1,1,129,107,0.054000," ","int(x^3*(c*x^2+b*x)^(1/2),x)","\frac{7 b^{5} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{256 c^{\frac{9}{2}}}-\frac{7 \sqrt{c \,x^{2}+b x}\, b^{3} x}{64 c^{3}}+\frac{\left(c \,x^{2}+b x \right)^{\frac{3}{2}} x^{2}}{5 c}-\frac{7 \sqrt{c \,x^{2}+b x}\, b^{4}}{128 c^{4}}-\frac{7 \left(c \,x^{2}+b x \right)^{\frac{3}{2}} b x}{40 c^{2}}+\frac{7 \left(c \,x^{2}+b x \right)^{\frac{3}{2}} b^{2}}{48 c^{3}}"," ",0,"1/5*x^2*(c*x^2+b*x)^(3/2)/c-7/40*b*x*(c*x^2+b*x)^(3/2)/c^2+7/48*b^2*(c*x^2+b*x)^(3/2)/c^3-7/64*b^3/c^3*(c*x^2+b*x)^(1/2)*x-7/128*b^4/c^4*(c*x^2+b*x)^(1/2)+7/256*b^5/c^(9/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))","A"
2,1,107,85,0.049000," ","int(x^2*(c*x^2+b*x)^(1/2),x)","-\frac{5 b^{4} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{128 c^{\frac{7}{2}}}+\frac{5 \sqrt{c \,x^{2}+b x}\, b^{2} x}{32 c^{2}}+\frac{5 \sqrt{c \,x^{2}+b x}\, b^{3}}{64 c^{3}}+\frac{\left(c \,x^{2}+b x \right)^{\frac{3}{2}} x}{4 c}-\frac{5 \left(c \,x^{2}+b x \right)^{\frac{3}{2}} b}{24 c^{2}}"," ",0,"1/4*x*(c*x^2+b*x)^(3/2)/c-5/24*b*(c*x^2+b*x)^(3/2)/c^2+5/32*b^2/c^2*(c*x^2+b*x)^(1/2)*x+5/64*b^3/c^3*(c*x^2+b*x)^(1/2)-5/128*b^4/c^(7/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))","A"
3,1,87,65,0.045000," ","int(x*(c*x^2+b*x)^(1/2),x)","\frac{b^{3} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{16 c^{\frac{5}{2}}}-\frac{\sqrt{c \,x^{2}+b x}\, b x}{4 c}-\frac{\sqrt{c \,x^{2}+b x}\, b^{2}}{8 c^{2}}+\frac{\left(c \,x^{2}+b x \right)^{\frac{3}{2}}}{3 c}"," ",0,"1/3*(c*x^2+b*x)^(3/2)/c-1/4*b/c*x*(c*x^2+b*x)^(1/2)-1/8*b^2/c^2*(c*x^2+b*x)^(1/2)+1/16*b^3/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))","A"
4,1,56,48,0.042000," ","int((c*x^2+b*x)^(1/2),x)","-\frac{b^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{8 c^{\frac{3}{2}}}+\frac{\left(2 c x +b \right) \sqrt{c \,x^{2}+b x}}{4 c}"," ",0,"1/4*(2*c*x+b)*(c*x^2+b*x)^(1/2)/c-1/8*b^2/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))","A"
5,1,43,34,0.042000," ","int((c*x^2+b*x)^(1/2)/x,x)","\frac{b \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{2 \sqrt{c}}+\sqrt{c \,x^{2}+b x}"," ",0,"(c*x^2+b*x)^(1/2)+1/2*b*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))/c^(1/2)","A"
6,1,66,39,0.042000," ","int((c*x^2+b*x)^(1/2)/x^2,x)","\sqrt{c}\, \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)+\frac{2 \sqrt{c \,x^{2}+b x}\, c}{b}-\frac{2 \left(c \,x^{2}+b x \right)^{\frac{3}{2}}}{b \,x^{2}}"," ",0,"-2/b/x^2*(c*x^2+b*x)^(3/2)+2/b*c*(c*x^2+b*x)^(1/2)+c^(1/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))","A"
7,1,25,19,0.045000," ","int((c*x^2+b*x)^(1/2)/x^3,x)","-\frac{2 \left(c x +b \right) \sqrt{c \,x^{2}+b x}}{3 b \,x^{2}}"," ",0,"-2/3*(c*x+b)/x^2/b*(c*x^2+b*x)^(1/2)","A"
8,1,33,40,0.047000," ","int((c*x^2+b*x)^(1/2)/x^4,x)","-\frac{2 \left(c x +b \right) \left(-2 c x +3 b \right) \sqrt{c \,x^{2}+b x}}{15 b^{2} x^{3}}"," ",0,"-2/15*(c*x+b)*(-2*c*x+3*b)*(c*x^2+b*x)^(1/2)/b^2/x^3","A"
9,1,44,62,0.045000," ","int((c*x^2+b*x)^(1/2)/x^5,x)","-\frac{2 \left(c x +b \right) \left(8 c^{2} x^{2}-12 b c x +15 b^{2}\right) \sqrt{c \,x^{2}+b x}}{105 b^{3} x^{4}}"," ",0,"-2/105*(c*x+b)*(8*c^2*x^2-12*b*c*x+15*b^2)*(c*x^2+b*x)^(1/2)/b^3/x^4","A"
10,1,55,84,0.046000," ","int((c*x^2+b*x)^(1/2)/x^6,x)","-\frac{2 \left(c x +b \right) \left(-16 x^{3} c^{3}+24 b \,x^{2} c^{2}-30 b^{2} x c +35 b^{3}\right) \sqrt{c \,x^{2}+b x}}{315 b^{4} x^{5}}"," ",0,"-2/315*(c*x+b)*(-16*c^3*x^3+24*b*c^2*x^2-30*b^2*c*x+35*b^3)*(c*x^2+b*x)^(1/2)/b^4/x^5","A"
11,1,66,106,0.045000," ","int((c*x^2+b*x)^(1/2)/x^7,x)","-\frac{2 \left(c x +b \right) \left(128 c^{4} x^{4}-192 x^{3} c^{3} b +240 c^{2} x^{2} b^{2}-280 c x \,b^{3}+315 b^{4}\right) \sqrt{c \,x^{2}+b x}}{3465 b^{5} x^{6}}"," ",0,"-2/3465*(c*x+b)*(128*c^4*x^4-192*b*c^3*x^3+240*b^2*c^2*x^2-280*b^3*c*x+315*b^4)*(c*x^2+b*x)^(1/2)/b^5/x^6","A"
12,1,146,110,0.047000," ","int(x^2*(c*x^2+b*x)^(3/2),x)","\frac{7 b^{6} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{1024 c^{\frac{9}{2}}}-\frac{7 \sqrt{c \,x^{2}+b x}\, b^{4} x}{256 c^{3}}-\frac{7 \sqrt{c \,x^{2}+b x}\, b^{5}}{512 c^{4}}+\frac{7 \left(c \,x^{2}+b x \right)^{\frac{3}{2}} b^{2} x}{96 c^{2}}+\frac{7 \left(c \,x^{2}+b x \right)^{\frac{3}{2}} b^{3}}{192 c^{3}}+\frac{\left(c \,x^{2}+b x \right)^{\frac{5}{2}} x}{6 c}-\frac{7 \left(c \,x^{2}+b x \right)^{\frac{5}{2}} b}{60 c^{2}}"," ",0,"1/6*x*(c*x^2+b*x)^(5/2)/c-7/60*b*(c*x^2+b*x)^(5/2)/c^2+7/96*b^2/c^2*(c*x^2+b*x)^(3/2)*x+7/192*b^3/c^3*(c*x^2+b*x)^(3/2)-7/256*b^4/c^3*(c*x^2+b*x)^(1/2)*x-7/512*b^5/c^4*(c*x^2+b*x)^(1/2)+7/1024*b^6/c^(9/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))","A"
13,1,126,90,0.048000," ","int(x*(c*x^2+b*x)^(3/2),x)","-\frac{3 b^{5} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{256 c^{\frac{7}{2}}}+\frac{3 \sqrt{c \,x^{2}+b x}\, b^{3} x}{64 c^{2}}+\frac{3 \sqrt{c \,x^{2}+b x}\, b^{4}}{128 c^{3}}-\frac{\left(c \,x^{2}+b x \right)^{\frac{3}{2}} b x}{8 c}-\frac{\left(c \,x^{2}+b x \right)^{\frac{3}{2}} b^{2}}{16 c^{2}}+\frac{\left(c \,x^{2}+b x \right)^{\frac{5}{2}}}{5 c}"," ",0,"1/5*(c*x^2+b*x)^(5/2)/c-1/8*b/c*x*(c*x^2+b*x)^(3/2)-1/16*b^2/c^2*(c*x^2+b*x)^(3/2)+3/64*b^3/c^2*(c*x^2+b*x)^(1/2)*x+3/128*b^4/c^3*(c*x^2+b*x)^(1/2)-3/256*b^5/c^(7/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))","A"
14,1,95,73,0.043000," ","int((c*x^2+b*x)^(3/2),x)","\frac{3 b^{4} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{128 c^{\frac{5}{2}}}-\frac{3 \sqrt{c \,x^{2}+b x}\, b^{2} x}{32 c}-\frac{3 \sqrt{c \,x^{2}+b x}\, b^{3}}{64 c^{2}}+\frac{\left(2 c x +b \right) \left(c \,x^{2}+b x \right)^{\frac{3}{2}}}{8 c}"," ",0,"1/8*(2*c*x+b)*(c*x^2+b*x)^(3/2)/c-3/32*b^2/c*(c*x^2+b*x)^(1/2)*x-3/64*b^3/c^2*(c*x^2+b*x)^(1/2)+3/128*b^4/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))","A"
15,1,81,62,0.046000," ","int((c*x^2+b*x)^(3/2)/x,x)","-\frac{b^{3} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{16 c^{\frac{3}{2}}}+\frac{\sqrt{c \,x^{2}+b x}\, b x}{4}+\frac{\sqrt{c \,x^{2}+b x}\, b^{2}}{8 c}+\frac{\left(c \,x^{2}+b x \right)^{\frac{3}{2}}}{3}"," ",0,"1/3*(c*x^2+b*x)^(3/2)+1/4*b*(c*x^2+b*x)^(1/2)*x+1/8/c*(c*x^2+b*x)^(1/2)*b^2-1/16*b^3/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))","A"
16,1,99,56,0.046000," ","int((c*x^2+b*x)^(3/2)/x^2,x)","\frac{3 b^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{8 \sqrt{c}}-\frac{3 \sqrt{c \,x^{2}+b x}\, c x}{2}-\frac{3 \sqrt{c \,x^{2}+b x}\, b}{4}-\frac{2 \left(c \,x^{2}+b x \right)^{\frac{3}{2}} c}{b}+\frac{2 \left(c \,x^{2}+b x \right)^{\frac{5}{2}}}{b \,x^{2}}"," ",0,"2/b/x^2*(c*x^2+b*x)^(5/2)-2/b*c*(c*x^2+b*x)^(3/2)-3/2*c*(c*x^2+b*x)^(1/2)*x-3/4*b*(c*x^2+b*x)^(1/2)+3/8*b^2/c^(1/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))","A"
17,1,124,54,0.044000," ","int((c*x^2+b*x)^(3/2)/x^3,x)","\frac{3 b \sqrt{c}\, \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{2}-\frac{6 \sqrt{c \,x^{2}+b x}\, c^{2} x}{b}-3 \sqrt{c \,x^{2}+b x}\, c -\frac{8 \left(c \,x^{2}+b x \right)^{\frac{3}{2}} c^{2}}{b^{2}}+\frac{8 \left(c \,x^{2}+b x \right)^{\frac{5}{2}} c}{b^{2} x^{2}}-\frac{2 \left(c \,x^{2}+b x \right)^{\frac{5}{2}}}{b \,x^{3}}"," ",0,"-2/b/x^3*(c*x^2+b*x)^(5/2)+8/b^2*c/x^2*(c*x^2+b*x)^(5/2)-8/b^2*c^2*(c*x^2+b*x)^(3/2)-6/b*c^2*(c*x^2+b*x)^(1/2)*x-3*c*(c*x^2+b*x)^(1/2)+3/2*b*c^(1/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))","B"
18,1,149,56,0.046000," ","int((c*x^2+b*x)^(3/2)/x^4,x)","c^{\frac{3}{2}} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)-\frac{4 \sqrt{c \,x^{2}+b x}\, c^{3} x}{b^{2}}-\frac{2 \sqrt{c \,x^{2}+b x}\, c^{2}}{b}-\frac{16 \left(c \,x^{2}+b x \right)^{\frac{3}{2}} c^{3}}{3 b^{3}}+\frac{16 \left(c \,x^{2}+b x \right)^{\frac{5}{2}} c^{2}}{3 b^{3} x^{2}}-\frac{4 \left(c \,x^{2}+b x \right)^{\frac{5}{2}} c}{3 b^{2} x^{3}}-\frac{2 \left(c \,x^{2}+b x \right)^{\frac{5}{2}}}{3 b \,x^{4}}"," ",0,"-2/3/b/x^4*(c*x^2+b*x)^(5/2)-4/3/b^2*c/x^3*(c*x^2+b*x)^(5/2)+16/3/b^3*c^2/x^2*(c*x^2+b*x)^(5/2)-16/3/b^3*c^3*(c*x^2+b*x)^(3/2)-4/b^2*c^3*(c*x^2+b*x)^(1/2)*x-2/b*c^2*(c*x^2+b*x)^(1/2)+c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))","B"
19,1,25,19,0.045000," ","int((c*x^2+b*x)^(3/2)/x^5,x)","-\frac{2 \left(c x +b \right) \left(c \,x^{2}+b x \right)^{\frac{3}{2}}}{5 b \,x^{4}}"," ",0,"-2/5*(c*x+b)/x^4/b*(c*x^2+b*x)^(3/2)","A"
20,1,33,40,0.046000," ","int((c*x^2+b*x)^(3/2)/x^6,x)","-\frac{2 \left(c x +b \right) \left(-2 c x +5 b \right) \left(c \,x^{2}+b x \right)^{\frac{3}{2}}}{35 b^{2} x^{5}}"," ",0,"-2/35*(c*x+b)*(-2*c*x+5*b)*(c*x^2+b*x)^(3/2)/b^2/x^5","A"
21,1,44,62,0.046000," ","int((c*x^2+b*x)^(3/2)/x^7,x)","-\frac{2 \left(c x +b \right) \left(8 c^{2} x^{2}-20 b c x +35 b^{2}\right) \left(c \,x^{2}+b x \right)^{\frac{3}{2}}}{315 b^{3} x^{6}}"," ",0,"-2/315*(c*x+b)*(8*c^2*x^2-20*b*c*x+35*b^2)*(c*x^2+b*x)^(3/2)/b^3/x^6","A"
22,1,55,84,0.047000," ","int((c*x^2+b*x)^(3/2)/x^8,x)","-\frac{2 \left(c x +b \right) \left(-16 x^{3} c^{3}+40 b \,x^{2} c^{2}-70 b^{2} x c +105 b^{3}\right) \left(c \,x^{2}+b x \right)^{\frac{3}{2}}}{1155 b^{4} x^{7}}"," ",0,"-2/1155*(c*x+b)*(-16*c^3*x^3+40*b*c^2*x^2-70*b^2*c*x+105*b^3)*(c*x^2+b*x)^(3/2)/x^7/b^4","A"
23,1,66,106,0.041000," ","int((c*x^2+b*x)^(3/2)/x^9,x)","-\frac{2 \left(c x +b \right) \left(128 c^{4} x^{4}-320 x^{3} c^{3} b +560 c^{2} x^{2} b^{2}-840 c x \,b^{3}+1155 b^{4}\right) \left(c \,x^{2}+b x \right)^{\frac{3}{2}}}{15015 b^{5} x^{8}}"," ",0,"-2/15015*(c*x+b)*(128*c^4*x^4-320*b*c^3*x^3+560*b^2*c^2*x^2-840*b^3*c*x+1155*b^4)*(c*x^2+b*x)^(3/2)/b^5/x^8","A"
24,1,185,135,0.048000," ","int(x^2*(b*x^2+a*x)^(5/2),x)","-\frac{45 a^{8} \ln \left(\frac{b x +\frac{a}{2}}{\sqrt{b}}+\sqrt{b \,x^{2}+a x}\right)}{32768 b^{\frac{11}{2}}}+\frac{45 \sqrt{b \,x^{2}+a x}\, a^{6} x}{8192 b^{4}}+\frac{45 \sqrt{b \,x^{2}+a x}\, a^{7}}{16384 b^{5}}-\frac{15 \left(b \,x^{2}+a x \right)^{\frac{3}{2}} a^{4} x}{1024 b^{3}}-\frac{15 \left(b \,x^{2}+a x \right)^{\frac{3}{2}} a^{5}}{2048 b^{4}}+\frac{3 \left(b \,x^{2}+a x \right)^{\frac{5}{2}} a^{2} x}{64 b^{2}}+\frac{3 \left(b \,x^{2}+a x \right)^{\frac{5}{2}} a^{3}}{128 b^{3}}+\frac{\left(b \,x^{2}+a x \right)^{\frac{7}{2}} x}{8 b}-\frac{9 \left(b \,x^{2}+a x \right)^{\frac{7}{2}} a}{112 b^{2}}"," ",0,"1/8*x*(b*x^2+a*x)^(7/2)/b-9/112*a*(b*x^2+a*x)^(7/2)/b^2+3/64*a^2/b^2*(b*x^2+a*x)^(5/2)*x+3/128*a^3/b^3*(b*x^2+a*x)^(5/2)-15/1024*a^4/b^3*(b*x^2+a*x)^(3/2)*x-15/2048*a^5/b^4*(b*x^2+a*x)^(3/2)+45/8192*a^6/b^4*(b*x^2+a*x)^(1/2)*x+45/16384*a^7/b^5*(b*x^2+a*x)^(1/2)-45/32768*a^8/b^(11/2)*ln((1/2*a+b*x)/b^(1/2)+(b*x^2+a*x)^(1/2))","A"
25,1,165,115,0.116000," ","int(x*(b*x^2+a*x)^(5/2),x)","\frac{5 a^{7} \ln \left(\frac{b x +\frac{a}{2}}{\sqrt{b}}+\sqrt{b \,x^{2}+a x}\right)}{2048 b^{\frac{9}{2}}}-\frac{5 \sqrt{b \,x^{2}+a x}\, a^{5} x}{512 b^{3}}-\frac{5 \sqrt{b \,x^{2}+a x}\, a^{6}}{1024 b^{4}}+\frac{5 \left(b \,x^{2}+a x \right)^{\frac{3}{2}} a^{3} x}{192 b^{2}}+\frac{5 \left(b \,x^{2}+a x \right)^{\frac{3}{2}} a^{4}}{384 b^{3}}-\frac{\left(b \,x^{2}+a x \right)^{\frac{5}{2}} a x}{12 b}-\frac{\left(b \,x^{2}+a x \right)^{\frac{5}{2}} a^{2}}{24 b^{2}}+\frac{\left(b \,x^{2}+a x \right)^{\frac{7}{2}}}{7 b}"," ",0,"1/7*(b*x^2+a*x)^(7/2)/b-1/12*a/b*x*(b*x^2+a*x)^(5/2)-1/24*a^2/b^2*(b*x^2+a*x)^(5/2)+5/192*a^3/b^2*(b*x^2+a*x)^(3/2)*x+5/384*a^4/b^3*(b*x^2+a*x)^(3/2)-5/512*a^5/b^3*(b*x^2+a*x)^(1/2)*x-5/1024*a^6/b^4*(b*x^2+a*x)^(1/2)+5/2048*a^7/b^(9/2)*ln((b*x+1/2*a)/b^(1/2)+(b*x^2+a*x)^(1/2))","A"
26,1,134,98,0.046000," ","int((b*x^2+a*x)^(5/2),x)","-\frac{5 a^{6} \ln \left(\frac{b x +\frac{a}{2}}{\sqrt{b}}+\sqrt{b \,x^{2}+a x}\right)}{1024 b^{\frac{7}{2}}}+\frac{5 \sqrt{b \,x^{2}+a x}\, a^{4} x}{256 b^{2}}+\frac{5 \sqrt{b \,x^{2}+a x}\, a^{5}}{512 b^{3}}-\frac{5 \left(b \,x^{2}+a x \right)^{\frac{3}{2}} a^{2} x}{96 b}-\frac{5 \left(b \,x^{2}+a x \right)^{\frac{3}{2}} a^{3}}{192 b^{2}}+\frac{\left(2 b x +a \right) \left(b \,x^{2}+a x \right)^{\frac{5}{2}}}{12 b}"," ",0,"1/12*(2*b*x+a)*(b*x^2+a*x)^(5/2)/b-5/96*a^2/b*(b*x^2+a*x)^(3/2)*x-5/192*a^3/b^2*(b*x^2+a*x)^(3/2)+5/256*a^4/b^2*(b*x^2+a*x)^(1/2)*x+5/512*a^5/b^3*(b*x^2+a*x)^(1/2)-5/1024*a^6/b^(7/2)*ln((b*x+1/2*a)/b^(1/2)+(b*x^2+a*x)^(1/2))","A"
27,1,120,87,0.044000," ","int((b*x^2+a*x)^(5/2)/x,x)","\frac{3 a^{5} \ln \left(\frac{b x +\frac{a}{2}}{\sqrt{b}}+\sqrt{b \,x^{2}+a x}\right)}{256 b^{\frac{5}{2}}}-\frac{3 \sqrt{b \,x^{2}+a x}\, a^{3} x}{64 b}-\frac{3 \sqrt{b \,x^{2}+a x}\, a^{4}}{128 b^{2}}+\frac{\left(b \,x^{2}+a x \right)^{\frac{3}{2}} a x}{8}+\frac{\left(b \,x^{2}+a x \right)^{\frac{3}{2}} a^{2}}{16 b}+\frac{\left(b \,x^{2}+a x \right)^{\frac{5}{2}}}{5}"," ",0,"1/5*(b*x^2+a*x)^(5/2)+1/8*a*(b*x^2+a*x)^(3/2)*x+1/16/b*(b*x^2+a*x)^(3/2)*a^2-3/64*a^3/b*(b*x^2+a*x)^(1/2)*x-3/128*a^4/b^2*(b*x^2+a*x)^(1/2)+3/256*a^5/b^(5/2)*ln((b*x+1/2*a)/b^(1/2)+(b*x^2+a*x)^(1/2))","A"
28,1,135,81,0.042000," ","int((b*x^2+a*x)^(5/2)/x^2,x)","-\frac{5 a^{4} \ln \left(\frac{b x +\frac{a}{2}}{\sqrt{b}}+\sqrt{b \,x^{2}+a x}\right)}{128 b^{\frac{3}{2}}}+\frac{5 \sqrt{b \,x^{2}+a x}\, a^{2} x}{32}+\frac{5 \sqrt{b \,x^{2}+a x}\, a^{3}}{64 b}-\frac{5 \left(b \,x^{2}+a x \right)^{\frac{3}{2}} b x}{12}-\frac{5 \left(b \,x^{2}+a x \right)^{\frac{3}{2}} a}{24}-\frac{2 \left(b \,x^{2}+a x \right)^{\frac{5}{2}} b}{3 a}+\frac{2 \left(b \,x^{2}+a x \right)^{\frac{7}{2}}}{3 a \,x^{2}}"," ",0,"2/3/a/x^2*(b*x^2+a*x)^(7/2)-2/3/a*b*(b*x^2+a*x)^(5/2)-5/12*b*(b*x^2+a*x)^(3/2)*x-5/24*a*(b*x^2+a*x)^(3/2)+5/32*a^2*(b*x^2+a*x)^(1/2)*x+5/64*a^3/b*(b*x^2+a*x)^(1/2)-5/128*a^4/b^(3/2)*ln((b*x+1/2*a)/b^(1/2)+(b*x^2+a*x)^(1/2))","A"
29,1,158,76,0.046000," ","int((b*x^2+a*x)^(5/2)/x^3,x)","\frac{5 a^{3} \ln \left(\frac{b x +\frac{a}{2}}{\sqrt{b}}+\sqrt{b \,x^{2}+a x}\right)}{16 \sqrt{b}}-\frac{5 \sqrt{b \,x^{2}+a x}\, a b x}{4}-\frac{5 \sqrt{b \,x^{2}+a x}\, a^{2}}{8}+\frac{10 \left(b \,x^{2}+a x \right)^{\frac{3}{2}} b^{2} x}{3 a}+\frac{5 \left(b \,x^{2}+a x \right)^{\frac{3}{2}} b}{3}+\frac{16 \left(b \,x^{2}+a x \right)^{\frac{5}{2}} b^{2}}{3 a^{2}}-\frac{16 \left(b \,x^{2}+a x \right)^{\frac{7}{2}} b}{3 a^{2} x^{2}}+\frac{2 \left(b \,x^{2}+a x \right)^{\frac{7}{2}}}{a \,x^{3}}"," ",0,"2/a/x^3*(b*x^2+a*x)^(7/2)-16/3/a^2*b/x^2*(b*x^2+a*x)^(7/2)+16/3/a^2*b^2*(b*x^2+a*x)^(5/2)+10/3/a*b^2*(b*x^2+a*x)^(3/2)*x+5/3*b*(b*x^2+a*x)^(3/2)-5/4*a*b*(b*x^2+a*x)^(1/2)*x-5/8*a^2*(b*x^2+a*x)^(1/2)+5/16*a^3/b^(1/2)*ln((b*x+1/2*a)/b^(1/2)+(b*x^2+a*x)^(1/2))","B"
30,1,185,74,0.042000," ","int((b*x^2+a*x)^(5/2)/x^4,x)","\frac{15 a^{2} \sqrt{b}\, \ln \left(\frac{b x +\frac{a}{2}}{\sqrt{b}}+\sqrt{b \,x^{2}+a x}\right)}{8}-\frac{15 \sqrt{b \,x^{2}+a x}\, b^{2} x}{2}-\frac{15 \sqrt{b \,x^{2}+a x}\, a b}{4}+\frac{20 \left(b \,x^{2}+a x \right)^{\frac{3}{2}} b^{3} x}{a^{2}}+\frac{10 \left(b \,x^{2}+a x \right)^{\frac{3}{2}} b^{2}}{a}+\frac{32 \left(b \,x^{2}+a x \right)^{\frac{5}{2}} b^{3}}{a^{3}}-\frac{32 \left(b \,x^{2}+a x \right)^{\frac{7}{2}} b^{2}}{a^{3} x^{2}}+\frac{12 \left(b \,x^{2}+a x \right)^{\frac{7}{2}} b}{a^{2} x^{3}}-\frac{2 \left(b \,x^{2}+a x \right)^{\frac{7}{2}}}{a \,x^{4}}"," ",0,"-2/a/x^4*(b*x^2+a*x)^(7/2)+12/a^2*b/x^3*(b*x^2+a*x)^(7/2)-32/a^3*b^2/x^2*(b*x^2+a*x)^(7/2)+32/a^3*b^3*(b*x^2+a*x)^(5/2)+20/a^2*b^3*(b*x^2+a*x)^(3/2)*x+10/a*b^2*(b*x^2+a*x)^(3/2)-15/2*b^2*(b*x^2+a*x)^(1/2)*x-15/4*a*b*(b*x^2+a*x)^(1/2)+15/8*a^2*b^(1/2)*ln((b*x+1/2*a)/b^(1/2)+(b*x^2+a*x)^(1/2))","B"
31,1,209,73,0.043000," ","int((b*x^2+a*x)^(5/2)/x^5,x)","\frac{5 a \,b^{\frac{3}{2}} \ln \left(\frac{b x +\frac{a}{2}}{\sqrt{b}}+\sqrt{b \,x^{2}+a x}\right)}{2}-\frac{10 \sqrt{b \,x^{2}+a x}\, b^{3} x}{a}+\frac{80 \left(b \,x^{2}+a x \right)^{\frac{3}{2}} b^{4} x}{3 a^{3}}-5 \sqrt{b \,x^{2}+a x}\, b^{2}+\frac{40 \left(b \,x^{2}+a x \right)^{\frac{3}{2}} b^{3}}{3 a^{2}}+\frac{128 \left(b \,x^{2}+a x \right)^{\frac{5}{2}} b^{4}}{3 a^{4}}-\frac{128 \left(b \,x^{2}+a x \right)^{\frac{7}{2}} b^{3}}{3 a^{4} x^{2}}+\frac{16 \left(b \,x^{2}+a x \right)^{\frac{7}{2}} b^{2}}{a^{3} x^{3}}-\frac{8 \left(b \,x^{2}+a x \right)^{\frac{7}{2}} b}{3 a^{2} x^{4}}-\frac{2 \left(b \,x^{2}+a x \right)^{\frac{7}{2}}}{3 a \,x^{5}}"," ",0,"-2/3/a/x^5*(b*x^2+a*x)^(7/2)-8/3/a^2*b/x^4*(b*x^2+a*x)^(7/2)+16/a^3*b^2/x^3*(b*x^2+a*x)^(7/2)-128/3/a^4*b^3/x^2*(b*x^2+a*x)^(7/2)+128/3/a^4*b^4*(b*x^2+a*x)^(5/2)+80/3/a^3*b^4*(b*x^2+a*x)^(3/2)*x+40/3/a^2*b^3*(b*x^2+a*x)^(3/2)-10/a*b^3*(b*x^2+a*x)^(1/2)*x-5*b^2*(b*x^2+a*x)^(1/2)+5/2*a*b^(3/2)*ln((b*x+1/2*a)/b^(1/2)+(b*x^2+a*x)^(1/2))","B"
32,1,232,75,0.045000," ","int((b*x^2+a*x)^(5/2)/x^6,x)","b^{\frac{5}{2}} \ln \left(\frac{b x +\frac{a}{2}}{\sqrt{b}}+\sqrt{b \,x^{2}+a x}\right)-\frac{4 \sqrt{b \,x^{2}+a x}\, b^{4} x}{a^{2}}-\frac{2 \sqrt{b \,x^{2}+a x}\, b^{3}}{a}+\frac{32 \left(b \,x^{2}+a x \right)^{\frac{3}{2}} b^{5} x}{3 a^{4}}+\frac{16 \left(b \,x^{2}+a x \right)^{\frac{3}{2}} b^{4}}{3 a^{3}}+\frac{256 \left(b \,x^{2}+a x \right)^{\frac{5}{2}} b^{5}}{15 a^{5}}-\frac{256 \left(b \,x^{2}+a x \right)^{\frac{7}{2}} b^{4}}{15 a^{5} x^{2}}+\frac{32 \left(b \,x^{2}+a x \right)^{\frac{7}{2}} b^{3}}{5 a^{4} x^{3}}-\frac{16 \left(b \,x^{2}+a x \right)^{\frac{7}{2}} b^{2}}{15 a^{3} x^{4}}-\frac{4 \left(b \,x^{2}+a x \right)^{\frac{7}{2}} b}{15 a^{2} x^{5}}-\frac{2 \left(b \,x^{2}+a x \right)^{\frac{7}{2}}}{5 a \,x^{6}}"," ",0,"-2/5/a/x^6*(b*x^2+a*x)^(7/2)-4/15/a^2*b/x^5*(b*x^2+a*x)^(7/2)-16/15/a^3*b^2/x^4*(b*x^2+a*x)^(7/2)+32/5/a^4*b^3/x^3*(b*x^2+a*x)^(7/2)-256/15/a^5*b^4/x^2*(b*x^2+a*x)^(7/2)+256/15/a^5*b^5*(b*x^2+a*x)^(5/2)+32/3/a^4*b^5*(b*x^2+a*x)^(3/2)*x+16/3/a^3*b^4*(b*x^2+a*x)^(3/2)-4/a^2*b^4*(b*x^2+a*x)^(1/2)*x-2/a*b^3*(b*x^2+a*x)^(1/2)+b^(5/2)*ln((b*x+1/2*a)/b^(1/2)+(b*x^2+a*x)^(1/2))","B"
33,1,25,19,0.039000," ","int((b*x^2+a*x)^(5/2)/x^7,x)","-\frac{2 \left(b x +a \right) \left(b \,x^{2}+a x \right)^{\frac{5}{2}}}{7 a \,x^{6}}"," ",0,"-2/7*(b*x+a)/x^6/a*(b*x^2+a*x)^(5/2)","A"
34,1,33,40,0.053000," ","int((b*x^2+a*x)^(5/2)/x^8,x)","-\frac{2 \left(b x +a \right) \left(-2 b x +7 a \right) \left(b \,x^{2}+a x \right)^{\frac{5}{2}}}{63 a^{2} x^{7}}"," ",0,"-2/63*(b*x+a)*(-2*b*x+7*a)*(b*x^2+a*x)^(5/2)/a^2/x^7","A"
35,1,44,62,0.041000," ","int((b*x^2+a*x)^(5/2)/x^9,x)","-\frac{2 \left(b x +a \right) \left(8 b^{2} x^{2}-28 a b x +63 a^{2}\right) \left(b \,x^{2}+a x \right)^{\frac{5}{2}}}{693 a^{3} x^{8}}"," ",0,"-2/693*(b*x+a)*(8*b^2*x^2-28*a*b*x+63*a^2)*(b*x^2+a*x)^(5/2)/x^8/a^3","A"
36,1,55,84,0.046000," ","int((b*x^2+a*x)^(5/2)/x^10,x)","-\frac{2 \left(b x +a \right) \left(-16 b^{3} x^{3}+56 a \,b^{2} x^{2}-126 a^{2} b x +231 a^{3}\right) \left(b \,x^{2}+a x \right)^{\frac{5}{2}}}{3003 a^{4} x^{9}}"," ",0,"-2/3003*(b*x+a)*(-16*b^3*x^3+56*a*b^2*x^2-126*a^2*b*x+231*a^3)*(b*x^2+a*x)^(5/2)/x^9/a^4","A"
37,1,66,106,0.046000," ","int((b*x^2+a*x)^(5/2)/x^11,x)","-\frac{2 \left(b x +a \right) \left(128 b^{4} x^{4}-448 a \,b^{3} x^{3}+1008 b^{2} x^{2} a^{2}-1848 b x \,a^{3}+3003 a^{4}\right) \left(b \,x^{2}+a x \right)^{\frac{5}{2}}}{45045 a^{5} x^{10}}"," ",0,"-2/45045*(b*x+a)*(128*b^4*x^4-448*a*b^3*x^3+1008*a^2*b^2*x^2-1848*a^3*b*x+3003*a^4)*(b*x^2+a*x)^(5/2)/x^10/a^5","A"
38,1,77,128,0.046000," ","int((b*x^2+a*x)^(5/2)/x^12,x)","-\frac{2 \left(b x +a \right) \left(-256 b^{5} x^{5}+896 a \,b^{4} x^{4}-2016 a^{2} b^{3} x^{3}+3696 a^{3} b^{2} x^{2}-6006 a^{4} b x +9009 a^{5}\right) \left(b \,x^{2}+a x \right)^{\frac{5}{2}}}{153153 a^{6} x^{11}}"," ",0,"-2/153153*(b*x+a)*(-256*b^5*x^5+896*a*b^4*x^4-2016*a^2*b^3*x^3+3696*a^3*b^2*x^2-6006*a^4*b*x+9009*a^5)*(b*x^2+a*x)^(5/2)/x^11/a^6","A"
39,1,39,38,0.045000," ","int(x*(-x^2+2*x)^(1/2),x)","\frac{\arcsin \left(x -1\right)}{2}-\frac{\left(-x^{2}+2 x \right)^{\frac{3}{2}}}{3}-\frac{\left(-2 x +2\right) \sqrt{-x^{2}+2 x}}{4}"," ",0,"-1/3*(-x^2+2*x)^(3/2)-1/4*(2-2*x)*(-x^2+2*x)^(1/2)+1/2*arcsin(x-1)","A"
40,1,41,40,0.044000," ","int(x*(-4*x^2+3*x)^(1/2),x)","\frac{27 \arcsin \left(\frac{8 x}{3}-1\right)}{512}-\frac{\left(-4 x^{2}+3 x \right)^{\frac{3}{2}}}{12}-\frac{3 \left(-8 x +3\right) \sqrt{-4 x^{2}+3 x}}{128}"," ",0,"-1/12*(-4*x^2+3*x)^(3/2)+27/512*arcsin(8/3*x-1)-3/128*(-8*x+3)*(-4*x^2+3*x)^(1/2)","A"
41,1,38,36,0.043000," ","int(x*(x^2+x)^(1/2),x)","\frac{\ln \left(x +\frac{1}{2}+\sqrt{x^{2}+x}\right)}{16}+\frac{\left(x^{2}+x \right)^{\frac{3}{2}}}{3}-\frac{\left(2 x +1\right) \sqrt{x^{2}+x}}{8}"," ",0,"1/3*(x^2+x)^(3/2)-1/8*(2*x+1)*(x^2+x)^(1/2)+1/16*ln(x+1/2+(x^2+x)^(1/2))","A"
42,1,112,104,0.045000," ","int(x^4/(c*x^2+b*x)^(1/2),x)","\frac{\sqrt{c \,x^{2}+b x}\, x^{3}}{4 c}-\frac{7 \sqrt{c \,x^{2}+b x}\, b \,x^{2}}{24 c^{2}}+\frac{35 b^{4} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{128 c^{\frac{9}{2}}}+\frac{35 \sqrt{c \,x^{2}+b x}\, b^{2} x}{96 c^{3}}-\frac{35 \sqrt{c \,x^{2}+b x}\, b^{3}}{64 c^{4}}"," ",0,"1/4*x^3*(c*x^2+b*x)^(1/2)/c-7/24*b*x^2*(c*x^2+b*x)^(1/2)/c^2+35/96*b^2*x*(c*x^2+b*x)^(1/2)/c^3-35/64*b^3*(c*x^2+b*x)^(1/2)/c^4+35/128*b^4/c^(9/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))","A"
43,1,90,82,0.044000," ","int(x^3/(c*x^2+b*x)^(1/2),x)","\frac{\sqrt{c \,x^{2}+b x}\, x^{2}}{3 c}-\frac{5 b^{3} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{16 c^{\frac{7}{2}}}-\frac{5 \sqrt{c \,x^{2}+b x}\, b x}{12 c^{2}}+\frac{5 \sqrt{c \,x^{2}+b x}\, b^{2}}{8 c^{3}}"," ",0,"1/3*x^2*(c*x^2+b*x)^(1/2)/c-5/12*b*x*(c*x^2+b*x)^(1/2)/c^2+5/8*b^2*(c*x^2+b*x)^(1/2)/c^3-5/16*b^3/c^(7/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))","A"
44,1,68,60,0.048000," ","int(x^2/(c*x^2+b*x)^(1/2),x)","\frac{3 b^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{8 c^{\frac{5}{2}}}+\frac{\sqrt{c \,x^{2}+b x}\, x}{2 c}-\frac{3 \sqrt{c \,x^{2}+b x}\, b}{4 c^{2}}"," ",0,"1/2*x*(c*x^2+b*x)^(1/2)/c-3/4*b*(c*x^2+b*x)^(1/2)/c^2+3/8*b^2/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))","A"
45,1,47,39,0.044000," ","int(x/(c*x^2+b*x)^(1/2),x)","-\frac{b \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{2 c^{\frac{3}{2}}}+\frac{\sqrt{c \,x^{2}+b x}}{c}"," ",0,"(c*x^2+b*x)^(1/2)/c-1/2*b/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))","A"
46,1,29,22,0.040000," ","int(1/(c*x^2+b*x)^(1/2),x)","\frac{\ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{\sqrt{c}}"," ",0,"ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))/c^(1/2)","A"
47,1,22,19,0.043000," ","int(1/x/(c*x^2+b*x)^(1/2),x)","-\frac{2 \left(c x +b \right)}{\sqrt{c \,x^{2}+b x}\, b}"," ",0,"-2*(c*x+b)/b/(c*x^2+b*x)^(1/2)","A"
48,1,31,40,0.045000," ","int(1/x^2/(c*x^2+b*x)^(1/2),x)","-\frac{2 \left(c x +b \right) \left(-2 c x +b \right)}{3 \sqrt{c \,x^{2}+b x}\, b^{2} x}"," ",0,"-2/3*(c*x+b)*(-2*c*x+b)/x/b^2/(c*x^2+b*x)^(1/2)","A"
49,1,44,62,0.044000," ","int(1/x^3/(c*x^2+b*x)^(1/2),x)","-\frac{2 \left(c x +b \right) \left(8 c^{2} x^{2}-4 b c x +3 b^{2}\right)}{15 \sqrt{c \,x^{2}+b x}\, b^{3} x^{2}}"," ",0,"-2/15*(c*x+b)*(8*c^2*x^2-4*b*c*x+3*b^2)/x^2/b^3/(c*x^2+b*x)^(1/2)","A"
50,1,55,84,0.047000," ","int(1/x^4/(c*x^2+b*x)^(1/2),x)","-\frac{2 \left(c x +b \right) \left(-16 x^{3} c^{3}+8 b \,x^{2} c^{2}-6 b^{2} x c +5 b^{3}\right)}{35 \sqrt{c \,x^{2}+b x}\, b^{4} x^{3}}"," ",0,"-2/35*(c*x+b)*(-16*c^3*x^3+8*b*c^2*x^2-6*b^2*c*x+5*b^3)/x^3/b^4/(c*x^2+b*x)^(1/2)","A"
51,1,66,106,0.043000," ","int(1/x^5/(c*x^2+b*x)^(1/2),x)","-\frac{2 \left(c x +b \right) \left(128 c^{4} x^{4}-64 x^{3} c^{3} b +48 c^{2} x^{2} b^{2}-40 c x \,b^{3}+35 b^{4}\right)}{315 \sqrt{c \,x^{2}+b x}\, b^{5} x^{4}}"," ",0,"-2/315*(c*x+b)*(128*c^4*x^4-64*b*c^3*x^3+48*b^2*c^2*x^2-40*b^3*c*x+35*b^4)/x^4/b^5/(c*x^2+b*x)^(1/2)","A"
52,1,93,79,0.042000," ","int(x^4/(c*x^2+b*x)^(3/2),x)","\frac{x^{3}}{2 \sqrt{c \,x^{2}+b x}\, c}-\frac{5 b \,x^{2}}{4 \sqrt{c \,x^{2}+b x}\, c^{2}}-\frac{15 b^{2} x}{4 \sqrt{c \,x^{2}+b x}\, c^{3}}+\frac{15 b^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{8 c^{\frac{7}{2}}}"," ",0,"1/2*x^3/c/(c*x^2+b*x)^(1/2)-5/4*b/c^2*x^2/(c*x^2+b*x)^(1/2)-15/4*b^2/c^3/(c*x^2+b*x)^(1/2)*x+15/8*b^2/c^(7/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))","A"
53,1,68,59,0.046000," ","int(x^3/(c*x^2+b*x)^(3/2),x)","\frac{x^{2}}{\sqrt{c \,x^{2}+b x}\, c}+\frac{3 b x}{\sqrt{c \,x^{2}+b x}\, c^{2}}-\frac{3 b \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{2 c^{\frac{5}{2}}}"," ",0,"x^2/c/(c*x^2+b*x)^(1/2)+3*b/c^2/(c*x^2+b*x)^(1/2)*x-3/2*b/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))","A"
54,1,47,40,0.046000," ","int(x^2/(c*x^2+b*x)^(3/2),x)","-\frac{2 x}{\sqrt{c \,x^{2}+b x}\, c}+\frac{\ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{c^{\frac{3}{2}}}"," ",0,"-2*x/c/(c*x^2+b*x)^(1/2)+1/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))","A"
55,1,25,17,0.046000," ","int(x/(c*x^2+b*x)^(3/2),x)","\frac{2 \left(c x +b \right) x^{2}}{\left(c \,x^{2}+b x \right)^{\frac{3}{2}} b}"," ",0,"2*(c*x+b)*x^2/b/(c*x^2+b*x)^(3/2)","A"
56,1,29,22,0.043000," ","int(1/(c*x^2+b*x)^(3/2),x)","-\frac{2 \left(c x +b \right) \left(2 c x +b \right) x}{\left(c \,x^{2}+b x \right)^{\frac{3}{2}} b^{2}}"," ",0,"-2*(c*x+b)*x*(2*c*x+b)/b^2/(c*x^2+b*x)^(3/2)","A"
57,1,39,43,0.039000," ","int(1/x/(c*x^2+b*x)^(3/2),x)","-\frac{2 \left(c x +b \right) \left(-8 c^{2} x^{2}-4 b c x +b^{2}\right)}{3 \left(c \,x^{2}+b x \right)^{\frac{3}{2}} b^{3}}"," ",0,"-2/3*(c*x+b)*(-8*c^2*x^2-4*b*c*x+b^2)/b^3/(c*x^2+b*x)^(3/2)","A"
58,1,53,65,0.048000," ","int(1/x^2/(c*x^2+b*x)^(3/2),x)","-\frac{2 \left(c x +b \right) \left(16 x^{3} c^{3}+8 b \,x^{2} c^{2}-2 b^{2} x c +b^{3}\right)}{5 \left(c \,x^{2}+b x \right)^{\frac{3}{2}} b^{4} x}"," ",0,"-2/5*(c*x+b)*(16*c^3*x^3+8*b*c^2*x^2-2*b^2*c*x+b^3)/x/b^4/(c*x^2+b*x)^(3/2)","A"
59,1,66,87,0.042000," ","int(1/x^3/(c*x^2+b*x)^(3/2),x)","-\frac{2 \left(c x +b \right) \left(-128 c^{4} x^{4}-64 x^{3} c^{3} b +16 c^{2} x^{2} b^{2}-8 c x \,b^{3}+5 b^{4}\right)}{35 \left(c \,x^{2}+b x \right)^{\frac{3}{2}} b^{5} x^{2}}"," ",0,"-2/35*(c*x+b)*(-128*c^4*x^4-64*b*c^3*x^3+16*b^2*c^2*x^2-8*b^3*c*x+5*b^4)/x^2/b^5/(c*x^2+b*x)^(3/2)","A"
60,1,176,98,0.047000," ","int(x^6/(b*x^2+a*x)^(5/2),x)","\frac{x^{5}}{2 \left(b \,x^{2}+a x \right)^{\frac{3}{2}} b}-\frac{7 a \,x^{4}}{4 \left(b \,x^{2}+a x \right)^{\frac{3}{2}} b^{2}}-\frac{35 a^{2} x^{3}}{24 \left(b \,x^{2}+a x \right)^{\frac{3}{2}} b^{3}}+\frac{35 a^{3} x^{2}}{16 \left(b \,x^{2}+a x \right)^{\frac{3}{2}} b^{4}}+\frac{35 a^{4} x}{48 \left(b \,x^{2}+a x \right)^{\frac{3}{2}} b^{5}}-\frac{245 a^{2} x}{24 \sqrt{b \,x^{2}+a x}\, b^{4}}+\frac{35 a^{2} \ln \left(\frac{b x +\frac{a}{2}}{\sqrt{b}}+\sqrt{b \,x^{2}+a x}\right)}{8 b^{\frac{9}{2}}}-\frac{35 a^{3}}{48 \sqrt{b \,x^{2}+a x}\, b^{5}}"," ",0,"1/2*x^5/b/(b*x^2+a*x)^(3/2)-7/4*a/b^2*x^4/(b*x^2+a*x)^(3/2)-35/24*a^2/b^3*x^3/(b*x^2+a*x)^(3/2)+35/16*a^3/b^4*x^2/(b*x^2+a*x)^(3/2)+35/48*a^4/b^5/(b*x^2+a*x)^(3/2)*x-245/24*a^2/b^4/(b*x^2+a*x)^(1/2)*x-35/48*a^3/b^5/(b*x^2+a*x)^(1/2)+35/8*a^2/b^(9/2)*ln((b*x+1/2*a)/b^(1/2)+(b*x^2+a*x)^(1/2))","A"
61,1,149,78,0.047000," ","int(x^5/(b*x^2+a*x)^(5/2),x)","\frac{x^{4}}{\left(b \,x^{2}+a x \right)^{\frac{3}{2}} b}+\frac{5 a \,x^{3}}{6 \left(b \,x^{2}+a x \right)^{\frac{3}{2}} b^{2}}-\frac{5 a^{2} x^{2}}{4 \left(b \,x^{2}+a x \right)^{\frac{3}{2}} b^{3}}-\frac{5 a^{3} x}{12 \left(b \,x^{2}+a x \right)^{\frac{3}{2}} b^{4}}+\frac{35 a x}{6 \sqrt{b \,x^{2}+a x}\, b^{3}}-\frac{5 a \ln \left(\frac{b x +\frac{a}{2}}{\sqrt{b}}+\sqrt{b \,x^{2}+a x}\right)}{2 b^{\frac{7}{2}}}+\frac{5 a^{2}}{12 \sqrt{b \,x^{2}+a x}\, b^{4}}"," ",0,"x^4/b/(b*x^2+a*x)^(3/2)+5/6*a/b^2*x^3/(b*x^2+a*x)^(3/2)-5/4*a^2/b^3*x^2/(b*x^2+a*x)^(3/2)-5/12*a^3/b^4/(b*x^2+a*x)^(3/2)*x+35/6*a/b^3/(b*x^2+a*x)^(1/2)*x+5/12*a^2/b^4/(b*x^2+a*x)^(1/2)-5/2*a/b^(7/2)*ln((b*x+1/2*a)/b^(1/2)+(b*x^2+a*x)^(1/2))","A"
62,1,123,59,0.046000," ","int(x^4/(b*x^2+a*x)^(5/2),x)","-\frac{x^{3}}{3 \left(b \,x^{2}+a x \right)^{\frac{3}{2}} b}+\frac{a \,x^{2}}{2 \left(b \,x^{2}+a x \right)^{\frac{3}{2}} b^{2}}+\frac{a^{2} x}{6 \left(b \,x^{2}+a x \right)^{\frac{3}{2}} b^{3}}-\frac{7 x}{3 \sqrt{b \,x^{2}+a x}\, b^{2}}+\frac{\ln \left(\frac{b x +\frac{a}{2}}{\sqrt{b}}+\sqrt{b \,x^{2}+a x}\right)}{b^{\frac{5}{2}}}-\frac{a}{6 \sqrt{b \,x^{2}+a x}\, b^{3}}"," ",0,"-1/3*x^3/b/(b*x^2+a*x)^(3/2)+1/2*a/b^2*x^2/(b*x^2+a*x)^(3/2)+1/6*a^2/b^3/(b*x^2+a*x)^(3/2)*x-7/3*x/b^2/(b*x^2+a*x)^(1/2)-1/6*a/b^3/(b*x^2+a*x)^(1/2)+1/b^(5/2)*ln((b*x+1/2*a)/b^(1/2)+(b*x^2+a*x)^(1/2))","B"
63,1,25,19,0.048000," ","int(x^3/(b*x^2+a*x)^(5/2),x)","\frac{2 \left(b x +a \right) x^{4}}{3 \left(b \,x^{2}+a x \right)^{\frac{5}{2}} a}"," ",0,"2/3*(b*x+a)*x^4/a/(b*x^2+a*x)^(5/2)","A"
64,1,33,43,0.045000," ","int(x^2/(b*x^2+a*x)^(5/2),x)","\frac{2 \left(b x +a \right) \left(2 b x +3 a \right) x^{3}}{3 \left(b \,x^{2}+a x \right)^{\frac{5}{2}} a^{2}}"," ",0,"2/3*(b*x+a)*x^3*(2*b*x+3*a)/a^2/(b*x^2+a*x)^(5/2)","A"
65,1,44,40,0.049000," ","int(x/(b*x^2+a*x)^(5/2),x)","-\frac{2 \left(b x +a \right) \left(8 b^{2} x^{2}+12 a b x +3 a^{2}\right) x^{2}}{3 \left(b \,x^{2}+a x \right)^{\frac{5}{2}} a^{3}}"," ",0,"-2/3*(b*x+a)*x^2*(8*b^2*x^2+12*a*b*x+3*a^2)/a^3/(b*x^2+a*x)^(5/2)","A"
66,1,51,46,0.046000," ","int(1/(b*x^2+a*x)^(5/2),x)","-\frac{2 \left(b x +a \right) \left(-16 b^{3} x^{3}-24 a \,b^{2} x^{2}-6 a^{2} b x +a^{3}\right) x}{3 \left(b \,x^{2}+a x \right)^{\frac{5}{2}} a^{4}}"," ",0,"-2/3*(b*x+a)*x*(-16*b^3*x^3-24*a*b^2*x^2-6*a^2*b*x+a^3)/a^4/(b*x^2+a*x)^(5/2)","A"
67,1,63,68,0.043000," ","int(1/x/(b*x^2+a*x)^(5/2),x)","-\frac{2 \left(b x +a \right) \left(128 b^{4} x^{4}+192 a \,b^{3} x^{3}+48 b^{2} x^{2} a^{2}-8 b x \,a^{3}+3 a^{4}\right)}{15 \left(b \,x^{2}+a x \right)^{\frac{5}{2}} a^{5}}"," ",0,"-2/15*(b*x+a)*(128*b^4*x^4+192*a*b^3*x^3+48*a^2*b^2*x^2-8*a^3*b*x+3*a^4)/a^5/(b*x^2+a*x)^(5/2)","A"
68,1,77,90,0.044000," ","int(1/x^2/(b*x^2+a*x)^(5/2),x)","-\frac{2 \left(b x +a \right) \left(-256 b^{5} x^{5}-384 a \,b^{4} x^{4}-96 a^{2} b^{3} x^{3}+16 a^{3} b^{2} x^{2}-6 a^{4} b x +3 a^{5}\right)}{21 \left(b \,x^{2}+a x \right)^{\frac{5}{2}} a^{6} x}"," ",0,"-2/21*(b*x+a)*(-256*b^5*x^5-384*a*b^4*x^4-96*a^2*b^3*x^3+16*a^3*b^2*x^2-6*a^4*b*x+3*a^5)/x/a^6/(b*x^2+a*x)^(5/2)","A"
69,1,23,22,0.043000," ","int(x/(-x^2+4*x)^(1/2),x)","2 \arcsin \left(\frac{x}{2}-1\right)-\sqrt{-x^{2}+4 x}"," ",0,"2*arcsin(-1+1/2*x)-(-x^2+4*x)^(1/2)","A"
70,1,26,24,0.043000," ","int(x/(x^2-4*x)^(1/2),x)","2 \ln \left(x -2+\sqrt{x^{2}-4 x}\right)+\sqrt{x^{2}-4 x}"," ",0,"(x^2-4*x)^(1/2)+2*ln(x-2+(x^2-4*x)^(1/2))","A"
71,1,35,34,0.043000," ","int(x^2/(-x^2+2*x)^(1/2),x)","-\frac{\sqrt{-x^{2}+2 x}\, x}{2}+\frac{3 \arcsin \left(x -1\right)}{2}-\frac{3 \sqrt{-x^{2}+2 x}}{2}"," ",0,"3/2*arcsin(x-1)-3/2*(-x^2+2*x)^(1/2)-1/2*x*(-x^2+2*x)^(1/2)","A"
72,1,66,106,0.045000," ","int(x^(7/2)*(c*x^2+b*x)^(1/2),x)","\frac{2 \left(c x +b \right) \left(315 x^{4} c^{4}-280 x^{3} c^{3} b +240 c^{2} x^{2} b^{2}-192 c x \,b^{3}+128 b^{4}\right) \sqrt{c \,x^{2}+b x}}{3465 c^{5} \sqrt{x}}"," ",0,"2/3465*(c*x+b)*(315*c^4*x^4-280*b*c^3*x^3+240*b^2*c^2*x^2-192*b^3*c*x+128*b^4)*(c*x^2+b*x)^(1/2)/c^5/x^(1/2)","A"
73,1,55,84,0.047000," ","int(x^(5/2)*(c*x^2+b*x)^(1/2),x)","-\frac{2 \left(c x +b \right) \left(-35 x^{3} c^{3}+30 b \,x^{2} c^{2}-24 b^{2} x c +16 b^{3}\right) \sqrt{c \,x^{2}+b x}}{315 c^{4} \sqrt{x}}"," ",0,"-2/315*(c*x+b)*(-35*c^3*x^3+30*b*c^2*x^2-24*b^2*c*x+16*b^3)*(c*x^2+b*x)^(1/2)/c^4/x^(1/2)","A"
74,1,44,62,0.048000," ","int(x^(3/2)*(c*x^2+b*x)^(1/2),x)","\frac{2 \left(c x +b \right) \left(15 c^{2} x^{2}-12 b c x +8 b^{2}\right) \sqrt{c \,x^{2}+b x}}{105 c^{3} \sqrt{x}}"," ",0,"2/105*(c*x+b)*(15*c^2*x^2-12*b*c*x+8*b^2)*(c*x^2+b*x)^(1/2)/c^3/x^(1/2)","A"
75,1,33,40,0.156000," ","int(x^(1/2)*(c*x^2+b*x)^(1/2),x)","-\frac{2 \left(c x +b \right) \left(-3 c x +2 b \right) \sqrt{c \,x^{2}+b x}}{15 c^{2} \sqrt{x}}"," ",0,"-2/15*(c*x+b)*(-3*c*x+2*b)*(c*x^2+b*x)^(1/2)/c^2/x^(1/2)","A"
76,1,25,19,0.039000," ","int((c*x^2+b*x)^(1/2)/x^(1/2),x)","\frac{2 \left(c x +b \right) \sqrt{c \,x^{2}+b x}}{3 c \sqrt{x}}"," ",0,"2/3*(c*x+b)*(c*x^2+b*x)^(1/2)/c/x^(1/2)","A"
77,1,48,41,0.081000," ","int((c*x^2+b*x)^(1/2)/x^(3/2),x)","-\frac{2 \sqrt{\left(c x +b \right) x}\, \left(\sqrt{b}\, \arctanh \left(\frac{\sqrt{c x +b}}{\sqrt{b}}\right)-\sqrt{c x +b}\right)}{\sqrt{c x +b}\, \sqrt{x}}"," ",0,"-2*((c*x+b)*x)^(1/2)/x^(1/2)*(b^(1/2)*arctanh((c*x+b)^(1/2)/b^(1/2))-(c*x+b)^(1/2))/(c*x+b)^(1/2)","A"
78,1,53,42,0.055000," ","int((c*x^2+b*x)^(1/2)/x^(5/2),x)","\frac{\left(-c x \arctanh \left(\frac{\sqrt{c x +b}}{\sqrt{b}}\right)-\sqrt{c x +b}\, \sqrt{b}\right) \sqrt{\left(c x +b \right) x}}{\sqrt{c x +b}\, \sqrt{b}\, x^{\frac{3}{2}}}"," ",0,"(-arctanh((c*x+b)^(1/2)/b^(1/2))*c*x-(c*x+b)^(1/2)*b^(1/2))*((c*x+b)*x)^(1/2)/x^(3/2)/(c*x+b)^(1/2)/b^(1/2)","A"
79,1,71,64,0.066000," ","int((c*x^2+b*x)^(1/2)/x^(7/2),x)","\frac{\sqrt{\left(c x +b \right) x}\, \left(c^{2} x^{2} \arctanh \left(\frac{\sqrt{c x +b}}{\sqrt{b}}\right)-\sqrt{c x +b}\, \sqrt{b}\, c x -2 \sqrt{c x +b}\, b^{\frac{3}{2}}\right)}{4 \sqrt{c x +b}\, b^{\frac{3}{2}} x^{\frac{5}{2}}}"," ",0,"1/4*((c*x+b)*x)^(1/2)/b^(3/2)*(arctanh((c*x+b)^(1/2)/b^(1/2))*c^2*x^2-x*c*(c*x+b)^(1/2)*b^(1/2)-2*(c*x+b)^(1/2)*b^(3/2))/x^(5/2)/(c*x+b)^(1/2)","A"
80,1,90,86,0.060000," ","int((c*x^2+b*x)^(1/2)/x^(9/2),x)","-\frac{\sqrt{\left(c x +b \right) x}\, \left(3 c^{3} x^{3} \arctanh \left(\frac{\sqrt{c x +b}}{\sqrt{b}}\right)-3 \sqrt{c x +b}\, \sqrt{b}\, c^{2} x^{2}+2 \sqrt{c x +b}\, b^{\frac{3}{2}} c x +8 \sqrt{c x +b}\, b^{\frac{5}{2}}\right)}{24 \sqrt{c x +b}\, b^{\frac{5}{2}} x^{\frac{7}{2}}}"," ",0,"-1/24*((c*x+b)*x)^(1/2)/b^(5/2)*(3*arctanh((c*x+b)^(1/2)/b^(1/2))*c^3*x^3-3*x^2*c^2*b^(1/2)*(c*x+b)^(1/2)+2*x*b^(3/2)*c*(c*x+b)^(1/2)+8*(c*x+b)^(1/2)*b^(5/2))/x^(7/2)/(c*x+b)^(1/2)","A"
81,1,108,108,0.062000," ","int((c*x^2+b*x)^(1/2)/x^(11/2),x)","\frac{\sqrt{\left(c x +b \right) x}\, \left(15 c^{4} x^{4} \arctanh \left(\frac{\sqrt{c x +b}}{\sqrt{b}}\right)-15 \sqrt{c x +b}\, \sqrt{b}\, c^{3} x^{3}+10 \sqrt{c x +b}\, b^{\frac{3}{2}} c^{2} x^{2}-8 \sqrt{c x +b}\, b^{\frac{5}{2}} c x -48 \sqrt{c x +b}\, b^{\frac{7}{2}}\right)}{192 \sqrt{c x +b}\, b^{\frac{7}{2}} x^{\frac{9}{2}}}"," ",0,"1/192*((c*x+b)*x)^(1/2)/b^(7/2)*(15*arctanh((c*x+b)^(1/2)/b^(1/2))*c^4*x^4-15*x^3*c^3*b^(1/2)*(c*x+b)^(1/2)+10*x^2*b^(3/2)*c^2*(c*x+b)^(1/2)-8*x*b^(5/2)*c*(c*x+b)^(1/2)-48*b^(7/2)*(c*x+b)^(1/2))/x^(9/2)/(c*x+b)^(1/2)","A"
82,1,77,128,0.043000," ","int(x^(7/2)*(c*x^2+b*x)^(3/2),x)","-\frac{2 \left(c x +b \right) \left(-3003 c^{5} x^{5}+2310 b \,x^{4} c^{4}-1680 b^{2} x^{3} c^{3}+1120 b^{3} x^{2} c^{2}-640 b^{4} x c +256 b^{5}\right) \left(c \,x^{2}+b x \right)^{\frac{3}{2}}}{45045 c^{6} x^{\frac{3}{2}}}"," ",0,"-2/45045*(c*x+b)*(-3003*c^5*x^5+2310*b*c^4*x^4-1680*b^2*c^3*x^3+1120*b^3*c^2*x^2-640*b^4*c*x+256*b^5)*(c*x^2+b*x)^(3/2)/c^6/x^(3/2)","A"
83,1,66,106,0.050000," ","int(x^(5/2)*(c*x^2+b*x)^(3/2),x)","\frac{2 \left(c x +b \right) \left(1155 x^{4} c^{4}-840 x^{3} c^{3} b +560 c^{2} x^{2} b^{2}-320 c x \,b^{3}+128 b^{4}\right) \left(c \,x^{2}+b x \right)^{\frac{3}{2}}}{15015 c^{5} x^{\frac{3}{2}}}"," ",0,"2/15015*(c*x+b)*(1155*c^4*x^4-840*b*c^3*x^3+560*b^2*c^2*x^2-320*b^3*c*x+128*b^4)*(c*x^2+b*x)^(3/2)/c^5/x^(3/2)","A"
84,1,55,84,0.041000," ","int(x^(3/2)*(c*x^2+b*x)^(3/2),x)","-\frac{2 \left(c x +b \right) \left(-105 x^{3} c^{3}+70 b \,x^{2} c^{2}-40 b^{2} x c +16 b^{3}\right) \left(c \,x^{2}+b x \right)^{\frac{3}{2}}}{1155 c^{4} x^{\frac{3}{2}}}"," ",0,"-2/1155*(c*x+b)*(-105*c^3*x^3+70*b*c^2*x^2-40*b^2*c*x+16*b^3)*(c*x^2+b*x)^(3/2)/c^4/x^(3/2)","A"
85,1,44,62,0.049000," ","int(x^(1/2)*(c*x^2+b*x)^(3/2),x)","\frac{2 \left(c x +b \right) \left(35 c^{2} x^{2}-20 b c x +8 b^{2}\right) \left(c \,x^{2}+b x \right)^{\frac{3}{2}}}{315 c^{3} x^{\frac{3}{2}}}"," ",0,"2/315*(c*x+b)*(35*c^2*x^2-20*b*c*x+8*b^2)*(c*x^2+b*x)^(3/2)/c^3/x^(3/2)","A"
86,1,33,40,0.042000," ","int((c*x^2+b*x)^(3/2)/x^(1/2),x)","-\frac{2 \left(c x +b \right) \left(-5 c x +2 b \right) \left(c \,x^{2}+b x \right)^{\frac{3}{2}}}{35 c^{2} x^{\frac{3}{2}}}"," ",0,"-2/35*(c*x+b)*(-5*c*x+2*b)*(c*x^2+b*x)^(3/2)/c^2/x^(3/2)","A"
87,1,25,19,0.045000," ","int((c*x^2+b*x)^(3/2)/x^(3/2),x)","\frac{2 \left(c x +b \right) \left(c \,x^{2}+b x \right)^{\frac{3}{2}}}{5 c \,x^{\frac{3}{2}}}"," ",0,"2/5*(c*x+b)*(c*x^2+b*x)^(3/2)/c/x^(3/2)","A"
88,1,61,58,0.055000," ","int((c*x^2+b*x)^(3/2)/x^(5/2),x)","-\frac{2 \sqrt{\left(c x +b \right) x}\, \left(3 b^{\frac{3}{2}} \arctanh \left(\frac{\sqrt{c x +b}}{\sqrt{b}}\right)-\sqrt{c x +b}\, c x -4 \sqrt{c x +b}\, b \right)}{3 \sqrt{c x +b}\, \sqrt{x}}"," ",0,"-2/3*((c*x+b)*x)^(1/2)*(3*b^(3/2)*arctanh((c*x+b)^(1/2)/b^(1/2))-x*c*(c*x+b)^(1/2)-4*(c*x+b)^(1/2)*b)/x^(1/2)/(c*x+b)^(1/2)","A"
89,1,68,59,0.061000," ","int((c*x^2+b*x)^(3/2)/x^(7/2),x)","\frac{\left(-3 b c x \arctanh \left(\frac{\sqrt{c x +b}}{\sqrt{b}}\right)+2 \sqrt{c x +b}\, \sqrt{b}\, c x -\sqrt{c x +b}\, b^{\frac{3}{2}}\right) \sqrt{\left(c x +b \right) x}}{\sqrt{c x +b}\, \sqrt{b}\, x^{\frac{3}{2}}}"," ",0,"(2*(c*x+b)^(1/2)*b^(1/2)*c*x-3*arctanh((c*x+b)^(1/2)/b^(1/2))*x*b*c-(c*x+b)^(1/2)*b^(3/2))*((c*x+b)*x)^(1/2)/x^(3/2)/(c*x+b)^(1/2)/b^(1/2)","A"
90,1,72,61,0.058000," ","int((c*x^2+b*x)^(3/2)/x^(9/2),x)","-\frac{\sqrt{\left(c x +b \right) x}\, \left(3 c^{2} x^{2} \arctanh \left(\frac{\sqrt{c x +b}}{\sqrt{b}}\right)+5 \sqrt{c x +b}\, \sqrt{b}\, c x +2 \sqrt{c x +b}\, b^{\frac{3}{2}}\right)}{4 \sqrt{c x +b}\, \sqrt{b}\, x^{\frac{5}{2}}}"," ",0,"-1/4*((c*x+b)*x)^(1/2)*(3*arctanh((c*x+b)^(1/2)/b^(1/2))*c^2*x^2+5*(c*x+b)^(1/2)*b^(1/2)*c*x+2*(c*x+b)^(1/2)*b^(3/2))/x^(5/2)/(c*x+b)^(1/2)/b^(1/2)","A"
91,1,90,83,0.059000," ","int((c*x^2+b*x)^(3/2)/x^(11/2),x)","\frac{\sqrt{\left(c x +b \right) x}\, \left(3 c^{3} x^{3} \arctanh \left(\frac{\sqrt{c x +b}}{\sqrt{b}}\right)-3 \sqrt{c x +b}\, \sqrt{b}\, c^{2} x^{2}-14 \sqrt{c x +b}\, b^{\frac{3}{2}} c x -8 \sqrt{c x +b}\, b^{\frac{5}{2}}\right)}{24 \sqrt{c x +b}\, b^{\frac{3}{2}} x^{\frac{7}{2}}}"," ",0,"1/24*((c*x+b)*x)^(1/2)/b^(3/2)*(3*arctanh((c*x+b)^(1/2)/b^(1/2))*c^3*x^3-3*(c*x+b)^(1/2)*b^(1/2)*c^2*x^2-14*(c*x+b)^(1/2)*b^(3/2)*c*x-8*(c*x+b)^(1/2)*b^(5/2))/x^(7/2)/(c*x+b)^(1/2)","A"
92,1,108,105,0.059000," ","int((c*x^2+b*x)^(3/2)/x^(13/2),x)","-\frac{\sqrt{\left(c x +b \right) x}\, \left(3 c^{4} x^{4} \arctanh \left(\frac{\sqrt{c x +b}}{\sqrt{b}}\right)-3 \sqrt{c x +b}\, \sqrt{b}\, c^{3} x^{3}+2 \sqrt{c x +b}\, b^{\frac{3}{2}} c^{2} x^{2}+24 \sqrt{c x +b}\, b^{\frac{5}{2}} c x +16 \sqrt{c x +b}\, b^{\frac{7}{2}}\right)}{64 \sqrt{c x +b}\, b^{\frac{5}{2}} x^{\frac{9}{2}}}"," ",0,"-1/64*((c*x+b)*x)^(1/2)/b^(5/2)*(3*arctanh((c*x+b)^(1/2)/b^(1/2))*c^4*x^4-3*(c*x+b)^(1/2)*b^(1/2)*c^3*x^3+2*(c*x+b)^(1/2)*b^(3/2)*c^2*x^2+24*(c*x+b)^(1/2)*b^(5/2)*c*x+16*(c*x+b)^(1/2)*b^(7/2))/x^(9/2)/(c*x+b)^(1/2)","A"
93,1,126,127,0.062000," ","int((c*x^2+b*x)^(3/2)/x^(15/2),x)","\frac{\sqrt{\left(c x +b \right) x}\, \left(15 c^{5} x^{5} \arctanh \left(\frac{\sqrt{c x +b}}{\sqrt{b}}\right)-15 \sqrt{c x +b}\, \sqrt{b}\, c^{4} x^{4}+10 \sqrt{c x +b}\, b^{\frac{3}{2}} c^{3} x^{3}-8 \sqrt{c x +b}\, b^{\frac{5}{2}} c^{2} x^{2}-176 \sqrt{c x +b}\, b^{\frac{7}{2}} c x -128 \sqrt{c x +b}\, b^{\frac{9}{2}}\right)}{640 \sqrt{c x +b}\, b^{\frac{7}{2}} x^{\frac{11}{2}}}"," ",0,"1/640*((c*x+b)*x)^(1/2)/b^(7/2)*(15*arctanh((c*x+b)^(1/2)/b^(1/2))*c^5*x^5-15*x^4*c^4*b^(1/2)*(c*x+b)^(1/2)+10*x^3*b^(3/2)*c^3*(c*x+b)^(1/2)-8*x^2*b^(5/2)*c^2*(c*x+b)^(1/2)-176*x*b^(7/2)*c*(c*x+b)^(1/2)-128*b^(9/2)*(c*x+b)^(1/2))/x^(11/2)/(c*x+b)^(1/2)","A"
94,1,55,84,0.041000," ","int(x^(7/2)/(c*x^2+b*x)^(1/2),x)","-\frac{2 \left(c x +b \right) \left(-5 x^{3} c^{3}+6 b \,x^{2} c^{2}-8 b^{2} x c +16 b^{3}\right) \sqrt{x}}{35 \sqrt{c \,x^{2}+b x}\, c^{4}}"," ",0,"-2/35*(c*x+b)*(-5*c^3*x^3+6*b*c^2*x^2-8*b^2*c*x+16*b^3)*x^(1/2)/c^4/(c*x^2+b*x)^(1/2)","A"
95,1,44,62,0.047000," ","int(x^(5/2)/(c*x^2+b*x)^(1/2),x)","\frac{2 \left(c x +b \right) \left(3 c^{2} x^{2}-4 b c x +8 b^{2}\right) \sqrt{x}}{15 \sqrt{c \,x^{2}+b x}\, c^{3}}"," ",0,"2/15*(c*x+b)*(3*c^2*x^2-4*b*c*x+8*b^2)*x^(1/2)/c^3/(c*x^2+b*x)^(1/2)","A"
96,1,33,40,0.044000," ","int(x^(3/2)/(c*x^2+b*x)^(1/2),x)","-\frac{2 \left(c x +b \right) \left(-c x +2 b \right) \sqrt{x}}{3 \sqrt{c \,x^{2}+b x}\, c^{2}}"," ",0,"-2/3*(c*x+b)*(-c*x+2*b)*x^(1/2)/c^2/(c*x^2+b*x)^(1/2)","A"
97,1,25,19,0.043000," ","int(x^(1/2)/(c*x^2+b*x)^(1/2),x)","\frac{2 \left(c x +b \right) \sqrt{x}}{\sqrt{c \,x^{2}+b x}\, c}"," ",0,"2*(c*x+b)*x^(1/2)/c/(c*x^2+b*x)^(1/2)","A"
98,1,37,24,0.048000," ","int(1/x^(1/2)/(c*x^2+b*x)^(1/2),x)","-\frac{2 \sqrt{\left(c x +b \right) x}\, \arctanh \left(\frac{\sqrt{c x +b}}{\sqrt{b}}\right)}{\sqrt{c x +b}\, \sqrt{b}\, \sqrt{x}}"," ",0,"-2/x^(1/2)*((c*x+b)*x)^(1/2)/(c*x+b)^(1/2)/b^(1/2)*arctanh((c*x+b)^(1/2)/b^(1/2))","A"
99,1,52,44,0.062000," ","int(1/x^(3/2)/(c*x^2+b*x)^(1/2),x)","\frac{\sqrt{\left(c x +b \right) x}\, \left(c x \arctanh \left(\frac{\sqrt{c x +b}}{\sqrt{b}}\right)-\sqrt{c x +b}\, \sqrt{b}\right)}{\sqrt{c x +b}\, b^{\frac{3}{2}} x^{\frac{3}{2}}}"," ",0,"((c*x+b)*x)^(1/2)/b^(3/2)*(arctanh((c*x+b)^(1/2)/b^(1/2))*c*x-(c*x+b)^(1/2)*b^(1/2))/x^(3/2)/(c*x+b)^(1/2)","A"
100,1,72,67,0.053000," ","int(1/x^(5/2)/(c*x^2+b*x)^(1/2),x)","-\frac{\sqrt{\left(c x +b \right) x}\, \left(3 c^{2} x^{2} \arctanh \left(\frac{\sqrt{c x +b}}{\sqrt{b}}\right)-3 \sqrt{c x +b}\, \sqrt{b}\, c x +2 \sqrt{c x +b}\, b^{\frac{3}{2}}\right)}{4 \sqrt{c x +b}\, b^{\frac{5}{2}} x^{\frac{5}{2}}}"," ",0,"-1/4*((c*x+b)*x)^(1/2)/b^(5/2)*(3*arctanh((c*x+b)^(1/2)/b^(1/2))*c^2*x^2-3*(c*x+b)^(1/2)*b^(1/2)*c*x+2*(c*x+b)^(1/2)*b^(3/2))/x^(5/2)/(c*x+b)^(1/2)","A"
101,1,90,89,0.062000," ","int(1/x^(7/2)/(c*x^2+b*x)^(1/2),x)","\frac{\sqrt{\left(c x +b \right) x}\, \left(15 c^{3} x^{3} \arctanh \left(\frac{\sqrt{c x +b}}{\sqrt{b}}\right)-15 \sqrt{c x +b}\, \sqrt{b}\, c^{2} x^{2}+10 \sqrt{c x +b}\, b^{\frac{3}{2}} c x -8 \sqrt{c x +b}\, b^{\frac{5}{2}}\right)}{24 \sqrt{c x +b}\, b^{\frac{7}{2}} x^{\frac{7}{2}}}"," ",0,"1/24*((c*x+b)*x)^(1/2)/b^(7/2)*(15*arctanh((c*x+b)^(1/2)/b^(1/2))*c^3*x^3-15*(c*x+b)^(1/2)*b^(1/2)*c^2*x^2+10*(c*x+b)^(1/2)*b^(3/2)*c*x-8*(c*x+b)^(1/2)*b^(5/2))/x^(7/2)/(c*x+b)^(1/2)","A"
102,1,77,128,0.041000," ","int(x^(13/2)/(c*x^2+b*x)^(3/2),x)","\frac{2 \left(c x +b \right) \left(7 c^{5} x^{5}-10 b \,x^{4} c^{4}+16 b^{2} x^{3} c^{3}-32 b^{3} x^{2} c^{2}+128 b^{4} x c +256 b^{5}\right) x^{\frac{3}{2}}}{63 \left(c \,x^{2}+b x \right)^{\frac{3}{2}} c^{6}}"," ",0,"2/63*(c*x+b)*(7*c^5*x^5-10*b*c^4*x^4+16*b^2*c^3*x^3-32*b^3*c^2*x^2+128*b^4*c*x+256*b^5)*x^(3/2)/c^6/(c*x^2+b*x)^(3/2)","A"
103,1,66,106,0.049000," ","int(x^(11/2)/(c*x^2+b*x)^(3/2),x)","-\frac{2 \left(c x +b \right) \left(-5 x^{4} c^{4}+8 x^{3} c^{3} b -16 c^{2} x^{2} b^{2}+64 c x \,b^{3}+128 b^{4}\right) x^{\frac{3}{2}}}{35 \left(c \,x^{2}+b x \right)^{\frac{3}{2}} c^{5}}"," ",0,"-2/35*(c*x+b)*(-5*c^4*x^4+8*b*c^3*x^3-16*b^2*c^2*x^2+64*b^3*c*x+128*b^4)*x^(3/2)/c^5/(c*x^2+b*x)^(3/2)","A"
104,1,54,84,0.040000," ","int(x^(9/2)/(c*x^2+b*x)^(3/2),x)","\frac{2 \left(c x +b \right) \left(x^{3} c^{3}-2 b \,x^{2} c^{2}+8 b^{2} x c +16 b^{3}\right) x^{\frac{3}{2}}}{5 \left(c \,x^{2}+b x \right)^{\frac{3}{2}} c^{4}}"," ",0,"2/5*(c*x+b)*(c^3*x^3-2*b*c^2*x^2+8*b^2*c*x+16*b^3)*x^(3/2)/c^4/(c*x^2+b*x)^(3/2)","A"
105,1,44,62,0.042000," ","int(x^(7/2)/(c*x^2+b*x)^(3/2),x)","-\frac{2 \left(c x +b \right) \left(-c^{2} x^{2}+4 b c x +8 b^{2}\right) x^{\frac{3}{2}}}{3 \left(c \,x^{2}+b x \right)^{\frac{3}{2}} c^{3}}"," ",0,"-2/3*(c*x+b)*(-c^2*x^2+4*b*c*x+8*b^2)*x^(3/2)/c^3/(c*x^2+b*x)^(3/2)","A"
106,1,32,40,0.045000," ","int(x^(5/2)/(c*x^2+b*x)^(3/2),x)","\frac{2 \left(c x +b \right) \left(c x +2 b \right) x^{\frac{3}{2}}}{\left(c \,x^{2}+b x \right)^{\frac{3}{2}} c^{2}}"," ",0,"2*(c*x+b)*(c*x+2*b)*x^(3/2)/c^2/(c*x^2+b*x)^(3/2)","A"
107,1,25,19,0.040000," ","int(x^(3/2)/(c*x^2+b*x)^(3/2),x)","-\frac{2 \left(c x +b \right) x^{\frac{3}{2}}}{\left(c \,x^{2}+b x \right)^{\frac{3}{2}} c}"," ",0,"-2*(c*x+b)*x^(3/2)/c/(c*x^2+b*x)^(3/2)","A"
108,1,51,44,0.059000," ","int(x^(1/2)/(c*x^2+b*x)^(3/2),x)","-\frac{2 \sqrt{\left(c x +b \right) x}\, \left(\sqrt{c x +b}\, \arctanh \left(\frac{\sqrt{c x +b}}{\sqrt{b}}\right)-\sqrt{b}\right)}{\left(c x +b \right) b^{\frac{3}{2}} \sqrt{x}}"," ",0,"-2*((c*x+b)*x)^(1/2)/b^(3/2)*(arctanh((c*x+b)^(1/2)/b^(1/2))*(c*x+b)^(1/2)-b^(1/2))/x^(1/2)/(c*x+b)","A"
109,1,60,65,0.064000," ","int(1/x^(1/2)/(c*x^2+b*x)^(3/2),x)","\frac{\sqrt{\left(c x +b \right) x}\, \left(3 \sqrt{c x +b}\, c x \arctanh \left(\frac{\sqrt{c x +b}}{\sqrt{b}}\right)-3 \sqrt{b}\, c x -b^{\frac{3}{2}}\right)}{\left(c x +b \right) b^{\frac{5}{2}} x^{\frac{3}{2}}}"," ",0,"((c*x+b)*x)^(1/2)*(3*arctanh((c*x+b)^(1/2)/b^(1/2))*(c*x+b)^(1/2)*x*c-3*c*x*b^(1/2)-b^(3/2))/x^(3/2)/(c*x+b)/b^(5/2)","A"
110,1,76,89,0.058000," ","int(1/x^(3/2)/(c*x^2+b*x)^(3/2),x)","-\frac{\sqrt{\left(c x +b \right) x}\, \left(15 \sqrt{c x +b}\, c^{2} x^{2} \arctanh \left(\frac{\sqrt{c x +b}}{\sqrt{b}}\right)-15 \sqrt{b}\, c^{2} x^{2}-5 b^{\frac{3}{2}} c x +2 b^{\frac{5}{2}}\right)}{4 \left(c x +b \right) b^{\frac{7}{2}} x^{\frac{5}{2}}}"," ",0,"-1/4/x^(5/2)*((c*x+b)*x)^(1/2)*(15*(c*x+b)^(1/2)*arctanh((c*x+b)^(1/2)/b^(1/2))*x^2*c^2-5*b^(3/2)*x*c-15*x^2*c^2*b^(1/2)+2*b^(5/2))/(c*x+b)/b^(7/2)","A"
111,1,87,111,0.065000," ","int(1/x^(5/2)/(c*x^2+b*x)^(3/2),x)","\frac{\sqrt{\left(c x +b \right) x}\, \left(105 \sqrt{c x +b}\, c^{3} x^{3} \arctanh \left(\frac{\sqrt{c x +b}}{\sqrt{b}}\right)-105 \sqrt{b}\, c^{3} x^{3}-35 b^{\frac{3}{2}} c^{2} x^{2}+14 b^{\frac{5}{2}} c x -8 b^{\frac{7}{2}}\right)}{24 \left(c x +b \right) b^{\frac{9}{2}} x^{\frac{7}{2}}}"," ",0,"1/24/x^(7/2)*((c*x+b)*x)^(1/2)*(105*(c*x+b)^(1/2)*arctanh((c*x+b)^(1/2)/b^(1/2))*x^3*c^3+14*b^(5/2)*x*c-35*b^(3/2)*x^2*c^2-105*c^3*x^3*b^(1/2)-8*b^(7/2))/(c*x+b)/b^(9/2)","A"
112,1,173,81,0.044000," ","int((d*x)^m*(c*x^2+b*x)^3,x)","\frac{\left(c^{3} m^{3} x^{3}+3 b \,c^{2} m^{3} x^{2}+15 c^{3} m^{2} x^{3}+3 b^{2} c \,m^{3} x +48 b \,c^{2} m^{2} x^{2}+74 c^{3} m \,x^{3}+b^{3} m^{3}+51 b^{2} c \,m^{2} x +249 b \,c^{2} m \,x^{2}+120 x^{3} c^{3}+18 b^{3} m^{2}+282 b^{2} c m x +420 b \,x^{2} c^{2}+107 b^{3} m +504 b^{2} x c +210 b^{3}\right) x^{4} \left(d x \right)^{m}}{\left(m +7\right) \left(m +6\right) \left(m +5\right) \left(m +4\right)}"," ",0,"(d*x)^m*(c^3*m^3*x^3+3*b*c^2*m^3*x^2+15*c^3*m^2*x^3+3*b^2*c*m^3*x+48*b*c^2*m^2*x^2+74*c^3*m*x^3+b^3*m^3+51*b^2*c*m^2*x+249*b*c^2*m*x^2+120*c^3*x^3+18*b^3*m^2+282*b^2*c*m*x+420*b*c^2*x^2+107*b^3*m+504*b^2*c*x+210*b^3)*x^4/(m+7)/(6+m)/(m+5)/(m+4)","B"
113,1,90,58,0.042000," ","int((d*x)^m*(c*x^2+b*x)^2,x)","\frac{\left(c^{2} m^{2} x^{2}+2 b c \,m^{2} x +7 c^{2} m \,x^{2}+b^{2} m^{2}+16 b c m x +12 c^{2} x^{2}+9 b^{2} m +30 b c x +20 b^{2}\right) x^{3} \left(d x \right)^{m}}{\left(m +5\right) \left(m +4\right) \left(m +3\right)}"," ",0,"(d*x)^m*(c^2*m^2*x^2+2*b*c*m^2*x+7*c^2*m*x^2+b^2*m^2+16*b*c*m*x+12*c^2*x^2+9*b^2*m+30*b*c*x+20*b^2)*x^3/(m+5)/(m+4)/(m+3)","A"
114,1,35,35,0.038000," ","int((d*x)^m*(c*x^2+b*x),x)","\frac{\left(c m x +b m +2 c x +3 b \right) x^{2} \left(d x \right)^{m}}{\left(m +3\right) \left(m +2\right)}"," ",0,"(d*x)^m*(c*m*x+b*m+2*c*x+3*b)*x^2/(m+3)/(m+2)","A"
115,0,0,27,0.529000," ","int((d*x)^m/(c*x^2+b*x),x)","\int \frac{\left(d x \right)^{m}}{c \,x^{2}+b x}\, dx"," ",0,"int((d*x)^m/(c*x^2+b*x),x)","F"
116,0,0,35,0.510000," ","int((d*x)^m/(c*x^2+b*x)^2,x)","\int \frac{\left(d x \right)^{m}}{\left(c \,x^{2}+b x \right)^{2}}\, dx"," ",0,"int((d*x)^m/(c*x^2+b*x)^2,x)","F"
117,0,0,39,0.510000," ","int((d*x)^m/(c*x^2+b*x)^3,x)","\int \frac{\left(d x \right)^{m}}{\left(c \,x^{2}+b x \right)^{3}}\, dx"," ",0,"int((d*x)^m/(c*x^2+b*x)^3,x)","F"
118,0,0,63,0.513000," ","int((d*x)^m*(c*x^2+b*x)^(5/2),x)","\int \left(c \,x^{2}+b x \right)^{\frac{5}{2}} \left(d x \right)^{m}\, dx"," ",0,"int((d*x)^m*(c*x^2+b*x)^(5/2),x)","F"
119,0,0,61,0.510000," ","int((d*x)^m*(c*x^2+b*x)^(3/2),x)","\int \left(c \,x^{2}+b x \right)^{\frac{3}{2}} \left(d x \right)^{m}\, dx"," ",0,"int((d*x)^m*(c*x^2+b*x)^(3/2),x)","F"
120,0,0,57,0.506000," ","int((d*x)^m*(c*x^2+b*x)^(1/2),x)","\int \sqrt{c \,x^{2}+b x}\, \left(d x \right)^{m}\, dx"," ",0,"int((d*x)^m*(c*x^2+b*x)^(1/2),x)","F"
121,0,0,57,0.612000," ","int((d*x)^m/(c*x^2+b*x)^(1/2),x)","\int \frac{\left(d x \right)^{m}}{\sqrt{c \,x^{2}+b x}}\, dx"," ",0,"int((d*x)^m/(c*x^2+b*x)^(1/2),x)","F"
122,0,0,58,0.508000," ","int((d*x)^m/(c*x^2+b*x)^(3/2),x)","\int \frac{\left(d x \right)^{m}}{\left(c \,x^{2}+b x \right)^{\frac{3}{2}}}\, dx"," ",0,"int((d*x)^m/(c*x^2+b*x)^(3/2),x)","F"
123,0,0,61,0.511000," ","int((d*x)^m/(c*x^2+b*x)^(5/2),x)","\int \frac{\left(d x \right)^{m}}{\left(c \,x^{2}+b x \right)^{\frac{5}{2}}}\, dx"," ",0,"int((d*x)^m/(c*x^2+b*x)^(5/2),x)","F"
124,0,0,57,0.511000," ","int((d*x)^m*(c*x^2+b*x)^p,x)","\int \left(d x \right)^{m} \left(c \,x^{2}+b x \right)^{p}\, dx"," ",0,"int((d*x)^m*(c*x^2+b*x)^p,x)","F"
125,0,0,51,0.508000," ","int(x^3*(c*x^2+b*x)^p,x)","\int x^{3} \left(c \,x^{2}+b x \right)^{p}\, dx"," ",0,"int(x^3*(c*x^2+b*x)^p,x)","F"
126,0,0,51,0.511000," ","int(x^2*(c*x^2+b*x)^p,x)","\int x^{2} \left(c \,x^{2}+b x \right)^{p}\, dx"," ",0,"int(x^2*(c*x^2+b*x)^p,x)","F"
127,0,0,51,0.507000," ","int(x*(c*x^2+b*x)^p,x)","\int x \left(c \,x^{2}+b x \right)^{p}\, dx"," ",0,"int(x*(c*x^2+b*x)^p,x)","F"
128,0,0,44,0.503000," ","int((c*x^2+b*x)^p/x,x)","\int \frac{\left(c \,x^{2}+b x \right)^{p}}{x}\, dx"," ",0,"int((c*x^2+b*x)^p/x,x)","F"
129,0,0,52,0.498000," ","int((c*x^2+b*x)^p/x^2,x)","\int \frac{\left(c \,x^{2}+b x \right)^{p}}{x^{2}}\, dx"," ",0,"int((c*x^2+b*x)^p/x^2,x)","F"
130,0,0,54,0.504000," ","int((c*x^2+b*x)^p/x^3,x)","\int \frac{\left(c \,x^{2}+b x \right)^{p}}{x^{3}}\, dx"," ",0,"int((c*x^2+b*x)^p/x^3,x)","F"
131,0,0,57,0.591000," ","int((d*x)^(5/2)*(c*x^2+b*x)^p,x)","\int \left(d x \right)^{\frac{5}{2}} \left(c \,x^{2}+b x \right)^{p}\, dx"," ",0,"int((d*x)^(5/2)*(c*x^2+b*x)^p,x)","F"
132,0,0,57,0.519000," ","int((d*x)^(3/2)*(c*x^2+b*x)^p,x)","\int \left(d x \right)^{\frac{3}{2}} \left(c \,x^{2}+b x \right)^{p}\, dx"," ",0,"int((d*x)^(3/2)*(c*x^2+b*x)^p,x)","F"
133,0,0,57,0.513000," ","int((d*x)^(1/2)*(c*x^2+b*x)^p,x)","\int \sqrt{d x}\, \left(c \,x^{2}+b x \right)^{p}\, dx"," ",0,"int((d*x)^(1/2)*(c*x^2+b*x)^p,x)","F"
134,0,0,57,0.517000," ","int((c*x^2+b*x)^p/(d*x)^(1/2),x)","\int \frac{\left(c \,x^{2}+b x \right)^{p}}{\sqrt{d x}}\, dx"," ",0,"int((c*x^2+b*x)^p/(d*x)^(1/2),x)","F"
135,0,0,57,0.524000," ","int((c*x^2+b*x)^p/(d*x)^(3/2),x)","\int \frac{\left(c \,x^{2}+b x \right)^{p}}{\left(d x \right)^{\frac{3}{2}}}\, dx"," ",0,"int((c*x^2+b*x)^p/(d*x)^(3/2),x)","F"
136,-1,0,57,180.000000," ","int((c*x^2+b*x)^p/(d*x)^(5/2),x)","\text{hanged}"," ",0,"int((c*x^2+b*x)^p/(d*x)^(5/2),x)","F"
137,1,30,45,0.048000," ","int(x^4*((b*x+a)^2)^(1/2),x)","\frac{\left(5 b x +6 a \right) \sqrt{\left(b x +a \right)^{2}}\, x^{5}}{30 b x +30 a}"," ",0,"1/30*x^5*(5*b*x+6*a)*((b*x+a)^2)^(1/2)/(b*x+a)","A"
138,1,30,45,0.047000," ","int(x^3*((b*x+a)^2)^(1/2),x)","\frac{\left(4 b x +5 a \right) \sqrt{\left(b x +a \right)^{2}}\, x^{4}}{20 b x +20 a}"," ",0,"1/20*x^4*(4*b*x+5*a)*((b*x+a)^2)^(1/2)/(b*x+a)","A"
139,1,30,45,0.043000," ","int(x^2*((b*x+a)^2)^(1/2),x)","\frac{\left(3 b x +4 a \right) \sqrt{\left(b x +a \right)^{2}}\, x^{3}}{12 b x +12 a}"," ",0,"1/12*x^3*(3*b*x+4*a)*((b*x+a)^2)^(1/2)/(b*x+a)","A"
140,1,30,44,0.049000," ","int(x*((b*x+a)^2)^(1/2),x)","\frac{\left(2 b x +3 a \right) \sqrt{\left(b x +a \right)^{2}}\, x^{2}}{6 b x +6 a}"," ",0,"1/6*x^2*(2*b*x+3*a)*((b*x+a)^2)^(1/2)/(b*x+a)","A"
141,1,27,19,0.040000," ","int(((b*x+a)^2)^(1/2),x)","\frac{\left(b x +2 a \right) \sqrt{\left(b x +a \right)^{2}}\, x}{2 b x +2 a}"," ",0,"1/2*x*(b*x+2*a)*((b*x+a)^2)^(1/2)/(b*x+a)","A"
142,1,19,40,0.172000," ","int(((b*x+a)^2)^(1/2)/x,x)","\left(a \ln \left(b x \right)+b x +a \right) \mathrm{csgn}\left(b x +a \right)"," ",0,"csgn(b*x+a)*(b*x+a+a*ln(b*x))","C"
143,1,22,43,0.053000," ","int(((b*x+a)^2)^(1/2)/x^2,x)","\frac{\left(b x \ln \left(b x \right)-a \right) \mathrm{csgn}\left(b x +a \right)}{x}"," ",0,"csgn(b*x+a)*(ln(b*x)*x*b-a)/x","C"
144,1,28,22,0.043000," ","int(((b*x+a)^2)^(1/2)/x^3,x)","-\frac{\left(2 b x +a \right) \sqrt{\left(b x +a \right)^{2}}}{2 \left(b x +a \right) x^{2}}"," ",0,"-1/2*(2*b*x+a)*((b*x+a)^2)^(1/2)/x^2/(b*x+a)","A"
145,1,30,45,0.043000," ","int(((b*x+a)^2)^(1/2)/x^4,x)","-\frac{\left(3 b x +2 a \right) \sqrt{\left(b x +a \right)^{2}}}{6 \left(b x +a \right) x^{3}}"," ",0,"-1/6*(3*b*x+2*a)*((b*x+a)^2)^(1/2)/x^3/(b*x+a)","A"
146,1,30,45,0.045000," ","int(((b*x+a)^2)^(1/2)/x^5,x)","-\frac{\left(4 b x +3 a \right) \sqrt{\left(b x +a \right)^{2}}}{12 \left(b x +a \right) x^{4}}"," ",0,"-1/12*(4*b*x+3*a)*((b*x+a)^2)^(1/2)/x^4/(b*x+a)","A"
147,1,30,45,0.042000," ","int(((b*x+a)^2)^(1/2)/x^6,x)","-\frac{\left(5 b x +4 a \right) \sqrt{\left(b x +a \right)^{2}}}{20 \left(b x +a \right) x^{5}}"," ",0,"-1/20*(5*b*x+4*a)*((b*x+a)^2)^(1/2)/x^5/(b*x+a)","A"
148,1,52,99,0.051000," ","int(x^5*(b^2*x^2+2*a*b*x+a^2)^(3/2),x)","\frac{\left(56 b^{3} x^{3}+189 a \,b^{2} x^{2}+216 a^{2} b x +84 a^{3}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}} x^{6}}{504 \left(b x +a \right)^{3}}"," ",0,"1/504*x^6*(56*b^3*x^3+189*a*b^2*x^2+216*a^2*b*x+84*a^3)*((b*x+a)^2)^(3/2)/(b*x+a)^3","A"
149,1,52,99,0.046000," ","int(x^4*(b^2*x^2+2*a*b*x+a^2)^(3/2),x)","\frac{\left(35 b^{3} x^{3}+120 a \,b^{2} x^{2}+140 a^{2} b x +56 a^{3}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}} x^{5}}{280 \left(b x +a \right)^{3}}"," ",0,"1/280*x^5*(35*b^3*x^3+120*a*b^2*x^2+140*a^2*b*x+56*a^3)*((b*x+a)^2)^(3/2)/(b*x+a)^3","A"
150,1,52,99,0.049000," ","int(x^3*(b^2*x^2+2*a*b*x+a^2)^(3/2),x)","\frac{\left(20 b^{3} x^{3}+70 a \,b^{2} x^{2}+84 a^{2} b x +35 a^{3}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}} x^{4}}{140 \left(b x +a \right)^{3}}"," ",0,"1/140*x^4*(20*b^3*x^3+70*a*b^2*x^2+84*a^2*b*x+35*a^3)*((b*x+a)^2)^(3/2)/(b*x+a)^3","A"
151,1,52,84,0.046000," ","int(x^2*(b^2*x^2+2*a*b*x+a^2)^(3/2),x)","\frac{\left(10 b^{3} x^{3}+36 a \,b^{2} x^{2}+45 a^{2} b x +20 a^{3}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}} x^{3}}{60 \left(b x +a \right)^{3}}"," ",0,"1/60*x^3*(10*b^3*x^3+36*a*b^2*x^2+45*a^2*b*x+20*a^3)*((b*x+a)^2)^(3/2)/(b*x+a)^3","A"
152,1,52,53,0.044000," ","int(x*(b^2*x^2+2*a*b*x+a^2)^(3/2),x)","\frac{\left(4 b^{3} x^{3}+15 a \,b^{2} x^{2}+20 a^{2} b x +10 a^{3}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}} x^{2}}{20 \left(b x +a \right)^{3}}"," ",0,"1/20*x^2*(4*b^3*x^3+15*a*b^2*x^2+20*a^2*b*x+10*a^3)*((b*x+a)^2)^(3/2)/(b*x+a)^3","A"
153,1,49,28,0.043000," ","int((b^2*x^2+2*a*b*x+a^2)^(3/2),x)","\frac{\left(b^{3} x^{3}+4 a \,b^{2} x^{2}+6 a^{2} b x +4 a^{3}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}} x}{4 \left(b x +a \right)^{3}}"," ",0,"1/4*x*(b^3*x^3+4*a*b^2*x^2+6*a^2*b*x+4*a^3)*((b*x+a)^2)^(3/2)/(b*x+a)^3","A"
154,1,51,95,0.053000," ","int((b^2*x^2+2*a*b*x+a^2)^(3/2)/x,x)","\frac{\left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}} \left(2 b^{3} x^{3}+9 a \,b^{2} x^{2}+6 a^{3} \ln \left(x \right)+18 a^{2} b x \right)}{6 \left(b x +a \right)^{3}}"," ",0,"1/6*((b*x+a)^2)^(3/2)*(2*b^3*x^3+9*a*b^2*x^2+6*a^3*ln(x)+18*a^2*b*x)/(b*x+a)^3","A"
155,1,53,96,0.054000," ","int((b^2*x^2+2*a*b*x+a^2)^(3/2)/x^2,x)","\frac{\left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}} \left(b^{3} x^{3}+6 a^{2} b x \ln \left(x \right)+6 a \,b^{2} x^{2}-2 a^{3}\right)}{2 \left(b x +a \right)^{3} x}"," ",0,"1/2*((b*x+a)^2)^(3/2)*(b^3*x^3+6*a^2*b*ln(x)*x+6*a*b^2*x^2-2*a^3)/(b*x+a)^3/x","A"
156,1,54,95,0.057000," ","int((b^2*x^2+2*a*b*x+a^2)^(3/2)/x^3,x)","\frac{\left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}} \left(6 a \,b^{2} x^{2} \ln \left(x \right)+2 b^{3} x^{3}-6 a^{2} b x -a^{3}\right)}{2 \left(b x +a \right)^{3} x^{2}}"," ",0,"1/2*((b*x+a)^2)^(3/2)*(6*a*b^2*ln(x)*x^2+2*b^3*x^3-6*a^2*b*x-a^3)/(b*x+a)^3/x^2","A"
157,1,54,97,0.056000," ","int((b^2*x^2+2*a*b*x+a^2)^(3/2)/x^4,x)","\frac{\left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}} \left(6 b^{3} x^{3} \ln \left(x \right)-18 a \,b^{2} x^{2}-9 a^{2} b x -2 a^{3}\right)}{6 \left(b x +a \right)^{3} x^{3}}"," ",0,"1/6*((b*x+a)^2)^(3/2)*(6*b^3*ln(x)*x^3-18*a*b^2*x^2-9*a^2*b*x-2*a^3)/(b*x+a)^3/x^3","A"
158,1,50,24,0.046000," ","int((b^2*x^2+2*a*b*x+a^2)^(3/2)/x^5,x)","-\frac{\left(4 b^{3} x^{3}+6 a \,b^{2} x^{2}+4 a^{2} b x +a^{3}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}}}{4 \left(b x +a \right)^{3} x^{4}}"," ",0,"-1/4*(4*b^3*x^3+6*a*b^2*x^2+4*a^2*b*x+a^3)*((b*x+a)^2)^(3/2)/x^4/(b*x+a)^3","B"
159,1,52,50,0.047000," ","int((b^2*x^2+2*a*b*x+a^2)^(3/2)/x^6,x)","-\frac{\left(10 b^{3} x^{3}+20 a \,b^{2} x^{2}+15 a^{2} b x +4 a^{3}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}}}{20 \left(b x +a \right)^{3} x^{5}}"," ",0,"-1/20*(10*b^3*x^3+20*a*b^2*x^2+15*a^2*b*x+4*a^3)*((b*x+a)^2)^(3/2)/x^5/(b*x+a)^3","A"
160,1,52,99,0.046000," ","int((b^2*x^2+2*a*b*x+a^2)^(3/2)/x^7,x)","-\frac{\left(20 b^{3} x^{3}+45 a \,b^{2} x^{2}+36 a^{2} b x +10 a^{3}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}}}{60 \left(b x +a \right)^{3} x^{6}}"," ",0,"-1/60*(20*b^3*x^3+45*a*b^2*x^2+36*a^2*b*x+10*a^3)*((b*x+a)^2)^(3/2)/x^6/(b*x+a)^3","A"
161,1,52,99,0.047000," ","int((b^2*x^2+2*a*b*x+a^2)^(3/2)/x^8,x)","-\frac{\left(35 b^{3} x^{3}+84 a \,b^{2} x^{2}+70 a^{2} b x +20 a^{3}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}}}{140 \left(b x +a \right)^{3} x^{7}}"," ",0,"-1/140*(35*b^3*x^3+84*a*b^2*x^2+70*a^2*b*x+20*a^3)*((b*x+a)^2)^(3/2)/x^7/(b*x+a)^3","A"
162,1,52,99,0.046000," ","int((b^2*x^2+2*a*b*x+a^2)^(3/2)/x^9,x)","-\frac{\left(56 b^{3} x^{3}+140 a \,b^{2} x^{2}+120 a^{2} b x +35 a^{3}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}}}{280 \left(b x +a \right)^{3} x^{8}}"," ",0,"-1/280*(56*b^3*x^3+140*a*b^2*x^2+120*a^2*b*x+35*a^3)*((b*x+a)^2)^(3/2)/x^8/(b*x+a)^3","A"
163,1,74,153,0.047000," ","int(x^5*(b^2*x^2+2*a*b*x+a^2)^(5/2),x)","\frac{\left(252 b^{5} x^{5}+1386 a \,b^{4} x^{4}+3080 a^{2} b^{3} x^{3}+3465 a^{3} b^{2} x^{2}+1980 a^{4} b x +462 a^{5}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}} x^{6}}{2772 \left(b x +a \right)^{5}}"," ",0,"1/2772*x^6*(252*b^5*x^5+1386*a*b^4*x^4+3080*a^2*b^3*x^3+3465*a^3*b^2*x^2+1980*a^4*b*x+462*a^5)*((b*x+a)^2)^(5/2)/(b*x+a)^5","A"
164,1,74,116,0.048000," ","int(x^4*(b^2*x^2+2*a*b*x+a^2)^(5/2),x)","\frac{\left(126 b^{5} x^{5}+700 a \,b^{4} x^{4}+1575 a^{2} b^{3} x^{3}+1800 a^{3} b^{2} x^{2}+1050 a^{4} b x +252 a^{5}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}} x^{5}}{1260 \left(b x +a \right)^{5}}"," ",0,"1/1260*x^5*(126*b^5*x^5+700*a*b^4*x^4+1575*a^2*b^3*x^3+1800*a^3*b^2*x^2+1050*a^4*b*x+252*a^5)*((b*x+a)^2)^(5/2)/(b*x+a)^5","A"
165,1,74,92,0.052000," ","int(x^3*(b^2*x^2+2*a*b*x+a^2)^(5/2),x)","\frac{\left(56 b^{5} x^{5}+315 a \,b^{4} x^{4}+720 a^{2} b^{3} x^{3}+840 a^{3} b^{2} x^{2}+504 a^{4} b x +126 a^{5}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}} x^{4}}{504 \left(b x +a \right)^{5}}"," ",0,"1/504*x^4*(56*b^5*x^5+315*a*b^4*x^4+720*a^2*b^3*x^3+840*a^3*b^2*x^2+504*a^4*b*x+126*a^5)*((b*x+a)^2)^(5/2)/(b*x+a)^5","A"
166,1,74,68,0.050000," ","int(x^2*(b^2*x^2+2*a*b*x+a^2)^(5/2),x)","\frac{\left(21 b^{5} x^{5}+120 a \,b^{4} x^{4}+280 a^{2} b^{3} x^{3}+336 a^{3} b^{2} x^{2}+210 a^{4} b x +56 a^{5}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}} x^{3}}{168 \left(b x +a \right)^{5}}"," ",0,"1/168*x^3*(21*b^5*x^5+120*a*b^4*x^4+280*a^2*b^3*x^3+336*a^3*b^2*x^2+210*a^4*b*x+56*a^5)*((b*x+a)^2)^(5/2)/(b*x+a)^5","A"
167,1,74,53,0.042000," ","int(x*(b^2*x^2+2*a*b*x+a^2)^(5/2),x)","\frac{\left(6 b^{5} x^{5}+35 a \,b^{4} x^{4}+84 a^{2} b^{3} x^{3}+105 a^{3} b^{2} x^{2}+70 a^{4} b x +21 a^{5}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}} x^{2}}{42 \left(b x +a \right)^{5}}"," ",0,"1/42*x^2*(6*b^5*x^5+35*a*b^4*x^4+84*a^2*b^3*x^3+105*a^3*b^2*x^2+70*a^4*b*x+21*a^5)*((b*x+a)^2)^(5/2)/(b*x+a)^5","A"
168,1,71,28,0.042000," ","int((b^2*x^2+2*a*b*x+a^2)^(5/2),x)","\frac{\left(b^{5} x^{5}+6 a \,b^{4} x^{4}+15 a^{2} b^{3} x^{3}+20 a^{3} b^{2} x^{2}+15 a^{4} b x +6 a^{5}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}} x}{6 \left(b x +a \right)^{5}}"," ",0,"1/6*x*(b^5*x^5+6*a*b^4*x^4+15*a^2*b^3*x^3+20*a^3*b^2*x^2+15*a^4*b*x+6*a^5)*((b*x+a)^2)^(5/2)/(b*x+a)^5","B"
169,1,73,149,0.051000," ","int((b^2*x^2+2*a*b*x+a^2)^(5/2)/x,x)","\frac{\left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}} \left(12 b^{5} x^{5}+75 a \,b^{4} x^{4}+200 a^{2} b^{3} x^{3}+300 a^{3} b^{2} x^{2}+60 a^{5} \ln \left(x \right)+300 a^{4} b x \right)}{60 \left(b x +a \right)^{5}}"," ",0,"1/60*((b*x+a)^2)^(5/2)*(12*b^5*x^5+75*a*b^4*x^4+200*a^2*b^3*x^3+300*a^3*b^2*x^2+60*a^5*ln(x)+300*a^4*b*x)/(b*x+a)^5","A"
170,1,76,150,0.060000," ","int((b^2*x^2+2*a*b*x+a^2)^(5/2)/x^2,x)","\frac{\left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}} \left(3 b^{5} x^{5}+20 a \,b^{4} x^{4}+60 a^{2} b^{3} x^{3}+60 a^{4} b x \ln \left(x \right)+120 a^{3} b^{2} x^{2}-12 a^{5}\right)}{12 \left(b x +a \right)^{5} x}"," ",0,"1/12*((b*x+a)^2)^(5/2)*(3*b^5*x^5+20*a*b^4*x^4+60*a^2*b^3*x^3+60*a^4*b*ln(x)*x+120*a^3*b^2*x^2-12*a^5)/(b*x+a)^5/x","A"
171,1,76,150,0.056000," ","int((b^2*x^2+2*a*b*x+a^2)^(5/2)/x^3,x)","\frac{\left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}} \left(2 b^{5} x^{5}+15 a \,b^{4} x^{4}+60 a^{3} b^{2} x^{2} \ln \left(x \right)+60 a^{2} b^{3} x^{3}-30 a^{4} b x -3 a^{5}\right)}{6 \left(b x +a \right)^{5} x^{2}}"," ",0,"1/6*((b*x+a)^2)^(5/2)*(2*b^5*x^5+15*a*b^4*x^4+60*a^3*b^2*ln(x)*x^2+60*a^2*b^3*x^3-30*a^4*b*x-3*a^5)/(b*x+a)^5/x^2","A"
172,1,76,150,0.057000," ","int((b^2*x^2+2*a*b*x+a^2)^(5/2)/x^4,x)","\frac{\left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}} \left(3 b^{5} x^{5}+60 a^{2} b^{3} x^{3} \ln \left(x \right)+30 a \,b^{4} x^{4}-60 a^{3} b^{2} x^{2}-15 a^{4} b x -2 a^{5}\right)}{6 \left(b x +a \right)^{5} x^{3}}"," ",0,"1/6*((b*x+a)^2)^(5/2)*(3*b^5*x^5+60*a^2*b^3*ln(x)*x^3+30*a*b^4*x^4-60*a^3*b^2*x^2-15*a^4*b*x-2*a^5)/(b*x+a)^5/x^3","A"
173,1,76,149,0.058000," ","int((b^2*x^2+2*a*b*x+a^2)^(5/2)/x^5,x)","\frac{\left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}} \left(60 a \,b^{4} x^{4} \ln \left(x \right)+12 b^{5} x^{5}-120 a^{2} b^{3} x^{3}-60 a^{3} b^{2} x^{2}-20 a^{4} b x -3 a^{5}\right)}{12 \left(b x +a \right)^{5} x^{4}}"," ",0,"1/12*((b*x+a)^2)^(5/2)*(60*a*b^4*ln(x)*x^4+12*b^5*x^5-120*a^2*b^3*x^3-60*a^3*b^2*x^2-20*a^4*b*x-3*a^5)/(b*x+a)^5/x^4","A"
174,1,76,151,0.058000," ","int((b^2*x^2+2*a*b*x+a^2)^(5/2)/x^6,x)","\frac{\left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}} \left(60 b^{5} x^{5} \ln \left(x \right)-300 a \,b^{4} x^{4}-300 a^{2} b^{3} x^{3}-200 a^{3} b^{2} x^{2}-75 a^{4} b x -12 a^{5}\right)}{60 \left(b x +a \right)^{5} x^{5}}"," ",0,"1/60*((b*x+a)^2)^(5/2)*(60*b^5*ln(x)*x^5-300*a*b^4*x^4-300*a^2*b^3*x^3-200*a^3*b^2*x^2-75*a^4*b*x-12*a^5)/(b*x+a)^5/x^5","A"
175,1,72,24,0.046000," ","int((b^2*x^2+2*a*b*x+a^2)^(5/2)/x^7,x)","-\frac{\left(6 b^{5} x^{5}+15 a \,b^{4} x^{4}+20 a^{2} b^{3} x^{3}+15 a^{3} b^{2} x^{2}+6 a^{4} b x +a^{5}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}}}{6 \left(b x +a \right)^{5} x^{6}}"," ",0,"-1/6*(6*b^5*x^5+15*a*b^4*x^4+20*a^2*b^3*x^3+15*a^3*b^2*x^2+6*a^4*b*x+a^5)*((b*x+a)^2)^(5/2)/x^6/(b*x+a)^5","B"
176,1,74,50,0.045000," ","int((b^2*x^2+2*a*b*x+a^2)^(5/2)/x^8,x)","-\frac{\left(21 b^{5} x^{5}+70 a \,b^{4} x^{4}+105 a^{2} b^{3} x^{3}+84 a^{3} b^{2} x^{2}+35 a^{4} b x +6 a^{5}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}}}{42 \left(b x +a \right)^{5} x^{7}}"," ",0,"-1/42*(21*b^5*x^5+70*a*b^4*x^4+105*a^2*b^3*x^3+84*a^3*b^2*x^2+35*a^4*b*x+6*a^5)*((b*x+a)^2)^(5/2)/x^7/(b*x+a)^5","A"
177,1,74,77,0.047000," ","int((b^2*x^2+2*a*b*x+a^2)^(5/2)/x^9,x)","-\frac{\left(56 b^{5} x^{5}+210 a \,b^{4} x^{4}+336 a^{2} b^{3} x^{3}+280 a^{3} b^{2} x^{2}+120 a^{4} b x +21 a^{5}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}}}{168 \left(b x +a \right)^{5} x^{8}}"," ",0,"-1/168*(56*b^5*x^5+210*a*b^4*x^4+336*a^2*b^3*x^3+280*a^3*b^2*x^2+120*a^4*b*x+21*a^5)*((b*x+a)^2)^(5/2)/x^8/(b*x+a)^5","A"
178,1,74,153,0.046000," ","int((b^2*x^2+2*a*b*x+a^2)^(5/2)/x^10,x)","-\frac{\left(126 b^{5} x^{5}+504 a \,b^{4} x^{4}+840 a^{2} b^{3} x^{3}+720 a^{3} b^{2} x^{2}+315 a^{4} b x +56 a^{5}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}}}{504 \left(b x +a \right)^{5} x^{9}}"," ",0,"-1/504*(126*b^5*x^5+504*a*b^4*x^4+840*a^2*b^3*x^3+720*a^3*b^2*x^2+315*a^4*b*x+56*a^5)*((b*x+a)^2)^(5/2)/x^9/(b*x+a)^5","A"
179,1,74,153,0.046000," ","int((b^2*x^2+2*a*b*x+a^2)^(5/2)/x^11,x)","-\frac{\left(252 b^{5} x^{5}+1050 a \,b^{4} x^{4}+1800 a^{2} b^{3} x^{3}+1575 a^{3} b^{2} x^{2}+700 a^{4} b x +126 a^{5}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}}}{1260 \left(b x +a \right)^{5} x^{10}}"," ",0,"-1/1260*(252*b^5*x^5+1050*a*b^4*x^4+1800*a^2*b^3*x^3+1575*a^3*b^2*x^2+700*a^4*b*x+126*a^5)*((b*x+a)^2)^(5/2)/x^10/(b*x+a)^5","A"
180,1,74,153,0.049000," ","int((b^2*x^2+2*a*b*x+a^2)^(5/2)/x^12,x)","-\frac{\left(462 b^{5} x^{5}+1980 a \,b^{4} x^{4}+3465 a^{2} b^{3} x^{3}+3080 a^{3} b^{2} x^{2}+1386 a^{4} b x +252 a^{5}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}}}{2772 \left(b x +a \right)^{5} x^{11}}"," ",0,"-1/2772*(462*b^5*x^5+1980*a*b^4*x^4+3465*a^2*b^3*x^3+3080*a^3*b^2*x^2+1386*a^4*b*x+252*a^5)*((b*x+a)^2)^(5/2)/x^11/(b*x+a)^5","A"
181,1,67,121,0.051000," ","int(x^4/((b*x+a)^2)^(1/2),x)","\frac{\left(b x +a \right) \left(3 b^{4} x^{4}-4 a \,b^{3} x^{3}+6 a^{2} b^{2} x^{2}+12 a^{4} \ln \left(b x +a \right)-12 a^{3} b x \right)}{12 \sqrt{\left(b x +a \right)^{2}}\, b^{5}}"," ",0,"1/12*(b*x+a)*(3*b^4*x^4-4*a*b^3*x^3+6*b^2*x^2*a^2+12*a^4*ln(b*x+a)-12*x*a^3*b)/((b*x+a)^2)^(1/2)/b^5","A"
182,1,56,96,0.047000," ","int(x^3/((b*x+a)^2)^(1/2),x)","-\frac{\left(b x +a \right) \left(-2 b^{3} x^{3}+3 a \,b^{2} x^{2}+6 a^{3} \ln \left(b x +a \right)-6 a^{2} b x \right)}{6 \sqrt{\left(b x +a \right)^{2}}\, b^{4}}"," ",0,"-1/6*(b*x+a)*(-2*b^3*x^3+3*a*b^2*x^2+6*a^3*ln(b*x+a)-6*a^2*b*x)/((b*x+a)^2)^(1/2)/b^4","A"
183,1,44,71,0.048000," ","int(x^2/((b*x+a)^2)^(1/2),x)","\frac{\left(b x +a \right) \left(b^{2} x^{2}+2 a^{2} \ln \left(b x +a \right)-2 a b x \right)}{2 \sqrt{\left(b x +a \right)^{2}}\, b^{3}}"," ",0,"1/2*(b*x+a)*(b^2*x^2+2*a^2*ln(b*x+a)-2*a*b*x)/((b*x+a)^2)^(1/2)/b^3","A"
184,1,33,40,0.046000," ","int(x/((b*x+a)^2)^(1/2),x)","-\frac{\left(b x +a \right) \left(a \ln \left(b x +a \right)-b x \right)}{\sqrt{\left(b x +a \right)^{2}}\, b^{2}}"," ",0,"-(b*x+a)*(a*ln(b*x+a)-b*x)/((b*x+a)^2)^(1/2)/b^2","A"
185,1,25,24,0.044000," ","int(1/((b*x+a)^2)^(1/2),x)","\frac{\left(b x +a \right) \ln \left(b x +a \right)}{\sqrt{\left(b x +a \right)^{2}}\, b}"," ",0,"(b*x+a)*ln(b*x+a)/b/((b*x+a)^2)^(1/2)","A"
186,1,31,46,0.050000," ","int(1/x/((b*x+a)^2)^(1/2),x)","-\frac{\left(b x +a \right) \left(-\ln \left(x \right)+\ln \left(b x +a \right)\right)}{\sqrt{\left(b x +a \right)^{2}}\, a}"," ",0,"-(b*x+a)*(ln(b*x+a)-ln(x))/((b*x+a)^2)^(1/2)/a","A"
187,1,41,72,0.056000," ","int(1/x^2/((b*x+a)^2)^(1/2),x)","\frac{\left(b x +a \right) \left(-b x \ln \left(x \right)+b x \ln \left(b x +a \right)-a \right)}{\sqrt{\left(b x +a \right)^{2}}\, a^{2} x}"," ",0,"(b*x+a)*(b*ln(b*x+a)*x-b*ln(x)*x-a)/((b*x+a)^2)^(1/2)/x/a^2","A"
188,1,56,99,0.063000," ","int(1/x^3/((b*x+a)^2)^(1/2),x)","-\frac{\left(b x +a \right) \left(-2 b^{2} x^{2} \ln \left(x \right)+2 b^{2} x^{2} \ln \left(b x +a \right)-2 a b x +a^{2}\right)}{2 \sqrt{\left(b x +a \right)^{2}}\, a^{3} x^{2}}"," ",0,"-1/2*(b*x+a)*(2*b^2*ln(b*x+a)*x^2-2*b^2*ln(x)*x^2-2*a*b*x+a^2)/((b*x+a)^2)^(1/2)/x^2/a^3","A"
189,1,69,125,0.058000," ","int(1/x^4/((b*x+a)^2)^(1/2),x)","\frac{\left(b x +a \right) \left(-6 b^{3} x^{3} \ln \left(x \right)+6 b^{3} x^{3} \ln \left(b x +a \right)-6 a \,b^{2} x^{2}+3 a^{2} b x -2 a^{3}\right)}{6 \sqrt{\left(b x +a \right)^{2}}\, a^{4} x^{3}}"," ",0,"1/6*(b*x+a)*(6*b^3*ln(b*x+a)*x^3-6*b^3*ln(x)*x^3-6*a*b^2*x^2+3*a^2*b*x-2*a^3)/((b*x+a)^2)^(1/2)/a^4/x^3","A"
190,1,101,113,0.058000," ","int(x^4/(b^2*x^2+2*a*b*x+a^2)^(3/2),x)","\frac{\left(b^{4} x^{4}+12 a^{2} b^{2} x^{2} \ln \left(b x +a \right)-4 a \,b^{3} x^{3}+24 a^{3} b x \ln \left(b x +a \right)-11 a^{2} b^{2} x^{2}+12 a^{4} \ln \left(b x +a \right)+2 a^{3} b x +7 a^{4}\right) \left(b x +a \right)}{2 \left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}} b^{5}}"," ",0,"1/2*(b^4*x^4+12*ln(b*x+a)*x^2*a^2*b^2-4*a*b^3*x^3+24*ln(b*x+a)*x*a^3*b-11*a^2*b^2*x^2+12*a^4*ln(b*x+a)+2*a^3*b*x+7*a^4)*(b*x+a)/b^5/((b*x+a)^2)^(3/2)","A"
191,1,89,87,0.056000," ","int(x^3/(b^2*x^2+2*a*b*x+a^2)^(3/2),x)","-\frac{\left(6 a \,b^{2} x^{2} \ln \left(b x +a \right)-2 b^{3} x^{3}+12 a^{2} b x \ln \left(b x +a \right)-4 a \,b^{2} x^{2}+6 a^{3} \ln \left(b x +a \right)+4 a^{2} b x +5 a^{3}\right) \left(b x +a \right)}{2 \left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}} b^{4}}"," ",0,"-1/2*(6*ln(b*x+a)*x^2*a*b^2-2*b^3*x^3+12*ln(b*x+a)*x*a^2*b-4*a*b^2*x^2+6*a^3*ln(b*x+a)+4*a^2*b*x+5*a^3)*(b*x+a)/b^4/((b*x+a)^2)^(3/2)","A"
192,1,67,64,0.054000," ","int(x^2/(b^2*x^2+2*a*b*x+a^2)^(3/2),x)","\frac{\left(2 b^{2} x^{2} \ln \left(b x +a \right)+4 a b x \ln \left(b x +a \right)+2 a^{2} \ln \left(b x +a \right)+4 a b x +3 a^{2}\right) \left(b x +a \right)}{2 \left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}} b^{3}}"," ",0,"1/2*(2*b^2*x^2*ln(b*x+a)+4*ln(b*x+a)*x*a*b+2*a^2*ln(b*x+a)+4*a*b*x+3*a^2)*(b*x+a)/b^3/((b*x+a)^2)^(3/2)","A"
193,1,26,37,0.043000," ","int(x/(b^2*x^2+2*a*b*x+a^2)^(3/2),x)","-\frac{\left(b x +a \right) \left(2 b x +a \right)}{2 \left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}} b^{2}}"," ",0,"-1/2*(b*x+a)*(2*b*x+a)/b^2/((b*x+a)^2)^(3/2)","A"
194,1,20,21,0.042000," ","int(1/(b^2*x^2+2*a*b*x+a^2)^(3/2),x)","-\frac{b x +a}{2 \left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}} b}"," ",0,"-1/2*(b*x+a)/b/((b*x+a)^2)^(3/2)","A"
195,1,91,80,0.058000," ","int(1/x/(b^2*x^2+2*a*b*x+a^2)^(3/2),x)","-\frac{\left(-2 b^{2} x^{2} \ln \left(x \right)+2 b^{2} x^{2} \ln \left(b x +a \right)-4 a b x \ln \left(x \right)+4 a b x \ln \left(b x +a \right)-2 a^{2} \ln \left(x \right)+2 a^{2} \ln \left(b x +a \right)-2 a b x -3 a^{2}\right) \left(b x +a \right)}{2 \left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}} a^{3}}"," ",0,"-1/2*(2*b^2*x^2*ln(b*x+a)-2*b^2*x^2*ln(x)+4*a*b*x*ln(b*x+a)-4*ln(x)*x*a*b+2*a^2*ln(b*x+a)-2*a^2*ln(x)-2*a*b*x-3*a^2)*(b*x+a)/a^3/((b*x+a)^2)^(3/2)","A"
196,1,117,110,0.063000," ","int(1/x^2/(b^2*x^2+2*a*b*x+a^2)^(3/2),x)","\frac{\left(-6 b^{3} x^{3} \ln \left(x \right)+6 b^{3} x^{3} \ln \left(b x +a \right)-12 a \,b^{2} x^{2} \ln \left(x \right)+12 a \,b^{2} x^{2} \ln \left(b x +a \right)-6 a^{2} b x \ln \left(x \right)+6 a^{2} b x \ln \left(b x +a \right)-6 a \,b^{2} x^{2}-9 a^{2} b x -2 a^{3}\right) \left(b x +a \right)}{2 \left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}} a^{4} x}"," ",0,"1/2*(6*b^3*x^3*ln(b*x+a)-6*b^3*x^3*ln(x)+12*a*b^2*x^2*ln(b*x+a)-12*a*b^2*x^2*ln(x)+6*a^2*b*x*ln(b*x+a)-6*a^2*b*x*ln(x)-6*a*b^2*x^2-9*a^2*b*x-2*a^3)*(b*x+a)/x/a^4/((b*x+a)^2)^(3/2)","A"
197,1,134,142,0.058000," ","int(1/x^3/(b^2*x^2+2*a*b*x+a^2)^(3/2),x)","-\frac{\left(-12 b^{4} x^{4} \ln \left(x \right)+12 b^{4} x^{4} \ln \left(b x +a \right)-24 a \,b^{3} x^{3} \ln \left(x \right)+24 a \,b^{3} x^{3} \ln \left(b x +a \right)-12 a^{2} b^{2} x^{2} \ln \left(x \right)+12 a^{2} b^{2} x^{2} \ln \left(b x +a \right)-12 a \,b^{3} x^{3}-18 a^{2} b^{2} x^{2}-4 a^{3} b x +a^{4}\right) \left(b x +a \right)}{2 \left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}} a^{5} x^{2}}"," ",0,"-1/2*(12*ln(b*x+a)*x^4*b^4-12*ln(x)*x^4*b^4+24*ln(b*x+a)*x^3*a*b^3-24*ln(x)*x^3*a*b^3+12*a^2*b^2*x^2*ln(b*x+a)-12*ln(x)*x^2*a^2*b^2-12*a*b^3*x^3-18*a^2*b^2*x^2-4*a^3*b*x+a^4)*(b*x+a)/x^2/a^5/((b*x+a)^2)^(3/2)","A"
198,1,158,161,0.239000," ","int(x^6/(b^2*x^2+2*a*b*x+a^2)^(5/2),x)","\frac{\left(2 b^{6} x^{6}+60 a^{2} b^{4} x^{4} \ln \left(b x +a \right)-12 a \,b^{5} x^{5}+240 a^{3} b^{3} x^{3} \ln \left(b x +a \right)-68 a^{2} b^{4} x^{4}+360 a^{4} b^{2} x^{2} \ln \left(b x +a \right)-32 a^{3} b^{3} x^{3}+240 a^{5} b x \ln \left(b x +a \right)+132 a^{4} b^{2} x^{2}+60 a^{6} \ln \left(b x +a \right)+168 a^{5} b x +57 a^{6}\right) \left(b x +a \right)}{4 \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}} b^{7}}"," ",0,"1/4*(2*b^6*x^6+60*ln(b*x+a)*x^4*a^2*b^4-12*x^5*a*b^5+240*ln(b*x+a)*x^3*a^3*b^3-68*a^2*x^4*b^4+360*ln(b*x+a)*x^2*a^4*b^2-32*a^3*x^3*b^3+240*ln(b*x+a)*x*a^5*b+132*a^4*x^2*b^2+60*ln(b*x+a)*a^6+168*x*a^5*b+57*a^6)*(b*x+a)/b^7/((b*x+a)^2)^(5/2)","A"
199,1,145,135,0.056000," ","int(x^5/(b^2*x^2+2*a*b*x+a^2)^(5/2),x)","-\frac{\left(60 a \,b^{4} x^{4} \ln \left(b x +a \right)-12 b^{5} x^{5}+240 a^{2} b^{3} x^{3} \ln \left(b x +a \right)-48 a \,b^{4} x^{4}+360 a^{3} b^{2} x^{2} \ln \left(b x +a \right)+48 a^{2} b^{3} x^{3}+240 a^{4} b x \ln \left(b x +a \right)+252 a^{3} b^{2} x^{2}+60 a^{5} \ln \left(b x +a \right)+248 a^{4} b x +77 a^{5}\right) \left(b x +a \right)}{12 \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}} b^{6}}"," ",0,"-1/12*(60*ln(b*x+a)*x^4*a*b^4-12*b^5*x^5+240*ln(b*x+a)*x^3*a^2*b^3-48*a*b^4*x^4+360*ln(b*x+a)*x^2*a^3*b^2+48*a^2*b^3*x^3+240*ln(b*x+a)*x*a^4*b+252*a^3*b^2*x^2+60*ln(b*x+a)*a^5+248*a^4*b*x+77*a^5)*(b*x+a)/b^6/((b*x+a)^2)^(5/2)","A"
200,1,123,112,0.056000," ","int(x^4/(b^2*x^2+2*a*b*x+a^2)^(5/2),x)","\frac{\left(12 b^{4} x^{4} \ln \left(b x +a \right)+48 a \,b^{3} x^{3} \ln \left(b x +a \right)+72 a^{2} b^{2} x^{2} \ln \left(b x +a \right)+48 a \,b^{3} x^{3}+48 a^{3} b x \ln \left(b x +a \right)+108 a^{2} b^{2} x^{2}+12 a^{4} \ln \left(b x +a \right)+88 a^{3} b x +25 a^{4}\right) \left(b x +a \right)}{12 \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}} b^{5}}"," ",0,"1/12*(12*b^4*x^4*ln(b*x+a)+48*a*b^3*x^3*ln(b*x+a)+72*a^2*b^2*x^2*ln(b*x+a)+48*a*b^3*x^3+48*a^3*b*x*ln(b*x+a)+108*a^2*b^2*x^2+12*a^4*ln(b*x+a)+88*a^3*b*x+25*a^4)*(b*x+a)/b^5/((b*x+a)^2)^(5/2)","A"
201,1,48,24,0.042000," ","int(x^3/(b^2*x^2+2*a*b*x+a^2)^(5/2),x)","-\frac{\left(b x +a \right) \left(4 b^{3} x^{3}+6 a \,b^{2} x^{2}+4 a^{2} b x +a^{3}\right)}{4 \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}} b^{4}}"," ",0,"-1/4*(b*x+a)*(4*b^3*x^3+6*a*b^2*x^2+4*a^2*b*x+a^3)/b^4/((b*x+a)^2)^(5/2)","A"
202,1,37,68,0.048000," ","int(x^2/(b^2*x^2+2*a*b*x+a^2)^(5/2),x)","-\frac{\left(b x +a \right) \left(6 b^{2} x^{2}+4 a b x +a^{2}\right)}{12 \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}} b^{3}}"," ",0,"-1/12*(b*x+a)*(6*b^2*x^2+4*a*b*x+a^2)/b^3/((b*x+a)^2)^(5/2)","A"
203,1,26,55,0.046000," ","int(x/(b^2*x^2+2*a*b*x+a^2)^(5/2),x)","-\frac{\left(b x +a \right) \left(4 b x +a \right)}{12 \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}} b^{2}}"," ",0,"-1/12*(b*x+a)*(4*b*x+a)/b^2/((b*x+a)^2)^(5/2)","A"
204,1,20,30,0.042000," ","int(1/(b^2*x^2+2*a*b*x+a^2)^(5/2),x)","-\frac{b x +a}{4 \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}} b}"," ",0,"-1/4*(b*x+a)/b/((b*x+a)^2)^(5/2)","A"
205,1,173,122,0.063000," ","int(1/x/(b^2*x^2+2*a*b*x+a^2)^(5/2),x)","-\frac{\left(-12 b^{4} x^{4} \ln \left(x \right)+12 b^{4} x^{4} \ln \left(b x +a \right)-48 a \,b^{3} x^{3} \ln \left(x \right)+48 a \,b^{3} x^{3} \ln \left(b x +a \right)-72 a^{2} b^{2} x^{2} \ln \left(x \right)+72 a^{2} b^{2} x^{2} \ln \left(b x +a \right)-12 a \,b^{3} x^{3}-48 a^{3} b x \ln \left(x \right)+48 a^{3} b x \ln \left(b x +a \right)-42 a^{2} b^{2} x^{2}-12 a^{4} \ln \left(x \right)+12 a^{4} \ln \left(b x +a \right)-52 a^{3} b x -25 a^{4}\right) \left(b x +a \right)}{12 \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}} a^{5}}"," ",0,"-1/12*(12*b^4*x^4*ln(b*x+a)-12*b^4*x^4*ln(x)+48*a*b^3*x^3*ln(b*x+a)-48*a*b^3*x^3*ln(x)+72*a^2*b^2*x^2*ln(b*x+a)-72*a^2*b^2*x^2*ln(x)-12*a*b^3*x^3+48*a^3*b*x*ln(b*x+a)-48*ln(x)*x*a^3*b-42*a^2*b^2*x^2+12*a^4*ln(b*x+a)-12*ln(x)*a^4-52*a^3*b*x-25*a^4)*(b*x+a)/a^5/((b*x+a)^2)^(5/2)","A"
206,1,199,154,0.149000," ","int(1/x^2/(b^2*x^2+2*a*b*x+a^2)^(5/2),x)","\frac{\left(-60 b^{5} x^{5} \ln \left(x \right)+60 b^{5} x^{5} \ln \left(b x +a \right)-240 a \,b^{4} x^{4} \ln \left(x \right)+240 a \,b^{4} x^{4} \ln \left(b x +a \right)-360 a^{2} b^{3} x^{3} \ln \left(x \right)+360 a^{2} b^{3} x^{3} \ln \left(b x +a \right)-60 a \,b^{4} x^{4}-240 a^{3} b^{2} x^{2} \ln \left(x \right)+240 a^{3} b^{2} x^{2} \ln \left(b x +a \right)-210 a^{2} b^{3} x^{3}-60 a^{4} b x \ln \left(x \right)+60 a^{4} b x \ln \left(b x +a \right)-260 a^{3} b^{2} x^{2}-125 a^{4} b x -12 a^{5}\right) \left(b x +a \right)}{12 \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}} a^{6} x}"," ",0,"1/12*(60*ln(b*x+a)*x^5*b^5-60*b^5*x^5*ln(x)+240*a*b^4*x^4*ln(b*x+a)-240*a*b^4*x^4*ln(x)+360*a^2*b^3*x^3*ln(b*x+a)-360*a^2*b^3*x^3*ln(x)-60*a*b^4*x^4+240*a^3*b^2*x^2*ln(b*x+a)-240*a^3*b^2*x^2*ln(x)-210*a^2*b^3*x^3+60*a^4*b*x*ln(b*x+a)-60*a^4*b*x*ln(x)-260*a^3*b^2*x^2-125*a^4*b*x-12*a^5)*(b*x+a)/x/a^6/((b*x+a)^2)^(5/2)","A"
207,1,218,189,0.068000," ","int(1/x^3/(b^2*x^2+2*a*b*x+a^2)^(5/2),x)","-\frac{\left(-60 b^{6} x^{6} \ln \left(x \right)+60 b^{6} x^{6} \ln \left(b x +a \right)-240 a \,b^{5} x^{5} \ln \left(x \right)+240 a \,b^{5} x^{5} \ln \left(b x +a \right)-360 a^{2} b^{4} x^{4} \ln \left(x \right)+360 a^{2} b^{4} x^{4} \ln \left(b x +a \right)-60 a \,b^{5} x^{5}-240 a^{3} b^{3} x^{3} \ln \left(x \right)+240 a^{3} b^{3} x^{3} \ln \left(b x +a \right)-210 a^{2} b^{4} x^{4}-60 a^{4} b^{2} x^{2} \ln \left(x \right)+60 a^{4} b^{2} x^{2} \ln \left(b x +a \right)-260 a^{3} b^{3} x^{3}-125 a^{4} b^{2} x^{2}-12 a^{5} b x +2 a^{6}\right) \left(b x +a \right)}{4 \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}} a^{7} x^{2}}"," ",0,"-1/4*(60*ln(b*x+a)*x^6*b^6-60*ln(x)*x^6*b^6+240*ln(b*x+a)*x^5*a*b^5-240*ln(x)*x^5*a*b^5+360*a^2*b^4*x^4*ln(b*x+a)-360*ln(x)*x^4*a^2*b^4-60*a*b^5*x^5+240*a^3*b^3*x^3*ln(b*x+a)-240*ln(x)*x^3*a^3*b^3-210*a^2*b^4*x^4+60*a^4*b^2*x^2*ln(b*x+a)-60*ln(x)*x^2*a^4*b^2-260*a^3*b^3*x^3-125*a^4*b^2*x^2-12*a^5*b*x+2*a^6)*(b*x+a)/x^2/a^7/((b*x+a)^2)^(5/2)","A"
208,1,47,34,0.046000," ","int(x*(4*x^2+12*x+9)^(5/2),x)","\frac{\left(64 x^{5}+560 x^{4}+2016 x^{3}+3780 x^{2}+3780 x +1701\right) \left(\left(2 x +3\right)^{2}\right)^{\frac{5}{2}} x^{2}}{14 \left(2 x +3\right)^{5}}"," ",0,"1/14*x^2*(64*x^5+560*x^4+2016*x^3+3780*x^2+3780*x+1701)*((2*x+3)^2)^(5/2)/(2*x+3)^5","A"
209,1,37,34,0.044000," ","int(x*(4*x^2+12*x+9)^(3/2),x)","\frac{\left(16 x^{3}+90 x^{2}+180 x +135\right) \left(\left(2 x +3\right)^{2}\right)^{\frac{3}{2}} x^{2}}{10 \left(2 x +3\right)^{3}}"," ",0,"1/10*x^2*(16*x^3+90*x^2+180*x+135)*((2*x+3)^2)^(3/2)/(2*x+3)^3","A"
210,1,27,31,0.044000," ","int(x*(4*x^2+12*x+9)^(1/2),x)","\frac{\left(4 x +9\right) \sqrt{\left(2 x +3\right)^{2}}\, x^{2}}{12 x +18}"," ",0,"1/6*x^2*(4*x+9)*((2*x+3)^2)^(1/2)/(2*x+3)","A"
211,1,29,34,0.051000," ","int(x/(4*x^2+12*x+9)^(1/2),x)","-\frac{\left(2 x +3\right) \left(-2 x +3 \ln \left(2 x +3\right)\right)}{4 \sqrt{\left(2 x +3\right)^{2}}}"," ",0,"-1/4*(2*x+3)*(-2*x+3*ln(2*x+3))/((2*x+3)^2)^(1/2)","A"
212,1,22,30,0.049000," ","int(x/(4*x^2+12*x+9)^(3/2),x)","-\frac{\left(2 x +3\right) \left(4 x +3\right)}{8 \left(\left(2 x +3\right)^{2}\right)^{\frac{3}{2}}}"," ",0,"-1/8*(2*x+3)*(4*x+3)/((2*x+3)^2)^(3/2)","A"
213,1,22,36,0.054000," ","int(x/(4*x^2+12*x+9)^(5/2),x)","-\frac{\left(2 x +3\right) \left(8 x +3\right)}{48 \left(\left(2 x +3\right)^{2}\right)^{\frac{5}{2}}}"," ",0,"-1/48*(2*x+3)*(8*x+3)/((2*x+3)^2)^(5/2)","A"
214,1,22,36,0.046000," ","int(x/(4*x^2+12*x+9)^(7/2),x)","-\frac{\left(2 x +3\right) \left(4 x +1\right)}{40 \left(\left(2 x +3\right)^{2}\right)^{\frac{7}{2}}}"," ",0,"-1/40*(2*x+3)*(1+4*x)/((2*x+3)^2)^(7/2)","A"
215,1,29,34,0.046000," ","int(x/((3*x+2)^2)^(1/2),x)","-\frac{\left(3 x +2\right) \left(-3 x +2 \ln \left(3 x +2\right)\right)}{9 \sqrt{\left(3 x +2\right)^{2}}}"," ",0,"-1/9*(3*x+2)*(-3*x+2*ln(3*x+2))/((3*x+2)^2)^(1/2)","A"
216,1,29,34,0.048000," ","int(x/((3*x-2)^2)^(1/2),x)","\frac{\left(3 x -2\right) \left(3 x +2 \ln \left(3 x -2\right)\right)}{9 \sqrt{\left(3 x -2\right)^{2}}}"," ",0,"1/9*(3*x-2)*(3*x+2*ln(3*x-2))/((3*x-2)^2)^(1/2)","A"
217,1,31,38,0.122000," ","int(x/(-(3*x-2)^2)^(1/2),x)","\frac{\left(3 x -2\right) \left(3 x +2 \ln \left(3 x -2\right)\right)}{9 \sqrt{-\left(3 x -2\right)^{2}}}"," ",0,"1/9*(3*x-2)*(3*x+2*ln(3*x-2))/(-(3*x-2)^2)^(1/2)","A"
218,1,31,38,0.049000," ","int(x/(-(3*x+2)^2)^(1/2),x)","-\frac{\left(3 x +2\right) \left(-3 x +2 \ln \left(3 x +2\right)\right)}{9 \sqrt{-\left(3 x +2\right)^{2}}}"," ",0,"-1/9*(3*x+2)*(-3*x+2*ln(3*x+2))/(-(3*x+2)^2)^(1/2)","A"
219,1,9,10,0.041000," ","int((x+1)/(x^2+2*x),x)","\frac{\ln \left(\left(x +2\right) x \right)}{2}"," ",0,"1/2*ln(x*(x+2))","A"
220,1,9,10,0.046000," ","int((2*b*x+a)/(b*x^2+a*x),x)","\ln \left(\left(b x +a \right) x \right)"," ",0,"ln((b*x+a)*x)","A"
221,1,100,56,0.050000," ","int((e*x+d)^4*(c*x^2+b*x),x)","\frac{c \,e^{4} x^{7}}{7}+\frac{b \,d^{4} x^{2}}{2}+\frac{\left(e^{4} b +4 d \,e^{3} c \right) x^{6}}{6}+\frac{\left(4 d \,e^{3} b +6 d^{2} e^{2} c \right) x^{5}}{5}+\frac{\left(6 d^{2} e^{2} b +4 d^{3} e c \right) x^{4}}{4}+\frac{\left(4 d^{3} e b +d^{4} c \right) x^{3}}{3}"," ",0,"1/7*e^4*c*x^7+1/6*(b*e^4+4*c*d*e^3)*x^6+1/5*(4*b*d*e^3+6*c*d^2*e^2)*x^5+1/4*(6*b*d^2*e^2+4*c*d^3*e)*x^4+1/3*(4*b*d^3*e+c*d^4)*x^3+1/2*b*d^4*x^2","A"
222,1,76,56,0.042000," ","int((e*x+d)^3*(c*x^2+b*x),x)","\frac{c \,e^{3} x^{6}}{6}+\frac{b \,d^{3} x^{2}}{2}+\frac{\left(e^{3} b +3 d \,e^{2} c \right) x^{5}}{5}+\frac{\left(3 d \,e^{2} b +3 d^{2} e c \right) x^{4}}{4}+\frac{\left(3 d^{2} e b +d^{3} c \right) x^{3}}{3}"," ",0,"1/6*e^3*c*x^6+1/5*(b*e^3+3*c*d*e^2)*x^5+1/4*(3*b*d*e^2+3*c*d^2*e)*x^4+1/3*(3*b*d^2*e+c*d^3)*x^3+1/2*b*d^3*x^2","A"
223,1,52,47,0.045000," ","int((e*x+d)^2*(c*x^2+b*x),x)","\frac{c \,e^{2} x^{5}}{5}+\frac{b \,d^{2} x^{2}}{2}+\frac{\left(b \,e^{2}+2 d e c \right) x^{4}}{4}+\frac{\left(2 b d e +c \,d^{2}\right) x^{3}}{3}"," ",0,"1/5*c*e^2*x^5+1/4*(b*e^2+2*c*d*e)*x^4+1/3*(2*b*d*e+c*d^2)*x^3+1/2*b*d^2*x^2","A"
224,1,28,27,0.042000," ","int((e*x+d)*(c*x^2+b*x),x)","\frac{c e \,x^{4}}{4}+\frac{b d \,x^{2}}{2}+\frac{\left(b e +c d \right) x^{3}}{3}"," ",0,"1/2*b*d*x^2+1/3*(b*e+c*d)*x^3+1/4*c*e*x^4","A"
225,1,14,13,0.049000," ","int(c*x^2+b*x,x)","\frac{1}{3} c \,x^{3}+\frac{1}{2} b \,x^{2}"," ",0,"1/2*b*x^2+1/3*c*x^3","A"
226,1,52,43,0.121000," ","int((c*x^2+b*x)/(e*x+d),x)","\frac{c \,x^{2}}{2 e}-\frac{b d \ln \left(e x +d \right)}{e^{2}}+\frac{b x}{e}+\frac{c \,d^{2} \ln \left(e x +d \right)}{e^{3}}-\frac{c d x}{e^{2}}"," ",0,"1/2*c*x^2/e+1/e*x*b-c*d*x/e^2-d/e^2*ln(e*x+d)*b+d^2/e^3*ln(e*x+d)*c","A"
227,1,61,48,0.054000," ","int((c*x^2+b*x)/(e*x+d)^2,x)","\frac{b d}{\left(e x +d \right) e^{2}}+\frac{b \ln \left(e x +d \right)}{e^{2}}-\frac{c \,d^{2}}{\left(e x +d \right) e^{3}}-\frac{2 c d \ln \left(e x +d \right)}{e^{3}}+\frac{c x}{e^{2}}"," ",0,"c*x/e^2+d/e^2/(e*x+d)*b-d^2/e^3/(e*x+d)*c+1/e^2*ln(e*x+d)*b-2*c*d*ln(e*x+d)/e^3","A"
228,1,70,53,0.047000," ","int((c*x^2+b*x)/(e*x+d)^3,x)","\frac{b d}{2 \left(e x +d \right)^{2} e^{2}}-\frac{c \,d^{2}}{2 \left(e x +d \right)^{2} e^{3}}-\frac{b}{\left(e x +d \right) e^{2}}+\frac{2 c d}{\left(e x +d \right) e^{3}}+\frac{c \ln \left(e x +d \right)}{e^{3}}"," ",0,"1/2*d/e^2/(e*x+d)^2*b-1/2*d^2/e^3/(e*x+d)^2*c-1/e^2/(e*x+d)*b+2*c*d/e^3/(e*x+d)+c*ln(e*x+d)/e^3","A"
229,1,56,56,0.048000," ","int((c*x^2+b*x)/(e*x+d)^4,x)","-\frac{c}{\left(e x +d \right) e^{3}}+\frac{\left(b e -c d \right) d}{3 \left(e x +d \right)^{3} e^{3}}-\frac{b e -2 c d}{2 \left(e x +d \right)^{2} e^{3}}"," ",0,"1/3*d*(b*e-c*d)/e^3/(e*x+d)^3-1/2*(b*e-2*c*d)/e^3/(e*x+d)^2-c/e^3/(e*x+d)","A"
230,1,56,56,0.046000," ","int((c*x^2+b*x)/(e*x+d)^5,x)","-\frac{c}{2 \left(e x +d \right)^{2} e^{3}}+\frac{\left(b e -c d \right) d}{4 \left(e x +d \right)^{4} e^{3}}-\frac{b e -2 c d}{3 \left(e x +d \right)^{3} e^{3}}"," ",0,"-1/3*(b*e-2*c*d)/e^3/(e*x+d)^3-1/2*c/e^3/(e*x+d)^2+1/4*d*(b*e-c*d)/e^3/(e*x+d)^4","A"
231,1,166,127,0.042000," ","int((e*x+d)^4*(c*x^2+b*x)^2,x)","\frac{c^{2} e^{4} x^{9}}{9}+\frac{b^{2} d^{4} x^{3}}{3}+\frac{\left(2 e^{4} b c +4 d \,e^{3} c^{2}\right) x^{8}}{8}+\frac{\left(e^{4} b^{2}+8 d \,e^{3} b c +6 d^{2} e^{2} c^{2}\right) x^{7}}{7}+\frac{\left(4 d \,e^{3} b^{2}+12 d^{2} e^{2} b c +4 d^{3} e \,c^{2}\right) x^{6}}{6}+\frac{\left(6 d^{2} e^{2} b^{2}+8 d^{3} e b c +c^{2} d^{4}\right) x^{5}}{5}+\frac{\left(4 d^{3} e \,b^{2}+2 d^{4} b c \right) x^{4}}{4}"," ",0,"1/9*e^4*c^2*x^9+1/8*(2*b*c*e^4+4*c^2*d*e^3)*x^8+1/7*(b^2*e^4+8*b*c*d*e^3+6*c^2*d^2*e^2)*x^7+1/6*(4*b^2*d*e^3+12*b*c*d^2*e^2+4*c^2*d^3*e)*x^6+1/5*(6*b^2*d^2*e^2+8*b*c*d^3*e+c^2*d^4)*x^5+1/4*(4*b^2*d^3*e+2*b*c*d^4)*x^4+1/3*d^4*b^2*x^3","A"
232,1,128,115,0.041000," ","int((e*x+d)^3*(c*x^2+b*x)^2,x)","\frac{c^{2} e^{3} x^{8}}{8}+\frac{b^{2} d^{3} x^{3}}{3}+\frac{\left(2 e^{3} b c +3 d \,e^{2} c^{2}\right) x^{7}}{7}+\frac{\left(e^{3} b^{2}+6 d \,e^{2} b c +3 d^{2} e \,c^{2}\right) x^{6}}{6}+\frac{\left(3 d \,e^{2} b^{2}+6 d^{2} e b c +c^{2} d^{3}\right) x^{5}}{5}+\frac{\left(3 d^{2} e \,b^{2}+2 b c \,d^{3}\right) x^{4}}{4}"," ",0,"1/8*c^2*e^3*x^8+1/7*(2*b*c*e^3+3*c^2*d*e^2)*x^7+1/6*(b^2*e^3+6*b*c*d*e^2+3*c^2*d^2*e)*x^6+1/5*(3*b^2*d*e^2+6*b*c*d^2*e+c^2*d^3)*x^5+1/4*(3*b^2*d^2*e+2*b*c*d^3)*x^4+1/3*b^2*d^3*x^3","A"
233,1,90,77,0.046000," ","int((e*x+d)^2*(c*x^2+b*x)^2,x)","\frac{c^{2} e^{2} x^{7}}{7}+\frac{b^{2} d^{2} x^{3}}{3}+\frac{\left(2 e^{2} b c +2 d e \,c^{2}\right) x^{6}}{6}+\frac{\left(b^{2} e^{2}+4 b c d e +c^{2} d^{2}\right) x^{5}}{5}+\frac{\left(2 b^{2} d e +2 b c \,d^{2}\right) x^{4}}{4}"," ",0,"1/7*c^2*e^2*x^7+1/6*(2*b*c*e^2+2*c^2*d*e)*x^6+1/5*(b^2*e^2+4*b*c*d*e+c^2*d^2)*x^5+1/4*(2*b^2*d*e+2*b*c*d^2)*x^4+1/3*b^2*d^2*x^3","A"
234,1,52,47,0.034000," ","int((e*x+d)*(c*x^2+b*x)^2,x)","\frac{c^{2} e \,x^{6}}{6}+\frac{b^{2} d \,x^{3}}{3}+\frac{\left(2 b c e +d \,c^{2}\right) x^{5}}{5}+\frac{\left(e \,b^{2}+2 b c d \right) x^{4}}{4}"," ",0,"1/6*c^2*e*x^6+1/5*(2*b*c*e+c^2*d)*x^5+1/4*(b^2*e+2*b*c*d)*x^4+1/3*b^2*d*x^3","A"
235,1,25,24,0.041000," ","int((c*x^2+b*x)^2,x)","\frac{1}{5} c^{2} x^{5}+\frac{1}{2} b c \,x^{4}+\frac{1}{3} b^{2} x^{3}"," ",0,"1/3*b^2*x^3+1/2*b*c*x^4+1/5*c^2*x^5","A"
236,1,152,87,0.039000," ","int((c*x^2+b*x)^2/(e*x+d),x)","\frac{c^{2} x^{4}}{4 e}+\frac{2 b c \,x^{3}}{3 e}-\frac{c^{2} d \,x^{3}}{3 e^{2}}+\frac{b^{2} x^{2}}{2 e}-\frac{b c d \,x^{2}}{e^{2}}+\frac{c^{2} d^{2} x^{2}}{2 e^{3}}+\frac{b^{2} d^{2} \ln \left(e x +d \right)}{e^{3}}-\frac{b^{2} d x}{e^{2}}-\frac{2 b c \,d^{3} \ln \left(e x +d \right)}{e^{4}}+\frac{2 b c \,d^{2} x}{e^{3}}+\frac{c^{2} d^{4} \ln \left(e x +d \right)}{e^{5}}-\frac{c^{2} d^{3} x}{e^{4}}"," ",0,"1/4*c^2*x^4/e+2/3/e*x^3*b*c-1/3*c^2*d*x^3/e^2+1/2/e*x^2*b^2-1/e^2*x^2*b*c*d+1/2/e^3*x^2*c^2*d^2-1/e^2*x*b^2*d+2/e^3*x*b*c*d^2-1/e^4*x*c^2*d^3+d^2/e^3*ln(e*x+d)*b^2-2*d^3/e^4*ln(e*x+d)*b*c+d^4/e^5*ln(e*x+d)*c^2","A"
237,1,164,105,0.129000," ","int((c*x^2+b*x)^2/(e*x+d)^2,x)","\frac{c^{2} x^{3}}{3 e^{2}}+\frac{b c \,x^{2}}{e^{2}}-\frac{c^{2} d \,x^{2}}{e^{3}}-\frac{b^{2} d^{2}}{\left(e x +d \right) e^{3}}-\frac{2 b^{2} d \ln \left(e x +d \right)}{e^{3}}+\frac{b^{2} x}{e^{2}}+\frac{2 b c \,d^{3}}{\left(e x +d \right) e^{4}}+\frac{6 b c \,d^{2} \ln \left(e x +d \right)}{e^{4}}-\frac{4 b c d x}{e^{3}}-\frac{c^{2} d^{4}}{\left(e x +d \right) e^{5}}-\frac{4 c^{2} d^{3} \ln \left(e x +d \right)}{e^{5}}+\frac{3 c^{2} d^{2} x}{e^{4}}"," ",0,"1/3*c^2*x^3/e^2+1/e^2*x^2*b*c-c^2*d*x^2/e^3+b^2*x/e^2-4/e^3*b*c*d*x+3/e^4*c^2*d^2*x-d^2/e^3/(e*x+d)*b^2+2*d^3/e^4/(e*x+d)*b*c-d^4/e^5/(e*x+d)*c^2-2*d/e^3*ln(e*x+d)*b^2+6*d^2/e^4*ln(e*x+d)*b*c-4*d^3/e^5*ln(e*x+d)*c^2","A"
238,1,178,115,0.079000," ","int((c*x^2+b*x)^2/(e*x+d)^3,x)","-\frac{b^{2} d^{2}}{2 \left(e x +d \right)^{2} e^{3}}+\frac{b c \,d^{3}}{\left(e x +d \right)^{2} e^{4}}-\frac{c^{2} d^{4}}{2 \left(e x +d \right)^{2} e^{5}}+\frac{c^{2} x^{2}}{2 e^{3}}+\frac{2 b^{2} d}{\left(e x +d \right) e^{3}}+\frac{b^{2} \ln \left(e x +d \right)}{e^{3}}-\frac{6 b c \,d^{2}}{\left(e x +d \right) e^{4}}-\frac{6 b c d \ln \left(e x +d \right)}{e^{4}}+\frac{2 b c x}{e^{3}}+\frac{4 c^{2} d^{3}}{\left(e x +d \right) e^{5}}+\frac{6 c^{2} d^{2} \ln \left(e x +d \right)}{e^{5}}-\frac{3 c^{2} d x}{e^{4}}"," ",0,"1/2*c^2*x^2/e^3+2*c/e^3*x*b-3*c^2*d*x/e^4-1/2*d^2/e^3/(e*x+d)^2*b^2+d^3/e^4/(e*x+d)^2*b*c-1/2*d^4/e^5/(e*x+d)^2*c^2+2*d/e^3/(e*x+d)*b^2-6*d^2/e^4/(e*x+d)*b*c+4*d^3/e^5/(e*x+d)*c^2+b^2*ln(e*x+d)/e^3-6/e^4*ln(e*x+d)*b*c*d+6/e^5*ln(e*x+d)*c^2*d^2","A"
239,1,189,118,0.046000," ","int((c*x^2+b*x)^2/(e*x+d)^4,x)","-\frac{b^{2} d^{2}}{3 \left(e x +d \right)^{3} e^{3}}+\frac{2 b c \,d^{3}}{3 \left(e x +d \right)^{3} e^{4}}-\frac{c^{2} d^{4}}{3 \left(e x +d \right)^{3} e^{5}}+\frac{b^{2} d}{\left(e x +d \right)^{2} e^{3}}-\frac{3 b c \,d^{2}}{\left(e x +d \right)^{2} e^{4}}+\frac{2 c^{2} d^{3}}{\left(e x +d \right)^{2} e^{5}}-\frac{b^{2}}{\left(e x +d \right) e^{3}}+\frac{6 b c d}{\left(e x +d \right) e^{4}}+\frac{2 b c \ln \left(e x +d \right)}{e^{4}}-\frac{6 c^{2} d^{2}}{\left(e x +d \right) e^{5}}-\frac{4 c^{2} d \ln \left(e x +d \right)}{e^{5}}+\frac{c^{2} x}{e^{4}}"," ",0,"c^2*x/e^4-1/3*d^2/e^3/(e*x+d)^3*b^2+2/3*d^3/e^4/(e*x+d)^3*b*c-1/3*d^4/e^5/(e*x+d)^3*c^2+d/e^3/(e*x+d)^2*b^2-3*d^2/e^4/(e*x+d)^2*b*c+2*d^3/e^5/(e*x+d)^2*c^2-1/e^3/(e*x+d)*b^2+6/e^4/(e*x+d)*b*c*d-6/e^5/(e*x+d)*c^2*d^2+2*c/e^4*ln(e*x+d)*b-4*c^2*d*ln(e*x+d)/e^5","A"
240,1,197,126,0.054000," ","int((c*x^2+b*x)^2/(e*x+d)^5,x)","-\frac{b^{2} d^{2}}{4 \left(e x +d \right)^{4} e^{3}}+\frac{b c \,d^{3}}{2 \left(e x +d \right)^{4} e^{4}}-\frac{c^{2} d^{4}}{4 \left(e x +d \right)^{4} e^{5}}+\frac{2 b^{2} d}{3 \left(e x +d \right)^{3} e^{3}}-\frac{2 b c \,d^{2}}{\left(e x +d \right)^{3} e^{4}}+\frac{4 c^{2} d^{3}}{3 \left(e x +d \right)^{3} e^{5}}-\frac{b^{2}}{2 \left(e x +d \right)^{2} e^{3}}+\frac{3 b c d}{\left(e x +d \right)^{2} e^{4}}-\frac{3 c^{2} d^{2}}{\left(e x +d \right)^{2} e^{5}}-\frac{2 b c}{\left(e x +d \right) e^{4}}+\frac{4 c^{2} d}{\left(e x +d \right) e^{5}}+\frac{c^{2} \ln \left(e x +d \right)}{e^{5}}"," ",0,"2/3*d/e^3/(e*x+d)^3*b^2-2*d^2/e^4/(e*x+d)^3*b*c+4/3*d^3/e^5/(e*x+d)^3*c^2-1/2*b^2/e^3/(e*x+d)^2+3/e^4/(e*x+d)^2*b*c*d-3/e^5/(e*x+d)^2*c^2*d^2-2*c/e^4/(e*x+d)*b+4*c^2*d/e^5/(e*x+d)+c^2*ln(e*x+d)/e^5-1/4*d^2/e^3/(e*x+d)^4*b^2+1/2*d^3/e^4/(e*x+d)^4*b*c-1/4*d^4/e^5/(e*x+d)^4*c^2","A"
241,1,143,127,0.068000," ","int((c*x^2+b*x)^2/(e*x+d)^6,x)","-\frac{c^{2}}{\left(e x +d \right) e^{5}}-\frac{\left(b^{2} e^{2}-2 b c d e +c^{2} d^{2}\right) d^{2}}{5 \left(e x +d \right)^{5} e^{5}}-\frac{\left(b e -2 c d \right) c}{\left(e x +d \right)^{2} e^{5}}+\frac{\left(b^{2} e^{2}-3 b c d e +2 c^{2} d^{2}\right) d}{2 \left(e x +d \right)^{4} e^{5}}-\frac{b^{2} e^{2}-6 b c d e +6 c^{2} d^{2}}{3 \left(e x +d \right)^{3} e^{5}}"," ",0,"-1/3*(b^2*e^2-6*b*c*d*e+6*c^2*d^2)/e^5/(e*x+d)^3-1/5*d^2*(b^2*e^2-2*b*c*d*e+c^2*d^2)/e^5/(e*x+d)^5-c*(b*e-2*c*d)/e^5/(e*x+d)^2-c^2/e^5/(e*x+d)+1/2*d*(b^2*e^2-3*b*c*d*e+2*c^2*d^2)/e^5/(e*x+d)^4","A"
242,1,143,128,0.065000," ","int((c*x^2+b*x)^2/(e*x+d)^7,x)","-\frac{c^{2}}{2 \left(e x +d \right)^{2} e^{5}}-\frac{\left(b^{2} e^{2}-2 b c d e +c^{2} d^{2}\right) d^{2}}{6 \left(e x +d \right)^{6} e^{5}}-\frac{2 \left(b e -2 c d \right) c}{3 \left(e x +d \right)^{3} e^{5}}+\frac{2 \left(b^{2} e^{2}-3 b c d e +2 c^{2} d^{2}\right) d}{5 \left(e x +d \right)^{5} e^{5}}-\frac{b^{2} e^{2}-6 b c d e +6 c^{2} d^{2}}{4 \left(e x +d \right)^{4} e^{5}}"," ",0,"-2/3*c*(b*e-2*c*d)/e^5/(e*x+d)^3+2/5*d*(b^2*e^2-3*b*c*d*e+2*c^2*d^2)/e^5/(e*x+d)^5-1/2*c^2/e^5/(e*x+d)^2-1/4*(b^2*e^2-6*b*c*d*e+6*c^2*d^2)/e^5/(e*x+d)^4-1/6*d^2*(b^2*e^2-2*b*c*d*e+c^2*d^2)/e^5/(e*x+d)^6","A"
243,1,143,128,0.043000," ","int((c*x^2+b*x)^2/(e*x+d)^8,x)","-\frac{c^{2}}{3 \left(e x +d \right)^{3} e^{5}}-\frac{\left(b^{2} e^{2}-2 b c d e +c^{2} d^{2}\right) d^{2}}{7 \left(e x +d \right)^{7} e^{5}}-\frac{\left(b e -2 c d \right) c}{2 \left(e x +d \right)^{4} e^{5}}+\frac{\left(b^{2} e^{2}-3 b c d e +2 c^{2} d^{2}\right) d}{3 \left(e x +d \right)^{6} e^{5}}-\frac{b^{2} e^{2}-6 b c d e +6 c^{2} d^{2}}{5 \left(e x +d \right)^{5} e^{5}}"," ",0,"-1/3*c^2/e^5/(e*x+d)^3-1/5*(b^2*e^2-6*b*c*d*e+6*c^2*d^2)/e^5/(e*x+d)^5-1/2*c*(b*e-2*c*d)/e^5/(e*x+d)^4+1/3*d*(b^2*e^2-3*b*c*d*e+2*c^2*d^2)/e^5/(e*x+d)^6-1/7*d^2*(b^2*e^2-2*b*c*d*e+c^2*d^2)/e^5/(e*x+d)^7","A"
244,1,232,209,0.047000," ","int((e*x+d)^4*(c*x^2+b*x)^3,x)","\frac{c^{3} e^{4} x^{11}}{11}+\frac{b^{3} d^{4} x^{4}}{4}+\frac{\left(3 e^{4} b \,c^{2}+4 d \,e^{3} c^{3}\right) x^{10}}{10}+\frac{\left(3 e^{4} c \,b^{2}+12 d \,e^{3} b \,c^{2}+6 d^{2} e^{2} c^{3}\right) x^{9}}{9}+\frac{\left(e^{4} b^{3}+12 d \,e^{3} c \,b^{2}+18 d^{2} e^{2} b \,c^{2}+4 d^{3} e \,c^{3}\right) x^{8}}{8}+\frac{\left(4 d \,e^{3} b^{3}+18 d^{2} e^{2} c \,b^{2}+12 d^{3} e b \,c^{2}+d^{4} c^{3}\right) x^{7}}{7}+\frac{\left(6 d^{2} e^{2} b^{3}+12 d^{3} e c \,b^{2}+3 d^{4} b \,c^{2}\right) x^{6}}{6}+\frac{\left(4 d^{3} e \,b^{3}+3 d^{4} c \,b^{2}\right) x^{5}}{5}"," ",0,"1/11*c^3*e^4*x^11+1/10*(3*b*c^2*e^4+4*c^3*d*e^3)*x^10+1/9*(3*b^2*c*e^4+12*b*c^2*d*e^3+6*c^3*d^2*e^2)*x^9+1/8*(b^3*e^4+12*b^2*c*d*e^3+18*b*c^2*d^2*e^2+4*c^3*d^3*e)*x^8+1/7*(4*b^3*d*e^3+18*b^2*c*d^2*e^2+12*b*c^2*d^3*e+c^3*d^4)*x^7+1/6*(6*b^3*d^2*e^2+12*b^2*c*d^3*e+3*b*c^2*d^4)*x^6+1/5*(4*b^3*d^3*e+3*b^2*c*d^4)*x^5+1/4*b^3*d^4*x^4","A"
245,1,180,148,0.041000," ","int((e*x+d)^3*(c*x^2+b*x)^3,x)","\frac{c^{3} e^{3} x^{10}}{10}+\frac{b^{3} d^{3} x^{4}}{4}+\frac{\left(3 e^{3} b \,c^{2}+3 d \,e^{2} c^{3}\right) x^{9}}{9}+\frac{\left(3 e^{3} c \,b^{2}+9 d \,e^{2} b \,c^{2}+3 d^{2} e \,c^{3}\right) x^{8}}{8}+\frac{\left(b^{3} e^{3}+9 b^{2} c d \,e^{2}+9 b \,c^{2} d^{2} e +c^{3} d^{3}\right) x^{7}}{7}+\frac{\left(3 b^{3} d \,e^{2}+9 d^{2} e c \,b^{2}+3 d^{3} b \,c^{2}\right) x^{6}}{6}+\frac{\left(3 d^{2} e \,b^{3}+3 d^{3} c \,b^{2}\right) x^{5}}{5}"," ",0,"1/10*c^3*e^3*x^10+1/9*(3*b*c^2*e^3+3*c^3*d*e^2)*x^9+1/8*(3*b^2*c*e^3+9*b*c^2*d*e^2+3*c^3*d^2*e)*x^8+1/7*(b^3*e^3+9*b^2*c*d*e^2+9*b*c^2*d^2*e+c^3*d^3)*x^7+1/6*(3*b^3*d*e^2+9*b^2*c*d^2*e+3*b*c^2*d^3)*x^6+1/5*(3*b^3*d^2*e+3*b^2*c*d^3)*x^5+1/4*b^3*d^3*x^4","A"
246,1,128,115,0.038000," ","int((e*x+d)^2*(c*x^2+b*x)^3,x)","\frac{c^{3} e^{2} x^{9}}{9}+\frac{b^{3} d^{2} x^{4}}{4}+\frac{\left(3 e^{2} b \,c^{2}+2 d e \,c^{3}\right) x^{8}}{8}+\frac{\left(3 e^{2} c \,b^{2}+6 d e b \,c^{2}+c^{3} d^{2}\right) x^{7}}{7}+\frac{\left(b^{3} e^{2}+6 b^{2} c d e +3 c^{2} d^{2} b \right) x^{6}}{6}+\frac{\left(2 b^{3} d e +3 d^{2} c \,b^{2}\right) x^{5}}{5}"," ",0,"1/9*c^3*e^2*x^9+1/8*(3*b*c^2*e^2+2*c^3*d*e)*x^8+1/7*(3*b^2*c*e^2+6*b*c^2*d*e+c^3*d^2)*x^7+1/6*(b^3*e^2+6*b^2*c*d*e+3*b*c^2*d^2)*x^6+1/5*(2*b^3*d*e+3*b^2*c*d^2)*x^5+1/4*b^3*d^2*x^4","A"
247,1,76,65,0.036000," ","int((e*x+d)*(c*x^2+b*x)^3,x)","\frac{c^{3} e \,x^{8}}{8}+\frac{b^{3} d \,x^{4}}{4}+\frac{\left(3 e b \,c^{2}+d \,c^{3}\right) x^{7}}{7}+\frac{\left(3 b^{2} c e +3 b \,c^{2} d \right) x^{6}}{6}+\frac{\left(e \,b^{3}+3 d c \,b^{2}\right) x^{5}}{5}"," ",0,"1/8*c^3*e*x^8+1/7*(3*b*c^2*e+c^3*d)*x^7+1/6*(3*b^2*c*e+3*b*c^2*d)*x^6+1/5*(b^3*e+3*b^2*c*d)*x^5+1/4*b^3*d*x^4","A"
248,1,36,35,0.038000," ","int((c*x^2+b*x)^3,x)","\frac{1}{7} c^{3} x^{7}+\frac{1}{2} b \,c^{2} x^{6}+\frac{3}{5} b^{2} c \,x^{5}+\frac{1}{4} b^{3} x^{4}"," ",0,"1/4*b^3*x^4+3/5*b^2*c*x^5+1/2*b*c^2*x^6+1/7*c^3*x^7","A"
249,1,302,141,0.131000," ","int((c*x^2+b*x)^3/(e*x+d),x)","\frac{c^{3} x^{6}}{6 e}+\frac{3 b \,c^{2} x^{5}}{5 e}-\frac{c^{3} d \,x^{5}}{5 e^{2}}+\frac{3 b^{2} c \,x^{4}}{4 e}-\frac{3 b \,c^{2} d \,x^{4}}{4 e^{2}}+\frac{c^{3} d^{2} x^{4}}{4 e^{3}}+\frac{b^{3} x^{3}}{3 e}-\frac{b^{2} c d \,x^{3}}{e^{2}}+\frac{b \,c^{2} d^{2} x^{3}}{e^{3}}-\frac{c^{3} d^{3} x^{3}}{3 e^{4}}-\frac{b^{3} d \,x^{2}}{2 e^{2}}+\frac{3 b^{2} c \,d^{2} x^{2}}{2 e^{3}}-\frac{3 b \,c^{2} d^{3} x^{2}}{2 e^{4}}+\frac{c^{3} d^{4} x^{2}}{2 e^{5}}-\frac{b^{3} d^{3} \ln \left(e x +d \right)}{e^{4}}+\frac{b^{3} d^{2} x}{e^{3}}+\frac{3 b^{2} c \,d^{4} \ln \left(e x +d \right)}{e^{5}}-\frac{3 b^{2} c \,d^{3} x}{e^{4}}-\frac{3 b \,c^{2} d^{5} \ln \left(e x +d \right)}{e^{6}}+\frac{3 b \,c^{2} d^{4} x}{e^{5}}+\frac{c^{3} d^{6} \ln \left(e x +d \right)}{e^{7}}-\frac{c^{3} d^{5} x}{e^{6}}"," ",0,"1/6*c^3*x^6/e+3/5/e*x^5*b*c^2-1/5*c^3*d*x^5/e^2+3/4/e*x^4*b^2*c-3/4/e^2*x^4*b*c^2*d+1/4/e^3*x^4*c^3*d^2+1/3/e*x^3*b^3-1/e^2*x^3*b^2*c*d+1/e^3*x^3*b*c^2*d^2-1/3/e^4*x^3*c^3*d^3-1/2/e^2*x^2*b^3*d+3/2/e^3*x^2*b^2*c*d^2-3/2/e^4*x^2*b*c^2*d^3+1/2/e^5*x^2*c^3*d^4+1/e^3*x*b^3*d^2-3/e^4*x*b^2*c*d^3+3/e^5*x*b*c^2*d^4-1/e^6*x*c^3*d^5-d^3/e^4*ln(e*x+d)*b^3+3*d^4/e^5*ln(e*x+d)*b^2*c-3*d^5/e^6*ln(e*x+d)*b*c^2+d^6/e^7*ln(e*x+d)*c^3","B"
250,1,318,160,0.064000," ","int((c*x^2+b*x)^3/(e*x+d)^2,x)","\frac{c^{3} x^{5}}{5 e^{2}}+\frac{3 b \,c^{2} x^{4}}{4 e^{2}}-\frac{c^{3} d \,x^{4}}{2 e^{3}}+\frac{b^{2} c \,x^{3}}{e^{2}}-\frac{2 b \,c^{2} d \,x^{3}}{e^{3}}+\frac{c^{3} d^{2} x^{3}}{e^{4}}+\frac{b^{3} x^{2}}{2 e^{2}}-\frac{3 b^{2} c d \,x^{2}}{e^{3}}+\frac{9 b \,c^{2} d^{2} x^{2}}{2 e^{4}}-\frac{2 c^{3} d^{3} x^{2}}{e^{5}}+\frac{b^{3} d^{3}}{\left(e x +d \right) e^{4}}+\frac{3 b^{3} d^{2} \ln \left(e x +d \right)}{e^{4}}-\frac{2 b^{3} d x}{e^{3}}-\frac{3 b^{2} c \,d^{4}}{\left(e x +d \right) e^{5}}-\frac{12 b^{2} c \,d^{3} \ln \left(e x +d \right)}{e^{5}}+\frac{9 b^{2} c \,d^{2} x}{e^{4}}+\frac{3 b \,c^{2} d^{5}}{\left(e x +d \right) e^{6}}+\frac{15 b \,c^{2} d^{4} \ln \left(e x +d \right)}{e^{6}}-\frac{12 b \,c^{2} d^{3} x}{e^{5}}-\frac{c^{3} d^{6}}{\left(e x +d \right) e^{7}}-\frac{6 c^{3} d^{5} \ln \left(e x +d \right)}{e^{7}}+\frac{5 c^{3} d^{4} x}{e^{6}}"," ",0,"1/5*c^3*x^5/e^2+3/4/e^2*x^4*b*c^2-1/2*c^3*d*x^4/e^3+1/e^2*x^3*b^2*c-2/e^3*x^3*b*c^2*d+1/e^4*x^3*c^3*d^2+1/2/e^2*x^2*b^3-3/e^3*x^2*b^2*c*d+9/2/e^4*x^2*b*c^2*d^2-2/e^5*x^2*c^3*d^3-2/e^3*d*b^3*x+9/e^4*b^2*c*d^2*x-12/e^5*b*c^2*d^3*x+5/e^6*c^3*d^4*x+d^3/e^4/(e*x+d)*b^3-3*d^4/e^5/(e*x+d)*b^2*c+3*d^5/e^6/(e*x+d)*b*c^2-d^6/e^7/(e*x+d)*c^3+3*d^2/e^4*ln(e*x+d)*b^3-12*d^3/e^5*ln(e*x+d)*b^2*c+15*d^4/e^6*ln(e*x+d)*b*c^2-6*d^5/e^7*ln(e*x+d)*c^3","A"
251,1,335,194,0.056000," ","int((c*x^2+b*x)^3/(e*x+d)^3,x)","\frac{c^{3} x^{4}}{4 e^{3}}+\frac{b \,c^{2} x^{3}}{e^{3}}-\frac{c^{3} d \,x^{3}}{e^{4}}+\frac{b^{3} d^{3}}{2 \left(e x +d \right)^{2} e^{4}}-\frac{3 b^{2} c \,d^{4}}{2 \left(e x +d \right)^{2} e^{5}}+\frac{3 b^{2} c \,x^{2}}{2 e^{3}}+\frac{3 b \,c^{2} d^{5}}{2 \left(e x +d \right)^{2} e^{6}}-\frac{9 b \,c^{2} d \,x^{2}}{2 e^{4}}-\frac{c^{3} d^{6}}{2 \left(e x +d \right)^{2} e^{7}}+\frac{3 c^{3} d^{2} x^{2}}{e^{5}}-\frac{3 b^{3} d^{2}}{\left(e x +d \right) e^{4}}-\frac{3 b^{3} d \ln \left(e x +d \right)}{e^{4}}+\frac{b^{3} x}{e^{3}}+\frac{12 b^{2} c \,d^{3}}{\left(e x +d \right) e^{5}}+\frac{18 b^{2} c \,d^{2} \ln \left(e x +d \right)}{e^{5}}-\frac{9 b^{2} c d x}{e^{4}}-\frac{15 b \,c^{2} d^{4}}{\left(e x +d \right) e^{6}}-\frac{30 b \,c^{2} d^{3} \ln \left(e x +d \right)}{e^{6}}+\frac{18 b \,c^{2} d^{2} x}{e^{5}}+\frac{6 c^{3} d^{5}}{\left(e x +d \right) e^{7}}+\frac{15 c^{3} d^{4} \ln \left(e x +d \right)}{e^{7}}-\frac{10 c^{3} d^{3} x}{e^{6}}"," ",0,"1/4*c^3*x^4/e^3+1/e^3*x^3*b*c^2-c^3*d*x^3/e^4+3/2/e^3*x^2*b^2*c-9/2/e^4*x^2*b*c^2*d+3/e^5*x^2*c^3*d^2+1/e^3*b^3*x-9/e^4*b^2*c*d*x+18/e^5*b*c^2*d^2*x-10/e^6*c^3*d^3*x+1/2*d^3/e^4/(e*x+d)^2*b^3-3/2*d^4/e^5/(e*x+d)^2*b^2*c+3/2*d^5/e^6/(e*x+d)^2*b*c^2-1/2*d^6/e^7/(e*x+d)^2*c^3-3*d^2/e^4/(e*x+d)*b^3+12*d^3/e^5/(e*x+d)*b^2*c-15*d^4/e^6/(e*x+d)*b*c^2+6*d^5/e^7/(e*x+d)*c^3-3*d/e^4*ln(e*x+d)*b^3+18*d^2/e^5*ln(e*x+d)*b^2*c-30*d^3/e^6*ln(e*x+d)*b*c^2+15*d^4/e^7*ln(e*x+d)*c^3","A"
252,1,353,205,0.053000," ","int((c*x^2+b*x)^3/(e*x+d)^4,x)","\frac{b^{3} d^{3}}{3 \left(e x +d \right)^{3} e^{4}}-\frac{b^{2} c \,d^{4}}{\left(e x +d \right)^{3} e^{5}}+\frac{b \,c^{2} d^{5}}{\left(e x +d \right)^{3} e^{6}}-\frac{c^{3} d^{6}}{3 \left(e x +d \right)^{3} e^{7}}+\frac{c^{3} x^{3}}{3 e^{4}}-\frac{3 b^{3} d^{2}}{2 \left(e x +d \right)^{2} e^{4}}+\frac{6 b^{2} c \,d^{3}}{\left(e x +d \right)^{2} e^{5}}-\frac{15 b \,c^{2} d^{4}}{2 \left(e x +d \right)^{2} e^{6}}+\frac{3 b \,c^{2} x^{2}}{2 e^{4}}+\frac{3 c^{3} d^{5}}{\left(e x +d \right)^{2} e^{7}}-\frac{2 c^{3} d \,x^{2}}{e^{5}}+\frac{3 b^{3} d}{\left(e x +d \right) e^{4}}+\frac{b^{3} \ln \left(e x +d \right)}{e^{4}}-\frac{18 b^{2} c \,d^{2}}{\left(e x +d \right) e^{5}}-\frac{12 b^{2} c d \ln \left(e x +d \right)}{e^{5}}+\frac{3 b^{2} c x}{e^{4}}+\frac{30 b \,c^{2} d^{3}}{\left(e x +d \right) e^{6}}+\frac{30 b \,c^{2} d^{2} \ln \left(e x +d \right)}{e^{6}}-\frac{12 b \,c^{2} d x}{e^{5}}-\frac{15 c^{3} d^{4}}{\left(e x +d \right) e^{7}}-\frac{20 c^{3} d^{3} \ln \left(e x +d \right)}{e^{7}}+\frac{10 c^{3} d^{2} x}{e^{6}}"," ",0,"1/3*c^3*x^3/e^4+3/2*c^2/e^4*x^2*b-2*c^3*d*x^2/e^5+3*c/e^4*b^2*x-12*c^2/e^5*b*d*x+10*c^3/e^6*d^2*x+1/3*d^3/e^4/(e*x+d)^3*b^3-d^4/e^5/(e*x+d)^3*b^2*c+d^5/e^6/(e*x+d)^3*b*c^2-1/3*d^6/e^7/(e*x+d)^3*c^3-3/2*d^2/e^4/(e*x+d)^2*b^3+6*d^3/e^5/(e*x+d)^2*b^2*c-15/2*d^4/e^6/(e*x+d)^2*b*c^2+3*d^5/e^7/(e*x+d)^2*c^3+3*d/e^4/(e*x+d)*b^3-18*d^2/e^5/(e*x+d)*b^2*c+30*d^3/e^6/(e*x+d)*b*c^2-15*d^4/e^7/(e*x+d)*c^3+1/e^4*ln(e*x+d)*b^3-12/e^5*ln(e*x+d)*b^2*c*d+30/e^6*ln(e*x+d)*b*c^2*d^2-20/e^7*ln(e*x+d)*c^3*d^3","A"
253,1,370,207,0.051000," ","int((c*x^2+b*x)^3/(e*x+d)^5,x)","\frac{b^{3} d^{3}}{4 \left(e x +d \right)^{4} e^{4}}-\frac{3 b^{2} c \,d^{4}}{4 \left(e x +d \right)^{4} e^{5}}+\frac{3 b \,c^{2} d^{5}}{4 \left(e x +d \right)^{4} e^{6}}-\frac{c^{3} d^{6}}{4 \left(e x +d \right)^{4} e^{7}}-\frac{b^{3} d^{2}}{\left(e x +d \right)^{3} e^{4}}+\frac{4 b^{2} c \,d^{3}}{\left(e x +d \right)^{3} e^{5}}-\frac{5 b \,c^{2} d^{4}}{\left(e x +d \right)^{3} e^{6}}+\frac{2 c^{3} d^{5}}{\left(e x +d \right)^{3} e^{7}}+\frac{3 b^{3} d}{2 \left(e x +d \right)^{2} e^{4}}-\frac{9 b^{2} c \,d^{2}}{\left(e x +d \right)^{2} e^{5}}+\frac{15 b \,c^{2} d^{3}}{\left(e x +d \right)^{2} e^{6}}-\frac{15 c^{3} d^{4}}{2 \left(e x +d \right)^{2} e^{7}}+\frac{c^{3} x^{2}}{2 e^{5}}-\frac{b^{3}}{\left(e x +d \right) e^{4}}+\frac{12 b^{2} c d}{\left(e x +d \right) e^{5}}+\frac{3 b^{2} c \ln \left(e x +d \right)}{e^{5}}-\frac{30 b \,c^{2} d^{2}}{\left(e x +d \right) e^{6}}-\frac{15 b \,c^{2} d \ln \left(e x +d \right)}{e^{6}}+\frac{3 b \,c^{2} x}{e^{5}}+\frac{20 c^{3} d^{3}}{\left(e x +d \right) e^{7}}+\frac{15 c^{3} d^{2} \ln \left(e x +d \right)}{e^{7}}-\frac{5 c^{3} d x}{e^{6}}"," ",0,"1/2*c^3*x^2/e^5+3*c^2/e^5*x*b-5*c^3*d*x/e^6-d^2/e^4/(e*x+d)^3*b^3+4*d^3/e^5/(e*x+d)^3*b^2*c-5*d^4/e^6/(e*x+d)^3*b*c^2+2*d^5/e^7/(e*x+d)^3*c^3+3/2*d/e^4/(e*x+d)^2*b^3-9*d^2/e^5/(e*x+d)^2*b^2*c+15*d^3/e^6/(e*x+d)^2*b*c^2-15/2*d^4/e^7/(e*x+d)^2*c^3-1/e^4/(e*x+d)*b^3+12/e^5/(e*x+d)*b^2*c*d-30/e^6/(e*x+d)*b*c^2*d^2+20/e^7/(e*x+d)*c^3*d^3+3*c/e^5*ln(e*x+d)*b^2-15*c^2/e^6*ln(e*x+d)*b*d+15*c^3/e^7*ln(e*x+d)*d^2+1/4*d^3/e^4/(e*x+d)^4*b^3-3/4*d^4/e^5/(e*x+d)^4*b^2*c+3/4*d^5/e^6/(e*x+d)^4*b*c^2-1/4*d^6/e^7/(e*x+d)^4*c^3","A"
254,1,379,212,0.054000," ","int((c*x^2+b*x)^3/(e*x+d)^6,x)","\frac{b^{3} d^{3}}{5 \left(e x +d \right)^{5} e^{4}}-\frac{3 b^{2} c \,d^{4}}{5 \left(e x +d \right)^{5} e^{5}}+\frac{3 b \,c^{2} d^{5}}{5 \left(e x +d \right)^{5} e^{6}}-\frac{c^{3} d^{6}}{5 \left(e x +d \right)^{5} e^{7}}-\frac{3 b^{3} d^{2}}{4 \left(e x +d \right)^{4} e^{4}}+\frac{3 b^{2} c \,d^{3}}{\left(e x +d \right)^{4} e^{5}}-\frac{15 b \,c^{2} d^{4}}{4 \left(e x +d \right)^{4} e^{6}}+\frac{3 c^{3} d^{5}}{2 \left(e x +d \right)^{4} e^{7}}+\frac{b^{3} d}{\left(e x +d \right)^{3} e^{4}}-\frac{6 b^{2} c \,d^{2}}{\left(e x +d \right)^{3} e^{5}}+\frac{10 b \,c^{2} d^{3}}{\left(e x +d \right)^{3} e^{6}}-\frac{5 c^{3} d^{4}}{\left(e x +d \right)^{3} e^{7}}-\frac{b^{3}}{2 \left(e x +d \right)^{2} e^{4}}+\frac{6 b^{2} c d}{\left(e x +d \right)^{2} e^{5}}-\frac{15 b \,c^{2} d^{2}}{\left(e x +d \right)^{2} e^{6}}+\frac{10 c^{3} d^{3}}{\left(e x +d \right)^{2} e^{7}}-\frac{3 b^{2} c}{\left(e x +d \right) e^{5}}+\frac{15 b \,c^{2} d}{\left(e x +d \right) e^{6}}+\frac{3 b \,c^{2} \ln \left(e x +d \right)}{e^{6}}-\frac{15 c^{3} d^{2}}{\left(e x +d \right) e^{7}}-\frac{6 c^{3} d \ln \left(e x +d \right)}{e^{7}}+\frac{c^{3} x}{e^{6}}"," ",0,"c^3*x/e^6+d/e^4/(e*x+d)^3*b^3-6*d^2/e^5/(e*x+d)^3*b^2*c+10*d^3/e^6/(e*x+d)^3*b*c^2-5*d^4/e^7/(e*x+d)^3*c^3+1/5*d^3/e^4/(e*x+d)^5*b^3-3/5*d^4/e^5/(e*x+d)^5*b^2*c+3/5*d^5/e^6/(e*x+d)^5*b*c^2-1/5*d^6/e^7/(e*x+d)^5*c^3-1/2/e^4/(e*x+d)^2*b^3+6/e^5/(e*x+d)^2*b^2*c*d-15/e^6/(e*x+d)^2*b*c^2*d^2+10/e^7/(e*x+d)^2*c^3*d^3-3*c/e^5/(e*x+d)*b^2+15*c^2/e^6/(e*x+d)*b*d-15*c^3/e^7/(e*x+d)*d^2+3*c^2/e^6*ln(e*x+d)*b-6*c^3*d*ln(e*x+d)/e^7-3/4*d^2/e^4/(e*x+d)^4*b^3+3*d^3/e^5/(e*x+d)^4*b^2*c-15/4*d^4/e^6/(e*x+d)^4*b*c^2+3/2*d^5/e^7/(e*x+d)^4*c^3","A"
255,1,387,218,0.050000," ","int((c*x^2+b*x)^3/(e*x+d)^7,x)","\frac{b^{3} d^{3}}{6 \left(e x +d \right)^{6} e^{4}}-\frac{b^{2} c \,d^{4}}{2 \left(e x +d \right)^{6} e^{5}}+\frac{b \,c^{2} d^{5}}{2 \left(e x +d \right)^{6} e^{6}}-\frac{c^{3} d^{6}}{6 \left(e x +d \right)^{6} e^{7}}-\frac{3 b^{3} d^{2}}{5 \left(e x +d \right)^{5} e^{4}}+\frac{12 b^{2} c \,d^{3}}{5 \left(e x +d \right)^{5} e^{5}}-\frac{3 b \,c^{2} d^{4}}{\left(e x +d \right)^{5} e^{6}}+\frac{6 c^{3} d^{5}}{5 \left(e x +d \right)^{5} e^{7}}+\frac{3 b^{3} d}{4 \left(e x +d \right)^{4} e^{4}}-\frac{9 b^{2} c \,d^{2}}{2 \left(e x +d \right)^{4} e^{5}}+\frac{15 b \,c^{2} d^{3}}{2 \left(e x +d \right)^{4} e^{6}}-\frac{15 c^{3} d^{4}}{4 \left(e x +d \right)^{4} e^{7}}-\frac{b^{3}}{3 \left(e x +d \right)^{3} e^{4}}+\frac{4 b^{2} c d}{\left(e x +d \right)^{3} e^{5}}-\frac{10 b \,c^{2} d^{2}}{\left(e x +d \right)^{3} e^{6}}+\frac{20 c^{3} d^{3}}{3 \left(e x +d \right)^{3} e^{7}}-\frac{3 b^{2} c}{2 \left(e x +d \right)^{2} e^{5}}+\frac{15 b \,c^{2} d}{2 \left(e x +d \right)^{2} e^{6}}-\frac{15 c^{3} d^{2}}{2 \left(e x +d \right)^{2} e^{7}}-\frac{3 b \,c^{2}}{\left(e x +d \right) e^{6}}+\frac{6 c^{3} d}{\left(e x +d \right) e^{7}}+\frac{c^{3} \ln \left(e x +d \right)}{e^{7}}"," ",0,"-1/3/e^4/(e*x+d)^3*b^3+4/e^5/(e*x+d)^3*b^2*c*d-10/e^6/(e*x+d)^3*b*c^2*d^2+20/3/e^7/(e*x+d)^3*c^3*d^3-3/5*d^2/e^4/(e*x+d)^5*b^3+12/5*d^3/e^5/(e*x+d)^5*b^2*c-3*d^4/e^6/(e*x+d)^5*b*c^2+6/5*d^5/e^7/(e*x+d)^5*c^3-3/2*c/e^5/(e*x+d)^2*b^2+15/2*c^2/e^6/(e*x+d)^2*b*d-15/2*c^3/e^7/(e*x+d)^2*d^2-3*c^2/e^6/(e*x+d)*b+6*c^3*d/e^7/(e*x+d)+c^3*ln(e*x+d)/e^7+3/4*d/e^4/(e*x+d)^4*b^3-9/2*d^2/e^5/(e*x+d)^4*b^2*c+15/2*d^3/e^6/(e*x+d)^4*b*c^2-15/4*d^4/e^7/(e*x+d)^4*c^3+1/6*d^3/e^4/(e*x+d)^6*b^3-1/2*d^4/e^5/(e*x+d)^6*b^2*c+1/2*d^5/e^6/(e*x+d)^6*b*c^2-1/6*d^6/e^7/(e*x+d)^6*c^3","A"
256,1,274,220,0.046000," ","int((c*x^2+b*x)^3/(e*x+d)^8,x)","-\frac{c^{3}}{\left(e x +d \right) e^{7}}+\frac{\left(b^{3} e^{3}-3 b^{2} c d \,e^{2}+3 b \,c^{2} d^{2} e -c^{3} d^{3}\right) d^{3}}{7 \left(e x +d \right)^{7} e^{7}}-\frac{3 \left(b e -2 c d \right) c^{2}}{2 \left(e x +d \right)^{2} e^{7}}-\frac{\left(b^{3} e^{3}-4 b^{2} c d \,e^{2}+5 b \,c^{2} d^{2} e -2 c^{3} d^{3}\right) d^{2}}{2 \left(e x +d \right)^{6} e^{7}}-\frac{\left(b^{2} e^{2}-5 b c d e +5 c^{2} d^{2}\right) c}{\left(e x +d \right)^{3} e^{7}}+\frac{3 \left(b^{3} e^{3}-6 b^{2} c d \,e^{2}+10 b \,c^{2} d^{2} e -5 c^{3} d^{3}\right) d}{5 \left(e x +d \right)^{5} e^{7}}-\frac{b^{3} e^{3}-12 b^{2} c d \,e^{2}+30 b \,c^{2} d^{2} e -20 c^{3} d^{3}}{4 \left(e x +d \right)^{4} e^{7}}"," ",0,"-c*(b^2*e^2-5*b*c*d*e+5*c^2*d^2)/e^7/(e*x+d)^3+3/5*d*(b^3*e^3-6*b^2*c*d*e^2+10*b*c^2*d^2*e-5*c^3*d^3)/e^7/(e*x+d)^5-3/2*c^2*(b*e-2*c*d)/e^7/(e*x+d)^2-c^3/e^7/(e*x+d)-1/4*(b^3*e^3-12*b^2*c*d*e^2+30*b*c^2*d^2*e-20*c^3*d^3)/e^7/(e*x+d)^4-1/2*d^2*(b^3*e^3-4*b^2*c*d*e^2+5*b*c^2*d^2*e-2*c^3*d^3)/e^7/(e*x+d)^6+1/7*d^3*(b^3*e^3-3*b^2*c*d*e^2+3*b*c^2*d^2*e-c^3*d^3)/e^7/(e*x+d)^7","A"
257,1,274,219,0.047000," ","int((c*x^2+b*x)^3/(e*x+d)^9,x)","-\frac{c^{3}}{2 \left(e x +d \right)^{2} e^{7}}+\frac{\left(b^{3} e^{3}-3 b^{2} c d \,e^{2}+3 b \,c^{2} d^{2} e -c^{3} d^{3}\right) d^{3}}{8 \left(e x +d \right)^{8} e^{7}}-\frac{\left(b e -2 c d \right) c^{2}}{\left(e x +d \right)^{3} e^{7}}-\frac{3 \left(b^{3} e^{3}-4 b^{2} c d \,e^{2}+5 b \,c^{2} d^{2} e -2 c^{3} d^{3}\right) d^{2}}{7 \left(e x +d \right)^{7} e^{7}}-\frac{3 \left(b^{2} e^{2}-5 b c d e +5 c^{2} d^{2}\right) c}{4 \left(e x +d \right)^{4} e^{7}}+\frac{\left(b^{3} e^{3}-6 b^{2} c d \,e^{2}+10 b \,c^{2} d^{2} e -5 c^{3} d^{3}\right) d}{2 \left(e x +d \right)^{6} e^{7}}-\frac{b^{3} e^{3}-12 b^{2} c d \,e^{2}+30 b \,c^{2} d^{2} e -20 c^{3} d^{3}}{5 \left(e x +d \right)^{5} e^{7}}"," ",0,"-c^2*(b*e-2*c*d)/e^7/(e*x+d)^3-1/5*(b^3*e^3-12*b^2*c*d*e^2+30*b*c^2*d^2*e-20*c^3*d^3)/e^7/(e*x+d)^5-1/2*c^3/e^7/(e*x+d)^2+1/8*d^3*(b^3*e^3-3*b^2*c*d*e^2+3*b*c^2*d^2*e-c^3*d^3)/e^7/(e*x+d)^8-3/4*c*(b^2*e^2-5*b*c*d*e+5*c^2*d^2)/e^7/(e*x+d)^4+1/2*d*(b^3*e^3-6*b^2*c*d*e^2+10*b*c^2*d^2*e-5*c^3*d^3)/e^7/(e*x+d)^6-3/7*d^2*(b^3*e^3-4*b^2*c*d*e^2+5*b*c^2*d^2*e-2*c^3*d^3)/e^7/(e*x+d)^7","A"
258,1,274,220,0.048000," ","int((c*x^2+b*x)^3/(e*x+d)^10,x)","-\frac{c^{3}}{3 \left(e x +d \right)^{3} e^{7}}+\frac{\left(b^{3} e^{3}-3 b^{2} c d \,e^{2}+3 b \,c^{2} d^{2} e -c^{3} d^{3}\right) d^{3}}{9 \left(e x +d \right)^{9} e^{7}}-\frac{3 \left(b e -2 c d \right) c^{2}}{4 \left(e x +d \right)^{4} e^{7}}-\frac{3 \left(b^{3} e^{3}-4 b^{2} c d \,e^{2}+5 b \,c^{2} d^{2} e -2 c^{3} d^{3}\right) d^{2}}{8 \left(e x +d \right)^{8} e^{7}}-\frac{3 \left(b^{2} e^{2}-5 b c d e +5 c^{2} d^{2}\right) c}{5 \left(e x +d \right)^{5} e^{7}}+\frac{3 \left(b^{3} e^{3}-6 b^{2} c d \,e^{2}+10 b \,c^{2} d^{2} e -5 c^{3} d^{3}\right) d}{7 \left(e x +d \right)^{7} e^{7}}-\frac{b^{3} e^{3}-12 b^{2} c d \,e^{2}+30 b \,c^{2} d^{2} e -20 c^{3} d^{3}}{6 \left(e x +d \right)^{6} e^{7}}"," ",0,"-1/3*c^3/e^7/(e*x+d)^3-3/5*c*(b^2*e^2-5*b*c*d*e+5*c^2*d^2)/e^7/(e*x+d)^5-3/8*d^2*(b^3*e^3-4*b^2*c*d*e^2+5*b*c^2*d^2*e-2*c^3*d^3)/e^7/(e*x+d)^8+1/9*d^3*(b^3*e^3-3*b^2*c*d*e^2+3*b*c^2*d^2*e-c^3*d^3)/e^7/(e*x+d)^9-3/4*c^2*(b*e-2*c*d)/e^7/(e*x+d)^4-1/6*(b^3*e^3-12*b^2*c*d*e^2+30*b*c^2*d^2*e-20*c^3*d^3)/e^7/(e*x+d)^6+3/7*d*(b^3*e^3-6*b^2*c*d*e^2+10*b*c^2*d^2*e-5*c^3*d^3)/e^7/(e*x+d)^7","A"
259,1,162,95,0.046000," ","int((e*x+d)^4/(c*x^2+b*x),x)","\frac{e^{4} x^{3}}{3 c}-\frac{b \,e^{4} x^{2}}{2 c^{2}}+\frac{2 d \,e^{3} x^{2}}{c}-\frac{b^{3} e^{4} \ln \left(c x +b \right)}{c^{4}}+\frac{4 b^{2} d \,e^{3} \ln \left(c x +b \right)}{c^{3}}+\frac{b^{2} e^{4} x}{c^{3}}-\frac{6 b \,d^{2} e^{2} \ln \left(c x +b \right)}{c^{2}}-\frac{4 b d \,e^{3} x}{c^{2}}+\frac{d^{4} \ln \left(x \right)}{b}-\frac{d^{4} \ln \left(c x +b \right)}{b}+\frac{4 d^{3} e \ln \left(c x +b \right)}{c}+\frac{6 d^{2} e^{2} x}{c}"," ",0,"1/3*e^4*x^3/c-1/2*e^4/c^2*x^2*b+2*d*e^3*x^2/c+e^4/c^3*b^2*x-4*e^3/c^2*b*d*x+6*e^2/c*d^2*x-b^3/c^4*ln(c*x+b)*e^4+4*b^2/c^3*ln(c*x+b)*d*e^3-6*b/c^2*ln(c*x+b)*d^2*e^2+4/c*ln(c*x+b)*d^3*e-1/b*ln(c*x+b)*d^4+d^4*ln(x)/b","A"
260,1,103,62,0.051000," ","int((e*x+d)^3/(c*x^2+b*x),x)","\frac{e^{3} x^{2}}{2 c}+\frac{b^{2} e^{3} \ln \left(c x +b \right)}{c^{3}}-\frac{3 b d \,e^{2} \ln \left(c x +b \right)}{c^{2}}-\frac{b \,e^{3} x}{c^{2}}+\frac{d^{3} \ln \left(x \right)}{b}-\frac{d^{3} \ln \left(c x +b \right)}{b}+\frac{3 d^{2} e \ln \left(c x +b \right)}{c}+\frac{3 d \,e^{2} x}{c}"," ",0,"1/2*e^3*x^2/c-e^3/c^2*x*b+3*d*e^2*x/c+1/c^3*b^2*ln(c*x+b)*e^3-3/c^2*b*ln(c*x+b)*d*e^2+3/c*ln(c*x+b)*d^2*e-1/b*ln(c*x+b)*d^3+d^3*ln(x)/b","A"
261,1,61,42,0.123000," ","int((e*x+d)^2/(c*x^2+b*x),x)","-\frac{b \,e^{2} \ln \left(c x +b \right)}{c^{2}}+\frac{d^{2} \ln \left(x \right)}{b}-\frac{d^{2} \ln \left(c x +b \right)}{b}+\frac{2 d e \ln \left(c x +b \right)}{c}+\frac{e^{2} x}{c}"," ",0,"e^2*x/c-b/c^2*ln(c*x+b)*e^2+2/c*ln(c*x+b)*d*e-1/b*ln(c*x+b)*d^2+d^2*ln(x)/b","A"
262,1,32,30,0.046000," ","int((e*x+d)/(c*x^2+b*x),x)","\frac{d \ln \left(x \right)}{b}-\frac{d \ln \left(c x +b \right)}{b}+\frac{e \ln \left(c x +b \right)}{c}"," ",0,"1/c*ln(c*x+b)*e-1/b*ln(c*x+b)*d+1/b*d*ln(x)","A"
263,1,19,18,0.050000," ","int(1/(c*x^2+b*x),x)","\frac{\ln \left(x \right)}{b}-\frac{\ln \left(c x +b \right)}{b}"," ",0,"1/b*ln(x)-ln(c*x+b)/b","A"
264,1,54,53,0.051000," ","int(1/(e*x+d)/(c*x^2+b*x),x)","\frac{c \ln \left(c x +b \right)}{\left(b e -c d \right) b}-\frac{e \ln \left(e x +d \right)}{\left(b e -c d \right) d}+\frac{\ln \left(x \right)}{b d}"," ",0,"c/(b*e-c*d)/b*ln(c*x+b)-e/(b*e-c*d)/d*ln(e*x+d)+ln(x)/b/d","A"
265,1,105,87,0.059000," ","int(1/(e*x+d)^2/(c*x^2+b*x),x)","-\frac{b \,e^{2} \ln \left(e x +d \right)}{\left(b e -c d \right)^{2} d^{2}}-\frac{c^{2} \ln \left(c x +b \right)}{\left(b e -c d \right)^{2} b}+\frac{2 c e \ln \left(e x +d \right)}{\left(b e -c d \right)^{2} d}+\frac{e}{\left(b e -c d \right) \left(e x +d \right) d}+\frac{\ln \left(x \right)}{b \,d^{2}}"," ",0,"-c^2/(b*e-c*d)^2/b*ln(c*x+b)+e/(b*e-c*d)/d/(e*x+d)-e^2/(b*e-c*d)^2/d^2*ln(e*x+d)*b+2*e/(b*e-c*d)^2/d*ln(e*x+d)*c+ln(x)/b/d^2","A"
266,1,184,132,0.067000," ","int(1/(e*x+d)^3/(c*x^2+b*x),x)","-\frac{b^{2} e^{3} \ln \left(e x +d \right)}{\left(b e -c d \right)^{3} d^{3}}+\frac{3 b c \,e^{2} \ln \left(e x +d \right)}{\left(b e -c d \right)^{3} d^{2}}+\frac{c^{3} \ln \left(c x +b \right)}{\left(b e -c d \right)^{3} b}-\frac{3 c^{2} e \ln \left(e x +d \right)}{\left(b e -c d \right)^{3} d}+\frac{b \,e^{2}}{\left(b e -c d \right)^{2} \left(e x +d \right) d^{2}}-\frac{2 c e}{\left(b e -c d \right)^{2} \left(e x +d \right) d}+\frac{e}{2 \left(b e -c d \right) \left(e x +d \right)^{2} d}+\frac{\ln \left(x \right)}{b \,d^{3}}"," ",0,"c^3/(b*e-c*d)^3/b*ln(c*x+b)+1/2*e/(b*e-c*d)/d/(e*x+d)^2+e^2/(b*e-c*d)^2/d^2/(e*x+d)*b-2*e/(b*e-c*d)^2/d/(e*x+d)*c-e^3/(b*e-c*d)^3/d^3*ln(e*x+d)*b^2+3*e^2/(b*e-c*d)^3/d^2*ln(e*x+d)*b*c-3*e/(b*e-c*d)^3/d*ln(e*x+d)*c^2+ln(x)/b/d^3","A"
267,1,251,116,0.155000," ","int((e*x+d)^5/(c*x^2+b*x)^2,x)","\frac{e^{5} x^{2}}{2 c^{2}}+\frac{b^{3} e^{5}}{\left(c x +b \right) c^{4}}-\frac{5 b^{2} d \,e^{4}}{\left(c x +b \right) c^{3}}+\frac{3 b^{2} e^{5} \ln \left(c x +b \right)}{c^{4}}+\frac{10 b \,d^{2} e^{3}}{\left(c x +b \right) c^{2}}-\frac{10 b d \,e^{4} \ln \left(c x +b \right)}{c^{3}}-\frac{2 b \,e^{5} x}{c^{3}}+\frac{5 d^{4} e}{\left(c x +b \right) b}-\frac{c \,d^{5}}{\left(c x +b \right) b^{2}}+\frac{5 d^{4} e \ln \left(x \right)}{b^{2}}-\frac{5 d^{4} e \ln \left(c x +b \right)}{b^{2}}-\frac{2 c \,d^{5} \ln \left(x \right)}{b^{3}}+\frac{2 c \,d^{5} \ln \left(c x +b \right)}{b^{3}}-\frac{10 d^{3} e^{2}}{\left(c x +b \right) c}+\frac{10 d^{2} e^{3} \ln \left(c x +b \right)}{c^{2}}+\frac{5 d \,e^{4} x}{c^{2}}-\frac{d^{5}}{b^{2} x}"," ",0,"1/2*e^5*x^2/c^2-2*e^5/c^3*x*b+5*e^4/c^2*x*d+3/c^4*b^2*ln(c*x+b)*e^5-10/c^3*b*ln(c*x+b)*d*e^4+10/c^2*ln(c*x+b)*d^2*e^3-5/b^2*ln(c*x+b)*d^4*e+2*c/b^3*ln(c*x+b)*d^5+b^3/c^4/(c*x+b)*e^5-5*b^2/c^3/(c*x+b)*d*e^4+10*b/c^2/(c*x+b)*d^2*e^3-10/c/(c*x+b)*d^3*e^2+5/b/(c*x+b)*d^4*e-1/b^2*c/(c*x+b)*d^5-d^5/b^2/x+5*d^4/b^2*ln(x)*e-2*d^5/b^3*ln(x)*c","B"
268,1,188,94,0.052000," ","int((e*x+d)^4/(c*x^2+b*x)^2,x)","-\frac{b^{2} e^{4}}{\left(c x +b \right) c^{3}}+\frac{4 b d \,e^{3}}{\left(c x +b \right) c^{2}}-\frac{2 b \,e^{4} \ln \left(c x +b \right)}{c^{3}}+\frac{4 d^{3} e}{\left(c x +b \right) b}-\frac{c \,d^{4}}{\left(c x +b \right) b^{2}}+\frac{4 d^{3} e \ln \left(x \right)}{b^{2}}-\frac{4 d^{3} e \ln \left(c x +b \right)}{b^{2}}-\frac{2 c \,d^{4} \ln \left(x \right)}{b^{3}}+\frac{2 c \,d^{4} \ln \left(c x +b \right)}{b^{3}}-\frac{6 d^{2} e^{2}}{\left(c x +b \right) c}+\frac{4 d \,e^{3} \ln \left(c x +b \right)}{c^{2}}+\frac{e^{4} x}{c^{2}}-\frac{d^{4}}{b^{2} x}"," ",0,"e^4*x/c^2-2*b/c^3*ln(c*x+b)*e^4+4/c^2*ln(c*x+b)*d*e^3-4/b^2*ln(c*x+b)*d^3*e+2/b^3*c*ln(c*x+b)*d^4-1/c^3*b^2/(c*x+b)*e^4+4/c^2*b/(c*x+b)*d*e^3-6/c/(c*x+b)*d^2*e^2+4/b/(c*x+b)*d^3*e-c/b^2/(c*x+b)*d^4-d^4/b^2/x+4*d^3/b^2*ln(x)*e-2*d^4/b^3*ln(x)*c","A"
269,1,141,87,0.059000," ","int((e*x+d)^3/(c*x^2+b*x)^2,x)","\frac{b \,e^{3}}{\left(c x +b \right) c^{2}}+\frac{3 d^{2} e}{\left(c x +b \right) b}-\frac{c \,d^{3}}{\left(c x +b \right) b^{2}}+\frac{3 d^{2} e \ln \left(x \right)}{b^{2}}-\frac{3 d^{2} e \ln \left(c x +b \right)}{b^{2}}-\frac{2 c \,d^{3} \ln \left(x \right)}{b^{3}}+\frac{2 c \,d^{3} \ln \left(c x +b \right)}{b^{3}}-\frac{3 d \,e^{2}}{\left(c x +b \right) c}+\frac{e^{3} \ln \left(c x +b \right)}{c^{2}}-\frac{d^{3}}{b^{2} x}"," ",0,"1/c^2*ln(c*x+b)*e^3-3/b^2*ln(c*x+b)*d^2*e+2/b^3*c*ln(c*x+b)*d^3+1/c^2*b/(c*x+b)*e^3-3/c/(c*x+b)*d*e^2+3/b/(c*x+b)*d^2*e-c/b^2/(c*x+b)*d^3-d^3/b^2/x+3*d^2/b^2*ln(x)*e-2*d^3/b^3*ln(x)*c","A"
270,1,106,73,0.066000," ","int((e*x+d)^2/(c*x^2+b*x)^2,x)","\frac{2 d e}{\left(c x +b \right) b}-\frac{c \,d^{2}}{\left(c x +b \right) b^{2}}+\frac{2 d e \ln \left(x \right)}{b^{2}}-\frac{2 d e \ln \left(c x +b \right)}{b^{2}}-\frac{2 c \,d^{2} \ln \left(x \right)}{b^{3}}+\frac{2 c \,d^{2} \ln \left(c x +b \right)}{b^{3}}-\frac{e^{2}}{\left(c x +b \right) c}-\frac{d^{2}}{b^{2} x}"," ",0,"-1/c/(c*x+b)*e^2+2/b/(c*x+b)*d*e-1/b^2*c/(c*x+b)*d^2-2*d/b^2*ln(c*x+b)*e+2*d^2/b^3*ln(c*x+b)*c-d^2/b^2/x+2*d/b^2*ln(x)*e-2*d^2/b^3*ln(x)*c","A"
271,1,78,64,0.052000," ","int((e*x+d)/(c*x^2+b*x)^2,x)","\frac{e}{\left(c x +b \right) b}-\frac{c d}{\left(c x +b \right) b^{2}}+\frac{e \ln \left(x \right)}{b^{2}}-\frac{e \ln \left(c x +b \right)}{b^{2}}-\frac{2 c d \ln \left(x \right)}{b^{3}}+\frac{2 c d \ln \left(c x +b \right)}{b^{3}}-\frac{d}{b^{2} x}"," ",0,"-1/b^2*ln(c*x+b)*e+2/b^3*ln(c*x+b)*c*d+1/b/(c*x+b)*e-1/b^2/(c*x+b)*c*d-d/b^2/x+1/b^2*ln(x)*e-2/b^3*ln(x)*c*d","A"
272,1,43,44,0.048000," ","int(1/(c*x^2+b*x)^2,x)","-\frac{c}{\left(c x +b \right) b^{2}}-\frac{2 c \ln \left(x \right)}{b^{3}}+\frac{2 c \ln \left(c x +b \right)}{b^{3}}-\frac{1}{b^{2} x}"," ",0,"-1/b^2*c/(c*x+b)+2*c*ln(c*x+b)/b^3-1/b^2/x-2*c*ln(x)/b^3","A"
273,1,132,110,0.050000," ","int(1/(e*x+d)/(c*x^2+b*x)^2,x)","-\frac{3 c^{2} e \ln \left(c x +b \right)}{\left(b e -c d \right)^{2} b^{2}}+\frac{2 c^{3} d \ln \left(c x +b \right)}{\left(b e -c d \right)^{2} b^{3}}+\frac{e^{3} \ln \left(e x +d \right)}{\left(b e -c d \right)^{2} d^{2}}+\frac{c^{2}}{\left(b e -c d \right) \left(c x +b \right) b^{2}}-\frac{e \ln \left(x \right)}{b^{2} d^{2}}-\frac{2 c \ln \left(x \right)}{b^{3} d}-\frac{1}{b^{2} d x}"," ",0,"c^2/(b*e-c*d)/b^2/(c*x+b)-3*c^2/(b*e-c*d)^2/b^2*ln(c*x+b)*e+2*c^3/(b*e-c*d)^2/b^3*ln(c*x+b)*d+e^3/(b*e-c*d)^2/d^2*ln(e*x+d)-1/b^2/d/x-1/b^2/d^2*ln(x)*e-2/b^3/d*ln(x)*c","A"
274,1,185,144,0.110000," ","int(1/(e*x+d)^2/(c*x^2+b*x)^2,x)","\frac{2 b \,e^{4} \ln \left(e x +d \right)}{\left(b e -c d \right)^{3} d^{3}}+\frac{4 c^{3} e \ln \left(c x +b \right)}{\left(b e -c d \right)^{3} b^{2}}-\frac{2 c^{4} d \ln \left(c x +b \right)}{\left(b e -c d \right)^{3} b^{3}}-\frac{4 c \,e^{3} \ln \left(e x +d \right)}{\left(b e -c d \right)^{3} d^{2}}-\frac{c^{3}}{\left(b e -c d \right)^{2} \left(c x +b \right) b^{2}}-\frac{e^{3}}{\left(b e -c d \right)^{2} \left(e x +d \right) d^{2}}-\frac{2 e \ln \left(x \right)}{b^{2} d^{3}}-\frac{2 c \ln \left(x \right)}{b^{3} d^{2}}-\frac{1}{b^{2} d^{2} x}"," ",0,"-c^3/(b*e-c*d)^2/b^2/(c*x+b)+4*c^3/(b*e-c*d)^3/b^2*ln(c*x+b)*e-2*c^4/(b*e-c*d)^3/b^3*ln(c*x+b)*d-e^3/(b*e-c*d)^2/d^2/(e*x+d)+2*e^4/(b*e-c*d)^3/d^3*ln(e*x+d)*b-4*e^3/(b*e-c*d)^3/d^2*ln(e*x+d)*c-1/b^2/d^2/x-2/b^2/d^3*ln(x)*e-2/b^3/d^2*ln(x)*c","A"
275,1,481,197,0.069000," ","int((e*x+d)^7/(c*x^2+b*x)^3,x)","-\frac{b^{4} e^{7}}{2 \left(c x +b \right)^{2} c^{5}}+\frac{7 b^{3} d \,e^{6}}{2 \left(c x +b \right)^{2} c^{4}}-\frac{21 b^{2} d^{2} e^{5}}{2 \left(c x +b \right)^{2} c^{3}}+\frac{35 b \,d^{3} e^{4}}{2 \left(c x +b \right)^{2} c^{2}}+\frac{21 d^{5} e^{2}}{2 \left(c x +b \right)^{2} b}-\frac{7 c \,d^{6} e}{2 \left(c x +b \right)^{2} b^{2}}+\frac{c^{2} d^{7}}{2 \left(c x +b \right)^{2} b^{3}}-\frac{35 d^{4} e^{3}}{2 \left(c x +b \right)^{2} c}+\frac{e^{7} x^{2}}{2 c^{3}}+\frac{4 b^{3} e^{7}}{\left(c x +b \right) c^{5}}-\frac{21 b^{2} d \,e^{6}}{\left(c x +b \right) c^{4}}+\frac{6 b^{2} e^{7} \ln \left(c x +b \right)}{c^{5}}+\frac{42 b \,d^{2} e^{5}}{\left(c x +b \right) c^{3}}-\frac{21 b d \,e^{6} \ln \left(c x +b \right)}{c^{4}}-\frac{3 b \,e^{7} x}{c^{4}}+\frac{21 d^{5} e^{2}}{\left(c x +b \right) b^{2}}-\frac{14 c \,d^{6} e}{\left(c x +b \right) b^{3}}+\frac{21 d^{5} e^{2} \ln \left(x \right)}{b^{3}}-\frac{21 d^{5} e^{2} \ln \left(c x +b \right)}{b^{3}}+\frac{3 c^{2} d^{7}}{\left(c x +b \right) b^{4}}-\frac{21 c \,d^{6} e \ln \left(x \right)}{b^{4}}+\frac{21 c \,d^{6} e \ln \left(c x +b \right)}{b^{4}}+\frac{6 c^{2} d^{7} \ln \left(x \right)}{b^{5}}-\frac{6 c^{2} d^{7} \ln \left(c x +b \right)}{b^{5}}-\frac{35 d^{3} e^{4}}{\left(c x +b \right) c^{2}}+\frac{21 d^{2} e^{5} \ln \left(c x +b \right)}{c^{3}}+\frac{7 d \,e^{6} x}{c^{3}}-\frac{7 d^{6} e}{b^{3} x}+\frac{3 c \,d^{7}}{b^{4} x}-\frac{d^{7}}{2 b^{3} x^{2}}"," ",0,"-7*d^6/b^3/x*e+3*d^7/b^4/x*c+21*d^5/b^3*ln(x)*e^2+6*d^7/b^5*ln(x)*c^2-3*e^7/c^4*x*b+7*e^6/c^3*x*d+6/c^5*b^2*ln(c*x+b)*e^7+21/c^3*ln(c*x+b)*d^2*e^5-21/b^3*ln(c*x+b)*d^5*e^2-6*c^2/b^5*ln(c*x+b)*d^7+4/c^5*b^3/(c*x+b)*e^7+3*c^2/b^4/(c*x+b)*d^7-1/2/c^5*b^4/(c*x+b)^2*e^7+1/2*c^2/b^3/(c*x+b)^2*d^7-35/c^2/(c*x+b)*d^3*e^4+21/b^2/(c*x+b)*d^5*e^2-35/2/c/(c*x+b)^2*d^4*e^3+21/2/b/(c*x+b)^2*d^5*e^2-21/c^4*b*ln(c*x+b)*d*e^6+21*c/b^4*ln(c*x+b)*d^6*e+1/2*e^7*x^2/c^3-1/2*d^7/b^3/x^2-21/c^4*b^2/(c*x+b)*d*e^6+42/c^3*b/(c*x+b)*d^2*e^5-14*c/b^3/(c*x+b)*d^6*e+7/2/c^4*b^3/(c*x+b)^2*d*e^6-21/2/c^3*b^2/(c*x+b)^2*d^2*e^5+35/2/c^2*b/(c*x+b)^2*d^3*e^4-7/2*c/b^2/(c*x+b)^2*d^6*e-21*d^6/b^4*ln(x)*c*e","B"
276,1,396,175,0.055000," ","int((e*x+d)^6/(c*x^2+b*x)^3,x)","\frac{b^{3} e^{6}}{2 \left(c x +b \right)^{2} c^{4}}-\frac{3 b^{2} d \,e^{5}}{\left(c x +b \right)^{2} c^{3}}+\frac{15 b \,d^{2} e^{4}}{2 \left(c x +b \right)^{2} c^{2}}+\frac{15 d^{4} e^{2}}{2 \left(c x +b \right)^{2} b}-\frac{3 c \,d^{5} e}{\left(c x +b \right)^{2} b^{2}}+\frac{c^{2} d^{6}}{2 \left(c x +b \right)^{2} b^{3}}-\frac{10 d^{3} e^{3}}{\left(c x +b \right)^{2} c}-\frac{3 b^{2} e^{6}}{\left(c x +b \right) c^{4}}+\frac{12 b d \,e^{5}}{\left(c x +b \right) c^{3}}-\frac{3 b \,e^{6} \ln \left(c x +b \right)}{c^{4}}+\frac{15 d^{4} e^{2}}{\left(c x +b \right) b^{2}}-\frac{12 c \,d^{5} e}{\left(c x +b \right) b^{3}}+\frac{15 d^{4} e^{2} \ln \left(x \right)}{b^{3}}-\frac{15 d^{4} e^{2} \ln \left(c x +b \right)}{b^{3}}+\frac{3 c^{2} d^{6}}{\left(c x +b \right) b^{4}}-\frac{18 c \,d^{5} e \ln \left(x \right)}{b^{4}}+\frac{18 c \,d^{5} e \ln \left(c x +b \right)}{b^{4}}+\frac{6 c^{2} d^{6} \ln \left(x \right)}{b^{5}}-\frac{6 c^{2} d^{6} \ln \left(c x +b \right)}{b^{5}}-\frac{15 d^{2} e^{4}}{\left(c x +b \right) c^{2}}+\frac{6 d \,e^{5} \ln \left(c x +b \right)}{c^{3}}+\frac{e^{6} x}{c^{3}}-\frac{6 d^{5} e}{b^{3} x}+\frac{3 c \,d^{6}}{b^{4} x}-\frac{d^{6}}{2 b^{3} x^{2}}"," ",0,"e^6*x/c^3+18*c/b^4*ln(c*x+b)*d^5*e+12/c^3*b/(c*x+b)*d*e^5-6*d^5/b^3/x*e+3*d^6/b^4/x*c-3/c^4*b*ln(c*x+b)*e^6+6/c^3*ln(c*x+b)*d*e^5-15/b^3*ln(c*x+b)*d^4*e^2-6*c^2/b^5*ln(c*x+b)*d^6-3/c^4*b^2/(c*x+b)*e^6+3*c^2/b^4/(c*x+b)*d^6+1/2/c^4*b^3/(c*x+b)^2*e^6+1/2*c^2/b^3/(c*x+b)^2*d^6+15*d^4/b^3*ln(x)*e^2+6*d^6/b^5*ln(x)*c^2-15/c^2/(c*x+b)*d^2*e^4+15/b^2/(c*x+b)*d^4*e^2-10/c/(c*x+b)^2*d^3*e^3+15/2/b/(c*x+b)^2*d^4*e^2-12*c/b^3/(c*x+b)*d^5*e-18*d^5/b^4*ln(x)*c*e-3/c^3*b^2/(c*x+b)^2*d*e^5+15/2/c^2*b/(c*x+b)^2*d^2*e^4-3*c/b^2/(c*x+b)^2*d^5*e-1/2*d^6/b^3/x^2","B"
277,1,329,167,0.059000," ","int((e*x+d)^5/(c*x^2+b*x)^3,x)","-\frac{b^{2} e^{5}}{2 \left(c x +b \right)^{2} c^{3}}+\frac{5 b d \,e^{4}}{2 \left(c x +b \right)^{2} c^{2}}+\frac{5 d^{3} e^{2}}{\left(c x +b \right)^{2} b}-\frac{5 c \,d^{4} e}{2 \left(c x +b \right)^{2} b^{2}}+\frac{c^{2} d^{5}}{2 \left(c x +b \right)^{2} b^{3}}-\frac{5 d^{2} e^{3}}{\left(c x +b \right)^{2} c}+\frac{2 b \,e^{5}}{\left(c x +b \right) c^{3}}+\frac{10 d^{3} e^{2}}{\left(c x +b \right) b^{2}}-\frac{10 c \,d^{4} e}{\left(c x +b \right) b^{3}}+\frac{10 d^{3} e^{2} \ln \left(x \right)}{b^{3}}-\frac{10 d^{3} e^{2} \ln \left(c x +b \right)}{b^{3}}+\frac{3 c^{2} d^{5}}{\left(c x +b \right) b^{4}}-\frac{15 c \,d^{4} e \ln \left(x \right)}{b^{4}}+\frac{15 c \,d^{4} e \ln \left(c x +b \right)}{b^{4}}+\frac{6 c^{2} d^{5} \ln \left(x \right)}{b^{5}}-\frac{6 c^{2} d^{5} \ln \left(c x +b \right)}{b^{5}}-\frac{5 d \,e^{4}}{\left(c x +b \right) c^{2}}+\frac{e^{5} \ln \left(c x +b \right)}{c^{3}}-\frac{5 d^{4} e}{b^{3} x}+\frac{3 c \,d^{5}}{b^{4} x}-\frac{d^{5}}{2 b^{3} x^{2}}"," ",0,"1/c^3*ln(c*x+b)*e^5-10/b^3*ln(c*x+b)*d^3*e^2+15/b^4*c*ln(c*x+b)*d^4*e-6/b^5*c^2*ln(c*x+b)*d^5+2/c^3*b/(c*x+b)*e^5-5/c^2/(c*x+b)*d*e^4+10/b^2/(c*x+b)*d^3*e^2-10*c/b^3/(c*x+b)*d^4*e+3*c^2/b^4/(c*x+b)*d^5-1/2/c^3*b^2/(c*x+b)^2*e^5+5/2/c^2*b/(c*x+b)^2*d*e^4-5/c/(c*x+b)^2*d^2*e^3+5/b/(c*x+b)^2*d^3*e^2-5/2*c/b^2/(c*x+b)^2*d^4*e+1/2*c^2/b^3/(c*x+b)^2*d^5-1/2*d^5/b^3/x^2+10*d^3/b^3*ln(x)*e^2-15*d^4/b^4*ln(x)*c*e+6*d^5/b^5*ln(x)*c^2-5*d^4/b^3/x*e+3*d^5/b^4/x*c","A"
278,1,278,132,0.060000," ","int((e*x+d)^4/(c*x^2+b*x)^3,x)","\frac{b \,e^{4}}{2 \left(c x +b \right)^{2} c^{2}}+\frac{3 d^{2} e^{2}}{\left(c x +b \right)^{2} b}-\frac{2 c \,d^{3} e}{\left(c x +b \right)^{2} b^{2}}+\frac{c^{2} d^{4}}{2 \left(c x +b \right)^{2} b^{3}}-\frac{2 d \,e^{3}}{\left(c x +b \right)^{2} c}+\frac{6 d^{2} e^{2}}{\left(c x +b \right) b^{2}}-\frac{8 c \,d^{3} e}{\left(c x +b \right) b^{3}}+\frac{6 d^{2} e^{2} \ln \left(x \right)}{b^{3}}-\frac{6 d^{2} e^{2} \ln \left(c x +b \right)}{b^{3}}+\frac{3 c^{2} d^{4}}{\left(c x +b \right) b^{4}}-\frac{12 c \,d^{3} e \ln \left(x \right)}{b^{4}}+\frac{12 c \,d^{3} e \ln \left(c x +b \right)}{b^{4}}+\frac{6 c^{2} d^{4} \ln \left(x \right)}{b^{5}}-\frac{6 c^{2} d^{4} \ln \left(c x +b \right)}{b^{5}}-\frac{e^{4}}{\left(c x +b \right) c^{2}}-\frac{4 d^{3} e}{b^{3} x}+\frac{3 c \,d^{4}}{b^{4} x}-\frac{d^{4}}{2 b^{3} x^{2}}"," ",0,"-1/c^2/(c*x+b)*e^4+6/b^2/(c*x+b)*d^2*e^2-8/b^3*c/(c*x+b)*d^3*e+3/b^4*c^2/(c*x+b)*d^4+1/2*b/c^2/(c*x+b)^2*e^4-2/c/(c*x+b)^2*d*e^3+3/b/(c*x+b)^2*d^2*e^2-2/b^2*c/(c*x+b)^2*d^3*e+1/2/b^3*c^2/(c*x+b)^2*d^4-6*d^2/b^3*ln(c*x+b)*e^2+12*d^3/b^4*ln(c*x+b)*c*e-6*d^4/b^5*ln(c*x+b)*c^2-1/2*d^4/b^3/x^2-4*d^3/b^3/x*e+3*d^4/b^4/x*c+6*d^2/b^3*ln(x)*e^2-12*d^3/b^4*ln(x)*c*e+6*d^4/b^5*ln(x)*c^2","B"
279,1,238,133,0.063000," ","int((e*x+d)^3/(c*x^2+b*x)^3,x)","\frac{3 d \,e^{2}}{2 \left(c x +b \right)^{2} b}-\frac{3 c \,d^{2} e}{2 \left(c x +b \right)^{2} b^{2}}+\frac{c^{2} d^{3}}{2 \left(c x +b \right)^{2} b^{3}}-\frac{e^{3}}{2 \left(c x +b \right)^{2} c}+\frac{3 d \,e^{2}}{\left(c x +b \right) b^{2}}-\frac{6 c \,d^{2} e}{\left(c x +b \right) b^{3}}+\frac{3 d \,e^{2} \ln \left(x \right)}{b^{3}}-\frac{3 d \,e^{2} \ln \left(c x +b \right)}{b^{3}}+\frac{3 c^{2} d^{3}}{\left(c x +b \right) b^{4}}-\frac{9 c \,d^{2} e \ln \left(x \right)}{b^{4}}+\frac{9 c \,d^{2} e \ln \left(c x +b \right)}{b^{4}}+\frac{6 c^{2} d^{3} \ln \left(x \right)}{b^{5}}-\frac{6 c^{2} d^{3} \ln \left(c x +b \right)}{b^{5}}-\frac{3 d^{2} e}{b^{3} x}+\frac{3 c \,d^{3}}{b^{4} x}-\frac{d^{3}}{2 b^{3} x^{2}}"," ",0,"-1/2/c/(c*x+b)^2*e^3+3/2/b/(c*x+b)^2*d*e^2-3/2/b^2*c/(c*x+b)^2*d^2*e+1/2/b^3*c^2/(c*x+b)^2*d^3-3*d/b^3*ln(c*x+b)*e^2+9*d^2/b^4*ln(c*x+b)*c*e-6*d^3/b^5*ln(c*x+b)*c^2+3*d/b^2/(c*x+b)*e^2-6*d^2/b^3/(c*x+b)*c*e+3*d^3/b^4/(c*x+b)*c^2-1/2*d^3/b^3/x^2+3*d/b^3*ln(x)*e^2-9*d^2/b^4*ln(x)*c*e+6*d^3/b^5*ln(x)*c^2-3*d^2/b^3/x*e+3*d^3/b^4/x*c","A"
280,1,207,140,0.058000," ","int((e*x+d)^2/(c*x^2+b*x)^3,x)","\frac{e^{2}}{2 \left(c x +b \right)^{2} b}-\frac{c d e}{\left(c x +b \right)^{2} b^{2}}+\frac{c^{2} d^{2}}{2 \left(c x +b \right)^{2} b^{3}}+\frac{e^{2}}{\left(c x +b \right) b^{2}}-\frac{4 c d e}{\left(c x +b \right) b^{3}}+\frac{e^{2} \ln \left(x \right)}{b^{3}}-\frac{e^{2} \ln \left(c x +b \right)}{b^{3}}+\frac{3 c^{2} d^{2}}{\left(c x +b \right) b^{4}}-\frac{6 c d e \ln \left(x \right)}{b^{4}}+\frac{6 c d e \ln \left(c x +b \right)}{b^{4}}+\frac{6 c^{2} d^{2} \ln \left(x \right)}{b^{5}}-\frac{6 c^{2} d^{2} \ln \left(c x +b \right)}{b^{5}}-\frac{2 d e}{b^{3} x}+\frac{3 c \,d^{2}}{b^{4} x}-\frac{d^{2}}{2 b^{3} x^{2}}"," ",0,"-1/b^3*ln(c*x+b)*e^2+6/b^4*ln(c*x+b)*c*d*e-6/b^5*ln(c*x+b)*c^2*d^2+1/b^2/(c*x+b)*e^2-4/b^3/(c*x+b)*c*d*e+3/b^4/(c*x+b)*c^2*d^2+1/2/b/(c*x+b)^2*e^2-1/b^2/(c*x+b)^2*c*d*e+1/2/b^3/(c*x+b)^2*c^2*d^2-1/2*d^2/b^3/x^2+1/b^3*ln(x)*e^2-6/b^4*ln(x)*c*d*e+6/b^5*ln(x)*c^2*d^2-2*d/b^3/x*e+3*d^2/b^4/x*c","A"
281,1,138,106,0.059000," ","int((e*x+d)/(c*x^2+b*x)^3,x)","-\frac{c e}{2 \left(c x +b \right)^{2} b^{2}}+\frac{c^{2} d}{2 \left(c x +b \right)^{2} b^{3}}-\frac{2 c e}{\left(c x +b \right) b^{3}}+\frac{3 c^{2} d}{\left(c x +b \right) b^{4}}-\frac{3 c e \ln \left(x \right)}{b^{4}}+\frac{3 c e \ln \left(c x +b \right)}{b^{4}}+\frac{6 c^{2} d \ln \left(x \right)}{b^{5}}-\frac{6 c^{2} d \ln \left(c x +b \right)}{b^{5}}-\frac{e}{b^{3} x}+\frac{3 c d}{b^{4} x}-\frac{d}{2 b^{3} x^{2}}"," ",0,"-2*c/b^3/(c*x+b)*e+3*c^2/b^4/(c*x+b)*d-1/2*c/b^2/(c*x+b)^2*e+1/2*c^2/b^3/(c*x+b)^2*d+3*c/b^4*ln(c*x+b)*e-6*c^2/b^5*ln(c*x+b)*d-1/2*d/b^3/x^2-1/b^3/x*e+3/b^4/x*c*d-3*c/b^4*ln(x)*e+6*c^2/b^5*ln(x)*d","A"
282,1,73,72,0.054000," ","int(1/(c*x^2+b*x)^3,x)","\frac{c^{2}}{2 \left(c x +b \right)^{2} b^{3}}+\frac{3 c^{2}}{\left(c x +b \right) b^{4}}+\frac{6 c^{2} \ln \left(x \right)}{b^{5}}-\frac{6 c^{2} \ln \left(c x +b \right)}{b^{5}}+\frac{3 c}{b^{4} x}-\frac{1}{2 b^{3} x^{2}}"," ",0,"-6*c^2*ln(c*x+b)/b^5+3/b^4*c^2/(c*x+b)+1/2/b^3*c^2/(c*x+b)^2-1/2/b^3/x^2+6*c^2*ln(x)/b^5+3/b^4*c/x","A"
283,1,254,189,0.060000," ","int(1/(e*x+d)/(c*x^2+b*x)^3,x)","\frac{10 c^{3} e^{2} \ln \left(c x +b \right)}{\left(b e -c d \right)^{3} b^{3}}-\frac{15 c^{4} d e \ln \left(c x +b \right)}{\left(b e -c d \right)^{3} b^{4}}+\frac{6 c^{5} d^{2} \ln \left(c x +b \right)}{\left(b e -c d \right)^{3} b^{5}}-\frac{e^{5} \ln \left(e x +d \right)}{\left(b e -c d \right)^{3} d^{3}}-\frac{4 c^{3} e}{\left(b e -c d \right)^{2} \left(c x +b \right) b^{3}}+\frac{3 c^{4} d}{\left(b e -c d \right)^{2} \left(c x +b \right) b^{4}}-\frac{c^{3}}{2 \left(b e -c d \right) \left(c x +b \right)^{2} b^{3}}+\frac{e^{2} \ln \left(x \right)}{b^{3} d^{3}}+\frac{3 c e \ln \left(x \right)}{b^{4} d^{2}}+\frac{6 c^{2} \ln \left(x \right)}{b^{5} d}+\frac{e}{b^{3} d^{2} x}+\frac{3 c}{b^{4} d x}-\frac{1}{2 b^{3} d \,x^{2}}"," ",0,"-1/2*c^3/(b*e-c*d)/b^3/(c*x+b)^2-4*c^3/(b*e-c*d)^2/b^3/(c*x+b)*e+3*c^4/(b*e-c*d)^2/b^4/(c*x+b)*d+10*c^3/(b*e-c*d)^3/b^3*ln(c*x+b)*e^2-15*c^4/(b*e-c*d)^3/b^4*ln(c*x+b)*d*e+6*c^5/(b*e-c*d)^3/b^5*ln(c*x+b)*d^2-e^5/(b*e-c*d)^3/d^3*ln(e*x+d)-1/2/b^3/d/x^2+1/b^3/d^2/x*e+3/b^4/d/x*c+1/b^3/d^3*ln(x)*e^2+3/b^4/d^2*ln(x)*c*e+6/b^5/d*ln(x)*c^2","A"
284,1,306,226,0.063000," ","int(1/(e*x+d)^2/(c*x^2+b*x)^3,x)","-\frac{3 b \,e^{6} \ln \left(e x +d \right)}{\left(b e -c d \right)^{4} d^{4}}-\frac{15 c^{4} e^{2} \ln \left(c x +b \right)}{\left(b e -c d \right)^{4} b^{3}}+\frac{18 c^{5} d e \ln \left(c x +b \right)}{\left(b e -c d \right)^{4} b^{4}}-\frac{6 c^{6} d^{2} \ln \left(c x +b \right)}{\left(b e -c d \right)^{4} b^{5}}+\frac{6 c \,e^{5} \ln \left(e x +d \right)}{\left(b e -c d \right)^{4} d^{3}}+\frac{5 c^{4} e}{\left(b e -c d \right)^{3} \left(c x +b \right) b^{3}}-\frac{3 c^{5} d}{\left(b e -c d \right)^{3} \left(c x +b \right) b^{4}}+\frac{e^{5}}{\left(b e -c d \right)^{3} \left(e x +d \right) d^{3}}+\frac{c^{4}}{2 \left(b e -c d \right)^{2} \left(c x +b \right)^{2} b^{3}}+\frac{3 e^{2} \ln \left(x \right)}{b^{3} d^{4}}+\frac{6 c e \ln \left(x \right)}{b^{4} d^{3}}+\frac{6 c^{2} \ln \left(x \right)}{b^{5} d^{2}}+\frac{2 e}{b^{3} d^{3} x}+\frac{3 c}{b^{4} d^{2} x}-\frac{1}{2 b^{3} d^{2} x^{2}}"," ",0,"1/2*c^4/(b*e-c*d)^2/b^3/(c*x+b)^2+5*c^4/(b*e-c*d)^3/b^3/(c*x+b)*e-3*c^5/(b*e-c*d)^3/b^4/(c*x+b)*d-15*c^4/(b*e-c*d)^4/b^3*ln(c*x+b)*e^2+18*c^5/(b*e-c*d)^4/b^4*ln(c*x+b)*d*e-6*c^6/(b*e-c*d)^4/b^5*ln(c*x+b)*d^2+e^5/(b*e-c*d)^3/d^3/(e*x+d)-3*e^6/(b*e-c*d)^4/d^4*ln(e*x+d)*b+6*e^5/(b*e-c*d)^4/d^3*ln(e*x+d)*c-1/2/b^3/d^2/x^2+2/b^3/d^3/x*e+3/b^4/d^2/x*c+3/b^3/d^4*ln(x)*e^2+6/b^4/d^3*ln(x)*c*e+6/b^5/d^2*ln(x)*c^2","A"
285,1,444,190,0.052000," ","int((e*x+d)^3*(c*x^2+b*x)^(1/2),x)","\frac{7 b^{5} e^{3} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{256 c^{\frac{9}{2}}}-\frac{15 b^{4} d \,e^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{128 c^{\frac{7}{2}}}+\frac{3 b^{3} d^{2} e \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{16 c^{\frac{5}{2}}}-\frac{b^{2} d^{3} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{8 c^{\frac{3}{2}}}-\frac{7 \sqrt{c \,x^{2}+b x}\, b^{3} e^{3} x}{64 c^{3}}+\frac{15 \sqrt{c \,x^{2}+b x}\, b^{2} d \,e^{2} x}{32 c^{2}}-\frac{3 \sqrt{c \,x^{2}+b x}\, b \,d^{2} e x}{4 c}+\frac{\left(c \,x^{2}+b x \right)^{\frac{3}{2}} e^{3} x^{2}}{5 c}+\frac{\sqrt{c \,x^{2}+b x}\, d^{3} x}{2}-\frac{7 \sqrt{c \,x^{2}+b x}\, b^{4} e^{3}}{128 c^{4}}+\frac{15 \sqrt{c \,x^{2}+b x}\, b^{3} d \,e^{2}}{64 c^{3}}-\frac{3 \sqrt{c \,x^{2}+b x}\, b^{2} d^{2} e}{8 c^{2}}+\frac{\sqrt{c \,x^{2}+b x}\, b \,d^{3}}{4 c}-\frac{7 \left(c \,x^{2}+b x \right)^{\frac{3}{2}} b \,e^{3} x}{40 c^{2}}+\frac{3 \left(c \,x^{2}+b x \right)^{\frac{3}{2}} d \,e^{2} x}{4 c}+\frac{7 \left(c \,x^{2}+b x \right)^{\frac{3}{2}} b^{2} e^{3}}{48 c^{3}}-\frac{5 \left(c \,x^{2}+b x \right)^{\frac{3}{2}} b d \,e^{2}}{8 c^{2}}+\frac{\left(c \,x^{2}+b x \right)^{\frac{3}{2}} d^{2} e}{c}"," ",0,"1/5*e^3*x^2*(c*x^2+b*x)^(3/2)/c-7/40*e^3*b/c^2*x*(c*x^2+b*x)^(3/2)+7/48*e^3*b^2/c^3*(c*x^2+b*x)^(3/2)-7/64*e^3*b^3/c^3*x*(c*x^2+b*x)^(1/2)-7/128*e^3*b^4/c^4*(c*x^2+b*x)^(1/2)+7/256*e^3*b^5/c^(9/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))+3/4*d*e^2*x*(c*x^2+b*x)^(3/2)/c-5/8*d*e^2*b/c^2*(c*x^2+b*x)^(3/2)+15/32*d*e^2*b^2/c^2*x*(c*x^2+b*x)^(1/2)+15/64*d*e^2*b^3/c^3*(c*x^2+b*x)^(1/2)-15/128*d*e^2*b^4/c^(7/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))+d^2*e*(c*x^2+b*x)^(3/2)/c-3/4*d^2*e*b/c*x*(c*x^2+b*x)^(1/2)-3/8*d^2*e*b^2/c^2*(c*x^2+b*x)^(1/2)+3/16*d^2*e*b^3/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))+1/2*d^3*x*(c*x^2+b*x)^(1/2)+1/4*d^3/c*(c*x^2+b*x)^(1/2)*b-1/8*d^3*b^2/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))","B"
286,1,287,142,0.053000," ","int((e*x+d)^2*(c*x^2+b*x)^(1/2),x)","-\frac{5 b^{4} e^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{128 c^{\frac{7}{2}}}+\frac{b^{3} d e \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{8 c^{\frac{5}{2}}}-\frac{b^{2} d^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{8 c^{\frac{3}{2}}}+\frac{5 \sqrt{c \,x^{2}+b x}\, b^{2} e^{2} x}{32 c^{2}}-\frac{\sqrt{c \,x^{2}+b x}\, b d e x}{2 c}+\frac{\sqrt{c \,x^{2}+b x}\, d^{2} x}{2}+\frac{5 \sqrt{c \,x^{2}+b x}\, b^{3} e^{2}}{64 c^{3}}-\frac{\sqrt{c \,x^{2}+b x}\, b^{2} d e}{4 c^{2}}+\frac{\sqrt{c \,x^{2}+b x}\, b \,d^{2}}{4 c}+\frac{\left(c \,x^{2}+b x \right)^{\frac{3}{2}} e^{2} x}{4 c}-\frac{5 \left(c \,x^{2}+b x \right)^{\frac{3}{2}} b \,e^{2}}{24 c^{2}}+\frac{2 \left(c \,x^{2}+b x \right)^{\frac{3}{2}} d e}{3 c}"," ",0,"1/4*e^2*x*(c*x^2+b*x)^(3/2)/c-5/24*e^2*b/c^2*(c*x^2+b*x)^(3/2)+5/32*e^2*b^2/c^2*x*(c*x^2+b*x)^(1/2)+5/64*e^2*b^3/c^3*(c*x^2+b*x)^(1/2)-5/128*e^2*b^4/c^(7/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))+2/3*d*e*(c*x^2+b*x)^(3/2)/c-1/2*d*e*b/c*x*(c*x^2+b*x)^(1/2)-1/4*d*e*b^2/c^2*(c*x^2+b*x)^(1/2)+1/8*d*e*b^3/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))+1/2*d^2*x*(c*x^2+b*x)^(1/2)+1/4*d^2/c*(c*x^2+b*x)^(1/2)*b-1/8*d^2*b^2/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))","B"
287,1,157,83,0.050000," ","int((e*x+d)*(c*x^2+b*x)^(1/2),x)","\frac{b^{3} e \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{16 c^{\frac{5}{2}}}-\frac{b^{2} d \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{8 c^{\frac{3}{2}}}-\frac{\sqrt{c \,x^{2}+b x}\, b e x}{4 c}+\frac{\sqrt{c \,x^{2}+b x}\, d x}{2}-\frac{\sqrt{c \,x^{2}+b x}\, b^{2} e}{8 c^{2}}+\frac{\sqrt{c \,x^{2}+b x}\, b d}{4 c}+\frac{\left(c \,x^{2}+b x \right)^{\frac{3}{2}} e}{3 c}"," ",0,"1/3*e*(c*x^2+b*x)^(3/2)/c-1/4*e*b/c*x*(c*x^2+b*x)^(1/2)-1/8*e*b^2/c^2*(c*x^2+b*x)^(1/2)+1/16*e*b^3/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))+1/2*d*x*(c*x^2+b*x)^(1/2)+1/4*d/c*(c*x^2+b*x)^(1/2)*b-1/8*d*b^2/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))","A"
288,1,56,48,0.044000," ","int((c*x^2+b*x)^(1/2),x)","-\frac{b^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{8 c^{\frac{3}{2}}}+\frac{\left(2 c x +b \right) \sqrt{c \,x^{2}+b x}}{4 c}"," ",0,"-1/8*b^2/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))+1/4*(2*c*x+b)*(c*x^2+b*x)^(1/2)/c","A"
289,1,490,109,0.080000," ","int((c*x^2+b*x)^(1/2)/(e*x+d),x)","\frac{b d \ln \left(\frac{-\frac{2 \left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+2 \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}}{x +\frac{d}{e}}\right)}{\sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, e^{2}}-\frac{c \,d^{2} \ln \left(\frac{-\frac{2 \left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+2 \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}}{x +\frac{d}{e}}\right)}{\sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, e^{3}}+\frac{b \ln \left(\frac{\left(x +\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\right)}{2 \sqrt{c}\, e}-\frac{\sqrt{c}\, d \ln \left(\frac{\left(x +\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\right)}{e^{2}}+\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}}{e}"," ",0,"1/e*(c*(d/e+x)^2+(b*e-2*c*d)/e*(d/e+x)-d*(b*e-c*d)/e^2)^(1/2)+1/2/e*ln((1/2*(b*e-2*c*d)/e+c*(d/e+x))/c^(1/2)+(c*(d/e+x)^2+(b*e-2*c*d)/e*(d/e+x)-d*(b*e-c*d)/e^2)^(1/2))/c^(1/2)*b-1/e^2*ln((1/2*(b*e-2*c*d)/e+c*(d/e+x))/c^(1/2)+(c*(d/e+x)^2+(b*e-2*c*d)/e*(d/e+x)-d*(b*e-c*d)/e^2)^(1/2))*c^(1/2)*d+1/e^2*d/(-d*(b*e-c*d)/e^2)^(1/2)*ln((-2*d*(b*e-c*d)/e^2+(b*e-2*c*d)/e*(d/e+x)+2*(-d*(b*e-c*d)/e^2)^(1/2)*(c*(d/e+x)^2+(b*e-2*c*d)/e*(d/e+x)-d*(b*e-c*d)/e^2)^(1/2))/(d/e+x))*b-1/e^3*d^2/(-d*(b*e-c*d)/e^2)^(1/2)*ln((-2*d*(b*e-c*d)/e^2+(b*e-2*c*d)/e*(d/e+x)+2*(-d*(b*e-c*d)/e^2)^(1/2)*(c*(d/e+x)^2+(b*e-2*c*d)/e*(d/e+x)-d*(b*e-c*d)/e^2)^(1/2))/(d/e+x))*c","B"
290,1,885,118,0.058000," ","int((c*x^2+b*x)^(1/2)/(e*x+d)^2,x)","-\frac{b^{2} \ln \left(\frac{-\frac{2 \left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+2 \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}}{x +\frac{d}{e}}\right)}{2 \left(b e -c d \right) \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, e}+\frac{3 b c d \ln \left(\frac{-\frac{2 \left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+2 \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}}{x +\frac{d}{e}}\right)}{2 \left(b e -c d \right) \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, e^{2}}-\frac{c^{2} d^{2} \ln \left(\frac{-\frac{2 \left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+2 \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}}{x +\frac{d}{e}}\right)}{\left(b e -c d \right) \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, e^{3}}+\frac{b \sqrt{c}\, \ln \left(\frac{\left(x +\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\right)}{\left(b e -c d \right) e}-\frac{c^{\frac{3}{2}} d \ln \left(\frac{\left(x +\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\right)}{\left(b e -c d \right) e^{2}}-\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, c x}{\left(b e -c d \right) d}-\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, b}{\left(b e -c d \right) d}+\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, c}{\left(b e -c d \right) e}+\frac{\left(\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}\right)^{\frac{3}{2}}}{\left(b e -c d \right) \left(x +\frac{d}{e}\right) d}"," ",0,"1/(b*e-c*d)/d/(x+d/e)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(3/2)-1/(b*e-c*d)/d*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*b+1/e/(b*e-c*d)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*c+1/e/(b*e-c*d)*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))*c^(1/2)*b-1/e^2/(b*e-c*d)*d*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))*c^(3/2)-1/2/e/(b*e-c*d)/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))*b^2+3/2/e^2/(b*e-c*d)*d/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))*b*c-1/e^3/(b*e-c*d)*d^2/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))*c^2-c/(b*e-c*d)/d*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*x","B"
291,1,1963,109,0.070000," ","int((c*x^2+b*x)^(1/2)/(e*x+d)^3,x)","-\frac{b^{3} \ln \left(\frac{-\frac{2 \left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+2 \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}}{x +\frac{d}{e}}\right)}{8 \left(b e -c d \right)^{2} \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, d}+\frac{5 b^{2} c \ln \left(\frac{-\frac{2 \left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+2 \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}}{x +\frac{d}{e}}\right)}{8 \left(b e -c d \right)^{2} \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, e}-\frac{b \,c^{2} d \ln \left(\frac{-\frac{2 \left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+2 \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}}{x +\frac{d}{e}}\right)}{\left(b e -c d \right)^{2} \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, e^{2}}+\frac{c^{3} d^{2} \ln \left(\frac{-\frac{2 \left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+2 \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}}{x +\frac{d}{e}}\right)}{2 \left(b e -c d \right)^{2} \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, e^{3}}+\frac{b^{2} \sqrt{c}\, \ln \left(\frac{\left(x +\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\right)}{4 \left(b e -c d \right)^{2} d}-\frac{3 b \,c^{\frac{3}{2}} \ln \left(\frac{\left(x +\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\right)}{4 \left(b e -c d \right)^{2} e}+\frac{c^{\frac{5}{2}} d \ln \left(\frac{\left(x +\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\right)}{2 \left(b e -c d \right)^{2} e^{2}}-\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, b c e x}{4 \left(b e -c d \right)^{2} d^{2}}+\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, c^{2} x}{2 \left(b e -c d \right)^{2} d}-\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, b^{2} e}{4 \left(b e -c d \right)^{2} d^{2}}+\frac{3 \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, b c}{4 \left(b e -c d \right)^{2} d}-\frac{b c \ln \left(\frac{-\frac{2 \left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+2 \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}}{x +\frac{d}{e}}\right)}{2 \left(b e -c d \right) \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, e^{2}}+\frac{c^{2} d \ln \left(\frac{-\frac{2 \left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+2 \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}}{x +\frac{d}{e}}\right)}{2 \left(b e -c d \right) \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, e^{3}}-\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, c^{2}}{2 \left(b e -c d \right)^{2} e}-\frac{b \sqrt{c}\, \ln \left(\frac{\left(x +\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\right)}{4 \left(b e -c d \right) d e}+\frac{c^{\frac{3}{2}} \ln \left(\frac{\left(x +\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\right)}{2 \left(b e -c d \right) e^{2}}+\frac{\left(\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}\right)^{\frac{3}{2}} b e}{4 \left(b e -c d \right)^{2} \left(x +\frac{d}{e}\right) d^{2}}-\frac{\left(\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}\right)^{\frac{3}{2}} c}{2 \left(b e -c d \right)^{2} \left(x +\frac{d}{e}\right) d}-\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, c}{2 \left(b e -c d \right) d e}+\frac{\left(\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}\right)^{\frac{3}{2}}}{2 \left(b e -c d \right) \left(x +\frac{d}{e}\right)^{2} d e}"," ",0,"1/2/e/(b*e-c*d)/d/(x+d/e)^2*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(3/2)+1/4*e/(b*e-c*d)^2/d^2/(x+d/e)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(3/2)*b-1/2/(b*e-c*d)^2/d/(x+d/e)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(3/2)*c-1/4*e/(b*e-c*d)^2/d^2*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*b^2+3/4/(b*e-c*d)^2/d*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*b*c-1/2/e/(b*e-c*d)^2*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*c^2+1/4/(b*e-c*d)^2/d*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))*c^(1/2)*b^2-3/4/e/(b*e-c*d)^2*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))*c^(3/2)*b+1/2/e^2/(b*e-c*d)^2*d*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))*c^(5/2)-1/8/(b*e-c*d)^2/d/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))*b^3+5/8/e/(b*e-c*d)^2/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))*b^2*c-1/e^2/(b*e-c*d)^2*d/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))*b*c^2+1/2/e^3/(b*e-c*d)^2*d^2/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))*c^3-1/4*e/(b*e-c*d)^2/d^2*c*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*x*b+1/2/(b*e-c*d)^2/d*c^2*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*x-1/2/e*c/(b*e-c*d)/d*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)-1/4/e*c^(1/2)/(b*e-c*d)/d*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))*b+1/2/e^2*c^(3/2)/(b*e-c*d)*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))-1/2/e^2*c/(b*e-c*d)/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))*b+1/2/e^3*c^2/(b*e-c*d)*d/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))","B"
292,1,2891,161,0.055000," ","int((c*x^2+b*x)^(1/2)/(e*x+d)^4,x)","\text{output too large to display}"," ",0,"1/2/e/(b*e-c*d)^3*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*c^3-1/2/e^2/(b*e-c*d)^2*c^(5/2)*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))+1/8*e^2/(b*e-c*d)^3/d^3/(x+d/e)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(3/2)*b^2+5/8*e/(b*e-c*d)^3/d^2*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*b^2*c+1/8*e/(b*e-c*d)^3/d^2*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))*c^(1/2)*b^3-1/16*e/(b*e-c*d)^3/d^2/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))*b^4+3/4/e^2/(b*e-c*d)^2*c^2/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))*b-9/8/e/(b*e-c*d)^3/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))*b^2*c^2+7/16/(b*e-c*d)^3/d/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))*b^3*c-1/2/e/(b*e-c*d)^2/d/(x+d/e)^2*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(3/2)*c-1/2/e^3/(b*e-c*d)^3*d^2/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))*c^4+1/2/e/(b*e-c*d)^2/d*c^(3/2)*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))*b-1/2/e^3/(b*e-c*d)^2*d*c^3/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))+5/4/e^2/(b*e-c*d)^3*d/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))*b*c^3-1/8*e^2/(b*e-c*d)^3/d^3*c*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*x*b^2+1/2*e/(b*e-c*d)^3/d^2*c^2*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*x*b-1/4/e/(b*e-c*d)^2/d*c/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))*b^2-1/2*e/(b*e-c*d)^3/d^2/(x+d/e)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(3/2)*b*c-1/8/(b*e-c*d)^2/d^2*c^(1/2)*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))*b^2+1/3/e^2/(b*e-c*d)/d/(x+d/e)^3*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(3/2)-1/8*e^2/(b*e-c*d)^3/d^3*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*b^3+1/2/e/(b*e-c*d)^2/d*c^2*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)+1/4/(b*e-c*d)^2/d^2/(x+d/e)^2*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(3/2)*b-5/8/(b*e-c*d)^3/d*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))*c^(3/2)*b^2-1/4/(b*e-c*d)^2/d^2*c*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*b+1/2/(b*e-c*d)^3/d/(x+d/e)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(3/2)*c^2-1/(b*e-c*d)^3/d*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*b*c^2-1/2/(b*e-c*d)^3/d*c^3*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*x+1/e/(b*e-c*d)^3*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))*c^(5/2)*b-1/2/e^2/(b*e-c*d)^3*d*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))*c^(7/2)","B"
293,1,4819,232,0.053000," ","int((c*x^2+b*x)^(1/2)/(e*x+d)^5,x)","\text{output too large to display}"," ",0,"5/8/(b*e-c*d)^4/d*c^4*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*x+3/4/e^2/(b*e-c*d)^3*c^(7/2)*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))-5/8/e/(b*e-c*d)^4*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*c^4+17/32/(b*e-c*d)^3/d^2*c^(3/2)*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))*b^2+13/16/(b*e-c*d)^3/d^2*c^2*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*b-5/8/(b*e-c*d)^4/d/(x+d/e)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(3/2)*c^3+5/64*e^3/(b*e-c*d)^4/d^4/(x+d/e)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(3/2)*b^3+5/24/e/(b*e-c*d)^2/d^2/(x+d/e)^3*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(3/2)*b-5/12/e^2/(b*e-c*d)^2/d/(x+d/e)^3*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(3/2)*c+35/16/e/(b*e-c*d)^4/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))*b^2*c^3-3/2/e^2/(b*e-c*d)^3*c^3/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))*b+5/8/e^3/(b*e-c*d)^4*d^2/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))*c^5+3/4/e^3/(b*e-c*d)^3*d*c^4/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))-35/64*e/(b*e-c*d)^4/d^2*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))*c^(3/2)*b^3-7/32*e/(b*e-c*d)^3/d^3*c*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*b^2-5/64*e/(b*e-c*d)^3/d^3*c^(1/2)*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))*b^3+5/64*e^2/(b*e-c*d)^4/d^3*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))*c^(1/2)*b^4-5/128*e^2/(b*e-c*d)^4/d^3/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))*b^5-1/16/e*c^(3/2)/(b*e-c*d)^2/d^2*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))*b+1/8/e*c/(b*e-c*d)^2/d^2/(x+d/e)^2*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(3/2)+35/64*e^2/(b*e-c*d)^4/d^3*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*b^3*c-45/32*e/(b*e-c*d)^4/d^2*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*b^2*c^2+5/32*e/(b*e-c*d)^3/d^3/(x+d/e)^2*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(3/2)*b^2-9/8/e/(b*e-c*d)^3/d*c^(5/2)*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))*b+5/8/e/(b*e-c*d)^3/d/(x+d/e)^2*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(3/2)*c^2+25/16/(b*e-c*d)^4/d*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*b*c^3+1/8*c^3/(b*e-c*d)^3/d^2*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*x-1/8*c^2/(b*e-c*d)^3/d^2/(x+d/e)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(3/2)+45/32/(b*e-c*d)^4/d*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))*c^(5/2)*b^2-25/16/e/(b*e-c*d)^4*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))*c^(7/2)*b-5/64*e^3/(b*e-c*d)^4/d^4*c*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*x*b^3-1/16*e*c^2/(b*e-c*d)^3/d^3*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*x*b-1/8/e^2*c^2/(b*e-c*d)^2/d/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))*b+45/128*e/(b*e-c*d)^4/d^2/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))*b^4*c-15/16*e/(b*e-c*d)^4/d^2*c^3*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*x*b+1/16*e*c/(b*e-c*d)^3/d^3/(x+d/e)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(3/2)*b-15/8/e^2/(b*e-c*d)^4*d/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))*c^4*b+15/16*e/(b*e-c*d)^4/d^2/(x+d/e)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(3/2)*c^2*b-15/32*e^2/(b*e-c*d)^4/d^3/(x+d/e)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(3/2)*b^2*c+15/16/e/(b*e-c*d)^3/d*c^2/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))*b^2+15/32*e^2/(b*e-c*d)^4/d^3*c^2*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*x*b^2-1/8/e*c^2/(b*e-c*d)^2/d^2*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)+1/8/e^3*c^3/(b*e-c*d)^2/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))+1/8/e^2*c^(5/2)/(b*e-c*d)^2/d*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))-3/4/e/(b*e-c*d)^3/d*c^3*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)-5/64*e^3/(b*e-c*d)^4/d^4*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*b^4+5/8/e^2/(b*e-c*d)^4*d*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))*c^(9/2)+1/4/e^3/(b*e-c*d)/d/(x+d/e)^4*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(3/2)-5/4/(b*e-c*d)^4/d/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))*b^3*c^2-5/8/(b*e-c*d)^3/d^2/(x+d/e)^2*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(3/2)*b*c-3/16/(b*e-c*d)^3/d^2*c/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))*b^3","B"
294,1,6533,307,0.055000," ","int((c*x^2+b*x)^(1/2)/(e*x+d)^6,x)","\text{output too large to display}"," ",0,"result too large to display","B"
295,1,629,247,0.054000," ","int((e*x+d)^3*(c*x^2+b*x)^(3/2),x)","-\frac{9 b^{7} e^{3} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{2048 c^{\frac{11}{2}}}+\frac{21 b^{6} d \,e^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{1024 c^{\frac{9}{2}}}-\frac{9 b^{5} d^{2} e \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{256 c^{\frac{7}{2}}}+\frac{3 b^{4} d^{3} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{128 c^{\frac{5}{2}}}+\frac{9 \sqrt{c \,x^{2}+b x}\, b^{5} e^{3} x}{512 c^{4}}-\frac{21 \sqrt{c \,x^{2}+b x}\, b^{4} d \,e^{2} x}{256 c^{3}}+\frac{9 \sqrt{c \,x^{2}+b x}\, b^{3} d^{2} e x}{64 c^{2}}-\frac{3 \sqrt{c \,x^{2}+b x}\, b^{2} d^{3} x}{32 c}+\frac{9 \sqrt{c \,x^{2}+b x}\, b^{6} e^{3}}{1024 c^{5}}-\frac{21 \sqrt{c \,x^{2}+b x}\, b^{5} d \,e^{2}}{512 c^{4}}+\frac{9 \sqrt{c \,x^{2}+b x}\, b^{4} d^{2} e}{128 c^{3}}-\frac{3 \sqrt{c \,x^{2}+b x}\, b^{3} d^{3}}{64 c^{2}}-\frac{3 \left(c \,x^{2}+b x \right)^{\frac{3}{2}} b^{3} e^{3} x}{64 c^{3}}+\frac{7 \left(c \,x^{2}+b x \right)^{\frac{3}{2}} b^{2} d \,e^{2} x}{32 c^{2}}-\frac{3 \left(c \,x^{2}+b x \right)^{\frac{3}{2}} b \,d^{2} e x}{8 c}+\frac{\left(c \,x^{2}+b x \right)^{\frac{5}{2}} e^{3} x^{2}}{7 c}+\frac{\left(c \,x^{2}+b x \right)^{\frac{3}{2}} d^{3} x}{4}-\frac{3 \left(c \,x^{2}+b x \right)^{\frac{3}{2}} b^{4} e^{3}}{128 c^{4}}+\frac{7 \left(c \,x^{2}+b x \right)^{\frac{3}{2}} b^{3} d \,e^{2}}{64 c^{3}}-\frac{3 \left(c \,x^{2}+b x \right)^{\frac{3}{2}} b^{2} d^{2} e}{16 c^{2}}+\frac{\left(c \,x^{2}+b x \right)^{\frac{3}{2}} b \,d^{3}}{8 c}-\frac{3 \left(c \,x^{2}+b x \right)^{\frac{5}{2}} b \,e^{3} x}{28 c^{2}}+\frac{\left(c \,x^{2}+b x \right)^{\frac{5}{2}} d \,e^{2} x}{2 c}+\frac{3 \left(c \,x^{2}+b x \right)^{\frac{5}{2}} b^{2} e^{3}}{40 c^{3}}-\frac{7 \left(c \,x^{2}+b x \right)^{\frac{5}{2}} b d \,e^{2}}{20 c^{2}}+\frac{3 \left(c \,x^{2}+b x \right)^{\frac{5}{2}} d^{2} e}{5 c}"," ",0,"3/128*d^3*b^4/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))+3/5*d^2*e*(c*x^2+b*x)^(5/2)/c-3/128*e^3*b^4/c^4*(c*x^2+b*x)^(3/2)+9/1024*e^3*b^6/c^5*(c*x^2+b*x)^(1/2)-9/2048*e^3*b^7/c^(11/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))+1/7*e^3*x^2*(c*x^2+b*x)^(5/2)/c+3/40*e^3*b^2/c^3*(c*x^2+b*x)^(5/2)+1/8*d^3/c*(c*x^2+b*x)^(3/2)*b-3/64*d^3*b^3/c^2*(c*x^2+b*x)^(1/2)+7/32*d*e^2*b^2/c^2*x*(c*x^2+b*x)^(3/2)-21/256*d*e^2*b^4/c^3*(c*x^2+b*x)^(1/2)*x+9/64*d^2*e*b^3/c^2*(c*x^2+b*x)^(1/2)*x-3/8*d^2*e*b/c*x*(c*x^2+b*x)^(3/2)-3/16*d^2*e*b^2/c^2*(c*x^2+b*x)^(3/2)+1/4*d^3*x*(c*x^2+b*x)^(3/2)+9/512*e^3*b^5/c^4*(c*x^2+b*x)^(1/2)*x-3/32*d^3*b^2/c*(c*x^2+b*x)^(1/2)*x-3/64*e^3*b^3/c^3*x*(c*x^2+b*x)^(3/2)+9/128*d^2*e*b^4/c^3*(c*x^2+b*x)^(1/2)-9/256*d^2*e*b^5/c^(7/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))-21/512*d*e^2*b^5/c^4*(c*x^2+b*x)^(1/2)+1/2*d*e^2*x*(c*x^2+b*x)^(5/2)/c+21/1024*d*e^2*b^6/c^(9/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))-3/28*e^3*b/c^2*x*(c*x^2+b*x)^(5/2)-7/20*d*e^2*b/c^2*(c*x^2+b*x)^(5/2)+7/64*d*e^2*b^3/c^3*(c*x^2+b*x)^(3/2)","B"
296,1,420,190,0.051000," ","int((e*x+d)^2*(c*x^2+b*x)^(3/2),x)","\frac{7 b^{6} e^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{1024 c^{\frac{9}{2}}}-\frac{3 b^{5} d e \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{128 c^{\frac{7}{2}}}+\frac{3 b^{4} d^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{128 c^{\frac{5}{2}}}-\frac{7 \sqrt{c \,x^{2}+b x}\, b^{4} e^{2} x}{256 c^{3}}+\frac{3 \sqrt{c \,x^{2}+b x}\, b^{3} d e x}{32 c^{2}}-\frac{3 \sqrt{c \,x^{2}+b x}\, b^{2} d^{2} x}{32 c}-\frac{7 \sqrt{c \,x^{2}+b x}\, b^{5} e^{2}}{512 c^{4}}+\frac{3 \sqrt{c \,x^{2}+b x}\, b^{4} d e}{64 c^{3}}-\frac{3 \sqrt{c \,x^{2}+b x}\, b^{3} d^{2}}{64 c^{2}}+\frac{7 \left(c \,x^{2}+b x \right)^{\frac{3}{2}} b^{2} e^{2} x}{96 c^{2}}-\frac{\left(c \,x^{2}+b x \right)^{\frac{3}{2}} b d e x}{4 c}+\frac{\left(c \,x^{2}+b x \right)^{\frac{3}{2}} d^{2} x}{4}+\frac{7 \left(c \,x^{2}+b x \right)^{\frac{3}{2}} b^{3} e^{2}}{192 c^{3}}-\frac{\left(c \,x^{2}+b x \right)^{\frac{3}{2}} b^{2} d e}{8 c^{2}}+\frac{\left(c \,x^{2}+b x \right)^{\frac{3}{2}} b \,d^{2}}{8 c}+\frac{\left(c \,x^{2}+b x \right)^{\frac{5}{2}} e^{2} x}{6 c}-\frac{7 \left(c \,x^{2}+b x \right)^{\frac{5}{2}} b \,e^{2}}{60 c^{2}}+\frac{2 \left(c \,x^{2}+b x \right)^{\frac{5}{2}} d e}{5 c}"," ",0,"1/6*e^2*x*(c*x^2+b*x)^(5/2)/c-7/60*e^2*b/c^2*(c*x^2+b*x)^(5/2)+7/96*e^2*b^2/c^2*x*(c*x^2+b*x)^(3/2)+7/192*e^2*b^3/c^3*(c*x^2+b*x)^(3/2)-7/256*e^2*b^4/c^3*(c*x^2+b*x)^(1/2)*x-7/512*e^2*b^5/c^4*(c*x^2+b*x)^(1/2)+7/1024*e^2*b^6/c^(9/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))+2/5*d*e*(c*x^2+b*x)^(5/2)/c-1/4*d*e*b/c*x*(c*x^2+b*x)^(3/2)-1/8*d*e*b^2/c^2*(c*x^2+b*x)^(3/2)+3/32*d*e*b^3/c^2*(c*x^2+b*x)^(1/2)*x+3/64*d*e*b^4/c^3*(c*x^2+b*x)^(1/2)-3/128*d*e*b^5/c^(7/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))+1/4*d^2*x*(c*x^2+b*x)^(3/2)+1/8*d^2/c*(c*x^2+b*x)^(3/2)*b-3/32*d^2*b^2/c*(c*x^2+b*x)^(1/2)*x-3/64*d^2*b^3/c^2*(c*x^2+b*x)^(1/2)+3/128*d^2*b^4/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))","B"
297,1,239,117,0.048000," ","int((e*x+d)*(c*x^2+b*x)^(3/2),x)","-\frac{3 b^{5} e \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{256 c^{\frac{7}{2}}}+\frac{3 b^{4} d \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{128 c^{\frac{5}{2}}}+\frac{3 \sqrt{c \,x^{2}+b x}\, b^{3} e x}{64 c^{2}}-\frac{3 \sqrt{c \,x^{2}+b x}\, b^{2} d x}{32 c}+\frac{3 \sqrt{c \,x^{2}+b x}\, b^{4} e}{128 c^{3}}-\frac{3 \sqrt{c \,x^{2}+b x}\, b^{3} d}{64 c^{2}}-\frac{\left(c \,x^{2}+b x \right)^{\frac{3}{2}} b e x}{8 c}+\frac{\left(c \,x^{2}+b x \right)^{\frac{3}{2}} d x}{4}-\frac{\left(c \,x^{2}+b x \right)^{\frac{3}{2}} b^{2} e}{16 c^{2}}+\frac{\left(c \,x^{2}+b x \right)^{\frac{3}{2}} b d}{8 c}+\frac{\left(c \,x^{2}+b x \right)^{\frac{5}{2}} e}{5 c}"," ",0,"1/5*e*(c*x^2+b*x)^(5/2)/c-1/8*e*b/c*x*(c*x^2+b*x)^(3/2)-1/16*e*b^2/c^2*(c*x^2+b*x)^(3/2)+3/64*e*b^3/c^2*(c*x^2+b*x)^(1/2)*x+3/128*e*b^4/c^3*(c*x^2+b*x)^(1/2)-3/256*e*b^5/c^(7/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))+1/4*d*x*(c*x^2+b*x)^(3/2)+1/8*d/c*(c*x^2+b*x)^(3/2)*b-3/32*d*b^2/c*(c*x^2+b*x)^(1/2)*x-3/64*d*b^3/c^2*(c*x^2+b*x)^(1/2)+3/128*d*b^4/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))","B"
298,1,95,73,0.038000," ","int((c*x^2+b*x)^(3/2),x)","\frac{3 b^{4} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{128 c^{\frac{5}{2}}}-\frac{3 \sqrt{c \,x^{2}+b x}\, b^{2} x}{32 c}-\frac{3 \sqrt{c \,x^{2}+b x}\, b^{3}}{64 c^{2}}+\frac{\left(2 c x +b \right) \left(c \,x^{2}+b x \right)^{\frac{3}{2}}}{8 c}"," ",0,"1/8*(2*c*x+b)*(c*x^2+b*x)^(3/2)/c-3/32*b^2/c*(c*x^2+b*x)^(1/2)*x-3/64*b^3/c^2*(c*x^2+b*x)^(1/2)+3/128*b^4/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))","A"
299,1,1090,188,0.056000," ","int((c*x^2+b*x)^(3/2)/(e*x+d),x)","-\frac{b^{2} d^{2} \ln \left(\frac{-\frac{2 \left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+2 \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}}{x +\frac{d}{e}}\right)}{\sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, e^{3}}+\frac{2 b c \,d^{3} \ln \left(\frac{-\frac{2 \left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+2 \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}}{x +\frac{d}{e}}\right)}{\sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, e^{4}}-\frac{c^{2} d^{4} \ln \left(\frac{-\frac{2 \left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+2 \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}}{x +\frac{d}{e}}\right)}{\sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, e^{5}}-\frac{b^{3} \ln \left(\frac{\left(x +\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\right)}{16 c^{\frac{3}{2}} e}-\frac{3 b^{2} d \ln \left(\frac{\left(x +\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\right)}{8 \sqrt{c}\, e^{2}}+\frac{3 b \sqrt{c}\, d^{2} \ln \left(\frac{\left(x +\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\right)}{2 e^{3}}-\frac{c^{\frac{3}{2}} d^{3} \ln \left(\frac{\left(x +\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\right)}{e^{4}}+\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, b x}{4 e}-\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, c d x}{2 e^{2}}+\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, b^{2}}{8 c e}-\frac{5 \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, b d}{4 e^{2}}+\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, c \,d^{2}}{e^{3}}+\frac{\left(\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}\right)^{\frac{3}{2}}}{3 e}"," ",0,"1/3/e*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(3/2)+1/4/e*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*x*b-1/2/e^2*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*x*c*d+1/8/e/c*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*b^2-5/4/e^2*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*b*d-1/16/e/c^(3/2)*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))*b^3-3/8/e^2*d*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/c^(1/2)*b^2+1/e^3*d^2*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*c+3/2/e^3*d^2*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))*c^(1/2)*b-1/e^4*d^3*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))*c^(3/2)-1/e^3*d^2/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))*b^2+2/e^4*d^3/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))*b*c-1/e^5*d^4/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))*c^2","B"
300,1,1569,170,0.054000," ","int((c*x^2+b*x)^(3/2)/(e*x+d)^2,x)","\frac{3 b^{3} d \ln \left(\frac{-\frac{2 \left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+2 \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}}{x +\frac{d}{e}}\right)}{2 \left(b e -c d \right) \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, e^{2}}-\frac{6 b^{2} c \,d^{2} \ln \left(\frac{-\frac{2 \left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+2 \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}}{x +\frac{d}{e}}\right)}{\left(b e -c d \right) \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, e^{3}}+\frac{15 b \,c^{2} d^{3} \ln \left(\frac{-\frac{2 \left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+2 \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}}{x +\frac{d}{e}}\right)}{2 \left(b e -c d \right) \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, e^{4}}-\frac{3 c^{3} d^{4} \ln \left(\frac{-\frac{2 \left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+2 \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}}{x +\frac{d}{e}}\right)}{\left(b e -c d \right) \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, e^{5}}+\frac{3 b^{3} \ln \left(\frac{\left(x +\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\right)}{8 \left(b e -c d \right) \sqrt{c}\, e}-\frac{27 b^{2} \sqrt{c}\, d \ln \left(\frac{\left(x +\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\right)}{8 \left(b e -c d \right) e^{2}}+\frac{6 b \,c^{\frac{3}{2}} d^{2} \ln \left(\frac{\left(x +\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\right)}{\left(b e -c d \right) e^{3}}-\frac{3 c^{\frac{5}{2}} d^{3} \ln \left(\frac{\left(x +\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\right)}{\left(b e -c d \right) e^{4}}+\frac{3 \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, b c x}{2 \left(b e -c d \right) e}-\frac{3 \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, c^{2} d x}{2 \left(b e -c d \right) e^{2}}+\frac{9 \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, b^{2}}{4 \left(b e -c d \right) e}-\frac{21 \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, b c d}{4 \left(b e -c d \right) e^{2}}+\frac{3 \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, c^{2} d^{2}}{\left(b e -c d \right) e^{3}}-\frac{\left(\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}\right)^{\frac{3}{2}} c x}{\left(b e -c d \right) d}-\frac{\left(\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}\right)^{\frac{3}{2}} b}{\left(b e -c d \right) d}+\frac{\left(\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}\right)^{\frac{3}{2}} c}{\left(b e -c d \right) e}+\frac{\left(\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}\right)^{\frac{5}{2}}}{\left(b e -c d \right) \left(x +\frac{d}{e}\right) d}"," ",0,"1/(b*e-c*d)/d/(x+d/e)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(5/2)+6/e^3/(b*e-c*d)*d^2*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))*c^(3/2)*b-3/e^4/(b*e-c*d)*d^3*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))*c^(5/2)+3/2/e^2/(b*e-c*d)*d/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))*b^3-3/e^5/(b*e-c*d)*d^4/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))*c^3+3/e^3/(b*e-c*d)*d^2*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*c^2+9/4/e/(b*e-c*d)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*b^2-6/e^3/(b*e-c*d)*d^2/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))*b^2*c+15/2/e^4/(b*e-c*d)*d^3/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))*b*c^2-27/8/e^2/(b*e-c*d)*d*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))*c^(1/2)*b^2+1/e/(b*e-c*d)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(3/2)*c-1/(b*e-c*d)/d*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(3/2)*b+3/2/e/(b*e-c*d)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*x*b*c-3/2/e^2/(b*e-c*d)*d*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*x*c^2-21/4/e^2/(b*e-c*d)*d*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*b*c+3/8/e/(b*e-c*d)*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/c^(1/2)*b^3-c/(b*e-c*d)/d*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(3/2)*x","B"
301,1,3466,177,0.057000," ","int((c*x^2+b*x)^(3/2)/(e*x+d)^3,x)","\text{output too large to display}"," ",0,"1/2/e/(b*e-c*d)^2*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(3/2)*c^2-9/16/(b*e-c*d)^2/d*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*b^3-9/4/e^3*c^(3/2)/(b*e-c*d)*d*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))*b+9/8/e/(b*e-c*d)^2*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*x*b*c^2-3/4/e^2/(b*e-c*d)^2*d*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*x*c^3-27/8/e^2/(b*e-c*d)^2*d*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*c^2*b-51/16/e^2/(b*e-c*d)^2*d*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))*c^(3/2)*b^2-3/2/e^5/(b*e-c*d)^2*d^4/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))*c^4+3/32/e/c^(1/2)/(b*e-c*d)/d*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))*b^3+3/2/e^5*c^3/(b*e-c*d)*d^3/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))+15/4/e^3/(b*e-c*d)^2*d^2*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))*c^(5/2)*b-1/4*e/(b*e-c*d)^2/d^2/(x+d/e)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(5/2)*b-3/8/(b*e-c*d)^2/d*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*x*b^2*c+9/4/e^2/(b*e-c*d)^2*d/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))*b^3*c-3/e^4*c^2/(b*e-c*d)*d^2/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))*b+1/4*e/(b*e-c*d)^2/d^2*c*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(3/2)*x*b+39/16/e/(b*e-c*d)^2*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*b^2*c-3/8/e/(b*e-c*d)^2/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))*b^4+15/8/e^2*c/(b*e-c*d)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*b-39/8/e^3/(b*e-c*d)^2*d^2/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))*b^2*c^2-3/8/e*c/(b*e-c*d)/d*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*x*b+3/2/e^3*c/(b*e-c*d)*d/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))*b^2+9/2/e^4/(b*e-c*d)^2*d^3/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))*b*c^3+1/4*e/(b*e-c*d)^2/d^2*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(3/2)*b^2+1/2/e/(b*e-c*d)/d/(x+d/e)^2*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(5/2)+9/16/e^2*c^(1/2)/(b*e-c*d)*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))*b^2+3/2/e^3/(b*e-c*d)^2*d^2*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*c^3-1/2/e*c/(b*e-c*d)/d*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(3/2)-3/2/e^3*c^2/(b*e-c*d)*d*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)-3/16/e/(b*e-c*d)/d*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*b^2+33/32/e/(b*e-c*d)^2*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))*c^(1/2)*b^3-1/2/(b*e-c*d)^2/d*c^2*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(3/2)*x+3/4/e^2*c^2/(b*e-c*d)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*x+3/2/e^4*c^(5/2)/(b*e-c*d)*d^2*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))-3/2/e^4/(b*e-c*d)^2*d^3*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))*c^(7/2)-3/4/(b*e-c*d)^2/d*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(3/2)*b*c+1/2/(b*e-c*d)^2/d/(x+d/e)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(5/2)*c-3/32/(b*e-c*d)^2/d*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/c^(1/2)*b^4","B"
302,1,813,304,0.051000," ","int((e*x+d)^3*(c*x^2+b*x)^(5/2),x)","\frac{55 b^{9} e^{3} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{65536 c^{\frac{13}{2}}}-\frac{135 b^{8} d \,e^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{32768 c^{\frac{11}{2}}}+\frac{15 b^{7} d^{2} e \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{2048 c^{\frac{9}{2}}}-\frac{5 b^{6} d^{3} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{1024 c^{\frac{7}{2}}}-\frac{55 \sqrt{c \,x^{2}+b x}\, b^{7} e^{3} x}{16384 c^{5}}+\frac{135 \sqrt{c \,x^{2}+b x}\, b^{6} d \,e^{2} x}{8192 c^{4}}-\frac{15 \sqrt{c \,x^{2}+b x}\, b^{5} d^{2} e x}{512 c^{3}}+\frac{5 \sqrt{c \,x^{2}+b x}\, b^{4} d^{3} x}{256 c^{2}}-\frac{55 \sqrt{c \,x^{2}+b x}\, b^{8} e^{3}}{32768 c^{6}}+\frac{135 \sqrt{c \,x^{2}+b x}\, b^{7} d \,e^{2}}{16384 c^{5}}-\frac{15 \sqrt{c \,x^{2}+b x}\, b^{6} d^{2} e}{1024 c^{4}}+\frac{5 \sqrt{c \,x^{2}+b x}\, b^{5} d^{3}}{512 c^{3}}+\frac{55 \left(c \,x^{2}+b x \right)^{\frac{3}{2}} b^{5} e^{3} x}{6144 c^{4}}-\frac{45 \left(c \,x^{2}+b x \right)^{\frac{3}{2}} b^{4} d \,e^{2} x}{1024 c^{3}}+\frac{5 \left(c \,x^{2}+b x \right)^{\frac{3}{2}} b^{3} d^{2} e x}{64 c^{2}}-\frac{5 \left(c \,x^{2}+b x \right)^{\frac{3}{2}} b^{2} d^{3} x}{96 c}+\frac{55 \left(c \,x^{2}+b x \right)^{\frac{3}{2}} b^{6} e^{3}}{12288 c^{5}}-\frac{45 \left(c \,x^{2}+b x \right)^{\frac{3}{2}} b^{5} d \,e^{2}}{2048 c^{4}}+\frac{5 \left(c \,x^{2}+b x \right)^{\frac{3}{2}} b^{4} d^{2} e}{128 c^{3}}-\frac{5 \left(c \,x^{2}+b x \right)^{\frac{3}{2}} b^{3} d^{3}}{192 c^{2}}-\frac{11 \left(c \,x^{2}+b x \right)^{\frac{5}{2}} b^{3} e^{3} x}{384 c^{3}}+\frac{9 \left(c \,x^{2}+b x \right)^{\frac{5}{2}} b^{2} d \,e^{2} x}{64 c^{2}}-\frac{\left(c \,x^{2}+b x \right)^{\frac{5}{2}} b \,d^{2} e x}{4 c}+\frac{\left(c \,x^{2}+b x \right)^{\frac{7}{2}} e^{3} x^{2}}{9 c}+\frac{\left(c \,x^{2}+b x \right)^{\frac{5}{2}} d^{3} x}{6}-\frac{11 \left(c \,x^{2}+b x \right)^{\frac{5}{2}} b^{4} e^{3}}{768 c^{4}}+\frac{9 \left(c \,x^{2}+b x \right)^{\frac{5}{2}} b^{3} d \,e^{2}}{128 c^{3}}-\frac{\left(c \,x^{2}+b x \right)^{\frac{5}{2}} b^{2} d^{2} e}{8 c^{2}}+\frac{\left(c \,x^{2}+b x \right)^{\frac{5}{2}} b \,d^{3}}{12 c}-\frac{11 \left(c \,x^{2}+b x \right)^{\frac{7}{2}} b \,e^{3} x}{144 c^{2}}+\frac{3 \left(c \,x^{2}+b x \right)^{\frac{7}{2}} d \,e^{2} x}{8 c}+\frac{11 \left(c \,x^{2}+b x \right)^{\frac{7}{2}} b^{2} e^{3}}{224 c^{3}}-\frac{27 \left(c \,x^{2}+b x \right)^{\frac{7}{2}} b d \,e^{2}}{112 c^{2}}+\frac{3 \left(c \,x^{2}+b x \right)^{\frac{7}{2}} d^{2} e}{7 c}"," ",0,"-27/112*d*e^2*b/c^2*(c*x^2+b*x)^(7/2)+9/128*d*e^2*b^3/c^3*(c*x^2+b*x)^(5/2)-45/2048*d*e^2*b^5/c^4*(c*x^2+b*x)^(3/2)+135/16384*d*e^2*b^7/c^5*(c*x^2+b*x)^(1/2)-135/32768*d*e^2*b^8/c^(11/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))-1/8*d^2*e*b^2/c^2*(c*x^2+b*x)^(5/2)-5/96*d^3*b^2/c*(c*x^2+b*x)^(3/2)*x+5/256*d^3*b^4/c^2*(c*x^2+b*x)^(1/2)*x+5/64*d^2*e*b^3/c^2*(c*x^2+b*x)^(3/2)*x-15/512*d^2*e*b^5/c^3*(c*x^2+b*x)^(1/2)*x-1/4*d^2*e*b/c*x*(c*x^2+b*x)^(5/2)+9/64*d*e^2*b^2/c^2*x*(c*x^2+b*x)^(5/2)-45/1024*d*e^2*b^4/c^3*(c*x^2+b*x)^(3/2)*x+135/8192*d*e^2*b^6/c^4*(c*x^2+b*x)^(1/2)*x+1/6*d^3*x*(c*x^2+b*x)^(5/2)+1/9*e^3*x^2*(c*x^2+b*x)^(7/2)/c+11/224*e^3*b^2/c^3*(c*x^2+b*x)^(7/2)-11/768*e^3*b^4/c^4*(c*x^2+b*x)^(5/2)+55/12288*e^3*b^6/c^5*(c*x^2+b*x)^(3/2)-55/32768*e^3*b^8/c^6*(c*x^2+b*x)^(1/2)+55/65536*e^3*b^9/c^(13/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))+1/12*d^3/c*(c*x^2+b*x)^(5/2)*b-5/192*d^3*b^3/c^2*(c*x^2+b*x)^(3/2)+5/512*d^3*b^5/c^3*(c*x^2+b*x)^(1/2)-5/1024*d^3*b^6/c^(7/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))+3/7*d^2*e*(c*x^2+b*x)^(7/2)/c+5/128*d^2*e*b^4/c^3*(c*x^2+b*x)^(3/2)-15/1024*d^2*e*b^6/c^4*(c*x^2+b*x)^(1/2)+15/2048*d^2*e*b^7/c^(9/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))-11/144*e^3*b/c^2*x*(c*x^2+b*x)^(7/2)-11/384*e^3*b^3/c^3*x*(c*x^2+b*x)^(5/2)+55/6144*e^3*b^5/c^4*(c*x^2+b*x)^(3/2)*x-55/16384*e^3*b^7/c^5*(c*x^2+b*x)^(1/2)*x+3/8*d*e^2*x*(c*x^2+b*x)^(7/2)/c","B"
303,1,553,238,0.067000," ","int((e*x+d)^2*(c*x^2+b*x)^(5/2),x)","-\frac{45 b^{8} e^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{32768 c^{\frac{11}{2}}}+\frac{5 b^{7} d e \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{1024 c^{\frac{9}{2}}}-\frac{5 b^{6} d^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{1024 c^{\frac{7}{2}}}+\frac{45 \sqrt{c \,x^{2}+b x}\, b^{6} e^{2} x}{8192 c^{4}}-\frac{5 \sqrt{c \,x^{2}+b x}\, b^{5} d e x}{256 c^{3}}+\frac{5 \sqrt{c \,x^{2}+b x}\, b^{4} d^{2} x}{256 c^{2}}+\frac{45 \sqrt{c \,x^{2}+b x}\, b^{7} e^{2}}{16384 c^{5}}-\frac{5 \sqrt{c \,x^{2}+b x}\, b^{6} d e}{512 c^{4}}+\frac{5 \sqrt{c \,x^{2}+b x}\, b^{5} d^{2}}{512 c^{3}}-\frac{15 \left(c \,x^{2}+b x \right)^{\frac{3}{2}} b^{4} e^{2} x}{1024 c^{3}}+\frac{5 \left(c \,x^{2}+b x \right)^{\frac{3}{2}} b^{3} d e x}{96 c^{2}}-\frac{5 \left(c \,x^{2}+b x \right)^{\frac{3}{2}} b^{2} d^{2} x}{96 c}-\frac{15 \left(c \,x^{2}+b x \right)^{\frac{3}{2}} b^{5} e^{2}}{2048 c^{4}}+\frac{5 \left(c \,x^{2}+b x \right)^{\frac{3}{2}} b^{4} d e}{192 c^{3}}-\frac{5 \left(c \,x^{2}+b x \right)^{\frac{3}{2}} b^{3} d^{2}}{192 c^{2}}+\frac{3 \left(c \,x^{2}+b x \right)^{\frac{5}{2}} b^{2} e^{2} x}{64 c^{2}}-\frac{\left(c \,x^{2}+b x \right)^{\frac{5}{2}} b d e x}{6 c}+\frac{\left(c \,x^{2}+b x \right)^{\frac{5}{2}} d^{2} x}{6}+\frac{3 \left(c \,x^{2}+b x \right)^{\frac{5}{2}} b^{3} e^{2}}{128 c^{3}}-\frac{\left(c \,x^{2}+b x \right)^{\frac{5}{2}} b^{2} d e}{12 c^{2}}+\frac{\left(c \,x^{2}+b x \right)^{\frac{5}{2}} b \,d^{2}}{12 c}+\frac{\left(c \,x^{2}+b x \right)^{\frac{7}{2}} e^{2} x}{8 c}-\frac{9 \left(c \,x^{2}+b x \right)^{\frac{7}{2}} b \,e^{2}}{112 c^{2}}+\frac{2 \left(c \,x^{2}+b x \right)^{\frac{7}{2}} d e}{7 c}"," ",0,"1/8*e^2*x*(c*x^2+b*x)^(7/2)/c-9/112*e^2*b/c^2*(c*x^2+b*x)^(7/2)+3/64*e^2*b^2/c^2*x*(c*x^2+b*x)^(5/2)+3/128*e^2*b^3/c^3*(c*x^2+b*x)^(5/2)-15/1024*e^2*b^4/c^3*(c*x^2+b*x)^(3/2)*x-15/2048*e^2*b^5/c^4*(c*x^2+b*x)^(3/2)+45/8192*e^2*b^6/c^4*(c*x^2+b*x)^(1/2)*x+45/16384*e^2*b^7/c^5*(c*x^2+b*x)^(1/2)-45/32768*e^2*b^8/c^(11/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))+2/7*d*e*(c*x^2+b*x)^(7/2)/c-1/6*d*e*b/c*x*(c*x^2+b*x)^(5/2)-1/12*d*e*b^2/c^2*(c*x^2+b*x)^(5/2)+5/96*d*e*b^3/c^2*(c*x^2+b*x)^(3/2)*x+5/192*d*e*b^4/c^3*(c*x^2+b*x)^(3/2)-5/256*d*e*b^5/c^3*(c*x^2+b*x)^(1/2)*x-5/512*d*e*b^6/c^4*(c*x^2+b*x)^(1/2)+5/1024*d*e*b^7/c^(9/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))+1/6*d^2*x*(c*x^2+b*x)^(5/2)+1/12*d^2/c*(c*x^2+b*x)^(5/2)*b-5/96*d^2*b^2/c*(c*x^2+b*x)^(3/2)*x-5/192*d^2*b^3/c^2*(c*x^2+b*x)^(3/2)+5/256*d^2*b^4/c^2*(c*x^2+b*x)^(1/2)*x+5/512*d^2*b^5/c^3*(c*x^2+b*x)^(1/2)-5/1024*d^2*b^6/c^(7/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))","B"
304,1,321,151,0.045000," ","int((e*x+d)*(c*x^2+b*x)^(5/2),x)","\frac{5 b^{7} e \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{2048 c^{\frac{9}{2}}}-\frac{5 b^{6} d \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{1024 c^{\frac{7}{2}}}-\frac{5 \sqrt{c \,x^{2}+b x}\, b^{5} e x}{512 c^{3}}+\frac{5 \sqrt{c \,x^{2}+b x}\, b^{4} d x}{256 c^{2}}-\frac{5 \sqrt{c \,x^{2}+b x}\, b^{6} e}{1024 c^{4}}+\frac{5 \sqrt{c \,x^{2}+b x}\, b^{5} d}{512 c^{3}}+\frac{5 \left(c \,x^{2}+b x \right)^{\frac{3}{2}} b^{3} e x}{192 c^{2}}-\frac{5 \left(c \,x^{2}+b x \right)^{\frac{3}{2}} b^{2} d x}{96 c}+\frac{5 \left(c \,x^{2}+b x \right)^{\frac{3}{2}} b^{4} e}{384 c^{3}}-\frac{5 \left(c \,x^{2}+b x \right)^{\frac{3}{2}} b^{3} d}{192 c^{2}}-\frac{\left(c \,x^{2}+b x \right)^{\frac{5}{2}} b e x}{12 c}+\frac{\left(c \,x^{2}+b x \right)^{\frac{5}{2}} d x}{6}-\frac{\left(c \,x^{2}+b x \right)^{\frac{5}{2}} b^{2} e}{24 c^{2}}+\frac{\left(c \,x^{2}+b x \right)^{\frac{5}{2}} b d}{12 c}+\frac{\left(c \,x^{2}+b x \right)^{\frac{7}{2}} e}{7 c}"," ",0,"1/7*e*(c*x^2+b*x)^(7/2)/c-1/12*e*b/c*x*(c*x^2+b*x)^(5/2)-1/24*e*b^2/c^2*(c*x^2+b*x)^(5/2)+5/192*e*b^3/c^2*(c*x^2+b*x)^(3/2)*x+5/384*e*b^4/c^3*(c*x^2+b*x)^(3/2)-5/512*e*b^5/c^3*(c*x^2+b*x)^(1/2)*x-5/1024*e*b^6/c^4*(c*x^2+b*x)^(1/2)+5/2048*e*b^7/c^(9/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))+1/6*d*x*(c*x^2+b*x)^(5/2)+1/12*d/c*(c*x^2+b*x)^(5/2)*b-5/96*d*b^2/c*(c*x^2+b*x)^(3/2)*x-5/192*d*b^3/c^2*(c*x^2+b*x)^(3/2)+5/256*d*b^4/c^2*(c*x^2+b*x)^(1/2)*x+5/512*d*b^5/c^3*(c*x^2+b*x)^(1/2)-5/1024*d*b^6/c^(7/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))","B"
305,1,134,98,0.042000," ","int((c*x^2+b*x)^(5/2),x)","-\frac{5 b^{6} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{1024 c^{\frac{7}{2}}}+\frac{5 \sqrt{c \,x^{2}+b x}\, b^{4} x}{256 c^{2}}+\frac{5 \sqrt{c \,x^{2}+b x}\, b^{5}}{512 c^{3}}-\frac{5 \left(c \,x^{2}+b x \right)^{\frac{3}{2}} b^{2} x}{96 c}-\frac{5 \left(c \,x^{2}+b x \right)^{\frac{3}{2}} b^{3}}{192 c^{2}}+\frac{\left(2 c x +b \right) \left(c \,x^{2}+b x \right)^{\frac{5}{2}}}{12 c}"," ",0,"1/12*(2*c*x+b)*(c*x^2+b*x)^(5/2)/c-5/96*b^2/c*(c*x^2+b*x)^(3/2)*x-5/192*b^3/c^2*(c*x^2+b*x)^(3/2)+5/256*b^4/c^2*(c*x^2+b*x)^(1/2)*x+5/512*b^5/c^3*(c*x^2+b*x)^(1/2)-5/1024*b^6/c^(7/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))","A"
306,1,1932,324,0.051000," ","int((c*x^2+b*x)^(5/2)/(e*x+d),x)","\frac{b^{3} d^{3} \ln \left(\frac{-\frac{2 \left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+2 \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}}{x +\frac{d}{e}}\right)}{\sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, e^{4}}-\frac{3 b^{2} c \,d^{4} \ln \left(\frac{-\frac{2 \left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+2 \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}}{x +\frac{d}{e}}\right)}{\sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, e^{5}}+\frac{3 b \,c^{2} d^{5} \ln \left(\frac{-\frac{2 \left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+2 \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}}{x +\frac{d}{e}}\right)}{\sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, e^{6}}-\frac{c^{3} d^{6} \ln \left(\frac{-\frac{2 \left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+2 \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}}{x +\frac{d}{e}}\right)}{\sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, e^{7}}+\frac{3 b^{5} \ln \left(\frac{\left(x +\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\right)}{256 c^{\frac{5}{2}} e}+\frac{5 b^{4} d \ln \left(\frac{\left(x +\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\right)}{128 c^{\frac{3}{2}} e^{2}}+\frac{5 b^{3} d^{2} \ln \left(\frac{\left(x +\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\right)}{16 \sqrt{c}\, e^{3}}-\frac{15 b^{2} \sqrt{c}\, d^{3} \ln \left(\frac{\left(x +\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\right)}{8 e^{4}}+\frac{5 b \,c^{\frac{3}{2}} d^{4} \ln \left(\frac{\left(x +\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\right)}{2 e^{5}}-\frac{c^{\frac{5}{2}} d^{5} \ln \left(\frac{\left(x +\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\right)}{e^{6}}-\frac{3 \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, b^{3} x}{64 c e}-\frac{5 \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, b^{2} d x}{32 e^{2}}+\frac{3 \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, b c \,d^{2} x}{4 e^{3}}-\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, c^{2} d^{3} x}{2 e^{4}}-\frac{3 \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, b^{4}}{128 c^{2} e}-\frac{5 \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, b^{3} d}{64 c \,e^{2}}+\frac{11 \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, b^{2} d^{2}}{8 e^{3}}-\frac{9 \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, b c \,d^{3}}{4 e^{4}}+\frac{\left(\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}\right)^{\frac{3}{2}} b x}{8 e}+\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, c^{2} d^{4}}{e^{5}}-\frac{\left(\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}\right)^{\frac{3}{2}} c d x}{4 e^{2}}+\frac{\left(\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}\right)^{\frac{3}{2}} b^{2}}{16 c e}-\frac{11 \left(\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}\right)^{\frac{3}{2}} b d}{24 e^{2}}+\frac{\left(\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}\right)^{\frac{3}{2}} c \,d^{2}}{3 e^{3}}+\frac{\left(\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}\right)^{\frac{5}{2}}}{5 e}"," ",0,"3/256/e/c^(5/2)*b^5*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))+1/8/e*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(3/2)*x*b+1/16/e/c*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(3/2)*b^2-11/24/e^2*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(3/2)*b*d-3/128/e/c^2*b^4*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)+1/e^5*d^4*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*c^2-1/e^6*d^5*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))*c^(5/2)+1/3/e^3*d^2*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(3/2)*c+11/8/e^3*d^2*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*b^2+3/4/e^3*d^2*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*x*b*c-3/e^5*d^4/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))*b^2*c+3/e^6*d^5/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))*b*c^2+1/5/e*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(5/2)+5/128/e^2*d/c^(3/2)*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))*b^4-1/2/e^4*d^3*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*x*c^2-5/32/e^2*b^2*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*x*d-5/64/e^2/c*b^3*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*d-1/e^7*d^6/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))*c^3+5/2/e^5*d^4*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))*c^(3/2)*b-1/4/e^2*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(3/2)*x*c*d-9/4/e^4*d^3*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*b*c+5/16/e^3*d^2*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/c^(1/2)*b^3-15/8/e^4*d^3*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))*c^(1/2)*b^2+1/e^4*d^3/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))*b^3-3/64/e/c*b^3*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*x","B"
307,1,2534,282,0.059000," ","int((c*x^2+b*x)^(5/2)/(e*x+d)^2,x)","-\frac{5 b^{4} d^{2} \ln \left(\frac{-\frac{2 \left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+2 \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}}{x +\frac{d}{e}}\right)}{2 \left(b e -c d \right) \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, e^{3}}+\frac{25 b^{3} c \,d^{3} \ln \left(\frac{-\frac{2 \left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+2 \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}}{x +\frac{d}{e}}\right)}{2 \left(b e -c d \right) \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, e^{4}}-\frac{45 b^{2} c^{2} d^{4} \ln \left(\frac{-\frac{2 \left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+2 \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}}{x +\frac{d}{e}}\right)}{2 \left(b e -c d \right) \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, e^{5}}+\frac{35 b \,c^{3} d^{5} \ln \left(\frac{-\frac{2 \left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+2 \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}}{x +\frac{d}{e}}\right)}{2 \left(b e -c d \right) \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, e^{6}}-\frac{5 c^{4} d^{6} \ln \left(\frac{-\frac{2 \left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+2 \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}}{x +\frac{d}{e}}\right)}{\left(b e -c d \right) \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, e^{7}}-\frac{5 b^{5} \ln \left(\frac{\left(x +\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\right)}{128 \left(b e -c d \right) c^{\frac{3}{2}} e}-\frac{75 b^{4} d \ln \left(\frac{\left(x +\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\right)}{128 \left(b e -c d \right) \sqrt{c}\, e^{2}}+\frac{25 b^{3} \sqrt{c}\, d^{2} \ln \left(\frac{\left(x +\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\right)}{4 \left(b e -c d \right) e^{3}}-\frac{125 b^{2} c^{\frac{3}{2}} d^{3} \ln \left(\frac{\left(x +\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\right)}{8 \left(b e -c d \right) e^{4}}+\frac{15 b \,c^{\frac{5}{2}} d^{4} \ln \left(\frac{\left(x +\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\right)}{\left(b e -c d \right) e^{5}}-\frac{5 c^{\frac{7}{2}} d^{5} \ln \left(\frac{\left(x +\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\right)}{\left(b e -c d \right) e^{6}}+\frac{5 \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, b^{3} x}{32 \left(b e -c d \right) e}-\frac{85 \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, b^{2} c d x}{32 \left(b e -c d \right) e^{2}}+\frac{5 \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, b \,c^{2} d^{2} x}{\left(b e -c d \right) e^{3}}-\frac{5 \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, c^{3} d^{3} x}{2 \left(b e -c d \right) e^{4}}+\frac{5 \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, b^{4}}{64 \left(b e -c d \right) c e}-\frac{245 \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, b^{3} d}{64 \left(b e -c d \right) e^{2}}+\frac{25 \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, b^{2} c \,d^{2}}{2 \left(b e -c d \right) e^{3}}-\frac{55 \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, b \,c^{2} d^{3}}{4 \left(b e -c d \right) e^{4}}+\frac{5 \left(\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}\right)^{\frac{3}{2}} b c x}{4 \left(b e -c d \right) e}+\frac{5 \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, c^{3} d^{4}}{\left(b e -c d \right) e^{5}}-\frac{5 \left(\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}\right)^{\frac{3}{2}} c^{2} d x}{4 \left(b e -c d \right) e^{2}}+\frac{35 \left(\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}\right)^{\frac{3}{2}} b^{2}}{24 \left(b e -c d \right) e}-\frac{25 \left(\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}\right)^{\frac{3}{2}} b c d}{8 \left(b e -c d \right) e^{2}}+\frac{5 \left(\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}\right)^{\frac{3}{2}} c^{2} d^{2}}{3 \left(b e -c d \right) e^{3}}-\frac{\left(\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}\right)^{\frac{5}{2}} c x}{\left(b e -c d \right) d}-\frac{\left(\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}\right)^{\frac{5}{2}} b}{\left(b e -c d \right) d}+\frac{\left(\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}\right)^{\frac{5}{2}} c}{\left(b e -c d \right) e}+\frac{\left(\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}\right)^{\frac{7}{2}}}{\left(b e -c d \right) \left(x +\frac{d}{e}\right) d}"," ",0,"5/4/e/(b*e-c*d)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(3/2)*x*b*c-55/4/e^4/(b*e-c*d)*d^3*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*b*c^2+25/4/e^3/(b*e-c*d)*d^2*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))*c^(1/2)*b^3-125/8/e^4/(b*e-c*d)*d^3*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))*c^(3/2)*b^2-5/e^7/(b*e-c*d)*d^6/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))*c^4-5/4/e^2/(b*e-c*d)*d*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(3/2)*x*c^2-75/128/e^2/(b*e-c*d)*d*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/c^(1/2)*b^4-25/8/e^2/(b*e-c*d)*d*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(3/2)*b*c-5/2/e^4/(b*e-c*d)*d^3*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*x*c^3+15/e^5/(b*e-c*d)*d^4*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))*c^(5/2)*b+25/2/e^3/(b*e-c*d)*d^2*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*b^2*c-5/2/e^3/(b*e-c*d)*d^2/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))*b^4+1/e/(b*e-c*d)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(5/2)*c+35/24/e/(b*e-c*d)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(3/2)*b^2+1/(b*e-c*d)/d/(x+d/e)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(7/2)-1/(b*e-c*d)/d*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(5/2)*b-5/e^6/(b*e-c*d)*d^5*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))*c^(7/2)-245/64/e^2/(b*e-c*d)*d*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*b^3+5/e^5/(b*e-c*d)*d^4*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*c^3+5/32/e/(b*e-c*d)*b^3*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*x+5/64/e/(b*e-c*d)/c*b^4*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)-5/128/e/(b*e-c*d)/c^(3/2)*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))*b^5+5/3/e^3/(b*e-c*d)*d^2*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(3/2)*c^2-c/(b*e-c*d)/d*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(5/2)*x-45/2/e^5/(b*e-c*d)*d^4/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))*b^2*c^2+35/2/e^6/(b*e-c*d)*d^5/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))*b*c^3-85/32/e^2/(b*e-c*d)*d*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*x*b^2*c+5/e^3/(b*e-c*d)*d^2*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*x*b*c^2+25/2/e^4/(b*e-c*d)*d^3/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))*b^3*c","B"
308,1,5534,248,0.075000," ","int((c*x^2+b*x)^(5/2)/(e*x+d)^3,x)","\text{output too large to display}"," ",0,"result too large to display","B"
309,1,21,22,0.171000," ","int((x^2+2*x)^(1/2)/(x+1),x)","\arctan \left(\frac{1}{\sqrt{\left(x +1\right)^{2}-1}}\right)+\sqrt{\left(x +1\right)^{2}-1}"," ",0,"((x+1)^2-1)^(1/2)+arctan(1/((x+1)^2-1)^(1/2))","A"
310,1,42,41,0.041000," ","int((-x^2+2*x)^(3/2)/(-2*x+2),x)","\frac{\arctanh \left(\frac{1}{\sqrt{-\left(x -1\right)^{2}+1}}\right)}{2}-\frac{\left(-\left(x -1\right)^{2}+1\right)^{\frac{3}{2}}}{6}-\frac{\sqrt{-\left(x -1\right)^{2}+1}}{2}"," ",0,"-1/6*(-(x-1)^2+1)^(3/2)-1/2*(-(x-1)^2+1)^(1/2)+1/2*arctanh(1/(-(x-1)^2+1)^(1/2))","A"
311,1,29,28,0.048000," ","int((-x^2+2*x)^(1/2)/(-2*x+2),x)","\frac{\arctanh \left(\frac{1}{\sqrt{-\left(x -1\right)^{2}+1}}\right)}{2}-\frac{\sqrt{-\left(x -1\right)^{2}+1}}{2}"," ",0,"-1/2*(-(x-1)^2+1)^(1/2)+1/2*arctanh(1/(-(x-1)^2+1)^(1/2))","A"
312,1,15,14,0.047000," ","int(1/(-2*x+2)/(-x^2+2*x)^(1/2),x)","\frac{\arctanh \left(\frac{1}{\sqrt{-\left(x -1\right)^{2}+1}}\right)}{2}"," ",0,"1/2*arctanh(1/(-(x-1)^2+1)^(1/2))","A"
313,1,29,28,0.045000," ","int(1/(-2*x+2)/(-x^2+2*x)^(3/2),x)","\frac{\arctanh \left(\frac{1}{\sqrt{-\left(x -1\right)^{2}+1}}\right)}{2}-\frac{1}{2 \sqrt{-\left(x -1\right)^{2}+1}}"," ",0,"-1/2/(-(x-1)^2+1)^(1/2)+1/2*arctanh(1/(-(x-1)^2+1)^(1/2))","A"
314,1,42,41,0.048000," ","int(1/(-2*x+2)/(-x^2+2*x)^(5/2),x)","\frac{\arctanh \left(\frac{1}{\sqrt{-\left(x -1\right)^{2}+1}}\right)}{2}-\frac{1}{6 \left(-\left(x -1\right)^{2}+1\right)^{\frac{3}{2}}}-\frac{1}{2 \sqrt{-\left(x -1\right)^{2}+1}}"," ",0,"-1/6/(-(x-1)^2+1)^(3/2)-1/2/(-(x-1)^2+1)^(1/2)+1/2*arctanh(1/(-(x-1)^2+1)^(1/2))","A"
315,1,265,133,0.052000," ","int((e*x+d)^3/(c*x^2+b*x)^(1/2),x)","\frac{\sqrt{c \,x^{2}+b x}\, e^{3} x^{2}}{3 c}-\frac{5 b^{3} e^{3} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{16 c^{\frac{7}{2}}}+\frac{9 b^{2} d \,e^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{8 c^{\frac{5}{2}}}-\frac{3 b \,d^{2} e \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{2 c^{\frac{3}{2}}}+\frac{d^{3} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{\sqrt{c}}-\frac{5 \sqrt{c \,x^{2}+b x}\, b \,e^{3} x}{12 c^{2}}+\frac{3 \sqrt{c \,x^{2}+b x}\, d \,e^{2} x}{2 c}+\frac{5 \sqrt{c \,x^{2}+b x}\, b^{2} e^{3}}{8 c^{3}}-\frac{9 \sqrt{c \,x^{2}+b x}\, b d \,e^{2}}{4 c^{2}}+\frac{3 \sqrt{c \,x^{2}+b x}\, d^{2} e}{c}"," ",0,"1/3*e^3*x^2/c*(c*x^2+b*x)^(1/2)-5/12*e^3*b/c^2*x*(c*x^2+b*x)^(1/2)+5/8*e^3*b^2/c^3*(c*x^2+b*x)^(1/2)-5/16*e^3*b^3/c^(7/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))+3/2*d*e^2*x/c*(c*x^2+b*x)^(1/2)-9/4*d*e^2*b/c^2*(c*x^2+b*x)^(1/2)+9/8*d*e^2*b^2/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))+3*d^2*e/c*(c*x^2+b*x)^(1/2)-3/2*d^2*e*b/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))+d^3*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))/c^(1/2)","A"
316,1,158,94,0.052000," ","int((e*x+d)^2/(c*x^2+b*x)^(1/2),x)","\frac{3 b^{2} e^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{8 c^{\frac{5}{2}}}-\frac{b d e \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{c^{\frac{3}{2}}}+\frac{d^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{\sqrt{c}}+\frac{\sqrt{c \,x^{2}+b x}\, e^{2} x}{2 c}-\frac{3 \sqrt{c \,x^{2}+b x}\, b \,e^{2}}{4 c^{2}}+\frac{2 \sqrt{c \,x^{2}+b x}\, d e}{c}"," ",0,"1/2*e^2*x/c*(c*x^2+b*x)^(1/2)-3/4*e^2*b/c^2*(c*x^2+b*x)^(1/2)+3/8*e^2*b^2/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))+2*d*e/c*(c*x^2+b*x)^(1/2)-d*e*b/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))+d^2*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))/c^(1/2)","A"
317,1,78,47,0.120000," ","int((e*x+d)/(c*x^2+b*x)^(1/2),x)","-\frac{b e \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{2 c^{\frac{3}{2}}}+\frac{d \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{\sqrt{c}}+\frac{\sqrt{c \,x^{2}+b x}\, e}{c}"," ",0,"e*(c*x^2+b*x)^(1/2)/c-1/2*e*b/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))+d*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))/c^(1/2)","A"
318,1,29,22,0.043000," ","int(1/(c*x^2+b*x)^(1/2),x)","\frac{\ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{\sqrt{c}}"," ",0,"ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))/c^(1/2)","A"
319,1,132,56,0.049000," ","int(1/(e*x+d)/(c*x^2+b*x)^(1/2),x)","-\frac{\ln \left(\frac{-\frac{2 \left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+2 \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}}{x +\frac{d}{e}}\right)}{\sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, e}"," ",0,"-1/e/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))","B"
320,1,355,101,0.051000," ","int(1/(e*x+d)^2/(c*x^2+b*x)^(1/2),x)","-\frac{b \ln \left(\frac{-\frac{2 \left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+2 \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}}{x +\frac{d}{e}}\right)}{2 \left(b e -c d \right) \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, d}+\frac{c \ln \left(\frac{-\frac{2 \left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+2 \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}}{x +\frac{d}{e}}\right)}{\left(b e -c d \right) \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, e}+\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}}{\left(b e -c d \right) \left(x +\frac{d}{e}\right) d}"," ",0,"1/(b*e-c*d)/d/(x+d/e)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)-1/2/(b*e-c*d)/d/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))*b+1/e/(b*e-c*d)/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))*c","B"
321,1,798,158,0.058000," ","int(1/(e*x+d)^3/(c*x^2+b*x)^(1/2),x)","-\frac{3 b^{2} e \ln \left(\frac{-\frac{2 \left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+2 \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}}{x +\frac{d}{e}}\right)}{8 \left(b e -c d \right)^{2} \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, d^{2}}+\frac{3 b c \ln \left(\frac{-\frac{2 \left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+2 \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}}{x +\frac{d}{e}}\right)}{2 \left(b e -c d \right)^{2} \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, d}-\frac{3 c^{2} \ln \left(\frac{-\frac{2 \left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+2 \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}}{x +\frac{d}{e}}\right)}{2 \left(b e -c d \right)^{2} \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, e}+\frac{3 \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, b e}{4 \left(b e -c d \right)^{2} \left(x +\frac{d}{e}\right) d^{2}}-\frac{c \ln \left(\frac{-\frac{2 \left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+2 \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}}{x +\frac{d}{e}}\right)}{2 \left(b e -c d \right) \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, d e}-\frac{3 \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, c}{2 \left(b e -c d \right)^{2} \left(x +\frac{d}{e}\right) d}+\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}}{2 \left(b e -c d \right) \left(x +\frac{d}{e}\right)^{2} d e}"," ",0,"1/2/e/(b*e-c*d)/d/(x+d/e)^2*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)+3/4*e/(b*e-c*d)^2/d^2/(x+d/e)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*b-3/2/(b*e-c*d)^2/d/(x+d/e)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*c-3/8*e/(b*e-c*d)^2/d^2/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))*b^2+3/2/(b*e-c*d)^2/d/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))*b*c-3/2/e/(b*e-c*d)^2/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))*c^2-1/2/e*c/(b*e-c*d)/d/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))","B"
322,1,177,129,0.050000," ","int((e*x+d)^3/(c*x^2+b*x)^(3/2),x)","\frac{e^{3} x^{2}}{\sqrt{c \,x^{2}+b x}\, c}+\frac{3 b \,e^{3} x}{\sqrt{c \,x^{2}+b x}\, c^{2}}+\frac{6 d^{2} e x}{\sqrt{c \,x^{2}+b x}\, b}-\frac{6 d \,e^{2} x}{\sqrt{c \,x^{2}+b x}\, c}-\frac{3 b \,e^{3} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{2 c^{\frac{5}{2}}}+\frac{3 d \,e^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{c^{\frac{3}{2}}}-\frac{2 \left(2 c x +b \right) d^{3}}{\sqrt{c \,x^{2}+b x}\, b^{2}}"," ",0,"e^3*x^2/c/(c*x^2+b*x)^(1/2)+3*e^3*b/c^2/(c*x^2+b*x)^(1/2)*x-3/2*e^3*b/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))-6*d*e^2/c/(c*x^2+b*x)^(1/2)*x+3*d*e^2/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))+6*d^2*e/b/(c*x^2+b*x)^(1/2)*x-2*d^3*(2*c*x+b)/b^2/(c*x^2+b*x)^(1/2)","A"
323,1,97,91,0.052000," ","int((e*x+d)^2/(c*x^2+b*x)^(3/2),x)","\frac{4 d e x}{\sqrt{c \,x^{2}+b x}\, b}-\frac{2 e^{2} x}{\sqrt{c \,x^{2}+b x}\, c}+\frac{e^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{c^{\frac{3}{2}}}-\frac{2 \left(2 c x +b \right) d^{2}}{\sqrt{c \,x^{2}+b x}\, b^{2}}"," ",0,"-2*e^2/c/(c*x^2+b*x)^(1/2)*x+e^2/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))+4*d*e/b/(c*x^2+b*x)^(1/2)*x-2*d^2*(2*c*x+b)/b^2/(c*x^2+b*x)^(1/2)","A"
324,1,37,31,0.047000," ","int((e*x+d)/(c*x^2+b*x)^(3/2),x)","-\frac{2 \left(c x +b \right) \left(-b e x +2 c d x +b d \right) x}{\left(c \,x^{2}+b x \right)^{\frac{3}{2}} b^{2}}"," ",0,"-2*(c*x+b)*x*(-b*e*x+2*c*d*x+b*d)/b^2/(c*x^2+b*x)^(3/2)","A"
325,1,29,22,0.043000," ","int(1/(c*x^2+b*x)^(3/2),x)","-\frac{2 \left(c x +b \right) \left(2 c x +b \right) x}{\left(c \,x^{2}+b x \right)^{\frac{3}{2}} b^{2}}"," ",0,"-2*(c*x+b)*x*(2*c*x+b)/b^2/(c*x^2+b*x)^(3/2)","A"
326,1,403,112,0.063000," ","int(1/(e*x+d)/(c*x^2+b*x)^(3/2),x)","-\frac{2 c e x}{\left(b e -c d \right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, b d}+\frac{4 c^{2} x}{\left(b e -c d \right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, b^{2}}+\frac{e \ln \left(\frac{-\frac{2 \left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+2 \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}}{x +\frac{d}{e}}\right)}{\left(b e -c d \right) \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, d}+\frac{2 c}{\left(b e -c d \right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, b}-\frac{2 e}{\left(b e -c d \right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, d}"," ",0,"-2*e/(b*e-c*d)/d/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)-2*e/(b*e-c*d)/d/b/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*x*c+4/(b*e-c*d)/b^2/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*x*c^2+2/(b*e-c*d)/b/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*c+e/(b*e-c*d)/d/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))","B"
327,1,893,189,0.074000," ","int(1/(e*x+d)^2/(c*x^2+b*x)^(3/2),x)","\frac{3 b \,e^{2} \ln \left(\frac{-\frac{2 \left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+2 \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}}{x +\frac{d}{e}}\right)}{2 \left(b e -c d \right)^{2} \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, d^{2}}+\frac{12 c^{2} e x}{\left(b e -c d \right)^{2} \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, b d}-\frac{12 c^{3} x}{\left(b e -c d \right)^{2} \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, b^{2}}-\frac{3 c e \ln \left(\frac{-\frac{2 \left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+2 \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}}{x +\frac{d}{e}}\right)}{\left(b e -c d \right)^{2} \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, d}-\frac{3 c \,e^{2} x}{\left(b e -c d \right)^{2} \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, d^{2}}-\frac{3 b \,e^{2}}{\left(b e -c d \right)^{2} \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, d^{2}}-\frac{6 c^{2}}{\left(b e -c d \right)^{2} \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, b}+\frac{9 c e}{\left(b e -c d \right)^{2} \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, d}-\frac{8 c^{2} x}{\left(b e -c d \right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, b^{2} d}-\frac{4 c}{\left(b e -c d \right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, b d}+\frac{1}{\left(b e -c d \right) \left(x +\frac{d}{e}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, d}"," ",0,"1/(b*e-c*d)/d/(x+d/e)/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)-3*e^2/(b*e-c*d)^2/d^2/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*b+9*e/(b*e-c*d)^2/d/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*c-3*e^2/(b*e-c*d)^2/d^2/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*x*c+12*e/(b*e-c*d)^2/d/b/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*x*c^2-12/(b*e-c*d)^2/b^2/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*x*c^3-6/(b*e-c*d)^2/b/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*c^2+3/2*e^2/(b*e-c*d)^2/d^2/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))*b-3*e/(b*e-c*d)^2/d/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))*c-8*c^2/(b*e-c*d)/d/b^2/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*x-4*c/(b*e-c*d)/d/b/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)","B"
328,1,1612,272,0.053000," ","int(1/(e*x+d)^3/(c*x^2+b*x)^(3/2),x)","\frac{15 b^{2} e^{3} \ln \left(\frac{-\frac{2 \left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+2 \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}}{x +\frac{d}{e}}\right)}{8 \left(b e -c d \right)^{3} \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, d^{3}}-\frac{15 b c \,e^{2} \ln \left(\frac{-\frac{2 \left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+2 \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}}{x +\frac{d}{e}}\right)}{2 \left(b e -c d \right)^{3} \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, d^{2}}-\frac{15 b c \,e^{3} x}{4 \left(b e -c d \right)^{3} \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, d^{3}}-\frac{45 c^{3} e x}{\left(b e -c d \right)^{3} \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, b d}+\frac{30 c^{4} x}{\left(b e -c d \right)^{3} \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, b^{2}}+\frac{15 c^{2} e \ln \left(\frac{-\frac{2 \left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+2 \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}}{x +\frac{d}{e}}\right)}{2 \left(b e -c d \right)^{3} \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, d}+\frac{45 c^{2} e^{2} x}{2 \left(b e -c d \right)^{3} \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, d^{2}}-\frac{15 b^{2} e^{3}}{4 \left(b e -c d \right)^{3} \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, d^{3}}+\frac{75 b c \,e^{2}}{4 \left(b e -c d \right)^{3} \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, d^{2}}+\frac{15 c^{3}}{\left(b e -c d \right)^{3} \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, b}-\frac{30 c^{2} e}{\left(b e -c d \right)^{3} \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, d}-\frac{13 c^{2} e x}{\left(b e -c d \right)^{2} \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, b \,d^{2}}+\frac{26 c^{3} x}{\left(b e -c d \right)^{2} \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, b^{2} d}+\frac{3 c e \ln \left(\frac{-\frac{2 \left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+2 \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}}{x +\frac{d}{e}}\right)}{2 \left(b e -c d \right)^{2} \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, d^{2}}+\frac{5 b e}{4 \left(b e -c d \right)^{2} \left(x +\frac{d}{e}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, d^{2}}+\frac{13 c^{2}}{\left(b e -c d \right)^{2} \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, b d}-\frac{5 c}{2 \left(b e -c d \right)^{2} \left(x +\frac{d}{e}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, d}-\frac{8 c e}{\left(b e -c d \right)^{2} \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, d^{2}}+\frac{1}{2 \left(b e -c d \right) \left(x +\frac{d}{e}\right)^{2} \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, d e}"," ",0,"1/2/e/(b*e-c*d)/d/(x+d/e)^2/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)+5/4*e/(b*e-c*d)^2/d^2/(x+d/e)/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*b-5/2/(b*e-c*d)^2/d/(x+d/e)/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*c-15/4*e^3/(b*e-c*d)^3/d^3/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*b^2+75/4*e^2/(b*e-c*d)^3/d^2/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*b*c-30*e/(b*e-c*d)^3/d/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*c^2-15/4*e^3/(b*e-c*d)^3/d^3/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*x*c*b+45/2*e^2/(b*e-c*d)^3/d^2/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*x*c^2-45*e/(b*e-c*d)^3/d/b/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*x*c^3+30/(b*e-c*d)^3/b^2/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*x*c^4+15/(b*e-c*d)^3/b/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*c^3+15/8*e^3/(b*e-c*d)^3/d^3/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))*b^2-15/2*e^2/(b*e-c*d)^3/d^2/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))*b*c+15/2*e/(b*e-c*d)^3/d/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))*c^2-13*e/(b*e-c*d)^2/d^2*c^2/b/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*x+26/(b*e-c*d)^2/d*c^3/b^2/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*x-8*e/(b*e-c*d)^2/d^2*c/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)+13/(b*e-c*d)^2/d*c^2/b/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)+3/2*e*c/(b*e-c*d)^2/d^2/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))","B"
329,1,447,190,0.122000," ","int((e*x+d)^4/(c*x^2+b*x)^(5/2),x)","-\frac{e^{4} x^{3}}{3 \left(c \,x^{2}+b x \right)^{\frac{3}{2}} c}+\frac{b \,e^{4} x^{2}}{2 \left(c \,x^{2}+b x \right)^{\frac{3}{2}} c^{2}}-\frac{4 d \,e^{3} x^{2}}{\left(c \,x^{2}+b x \right)^{\frac{3}{2}} c}+\frac{b^{2} e^{4} x}{6 \left(c \,x^{2}+b x \right)^{\frac{3}{2}} c^{3}}-\frac{4 b d \,e^{3} x}{3 \left(c \,x^{2}+b x \right)^{\frac{3}{2}} c^{2}}+\frac{8 d^{3} e x}{3 \left(c \,x^{2}+b x \right)^{\frac{3}{2}} b}-\frac{4 c \,d^{4} x}{3 \left(c \,x^{2}+b x \right)^{\frac{3}{2}} b^{2}}-\frac{4 d^{2} e^{2} x}{\left(c \,x^{2}+b x \right)^{\frac{3}{2}} c}+\frac{8 d \,e^{3} x}{3 \sqrt{c \,x^{2}+b x}\, b c}-\frac{2 d^{4}}{3 \left(c \,x^{2}+b x \right)^{\frac{3}{2}} b}+\frac{8 d^{2} e^{2} x}{\sqrt{c \,x^{2}+b x}\, b^{2}}-\frac{64 c \,d^{3} e x}{3 \sqrt{c \,x^{2}+b x}\, b^{3}}+\frac{32 c^{2} d^{4} x}{3 \sqrt{c \,x^{2}+b x}\, b^{4}}-\frac{7 e^{4} x}{3 \sqrt{c \,x^{2}+b x}\, c^{2}}+\frac{e^{4} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x}\right)}{c^{\frac{5}{2}}}-\frac{b \,e^{4}}{6 \sqrt{c \,x^{2}+b x}\, c^{3}}+\frac{4 d^{2} e^{2}}{\sqrt{c \,x^{2}+b x}\, b c}-\frac{32 d^{3} e}{3 \sqrt{c \,x^{2}+b x}\, b^{2}}+\frac{16 c \,d^{4}}{3 \sqrt{c \,x^{2}+b x}\, b^{3}}+\frac{4 d \,e^{3}}{3 \sqrt{c \,x^{2}+b x}\, c^{2}}"," ",0,"-1/3*e^4*x^3/c/(c*x^2+b*x)^(3/2)+1/2*e^4*b/c^2*x^2/(c*x^2+b*x)^(3/2)+1/6*e^4*b^2/c^3/(c*x^2+b*x)^(3/2)*x-7/3*e^4/c^2/(c*x^2+b*x)^(1/2)*x-1/6*e^4*b/c^3/(c*x^2+b*x)^(1/2)+e^4/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x)^(1/2))-4*d*e^3*x^2/c/(c*x^2+b*x)^(3/2)-4/3*d*e^3*b/c^2/(c*x^2+b*x)^(3/2)*x+8/3*d*e^3/b/c/(c*x^2+b*x)^(1/2)*x+4/3*d*e^3/c^2/(c*x^2+b*x)^(1/2)-4*d^2*e^2/c/(c*x^2+b*x)^(3/2)*x+8*d^2*e^2/b^2/(c*x^2+b*x)^(1/2)*x+4*d^2*e^2/b/c/(c*x^2+b*x)^(1/2)+8/3*d^3*e/b/(c*x^2+b*x)^(3/2)*x-64/3*d^3*e/b^3*c/(c*x^2+b*x)^(1/2)*x-32/3*d^3*e/b^2/(c*x^2+b*x)^(1/2)-4/3*d^4/b^2/(c*x^2+b*x)^(3/2)*c*x-2/3*d^4/b/(c*x^2+b*x)^(3/2)+32/3*d^4*c^2/b^4/(c*x^2+b*x)^(1/2)*x+16/3*d^4*c/b^3/(c*x^2+b*x)^(1/2)","B"
330,1,136,79,0.047000," ","int((e*x+d)^3/(c*x^2+b*x)^(5/2),x)","-\frac{2 \left(c x +b \right) \left(-b^{3} e^{3} x^{3}-6 b^{2} c d \,e^{2} x^{3}+24 b \,c^{2} d^{2} e \,x^{3}-16 c^{3} d^{3} x^{3}-9 b^{3} d \,e^{2} x^{2}+36 b^{2} c \,d^{2} e \,x^{2}-24 b \,c^{2} d^{3} x^{2}+9 b^{3} d^{2} e x -6 b^{2} c \,d^{3} x +d^{3} b^{3}\right) x}{3 \left(c \,x^{2}+b x \right)^{\frac{5}{2}} b^{4}}"," ",0,"-2/3*(c*x+b)*x*(-b^3*e^3*x^3-6*b^2*c*d*e^2*x^3+24*b*c^2*d^2*e*x^3-16*c^3*d^3*x^3-9*b^3*d*e^2*x^2+36*b^2*c*d^2*e*x^2-24*b*c^2*d^3*x^2+9*b^3*d^2*e*x-6*b^2*c*d^3*x+b^3*d^3)/b^4/(c*x^2+b*x)^(5/2)","A"
331,1,117,70,0.046000," ","int((e*x+d)^2/(c*x^2+b*x)^(5/2),x)","-\frac{2 \left(c x +b \right) \left(-2 b^{2} c \,e^{2} x^{3}+16 b \,c^{2} d e \,x^{3}-16 c^{3} d^{2} x^{3}-3 b^{3} e^{2} x^{2}+24 b^{2} c d e \,x^{2}-24 b \,c^{2} d^{2} x^{2}+6 b^{3} d e x -6 b^{2} c \,d^{2} x +d^{2} b^{3}\right) x}{3 \left(c \,x^{2}+b x \right)^{\frac{5}{2}} b^{4}}"," ",0,"-2/3*(c*x+b)*x*(-2*b^2*c*e^2*x^3+16*b*c^2*d*e*x^3-16*c^3*d^2*x^3-3*b^3*e^2*x^2+24*b^2*c*d*e*x^2-24*b*c^2*d^2*x^2+6*b^3*d*e*x-6*b^2*c*d^2*x+b^3*d^2)/b^4/(c*x^2+b*x)^(5/2)","A"
332,1,83,63,0.045000," ","int((e*x+d)/(c*x^2+b*x)^(5/2),x)","-\frac{2 \left(c x +b \right) \left(8 b \,c^{2} e \,x^{3}-16 c^{3} d \,x^{3}+12 b^{2} c e \,x^{2}-24 b \,c^{2} d \,x^{2}+3 b^{3} e x -6 b^{2} c d x +b^{3} d \right) x}{3 \left(c \,x^{2}+b x \right)^{\frac{5}{2}} b^{4}}"," ",0,"-2/3*(c*x+b)*x*(8*b*c^2*e*x^3-16*c^3*d*x^3+12*b^2*c*e*x^2-24*b*c^2*d*x^2+3*b^3*e*x-6*b^2*c*d*x+b^3*d)/b^4/(c*x^2+b*x)^(5/2)","A"
333,1,51,46,0.041000," ","int(1/(c*x^2+b*x)^(5/2),x)","-\frac{2 \left(c x +b \right) \left(-16 x^{3} c^{3}-24 b \,x^{2} c^{2}-6 b^{2} x c +b^{3}\right) x}{3 \left(c \,x^{2}+b x \right)^{\frac{5}{2}} b^{4}}"," ",0,"-2/3*(c*x+b)*x*(-16*c^3*x^3-24*b*c^2*x^2-6*b^2*c*x+b^3)/b^4/(c*x^2+b*x)^(5/2)","A"
334,1,950,210,0.048000," ","int(1/(e*x+d)/(c*x^2+b*x)^(5/2),x)","\frac{2 c \,e^{3} x}{\left(b e -c d \right)^{2} \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, b \,d^{2}}-\frac{4 c^{2} e^{2} x}{\left(b e -c d \right)^{2} \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, b^{2} d}-\frac{e^{3} \ln \left(\frac{-\frac{2 \left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+2 \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}}{x +\frac{d}{e}}\right)}{\left(b e -c d \right)^{2} \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, d^{2}}-\frac{2 c \,e^{2}}{\left(b e -c d \right)^{2} \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, b d}-\frac{2 c e x}{3 \left(b e -c d \right) \left(\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}\right)^{\frac{3}{2}} b d}+\frac{4 c^{2} x}{3 \left(b e -c d \right) \left(\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}\right)^{\frac{3}{2}} b^{2}}+\frac{2 e^{3}}{\left(b e -c d \right)^{2} \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, d^{2}}+\frac{2 c}{3 \left(b e -c d \right) \left(\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}\right)^{\frac{3}{2}} b}+\frac{16 c^{2} e x}{3 \left(b e -c d \right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, b^{3} d}-\frac{32 c^{3} x}{3 \left(b e -c d \right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, b^{4}}-\frac{2 e}{3 \left(b e -c d \right) \left(\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}\right)^{\frac{3}{2}} d}+\frac{8 c e}{3 \left(b e -c d \right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, b^{2} d}-\frac{16 c^{2}}{3 \left(b e -c d \right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, b^{3}}"," ",0,"-2/3*e/(b*e-c*d)/d/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(3/2)-2/3*e/(b*e-c*d)/d/b/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(3/2)*c*x+4/3/(b*e-c*d)/b^2/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(3/2)*c^2*x+2/3/(b*e-c*d)/b/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(3/2)*c+16/3*e/(b*e-c*d)/d*c^2/b^3/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*x-32/3/(b*e-c*d)*c^3/b^4/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*x+8/3*e/(b*e-c*d)/d*c/b^2/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)-16/3/(b*e-c*d)*c^2/b^3/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)+2*e^3/(b*e-c*d)^2/d^2/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)+2*e^3/(b*e-c*d)^2/d^2/b/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*x*c-4*e^2/(b*e-c*d)^2/d/b^2/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*x*c^2-2*e^2/(b*e-c*d)^2/d/b/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*c-e^3/(b*e-c*d)^2/d^2/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))","B"
335,1,1857,322,0.059000," ","int(1/(e*x+d)^2/(c*x^2+b*x)^(5/2),x)","-\frac{5 b \,e^{4} \ln \left(\frac{-\frac{2 \left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+2 \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}}{x +\frac{d}{e}}\right)}{2 \left(b e -c d \right)^{3} \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, d^{3}}-\frac{20 c^{2} e^{3} x}{\left(b e -c d \right)^{3} \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, b \,d^{2}}+\frac{20 c^{3} e^{2} x}{\left(b e -c d \right)^{3} \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, b^{2} d}+\frac{5 c \,e^{3} \ln \left(\frac{-\frac{2 \left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+2 \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}}{x +\frac{d}{e}}\right)}{\left(b e -c d \right)^{3} \sqrt{-\frac{\left(b e -c d \right) d}{e^{2}}}\, d^{2}}+\frac{5 c \,e^{4} x}{\left(b e -c d \right)^{3} \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, d^{3}}+\frac{5 b \,e^{4}}{\left(b e -c d \right)^{3} \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, d^{3}}+\frac{10 c^{2} e^{2}}{\left(b e -c d \right)^{3} \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, b d}+\frac{20 c^{2} e x}{3 \left(b e -c d \right)^{2} \left(\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}\right)^{\frac{3}{2}} b d}-\frac{20 c^{3} x}{3 \left(b e -c d \right)^{2} \left(\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}\right)^{\frac{3}{2}} b^{2}}-\frac{15 c \,e^{3}}{\left(b e -c d \right)^{3} \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, d^{2}}-\frac{5 c \,e^{2} x}{3 \left(b e -c d \right)^{2} \left(\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}\right)^{\frac{3}{2}} d^{2}}-\frac{5 b \,e^{2}}{3 \left(b e -c d \right)^{2} \left(\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}\right)^{\frac{3}{2}} d^{2}}-\frac{10 c^{2}}{3 \left(b e -c d \right)^{2} \left(\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}\right)^{\frac{3}{2}} b}+\frac{40 c^{2} e^{2} x}{3 \left(b e -c d \right)^{2} \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, b^{2} d^{2}}-\frac{160 c^{3} e x}{3 \left(b e -c d \right)^{2} \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, b^{3} d}+\frac{160 c^{4} x}{3 \left(b e -c d \right)^{2} \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, b^{4}}+\frac{5 c e}{\left(b e -c d \right)^{2} \left(\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}\right)^{\frac{3}{2}} d}+\frac{20 c \,e^{2}}{3 \left(b e -c d \right)^{2} \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, b \,d^{2}}-\frac{80 c^{2} e}{3 \left(b e -c d \right)^{2} \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, b^{2} d}-\frac{16 c^{2} x}{3 \left(b e -c d \right) \left(\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}\right)^{\frac{3}{2}} b^{2} d}+\frac{80 c^{3}}{3 \left(b e -c d \right)^{2} \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, b^{3}}-\frac{8 c}{3 \left(b e -c d \right) \left(\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}\right)^{\frac{3}{2}} b d}+\frac{128 c^{3} x}{3 \left(b e -c d \right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, b^{4} d}+\frac{1}{\left(b e -c d \right) \left(x +\frac{d}{e}\right) \left(\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}\right)^{\frac{3}{2}} d}+\frac{64 c^{2}}{3 \left(b e -c d \right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c -\frac{\left(b e -c d \right) d}{e^{2}}+\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}}\, b^{3} d}"," ",0,"80/3/(b*e-c*d)^2*c^3/b^3/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)+1/(b*e-c*d)/d/(x+d/e)/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(3/2)-10/3/(b*e-c*d)^2/b/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(3/2)*c^2+5*e^3/(b*e-c*d)^3/d^2/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))*c+20/3*e^2/(b*e-c*d)^2/d^2*c/b/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)-5/3*e^2/(b*e-c*d)^2/d^2/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(3/2)*c*x-16/3*c^2/(b*e-c*d)/d/b^2/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(3/2)*x+128/3*c^3/(b*e-c*d)/d/b^4/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*x-80/3*e/(b*e-c*d)^2/d*c^2/b^2/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)+10*e^2/(b*e-c*d)^3/d/b/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*c^2+5*e^4/(b*e-c*d)^3/d^3/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*x*c-5/2*e^4/(b*e-c*d)^3/d^3/(-(b*e-c*d)*d/e^2)^(1/2)*ln((-2*(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e+2*(-(b*e-c*d)*d/e^2)^(1/2)*((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2))/(x+d/e))*b-20/3/(b*e-c*d)^2/b^2/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(3/2)*c^3*x-8/3*c/(b*e-c*d)/d/b/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(3/2)+64/3*c^2/(b*e-c*d)/d/b^3/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)+5*e^4/(b*e-c*d)^3/d^3/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*b-15*e^3/(b*e-c*d)^3/d^2/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*c-5/3*e^2/(b*e-c*d)^2/d^2/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(3/2)*b+5*e/(b*e-c*d)^2/d/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(3/2)*c+160/3/(b*e-c*d)^2*c^4/b^4/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*x+20*e^2/(b*e-c*d)^3/d/b^2/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*x*c^3+20/3*e/(b*e-c*d)^2/d/b/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(3/2)*c^2*x-20*e^3/(b*e-c*d)^3/d^2/b/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*x*c^2+40/3*e^2/(b*e-c*d)^2/d^2*c^2/b^2/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*x-160/3*e/(b*e-c*d)^2/d*c^3/b^3/((x+d/e)^2*c-(b*e-c*d)*d/e^2+(b*e-2*c*d)*(x+d/e)/e)^(1/2)*x","B"
336,1,12,15,0.036000," ","int(1/(x+2)/(x^2+2*x)^(1/2),x)","\frac{x}{\sqrt{x^{2}+2 x}}"," ",0,"x/(x^2+2*x)^(1/2)","A"
337,1,47,56,0.123000," ","int((e*x+d)^(7/2)*(c*x^2+b*x),x)","-\frac{2 \left(e x +d \right)^{\frac{9}{2}} \left(-99 c \,e^{2} x^{2}-117 b \,e^{2} x +36 c d e x +26 b d e -8 c \,d^{2}\right)}{1287 e^{3}}"," ",0,"-2/1287*(e*x+d)^(9/2)*(-99*c*e^2*x^2-117*b*e^2*x+36*c*d*e*x+26*b*d*e-8*c*d^2)/e^3","A"
338,1,47,56,0.046000," ","int((e*x+d)^(5/2)*(c*x^2+b*x),x)","-\frac{2 \left(e x +d \right)^{\frac{7}{2}} \left(-63 c \,e^{2} x^{2}-77 b \,e^{2} x +28 c d e x +22 b d e -8 c \,d^{2}\right)}{693 e^{3}}"," ",0,"-2/693*(e*x+d)^(7/2)*(-63*c*e^2*x^2-77*b*e^2*x+28*c*d*e*x+22*b*d*e-8*c*d^2)/e^3","A"
339,1,47,56,0.047000," ","int((e*x+d)^(3/2)*(c*x^2+b*x),x)","-\frac{2 \left(e x +d \right)^{\frac{5}{2}} \left(-35 c \,e^{2} x^{2}-45 b \,e^{2} x +20 c d e x +18 b d e -8 c \,d^{2}\right)}{315 e^{3}}"," ",0,"-2/315*(e*x+d)^(5/2)*(-35*c*e^2*x^2-45*b*e^2*x+20*c*d*e*x+18*b*d*e-8*c*d^2)/e^3","A"
340,1,47,56,0.046000," ","int((e*x+d)^(1/2)*(c*x^2+b*x),x)","-\frac{2 \left(e x +d \right)^{\frac{3}{2}} \left(-15 c \,e^{2} x^{2}-21 b \,e^{2} x +12 c d e x +14 b d e -8 c \,d^{2}\right)}{105 e^{3}}"," ",0,"-2/105*(e*x+d)^(3/2)*(-15*c*e^2*x^2-21*b*e^2*x+12*c*d*e*x+14*b*d*e-8*c*d^2)/e^3","A"
341,1,47,56,0.041000," ","int((c*x^2+b*x)/(e*x+d)^(1/2),x)","-\frac{2 \left(-3 c \,e^{2} x^{2}-5 b \,e^{2} x +4 c d e x +10 b d e -8 c \,d^{2}\right) \sqrt{e x +d}}{15 e^{3}}"," ",0,"-2/15*(-3*c*e^2*x^2-5*b*e^2*x+4*c*d*e*x+10*b*d*e-8*c*d^2)*(e*x+d)^(1/2)/e^3","A"
342,1,46,56,0.042000," ","int((c*x^2+b*x)/(e*x+d)^(3/2),x)","\frac{\frac{2}{3} c \,e^{2} x^{2}+2 b \,e^{2} x -\frac{8}{3} c d e x +4 b d e -\frac{16}{3} c \,d^{2}}{\sqrt{e x +d}\, e^{3}}"," ",0,"2/3*(c*e^2*x^2+3*b*e^2*x-4*c*d*e*x+6*b*d*e-8*c*d^2)/(e*x+d)^(1/2)/e^3","A"
343,1,47,56,0.043000," ","int((c*x^2+b*x)/(e*x+d)^(5/2),x)","-\frac{2 \left(-3 c \,e^{2} x^{2}+3 b \,e^{2} x -12 c d e x +2 b d e -8 c \,d^{2}\right)}{3 \left(e x +d \right)^{\frac{3}{2}} e^{3}}"," ",0,"-2/3*(-3*c*e^2*x^2+3*b*e^2*x-12*c*d*e*x+2*b*d*e-8*c*d^2)/(e*x+d)^(3/2)/e^3","A"
344,1,47,56,0.055000," ","int((c*x^2+b*x)/(e*x+d)^(7/2),x)","-\frac{2 \left(15 c \,e^{2} x^{2}+5 b \,e^{2} x +20 c d e x +2 b d e +8 c \,d^{2}\right)}{15 \left(e x +d \right)^{\frac{5}{2}} e^{3}}"," ",0,"-2/15*(15*c*e^2*x^2+5*b*e^2*x+20*c*d*e*x+2*b*d*e+8*c*d^2)/(e*x+d)^(5/2)/e^3","A"
345,1,141,127,0.049000," ","int((e*x+d)^(7/2)*(c*x^2+b*x)^2,x)","\frac{2 \left(e x +d \right)^{\frac{9}{2}} \left(6435 c^{2} x^{4} e^{4}+14586 b c \,e^{4} x^{3}-3432 c^{2} d \,e^{3} x^{3}+8415 b^{2} e^{4} x^{2}-6732 b c d \,e^{3} x^{2}+1584 c^{2} d^{2} e^{2} x^{2}-3060 b^{2} d \,e^{3} x +2448 b c \,d^{2} e^{2} x -576 c^{2} d^{3} e x +680 b^{2} d^{2} e^{2}-544 b c \,d^{3} e +128 c^{2} d^{4}\right)}{109395 e^{5}}"," ",0,"2/109395*(e*x+d)^(9/2)*(6435*c^2*e^4*x^4+14586*b*c*e^4*x^3-3432*c^2*d*e^3*x^3+8415*b^2*e^4*x^2-6732*b*c*d*e^3*x^2+1584*c^2*d^2*e^2*x^2-3060*b^2*d*e^3*x+2448*b*c*d^2*e^2*x-576*c^2*d^3*e*x+680*b^2*d^2*e^2-544*b*c*d^3*e+128*c^2*d^4)/e^5","A"
346,1,141,127,0.052000," ","int((e*x+d)^(5/2)*(c*x^2+b*x)^2,x)","\frac{2 \left(e x +d \right)^{\frac{7}{2}} \left(3003 c^{2} x^{4} e^{4}+6930 b c \,e^{4} x^{3}-1848 c^{2} d \,e^{3} x^{3}+4095 b^{2} e^{4} x^{2}-3780 b c d \,e^{3} x^{2}+1008 c^{2} d^{2} e^{2} x^{2}-1820 b^{2} d \,e^{3} x +1680 b c \,d^{2} e^{2} x -448 c^{2} d^{3} e x +520 b^{2} d^{2} e^{2}-480 b c \,d^{3} e +128 c^{2} d^{4}\right)}{45045 e^{5}}"," ",0,"2/45045*(e*x+d)^(7/2)*(3003*c^2*e^4*x^4+6930*b*c*e^4*x^3-1848*c^2*d*e^3*x^3+4095*b^2*e^4*x^2-3780*b*c*d*e^3*x^2+1008*c^2*d^2*e^2*x^2-1820*b^2*d*e^3*x+1680*b*c*d^2*e^2*x-448*c^2*d^3*e*x+520*b^2*d^2*e^2-480*b*c*d^3*e+128*c^2*d^4)/e^5","A"
347,1,141,127,0.042000," ","int((e*x+d)^(3/2)*(c*x^2+b*x)^2,x)","\frac{2 \left(e x +d \right)^{\frac{5}{2}} \left(3465 c^{2} x^{4} e^{4}+8190 b c \,e^{4} x^{3}-2520 c^{2} d \,e^{3} x^{3}+5005 b^{2} e^{4} x^{2}-5460 b c d \,e^{3} x^{2}+1680 c^{2} d^{2} e^{2} x^{2}-2860 b^{2} d \,e^{3} x +3120 b c \,d^{2} e^{2} x -960 c^{2} d^{3} e x +1144 b^{2} d^{2} e^{2}-1248 b c \,d^{3} e +384 c^{2} d^{4}\right)}{45045 e^{5}}"," ",0,"2/45045*(e*x+d)^(5/2)*(3465*c^2*e^4*x^4+8190*b*c*e^4*x^3-2520*c^2*d*e^3*x^3+5005*b^2*e^4*x^2-5460*b*c*d*e^3*x^2+1680*c^2*d^2*e^2*x^2-2860*b^2*d*e^3*x+3120*b*c*d^2*e^2*x-960*c^2*d^3*e*x+1144*b^2*d^2*e^2-1248*b*c*d^3*e+384*c^2*d^4)/e^5","A"
348,1,141,127,0.058000," ","int((e*x+d)^(1/2)*(c*x^2+b*x)^2,x)","\frac{2 \left(e x +d \right)^{\frac{3}{2}} \left(315 c^{2} x^{4} e^{4}+770 b c \,e^{4} x^{3}-280 c^{2} d \,e^{3} x^{3}+495 b^{2} e^{4} x^{2}-660 b c d \,e^{3} x^{2}+240 c^{2} d^{2} e^{2} x^{2}-396 b^{2} d \,e^{3} x +528 b c \,d^{2} e^{2} x -192 c^{2} d^{3} e x +264 b^{2} d^{2} e^{2}-352 b c \,d^{3} e +128 c^{2} d^{4}\right)}{3465 e^{5}}"," ",0,"2/3465*(e*x+d)^(3/2)*(315*c^2*e^4*x^4+770*b*c*e^4*x^3-280*c^2*d*e^3*x^3+495*b^2*e^4*x^2-660*b*c*d*e^3*x^2+240*c^2*d^2*e^2*x^2-396*b^2*d*e^3*x+528*b*c*d^2*e^2*x-192*c^2*d^3*e*x+264*b^2*d^2*e^2-352*b*c*d^3*e+128*c^2*d^4)/e^5","A"
349,1,141,127,0.054000," ","int((c*x^2+b*x)^2/(e*x+d)^(1/2),x)","\frac{2 \left(35 c^{2} x^{4} e^{4}+90 b c \,e^{4} x^{3}-40 c^{2} d \,e^{3} x^{3}+63 b^{2} e^{4} x^{2}-108 b c d \,e^{3} x^{2}+48 c^{2} d^{2} e^{2} x^{2}-84 b^{2} d \,e^{3} x +144 b c \,d^{2} e^{2} x -64 c^{2} d^{3} e x +168 b^{2} d^{2} e^{2}-288 b c \,d^{3} e +128 c^{2} d^{4}\right) \sqrt{e x +d}}{315 e^{5}}"," ",0,"2/315*(35*c^2*e^4*x^4+90*b*c*e^4*x^3-40*c^2*d*e^3*x^3+63*b^2*e^4*x^2-108*b*c*d*e^3*x^2+48*c^2*d^2*e^2*x^2-84*b^2*d*e^3*x+144*b*c*d^2*e^2*x-64*c^2*d^3*e*x+168*b^2*d^2*e^2-288*b*c*d^3*e+128*c^2*d^4)*(e*x+d)^(1/2)/e^5","A"
350,1,141,127,0.045000," ","int((c*x^2+b*x)^2/(e*x+d)^(3/2),x)","-\frac{2 \left(-15 c^{2} x^{4} e^{4}-42 b c \,e^{4} x^{3}+24 c^{2} d \,e^{3} x^{3}-35 b^{2} e^{4} x^{2}+84 b c d \,e^{3} x^{2}-48 c^{2} d^{2} e^{2} x^{2}+140 b^{2} d \,e^{3} x -336 b c \,d^{2} e^{2} x +192 c^{2} d^{3} e x +280 b^{2} d^{2} e^{2}-672 b c \,d^{3} e +384 c^{2} d^{4}\right)}{105 \sqrt{e x +d}\, e^{5}}"," ",0,"-2/105*(-15*c^2*e^4*x^4-42*b*c*e^4*x^3+24*c^2*d*e^3*x^3-35*b^2*e^4*x^2+84*b*c*d*e^3*x^2-48*c^2*d^2*e^2*x^2+140*b^2*d*e^3*x-336*b*c*d^2*e^2*x+192*c^2*d^3*e*x+280*b^2*d^2*e^2-672*b*c*d^3*e+384*c^2*d^4)/(e*x+d)^(1/2)/e^5","A"
351,1,141,127,0.046000," ","int((c*x^2+b*x)^2/(e*x+d)^(5/2),x)","\frac{\frac{2}{5} c^{2} x^{4} e^{4}+\frac{4}{3} b c \,e^{4} x^{3}-\frac{16}{15} c^{2} d \,e^{3} x^{3}+2 b^{2} e^{4} x^{2}-8 b c d \,e^{3} x^{2}+\frac{32}{5} c^{2} d^{2} e^{2} x^{2}+8 b^{2} d \,e^{3} x -32 b c \,d^{2} e^{2} x +\frac{128}{5} c^{2} d^{3} e x +\frac{16}{3} b^{2} d^{2} e^{2}-\frac{64}{3} b c \,d^{3} e +\frac{256}{15} c^{2} d^{4}}{\left(e x +d \right)^{\frac{3}{2}} e^{5}}"," ",0,"2/15*(3*c^2*e^4*x^4+10*b*c*e^4*x^3-8*c^2*d*e^3*x^3+15*b^2*e^4*x^2-60*b*c*d*e^3*x^2+48*c^2*d^2*e^2*x^2+60*b^2*d*e^3*x-240*b*c*d^2*e^2*x+192*c^2*d^3*e*x+40*b^2*d^2*e^2-160*b*c*d^3*e+128*c^2*d^4)/(e*x+d)^(3/2)/e^5","A"
352,1,141,127,0.049000," ","int((c*x^2+b*x)^2/(e*x+d)^(7/2),x)","-\frac{2 \left(-5 c^{2} x^{4} e^{4}-30 b c \,e^{4} x^{3}+40 c^{2} d \,e^{3} x^{3}+15 b^{2} e^{4} x^{2}-180 b c d \,e^{3} x^{2}+240 c^{2} d^{2} e^{2} x^{2}+20 b^{2} d \,e^{3} x -240 b c \,d^{2} e^{2} x +320 c^{2} d^{3} e x +8 b^{2} d^{2} e^{2}-96 b c \,d^{3} e +128 c^{2} d^{4}\right)}{15 \left(e x +d \right)^{\frac{5}{2}} e^{5}}"," ",0,"-2/15*(-5*c^2*e^4*x^4-30*b*c*e^4*x^3+40*c^2*d*e^3*x^3+15*b^2*e^4*x^2-180*b*c*d*e^3*x^2+240*c^2*d^2*e^2*x^2+20*b^2*d*e^3*x-240*b*c*d^2*e^2*x+320*c^2*d^3*e*x+8*b^2*d^2*e^2-96*b*c*d^3*e+128*c^2*d^4)/(e*x+d)^(5/2)/e^5","A"
353,1,286,220,0.124000," ","int((e*x+d)^(7/2)*(c*x^2+b*x)^3,x)","-\frac{2 \left(e x +d \right)^{\frac{9}{2}} \left(-692835 c^{3} x^{6} e^{6}-2297295 b \,c^{2} e^{6} x^{5}+437580 c^{3} d \,e^{5} x^{5}-2567565 b^{2} c \,e^{6} x^{4}+1351350 b \,c^{2} d \,e^{5} x^{4}-257400 c^{3} d^{2} e^{4} x^{4}-969969 b^{3} e^{6} x^{3}+1369368 b^{2} c d \,e^{5} x^{3}-720720 b \,c^{2} d^{2} e^{4} x^{3}+137280 c^{3} d^{3} e^{3} x^{3}+447678 b^{3} d \,e^{5} x^{2}-632016 b^{2} c \,d^{2} e^{4} x^{2}+332640 b \,c^{2} d^{3} e^{3} x^{2}-63360 c^{3} d^{4} e^{2} x^{2}-162792 b^{3} d^{2} e^{4} x +229824 b^{2} c \,d^{3} e^{3} x -120960 b \,c^{2} d^{4} e^{2} x +23040 c^{3} d^{5} e x +36176 b^{3} d^{3} e^{3}-51072 b^{2} c \,d^{4} e^{2}+26880 b \,c^{2} d^{5} e -5120 c^{3} d^{6}\right)}{14549535 e^{7}}"," ",0,"-2/14549535*(e*x+d)^(9/2)*(-692835*c^3*e^6*x^6-2297295*b*c^2*e^6*x^5+437580*c^3*d*e^5*x^5-2567565*b^2*c*e^6*x^4+1351350*b*c^2*d*e^5*x^4-257400*c^3*d^2*e^4*x^4-969969*b^3*e^6*x^3+1369368*b^2*c*d*e^5*x^3-720720*b*c^2*d^2*e^4*x^3+137280*c^3*d^3*e^3*x^3+447678*b^3*d*e^5*x^2-632016*b^2*c*d^2*e^4*x^2+332640*b*c^2*d^3*e^3*x^2-63360*c^3*d^4*e^2*x^2-162792*b^3*d^2*e^4*x+229824*b^2*c*d^3*e^3*x-120960*b*c^2*d^4*e^2*x+23040*c^3*d^5*e*x+36176*b^3*d^3*e^3-51072*b^2*c*d^4*e^2+26880*b*c^2*d^5*e-5120*c^3*d^6)/e^7","A"
354,1,286,220,0.048000," ","int((e*x+d)^(5/2)*(c*x^2+b*x)^3,x)","-\frac{2 \left(e x +d \right)^{\frac{7}{2}} \left(-255255 c^{3} x^{6} e^{6}-855855 b \,c^{2} e^{6} x^{5}+180180 c^{3} d \,e^{5} x^{5}-969969 b^{2} c \,e^{6} x^{4}+570570 b \,c^{2} d \,e^{5} x^{4}-120120 c^{3} d^{2} e^{4} x^{4}-373065 b^{3} e^{6} x^{3}+596904 b^{2} c d \,e^{5} x^{3}-351120 b \,c^{2} d^{2} e^{4} x^{3}+73920 c^{3} d^{3} e^{3} x^{3}+203490 b^{3} d \,e^{5} x^{2}-325584 b^{2} c \,d^{2} e^{4} x^{2}+191520 b \,c^{2} d^{3} e^{3} x^{2}-40320 c^{3} d^{4} e^{2} x^{2}-90440 b^{3} d^{2} e^{4} x +144704 b^{2} c \,d^{3} e^{3} x -85120 b \,c^{2} d^{4} e^{2} x +17920 c^{3} d^{5} e x +25840 b^{3} d^{3} e^{3}-41344 b^{2} c \,d^{4} e^{2}+24320 b \,c^{2} d^{5} e -5120 c^{3} d^{6}\right)}{4849845 e^{7}}"," ",0,"-2/4849845*(e*x+d)^(7/2)*(-255255*c^3*e^6*x^6-855855*b*c^2*e^6*x^5+180180*c^3*d*e^5*x^5-969969*b^2*c*e^6*x^4+570570*b*c^2*d*e^5*x^4-120120*c^3*d^2*e^4*x^4-373065*b^3*e^6*x^3+596904*b^2*c*d*e^5*x^3-351120*b*c^2*d^2*e^4*x^3+73920*c^3*d^3*e^3*x^3+203490*b^3*d*e^5*x^2-325584*b^2*c*d^2*e^4*x^2+191520*b*c^2*d^3*e^3*x^2-40320*c^3*d^4*e^2*x^2-90440*b^3*d^2*e^4*x+144704*b^2*c*d^3*e^3*x-85120*b*c^2*d^4*e^2*x+17920*c^3*d^5*e*x+25840*b^3*d^3*e^3-41344*b^2*c*d^4*e^2+24320*b*c^2*d^5*e-5120*c^3*d^6)/e^7","A"
355,1,286,220,0.054000," ","int((e*x+d)^(3/2)*(c*x^2+b*x)^3,x)","-\frac{2 \left(e x +d \right)^{\frac{5}{2}} \left(-15015 c^{3} x^{6} e^{6}-51051 b \,c^{2} e^{6} x^{5}+12012 c^{3} d \,e^{5} x^{5}-58905 b^{2} c \,e^{6} x^{4}+39270 b \,c^{2} d \,e^{5} x^{4}-9240 c^{3} d^{2} e^{4} x^{4}-23205 b^{3} e^{6} x^{3}+42840 b^{2} c d \,e^{5} x^{3}-28560 b \,c^{2} d^{2} e^{4} x^{3}+6720 c^{3} d^{3} e^{3} x^{3}+15470 b^{3} d \,e^{5} x^{2}-28560 b^{2} c \,d^{2} e^{4} x^{2}+19040 b \,c^{2} d^{3} e^{3} x^{2}-4480 c^{3} d^{4} e^{2} x^{2}-8840 b^{3} d^{2} e^{4} x +16320 b^{2} c \,d^{3} e^{3} x -10880 b \,c^{2} d^{4} e^{2} x +2560 c^{3} d^{5} e x +3536 b^{3} d^{3} e^{3}-6528 b^{2} c \,d^{4} e^{2}+4352 b \,c^{2} d^{5} e -1024 c^{3} d^{6}\right)}{255255 e^{7}}"," ",0,"-2/255255*(e*x+d)^(5/2)*(-15015*c^3*e^6*x^6-51051*b*c^2*e^6*x^5+12012*c^3*d*e^5*x^5-58905*b^2*c*e^6*x^4+39270*b*c^2*d*e^5*x^4-9240*c^3*d^2*e^4*x^4-23205*b^3*e^6*x^3+42840*b^2*c*d*e^5*x^3-28560*b*c^2*d^2*e^4*x^3+6720*c^3*d^3*e^3*x^3+15470*b^3*d*e^5*x^2-28560*b^2*c*d^2*e^4*x^2+19040*b*c^2*d^3*e^3*x^2-4480*c^3*d^4*e^2*x^2-8840*b^3*d^2*e^4*x+16320*b^2*c*d^3*e^3*x-10880*b*c^2*d^4*e^2*x+2560*c^3*d^5*e*x+3536*b^3*d^3*e^3-6528*b^2*c*d^4*e^2+4352*b*c^2*d^5*e-1024*c^3*d^6)/e^7","A"
356,1,286,220,0.045000," ","int((e*x+d)^(1/2)*(c*x^2+b*x)^3,x)","-\frac{2 \left(e x +d \right)^{\frac{3}{2}} \left(-3003 c^{3} x^{6} e^{6}-10395 b \,c^{2} e^{6} x^{5}+2772 c^{3} d \,e^{5} x^{5}-12285 b^{2} c \,e^{6} x^{4}+9450 b \,c^{2} d \,e^{5} x^{4}-2520 c^{3} d^{2} e^{4} x^{4}-5005 b^{3} e^{6} x^{3}+10920 b^{2} c d \,e^{5} x^{3}-8400 b \,c^{2} d^{2} e^{4} x^{3}+2240 c^{3} d^{3} e^{3} x^{3}+4290 b^{3} d \,e^{5} x^{2}-9360 b^{2} c \,d^{2} e^{4} x^{2}+7200 b \,c^{2} d^{3} e^{3} x^{2}-1920 c^{3} d^{4} e^{2} x^{2}-3432 b^{3} d^{2} e^{4} x +7488 b^{2} c \,d^{3} e^{3} x -5760 b \,c^{2} d^{4} e^{2} x +1536 c^{3} d^{5} e x +2288 b^{3} d^{3} e^{3}-4992 b^{2} c \,d^{4} e^{2}+3840 b \,c^{2} d^{5} e -1024 c^{3} d^{6}\right)}{45045 e^{7}}"," ",0,"-2/45045*(e*x+d)^(3/2)*(-3003*c^3*e^6*x^6-10395*b*c^2*e^6*x^5+2772*c^3*d*e^5*x^5-12285*b^2*c*e^6*x^4+9450*b*c^2*d*e^5*x^4-2520*c^3*d^2*e^4*x^4-5005*b^3*e^6*x^3+10920*b^2*c*d*e^5*x^3-8400*b*c^2*d^2*e^4*x^3+2240*c^3*d^3*e^3*x^3+4290*b^3*d*e^5*x^2-9360*b^2*c*d^2*e^4*x^2+7200*b*c^2*d^3*e^3*x^2-1920*c^3*d^4*e^2*x^2-3432*b^3*d^2*e^4*x+7488*b^2*c*d^3*e^3*x-5760*b*c^2*d^4*e^2*x+1536*c^3*d^5*e*x+2288*b^3*d^3*e^3-4992*b^2*c*d^4*e^2+3840*b*c^2*d^5*e-1024*c^3*d^6)/e^7","A"
357,1,286,220,0.056000," ","int((c*x^2+b*x)^3/(e*x+d)^(1/2),x)","-\frac{2 \left(-1155 c^{3} x^{6} e^{6}-4095 b \,c^{2} e^{6} x^{5}+1260 c^{3} d \,e^{5} x^{5}-5005 b^{2} c \,e^{6} x^{4}+4550 b \,c^{2} d \,e^{5} x^{4}-1400 c^{3} d^{2} e^{4} x^{4}-2145 b^{3} e^{6} x^{3}+5720 b^{2} c d \,e^{5} x^{3}-5200 b \,c^{2} d^{2} e^{4} x^{3}+1600 c^{3} d^{3} e^{3} x^{3}+2574 b^{3} d \,e^{5} x^{2}-6864 b^{2} c \,d^{2} e^{4} x^{2}+6240 b \,c^{2} d^{3} e^{3} x^{2}-1920 c^{3} d^{4} e^{2} x^{2}-3432 b^{3} d^{2} e^{4} x +9152 b^{2} c \,d^{3} e^{3} x -8320 b \,c^{2} d^{4} e^{2} x +2560 c^{3} d^{5} e x +6864 b^{3} d^{3} e^{3}-18304 b^{2} c \,d^{4} e^{2}+16640 b \,c^{2} d^{5} e -5120 c^{3} d^{6}\right) \sqrt{e x +d}}{15015 e^{7}}"," ",0,"-2/15015*(-1155*c^3*e^6*x^6-4095*b*c^2*e^6*x^5+1260*c^3*d*e^5*x^5-5005*b^2*c*e^6*x^4+4550*b*c^2*d*e^5*x^4-1400*c^3*d^2*e^4*x^4-2145*b^3*e^6*x^3+5720*b^2*c*d*e^5*x^3-5200*b*c^2*d^2*e^4*x^3+1600*c^3*d^3*e^3*x^3+2574*b^3*d*e^5*x^2-6864*b^2*c*d^2*e^4*x^2+6240*b*c^2*d^3*e^3*x^2-1920*c^3*d^4*e^2*x^2-3432*b^3*d^2*e^4*x+9152*b^2*c*d^3*e^3*x-8320*b*c^2*d^4*e^2*x+2560*c^3*d^5*e*x+6864*b^3*d^3*e^3-18304*b^2*c*d^4*e^2+16640*b*c^2*d^5*e-5120*c^3*d^6)*(e*x+d)^(1/2)/e^7","A"
358,1,286,220,0.068000," ","int((c*x^2+b*x)^3/(e*x+d)^(3/2),x)","\frac{\frac{2}{11} c^{3} x^{6} e^{6}+\frac{2}{3} b \,c^{2} e^{6} x^{5}-\frac{8}{33} c^{3} d \,e^{5} x^{5}+\frac{6}{7} b^{2} c \,e^{6} x^{4}-\frac{20}{21} b \,c^{2} d \,e^{5} x^{4}+\frac{80}{231} c^{3} d^{2} e^{4} x^{4}+\frac{2}{5} b^{3} e^{6} x^{3}-\frac{48}{35} b^{2} c d \,e^{5} x^{3}+\frac{32}{21} b \,c^{2} d^{2} e^{4} x^{3}-\frac{128}{231} c^{3} d^{3} e^{3} x^{3}-\frac{4}{5} b^{3} d \,e^{5} x^{2}+\frac{96}{35} b^{2} c \,d^{2} e^{4} x^{2}-\frac{64}{21} b \,c^{2} d^{3} e^{3} x^{2}+\frac{256}{231} c^{3} d^{4} e^{2} x^{2}+\frac{16}{5} b^{3} d^{2} e^{4} x -\frac{384}{35} b^{2} c \,d^{3} e^{3} x +\frac{256}{21} b \,c^{2} d^{4} e^{2} x -\frac{1024}{231} c^{3} d^{5} e x +\frac{32}{5} b^{3} d^{3} e^{3}-\frac{768}{35} b^{2} c \,d^{4} e^{2}+\frac{512}{21} b \,c^{2} d^{5} e -\frac{2048}{231} c^{3} d^{6}}{\sqrt{e x +d}\, e^{7}}"," ",0,"2/1155*(105*c^3*e^6*x^6+385*b*c^2*e^6*x^5-140*c^3*d*e^5*x^5+495*b^2*c*e^6*x^4-550*b*c^2*d*e^5*x^4+200*c^3*d^2*e^4*x^4+231*b^3*e^6*x^3-792*b^2*c*d*e^5*x^3+880*b*c^2*d^2*e^4*x^3-320*c^3*d^3*e^3*x^3-462*b^3*d*e^5*x^2+1584*b^2*c*d^2*e^4*x^2-1760*b*c^2*d^3*e^3*x^2+640*c^3*d^4*e^2*x^2+1848*b^3*d^2*e^4*x-6336*b^2*c*d^3*e^3*x+7040*b*c^2*d^4*e^2*x-2560*c^3*d^5*e*x+3696*b^3*d^3*e^3-12672*b^2*c*d^4*e^2+14080*b*c^2*d^5*e-5120*c^3*d^6)/(e*x+d)^(1/2)/e^7","A"
359,1,286,220,0.046000," ","int((c*x^2+b*x)^3/(e*x+d)^(5/2),x)","-\frac{2 \left(-35 c^{3} x^{6} e^{6}-135 b \,c^{2} e^{6} x^{5}+60 c^{3} d \,e^{5} x^{5}-189 b^{2} c \,e^{6} x^{4}+270 b \,c^{2} d \,e^{5} x^{4}-120 c^{3} d^{2} e^{4} x^{4}-105 b^{3} e^{6} x^{3}+504 b^{2} c d \,e^{5} x^{3}-720 b \,c^{2} d^{2} e^{4} x^{3}+320 c^{3} d^{3} e^{3} x^{3}+630 b^{3} d \,e^{5} x^{2}-3024 b^{2} c \,d^{2} e^{4} x^{2}+4320 b \,c^{2} d^{3} e^{3} x^{2}-1920 c^{3} d^{4} e^{2} x^{2}+2520 b^{3} d^{2} e^{4} x -12096 b^{2} c \,d^{3} e^{3} x +17280 b \,c^{2} d^{4} e^{2} x -7680 c^{3} d^{5} e x +1680 b^{3} d^{3} e^{3}-8064 b^{2} c \,d^{4} e^{2}+11520 b \,c^{2} d^{5} e -5120 c^{3} d^{6}\right)}{315 \left(e x +d \right)^{\frac{3}{2}} e^{7}}"," ",0,"-2/315*(-35*c^3*e^6*x^6-135*b*c^2*e^6*x^5+60*c^3*d*e^5*x^5-189*b^2*c*e^6*x^4+270*b*c^2*d*e^5*x^4-120*c^3*d^2*e^4*x^4-105*b^3*e^6*x^3+504*b^2*c*d*e^5*x^3-720*b*c^2*d^2*e^4*x^3+320*c^3*d^3*e^3*x^3+630*b^3*d*e^5*x^2-3024*b^2*c*d^2*e^4*x^2+4320*b*c^2*d^3*e^3*x^2-1920*c^3*d^4*e^2*x^2+2520*b^3*d^2*e^4*x-12096*b^2*c*d^3*e^3*x+17280*b*c^2*d^4*e^2*x-7680*c^3*d^5*e*x+1680*b^3*d^3*e^3-8064*b^2*c*d^4*e^2+11520*b*c^2*d^5*e-5120*c^3*d^6)/(e*x+d)^(3/2)/e^7","A"
360,1,286,220,0.051000," ","int((c*x^2+b*x)^3/(e*x+d)^(7/2),x)","\frac{\frac{2}{7} c^{3} x^{6} e^{6}+\frac{6}{5} b \,c^{2} e^{6} x^{5}-\frac{24}{35} c^{3} d \,e^{5} x^{5}+2 b^{2} c \,e^{6} x^{4}-4 b \,c^{2} d \,e^{5} x^{4}+\frac{16}{7} c^{3} d^{2} e^{4} x^{4}+2 b^{3} e^{6} x^{3}-16 b^{2} c d \,e^{5} x^{3}+32 b \,c^{2} d^{2} e^{4} x^{3}-\frac{128}{7} c^{3} d^{3} e^{3} x^{3}+12 b^{3} d \,e^{5} x^{2}-96 b^{2} c \,d^{2} e^{4} x^{2}+192 b \,c^{2} d^{3} e^{3} x^{2}-\frac{768}{7} c^{3} d^{4} e^{2} x^{2}+16 b^{3} d^{2} e^{4} x -128 b^{2} c \,d^{3} e^{3} x +256 b \,c^{2} d^{4} e^{2} x -\frac{1024}{7} c^{3} d^{5} e x +\frac{32}{5} b^{3} d^{3} e^{3}-\frac{256}{5} b^{2} c \,d^{4} e^{2}+\frac{512}{5} b \,c^{2} d^{5} e -\frac{2048}{35} c^{3} d^{6}}{\left(e x +d \right)^{\frac{5}{2}} e^{7}}"," ",0,"2/35*(5*c^3*e^6*x^6+21*b*c^2*e^6*x^5-12*c^3*d*e^5*x^5+35*b^2*c*e^6*x^4-70*b*c^2*d*e^5*x^4+40*c^3*d^2*e^4*x^4+35*b^3*e^6*x^3-280*b^2*c*d*e^5*x^3+560*b*c^2*d^2*e^4*x^3-320*c^3*d^3*e^3*x^3+210*b^3*d*e^5*x^2-1680*b^2*c*d^2*e^4*x^2+3360*b*c^2*d^3*e^3*x^2-1920*c^3*d^4*e^2*x^2+280*b^3*d^2*e^4*x-2240*b^2*c*d^3*e^3*x+4480*b*c^2*d^4*e^2*x-2560*c^3*d^5*e*x+112*b^3*d^3*e^3-896*b^2*c*d^4*e^2+1792*b*c^2*d^5*e-1024*c^3*d^6)/(e*x+d)^(5/2)/e^7","A"
361,1,336,131,0.081000," ","int((e*x+d)^(7/2)/(c*x^2+b*x),x)","-\frac{2 b^{3} e^{4} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\sqrt{\left(b e -c d \right) c}\, c^{3}}+\frac{8 b^{2} d \,e^{3} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\sqrt{\left(b e -c d \right) c}\, c^{2}}-\frac{12 b \,d^{2} e^{2} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\sqrt{\left(b e -c d \right) c}\, c}-\frac{2 c \,d^{4} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\sqrt{\left(b e -c d \right) c}\, b}+\frac{8 d^{3} e \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\sqrt{\left(b e -c d \right) c}}-\frac{2 d^{\frac{7}{2}} \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{b}+\frac{2 \sqrt{e x +d}\, b^{2} e^{3}}{c^{3}}-\frac{6 \sqrt{e x +d}\, b d \,e^{2}}{c^{2}}+\frac{6 \sqrt{e x +d}\, d^{2} e}{c}-\frac{2 \left(e x +d \right)^{\frac{3}{2}} b \,e^{2}}{3 c^{2}}+\frac{4 \left(e x +d \right)^{\frac{3}{2}} d e}{3 c}+\frac{2 \left(e x +d \right)^{\frac{5}{2}} e}{5 c}"," ",0,"2/5*e*(e*x+d)^(5/2)/c-2/3/c^2*(e*x+d)^(3/2)*b*e^2+4/3*e/c*(e*x+d)^(3/2)*d+2/c^3*b^2*e^3*(e*x+d)^(1/2)-6/c^2*b*d*e^2*(e*x+d)^(1/2)+6*e/c*d^2*(e*x+d)^(1/2)-2/c^3*b^3*e^4/((b*e-c*d)*c)^(1/2)*arctan(c*(e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2))+8/c^2*b^2*e^3/((b*e-c*d)*c)^(1/2)*arctan(c*(e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2))*d-12/c*b*e^2/((b*e-c*d)*c)^(1/2)*arctan(c*(e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2))*d^2+8*e/((b*e-c*d)*c)^(1/2)*arctan(c*(e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2))*d^3-2*c/b/((b*e-c*d)*c)^(1/2)*arctan(c*(e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2))*d^4-2*d^(7/2)*arctanh((e*x+d)^(1/2)/d^(1/2))/b","B"
362,1,237,96,0.059000," ","int((e*x+d)^(5/2)/(c*x^2+b*x),x)","\frac{2 b^{2} e^{3} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\sqrt{\left(b e -c d \right) c}\, c^{2}}-\frac{6 b d \,e^{2} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\sqrt{\left(b e -c d \right) c}\, c}-\frac{2 c \,d^{3} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\sqrt{\left(b e -c d \right) c}\, b}+\frac{6 d^{2} e \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\sqrt{\left(b e -c d \right) c}}-\frac{2 d^{\frac{5}{2}} \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{b}-\frac{2 \sqrt{e x +d}\, b \,e^{2}}{c^{2}}+\frac{4 \sqrt{e x +d}\, d e}{c}+\frac{2 \left(e x +d \right)^{\frac{3}{2}} e}{3 c}"," ",0,"2/3*e*(e*x+d)^(3/2)/c-2/c^2*(e*x+d)^(1/2)*b*e^2+4*d*e*(e*x+d)^(1/2)/c+2/c^2*b^2*e^3/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)-6/c*b*e^2/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)*d+6*e/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)*d^2-2*c/b/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)*d^3-2*d^(5/2)*arctanh((e*x+d)^(1/2)/d^(1/2))/b","B"
363,1,159,74,0.051000," ","int((e*x+d)^(3/2)/(c*x^2+b*x),x)","-\frac{2 b \,e^{2} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\sqrt{\left(b e -c d \right) c}\, c}-\frac{2 c \,d^{2} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\sqrt{\left(b e -c d \right) c}\, b}+\frac{4 d e \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\sqrt{\left(b e -c d \right) c}}-\frac{2 d^{\frac{3}{2}} \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{b}+\frac{2 \sqrt{e x +d}\, e}{c}"," ",0,"2*e*(e*x+d)^(1/2)/c-2*b/c*e^2/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)+4*e/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)*d-2/b*c/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)*d^2-2*d^(3/2)*arctanh((e*x+d)^(1/2)/d^(1/2))/b","B"
364,1,100,61,0.063000," ","int((e*x+d)^(1/2)/(c*x^2+b*x),x)","-\frac{2 c d \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\sqrt{\left(b e -c d \right) c}\, b}+\frac{2 e \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\sqrt{\left(b e -c d \right) c}}-\frac{2 \sqrt{d}\, \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{b}"," ",0,"2*e/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)-2/b/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)*c*d-2*arctanh((e*x+d)^(1/2)/d^(1/2))*d^(1/2)/b","A"
365,1,62,61,0.059000," ","int(1/(e*x+d)^(1/2)/(c*x^2+b*x),x)","-\frac{2 c \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\sqrt{\left(b e -c d \right) c}\, b}-\frac{2 \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{b \sqrt{d}}"," ",0,"-2*c/b/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)-2*arctanh((e*x+d)^(1/2)/d^(1/2))/b/d^(1/2)","A"
366,1,97,84,0.061000," ","int(1/(e*x+d)^(3/2)/(c*x^2+b*x),x)","\frac{2 c^{2} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\left(b e -c d \right) \sqrt{\left(b e -c d \right) c}\, b}+\frac{2 e}{\left(b e -c d \right) \sqrt{e x +d}\, d}-\frac{2 \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{b \,d^{\frac{3}{2}}}"," ",0,"2/(b*e-c*d)*c^2/b/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)-2*arctanh((e*x+d)^(1/2)/d^(1/2))/b/d^(3/2)+2*e/(b*e-c*d)/d/(e*x+d)^(1/2)","A"
367,1,147,116,0.066000," ","int(1/(e*x+d)^(5/2)/(c*x^2+b*x),x)","-\frac{2 c^{3} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\left(b e -c d \right)^{2} \sqrt{\left(b e -c d \right) c}\, b}+\frac{2 b \,e^{2}}{\left(b e -c d \right)^{2} \sqrt{e x +d}\, d^{2}}-\frac{4 c e}{\left(b e -c d \right)^{2} \sqrt{e x +d}\, d}+\frac{2 e}{3 \left(b e -c d \right) \left(e x +d \right)^{\frac{3}{2}} d}-\frac{2 \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{b \,d^{\frac{5}{2}}}"," ",0,"-2/(b*e-c*d)^2*c^3/b/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)-2*arctanh((e*x+d)^(1/2)/d^(1/2))/b/d^(5/2)+2/(b*e-c*d)^2/d^2/(e*x+d)^(1/2)*b*e^2-4*e/(b*e-c*d)^2/d/(e*x+d)^(1/2)*c+2/3*e/(b*e-c*d)/d/(e*x+d)^(3/2)","A"
368,1,228,161,0.061000," ","int(1/(e*x+d)^(7/2)/(c*x^2+b*x),x)","\frac{2 c^{4} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\left(b e -c d \right)^{3} \sqrt{\left(b e -c d \right) c}\, b}+\frac{2 b^{2} e^{3}}{\left(b e -c d \right)^{3} \sqrt{e x +d}\, d^{3}}-\frac{6 b c \,e^{2}}{\left(b e -c d \right)^{3} \sqrt{e x +d}\, d^{2}}+\frac{6 c^{2} e}{\left(b e -c d \right)^{3} \sqrt{e x +d}\, d}+\frac{2 b \,e^{2}}{3 \left(b e -c d \right)^{2} \left(e x +d \right)^{\frac{3}{2}} d^{2}}-\frac{4 c e}{3 \left(b e -c d \right)^{2} \left(e x +d \right)^{\frac{3}{2}} d}+\frac{2 e}{5 \left(b e -c d \right) \left(e x +d \right)^{\frac{5}{2}} d}-\frac{2 \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{b \,d^{\frac{7}{2}}}"," ",0,"2/(b*e-c*d)^3*c^4/b/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)-2*arctanh((e*x+d)^(1/2)/d^(1/2))/b/d^(7/2)+2/3/(b*e-c*d)^2/d^2/(e*x+d)^(3/2)*b*e^2-4/3*e/(b*e-c*d)^2/d/(e*x+d)^(3/2)*c+2/(b*e-c*d)^3/d^3/(e*x+d)^(1/2)*b^2*e^3-6/(b*e-c*d)^3/d^2/(e*x+d)^(1/2)*b*c*e^2+6*e/(b*e-c*d)^3/d/(e*x+d)^(1/2)*c^2+2/5*e/(b*e-c*d)/d/(e*x+d)^(5/2)","A"
369,1,515,225,0.078000," ","int((e*x+d)^(9/2)/(c*x^2+b*x)^2,x)","\frac{5 b^{2} e^{5} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\sqrt{\left(b e -c d \right) c}\, c^{3}}-\frac{16 b d \,e^{4} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\sqrt{\left(b e -c d \right) c}\, c^{2}}+\frac{4 d^{3} e^{2} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\sqrt{\left(b e -c d \right) c}\, b}-\frac{11 c \,d^{4} e \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\sqrt{\left(b e -c d \right) c}\, b^{2}}+\frac{4 c^{2} d^{5} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\sqrt{\left(b e -c d \right) c}\, b^{3}}+\frac{14 d^{2} e^{3} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\sqrt{\left(b e -c d \right) c}\, c}-\frac{\sqrt{e x +d}\, b^{2} e^{5}}{\left(c e x +b e \right) c^{3}}+\frac{4 \sqrt{e x +d}\, b d \,e^{4}}{\left(c e x +b e \right) c^{2}}+\frac{4 \sqrt{e x +d}\, d^{3} e^{2}}{\left(c e x +b e \right) b}-\frac{\sqrt{e x +d}\, c \,d^{4} e}{\left(c e x +b e \right) b^{2}}-\frac{6 \sqrt{e x +d}\, d^{2} e^{3}}{\left(c e x +b e \right) c}-\frac{9 d^{\frac{7}{2}} e \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{b^{2}}+\frac{4 c \,d^{\frac{9}{2}} \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{b^{3}}-\frac{4 \sqrt{e x +d}\, b \,e^{4}}{c^{3}}+\frac{8 \sqrt{e x +d}\, d \,e^{3}}{c^{2}}-\frac{\sqrt{e x +d}\, d^{4}}{b^{2} x}+\frac{2 \left(e x +d \right)^{\frac{3}{2}} e^{3}}{3 c^{2}}"," ",0,"2/3*e^3/c^2*(e*x+d)^(3/2)-4*e^4/c^3*(e*x+d)^(1/2)*b+8*e^3/c^2*(e*x+d)^(1/2)*d-e^5/c^3*b^2*(e*x+d)^(1/2)/(c*e*x+b*e)+4*e^4/c^2*b*(e*x+d)^(1/2)/(c*e*x+b*e)*d-6*e^3/c*(e*x+d)^(1/2)/(c*e*x+b*e)*d^2+4*e^2/b*(e*x+d)^(1/2)/(c*e*x+b*e)*d^3-e*c/b^2*(e*x+d)^(1/2)/(c*e*x+b*e)*d^4+5*e^5/c^3*b^2/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)-16*e^4/c^2*b/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)*d+14*e^3/c/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)*d^2+4*e^2/b/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)*d^3-11*e*c/b^2/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)*d^4+4*c^2/b^3/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)*d^5-d^4/b^2*(e*x+d)^(1/2)/x-9*e*d^(7/2)/b^2*arctanh((e*x+d)^(1/2)/d^(1/2))+4*d^(9/2)/b^3*arctanh((e*x+d)^(1/2)/d^(1/2))*c","B"
370,1,403,178,0.072000," ","int((e*x+d)^(7/2)/(c*x^2+b*x)^2,x)","-\frac{3 b \,e^{4} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\sqrt{\left(b e -c d \right) c}\, c^{2}}+\frac{3 d^{2} e^{2} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\sqrt{\left(b e -c d \right) c}\, b}-\frac{9 c \,d^{3} e \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\sqrt{\left(b e -c d \right) c}\, b^{2}}+\frac{4 c^{2} d^{4} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\sqrt{\left(b e -c d \right) c}\, b^{3}}+\frac{5 d \,e^{3} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\sqrt{\left(b e -c d \right) c}\, c}+\frac{\sqrt{e x +d}\, b \,e^{4}}{\left(c e x +b e \right) c^{2}}+\frac{3 \sqrt{e x +d}\, d^{2} e^{2}}{\left(c e x +b e \right) b}-\frac{\sqrt{e x +d}\, c \,d^{3} e}{\left(c e x +b e \right) b^{2}}-\frac{3 \sqrt{e x +d}\, d \,e^{3}}{\left(c e x +b e \right) c}-\frac{7 d^{\frac{5}{2}} e \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{b^{2}}+\frac{4 c \,d^{\frac{7}{2}} \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{b^{3}}+\frac{2 \sqrt{e x +d}\, e^{3}}{c^{2}}-\frac{\sqrt{e x +d}\, d^{3}}{b^{2} x}"," ",0,"2*e^3/c^2*(e*x+d)^(1/2)+e^4/c^2*b*(e*x+d)^(1/2)/(c*e*x+b*e)-3*e^3/c*(e*x+d)^(1/2)/(c*e*x+b*e)*d+3*e^2/b*(e*x+d)^(1/2)/(c*e*x+b*e)*d^2-e*c/b^2*(e*x+d)^(1/2)/(c*e*x+b*e)*d^3-3*e^4/c^2*b/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)+5*e^3/c/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)*d+3*e^2/b/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)*d^2-9*e*c/b^2/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)*d^3+4*c^2/b^3/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)*d^4-d^3/b^2*(e*x+d)^(1/2)/x-7*e*d^(5/2)/b^2*arctanh((e*x+d)^(1/2)/d^(1/2))+4*d^(7/2)/b^3*arctanh((e*x+d)^(1/2)/d^(1/2))*c","B"
371,1,313,139,0.069000," ","int((e*x+d)^(5/2)/(c*x^2+b*x)^2,x)","\frac{2 d \,e^{2} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\sqrt{\left(b e -c d \right) c}\, b}-\frac{7 c \,d^{2} e \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\sqrt{\left(b e -c d \right) c}\, b^{2}}+\frac{4 c^{2} d^{3} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\sqrt{\left(b e -c d \right) c}\, b^{3}}+\frac{e^{3} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\sqrt{\left(b e -c d \right) c}\, c}+\frac{2 \sqrt{e x +d}\, d \,e^{2}}{\left(c e x +b e \right) b}-\frac{\sqrt{e x +d}\, c \,d^{2} e}{\left(c e x +b e \right) b^{2}}-\frac{\sqrt{e x +d}\, e^{3}}{\left(c e x +b e \right) c}-\frac{5 d^{\frac{3}{2}} e \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{b^{2}}+\frac{4 c \,d^{\frac{5}{2}} \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{b^{3}}-\frac{\sqrt{e x +d}\, d^{2}}{b^{2} x}"," ",0,"-e^3/c*(e*x+d)^(1/2)/(c*e*x+b*e)+2*e^2/b*(e*x+d)^(1/2)/(c*e*x+b*e)*d-e/b^2*c*(e*x+d)^(1/2)/(c*e*x+b*e)*d^2+e^3/c/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)+2*e^2/b/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)*d-7*e/b^2*c/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)*d^2+4/b^3/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)*d^3*c^2-d^2/b^2*(e*x+d)^(1/2)/x-5*e*d^(3/2)/b^2*arctanh((e*x+d)^(1/2)/d^(1/2))+4*d^(5/2)/b^3*arctanh((e*x+d)^(1/2)/d^(1/2))*c","B"
372,1,237,116,0.069000," ","int((e*x+d)^(3/2)/(c*x^2+b*x)^2,x)","\frac{e^{2} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\sqrt{\left(b e -c d \right) c}\, b}-\frac{5 c d e \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\sqrt{\left(b e -c d \right) c}\, b^{2}}+\frac{4 c^{2} d^{2} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\sqrt{\left(b e -c d \right) c}\, b^{3}}+\frac{\sqrt{e x +d}\, e^{2}}{\left(c e x +b e \right) b}-\frac{\sqrt{e x +d}\, c d e}{\left(c e x +b e \right) b^{2}}-\frac{3 \sqrt{d}\, e \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{b^{2}}+\frac{4 c \,d^{\frac{3}{2}} \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{b^{3}}-\frac{\sqrt{e x +d}\, d}{b^{2} x}"," ",0,"e^2/b*(e*x+d)^(1/2)/(c*e*x+b*e)-e/b^2*(e*x+d)^(1/2)/(c*e*x+b*e)*c*d+e^2/b/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)-5*e/b^2/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)*c*d+4/b^3/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)*c^2*d^2-d/b^2*(e*x+d)^(1/2)/x-3*e*d^(1/2)/b^2*arctanh((e*x+d)^(1/2)/d^(1/2))+4*d^(3/2)/b^3*arctanh((e*x+d)^(1/2)/d^(1/2))*c","B"
373,1,167,107,0.069000," ","int((e*x+d)^(1/2)/(c*x^2+b*x)^2,x)","-\frac{3 c e \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\sqrt{\left(b e -c d \right) c}\, b^{2}}+\frac{4 c^{2} d \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\sqrt{\left(b e -c d \right) c}\, b^{3}}-\frac{\sqrt{e x +d}\, c e}{\left(c e x +b e \right) b^{2}}-\frac{e \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{b^{2} \sqrt{d}}+\frac{4 c \sqrt{d}\, \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{b^{3}}-\frac{\sqrt{e x +d}}{b^{2} x}"," ",0,"-e/b^2*c*(e*x+d)^(1/2)/(c*e*x+b*e)-3*e/b^2*c/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)+4/b^3*c^2/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)*d-1/b^2*(e*x+d)^(1/2)/x-e/b^2/d^(1/2)*arctanh((e*x+d)^(1/2)/d^(1/2))+4/b^3*d^(1/2)*arctanh((e*x+d)^(1/2)/d^(1/2))*c","A"
374,1,202,136,0.058000," ","int(1/(e*x+d)^(1/2)/(c*x^2+b*x)^2,x)","\frac{5 c^{2} e \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\left(b e -c d \right) \sqrt{\left(b e -c d \right) c}\, b^{2}}-\frac{4 c^{3} d \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\left(b e -c d \right) \sqrt{\left(b e -c d \right) c}\, b^{3}}+\frac{\sqrt{e x +d}\, c^{2} e}{\left(b e -c d \right) \left(c e x +b e \right) b^{2}}+\frac{e \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{b^{2} d^{\frac{3}{2}}}+\frac{4 c \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{b^{3} \sqrt{d}}-\frac{\sqrt{e x +d}}{b^{2} d x}"," ",0,"e/b^2*c^2/(b*e-c*d)*(e*x+d)^(1/2)/(c*e*x+b*e)+5*e/b^2*c^2/(b*e-c*d)/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)-4/b^3*c^3/(b*e-c*d)/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)*d-1/b^2/d*(e*x+d)^(1/2)/x+e/b^2/d^(3/2)*arctanh((e*x+d)^(1/2)/d^(1/2))+4/b^3/d^(1/2)*arctanh((e*x+d)^(1/2)/d^(1/2))*c","A"
375,1,229,187,0.078000," ","int(1/(e*x+d)^(3/2)/(c*x^2+b*x)^2,x)","-\frac{7 c^{3} e \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\left(b e -c d \right)^{2} \sqrt{\left(b e -c d \right) c}\, b^{2}}+\frac{4 c^{4} d \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\left(b e -c d \right)^{2} \sqrt{\left(b e -c d \right) c}\, b^{3}}-\frac{\sqrt{e x +d}\, c^{3} e}{\left(b e -c d \right)^{2} \left(c e x +b e \right) b^{2}}-\frac{2 e^{3}}{\left(b e -c d \right)^{2} \sqrt{e x +d}\, d^{2}}+\frac{3 e \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{b^{2} d^{\frac{5}{2}}}+\frac{4 c \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{b^{3} d^{\frac{3}{2}}}-\frac{\sqrt{e x +d}}{b^{2} d^{2} x}"," ",0,"-e*c^3/b^2/(b*e-c*d)^2*(e*x+d)^(1/2)/(c*e*x+b*e)-7*e*c^3/b^2/(b*e-c*d)^2/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)+4*c^4/b^3/(b*e-c*d)^2/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)*d-1/b^2/d^2*(e*x+d)^(1/2)/x+3*e/b^2/d^(5/2)*arctanh((e*x+d)^(1/2)/d^(1/2))+4/b^3/d^(3/2)*arctanh((e*x+d)^(1/2)/d^(1/2))*c-2*e^3/(b*e-c*d)^2/d^2/(e*x+d)^(1/2)","A"
376,1,280,244,0.074000," ","int(1/(e*x+d)^(5/2)/(c*x^2+b*x)^2,x)","\frac{9 c^{4} e \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\left(b e -c d \right)^{3} \sqrt{\left(b e -c d \right) c}\, b^{2}}-\frac{4 c^{5} d \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\left(b e -c d \right)^{3} \sqrt{\left(b e -c d \right) c}\, b^{3}}+\frac{\sqrt{e x +d}\, c^{4} e}{\left(b e -c d \right)^{3} \left(c e x +b e \right) b^{2}}-\frac{4 b \,e^{4}}{\left(b e -c d \right)^{3} \sqrt{e x +d}\, d^{3}}+\frac{8 c \,e^{3}}{\left(b e -c d \right)^{3} \sqrt{e x +d}\, d^{2}}-\frac{2 e^{3}}{3 \left(b e -c d \right)^{2} \left(e x +d \right)^{\frac{3}{2}} d^{2}}+\frac{5 e \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{b^{2} d^{\frac{7}{2}}}+\frac{4 c \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{b^{3} d^{\frac{5}{2}}}-\frac{\sqrt{e x +d}}{b^{2} d^{3} x}"," ",0,"e*c^4/b^2/(b*e-c*d)^3*(e*x+d)^(1/2)/(c*e*x+b*e)+9*e*c^4/b^2/(b*e-c*d)^3/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)-4*c^5/b^3/(b*e-c*d)^3/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)*d-1/b^2/d^3*(e*x+d)^(1/2)/x+5*e/b^2/d^(7/2)*arctanh((e*x+d)^(1/2)/d^(1/2))+4/b^3/d^(5/2)*arctanh((e*x+d)^(1/2)/d^(1/2))*c-2/3*e^3/(b*e-c*d)^2/d^2/(e*x+d)^(3/2)-4*e^4/(b*e-c*d)^3/d^3/(e*x+d)^(1/2)*b+8*e^3/(b*e-c*d)^3/d^2/(e*x+d)^(1/2)*c","A"
377,1,364,322,0.073000," ","int(1/(e*x+d)^(7/2)/(c*x^2+b*x)^2,x)","-\frac{11 c^{5} e \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\left(b e -c d \right)^{4} \sqrt{\left(b e -c d \right) c}\, b^{2}}+\frac{4 c^{6} d \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\left(b e -c d \right)^{4} \sqrt{\left(b e -c d \right) c}\, b^{3}}-\frac{\sqrt{e x +d}\, c^{5} e}{\left(b e -c d \right)^{4} \left(c e x +b e \right) b^{2}}-\frac{6 b^{2} e^{5}}{\left(b e -c d \right)^{4} \sqrt{e x +d}\, d^{4}}+\frac{20 b c \,e^{4}}{\left(b e -c d \right)^{4} \sqrt{e x +d}\, d^{3}}-\frac{20 c^{2} e^{3}}{\left(b e -c d \right)^{4} \sqrt{e x +d}\, d^{2}}-\frac{4 b \,e^{4}}{3 \left(b e -c d \right)^{3} \left(e x +d \right)^{\frac{3}{2}} d^{3}}+\frac{8 c \,e^{3}}{3 \left(b e -c d \right)^{3} \left(e x +d \right)^{\frac{3}{2}} d^{2}}-\frac{2 e^{3}}{5 \left(b e -c d \right)^{2} \left(e x +d \right)^{\frac{5}{2}} d^{2}}+\frac{7 e \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{b^{2} d^{\frac{9}{2}}}+\frac{4 c \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{b^{3} d^{\frac{7}{2}}}-\frac{\sqrt{e x +d}}{b^{2} d^{4} x}"," ",0,"-e*c^5/b^2/(b*e-c*d)^4*(e*x+d)^(1/2)/(c*e*x+b*e)-11*e*c^5/b^2/(b*e-c*d)^4/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)+4*c^6/b^3/(b*e-c*d)^4/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)*d-1/b^2/d^4*(e*x+d)^(1/2)/x+7*e/b^2/d^(9/2)*arctanh((e*x+d)^(1/2)/d^(1/2))+4/b^3/d^(7/2)*arctanh((e*x+d)^(1/2)/d^(1/2))*c-2/5*e^3/(b*e-c*d)^2/d^2/(e*x+d)^(5/2)-4/3*e^4/(b*e-c*d)^3/d^3/(e*x+d)^(3/2)*b+8/3*e^3/(b*e-c*d)^3/d^2/(e*x+d)^(3/2)*c-6*e^5/(b*e-c*d)^4/d^4/(e*x+d)^(1/2)*b^2+20*e^4/(b*e-c*d)^4/d^3/(e*x+d)^(1/2)*b*c-20*e^3/(b*e-c*d)^4/d^2/(e*x+d)^(1/2)*c^2","A"
378,1,703,268,0.079000," ","int((e*x+d)^(9/2)/(c*x^2+b*x)^3,x)","-\frac{3 \sqrt{e x +d}\, b \,e^{6}}{4 \left(c e x +b e \right)^{2} c^{2}}+\frac{15 \sqrt{e x +d}\, d^{2} e^{4}}{2 \left(c e x +b e \right)^{2} b}-\frac{15 \sqrt{e x +d}\, c \,d^{3} e^{3}}{\left(c e x +b e \right)^{2} b^{2}}+\frac{45 \sqrt{e x +d}\, c^{2} d^{4} e^{2}}{4 \left(c e x +b e \right)^{2} b^{3}}-\frac{3 \sqrt{e x +d}\, c^{3} d^{5} e}{\left(c e x +b e \right)^{2} b^{4}}+\frac{3 d \,e^{4} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{4 \sqrt{\left(b e -c d \right) c}\, b c}+\frac{3 \left(e x +d \right)^{\frac{3}{2}} d \,e^{4}}{4 \left(c e x +b e \right)^{2} b}+\frac{21 \left(e x +d \right)^{\frac{3}{2}} c \,d^{2} e^{3}}{4 \left(c e x +b e \right)^{2} b^{2}}+\frac{21 d^{2} e^{3} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{4 \sqrt{\left(b e -c d \right) c}\, b^{2}}-\frac{31 \left(e x +d \right)^{\frac{3}{2}} c^{2} d^{3} e^{2}}{4 \left(c e x +b e \right)^{2} b^{3}}-\frac{111 c \,d^{3} e^{2} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{4 \sqrt{\left(b e -c d \right) c}\, b^{3}}+\frac{3 \left(e x +d \right)^{\frac{3}{2}} c^{3} d^{4} e}{\left(c e x +b e \right)^{2} b^{4}}+\frac{33 c^{2} d^{4} e \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\sqrt{\left(b e -c d \right) c}\, b^{4}}-\frac{12 c^{3} d^{5} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\sqrt{\left(b e -c d \right) c}\, b^{5}}-\frac{5 \left(e x +d \right)^{\frac{3}{2}} e^{5}}{4 \left(c e x +b e \right)^{2} c}+\frac{3 e^{5} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{4 \sqrt{\left(b e -c d \right) c}\, c^{2}}-\frac{63 d^{\frac{5}{2}} e^{2} \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{4 b^{3}}+\frac{27 c \,d^{\frac{7}{2}} e \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{b^{4}}-\frac{12 c^{2} d^{\frac{9}{2}} \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{b^{5}}+\frac{15 \sqrt{e x +d}\, d^{4}}{4 b^{3} x^{2}}-\frac{3 \sqrt{e x +d}\, c \,d^{5}}{b^{4} e \,x^{2}}-\frac{17 \left(e x +d \right)^{\frac{3}{2}} d^{3}}{4 b^{3} x^{2}}+\frac{3 \left(e x +d \right)^{\frac{3}{2}} c \,d^{4}}{b^{4} e \,x^{2}}"," ",0,"-5/4*e^5/(c*e*x+b*e)^2/c*(e*x+d)^(3/2)-3/4*e^6*b/(c*e*x+b*e)^2/c^2*(e*x+d)^(1/2)+3/4*e^5/c^2/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)-111/4*e^2/b^3*c/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)*d^3+33*e/b^4*c^2/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)*d^4+21/4*e^3/b^2/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)*d^2-3*e/b^4/(c*e*x+b*e)^2*(e*x+d)^(1/2)*d^5*c^3+3/4*e^4/b/c/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)*d+45/4*e^2/b^3/(c*e*x+b*e)^2*c^2*(e*x+d)^(1/2)*d^4+3/4*e^4/b/(c*e*x+b*e)^2*(e*x+d)^(3/2)*d+21/4*e^3/b^2/(c*e*x+b*e)^2*c*(e*x+d)^(3/2)*d^2-31/4*e^2/b^3/(c*e*x+b*e)^2*c^2*(e*x+d)^(3/2)*d^3+3*e/b^4/(c*e*x+b*e)^2*(e*x+d)^(3/2)*d^4*c^3+15/2*e^4/b/(c*e*x+b*e)^2*(e*x+d)^(1/2)*d^2-15*e^3/b^2/(c*e*x+b*e)^2*c*(e*x+d)^(1/2)*d^3-12/b^5/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)*d^5*c^3-17/4*d^3/b^3/x^2*(e*x+d)^(3/2)+3/e*d^4/b^4/x^2*(e*x+d)^(3/2)*c+15/4*d^4/b^3/x^2*(e*x+d)^(1/2)-3/e*d^5/b^4/x^2*(e*x+d)^(1/2)*c-63/4*e^2*d^(5/2)/b^3*arctanh((e*x+d)^(1/2)/d^(1/2))+27*e*d^(7/2)/b^4*arctanh((e*x+d)^(1/2)/d^(1/2))*c-12*d^(9/2)/b^5*arctanh((e*x+d)^(1/2)/d^(1/2))*c^2","B"
379,1,627,220,0.063000," ","int((e*x+d)^(7/2)/(c*x^2+b*x)^3,x)","\frac{15 \sqrt{e x +d}\, d \,e^{4}}{4 \left(c e x +b e \right)^{2} b}-\frac{39 \sqrt{e x +d}\, c \,d^{2} e^{3}}{4 \left(c e x +b e \right)^{2} b^{2}}+\frac{37 \sqrt{e x +d}\, c^{2} d^{3} e^{2}}{4 \left(c e x +b e \right)^{2} b^{3}}-\frac{3 \sqrt{e x +d}\, c^{3} d^{4} e}{\left(c e x +b e \right)^{2} b^{4}}-\frac{\sqrt{e x +d}\, e^{5}}{4 \left(c e x +b e \right)^{2} c}+\frac{e^{4} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{4 \sqrt{\left(b e -c d \right) c}\, b c}+\frac{\left(e x +d \right)^{\frac{3}{2}} e^{4}}{4 \left(c e x +b e \right)^{2} b}+\frac{5 \left(e x +d \right)^{\frac{3}{2}} c d \,e^{3}}{2 \left(c e x +b e \right)^{2} b^{2}}+\frac{5 d \,e^{3} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{2 \sqrt{\left(b e -c d \right) c}\, b^{2}}-\frac{23 \left(e x +d \right)^{\frac{3}{2}} c^{2} d^{2} e^{2}}{4 \left(c e x +b e \right)^{2} b^{3}}-\frac{71 c \,d^{2} e^{2} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{4 \sqrt{\left(b e -c d \right) c}\, b^{3}}+\frac{3 \left(e x +d \right)^{\frac{3}{2}} c^{3} d^{3} e}{\left(c e x +b e \right)^{2} b^{4}}+\frac{27 c^{2} d^{3} e \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\sqrt{\left(b e -c d \right) c}\, b^{4}}-\frac{12 c^{3} d^{4} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\sqrt{\left(b e -c d \right) c}\, b^{5}}-\frac{35 d^{\frac{3}{2}} e^{2} \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{4 b^{3}}+\frac{21 c \,d^{\frac{5}{2}} e \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{b^{4}}-\frac{12 c^{2} d^{\frac{7}{2}} \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{b^{5}}+\frac{11 \sqrt{e x +d}\, d^{3}}{4 b^{3} x^{2}}-\frac{3 \sqrt{e x +d}\, c \,d^{4}}{b^{4} e \,x^{2}}-\frac{13 \left(e x +d \right)^{\frac{3}{2}} d^{2}}{4 b^{3} x^{2}}+\frac{3 \left(e x +d \right)^{\frac{3}{2}} c \,d^{3}}{b^{4} e \,x^{2}}"," ",0,"1/4*e^4/b/(c*e*x+b*e)^2*(e*x+d)^(3/2)+5/2*e^3/b^2/(c*e*x+b*e)^2*(e*x+d)^(3/2)*c*d-23/4*e^2/b^3/(c*e*x+b*e)^2*(e*x+d)^(3/2)*c^2*d^2+3*e/b^4/(c*e*x+b*e)^2*(e*x+d)^(3/2)*c^3*d^3-1/4*e^5/(c*e*x+b*e)^2/c*(e*x+d)^(1/2)+15/4*e^4/b/(c*e*x+b*e)^2*(e*x+d)^(1/2)*d-39/4*e^3/b^2/(c*e*x+b*e)^2*c*(e*x+d)^(1/2)*d^2+37/4*e^2/b^3/(c*e*x+b*e)^2*(e*x+d)^(1/2)*d^3*c^2-3*e/b^4/(c*e*x+b*e)^2*c^3*(e*x+d)^(1/2)*d^4+1/4*e^4/b/c/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)+5/2*e^3/b^2/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)*d-71/4*e^2/b^3*c/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)*d^2+27*e/b^4/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)*d^3*c^2-12/b^5*c^3/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)*d^4-13/4*d^2/b^3/x^2*(e*x+d)^(3/2)+3/e*d^3/b^4/x^2*(e*x+d)^(3/2)*c+11/4*d^3/b^3/x^2*(e*x+d)^(1/2)-3/e*d^4/b^4/x^2*c*(e*x+d)^(1/2)-35/4*e^2*d^(3/2)/b^3*arctanh((e*x+d)^(1/2)/d^(1/2))+21*e*d^(5/2)/b^4*arctanh((e*x+d)^(1/2)/d^(1/2))*c-12*d^(7/2)/b^5*arctanh((e*x+d)^(1/2)/d^(1/2))*c^2","B"
380,1,521,204,0.067000," ","int((e*x+d)^(5/2)/(c*x^2+b*x)^3,x)","\frac{5 \sqrt{e x +d}\, e^{4}}{4 \left(c e x +b e \right)^{2} b}-\frac{11 \sqrt{e x +d}\, c d \,e^{3}}{2 \left(c e x +b e \right)^{2} b^{2}}+\frac{29 \sqrt{e x +d}\, c^{2} d^{2} e^{2}}{4 \left(c e x +b e \right)^{2} b^{3}}-\frac{3 \sqrt{e x +d}\, c^{3} d^{3} e}{\left(c e x +b e \right)^{2} b^{4}}+\frac{3 \left(e x +d \right)^{\frac{3}{2}} c \,e^{3}}{4 \left(c e x +b e \right)^{2} b^{2}}+\frac{3 e^{3} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{4 \sqrt{\left(b e -c d \right) c}\, b^{2}}-\frac{15 \left(e x +d \right)^{\frac{3}{2}} c^{2} d \,e^{2}}{4 \left(c e x +b e \right)^{2} b^{3}}-\frac{39 c d \,e^{2} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{4 \sqrt{\left(b e -c d \right) c}\, b^{3}}+\frac{3 \left(e x +d \right)^{\frac{3}{2}} c^{3} d^{2} e}{\left(c e x +b e \right)^{2} b^{4}}+\frac{21 c^{2} d^{2} e \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\sqrt{\left(b e -c d \right) c}\, b^{4}}-\frac{12 c^{3} d^{3} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\sqrt{\left(b e -c d \right) c}\, b^{5}}-\frac{15 \sqrt{d}\, e^{2} \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{4 b^{3}}+\frac{15 c \,d^{\frac{3}{2}} e \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{b^{4}}-\frac{12 c^{2} d^{\frac{5}{2}} \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{b^{5}}+\frac{7 \sqrt{e x +d}\, d^{2}}{4 b^{3} x^{2}}-\frac{3 \sqrt{e x +d}\, c \,d^{3}}{b^{4} e \,x^{2}}-\frac{9 \left(e x +d \right)^{\frac{3}{2}} d}{4 b^{3} x^{2}}+\frac{3 \left(e x +d \right)^{\frac{3}{2}} c \,d^{2}}{b^{4} e \,x^{2}}"," ",0,"3/4*e^3/b^2/(c*e*x+b*e)^2*(e*x+d)^(3/2)*c-15/4*e^2/b^3/(c*e*x+b*e)^2*(e*x+d)^(3/2)*c^2*d+3*e/b^4/(c*e*x+b*e)^2*(e*x+d)^(3/2)*d^2*c^3+5/4*e^4/b/(c*e*x+b*e)^2*(e*x+d)^(1/2)-11/2*e^3/b^2/(c*e*x+b*e)^2*(e*x+d)^(1/2)*c*d+29/4*e^2/b^3/(c*e*x+b*e)^2*(e*x+d)^(1/2)*c^2*d^2-3*e/b^4/(c*e*x+b*e)^2*(e*x+d)^(1/2)*c^3*d^3+3/4*e^3/b^2/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)-39/4*e^2/b^3/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)*c*d+21*e/b^4/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)*c^2*d^2-12/b^5/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)*c^3*d^3-9/4*d/b^3/x^2*(e*x+d)^(3/2)+3/e*d^2/b^4/x^2*(e*x+d)^(3/2)*c+7/4*d^2/b^3/x^2*(e*x+d)^(1/2)-3/e*d^3/b^4/x^2*(e*x+d)^(1/2)*c-15/4*e^2*d^(1/2)/b^3*arctanh((e*x+d)^(1/2)/d^(1/2))+15*e*d^(3/2)/b^4*arctanh((e*x+d)^(1/2)/d^(1/2))*c-12*d^(5/2)/b^5*arctanh((e*x+d)^(1/2)/d^(1/2))*c^2","B"
381,1,414,218,0.061000," ","int((e*x+d)^(3/2)/(c*x^2+b*x)^3,x)","-\frac{9 \sqrt{e x +d}\, c \,e^{3}}{4 \left(c e x +b e \right)^{2} b^{2}}+\frac{21 \sqrt{e x +d}\, c^{2} d \,e^{2}}{4 \left(c e x +b e \right)^{2} b^{3}}-\frac{3 \sqrt{e x +d}\, c^{3} d^{2} e}{\left(c e x +b e \right)^{2} b^{4}}-\frac{7 \left(e x +d \right)^{\frac{3}{2}} c^{2} e^{2}}{4 \left(c e x +b e \right)^{2} b^{3}}-\frac{15 c \,e^{2} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{4 \sqrt{\left(b e -c d \right) c}\, b^{3}}+\frac{3 \left(e x +d \right)^{\frac{3}{2}} c^{3} d e}{\left(c e x +b e \right)^{2} b^{4}}+\frac{15 c^{2} d e \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\sqrt{\left(b e -c d \right) c}\, b^{4}}-\frac{12 c^{3} d^{2} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\sqrt{\left(b e -c d \right) c}\, b^{5}}-\frac{3 e^{2} \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{4 b^{3} \sqrt{d}}+\frac{9 c \sqrt{d}\, e \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{b^{4}}-\frac{12 c^{2} d^{\frac{3}{2}} \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{b^{5}}+\frac{3 \sqrt{e x +d}\, d}{4 b^{3} x^{2}}-\frac{3 \sqrt{e x +d}\, c \,d^{2}}{b^{4} e \,x^{2}}-\frac{5 \left(e x +d \right)^{\frac{3}{2}}}{4 b^{3} x^{2}}+\frac{3 \left(e x +d \right)^{\frac{3}{2}} c d}{b^{4} e \,x^{2}}"," ",0,"-7/4*e^2*c^2/b^3/(c*e*x+b*e)^2*(e*x+d)^(3/2)+3*e*c^3/b^4/(c*e*x+b*e)^2*(e*x+d)^(3/2)*d-9/4*e^3*c/b^2/(c*e*x+b*e)^2*(e*x+d)^(1/2)+21/4*e^2*c^2/b^3/(c*e*x+b*e)^2*(e*x+d)^(1/2)*d-3*e*c^3/b^4/(c*e*x+b*e)^2*(e*x+d)^(1/2)*d^2-15/4*e^2*c/b^3/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)+15*e*c^2/b^4/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)*d-12*c^3/b^5/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)*d^2-5/4/b^3/x^2*(e*x+d)^(3/2)+3/e/b^4/x^2*(e*x+d)^(3/2)*c*d-3/e/b^4/x^2*(e*x+d)^(1/2)*c*d^2+3/4/b^3/x^2*(e*x+d)^(1/2)*d-3/4*e^2/b^3/d^(1/2)*arctanh((e*x+d)^(1/2)/d^(1/2))+9*e/b^4*d^(1/2)*arctanh((e*x+d)^(1/2)/d^(1/2))*c-12/b^5*d^(3/2)*arctanh((e*x+d)^(1/2)/d^(1/2))*c^2","A"
382,1,436,217,0.211000," ","int((e*x+d)^(1/2)/(c*x^2+b*x)^3,x)","\frac{11 \left(e x +d \right)^{\frac{3}{2}} c^{3} e^{2}}{4 \left(c e x +b e \right)^{2} \left(b e -c d \right) b^{3}}+\frac{35 c^{2} e^{2} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{4 \left(b e -c d \right) \sqrt{\left(b e -c d \right) c}\, b^{3}}-\frac{3 \left(e x +d \right)^{\frac{3}{2}} c^{4} d e}{\left(c e x +b e \right)^{2} \left(b e -c d \right) b^{4}}-\frac{21 c^{3} d e \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\left(b e -c d \right) \sqrt{\left(b e -c d \right) c}\, b^{4}}+\frac{12 c^{4} d^{2} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\left(b e -c d \right) \sqrt{\left(b e -c d \right) c}\, b^{5}}+\frac{13 \sqrt{e x +d}\, c^{2} e^{2}}{4 \left(c e x +b e \right)^{2} b^{3}}-\frac{3 \sqrt{e x +d}\, c^{3} d e}{\left(c e x +b e \right)^{2} b^{4}}+\frac{e^{2} \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{4 b^{3} d^{\frac{3}{2}}}+\frac{3 c e \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{b^{4} \sqrt{d}}-\frac{12 c^{2} \sqrt{d}\, \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{b^{5}}-\frac{\sqrt{e x +d}}{4 b^{3} x^{2}}-\frac{3 \sqrt{e x +d}\, c d}{b^{4} e \,x^{2}}-\frac{\left(e x +d \right)^{\frac{3}{2}}}{4 b^{3} d \,x^{2}}+\frac{3 \left(e x +d \right)^{\frac{3}{2}} c}{b^{4} e \,x^{2}}"," ",0,"11/4*e^2/b^3*c^3/(c*e*x+b*e)^2/(b*e-c*d)*(e*x+d)^(3/2)-3*e/b^4*c^4/(c*e*x+b*e)^2/(b*e-c*d)*(e*x+d)^(3/2)*d+13/4*e^2/b^3*c^2/(c*e*x+b*e)^2*(e*x+d)^(1/2)-3*e/b^4*c^3/(c*e*x+b*e)^2*(e*x+d)^(1/2)*d+35/4*e^2/b^3*c^2/(b*e-c*d)/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)-21*e/b^4*c^3/(b*e-c*d)/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)*d+12/b^5*c^4/(b*e-c*d)/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)*d^2-1/4/b^3/x^2/d*(e*x+d)^(3/2)+3/e/b^4/x^2*(e*x+d)^(3/2)*c-3/e/b^4/x^2*(e*x+d)^(1/2)*c*d-1/4/b^3/x^2*(e*x+d)^(1/2)+1/4*e^2/b^3/d^(3/2)*arctanh((e*x+d)^(1/2)/d^(1/2))+3*e/b^4/d^(1/2)*arctanh((e*x+d)^(1/2)/d^(1/2))*c-12/b^5*d^(1/2)*arctanh((e*x+d)^(1/2)/d^(1/2))*c^2","B"
383,1,526,271,0.086000," ","int(1/(e*x+d)^(1/2)/(c*x^2+b*x)^3,x)","-\frac{15 \left(e x +d \right)^{\frac{3}{2}} c^{4} e^{2}}{4 \left(c e x +b e \right)^{2} \left(b^{2} e^{2}-2 b c d e +c^{2} d^{2}\right) b^{3}}-\frac{63 c^{3} e^{2} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{4 \left(b^{2} e^{2}-2 b c d e +c^{2} d^{2}\right) \sqrt{\left(b e -c d \right) c}\, b^{3}}+\frac{3 \left(e x +d \right)^{\frac{3}{2}} c^{5} d e}{\left(c e x +b e \right)^{2} \left(b^{2} e^{2}-2 b c d e +c^{2} d^{2}\right) b^{4}}+\frac{27 c^{4} d e \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\left(b^{2} e^{2}-2 b c d e +c^{2} d^{2}\right) \sqrt{\left(b e -c d \right) c}\, b^{4}}-\frac{12 c^{5} d^{2} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\left(b^{2} e^{2}-2 b c d e +c^{2} d^{2}\right) \sqrt{\left(b e -c d \right) c}\, b^{5}}-\frac{17 \sqrt{e x +d}\, c^{3} e^{2}}{4 \left(c e x +b e \right)^{2} \left(b e -c d \right) b^{3}}+\frac{3 \sqrt{e x +d}\, c^{4} d e}{\left(c e x +b e \right)^{2} \left(b e -c d \right) b^{4}}-\frac{3 e^{2} \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{4 b^{3} d^{\frac{5}{2}}}-\frac{3 c e \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{b^{4} d^{\frac{3}{2}}}-\frac{12 c^{2} \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{b^{5} \sqrt{d}}-\frac{5 \sqrt{e x +d}}{4 b^{3} d \,x^{2}}-\frac{3 \sqrt{e x +d}\, c}{b^{4} e \,x^{2}}+\frac{3 \left(e x +d \right)^{\frac{3}{2}}}{4 b^{3} d^{2} x^{2}}+\frac{3 \left(e x +d \right)^{\frac{3}{2}} c}{b^{4} d e \,x^{2}}"," ",0,"-15/4*e^2/b^3*c^4/(c*e*x+b*e)^2/(b^2*e^2-2*b*c*d*e+c^2*d^2)*(e*x+d)^(3/2)+3*e/b^4*c^5/(c*e*x+b*e)^2/(b^2*e^2-2*b*c*d*e+c^2*d^2)*(e*x+d)^(3/2)*d-17/4*e^2/b^3*c^3/(c*e*x+b*e)^2/(b*e-c*d)*(e*x+d)^(1/2)+3*e/b^4*c^4/(c*e*x+b*e)^2/(b*e-c*d)*(e*x+d)^(1/2)*d-63/4*e^2/b^3*c^3/(b^2*e^2-2*b*c*d*e+c^2*d^2)/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)+27*e/b^4*c^4/(b^2*e^2-2*b*c*d*e+c^2*d^2)/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)*d-12/b^5*c^5/(b^2*e^2-2*b*c*d*e+c^2*d^2)/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)*d^2+3/4/b^3/x^2/d^2*(e*x+d)^(3/2)+3/e/b^4/x^2/d*(e*x+d)^(3/2)*c-5/4/b^3/x^2/d*(e*x+d)^(1/2)-3/e/b^4/x^2*(e*x+d)^(1/2)*c-3/4*e^2/b^3/d^(5/2)*arctanh((e*x+d)^(1/2)/d^(1/2))-3*e/b^4/d^(3/2)*arctanh((e*x+d)^(1/2)/d^(1/2))*c-12/b^5/d^(1/2)*arctanh((e*x+d)^(1/2)/d^(1/2))*c^2","A"
384,1,530,340,0.071000," ","int(1/(e*x+d)^(3/2)/(c*x^2+b*x)^3,x)","\frac{21 \sqrt{e x +d}\, c^{4} e^{3}}{4 \left(b e -c d \right)^{3} \left(c e x +b e \right)^{2} b^{2}}-\frac{33 \sqrt{e x +d}\, c^{5} d \,e^{2}}{4 \left(b e -c d \right)^{3} \left(c e x +b e \right)^{2} b^{3}}+\frac{3 \sqrt{e x +d}\, c^{6} d^{2} e}{\left(b e -c d \right)^{3} \left(c e x +b e \right)^{2} b^{4}}+\frac{19 \left(e x +d \right)^{\frac{3}{2}} c^{5} e^{2}}{4 \left(b e -c d \right)^{3} \left(c e x +b e \right)^{2} b^{3}}+\frac{99 c^{4} e^{2} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{4 \left(b e -c d \right)^{3} \sqrt{\left(b e -c d \right) c}\, b^{3}}-\frac{3 \left(e x +d \right)^{\frac{3}{2}} c^{6} d e}{\left(b e -c d \right)^{3} \left(c e x +b e \right)^{2} b^{4}}-\frac{33 c^{5} d e \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\left(b e -c d \right)^{3} \sqrt{\left(b e -c d \right) c}\, b^{4}}+\frac{12 c^{6} d^{2} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\left(b e -c d \right)^{3} \sqrt{\left(b e -c d \right) c}\, b^{5}}+\frac{2 e^{5}}{\left(b e -c d \right)^{3} \sqrt{e x +d}\, d^{3}}-\frac{15 e^{2} \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{4 b^{3} d^{\frac{7}{2}}}-\frac{9 c e \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{b^{4} d^{\frac{5}{2}}}-\frac{12 c^{2} \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{b^{5} d^{\frac{3}{2}}}-\frac{9 \sqrt{e x +d}}{4 b^{3} d^{2} x^{2}}-\frac{3 \sqrt{e x +d}\, c}{b^{4} d e \,x^{2}}+\frac{7 \left(e x +d \right)^{\frac{3}{2}}}{4 b^{3} d^{3} x^{2}}+\frac{3 \left(e x +d \right)^{\frac{3}{2}} c}{b^{4} d^{2} e \,x^{2}}"," ",0,"19/4*e^2*c^5/b^3/(b*e-c*d)^3/(c*e*x+b*e)^2*(e*x+d)^(3/2)-3*e*c^6/b^4/(b*e-c*d)^3/(c*e*x+b*e)^2*(e*x+d)^(3/2)*d+21/4*e^3*c^4/b^2/(b*e-c*d)^3/(c*e*x+b*e)^2*(e*x+d)^(1/2)-33/4*e^2*c^5/b^3/(b*e-c*d)^3/(c*e*x+b*e)^2*(e*x+d)^(1/2)*d+3*e*c^6/b^4/(b*e-c*d)^3/(c*e*x+b*e)^2*(e*x+d)^(1/2)*d^2+99/4*e^2*c^4/b^3/(b*e-c*d)^3/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)-33*e*c^5/b^4/(b*e-c*d)^3/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)*d+12*c^6/b^5/(b*e-c*d)^3/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)*d^2+7/4/b^3/d^3/x^2*(e*x+d)^(3/2)+3/e/b^4/d^2/x^2*(e*x+d)^(3/2)*c-9/4/b^3/d^2/x^2*(e*x+d)^(1/2)-3/e/b^4/d/x^2*(e*x+d)^(1/2)*c-15/4*e^2/b^3/d^(7/2)*arctanh((e*x+d)^(1/2)/d^(1/2))-9*e/b^4/d^(5/2)*arctanh((e*x+d)^(1/2)/d^(1/2))*c-12/b^5/d^(3/2)*arctanh((e*x+d)^(1/2)/d^(1/2))*c^2+2*e^5/(b*e-c*d)^3/d^3/(e*x+d)^(1/2)","A"
385,1,582,436,0.086000," ","int(1/(e*x+d)^(5/2)/(c*x^2+b*x)^3,x)","-\frac{25 \sqrt{e x +d}\, c^{5} e^{3}}{4 \left(b e -c d \right)^{4} \left(c e x +b e \right)^{2} b^{2}}+\frac{37 \sqrt{e x +d}\, c^{6} d \,e^{2}}{4 \left(b e -c d \right)^{4} \left(c e x +b e \right)^{2} b^{3}}-\frac{3 \sqrt{e x +d}\, c^{7} d^{2} e}{\left(b e -c d \right)^{4} \left(c e x +b e \right)^{2} b^{4}}-\frac{23 \left(e x +d \right)^{\frac{3}{2}} c^{6} e^{2}}{4 \left(b e -c d \right)^{4} \left(c e x +b e \right)^{2} b^{3}}-\frac{143 c^{5} e^{2} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{4 \left(b e -c d \right)^{4} \sqrt{\left(b e -c d \right) c}\, b^{3}}+\frac{3 \left(e x +d \right)^{\frac{3}{2}} c^{7} d e}{\left(b e -c d \right)^{4} \left(c e x +b e \right)^{2} b^{4}}+\frac{39 c^{6} d e \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\left(b e -c d \right)^{4} \sqrt{\left(b e -c d \right) c}\, b^{4}}-\frac{12 c^{7} d^{2} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(b e -c d \right) c}}\right)}{\left(b e -c d \right)^{4} \sqrt{\left(b e -c d \right) c}\, b^{5}}+\frac{6 b \,e^{6}}{\left(b e -c d \right)^{4} \sqrt{e x +d}\, d^{4}}-\frac{12 c \,e^{5}}{\left(b e -c d \right)^{4} \sqrt{e x +d}\, d^{3}}+\frac{2 e^{5}}{3 \left(b e -c d \right)^{3} \left(e x +d \right)^{\frac{3}{2}} d^{3}}-\frac{35 e^{2} \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{4 b^{3} d^{\frac{9}{2}}}-\frac{15 c e \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{b^{4} d^{\frac{7}{2}}}-\frac{12 c^{2} \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{b^{5} d^{\frac{5}{2}}}-\frac{13 \sqrt{e x +d}}{4 b^{3} d^{3} x^{2}}-\frac{3 \sqrt{e x +d}\, c}{b^{4} d^{2} e \,x^{2}}+\frac{11 \left(e x +d \right)^{\frac{3}{2}}}{4 b^{3} d^{4} x^{2}}+\frac{3 \left(e x +d \right)^{\frac{3}{2}} c}{b^{4} d^{3} e \,x^{2}}"," ",0,"-23/4*e^2*c^6/b^3/(b*e-c*d)^4/(c*e*x+b*e)^2*(e*x+d)^(3/2)+3*e*c^7/b^4/(b*e-c*d)^4/(c*e*x+b*e)^2*(e*x+d)^(3/2)*d-25/4*e^3*c^5/b^2/(b*e-c*d)^4/(c*e*x+b*e)^2*(e*x+d)^(1/2)+37/4*e^2*c^6/b^3/(b*e-c*d)^4/(c*e*x+b*e)^2*(e*x+d)^(1/2)*d-3*e*c^7/b^4/(b*e-c*d)^4/(c*e*x+b*e)^2*(e*x+d)^(1/2)*d^2-143/4*e^2*c^5/b^3/(b*e-c*d)^4/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)+39*e*c^6/b^4/(b*e-c*d)^4/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)*d-12*c^7/b^5/(b*e-c*d)^4/((b*e-c*d)*c)^(1/2)*arctan((e*x+d)^(1/2)/((b*e-c*d)*c)^(1/2)*c)*d^2+11/4/d^4/b^3/x^2*(e*x+d)^(3/2)+3/e/d^3/b^4/x^2*(e*x+d)^(3/2)*c-13/4/d^3/b^3/x^2*(e*x+d)^(1/2)-3/e/d^2/b^4/x^2*(e*x+d)^(1/2)*c-35/4*e^2/d^(9/2)/b^3*arctanh((e*x+d)^(1/2)/d^(1/2))-15*e/d^(7/2)/b^4*arctanh((e*x+d)^(1/2)/d^(1/2))*c-12/d^(5/2)/b^5*arctanh((e*x+d)^(1/2)/d^(1/2))*c^2+6*e^6/(b*e-c*d)^4/d^4/(e*x+d)^(1/2)*b-12*e^5/(b*e-c*d)^4/d^3/(e*x+d)^(1/2)*c+2/3*e^5/(b*e-c*d)^3/d^3/(e*x+d)^(3/2)","A"
386,1,920,308,0.169000," ","int((e*x+d)^(3/2)*(c*x^2+b*x)^(1/2),x)","-\frac{2 \sqrt{e x +d}\, \sqrt{\left(c x +b \right) x}\, \left(-15 c^{5} e^{4} x^{5}-18 b \,c^{4} e^{4} x^{4}-39 c^{5} d \,e^{3} x^{4}+b^{2} c^{3} e^{4} x^{3}-51 b \,c^{4} d \,e^{3} x^{3}-27 c^{5} d^{2} e^{2} x^{3}+4 b^{3} c^{2} e^{4} x^{2}-8 b^{2} c^{3} d \,e^{3} x^{2}-36 b \,c^{4} d^{2} e^{2} x^{2}-3 c^{5} d^{3} e \,x^{2}+8 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{5} e^{4} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-27 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{4} c d \,e^{3} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+4 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{4} c d \,e^{3} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+28 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c^{2} d^{2} e^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-10 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c^{2} d^{2} e^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+4 b^{3} c^{2} d \,e^{3} x -15 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{3} d^{3} e \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+12 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{3} d^{3} e \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-9 b^{2} c^{3} d^{2} e^{2} x +6 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{4} d^{4} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-6 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{4} d^{4} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-3 b \,c^{4} d^{3} e x \right)}{105 \left(c e \,x^{2}+b e x +c d x +b d \right) c^{4} e^{2} x}"," ",0,"-2/105*(e*x+d)^(1/2)*((c*x+b)*x)^(1/2)*(-15*x^5*c^5*e^4+4*((c*x+b)/b)^(1/2)*(-(e*x+d)*c/(b*e-c*d))^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(b*e/(b*e-c*d))^(1/2))*b^4*c*d*e^3-10*((c*x+b)/b)^(1/2)*(-(e*x+d)*c/(b*e-c*d))^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(b*e/(b*e-c*d))^(1/2))*b^3*c^2*d^2*e^2+12*((c*x+b)/b)^(1/2)*(-(e*x+d)*c/(b*e-c*d))^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(b*e/(b*e-c*d))^(1/2))*b^2*c^3*d^3*e-6*((c*x+b)/b)^(1/2)*(-(e*x+d)*c/(b*e-c*d))^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(b*e/(b*e-c*d))^(1/2))*b*c^4*d^4+8*((c*x+b)/b)^(1/2)*(-(e*x+d)*c/(b*e-c*d))^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(b*e/(b*e-c*d))^(1/2))*b^5*e^4-27*((c*x+b)/b)^(1/2)*(-(e*x+d)*c/(b*e-c*d))^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(b*e/(b*e-c*d))^(1/2))*b^4*c*d*e^3+28*((c*x+b)/b)^(1/2)*(-(e*x+d)*c/(b*e-c*d))^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(b*e/(b*e-c*d))^(1/2))*b^3*c^2*d^2*e^2-15*((c*x+b)/b)^(1/2)*(-(e*x+d)*c/(b*e-c*d))^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(b*e/(b*e-c*d))^(1/2))*b^2*c^3*d^3*e+6*((c*x+b)/b)^(1/2)*(-(e*x+d)*c/(b*e-c*d))^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(b*e/(b*e-c*d))^(1/2))*b*c^4*d^4-18*x^4*b*c^4*e^4-39*x^4*c^5*d*e^3+x^3*b^2*c^3*e^4-51*x^3*b*c^4*d*e^3-27*x^3*c^5*d^2*e^2+4*x^2*b^3*c^2*e^4-8*x^2*b^2*c^3*d*e^3-36*x^2*b*c^4*d^2*e^2-3*x^2*c^5*d^3*e+4*x*b^3*c^2*d*e^3-9*x*b^2*c^3*d^2*e^2-3*x*b*c^4*d^3*e)/e^2/x/(c*e*x^2+b*e*x+c*d*x+b*d)/c^4","B"
387,1,681,254,0.059000," ","int((e*x+d)^(1/2)*(c*x^2+b*x)^(1/2),x)","\frac{2 \sqrt{e x +d}\, \sqrt{\left(c x +b \right) x}\, \left(3 c^{4} e^{3} x^{4}+4 b \,c^{3} e^{3} x^{3}+4 c^{4} d \,e^{2} x^{3}+b^{2} c^{2} e^{3} x^{2}+5 b \,c^{3} d \,e^{2} x^{2}+c^{4} d^{2} e \,x^{2}+2 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{4} e^{3} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-4 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c d \,e^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+\sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c d \,e^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+4 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{2} d^{2} e \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-3 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{2} d^{2} e \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+b^{2} c^{2} d \,e^{2} x -2 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{3} d^{3} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+2 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{3} d^{3} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+b \,c^{3} d^{2} e x \right)}{15 \left(c e \,x^{2}+b e x +c d x +b d \right) c^{3} e^{2} x}"," ",0,"2/15*(e*x+d)^(1/2)*((c*x+b)*x)^(1/2)*(((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^3*c*d*e^2-3*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^2*c^2*d^2*e+2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b*c^3*d^3+2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^4*e^3-4*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^3*c*d*e^2+4*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^2*c^2*d^2*e-2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b*c^3*d^3+3*x^4*c^4*e^3+4*x^3*b*c^3*e^3+4*x^3*c^4*d*e^2+x^2*b^2*c^2*e^3+5*x^2*b*c^3*d*e^2+x^2*c^4*d^2*e+x*b^2*c^2*d*e^2+x*b*c^3*d^2*e)/x/(c*e*x^2+b*e*x+c*d*x+b*d)/c^3/e^2","B"
388,1,467,198,0.176000," ","int((c*x^2+b*x)^(1/2)/(e*x+d)^(1/2),x)","-\frac{2 \sqrt{\left(c x +b \right) x}\, \sqrt{e x +d}\, \left(-c^{3} e^{2} x^{3}-b \,c^{2} e^{2} x^{2}-c^{3} d e \,x^{2}+\sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} e^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-3 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c d e \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+2 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c d e \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+2 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{2} d^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-2 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{2} d^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-b \,c^{2} d e x \right)}{3 \left(c e \,x^{2}+b e x +c d x +b d \right) c^{2} e^{2} x}"," ",0,"-2/3*((c*x+b)*x)^(1/2)*(e*x+d)^(1/2)*(2*b^2*d*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*e*c-2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b*c^2*d^2+((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^3*e^2-3*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^2*c*d*e+2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b*c^2*d^2-x^3*c^3*e^2-x^2*b*c^2*e^2-x^2*c^3*d*e-x*b*c^2*d*e)/x/(c*e*x^2+b*e*x+c*d*x+b*d)/e^2/c^2","B"
389,1,353,189,0.152000," ","int((c*x^2+b*x)^(1/2)/(e*x+d)^(3/2),x)","\frac{2 \sqrt{\left(c x +b \right) x}\, \sqrt{e x +d}\, \left(-c^{2} e \,x^{2}-2 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} e \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+\sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} e \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+2 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b c d \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-2 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b c d \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-b c e x \right)}{\left(c e \,x^{2}+b e x +c d x +b d \right) c \,e^{2} x}"," ",0,"2*((c*x+b)*x)^(1/2)*(e*x+d)^(1/2)*(EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^2*e*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-2*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b*c*d*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-2*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^2*e*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+2*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b*c*d*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-x^2*c^2*e-c*e*x*b)/x/(c*e*x^2+b*e*x+c*d*x+b*d)/e^2/c","A"
390,1,887,247,0.105000," ","int((c*x^2+b*x)^(1/2)/(e*x+d)^(5/2),x)","\frac{2 \left(b \,c^{2} e^{3} x^{3}-2 c^{3} d \,e^{2} x^{3}+\sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} e^{3} x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-3 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c d \,e^{2} x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+2 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c d \,e^{2} x \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+b^{2} c \,e^{3} x^{2}+2 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{2} d^{2} e x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-2 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{2} d^{2} e x \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-2 b \,c^{2} d \,e^{2} x^{2}-c^{3} d^{2} e \,x^{2}+\sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} d \,e^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-3 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c \,d^{2} e \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+2 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c \,d^{2} e \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+2 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{2} d^{3} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-2 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{2} d^{3} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-b \,c^{2} d^{2} e x \right) \sqrt{\left(c x +b \right) x}}{3 \left(b e -c d \right) \left(c x +b \right) \left(e x +d \right)^{\frac{3}{2}} c d \,e^{2} x}"," ",0,"2/3*(2*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^2*c*d*e^2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-2*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b*c^2*d^2*e*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^3*e^3*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-3*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^2*c*d*e^2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+2*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b*c^2*d^2*e*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+2*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^2*c*d^2*e*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-2*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b*c^2*d^3*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^3*d*e^2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-3*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^2*c*d^2*e*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+2*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b*c^2*d^3*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+x^3*b*c^2*e^3-2*x^3*c^3*d*e^2+x^2*b^2*c*e^3-2*x^2*b*c^2*d*e^2-x^2*c^3*d^2*e-b*c^2*d^2*e*x)*((c*x+b)*x)^(1/2)/c/(b*e-c*d)/d/(c*x+b)/x/e^2/(e*x+d)^(3/2)","B"
391,1,1897,338,0.160000," ","int((c*x^2+b*x)^(1/2)/(e*x+d)^(7/2),x)","\frac{2 \left(2 b^{2} c^{2} e^{5} x^{4}-2 b \,c^{3} d \,e^{4} x^{4}+2 c^{4} d^{2} e^{3} x^{4}+2 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{4} e^{5} x^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-4 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c d \,e^{4} x^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+\sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c d \,e^{4} x^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+2 b^{3} c \,e^{5} x^{3}+4 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{2} d^{2} e^{3} x^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-3 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{2} d^{2} e^{3} x^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+3 b^{2} c^{2} d \,e^{4} x^{3}-2 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{3} d^{3} e^{2} x^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+2 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{3} d^{3} e^{2} x^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-5 b \,c^{3} d^{2} e^{3} x^{3}+6 c^{4} d^{3} e^{2} x^{3}+4 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{4} d \,e^{4} x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-8 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c \,d^{2} e^{3} x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+2 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c \,d^{2} e^{3} x \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+5 b^{3} c d \,e^{4} x^{2}+8 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{2} d^{3} e^{2} x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-6 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{2} d^{3} e^{2} x \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-7 b^{2} c^{2} d^{2} e^{3} x^{2}-4 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{3} d^{4} e x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+4 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{3} d^{4} e x \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+7 b \,c^{3} d^{3} e^{2} x^{2}+c^{4} d^{4} e \,x^{2}+2 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{4} d^{2} e^{3} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-4 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c \,d^{3} e^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+\sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c \,d^{3} e^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+4 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{2} d^{4} e \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-3 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{2} d^{4} e \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+b^{2} c^{2} d^{3} e^{2} x -2 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{3} d^{5} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+2 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{3} d^{5} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+b \,c^{3} d^{4} e x \right) \sqrt{\left(c x +b \right) x}}{15 \left(b e -c d \right)^{2} \left(c x +b \right) \left(e x +d \right)^{\frac{5}{2}} c \,d^{2} e^{2} x}"," ",0,"2/15*(-2*x^4*b*c^3*d*e^4+2*x^4*b^2*c^2*e^5+2*x^4*c^4*d^2*e^3+2*x^3*b^3*c*e^5+x^2*c^4*d^4*e-2*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b*c^3*d^3*e^2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+2*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^3*c*d^2*e^3*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-6*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^2*c^2*d^3*e^2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+4*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b*c^3*d^4*e*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-8*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^3*c*d^2*e^3*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+8*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^2*c^2*d^3*e^2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-4*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b*c^3*d^4*e*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^3*c*d*e^4*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-3*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^2*c^2*d^2*e^3*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+2*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b*c^3*d^3*e^2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-4*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^3*c*d*e^4*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+4*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^2*c^2*d^2*e^3*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+2*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^4*e^5*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+2*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b*c^3*d^5*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+2*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^4*d^2*e^3*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+4*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^4*d*e^4*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+6*x^3*c^4*d^3*e^2+EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^3*c*d^3*e^2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-3*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^2*c^2*d^4*e*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-4*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^3*c*d^3*e^2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+4*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^2*c^2*d^4*e*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+3*x^3*b^2*c^2*d*e^4-5*x^3*b*c^3*d^2*e^3+5*x^2*b^3*c*d*e^4-7*x^2*b^2*c^2*d^2*e^3+7*x^2*b*c^3*d^3*e^2+x*b^2*c^2*d^3*e^2+x*b*c^3*d^4*e-2*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b*c^3*d^5*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2))*((c*x+b)*x)^(1/2)/c/(b*e-c*d)^2/d^2/(c*x+b)/x/e^2/(e*x+d)^(5/2)","B"
392,1,1359,461,0.105000," ","int((e*x+d)^(3/2)*(c*x^2+b*x)^(3/2),x)","\frac{2 \sqrt{e x +d}\, \sqrt{\left(c x +b \right) x}\, \left(105 c^{7} e^{6} x^{7}+245 b \,c^{6} e^{6} x^{6}+245 c^{7} d \,e^{5} x^{6}+145 b^{2} c^{5} e^{6} x^{5}+590 b \,c^{6} d \,e^{5} x^{5}+145 c^{7} d^{2} e^{4} x^{5}-b^{3} c^{4} e^{6} x^{4}+364 b^{2} c^{5} d \,e^{5} x^{4}+364 b \,c^{6} d^{2} e^{4} x^{4}-c^{7} d^{3} e^{3} x^{4}+2 b^{4} c^{3} e^{6} x^{3}-6 b^{3} c^{4} d \,e^{5} x^{3}+239 b^{2} c^{5} d^{2} e^{4} x^{3}-6 b \,c^{6} d^{3} e^{3} x^{3}+2 c^{7} d^{4} e^{2} x^{3}+8 b^{5} c^{2} e^{6} x^{2}-17 b^{4} c^{3} d \,e^{5} x^{2}+b^{3} c^{4} d^{2} e^{4} x^{2}+b^{2} c^{5} d^{3} e^{3} x^{2}-17 b \,c^{6} d^{4} e^{2} x^{2}+8 c^{7} d^{5} e \,x^{2}+16 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{7} e^{6} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-56 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{6} c d \,e^{5} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+8 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{6} c d \,e^{5} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+56 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{5} c^{2} d^{2} e^{4} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-21 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{5} c^{2} d^{2} e^{4} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+8 b^{5} c^{2} d \,e^{5} x +10 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{4} c^{3} d^{3} e^{3} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-19 b^{4} c^{3} d^{2} e^{4} x -56 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c^{4} d^{4} e^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+35 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c^{4} d^{4} e^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+6 b^{3} c^{4} d^{3} e^{3} x +56 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{5} d^{5} e \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-48 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{5} d^{5} e \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-19 b^{2} c^{5} d^{4} e^{2} x -16 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{6} d^{6} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+16 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{6} d^{6} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+8 b \,c^{6} d^{5} e x \right)}{1155 \left(c e \,x^{2}+b e x +c d x +b d \right) c^{5} e^{4} x}"," ",0,"2/1155*(e*x+d)^(1/2)*((c*x+b)*x)^(1/2)*(590*x^5*b*c^6*d*e^5+16*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^7*e^6+105*x^7*c^7*e^6+245*x^6*b*c^6*e^6+245*x^6*c^7*d*e^5+145*x^5*b^2*c^5*e^6+145*x^5*c^7*d^2*e^4-x^4*b^3*c^4*e^6-x^4*c^7*d^3*e^3+2*x^3*b^4*c^3*e^6+2*x^3*c^7*d^4*e^2+8*x^2*b^5*c^2*e^6+8*x^2*c^7*d^5*e-48*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^2*c^5*d^5*e-56*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^6*c*d*e^5+56*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^5*c^2*d^2*e^4-56*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^3*c^4*d^4*e^2+56*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^2*c^5*d^5*e-21*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^5*c^2*d^2*e^4+10*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^4*c^3*d^3*e^3+8*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^6*c*d*e^5+364*x^4*b^2*c^5*d*e^5+364*x^4*b*c^6*d^2*e^4-6*x^3*b^3*c^4*d*e^5+239*x^3*b^2*c^5*d^2*e^4+35*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^3*c^4*d^4*e^2-6*x^3*b*c^6*d^3*e^3-17*x^2*b^4*c^3*d*e^5+x^2*b^3*c^4*d^2*e^4+x^2*b^2*c^5*d^3*e^3-17*x^2*b*c^6*d^4*e^2+8*x*b^5*c^2*d*e^5-19*x*b^4*c^3*d^2*e^4+6*x*b^3*c^4*d^3*e^3-19*x*b^2*c^5*d^4*e^2+8*x*b*c^6*d^5*e+16*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b*c^6*d^6-16*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b*c^6*d^6)/c^5/e^4/x/(c*e*x^2+b*e*x+c*d*x+b*d)","B"
393,1,1170,397,0.066000," ","int((c*x^2+b*x)^(3/2)*(e*x+d)^(1/2),x)","-\frac{2 \sqrt{\left(c x +b \right) x}\, \sqrt{e x +d}\, \left(-35 c^{6} e^{5} x^{6}-85 b \,c^{5} e^{5} x^{5}-40 c^{6} d \,e^{4} x^{5}-53 b^{2} c^{4} e^{5} x^{4}-101 b \,c^{5} d \,e^{4} x^{4}+c^{6} d^{2} e^{3} x^{4}+b^{3} c^{3} e^{5} x^{3}-67 b^{2} c^{4} d \,e^{4} x^{3}+5 b \,c^{5} d^{2} e^{3} x^{3}-2 c^{6} d^{3} e^{2} x^{3}+4 b^{4} c^{2} e^{5} x^{2}-2 b^{3} c^{3} d \,e^{4} x^{2}+b^{2} c^{4} d^{2} e^{3} x^{2}+13 b \,c^{5} d^{3} e^{2} x^{2}-8 c^{6} d^{4} e \,x^{2}+8 \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, b^{6} e^{5} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-15 \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, b^{5} c d \,e^{4} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+4 \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, b^{5} c d \,e^{4} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-2 \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, b^{4} c^{2} d^{2} e^{3} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-4 \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, b^{4} c^{2} d^{2} e^{3} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+4 b^{4} c^{2} d \,e^{4} x +41 \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, b^{3} c^{3} d^{3} e^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-24 \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, b^{3} c^{3} d^{3} e^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-3 b^{3} c^{3} d^{2} e^{3} x -48 \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, b^{2} c^{4} d^{4} e \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+40 \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, b^{2} c^{4} d^{4} e \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+15 b^{2} c^{4} d^{3} e^{2} x +16 \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, b \,c^{5} d^{5} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-16 \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, b \,c^{5} d^{5} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-8 b \,c^{5} d^{4} e x \right)}{315 \left(c e \,x^{2}+b e x +c d x +b d \right) c^{4} e^{4} x}"," ",0,"-2/315*((c*x+b)*x)^(1/2)*(e*x+d)^(1/2)*(8*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*b^6*e^5+5*x^3*b*c^5*d^2*e^3+x^2*b^2*c^4*d^2*e^3-67*x^3*b^2*c^4*d*e^4-101*x^4*b*c^5*d*e^4+13*x^2*b*c^5*d^3*e^2+4*x*b^4*c^2*d*e^4-3*x*b^3*c^3*d^2*e^3+x^3*b^3*c^3*e^5-2*x^3*c^6*d^3*e^2+4*x^2*b^4*c^2*e^5-8*x^2*c^6*d^4*e-85*x^5*b*c^5*e^5-40*x^5*c^6*d*e^4-53*x^4*b^2*c^4*e^5+x^4*c^6*d^2*e^3+40*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*b^2*c^4*d^4*e+41*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*b^3*c^3*d^3*e^2-48*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*b^2*c^4*d^4*e-15*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*b^5*c*d*e^4+4*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*b^5*c*d*e^4-4*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*b^4*c^2*d^2*e^3-2*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*b^4*c^2*d^2*e^3-24*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*b^3*c^3*d^3*e^2+15*x*b^2*c^4*d^3*e^2-8*x*b*c^5*d^4*e-35*x^6*c^6*e^5-16*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*b*c^5*d^5+16*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*b*c^5*d^5-2*x^2*b^3*c^3*d*e^4)/c^4/x/(c*e*x^2+b*e*x+c*d*x+b*d)/e^4","B"
394,1,918,306,0.079000," ","int((c*x^2+b*x)^(3/2)/(e*x+d)^(1/2),x)","\frac{2 \sqrt{\left(c x +b \right) x}\, \sqrt{e x +d}\, \left(5 c^{5} e^{4} x^{5}+13 b \,c^{4} e^{4} x^{4}-c^{5} d \,e^{3} x^{4}+9 b^{2} c^{3} e^{4} x^{3}-4 b \,c^{4} d \,e^{3} x^{3}+2 c^{5} d^{2} e^{2} x^{3}+b^{3} c^{2} e^{4} x^{2}-2 b^{2} c^{3} d \,e^{3} x^{2}-9 b \,c^{4} d^{2} e^{2} x^{2}+8 c^{5} d^{3} e \,x^{2}+2 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{5} e^{4} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+2 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{4} c d \,e^{3} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+\sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{4} c d \,e^{3} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-28 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c^{2} d^{2} e^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+15 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c^{2} d^{2} e^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+b^{3} c^{2} d \,e^{3} x +40 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{3} d^{3} e \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-32 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{3} d^{3} e \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-11 b^{2} c^{3} d^{2} e^{2} x -16 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{4} d^{4} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+16 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{4} d^{4} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+8 b \,c^{4} d^{3} e x \right)}{35 \left(c e \,x^{2}+b e x +c d x +b d \right) c^{3} e^{4} x}"," ",0,"2/35*((c*x+b)*x)^(1/2)*(e*x+d)^(1/2)*(5*c^5*e^4*x^5+((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^4*c*d*e^3+15*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^3*c^2*d^2*e^2-32*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^2*c^3*d^3*e+16*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b*c^4*d^4+2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^5*e^4+2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^4*c*d*e^3-28*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^3*c^2*d^2*e^2+40*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^2*c^3*d^3*e-16*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b*c^4*d^4+13*b*c^4*e^4*x^4-c^5*d*e^3*x^4+9*b^2*c^3*e^4*x^3-4*b*c^4*d*e^3*x^3+2*c^5*d^2*e^2*x^3+b^3*c^2*e^4*x^2-2*b^2*c^3*d*e^3*x^2-9*b*c^4*d^2*e^2*x^2+8*c^5*d^3*e*x^2+b^3*c^2*d*e^3*x-11*b^2*c^3*d^2*e^2*x+8*b*c^4*d^3*e*x)/c^3/e^4/x/(c*e*x^2+b*e*x+c*d*x+b*d)","B"
395,1,685,257,0.084000," ","int((c*x^2+b*x)^(3/2)/(e*x+d)^(3/2),x)","-\frac{2 \sqrt{\left(c x +b \right) x}\, \sqrt{e x +d}\, \left(-c^{4} e^{3} x^{4}-3 b \,c^{3} e^{3} x^{3}+2 c^{4} d \,e^{2} x^{3}-2 b^{2} c^{2} e^{3} x^{2}-5 b \,c^{3} d \,e^{2} x^{2}+8 c^{4} d^{2} e \,x^{2}+\sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{4} e^{3} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-17 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c d \,e^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+8 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c d \,e^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+32 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{2} d^{2} e \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-24 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{2} d^{2} e \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-7 b^{2} c^{2} d \,e^{2} x -16 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{3} d^{3} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+16 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{3} d^{3} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+8 b \,c^{3} d^{2} e x \right)}{5 \left(c e \,x^{2}+b e x +c d x +b d \right) c^{2} e^{4} x}"," ",0,"-2/5*((c*x+b)*x)^(1/2)*(e*x+d)^(1/2)*(8*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^3*c*d*e^2-24*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^2*c^2*d^2*e+16*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b*c^3*d^3+((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^4*e^3-17*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^3*c*d*e^2+32*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^2*c^2*d^2*e-16*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b*c^3*d^3-x^4*c^4*e^3-3*x^3*b*c^3*e^3+2*x^3*c^4*d*e^2-2*b^2*c^2*e^3*x^2-5*b*c^3*d*e^2*x^2+8*x^2*c^4*d^2*e-7*x*b^2*c^2*d*e^2+8*x*b*c^3*d^2*e)/c^2/x/(c*e*x^2+b*e*x+c*d*x+b*d)/e^4","B"
396,1,1051,244,0.095000," ","int((c*x^2+b*x)^(3/2)/(e*x+d)^(5/2),x)","\frac{2 \sqrt{\left(c x +b \right) x}\, \left(c^{3} e^{3} x^{4}-3 b \,c^{2} e^{3} x^{3}+10 c^{3} d \,e^{2} x^{3}-8 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} e^{3} x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+3 \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, b^{3} e^{3} x \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+24 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c d \,e^{2} x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-16 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c d \,e^{2} x \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-4 b^{2} c \,e^{3} x^{2}-16 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{2} d^{2} e x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+16 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{2} d^{2} e x \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+7 b \,c^{2} d \,e^{2} x^{2}+8 c^{3} d^{2} e \,x^{2}-8 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} d \,e^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+3 \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, b^{3} d \,e^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+24 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c \,d^{2} e \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-16 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c \,d^{2} e \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-3 b^{2} c d \,e^{2} x -16 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{2} d^{3} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+16 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{2} d^{3} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+8 b \,c^{2} d^{2} e x \right)}{3 \left(c x +b \right) \left(e x +d \right)^{\frac{3}{2}} c \,e^{4} x}"," ",0,"2/3*((c*x+b)*x)^(1/2)*(3*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^3*e^3*(-1/b*c*x)^(1/2)*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)-16*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^2*c*d*e^2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+16*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b*c^2*d^2*e*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-8*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^3*e^3*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+24*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^2*c*d*e^2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-16*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b*c^2*d^2*e*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+3*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^3*d*e^2*(-1/b*c*x)^(1/2)*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)-16*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^2*c*d^2*e*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+16*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b*c^2*d^3*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-8*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^3*d*e^2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+24*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^2*c*d^2*e*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-16*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b*c^2*d^3*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+c^3*x^4*e^3-3*b*c^2*e^3*x^3+10*c^3*d*e^2*x^3-4*b^2*c*e^3*x^2+7*b*c^2*d*e^2*x^2+8*c^3*d^2*e*x^2-3*b^2*c*d*e^2*x+8*b*c^2*d^2*e*x)/(c*x+b)/x/(e*x+d)^(3/2)/e^4/c","B"
397,1,1885,300,0.101000," ","int((c*x^2+b*x)^(3/2)/(e*x+d)^(7/2),x)","\frac{2 \sqrt{\left(c x +b \right) x}\, \left(b^{2} c^{2} e^{5} x^{4}-11 b \,c^{3} d \,e^{4} x^{4}+11 c^{4} d^{2} e^{3} x^{4}+\sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{4} e^{5} x^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-17 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c d \,e^{4} x^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+8 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c d \,e^{4} x^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+b^{3} c \,e^{5} x^{3}+32 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{2} d^{2} e^{3} x^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-24 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{2} d^{2} e^{3} x^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-11 b^{2} c^{2} d \,e^{4} x^{3}-16 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{3} d^{3} e^{2} x^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+16 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{3} d^{3} e^{2} x^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-5 b \,c^{3} d^{2} e^{3} x^{3}+18 c^{4} d^{3} e^{2} x^{3}+2 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{4} d \,e^{4} x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-34 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c \,d^{2} e^{3} x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+16 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c \,d^{2} e^{3} x \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+64 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{2} d^{3} e^{2} x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-48 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{2} d^{3} e^{2} x \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-16 b^{2} c^{2} d^{2} e^{3} x^{2}-32 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{3} d^{4} e x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+32 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{3} d^{4} e x \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+11 b \,c^{3} d^{3} e^{2} x^{2}+8 c^{4} d^{4} e \,x^{2}+\sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{4} d^{2} e^{3} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-17 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c \,d^{3} e^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+8 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c \,d^{3} e^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+32 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{2} d^{4} e \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-24 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{2} d^{4} e \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-7 b^{2} c^{2} d^{3} e^{2} x -16 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{3} d^{5} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+16 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{3} d^{5} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+8 b \,c^{3} d^{4} e x \right)}{5 \left(c x +b \right) \left(b e -c d \right) \left(e x +d \right)^{\frac{5}{2}} c d \,e^{4} x}"," ",0,"2/5*((c*x+b)*x)^(1/2)*(-11*b*c^3*d*e^4*x^4+b^2*c^2*e^5*x^4+11*c^4*d^2*e^3*x^4+b^3*c*e^5*x^3+8*c^4*d^4*e*x^2-16*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b*c^3*d^3*e^2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+16*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^3*c*d^2*e^3*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-48*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^2*c^2*d^3*e^2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+32*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b*c^3*d^4*e*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-34*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^3*c*d^2*e^3*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+64*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^2*c^2*d^3*e^2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-32*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b*c^3*d^4*e*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+8*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^3*c*d*e^4*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-24*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^2*c^2*d^2*e^3*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+16*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b*c^3*d^3*e^2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-17*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^3*c*d*e^4*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+32*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^2*c^2*d^2*e^3*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^4*e^5*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+16*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b*c^3*d^5*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^4*d^2*e^3*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+2*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^4*d*e^4*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+18*c^4*d^3*e^2*x^3+8*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^3*c*d^3*e^2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-24*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^2*c^2*d^4*e*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-17*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^3*c*d^3*e^2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+32*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^2*c^2*d^4*e*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-11*b^2*c^2*d*e^4*x^3-5*b*c^3*d^2*e^3*x^3-16*b^2*c^2*d^2*e^3*x^2+11*b*c^3*d^3*e^2*x^2-7*b^2*c^2*d^3*e^2*x+8*b*c^3*d^4*e*x-16*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b*c^3*d^5*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2))/(c*x+b)/x/(b*e-c*d)/c/(e*x+d)^(5/2)/e^4/d","B"
398,1,3267,416,0.165000," ","int((c*x^2+b*x)^(3/2)/(e*x+d)^(9/2),x)","\text{output too large to display}"," ",0,"2/35*((c*x+b)*x)^(1/2)*(-35*x^2*b^2*c^3*d^4*e^3+6*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^5*d*e^6*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-32*x^4*b^2*c^3*d^2*e^5-16*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^3*b*c^4*d^4*e^3*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^3*b^4*c*d*e^6*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+15*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^3*b^3*c^2*d^2*e^5*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-32*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^3*b^2*c^3*d^3*e^4*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+16*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^3*b*c^4*d^4*e^3*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+6*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^4*c*d^2*e^5*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-84*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^3*c^2*d^3*e^4*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+120*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^2*c^3*d^4*e^3*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-48*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b*c^4*d^5*e^2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+3*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^4*c*d^2*e^5*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+45*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^3*c^2*d^3*e^4*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-96*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^2*c^3*d^4*e^3*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+48*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b*c^4*d^5*e^2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+6*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^4*c*d^3*e^4*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-84*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^3*c^2*d^4*e^3*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+120*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^2*c^3*d^5*e^2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-48*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b*c^4*d^6*e*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+3*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^4*c*d^3*e^4*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+45*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^3*c^2*d^4*e^3*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-96*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^2*c^3*d^5*e^2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+48*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b*c^4*d^6*e*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+2*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^3*b^4*c*d*e^6*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-28*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^3*b^3*c^2*d^2*e^5*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+40*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^3*b^2*c^3*d^3*e^4*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+2*x^5*b^3*c^2*e^7+16*x^5*c^5*d^3*e^4+2*x^4*b^4*c*e^7+29*x^4*c^5*d^4*e^3+26*x^3*c^5*d^5*e^2+8*x^2*c^5*d^6*e+2*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^4*c*d^4*e^3*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-28*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^3*c^2*d^5*e^2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+40*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^2*c^3*d^6*e*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^4*c*d^4*e^3*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+15*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^3*c^2*d^5*e^2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-32*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^2*c^3*d^6*e*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+6*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^5*d^2*e^5*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+15*x^2*b*c^4*d^5*e^2+x*b^3*c^2*d^4*e^3-11*x*b^2*c^3*d^5*e^2+8*x*b*c^4*d^6*e-18*x^4*b*c^4*d^3*e^4+7*x^3*b^4*c*d*e^6-8*x^3*b^3*c^2*d^2*e^5-30*x^3*b^2*c^3*d^3*e^4-7*x^3*b*c^4*d^4*e^3+4*x^2*b^3*c^2*d^3*e^4+4*x^5*b^2*c^3*d*e^6-24*x^5*b*c^4*d^2*e^5+11*x^4*b^3*c^2*d*e^6+2*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^3*b^5*e^7*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+2*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^5*d^3*e^4*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-16*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b*c^4*d^7*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+16*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b*c^4*d^7*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2))/(c*x+b)/x/(b*e-c*d)^2/c/(e*x+d)^(7/2)/e^4/d^2","B"
399,1,1728,600,0.101000," ","int((c*x^2+b*x)^(5/2)*(e*x+d)^(1/2),x)","\frac{2 \sqrt{\left(c x +b \right) x}\, \sqrt{e x +d}\, \left(693 c^{8} e^{7} x^{8}+2394 b \,c^{7} e^{7} x^{7}+756 c^{8} d \,e^{6} x^{7}+2814 b^{2} c^{6} e^{7} x^{6}+2653 b \,c^{7} d \,e^{6} x^{6}-7 c^{8} d^{2} e^{5} x^{6}+1128 b^{3} c^{5} e^{7} x^{5}+3188 b^{2} c^{6} d \,e^{6} x^{5}-36 b \,c^{7} d^{2} e^{5} x^{5}+10 c^{8} d^{3} e^{4} x^{5}-3 b^{4} c^{4} e^{7} x^{4}+1318 b^{3} c^{5} d \,e^{6} x^{4}-69 b^{2} c^{6} d^{2} e^{5} x^{4}+57 b \,c^{7} d^{3} e^{4} x^{4}-16 c^{8} d^{4} e^{3} x^{4}+6 b^{5} c^{3} e^{7} x^{3}-8 b^{4} c^{4} d \,e^{6} x^{3}-50 b^{3} c^{5} d^{2} e^{5} x^{3}+132 b^{2} c^{6} d^{3} e^{4} x^{3}-112 b \,c^{7} d^{4} e^{3} x^{3}+32 c^{8} d^{5} e^{2} x^{3}+24 b^{6} c^{2} e^{7} x^{2}-11 b^{5} c^{3} d \,e^{6} x^{2}-27 b^{4} c^{4} d^{2} e^{5} x^{2}+63 b^{3} c^{5} d^{3} e^{4} x^{2}+207 b^{2} c^{6} d^{4} e^{3} x^{2}-336 b \,c^{7} d^{5} e^{2} x^{2}+128 c^{8} d^{6} e \,x^{2}+48 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{8} e^{7} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-88 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{7} c d \,e^{6} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+24 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{7} c d \,e^{6} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-2 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{6} c^{2} d^{2} e^{5} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-23 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{6} c^{2} d^{2} e^{5} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+24 b^{6} c^{2} d \,e^{6} x -50 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{5} c^{3} d^{3} e^{4} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-20 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{5} c^{3} d^{3} e^{4} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-17 b^{5} c^{3} d^{2} e^{5} x +778 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{4} c^{4} d^{4} e^{3} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-395 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{4} c^{4} d^{4} e^{3} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-22 b^{4} c^{4} d^{3} e^{4} x -1454 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c^{5} d^{5} e^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+1054 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c^{5} d^{5} e^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+303 b^{3} c^{5} d^{4} e^{3} x +1024 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{6} d^{6} e \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-896 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{6} d^{6} e \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-368 b^{2} c^{6} d^{5} e^{2} x -256 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{7} d^{7} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+256 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{7} d^{7} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+128 b \,c^{7} d^{6} e x \right)}{9009 \left(c e \,x^{2}+b e x +c d x +b d \right) c^{5} e^{6} x}"," ",0,"2/9009*((c*x+b)*x)^(1/2)*(e*x+d)^(1/2)*(48*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^8*e^7-896*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^2*c^6*d^6*e-88*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^7*c*d*e^6-2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^6*c^2*d^2*e^5-50*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^5*c^3*d^3*e^4-20*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^5*c^3*d^3*e^4-395*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^4*c^4*d^4*e^3+1054*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^3*c^5*d^5*e^2+2653*x^6*b*c^7*d*e^6+693*x^8*c^8*e^7+24*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^7*c*d*e^6-3*x^4*b^4*c^4*e^7-16*x^4*c^8*d^4*e^3+6*x^3*b^5*c^3*e^7+32*x^3*c^8*d^5*e^2+24*x^2*b^6*c^2*e^7+128*x^2*c^8*d^6*e+2394*x^7*b*c^7*e^7+756*x^7*c^8*d*e^6+2814*x^6*b^2*c^6*e^7-7*x^6*c^8*d^2*e^5+1128*x^5*b^3*c^5*e^7+10*x^5*c^8*d^3*e^4-23*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^6*c^2*d^2*e^5+778*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^4*c^4*d^4*e^3-1454*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^3*c^5*d^5*e^2+1024*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^2*c^6*d^6*e+128*x*b*c^7*d^6*e+3188*x^5*b^2*c^6*d*e^6-36*x^5*b*c^7*d^2*e^5+1318*x^4*b^3*c^5*d*e^6-69*x^4*b^2*c^6*d^2*e^5+57*x^4*b*c^7*d^3*e^4-8*x^3*b^4*c^4*d*e^6-50*x^3*b^3*c^5*d^2*e^5+132*x^3*b^2*c^6*d^3*e^4-112*x^3*b*c^7*d^4*e^3-11*x^2*b^5*c^3*d*e^6-27*x^2*b^4*c^4*d^2*e^5+63*x^2*b^3*c^5*d^3*e^4+207*x^2*b^2*c^6*d^4*e^3-336*x^2*b*c^7*d^5*e^2+24*x*b^6*c^2*d*e^6-17*x*b^5*c^3*d^2*e^5-22*x*b^4*c^4*d^3*e^4+303*x*b^3*c^5*d^4*e^3-368*x*b^2*c^6*d^5*e^2+256*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b*c^7*d^7-256*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b*c^7*d^7)/c^5/x/(c*e*x^2+b*e*x+c*d*x+b*d)/e^6","B"
400,1,1441,477,0.088000," ","int((c*x^2+b*x)^(5/2)/(e*x+d)^(1/2),x)","-\frac{2 \sqrt{\left(c x +b \right) x}\, \sqrt{e x +d}\, \left(-63 c^{7} e^{6} x^{7}-224 b \,c^{6} e^{6} x^{6}+7 c^{7} d \,e^{5} x^{6}-274 b^{2} c^{5} e^{6} x^{5}+31 b \,c^{6} d \,e^{5} x^{5}-10 c^{7} d^{2} e^{4} x^{5}-116 b^{3} c^{4} e^{6} x^{4}+50 b^{2} c^{5} d \,e^{5} x^{4}-49 b \,c^{6} d^{2} e^{4} x^{4}+16 c^{7} d^{3} e^{3} x^{4}+b^{4} c^{3} e^{6} x^{3}+30 b^{3} c^{4} d \,e^{5} x^{3}-95 b^{2} c^{5} d^{2} e^{4} x^{3}+96 b \,c^{6} d^{3} e^{3} x^{3}-32 c^{7} d^{4} e^{2} x^{3}+4 b^{5} c^{2} e^{6} x^{2}+8 b^{4} c^{3} d \,e^{5} x^{2}-49 b^{3} c^{4} d^{2} e^{4} x^{2}-115 b^{2} c^{5} d^{3} e^{3} x^{2}+272 b \,c^{6} d^{4} e^{2} x^{2}-128 c^{7} d^{5} e \,x^{2}+8 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{7} e^{6} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+5 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{6} c d \,e^{5} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+4 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{6} c d \,e^{5} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+28 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{5} c^{2} d^{2} e^{4} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+6 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{5} c^{2} d^{2} e^{4} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+4 b^{5} c^{2} d \,e^{5} x -495 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{4} c^{3} d^{3} e^{3} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+236 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{4} c^{3} d^{3} e^{3} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+7 b^{4} c^{3} d^{2} e^{4} x +1094 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c^{4} d^{4} e^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-758 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c^{4} d^{4} e^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-195 b^{3} c^{4} d^{3} e^{3} x -896 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{5} d^{5} e \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+768 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{5} d^{5} e \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+304 b^{2} c^{5} d^{4} e^{2} x +256 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{6} d^{6} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-256 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{6} d^{6} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-128 b \,c^{6} d^{5} e x \right)}{693 \left(c e \,x^{2}+b e x +c d x +b d \right) c^{4} e^{6} x}"," ",0,"-2/693*((c*x+b)*x)^(1/2)*(e*x+d)^(1/2)*(8*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^7*e^6+31*x^5*b*c^6*d*e^5-224*b*c^6*e^6*x^6+7*c^7*d*e^5*x^6-274*b^2*c^5*e^6*x^5+16*c^7*d^3*e^3*x^4+b^4*c^3*e^6*x^3-32*c^7*d^4*e^2*x^3-128*c^7*d^5*e*x^2+50*b^2*c^5*d*e^5*x^4-49*b*c^6*d^2*e^4*x^4-95*b^2*c^5*d^2*e^4*x^3-10*x^5*c^7*d^2*e^4-116*x^4*b^3*c^4*e^6-63*x^7*c^7*e^6-495*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^4*c^3*d^3*e^3+4*x^2*b^5*c^2*e^6+8*b^4*c^3*d*e^5*x^2+272*b*c^6*d^4*e^2*x^2+304*b^2*c^5*d^4*e^2*x+4*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^6*c*d*e^5-256*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b*c^6*d^6+256*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b*c^6*d^6-758*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^3*c^4*d^4*e^2+768*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^2*c^5*d^5*e+5*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^6*c*d*e^5+28*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^5*c^2*d^2*e^4+1094*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^3*c^4*d^4*e^2-896*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^2*c^5*d^5*e+6*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^5*c^2*d^2*e^4+236*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^4*c^3*d^3*e^3+30*x^3*b^3*c^4*d*e^5+96*x^3*b*c^6*d^3*e^3-49*x^2*b^3*c^4*d^2*e^4-115*x^2*b^2*c^5*d^3*e^3+4*x*b^5*c^2*d*e^5+7*x*b^4*c^3*d^2*e^4-195*x*b^3*c^4*d^3*e^3-128*x*b*c^6*d^5*e)/c^4/e^6/x/(c*e*x^2+b*e*x+c*d*x+b*d)","B"
401,1,1170,399,0.116000," ","int((c*x^2+b*x)^(5/2)/(e*x+d)^(3/2),x)","\frac{2 \sqrt{\left(c x +b \right) x}\, \sqrt{e x +d}\, \left(7 c^{6} e^{5} x^{6}+26 b \,c^{5} e^{5} x^{5}-10 c^{6} d \,e^{4} x^{5}+34 b^{2} c^{4} e^{5} x^{4}-41 b \,c^{5} d \,e^{4} x^{4}+16 c^{6} d^{2} e^{3} x^{4}+16 b^{3} c^{3} e^{5} x^{3}-64 b^{2} c^{4} d \,e^{4} x^{3}+80 b \,c^{5} d^{2} e^{3} x^{3}-32 c^{6} d^{3} e^{2} x^{3}+b^{4} c^{2} e^{5} x^{2}-32 b^{3} c^{3} d \,e^{4} x^{2}-47 b^{2} c^{4} d^{2} e^{3} x^{2}+208 b \,c^{5} d^{3} e^{2} x^{2}-128 c^{6} d^{4} e \,x^{2}+2 \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, b^{6} e^{5} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+12 \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, b^{5} c d \,e^{4} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+\sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, b^{5} c d \,e^{4} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-284 \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, b^{4} c^{2} d^{2} e^{3} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+125 \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, b^{4} c^{2} d^{2} e^{3} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+b^{4} c^{2} d \,e^{4} x +782 \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, b^{3} c^{3} d^{3} e^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-510 \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, b^{3} c^{3} d^{3} e^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-111 b^{3} c^{3} d^{2} e^{3} x -768 \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, b^{2} c^{4} d^{4} e \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+640 \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, b^{2} c^{4} d^{4} e \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+240 b^{2} c^{4} d^{3} e^{2} x +256 \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, b \,c^{5} d^{5} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-256 \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, b \,c^{5} d^{5} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-128 b \,c^{5} d^{4} e x \right)}{63 \left(c e \,x^{2}+b e x +c d x +b d \right) c^{3} e^{6} x}"," ",0,"2/63*((c*x+b)*x)^(1/2)*(e*x+d)^(1/2)*(2*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*b^6*e^5+80*b*c^5*d^2*e^3*x^3-47*b^2*c^4*d^2*e^3*x^2-64*b^2*c^4*d*e^4*x^3-41*b*c^5*d*e^4*x^4+208*b*c^5*d^3*e^2*x^2+b^4*c^2*d*e^4*x-111*b^3*c^3*d^2*e^3*x+16*b^3*c^3*e^5*x^3-32*c^6*d^3*e^2*x^3+b^4*c^2*e^5*x^2-128*c^6*d^4*e*x^2+26*b*c^5*e^5*x^5-10*c^6*d*e^4*x^5+34*b^2*c^4*e^5*x^4+16*c^6*d^2*e^3*x^4+640*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*b^2*c^4*d^4*e+782*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*b^3*c^3*d^3*e^2-768*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*b^2*c^4*d^4*e+12*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*b^5*c*d*e^4+(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*b^5*c*d*e^4+125*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*b^4*c^2*d^2*e^3-284*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*b^4*c^2*d^2*e^3-510*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*b^3*c^3*d^3*e^2+240*b^2*c^4*d^3*e^2*x-128*b*c^5*d^4*e*x+7*c^6*e^5*x^6-256*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*b*c^5*d^5+256*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*b*c^5*d^5-32*b^3*c^3*d*e^4*x^2)/c^3/e^6/x/(c*e*x^2+b*e*x+c*d*x+b*d)","B"
402,1,1692,341,0.111000," ","int((c*x^2+b*x)^(5/2)/(e*x+d)^(5/2),x)","-\frac{2 \sqrt{\left(c x +b \right) x}\, \left(-3 c^{5} e^{5} x^{6}-12 b \,c^{4} e^{5} x^{5}+6 c^{5} d \,e^{4} x^{5}-18 b^{2} c^{3} e^{5} x^{4}+31 b \,c^{4} d \,e^{4} x^{4}-16 c^{5} d^{2} e^{3} x^{4}-9 b^{3} c^{2} e^{5} x^{3}-42 b^{2} c^{3} d \,e^{4} x^{3}+208 b \,c^{4} d^{2} e^{3} x^{3}-160 c^{5} d^{3} e^{2} x^{3}+3 \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, b^{5} e^{5} x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-137 \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, b^{4} c d \,e^{4} x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+54 \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, b^{4} c d \,e^{4} x \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+518 \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, b^{3} c^{2} d^{2} e^{3} x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-310 \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, b^{3} c^{2} d^{2} e^{3} x \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-67 b^{3} c^{2} d \,e^{4} x^{2}-640 \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, b^{2} c^{3} d^{3} e^{2} x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+512 \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, b^{2} c^{3} d^{3} e^{2} x \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+173 b^{2} c^{3} d^{2} e^{3} x^{2}+256 \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, b \,c^{4} d^{4} e x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-256 \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, b \,c^{4} d^{4} e x \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+16 b \,c^{4} d^{3} e^{2} x^{2}-128 c^{5} d^{4} e \,x^{2}+3 \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, b^{5} d \,e^{4} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-137 \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, b^{4} c \,d^{2} e^{3} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+54 \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, b^{4} c \,d^{2} e^{3} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+518 \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, b^{3} c^{2} d^{3} e^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-310 \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, b^{3} c^{2} d^{3} e^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-51 b^{3} c^{2} d^{2} e^{3} x -640 \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, b^{2} c^{3} d^{4} e \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+512 \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, b^{2} c^{3} d^{4} e \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+176 b^{2} c^{3} d^{3} e^{2} x +256 \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, b \,c^{4} d^{5} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-256 \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, b \,c^{4} d^{5} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-128 b \,c^{4} d^{4} e x \right)}{21 \left(c x +b \right) \left(e x +d \right)^{\frac{3}{2}} c^{2} e^{6} x}"," ",0,"-2/21*((c*x+b)*x)^(1/2)*(173*x^2*b^2*c^3*d^2*e^3+16*x^2*b*c^4*d^3*e^2-51*x*b^3*c^2*d^2*e^3+176*x*b^2*c^3*d^3*e^2-128*x*b*c^4*d^4*e+31*x^4*b*c^4*d*e^4+512*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^2*c^3*d^3*e^2*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*((c*x+b)/b)^(1/2)-256*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b*c^4*d^4*e*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*((c*x+b)/b)^(1/2)-137*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^4*c*d*e^4*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*((c*x+b)/b)^(1/2)+518*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^3*c^2*d^2*e^3*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*((c*x+b)/b)^(1/2)-640*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^2*c^3*d^3*e^2*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*((c*x+b)/b)^(1/2)+256*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b*c^4*d^4*e*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*((c*x+b)/b)^(1/2)+54*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^4*c*d*e^4*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*((c*x+b)/b)^(1/2)-310*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^3*c^2*d^2*e^3*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*((c*x+b)/b)^(1/2)-640*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^2*c^3*d^4*e*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*((c*x+b)/b)^(1/2)-3*x^6*c^5*e^5-12*x^5*b*c^4*e^5+6*x^5*c^5*d*e^4-18*x^4*b^2*c^3*e^5-16*x^4*c^5*d^2*e^3-9*x^3*b^3*c^2*e^5-160*x^3*c^5*d^3*e^2-128*x^2*c^5*d^4*e+54*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^4*c*d^2*e^3*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*((c*x+b)/b)^(1/2)-310*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^3*c^2*d^3*e^2*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*((c*x+b)/b)^(1/2)+512*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^2*c^3*d^4*e*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*((c*x+b)/b)^(1/2)-137*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^4*c*d^2*e^3*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*((c*x+b)/b)^(1/2)+518*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^3*c^2*d^3*e^2*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*((c*x+b)/b)^(1/2)-42*x^3*b^2*c^3*d*e^4+208*x^3*b*c^4*d^2*e^3-67*x^2*b^3*c^2*d*e^4+3*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^5*d*e^4*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*((c*x+b)/b)^(1/2)+256*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b*c^4*d^5*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*((c*x+b)/b)^(1/2)+3*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^5*e^5*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*((c*x+b)/b)^(1/2)-256*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b*c^4*d^5*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*((c*x+b)/b)^(1/2))/(c*x+b)/x/(e*x+d)^(3/2)/c^2/e^6","B"
403,1,2170,332,0.115000," ","int((c*x^2+b*x)^(5/2)/(e*x+d)^(7/2),x)","\frac{2 \sqrt{\left(c x +b \right) x}\, \left(3 c^{4} e^{5} x^{6}+14 b \,c^{3} e^{5} x^{5}-10 c^{4} d \,e^{4} x^{5}-12 b^{2} c^{2} e^{5} x^{4}+151 b \,c^{3} d \,e^{4} x^{4}-176 c^{4} d^{2} e^{3} x^{4}-46 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{4} e^{5} x^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+15 \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, b^{4} e^{5} x^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+302 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c d \,e^{4} x^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-158 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c d \,e^{4} x^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-23 b^{3} c \,e^{5} x^{3}-512 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{2} d^{2} e^{3} x^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+384 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{2} d^{2} e^{3} x^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+126 b^{2} c^{2} d \,e^{4} x^{3}+256 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{3} d^{3} e^{2} x^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-256 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{3} d^{3} e^{2} x^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+80 b \,c^{3} d^{2} e^{3} x^{3}-288 c^{4} d^{3} e^{2} x^{3}-92 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{4} d \,e^{4} x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+30 \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, b^{4} d \,e^{4} x \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+604 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c \,d^{2} e^{3} x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-316 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c \,d^{2} e^{3} x \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-35 b^{3} c d \,e^{4} x^{2}-1024 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{2} d^{3} e^{2} x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+768 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{2} d^{3} e^{2} x \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+241 b^{2} c^{2} d^{2} e^{3} x^{2}+512 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{3} d^{4} e x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-512 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{3} d^{4} e x \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-176 b \,c^{3} d^{3} e^{2} x^{2}-128 c^{4} d^{4} e \,x^{2}-46 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{4} d^{2} e^{3} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+15 \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, b^{4} d^{2} e^{3} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+302 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c \,d^{3} e^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-158 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c \,d^{3} e^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-15 b^{3} c \,d^{2} e^{3} x -512 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{2} d^{4} e \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+384 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{2} d^{4} e \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+112 b^{2} c^{2} d^{3} e^{2} x +256 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{3} d^{5} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-256 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{3} d^{5} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-128 b \,c^{3} d^{4} e x \right)}{15 \left(c x +b \right) \left(e x +d \right)^{\frac{5}{2}} c \,e^{6} x}"," ",0,"2/15*((c*x+b)*x)^(1/2)*(151*b*c^3*d*e^4*x^4+30*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^4*d*e^4*(-1/b*c*x)^(1/2)*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)-12*b^2*c^2*e^5*x^4-176*c^4*d^2*e^3*x^4-23*b^3*c*e^5*x^3-128*c^4*d^4*e*x^2+256*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b*c^3*d^3*e^2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-316*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^3*c*d^2*e^3*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+768*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^2*c^2*d^3*e^2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-512*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b*c^3*d^4*e*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+604*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^3*c*d^2*e^3*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-1024*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^2*c^2*d^3*e^2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+512*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b*c^3*d^4*e*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-158*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^3*c*d*e^4*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+384*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^2*c^2*d^2*e^3*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-256*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b*c^3*d^3*e^2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+302*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^3*c*d*e^4*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-512*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^2*c^2*d^2*e^3*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-46*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^4*e^5*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-256*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b*c^3*d^5*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-46*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^4*d^2*e^3*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-15*x*b^3*c*d^2*e^3-92*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^4*d*e^4*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+3*x^6*c^4*e^5+14*x^5*b*c^3*e^5-10*x^5*c^4*d*e^4-288*c^4*d^3*e^2*x^3-158*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^3*c*d^3*e^2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+384*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^2*c^2*d^4*e*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+302*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^3*c*d^3*e^2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-512*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^2*c^2*d^4*e*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+126*b^2*c^2*d*e^4*x^3+80*b*c^3*d^2*e^3*x^3-35*b^3*c*d*e^4*x^2+241*b^2*c^2*d^2*e^3*x^2-176*b*c^3*d^3*e^2*x^2+112*b^2*c^2*d^3*e^2*x-128*b*c^3*d^4*e*x+256*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b*c^3*d^5*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+15*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^4*d^2*e^3*(-1/b*c*x)^(1/2)*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)+15*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^4*e^5*(-1/b*c*x)^(1/2)*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2))/(c*x+b)/x/(e*x+d)^(5/2)/e^6/c","B"
404,1,3284,414,0.156000," ","int((c*x^2+b*x)^(5/2)/(e*x+d)^(9/2),x)","\text{output too large to display}"," ",0,"2/21*((c*x+b)*x)^(1/2)*(525*x^2*b^2*c^3*d^4*e^3+7*x^6*b*c^4*d*e^6+9*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^5*d*e^6*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+71*x^4*b^2*c^3*d^2*e^5+256*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^3*b*c^4*d^4*e^3*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+54*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^3*b^4*c*d*e^6*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-310*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^3*b^3*c^2*d^2*e^5*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+512*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^3*b^2*c^3*d^3*e^4*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-256*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^3*b*c^4*d^4*e^3*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-411*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^4*c*d^2*e^5*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+1554*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^3*c^2*d^3*e^4*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-1920*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^2*c^3*d^4*e^3*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+768*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b*c^4*d^5*e^2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+162*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^4*c*d^2*e^5*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-930*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^3*c^2*d^3*e^4*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+1536*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^2*c^3*d^4*e^3*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-768*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b*c^4*d^5*e^2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-411*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^4*c*d^3*e^4*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+1554*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^3*c^2*d^4*e^3*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-1920*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^2*c^3*d^5*e^2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+768*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b*c^4*d^6*e*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+162*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^4*c*d^3*e^4*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-930*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^3*c^2*d^4*e^3*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+1536*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^2*c^3*d^5*e^2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-768*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b*c^4*d^6*e*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-137*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^3*b^4*c*d*e^6*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+518*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^3*b^3*c^2*d^2*e^5*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-640*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^3*b^2*c^3*d^3*e^4*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-7*x^6*c^5*d^2*e^5+3*x^5*b^3*c^2*e^7-186*x^5*c^5*d^3*e^4+3*x^4*b^4*c*e^7-464*x^4*c^5*d^4*e^3-416*x^3*c^5*d^5*e^2-128*x^2*c^5*d^6*e-137*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^4*c*d^4*e^3*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+518*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^3*c^2*d^5*e^2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-640*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^2*c^3*d^6*e*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+54*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^4*c*d^4*e^3*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-310*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^3*c^2*d^5*e^2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+512*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^2*c^3*d^6*e*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+9*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^5*d^2*e^5*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-240*x^2*b*c^4*d^5*e^2-51*x*b^3*c^2*d^4*e^3+176*x*b^2*c^3*d^5*e^2-128*x*b*c^4*d^6*e+463*x^4*b*c^4*d^3*e^4-194*x^3*b^3*c^2*d^2*e^5+480*x^3*b^2*c^3*d^3*e^4+112*x^3*b*c^4*d^4*e^3-169*x^2*b^3*c^2*d^3*e^4-78*x^5*b^2*c^3*d*e^6+258*x^5*b*c^4*d^2*e^5-85*x^4*b^3*c^2*d*e^6+3*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^3*b^5*e^7*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+3*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^5*d^3*e^4*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+256*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b*c^4*d^7*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-256*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b*c^4*d^7*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2))/(c*x+b)/x/(b*e-c*d)/(e*x+d)^(7/2)/c/d/e^6","B"
405,1,5005,510,0.173000," ","int((c*x^2+b*x)^(5/2)/(e*x+d)^(11/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
406,1,918,319,0.098000," ","int((e*x+d)^(7/2)/(c*x^2+b*x)^(1/2),x)","\frac{2 \sqrt{e x +d}\, \sqrt{\left(c x +b \right) x}\, \left(15 c^{5} e^{4} x^{5}-3 b \,c^{4} e^{4} x^{4}+81 c^{5} d \,e^{3} x^{4}+6 b^{2} c^{3} e^{4} x^{3}-26 b \,c^{4} d \,e^{3} x^{3}+188 c^{5} d^{2} e^{2} x^{3}+24 b^{3} c^{2} e^{4} x^{2}-83 b^{2} c^{3} d \,e^{3} x^{2}+99 b \,c^{4} d^{2} e^{2} x^{2}+122 c^{5} d^{3} e \,x^{2}+48 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{5} e^{4} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-232 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{4} c d \,e^{3} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+24 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{4} c d \,e^{3} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+448 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c^{2} d^{2} e^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-95 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c^{2} d^{2} e^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+24 b^{3} c^{2} d \,e^{3} x -440 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{3} d^{3} e \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+142 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{3} d^{3} e \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-89 b^{2} c^{3} d^{2} e^{2} x +176 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{4} d^{4} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-71 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{4} d^{4} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+122 b \,c^{4} d^{3} e x \right)}{105 \left(c e \,x^{2}+b e x +c d x +b d \right) c^{5} x}"," ",0,"2/105*(e*x+d)^(1/2)*((c*x+b)*x)^(1/2)*(15*c^5*e^4*x^5+24*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^4*c*d*e^3-95*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^3*c^2*d^2*e^2+142*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^2*c^3*d^3*e-71*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b*c^4*d^4+48*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^5*e^4-232*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^4*c*d*e^3+448*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^3*c^2*d^2*e^2-440*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^2*c^3*d^3*e+176*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b*c^4*d^4-3*b*c^4*e^4*x^4+81*c^5*d*e^3*x^4+6*b^2*c^3*e^4*x^3-26*b*c^4*d*e^3*x^3+188*c^5*d^2*e^2*x^3+24*b^3*c^2*e^4*x^2-83*b^2*c^3*d*e^3*x^2+99*b*c^4*d^2*e^2*x^2+122*c^5*d^3*e*x^2+24*b^3*c^2*d*e^3*x-89*b^2*c^3*d^2*e^2*x+122*b*c^4*d^3*e*x)/c^5/x/(c*e*x^2+b*e*x+c*d*x+b*d)","B"
407,1,682,249,0.082000," ","int((e*x+d)^(5/2)/(c*x^2+b*x)^(1/2),x)","-\frac{2 \sqrt{e x +d}\, \sqrt{\left(c x +b \right) x}\, \left(-3 c^{4} e^{3} x^{4}+b \,c^{3} e^{3} x^{3}-14 c^{4} d \,e^{2} x^{3}+4 b^{2} c^{2} e^{3} x^{2}-10 b \,c^{3} d \,e^{2} x^{2}-11 c^{4} d^{2} e \,x^{2}+8 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{4} e^{3} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-31 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c d \,e^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+4 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c d \,e^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+46 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{2} d^{2} e \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-12 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{2} d^{2} e \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+4 b^{2} c^{2} d \,e^{2} x -23 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{3} d^{3} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+8 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{3} d^{3} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-11 b \,c^{3} d^{2} e x \right)}{15 \left(c e \,x^{2}+b e x +c d x +b d \right) c^{4} x}"," ",0,"-2/15*(e*x+d)^(1/2)*((c*x+b)*x)^(1/2)*(4*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^3*c*d*e^2-12*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^2*c^2*d^2*e+8*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b*c^3*d^3+8*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^4*e^3-31*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^3*c*d*e^2+46*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^2*c^2*d^2*e-23*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b*c^3*d^3-3*c^4*e^3*x^4+b*c^3*e^3*x^3-14*c^4*d*e^2*x^3+4*b^2*c^2*e^3*x^2-10*b*c^3*d*e^2*x^2-11*c^4*d^2*e*x^2+4*b^2*c^2*d*e^2*x-11*b*c^3*d^2*e*x)/x/(c*e*x^2+b*e*x+c*d*x+b*d)/c^4","B"
408,1,460,193,0.074000," ","int((e*x+d)^(3/2)/(c*x^2+b*x)^(1/2),x)","\frac{2 \sqrt{e x +d}\, \sqrt{\left(c x +b \right) x}\, \left(c^{3} e^{2} x^{3}+b \,c^{2} e^{2} x^{2}+c^{3} d e \,x^{2}+2 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} e^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-6 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c d e \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+\sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c d e \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+4 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{2} d^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-\sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{2} d^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+b \,c^{2} d e x \right)}{3 \left(c e \,x^{2}+b e x +c d x +b d \right) c^{3} x}"," ",0,"2/3*(e*x+d)^(1/2)*((c*x+b)*x)^(1/2)*(b^2*d*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*e*c-((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b*c^2*d^2+2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^3*e^2-6*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^2*c*d*e+4*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b*c^2*d^2+c^3*e^2*x^3+x^2*b*c^2*e^2+x^2*c^3*d*e+x*b*c^2*d*e)/x/(c*e*x^2+b*e*x+c*d*x+b*d)/c^3","B"
409,1,121,75,0.071000," ","int((e*x+d)^(1/2)/(c*x^2+b*x)^(1/2),x)","-\frac{2 \sqrt{e x +d}\, \sqrt{\left(c x +b \right) x}\, \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, \left(b e -c d \right) b \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)}{\left(c e \,x^{2}+b e x +c d x +b d \right) c^{2} x}"," ",0,"-2*(e*x+d)^(1/2)*((c*x+b)*x)^(1/2)*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b*(b*e-c*d)/c^2/x/(c*e*x^2+b*e*x+c*d*x+b*d)","A"
410,1,113,75,0.070000," ","int(1/(e*x+d)^(1/2)/(c*x^2+b*x)^(1/2),x)","\frac{2 \sqrt{-\frac{c x}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{\frac{c x +b}{b}}\, \sqrt{e x +d}\, \sqrt{\left(c x +b \right) x}\, b \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)}{\left(c e \,x^{2}+b e x +c d x +b d \right) c x}"," ",0,"2*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*(-1/b*c*x)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*((c*x+b)/b)^(1/2)*b*(e*x+d)^(1/2)*((c*x+b)*x)^(1/2)/c/x/(c*e*x^2+b*e*x+c*d*x+b*d)","A"
411,1,216,123,0.093000," ","int(1/(e*x+d)^(3/2)/(c*x^2+b*x)^(1/2),x)","\frac{2 \left(c^{2} e \,x^{2}+\sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} e \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-\sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b c d \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+b c e x \right) \sqrt{\left(c x +b \right) x}\, \sqrt{e x +d}}{\left(b e -c d \right) \left(c e \,x^{2}+b e x +c d x +b d \right) c d x}"," ",0,"2*(EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^2*e*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b*c*d*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+c^2*e*x^2+b*c*e*x)*((c*x+b)*x)^(1/2)*(e*x+d)^(1/2)/d/c/(b*e-c*d)/x/(c*e*x^2+b*e*x+c*d*x+b*d)","A"
412,1,897,263,0.099000," ","int(1/(e*x+d)^(5/2)/(c*x^2+b*x)^(1/2),x)","\frac{2 \sqrt{\left(c x +b \right) x}\, \left(2 b \,c^{2} e^{3} x^{3}-4 c^{3} d \,e^{2} x^{3}+2 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} e^{3} x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-6 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c d \,e^{2} x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+\sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c d \,e^{2} x \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+2 b^{2} c \,e^{3} x^{2}+4 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{2} d^{2} e x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-\sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{2} d^{2} e x \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-b \,c^{2} d \,e^{2} x^{2}-5 c^{3} d^{2} e \,x^{2}+2 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} d \,e^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-6 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c \,d^{2} e \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+\sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c \,d^{2} e \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+3 b^{2} c d \,e^{2} x +4 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{2} d^{3} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-\sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{2} d^{3} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-5 b \,c^{2} d^{2} e x \right)}{3 \left(c x +b \right) \left(b e -c d \right)^{2} \left(e x +d \right)^{\frac{3}{2}} c \,d^{2} x}"," ",0,"2/3*((c*x+b)*x)^(1/2)*(EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^2*c*d*e^2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b*c^2*d^2*e*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+2*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^3*e^3*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-6*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^2*c*d*e^2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+4*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b*c^2*d^2*e*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^2*c*d^2*e*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b*c^2*d^3*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+2*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^3*d*e^2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-6*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^2*c*d^2*e*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+4*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b*c^2*d^3*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+2*b*c^2*e^3*x^3-4*c^3*d*e^2*x^3+2*b^2*c*e^3*x^2-b*c^2*d*e^2*x^2-5*c^3*d^2*e*x^2+3*b^2*c*d*e^2*x-5*b*c^2*d^2*e*x)/(c*x+b)/x/(b*e-c*d)^2/(e*x+d)^(3/2)/c/d^2","B"
413,1,1912,343,0.122000," ","int(1/(e*x+d)^(7/2)/(c*x^2+b*x)^(1/2),x)","\frac{2 \sqrt{\left(c x +b \right) x}\, \left(8 b^{2} c^{2} e^{5} x^{4}-23 b \,c^{3} d \,e^{4} x^{4}+23 c^{4} d^{2} e^{3} x^{4}+8 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{4} e^{5} x^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-31 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c d \,e^{4} x^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+4 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c d \,e^{4} x^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+8 b^{3} c \,e^{5} x^{3}+46 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{2} d^{2} e^{3} x^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-12 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{2} d^{2} e^{3} x^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-3 b^{2} c^{2} d \,e^{4} x^{3}-23 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{3} d^{3} e^{2} x^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+8 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{3} d^{3} e^{2} x^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-35 b \,c^{3} d^{2} e^{3} x^{3}+54 c^{4} d^{3} e^{2} x^{3}+16 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{4} d \,e^{4} x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-62 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c \,d^{2} e^{3} x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+8 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c \,d^{2} e^{3} x \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+20 b^{3} c d \,e^{4} x^{2}+92 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{2} d^{3} e^{2} x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-24 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{2} d^{3} e^{2} x \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-43 b^{2} c^{2} d^{2} e^{3} x^{2}-46 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{3} d^{4} e x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+16 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{3} d^{4} e x \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+13 b \,c^{3} d^{3} e^{2} x^{2}+34 c^{4} d^{4} e \,x^{2}+8 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{4} d^{2} e^{3} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-31 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c \,d^{3} e^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+4 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c \,d^{3} e^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+15 b^{3} c \,d^{2} e^{3} x +46 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{2} d^{4} e \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-12 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{2} d^{4} e \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-41 b^{2} c^{2} d^{3} e^{2} x -23 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{3} d^{5} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+8 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{3} d^{5} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+34 b \,c^{3} d^{4} e x \right)}{15 \left(c x +b \right) \left(b e -c d \right)^{3} \left(e x +d \right)^{\frac{5}{2}} c \,d^{3} x}"," ",0,"2/15*((c*x+b)*x)^(1/2)*(-23*b*c^3*d*e^4*x^4+8*b^2*c^2*e^5*x^4+23*c^4*d^2*e^3*x^4+8*b^3*c*e^5*x^3+34*c^4*d^4*e*x^2-23*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b*c^3*d^3*e^2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+8*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^3*c*d^2*e^3*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-24*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^2*c^2*d^3*e^2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+16*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b*c^3*d^4*e*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-62*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^3*c*d^2*e^3*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+92*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^2*c^2*d^3*e^2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-46*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b*c^3*d^4*e*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+4*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^3*c*d*e^4*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-12*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^2*c^2*d^2*e^3*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+8*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b*c^3*d^3*e^2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-31*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^3*c*d*e^4*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+46*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^2*c^2*d^2*e^3*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+8*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^4*e^5*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+8*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b*c^3*d^5*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+8*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^4*d^2*e^3*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+15*b^3*c*d^2*e^3*x+16*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^4*d*e^4*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+54*c^4*d^3*e^2*x^3+4*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^3*c*d^3*e^2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-12*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^2*c^2*d^4*e*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-31*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^3*c*d^3*e^2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+46*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^2*c^2*d^4*e*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-3*b^2*c^2*d*e^4*x^3-35*b*c^3*d^2*e^3*x^3+20*b^3*c*d*e^4*x^2-43*b^2*c^2*d^2*e^3*x^2+13*b*c^3*d^3*e^2*x^2-41*b^2*c^2*d^3*e^2*x+34*b*c^3*d^4*e*x-23*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b*c^3*d^5*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2))/(c*x+b)/x/(b*e-c*d)^3/(e*x+d)^(5/2)/c/d^3","B"
414,1,863,339,0.257000," ","int((e*x+d)^(7/2)/(c*x^2+b*x)^(3/2),x)","\frac{2 \left(b^{2} c^{3} e^{4} x^{3}+4 b^{3} c^{2} e^{4} x^{2}-8 b^{2} c^{3} d \,e^{3} x^{2}+9 b \,c^{4} d^{2} e^{2} x^{2}-6 c^{5} d^{3} e \,x^{2}+8 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{5} e^{4} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-27 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{4} c d \,e^{3} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+4 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{4} c d \,e^{3} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+28 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c^{2} d^{2} e^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-10 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c^{2} d^{2} e^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+4 b^{3} c^{2} d \,e^{3} x -15 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{3} d^{3} e \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+12 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{3} d^{3} e \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-9 b^{2} c^{3} d^{2} e^{2} x +6 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{4} d^{4} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-6 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{4} d^{4} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+6 b \,c^{4} d^{3} e x -6 c^{5} d^{4} x -3 b \,c^{4} d^{4}\right) \sqrt{\left(c x +b \right) x}}{3 \left(c x +b \right) \sqrt{e x +d}\, b^{2} c^{4} x}"," ",0,"2/3*(4*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^4*c*d*e^3-10*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^3*c^2*d^2*e^2+12*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^2*c^3*d^3*e-6*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b*c^4*d^4+8*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^5*e^4-27*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^4*c*d*e^3+28*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^3*c^2*d^2*e^2-15*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^2*c^3*d^3*e+6*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b*c^4*d^4+b^2*c^3*e^4*x^3+4*b^3*c^2*e^4*x^2-8*b^2*c^3*d*e^3*x^2+9*b*c^4*d^2*e^2*x^2-6*c^5*d^3*e*x^2+4*b^3*c^2*d*e^3*x-9*b^2*c^3*d^2*e^2*x+6*b*c^4*d^3*e*x-6*x*c^5*d^4-3*b*c^4*d^4)/x*((c*x+b)*x)^(1/2)/(c*x+b)/c^4/b^2/(e*x+d)^(1/2)","B"
415,1,652,264,0.114000," ","int((e*x+d)^(5/2)/(c*x^2+b*x)^(3/2),x)","-\frac{2 \left(b^{2} c^{2} e^{3} x^{2}-2 b \,c^{3} d \,e^{2} x^{2}+2 c^{4} d^{2} e \,x^{2}+2 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{4} e^{3} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-4 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c d \,e^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+\sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c d \,e^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+4 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{2} d^{2} e \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-3 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{2} d^{2} e \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+b^{2} c^{2} d \,e^{2} x -2 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{3} d^{3} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+2 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{3} d^{3} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-b \,c^{3} d^{2} e x +2 c^{4} d^{3} x +b \,c^{3} d^{3}\right) \sqrt{\left(c x +b \right) x}}{\left(c x +b \right) \sqrt{e x +d}\, b^{2} c^{3} x}"," ",0,"-2*(((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^3*c*d*e^2-3*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^2*c^2*d^2*e+2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b*c^3*d^3+2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^4*e^3-4*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^3*c*d*e^2+4*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^2*c^2*d^2*e-2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b*c^3*d^3+b^2*c^2*e^3*x^2-2*b*c^3*d*e^2*x^2+2*c^4*d^2*e*x^2+b^2*c^2*d*e^2*x-b*c^3*d^2*e*x+2*x*c^4*d^3+b*c^3*d^3)/x*((c*x+b)*x)^(1/2)/(c*x+b)/c^3/b^2/(e*x+d)^(1/2)","B"
416,1,451,207,0.096000," ","int((e*x+d)^(3/2)/(c*x^2+b*x)^(3/2),x)","\frac{2 \left(b \,c^{2} e^{2} x^{2}-2 c^{3} d e \,x^{2}+\sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} e^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-3 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c d e \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+2 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c d e \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+2 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{2} d^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-2 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{2} d^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-2 c^{3} d^{2} x -b \,c^{2} d^{2}\right) \sqrt{\left(c x +b \right) x}}{\left(c x +b \right) \sqrt{e x +d}\, b^{2} c^{2} x}"," ",0,"2*(2*b^2*d*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*e*c-2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b*c^2*d^2+((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^3*e^2-3*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^2*c*d*e+2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b*c^2*d^2+b*c^2*e^2*x^2-2*c^3*d*e*x^2-2*x*c^3*d^2-c^2*d^2*b)/x*((c*x+b)*x)^(1/2)/(c*x+b)/b^2/c^2/(e*x+d)^(1/2)","B"
417,1,352,189,0.109000," ","int((e*x+d)^(1/2)/(c*x^2+b*x)^(3/2),x)","\frac{2 \left(-2 c^{2} e \,x^{2}-2 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} e \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+\sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} e \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+2 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b c d \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-2 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b c d \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-b c e x -2 c^{2} d x -b c d \right) \sqrt{\left(c x +b \right) x}}{\left(c x +b \right) \sqrt{e x +d}\, b^{2} c x}"," ",0,"2*(EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^2*e*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-2*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b*c*d*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-2*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^2*e*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)+2*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b*c*d*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)-2*c^2*e*x^2-b*c*e*x-2*x*c^2*d-b*c*d)/x*((c*x+b)*x)^(1/2)/(c*x+b)/b^2/c/(e*x+d)^(1/2)","A"
418,1,480,232,0.207000," ","int(1/(c*x^2+b*x)^(3/2)/(e*x+d)^(1/2),x)","-\frac{2 \left(b \,c^{2} e^{2} x^{2}-2 c^{3} d e \,x^{2}+\sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} e^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-3 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c d e \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+2 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c d e \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+b^{2} c \,e^{2} x +2 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{2} d^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-2 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{2} d^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-2 c^{3} d^{2} x +b^{2} c d e -b \,c^{2} d^{2}\right) \sqrt{\left(c x +b \right) x}}{\left(c x +b \right) \left(b e -c d \right) \sqrt{e x +d}\, b^{2} c d x}"," ",0,"-2/x*(2*b^2*d*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*e*c-2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b*c^2*d^2+((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^3*e^2-3*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^2*c*d*e+2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b*c^2*d^2+b*c^2*e^2*x^2-2*c^3*d*e*x^2+x*b^2*c*e^2-2*c^3*d^2*x+b^2*c*d*e-b*c^2*d^2)*((c*x+b)*x)^(1/2)/(c*x+b)/(b*e-c*d)/c/b^2/d/(e*x+d)^(1/2)","B"
419,1,698,324,0.144000," ","int(1/(e*x+d)^(3/2)/(c*x^2+b*x)^(3/2),x)","-\frac{2 \left(2 b^{2} c^{2} e^{3} x^{2}-2 b \,c^{3} d \,e^{2} x^{2}+2 c^{4} d^{2} e \,x^{2}+2 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{4} e^{3} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-4 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c d \,e^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+\sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c d \,e^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+2 b^{3} c \,e^{3} x +4 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{2} d^{2} e \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-3 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{2} d^{2} e \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-b^{2} c^{2} d \,e^{2} x -2 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{3} d^{3} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+2 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{3} d^{3} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-b \,c^{3} d^{2} e x +2 c^{4} d^{3} x +b^{3} c d \,e^{2}-2 b^{2} c^{2} d^{2} e +b \,c^{3} d^{3}\right) \sqrt{\left(c x +b \right) x}}{\left(c x +b \right) \left(b e -c d \right)^{2} \sqrt{e x +d}\, b^{2} c \,d^{2} x}"," ",0,"-2/x*(((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^3*c*d*e^2-3*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^2*c^2*d^2*e+2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b*c^3*d^3+2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^4*e^3-4*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^3*c*d*e^2+4*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^2*c^2*d^2*e-2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b*c^3*d^3+2*b^2*c^2*e^3*x^2-2*b*c^3*d*e^2*x^2+2*c^4*d^2*e*x^2+2*x*b^3*c*e^3-b^2*c^2*d*e^2*x-b*c^3*d^2*e*x+2*c^4*d^3*x+b^3*c*d*e^2-2*b^2*c^2*d^2*e+b*c^3*d^3)*((c*x+b)*x)^(1/2)/(c*x+b)/(b*e-c*d)^2/c/b^2/d^2/(e*x+d)^(1/2)","B"
420,1,1708,420,0.191000," ","int(1/(e*x+d)^(5/2)/(c*x^2+b*x)^(3/2),x)","-\frac{2 \sqrt{\left(c x +b \right) x}\, \left(8 b^{3} c^{2} e^{5} x^{3}-19 b^{2} c^{3} d \,e^{4} x^{3}+9 b \,c^{4} d^{2} e^{3} x^{3}-6 c^{5} d^{3} e^{2} x^{3}+8 \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, b^{5} e^{5} x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-27 \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, b^{4} c d \,e^{4} x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+4 \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, b^{4} c d \,e^{4} x \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+8 b^{4} c \,e^{5} x^{2}+28 \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, b^{3} c^{2} d^{2} e^{3} x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-10 \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, b^{3} c^{2} d^{2} e^{3} x \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-7 b^{3} c^{2} d \,e^{4} x^{2}-15 \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, b^{2} c^{3} d^{3} e^{2} x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+12 \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, b^{2} c^{3} d^{3} e^{2} x \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-20 b^{2} c^{3} d^{2} e^{3} x^{2}+6 \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, b \,c^{4} d^{4} e x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-6 \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, b \,c^{4} d^{4} e x \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+15 b \,c^{4} d^{3} e^{2} x^{2}-12 c^{5} d^{4} e \,x^{2}+8 \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, b^{5} d \,e^{4} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-27 \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, b^{4} c \,d^{2} e^{3} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+4 \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, b^{4} c \,d^{2} e^{3} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+12 b^{4} c d \,e^{4} x +28 \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, b^{3} c^{2} d^{3} e^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-10 \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, b^{3} c^{2} d^{3} e^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-26 b^{3} c^{2} d^{2} e^{3} x -15 \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, b^{2} c^{3} d^{4} e \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+12 \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, b^{2} c^{3} d^{4} e \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+9 b^{2} c^{3} d^{3} e^{2} x +6 \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, b \,c^{4} d^{5} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-6 \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, \sqrt{\frac{c x +b}{b}}\, b \,c^{4} d^{5} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+3 b \,c^{4} d^{4} e x -6 c^{5} d^{5} x +3 b^{4} c \,d^{2} e^{3}-9 b^{3} c^{2} d^{3} e^{2}+9 b^{2} c^{3} d^{4} e -3 b \,c^{4} d^{5}\right)}{3 \left(e x +d \right)^{\frac{3}{2}} \left(b e -c d \right)^{3} \left(c x +b \right) b^{2} c \,d^{3} x}"," ",0,"-2/3*((c*x+b)*x)^(1/2)/x*(-20*b^2*c^3*d^2*e^3*x^2+15*b*c^4*d^3*e^2*x^2-26*b^3*c^2*d^2*e^3*x+9*b^2*c^3*d^3*e^2*x+3*b*c^4*d^4*e*x+8*x^2*b^4*c*e^5+12*x*b^4*c*d*e^4+12*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^2*c^3*d^3*e^2*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*((c*x+b)/b)^(1/2)-6*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b*c^4*d^4*e*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*((c*x+b)/b)^(1/2)-27*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^4*c*d*e^4*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*((c*x+b)/b)^(1/2)+28*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^3*c^2*d^2*e^3*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*((c*x+b)/b)^(1/2)-15*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^2*c^3*d^3*e^2*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*((c*x+b)/b)^(1/2)+6*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b*c^4*d^4*e*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*((c*x+b)/b)^(1/2)+4*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^4*c*d*e^4*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*((c*x+b)/b)^(1/2)-10*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^3*c^2*d^2*e^3*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*((c*x+b)/b)^(1/2)-15*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^2*c^3*d^4*e*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*((c*x+b)/b)^(1/2)-6*x*c^5*d^5+3*b^4*c*d^2*e^3-9*b^3*c^2*d^3*e^2+9*b^2*c^3*d^4*e+8*b^3*c^2*e^5*x^3-6*c^5*d^3*e^2*x^3-12*c^5*d^4*e*x^2+4*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^4*c*d^2*e^3*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*((c*x+b)/b)^(1/2)-10*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^3*c^2*d^3*e^2*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*((c*x+b)/b)^(1/2)+12*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^2*c^3*d^4*e*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*((c*x+b)/b)^(1/2)-27*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^4*c*d^2*e^3*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*((c*x+b)/b)^(1/2)+28*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^3*c^2*d^3*e^2*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*((c*x+b)/b)^(1/2)-19*b^2*c^3*d*e^4*x^3+9*b*c^4*d^2*e^3*x^3-7*b^3*c^2*d*e^4*x^2-3*b*c^4*d^5+8*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b^5*d*e^4*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*((c*x+b)/b)^(1/2)+6*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b*c^4*d^5*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*((c*x+b)/b)^(1/2)+8*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^5*e^5*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*((c*x+b)/b)^(1/2)-6*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*b*c^4*d^5*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*((c*x+b)/b)^(1/2))/d^3/b^2/c/(e*x+d)^(3/2)/(b*e-c*d)^3/(c*x+b)","B"
421,1,2086,410,0.176000," ","int((e*x+d)^(9/2)/(c*x^2+b*x)^(5/2),x)","-\frac{2 \left(5 b^{4} c^{3} e^{5} x^{4}-7 b^{3} c^{4} d \,e^{4} x^{4}-9 b^{2} c^{5} d^{2} e^{3} x^{4}+32 b \,c^{6} d^{3} e^{2} x^{4}-16 c^{7} d^{4} e \,x^{4}+8 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{6} c \,e^{5} x^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-15 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{5} c^{2} d \,e^{4} x^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+4 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{5} c^{2} d \,e^{4} x^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+4 b^{5} c^{2} e^{5} x^{3}-2 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{4} c^{3} d^{2} e^{3} x^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-4 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{4} c^{3} d^{2} e^{3} x^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+2 b^{4} c^{3} d \,e^{4} x^{3}+41 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c^{4} d^{3} e^{2} x^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-24 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c^{4} d^{3} e^{2} x^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-22 b^{3} c^{4} d^{2} e^{3} x^{3}-48 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{5} d^{4} e \,x^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+40 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{5} d^{4} e \,x^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+40 b^{2} c^{5} d^{3} e^{2} x^{3}+16 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{6} d^{5} x^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-16 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{6} d^{5} x^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+8 b \,c^{6} d^{4} e \,x^{3}-16 c^{7} d^{5} x^{3}+8 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{7} e^{5} x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-15 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{6} c d \,e^{4} x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+4 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{6} c d \,e^{4} x \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-2 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{5} c^{2} d^{2} e^{3} x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-4 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{5} c^{2} d^{2} e^{3} x \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+4 b^{5} c^{2} d \,e^{4} x^{2}+41 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{4} c^{3} d^{3} e^{2} x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-24 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{4} c^{3} d^{3} e^{2} x \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-3 b^{4} c^{3} d^{2} e^{3} x^{2}-48 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c^{4} d^{4} e x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+40 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c^{4} d^{4} e x \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-2 b^{3} c^{4} d^{3} e^{2} x^{2}+16 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{5} d^{5} x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-16 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{5} d^{5} x \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+43 b^{2} c^{5} d^{4} e \,x^{2}-24 b \,c^{6} d^{5} x^{2}+14 b^{3} c^{4} d^{4} e x -6 b^{2} c^{5} d^{5} x +b^{3} c^{4} d^{5}\right) \sqrt{\left(c x +b \right) x}}{3 \left(c x +b \right)^{2} \sqrt{e x +d}\, b^{4} c^{4} x^{2}}"," ",0,"-2/3*(-7*x^4*b^3*c^4*d*e^4-15*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^6*c*d*e^4-2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^5*c^2*d^2*e^3-4*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^5*c^2*d^2*e^3-24*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^4*c^3*d^3*e^2+4*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^5*c^2*d*e^4-4*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^4*c^3*d^2*e^3-24*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^3*c^4*d^3*e^2+40*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^3*c^4*d^4*e+41*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^4*c^3*d^3*e^2-48*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^3*c^4*d^4*e-2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^4*c^3*d^2*e^3+41*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^3*c^4*d^3*e^2+40*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^2*c^5*d^4*e-15*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^5*c^2*d*e^4-48*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^2*c^5*d^4*e+4*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^6*c*d*e^4-16*x^3*c^7*d^5+5*x^4*b^4*c^3*e^5-16*x^4*c^7*d^4*e-24*x^2*b*c^6*d^5+4*x^3*b^5*c^2*e^5-6*x*b^2*c^5*d^5+b^3*c^4*d^5-3*x^2*b^4*c^3*d^2*e^3-2*x^2*b^3*c^4*d^3*e^2+43*x^2*b^2*c^5*d^4*e+2*x^3*b^4*c^3*d*e^4-22*x^3*b^3*c^4*d^2*e^3+40*x^3*b^2*c^5*d^3*e^2+16*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b*c^6*d^5-16*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^2*c^5*d^5+16*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^2*c^5*d^5-16*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b*c^6*d^5+8*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^6*c*e^5-9*x^4*b^2*c^5*d^2*e^3+32*x^4*b*c^6*d^3*e^2+8*x^3*b*c^6*d^4*e+14*x*b^3*c^4*d^4*e+4*x^2*b^5*c^2*d*e^4+8*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^7*e^5)/x^2*((c*x+b)*x)^(1/2)/b^4/(c*x+b)^2/c^4/(e*x+d)^(1/2)","B"
422,1,1687,329,0.139000," ","int((e*x+d)^(7/2)/(c*x^2+b*x)^(5/2),x)","\frac{2 \left(2 b^{3} c^{3} e^{4} x^{4}+4 b^{2} c^{4} d \,e^{3} x^{4}-24 b \,c^{5} d^{2} e^{2} x^{4}+16 c^{6} d^{3} e \,x^{4}+2 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{5} c \,e^{4} x^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+2 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{4} c^{2} d \,e^{3} x^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+\sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{4} c^{2} d \,e^{3} x^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+b^{4} c^{2} e^{4} x^{3}-28 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c^{3} d^{2} e^{2} x^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+15 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c^{3} d^{2} e^{2} x^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+9 b^{3} c^{3} d \,e^{3} x^{3}+40 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{4} d^{3} e \,x^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-32 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{4} d^{3} e \,x^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-33 b^{2} c^{4} d^{2} e^{2} x^{3}-16 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{5} d^{4} x^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+16 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{5} d^{4} x^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+16 c^{6} d^{4} x^{3}+2 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{6} e^{4} x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+2 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{5} c d \,e^{3} x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+\sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{5} c d \,e^{3} x \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-28 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{4} c^{2} d^{2} e^{2} x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+15 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{4} c^{2} d^{2} e^{2} x \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+b^{4} c^{2} d \,e^{3} x^{2}+40 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c^{3} d^{3} e x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-32 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c^{3} d^{3} e x \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-3 b^{3} c^{3} d^{2} e^{2} x^{2}-16 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{4} d^{4} x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+16 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{4} d^{4} x \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-31 b^{2} c^{4} d^{3} e \,x^{2}+24 b \,c^{5} d^{4} x^{2}-11 b^{3} c^{3} d^{3} e x +6 b^{2} c^{4} d^{4} x -b^{3} c^{3} d^{4}\right) \sqrt{\left(c x +b \right) x}}{3 \left(c x +b \right)^{2} \sqrt{e x +d}\, b^{4} c^{3} x^{2}}"," ",0,"2/3*(4*x^4*b^2*c^4*d*e^3+16*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^2*c^4*d^4-16*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^2*c^4*d^4+x^3*b^4*c^2*e^4+6*x*b^2*c^4*d^4+16*x^4*c^6*d^3*e+24*x^2*b*c^5*d^4+2*x^4*b^3*c^3*e^4-33*x^3*b^2*c^4*d^2*e^2-3*x^2*b^3*c^3*d^2*e^2+x^2*b^4*c^2*d*e^3+2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^5*c*d*e^3-28*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^4*c^2*d^2*e^2+40*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^3*c^3*d^3*e+((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^4*c^2*d*e^3+15*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^3*c^3*d^2*e^2-32*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^2*c^4*d^3*e+2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^4*c^2*d*e^3+((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^5*c*d*e^3+15*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^4*c^2*d^2*e^2-28*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^3*c^3*d^2*e^2+40*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^2*c^4*d^3*e-32*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^3*c^3*d^3*e+16*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b*c^5*d^4-31*x^2*b^2*c^4*d^3*e-11*x*b^3*c^3*d^3*e-24*x^4*b*c^5*d^2*e^2+9*x^3*b^3*c^3*d*e^3+16*x^3*c^6*d^4+2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^5*c*e^4-16*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b*c^5*d^4-b^3*c^3*d^4+2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^6*e^4)/x^2*((c*x+b)*x)^(1/2)/b^4/(c*x+b)^2/c^3/(e*x+d)^(1/2)","B"
423,1,1318,289,0.122000," ","int((e*x+d)^(5/2)/(c*x^2+b*x)^(5/2),x)","\frac{2 \left(b^{2} c^{3} e^{3} x^{4}-16 b \,c^{4} d \,e^{2} x^{4}+16 c^{5} d^{2} e \,x^{4}+\sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{4} c \,e^{3} x^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-17 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c^{2} d \,e^{2} x^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+8 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c^{2} d \,e^{2} x^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+2 b^{3} c^{2} e^{3} x^{3}+32 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{3} d^{2} e \,x^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-24 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{3} d^{2} e \,x^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-24 b^{2} c^{3} d \,e^{2} x^{3}-16 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{4} d^{3} x^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+16 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{4} d^{3} x^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+8 b \,c^{4} d^{2} e \,x^{3}+16 c^{5} d^{3} x^{3}+\sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{5} e^{3} x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-17 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{4} c d \,e^{2} x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+8 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{4} c d \,e^{2} x \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+32 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c^{2} d^{2} e x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-24 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c^{2} d^{2} e x \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-5 b^{3} c^{2} d \,e^{2} x^{2}-16 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{3} d^{3} x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+16 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{3} d^{3} x \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-19 b^{2} c^{3} d^{2} e \,x^{2}+24 b \,c^{4} d^{3} x^{2}-8 b^{3} c^{2} d^{2} e x +6 b^{2} c^{3} d^{3} x -b^{3} c^{2} d^{3}\right) \sqrt{\left(c x +b \right) x}}{3 \left(c x +b \right)^{2} \sqrt{e x +d}\, b^{4} c^{2} x^{2}}"," ",0,"2/3*(-5*x^2*b^3*c^2*d*e^2-17*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^3*c^2*d*e^2+32*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^2*c^3*d^2*e+8*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^3*c^2*d*e^2-24*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^2*c^3*d^2*e-17*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^4*c*d*e^2+32*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^3*c^2*d^2*e+8*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^4*c*d*e^2-24*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^3*c^2*d^2*e+16*x^3*c^5*d^3+((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^4*c*e^3+6*x*b^2*c^3*d^3+16*x^4*c^5*d^2*e+24*x^2*b*c^4*d^3+2*x^3*b^3*c^2*e^3+x^4*b^2*c^3*e^3-16*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b*c^4*d^3+16*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b*c^4*d^3-16*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^2*c^3*d^3+16*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^2*c^3*d^3-b^3*c^2*d^3-16*x^4*b*c^4*d*e^2+8*x^3*b*c^4*d^2*e-19*x^2*b^2*c^3*d^2*e-8*x*b^3*c^2*d^2*e-24*x^3*b^2*c^3*d*e^2+((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^5*e^3)/x^2*((c*x+b)*x)^(1/2)/b^4/c^2/(c*x+b)^2/(e*x+d)^(1/2)","B"
424,1,1099,290,0.116000," ","int((e*x+d)^(3/2)/(c*x^2+b*x)^(5/2),x)","\frac{2 \left(-8 b \,c^{3} e^{2} x^{4}+16 c^{4} d e \,x^{4}-8 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c \,e^{2} x^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+3 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c \,e^{2} x^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+24 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{2} d e \,x^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-16 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{2} d e \,x^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-13 b^{2} c^{2} e^{2} x^{3}-16 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{3} d^{2} x^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+16 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{3} d^{2} x^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+16 b \,c^{3} d e \,x^{3}+16 c^{4} d^{2} x^{3}-8 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{4} e^{2} x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+3 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{4} e^{2} x \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+24 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c d e x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-16 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c d e x \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-4 b^{3} c \,e^{2} x^{2}-16 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{2} d^{2} x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+16 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{2} d^{2} x \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-7 b^{2} c^{2} d e \,x^{2}+24 b \,c^{3} d^{2} x^{2}-5 b^{3} c d e x +6 b^{2} c^{2} d^{2} x -b^{3} c \,d^{2}\right) \sqrt{\left(c x +b \right) x}}{3 \left(c x +b \right)^{2} \sqrt{e x +d}\, b^{4} c \,x^{2}}"," ",0,"2/3*(3*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^3*c*e^2-16*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^2*c^2*d*e+16*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b*c^3*d^2-8*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^3*c*e^2+24*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^2*c^2*d*e-16*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b*c^3*d^2+3*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^4*e^2-16*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^3*c*d*e+16*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^2*c^2*d^2-8*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^4*e^2+24*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^3*c*d*e-16*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^2*c^2*d^2-8*x^4*b*c^3*e^2+16*x^4*c^4*d*e-13*x^3*b^2*c^2*e^2+16*x^3*b*c^3*d*e+16*x^3*c^4*d^2-4*x^2*b^3*c*e^2-7*x^2*b^2*c^2*d*e+24*x^2*b*c^3*d^2-5*x*b^3*c*d*e+6*x*b^2*c^2*d^2-b^3*c*d^2)/x^2*((c*x+b)*x)^(1/2)/b^4/c/(c*x+b)^2/(e*x+d)^(1/2)","B"
425,1,1362,305,0.120000," ","int((e*x+d)^(1/2)/(c*x^2+b*x)^(5/2),x)","-\frac{2 \left(b^{2} c^{3} e^{3} x^{4}-16 b \,c^{4} d \,e^{2} x^{4}+16 c^{5} d^{2} e \,x^{4}+\sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{4} c \,e^{3} x^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-17 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c^{2} d \,e^{2} x^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+8 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c^{2} d \,e^{2} x^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+2 b^{3} c^{2} e^{3} x^{3}+32 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{3} d^{2} e \,x^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-24 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{3} d^{2} e \,x^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-24 b^{2} c^{3} d \,e^{2} x^{3}-16 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{4} d^{3} x^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+16 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{4} d^{3} x^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+8 b \,c^{4} d^{2} e \,x^{3}+16 c^{5} d^{3} x^{3}+\sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{5} e^{3} x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-17 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{4} c d \,e^{2} x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+8 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{4} c d \,e^{2} x \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+b^{4} c \,e^{3} x^{2}+32 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c^{2} d^{2} e x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-24 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c^{2} d^{2} e x \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-5 b^{3} c^{2} d \,e^{2} x^{2}-16 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{3} d^{3} x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+16 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{3} d^{3} x \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-19 b^{2} c^{3} d^{2} e \,x^{2}+24 b \,c^{4} d^{3} x^{2}+2 b^{4} c d \,e^{2} x -8 b^{3} c^{2} d^{2} e x +6 b^{2} c^{3} d^{3} x +b^{4} c \,d^{2} e -b^{3} c^{2} d^{3}\right) \sqrt{\left(c x +b \right) x}}{3 \left(b e -c d \right) \left(c x +b \right)^{2} \sqrt{e x +d}\, b^{4} c d \,x^{2}}"," ",0,"-2/3/x^2*(2*x*b^4*c*d*e^2-5*b^3*c^2*d*e^2*x^2+b^4*c*d^2*e-17*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^3*c^2*d*e^2+32*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^2*c^3*d^2*e+8*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^3*c^2*d*e^2-24*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^2*c^3*d^2*e-17*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^4*c*d*e^2+32*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^3*c^2*d^2*e+8*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^4*c*d*e^2-24*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^3*c^2*d^2*e+16*c^5*d^3*x^3+((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^4*c*e^3+6*b^2*c^3*d^3*x+16*c^5*d^2*e*x^4+24*b*c^4*d^3*x^2+2*b^3*c^2*e^3*x^3+b^2*c^3*e^3*x^4-16*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b*c^4*d^3+16*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b*c^4*d^3-16*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^2*c^3*d^3+16*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^2*c^3*d^3+x^2*b^4*c*e^3-b^3*c^2*d^3-16*b*c^4*d*e^2*x^4+8*b*c^4*d^2*e*x^3-19*b^2*c^3*d^2*e*x^2-8*b^3*c^2*d^2*e*x-24*b^2*c^3*d*e^2*x^3+((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^5*e^3)*((c*x+b)*x)^(1/2)/c/b^4/d/(b*e-c*d)/(c*x+b)^2/(e*x+d)^(1/2)","B"
426,1,1763,397,0.220000," ","int(1/(c*x^2+b*x)^(5/2)/(e*x+d)^(1/2),x)","\frac{2 \left(2 b^{3} c^{3} e^{4} x^{4}+4 b^{2} c^{4} d \,e^{3} x^{4}-24 b \,c^{5} d^{2} e^{2} x^{4}+16 c^{6} d^{3} e \,x^{4}+2 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{5} c \,e^{4} x^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+2 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{4} c^{2} d \,e^{3} x^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+\sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{4} c^{2} d \,e^{3} x^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+4 b^{4} c^{2} e^{4} x^{3}-28 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c^{3} d^{2} e^{2} x^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+15 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c^{3} d^{2} e^{2} x^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+9 b^{3} c^{3} d \,e^{3} x^{3}+40 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{4} d^{3} e \,x^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-32 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{4} d^{3} e \,x^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-33 b^{2} c^{4} d^{2} e^{2} x^{3}-16 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{5} d^{4} x^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+16 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{5} d^{4} x^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+16 c^{6} d^{4} x^{3}+2 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{6} e^{4} x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+2 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{5} c d \,e^{3} x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+\sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{5} c d \,e^{3} x \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+2 b^{5} c \,e^{4} x^{2}-28 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{4} c^{2} d^{2} e^{2} x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+15 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{4} c^{2} d^{2} e^{2} x \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+6 b^{4} c^{2} d \,e^{3} x^{2}+40 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c^{3} d^{3} e x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-32 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c^{3} d^{3} e x \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-3 b^{3} c^{3} d^{2} e^{2} x^{2}-16 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{4} d^{4} x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+16 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{4} d^{4} x \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-31 b^{2} c^{4} d^{3} e \,x^{2}+24 b \,c^{5} d^{4} x^{2}+b^{5} c d \,e^{3} x +4 b^{4} c^{2} d^{2} e^{2} x -11 b^{3} c^{3} d^{3} e x +6 b^{2} c^{4} d^{4} x -b^{5} c \,d^{2} e^{2}+2 b^{4} c^{2} d^{3} e -b^{3} c^{3} d^{4}\right) \sqrt{\left(c x +b \right) x}}{3 \left(c x +b \right)^{2} \left(b e -c d \right)^{2} \sqrt{e x +d}\, b^{4} c \,d^{2} x^{2}}"," ",0,"2/3*(4*b^2*c^4*d*e^3*x^4+16*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^2*c^4*d^4-16*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^2*c^4*d^4+2*x^2*b^5*c*e^4+4*b^4*c^2*e^4*x^3+6*b^2*c^4*d^4*x+16*c^6*d^3*e*x^4+24*b*c^5*d^4*x^2+2*b^3*c^3*e^4*x^4-33*b^2*c^4*d^2*e^2*x^3-3*b^3*c^3*d^2*e^2*x^2+6*b^4*c^2*d*e^3*x^2-b^5*c*d^2*e^2+2*b^4*c^2*d^3*e+2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^5*c*d*e^3-28*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^4*c^2*d^2*e^2+40*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^3*c^3*d^3*e+((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^4*c^2*d*e^3+15*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^3*c^3*d^2*e^2-32*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^2*c^4*d^3*e+2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^4*c^2*d*e^3+((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^5*c*d*e^3+15*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^4*c^2*d^2*e^2-28*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^3*c^3*d^2*e^2+40*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^2*c^4*d^3*e-32*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^3*c^3*d^3*e+16*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b*c^5*d^4+x*b^5*c*d*e^3+4*x*b^4*c^2*d^2*e^2-31*b^2*c^4*d^3*e*x^2-11*b^3*c^3*d^3*e*x-24*b*c^5*d^2*e^2*x^4+9*b^3*c^3*d*e^3*x^3+16*c^6*d^4*x^3+2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^5*c*e^4-16*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b*c^5*d^4-b^3*c^3*d^4+2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^6*e^4)/x^2*((c*x+b)*x)^(1/2)/d^2/b^4/c/(c*x+b)^2/(b*e-c*d)^2/(e*x+d)^(1/2)","B"
427,1,2189,507,0.132000," ","int(1/(e*x+d)^(3/2)/(c*x^2+b*x)^(5/2),x)","\frac{2 \left(8 b^{4} c^{3} e^{5} x^{4}-7 b^{3} c^{4} d \,e^{4} x^{4}-9 b^{2} c^{5} d^{2} e^{3} x^{4}+32 b \,c^{6} d^{3} e^{2} x^{4}-16 c^{7} d^{4} e \,x^{4}+8 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{6} c \,e^{5} x^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-15 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{5} c^{2} d \,e^{4} x^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+4 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{5} c^{2} d \,e^{4} x^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+16 b^{5} c^{2} e^{5} x^{3}-2 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{4} c^{3} d^{2} e^{3} x^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-4 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{4} c^{3} d^{2} e^{3} x^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-10 b^{4} c^{3} d \,e^{4} x^{3}+41 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c^{4} d^{3} e^{2} x^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-24 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c^{4} d^{3} e^{2} x^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-22 b^{3} c^{4} d^{2} e^{3} x^{3}-48 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{5} d^{4} e \,x^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+40 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{5} d^{4} e \,x^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+40 b^{2} c^{5} d^{3} e^{2} x^{3}+16 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{6} d^{5} x^{2} \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-16 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b \,c^{6} d^{5} x^{2} \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+8 b \,c^{6} d^{4} e \,x^{3}-16 c^{7} d^{5} x^{3}+8 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{7} e^{5} x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-15 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{6} c d \,e^{4} x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+4 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{6} c d \,e^{4} x \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+8 b^{6} c \,e^{5} x^{2}-2 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{5} c^{2} d^{2} e^{3} x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-4 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{5} c^{2} d^{2} e^{3} x \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+b^{5} c^{2} d \,e^{4} x^{2}+41 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{4} c^{3} d^{3} e^{2} x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-24 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{4} c^{3} d^{3} e^{2} x \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-18 b^{4} c^{3} d^{2} e^{3} x^{2}-48 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c^{4} d^{4} e x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+40 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{3} c^{4} d^{4} e x \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-2 b^{3} c^{4} d^{3} e^{2} x^{2}+16 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{5} d^{5} x \EllipticE \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)-16 \sqrt{\frac{c x +b}{b}}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -c d}}\, \sqrt{-\frac{c x}{b}}\, b^{2} c^{5} d^{5} x \EllipticF \left(\sqrt{\frac{c x +b}{b}}, \sqrt{\frac{b e}{b e -c d}}\right)+43 b^{2} c^{5} d^{4} e \,x^{2}-24 b \,c^{6} d^{5} x^{2}+4 b^{6} c d \,e^{4} x -6 b^{5} c^{2} d^{2} e^{3} x -6 b^{4} c^{3} d^{3} e^{2} x +14 b^{3} c^{4} d^{4} e x -6 b^{2} c^{5} d^{5} x -b^{6} c \,d^{2} e^{3}+3 b^{5} c^{2} d^{3} e^{2}-3 b^{4} c^{3} d^{4} e +b^{3} c^{4} d^{5}\right) \sqrt{\left(c x +b \right) x}}{3 \left(c x +b \right)^{2} \left(b e -c d \right)^{3} \sqrt{e x +d}\, b^{4} c \,d^{3} x^{2}}"," ",0,"2/3*(-7*b^3*c^4*d*e^4*x^4+8*x^2*b^6*c*e^5-15*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^6*c*d*e^4-2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^5*c^2*d^2*e^3-4*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^5*c^2*d^2*e^3-24*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^4*c^3*d^3*e^2+4*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^5*c^2*d*e^4-4*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^4*c^3*d^2*e^3-24*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^3*c^4*d^3*e^2+40*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^3*c^4*d^4*e+41*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^4*c^3*d^3*e^2-48*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^3*c^4*d^4*e-2*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^4*c^3*d^2*e^3+41*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^3*c^4*d^3*e^2+40*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^2*c^5*d^4*e-15*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^5*c^2*d*e^4-48*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^2*c^5*d^4*e+4*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^6*c*d*e^4-b^6*c*d^2*e^3+3*b^5*c^2*d^3*e^2-3*b^4*c^3*d^4*e-16*c^7*d^5*x^3+8*b^4*c^3*e^5*x^4-16*c^7*d^4*e*x^4-24*b*c^6*d^5*x^2+16*b^5*c^2*e^5*x^3-6*b^2*c^5*d^5*x+b^3*c^4*d^5-18*b^4*c^3*d^2*e^3*x^2-2*b^3*c^4*d^3*e^2*x^2+43*b^2*c^5*d^4*e*x^2-10*b^4*c^3*d*e^4*x^3-22*b^3*c^4*d^2*e^3*x^3+40*b^2*c^5*d^3*e^2*x^3+16*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b*c^6*d^5-16*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^2*c^5*d^5+16*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^2*c^5*d^5-16*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticF(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b*c^6*d^5+8*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x^2*b^6*c*e^5-9*b^2*c^5*d^2*e^3*x^4+32*b*c^6*d^3*e^2*x^4+8*b*c^6*d^4*e*x^3+14*b^3*c^4*d^4*e*x+b^5*c^2*d*e^4*x^2-6*x*b^5*c^2*d^2*e^3-6*x*b^4*c^3*d^3*e^2+4*x*b^6*c*d*e^4+8*((c*x+b)/b)^(1/2)*(-(e*x+d)/(b*e-c*d)*c)^(1/2)*(-1/b*c*x)^(1/2)*EllipticE(((c*x+b)/b)^(1/2),(1/(b*e-c*d)*b*e)^(1/2))*x*b^7*e^5)/x^2*((c*x+b)*x)^(1/2)/d^3/b^4/c/(c*x+b)^2/(b*e-c*d)^3/(e*x+d)^(1/2)","B"
428,1,215,41,0.120000," ","int((e*x+d)^(1/2)/(-3*x^2+2*x)^(1/2),x)","-\frac{2 \sqrt{e x +d}\, \sqrt{-\left(3 x -2\right) x}\, \sqrt{\frac{e x +d}{d}}\, \sqrt{-\frac{\left(3 x -2\right) e}{3 d +2 e}}\, \sqrt{-\frac{e x}{d}}\, \left(-3 d \EllipticE \left(\sqrt{\frac{e x +d}{d}}, \sqrt{3}\, \sqrt{\frac{d}{3 d +2 e}}\right)+3 d \EllipticF \left(\sqrt{\frac{e x +d}{d}}, \sqrt{3}\, \sqrt{\frac{d}{3 d +2 e}}\right)-2 e \EllipticE \left(\sqrt{\frac{e x +d}{d}}, \sqrt{3}\, \sqrt{\frac{d}{3 d +2 e}}\right)+2 e \EllipticF \left(\sqrt{\frac{e x +d}{d}}, \sqrt{3}\, \sqrt{\frac{d}{3 d +2 e}}\right)\right) d}{3 \left(3 e \,x^{2}+3 d x -2 e x -2 d \right) e x}"," ",0,"-2/3*(e*x+d)^(1/2)*(-x*(3*x-2))^(1/2)*d*((e*x+d)/d)^(1/2)*(-(3*x-2)*e/(3*d+2*e))^(1/2)*(-e*x/d)^(1/2)*(3*d*EllipticF(((e*x+d)/d)^(1/2),3^(1/2)*(d/(3*d+2*e))^(1/2))+2*EllipticF(((e*x+d)/d)^(1/2),3^(1/2)*(d/(3*d+2*e))^(1/2))*e-3*EllipticE(((e*x+d)/d)^(1/2),3^(1/2)*(d/(3*d+2*e))^(1/2))*d-2*EllipticE(((e*x+d)/d)^(1/2),3^(1/2)*(d/(3*d+2*e))^(1/2))*e)/e/x/(3*e*x^2+3*d*x-2*e*x-2*d)","B"
429,1,115,41,0.076000," ","int(1/(e*x+d)^(1/2)/(-3*x^2+2*x)^(1/2),x)","-\frac{2 \sqrt{-\frac{e x}{d}}\, \sqrt{-\frac{\left(3 x -2\right) e}{3 d +2 e}}\, \sqrt{\frac{e x +d}{d}}\, \sqrt{e x +d}\, \sqrt{-\left(3 x -2\right) x}\, d \EllipticF \left(\sqrt{\frac{e x +d}{d}}, \sqrt{3}\, \sqrt{\frac{d}{3 d +2 e}}\right)}{\left(3 e \,x^{2}+3 d x -2 e x -2 d \right) e x}"," ",0,"-2*EllipticF(((e*x+d)/d)^(1/2),3^(1/2)*(1/(3*d+2*e)*d)^(1/2))*(-1/d*e*x)^(1/2)*(-(3*x-2)/(3*d+2*e)*e)^(1/2)*((e*x+d)/d)^(1/2)*d*(e*x+d)^(1/2)*(-(3*x-2)*x)^(1/2)/e/x/(3*e*x^2+3*d*x-2*e*x-2*d)","B"
430,1,215,45,0.117000," ","int((e*x+d)^(1/2)/(-3*x^2-2*x)^(1/2),x)","-\frac{2 \sqrt{e x +d}\, \sqrt{-\left(3 x +2\right) x}\, \sqrt{\frac{e x +d}{d}}\, \sqrt{-\frac{\left(3 x +2\right) e}{3 d -2 e}}\, \sqrt{-\frac{e x}{d}}\, \left(-3 d \EllipticE \left(\sqrt{\frac{e x +d}{d}}, \sqrt{3}\, \sqrt{\frac{d}{3 d -2 e}}\right)+3 d \EllipticF \left(\sqrt{\frac{e x +d}{d}}, \sqrt{3}\, \sqrt{\frac{d}{3 d -2 e}}\right)+2 e \EllipticE \left(\sqrt{\frac{e x +d}{d}}, \sqrt{3}\, \sqrt{\frac{d}{3 d -2 e}}\right)-2 e \EllipticF \left(\sqrt{\frac{e x +d}{d}}, \sqrt{3}\, \sqrt{\frac{d}{3 d -2 e}}\right)\right) d}{3 \left(3 e \,x^{2}+3 d x +2 e x +2 d \right) e x}"," ",0,"-2/3*(e*x+d)^(1/2)*(-x*(3*x+2))^(1/2)*d*((e*x+d)/d)^(1/2)*(-(3*x+2)*e/(3*d-2*e))^(1/2)*(-1/d*e*x)^(1/2)*(3*d*EllipticF(((e*x+d)/d)^(1/2),3^(1/2)*(d/(3*d-2*e))^(1/2))-2*EllipticF(((e*x+d)/d)^(1/2),3^(1/2)*(d/(3*d-2*e))^(1/2))*e-3*EllipticE(((e*x+d)/d)^(1/2),3^(1/2)*(d/(3*d-2*e))^(1/2))*d+2*EllipticE(((e*x+d)/d)^(1/2),3^(1/2)*(d/(3*d-2*e))^(1/2))*e)/e/x/(3*e*x^2+3*d*x+2*e*x+2*d)","B"
431,1,115,45,0.085000," ","int(1/(e*x+d)^(1/2)/(-3*x^2-2*x)^(1/2),x)","-\frac{2 \sqrt{-\frac{e x}{d}}\, \sqrt{-\frac{\left(3 x +2\right) e}{3 d -2 e}}\, \sqrt{\frac{e x +d}{d}}\, \sqrt{e x +d}\, \sqrt{-\left(3 x +2\right) x}\, d \EllipticF \left(\sqrt{\frac{e x +d}{d}}, \sqrt{3}\, \sqrt{\frac{d}{3 d -2 e}}\right)}{\left(3 e \,x^{2}+3 d x +2 e x +2 d \right) e x}"," ",0,"-2*EllipticF(((e*x+d)/d)^(1/2),3^(1/2)*(1/(3*d-2*e)*d)^(1/2))*(-1/d*e*x)^(1/2)*(-(3*x+2)/(3*d-2*e)*e)^(1/2)*((e*x+d)/d)^(1/2)*d*(e*x+d)^(1/2)*(-(3*x+2)*x)^(1/2)/e/x/(3*e*x^2+3*d*x+2*e*x+2*d)","B"
432,1,17,10,0.064000," ","int((1-x)^(1/2)/(-x)^(1/2)/(x+1)^(1/2),x)","2 \sqrt{2}\, \EllipticE \left(\sqrt{x +1}, \frac{\sqrt{2}}{2}\right)"," ",0,"2*2^(1/2)*EllipticE((x+1)^(1/2),1/2*2^(1/2))","A"
433,1,50,10,0.055000," ","int((1-x)^(1/2)/(-x^2-x)^(1/2),x)","\frac{2 \left(-x +1\right) \sqrt{-\left(x +1\right) x}\, \sqrt{x +1}\, \sqrt{2}\, \sqrt{-x}\, \EllipticE \left(\sqrt{x +1}, \frac{\sqrt{2}}{2}\right)}{\left(x^{2}-1\right) x}"," ",0,"2*(1-x)*(-x*(x+1))^(1/2)*(x+1)^(1/2)*2^(1/2)*(-x)^(1/2)*EllipticE((x+1)^(1/2),1/2*2^(1/2))/x/(x^2-1)","B"
434,1,129,95,0.047000," ","int((e*x+d)^m*(c*e*x^2+c*d*x)^3,x)","-\frac{\left(-e^{3} m^{3} x^{3}-15 e^{3} m^{2} x^{3}+3 d \,e^{2} m^{2} x^{2}-74 e^{3} m \,x^{3}+27 d \,e^{2} m \,x^{2}-120 x^{3} e^{3}-6 d^{2} e m x +60 d \,x^{2} e^{2}-24 d^{2} x e +6 d^{3}\right) c^{3} \left(e x +d \right)^{m +4}}{\left(m^{4}+22 m^{3}+179 m^{2}+638 m +840\right) e^{4}}"," ",0,"-c^3*(e*x+d)^(m+4)*(-e^3*m^3*x^3-15*e^3*m^2*x^3+3*d*e^2*m^2*x^2-74*e^3*m*x^3+27*d*e^2*m*x^2-120*e^3*x^3-6*d^2*e*m*x+60*d*e^2*x^2-24*d^2*e*x+6*d^3)/e^4/(m^4+22*m^3+179*m^2+638*m+840)","A"
435,1,76,69,0.043000," ","int((e*x+d)^m*(c*e*x^2+c*d*x)^2,x)","\frac{\left(e^{2} m^{2} x^{2}+7 e^{2} m \,x^{2}-2 d e m x +12 x^{2} e^{2}-6 e x d +2 d^{2}\right) c^{2} \left(e x +d \right)^{m +3}}{\left(m^{3}+12 m^{2}+47 m +60\right) e^{3}}"," ",0,"(e*x+d)^(m+3)*(e^2*m^2*x^2+7*e^2*m*x^2-2*d*e*m*x+12*e^2*x^2-6*d*e*x+2*d^2)*c^2/e^3/(m^3+12*m^2+47*m+60)","A"
436,1,37,41,0.036000," ","int((e*x+d)^m*(c*e*x^2+c*d*x),x)","-\frac{\left(-m e x -2 e x +d \right) c \left(e x +d \right)^{m +2}}{\left(m^{2}+5 m +6\right) e^{2}}"," ",0,"-c*(e*x+d)^(m+2)*(-e*m*x-2*e*x+d)/e^2/(m^2+5*m+6)","A"
437,1,19,18,0.038000," ","int((e*x+d)^m,x)","\frac{\left(e x +d \right)^{m +1}}{\left(m +1\right) e}"," ",0,"(e*x+d)^(m+1)/e/(m+1)","A"
438,0,0,34,0.698000," ","int((e*x+d)^m/(c*e*x^2+c*d*x),x)","\int \frac{\left(e x +d \right)^{m}}{c e \,x^{2}+c d x}\, dx"," ",0,"int((e*x+d)^m/(c*e*x^2+c*d*x),x)","F"
439,0,0,41,0.696000," ","int((e*x+d)^m/(c*e*x^2+c*d*x)^2,x)","\int \frac{\left(e x +d \right)^{m}}{\left(c e \,x^{2}+c d x \right)^{2}}\, dx"," ",0,"int((e*x+d)^m/(c*e*x^2+c*d*x)^2,x)","F"
440,1,1528,267,0.056000," ","int((e*x+d)^m*(c*x^2+b*x)^3,x)","-\frac{\left(-c^{3} e^{6} m^{6} x^{6}-3 b \,c^{2} e^{6} m^{6} x^{5}-21 c^{3} e^{6} m^{5} x^{6}-3 b^{2} c \,e^{6} m^{6} x^{4}-66 b \,c^{2} e^{6} m^{5} x^{5}+6 c^{3} d \,e^{5} m^{5} x^{5}-175 c^{3} e^{6} m^{4} x^{6}-b^{3} e^{6} m^{6} x^{3}-69 b^{2} c \,e^{6} m^{5} x^{4}+15 b \,c^{2} d \,e^{5} m^{5} x^{4}-570 b \,c^{2} e^{6} m^{4} x^{5}+90 c^{3} d \,e^{5} m^{4} x^{5}-735 c^{3} e^{6} m^{3} x^{6}-24 b^{3} e^{6} m^{5} x^{3}+12 b^{2} c d \,e^{5} m^{5} x^{3}-621 b^{2} c \,e^{6} m^{4} x^{4}+255 b \,c^{2} d \,e^{5} m^{4} x^{4}-2460 b \,c^{2} e^{6} m^{3} x^{5}-30 c^{3} d^{2} e^{4} m^{4} x^{4}+510 c^{3} d \,e^{5} m^{3} x^{5}-1624 c^{3} e^{6} m^{2} x^{6}+3 b^{3} d \,e^{5} m^{5} x^{2}-226 b^{3} e^{6} m^{4} x^{3}+228 b^{2} c d \,e^{5} m^{4} x^{3}-2775 b^{2} c \,e^{6} m^{3} x^{4}-60 b \,c^{2} d^{2} e^{4} m^{4} x^{3}+1575 b \,c^{2} d \,e^{5} m^{3} x^{4}-5547 b \,c^{2} e^{6} m^{2} x^{5}-300 c^{3} d^{2} e^{4} m^{3} x^{4}+1350 c^{3} d \,e^{5} m^{2} x^{5}-1764 c^{3} e^{6} m \,x^{6}+63 b^{3} d \,e^{5} m^{4} x^{2}-1056 b^{3} e^{6} m^{3} x^{3}-36 b^{2} c \,d^{2} e^{4} m^{4} x^{2}+1572 b^{2} c d \,e^{5} m^{3} x^{3}-6432 b^{2} c \,e^{6} m^{2} x^{4}-780 b \,c^{2} d^{2} e^{4} m^{3} x^{3}+4425 b \,c^{2} d \,e^{5} m^{2} x^{4}-6114 b \,c^{2} e^{6} m \,x^{5}+120 c^{3} d^{3} e^{3} m^{3} x^{3}-1050 c^{3} d^{2} e^{4} m^{2} x^{4}+1644 c^{3} d \,e^{5} m \,x^{5}-720 c^{3} x^{6} e^{6}-6 b^{3} d^{2} e^{4} m^{4} x +489 b^{3} d \,e^{5} m^{3} x^{2}-2545 b^{3} e^{6} m^{2} x^{3}-576 b^{2} c \,d^{2} e^{4} m^{3} x^{2}+4812 b^{2} c d \,e^{5} m^{2} x^{3}-7236 b^{2} c \,e^{6} m \,x^{4}+180 b \,c^{2} d^{3} e^{3} m^{3} x^{2}-3180 b \,c^{2} d^{2} e^{4} m^{2} x^{3}+5610 b \,c^{2} d \,e^{5} m \,x^{4}-2520 b \,c^{2} e^{6} x^{5}+720 c^{3} d^{3} e^{3} m^{2} x^{3}-1500 c^{3} d^{2} e^{4} m \,x^{4}+720 c^{3} d \,e^{5} x^{5}-114 b^{3} d^{2} e^{4} m^{3} x +1701 b^{3} d \,e^{5} m^{2} x^{2}-2952 b^{3} e^{6} m \,x^{3}+72 b^{2} c \,d^{3} e^{3} m^{3} x -2988 b^{2} c \,d^{2} e^{4} m^{2} x^{2}+6480 b^{2} c d \,e^{5} m \,x^{3}-3024 b^{2} c \,e^{6} x^{4}+1800 b \,c^{2} d^{3} e^{3} m^{2} x^{2}-4980 b \,c^{2} d^{2} e^{4} m \,x^{3}+2520 b \,c^{2} d \,e^{5} x^{4}-360 c^{3} d^{4} e^{2} m^{2} x^{2}+1320 c^{3} d^{3} e^{3} m \,x^{3}-720 c^{3} d^{2} e^{4} x^{4}+6 b^{3} d^{3} e^{3} m^{3}-750 b^{3} d^{2} e^{4} m^{2} x +2532 b^{3} d \,e^{5} m \,x^{2}-1260 b^{3} e^{6} x^{3}+1008 b^{2} c \,d^{3} e^{3} m^{2} x -5472 b^{2} c \,d^{2} e^{4} m \,x^{2}+3024 b^{2} c d \,e^{5} x^{3}-360 b \,c^{2} d^{4} e^{2} m^{2} x +4140 b \,c^{2} d^{3} e^{3} m \,x^{2}-2520 b \,c^{2} d^{2} e^{4} x^{3}-1080 c^{3} d^{4} e^{2} m \,x^{2}+720 c^{3} d^{3} e^{3} x^{3}+108 b^{3} d^{3} e^{3} m^{2}-1902 b^{3} d^{2} e^{4} m x +1260 b^{3} d \,e^{5} x^{2}-72 b^{2} c \,d^{4} e^{2} m^{2}+3960 b^{2} c \,d^{3} e^{3} m x -3024 b^{2} c \,d^{2} e^{4} x^{2}-2880 b \,c^{2} d^{4} e^{2} m x +2520 b \,c^{2} d^{3} e^{3} x^{2}+720 c^{3} d^{5} e m x -720 c^{3} d^{4} e^{2} x^{2}+642 b^{3} d^{3} e^{3} m -1260 b^{3} d^{2} e^{4} x -936 b^{2} c \,d^{4} e^{2} m +3024 b^{2} c \,d^{3} e^{3} x +360 b \,c^{2} d^{5} e m -2520 b \,c^{2} d^{4} e^{2} x +720 c^{3} d^{5} e x +1260 b^{3} d^{3} e^{3}-3024 b^{2} c \,d^{4} e^{2}+2520 b \,c^{2} d^{5} e -720 c^{3} d^{6}\right) \left(e x +d \right)^{m +1}}{\left(m^{7}+28 m^{6}+322 m^{5}+1960 m^{4}+6769 m^{3}+13132 m^{2}+13068 m +5040\right) e^{7}}"," ",0,"-(e*x+d)^(m+1)*(-c^3*e^6*m^6*x^6-3*b*c^2*e^6*m^6*x^5-21*c^3*e^6*m^5*x^6-3*b^2*c*e^6*m^6*x^4-66*b*c^2*e^6*m^5*x^5+6*c^3*d*e^5*m^5*x^5-175*c^3*e^6*m^4*x^6-b^3*e^6*m^6*x^3-69*b^2*c*e^6*m^5*x^4+15*b*c^2*d*e^5*m^5*x^4-570*b*c^2*e^6*m^4*x^5+90*c^3*d*e^5*m^4*x^5-735*c^3*e^6*m^3*x^6-24*b^3*e^6*m^5*x^3+12*b^2*c*d*e^5*m^5*x^3-621*b^2*c*e^6*m^4*x^4+255*b*c^2*d*e^5*m^4*x^4-2460*b*c^2*e^6*m^3*x^5-30*c^3*d^2*e^4*m^4*x^4+510*c^3*d*e^5*m^3*x^5-1624*c^3*e^6*m^2*x^6+3*b^3*d*e^5*m^5*x^2-226*b^3*e^6*m^4*x^3+228*b^2*c*d*e^5*m^4*x^3-2775*b^2*c*e^6*m^3*x^4-60*b*c^2*d^2*e^4*m^4*x^3+1575*b*c^2*d*e^5*m^3*x^4-5547*b*c^2*e^6*m^2*x^5-300*c^3*d^2*e^4*m^3*x^4+1350*c^3*d*e^5*m^2*x^5-1764*c^3*e^6*m*x^6+63*b^3*d*e^5*m^4*x^2-1056*b^3*e^6*m^3*x^3-36*b^2*c*d^2*e^4*m^4*x^2+1572*b^2*c*d*e^5*m^3*x^3-6432*b^2*c*e^6*m^2*x^4-780*b*c^2*d^2*e^4*m^3*x^3+4425*b*c^2*d*e^5*m^2*x^4-6114*b*c^2*e^6*m*x^5+120*c^3*d^3*e^3*m^3*x^3-1050*c^3*d^2*e^4*m^2*x^4+1644*c^3*d*e^5*m*x^5-720*c^3*e^6*x^6-6*b^3*d^2*e^4*m^4*x+489*b^3*d*e^5*m^3*x^2-2545*b^3*e^6*m^2*x^3-576*b^2*c*d^2*e^4*m^3*x^2+4812*b^2*c*d*e^5*m^2*x^3-7236*b^2*c*e^6*m*x^4+180*b*c^2*d^3*e^3*m^3*x^2-3180*b*c^2*d^2*e^4*m^2*x^3+5610*b*c^2*d*e^5*m*x^4-2520*b*c^2*e^6*x^5+720*c^3*d^3*e^3*m^2*x^3-1500*c^3*d^2*e^4*m*x^4+720*c^3*d*e^5*x^5-114*b^3*d^2*e^4*m^3*x+1701*b^3*d*e^5*m^2*x^2-2952*b^3*e^6*m*x^3+72*b^2*c*d^3*e^3*m^3*x-2988*b^2*c*d^2*e^4*m^2*x^2+6480*b^2*c*d*e^5*m*x^3-3024*b^2*c*e^6*x^4+1800*b*c^2*d^3*e^3*m^2*x^2-4980*b*c^2*d^2*e^4*m*x^3+2520*b*c^2*d*e^5*x^4-360*c^3*d^4*e^2*m^2*x^2+1320*c^3*d^3*e^3*m*x^3-720*c^3*d^2*e^4*x^4+6*b^3*d^3*e^3*m^3-750*b^3*d^2*e^4*m^2*x+2532*b^3*d*e^5*m*x^2-1260*b^3*e^6*x^3+1008*b^2*c*d^3*e^3*m^2*x-5472*b^2*c*d^2*e^4*m*x^2+3024*b^2*c*d*e^5*x^3-360*b*c^2*d^4*e^2*m^2*x+4140*b*c^2*d^3*e^3*m*x^2-2520*b*c^2*d^2*e^4*x^3-1080*c^3*d^4*e^2*m*x^2+720*c^3*d^3*e^3*x^3+108*b^3*d^3*e^3*m^2-1902*b^3*d^2*e^4*m*x+1260*b^3*d*e^5*x^2-72*b^2*c*d^4*e^2*m^2+3960*b^2*c*d^3*e^3*m*x-3024*b^2*c*d^2*e^4*x^2-2880*b*c^2*d^4*e^2*m*x+2520*b*c^2*d^3*e^3*x^2+720*c^3*d^5*e*m*x-720*c^3*d^4*e^2*x^2+642*b^3*d^3*e^3*m-1260*b^3*d^2*e^4*x-936*b^2*c*d^4*e^2*m+3024*b^2*c*d^3*e^3*x+360*b*c^2*d^5*e*m-2520*b*c^2*d^4*e^2*x+720*c^3*d^5*e*x+1260*b^3*d^3*e^3-3024*b^2*c*d^4*e^2+2520*b*c^2*d^5*e-720*c^3*d^6)/e^7/(m^7+28*m^6+322*m^5+1960*m^4+6769*m^3+13132*m^2+13068*m+5040)","B"
441,1,547,159,0.051000," ","int((e*x+d)^m*(c*x^2+b*x)^2,x)","\frac{\left(c^{2} e^{4} m^{4} x^{4}+2 b c \,e^{4} m^{4} x^{3}+10 c^{2} e^{4} m^{3} x^{4}+b^{2} e^{4} m^{4} x^{2}+22 b c \,e^{4} m^{3} x^{3}-4 c^{2} d \,e^{3} m^{3} x^{3}+35 c^{2} e^{4} m^{2} x^{4}+12 b^{2} e^{4} m^{3} x^{2}-6 b c d \,e^{3} m^{3} x^{2}+82 b c \,e^{4} m^{2} x^{3}-24 c^{2} d \,e^{3} m^{2} x^{3}+50 c^{2} e^{4} m \,x^{4}-2 b^{2} d \,e^{3} m^{3} x +49 b^{2} e^{4} m^{2} x^{2}-48 b c d \,e^{3} m^{2} x^{2}+122 b c \,e^{4} m \,x^{3}+12 c^{2} d^{2} e^{2} m^{2} x^{2}-44 c^{2} d \,e^{3} m \,x^{3}+24 c^{2} x^{4} e^{4}-20 b^{2} d \,e^{3} m^{2} x +78 b^{2} e^{4} m \,x^{2}+12 b c \,d^{2} e^{2} m^{2} x -102 b c d \,e^{3} m \,x^{2}+60 b c \,e^{4} x^{3}+36 c^{2} d^{2} e^{2} m \,x^{2}-24 c^{2} d \,e^{3} x^{3}+2 b^{2} d^{2} e^{2} m^{2}-58 b^{2} d \,e^{3} m x +40 b^{2} e^{4} x^{2}+72 b c \,d^{2} e^{2} m x -60 b c d \,e^{3} x^{2}-24 c^{2} d^{3} e m x +24 c^{2} d^{2} e^{2} x^{2}+18 b^{2} d^{2} e^{2} m -40 b^{2} d \,e^{3} x -12 b c \,d^{3} e m +60 b c \,d^{2} e^{2} x -24 c^{2} d^{3} e x +40 b^{2} d^{2} e^{2}-60 b c \,d^{3} e +24 c^{2} d^{4}\right) \left(e x +d \right)^{m +1}}{\left(m^{5}+15 m^{4}+85 m^{3}+225 m^{2}+274 m +120\right) e^{5}}"," ",0,"(e*x+d)^(m+1)*(c^2*e^4*m^4*x^4+2*b*c*e^4*m^4*x^3+10*c^2*e^4*m^3*x^4+b^2*e^4*m^4*x^2+22*b*c*e^4*m^3*x^3-4*c^2*d*e^3*m^3*x^3+35*c^2*e^4*m^2*x^4+12*b^2*e^4*m^3*x^2-6*b*c*d*e^3*m^3*x^2+82*b*c*e^4*m^2*x^3-24*c^2*d*e^3*m^2*x^3+50*c^2*e^4*m*x^4-2*b^2*d*e^3*m^3*x+49*b^2*e^4*m^2*x^2-48*b*c*d*e^3*m^2*x^2+122*b*c*e^4*m*x^3+12*c^2*d^2*e^2*m^2*x^2-44*c^2*d*e^3*m*x^3+24*c^2*e^4*x^4-20*b^2*d*e^3*m^2*x+78*b^2*e^4*m*x^2+12*b*c*d^2*e^2*m^2*x-102*b*c*d*e^3*m*x^2+60*b*c*e^4*x^3+36*c^2*d^2*e^2*m*x^2-24*c^2*d*e^3*x^3+2*b^2*d^2*e^2*m^2-58*b^2*d*e^3*m*x+40*b^2*e^4*x^2+72*b*c*d^2*e^2*m*x-60*b*c*d*e^3*x^2-24*c^2*d^3*e*m*x+24*c^2*d^2*e^2*x^2+18*b^2*d^2*e^2*m-40*b^2*d*e^3*x-12*b*c*d^3*e*m+60*b*c*d^2*e^2*x-24*c^2*d^3*e*x+40*b^2*d^2*e^2-60*b*c*d^3*e+24*c^2*d^4)/e^5/(m^5+15*m^4+85*m^3+225*m^2+274*m+120)","B"
442,1,116,75,0.044000," ","int((e*x+d)^m*(c*x^2+b*x),x)","-\frac{\left(-c \,e^{2} m^{2} x^{2}-b \,e^{2} m^{2} x -3 c \,e^{2} m \,x^{2}-4 b \,e^{2} m x +2 c d e m x -2 c \,e^{2} x^{2}+b d e m -3 b \,e^{2} x +2 c d e x +3 b d e -2 c \,d^{2}\right) \left(e x +d \right)^{m +1}}{\left(m^{3}+6 m^{2}+11 m +6\right) e^{3}}"," ",0,"-(e*x+d)^(m+1)*(-c*e^2*m^2*x^2-b*e^2*m^2*x-3*c*e^2*m*x^2-4*b*e^2*m*x+2*c*d*e*m*x-2*c*e^2*x^2+b*d*e*m-3*b*e^2*x+2*c*d*e*x+3*b*d*e-2*c*d^2)/e^3/(m^3+6*m^2+11*m+6)","A"
443,0,0,97,0.729000," ","int((e*x+d)^m/(c*x^2+b*x),x)","\int \frac{\left(e x +d \right)^{m}}{c \,x^{2}+b x}\, dx"," ",0,"int((e*x+d)^m/(c*x^2+b*x),x)","F"
444,0,0,184,0.643000," ","int((e*x+d)^m/(c*x^2+b*x)^2,x)","\int \frac{\left(e x +d \right)^{m}}{\left(c \,x^{2}+b x \right)^{2}}\, dx"," ",0,"int((e*x+d)^m/(c*x^2+b*x)^2,x)","F"
445,0,0,346,0.727000," ","int((e*x+d)^m/(c*x^2+b*x)^3,x)","\int \frac{\left(e x +d \right)^{m}}{\left(c \,x^{2}+b x \right)^{3}}\, dx"," ",0,"int((e*x+d)^m/(c*x^2+b*x)^3,x)","F"
446,0,0,95,0.777000," ","int((e*x+d)^m*(c*x^2+b*x)^(3/2),x)","\int \left(c \,x^{2}+b x \right)^{\frac{3}{2}} \left(e x +d \right)^{m}\, dx"," ",0,"int((e*x+d)^m*(c*x^2+b*x)^(3/2),x)","F"
447,0,0,95,0.694000," ","int((e*x+d)^m*(c*x^2+b*x)^(1/2),x)","\int \sqrt{c \,x^{2}+b x}\, \left(e x +d \right)^{m}\, dx"," ",0,"int((e*x+d)^m*(c*x^2+b*x)^(1/2),x)","F"
448,0,0,95,0.701000," ","int((e*x+d)^m/(c*x^2+b*x)^(1/2),x)","\int \frac{\left(e x +d \right)^{m}}{\sqrt{c \,x^{2}+b x}}\, dx"," ",0,"int((e*x+d)^m/(c*x^2+b*x)^(1/2),x)","F"
449,0,0,95,0.654000," ","int((e*x+d)^m/(c*x^2+b*x)^(3/2),x)","\int \frac{\left(e x +d \right)^{m}}{\left(c \,x^{2}+b x \right)^{\frac{3}{2}}}\, dx"," ",0,"int((e*x+d)^m/(c*x^2+b*x)^(3/2),x)","F"
450,0,0,103,0.679000," ","int((e*x+d)^m*(c*x^2+b*x)^p,x)","\int \left(c \,x^{2}+b x \right)^{p} \left(e x +d \right)^{m}\, dx"," ",0,"int((e*x+d)^m*(c*x^2+b*x)^p,x)","F"
451,1,97,51,0.036000," ","int((e*x+d)^4*(c*x^2+a),x)","\frac{c \,e^{4} x^{7}}{7}+\frac{2 c d \,e^{3} x^{6}}{3}+2 a \,d^{3} e \,x^{2}+a \,d^{4} x +\frac{\left(e^{4} a +6 d^{2} e^{2} c \right) x^{5}}{5}+\frac{\left(4 d \,e^{3} a +4 d^{3} e c \right) x^{4}}{4}+\frac{\left(6 d^{2} e^{2} a +d^{4} c \right) x^{3}}{3}"," ",0,"1/7*e^4*c*x^7+2/3*d*e^3*c*x^6+1/5*(a*e^4+6*c*d^2*e^2)*x^5+1/4*(4*a*d*e^3+4*c*d^3*e)*x^4+1/3*(6*a*d^2*e^2+c*d^4)*x^3+2*d^3*e*a*x^2+d^4*a*x","A"
452,1,73,51,0.035000," ","int((e*x+d)^3*(c*x^2+a),x)","\frac{c \,e^{3} x^{6}}{6}+\frac{3 c d \,e^{2} x^{5}}{5}+\frac{3 a \,d^{2} e \,x^{2}}{2}+a \,d^{3} x +\frac{\left(e^{3} a +3 d^{2} e c \right) x^{4}}{4}+\frac{\left(3 d \,e^{2} a +d^{3} c \right) x^{3}}{3}"," ",0,"1/6*e^3*c*x^6+3/5*d*e^2*c*x^5+1/4*(a*e^3+3*c*d^2*e)*x^4+1/3*(3*a*d*e^2+c*d^3)*x^3+3/2*d^2*e*a*x^2+d^3*a*x","A"
453,1,48,51,0.036000," ","int((e*x+d)^2*(c*x^2+a),x)","\frac{c \,e^{2} x^{5}}{5}+\frac{c d e \,x^{4}}{2}+a d e \,x^{2}+a \,d^{2} x +\frac{\left(a \,e^{2}+c \,d^{2}\right) x^{3}}{3}"," ",0,"1/5*c*e^2*x^5+1/2*c*d*e*x^4+1/3*(a*e^2+c*d^2)*x^3+a*d*e*x^2+a*d^2*x","A"
454,1,27,27,0.042000," ","int((e*x+d)*(c*x^2+a),x)","\frac{1}{4} c e \,x^{4}+\frac{1}{3} c d \,x^{3}+\frac{1}{2} a e \,x^{2}+a d x"," ",0,"1/4*c*e*x^4+1/3*c*d*x^3+1/2*a*e*x^2+a*d*x","A"
455,1,44,39,0.043000," ","int((c*x^2+a)/(e*x+d),x)","\frac{c \,x^{2}}{2 e}+\frac{a \ln \left(e x +d \right)}{e}+\frac{c \,d^{2} \ln \left(e x +d \right)}{e^{3}}-\frac{c d x}{e^{2}}"," ",0,"1/2*c/e*x^2-c*d/e^2*x+1/e*ln(e*x+d)*a+d^2/e^3*ln(e*x+d)*c","A"
456,1,50,44,0.049000," ","int((c*x^2+a)/(e*x+d)^2,x)","-\frac{a}{\left(e x +d \right) e}-\frac{c \,d^{2}}{\left(e x +d \right) e^{3}}-\frac{2 c d \ln \left(e x +d \right)}{e^{3}}+\frac{c x}{e^{2}}"," ",0,"c/e^2*x-1/e/(e*x+d)*a-1/e^3/(e*x+d)*c*d^2-2*c*d/e^3*ln(e*x+d)","A"
457,1,56,51,0.047000," ","int((c*x^2+a)/(e*x+d)^3,x)","-\frac{a}{2 \left(e x +d \right)^{2} e}-\frac{c \,d^{2}}{2 \left(e x +d \right)^{2} e^{3}}+\frac{2 c d}{\left(e x +d \right) e^{3}}+\frac{c \ln \left(e x +d \right)}{e^{3}}"," ",0,"-1/2/e/(e*x+d)^2*a-1/2/e^3/(e*x+d)^2*c*d^2+2/(e*x+d)*c*d/e^3+c/e^3*ln(e*x+d)","A"
458,1,51,52,0.044000," ","int((c*x^2+a)/(e*x+d)^4,x)","\frac{c d}{\left(e x +d \right)^{2} e^{3}}-\frac{c}{\left(e x +d \right) e^{3}}-\frac{a \,e^{2}+c \,d^{2}}{3 \left(e x +d \right)^{3} e^{3}}"," ",0,"c*d/e^3/(e*x+d)^2-1/(e*x+d)*c/e^3-1/3*(a*e^2+c*d^2)/e^3/(e*x+d)^3","A"
459,1,52,53,0.048000," ","int((c*x^2+a)/(e*x+d)^5,x)","\frac{2 c d}{3 \left(e x +d \right)^{3} e^{3}}-\frac{c}{2 \left(e x +d \right)^{2} e^{3}}-\frac{a \,e^{2}+c \,d^{2}}{4 \left(e x +d \right)^{4} e^{3}}"," ",0,"-1/2/(e*x+d)^2*c/e^3-1/4*(a*e^2+c*d^2)/e^3/(e*x+d)^4+2/3*c*d/e^3/(e*x+d)^3","A"
460,1,169,107,0.039000," ","int((e*x+d)^4*(c*x^2+a)^2,x)","\frac{c^{2} e^{4} x^{9}}{9}+\frac{c^{2} d \,e^{3} x^{8}}{2}+2 a^{2} d^{3} e \,x^{2}+a^{2} d^{4} x +\frac{\left(2 e^{4} a c +6 d^{2} e^{2} c^{2}\right) x^{7}}{7}+\frac{\left(8 d \,e^{3} a c +4 d^{3} e \,c^{2}\right) x^{6}}{6}+\frac{\left(a^{2} e^{4}+12 a c \,d^{2} e^{2}+c^{2} d^{4}\right) x^{5}}{5}+\frac{\left(4 d \,e^{3} a^{2}+8 d^{3} e a c \right) x^{4}}{4}+\frac{\left(6 d^{2} e^{2} a^{2}+2 d^{4} a c \right) x^{3}}{3}"," ",0,"1/9*e^4*c^2*x^9+1/2*d*e^3*c^2*x^8+1/7*(2*a*c*e^4+6*c^2*d^2*e^2)*x^7+1/6*(8*a*c*d*e^3+4*c^2*d^3*e)*x^6+1/5*(a^2*e^4+12*a*c*d^2*e^2+c^2*d^4)*x^5+1/4*(4*a^2*d*e^3+8*a*c*d^3*e)*x^4+1/3*(6*a^2*d^2*e^2+2*a*c*d^4)*x^3+2*d^3*e*a^2*x^2+d^4*a^2*x","A"
461,1,131,107,0.040000," ","int((e*x+d)^3*(c*x^2+a)^2,x)","\frac{c^{2} e^{3} x^{8}}{8}+\frac{3 c^{2} d \,e^{2} x^{7}}{7}+\frac{3 a^{2} d^{2} e \,x^{2}}{2}+a^{2} d^{3} x +\frac{\left(2 e^{3} a c +3 d^{2} e \,c^{2}\right) x^{6}}{6}+\frac{\left(6 d \,e^{2} a c +c^{2} d^{3}\right) x^{5}}{5}+\frac{\left(a^{2} e^{3}+6 d^{2} e a c \right) x^{4}}{4}+\frac{\left(3 d \,e^{2} a^{2}+2 d^{3} a c \right) x^{3}}{3}"," ",0,"1/8*c^2*e^3*x^8+3/7*d*e^2*c^2*x^7+1/6*(2*a*c*e^3+3*c^2*d^2*e)*x^6+1/5*(6*a*c*d*e^2+c^2*d^3)*x^5+1/4*(a^2*e^3+6*a*c*d^2*e)*x^4+1/3*(3*a^2*d*e^2+2*a*c*d^3)*x^3+3/2*d^2*e*a^2*x^2+a^2*d^3*x","A"
462,1,88,72,0.039000," ","int((e*x+d)^2*(c*x^2+a)^2,x)","\frac{c^{2} e^{2} x^{7}}{7}+\frac{c^{2} d e \,x^{6}}{3}+a c d e \,x^{4}+a^{2} d e \,x^{2}+a^{2} d^{2} x +\frac{\left(2 e^{2} a c +c^{2} d^{2}\right) x^{5}}{5}+\frac{\left(a^{2} e^{2}+2 d^{2} a c \right) x^{3}}{3}"," ",0,"1/7*c^2*e^2*x^7+1/3*d*e*c^2*x^6+1/5*(2*a*c*e^2+c^2*d^2)*x^5+a*c*d*e*x^4+1/3*(a^2*e^2+2*a*c*d^2)*x^3+d*e*a^2*x^2+a^2*d^2*x","A"
463,1,51,39,0.039000," ","int((e*x+d)*(c*x^2+a)^2,x)","\frac{1}{6} c^{2} e \,x^{6}+\frac{1}{5} c^{2} d \,x^{5}+\frac{1}{2} a c e \,x^{4}+\frac{2}{3} a c d \,x^{3}+\frac{1}{2} a^{2} e \,x^{2}+a^{2} d x"," ",0,"1/6*c^2*e*x^6+1/5*c^2*d*x^5+1/2*a*c*e*x^4+2/3*a*c*d*x^3+1/2*a^2*e*x^2+a^2*d*x","A"
464,1,114,88,0.042000," ","int((c*x^2+a)^2/(e*x+d),x)","\frac{c^{2} x^{4}}{4 e}-\frac{c^{2} d \,x^{3}}{3 e^{2}}+\frac{a c \,x^{2}}{e}+\frac{c^{2} d^{2} x^{2}}{2 e^{3}}+\frac{a^{2} \ln \left(e x +d \right)}{e}+\frac{2 a c \,d^{2} \ln \left(e x +d \right)}{e^{3}}-\frac{2 a c d x}{e^{2}}+\frac{c^{2} d^{4} \ln \left(e x +d \right)}{e^{5}}-\frac{c^{2} d^{3} x}{e^{4}}"," ",0,"1/4*c^2/e*x^4-1/3*c^2*d/e^2*x^3+c/e*x^2*a+1/2*c^2/e^3*x^2*d^2-2*c/e^2*d*a*x-c^2/e^4*d^3*x+1/e*ln(e*x+d)*a^2+2/e^3*ln(e*x+d)*a*c*d^2+1/e^5*ln(e*x+d)*c^2*d^4","A"
465,1,126,92,0.048000," ","int((c*x^2+a)^2/(e*x+d)^2,x)","\frac{c^{2} x^{3}}{3 e^{2}}-\frac{c^{2} d \,x^{2}}{e^{3}}-\frac{a^{2}}{\left(e x +d \right) e}-\frac{2 a c \,d^{2}}{\left(e x +d \right) e^{3}}-\frac{4 a c d \ln \left(e x +d \right)}{e^{3}}+\frac{2 a c x}{e^{2}}-\frac{c^{2} d^{4}}{\left(e x +d \right) e^{5}}-\frac{4 c^{2} d^{3} \ln \left(e x +d \right)}{e^{5}}+\frac{3 c^{2} d^{2} x}{e^{4}}"," ",0,"1/3*c^2/e^2*x^3-c^2*d/e^3*x^2+2*c/e^2*a*x+3*c^2/e^4*d^2*x-1/e/(e*x+d)*a^2-2/e^3/(e*x+d)*a*c*d^2-1/e^5/(e*x+d)*c^2*d^4-4*c*d/e^3*ln(e*x+d)*a-4*c^2*d^3/e^5*ln(e*x+d)","A"
466,1,136,96,0.052000," ","int((c*x^2+a)^2/(e*x+d)^3,x)","-\frac{a^{2}}{2 \left(e x +d \right)^{2} e}-\frac{a c \,d^{2}}{\left(e x +d \right)^{2} e^{3}}-\frac{c^{2} d^{4}}{2 \left(e x +d \right)^{2} e^{5}}+\frac{c^{2} x^{2}}{2 e^{3}}+\frac{4 a c d}{\left(e x +d \right) e^{3}}+\frac{2 a c \ln \left(e x +d \right)}{e^{3}}+\frac{4 c^{2} d^{3}}{\left(e x +d \right) e^{5}}+\frac{6 c^{2} d^{2} \ln \left(e x +d \right)}{e^{5}}-\frac{3 c^{2} d x}{e^{4}}"," ",0,"1/2*c^2/e^3*x^2-3*c^2*d/e^4*x-1/2/e/(e*x+d)^2*a^2-1/e^3/(e*x+d)^2*a*c*d^2-1/2/(e*x+d)^2*c^2*d^4/e^5+4*c*d/e^3/(e*x+d)*a+4/(e*x+d)*c^2*d^3/e^5+2*c/e^3*ln(e*x+d)*a+6*c^2*d^2/e^5*ln(e*x+d)","A"
467,1,140,99,0.050000," ","int((c*x^2+a)^2/(e*x+d)^4,x)","-\frac{a^{2}}{3 \left(e x +d \right)^{3} e}-\frac{2 a c \,d^{2}}{3 \left(e x +d \right)^{3} e^{3}}-\frac{c^{2} d^{4}}{3 \left(e x +d \right)^{3} e^{5}}+\frac{2 a c d}{\left(e x +d \right)^{2} e^{3}}+\frac{2 c^{2} d^{3}}{\left(e x +d \right)^{2} e^{5}}-\frac{2 a c}{\left(e x +d \right) e^{3}}-\frac{6 c^{2} d^{2}}{\left(e x +d \right) e^{5}}-\frac{4 c^{2} d \ln \left(e x +d \right)}{e^{5}}+\frac{c^{2} x}{e^{4}}"," ",0,"c^2/e^4*x+2*c*d/e^3/(e*x+d)^2*a+2*c^2*d^3/e^5/(e*x+d)^2-2*c/e^3/(e*x+d)*a-6*c^2/e^5/(e*x+d)*d^2-4*c^2*d/e^5*ln(e*x+d)-1/3/e/(e*x+d)^3*a^2-2/3/e^3/(e*x+d)^3*a*c*d^2-1/3/e^5/(e*x+d)^3*c^2*d^4","A"
468,1,146,105,0.047000," ","int((c*x^2+a)^2/(e*x+d)^5,x)","-\frac{a^{2}}{4 \left(e x +d \right)^{4} e}-\frac{a c \,d^{2}}{2 \left(e x +d \right)^{4} e^{3}}-\frac{c^{2} d^{4}}{4 \left(e x +d \right)^{4} e^{5}}+\frac{4 a c d}{3 \left(e x +d \right)^{3} e^{3}}+\frac{4 c^{2} d^{3}}{3 \left(e x +d \right)^{3} e^{5}}-\frac{a c}{\left(e x +d \right)^{2} e^{3}}-\frac{3 c^{2} d^{2}}{\left(e x +d \right)^{2} e^{5}}+\frac{4 c^{2} d}{\left(e x +d \right) e^{5}}+\frac{c^{2} \ln \left(e x +d \right)}{e^{5}}"," ",0,"-c/e^3/(e*x+d)^2*a-3*c^2/e^5/(e*x+d)^2*d^2-1/4/e/(e*x+d)^4*a^2-1/2/e^3/(e*x+d)^4*a*c*d^2-1/4/e^5/(e*x+d)^4*c^2*d^4+4/(e*x+d)*c^2*d/e^5+c^2/e^5*ln(e*x+d)+4/3*c*d/e^3/(e*x+d)^3*a+4/3*c^2*d^3/e^5/(e*x+d)^3","A"
469,1,119,106,0.052000," ","int((c*x^2+a)^2/(e*x+d)^6,x)","\frac{2 c^{2} d}{\left(e x +d \right)^{2} e^{5}}-\frac{c^{2}}{\left(e x +d \right) e^{5}}+\frac{\left(a \,e^{2}+c \,d^{2}\right) c d}{\left(e x +d \right)^{4} e^{5}}-\frac{2 \left(a \,e^{2}+3 c \,d^{2}\right) c}{3 \left(e x +d \right)^{3} e^{5}}-\frac{a^{2} e^{4}+2 a c \,d^{2} e^{2}+c^{2} d^{4}}{5 \left(e x +d \right)^{5} e^{5}}"," ",0,"2*c^2*d/e^5/(e*x+d)^2+c*d*(a*e^2+c*d^2)/e^5/(e*x+d)^4-1/(e*x+d)*c^2/e^5-2/3*c*(a*e^2+3*c*d^2)/e^5/(e*x+d)^3-1/5*(a^2*e^4+2*a*c*d^2*e^2+c^2*d^4)/e^5/(e*x+d)^5","A"
470,1,120,107,0.044000," ","int((c*x^2+a)^2/(e*x+d)^7,x)","\frac{4 c^{2} d}{3 \left(e x +d \right)^{3} e^{5}}-\frac{c^{2}}{2 \left(e x +d \right)^{2} e^{5}}+\frac{4 \left(a \,e^{2}+c \,d^{2}\right) c d}{5 \left(e x +d \right)^{5} e^{5}}-\frac{\left(a \,e^{2}+3 c \,d^{2}\right) c}{2 \left(e x +d \right)^{4} e^{5}}-\frac{a^{2} e^{4}+2 a c \,d^{2} e^{2}+c^{2} d^{4}}{6 \left(e x +d \right)^{6} e^{5}}"," ",0,"-1/6*(a^2*e^4+2*a*c*d^2*e^2+c^2*d^4)/e^5/(e*x+d)^6-1/2/(e*x+d)^2*c^2/e^5-1/2*c*(a*e^2+3*c*d^2)/e^5/(e*x+d)^4+4/3*c^2*d/e^5/(e*x+d)^3+4/5*c*d*(a*e^2+c*d^2)/e^5/(e*x+d)^5","A"
471,1,119,106,0.049000," ","int((c*x^2+a)^2/(e*x+d)^8,x)","\frac{c^{2} d}{\left(e x +d \right)^{4} e^{5}}-\frac{c^{2}}{3 \left(e x +d \right)^{3} e^{5}}+\frac{2 \left(a \,e^{2}+c \,d^{2}\right) c d}{3 \left(e x +d \right)^{6} e^{5}}-\frac{2 \left(a \,e^{2}+3 c \,d^{2}\right) c}{5 \left(e x +d \right)^{5} e^{5}}-\frac{a^{2} e^{4}+2 a c \,d^{2} e^{2}+c^{2} d^{4}}{7 \left(e x +d \right)^{7} e^{5}}"," ",0,"2/3*c*d*(a*e^2+c*d^2)/e^5/(e*x+d)^6+c^2*d/e^5/(e*x+d)^4-1/7*(a^2*e^4+2*a*c*d^2*e^2+c^2*d^4)/e^5/(e*x+d)^7-1/3/(e*x+d)^3*c^2/e^5-2/5*c*(a*e^2+3*c*d^2)/e^5/(e*x+d)^5","A"
472,1,345,176,0.038000," ","int((e*x+d)^6*(c*x^2+a)^3,x)","\frac{c^{3} e^{6} x^{13}}{13}+\frac{c^{3} d \,e^{5} x^{12}}{2}+3 a^{3} d^{5} e \,x^{2}+\frac{\left(3 e^{6} a \,c^{2}+15 d^{2} e^{4} c^{3}\right) x^{11}}{11}+a^{3} d^{6} x +\frac{\left(18 d \,e^{5} a \,c^{2}+20 d^{3} e^{3} c^{3}\right) x^{10}}{10}+\frac{\left(3 e^{6} a^{2} c +45 d^{2} e^{4} a \,c^{2}+15 d^{4} e^{2} c^{3}\right) x^{9}}{9}+\frac{\left(18 d \,e^{5} a^{2} c +60 d^{3} e^{3} a \,c^{2}+6 d^{5} e \,c^{3}\right) x^{8}}{8}+\frac{\left(e^{6} a^{3}+45 d^{2} e^{4} a^{2} c +45 d^{4} e^{2} a \,c^{2}+c^{3} d^{6}\right) x^{7}}{7}+\frac{\left(6 d \,e^{5} a^{3}+60 d^{3} e^{3} a^{2} c +18 d^{5} e a \,c^{2}\right) x^{6}}{6}+\frac{\left(15 d^{2} e^{4} a^{3}+45 d^{4} e^{2} a^{2} c +3 d^{6} a \,c^{2}\right) x^{5}}{5}+\frac{\left(20 d^{3} e^{3} a^{3}+18 d^{5} e \,a^{2} c \right) x^{4}}{4}+\frac{\left(15 d^{4} e^{2} a^{3}+3 d^{6} a^{2} c \right) x^{3}}{3}"," ",0,"1/13*e^6*c^3*x^13+1/2*d*e^5*c^3*x^12+1/11*(3*a*c^2*e^6+15*c^3*d^2*e^4)*x^11+1/10*(18*a*c^2*d*e^5+20*c^3*d^3*e^3)*x^10+1/9*(3*a^2*c*e^6+45*a*c^2*d^2*e^4+15*c^3*d^4*e^2)*x^9+1/8*(18*a^2*c*d*e^5+60*a*c^2*d^3*e^3+6*c^3*d^5*e)*x^8+1/7*(a^3*e^6+45*a^2*c*d^2*e^4+45*a*c^2*d^4*e^2+c^3*d^6)*x^7+1/6*(6*a^3*d*e^5+60*a^2*c*d^3*e^3+18*a*c^2*d^5*e)*x^6+1/5*(15*a^3*d^2*e^4+45*a^2*c*d^4*e^2+3*a*c^2*d^6)*x^5+1/4*(20*a^3*d^3*e^3+18*a^2*c*d^5*e)*x^4+1/3*(15*a^3*d^4*e^2+3*a^2*c*d^6)*x^3+3*d^5*e*a^3*x^2+d^6*a^3*x","A"
473,1,293,176,0.038000," ","int((e*x+d)^5*(c*x^2+a)^3,x)","\frac{c^{3} e^{5} x^{12}}{12}+\frac{5 c^{3} d \,e^{4} x^{11}}{11}+\frac{5 a^{3} d^{4} e \,x^{2}}{2}+\frac{\left(3 e^{5} a \,c^{2}+10 d^{2} e^{3} c^{3}\right) x^{10}}{10}+a^{3} d^{5} x +\frac{\left(15 d \,e^{4} a \,c^{2}+10 d^{3} e^{2} c^{3}\right) x^{9}}{9}+\frac{\left(3 e^{5} a^{2} c +30 d^{2} e^{3} a \,c^{2}+5 d^{4} e \,c^{3}\right) x^{8}}{8}+\frac{\left(15 d \,e^{4} a^{2} c +30 d^{3} e^{2} a \,c^{2}+d^{5} c^{3}\right) x^{7}}{7}+\frac{\left(a^{3} e^{5}+30 d^{2} e^{3} a^{2} c +15 d^{4} e a \,c^{2}\right) x^{6}}{6}+\frac{\left(5 d \,e^{4} a^{3}+30 d^{3} e^{2} a^{2} c +3 d^{5} a \,c^{2}\right) x^{5}}{5}+\frac{\left(10 d^{2} e^{3} a^{3}+15 d^{4} e \,a^{2} c \right) x^{4}}{4}+\frac{\left(10 d^{3} e^{2} a^{3}+3 d^{5} a^{2} c \right) x^{3}}{3}"," ",0,"1/12*e^5*c^3*x^12+5/11*d*e^4*c^3*x^11+1/10*(3*a*c^2*e^5+10*c^3*d^2*e^3)*x^10+1/9*(15*a*c^2*d*e^4+10*c^3*d^3*e^2)*x^9+1/8*(3*a^2*c*e^5+30*a*c^2*d^2*e^3+5*c^3*d^4*e)*x^8+1/7*(15*a^2*c*d*e^4+30*a*c^2*d^3*e^2+c^3*d^5)*x^7+1/6*(a^3*e^5+30*a^2*c*d^2*e^3+15*a*c^2*d^4*e)*x^6+1/5*(5*a^3*d*e^4+30*a^2*c*d^3*e^2+3*a*c^2*d^5)*x^5+1/4*(10*a^3*d^2*e^3+15*a^2*c*d^4*e)*x^4+1/3*(10*a^3*d^3*e^2+3*a^2*c*d^5)*x^3+5/2*d^4*e*a^3*x^2+d^5*a^3*x","A"
474,1,241,176,0.037000," ","int((e*x+d)^4*(c*x^2+a)^3,x)","\frac{c^{3} e^{4} x^{11}}{11}+\frac{2 c^{3} d \,e^{3} x^{10}}{5}+2 a^{3} d^{3} e \,x^{2}+\frac{\left(3 e^{4} a \,c^{2}+6 d^{2} e^{2} c^{3}\right) x^{9}}{9}+a^{3} d^{4} x +\frac{\left(12 d \,e^{3} a \,c^{2}+4 d^{3} e \,c^{3}\right) x^{8}}{8}+\frac{\left(3 e^{4} a^{2} c +18 d^{2} e^{2} a \,c^{2}+d^{4} c^{3}\right) x^{7}}{7}+\frac{\left(12 d \,e^{3} a^{2} c +12 d^{3} e a \,c^{2}\right) x^{6}}{6}+\frac{\left(e^{4} a^{3}+18 d^{2} e^{2} a^{2} c +3 d^{4} a \,c^{2}\right) x^{5}}{5}+\frac{\left(4 d \,e^{3} a^{3}+12 d^{3} e \,a^{2} c \right) x^{4}}{4}+\frac{\left(6 d^{2} e^{2} a^{3}+3 d^{4} a^{2} c \right) x^{3}}{3}"," ",0,"1/11*c^3*e^4*x^11+2/5*d*e^3*c^3*x^10+1/9*(3*a*c^2*e^4+6*c^3*d^2*e^2)*x^9+1/8*(12*a*c^2*d*e^3+4*c^3*d^3*e)*x^8+1/7*(3*a^2*c*e^4+18*a*c^2*d^2*e^2+c^3*d^4)*x^7+1/6*(12*a^2*c*d*e^3+12*a*c^2*d^3*e)*x^6+1/5*(a^3*e^4+18*a^2*c*d^2*e^2+3*a*c^2*d^4)*x^5+1/4*(4*a^3*d*e^3+12*a^2*c*d^3*e)*x^4+1/3*(6*a^3*d^2*e^2+3*a^2*c*d^4)*x^3+2*d^3*e*a^3*x^2+d^4*a^3*x","A"
475,1,189,145,0.038000," ","int((e*x+d)^3*(c*x^2+a)^3,x)","\frac{c^{3} e^{3} x^{10}}{10}+\frac{c^{3} d \,e^{2} x^{9}}{3}+\frac{3 a^{3} d^{2} e \,x^{2}}{2}+\frac{\left(3 e^{3} a \,c^{2}+3 d^{2} e \,c^{3}\right) x^{8}}{8}+a^{3} d^{3} x +\frac{\left(9 d \,e^{2} a \,c^{2}+c^{3} d^{3}\right) x^{7}}{7}+\frac{\left(3 a^{2} c \,e^{3}+9 d^{2} e a \,c^{2}\right) x^{6}}{6}+\frac{\left(9 d \,e^{2} a^{2} c +3 d^{3} a \,c^{2}\right) x^{5}}{5}+\frac{\left(e^{3} a^{3}+9 d^{2} e \,a^{2} c \right) x^{4}}{4}+\frac{\left(3 d \,e^{2} a^{3}+3 d^{3} a^{2} c \right) x^{3}}{3}"," ",0,"1/10*c^3*e^3*x^10+1/3*c^3*d*e^2*x^9+1/8*(3*a*c^2*e^3+3*c^3*d^2*e)*x^8+1/7*(9*a*c^2*d*e^2+c^3*d^3)*x^7+1/6*(3*a^2*c*e^3+9*a*c^2*d^2*e)*x^6+1/5*(9*a^2*c*d*e^2+3*a*c^2*d^3)*x^5+1/4*(a^3*e^3+9*a^2*c*d^2*e)*x^4+1/3*(3*a^3*d*e^2+3*a^2*c*d^3)*x^3+3/2*d^2*e*a^3*x^2+a^3*d^3*x","A"
476,1,129,94,0.039000," ","int((e*x+d)^2*(c*x^2+a)^3,x)","\frac{c^{3} e^{2} x^{9}}{9}+\frac{c^{3} d e \,x^{8}}{4}+a \,c^{2} d e \,x^{6}+\frac{3 a^{2} c d e \,x^{4}}{2}+a^{3} d e \,x^{2}+\frac{\left(3 e^{2} a \,c^{2}+c^{3} d^{2}\right) x^{7}}{7}+a^{3} d^{2} x +\frac{\left(3 e^{2} a^{2} c +3 d^{2} a \,c^{2}\right) x^{5}}{5}+\frac{\left(a^{3} e^{2}+3 a^{2} c \,d^{2}\right) x^{3}}{3}"," ",0,"1/9*c^3*e^2*x^9+1/4*d*e*c^3*x^8+1/7*(3*a*c^2*e^2+c^3*d^2)*x^7+a*c^2*d*e*x^6+1/5*(3*a^2*c*e^2+3*a*c^2*d^2)*x^5+3/2*d*e*a^2*c*x^4+1/3*(a^3*e^2+3*a^2*c*d^2)*x^3+d*e*a^3*x^2+a^3*d^2*x","A"
477,1,74,50,0.037000," ","int((e*x+d)*(c*x^2+a)^3,x)","\frac{1}{8} c^{3} e \,x^{8}+\frac{1}{7} c^{3} d \,x^{7}+\frac{1}{2} a \,c^{2} e \,x^{6}+\frac{3}{5} a \,c^{2} d \,x^{5}+\frac{3}{4} a^{2} c e \,x^{4}+a^{2} c d \,x^{3}+\frac{1}{2} a^{3} e \,x^{2}+a^{3} d x"," ",0,"1/8*c^3*e*x^8+1/7*c^3*d*x^7+1/2*e*a*c^2*x^6+3/5*a*c^2*d*x^5+3/4*e*a^2*c*x^4+a^2*c*d*x^3+1/2*a^3*e*x^2+a^3*d*x","A"
478,1,220,163,0.045000," ","int((c*x^2+a)^3/(e*x+d),x)","\frac{c^{3} x^{6}}{6 e}-\frac{c^{3} d \,x^{5}}{5 e^{2}}+\frac{3 a \,c^{2} x^{4}}{4 e}+\frac{c^{3} d^{2} x^{4}}{4 e^{3}}-\frac{a \,c^{2} d \,x^{3}}{e^{2}}-\frac{c^{3} d^{3} x^{3}}{3 e^{4}}+\frac{3 a^{2} c \,x^{2}}{2 e}+\frac{3 a \,c^{2} d^{2} x^{2}}{2 e^{3}}+\frac{c^{3} d^{4} x^{2}}{2 e^{5}}+\frac{a^{3} \ln \left(e x +d \right)}{e}+\frac{3 a^{2} c \,d^{2} \ln \left(e x +d \right)}{e^{3}}-\frac{3 a^{2} c d x}{e^{2}}+\frac{3 a \,c^{2} d^{4} \ln \left(e x +d \right)}{e^{5}}-\frac{3 a \,c^{2} d^{3} x}{e^{4}}+\frac{c^{3} d^{6} \ln \left(e x +d \right)}{e^{7}}-\frac{c^{3} d^{5} x}{e^{6}}"," ",0,"1/6*c^3/e*x^6-1/5*c^3*d/e^2*x^5+3/4*c^2/e*x^4*a+1/4*c^3*d^2/e^3*x^4-c^2/e^2*x^3*a*d-1/3*c^3*d^3/e^4*x^3+3/2*c/e*x^2*a^2+3/2*c^2/e^3*x^2*a*d^2+1/2*c^3*d^4/e^5*x^2-3*c/e^2*a^2*d*x-3*c^2/e^4*a*d^3*x-c^3*d^5/e^6*x+1/e*ln(e*x+d)*a^3+3/e^3*ln(e*x+d)*d^2*a^2*c+3/e^5*ln(e*x+d)*a*c^2*d^4+c^3*d^6/e^7*ln(e*x+d)","A"
479,1,233,154,0.050000," ","int((c*x^2+a)^3/(e*x+d)^2,x)","\frac{c^{3} x^{5}}{5 e^{2}}-\frac{c^{3} d \,x^{4}}{2 e^{3}}+\frac{a \,c^{2} x^{3}}{e^{2}}+\frac{c^{3} d^{2} x^{3}}{e^{4}}-\frac{3 a \,c^{2} d \,x^{2}}{e^{3}}-\frac{2 c^{3} d^{3} x^{2}}{e^{5}}-\frac{a^{3}}{\left(e x +d \right) e}-\frac{3 a^{2} c \,d^{2}}{\left(e x +d \right) e^{3}}-\frac{6 a^{2} c d \ln \left(e x +d \right)}{e^{3}}+\frac{3 a^{2} c x}{e^{2}}-\frac{3 a \,c^{2} d^{4}}{\left(e x +d \right) e^{5}}-\frac{12 a \,c^{2} d^{3} \ln \left(e x +d \right)}{e^{5}}+\frac{9 a \,c^{2} d^{2} x}{e^{4}}-\frac{c^{3} d^{6}}{\left(e x +d \right) e^{7}}-\frac{6 c^{3} d^{5} \ln \left(e x +d \right)}{e^{7}}+\frac{5 c^{3} d^{4} x}{e^{6}}"," ",0,"1/5*c^3/e^2*x^5-1/2*c^3*d/e^3*x^4+c^2/e^2*x^3*a+c^3*d^2/e^4*x^3-3*c^2/e^3*x^2*a*d-2*c^3*d^3/e^5*x^2+3*c/e^2*a^2*x+9*c^2/e^4*a*d^2*x+5*c^3*d^4/e^6*x-1/e/(e*x+d)*a^3-3/e^3/(e*x+d)*d^2*a^2*c-3/e^5/(e*x+d)*a*c^2*d^4-1/(e*x+d)*c^3*d^6/e^7-6*c*d/e^3*ln(e*x+d)*a^2-12*c^2*d^3/e^5*ln(e*x+d)*a-6*c^3*d^5/e^7*ln(e*x+d)","A"
480,1,249,157,0.051000," ","int((c*x^2+a)^3/(e*x+d)^3,x)","\frac{c^{3} x^{4}}{4 e^{3}}-\frac{c^{3} d \,x^{3}}{e^{4}}-\frac{a^{3}}{2 \left(e x +d \right)^{2} e}-\frac{3 a^{2} c \,d^{2}}{2 \left(e x +d \right)^{2} e^{3}}-\frac{3 a \,c^{2} d^{4}}{2 \left(e x +d \right)^{2} e^{5}}+\frac{3 a \,c^{2} x^{2}}{2 e^{3}}-\frac{c^{3} d^{6}}{2 \left(e x +d \right)^{2} e^{7}}+\frac{3 c^{3} d^{2} x^{2}}{e^{5}}+\frac{6 a^{2} c d}{\left(e x +d \right) e^{3}}+\frac{3 a^{2} c \ln \left(e x +d \right)}{e^{3}}+\frac{12 a \,c^{2} d^{3}}{\left(e x +d \right) e^{5}}+\frac{18 a \,c^{2} d^{2} \ln \left(e x +d \right)}{e^{5}}-\frac{9 a \,c^{2} d x}{e^{4}}+\frac{6 c^{3} d^{5}}{\left(e x +d \right) e^{7}}+\frac{15 c^{3} d^{4} \ln \left(e x +d \right)}{e^{7}}-\frac{10 c^{3} d^{3} x}{e^{6}}"," ",0,"1/4*c^3/e^3*x^4-c^3*d/e^4*x^3+3/2*c^2/e^3*x^2*a+3*c^3/e^5*x^2*d^2-9*c^2/e^4*d*a*x-10*c^3/e^6*d^3*x-1/2/e/(e*x+d)^2*a^3-3/2/e^3/(e*x+d)^2*d^2*a^2*c-3/2/e^5/(e*x+d)^2*a*c^2*d^4-1/2/e^7/(e*x+d)^2*c^3*d^6+6*c*d/e^3/(e*x+d)*a^2+12*c^2*d^3/e^5/(e*x+d)*a+6*c^3*d^5/e^7/(e*x+d)+3*c/e^3*ln(e*x+d)*a^2+18*c^2/e^5*ln(e*x+d)*a*d^2+15*c^3/e^7*ln(e*x+d)*d^4","A"
481,1,258,161,0.053000," ","int((c*x^2+a)^3/(e*x+d)^4,x)","-\frac{a^{3}}{3 \left(e x +d \right)^{3} e}-\frac{a^{2} c \,d^{2}}{\left(e x +d \right)^{3} e^{3}}-\frac{a \,c^{2} d^{4}}{\left(e x +d \right)^{3} e^{5}}-\frac{c^{3} d^{6}}{3 \left(e x +d \right)^{3} e^{7}}+\frac{c^{3} x^{3}}{3 e^{4}}+\frac{3 a^{2} c d}{\left(e x +d \right)^{2} e^{3}}+\frac{6 a \,c^{2} d^{3}}{\left(e x +d \right)^{2} e^{5}}+\frac{3 c^{3} d^{5}}{\left(e x +d \right)^{2} e^{7}}-\frac{2 c^{3} d \,x^{2}}{e^{5}}-\frac{3 a^{2} c}{\left(e x +d \right) e^{3}}-\frac{18 a \,c^{2} d^{2}}{\left(e x +d \right) e^{5}}-\frac{12 a \,c^{2} d \ln \left(e x +d \right)}{e^{5}}+\frac{3 a \,c^{2} x}{e^{4}}-\frac{15 c^{3} d^{4}}{\left(e x +d \right) e^{7}}-\frac{20 c^{3} d^{3} \ln \left(e x +d \right)}{e^{7}}+\frac{10 c^{3} d^{2} x}{e^{6}}"," ",0,"1/3*c^3/e^4*x^3-2*c^3*d/e^5*x^2+3*c^2/e^4*a*x+10*c^3/e^6*d^2*x+3*c*d/e^3/(e*x+d)^2*a^2+6*c^2*d^3/e^5/(e*x+d)^2*a+3*c^3*d^5/e^7/(e*x+d)^2-3*c/e^3/(e*x+d)*a^2-18*c^2/e^5/(e*x+d)*a*d^2-15*c^3/e^7/(e*x+d)*d^4-12*c^2*d/e^5*ln(e*x+d)*a-20*c^3*d^3/e^7*ln(e*x+d)-1/3/e/(e*x+d)^3*a^3-1/e^3/(e*x+d)^3*d^2*a^2*c-1/e^5/(e*x+d)^3*a*c^2*d^4-1/3/e^7/(e*x+d)^3*c^3*d^6","A"
482,1,268,165,0.051000," ","int((c*x^2+a)^3/(e*x+d)^5,x)","-\frac{a^{3}}{4 \left(e x +d \right)^{4} e}-\frac{3 a^{2} c \,d^{2}}{4 \left(e x +d \right)^{4} e^{3}}-\frac{3 a \,c^{2} d^{4}}{4 \left(e x +d \right)^{4} e^{5}}-\frac{c^{3} d^{6}}{4 \left(e x +d \right)^{4} e^{7}}+\frac{2 a^{2} c d}{\left(e x +d \right)^{3} e^{3}}+\frac{4 a \,c^{2} d^{3}}{\left(e x +d \right)^{3} e^{5}}+\frac{2 c^{3} d^{5}}{\left(e x +d \right)^{3} e^{7}}-\frac{3 a^{2} c}{2 \left(e x +d \right)^{2} e^{3}}-\frac{9 a \,c^{2} d^{2}}{\left(e x +d \right)^{2} e^{5}}-\frac{15 c^{3} d^{4}}{2 \left(e x +d \right)^{2} e^{7}}+\frac{c^{3} x^{2}}{2 e^{5}}+\frac{12 a \,c^{2} d}{\left(e x +d \right) e^{5}}+\frac{3 a \,c^{2} \ln \left(e x +d \right)}{e^{5}}+\frac{20 c^{3} d^{3}}{\left(e x +d \right) e^{7}}+\frac{15 c^{3} d^{2} \ln \left(e x +d \right)}{e^{7}}-\frac{5 c^{3} d x}{e^{6}}"," ",0,"1/2*c^3/e^5*x^2-5*c^3*d/e^6*x-3/2*c/e^3/(e*x+d)^2*a^2-9*c^2/e^5/(e*x+d)^2*a*d^2-15/2/(e*x+d)^2*c^3*d^4/e^7-1/4/e/(e*x+d)^4*a^3-3/4/e^3/(e*x+d)^4*d^2*a^2*c-3/4/e^5/(e*x+d)^4*d^4*a*c^2-1/4/e^7/(e*x+d)^4*c^3*d^6+12*c^2*d/e^5/(e*x+d)*a+20*c^3*d^3/e^7/(e*x+d)+3*c^2/e^5*ln(e*x+d)*a+15*c^3/e^7*ln(e*x+d)*d^2+2*c*d/e^3/(e*x+d)^3*a^2+4*c^2*d^3/e^5/(e*x+d)^3*a+2*c^3*d^5/e^7/(e*x+d)^3","A"
483,1,272,168,0.051000," ","int((c*x^2+a)^3/(e*x+d)^6,x)","-\frac{a^{3}}{5 \left(e x +d \right)^{5} e}-\frac{3 a^{2} c \,d^{2}}{5 \left(e x +d \right)^{5} e^{3}}-\frac{3 a \,c^{2} d^{4}}{5 \left(e x +d \right)^{5} e^{5}}-\frac{c^{3} d^{6}}{5 \left(e x +d \right)^{5} e^{7}}+\frac{3 a^{2} c d}{2 \left(e x +d \right)^{4} e^{3}}+\frac{3 a \,c^{2} d^{3}}{\left(e x +d \right)^{4} e^{5}}+\frac{3 c^{3} d^{5}}{2 \left(e x +d \right)^{4} e^{7}}-\frac{a^{2} c}{\left(e x +d \right)^{3} e^{3}}-\frac{6 a \,c^{2} d^{2}}{\left(e x +d \right)^{3} e^{5}}-\frac{5 c^{3} d^{4}}{\left(e x +d \right)^{3} e^{7}}+\frac{6 a \,c^{2} d}{\left(e x +d \right)^{2} e^{5}}+\frac{10 c^{3} d^{3}}{\left(e x +d \right)^{2} e^{7}}-\frac{3 a \,c^{2}}{\left(e x +d \right) e^{5}}-\frac{15 c^{3} d^{2}}{\left(e x +d \right) e^{7}}-\frac{6 c^{3} d \ln \left(e x +d \right)}{e^{7}}+\frac{c^{3} x}{e^{6}}"," ",0,"c^3/e^6*x+6*c^2*d/e^5/(e*x+d)^2*a+10*c^3*d^3/e^7/(e*x+d)^2+3/2*c*d/e^3/(e*x+d)^4*a^2+3*c^2*d^3/e^5/(e*x+d)^4*a+3/2*c^3*d^5/e^7/(e*x+d)^4-3*c^2/e^5/(e*x+d)*a-15*c^3/e^7/(e*x+d)*d^2-6*c^3*d/e^7*ln(e*x+d)-c/e^3/(e*x+d)^3*a^2-6*c^2/e^5/(e*x+d)^3*a*d^2-5*c^3/e^7/(e*x+d)^3*d^4-1/5/e/(e*x+d)^5*a^3-3/5/e^3/(e*x+d)^5*d^2*a^2*c-3/5/e^5/(e*x+d)^5*d^4*a*c^2-1/5/e^7/(e*x+d)^5*c^3*d^6","A"
484,1,278,174,0.049000," ","int((c*x^2+a)^3/(e*x+d)^7,x)","-\frac{a^{3}}{6 \left(e x +d \right)^{6} e}-\frac{a^{2} c \,d^{2}}{2 \left(e x +d \right)^{6} e^{3}}-\frac{a \,c^{2} d^{4}}{2 \left(e x +d \right)^{6} e^{5}}-\frac{c^{3} d^{6}}{6 \left(e x +d \right)^{6} e^{7}}+\frac{6 a^{2} c d}{5 \left(e x +d \right)^{5} e^{3}}+\frac{12 a \,c^{2} d^{3}}{5 \left(e x +d \right)^{5} e^{5}}+\frac{6 c^{3} d^{5}}{5 \left(e x +d \right)^{5} e^{7}}-\frac{3 a^{2} c}{4 \left(e x +d \right)^{4} e^{3}}-\frac{9 a \,c^{2} d^{2}}{2 \left(e x +d \right)^{4} e^{5}}-\frac{15 c^{3} d^{4}}{4 \left(e x +d \right)^{4} e^{7}}+\frac{4 a \,c^{2} d}{\left(e x +d \right)^{3} e^{5}}+\frac{20 c^{3} d^{3}}{3 \left(e x +d \right)^{3} e^{7}}-\frac{3 a \,c^{2}}{2 \left(e x +d \right)^{2} e^{5}}-\frac{15 c^{3} d^{2}}{2 \left(e x +d \right)^{2} e^{7}}+\frac{6 c^{3} d}{\left(e x +d \right) e^{7}}+\frac{c^{3} \ln \left(e x +d \right)}{e^{7}}"," ",0,"-1/6/e/(e*x+d)^6*a^3-1/2/e^3/(e*x+d)^6*d^2*a^2*c-1/2/e^5/(e*x+d)^6*d^4*a*c^2-1/6/e^7/(e*x+d)^6*c^3*d^6-3/2*c^2/e^5/(e*x+d)^2*a-15/2*c^3/e^7/(e*x+d)^2*d^2-3/4*c/e^3/(e*x+d)^4*a^2-9/2*c^2/e^5/(e*x+d)^4*a*d^2-15/4*c^3/e^7/(e*x+d)^4*d^4+6/(e*x+d)*c^3*d/e^7+c^3/e^7*ln(e*x+d)+4*c^2*d/e^5/(e*x+d)^3*a+20/3*c^3*d^3/e^7/(e*x+d)^3+6/5*c*d/e^3/(e*x+d)^5*a^2+12/5*c^2*d^3/e^5/(e*x+d)^5*a+6/5*c^3*d^5/e^7/(e*x+d)^5","A"
485,1,216,174,0.048000," ","int((c*x^2+a)^3/(e*x+d)^8,x)","\frac{3 c^{3} d}{\left(e x +d \right)^{2} e^{7}}-\frac{c^{3}}{\left(e x +d \right) e^{7}}+\frac{\left(3 a \,e^{2}+5 c \,d^{2}\right) c^{2} d}{\left(e x +d \right)^{4} e^{7}}-\frac{\left(a \,e^{2}+5 c \,d^{2}\right) c^{2}}{\left(e x +d \right)^{3} e^{7}}+\frac{\left(a^{2} e^{4}+2 a c \,d^{2} e^{2}+c^{2} d^{4}\right) c d}{\left(e x +d \right)^{6} e^{7}}-\frac{3 \left(a^{2} e^{4}+6 a c \,d^{2} e^{2}+5 c^{2} d^{4}\right) c}{5 \left(e x +d \right)^{5} e^{7}}-\frac{e^{6} a^{3}+3 d^{2} e^{4} a^{2} c +3 a \,c^{2} d^{4} e^{2}+c^{3} d^{6}}{7 \left(e x +d \right)^{7} e^{7}}"," ",0,"c*d*(a^2*e^4+2*a*c*d^2*e^2+c^2*d^4)/e^7/(e*x+d)^6+3*c^3*d/e^7/(e*x+d)^2+c^2*d*(3*a*e^2+5*c*d^2)/e^7/(e*x+d)^4-1/(e*x+d)*c^3/e^7-1/7*(a^3*e^6+3*a^2*c*d^2*e^4+3*a*c^2*d^4*e^2+c^3*d^6)/e^7/(e*x+d)^7-c^2*(a*e^2+5*c*d^2)/e^7/(e*x+d)^3-3/5*c*(a^2*e^4+6*a*c*d^2*e^2+5*c^2*d^4)/e^7/(e*x+d)^5","A"
486,1,218,176,0.046000," ","int((c*x^2+a)^3/(e*x+d)^9,x)","\frac{2 c^{3} d}{\left(e x +d \right)^{3} e^{7}}-\frac{c^{3}}{2 \left(e x +d \right)^{2} e^{7}}+\frac{4 \left(3 a \,e^{2}+5 c \,d^{2}\right) c^{2} d}{5 \left(e x +d \right)^{5} e^{7}}-\frac{3 \left(a \,e^{2}+5 c \,d^{2}\right) c^{2}}{4 \left(e x +d \right)^{4} e^{7}}+\frac{6 \left(a^{2} e^{4}+2 a c \,d^{2} e^{2}+c^{2} d^{4}\right) c d}{7 \left(e x +d \right)^{7} e^{7}}-\frac{\left(a^{2} e^{4}+6 a c \,d^{2} e^{2}+5 c^{2} d^{4}\right) c}{2 \left(e x +d \right)^{6} e^{7}}-\frac{e^{6} a^{3}+3 d^{2} e^{4} a^{2} c +3 a \,c^{2} d^{4} e^{2}+c^{3} d^{6}}{8 \left(e x +d \right)^{8} e^{7}}"," ",0,"-1/2*c*(a^2*e^4+6*a*c*d^2*e^2+5*c^2*d^4)/e^7/(e*x+d)^6-1/2/(e*x+d)^2*c^3/e^7-3/4*c^2*(a*e^2+5*c*d^2)/e^7/(e*x+d)^4-1/8*(a^3*e^6+3*a^2*c*d^2*e^4+3*a*c^2*d^4*e^2+c^3*d^6)/e^7/(e*x+d)^8+6/7*c*d*(a^2*e^4+2*a*c*d^2*e^2+c^2*d^4)/e^7/(e*x+d)^7+2*c^3*d/e^7/(e*x+d)^3+4/5*c^2*d*(3*a*e^2+5*c*d^2)/e^7/(e*x+d)^5","A"
487,1,218,176,0.048000," ","int((c*x^2+a)^3/(e*x+d)^10,x)","\frac{3 c^{3} d}{2 \left(e x +d \right)^{4} e^{7}}-\frac{c^{3}}{3 \left(e x +d \right)^{3} e^{7}}+\frac{2 \left(3 a \,e^{2}+5 c \,d^{2}\right) c^{2} d}{3 \left(e x +d \right)^{6} e^{7}}-\frac{3 \left(a \,e^{2}+5 c \,d^{2}\right) c^{2}}{5 \left(e x +d \right)^{5} e^{7}}+\frac{3 \left(a^{2} e^{4}+2 a c \,d^{2} e^{2}+c^{2} d^{4}\right) c d}{4 \left(e x +d \right)^{8} e^{7}}-\frac{3 \left(a^{2} e^{4}+6 a c \,d^{2} e^{2}+5 c^{2} d^{4}\right) c}{7 \left(e x +d \right)^{7} e^{7}}-\frac{e^{6} a^{3}+3 d^{2} e^{4} a^{2} c +3 a \,c^{2} d^{4} e^{2}+c^{3} d^{6}}{9 \left(e x +d \right)^{9} e^{7}}"," ",0,"2/3*c^2*d*(3*a*e^2+5*c*d^2)/e^7/(e*x+d)^6-1/9*(a^3*e^6+3*a^2*c*d^2*e^4+3*a*c^2*d^4*e^2+c^3*d^6)/e^7/(e*x+d)^9+3/2*c^3*d/e^7/(e*x+d)^4+3/4*c*d*(a^2*e^4+2*a*c*d^2*e^2+c^2*d^4)/e^7/(e*x+d)^8-3/7*c*(a^2*e^4+6*a*c*d^2*e^2+5*c^2*d^4)/e^7/(e*x+d)^7-1/3/(e*x+d)^3*c^3/e^7-3/5*c^2*(a*e^2+5*c*d^2)/e^7/(e*x+d)^5","A"
488,1,511,260,0.039000," ","int((e*x+d)^7*(c*x^2+a)^4,x)","\frac{c^{4} e^{7} x^{16}}{16}+\frac{7 c^{4} d \,e^{6} x^{15}}{15}+\frac{\left(4 e^{7} a \,c^{3}+21 d^{2} e^{5} c^{4}\right) x^{14}}{14}+\frac{7 a^{4} d^{6} e \,x^{2}}{2}+\frac{\left(28 d \,e^{6} a \,c^{3}+35 d^{3} e^{4} c^{4}\right) x^{13}}{13}+a^{4} d^{7} x +\frac{\left(6 e^{7} a^{2} c^{2}+84 d^{2} e^{5} a \,c^{3}+35 d^{4} e^{3} c^{4}\right) x^{12}}{12}+\frac{\left(42 d \,e^{6} a^{2} c^{2}+140 d^{3} e^{4} a \,c^{3}+21 d^{5} e^{2} c^{4}\right) x^{11}}{11}+\frac{\left(4 e^{7} a^{3} c +126 d^{2} e^{5} a^{2} c^{2}+140 d^{4} e^{3} a \,c^{3}+7 d^{6} e \,c^{4}\right) x^{10}}{10}+\frac{\left(28 d \,e^{6} a^{3} c +210 d^{3} e^{4} a^{2} c^{2}+84 d^{5} e^{2} a \,c^{3}+d^{7} c^{4}\right) x^{9}}{9}+\frac{\left(e^{7} a^{4}+84 d^{2} e^{5} a^{3} c +210 d^{4} e^{3} a^{2} c^{2}+28 d^{6} e a \,c^{3}\right) x^{8}}{8}+\frac{\left(7 d \,e^{6} a^{4}+140 d^{3} e^{4} a^{3} c +126 d^{5} e^{2} a^{2} c^{2}+4 d^{7} a \,c^{3}\right) x^{7}}{7}+\frac{\left(21 d^{2} e^{5} a^{4}+140 d^{4} e^{3} a^{3} c +42 d^{6} e \,a^{2} c^{2}\right) x^{6}}{6}+\frac{\left(35 d^{3} e^{4} a^{4}+84 d^{5} e^{2} a^{3} c +6 d^{7} a^{2} c^{2}\right) x^{5}}{5}+\frac{\left(35 d^{4} e^{3} a^{4}+28 d^{6} e \,a^{3} c \right) x^{4}}{4}+\frac{\left(21 d^{5} e^{2} a^{4}+4 d^{7} a^{3} c \right) x^{3}}{3}"," ",0,"1/16*e^7*c^4*x^16+7/15*d*e^6*c^4*x^15+1/14*(4*a*c^3*e^7+21*c^4*d^2*e^5)*x^14+1/13*(28*a*c^3*d*e^6+35*c^4*d^3*e^4)*x^13+1/12*(6*a^2*c^2*e^7+84*a*c^3*d^2*e^5+35*c^4*d^4*e^3)*x^12+1/11*(42*a^2*c^2*d*e^6+140*a*c^3*d^3*e^4+21*c^4*d^5*e^2)*x^11+1/10*(4*a^3*c*e^7+126*a^2*c^2*d^2*e^5+140*a*c^3*d^4*e^3+7*c^4*d^6*e)*x^10+1/9*(28*a^3*c*d*e^6+210*a^2*c^2*d^3*e^4+84*a*c^3*d^5*e^2+c^4*d^7)*x^9+1/8*(a^4*e^7+84*a^3*c*d^2*e^5+210*a^2*c^2*d^4*e^3+28*a*c^3*d^6*e)*x^8+1/7*(7*a^4*d*e^6+140*a^3*c*d^3*e^4+126*a^2*c^2*d^5*e^2+4*a*c^3*d^7)*x^7+1/6*(21*a^4*d^2*e^5+140*a^3*c*d^4*e^3+42*a^2*c^2*d^6*e)*x^6+1/5*(35*a^4*d^3*e^4+84*a^3*c*d^5*e^2+6*a^2*c^2*d^7)*x^5+1/4*(35*a^4*d^4*e^3+28*a^3*c*d^6*e)*x^4+1/3*(21*a^4*d^5*e^2+4*a^3*c*d^7)*x^3+7/2*d^6*e*a^4*x^2+d^7*a^4*x","A"
489,1,445,260,0.040000," ","int((e*x+d)^6*(c*x^2+a)^4,x)","\frac{c^{4} e^{6} x^{15}}{15}+\frac{3 c^{4} d \,e^{5} x^{14}}{7}+\frac{\left(4 e^{6} a \,c^{3}+15 d^{2} e^{4} c^{4}\right) x^{13}}{13}+3 a^{4} d^{5} e \,x^{2}+\frac{\left(24 d \,e^{5} a \,c^{3}+20 d^{3} e^{3} c^{4}\right) x^{12}}{12}+a^{4} d^{6} x +\frac{\left(6 e^{6} a^{2} c^{2}+60 d^{2} e^{4} a \,c^{3}+15 d^{4} e^{2} c^{4}\right) x^{11}}{11}+\frac{\left(36 d \,e^{5} a^{2} c^{2}+80 d^{3} e^{3} a \,c^{3}+6 d^{5} e \,c^{4}\right) x^{10}}{10}+\frac{\left(4 e^{6} a^{3} c +90 d^{2} e^{4} a^{2} c^{2}+60 d^{4} e^{2} a \,c^{3}+d^{6} c^{4}\right) x^{9}}{9}+\frac{\left(24 d \,e^{5} a^{3} c +120 d^{3} e^{3} a^{2} c^{2}+24 d^{5} e a \,c^{3}\right) x^{8}}{8}+\frac{\left(e^{6} a^{4}+60 d^{2} e^{4} a^{3} c +90 d^{4} e^{2} a^{2} c^{2}+4 d^{6} a \,c^{3}\right) x^{7}}{7}+\frac{\left(6 d \,e^{5} a^{4}+80 d^{3} e^{3} a^{3} c +36 d^{5} e \,a^{2} c^{2}\right) x^{6}}{6}+\frac{\left(15 d^{2} e^{4} a^{4}+60 d^{4} e^{2} a^{3} c +6 d^{6} a^{2} c^{2}\right) x^{5}}{5}+\frac{\left(20 d^{3} e^{3} a^{4}+24 d^{5} e \,a^{3} c \right) x^{4}}{4}+\frac{\left(15 d^{4} e^{2} a^{4}+4 d^{6} a^{3} c \right) x^{3}}{3}"," ",0,"1/15*e^6*c^4*x^15+3/7*d*e^5*c^4*x^14+1/13*(4*a*c^3*e^6+15*c^4*d^2*e^4)*x^13+1/12*(24*a*c^3*d*e^5+20*c^4*d^3*e^3)*x^12+1/11*(6*a^2*c^2*e^6+60*a*c^3*d^2*e^4+15*c^4*d^4*e^2)*x^11+1/10*(36*a^2*c^2*d*e^5+80*a*c^3*d^3*e^3+6*c^4*d^5*e)*x^10+1/9*(4*a^3*c*e^6+90*a^2*c^2*d^2*e^4+60*a*c^3*d^4*e^2+c^4*d^6)*x^9+1/8*(24*a^3*c*d*e^5+120*a^2*c^2*d^3*e^3+24*a*c^3*d^5*e)*x^8+1/7*(a^4*e^6+60*a^3*c*d^2*e^4+90*a^2*c^2*d^4*e^2+4*a*c^3*d^6)*x^7+1/6*(6*a^4*d*e^5+80*a^3*c*d^3*e^3+36*a^2*c^2*d^5*e)*x^6+1/5*(15*a^4*d^2*e^4+60*a^3*c*d^4*e^2+6*a^2*c^2*d^6)*x^5+1/4*(20*a^4*d^3*e^3+24*a^3*c*d^5*e)*x^4+1/3*(15*a^4*d^4*e^2+4*a^3*c*d^6)*x^3+3*d^5*e*a^4*x^2+d^6*a^4*x","A"
490,1,379,260,0.042000," ","int((e*x+d)^5*(c*x^2+a)^4,x)","\frac{c^{4} e^{5} x^{14}}{14}+\frac{5 c^{4} d \,e^{4} x^{13}}{13}+\frac{\left(4 e^{5} a \,c^{3}+10 d^{2} e^{3} c^{4}\right) x^{12}}{12}+\frac{5 a^{4} d^{4} e \,x^{2}}{2}+\frac{\left(20 d \,e^{4} a \,c^{3}+10 d^{3} e^{2} c^{4}\right) x^{11}}{11}+a^{4} d^{5} x +\frac{\left(6 e^{5} a^{2} c^{2}+40 d^{2} e^{3} a \,c^{3}+5 d^{4} e \,c^{4}\right) x^{10}}{10}+\frac{\left(30 d \,e^{4} a^{2} c^{2}+40 d^{3} e^{2} a \,c^{3}+c^{4} d^{5}\right) x^{9}}{9}+\frac{\left(4 e^{5} a^{3} c +60 d^{2} e^{3} a^{2} c^{2}+20 d^{4} e a \,c^{3}\right) x^{8}}{8}+\frac{\left(20 d \,e^{4} a^{3} c +60 d^{3} e^{2} a^{2} c^{2}+4 d^{5} a \,c^{3}\right) x^{7}}{7}+\frac{\left(e^{5} a^{4}+40 d^{2} e^{3} a^{3} c +30 d^{4} e \,a^{2} c^{2}\right) x^{6}}{6}+\frac{\left(5 d \,e^{4} a^{4}+40 d^{3} e^{2} a^{3} c +6 d^{5} a^{2} c^{2}\right) x^{5}}{5}+\frac{\left(10 d^{2} e^{3} a^{4}+20 d^{4} e \,a^{3} c \right) x^{4}}{4}+\frac{\left(10 d^{3} e^{2} a^{4}+4 d^{5} a^{3} c \right) x^{3}}{3}"," ",0,"1/14*e^5*c^4*x^14+5/13*d*e^4*c^4*x^13+1/12*(4*a*c^3*e^5+10*c^4*d^2*e^3)*x^12+1/11*(20*a*c^3*d*e^4+10*c^4*d^3*e^2)*x^11+1/10*(6*a^2*c^2*e^5+40*a*c^3*d^2*e^3+5*c^4*d^4*e)*x^10+1/9*(30*a^2*c^2*d*e^4+40*a*c^3*d^3*e^2+c^4*d^5)*x^9+1/8*(4*a^3*c*e^5+60*a^2*c^2*d^2*e^3+20*a*c^3*d^4*e)*x^8+1/7*(20*a^3*c*d*e^4+60*a^2*c^2*d^3*e^2+4*a*c^3*d^5)*x^7+1/6*(a^4*e^5+40*a^3*c*d^2*e^3+30*a^2*c^2*d^4*e)*x^6+1/5*(5*a^4*d*e^4+40*a^3*c*d^3*e^2+6*a^2*c^2*d^5)*x^5+1/4*(10*a^4*d^2*e^3+20*a^3*c*d^4*e)*x^4+1/3*(10*a^4*d^3*e^2+4*a^3*c*d^5)*x^3+5/2*d^4*e*a^4*x^2+d^5*a^4*x","A"
491,1,313,250,0.042000," ","int((e*x+d)^4*(c*x^2+a)^4,x)","\frac{c^{4} e^{4} x^{13}}{13}+\frac{c^{4} d \,e^{3} x^{12}}{3}+\frac{\left(4 e^{4} a \,c^{3}+6 d^{2} e^{2} c^{4}\right) x^{11}}{11}+2 a^{4} d^{3} e \,x^{2}+\frac{\left(16 d \,e^{3} a \,c^{3}+4 d^{3} e \,c^{4}\right) x^{10}}{10}+a^{4} d^{4} x +\frac{\left(6 e^{4} a^{2} c^{2}+24 d^{2} e^{2} a \,c^{3}+c^{4} d^{4}\right) x^{9}}{9}+\frac{\left(24 d \,e^{3} a^{2} c^{2}+16 d^{3} e a \,c^{3}\right) x^{8}}{8}+\frac{\left(4 e^{4} a^{3} c +36 d^{2} e^{2} a^{2} c^{2}+4 d^{4} a \,c^{3}\right) x^{7}}{7}+\frac{\left(16 d \,e^{3} a^{3} c +24 d^{3} e \,a^{2} c^{2}\right) x^{6}}{6}+\frac{\left(e^{4} a^{4}+24 d^{2} e^{2} a^{3} c +6 d^{4} a^{2} c^{2}\right) x^{5}}{5}+\frac{\left(4 d \,e^{3} a^{4}+16 d^{3} e \,a^{3} c \right) x^{4}}{4}+\frac{\left(6 d^{2} e^{2} a^{4}+4 d^{4} a^{3} c \right) x^{3}}{3}"," ",0,"1/13*c^4*e^4*x^13+1/3*c^4*d*e^3*x^12+1/11*(4*a*c^3*e^4+6*c^4*d^2*e^2)*x^11+1/10*(16*a*c^3*d*e^3+4*c^4*d^3*e)*x^10+1/9*(6*a^2*c^2*e^4+24*a*c^3*d^2*e^2+c^4*d^4)*x^9+1/8*(24*a^2*c^2*d*e^3+16*a*c^3*d^3*e)*x^8+1/7*(4*a^3*c*e^4+36*a^2*c^2*d^2*e^2+4*a*c^3*d^4)*x^7+1/6*(16*a^3*c*d*e^3+24*a^2*c^2*d^3*e)*x^6+1/5*(a^4*e^4+24*a^3*c*d^2*e^2+6*a^2*c^2*d^4)*x^5+1/4*(4*a^4*d*e^3+16*a^3*c*d^3*e)*x^4+1/3*(6*a^4*d^2*e^2+4*a^3*c*d^4)*x^3+2*d^3*e*a^4*x^2+a^4*d^4*x","A"
492,1,247,187,0.041000," ","int((e*x+d)^3*(c*x^2+a)^4,x)","\frac{c^{4} e^{3} x^{12}}{12}+\frac{3 c^{4} d \,e^{2} x^{11}}{11}+\frac{\left(4 e^{3} a \,c^{3}+3 d^{2} e \,c^{4}\right) x^{10}}{10}+\frac{3 a^{4} d^{2} e \,x^{2}}{2}+\frac{\left(12 d \,e^{2} a \,c^{3}+d^{3} c^{4}\right) x^{9}}{9}+a^{4} d^{3} x +\frac{\left(6 e^{3} a^{2} c^{2}+12 d^{2} e a \,c^{3}\right) x^{8}}{8}+\frac{\left(18 d \,e^{2} a^{2} c^{2}+4 d^{3} a \,c^{3}\right) x^{7}}{7}+\frac{\left(4 e^{3} a^{3} c +18 d^{2} e \,a^{2} c^{2}\right) x^{6}}{6}+\frac{\left(12 d \,e^{2} a^{3} c +6 d^{3} a^{2} c^{2}\right) x^{5}}{5}+\frac{\left(e^{3} a^{4}+12 d^{2} e \,a^{3} c \right) x^{4}}{4}+\frac{\left(3 d \,e^{2} a^{4}+4 a^{3} c \,d^{3}\right) x^{3}}{3}"," ",0,"1/12*c^4*e^3*x^12+3/11*c^4*d*e^2*x^11+1/10*(4*a*c^3*e^3+3*c^4*d^2*e)*x^10+1/9*(12*a*c^3*d*e^2+c^4*d^3)*x^9+1/8*(6*a^2*c^2*e^3+12*a*c^3*d^2*e)*x^8+1/7*(18*a^2*c^2*d*e^2+4*a*c^3*d^3)*x^7+1/6*(4*a^3*c*e^3+18*a^2*c^2*d^2*e)*x^6+1/5*(12*a^3*c*d*e^2+6*a^2*c^2*d^3)*x^5+1/4*(a^4*e^3+12*a^3*c*d^2*e)*x^4+1/3*(3*a^4*d*e^2+4*a^3*c*d^3)*x^3+3/2*d^2*e*a^4*x^2+a^4*d^3*x","A"
493,1,170,120,0.037000," ","int((e*x+d)^2*(c*x^2+a)^4,x)","\frac{c^{4} e^{2} x^{11}}{11}+\frac{c^{4} d e \,x^{10}}{5}+a \,c^{3} d e \,x^{8}+2 a^{2} c^{2} d e \,x^{6}+2 a^{3} c d e \,x^{4}+\frac{\left(4 e^{2} a \,c^{3}+c^{4} d^{2}\right) x^{9}}{9}+a^{4} d e \,x^{2}+a^{4} d^{2} x +\frac{\left(6 e^{2} a^{2} c^{2}+4 d^{2} a \,c^{3}\right) x^{7}}{7}+\frac{\left(4 e^{2} a^{3} c +6 d^{2} a^{2} c^{2}\right) x^{5}}{5}+\frac{\left(e^{2} a^{4}+4 d^{2} a^{3} c \right) x^{3}}{3}"," ",0,"1/11*c^4*e^2*x^11+1/5*d*e*c^4*x^10+1/9*(4*a*c^3*e^2+c^4*d^2)*x^9+d*e*a*c^3*x^8+1/7*(6*a^2*c^2*e^2+4*a*c^3*d^2)*x^7+2*a^2*c^2*d*e*x^6+1/5*(4*a^3*c*e^2+6*a^2*c^2*d^2)*x^5+2*d*e*a^3*c*x^4+1/3*(a^4*e^2+4*a^3*c*d^2)*x^3+d*e*a^4*x^2+a^4*d^2*x","A"
494,1,97,63,0.046000," ","int((e*x+d)*(c*x^2+a)^4,x)","\frac{1}{10} c^{4} e \,x^{10}+\frac{1}{9} c^{4} d \,x^{9}+\frac{1}{2} a \,c^{3} e \,x^{8}+\frac{4}{7} a \,c^{3} d \,x^{7}+a^{2} c^{2} e \,x^{6}+\frac{6}{5} a^{2} c^{2} d \,x^{5}+a^{3} c e \,x^{4}+\frac{4}{3} a^{3} c d \,x^{3}+\frac{1}{2} a^{4} e \,x^{2}+a^{4} d x"," ",0,"1/10*c^4*e*x^10+1/9*c^4*d*x^9+1/2*e*a*c^3*x^8+4/7*a*c^3*d*x^7+e*a^2*c^2*x^6+6/5*a^2*c^2*d*x^5+e*a^3*c*x^4+4/3*a^3*c*d*x^3+1/2*a^4*e*x^2+a^4*d*x","A"
495,1,358,252,0.041000," ","int((c*x^2+a)^4/(e*x+d),x)","\frac{c^{4} x^{8}}{8 e}-\frac{c^{4} d \,x^{7}}{7 e^{2}}+\frac{2 a \,c^{3} x^{6}}{3 e}+\frac{c^{4} d^{2} x^{6}}{6 e^{3}}-\frac{4 a \,c^{3} d \,x^{5}}{5 e^{2}}-\frac{c^{4} d^{3} x^{5}}{5 e^{4}}+\frac{3 a^{2} c^{2} x^{4}}{2 e}+\frac{a \,c^{3} d^{2} x^{4}}{e^{3}}+\frac{c^{4} d^{4} x^{4}}{4 e^{5}}-\frac{2 a^{2} c^{2} d \,x^{3}}{e^{2}}-\frac{4 a \,c^{3} d^{3} x^{3}}{3 e^{4}}-\frac{c^{4} d^{5} x^{3}}{3 e^{6}}+\frac{2 a^{3} c \,x^{2}}{e}+\frac{3 a^{2} c^{2} d^{2} x^{2}}{e^{3}}+\frac{2 a \,c^{3} d^{4} x^{2}}{e^{5}}+\frac{c^{4} d^{6} x^{2}}{2 e^{7}}+\frac{a^{4} \ln \left(e x +d \right)}{e}+\frac{4 a^{3} c \,d^{2} \ln \left(e x +d \right)}{e^{3}}-\frac{4 a^{3} c d x}{e^{2}}+\frac{6 a^{2} c^{2} d^{4} \ln \left(e x +d \right)}{e^{5}}-\frac{6 a^{2} c^{2} d^{3} x}{e^{4}}+\frac{4 a \,c^{3} d^{6} \ln \left(e x +d \right)}{e^{7}}-\frac{4 a \,c^{3} d^{5} x}{e^{6}}+\frac{c^{4} d^{8} \ln \left(e x +d \right)}{e^{9}}-\frac{c^{4} d^{7} x}{e^{8}}"," ",0,"-4/5*c^3/e^2*x^5*a*d+c^3/e^3*x^4*a*d^2+1/6*c^4/e^3*x^6*d^2-1/5*c^4/e^4*x^5*d^3+3/2*c^2/e*x^4*a^2-1/7*c^4/e^2*d*x^7-c^4/e^8*d^7*x+2/3*c^3/e*x^6*a+1/4*c^4/e^5*x^4*d^4-1/3*c^4/e^6*x^3*d^5+2*c/e*x^2*a^3+1/2*c^4/e^7*x^2*d^6+1/e^9*ln(e*x+d)*c^4*d^8+1/e*ln(e*x+d)*a^4+4/e^3*ln(e*x+d)*a^3*c*d^2+6/e^5*ln(e*x+d)*a^2*c^2*d^4+4/e^7*ln(e*x+d)*a*c^3*d^6-2*c^2/e^2*x^3*a^2*d-4*c^3/e^6*a*d^5*x+1/8*c^4/e*x^8-6*c^2/e^4*a^2*d^3*x+2*c^3/e^5*x^2*a*d^4-4*c/e^2*a^3*d*x-4/3*c^3/e^4*x^3*a*d^3+3*c^2/e^3*x^2*a^2*d^2","A"
496,1,378,247,0.052000," ","int((c*x^2+a)^4/(e*x+d)^2,x)","\frac{c^{4} x^{7}}{7 e^{2}}-\frac{c^{4} d \,x^{6}}{3 e^{3}}+\frac{4 a \,c^{3} x^{5}}{5 e^{2}}+\frac{3 c^{4} d^{2} x^{5}}{5 e^{4}}-\frac{2 a \,c^{3} d \,x^{4}}{e^{3}}-\frac{c^{4} d^{3} x^{4}}{e^{5}}+\frac{2 a^{2} c^{2} x^{3}}{e^{2}}+\frac{4 a \,c^{3} d^{2} x^{3}}{e^{4}}+\frac{5 c^{4} d^{4} x^{3}}{3 e^{6}}-\frac{6 a^{2} c^{2} d \,x^{2}}{e^{3}}-\frac{8 a \,c^{3} d^{3} x^{2}}{e^{5}}-\frac{3 c^{4} d^{5} x^{2}}{e^{7}}-\frac{a^{4}}{\left(e x +d \right) e}-\frac{4 a^{3} c \,d^{2}}{\left(e x +d \right) e^{3}}-\frac{8 a^{3} c d \ln \left(e x +d \right)}{e^{3}}+\frac{4 a^{3} c x}{e^{2}}-\frac{6 a^{2} c^{2} d^{4}}{\left(e x +d \right) e^{5}}-\frac{24 a^{2} c^{2} d^{3} \ln \left(e x +d \right)}{e^{5}}+\frac{18 a^{2} c^{2} d^{2} x}{e^{4}}-\frac{4 a \,c^{3} d^{6}}{\left(e x +d \right) e^{7}}-\frac{24 a \,c^{3} d^{5} \ln \left(e x +d \right)}{e^{7}}+\frac{20 a \,c^{3} d^{4} x}{e^{6}}-\frac{c^{4} d^{8}}{\left(e x +d \right) e^{9}}-\frac{8 c^{4} d^{7} \ln \left(e x +d \right)}{e^{9}}+\frac{7 c^{4} d^{6} x}{e^{8}}"," ",0,"4/5*c^3/e^2*x^5*a+3/5*c^4/e^4*x^5*d^2-c^4/e^5*x^4*d^3+2*c^2/e^2*x^3*a^2-8*c^4*d^7/e^9*ln(e*x+d)-1/e^9/(e*x+d)*c^4*d^8+5/3*c^4/e^6*x^3*d^4-3*c^4/e^7*x^2*d^5+4*c/e^2*a^3*x+7*c^4/e^8*d^6*x-1/e/(e*x+d)*a^4+18*c^2/e^4*a^2*d^2*x+20*c^3/e^6*a*d^4*x-4/e^3/(e*x+d)*a^3*c*d^2-6/e^5/(e*x+d)*a^2*c^2*d^4-4/e^7/(e*x+d)*a*c^3*d^6-6*c^2/e^3*x^2*a^2*d-8*c^3/e^5*x^2*a*d^3-2*c^3/e^3*x^4*a*d+4*c^3/e^4*x^3*a*d^2-24*c^2*d^3/e^5*ln(e*x+d)*a^2-24*c^3*d^5/e^7*ln(e*x+d)*a-8*c*d/e^3*ln(e*x+d)*a^3+1/7*c^4*x^7/e^2-1/3*c^4*d*x^6/e^3","A"
497,1,97,63,0.038000," ","int((d*x+c)*(b*x^2+a)^4,x)","\frac{1}{10} b^{4} d \,x^{10}+\frac{1}{9} b^{4} c \,x^{9}+\frac{1}{2} a \,b^{3} d \,x^{8}+\frac{4}{7} a \,b^{3} c \,x^{7}+a^{2} b^{2} d \,x^{6}+\frac{6}{5} a^{2} b^{2} c \,x^{5}+a^{3} b d \,x^{4}+\frac{4}{3} a^{3} b c \,x^{3}+\frac{1}{2} a^{4} d \,x^{2}+a^{4} c x"," ",0,"1/10*d*b^4*x^10+1/9*b^4*c*x^9+1/2*a*b^3*d*x^8+4/7*a*b^3*c*x^7+a^2*b^2*d*x^6+6/5*a^2*b^2*c*x^5+a^3*b*d*x^4+4/3*a^3*b*c*x^3+1/2*a^4*d*x^2+a^4*c*x","A"
498,1,150,113,0.043000," ","int((e*x+d)^4/(c*x^2+a),x)","\frac{e^{4} x^{3}}{3 c}+\frac{a^{2} e^{4} \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{\sqrt{a c}\, c^{2}}-\frac{6 a \,d^{2} e^{2} \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{\sqrt{a c}\, c}+\frac{2 d \,e^{3} x^{2}}{c}+\frac{d^{4} \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{\sqrt{a c}}-\frac{2 a d \,e^{3} \ln \left(c \,x^{2}+a \right)}{c^{2}}-\frac{a \,e^{4} x}{c^{2}}+\frac{2 d^{3} e \ln \left(c \,x^{2}+a \right)}{c}+\frac{6 d^{2} e^{2} x}{c}"," ",0,"1/3/c*e^4*x^3+2/c*d*e^3*x^2-e^4/c^2*a*x+6*e^2/c*d^2*x-2/c^2*ln(c*x^2+a)*a*d*e^3+2/c*ln(c*x^2+a)*d^3*e+1/c^2/(a*c)^(1/2)*arctan(c*x/(a*c)^(1/2))*a^2*e^4-6/c/(a*c)^(1/2)*arctan(c*x/(a*c)^(1/2))*a*d^2*e^2+1/(a*c)^(1/2)*arctan(c*x/(a*c)^(1/2))*d^4","A"
499,1,99,78,0.042000," ","int((e*x+d)^3/(c*x^2+a),x)","-\frac{3 a d \,e^{2} \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{\sqrt{a c}\, c}+\frac{e^{3} x^{2}}{2 c}+\frac{d^{3} \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{\sqrt{a c}}-\frac{a \,e^{3} \ln \left(c \,x^{2}+a \right)}{2 c^{2}}+\frac{3 d^{2} e \ln \left(c \,x^{2}+a \right)}{2 c}+\frac{3 d \,e^{2} x}{c}"," ",0,"1/2/c*e^3*x^2+3/c*d*e^2*x-1/2/c^2*ln(c*x^2+a)*e^3*a+3/2/c*ln(c*x^2+a)*d^2*e-3/c/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)*d*e^2*a+1/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)*d^3","A"
500,1,65,51,0.043000," ","int((e*x+d)^2/(c*x^2+a),x)","-\frac{a \,e^{2} \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{\sqrt{a c}\, c}+\frac{d^{2} \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{\sqrt{a c}}+\frac{d e \ln \left(c \,x^{2}+a \right)}{c}+\frac{e^{2} x}{c}"," ",0,"1/c*e^2*x+d*e*ln(c*x^2+a)/c-1/c/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)*a*e^2+1/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)*d^2","A"
501,1,32,32,0.042000," ","int((e*x+d)/(c*x^2+a),x)","\frac{d \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{\sqrt{a c}}+\frac{e \ln \left(c \,x^{2}+a \right)}{2 c}"," ",0,"1/2*e*ln(c*x^2+a)/c+d/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)","A"
502,1,77,76,0.050000," ","int(1/(e*x+d)/(c*x^2+a),x)","\frac{c d \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{\left(a \,e^{2}+c \,d^{2}\right) \sqrt{a c}}-\frac{e \ln \left(c \,x^{2}+a \right)}{2 \left(a \,e^{2}+c \,d^{2}\right)}+\frac{e \ln \left(e x +d \right)}{a \,e^{2}+c \,d^{2}}"," ",0,"-1/2*e*ln(c*x^2+a)/(a*e^2+c*d^2)+c/(a*e^2+c*d^2)*d/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)+e*ln(e*x+d)/(a*e^2+c*d^2)","A"
503,1,143,115,0.051000," ","int(1/(e*x+d)^2/(c*x^2+a),x)","-\frac{a c \,e^{2} \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{\left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{a c}}+\frac{c^{2} d^{2} \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{\left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{a c}}-\frac{c d e \ln \left(c \,x^{2}+a \right)}{\left(a \,e^{2}+c \,d^{2}\right)^{2}}+\frac{2 c d e \ln \left(e x +d \right)}{\left(a \,e^{2}+c \,d^{2}\right)^{2}}-\frac{e}{\left(a \,e^{2}+c \,d^{2}\right) \left(e x +d \right)}"," ",0,"-c*d*e*ln(c*x^2+a)/(a*e^2+c*d^2)^2-c/(a*e^2+c*d^2)^2/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)*a*e^2+c^2/(a*e^2+c*d^2)^2/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)*d^2-e/(a*e^2+c*d^2)/(e*x+d)+2*c*d*e*ln(e*x+d)/(a*e^2+c*d^2)^2","A"
504,1,233,164,0.053000," ","int(1/(e*x+d)^3/(c*x^2+a),x)","-\frac{3 a \,c^{2} d \,e^{2} \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{\left(a \,e^{2}+c \,d^{2}\right)^{3} \sqrt{a c}}+\frac{c^{3} d^{3} \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{\left(a \,e^{2}+c \,d^{2}\right)^{3} \sqrt{a c}}+\frac{a c \,e^{3} \ln \left(c \,x^{2}+a \right)}{2 \left(a \,e^{2}+c \,d^{2}\right)^{3}}-\frac{a c \,e^{3} \ln \left(e x +d \right)}{\left(a \,e^{2}+c \,d^{2}\right)^{3}}-\frac{3 c^{2} d^{2} e \ln \left(c \,x^{2}+a \right)}{2 \left(a \,e^{2}+c \,d^{2}\right)^{3}}+\frac{3 c^{2} d^{2} e \ln \left(e x +d \right)}{\left(a \,e^{2}+c \,d^{2}\right)^{3}}-\frac{2 c d e}{\left(a \,e^{2}+c \,d^{2}\right)^{2} \left(e x +d \right)}-\frac{e}{2 \left(a \,e^{2}+c \,d^{2}\right) \left(e x +d \right)^{2}}"," ",0,"1/2*c/(a*e^2+c*d^2)^3*ln(c*x^2+a)*e^3*a-3/2*c^2/(a*e^2+c*d^2)^3*ln(c*x^2+a)*d^2*e-3*c^2/(a*e^2+c*d^2)^3/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)*d*e^2*a+c^3/(a*e^2+c*d^2)^3/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)*d^3-1/2*e/(a*e^2+c*d^2)/(e*x+d)^2-2*c*d*e/(a*e^2+c*d^2)^2/(e*x+d)-e^3*c/(a*e^2+c*d^2)^3*ln(e*x+d)*a+3*e*c^2/(a*e^2+c*d^2)^3*ln(e*x+d)*d^2","A"
505,1,248,174,0.054000," ","int((e*x+d)^5/(c*x^2+a)^2,x)","\frac{5 a d \,e^{4} x}{2 \left(c \,x^{2}+a \right) c^{2}}-\frac{15 a d \,e^{4} \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{2 \sqrt{a c}\, c^{2}}+\frac{d^{5} x}{2 \left(c \,x^{2}+a \right) a}+\frac{d^{5} \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{2 \sqrt{a c}\, a}-\frac{5 d^{3} e^{2} x}{\left(c \,x^{2}+a \right) c}+\frac{5 d^{3} e^{2} \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{\sqrt{a c}\, c}+\frac{e^{5} x^{2}}{2 c^{2}}-\frac{a^{2} e^{5}}{2 \left(c \,x^{2}+a \right) c^{3}}+\frac{5 a \,d^{2} e^{3}}{\left(c \,x^{2}+a \right) c^{2}}-\frac{a \,e^{5} \ln \left(c \,x^{2}+a \right)}{c^{3}}-\frac{5 d^{4} e}{2 \left(c \,x^{2}+a \right) c}+\frac{5 d^{2} e^{3} \ln \left(c \,x^{2}+a \right)}{c^{2}}+\frac{5 d \,e^{4} x}{c^{2}}"," ",0,"1/2/c^2*e^5*x^2+5/c^2*d*e^4*x+5/2/c^2/(c*x^2+a)*d*a*x*e^4-5/c/(c*x^2+a)*d^3*x*e^2+1/2/(c*x^2+a)*d^5/a*x-1/2/c^3/(c*x^2+a)*e^5*a^2+5/c^2/(c*x^2+a)*a*d^2*e^3-5/2/c/(c*x^2+a)*e*d^4-1/c^3*a*ln(c*x^2+a)*e^5+5/c^2*ln(c*x^2+a)*d^2*e^3-15/2/c^2*a/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)*d*e^4+5/c/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)*d^3*e^2+1/2/a/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)*d^5","A"
506,1,192,133,0.051000," ","int((e*x+d)^4/(c*x^2+a)^2,x)","\frac{a \,e^{4} x}{2 \left(c \,x^{2}+a \right) c^{2}}-\frac{3 a \,e^{4} \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{2 \sqrt{a c}\, c^{2}}+\frac{d^{4} x}{2 \left(c \,x^{2}+a \right) a}+\frac{d^{4} \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{2 \sqrt{a c}\, a}-\frac{3 d^{2} e^{2} x}{\left(c \,x^{2}+a \right) c}+\frac{3 d^{2} e^{2} \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{\sqrt{a c}\, c}+\frac{2 a d \,e^{3}}{\left(c \,x^{2}+a \right) c^{2}}-\frac{2 d^{3} e}{\left(c \,x^{2}+a \right) c}+\frac{2 d \,e^{3} \ln \left(c \,x^{2}+a \right)}{c^{2}}+\frac{e^{4} x}{c^{2}}"," ",0,"1/c^2*e^4*x+1/2/c^2/(c*x^2+a)*a*x*e^4-3/c/(c*x^2+a)*x*d^2*e^2+1/2/(c*x^2+a)/a*x*d^4+2/c^2/(c*x^2+a)*d*e^3*a-2/c/(c*x^2+a)*d^3*e+2*d*e^3*ln(c*x^2+a)/c^2-3/2/c^2*a/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)*e^4+3/c/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)*d^2*e^2+1/2/a/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)*d^4","A"
507,1,115,93,0.063000," ","int((e*x+d)^3/(c*x^2+a)^2,x)","\frac{d^{3} \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{2 \sqrt{a c}\, a}+\frac{3 d \,e^{2} \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{2 \sqrt{a c}\, c}+\frac{e^{3} \ln \left(c \,x^{2}+a \right)}{2 c^{2}}+\frac{-\frac{\left(3 a \,e^{2}-c \,d^{2}\right) d x}{2 a c}+\frac{\left(a \,e^{2}-3 c \,d^{2}\right) e}{2 c^{2}}}{c \,x^{2}+a}"," ",0,"(-1/2*d*(3*a*e^2-c*d^2)/a/c*x+1/2*e*(a*e^2-3*c*d^2)/c^2)/(c*x^2+a)+1/2*e^3*ln(c*x^2+a)/c^2+3/2/c/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)*d*e^2+1/2/a/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)*d^3","A"
508,1,85,60,0.049000," ","int((e*x+d)^2/(c*x^2+a)^2,x)","\frac{d^{2} \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{2 \sqrt{a c}\, a}+\frac{e^{2} \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{2 \sqrt{a c}\, c}+\frac{-\frac{d e}{c}-\frac{\left(a \,e^{2}-c \,d^{2}\right) x}{2 a c}}{c \,x^{2}+a}"," ",0,"(-1/2*(a*e^2-c*d^2)/a/c*x-d*e/c)/(c*x^2+a)+1/2/c/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)*e^2+1/2/a/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)*d^2","A"
509,1,49,45,0.046000," ","int((e*x+d)/(c*x^2+a)^2,x)","\frac{d \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{2 \sqrt{a c}\, a}+\frac{2 c d x -2 a e}{4 \left(c \,x^{2}+a \right) a c}"," ",0,"1/4*(2*c*d*x-2*a*e)/a/c/(c*x^2+a)+1/2*d/a/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)","A"
510,1,244,128,0.063000," ","int(1/(e*x+d)/(c*x^2+a)^2,x)","\frac{c^{2} d^{3} x}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{2}+a \right) a}+\frac{c^{2} d^{3} \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{a c}\, a}+\frac{c d \,e^{2} x}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{2}+a \right)}+\frac{3 c d \,e^{2} \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{a c}}+\frac{a \,e^{3}}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{2}+a \right)}+\frac{c \,d^{2} e}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{2}+a \right)}-\frac{e^{3} \ln \left(c \,x^{2}+a \right)}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2}}+\frac{e^{3} \ln \left(e x +d \right)}{\left(a \,e^{2}+c \,d^{2}\right)^{2}}"," ",0,"1/2*c/(a*e^2+c*d^2)^2/(c*x^2+a)*d*x*e^2+1/2*c^2/(a*e^2+c*d^2)^2/(c*x^2+a)*d^3/a*x+1/2/(a*e^2+c*d^2)^2/(c*x^2+a)*e^3*a+1/2*c/(a*e^2+c*d^2)^2/(c*x^2+a)*d^2*e-1/2*e^3*ln(c*x^2+a)/(a*e^2+c*d^2)^2+3/2*c/(a*e^2+c*d^2)^2/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)*d*e^2+1/2*c^2/(a*e^2+c*d^2)^2/a/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)*d^3+e^3*ln(e*x+d)/(a*e^2+c*d^2)^2","A"
511,1,314,191,0.067000," ","int(1/(e*x+d)^2/(c*x^2+a)^2,x)","-\frac{a c \,e^{4} x}{2 \left(a \,e^{2}+c \,d^{2}\right)^{3} \left(c \,x^{2}+a \right)}-\frac{3 a c \,e^{4} \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right)^{3} \sqrt{a c}}+\frac{c^{3} d^{4} x}{2 \left(a \,e^{2}+c \,d^{2}\right)^{3} \left(c \,x^{2}+a \right) a}+\frac{c^{3} d^{4} \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right)^{3} \sqrt{a c}\, a}+\frac{3 c^{2} d^{2} e^{2} \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{\left(a \,e^{2}+c \,d^{2}\right)^{3} \sqrt{a c}}+\frac{a c d \,e^{3}}{\left(a \,e^{2}+c \,d^{2}\right)^{3} \left(c \,x^{2}+a \right)}+\frac{c^{2} d^{3} e}{\left(a \,e^{2}+c \,d^{2}\right)^{3} \left(c \,x^{2}+a \right)}-\frac{2 c d \,e^{3} \ln \left(c \,x^{2}+a \right)}{\left(a \,e^{2}+c \,d^{2}\right)^{3}}+\frac{4 c d \,e^{3} \ln \left(e x +d \right)}{\left(a \,e^{2}+c \,d^{2}\right)^{3}}-\frac{e^{3}}{\left(a \,e^{2}+c \,d^{2}\right)^{2} \left(e x +d \right)}"," ",0,"-1/2*c/(a*e^2+c*d^2)^3/(c*x^2+a)*a*x*e^4+1/2*c^3/(a*e^2+c*d^2)^3/(c*x^2+a)/a*x*d^4+c/(a*e^2+c*d^2)^3/(c*x^2+a)*d*e^3*a+c^2/(a*e^2+c*d^2)^3/(c*x^2+a)*d^3*e-2*c*d*e^3*ln(c*x^2+a)/(a*e^2+c*d^2)^3-3/2*c/(a*e^2+c*d^2)^3*a/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)*e^4+3*c^2/(a*e^2+c*d^2)^3/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)*d^2*e^2+1/2*c^3/(a*e^2+c*d^2)^3/a/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)*d^4-e^3/(a*e^2+c*d^2)^2/(e*x+d)+4*c*d*e^3*ln(e*x+d)/(a*e^2+c*d^2)^3","A"
512,1,233,180,0.062000," ","int((e*x+d)^5/(c*x^2+a)^3,x)","\frac{5 d^{3} e^{2} \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{4 \sqrt{a c}\, a c}+\frac{3 d^{5} \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{8 \sqrt{a c}\, a^{2}}+\frac{15 d \,e^{4} \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{8 \sqrt{a c}\, c^{2}}+\frac{e^{5} \ln \left(c \,x^{2}+a \right)}{2 c^{3}}+\frac{\frac{\left(a \,e^{2}-5 c \,d^{2}\right) e^{3} x^{2}}{c^{2}}-\frac{\left(25 a^{2} e^{4}-10 a c \,d^{2} e^{2}-3 c^{2} d^{4}\right) d \,x^{3}}{8 a^{2} c}-\frac{5 \left(3 a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) d x}{8 a \,c^{2}}+\frac{\left(3 a^{2} e^{4}-10 a c \,d^{2} e^{2}-5 c^{2} d^{4}\right) e}{4 c^{3}}}{\left(c \,x^{2}+a \right)^{2}}"," ",0,"(-1/8*d*(25*a^2*e^4-10*a*c*d^2*e^2-3*c^2*d^4)/a^2/c*x^3+e^3*(a*e^2-5*c*d^2)/c^2*x^2-5/8*d*(3*a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/a/c^2*x+1/4*e*(3*a^2*e^4-10*a*c*d^2*e^2-5*c^2*d^4)/c^3)/(c*x^2+a)^2+1/2*e^5*ln(c*x^2+a)/c^3+15/8/c^2/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)*d*e^4+5/4/a/c/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)*d^3*e^2+3/8/a^2/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)*d^5","A"
513,1,189,106,0.051000," ","int((e*x+d)^4/(c*x^2+a)^3,x)","\frac{3 d^{2} e^{2} \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{4 \sqrt{a c}\, a c}+\frac{3 d^{4} \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{8 \sqrt{a c}\, a^{2}}+\frac{3 e^{4} \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{8 \sqrt{a c}\, c^{2}}+\frac{-\frac{2 d \,e^{3} x^{2}}{c}-\frac{\left(5 a^{2} e^{4}-6 a c \,d^{2} e^{2}-3 c^{2} d^{4}\right) x^{3}}{8 a^{2} c}-\frac{\left(a \,e^{2}+c \,d^{2}\right) d e}{c^{2}}-\frac{\left(3 a^{2} e^{4}+6 a c \,d^{2} e^{2}-5 c^{2} d^{4}\right) x}{8 a \,c^{2}}}{\left(c \,x^{2}+a \right)^{2}}"," ",0,"(-1/8*(5*a^2*e^4-6*a*c*d^2*e^2-3*c^2*d^4)/a^2/c*x^3-2/c*d*e^3*x^2-1/8*(3*a^2*e^4+6*a*c*d^2*e^2-5*c^2*d^4)/a/c^2*x-d*e*(a*e^2+c*d^2)/c^2)/(c*x^2+a)^2+3/8/c^2/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)*e^4+3/4/a/c/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)*d^2*e^2+3/8/a^2/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)*d^4","A"
514,1,133,84,0.054000," ","int((e*x+d)^3/(c*x^2+a)^3,x)","\frac{3 d \,e^{2} \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{8 \sqrt{a c}\, a c}+\frac{3 d^{3} \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{8 \sqrt{a c}\, a^{2}}+\frac{-\frac{e^{3} x^{2}}{2 c}+\frac{3 \left(a \,e^{2}+c \,d^{2}\right) d \,x^{3}}{8 a^{2}}-\frac{\left(3 a \,e^{2}-5 c \,d^{2}\right) d x}{8 a c}-\frac{\left(a \,e^{2}+3 c \,d^{2}\right) e}{4 c^{2}}}{\left(c \,x^{2}+a \right)^{2}}"," ",0,"(3/8*d*(a*e^2+c*d^2)/a^2*x^3-1/2/c*e^3*x^2-1/8*d*(3*a*e^2-5*c*d^2)/a/c*x-1/4*e*(a*e^2+3*c*d^2)/c^2)/(c*x^2+a)^2+3/8*d/a/c/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)*e^2+3/8*d^3/a^2/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)","A"
515,1,108,98,0.053000," ","int((e*x+d)^2/(c*x^2+a)^3,x)","\frac{e^{2} \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{8 \sqrt{a c}\, a c}+\frac{3 d^{2} \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{8 \sqrt{a c}\, a^{2}}+\frac{\frac{\left(a \,e^{2}+3 c \,d^{2}\right) x^{3}}{8 a^{2}}-\frac{d e}{2 c}-\frac{\left(a \,e^{2}-5 c \,d^{2}\right) x}{8 a c}}{\left(c \,x^{2}+a \right)^{2}}"," ",0,"(1/8*(a*e^2+3*c*d^2)/a^2*x^3-1/8*(a*e^2-5*c*d^2)/a/c*x-1/2/c*d*e)/(c*x^2+a)^2+1/8/a/c/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)*e^2+3/8/a^2/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)*d^2","A"
516,1,65,61,0.049000," ","int((e*x+d)/(c*x^2+a)^3,x)","\frac{3 d x}{8 \left(c \,x^{2}+a \right) a^{2}}+\frac{3 d \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{8 \sqrt{a c}\, a^{2}}+\frac{2 c d x -2 a e}{8 \left(c \,x^{2}+a \right)^{2} a c}"," ",0,"1/8*(2*c*d*x-2*a*e)/a/c/(c*x^2+a)^2+3/8*d*x/a^2/(c*x^2+a)+3/8*d/a^2/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)","A"
517,1,532,196,0.063000," ","int(1/(e*x+d)/(c*x^2+a)^3,x)","\frac{5 c^{3} d^{3} e^{2} x^{3}}{4 \left(a \,e^{2}+c \,d^{2}\right)^{3} \left(c \,x^{2}+a \right)^{2} a}+\frac{3 c^{4} d^{5} x^{3}}{8 \left(a \,e^{2}+c \,d^{2}\right)^{3} \left(c \,x^{2}+a \right)^{2} a^{2}}+\frac{7 c^{2} d \,e^{4} x^{3}}{8 \left(a \,e^{2}+c \,d^{2}\right)^{3} \left(c \,x^{2}+a \right)^{2}}+\frac{a c \,e^{5} x^{2}}{2 \left(a \,e^{2}+c \,d^{2}\right)^{3} \left(c \,x^{2}+a \right)^{2}}+\frac{c^{2} d^{2} e^{3} x^{2}}{2 \left(a \,e^{2}+c \,d^{2}\right)^{3} \left(c \,x^{2}+a \right)^{2}}+\frac{9 a c d \,e^{4} x}{8 \left(a \,e^{2}+c \,d^{2}\right)^{3} \left(c \,x^{2}+a \right)^{2}}+\frac{5 c^{3} d^{5} x}{8 \left(a \,e^{2}+c \,d^{2}\right)^{3} \left(c \,x^{2}+a \right)^{2} a}+\frac{7 c^{2} d^{3} e^{2} x}{4 \left(a \,e^{2}+c \,d^{2}\right)^{3} \left(c \,x^{2}+a \right)^{2}}+\frac{3 a^{2} e^{5}}{4 \left(a \,e^{2}+c \,d^{2}\right)^{3} \left(c \,x^{2}+a \right)^{2}}+\frac{a c \,d^{2} e^{3}}{\left(a \,e^{2}+c \,d^{2}\right)^{3} \left(c \,x^{2}+a \right)^{2}}+\frac{5 c^{2} d^{3} e^{2} \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{4 \left(a \,e^{2}+c \,d^{2}\right)^{3} \sqrt{a c}\, a}+\frac{3 c^{3} d^{5} \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{8 \left(a \,e^{2}+c \,d^{2}\right)^{3} \sqrt{a c}\, a^{2}}+\frac{c^{2} d^{4} e}{4 \left(a \,e^{2}+c \,d^{2}\right)^{3} \left(c \,x^{2}+a \right)^{2}}+\frac{15 c d \,e^{4} \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{8 \left(a \,e^{2}+c \,d^{2}\right)^{3} \sqrt{a c}}-\frac{e^{5} \ln \left(c \,x^{2}+a \right)}{2 \left(a \,e^{2}+c \,d^{2}\right)^{3}}+\frac{e^{5} \ln \left(e x +d \right)}{\left(a \,e^{2}+c \,d^{2}\right)^{3}}"," ",0,"7/8*c^2/(a*e^2+c*d^2)^3/(c*x^2+a)^2*d*x^3*e^4+5/4*c^3/(a*e^2+c*d^2)^3/(c*x^2+a)^2*d^3/a*x^3*e^2+3/8*c^4/(a*e^2+c*d^2)^3/(c*x^2+a)^2*d^5/a^2*x^3+1/2*c/(a*e^2+c*d^2)^3/(c*x^2+a)^2*x^2*a*e^5+1/2*c^2/(a*e^2+c*d^2)^3/(c*x^2+a)^2*x^2*d^2*e^3+9/8*c/(a*e^2+c*d^2)^3/(c*x^2+a)^2*d*a*x*e^4+7/4*c^2/(a*e^2+c*d^2)^3/(c*x^2+a)^2*d^3*x*e^2+5/8*c^3/(a*e^2+c*d^2)^3/(c*x^2+a)^2*d^5/a*x+3/4/(a*e^2+c*d^2)^3/(c*x^2+a)^2*a^2*e^5+c/(a*e^2+c*d^2)^3/(c*x^2+a)^2*a*d^2*e^3+1/4*c^2/(a*e^2+c*d^2)^3/(c*x^2+a)^2*e*d^4-1/2*e^5*ln(c*x^2+a)/(a*e^2+c*d^2)^3+15/8*c/(a*e^2+c*d^2)^3/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)*d*e^4+5/4*c^2/(a*e^2+c*d^2)^3/a/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)*d^3*e^2+3/8*c^3/(a*e^2+c*d^2)^3/a^2/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)*d^5+e^5*ln(e*x+d)/(a*e^2+c*d^2)^3","B"
518,1,680,285,0.066000," ","int(1/(e*x+d)^2/(c*x^2+a)^3,x)","-\frac{7 a \,c^{2} e^{6} x^{3}}{8 \left(a \,e^{2}+c \,d^{2}\right)^{4} \left(c \,x^{2}+a \right)^{2}}+\frac{15 c^{4} d^{4} e^{2} x^{3}}{8 \left(a \,e^{2}+c \,d^{2}\right)^{4} \left(c \,x^{2}+a \right)^{2} a}+\frac{3 c^{5} d^{6} x^{3}}{8 \left(a \,e^{2}+c \,d^{2}\right)^{4} \left(c \,x^{2}+a \right)^{2} a^{2}}+\frac{5 c^{3} d^{2} e^{4} x^{3}}{8 \left(a \,e^{2}+c \,d^{2}\right)^{4} \left(c \,x^{2}+a \right)^{2}}+\frac{2 a \,c^{2} d \,e^{5} x^{2}}{\left(a \,e^{2}+c \,d^{2}\right)^{4} \left(c \,x^{2}+a \right)^{2}}+\frac{2 c^{3} d^{3} e^{3} x^{2}}{\left(a \,e^{2}+c \,d^{2}\right)^{4} \left(c \,x^{2}+a \right)^{2}}-\frac{9 a^{2} c \,e^{6} x}{8 \left(a \,e^{2}+c \,d^{2}\right)^{4} \left(c \,x^{2}+a \right)^{2}}+\frac{3 a \,c^{2} d^{2} e^{4} x}{8 \left(a \,e^{2}+c \,d^{2}\right)^{4} \left(c \,x^{2}+a \right)^{2}}+\frac{5 c^{4} d^{6} x}{8 \left(a \,e^{2}+c \,d^{2}\right)^{4} \left(c \,x^{2}+a \right)^{2} a}+\frac{17 c^{3} d^{4} e^{2} x}{8 \left(a \,e^{2}+c \,d^{2}\right)^{4} \left(c \,x^{2}+a \right)^{2}}+\frac{5 a^{2} c d \,e^{5}}{2 \left(a \,e^{2}+c \,d^{2}\right)^{4} \left(c \,x^{2}+a \right)^{2}}+\frac{3 a \,c^{2} d^{3} e^{3}}{\left(a \,e^{2}+c \,d^{2}\right)^{4} \left(c \,x^{2}+a \right)^{2}}-\frac{15 a c \,e^{6} \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{8 \left(a \,e^{2}+c \,d^{2}\right)^{4} \sqrt{a c}}+\frac{15 c^{3} d^{4} e^{2} \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{8 \left(a \,e^{2}+c \,d^{2}\right)^{4} \sqrt{a c}\, a}+\frac{3 c^{4} d^{6} \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{8 \left(a \,e^{2}+c \,d^{2}\right)^{4} \sqrt{a c}\, a^{2}}+\frac{c^{3} d^{5} e}{2 \left(a \,e^{2}+c \,d^{2}\right)^{4} \left(c \,x^{2}+a \right)^{2}}+\frac{45 c^{2} d^{2} e^{4} \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{8 \left(a \,e^{2}+c \,d^{2}\right)^{4} \sqrt{a c}}-\frac{3 c d \,e^{5} \ln \left(c \,x^{2}+a \right)}{\left(a \,e^{2}+c \,d^{2}\right)^{4}}+\frac{6 c d \,e^{5} \ln \left(e x +d \right)}{\left(a \,e^{2}+c \,d^{2}\right)^{4}}-\frac{e^{5}}{\left(a \,e^{2}+c \,d^{2}\right)^{3} \left(e x +d \right)}"," ",0,"-7/8*c^2/(a*e^2+c*d^2)^4/(c*x^2+a)^2*a*x^3*e^6+5/8*c^3/(a*e^2+c*d^2)^4/(c*x^2+a)^2*x^3*d^2*e^4+15/8*c^4/(a*e^2+c*d^2)^4/(c*x^2+a)^2/a*x^3*d^4*e^2+3/8*c^5/(a*e^2+c*d^2)^4/(c*x^2+a)^2/a^2*x^3*d^6+2*c^2/(a*e^2+c*d^2)^4/(c*x^2+a)^2*x^2*a*d*e^5+2*c^3/(a*e^2+c*d^2)^4/(c*x^2+a)^2*x^2*d^3*e^3-9/8*c/(a*e^2+c*d^2)^4/(c*x^2+a)^2*a^2*x*e^6+3/8*c^2/(a*e^2+c*d^2)^4/(c*x^2+a)^2*a*x*d^2*e^4+17/8*c^3/(a*e^2+c*d^2)^4/(c*x^2+a)^2*x*d^4*e^2+5/8*c^4/(a*e^2+c*d^2)^4/(c*x^2+a)^2/a*x*d^6+5/2*c/(a*e^2+c*d^2)^4/(c*x^2+a)^2*a^2*d*e^5+3*c^2/(a*e^2+c*d^2)^4/(c*x^2+a)^2*a*d^3*e^3+1/2*c^3/(a*e^2+c*d^2)^4/(c*x^2+a)^2*d^5*e-3*c*d*e^5*ln(c*x^2+a)/(a*e^2+c*d^2)^4-15/8*c/(a*e^2+c*d^2)^4*a/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)*e^6+45/8*c^2/(a*e^2+c*d^2)^4/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)*d^2*e^4+15/8*c^3/(a*e^2+c*d^2)^4/a/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)*d^4*e^2+3/8*c^4/(a*e^2+c*d^2)^4/a^2/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)*d^6-e^5/(a*e^2+c*d^2)^3/(e*x+d)+6*c*d*e^5*ln(e*x+d)/(a*e^2+c*d^2)^4","B"
519,1,225,139,0.050000," ","int((e*x+d)^4/(c*x^2+a)^4,x)","\frac{e^{4} \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{16 \sqrt{a c}\, a \,c^{2}}+\frac{3 d^{2} e^{2} \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{8 \sqrt{a c}\, a^{2} c}+\frac{5 d^{4} \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{16 \sqrt{a c}\, a^{3}}+\frac{-\frac{d \,e^{3} x^{2}}{c}+\frac{\left(a^{2} e^{4}+6 a c \,d^{2} e^{2}+5 c^{2} d^{4}\right) x^{5}}{16 a^{3}}-\frac{\left(a^{2} e^{4}-6 a c \,d^{2} e^{2}-5 c^{2} d^{4}\right) x^{3}}{6 a^{2} c}-\frac{\left(a \,e^{2}+2 c \,d^{2}\right) d e}{3 c^{2}}-\frac{\left(a^{2} e^{4}+6 a c \,d^{2} e^{2}-11 c^{2} d^{4}\right) x}{16 a \,c^{2}}}{\left(c \,x^{2}+a \right)^{3}}"," ",0,"(1/16*(a^2*e^4+6*a*c*d^2*e^2+5*c^2*d^4)/a^3*x^5-1/6*(a^2*e^4-6*a*c*d^2*e^2-5*c^2*d^4)/a^2/c*x^3-1/c*d*e^3*x^2-1/16*(a^2*e^4+6*a*c*d^2*e^2-11*c^2*d^4)/a/c^2*x-1/3*d*e*(a*e^2+2*c*d^2)/c^2)/(c*x^2+a)^3+1/16/a/c^2/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)*e^4+3/8/a^2/c/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)*d^2*e^2+5/16/a^3/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)*d^4","A"
520,1,158,139,0.053000," ","int((e*x+d)^3/(c*x^2+a)^4,x)","\frac{3 d \,e^{2} \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{16 \sqrt{a c}\, a^{2} c}+\frac{5 d^{3} \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{16 \sqrt{a c}\, a^{3}}+\frac{\frac{\left(3 a \,e^{2}+5 c \,d^{2}\right) c d \,x^{5}}{16 a^{3}}-\frac{e^{3} x^{2}}{4 c}+\frac{\left(3 a \,e^{2}+5 c \,d^{2}\right) d \,x^{3}}{6 a^{2}}-\frac{\left(3 a \,e^{2}-11 c \,d^{2}\right) d x}{16 a c}-\frac{\left(a \,e^{2}+6 c \,d^{2}\right) e}{12 c^{2}}}{\left(c \,x^{2}+a \right)^{3}}"," ",0,"(1/16*d*(3*a*e^2+5*c*d^2)/a^3*c*x^5+1/6/a^2*d*(3*a*e^2+5*c*d^2)*x^3-1/4/c*e^3*x^2-1/16*d*(3*a*e^2-11*c*d^2)/a/c*x-1/12*e*(a*e^2+6*c*d^2)/c^2)/(c*x^2+a)^3+3/16*d/a^2/c/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)*e^2+5/16*d^3/a^3/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)","A"
521,1,129,128,0.051000," ","int((e*x+d)^2/(c*x^2+a)^4,x)","\frac{e^{2} \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{16 \sqrt{a c}\, a^{2} c}+\frac{5 d^{2} \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{16 \sqrt{a c}\, a^{3}}+\frac{\frac{\left(a \,e^{2}+5 c \,d^{2}\right) c \,x^{5}}{16 a^{3}}+\frac{\left(a \,e^{2}+5 c \,d^{2}\right) x^{3}}{6 a^{2}}-\frac{d e}{3 c}-\frac{\left(a \,e^{2}-11 c \,d^{2}\right) x}{16 a c}}{\left(c \,x^{2}+a \right)^{3}}"," ",0,"(1/16*(a*e^2+5*c*d^2)/a^3*c*x^5+1/6/a^2*(a*e^2+5*c*d^2)*x^3-1/16*(a*e^2-11*c*d^2)/a/c*x-1/3/c*d*e)/(c*x^2+a)^3+1/16/a^2/c/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)*e^2+5/16/a^3/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)*d^2","A"
522,1,81,77,0.048000," ","int((e*x+d)/(c*x^2+a)^4,x)","\frac{5 d x}{24 \left(c \,x^{2}+a \right)^{2} a^{2}}+\frac{5 d x}{16 \left(c \,x^{2}+a \right) a^{3}}+\frac{5 d \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{16 \sqrt{a c}\, a^{3}}+\frac{2 c d x -2 a e}{12 \left(c \,x^{2}+a \right)^{3} a c}"," ",0,"1/12*(2*c*d*x-2*a*e)/a/c/(c*x^2+a)^3+5/24*d*x/a^2/(c*x^2+a)^2+5/16*d*x/a^3/(c*x^2+a)+5/16*d/a^3/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)","A"
523,1,941,277,0.063000," ","int(1/(e*x+d)/(c*x^2+a)^4,x)","\frac{35 c^{4} d^{3} e^{4} x^{5}}{16 \left(a \,e^{2}+c \,d^{2}\right)^{4} \left(c \,x^{2}+a \right)^{3} a}+\frac{21 c^{5} d^{5} e^{2} x^{5}}{16 \left(a \,e^{2}+c \,d^{2}\right)^{4} \left(c \,x^{2}+a \right)^{3} a^{2}}+\frac{5 c^{6} d^{7} x^{5}}{16 \left(a \,e^{2}+c \,d^{2}\right)^{4} \left(c \,x^{2}+a \right)^{3} a^{3}}+\frac{19 c^{3} d \,e^{6} x^{5}}{16 \left(a \,e^{2}+c \,d^{2}\right)^{4} \left(c \,x^{2}+a \right)^{3}}+\frac{a \,c^{2} e^{7} x^{4}}{2 \left(a \,e^{2}+c \,d^{2}\right)^{4} \left(c \,x^{2}+a \right)^{3}}+\frac{c^{3} d^{2} e^{5} x^{4}}{2 \left(a \,e^{2}+c \,d^{2}\right)^{4} \left(c \,x^{2}+a \right)^{3}}+\frac{17 a \,c^{2} d \,e^{6} x^{3}}{6 \left(a \,e^{2}+c \,d^{2}\right)^{4} \left(c \,x^{2}+a \right)^{3}}+\frac{7 c^{4} d^{5} e^{2} x^{3}}{2 \left(a \,e^{2}+c \,d^{2}\right)^{4} \left(c \,x^{2}+a \right)^{3} a}+\frac{5 c^{5} d^{7} x^{3}}{6 \left(a \,e^{2}+c \,d^{2}\right)^{4} \left(c \,x^{2}+a \right)^{3} a^{2}}+\frac{11 c^{3} d^{3} e^{4} x^{3}}{2 \left(a \,e^{2}+c \,d^{2}\right)^{4} \left(c \,x^{2}+a \right)^{3}}+\frac{5 a^{2} c \,e^{7} x^{2}}{4 \left(a \,e^{2}+c \,d^{2}\right)^{4} \left(c \,x^{2}+a \right)^{3}}+\frac{3 a \,c^{2} d^{2} e^{5} x^{2}}{2 \left(a \,e^{2}+c \,d^{2}\right)^{4} \left(c \,x^{2}+a \right)^{3}}+\frac{c^{3} d^{4} e^{3} x^{2}}{4 \left(a \,e^{2}+c \,d^{2}\right)^{4} \left(c \,x^{2}+a \right)^{3}}+\frac{29 a^{2} c d \,e^{6} x}{16 \left(a \,e^{2}+c \,d^{2}\right)^{4} \left(c \,x^{2}+a \right)^{3}}+\frac{61 a \,c^{2} d^{3} e^{4} x}{16 \left(a \,e^{2}+c \,d^{2}\right)^{4} \left(c \,x^{2}+a \right)^{3}}+\frac{11 c^{4} d^{7} x}{16 \left(a \,e^{2}+c \,d^{2}\right)^{4} \left(c \,x^{2}+a \right)^{3} a}+\frac{43 c^{3} d^{5} e^{2} x}{16 \left(a \,e^{2}+c \,d^{2}\right)^{4} \left(c \,x^{2}+a \right)^{3}}+\frac{11 a^{3} e^{7}}{12 \left(a \,e^{2}+c \,d^{2}\right)^{4} \left(c \,x^{2}+a \right)^{3}}+\frac{3 a^{2} c \,d^{2} e^{5}}{2 \left(a \,e^{2}+c \,d^{2}\right)^{4} \left(c \,x^{2}+a \right)^{3}}+\frac{3 a \,c^{2} d^{4} e^{3}}{4 \left(a \,e^{2}+c \,d^{2}\right)^{4} \left(c \,x^{2}+a \right)^{3}}+\frac{c^{3} d^{6} e}{6 \left(a \,e^{2}+c \,d^{2}\right)^{4} \left(c \,x^{2}+a \right)^{3}}+\frac{35 c^{2} d^{3} e^{4} \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{4} \sqrt{a c}\, a}+\frac{21 c^{3} d^{5} e^{2} \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{4} \sqrt{a c}\, a^{2}}+\frac{5 c^{4} d^{7} \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{4} \sqrt{a c}\, a^{3}}+\frac{35 c d \,e^{6} \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{4} \sqrt{a c}}-\frac{e^{7} \ln \left(c \,x^{2}+a \right)}{2 \left(a \,e^{2}+c \,d^{2}\right)^{4}}+\frac{e^{7} \ln \left(e x +d \right)}{\left(a \,e^{2}+c \,d^{2}\right)^{4}}"," ",0,"43/16*c^3/(a*e^2+c*d^2)^4/(c*x^2+a)^3*d^5*x*e^2+5/4*c/(a*e^2+c*d^2)^4/(c*x^2+a)^3*x^2*a^2*e^7+3/2*c/(a*e^2+c*d^2)^4/(c*x^2+a)^3*a^2*d^2*e^5+1/4*c^3/(a*e^2+c*d^2)^4/(c*x^2+a)^3*x^2*d^4*e^3+11/2*c^3/(a*e^2+c*d^2)^4/(c*x^2+a)^3*d^3*x^3*e^4+5/6*c^5/(a*e^2+c*d^2)^4/(c*x^2+a)^3*d^7/a^2*x^3+35/16*c/(a*e^2+c*d^2)^4/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)*d*e^6+5/16*c^4/(a*e^2+c*d^2)^4/a^3/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)*d^7+1/2*c^2/(a*e^2+c*d^2)^4/(c*x^2+a)^3*x^4*a*e^7+1/2*c^3/(a*e^2+c*d^2)^4/(c*x^2+a)^3*x^4*d^2*e^5+5/16*c^6/(a*e^2+c*d^2)^4/(c*x^2+a)^3*d^7/a^3*x^5+11/16*c^4/(a*e^2+c*d^2)^4/(c*x^2+a)^3*d^7/a*x+3/4*c^2/(a*e^2+c*d^2)^4/(c*x^2+a)^3*e^3*a*d^4+19/16*c^3/(a*e^2+c*d^2)^4/(c*x^2+a)^3*d*x^5*e^6+29/16*c/(a*e^2+c*d^2)^4/(c*x^2+a)^3*d*a^2*x*e^6+35/16*c^2/(a*e^2+c*d^2)^4/a/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)*d^3*e^4+35/16*c^4/(a*e^2+c*d^2)^4/(c*x^2+a)^3*d^3/a*x^5*e^4+61/16*c^2/(a*e^2+c*d^2)^4/(c*x^2+a)^3*d^3*a*x*e^4+3/2*c^2/(a*e^2+c*d^2)^4/(c*x^2+a)^3*x^2*a*d^2*e^5+7/2*c^4/(a*e^2+c*d^2)^4/(c*x^2+a)^3*d^5/a*x^3*e^2+11/12/(a*e^2+c*d^2)^4/(c*x^2+a)^3*a^3*e^7+21/16*c^3/(a*e^2+c*d^2)^4/a^2/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)*d^5*e^2+21/16*c^5/(a*e^2+c*d^2)^4/(c*x^2+a)^3*d^5/a^2*x^5*e^2+17/6*c^2/(a*e^2+c*d^2)^4/(c*x^2+a)^3*d*a*x^3*e^6+1/6*c^3/(a*e^2+c*d^2)^4/(c*x^2+a)^3*e*d^6+e^7*ln(e*x+d)/(a*e^2+c*d^2)^4-1/2*e^7*ln(c*x^2+a)/(a*e^2+c*d^2)^4","B"
524,1,1126,413,0.075000," ","int(1/(e*x+d)^2/(c*x^2+a)^4,x)","-\frac{19 a \,c^{3} e^{8} x^{5}}{16 \left(a \,e^{2}+c \,d^{2}\right)^{5} \left(c \,x^{2}+a \right)^{3}}+\frac{35 c^{5} d^{4} e^{4} x^{5}}{8 \left(a \,e^{2}+c \,d^{2}\right)^{5} \left(c \,x^{2}+a \right)^{3} a}+\frac{7 c^{6} d^{6} e^{2} x^{5}}{4 \left(a \,e^{2}+c \,d^{2}\right)^{5} \left(c \,x^{2}+a \right)^{3} a^{2}}+\frac{5 c^{7} d^{8} x^{5}}{16 \left(a \,e^{2}+c \,d^{2}\right)^{5} \left(c \,x^{2}+a \right)^{3} a^{3}}+\frac{7 c^{4} d^{2} e^{6} x^{5}}{4 \left(a \,e^{2}+c \,d^{2}\right)^{5} \left(c \,x^{2}+a \right)^{3}}+\frac{3 a \,c^{3} d \,e^{7} x^{4}}{\left(a \,e^{2}+c \,d^{2}\right)^{5} \left(c \,x^{2}+a \right)^{3}}+\frac{3 c^{4} d^{3} e^{5} x^{4}}{\left(a \,e^{2}+c \,d^{2}\right)^{5} \left(c \,x^{2}+a \right)^{3}}-\frac{17 a^{2} c^{2} e^{8} x^{3}}{6 \left(a \,e^{2}+c \,d^{2}\right)^{5} \left(c \,x^{2}+a \right)^{3}}+\frac{10 a \,c^{3} d^{2} e^{6} x^{3}}{3 \left(a \,e^{2}+c \,d^{2}\right)^{5} \left(c \,x^{2}+a \right)^{3}}+\frac{14 c^{5} d^{6} e^{2} x^{3}}{3 \left(a \,e^{2}+c \,d^{2}\right)^{5} \left(c \,x^{2}+a \right)^{3} a}+\frac{5 c^{6} d^{8} x^{3}}{6 \left(a \,e^{2}+c \,d^{2}\right)^{5} \left(c \,x^{2}+a \right)^{3} a^{2}}+\frac{10 c^{4} d^{4} e^{4} x^{3}}{\left(a \,e^{2}+c \,d^{2}\right)^{5} \left(c \,x^{2}+a \right)^{3}}+\frac{7 a^{2} c^{2} d \,e^{7} x^{2}}{\left(a \,e^{2}+c \,d^{2}\right)^{5} \left(c \,x^{2}+a \right)^{3}}+\frac{8 a \,c^{3} d^{3} e^{5} x^{2}}{\left(a \,e^{2}+c \,d^{2}\right)^{5} \left(c \,x^{2}+a \right)^{3}}+\frac{c^{4} d^{5} e^{3} x^{2}}{\left(a \,e^{2}+c \,d^{2}\right)^{5} \left(c \,x^{2}+a \right)^{3}}-\frac{29 a^{3} c \,e^{8} x}{16 \left(a \,e^{2}+c \,d^{2}\right)^{5} \left(c \,x^{2}+a \right)^{3}}+\frac{5 a^{2} c^{2} d^{2} e^{6} x}{4 \left(a \,e^{2}+c \,d^{2}\right)^{5} \left(c \,x^{2}+a \right)^{3}}+\frac{45 a \,c^{3} d^{4} e^{4} x}{8 \left(a \,e^{2}+c \,d^{2}\right)^{5} \left(c \,x^{2}+a \right)^{3}}+\frac{11 c^{5} d^{8} x}{16 \left(a \,e^{2}+c \,d^{2}\right)^{5} \left(c \,x^{2}+a \right)^{3} a}+\frac{13 c^{4} d^{6} e^{2} x}{4 \left(a \,e^{2}+c \,d^{2}\right)^{5} \left(c \,x^{2}+a \right)^{3}}+\frac{13 a^{3} c d \,e^{7}}{3 \left(a \,e^{2}+c \,d^{2}\right)^{5} \left(c \,x^{2}+a \right)^{3}}+\frac{6 a^{2} c^{2} d^{3} e^{5}}{\left(a \,e^{2}+c \,d^{2}\right)^{5} \left(c \,x^{2}+a \right)^{3}}+\frac{2 a \,c^{3} d^{5} e^{3}}{\left(a \,e^{2}+c \,d^{2}\right)^{5} \left(c \,x^{2}+a \right)^{3}}+\frac{c^{4} d^{7} e}{3 \left(a \,e^{2}+c \,d^{2}\right)^{5} \left(c \,x^{2}+a \right)^{3}}-\frac{35 a c \,e^{8} \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{5} \sqrt{a c}}+\frac{35 c^{3} d^{4} e^{4} \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{8 \left(a \,e^{2}+c \,d^{2}\right)^{5} \sqrt{a c}\, a}+\frac{7 c^{4} d^{6} e^{2} \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{4 \left(a \,e^{2}+c \,d^{2}\right)^{5} \sqrt{a c}\, a^{2}}+\frac{5 c^{5} d^{8} \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{5} \sqrt{a c}\, a^{3}}+\frac{35 c^{2} d^{2} e^{6} \arctan \left(\frac{c x}{\sqrt{a c}}\right)}{4 \left(a \,e^{2}+c \,d^{2}\right)^{5} \sqrt{a c}}-\frac{4 c d \,e^{7} \ln \left(c \,x^{2}+a \right)}{\left(a \,e^{2}+c \,d^{2}\right)^{5}}+\frac{8 c d \,e^{7} \ln \left(e x +d \right)}{\left(a \,e^{2}+c \,d^{2}\right)^{5}}-\frac{e^{7}}{\left(a \,e^{2}+c \,d^{2}\right)^{4} \left(e x +d \right)}"," ",0,"2*c^3/(a*e^2+c*d^2)^5/(c*x^2+a)^3*a*d^5*e^3-35/16*c/(a*e^2+c*d^2)^5*a/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)*e^8+35/4*c^2/(a*e^2+c*d^2)^5/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)*d^2*e^6+5/16*c^5/(a*e^2+c*d^2)^5/a^3/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)*d^8-29/16*c/(a*e^2+c*d^2)^5/(c*x^2+a)^3*a^3*x*e^8+13/3*c/(a*e^2+c*d^2)^5/(c*x^2+a)^3*a^3*d*e^7-19/16*c^3/(a*e^2+c*d^2)^5/(c*x^2+a)^3*a*x^5*e^8+7/4*c^4/(a*e^2+c*d^2)^5/(c*x^2+a)^3*x^5*d^2*e^6+5/16*c^7/(a*e^2+c*d^2)^5/(c*x^2+a)^3/a^3*x^5*d^8+3*c^4/(a*e^2+c*d^2)^5/(c*x^2+a)^3*x^4*d^3*e^5-17/6*c^2/(a*e^2+c*d^2)^5/(c*x^2+a)^3*a^2*x^3*e^8+10*c^4/(a*e^2+c*d^2)^5/(c*x^2+a)^3*x^3*d^4*e^4+5/6*c^6/(a*e^2+c*d^2)^5/(c*x^2+a)^3/a^2*x^3*d^8+c^4/(a*e^2+c*d^2)^5/(c*x^2+a)^3*x^2*d^5*e^3+13/4*c^4/(a*e^2+c*d^2)^5/(c*x^2+a)^3*x*d^6*e^2+11/16*c^5/(a*e^2+c*d^2)^5/(c*x^2+a)^3/a*x*d^8-e^7/(a*e^2+c*d^2)^4/(e*x+d)+7*c^2/(a*e^2+c*d^2)^5/(c*x^2+a)^3*x^2*a^2*d*e^7+8*c^3/(a*e^2+c*d^2)^5/(c*x^2+a)^3*x^2*a*d^3*e^5+5/4*c^2/(a*e^2+c*d^2)^5/(c*x^2+a)^3*a^2*x*d^2*e^6+45/8*c^3/(a*e^2+c*d^2)^5/(c*x^2+a)^3*a*x*d^4*e^4+35/8*c^3/(a*e^2+c*d^2)^5/a/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)*d^4*e^4+7/4*c^4/(a*e^2+c*d^2)^5/a^2/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x)*d^6*e^2+7/4*c^6/(a*e^2+c*d^2)^5/(c*x^2+a)^3/a^2*x^5*d^6*e^2+3*c^3/(a*e^2+c*d^2)^5/(c*x^2+a)^3*x^4*a*d*e^7+10/3*c^3/(a*e^2+c*d^2)^5/(c*x^2+a)^3*a*x^3*d^2*e^6+14/3*c^5/(a*e^2+c*d^2)^5/(c*x^2+a)^3/a*x^3*d^6*e^2+35/8*c^5/(a*e^2+c*d^2)^5/(c*x^2+a)^3/a*x^5*d^4*e^4+6*c^2/(a*e^2+c*d^2)^5/(c*x^2+a)^3*a^2*d^3*e^5+1/3*c^4/(a*e^2+c*d^2)^5/(c*x^2+a)^3*d^7*e+8*c*d*e^7*ln(e*x+d)/(a*e^2+c*d^2)^5-4*c*d*e^7*ln(c*x^2+a)/(a*e^2+c*d^2)^5","B"
525,1,260,183,0.053000," ","int((e*x+d)^4*(c*x^2+a)^(1/2),x)","\frac{\left(c \,x^{2}+a \right)^{\frac{3}{2}} e^{4} x^{3}}{6 c}+\frac{a^{3} e^{4} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{16 c^{\frac{5}{2}}}-\frac{3 a^{2} d^{2} e^{2} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{4 c^{\frac{3}{2}}}+\frac{a \,d^{4} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{2 \sqrt{c}}+\frac{\sqrt{c \,x^{2}+a}\, a^{2} e^{4} x}{16 c^{2}}-\frac{3 \sqrt{c \,x^{2}+a}\, a \,d^{2} e^{2} x}{4 c}+\frac{4 \left(c \,x^{2}+a \right)^{\frac{3}{2}} d \,e^{3} x^{2}}{5 c}+\frac{\sqrt{c \,x^{2}+a}\, d^{4} x}{2}-\frac{\left(c \,x^{2}+a \right)^{\frac{3}{2}} a \,e^{4} x}{8 c^{2}}+\frac{3 \left(c \,x^{2}+a \right)^{\frac{3}{2}} d^{2} e^{2} x}{2 c}-\frac{8 \left(c \,x^{2}+a \right)^{\frac{3}{2}} a d \,e^{3}}{15 c^{2}}+\frac{4 \left(c \,x^{2}+a \right)^{\frac{3}{2}} d^{3} e}{3 c}"," ",0,"1/6*e^4*x^3*(c*x^2+a)^(3/2)/c-1/8*e^4*a/c^2*x*(c*x^2+a)^(3/2)+1/16*e^4*a^2/c^2*x*(c*x^2+a)^(1/2)+1/16*e^4*a^3/c^(5/2)*ln(c^(1/2)*x+(c*x^2+a)^(1/2))+4/5*d*e^3*x^2*(c*x^2+a)^(3/2)/c-8/15*d*e^3*a/c^2*(c*x^2+a)^(3/2)+3/2*d^2*e^2*x*(c*x^2+a)^(3/2)/c-3/4*d^2*e^2*a/c*x*(c*x^2+a)^(1/2)-3/4*d^2*e^2*a^2/c^(3/2)*ln(c^(1/2)*x+(c*x^2+a)^(1/2))+4/3*d^3*e*(c*x^2+a)^(3/2)/c+1/2*d^4*x*(c*x^2+a)^(1/2)+1/2*d^4*a/c^(1/2)*ln(c^(1/2)*x+(c*x^2+a)^(1/2))","A"
526,1,164,121,0.053000," ","int((e*x+d)^3*(c*x^2+a)^(1/2),x)","-\frac{3 a^{2} d \,e^{2} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{8 c^{\frac{3}{2}}}+\frac{a \,d^{3} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{2 \sqrt{c}}-\frac{3 \sqrt{c \,x^{2}+a}\, a d \,e^{2} x}{8 c}+\frac{\left(c \,x^{2}+a \right)^{\frac{3}{2}} e^{3} x^{2}}{5 c}+\frac{\sqrt{c \,x^{2}+a}\, d^{3} x}{2}+\frac{3 \left(c \,x^{2}+a \right)^{\frac{3}{2}} d \,e^{2} x}{4 c}-\frac{2 \left(c \,x^{2}+a \right)^{\frac{3}{2}} a \,e^{3}}{15 c^{2}}+\frac{\left(c \,x^{2}+a \right)^{\frac{3}{2}} d^{2} e}{c}"," ",0,"1/5*e^3*x^2*(c*x^2+a)^(3/2)/c-2/15*e^3*a/c^2*(c*x^2+a)^(3/2)+3/4*d*e^2*x*(c*x^2+a)^(3/2)/c-3/8*d*e^2*a/c*x*(c*x^2+a)^(1/2)-3/8*d*e^2*a^2/c^(3/2)*ln(c^(1/2)*x+(c*x^2+a)^(1/2))+d^2*e*(c*x^2+a)^(3/2)/c+1/2*d^3*x*(c*x^2+a)^(1/2)+1/2*d^3*a/c^(1/2)*ln(c^(1/2)*x+(c*x^2+a)^(1/2))","A"
527,1,122,99,0.050000," ","int((e*x+d)^2*(c*x^2+a)^(1/2),x)","-\frac{a^{2} e^{2} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{8 c^{\frac{3}{2}}}+\frac{a \,d^{2} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{2 \sqrt{c}}-\frac{\sqrt{c \,x^{2}+a}\, a \,e^{2} x}{8 c}+\frac{\sqrt{c \,x^{2}+a}\, d^{2} x}{2}+\frac{\left(c \,x^{2}+a \right)^{\frac{3}{2}} e^{2} x}{4 c}+\frac{2 \left(c \,x^{2}+a \right)^{\frac{3}{2}} d e}{3 c}"," ",0,"1/4*e^2*x*(c*x^2+a)^(3/2)/c-1/8*e^2*a/c*x*(c*x^2+a)^(1/2)-1/8*e^2*a^2/c^(3/2)*ln(c^(1/2)*x+(c*x^2+a)^(1/2))+2/3*d*e*(c*x^2+a)^(3/2)/c+1/2*d^2*x*(c*x^2+a)^(1/2)+1/2*d^2*a/c^(1/2)*ln(c^(1/2)*x+(c*x^2+a)^(1/2))","A"
528,1,53,51,0.043000," ","int((e*x+d)*(c*x^2+a)^(1/2),x)","\frac{a d \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{2 \sqrt{c}}+\frac{\sqrt{c \,x^{2}+a}\, d x}{2}+\frac{\left(c \,x^{2}+a \right)^{\frac{3}{2}} e}{3 c}"," ",0,"1/3*e*(c*x^2+a)^(3/2)/c+1/2*d*x*(c*x^2+a)^(1/2)+1/2*d*a/c^(1/2)*ln(c^(1/2)*x+(c*x^2+a)^(1/2))","A"
529,1,381,89,0.082000," ","int((c*x^2+a)^(1/2)/(e*x+d),x)","-\frac{a \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e}-\frac{c \,d^{2} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{3}}-\frac{\sqrt{c}\, d \ln \left(\frac{-\frac{c d}{e}+\left(x +\frac{d}{e}\right) c}{\sqrt{c}}+\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\right)}{e^{2}}+\frac{\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{e}"," ",0,"1/e*((x+d/e)^2*c-2*c*d/e*(x+d/e)+(a*e^2+c*d^2)/e^2)^(1/2)-1/e^2*c^(1/2)*d*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+((x+d/e)^2*c-2*c*d/e*(x+d/e)+(a*e^2+c*d^2)/e^2)^(1/2))-1/e/((a*e^2+c*d^2)/e^2)^(1/2)*ln((2*(a*e^2+c*d^2)/e^2-2*c*d/e*(x+d/e)+2*((a*e^2+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c-2*c*d/e*(x+d/e)+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a-1/e^3/((a*e^2+c*d^2)/e^2)^(1/2)*ln((2*(a*e^2+c*d^2)/e^2-2*c*d/e*(x+d/e)+2*((a*e^2+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c-2*c*d/e*(x+d/e)+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*c*d^2","B"
530,1,649,96,0.056000," ","int((c*x^2+a)^(1/2)/(e*x+d)^2,x)","\frac{a c d \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\left(a \,e^{2}+c \,d^{2}\right) \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e}+\frac{c^{2} d^{3} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\left(a \,e^{2}+c \,d^{2}\right) \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{3}}+\frac{a \sqrt{c}\, \ln \left(\frac{-\frac{c d}{e}+\left(x +\frac{d}{e}\right) c}{\sqrt{c}}+\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\right)}{a \,e^{2}+c \,d^{2}}+\frac{c^{\frac{3}{2}} d^{2} \ln \left(\frac{-\frac{c d}{e}+\left(x +\frac{d}{e}\right) c}{\sqrt{c}}+\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\right)}{\left(a \,e^{2}+c \,d^{2}\right) e^{2}}+\frac{\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, c x}{a \,e^{2}+c \,d^{2}}-\frac{\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, c d}{\left(a \,e^{2}+c \,d^{2}\right) e}-\frac{\left(-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}\right)^{\frac{3}{2}}}{\left(a \,e^{2}+c \,d^{2}\right) \left(x +\frac{d}{e}\right)}"," ",0,"-1/(a*e^2+c*d^2)/(x+d/e)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)-1/e*c*d/(a*e^2+c*d^2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)+1/e^2*c^(3/2)*d^2/(a*e^2+c*d^2)*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))+1/e*c*d/(a*e^2+c*d^2)/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a+1/e^3*c^2*d^3/(a*e^2+c*d^2)/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))+1/(a*e^2+c*d^2)*c*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*x+1/(a*e^2+c*d^2)*c^(1/2)*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))*a","B"
531,1,1174,91,0.055000," ","int((c*x^2+a)^(1/2)/(e*x+d)^3,x)","\frac{a \,c^{2} d^{2} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e}+\frac{c^{3} d^{4} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{3}}+\frac{a \,c^{\frac{3}{2}} d \ln \left(\frac{-\frac{c d}{e}+\left(x +\frac{d}{e}\right) c}{\sqrt{c}}+\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2}}+\frac{c^{\frac{5}{2}} d^{3} \ln \left(\frac{-\frac{c d}{e}+\left(x +\frac{d}{e}\right) c}{\sqrt{c}}+\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2} e^{2}}+\frac{\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, c^{2} d x}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2}}-\frac{\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, c^{2} d^{2}}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2} e}-\frac{a c \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right) \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e}-\frac{c^{2} d^{2} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right) \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{3}}-\frac{\left(-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}\right)^{\frac{3}{2}} c d}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(x +\frac{d}{e}\right)}-\frac{c^{\frac{3}{2}} d \ln \left(\frac{-\frac{c d}{e}+\left(x +\frac{d}{e}\right) c}{\sqrt{c}}+\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right) e^{2}}+\frac{\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, c}{2 \left(a \,e^{2}+c \,d^{2}\right) e}-\frac{\left(-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}\right)^{\frac{3}{2}}}{2 \left(a \,e^{2}+c \,d^{2}\right) \left(x +\frac{d}{e}\right)^{2} e}"," ",0,"-1/2/e/(a*e^2+c*d^2)/(x+d/e)^2*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)-1/2*c*d/(a*e^2+c*d^2)^2/(x+d/e)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)-1/2/e*c^2*d^2/(a*e^2+c*d^2)^2*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)+1/2/e^2*c^(5/2)*d^3/(a*e^2+c*d^2)^2*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))+1/2/e*c^2*d^2/(a*e^2+c*d^2)^2/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a+1/2/e^3*c^3*d^4/(a*e^2+c*d^2)^2/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))+1/2*c^2*d/(a*e^2+c*d^2)^2*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*x+1/2*c^(3/2)*d/(a*e^2+c*d^2)^2*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))*a+1/2/e/(a*e^2+c*d^2)*c*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)-1/2/e^2/(a*e^2+c*d^2)*c^(3/2)*d*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))-1/2/e/(a*e^2+c*d^2)*c/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a-1/2/e^3/(a*e^2+c*d^2)*c^2/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*d^2","B"
532,1,1262,128,0.059000," ","int((c*x^2+a)^(1/2)/(e*x+d)^4,x)","\frac{a \,c^{3} d^{3} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right)^{3} \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e}+\frac{c^{4} d^{5} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right)^{3} \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{3}}+\frac{a \,c^{\frac{5}{2}} d^{2} \ln \left(\frac{-\frac{c d}{e}+\left(x +\frac{d}{e}\right) c}{\sqrt{c}}+\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right)^{3}}+\frac{c^{\frac{7}{2}} d^{4} \ln \left(\frac{-\frac{c d}{e}+\left(x +\frac{d}{e}\right) c}{\sqrt{c}}+\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right)^{3} e^{2}}+\frac{\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, c^{3} d^{2} x}{2 \left(a \,e^{2}+c \,d^{2}\right)^{3}}-\frac{\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, c^{3} d^{3}}{2 \left(a \,e^{2}+c \,d^{2}\right)^{3} e}-\frac{a \,c^{2} d \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e}-\frac{c^{3} d^{3} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{3}}-\frac{\left(-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}\right)^{\frac{3}{2}} c^{2} d^{2}}{2 \left(a \,e^{2}+c \,d^{2}\right)^{3} \left(x +\frac{d}{e}\right)}-\frac{c^{\frac{5}{2}} d^{2} \ln \left(\frac{-\frac{c d}{e}+\left(x +\frac{d}{e}\right) c}{\sqrt{c}}+\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2} e^{2}}+\frac{\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, c^{2} d}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2} e}-\frac{\left(-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}\right)^{\frac{3}{2}} c d}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(x +\frac{d}{e}\right)^{2} e}-\frac{\left(-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}\right)^{\frac{3}{2}}}{3 \left(a \,e^{2}+c \,d^{2}\right) \left(x +\frac{d}{e}\right)^{3} e^{2}}"," ",0,"-1/3/e^2/(a*e^2+c*d^2)/(x+d/e)^3*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)-1/2/e*c*d/(a*e^2+c*d^2)^2/(x+d/e)^2*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)-1/2*c^2*d^2/(a*e^2+c*d^2)^3/(x+d/e)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)-1/2/e*c^3*d^3/(a*e^2+c*d^2)^3*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)+1/2/e^2*c^(7/2)*d^4/(a*e^2+c*d^2)^3*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))+1/2/e*c^3*d^3/(a*e^2+c*d^2)^3/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a+1/2/e^3*c^4*d^5/(a*e^2+c*d^2)^3/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))+1/2*c^3*d^2/(a*e^2+c*d^2)^3*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*x+1/2*c^(5/2)*d^2/(a*e^2+c*d^2)^3*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))*a+1/2/e*c^2*d/(a*e^2+c*d^2)^2*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)-1/2/e^2*c^(5/2)*d^2/(a*e^2+c*d^2)^2*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))-1/2/e*c^2*d/(a*e^2+c*d^2)^2/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a-1/2/e^3*c^3*d^3/(a*e^2+c*d^2)^2/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))","B"
533,1,2073,186,0.060000," ","int((c*x^2+a)^(1/2)/(e*x+d)^5,x)","\frac{5 a \,c^{4} d^{4} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{8 \left(a \,e^{2}+c \,d^{2}\right)^{4} \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e}+\frac{5 c^{5} d^{6} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{8 \left(a \,e^{2}+c \,d^{2}\right)^{4} \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{3}}+\frac{5 a \,c^{\frac{7}{2}} d^{3} \ln \left(\frac{-\frac{c d}{e}+\left(x +\frac{d}{e}\right) c}{\sqrt{c}}+\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\right)}{8 \left(a \,e^{2}+c \,d^{2}\right)^{4}}+\frac{5 c^{\frac{9}{2}} d^{5} \ln \left(\frac{-\frac{c d}{e}+\left(x +\frac{d}{e}\right) c}{\sqrt{c}}+\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\right)}{8 \left(a \,e^{2}+c \,d^{2}\right)^{4} e^{2}}+\frac{5 \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, c^{4} d^{3} x}{8 \left(a \,e^{2}+c \,d^{2}\right)^{4}}-\frac{5 \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, c^{4} d^{4}}{8 \left(a \,e^{2}+c \,d^{2}\right)^{4} e}-\frac{3 a \,c^{3} d^{2} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{4 \left(a \,e^{2}+c \,d^{2}\right)^{3} \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e}-\frac{3 c^{4} d^{4} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{4 \left(a \,e^{2}+c \,d^{2}\right)^{3} \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{3}}-\frac{5 \left(-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}\right)^{\frac{3}{2}} c^{3} d^{3}}{8 \left(a \,e^{2}+c \,d^{2}\right)^{4} \left(x +\frac{d}{e}\right)}-\frac{a \,c^{\frac{5}{2}} d \ln \left(\frac{-\frac{c d}{e}+\left(x +\frac{d}{e}\right) c}{\sqrt{c}}+\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\right)}{8 \left(a \,e^{2}+c \,d^{2}\right)^{3}}-\frac{3 c^{\frac{7}{2}} d^{3} \ln \left(\frac{-\frac{c d}{e}+\left(x +\frac{d}{e}\right) c}{\sqrt{c}}+\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\right)}{4 \left(a \,e^{2}+c \,d^{2}\right)^{3} e^{2}}-\frac{\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, c^{3} d x}{8 \left(a \,e^{2}+c \,d^{2}\right)^{3}}+\frac{3 \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, c^{3} d^{2}}{4 \left(a \,e^{2}+c \,d^{2}\right)^{3} e}+\frac{a \,c^{2} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{8 \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e}+\frac{c^{3} d^{2} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{8 \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{3}}-\frac{5 \left(-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}\right)^{\frac{3}{2}} c^{2} d^{2}}{8 \left(a \,e^{2}+c \,d^{2}\right)^{3} \left(x +\frac{d}{e}\right)^{2} e}+\frac{\left(-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}\right)^{\frac{3}{2}} c^{2} d}{8 \left(a \,e^{2}+c \,d^{2}\right)^{3} \left(x +\frac{d}{e}\right)}+\frac{c^{\frac{5}{2}} d \ln \left(\frac{-\frac{c d}{e}+\left(x +\frac{d}{e}\right) c}{\sqrt{c}}+\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\right)}{8 \left(a \,e^{2}+c \,d^{2}\right)^{2} e^{2}}-\frac{\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, c^{2}}{8 \left(a \,e^{2}+c \,d^{2}\right)^{2} e}-\frac{5 \left(-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}\right)^{\frac{3}{2}} c d}{12 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(x +\frac{d}{e}\right)^{3} e^{2}}+\frac{\left(-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}\right)^{\frac{3}{2}} c}{8 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(x +\frac{d}{e}\right)^{2} e}-\frac{\left(-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}\right)^{\frac{3}{2}}}{4 \left(a \,e^{2}+c \,d^{2}\right) \left(x +\frac{d}{e}\right)^{4} e^{3}}"," ",0,"5/8/e^3*c^5*d^6/(a*e^2+c*d^2)^4/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))+5/8*c^4*d^3/(a*e^2+c*d^2)^4*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*x-3/4/e^2*c^(7/2)*d^3/(a*e^2+c*d^2)^3*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))-3/4/e^3*c^4*d^4/(a*e^2+c*d^2)^3/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))+5/8/e^2*c^(9/2)*d^5/(a*e^2+c*d^2)^4*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))-5/8*c^3*d^3/(a*e^2+c*d^2)^4/(x+d/e)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)-5/12/e^2*c*d/(a*e^2+c*d^2)^2/(x+d/e)^3*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)-5/8/e*c^2*d^2/(a*e^2+c*d^2)^3/(x+d/e)^2*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)-1/4/e^3/(a*e^2+c*d^2)/(x+d/e)^4*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)-5/8/e*c^4*d^4/(a*e^2+c*d^2)^4*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)+3/4/e*c^3*d^2/(a*e^2+c*d^2)^3*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)-1/8/e/(a*e^2+c*d^2)^2*c^2*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)+1/8/(a*e^2+c*d^2)^3*c^2*d/(x+d/e)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)+5/8/e*c^4*d^4/(a*e^2+c*d^2)^4/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a+5/8*c^(7/2)*d^3/(a*e^2+c*d^2)^4*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))*a-3/4/e*c^3*d^2/(a*e^2+c*d^2)^3/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a-1/8/(a*e^2+c*d^2)^3*c^(5/2)*d*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))*a-1/8/(a*e^2+c*d^2)^3*c^3*d*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*x+1/8/e^2/(a*e^2+c*d^2)^2*c^(5/2)*d*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))+1/8/e/(a*e^2+c*d^2)^2*c^2/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a+1/8/e^3/(a*e^2+c*d^2)^2*c^3/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*d^2+1/8/e/(a*e^2+c*d^2)^2*c/(x+d/e)^2*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)","B"
534,1,322,227,0.063000," ","int((e*x+d)^4*(c*x^2+a)^(3/2),x)","\frac{3 a^{4} e^{4} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{128 c^{\frac{5}{2}}}-\frac{3 a^{3} d^{2} e^{2} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{8 c^{\frac{3}{2}}}+\frac{3 a^{2} d^{4} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{8 \sqrt{c}}+\frac{3 \sqrt{c \,x^{2}+a}\, a^{3} e^{4} x}{128 c^{2}}-\frac{3 \sqrt{c \,x^{2}+a}\, a^{2} d^{2} e^{2} x}{8 c}+\frac{3 \sqrt{c \,x^{2}+a}\, a \,d^{4} x}{8}+\frac{\left(c \,x^{2}+a \right)^{\frac{5}{2}} e^{4} x^{3}}{8 c}+\frac{\left(c \,x^{2}+a \right)^{\frac{3}{2}} a^{2} e^{4} x}{64 c^{2}}-\frac{\left(c \,x^{2}+a \right)^{\frac{3}{2}} a \,d^{2} e^{2} x}{4 c}+\frac{4 \left(c \,x^{2}+a \right)^{\frac{5}{2}} d \,e^{3} x^{2}}{7 c}+\frac{\left(c \,x^{2}+a \right)^{\frac{3}{2}} d^{4} x}{4}-\frac{\left(c \,x^{2}+a \right)^{\frac{5}{2}} a \,e^{4} x}{16 c^{2}}+\frac{\left(c \,x^{2}+a \right)^{\frac{5}{2}} d^{2} e^{2} x}{c}-\frac{8 \left(c \,x^{2}+a \right)^{\frac{5}{2}} a d \,e^{3}}{35 c^{2}}+\frac{4 \left(c \,x^{2}+a \right)^{\frac{5}{2}} d^{3} e}{5 c}"," ",0,"1/8*e^4*x^3*(c*x^2+a)^(5/2)/c-1/16*e^4*a/c^2*x*(c*x^2+a)^(5/2)+1/64*e^4*a^2/c^2*x*(c*x^2+a)^(3/2)+3/128*e^4*a^3/c^2*x*(c*x^2+a)^(1/2)+3/128*e^4*a^4/c^(5/2)*ln(c^(1/2)*x+(c*x^2+a)^(1/2))+4/7*d*e^3*x^2*(c*x^2+a)^(5/2)/c-8/35*d*e^3*a/c^2*(c*x^2+a)^(5/2)+d^2*e^2*x*(c*x^2+a)^(5/2)/c-1/4*d^2*e^2*a/c*x*(c*x^2+a)^(3/2)-3/8*d^2*e^2*a^2/c*x*(c*x^2+a)^(1/2)-3/8*d^2*e^2*a^3/c^(3/2)*ln(c^(1/2)*x+(c*x^2+a)^(1/2))+4/5*d^3*e*(c*x^2+a)^(5/2)/c+1/4*d^4*x*(c*x^2+a)^(3/2)+3/8*d^4*a*x*(c*x^2+a)^(1/2)+3/8*d^4*a^2/c^(1/2)*ln(c^(1/2)*x+(c*x^2+a)^(1/2))","A"
535,1,205,153,0.061000," ","int((e*x+d)^3*(c*x^2+a)^(3/2),x)","-\frac{3 a^{3} d \,e^{2} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{16 c^{\frac{3}{2}}}+\frac{3 a^{2} d^{3} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{8 \sqrt{c}}-\frac{3 \sqrt{c \,x^{2}+a}\, a^{2} d \,e^{2} x}{16 c}+\frac{3 \sqrt{c \,x^{2}+a}\, a \,d^{3} x}{8}-\frac{\left(c \,x^{2}+a \right)^{\frac{3}{2}} a d \,e^{2} x}{8 c}+\frac{\left(c \,x^{2}+a \right)^{\frac{5}{2}} e^{3} x^{2}}{7 c}+\frac{\left(c \,x^{2}+a \right)^{\frac{3}{2}} d^{3} x}{4}+\frac{\left(c \,x^{2}+a \right)^{\frac{5}{2}} d \,e^{2} x}{2 c}-\frac{2 \left(c \,x^{2}+a \right)^{\frac{5}{2}} a \,e^{3}}{35 c^{2}}+\frac{3 \left(c \,x^{2}+a \right)^{\frac{5}{2}} d^{2} e}{5 c}"," ",0,"1/7*e^3*x^2*(c*x^2+a)^(5/2)/c-2/35*e^3*a/c^2*(c*x^2+a)^(5/2)+1/2*d*e^2*x*(c*x^2+a)^(5/2)/c-1/8*d*e^2*a/c*x*(c*x^2+a)^(3/2)-3/16*d*e^2*a^2/c*x*(c*x^2+a)^(1/2)-3/16*d*e^2*a^3/c^(3/2)*ln(c^(1/2)*x+(c*x^2+a)^(1/2))+3/5*d^2*e*(c*x^2+a)^(5/2)/c+1/4*d^3*x*(c*x^2+a)^(3/2)+3/8*d^3*a*x*(c*x^2+a)^(1/2)+3/8*d^3*a^2/c^(1/2)*ln(c^(1/2)*x+(c*x^2+a)^(1/2))","A"
536,1,161,130,0.056000," ","int((e*x+d)^2*(c*x^2+a)^(3/2),x)","-\frac{a^{3} e^{2} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{16 c^{\frac{3}{2}}}+\frac{3 a^{2} d^{2} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{8 \sqrt{c}}-\frac{\sqrt{c \,x^{2}+a}\, a^{2} e^{2} x}{16 c}+\frac{3 \sqrt{c \,x^{2}+a}\, a \,d^{2} x}{8}-\frac{\left(c \,x^{2}+a \right)^{\frac{3}{2}} a \,e^{2} x}{24 c}+\frac{\left(c \,x^{2}+a \right)^{\frac{3}{2}} d^{2} x}{4}+\frac{\left(c \,x^{2}+a \right)^{\frac{5}{2}} e^{2} x}{6 c}+\frac{2 \left(c \,x^{2}+a \right)^{\frac{5}{2}} d e}{5 c}"," ",0,"1/6*e^2*x*(c*x^2+a)^(5/2)/c-1/24*e^2*a/c*x*(c*x^2+a)^(3/2)-1/16*e^2*a^2/c*x*(c*x^2+a)^(1/2)-1/16*e^2*a^3/c^(3/2)*ln(c^(1/2)*x+(c*x^2+a)^(1/2))+2/5*d*e*(c*x^2+a)^(5/2)/c+1/4*d^2*x*(c*x^2+a)^(3/2)+3/8*d^2*a*x*(c*x^2+a)^(1/2)+3/8*d^2*a^2/c^(1/2)*ln(c^(1/2)*x+(c*x^2+a)^(1/2))","A"
537,1,69,67,0.057000," ","int((e*x+d)*(c*x^2+a)^(3/2),x)","\frac{3 a^{2} d \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{8 \sqrt{c}}+\frac{3 \sqrt{c \,x^{2}+a}\, a d x}{8}+\frac{\left(c \,x^{2}+a \right)^{\frac{3}{2}} d x}{4}+\frac{\left(c \,x^{2}+a \right)^{\frac{5}{2}} e}{5 c}"," ",0,"1/5*e*(c*x^2+a)^(5/2)/c+1/4*d*x*(c*x^2+a)^(3/2)+3/8*a*d*x*(c*x^2+a)^(1/2)+3/8*d*a^2/c^(1/2)*ln(c^(1/2)*x+(c*x^2+a)^(1/2))","A"
538,1,745,136,0.056000," ","int((c*x^2+a)^(3/2)/(e*x+d),x)","-\frac{a^{2} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e}-\frac{2 a c \,d^{2} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{3}}-\frac{c^{2} d^{4} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{5}}-\frac{3 a \sqrt{c}\, d \ln \left(\frac{-\frac{c d}{e}+\left(x +\frac{d}{e}\right) c}{\sqrt{c}}+\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\right)}{2 e^{2}}-\frac{c^{\frac{3}{2}} d^{3} \ln \left(\frac{-\frac{c d}{e}+\left(x +\frac{d}{e}\right) c}{\sqrt{c}}+\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\right)}{e^{4}}-\frac{\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, c d x}{2 e^{2}}+\frac{\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, a}{e}+\frac{\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, c \,d^{2}}{e^{3}}+\frac{\left(-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}\right)^{\frac{3}{2}}}{3 e}"," ",0,"1/3/e*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)-1/2/e^2*c*d*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*x-3/2/e^2*c^(1/2)*d*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))*a+1/e*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*a+1/e^3*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*c*d^2-1/e^4*c^(3/2)*d^3*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))-1/e/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a^2-2/e^3/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a*c*d^2-1/e^5/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*c^2*d^4","B"
539,1,1154,133,0.055000," ","int((c*x^2+a)^(3/2)/(e*x+d)^2,x)","\frac{3 a^{2} c d \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\left(a \,e^{2}+c \,d^{2}\right) \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e}+\frac{6 a \,c^{2} d^{3} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\left(a \,e^{2}+c \,d^{2}\right) \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{3}}+\frac{3 c^{3} d^{5} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\left(a \,e^{2}+c \,d^{2}\right) \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{5}}+\frac{3 a^{2} \sqrt{c}\, \ln \left(\frac{-\frac{c d}{e}+\left(x +\frac{d}{e}\right) c}{\sqrt{c}}+\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right)}+\frac{9 a \,c^{\frac{3}{2}} d^{2} \ln \left(\frac{-\frac{c d}{e}+\left(x +\frac{d}{e}\right) c}{\sqrt{c}}+\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right) e^{2}}+\frac{3 c^{\frac{5}{2}} d^{4} \ln \left(\frac{-\frac{c d}{e}+\left(x +\frac{d}{e}\right) c}{\sqrt{c}}+\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\right)}{\left(a \,e^{2}+c \,d^{2}\right) e^{4}}+\frac{3 \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, a c x}{2 \left(a \,e^{2}+c \,d^{2}\right)}+\frac{3 \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, c^{2} d^{2} x}{2 \left(a \,e^{2}+c \,d^{2}\right) e^{2}}-\frac{3 \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, a c d}{\left(a \,e^{2}+c \,d^{2}\right) e}-\frac{3 \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, c^{2} d^{3}}{\left(a \,e^{2}+c \,d^{2}\right) e^{3}}+\frac{\left(-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}\right)^{\frac{3}{2}} c x}{a \,e^{2}+c \,d^{2}}-\frac{\left(-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}\right)^{\frac{3}{2}} c d}{\left(a \,e^{2}+c \,d^{2}\right) e}-\frac{\left(-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}\right)^{\frac{5}{2}}}{\left(a \,e^{2}+c \,d^{2}\right) \left(x +\frac{d}{e}\right)}"," ",0,"-1/(a*e^2+c*d^2)/(x+d/e)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(5/2)-1/e*c*d/(a*e^2+c*d^2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)+3/2/e^2*c^2*d^2/(a*e^2+c*d^2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*x+9/2/e^2*c^(3/2)*d^2/(a*e^2+c*d^2)*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))*a-3/e*c*d/(a*e^2+c*d^2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*a-3/e^3*c^2*d^3/(a*e^2+c*d^2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)+3/e^4*c^(5/2)*d^4/(a*e^2+c*d^2)*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))+3/e*c*d/(a*e^2+c*d^2)/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a^2+6/e^3*c^2*d^3/(a*e^2+c*d^2)/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a+3/e^5*c^3*d^5/(a*e^2+c*d^2)/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))+1/(a*e^2+c*d^2)*c*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)*x+3/2/(a*e^2+c*d^2)*c*a*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*x+3/2/(a*e^2+c*d^2)*c^(1/2)*a^2*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))","B"
540,1,2117,139,0.061000," ","int((c*x^2+a)^(3/2)/(e*x+d)^3,x)","-\frac{3 a^{2} c^{2} d^{2} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e}-\frac{3 a \,c^{3} d^{4} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{3}}-\frac{3 c^{4} d^{6} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{5}}-\frac{3 a^{2} c^{\frac{3}{2}} d \ln \left(\frac{-\frac{c d}{e}+\left(x +\frac{d}{e}\right) c}{\sqrt{c}}+\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\right)}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2}}-\frac{9 a \,c^{\frac{5}{2}} d^{3} \ln \left(\frac{-\frac{c d}{e}+\left(x +\frac{d}{e}\right) c}{\sqrt{c}}+\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\right)}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} e^{2}}-\frac{3 c^{\frac{7}{2}} d^{5} \ln \left(\frac{-\frac{c d}{e}+\left(x +\frac{d}{e}\right) c}{\sqrt{c}}+\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2} e^{4}}-\frac{3 \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, a \,c^{2} d x}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2}}-\frac{3 \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, c^{3} d^{3} x}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} e^{2}}+\frac{3 \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, a \,c^{2} d^{2}}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2} e}+\frac{3 \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, c^{3} d^{4}}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2} e^{3}}-\frac{\left(-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}\right)^{\frac{3}{2}} c^{2} d x}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2}}-\frac{3 a^{2} c \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right) \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e}-\frac{3 a \,c^{2} d^{2} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\left(a \,e^{2}+c \,d^{2}\right) \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{3}}-\frac{3 c^{3} d^{4} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right) \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{5}}+\frac{\left(-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}\right)^{\frac{3}{2}} c^{2} d^{2}}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2} e}-\frac{9 a \,c^{\frac{3}{2}} d \ln \left(\frac{-\frac{c d}{e}+\left(x +\frac{d}{e}\right) c}{\sqrt{c}}+\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\right)}{4 \left(a \,e^{2}+c \,d^{2}\right) e^{2}}-\frac{3 c^{\frac{5}{2}} d^{3} \ln \left(\frac{-\frac{c d}{e}+\left(x +\frac{d}{e}\right) c}{\sqrt{c}}+\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right) e^{4}}-\frac{3 \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, c^{2} d x}{4 \left(a \,e^{2}+c \,d^{2}\right) e^{2}}+\frac{\left(-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}\right)^{\frac{5}{2}} c d}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(x +\frac{d}{e}\right)}+\frac{3 \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, a c}{2 \left(a \,e^{2}+c \,d^{2}\right) e}+\frac{3 \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, c^{2} d^{2}}{2 \left(a \,e^{2}+c \,d^{2}\right) e^{3}}+\frac{\left(-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}\right)^{\frac{3}{2}} c}{2 \left(a \,e^{2}+c \,d^{2}\right) e}-\frac{\left(-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}\right)^{\frac{5}{2}}}{2 \left(a \,e^{2}+c \,d^{2}\right) \left(x +\frac{d}{e}\right)^{2} e}"," ",0,"-1/2/e/(a*e^2+c*d^2)/(x+d/e)^2*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(5/2)+1/2*c*d/(a*e^2+c*d^2)^2/(x+d/e)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(5/2)+1/2/e*c^2*d^2/(a*e^2+c*d^2)^2*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)-3/4/e^2*c^3*d^3/(a*e^2+c*d^2)^2*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*x-9/4/e^2*c^(5/2)*d^3/(a*e^2+c*d^2)^2*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))*a+3/2/e*c^2*d^2/(a*e^2+c*d^2)^2*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*a+3/2/e^3*c^3*d^4/(a*e^2+c*d^2)^2*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)-3/2/e^4*c^(7/2)*d^5/(a*e^2+c*d^2)^2*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))-3/2/e*c^2*d^2/(a*e^2+c*d^2)^2/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a^2-3/e^3*c^3*d^4/(a*e^2+c*d^2)^2/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a-3/2/e^5*c^4*d^6/(a*e^2+c*d^2)^2/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))-1/2*c^2*d/(a*e^2+c*d^2)^2*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)*x-3/4*c^2*d/(a*e^2+c*d^2)^2*a*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*x-3/4*c^(3/2)*d/(a*e^2+c*d^2)^2*a^2*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))+1/2/e/(a*e^2+c*d^2)*c*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)-3/4/e^2/(a*e^2+c*d^2)*c^2*d*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*x-9/4/e^2/(a*e^2+c*d^2)*c^(3/2)*d*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))*a+3/2/e/(a*e^2+c*d^2)*c*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*a+3/2/e^3/(a*e^2+c*d^2)*c^2*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*d^2-3/2/e^4/(a*e^2+c*d^2)*c^(5/2)*d^3*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))-3/2/e/(a*e^2+c*d^2)*c/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a^2-3/e^3/(a*e^2+c*d^2)*c^2/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a*d^2-3/2/e^5/(a*e^2+c*d^2)*c^3/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*d^4","B"
541,1,2490,178,0.063000," ","int((c*x^2+a)^(3/2)/(e*x+d)^4,x)","\frac{3 c^{4} d^{5} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{5}}-\frac{\left(-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}\right)^{\frac{5}{2}}}{3 \left(a \,e^{2}+c \,d^{2}\right) \left(x +\frac{d}{e}\right)^{3} e^{2}}-\frac{2 \left(-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}\right)^{\frac{5}{2}} c}{3 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(x +\frac{d}{e}\right)}+\frac{2 \left(-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}\right)^{\frac{3}{2}} c^{2} x}{3 \left(a \,e^{2}+c \,d^{2}\right)^{2}}+\frac{a^{2} c^{\frac{3}{2}} \ln \left(\frac{-\frac{c d}{e}+\left(x +\frac{d}{e}\right) c}{\sqrt{c}}+\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\right)}{\left(a \,e^{2}+c \,d^{2}\right)^{2}}+\frac{3 a^{2} c^{2} d \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e}+\frac{3 a \,c^{3} d^{3} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{3}}-\frac{a^{2} c^{3} d^{3} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right)^{3} \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e}-\frac{a \,c^{4} d^{5} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\left(a \,e^{2}+c \,d^{2}\right)^{3} \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{3}}-\frac{a^{2} c^{\frac{5}{2}} d^{2} \ln \left(\frac{-\frac{c d}{e}+\left(x +\frac{d}{e}\right) c}{\sqrt{c}}+\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\right)}{4 \left(a \,e^{2}+c \,d^{2}\right)^{3}}-\frac{c^{5} d^{7} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right)^{3} \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{5}}-\frac{\left(-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}\right)^{\frac{5}{2}} c d}{6 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(x +\frac{d}{e}\right)^{2} e}-\frac{\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, c^{4} d^{4} x}{4 \left(a \,e^{2}+c \,d^{2}\right)^{3} e^{2}}+\frac{\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, a \,c^{3} d^{3}}{2 \left(a \,e^{2}+c \,d^{2}\right)^{3} e}+\frac{3 \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, c^{3} d^{2} x}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} e^{2}}-\frac{3 \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, a \,c^{2} d}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2} e}-\frac{3 a \,c^{\frac{7}{2}} d^{4} \ln \left(\frac{-\frac{c d}{e}+\left(x +\frac{d}{e}\right) c}{\sqrt{c}}+\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\right)}{4 \left(a \,e^{2}+c \,d^{2}\right)^{3} e^{2}}+\frac{9 a \,c^{\frac{5}{2}} d^{2} \ln \left(\frac{-\frac{c d}{e}+\left(x +\frac{d}{e}\right) c}{\sqrt{c}}+\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\right)}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} e^{2}}-\frac{\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, a \,c^{3} d^{2} x}{4 \left(a \,e^{2}+c \,d^{2}\right)^{3}}-\frac{c^{\frac{9}{2}} d^{6} \ln \left(\frac{-\frac{c d}{e}+\left(x +\frac{d}{e}\right) c}{\sqrt{c}}+\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right)^{3} e^{4}}+\frac{3 c^{\frac{7}{2}} d^{4} \ln \left(\frac{-\frac{c d}{e}+\left(x +\frac{d}{e}\right) c}{\sqrt{c}}+\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2} e^{4}}-\frac{\left(-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}\right)^{\frac{3}{2}} c^{2} d}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2} e}-\frac{3 \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, c^{3} d^{3}}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2} e^{3}}+\frac{\left(-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}\right)^{\frac{3}{2}} c^{3} d^{3}}{6 \left(a \,e^{2}+c \,d^{2}\right)^{3} e}+\frac{\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, c^{4} d^{5}}{2 \left(a \,e^{2}+c \,d^{2}\right)^{3} e^{3}}+\frac{\left(-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}\right)^{\frac{5}{2}} c^{2} d^{2}}{6 \left(a \,e^{2}+c \,d^{2}\right)^{3} \left(x +\frac{d}{e}\right)}-\frac{\left(-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}\right)^{\frac{3}{2}} c^{3} d^{2} x}{6 \left(a \,e^{2}+c \,d^{2}\right)^{3}}+\frac{\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, a \,c^{2} x}{\left(a \,e^{2}+c \,d^{2}\right)^{2}}"," ",0,"-1/3/e^2/(a*e^2+c*d^2)/(x+d/e)^3*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(5/2)-2/3/(a*e^2+c*d^2)^2*c/(x+d/e)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(5/2)+2/3/(a*e^2+c*d^2)^2*c^2*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)*x+1/(a*e^2+c*d^2)^2*c^(3/2)*a^2*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))+3/e^3*c^3*d^3/(a*e^2+c*d^2)^2/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a-1/2/e*c^3*d^3/(a*e^2+c*d^2)^3/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a^2-1/e^3*c^4*d^5/(a*e^2+c*d^2)^3/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a+3/2/e*c^2*d/(a*e^2+c*d^2)^2/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a^2-1/4*c^(5/2)*d^2/(a*e^2+c*d^2)^3*a^2*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))+3/2/e^5*c^4*d^5/(a*e^2+c*d^2)^2/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))-1/6/e*c*d/(a*e^2+c*d^2)^2/(x+d/e)^2*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(5/2)-1/4/e^2*c^4*d^4/(a*e^2+c*d^2)^3*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*x+1/2/e*c^3*d^3/(a*e^2+c*d^2)^3*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*a-1/2/e^5*c^5*d^7/(a*e^2+c*d^2)^3/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))+3/4/e^2*c^3*d^2/(a*e^2+c*d^2)^2*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*x-3/2/e*c^2*d/(a*e^2+c*d^2)^2*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*a-3/4/e^2*c^(7/2)*d^4/(a*e^2+c*d^2)^3*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))*a+9/4/e^2*c^(5/2)*d^2/(a*e^2+c*d^2)^2*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))*a-1/4*c^3*d^2/(a*e^2+c*d^2)^3*a*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*x-1/2/e^4*c^(9/2)*d^6/(a*e^2+c*d^2)^3*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))+3/2/e^4*c^(7/2)*d^4/(a*e^2+c*d^2)^2*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))-1/2/e*c^2*d/(a*e^2+c*d^2)^2*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)-3/2/e^3*c^3*d^3/(a*e^2+c*d^2)^2*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)+1/6/e*c^3*d^3/(a*e^2+c*d^2)^3*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)+1/2/e^3*c^4*d^5/(a*e^2+c*d^2)^3*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)+1/6*c^2*d^2/(a*e^2+c*d^2)^3/(x+d/e)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(5/2)-1/6*c^3*d^2/(a*e^2+c*d^2)^3*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)*x+1/(a*e^2+c*d^2)^2*c^2*a*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*x","B"
542,1,3528,137,0.074000," ","int((c*x^2+a)^(3/2)/(e*x+d)^5,x)","\text{output too large to display}"," ",0,"9/8/e^2*c^(7/2)*d^3/(a*e^2+c*d^2)^3*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))*a-9/16/e^2/(a*e^2+c*d^2)^2*c^(5/2)*d*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))*a-3/16/e^2/(a*e^2+c*d^2)^2*c^3*d*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*x-3/8/e/(a*e^2+c*d^2)^2*c^2/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a^2-3/8/e^5/(a*e^2+c*d^2)^2*c^4/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*d^4-1/4/e^2*c*d/(a*e^2+c*d^2)^2/(x+d/e)^3*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(5/2)-1/8/e*c^2*d^2/(a*e^2+c*d^2)^3/(x+d/e)^2*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(5/2)+1/8/e/(a*e^2+c*d^2)^2*c^2*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)-1/4/e^3/(a*e^2+c*d^2)/(x+d/e)^4*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(5/2)-3/8*c^2*d/(a*e^2+c*d^2)^3/(x+d/e)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(5/2)-3/8/e^4/(a*e^2+c*d^2)^2*c^(7/2)*d^3*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))-1/8*c^4*d^3/(a*e^2+c*d^2)^4*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)*x+9/16*c^(5/2)*d/(a*e^2+c*d^2)^3*a^2*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))-3/16*c^(7/2)*d^3/(a*e^2+c*d^2)^4*a^2*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))+3/8*c^3*d/(a*e^2+c*d^2)^3*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)*x+3/8/e^3*c^5*d^6/(a*e^2+c*d^2)^4*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)-1/4/e*c^3*d^2/(a*e^2+c*d^2)^3*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)-3/4/e^3*c^4*d^4/(a*e^2+c*d^2)^3*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)+3/8/e/(a*e^2+c*d^2)^2*c^2*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*a+3/8/e^3/(a*e^2+c*d^2)^2*c^3*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*d^2-3/16/e^2*c^5*d^5/(a*e^2+c*d^2)^4*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*x+3/8/e*c^4*d^4/(a*e^2+c*d^2)^4*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*a+3/2/e^3*c^4*d^4/(a*e^2+c*d^2)^3/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a-3/8/e*c^4*d^4/(a*e^2+c*d^2)^4/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a^2+3/4/e*c^3*d^2/(a*e^2+c*d^2)^3/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a^2-3/4/e^3*c^5*d^6/(a*e^2+c*d^2)^4/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a-3/4/e^3/(a*e^2+c*d^2)^2*c^3/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a*d^2+1/8*c^3*d^3/(a*e^2+c*d^2)^4/(x+d/e)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(5/2)+1/8/e*c^4*d^4/(a*e^2+c*d^2)^4*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)-3/8/e^4*c^(11/2)*d^7/(a*e^2+c*d^2)^4*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))+3/4/e^4*c^(9/2)*d^5/(a*e^2+c*d^2)^3*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))-1/8/e/(a*e^2+c*d^2)^2*c/(x+d/e)^2*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(5/2)+9/16*c^3*d/(a*e^2+c*d^2)^3*a*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*x-3/16*c^4*d^3/(a*e^2+c*d^2)^4*a*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*x-3/8/e^5*c^6*d^8/(a*e^2+c*d^2)^4/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))+3/8/e^2*c^4*d^3/(a*e^2+c*d^2)^3*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*x-3/4/e*c^3*d^2/(a*e^2+c*d^2)^3*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*a+3/4/e^5*c^5*d^6/(a*e^2+c*d^2)^3/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))-9/16/e^2*c^(9/2)*d^5/(a*e^2+c*d^2)^4*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))*a","B"
543,1,3622,175,0.067000," ","int((c*x^2+a)^(3/2)/(e*x+d)^6,x)","\text{output too large to display}"," ",0,"-1/5/e^4/(a*e^2+c*d^2)/(x+d/e)^5*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(5/2)-3/8/e^4*c^(13/2)*d^8/(a*e^2+c*d^2)^5*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))+1/8/e*c^3*d/(a*e^2+c*d^2)^3*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)-1/8/e*c^2*d/(a*e^2+c*d^2)^3/(x+d/e)^2*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(5/2)+9/8/e^2*c^(9/2)*d^4/(a*e^2+c*d^2)^4*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))*a-1/4/e^2*c^2*d^2/(a*e^2+c*d^2)^3/(x+d/e)^3*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(5/2)-1/8/e*c^3*d^3/(a*e^2+c*d^2)^4/(x+d/e)^2*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(5/2)+3/4/e^5*c^6*d^7/(a*e^2+c*d^2)^4/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))-3/16*c^5*d^4/(a*e^2+c*d^2)^5*a*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*x+9/16*c^4*d^2/(a*e^2+c*d^2)^4*a*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*x+3/8/e^2*c^5*d^4/(a*e^2+c*d^2)^4*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*x-3/4/e^3*c^6*d^7/(a*e^2+c*d^2)^5/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a-3/8/e*c^3*d/(a*e^2+c*d^2)^3/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a^2-3/4/e^3*c^4*d^3/(a*e^2+c*d^2)^3/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a+3/4/e*c^4*d^3/(a*e^2+c*d^2)^4/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a^2+3/2/e^3*c^5*d^5/(a*e^2+c*d^2)^4/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a-3/8/e*c^5*d^5/(a*e^2+c*d^2)^5/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a^2+1/8*c^4*d^4/(a*e^2+c*d^2)^5/(x+d/e)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(5/2)+1/8/e*c^5*d^5/(a*e^2+c*d^2)^5*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)+3/8/e^3*c^6*d^7/(a*e^2+c*d^2)^5*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)-3/16*c^(9/2)*d^4/(a*e^2+c*d^2)^5*a^2*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))+9/16*c^(7/2)*d^2/(a*e^2+c*d^2)^4*a^2*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))+3/8*c^4*d^2/(a*e^2+c*d^2)^4*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)*x-3/8*c^3*d^2/(a*e^2+c*d^2)^4/(x+d/e)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(5/2)-1/8*c^5*d^4/(a*e^2+c*d^2)^5*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)*x-1/4/e*c^4*d^3/(a*e^2+c*d^2)^4*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)-3/4/e^3*c^5*d^5/(a*e^2+c*d^2)^4*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)-3/8/e^4*c^(9/2)*d^4/(a*e^2+c*d^2)^3*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))+3/4/e^4*c^(11/2)*d^6/(a*e^2+c*d^2)^4*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))-3/4/e*c^4*d^3/(a*e^2+c*d^2)^4*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*a-3/16/e^2*c^6*d^6/(a*e^2+c*d^2)^5*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*x-9/16/e^2*c^(11/2)*d^6/(a*e^2+c*d^2)^5*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))*a-9/16/e^2*c^(7/2)*d^2/(a*e^2+c*d^2)^3*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))*a+3/8/e*c^5*d^5/(a*e^2+c*d^2)^5*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*a-3/8/e^5*c^7*d^9/(a*e^2+c*d^2)^5/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))-1/4/e^3*c*d/(a*e^2+c*d^2)^2/(x+d/e)^4*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(5/2)-3/16/e^2*c^4*d^2/(a*e^2+c*d^2)^3*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*x-3/8/e^5*c^5*d^5/(a*e^2+c*d^2)^3/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))+3/8/e*c^3*d/(a*e^2+c*d^2)^3*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*a+3/8/e^3*c^4*d^3/(a*e^2+c*d^2)^3*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)","B"
544,1,5087,245,0.075000," ","int((c*x^2+a)^(3/2)/(e*x+d)^7,x)","\text{output too large to display}"," ",0,"result too large to display","B"
545,1,386,275,0.054000," ","int((e*x+d)^4*(c*x^2+a)^(5/2),x)","\frac{3 a^{5} e^{4} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{256 c^{\frac{5}{2}}}-\frac{15 a^{4} d^{2} e^{2} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{64 c^{\frac{3}{2}}}+\frac{5 a^{3} d^{4} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{16 \sqrt{c}}+\frac{3 \sqrt{c \,x^{2}+a}\, a^{4} e^{4} x}{256 c^{2}}-\frac{15 \sqrt{c \,x^{2}+a}\, a^{3} d^{2} e^{2} x}{64 c}+\frac{5 \sqrt{c \,x^{2}+a}\, a^{2} d^{4} x}{16}+\frac{\left(c \,x^{2}+a \right)^{\frac{3}{2}} a^{3} e^{4} x}{128 c^{2}}-\frac{5 \left(c \,x^{2}+a \right)^{\frac{3}{2}} a^{2} d^{2} e^{2} x}{32 c}+\frac{5 \left(c \,x^{2}+a \right)^{\frac{3}{2}} a \,d^{4} x}{24}+\frac{\left(c \,x^{2}+a \right)^{\frac{7}{2}} e^{4} x^{3}}{10 c}+\frac{\left(c \,x^{2}+a \right)^{\frac{5}{2}} a^{2} e^{4} x}{160 c^{2}}-\frac{\left(c \,x^{2}+a \right)^{\frac{5}{2}} a \,d^{2} e^{2} x}{8 c}+\frac{4 \left(c \,x^{2}+a \right)^{\frac{7}{2}} d \,e^{3} x^{2}}{9 c}+\frac{\left(c \,x^{2}+a \right)^{\frac{5}{2}} d^{4} x}{6}-\frac{3 \left(c \,x^{2}+a \right)^{\frac{7}{2}} a \,e^{4} x}{80 c^{2}}+\frac{3 \left(c \,x^{2}+a \right)^{\frac{7}{2}} d^{2} e^{2} x}{4 c}-\frac{8 \left(c \,x^{2}+a \right)^{\frac{7}{2}} a d \,e^{3}}{63 c^{2}}+\frac{4 \left(c \,x^{2}+a \right)^{\frac{7}{2}} d^{3} e}{7 c}"," ",0,"1/10*e^4*x^3*(c*x^2+a)^(7/2)/c-3/80*e^4*a/c^2*x*(c*x^2+a)^(7/2)+1/160*e^4*a^2/c^2*x*(c*x^2+a)^(5/2)+1/128*e^4*a^3/c^2*x*(c*x^2+a)^(3/2)+3/256*e^4*a^4/c^2*x*(c*x^2+a)^(1/2)+3/256*e^4*a^5/c^(5/2)*ln(c^(1/2)*x+(c*x^2+a)^(1/2))+4/9*d*e^3*x^2*(c*x^2+a)^(7/2)/c-8/63*d*e^3*a/c^2*(c*x^2+a)^(7/2)+3/4*d^2*e^2*x*(c*x^2+a)^(7/2)/c-1/8*d^2*e^2*a/c*x*(c*x^2+a)^(5/2)-5/32*d^2*e^2*a^2/c*x*(c*x^2+a)^(3/2)-15/64*d^2*e^2*a^3/c*x*(c*x^2+a)^(1/2)-15/64*d^2*e^2*a^4/c^(3/2)*ln(c^(1/2)*x+(c*x^2+a)^(1/2))+4/7*d^3*e*(c*x^2+a)^(7/2)/c+1/6*d^4*x*(c*x^2+a)^(5/2)+5/24*d^4*a*x*(c*x^2+a)^(3/2)+5/16*d^4*a^2*x*(c*x^2+a)^(1/2)+5/16*d^4*a^3/c^(1/2)*ln(c^(1/2)*x+(c*x^2+a)^(1/2))","A"
546,1,245,185,0.052000," ","int((e*x+d)^3*(c*x^2+a)^(5/2),x)","-\frac{15 a^{4} d \,e^{2} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{128 c^{\frac{3}{2}}}+\frac{5 a^{3} d^{3} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{16 \sqrt{c}}-\frac{15 \sqrt{c \,x^{2}+a}\, a^{3} d \,e^{2} x}{128 c}+\frac{5 \sqrt{c \,x^{2}+a}\, a^{2} d^{3} x}{16}-\frac{5 \left(c \,x^{2}+a \right)^{\frac{3}{2}} a^{2} d \,e^{2} x}{64 c}+\frac{5 \left(c \,x^{2}+a \right)^{\frac{3}{2}} a \,d^{3} x}{24}-\frac{\left(c \,x^{2}+a \right)^{\frac{5}{2}} a d \,e^{2} x}{16 c}+\frac{\left(c \,x^{2}+a \right)^{\frac{7}{2}} e^{3} x^{2}}{9 c}+\frac{\left(c \,x^{2}+a \right)^{\frac{5}{2}} d^{3} x}{6}+\frac{3 \left(c \,x^{2}+a \right)^{\frac{7}{2}} d \,e^{2} x}{8 c}-\frac{2 \left(c \,x^{2}+a \right)^{\frac{7}{2}} a \,e^{3}}{63 c^{2}}+\frac{3 \left(c \,x^{2}+a \right)^{\frac{7}{2}} d^{2} e}{7 c}"," ",0,"1/9*e^3*x^2*(c*x^2+a)^(7/2)/c-2/63*e^3*a/c^2*(c*x^2+a)^(7/2)+3/8*d*e^2*x*(c*x^2+a)^(7/2)/c-1/16*d*e^2*a/c*x*(c*x^2+a)^(5/2)-5/64*d*e^2*a^2/c*x*(c*x^2+a)^(3/2)-15/128*d*e^2*a^3/c*x*(c*x^2+a)^(1/2)-15/128*d*e^2*a^4/c^(3/2)*ln(c^(1/2)*x+(c*x^2+a)^(1/2))+3/7*d^2*e*(c*x^2+a)^(7/2)/c+1/6*d^3*x*(c*x^2+a)^(5/2)+5/24*d^3*a*x*(c*x^2+a)^(3/2)+5/16*d^3*a^2*x*(c*x^2+a)^(1/2)+5/16*d^3*a^3/c^(1/2)*ln(c^(1/2)*x+(c*x^2+a)^(1/2))","A"
547,1,200,161,0.051000," ","int((e*x+d)^2*(c*x^2+a)^(5/2),x)","-\frac{5 a^{4} e^{2} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{128 c^{\frac{3}{2}}}+\frac{5 a^{3} d^{2} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{16 \sqrt{c}}-\frac{5 \sqrt{c \,x^{2}+a}\, a^{3} e^{2} x}{128 c}+\frac{5 \sqrt{c \,x^{2}+a}\, a^{2} d^{2} x}{16}-\frac{5 \left(c \,x^{2}+a \right)^{\frac{3}{2}} a^{2} e^{2} x}{192 c}+\frac{5 \left(c \,x^{2}+a \right)^{\frac{3}{2}} a \,d^{2} x}{24}-\frac{\left(c \,x^{2}+a \right)^{\frac{5}{2}} a \,e^{2} x}{48 c}+\frac{\left(c \,x^{2}+a \right)^{\frac{5}{2}} d^{2} x}{6}+\frac{\left(c \,x^{2}+a \right)^{\frac{7}{2}} e^{2} x}{8 c}+\frac{2 \left(c \,x^{2}+a \right)^{\frac{7}{2}} d e}{7 c}"," ",0,"1/8*e^2*x*(c*x^2+a)^(7/2)/c-1/48*e^2*a/c*x*(c*x^2+a)^(5/2)-5/192*e^2*a^2/c*x*(c*x^2+a)^(3/2)-5/128*e^2*a^3/c*x*(c*x^2+a)^(1/2)-5/128*e^2*a^4/c^(3/2)*ln(c^(1/2)*x+(c*x^2+a)^(1/2))+2/7*d*e*(c*x^2+a)^(7/2)/c+1/6*d^2*x*(c*x^2+a)^(5/2)+5/24*d^2*a*x*(c*x^2+a)^(3/2)+5/16*d^2*a^2*x*(c*x^2+a)^(1/2)+5/16*d^2*a^3/c^(1/2)*ln(c^(1/2)*x+(c*x^2+a)^(1/2))","A"
548,1,85,83,0.047000," ","int((e*x+d)*(c*x^2+a)^(5/2),x)","\frac{5 a^{3} d \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{16 \sqrt{c}}+\frac{5 \sqrt{c \,x^{2}+a}\, a^{2} d x}{16}+\frac{5 \left(c \,x^{2}+a \right)^{\frac{3}{2}} a d x}{24}+\frac{\left(c \,x^{2}+a \right)^{\frac{5}{2}} d x}{6}+\frac{\left(c \,x^{2}+a \right)^{\frac{7}{2}} e}{7 c}"," ",0,"1/7*e*(c*x^2+a)^(7/2)/c+1/6*d*x*(c*x^2+a)^(5/2)+5/24*a*d*x*(c*x^2+a)^(3/2)+5/16*a^2*d*x*(c*x^2+a)^(1/2)+5/16*d*a^3/c^(1/2)*ln(c^(1/2)*x+(c*x^2+a)^(1/2))","A"
549,1,1225,199,0.059000," ","int((c*x^2+a)^(5/2)/(e*x+d),x)","-\frac{a^{3} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e}-\frac{3 a^{2} c \,d^{2} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{3}}-\frac{3 a \,c^{2} d^{4} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{5}}-\frac{c^{3} d^{6} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{7}}-\frac{15 a^{2} \sqrt{c}\, d \ln \left(\frac{-\frac{c d}{e}+\left(x +\frac{d}{e}\right) c}{\sqrt{c}}+\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\right)}{8 e^{2}}-\frac{5 a \,c^{\frac{3}{2}} d^{3} \ln \left(\frac{-\frac{c d}{e}+\left(x +\frac{d}{e}\right) c}{\sqrt{c}}+\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\right)}{2 e^{4}}-\frac{c^{\frac{5}{2}} d^{5} \ln \left(\frac{-\frac{c d}{e}+\left(x +\frac{d}{e}\right) c}{\sqrt{c}}+\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\right)}{e^{6}}-\frac{7 \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, a c d x}{8 e^{2}}-\frac{\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, c^{2} d^{3} x}{2 e^{4}}+\frac{\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, a^{2}}{e}+\frac{2 \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, a c \,d^{2}}{e^{3}}+\frac{\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, c^{2} d^{4}}{e^{5}}-\frac{\left(-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}\right)^{\frac{3}{2}} c d x}{4 e^{2}}+\frac{\left(-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}\right)^{\frac{3}{2}} a}{3 e}+\frac{\left(-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}\right)^{\frac{3}{2}} c \,d^{2}}{3 e^{3}}+\frac{\left(-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}\right)^{\frac{5}{2}}}{5 e}"," ",0,"1/5/e*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(5/2)-1/4/e^2*c*d*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)*x-7/8/e^2*c*d*a*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*x-15/8/e^2*c^(1/2)*d*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))*a^2+1/3/e*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)*a+1/3/e^3*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)*c*d^2-1/2/e^4*c^2*d^3*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*x-5/2/e^4*c^(3/2)*d^3*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))*a+1/e*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*a^2+2/e^3*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*a*c*d^2+1/e^5*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*c^2*d^4-1/e^6*c^(5/2)*d^5*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))-1/e/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a^3-3/e^3/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a^2*c*d^2-3/e^5/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a*c^2*d^4-1/e^7/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*c^3*d^6","B"
550,1,1796,195,0.067000," ","int((c*x^2+a)^(5/2)/(e*x+d)^2,x)","\frac{5 a^{3} c d \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\left(a \,e^{2}+c \,d^{2}\right) \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e}+\frac{15 a^{2} c^{2} d^{3} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\left(a \,e^{2}+c \,d^{2}\right) \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{3}}+\frac{15 a \,c^{3} d^{5} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\left(a \,e^{2}+c \,d^{2}\right) \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{5}}+\frac{5 c^{4} d^{7} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\left(a \,e^{2}+c \,d^{2}\right) \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{7}}+\frac{15 a^{3} \sqrt{c}\, \ln \left(\frac{-\frac{c d}{e}+\left(x +\frac{d}{e}\right) c}{\sqrt{c}}+\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\right)}{8 \left(a \,e^{2}+c \,d^{2}\right)}+\frac{75 a^{2} c^{\frac{3}{2}} d^{2} \ln \left(\frac{-\frac{c d}{e}+\left(x +\frac{d}{e}\right) c}{\sqrt{c}}+\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\right)}{8 \left(a \,e^{2}+c \,d^{2}\right) e^{2}}+\frac{25 a \,c^{\frac{5}{2}} d^{4} \ln \left(\frac{-\frac{c d}{e}+\left(x +\frac{d}{e}\right) c}{\sqrt{c}}+\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right) e^{4}}+\frac{5 c^{\frac{7}{2}} d^{6} \ln \left(\frac{-\frac{c d}{e}+\left(x +\frac{d}{e}\right) c}{\sqrt{c}}+\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\right)}{\left(a \,e^{2}+c \,d^{2}\right) e^{6}}+\frac{15 \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, a^{2} c x}{8 \left(a \,e^{2}+c \,d^{2}\right)}+\frac{35 \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, a \,c^{2} d^{2} x}{8 \left(a \,e^{2}+c \,d^{2}\right) e^{2}}+\frac{5 \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, c^{3} d^{4} x}{2 \left(a \,e^{2}+c \,d^{2}\right) e^{4}}-\frac{5 \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, a^{2} c d}{\left(a \,e^{2}+c \,d^{2}\right) e}-\frac{10 \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, a \,c^{2} d^{3}}{\left(a \,e^{2}+c \,d^{2}\right) e^{3}}+\frac{5 \left(-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}\right)^{\frac{3}{2}} a c x}{4 \left(a \,e^{2}+c \,d^{2}\right)}-\frac{5 \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, c^{3} d^{5}}{\left(a \,e^{2}+c \,d^{2}\right) e^{5}}+\frac{5 \left(-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}\right)^{\frac{3}{2}} c^{2} d^{2} x}{4 \left(a \,e^{2}+c \,d^{2}\right) e^{2}}-\frac{5 \left(-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}\right)^{\frac{3}{2}} a c d}{3 \left(a \,e^{2}+c \,d^{2}\right) e}-\frac{5 \left(-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}\right)^{\frac{3}{2}} c^{2} d^{3}}{3 \left(a \,e^{2}+c \,d^{2}\right) e^{3}}+\frac{\left(-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}\right)^{\frac{5}{2}} c x}{a \,e^{2}+c \,d^{2}}-\frac{\left(-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}\right)^{\frac{5}{2}} c d}{\left(a \,e^{2}+c \,d^{2}\right) e}-\frac{\left(-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}\right)^{\frac{7}{2}}}{\left(a \,e^{2}+c \,d^{2}\right) \left(x +\frac{d}{e}\right)}"," ",0,"-1/(a*e^2+c*d^2)/(x+d/e)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(7/2)-1/e*c*d/(a*e^2+c*d^2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(5/2)+5/4/e^2*c^2*d^2/(a*e^2+c*d^2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)*x+35/8/e^2*c^2*d^2/(a*e^2+c*d^2)*a*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*x+75/8/e^2*c^(3/2)*d^2/(a*e^2+c*d^2)*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))*a^2-5/3/e*c*d/(a*e^2+c*d^2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)*a-5/3/e^3*c^2*d^3/(a*e^2+c*d^2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)+5/2/e^4*c^3*d^4/(a*e^2+c*d^2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*x+25/2/e^4*c^(5/2)*d^4/(a*e^2+c*d^2)*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))*a-5/e*c*d/(a*e^2+c*d^2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*a^2-10/e^3*c^2*d^3/(a*e^2+c*d^2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*a-5/e^5*c^3*d^5/(a*e^2+c*d^2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)+5/e^6*c^(7/2)*d^6/(a*e^2+c*d^2)*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))+5/e*c*d/(a*e^2+c*d^2)/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a^3+15/e^3*c^2*d^3/(a*e^2+c*d^2)/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a^2+15/e^5*c^3*d^5/(a*e^2+c*d^2)/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a+5/e^7*c^4*d^7/(a*e^2+c*d^2)/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))+1/(a*e^2+c*d^2)*c*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(5/2)*x+5/4/(a*e^2+c*d^2)*c*a*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)*x+15/8/(a*e^2+c*d^2)*c*a^2*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*x+15/8/(a*e^2+c*d^2)*c^(1/2)*a^3*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))","B"
551,1,3342,185,0.066000," ","int((c*x^2+a)^(5/2)/(e*x+d)^3,x)","\text{output too large to display}"," ",0,"5/2/e/(a*e^2+c*d^2)*c*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*a^2+5/2/e^5/(a*e^2+c*d^2)*c^3*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*d^4+3/2/e*c^2*d^2/(a*e^2+c*d^2)^2*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(5/2)-15/2/e^6*c^(9/2)*d^7/(a*e^2+c*d^2)^2*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))-5/2/e^6/(a*e^2+c*d^2)*c^(7/2)*d^5*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))+5/2/e^3*c^3*d^4/(a*e^2+c*d^2)^2*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)+15/2/e^5*c^4*d^6/(a*e^2+c*d^2)^2*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)+5/6/e/(a*e^2+c*d^2)*c*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)*a+3/2*c*d/(a*e^2+c*d^2)^2/(x+d/e)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(7/2)-3/2*c^2*d/(a*e^2+c*d^2)^2*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(5/2)*x-45/16*c^(3/2)*d/(a*e^2+c*d^2)^2*a^3*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))-5/2/e/(a*e^2+c*d^2)*c/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a^3-5/2/e^7/(a*e^2+c*d^2)*c^4/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*d^6+5/2/e*c^2*d^2/(a*e^2+c*d^2)^2*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)*a-5/8/e^2/(a*e^2+c*d^2)*c^2*d*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)*x-5/4/e^4/(a*e^2+c*d^2)*c^3*d^3*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*x+5/e^3/(a*e^2+c*d^2)*c^2*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*a*d^2-15/4/e^4*c^4*d^5/(a*e^2+c*d^2)^2*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*x-15/8/e^2*c^3*d^3/(a*e^2+c*d^2)^2*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)*x-45/16*c^2*d/(a*e^2+c*d^2)^2*a^2*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*x-1/2/e/(a*e^2+c*d^2)/(x+d/e)^2*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(7/2)+1/2/e/(a*e^2+c*d^2)*c*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(5/2)+5/6/e^3/(a*e^2+c*d^2)*c^2*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)*d^2-35/16/e^2/(a*e^2+c*d^2)*c^2*d*a*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*x-15/2/e^3/(a*e^2+c*d^2)*c^2/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a^2*d^2-105/16/e^2*c^3*d^3/(a*e^2+c*d^2)^2*a*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*x-15/2/e*c^2*d^2/(a*e^2+c*d^2)^2/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a^3-45/2/e^3*c^3*d^4/(a*e^2+c*d^2)^2/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a^2-45/2/e^5*c^4*d^6/(a*e^2+c*d^2)^2/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a-15/2/e^5/(a*e^2+c*d^2)*c^3/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a*d^4-75/16/e^2/(a*e^2+c*d^2)*c^(3/2)*d*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))*a^2-25/4/e^4/(a*e^2+c*d^2)*c^(5/2)*d^3*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))*a-15/2/e^7*c^5*d^8/(a*e^2+c*d^2)^2/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))+15/e^3*c^3*d^4/(a*e^2+c*d^2)^2*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*a+15/2/e*c^2*d^2/(a*e^2+c*d^2)^2*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*a^2-75/4/e^4*c^(7/2)*d^5/(a*e^2+c*d^2)^2*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))*a-225/16/e^2*c^(5/2)*d^3/(a*e^2+c*d^2)^2*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))*a^2-15/8*c^2*d/(a*e^2+c*d^2)^2*a*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)*x","B"
552,1,3789,194,0.056000," ","int((c*x^2+a)^(5/2)/(e*x+d)^4,x)","\text{output too large to display}"," ",0,"15/8/e^2*c^3*d^2/(a*e^2+c*d^2)^2*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)*x+15/4/e^4*c^4*d^4/(a*e^2+c*d^2)^2*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*x-15/e^3*c^3*d^3/(a*e^2+c*d^2)^2*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*a+15/2/e^7*c^5*d^7/(a*e^2+c*d^2)^2/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))+1/6/e*c*d/(a*e^2+c*d^2)^2/(x+d/e)^2*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(7/2)+5/8/e^2*c^4*d^4/(a*e^2+c*d^2)^3*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)*x-5/6/e*c^3*d^3/(a*e^2+c*d^2)^3*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)*a+5/4/e^4*c^5*d^6/(a*e^2+c*d^2)^3*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*x-5/2/e*c^2*d/(a*e^2+c*d^2)^2*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)*a+5/2/(a*e^2+c*d^2)^2*c^2*a^2*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*x-4/3/(a*e^2+c*d^2)^2*c/(x+d/e)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(7/2)+4/3/(a*e^2+c*d^2)^2*c^2*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(5/2)*x+5/2/(a*e^2+c*d^2)^2*c^(3/2)*a^3*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))-1/3/e^2/(a*e^2+c*d^2)/(x+d/e)^3*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(7/2)-15/2/e*c^2*d/(a*e^2+c*d^2)^2*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*a^2+75/4/e^4*c^(7/2)*d^4/(a*e^2+c*d^2)^2*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))*a+25/4/e^4*c^(9/2)*d^6/(a*e^2+c*d^2)^3*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))*a-5/2/e*c^3*d^3/(a*e^2+c*d^2)^3*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*a^2+5/8*c^3*d^2/(a*e^2+c*d^2)^3*a*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)*x+15/16*c^3*d^2/(a*e^2+c*d^2)^3*a^2*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*x-5/e^3*c^4*d^5/(a*e^2+c*d^2)^3*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*a+5/2/e^7*c^6*d^9/(a*e^2+c*d^2)^3/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))+75/16/e^2*c^(7/2)*d^4/(a*e^2+c*d^2)^3*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))*a^2+225/16/e^2*c^(5/2)*d^2/(a*e^2+c*d^2)^2*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))*a^2-5/2/e^5*c^5*d^7/(a*e^2+c*d^2)^3*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)-5/2/e^3*c^3*d^3/(a*e^2+c*d^2)^2*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)+5/2/e^6*c^(11/2)*d^8/(a*e^2+c*d^2)^3*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))+15/2/e^6*c^(9/2)*d^6/(a*e^2+c*d^2)^2*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))-15/2/e^5*c^4*d^5/(a*e^2+c*d^2)^2*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)+15/16*c^(5/2)*d^2/(a*e^2+c*d^2)^3*a^3*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))+5/3/(a*e^2+c*d^2)^2*c^2*a*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)*x-5/6/e^3*c^4*d^5/(a*e^2+c*d^2)^3*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)-3/2/e*c^2*d/(a*e^2+c*d^2)^2*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(5/2)+45/2/e^3*c^3*d^3/(a*e^2+c*d^2)^2/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a^2+45/2/e^5*c^4*d^5/(a*e^2+c*d^2)^2/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a+35/16/e^2*c^4*d^4/(a*e^2+c*d^2)^3*a*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*x+15/2/e^3*c^4*d^5/(a*e^2+c*d^2)^3/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a^2+15/2/e^5*c^5*d^7/(a*e^2+c*d^2)^3/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a+105/16/e^2*c^3*d^2/(a*e^2+c*d^2)^2*a*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*x+15/2/e*c^2*d/(a*e^2+c*d^2)^2/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a^3+5/2/e*c^3*d^3/(a*e^2+c*d^2)^3/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a^3-1/2*c^2*d^2/(a*e^2+c*d^2)^3/(x+d/e)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(7/2)+1/2*c^3*d^2/(a*e^2+c*d^2)^3*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(5/2)*x-1/2/e*c^3*d^3/(a*e^2+c*d^2)^3*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(5/2)","B"
553,1,5406,261,0.074000," ","int((c*x^2+a)^(5/2)/(e*x+d)^5,x)","\text{output too large to display}"," ",0,"result too large to display","B"
554,1,5921,288,0.072000," ","int((c*x^2+a)^(5/2)/(e*x+d)^6,x)","\text{output too large to display}"," ",0,"result too large to display","B"
555,1,7616,183,0.092000," ","int((c*x^2+a)^(5/2)/(e*x+d)^7,x)","\text{output too large to display}"," ",0,"result too large to display","B"
556,1,7718,222,0.090000," ","int((c*x^2+a)^(5/2)/(e*x+d)^8,x)","\text{output too large to display}"," ",0,"result too large to display","B"
557,1,9978,304,0.127000," ","int((c*x^2+a)^(5/2)/(e*x+d)^9,x)","\text{output too large to display}"," ",0,"result too large to display","B"
558,1,57,42,0.046000," ","int((x^2+2)^(1/2)/(4*x+1),x)","-\frac{\arcsinh \left(\frac{\sqrt{2}\, x}{2}\right)}{16}-\frac{\sqrt{33}\, \arctanh \left(\frac{8 \left(-\frac{x}{2}+4\right) \sqrt{33}}{33 \sqrt{-8 x +16 \left(x +\frac{1}{4}\right)^{2}+31}}\right)}{16}+\frac{\sqrt{-8 x +16 \left(x +\frac{1}{4}\right)^{2}+31}}{16}"," ",0,"1/16*(16*(x+1/4)^2-8*x+31)^(1/2)-1/16*arcsinh(1/2*2^(1/2)*x)-1/16*33^(1/2)*arctanh(8/33*(4-1/2*x)*33^(1/2)/(16*(x+1/4)^2-8*x+31)^(1/2))","A"
559,1,56,48,0.055000," ","int((4*x^2+2)^(1/2)/(5+4*x),x)","-\frac{5 \arcsinh \left(\sqrt{2}\, x \right)}{8}-\frac{\sqrt{33}\, \arctanh \left(\frac{2 \left(-10 x +4\right) \sqrt{33}}{33 \sqrt{-40 x +16 \left(x +\frac{5}{4}\right)^{2}-17}}\right)}{8}+\frac{\sqrt{-40 x +16 \left(x +\frac{5}{4}\right)^{2}-17}}{8}"," ",0,"1/8*(16*(x+5/4)^2-40*x-17)^(1/2)-5/8*arcsinh(2^(1/2)*x)-1/8*33^(1/2)*arctanh(2/33*(-10*x+4)*33^(1/2)/(16*(x+5/4)^2-40*x-17)^(1/2))","A"
560,1,45,43,0.048000," ","int((3*x+2)*(7*x^2-5)^(1/2),x)","\sqrt{7 x^{2}-5}\, x -\frac{5 \sqrt{7}\, \ln \left(\sqrt{7}\, x +\sqrt{7 x^{2}-5}\right)}{7}+\frac{\left(7 x^{2}-5\right)^{\frac{3}{2}}}{7}"," ",0,"x*(7*x^2-5)^(1/2)-5/7*ln(x*7^(1/2)+(7*x^2-5)^(1/2))*7^(1/2)+1/7*(7*x^2-5)^(3/2)","A"
561,1,198,141,0.050000," ","int((e*x+d)^4/(c*x^2+a)^(1/2),x)","\frac{\sqrt{c \,x^{2}+a}\, e^{4} x^{3}}{4 c}+\frac{4 \sqrt{c \,x^{2}+a}\, d \,e^{3} x^{2}}{3 c}+\frac{3 a^{2} e^{4} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{8 c^{\frac{5}{2}}}-\frac{3 a \,d^{2} e^{2} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{c^{\frac{3}{2}}}+\frac{d^{4} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{\sqrt{c}}-\frac{3 \sqrt{c \,x^{2}+a}\, a \,e^{4} x}{8 c^{2}}+\frac{3 \sqrt{c \,x^{2}+a}\, d^{2} e^{2} x}{c}-\frac{8 \sqrt{c \,x^{2}+a}\, a d \,e^{3}}{3 c^{2}}+\frac{4 \sqrt{c \,x^{2}+a}\, d^{3} e}{c}"," ",0,"1/4*e^4*x^3/c*(c*x^2+a)^(1/2)-3/8*e^4*a/c^2*x*(c*x^2+a)^(1/2)+3/8*e^4*a^2/c^(5/2)*ln(c^(1/2)*x+(c*x^2+a)^(1/2))+4/3*d*e^3*x^2/c*(c*x^2+a)^(1/2)-8/3*d*e^3*a/c^2*(c*x^2+a)^(1/2)+3*d^2*e^2*x/c*(c*x^2+a)^(1/2)-3*d^2*e^2*a/c^(3/2)*ln(c^(1/2)*x+(c*x^2+a)^(1/2))+4*d^3*e/c*(c*x^2+a)^(1/2)+d^4*ln(c^(1/2)*x+(c*x^2+a)^(1/2))/c^(1/2)","A"
562,1,126,91,0.049000," ","int((e*x+d)^3/(c*x^2+a)^(1/2),x)","\frac{\sqrt{c \,x^{2}+a}\, e^{3} x^{2}}{3 c}-\frac{3 a d \,e^{2} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{2 c^{\frac{3}{2}}}+\frac{d^{3} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{\sqrt{c}}+\frac{3 \sqrt{c \,x^{2}+a}\, d \,e^{2} x}{2 c}-\frac{2 \sqrt{c \,x^{2}+a}\, a \,e^{3}}{3 c^{2}}+\frac{3 \sqrt{c \,x^{2}+a}\, d^{2} e}{c}"," ",0,"1/3*e^3*x^2/c*(c*x^2+a)^(1/2)-2/3*e^3*a/c^2*(c*x^2+a)^(1/2)+3/2*d*e^2*x/c*(c*x^2+a)^(1/2)-3/2*d*e^2*a/c^(3/2)*ln(c^(1/2)*x+(c*x^2+a)^(1/2))+3*d^2*e/c*(c*x^2+a)^(1/2)+d^3*ln(c^(1/2)*x+(c*x^2+a)^(1/2))/c^(1/2)","A"
563,1,84,70,0.053000," ","int((e*x+d)^2/(c*x^2+a)^(1/2),x)","-\frac{a \,e^{2} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{2 c^{\frac{3}{2}}}+\frac{d^{2} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{\sqrt{c}}+\frac{\sqrt{c \,x^{2}+a}\, e^{2} x}{2 c}+\frac{2 \sqrt{c \,x^{2}+a}\, d e}{c}"," ",0,"1/2*e^2*x/c*(c*x^2+a)^(1/2)-1/2*e^2*a/c^(3/2)*ln(c^(1/2)*x+(c*x^2+a)^(1/2))+2*d*e*(c*x^2+a)^(1/2)/c+d^2*ln(c^(1/2)*x+(c*x^2+a)^(1/2))/c^(1/2)","A"
564,1,37,35,0.044000," ","int((e*x+d)/(c*x^2+a)^(1/2),x)","\frac{d \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{\sqrt{c}}+\frac{\sqrt{c \,x^{2}+a}\, e}{c}"," ",0,"e*(c*x^2+a)^(1/2)/c+d*ln(c^(1/2)*x+(c*x^2+a)^(1/2))/c^(1/2)","A"
565,1,127,48,0.055000," ","int(1/(e*x+d)/(c*x^2+a)^(1/2),x)","-\frac{\ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e}"," ",0,"-1/e/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))","B"
566,1,210,83,0.056000," ","int(1/(e*x+d)^2/(c*x^2+a)^(1/2),x)","-\frac{c d \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\left(a \,e^{2}+c \,d^{2}\right) \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e}-\frac{\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{\left(a \,e^{2}+c \,d^{2}\right) \left(x +\frac{d}{e}\right)}"," ",0,"-1/(a*e^2+c*d^2)/(x+d/e)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)-1/e*c*d/(a*e^2+c*d^2)/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))","B"
567,1,426,129,0.060000," ","int(1/(e*x+d)^3/(c*x^2+a)^(1/2),x)","-\frac{3 c^{2} d^{2} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e}-\frac{3 \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, c d}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(x +\frac{d}{e}\right)}+\frac{c \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right) \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e}-\frac{\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{2 \left(a \,e^{2}+c \,d^{2}\right) \left(x +\frac{d}{e}\right)^{2} e}"," ",0,"-1/2/e/(a*e^2+c*d^2)/(x+d/e)^2*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)-3/2*c*d/(a*e^2+c*d^2)^2/(x+d/e)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)-3/2/e*c^2*d^2/(a*e^2+c*d^2)^2/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))+1/2/e*c/(a*e^2+c*d^2)/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))","B"
568,1,573,178,0.059000," ","int(1/(e*x+d)^4/(c*x^2+a)^(1/2),x)","-\frac{5 c^{3} d^{3} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right)^{3} \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e}-\frac{5 \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, c^{2} d^{2}}{2 \left(a \,e^{2}+c \,d^{2}\right)^{3} \left(x +\frac{d}{e}\right)}+\frac{3 c^{2} d \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e}-\frac{5 \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, c d}{6 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(x +\frac{d}{e}\right)^{2} e}+\frac{2 \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, c}{3 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(x +\frac{d}{e}\right)}-\frac{\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{3 \left(a \,e^{2}+c \,d^{2}\right) \left(x +\frac{d}{e}\right)^{3} e^{2}}"," ",0,"-1/3/e^2/(a*e^2+c*d^2)/(x+d/e)^3*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)-5/6/e*c*d/(a*e^2+c*d^2)^2/(x+d/e)^2*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)-5/2*c^2*d^2/(a*e^2+c*d^2)^3/(x+d/e)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)-5/2/e*c^3*d^3/(a*e^2+c*d^2)^3/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))+3/2/e*c^2*d/(a*e^2+c*d^2)^2/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))+2/3/(a*e^2+c*d^2)^2*c/(x+d/e)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)","B"
569,1,189,146,0.054000," ","int((e*x+d)^4/(c*x^2+a)^(3/2),x)","\frac{e^{4} x^{3}}{2 \sqrt{c \,x^{2}+a}\, c}+\frac{4 d \,e^{3} x^{2}}{\sqrt{c \,x^{2}+a}\, c}+\frac{3 a \,e^{4} x}{2 \sqrt{c \,x^{2}+a}\, c^{2}}+\frac{d^{4} x}{\sqrt{c \,x^{2}+a}\, a}-\frac{6 d^{2} e^{2} x}{\sqrt{c \,x^{2}+a}\, c}-\frac{3 a \,e^{4} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{2 c^{\frac{5}{2}}}+\frac{6 d^{2} e^{2} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{c^{\frac{3}{2}}}+\frac{8 a d \,e^{3}}{\sqrt{c \,x^{2}+a}\, c^{2}}-\frac{4 d^{3} e}{\sqrt{c \,x^{2}+a}\, c}"," ",0,"1/2*e^4*x^3/c/(c*x^2+a)^(1/2)+3/2*e^4*a/c^2*x/(c*x^2+a)^(1/2)-3/2*e^4*a/c^(5/2)*ln(c^(1/2)*x+(c*x^2+a)^(1/2))+4*d*e^3*x^2/c/(c*x^2+a)^(1/2)+8*d*e^3*a/c^2/(c*x^2+a)^(1/2)-6*d^2*e^2*x/c/(c*x^2+a)^(1/2)+6*d^2*e^2/c^(3/2)*ln(c^(1/2)*x+(c*x^2+a)^(1/2))-4*d^3*e/c/(c*x^2+a)^(1/2)+d^4*x/a/(c*x^2+a)^(1/2)","A"
570,1,118,94,0.054000," ","int((e*x+d)^3/(c*x^2+a)^(3/2),x)","\frac{e^{3} x^{2}}{\sqrt{c \,x^{2}+a}\, c}+\frac{d^{3} x}{\sqrt{c \,x^{2}+a}\, a}-\frac{3 d \,e^{2} x}{\sqrt{c \,x^{2}+a}\, c}+\frac{3 d \,e^{2} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{c^{\frac{3}{2}}}+\frac{2 a \,e^{3}}{\sqrt{c \,x^{2}+a}\, c^{2}}-\frac{3 d^{2} e}{\sqrt{c \,x^{2}+a}\, c}"," ",0,"e^3*x^2/c/(c*x^2+a)^(1/2)+2*e^3*a/c^2/(c*x^2+a)^(1/2)-3*d*e^2*x/c/(c*x^2+a)^(1/2)+3*d*e^2/c^(3/2)*ln(c^(1/2)*x+(c*x^2+a)^(1/2))-3*d^2*e/c/(c*x^2+a)^(1/2)+d^3*x/a/(c*x^2+a)^(1/2)","A"
571,1,76,73,0.053000," ","int((e*x+d)^2/(c*x^2+a)^(3/2),x)","\frac{d^{2} x}{\sqrt{c \,x^{2}+a}\, a}-\frac{e^{2} x}{\sqrt{c \,x^{2}+a}\, c}+\frac{e^{2} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{c^{\frac{3}{2}}}-\frac{2 d e}{\sqrt{c \,x^{2}+a}\, c}"," ",0,"-e^2*x/c/(c*x^2+a)^(1/2)+e^2/c^(3/2)*ln(c^(1/2)*x+(c*x^2+a)^(1/2))-2*d*e/c/(c*x^2+a)^(1/2)+d^2*x/a/(c*x^2+a)^(1/2)","A"
572,1,27,25,0.044000," ","int((e*x+d)/(c*x^2+a)^(3/2),x)","-\frac{-c d x +a e}{\sqrt{c \,x^{2}+a}\, a c}"," ",0,"-(-c*d*x+a*e)/(c*x^2+a)^(1/2)/a/c","A"
573,1,260,86,0.051000," ","int(1/(e*x+d)/(c*x^2+a)^(3/2),x)","\frac{c d x}{\left(a \,e^{2}+c \,d^{2}\right) \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, a}-\frac{e \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\left(a \,e^{2}+c \,d^{2}\right) \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}+\frac{e}{\left(a \,e^{2}+c \,d^{2}\right) \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}"," ",0,"e/(a*e^2+c*d^2)/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)+d/(a*e^2+c*d^2)/a/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*c*x-e/(a*e^2+c*d^2)/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))","B"
574,1,400,141,0.058000," ","int(1/(e*x+d)^2/(c*x^2+a)^(3/2),x)","\frac{3 c^{2} d^{2} x}{\left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, a}-\frac{3 c d e \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}+\frac{3 c d e}{\left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}-\frac{2 c x}{\left(a \,e^{2}+c \,d^{2}\right) \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, a}-\frac{1}{\left(a \,e^{2}+c \,d^{2}\right) \left(x +\frac{d}{e}\right) \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}"," ",0,"-1/(a*e^2+c*d^2)/(x+d/e)/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)+3*e*c*d/(a*e^2+c*d^2)^2/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)+3*c^2*d^2/(a*e^2+c*d^2)^2/a/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*x-3*e*c*d/(a*e^2+c*d^2)^2/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))-2/(a*e^2+c*d^2)/a/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*c*x","B"
575,1,681,205,0.063000," ","int(1/(e*x+d)^3/(c*x^2+a)^(3/2),x)","\frac{15 c^{3} d^{3} x}{2 \left(a \,e^{2}+c \,d^{2}\right)^{3} \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, a}-\frac{15 c^{2} d^{2} e \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right)^{3} \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}+\frac{15 c^{2} d^{2} e}{2 \left(a \,e^{2}+c \,d^{2}\right)^{3} \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}-\frac{13 c^{2} d x}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, a}+\frac{3 c e \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}-\frac{5 c d}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(x +\frac{d}{e}\right) \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}-\frac{3 c e}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}-\frac{1}{2 \left(a \,e^{2}+c \,d^{2}\right) \left(x +\frac{d}{e}\right)^{2} \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e}"," ",0,"-1/2/e/(a*e^2+c*d^2)/(x+d/e)^2/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)-5/2*c*d/(a*e^2+c*d^2)^2/(x+d/e)/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)+15/2*e*c^2*d^2/(a*e^2+c*d^2)^3/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)+15/2*c^3*d^3/(a*e^2+c*d^2)^3/a/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*x-15/2*e*c^2*d^2/(a*e^2+c*d^2)^3/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))-13/2*c^2*d/(a*e^2+c*d^2)^2/a/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*x-3/2*e/(a*e^2+c*d^2)^2*c/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)+3/2*e/(a*e^2+c*d^2)^2*c/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))","B"
576,1,898,271,0.062000," ","int(1/(e*x+d)^4/(c*x^2+a)^(3/2),x)","\frac{35 c^{4} d^{4} x}{2 \left(a \,e^{2}+c \,d^{2}\right)^{4} \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, a}-\frac{35 c^{3} d^{3} e \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right)^{4} \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}+\frac{35 c^{3} d^{3} e}{2 \left(a \,e^{2}+c \,d^{2}\right)^{4} \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}-\frac{115 c^{3} d^{2} x}{6 \left(a \,e^{2}+c \,d^{2}\right)^{3} \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, a}+\frac{15 c^{2} d e \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right)^{3} \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}-\frac{35 c^{2} d^{2}}{6 \left(a \,e^{2}+c \,d^{2}\right)^{3} \left(x +\frac{d}{e}\right) \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}-\frac{15 c^{2} d e}{2 \left(a \,e^{2}+c \,d^{2}\right)^{3} \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}+\frac{8 c^{2} x}{3 \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, a}-\frac{7 c d}{6 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(x +\frac{d}{e}\right)^{2} \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e}+\frac{4 c}{3 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(x +\frac{d}{e}\right) \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}-\frac{1}{3 \left(a \,e^{2}+c \,d^{2}\right) \left(x +\frac{d}{e}\right)^{3} \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{2}}"," ",0,"-1/3/e^2/(a*e^2+c*d^2)/(x+d/e)^3/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)-7/6/e*c*d/(a*e^2+c*d^2)^2/(x+d/e)^2/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)-35/6*c^2*d^2/(a*e^2+c*d^2)^3/(x+d/e)/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)+35/2*e*c^3*d^3/(a*e^2+c*d^2)^4/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)+35/2*c^4*d^4/(a*e^2+c*d^2)^4/a/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*x-35/2*e*c^3*d^3/(a*e^2+c*d^2)^4/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))-115/6*c^3*d^2/(a*e^2+c*d^2)^3/a/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*x-15/2*e*c^2*d/(a*e^2+c*d^2)^3/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)+15/2*e*c^2*d/(a*e^2+c*d^2)^3/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))+4/3/(a*e^2+c*d^2)^2*c/(x+d/e)/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)+8/3/(a*e^2+c*d^2)^2*c^2/a/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*x","B"
577,1,270,171,0.066000," ","int((e*x+d)^5/(c*x^2+a)^(5/2),x)","\frac{e^{5} x^{4}}{\left(c \,x^{2}+a \right)^{\frac{3}{2}} c}-\frac{5 d \,e^{4} x^{3}}{3 \left(c \,x^{2}+a \right)^{\frac{3}{2}} c}+\frac{4 a \,e^{5} x^{2}}{\left(c \,x^{2}+a \right)^{\frac{3}{2}} c^{2}}-\frac{10 d^{2} e^{3} x^{2}}{\left(c \,x^{2}+a \right)^{\frac{3}{2}} c}+\frac{d^{5} x}{3 \left(c \,x^{2}+a \right)^{\frac{3}{2}} a}-\frac{10 d^{3} e^{2} x}{3 \left(c \,x^{2}+a \right)^{\frac{3}{2}} c}+\frac{8 a^{2} e^{5}}{3 \left(c \,x^{2}+a \right)^{\frac{3}{2}} c^{3}}-\frac{20 a \,d^{2} e^{3}}{3 \left(c \,x^{2}+a \right)^{\frac{3}{2}} c^{2}}+\frac{10 d^{3} e^{2} x}{3 \sqrt{c \,x^{2}+a}\, a c}+\frac{2 d^{5} x}{3 \sqrt{c \,x^{2}+a}\, a^{2}}-\frac{5 d^{4} e}{3 \left(c \,x^{2}+a \right)^{\frac{3}{2}} c}-\frac{5 d \,e^{4} x}{\sqrt{c \,x^{2}+a}\, c^{2}}+\frac{5 d \,e^{4} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{c^{\frac{5}{2}}}"," ",0,"e^5*x^4/c/(c*x^2+a)^(3/2)+4*e^5*a/c^2*x^2/(c*x^2+a)^(3/2)+8/3*e^5*a^2/c^3/(c*x^2+a)^(3/2)-5/3*d*e^4*x^3/c/(c*x^2+a)^(3/2)-5*d*e^4/c^2*x/(c*x^2+a)^(1/2)+5*d*e^4/c^(5/2)*ln(c^(1/2)*x+(c*x^2+a)^(1/2))-10*d^2*e^3*x^2/c/(c*x^2+a)^(3/2)-20/3*d^2*e^3*a/c^2/(c*x^2+a)^(3/2)-10/3*d^3*e^2/c*x/(c*x^2+a)^(3/2)+10/3*d^3*e^2/a/c*x/(c*x^2+a)^(1/2)-5/3*d^4*e/c/(c*x^2+a)^(3/2)+1/3*d^5*x/a/(c*x^2+a)^(3/2)+2/3*d^5/a^2*x/(c*x^2+a)^(1/2)","A"
578,1,202,143,0.050000," ","int((e*x+d)^4/(c*x^2+a)^(5/2),x)","-\frac{e^{4} x^{3}}{3 \left(c \,x^{2}+a \right)^{\frac{3}{2}} c}-\frac{4 d \,e^{3} x^{2}}{\left(c \,x^{2}+a \right)^{\frac{3}{2}} c}+\frac{d^{4} x}{3 \left(c \,x^{2}+a \right)^{\frac{3}{2}} a}-\frac{2 d^{2} e^{2} x}{\left(c \,x^{2}+a \right)^{\frac{3}{2}} c}-\frac{8 a d \,e^{3}}{3 \left(c \,x^{2}+a \right)^{\frac{3}{2}} c^{2}}+\frac{2 d^{2} e^{2} x}{\sqrt{c \,x^{2}+a}\, a c}+\frac{2 d^{4} x}{3 \sqrt{c \,x^{2}+a}\, a^{2}}-\frac{4 d^{3} e}{3 \left(c \,x^{2}+a \right)^{\frac{3}{2}} c}-\frac{e^{4} x}{\sqrt{c \,x^{2}+a}\, c^{2}}+\frac{e^{4} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{c^{\frac{5}{2}}}"," ",0,"-1/3*e^4*x^3/c/(c*x^2+a)^(3/2)-e^4/c^2*x/(c*x^2+a)^(1/2)+e^4/c^(5/2)*ln(c^(1/2)*x+(c*x^2+a)^(1/2))-4*d*e^3*x^2/c/(c*x^2+a)^(3/2)-8/3*d*e^3*a/c^2/(c*x^2+a)^(3/2)-2*d^2*e^2/c*x/(c*x^2+a)^(3/2)+2*d^2*e^2/a/c*x/(c*x^2+a)^(1/2)-4/3*d^3*e/c/(c*x^2+a)^(3/2)+1/3*d^4*x/a/(c*x^2+a)^(3/2)+2/3*d^4/a^2*x/(c*x^2+a)^(1/2)","A"
579,1,83,71,0.047000," ","int((e*x+d)^3/(c*x^2+a)^(5/2),x)","-\frac{-3 a \,c^{2} d \,e^{2} x^{3}-2 c^{3} d^{3} x^{3}+3 e^{3} x^{2} a^{2} c -3 d^{3} x a \,c^{2}+2 e^{3} a^{3}+3 d^{2} e \,a^{2} c}{3 \left(c \,x^{2}+a \right)^{\frac{3}{2}} a^{2} c^{2}}"," ",0,"-1/3*(-3*a*c^2*d*e^2*x^3-2*c^3*d^3*x^3+3*a^2*c*e^3*x^2-3*a*c^2*d^3*x+2*a^3*e^3+3*a^2*c*d^2*e)/(c*x^2+a)^(3/2)/a^2/c^2","A"
580,1,55,50,0.048000," ","int((e*x+d)^2/(c*x^2+a)^(5/2),x)","-\frac{-a c \,e^{2} x^{3}-2 c^{2} d^{2} x^{3}-3 d^{2} x a c +2 a^{2} d e}{3 \left(c \,x^{2}+a \right)^{\frac{3}{2}} a^{2} c}"," ",0,"-1/3*(-a*c*e^2*x^3-2*c^2*d^2*x^3-3*a*c*d^2*x+2*a^2*d*e)/(c*x^2+a)^(3/2)/a^2/c","A"
581,1,39,43,0.041000," ","int((e*x+d)/(c*x^2+a)^(5/2),x)","-\frac{-2 c^{2} d \,x^{3}-3 d x a c +e \,a^{2}}{3 \left(c \,x^{2}+a \right)^{\frac{3}{2}} a^{2} c}"," ",0,"-1/3*(-2*c^2*d*x^3-3*a*c*d*x+a^2*e)/(c*x^2+a)^(3/2)/a^2/c","A"
582,1,454,140,0.053000," ","int(1/(e*x+d)/(c*x^2+a)^(5/2),x)","\frac{c d \,e^{2} x}{\left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, a}-\frac{e^{3} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}+\frac{e^{3}}{\left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}+\frac{c d x}{3 \left(a \,e^{2}+c \,d^{2}\right) \left(-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}\right)^{\frac{3}{2}} a}+\frac{2 c d x}{3 \left(a \,e^{2}+c \,d^{2}\right) \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, a^{2}}+\frac{e}{3 \left(a \,e^{2}+c \,d^{2}\right) \left(-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}\right)^{\frac{3}{2}}}"," ",0,"1/3*e/(a*e^2+c*d^2)/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)+1/3*c*d/(a*e^2+c*d^2)/a/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)*x+2/3*c*d/(a*e^2+c*d^2)/a^2/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*x+e^3/(a*e^2+c*d^2)^2/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)+e^2/(a*e^2+c*d^2)^2*d/a/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*c*x-e^3/(a*e^2+c*d^2)^2/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))","B"
583,1,667,226,0.058000," ","int(1/(e*x+d)^2/(c*x^2+a)^(5/2),x)","\frac{5 c^{2} d^{2} e^{2} x}{\left(a \,e^{2}+c \,d^{2}\right)^{3} \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, a}-\frac{5 c d \,e^{3} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\left(a \,e^{2}+c \,d^{2}\right)^{3} \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}+\frac{5 c d \,e^{3}}{\left(a \,e^{2}+c \,d^{2}\right)^{3} \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}+\frac{5 c^{2} d^{2} x}{3 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}\right)^{\frac{3}{2}} a}+\frac{10 c^{2} d^{2} x}{3 \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, a^{2}}+\frac{5 c d e}{3 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}\right)^{\frac{3}{2}}}-\frac{4 c x}{3 \left(a \,e^{2}+c \,d^{2}\right) \left(-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}\right)^{\frac{3}{2}} a}-\frac{8 c x}{3 \left(a \,e^{2}+c \,d^{2}\right) \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, a^{2}}-\frac{1}{\left(a \,e^{2}+c \,d^{2}\right) \left(x +\frac{d}{e}\right) \left(-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}\right)^{\frac{3}{2}}}"," ",0,"-1/(a*e^2+c*d^2)/(x+d/e)/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)+5/3*e*c*d/(a*e^2+c*d^2)^2/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)+5/3*c^2*d^2/(a*e^2+c*d^2)^2/a/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)*x+10/3*c^2*d^2/(a*e^2+c*d^2)^2/a^2/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*x+5*e^3*c*d/(a*e^2+c*d^2)^3/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)+5*e^2*c^2*d^2/(a*e^2+c*d^2)^3/a/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*x-5*e^3*c*d/(a*e^2+c*d^2)^3/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))-4/3/(a*e^2+c*d^2)*c/a/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)*x-8/3/(a*e^2+c*d^2)*c/a^2/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*x","B"
584,1,1088,303,0.061000," ","int(1/(e*x+d)^3/(c*x^2+a)^(5/2),x)","\frac{35 c^{3} d^{3} e^{2} x}{2 \left(a \,e^{2}+c \,d^{2}\right)^{4} \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, a}-\frac{35 c^{2} d^{2} e^{3} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right)^{4} \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}+\frac{35 c^{2} d^{2} e^{3}}{2 \left(a \,e^{2}+c \,d^{2}\right)^{4} \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}+\frac{35 c^{3} d^{3} x}{6 \left(a \,e^{2}+c \,d^{2}\right)^{3} \left(-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}\right)^{\frac{3}{2}} a}-\frac{5 c^{2} d \,e^{2} x}{2 \left(a \,e^{2}+c \,d^{2}\right)^{3} \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, a}+\frac{35 c^{3} d^{3} x}{3 \left(a \,e^{2}+c \,d^{2}\right)^{3} \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, a^{2}}+\frac{35 c^{2} d^{2} e}{6 \left(a \,e^{2}+c \,d^{2}\right)^{3} \left(-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}\right)^{\frac{3}{2}}}+\frac{5 c \,e^{3} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right)^{3} \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}-\frac{5 c \,e^{3}}{2 \left(a \,e^{2}+c \,d^{2}\right)^{3} \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}-\frac{11 c^{2} d x}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}\right)^{\frac{3}{2}} a}-\frac{11 c^{2} d x}{\left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, a^{2}}-\frac{7 c d}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(x +\frac{d}{e}\right) \left(-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}\right)^{\frac{3}{2}}}-\frac{5 c e}{6 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}\right)^{\frac{3}{2}}}-\frac{1}{2 \left(a \,e^{2}+c \,d^{2}\right) \left(x +\frac{d}{e}\right)^{2} \left(-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}\right)^{\frac{3}{2}} e}"," ",0,"-1/2/e/(a*e^2+c*d^2)/(x+d/e)^2/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)-7/2*c*d/(a*e^2+c*d^2)^2/(x+d/e)/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)+35/6*e*c^2*d^2/(a*e^2+c*d^2)^3/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)+35/6*c^3*d^3/(a*e^2+c*d^2)^3/a/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)*x+35/3*c^3*d^3/(a*e^2+c*d^2)^3/a^2/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*x+35/2*e^3*c^2*d^2/(a*e^2+c*d^2)^4/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)+35/2*e^2*c^3*d^3/(a*e^2+c*d^2)^4/a/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*x-35/2*e^3*c^2*d^2/(a*e^2+c*d^2)^4/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))-11/2*c^2*d/(a*e^2+c*d^2)^2/a/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)*x-11*c^2*d/(a*e^2+c*d^2)^2/a^2/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*x-5/6*e/(a*e^2+c*d^2)^2*c/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(3/2)-5/2*e^3/(a*e^2+c*d^2)^3*c/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)-5/2*e^2/(a*e^2+c*d^2)^3*c^2*d/a/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*x+5/2*e^3/(a*e^2+c*d^2)^3*c/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))","B"
585,1,17,16,0.046000," ","int((x+3)/(-x^2+1)^(1/2),x)","3 \arcsin \left(x \right)-\sqrt{-x^{2}+1}"," ",0,"3*arcsin(x)-(-x^2+1)^(1/2)","A"
586,1,17,16,0.048000," ","int((x+1)/(-x^2+4)^(1/2),x)","\arcsin \left(\frac{x}{2}\right)-\sqrt{-x^{2}+4}"," ",0,"arcsin(1/2*x)-(-x^2+4)^(1/2)","A"
587,1,15,14,0.044000," ","int((x+2)/(x^2+9)^(1/2),x)","2 \arcsinh \left(\frac{x}{3}\right)+\sqrt{x^{2}+9}"," ",0,"2*arcsinh(1/3*x)+(x^2+9)^(1/2)","A"
588,1,42,44,0.049000," ","int((b*x+a)^2/(-x^2+1)^(1/2),x)","a^{2} \arcsin \left(x \right)-2 \sqrt{-x^{2}+1}\, a b +\left(-\frac{\sqrt{-x^{2}+1}\, x}{2}+\frac{\arcsin \left(x \right)}{2}\right) b^{2}"," ",0,"b^2*(-1/2*x*(-x^2+1)^(1/2)+1/2*arcsin(x))-2*a*b*(-x^2+1)^(1/2)+a^2*arcsin(x)","A"
589,1,38,42,0.052000," ","int((b*x+a)^2/(x^2+1)^(1/2),x)","a^{2} \arcsinh \left(x \right)+2 \sqrt{x^{2}+1}\, a b +\left(\frac{\sqrt{x^{2}+1}\, x}{2}-\frac{\arcsinh \left(x \right)}{2}\right) b^{2}"," ",0,"b^2*(1/2*x*(x^2+1)^(1/2)-1/2*arcsinh(x))+2*a*b*(x^2+1)^(1/2)+a^2*arcsinh(x)","A"
590,1,13,12,0.043000," ","int((3*x+2)/(x^2+4)^(3/2),x)","\frac{x -6}{2 \sqrt{x^{2}+4}}"," ",0,"1/2*(-6+x)/(x^2+4)^(1/2)","A"
591,1,41,51,0.046000," ","int((e*x+d)^(5/2)*(c*x^2+a),x)","\frac{2 \left(e x +d \right)^{\frac{7}{2}} \left(63 c \,e^{2} x^{2}-28 c d e x +99 a \,e^{2}+8 c \,d^{2}\right)}{693 e^{3}}"," ",0,"2/693*(e*x+d)^(7/2)*(63*c*e^2*x^2-28*c*d*e*x+99*a*e^2+8*c*d^2)/e^3","A"
592,1,41,51,0.048000," ","int((e*x+d)^(3/2)*(c*x^2+a),x)","\frac{2 \left(e x +d \right)^{\frac{5}{2}} \left(35 c \,e^{2} x^{2}-20 c d e x +63 a \,e^{2}+8 c \,d^{2}\right)}{315 e^{3}}"," ",0,"2/315*(e*x+d)^(5/2)*(35*c*e^2*x^2-20*c*d*e*x+63*a*e^2+8*c*d^2)/e^3","A"
593,1,41,51,0.051000," ","int((c*x^2+a)*(e*x+d)^(1/2),x)","\frac{2 \left(e x +d \right)^{\frac{3}{2}} \left(15 c \,e^{2} x^{2}-12 c d e x +35 a \,e^{2}+8 c \,d^{2}\right)}{105 e^{3}}"," ",0,"2/105*(e*x+d)^(3/2)*(15*c*e^2*x^2-12*c*d*e*x+35*a*e^2+8*c*d^2)/e^3","A"
594,1,41,51,0.046000," ","int((c*x^2+a)/(e*x+d)^(1/2),x)","\frac{2 \sqrt{e x +d}\, \left(3 c \,e^{2} x^{2}-4 c d e x +15 a \,e^{2}+8 c \,d^{2}\right)}{15 e^{3}}"," ",0,"2/15*(e*x+d)^(1/2)*(3*c*e^2*x^2-4*c*d*e*x+15*a*e^2+8*c*d^2)/e^3","A"
595,1,41,51,0.054000," ","int((c*x^2+a)/(e*x+d)^(3/2),x)","-\frac{2 \left(-c \,e^{2} x^{2}+4 c d e x +3 a \,e^{2}+8 c \,d^{2}\right)}{3 \sqrt{e x +d}\, e^{3}}"," ",0,"-2/3/(e*x+d)^(1/2)*(-c*e^2*x^2+4*c*d*e*x+3*a*e^2+8*c*d^2)/e^3","A"
596,1,40,51,0.048000," ","int((c*x^2+a)/(e*x+d)^(5/2),x)","-\frac{2 \left(-3 c \,e^{2} x^{2}-12 c d e x +a \,e^{2}-8 c \,d^{2}\right)}{3 \left(e x +d \right)^{\frac{3}{2}} e^{3}}"," ",0,"-2/3/(e*x+d)^(3/2)*(-3*c*e^2*x^2-12*c*d*e*x+a*e^2-8*c*d^2)/e^3","A"
597,1,41,51,0.040000," ","int((c*x^2+a)/(e*x+d)^(7/2),x)","-\frac{2 \left(15 c \,e^{2} x^{2}+20 c d e x +3 a \,e^{2}+8 c \,d^{2}\right)}{15 \left(e x +d \right)^{\frac{5}{2}} e^{3}}"," ",0,"-2/15/(e*x+d)^(5/2)*(15*c*e^2*x^2+20*c*d*e*x+3*a*e^2+8*c*d^2)/e^3","A"
598,1,106,107,0.046000," ","int((e*x+d)^(5/2)*(c*x^2+a)^2,x)","\frac{2 \left(e x +d \right)^{\frac{7}{2}} \left(3003 c^{2} x^{4} e^{4}-1848 c^{2} d \,x^{3} e^{3}+8190 a c \,e^{4} x^{2}+1008 c^{2} d^{2} e^{2} x^{2}-3640 a c d \,e^{3} x -448 c^{2} d^{3} e x +6435 a^{2} e^{4}+1040 a c \,d^{2} e^{2}+128 c^{2} d^{4}\right)}{45045 e^{5}}"," ",0,"2/45045*(e*x+d)^(7/2)*(3003*c^2*e^4*x^4-1848*c^2*d*e^3*x^3+8190*a*c*e^4*x^2+1008*c^2*d^2*e^2*x^2-3640*a*c*d*e^3*x-448*c^2*d^3*e*x+6435*a^2*e^4+1040*a*c*d^2*e^2+128*c^2*d^4)/e^5","A"
599,1,106,107,0.053000," ","int((e*x+d)^(3/2)*(c*x^2+a)^2,x)","\frac{2 \left(e x +d \right)^{\frac{5}{2}} \left(3465 c^{2} x^{4} e^{4}-2520 c^{2} d \,x^{3} e^{3}+10010 a c \,e^{4} x^{2}+1680 c^{2} d^{2} e^{2} x^{2}-5720 a c d \,e^{3} x -960 c^{2} d^{3} e x +9009 a^{2} e^{4}+2288 a c \,d^{2} e^{2}+384 c^{2} d^{4}\right)}{45045 e^{5}}"," ",0,"2/45045*(e*x+d)^(5/2)*(3465*c^2*e^4*x^4-2520*c^2*d*e^3*x^3+10010*a*c*e^4*x^2+1680*c^2*d^2*e^2*x^2-5720*a*c*d*e^3*x-960*c^2*d^3*e*x+9009*a^2*e^4+2288*a*c*d^2*e^2+384*c^2*d^4)/e^5","A"
600,1,106,107,0.043000," ","int((c*x^2+a)^2*(e*x+d)^(1/2),x)","\frac{2 \left(e x +d \right)^{\frac{3}{2}} \left(315 c^{2} x^{4} e^{4}-280 c^{2} d \,x^{3} e^{3}+990 a c \,e^{4} x^{2}+240 c^{2} d^{2} e^{2} x^{2}-792 a c d \,e^{3} x -192 c^{2} d^{3} e x +1155 a^{2} e^{4}+528 a c \,d^{2} e^{2}+128 c^{2} d^{4}\right)}{3465 e^{5}}"," ",0,"2/3465*(e*x+d)^(3/2)*(315*c^2*e^4*x^4-280*c^2*d*e^3*x^3+990*a*c*e^4*x^2+240*c^2*d^2*e^2*x^2-792*a*c*d*e^3*x-192*c^2*d^3*e*x+1155*a^2*e^4+528*a*c*d^2*e^2+128*c^2*d^4)/e^5","A"
601,1,106,107,0.050000," ","int((c*x^2+a)^2/(e*x+d)^(1/2),x)","\frac{2 \sqrt{e x +d}\, \left(35 c^{2} x^{4} e^{4}-40 c^{2} d \,x^{3} e^{3}+126 a c \,e^{4} x^{2}+48 c^{2} d^{2} e^{2} x^{2}-168 a c d \,e^{3} x -64 c^{2} d^{3} e x +315 a^{2} e^{4}+336 a c \,d^{2} e^{2}+128 c^{2} d^{4}\right)}{315 e^{5}}"," ",0,"2/315*(e*x+d)^(1/2)*(35*c^2*e^4*x^4-40*c^2*d*e^3*x^3+126*a*c*e^4*x^2+48*c^2*d^2*e^2*x^2-168*a*c*d*e^3*x-64*c^2*d^3*e*x+315*a^2*e^4+336*a*c*d^2*e^2+128*c^2*d^4)/e^5","A"
602,1,106,107,0.052000," ","int((c*x^2+a)^2/(e*x+d)^(3/2),x)","-\frac{2 \left(-15 c^{2} x^{4} e^{4}+24 c^{2} d \,x^{3} e^{3}-70 a c \,e^{4} x^{2}-48 c^{2} d^{2} e^{2} x^{2}+280 a c d \,e^{3} x +192 c^{2} d^{3} e x +105 a^{2} e^{4}+560 a c \,d^{2} e^{2}+384 c^{2} d^{4}\right)}{105 \sqrt{e x +d}\, e^{5}}"," ",0,"-2/105/(e*x+d)^(1/2)*(-15*c^2*e^4*x^4+24*c^2*d*e^3*x^3-70*a*c*e^4*x^2-48*c^2*d^2*e^2*x^2+280*a*c*d*e^3*x+192*c^2*d^3*e*x+105*a^2*e^4+560*a*c*d^2*e^2+384*c^2*d^4)/e^5","A"
603,1,106,107,0.049000," ","int((c*x^2+a)^2/(e*x+d)^(5/2),x)","-\frac{2 \left(-3 c^{2} x^{4} e^{4}+8 c^{2} d \,x^{3} e^{3}-30 a c \,e^{4} x^{2}-48 c^{2} d^{2} e^{2} x^{2}-120 a c d \,e^{3} x -192 c^{2} d^{3} e x +5 a^{2} e^{4}-80 a c \,d^{2} e^{2}-128 c^{2} d^{4}\right)}{15 \left(e x +d \right)^{\frac{3}{2}} e^{5}}"," ",0,"-2/15/(e*x+d)^(3/2)*(-3*c^2*e^4*x^4+8*c^2*d*e^3*x^3-30*a*c*e^4*x^2-48*c^2*d^2*e^2*x^2-120*a*c*d*e^3*x-192*c^2*d^3*e*x+5*a^2*e^4-80*a*c*d^2*e^2-128*c^2*d^4)/e^5","A"
604,1,106,107,0.050000," ","int((c*x^2+a)^2/(e*x+d)^(7/2),x)","-\frac{2 \left(-5 c^{2} x^{4} e^{4}+40 c^{2} d \,x^{3} e^{3}+30 a c \,e^{4} x^{2}+240 c^{2} d^{2} e^{2} x^{2}+40 a c d \,e^{3} x +320 c^{2} d^{3} e x +3 a^{2} e^{4}+16 a c \,d^{2} e^{2}+128 c^{2} d^{4}\right)}{15 \left(e x +d \right)^{\frac{5}{2}} e^{5}}"," ",0,"-2/15/(e*x+d)^(5/2)*(-5*c^2*e^4*x^4+40*c^2*d*e^3*x^3+30*a*c*e^4*x^2+240*c^2*d^2*e^2*x^2+40*a*c*d*e^3*x+320*c^2*d^3*e*x+3*a^2*e^4+16*a*c*d^2*e^2+128*c^2*d^4)/e^5","A"
605,1,205,176,0.049000," ","int((e*x+d)^(5/2)*(c*x^2+a)^3,x)","\frac{2 \left(e x +d \right)^{\frac{7}{2}} \left(255255 c^{3} x^{6} e^{6}-180180 c^{3} d \,e^{5} x^{5}+969969 a \,c^{2} e^{6} x^{4}+120120 c^{3} d^{2} e^{4} x^{4}-596904 a \,c^{2} d \,e^{5} x^{3}-73920 c^{3} d^{3} e^{3} x^{3}+1322685 a^{2} c \,e^{6} x^{2}+325584 a \,c^{2} d^{2} e^{4} x^{2}+40320 c^{3} d^{4} e^{2} x^{2}-587860 a^{2} c d \,e^{5} x -144704 a \,c^{2} d^{3} e^{3} x -17920 c^{3} d^{5} e x +692835 e^{6} a^{3}+167960 a^{2} c \,d^{2} e^{4}+41344 a \,c^{2} d^{4} e^{2}+5120 c^{3} d^{6}\right)}{4849845 e^{7}}"," ",0,"2/4849845*(e*x+d)^(7/2)*(255255*c^3*e^6*x^6-180180*c^3*d*e^5*x^5+969969*a*c^2*e^6*x^4+120120*c^3*d^2*e^4*x^4-596904*a*c^2*d*e^5*x^3-73920*c^3*d^3*e^3*x^3+1322685*a^2*c*e^6*x^2+325584*a*c^2*d^2*e^4*x^2+40320*c^3*d^4*e^2*x^2-587860*a^2*c*d*e^5*x-144704*a*c^2*d^3*e^3*x-17920*c^3*d^5*e*x+692835*a^3*e^6+167960*a^2*c*d^2*e^4+41344*a*c^2*d^4*e^2+5120*c^3*d^6)/e^7","A"
606,1,205,176,0.055000," ","int((e*x+d)^(3/2)*(c*x^2+a)^3,x)","\frac{2 \left(e x +d \right)^{\frac{5}{2}} \left(15015 c^{3} x^{6} e^{6}-12012 c^{3} d \,e^{5} x^{5}+58905 a \,c^{2} e^{6} x^{4}+9240 c^{3} d^{2} e^{4} x^{4}-42840 a \,c^{2} d \,e^{5} x^{3}-6720 c^{3} d^{3} e^{3} x^{3}+85085 a^{2} c \,e^{6} x^{2}+28560 a \,c^{2} d^{2} e^{4} x^{2}+4480 c^{3} d^{4} e^{2} x^{2}-48620 a^{2} c d \,e^{5} x -16320 a \,c^{2} d^{3} e^{3} x -2560 c^{3} d^{5} e x +51051 e^{6} a^{3}+19448 a^{2} c \,d^{2} e^{4}+6528 a \,c^{2} d^{4} e^{2}+1024 c^{3} d^{6}\right)}{255255 e^{7}}"," ",0,"2/255255*(e*x+d)^(5/2)*(15015*c^3*e^6*x^6-12012*c^3*d*e^5*x^5+58905*a*c^2*e^6*x^4+9240*c^3*d^2*e^4*x^4-42840*a*c^2*d*e^5*x^3-6720*c^3*d^3*e^3*x^3+85085*a^2*c*e^6*x^2+28560*a*c^2*d^2*e^4*x^2+4480*c^3*d^4*e^2*x^2-48620*a^2*c*d*e^5*x-16320*a*c^2*d^3*e^3*x-2560*c^3*d^5*e*x+51051*a^3*e^6+19448*a^2*c*d^2*e^4+6528*a*c^2*d^4*e^2+1024*c^3*d^6)/e^7","A"
607,1,205,176,0.059000," ","int((c*x^2+a)^3*(e*x+d)^(1/2),x)","\frac{2 \left(e x +d \right)^{\frac{3}{2}} \left(3003 c^{3} x^{6} e^{6}-2772 c^{3} d \,e^{5} x^{5}+12285 a \,c^{2} e^{6} x^{4}+2520 c^{3} d^{2} e^{4} x^{4}-10920 a \,c^{2} d \,e^{5} x^{3}-2240 c^{3} d^{3} e^{3} x^{3}+19305 a^{2} c \,e^{6} x^{2}+9360 a \,c^{2} d^{2} e^{4} x^{2}+1920 c^{3} d^{4} e^{2} x^{2}-15444 a^{2} c d \,e^{5} x -7488 a \,c^{2} d^{3} e^{3} x -1536 c^{3} d^{5} e x +15015 e^{6} a^{3}+10296 a^{2} c \,d^{2} e^{4}+4992 a \,c^{2} d^{4} e^{2}+1024 c^{3} d^{6}\right)}{45045 e^{7}}"," ",0,"2/45045*(e*x+d)^(3/2)*(3003*c^3*e^6*x^6-2772*c^3*d*e^5*x^5+12285*a*c^2*e^6*x^4+2520*c^3*d^2*e^4*x^4-10920*a*c^2*d*e^5*x^3-2240*c^3*d^3*e^3*x^3+19305*a^2*c*e^6*x^2+9360*a*c^2*d^2*e^4*x^2+1920*c^3*d^4*e^2*x^2-15444*a^2*c*d*e^5*x-7488*a*c^2*d^3*e^3*x-1536*c^3*d^5*e*x+15015*a^3*e^6+10296*a^2*c*d^2*e^4+4992*a*c^2*d^4*e^2+1024*c^3*d^6)/e^7","A"
608,1,205,176,0.051000," ","int((c*x^2+a)^3/(e*x+d)^(1/2),x)","\frac{2 \sqrt{e x +d}\, \left(1155 c^{3} x^{6} e^{6}-1260 c^{3} d \,e^{5} x^{5}+5005 a \,c^{2} e^{6} x^{4}+1400 c^{3} d^{2} e^{4} x^{4}-5720 a \,c^{2} d \,e^{5} x^{3}-1600 c^{3} d^{3} e^{3} x^{3}+9009 a^{2} c \,e^{6} x^{2}+6864 a \,c^{2} d^{2} e^{4} x^{2}+1920 c^{3} d^{4} e^{2} x^{2}-12012 a^{2} c d \,e^{5} x -9152 a \,c^{2} d^{3} e^{3} x -2560 c^{3} d^{5} e x +15015 e^{6} a^{3}+24024 a^{2} c \,d^{2} e^{4}+18304 a \,c^{2} d^{4} e^{2}+5120 c^{3} d^{6}\right)}{15015 e^{7}}"," ",0,"2/15015*(e*x+d)^(1/2)*(1155*c^3*e^6*x^6-1260*c^3*d*e^5*x^5+5005*a*c^2*e^6*x^4+1400*c^3*d^2*e^4*x^4-5720*a*c^2*d*e^5*x^3-1600*c^3*d^3*e^3*x^3+9009*a^2*c*e^6*x^2+6864*a*c^2*d^2*e^4*x^2+1920*c^3*d^4*e^2*x^2-12012*a^2*c*d*e^5*x-9152*a*c^2*d^3*e^3*x-2560*c^3*d^5*e*x+15015*a^3*e^6+24024*a^2*c*d^2*e^4+18304*a*c^2*d^4*e^2+5120*c^3*d^6)/e^7","A"
609,1,205,176,0.050000," ","int((c*x^2+a)^3/(e*x+d)^(3/2),x)","-\frac{2 \left(-105 c^{3} x^{6} e^{6}+140 c^{3} d \,e^{5} x^{5}-495 a \,c^{2} e^{6} x^{4}-200 c^{3} d^{2} e^{4} x^{4}+792 a \,c^{2} d \,e^{5} x^{3}+320 c^{3} d^{3} e^{3} x^{3}-1155 a^{2} c \,e^{6} x^{2}-1584 a \,c^{2} d^{2} e^{4} x^{2}-640 c^{3} d^{4} e^{2} x^{2}+4620 a^{2} c d \,e^{5} x +6336 a \,c^{2} d^{3} e^{3} x +2560 c^{3} d^{5} e x +1155 e^{6} a^{3}+9240 a^{2} c \,d^{2} e^{4}+12672 a \,c^{2} d^{4} e^{2}+5120 c^{3} d^{6}\right)}{1155 \sqrt{e x +d}\, e^{7}}"," ",0,"-2/1155/(e*x+d)^(1/2)*(-105*c^3*e^6*x^6+140*c^3*d*e^5*x^5-495*a*c^2*e^6*x^4-200*c^3*d^2*e^4*x^4+792*a*c^2*d*e^5*x^3+320*c^3*d^3*e^3*x^3-1155*a^2*c*e^6*x^2-1584*a*c^2*d^2*e^4*x^2-640*c^3*d^4*e^2*x^2+4620*a^2*c*d*e^5*x+6336*a*c^2*d^3*e^3*x+2560*c^3*d^5*e*x+1155*a^3*e^6+9240*a^2*c*d^2*e^4+12672*a*c^2*d^4*e^2+5120*c^3*d^6)/e^7","A"
610,1,205,176,0.048000," ","int((c*x^2+a)^3/(e*x+d)^(5/2),x)","-\frac{2 \left(-35 c^{3} x^{6} e^{6}+60 c^{3} d \,e^{5} x^{5}-189 a \,c^{2} e^{6} x^{4}-120 c^{3} d^{2} e^{4} x^{4}+504 a \,c^{2} d \,e^{5} x^{3}+320 c^{3} d^{3} e^{3} x^{3}-945 a^{2} c \,e^{6} x^{2}-3024 a \,c^{2} d^{2} e^{4} x^{2}-1920 c^{3} d^{4} e^{2} x^{2}-3780 a^{2} c d \,e^{5} x -12096 a \,c^{2} d^{3} e^{3} x -7680 c^{3} d^{5} e x +105 e^{6} a^{3}-2520 a^{2} c \,d^{2} e^{4}-8064 a \,c^{2} d^{4} e^{2}-5120 c^{3} d^{6}\right)}{315 \left(e x +d \right)^{\frac{3}{2}} e^{7}}"," ",0,"-2/315/(e*x+d)^(3/2)*(-35*c^3*e^6*x^6+60*c^3*d*e^5*x^5-189*a*c^2*e^6*x^4-120*c^3*d^2*e^4*x^4+504*a*c^2*d*e^5*x^3+320*c^3*d^3*e^3*x^3-945*a^2*c*e^6*x^2-3024*a*c^2*d^2*e^4*x^2-1920*c^3*d^4*e^2*x^2-3780*a^2*c*d*e^5*x-12096*a*c^2*d^3*e^3*x-7680*c^3*d^5*e*x+105*a^3*e^6-2520*a^2*c*d^2*e^4-8064*a*c^2*d^4*e^2-5120*c^3*d^6)/e^7","A"
611,1,205,176,0.056000," ","int((c*x^2+a)^3/(e*x+d)^(7/2),x)","-\frac{2 \left(-5 c^{3} x^{6} e^{6}+12 c^{3} d \,e^{5} x^{5}-35 a \,c^{2} e^{6} x^{4}-40 c^{3} d^{2} e^{4} x^{4}+280 a \,c^{2} d \,e^{5} x^{3}+320 c^{3} d^{3} e^{3} x^{3}+105 a^{2} c \,e^{6} x^{2}+1680 a \,c^{2} d^{2} e^{4} x^{2}+1920 c^{3} d^{4} e^{2} x^{2}+140 a^{2} c d \,e^{5} x +2240 a \,c^{2} d^{3} e^{3} x +2560 c^{3} d^{5} e x +7 e^{6} a^{3}+56 a^{2} c \,d^{2} e^{4}+896 a \,c^{2} d^{4} e^{2}+1024 c^{3} d^{6}\right)}{35 \left(e x +d \right)^{\frac{5}{2}} e^{7}}"," ",0,"-2/35/(e*x+d)^(5/2)*(-5*c^3*e^6*x^6+12*c^3*d*e^5*x^5-35*a*c^2*e^6*x^4-40*c^3*d^2*e^4*x^4+280*a*c^2*d*e^5*x^3+320*c^3*d^3*e^3*x^3+105*a^2*c*e^6*x^2+1680*a*c^2*d^2*e^4*x^2+1920*c^3*d^4*e^2*x^2+140*a^2*c*d*e^5*x+2240*a*c^2*d^3*e^3*x+2560*c^3*d^5*e*x+7*a^3*e^6+56*a^2*c*d^2*e^4+896*a*c^2*d^4*e^2+1024*c^3*d^6)/e^7","A"
612,1,460,121,0.148000," ","int((e*x+d)^(5/2)/(-c*x^2+a),x)","\frac{3 a d \,e^{3} \arctanh \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{\sqrt{a c \,e^{2}}\, \sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}+\frac{3 a d \,e^{3} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{\sqrt{a c \,e^{2}}\, \sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}+\frac{c \,d^{3} e \arctanh \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{\sqrt{a c \,e^{2}}\, \sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}+\frac{c \,d^{3} e \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{\sqrt{a c \,e^{2}}\, \sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}+\frac{a \,e^{3} \arctanh \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}\, c}-\frac{a \,e^{3} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}\, c}+\frac{3 d^{2} e \arctanh \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}-\frac{3 d^{2} e \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}-\frac{4 \sqrt{e x +d}\, d e}{c}-\frac{2 \left(e x +d \right)^{\frac{3}{2}} e}{3 c}"," ",0,"-2/3*(e*x+d)^(3/2)/c*e-4*(e*x+d)^(1/2)/c*d*e+3/(a*c*e^2)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctanh(c*(e*x+d)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2))*a*d*e^3+e*c/(a*c*e^2)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctanh(c*(e*x+d)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2))*d^3+1/c/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctanh(c*(e*x+d)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2))*a*e^3+3*e/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctanh(c*(e*x+d)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2))*d^2+3/(a*c*e^2)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctan(c*(e*x+d)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2))*a*d*e^3+e*c/(a*c*e^2)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctan(c*(e*x+d)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2))*d^3-1/c/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctan(c*(e*x+d)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2))*a*e^3-3*e/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctan(c*(e*x+d)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2))*d^2","B"
613,1,335,107,0.072000," ","int((e*x+d)^(3/2)/(-c*x^2+a),x)","\frac{a \,e^{3} \arctanh \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{\sqrt{a c \,e^{2}}\, \sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}+\frac{a \,e^{3} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{\sqrt{a c \,e^{2}}\, \sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}+\frac{c \,d^{2} e \arctanh \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{\sqrt{a c \,e^{2}}\, \sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}+\frac{c \,d^{2} e \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{\sqrt{a c \,e^{2}}\, \sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}+\frac{2 d e \arctanh \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}-\frac{2 d e \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}-\frac{2 \sqrt{e x +d}\, e}{c}"," ",0,"-2*(e*x+d)^(1/2)/c*e+1/(a*c*e^2)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*a*e^3+e/(a*c*e^2)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*c*d^2+2*e/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d+1/(a*c*e^2)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*a*e^3+e/(a*c*e^2)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*c*d^2-2*e/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d","B"
614,1,203,94,0.066000," ","int((e*x+d)^(1/2)/(-c*x^2+a),x)","\frac{c d e \arctanh \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{\sqrt{a c \,e^{2}}\, \sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}+\frac{c d e \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{\sqrt{a c \,e^{2}}\, \sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}+\frac{e \arctanh \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}-\frac{e \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}"," ",0,"c*e/(a*c*e^2)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d+e/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)+c*e/(a*c*e^2)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d-e/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)","B"
615,1,110,94,0.080000," ","int(1/(-c*x^2+a)/(e*x+d)^(1/2),x)","\frac{c e \arctanh \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{\sqrt{a c \,e^{2}}\, \sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}+\frac{c e \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{\sqrt{a c \,e^{2}}\, \sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}"," ",0,"c*e/(a*c*e^2)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)+c*e/(a*c*e^2)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)","A"
616,1,291,118,0.071000," ","int(1/(e*x+d)^(3/2)/(-c*x^2+a),x)","-\frac{c^{2} d e \arctanh \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{\left(a \,e^{2}-c \,d^{2}\right) \sqrt{a c \,e^{2}}\, \sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}-\frac{c^{2} d e \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{\left(a \,e^{2}-c \,d^{2}\right) \sqrt{a c \,e^{2}}\, \sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}+\frac{c e \arctanh \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{\left(a \,e^{2}-c \,d^{2}\right) \sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}-\frac{c e \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{\left(a \,e^{2}-c \,d^{2}\right) \sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}-\frac{2 e}{\left(a \,e^{2}-c \,d^{2}\right) \sqrt{e x +d}}"," ",0,"-2*e/(a*e^2-c*d^2)/(e*x+d)^(1/2)-e*c^2/(a*e^2-c*d^2)/(a*c*e^2)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d+e*c/(a*e^2-c*d^2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)-e*c^2/(a*e^2-c*d^2)/(a*c*e^2)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d-e*c/(a*e^2-c*d^2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)","B"
617,1,472,144,0.074000," ","int(1/(e*x+d)^(5/2)/(-c*x^2+a),x)","\frac{a \,c^{2} e^{3} \arctanh \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{\left(a \,e^{2}-c \,d^{2}\right)^{2} \sqrt{a c \,e^{2}}\, \sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}+\frac{a \,c^{2} e^{3} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{\left(a \,e^{2}-c \,d^{2}\right)^{2} \sqrt{a c \,e^{2}}\, \sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}+\frac{c^{3} d^{2} e \arctanh \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{\left(a \,e^{2}-c \,d^{2}\right)^{2} \sqrt{a c \,e^{2}}\, \sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}+\frac{c^{3} d^{2} e \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{\left(a \,e^{2}-c \,d^{2}\right)^{2} \sqrt{a c \,e^{2}}\, \sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}-\frac{2 c^{2} d e \arctanh \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{\left(a \,e^{2}-c \,d^{2}\right)^{2} \sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}+\frac{2 c^{2} d e \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{\left(a \,e^{2}-c \,d^{2}\right)^{2} \sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}+\frac{4 c d e}{\left(a \,e^{2}-c \,d^{2}\right)^{2} \sqrt{e x +d}}-\frac{2 e}{3 \left(a \,e^{2}-c \,d^{2}\right) \left(e x +d \right)^{\frac{3}{2}}}"," ",0,"c^2/(a*e^2-c*d^2)^2/(a*c*e^2)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*a*e^3+e*c^3/(a*e^2-c*d^2)^2/(a*c*e^2)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d^2-2*e*c^2/(a*e^2-c*d^2)^2/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d+c^2/(a*e^2-c*d^2)^2/(a*c*e^2)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*a*e^3+e*c^3/(a*e^2-c*d^2)^2/(a*c*e^2)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d^2+2*e*c^2/(a*e^2-c*d^2)^2/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d-2/3*e/(a*e^2-c*d^2)/(e*x+d)^(3/2)+4*e*c*d/(a*e^2-c*d^2)^2/(e*x+d)^(1/2)","B"
618,1,3931,632,0.390000," ","int((e*x+d)^(5/2)/(c*x^2+a),x)","\text{output too large to display}"," ",0,"-3/2/c^(3/2)/a/e/(4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*(c*(a*e^2+c*d^2))^(1/2)-2*c*d)^(1/2)*arctan((-2*c^(1/2)*(e*x+d)^(1/2)+(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2))/(4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*(c*(a*e^2+c*d^2))^(1/2)-2*c*d)^(1/2))*(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2)*(2*(a*c*e^2+c^2*d^2)^(1/2)+2*c*d)^(1/2)*(a*c*e^2+c^2*d^2)^(1/2)*d^2-1/c/a/e/(4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*(c*(a*e^2+c*d^2))^(1/2)-2*c*d)^(1/2)*arctan((2*c^(1/2)*(e*x+d)^(1/2)+(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2))/(4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*(c*(a*e^2+c*d^2))^(1/2)-2*c*d)^(1/2))*(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2)*(2*(a*c*e^2+c^2*d^2)^(1/2)+2*c*d)^(1/2)*(a*e^2+c*d^2)^(1/2)*d^2+1/c/a/e/(4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*(c*(a*e^2+c*d^2))^(1/2)-2*c*d)^(1/2)*arctan((-2*c^(1/2)*(e*x+d)^(1/2)+(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2))/(4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*(c*(a*e^2+c*d^2))^(1/2)-2*c*d)^(1/2))*(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2)*(2*(a*c*e^2+c^2*d^2)^(1/2)+2*c*d)^(1/2)*(a*e^2+c*d^2)^(1/2)*d^2+3/2/c^(3/2)/a/e/(4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*(c*(a*e^2+c*d^2))^(1/2)-2*c*d)^(1/2)*arctan((2*c^(1/2)*(e*x+d)^(1/2)+(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2))/(4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*(c*(a*e^2+c*d^2))^(1/2)-2*c*d)^(1/2))*(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2)*(2*(a*c*e^2+c^2*d^2)^(1/2)+2*c*d)^(1/2)*(a*c*e^2+c^2*d^2)^(1/2)*d^2+1/c^2/a/e/(4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*(c*(a*e^2+c*d^2))^(1/2)-2*c*d)^(1/2)*arctan((2*c^(1/2)*(e*x+d)^(1/2)+(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2))/(4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*(c*(a*e^2+c*d^2))^(1/2)-2*c*d)^(1/2))*(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2)*(2*(a*c*e^2+c^2*d^2)^(1/2)+2*c*d)^(1/2)*(a*e^2+c*d^2)^(1/2)*(a*c*e^2+c^2*d^2)^(1/2)*d-1/c^2/a/e/(4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*(c*(a*e^2+c*d^2))^(1/2)-2*c*d)^(1/2)*arctan((-2*c^(1/2)*(e*x+d)^(1/2)+(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2))/(4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*(c*(a*e^2+c*d^2))^(1/2)-2*c*d)^(1/2))*(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2)*(2*(a*c*e^2+c^2*d^2)^(1/2)+2*c*d)^(1/2)*(a*e^2+c*d^2)^(1/2)*(a*c*e^2+c^2*d^2)^(1/2)*d-3/2/c^(1/2)/a/e/(4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*(c*(a*e^2+c*d^2))^(1/2)-2*c*d)^(1/2)*arctan((2*c^(1/2)*(e*x+d)^(1/2)+(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2))/(4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*(c*(a*e^2+c*d^2))^(1/2)-2*c*d)^(1/2))*(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2)*(2*(a*c*e^2+c^2*d^2)^(1/2)+2*c*d)^(1/2)*d^3+3/2/c^(1/2)/a/e/(4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*(c*(a*e^2+c*d^2))^(1/2)-2*c*d)^(1/2)*arctan((-2*c^(1/2)*(e*x+d)^(1/2)+(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2))/(4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*(c*(a*e^2+c*d^2))^(1/2)-2*c*d)^(1/2))*(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2)*(2*(a*c*e^2+c^2*d^2)^(1/2)+2*c*d)^(1/2)*d^3-1/2/c^2/a/e*ln((e*x+d)*c^(1/2)+(e*x+d)^(1/2)*(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2)+(a*e^2+c*d^2)^(1/2))*(2*(a*c*e^2+c^2*d^2)^(1/2)+2*c*d)^(1/2)*(a*e^2+c*d^2)^(1/2)*(a*c*e^2+c^2*d^2)^(1/2)*d+1/2/c^2/a/e*ln(-(e*x+d)*c^(1/2)+(e*x+d)^(1/2)*(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2)-(a*e^2+c*d^2)^(1/2))*(2*(a*c*e^2+c^2*d^2)^(1/2)+2*c*d)^(1/2)*(a*e^2+c*d^2)^(1/2)*(a*c*e^2+c^2*d^2)^(1/2)*d+1/2/c/a/e*ln((e*x+d)*c^(1/2)+(e*x+d)^(1/2)*(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2)+(a*e^2+c*d^2)^(1/2))*(2*(a*c*e^2+c^2*d^2)^(1/2)+2*c*d)^(1/2)*(a*e^2+c*d^2)^(1/2)*d^2-1/2/c/a/e*ln(-(e*x+d)*c^(1/2)+(e*x+d)^(1/2)*(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2)-(a*e^2+c*d^2)^(1/2))*(2*(a*c*e^2+c^2*d^2)^(1/2)+2*c*d)^(1/2)*(a*e^2+c*d^2)^(1/2)*d^2+1/2*e/c^(3/2)/(4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*(c*(a*e^2+c*d^2))^(1/2)-2*c*d)^(1/2)*arctan((2*c^(1/2)*(e*x+d)^(1/2)+(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2))/(4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*(c*(a*e^2+c*d^2))^(1/2)-2*c*d)^(1/2))*(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2)*(2*(a*c*e^2+c^2*d^2)^(1/2)+2*c*d)^(1/2)*d-1/2*e/c^(5/2)/(4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*(c*(a*e^2+c*d^2))^(1/2)-2*c*d)^(1/2)*arctan((2*c^(1/2)*(e*x+d)^(1/2)+(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2))/(4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*(c*(a*e^2+c*d^2))^(1/2)-2*c*d)^(1/2))*(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2)*(2*(a*c*e^2+c^2*d^2)^(1/2)+2*c*d)^(1/2)*(a*c*e^2+c^2*d^2)^(1/2)-1/2*e/c^(3/2)/(4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*(c*(a*e^2+c*d^2))^(1/2)-2*c*d)^(1/2)*arctan((-2*c^(1/2)*(e*x+d)^(1/2)+(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2))/(4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*(c*(a*e^2+c*d^2))^(1/2)-2*c*d)^(1/2))*(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2)*(2*(a*c*e^2+c^2*d^2)^(1/2)+2*c*d)^(1/2)*d+1/2*e/c^(5/2)/(4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*(c*(a*e^2+c*d^2))^(1/2)-2*c*d)^(1/2)*arctan((-2*c^(1/2)*(e*x+d)^(1/2)+(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2))/(4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*(c*(a*e^2+c*d^2))^(1/2)-2*c*d)^(1/2))*(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2)*(2*(a*c*e^2+c^2*d^2)^(1/2)+2*c*d)^(1/2)*(a*c*e^2+c^2*d^2)^(1/2)+2/3*(e*x+d)^(3/2)/c*e-1/4*e/c^(5/2)*ln(-(e*x+d)*c^(1/2)+(e*x+d)^(1/2)*(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2)-(a*e^2+c*d^2)^(1/2))*(2*(a*c*e^2+c^2*d^2)^(1/2)+2*c*d)^(1/2)*(a*c*e^2+c^2*d^2)^(1/2)-1/4*e/c^(3/2)*ln((e*x+d)*c^(1/2)+(e*x+d)^(1/2)*(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2)+(a*e^2+c*d^2)^(1/2))*(2*(a*c*e^2+c^2*d^2)^(1/2)+2*c*d)^(1/2)*d+1/4*e/c^(5/2)*ln((e*x+d)*c^(1/2)+(e*x+d)^(1/2)*(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2)+(a*e^2+c*d^2)^(1/2))*(2*(a*c*e^2+c^2*d^2)^(1/2)+2*c*d)^(1/2)*(a*c*e^2+c^2*d^2)^(1/2)+1/4*e/c^(3/2)*ln(-(e*x+d)*c^(1/2)+(e*x+d)^(1/2)*(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2)-(a*e^2+c*d^2)^(1/2))*(2*(a*c*e^2+c^2*d^2)^(1/2)+2*c*d)^(1/2)*d-3/4/c^(3/2)/a/e*ln((e*x+d)*c^(1/2)+(e*x+d)^(1/2)*(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2)+(a*e^2+c*d^2)^(1/2))*(2*(a*c*e^2+c^2*d^2)^(1/2)+2*c*d)^(1/2)*(a*c*e^2+c^2*d^2)^(1/2)*d^2+3/4/c^(3/2)/a/e*ln(-(e*x+d)*c^(1/2)+(e*x+d)^(1/2)*(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2)-(a*e^2+c*d^2)^(1/2))*(2*(a*c*e^2+c^2*d^2)^(1/2)+2*c*d)^(1/2)*(a*c*e^2+c^2*d^2)^(1/2)*d^2-3/4/c^(1/2)/a/e*ln(-(e*x+d)*c^(1/2)+(e*x+d)^(1/2)*(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2)-(a*e^2+c*d^2)^(1/2))*(2*(a*c*e^2+c^2*d^2)^(1/2)+2*c*d)^(1/2)*d^3+4*e/c/(4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*(c*(a*e^2+c*d^2))^(1/2)-2*c*d)^(1/2)*arctan((-2*c^(1/2)*(e*x+d)^(1/2)+(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2))/(4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*(c*(a*e^2+c*d^2))^(1/2)-2*c*d)^(1/2))*(a*e^2+c*d^2)^(1/2)*d-4*e/c/(4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*(c*(a*e^2+c*d^2))^(1/2)-2*c*d)^(1/2)*arctan((2*c^(1/2)*(e*x+d)^(1/2)+(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2))/(4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*(c*(a*e^2+c*d^2))^(1/2)-2*c*d)^(1/2))*(a*e^2+c*d^2)^(1/2)*d+3/4/c^(1/2)/a/e*ln((e*x+d)*c^(1/2)+(e*x+d)^(1/2)*(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2)+(a*e^2+c*d^2)^(1/2))*(2*(a*c*e^2+c^2*d^2)^(1/2)+2*c*d)^(1/2)*d^3+4*(e*x+d)^(1/2)/c*d*e","B"
619,1,2763,552,0.183000," ","int((e*x+d)^(3/2)/(c*x^2+a),x)","-\frac{2 \sqrt{a \,e^{2}+c \,d^{2}}\, e \arctan \left(\frac{2 \sqrt{e x +d}\, \sqrt{c}-\sqrt{2 c d +2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}}{\sqrt{-2 c d +4 \sqrt{a \,e^{2}+c \,d^{2}}\, \sqrt{c}-2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}}\right)}{\sqrt{-2 c d +4 \sqrt{a \,e^{2}+c \,d^{2}}\, \sqrt{c}-2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}\, c}-\frac{2 \sqrt{a \,e^{2}+c \,d^{2}}\, e \arctan \left(\frac{2 \sqrt{e x +d}\, \sqrt{c}+\sqrt{2 c d +2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}}{\sqrt{-2 c d +4 \sqrt{a \,e^{2}+c \,d^{2}}\, \sqrt{c}-2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}}\right)}{\sqrt{-2 c d +4 \sqrt{a \,e^{2}+c \,d^{2}}\, \sqrt{c}-2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}\, c}-\frac{\sqrt{2 c d +2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}\, \sqrt{2 c d +2 \sqrt{a c \,e^{2}+c^{2} d^{2}}}\, d^{2} \arctan \left(\frac{2 \sqrt{e x +d}\, \sqrt{c}-\sqrt{2 c d +2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}}{\sqrt{-2 c d +4 \sqrt{a \,e^{2}+c \,d^{2}}\, \sqrt{c}-2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}}\right)}{\sqrt{-2 c d +4 \sqrt{a \,e^{2}+c \,d^{2}}\, \sqrt{c}-2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}\, a \sqrt{c}\, e}-\frac{\sqrt{2 c d +2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}\, \sqrt{2 c d +2 \sqrt{a c \,e^{2}+c^{2} d^{2}}}\, d^{2} \arctan \left(\frac{2 \sqrt{e x +d}\, \sqrt{c}+\sqrt{2 c d +2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}}{\sqrt{-2 c d +4 \sqrt{a \,e^{2}+c \,d^{2}}\, \sqrt{c}-2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}}\right)}{\sqrt{-2 c d +4 \sqrt{a \,e^{2}+c \,d^{2}}\, \sqrt{c}-2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}\, a \sqrt{c}\, e}-\frac{\sqrt{2 c d +2 \sqrt{a c \,e^{2}+c^{2} d^{2}}}\, d^{2} \ln \left(\left(e x +d \right) \sqrt{c}-\sqrt{e x +d}\, \sqrt{2 c d +2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}+\sqrt{a \,e^{2}+c \,d^{2}}\right)}{2 a \sqrt{c}\, e}+\frac{\sqrt{2 c d +2 \sqrt{a c \,e^{2}+c^{2} d^{2}}}\, d^{2} \ln \left(\left(e x +d \right) \sqrt{c}+\sqrt{e x +d}\, \sqrt{2 c d +2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}+\sqrt{a \,e^{2}+c \,d^{2}}\right)}{2 a \sqrt{c}\, e}+\frac{2 \sqrt{e x +d}\, e}{c}-\frac{\sqrt{2 c d +2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}\, \sqrt{a \,e^{2}+c \,d^{2}}\, \sqrt{2 c d +2 \sqrt{a c \,e^{2}+c^{2} d^{2}}}\, d \arctan \left(\frac{2 \sqrt{e x +d}\, \sqrt{c}-\sqrt{2 c d +2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}}{\sqrt{-2 c d +4 \sqrt{a \,e^{2}+c \,d^{2}}\, \sqrt{c}-2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}}\right)}{2 \sqrt{-2 c d +4 \sqrt{a \,e^{2}+c \,d^{2}}\, \sqrt{c}-2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}\, a c e}-\frac{\sqrt{2 c d +2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}\, \sqrt{a \,e^{2}+c \,d^{2}}\, \sqrt{2 c d +2 \sqrt{a c \,e^{2}+c^{2} d^{2}}}\, d \arctan \left(\frac{2 \sqrt{e x +d}\, \sqrt{c}+\sqrt{2 c d +2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}}{\sqrt{-2 c d +4 \sqrt{a \,e^{2}+c \,d^{2}}\, \sqrt{c}-2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}}\right)}{2 \sqrt{-2 c d +4 \sqrt{a \,e^{2}+c \,d^{2}}\, \sqrt{c}-2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}\, a c e}-\frac{\sqrt{a \,e^{2}+c \,d^{2}}\, \sqrt{2 c d +2 \sqrt{a c \,e^{2}+c^{2} d^{2}}}\, d \ln \left(\left(e x +d \right) \sqrt{c}-\sqrt{e x +d}\, \sqrt{2 c d +2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}+\sqrt{a \,e^{2}+c \,d^{2}}\right)}{4 a c e}+\frac{\sqrt{a \,e^{2}+c \,d^{2}}\, \sqrt{2 c d +2 \sqrt{a c \,e^{2}+c^{2} d^{2}}}\, d \ln \left(\left(e x +d \right) \sqrt{c}+\sqrt{e x +d}\, \sqrt{2 c d +2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}+\sqrt{a \,e^{2}+c \,d^{2}}\right)}{4 a c e}+\frac{\sqrt{2 c d +2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}\, \sqrt{2 c d +2 \sqrt{a c \,e^{2}+c^{2} d^{2}}}\, \sqrt{a c \,e^{2}+c^{2} d^{2}}\, d \arctan \left(\frac{2 \sqrt{e x +d}\, \sqrt{c}-\sqrt{2 c d +2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}}{\sqrt{-2 c d +4 \sqrt{a \,e^{2}+c \,d^{2}}\, \sqrt{c}-2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}}\right)}{\sqrt{-2 c d +4 \sqrt{a \,e^{2}+c \,d^{2}}\, \sqrt{c}-2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}\, a \,c^{\frac{3}{2}} e}+\frac{\sqrt{2 c d +2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}\, \sqrt{2 c d +2 \sqrt{a c \,e^{2}+c^{2} d^{2}}}\, \sqrt{a c \,e^{2}+c^{2} d^{2}}\, d \arctan \left(\frac{2 \sqrt{e x +d}\, \sqrt{c}+\sqrt{2 c d +2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}}{\sqrt{-2 c d +4 \sqrt{a \,e^{2}+c \,d^{2}}\, \sqrt{c}-2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}}\right)}{\sqrt{-2 c d +4 \sqrt{a \,e^{2}+c \,d^{2}}\, \sqrt{c}-2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}\, a \,c^{\frac{3}{2}} e}+\frac{\sqrt{2 c d +2 \sqrt{a c \,e^{2}+c^{2} d^{2}}}\, \sqrt{a c \,e^{2}+c^{2} d^{2}}\, d \ln \left(\left(e x +d \right) \sqrt{c}-\sqrt{e x +d}\, \sqrt{2 c d +2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}+\sqrt{a \,e^{2}+c \,d^{2}}\right)}{2 a \,c^{\frac{3}{2}} e}-\frac{\sqrt{2 c d +2 \sqrt{a c \,e^{2}+c^{2} d^{2}}}\, \sqrt{a c \,e^{2}+c^{2} d^{2}}\, d \ln \left(\left(e x +d \right) \sqrt{c}+\sqrt{e x +d}\, \sqrt{2 c d +2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}+\sqrt{a \,e^{2}+c \,d^{2}}\right)}{2 a \,c^{\frac{3}{2}} e}+\frac{\sqrt{2 c d +2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}\, \sqrt{a \,e^{2}+c \,d^{2}}\, \sqrt{2 c d +2 \sqrt{a c \,e^{2}+c^{2} d^{2}}}\, \sqrt{a c \,e^{2}+c^{2} d^{2}}\, \arctan \left(\frac{2 \sqrt{e x +d}\, \sqrt{c}-\sqrt{2 c d +2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}}{\sqrt{-2 c d +4 \sqrt{a \,e^{2}+c \,d^{2}}\, \sqrt{c}-2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}}\right)}{2 \sqrt{-2 c d +4 \sqrt{a \,e^{2}+c \,d^{2}}\, \sqrt{c}-2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}\, a \,c^{2} e}+\frac{\sqrt{2 c d +2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}\, \sqrt{a \,e^{2}+c \,d^{2}}\, \sqrt{2 c d +2 \sqrt{a c \,e^{2}+c^{2} d^{2}}}\, \sqrt{a c \,e^{2}+c^{2} d^{2}}\, \arctan \left(\frac{2 \sqrt{e x +d}\, \sqrt{c}+\sqrt{2 c d +2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}}{\sqrt{-2 c d +4 \sqrt{a \,e^{2}+c \,d^{2}}\, \sqrt{c}-2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}}\right)}{2 \sqrt{-2 c d +4 \sqrt{a \,e^{2}+c \,d^{2}}\, \sqrt{c}-2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}\, a \,c^{2} e}+\frac{\sqrt{a \,e^{2}+c \,d^{2}}\, \sqrt{2 c d +2 \sqrt{a c \,e^{2}+c^{2} d^{2}}}\, \sqrt{a c \,e^{2}+c^{2} d^{2}}\, \ln \left(\left(e x +d \right) \sqrt{c}-\sqrt{e x +d}\, \sqrt{2 c d +2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}+\sqrt{a \,e^{2}+c \,d^{2}}\right)}{4 a \,c^{2} e}-\frac{\sqrt{a \,e^{2}+c \,d^{2}}\, \sqrt{2 c d +2 \sqrt{a c \,e^{2}+c^{2} d^{2}}}\, \sqrt{a c \,e^{2}+c^{2} d^{2}}\, \ln \left(\left(e x +d \right) \sqrt{c}+\sqrt{e x +d}\, \sqrt{2 c d +2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}+\sqrt{a \,e^{2}+c \,d^{2}}\right)}{4 a \,c^{2} e}"," ",0,"2*(e*x+d)^(1/2)/c*e-1/4/c/a/e*ln((e*x+d)*c^(1/2)-(e*x+d)^(1/2)*(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2)+(a*e^2+c*d^2)^(1/2))*(a*e^2+c*d^2)^(1/2)*(2*(a*c*e^2+c^2*d^2)^(1/2)+2*c*d)^(1/2)*d-1/2/c^(1/2)/a/e*ln((e*x+d)*c^(1/2)-(e*x+d)^(1/2)*(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2)+(a*e^2+c*d^2)^(1/2))*(2*(a*c*e^2+c^2*d^2)^(1/2)+2*c*d)^(1/2)*d^2+1/4/c^2/a/e*ln((e*x+d)*c^(1/2)-(e*x+d)^(1/2)*(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2)+(a*e^2+c*d^2)^(1/2))*(a*e^2+c*d^2)^(1/2)*(2*(a*c*e^2+c^2*d^2)^(1/2)+2*c*d)^(1/2)*(a*c*e^2+c^2*d^2)^(1/2)+1/2/c^(3/2)/a/e*ln((e*x+d)*c^(1/2)-(e*x+d)^(1/2)*(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2)+(a*e^2+c*d^2)^(1/2))*(2*(a*c*e^2+c^2*d^2)^(1/2)+2*c*d)^(1/2)*(a*c*e^2+c^2*d^2)^(1/2)*d-2*e/c/(4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*(c*(a*e^2+c*d^2))^(1/2)-2*c*d)^(1/2)*arctan((2*c^(1/2)*(e*x+d)^(1/2)-(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2))/(4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*(c*(a*e^2+c*d^2))^(1/2)-2*c*d)^(1/2))*(a*e^2+c*d^2)^(1/2)-1/2/c/a/e/(4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*(c*(a*e^2+c*d^2))^(1/2)-2*c*d)^(1/2)*arctan((2*c^(1/2)*(e*x+d)^(1/2)-(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2))/(4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*(c*(a*e^2+c*d^2))^(1/2)-2*c*d)^(1/2))*(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2)*(a*e^2+c*d^2)^(1/2)*(2*(a*c*e^2+c^2*d^2)^(1/2)+2*c*d)^(1/2)*d-1/c^(1/2)/a/e/(4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*(c*(a*e^2+c*d^2))^(1/2)-2*c*d)^(1/2)*arctan((2*c^(1/2)*(e*x+d)^(1/2)-(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2))/(4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*(c*(a*e^2+c*d^2))^(1/2)-2*c*d)^(1/2))*(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2)*(2*(a*c*e^2+c^2*d^2)^(1/2)+2*c*d)^(1/2)*d^2+1/2/c^2/a/e/(4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*(c*(a*e^2+c*d^2))^(1/2)-2*c*d)^(1/2)*arctan((2*c^(1/2)*(e*x+d)^(1/2)-(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2))/(4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*(c*(a*e^2+c*d^2))^(1/2)-2*c*d)^(1/2))*(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2)*(a*e^2+c*d^2)^(1/2)*(2*(a*c*e^2+c^2*d^2)^(1/2)+2*c*d)^(1/2)*(a*c*e^2+c^2*d^2)^(1/2)+1/c^(3/2)/a/e/(4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*(c*(a*e^2+c*d^2))^(1/2)-2*c*d)^(1/2)*arctan((2*c^(1/2)*(e*x+d)^(1/2)-(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2))/(4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*(c*(a*e^2+c*d^2))^(1/2)-2*c*d)^(1/2))*(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2)*(2*(a*c*e^2+c^2*d^2)^(1/2)+2*c*d)^(1/2)*(a*c*e^2+c^2*d^2)^(1/2)*d+1/4/c/a/e*ln((e*x+d)*c^(1/2)+(e*x+d)^(1/2)*(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2)+(a*e^2+c*d^2)^(1/2))*(a*e^2+c*d^2)^(1/2)*(2*(a*c*e^2+c^2*d^2)^(1/2)+2*c*d)^(1/2)*d+1/2/c^(1/2)/a/e*ln((e*x+d)*c^(1/2)+(e*x+d)^(1/2)*(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2)+(a*e^2+c*d^2)^(1/2))*(2*(a*c*e^2+c^2*d^2)^(1/2)+2*c*d)^(1/2)*d^2-1/4/c^2/a/e*ln((e*x+d)*c^(1/2)+(e*x+d)^(1/2)*(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2)+(a*e^2+c*d^2)^(1/2))*(a*e^2+c*d^2)^(1/2)*(2*(a*c*e^2+c^2*d^2)^(1/2)+2*c*d)^(1/2)*(a*c*e^2+c^2*d^2)^(1/2)-1/2/c^(3/2)/a/e*ln((e*x+d)*c^(1/2)+(e*x+d)^(1/2)*(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2)+(a*e^2+c*d^2)^(1/2))*(2*(a*c*e^2+c^2*d^2)^(1/2)+2*c*d)^(1/2)*(a*c*e^2+c^2*d^2)^(1/2)*d-2*e/c/(4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*(c*(a*e^2+c*d^2))^(1/2)-2*c*d)^(1/2)*arctan((2*c^(1/2)*(e*x+d)^(1/2)+(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2))/(4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*(c*(a*e^2+c*d^2))^(1/2)-2*c*d)^(1/2))*(a*e^2+c*d^2)^(1/2)-1/2/c/a/e/(4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*(c*(a*e^2+c*d^2))^(1/2)-2*c*d)^(1/2)*arctan((2*c^(1/2)*(e*x+d)^(1/2)+(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2))/(4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*(c*(a*e^2+c*d^2))^(1/2)-2*c*d)^(1/2))*(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2)*(a*e^2+c*d^2)^(1/2)*(2*(a*c*e^2+c^2*d^2)^(1/2)+2*c*d)^(1/2)*d-1/c^(1/2)/a/e/(4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*(c*(a*e^2+c*d^2))^(1/2)-2*c*d)^(1/2)*arctan((2*c^(1/2)*(e*x+d)^(1/2)+(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2))/(4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*(c*(a*e^2+c*d^2))^(1/2)-2*c*d)^(1/2))*(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2)*(2*(a*c*e^2+c^2*d^2)^(1/2)+2*c*d)^(1/2)*d^2+1/2/c^2/a/e/(4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*(c*(a*e^2+c*d^2))^(1/2)-2*c*d)^(1/2)*arctan((2*c^(1/2)*(e*x+d)^(1/2)+(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2))/(4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*(c*(a*e^2+c*d^2))^(1/2)-2*c*d)^(1/2))*(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2)*(a*e^2+c*d^2)^(1/2)*(2*(a*c*e^2+c^2*d^2)^(1/2)+2*c*d)^(1/2)*(a*c*e^2+c^2*d^2)^(1/2)+1/c^(3/2)/a/e/(4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*(c*(a*e^2+c*d^2))^(1/2)-2*c*d)^(1/2)*arctan((2*c^(1/2)*(e*x+d)^(1/2)+(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2))/(4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*(c*(a*e^2+c*d^2))^(1/2)-2*c*d)^(1/2))*(2*(c*(a*e^2+c*d^2))^(1/2)+2*c*d)^(1/2)*(2*(a*c*e^2+c^2*d^2)^(1/2)+2*c*d)^(1/2)*(a*c*e^2+c^2*d^2)^(1/2)*d","B"
620,1,1176,367,0.194000," ","int((e*x+d)^(1/2)/(c*x^2+a),x)","-\frac{\sqrt{2 c d +2 \sqrt{a c \,e^{2}+c^{2} d^{2}}}\, \sqrt{2 c d +2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}\, d \arctan \left(\frac{2 \sqrt{e x +d}\, \sqrt{c}-\sqrt{2 c d +2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}}{\sqrt{-2 c d +4 \sqrt{a \,e^{2}+c \,d^{2}}\, \sqrt{c}-2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}}\right)}{2 \sqrt{-2 c d +4 \sqrt{a \,e^{2}+c \,d^{2}}\, \sqrt{c}-2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}\, a \sqrt{c}\, e}-\frac{\sqrt{2 c d +2 \sqrt{a c \,e^{2}+c^{2} d^{2}}}\, \sqrt{2 c d +2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}\, d \arctan \left(\frac{2 \sqrt{e x +d}\, \sqrt{c}+\sqrt{2 c d +2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}}{\sqrt{-2 c d +4 \sqrt{a \,e^{2}+c \,d^{2}}\, \sqrt{c}-2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}}\right)}{2 \sqrt{-2 c d +4 \sqrt{a \,e^{2}+c \,d^{2}}\, \sqrt{c}-2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}\, a \sqrt{c}\, e}-\frac{\sqrt{2 c d +2 \sqrt{a c \,e^{2}+c^{2} d^{2}}}\, d \ln \left(\left(e x +d \right) \sqrt{c}-\sqrt{e x +d}\, \sqrt{2 c d +2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}+\sqrt{a \,e^{2}+c \,d^{2}}\right)}{4 a \sqrt{c}\, e}+\frac{\sqrt{2 c d +2 \sqrt{a c \,e^{2}+c^{2} d^{2}}}\, d \ln \left(\left(e x +d \right) \sqrt{c}+\sqrt{e x +d}\, \sqrt{2 c d +2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}+\sqrt{a \,e^{2}+c \,d^{2}}\right)}{4 a \sqrt{c}\, e}+\frac{\sqrt{2 c d +2 \sqrt{a c \,e^{2}+c^{2} d^{2}}}\, \sqrt{2 c d +2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}\, \sqrt{a c \,e^{2}+c^{2} d^{2}}\, \arctan \left(\frac{2 \sqrt{e x +d}\, \sqrt{c}-\sqrt{2 c d +2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}}{\sqrt{-2 c d +4 \sqrt{a \,e^{2}+c \,d^{2}}\, \sqrt{c}-2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}}\right)}{2 \sqrt{-2 c d +4 \sqrt{a \,e^{2}+c \,d^{2}}\, \sqrt{c}-2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}\, a \,c^{\frac{3}{2}} e}+\frac{\sqrt{2 c d +2 \sqrt{a c \,e^{2}+c^{2} d^{2}}}\, \sqrt{2 c d +2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}\, \sqrt{a c \,e^{2}+c^{2} d^{2}}\, \arctan \left(\frac{2 \sqrt{e x +d}\, \sqrt{c}+\sqrt{2 c d +2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}}{\sqrt{-2 c d +4 \sqrt{a \,e^{2}+c \,d^{2}}\, \sqrt{c}-2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}}\right)}{2 \sqrt{-2 c d +4 \sqrt{a \,e^{2}+c \,d^{2}}\, \sqrt{c}-2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}\, a \,c^{\frac{3}{2}} e}+\frac{\sqrt{2 c d +2 \sqrt{a c \,e^{2}+c^{2} d^{2}}}\, \sqrt{a c \,e^{2}+c^{2} d^{2}}\, \ln \left(\left(e x +d \right) \sqrt{c}-\sqrt{e x +d}\, \sqrt{2 c d +2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}+\sqrt{a \,e^{2}+c \,d^{2}}\right)}{4 a \,c^{\frac{3}{2}} e}-\frac{\sqrt{2 c d +2 \sqrt{a c \,e^{2}+c^{2} d^{2}}}\, \sqrt{a c \,e^{2}+c^{2} d^{2}}\, \ln \left(\left(e x +d \right) \sqrt{c}+\sqrt{e x +d}\, \sqrt{2 c d +2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}+\sqrt{a \,e^{2}+c \,d^{2}}\right)}{4 a \,c^{\frac{3}{2}} e}"," ",0,"-1/4*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)/a/e/c^(1/2)*ln((e*x+d)*c^(1/2)-(e*x+d)^(1/2)*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)+(a*e^2+c*d^2)^(1/2))*d+1/4*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)/a/c^(3/2)/e*ln((e*x+d)*c^(1/2)-(e*x+d)^(1/2)*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)+(a*e^2+c*d^2)^(1/2))*(a*c*e^2+c^2*d^2)^(1/2)-1/2*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)/a/e/c^(1/2)*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*arctan((2*(e*x+d)^(1/2)*c^(1/2)-(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))*d+1/2*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)/a/c^(3/2)/e*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*arctan((2*(e*x+d)^(1/2)*c^(1/2)-(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))*(a*c*e^2+c^2*d^2)^(1/2)+1/4*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)/a/e/c^(1/2)*ln((e*x+d)*c^(1/2)+(e*x+d)^(1/2)*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)+(a*e^2+c*d^2)^(1/2))*d-1/4*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)/a/c^(3/2)/e*ln((e*x+d)*c^(1/2)+(e*x+d)^(1/2)*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)+(a*e^2+c*d^2)^(1/2))*(a*c*e^2+c^2*d^2)^(1/2)-1/2*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)/a/e/c^(1/2)*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*arctan((2*(e*x+d)^(1/2)*c^(1/2)+(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))*d+1/2*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)/a/c^(3/2)/e*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*arctan((2*(e*x+d)^(1/2)*c^(1/2)+(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))*(a*c*e^2+c^2*d^2)^(1/2)","B"
621,1,1548,419,0.246000," ","int(1/(c*x^2+a)/(e*x+d)^(1/2),x)","\frac{2 e \arctan \left(\frac{2 \sqrt{e x +d}\, \sqrt{c}-\sqrt{2 c d +2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}}{\sqrt{-2 c d +4 \sqrt{a \,e^{2}+c \,d^{2}}\, \sqrt{c}-2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}}\right)}{\sqrt{a \,e^{2}+c \,d^{2}}\, \sqrt{-2 c d +4 \sqrt{a \,e^{2}+c \,d^{2}}\, \sqrt{c}-2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}}+\frac{2 e \arctan \left(\frac{2 \sqrt{e x +d}\, \sqrt{c}+\sqrt{2 c d +2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}}{\sqrt{-2 c d +4 \sqrt{a \,e^{2}+c \,d^{2}}\, \sqrt{c}-2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}}\right)}{\sqrt{a \,e^{2}+c \,d^{2}}\, \sqrt{-2 c d +4 \sqrt{a \,e^{2}+c \,d^{2}}\, \sqrt{c}-2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}}+\frac{\sqrt{2 c d +2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}\, \sqrt{2 c d +2 \sqrt{a c \,e^{2}+c^{2} d^{2}}}\, d \arctan \left(\frac{2 \sqrt{e x +d}\, \sqrt{c}-\sqrt{2 c d +2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}}{\sqrt{-2 c d +4 \sqrt{a \,e^{2}+c \,d^{2}}\, \sqrt{c}-2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}}\right)}{2 \sqrt{a \,e^{2}+c \,d^{2}}\, \sqrt{-2 c d +4 \sqrt{a \,e^{2}+c \,d^{2}}\, \sqrt{c}-2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}\, a e}+\frac{\sqrt{2 c d +2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}\, \sqrt{2 c d +2 \sqrt{a c \,e^{2}+c^{2} d^{2}}}\, d \arctan \left(\frac{2 \sqrt{e x +d}\, \sqrt{c}+\sqrt{2 c d +2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}}{\sqrt{-2 c d +4 \sqrt{a \,e^{2}+c \,d^{2}}\, \sqrt{c}-2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}}\right)}{2 \sqrt{a \,e^{2}+c \,d^{2}}\, \sqrt{-2 c d +4 \sqrt{a \,e^{2}+c \,d^{2}}\, \sqrt{c}-2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}\, a e}+\frac{\sqrt{2 c d +2 \sqrt{a c \,e^{2}+c^{2} d^{2}}}\, d \ln \left(\left(e x +d \right) \sqrt{c}-\sqrt{e x +d}\, \sqrt{2 c d +2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}+\sqrt{a \,e^{2}+c \,d^{2}}\right)}{4 \sqrt{a \,e^{2}+c \,d^{2}}\, a e}-\frac{\sqrt{2 c d +2 \sqrt{a c \,e^{2}+c^{2} d^{2}}}\, d \ln \left(\left(e x +d \right) \sqrt{c}+\sqrt{e x +d}\, \sqrt{2 c d +2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}+\sqrt{a \,e^{2}+c \,d^{2}}\right)}{4 \sqrt{a \,e^{2}+c \,d^{2}}\, a e}-\frac{\sqrt{2 c d +2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}\, \sqrt{2 c d +2 \sqrt{a c \,e^{2}+c^{2} d^{2}}}\, \sqrt{a c \,e^{2}+c^{2} d^{2}}\, \arctan \left(\frac{2 \sqrt{e x +d}\, \sqrt{c}-\sqrt{2 c d +2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}}{\sqrt{-2 c d +4 \sqrt{a \,e^{2}+c \,d^{2}}\, \sqrt{c}-2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}}\right)}{2 \sqrt{a \,e^{2}+c \,d^{2}}\, \sqrt{-2 c d +4 \sqrt{a \,e^{2}+c \,d^{2}}\, \sqrt{c}-2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}\, a c e}-\frac{\sqrt{2 c d +2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}\, \sqrt{2 c d +2 \sqrt{a c \,e^{2}+c^{2} d^{2}}}\, \sqrt{a c \,e^{2}+c^{2} d^{2}}\, \arctan \left(\frac{2 \sqrt{e x +d}\, \sqrt{c}+\sqrt{2 c d +2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}}{\sqrt{-2 c d +4 \sqrt{a \,e^{2}+c \,d^{2}}\, \sqrt{c}-2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}}\right)}{2 \sqrt{a \,e^{2}+c \,d^{2}}\, \sqrt{-2 c d +4 \sqrt{a \,e^{2}+c \,d^{2}}\, \sqrt{c}-2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}\, a c e}-\frac{\sqrt{2 c d +2 \sqrt{a c \,e^{2}+c^{2} d^{2}}}\, \sqrt{a c \,e^{2}+c^{2} d^{2}}\, \ln \left(\left(e x +d \right) \sqrt{c}-\sqrt{e x +d}\, \sqrt{2 c d +2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}+\sqrt{a \,e^{2}+c \,d^{2}}\right)}{4 \sqrt{a \,e^{2}+c \,d^{2}}\, a c e}+\frac{\sqrt{2 c d +2 \sqrt{a c \,e^{2}+c^{2} d^{2}}}\, \sqrt{a c \,e^{2}+c^{2} d^{2}}\, \ln \left(\left(e x +d \right) \sqrt{c}+\sqrt{e x +d}\, \sqrt{2 c d +2 \sqrt{\left(a \,e^{2}+c \,d^{2}\right) c}}+\sqrt{a \,e^{2}+c \,d^{2}}\right)}{4 \sqrt{a \,e^{2}+c \,d^{2}}\, a c e}"," ",0,"1/4/(a*e^2+c*d^2)^(1/2)/a/e*ln((e*x+d)*c^(1/2)-(e*x+d)^(1/2)*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)+(a*e^2+c*d^2)^(1/2))*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*d-1/4/(a*e^2+c*d^2)^(1/2)/c/a/e*ln((e*x+d)*c^(1/2)-(e*x+d)^(1/2)*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)+(a*e^2+c*d^2)^(1/2))*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*(a*c*e^2+c^2*d^2)^(1/2)+2*e/(a*e^2+c*d^2)^(1/2)/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*arctan((2*(e*x+d)^(1/2)*c^(1/2)-(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))+1/2/(a*e^2+c*d^2)^(1/2)/a/e/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*arctan((2*(e*x+d)^(1/2)*c^(1/2)-(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*d-1/2/(a*e^2+c*d^2)^(1/2)/c/a/e/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*arctan((2*(e*x+d)^(1/2)*c^(1/2)-(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*(a*c*e^2+c^2*d^2)^(1/2)-1/4/(a*e^2+c*d^2)^(1/2)/a/e*ln((e*x+d)*c^(1/2)+(e*x+d)^(1/2)*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)+(a*e^2+c*d^2)^(1/2))*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*d+1/4/(a*e^2+c*d^2)^(1/2)/c/a/e*ln((e*x+d)*c^(1/2)+(e*x+d)^(1/2)*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)+(a*e^2+c*d^2)^(1/2))*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*(a*c*e^2+c^2*d^2)^(1/2)+2*e/(a*e^2+c*d^2)^(1/2)/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*arctan((2*(e*x+d)^(1/2)*c^(1/2)+(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))+1/2/(a*e^2+c*d^2)^(1/2)/a/e/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*arctan((2*(e*x+d)^(1/2)*c^(1/2)+(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*d-1/2/(a*e^2+c*d^2)^(1/2)/c/a/e/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*arctan((2*(e*x+d)^(1/2)*c^(1/2)+(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*(a*c*e^2+c^2*d^2)^(1/2)","B"
622,1,5659,526,0.214000," ","int(1/(e*x+d)^(3/2)/(c*x^2+a),x)","\text{output too large to display}"," ",0,"result too large to display","B"
623,1,7264,595,0.309000," ","int(1/(e*x+d)^(5/2)/(c*x^2+a),x)","\text{output too large to display}"," ",0,"result too large to display","B"
624,1,717,199,0.099000," ","int((e*x+d)^(7/2)/(-c*x^2+a)^2,x)","-\frac{5 a \,e^{5} \arctanh \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{4 \sqrt{a c \,e^{2}}\, \sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}\, c}-\frac{5 a \,e^{5} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{4 \sqrt{a c \,e^{2}}\, \sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}\, c}+\frac{c \,d^{4} e \arctanh \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{2 \sqrt{a c \,e^{2}}\, \sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}\, a}+\frac{c \,d^{4} e \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{2 \sqrt{a c \,e^{2}}\, \sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}\, a}-\frac{9 d^{2} e^{3} \arctanh \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{4 \sqrt{a c \,e^{2}}\, \sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}-\frac{9 d^{2} e^{3} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{4 \sqrt{a c \,e^{2}}\, \sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}-\frac{\sqrt{e x +d}\, a \,e^{5}}{2 \left(c \,e^{2} x^{2}-a \,e^{2}\right) c^{2}}+\frac{\sqrt{e x +d}\, d^{4} e}{2 \left(c \,e^{2} x^{2}-a \,e^{2}\right) a}+\frac{d^{3} e \arctanh \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{4 \sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}\, a}-\frac{d^{3} e \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{4 \sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}\, a}-\frac{13 d \,e^{3} \arctanh \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{4 \sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}\, c}+\frac{13 d \,e^{3} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{4 \sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}\, c}-\frac{\left(e x +d \right)^{\frac{3}{2}} d^{3} e}{2 \left(c \,e^{2} x^{2}-a \,e^{2}\right) a}-\frac{3 \left(e x +d \right)^{\frac{3}{2}} d \,e^{3}}{2 \left(c \,e^{2} x^{2}-a \,e^{2}\right) c}+\frac{2 \sqrt{e x +d}\, e^{3}}{c^{2}}"," ",0,"2*e^3/c^2*(e*x+d)^(1/2)-3/2*e^3/c/(c*e^2*x^2-a*e^2)*d*(e*x+d)^(3/2)-1/2*e/(c*e^2*x^2-a*e^2)*d^3/a*(e*x+d)^(3/2)-1/2*e^5/c^2/(c*e^2*x^2-a*e^2)*a*(e*x+d)^(1/2)+1/2*e/(c*e^2*x^2-a*e^2)/a*(e*x+d)^(1/2)*d^4-5/4*e^5/c*a/(a*c*e^2)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)-9/4*e^3/(a*c*e^2)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d^2+1/2*e*c/a/(a*c*e^2)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d^4-13/4*e^3/c/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d+1/4*e/a/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d^3-5/4*e^5/c*a/(a*c*e^2)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)-9/4*e^3/(a*c*e^2)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d^2+1/2*e*c/a/(a*c*e^2)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d^4+13/4*e^3/c/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d-1/4*e/a/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d^3","B"
625,1,575,171,0.085000," ","int((e*x+d)^(5/2)/(-c*x^2+a)^2,x)","\frac{c \,d^{3} e \arctanh \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{2 \sqrt{a c \,e^{2}}\, \sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}\, a}+\frac{c \,d^{3} e \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{2 \sqrt{a c \,e^{2}}\, \sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}\, a}-\frac{d \,e^{3} \arctanh \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{\sqrt{a c \,e^{2}}\, \sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}-\frac{d \,e^{3} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{\sqrt{a c \,e^{2}}\, \sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}+\frac{\sqrt{e x +d}\, d^{3} e}{2 \left(c \,e^{2} x^{2}-a \,e^{2}\right) a}+\frac{d^{2} e \arctanh \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{4 \sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}\, a}-\frac{d^{2} e \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{4 \sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}\, a}-\frac{\sqrt{e x +d}\, d \,e^{3}}{2 \left(c \,e^{2} x^{2}-a \,e^{2}\right) c}-\frac{3 e^{3} \arctanh \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{4 \sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}\, c}+\frac{3 e^{3} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{4 \sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}\, c}-\frac{\left(e x +d \right)^{\frac{3}{2}} d^{2} e}{2 \left(c \,e^{2} x^{2}-a \,e^{2}\right) a}-\frac{\left(e x +d \right)^{\frac{3}{2}} e^{3}}{2 \left(c \,e^{2} x^{2}-a \,e^{2}\right) c}"," ",0,"-1/2*e^3/(c*e^2*x^2-a*e^2)/c*(e*x+d)^(3/2)-1/2*e/(c*e^2*x^2-a*e^2)/a*(e*x+d)^(3/2)*d^2-1/2*e^3/(c*e^2*x^2-a*e^2)*d/c*(e*x+d)^(1/2)+1/2*e/(c*e^2*x^2-a*e^2)*d^3/a*(e*x+d)^(1/2)-e^3/(a*c*e^2)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d+1/2*e/a*c/(a*c*e^2)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d^3-3/4*e^3/c/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)+1/4*e/a/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d^2-e^3/(a*c*e^2)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d+1/2*e/a*c/(a*c*e^2)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d^3+3/4*e^3/c/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)-1/4*e/a/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d^2","B"
626,1,432,153,0.089000," ","int((e*x+d)^(3/2)/(-c*x^2+a)^2,x)","\frac{c \,d^{2} e \arctanh \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{2 \sqrt{a c \,e^{2}}\, \sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}\, a}+\frac{c \,d^{2} e \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{2 \sqrt{a c \,e^{2}}\, \sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}\, a}-\frac{e^{3} \arctanh \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{4 \sqrt{a c \,e^{2}}\, \sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}-\frac{e^{3} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{4 \sqrt{a c \,e^{2}}\, \sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}+\frac{\sqrt{e x +d}\, d^{2} e}{2 \left(c \,e^{2} x^{2}-a \,e^{2}\right) a}+\frac{d e \arctanh \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{4 \sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}\, a}-\frac{d e \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{4 \sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}\, a}-\frac{\sqrt{e x +d}\, e^{3}}{2 \left(c \,e^{2} x^{2}-a \,e^{2}\right) c}-\frac{\left(e x +d \right)^{\frac{3}{2}} d e}{2 \left(c \,e^{2} x^{2}-a \,e^{2}\right) a}"," ",0,"-1/2*e/(c*e^2*x^2-a*e^2)*d/a*(e*x+d)^(3/2)-1/2*e^3/(c*e^2*x^2-a*e^2)/c*(e*x+d)^(1/2)+1/2*e/(c*e^2*x^2-a*e^2)/a*(e*x+d)^(1/2)*d^2-1/4*e^3/(a*c*e^2)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)+1/2*e/a/(a*c*e^2)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*c*d^2+1/4*e/a/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d-1/4*e^3/(a*c*e^2)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)+1/2*e/a/(a*c*e^2)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*c*d^2-1/4*e/a/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d","B"
627,1,287,142,0.297000," ","int((e*x+d)^(1/2)/(-c*x^2+a)^2,x)","\frac{c d e \arctanh \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{2 \sqrt{a c \,e^{2}}\, \sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}\, a}+\frac{c d e \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{2 \sqrt{a c \,e^{2}}\, \sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}\, a}+\frac{e \arctanh \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{4 \sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}\, a}-\frac{e \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{4 \sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}\, a}-\frac{\sqrt{e x +d}\, e}{4 \left(e x -\frac{\sqrt{a c \,e^{2}}}{c}\right) a c}-\frac{\sqrt{e x +d}\, e}{4 \left(e x +\frac{\sqrt{a c \,e^{2}}}{c}\right) a c}"," ",0,"-1/4*e/c/a*(e*x+d)^(1/2)/(e*x-(a*c*e^2)^(1/2)/c)+1/2*e*c/a/(a*c*e^2)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d+1/4*e/a/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)-1/4*e/c/a*(e*x+d)^(1/2)/(e*x+(a*c*e^2)^(1/2)/c)+1/2*e*c/a/(a*c*e^2)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d-1/4*e/a/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)","B"
628,1,375,166,0.278000," ","int(1/(-c*x^2+a)^2/(e*x+d)^(1/2),x)","\frac{c^{2} d e \arctanh \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{2 \sqrt{a c \,e^{2}}\, \left(c d +\sqrt{a c \,e^{2}}\right) \sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}\, a}-\frac{c^{2} d e \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{2 \sqrt{a c \,e^{2}}\, \left(-c d +\sqrt{a c \,e^{2}}\right) \sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}\, a}+\frac{3 c e \arctanh \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{4 \left(c d +\sqrt{a c \,e^{2}}\right) \sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}\, a}+\frac{3 c e \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{4 \left(-c d +\sqrt{a c \,e^{2}}\right) \sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}\, a}-\frac{\sqrt{e x +d}\, e}{4 \left(c d +\sqrt{a c \,e^{2}}\right) \left(e x -\frac{\sqrt{a c \,e^{2}}}{c}\right) a}-\frac{\sqrt{e x +d}\, e}{4 \left(c d -\sqrt{a c \,e^{2}}\right) \left(e x +\frac{\sqrt{a c \,e^{2}}}{c}\right) a}"," ",0,"-1/4*e/a/(c*d+(a*c*e^2)^(1/2))*(e*x+d)^(1/2)/(e*x-(a*c*e^2)^(1/2)/c)+1/2*e*c^2/a/(a*c*e^2)^(1/2)/(c*d+(a*c*e^2)^(1/2))/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d+3/4*e*c/a/(c*d+(a*c*e^2)^(1/2))/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)-1/4*e/a/(c*d-(a*c*e^2)^(1/2))*(e*x+d)^(1/2)/(e*x+(a*c*e^2)^(1/2)/c)-1/2*e*c^2/a/(a*c*e^2)^(1/2)/(-c*d+(a*c*e^2)^(1/2))/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d+3/4*e*c/a/(-c*d+(a*c*e^2)^(1/2))/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)","B"
629,1,783,205,0.092000," ","int(1/(e*x+d)^(3/2)/(-c*x^2+a)^2,x)","\frac{c^{3} d^{3} e \arctanh \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-c \,d^{2}\right)^{2} \sqrt{a c \,e^{2}}\, \sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}\, a}+\frac{c^{3} d^{3} e \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-c \,d^{2}\right)^{2} \sqrt{a c \,e^{2}}\, \sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}\, a}-\frac{2 c^{2} d \,e^{3} \arctanh \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{\left(a \,e^{2}-c \,d^{2}\right)^{2} \sqrt{a c \,e^{2}}\, \sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}-\frac{2 c^{2} d \,e^{3} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{\left(a \,e^{2}-c \,d^{2}\right)^{2} \sqrt{a c \,e^{2}}\, \sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}+\frac{\sqrt{e x +d}\, c^{2} d^{3} e}{2 \left(a \,e^{2}-c \,d^{2}\right)^{2} \left(c \,e^{2} x^{2}-a \,e^{2}\right) a}+\frac{c^{2} d^{2} e \arctanh \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{4 \left(a \,e^{2}-c \,d^{2}\right)^{2} \sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}\, a}-\frac{c^{2} d^{2} e \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{4 \left(a \,e^{2}-c \,d^{2}\right)^{2} \sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}\, a}+\frac{3 \sqrt{e x +d}\, c d \,e^{3}}{2 \left(a \,e^{2}-c \,d^{2}\right)^{2} \left(c \,e^{2} x^{2}-a \,e^{2}\right)}+\frac{5 c \,e^{3} \arctanh \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{4 \left(a \,e^{2}-c \,d^{2}\right)^{2} \sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}-\frac{5 c \,e^{3} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{4 \left(a \,e^{2}-c \,d^{2}\right)^{2} \sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}-\frac{\left(e x +d \right)^{\frac{3}{2}} c^{2} d^{2} e}{2 \left(a \,e^{2}-c \,d^{2}\right)^{2} \left(c \,e^{2} x^{2}-a \,e^{2}\right) a}-\frac{\left(e x +d \right)^{\frac{3}{2}} c \,e^{3}}{2 \left(a \,e^{2}-c \,d^{2}\right)^{2} \left(c \,e^{2} x^{2}-a \,e^{2}\right)}-\frac{2 e^{3}}{\left(a \,e^{2}-c \,d^{2}\right)^{2} \sqrt{e x +d}}"," ",0,"-1/2*e^3*c/(a*e^2-c*d^2)^2/(c*e^2*x^2-a*e^2)*(e*x+d)^(3/2)-1/2*e*c^2/(a*e^2-c*d^2)^2/(c*e^2*x^2-a*e^2)/a*(e*x+d)^(3/2)*d^2+3/2*e^3*c/(a*e^2-c*d^2)^2/(c*e^2*x^2-a*e^2)*d*(e*x+d)^(1/2)+1/2*e*c^2/(a*e^2-c*d^2)^2/(c*e^2*x^2-a*e^2)*d^3/a*(e*x+d)^(1/2)-2*e^3*c^2/(a*e^2-c*d^2)^2/(a*c*e^2)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d+1/2*e*c^3/(a*e^2-c*d^2)^2/a/(a*c*e^2)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d^3+5/4*e^3*c/(a*e^2-c*d^2)^2/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)+1/4*e*c^2/(a*e^2-c*d^2)^2/a/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d^2-2*e^3*c^2/(a*e^2-c*d^2)^2/(a*c*e^2)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d+1/2*e*c^3/(a*e^2-c*d^2)^2/a/(a*c*e^2)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d^3-5/4*e^3*c/(a*e^2-c*d^2)^2/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)-1/4*e*c^2/(a*e^2-c*d^2)^2/a/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d^2-2*e^3/(a*e^2-c*d^2)^2/(e*x+d)^(1/2)","B"
630,1,1021,247,0.097000," ","int(1/(e*x+d)^(5/2)/(-c*x^2+a)^2,x)","\frac{7 a \,c^{2} e^{5} \arctanh \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{4 \left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{a c \,e^{2}}\, \sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}+\frac{7 a \,c^{2} e^{5} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{4 \left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{a c \,e^{2}}\, \sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}-\frac{c^{4} d^{4} e \arctanh \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{a c \,e^{2}}\, \sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}\, a}-\frac{c^{4} d^{4} e \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{a c \,e^{2}}\, \sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}\, a}+\frac{15 c^{3} d^{2} e^{3} \arctanh \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{4 \left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{a c \,e^{2}}\, \sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}+\frac{15 c^{3} d^{2} e^{3} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{4 \left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{a c \,e^{2}}\, \sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}-\frac{\sqrt{e x +d}\, a c \,e^{5}}{2 \left(a \,e^{2}-c \,d^{2}\right)^{3} \left(c \,e^{2} x^{2}-a \,e^{2}\right)}-\frac{\sqrt{e x +d}\, c^{3} d^{4} e}{2 \left(a \,e^{2}-c \,d^{2}\right)^{3} \left(c \,e^{2} x^{2}-a \,e^{2}\right) a}-\frac{c^{3} d^{3} e \arctanh \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{4 \left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}\, a}+\frac{c^{3} d^{3} e \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{4 \left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}\, a}-\frac{3 \sqrt{e x +d}\, c^{2} d^{2} e^{3}}{\left(a \,e^{2}-c \,d^{2}\right)^{3} \left(c \,e^{2} x^{2}-a \,e^{2}\right)}-\frac{19 c^{2} d \,e^{3} \arctanh \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{4 \left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}+\frac{19 c^{2} d \,e^{3} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{4 \left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}+\frac{\left(e x +d \right)^{\frac{3}{2}} c^{3} d^{3} e}{2 \left(a \,e^{2}-c \,d^{2}\right)^{3} \left(c \,e^{2} x^{2}-a \,e^{2}\right) a}+\frac{3 \left(e x +d \right)^{\frac{3}{2}} c^{2} d \,e^{3}}{2 \left(a \,e^{2}-c \,d^{2}\right)^{3} \left(c \,e^{2} x^{2}-a \,e^{2}\right)}+\frac{8 c d \,e^{3}}{\left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{e x +d}}-\frac{2 e^{3}}{3 \left(a \,e^{2}-c \,d^{2}\right)^{2} \left(e x +d \right)^{\frac{3}{2}}}"," ",0,"3/2*e^3/(a*e^2-c*d^2)^3*c^2/(c*e^2*x^2-a*e^2)*d*(e*x+d)^(3/2)+1/2*e/(a*e^2-c*d^2)^3*c^3/(c*e^2*x^2-a*e^2)*d^3/a*(e*x+d)^(3/2)-1/2*e^5/(a*e^2-c*d^2)^3*c/(c*e^2*x^2-a*e^2)*a*(e*x+d)^(1/2)-3*e^3/(a*e^2-c*d^2)^3*c^2/(c*e^2*x^2-a*e^2)*(e*x+d)^(1/2)*d^2-1/2*e/(a*e^2-c*d^2)^3*c^3/(c*e^2*x^2-a*e^2)/a*(e*x+d)^(1/2)*d^4+7/4*e^5/(a*e^2-c*d^2)^3*c^2*a/(a*c*e^2)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)+15/4*e^3/(a*e^2-c*d^2)^3*c^3/(a*c*e^2)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d^2-1/2*e/(a*e^2-c*d^2)^3*c^4/a/(a*c*e^2)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d^4-19/4*e^3/(a*e^2-c*d^2)^3*c^2/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d-1/4*e/(a*e^2-c*d^2)^3*c^3/a/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d^3+7/4*e^5/(a*e^2-c*d^2)^3*c^2*a/(a*c*e^2)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)+15/4*e^3/(a*e^2-c*d^2)^3*c^3/(a*c*e^2)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d^2-1/2*e/(a*e^2-c*d^2)^3*c^4/a/(a*c*e^2)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d^4+19/4*e^3/(a*e^2-c*d^2)^3*c^2/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d+1/4*e/(a*e^2-c*d^2)^3*c^3/a/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d^3-2/3*e^3/(a*e^2-c*d^2)^2/(e*x+d)^(3/2)+8*e^3/(a*e^2-c*d^2)^3*c*d/(e*x+d)^(1/2)","B"
631,1,5657,735,0.214000," ","int((e*x+d)^(7/2)/(c*x^2+a)^2,x)","\text{output too large to display}"," ",0,"result too large to display","B"
632,1,4065,655,0.204000," ","int((e*x+d)^(5/2)/(c*x^2+a)^2,x)","\text{output too large to display}"," ",0,"1/8/e/a^2/c^(3/2)/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*arctan((2*(e*x+d)^(1/2)*c^(1/2)+(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*(a*c*e^2+c^2*d^2)^(1/2)*d^2+1/8/e/a^2/c^(3/2)/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*arctan((2*(e*x+d)^(1/2)*c^(1/2)-(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*(a*c*e^2+c^2*d^2)^(1/2)*d^2+1/8/e/a^2/c/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*arctan((2*(e*x+d)^(1/2)*c^(1/2)-(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*(a*e^2+c*d^2)^(1/2)*d^2+1/8/e/a^2/c/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*arctan((2*(e*x+d)^(1/2)*c^(1/2)+(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*(a*e^2+c*d^2)^(1/2)*d^2+1/16/e/a^2/c^(1/2)*ln((e*x+d)*c^(1/2)+(e*x+d)^(1/2)*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)+(a*e^2+c*d^2)^(1/2))*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*d^3-1/16/e/a^2/c^(1/2)*ln((e*x+d)*c^(1/2)-(e*x+d)^(1/2)*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)+(a*e^2+c*d^2)^(1/2))*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*d^3-3/16*e/a/c^(3/2)*ln((e*x+d)*c^(1/2)-(e*x+d)^(1/2)*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)+(a*e^2+c*d^2)^(1/2))*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*d+3/16*e/a/c^(3/2)*ln((e*x+d)*c^(1/2)+(e*x+d)^(1/2)*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)+(a*e^2+c*d^2)^(1/2))*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*d-3/16*e/a/c^(5/2)*ln((e*x+d)*c^(1/2)+(e*x+d)^(1/2)*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)+(a*e^2+c*d^2)^(1/2))*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*(a*c*e^2+c^2*d^2)^(1/2)+3/16*e/a/c^(5/2)*ln((e*x+d)*c^(1/2)-(e*x+d)^(1/2)*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)+(a*e^2+c*d^2)^(1/2))*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*(a*c*e^2+c^2*d^2)^(1/2)-1/8/e/a^2/c^2/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*arctan((2*(e*x+d)^(1/2)*c^(1/2)+(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*(a*c*e^2+c^2*d^2)^(1/2)*(a*e^2+c*d^2)^(1/2)*d-1/8/e/a^2/c^2/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*arctan((2*(e*x+d)^(1/2)*c^(1/2)-(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*(a*c*e^2+c^2*d^2)^(1/2)*(a*e^2+c*d^2)^(1/2)*d+1/16/e/a^2/c^2*ln((e*x+d)*c^(1/2)+(e*x+d)^(1/2)*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)+(a*e^2+c*d^2)^(1/2))*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*(a*c*e^2+c^2*d^2)^(1/2)*(a*e^2+c*d^2)^(1/2)*d-1/16/e/a^2/c^2*ln((e*x+d)*c^(1/2)-(e*x+d)^(1/2)*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)+(a*e^2+c*d^2)^(1/2))*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*(a*c*e^2+c^2*d^2)^(1/2)*(a*e^2+c*d^2)^(1/2)*d-3/8*e/a/c^(3/2)/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*arctan((2*(e*x+d)^(1/2)*c^(1/2)+(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*d+3/8*e/a/c^(5/2)/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*arctan((2*(e*x+d)^(1/2)*c^(1/2)+(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*(a*c*e^2+c^2*d^2)^(1/2)-3/8*e/a/c^(3/2)/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*arctan((2*(e*x+d)^(1/2)*c^(1/2)-(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*d-1/8/e/a^2/c^(1/2)/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*arctan((2*(e*x+d)^(1/2)*c^(1/2)+(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*d^3+3/8*e/a/c^(5/2)/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*arctan((2*(e*x+d)^(1/2)*c^(1/2)-(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*(a*c*e^2+c^2*d^2)^(1/2)-1/8/e/a^2/c^(1/2)/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*arctan((2*(e*x+d)^(1/2)*c^(1/2)-(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*d^3-1/2*e/(c*e^2*x^2+a*e^2)*d^3/a*(e*x+d)^(1/2)-1/2*e^3/(c*e^2*x^2+a*e^2)*d/c*(e*x+d)^(1/2)+1/2*e/(c*e^2*x^2+a*e^2)/a*(e*x+d)^(3/2)*d^2-1/2*e^3/(c*e^2*x^2+a*e^2)/c*(e*x+d)^(3/2)+1/16/e/a^2/c*ln((e*x+d)*c^(1/2)-(e*x+d)^(1/2)*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)+(a*e^2+c*d^2)^(1/2))*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*(a*e^2+c*d^2)^(1/2)*d^2+1/2*e/a/c/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*arctan((2*(e*x+d)^(1/2)*c^(1/2)-(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))*(a*e^2+c*d^2)^(1/2)*d+1/16/e/a^2/c^(3/2)*ln((e*x+d)*c^(1/2)-(e*x+d)^(1/2)*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)+(a*e^2+c*d^2)^(1/2))*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*(a*c*e^2+c^2*d^2)^(1/2)*d^2-1/16/e/a^2/c^(3/2)*ln((e*x+d)*c^(1/2)+(e*x+d)^(1/2)*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)+(a*e^2+c*d^2)^(1/2))*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*(a*c*e^2+c^2*d^2)^(1/2)*d^2-1/16/e/a^2/c*ln((e*x+d)*c^(1/2)+(e*x+d)^(1/2)*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)+(a*e^2+c*d^2)^(1/2))*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*(a*e^2+c*d^2)^(1/2)*d^2+1/2*e/a/c/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*arctan((2*(e*x+d)^(1/2)*c^(1/2)+(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))*(a*e^2+c*d^2)^(1/2)*d","B"
633,1,2851,582,0.192000," ","int((e*x+d)^(3/2)/(c*x^2+a)^2,x)","\text{output too large to display}"," ",0,"1/2*e/(c*e^2*x^2+a*e^2)*d/a*(e*x+d)^(3/2)-1/2*e^3/(c*e^2*x^2+a*e^2)/c*(e*x+d)^(1/2)-1/2*e/(c*e^2*x^2+a*e^2)/a*(e*x+d)^(1/2)*d^2+1/16/e/a^2/c*ln((e*x+d)*c^(1/2)-(e*x+d)^(1/2)*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)+(a*e^2+c*d^2)^(1/2))*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*(a*e^2+c*d^2)^(1/2)*d-1/16/e/a^2/c^(1/2)*ln((e*x+d)*c^(1/2)-(e*x+d)^(1/2)*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)+(a*e^2+c*d^2)^(1/2))*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*d^2-1/16/e/a^2/c^2*ln((e*x+d)*c^(1/2)-(e*x+d)^(1/2)*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)+(a*e^2+c*d^2)^(1/2))*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*(a*c*e^2+c^2*d^2)^(1/2)*(a*e^2+c*d^2)^(1/2)+1/16/e/a^2/c^(3/2)*ln((e*x+d)*c^(1/2)-(e*x+d)^(1/2)*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)+(a*e^2+c*d^2)^(1/2))*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*(a*c*e^2+c^2*d^2)^(1/2)*d+1/2*e/a/c/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*arctan((2*(e*x+d)^(1/2)*c^(1/2)-(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))*(a*e^2+c*d^2)^(1/2)+1/8/e/a^2/c/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*arctan((2*(e*x+d)^(1/2)*c^(1/2)-(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*(a*e^2+c*d^2)^(1/2)*d-1/8/e/a^2/c^(1/2)/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*arctan((2*(e*x+d)^(1/2)*c^(1/2)-(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*d^2-1/8/e/a^2/c^2/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*arctan((2*(e*x+d)^(1/2)*c^(1/2)-(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*(a*c*e^2+c^2*d^2)^(1/2)*(a*e^2+c*d^2)^(1/2)+1/8/e/a^2/c^(3/2)/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*arctan((2*(e*x+d)^(1/2)*c^(1/2)-(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*(a*c*e^2+c^2*d^2)^(1/2)*d-1/16/e/a^2/c*ln((e*x+d)*c^(1/2)+(e*x+d)^(1/2)*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)+(a*e^2+c*d^2)^(1/2))*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*(a*e^2+c*d^2)^(1/2)*d+1/16/e/a^2/c^(1/2)*ln((e*x+d)*c^(1/2)+(e*x+d)^(1/2)*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)+(a*e^2+c*d^2)^(1/2))*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*d^2+1/16/e/a^2/c^2*ln((e*x+d)*c^(1/2)+(e*x+d)^(1/2)*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)+(a*e^2+c*d^2)^(1/2))*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*(a*c*e^2+c^2*d^2)^(1/2)*(a*e^2+c*d^2)^(1/2)-1/16/e/a^2/c^(3/2)*ln((e*x+d)*c^(1/2)+(e*x+d)^(1/2)*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)+(a*e^2+c*d^2)^(1/2))*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*(a*c*e^2+c^2*d^2)^(1/2)*d+1/2*e/a/c/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*arctan((2*(e*x+d)^(1/2)*c^(1/2)+(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))*(a*e^2+c*d^2)^(1/2)+1/8/e/a^2/c/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*arctan((2*(e*x+d)^(1/2)*c^(1/2)+(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*(a*e^2+c*d^2)^(1/2)*d-1/8/e/a^2/c^(1/2)/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*arctan((2*(e*x+d)^(1/2)*c^(1/2)+(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*d^2-1/8/e/a^2/c^2/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*arctan((2*(e*x+d)^(1/2)*c^(1/2)+(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*(a*c*e^2+c^2*d^2)^(1/2)*(a*e^2+c*d^2)^(1/2)+1/8/e/a^2/c^(3/2)/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*arctan((2*(e*x+d)^(1/2)*c^(1/2)+(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*(a*c*e^2+c^2*d^2)^(1/2)*d","B"
634,-2,0,531,180.000000," ","int((e*x+d)^(1/2)/(c*x^2+a)^2,x)","\int \frac{\sqrt{e x +d}}{\left(c \,x^{2}+a \right)^{2}}\, dx"," ",0,"int((e*x+d)^(1/2)/(c*x^2+a)^2,x)","F"
635,-2,0,595,180.000000," ","int(1/(c*x^2+a)^2/(e*x+d)^(1/2),x)","\int \frac{1}{\left(c \,x^{2}+a \right)^{2} \sqrt{e x +d}}\, dx"," ",0,"int(1/(c*x^2+a)^2/(e*x+d)^(1/2),x)","F"
636,1,8744,689,0.236000," ","int(1/(e*x+d)^(3/2)/(c*x^2+a)^2,x)","\text{output too large to display}"," ",0,"result too large to display","B"
637,1,10403,778,0.325000," ","int(1/(e*x+d)^(5/2)/(c*x^2+a)^2,x)","\text{output too large to display}"," ",0,"result too large to display","B"
638,1,986,234,0.095000," ","int((e*x+d)^(7/2)/(-c*x^2+a)^3,x)","-\frac{5 \sqrt{e x +d}\, a \,e^{7}}{16 \left(c \,e^{2} x^{2}-a \,e^{2}\right)^{2} c^{2}}-\frac{17 \sqrt{e x +d}\, d^{4} e^{3}}{16 \left(c \,e^{2} x^{2}-a \,e^{2}\right)^{2} a}+\frac{3 \sqrt{e x +d}\, c \,d^{6} e}{8 \left(c \,e^{2} x^{2}-a \,e^{2}\right)^{2} a^{2}}+\frac{\sqrt{e x +d}\, d^{2} e^{5}}{\left(c \,e^{2} x^{2}-a \,e^{2}\right)^{2} c}+\frac{2 \left(e x +d \right)^{\frac{3}{2}} d^{3} e^{3}}{\left(c \,e^{2} x^{2}-a \,e^{2}\right)^{2} a}-\frac{19 d^{2} e^{3} \arctanh \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{32 \sqrt{a c \,e^{2}}\, \sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}\, a}-\frac{19 d^{2} e^{3} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{32 \sqrt{a c \,e^{2}}\, \sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}\, a}-\frac{9 \left(e x +d \right)^{\frac{3}{2}} c \,d^{5} e}{8 \left(c \,e^{2} x^{2}-a \,e^{2}\right)^{2} a^{2}}+\frac{3 c \,d^{4} e \arctanh \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{8 \sqrt{a c \,e^{2}}\, \sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}\, a^{2}}+\frac{3 c \,d^{4} e \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{8 \sqrt{a c \,e^{2}}\, \sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}\, a^{2}}-\frac{7 \left(e x +d \right)^{\frac{3}{2}} d \,e^{5}}{8 \left(c \,e^{2} x^{2}-a \,e^{2}\right)^{2} c}+\frac{5 e^{5} \arctanh \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{32 \sqrt{a c \,e^{2}}\, \sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}\, c}+\frac{5 e^{5} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{32 \sqrt{a c \,e^{2}}\, \sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}\, c}-\frac{23 \left(e x +d \right)^{\frac{5}{2}} d^{2} e^{3}}{16 \left(c \,e^{2} x^{2}-a \,e^{2}\right)^{2} a}+\frac{9 \left(e x +d \right)^{\frac{5}{2}} c \,d^{4} e}{8 \left(c \,e^{2} x^{2}-a \,e^{2}\right)^{2} a^{2}}+\frac{9 \left(e x +d \right)^{\frac{5}{2}} e^{5}}{16 \left(c \,e^{2} x^{2}-a \,e^{2}\right)^{2} c}-\frac{d \,e^{3} \arctanh \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{4 \sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}\, a c}+\frac{d \,e^{3} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{4 \sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}\, a c}+\frac{\left(e x +d \right)^{\frac{7}{2}} d \,e^{3}}{2 \left(c \,e^{2} x^{2}-a \,e^{2}\right)^{2} a}-\frac{3 \left(e x +d \right)^{\frac{7}{2}} c \,d^{3} e}{8 \left(c \,e^{2} x^{2}-a \,e^{2}\right)^{2} a^{2}}+\frac{3 d^{3} e \arctanh \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{16 \sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}\, a^{2}}-\frac{3 d^{3} e \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{16 \sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}\, a^{2}}"," ",0,"1/2*e^3/(c*e^2*x^2-a*e^2)^2*d/a*(e*x+d)^(7/2)-3/8*e/(c*e^2*x^2-a*e^2)^2*d^3/a^2*(e*x+d)^(7/2)*c+9/16*e^5/(c*e^2*x^2-a*e^2)^2/c*(e*x+d)^(5/2)-23/16*e^3/(c*e^2*x^2-a*e^2)^2/a*(e*x+d)^(5/2)*d^2+9/8*e/(c*e^2*x^2-a*e^2)^2/a^2*c*(e*x+d)^(5/2)*d^4-7/8*e^5/(c*e^2*x^2-a*e^2)^2*d/c*(e*x+d)^(3/2)+2*e^3/(c*e^2*x^2-a*e^2)^2*d^3/a*(e*x+d)^(3/2)-9/8*e/(c*e^2*x^2-a*e^2)^2*d^5/a^2*c*(e*x+d)^(3/2)-5/16*e^7/(c*e^2*x^2-a*e^2)^2/c^2*a*(e*x+d)^(1/2)+e^5/(c*e^2*x^2-a*e^2)^2/c*(e*x+d)^(1/2)*d^2-17/16*e^3/(c*e^2*x^2-a*e^2)^2/a*(e*x+d)^(1/2)*d^4+3/8*e/(c*e^2*x^2-a*e^2)^2*c/a^2*(e*x+d)^(1/2)*d^6+5/32*e^5/c/(a*c*e^2)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)-19/32*e^3/a/(a*c*e^2)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d^2+3/8*e/a^2*c/(a*c*e^2)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d^4-1/4*e^3/a/c/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d+3/16*e/a^2/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d^3+5/32*e^5/c/(a*c*e^2)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)-19/32*e^3/a/(a*c*e^2)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d^2+3/8*e/a^2*c/(a*c*e^2)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d^4+1/4*e^3/a/c/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d-3/16*e/a^2/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d^3","B"
639,1,792,219,0.104000," ","int((e*x+d)^(5/2)/(-c*x^2+a)^3,x)","-\frac{3 \sqrt{e x +d}\, d^{3} e^{3}}{4 \left(c \,e^{2} x^{2}-a \,e^{2}\right)^{2} a}+\frac{3 \sqrt{e x +d}\, c \,d^{5} e}{8 \left(c \,e^{2} x^{2}-a \,e^{2}\right)^{2} a^{2}}+\frac{3 \sqrt{e x +d}\, d \,e^{5}}{8 \left(c \,e^{2} x^{2}-a \,e^{2}\right)^{2} c}+\frac{17 \left(e x +d \right)^{\frac{3}{2}} d^{2} e^{3}}{16 \left(c \,e^{2} x^{2}-a \,e^{2}\right)^{2} a}-\frac{9 d \,e^{3} \arctanh \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{32 \sqrt{a c \,e^{2}}\, \sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}\, a}-\frac{9 d \,e^{3} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{32 \sqrt{a c \,e^{2}}\, \sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}\, a}-\frac{9 \left(e x +d \right)^{\frac{3}{2}} c \,d^{4} e}{8 \left(c \,e^{2} x^{2}-a \,e^{2}\right)^{2} a^{2}}+\frac{3 c \,d^{3} e \arctanh \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{8 \sqrt{a c \,e^{2}}\, \sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}\, a^{2}}+\frac{3 c \,d^{3} e \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{8 \sqrt{a c \,e^{2}}\, \sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}\, a^{2}}+\frac{\left(e x +d \right)^{\frac{3}{2}} e^{5}}{16 \left(c \,e^{2} x^{2}-a \,e^{2}\right)^{2} c}-\frac{\left(e x +d \right)^{\frac{5}{2}} d \,e^{3}}{2 \left(c \,e^{2} x^{2}-a \,e^{2}\right)^{2} a}+\frac{9 \left(e x +d \right)^{\frac{5}{2}} c \,d^{3} e}{8 \left(c \,e^{2} x^{2}-a \,e^{2}\right)^{2} a^{2}}-\frac{3 e^{3} \arctanh \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{32 \sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}\, a c}+\frac{3 e^{3} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{32 \sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}\, a c}+\frac{3 \left(e x +d \right)^{\frac{7}{2}} e^{3}}{16 \left(c \,e^{2} x^{2}-a \,e^{2}\right)^{2} a}-\frac{3 \left(e x +d \right)^{\frac{7}{2}} c \,d^{2} e}{8 \left(c \,e^{2} x^{2}-a \,e^{2}\right)^{2} a^{2}}+\frac{3 d^{2} e \arctanh \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{16 \sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}\, a^{2}}-\frac{3 d^{2} e \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{16 \sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}\, a^{2}}"," ",0,"3/16*e^3/(c*e^2*x^2-a*e^2)^2/a*(e*x+d)^(7/2)-3/8*e/(c*e^2*x^2-a*e^2)^2/a^2*(e*x+d)^(7/2)*c*d^2-1/2*e^3/(c*e^2*x^2-a*e^2)^2*d/a*(e*x+d)^(5/2)+9/8*e/(c*e^2*x^2-a*e^2)^2*d^3/a^2*(e*x+d)^(5/2)*c+1/16*e^5/(c*e^2*x^2-a*e^2)^2/c*(e*x+d)^(3/2)+17/16*e^3/(c*e^2*x^2-a*e^2)^2/a*(e*x+d)^(3/2)*d^2-9/8*e/(c*e^2*x^2-a*e^2)^2/a^2*c*(e*x+d)^(3/2)*d^4+3/8*e^5/(c*e^2*x^2-a*e^2)^2*d/c*(e*x+d)^(1/2)-3/4*e^3/(c*e^2*x^2-a*e^2)^2*d^3/a*(e*x+d)^(1/2)+3/8*e/(c*e^2*x^2-a*e^2)^2*d^5/a^2*c*(e*x+d)^(1/2)-9/32*e^3/a/(a*c*e^2)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d+3/8*e/a^2*c/(a*c*e^2)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d^3-3/32*e^3/a/c/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)+3/16*e/a^2/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d^2-9/32*e^3/a/(a*c*e^2)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d+3/8*e/a^2*c/(a*c*e^2)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d^3+3/32*e^3/a/c/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)-3/16*e/a^2/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d^2","B"
640,1,608,208,0.116000," ","int((e*x+d)^(3/2)/(-c*x^2+a)^3,x)","-\frac{9 \sqrt{e x +d}\, d^{2} e^{3}}{16 \left(c \,e^{2} x^{2}-a \,e^{2}\right)^{2} a}+\frac{3 \sqrt{e x +d}\, c \,d^{4} e}{8 \left(c \,e^{2} x^{2}-a \,e^{2}\right)^{2} a^{2}}+\frac{3 \sqrt{e x +d}\, e^{5}}{16 \left(c \,e^{2} x^{2}-a \,e^{2}\right)^{2} c}+\frac{\left(e x +d \right)^{\frac{3}{2}} d \,e^{3}}{2 \left(c \,e^{2} x^{2}-a \,e^{2}\right)^{2} a}-\frac{3 e^{3} \arctanh \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{32 \sqrt{a c \,e^{2}}\, \sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}\, a}-\frac{3 e^{3} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{32 \sqrt{a c \,e^{2}}\, \sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}\, a}-\frac{9 \left(e x +d \right)^{\frac{3}{2}} c \,d^{3} e}{8 \left(c \,e^{2} x^{2}-a \,e^{2}\right)^{2} a^{2}}+\frac{3 c \,d^{2} e \arctanh \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{8 \sqrt{a c \,e^{2}}\, \sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}\, a^{2}}+\frac{3 c \,d^{2} e \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{8 \sqrt{a c \,e^{2}}\, \sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}\, a^{2}}+\frac{\left(e x +d \right)^{\frac{5}{2}} e^{3}}{16 \left(c \,e^{2} x^{2}-a \,e^{2}\right)^{2} a}+\frac{9 \left(e x +d \right)^{\frac{5}{2}} c \,d^{2} e}{8 \left(c \,e^{2} x^{2}-a \,e^{2}\right)^{2} a^{2}}-\frac{3 \left(e x +d \right)^{\frac{7}{2}} c d e}{8 \left(c \,e^{2} x^{2}-a \,e^{2}\right)^{2} a^{2}}+\frac{3 d e \arctanh \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{16 \sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}\, a^{2}}-\frac{3 d e \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{16 \sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}\, a^{2}}"," ",0,"-3/8*e/(c*e^2*x^2-a*e^2)^2*c*d/a^2*(e*x+d)^(7/2)+1/16*e^3/(c*e^2*x^2-a*e^2)^2/a*(e*x+d)^(5/2)+9/8*e/(c*e^2*x^2-a*e^2)^2/a^2*(e*x+d)^(5/2)*c*d^2+1/2*e^3/(c*e^2*x^2-a*e^2)^2*d/a*(e*x+d)^(3/2)-9/8*e/(c*e^2*x^2-a*e^2)^2*d^3/a^2*(e*x+d)^(3/2)*c+3/16*e^5/(c*e^2*x^2-a*e^2)^2/c*(e*x+d)^(1/2)-9/16*e^3/(c*e^2*x^2-a*e^2)^2/a*(e*x+d)^(1/2)*d^2+3/8*e/(c*e^2*x^2-a*e^2)^2/a^2*c*(e*x+d)^(1/2)*d^4-3/32*e^3/a/(a*c*e^2)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)+3/8*e/a^2/(a*c*e^2)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*c*d^2+3/16*e/a^2/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d-3/32*e^3/a/(a*c*e^2)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)+3/8*e/a^2/(a*c*e^2)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*c*d^2-3/16*e/a^2/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d","B"
641,1,803,221,0.642000," ","int((e*x+d)^(1/2)/(-c*x^2+a)^3,x)","\frac{5 c \,e^{3} \arctanh \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{32 \sqrt{a c \,e^{2}}\, \left(c d +\sqrt{a c \,e^{2}}\right) \sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}\, a}-\frac{5 c \,e^{3} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{32 \sqrt{a c \,e^{2}}\, \left(-c d +\sqrt{a c \,e^{2}}\right) \sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}\, a}+\frac{3 c^{2} d^{2} e \arctanh \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{8 \sqrt{a c \,e^{2}}\, \left(c d +\sqrt{a c \,e^{2}}\right) \sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}\, a^{2}}-\frac{3 c^{2} d^{2} e \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{8 \sqrt{a c \,e^{2}}\, \left(-c d +\sqrt{a c \,e^{2}}\right) \sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}\, a^{2}}+\frac{9 c d e \arctanh \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{16 \left(c d +\sqrt{a c \,e^{2}}\right) \sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}\, a^{2}}+\frac{9 c d e \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{16 \left(-c d +\sqrt{a c \,e^{2}}\right) \sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}\, a^{2}}-\frac{3 \left(e x +d \right)^{\frac{3}{2}} d e}{16 \left(e x -\frac{\sqrt{a c \,e^{2}}}{c}\right)^{2} \left(c d +\sqrt{a c \,e^{2}}\right) a^{2}}-\frac{3 \left(e x +d \right)^{\frac{3}{2}} d e}{16 \left(e x +\frac{\sqrt{a c \,e^{2}}}{c}\right)^{2} \left(c d -\sqrt{a c \,e^{2}}\right) a^{2}}+\frac{3 \sqrt{e x +d}\, d e}{16 \left(e x -\frac{\sqrt{a c \,e^{2}}}{c}\right)^{2} a^{2} c}+\frac{3 \sqrt{e x +d}\, d e}{16 \left(e x +\frac{\sqrt{a c \,e^{2}}}{c}\right)^{2} a^{2} c}-\frac{5 \sqrt{a c \,e^{2}}\, \left(e x +d \right)^{\frac{3}{2}} e}{32 \left(e x -\frac{\sqrt{a c \,e^{2}}}{c}\right)^{2} \left(c d +\sqrt{a c \,e^{2}}\right) a^{2} c}+\frac{5 \sqrt{a c \,e^{2}}\, \left(e x +d \right)^{\frac{3}{2}} e}{32 \left(e x +\frac{\sqrt{a c \,e^{2}}}{c}\right)^{2} \left(c d -\sqrt{a c \,e^{2}}\right) a^{2} c}+\frac{7 \sqrt{a c \,e^{2}}\, \sqrt{e x +d}\, e}{32 \left(e x -\frac{\sqrt{a c \,e^{2}}}{c}\right)^{2} a^{2} c^{2}}-\frac{7 \sqrt{a c \,e^{2}}\, \sqrt{e x +d}\, e}{32 \left(e x +\frac{\sqrt{a c \,e^{2}}}{c}\right)^{2} a^{2} c^{2}}"," ",0,"-3/16*e/a^2/(e*x-(a*c*e^2)^(1/2)/c)^2/(c*d+(a*c*e^2)^(1/2))*(e*x+d)^(3/2)*d-5/32*e/c/a^2*(a*c*e^2)^(1/2)/(e*x-(a*c*e^2)^(1/2)/c)^2/(c*d+(a*c*e^2)^(1/2))*(e*x+d)^(3/2)+3/16*e/c/a^2/(e*x-(a*c*e^2)^(1/2)/c)^2*(e*x+d)^(1/2)*d+7/32*e/c^2/a^2*(a*c*e^2)^(1/2)/(e*x-(a*c*e^2)^(1/2)/c)^2*(e*x+d)^(1/2)+5/32*e^3*c/a/(a*c*e^2)^(1/2)/(c*d+(a*c*e^2)^(1/2))/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)+3/8*e*c^2/a^2/(a*c*e^2)^(1/2)/(c*d+(a*c*e^2)^(1/2))/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d^2+9/16*e*c/a^2/(c*d+(a*c*e^2)^(1/2))/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d-3/16*e/a^2/(e*x+(a*c*e^2)^(1/2)/c)^2/(c*d-(a*c*e^2)^(1/2))*(e*x+d)^(3/2)*d+5/32*e/c/a^2*(a*c*e^2)^(1/2)/(e*x+(a*c*e^2)^(1/2)/c)^2/(c*d-(a*c*e^2)^(1/2))*(e*x+d)^(3/2)+3/16*e/c/a^2/(e*x+(a*c*e^2)^(1/2)/c)^2*(e*x+d)^(1/2)*d-7/32*e/c^2/a^2*(a*c*e^2)^(1/2)/(e*x+(a*c*e^2)^(1/2)/c)^2*(e*x+d)^(1/2)-5/32*e^3*c/a/(a*c*e^2)^(1/2)/(-c*d+(a*c*e^2)^(1/2))/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)-3/8*e*c^2/a^2/(a*c*e^2)^(1/2)/(-c*d+(a*c*e^2)^(1/2))/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d^2+9/16*e*c/a^2/(-c*d+(a*c*e^2)^(1/2))/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d","B"
642,1,956,255,0.601000," ","int(1/(-c*x^2+a)^3/(e*x+d)^(1/2),x)","\frac{21 c \,e^{3} \arctanh \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{32 \sqrt{a c \,e^{2}}\, \left(a \,e^{2}+c \,d^{2}+2 \sqrt{a c \,e^{2}}\, d \right) \sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}\, a}-\frac{21 c \,e^{3} \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{32 \sqrt{a c \,e^{2}}\, \left(-a \,e^{2}-c \,d^{2}+2 \sqrt{a c \,e^{2}}\, d \right) \sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}\, a}+\frac{3 c^{2} d^{2} e \arctanh \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{8 \sqrt{a c \,e^{2}}\, \left(a \,e^{2}+c \,d^{2}+2 \sqrt{a c \,e^{2}}\, d \right) \sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}\, a^{2}}-\frac{3 c^{2} d^{2} e \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{8 \sqrt{a c \,e^{2}}\, \left(-a \,e^{2}-c \,d^{2}+2 \sqrt{a c \,e^{2}}\, d \right) \sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}\, a^{2}}+\frac{15 c d e \arctanh \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{16 \left(a \,e^{2}+c \,d^{2}+2 \sqrt{a c \,e^{2}}\, d \right) \sqrt{\left(c d +\sqrt{a c \,e^{2}}\right) c}\, a^{2}}+\frac{15 c d e \arctan \left(\frac{\sqrt{e x +d}\, c}{\sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}}\right)}{16 \left(-a \,e^{2}-c \,d^{2}+2 \sqrt{a c \,e^{2}}\, d \right) \sqrt{\left(-c d +\sqrt{a c \,e^{2}}\right) c}\, a^{2}}-\frac{3 \left(e x +d \right)^{\frac{3}{2}} d e}{16 \left(e x -\frac{\sqrt{a c \,e^{2}}}{c}\right)^{2} \left(a \,e^{2}+c \,d^{2}+2 \sqrt{a c \,e^{2}}\, d \right) a^{2}}+\frac{3 \sqrt{e x +d}\, d e}{16 \left(e x -\frac{\sqrt{a c \,e^{2}}}{c}\right)^{2} \left(c d +\sqrt{a c \,e^{2}}\right) a^{2}}-\frac{3 \left(e x +d \right)^{\frac{3}{2}} d e}{16 \left(e x +\frac{\sqrt{a c \,e^{2}}}{c}\right)^{2} \left(a \,e^{2}+c \,d^{2}-2 \sqrt{a c \,e^{2}}\, d \right) a^{2}}+\frac{3 \sqrt{e x +d}\, d e}{16 \left(e x +\frac{\sqrt{a c \,e^{2}}}{c}\right)^{2} \left(c d -\sqrt{a c \,e^{2}}\right) a^{2}}-\frac{9 \sqrt{a c \,e^{2}}\, \left(e x +d \right)^{\frac{3}{2}} e}{32 \left(e x -\frac{\sqrt{a c \,e^{2}}}{c}\right)^{2} \left(a \,e^{2}+c \,d^{2}+2 \sqrt{a c \,e^{2}}\, d \right) a^{2} c}+\frac{11 \sqrt{a c \,e^{2}}\, \sqrt{e x +d}\, e}{32 \left(e x -\frac{\sqrt{a c \,e^{2}}}{c}\right)^{2} \left(c d +\sqrt{a c \,e^{2}}\right) a^{2} c}+\frac{9 \sqrt{a c \,e^{2}}\, \left(e x +d \right)^{\frac{3}{2}} e}{32 \left(e x +\frac{\sqrt{a c \,e^{2}}}{c}\right)^{2} \left(a \,e^{2}+c \,d^{2}-2 \sqrt{a c \,e^{2}}\, d \right) a^{2} c}-\frac{11 \sqrt{a c \,e^{2}}\, \sqrt{e x +d}\, e}{32 \left(e x +\frac{\sqrt{a c \,e^{2}}}{c}\right)^{2} \left(c d -\sqrt{a c \,e^{2}}\right) a^{2} c}"," ",0,"-3/16*e/a^2/(e*x-(a*c*e^2)^(1/2)/c)^2/(a*e^2+c*d^2+2*(a*c*e^2)^(1/2)*d)*(e*x+d)^(3/2)*d-9/32*e/c*(a*c*e^2)^(1/2)/a^2/(e*x-(a*c*e^2)^(1/2)/c)^2/(a*e^2+c*d^2+2*(a*c*e^2)^(1/2)*d)*(e*x+d)^(3/2)+3/16*e/a^2/(e*x-(a*c*e^2)^(1/2)/c)^2/(c*d+(a*c*e^2)^(1/2))*(e*x+d)^(1/2)*d+11/32*e/c*(a*c*e^2)^(1/2)/a^2/(e*x-(a*c*e^2)^(1/2)/c)^2/(c*d+(a*c*e^2)^(1/2))*(e*x+d)^(1/2)+21/32*e^3*c/(a*c*e^2)^(1/2)/a/(a*e^2+c*d^2+2*(a*c*e^2)^(1/2)*d)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)+3/8*e*c^2/(a*c*e^2)^(1/2)/a^2/(a*e^2+c*d^2+2*(a*c*e^2)^(1/2)*d)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d^2+15/16*e*c/a^2/(a*e^2+c*d^2+2*(a*c*e^2)^(1/2)*d)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)/((c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d-3/16*e/a^2/(e*x+(a*c*e^2)^(1/2)/c)^2/(a*e^2+c*d^2-2*(a*c*e^2)^(1/2)*d)*(e*x+d)^(3/2)*d+9/32*e/c*(a*c*e^2)^(1/2)/a^2/(e*x+(a*c*e^2)^(1/2)/c)^2/(a*e^2+c*d^2-2*(a*c*e^2)^(1/2)*d)*(e*x+d)^(3/2)+3/16*e/a^2/(e*x+(a*c*e^2)^(1/2)/c)^2/(c*d-(a*c*e^2)^(1/2))*(e*x+d)^(1/2)*d-11/32*e/c*(a*c*e^2)^(1/2)/a^2/(e*x+(a*c*e^2)^(1/2)/c)^2/(c*d-(a*c*e^2)^(1/2))*(e*x+d)^(1/2)-21/32*e^3*c/(a*c*e^2)^(1/2)/a/(-a*e^2-c*d^2+2*(a*c*e^2)^(1/2)*d)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)-3/8*e*c^2/(a*c*e^2)^(1/2)/a^2/(-a*e^2-c*d^2+2*(a*c*e^2)^(1/2)*d)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d^2+15/16*e*c/a^2/(-a*e^2-c*d^2+2*(a*c*e^2)^(1/2)*d)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)/((-c*d+(a*c*e^2)^(1/2))*c)^(1/2)*c)*d","B"
643,1,5915,757,0.224000," ","int((e*x+d)^(7/2)/(c*x^2+a)^3,x)","\text{output too large to display}"," ",0,"result too large to display","B"
644,1,4264,690,0.204000," ","int((e*x+d)^(5/2)/(c*x^2+a)^3,x)","\text{output too large to display}"," ",0,"3/16*e^3/(c*e^2*x^2+a*e^2)^2/a*(e*x+d)^(7/2)-1/16*e^5/(c*e^2*x^2+a*e^2)^2/c*(e*x+d)^(3/2)+3/64*e/a^2/c^(5/2)/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*arctan((2*(e*x+d)^(1/2)*c^(1/2)-(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*(a*c*e^2+c^2*d^2)^(1/2)-3/64*e/a^2/c^(3/2)/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*arctan((2*(e*x+d)^(1/2)*c^(1/2)+(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*d+3/64/e/a^3/c^2*ln((e*x+d)*c^(1/2)+(e*x+d)^(1/2)*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)+(a*e^2+c*d^2)^(1/2))*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*(a*c*e^2+c^2*d^2)^(1/2)*(a*e^2+c*d^2)^(1/2)*d-3/64/e/a^3/c^2*ln((e*x+d)*c^(1/2)-(e*x+d)^(1/2)*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)+(a*e^2+c*d^2)^(1/2))*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*(a*c*e^2+c^2*d^2)^(1/2)*(a*e^2+c*d^2)^(1/2)*d-3/32/e/a^3/c^(1/2)/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*arctan((2*(e*x+d)^(1/2)*c^(1/2)-(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*d^3+3/64*e/a^2/c^(5/2)/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*arctan((2*(e*x+d)^(1/2)*c^(1/2)+(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*(a*c*e^2+c^2*d^2)^(1/2)-3/32/e/a^3/c^(1/2)/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*arctan((2*(e*x+d)^(1/2)*c^(1/2)+(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*d^3-3/64*e/a^2/c^(3/2)/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*arctan((2*(e*x+d)^(1/2)*c^(1/2)-(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*d-3/32/e/a^3/c^2/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*arctan((2*(e*x+d)^(1/2)*c^(1/2)+(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*(a*c*e^2+c^2*d^2)^(1/2)*(a*e^2+c*d^2)^(1/2)*d-3/32/e/a^3/c^2/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*arctan((2*(e*x+d)^(1/2)*c^(1/2)-(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*(a*c*e^2+c^2*d^2)^(1/2)*(a*e^2+c*d^2)^(1/2)*d+3/32/e/a^3/c/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*arctan((2*(e*x+d)^(1/2)*c^(1/2)-(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*(a*e^2+c*d^2)^(1/2)*d^2+3/32/e/a^3/c^(3/2)/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*arctan((2*(e*x+d)^(1/2)*c^(1/2)-(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*(a*c*e^2+c^2*d^2)^(1/2)*d^2+3/32/e/a^3/c^(3/2)/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*arctan((2*(e*x+d)^(1/2)*c^(1/2)+(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*(a*c*e^2+c^2*d^2)^(1/2)*d^2+3/32/e/a^3/c/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*arctan((2*(e*x+d)^(1/2)*c^(1/2)+(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*(a*e^2+c*d^2)^(1/2)*d^2-3/64/e/a^3/c^(3/2)*ln((e*x+d)*c^(1/2)+(e*x+d)^(1/2)*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)+(a*e^2+c*d^2)^(1/2))*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*(a*c*e^2+c^2*d^2)^(1/2)*d^2+3/64/e/a^3/c^(3/2)*ln((e*x+d)*c^(1/2)-(e*x+d)^(1/2)*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)+(a*e^2+c*d^2)^(1/2))*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*(a*c*e^2+c^2*d^2)^(1/2)*d^2-3/64/e/a^3/c*ln((e*x+d)*c^(1/2)+(e*x+d)^(1/2)*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)+(a*e^2+c*d^2)^(1/2))*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*(a*e^2+c*d^2)^(1/2)*d^2+3/8*e/a^2/c/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*arctan((2*(e*x+d)^(1/2)*c^(1/2)+(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))*(a*e^2+c*d^2)^(1/2)*d+3/64/e/a^3/c*ln((e*x+d)*c^(1/2)-(e*x+d)^(1/2)*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)+(a*e^2+c*d^2)^(1/2))*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*(a*e^2+c*d^2)^(1/2)*d^2+3/8*e/a^2/c/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)*arctan((2*(e*x+d)^(1/2)*c^(1/2)-(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))/(-2*c*d+4*(a*e^2+c*d^2)^(1/2)*c^(1/2)-2*((a*e^2+c*d^2)*c)^(1/2))^(1/2))*(a*e^2+c*d^2)^(1/2)*d-3/64/e/a^3/c^(1/2)*ln((e*x+d)*c^(1/2)-(e*x+d)^(1/2)*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)+(a*e^2+c*d^2)^(1/2))*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*d^3+3/8*e/(c*e^2*x^2+a*e^2)^2/a^2*(e*x+d)^(7/2)*c*d^2-9/8*e/(c*e^2*x^2+a*e^2)^2*d^3/a^2*(e*x+d)^(5/2)*c-3/128*e/a^2/c^(5/2)*ln((e*x+d)*c^(1/2)+(e*x+d)^(1/2)*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)+(a*e^2+c*d^2)^(1/2))*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*(a*c*e^2+c^2*d^2)^(1/2)+9/8*e/(c*e^2*x^2+a*e^2)^2/a^2*c*(e*x+d)^(3/2)*d^4-3/8*e/(c*e^2*x^2+a*e^2)^2*d^5/a^2*c*(e*x+d)^(1/2)+3/128*e/a^2/c^(5/2)*ln((e*x+d)*c^(1/2)-(e*x+d)^(1/2)*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)+(a*e^2+c*d^2)^(1/2))*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*(a*c*e^2+c^2*d^2)^(1/2)+3/128*e/a^2/c^(3/2)*ln((e*x+d)*c^(1/2)+(e*x+d)^(1/2)*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)+(a*e^2+c*d^2)^(1/2))*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*d-3/128*e/a^2/c^(3/2)*ln((e*x+d)*c^(1/2)-(e*x+d)^(1/2)*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)+(a*e^2+c*d^2)^(1/2))*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*d+3/64/e/a^3/c^(1/2)*ln((e*x+d)*c^(1/2)+(e*x+d)^(1/2)*(2*c*d+2*((a*e^2+c*d^2)*c)^(1/2))^(1/2)+(a*e^2+c*d^2)^(1/2))*(2*c*d+2*(a*c*e^2+c^2*d^2)^(1/2))^(1/2)*d^3-3/4*e^3/(c*e^2*x^2+a*e^2)^2*d^3/a*(e*x+d)^(1/2)-3/8*e^5/(c*e^2*x^2+a*e^2)^2*d/c*(e*x+d)^(1/2)-1/2*e^3/(c*e^2*x^2+a*e^2)^2*d/a*(e*x+d)^(5/2)+17/16*e^3/(c*e^2*x^2+a*e^2)^2/a*(e*x+d)^(3/2)*d^2","B"
645,1,7538,621,0.247000," ","int((e*x+d)^(3/2)/(c*x^2+a)^3,x)","\text{output too large to display}"," ",0,"result too large to display","B"
646,-2,0,693,180.000000," ","int((e*x+d)^(1/2)/(c*x^2+a)^3,x)","\int \frac{\sqrt{e x +d}}{\left(c \,x^{2}+a \right)^{3}}\, dx"," ",0,"int((e*x+d)^(1/2)/(c*x^2+a)^3,x)","F"
647,-2,0,772,180.000000," ","int(1/(c*x^2+a)^3/(e*x+d)^(1/2),x)","\int \frac{1}{\left(c \,x^{2}+a \right)^{3} \sqrt{e x +d}}\, dx"," ",0,"int(1/(c*x^2+a)^3/(e*x+d)^(1/2),x)","F"
648,1,360,158,0.701000," ","int((3*x+2)^(1/2)/(x^2+1),x)","-\frac{\left(4+2 \sqrt{13}\right) \arctan \left(\frac{2 \sqrt{3 x +2}-\sqrt{4+2 \sqrt{13}}}{\sqrt{-4+2 \sqrt{13}}}\right)}{3 \sqrt{-4+2 \sqrt{13}}}+\frac{\sqrt{13}\, \left(4+2 \sqrt{13}\right) \arctan \left(\frac{2 \sqrt{3 x +2}-\sqrt{4+2 \sqrt{13}}}{\sqrt{-4+2 \sqrt{13}}}\right)}{6 \sqrt{-4+2 \sqrt{13}}}-\frac{\left(4+2 \sqrt{13}\right) \arctan \left(\frac{2 \sqrt{3 x +2}+\sqrt{4+2 \sqrt{13}}}{\sqrt{-4+2 \sqrt{13}}}\right)}{3 \sqrt{-4+2 \sqrt{13}}}+\frac{\sqrt{13}\, \left(4+2 \sqrt{13}\right) \arctan \left(\frac{2 \sqrt{3 x +2}+\sqrt{4+2 \sqrt{13}}}{\sqrt{-4+2 \sqrt{13}}}\right)}{6 \sqrt{-4+2 \sqrt{13}}}-\frac{\sqrt{4+2 \sqrt{13}}\, \ln \left(3 x +2+\sqrt{13}-\sqrt{3 x +2}\, \sqrt{4+2 \sqrt{13}}\right)}{6}+\frac{\sqrt{4+2 \sqrt{13}}\, \sqrt{13}\, \ln \left(3 x +2+\sqrt{13}-\sqrt{3 x +2}\, \sqrt{4+2 \sqrt{13}}\right)}{12}+\frac{\sqrt{4+2 \sqrt{13}}\, \ln \left(3 x +2+\sqrt{13}+\sqrt{3 x +2}\, \sqrt{4+2 \sqrt{13}}\right)}{6}-\frac{\sqrt{4+2 \sqrt{13}}\, \sqrt{13}\, \ln \left(3 x +2+\sqrt{13}+\sqrt{3 x +2}\, \sqrt{4+2 \sqrt{13}}\right)}{12}"," ",0,"-1/6*(4+2*13^(1/2))^(1/2)*ln(2+3*x+13^(1/2)-(3*x+2)^(1/2)*(4+2*13^(1/2))^(1/2))-1/3*(4+2*13^(1/2))/(-4+2*13^(1/2))^(1/2)*arctan((2*(3*x+2)^(1/2)-(4+2*13^(1/2))^(1/2))/(-4+2*13^(1/2))^(1/2))+1/12*(4+2*13^(1/2))^(1/2)*13^(1/2)*ln(2+3*x+13^(1/2)-(3*x+2)^(1/2)*(4+2*13^(1/2))^(1/2))+1/6*13^(1/2)*(4+2*13^(1/2))/(-4+2*13^(1/2))^(1/2)*arctan((2*(3*x+2)^(1/2)-(4+2*13^(1/2))^(1/2))/(-4+2*13^(1/2))^(1/2))+1/6*(4+2*13^(1/2))^(1/2)*ln(2+3*x+13^(1/2)+(3*x+2)^(1/2)*(4+2*13^(1/2))^(1/2))-1/3*(4+2*13^(1/2))/(-4+2*13^(1/2))^(1/2)*arctan((2*(3*x+2)^(1/2)+(4+2*13^(1/2))^(1/2))/(-4+2*13^(1/2))^(1/2))-1/12*(4+2*13^(1/2))^(1/2)*13^(1/2)*ln(2+3*x+13^(1/2)+(3*x+2)^(1/2)*(4+2*13^(1/2))^(1/2))+1/6*13^(1/2)*(4+2*13^(1/2))/(-4+2*13^(1/2))^(1/2)*arctan((2*(3*x+2)^(1/2)+(4+2*13^(1/2))^(1/2))/(-4+2*13^(1/2))^(1/2))","B"
649,1,566,245,0.292000," ","int((d*x+c)^(1/2)/(x^2+1),x)","-\frac{c^{2} \arctan \left(\frac{2 \sqrt{d x +c}-\sqrt{2 c +2 \sqrt{c^{2}+d^{2}}}}{\sqrt{-2 c +2 \sqrt{c^{2}+d^{2}}}}\right)}{\sqrt{-2 c +2 \sqrt{c^{2}+d^{2}}}\, d}-\frac{c^{2} \arctan \left(\frac{2 \sqrt{d x +c}+\sqrt{2 c +2 \sqrt{c^{2}+d^{2}}}}{\sqrt{-2 c +2 \sqrt{c^{2}+d^{2}}}}\right)}{\sqrt{-2 c +2 \sqrt{c^{2}+d^{2}}}\, d}-\frac{\sqrt{2 c +2 \sqrt{c^{2}+d^{2}}}\, c \ln \left(d x +c -\sqrt{d x +c}\, \sqrt{2 c +2 \sqrt{c^{2}+d^{2}}}+\sqrt{c^{2}+d^{2}}\right)}{4 d}+\frac{\sqrt{2 c +2 \sqrt{c^{2}+d^{2}}}\, c \ln \left(d x +c +\sqrt{d x +c}\, \sqrt{2 c +2 \sqrt{c^{2}+d^{2}}}+\sqrt{c^{2}+d^{2}}\right)}{4 d}+\frac{\left(c^{2}+d^{2}\right) \arctan \left(\frac{2 \sqrt{d x +c}-\sqrt{2 c +2 \sqrt{c^{2}+d^{2}}}}{\sqrt{-2 c +2 \sqrt{c^{2}+d^{2}}}}\right)}{\sqrt{-2 c +2 \sqrt{c^{2}+d^{2}}}\, d}+\frac{\left(c^{2}+d^{2}\right) \arctan \left(\frac{2 \sqrt{d x +c}+\sqrt{2 c +2 \sqrt{c^{2}+d^{2}}}}{\sqrt{-2 c +2 \sqrt{c^{2}+d^{2}}}}\right)}{\sqrt{-2 c +2 \sqrt{c^{2}+d^{2}}}\, d}+\frac{\sqrt{2 c +2 \sqrt{c^{2}+d^{2}}}\, \sqrt{c^{2}+d^{2}}\, \ln \left(d x +c -\sqrt{d x +c}\, \sqrt{2 c +2 \sqrt{c^{2}+d^{2}}}+\sqrt{c^{2}+d^{2}}\right)}{4 d}-\frac{\sqrt{2 c +2 \sqrt{c^{2}+d^{2}}}\, \sqrt{c^{2}+d^{2}}\, \ln \left(d x +c +\sqrt{d x +c}\, \sqrt{2 c +2 \sqrt{c^{2}+d^{2}}}+\sqrt{c^{2}+d^{2}}\right)}{4 d}"," ",0,"1/4*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/d*c*ln(d*x+c+(d*x+c)^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))-1/d*c^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(d*x+c)^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))-1/4*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/d*(c^2+d^2)^(1/2)*ln(d*x+c+(d*x+c)^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))+1/d*(c^2+d^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(d*x+c)^(1/2)+(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))-1/4*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/d*c*ln(d*x+c-(d*x+c)^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))-1/d*c^2/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(d*x+c)^(1/2)-(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))+1/4*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)/d*(c^2+d^2)^(1/2)*ln(d*x+c-(d*x+c)^(1/2)*(2*(c^2+d^2)^(1/2)+2*c)^(1/2)+(c^2+d^2)^(1/2))+1/d*(c^2+d^2)/(2*(c^2+d^2)^(1/2)-2*c)^(1/2)*arctan((2*(d*x+c)^(1/2)-(2*(c^2+d^2)^(1/2)+2*c)^(1/2))/(2*(c^2+d^2)^(1/2)-2*c)^(1/2))","B"
650,1,29,28,0.057000," ","int((3*x+2)^(1/2)/(-x^2+1),x)","\sqrt{5}\, \arctanh \left(\frac{\sqrt{3 x +2}\, \sqrt{5}}{5}\right)-\arctan \left(\sqrt{3 x +2}\right)"," ",0,"-arctan((3*x+2)^(1/2))+arctanh(1/5*(3*x+2)^(1/2)*5^(1/2))*5^(1/2)","A"
651,1,47,46,0.087000," ","int((d*x+c)^(1/2)/(-x^2+1),x)","\sqrt{c +d}\, \arctanh \left(\frac{\sqrt{d x +c}}{\sqrt{c +d}}\right)-\sqrt{-c +d}\, \arctan \left(\frac{\sqrt{d x +c}}{\sqrt{-c +d}}\right)"," ",0,"arctanh((d*x+c)^(1/2)/(c+d)^(1/2))*(c+d)^(1/2)-(-c+d)^(1/2)*arctan((d*x+c)^(1/2)/(-c+d)^(1/2))","A"
652,1,944,315,0.366000," ","int((3*x+2)^(1/2)/(b*x^2+a),x)","-\frac{\sqrt{4 b +2 \sqrt{9 a b +4 b^{2}}}\, \sqrt{4 b +2 \sqrt{\left(9 a +4 b \right) b}}\, \arctan \left(\frac{2 \sqrt{3 x +2}\, \sqrt{b}-\sqrt{4 b +2 \sqrt{\left(9 a +4 b \right) b}}}{\sqrt{-4 b +4 \sqrt{9 a +4 b}\, \sqrt{b}-2 \sqrt{\left(9 a +4 b \right) b}}}\right)}{3 \sqrt{-4 b +4 \sqrt{9 a +4 b}\, \sqrt{b}-2 \sqrt{\left(9 a +4 b \right) b}}\, a \sqrt{b}}-\frac{\sqrt{4 b +2 \sqrt{9 a b +4 b^{2}}}\, \sqrt{4 b +2 \sqrt{\left(9 a +4 b \right) b}}\, \arctan \left(\frac{2 \sqrt{3 x +2}\, \sqrt{b}+\sqrt{4 b +2 \sqrt{\left(9 a +4 b \right) b}}}{\sqrt{-4 b +4 \sqrt{9 a +4 b}\, \sqrt{b}-2 \sqrt{\left(9 a +4 b \right) b}}}\right)}{3 \sqrt{-4 b +4 \sqrt{9 a +4 b}\, \sqrt{b}-2 \sqrt{\left(9 a +4 b \right) b}}\, a \sqrt{b}}-\frac{\sqrt{4 b +2 \sqrt{9 a b +4 b^{2}}}\, \ln \left(\left(3 x +2\right) \sqrt{b}-\sqrt{3 x +2}\, \sqrt{4 b +2 \sqrt{\left(9 a +4 b \right) b}}+\sqrt{9 a +4 b}\right)}{6 a \sqrt{b}}+\frac{\sqrt{4 b +2 \sqrt{9 a b +4 b^{2}}}\, \ln \left(\left(3 x +2\right) \sqrt{b}+\sqrt{3 x +2}\, \sqrt{4 b +2 \sqrt{\left(9 a +4 b \right) b}}+\sqrt{9 a +4 b}\right)}{6 a \sqrt{b}}+\frac{\sqrt{4 b +2 \sqrt{9 a b +4 b^{2}}}\, \sqrt{9 a b +4 b^{2}}\, \sqrt{4 b +2 \sqrt{\left(9 a +4 b \right) b}}\, \arctan \left(\frac{2 \sqrt{3 x +2}\, \sqrt{b}-\sqrt{4 b +2 \sqrt{\left(9 a +4 b \right) b}}}{\sqrt{-4 b +4 \sqrt{9 a +4 b}\, \sqrt{b}-2 \sqrt{\left(9 a +4 b \right) b}}}\right)}{6 \sqrt{-4 b +4 \sqrt{9 a +4 b}\, \sqrt{b}-2 \sqrt{\left(9 a +4 b \right) b}}\, a \,b^{\frac{3}{2}}}+\frac{\sqrt{4 b +2 \sqrt{9 a b +4 b^{2}}}\, \sqrt{9 a b +4 b^{2}}\, \sqrt{4 b +2 \sqrt{\left(9 a +4 b \right) b}}\, \arctan \left(\frac{2 \sqrt{3 x +2}\, \sqrt{b}+\sqrt{4 b +2 \sqrt{\left(9 a +4 b \right) b}}}{\sqrt{-4 b +4 \sqrt{9 a +4 b}\, \sqrt{b}-2 \sqrt{\left(9 a +4 b \right) b}}}\right)}{6 \sqrt{-4 b +4 \sqrt{9 a +4 b}\, \sqrt{b}-2 \sqrt{\left(9 a +4 b \right) b}}\, a \,b^{\frac{3}{2}}}+\frac{\sqrt{4 b +2 \sqrt{9 a b +4 b^{2}}}\, \sqrt{9 a b +4 b^{2}}\, \ln \left(\left(3 x +2\right) \sqrt{b}-\sqrt{3 x +2}\, \sqrt{4 b +2 \sqrt{\left(9 a +4 b \right) b}}+\sqrt{9 a +4 b}\right)}{12 a \,b^{\frac{3}{2}}}-\frac{\sqrt{4 b +2 \sqrt{9 a b +4 b^{2}}}\, \sqrt{9 a b +4 b^{2}}\, \ln \left(\left(3 x +2\right) \sqrt{b}+\sqrt{3 x +2}\, \sqrt{4 b +2 \sqrt{\left(9 a +4 b \right) b}}+\sqrt{9 a +4 b}\right)}{12 a \,b^{\frac{3}{2}}}"," ",0,"1/12*(2*(9*a*b+4*b^2)^(1/2)+4*b)^(1/2)/a/b^(3/2)*(9*a*b+4*b^2)^(1/2)*ln((3*x+2)*b^(1/2)-(3*x+2)^(1/2)*(2*(b*(9*a+4*b))^(1/2)+4*b)^(1/2)+(9*a+4*b)^(1/2))+1/6*(2*(9*a*b+4*b^2)^(1/2)+4*b)^(1/2)/a/b^(3/2)*(9*a*b+4*b^2)^(1/2)*(2*(b*(9*a+4*b))^(1/2)+4*b)^(1/2)/(4*(9*a+4*b)^(1/2)*b^(1/2)-2*(b*(9*a+4*b))^(1/2)-4*b)^(1/2)*arctan((2*b^(1/2)*(3*x+2)^(1/2)-(2*(b*(9*a+4*b))^(1/2)+4*b)^(1/2))/(4*(9*a+4*b)^(1/2)*b^(1/2)-2*(b*(9*a+4*b))^(1/2)-4*b)^(1/2))-1/6*(2*(9*a*b+4*b^2)^(1/2)+4*b)^(1/2)/a/b^(1/2)*ln((3*x+2)*b^(1/2)-(3*x+2)^(1/2)*(2*(b*(9*a+4*b))^(1/2)+4*b)^(1/2)+(9*a+4*b)^(1/2))-1/3*(2*(9*a*b+4*b^2)^(1/2)+4*b)^(1/2)/a/b^(1/2)*(2*(b*(9*a+4*b))^(1/2)+4*b)^(1/2)/(4*(9*a+4*b)^(1/2)*b^(1/2)-2*(b*(9*a+4*b))^(1/2)-4*b)^(1/2)*arctan((2*b^(1/2)*(3*x+2)^(1/2)-(2*(b*(9*a+4*b))^(1/2)+4*b)^(1/2))/(4*(9*a+4*b)^(1/2)*b^(1/2)-2*(b*(9*a+4*b))^(1/2)-4*b)^(1/2))-1/12*(2*(9*a*b+4*b^2)^(1/2)+4*b)^(1/2)/a/b^(3/2)*(9*a*b+4*b^2)^(1/2)*ln((3*x+2)*b^(1/2)+(3*x+2)^(1/2)*(2*(b*(9*a+4*b))^(1/2)+4*b)^(1/2)+(9*a+4*b)^(1/2))+1/6*(2*(9*a*b+4*b^2)^(1/2)+4*b)^(1/2)/a/b^(3/2)*(9*a*b+4*b^2)^(1/2)*(2*(b*(9*a+4*b))^(1/2)+4*b)^(1/2)/(4*(9*a+4*b)^(1/2)*b^(1/2)-2*(b*(9*a+4*b))^(1/2)-4*b)^(1/2)*arctan((2*b^(1/2)*(3*x+2)^(1/2)+(2*(b*(9*a+4*b))^(1/2)+4*b)^(1/2))/(4*(9*a+4*b)^(1/2)*b^(1/2)-2*(b*(9*a+4*b))^(1/2)-4*b)^(1/2))+1/6*(2*(9*a*b+4*b^2)^(1/2)+4*b)^(1/2)/a/b^(1/2)*ln((3*x+2)*b^(1/2)+(3*x+2)^(1/2)*(2*(b*(9*a+4*b))^(1/2)+4*b)^(1/2)+(9*a+4*b)^(1/2))-1/3*(2*(9*a*b+4*b^2)^(1/2)+4*b)^(1/2)/a/b^(1/2)*(2*(b*(9*a+4*b))^(1/2)+4*b)^(1/2)/(4*(9*a+4*b)^(1/2)*b^(1/2)-2*(b*(9*a+4*b))^(1/2)-4*b)^(1/2)*arctan((2*b^(1/2)*(3*x+2)^(1/2)+(2*(b*(9*a+4*b))^(1/2)+4*b)^(1/2))/(4*(9*a+4*b)^(1/2)*b^(1/2)-2*(b*(9*a+4*b))^(1/2)-4*b)^(1/2))","B"
653,1,182,92,0.100000," ","int((3*x+2)^(1/2)/(-b*x^2+a),x)","\frac{2 b \arctanh \left(\frac{\sqrt{3 x +2}\, b}{\sqrt{\left(2 b +3 \sqrt{a b}\right) b}}\right)}{\sqrt{a b}\, \sqrt{\left(2 b +3 \sqrt{a b}\right) b}}+\frac{2 b \arctan \left(\frac{\sqrt{3 x +2}\, b}{\sqrt{\left(-2 b +3 \sqrt{a b}\right) b}}\right)}{\sqrt{a b}\, \sqrt{\left(-2 b +3 \sqrt{a b}\right) b}}+\frac{3 \arctanh \left(\frac{\sqrt{3 x +2}\, b}{\sqrt{\left(2 b +3 \sqrt{a b}\right) b}}\right)}{\sqrt{\left(2 b +3 \sqrt{a b}\right) b}}-\frac{3 \arctan \left(\frac{\sqrt{3 x +2}\, b}{\sqrt{\left(-2 b +3 \sqrt{a b}\right) b}}\right)}{\sqrt{\left(-2 b +3 \sqrt{a b}\right) b}}"," ",0,"3/((3*(a*b)^(1/2)+2*b)*b)^(1/2)*arctanh((3*x+2)^(1/2)*b/((3*(a*b)^(1/2)+2*b)*b)^(1/2))+2*b/(a*b)^(1/2)/((3*(a*b)^(1/2)+2*b)*b)^(1/2)*arctanh((3*x+2)^(1/2)*b/((3*(a*b)^(1/2)+2*b)*b)^(1/2))-3/((3*(a*b)^(1/2)-2*b)*b)^(1/2)*arctan((3*x+2)^(1/2)*b/((3*(a*b)^(1/2)-2*b)*b)^(1/2))+2*b/(a*b)^(1/2)/((3*(a*b)^(1/2)-2*b)*b)^(1/2)*arctan((3*x+2)^(1/2)*b/((3*(a*b)^(1/2)-2*b)*b)^(1/2))","A"
654,1,336,146,0.701000," ","int((x+1)^(1/2)/(x^2+1),x)","\frac{\sqrt{2}\, \left(2+2 \sqrt{2}\right) \arctan \left(\frac{2 \sqrt{x +1}-\sqrt{2+2 \sqrt{2}}}{\sqrt{-2+2 \sqrt{2}}}\right)}{2 \sqrt{-2+2 \sqrt{2}}}-\frac{\left(2+2 \sqrt{2}\right) \arctan \left(\frac{2 \sqrt{x +1}-\sqrt{2+2 \sqrt{2}}}{\sqrt{-2+2 \sqrt{2}}}\right)}{2 \sqrt{-2+2 \sqrt{2}}}+\frac{\sqrt{2}\, \left(2+2 \sqrt{2}\right) \arctan \left(\frac{2 \sqrt{x +1}+\sqrt{2+2 \sqrt{2}}}{\sqrt{-2+2 \sqrt{2}}}\right)}{2 \sqrt{-2+2 \sqrt{2}}}-\frac{\left(2+2 \sqrt{2}\right) \arctan \left(\frac{2 \sqrt{x +1}+\sqrt{2+2 \sqrt{2}}}{\sqrt{-2+2 \sqrt{2}}}\right)}{2 \sqrt{-2+2 \sqrt{2}}}+\frac{\sqrt{2+2 \sqrt{2}}\, \sqrt{2}\, \ln \left(x +1+\sqrt{2}-\sqrt{x +1}\, \sqrt{2+2 \sqrt{2}}\right)}{4}-\frac{\sqrt{2+2 \sqrt{2}}\, \ln \left(x +1+\sqrt{2}-\sqrt{x +1}\, \sqrt{2+2 \sqrt{2}}\right)}{4}-\frac{\sqrt{2+2 \sqrt{2}}\, \sqrt{2}\, \ln \left(x +1+\sqrt{2}+\sqrt{x +1}\, \sqrt{2+2 \sqrt{2}}\right)}{4}+\frac{\sqrt{2+2 \sqrt{2}}\, \ln \left(x +1+\sqrt{2}+\sqrt{x +1}\, \sqrt{2+2 \sqrt{2}}\right)}{4}"," ",0,"-1/4*(2+2*2^(1/2))^(1/2)*2^(1/2)*ln(1+x+2^(1/2)+(x+1)^(1/2)*(2+2*2^(1/2))^(1/2))+1/2*2^(1/2)*(2+2*2^(1/2))/(-2+2*2^(1/2))^(1/2)*arctan((2*(x+1)^(1/2)+(2+2*2^(1/2))^(1/2))/(-2+2*2^(1/2))^(1/2))+1/4*(2+2*2^(1/2))^(1/2)*ln(1+x+2^(1/2)+(x+1)^(1/2)*(2+2*2^(1/2))^(1/2))-1/2*(2+2*2^(1/2))/(-2+2*2^(1/2))^(1/2)*arctan((2*(x+1)^(1/2)+(2+2*2^(1/2))^(1/2))/(-2+2*2^(1/2))^(1/2))+1/4*(2+2*2^(1/2))^(1/2)*2^(1/2)*ln(1+x+2^(1/2)-(x+1)^(1/2)*(2+2*2^(1/2))^(1/2))+1/2*2^(1/2)*(2+2*2^(1/2))/(-2+2*2^(1/2))^(1/2)*arctan((2*(x+1)^(1/2)-(2+2*2^(1/2))^(1/2))/(-2+2*2^(1/2))^(1/2))-1/4*(2+2*2^(1/2))^(1/2)*ln(1+x+2^(1/2)-(x+1)^(1/2)*(2+2*2^(1/2))^(1/2))-1/2*(2+2*2^(1/2))/(-2+2*2^(1/2))^(1/2)*arctan((2*(x+1)^(1/2)-(2+2*2^(1/2))^(1/2))/(-2+2*2^(1/2))^(1/2))","B"
655,1,420,138,0.126000," ","int(1/(x^2+1)/(x+1)^(1/2),x)","\frac{\sqrt{2}\, \left(2+2 \sqrt{2}\right) \arctan \left(\frac{2 \sqrt{x +1}-\sqrt{2+2 \sqrt{2}}}{\sqrt{-2+2 \sqrt{2}}}\right)}{4 \sqrt{-2+2 \sqrt{2}}}-\frac{\left(2+2 \sqrt{2}\right) \arctan \left(\frac{2 \sqrt{x +1}-\sqrt{2+2 \sqrt{2}}}{\sqrt{-2+2 \sqrt{2}}}\right)}{2 \sqrt{-2+2 \sqrt{2}}}+\frac{\sqrt{2}\, \arctan \left(\frac{2 \sqrt{x +1}-\sqrt{2+2 \sqrt{2}}}{\sqrt{-2+2 \sqrt{2}}}\right)}{\sqrt{-2+2 \sqrt{2}}}+\frac{\sqrt{2}\, \left(2+2 \sqrt{2}\right) \arctan \left(\frac{2 \sqrt{x +1}+\sqrt{2+2 \sqrt{2}}}{\sqrt{-2+2 \sqrt{2}}}\right)}{4 \sqrt{-2+2 \sqrt{2}}}-\frac{\left(2+2 \sqrt{2}\right) \arctan \left(\frac{2 \sqrt{x +1}+\sqrt{2+2 \sqrt{2}}}{\sqrt{-2+2 \sqrt{2}}}\right)}{2 \sqrt{-2+2 \sqrt{2}}}+\frac{\sqrt{2}\, \arctan \left(\frac{2 \sqrt{x +1}+\sqrt{2+2 \sqrt{2}}}{\sqrt{-2+2 \sqrt{2}}}\right)}{\sqrt{-2+2 \sqrt{2}}}-\frac{\sqrt{2+2 \sqrt{2}}\, \ln \left(x +1+\sqrt{2}-\sqrt{x +1}\, \sqrt{2+2 \sqrt{2}}\right)}{4}+\frac{\sqrt{2+2 \sqrt{2}}\, \sqrt{2}\, \ln \left(x +1+\sqrt{2}-\sqrt{x +1}\, \sqrt{2+2 \sqrt{2}}\right)}{8}+\frac{\sqrt{2+2 \sqrt{2}}\, \ln \left(x +1+\sqrt{2}+\sqrt{x +1}\, \sqrt{2+2 \sqrt{2}}\right)}{4}-\frac{\sqrt{2+2 \sqrt{2}}\, \sqrt{2}\, \ln \left(x +1+\sqrt{2}+\sqrt{x +1}\, \sqrt{2+2 \sqrt{2}}\right)}{8}"," ",0,"1/4*(2+2*2^(1/2))^(1/2)*ln(x+1+2^(1/2)+(x+1)^(1/2)*(2+2*2^(1/2))^(1/2))-1/8*(2+2*2^(1/2))^(1/2)*2^(1/2)*ln(x+1+2^(1/2)+(x+1)^(1/2)*(2+2*2^(1/2))^(1/2))+1/4*2^(1/2)*(2+2*2^(1/2))/(-2+2*2^(1/2))^(1/2)*arctan((2*(x+1)^(1/2)+(2+2*2^(1/2))^(1/2))/(-2+2*2^(1/2))^(1/2))-1/2*(2+2*2^(1/2))/(-2+2*2^(1/2))^(1/2)*arctan((2*(x+1)^(1/2)+(2+2*2^(1/2))^(1/2))/(-2+2*2^(1/2))^(1/2))+1/(-2+2*2^(1/2))^(1/2)*arctan((2*(x+1)^(1/2)+(2+2*2^(1/2))^(1/2))/(-2+2*2^(1/2))^(1/2))*2^(1/2)-1/4*(2+2*2^(1/2))^(1/2)*ln(x+1+2^(1/2)-(x+1)^(1/2)*(2+2*2^(1/2))^(1/2))+1/8*(2+2*2^(1/2))^(1/2)*2^(1/2)*ln(x+1+2^(1/2)-(x+1)^(1/2)*(2+2*2^(1/2))^(1/2))+1/4*2^(1/2)*(2+2*2^(1/2))/(-2+2*2^(1/2))^(1/2)*arctan((2*(x+1)^(1/2)-(2+2*2^(1/2))^(1/2))/(-2+2*2^(1/2))^(1/2))-1/2*(2+2*2^(1/2))/(-2+2*2^(1/2))^(1/2)*arctan((2*(x+1)^(1/2)-(2+2*2^(1/2))^(1/2))/(-2+2*2^(1/2))^(1/2))+1/(-2+2*2^(1/2))^(1/2)*arctan((2*(x+1)^(1/2)-(2+2*2^(1/2))^(1/2))/(-2+2*2^(1/2))^(1/2))*2^(1/2)","B"
656,1,639,188,1.071000," ","int((x-1)^(1/2)/(x^2+1)^3,x)","\frac{\sqrt{2}\, \arctan \left(\frac{2 \sqrt{x -1}-\sqrt{-2+2 \sqrt{2}}}{\sqrt{2+2 \sqrt{2}}}\right)}{64 \left(3+2 \sqrt{2}\right) \sqrt{2+2 \sqrt{2}}}+\frac{5 \arctan \left(\frac{2 \sqrt{x -1}-\sqrt{-2+2 \sqrt{2}}}{\sqrt{2+2 \sqrt{2}}}\right)}{64 \left(3+2 \sqrt{2}\right) \sqrt{2+2 \sqrt{2}}}+\frac{\sqrt{2}\, \arctan \left(\frac{2 \sqrt{x -1}+\sqrt{-2+2 \sqrt{2}}}{\sqrt{2+2 \sqrt{2}}}\right)}{64 \left(3+2 \sqrt{2}\right) \sqrt{2+2 \sqrt{2}}}+\frac{5 \arctan \left(\frac{2 \sqrt{x -1}+\sqrt{-2+2 \sqrt{2}}}{\sqrt{2+2 \sqrt{2}}}\right)}{64 \left(3+2 \sqrt{2}\right) \sqrt{2+2 \sqrt{2}}}+\frac{13 \sqrt{2}\, \sqrt{-2+2 \sqrt{2}}\, \ln \left(x -1-\sqrt{x -1}\, \sqrt{-2+2 \sqrt{2}}+\sqrt{2}\right)}{32 \left(3+2 \sqrt{2}\right)}+\frac{147 \sqrt{-2+2 \sqrt{2}}\, \ln \left(x -1-\sqrt{x -1}\, \sqrt{-2+2 \sqrt{2}}+\sqrt{2}\right)}{256 \left(3+2 \sqrt{2}\right)}-\frac{13 \sqrt{2}\, \sqrt{-2+2 \sqrt{2}}\, \ln \left(x -1+\sqrt{x -1}\, \sqrt{-2+2 \sqrt{2}}+\sqrt{2}\right)}{32 \left(3+2 \sqrt{2}\right)}-\frac{147 \sqrt{-2+2 \sqrt{2}}\, \ln \left(x -1+\sqrt{x -1}\, \sqrt{-2+2 \sqrt{2}}+\sqrt{2}\right)}{256 \left(3+2 \sqrt{2}\right)}-\frac{-\frac{4 \left(-759-506 \sqrt{2}\right) \left(x -1\right)^{\frac{3}{2}}}{23 \left(-6-4 \sqrt{2}\right)}-\frac{\left(-5336-3588 \sqrt{2}\right) \sqrt{-2+2 \sqrt{2}}\, \left(x -1\right)}{23 \left(-6-4 \sqrt{2}\right)}-\frac{2 \left(-2392 \sqrt{2}-3036\right) \sqrt{x -1}}{23 \left(-6-4 \sqrt{2}\right)}-\frac{\left(-3312 \sqrt{2}-4416\right) \sqrt{-2+2 \sqrt{2}}}{46 \left(-6-4 \sqrt{2}\right)}}{128 \left(x -1+\sqrt{x -1}\, \sqrt{-2+2 \sqrt{2}}+\sqrt{2}\right)^{2}}+\frac{\frac{4 \left(-759-506 \sqrt{2}\right) \left(x -1\right)^{\frac{3}{2}}}{23 \left(-6-4 \sqrt{2}\right)}-\frac{\left(-5336-3588 \sqrt{2}\right) \sqrt{-2+2 \sqrt{2}}\, \left(x -1\right)}{23 \left(-6-4 \sqrt{2}\right)}+\frac{2 \left(-2392 \sqrt{2}-3036\right) \sqrt{x -1}}{23 \left(-6-4 \sqrt{2}\right)}-\frac{\left(-3312 \sqrt{2}-4416\right) \sqrt{-2+2 \sqrt{2}}}{46 \left(-6-4 \sqrt{2}\right)}}{128 \left(x -1-\sqrt{x -1}\, \sqrt{-2+2 \sqrt{2}}+\sqrt{2}\right)^{2}}"," ",0,"-1/128*(-4/23*(-759-506*2^(1/2))/(-6-4*2^(1/2))*(x-1)^(3/2)-1/23/(-6-4*2^(1/2))*(-5336-3588*2^(1/2))*(-2+2*2^(1/2))^(1/2)*(x-1)-2/23*(-2392*2^(1/2)-3036)/(-6-4*2^(1/2))*(x-1)^(1/2)-1/46*(-3312*2^(1/2)-4416)*(-2+2*2^(1/2))^(1/2)/(-6-4*2^(1/2)))/(x-1+(x-1)^(1/2)*(-2+2*2^(1/2))^(1/2)+2^(1/2))^2-13/32/(3+2*2^(1/2))*ln(x-1+(x-1)^(1/2)*(-2+2*2^(1/2))^(1/2)+2^(1/2))*2^(1/2)*(-2+2*2^(1/2))^(1/2)-147/256/(3+2*2^(1/2))*ln(x-1+(x-1)^(1/2)*(-2+2*2^(1/2))^(1/2)+2^(1/2))*(-2+2*2^(1/2))^(1/2)+1/64/(3+2*2^(1/2))/(2+2*2^(1/2))^(1/2)*arctan((2*(x-1)^(1/2)+(-2+2*2^(1/2))^(1/2))/(2+2*2^(1/2))^(1/2))*2^(1/2)+5/64/(3+2*2^(1/2))/(2+2*2^(1/2))^(1/2)*arctan((2*(x-1)^(1/2)+(-2+2*2^(1/2))^(1/2))/(2+2*2^(1/2))^(1/2))+1/128*(4/23*(-759-506*2^(1/2))/(-6-4*2^(1/2))*(x-1)^(3/2)-1/23/(-6-4*2^(1/2))*(-5336-3588*2^(1/2))*(-2+2*2^(1/2))^(1/2)*(x-1)+2/23*(-2392*2^(1/2)-3036)/(-6-4*2^(1/2))*(x-1)^(1/2)-1/46*(-3312*2^(1/2)-4416)*(-2+2*2^(1/2))^(1/2)/(-6-4*2^(1/2)))/(x-1-(x-1)^(1/2)*(-2+2*2^(1/2))^(1/2)+2^(1/2))^2+13/32/(3+2*2^(1/2))*ln(x-1-(x-1)^(1/2)*(-2+2*2^(1/2))^(1/2)+2^(1/2))*2^(1/2)*(-2+2*2^(1/2))^(1/2)+147/256/(3+2*2^(1/2))*ln(x-1-(x-1)^(1/2)*(-2+2*2^(1/2))^(1/2)+2^(1/2))*(-2+2*2^(1/2))^(1/2)+1/64/(3+2*2^(1/2))/(2+2*2^(1/2))^(1/2)*arctan((2*(x-1)^(1/2)-(-2+2*2^(1/2))^(1/2))/(2+2*2^(1/2))^(1/2))*2^(1/2)+5/64/(3+2*2^(1/2))/(2+2*2^(1/2))^(1/2)*arctan((2*(x-1)^(1/2)-(-2+2*2^(1/2))^(1/2))/(2+2*2^(1/2))^(1/2))","B"
657,1,1386,326,0.303000," ","int((e*x+d)^(3/2)*(c*x^2+a)^(1/2),x)","\frac{2 \sqrt{e x +d}\, \sqrt{c \,x^{2}+a}\, \left(15 c^{3} e^{5} x^{5}+39 c^{3} d \,e^{4} x^{4}+25 a \,c^{2} e^{5} x^{3}+27 c^{3} d^{2} e^{3} x^{3}+49 a \,c^{2} d \,e^{4} x^{2}+3 c^{3} d^{3} e^{2} x^{2}-58 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} c d \,e^{4} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+48 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} c d \,e^{4} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+10 a^{2} c \,e^{5} x -52 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a \,c^{2} d^{3} e^{2} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+48 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a \,c^{2} d^{3} e^{2} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+27 a \,c^{2} d^{2} e^{3} x +6 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, c^{3} d^{5} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+10 a^{2} c d \,e^{4}+10 \sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} e^{5} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+3 a \,c^{2} d^{3} e^{2}+4 \sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a c \,d^{2} e^{3} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-6 \sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, c^{2} d^{4} e \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)\right)}{105 \left(c e \,x^{3}+c d \,x^{2}+a e x +a d \right) c^{2} e^{3}}"," ",0,"2/105*(e*x+d)^(1/2)*(c*x^2+a)^(1/2)*(15*x^5*c^3*e^5+10*(-a*c)^(1/2)*(-(e*x+d)*c/((-a*c)^(1/2)*e-c*d))^(1/2)*((-c*x+(-a*c)^(1/2))*e/((-a*c)^(1/2)*e+c*d))^(1/2)*((c*x+(-a*c)^(1/2))*e/((-a*c)^(1/2)*e-c*d))^(1/2)*EllipticF((-(e*x+d)*c/((-a*c)^(1/2)*e-c*d))^(1/2),(-((-a*c)^(1/2)*e-c*d)/((-a*c)^(1/2)*e+c*d))^(1/2))*a^2*e^5+4*(-a*c)^(1/2)*(-(e*x+d)*c/((-a*c)^(1/2)*e-c*d))^(1/2)*((-c*x+(-a*c)^(1/2))*e/((-a*c)^(1/2)*e+c*d))^(1/2)*((c*x+(-a*c)^(1/2))*e/((-a*c)^(1/2)*e-c*d))^(1/2)*EllipticF((-(e*x+d)*c/((-a*c)^(1/2)*e-c*d))^(1/2),(-((-a*c)^(1/2)*e-c*d)/((-a*c)^(1/2)*e+c*d))^(1/2))*a*c*d^2*e^3-6*(-a*c)^(1/2)*(-(e*x+d)*c/((-a*c)^(1/2)*e-c*d))^(1/2)*((-c*x+(-a*c)^(1/2))*e/((-a*c)^(1/2)*e+c*d))^(1/2)*((c*x+(-a*c)^(1/2))*e/((-a*c)^(1/2)*e-c*d))^(1/2)*EllipticF((-(e*x+d)*c/((-a*c)^(1/2)*e-c*d))^(1/2),(-((-a*c)^(1/2)*e-c*d)/((-a*c)^(1/2)*e+c*d))^(1/2))*c^2*d^4*e+48*a^2*c*(-(e*x+d)*c/((-a*c)^(1/2)*e-c*d))^(1/2)*((-c*x+(-a*c)^(1/2))*e/((-a*c)^(1/2)*e+c*d))^(1/2)*((c*x+(-a*c)^(1/2))*e/((-a*c)^(1/2)*e-c*d))^(1/2)*EllipticF((-(e*x+d)*c/((-a*c)^(1/2)*e-c*d))^(1/2),(-((-a*c)^(1/2)*e-c*d)/((-a*c)^(1/2)*e+c*d))^(1/2))*d*e^4+48*a*c^2*(-(e*x+d)*c/((-a*c)^(1/2)*e-c*d))^(1/2)*((-c*x+(-a*c)^(1/2))*e/((-a*c)^(1/2)*e+c*d))^(1/2)*((c*x+(-a*c)^(1/2))*e/((-a*c)^(1/2)*e-c*d))^(1/2)*EllipticF((-(e*x+d)*c/((-a*c)^(1/2)*e-c*d))^(1/2),(-((-a*c)^(1/2)*e-c*d)/((-a*c)^(1/2)*e+c*d))^(1/2))*d^3*e^2-58*a^2*c*(-(e*x+d)*c/((-a*c)^(1/2)*e-c*d))^(1/2)*((-c*x+(-a*c)^(1/2))*e/((-a*c)^(1/2)*e+c*d))^(1/2)*((c*x+(-a*c)^(1/2))*e/((-a*c)^(1/2)*e-c*d))^(1/2)*EllipticE((-(e*x+d)*c/((-a*c)^(1/2)*e-c*d))^(1/2),(-((-a*c)^(1/2)*e-c*d)/((-a*c)^(1/2)*e+c*d))^(1/2))*d*e^4-52*a*c^2*(-(e*x+d)*c/((-a*c)^(1/2)*e-c*d))^(1/2)*((-c*x+(-a*c)^(1/2))*e/((-a*c)^(1/2)*e+c*d))^(1/2)*((c*x+(-a*c)^(1/2))*e/((-a*c)^(1/2)*e-c*d))^(1/2)*EllipticE((-(e*x+d)*c/((-a*c)^(1/2)*e-c*d))^(1/2),(-((-a*c)^(1/2)*e-c*d)/((-a*c)^(1/2)*e+c*d))^(1/2))*d^3*e^2+6*(-(e*x+d)*c/((-a*c)^(1/2)*e-c*d))^(1/2)*((-c*x+(-a*c)^(1/2))*e/((-a*c)^(1/2)*e+c*d))^(1/2)*((c*x+(-a*c)^(1/2))*e/((-a*c)^(1/2)*e-c*d))^(1/2)*EllipticE((-(e*x+d)*c/((-a*c)^(1/2)*e-c*d))^(1/2),(-((-a*c)^(1/2)*e-c*d)/((-a*c)^(1/2)*e+c*d))^(1/2))*c^3*d^5+39*x^4*c^3*d*e^4+25*x^3*a*c^2*e^5+27*x^3*c^3*d^2*e^3+49*x^2*a*c^2*d*e^4+3*x^2*c^3*d^3*e^2+10*x*a^2*c*e^5+27*x*a*c^2*d^2*e^3+10*d*e^4*a^2*c+3*a*c^2*d^3*e^2)/e^3/(c*e*x^3+c*d*x^2+a*e*x+a*d)/c^2","B"
658,1,1162,290,0.077000," ","int((e*x+d)^(1/2)*(c*x^2+a)^(1/2),x)","\frac{2 \sqrt{e x +d}\, \sqrt{c \,x^{2}+a}\, \left(3 c^{2} e^{4} x^{4}+4 c^{2} d \,e^{3} x^{3}+3 a c \,e^{4} x^{2}+c^{2} d^{2} e^{2} x^{2}-6 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} e^{4} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+6 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} e^{4} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-4 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a c \,d^{2} e^{2} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+6 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a c \,d^{2} e^{2} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+4 a c d \,e^{3} x +2 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, c^{2} d^{4} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+a c \,d^{2} e^{2}-2 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, \sqrt{-a c}\, a d \,e^{3} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-2 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, \sqrt{-a c}\, c \,d^{3} e \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)\right)}{15 \left(c e \,x^{3}+c d \,x^{2}+a e x +a d \right) c \,e^{3}}"," ",0,"2/15*(e*x+d)^(1/2)*(c*x^2+a)^(1/2)*(6*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^2*e^4+6*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c*d^2*e^2-2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*(-a*c)^(1/2)*a*d*e^3-2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*(-a*c)^(1/2)*c*d^3*e-6*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^2*e^4-4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c*d^2*e^2+2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*c^2*d^4+3*c^2*x^4*e^4+4*c^2*d*x^3*e^3+3*a*c*e^4*x^2+c^2*d^2*e^2*x^2+4*a*c*d*e^3*x+a*c*d^2*e^2)/c/(c*e*x^3+c*d*x^2+a*e*x+a*d)/e^3","B"
659,1,688,256,0.153000," ","int((c*x^2+a)^(1/2)/(e*x+d)^(1/2),x)","-\frac{2 \sqrt{c \,x^{2}+a}\, \sqrt{e x +d}\, \left(-c^{2} e^{3} x^{3}-c^{2} d \,e^{2} x^{2}-2 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a c d \,e^{2} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-a c \,e^{3} x -2 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, c^{2} d^{3} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-a c d \,e^{2}+2 \sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a \,e^{3} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+2 \sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, c \,d^{2} e \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)\right)}{3 \left(c e \,x^{3}+c d \,x^{2}+a e x +a d \right) c \,e^{3}}"," ",0,"-2/3*(c*x^2+a)^(1/2)*(e*x+d)^(1/2)*(2*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*e^3+2*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*c*d^2*e-2*a*c*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*d*e^2-2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*c^2*d^3-x^3*c^2*e^3-x^2*c^2*d*e^2-a*c*e^3*x-a*d*e^2*c)/c/(c*e*x^3+c*d*x^2+a*e*x+a*d)/e^3","B"
660,1,648,245,0.201000," ","int((c*x^2+a)^(1/2)/(e*x+d)^(3/2),x)","\frac{2 \sqrt{c \,x^{2}+a}\, \sqrt{e x +d}\, \left(-c \,e^{2} x^{2}-2 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a \,e^{2} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+2 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a \,e^{2} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-2 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, c \,d^{2} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-a \,e^{2}+2 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, \sqrt{-a c}\, d e \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)\right)}{\left(c e \,x^{3}+c d \,x^{2}+a e x +a d \right) e^{3}}"," ",0,"2*(c*x^2+a)^(1/2)*(e*x+d)^(1/2)*(2*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*e^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+2*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*d*e*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*(-a*c)^(1/2)-2*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*e^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-2*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*c*d^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-c*e^2*x^2-a*e^2)/(c*e*x^3+c*d*x^2+a*e*x+a*d)/e^3","B"
661,1,1309,294,0.126000," ","int((c*x^2+a)^(1/2)/(e*x+d)^(5/2),x)","-\frac{2 \left(-2 c^{2} d \,e^{3} x^{3}-2 \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, a c d \,e^{3} x \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+a c \,e^{4} x^{2}-2 \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, c^{2} d^{3} e x \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-c^{2} d^{2} e^{2} x^{2}-2 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a c \,d^{2} e^{2} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-2 a c d \,e^{3} x +2 \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, \sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, a \,e^{4} x \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-2 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, c^{2} d^{4} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+2 \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, \sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, c \,d^{2} e^{2} x \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+a^{2} e^{4}-a c \,d^{2} e^{2}+2 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, \sqrt{-a c}\, a d \,e^{3} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+2 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, \sqrt{-a c}\, c \,d^{3} e \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)\right)}{3 \sqrt{c \,x^{2}+a}\, \left(a \,e^{2}+c \,d^{2}\right) \left(e x +d \right)^{\frac{3}{2}} e^{3}}"," ",0,"-2/3*(2*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x*a*e^4*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)+2*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x*c*d^2*e^2*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)-2*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x*a*c*d*e^3*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)-2*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x*c^2*d^3*e*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)+2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*(-a*c)^(1/2)*a*d*e^3+2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*(-a*c)^(1/2)*c*d^3*e-2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c*d^2*e^2-2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*c^2*d^4-2*c^2*d*e^3*x^3+a*c*e^4*x^2-c^2*d^2*e^2*x^2-2*a*c*d*e^3*x+a^2*e^4-a*c*d^2*e^2)/(c*x^2+a)^(1/2)/(a*e^2+c*d^2)/e^3/(e*x+d)^(3/2)","B"
662,1,3409,366,0.134000," ","int((c*x^2+a)^(1/2)/(e*x+d)^(7/2),x)","\text{output too large to display}"," ",0,"2/15*(-10*a*c^2*d*e^5*x^3-8*a*c^2*d^2*e^4*x^2+6*a*c^2*d^3*e^3*x+6*c^3*d^3*e^3*x^3-9*a^2*c*e^6*x^2-6*a*c^2*e^6*x^4+2*c^3*d^2*e^4*x^4-10*a^2*c*d^2*e^4+a*c^2*d^4*e^2+2*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*c^3*d^6*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-3*e^6*a^3+x^2*c^3*d^4*e^2+6*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a*c^2*d^2*e^4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-2*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*c^2*d^3*e^3*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-4*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a*c^2*d^2*e^4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+12*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x*a^2*c*d*e^5*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+12*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x*a*c^2*d^3*e^3*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-4*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x*c^2*d^4*e^2*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-12*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x*a^2*c*d*e^5*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-8*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x*a*c^2*d^3*e^3*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-2*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c*d^3*e^3*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-2*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a*c*d*e^5*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-4*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x*a*c*d^2*e^4*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+2*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*c^3*d^4*e^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-4*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c^2*d^4*e^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+6*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^2*c*d^2*e^4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+6*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c^2*d^4*e^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+4*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x*c^3*d^5*e*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+6*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a^2*c*e^6*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-6*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a^2*c*e^6*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-2*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*c^2*d^5*e*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-6*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^2*c*d^2*e^4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-10*x*a^2*c*d*e^5)/(c*x^2+a)^(1/2)/(a*e^2+c*d^2)^2/e^3/(e*x+d)^(5/2)","B"
663,1,1970,419,0.124000," ","int((e*x+d)^(3/2)*(c*x^2+a)^(3/2),x)","\frac{2 \sqrt{e x +d}\, \sqrt{c \,x^{2}+a}\, \left(105 c^{4} e^{7} x^{7}+245 c^{4} d \,e^{6} x^{6}+300 a \,c^{3} e^{7} x^{5}+145 c^{4} d^{2} e^{5} x^{5}+766 a \,c^{3} d \,e^{6} x^{4}-c^{4} d^{3} e^{4} x^{4}+255 a^{2} c^{2} e^{7} x^{3}+518 a \,c^{3} d^{2} e^{5} x^{3}+2 c^{4} d^{4} e^{3} x^{3}+581 a^{2} c^{2} d \,e^{6} x^{2}+46 a \,c^{3} d^{3} e^{4} x^{2}+8 c^{4} d^{5} e^{2} x^{2}-432 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{3} c d \,e^{6} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+372 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{3} c d \,e^{6} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+60 a^{3} c \,e^{7} x -336 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} c^{2} d^{3} e^{4} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+360 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} c^{2} d^{3} e^{4} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+373 a^{2} c^{2} d^{2} e^{5} x +112 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a \,c^{3} d^{5} e^{2} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-12 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a \,c^{3} d^{5} e^{2} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+2 a \,c^{3} d^{4} e^{3} x +16 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, c^{4} d^{7} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+60 a^{3} c d \,e^{6}+60 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, \sqrt{-a c}\, a^{3} e^{7} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+47 a^{2} c^{2} d^{3} e^{4}-24 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, \sqrt{-a c}\, a^{2} c \,d^{2} e^{5} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+8 a \,c^{3} d^{5} e^{2}-100 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, \sqrt{-a c}\, a \,c^{2} d^{4} e^{3} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-16 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, \sqrt{-a c}\, c^{3} d^{6} e \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)\right)}{1155 \left(c e \,x^{3}+c d \,x^{2}+a e x +a d \right) c^{2} e^{5}}"," ",0,"2/1155*(e*x+d)^(1/2)*(c*x^2+a)^(1/2)*(518*x^3*a*c^3*d^2*e^5-432*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^3*c*d*e^6-336*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^2*c^2*d^3*e^4+16*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*c^4*d^7+2*x^3*c^4*d^4*e^3+8*x^2*c^4*d^5*e^2+60*x*a^3*c*e^7+245*x^6*c^4*d*e^6+300*x^5*a*c^3*e^7+145*x^5*c^4*d^2*e^5-x^4*c^4*d^3*e^4+255*x^3*a^2*c^2*e^7-24*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*(-a*c)^(1/2)*a^2*c*d^2*e^5-100*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*(-a*c)^(1/2)*a*c^2*d^4*e^3-16*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*(-a*c)^(1/2)*c^3*d^6*e+372*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^3*c*d*e^6+360*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^2*c^2*d^3*e^4+112*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c^3*d^5*e^2-12*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c^3*d^5*e^2+105*x^7*c^4*e^7+60*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*(-a*c)^(1/2)*a^3*e^7+373*x*a^2*c^2*d^2*e^5+2*x*a*c^3*d^4*e^3+581*x^2*a^2*c^2*d*e^6+766*x^4*a*c^3*d*e^6+46*x^2*a*c^3*d^3*e^4+60*a^3*c*d*e^6+47*a^2*c^2*d^3*e^4+8*a*c^3*d^5*e^2)/c^2/e^5/(c*e*x^3+c*d*x^2+a*e*x+a*d)","B"
664,1,1731,370,0.085000," ","int((c*x^2+a)^(3/2)*(e*x+d)^(1/2),x)","\frac{2 \sqrt{c \,x^{2}+a}\, \sqrt{e x +d}\, \left(35 c^{3} e^{6} x^{6}+40 c^{3} d \,e^{5} x^{5}+112 a \,c^{2} e^{6} x^{4}-c^{3} d^{2} e^{4} x^{4}+146 a \,c^{2} d \,e^{5} x^{3}+2 c^{3} d^{3} e^{3} x^{3}+77 a^{2} c \,e^{6} x^{2}+28 a \,c^{2} d^{2} e^{4} x^{2}+8 c^{3} d^{4} e^{2} x^{2}-84 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{3} e^{6} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+84 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{3} e^{6} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-24 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} c \,d^{2} e^{4} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+72 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} c \,d^{2} e^{4} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+106 a^{2} c d \,e^{5} x +76 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a \,c^{2} d^{4} e^{2} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-12 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a \,c^{2} d^{4} e^{2} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+2 a \,c^{2} d^{3} e^{3} x +16 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, c^{3} d^{6} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+29 a^{2} c \,d^{2} e^{4}-48 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, \sqrt{-a c}\, a^{2} d \,e^{5} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+8 a \,c^{2} d^{4} e^{2}-64 \sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a c \,d^{3} e^{3} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-16 \sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, c^{2} d^{5} e \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)\right)}{315 \left(c e \,x^{3}+c d \,x^{2}+a e x +a d \right) c \,e^{5}}"," ",0,"2/315*(c*x^2+a)^(1/2)*(e*x+d)^(1/2)*(35*c^3*x^6*e^6+40*c^3*d*e^5*x^5+84*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^3*e^6+72*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^2*c*d^2*e^4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-48*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*(-a*c)^(1/2)*a^2*d*e^5-12*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c^2*d^4*e^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-64*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c*d^3*e^3*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-16*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*c^2*d^5*e*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-84*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^3*e^6-24*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^2*c*d^2*e^4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+76*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c^2*d^4*e^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+16*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*c^3*d^6*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+112*a*c^2*e^6*x^4-c^3*d^2*e^4*x^4+146*a*c^2*d*e^5*x^3+2*c^3*d^3*e^3*x^3+77*a^2*c*e^6*x^2+28*a*c^2*d^2*e^4*x^2+8*x^2*c^3*d^4*e^2+106*x*a^2*c*d*e^5+2*a*c^2*d^3*e^3*x+29*a^2*c*d^2*e^4+8*a*c^2*d^4*e^2)/c/(c*e*x^3+c*d*x^2+a*e*x+a*d)/e^5","B"
665,1,1385,321,0.082000," ","int((c*x^2+a)^(3/2)/(e*x+d)^(1/2),x)","-\frac{2 \sqrt{c \,x^{2}+a}\, \sqrt{e x +d}\, \left(-5 c^{3} e^{5} x^{5}+c^{3} d \,e^{4} x^{4}-20 a \,c^{2} e^{5} x^{3}-2 c^{3} d^{2} e^{3} x^{3}-14 a \,c^{2} d \,e^{4} x^{2}-8 c^{3} d^{3} e^{2} x^{2}-32 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} c d \,e^{4} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+12 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} c d \,e^{4} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-15 a^{2} c \,e^{5} x -48 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a \,c^{2} d^{3} e^{2} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+12 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a \,c^{2} d^{3} e^{2} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-2 a \,c^{2} d^{2} e^{3} x -16 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, c^{3} d^{5} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-15 a^{2} c d \,e^{4}+20 \sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} e^{5} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-8 a \,c^{2} d^{3} e^{2}+36 \sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a c \,d^{2} e^{3} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+16 \sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, c^{2} d^{4} e \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)\right)}{35 \left(c e \,x^{3}+c d \,x^{2}+a e x +a d \right) c \,e^{5}}"," ",0,"-2/35*(c*x^2+a)^(1/2)*(e*x+d)^(1/2)*(-5*c^3*e^5*x^5+20*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^2*e^5+36*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c*d^2*e^3+16*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*c^2*d^4*e+12*a^2*c*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*d*e^4+12*a*c^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*d^3*e^2-32*a^2*c*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*d*e^4-48*a*c^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*d^3*e^2-16*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*c^3*d^5+c^3*d*e^4*x^4-20*a*c^2*e^5*x^3-2*c^3*d^2*e^3*x^3-14*a*c^2*d*e^4*x^2-8*c^3*d^3*e^2*x^2-15*a^2*c*e^5*x-2*a*c^2*d^2*e^3*x-15*a^2*c*d*e^4-8*a*c^2*d^3*e^2)/c/e^5/(c*e*x^3+c*d*x^2+a*e*x+a*d)","B"
666,1,1168,299,0.096000," ","int((c*x^2+a)^(3/2)/(e*x+d)^(3/2),x)","\frac{2 \sqrt{c \,x^{2}+a}\, \sqrt{e x +d}\, \left(c^{2} e^{4} x^{4}-2 c^{2} d \,e^{3} x^{3}-4 a c \,e^{4} x^{2}-8 c^{2} d^{2} e^{2} x^{2}-12 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} e^{4} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+12 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} e^{4} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-28 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a c \,d^{2} e^{2} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+12 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a c \,d^{2} e^{2} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-2 a c d \,e^{3} x -16 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, c^{2} d^{4} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-5 a^{2} e^{4}-8 a c \,d^{2} e^{2}+16 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, \sqrt{-a c}\, a d \,e^{3} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+16 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, \sqrt{-a c}\, c \,d^{3} e \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)\right)}{5 \left(c e \,x^{3}+c d \,x^{2}+a e x +a d \right) e^{5}}"," ",0,"2/5*(c*x^2+a)^(1/2)*(e*x+d)^(1/2)*(12*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^2*e^4+12*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c*d^2*e^2+16*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*(-a*c)^(1/2)*a*d*e^3+16*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*(-a*c)^(1/2)*c*d^3*e-12*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^2*e^4-28*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c*d^2*e^2-16*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*c^2*d^4+c^2*e^4*x^4-2*c^2*d*e^3*x^3-4*a*c*e^4*x^2-8*c^2*d^2*e^2*x^2-2*a*c*d*e^3*x-5*a^2*e^4-8*a*c*d^2*e^2)/(c*e*x^3+c*d*x^2+a*e*x+a*d)/e^5","B"
667,1,1597,286,0.106000," ","int((c*x^2+a)^(3/2)/(e*x+d)^(5/2),x)","-\frac{2 \left(-c^{2} e^{4} x^{4}-10 c^{2} d \,e^{3} x^{3}-16 \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, a c d \,e^{3} x \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+12 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a c d \,e^{3} x \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-16 \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, c^{2} d^{3} e x \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-8 c^{2} d^{2} e^{2} x^{2}-16 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a c \,d^{2} e^{2} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+12 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a c \,d^{2} e^{2} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-10 a c d \,e^{3} x +4 \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, \sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, a \,e^{4} x \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-16 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, c^{2} d^{4} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+16 \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, \sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, c \,d^{2} e^{2} x \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+a^{2} e^{4}-8 a c \,d^{2} e^{2}+4 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, \sqrt{-a c}\, a d \,e^{3} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+16 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, \sqrt{-a c}\, c \,d^{3} e \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)\right)}{3 \sqrt{c \,x^{2}+a}\, \left(e x +d \right)^{\frac{3}{2}} e^{5}}"," ",0,"-2/3*(12*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x*a*c*d*e^3*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+4*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x*a*e^4*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)+16*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x*c*d^2*e^2*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)-16*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x*a*c*d*e^3*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)-16*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x*c^2*d^3*e*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)+12*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c*d^2*e^2+4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*(-a*c)^(1/2)*a*d*e^3+16*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*(-a*c)^(1/2)*c*d^3*e-16*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c*d^2*e^2-16*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*c^2*d^4-c^2*e^4*x^4-10*c^2*d*e^3*x^3-8*c^2*d^2*e^2*x^2-10*a*c*d*e^3*x+a^2*e^4-8*a*c*d^2*e^2)/(c*x^2+a)^(1/2)/e^5/(e*x+d)^(3/2)","B"
668,1,3411,338,0.109000," ","int((c*x^2+a)^(3/2)/(e*x+d)^(7/2),x)","\text{output too large to display}"," ",0,"2/5*(-10*a*c^2*d*e^5*x^3-16*a*c^2*d^2*e^4*x^2-18*a*c^2*d^3*e^3*x-18*c^3*d^3*e^3*x^3-8*a^2*c*e^6*x^2-7*a*c^2*e^6*x^4-11*c^3*d^2*e^4*x^4-5*a^2*c*d^2*e^4-8*a*c^2*d^4*e^2-16*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*c^3*d^6*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-e^6*a^3-8*c^3*d^4*e^2*x^2+12*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a*c^2*d^2*e^4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+16*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*c^2*d^3*e^3*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-28*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a*c^2*d^2*e^4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+24*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x*a^2*c*d*e^5*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+24*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x*a*c^2*d^3*e^3*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+32*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x*c^2*d^4*e^2*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-24*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x*a^2*c*d*e^5*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-56*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x*a*c^2*d^3*e^3*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+16*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c*d^3*e^3*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+16*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a*c*d*e^5*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+32*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x*a*c*d^2*e^4*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-16*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*c^3*d^4*e^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-28*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c^2*d^4*e^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+12*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^2*c*d^2*e^4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+12*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c^2*d^4*e^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-32*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x*c^3*d^5*e*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+12*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a^2*c*e^6*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-12*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a^2*c*e^6*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+16*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*c^2*d^5*e*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-12*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^2*c*d^2*e^4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-10*a^2*c*d*e^5*x)/(c*x^2+a)^(1/2)/(a*e^2+c*d^2)/(e*x+d)^(5/2)/e^5","B"
669,1,5277,413,0.173000," ","int((c*x^2+a)^(3/2)/(e*x+d)^(9/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
670,1,2332,482,0.106000," ","int((c*x^2+a)^(5/2)*(e*x+d)^(1/2),x)","-\frac{2 \sqrt{c \,x^{2}+a}\, \sqrt{e x +d}\, \left(-693 c^{4} e^{8} x^{8}-756 c^{4} d \,e^{7} x^{7}-2849 a \,c^{3} e^{8} x^{6}+7 c^{4} d^{2} e^{6} x^{6}-3238 a \,c^{3} d \,e^{7} x^{5}-10 c^{4} d^{3} e^{5} x^{5}-4543 a^{2} c^{2} e^{8} x^{4}+75 a \,c^{3} d^{2} e^{6} x^{4}+16 c^{4} d^{4} e^{4} x^{4}-5840 a^{2} c^{2} d \,e^{7} x^{3}-148 a \,c^{3} d^{3} e^{5} x^{3}-32 c^{4} d^{5} e^{3} x^{3}-2387 a^{3} c \,e^{8} x^{2}-903 a^{2} c^{2} d^{2} e^{6} x^{2}-516 a \,c^{3} d^{4} e^{4} x^{2}-128 c^{4} d^{6} e^{2} x^{2}+1848 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{4} e^{8} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-1848 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{4} e^{8} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-216 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{3} c \,d^{2} e^{6} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-1200 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{3} c \,d^{2} e^{6} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-3358 a^{3} c d \,e^{7} x -3160 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} c^{2} d^{4} e^{4} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+840 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} c^{2} d^{4} e^{4} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-138 a^{2} c^{2} d^{3} e^{5} x -1352 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a \,c^{3} d^{6} e^{2} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+192 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a \,c^{3} d^{6} e^{2} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-32 a \,c^{3} d^{5} e^{3} x -256 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, c^{4} d^{8} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-971 a^{3} c \,d^{2} e^{6}+1416 \sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{3} d \,e^{7} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-532 a^{2} c^{2} d^{4} e^{4}+2320 \sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} c \,d^{3} e^{5} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-128 a \,c^{3} d^{6} e^{2}+1160 \sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a \,c^{2} d^{5} e^{3} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+256 \sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, c^{3} d^{7} e \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)\right)}{9009 \left(c e \,x^{3}+c d \,x^{2}+a e x +a d \right) c \,e^{7}}"," ",0,"-2/9009*(c*x^2+a)^(1/2)*(e*x+d)^(1/2)/c*(-256*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*c^4*d^8*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-138*x*a^2*c^2*d^3*e^5-128*x^2*c^4*d^6*e^2-10*x^5*c^4*d^3*e^5-4543*x^4*a^2*c^2*e^8+16*x^4*c^4*d^4*e^4-32*x^3*c^4*d^5*e^3-2387*x^2*a^3*c*e^8-2849*x^6*a*c^3*e^8+7*x^6*c^4*d^2*e^6-756*x^7*c^4*d*e^7-693*x^8*c^4*e^8+1848*a^4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*e^8-1848*a^4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*e^8-3160*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^2*c^2*d^4*e^4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+840*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^2*c^2*d^4*e^4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+192*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c^3*d^6*e^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+256*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*c^3*d^7*e*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+1416*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^3*d*e^7-1200*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^3*c*d^2*e^6-216*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^3*c*d^2*e^6-1352*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c^3*d^6*e^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+2320*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^2*c*d^3*e^5*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+1160*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c^2*d^5*e^3*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-32*x*a*c^3*d^5*e^3-3238*x^5*a*c^3*d*e^7+75*x^4*a*c^3*d^2*e^6-5840*x^3*a^2*c^2*d*e^7-148*x^3*a*c^3*d^3*e^5-903*x^2*a^2*c^2*d^2*e^6-516*x^2*a*c^3*d^4*e^4-3358*x*a^3*c*d*e^7-971*a^3*c*d^2*e^6-532*a^2*c^2*d^4*e^4-128*a*c^3*d^6*e^2)/(c*e*x^3+c*d*x^2+a*e*x+a*d)/e^7","B"
671,1,1970,416,0.096000," ","int((c*x^2+a)^(5/2)/(e*x+d)^(1/2),x)","\frac{2 \sqrt{c \,x^{2}+a}\, \sqrt{e x +d}\, \left(63 c^{4} e^{7} x^{7}-7 c^{4} d \,e^{6} x^{6}+279 a \,c^{3} e^{7} x^{5}+10 c^{4} d^{2} e^{5} x^{5}-53 a \,c^{3} d \,e^{6} x^{4}-16 c^{4} d^{3} e^{4} x^{4}+549 a^{2} c^{2} e^{7} x^{3}+104 a \,c^{3} d^{2} e^{5} x^{3}+32 c^{4} d^{4} e^{3} x^{3}+287 a^{2} c^{2} d \,e^{6} x^{2}+340 a \,c^{3} d^{3} e^{4} x^{2}+128 c^{4} d^{5} e^{2} x^{2}+744 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{3} c d \,e^{6} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-384 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{3} c d \,e^{6} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+333 a^{3} c \,e^{7} x +1488 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} c^{2} d^{3} e^{4} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-576 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} c^{2} d^{3} e^{4} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+94 a^{2} c^{2} d^{2} e^{5} x +1000 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a \,c^{3} d^{5} e^{2} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-192 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a \,c^{3} d^{5} e^{2} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+32 a \,c^{3} d^{4} e^{3} x +256 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, c^{4} d^{7} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+333 a^{3} c d \,e^{6}-360 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, \sqrt{-a c}\, a^{3} e^{7} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+356 a^{2} c^{2} d^{3} e^{4}-912 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, \sqrt{-a c}\, a^{2} c \,d^{2} e^{5} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+128 a \,c^{3} d^{5} e^{2}-808 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, \sqrt{-a c}\, a \,c^{2} d^{4} e^{3} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-256 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, \sqrt{-a c}\, c^{3} d^{6} e \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)\right)}{693 \left(c e \,x^{3}+c d \,x^{2}+a e x +a d \right) c \,e^{7}}"," ",0,"2/693*(c*x^2+a)^(1/2)*(e*x+d)^(1/2)*(104*a*c^3*d^2*e^5*x^3+744*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^3*c*d*e^6+1488*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^2*c^2*d^3*e^4+256*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*c^4*d^7+32*c^4*d^4*e^3*x^3+128*c^4*d^5*e^2*x^2+333*a^3*c*e^7*x-7*c^4*d*e^6*x^6+279*a*c^3*e^7*x^5+10*c^4*d^2*e^5*x^5-16*c^4*d^3*e^4*x^4+549*a^2*c^2*e^7*x^3-912*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*(-a*c)^(1/2)*a^2*c*d^2*e^5-808*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*(-a*c)^(1/2)*a*c^2*d^4*e^3-256*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*(-a*c)^(1/2)*c^3*d^6*e-384*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^3*c*d*e^6-576*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^2*c^2*d^3*e^4+1000*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c^3*d^5*e^2-192*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c^3*d^5*e^2+63*c^4*e^7*x^7-360*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*(-a*c)^(1/2)*a^3*e^7+94*a^2*c^2*d^2*e^5*x+32*a*c^3*d^4*e^3*x+287*a^2*c^2*d*e^6*x^2-53*a*c^3*d*e^6*x^4+340*a*c^3*d^3*e^4*x^2+333*a^3*c*d*e^6+356*a^2*c^2*d^3*e^4+128*a*c^3*d^5*e^2)/c/e^7/(c*e*x^3+c*d*x^2+a*e*x+a*d)","B"
672,1,1736,381,0.118000," ","int((c*x^2+a)^(5/2)/(e*x+d)^(3/2),x)","-\frac{2 \sqrt{c \,x^{2}+a}\, \sqrt{e x +d}\, \left(-7 c^{3} e^{6} x^{6}+10 c^{3} d \,e^{5} x^{5}-35 a \,c^{2} e^{6} x^{4}-16 c^{3} d^{2} e^{4} x^{4}+68 a \,c^{2} d \,e^{5} x^{3}+32 c^{3} d^{3} e^{3} x^{3}+35 a^{2} c \,e^{6} x^{2}+196 a \,c^{2} d^{2} e^{4} x^{2}+128 c^{3} d^{4} e^{2} x^{2}+168 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{3} e^{6} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-168 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{3} e^{6} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+624 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} c \,d^{2} e^{4} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-360 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} c \,d^{2} e^{4} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+58 a^{2} c d \,e^{5} x +712 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a \,c^{2} d^{4} e^{2} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-192 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a \,c^{2} d^{4} e^{2} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+32 a \,c^{2} d^{3} e^{3} x +256 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, c^{3} d^{6} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+63 a^{3} e^{6}+212 a^{2} c \,d^{2} e^{4}-264 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, \sqrt{-a c}\, a^{2} d \,e^{5} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+128 a \,c^{2} d^{4} e^{2}-520 \sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a c \,d^{3} e^{3} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-256 \sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, c^{2} d^{5} e \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)\right)}{63 \left(c e \,x^{3}+c d \,x^{2}+a e x +a d \right) e^{7}}"," ",0,"-2/63*(c*x^2+a)^(1/2)*(e*x+d)^(1/2)*(-7*c^3*e^6*x^6+10*c^3*d*e^5*x^5+168*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^3*e^6+624*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^2*c*d^2*e^4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+712*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c^2*d^4*e^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+256*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*c^3*d^6*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-168*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^3*e^6-360*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^2*c*d^2*e^4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-264*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*(-a*c)^(1/2)*a^2*d*e^5-192*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c^2*d^4*e^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-520*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c*d^3*e^3*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-256*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*c^2*d^5*e*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-35*a*c^2*e^6*x^4-16*c^3*d^2*e^4*x^4+68*a*c^2*d*e^5*x^3+32*c^3*d^3*e^3*x^3+35*a^2*c*e^6*x^2+196*a*c^2*d^2*e^4*x^2+128*c^3*d^4*e^2*x^2+58*a^2*c*d*e^5*x+32*a*c^2*d^3*e^3*x+63*e^6*a^3+212*a^2*c*d^2*e^4+128*a*c^2*d^4*e^2)/e^7/(c*e*x^3+c*d*x^2+a*e*x+a*d)","B"
673,1,2646,352,0.122000," ","int((c*x^2+a)^(5/2)/(e*x+d)^(5/2),x)","-\frac{2 \left(-3 c^{3} e^{6} x^{6}+6 c^{3} d \,e^{5} x^{5}-19 a \,c^{2} e^{6} x^{4}-16 c^{3} d^{2} e^{4} x^{4}-124 a \,c^{2} d \,e^{5} x^{3}-160 c^{3} d^{3} e^{3} x^{3}-232 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} c d \,e^{5} x \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+192 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} c d \,e^{5} x \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-9 a^{2} c \,e^{6} x^{2}-488 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a \,c^{2} d^{3} e^{3} x \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+192 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a \,c^{2} d^{3} e^{3} x \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-116 a \,c^{2} d^{2} e^{4} x^{2}-256 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, c^{3} d^{5} e x \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-128 c^{3} d^{4} e^{2} x^{2}-232 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} c \,d^{2} e^{4} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+192 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} c \,d^{2} e^{4} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-130 a^{2} c d \,e^{5} x +40 \sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} e^{6} x \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-488 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a \,c^{2} d^{4} e^{2} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+192 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a \,c^{2} d^{4} e^{2} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-160 a \,c^{2} d^{3} e^{3} x +296 \sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a c \,d^{2} e^{4} x \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-256 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, c^{3} d^{6} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+256 \sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, c^{2} d^{4} e^{2} x \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+7 a^{3} e^{6}-100 a^{2} c \,d^{2} e^{4}+40 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, \sqrt{-a c}\, a^{2} d \,e^{5} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-128 a \,c^{2} d^{4} e^{2}+296 \sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a c \,d^{3} e^{3} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+256 \sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, c^{2} d^{5} e \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)\right)}{21 \sqrt{c \,x^{2}+a}\, \left(e x +d \right)^{\frac{3}{2}} e^{7}}"," ",0,"-2/21*(40*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*(-a*c)^(1/2)*a^2*d*e^5-124*a*c^2*d*e^5*x^3-116*a*c^2*d^2*e^4*x^2-160*a*c^2*d^3*e^3*x+6*c^3*d*e^5*x^5-160*c^3*d^3*e^3*x^3-9*a^2*c*e^6*x^2-19*a*c^2*e^6*x^4-16*c^3*d^2*e^4*x^4-3*c^3*e^6*x^6-100*a^2*c*d^2*e^4-128*a*c^2*d^4*e^2-256*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*c^3*d^6*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+7*a^3*e^6-128*c^3*d^4*e^2*x^2+192*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x*a^2*c*d*e^5*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+192*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x*a*c^2*d^3*e^3*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+256*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x*c^2*d^4*e^2*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-232*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x*a^2*c*d*e^5*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-488*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x*a*c^2*d^3*e^3*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+296*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c*d^3*e^3*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+296*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x*a*c*d^2*e^4*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-488*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c^2*d^4*e^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+192*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^2*c*d^2*e^4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+192*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c^2*d^4*e^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-256*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x*c^3*d^5*e*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+256*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*c^2*d^5*e*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-232*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^2*c*d^2*e^4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+40*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x*a^2*e^6*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-130*a^2*c*d*e^5*x)/(c*x^2+a)^(1/2)/(e*x+d)^(3/2)/e^7","B"
674,1,3421,342,0.117000," ","int((c*x^2+a)^(5/2)/(e*x+d)^(7/2),x)","\text{output too large to display}"," ",0,"2/15*(-60*a*c^2*d*e^5*x^3-196*a*c^2*d^2*e^4*x^2-288*a*c^2*d^3*e^3*x-10*c^3*d*e^5*x^5-288*c^3*d^3*e^3*x^3-39*a^2*c*e^6*x^2-33*a*c^2*e^6*x^4-176*c^3*d^2*e^4*x^4+3*c^3*e^6*x^6-20*a^2*c*d^2*e^4-128*a*c^2*d^4*e^2-256*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*c^3*d^6*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-3*a^3*e^6-128*c^3*d^4*e^2*x^2+192*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a*c^2*d^2*e^4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+256*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*c^2*d^3*e^3*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-328*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a*c^2*d^2*e^4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+144*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x*a^2*c*d*e^5*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+384*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x*a*c^2*d^3*e^3*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+512*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x*c^2*d^4*e^2*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-144*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x*a^2*c*d*e^5*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-656*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x*a*c^2*d^3*e^3*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+136*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c*d^3*e^3*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+136*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a*c*d*e^5*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+272*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x*a*c*d^2*e^4*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-256*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*c^3*d^4*e^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-328*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c^2*d^4*e^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+72*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^2*c*d^2*e^4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+192*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c^2*d^4*e^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-512*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x*c^3*d^5*e*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+72*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a^2*c*e^6*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-72*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a^2*c*e^6*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+256*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*c^2*d^5*e*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-72*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^2*c*d^2*e^4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-50*a^2*c*d*e^5*x)/(c*x^2+a)^(1/2)/(e*x+d)^(5/2)/e^7","B"
675,1,5303,420,0.120000," ","int((c*x^2+a)^(5/2)/(e*x+d)^(9/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
676,1,8244,475,0.171000," ","int((c*x^2+a)^(5/2)/(e*x+d)^(11/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
677,1,1534,335,0.118000," ","int((e*x+d)^(7/2)/(c*x^2+a)^(1/2),x)","-\frac{2 \sqrt{e x +d}\, \sqrt{c \,x^{2}+a}\, \left(-15 c^{3} e^{5} x^{5}-81 c^{3} d \,e^{4} x^{4}+10 a \,c^{2} e^{5} x^{3}-188 c^{3} d^{2} e^{3} x^{3}-56 a \,c^{2} d \,e^{4} x^{2}-122 c^{3} d^{3} e^{2} x^{2}-208 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} c d \,e^{4} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+183 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} c d \,e^{4} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+25 a^{2} c \,e^{5} x -32 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a \,c^{2} d^{3} e^{2} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+78 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a \,c^{2} d^{3} e^{2} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-188 a \,c^{2} d^{2} e^{3} x +176 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, c^{3} d^{5} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-105 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, c^{3} d^{5} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+25 a^{2} c d \,e^{4}+25 \sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} e^{5} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-122 a \,c^{2} d^{3} e^{2}-46 \sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a c \,d^{2} e^{3} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-71 \sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, c^{2} d^{4} e \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)\right)}{105 \left(c e \,x^{3}+c d \,x^{2}+a e x +a d \right) c^{3} e}"," ",0,"-2/105*(e*x+d)^(1/2)*(c*x^2+a)^(1/2)*(-15*c^3*e^5*x^5+25*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^2*e^5-46*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c*d^2*e^3-71*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*c^2*d^4*e+183*a^2*c*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*d*e^4+78*a*c^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*d^3*e^2-105*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*c^3*d^5-208*a^2*c*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*d*e^4-32*a*c^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*d^3*e^2+176*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*c^3*d^5-81*c^3*d*e^4*x^4+10*a*c^2*e^5*x^3-188*c^3*d^2*e^3*x^3-56*a*c^2*d*e^4*x^2-122*c^3*d^3*e^2*x^2+25*a^2*c*e^5*x-188*a*c^2*d^2*e^3*x+25*a^2*c*d*e^4-122*a*c^2*d^3*e^2)/e/(c*e*x^3+c*d*x^2+a*e*x+a*d)/c^3","B"
678,1,1312,287,0.105000," ","int((e*x+d)^(5/2)/(c*x^2+a)^(1/2),x)","-\frac{2 \sqrt{e x +d}\, \sqrt{c \,x^{2}+a}\, \left(-3 c^{2} e^{4} x^{4}-14 c^{2} d \,e^{3} x^{3}-3 a c \,e^{4} x^{2}-11 c^{2} d^{2} e^{2} x^{2}-9 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} e^{4} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+9 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} e^{4} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+14 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a c \,d^{2} e^{2} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-6 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a c \,d^{2} e^{2} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-14 a c d \,e^{3} x +23 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, c^{2} d^{4} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-15 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, c^{2} d^{4} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-11 a c \,d^{2} e^{2}-8 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, \sqrt{-a c}\, a d \,e^{3} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-8 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, \sqrt{-a c}\, c \,d^{3} e \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)\right)}{15 \left(c e \,x^{3}+c d \,x^{2}+a e x +a d \right) c^{2} e}"," ",0,"-2/15*(e*x+d)^(1/2)*(c*x^2+a)^(1/2)*(9*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^2*e^4-6*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c*d^2*e^2-8*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*(-a*c)^(1/2)*a*d*e^3-15*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*c^2*d^4-8*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*(-a*c)^(1/2)*c*d^3*e-9*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^2*e^4+14*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c*d^2*e^2+23*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*c^2*d^4-3*c^2*e^4*x^4-14*c^2*d*e^3*x^3-3*a*c*e^4*x^2-11*c^2*d^2*e^2*x^2-14*a*c*d*e^3*x-11*a*c*d^2*e^2)/c^2/e/(c*e*x^3+c*d*x^2+a*e*x+a*d)","B"
679,1,978,251,0.097000," ","int((e*x+d)^(3/2)/(c*x^2+a)^(1/2),x)","\frac{2 \sqrt{e x +d}\, \sqrt{c \,x^{2}+a}\, \left(c^{2} e^{3} x^{3}+c^{2} d \,e^{2} x^{2}-4 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a c d \,e^{2} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+3 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a c d \,e^{2} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+a c \,e^{3} x -4 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, c^{2} d^{3} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+3 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, c^{2} d^{3} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+a c d \,e^{2}+\sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a \,e^{3} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+\sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, c \,d^{2} e \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)\right)}{3 \left(c e \,x^{3}+c d \,x^{2}+a e x +a d \right) c^{2} e}"," ",0,"2/3*(e*x+d)^(1/2)*(c*x^2+a)^(1/2)*((-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*e^3+(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*c*d^2*e+3*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c*d*e^2+3*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*c^2*d^3-4*a*c*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*d*e^2-4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*c^2*d^3+c^2*e^3*x^3+c^2*d*e^2*x^2+a*c*e^3*x+a*c*d*e^2)/e/(c*e*x^3+c*d*x^2+a*e*x+a*d)/c^2","B"
680,1,396,108,0.103000," ","int((e*x+d)^(1/2)/(c*x^2+a)^(1/2),x)","\frac{2 \sqrt{e x +d}\, \sqrt{c \,x^{2}+a}\, \left(c d -\sqrt{-a c}\, e \right) \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, \left(-c d \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+c d \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-\sqrt{-a c}\, e \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+\sqrt{-a c}\, e \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)\right)}{\left(c e \,x^{3}+c d \,x^{2}+a e x +a d \right) c^{2} e}"," ",0,"2*(e*x+d)^(1/2)*(c*x^2+a)^(1/2)*(-(-a*c)^(1/2)*e+c*d)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((-a*c)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*e-(-a*c)^(1/2)*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*e+d*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*c-EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*c*d)/e/(c*e*x^3+c*d*x^2+a*e*x+a*d)/c^2","B"
681,1,200,108,0.104000," ","int(1/(e*x+d)^(1/2)/(c*x^2+a)^(1/2),x)","\frac{2 \left(c d -\sqrt{-a c}\, e \right) \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{e x +d}\, \sqrt{c \,x^{2}+a}\, \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)}{\left(c e \,x^{3}+c d \,x^{2}+a e x +a d \right) c e}"," ",0,"2*(c*d-(-a*c)^(1/2)*e)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*(e*x+d)^(1/2)*(c*x^2+a)^(1/2)/e/c/(c*e*x^3+c*d*x^2+a*e*x+a*d)","A"
682,1,653,154,0.112000," ","int(1/(e*x+d)^(3/2)/(c*x^2+a)^(1/2),x)","-\frac{2 \left(c \,e^{2} x^{2}+\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a \,e^{2} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a \,e^{2} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, c \,d^{2} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, c \,d^{2} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+a \,e^{2}\right) \sqrt{c \,x^{2}+a}\, \sqrt{e x +d}}{\left(a \,e^{2}+c \,d^{2}\right) \left(c e \,x^{3}+c d \,x^{2}+a e x +a d \right) e}"," ",0,"-2*(EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*e^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*c*d^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*e^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*c*d^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+c*e^2*x^2+a*e^2)*(c*x^2+a)^(1/2)*(e*x+d)^(1/2)/e/(a*e^2+c*d^2)/(c*e*x^3+c*d*x^2+a*e*x+a*d)","B"
683,1,1906,310,0.141000," ","int(1/(e*x+d)^(5/2)/(c*x^2+a)^(1/2),x)","-\frac{2 \left(4 c^{2} d \,e^{3} x^{3}+4 \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, a c d \,e^{3} x \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-3 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a c d \,e^{3} x \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+a c \,e^{4} x^{2}+4 \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, c^{2} d^{3} e x \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-3 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, c^{2} d^{3} e x \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+5 c^{2} d^{2} e^{2} x^{2}+4 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a c \,d^{2} e^{2} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-3 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a c \,d^{2} e^{2} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+4 a c d \,e^{3} x -\sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, \sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, a \,e^{4} x \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+4 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, c^{2} d^{4} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-3 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, c^{2} d^{4} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-\sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, \sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, c \,d^{2} e^{2} x \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+a^{2} e^{4}+5 a c \,d^{2} e^{2}-\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, \sqrt{-a c}\, a d \,e^{3} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, \sqrt{-a c}\, c \,d^{3} e \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)\right)}{3 \sqrt{c \,x^{2}+a}\, \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(e x +d \right)^{\frac{3}{2}} e}"," ",0,"-2/3*(4*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x*a*c*d*e^3*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)+4*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x*c^2*d^3*e*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)-3*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x*a*c*d*e^3*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x*a*e^4*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)-3*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x*c^2*d^3*e*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x*c*d^2*e^2*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)+4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c*d^2*e^2+4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*c^2*d^4-3*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c*d^2*e^2-(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*(-a*c)^(1/2)*a*d*e^3-3*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*c^2*d^4-(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*(-a*c)^(1/2)*c*d^3*e+4*c^2*d*e^3*x^3+a*c*e^4*x^2+5*c^2*d^2*e^2*x^2+4*a*c*d*e^3*x+a^2*e^4+5*a*c*d^2*e^2)/(c*x^2+a)^(1/2)/(a*e^2+c*d^2)^2/(e*x+d)^(3/2)/e","B"
684,1,3863,369,0.135000," ","int(1/(e*x+d)^(7/2)/(c*x^2+a)^(1/2),x)","\text{output too large to display}"," ",0,"-2/15*(-10*a*c^2*d*e^5*x^3+28*a*c^2*d^2*e^4*x^2+54*a*c^2*d^3*e^3*x+54*c^3*d^3*e^3*x^3-6*a^2*c*e^6*x^2-9*a*c^2*e^6*x^4+23*c^3*d^2*e^4*x^4+5*a^2*c*d^2*e^4+34*a*c^2*d^4*e^2-15*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*c^3*d^6*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+23*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*c^3*d^6*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+3*a^3*e^6+34*c^3*d^4*e^2*x^2-6*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a*c^2*d^2*e^4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-8*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*c^2*d^3*e^3*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+14*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a*c^2*d^2*e^4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+18*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x*a^2*c*d*e^5*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-12*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x*a*c^2*d^3*e^3*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-16*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x*c^2*d^4*e^2*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-18*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x*a^2*c*d*e^5*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+28*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x*a*c^2*d^3*e^3*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-8*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c*d^3*e^3*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-8*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a*c*d*e^5*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-16*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x*a*c*d^2*e^4*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+23*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*c^3*d^4*e^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+14*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c^2*d^4*e^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+9*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^2*c*d^2*e^4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-6*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c^2*d^4*e^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+46*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x*c^3*d^5*e*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+9*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a^2*c*e^6*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-9*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a^2*c*e^6*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-8*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*c^2*d^5*e*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-9*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^2*c*d^2*e^4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-10*a^2*c*d*e^5*x-15*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*c^3*d^4*e^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-30*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x*c^3*d^5*e*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2))/(c*x^2+a)^(1/2)/(a*e^2+c*d^2)^3/(e*x+d)^(5/2)/e","B"
685,1,1362,352,0.230000," ","int((e*x+d)^(7/2)/(c*x^2+a)^(3/2),x)","\frac{\sqrt{e x +d}\, \sqrt{c \,x^{2}+a}\, \left(2 a \,c^{2} e^{5} x^{3}-7 a \,c^{2} d \,e^{4} x^{2}+3 c^{3} d^{3} e^{2} x^{2}-29 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} c d \,e^{4} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+24 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} c d \,e^{4} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+5 a^{2} c \,e^{5} x -26 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a \,c^{2} d^{3} e^{2} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+24 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a \,c^{2} d^{3} e^{2} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-18 a \,c^{2} d^{2} e^{3} x +3 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, c^{3} d^{5} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+3 c^{3} d^{4} e x +5 a^{2} c d \,e^{4}+5 \sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} e^{5} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-9 a \,c^{2} d^{3} e^{2}+2 \sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a c \,d^{2} e^{3} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-3 \sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, c^{2} d^{4} e \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)\right)}{3 \left(c e \,x^{3}+c d \,x^{2}+a e x +a d \right) a \,c^{3} e}"," ",0,"1/3*(e*x+d)^(1/2)*(c*x^2+a)^(1/2)*(24*a^2*c*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*d*e^4+5*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^2*e^5+24*a*c^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*d^3*e^2+2*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c*d^2*e^3-3*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*c^2*d^4*e-29*a^2*c*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*d*e^4-26*a*c^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*d^3*e^2+3*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*c^3*d^5+2*a*c^2*e^5*x^3-7*a*c^2*d*e^4*x^2+3*c^3*d^3*e^2*x^2+5*a^2*c*e^5*x-18*a*c^2*d^2*e^3*x+3*x*c^3*d^4*e+5*a^2*c*d*e^4-9*a*c^2*d^3*e^2)/e/(c*e*x^3+c*d*x^2+a*e*x+a*d)/c^3/a","B"
686,1,1150,299,0.118000," ","int((e*x+d)^(5/2)/(c*x^2+a)^(3/2),x)","\frac{\sqrt{e x +d}\, \sqrt{c \,x^{2}+a}\, \left(-a c \,e^{4} x^{2}+c^{2} d^{2} e^{2} x^{2}-3 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} e^{4} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+3 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} e^{4} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-2 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a c \,d^{2} e^{2} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+3 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a c \,d^{2} e^{2} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-3 a c d \,e^{3} x +\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, c^{2} d^{4} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+c^{2} d^{3} e x -2 a c \,d^{2} e^{2}-\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, \sqrt{-a c}\, a d \,e^{3} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, \sqrt{-a c}\, c \,d^{3} e \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)\right)}{\left(c e \,x^{3}+c d \,x^{2}+a e x +a d \right) a \,c^{2} e}"," ",0,"(e*x+d)^(1/2)*(c*x^2+a)^(1/2)*(3*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^2*e^4+3*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c*d^2*e^2-(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*(-a*c)^(1/2)*a*d*e^3-(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*(-a*c)^(1/2)*c*d^3*e-3*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^2*e^4-2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c*d^2*e^2+(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*c^2*d^4-a*c*e^4*x^2+c^2*d^2*e^2*x^2-3*a*c*d*e^3*x+c^2*d^3*e*x-2*a*c*d^2*e^2)/c^2/e/(c*e*x^3+c*d*x^2+a*e*x+a*d)/a","B"
687,1,685,261,0.113000," ","int((e*x+d)^(3/2)/(c*x^2+a)^(3/2),x)","\frac{\left(c^{2} d \,e^{2} x^{2}+\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a c d \,e^{2} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-a c \,e^{3} x +\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, c^{2} d^{3} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+c^{2} d^{2} e x -a c d \,e^{2}-\sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a \,e^{3} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-\sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, c \,d^{2} e \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)\right) \sqrt{e x +d}\, \sqrt{c \,x^{2}+a}}{\left(c e \,x^{3}+c d \,x^{2}+a e x +a d \right) a \,c^{2} e}"," ",0,"(-(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*e^3-(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*c*d^2*e+a*c*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*d*e^2+(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*c^2*d^3+c^2*d*e^2*x^2-a*c*e^3*x+x*c^2*d^2*e-a*c*d*e^2)*(e*x+d)^(1/2)*(c*x^2+a)^(1/2)/e/(c*e*x^3+c*d*x^2+a*e*x+a*d)/a/c^2","B"
688,1,649,238,0.110000," ","int((e*x+d)^(1/2)/(c*x^2+a)^(3/2),x)","\frac{\sqrt{e x +d}\, \sqrt{c \,x^{2}+a}\, \left(c \,e^{2} x^{2}+\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a \,e^{2} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a \,e^{2} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, c \,d^{2} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+c d e x -\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, \sqrt{-a c}\, d e \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)\right)}{\left(c e \,x^{3}+c d \,x^{2}+a e x +a d \right) a c e}"," ",0,"(e*x+d)^(1/2)*(c*x^2+a)^(1/2)*(EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*e^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*c*d^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*e^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*d*e*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*(-a*c)^(1/2)+c*e^2*x^2+c*d*e*x)/c/e/(c*e*x^3+c*d*x^2+a*e*x+a*d)/a","B"
689,1,696,271,0.129000," ","int(1/(c*x^2+a)^(3/2)/(e*x+d)^(1/2),x)","\frac{\left(c^{2} d \,e^{2} x^{2}+\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a c d \,e^{2} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+a c \,e^{3} x +\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, c^{2} d^{3} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+c^{2} d^{2} e x +a c d \,e^{2}-\sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a \,e^{3} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-\sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, c \,d^{2} e \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)\right) \sqrt{e x +d}\, \sqrt{c \,x^{2}+a}}{\left(a \,e^{2}+c \,d^{2}\right) \left(c e \,x^{3}+c d \,x^{2}+a e x +a d \right) a c e}"," ",0,"(-(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*e^3-(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*c*d^2*e+a*c*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*d*e^2+(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*c^2*d^3+c^2*d*e^2*x^2+a*c*e^3*x+c^2*d^2*e*x+a*c*d*e^2)*(e*x+d)^(1/2)*(c*x^2+a)^(1/2)/e/c/a/(a*e^2+c*d^2)/(c*e*x^3+c*d*x^2+a*e*x+a*d)","B"
690,1,1167,342,0.151000," ","int(1/(e*x+d)^(3/2)/(c*x^2+a)^(3/2),x)","\frac{\left(-3 a c \,e^{4} x^{2}+c^{2} d^{2} e^{2} x^{2}-3 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} e^{4} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+3 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} e^{4} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-2 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a c \,d^{2} e^{2} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+3 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a c \,d^{2} e^{2} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+a c d \,e^{3} x +\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, c^{2} d^{4} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+c^{2} d^{3} e x -2 a^{2} e^{4}+2 a c \,d^{2} e^{2}-\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, \sqrt{-a c}\, a d \,e^{3} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, \sqrt{-a c}\, c \,d^{3} e \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)\right) \sqrt{c \,x^{2}+a}\, \sqrt{e x +d}}{\left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c e \,x^{3}+c d \,x^{2}+a e x +a d \right) a e}"," ",0,"(3*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^2*e^4+3*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c*d^2*e^2-(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*(-a*c)^(1/2)*a*d*e^3-(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*(-a*c)^(1/2)*c*d^3*e-3*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^2*e^4-2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c*d^2*e^2+(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*c^2*d^4-3*a*c*e^4*x^2+c^2*d^2*e^2*x^2+a*c*d*e^3*x+c^2*d^3*e*x-2*a^2*e^4+2*a*c*d^2*e^2)*(c*x^2+a)^(1/2)*(e*x+d)^(1/2)/e/a/(a*e^2+c*d^2)^2/(c*e*x^3+c*d*x^2+a*e*x+a*d)","B"
691,1,2623,409,0.160000," ","int(1/(e*x+d)^(5/2)/(c*x^2+a)^(3/2),x)","\frac{-29 a \,c^{2} d \,e^{5} x^{3}+3 c^{3} d^{3} e^{3} x^{3}-29 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} c d \,e^{5} x \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+24 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} c d \,e^{5} x \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-5 a^{2} c \,e^{6} x^{2}-26 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a \,c^{2} d^{3} e^{3} x \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+24 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a \,c^{2} d^{3} e^{3} x \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-31 a \,c^{2} d^{2} e^{4} x^{2}+3 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, c^{3} d^{5} e x \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+6 c^{3} d^{4} e^{2} x^{2}-29 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} c \,d^{2} e^{4} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+24 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} c \,d^{2} e^{4} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-26 a^{2} c d \,e^{5} x +5 \sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} e^{6} x \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-26 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a \,c^{2} d^{4} e^{2} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+24 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a \,c^{2} d^{4} e^{2} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+9 a \,c^{2} d^{3} e^{3} x +2 \sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a c \,d^{2} e^{4} x \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+3 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, c^{3} d^{6} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+3 c^{3} d^{5} e x -3 \sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, c^{2} d^{4} e^{2} x \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-2 a^{3} e^{6}-25 a^{2} c \,d^{2} e^{4}+5 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, \sqrt{-a c}\, a^{2} d \,e^{5} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+9 a \,c^{2} d^{4} e^{2}+2 \sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a c \,d^{3} e^{3} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-3 \sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, c^{2} d^{5} e \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)}{3 \sqrt{c \,x^{2}+a}\, \left(a \,e^{2}+c \,d^{2}\right)^{3} \left(e x +d \right)^{\frac{3}{2}} a e}"," ",0,"1/3*(5*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*(-a*c)^(1/2)*a^2*d*e^5-29*a*c^2*d*e^5*x^3-31*a*c^2*d^2*e^4*x^2+9*a*c^2*d^3*e^3*x+3*c^3*d^5*e*x+3*c^3*d^3*e^3*x^3-5*a^2*c*e^6*x^2-25*a^2*c*d^2*e^4+9*a*c^2*d^4*e^2+3*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*c^3*d^6*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-2*a^3*e^6+6*c^3*d^4*e^2*x^2+24*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x*a^2*c*d*e^5*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+24*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x*a*c^2*d^3*e^3*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-3*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x*c^2*d^4*e^2*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-29*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x*a^2*c*d*e^5*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-26*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x*a*c^2*d^3*e^3*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+2*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c*d^3*e^3*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+2*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x*a*c*d^2*e^4*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-26*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c^2*d^4*e^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+24*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^2*c*d^2*e^4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+24*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c^2*d^4*e^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+3*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x*c^3*d^5*e*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-3*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*c^2*d^5*e*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-29*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^2*c*d^2*e^4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-26*a^2*c*d*e^5*x+5*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x*a^2*e^6*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2))/(c*x^2+a)^(1/2)/(a*e^2+c*d^2)^3/a/(e*x+d)^(3/2)/e","B"
692,1,3304,397,0.156000," ","int((e*x+d)^(9/2)/(c*x^2+a)^(5/2),x)","\text{output too large to display}"," ",0,"-1/6*(21*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a^3*c*e^6*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+3*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^2*c^2*d^4*e^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+21*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^4*e^6*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-7*x^2*a*c^3*d^4*e^2-21*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a^3*c*e^6*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-21*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^4*e^6*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+12*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a^2*c*d*e^5*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+16*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a*c^2*d^3*e^3*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-4*x^3*c^4*d^5*e+9*x^4*a^2*c^2*e^6-4*x^4*c^4*d^4*e^2+7*x^2*a^3*c*e^6-15*x^4*a*c^3*d^2*e^4+36*x^3*a^2*c^2*d*e^5-16*x^3*a*c^3*d^3*e^3+26*x*a^3*c*d*e^5+24*x^2*a^2*c^2*d^2*e^4+4*x*a^2*c^2*d^3*e^3+19*a^3*c*d^2*e^4+7*a^2*c^2*d^4*e^2+6*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a^2*c^2*d^2*e^4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-19*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a*c^3*d^4*e^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-18*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a^2*c^2*d^2*e^4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+3*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a*c^3*d^4*e^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+4*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*c^3*d^5*e*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+16*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^2*c*d^3*e^3*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+4*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c^2*d^5*e*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+6*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^3*c*d^2*e^4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-19*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^2*c^2*d^4*e^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-18*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^3*c*d^2*e^4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+12*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^3*d*e^5*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-6*x*a*c^3*d^5*e-4*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c^3*d^6*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-4*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*c^4*d^6*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2))/c^3/(e*x+d)^(1/2)/a^2/e/(c*x^2+a)^(3/2)","B"
693,1,2660,346,0.157000," ","int((e*x+d)^(7/2)/(c*x^2+a)^(5/2),x)","-\frac{-8 a \,c^{3} d \,e^{4} x^{4}-4 c^{4} d^{3} e^{2} x^{4}-8 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} c^{2} d \,e^{4} x^{2} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+3 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} c^{2} d \,e^{4} x^{2} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+7 a^{2} c^{2} e^{5} x^{3}-12 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a \,c^{3} d^{3} e^{2} x^{2} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+3 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a \,c^{3} d^{3} e^{2} x^{2} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-9 a \,c^{3} d^{2} e^{3} x^{3}-4 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, c^{4} d^{5} x^{2} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-4 c^{4} d^{4} e \,x^{3}+5 a^{2} c^{2} d \,e^{4} x^{2}+5 \sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} c \,e^{5} x^{2} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-7 a \,c^{3} d^{3} e^{2} x^{2}+9 \sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a \,c^{2} d^{2} e^{3} x^{2} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+4 \sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, c^{3} d^{4} e \,x^{2} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-8 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{3} c d \,e^{4} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+3 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{3} c d \,e^{4} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+5 a^{3} c \,e^{5} x -12 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} c^{2} d^{3} e^{2} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+3 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} c^{2} d^{3} e^{2} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+3 a^{2} c^{2} d^{2} e^{3} x -4 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a \,c^{3} d^{5} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-6 a \,c^{3} d^{4} e x +5 a^{3} c d \,e^{4}+5 \sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{3} e^{5} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+5 a^{2} c^{2} d^{3} e^{2}+9 \sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} c \,d^{2} e^{3} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+4 \sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a \,c^{2} d^{4} e \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)}{6 \sqrt{e x +d}\, \left(c \,x^{2}+a \right)^{\frac{3}{2}} a^{2} c^{3} e}"," ",0,"-1/6*(-8*x^4*a*c^3*d*e^4-4*x^4*c^4*d^3*e^2+7*x^3*a^2*c^2*e^5-4*x^3*c^4*d^4*e+5*x*a^3*c*e^5+5*a^3*c*d*e^4+5*a^2*c^2*d^3*e^2+3*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a^2*c^2*d*e^4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+5*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a^2*c*e^5*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-12*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a*c^3*d^3*e^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+9*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^2*c*d^2*e^3*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+4*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c^2*d^4*e*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+3*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a*c^3*d^3*e^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+4*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*c^3*d^4*e*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-8*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a^2*c^2*d*e^4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+9*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a*c^2*d^2*e^3*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+3*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^2*c^2*d^3*e^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-8*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^3*c*d*e^4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-12*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^2*c^2*d^3*e^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+3*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^3*c*d*e^4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-9*x^3*a*c^3*d^2*e^3+5*x^2*a^2*c^2*d*e^4-7*x^2*a*c^3*d^3*e^2+3*x*a^2*c^2*d^2*e^3-6*x*a*c^3*d^4*e-4*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c^3*d^5*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-4*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*c^4*d^5*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+5*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^3*e^5*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2))/(e*x+d)^(1/2)/a^2/e/c^3/(c*x^2+a)^(3/2)","B"
694,1,2279,320,0.136000," ","int((e*x+d)^(5/2)/(c*x^2+a)^(5/2),x)","-\frac{-3 a \,c^{2} e^{4} x^{4}-4 c^{3} d^{2} e^{2} x^{4}-3 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} c \,e^{4} x^{2} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+3 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} c \,e^{4} x^{2} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-7 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a \,c^{2} d^{2} e^{2} x^{2} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+3 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a \,c^{2} d^{2} e^{2} x^{2} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-4 a \,c^{2} d \,e^{3} x^{3}-4 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, c^{3} d^{4} x^{2} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-4 c^{3} d^{3} e \,x^{3}-a^{2} c \,e^{4} x^{2}-7 a \,c^{2} d^{2} e^{2} x^{2}+4 \sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a c d \,e^{3} x^{2} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+4 \sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, c^{2} d^{3} e \,x^{2} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-3 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{3} e^{4} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+3 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{3} e^{4} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-7 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} c \,d^{2} e^{2} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+3 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} c \,d^{2} e^{2} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+2 a^{2} c d \,e^{3} x -4 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a \,c^{2} d^{4} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-6 a \,c^{2} d^{3} e x +3 a^{2} c \,d^{2} e^{2}+4 \sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} d \,e^{3} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+4 \sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a c \,d^{3} e \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)}{6 \sqrt{e x +d}\, \left(c \,x^{2}+a \right)^{\frac{3}{2}} a^{2} c^{2} e}"," ",0,"-1/6*(3*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a^2*c*e^4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+3*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a*c^2*d^2*e^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+4*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a*c*d*e^3*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+4*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*c^2*d^3*e*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-3*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a^2*c*e^4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-7*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a*c^2*d^2*e^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-4*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*c^3*d^4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+3*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^3*e^4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+3*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^2*c*d^2*e^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+4*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^2*d*e^3*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+4*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c*d^3*e*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-3*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^3*e^4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-7*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^2*c*d^2*e^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-4*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c^2*d^4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-3*x^4*a*c^2*e^4-4*x^4*c^3*d^2*e^2-4*x^3*a*c^2*d*e^3-4*x^3*c^3*d^3*e-x^2*a^2*c*e^4-7*x^2*a*c^2*d^2*e^2+2*x*a^2*c*d*e^3-6*x*a*c^2*d^3*e+3*a^2*c*d^2*e^2)/c^2/(e*x+d)^(1/2)/a^2/e/(c*x^2+a)^(3/2)","B"
695,1,1633,296,0.137000," ","int((e*x+d)^(3/2)/(c*x^2+a)^(5/2),x)","-\frac{-4 c^{3} d \,e^{2} x^{4}-4 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a \,c^{2} d \,e^{2} x^{2} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+3 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a \,c^{2} d \,e^{2} x^{2} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-a \,c^{2} e^{3} x^{3}-4 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, c^{3} d^{3} x^{2} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-4 c^{3} d^{2} e \,x^{3}-7 a \,c^{2} d \,e^{2} x^{2}+\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, \sqrt{-a c}\, a c \,e^{3} x^{2} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+4 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, \sqrt{-a c}\, c^{2} d^{2} e \,x^{2} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-4 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} c d \,e^{2} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+3 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} c d \,e^{2} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+a^{2} c \,e^{3} x -4 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a \,c^{2} d^{3} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-6 a \,c^{2} d^{2} e x +a^{2} c d \,e^{2}+\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, \sqrt{-a c}\, a^{2} e^{3} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+4 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, \sqrt{-a c}\, a c \,d^{2} e \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)}{6 \sqrt{e x +d}\, \left(c \,x^{2}+a \right)^{\frac{3}{2}} a^{2} c^{2} e}"," ",0,"-1/6*(3*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a*c^2*d*e^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a*c*e^3*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*(-a*c)^(1/2)+4*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*c^2*d^2*e*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*(-a*c)^(1/2)-4*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a*c^2*d*e^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-4*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*c^3*d^3*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+3*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^2*c*d*e^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^2*e^3*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*(-a*c)^(1/2)+4*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c*d^2*e*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)*(-a*c)^(1/2)-4*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^2*c*d*e^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-4*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c^2*d^3*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-4*x^4*c^3*d*e^2-x^3*a*c^2*e^3-4*x^3*c^3*d^2*e-7*x^2*a*c^2*d*e^2+x*a^2*c*e^3-6*x*a*c^2*d^2*e+a^2*c*d*e^2)/(e*x+d)^(1/2)/a^2/e/c^2/(c*x^2+a)^(3/2)","B"
696,1,2292,320,0.133000," ","int((e*x+d)^(1/2)/(c*x^2+a)^(5/2),x)","-\frac{-3 a \,c^{2} e^{4} x^{4}-4 c^{3} d^{2} e^{2} x^{4}-3 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} c \,e^{4} x^{2} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+3 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} c \,e^{4} x^{2} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-7 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a \,c^{2} d^{2} e^{2} x^{2} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+3 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a \,c^{2} d^{2} e^{2} x^{2} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-4 a \,c^{2} d \,e^{3} x^{3}-4 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, c^{3} d^{4} x^{2} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-4 c^{3} d^{3} e \,x^{3}-5 a^{2} c \,e^{4} x^{2}-7 a \,c^{2} d^{2} e^{2} x^{2}+4 \sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a c d \,e^{3} x^{2} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+4 \sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, c^{2} d^{3} e \,x^{2} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-3 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{3} e^{4} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+3 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{3} e^{4} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-7 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} c \,d^{2} e^{2} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+3 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} c \,d^{2} e^{2} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-6 a^{2} c d \,e^{3} x -4 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a \,c^{2} d^{4} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-6 a \,c^{2} d^{3} e x -a^{2} c \,d^{2} e^{2}+4 \sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} d \,e^{3} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+4 \sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a c \,d^{3} e \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)}{6 \sqrt{e x +d}\, \left(a \,e^{2}+c \,d^{2}\right) \left(c \,x^{2}+a \right)^{\frac{3}{2}} a^{2} c e}"," ",0,"-1/6*(3*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a^2*c*e^4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+3*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a*c^2*d^2*e^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+4*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a*c*d*e^3*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+4*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*c^2*d^3*e*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-3*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a^2*c*e^4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-7*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a*c^2*d^2*e^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-4*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*c^3*d^4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+3*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^3*e^4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+3*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^2*c*d^2*e^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+4*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^2*d*e^3*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+4*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c*d^3*e*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-3*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^3*e^4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-7*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^2*c*d^2*e^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-4*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c^2*d^4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-3*a*c^2*e^4*x^4-4*c^3*d^2*e^2*x^4-4*a*c^2*d*e^3*x^3-4*c^3*d^3*e*x^3-5*a^2*c*e^4*x^2-7*a*c^2*d^2*e^2*x^2-6*a^2*c*d*e^3*x-6*a*c^2*d^3*e*x-a^2*c*d^2*e^2)/c/(e*x+d)^(1/2)/(a*e^2+c*d^2)/a^2/e/(c*x^2+a)^(3/2)","B"
697,1,2673,378,0.145000," ","int(1/(c*x^2+a)^(5/2)/(e*x+d)^(1/2),x)","\frac{8 a \,c^{3} d \,e^{4} x^{4}+4 c^{4} d^{3} e^{2} x^{4}+8 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} c^{2} d \,e^{4} x^{2} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-3 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} c^{2} d \,e^{4} x^{2} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+5 a^{2} c^{2} e^{5} x^{3}+12 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a \,c^{3} d^{3} e^{2} x^{2} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-3 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a \,c^{3} d^{3} e^{2} x^{2} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+9 a \,c^{3} d^{2} e^{3} x^{3}+4 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, c^{4} d^{5} x^{2} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+4 c^{4} d^{4} e \,x^{3}+15 a^{2} c^{2} d \,e^{4} x^{2}-5 \sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} c \,e^{5} x^{2} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+7 a \,c^{3} d^{3} e^{2} x^{2}-9 \sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a \,c^{2} d^{2} e^{3} x^{2} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-4 \sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, c^{3} d^{4} e \,x^{2} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+8 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{3} c d \,e^{4} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-3 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{3} c d \,e^{4} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+7 a^{3} c \,e^{5} x +12 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} c^{2} d^{3} e^{2} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-3 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} c^{2} d^{3} e^{2} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+13 a^{2} c^{2} d^{2} e^{3} x +4 \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a \,c^{3} d^{5} \EllipticE \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+6 a \,c^{3} d^{4} e x +7 a^{3} c d \,e^{4}-5 \sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{3} e^{5} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)+3 a^{2} c^{2} d^{3} e^{2}-9 \sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a^{2} c \,d^{2} e^{3} \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)-4 \sqrt{-a c}\, \sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) e}{c d +\sqrt{-a c}\, e}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) e}{-c d +\sqrt{-a c}\, e}}\, a \,c^{2} d^{4} e \EllipticF \left(\sqrt{-\frac{\left(e x +d \right) c}{-c d +\sqrt{-a c}\, e}}, \sqrt{-\frac{-c d +\sqrt{-a c}\, e}{c d +\sqrt{-a c}\, e}}\right)}{6 \sqrt{e x +d}\, \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{2}+a \right)^{\frac{3}{2}} a^{2} c e}"," ",0,"1/6*(8*a*c^3*d*e^4*x^4+4*c^4*d^3*e^2*x^4+5*a^2*c^2*e^5*x^3+4*c^4*d^4*e*x^3+7*a^3*c*e^5*x+7*a^3*c*d*e^4+3*a^2*c^2*d^3*e^2-3*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a^2*c^2*d*e^4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-5*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a^2*c*e^5*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+12*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a*c^3*d^3*e^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-9*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^2*c*d^2*e^3*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-4*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c^2*d^4*e*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-3*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a*c^3*d^3*e^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-4*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*c^3*d^4*e*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+8*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a^2*c^2*d*e^4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-9*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a*c^2*d^2*e^3*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-3*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^2*c^2*d^3*e^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+8*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^3*c*d*e^4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+12*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^2*c^2*d^3*e^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-3*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^3*c*d*e^4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+9*a*c^3*d^2*e^3*x^3+15*a^2*c^2*d*e^4*x^2+7*a*c^3*d^3*e^2*x^2+13*a^2*c^2*d^2*e^3*x+6*a*c^3*d^4*e*x+4*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c^3*d^5*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+4*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*c^4*d^5*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-5*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^3*e^5*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2))/(e*x+d)^(1/2)/(a*e^2+c*d^2)^2/a^2/(c*x^2+a)^(3/2)/c/e","B"
698,1,3322,455,0.185000," ","int(1/(e*x+d)^(3/2)/(c*x^2+a)^(5/2),x)","\text{output too large to display}"," ",0,"-1/6*(21*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a^3*c*e^6*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+3*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^2*c^2*d^4*e^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+21*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^4*e^6*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-7*x^2*a*c^3*d^4*e^2-21*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a^3*c*e^6*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-21*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^4*e^6*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+12*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a^2*c*d*e^5*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+16*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a*c^2*d^3*e^3*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-4*x^3*c^4*d^5*e+21*x^4*a^2*c^2*e^6-4*x^4*c^4*d^4*e^2+35*x^2*a^3*c*e^6-15*x^4*a*c^3*d^2*e^4-12*x^3*a^2*c^2*d*e^5-16*x^3*a*c^3*d^3*e^3-14*x*a^3*c*d*e^5-36*x^2*a^2*c^2*d^2*e^4-20*x*a^2*c^2*d^3*e^3-25*a^3*c*d^2*e^4-5*a^2*c^2*d^4*e^2+6*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a^2*c^2*d^2*e^4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-19*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a*c^3*d^4*e^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-18*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a^2*c^2*d^2*e^4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+3*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*a*c^3*d^4*e^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+4*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*c^3*d^5*e*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+16*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^2*c*d^3*e^3*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+4*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c^2*d^5*e*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+12*a^4*e^6+6*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^3*c*d^2*e^4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-19*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^2*c^2*d^4*e^2*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-18*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^3*c*d^2*e^4*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)+12*EllipticF((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a^3*d*e^5*(-a*c)^(1/2)*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-6*x*a*c^3*d^5*e-4*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*a*c^3*d^6*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2)-4*EllipticE((-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2),(-(-c*d+(-a*c)^(1/2)*e)/(c*d+(-a*c)^(1/2)*e))^(1/2))*x^2*c^4*d^6*(-(e*x+d)/(-c*d+(-a*c)^(1/2)*e)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*d+(-a*c)^(1/2)*e)*e)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*d+(-a*c)^(1/2)*e)*e)^(1/2))/(e*x+d)^(1/2)/(a*e^2+c*d^2)^3/a^2/(c*x^2+a)^(3/2)/e","B"
699,0,0,120,0.833000," ","int(1/(e*x+d)/(3*e^2*x^2+d^2)^(1/3),x)","\int \frac{1}{\left(e x +d \right) \left(3 e^{2} x^{2}+d^{2}\right)^{\frac{1}{3}}}\, dx"," ",0,"int(1/(e*x+d)/(3*e^2*x^2+d^2)^(1/3),x)","F"
700,1,40,438,0.560000," ","int((3*x+2)^3/(27*x^2+4)^(1/3),x)","\frac{16 \,2^{\frac{1}{3}} x \hypergeom \left(\left[\frac{1}{3}, \frac{1}{2}\right], \left[\frac{3}{2}\right], -\frac{27 x^{2}}{4}\right)}{7}+\frac{\left(63 x^{2}+180 x +196\right) \left(27 x^{2}+4\right)^{\frac{2}{3}}}{210}"," ",0,"1/210*(63*x^2+180*x+196)*(27*x^2+4)^(2/3)+16/7*2^(1/3)*x*hypergeom([1/3,1/2],[3/2],-27/4*x^2)","C"
701,1,35,431,0.536000," ","int((3*x+2)^2/(27*x^2+4)^(1/3),x)","\frac{12 \,2^{\frac{1}{3}} x \hypergeom \left(\left[\frac{1}{3}, \frac{1}{2}\right], \left[\frac{3}{2}\right], -\frac{27 x^{2}}{4}\right)}{7}+\frac{\left(3 x +7\right) \left(27 x^{2}+4\right)^{\frac{2}{3}}}{21}"," ",0,"1/21*(7+3*x)*(27*x^2+4)^(2/3)+12/7*2^(1/3)*x*hypergeom([1/3,1/2],[3/2],-27/4*x^2)","C"
702,1,29,415,0.542000," ","int((3*x+2)/(27*x^2+4)^(1/3),x)","2^{\frac{1}{3}} x \hypergeom \left(\left[\frac{1}{3}, \frac{1}{2}\right], \left[\frac{3}{2}\right], -\frac{27 x^{2}}{4}\right)+\frac{\left(27 x^{2}+4\right)^{\frac{2}{3}}}{12}"," ",0,"1/12*(27*x^2+4)^(2/3)+2^(1/3)*x*hypergeom([1/3,1/2],[3/2],-27/4*x^2)","C"
703,0,0,74,2.797000," ","int(1/(3*x+2)/(27*x^2+4)^(1/3),x)","\int \frac{1}{\left(3 x +2\right) \left(27 x^{2}+4\right)^{\frac{1}{3}}}\, dx"," ",0,"int(1/(3*x+2)/(27*x^2+4)^(1/3),x)","F"
704,0,0,495,0.767000," ","int(1/(3*x+2)^2/(27*x^2+4)^(1/3),x)","\int \frac{1}{\left(3 x +2\right)^{2} \left(27 x^{2}+4\right)^{\frac{1}{3}}}\, dx"," ",0,"int(1/(3*x+2)^2/(27*x^2+4)^(1/3),x)","F"
705,0,0,513,0.661000," ","int(1/(3*x+2)^3/(27*x^2+4)^(1/3),x)","\int \frac{1}{\left(3 x +2\right)^{3} \left(27 x^{2}+4\right)^{\frac{1}{3}}}\, dx"," ",0,"int(1/(3*x+2)^3/(27*x^2+4)^(1/3),x)","F"
706,1,49,441,0.562000," ","int((2+3*I*x)^3/(-27*x^2+4)^(1/3),x)","\frac{16 \,2^{\frac{1}{3}} x \hypergeom \left(\left[\frac{1}{3}, \frac{1}{2}\right], \left[\frac{3}{2}\right], \frac{27 x^{2}}{4}\right)}{7}-\frac{i \left(63 x^{2}-180 i x -196\right) \left(27 x^{2}-4\right)}{210 \left(-27 x^{2}+4\right)^{\frac{1}{3}}}"," ",0,"-1/210*I*(-180*I*x+63*x^2-196)*(27*x^2-4)/(-27*x^2+4)^(1/3)+16/7*2^(1/3)*x*hypergeom([1/3,1/2],[3/2],27/4*x^2)","C"
707,1,43,434,0.543000," ","int((2+3*I*x)^2/(-27*x^2+4)^(1/3),x)","\frac{12 \,2^{\frac{1}{3}} x \hypergeom \left(\left[\frac{1}{3}, \frac{1}{2}\right], \left[\frac{3}{2}\right], \frac{27 x^{2}}{4}\right)}{7}-\frac{\left(3 x -7 i\right) \left(27 x^{2}-4\right)}{21 \left(-27 x^{2}+4\right)^{\frac{1}{3}}}"," ",0,"-1/21*(-7*I+3*x)*(27*x^2-4)/(-27*x^2+4)^(1/3)+12/7*2^(1/3)*x*hypergeom([1/3,1/2],[3/2],27/4*x^2)","C"
708,1,37,416,0.554000," ","int((2+3*I*x)/(-27*x^2+4)^(1/3),x)","2^{\frac{1}{3}} x \hypergeom \left(\left[\frac{1}{3}, \frac{1}{2}\right], \left[\frac{3}{2}\right], \frac{27 x^{2}}{4}\right)+\frac{i \left(27 x^{2}-4\right)}{12 \left(-27 x^{2}+4\right)^{\frac{1}{3}}}"," ",0,"1/12*I*(27*x^2-4)/(-27*x^2+4)^(1/3)+2^(1/3)*x*hypergeom([1/3,1/2],[3/2],27/4*x^2)","C"
709,0,0,80,0.742000," ","int(1/(2+3*I*x)/(-27*x^2+4)^(1/3),x)","\int \frac{1}{\left(3 i x +2\right) \left(-27 x^{2}+4\right)^{\frac{1}{3}}}\, dx"," ",0,"int(1/(2+3*I*x)/(-27*x^2+4)^(1/3),x)","F"
710,0,0,503,0.773000," ","int(1/(3*I*x+2)^2/(-27*x^2+4)^(1/3),x)","\int \frac{1}{\left(3 i x +2\right)^{2} \left(-27 x^{2}+4\right)^{\frac{1}{3}}}\, dx"," ",0,"int(1/(3*I*x+2)^2/(-27*x^2+4)^(1/3),x)","F"
711,0,0,523,0.762000," ","int(1/(3*I*x+2)^3/(-27*x^2+4)^(1/3),x)","\int \frac{1}{\left(3 i x +2\right)^{3} \left(-27 x^{2}+4\right)^{\frac{1}{3}}}\, dx"," ",0,"int(1/(3*I*x+2)^3/(-27*x^2+4)^(1/3),x)","F"
712,1,2422,74,47.004000," ","int(1/(x^2+1)^(1/3)/(x+3^(1/2)),x)","\text{Expression too large to display}"," ",0,"-1/18*3^(1/2)*(6*ln((12*RootOf(_Z^3-6*3^(1/2))^2*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)^2*x^3-144*3^(1/2)*RootOf(_Z^3-6*3^(1/2))^2*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*(x^2+1)^(2/3)*x+10*RootOf(_Z^3-6*3^(1/2))^3*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*x^3+540*RootOf(_Z^3-6*3^(1/2))*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*(x^2+1)^(1/3)*x-90*3^(1/2)*RootOf(_Z^3-6*3^(1/2))*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*(x^2+1)^(1/3)*x^2-54*RootOf(_Z^3-6*3^(1/2))^2*(x^2+1)^(1/3)*x+9*3^(1/2)*RootOf(_Z^3-6*3^(1/2))^2*(x^2+1)^(1/3)*x^2+108*RootOf(_Z^3-6*3^(1/2))^2*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)^2*x+18*3^(1/2)*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*x^3+90*RootOf(_Z^3-6*3^(1/2))^3*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*x+432*RootOf(_Z^3-6*3^(1/2))^2*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*(x^2+1)^(2/3)-270*(x^2+1)^(2/3)*x+15*3^(1/2)*RootOf(_Z^3-6*3^(1/2))*x^3-270*3^(1/2)*RootOf(_Z^3-6*3^(1/2))*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*(x^2+1)^(1/3)+27*3^(1/2)*RootOf(_Z^3-6*3^(1/2))^2*(x^2+1)^(1/3)+162*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*3^(1/2)*x-378*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*x^2+135*RootOf(_Z^3-6*3^(1/2))*3^(1/2)*x+270*3^(1/2)*(x^2+1)^(2/3)-315*x^2*RootOf(_Z^3-6*3^(1/2))-378*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)-315*RootOf(_Z^3-6*3^(1/2)))/(3^(1/2)*x+3)^3)*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)+ln((12*RootOf(_Z^3-6*3^(1/2))^2*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)^2*x^3-144*3^(1/2)*RootOf(_Z^3-6*3^(1/2))^2*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*(x^2+1)^(2/3)*x+10*RootOf(_Z^3-6*3^(1/2))^3*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*x^3+540*RootOf(_Z^3-6*3^(1/2))*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*(x^2+1)^(1/3)*x-90*3^(1/2)*RootOf(_Z^3-6*3^(1/2))*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*(x^2+1)^(1/3)*x^2-54*RootOf(_Z^3-6*3^(1/2))^2*(x^2+1)^(1/3)*x+9*3^(1/2)*RootOf(_Z^3-6*3^(1/2))^2*(x^2+1)^(1/3)*x^2+108*RootOf(_Z^3-6*3^(1/2))^2*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)^2*x+18*3^(1/2)*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*x^3+90*RootOf(_Z^3-6*3^(1/2))^3*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*x+432*RootOf(_Z^3-6*3^(1/2))^2*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*(x^2+1)^(2/3)-270*(x^2+1)^(2/3)*x+15*3^(1/2)*RootOf(_Z^3-6*3^(1/2))*x^3-270*3^(1/2)*RootOf(_Z^3-6*3^(1/2))*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*(x^2+1)^(1/3)+27*3^(1/2)*RootOf(_Z^3-6*3^(1/2))^2*(x^2+1)^(1/3)+162*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*3^(1/2)*x-378*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*x^2+135*RootOf(_Z^3-6*3^(1/2))*3^(1/2)*x+270*3^(1/2)*(x^2+1)^(2/3)-315*x^2*RootOf(_Z^3-6*3^(1/2))-378*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)-315*RootOf(_Z^3-6*3^(1/2)))/(3^(1/2)*x+3)^3)*RootOf(_Z^3-6*3^(1/2))-RootOf(_Z^3-6*3^(1/2))*ln((48*RootOf(_Z^3-6*3^(1/2))^2*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)^2*x^3+144*3^(1/2)*RootOf(_Z^3-6*3^(1/2))^2*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*(x^2+1)^(2/3)*x+10*RootOf(_Z^3-6*3^(1/2))^3*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*x^3-324*RootOf(_Z^3-6*3^(1/2))*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*(x^2+1)^(1/3)*x+54*3^(1/2)*RootOf(_Z^3-6*3^(1/2))*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*(x^2+1)^(1/3)*x^2+90*RootOf(_Z^3-6*3^(1/2))^2*(x^2+1)^(1/3)*x-15*3^(1/2)*RootOf(_Z^3-6*3^(1/2))^2*(x^2+1)^(1/3)*x^2+432*RootOf(_Z^3-6*3^(1/2))^2*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)^2*x-24*3^(1/2)*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*x^3+90*RootOf(_Z^3-6*3^(1/2))^3*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*x-432*RootOf(_Z^3-6*3^(1/2))^2*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*(x^2+1)^(2/3)+162*(x^2+1)^(2/3)*x-5*3^(1/2)*RootOf(_Z^3-6*3^(1/2))*x^3+162*3^(1/2)*RootOf(_Z^3-6*3^(1/2))*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*(x^2+1)^(1/3)-45*3^(1/2)*RootOf(_Z^3-6*3^(1/2))^2*(x^2+1)^(1/3)-216*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*3^(1/2)*x+1512*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*x^2-45*RootOf(_Z^3-6*3^(1/2))*3^(1/2)*x-162*3^(1/2)*(x^2+1)^(2/3)+315*x^2*RootOf(_Z^3-6*3^(1/2))+1512*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)+315*RootOf(_Z^3-6*3^(1/2)))/(3^(1/2)*x+3)^3))","C"
713,1,2443,72,41.218000," ","int(1/(x^2+1)^(1/3)/(-x+3^(1/2)),x)","\text{Expression too large to display}"," ",0,"1/18*3^(1/2)*(ln((144*3^(1/2)*RootOf(_Z^3-6*3^(1/2))^2*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*(x^2+1)^(2/3)*x-2*RootOf(_Z^3-6*3^(1/2))^3*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*x^3-60*RootOf(_Z^3-6*3^(1/2))^2*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)^2*x^3+54*RootOf(_Z^3-6*3^(1/2))^2*(x^2+1)^(1/3)*x+864*RootOf(_Z^3-6*3^(1/2))*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*(x^2+1)^(1/3)*x+9*3^(1/2)*RootOf(_Z^3-6*3^(1/2))^2*(x^2+1)^(1/3)*x^2+144*3^(1/2)*RootOf(_Z^3-6*3^(1/2))*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*(x^2+1)^(1/3)*x^2+162*(x^2+1)^(2/3)*x+3^(1/2)*RootOf(_Z^3-6*3^(1/2))*x^3+30*3^(1/2)*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*x^3-18*RootOf(_Z^3-6*3^(1/2))^3*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*x-540*RootOf(_Z^3-6*3^(1/2))^2*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)^2*x+432*RootOf(_Z^3-6*3^(1/2))^2*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*(x^2+1)^(2/3)+27*3^(1/2)*RootOf(_Z^3-6*3^(1/2))^2*(x^2+1)^(1/3)+432*3^(1/2)*RootOf(_Z^3-6*3^(1/2))*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*(x^2+1)^(1/3)+9*RootOf(_Z^3-6*3^(1/2))*3^(1/2)*x+270*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*3^(1/2)*x+162*3^(1/2)*(x^2+1)^(2/3)+63*x^2*RootOf(_Z^3-6*3^(1/2))+1890*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*x^2+63*RootOf(_Z^3-6*3^(1/2))+1890*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2))/(3^(1/2)*x-3)^3)*RootOf(_Z^3-6*3^(1/2))+6*ln((144*3^(1/2)*RootOf(_Z^3-6*3^(1/2))^2*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*(x^2+1)^(2/3)*x-2*RootOf(_Z^3-6*3^(1/2))^3*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*x^3-60*RootOf(_Z^3-6*3^(1/2))^2*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)^2*x^3+54*RootOf(_Z^3-6*3^(1/2))^2*(x^2+1)^(1/3)*x+864*RootOf(_Z^3-6*3^(1/2))*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*(x^2+1)^(1/3)*x+9*3^(1/2)*RootOf(_Z^3-6*3^(1/2))^2*(x^2+1)^(1/3)*x^2+144*3^(1/2)*RootOf(_Z^3-6*3^(1/2))*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*(x^2+1)^(1/3)*x^2+162*(x^2+1)^(2/3)*x+3^(1/2)*RootOf(_Z^3-6*3^(1/2))*x^3+30*3^(1/2)*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*x^3-18*RootOf(_Z^3-6*3^(1/2))^3*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*x-540*RootOf(_Z^3-6*3^(1/2))^2*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)^2*x+432*RootOf(_Z^3-6*3^(1/2))^2*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*(x^2+1)^(2/3)+27*3^(1/2)*RootOf(_Z^3-6*3^(1/2))^2*(x^2+1)^(1/3)+432*3^(1/2)*RootOf(_Z^3-6*3^(1/2))*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*(x^2+1)^(1/3)+9*RootOf(_Z^3-6*3^(1/2))*3^(1/2)*x+270*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*3^(1/2)*x+162*3^(1/2)*(x^2+1)^(2/3)+63*x^2*RootOf(_Z^3-6*3^(1/2))+1890*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*x^2+63*RootOf(_Z^3-6*3^(1/2))+1890*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2))/(3^(1/2)*x-3)^3)*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)-6*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*ln(-(144*3^(1/2)*RootOf(_Z^3-6*3^(1/2))^2*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*(x^2+1)^(2/3)*x+8*RootOf(_Z^3-6*3^(1/2))^3*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*x^3+60*RootOf(_Z^3-6*3^(1/2))^2*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)^2*x^3+90*RootOf(_Z^3-6*3^(1/2))^2*(x^2+1)^(1/3)*x+864*RootOf(_Z^3-6*3^(1/2))*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*(x^2+1)^(1/3)*x+15*3^(1/2)*RootOf(_Z^3-6*3^(1/2))^2*(x^2+1)^(1/3)*x^2+144*3^(1/2)*RootOf(_Z^3-6*3^(1/2))*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*(x^2+1)^(1/3)*x^2+270*(x^2+1)^(2/3)*x+12*3^(1/2)*RootOf(_Z^3-6*3^(1/2))*x^3+90*3^(1/2)*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*x^3+72*RootOf(_Z^3-6*3^(1/2))^3*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*x+540*RootOf(_Z^3-6*3^(1/2))^2*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)^2*x+432*RootOf(_Z^3-6*3^(1/2))^2*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*(x^2+1)^(2/3)+45*3^(1/2)*RootOf(_Z^3-6*3^(1/2))^2*(x^2+1)^(1/3)+432*3^(1/2)*RootOf(_Z^3-6*3^(1/2))*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*(x^2+1)^(1/3)+108*RootOf(_Z^3-6*3^(1/2))*3^(1/2)*x+810*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*3^(1/2)*x+270*3^(1/2)*(x^2+1)^(2/3)+252*x^2*RootOf(_Z^3-6*3^(1/2))+1890*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2)*x^2+252*RootOf(_Z^3-6*3^(1/2))+1890*RootOf(RootOf(_Z^3-6*3^(1/2))^2+6*RootOf(_Z^3-6*3^(1/2))*_Z+36*_Z^2))/(3^(1/2)*x-3)^3))","C"
714,1,618,58,2.796000," ","int(1/(3-x)/(-x^2+1)^(1/3),x)","\frac{\RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \ln \left(-\frac{48 x^{2} \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2}-91 x^{2} \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)+144 x \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2}-49 x^{2}+216 \left(-x^{2}+1\right)^{\frac{1}{3}} x \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)-102 x \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)+237 \left(-x^{2}+1\right)^{\frac{1}{3}} x -546 x -432 \left(-x^{2}+1\right)^{\frac{2}{3}} \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)+216 \left(-x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)-171 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)-474 \left(-x^{2}+1\right)^{\frac{2}{3}}+237 \left(-x^{2}+1\right)^{\frac{1}{3}}+399}{\left(x -3\right)^{2}}\right)}{2}-\frac{\RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \ln \left(-\frac{96 x^{2} \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2}+278 x^{2} \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)+288 x \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2}+17 x^{2}-432 \left(-x^{2}+1\right)^{\frac{1}{3}} x \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)+492 x \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)+258 \left(-x^{2}+1\right)^{\frac{1}{3}} x -918 x +864 \left(-x^{2}+1\right)^{\frac{2}{3}} \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)-432 \left(-x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)+342 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)-516 \left(-x^{2}+1\right)^{\frac{2}{3}}+258 \left(-x^{2}+1\right)^{\frac{1}{3}}+969}{\left(x -3\right)^{2}}\right)}{2}-\frac{\ln \left(-\frac{96 x^{2} \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2}+278 x^{2} \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)+288 x \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2}+17 x^{2}-432 \left(-x^{2}+1\right)^{\frac{1}{3}} x \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)+492 x \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)+258 \left(-x^{2}+1\right)^{\frac{1}{3}} x -918 x +864 \left(-x^{2}+1\right)^{\frac{2}{3}} \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)-432 \left(-x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)+342 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)-516 \left(-x^{2}+1\right)^{\frac{2}{3}}+258 \left(-x^{2}+1\right)^{\frac{1}{3}}+969}{\left(x -3\right)^{2}}\right)}{4}"," ",0,"1/2*RootOf(4*_Z^2+2*_Z+1)*ln(-(48*RootOf(4*_Z^2+2*_Z+1)^2*x^2+144*RootOf(4*_Z^2+2*_Z+1)^2*x-432*RootOf(4*_Z^2+2*_Z+1)*(-x^2+1)^(2/3)+216*RootOf(4*_Z^2+2*_Z+1)*(-x^2+1)^(1/3)*x-91*RootOf(4*_Z^2+2*_Z+1)*x^2+216*RootOf(4*_Z^2+2*_Z+1)*(-x^2+1)^(1/3)-102*RootOf(4*_Z^2+2*_Z+1)*x-474*(-x^2+1)^(2/3)+237*(-x^2+1)^(1/3)*x-49*x^2-171*RootOf(4*_Z^2+2*_Z+1)+237*(-x^2+1)^(1/3)-546*x+399)/(x-3)^2)-1/4*ln(-(96*RootOf(4*_Z^2+2*_Z+1)^2*x^2+288*RootOf(4*_Z^2+2*_Z+1)^2*x+864*RootOf(4*_Z^2+2*_Z+1)*(-x^2+1)^(2/3)-432*RootOf(4*_Z^2+2*_Z+1)*(-x^2+1)^(1/3)*x+278*RootOf(4*_Z^2+2*_Z+1)*x^2-432*RootOf(4*_Z^2+2*_Z+1)*(-x^2+1)^(1/3)+492*RootOf(4*_Z^2+2*_Z+1)*x-516*(-x^2+1)^(2/3)+258*(-x^2+1)^(1/3)*x+17*x^2+342*RootOf(4*_Z^2+2*_Z+1)+258*(-x^2+1)^(1/3)-918*x+969)/(x-3)^2)-1/2*ln(-(96*RootOf(4*_Z^2+2*_Z+1)^2*x^2+288*RootOf(4*_Z^2+2*_Z+1)^2*x+864*RootOf(4*_Z^2+2*_Z+1)*(-x^2+1)^(2/3)-432*RootOf(4*_Z^2+2*_Z+1)*(-x^2+1)^(1/3)*x+278*RootOf(4*_Z^2+2*_Z+1)*x^2-432*RootOf(4*_Z^2+2*_Z+1)*(-x^2+1)^(1/3)+492*RootOf(4*_Z^2+2*_Z+1)*x-516*(-x^2+1)^(2/3)+258*(-x^2+1)^(1/3)*x+17*x^2+342*RootOf(4*_Z^2+2*_Z+1)+258*(-x^2+1)^(1/3)-918*x+969)/(x-3)^2)*RootOf(4*_Z^2+2*_Z+1)","C"
715,1,618,56,2.871000," ","int(1/(x+3)/(-x^2+1)^(1/3),x)","\frac{\RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) \ln \left(-\frac{48 x^{2} \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)^{2}+91 x^{2} \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)-144 x \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)^{2}-49 x^{2}+216 \left(-x^{2}+1\right)^{\frac{1}{3}} x \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)-102 x \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)-237 \left(-x^{2}+1\right)^{\frac{1}{3}} x +546 x +432 \left(-x^{2}+1\right)^{\frac{2}{3}} \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)-216 \left(-x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)+171 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)-474 \left(-x^{2}+1\right)^{\frac{2}{3}}+237 \left(-x^{2}+1\right)^{\frac{1}{3}}+399}{\left(x +3\right)^{2}}\right)}{2}-\frac{\RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right) \ln \left(-\frac{96 x^{2} \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)^{2}-278 x^{2} \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)-288 x \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)^{2}+17 x^{2}-432 \left(-x^{2}+1\right)^{\frac{1}{3}} x \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)+492 x \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)-258 \left(-x^{2}+1\right)^{\frac{1}{3}} x +918 x -864 \left(-x^{2}+1\right)^{\frac{2}{3}} \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)+432 \left(-x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)-342 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)-516 \left(-x^{2}+1\right)^{\frac{2}{3}}+258 \left(-x^{2}+1\right)^{\frac{1}{3}}+969}{\left(x +3\right)^{2}}\right)}{2}+\frac{\ln \left(-\frac{96 x^{2} \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)^{2}-278 x^{2} \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)-288 x \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)^{2}+17 x^{2}-432 \left(-x^{2}+1\right)^{\frac{1}{3}} x \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)+492 x \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)-258 \left(-x^{2}+1\right)^{\frac{1}{3}} x +918 x -864 \left(-x^{2}+1\right)^{\frac{2}{3}} \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)+432 \left(-x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)-342 \RootOf \left(4 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)-516 \left(-x^{2}+1\right)^{\frac{2}{3}}+258 \left(-x^{2}+1\right)^{\frac{1}{3}}+969}{\left(x +3\right)^{2}}\right)}{4}"," ",0,"1/2*RootOf(4*_Z^2-2*_Z+1)*ln(-(48*RootOf(4*_Z^2-2*_Z+1)^2*x^2-144*RootOf(4*_Z^2-2*_Z+1)^2*x+432*RootOf(4*_Z^2-2*_Z+1)*(-x^2+1)^(2/3)+216*RootOf(4*_Z^2-2*_Z+1)*(-x^2+1)^(1/3)*x+91*RootOf(4*_Z^2-2*_Z+1)*x^2-216*RootOf(4*_Z^2-2*_Z+1)*(-x^2+1)^(1/3)-102*RootOf(4*_Z^2-2*_Z+1)*x-474*(-x^2+1)^(2/3)-237*(-x^2+1)^(1/3)*x-49*x^2+171*RootOf(4*_Z^2-2*_Z+1)+237*(-x^2+1)^(1/3)+546*x+399)/(x+3)^2)+1/4*ln(-(96*RootOf(4*_Z^2-2*_Z+1)^2*x^2-288*RootOf(4*_Z^2-2*_Z+1)^2*x-864*RootOf(4*_Z^2-2*_Z+1)*(-x^2+1)^(2/3)-432*RootOf(4*_Z^2-2*_Z+1)*(-x^2+1)^(1/3)*x-278*RootOf(4*_Z^2-2*_Z+1)*x^2+432*RootOf(4*_Z^2-2*_Z+1)*(-x^2+1)^(1/3)+492*RootOf(4*_Z^2-2*_Z+1)*x-516*(-x^2+1)^(2/3)-258*(-x^2+1)^(1/3)*x+17*x^2-342*RootOf(4*_Z^2-2*_Z+1)+258*(-x^2+1)^(1/3)+918*x+969)/(x+3)^2)-1/2*ln(-(96*RootOf(4*_Z^2-2*_Z+1)^2*x^2-288*RootOf(4*_Z^2-2*_Z+1)^2*x-864*RootOf(4*_Z^2-2*_Z+1)*(-x^2+1)^(2/3)-432*RootOf(4*_Z^2-2*_Z+1)*(-x^2+1)^(1/3)*x-278*RootOf(4*_Z^2-2*_Z+1)*x^2+432*RootOf(4*_Z^2-2*_Z+1)*(-x^2+1)^(1/3)+492*RootOf(4*_Z^2-2*_Z+1)*x-516*(-x^2+1)^(2/3)-258*(-x^2+1)^(1/3)*x+17*x^2-342*RootOf(4*_Z^2-2*_Z+1)+258*(-x^2+1)^(1/3)+918*x+969)/(x+3)^2)*RootOf(4*_Z^2-2*_Z+1)","C"
716,0,0,174,0.849000," ","int(1/(e*x+d)/(-9*e^2*x^2+d^2)^(1/3),x)","\int \frac{1}{\left(e x +d \right) \left(-9 e^{2} x^{2}+d^{2}\right)^{\frac{1}{3}}}\, dx"," ",0,"int(1/(e*x+d)/(-9*e^2*x^2+d^2)^(1/3),x)","F"
717,0,0,230,0.804000," ","int(1/(b*x+a)/(d*x^2+c)^(1/4),x)","\int \frac{1}{\left(b x +a \right) \left(d \,x^{2}+c \right)^{\frac{1}{4}}}\, dx"," ",0,"int(1/(b*x+a)/(d*x^2+c)^(1/4),x)","F"
718,0,0,224,0.757000," ","int(1/(b*x+a)/(d*x^2+c)^(3/4),x)","\int \frac{1}{\left(b x +a \right) \left(d \,x^{2}+c \right)^{\frac{3}{4}}}\, dx"," ",0,"int(1/(b*x+a)/(d*x^2+c)^(3/4),x)","F"
719,0,0,154,0.899000," ","int(1/(e*x+d)^(3/2)/(c*x^2+a)^(1/4),x)","\int \frac{1}{\left(e x +d \right)^{\frac{3}{2}} \left(c \,x^{2}+a \right)^{\frac{1}{4}}}\, dx"," ",0,"int(1/(e*x+d)^(3/2)/(c*x^2+a)^(1/4),x)","F"
720,-1,0,146,180.000000," ","int(1/(x+1)/(x^2+1)^(1/6),x)","\int \frac{1}{\left(x +1\right) \left(x^{2}+1\right)^{\frac{1}{6}}}\, dx"," ",0,"int(1/(x+1)/(x^2+1)^(1/6),x)","F"
721,1,1140,223,0.054000," ","int((e*x+d)^m*(c*x^2+a)^3,x)","\frac{\left(c^{3} e^{6} m^{6} x^{6}+21 c^{3} e^{6} m^{5} x^{6}+3 a \,c^{2} e^{6} m^{6} x^{4}-6 c^{3} d \,e^{5} m^{5} x^{5}+175 c^{3} e^{6} m^{4} x^{6}+69 a \,c^{2} e^{6} m^{5} x^{4}-90 c^{3} d \,e^{5} m^{4} x^{5}+735 c^{3} e^{6} m^{3} x^{6}+3 a^{2} c \,e^{6} m^{6} x^{2}-12 a \,c^{2} d \,e^{5} m^{5} x^{3}+621 a \,c^{2} e^{6} m^{4} x^{4}+30 c^{3} d^{2} e^{4} m^{4} x^{4}-510 c^{3} d \,e^{5} m^{3} x^{5}+1624 c^{3} e^{6} m^{2} x^{6}+75 a^{2} c \,e^{6} m^{5} x^{2}-228 a \,c^{2} d \,e^{5} m^{4} x^{3}+2775 a \,c^{2} e^{6} m^{3} x^{4}+300 c^{3} d^{2} e^{4} m^{3} x^{4}-1350 c^{3} d \,e^{5} m^{2} x^{5}+1764 c^{3} e^{6} m \,x^{6}+a^{3} e^{6} m^{6}-6 a^{2} c d \,e^{5} m^{5} x +741 a^{2} c \,e^{6} m^{4} x^{2}+36 a \,c^{2} d^{2} e^{4} m^{4} x^{2}-1572 a \,c^{2} d \,e^{5} m^{3} x^{3}+6432 a \,c^{2} e^{6} m^{2} x^{4}-120 c^{3} d^{3} e^{3} m^{3} x^{3}+1050 c^{3} d^{2} e^{4} m^{2} x^{4}-1644 c^{3} d \,e^{5} m \,x^{5}+720 c^{3} e^{6} x^{6}+27 a^{3} e^{6} m^{5}-138 a^{2} c d \,e^{5} m^{4} x +3657 a^{2} c \,e^{6} m^{3} x^{2}+576 a \,c^{2} d^{2} e^{4} m^{3} x^{2}-4812 a \,c^{2} d \,e^{5} m^{2} x^{3}+7236 a \,c^{2} e^{6} m \,x^{4}-720 c^{3} d^{3} e^{3} m^{2} x^{3}+1500 c^{3} d^{2} e^{4} m \,x^{4}-720 c^{3} d \,e^{5} x^{5}+295 a^{3} e^{6} m^{4}+6 a^{2} c \,d^{2} e^{4} m^{4}-1206 a^{2} c d \,e^{5} m^{3} x +9336 a^{2} c \,e^{6} m^{2} x^{2}-72 a \,c^{2} d^{3} e^{3} m^{3} x +2988 a \,c^{2} d^{2} e^{4} m^{2} x^{2}-6480 a \,c^{2} d \,e^{5} m \,x^{3}+3024 a \,c^{2} e^{6} x^{4}+360 c^{3} d^{4} e^{2} m^{2} x^{2}-1320 c^{3} d^{3} e^{3} m \,x^{3}+720 c^{3} d^{2} e^{4} x^{4}+1665 a^{3} e^{6} m^{3}+132 a^{2} c \,d^{2} e^{4} m^{3}-4902 a^{2} c d \,e^{5} m^{2} x +11388 a^{2} c \,e^{6} m \,x^{2}-1008 a \,c^{2} d^{3} e^{3} m^{2} x +5472 a \,c^{2} d^{2} e^{4} m \,x^{2}-3024 a \,c^{2} d \,e^{5} x^{3}+1080 c^{3} d^{4} e^{2} m \,x^{2}-720 c^{3} d^{3} e^{3} x^{3}+5104 a^{3} e^{6} m^{2}+1074 a^{2} c \,d^{2} e^{4} m^{2}-8868 a^{2} c d \,e^{5} m x +5040 a^{2} c \,e^{6} x^{2}+72 a \,c^{2} d^{4} e^{2} m^{2}-3960 a \,c^{2} d^{3} e^{3} m x +3024 a \,c^{2} d^{2} e^{4} x^{2}-720 c^{3} d^{5} e m x +720 c^{3} d^{4} e^{2} x^{2}+8028 a^{3} e^{6} m +3828 a^{2} c \,d^{2} e^{4} m -5040 a^{2} c d \,e^{5} x +936 a \,c^{2} d^{4} e^{2} m -3024 a \,c^{2} d^{3} e^{3} x -720 c^{3} d^{5} e x +5040 a^{3} e^{6}+5040 a^{2} c \,d^{2} e^{4}+3024 a \,c^{2} d^{4} e^{2}+720 c^{3} d^{6}\right) \left(e x +d \right)^{m +1}}{\left(m^{7}+28 m^{6}+322 m^{5}+1960 m^{4}+6769 m^{3}+13132 m^{2}+13068 m +5040\right) e^{7}}"," ",0,"(e*x+d)^(m+1)*(c^3*e^6*m^6*x^6+21*c^3*e^6*m^5*x^6+3*a*c^2*e^6*m^6*x^4-6*c^3*d*e^5*m^5*x^5+175*c^3*e^6*m^4*x^6+69*a*c^2*e^6*m^5*x^4-90*c^3*d*e^5*m^4*x^5+735*c^3*e^6*m^3*x^6+3*a^2*c*e^6*m^6*x^2-12*a*c^2*d*e^5*m^5*x^3+621*a*c^2*e^6*m^4*x^4+30*c^3*d^2*e^4*m^4*x^4-510*c^3*d*e^5*m^3*x^5+1624*c^3*e^6*m^2*x^6+75*a^2*c*e^6*m^5*x^2-228*a*c^2*d*e^5*m^4*x^3+2775*a*c^2*e^6*m^3*x^4+300*c^3*d^2*e^4*m^3*x^4-1350*c^3*d*e^5*m^2*x^5+1764*c^3*e^6*m*x^6+a^3*e^6*m^6-6*a^2*c*d*e^5*m^5*x+741*a^2*c*e^6*m^4*x^2+36*a*c^2*d^2*e^4*m^4*x^2-1572*a*c^2*d*e^5*m^3*x^3+6432*a*c^2*e^6*m^2*x^4-120*c^3*d^3*e^3*m^3*x^3+1050*c^3*d^2*e^4*m^2*x^4-1644*c^3*d*e^5*m*x^5+720*c^3*e^6*x^6+27*a^3*e^6*m^5-138*a^2*c*d*e^5*m^4*x+3657*a^2*c*e^6*m^3*x^2+576*a*c^2*d^2*e^4*m^3*x^2-4812*a*c^2*d*e^5*m^2*x^3+7236*a*c^2*e^6*m*x^4-720*c^3*d^3*e^3*m^2*x^3+1500*c^3*d^2*e^4*m*x^4-720*c^3*d*e^5*x^5+295*a^3*e^6*m^4+6*a^2*c*d^2*e^4*m^4-1206*a^2*c*d*e^5*m^3*x+9336*a^2*c*e^6*m^2*x^2-72*a*c^2*d^3*e^3*m^3*x+2988*a*c^2*d^2*e^4*m^2*x^2-6480*a*c^2*d*e^5*m*x^3+3024*a*c^2*e^6*x^4+360*c^3*d^4*e^2*m^2*x^2-1320*c^3*d^3*e^3*m*x^3+720*c^3*d^2*e^4*x^4+1665*a^3*e^6*m^3+132*a^2*c*d^2*e^4*m^3-4902*a^2*c*d*e^5*m^2*x+11388*a^2*c*e^6*m*x^2-1008*a*c^2*d^3*e^3*m^2*x+5472*a*c^2*d^2*e^4*m*x^2-3024*a*c^2*d*e^5*x^3+1080*c^3*d^4*e^2*m*x^2-720*c^3*d^3*e^3*x^3+5104*a^3*e^6*m^2+1074*a^2*c*d^2*e^4*m^2-8868*a^2*c*d*e^5*m*x+5040*a^2*c*e^6*x^2+72*a*c^2*d^4*e^2*m^2-3960*a*c^2*d^3*e^3*m*x+3024*a*c^2*d^2*e^4*x^2-720*c^3*d^5*e*m*x+720*c^3*d^4*e^2*x^2+8028*a^3*e^6*m+3828*a^2*c*d^2*e^4*m-5040*a^2*c*d*e^5*x+936*a*c^2*d^4*e^2*m-3024*a*c^2*d^3*e^3*x-720*c^3*d^5*e*x+5040*a^3*e^6+5040*a^2*c*d^2*e^4+3024*a*c^2*d^4*e^2+720*c^3*d^6)/e^7/(m^7+28*m^6+322*m^5+1960*m^4+6769*m^3+13132*m^2+13068*m+5040)","B"
722,1,420,140,0.054000," ","int((e*x+d)^m*(c*x^2+a)^2,x)","\frac{\left(c^{2} e^{4} m^{4} x^{4}+10 c^{2} e^{4} m^{3} x^{4}+2 a c \,e^{4} m^{4} x^{2}-4 c^{2} d \,e^{3} m^{3} x^{3}+35 c^{2} e^{4} m^{2} x^{4}+24 a c \,e^{4} m^{3} x^{2}-24 c^{2} d \,e^{3} m^{2} x^{3}+50 c^{2} e^{4} m \,x^{4}+a^{2} e^{4} m^{4}-4 a c d \,e^{3} m^{3} x +98 a c \,e^{4} m^{2} x^{2}+12 c^{2} d^{2} e^{2} m^{2} x^{2}-44 c^{2} d \,e^{3} m \,x^{3}+24 c^{2} e^{4} x^{4}+14 a^{2} e^{4} m^{3}-40 a c d \,e^{3} m^{2} x +156 a c \,e^{4} m \,x^{2}+36 c^{2} d^{2} e^{2} m \,x^{2}-24 c^{2} d \,e^{3} x^{3}+71 a^{2} e^{4} m^{2}+4 a c \,d^{2} e^{2} m^{2}-116 a c d \,e^{3} m x +80 a c \,e^{4} x^{2}-24 c^{2} d^{3} e m x +24 c^{2} d^{2} e^{2} x^{2}+154 a^{2} e^{4} m +36 a c \,d^{2} e^{2} m -80 a c d \,e^{3} x -24 c^{2} d^{3} e x +120 a^{2} e^{4}+80 a c \,d^{2} e^{2}+24 c^{2} d^{4}\right) \left(e x +d \right)^{m +1}}{\left(m^{5}+15 m^{4}+85 m^{3}+225 m^{2}+274 m +120\right) e^{5}}"," ",0,"(e*x+d)^(m+1)*(c^2*e^4*m^4*x^4+10*c^2*e^4*m^3*x^4+2*a*c*e^4*m^4*x^2-4*c^2*d*e^3*m^3*x^3+35*c^2*e^4*m^2*x^4+24*a*c*e^4*m^3*x^2-24*c^2*d*e^3*m^2*x^3+50*c^2*e^4*m*x^4+a^2*e^4*m^4-4*a*c*d*e^3*m^3*x+98*a*c*e^4*m^2*x^2+12*c^2*d^2*e^2*m^2*x^2-44*c^2*d*e^3*m*x^3+24*c^2*e^4*x^4+14*a^2*e^4*m^3-40*a*c*d*e^3*m^2*x+156*a*c*e^4*m*x^2+36*c^2*d^2*e^2*m*x^2-24*c^2*d*e^3*x^3+71*a^2*e^4*m^2+4*a*c*d^2*e^2*m^2-116*a*c*d*e^3*m*x+80*a*c*e^4*x^2-24*c^2*d^3*e*m*x+24*c^2*d^2*e^2*x^2+154*a^2*e^4*m+36*a*c*d^2*e^2*m-80*a*c*d*e^3*x-24*c^2*d^3*e*x+120*a^2*e^4+80*a*c*d^2*e^2+24*c^2*d^4)/e^5/(m^5+15*m^4+85*m^3+225*m^2+274*m+120)","B"
723,1,100,70,0.049000," ","int((e*x+d)^m*(c*x^2+a),x)","\frac{\left(c \,e^{2} m^{2} x^{2}+3 c \,e^{2} m \,x^{2}+a \,e^{2} m^{2}-2 c d e m x +2 c \,e^{2} x^{2}+5 a \,e^{2} m -2 c d e x +6 a \,e^{2}+2 c \,d^{2}\right) \left(e x +d \right)^{m +1}}{\left(m^{3}+6 m^{2}+11 m +6\right) e^{3}}"," ",0,"(e*x+d)^(m+1)*(c*e^2*m^2*x^2+3*c*e^2*m*x^2+a*e^2*m^2-2*c*d*e*m*x+2*c*e^2*x^2+5*a*e^2*m-2*c*d*e*x+6*a*e^2+2*c*d^2)/e^3/(m^3+6*m^2+11*m+6)","A"
724,0,0,143,0.783000," ","int((e*x+d)^m/(c*x^2+a),x)","\int \frac{\left(e x +d \right)^{m}}{c \,x^{2}+a}\, dx"," ",0,"int((e*x+d)^m/(c*x^2+a),x)","F"
725,0,0,270,0.832000," ","int((e*x+d)^m/(c*x^2+a)^2,x)","\int \frac{\left(e x +d \right)^{m}}{\left(c \,x^{2}+a \right)^{2}}\, dx"," ",0,"int((e*x+d)^m/(c*x^2+a)^2,x)","F"
726,0,0,440,0.716000," ","int((e*x+d)^m/(c*x^2+a)^3,x)","\int \frac{\left(e x +d \right)^{m}}{\left(c \,x^{2}+a \right)^{3}}\, dx"," ",0,"int((e*x+d)^m/(c*x^2+a)^3,x)","F"
727,0,0,132,0.716000," ","int((e*x+d)^m*(c*x^2+a)^(3/2),x)","\int \left(c \,x^{2}+a \right)^{\frac{3}{2}} \left(e x +d \right)^{m}\, dx"," ",0,"int((e*x+d)^m*(c*x^2+a)^(3/2),x)","F"
728,0,0,132,0.712000," ","int((e*x+d)^m*(c*x^2+a)^(1/2),x)","\int \sqrt{c \,x^{2}+a}\, \left(e x +d \right)^{m}\, dx"," ",0,"int((e*x+d)^m*(c*x^2+a)^(1/2),x)","F"
729,0,0,132,0.781000," ","int((e*x+d)^m/(c*x^2+a)^(1/2),x)","\int \frac{\left(e x +d \right)^{m}}{\sqrt{c \,x^{2}+a}}\, dx"," ",0,"int((e*x+d)^m/(c*x^2+a)^(1/2),x)","F"
730,0,0,132,0.750000," ","int((e*x+d)^m/(c*x^2+a)^(3/2),x)","\int \frac{\left(e x +d \right)^{m}}{\left(c \,x^{2}+a \right)^{\frac{3}{2}}}\, dx"," ",0,"int((e*x+d)^m/(c*x^2+a)^(3/2),x)","F"
731,0,0,140,0.719000," ","int((e*x+d)^m*(c*x^2+a)^p,x)","\int \left(c \,x^{2}+a \right)^{p} \left(e x +d \right)^{m}\, dx"," ",0,"int((e*x+d)^m*(c*x^2+a)^p,x)","F"
732,0,0,172,0.674000," ","int((e*x+d)^3*(c*x^2+a)^p,x)","\int \left(e x +d \right)^{3} \left(c \,x^{2}+a \right)^{p}\, dx"," ",0,"int((e*x+d)^3*(c*x^2+a)^p,x)","F"
733,0,0,131,0.681000," ","int((e*x+d)^2*(c*x^2+a)^p,x)","\int \left(e x +d \right)^{2} \left(c \,x^{2}+a \right)^{p}\, dx"," ",0,"int((e*x+d)^2*(c*x^2+a)^p,x)","F"
734,0,0,57,0.525000," ","int((e*x+d)*(c*x^2+a)^p,x)","\int \left(e x +d \right) \left(c \,x^{2}+a \right)^{p}\, dx"," ",0,"int((e*x+d)*(c*x^2+a)^p,x)","F"
735,0,0,33,0.537000," ","int((c*x^2+a)^p,x)","\int \left(c \,x^{2}+a \right)^{p}\, dx"," ",0,"int((c*x^2+a)^p,x)","F"
736,0,0,121,0.698000," ","int((c*x^2+a)^p/(e*x+d),x)","\int \frac{\left(c \,x^{2}+a \right)^{p}}{e x +d}\, dx"," ",0,"int((c*x^2+a)^p/(e*x+d),x)","F"
737,0,0,183,0.752000," ","int((c*x^2+a)^p/(e*x+d)^2,x)","\int \frac{\left(c \,x^{2}+a \right)^{p}}{\left(e x +d \right)^{2}}\, dx"," ",0,"int((c*x^2+a)^p/(e*x+d)^2,x)","F"
738,0,0,312,0.678000," ","int((c*x^2+a)^p/(e*x+d)^3,x)","\int \frac{\left(c \,x^{2}+a \right)^{p}}{\left(e x +d \right)^{3}}\, dx"," ",0,"int((c*x^2+a)^p/(e*x+d)^3,x)","F"
739,0,0,148,0.715000," ","int((c*x^2+a)^p/((e*x+d)^(2*p)),x)","\int \left(c \,x^{2}+a \right)^{p} \left(e x +d \right)^{-2 p}\, dx"," ",0,"int((c*x^2+a)^p/((e*x+d)^(2*p)),x)","F"
740,0,0,143,0.704000," ","int((e*x+d)^(-2*p-1)*(c*x^2+a)^p,x)","\int \left(c \,x^{2}+a \right)^{p} \left(e x +d \right)^{-2 p -1}\, dx"," ",0,"int((e*x+d)^(-2*p-1)*(c*x^2+a)^p,x)","F"
741,0,0,175,0.692000," ","int((e*x+d)^(-2*p-2)*(c*x^2+a)^p,x)","\int \left(c \,x^{2}+a \right)^{p} \left(e x +d \right)^{-2 p -2}\, dx"," ",0,"int((e*x+d)^(-2*p-2)*(c*x^2+a)^p,x)","F"
742,0,0,236,0.685000," ","int((e*x+d)^(-3-2*p)*(c*x^2+a)^p,x)","\int \left(c \,x^{2}+a \right)^{p} \left(e x +d \right)^{-2 p -3}\, dx"," ",0,"int((e*x+d)^(-3-2*p)*(c*x^2+a)^p,x)","F"
743,0,0,315,0.743000," ","int((e*x+d)^(-4-2*p)*(c*x^2+a)^p,x)","\int \left(c \,x^{2}+a \right)^{p} \left(e x +d \right)^{-2 p -4}\, dx"," ",0,"int((e*x+d)^(-4-2*p)*(c*x^2+a)^p,x)","F"
744,0,0,402,0.769000," ","int((e*x+d)^(-5-2*p)*(c*x^2+a)^p,x)","\int \left(c \,x^{2}+a \right)^{p} \left(e x +d \right)^{-2 p -5}\, dx"," ",0,"int((e*x+d)^(-5-2*p)*(c*x^2+a)^p,x)","F"
745,0,0,529,0.724000," ","int((e*x+d)^(-6-2*p)*(c*x^2+a)^p,x)","\int \left(c \,x^{2}+a \right)^{p} \left(e x +d \right)^{-2 p -6}\, dx"," ",0,"int((e*x+d)^(-6-2*p)*(c*x^2+a)^p,x)","F"
746,0,0,29,0.883000," ","int((3-4*x)^n/(-x^2+1)^(1/2),x)","\int \frac{\left(-4 x +3\right)^{n}}{\sqrt{-x^{2}+1}}\, dx"," ",0,"int((3-4*x)^n/(-x^2+1)^(1/2),x)","F"
747,1,61,77,0.041000," ","int((b*x+a)^6/(-b^2*x^2+a^2),x)","-\frac{b^{4} x^{5}}{5}-\frac{3 a \,b^{3} x^{4}}{2}-\frac{16 a^{2} b^{2} x^{3}}{3}-13 a^{3} b \,x^{2}-\frac{32 a^{5} \ln \left(b x -a \right)}{b}-31 a^{4} x"," ",0,"-1/5*b^4*x^5-3/2*x^4*a*b^3-16/3*b^2*a^2*x^3-13*a^3*b*x^2-31*a^4*x-32*a^5/b*ln(b*x-a)","A"
748,1,50,62,0.046000," ","int((b*x+a)^5/(-b^2*x^2+a^2),x)","-\frac{b^{3} x^{4}}{4}-\frac{5 a \,b^{2} x^{3}}{3}-\frac{11 a^{2} b \,x^{2}}{2}-\frac{16 a^{4} \ln \left(b x -a \right)}{b}-15 a^{3} x"," ",0,"-1/4*b^3*x^4-5/3*a*b^2*x^3-11/2*a^2*b*x^2-15*a^3*x-16*a^4/b*ln(b*x-a)","A"
749,1,39,47,0.042000," ","int((b*x+a)^4/(-b^2*x^2+a^2),x)","-\frac{b^{2} x^{3}}{3}-2 a b \,x^{2}-\frac{8 a^{3} \ln \left(b x -a \right)}{b}-7 a^{2} x"," ",0,"-1/3*b^2*x^3-2*a*b*x^2-7*a^2*x-8*a^3/b*ln(b*x-a)","A"
750,1,28,26,0.048000," ","int((b*x+a)^3/(-b^2*x^2+a^2),x)","-\frac{b \,x^{2}}{2}-\frac{4 a^{2} \ln \left(b x -a \right)}{b}-3 a x"," ",0,"-1/2*b*x^2-3*a*x-4*a^2/b*ln(b*x-a)","A"
751,1,19,17,0.046000," ","int((b*x+a)^2/(-b^2*x^2+a^2),x)","-\frac{2 a \ln \left(b x -a \right)}{b}-x"," ",0,"-x-2*a/b*ln(b*x-a)","A"
752,1,14,12,0.045000," ","int((b*x+a)/(-b^2*x^2+a^2),x)","-\frac{\ln \left(b x -a \right)}{b}"," ",0,"-1/b*ln(b*x-a)","A"
753,1,47,31,0.050000," ","int(1/(b*x+a)/(-b^2*x^2+a^2),x)","-\frac{1}{2 \left(b x +a \right) a b}-\frac{\ln \left(b x -a \right)}{4 a^{2} b}+\frac{\ln \left(b x +a \right)}{4 a^{2} b}"," ",0,"-1/4/a^2/b*ln(b*x-a)+1/4/a^2/b*ln(b*x+a)-1/2/a/b/(b*x+a)","A"
754,1,62,46,0.052000," ","int(1/(b*x+a)^2/(-b^2*x^2+a^2),x)","-\frac{1}{4 \left(b x +a \right)^{2} a b}-\frac{1}{4 \left(b x +a \right) a^{2} b}-\frac{\ln \left(b x -a \right)}{8 a^{3} b}+\frac{\ln \left(b x +a \right)}{8 a^{3} b}"," ",0,"-1/8/a^3/b*ln(b*x-a)+1/8/a^3/b*ln(b*x+a)-1/4/a^2/b/(b*x+a)-1/4/a/b/(b*x+a)^2","A"
755,1,77,61,0.050000," ","int(1/(b*x+a)^3/(-b^2*x^2+a^2),x)","-\frac{1}{6 \left(b x +a \right)^{3} a b}-\frac{1}{8 \left(b x +a \right)^{2} a^{2} b}-\frac{1}{8 \left(b x +a \right) a^{3} b}-\frac{\ln \left(b x -a \right)}{16 a^{4} b}+\frac{\ln \left(b x +a \right)}{16 a^{4} b}"," ",0,"-1/16/a^4/b*ln(b*x-a)+1/16/a^4/b*ln(b*x+a)-1/8/a^3/b/(b*x+a)-1/8/a^2/b/(b*x+a)^2-1/6/a/b/(b*x+a)^3","A"
756,1,92,76,0.050000," ","int(1/(b*x+a)^4/(-b^2*x^2+a^2),x)","-\frac{1}{8 \left(b x +a \right)^{4} a b}-\frac{1}{12 \left(b x +a \right)^{3} a^{2} b}-\frac{1}{16 \left(b x +a \right)^{2} a^{3} b}-\frac{1}{16 \left(b x +a \right) a^{4} b}-\frac{\ln \left(b x -a \right)}{32 a^{5} b}+\frac{\ln \left(b x +a \right)}{32 a^{5} b}"," ",0,"-1/32/a^5/b*ln(b*x-a)+1/32/a^5/b*ln(b*x+a)-1/16/a^4/b/(b*x+a)-1/16/a^3/b/(b*x+a)^2-1/12/a^2/b/(b*x+a)^3-1/8/a/b/(b*x+a)^4","A"
757,1,67,64,0.077000," ","int((b*x+a)^7/(-b^2*x^2+a^2)^2,x)","\frac{b^{3} x^{4}}{4}+\frac{7 a \,b^{2} x^{3}}{3}+\frac{23 a^{2} b \,x^{2}}{2}-\frac{32 a^{5}}{\left(b x -a \right) b}+\frac{80 a^{4} \ln \left(b x -a \right)}{b}+49 a^{3} x"," ",0,"1/4*b^3*x^4+7/3*a*b^2*x^3+23/2*a^2*b*x^2+49*a^3*x+80*a^4/b*ln(b*x-a)-32*a^5/b/(b*x-a)","A"
758,1,56,53,0.051000," ","int((b*x+a)^6/(-b^2*x^2+a^2)^2,x)","\frac{b^{2} x^{3}}{3}+3 a b \,x^{2}-\frac{16 a^{4}}{\left(b x -a \right) b}+\frac{32 a^{3} \ln \left(b x -a \right)}{b}+17 a^{2} x"," ",0,"1/3*b^2*x^3+3*a*b*x^2+17*a^2*x+32*a^3/b*ln(b*x-a)-16*a^4/b/(b*x-a)","A"
759,1,45,42,0.050000," ","int((b*x+a)^5/(-b^2*x^2+a^2)^2,x)","\frac{b \,x^{2}}{2}-\frac{8 a^{3}}{\left(b x -a \right) b}+\frac{12 a^{2} \ln \left(b x -a \right)}{b}+5 a x"," ",0,"1/2*b*x^2+5*a*x+12*a^2/b*ln(b*x-a)-8*a^3/b/(b*x-a)","A"
760,1,34,31,0.049000," ","int((b*x+a)^4/(-b^2*x^2+a^2)^2,x)","-\frac{4 a^{2}}{\left(b x -a \right) b}+\frac{4 a \ln \left(b x -a \right)}{b}+x"," ",0,"x+4*a/b*ln(b*x-a)-4*a^2/b/(b*x-a)","A"
761,1,29,26,0.055000," ","int((b*x+a)^3/(-b^2*x^2+a^2)^2,x)","-\frac{2 a}{\left(b x -a \right) b}+\frac{\ln \left(b x -a \right)}{b}"," ",0,"1/b*ln(b*x-a)-2*a/b/(b*x-a)","A"
762,1,15,12,0.033000," ","int((b*x+a)^2/(-b^2*x^2+a^2)^2,x)","-\frac{1}{\left(b x -a \right) b}"," ",0,"-1/b/(b*x-a)","A"
763,1,49,32,0.051000," ","int((b*x+a)/(-b^2*x^2+a^2)^2,x)","-\frac{1}{2 \left(b x -a \right) a b}-\frac{\ln \left(b x -a \right)}{4 a^{2} b}+\frac{\ln \left(b x +a \right)}{4 a^{2} b}"," ",0,"-1/4/a^2/b*ln(b*x-a)-1/2/b/a/(b*x-a)+1/4/a^2/b*ln(b*x+a)","A"
764,1,79,62,0.050000," ","int(1/(b*x+a)/(-b^2*x^2+a^2)^2,x)","-\frac{1}{8 \left(b x +a \right)^{2} a^{2} b}-\frac{1}{8 \left(b x -a \right) a^{3} b}-\frac{1}{4 \left(b x +a \right) a^{3} b}-\frac{3 \ln \left(b x -a \right)}{16 a^{4} b}+\frac{3 \ln \left(b x +a \right)}{16 a^{4} b}"," ",0,"-3/16/a^4/b*ln(b*x-a)-1/8/a^3/b/(b*x-a)+3/16/a^4/b*ln(b*x+a)-1/4/(b*x+a)/a^3/b-1/8/(b*x+a)^2/a^2/b","A"
765,1,94,77,0.056000," ","int(1/(b*x+a)^2/(-b^2*x^2+a^2)^2,x)","-\frac{1}{12 \left(b x +a \right)^{3} a^{2} b}-\frac{1}{8 \left(b x +a \right)^{2} a^{3} b}-\frac{1}{16 \left(b x -a \right) a^{4} b}-\frac{3}{16 \left(b x +a \right) a^{4} b}-\frac{\ln \left(b x -a \right)}{8 a^{5} b}+\frac{\ln \left(b x +a \right)}{8 a^{5} b}"," ",0,"-1/8/a^5/b*ln(b*x-a)-1/16/a^4/b/(b*x-a)+1/8/a^5/b*ln(b*x+a)-3/16/(b*x+a)/a^4/b-1/8/(b*x+a)^2/a^3/b-1/12/(b*x+a)^3/a^2/b","A"
766,1,109,92,0.053000," ","int(1/(b*x+a)^3/(-b^2*x^2+a^2)^2,x)","-\frac{1}{16 \left(b x +a \right)^{4} a^{2} b}-\frac{1}{12 \left(b x +a \right)^{3} a^{3} b}-\frac{3}{32 \left(b x +a \right)^{2} a^{4} b}-\frac{1}{32 \left(b x -a \right) a^{5} b}-\frac{1}{8 \left(b x +a \right) a^{5} b}-\frac{5 \ln \left(b x -a \right)}{64 a^{6} b}+\frac{5 \ln \left(b x +a \right)}{64 a^{6} b}"," ",0,"-5/64/a^6/b*ln(b*x-a)-1/32/a^5/b/(b*x-a)+5/64/a^6/b*ln(b*x+a)-1/8/a^5/b/(b*x+a)-3/32/a^4/b/(b*x+a)^2-1/12/a^3/b/(b*x+a)^3-1/16/a^2/b/(b*x+a)^4","A"
767,1,73,69,0.044000," ","int((b*x+a)^8/(-b^2*x^2+a^2)^3,x)","-\frac{b^{2} x^{3}}{3}+\frac{16 a^{5}}{\left(b x -a \right)^{2} b}-4 a b \,x^{2}+\frac{80 a^{4}}{\left(b x -a \right) b}-\frac{80 a^{3} \ln \left(b x -a \right)}{b}-31 a^{2} x"," ",0,"-1/3*b^2*x^3-4*a*b*x^2-31*a^2*x-80*a^3/b*ln(b*x-a)+16*a^5/b/(b*x-a)^2+80/(b*x-a)*a^4/b","A"
768,1,62,58,0.050000," ","int((b*x+a)^7/(-b^2*x^2+a^2)^3,x)","\frac{8 a^{4}}{\left(b x -a \right)^{2} b}-\frac{b \,x^{2}}{2}+\frac{32 a^{3}}{\left(b x -a \right) b}-\frac{24 a^{2} \ln \left(b x -a \right)}{b}-7 a x"," ",0,"-1/2*b*x^2-7*a*x-24*a^2/b*ln(b*x-a)+8*a^4/b/(b*x-a)^2+32/(b*x-a)*a^3/b","A"
769,1,53,49,0.044000," ","int((b*x+a)^6/(-b^2*x^2+a^2)^3,x)","\frac{4 a^{3}}{\left(b x -a \right)^{2} b}+\frac{12 a^{2}}{\left(b x -a \right) b}-\frac{6 a \ln \left(b x -a \right)}{b}-x"," ",0,"-x-6*a/b*ln(b*x-a)+4*a^3/b/(b*x-a)^2+12/(b*x-a)*a^2/b","A"
770,1,47,43,0.044000," ","int((b*x+a)^5/(-b^2*x^2+a^2)^3,x)","\frac{2 a^{2}}{\left(b x -a \right)^{2} b}+\frac{4 a}{\left(b x -a \right) b}-\frac{\ln \left(b x -a \right)}{b}"," ",0,"-1/b*ln(b*x-a)+2*a^2/b/(b*x-a)^2+4/(b*x-a)*a/b","A"
771,1,29,10,0.042000," ","int((b*x+a)^4/(-b^2*x^2+a^2)^3,x)","\frac{a}{\left(b x -a \right)^{2} b}+\frac{1}{\left(b x -a \right) b}"," ",0,"a/b/(b*x-a)^2+1/(b*x-a)/b","B"
772,1,15,13,0.041000," ","int((b*x+a)^3/(-b^2*x^2+a^2)^3,x)","\frac{1}{2 \left(b x -a \right)^{2} b}"," ",0,"1/2/b/(b*x-a)^2","A"
773,1,66,48,0.049000," ","int((b*x+a)^2/(-b^2*x^2+a^2)^3,x)","\frac{1}{4 \left(b x -a \right)^{2} a b}-\frac{1}{4 \left(b x -a \right) a^{2} b}-\frac{\ln \left(b x -a \right)}{8 a^{3} b}+\frac{\ln \left(b x +a \right)}{8 a^{3} b}"," ",0,"-1/8/a^3/b*ln(b*x-a)-1/4/a^2/b/(b*x-a)+1/4/b/a/(b*x-a)^2+1/8/a^3/b*ln(b*x+a)","A"
774,1,81,63,0.050000," ","int((b*x+a)/(-b^2*x^2+a^2)^3,x)","\frac{1}{8 \left(b x -a \right)^{2} a^{2} b}-\frac{1}{4 \left(b x -a \right) a^{3} b}-\frac{1}{8 \left(b x +a \right) a^{3} b}-\frac{3 \ln \left(b x -a \right)}{16 a^{4} b}+\frac{3 \ln \left(b x +a \right)}{16 a^{4} b}"," ",0,"-3/16/a^4/b*ln(b*x-a)-1/4/(b*x-a)/a^3/b+1/8/a^2/b/(b*x-a)^2+3/16/a^4/b*ln(b*x+a)-1/8/(b*x+a)/a^3/b","A"
775,1,111,93,0.055000," ","int(1/(b*x+a)/(-b^2*x^2+a^2)^3,x)","-\frac{1}{24 \left(b x +a \right)^{3} a^{3} b}+\frac{1}{32 \left(b x -a \right)^{2} a^{4} b}-\frac{3}{32 \left(b x +a \right)^{2} a^{4} b}-\frac{1}{8 \left(b x -a \right) a^{5} b}-\frac{3}{16 \left(b x +a \right) a^{5} b}-\frac{5 \ln \left(b x -a \right)}{32 a^{6} b}+\frac{5 \ln \left(b x +a \right)}{32 a^{6} b}"," ",0,"-5/32/a^6/b*ln(b*x-a)-1/8/(b*x-a)/a^5/b+1/32/a^4/b/(b*x-a)^2+5/32/a^6/b*ln(b*x+a)-3/16/(b*x+a)/a^5/b-3/32/(b*x+a)^2/a^4/b-1/24/(b*x+a)^3/a^3/b","A"
776,1,126,108,0.052000," ","int(1/(b*x+a)^2/(-b^2*x^2+a^2)^3,x)","-\frac{1}{32 \left(b x +a \right)^{4} a^{3} b}-\frac{1}{16 \left(b x +a \right)^{3} a^{4} b}+\frac{1}{64 \left(b x -a \right)^{2} a^{5} b}-\frac{3}{32 \left(b x +a \right)^{2} a^{5} b}-\frac{5}{64 \left(b x -a \right) a^{6} b}-\frac{5}{32 \left(b x +a \right) a^{6} b}-\frac{15 \ln \left(b x -a \right)}{128 a^{7} b}+\frac{15 \ln \left(b x +a \right)}{128 a^{7} b}"," ",0,"-15/128/a^7/b*ln(b*x-a)-5/64/a^6/b/(b*x-a)+1/64/a^5/b/(b*x-a)^2+15/128/a^7/b*ln(b*x+a)-5/32/a^6/b/(b*x+a)-3/32/a^5/b/(b*x+a)^2-1/16/a^4/b/(b*x+a)^3-1/32/a^3/b/(b*x+a)^4","A"
777,1,139,149,0.054000," ","int((b*x+a)^4*(-b^2*x^2+a^2)^(1/2),x)","\frac{21 a^{6} \arctan \left(\frac{\sqrt{b^{2}}\, x}{\sqrt{-b^{2} x^{2}+a^{2}}}\right)}{16 \sqrt{b^{2}}}+\frac{21 \sqrt{-b^{2} x^{2}+a^{2}}\, a^{4} x}{16}-\frac{\left(-b^{2} x^{2}+a^{2}\right)^{\frac{3}{2}} b^{2} x^{3}}{6}-\frac{4 \left(-b^{2} x^{2}+a^{2}\right)^{\frac{3}{2}} a b \,x^{2}}{5}-\frac{13 \left(-b^{2} x^{2}+a^{2}\right)^{\frac{3}{2}} a^{2} x}{8}-\frac{28 \left(-b^{2} x^{2}+a^{2}\right)^{\frac{3}{2}} a^{3}}{15 b}"," ",0,"-1/6*b^2*x^3*(-b^2*x^2+a^2)^(3/2)-13/8*a^2*x*(-b^2*x^2+a^2)^(3/2)+21/16*a^4*x*(-b^2*x^2+a^2)^(1/2)+21/16*a^6/(b^2)^(1/2)*arctan((b^2)^(1/2)*x/(-b^2*x^2+a^2)^(1/2))-4/5*a*b*x^2*(-b^2*x^2+a^2)^(3/2)-28/15*a^3*(-b^2*x^2+a^2)^(3/2)/b","A"
778,1,114,120,0.059000," ","int((b*x+a)^3*(-b^2*x^2+a^2)^(1/2),x)","\frac{7 a^{5} \arctan \left(\frac{\sqrt{b^{2}}\, x}{\sqrt{-b^{2} x^{2}+a^{2}}}\right)}{8 \sqrt{b^{2}}}+\frac{7 \sqrt{-b^{2} x^{2}+a^{2}}\, a^{3} x}{8}-\frac{\left(-b^{2} x^{2}+a^{2}\right)^{\frac{3}{2}} b \,x^{2}}{5}-\frac{3 \left(-b^{2} x^{2}+a^{2}\right)^{\frac{3}{2}} a x}{4}-\frac{17 \left(-b^{2} x^{2}+a^{2}\right)^{\frac{3}{2}} a^{2}}{15 b}"," ",0,"-1/5*b*x^2*(-b^2*x^2+a^2)^(3/2)-17/15*a^2*(-b^2*x^2+a^2)^(3/2)/b-3/4*a*x*(-b^2*x^2+a^2)^(3/2)+7/8*a^3*x*(-b^2*x^2+a^2)^(1/2)+7/8*a^5/(b^2)^(1/2)*arctan((b^2)^(1/2)/(-b^2*x^2+a^2)^(1/2)*x)","A"
779,1,91,91,0.049000," ","int((b*x+a)^2*(-b^2*x^2+a^2)^(1/2),x)","\frac{5 a^{4} \arctan \left(\frac{\sqrt{b^{2}}\, x}{\sqrt{-b^{2} x^{2}+a^{2}}}\right)}{8 \sqrt{b^{2}}}+\frac{5 \sqrt{-b^{2} x^{2}+a^{2}}\, a^{2} x}{8}-\frac{\left(-b^{2} x^{2}+a^{2}\right)^{\frac{3}{2}} x}{4}-\frac{2 \left(-b^{2} x^{2}+a^{2}\right)^{\frac{3}{2}} a}{3 b}"," ",0,"-1/4*x*(-b^2*x^2+a^2)^(3/2)+5/8*a^2*x*(-b^2*x^2+a^2)^(1/2)+5/8*a^4/(b^2)^(1/2)*arctan((b^2)^(1/2)/(-b^2*x^2+a^2)^(1/2)*x)-2/3*a*(-b^2*x^2+a^2)^(3/2)/b","A"
780,1,71,64,0.046000," ","int((b*x+a)*(-b^2*x^2+a^2)^(1/2),x)","\frac{a^{3} \arctan \left(\frac{\sqrt{b^{2}}\, x}{\sqrt{-b^{2} x^{2}+a^{2}}}\right)}{2 \sqrt{b^{2}}}+\frac{\sqrt{-b^{2} x^{2}+a^{2}}\, a x}{2}-\frac{\left(-b^{2} x^{2}+a^{2}\right)^{\frac{3}{2}}}{3 b}"," ",0,"-1/3*(-b^2*x^2+a^2)^(3/2)/b+1/2*a*x*(-b^2*x^2+a^2)^(1/2)+1/2*a^3/(b^2)^(1/2)*arctan((b^2)^(1/2)/(-b^2*x^2+a^2)^(1/2)*x)","A"
781,1,77,42,0.044000," ","int((-b^2*x^2+a^2)^(1/2)/(b*x+a),x)","\frac{a \arctan \left(\frac{\sqrt{b^{2}}\, x}{\sqrt{2 \left(x +\frac{a}{b}\right) a b -\left(x +\frac{a}{b}\right)^{2} b^{2}}}\right)}{\sqrt{b^{2}}}+\frac{\sqrt{2 \left(x +\frac{a}{b}\right) a b -\left(x +\frac{a}{b}\right)^{2} b^{2}}}{b}"," ",0,"1/b*(-(x+a/b)^2*b^2+2*(x+a/b)*a*b)^(1/2)+a/(b^2)^(1/2)*arctan((b^2)^(1/2)*x/(-(x+a/b)^2*b^2+2*(x+a/b)*a*b)^(1/2))","A"
782,1,126,50,0.049000," ","int((-b^2*x^2+a^2)^(1/2)/(b*x+a)^2,x)","-\frac{\arctan \left(\frac{\sqrt{b^{2}}\, x}{\sqrt{2 \left(x +\frac{a}{b}\right) a b -\left(x +\frac{a}{b}\right)^{2} b^{2}}}\right)}{\sqrt{b^{2}}}-\frac{\sqrt{2 \left(x +\frac{a}{b}\right) a b -\left(x +\frac{a}{b}\right)^{2} b^{2}}}{a b}-\frac{\left(2 \left(x +\frac{a}{b}\right) a b -\left(x +\frac{a}{b}\right)^{2} b^{2}\right)^{\frac{3}{2}}}{\left(x +\frac{a}{b}\right)^{2} a \,b^{3}}"," ",0,"-1/b^3/a/(x+a/b)^2*(2*(x+a/b)*a*b-(x+a/b)^2*b^2)^(3/2)-1/b/a*(2*(x+a/b)*a*b-(x+a/b)^2*b^2)^(1/2)-1/(b^2)^(1/2)*arctan((b^2)^(1/2)/(2*(x+a/b)*a*b-(x+a/b)^2*b^2)^(1/2)*x)","B"
783,1,36,29,0.042000," ","int((-b^2*x^2+a^2)^(1/2)/(b*x+a)^3,x)","-\frac{\left(-b x +a \right) \sqrt{-b^{2} x^{2}+a^{2}}}{3 \left(b x +a \right)^{2} a b}"," ",0,"-1/3*(-b*x+a)/(b*x+a)^2/b/a*(-b^2*x^2+a^2)^(1/2)","A"
784,1,43,59,0.040000," ","int((-b^2*x^2+a^2)^(1/2)/(b*x+a)^4,x)","-\frac{\left(-b x +a \right) \left(b x +4 a \right) \sqrt{-b^{2} x^{2}+a^{2}}}{15 \left(b x +a \right)^{3} a^{2} b}"," ",0,"-1/15*(-b*x+a)*(b*x+4*a)*(-b^2*x^2+a^2)^(1/2)/(b*x+a)^3/a^2/b","A"
785,1,55,88,0.045000," ","int((-b^2*x^2+a^2)^(1/2)/(b*x+a)^5,x)","-\frac{\left(-b x +a \right) \left(2 b^{2} x^{2}+10 a b x +23 a^{2}\right) \sqrt{-b^{2} x^{2}+a^{2}}}{105 \left(b x +a \right)^{4} a^{3} b}"," ",0,"-1/105*(-b*x+a)*(2*b^2*x^2+10*a*b*x+23*a^2)*(-b^2*x^2+a^2)^(1/2)/(b*x+a)^4/a^3/b","A"
786,1,66,117,0.043000," ","int((-b^2*x^2+a^2)^(1/2)/(b*x+a)^6,x)","-\frac{\left(-b x +a \right) \left(2 b^{3} x^{3}+12 a \,b^{2} x^{2}+33 a^{2} b x +58 a^{3}\right) \sqrt{-b^{2} x^{2}+a^{2}}}{315 \left(b x +a \right)^{5} a^{4} b}"," ",0,"-1/315*(-b*x+a)*(2*b^3*x^3+12*a*b^2*x^2+33*a^2*b*x+58*a^3)*(-b^2*x^2+a^2)^(1/2)/(b*x+a)^5/a^4/b","A"
787,1,77,146,0.046000," ","int((-b^2*x^2+a^2)^(1/2)/(b*x+a)^7,x)","-\frac{\left(-b x +a \right) \left(8 b^{4} x^{4}+56 a \,b^{3} x^{3}+180 b^{2} x^{2} a^{2}+364 x \,a^{3} b +547 a^{4}\right) \sqrt{-b^{2} x^{2}+a^{2}}}{3465 \left(b x +a \right)^{6} a^{5} b}"," ",0,"-1/3465*(-b*x+a)*(8*b^4*x^4+56*a*b^3*x^3+180*a^2*b^2*x^2+364*a^3*b*x+547*a^4)*(-b^2*x^2+a^2)^(1/2)/(b*x+a)^6/a^5/b","A"
788,1,134,140,0.080000," ","int((b*x+a)^3*(-b^2*x^2+a^2)^(3/2),x)","\frac{9 a^{7} \arctan \left(\frac{\sqrt{b^{2}}\, x}{\sqrt{-b^{2} x^{2}+a^{2}}}\right)}{16 \sqrt{b^{2}}}+\frac{9 \sqrt{-b^{2} x^{2}+a^{2}}\, a^{5} x}{16}+\frac{3 \left(-b^{2} x^{2}+a^{2}\right)^{\frac{3}{2}} a^{3} x}{8}-\frac{\left(-b^{2} x^{2}+a^{2}\right)^{\frac{5}{2}} b \,x^{2}}{7}-\frac{\left(-b^{2} x^{2}+a^{2}\right)^{\frac{5}{2}} a x}{2}-\frac{23 \left(-b^{2} x^{2}+a^{2}\right)^{\frac{5}{2}} a^{2}}{35 b}"," ",0,"-1/7*b*x^2*(-b^2*x^2+a^2)^(5/2)-23/35*a^2*(-b^2*x^2+a^2)^(5/2)/b-1/2*a*x*(-b^2*x^2+a^2)^(5/2)+3/8*a^3*x*(-b^2*x^2+a^2)^(3/2)+9/16*a^5*x*(-b^2*x^2+a^2)^(1/2)+9/16*a^7/(b^2)^(1/2)*arctan((b^2)^(1/2)/(-b^2*x^2+a^2)^(1/2)*x)","A"
789,1,111,111,0.049000," ","int((b*x+a)^2*(-b^2*x^2+a^2)^(3/2),x)","\frac{7 a^{6} \arctan \left(\frac{\sqrt{b^{2}}\, x}{\sqrt{-b^{2} x^{2}+a^{2}}}\right)}{16 \sqrt{b^{2}}}+\frac{7 \sqrt{-b^{2} x^{2}+a^{2}}\, a^{4} x}{16}+\frac{7 \left(-b^{2} x^{2}+a^{2}\right)^{\frac{3}{2}} a^{2} x}{24}-\frac{\left(-b^{2} x^{2}+a^{2}\right)^{\frac{5}{2}} x}{6}-\frac{2 \left(-b^{2} x^{2}+a^{2}\right)^{\frac{5}{2}} a}{5 b}"," ",0,"-1/6*x*(-b^2*x^2+a^2)^(5/2)+7/24*(-b^2*x^2+a^2)^(3/2)*a^2*x+7/16*(-b^2*x^2+a^2)^(1/2)*a^4*x+7/16/(b^2)^(1/2)*a^6*arctan((b^2)^(1/2)/(-b^2*x^2+a^2)^(1/2)*x)-2/5*a*(-b^2*x^2+a^2)^(5/2)/b","A"
790,1,91,84,0.056000," ","int((b*x+a)*(-b^2*x^2+a^2)^(3/2),x)","\frac{3 a^{5} \arctan \left(\frac{\sqrt{b^{2}}\, x}{\sqrt{-b^{2} x^{2}+a^{2}}}\right)}{8 \sqrt{b^{2}}}+\frac{3 \sqrt{-b^{2} x^{2}+a^{2}}\, a^{3} x}{8}+\frac{\left(-b^{2} x^{2}+a^{2}\right)^{\frac{3}{2}} a x}{4}-\frac{\left(-b^{2} x^{2}+a^{2}\right)^{\frac{5}{2}}}{5 b}"," ",0,"-1/5*(-b^2*x^2+a^2)^(5/2)/b+1/4*(-b^2*x^2+a^2)^(3/2)*a*x+3/8*(-b^2*x^2+a^2)^(1/2)*a^3*x+3/8/(b^2)^(1/2)*a^5*arctan((b^2)^(1/2)/(-b^2*x^2+a^2)^(1/2)*x)","A"
791,1,113,64,0.050000," ","int((-b^2*x^2+a^2)^(3/2)/(b*x+a),x)","\frac{a^{3} \arctan \left(\frac{\sqrt{b^{2}}\, x}{\sqrt{2 \left(x +\frac{a}{b}\right) a b -\left(x +\frac{a}{b}\right)^{2} b^{2}}}\right)}{2 \sqrt{b^{2}}}+\frac{\sqrt{2 \left(x +\frac{a}{b}\right) a b -\left(x +\frac{a}{b}\right)^{2} b^{2}}\, a x}{2}+\frac{\left(2 \left(x +\frac{a}{b}\right) a b -\left(x +\frac{a}{b}\right)^{2} b^{2}\right)^{\frac{3}{2}}}{3 b}"," ",0,"1/3/b*(2*(x+a/b)*a*b-(x+a/b)^2*b^2)^(3/2)+1/2*a*(2*(x+a/b)*a*b-(x+a/b)^2*b^2)^(1/2)*x+1/2*a^3/(b^2)^(1/2)*arctan((b^2)^(1/2)/(2*(x+a/b)*a*b-(x+a/b)^2*b^2)^(1/2)*x)","A"
792,1,158,73,0.050000," ","int((-b^2*x^2+a^2)^(3/2)/(b*x+a)^2,x)","\frac{3 a^{2} \arctan \left(\frac{\sqrt{b^{2}}\, x}{\sqrt{2 \left(x +\frac{a}{b}\right) a b -\left(x +\frac{a}{b}\right)^{2} b^{2}}}\right)}{2 \sqrt{b^{2}}}+\frac{3 \sqrt{2 \left(x +\frac{a}{b}\right) a b -\left(x +\frac{a}{b}\right)^{2} b^{2}}\, x}{2}+\frac{\left(2 \left(x +\frac{a}{b}\right) a b -\left(x +\frac{a}{b}\right)^{2} b^{2}\right)^{\frac{3}{2}}}{a b}+\frac{\left(2 \left(x +\frac{a}{b}\right) a b -\left(x +\frac{a}{b}\right)^{2} b^{2}\right)^{\frac{5}{2}}}{\left(x +\frac{a}{b}\right)^{2} a \,b^{3}}"," ",0,"1/b^3/a/(x+a/b)^2*(2*(x+a/b)*a*b-(x+a/b)^2*b^2)^(5/2)+1/b/a*(2*(x+a/b)*a*b-(x+a/b)^2*b^2)^(3/2)+3/2*(2*(x+a/b)*a*b-(x+a/b)^2*b^2)^(1/2)*x+3/2*a^2/(b^2)^(1/2)*arctan((b^2)^(1/2)/(2*(x+a/b)*a*b-(x+a/b)^2*b^2)^(1/2)*x)","B"
793,1,206,70,0.050000," ","int((-b^2*x^2+a^2)^(3/2)/(b*x+a)^3,x)","-\frac{3 a \arctan \left(\frac{\sqrt{b^{2}}\, x}{\sqrt{2 \left(x +\frac{a}{b}\right) a b -\left(x +\frac{a}{b}\right)^{2} b^{2}}}\right)}{\sqrt{b^{2}}}-\frac{3 \sqrt{2 \left(x +\frac{a}{b}\right) a b -\left(x +\frac{a}{b}\right)^{2} b^{2}}\, x}{a}-\frac{2 \left(2 \left(x +\frac{a}{b}\right) a b -\left(x +\frac{a}{b}\right)^{2} b^{2}\right)^{\frac{3}{2}}}{a^{2} b}-\frac{\left(2 \left(x +\frac{a}{b}\right) a b -\left(x +\frac{a}{b}\right)^{2} b^{2}\right)^{\frac{5}{2}}}{\left(x +\frac{a}{b}\right)^{3} a \,b^{4}}-\frac{2 \left(2 \left(x +\frac{a}{b}\right) a b -\left(x +\frac{a}{b}\right)^{2} b^{2}\right)^{\frac{5}{2}}}{\left(x +\frac{a}{b}\right)^{2} a^{2} b^{3}}"," ",0,"-1/b^4/a/(x+a/b)^3*(2*(x+a/b)*a*b-(x+a/b)^2*b^2)^(5/2)-2/b^3/a^2/(x+a/b)^2*(2*(x+a/b)*a*b-(x+a/b)^2*b^2)^(5/2)-2/b/a^2*(2*(x+a/b)*a*b-(x+a/b)^2*b^2)^(3/2)-3/a*(2*(x+a/b)*a*b-(x+a/b)^2*b^2)^(1/2)*x-3/(b^2)^(1/2)*a*arctan((b^2)^(1/2)/(2*(x+a/b)*a*b-(x+a/b)^2*b^2)^(1/2)*x)","B"
794,1,248,75,0.050000," ","int((-b^2*x^2+a^2)^(3/2)/(b*x+a)^4,x)","\frac{\arctan \left(\frac{\sqrt{b^{2}}\, x}{\sqrt{2 \left(x +\frac{a}{b}\right) a b -\left(x +\frac{a}{b}\right)^{2} b^{2}}}\right)}{\sqrt{b^{2}}}+\frac{\sqrt{2 \left(x +\frac{a}{b}\right) a b -\left(x +\frac{a}{b}\right)^{2} b^{2}}\, x}{a^{2}}+\frac{2 \left(2 \left(x +\frac{a}{b}\right) a b -\left(x +\frac{a}{b}\right)^{2} b^{2}\right)^{\frac{3}{2}}}{3 a^{3} b}-\frac{\left(2 \left(x +\frac{a}{b}\right) a b -\left(x +\frac{a}{b}\right)^{2} b^{2}\right)^{\frac{5}{2}}}{3 \left(x +\frac{a}{b}\right)^{4} a \,b^{5}}+\frac{\left(2 \left(x +\frac{a}{b}\right) a b -\left(x +\frac{a}{b}\right)^{2} b^{2}\right)^{\frac{5}{2}}}{3 \left(x +\frac{a}{b}\right)^{3} a^{2} b^{4}}+\frac{2 \left(2 \left(x +\frac{a}{b}\right) a b -\left(x +\frac{a}{b}\right)^{2} b^{2}\right)^{\frac{5}{2}}}{3 \left(x +\frac{a}{b}\right)^{2} a^{3} b^{3}}"," ",0,"-1/3/b^5/a/(x+a/b)^4*(2*(x+a/b)*a*b-(x+a/b)^2*b^2)^(5/2)+1/3/b^4/a^2/(x+a/b)^3*(2*(x+a/b)*a*b-(x+a/b)^2*b^2)^(5/2)+2/3/b^3/a^3/(x+a/b)^2*(2*(x+a/b)*a*b-(x+a/b)^2*b^2)^(5/2)+2/3/b/a^3*(2*(x+a/b)*a*b-(x+a/b)^2*b^2)^(3/2)+1/a^2*(2*(x+a/b)*a*b-(x+a/b)^2*b^2)^(1/2)*x+1/(b^2)^(1/2)*arctan((b^2)^(1/2)/(2*(x+a/b)*a*b-(x+a/b)^2*b^2)^(1/2)*x)","B"
795,1,36,29,0.045000," ","int((-b^2*x^2+a^2)^(3/2)/(b*x+a)^5,x)","-\frac{\left(-b x +a \right) \left(-b^{2} x^{2}+a^{2}\right)^{\frac{3}{2}}}{5 \left(b x +a \right)^{4} a b}"," ",0,"-1/5*(-b*x+a)/(b*x+a)^4/b/a*(-b^2*x^2+a^2)^(3/2)","A"
796,1,43,59,0.206000," ","int((-b^2*x^2+a^2)^(3/2)/(b*x+a)^6,x)","-\frac{\left(-b x +a \right) \left(b x +6 a \right) \left(-b^{2} x^{2}+a^{2}\right)^{\frac{3}{2}}}{35 \left(b x +a \right)^{5} a^{2} b}"," ",0,"-1/35*(-b*x+a)*(b*x+6*a)*(-b^2*x^2+a^2)^(3/2)/(b*x+a)^5/a^2/b","A"
797,1,55,88,0.045000," ","int((-b^2*x^2+a^2)^(3/2)/(b*x+a)^7,x)","-\frac{\left(-b x +a \right) \left(2 b^{2} x^{2}+14 a b x +47 a^{2}\right) \left(-b^{2} x^{2}+a^{2}\right)^{\frac{3}{2}}}{315 \left(b x +a \right)^{6} a^{3} b}"," ",0,"-1/315*(-b*x+a)*(2*b^2*x^2+14*a*b*x+47*a^2)*(-b^2*x^2+a^2)^(3/2)/(b*x+a)^6/a^3/b","A"
798,1,66,117,0.048000," ","int((-b^2*x^2+a^2)^(3/2)/(b*x+a)^8,x)","-\frac{\left(-b x +a \right) \left(2 b^{3} x^{3}+16 a \,b^{2} x^{2}+61 a^{2} b x +152 a^{3}\right) \left(-b^{2} x^{2}+a^{2}\right)^{\frac{3}{2}}}{1155 \left(b x +a \right)^{7} a^{4} b}"," ",0,"-1/1155*(-b*x+a)*(2*b^3*x^3+16*a*b^2*x^2+61*a^2*b*x+152*a^3)*(-b^2*x^2+a^2)^(3/2)/(b*x+a)^7/a^4/b","A"
799,1,77,146,0.046000," ","int((-b^2*x^2+a^2)^(3/2)/(b*x+a)^9,x)","-\frac{\left(-b x +a \right) \left(8 b^{4} x^{4}+72 a \,b^{3} x^{3}+308 b^{2} x^{2} a^{2}+852 x \,a^{3} b +1763 a^{4}\right) \left(-b^{2} x^{2}+a^{2}\right)^{\frac{3}{2}}}{15015 \left(b x +a \right)^{8} a^{5} b}"," ",0,"-1/15015*(-b*x+a)*(8*b^4*x^4+72*a*b^3*x^3+308*a^2*b^2*x^2+852*a^3*b*x+1763*a^4)*(-b^2*x^2+a^2)^(3/2)/(b*x+a)^8/a^5/b","A"
800,1,174,180,0.093000," ","int((e*x+d)^3*(-e^2*x^2+d^2)^(7/2),x)","\frac{91 d^{11} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{256 \sqrt{e^{2}}}+\frac{91 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{9} x}{256}+\frac{91 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{7} x}{384}+\frac{91 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d^{5} x}{480}+\frac{13 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d^{3} x}{80}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{9}{2}} e \,x^{2}}{11}-\frac{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{9}{2}} d x}{10}-\frac{35 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{9}{2}} d^{2}}{99 e}"," ",0,"-1/11*e*x^2*(-e^2*x^2+d^2)^(9/2)-35/99*d^2*(-e^2*x^2+d^2)^(9/2)/e-3/10*d*x*(-e^2*x^2+d^2)^(9/2)+13/80*d^3*x*(-e^2*x^2+d^2)^(7/2)+91/480*d^5*x*(-e^2*x^2+d^2)^(5/2)+91/384*d^7*x*(-e^2*x^2+d^2)^(3/2)+91/256*d^9*x*(-e^2*x^2+d^2)^(1/2)+91/256*d^11/(e^2)^(1/2)*arctan((e^2)^(1/2)*x/(-e^2*x^2+d^2)^(1/2))","A"
801,1,151,151,0.061000," ","int((e*x+d)^2*(-e^2*x^2+d^2)^(7/2),x)","\frac{77 d^{10} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{256 \sqrt{e^{2}}}+\frac{77 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{8} x}{256}+\frac{77 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{6} x}{384}+\frac{77 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d^{4} x}{480}+\frac{11 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d^{2} x}{80}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{9}{2}} x}{10}-\frac{2 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{9}{2}} d}{9 e}"," ",0,"-1/10*x*(-e^2*x^2+d^2)^(9/2)+11/80*d^2*x*(-e^2*x^2+d^2)^(7/2)+77/480*d^4*x*(-e^2*x^2+d^2)^(5/2)+77/384*d^6*x*(-e^2*x^2+d^2)^(3/2)+77/256*d^8*x*(-e^2*x^2+d^2)^(1/2)+77/256*d^10/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)-2/9*d*(-e^2*x^2+d^2)^(9/2)/e","A"
802,1,131,124,0.046000," ","int((e*x+d)*(-e^2*x^2+d^2)^(7/2),x)","\frac{35 d^{9} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{128 \sqrt{e^{2}}}+\frac{35 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{7} x}{128}+\frac{35 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{5} x}{192}+\frac{7 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d^{3} x}{48}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d x}{8}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{9}{2}}}{9 e}"," ",0,"-1/9*(-e^2*x^2+d^2)^(9/2)/e+1/8*d*x*(-e^2*x^2+d^2)^(7/2)+7/48*d^3*x*(-e^2*x^2+d^2)^(5/2)+35/192*d^5*x*(-e^2*x^2+d^2)^(3/2)+35/128*d^7*x*(-e^2*x^2+d^2)^(1/2)+35/128*d^9/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)","A"
803,1,181,104,0.053000," ","int((-e^2*x^2+d^2)^(7/2)/(e*x+d),x)","\frac{5 d^{7} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{16 \sqrt{e^{2}}}+\frac{5 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d^{5} x}{16}+\frac{5 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} d^{3} x}{24}+\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{5}{2}} d x}{6}+\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{7}{2}}}{7 e}"," ",0,"1/7/e*(-(x+d/e)^2*e^2+2*d*e*(x+d/e))^(7/2)+1/6*d*(-(x+d/e)^2*e^2+2*d*e*(x+d/e))^(5/2)*x+5/24*d^3*(-(x+d/e)^2*e^2+2*d*e*(x+d/e))^(3/2)*x+5/16*d^5*(-(x+d/e)^2*e^2+2*d*e*(x+d/e))^(1/2)*x+5/16*d^7/(e^2)^(1/2)*arctan((e^2)^(1/2)*x/(-(x+d/e)^2*e^2+2*d*e*(x+d/e))^(1/2))","A"
804,1,228,112,0.053000," ","int((-e^2*x^2+d^2)^(7/2)/(e*x+d)^2,x)","\frac{7 d^{6} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{16 \sqrt{e^{2}}}+\frac{7 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d^{4} x}{16}+\frac{7 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} d^{2} x}{24}+\frac{7 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{5}{2}} x}{30}+\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{7}{2}}}{5 d e}+\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{9}{2}}}{5 \left(x +\frac{d}{e}\right)^{2} d \,e^{3}}"," ",0,"1/5/e^3/d/(x+d/e)^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(9/2)+1/5/e/d*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(7/2)+7/30*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(5/2)*x+7/24*d^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)*x+7/16*d^4*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x+7/16*d^6/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)","B"
805,1,274,122,0.053000," ","int((-e^2*x^2+d^2)^(7/2)/(e*x+d)^3,x)","\frac{7 d^{5} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{8 \sqrt{e^{2}}}+\frac{7 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d^{3} x}{8}+\frac{7 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} d x}{12}+\frac{7 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{5}{2}} x}{15 d}+\frac{2 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{7}{2}}}{5 d^{2} e}+\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{9}{2}}}{3 \left(x +\frac{d}{e}\right)^{3} d \,e^{4}}+\frac{2 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{9}{2}}}{5 \left(x +\frac{d}{e}\right)^{2} d^{2} e^{3}}"," ",0,"1/3/e^4/d/(x+d/e)^3*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(9/2)+2/5/e^3/d^2/(x+d/e)^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(9/2)+2/5/e/d^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(7/2)+7/15/d*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(5/2)*x+7/12*d*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)*x+7/8*d^3*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x+7/8*d^5/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)","B"
806,1,317,118,0.058000," ","int((-e^2*x^2+d^2)^(7/2)/(e*x+d)^4,x)","\frac{35 d^{4} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{8 \sqrt{e^{2}}}+\frac{35 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d^{2} x}{8}+\frac{35 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} x}{12}+\frac{7 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{5}{2}} x}{3 d^{2}}+\frac{2 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{7}{2}}}{d^{3} e}+\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{9}{2}}}{\left(x +\frac{d}{e}\right)^{4} d \,e^{5}}+\frac{5 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{9}{2}}}{3 \left(x +\frac{d}{e}\right)^{3} d^{2} e^{4}}+\frac{2 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{9}{2}}}{\left(x +\frac{d}{e}\right)^{2} d^{3} e^{3}}"," ",0,"1/e^5/d/(x+d/e)^4*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(9/2)+5/3/e^4/d^2/(x+d/e)^3*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(9/2)+2/e^3/d^3/(x+d/e)^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(9/2)+2/e/d^3*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(7/2)+7/3/d^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(5/2)*x+35/12*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)*x+35/8*d^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x+35/8*d^4/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)","B"
807,1,364,116,0.056000," ","int((-e^2*x^2+d^2)^(7/2)/(e*x+d)^5,x)","-\frac{35 d^{3} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{2 \sqrt{e^{2}}}-\frac{35 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d x}{2}-\frac{35 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} x}{3 d}-\frac{28 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{5}{2}} x}{3 d^{3}}-\frac{8 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{7}{2}}}{d^{4} e}-\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{9}{2}}}{\left(x +\frac{d}{e}\right)^{5} d \,e^{6}}-\frac{4 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{9}{2}}}{\left(x +\frac{d}{e}\right)^{4} d^{2} e^{5}}-\frac{20 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{9}{2}}}{3 \left(x +\frac{d}{e}\right)^{3} d^{3} e^{4}}-\frac{8 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{9}{2}}}{\left(x +\frac{d}{e}\right)^{2} d^{4} e^{3}}"," ",0,"-1/e^6/d/(x+d/e)^5*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(9/2)-4/e^5/d^2/(x+d/e)^4*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(9/2)-20/3/e^4/d^3/(x+d/e)^3*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(9/2)-8/e^3/d^4/(x+d/e)^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(9/2)-8/e/d^4*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(7/2)-28/3/d^3*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(5/2)*x-35/3/d*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)*x-35/2*d*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x-35/2*d^3/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)","B"
808,1,407,125,0.049000," ","int((-e^2*x^2+d^2)^(7/2)/(e*x+d)^6,x)","\frac{35 d^{2} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{2 \sqrt{e^{2}}}+\frac{35 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, x}{2}+\frac{35 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} x}{3 d^{2}}+\frac{28 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{5}{2}} x}{3 d^{4}}+\frac{8 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{7}{2}}}{d^{5} e}-\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{9}{2}}}{3 \left(x +\frac{d}{e}\right)^{6} d \,e^{7}}+\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{9}{2}}}{\left(x +\frac{d}{e}\right)^{5} d^{2} e^{6}}+\frac{4 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{9}{2}}}{\left(x +\frac{d}{e}\right)^{4} d^{3} e^{5}}+\frac{20 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{9}{2}}}{3 \left(x +\frac{d}{e}\right)^{3} d^{4} e^{4}}+\frac{8 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{9}{2}}}{\left(x +\frac{d}{e}\right)^{2} d^{5} e^{3}}"," ",0,"-1/3/e^7/d/(x+d/e)^6*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(9/2)+1/e^6/d^2/(x+d/e)^5*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(9/2)+4/e^5/d^3/(x+d/e)^4*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(9/2)+20/3/e^4/d^4/(x+d/e)^3*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(9/2)+8/e^3/d^5/(x+d/e)^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(9/2)+8/e/d^5*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(7/2)+28/3/d^4*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(5/2)*x+35/3/d^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)*x+35/2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x+35/2*d^2/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)","B"
809,1,454,122,0.052000," ","int((-e^2*x^2+d^2)^(7/2)/(e*x+d)^7,x)","-\frac{7 d \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{\sqrt{e^{2}}}-\frac{7 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, x}{d}-\frac{14 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} x}{3 d^{3}}-\frac{56 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{5}{2}} x}{15 d^{5}}-\frac{16 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{7}{2}}}{5 d^{6} e}-\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{9}{2}}}{5 \left(x +\frac{d}{e}\right)^{7} d \,e^{8}}+\frac{2 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{9}{2}}}{15 \left(x +\frac{d}{e}\right)^{6} d^{2} e^{7}}-\frac{2 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{9}{2}}}{5 \left(x +\frac{d}{e}\right)^{5} d^{3} e^{6}}-\frac{8 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{9}{2}}}{5 \left(x +\frac{d}{e}\right)^{4} d^{4} e^{5}}-\frac{8 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{9}{2}}}{3 \left(x +\frac{d}{e}\right)^{3} d^{5} e^{4}}-\frac{16 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{9}{2}}}{5 \left(x +\frac{d}{e}\right)^{2} d^{6} e^{3}}"," ",0,"-1/5/e^8/d/(x+d/e)^7*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(9/2)+2/15/e^7/d^2/(x+d/e)^6*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(9/2)-2/5/e^6/d^3/(x+d/e)^5*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(9/2)-8/5/e^5/d^4/(x+d/e)^4*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(9/2)-8/3/e^4/d^5/(x+d/e)^3*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(9/2)-16/5/e^3/d^6/(x+d/e)^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(9/2)-16/5/e/d^6*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(7/2)-56/15/d^5*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(5/2)*x-14/3/d^3*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)*x-7/d*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x-7*d/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)","B"
810,1,496,127,0.052000," ","int((-e^2*x^2+d^2)^(7/2)/(e*x+d)^8,x)","\frac{\arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{\sqrt{e^{2}}}+\frac{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, x}{d^{2}}+\frac{2 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} x}{3 d^{4}}+\frac{8 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{5}{2}} x}{15 d^{6}}+\frac{16 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{7}{2}}}{35 d^{7} e}-\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{9}{2}}}{7 \left(x +\frac{d}{e}\right)^{8} d \,e^{9}}+\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{9}{2}}}{35 \left(x +\frac{d}{e}\right)^{7} d^{2} e^{8}}-\frac{2 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{9}{2}}}{105 \left(x +\frac{d}{e}\right)^{6} d^{3} e^{7}}+\frac{2 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{9}{2}}}{35 \left(x +\frac{d}{e}\right)^{5} d^{4} e^{6}}+\frac{8 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{9}{2}}}{35 \left(x +\frac{d}{e}\right)^{4} d^{5} e^{5}}+\frac{8 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{9}{2}}}{21 \left(x +\frac{d}{e}\right)^{3} d^{6} e^{4}}+\frac{16 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{9}{2}}}{35 \left(x +\frac{d}{e}\right)^{2} d^{7} e^{3}}"," ",0,"-1/7/e^9/d/(x+d/e)^8*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(9/2)+1/35/e^8/d^2/(x+d/e)^7*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(9/2)-2/105/e^7/d^3/(x+d/e)^6*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(9/2)+2/35/e^6/d^4/(x+d/e)^5*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(9/2)+8/35/e^5/d^5/(x+d/e)^4*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(9/2)+8/21/e^4/d^6/(x+d/e)^3*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(9/2)+16/35/e^3/d^7/(x+d/e)^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(9/2)+16/35/e/d^7*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(7/2)+8/15/d^6*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(5/2)*x+2/3/d^4*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)*x+1/d^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x+1/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)","B"
811,1,36,29,0.043000," ","int((-e^2*x^2+d^2)^(7/2)/(e*x+d)^9,x)","-\frac{\left(-e x +d \right) \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}}}{9 \left(e x +d \right)^{8} d e}"," ",0,"-1/9/(e*x+d)^8*(-e*x+d)/d/e*(-e^2*x^2+d^2)^(7/2)","A"
812,1,43,59,0.041000," ","int((-e^2*x^2+d^2)^(7/2)/(e*x+d)^10,x)","-\frac{\left(-e x +d \right) \left(e x +10 d \right) \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}}}{99 \left(e x +d \right)^{9} d^{2} e}"," ",0,"-1/99*(-e*x+d)*(e*x+10*d)*(-e^2*x^2+d^2)^(7/2)/(e*x+d)^9/d^2/e","A"
813,1,55,88,0.040000," ","int((-e^2*x^2+d^2)^(7/2)/(e*x+d)^11,x)","-\frac{\left(-e x +d \right) \left(2 e^{2} x^{2}+22 d e x +119 d^{2}\right) \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}}}{1287 \left(e x +d \right)^{10} d^{3} e}"," ",0,"-1/1287*(-e*x+d)*(2*e^2*x^2+22*d*e*x+119*d^2)*(-e^2*x^2+d^2)^(7/2)/(e*x+d)^10/d^3/e","A"
814,1,66,117,0.045000," ","int((-e^2*x^2+d^2)^(7/2)/(e*x+d)^12,x)","-\frac{\left(-e x +d \right) \left(2 e^{3} x^{3}+24 e^{2} x^{2} d +141 x \,d^{2} e +548 d^{3}\right) \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}}}{6435 \left(e x +d \right)^{11} d^{4} e}"," ",0,"-1/6435*(-e*x+d)*(2*e^3*x^3+24*d*e^2*x^2+141*d^2*e*x+548*d^3)*(-e^2*x^2+d^2)^(7/2)/(e*x+d)^11/d^4/e","A"
815,1,77,146,0.046000," ","int((-e^2*x^2+d^2)^(7/2)/(e*x+d)^13,x)","-\frac{\left(-e x +d \right) \left(8 e^{4} x^{4}+104 e^{3} x^{3} d +660 e^{2} x^{2} d^{2}+2756 x \,d^{3} e +8627 d^{4}\right) \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}}}{109395 \left(e x +d \right)^{12} d^{5} e}"," ",0,"-1/109395*(-e*x+d)*(8*e^4*x^4+104*d*e^3*x^3+660*d^2*e^2*x^2+2756*d^3*e*x+8627*d^4)*(-e^2*x^2+d^2)^(7/2)/(e*x+d)^12/d^5/e","A"
816,1,82,43,0.045000," ","int((-b^2*x^2+a^2)^(1/2)/(-b*x+a),x)","\frac{a \arctan \left(\frac{\sqrt{b^{2}}\, x}{\sqrt{-2 \left(x -\frac{a}{b}\right) a b -\left(x -\frac{a}{b}\right)^{2} b^{2}}}\right)}{\sqrt{b^{2}}}-\frac{\sqrt{-2 \left(x -\frac{a}{b}\right) a b -\left(x -\frac{a}{b}\right)^{2} b^{2}}}{b}"," ",0,"-1/b*(-(x-a/b)^2*b^2-2*(x-a/b)*a*b)^(1/2)+a/(b^2)^(1/2)*arctan((b^2)^(1/2)*x/(-(x-a/b)^2*b^2-2*(x-a/b)*a*b)^(1/2))","A"
817,1,113,110,0.102000," ","int((b*x+a)^2*(-a^2*c/b^2+c*x^2)^(1/2),x)","-\frac{5 a^{4} \sqrt{c}\, \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}-\frac{a^{2} c}{b^{2}}}\right)}{8 b^{2}}+\frac{5 \sqrt{c \,x^{2}-\frac{a^{2} c}{b^{2}}}\, a^{2} x}{8}+\frac{\left(c \,x^{2}-\frac{a^{2} c}{b^{2}}\right)^{\frac{3}{2}} b^{2} x}{4 c}+\frac{2 \left(\frac{\left(b^{2} x^{2}-a^{2}\right) c}{b^{2}}\right)^{\frac{3}{2}} a b}{3 c}"," ",0,"1/4*b^2*x*(-a^2*c/b^2+c*x^2)^(3/2)/c+5/8*a^2*x*(-a^2*c/b^2+c*x^2)^(1/2)-5/8/b^2*a^4*c^(1/2)*ln(c^(1/2)*x+(-a^2*c/b^2+c*x^2)^(1/2))+2/3*a*b/c*(c*(b^2*x^2-a^2)/b^2)^(3/2)","A"
818,1,169,143,0.053000," ","int((b*x+a)^3*(c*x^2-a^2/b^2*c)^(1/2),x)","-\frac{7 a^{5} \sqrt{c}\, \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}-\frac{a^{2} c}{b^{2}}}\right)}{8 b^{2}}+\frac{7 \sqrt{c \,x^{2}-\frac{a^{2} c}{b^{2}}}\, a^{3} x}{8}+\frac{\left(c \,x^{2}-\frac{a^{2} c}{b^{2}}\right)^{\frac{3}{2}} b^{3} x^{2}}{5 c}+\frac{3 \left(c \,x^{2}-\frac{a^{2} c}{b^{2}}\right)^{\frac{3}{2}} a \,b^{2} x}{4 c}+\frac{2 \left(c \,x^{2}-\frac{a^{2} c}{b^{2}}\right)^{\frac{3}{2}} a^{2} b}{15 c}+\frac{\left(\frac{\left(b^{2} x^{2}-a^{2}\right) c}{b^{2}}\right)^{\frac{3}{2}} a^{2} b}{c}"," ",0,"1/5*b^3*x^2*(c*x^2-a^2/b^2*c)^(3/2)/c+2/15*a^2*b*(c*x^2-a^2/b^2*c)^(3/2)/c+3/4*a*b^2*x*(c*x^2-a^2/b^2*c)^(3/2)/c+7/8*a^3*x*(c*x^2-a^2/b^2*c)^(1/2)-7/8*a^5/b^2*c^(1/2)*ln(c^(1/2)*x+(c*x^2-a^2/b^2*c)^(1/2))+a^2*b/c*((b^2*x^2-a^2)/b^2*c)^(3/2)","A"
819,1,33,32,0.040000," ","int((x+1)*(x^2-1)^(1/2),x)","\frac{\sqrt{x^{2}-1}\, x}{2}-\frac{\ln \left(x +\sqrt{x^{2}-1}\right)}{2}+\frac{\left(x^{2}-1\right)^{\frac{3}{2}}}{3}"," ",0,"1/3*(x^2-1)^(3/2)+1/2*x*(x^2-1)^(1/2)-1/2*ln(x+(x^2-1)^(1/2))","A"
820,1,29,28,0.040000," ","int((x+1)*(-x^2+1)^(1/2),x)","\frac{\sqrt{-x^{2}+1}\, x}{2}+\frac{\arcsin \left(x \right)}{2}-\frac{\left(-x^{2}+1\right)^{\frac{3}{2}}}{3}"," ",0,"-1/3*(-x^2+1)^(3/2)+1/2*arcsin(x)+1/2*(-x^2+1)^(1/2)*x","A"
821,1,18,12,0.046000," ","int((-x^2+1)^(1/2)/(x+1),x)","\arcsin \left(x \right)+\sqrt{2 x -\left(x +1\right)^{2}+2}"," ",0,"(-(x+1)^2+2*x+2)^(1/2)+arcsin(x)","A"
822,1,29,28,0.045000," ","int((-x+1)*(-x^2+1)^(1/2),x)","\frac{\sqrt{-x^{2}+1}\, x}{2}+\frac{\arcsin \left(x \right)}{2}+\frac{\left(-x^{2}+1\right)^{\frac{3}{2}}}{3}"," ",0,"1/3*(-x^2+1)^(3/2)+1/2*arcsin(x)+1/2*(-x^2+1)^(1/2)*x","A"
823,1,20,14,0.043000," ","int((-x^2+1)^(1/2)/(-x+1),x)","\arcsin \left(x \right)-\sqrt{-2 x -\left(x -1\right)^{2}+2}"," ",0,"-(-(x-1)^2-2*x+2)^(1/2)+arcsin(x)","A"
824,1,40,23,0.045000," ","int((-x^2+1)^(1/2)/(-x+1)^2,x)","-\arcsin \left(x \right)+\frac{\left(-2 x -\left(x -1\right)^{2}+2\right)^{\frac{3}{2}}}{\left(x -1\right)^{2}}+\sqrt{-2 x -\left(x -1\right)^{2}+2}"," ",0,"1/(x-1)^2*(-2*x-(x-1)^2+2)^(3/2)+(-2*x-(x-1)^2+2)^(1/2)-arcsin(x)","A"
825,1,20,18,0.036000," ","int((-x^2+1)^(1/2)/(-x+1)^3,x)","\frac{\left(x +1\right) \sqrt{-x^{2}+1}}{3 \left(x -1\right)^{2}}"," ",0,"1/3*(x+1)*(-x^2+1)^(1/2)/(x-1)^2","A"
826,1,144,158,0.069000," ","int((e*x+d)^5/(-e^2*x^2+d^2)^(1/2),x)","-\frac{\sqrt{-e^{2} x^{2}+d^{2}}\, e^{3} x^{4}}{5}+\frac{63 d^{5} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{8 \sqrt{e^{2}}}-\frac{5 \sqrt{-e^{2} x^{2}+d^{2}}\, d \,e^{2} x^{3}}{4}-\frac{18 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{2} e \,x^{2}}{5}-\frac{55 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{3} x}{8}-\frac{61 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{4}}{5 e}"," ",0,"-1/5*e^3*x^4*(-e^2*x^2+d^2)^(1/2)-18/5*e*d^2*x^2*(-e^2*x^2+d^2)^(1/2)-61/5*d^4*(-e^2*x^2+d^2)^(1/2)/e-5/4*d*e^2*x^3*(-e^2*x^2+d^2)^(1/2)-55/8*d^3*x*(-e^2*x^2+d^2)^(1/2)+63/8*d^5/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)","A"
827,1,119,129,0.062000," ","int((e*x+d)^4/(-e^2*x^2+d^2)^(1/2),x)","\frac{35 d^{4} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{8 \sqrt{e^{2}}}-\frac{\sqrt{-e^{2} x^{2}+d^{2}}\, e^{2} x^{3}}{4}-\frac{4 \sqrt{-e^{2} x^{2}+d^{2}}\, d e \,x^{2}}{3}-\frac{27 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{2} x}{8}-\frac{20 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{3}}{3 e}"," ",0,"-1/4*e^2*x^3*(-e^2*x^2+d^2)^(1/2)-27/8*d^2*x*(-e^2*x^2+d^2)^(1/2)+35/8*d^4/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)-4/3*e*d*x^2*(-e^2*x^2+d^2)^(1/2)-20/3*d^3*(-e^2*x^2+d^2)^(1/2)/e","A"
828,1,94,100,0.054000," ","int((e*x+d)^3/(-e^2*x^2+d^2)^(1/2),x)","\frac{5 d^{3} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{2 \sqrt{e^{2}}}-\frac{\sqrt{-e^{2} x^{2}+d^{2}}\, e \,x^{2}}{3}-\frac{3 \sqrt{-e^{2} x^{2}+d^{2}}\, d x}{2}-\frac{11 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{2}}{3 e}"," ",0,"-1/3*e*x^2*(-e^2*x^2+d^2)^(1/2)-11/3*d^2*(-e^2*x^2+d^2)^(1/2)/e-3/2*d*x*(-e^2*x^2+d^2)^(1/2)+5/2*d^3/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)","A"
829,1,71,64,0.049000," ","int((e*x+d)^2/(-e^2*x^2+d^2)^(1/2),x)","\frac{3 d^{2} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{2 \sqrt{e^{2}}}-\frac{\sqrt{-e^{2} x^{2}+d^{2}}\, x}{2}-\frac{2 \sqrt{-e^{2} x^{2}+d^{2}}\, d}{e}"," ",0,"-1/2*x*(-e^2*x^2+d^2)^(1/2)+3/2*d^2/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)-2*d*(-e^2*x^2+d^2)^(1/2)/e","A"
830,1,50,43,0.044000," ","int((e*x+d)/(-e^2*x^2+d^2)^(1/2),x)","\frac{d \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{\sqrt{e^{2}}}-\frac{\sqrt{-e^{2} x^{2}+d^{2}}}{e}"," ",0,"-(-e^2*x^2+d^2)^(1/2)/e+d/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)","A"
831,1,29,29,0.045000," ","int(1/(e*x+d)/(-e^2*x^2+d^2)^(1/2),x)","-\frac{-e x +d}{\sqrt{-e^{2} x^{2}+d^{2}}\, d e}"," ",0,"-(-e*x+d)/d/e/(-e^2*x^2+d^2)^(1/2)","A"
832,1,43,59,0.048000," ","int(1/(e*x+d)^2/(-e^2*x^2+d^2)^(1/2),x)","-\frac{\left(-e x +d \right) \left(e x +2 d \right)}{3 \left(e x +d \right) \sqrt{-e^{2} x^{2}+d^{2}}\, d^{2} e}"," ",0,"-1/3*(-e*x+d)*(e*x+2*d)/(e*x+d)/d^2/e/(-e^2*x^2+d^2)^(1/2)","A"
833,1,55,88,0.044000," ","int(1/(e*x+d)^3/(-e^2*x^2+d^2)^(1/2),x)","-\frac{\left(-e x +d \right) \left(2 e^{2} x^{2}+6 d e x +7 d^{2}\right)}{15 \left(e x +d \right)^{2} \sqrt{-e^{2} x^{2}+d^{2}}\, d^{3} e}"," ",0,"-1/15*(-e*x+d)*(2*e^2*x^2+6*d*e*x+7*d^2)/(e*x+d)^2/d^3/e/(-e^2*x^2+d^2)^(1/2)","A"
834,1,66,117,0.046000," ","int(1/(e*x+d)^4/(-e^2*x^2+d^2)^(1/2),x)","-\frac{\left(-e x +d \right) \left(2 e^{3} x^{3}+8 e^{2} x^{2} d +13 x \,d^{2} e +12 d^{3}\right)}{35 \left(e x +d \right)^{3} \sqrt{-e^{2} x^{2}+d^{2}}\, d^{4} e}"," ",0,"-1/35*(-e*x+d)*(2*e^3*x^3+8*d*e^2*x^2+13*d^2*e*x+12*d^3)/(e*x+d)^3/d^4/e/(-e^2*x^2+d^2)^(1/2)","A"
835,1,77,146,0.057000," ","int(1/(e*x+d)^5/(-e^2*x^2+d^2)^(1/2),x)","-\frac{\left(-e x +d \right) \left(8 e^{4} x^{4}+40 e^{3} x^{3} d +84 e^{2} x^{2} d^{2}+100 x \,d^{3} e +83 d^{4}\right)}{315 \left(e x +d \right)^{4} \sqrt{-e^{2} x^{2}+d^{2}}\, d^{5} e}"," ",0,"-1/315*(-e*x+d)*(8*e^4*x^4+40*d*e^3*x^3+84*d^2*e^2*x^2+100*d^3*e*x+83*d^4)/(e*x+d)^4/d^5/e/(-e^2*x^2+d^2)^(1/2)","A"
836,1,189,123,0.095000," ","int((e*x+d)^6/(-e^2*x^2+d^2)^(5/2),x)","-\frac{e^{4} x^{5}}{2 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}}}-\frac{6 d \,e^{3} x^{4}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}}}+\frac{35 d^{2} e^{2} x^{3}}{6 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}}}+\frac{44 d^{3} e \,x^{2}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}}}+\frac{16 d^{4} x}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}}}-\frac{82 d^{5}}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e}-\frac{131 d^{2} x}{6 \sqrt{-e^{2} x^{2}+d^{2}}}+\frac{35 d^{2} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{2 \sqrt{e^{2}}}"," ",0,"-1/2*e^4*x^5/(-e^2*x^2+d^2)^(3/2)+35/6*e^2*d^2*x^3/(-e^2*x^2+d^2)^(3/2)-131/6*d^2*x/(-e^2*x^2+d^2)^(1/2)+35/2/(e^2)^(1/2)*d^2*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)-6*d*e^3*x^4/(-e^2*x^2+d^2)^(3/2)+44*d^3*e*x^2/(-e^2*x^2+d^2)^(3/2)-82/3*d^5/e/(-e^2*x^2+d^2)^(3/2)+16/3*d^4*x/(-e^2*x^2+d^2)^(3/2)","A"
837,1,160,96,0.066000," ","int((e*x+d)^5/(-e^2*x^2+d^2)^(5/2),x)","-\frac{e^{3} x^{4}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}}}+\frac{5 d \,e^{2} x^{3}}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}}}+\frac{14 d^{2} e \,x^{2}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}}}+\frac{11 d^{3} x}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}}}-\frac{23 d^{4}}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e}-\frac{23 d x}{3 \sqrt{-e^{2} x^{2}+d^{2}}}+\frac{5 d \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{\sqrt{e^{2}}}"," ",0,"-e^3*x^4/(-e^2*x^2+d^2)^(3/2)+14*e*d^2*x^2/(-e^2*x^2+d^2)^(3/2)-23/3*d^4/e/(-e^2*x^2+d^2)^(3/2)+5/3*d*e^2*x^3/(-e^2*x^2+d^2)^(3/2)-23/3*d*x/(-e^2*x^2+d^2)^(1/2)+5/(e^2)^(1/2)*d*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)+11/3*d^3*x/(-e^2*x^2+d^2)^(3/2)","A"
838,1,132,73,0.074000," ","int((e*x+d)^4/(-e^2*x^2+d^2)^(5/2),x)","\frac{e^{2} x^{3}}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}}}+\frac{4 d e \,x^{2}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}}}+\frac{7 d^{2} x}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}}}-\frac{4 d^{3}}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e}-\frac{7 x}{3 \sqrt{-e^{2} x^{2}+d^{2}}}+\frac{\arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{\sqrt{e^{2}}}"," ",0,"1/3*e^2*x^3/(-e^2*x^2+d^2)^(3/2)-7/3*x/(-e^2*x^2+d^2)^(1/2)+1/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)+4*e*d*x^2/(-e^2*x^2+d^2)^(3/2)-4/3*d^3/e/(-e^2*x^2+d^2)^(3/2)+7/3*d^2*x/(-e^2*x^2+d^2)^(3/2)","A"
839,1,36,29,0.049000," ","int((e*x+d)^3/(-e^2*x^2+d^2)^(5/2),x)","\frac{\left(e x +d \right)^{4} \left(-e x +d \right)}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d e}"," ",0,"1/3*(e*x+d)^4*(-e*x+d)/d/e/(-e^2*x^2+d^2)^(5/2)","A"
840,1,44,45,0.054000," ","int((e*x+d)^2/(-e^2*x^2+d^2)^(5/2),x)","\frac{\left(e x +d \right)^{3} \left(-e x +d \right) \left(-e x +2 d \right)}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d^{2} e}"," ",0,"1/3*(e*x+d)^3*(-e*x+d)*(-e*x+2*d)/d^2/e/(-e^2*x^2+d^2)^(5/2)","A"
841,1,53,48,0.050000," ","int((e*x+d)/(-e^2*x^2+d^2)^(5/2),x)","\frac{\left(e x +d \right)^{2} \left(-e x +d \right) \left(-2 e^{2} x^{2}+2 d e x +d^{2}\right)}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d^{3} e}"," ",0,"1/3*(e*x+d)^2*(-e*x+d)*(-2*e^2*x^2+2*d*e*x+d^2)/d^3/e/(-e^2*x^2+d^2)^(5/2)","A"
842,1,70,70,0.050000," ","int(1/(e*x+d)/(-e^2*x^2+d^2)^(5/2),x)","-\frac{\left(-e x +d \right) \left(8 e^{4} x^{4}+8 e^{3} x^{3} d -12 e^{2} x^{2} d^{2}-12 x \,d^{3} e +3 d^{4}\right)}{15 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d^{5} e}"," ",0,"-1/15*(-e*x+d)*(8*e^4*x^4+8*d*e^3*x^3-12*d^2*e^2*x^2-12*d^3*e*x+3*d^4)/d^5/e/(-e^2*x^2+d^2)^(5/2)","A"
843,1,88,99,0.045000," ","int(1/(e*x+d)^2/(-e^2*x^2+d^2)^(5/2),x)","-\frac{\left(-e x +d \right) \left(8 e^{5} x^{5}+16 e^{4} x^{4} d -4 e^{3} x^{3} d^{2}-24 e^{2} x^{2} d^{3}-9 x \,d^{4} e +6 d^{5}\right)}{21 \left(e x +d \right) \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d^{6} e}"," ",0,"-1/21*(-e*x+d)*(8*e^5*x^5+16*d*e^4*x^4-4*d^2*e^3*x^3-24*d^3*e^2*x^2-9*d^4*e*x+6*d^5)/(e*x+d)/d^6/e/(-e^2*x^2+d^2)^(5/2)","A"
844,1,99,128,0.059000," ","int(1/(e*x+d)^3/(-e^2*x^2+d^2)^(5/2),x)","-\frac{\left(-e x +d \right) \left(16 e^{6} x^{6}+48 e^{5} x^{5} d +24 e^{4} x^{4} d^{2}-56 e^{3} x^{3} d^{3}-66 e^{2} x^{2} d^{4}-6 x \,d^{5} e +19 d^{6}\right)}{63 \left(e x +d \right)^{2} \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d^{7} e}"," ",0,"-1/63*(-e*x+d)*(16*e^6*x^6+48*d*e^5*x^5+24*d^2*e^4*x^4-56*d^3*e^3*x^3-66*d^4*e^2*x^2-6*d^5*e*x+19*d^6)/(e*x+d)^2/d^7/e/(-e^2*x^2+d^2)^(5/2)","A"
845,1,110,157,0.052000," ","int(1/(e*x+d)^4/(-e^2*x^2+d^2)^(5/2),x)","-\frac{\left(-e x +d \right) \left(16 e^{7} x^{7}+64 e^{6} x^{6} d +72 e^{5} x^{5} d^{2}-32 e^{4} x^{4} d^{3}-122 e^{3} x^{3} d^{4}-72 e^{2} x^{2} d^{5}+13 x \,d^{6} e +28 d^{7}\right)}{99 \left(e x +d \right)^{3} \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d^{8} e}"," ",0,"-1/99*(-e*x+d)*(16*e^7*x^7+64*d*e^6*x^6+72*d^2*e^5*x^5-32*d^3*e^4*x^4-122*d^4*e^3*x^3-72*d^5*e^2*x^2+13*d^6*e*x+28*d^7)/(e*x+d)^3/d^8/e/(-e^2*x^2+d^2)^(5/2)","A"
846,1,309,178,0.287000," ","int((e*x+d)^9/(-e^2*x^2+d^2)^(7/2),x)","-\frac{e^{7} x^{8}}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}-\frac{9 d \,e^{6} x^{7}}{2 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}-\frac{116 d^{2} e^{5} x^{6}}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}+\frac{231 d^{3} e^{4} x^{5}}{10 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}+\frac{358 d^{4} e^{3} x^{4}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}+\frac{63 d^{5} e^{2} x^{3}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}-\frac{1348 d^{6} e \,x^{2}}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}-\frac{152 d^{7} x}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}-\frac{77 d^{3} e^{2} x^{3}}{2 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}}}+\frac{2723 d^{8}}{15 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e}+\frac{157 d^{5} x}{15 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}}}+\frac{4093 d^{3} x}{30 \sqrt{-e^{2} x^{2}+d^{2}}}-\frac{231 d^{3} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{2 \sqrt{e^{2}}}"," ",0,"63*d^5*e^2*x^3/(-e^2*x^2+d^2)^(5/2)-9/2*d*e^6*x^7/(-e^2*x^2+d^2)^(5/2)+231/10*d^3*e^4*x^5/(-e^2*x^2+d^2)^(5/2)-77/2*d^3*e^2*x^3/(-e^2*x^2+d^2)^(3/2)-116/3*e^5*d^2*x^6/(-e^2*x^2+d^2)^(5/2)+358*e^3*d^4*x^4/(-e^2*x^2+d^2)^(5/2)-1348/3*e*d^6*x^2/(-e^2*x^2+d^2)^(5/2)-231/2/(e^2)^(1/2)*d^3*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)-152/5*d^7*x/(-e^2*x^2+d^2)^(5/2)+157/15*d^5*x/(-e^2*x^2+d^2)^(3/2)+2723/15*d^8/e/(-e^2*x^2+d^2)^(5/2)+4093/30*d^3*x/(-e^2*x^2+d^2)^(1/2)-1/3*e^7*x^8/(-e^2*x^2+d^2)^(5/2)","A"
847,1,284,149,0.186000," ","int((e*x+d)^8/(-e^2*x^2+d^2)^(7/2),x)","-\frac{e^{6} x^{7}}{2 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}-\frac{8 d \,e^{5} x^{6}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}+\frac{63 d^{2} e^{4} x^{5}}{10 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}+\frac{104 d^{3} e^{3} x^{4}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}+\frac{35 d^{4} e^{2} x^{3}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}-\frac{120 d^{5} e \,x^{2}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}-\frac{76 d^{6} x}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}-\frac{21 d^{2} e^{2} x^{3}}{2 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}}}+\frac{248 d^{7}}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e}+\frac{27 d^{4} x}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}}}+\frac{423 d^{2} x}{10 \sqrt{-e^{2} x^{2}+d^{2}}}-\frac{63 d^{2} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{2 \sqrt{e^{2}}}"," ",0,"-21/2/(-e^2*x^2+d^2)^(3/2)*d^2*e^2*x^3+423/10/(-e^2*x^2+d^2)^(1/2)*d^2*x+35*d^4*e^2*x^3/(-e^2*x^2+d^2)^(5/2)-8*e^5*d*x^6/(-e^2*x^2+d^2)^(5/2)+104*e^3*d^3*x^4/(-e^2*x^2+d^2)^(5/2)-120*e*d^5*x^2/(-e^2*x^2+d^2)^(5/2)+63/10*e^4*d^2*x^5/(-e^2*x^2+d^2)^(5/2)-63/2/(e^2)^(1/2)*d^2*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)+27/5/(-e^2*x^2+d^2)^(3/2)*d^4*x-76/5*d^6*x/(-e^2*x^2+d^2)^(5/2)-1/2*e^6*x^7/(-e^2*x^2+d^2)^(5/2)+248/5*d^7/e/(-e^2*x^2+d^2)^(5/2)","A"
848,1,253,122,0.120000," ","int((e*x+d)^7/(-e^2*x^2+d^2)^(7/2),x)","-\frac{e^{5} x^{6}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}+\frac{7 d \,e^{4} x^{5}}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}+\frac{27 d^{2} e^{3} x^{4}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}+\frac{35 d^{3} e^{2} x^{3}}{2 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}-\frac{73 d^{4} e \,x^{2}}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}-\frac{61 d^{5} x}{10 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}-\frac{7 d \,e^{2} x^{3}}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}}}+\frac{167 d^{6}}{15 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e}+\frac{71 d^{3} x}{30 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}}}+\frac{176 d x}{15 \sqrt{-e^{2} x^{2}+d^{2}}}-\frac{7 d \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{\sqrt{e^{2}}}"," ",0,"-e^5*x^6/(-e^2*x^2+d^2)^(5/2)+27*e^3*d^2*x^4/(-e^2*x^2+d^2)^(5/2)-73/3*e*d^4*x^2/(-e^2*x^2+d^2)^(5/2)+167/15*d^6/e/(-e^2*x^2+d^2)^(5/2)+7/5*d*e^4*x^5/(-e^2*x^2+d^2)^(5/2)-7/3/(-e^2*x^2+d^2)^(3/2)*d*e^2*x^3+176/15/(-e^2*x^2+d^2)^(1/2)*d*x-7/(e^2)^(1/2)*d*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)+35/2*d^3*e^2*x^3/(-e^2*x^2+d^2)^(5/2)-61/10*d^5*x/(-e^2*x^2+d^2)^(5/2)+71/30/(-e^2*x^2+d^2)^(3/2)*d^3*x","B"
849,1,225,100,0.094000," ","int((e*x+d)^6/(-e^2*x^2+d^2)^(7/2),x)","\frac{e^{4} x^{5}}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}+\frac{6 d \,e^{3} x^{4}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}+\frac{15 d^{2} e^{2} x^{3}}{2 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}-\frac{4 d^{3} e \,x^{2}}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}-\frac{13 d^{4} x}{10 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}-\frac{e^{2} x^{3}}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}}}+\frac{26 d^{5}}{15 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e}+\frac{23 d^{2} x}{30 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}}}+\frac{38 x}{15 \sqrt{-e^{2} x^{2}+d^{2}}}-\frac{\arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{\sqrt{e^{2}}}"," ",0,"1/5*e^4*x^5/(-e^2*x^2+d^2)^(5/2)-1/3/(-e^2*x^2+d^2)^(3/2)*e^2*x^3+38/15/(-e^2*x^2+d^2)^(1/2)*x-1/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)+6*d*e^3*x^4/(-e^2*x^2+d^2)^(5/2)-4/3*d^3*e*x^2/(-e^2*x^2+d^2)^(5/2)+26/15*d^5/e/(-e^2*x^2+d^2)^(5/2)+15/2*e^2*d^2*x^3/(-e^2*x^2+d^2)^(5/2)-13/10*d^4*x/(-e^2*x^2+d^2)^(5/2)+23/30/(-e^2*x^2+d^2)^(3/2)*d^2*x","B"
850,1,36,29,0.043000," ","int((e*x+d)^5/(-e^2*x^2+d^2)^(7/2),x)","\frac{\left(e x +d \right)^{6} \left(-e x +d \right)}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d e}"," ",0,"1/5*(e*x+d)^6*(-e*x+d)/d/e/(-e^2*x^2+d^2)^(7/2)","A"
851,1,44,59,0.049000," ","int((e*x+d)^4/(-e^2*x^2+d^2)^(7/2),x)","\frac{\left(e x +d \right)^{5} \left(-e x +d \right) \left(-e x +4 d \right)}{15 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d^{2} e}"," ",0,"1/15*(e*x+d)^5*(-e*x+d)*(-e*x+4*d)/d^2/e/(-e^2*x^2+d^2)^(7/2)","A"
852,1,55,91,0.046000," ","int((e*x+d)^3/(-e^2*x^2+d^2)^(7/2),x)","\frac{\left(e x +d \right)^{4} \left(-e x +d \right) \left(2 e^{2} x^{2}-6 d e x +7 d^{2}\right)}{15 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d^{3} e}"," ",0,"1/15*(e*x+d)^4*(-e*x+d)*(2*e^2*x^2-6*d*e*x+7*d^2)/d^3/e/(-e^2*x^2+d^2)^(7/2)","A"
853,1,65,65,0.047000," ","int((e*x+d)^2/(-e^2*x^2+d^2)^(7/2),x)","\frac{\left(e x +d \right)^{3} \left(-e x +d \right) \left(2 e^{3} x^{3}-4 e^{2} x^{2} d +x \,d^{2} e +2 d^{3}\right)}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d^{4} e}"," ",0,"1/5*(e*x+d)^3*(-e*x+d)*(2*e^3*x^3-4*d*e^2*x^2+d^2*e*x+2*d^3)/d^4/e/(-e^2*x^2+d^2)^(7/2)","A"
854,1,77,68,0.049000," ","int((e*x+d)/(-e^2*x^2+d^2)^(7/2),x)","\frac{\left(e x +d \right)^{2} \left(-e x +d \right) \left(8 e^{4} x^{4}-8 e^{3} x^{3} d -12 e^{2} x^{2} d^{2}+12 x \,d^{3} e +3 d^{4}\right)}{15 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d^{5} e}"," ",0,"1/15*(e*x+d)^2*(-e*x+d)*(8*e^4*x^4-8*d*e^3*x^3-12*d^2*e^2*x^2+12*d^3*e*x+3*d^4)/d^5/e/(-e^2*x^2+d^2)^(7/2)","A"
855,1,92,90,0.052000," ","int(1/(e*x+d)/(-e^2*x^2+d^2)^(7/2),x)","-\frac{\left(-e x +d \right) \left(-16 e^{6} x^{6}-16 e^{5} x^{5} d +40 e^{4} x^{4} d^{2}+40 e^{3} x^{3} d^{3}-30 e^{2} x^{2} d^{4}-30 x \,d^{5} e +5 d^{6}\right)}{35 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d^{7} e}"," ",0,"-1/35*(-e*x+d)*(-16*e^6*x^6-16*d*e^5*x^5+40*d^2*e^4*x^4+40*d^3*e^3*x^3-30*d^4*e^2*x^2-30*d^5*e*x+5*d^6)/d^7/e/(-e^2*x^2+d^2)^(7/2)","A"
856,1,110,119,0.052000," ","int(1/(e*x+d)^2/(-e^2*x^2+d^2)^(7/2),x)","-\frac{\left(-e x +d \right) \left(-16 e^{7} x^{7}-32 e^{6} x^{6} d +24 e^{5} x^{5} d^{2}+80 e^{4} x^{4} d^{3}+10 e^{3} x^{3} d^{4}-60 e^{2} x^{2} d^{5}-25 x \,d^{6} e +10 d^{7}\right)}{45 \left(e x +d \right) \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d^{8} e}"," ",0,"-1/45*(-e*x+d)*(-16*e^7*x^7-32*d*e^6*x^6+24*d^2*e^5*x^5+80*d^3*e^4*x^4+10*d^4*e^3*x^3-60*d^5*e^2*x^2-25*d^6*e*x+10*d^7)/(e*x+d)/d^8/e/(-e^2*x^2+d^2)^(7/2)","A"
857,1,121,148,0.063000," ","int(1/(e*x+d)^3/(-e^2*x^2+d^2)^(7/2),x)","-\frac{\left(-e x +d \right) \left(-128 e^{8} x^{8}-384 e^{7} x^{7} d -64 e^{6} x^{6} d^{2}+832 e^{5} x^{5} d^{3}+720 e^{4} x^{4} d^{4}-400 e^{3} x^{3} d^{5}-680 e^{2} x^{2} d^{6}-120 x \,d^{7} e +125 d^{8}\right)}{495 \left(e x +d \right)^{2} \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d^{9} e}"," ",0,"-1/495*(-e*x+d)*(-128*e^8*x^8-384*d*e^7*x^7-64*d^2*e^6*x^6+832*d^3*e^5*x^5+720*d^4*e^4*x^4-400*d^5*e^3*x^3-680*d^6*e^2*x^2-120*d^7*e*x+125*d^8)/(e*x+d)^2/d^9/e/(-e^2*x^2+d^2)^(7/2)","A"
858,1,132,177,0.051000," ","int(1/(e*x+d)^4/(-e^2*x^2+d^2)^(7/2),x)","-\frac{\left(-e x +d \right) \left(-128 e^{9} x^{9}-512 e^{8} x^{8} d -448 e^{7} x^{7} d^{2}+768 e^{6} x^{6} d^{3}+1552 e^{5} x^{5} d^{4}+320 e^{4} x^{4} d^{5}-1080 e^{3} x^{3} d^{6}-800 e^{2} x^{2} d^{7}+5 x \,d^{8} e +180 d^{9}\right)}{715 \left(e x +d \right)^{3} \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d^{10} e}"," ",0,"-1/715*(-e*x+d)*(-128*e^9*x^9-512*d*e^8*x^8-448*d^2*e^7*x^7+768*d^3*e^6*x^6+1552*d^4*e^5*x^5+320*d^5*e^4*x^4-1080*d^6*e^3*x^3-800*d^7*e^2*x^2+5*d^8*e*x+180*d^9)/(e*x+d)^3/d^10/e/(-e^2*x^2+d^2)^(7/2)","A"
859,1,143,206,0.046000," ","int(1/(e*x+d)^5/(-e^2*x^2+d^2)^(7/2),x)","-\frac{\left(-e x +d \right) \left(-256 e^{10} x^{10}-1280 e^{9} x^{9} d -1920 e^{8} x^{8} d^{2}+640 e^{7} x^{7} d^{3}+4640 e^{6} x^{6} d^{4}+3744 e^{5} x^{5} d^{5}-1520 e^{4} x^{4} d^{6}-3760 e^{3} x^{3} d^{7}-1590 e^{2} x^{2} d^{8}+370 x \,d^{9} e +503 d^{10}\right)}{2145 \left(e x +d \right)^{4} \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d^{11} e}"," ",0,"-1/2145*(-e*x+d)*(-256*e^10*x^10-1280*d*e^9*x^9-1920*d^2*e^8*x^8+640*d^3*e^7*x^7+4640*d^4*e^6*x^6+3744*d^5*e^5*x^5-1520*d^6*e^4*x^4-3760*d^7*e^3*x^3-1590*d^8*e^2*x^2+370*d^9*e*x+503*d^10)/(e*x+d)^4/d^11/e/(-e^2*x^2+d^2)^(7/2)","A"
860,1,15,14,0.047000," ","int((x+1)/(-x^2+1)^(1/2),x)","\arcsin \left(x \right)-\sqrt{-x^{2}+1}"," ",0,"arcsin(x)-(-x^2+1)^(1/2)","A"
861,1,13,12,0.052000," ","int((-x+1)/(-x^2+1)^(1/2),x)","\arcsin \left(x \right)+\sqrt{-x^{2}+1}"," ",0,"arcsin(x)+(-x^2+1)^(1/2)","A"
862,1,66,136,0.044000," ","int((e*x+d)^(5/2)*(-c*e^2*x^2+c*d^2)^(1/2),x)","-\frac{2 \left(-e x +d \right) \left(35 e^{3} x^{3}+165 e^{2} x^{2} d +321 d^{2} x e +319 d^{3}\right) \sqrt{-c \,e^{2} x^{2}+c \,d^{2}}}{315 \sqrt{e x +d}\, e}"," ",0,"-2/315*(-e*x+d)*(35*e^3*x^3+165*d*e^2*x^2+321*d^2*e*x+319*d^3)*(-c*e^2*x^2+c*d^2)^(1/2)/e/(e*x+d)^(1/2)","A"
863,1,55,101,0.050000," ","int((e*x+d)^(3/2)*(-c*e^2*x^2+c*d^2)^(1/2),x)","-\frac{2 \left(-e x +d \right) \left(15 e^{2} x^{2}+54 d e x +71 d^{2}\right) \sqrt{-c \,e^{2} x^{2}+c \,d^{2}}}{105 \sqrt{e x +d}\, e}"," ",0,"-2/105*(-e*x+d)*(15*e^2*x^2+54*d*e*x+71*d^2)*(-c*e^2*x^2+c*d^2)^(1/2)/(e*x+d)^(1/2)/e","A"
864,1,44,66,0.045000," ","int((e*x+d)^(1/2)*(-c*e^2*x^2+c*d^2)^(1/2),x)","-\frac{2 \left(-e x +d \right) \left(3 e x +7 d \right) \sqrt{-c \,e^{2} x^{2}+c \,d^{2}}}{15 \sqrt{e x +d}\, e}"," ",0,"-2/15*(-e*x+d)*(3*e*x+7*d)*(-c*e^2*x^2+c*d^2)^(1/2)/e/(e*x+d)^(1/2)","A"
865,1,36,32,0.046000," ","int((-c*e^2*x^2+c*d^2)^(1/2)/(e*x+d)^(1/2),x)","-\frac{2 \left(-e x +d \right) \sqrt{-c \,e^{2} x^{2}+c \,d^{2}}}{3 \sqrt{e x +d}\, e}"," ",0,"-2/3*(-e*x+d)*(-c*e^2*x^2+c*d^2)^(1/2)/e/(e*x+d)^(1/2)","A"
866,1,97,80,0.176000," ","int((-c*e^2*x^2+c*d^2)^(1/2)/(e*x+d)^(3/2),x)","-\frac{2 \sqrt{-\left(e^{2} x^{2}-d^{2}\right) c}\, \left(\sqrt{2}\, c d \arctanh \left(\frac{\sqrt{-\left(e x -d \right) c}\, \sqrt{2}}{2 \sqrt{c d}}\right)-\sqrt{-\left(e x -d \right) c}\, \sqrt{c d}\right)}{\sqrt{e x +d}\, \sqrt{-\left(e x -d \right) c}\, \sqrt{c d}\, e}"," ",0,"-2*(-c*(e^2*x^2-d^2))^(1/2)*(c*d*2^(1/2)*arctanh(1/2*(-(e*x-d)*c)^(1/2)*2^(1/2)/(c*d)^(1/2))-(-(e*x-d)*c)^(1/2)*(c*d)^(1/2))/(e*x+d)^(1/2)/(-(e*x-d)*c)^(1/2)/e/(c*d)^(1/2)","A"
867,1,127,80,0.072000," ","int((-c*e^2*x^2+c*d^2)^(1/2)/(e*x+d)^(5/2),x)","\frac{\sqrt{-\left(e^{2} x^{2}-d^{2}\right) c}\, \left(\sqrt{2}\, c e x \arctanh \left(\frac{\sqrt{-\left(e x -d \right) c}\, \sqrt{2}}{2 \sqrt{c d}}\right)+\sqrt{2}\, c d \arctanh \left(\frac{\sqrt{-\left(e x -d \right) c}\, \sqrt{2}}{2 \sqrt{c d}}\right)-2 \sqrt{-\left(e x -d \right) c}\, \sqrt{c d}\right)}{2 \left(e x +d \right)^{\frac{3}{2}} \sqrt{-\left(e x -d \right) c}\, \sqrt{c d}\, e}"," ",0,"1/2*(-(e^2*x^2-d^2)*c)^(1/2)*(2^(1/2)*arctanh(1/2*(-(e*x-d)*c)^(1/2)*2^(1/2)/(c*d)^(1/2))*x*c*e+c*d*2^(1/2)*arctanh(1/2*(-(e*x-d)*c)^(1/2)*2^(1/2)/(c*d)^(1/2))-2*(-(e*x-d)*c)^(1/2)*(c*d)^(1/2))/(e*x+d)^(3/2)/(-(e*x-d)*c)^(1/2)/e/(c*d)^(1/2)","A"
868,1,190,112,0.068000," ","int((-c*e^2*x^2+c*d^2)^(1/2)/(e*x+d)^(7/2),x)","\frac{\sqrt{-\left(e^{2} x^{2}-d^{2}\right) c}\, \left(\sqrt{2}\, c \,e^{2} x^{2} \arctanh \left(\frac{\sqrt{-\left(e x -d \right) c}\, \sqrt{2}}{2 \sqrt{c d}}\right)+2 \sqrt{2}\, c d e x \arctanh \left(\frac{\sqrt{-\left(e x -d \right) c}\, \sqrt{2}}{2 \sqrt{c d}}\right)+\sqrt{2}\, c \,d^{2} \arctanh \left(\frac{\sqrt{-\left(e x -d \right) c}\, \sqrt{2}}{2 \sqrt{c d}}\right)+2 \sqrt{c d}\, \sqrt{-\left(e x -d \right) c}\, e x -6 \sqrt{-\left(e x -d \right) c}\, \sqrt{c d}\, d \right)}{16 \left(e x +d \right)^{\frac{5}{2}} \sqrt{-\left(e x -d \right) c}\, \sqrt{c d}\, d e}"," ",0,"1/16*(-(e^2*x^2-d^2)*c)^(1/2)*(2^(1/2)*arctanh(1/2*(-(e*x-d)*c)^(1/2)*2^(1/2)/(c*d)^(1/2))*x^2*c*e^2+2*2^(1/2)*arctanh(1/2*(-(e*x-d)*c)^(1/2)*2^(1/2)/(c*d)^(1/2))*x*c*d*e+2^(1/2)*arctanh(1/2*(-(e*x-d)*c)^(1/2)*2^(1/2)/(c*d)^(1/2))*c*d^2+2*x*e*(c*d)^(1/2)*(-(e*x-d)*c)^(1/2)-6*(-(e*x-d)*c)^(1/2)*(c*d)^(1/2)*d)/(e*x+d)^(5/2)/(-(e*x-d)*c)^(1/2)/e/d/(c*d)^(1/2)","A"
869,1,77,171,0.050000," ","int((e*x+d)^(5/2)*(-c*e^2*x^2+c*d^2)^(3/2),x)","-\frac{2 \left(-e x +d \right) \left(1155 e^{4} x^{4}+6300 e^{3} x^{3} d +14210 d^{2} e^{2} x^{2}+16700 d^{3} x e +9683 d^{4}\right) \left(-c \,e^{2} x^{2}+c \,d^{2}\right)^{\frac{3}{2}}}{15015 \left(e x +d \right)^{\frac{3}{2}} e}"," ",0,"-2/15015*(-e*x+d)*(1155*e^4*x^4+6300*d*e^3*x^3+14210*d^2*e^2*x^2+16700*d^3*e*x+9683*d^4)*(-c*e^2*x^2+c*d^2)^(3/2)/e/(e*x+d)^(3/2)","A"
870,1,66,136,0.046000," ","int((e*x+d)^(3/2)*(-c*e^2*x^2+c*d^2)^(3/2),x)","-\frac{2 \left(-e x +d \right) \left(105 e^{3} x^{3}+455 e^{2} x^{2} d +755 d^{2} x e +533 d^{3}\right) \left(-c \,e^{2} x^{2}+c \,d^{2}\right)^{\frac{3}{2}}}{1155 \left(e x +d \right)^{\frac{3}{2}} e}"," ",0,"-2/1155*(-e*x+d)*(105*e^3*x^3+455*d*e^2*x^2+755*d^2*e*x+533*d^3)*(-c*e^2*x^2+c*d^2)^(3/2)/e/(e*x+d)^(3/2)","A"
871,1,55,101,0.051000," ","int((e*x+d)^(1/2)*(-c*e^2*x^2+c*d^2)^(3/2),x)","-\frac{2 \left(-e x +d \right) \left(35 e^{2} x^{2}+110 d e x +107 d^{2}\right) \left(-c \,e^{2} x^{2}+c \,d^{2}\right)^{\frac{3}{2}}}{315 \left(e x +d \right)^{\frac{3}{2}} e}"," ",0,"-2/315*(-e*x+d)*(35*e^2*x^2+110*d*e*x+107*d^2)*(-c*e^2*x^2+c*d^2)^(3/2)/e/(e*x+d)^(3/2)","A"
872,1,44,66,0.045000," ","int((-c*e^2*x^2+c*d^2)^(3/2)/(e*x+d)^(1/2),x)","-\frac{2 \left(-e x +d \right) \left(5 e x +9 d \right) \left(-c \,e^{2} x^{2}+c \,d^{2}\right)^{\frac{3}{2}}}{35 \left(e x +d \right)^{\frac{3}{2}} e}"," ",0,"-2/35*(-e*x+d)*(5*e*x+9*d)*(-c*e^2*x^2+c*d^2)^(3/2)/e/(e*x+d)^(3/2)","A"
873,1,36,32,0.046000," ","int((-c*e^2*x^2+c*d^2)^(3/2)/(e*x+d)^(3/2),x)","-\frac{2 \left(-e x +d \right) \left(-c \,e^{2} x^{2}+c \,d^{2}\right)^{\frac{3}{2}}}{5 \left(e x +d \right)^{\frac{3}{2}} e}"," ",0,"-2/5*(-e*x+d)*(-c*e^2*x^2+c*d^2)^(3/2)/e/(e*x+d)^(3/2)","A"
874,1,122,111,0.065000," ","int((-c*e^2*x^2+c*d^2)^(3/2)/(e*x+d)^(5/2),x)","-\frac{2 \sqrt{-\left(e^{2} x^{2}-d^{2}\right) c}\, \left(6 \sqrt{2}\, c \,d^{2} \arctanh \left(\frac{\sqrt{-\left(e x -d \right) c}\, \sqrt{2}}{2 \sqrt{c d}}\right)+\sqrt{c d}\, \sqrt{-\left(e x -d \right) c}\, e x -7 \sqrt{-\left(e x -d \right) c}\, \sqrt{c d}\, d \right) c}{3 \sqrt{e x +d}\, \sqrt{-\left(e x -d \right) c}\, \sqrt{c d}\, e}"," ",0,"-2/3*(-(e^2*x^2-d^2)*c)^(1/2)*c*(6*2^(1/2)*arctanh(1/2*(-(e*x-d)*c)^(1/2)*2^(1/2)/(c*d)^(1/2))*c*d^2+(c*d)^(1/2)*(-(e*x-d)*c)^(1/2)*e*x-7*(-(e*x-d)*c)^(1/2)*(c*d)^(1/2)*d)/(e*x+d)^(1/2)/(-(e*x-d)*c)^(1/2)/e/(c*d)^(1/2)","A"
875,1,154,110,0.074000," ","int((-c*e^2*x^2+c*d^2)^(3/2)/(e*x+d)^(7/2),x)","\frac{\sqrt{-\left(e^{2} x^{2}-d^{2}\right) c}\, \left(3 \sqrt{2}\, c d e x \arctanh \left(\frac{\sqrt{-\left(e x -d \right) c}\, \sqrt{2}}{2 \sqrt{c d}}\right)+3 \sqrt{2}\, c \,d^{2} \arctanh \left(\frac{\sqrt{-\left(e x -d \right) c}\, \sqrt{2}}{2 \sqrt{c d}}\right)-2 \sqrt{c d}\, \sqrt{-\left(e x -d \right) c}\, e x -4 \sqrt{-\left(e x -d \right) c}\, \sqrt{c d}\, d \right) c}{\left(e x +d \right)^{\frac{3}{2}} \sqrt{-\left(e x -d \right) c}\, \sqrt{c d}\, e}"," ",0,"(-(e^2*x^2-d^2)*c)^(1/2)*c*(3*2^(1/2)*arctanh(1/2*(-(e*x-d)*c)^(1/2)*2^(1/2)/(c*d)^(1/2))*x*c*d*e+3*2^(1/2)*arctanh(1/2*(-(e*x-d)*c)^(1/2)*2^(1/2)/(c*d)^(1/2))*c*d^2-2*(c*d)^(1/2)*(-(e*x-d)*c)^(1/2)*e*x-4*(-(e*x-d)*c)^(1/2)*(c*d)^(1/2)*d)/(e*x+d)^(3/2)/(-(e*x-d)*c)^(1/2)/e/(c*d)^(1/2)","A"
876,1,190,110,0.072000," ","int((-c*e^2*x^2+c*d^2)^(3/2)/(e*x+d)^(9/2),x)","-\frac{\sqrt{-\left(e^{2} x^{2}-d^{2}\right) c}\, \left(3 \sqrt{2}\, c \,e^{2} x^{2} \arctanh \left(\frac{\sqrt{-\left(e x -d \right) c}\, \sqrt{2}}{2 \sqrt{c d}}\right)+6 \sqrt{2}\, c d e x \arctanh \left(\frac{\sqrt{-\left(e x -d \right) c}\, \sqrt{2}}{2 \sqrt{c d}}\right)+3 \sqrt{2}\, c \,d^{2} \arctanh \left(\frac{\sqrt{-\left(e x -d \right) c}\, \sqrt{2}}{2 \sqrt{c d}}\right)-10 \sqrt{c d}\, \sqrt{-\left(e x -d \right) c}\, e x -2 \sqrt{-\left(e x -d \right) c}\, \sqrt{c d}\, d \right) c}{8 \left(e x +d \right)^{\frac{5}{2}} \sqrt{-\left(e x -d \right) c}\, \sqrt{c d}\, e}"," ",0,"-1/8*(-(e^2*x^2-d^2)*c)^(1/2)*c*(3*2^(1/2)*arctanh(1/2*(-(e*x-d)*c)^(1/2)*2^(1/2)/(c*d)^(1/2))*x^2*c*e^2+6*2^(1/2)*arctanh(1/2*(-(e*x-d)*c)^(1/2)*2^(1/2)/(c*d)^(1/2))*x*c*d*e+3*2^(1/2)*arctanh(1/2*(-(e*x-d)*c)^(1/2)*2^(1/2)/(c*d)^(1/2))*c*d^2-10*(c*d)^(1/2)*(-(e*x-d)*c)^(1/2)*e*x-2*(-(e*x-d)*c)^(1/2)*(c*d)^(1/2)*d)/(e*x+d)^(5/2)/(-(e*x-d)*c)^(1/2)/e/(c*d)^(1/2)","A"
877,1,259,143,0.066000," ","int((-c*e^2*x^2+c*d^2)^(3/2)/(e*x+d)^(11/2),x)","-\frac{\sqrt{-\left(e^{2} x^{2}-d^{2}\right) c}\, \left(3 \sqrt{2}\, c \,e^{3} x^{3} \arctanh \left(\frac{\sqrt{-\left(e x -d \right) c}\, \sqrt{2}}{2 \sqrt{c d}}\right)+9 \sqrt{2}\, c d \,e^{2} x^{2} \arctanh \left(\frac{\sqrt{-\left(e x -d \right) c}\, \sqrt{2}}{2 \sqrt{c d}}\right)+9 \sqrt{2}\, c \,d^{2} e x \arctanh \left(\frac{\sqrt{-\left(e x -d \right) c}\, \sqrt{2}}{2 \sqrt{c d}}\right)+3 \sqrt{2}\, c \,d^{3} \arctanh \left(\frac{\sqrt{-\left(e x -d \right) c}\, \sqrt{2}}{2 \sqrt{c d}}\right)+6 \sqrt{-\left(e x -d \right) c}\, \sqrt{c d}\, e^{2} x^{2}-44 \sqrt{-\left(e x -d \right) c}\, \sqrt{c d}\, d e x +14 \sqrt{-\left(e x -d \right) c}\, \sqrt{c d}\, d^{2}\right) c}{96 \left(e x +d \right)^{\frac{7}{2}} \sqrt{-\left(e x -d \right) c}\, \sqrt{c d}\, d e}"," ",0,"-1/96*(-(e^2*x^2-d^2)*c)^(1/2)*c*(3*2^(1/2)*arctanh(1/2*(-(e*x-d)*c)^(1/2)*2^(1/2)/(c*d)^(1/2))*x^3*c*e^3+9*2^(1/2)*arctanh(1/2*(-(e*x-d)*c)^(1/2)*2^(1/2)/(c*d)^(1/2))*x^2*c*d*e^2+9*2^(1/2)*arctanh(1/2*(-(e*x-d)*c)^(1/2)*2^(1/2)/(c*d)^(1/2))*x*c*d^2*e+3*2^(1/2)*arctanh(1/2*(-(e*x-d)*c)^(1/2)*2^(1/2)/(c*d)^(1/2))*c*d^3+6*x^2*e^2*(-(e*x-d)*c)^(1/2)*(c*d)^(1/2)-44*x*d*e*(-(e*x-d)*c)^(1/2)*(c*d)^(1/2)+14*(-(e*x-d)*c)^(1/2)*(c*d)^(1/2)*d^2)/(e*x+d)^(7/2)/(-(e*x-d)*c)^(1/2)/e/d/(c*d)^(1/2)","A"
878,1,325,176,0.075000," ","int((-c*e^2*x^2+c*d^2)^(3/2)/(e*x+d)^(13/2),x)","-\frac{\sqrt{-\left(e^{2} x^{2}-d^{2}\right) c}\, \left(3 \sqrt{2}\, c \,e^{4} x^{4} \arctanh \left(\frac{\sqrt{-\left(e x -d \right) c}\, \sqrt{2}}{2 \sqrt{c d}}\right)+12 \sqrt{2}\, c d \,e^{3} x^{3} \arctanh \left(\frac{\sqrt{-\left(e x -d \right) c}\, \sqrt{2}}{2 \sqrt{c d}}\right)+18 \sqrt{2}\, c \,d^{2} e^{2} x^{2} \arctanh \left(\frac{\sqrt{-\left(e x -d \right) c}\, \sqrt{2}}{2 \sqrt{c d}}\right)+12 \sqrt{2}\, c \,d^{3} e x \arctanh \left(\frac{\sqrt{-\left(e x -d \right) c}\, \sqrt{2}}{2 \sqrt{c d}}\right)+3 \sqrt{2}\, c \,d^{4} \arctanh \left(\frac{\sqrt{-\left(e x -d \right) c}\, \sqrt{2}}{2 \sqrt{c d}}\right)+6 \sqrt{c d}\, \sqrt{-\left(e x -d \right) c}\, e^{3} x^{3}+26 \sqrt{c d}\, \sqrt{-\left(e x -d \right) c}\, d \,e^{2} x^{2}-158 \sqrt{c d}\, \sqrt{-\left(e x -d \right) c}\, d^{2} e x +78 \sqrt{-\left(e x -d \right) c}\, \sqrt{c d}\, d^{3}\right) c}{512 \left(e x +d \right)^{\frac{9}{2}} \sqrt{-\left(e x -d \right) c}\, \sqrt{c d}\, d^{2} e}"," ",0,"-1/512*(-(e^2*x^2-d^2)*c)^(1/2)*c*(3*2^(1/2)*arctanh(1/2*(-(e*x-d)*c)^(1/2)*2^(1/2)/(c*d)^(1/2))*x^4*c*e^4+12*2^(1/2)*arctanh(1/2*(-(e*x-d)*c)^(1/2)*2^(1/2)/(c*d)^(1/2))*x^3*c*d*e^3+18*2^(1/2)*arctanh(1/2*(-(e*x-d)*c)^(1/2)*2^(1/2)/(c*d)^(1/2))*x^2*c*d^2*e^2+12*2^(1/2)*arctanh(1/2*(-(e*x-d)*c)^(1/2)*2^(1/2)/(c*d)^(1/2))*x*c*d^3*e+6*x^3*e^3*(c*d)^(1/2)*(-(e*x-d)*c)^(1/2)+3*2^(1/2)*arctanh(1/2*(-(e*x-d)*c)^(1/2)*2^(1/2)/(c*d)^(1/2))*c*d^4+26*x^2*d*e^2*(c*d)^(1/2)*(-(e*x-d)*c)^(1/2)-158*x*d^2*e*(c*d)^(1/2)*(-(e*x-d)*c)^(1/2)+78*(-(e*x-d)*c)^(1/2)*(c*d)^(1/2)*d^3)/(e*x+d)^(9/2)/(-(e*x-d)*c)^(1/2)/e/d^2/(c*d)^(1/2)","A"
879,1,66,136,0.042000," ","int((e*x+d)^(7/2)/(-c*e^2*x^2+c*d^2)^(1/2),x)","-\frac{2 \left(-e x +d \right) \left(5 e^{3} x^{3}+27 e^{2} x^{2} d +71 d^{2} x e +177 d^{3}\right) \sqrt{e x +d}}{35 \sqrt{-c \,e^{2} x^{2}+c \,d^{2}}\, e}"," ",0,"-2/35*(-e*x+d)*(5*e^3*x^3+27*d*e^2*x^2+71*d^2*e*x+177*d^3)*(e*x+d)^(1/2)/e/(-c*e^2*x^2+c*d^2)^(1/2)","A"
880,1,55,101,0.050000," ","int((e*x+d)^(5/2)/(-c*e^2*x^2+c*d^2)^(1/2),x)","-\frac{2 \left(-e x +d \right) \left(3 e^{2} x^{2}+14 d x e +43 d^{2}\right) \sqrt{e x +d}}{15 \sqrt{-c \,e^{2} x^{2}+c \,d^{2}}\, e}"," ",0,"-2/15*(-e*x+d)*(3*e^2*x^2+14*d*e*x+43*d^2)*(e*x+d)^(1/2)/e/(-c*e^2*x^2+c*d^2)^(1/2)","A"
881,1,43,66,0.046000," ","int((e*x+d)^(3/2)/(-c*e^2*x^2+c*d^2)^(1/2),x)","-\frac{2 \left(-e x +d \right) \left(e x +5 d \right) \sqrt{e x +d}}{3 \sqrt{-c \,e^{2} x^{2}+c \,d^{2}}\, e}"," ",0,"-2/3*(-e*x+d)*(e*x+5*d)*(e*x+d)^(1/2)/e/(-c*e^2*x^2+c*d^2)^(1/2)","A"
882,1,36,32,0.039000," ","int((e*x+d)^(1/2)/(-c*e^2*x^2+c*d^2)^(1/2),x)","-\frac{2 \left(-e x +d \right) \sqrt{e x +d}}{\sqrt{-c \,e^{2} x^{2}+c \,d^{2}}\, e}"," ",0,"-2*(-e*x+d)*(e*x+d)^(1/2)/e/(-c*e^2*x^2+c*d^2)^(1/2)","A"
883,1,74,50,0.061000," ","int(1/(e*x+d)^(1/2)/(-c*e^2*x^2+c*d^2)^(1/2),x)","-\frac{\sqrt{-\left(e^{2} x^{2}-d^{2}\right) c}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\left(e x -d \right) c}\, \sqrt{2}}{2 \sqrt{c d}}\right)}{\sqrt{e x +d}\, \sqrt{-\left(e x -d \right) c}\, \sqrt{c d}\, e}"," ",0,"-1/(e*x+d)^(1/2)*(-(e^2*x^2-d^2)*c)^(1/2)/(-(e*x-d)*c)^(1/2)/e*2^(1/2)/(c*d)^(1/2)*arctanh(1/2*(-(e*x-d)*c)^(1/2)*2^(1/2)/(c*d)^(1/2))","A"
884,1,133,86,0.066000," ","int(1/(e*x+d)^(3/2)/(-c*e^2*x^2+c*d^2)^(1/2),x)","-\frac{\sqrt{-\left(e^{2} x^{2}-d^{2}\right) c}\, \left(\sqrt{2}\, c e x \arctanh \left(\frac{\sqrt{-\left(e x -d \right) c}\, \sqrt{2}}{2 \sqrt{c d}}\right)+\sqrt{2}\, c d \arctanh \left(\frac{\sqrt{-\left(e x -d \right) c}\, \sqrt{2}}{2 \sqrt{c d}}\right)+2 \sqrt{-\left(e x -d \right) c}\, \sqrt{c d}\right)}{4 \left(e x +d \right)^{\frac{3}{2}} \sqrt{-\left(e x -d \right) c}\, \sqrt{c d}\, c d e}"," ",0,"-1/4/(e*x+d)^(3/2)*(-(e^2*x^2-d^2)*c)^(1/2)/c*(2^(1/2)*arctanh(1/2*(-(e*x-d)*c)^(1/2)*2^(1/2)/(c*d)^(1/2))*x*c*e+c*d*2^(1/2)*arctanh(1/2*(-(e*x-d)*c)^(1/2)*2^(1/2)/(c*d)^(1/2))+2*(-(e*x-d)*c)^(1/2)*(c*d)^(1/2))/(-(e*x-d)*c)^(1/2)/e/d/(c*d)^(1/2)","A"
885,1,195,121,0.065000," ","int(1/(e*x+d)^(5/2)/(-c*e^2*x^2+c*d^2)^(1/2),x)","-\frac{\sqrt{-\left(e^{2} x^{2}-d^{2}\right) c}\, \left(3 \sqrt{2}\, c \,e^{2} x^{2} \arctanh \left(\frac{\sqrt{-\left(e x -d \right) c}\, \sqrt{2}}{2 \sqrt{c d}}\right)+6 \sqrt{2}\, c d e x \arctanh \left(\frac{\sqrt{-\left(e x -d \right) c}\, \sqrt{2}}{2 \sqrt{c d}}\right)+3 \sqrt{2}\, c \,d^{2} \arctanh \left(\frac{\sqrt{-\left(e x -d \right) c}\, \sqrt{2}}{2 \sqrt{c d}}\right)+6 \sqrt{c d}\, \sqrt{-\left(e x -d \right) c}\, e x +14 \sqrt{-\left(e x -d \right) c}\, \sqrt{c d}\, d \right)}{32 \left(e x +d \right)^{\frac{5}{2}} \sqrt{-\left(e x -d \right) c}\, \sqrt{c d}\, c \,d^{2} e}"," ",0,"-1/32/(e*x+d)^(5/2)*(-(e^2*x^2-d^2)*c)^(1/2)/c*(3*2^(1/2)*arctanh(1/2*(-(e*x-d)*c)^(1/2)*2^(1/2)/(c*d)^(1/2))*x^2*c*e^2+6*2^(1/2)*arctanh(1/2*(-(e*x-d)*c)^(1/2)*2^(1/2)/(c*d)^(1/2))*x*c*d*e+3*2^(1/2)*arctanh(1/2*(-(e*x-d)*c)^(1/2)*2^(1/2)/(c*d)^(1/2))*c*d^2+6*(c*d)^(1/2)*(-(e*x-d)*c)^(1/2)*e*x+14*(-(e*x-d)*c)^(1/2)*(c*d)^(1/2)*d)/(-(e*x-d)*c)^(1/2)/e/d^2/(c*d)^(1/2)","A"
886,1,66,136,0.042000," ","int((e*x+d)^(9/2)/(-c*e^2*x^2+c*d^2)^(3/2),x)","\frac{2 \left(-e x +d \right) \left(-e^{3} x^{3}-7 e^{2} x^{2} d -43 d^{2} x e +91 d^{3}\right) \left(e x +d \right)^{\frac{3}{2}}}{5 \left(-c \,e^{2} x^{2}+c \,d^{2}\right)^{\frac{3}{2}} e}"," ",0,"2/5*(-e*x+d)*(-e^3*x^3-7*d*e^2*x^2-43*d^2*e*x+91*d^3)*(e*x+d)^(3/2)/e/(-c*e^2*x^2+c*d^2)^(3/2)","A"
887,1,55,101,0.049000," ","int((e*x+d)^(7/2)/(-c*e^2*x^2+c*d^2)^(3/2),x)","\frac{2 \left(-e x +d \right) \left(-e^{2} x^{2}-10 d x e +23 d^{2}\right) \left(e x +d \right)^{\frac{3}{2}}}{3 \left(-c \,e^{2} x^{2}+c \,d^{2}\right)^{\frac{3}{2}} e}"," ",0,"2/3*(-e*x+d)*(-e^2*x^2-10*d*e*x+23*d^2)*(e*x+d)^(3/2)/e/(-c*e^2*x^2+c*d^2)^(3/2)","A"
888,1,44,66,0.040000," ","int((e*x+d)^(5/2)/(-c*e^2*x^2+c*d^2)^(3/2),x)","\frac{2 \left(-e x +d \right) \left(-e x +3 d \right) \left(e x +d \right)^{\frac{3}{2}}}{\left(-c \,e^{2} x^{2}+c \,d^{2}\right)^{\frac{3}{2}} e}"," ",0,"2*(-e*x+d)*(-e*x+3*d)*(e*x+d)^(3/2)/e/(-c*e^2*x^2+c*d^2)^(3/2)","A"
889,1,36,32,0.049000," ","int((e*x+d)^(3/2)/(-c*e^2*x^2+c*d^2)^(3/2),x)","\frac{2 \left(-e x +d \right) \left(e x +d \right)^{\frac{3}{2}}}{\left(-c \,e^{2} x^{2}+c \,d^{2}\right)^{\frac{3}{2}} e}"," ",0,"2*(-e*x+d)*(e*x+d)^(3/2)/e/(-c*e^2*x^2+c*d^2)^(3/2)","A"
890,1,98,85,0.085000," ","int((e*x+d)^(1/2)/(-c*e^2*x^2+c*d^2)^(3/2),x)","\frac{\sqrt{-\left(e^{2} x^{2}-d^{2}\right) c}\, \left(\sqrt{2}\, \sqrt{-\left(e x -d \right) c}\, \arctanh \left(\frac{\sqrt{-\left(e x -d \right) c}\, \sqrt{2}}{2 \sqrt{c d}}\right)-2 \sqrt{c d}\right)}{2 \sqrt{e x +d}\, \left(e x -d \right) \sqrt{c d}\, c^{2} d e}"," ",0,"1/2/(e*x+d)^(1/2)*(-(e^2*x^2-d^2)*c)^(1/2)*(2^(1/2)*arctanh(1/2*(-(e*x-d)*c)^(1/2)*2^(1/2)/(c*d)^(1/2))*(-(e*x-d)*c)^(1/2)-2*(c*d)^(1/2))/c^2/(e*x-d)/e/d/(c*d)^(1/2)","A"
891,1,152,121,0.079000," ","int(1/(e*x+d)^(1/2)/(-c*e^2*x^2+c*d^2)^(3/2),x)","\frac{\sqrt{-\left(e^{2} x^{2}-d^{2}\right) c}\, \left(3 \sqrt{-\left(e x -d \right) c}\, \sqrt{2}\, e x \arctanh \left(\frac{\sqrt{-\left(e x -d \right) c}\, \sqrt{2}}{2 \sqrt{c d}}\right)+3 \sqrt{-\left(e x -d \right) c}\, \sqrt{2}\, d \arctanh \left(\frac{\sqrt{-\left(e x -d \right) c}\, \sqrt{2}}{2 \sqrt{c d}}\right)-6 \sqrt{c d}\, e x -2 \sqrt{c d}\, d \right)}{8 \left(e x +d \right)^{\frac{3}{2}} \left(e x -d \right) \sqrt{c d}\, c^{2} d^{2} e}"," ",0,"1/8/(e*x+d)^(3/2)*(-(e^2*x^2-d^2)*c)^(1/2)/c^2*(3*(-(e*x-d)*c)^(1/2)*2^(1/2)*arctanh(1/2*(-(e*x-d)*c)^(1/2)*2^(1/2)/(c*d)^(1/2))*x*e+3*(-(e*x-d)*c)^(1/2)*2^(1/2)*arctanh(1/2*(-(e*x-d)*c)^(1/2)*2^(1/2)/(c*d)^(1/2))*d-6*(c*d)^(1/2)*x*e-2*(c*d)^(1/2)*d)/(e*x-d)/e/d^2/(c*d)^(1/2)","A"
892,1,217,156,0.073000," ","int(1/(e*x+d)^(3/2)/(-c*e^2*x^2+c*d^2)^(3/2),x)","\frac{\sqrt{-\left(e^{2} x^{2}-d^{2}\right) c}\, \left(15 \sqrt{-\left(e x -d \right) c}\, \sqrt{2}\, e^{2} x^{2} \arctanh \left(\frac{\sqrt{-\left(e x -d \right) c}\, \sqrt{2}}{2 \sqrt{c d}}\right)+30 \sqrt{-\left(e x -d \right) c}\, \sqrt{2}\, d e x \arctanh \left(\frac{\sqrt{-\left(e x -d \right) c}\, \sqrt{2}}{2 \sqrt{c d}}\right)-30 \sqrt{c d}\, e^{2} x^{2}+15 \sqrt{-\left(e x -d \right) c}\, \sqrt{2}\, d^{2} \arctanh \left(\frac{\sqrt{-\left(e x -d \right) c}\, \sqrt{2}}{2 \sqrt{c d}}\right)-40 \sqrt{c d}\, d e x +6 \sqrt{c d}\, d^{2}\right)}{64 \left(e x +d \right)^{\frac{5}{2}} \left(e x -d \right) \sqrt{c d}\, c^{2} d^{3} e}"," ",0,"1/64/(e*x+d)^(5/2)*(-(e^2*x^2-d^2)*c)^(1/2)/c^2*(15*(-(e*x-d)*c)^(1/2)*2^(1/2)*arctanh(1/2*(-(e*x-d)*c)^(1/2)*2^(1/2)/(c*d)^(1/2))*x^2*e^2+30*(-(e*x-d)*c)^(1/2)*2^(1/2)*arctanh(1/2*(-(e*x-d)*c)^(1/2)*2^(1/2)/(c*d)^(1/2))*x*d*e+15*(-(e*x-d)*c)^(1/2)*2^(1/2)*arctanh(1/2*(-(e*x-d)*c)^(1/2)*2^(1/2)/(c*d)^(1/2))*d^2-30*(c*d)^(1/2)*x^2*e^2-40*(c*d)^(1/2)*x*d*e+6*(c*d)^(1/2)*d^2)/(e*x-d)/e/d^3/(c*d)^(1/2)","A"
893,1,39,24,0.056000," ","int(1/(x-1)^(1/2)/(-x^2+1)^(1/2),x)","\frac{\sqrt{-x^{2}+1}\, \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{-x -1}}{2}\right)}{\sqrt{x -1}\, \sqrt{-x -1}}"," ",0,"1/(x-1)^(1/2)*(-x^2+1)^(1/2)/(-1-x)^(1/2)*2^(1/2)*arctan(1/2*2^(1/2)*(-1-x)^(1/2))","A"
894,1,52,65,0.048000," ","int((e*x+2)^(5/2)*(-3*e^2*x^2+12)^(1/2),x)","\frac{2 \left(e x -2\right) \left(35 e^{3} x^{3}+330 e^{2} x^{2}+1284 e x +2552\right) \sqrt{-3 e^{2} x^{2}+12}}{315 \sqrt{e x +2}\, e}"," ",0,"2/315*(e*x-2)*(35*e^3*x^3+330*e^2*x^2+1284*e*x+2552)*(-3*e^2*x^2+12)^(1/2)/e/(e*x+2)^(1/2)","A"
895,1,44,49,0.049000," ","int((e*x+2)^(3/2)*(-3*e^2*x^2+12)^(1/2),x)","\frac{2 \left(e x -2\right) \left(15 e^{2} x^{2}+108 e x +284\right) \sqrt{-3 e^{2} x^{2}+12}}{105 \sqrt{e x +2}\, e}"," ",0,"2/105*(e*x-2)*(15*e^2*x^2+108*e*x+284)*(-3*e^2*x^2+12)^(1/2)/(e*x+2)^(1/2)/e","A"
896,1,36,33,0.049000," ","int((e*x+2)^(1/2)*(-3*e^2*x^2+12)^(1/2),x)","\frac{2 \left(e x -2\right) \left(3 e x +14\right) \sqrt{-3 e^{2} x^{2}+12}}{15 \sqrt{e x +2}\, e}"," ",0,"2/15*(e*x-2)*(3*e*x+14)*(-3*e^2*x^2+12)^(1/2)/e/(e*x+2)^(1/2)","A"
897,1,30,16,0.045000," ","int((-3*e^2*x^2+12)^(1/2)/(e*x+2)^(1/2),x)","\frac{2 \left(e x -2\right) \sqrt{-3 e^{2} x^{2}+12}}{3 \sqrt{e x +2}\, e}"," ",0,"2/3*(e*x-2)*(-3*e^2*x^2+12)^(1/2)/e/(e*x+2)^(1/2)","A"
898,1,66,36,0.074000," ","int((-3*e^2*x^2+12)^(1/2)/(e*x+2)^(3/2),x)","-\frac{2 \sqrt{-e^{2} x^{2}+4}\, \left(2 \sqrt{3}\, \arctanh \left(\frac{\sqrt{3}\, \sqrt{-3 e x +6}}{6}\right)-\sqrt{-3 e x +6}\right) \sqrt{3}}{\sqrt{e x +2}\, \sqrt{-3 e x +6}\, e}"," ",0,"-2*(-e^2*x^2+4)^(1/2)*(2*3^(1/2)*arctanh(1/6*3^(1/2)*(-3*e*x+6)^(1/2))-(-3*e*x+6)^(1/2))/(e*x+2)^(1/2)*3^(1/2)/(-3*e*x+6)^(1/2)/e","A"
899,1,88,43,0.100000," ","int((-3*e^2*x^2+12)^(1/2)/(e*x+2)^(5/2),x)","\frac{\sqrt{-e^{2} x^{2}+4}\, \left(\sqrt{3}\, e x \arctanh \left(\frac{\sqrt{3}\, \sqrt{-3 e x +6}}{6}\right)+2 \sqrt{3}\, \arctanh \left(\frac{\sqrt{3}\, \sqrt{-3 e x +6}}{6}\right)-2 \sqrt{-3 e x +6}\right) \sqrt{3}}{2 \sqrt{\left(e x +2\right)^{3}}\, \sqrt{-3 e x +6}\, e}"," ",0,"1/2*(-e^2*x^2+4)^(1/2)*(arctanh(1/6*3^(1/2)*(-3*e*x+6)^(1/2))*3^(1/2)*x*e+2*3^(1/2)*arctanh(1/6*3^(1/2)*(-3*e*x+6)^(1/2))-2*(-3*e*x+6)^(1/2))/((e*x+2)^3)^(1/2)*3^(1/2)/(-3*e*x+6)^(1/2)/e","B"
900,1,125,66,0.104000," ","int((-3*e^2*x^2+12)^(1/2)/(e*x+2)^(7/2),x)","\frac{\sqrt{-e^{2} x^{2}+4}\, \left(\sqrt{3}\, e^{2} x^{2} \arctanh \left(\frac{\sqrt{3}\, \sqrt{-3 e x +6}}{6}\right)+4 \sqrt{3}\, e x \arctanh \left(\frac{\sqrt{3}\, \sqrt{-3 e x +6}}{6}\right)+2 \sqrt{-3 e x +6}\, e x +4 \sqrt{3}\, \arctanh \left(\frac{\sqrt{3}\, \sqrt{-3 e x +6}}{6}\right)-12 \sqrt{-3 e x +6}\right) \sqrt{3}}{32 \sqrt{\left(e x +2\right)^{5}}\, \sqrt{-3 e x +6}\, e}"," ",0,"1/32*(-e^2*x^2+4)^(1/2)*(3^(1/2)*arctanh(1/6*3^(1/2)*(-3*e*x+6)^(1/2))*x^2*e^2+4*arctanh(1/6*3^(1/2)*(-3*e*x+6)^(1/2))*3^(1/2)*x*e+2*x*e*(-3*e*x+6)^(1/2)+4*3^(1/2)*arctanh(1/6*3^(1/2)*(-3*e*x+6)^(1/2))-12*(-3*e*x+6)^(1/2))*3^(1/2)/((e*x+2)^5)^(1/2)/(-3*e*x+6)^(1/2)/e","A"
901,1,60,81,0.042000," ","int((e*x+2)^(5/2)*(-3*e^2*x^2+12)^(3/2),x)","\frac{2 \left(e x -2\right) \left(1155 e^{4} x^{4}+12600 e^{3} x^{3}+56840 e^{2} x^{2}+133600 e x +154928\right) \left(-3 e^{2} x^{2}+12\right)^{\frac{3}{2}}}{15015 \left(e x +2\right)^{\frac{3}{2}} e}"," ",0,"2/15015*(e*x-2)*(1155*e^4*x^4+12600*e^3*x^3+56840*e^2*x^2+133600*e*x+154928)*(-3*e^2*x^2+12)^(3/2)/e/(e*x+2)^(3/2)","A"
902,1,52,65,0.040000," ","int((e*x+2)^(3/2)*(-3*e^2*x^2+12)^(3/2),x)","\frac{2 \left(e x -2\right) \left(105 e^{3} x^{3}+910 e^{2} x^{2}+3020 e x +4264\right) \left(-3 e^{2} x^{2}+12\right)^{\frac{3}{2}}}{1155 \left(e x +2\right)^{\frac{3}{2}} e}"," ",0,"2/1155*(e*x-2)*(105*e^3*x^3+910*e^2*x^2+3020*e*x+4264)*(-3*e^2*x^2+12)^(3/2)/e/(e*x+2)^(3/2)","A"
903,1,44,49,0.049000," ","int((e*x+2)^(1/2)*(-3*e^2*x^2+12)^(3/2),x)","\frac{2 \left(e x -2\right) \left(35 e^{2} x^{2}+220 e x +428\right) \left(-3 e^{2} x^{2}+12\right)^{\frac{3}{2}}}{315 \left(e x +2\right)^{\frac{3}{2}} e}"," ",0,"2/315*(e*x-2)*(35*e^2*x^2+220*e*x+428)*(-3*e^2*x^2+12)^(3/2)/e/(e*x+2)^(3/2)","A"
904,1,36,33,0.041000," ","int((-3*e^2*x^2+12)^(3/2)/(e*x+2)^(1/2),x)","\frac{2 \left(e x -2\right) \left(5 e x +18\right) \left(-3 e^{2} x^{2}+12\right)^{\frac{3}{2}}}{35 \left(e x +2\right)^{\frac{3}{2}} e}"," ",0,"2/35*(e*x-2)*(5*e*x+18)*(-3*e^2*x^2+12)^(3/2)/e/(e*x+2)^(3/2)","A"
905,1,30,16,0.039000," ","int((-3*e^2*x^2+12)^(3/2)/(e*x+2)^(3/2),x)","\frac{2 \left(e x -2\right) \left(-3 e^{2} x^{2}+12\right)^{\frac{3}{2}}}{5 \left(e x +2\right)^{\frac{3}{2}} e}"," ",0,"2/5*(e*x-2)*(-3*e^2*x^2+12)^(3/2)/e/(e*x+2)^(3/2)","A"
906,1,77,52,0.056000," ","int((-3*e^2*x^2+12)^(3/2)/(e*x+2)^(5/2),x)","-\frac{2 \sqrt{-e^{2} x^{2}+4}\, \left(\sqrt{-3 e x +6}\, e x +24 \sqrt{3}\, \arctanh \left(\frac{\sqrt{3}\, \sqrt{-3 e x +6}}{6}\right)-14 \sqrt{-3 e x +6}\right) \sqrt{3}}{\sqrt{e x +2}\, \sqrt{-3 e x +6}\, e}"," ",0,"-2*(-e^2*x^2+4)^(1/2)*((-3*e*x+6)^(1/2)*e*x+24*3^(1/2)*arctanh(1/6*3^(1/2)*(-3*e*x+6)^(1/2))-14*(-3*e*x+6)^(1/2))*3^(1/2)/(e*x+2)^(1/2)/(-3*e*x+6)^(1/2)/e","A"
907,1,101,59,0.059000," ","int((-3*e^2*x^2+12)^(3/2)/(e*x+2)^(7/2),x)","\frac{6 \sqrt{-e^{2} x^{2}+4}\, \left(3 \sqrt{3}\, e x \arctanh \left(\frac{\sqrt{3}\, \sqrt{-3 e x +6}}{6}\right)-\sqrt{-3 e x +6}\, e x +6 \sqrt{3}\, \arctanh \left(\frac{\sqrt{3}\, \sqrt{-3 e x +6}}{6}\right)-4 \sqrt{-3 e x +6}\right) \sqrt{3}}{\sqrt{\left(e x +2\right)^{3}}\, \sqrt{-3 e x +6}\, e}"," ",0,"6*(-e^2*x^2+4)^(1/2)*(3*arctanh(1/6*3^(1/2)*(-3*e*x+6)^(1/2))*3^(1/2)*x*e-(-3*e*x+6)^(1/2)*e*x+6*3^(1/2)*arctanh(1/6*3^(1/2)*(-3*e*x+6)^(1/2))-4*(-3*e*x+6)^(1/2))*3^(1/2)/((e*x+2)^3)^(1/2)/(-3*e*x+6)^(1/2)/e","A"
908,1,126,66,0.066000," ","int((-3*e^2*x^2+12)^(3/2)/(e*x+2)^(9/2),x)","-\frac{3 \sqrt{-e^{2} x^{2}+4}\, \left(3 \sqrt{3}\, e^{2} x^{2} \arctanh \left(\frac{\sqrt{3}\, \sqrt{-3 e x +6}}{6}\right)+12 \sqrt{3}\, e x \arctanh \left(\frac{\sqrt{3}\, \sqrt{-3 e x +6}}{6}\right)-10 \sqrt{-3 e x +6}\, e x +12 \sqrt{3}\, \arctanh \left(\frac{\sqrt{3}\, \sqrt{-3 e x +6}}{6}\right)-4 \sqrt{-3 e x +6}\right) \sqrt{3}}{8 \sqrt{\left(e x +2\right)^{5}}\, \sqrt{-3 e x +6}\, e}"," ",0,"-3/8*(-e^2*x^2+4)^(1/2)*(3*3^(1/2)*arctanh(1/6*3^(1/2)*(-3*e*x+6)^(1/2))*x^2*e^2+12*arctanh(1/6*3^(1/2)*(-3*e*x+6)^(1/2))*3^(1/2)*x*e-10*(-3*e*x+6)^(1/2)*e*x+12*3^(1/2)*arctanh(1/6*3^(1/2)*(-3*e*x+6)^(1/2))-4*(-3*e*x+6)^(1/2))*3^(1/2)/((e*x+2)^5)^(1/2)/(-3*e*x+6)^(1/2)/e","A"
909,1,167,89,0.097000," ","int((-3*e^2*x^2+12)^(3/2)/(e*x+2)^(11/2),x)","-\frac{\sqrt{-e^{2} x^{2}+4}\, \left(3 \sqrt{3}\, e^{3} x^{3} \arctanh \left(\frac{\sqrt{3}\, \sqrt{-3 e x +6}}{6}\right)+18 \sqrt{3}\, e^{2} x^{2} \arctanh \left(\frac{\sqrt{3}\, \sqrt{-3 e x +6}}{6}\right)+6 \sqrt{-3 e x +6}\, e^{2} x^{2}+36 \sqrt{3}\, e x \arctanh \left(\frac{\sqrt{3}\, \sqrt{-3 e x +6}}{6}\right)-88 \sqrt{-3 e x +6}\, e x +24 \sqrt{3}\, \arctanh \left(\frac{\sqrt{3}\, \sqrt{-3 e x +6}}{6}\right)+56 \sqrt{-3 e x +6}\right) \sqrt{3}}{64 \sqrt{\left(e x +2\right)^{7}}\, \sqrt{-3 e x +6}\, e}"," ",0,"-1/64*(-e^2*x^2+4)^(1/2)*(3*3^(1/2)*arctanh(1/6*3^(1/2)*(-3*e*x+6)^(1/2))*x^3*e^3+18*3^(1/2)*arctanh(1/6*3^(1/2)*(-3*e*x+6)^(1/2))*x^2*e^2+6*x^2*e^2*(-3*e*x+6)^(1/2)+36*arctanh(1/6*3^(1/2)*(-3*e*x+6)^(1/2))*3^(1/2)*x*e-88*(-3*e*x+6)^(1/2)*e*x+24*3^(1/2)*arctanh(1/6*3^(1/2)*(-3*e*x+6)^(1/2))+56*(-3*e*x+6)^(1/2))*3^(1/2)/((e*x+2)^7)^(1/2)/(-3*e*x+6)^(1/2)/e","A"
910,1,208,112,0.090000," ","int((-3*e^2*x^2+12)^(3/2)/(e*x+2)^(13/2),x)","-\frac{3 \sqrt{-e^{2} x^{2}+4}\, \left(3 \sqrt{3}\, e^{4} x^{4} \arctanh \left(\frac{\sqrt{3}\, \sqrt{-3 e x +6}}{6}\right)+24 \sqrt{3}\, e^{3} x^{3} \arctanh \left(\frac{\sqrt{3}\, \sqrt{-3 e x +6}}{6}\right)+6 \sqrt{-3 e x +6}\, e^{3} x^{3}+72 \sqrt{3}\, e^{2} x^{2} \arctanh \left(\frac{\sqrt{3}\, \sqrt{-3 e x +6}}{6}\right)+52 \sqrt{-3 e x +6}\, e^{2} x^{2}+96 \sqrt{3}\, e x \arctanh \left(\frac{\sqrt{3}\, \sqrt{-3 e x +6}}{6}\right)-632 \sqrt{-3 e x +6}\, e x +48 \sqrt{3}\, \arctanh \left(\frac{\sqrt{3}\, \sqrt{-3 e x +6}}{6}\right)+624 \sqrt{-3 e x +6}\right) \sqrt{3}}{2048 \sqrt{\left(e x +2\right)^{9}}\, \sqrt{-3 e x +6}\, e}"," ",0,"-3/2048*(-e^2*x^2+4)^(1/2)*(3*3^(1/2)*arctanh(1/6*3^(1/2)*(-3*e*x+6)^(1/2))*x^4*e^4+24*3^(1/2)*arctanh(1/6*3^(1/2)*(-3*e*x+6)^(1/2))*x^3*e^3+6*x^3*e^3*(-3*e*x+6)^(1/2)+72*3^(1/2)*arctanh(1/6*3^(1/2)*(-3*e*x+6)^(1/2))*x^2*e^2+52*(-3*e*x+6)^(1/2)*e^2*x^2+96*arctanh(1/6*3^(1/2)*(-3*e*x+6)^(1/2))*3^(1/2)*x*e-632*(-3*e*x+6)^(1/2)*e*x+48*3^(1/2)*arctanh(1/6*3^(1/2)*(-3*e*x+6)^(1/2))+624*(-3*e*x+6)^(1/2))*3^(1/2)/((e*x+2)^9)^(1/2)/(-3*e*x+6)^(1/2)/e","A"
911,1,52,65,0.050000," ","int((e*x+2)^(7/2)/(-3*e^2*x^2+12)^(1/2),x)","\frac{2 \left(e x -2\right) \left(5 e^{3} x^{3}+54 e^{2} x^{2}+284 e x +1416\right) \sqrt{e x +2}}{35 \sqrt{-3 e^{2} x^{2}+12}\, e}"," ",0,"2/35*(e*x-2)*(5*e^3*x^3+54*e^2*x^2+284*e*x+1416)*(e*x+2)^(1/2)/e/(-3*e^2*x^2+12)^(1/2)","A"
912,1,44,49,0.046000," ","int((e*x+2)^(5/2)/(-3*e^2*x^2+12)^(1/2),x)","\frac{2 \left(e x -2\right) \left(3 e^{2} x^{2}+28 e x +172\right) \sqrt{e x +2}}{15 \sqrt{-3 e^{2} x^{2}+12}\, e}"," ",0,"2/15*(e*x-2)*(3*e^2*x^2+28*e*x+172)*(e*x+2)^(1/2)/e/(-3*e^2*x^2+12)^(1/2)","A"
913,1,35,33,0.042000," ","int((e*x+2)^(3/2)/(-3*e^2*x^2+12)^(1/2),x)","\frac{2 \left(e x -2\right) \left(e x +10\right) \sqrt{e x +2}}{3 \sqrt{-3 e^{2} x^{2}+12}\, e}"," ",0,"2/3*(e*x-2)*(e*x+10)*(e*x+2)^(1/2)/e/(-3*e^2*x^2+12)^(1/2)","A"
914,1,30,16,0.043000," ","int((e*x+2)^(1/2)/(-3*e^2*x^2+12)^(1/2),x)","\frac{2 \left(e x -2\right) \sqrt{e x +2}}{\sqrt{-3 e^{2} x^{2}+12}\, e}"," ",0,"2*(e*x-2)*(e*x+2)^(1/2)/e/(-3*e^2*x^2+12)^(1/2)","A"
915,1,50,19,0.070000," ","int(1/(e*x+2)^(1/2)/(-3*e^2*x^2+12)^(1/2),x)","-\frac{\sqrt{-e^{2} x^{2}+4}\, \sqrt{3}\, \arctanh \left(\frac{\sqrt{3}\, \sqrt{-3 e x +6}}{6}\right)}{3 \sqrt{e x +2}\, \sqrt{-e x +2}\, e}"," ",0,"-1/3*(-e^2*x^2+4)^(1/2)*3^(1/2)*arctanh(1/6*3^(1/2)*(-3*e*x+6)^(1/2))/(e*x+2)^(1/2)/(-e*x+2)^(1/2)/e","B"
916,1,88,43,0.061000," ","int(1/(e*x+2)^(3/2)/(-3*e^2*x^2+12)^(1/2),x)","-\frac{\sqrt{-e^{2} x^{2}+4}\, \left(\sqrt{3}\, e x \arctanh \left(\frac{\sqrt{3}\, \sqrt{-3 e x +6}}{6}\right)+2 \sqrt{3}\, \arctanh \left(\frac{\sqrt{3}\, \sqrt{-3 e x +6}}{6}\right)+2 \sqrt{-3 e x +6}\right) \sqrt{3}}{24 \sqrt{\left(e x +2\right)^{3}}\, \sqrt{-3 e x +6}\, e}"," ",0,"-1/24*(-e^2*x^2+4)^(1/2)*(arctanh(1/6*3^(1/2)*(-3*e*x+6)^(1/2))*3^(1/2)*x*e+2*3^(1/2)*arctanh(1/6*3^(1/2)*(-3*e*x+6)^(1/2))+2*(-3*e*x+6)^(1/2))/((e*x+2)^3)^(1/2)*3^(1/2)/(-3*e*x+6)^(1/2)/e","B"
917,1,126,66,0.063000," ","int(1/(e*x+2)^(5/2)/(-3*e^2*x^2+12)^(1/2),x)","-\frac{\sqrt{-e^{2} x^{2}+4}\, \left(3 \sqrt{3}\, e^{2} x^{2} \arctanh \left(\frac{\sqrt{3}\, \sqrt{-3 e x +6}}{6}\right)+12 \sqrt{3}\, e x \arctanh \left(\frac{\sqrt{3}\, \sqrt{-3 e x +6}}{6}\right)+6 \sqrt{-3 e x +6}\, e x +12 \sqrt{3}\, \arctanh \left(\frac{\sqrt{3}\, \sqrt{-3 e x +6}}{6}\right)+28 \sqrt{-3 e x +6}\right) \sqrt{3}}{384 \sqrt{\left(e x +2\right)^{5}}\, \sqrt{-3 e x +6}\, e}"," ",0,"-1/384*(-e^2*x^2+4)^(1/2)*(3*3^(1/2)*arctanh(1/6*3^(1/2)*(-3*e*x+6)^(1/2))*x^2*e^2+12*arctanh(1/6*3^(1/2)*(-3*e*x+6)^(1/2))*3^(1/2)*x*e+6*(-3*e*x+6)^(1/2)*e*x+12*3^(1/2)*arctanh(1/6*3^(1/2)*(-3*e*x+6)^(1/2))+28*(-3*e*x+6)^(1/2))/((e*x+2)^5)^(1/2)*3^(1/2)/(-3*e*x+6)^(1/2)/e","A"
918,1,60,81,0.047000," ","int((e*x+2)^(11/2)/(-3*e^2*x^2+12)^(3/2),x)","\frac{2 \left(e x -2\right) \left(5 e^{4} x^{4}+72 e^{3} x^{3}+568 e^{2} x^{2}+5664 e x -23216\right) \left(e x +2\right)^{\frac{3}{2}}}{35 \left(-3 e^{2} x^{2}+12\right)^{\frac{3}{2}} e}"," ",0,"2/35*(e*x-2)*(5*e^4*x^4+72*e^3*x^3+568*e^2*x^2+5664*e*x-23216)*(e*x+2)^(3/2)/e/(-3*e^2*x^2+12)^(3/2)","A"
919,1,51,65,0.054000," ","int((e*x+2)^(9/2)/(-3*e^2*x^2+12)^(3/2),x)","\frac{2 \left(e x -2\right) \left(e^{3} x^{3}+14 e^{2} x^{2}+172 e x -728\right) \left(e x +2\right)^{\frac{3}{2}}}{5 \left(-3 e^{2} x^{2}+12\right)^{\frac{3}{2}} e}"," ",0,"2/5*(e*x-2)*(e^3*x^3+14*e^2*x^2+172*e*x-728)*(e*x+2)^(3/2)/e/(-3*e^2*x^2+12)^(3/2)","A"
920,1,43,49,0.055000," ","int((e*x+2)^(7/2)/(-3*e^2*x^2+12)^(3/2),x)","\frac{2 \left(e x -2\right) \left(e^{2} x^{2}+20 e x -92\right) \left(e x +2\right)^{\frac{3}{2}}}{3 \left(-3 e^{2} x^{2}+12\right)^{\frac{3}{2}} e}"," ",0,"2/3*(e*x-2)*(e^2*x^2+20*e*x-92)*(e*x+2)^(3/2)/e/(-3*e^2*x^2+12)^(3/2)","A"
921,1,35,33,0.052000," ","int((e*x+2)^(5/2)/(-3*e^2*x^2+12)^(3/2),x)","\frac{2 \left(e x -2\right) \left(e x -6\right) \left(e x +2\right)^{\frac{3}{2}}}{\left(-3 e^{2} x^{2}+12\right)^{\frac{3}{2}} e}"," ",0,"2*(e*x-2)*(e*x-6)*(e*x+2)^(3/2)/e/(-3*e^2*x^2+12)^(3/2)","A"
922,1,30,16,0.048000," ","int((e*x+2)^(3/2)/(-3*e^2*x^2+12)^(3/2),x)","-\frac{2 \left(e x -2\right) \left(e x +2\right)^{\frac{3}{2}}}{\left(-3 e^{2} x^{2}+12\right)^{\frac{3}{2}} e}"," ",0,"-2*(e*x-2)*(e*x+2)^(3/2)/e/(-3*e^2*x^2+12)^(3/2)","A"
923,1,60,36,0.064000," ","int((e*x+2)^(1/2)/(-3*e^2*x^2+12)^(3/2),x)","\frac{\sqrt{-3 e^{2} x^{2}+12}\, \left(\sqrt{3}\, \sqrt{-3 e x +6}\, \arctanh \left(\frac{\sqrt{3}\, \sqrt{-3 e x +6}}{6}\right)-6\right)}{108 \sqrt{e x +2}\, \left(e x -2\right) e}"," ",0,"1/108/(e*x+2)^(1/2)*(-3*e^2*x^2+12)^(1/2)*(3^(1/2)*arctanh(1/6*3^(1/2)*(-3*e*x+6)^(1/2))*(-3*e*x+6)^(1/2)-6)/(e*x-2)/e","A"
924,1,93,59,0.068000," ","int(1/(e*x+2)^(1/2)/(-3*e^2*x^2+12)^(3/2),x)","\frac{\sqrt{-3 e^{2} x^{2}+12}\, \left(\sqrt{3}\, \sqrt{-3 e x +6}\, e x \arctanh \left(\frac{\sqrt{3}\, \sqrt{-3 e x +6}}{6}\right)-6 e x +2 \sqrt{3}\, \sqrt{-3 e x +6}\, \arctanh \left(\frac{\sqrt{3}\, \sqrt{-3 e x +6}}{6}\right)-4\right)}{288 \left(e x +2\right)^{\frac{3}{2}} \left(e x -2\right) e}"," ",0,"1/288/(e*x+2)^(3/2)*(-3*e^2*x^2+12)^(1/2)*(3^(1/2)*(-3*e*x+6)^(1/2)*arctanh(1/6*3^(1/2)*(-3*e*x+6)^(1/2))*x*e+2*3^(1/2)*arctanh(1/6*3^(1/2)*(-3*e*x+6)^(1/2))*(-3*e*x+6)^(1/2)-6*e*x-4)/(e*x-2)/e","A"
925,1,135,82,0.068000," ","int(1/(e*x+2)^(3/2)/(-3*e^2*x^2+12)^(3/2),x)","\frac{\sqrt{-3 e^{2} x^{2}+12}\, \left(5 \sqrt{3}\, \sqrt{-3 e x +6}\, e^{2} x^{2} \arctanh \left(\frac{\sqrt{3}\, \sqrt{-3 e x +6}}{6}\right)-30 e^{2} x^{2}+20 \sqrt{3}\, \sqrt{-3 e x +6}\, e x \arctanh \left(\frac{\sqrt{3}\, \sqrt{-3 e x +6}}{6}\right)-80 e x +20 \sqrt{3}\, \sqrt{-3 e x +6}\, \arctanh \left(\frac{\sqrt{3}\, \sqrt{-3 e x +6}}{6}\right)+24\right)}{4608 \left(e x +2\right)^{\frac{5}{2}} \left(e x -2\right) e}"," ",0,"1/4608/(e*x+2)^(5/2)*(-3*e^2*x^2+12)^(1/2)*(5*3^(1/2)*(-3*e*x+6)^(1/2)*arctanh(1/6*3^(1/2)*(-3*e*x+6)^(1/2))*x^2*e^2+20*3^(1/2)*(-3*e*x+6)^(1/2)*arctanh(1/6*3^(1/2)*(-3*e*x+6)^(1/2))*x*e-30*e^2*x^2+20*3^(1/2)*arctanh(1/6*3^(1/2)*(-3*e*x+6)^(1/2))*(-3*e*x+6)^(1/2)-80*e*x+24)/(e*x-2)/e","A"
926,1,19,18,0.046000," ","int(1/(x+1)/(-x+1)^(1/2),x)","-\sqrt{2}\, \arctanh \left(\frac{\sqrt{-x +1}\, \sqrt{2}}{2}\right)"," ",0,"-arctanh(1/2*(-x+1)^(1/2)*2^(1/2))*2^(1/2)","A"
927,1,40,18,0.059000," ","int(1/(x+1)^(1/2)/(-x^2+1)^(1/2),x)","-\frac{\sqrt{-x^{2}+1}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{-x +1}\, \sqrt{2}}{2}\right)}{\sqrt{x +1}\, \sqrt{-x +1}}"," ",0,"-1/(x+1)^(1/2)*(-x^2+1)^(1/2)/(-x+1)^(1/2)*2^(1/2)*arctanh(1/2*(-x+1)^(1/2)*2^(1/2))","B"
928,1,23,22,0.052000," ","int(1/(a*x+1)/(-a*x+1)^(1/2),x)","-\frac{\sqrt{2}\, \arctanh \left(\frac{\sqrt{-a x +1}\, \sqrt{2}}{2}\right)}{a}"," ",0,"-arctanh(1/2*(-a*x+1)^(1/2)*2^(1/2))*2^(1/2)/a","A"
929,1,50,22,0.089000," ","int(1/(a*x+1)^(1/2)/(-a^2*x^2+1)^(1/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a x +1}\, \sqrt{2}}{2}\right)}{\sqrt{a x +1}\, \sqrt{-a x +1}\, a}"," ",0,"-1/(a*x+1)^(1/2)*(-a^2*x^2+1)^(1/2)/(-a*x+1)^(1/2)/a*2^(1/2)*arctanh(1/2*(-a*x+1)^(1/2)*2^(1/2))","B"
930,0,0,222,0.150000," ","int((e*x+2)^(1/2)*(-3*e^2*x^2+12)^(1/4),x)","\int \sqrt{e x +2}\, \left(-3 e^{2} x^{2}+12\right)^{\frac{1}{4}}\, dx"," ",0,"int((e*x+2)^(1/2)*(-3*e^2*x^2+12)^(1/4),x)","F"
931,0,0,198,0.112000," ","int((-3*e^2*x^2+12)^(1/4)/(e*x+2)^(1/2),x)","\int \frac{\left(-3 e^{2} x^{2}+12\right)^{\frac{1}{4}}}{\sqrt{e x +2}}\, dx"," ",0,"int((-3*e^2*x^2+12)^(1/4)/(e*x+2)^(1/2),x)","F"
932,0,0,197,0.816000," ","int((-3*e^2*x^2+12)^(1/4)/(e*x+2)^(3/2),x)","\int \frac{\left(-3 e^{2} x^{2}+12\right)^{\frac{1}{4}}}{\left(e x +2\right)^{\frac{3}{2}}}\, dx"," ",0,"int((-3*e^2*x^2+12)^(1/4)/(e*x+2)^(3/2),x)","F"
933,1,30,27,0.049000," ","int((-3*e^2*x^2+12)^(1/4)/(e*x+2)^(5/2),x)","\frac{\left(e x -2\right) \left(-3 e^{2} x^{2}+12\right)^{\frac{1}{4}}}{5 \left(e x +2\right)^{\frac{3}{2}} e}"," ",0,"1/5*(e*x-2)/(e*x+2)^(3/2)/e*(-3*e^2*x^2+12)^(1/4)","A"
934,1,35,55,0.058000," ","int((-3*e^2*x^2+12)^(1/4)/(e*x+2)^(7/2),x)","\frac{\left(e x -2\right) \left(e x +7\right) \left(-3 e^{2} x^{2}+12\right)^{\frac{1}{4}}}{45 \left(e x +2\right)^{\frac{5}{2}} e}"," ",0,"1/45*(e*x-2)*(e*x+7)*(-3*e^2*x^2+12)^(1/4)/(e*x+2)^(5/2)/e","A"
935,1,44,82,0.047000," ","int((-3*e^2*x^2+12)^(1/4)/(e*x+2)^(9/2),x)","\frac{\left(e x -2\right) \left(2 e^{2} x^{2}+18 e x +73\right) \left(-3 e^{2} x^{2}+12\right)^{\frac{1}{4}}}{585 \left(e x +2\right)^{\frac{7}{2}} e}"," ",0,"1/585*(e*x-2)*(2*e^2*x^2+18*e*x+73)*(-3*e^2*x^2+12)^(1/4)/(e*x+2)^(7/2)/e","A"
936,1,52,109,0.047000," ","int((-3*e^2*x^2+12)^(1/4)/(e*x+2)^(11/2),x)","\frac{\left(e x -2\right) \left(2 e^{3} x^{3}+22 e^{2} x^{2}+109 e x +341\right) \left(-3 e^{2} x^{2}+12\right)^{\frac{1}{4}}}{3315 \left(e x +2\right)^{\frac{9}{2}} e}"," ",0,"1/3315*(e*x-2)*(2*e^3*x^3+22*e^2*x^2+109*e*x+341)*(-3*e^2*x^2+12)^(1/4)/(e*x+2)^(9/2)/e","A"
937,0,0,245,0.171000," ","int((e*x+2)^(5/2)/(-3*e^2*x^2+12)^(1/4),x)","\int \frac{\left(e x +2\right)^{\frac{5}{2}}}{\left(-3 e^{2} x^{2}+12\right)^{\frac{1}{4}}}\, dx"," ",0,"int((e*x+2)^(5/2)/(-3*e^2*x^2+12)^(1/4),x)","F"
938,0,0,222,0.116000," ","int((e*x+2)^(3/2)/(-3*e^2*x^2+12)^(1/4),x)","\int \frac{\left(e x +2\right)^{\frac{3}{2}}}{\left(-3 e^{2} x^{2}+12\right)^{\frac{1}{4}}}\, dx"," ",0,"int((e*x+2)^(3/2)/(-3*e^2*x^2+12)^(1/4),x)","F"
939,0,0,199,0.124000," ","int((e*x+2)^(1/2)/(-3*e^2*x^2+12)^(1/4),x)","\int \frac{\sqrt{e x +2}}{\left(-3 e^{2} x^{2}+12\right)^{\frac{1}{4}}}\, dx"," ",0,"int((e*x+2)^(1/2)/(-3*e^2*x^2+12)^(1/4),x)","F"
940,0,0,176,0.797000," ","int(1/(e*x+2)^(1/2)/(-3*e^2*x^2+12)^(1/4),x)","\int \frac{1}{\sqrt{e x +2}\, \left(-3 e^{2} x^{2}+12\right)^{\frac{1}{4}}}\, dx"," ",0,"int(1/(e*x+2)^(1/2)/(-3*e^2*x^2+12)^(1/4),x)","F"
941,1,30,27,0.051000," ","int(1/(e*x+2)^(3/2)/(-3*e^2*x^2+12)^(1/4),x)","\frac{e x -2}{3 \sqrt{e x +2}\, \left(-3 e^{2} x^{2}+12\right)^{\frac{1}{4}} e}"," ",0,"1/3*(e*x-2)/(e*x+2)^(1/2)/e/(-3*e^2*x^2+12)^(1/4)","A"
942,1,35,55,0.055000," ","int(1/(e*x+2)^(5/2)/(-3*e^2*x^2+12)^(1/4),x)","\frac{\left(e x -2\right) \left(e x +5\right)}{21 \left(e x +2\right)^{\frac{3}{2}} \left(-3 e^{2} x^{2}+12\right)^{\frac{1}{4}} e}"," ",0,"1/21*(e*x-2)*(e*x+5)/(e*x+2)^(3/2)/e/(-3*e^2*x^2+12)^(1/4)","A"
943,1,44,82,0.050000," ","int(1/(e*x+2)^(7/2)/(-3*e^2*x^2+12)^(1/4),x)","\frac{\left(e x -2\right) \left(2 e^{2} x^{2}+14 e x +41\right)}{231 \left(e x +2\right)^{\frac{5}{2}} \left(-3 e^{2} x^{2}+12\right)^{\frac{1}{4}} e}"," ",0,"1/231*(e*x-2)*(2*e^2*x^2+14*e*x+41)/(e*x+2)^(5/2)/e/(-3*e^2*x^2+12)^(1/4)","A"
944,1,52,109,0.061000," ","int(1/(e*x+2)^(9/2)/(-3*e^2*x^2+12)^(1/4),x)","\frac{\left(e x -2\right) \left(2 e^{3} x^{3}+18 e^{2} x^{2}+69 e x +159\right)}{1155 \left(e x +2\right)^{\frac{7}{2}} \left(-3 e^{2} x^{2}+12\right)^{\frac{1}{4}} e}"," ",0,"1/1155*(e*x-2)*(2*e^3*x^3+18*e^2*x^2+69*e*x+159)/(e*x+2)^(7/2)/e/(-3*e^2*x^2+12)^(1/4)","A"
945,1,178,84,0.058000," ","int((b*x+a)^m*(-b^2*x^2+a^2)^3,x)","\frac{\left(-b^{3} m^{3} x^{3}+3 a \,b^{2} m^{3} x^{2}-15 b^{3} m^{2} x^{3}-3 a^{2} b \,m^{3} x +51 a \,b^{2} m^{2} x^{2}-74 b^{3} m \,x^{3}+a^{3} m^{3}-57 a^{2} b \,m^{2} x +276 a \,b^{2} m \,x^{2}-120 b^{3} x^{3}+21 a^{3} m^{2}-354 a^{2} b m x +480 a \,b^{2} x^{2}+152 a^{3} m -696 a^{2} b x +384 a^{3}\right) \left(b x +a \right)^{m +4}}{\left(m^{4}+22 m^{3}+179 m^{2}+638 m +840\right) b}"," ",0,"(b*x+a)^(m+4)*(-b^3*m^3*x^3+3*a*b^2*m^3*x^2-15*b^3*m^2*x^3-3*a^2*b*m^3*x+51*a*b^2*m^2*x^2-74*b^3*m*x^3+a^3*m^3-57*a^2*b*m^2*x+276*a*b^2*m*x^2-120*b^3*x^3+21*a^3*m^2-354*a^2*b*m*x+480*a*b^2*x^2+152*a^3*m-696*a^2*b*x+384*a^3)/b/(m^4+22*m^3+179*m^2+638*m+840)","B"
946,1,94,61,0.056000," ","int((b*x+a)^m*(-b^2*x^2+a^2)^2,x)","\frac{\left(b^{2} m^{2} x^{2}-2 a b \,m^{2} x +7 b^{2} m \,x^{2}+a^{2} m^{2}-18 a b m x +12 b^{2} x^{2}+11 a^{2} m -36 a b x +32 a^{2}\right) \left(b x +a \right)^{m +3}}{\left(m^{3}+12 m^{2}+47 m +60\right) b}"," ",0,"(b*x+a)^(m+3)*(b^2*m^2*x^2-2*a*b*m^2*x+7*b^2*m*x^2+a^2*m^2-18*a*b*m*x+12*b^2*x^2+11*a^2*m-36*a*b*x+32*a^2)/b/(m^3+12*m^2+47*m+60)","A"
947,1,40,40,0.053000," ","int((b*x+a)^m*(-b^2*x^2+a^2),x)","\frac{\left(-b m x +a m -2 b x +4 a \right) \left(b x +a \right)^{m +2}}{\left(m^{2}+5 m +6\right) b}"," ",0,"(b*x+a)^(m+2)*(-b*m*x+a*m-2*b*x+4*a)/b/(m^2+5*m+6)","A"
948,0,0,36,0.793000," ","int((b*x+a)^m/(-b^2*x^2+a^2),x)","\int \frac{\left(b x +a \right)^{m}}{-b^{2} x^{2}+a^{2}}\, dx"," ",0,"int((b*x+a)^m/(-b^2*x^2+a^2),x)","F"
949,0,0,42,0.786000," ","int((b*x+a)^m/(-b^2*x^2+a^2)^2,x)","\int \frac{\left(b x +a \right)^{m}}{\left(-b^{2} x^{2}+a^{2}\right)^{2}}\, dx"," ",0,"int((b*x+a)^m/(-b^2*x^2+a^2)^2,x)","F"
950,0,0,44,0.814000," ","int((b*x+a)^m/(-b^2*x^2+a^2)^3,x)","\int \frac{\left(b x +a \right)^{m}}{\left(-b^{2} x^{2}+a^{2}\right)^{3}}\, dx"," ",0,"int((b*x+a)^m/(-b^2*x^2+a^2)^3,x)","F"
951,0,0,55,0.800000," ","int((e*x+d)^m*(-e^2*x^2+d^2)^(7/2),x)","\int \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} \left(e x +d \right)^{m}\, dx"," ",0,"int((e*x+d)^m*(-e^2*x^2+d^2)^(7/2),x)","F"
952,0,0,69,0.785000," ","int((e*x+d)^m*(-e^2*x^2+d^2)^(5/2),x)","\int \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} \left(e x +d \right)^{m}\, dx"," ",0,"int((e*x+d)^m*(-e^2*x^2+d^2)^(5/2),x)","F"
953,0,0,55,0.755000," ","int((e*x+d)^m*(-e^2*x^2+d^2)^(3/2),x)","\int \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} \left(e x +d \right)^{m}\, dx"," ",0,"int((e*x+d)^m*(-e^2*x^2+d^2)^(3/2),x)","F"
954,0,0,63,0.797000," ","int((e*x+d)^m*(-e^2*x^2+d^2)^(1/2),x)","\int \sqrt{-e^{2} x^{2}+d^{2}}\, \left(e x +d \right)^{m}\, dx"," ",0,"int((e*x+d)^m*(-e^2*x^2+d^2)^(1/2),x)","F"
955,0,0,63,0.794000," ","int((e*x+d)^m/(-e^2*x^2+d^2)^(1/2),x)","\int \frac{\left(e x +d \right)^{m}}{\sqrt{-e^{2} x^{2}+d^{2}}}\, dx"," ",0,"int((e*x+d)^m/(-e^2*x^2+d^2)^(1/2),x)","F"
956,0,0,68,0.802000," ","int((e*x+d)^m/(-e^2*x^2+d^2)^(3/2),x)","\int \frac{\left(e x +d \right)^{m}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"int((e*x+d)^m/(-e^2*x^2+d^2)^(3/2),x)","F"
957,0,0,56,0.786000," ","int((e*x+d)^m/(-e^2*x^2+d^2)^(5/2),x)","\int \frac{\left(e x +d \right)^{m}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"int((e*x+d)^m/(-e^2*x^2+d^2)^(5/2),x)","F"
958,0,0,64,0.806000," ","int((e*x+d)^m/(-e^2*x^2+d^2)^(7/2),x)","\int \frac{\left(e x +d \right)^{m}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}}}\, dx"," ",0,"int((e*x+d)^m/(-e^2*x^2+d^2)^(7/2),x)","F"
959,0,0,61,0.825000," ","int((b*x+a)^m*(-b^2*x^2+a^2)^p,x)","\int \left(b x +a \right)^{m} \left(-b^{2} x^{2}+a^{2}\right)^{p}\, dx"," ",0,"int((b*x+a)^m*(-b^2*x^2+a^2)^p,x)","F"
960,1,104,57,0.819000," ","int((e*x+d)^3*(1-e^2*x^2/d^2)^p,x)","\frac{e^{3} x^{4} \hypergeom \left(\left[2, -p \right], \left[3\right], \frac{e^{2} x^{2}}{d^{2}}\right)}{4}+d \,e^{2} x^{3} \hypergeom \left(\left[\frac{3}{2}, -p \right], \left[\frac{5}{2}\right], \frac{e^{2} x^{2}}{d^{2}}\right)+\frac{3 d^{2} e \,x^{2} \hypergeom \left(\left[1, -p \right], \left[2\right], \frac{e^{2} x^{2}}{d^{2}}\right)}{2}+d^{3} x \hypergeom \left(\left[\frac{1}{2}, -p \right], \left[\frac{3}{2}\right], \frac{e^{2} x^{2}}{d^{2}}\right)"," ",0,"1/4*e^3*x^4*hypergeom([2,-p],[3],e^2*x^2/d^2)+d*e^2*x^3*hypergeom([3/2,-p],[5/2],e^2*x^2/d^2)+3/2*e*d^2*x^2*hypergeom([1,-p],[2],e^2*x^2/d^2)+d^3*x*hypergeom([1/2,-p],[3/2],e^2*x^2/d^2)","A"
961,1,75,57,0.739000," ","int((e*x+d)^2*(1-1/d^2*e^2*x^2)^p,x)","\frac{e^{2} x^{3} \hypergeom \left(\left[\frac{3}{2}, -p \right], \left[\frac{5}{2}\right], \frac{e^{2} x^{2}}{d^{2}}\right)}{3}+d e \,x^{2} \hypergeom \left(\left[1, -p \right], \left[2\right], \frac{e^{2} x^{2}}{d^{2}}\right)+d^{2} x \hypergeom \left(\left[\frac{1}{2}, -p \right], \left[\frac{3}{2}\right], \frac{e^{2} x^{2}}{d^{2}}\right)"," ",0,"1/3*e^2*x^3*hypergeom([3/2,-p],[5/2],1/d^2*e^2*x^2)+e*d*x^2*hypergeom([1,-p],[2],1/d^2*e^2*x^2)+d^2*x*hypergeom([1/2,-p],[3/2],1/d^2*e^2*x^2)","A"
962,1,47,57,0.600000," ","int((e*x+d)*(1-1/d^2*e^2*x^2)^p,x)","\frac{e \,x^{2} \hypergeom \left(\left[1, -p \right], \left[2\right], \frac{e^{2} x^{2}}{d^{2}}\right)}{2}+d x \hypergeom \left(\left[\frac{1}{2}, -p \right], \left[\frac{3}{2}\right], \frac{e^{2} x^{2}}{d^{2}}\right)"," ",0,"1/2*e*x^2*hypergeom([1,-p],[2],1/d^2*e^2*x^2)+d*x*hypergeom([1/2,-p],[3/2],1/d^2*e^2*x^2)","A"
963,1,21,20,0.569000," ","int((1-1/d^2*e^2*x^2)^p,x)","x \hypergeom \left(\left[\frac{1}{2}, -p \right], \left[\frac{3}{2}\right], \frac{e^{2} x^{2}}{d^{2}}\right)"," ",0,"x*hypergeom([1/2,-p],[3/2],1/d^2*e^2*x^2)","A"
964,0,0,41,0.822000," ","int((1-1/d^2*e^2*x^2)^p/(e*x+d),x)","\int \frac{\left(-\frac{e^{2} x^{2}}{d^{2}}+1\right)^{p}}{e x +d}\, dx"," ",0,"int((1-1/d^2*e^2*x^2)^p/(e*x+d),x)","F"
965,0,0,57,0.771000," ","int((-1/d^2*e^2*x^2+1)^p/(e*x+d)^2,x)","\int \frac{\left(-\frac{e^{2} x^{2}}{d^{2}}+1\right)^{p}}{\left(e x +d \right)^{2}}\, dx"," ",0,"int((-1/d^2*e^2*x^2+1)^p/(e*x+d)^2,x)","F"
966,0,0,57,0.831000," ","int((-1/d^2*e^2*x^2+1)^p/(e*x+d)^3,x)","\int \frac{\left(-\frac{e^{2} x^{2}}{d^{2}}+1\right)^{p}}{\left(e x +d \right)^{3}}\, dx"," ",0,"int((-1/d^2*e^2*x^2+1)^p/(e*x+d)^3,x)","F"
967,0,0,58,0.801000," ","int((b*x+a)^3*(-b^2*x^2+a^2)^p,x)","\int \left(b x +a \right)^{3} \left(-b^{2} x^{2}+a^{2}\right)^{p}\, dx"," ",0,"int((b*x+a)^3*(-b^2*x^2+a^2)^p,x)","F"
968,0,0,58,0.757000," ","int((b*x+a)^2*(-b^2*x^2+a^2)^p,x)","\int \left(b x +a \right)^{2} \left(-b^{2} x^{2}+a^{2}\right)^{p}\, dx"," ",0,"int((b*x+a)^2*(-b^2*x^2+a^2)^p,x)","F"
969,0,0,79,0.661000," ","int((b*x+a)*(-b^2*x^2+a^2)^p,x)","\int \left(b x +a \right) \left(-b^{2} x^{2}+a^{2}\right)^{p}\, dx"," ",0,"int((b*x+a)*(-b^2*x^2+a^2)^p,x)","F"
970,0,0,53,0.773000," ","int((-b^2*x^2+a^2)^p/(b*x+a),x)","\int \frac{\left(-b^{2} x^{2}+a^{2}\right)^{p}}{b x +a}\, dx"," ",0,"int((-b^2*x^2+a^2)^p/(b*x+a),x)","F"
971,0,0,56,0.802000," ","int((-b^2*x^2+a^2)^p/(b*x+a)^2,x)","\int \frac{\left(-b^{2} x^{2}+a^{2}\right)^{p}}{\left(b x +a \right)^{2}}\, dx"," ",0,"int((-b^2*x^2+a^2)^p/(b*x+a)^2,x)","F"
972,0,0,60,0.798000," ","int((-b^2*x^2+a^2)^p/(b*x+a)^3,x)","\int \frac{\left(-b^{2} x^{2}+a^{2}\right)^{p}}{\left(b x +a \right)^{3}}\, dx"," ",0,"int((-b^2*x^2+a^2)^p/(b*x+a)^3,x)","F"
973,0,0,77,0.792000," ","int((b*x+a)^(3/2)*(-b^2*x^2+a^2)^p,x)","\int \left(b x +a \right)^{\frac{3}{2}} \left(-b^{2} x^{2}+a^{2}\right)^{p}\, dx"," ",0,"int((b*x+a)^(3/2)*(-b^2*x^2+a^2)^p,x)","F"
974,0,0,80,0.799000," ","int((b*x+a)^(1/2)*(-b^2*x^2+a^2)^p,x)","\int \sqrt{b x +a}\, \left(-b^{2} x^{2}+a^{2}\right)^{p}\, dx"," ",0,"int((b*x+a)^(1/2)*(-b^2*x^2+a^2)^p,x)","F"
975,0,0,80,0.803000," ","int((-b^2*x^2+a^2)^p/(b*x+a)^(1/2),x)","\int \frac{\left(-b^{2} x^{2}+a^{2}\right)^{p}}{\sqrt{b x +a}}\, dx"," ",0,"int((-b^2*x^2+a^2)^p/(b*x+a)^(1/2),x)","F"
976,0,0,80,0.812000," ","int((-b^2*x^2+a^2)^p/(b*x+a)^(3/2),x)","\int \frac{\left(-b^{2} x^{2}+a^{2}\right)^{p}}{\left(b x +a \right)^{\frac{3}{2}}}\, dx"," ",0,"int((-b^2*x^2+a^2)^p/(b*x+a)^(3/2),x)","F"
977,1,36,26,0.047000," ","int(-a*(-b^2*x^2+a^2)^p+(b*x+a)*(-b^2*x^2+a^2)^p,x)","-\frac{\left(-b x +a \right) \left(b x +a \right) \left(-b^{2} x^{2}+a^{2}\right)^{p}}{2 \left(p +1\right) b}"," ",0,"-1/2*(-b*x+a)*(b*x+a)*(-b^2*x^2+a^2)^p/b/(p+1)","A"
978,1,48,13,0.043000," ","int((e*x+d)^2*(c*e^2*x^2+2*c*d*e*x+c*d^2),x)","\frac{1}{5} c \,e^{4} x^{5}+c d \,e^{3} x^{4}+2 c \,d^{2} e^{2} x^{3}+2 c \,d^{3} e \,x^{2}+c \,d^{4} x"," ",0,"1/5*e^4*c*x^5+c*d*e^3*x^4+2*d^2*c*e^2*x^3+2*c*d^3*e*x^2+c*d^4*x","B"
979,1,36,13,0.191000," ","int((e*x+d)*(c*e^2*x^2+2*c*d*e*x+c*d^2),x)","\frac{1}{4} c \,e^{3} x^{4}+c d \,e^{2} x^{3}+\frac{3}{2} c \,d^{2} e \,x^{2}+c \,d^{3} x"," ",0,"1/4*c*e^3*x^4+d*c*e^2*x^3+3/2*c*d^2*e*x^2+c*d^3*x","B"
980,1,24,23,0.147000," ","int(c*e^2*x^2+2*c*d*e*x+c*d^2,x)","\frac{1}{3} c \,e^{2} x^{3}+c d e \,x^{2}+c \,d^{2} x"," ",0,"c*d^2*x+c*d*e*x^2+1/3*c*e^2*x^3","A"
981,1,13,12,0.049000," ","int((c*e^2*x^2+2*c*d*e*x+c*d^2)/(e*x+d),x)","\left(\frac{1}{2} e \,x^{2}+d x \right) c"," ",0,"c*(1/2*e*x^2+d*x)","A"
982,1,4,3,0.049000," ","int((c*e^2*x^2+2*c*d*e*x+c*d^2)/(e*x+d)^2,x)","c x"," ",0,"c*x","A"
983,1,12,11,0.059000," ","int((c*e^2*x^2+2*c*d*e*x+c*d^2)/(e*x+d)^3,x)","\frac{c \ln \left(e x +d \right)}{e}"," ",0,"c*ln(e*x+d)/e","A"
984,1,14,13,0.046000," ","int((c*e^2*x^2+2*c*d*e*x+c*d^2)/(e*x+d)^4,x)","-\frac{c}{\left(e x +d \right) e}"," ",0,"-c/e/(e*x+d)","A"
985,1,14,13,0.043000," ","int((c*e^2*x^2+2*c*d*e*x+c*d^2)/(e*x+d)^5,x)","-\frac{c}{2 \left(e x +d \right)^{2} e}"," ",0,"-1/2*c/e/(e*x+d)^2","A"
986,1,14,13,0.046000," ","int((c*e^2*x^2+2*c*d*e*x+c*d^2)/(e*x+d)^6,x)","-\frac{c}{3 \left(e x +d \right)^{3} e}"," ",0,"-1/3*c/e/(e*x+d)^3","A"
987,1,86,15,0.045000," ","int((e*x+d)^2*(c*e^2*x^2+2*c*d*e*x+c*d^2)^2,x)","\frac{1}{7} c^{2} e^{6} x^{7}+c^{2} d \,e^{5} x^{6}+3 c^{2} d^{2} e^{4} x^{5}+5 c^{2} d^{3} e^{3} x^{4}+5 c^{2} d^{4} e^{2} x^{3}+3 c^{2} d^{5} e \,x^{2}+c^{2} d^{6} x"," ",0,"1/7*e^6*c^2*x^7+d*e^5*c^2*x^6+3*d^2*c^2*e^4*x^5+5*d^3*c^2*e^3*x^4+5*d^4*c^2*e^2*x^3+3*d^5*c^2*e*x^2+d^6*c^2*x","B"
988,1,72,15,0.059000," ","int((e*x+d)*(c*e^2*x^2+2*c*d*e*x+c*d^2)^2,x)","\frac{1}{6} c^{2} e^{5} x^{6}+c^{2} d \,e^{4} x^{5}+\frac{5}{2} c^{2} d^{2} e^{3} x^{4}+\frac{10}{3} c^{2} d^{3} e^{2} x^{3}+\frac{5}{2} c^{2} d^{4} e \,x^{2}+c^{2} d^{5} x"," ",0,"1/6*c^2*e^5*x^6+d*c^2*e^4*x^5+5/2*d^2*c^2*e^3*x^4+10/3*d^3*c^2*e^2*x^3+5/2*c^2*e*d^4*x^2+c^2*d^5*x","B"
989,1,58,15,0.043000," ","int((c*e^2*x^2+2*c*d*e*x+c*d^2)^2,x)","\frac{1}{5} c^{2} e^{4} x^{5}+c^{2} d \,e^{3} x^{4}+2 c^{2} d^{2} e^{2} x^{3}+2 c^{2} d^{3} e \,x^{2}+c^{2} d^{4} x"," ",0,"1/5*c^2*e^4*x^5+c^2*d*e^3*x^4+2*c^2*d^2*e^2*x^3+2*c^2*d^3*e*x^2+c^2*d^4*x","B"
990,1,36,15,0.046000," ","int((c*e^2*x^2+2*c*d*e*x+c*d^2)^2/(e*x+d),x)","\left(\frac{1}{4} e^{3} x^{4}+d \,e^{2} x^{3}+\frac{3}{2} d^{2} e \,x^{2}+d^{3} x \right) c^{2}"," ",0,"c^2*(1/4*e^3*x^4+d*e^2*x^3+3/2*d^2*e*x^2+d^3*x)","B"
991,1,16,15,0.063000," ","int((c*e^2*x^2+2*c*d*e*x+c*d^2)^2/(e*x+d)^2,x)","\frac{\left(e x +d \right)^{3} c^{2}}{3 e}"," ",0,"1/3*c^2*(e*x+d)^3/e","A"
992,1,15,15,0.065000," ","int((c*e^2*x^2+2*c*d*e*x+c*d^2)^2/(e*x+d)^3,x)","\left(\frac{1}{2} e \,x^{2}+d x \right) c^{2}"," ",0,"c^2*(1/2*e*x^2+d*x)","A"
993,1,6,5,0.038000," ","int((c*e^2*x^2+2*c*d*e*x+c*d^2)^2/(e*x+d)^4,x)","c^{2} x"," ",0,"c^2*x","A"
994,1,14,13,0.058000," ","int((c*e^2*x^2+2*c*d*e*x+c*d^2)^2/(e*x+d)^5,x)","\frac{c^{2} \ln \left(e x +d \right)}{e}"," ",0,"c^2*ln(e*x+d)/e","A"
995,1,16,15,0.049000," ","int((c*e^2*x^2+2*c*d*e*x+c*d^2)^2/(e*x+d)^6,x)","-\frac{c^{2}}{\left(e x +d \right) e}"," ",0,"-c^2/e/(e*x+d)","A"
996,1,16,15,0.069000," ","int((c*e^2*x^2+2*c*d*e*x+c*d^2)^2/(e*x+d)^7,x)","-\frac{c^{2}}{2 \left(e x +d \right)^{2} e}"," ",0,"-1/2*c^2/e/(e*x+d)^2","A"
997,1,16,15,0.049000," ","int((c*e^2*x^2+2*c*d*e*x+c*d^2)^2/(e*x+d)^8,x)","-\frac{c^{2}}{3 \left(e x +d \right)^{3} e}"," ",0,"-1/3*c^2/e/(e*x+d)^3","A"
998,1,16,15,0.059000," ","int((e*x+d)^5/(c*e^2*x^2+2*c*d*e*x+c*d^2),x)","\frac{\left(e x +d \right)^{4}}{4 c e}"," ",0,"1/4*(e*x+d)^4/c/e","A"
999,1,16,15,0.049000," ","int((e*x+d)^4/(c*e^2*x^2+2*c*d*e*x+c*d^2),x)","\frac{\left(e x +d \right)^{3}}{3 c e}"," ",0,"1/3*(e*x+d)^3/c/e","A"
1000,1,15,15,0.049000," ","int((e*x+d)^3/(c*e^2*x^2+2*c*d*e*x+c*d^2),x)","\frac{\frac{1}{2} e \,x^{2}+d x}{c}"," ",0,"1/c*(1/2*e*x^2+d*x)","A"
1001,1,6,5,0.064000," ","int((e*x+d)^2/(c*e^2*x^2+2*c*d*e*x+c*d^2),x)","\frac{x}{c}"," ",0,"1/c*x","A"
1002,1,14,13,0.045000," ","int((e*x+d)/(c*e^2*x^2+2*c*d*e*x+c*d^2),x)","\frac{\ln \left(e x +d \right)}{c e}"," ",0,"ln(e*x+d)/c/e","A"
1003,1,16,15,0.050000," ","int(1/(c*e^2*x^2+2*c*d*e*x+c*d^2),x)","-\frac{1}{\left(e x +d \right) c e}"," ",0,"-1/c/e/(e*x+d)","A"
1004,1,16,15,0.053000," ","int(1/(e*x+d)/(c*e^2*x^2+2*c*d*e*x+c*d^2),x)","-\frac{1}{2 \left(e x +d \right)^{2} c e}"," ",0,"-1/2/c/e/(e*x+d)^2","A"
1005,1,16,15,0.049000," ","int(1/(e*x+d)^2/(c*e^2*x^2+2*c*d*e*x+c*d^2),x)","-\frac{1}{3 \left(e x +d \right)^{3} c e}"," ",0,"-1/3/c/e/(e*x+d)^3","A"
1006,1,16,15,0.055000," ","int(1/(e*x+d)^3/(c*e^2*x^2+2*c*d*e*x+c*d^2),x)","-\frac{1}{4 \left(e x +d \right)^{4} c e}"," ",0,"-1/4/c/e/(e*x+d)^4","A"
1007,1,16,15,0.044000," ","int((e*x+d)^7/(c*e^2*x^2+2*c*d*e*x+c*d^2)^2,x)","\frac{\left(e x +d \right)^{4}}{4 c^{2} e}"," ",0,"1/4*(e*x+d)^4/c^2/e","A"
1008,1,16,15,0.047000," ","int((e*x+d)^6/(c*e^2*x^2+2*c*d*e*x+c*d^2)^2,x)","\frac{\left(e x +d \right)^{3}}{3 c^{2} e}"," ",0,"1/3*(e*x+d)^3/c^2/e","A"
1009,1,15,15,0.043000," ","int((e*x+d)^5/(c*e^2*x^2+2*c*d*e*x+c*d^2)^2,x)","\frac{\frac{1}{2} e \,x^{2}+d x}{c^{2}}"," ",0,"1/c^2*(1/2*e*x^2+d*x)","A"
1010,1,6,5,0.046000," ","int((e*x+d)^4/(c*e^2*x^2+2*c*d*e*x+c*d^2)^2,x)","\frac{x}{c^{2}}"," ",0,"x/c^2","A"
1011,1,14,13,0.046000," ","int((e*x+d)^3/(c*e^2*x^2+2*c*d*e*x+c*d^2)^2,x)","\frac{\ln \left(e x +d \right)}{c^{2} e}"," ",0,"ln(e*x+d)/c^2/e","A"
1012,1,16,15,0.051000," ","int((e*x+d)^2/(c*e^2*x^2+2*c*d*e*x+c*d^2)^2,x)","-\frac{1}{\left(e x +d \right) c^{2} e}"," ",0,"-1/c^2/e/(e*x+d)","A"
1013,1,16,15,0.046000," ","int((e*x+d)/(c*e^2*x^2+2*c*d*e*x+c*d^2)^2,x)","-\frac{1}{2 \left(e x +d \right)^{2} c^{2} e}"," ",0,"-1/2/c^2/e/(e*x+d)^2","A"
1014,1,16,15,0.048000," ","int(1/(c*e^2*x^2+2*c*d*e*x+c*d^2)^2,x)","-\frac{1}{3 \left(e x +d \right)^{3} c^{2} e}"," ",0,"-1/3/c^2/e/(e*x+d)^3","A"
1015,1,16,15,0.207000," ","int(1/(e*x+d)/(c*e^2*x^2+2*c*d*e*x+c*d^2)^2,x)","-\frac{1}{4 \left(e x +d \right)^{4} c^{2} e}"," ",0,"-1/4/c^2/e/(e*x+d)^4","A"
1016,1,16,15,0.048000," ","int(1/(e*x+d)^2/(c*e^2*x^2+2*c*d*e*x+c*d^2)^2,x)","-\frac{1}{5 \left(e x +d \right)^{5} c^{2} e}"," ",0,"-1/5/c^2/e/(e*x+d)^5","A"
1017,1,16,15,0.047000," ","int((e*x+d)^9/(c*e^2*x^2+2*c*d*e*x+c*d^2)^3,x)","\frac{\left(e x +d \right)^{4}}{4 c^{3} e}"," ",0,"1/4*(e*x+d)^4/c^3/e","A"
1018,1,16,15,0.046000," ","int((e*x+d)^8/(c*e^2*x^2+2*c*d*e*x+c*d^2)^3,x)","\frac{\left(e x +d \right)^{3}}{3 c^{3} e}"," ",0,"1/3*(e*x+d)^3/c^3/e","A"
1019,1,15,15,0.043000," ","int((e*x+d)^7/(c*e^2*x^2+2*c*d*e*x+c*d^2)^3,x)","\frac{\frac{1}{2} e \,x^{2}+d x}{c^{3}}"," ",0,"1/c^3*(1/2*e*x^2+d*x)","A"
1020,1,6,5,0.041000," ","int((e*x+d)^6/(c*e^2*x^2+2*c*d*e*x+c*d^2)^3,x)","\frac{x}{c^{3}}"," ",0,"x/c^3","A"
1021,1,14,13,0.047000," ","int((e*x+d)^5/(c*e^2*x^2+2*c*d*e*x+c*d^2)^3,x)","\frac{\ln \left(e x +d \right)}{c^{3} e}"," ",0,"ln(e*x+d)/c^3/e","A"
1022,1,16,15,0.047000," ","int((e*x+d)^4/(c*e^2*x^2+2*c*d*e*x+c*d^2)^3,x)","-\frac{1}{\left(e x +d \right) c^{3} e}"," ",0,"-1/c^3/e/(e*x+d)","A"
1023,1,16,15,0.048000," ","int((e*x+d)^3/(c*e^2*x^2+2*c*d*e*x+c*d^2)^3,x)","-\frac{1}{2 \left(e x +d \right)^{2} c^{3} e}"," ",0,"-1/2/c^3/e/(e*x+d)^2","A"
1024,1,16,15,0.048000," ","int((e*x+d)^2/(c*e^2*x^2+2*c*d*e*x+c*d^2)^3,x)","-\frac{1}{3 \left(e x +d \right)^{3} c^{3} e}"," ",0,"-1/3/c^3/e/(e*x+d)^3","A"
1025,1,16,15,0.049000," ","int((e*x+d)/(c*e^2*x^2+2*c*d*e*x+c*d^2)^3,x)","-\frac{1}{4 \left(e x +d \right)^{4} c^{3} e}"," ",0,"-1/4/c^3/e/(e*x+d)^4","A"
1026,1,16,15,0.050000," ","int(1/(c*e^2*x^2+2*c*d*e*x+c*d^2)^3,x)","-\frac{1}{5 \left(e x +d \right)^{5} c^{3} e}"," ",0,"-1/5/c^3/e/(e*x+d)^5","A"
1027,1,16,15,0.063000," ","int(1/(e*x+d)/(c*e^2*x^2+2*c*d*e*x+c*d^2)^3,x)","-\frac{1}{6 \left(e x +d \right)^{6} c^{3} e}"," ",0,"-1/6/c^3/e/(e*x+d)^6","A"
1028,1,16,15,0.053000," ","int(1/(e*x+d)^2/(c*e^2*x^2+2*c*d*e*x+c*d^2)^3,x)","-\frac{1}{7 \left(e x +d \right)^{7} c^{3} e}"," ",0,"-1/7/c^3/e/(e*x+d)^7","A"
1029,1,73,30,0.047000," ","int((e*x+d)^3*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2),x)","\frac{\left(e^{4} x^{4}+5 d \,e^{3} x^{3}+10 d^{2} e^{2} x^{2}+10 d^{3} e x +5 d^{4}\right) \sqrt{c \,e^{2} x^{2}+2 c d e x +c \,d^{2}}\, x}{5 e x +5 d}"," ",0,"1/5*x*(e^4*x^4+5*d*e^3*x^3+10*d^2*e^2*x^2+10*d^3*e*x+5*d^4)*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2)/(e*x+d)","B"
1030,1,62,35,0.050000," ","int((e*x+d)^2*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2),x)","\frac{\left(e^{3} x^{3}+4 e^{2} x^{2} d +6 d^{2} x e +4 d^{3}\right) \sqrt{c \,e^{2} x^{2}+2 c d e x +c \,d^{2}}\, x}{4 e x +4 d}"," ",0,"1/4*x*(e^3*x^3+4*d*e^2*x^2+6*d^2*e*x+4*d^3)*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2)/(e*x+d)","A"
1031,1,51,30,0.046000," ","int((e*x+d)*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2),x)","\frac{\left(e^{2} x^{2}+3 d x e +3 d^{2}\right) \sqrt{c \,e^{2} x^{2}+2 c d e x +c \,d^{2}}\, x}{3 e x +3 d}"," ",0,"1/3*x*(e^2*x^2+3*d*e*x+3*d^2)*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2)/(e*x+d)","A"
1032,1,40,32,0.044000," ","int((c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2),x)","\frac{\left(e x +2 d \right) \sqrt{c \,e^{2} x^{2}+2 c d e x +c \,d^{2}}\, x}{2 e x +2 d}"," ",0,"1/2*x*(e*x+2*d)*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2)/(e*x+d)","A"
1033,1,32,26,0.047000," ","int((c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2)/(e*x+d),x)","\frac{\sqrt{c \,e^{2} x^{2}+2 c d e x +c \,d^{2}}\, x}{e x +d}"," ",0,"(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2)/(e*x+d)*x","A"
1034,1,40,38,0.049000," ","int((c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2)/(e*x+d)^2,x)","\frac{\sqrt{c \,e^{2} x^{2}+2 c d e x +c \,d^{2}}\, \ln \left(e x +d \right)}{\left(e x +d \right) e}"," ",0,"(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2)/(e*x+d)*ln(e*x+d)/e","A"
1035,1,35,28,0.049000," ","int((c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2)/(e*x+d)^3,x)","-\frac{\sqrt{c \,e^{2} x^{2}+2 c d e x +c \,d^{2}}}{\left(e x +d \right)^{2} e}"," ",0,"-1/(e*x+d)^2/e*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2)","A"
1036,1,35,35,0.072000," ","int((c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2)/(e*x+d)^4,x)","-\frac{\sqrt{c \,e^{2} x^{2}+2 c d e x +c \,d^{2}}}{2 \left(e x +d \right)^{3} e}"," ",0,"-1/2/(e*x+d)^3/e*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2)","A"
1037,1,35,30,0.050000," ","int((c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2)/(e*x+d)^5,x)","-\frac{\sqrt{c \,e^{2} x^{2}+2 c d e x +c \,d^{2}}}{3 \left(e x +d \right)^{4} e}"," ",0,"-1/3/(e*x+d)^4/e*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2)","A"
1038,1,35,37,0.046000," ","int((c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2)/(e*x+d)^6,x)","-\frac{\sqrt{c \,e^{2} x^{2}+2 c d e x +c \,d^{2}}}{4 \left(e x +d \right)^{5} e}"," ",0,"-1/4/(e*x+d)^5/e*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2)","A"
1039,1,95,30,0.047000," ","int((e*x+d)^3*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2),x)","\frac{\left(e^{6} x^{6}+7 e^{5} x^{5} d +21 e^{4} x^{4} d^{2}+35 d^{3} e^{3} x^{3}+35 d^{4} e^{2} x^{2}+21 d^{5} e x +7 d^{6}\right) \left(c \,e^{2} x^{2}+2 c d e x +c \,d^{2}\right)^{\frac{3}{2}} x}{7 \left(e x +d \right)^{3}}"," ",0,"1/7*x*(e^6*x^6+7*d*e^5*x^5+21*d^2*e^4*x^4+35*d^3*e^3*x^3+35*d^4*e^2*x^2+21*d^5*e*x+7*d^6)*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2)/(e*x+d)^3","B"
1040,1,84,35,0.052000," ","int((e*x+d)^2*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2),x)","\frac{\left(e^{5} x^{5}+6 d \,e^{4} x^{4}+15 e^{3} x^{3} d^{2}+20 d^{3} e^{2} x^{2}+15 d^{4} e x +6 d^{5}\right) \left(c \,e^{2} x^{2}+2 c d e x +c \,d^{2}\right)^{\frac{3}{2}} x}{6 \left(e x +d \right)^{3}}"," ",0,"1/6*x*(e^5*x^5+6*d*e^4*x^4+15*d^2*e^3*x^3+20*d^3*e^2*x^2+15*d^4*e*x+6*d^5)*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2)/(e*x+d)^3","B"
1041,1,73,30,0.052000," ","int((e*x+d)*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2),x)","\frac{\left(e^{4} x^{4}+5 d \,e^{3} x^{3}+10 d^{2} e^{2} x^{2}+10 d^{3} e x +5 d^{4}\right) \left(c \,e^{2} x^{2}+2 c d e x +c \,d^{2}\right)^{\frac{3}{2}} x}{5 \left(e x +d \right)^{3}}"," ",0,"1/5*x*(e^4*x^4+5*d*e^3*x^3+10*d^2*e^2*x^2+10*d^3*e*x+5*d^4)*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2)/(e*x+d)^3","B"
1042,1,62,32,0.047000," ","int((c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2),x)","\frac{\left(e^{3} x^{3}+4 e^{2} x^{2} d +6 d^{2} x e +4 d^{3}\right) \left(c \,e^{2} x^{2}+2 c d e x +c \,d^{2}\right)^{\frac{3}{2}} x}{4 \left(e x +d \right)^{3}}"," ",0,"1/4*x*(e^3*x^3+4*d*e^2*x^2+6*d^2*e*x+4*d^3)*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2)/(e*x+d)^3","A"
1043,1,51,27,0.053000," ","int((c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2)/(e*x+d),x)","\frac{\left(e^{2} x^{2}+3 d x e +3 d^{2}\right) \left(c \,e^{2} x^{2}+2 c d e x +c \,d^{2}\right)^{\frac{3}{2}} x}{3 \left(e x +d \right)^{3}}"," ",0,"1/3*x*(e^2*x^2+3*d*e*x+3*d^2)*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2)/(e*x+d)^3","A"
1044,1,40,33,0.044000," ","int((c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2)/(e*x+d)^2,x)","\frac{\left(e x +2 d \right) \left(c \,e^{2} x^{2}+2 c d e x +c \,d^{2}\right)^{\frac{3}{2}} x}{2 \left(e x +d \right)^{3}}"," ",0,"1/2*x*(e*x+2*d)*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2)/(e*x+d)^3","A"
1045,1,32,27,0.043000," ","int((c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2)/(e*x+d)^3,x)","\frac{\left(c \,e^{2} x^{2}+2 c d e x +c \,d^{2}\right)^{\frac{3}{2}} x}{\left(e x +d \right)^{3}}"," ",0,"(c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2)/(e*x+d)^3*x","A"
1046,1,40,40,0.048000," ","int((c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2)/(e*x+d)^4,x)","\frac{\left(c \,e^{2} x^{2}+2 c d e x +c \,d^{2}\right)^{\frac{3}{2}} \ln \left(e x +d \right)}{\left(e x +d \right)^{3} e}"," ",0,"(c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2)/(e*x+d)^3*ln(e*x+d)/e","A"
1047,1,35,30,0.045000," ","int((c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2)/(e*x+d)^5,x)","-\frac{\left(c \,e^{2} x^{2}+2 c d e x +c \,d^{2}\right)^{\frac{3}{2}}}{\left(e x +d \right)^{4} e}"," ",0,"-1/(e*x+d)^4/e*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2)","A"
1048,1,35,37,0.050000," ","int((c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2)/(e*x+d)^6,x)","-\frac{\left(c \,e^{2} x^{2}+2 c d e x +c \,d^{2}\right)^{\frac{3}{2}}}{2 \left(e x +d \right)^{5} e}"," ",0,"-1/2/(e*x+d)^5/e*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2)","A"
1049,1,35,30,0.042000," ","int((c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2)/(e*x+d)^7,x)","-\frac{\left(c \,e^{2} x^{2}+2 c d e x +c \,d^{2}\right)^{\frac{3}{2}}}{3 \left(e x +d \right)^{6} e}"," ",0,"-1/3/(e*x+d)^6/e*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2)","A"
1050,1,117,30,0.042000," ","int((e*x+d)^3*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2),x)","\frac{\left(e^{8} x^{8}+9 d \,e^{7} x^{7}+36 d^{2} e^{6} x^{6}+84 d^{3} e^{5} x^{5}+126 d^{4} e^{4} x^{4}+126 d^{5} e^{3} x^{3}+84 d^{6} e^{2} x^{2}+36 x \,d^{7} e +9 d^{8}\right) \left(c \,e^{2} x^{2}+2 c d e x +c \,d^{2}\right)^{\frac{5}{2}} x}{9 \left(e x +d \right)^{5}}"," ",0,"1/9*x*(e^8*x^8+9*d*e^7*x^7+36*d^2*e^6*x^6+84*d^3*e^5*x^5+126*d^4*e^4*x^4+126*d^5*e^3*x^3+84*d^6*e^2*x^2+36*d^7*e*x+9*d^8)*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2)/(e*x+d)^5","B"
1051,1,106,35,0.044000," ","int((e*x+d)^2*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2),x)","\frac{\left(e^{7} x^{7}+8 d \,e^{6} x^{6}+28 e^{5} x^{5} d^{2}+56 e^{4} x^{4} d^{3}+70 d^{4} e^{3} x^{3}+56 d^{5} e^{2} x^{2}+28 d^{6} e x +8 d^{7}\right) \left(c \,e^{2} x^{2}+2 c d e x +c \,d^{2}\right)^{\frac{5}{2}} x}{8 \left(e x +d \right)^{5}}"," ",0,"1/8*x*(e^7*x^7+8*d*e^6*x^6+28*d^2*e^5*x^5+56*d^3*e^4*x^4+70*d^4*e^3*x^3+56*d^5*e^2*x^2+28*d^6*e*x+8*d^7)*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2)/(e*x+d)^5","B"
1052,1,95,30,0.047000," ","int((e*x+d)*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2),x)","\frac{\left(e^{6} x^{6}+7 e^{5} x^{5} d +21 e^{4} x^{4} d^{2}+35 d^{3} e^{3} x^{3}+35 d^{4} e^{2} x^{2}+21 d^{5} e x +7 d^{6}\right) \left(c \,e^{2} x^{2}+2 c d e x +c \,d^{2}\right)^{\frac{5}{2}} x}{7 \left(e x +d \right)^{5}}"," ",0,"1/7*x*(e^6*x^6+7*d*e^5*x^5+21*d^2*e^4*x^4+35*d^3*e^3*x^3+35*d^4*e^2*x^2+21*d^5*e*x+7*d^6)*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2)/(e*x+d)^5","B"
1053,1,84,32,0.050000," ","int((c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2),x)","\frac{\left(e^{5} x^{5}+6 d \,e^{4} x^{4}+15 e^{3} x^{3} d^{2}+20 d^{3} e^{2} x^{2}+15 d^{4} e x +6 d^{5}\right) \left(c \,e^{2} x^{2}+2 c d e x +c \,d^{2}\right)^{\frac{5}{2}} x}{6 \left(e x +d \right)^{5}}"," ",0,"1/6*x*(e^5*x^5+6*d*e^4*x^4+15*d^2*e^3*x^3+20*d^3*e^2*x^2+15*d^4*e*x+6*d^5)*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2)/(e*x+d)^5","B"
1054,1,73,27,0.047000," ","int((c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2)/(e*x+d),x)","\frac{\left(e^{4} x^{4}+5 d \,e^{3} x^{3}+10 d^{2} e^{2} x^{2}+10 d^{3} e x +5 d^{4}\right) \left(c \,e^{2} x^{2}+2 c d e x +c \,d^{2}\right)^{\frac{5}{2}} x}{5 \left(e x +d \right)^{5}}"," ",0,"1/5*x*(e^4*x^4+5*d*e^3*x^3+10*d^2*e^2*x^2+10*d^3*e*x+5*d^4)*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2)/(e*x+d)^5","B"
1055,1,62,33,0.059000," ","int((c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2)/(e*x+d)^2,x)","\frac{\left(e^{3} x^{3}+4 e^{2} x^{2} d +6 d^{2} x e +4 d^{3}\right) \left(c \,e^{2} x^{2}+2 c d e x +c \,d^{2}\right)^{\frac{5}{2}} x}{4 \left(e x +d \right)^{5}}"," ",0,"1/4*x*(e^3*x^3+4*d*e^2*x^2+6*d^2*e*x+4*d^3)*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2)/(e*x+d)^5","A"
1056,1,51,28,0.040000," ","int((c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2)/(e*x+d)^3,x)","\frac{\left(e^{2} x^{2}+3 d x e +3 d^{2}\right) \left(c \,e^{2} x^{2}+2 c d e x +c \,d^{2}\right)^{\frac{5}{2}} x}{3 \left(e x +d \right)^{5}}"," ",0,"1/3*x*(e^2*x^2+3*d*e*x+3*d^2)*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2)/(e*x+d)^5","A"
1057,1,40,35,0.046000," ","int((c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2)/(e*x+d)^4,x)","\frac{\left(e x +2 d \right) \left(c \,e^{2} x^{2}+2 c d e x +c \,d^{2}\right)^{\frac{5}{2}} x}{2 \left(e x +d \right)^{5}}"," ",0,"1/2*x*(e*x+2*d)*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2)/(e*x+d)^5","A"
1058,1,32,29,0.050000," ","int((c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2)/(e*x+d)^5,x)","\frac{\left(c \,e^{2} x^{2}+2 c d e x +c \,d^{2}\right)^{\frac{5}{2}} x}{\left(e x +d \right)^{5}}"," ",0,"(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2)/(e*x+d)^5*x","A"
1059,1,40,40,0.048000," ","int((c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2)/(e*x+d)^6,x)","\frac{\left(c \,e^{2} x^{2}+2 c d e x +c \,d^{2}\right)^{\frac{5}{2}} \ln \left(e x +d \right)}{\left(e x +d \right)^{5} e}"," ",0,"(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2)/(e*x+d)^5*ln(e*x+d)/e","A"
1060,1,35,30,0.047000," ","int((c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2)/(e*x+d)^7,x)","-\frac{\left(c \,e^{2} x^{2}+2 c d e x +c \,d^{2}\right)^{\frac{5}{2}}}{\left(e x +d \right)^{6} e}"," ",0,"-1/(e*x+d)^6/e*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2)","A"
1061,1,35,37,0.051000," ","int((c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2)/(e*x+d)^8,x)","-\frac{\left(c \,e^{2} x^{2}+2 c d e x +c \,d^{2}\right)^{\frac{5}{2}}}{2 \left(e x +d \right)^{7} e}"," ",0,"-1/2/(e*x+d)^7/e*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2)","A"
1062,1,60,35,0.047000," ","int((e*x+d)^4/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2),x)","\frac{\left(e^{3} x^{3}+4 e^{2} x^{2} d +6 d^{2} x e +4 d^{3}\right) \left(e x +d \right) x}{4 \sqrt{c \,e^{2} x^{2}+2 c d e x +c \,d^{2}}}"," ",0,"1/4*x*(e^3*x^3+4*d*e^2*x^2+6*d^2*e*x+4*d^3)*(e*x+d)/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2)","A"
1063,1,49,30,0.053000," ","int((e*x+d)^3/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2),x)","\frac{\left(e^{2} x^{2}+3 d x e +3 d^{2}\right) \left(e x +d \right) x}{3 \sqrt{c \,e^{2} x^{2}+2 c d e x +c \,d^{2}}}"," ",0,"1/3*x*(e^2*x^2+3*d*e*x+3*d^2)*(e*x+d)/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2)","A"
1064,1,38,35,0.046000," ","int((e*x+d)^2/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2),x)","\frac{\left(e x +2 d \right) \left(e x +d \right) x}{2 \sqrt{c \,e^{2} x^{2}+2 c d e x +c \,d^{2}}}"," ",0,"1/2*x*(e*x+2*d)*(e*x+d)/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2)","A"
1065,1,30,29,0.046000," ","int((e*x+d)/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2),x)","\frac{\left(e x +d \right) x}{\sqrt{c \,e^{2} x^{2}+2 c d e x +c \,d^{2}}}"," ",0,"1/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2)*(e*x+d)*x","A"
1066,1,38,37,0.054000," ","int(1/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2),x)","\frac{\left(e x +d \right) \ln \left(e x +d \right)}{\sqrt{c \,e^{2} x^{2}+2 c d e x +c \,d^{2}}\, e}"," ",0,"(e*x+d)*ln(e*x+d)/e/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2)","A"
1067,1,28,27,0.048000," ","int(1/(e*x+d)/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2),x)","-\frac{1}{\sqrt{c \,e^{2} x^{2}+2 c d e x +c \,d^{2}}\, e}"," ",0,"-1/e/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2)","A"
1068,1,35,34,0.047000," ","int(1/(e*x+d)^2/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2),x)","-\frac{1}{2 \left(e x +d \right) \sqrt{c \,e^{2} x^{2}+2 c d e x +c \,d^{2}}\, e}"," ",0,"-1/2/e/(e*x+d)/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2)","A"
1069,1,35,28,0.047000," ","int(1/(e*x+d)^3/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2),x)","-\frac{1}{3 \left(e x +d \right)^{2} \sqrt{c \,e^{2} x^{2}+2 c d e x +c \,d^{2}}\, e}"," ",0,"-1/3/(e*x+d)^2/e/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2)","A"
1070,1,35,35,0.049000," ","int(1/(e*x+d)^4/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2),x)","-\frac{1}{4 \left(e x +d \right)^{3} \sqrt{c \,e^{2} x^{2}+2 c d e x +c \,d^{2}}\, e}"," ",0,"-1/4/(e*x+d)^3/e/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2)","A"
1071,1,40,35,0.043000," ","int((e*x+d)^4/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2),x)","\frac{\left(e x +2 d \right) \left(e x +d \right)^{3} x}{2 \left(c \,e^{2} x^{2}+2 c d e x +c \,d^{2}\right)^{\frac{3}{2}}}"," ",0,"1/2*x*(e*x+2*d)*(e*x+d)^3/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2)","A"
1072,1,32,29,0.043000," ","int((e*x+d)^3/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2),x)","\frac{\left(e x +d \right)^{3} x}{\left(c \,e^{2} x^{2}+2 c d e x +c \,d^{2}\right)^{\frac{3}{2}}}"," ",0,"1/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2)*(e*x+d)^3*x","A"
1073,1,40,40,0.046000," ","int((e*x+d)^2/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2),x)","\frac{\left(e x +d \right)^{3} \ln \left(e x +d \right)}{\left(c \,e^{2} x^{2}+2 c d e x +c \,d^{2}\right)^{\frac{3}{2}} e}"," ",0,"1/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2)*(e*x+d)^3*ln(e*x+d)/e","A"
1074,1,35,30,0.045000," ","int((e*x+d)/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2),x)","-\frac{\left(e x +d \right)^{2}}{\left(c \,e^{2} x^{2}+2 c d e x +c \,d^{2}\right)^{\frac{3}{2}} e}"," ",0,"-(e*x+d)^2/e/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2)","A"
1075,1,33,37,0.050000," ","int(1/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2),x)","-\frac{e x +d}{2 \left(c \,e^{2} x^{2}+2 c d e x +c \,d^{2}\right)^{\frac{3}{2}} e}"," ",0,"-1/2*(e*x+d)/e/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2)","A"
1076,1,28,27,0.048000," ","int(1/(e*x+d)/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2),x)","-\frac{1}{3 \left(c \,e^{2} x^{2}+2 c d e x +c \,d^{2}\right)^{\frac{3}{2}} e}"," ",0,"-1/3/e/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2)","A"
1077,1,35,34,0.046000," ","int(1/(e*x+d)^2/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2),x)","-\frac{1}{4 \left(e x +d \right) \left(c \,e^{2} x^{2}+2 c d e x +c \,d^{2}\right)^{\frac{3}{2}} e}"," ",0,"-1/4/e/(e*x+d)/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2)","A"
1078,1,35,28,0.042000," ","int(1/(e*x+d)^3/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2),x)","-\frac{1}{5 \left(e x +d \right)^{2} \left(c \,e^{2} x^{2}+2 c d e x +c \,d^{2}\right)^{\frac{3}{2}} e}"," ",0,"-1/5/(e*x+d)^2/e/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2)","A"
1079,1,40,35,0.047000," ","int((e*x+d)^6/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2),x)","\frac{\left(e x +2 d \right) \left(e x +d \right)^{5} x}{2 \left(c \,e^{2} x^{2}+2 c d e x +c \,d^{2}\right)^{\frac{5}{2}}}"," ",0,"1/2*x*(e*x+2*d)*(e*x+d)^5/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2)","A"
1080,1,32,29,0.044000," ","int((e*x+d)^5/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2),x)","\frac{\left(e x +d \right)^{5} x}{\left(c \,e^{2} x^{2}+2 c d e x +c \,d^{2}\right)^{\frac{5}{2}}}"," ",0,"1/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2)*(e*x+d)^5*x","A"
1081,1,40,40,0.050000," ","int((e*x+d)^4/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2),x)","\frac{\left(e x +d \right)^{5} \ln \left(e x +d \right)}{\left(c \,e^{2} x^{2}+2 c d e x +c \,d^{2}\right)^{\frac{5}{2}} e}"," ",0,"1/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2)*(e*x+d)^5*ln(e*x+d)/e","A"
1082,1,35,30,0.046000," ","int((e*x+d)^3/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2),x)","-\frac{\left(e x +d \right)^{4}}{\left(c \,e^{2} x^{2}+2 c d e x +c \,d^{2}\right)^{\frac{5}{2}} e}"," ",0,"-(e*x+d)^4/e/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2)","A"
1083,1,35,37,0.055000," ","int((e*x+d)^2/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2),x)","-\frac{\left(e x +d \right)^{3}}{2 \left(c \,e^{2} x^{2}+2 c d e x +c \,d^{2}\right)^{\frac{5}{2}} e}"," ",0,"-1/2*(e*x+d)^3/e/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2)","A"
1084,1,35,30,0.044000," ","int((e*x+d)/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2),x)","-\frac{\left(e x +d \right)^{2}}{3 \left(c \,e^{2} x^{2}+2 c d e x +c \,d^{2}\right)^{\frac{5}{2}} e}"," ",0,"-1/3*(e*x+d)^2/e/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2)","A"
1085,1,33,37,0.047000," ","int(1/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2),x)","-\frac{e x +d}{4 \left(c \,e^{2} x^{2}+2 c d e x +c \,d^{2}\right)^{\frac{5}{2}} e}"," ",0,"-1/4*(e*x+d)/e/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2)","A"
1086,1,28,27,0.046000," ","int(1/(e*x+d)/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2),x)","-\frac{1}{5 \left(c \,e^{2} x^{2}+2 c d e x +c \,d^{2}\right)^{\frac{5}{2}} e}"," ",0,"-1/5/e/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2)","A"
1087,1,35,34,0.047000," ","int(1/(e*x+d)^2/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2),x)","-\frac{1}{6 \left(e x +d \right) \left(c \,e^{2} x^{2}+2 c d e x +c \,d^{2}\right)^{\frac{5}{2}} e}"," ",0,"-1/6/e/(e*x+d)/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2)","A"
1088,1,35,28,0.048000," ","int(1/(e*x+d)^3/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2),x)","-\frac{1}{7 \left(e x +d \right)^{2} \left(c \,e^{2} x^{2}+2 c d e x +c \,d^{2}\right)^{\frac{5}{2}} e}"," ",0,"-1/7/(e*x+d)^2/e/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2)","A"
1089,1,40,21,0.051000," ","int((e*x+d)^m*(c*e^2*x^2+2*c*d*e*x+c*d^2)^2,x)","\frac{\left(e^{2} x^{2}+2 d x e +d^{2}\right)^{2} c^{2} \left(e x +d \right)^{m +1}}{\left(m +5\right) e}"," ",0,"(e*x+d)^(m+1)*c^2*(e^2*x^2+2*d*e*x+d^2)^2/e/(m+5)","A"
1090,1,36,19,0.046000," ","int((e*x+d)^m*(c*e^2*x^2+2*c*d*e*x+c*d^2),x)","\frac{\left(e^{2} x^{2}+2 d x e +d^{2}\right) c \left(e x +d \right)^{m +1}}{\left(m +3\right) e}"," ",0,"(e*x+d)^(m+1)*c*(e^2*x^2+2*d*e*x+d^2)/e/(m+3)","A"
1091,1,22,24,0.048000," ","int((e*x+d)^m/(c*e^2*x^2+2*c*d*e*x+c*d^2),x)","\frac{\left(e x +d \right)^{m -1}}{\left(m -1\right) c e}"," ",0,"(e*x+d)^(m-1)/c/e/(m-1)","A"
1092,1,40,24,0.046000," ","int((e*x+d)^m/(c*e^2*x^2+2*c*d*e*x+c*d^2)^2,x)","\frac{\left(e x +d \right)^{m -1}}{\left(e^{2} x^{2}+2 d x e +d^{2}\right) \left(m -3\right) c^{2} e}"," ",0,"(e*x+d)^(m-1)/(e^2*x^2+2*d*e*x+d^2)/c^2/e/(m-3)","A"
1093,1,40,24,0.046000," ","int((e*x+d)^m/(c*e^2*x^2+2*c*d*e*x+c*d^2)^3,x)","\frac{\left(e x +d \right)^{m -1}}{\left(e^{2} x^{2}+2 d x e +d^{2}\right)^{2} \left(m -5\right) c^{3} e}"," ",0,"(e*x+d)^(m-1)/(e^2*x^2+2*d*e*x+d^2)^2/c^3/e/(m-5)","A"
1094,1,41,40,0.047000," ","int((e*x+d)^m*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2),x)","\frac{\left(c \,e^{2} x^{2}+2 c d e x +c \,d^{2}\right)^{\frac{3}{2}} \left(e x +d \right)^{m +1}}{\left(m +4\right) e}"," ",0,"(e*x+d)^(m+1)*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2)/e/(m+4)","A"
1095,1,41,40,0.052000," ","int((e*x+d)^m*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2),x)","\frac{\sqrt{c \,e^{2} x^{2}+2 c d e x +c \,d^{2}}\, \left(e x +d \right)^{m +1}}{\left(m +2\right) e}"," ",0,"(e*x+d)^(m+1)*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2)/e/(m+2)","A"
1096,1,39,38,0.046000," ","int((e*x+d)^m/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2),x)","\frac{\left(e x +d \right)^{m +1}}{\sqrt{c \,e^{2} x^{2}+2 c d e x +c \,d^{2}}\, e m}"," ",0,"(e*x+d)^(m+1)/e/m/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2)","A"
1097,1,41,43,0.045000," ","int((e*x+d)^m/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2),x)","\frac{\left(e x +d \right)^{m +1}}{\left(m -2\right) \left(c \,e^{2} x^{2}+2 c d e x +c \,d^{2}\right)^{\frac{3}{2}} e}"," ",0,"(e*x+d)^(m+1)/e/(m-2)/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2)","A"
1098,1,44,43,0.041000," ","int((e*x+d)^m*(c*e^2*x^2+2*c*d*e*x+c*d^2)^p,x)","\frac{\left(e x +d \right)^{m +1} \left(c \,e^{2} x^{2}+2 c d e x +c \,d^{2}\right)^{p}}{\left(m +2 p +1\right) e}"," ",0,"(e*x+d)^(m+1)*(c*e^2*x^2+2*c*d*e*x+c*d^2)^p/e/(m+2*p+1)","A"
1099,1,44,44,0.045000," ","int((e*x+d)^p/((c*e^2*x^2+2*c*d*e*x+c*d^2)^p),x)","-\frac{\left(e x +d \right)^{p +1} \left(c \,e^{2} x^{2}+2 c d e x +c \,d^{2}\right)^{-p}}{\left(p -1\right) e}"," ",0,"-(e*x+d)^(p+1)/e/(p-1)/((c*e^2*x^2+2*c*d*e*x+c*d^2)^p)","A"
1100,1,40,37,0.053000," ","int((e*x+d)^3*(c*e^2*x^2+2*c*d*e*x+c*d^2)^p,x)","\frac{\left(e x +d \right)^{4} \left(c \,e^{2} x^{2}+2 c d e x +c \,d^{2}\right)^{p}}{2 \left(p +2\right) e}"," ",0,"1/2*(e*x+d)^4/e/(p+2)*(c*e^2*x^2+2*c*d*e*x+c*d^2)^p","A"
1101,1,41,43,0.044000," ","int((e*x+d)^2*(c*e^2*x^2+2*c*d*e*x+c*d^2)^p,x)","\frac{\left(e x +d \right)^{3} \left(c \,e^{2} x^{2}+2 c d e x +c \,d^{2}\right)^{p}}{\left(2 p +3\right) e}"," ",0,"(e*x+d)^3/e/(2*p+3)*(c*e^2*x^2+2*c*d*e*x+c*d^2)^p","A"
1102,1,40,37,0.046000," ","int((e*x+d)*(c*e^2*x^2+2*c*d*e*x+c*d^2)^p,x)","\frac{\left(e x +d \right)^{2} \left(c \,e^{2} x^{2}+2 c d e x +c \,d^{2}\right)^{p}}{2 \left(p +1\right) e}"," ",0,"1/2*(e*x+d)^2/e/(p+1)*(c*e^2*x^2+2*c*d*e*x+c*d^2)^p","A"
1103,1,39,38,0.043000," ","int((c*e^2*x^2+2*c*d*e*x+c*d^2)^p,x)","\frac{\left(e x +d \right) \left(c \,e^{2} x^{2}+2 c d e x +c \,d^{2}\right)^{p}}{\left(2 p +1\right) e}"," ",0,"(e*x+d)*(c*e^2*x^2+2*c*d*e*x+c*d^2)^p/e/(2*p+1)","A"
1104,1,31,30,0.044000," ","int((c*e^2*x^2+2*c*d*e*x+c*d^2)^p/(e*x+d),x)","\frac{\left(c \,e^{2} x^{2}+2 c d e x +c \,d^{2}\right)^{p}}{2 e p}"," ",0,"1/2*(c*e^2*x^2+2*c*d*e*x+c*d^2)^p/e/p","A"
1105,1,41,42,0.045000," ","int((c*e^2*x^2+2*c*d*e*x+c*d^2)^p/(e*x+d)^2,x)","\frac{\left(c \,e^{2} x^{2}+2 c d e x +c \,d^{2}\right)^{p}}{\left(e x +d \right) \left(2 p -1\right) e}"," ",0,"1/(e*x+d)/(-1+2*p)/e*(c*e^2*x^2+2*c*d*e*x+c*d^2)^p","A"
1106,1,40,37,0.041000," ","int((c*e^2*x^2+2*c*d*e*x+c*d^2)^p/(e*x+d)^3,x)","\frac{\left(c \,e^{2} x^{2}+2 c d e x +c \,d^{2}\right)^{p}}{2 \left(e x +d \right)^{2} \left(p -1\right) e}"," ",0,"1/2/(e*x+d)^2/(p-1)/e*(c*e^2*x^2+2*c*d*e*x+c*d^2)^p","A"
1107,1,95,43,0.114000," ","int((e*x+d)^(-2*p-1)*(c*e^2*x^2+2*c*d*e*x+c*d^2)^p,x)","x \,{\mathrm e}^{p \ln \left(c \,e^{2} x^{2}+2 c d e x +c \,d^{2}\right)} {\mathrm e}^{\left(-2 p -1\right) \ln \left(e x +d \right)} \ln \left(e x +d \right)+\frac{d \,{\mathrm e}^{p \ln \left(c \,e^{2} x^{2}+2 c d e x +c \,d^{2}\right)} {\mathrm e}^{\left(-2 p -1\right) \ln \left(e x +d \right)} \ln \left(e x +d \right)}{e}"," ",0,"x*ln(e*x+d)*exp((-2*p-1)*ln(e*x+d))*exp(p*ln(c*e^2*x^2+2*c*d*e*x+c*d^2))+d/e*ln(e*x+d)*exp((-2*p-1)*ln(e*x+d))*exp(p*ln(c*e^2*x^2+2*c*d*e*x+c*d^2))","B"
1108,1,74,43,0.098000," ","int((e*x+d)^(2*p-1)/((c*e^2*x^2+2*c*d*e*x+c*d^2)^p),x)","\left(x \,{\mathrm e}^{\left(2 p -1\right) \ln \left(e x +d \right)} \ln \left(e x +d \right)+\frac{d \,{\mathrm e}^{\left(2 p -1\right) \ln \left(e x +d \right)} \ln \left(e x +d \right)}{e}\right) {\mathrm e}^{-p \ln \left(c \,e^{2} x^{2}+2 c d e x +c \,d^{2}\right)}"," ",0,"(x*ln(e*x+d)*exp((2*p-1)*ln(e*x+d))+d/e*ln(e*x+d)*exp((2*p-1)*ln(e*x+d)))/exp(p*ln(c*e^2*x^2+2*c*d*e*x+c*d^2))","A"
1109,1,137,41,0.043000," ","int((2*c*d*x+b*d)^4*(c*x^2+b*x+a),x)","\frac{16 c^{5} d^{4} x^{7}}{7}+8 b \,c^{4} d^{4} x^{6}+a \,b^{4} d^{4} x +\frac{\left(16 c^{4} d^{4} a +56 b^{2} d^{4} c^{3}\right) x^{5}}{5}+\frac{\left(32 b \,c^{3} d^{4} a +32 b^{3} d^{4} c^{2}\right) x^{4}}{4}+\frac{\left(24 b^{2} d^{4} c^{2} a +9 b^{4} d^{4} c \right) x^{3}}{3}+\frac{\left(8 b^{3} d^{4} c a +b^{5} d^{4}\right) x^{2}}{2}"," ",0,"16/7*c^5*d^4*x^7+8*b*c^4*d^4*x^6+1/5*(16*a*c^4*d^4+56*b^2*c^3*d^4)*x^5+1/4*(32*a*b*c^3*d^4+32*b^3*c^2*d^4)*x^4+1/3*(24*a*b^2*c^2*d^4+9*b^4*c*d^4)*x^3+1/2*(8*a*b^3*c*d^4+b^5*d^4)*x^2+b^4*d^4*a*x","B"
1110,1,108,41,0.043000," ","int((2*c*d*x+b*d)^3*(c*x^2+b*x+a),x)","\frac{4 c^{4} d^{3} x^{6}}{3}+4 b \,c^{3} d^{3} x^{5}+a \,b^{3} d^{3} x +\frac{\left(8 c^{3} d^{3} a +18 b^{2} d^{3} c^{2}\right) x^{4}}{4}+\frac{\left(12 b \,d^{3} c^{2} a +7 b^{3} d^{3} c \right) x^{3}}{3}+\frac{\left(6 b^{2} d^{3} c a +b^{4} d^{3}\right) x^{2}}{2}"," ",0,"4/3*c^4*d^3*x^6+4*b*d^3*c^3*x^5+1/4*(8*a*c^3*d^3+18*b^2*c^2*d^3)*x^4+1/3*(12*a*b*c^2*d^3+7*b^3*c*d^3)*x^3+1/2*(6*a*b^2*c*d^3+b^4*d^3)*x^2+b^3*d^3*a*x","B"
1111,1,79,41,0.041000," ","int((2*c*d*x+b*d)^2*(c*x^2+b*x+a),x)","\frac{4 c^{3} d^{2} x^{5}}{5}+2 b \,c^{2} d^{2} x^{4}+a \,b^{2} d^{2} x +\frac{\left(4 c^{2} d^{2} a +5 b^{2} d^{2} c \right) x^{3}}{3}+\frac{\left(4 b c \,d^{2} a +b^{3} d^{2}\right) x^{2}}{2}"," ",0,"4/5*c^3*d^2*x^5+2*b*c^2*d^2*x^4+1/3*(4*a*c^2*d^2+5*b^2*c*d^2)*x^3+1/2*(4*a*b*c*d^2+b^3*d^2)*x^2+b^2*d^2*a*x","A"
1112,1,39,15,0.048000," ","int((2*c*d*x+b*d)*(c*x^2+b*x+a),x)","\frac{c^{2} d \,x^{4}}{2}+b c d \,x^{3}+a b d x +\frac{\left(2 a c d +b^{2} d \right) x^{2}}{2}"," ",0,"1/2*c^2*d*x^4+b*c*d*x^3+1/2*(2*a*c*d+b^2*d)*x^2+b*d*a*x","B"
1113,1,54,42,0.049000," ","int((c*x^2+b*x+a)/(2*c*d*x+b*d),x)","\frac{x^{2}}{4 d}+\frac{a \ln \left(2 c x +b \right)}{2 c d}-\frac{b^{2} \ln \left(2 c x +b \right)}{8 c^{2} d}+\frac{b x}{4 c d}"," ",0,"1/4*x^2/d+1/4*b*x/c/d+1/2/d/c*ln(2*c*x+b)*a-1/8/d/c^2*ln(2*c*x+b)*b^2","A"
1114,1,35,34,0.052000," ","int((c*x^2+b*x+a)/(2*c*d*x+b*d)^2,x)","\frac{\frac{x}{4 c}-\frac{4 a c -b^{2}}{8 \left(2 c x +b \right) c^{2}}}{d^{2}}"," ",0,"1/d^2*(1/4/c*x-1/8*(4*a*c-b^2)/c^2/(2*c*x+b))","A"
1115,1,53,40,0.052000," ","int((c*x^2+b*x+a)/(2*c*d*x+b*d)^3,x)","-\frac{a}{4 \left(2 c x +b \right)^{2} c \,d^{3}}+\frac{b^{2}}{16 \left(2 c x +b \right)^{2} c^{2} d^{3}}+\frac{\ln \left(2 c x +b \right)}{8 c^{2} d^{3}}"," ",0,"-1/4/d^3/c/(2*c*x+b)^2*a+1/16/d^3/c^2/(2*c*x+b)^2*b^2+1/8*ln(2*c*x+b)/c^2/d^3","A"
1116,1,42,41,0.049000," ","int((c*x^2+b*x+a)/(2*c*d*x+b*d)^4,x)","\frac{-\frac{4 a c -b^{2}}{24 \left(2 c x +b \right)^{3} c^{2}}-\frac{1}{8 \left(2 c x +b \right) c^{2}}}{d^{4}}"," ",0,"1/d^4*(-1/24*(4*a*c-b^2)/c^2/(2*c*x+b)^3-1/8/c^2/(2*c*x+b))","A"
1117,1,42,35,0.049000," ","int((c*x^2+b*x+a)/(2*c*d*x+b*d)^5,x)","\frac{-\frac{4 a c -b^{2}}{32 \left(2 c x +b \right)^{4} c^{2}}-\frac{1}{16 \left(2 c x +b \right)^{2} c^{2}}}{d^{5}}"," ",0,"1/d^5*(-1/32*(4*a*c-b^2)/c^2/(2*c*x+b)^4-1/16/c^2/(2*c*x+b)^2)","A"
1118,1,42,41,0.050000," ","int((c*x^2+b*x+a)/(2*c*d*x+b*d)^6,x)","\frac{-\frac{1}{24 \left(2 c x +b \right)^{3} c^{2}}-\frac{4 a c -b^{2}}{40 \left(2 c x +b \right)^{5} c^{2}}}{d^{6}}"," ",0,"1/d^6*(-1/24/c^2/(2*c*x+b)^3-1/40*(4*a*c-b^2)/c^2/(2*c*x+b)^5)","A"
1119,1,42,41,0.053000," ","int((c*x^2+b*x+a)/(2*c*d*x+b*d)^7,x)","\frac{-\frac{1}{32 \left(2 c x +b \right)^{4} c^{2}}-\frac{4 a c -b^{2}}{48 \left(2 c x +b \right)^{6} c^{2}}}{d^{7}}"," ",0,"1/d^7*(-1/32/c^2/(2*c*x+b)^4-1/48*(4*a*c-b^2)/c^2/(2*c*x+b)^6)","A"
1120,1,42,41,0.045000," ","int((c*x^2+b*x+a)/(2*c*d*x+b*d)^8,x)","\frac{-\frac{4 a c -b^{2}}{56 \left(2 c x +b \right)^{7} c^{2}}-\frac{1}{40 \left(2 c x +b \right)^{5} c^{2}}}{d^{8}}"," ",0,"1/d^8*(-1/56*(4*a*c-b^2)/c^2/(2*c*x+b)^7-1/40/c^2/(2*c*x+b)^5)","A"
1121,1,362,67,0.050000," ","int((2*c*d*x+b*d)^5*(c*x^2+b*x+a)^2,x)","\frac{16 c^{7} d^{5} x^{10}}{5}+16 b \,c^{6} d^{5} x^{9}+a^{2} b^{5} d^{5} x +\frac{\left(240 b^{2} c^{5} d^{5}+32 \left(2 a c +b^{2}\right) c^{5} d^{5}\right) x^{8}}{8}+\frac{\left(64 a b \,c^{5} d^{5}+200 b^{3} c^{4} d^{5}+80 \left(2 a c +b^{2}\right) b \,c^{4} d^{5}\right) x^{7}}{7}+\frac{\left(32 a^{2} c^{5} d^{5}+160 a \,b^{2} c^{4} d^{5}+90 b^{4} c^{3} d^{5}+80 \left(2 a c +b^{2}\right) b^{2} c^{3} d^{5}\right) x^{6}}{6}+\frac{\left(80 a^{2} b \,c^{4} d^{5}+160 a \,b^{3} c^{3} d^{5}+21 b^{5} c^{2} d^{5}+40 \left(2 a c +b^{2}\right) b^{3} c^{2} d^{5}\right) x^{5}}{5}+\frac{\left(80 a^{2} b^{2} c^{3} d^{5}+80 a \,b^{4} c^{2} d^{5}+2 b^{6} c \,d^{5}+10 \left(2 a c +b^{2}\right) b^{4} c \,d^{5}\right) x^{4}}{4}+\frac{\left(40 a^{2} b^{3} c^{2} d^{5}+20 a \,b^{5} c \,d^{5}+\left(2 a c +b^{2}\right) b^{5} d^{5}\right) x^{3}}{3}+\frac{\left(10 b^{4} d^{5} c \,a^{2}+2 b^{6} d^{5} a \right) x^{2}}{2}"," ",0,"16/5*c^7*d^5*x^10+16*b*d^5*c^6*x^9+1/8*(240*b^2*d^5*c^5+32*c^5*d^5*(2*a*c+b^2))*x^8+1/7*(200*b^3*d^5*c^4+80*b*d^5*c^4*(2*a*c+b^2)+64*c^5*d^5*a*b)*x^7+1/6*(90*b^4*d^5*c^3+80*b^2*d^5*c^3*(2*a*c+b^2)+160*b^2*d^5*c^4*a+32*c^5*d^5*a^2)*x^6+1/5*(21*b^5*d^5*c^2+40*b^3*d^5*c^2*(2*a*c+b^2)+160*b^3*d^5*c^3*a+80*b*d^5*c^4*a^2)*x^5+1/4*(2*b^6*d^5*c+10*b^4*d^5*c*(2*a*c+b^2)+80*b^4*d^5*c^2*a+80*b^2*d^5*c^3*a^2)*x^4+1/3*(b^5*d^5*(2*a*c+b^2)+20*b^5*d^5*c*a+40*b^3*d^5*c^2*a^2)*x^3+1/2*(10*a^2*b^4*c*d^5+2*a*b^6*d^5)*x^2+b^5*d^5*a^2*x","B"
1122,1,300,67,0.043000," ","int((2*c*d*x+b*d)^4*(c*x^2+b*x+a)^2,x)","\frac{16 c^{6} d^{4} x^{9}}{9}+8 b \,c^{5} d^{4} x^{8}+a^{2} b^{4} d^{4} x +\frac{\left(88 b^{2} c^{4} d^{4}+16 \left(2 a c +b^{2}\right) c^{4} d^{4}\right) x^{7}}{7}+\frac{\left(32 a b \,c^{4} d^{4}+56 b^{3} c^{3} d^{4}+32 \left(2 a c +b^{2}\right) b \,c^{3} d^{4}\right) x^{6}}{6}+\frac{\left(16 a^{2} c^{4} d^{4}+64 a \,b^{2} c^{3} d^{4}+17 b^{4} c^{2} d^{4}+24 \left(2 a c +b^{2}\right) b^{2} c^{2} d^{4}\right) x^{5}}{5}+\frac{\left(32 a^{2} b \,c^{3} d^{4}+48 a \,b^{3} c^{2} d^{4}+2 b^{5} c \,d^{4}+8 \left(2 a c +b^{2}\right) b^{3} c \,d^{4}\right) x^{4}}{4}+\frac{\left(24 a^{2} b^{2} c^{2} d^{4}+16 a \,b^{4} c \,d^{4}+\left(2 a c +b^{2}\right) b^{4} d^{4}\right) x^{3}}{3}+\frac{\left(8 b^{3} d^{4} c \,a^{2}+2 b^{5} d^{4} a \right) x^{2}}{2}"," ",0,"16/9*c^6*d^4*x^9+8*b*c^5*d^4*x^8+1/7*(88*b^2*d^4*c^4+16*c^4*d^4*(2*a*c+b^2))*x^7+1/6*(56*b^3*d^4*c^3+32*b*c^3*d^4*(2*a*c+b^2)+32*c^4*d^4*a*b)*x^6+1/5*(17*b^4*d^4*c^2+24*b^2*d^4*c^2*(2*a*c+b^2)+64*b^2*c^3*d^4*a+16*c^4*d^4*a^2)*x^5+1/4*(2*b^5*d^4*c+8*b^3*d^4*c*(2*a*c+b^2)+48*b^3*d^4*c^2*a+32*b*c^3*d^4*a^2)*x^4+1/3*(b^4*d^4*(2*a*c+b^2)+16*b^4*d^4*c*a+24*b^2*d^4*c^2*a^2)*x^3+1/2*(8*a^2*b^3*c*d^4+2*a*b^5*d^4)*x^2+b^4*d^4*a^2*x","B"
1123,1,237,51,0.037000," ","int((2*c*d*x+b*d)^3*(c*x^2+b*x+a)^2,x)","c^{5} d^{3} x^{8}+4 b \,c^{4} d^{3} x^{7}+a^{2} b^{3} d^{3} x +\frac{\left(30 b^{2} c^{3} d^{3}+8 \left(2 a c +b^{2}\right) c^{3} d^{3}\right) x^{6}}{6}+\frac{\left(16 a b \,c^{3} d^{3}+13 b^{3} c^{2} d^{3}+12 \left(2 a c +b^{2}\right) b \,c^{2} d^{3}\right) x^{5}}{5}+\frac{\left(8 a^{2} c^{3} d^{3}+24 a \,b^{2} c^{2} d^{3}+2 b^{4} c \,d^{3}+6 \left(2 a c +b^{2}\right) b^{2} c \,d^{3}\right) x^{4}}{4}+\frac{\left(12 a^{2} b \,c^{2} d^{3}+12 a \,b^{3} c \,d^{3}+\left(2 a c +b^{2}\right) b^{3} d^{3}\right) x^{3}}{3}+\frac{\left(6 b^{2} d^{3} c \,a^{2}+2 b^{4} d^{3} a \right) x^{2}}{2}"," ",0,"c^5*d^3*x^8+4*b*d^3*c^4*x^7+1/6*(30*b^2*c^3*d^3+8*c^3*d^3*(2*a*c+b^2))*x^6+1/5*(13*b^3*d^3*c^2+12*b*d^3*c^2*(2*a*c+b^2)+16*c^3*d^3*a*b)*x^5+1/4*(2*b^4*d^3*c+6*b^2*d^3*c*(2*a*c+b^2)+24*b^2*d^3*c^2*a+8*c^3*d^3*a^2)*x^4+1/3*(b^3*d^3*(2*a*c+b^2)+12*b^3*d^3*c*a+12*b*d^3*c^2*a^2)*x^3+1/2*(6*a^2*b^2*c*d^3+2*a*b^4*d^3)*x^2+b^3*d^3*a^2*x","B"
1124,1,176,67,0.041000," ","int((2*c*d*x+b*d)^2*(c*x^2+b*x+a)^2,x)","\frac{4 c^{4} d^{2} x^{7}}{7}+2 b \,c^{3} d^{2} x^{6}+a^{2} b^{2} d^{2} x +\frac{\left(9 b^{2} c^{2} d^{2}+4 \left(2 a c +b^{2}\right) c^{2} d^{2}\right) x^{5}}{5}+\frac{\left(8 a b \,c^{2} d^{2}+2 b^{3} c \,d^{2}+4 \left(2 a c +b^{2}\right) b c \,d^{2}\right) x^{4}}{4}+\frac{\left(4 a^{2} c^{2} d^{2}+8 a \,b^{2} c \,d^{2}+\left(2 a c +b^{2}\right) b^{2} d^{2}\right) x^{3}}{3}+\frac{\left(4 a^{2} b c \,d^{2}+2 b^{3} d^{2} a \right) x^{2}}{2}"," ",0,"4/7*c^4*d^2*x^7+2*b*c^3*d^2*x^6+1/5*(9*b^2*d^2*c^2+4*c^2*d^2*(2*a*c+b^2))*x^5+1/4*(2*b^3*d^2*c+4*b*c*d^2*(2*a*c+b^2)+8*c^2*d^2*a*b)*x^4+1/3*(b^2*d^2*(2*a*c+b^2)+8*b^2*c*d^2*a+4*c^2*d^2*a^2)*x^3+1/2*(4*a^2*b*c*d^2+2*a*b^3*d^2)*x^2+b^2*d^2*a^2*x","B"
1125,1,95,15,0.042000," ","int((2*c*d*x+b*d)*(c*x^2+b*x+a)^2,x)","\frac{c^{3} d \,x^{6}}{3}+b \,c^{2} d \,x^{5}+a^{2} b d x +\frac{\left(2 b^{2} c d +2 \left(2 a c +b^{2}\right) c d \right) x^{4}}{4}+\frac{\left(4 a b c d +\left(2 a c +b^{2}\right) b d \right) x^{3}}{3}+\frac{\left(2 c d \,a^{2}+2 a \,b^{2} d \right) x^{2}}{2}"," ",0,"1/3*c^3*d*x^6+b*c^2*d*x^5+1/4*(2*b^2*d*c+2*c*d*(2*a*c+b^2))*x^4+1/3*(b*d*(2*a*c+b^2)+4*a*b*c*d)*x^3+1/2*(2*a^2*c*d+2*a*b^2*d)*x^2+b*d*a^2*x","B"
1126,1,121,66,0.045000," ","int((c*x^2+b*x+a)^2/(2*c*d*x+b*d),x)","\frac{c \,x^{4}}{8 d}+\frac{b \,x^{3}}{4 d}+\frac{a \,x^{2}}{2 d}+\frac{b^{2} x^{2}}{16 c d}+\frac{a^{2} \ln \left(2 c x +b \right)}{2 c d}-\frac{a \,b^{2} \ln \left(2 c x +b \right)}{4 c^{2} d}+\frac{a b x}{2 c d}+\frac{b^{4} \ln \left(2 c x +b \right)}{32 c^{3} d}-\frac{b^{3} x}{16 c^{2} d}"," ",0,"1/8*c/d*x^4+1/4/d*b*x^3+1/2/d*x^2*a+1/16/d/c*x^2*b^2+1/2/d/c*x*a*b-1/16/d/c^2*b^3*x+1/2/d/c*ln(2*c*x+b)*a^2-1/4/d/c^2*ln(2*c*x+b)*a*b^2+1/32/d/c^3*ln(2*c*x+b)*b^4","A"
1127,1,70,64,0.057000," ","int((c*x^2+b*x+a)^2/(2*c*d*x+b*d)^2,x)","\frac{\frac{\frac{4}{3} c^{2} x^{3}+2 b c \,x^{2}+8 a c x -b^{2} x}{16 c^{2}}-\frac{16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}}{32 \left(2 c x +b \right) c^{3}}}{d^{2}}"," ",0,"1/d^2*(1/16/c^2*(4/3*x^3*c^2+2*b*c*x^2+8*a*c*x-b^2*x)-1/32*(16*a^2*c^2-8*a*b^2*c+b^4)/c^3/(2*c*x+b))","A"
1128,1,115,71,0.055000," ","int((c*x^2+b*x+a)^2/(2*c*d*x+b*d)^3,x)","-\frac{a^{2}}{4 \left(2 c x +b \right)^{2} c \,d^{3}}+\frac{a \,b^{2}}{8 \left(2 c x +b \right)^{2} c^{2} d^{3}}-\frac{b^{4}}{64 \left(2 c x +b \right)^{2} c^{3} d^{3}}+\frac{x^{2}}{16 c \,d^{3}}+\frac{a \ln \left(2 c x +b \right)}{4 c^{2} d^{3}}-\frac{b^{2} \ln \left(2 c x +b \right)}{16 c^{3} d^{3}}+\frac{b x}{16 c^{2} d^{3}}"," ",0,"1/16*x^2/c/d^3+1/16*b*x/c^2/d^3-1/4/d^3/c/(2*c*x+b)^2*a^2+1/8/d^3/c^2/(2*c*x+b)^2*a*b^2-1/64/d^3/c^3/(2*c*x+b)^2*b^4+1/4/d^3/c^2*ln(2*c*x+b)*a-1/16/d^3/c^3*ln(2*c*x+b)*b^2","A"
1129,1,67,60,0.046000," ","int((c*x^2+b*x+a)^2/(2*c*d*x+b*d)^4,x)","\frac{\frac{x}{16 c^{2}}-\frac{16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}}{96 \left(2 c x +b \right)^{3} c^{3}}-\frac{4 a c -b^{2}}{16 \left(2 c x +b \right) c^{3}}}{d^{4}}"," ",0,"1/d^4*(1/16/c^2*x-1/96/c^3*(16*a^2*c^2-8*a*b^2*c+b^4)/(2*c*x+b)^3-1/16/c^3*(4*a*c-b^2)/(2*c*x+b))","A"
1130,1,111,66,0.047000," ","int((c*x^2+b*x+a)^2/(2*c*d*x+b*d)^5,x)","-\frac{a^{2}}{8 \left(2 c x +b \right)^{4} c \,d^{5}}+\frac{a \,b^{2}}{16 \left(2 c x +b \right)^{4} c^{2} d^{5}}-\frac{b^{4}}{128 \left(2 c x +b \right)^{4} c^{3} d^{5}}-\frac{a}{8 \left(2 c x +b \right)^{2} c^{2} d^{5}}+\frac{b^{2}}{32 \left(2 c x +b \right)^{2} c^{3} d^{5}}+\frac{\ln \left(2 c x +b \right)}{32 c^{3} d^{5}}"," ",0,"-1/8/d^5/c/(2*c*x+b)^4*a^2+1/16/d^5/c^2/(2*c*x+b)^4*a*b^2-1/128/d^5/c^3/(2*c*x+b)^4*b^4-1/8/d^5/c^2/(2*c*x+b)^2*a+1/32/d^5/c^3/(2*c*x+b)^2*b^2+1/32*ln(2*c*x+b)/c^3/d^5","A"
1131,1,74,67,0.049000," ","int((c*x^2+b*x+a)^2/(2*c*d*x+b*d)^6,x)","\frac{-\frac{4 a c -b^{2}}{48 \left(2 c x +b \right)^{3} c^{3}}-\frac{16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}}{160 \left(2 c x +b \right)^{5} c^{3}}-\frac{1}{32 \left(2 c x +b \right) c^{3}}}{d^{6}}"," ",0,"1/d^6*(-1/48*(4*a*c-b^2)/c^3/(2*c*x+b)^3-1/160*(16*a^2*c^2-8*a*b^2*c+b^4)/c^3/(2*c*x+b)^5-1/32/c^3/(2*c*x+b))","A"
1132,1,74,35,0.047000," ","int((c*x^2+b*x+a)^2/(2*c*d*x+b*d)^7,x)","\frac{-\frac{4 a c -b^{2}}{64 \left(2 c x +b \right)^{4} c^{3}}-\frac{1}{64 \left(2 c x +b \right)^{2} c^{3}}-\frac{16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}}{192 \left(2 c x +b \right)^{6} c^{3}}}{d^{7}}"," ",0,"1/d^7*(-1/64*(4*a*c-b^2)/c^3/(2*c*x+b)^4-1/64/c^3/(2*c*x+b)^2-1/192*(16*a^2*c^2-8*a*b^2*c+b^4)/c^3/(2*c*x+b)^6)","B"
1133,1,74,67,0.046000," ","int((c*x^2+b*x+a)^2/(2*c*d*x+b*d)^8,x)","\frac{-\frac{1}{96 \left(2 c x +b \right)^{3} c^{3}}-\frac{16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}}{224 \left(2 c x +b \right)^{7} c^{3}}-\frac{4 a c -b^{2}}{80 \left(2 c x +b \right)^{5} c^{3}}}{d^{8}}"," ",0,"1/d^8*(-1/96/c^3/(2*c*x+b)^3-1/224*(16*a^2*c^2-8*a*b^2*c+b^4)/c^3/(2*c*x+b)^7-1/80*(4*a*c-b^2)/c^3/(2*c*x+b)^5)","A"
1134,1,74,67,0.111000," ","int((c*x^2+b*x+a)^2/(2*c*d*x+b*d)^9,x)","\frac{-\frac{1}{128 \left(2 c x +b \right)^{4} c^{3}}-\frac{16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}}{256 \left(2 c x +b \right)^{8} c^{3}}-\frac{4 a c -b^{2}}{96 \left(2 c x +b \right)^{6} c^{3}}}{d^{9}}"," ",0,"1/d^9*(-1/128/c^3/(2*c*x+b)^4-1/256*(16*a^2*c^2-8*a*b^2*c+b^4)/c^3/(2*c*x+b)^8-1/96*(4*a*c-b^2)/c^3/(2*c*x+b)^6)","A"
1135,1,74,67,0.046000," ","int((c*x^2+b*x+a)^2/(2*c*d*x+b*d)^10,x)","\frac{-\frac{4 a c -b^{2}}{112 \left(2 c x +b \right)^{7} c^{3}}-\frac{16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}}{288 \left(2 c x +b \right)^{9} c^{3}}-\frac{1}{160 \left(2 c x +b \right)^{5} c^{3}}}{d^{10}}"," ",0,"1/d^10*(-1/112*(4*a*c-b^2)/c^3/(2*c*x+b)^7-1/288*(16*a^2*c^2-8*a*b^2*c+b^4)/c^3/(2*c*x+b)^9-1/160/c^3/(2*c*x+b)^5)","A"
1136,1,74,67,0.051000," ","int((c*x^2+b*x+a)^2/(2*c*d*x+b*d)^11,x)","\frac{-\frac{4 a c -b^{2}}{128 \left(2 c x +b \right)^{8} c^{3}}-\frac{1}{192 \left(2 c x +b \right)^{6} c^{3}}-\frac{16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}}{320 \left(2 c x +b \right)^{10} c^{3}}}{d^{11}}"," ",0,"1/d^11*(-1/128*(4*a*c-b^2)/c^3/(2*c*x+b)^8-1/192/c^3/(2*c*x+b)^6-1/320*(16*a^2*c^2-8*a*b^2*c+b^4)/c^3/(2*c*x+b)^10)","A"
1137,1,810,93,0.044000," ","int((2*c*d*x+b*d)^5*(c*x^2+b*x+a)^3,x)","\frac{8 c^{8} d^{5} x^{12}}{3}+16 b \,c^{7} d^{5} x^{11}+a^{3} b^{5} d^{5} x +\frac{\left(320 b^{2} c^{6} d^{5}+32 \left(a \,c^{2}+2 b^{2} c +\left(2 a c +b^{2}\right) c \right) c^{5} d^{5}\right) x^{10}}{10}+\frac{\left(280 b^{3} c^{5} d^{5}+80 \left(a \,c^{2}+2 b^{2} c +\left(2 a c +b^{2}\right) c \right) b \,c^{4} d^{5}+32 \left(4 a b c +\left(2 a c +b^{2}\right) b \right) c^{5} d^{5}\right) x^{9}}{9}+\frac{\left(130 b^{4} c^{4} d^{5}+80 \left(a \,c^{2}+2 b^{2} c +\left(2 a c +b^{2}\right) c \right) b^{2} c^{3} d^{5}+80 \left(4 a b c +\left(2 a c +b^{2}\right) b \right) b \,c^{4} d^{5}+32 \left(a^{2} c +2 a \,b^{2}+\left(2 a c +b^{2}\right) a \right) c^{5} d^{5}\right) x^{8}}{8}+\frac{\left(96 a^{2} b \,c^{5} d^{5}+31 b^{5} c^{3} d^{5}+40 \left(a \,c^{2}+2 b^{2} c +\left(2 a c +b^{2}\right) c \right) b^{3} c^{2} d^{5}+80 \left(4 a b c +\left(2 a c +b^{2}\right) b \right) b^{2} c^{3} d^{5}+80 \left(a^{2} c +2 a \,b^{2}+\left(2 a c +b^{2}\right) a \right) b \,c^{4} d^{5}\right) x^{7}}{7}+\frac{\left(32 a^{3} c^{5} d^{5}+240 a^{2} b^{2} c^{4} d^{5}+3 b^{6} c^{2} d^{5}+10 \left(a \,c^{2}+2 b^{2} c +\left(2 a c +b^{2}\right) c \right) b^{4} c \,d^{5}+40 \left(4 a b c +\left(2 a c +b^{2}\right) b \right) b^{3} c^{2} d^{5}+80 \left(a^{2} c +2 a \,b^{2}+\left(2 a c +b^{2}\right) a \right) b^{2} c^{3} d^{5}\right) x^{6}}{6}+\frac{\left(80 a^{3} b \,c^{4} d^{5}+240 a^{2} b^{3} c^{3} d^{5}+\left(a \,c^{2}+2 b^{2} c +\left(2 a c +b^{2}\right) c \right) b^{5} d^{5}+10 \left(4 a b c +\left(2 a c +b^{2}\right) b \right) b^{4} c \,d^{5}+40 \left(a^{2} c +2 a \,b^{2}+\left(2 a c +b^{2}\right) a \right) b^{3} c^{2} d^{5}\right) x^{5}}{5}+\frac{\left(80 a^{3} b^{2} c^{3} d^{5}+120 a^{2} b^{4} c^{2} d^{5}+\left(4 a b c +\left(2 a c +b^{2}\right) b \right) b^{5} d^{5}+10 \left(a^{2} c +2 a \,b^{2}+\left(2 a c +b^{2}\right) a \right) b^{4} c \,d^{5}\right) x^{4}}{4}+\frac{\left(40 a^{3} b^{3} c^{2} d^{5}+30 a^{2} b^{5} c \,d^{5}+\left(a^{2} c +2 a \,b^{2}+\left(2 a c +b^{2}\right) a \right) b^{5} d^{5}\right) x^{3}}{3}+\frac{\left(10 b^{4} d^{5} c \,a^{3}+3 b^{6} d^{5} a^{2}\right) x^{2}}{2}"," ",0,"8/3*c^8*d^5*x^12+16*b*d^5*c^7*x^11+1/10*(320*b^2*d^5*c^6+32*c^5*d^5*(a*c^2+2*c*b^2+c*(2*a*c+b^2)))*x^10+1/9*(280*b^3*d^5*c^5+80*b*d^5*c^4*(a*c^2+2*c*b^2+c*(2*a*c+b^2))+32*c^5*d^5*(4*a*b*c+b*(2*a*c+b^2)))*x^9+1/8*(130*b^4*d^5*c^4+80*b^2*d^5*c^3*(a*c^2+2*c*b^2+c*(2*a*c+b^2))+80*b*d^5*c^4*(4*a*b*c+b*(2*a*c+b^2))+32*c^5*d^5*(a*(2*a*c+b^2)+2*a*b^2+c*a^2))*x^8+1/7*(31*b^5*d^5*c^3+40*b^3*d^5*c^2*(a*c^2+2*c*b^2+c*(2*a*c+b^2))+80*b^2*d^5*c^3*(4*a*b*c+b*(2*a*c+b^2))+80*b*d^5*c^4*(a*(2*a*c+b^2)+2*a*b^2+c*a^2)+96*c^5*d^5*a^2*b)*x^7+1/6*(3*b^6*d^5*c^2+10*b^4*d^5*c*(a*c^2+2*c*b^2+c*(2*a*c+b^2))+40*b^3*d^5*c^2*(4*a*b*c+b*(2*a*c+b^2))+80*b^2*d^5*c^3*(a*(2*a*c+b^2)+2*a*b^2+c*a^2)+240*b^2*d^5*c^4*a^2+32*c^5*d^5*a^3)*x^6+1/5*(b^5*d^5*(a*c^2+2*c*b^2+c*(2*a*c+b^2))+10*b^4*d^5*c*(4*a*b*c+b*(2*a*c+b^2))+40*b^3*d^5*c^2*(a*(2*a*c+b^2)+2*a*b^2+c*a^2)+240*b^3*d^5*c^3*a^2+80*b*d^5*c^4*a^3)*x^5+1/4*(b^5*d^5*(4*a*b*c+b*(2*a*c+b^2))+10*b^4*d^5*c*(a*(2*a*c+b^2)+2*a*b^2+c*a^2)+120*b^4*d^5*c^2*a^2+80*b^2*d^5*c^3*a^3)*x^4+1/3*(b^5*d^5*(a*(2*a*c+b^2)+2*a*b^2+c*a^2)+30*b^5*d^5*c*a^2+40*b^3*d^5*c^2*a^3)*x^3+1/2*(10*a^3*b^4*c*d^5+3*a^2*b^6*d^5)*x^2+b^5*d^5*a^3*x","B"
1138,1,672,93,0.049000," ","int((2*c*d*x+b*d)^4*(c*x^2+b*x+a)^3,x)","\frac{16 c^{7} d^{4} x^{11}}{11}+8 b \,c^{6} d^{4} x^{10}+a^{3} b^{4} d^{4} x +\frac{\left(120 b^{2} c^{5} d^{4}+16 \left(a \,c^{2}+2 b^{2} c +\left(2 a c +b^{2}\right) c \right) c^{4} d^{4}\right) x^{9}}{9}+\frac{\left(80 b^{3} c^{4} d^{4}+32 \left(a \,c^{2}+2 b^{2} c +\left(2 a c +b^{2}\right) c \right) b \,c^{3} d^{4}+16 \left(4 a b c +\left(2 a c +b^{2}\right) b \right) c^{4} d^{4}\right) x^{8}}{8}+\frac{\left(25 b^{4} c^{3} d^{4}+24 \left(a \,c^{2}+2 b^{2} c +\left(2 a c +b^{2}\right) c \right) b^{2} c^{2} d^{4}+32 \left(4 a b c +\left(2 a c +b^{2}\right) b \right) b \,c^{3} d^{4}+16 \left(a^{2} c +2 a \,b^{2}+\left(2 a c +b^{2}\right) a \right) c^{4} d^{4}\right) x^{7}}{7}+\frac{\left(48 a^{2} b \,c^{4} d^{4}+3 b^{5} c^{2} d^{4}+8 \left(a \,c^{2}+2 b^{2} c +\left(2 a c +b^{2}\right) c \right) b^{3} c \,d^{4}+24 \left(4 a b c +\left(2 a c +b^{2}\right) b \right) b^{2} c^{2} d^{4}+32 \left(a^{2} c +2 a \,b^{2}+\left(2 a c +b^{2}\right) a \right) b \,c^{3} d^{4}\right) x^{6}}{6}+\frac{\left(16 a^{3} c^{4} d^{4}+96 a^{2} b^{2} c^{3} d^{4}+\left(a \,c^{2}+2 b^{2} c +\left(2 a c +b^{2}\right) c \right) b^{4} d^{4}+8 \left(4 a b c +\left(2 a c +b^{2}\right) b \right) b^{3} c \,d^{4}+24 \left(a^{2} c +2 a \,b^{2}+\left(2 a c +b^{2}\right) a \right) b^{2} c^{2} d^{4}\right) x^{5}}{5}+\frac{\left(32 a^{3} b \,c^{3} d^{4}+72 a^{2} b^{3} c^{2} d^{4}+\left(4 a b c +\left(2 a c +b^{2}\right) b \right) b^{4} d^{4}+8 \left(a^{2} c +2 a \,b^{2}+\left(2 a c +b^{2}\right) a \right) b^{3} c \,d^{4}\right) x^{4}}{4}+\frac{\left(24 a^{3} b^{2} c^{2} d^{4}+24 a^{2} b^{4} c \,d^{4}+\left(a^{2} c +2 a \,b^{2}+\left(2 a c +b^{2}\right) a \right) b^{4} d^{4}\right) x^{3}}{3}+\frac{\left(8 b^{3} d^{4} c \,a^{3}+3 b^{5} d^{4} a^{2}\right) x^{2}}{2}"," ",0,"16/11*c^7*d^4*x^11+8*b*c^6*d^4*x^10+1/9*(120*b^2*c^5*d^4+16*c^4*d^4*(a*c^2+2*b^2*c+(2*a*c+b^2)*c))*x^9+1/8*(80*b^3*d^4*c^4+32*b*c^3*d^4*(a*c^2+2*b^2*c+(2*a*c+b^2)*c)+16*c^4*d^4*(4*a*b*c+(2*a*c+b^2)*b))*x^8+1/7*(25*b^4*d^4*c^3+24*b^2*d^4*c^2*(a*c^2+2*b^2*c+(2*a*c+b^2)*c)+32*b*c^3*d^4*(4*a*b*c+(2*a*c+b^2)*b)+16*c^4*d^4*(a^2*c+2*a*b^2+(2*a*c+b^2)*a))*x^7+1/6*(3*b^5*d^4*c^2+8*b^3*d^4*c*(a*c^2+2*b^2*c+(2*a*c+b^2)*c)+24*b^2*d^4*c^2*(4*a*b*c+(2*a*c+b^2)*b)+32*b*c^3*d^4*(a^2*c+2*a*b^2+(2*a*c+b^2)*a)+48*c^4*d^4*a^2*b)*x^6+1/5*(b^4*d^4*(a*c^2+2*b^2*c+(2*a*c+b^2)*c)+8*b^3*d^4*c*(4*a*b*c+(2*a*c+b^2)*b)+24*b^2*d^4*c^2*(a^2*c+2*a*b^2+(2*a*c+b^2)*a)+96*b^2*c^3*d^4*a^2+16*c^4*d^4*a^3)*x^5+1/4*(b^4*d^4*(4*a*b*c+(2*a*c+b^2)*b)+8*b^3*d^4*c*(a^2*c+2*a*b^2+(2*a*c+b^2)*a)+72*b^3*d^4*c^2*a^2+32*b*c^3*d^4*a^3)*x^4+1/3*(b^4*d^4*(a^2*c+2*a*b^2+(2*a*c+b^2)*a)+24*b^4*d^4*c*a^2+24*b^2*d^4*c^2*a^3)*x^3+1/2*(8*a^3*b^3*c*d^4+3*a^2*b^5*d^4)*x^2+b^4*d^4*a^3*x","B"
1139,1,534,51,0.042000," ","int((2*c*d*x+b*d)^3*(c*x^2+b*x+a)^3,x)","\frac{4 c^{6} d^{3} x^{10}}{5}+4 b \,c^{5} d^{3} x^{9}+a^{3} b^{3} d^{3} x +\frac{\left(42 b^{2} c^{4} d^{3}+8 \left(a \,c^{2}+2 b^{2} c +\left(2 a c +b^{2}\right) c \right) c^{3} d^{3}\right) x^{8}}{8}+\frac{\left(19 b^{3} c^{3} d^{3}+12 \left(a \,c^{2}+2 b^{2} c +\left(2 a c +b^{2}\right) c \right) b \,c^{2} d^{3}+8 \left(4 a b c +\left(2 a c +b^{2}\right) b \right) c^{3} d^{3}\right) x^{7}}{7}+\frac{\left(3 b^{4} c^{2} d^{3}+6 \left(a \,c^{2}+2 b^{2} c +\left(2 a c +b^{2}\right) c \right) b^{2} c \,d^{3}+12 \left(4 a b c +\left(2 a c +b^{2}\right) b \right) b \,c^{2} d^{3}+8 \left(a^{2} c +2 a \,b^{2}+\left(2 a c +b^{2}\right) a \right) c^{3} d^{3}\right) x^{6}}{6}+\frac{\left(24 a^{2} b \,c^{3} d^{3}+\left(a \,c^{2}+2 b^{2} c +\left(2 a c +b^{2}\right) c \right) b^{3} d^{3}+6 \left(4 a b c +\left(2 a c +b^{2}\right) b \right) b^{2} c \,d^{3}+12 \left(a^{2} c +2 a \,b^{2}+\left(2 a c +b^{2}\right) a \right) b \,c^{2} d^{3}\right) x^{5}}{5}+\frac{\left(8 a^{3} c^{3} d^{3}+36 a^{2} b^{2} c^{2} d^{3}+\left(4 a b c +\left(2 a c +b^{2}\right) b \right) b^{3} d^{3}+6 \left(a^{2} c +2 a \,b^{2}+\left(2 a c +b^{2}\right) a \right) b^{2} c \,d^{3}\right) x^{4}}{4}+\frac{\left(12 a^{3} b \,c^{2} d^{3}+18 a^{2} b^{3} c \,d^{3}+\left(a^{2} c +2 a \,b^{2}+\left(2 a c +b^{2}\right) a \right) b^{3} d^{3}\right) x^{3}}{3}+\frac{\left(6 b^{2} d^{3} c \,a^{3}+3 b^{4} d^{3} a^{2}\right) x^{2}}{2}"," ",0,"4/5*c^6*d^3*x^10+4*b*d^3*c^5*x^9+1/8*(42*b^2*d^3*c^4+8*c^3*d^3*(a*c^2+2*b^2*c+(2*a*c+b^2)*c))*x^8+1/7*(19*b^3*d^3*c^3+12*b*d^3*c^2*(a*c^2+2*b^2*c+(2*a*c+b^2)*c)+8*c^3*d^3*(4*a*b*c+(2*a*c+b^2)*b))*x^7+1/6*(3*b^4*d^3*c^2+6*b^2*d^3*c*(a*c^2+2*b^2*c+(2*a*c+b^2)*c)+12*b*d^3*c^2*(4*a*b*c+(2*a*c+b^2)*b)+8*c^3*d^3*(a^2*c+2*a*b^2+(2*a*c+b^2)*a))*x^6+1/5*(b^3*d^3*(a*c^2+2*b^2*c+(2*a*c+b^2)*c)+6*b^2*d^3*c*(4*a*b*c+(2*a*c+b^2)*b)+12*b*d^3*c^2*(a^2*c+2*a*b^2+(2*a*c+b^2)*a)+24*c^3*d^3*a^2*b)*x^5+1/4*(b^3*d^3*(4*a*b*c+(2*a*c+b^2)*b)+6*b^2*d^3*c*(a^2*c+2*a*b^2+(2*a*c+b^2)*a)+36*b^2*d^3*c^2*a^2+8*c^3*d^3*a^3)*x^4+1/3*(b^3*d^3*(a^2*c+2*a*b^2+(2*a*c+b^2)*a)+18*b^3*d^3*c*a^2+12*b*d^3*c^2*a^3)*x^3+1/2*(6*a^3*b^2*c*d^3+3*a^2*b^4*d^3)*x^2+b^3*d^3*a^3*x","B"
1140,1,396,93,0.045000," ","int((2*c*d*x+b*d)^2*(c*x^2+b*x+a)^3,x)","\frac{4 c^{5} d^{2} x^{9}}{9}+2 b \,c^{4} d^{2} x^{8}+a^{3} b^{2} d^{2} x +\frac{\left(13 b^{2} c^{3} d^{2}+4 \left(a \,c^{2}+2 b^{2} c +\left(2 a c +b^{2}\right) c \right) c^{2} d^{2}\right) x^{7}}{7}+\frac{\left(3 b^{3} c^{2} d^{2}+4 \left(a \,c^{2}+2 b^{2} c +\left(2 a c +b^{2}\right) c \right) b c \,d^{2}+4 \left(4 a b c +\left(2 a c +b^{2}\right) b \right) c^{2} d^{2}\right) x^{6}}{6}+\frac{\left(\left(a \,c^{2}+2 b^{2} c +\left(2 a c +b^{2}\right) c \right) b^{2} d^{2}+4 \left(4 a b c +\left(2 a c +b^{2}\right) b \right) b c \,d^{2}+4 \left(a^{2} c +2 a \,b^{2}+\left(2 a c +b^{2}\right) a \right) c^{2} d^{2}\right) x^{5}}{5}+\frac{\left(12 a^{2} b \,c^{2} d^{2}+\left(4 a b c +\left(2 a c +b^{2}\right) b \right) b^{2} d^{2}+4 \left(a^{2} c +2 a \,b^{2}+\left(2 a c +b^{2}\right) a \right) b c \,d^{2}\right) x^{4}}{4}+\frac{\left(4 a^{3} c^{2} d^{2}+12 a^{2} b^{2} c \,d^{2}+\left(a^{2} c +2 a \,b^{2}+\left(2 a c +b^{2}\right) a \right) b^{2} d^{2}\right) x^{3}}{3}+\frac{\left(4 b c \,d^{2} a^{3}+3 b^{3} d^{2} a^{2}\right) x^{2}}{2}"," ",0,"4/9*c^5*d^2*x^9+2*b*c^4*d^2*x^8+1/7*(13*b^2*d^2*c^3+4*c^2*d^2*(a*c^2+2*b^2*c+(2*a*c+b^2)*c))*x^7+1/6*(3*b^3*d^2*c^2+4*b*c*d^2*(a*c^2+2*b^2*c+(2*a*c+b^2)*c)+4*c^2*d^2*(4*a*b*c+(2*a*c+b^2)*b))*x^6+1/5*(b^2*d^2*(a*c^2+2*b^2*c+(2*a*c+b^2)*c)+4*b*c*d^2*(4*a*b*c+(2*a*c+b^2)*b)+4*c^2*d^2*(a^2*c+2*a*b^2+(2*a*c+b^2)*a))*x^5+1/4*(b^2*d^2*(4*a*b*c+(2*a*c+b^2)*b)+4*b*c*d^2*(a^2*c+2*a*b^2+(2*a*c+b^2)*a)+12*a^2*b*c^2*d^2)*x^4+1/3*(b^2*d^2*(a^2*c+2*a*b^2+(2*a*c+b^2)*a)+12*b^2*c*d^2*a^2+4*c^2*d^2*a^3)*x^3+1/2*(4*a^3*b*c*d^2+3*a^2*b^3*d^2)*x^2+b^2*d^2*a^3*x","B"
1141,1,231,15,0.043000," ","int((2*c*d*x+b*d)*(c*x^2+b*x+a)^3,x)","\frac{c^{4} d \,x^{8}}{4}+b \,c^{3} d \,x^{7}+a^{3} b d x +\frac{\left(3 b^{2} c^{2} d +2 \left(a \,c^{2}+2 b^{2} c +\left(2 a c +b^{2}\right) c \right) c d \right) x^{6}}{6}+\frac{\left(\left(a \,c^{2}+2 b^{2} c +\left(2 a c +b^{2}\right) c \right) b d +2 \left(4 a b c +\left(2 a c +b^{2}\right) b \right) c d \right) x^{5}}{5}+\frac{\left(\left(4 a b c +\left(2 a c +b^{2}\right) b \right) b d +2 \left(a^{2} c +2 a \,b^{2}+\left(2 a c +b^{2}\right) a \right) c d \right) x^{4}}{4}+\frac{\left(6 a^{2} b c d +\left(a^{2} c +2 a \,b^{2}+\left(2 a c +b^{2}\right) a \right) b d \right) x^{3}}{3}+\frac{\left(2 c d \,a^{3}+3 b^{2} d \,a^{2}\right) x^{2}}{2}"," ",0,"1/4*c^4*d*x^8+c^3*d*b*x^7+1/6*(3*b^2*d*c^2+2*c*d*(a*c^2+2*b^2*c+(2*a*c+b^2)*c))*x^6+1/5*(b*d*(a*c^2+2*b^2*c+(2*a*c+b^2)*c)+2*c*d*(4*a*b*c+(2*a*c+b^2)*b))*x^5+1/4*(b*d*(4*a*b*c+(2*a*c+b^2)*b)+2*c*d*(a^2*c+2*a*b^2+(2*a*c+b^2)*a))*x^4+1/3*(b*d*(a^2*c+2*a*b^2+(2*a*c+b^2)*a)+6*c*d*a^2*b)*x^3+1/2*(2*a^3*c*d+3*a^2*b^2*d)*x^2+b*d*a^3*x","B"
1142,1,222,92,0.048000," ","int((c*x^2+b*x+a)^3/(2*c*d*x+b*d),x)","\frac{c^{2} x^{6}}{12 d}+\frac{b c \,x^{5}}{4 d}+\frac{3 a c \,x^{4}}{8 d}+\frac{7 b^{2} x^{4}}{32 d}+\frac{3 a b \,x^{3}}{4 d}+\frac{b^{3} x^{3}}{48 c d}+\frac{3 a^{2} x^{2}}{4 d}+\frac{3 a \,b^{2} x^{2}}{16 c d}-\frac{b^{4} x^{2}}{64 c^{2} d}+\frac{a^{3} \ln \left(2 c x +b \right)}{2 c d}-\frac{3 a^{2} b^{2} \ln \left(2 c x +b \right)}{8 c^{2} d}+\frac{3 a^{2} b x}{4 c d}+\frac{3 a \,b^{4} \ln \left(2 c x +b \right)}{32 c^{3} d}-\frac{3 a \,b^{3} x}{16 c^{2} d}-\frac{b^{6} \ln \left(2 c x +b \right)}{128 c^{4} d}+\frac{b^{5} x}{64 c^{3} d}"," ",0,"1/12/d*c^2*x^6+1/4/d*c*b*x^5+3/8/d*x^4*a*c+7/32*b^2/d*x^4+3/4/d*x^3*a*b+1/48/d/c*x^3*b^3+3/4/d*a^2*x^2+3/16/d/c*x^2*a*b^2-1/64/d/c^2*x^2*b^4+3/4/d/c*x*a^2*b-3/16/d/c^2*x*a*b^3+1/64/d/c^3*x*b^5+1/2/d/c*ln(2*c*x+b)*a^3-3/8/d/c^2*ln(2*c*x+b)*a^2*b^2+3/32/d/c^3*ln(2*c*x+b)*a*b^4-1/128/d/c^4*ln(2*c*x+b)*b^6","B"
1143,1,135,86,0.046000," ","int((c*x^2+b*x+a)^3/(2*c*d*x+b*d)^2,x)","\frac{\frac{\frac{16}{5} c^{4} x^{5}+8 b \,c^{3} x^{4}+16 a \,c^{3} x^{3}+4 b^{2} c^{2} x^{3}+24 a b \,c^{2} x^{2}-2 b^{3} c \,x^{2}+48 a^{2} c^{2} x -12 a \,b^{2} c x +b^{4} x}{64 c^{3}}-\frac{64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}}{128 \left(2 c x +b \right) c^{4}}}{d^{2}}"," ",0,"1/d^2*(1/64/c^3*(16/5*c^4*x^5+8*b*x^4*c^3+16*x^3*a*c^3+4*b^2*c^2*x^3+24*x^2*a*b*c^2-2*x^2*b^3*c+48*a^2*c^2*x-12*x*a*b^2*c+b^4*x)-1/128*(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)/c^4/(2*c*x+b))","A"
1144,1,192,92,0.054000," ","int((c*x^2+b*x+a)^3/(2*c*d*x+b*d)^3,x)","\frac{x^{4}}{32 d^{3}}+\frac{b \,x^{3}}{16 c \,d^{3}}-\frac{a^{3}}{4 \left(2 c x +b \right)^{2} c \,d^{3}}+\frac{3 a^{2} b^{2}}{16 \left(2 c x +b \right)^{2} c^{2} d^{3}}-\frac{3 a \,b^{4}}{64 \left(2 c x +b \right)^{2} c^{3} d^{3}}+\frac{3 a \,x^{2}}{16 c \,d^{3}}+\frac{b^{6}}{256 \left(2 c x +b \right)^{2} c^{4} d^{3}}+\frac{3 a^{2} \ln \left(2 c x +b \right)}{8 c^{2} d^{3}}-\frac{3 a \,b^{2} \ln \left(2 c x +b \right)}{16 c^{3} d^{3}}+\frac{3 a b x}{16 c^{2} d^{3}}+\frac{3 b^{4} \ln \left(2 c x +b \right)}{128 c^{4} d^{3}}-\frac{b^{3} x}{32 c^{3} d^{3}}"," ",0,"1/32/d^3*x^4+1/16/d^3/c*x^3*b+3/16/d^3/c*x^2*a+3/16/d^3/c^2*a*b*x-1/32/d^3/c^3*b^3*x-1/4/d^3/c/(2*c*x+b)^2*a^3+3/16/d^3/c^2/(2*c*x+b)^2*a^2*b^2-3/64/d^3/c^3/(2*c*x+b)^2*a*b^4+1/256/d^3/c^4/(2*c*x+b)^2*b^6+3/8/d^3/c^2*ln(2*c*x+b)*a^2-3/16/d^3/c^3*ln(2*c*x+b)*a*b^2+3/128/d^3/c^4*ln(2*c*x+b)*b^4","B"
1145,1,116,93,0.056000," ","int((c*x^2+b*x+a)^3/(2*c*d*x+b*d)^4,x)","\frac{\frac{\frac{2}{3} c^{2} x^{3}+b c \,x^{2}+6 a c x -b^{2} x}{32 c^{3}}-\frac{64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}}{384 \left(2 c x +b \right)^{3} c^{4}}-\frac{48 a^{2} c^{2}-24 a \,b^{2} c +3 b^{4}}{128 \left(2 c x +b \right) c^{4}}}{d^{4}}"," ",0,"1/d^4*(1/32/c^3*(2/3*c^2*x^3+b*c*x^2+6*a*c*x-b^2*x)-1/384*(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)/c^4/(2*c*x+b)^3-1/128*(48*a^2*c^2-24*a*b^2*c+3*b^4)/c^4/(2*c*x+b))","A"
1146,1,195,97,0.057000," ","int((c*x^2+b*x+a)^3/(2*c*d*x+b*d)^5,x)","-\frac{a^{3}}{8 \left(2 c x +b \right)^{4} c \,d^{5}}+\frac{3 a^{2} b^{2}}{32 \left(2 c x +b \right)^{4} c^{2} d^{5}}-\frac{3 a \,b^{4}}{128 \left(2 c x +b \right)^{4} c^{3} d^{5}}+\frac{b^{6}}{512 \left(2 c x +b \right)^{4} c^{4} d^{5}}-\frac{3 a^{2}}{16 \left(2 c x +b \right)^{2} c^{2} d^{5}}+\frac{3 a \,b^{2}}{32 \left(2 c x +b \right)^{2} c^{3} d^{5}}-\frac{3 b^{4}}{256 \left(2 c x +b \right)^{2} c^{4} d^{5}}+\frac{x^{2}}{64 c^{2} d^{5}}+\frac{3 a \ln \left(2 c x +b \right)}{32 c^{3} d^{5}}-\frac{3 b^{2} \ln \left(2 c x +b \right)}{128 c^{4} d^{5}}+\frac{b x}{64 c^{3} d^{5}}"," ",0,"1/64*x^2/c^2/d^5+1/64*b*x/c^3/d^5-1/8/d^5/c/(2*c*x+b)^4*a^3+3/32/d^5/c^2/(2*c*x+b)^4*a^2*b^2-3/128/d^5/c^3/(2*c*x+b)^4*a*b^4+1/512/d^5/c^4/(2*c*x+b)^4*b^6-3/16/d^5/c^2/(2*c*x+b)^2*a^2+3/32/d^5/c^3/(2*c*x+b)^2*a*b^2-3/256/d^5/c^4/(2*c*x+b)^2*b^4+3/32/d^5/c^3*ln(2*c*x+b)*a-3/128/d^5/c^4*ln(2*c*x+b)*b^2","A"
1147,1,114,86,0.054000," ","int((c*x^2+b*x+a)^3/(2*c*d*x+b*d)^6,x)","\frac{\frac{x}{64 c^{3}}-\frac{48 a^{2} c^{2}-24 a \,b^{2} c +3 b^{4}}{384 \left(2 c x +b \right)^{3} c^{4}}-\frac{64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}}{640 \left(2 c x +b \right)^{5} c^{4}}-\frac{12 a c -3 b^{2}}{128 \left(2 c x +b \right) c^{4}}}{d^{6}}"," ",0,"1/d^6*(1/64/c^3*x-1/384*(48*a^2*c^2-24*a*b^2*c+3*b^4)/c^4/(2*c*x+b)^3-1/640/c^4*(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)/(2*c*x+b)^5-1/128*(12*a*c-3*b^2)/c^4/(2*c*x+b))","A"
1148,1,191,92,0.057000," ","int((c*x^2+b*x+a)^3/(2*c*d*x+b*d)^7,x)","-\frac{a^{3}}{12 \left(2 c x +b \right)^{6} c \,d^{7}}+\frac{a^{2} b^{2}}{16 \left(2 c x +b \right)^{6} c^{2} d^{7}}-\frac{a \,b^{4}}{64 \left(2 c x +b \right)^{6} c^{3} d^{7}}+\frac{b^{6}}{768 \left(2 c x +b \right)^{6} c^{4} d^{7}}-\frac{3 a^{2}}{32 \left(2 c x +b \right)^{4} c^{2} d^{7}}+\frac{3 a \,b^{2}}{64 \left(2 c x +b \right)^{4} c^{3} d^{7}}-\frac{3 b^{4}}{512 \left(2 c x +b \right)^{4} c^{4} d^{7}}-\frac{3 a}{64 \left(2 c x +b \right)^{2} c^{3} d^{7}}+\frac{3 b^{2}}{256 \left(2 c x +b \right)^{2} c^{4} d^{7}}+\frac{\ln \left(2 c x +b \right)}{128 c^{4} d^{7}}"," ",0,"-3/32/d^7/c^2/(2*c*x+b)^4*a^2+3/64/d^7/c^3/(2*c*x+b)^4*a*b^2-3/512/d^7/c^4/(2*c*x+b)^4*b^4-3/64/d^7/c^3/(2*c*x+b)^2*a+3/256/d^7/c^4/(2*c*x+b)^2*b^2-1/12/d^7/c/(2*c*x+b)^6*a^3+1/16/d^7/c^2/(2*c*x+b)^6*a^2*b^2-1/64/d^7/c^3/(2*c*x+b)^6*a*b^4+1/768/d^7/c^4/(2*c*x+b)^6*b^6+1/128*ln(2*c*x+b)/c^4/d^7","B"
1149,1,121,93,0.051000," ","int((c*x^2+b*x+a)^3/(2*c*d*x+b*d)^8,x)","\frac{-\frac{12 a c -3 b^{2}}{384 \left(2 c x +b \right)^{3} c^{4}}-\frac{64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}}{896 \left(2 c x +b \right)^{7} c^{4}}-\frac{48 a^{2} c^{2}-24 a \,b^{2} c +3 b^{4}}{640 \left(2 c x +b \right)^{5} c^{4}}-\frac{1}{128 \left(2 c x +b \right) c^{4}}}{d^{8}}"," ",0,"1/d^8*(-1/384*(12*a*c-3*b^2)/c^4/(2*c*x+b)^3-1/896*(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)/c^4/(2*c*x+b)^7-1/640*(48*a^2*c^2-24*a*b^2*c+3*b^4)/c^4/(2*c*x+b)^5-1/128/c^4/(2*c*x+b))","A"
1150,1,121,35,0.052000," ","int((c*x^2+b*x+a)^3/(2*c*d*x+b*d)^9,x)","\frac{-\frac{12 a c -3 b^{2}}{512 \left(2 c x +b \right)^{4} c^{4}}-\frac{64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}}{1024 \left(2 c x +b \right)^{8} c^{4}}-\frac{1}{256 \left(2 c x +b \right)^{2} c^{4}}-\frac{48 a^{2} c^{2}-24 a \,b^{2} c +3 b^{4}}{768 \left(2 c x +b \right)^{6} c^{4}}}{d^{9}}"," ",0,"1/d^9*(-1/512*(12*a*c-3*b^2)/c^4/(2*c*x+b)^4-1/1024*(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)/c^4/(2*c*x+b)^8-1/256/c^4/(2*c*x+b)^2-1/768*(48*a^2*c^2-24*a*b^2*c+3*b^4)/c^4/(2*c*x+b)^6)","B"
1151,1,121,93,0.053000," ","int((c*x^2+b*x+a)^3/(2*c*d*x+b*d)^10,x)","\frac{-\frac{1}{384 \left(2 c x +b \right)^{3} c^{4}}-\frac{48 a^{2} c^{2}-24 a \,b^{2} c +3 b^{4}}{896 \left(2 c x +b \right)^{7} c^{4}}-\frac{64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}}{1152 \left(2 c x +b \right)^{9} c^{4}}-\frac{12 a c -3 b^{2}}{640 \left(2 c x +b \right)^{5} c^{4}}}{d^{10}}"," ",0,"1/d^10*(-1/384/c^4/(2*c*x+b)^3-1/896*(48*a^2*c^2-24*a*b^2*c+3*b^4)/c^4/(2*c*x+b)^7-1/1152*(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)/c^4/(2*c*x+b)^9-1/640*(12*a*c-3*b^2)/c^4/(2*c*x+b)^5)","A"
1152,1,121,93,0.052000," ","int((c*x^2+b*x+a)^3/(2*c*d*x+b*d)^11,x)","\frac{-\frac{1}{512 \left(2 c x +b \right)^{4} c^{4}}-\frac{48 a^{2} c^{2}-24 a \,b^{2} c +3 b^{4}}{1024 \left(2 c x +b \right)^{8} c^{4}}-\frac{12 a c -3 b^{2}}{768 \left(2 c x +b \right)^{6} c^{4}}-\frac{64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}}{1280 \left(2 c x +b \right)^{10} c^{4}}}{d^{11}}"," ",0,"1/d^11*(-1/512/c^4/(2*c*x+b)^4-1/1024*(48*a^2*c^2-24*a*b^2*c+3*b^4)/c^4/(2*c*x+b)^8-1/768*(12*a*c-3*b^2)/c^4/(2*c*x+b)^6-1/1280*(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)/c^4/(2*c*x+b)^10)","A"
1153,1,121,93,0.051000," ","int((c*x^2+b*x+a)^3/(2*c*d*x+b*d)^12,x)","\frac{-\frac{64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}}{1408 \left(2 c x +b \right)^{11} c^{4}}-\frac{12 a c -3 b^{2}}{896 \left(2 c x +b \right)^{7} c^{4}}-\frac{48 a^{2} c^{2}-24 a \,b^{2} c +3 b^{4}}{1152 \left(2 c x +b \right)^{9} c^{4}}-\frac{1}{640 \left(2 c x +b \right)^{5} c^{4}}}{d^{12}}"," ",0,"1/d^12*(-1/1408*(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)/c^4/(2*c*x+b)^11-1/896*(12*a*c-3*b^2)/c^4/(2*c*x+b)^7-1/1152*(48*a^2*c^2-24*a*b^2*c+3*b^4)/c^4/(2*c*x+b)^9-1/640/c^4/(2*c*x+b)^5)","A"
1154,1,432,112,0.053000," ","int((2*c*d*x+b*d)^8/(c*x^2+b*x+a),x)","\frac{256 c^{7} d^{8} x^{7}}{7}+128 b \,c^{6} d^{8} x^{6}-\frac{256 a \,c^{6} d^{8} x^{5}}{5}+\frac{1024 b^{2} c^{5} d^{8} x^{5}}{5}-128 a b \,c^{5} d^{8} x^{4}+192 b^{3} c^{4} d^{8} x^{4}+\frac{256 a^{2} c^{5} d^{8} x^{3}}{3}-\frac{512 a \,b^{2} c^{4} d^{8} x^{3}}{3}+\frac{352 b^{4} c^{3} d^{8} x^{3}}{3}+\frac{512 a^{4} c^{4} d^{8} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}}-\frac{512 a^{3} b^{2} c^{3} d^{8} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}}+\frac{192 a^{2} b^{4} c^{2} d^{8} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}}+128 a^{2} b \,c^{4} d^{8} x^{2}-\frac{32 a \,b^{6} c \,d^{8} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}}-128 a \,b^{3} c^{3} d^{8} x^{2}+\frac{2 b^{8} d^{8} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}}+48 b^{5} c^{2} d^{8} x^{2}-256 a^{3} c^{4} d^{8} x +256 a^{2} b^{2} c^{3} d^{8} x -96 a \,b^{4} c^{2} d^{8} x +16 b^{6} c \,d^{8} x"," ",0,"256/7*d^8*c^7*x^7+128*d^8*b*c^6*x^6-256/5*d^8*x^5*a*c^6+1024/5*d^8*x^5*b^2*c^5-128*d^8*x^4*a*b*c^5+192*d^8*x^4*b^3*c^4+256/3*d^8*x^3*a^2*c^5-512/3*d^8*x^3*a*b^2*c^4+352/3*d^8*x^3*b^4*c^3+128*d^8*x^2*a^2*b*c^4-128*d^8*x^2*a*b^3*c^3+48*d^8*x^2*b^5*c^2-256*d^8*a^3*c^4*x+256*d^8*b^2*a^2*c^3*x-96*d^8*a*b^4*c^2*x+16*d^8*b^6*c*x+512*d^8/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a^4*c^4-512*d^8/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a^3*b^2*c^3+192*d^8/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a^2*b^4*c^2-32*d^8/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*b^6*c+2*d^8/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^8","B"
1155,1,243,82,0.048000," ","int((2*c*d*x+b*d)^7/(c*x^2+b*x+a),x)","\frac{64 c^{6} d^{7} x^{6}}{3}+64 b \,c^{5} d^{7} x^{5}-32 a \,c^{5} d^{7} x^{4}+88 b^{2} c^{4} d^{7} x^{4}-64 a b \,c^{4} d^{7} x^{3}+\frac{208 b^{3} c^{3} d^{7} x^{3}}{3}+64 a^{2} c^{4} d^{7} x^{2}-80 a \,b^{2} c^{3} d^{7} x^{2}+36 b^{4} c^{2} d^{7} x^{2}-64 a^{3} c^{3} d^{7} \ln \left(c \,x^{2}+b x +a \right)+48 a^{2} b^{2} c^{2} d^{7} \ln \left(c \,x^{2}+b x +a \right)+64 a^{2} b \,c^{3} d^{7} x -12 a \,b^{4} c \,d^{7} \ln \left(c \,x^{2}+b x +a \right)-48 a \,b^{3} c^{2} d^{7} x +b^{6} d^{7} \ln \left(c \,x^{2}+b x +a \right)+12 b^{5} c \,d^{7} x"," ",0,"64/3*d^7*c^6*x^6+64*d^7*b*c^5*x^5-32*d^7*x^4*a*c^5+88*d^7*x^4*b^2*c^4-64*d^7*x^3*a*b*c^4+208/3*d^7*x^3*b^3*c^3+64*d^7*x^2*a^2*c^4-80*d^7*x^2*a*b^2*c^3+36*d^7*x^2*b^4*c^2+64*d^7*a^2*b*c^3*x-48*d^7*a*b^3*c^2*x+12*d^7*b^5*c*x-64*d^7*ln(c*x^2+b*x+a)*a^3*c^3+48*d^7*ln(c*x^2+b*x+a)*a^2*b^2*c^2-12*d^7*ln(c*x^2+b*x+a)*a*b^4*c+d^7*ln(c*x^2+b*x+a)*b^6","B"
1156,1,284,89,0.048000," ","int((2*c*d*x+b*d)^6/(c*x^2+b*x+a),x)","\frac{64 c^{5} d^{6} x^{5}}{5}+32 b \,c^{4} d^{6} x^{4}-\frac{64 a \,c^{4} d^{6} x^{3}}{3}+\frac{112 b^{2} c^{3} d^{6} x^{3}}{3}-\frac{128 a^{3} c^{3} d^{6} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}}+\frac{96 a^{2} b^{2} c^{2} d^{6} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}}-\frac{24 a \,b^{4} c \,d^{6} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}}-32 a b \,c^{3} d^{6} x^{2}+\frac{2 b^{6} d^{6} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}}+24 b^{3} c^{2} d^{6} x^{2}+64 a^{2} c^{3} d^{6} x -48 a \,b^{2} c^{2} d^{6} x +12 b^{4} c \,d^{6} x"," ",0,"64/5*d^6*c^5*x^5+32*d^6*b*c^4*x^4-64/3*d^6*x^3*a*c^4+112/3*d^6*x^3*b^2*c^3-32*d^6*x^2*a*b*c^3+24*d^6*x^2*b^3*c^2+64*d^6*a^2*c^3*x-48*d^6*a*b^2*c^2*x+12*d^6*b^4*c*x-128*d^6/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a^3*c^3+96*d^6/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a^2*b^2*c^2-24*d^6/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*b^4*c+2*d^6/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^6","B"
1157,1,133,59,0.049000," ","int((2*c*d*x+b*d)^5/(c*x^2+b*x+a),x)","8 c^{4} d^{5} x^{4}+16 b \,c^{3} d^{5} x^{3}-16 a \,c^{3} d^{5} x^{2}+16 b^{2} c^{2} d^{5} x^{2}+16 a^{2} c^{2} d^{5} \ln \left(c \,x^{2}+b x +a \right)-8 a \,b^{2} c \,d^{5} \ln \left(c \,x^{2}+b x +a \right)-16 a b \,c^{2} d^{5} x +b^{4} d^{5} \ln \left(c \,x^{2}+b x +a \right)+8 b^{3} c \,d^{5} x"," ",0,"8*x^4*c^4*d^5+16*x^3*b*c^3*d^5-16*x^2*a*c^3*d^5+16*x^2*b^2*c^2*d^5+16*ln(c*x^2+b*x+a)*a^2*c^2*d^5-8*ln(c*x^2+b*x+a)*a*b^2*c*d^5+ln(c*x^2+b*x+a)*b^4*d^5-16*x*a*b*c^2*d^5+8*x*b^3*c*d^5","B"
1158,1,170,66,0.046000," ","int((2*c*d*x+b*d)^4/(c*x^2+b*x+a),x)","\frac{16 c^{3} d^{4} x^{3}}{3}+\frac{32 a^{2} c^{2} d^{4} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}}-\frac{16 a \,b^{2} c \,d^{4} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}}+\frac{2 b^{4} d^{4} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}}+8 b \,c^{2} d^{4} x^{2}-16 a \,c^{2} d^{4} x +8 b^{2} c \,d^{4} x"," ",0,"16/3*d^4*c^3*x^3+8*d^4*b*c^2*x^2-16*d^4*a*c^2*x+8*d^4*b^2*c*x+32*d^4/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a^2*c^2-16*d^4/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*b^2*c+2*d^4/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^4","B"
1159,1,57,36,0.048000," ","int((2*c*d*x+b*d)^3/(c*x^2+b*x+a),x)","4 c^{2} d^{3} x^{2}-4 a c \,d^{3} \ln \left(c \,x^{2}+b x +a \right)+b^{2} d^{3} \ln \left(c \,x^{2}+b x +a \right)+4 b c \,d^{3} x"," ",0,"4*x^2*c^2*d^3-4*ln(c*x^2+b*x+a)*a*c*d^3+ln(c*x^2+b*x+a)*b^2*d^3+4*x*b*c*d^3","A"
1160,1,88,45,0.041000," ","int((2*c*d*x+b*d)^2/(c*x^2+b*x+a),x)","-\frac{8 a c \,d^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}}+\frac{2 b^{2} d^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}}+4 c \,d^{2} x"," ",0,"4*c*d^2*x-8*d^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*c+2*d^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^2","A"
1161,1,14,13,0.042000," ","int((2*c*d*x+b*d)/(c*x^2+b*x+a),x)","d \ln \left(c \,x^{2}+b x +a \right)"," ",0,"d*ln(c*x^2+b*x+a)","A"
1162,1,54,48,0.054000," ","int(1/(2*c*d*x+b*d)/(c*x^2+b*x+a),x)","\frac{2 \ln \left(2 c x +b \right)}{\left(4 a c -b^{2}\right) d}-\frac{\ln \left(c \,x^{2}+b x +a \right)}{\left(4 a c -b^{2}\right) d}"," ",0,"2/d/(4*a*c-b^2)*ln(2*c*x+b)-1/d/(4*a*c-b^2)*ln(c*x^2+b*x+a)","A"
1163,1,64,57,0.050000," ","int(1/(2*c*d*x+b*d)^2/(c*x^2+b*x+a),x)","-\frac{2 \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} d^{2}}-\frac{2}{\left(4 a c -b^{2}\right) \left(2 c x +b \right) d^{2}}"," ",0,"-2/d^2/(4*a*c-b^2)/(2*c*x+b)-2/d^2/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))","A"
1164,1,78,70,0.053000," ","int(1/(2*c*d*x+b*d)^3/(c*x^2+b*x+a),x)","-\frac{2 \ln \left(2 c x +b \right)}{\left(4 a c -b^{2}\right)^{2} d^{3}}+\frac{\ln \left(c \,x^{2}+b x +a \right)}{\left(4 a c -b^{2}\right)^{2} d^{3}}-\frac{1}{\left(4 a c -b^{2}\right) \left(2 c x +b \right)^{2} d^{3}}"," ",0,"-2/d^3/(4*a*c-b^2)^2*ln(2*c*x+b)-1/d^3/(4*a*c-b^2)/(2*c*x+b)^2+1/d^3/(4*a*c-b^2)^2*ln(c*x^2+b*x+a)","A"
1165,1,89,80,0.047000," ","int(1/(2*c*d*x+b*d)^4/(c*x^2+b*x+a),x)","\frac{2 \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{5}{2}} d^{4}}+\frac{2}{\left(4 a c -b^{2}\right)^{2} \left(2 c x +b \right) d^{4}}-\frac{2}{3 \left(4 a c -b^{2}\right) \left(2 c x +b \right)^{3} d^{4}}"," ",0,"2/d^4/(4*a*c-b^2)^2/(2*c*x+b)-2/3/d^4/(4*a*c-b^2)/(2*c*x+b)^3+2/d^4/(4*a*c-b^2)^(5/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))","A"
1166,1,479,118,0.061000," ","int((2*c*d*x+b*d)^8/(c*x^2+b*x+a)^2,x)","\frac{256 c^{6} d^{8} x^{5}}{5}+128 b \,c^{5} d^{8} x^{4}-\frac{512 a \,c^{5} d^{8} x^{3}}{3}+\frac{512 b^{2} c^{4} d^{8} x^{3}}{3}+\frac{128 a^{3} c^{4} d^{8} x}{c \,x^{2}+b x +a}-\frac{1792 a^{3} c^{4} d^{8} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}}-\frac{96 a^{2} b^{2} c^{3} d^{8} x}{c \,x^{2}+b x +a}+\frac{1344 a^{2} b^{2} c^{3} d^{8} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}}+\frac{24 a \,b^{4} c^{2} d^{8} x}{c \,x^{2}+b x +a}-\frac{336 a \,b^{4} c^{2} d^{8} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}}-256 a b \,c^{4} d^{8} x^{2}-\frac{2 b^{6} c \,d^{8} x}{c \,x^{2}+b x +a}+\frac{28 b^{6} c \,d^{8} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}}+128 b^{3} c^{3} d^{8} x^{2}+\frac{64 a^{3} b \,c^{3} d^{8}}{c \,x^{2}+b x +a}-\frac{48 a^{2} b^{3} c^{2} d^{8}}{c \,x^{2}+b x +a}+768 a^{2} c^{4} d^{8} x +\frac{12 a \,b^{5} c \,d^{8}}{c \,x^{2}+b x +a}-512 a \,b^{2} c^{3} d^{8} x -\frac{b^{7} d^{8}}{c \,x^{2}+b x +a}+96 b^{4} c^{2} d^{8} x"," ",0,"256/5*d^8*c^6*x^5+128*d^8*b*c^5*x^4-512/3*d^8*x^3*a*c^5+512/3*d^8*x^3*b^2*c^4-256*d^8*x^2*a*b*c^4+128*d^8*x^2*b^3*c^3+768*d^8*a^2*c^4*x-512*d^8*a*b^2*c^3*x+96*d^8*b^4*c^2*x+128*d^8/(c*x^2+b*x+a)*a^3*c^4*x-96*d^8/(c*x^2+b*x+a)*b^2*a^2*c^3*x+24*d^8/(c*x^2+b*x+a)*a*b^4*c^2*x-2*d^8/(c*x^2+b*x+a)*b^6*c*x+64*d^8/(c*x^2+b*x+a)*a^3*b*c^3-48*d^8/(c*x^2+b*x+a)*a^2*b^3*c^2+12*d^8/(c*x^2+b*x+a)*a*b^5*c-d^8/(c*x^2+b*x+a)*b^7-1792*d^8*c^4/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a^3+1344*d^8*c^3/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a^2*b^2-336*d^8*c^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*b^4+28*d^8*c/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^6","B"
1167,1,230,89,0.057000," ","int((2*c*d*x+b*d)^7/(c*x^2+b*x+a)^2,x)","32 c^{5} d^{7} x^{4}+64 b \,c^{4} d^{7} x^{3}-128 a \,c^{4} d^{7} x^{2}+80 b^{2} c^{3} d^{7} x^{2}+\frac{64 a^{3} c^{3} d^{7}}{c \,x^{2}+b x +a}-\frac{48 a^{2} b^{2} c^{2} d^{7}}{c \,x^{2}+b x +a}+192 a^{2} c^{3} d^{7} \ln \left(c \,x^{2}+b x +a \right)+\frac{12 a \,b^{4} c \,d^{7}}{c \,x^{2}+b x +a}-96 a \,b^{2} c^{2} d^{7} \ln \left(c \,x^{2}+b x +a \right)-128 a b \,c^{3} d^{7} x -\frac{b^{6} d^{7}}{c \,x^{2}+b x +a}+12 b^{4} c \,d^{7} \ln \left(c \,x^{2}+b x +a \right)+48 b^{3} c^{2} d^{7} x"," ",0,"32*d^7*c^5*x^4+64*d^7*b*c^4*x^3-128*d^7*x^2*a*c^4+80*d^7*x^2*b^2*c^3-128*d^7*a*b*c^3*x+48*d^7*b^3*c^2*x+64*d^7/(c*x^2+b*x+a)*a^3*c^3-48*d^7/(c*x^2+b*x+a)*a^2*b^2*c^2+12*d^7/(c*x^2+b*x+a)*a*b^4*c-d^7/(c*x^2+b*x+a)*b^6+192*d^7*ln(c*x^2+b*x+a)*a^2*c^3-96*d^7*ln(c*x^2+b*x+a)*a*b^2*c^2+12*d^7*ln(c*x^2+b*x+a)*b^4*c","B"
1168,1,312,94,0.070000," ","int((2*c*d*x+b*d)^6/(c*x^2+b*x+a)^2,x)","\frac{64 c^{4} d^{6} x^{3}}{3}-\frac{32 a^{2} c^{3} d^{6} x}{c \,x^{2}+b x +a}+\frac{320 a^{2} c^{3} d^{6} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}}+\frac{16 a \,b^{2} c^{2} d^{6} x}{c \,x^{2}+b x +a}-\frac{160 a \,b^{2} c^{2} d^{6} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}}-\frac{2 b^{4} c \,d^{6} x}{c \,x^{2}+b x +a}+\frac{20 b^{4} c \,d^{6} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}}+32 b \,c^{3} d^{6} x^{2}-\frac{16 a^{2} b \,c^{2} d^{6}}{c \,x^{2}+b x +a}+\frac{8 a \,b^{3} c \,d^{6}}{c \,x^{2}+b x +a}-128 a \,c^{3} d^{6} x -\frac{b^{5} d^{6}}{c \,x^{2}+b x +a}+48 b^{2} c^{2} d^{6} x"," ",0,"64/3*d^6*c^4*x^3+32*d^6*b*c^3*x^2-128*d^6*a*c^3*x+48*d^6*b^2*c^2*x-32*d^6/(c*x^2+b*x+a)*a^2*c^3*x+16*d^6/(c*x^2+b*x+a)*a*b^2*c^2*x-2*d^6/(c*x^2+b*x+a)*b^4*c*x-16*d^6/(c*x^2+b*x+a)*a^2*b*c^2+8*d^6/(c*x^2+b*x+a)*a*b^3*c-d^6/(c*x^2+b*x+a)*b^5+320*d^6*c^3/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a^2-160*d^6*c^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*b^2+20*d^6*c/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^4","B"
1169,1,128,65,0.047000," ","int((2*c*d*x+b*d)^5/(c*x^2+b*x+a)^2,x)","16 c^{3} d^{5} x^{2}-\frac{16 a^{2} c^{2} d^{5}}{c \,x^{2}+b x +a}+\frac{8 a \,b^{2} c \,d^{5}}{c \,x^{2}+b x +a}-32 a \,c^{2} d^{5} \ln \left(c \,x^{2}+b x +a \right)-\frac{b^{4} d^{5}}{c \,x^{2}+b x +a}+8 b^{2} c \,d^{5} \ln \left(c \,x^{2}+b x +a \right)+16 b \,c^{2} d^{5} x"," ",0,"16*d^5*c^3*x^2+16*d^5*b*c^2*x-16*d^5/(c*x^2+b*x+a)*a^2*c^2+8*d^5/(c*x^2+b*x+a)*a*b^2*c-d^5/(c*x^2+b*x+a)*b^4-32*d^5*ln(c*x^2+b*x+a)*a*c^2+8*d^5*ln(c*x^2+b*x+a)*b^2*c","A"
1170,1,133,72,0.045000," ","int((2*c*d*x+b*d)^4/(c*x^2+b*x+a)^2,x)","\frac{8 a \,c^{2} d^{4} x}{c \,x^{2}+b x +a}-\frac{2 b^{2} c \,d^{4} x}{c \,x^{2}+b x +a}+\frac{4 a b c \,d^{4}}{c \,x^{2}+b x +a}-\frac{b^{3} d^{4}}{c \,x^{2}+b x +a}+16 c^{2} d^{4} x -12 \sqrt{4 a c -b^{2}}\, c \,d^{4} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)"," ",0,"16*d^4*c^2*x+8*d^4/(c*x^2+b*x+a)*a*c^2*x-2*d^4/(c*x^2+b*x+a)*b^2*c*x+4*d^4/(c*x^2+b*x+a)*a*b*c-d^4/(c*x^2+b*x+a)*b^3-12*d^4*c*(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))","A"
1171,1,58,43,0.049000," ","int((2*c*d*x+b*d)^3/(c*x^2+b*x+a)^2,x)","\frac{4 a c \,d^{3}}{c \,x^{2}+b x +a}-\frac{b^{2} d^{3}}{c \,x^{2}+b x +a}+4 c \,d^{3} \ln \left(c \,x^{2}+b x +a \right)"," ",0,"4*d^3/(c*x^2+b*x+a)*a*c-d^3/(c*x^2+b*x+a)*b^2+4*c*d^3*ln(c*x^2+b*x+a)","A"
1172,1,77,58,0.056000," ","int((2*c*d*x+b*d)^2/(c*x^2+b*x+a)^2,x)","-\frac{2 c \,d^{2} x}{c \,x^{2}+b x +a}+\frac{4 c \,d^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}}-\frac{b \,d^{2}}{c \,x^{2}+b x +a}"," ",0,"-2*d^2/(c*x^2+b*x+a)*c*x-d^2/(c*x^2+b*x+a)*b+4*d^2*c/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))","A"
1173,1,16,15,0.043000," ","int((2*c*d*x+b*d)/(c*x^2+b*x+a)^2,x)","-\frac{d}{c \,x^{2}+b x +a}"," ",0,"-d/(c*x^2+b*x+a)","A"
1174,1,119,78,0.060000," ","int(1/(2*c*d*x+b*d)/(c*x^2+b*x+a)^2,x)","\frac{4 a c}{\left(4 a c -b^{2}\right)^{2} \left(c \,x^{2}+b x +a \right) d}-\frac{b^{2}}{\left(4 a c -b^{2}\right)^{2} \left(c \,x^{2}+b x +a \right) d}+\frac{8 c \ln \left(2 c x +b \right)}{\left(4 a c -b^{2}\right)^{2} d}-\frac{4 c \ln \left(c \,x^{2}+b x +a \right)}{\left(4 a c -b^{2}\right)^{2} d}"," ",0,"8/d*c/(4*a*c-b^2)^2*ln(2*c*x+b)+4/d/(4*a*c-b^2)^2/(c*x^2+b*x+a)*a*c-1/d/(4*a*c-b^2)^2/(c*x^2+b*x+a)*b^2-4/d/(4*a*c-b^2)^2*c*ln(c*x^2+b*x+a)","A"
1175,1,127,94,0.061000," ","int(1/(2*c*d*x+b*d)^2/(c*x^2+b*x+a)^2,x)","-\frac{2 c x}{\left(4 a c -b^{2}\right)^{2} \left(c \,x^{2}+b x +a \right) d^{2}}-\frac{12 c \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{5}{2}} d^{2}}-\frac{b}{\left(4 a c -b^{2}\right)^{2} \left(c \,x^{2}+b x +a \right) d^{2}}-\frac{8 c}{\left(4 a c -b^{2}\right)^{2} \left(2 c x +b \right) d^{2}}"," ",0,"-8/d^2/(4*a*c-b^2)^2*c/(2*c*x+b)-2/d^2/(4*a*c-b^2)^2/(c*x^2+b*x+a)*c*x-1/d^2/(4*a*c-b^2)^2/(c*x^2+b*x+a)*b-12/d^2/(4*a*c-b^2)^(5/2)*c*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))","A"
1176,1,144,110,0.059000," ","int(1/(2*c*d*x+b*d)^3/(c*x^2+b*x+a)^2,x)","-\frac{4 a c}{\left(4 a c -b^{2}\right)^{3} \left(c \,x^{2}+b x +a \right) d^{3}}+\frac{b^{2}}{\left(4 a c -b^{2}\right)^{3} \left(c \,x^{2}+b x +a \right) d^{3}}-\frac{16 c \ln \left(2 c x +b \right)}{\left(4 a c -b^{2}\right)^{3} d^{3}}+\frac{8 c \ln \left(c \,x^{2}+b x +a \right)}{\left(4 a c -b^{2}\right)^{3} d^{3}}-\frac{4 c}{\left(4 a c -b^{2}\right)^{2} \left(2 c x +b \right)^{2} d^{3}}"," ",0,"-16/d^3*c/(4*a*c-b^2)^3*ln(2*c*x+b)-4/d^3*c/(4*a*c-b^2)^2/(2*c*x+b)^2-4/d^3/(4*a*c-b^2)^3/(c*x^2+b*x+a)*a*c+1/d^3/(4*a*c-b^2)^3/(c*x^2+b*x+a)*b^2+8/d^3/(4*a*c-b^2)^3*c*ln(c*x^2+b*x+a)","A"
1177,1,751,152,0.061000," ","int((2*c*d*x+b*d)^10/(c*x^2+b*x+a)^3,x)","\frac{2176 a^{3} c^{6} d^{10} x^{3}}{\left(c \,x^{2}+b x +a \right)^{2}}-\frac{1632 a^{2} b^{2} c^{5} d^{10} x^{3}}{\left(c \,x^{2}+b x +a \right)^{2}}+\frac{408 a \,b^{4} c^{4} d^{10} x^{3}}{\left(c \,x^{2}+b x +a \right)^{2}}-\frac{34 b^{6} c^{3} d^{10} x^{3}}{\left(c \,x^{2}+b x +a \right)^{2}}+\frac{1024 c^{7} d^{10} x^{5}}{5}+\frac{3264 a^{3} b \,c^{5} d^{10} x^{2}}{\left(c \,x^{2}+b x +a \right)^{2}}-\frac{2448 a^{2} b^{3} c^{4} d^{10} x^{2}}{\left(c \,x^{2}+b x +a \right)^{2}}+\frac{612 a \,b^{5} c^{3} d^{10} x^{2}}{\left(c \,x^{2}+b x +a \right)^{2}}-\frac{51 b^{7} c^{2} d^{10} x^{2}}{\left(c \,x^{2}+b x +a \right)^{2}}+512 b \,c^{6} d^{10} x^{4}+\frac{1920 a^{4} c^{5} d^{10} x}{\left(c \,x^{2}+b x +a \right)^{2}}-\frac{288 a^{3} b^{2} c^{4} d^{10} x}{\left(c \,x^{2}+b x +a \right)^{2}}-\frac{504 a^{2} b^{4} c^{3} d^{10} x}{\left(c \,x^{2}+b x +a \right)^{2}}+\frac{186 a \,b^{6} c^{2} d^{10} x}{\left(c \,x^{2}+b x +a \right)^{2}}-1024 a \,c^{6} d^{10} x^{3}-\frac{18 b^{8} c \,d^{10} x}{\left(c \,x^{2}+b x +a \right)^{2}}+768 b^{2} c^{5} d^{10} x^{3}+\frac{960 a^{4} b \,c^{4} d^{10}}{\left(c \,x^{2}+b x +a \right)^{2}}-\frac{688 a^{3} b^{3} c^{3} d^{10}}{\left(c \,x^{2}+b x +a \right)^{2}}-\frac{16128 a^{3} c^{5} d^{10} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}}+\frac{156 a^{2} b^{5} c^{2} d^{10}}{\left(c \,x^{2}+b x +a \right)^{2}}+\frac{12096 a^{2} b^{2} c^{4} d^{10} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}}-\frac{9 a \,b^{7} c \,d^{10}}{\left(c \,x^{2}+b x +a \right)^{2}}-\frac{3024 a \,b^{4} c^{3} d^{10} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}}-1536 a b \,c^{5} d^{10} x^{2}-\frac{b^{9} d^{10}}{2 \left(c \,x^{2}+b x +a \right)^{2}}+\frac{252 b^{6} c^{2} d^{10} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}}+640 b^{3} c^{4} d^{10} x^{2}+6144 a^{2} c^{5} d^{10} x -3840 a \,b^{2} c^{4} d^{10} x +640 b^{4} c^{3} d^{10} x"," ",0,"-1024*d^10*x^3*a*c^6+768*d^10*x^3*b^2*c^5+640*d^10*x^2*b^3*c^4+6144*d^10*a^2*c^5*x+640*d^10*b^4*c^3*x+512*d^10*b*c^6*x^4+156*d^10/(c*x^2+b*x+a)^2*a^2*b^5*c^2-1536*d^10*x^2*a*b*c^5-3840*d^10*a*b^2*c^4*x+612*d^10/(c*x^2+b*x+a)^2*x^2*a*b^5*c^3-504*d^10/(c*x^2+b*x+a)^2*x*a^2*b^4*c^3+186*d^10/(c*x^2+b*x+a)^2*x*a*b^6*c^2-288*d^10/(c*x^2+b*x+a)^2*x*a^3*b^2*c^4-3024*d^10*c^3/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*b^4+12096*d^10*c^4/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a^2*b^2-1632*d^10/(c*x^2+b*x+a)^2*x^3*a^2*b^2*c^5+408*d^10/(c*x^2+b*x+a)^2*x^3*a*b^4*c^4+3264*d^10/(c*x^2+b*x+a)^2*x^2*a^3*b*c^5-2448*d^10/(c*x^2+b*x+a)^2*x^2*a^2*b^3*c^4-1/2*d^10/(c*x^2+b*x+a)^2*b^9+1024/5*d^10*c^7*x^5+2176*d^10/(c*x^2+b*x+a)^2*x^3*a^3*c^6-34*d^10/(c*x^2+b*x+a)^2*x^3*b^6*c^3-51*d^10/(c*x^2+b*x+a)^2*x^2*b^7*c^2+1920*d^10/(c*x^2+b*x+a)^2*x*a^4*c^5-18*d^10/(c*x^2+b*x+a)^2*x*b^8*c+960*d^10/(c*x^2+b*x+a)^2*a^4*b*c^4-688*d^10/(c*x^2+b*x+a)^2*a^3*b^3*c^3-16128*d^10*c^5/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a^3+252*d^10*c^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^6-9*d^10/(c*x^2+b*x+a)^2*a*b^7*c","B"
1178,1,465,121,0.059000," ","int((2*c*d*x+b*d)^9/(c*x^2+b*x+a)^3,x)","\frac{1024 a^{3} c^{5} d^{9} x^{2}}{\left(c \,x^{2}+b x +a \right)^{2}}-\frac{768 a^{2} b^{2} c^{4} d^{9} x^{2}}{\left(c \,x^{2}+b x +a \right)^{2}}+\frac{192 a \,b^{4} c^{3} d^{9} x^{2}}{\left(c \,x^{2}+b x +a \right)^{2}}-\frac{16 b^{6} c^{2} d^{9} x^{2}}{\left(c \,x^{2}+b x +a \right)^{2}}+128 c^{6} d^{9} x^{4}+\frac{1024 a^{3} b \,c^{4} d^{9} x}{\left(c \,x^{2}+b x +a \right)^{2}}-\frac{768 a^{2} b^{3} c^{3} d^{9} x}{\left(c \,x^{2}+b x +a \right)^{2}}+\frac{192 a \,b^{5} c^{2} d^{9} x}{\left(c \,x^{2}+b x +a \right)^{2}}-\frac{16 b^{7} c \,d^{9} x}{\left(c \,x^{2}+b x +a \right)^{2}}+256 b \,c^{5} d^{9} x^{3}+\frac{896 a^{4} c^{4} d^{9}}{\left(c \,x^{2}+b x +a \right)^{2}}-\frac{640 a^{3} b^{2} c^{3} d^{9}}{\left(c \,x^{2}+b x +a \right)^{2}}+\frac{144 a^{2} b^{4} c^{2} d^{9}}{\left(c \,x^{2}+b x +a \right)^{2}}-\frac{8 a \,b^{6} c \,d^{9}}{\left(c \,x^{2}+b x +a \right)^{2}}-768 a \,c^{5} d^{9} x^{2}-\frac{b^{8} d^{9}}{2 \left(c \,x^{2}+b x +a \right)^{2}}+384 b^{2} c^{4} d^{9} x^{2}+1536 a^{2} c^{4} d^{9} \ln \left(c \,x^{2}+b x +a \right)-768 a \,b^{2} c^{3} d^{9} \ln \left(c \,x^{2}+b x +a \right)-768 a b \,c^{4} d^{9} x +96 b^{4} c^{2} d^{9} \ln \left(c \,x^{2}+b x +a \right)+256 b^{3} c^{3} d^{9} x"," ",0,"128*d^9*c^6*x^4+256*d^9*b*c^5*x^3-768*d^9*x^2*a*c^5+384*d^9*x^2*b^2*c^4-768*d^9*a*b*c^4*x+256*d^9*b^3*c^3*x+1024*d^9/(c*x^2+b*x+a)^2*x^2*a^3*c^5-768*d^9/(c*x^2+b*x+a)^2*x^2*a^2*b^2*c^4+192*d^9/(c*x^2+b*x+a)^2*x^2*a*b^4*c^3-16*d^9/(c*x^2+b*x+a)^2*x^2*b^6*c^2+1024*d^9/(c*x^2+b*x+a)^2*x*a^3*b*c^4-768*d^9/(c*x^2+b*x+a)^2*x*a^2*b^3*c^3+192*d^9/(c*x^2+b*x+a)^2*x*a*b^5*c^2-16*d^9/(c*x^2+b*x+a)^2*x*b^7*c+896*d^9/(c*x^2+b*x+a)^2*a^4*c^4-640*d^9/(c*x^2+b*x+a)^2*a^3*b^2*c^3+144*d^9/(c*x^2+b*x+a)^2*a^2*b^4*c^2-8*d^9/(c*x^2+b*x+a)^2*a*b^6*c-1/2*d^9/(c*x^2+b*x+a)^2*b^8+1536*d^9*ln(c*x^2+b*x+a)*a^2*c^4-768*d^9*ln(c*x^2+b*x+a)*a*b^2*c^3+96*d^9*ln(c*x^2+b*x+a)*b^4*c^2","B"
1179,1,526,126,0.061000," ","int((2*c*d*x+b*d)^8/(c*x^2+b*x+a)^3,x)","-\frac{416 a^{2} c^{5} d^{8} x^{3}}{\left(c \,x^{2}+b x +a \right)^{2}}+\frac{208 a \,b^{2} c^{4} d^{8} x^{3}}{\left(c \,x^{2}+b x +a \right)^{2}}-\frac{26 b^{4} c^{3} d^{8} x^{3}}{\left(c \,x^{2}+b x +a \right)^{2}}-\frac{624 a^{2} b \,c^{4} d^{8} x^{2}}{\left(c \,x^{2}+b x +a \right)^{2}}+\frac{312 a \,b^{3} c^{3} d^{8} x^{2}}{\left(c \,x^{2}+b x +a \right)^{2}}-\frac{39 b^{5} c^{2} d^{8} x^{2}}{\left(c \,x^{2}+b x +a \right)^{2}}-\frac{352 a^{3} c^{4} d^{8} x}{\left(c \,x^{2}+b x +a \right)^{2}}-\frac{48 a^{2} b^{2} c^{3} d^{8} x}{\left(c \,x^{2}+b x +a \right)^{2}}+\frac{90 a \,b^{4} c^{2} d^{8} x}{\left(c \,x^{2}+b x +a \right)^{2}}-\frac{14 b^{6} c \,d^{8} x}{\left(c \,x^{2}+b x +a \right)^{2}}+\frac{256 c^{5} d^{8} x^{3}}{3}-\frac{176 a^{3} b \,c^{3} d^{8}}{\left(c \,x^{2}+b x +a \right)^{2}}+\frac{80 a^{2} b^{3} c^{2} d^{8}}{\left(c \,x^{2}+b x +a \right)^{2}}+\frac{2240 a^{2} c^{4} d^{8} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}}-\frac{7 a \,b^{5} c \,d^{8}}{\left(c \,x^{2}+b x +a \right)^{2}}-\frac{1120 a \,b^{2} c^{3} d^{8} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}}-\frac{b^{7} d^{8}}{2 \left(c \,x^{2}+b x +a \right)^{2}}+\frac{140 b^{4} c^{2} d^{8} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}}+128 b \,c^{4} d^{8} x^{2}-768 a \,c^{4} d^{8} x +256 b^{2} c^{3} d^{8} x"," ",0,"256/3*d^8*c^5*x^3+128*d^8*b*c^4*x^2-768*d^8*a*c^4*x+256*d^8*b^2*c^3*x-416*d^8/(c*x^2+b*x+a)^2*x^3*a^2*c^5+208*d^8/(c*x^2+b*x+a)^2*x^3*a*b^2*c^4-26*d^8/(c*x^2+b*x+a)^2*x^3*b^4*c^3-624*d^8/(c*x^2+b*x+a)^2*x^2*a^2*b*c^4+312*d^8/(c*x^2+b*x+a)^2*x^2*a*b^3*c^3-39*d^8/(c*x^2+b*x+a)^2*x^2*b^5*c^2-352*d^8/(c*x^2+b*x+a)^2*a^3*c^4*x-48*d^8/(c*x^2+b*x+a)^2*b^2*a^2*c^3*x+90*d^8/(c*x^2+b*x+a)^2*a*b^4*c^2*x-14*d^8/(c*x^2+b*x+a)^2*b^6*c*x-176*d^8/(c*x^2+b*x+a)^2*a^3*b*c^3+80*d^8/(c*x^2+b*x+a)^2*a^2*b^3*c^2-7*d^8/(c*x^2+b*x+a)^2*a*b^5*c-1/2*d^8/(c*x^2+b*x+a)^2*b^7+2240*d^8*c^4/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a^2-1120*d^8*c^3/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*b^2+140*d^8*c^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^4","B"
1180,1,307,95,0.065000," ","int((2*c*d*x+b*d)^7/(c*x^2+b*x+a)^3,x)","-\frac{192 a^{2} c^{4} d^{7} x^{2}}{\left(c \,x^{2}+b x +a \right)^{2}}+\frac{96 a \,b^{2} c^{3} d^{7} x^{2}}{\left(c \,x^{2}+b x +a \right)^{2}}-\frac{12 b^{4} c^{2} d^{7} x^{2}}{\left(c \,x^{2}+b x +a \right)^{2}}-\frac{192 a^{2} b \,c^{3} d^{7} x}{\left(c \,x^{2}+b x +a \right)^{2}}+\frac{96 a \,b^{3} c^{2} d^{7} x}{\left(c \,x^{2}+b x +a \right)^{2}}-\frac{12 b^{5} c \,d^{7} x}{\left(c \,x^{2}+b x +a \right)^{2}}-\frac{160 a^{3} c^{3} d^{7}}{\left(c \,x^{2}+b x +a \right)^{2}}+\frac{72 a^{2} b^{2} c^{2} d^{7}}{\left(c \,x^{2}+b x +a \right)^{2}}-\frac{6 a \,b^{4} c \,d^{7}}{\left(c \,x^{2}+b x +a \right)^{2}}-\frac{b^{6} d^{7}}{2 \left(c \,x^{2}+b x +a \right)^{2}}+64 c^{4} d^{7} x^{2}-192 a \,c^{3} d^{7} \ln \left(c \,x^{2}+b x +a \right)+48 b^{2} c^{2} d^{7} \ln \left(c \,x^{2}+b x +a \right)+64 b \,c^{3} d^{7} x"," ",0,"64*d^7*c^4*x^2+64*d^7*b*c^3*x-192*d^7/(c*x^2+b*x+a)^2*x^2*a^2*c^4+96*d^7/(c*x^2+b*x+a)^2*x^2*a*b^2*c^3-12*d^7/(c*x^2+b*x+a)^2*x^2*b^4*c^2-192*d^7/(c*x^2+b*x+a)^2*a^2*b*c^3*x+96*d^7/(c*x^2+b*x+a)^2*a*b^3*c^2*x-12*d^7/(c*x^2+b*x+a)^2*b^5*c*x-160*d^7/(c*x^2+b*x+a)^2*a^3*c^3+72*d^7/(c*x^2+b*x+a)^2*a^2*b^2*c^2-6*d^7/(c*x^2+b*x+a)^2*a*b^4*c-1/2*d^7/(c*x^2+b*x+a)^2*b^6-192*d^7*ln(c*x^2+b*x+a)*a*c^3+48*d^7*ln(c*x^2+b*x+a)*b^2*c^2","B"
1181,1,289,102,0.061000," ","int((2*c*d*x+b*d)^6/(c*x^2+b*x+a)^3,x)","\frac{72 a \,c^{4} d^{6} x^{3}}{\left(c \,x^{2}+b x +a \right)^{2}}-\frac{18 b^{2} c^{3} d^{6} x^{3}}{\left(c \,x^{2}+b x +a \right)^{2}}+\frac{108 a b \,c^{3} d^{6} x^{2}}{\left(c \,x^{2}+b x +a \right)^{2}}-\frac{27 b^{3} c^{2} d^{6} x^{2}}{\left(c \,x^{2}+b x +a \right)^{2}}+\frac{56 a^{2} c^{3} d^{6} x}{\left(c \,x^{2}+b x +a \right)^{2}}+\frac{26 a \,b^{2} c^{2} d^{6} x}{\left(c \,x^{2}+b x +a \right)^{2}}-\frac{10 b^{4} c \,d^{6} x}{\left(c \,x^{2}+b x +a \right)^{2}}+\frac{28 a^{2} b \,c^{2} d^{6}}{\left(c \,x^{2}+b x +a \right)^{2}}-\frac{5 a \,b^{3} c \,d^{6}}{\left(c \,x^{2}+b x +a \right)^{2}}-\frac{b^{5} d^{6}}{2 \left(c \,x^{2}+b x +a \right)^{2}}+64 c^{3} d^{6} x -60 \sqrt{4 a c -b^{2}}\, c^{2} d^{6} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)"," ",0,"64*d^6*c^3*x+72*d^6/(c*x^2+b*x+a)^2*x^3*a*c^4-18*d^6/(c*x^2+b*x+a)^2*x^3*b^2*c^3+108*d^6/(c*x^2+b*x+a)^2*x^2*a*b*c^3-27*d^6/(c*x^2+b*x+a)^2*x^2*b^3*c^2+56*d^6/(c*x^2+b*x+a)^2*a^2*c^3*x+26*d^6/(c*x^2+b*x+a)^2*a*b^2*c^2*x-10*d^6/(c*x^2+b*x+a)^2*b^4*c*x+28*d^6/(c*x^2+b*x+a)^2*a^2*b*c^2-5*d^6/(c*x^2+b*x+a)^2*a*b^3*c-1/2*d^6/(c*x^2+b*x+a)^2*b^5-60*d^6*c^2*(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))","B"
1182,1,181,71,0.052000," ","int((2*c*d*x+b*d)^5/(c*x^2+b*x+a)^3,x)","\frac{32 a \,c^{3} d^{5} x^{2}}{\left(c \,x^{2}+b x +a \right)^{2}}-\frac{8 b^{2} c^{2} d^{5} x^{2}}{\left(c \,x^{2}+b x +a \right)^{2}}+\frac{32 a b \,c^{2} d^{5} x}{\left(c \,x^{2}+b x +a \right)^{2}}-\frac{8 b^{3} c \,d^{5} x}{\left(c \,x^{2}+b x +a \right)^{2}}+\frac{24 a^{2} c^{2} d^{5}}{\left(c \,x^{2}+b x +a \right)^{2}}-\frac{4 a \,b^{2} c \,d^{5}}{\left(c \,x^{2}+b x +a \right)^{2}}-\frac{b^{4} d^{5}}{2 \left(c \,x^{2}+b x +a \right)^{2}}+16 c^{2} d^{5} \ln \left(c \,x^{2}+b x +a \right)"," ",0,"32*d^5/(c*x^2+b*x+a)^2*x^2*a*c^3-8*d^5/(c*x^2+b*x+a)^2*x^2*b^2*c^2+32*d^5/(c*x^2+b*x+a)^2*b*a*c^2*x-8*d^5/(c*x^2+b*x+a)^2*b^3*c*x+24*d^5/(c*x^2+b*x+a)^2*a^2*c^2-4*d^5/(c*x^2+b*x+a)^2*a*b^2*c-1/2*d^5/(c*x^2+b*x+a)^2*b^4+16*c^2*d^5*ln(c*x^2+b*x+a)","B"
1183,1,173,86,0.056000," ","int((2*c*d*x+b*d)^4/(c*x^2+b*x+a)^3,x)","-\frac{10 c^{3} d^{4} x^{3}}{\left(c \,x^{2}+b x +a \right)^{2}}-\frac{15 b \,c^{2} d^{4} x^{2}}{\left(c \,x^{2}+b x +a \right)^{2}}-\frac{6 a \,c^{2} d^{4} x}{\left(c \,x^{2}+b x +a \right)^{2}}-\frac{6 b^{2} c \,d^{4} x}{\left(c \,x^{2}+b x +a \right)^{2}}-\frac{3 a b c \,d^{4}}{\left(c \,x^{2}+b x +a \right)^{2}}-\frac{b^{3} d^{4}}{2 \left(c \,x^{2}+b x +a \right)^{2}}+\frac{12 c^{2} d^{4} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}}"," ",0,"-10*d^4/(c*x^2+b*x+a)^2*c^3*x^3-15*d^4/(c*x^2+b*x+a)^2*b*c^2*x^2-6*d^4/(c*x^2+b*x+a)^2*a*c^2*x-6*d^4/(c*x^2+b*x+a)^2*b^2*c*x-3*d^4/(c*x^2+b*x+a)^2*a*b*c-1/2*d^4/(c*x^2+b*x+a)^2*b^3+12*d^4*c^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))","A"
1184,1,40,35,0.056000," ","int((2*c*d*x+b*d)^3/(c*x^2+b*x+a)^3,x)","\frac{\left(-4 c^{2} x^{2}-4 b c x -2 a c -\frac{1}{2} b^{2}\right) d^{3}}{\left(c \,x^{2}+b x +a \right)^{2}}"," ",0,"d^3*(-4*c^2*x^2-4*b*c*x-2*a*c-1/2*b^2)/(c*x^2+b*x+a)^2","A"
1185,1,245,94,0.056000," ","int((2*c*d*x+b*d)^2/(c*x^2+b*x+a)^3,x)","\frac{2 c^{3} d^{2} x^{3}}{\left(c \,x^{2}+b x +a \right)^{2} \left(4 a c -b^{2}\right)}+\frac{3 b \,c^{2} d^{2} x^{2}}{\left(c \,x^{2}+b x +a \right)^{2} \left(4 a c -b^{2}\right)}-\frac{2 a \,c^{2} d^{2} x}{\left(c \,x^{2}+b x +a \right)^{2} \left(4 a c -b^{2}\right)}+\frac{2 b^{2} c \,d^{2} x}{\left(c \,x^{2}+b x +a \right)^{2} \left(4 a c -b^{2}\right)}-\frac{a b c \,d^{2}}{\left(c \,x^{2}+b x +a \right)^{2} \left(4 a c -b^{2}\right)}+\frac{b^{3} d^{2}}{2 \left(c \,x^{2}+b x +a \right)^{2} \left(4 a c -b^{2}\right)}+\frac{4 c^{2} d^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}}}"," ",0,"2*d^2/(c*x^2+b*x+a)^2*c^3/(4*a*c-b^2)*x^3+3*d^2/(c*x^2+b*x+a)^2*b*c^2/(4*a*c-b^2)*x^2-2*d^2/(c*x^2+b*x+a)^2*c^2/(4*a*c-b^2)*x*a+2*d^2/(c*x^2+b*x+a)^2*c/(4*a*c-b^2)*x*b^2-d^2/(c*x^2+b*x+a)^2*b/(4*a*c-b^2)*a*c+1/2*d^2/(c*x^2+b*x+a)^2*b^3/(4*a*c-b^2)+4*d^2*c^2/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))","B"
1186,1,16,15,0.045000," ","int((2*c*d*x+b*d)/(c*x^2+b*x+a)^3,x)","-\frac{d}{2 \left(c \,x^{2}+b x +a \right)^{2}}"," ",0,"-1/2*d/(c*x^2+b*x+a)^2","A"
1187,1,304,110,0.070000," ","int(1/(2*c*d*x+b*d)/(c*x^2+b*x+a)^3,x)","\frac{16 a \,c^{3} x^{2}}{\left(4 a c -b^{2}\right)^{3} \left(c \,x^{2}+b x +a \right)^{2} d}-\frac{4 b^{2} c^{2} x^{2}}{\left(4 a c -b^{2}\right)^{3} \left(c \,x^{2}+b x +a \right)^{2} d}+\frac{16 a b \,c^{2} x}{\left(4 a c -b^{2}\right)^{3} \left(c \,x^{2}+b x +a \right)^{2} d}-\frac{4 b^{3} c x}{\left(4 a c -b^{2}\right)^{3} \left(c \,x^{2}+b x +a \right)^{2} d}+\frac{24 a^{2} c^{2}}{\left(4 a c -b^{2}\right)^{3} \left(c \,x^{2}+b x +a \right)^{2} d}-\frac{8 a \,b^{2} c}{\left(4 a c -b^{2}\right)^{3} \left(c \,x^{2}+b x +a \right)^{2} d}+\frac{b^{4}}{2 \left(4 a c -b^{2}\right)^{3} \left(c \,x^{2}+b x +a \right)^{2} d}+\frac{32 c^{2} \ln \left(2 c x +b \right)}{\left(4 a c -b^{2}\right)^{3} d}-\frac{16 c^{2} \ln \left(c \,x^{2}+b x +a \right)}{\left(4 a c -b^{2}\right)^{3} d}"," ",0,"32/d*c^2/(4*a*c-b^2)^3*ln(2*c*x+b)+16/d/(4*a*c-b^2)^3/(c*x^2+b*x+a)^2*x^2*a*c^3-4/d/(4*a*c-b^2)^3/(c*x^2+b*x+a)^2*x^2*b^2*c^2+16/d/(4*a*c-b^2)^3/(c*x^2+b*x+a)^2*b*a*c^2*x-4/d/(4*a*c-b^2)^3/(c*x^2+b*x+a)^2*b^3*c*x+24/d/(4*a*c-b^2)^3/(c*x^2+b*x+a)^2*a^2*c^2-8/d/(4*a*c-b^2)^3/(c*x^2+b*x+a)^2*a*b^2*c+1/2/d/(4*a*c-b^2)^3/(c*x^2+b*x+a)^2*b^4-16/d/(4*a*c-b^2)^3*c^2*ln(c*x^2+b*x+a)","B"
1188,1,273,134,0.062000," ","int(1/(2*c*d*x+b*d)^2/(c*x^2+b*x+a)^3,x)","-\frac{14 c^{3} x^{3}}{\left(4 a c -b^{2}\right)^{3} \left(c \,x^{2}+b x +a \right)^{2} d^{2}}-\frac{21 b \,c^{2} x^{2}}{\left(4 a c -b^{2}\right)^{3} \left(c \,x^{2}+b x +a \right)^{2} d^{2}}-\frac{18 a \,c^{2} x}{\left(4 a c -b^{2}\right)^{3} \left(c \,x^{2}+b x +a \right)^{2} d^{2}}-\frac{6 b^{2} c x}{\left(4 a c -b^{2}\right)^{3} \left(c \,x^{2}+b x +a \right)^{2} d^{2}}-\frac{9 a b c}{\left(4 a c -b^{2}\right)^{3} \left(c \,x^{2}+b x +a \right)^{2} d^{2}}+\frac{b^{3}}{2 \left(4 a c -b^{2}\right)^{3} \left(c \,x^{2}+b x +a \right)^{2} d^{2}}-\frac{60 c^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{7}{2}} d^{2}}-\frac{32 c^{2}}{\left(4 a c -b^{2}\right)^{3} \left(2 c x +b \right) d^{2}}"," ",0,"-32/d^2/(4*a*c-b^2)^3*c^2/(2*c*x+b)-14/d^2/(4*a*c-b^2)^3/(c*x^2+b*x+a)^2*c^3*x^3-21/d^2/(4*a*c-b^2)^3/(c*x^2+b*x+a)^2*b*c^2*x^2-18/d^2/(4*a*c-b^2)^3/(c*x^2+b*x+a)^2*a*c^2*x-6/d^2/(4*a*c-b^2)^3/(c*x^2+b*x+a)^2*b^2*c*x-9/d^2/(4*a*c-b^2)^3/(c*x^2+b*x+a)^2*a*b*c+1/2/d^2/(4*a*c-b^2)^3/(c*x^2+b*x+a)^2*b^3-60/d^2/(4*a*c-b^2)^(7/2)*c^2*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))","B"
1189,1,332,152,0.069000," ","int(1/(2*c*d*x+b*d)^3/(c*x^2+b*x+a)^3,x)","-\frac{32 a \,c^{3} x^{2}}{\left(4 a c -b^{2}\right)^{4} \left(c \,x^{2}+b x +a \right)^{2} d^{3}}+\frac{8 b^{2} c^{2} x^{2}}{\left(4 a c -b^{2}\right)^{4} \left(c \,x^{2}+b x +a \right)^{2} d^{3}}-\frac{32 a b \,c^{2} x}{\left(4 a c -b^{2}\right)^{4} \left(c \,x^{2}+b x +a \right)^{2} d^{3}}+\frac{8 b^{3} c x}{\left(4 a c -b^{2}\right)^{4} \left(c \,x^{2}+b x +a \right)^{2} d^{3}}-\frac{40 a^{2} c^{2}}{\left(4 a c -b^{2}\right)^{4} \left(c \,x^{2}+b x +a \right)^{2} d^{3}}+\frac{12 a \,b^{2} c}{\left(4 a c -b^{2}\right)^{4} \left(c \,x^{2}+b x +a \right)^{2} d^{3}}-\frac{b^{4}}{2 \left(4 a c -b^{2}\right)^{4} \left(c \,x^{2}+b x +a \right)^{2} d^{3}}-\frac{96 c^{2} \ln \left(2 c x +b \right)}{\left(4 a c -b^{2}\right)^{4} d^{3}}+\frac{48 c^{2} \ln \left(c \,x^{2}+b x +a \right)}{\left(4 a c -b^{2}\right)^{4} d^{3}}-\frac{16 c^{2}}{\left(4 a c -b^{2}\right)^{3} \left(2 c x +b \right)^{2} d^{3}}"," ",0,"-96/d^3*c^2/(4*a*c-b^2)^4*ln(2*c*x+b)-16/d^3*c^2/(4*a*c-b^2)^3/(2*c*x+b)^2-32/d^3/(4*a*c-b^2)^4/(c*x^2+b*x+a)^2*x^2*a*c^3+8/d^3/(4*a*c-b^2)^4/(c*x^2+b*x+a)^2*x^2*b^2*c^2-32/d^3/(4*a*c-b^2)^4/(c*x^2+b*x+a)^2*b*a*c^2*x+8/d^3/(4*a*c-b^2)^4/(c*x^2+b*x+a)^2*b^3*c*x-40/d^3/(4*a*c-b^2)^4/(c*x^2+b*x+a)^2*a^2*c^2+12/d^3/(4*a*c-b^2)^4/(c*x^2+b*x+a)^2*a*b^2*c-1/2/d^3/(4*a*c-b^2)^4/(c*x^2+b*x+a)^2*b^4+48/d^3/(4*a*c-b^2)^4*c^2*ln(c*x^2+b*x+a)","B"
1190,1,301,160,0.066000," ","int(1/(2*c*d*x+b*d)^4/(c*x^2+b*x+a)^3,x)","\frac{22 c^{3} x^{3}}{\left(4 a c -b^{2}\right)^{4} \left(c \,x^{2}+b x +a \right)^{2} d^{4}}+\frac{33 b \,c^{2} x^{2}}{\left(4 a c -b^{2}\right)^{4} \left(c \,x^{2}+b x +a \right)^{2} d^{4}}+\frac{26 a \,c^{2} x}{\left(4 a c -b^{2}\right)^{4} \left(c \,x^{2}+b x +a \right)^{2} d^{4}}+\frac{10 b^{2} c x}{\left(4 a c -b^{2}\right)^{4} \left(c \,x^{2}+b x +a \right)^{2} d^{4}}+\frac{13 a b c}{\left(4 a c -b^{2}\right)^{4} \left(c \,x^{2}+b x +a \right)^{2} d^{4}}-\frac{b^{3}}{2 \left(4 a c -b^{2}\right)^{4} \left(c \,x^{2}+b x +a \right)^{2} d^{4}}+\frac{140 c^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{9}{2}} d^{4}}+\frac{96 c^{2}}{\left(4 a c -b^{2}\right)^{4} \left(2 c x +b \right) d^{4}}-\frac{32 c^{2}}{3 \left(4 a c -b^{2}\right)^{3} \left(2 c x +b \right)^{3} d^{4}}"," ",0,"96/d^4/(4*a*c-b^2)^4*c^2/(2*c*x+b)-32/3/d^4*c^2/(4*a*c-b^2)^3/(2*c*x+b)^3+22/d^4/(4*a*c-b^2)^4/(c*x^2+b*x+a)^2*c^3*x^3+33/d^4/(4*a*c-b^2)^4/(c*x^2+b*x+a)^2*b*c^2*x^2+26/d^4/(4*a*c-b^2)^4/(c*x^2+b*x+a)^2*a*c^2*x+10/d^4/(4*a*c-b^2)^4/(c*x^2+b*x+a)^2*b^2*c*x+13/d^4/(4*a*c-b^2)^4/(c*x^2+b*x+a)^2*a*b*c-1/2/d^4/(4*a*c-b^2)^4/(c*x^2+b*x+a)^2*b^3+140/d^4/(4*a*c-b^2)^(9/2)*c^2*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))","A"
1191,1,413,143,0.063000," ","int((2*c*d*x+b*d)^4*(c*x^2+b*x+a)^(1/2),x)","\frac{8 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{3} d^{4} x^{3}}{3}+a^{3} c^{\frac{3}{2}} d^{4} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)-\frac{3 a^{2} b^{2} \sqrt{c}\, d^{4} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{4}+\frac{3 a \,b^{4} d^{4} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{16 \sqrt{c}}-\frac{b^{6} d^{4} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{64 c^{\frac{3}{2}}}+\sqrt{c \,x^{2}+b x +a}\, a^{2} c^{2} d^{4} x -\frac{\sqrt{c \,x^{2}+b x +a}\, a \,b^{2} c \,d^{4} x}{2}+\frac{\sqrt{c \,x^{2}+b x +a}\, b^{4} d^{4} x}{16}+4 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b \,c^{2} d^{4} x^{2}+\frac{\sqrt{c \,x^{2}+b x +a}\, a^{2} b c \,d^{4}}{2}-\frac{\sqrt{c \,x^{2}+b x +a}\, a \,b^{3} d^{4}}{4}-2 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a \,c^{2} d^{4} x +\frac{\sqrt{c \,x^{2}+b x +a}\, b^{5} d^{4}}{32 c}+\frac{5 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{2} c \,d^{4} x}{2}-\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a b c \,d^{4}+\frac{7 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{3} d^{4}}{12}"," ",0,"7/12*d^4*b^3*(c*x^2+b*x+a)^(3/2)+4*d^4*c^2*b*x^2*(c*x^2+b*x+a)^(3/2)+5/2*d^4*c*b^2*x*(c*x^2+b*x+a)^(3/2)-1/64*d^4*b^6/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-d^4*c*b*a*(c*x^2+b*x+a)^(3/2)-2*d^4*c^2*a*x*(c*x^2+b*x+a)^(3/2)+d^4*c^2*a^2*x*(c*x^2+b*x+a)^(1/2)+1/2*d^4*c*a^2*(c*x^2+b*x+a)^(1/2)*b+d^4*c^(3/2)*a^3*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+3/16*d^4*b^4/c^(1/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a-1/2*d^4*c*b^2*a*x*(c*x^2+b*x+a)^(1/2)-3/4*d^4*c^(1/2)*b^2*a^2*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+8/3*d^4*c^3*x^3*(c*x^2+b*x+a)^(3/2)+1/16*d^4*b^4*x*(c*x^2+b*x+a)^(1/2)+1/32*d^4/c*b^5*(c*x^2+b*x+a)^(1/2)-1/4*d^4*b^3*a*(c*x^2+b*x+a)^(1/2)","B"
1192,1,41,51,0.046000," ","int((2*c*d*x+b*d)^3*(c*x^2+b*x+a)^(1/2),x)","-\frac{2 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} \left(-12 c^{2} x^{2}-12 b c x +8 a c -5 b^{2}\right) d^{3}}{15}"," ",0,"-2/15*(c*x^2+b*x+a)^(3/2)*(-12*c^2*x^2-12*b*c*x+8*a*c-5*b^2)*d^3","A"
1193,1,230,105,0.051000," ","int((2*c*d*x+b*d)^2*(c*x^2+b*x+a)^(1/2),x)","-\frac{a^{2} \sqrt{c}\, d^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{2}+\frac{a \,b^{2} d^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{4 \sqrt{c}}-\frac{b^{4} d^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{32 c^{\frac{3}{2}}}-\frac{\sqrt{c \,x^{2}+b x +a}\, a c \,d^{2} x}{2}+\frac{\sqrt{c \,x^{2}+b x +a}\, b^{2} d^{2} x}{8}-\frac{\sqrt{c \,x^{2}+b x +a}\, a b \,d^{2}}{4}+\frac{\sqrt{c \,x^{2}+b x +a}\, b^{3} d^{2}}{16 c}+\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c \,d^{2} x +\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b \,d^{2}}{2}"," ",0,"d^2*c*x*(c*x^2+b*x+a)^(3/2)+1/2*d^2*b*(c*x^2+b*x+a)^(3/2)+1/8*d^2*b^2*x*(c*x^2+b*x+a)^(1/2)+1/16*d^2/c*b^3*(c*x^2+b*x+a)^(1/2)+1/4*d^2*b^2/c^(1/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a-1/32*d^2*b^4/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-1/2*d^2*c*a*x*(c*x^2+b*x+a)^(1/2)-1/4*d^2*a*(c*x^2+b*x+a)^(1/2)*b-1/2*d^2*c^(1/2)*a^2*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))","B"
1194,1,16,15,0.047000," ","int((2*c*d*x+b*d)*(c*x^2+b*x+a)^(1/2),x)","\frac{2 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} d}{3}"," ",0,"2/3*d*(c*x^2+b*x+a)^(3/2)","A"
1195,1,244,67,0.082000," ","int((c*x^2+b*x+a)^(1/2)/(2*c*d*x+b*d),x)","-\frac{a \ln \left(\frac{\frac{4 a c -b^{2}}{2 c}+\frac{\sqrt{\frac{4 a c -b^{2}}{c}}\, \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}}{2}}{x +\frac{b}{2 c}}\right)}{\sqrt{\frac{4 a c -b^{2}}{c}}\, c d}+\frac{b^{2} \ln \left(\frac{\frac{4 a c -b^{2}}{2 c}+\frac{\sqrt{\frac{4 a c -b^{2}}{c}}\, \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}}{2}}{x +\frac{b}{2 c}}\right)}{4 \sqrt{\frac{4 a c -b^{2}}{c}}\, c^{2} d}+\frac{\sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}}{4 c d}"," ",0,"1/4/c/d*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2)-1/c/d/((4*a*c-b^2)/c)^(1/2)*ln((1/2*(4*a*c-b^2)/c+1/2*((4*a*c-b^2)/c)^(1/2)*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2))/(x+1/2*b/c))*a+1/4/c^2/d/((4*a*c-b^2)/c)^(1/2)*ln((1/2*(4*a*c-b^2)/c+1/2*((4*a*c-b^2)/c)^(1/2)*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2))/(x+1/2*b/c))*b^2","B"
1196,1,291,61,0.059000," ","int((c*x^2+b*x+a)^(1/2)/(2*c*d*x+b*d)^2,x)","\frac{a \ln \left(\left(x +\frac{b}{2 c}\right) \sqrt{c}+\sqrt{\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{c}\, d^{2}}-\frac{b^{2} \ln \left(\left(x +\frac{b}{2 c}\right) \sqrt{c}+\sqrt{\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}}\right)}{4 \left(4 a c -b^{2}\right) c^{\frac{3}{2}} d^{2}}+\frac{\sqrt{\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}}\, x}{\left(4 a c -b^{2}\right) d^{2}}+\frac{\sqrt{\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}}\, b}{2 \left(4 a c -b^{2}\right) c \,d^{2}}-\frac{\left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{3}{2}}}{\left(4 a c -b^{2}\right) \left(x +\frac{b}{2 c}\right) c \,d^{2}}"," ",0,"-1/c/d^2/(4*a*c-b^2)/(x+1/2*b/c)*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(3/2)+1/d^2/(4*a*c-b^2)*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(1/2)*x+1/2/c/d^2/(4*a*c-b^2)*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(1/2)*b+1/c^(1/2)/d^2/(4*a*c-b^2)*ln(c^(1/2)*(x+1/2*b/c)+((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(1/2))*a-1/4/c^(3/2)/d^2/(4*a*c-b^2)*ln(c^(1/2)*(x+1/2*b/c)+((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(1/2))*b^2","B"
1197,1,340,75,0.059000," ","int((c*x^2+b*x+a)^(1/2)/(2*c*d*x+b*d)^3,x)","-\frac{a \ln \left(\frac{\frac{4 a c -b^{2}}{2 c}+\frac{\sqrt{\frac{4 a c -b^{2}}{c}}\, \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}}{2}}{x +\frac{b}{2 c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\frac{4 a c -b^{2}}{c}}\, c \,d^{3}}+\frac{b^{2} \ln \left(\frac{\frac{4 a c -b^{2}}{2 c}+\frac{\sqrt{\frac{4 a c -b^{2}}{c}}\, \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}}{2}}{x +\frac{b}{2 c}}\right)}{8 \left(4 a c -b^{2}\right) \sqrt{\frac{4 a c -b^{2}}{c}}\, c^{2} d^{3}}+\frac{\sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}}{8 \left(4 a c -b^{2}\right) c \,d^{3}}-\frac{\left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{3}{2}}}{4 \left(4 a c -b^{2}\right) \left(x +\frac{b}{2 c}\right)^{2} c^{2} d^{3}}"," ",0,"-1/4/d^3/c^2/(4*a*c-b^2)/(x+1/2*b/c)^2*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(3/2)+1/8/d^3/c/(4*a*c-b^2)*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2)-1/2/d^3/c/(4*a*c-b^2)/((4*a*c-b^2)/c)^(1/2)*ln((1/2*(4*a*c-b^2)/c+1/2*((4*a*c-b^2)/c)^(1/2)*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2))/(x+1/2*b/c))*a+1/8/d^3/c^2/(4*a*c-b^2)/((4*a*c-b^2)/c)^(1/2)*ln((1/2*(4*a*c-b^2)/c+1/2*((4*a*c-b^2)/c)^(1/2)*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2))/(x+1/2*b/c))*b^2","B"
1198,1,38,35,0.059000," ","int((c*x^2+b*x+a)^(1/2)/(2*c*d*x+b*d)^4,x)","-\frac{2 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}}}{3 \left(2 c x +b \right)^{3} \left(4 a c -b^{2}\right) d^{4}}"," ",0,"-2/3*(c*x^2+b*x+a)^(3/2)/(2*c*x+b)^3/d^4/(4*a*c-b^2)","A"
1199,1,400,113,0.059000," ","int((c*x^2+b*x+a)^(1/2)/(2*c*d*x+b*d)^5,x)","\frac{a \ln \left(\frac{\frac{4 a c -b^{2}}{2 c}+\frac{\sqrt{\frac{4 a c -b^{2}}{c}}\, \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}}{2}}{x +\frac{b}{2 c}}\right)}{8 \left(4 a c -b^{2}\right)^{2} \sqrt{\frac{4 a c -b^{2}}{c}}\, c \,d^{5}}-\frac{b^{2} \ln \left(\frac{\frac{4 a c -b^{2}}{2 c}+\frac{\sqrt{\frac{4 a c -b^{2}}{c}}\, \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}}{2}}{x +\frac{b}{2 c}}\right)}{32 \left(4 a c -b^{2}\right)^{2} \sqrt{\frac{4 a c -b^{2}}{c}}\, c^{2} d^{5}}-\frac{\sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}}{32 \left(4 a c -b^{2}\right)^{2} c \,d^{5}}+\frac{\left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{3}{2}}}{16 \left(4 a c -b^{2}\right)^{2} \left(x +\frac{b}{2 c}\right)^{2} c^{2} d^{5}}-\frac{\left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{3}{2}}}{32 \left(4 a c -b^{2}\right) \left(x +\frac{b}{2 c}\right)^{4} c^{4} d^{5}}"," ",0,"-1/32/d^5/c^4/(4*a*c-b^2)/(x+1/2*b/c)^4*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(3/2)+1/16/d^5/c^2/(4*a*c-b^2)^2/(x+1/2*b/c)^2*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(3/2)-1/32/d^5/c/(4*a*c-b^2)^2*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2)+1/8/d^5/c/(4*a*c-b^2)^2/((4*a*c-b^2)/c)^(1/2)*ln((1/2*(4*a*c-b^2)/c+1/2*((4*a*c-b^2)/c)^(1/2)*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2))/(x+1/2*b/c))*a-1/32/d^5/c^2/(4*a*c-b^2)^2/((4*a*c-b^2)/c)^(1/2)*ln((1/2*(4*a*c-b^2)/c+1/2*((4*a*c-b^2)/c)^(1/2)*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2))/(x+1/2*b/c))*b^2","B"
1200,1,70,71,0.048000," ","int((c*x^2+b*x+a)^(1/2)/(2*c*d*x+b*d)^6,x)","-\frac{2 \left(-8 c^{2} x^{2}-8 b c x +12 a c -5 b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}}}{15 \left(2 c x +b \right)^{5} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) d^{6}}"," ",0,"-2/15*(-8*c^2*x^2-8*b*c*x+12*a*c-5*b^2)*(c*x^2+b*x+a)^(3/2)/(2*c*x+b)^5/d^6/(16*a^2*c^2-8*a*b^2*c+b^4)","A"
1201,1,460,151,0.064000," ","int((c*x^2+b*x+a)^(1/2)/(2*c*d*x+b*d)^7,x)","-\frac{a \ln \left(\frac{\frac{4 a c -b^{2}}{2 c}+\frac{\sqrt{\frac{4 a c -b^{2}}{c}}\, \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}}{2}}{x +\frac{b}{2 c}}\right)}{16 \left(4 a c -b^{2}\right)^{3} \sqrt{\frac{4 a c -b^{2}}{c}}\, c \,d^{7}}+\frac{b^{2} \ln \left(\frac{\frac{4 a c -b^{2}}{2 c}+\frac{\sqrt{\frac{4 a c -b^{2}}{c}}\, \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}}{2}}{x +\frac{b}{2 c}}\right)}{64 \left(4 a c -b^{2}\right)^{3} \sqrt{\frac{4 a c -b^{2}}{c}}\, c^{2} d^{7}}+\frac{\sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}}{64 \left(4 a c -b^{2}\right)^{3} c \,d^{7}}-\frac{\left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{3}{2}}}{32 \left(4 a c -b^{2}\right)^{3} \left(x +\frac{b}{2 c}\right)^{2} c^{2} d^{7}}+\frac{\left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{3}{2}}}{64 \left(4 a c -b^{2}\right)^{2} \left(x +\frac{b}{2 c}\right)^{4} c^{4} d^{7}}-\frac{\left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{3}{2}}}{192 \left(4 a c -b^{2}\right) \left(x +\frac{b}{2 c}\right)^{6} c^{6} d^{7}}"," ",0,"-1/192/d^7/c^6/(4*a*c-b^2)/(x+1/2*b/c)^6*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(3/2)+1/64/d^7/c^4/(4*a*c-b^2)^2/(x+1/2*b/c)^4*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(3/2)-1/32/d^7/c^2/(4*a*c-b^2)^3/(x+1/2*b/c)^2*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(3/2)+1/64/d^7/c/(4*a*c-b^2)^3*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2)-1/16/d^7/c/(4*a*c-b^2)^3/((4*a*c-b^2)/c)^(1/2)*ln((1/2*(4*a*c-b^2)/c+1/2*((4*a*c-b^2)/c)^(1/2)*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2))/(x+1/2*b/c))*a+1/64/d^7/c^2/(4*a*c-b^2)^3/((4*a*c-b^2)/c)^(1/2)*ln((1/2*(4*a*c-b^2)/c+1/2*((4*a*c-b^2)/c)^(1/2)*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2))/(x+1/2*b/c))*b^2","B"
1202,1,91,86,0.047000," ","int((2*c*d*x+b*d)^5*(c*x^2+b*x+a)^(3/2),x)","\frac{2 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} \left(560 c^{4} x^{4}+1120 b \,c^{3} x^{3}-320 x^{2} a \,c^{3}+920 x^{2} b^{2} c^{2}-320 x b a \,c^{2}+360 x \,b^{3} c +128 a^{2} c^{2}-144 a \,b^{2} c +63 b^{4}\right) d^{5}}{315}"," ",0,"2/315*(c*x^2+b*x+a)^(5/2)*(560*c^4*x^4+1120*b*c^3*x^3-320*a*c^3*x^2+920*b^2*c^2*x^2-320*a*b*c^2*x+360*b^3*c*x+128*a^2*c^2-144*a*b^2*c+63*b^4)*d^5","A"
1203,1,641,181,0.066000," ","int((2*c*d*x+b*d)^4*(c*x^2+b*x+a)^(3/2),x)","\frac{3 a^{4} c^{\frac{3}{2}} d^{4} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{8}-\frac{3 a^{3} b^{2} \sqrt{c}\, d^{4} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{8}+\frac{9 a^{2} b^{4} d^{4} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{64 \sqrt{c}}-\frac{3 a \,b^{6} d^{4} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{128 c^{\frac{3}{2}}}+\frac{3 b^{8} d^{4} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{2048 c^{\frac{5}{2}}}+\frac{3 \sqrt{c \,x^{2}+b x +a}\, a^{3} c^{2} d^{4} x}{8}-\frac{9 \sqrt{c \,x^{2}+b x +a}\, a^{2} b^{2} c \,d^{4} x}{32}+\frac{9 \sqrt{c \,x^{2}+b x +a}\, a \,b^{4} d^{4} x}{128}-\frac{3 \sqrt{c \,x^{2}+b x +a}\, b^{6} d^{4} x}{512 c}+2 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} c^{3} d^{4} x^{3}+\frac{3 \sqrt{c \,x^{2}+b x +a}\, a^{3} b c \,d^{4}}{16}-\frac{9 \sqrt{c \,x^{2}+b x +a}\, a^{2} b^{3} d^{4}}{64}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a^{2} c^{2} d^{4} x}{4}+\frac{9 \sqrt{c \,x^{2}+b x +a}\, a \,b^{5} d^{4}}{256 c}-\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a \,b^{2} c \,d^{4} x}{8}-\frac{3 \sqrt{c \,x^{2}+b x +a}\, b^{7} d^{4}}{1024 c^{2}}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{4} d^{4} x}{64}+3 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} b \,c^{2} d^{4} x^{2}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a^{2} b c \,d^{4}}{8}-\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a \,b^{3} d^{4}}{16}-\left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} a \,c^{2} d^{4} x +\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{5} d^{4}}{128 c}+\frac{7 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} b^{2} c \,d^{4} x}{4}-\frac{\left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} a b c \,d^{4}}{2}+\frac{3 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} b^{3} d^{4}}{8}"," ",0,"-1/8*d^4*c*b^2*a*x*(c*x^2+b*x+a)^(3/2)-9/32*d^4*c*b^2*a^2*(c*x^2+b*x+a)^(1/2)*x+3/8*d^4*b^3*(c*x^2+b*x+a)^(5/2)-9/64*d^4*b^3*a^2*(c*x^2+b*x+a)^(1/2)+1/64*d^4*b^4*x*(c*x^2+b*x+a)^(3/2)-3/1024*d^4/c^2*b^7*(c*x^2+b*x+a)^(1/2)+2*d^4*c^3*x^3*(c*x^2+b*x+a)^(5/2)+1/128*d^4/c*b^5*(c*x^2+b*x+a)^(3/2)+3/2048*d^4*b^8/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+3/8*d^4*c^(3/2)*a^4*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-1/16*d^4*b^3*a*(c*x^2+b*x+a)^(3/2)-3/128*d^4*b^6/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a+7/4*d^4*c*b^2*x*(c*x^2+b*x+a)^(5/2)+3*d^4*c^2*b*x^2*(c*x^2+b*x+a)^(5/2)-1/2*d^4*c*b*a*(c*x^2+b*x+a)^(5/2)-3/8*d^4*c^(1/2)*b^2*a^3*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+9/64*d^4*b^4/c^(1/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a^2+3/8*d^4*c^2*a^3*(c*x^2+b*x+a)^(1/2)*x+1/8*d^4*c*a^2*(c*x^2+b*x+a)^(3/2)*b+1/4*d^4*c^2*a^2*x*(c*x^2+b*x+a)^(3/2)+3/16*d^4*c*a^3*(c*x^2+b*x+a)^(1/2)*b-d^4*c^2*a*x*(c*x^2+b*x+a)^(5/2)-3/512*d^4/c*b^6*(c*x^2+b*x+a)^(1/2)*x+9/256*d^4/c*b^5*(c*x^2+b*x+a)^(1/2)*a+9/128*d^4*b^4*(c*x^2+b*x+a)^(1/2)*x*a","B"
1204,1,41,51,0.051000," ","int((2*c*d*x+b*d)^3*(c*x^2+b*x+a)^(3/2),x)","-\frac{2 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} \left(-20 c^{2} x^{2}-20 b c x +8 a c -7 b^{2}\right) d^{3}}{35}"," ",0,"-2/35*(c*x^2+b*x+a)^(5/2)*(-20*c^2*x^2-20*b*c*x+8*a*c-7*b^2)*d^3","A"
1205,1,406,143,0.056000," ","int((2*c*d*x+b*d)^2*(c*x^2+b*x+a)^(3/2),x)","-\frac{a^{3} \sqrt{c}\, d^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{4}+\frac{3 a^{2} b^{2} d^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{16 \sqrt{c}}-\frac{3 a \,b^{4} d^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{64 c^{\frac{3}{2}}}+\frac{b^{6} d^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{256 c^{\frac{5}{2}}}-\frac{\sqrt{c \,x^{2}+b x +a}\, a^{2} c \,d^{2} x}{4}+\frac{\sqrt{c \,x^{2}+b x +a}\, a \,b^{2} d^{2} x}{8}-\frac{\sqrt{c \,x^{2}+b x +a}\, b^{4} d^{2} x}{64 c}-\frac{\sqrt{c \,x^{2}+b x +a}\, a^{2} b \,d^{2}}{8}+\frac{\sqrt{c \,x^{2}+b x +a}\, a \,b^{3} d^{2}}{16 c}-\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a c \,d^{2} x}{6}-\frac{\sqrt{c \,x^{2}+b x +a}\, b^{5} d^{2}}{128 c^{2}}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{2} d^{2} x}{24}-\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a b \,d^{2}}{12}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{3} d^{2}}{48 c}+\frac{2 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} c \,d^{2} x}{3}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} b \,d^{2}}{3}"," ",0,"1/256*d^2*b^6/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-1/6*d^2*c*a*x*(c*x^2+b*x+a)^(3/2)-1/4*d^2*c*a^2*(c*x^2+b*x+a)^(1/2)*x-1/4*d^2*c^(1/2)*a^3*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+1/8*d^2*b^2*(c*x^2+b*x+a)^(1/2)*x*a-1/64*d^2/c*b^4*(c*x^2+b*x+a)^(1/2)*x+1/16*d^2/c*b^3*(c*x^2+b*x+a)^(1/2)*a-3/64*d^2*b^4/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a+3/16*d^2*b^2/c^(1/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a^2+1/3*d^2*b*(c*x^2+b*x+a)^(5/2)-1/8*d^2*a^2*(c*x^2+b*x+a)^(1/2)*b+1/48*d^2/c*b^3*(c*x^2+b*x+a)^(3/2)-1/128*d^2/c^2*b^5*(c*x^2+b*x+a)^(1/2)-1/12*d^2*a*(c*x^2+b*x+a)^(3/2)*b+2/3*d^2*c*x*(c*x^2+b*x+a)^(5/2)+1/24*d^2*b^2*x*(c*x^2+b*x+a)^(3/2)","B"
1206,1,16,15,0.040000," ","int((2*c*d*x+b*d)*(c*x^2+b*x+a)^(3/2),x)","\frac{2 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} d}{5}"," ",0,"2/5*d*(c*x^2+b*x+a)^(5/2)","A"
1207,1,430,95,0.047000," ","int((c*x^2+b*x+a)^(3/2)/(2*c*d*x+b*d),x)","-\frac{a^{2} \ln \left(\frac{\frac{4 a c -b^{2}}{2 c}+\frac{\sqrt{\frac{4 a c -b^{2}}{c}}\, \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}}{2}}{x +\frac{b}{2 c}}\right)}{\sqrt{\frac{4 a c -b^{2}}{c}}\, c d}+\frac{a \,b^{2} \ln \left(\frac{\frac{4 a c -b^{2}}{2 c}+\frac{\sqrt{\frac{4 a c -b^{2}}{c}}\, \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}}{2}}{x +\frac{b}{2 c}}\right)}{2 \sqrt{\frac{4 a c -b^{2}}{c}}\, c^{2} d}-\frac{b^{4} \ln \left(\frac{\frac{4 a c -b^{2}}{2 c}+\frac{\sqrt{\frac{4 a c -b^{2}}{c}}\, \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}}{2}}{x +\frac{b}{2 c}}\right)}{16 \sqrt{\frac{4 a c -b^{2}}{c}}\, c^{3} d}+\frac{\sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}\, a}{4 c d}-\frac{\sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}\, b^{2}}{16 c^{2} d}+\frac{\left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{3}{2}}}{6 c d}"," ",0,"1/6/c/d*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(3/2)+1/4/c/d*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2)*a-1/16/c^2/d*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2)*b^2-1/c/d/((4*a*c-b^2)/c)^(1/2)*ln((1/2*(4*a*c-b^2)/c+1/2*((4*a*c-b^2)/c)^(1/2)*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2))/(x+1/2*b/c))*a^2+1/2/c^2/d/((4*a*c-b^2)/c)^(1/2)*ln((1/2*(4*a*c-b^2)/c+1/2*((4*a*c-b^2)/c)^(1/2)*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2))/(x+1/2*b/c))*a*b^2-1/16/c^3/d/((4*a*c-b^2)/c)^(1/2)*ln((1/2*(4*a*c-b^2)/c+1/2*((4*a*c-b^2)/c)^(1/2)*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2))/(x+1/2*b/c))*b^4","B"
1208,1,570,95,0.053000," ","int((c*x^2+b*x+a)^(3/2)/(2*c*d*x+b*d)^2,x)","\frac{3 a^{2} \ln \left(\left(x +\frac{b}{2 c}\right) \sqrt{c}+\sqrt{\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{c}\, d^{2}}-\frac{3 a \,b^{2} \ln \left(\left(x +\frac{b}{2 c}\right) \sqrt{c}+\sqrt{\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}}\right)}{4 \left(4 a c -b^{2}\right) c^{\frac{3}{2}} d^{2}}+\frac{3 b^{4} \ln \left(\left(x +\frac{b}{2 c}\right) \sqrt{c}+\sqrt{\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}}\right)}{32 \left(4 a c -b^{2}\right) c^{\frac{5}{2}} d^{2}}+\frac{3 \sqrt{\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}}\, a x}{2 \left(4 a c -b^{2}\right) d^{2}}-\frac{3 \sqrt{\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}}\, b^{2} x}{8 \left(4 a c -b^{2}\right) c \,d^{2}}+\frac{3 \sqrt{\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}}\, a b}{4 \left(4 a c -b^{2}\right) c \,d^{2}}-\frac{3 \sqrt{\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}}\, b^{3}}{16 \left(4 a c -b^{2}\right) c^{2} d^{2}}+\frac{\left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{3}{2}} x}{\left(4 a c -b^{2}\right) d^{2}}+\frac{\left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{3}{2}} b}{2 \left(4 a c -b^{2}\right) c \,d^{2}}-\frac{\left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{5}{2}}}{\left(4 a c -b^{2}\right) \left(x +\frac{b}{2 c}\right) c \,d^{2}}"," ",0,"-1/c/d^2/(4*a*c-b^2)/(x+1/2*b/c)*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(5/2)+1/d^2/(4*a*c-b^2)*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(3/2)*x+1/2/c/d^2/(4*a*c-b^2)*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(3/2)*b+3/2/d^2/(4*a*c-b^2)*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(1/2)*x*a-3/8/c/d^2/(4*a*c-b^2)*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(1/2)*x*b^2+3/4/c/d^2/(4*a*c-b^2)*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(1/2)*b*a-3/16/c^2/d^2/(4*a*c-b^2)*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(1/2)*b^3+3/2/c^(1/2)/d^2/(4*a*c-b^2)*ln((x+1/2*b/c)*c^(1/2)+((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(1/2))*a^2-3/4/c^(3/2)/d^2/(4*a*c-b^2)*ln((x+1/2*b/c)*c^(1/2)+((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(1/2))*b^2*a+3/32/c^(5/2)/d^2/(4*a*c-b^2)*ln((x+1/2*b/c)*c^(1/2)+((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(1/2))*b^4","B"
1209,1,562,95,0.059000," ","int((c*x^2+b*x+a)^(3/2)/(2*c*d*x+b*d)^3,x)","-\frac{3 a^{2} \ln \left(\frac{\frac{4 a c -b^{2}}{2 c}+\frac{\sqrt{\frac{4 a c -b^{2}}{c}}\, \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}}{2}}{x +\frac{b}{2 c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\frac{4 a c -b^{2}}{c}}\, c \,d^{3}}+\frac{3 a \,b^{2} \ln \left(\frac{\frac{4 a c -b^{2}}{2 c}+\frac{\sqrt{\frac{4 a c -b^{2}}{c}}\, \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}}{2}}{x +\frac{b}{2 c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\frac{4 a c -b^{2}}{c}}\, c^{2} d^{3}}-\frac{3 b^{4} \ln \left(\frac{\frac{4 a c -b^{2}}{2 c}+\frac{\sqrt{\frac{4 a c -b^{2}}{c}}\, \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}}{2}}{x +\frac{b}{2 c}}\right)}{32 \left(4 a c -b^{2}\right) \sqrt{\frac{4 a c -b^{2}}{c}}\, c^{3} d^{3}}+\frac{3 \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}\, a}{8 \left(4 a c -b^{2}\right) c \,d^{3}}-\frac{3 \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}\, b^{2}}{32 \left(4 a c -b^{2}\right) c^{2} d^{3}}+\frac{\left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{3}{2}}}{4 \left(4 a c -b^{2}\right) c \,d^{3}}-\frac{\left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{5}{2}}}{4 \left(4 a c -b^{2}\right) \left(x +\frac{b}{2 c}\right)^{2} c^{2} d^{3}}"," ",0,"-1/4/d^3/c^2/(4*a*c-b^2)/(x+1/2*b/c)^2*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(5/2)+1/4/d^3/c/(4*a*c-b^2)*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(3/2)+3/8/d^3/c/(4*a*c-b^2)*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2)*a-3/32/d^3/c^2/(4*a*c-b^2)*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2)*b^2-3/2/d^3/c/(4*a*c-b^2)/((4*a*c-b^2)/c)^(1/2)*ln((1/2*(4*a*c-b^2)/c+1/2*((4*a*c-b^2)/c)^(1/2)*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2))/(x+1/2*b/c))*a^2+3/4/d^3/c^2/(4*a*c-b^2)/((4*a*c-b^2)/c)^(1/2)*ln((1/2*(4*a*c-b^2)/c+1/2*((4*a*c-b^2)/c)^(1/2)*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2))/(x+1/2*b/c))*a*b^2-3/32/d^3/c^3/(4*a*c-b^2)/((4*a*c-b^2)/c)^(1/2)*ln((1/2*(4*a*c-b^2)/c+1/2*((4*a*c-b^2)/c)^(1/2)*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2))/(x+1/2*b/c))*b^4","B"
1210,1,629,89,0.056000," ","int((c*x^2+b*x+a)^(3/2)/(2*c*d*x+b*d)^4,x)","\frac{a^{2} \ln \left(\left(x +\frac{b}{2 c}\right) \sqrt{c}+\sqrt{\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{c}\, d^{4}}-\frac{a \,b^{2} \ln \left(\left(x +\frac{b}{2 c}\right) \sqrt{c}+\sqrt{\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}}\right)}{2 \left(4 a c -b^{2}\right)^{2} c^{\frac{3}{2}} d^{4}}+\frac{b^{4} \ln \left(\left(x +\frac{b}{2 c}\right) \sqrt{c}+\sqrt{\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}}\right)}{16 \left(4 a c -b^{2}\right)^{2} c^{\frac{5}{2}} d^{4}}+\frac{\sqrt{\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}}\, a x}{\left(4 a c -b^{2}\right)^{2} d^{4}}-\frac{\sqrt{\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}}\, b^{2} x}{4 \left(4 a c -b^{2}\right)^{2} c \,d^{4}}+\frac{\sqrt{\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}}\, a b}{2 \left(4 a c -b^{2}\right)^{2} c \,d^{4}}-\frac{\sqrt{\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}}\, b^{3}}{8 \left(4 a c -b^{2}\right)^{2} c^{2} d^{4}}+\frac{2 \left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{3}{2}} x}{3 \left(4 a c -b^{2}\right)^{2} d^{4}}+\frac{\left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{3}{2}} b}{3 \left(4 a c -b^{2}\right)^{2} c \,d^{4}}-\frac{2 \left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{5}{2}}}{3 \left(4 a c -b^{2}\right)^{2} \left(x +\frac{b}{2 c}\right) c \,d^{4}}-\frac{\left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{5}{2}}}{12 \left(4 a c -b^{2}\right) \left(x +\frac{b}{2 c}\right)^{3} c^{3} d^{4}}"," ",0,"-1/12/d^4/c^3/(4*a*c-b^2)/(x+1/2*b/c)^3*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(5/2)-2/3/d^4/c/(4*a*c-b^2)^2/(x+1/2*b/c)*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(5/2)+2/3/d^4/(4*a*c-b^2)^2*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(3/2)*x+1/3/d^4/c/(4*a*c-b^2)^2*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(3/2)*b+1/d^4/(4*a*c-b^2)^2*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(1/2)*x*a-1/4/d^4/c/(4*a*c-b^2)^2*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(1/2)*x*b^2+1/2/d^4/c/(4*a*c-b^2)^2*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(1/2)*b*a-1/8/d^4/c^2/(4*a*c-b^2)^2*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(1/2)*b^3+1/d^4/c^(1/2)/(4*a*c-b^2)^2*ln((x+1/2*b/c)*c^(1/2)+((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(1/2))*a^2-1/2/d^4/c^(3/2)/(4*a*c-b^2)^2*ln((x+1/2*b/c)*c^(1/2)+((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(1/2))*b^2*a+1/16/d^4/c^(5/2)/(4*a*c-b^2)^2*ln((x+1/2*b/c)*c^(1/2)+((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(1/2))*b^4","B"
1211,1,622,103,0.062000," ","int((c*x^2+b*x+a)^(3/2)/(2*c*d*x+b*d)^5,x)","-\frac{3 a^{2} \ln \left(\frac{\frac{4 a c -b^{2}}{2 c}+\frac{\sqrt{\frac{4 a c -b^{2}}{c}}\, \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}}{2}}{x +\frac{b}{2 c}}\right)}{8 \left(4 a c -b^{2}\right)^{2} \sqrt{\frac{4 a c -b^{2}}{c}}\, c \,d^{5}}+\frac{3 a \,b^{2} \ln \left(\frac{\frac{4 a c -b^{2}}{2 c}+\frac{\sqrt{\frac{4 a c -b^{2}}{c}}\, \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}}{2}}{x +\frac{b}{2 c}}\right)}{16 \left(4 a c -b^{2}\right)^{2} \sqrt{\frac{4 a c -b^{2}}{c}}\, c^{2} d^{5}}-\frac{3 b^{4} \ln \left(\frac{\frac{4 a c -b^{2}}{2 c}+\frac{\sqrt{\frac{4 a c -b^{2}}{c}}\, \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}}{2}}{x +\frac{b}{2 c}}\right)}{128 \left(4 a c -b^{2}\right)^{2} \sqrt{\frac{4 a c -b^{2}}{c}}\, c^{3} d^{5}}+\frac{3 \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}\, a}{32 \left(4 a c -b^{2}\right)^{2} c \,d^{5}}-\frac{3 \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}\, b^{2}}{128 \left(4 a c -b^{2}\right)^{2} c^{2} d^{5}}+\frac{\left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{3}{2}}}{16 \left(4 a c -b^{2}\right)^{2} c \,d^{5}}-\frac{\left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{5}{2}}}{16 \left(4 a c -b^{2}\right)^{2} \left(x +\frac{b}{2 c}\right)^{2} c^{2} d^{5}}-\frac{\left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{5}{2}}}{32 \left(4 a c -b^{2}\right) \left(x +\frac{b}{2 c}\right)^{4} c^{4} d^{5}}"," ",0,"-1/32/d^5/c^4/(4*a*c-b^2)/(x+1/2*b/c)^4*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(5/2)-1/16/d^5/c^2/(4*a*c-b^2)^2/(x+1/2*b/c)^2*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(5/2)+1/16/d^5/c/(4*a*c-b^2)^2*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(3/2)+3/32/d^5/c/(4*a*c-b^2)^2*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2)*a-3/128/d^5/c^2/(4*a*c-b^2)^2*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2)*b^2-3/8/d^5/c/(4*a*c-b^2)^2/((4*a*c-b^2)/c)^(1/2)*ln((1/2*(4*a*c-b^2)/c+1/2*((4*a*c-b^2)/c)^(1/2)*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2))/(x+1/2*b/c))*a^2+3/16/d^5/c^2/(4*a*c-b^2)^2/((4*a*c-b^2)/c)^(1/2)*ln((1/2*(4*a*c-b^2)/c+1/2*((4*a*c-b^2)/c)^(1/2)*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2))/(x+1/2*b/c))*a*b^2-3/128/d^5/c^3/(4*a*c-b^2)^2/((4*a*c-b^2)/c)^(1/2)*ln((1/2*(4*a*c-b^2)/c+1/2*((4*a*c-b^2)/c)^(1/2)*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2))/(x+1/2*b/c))*b^4","B"
1212,1,38,35,0.043000," ","int((c*x^2+b*x+a)^(3/2)/(2*c*d*x+b*d)^6,x)","-\frac{2 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}}}{5 \left(2 c x +b \right)^{5} \left(4 a c -b^{2}\right) d^{6}}"," ",0,"-2/5*(c*x^2+b*x+a)^(5/2)/(2*c*x+b)^5/d^6/(4*a*c-b^2)","A"
1213,1,682,141,0.070000," ","int((c*x^2+b*x+a)^(3/2)/(2*c*d*x+b*d)^7,x)","\frac{a^{2} \ln \left(\frac{\frac{4 a c -b^{2}}{2 c}+\frac{\sqrt{\frac{4 a c -b^{2}}{c}}\, \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}}{2}}{x +\frac{b}{2 c}}\right)}{16 \left(4 a c -b^{2}\right)^{3} \sqrt{\frac{4 a c -b^{2}}{c}}\, c \,d^{7}}-\frac{a \,b^{2} \ln \left(\frac{\frac{4 a c -b^{2}}{2 c}+\frac{\sqrt{\frac{4 a c -b^{2}}{c}}\, \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}}{2}}{x +\frac{b}{2 c}}\right)}{32 \left(4 a c -b^{2}\right)^{3} \sqrt{\frac{4 a c -b^{2}}{c}}\, c^{2} d^{7}}+\frac{b^{4} \ln \left(\frac{\frac{4 a c -b^{2}}{2 c}+\frac{\sqrt{\frac{4 a c -b^{2}}{c}}\, \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}}{2}}{x +\frac{b}{2 c}}\right)}{256 \left(4 a c -b^{2}\right)^{3} \sqrt{\frac{4 a c -b^{2}}{c}}\, c^{3} d^{7}}-\frac{\sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}\, a}{64 \left(4 a c -b^{2}\right)^{3} c \,d^{7}}+\frac{\sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}\, b^{2}}{256 \left(4 a c -b^{2}\right)^{3} c^{2} d^{7}}-\frac{\left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{3}{2}}}{96 \left(4 a c -b^{2}\right)^{3} c \,d^{7}}+\frac{\left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{5}{2}}}{96 \left(4 a c -b^{2}\right)^{3} \left(x +\frac{b}{2 c}\right)^{2} c^{2} d^{7}}+\frac{\left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{5}{2}}}{192 \left(4 a c -b^{2}\right)^{2} \left(x +\frac{b}{2 c}\right)^{4} c^{4} d^{7}}-\frac{\left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{5}{2}}}{192 \left(4 a c -b^{2}\right) \left(x +\frac{b}{2 c}\right)^{6} c^{6} d^{7}}"," ",0,"-1/192/d^7/c^6/(4*a*c-b^2)/(x+1/2*b/c)^6*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(5/2)+1/192/d^7/c^4/(4*a*c-b^2)^2/(x+1/2*b/c)^4*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(5/2)+1/96/d^7/c^2/(4*a*c-b^2)^3/(x+1/2*b/c)^2*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(5/2)-1/96/d^7/c/(4*a*c-b^2)^3*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(3/2)-1/64/d^7/c/(4*a*c-b^2)^3*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2)*a+1/256/d^7/c^2/(4*a*c-b^2)^3*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2)*b^2+1/16/d^7/c/(4*a*c-b^2)^3/((4*a*c-b^2)/c)^(1/2)*ln((1/2*(4*a*c-b^2)/c+1/2*((4*a*c-b^2)/c)^(1/2)*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2))/(x+1/2*b/c))*a^2-1/32/d^7/c^2/(4*a*c-b^2)^3/((4*a*c-b^2)/c)^(1/2)*ln((1/2*(4*a*c-b^2)/c+1/2*((4*a*c-b^2)/c)^(1/2)*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2))/(x+1/2*b/c))*a*b^2+1/256/d^7/c^3/(4*a*c-b^2)^3/((4*a*c-b^2)/c)^(1/2)*ln((1/2*(4*a*c-b^2)/c+1/2*((4*a*c-b^2)/c)^(1/2)*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2))/(x+1/2*b/c))*b^4","B"
1214,1,70,71,0.051000," ","int((c*x^2+b*x+a)^(3/2)/(2*c*d*x+b*d)^8,x)","-\frac{2 \left(-8 c^{2} x^{2}-8 b c x +20 a c -7 b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}}}{35 \left(2 c x +b \right)^{7} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) d^{8}}"," ",0,"-2/35*(-8*c^2*x^2-8*b*c*x+20*a*c-7*b^2)*(c*x^2+b*x+a)^(5/2)/(2*c*x+b)^7/d^8/(16*a^2*c^2-8*a*b^2*c+b^4)","A"
1215,1,742,179,0.077000," ","int((c*x^2+b*x+a)^(3/2)/(2*c*d*x+b*d)^9,x)","-\frac{3 a^{2} \ln \left(\frac{\frac{4 a c -b^{2}}{2 c}+\frac{\sqrt{\frac{4 a c -b^{2}}{c}}\, \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}}{2}}{x +\frac{b}{2 c}}\right)}{128 \left(4 a c -b^{2}\right)^{4} \sqrt{\frac{4 a c -b^{2}}{c}}\, c \,d^{9}}+\frac{3 a \,b^{2} \ln \left(\frac{\frac{4 a c -b^{2}}{2 c}+\frac{\sqrt{\frac{4 a c -b^{2}}{c}}\, \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}}{2}}{x +\frac{b}{2 c}}\right)}{256 \left(4 a c -b^{2}\right)^{4} \sqrt{\frac{4 a c -b^{2}}{c}}\, c^{2} d^{9}}-\frac{3 b^{4} \ln \left(\frac{\frac{4 a c -b^{2}}{2 c}+\frac{\sqrt{\frac{4 a c -b^{2}}{c}}\, \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}}{2}}{x +\frac{b}{2 c}}\right)}{2048 \left(4 a c -b^{2}\right)^{4} \sqrt{\frac{4 a c -b^{2}}{c}}\, c^{3} d^{9}}+\frac{3 \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}\, a}{512 \left(4 a c -b^{2}\right)^{4} c \,d^{9}}-\frac{3 \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}\, b^{2}}{2048 \left(4 a c -b^{2}\right)^{4} c^{2} d^{9}}+\frac{\left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{3}{2}}}{256 \left(4 a c -b^{2}\right)^{4} c \,d^{9}}-\frac{\left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{5}{2}}}{256 \left(4 a c -b^{2}\right)^{4} \left(x +\frac{b}{2 c}\right)^{2} c^{2} d^{9}}-\frac{\left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{5}{2}}}{512 \left(4 a c -b^{2}\right)^{3} \left(x +\frac{b}{2 c}\right)^{4} c^{4} d^{9}}+\frac{\left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{5}{2}}}{512 \left(4 a c -b^{2}\right)^{2} \left(x +\frac{b}{2 c}\right)^{6} c^{6} d^{9}}-\frac{\left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{5}{2}}}{1024 \left(4 a c -b^{2}\right) \left(x +\frac{b}{2 c}\right)^{8} c^{8} d^{9}}"," ",0,"-1/1024/d^9/c^8/(4*a*c-b^2)/(x+1/2*b/c)^8*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(5/2)+1/512/d^9/c^6/(4*a*c-b^2)^2/(x+1/2*b/c)^6*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(5/2)-1/512/d^9/c^4/(4*a*c-b^2)^3/(x+1/2*b/c)^4*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(5/2)-1/256/d^9/c^2/(4*a*c-b^2)^4/(x+1/2*b/c)^2*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(5/2)+1/256/d^9/c/(4*a*c-b^2)^4*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(3/2)+3/512/d^9/c/(4*a*c-b^2)^4*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2)*a-3/2048/d^9/c^2/(4*a*c-b^2)^4*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2)*b^2-3/128/d^9/c/(4*a*c-b^2)^4/((4*a*c-b^2)/c)^(1/2)*ln((1/2*(4*a*c-b^2)/c+1/2*((4*a*c-b^2)/c)^(1/2)*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2))/(x+1/2*b/c))*a^2+3/256/d^9/c^2/(4*a*c-b^2)^4/((4*a*c-b^2)/c)^(1/2)*ln((1/2*(4*a*c-b^2)/c+1/2*((4*a*c-b^2)/c)^(1/2)*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2))/(x+1/2*b/c))*a*b^2-3/2048/d^9/c^3/(4*a*c-b^2)^4/((4*a*c-b^2)/c)^(1/2)*ln((1/2*(4*a*c-b^2)/c+1/2*((4*a*c-b^2)/c)^(1/2)*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2))/(x+1/2*b/c))*b^4","B"
1216,1,133,106,0.052000," ","int((c*x^2+b*x+a)^(3/2)/(2*c*d*x+b*d)^10,x)","-\frac{2 \left(128 c^{4} x^{4}+256 b \,c^{3} x^{3}-320 a \,c^{3} x^{2}+272 x^{2} b^{2} c^{2}-320 x b a \,c^{2}+144 x \,b^{3} c +560 a^{2} c^{2}-360 a \,b^{2} c +63 b^{4}\right) \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}}}{315 \left(2 c x +b \right)^{9} \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) d^{10}}"," ",0,"-2/315*(128*c^4*x^4+256*b*c^3*x^3-320*a*c^3*x^2+272*b^2*c^2*x^2-320*a*b*c^2*x+144*b^3*c*x+560*a^2*c^2-360*a*b^2*c+63*b^4)*(c*x^2+b*x+a)^(5/2)/(2*c*x+b)^9/d^10/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)","A"
1217,1,91,86,0.047000," ","int((2*c*d*x+b*d)^5*(c*x^2+b*x+a)^(5/2),x)","\frac{2 \left(c \,x^{2}+b x +a \right)^{\frac{7}{2}} \left(1008 c^{4} x^{4}+2016 b \,c^{3} x^{3}-448 a \,c^{3} x^{2}+1624 x^{2} b^{2} c^{2}-448 x b a \,c^{2}+616 x \,b^{3} c +128 a^{2} c^{2}-176 a \,b^{2} c +99 b^{4}\right) d^{5}}{693}"," ",0,"2/693*(c*x^2+b*x+a)^(7/2)*(1008*c^4*x^4+2016*b*c^3*x^3-448*a*c^3*x^2+1624*b^2*c^2*x^2-448*a*b*c^2*x+616*b^3*c*x+128*a^2*c^2-176*a*b^2*c+99*b^4)*d^5","A"
1218,1,920,219,0.060000," ","int((2*c*d*x+b*d)^4*(c*x^2+b*x+a)^(5/2),x)","\frac{3 a^{5} c^{\frac{3}{2}} d^{4} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{16}-\frac{15 a^{4} b^{2} \sqrt{c}\, d^{4} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{64}+\frac{15 a^{3} b^{4} d^{4} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{128 \sqrt{c}}-\frac{15 a^{2} b^{6} d^{4} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{512 c^{\frac{3}{2}}}+\frac{15 a \,b^{8} d^{4} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{4096 c^{\frac{5}{2}}}-\frac{3 b^{10} d^{4} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{16384 c^{\frac{7}{2}}}+\frac{3 \sqrt{c \,x^{2}+b x +a}\, a^{4} c^{2} d^{4} x}{16}-\frac{3 \sqrt{c \,x^{2}+b x +a}\, a^{3} b^{2} c \,d^{4} x}{16}+\frac{9 \sqrt{c \,x^{2}+b x +a}\, a^{2} b^{4} d^{4} x}{128}-\frac{3 \sqrt{c \,x^{2}+b x +a}\, a \,b^{6} d^{4} x}{256 c}+\frac{3 \sqrt{c \,x^{2}+b x +a}\, b^{8} d^{4} x}{4096 c^{2}}+\frac{3 \sqrt{c \,x^{2}+b x +a}\, a^{4} b c \,d^{4}}{32}-\frac{3 \sqrt{c \,x^{2}+b x +a}\, a^{3} b^{3} d^{4}}{32}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a^{3} c^{2} d^{4} x}{8}+\frac{9 \sqrt{c \,x^{2}+b x +a}\, a^{2} b^{5} d^{4}}{256 c}-\frac{3 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a^{2} b^{2} c \,d^{4} x}{32}-\frac{3 \sqrt{c \,x^{2}+b x +a}\, a \,b^{7} d^{4}}{512 c^{2}}+\frac{3 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a \,b^{4} d^{4} x}{128}+\frac{3 \sqrt{c \,x^{2}+b x +a}\, b^{9} d^{4}}{8192 c^{3}}-\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{6} d^{4} x}{512 c}+\frac{8 \left(c \,x^{2}+b x +a \right)^{\frac{7}{2}} c^{3} d^{4} x^{3}}{5}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a^{3} b c \,d^{4}}{16}-\frac{3 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a^{2} b^{3} d^{4}}{64}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} a^{2} c^{2} d^{4} x}{10}+\frac{3 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a \,b^{5} d^{4}}{256 c}-\frac{\left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} a \,b^{2} c \,d^{4} x}{20}-\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{7} d^{4}}{1024 c^{2}}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} b^{4} d^{4} x}{160}+\frac{12 \left(c \,x^{2}+b x +a \right)^{\frac{7}{2}} b \,c^{2} d^{4} x^{2}}{5}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} a^{2} b c \,d^{4}}{20}-\frac{\left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} a \,b^{3} d^{4}}{40}-\frac{3 \left(c \,x^{2}+b x +a \right)^{\frac{7}{2}} a \,c^{2} d^{4} x}{5}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} b^{5} d^{4}}{320 c}+\frac{27 \left(c \,x^{2}+b x +a \right)^{\frac{7}{2}} b^{2} c \,d^{4} x}{20}-\frac{3 \left(c \,x^{2}+b x +a \right)^{\frac{7}{2}} a b c \,d^{4}}{10}+\frac{11 \left(c \,x^{2}+b x +a \right)^{\frac{7}{2}} b^{3} d^{4}}{40}"," ",0,"-3/5*d^4*c^2*a*x*(c*x^2+b*x+a)^(7/2)+3/32*d^4*c*a^4*(c*x^2+b*x+a)^(1/2)*b+1/10*d^4*c^2*a^2*x*(c*x^2+b*x+a)^(5/2)+1/20*d^4*c*a^2*(c*x^2+b*x+a)^(5/2)*b+1/8*d^4*c^2*a^3*(c*x^2+b*x+a)^(3/2)*x+1/16*d^4*c*a^3*(c*x^2+b*x+a)^(3/2)*b+3/16*d^4*c^2*a^4*(c*x^2+b*x+a)^(1/2)*x-1/512*d^4/c*b^6*(c*x^2+b*x+a)^(3/2)*x+3/256*d^4/c*b^5*(c*x^2+b*x+a)^(3/2)*a+3/4096*d^4/c^2*b^8*(c*x^2+b*x+a)^(1/2)*x-3/16*d^4*c*b^2*a^3*(c*x^2+b*x+a)^(1/2)*x-3/256*d^4/c*b^6*(c*x^2+b*x+a)^(1/2)*x*a-1/20*d^4*c*b^2*a*x*(c*x^2+b*x+a)^(5/2)-3/32*d^4*c*b^2*a^2*(c*x^2+b*x+a)^(3/2)*x-3/64*d^4*b^3*a^2*(c*x^2+b*x+a)^(3/2)+1/160*d^4*b^4*x*(c*x^2+b*x+a)^(5/2)-3/32*d^4*b^3*a^3*(c*x^2+b*x+a)^(1/2)+3/16*d^4*c^(3/2)*a^5*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+3/8192*d^4/c^3*b^9*(c*x^2+b*x+a)^(1/2)-3/16384*d^4*b^10/c^(7/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+8/5*d^4*c^3*x^3*(c*x^2+b*x+a)^(7/2)+15/4096*d^4*b^8/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a+1/320*d^4/c*b^5*(c*x^2+b*x+a)^(5/2)-1/1024*d^4/c^2*b^7*(c*x^2+b*x+a)^(3/2)-1/40*d^4*b^3*a*(c*x^2+b*x+a)^(5/2)+9/256*d^4/c*b^5*(c*x^2+b*x+a)^(1/2)*a^2-3/512*d^4/c^2*b^7*(c*x^2+b*x+a)^(1/2)*a+11/40*d^4*b^3*(c*x^2+b*x+a)^(7/2)-3/10*d^4*c*b*a*(c*x^2+b*x+a)^(7/2)+12/5*d^4*c^2*b*x^2*(c*x^2+b*x+a)^(7/2)+27/20*d^4*c*b^2*x*(c*x^2+b*x+a)^(7/2)+9/128*d^4*b^4*(c*x^2+b*x+a)^(1/2)*x*a^2+3/128*d^4*b^4*(c*x^2+b*x+a)^(3/2)*x*a-15/64*d^4*c^(1/2)*b^2*a^4*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+15/128*d^4*b^4/c^(1/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a^3-15/512*d^4*b^6/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a^2","B"
1219,1,41,51,0.051000," ","int((2*c*d*x+b*d)^3*(c*x^2+b*x+a)^(5/2),x)","-\frac{2 \left(c \,x^{2}+b x +a \right)^{\frac{7}{2}} \left(-28 c^{2} x^{2}-28 b c x +8 a c -9 b^{2}\right) d^{3}}{63}"," ",0,"-2/63*(c*x^2+b*x+a)^(7/2)*(-28*c^2*x^2-28*b*c*x+8*a*c-9*b^2)*d^3","A"
1220,1,634,181,0.050000," ","int((2*c*d*x+b*d)^2*(c*x^2+b*x+a)^(5/2),x)","-\frac{5 a^{4} \sqrt{c}\, d^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{32}+\frac{5 a^{3} b^{2} d^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{32 \sqrt{c}}-\frac{15 a^{2} b^{4} d^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{256 c^{\frac{3}{2}}}+\frac{5 a \,b^{6} d^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{512 c^{\frac{5}{2}}}-\frac{5 b^{8} d^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{8192 c^{\frac{7}{2}}}-\frac{5 \sqrt{c \,x^{2}+b x +a}\, a^{3} c \,d^{2} x}{32}+\frac{15 \sqrt{c \,x^{2}+b x +a}\, a^{2} b^{2} d^{2} x}{128}-\frac{15 \sqrt{c \,x^{2}+b x +a}\, a \,b^{4} d^{2} x}{512 c}+\frac{5 \sqrt{c \,x^{2}+b x +a}\, b^{6} d^{2} x}{2048 c^{2}}-\frac{5 \sqrt{c \,x^{2}+b x +a}\, a^{3} b \,d^{2}}{64}+\frac{15 \sqrt{c \,x^{2}+b x +a}\, a^{2} b^{3} d^{2}}{256 c}-\frac{5 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a^{2} c \,d^{2} x}{48}-\frac{15 \sqrt{c \,x^{2}+b x +a}\, a \,b^{5} d^{2}}{1024 c^{2}}+\frac{5 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a \,b^{2} d^{2} x}{96}+\frac{5 \sqrt{c \,x^{2}+b x +a}\, b^{7} d^{2}}{4096 c^{3}}-\frac{5 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{4} d^{2} x}{768 c}-\frac{5 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a^{2} b \,d^{2}}{96}+\frac{5 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a \,b^{3} d^{2}}{192 c}-\frac{\left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} a c \,d^{2} x}{12}-\frac{5 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{5} d^{2}}{1536 c^{2}}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} b^{2} d^{2} x}{48}-\frac{\left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} a b \,d^{2}}{24}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} b^{3} d^{2}}{96 c}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{7}{2}} c \,d^{2} x}{2}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{7}{2}} b \,d^{2}}{4}"," ",0,"-15/512*d^2/c*b^4*(c*x^2+b*x+a)^(1/2)*x*a-5/1536*d^2/c^2*b^5*(c*x^2+b*x+a)^(3/2)+5/4096*d^2/c^3*b^7*(c*x^2+b*x+a)^(1/2)+1/96*d^2/c*b^3*(c*x^2+b*x+a)^(5/2)-5/96*d^2*a^2*(c*x^2+b*x+a)^(3/2)*b-5/64*d^2*a^3*(c*x^2+b*x+a)^(1/2)*b-1/24*d^2*a*(c*x^2+b*x+a)^(5/2)*b+1/48*d^2*b^2*x*(c*x^2+b*x+a)^(5/2)-5/32*d^2*c^(1/2)*a^4*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-5/8192*d^2*b^8/c^(7/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+1/2*d^2*c*x*(c*x^2+b*x+a)^(7/2)+5/192*d^2/c*b^3*(c*x^2+b*x+a)^(3/2)*a+5/96*d^2*b^2*(c*x^2+b*x+a)^(3/2)*x*a+15/128*d^2*b^2*(c*x^2+b*x+a)^(1/2)*x*a^2-5/32*d^2*c*a^3*(c*x^2+b*x+a)^(1/2)*x-1/12*d^2*c*a*x*(c*x^2+b*x+a)^(5/2)-5/768*d^2/c*b^4*(c*x^2+b*x+a)^(3/2)*x-5/48*d^2*c*a^2*(c*x^2+b*x+a)^(3/2)*x-15/256*d^2*b^4/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a^2+5/512*d^2*b^6/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a-15/1024*d^2/c^2*b^5*(c*x^2+b*x+a)^(1/2)*a+5/2048*d^2/c^2*b^6*(c*x^2+b*x+a)^(1/2)*x+15/256*d^2/c*b^3*(c*x^2+b*x+a)^(1/2)*a^2+5/32*d^2*b^2/c^(1/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a^3+1/4*d^2*b*(c*x^2+b*x+a)^(7/2)","B"
1221,1,16,15,0.043000," ","int((2*c*d*x+b*d)*(c*x^2+b*x+a)^(5/2),x)","\frac{2 \left(c \,x^{2}+b x +a \right)^{\frac{7}{2}} d}{7}"," ",0,"2/7*d*(c*x^2+b*x+a)^(7/2)","A"
1222,1,660,125,0.051000," ","int((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d),x)","-\frac{a^{3} \ln \left(\frac{\frac{4 a c -b^{2}}{2 c}+\frac{\sqrt{\frac{4 a c -b^{2}}{c}}\, \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}}{2}}{x +\frac{b}{2 c}}\right)}{\sqrt{\frac{4 a c -b^{2}}{c}}\, c d}+\frac{3 a^{2} b^{2} \ln \left(\frac{\frac{4 a c -b^{2}}{2 c}+\frac{\sqrt{\frac{4 a c -b^{2}}{c}}\, \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}}{2}}{x +\frac{b}{2 c}}\right)}{4 \sqrt{\frac{4 a c -b^{2}}{c}}\, c^{2} d}-\frac{3 a \,b^{4} \ln \left(\frac{\frac{4 a c -b^{2}}{2 c}+\frac{\sqrt{\frac{4 a c -b^{2}}{c}}\, \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}}{2}}{x +\frac{b}{2 c}}\right)}{16 \sqrt{\frac{4 a c -b^{2}}{c}}\, c^{3} d}+\frac{b^{6} \ln \left(\frac{\frac{4 a c -b^{2}}{2 c}+\frac{\sqrt{\frac{4 a c -b^{2}}{c}}\, \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}}{2}}{x +\frac{b}{2 c}}\right)}{64 \sqrt{\frac{4 a c -b^{2}}{c}}\, c^{4} d}+\frac{\sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}\, a^{2}}{4 c d}-\frac{\sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}\, a \,b^{2}}{8 c^{2} d}+\frac{\sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}\, b^{4}}{64 c^{3} d}+\frac{\left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{3}{2}} a}{6 c d}-\frac{\left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{3}{2}} b^{2}}{24 c^{2} d}+\frac{\left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{5}{2}}}{10 c d}"," ",0,"1/10/c/d*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(5/2)+1/6/c/d*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(3/2)*a-1/24/c^2/d*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(3/2)*b^2+1/4/c/d*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2)*a^2-1/8/c^2/d*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2)*a*b^2+1/64/c^3/d*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2)*b^4-1/c/d/((4*a*c-b^2)/c)^(1/2)*ln((1/2*(4*a*c-b^2)/c+1/2*((4*a*c-b^2)/c)^(1/2)*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2))/(x+1/2*b/c))*a^3+3/4/c^2/d/((4*a*c-b^2)/c)^(1/2)*ln((1/2*(4*a*c-b^2)/c+1/2*((4*a*c-b^2)/c)^(1/2)*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2))/(x+1/2*b/c))*a^2*b^2-3/16/c^3/d/((4*a*c-b^2)/c)^(1/2)*ln((1/2*(4*a*c-b^2)/c+1/2*((4*a*c-b^2)/c)^(1/2)*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2))/(x+1/2*b/c))*a*b^4+1/64/c^4/d/((4*a*c-b^2)/c)^(1/2)*ln((1/2*(4*a*c-b^2)/c+1/2*((4*a*c-b^2)/c)^(1/2)*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2))/(x+1/2*b/c))*b^6","B"
1223,1,961,131,0.055000," ","int((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^2,x)","\frac{15 a^{3} \ln \left(\left(x +\frac{b}{2 c}\right) \sqrt{c}+\sqrt{\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}}\right)}{8 \left(4 a c -b^{2}\right) \sqrt{c}\, d^{2}}-\frac{45 a^{2} b^{2} \ln \left(\left(x +\frac{b}{2 c}\right) \sqrt{c}+\sqrt{\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}}\right)}{32 \left(4 a c -b^{2}\right) c^{\frac{3}{2}} d^{2}}+\frac{45 a \,b^{4} \ln \left(\left(x +\frac{b}{2 c}\right) \sqrt{c}+\sqrt{\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}}\right)}{128 \left(4 a c -b^{2}\right) c^{\frac{5}{2}} d^{2}}-\frac{15 b^{6} \ln \left(\left(x +\frac{b}{2 c}\right) \sqrt{c}+\sqrt{\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}}\right)}{512 \left(4 a c -b^{2}\right) c^{\frac{7}{2}} d^{2}}+\frac{15 \sqrt{\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}}\, a^{2} x}{8 \left(4 a c -b^{2}\right) d^{2}}-\frac{15 \sqrt{\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}}\, a \,b^{2} x}{16 \left(4 a c -b^{2}\right) c \,d^{2}}+\frac{15 \sqrt{\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}}\, b^{4} x}{128 \left(4 a c -b^{2}\right) c^{2} d^{2}}+\frac{15 \sqrt{\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}}\, a^{2} b}{16 \left(4 a c -b^{2}\right) c \,d^{2}}-\frac{15 \sqrt{\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}}\, a \,b^{3}}{32 \left(4 a c -b^{2}\right) c^{2} d^{2}}+\frac{5 \left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{3}{2}} a x}{4 \left(4 a c -b^{2}\right) d^{2}}+\frac{15 \sqrt{\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}}\, b^{5}}{256 \left(4 a c -b^{2}\right) c^{3} d^{2}}-\frac{5 \left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{3}{2}} b^{2} x}{16 \left(4 a c -b^{2}\right) c \,d^{2}}+\frac{5 \left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{3}{2}} a b}{8 \left(4 a c -b^{2}\right) c \,d^{2}}-\frac{5 \left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{3}{2}} b^{3}}{32 \left(4 a c -b^{2}\right) c^{2} d^{2}}+\frac{\left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{5}{2}} x}{\left(4 a c -b^{2}\right) d^{2}}+\frac{\left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{5}{2}} b}{2 \left(4 a c -b^{2}\right) c \,d^{2}}-\frac{\left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{7}{2}}}{\left(4 a c -b^{2}\right) \left(x +\frac{b}{2 c}\right) c \,d^{2}}"," ",0,"-1/c/d^2/(4*a*c-b^2)/(x+1/2*b/c)*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(7/2)+1/d^2/(4*a*c-b^2)*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(5/2)*x+1/2/c/d^2/(4*a*c-b^2)*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(5/2)*b+5/4/d^2/(4*a*c-b^2)*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(3/2)*x*a-5/16/c/d^2/(4*a*c-b^2)*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(3/2)*x*b^2+5/8/c/d^2/(4*a*c-b^2)*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(3/2)*b*a-5/32/c^2/d^2/(4*a*c-b^2)*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(3/2)*b^3+15/8/d^2/(4*a*c-b^2)*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(1/2)*x*a^2-15/16/c/d^2/(4*a*c-b^2)*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(1/2)*x*a*b^2+15/128/c^2/d^2/(4*a*c-b^2)*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(1/2)*x*b^4+15/16/c/d^2/(4*a*c-b^2)*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(1/2)*b*a^2-15/32/c^2/d^2/(4*a*c-b^2)*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(1/2)*b^3*a+15/256/c^3/d^2/(4*a*c-b^2)*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(1/2)*b^5+15/8/c^(1/2)/d^2/(4*a*c-b^2)*ln((x+1/2*b/c)*c^(1/2)+((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(1/2))*a^3-45/32/c^(3/2)/d^2/(4*a*c-b^2)*ln((x+1/2*b/c)*c^(1/2)+((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(1/2))*b^2*a^2+45/128/c^(5/2)/d^2/(4*a*c-b^2)*ln((x+1/2*b/c)*c^(1/2)+((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(1/2))*b^4*a-15/512/c^(7/2)/d^2/(4*a*c-b^2)*ln((x+1/2*b/c)*c^(1/2)+((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(1/2))*b^6","B"
1224,1,840,123,0.055000," ","int((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^3,x)","-\frac{5 a^{3} \ln \left(\frac{\frac{4 a c -b^{2}}{2 c}+\frac{\sqrt{\frac{4 a c -b^{2}}{c}}\, \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}}{2}}{x +\frac{b}{2 c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\frac{4 a c -b^{2}}{c}}\, c \,d^{3}}+\frac{15 a^{2} b^{2} \ln \left(\frac{\frac{4 a c -b^{2}}{2 c}+\frac{\sqrt{\frac{4 a c -b^{2}}{c}}\, \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}}{2}}{x +\frac{b}{2 c}}\right)}{8 \left(4 a c -b^{2}\right) \sqrt{\frac{4 a c -b^{2}}{c}}\, c^{2} d^{3}}-\frac{15 a \,b^{4} \ln \left(\frac{\frac{4 a c -b^{2}}{2 c}+\frac{\sqrt{\frac{4 a c -b^{2}}{c}}\, \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}}{2}}{x +\frac{b}{2 c}}\right)}{32 \left(4 a c -b^{2}\right) \sqrt{\frac{4 a c -b^{2}}{c}}\, c^{3} d^{3}}+\frac{5 b^{6} \ln \left(\frac{\frac{4 a c -b^{2}}{2 c}+\frac{\sqrt{\frac{4 a c -b^{2}}{c}}\, \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}}{2}}{x +\frac{b}{2 c}}\right)}{128 \left(4 a c -b^{2}\right) \sqrt{\frac{4 a c -b^{2}}{c}}\, c^{4} d^{3}}+\frac{5 \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}\, a^{2}}{8 \left(4 a c -b^{2}\right) c \,d^{3}}-\frac{5 \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}\, a \,b^{2}}{16 \left(4 a c -b^{2}\right) c^{2} d^{3}}+\frac{5 \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}\, b^{4}}{128 \left(4 a c -b^{2}\right) c^{3} d^{3}}+\frac{5 \left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{3}{2}} a}{12 \left(4 a c -b^{2}\right) c \,d^{3}}-\frac{5 \left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{3}{2}} b^{2}}{48 \left(4 a c -b^{2}\right) c^{2} d^{3}}+\frac{\left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{5}{2}}}{4 \left(4 a c -b^{2}\right) c \,d^{3}}-\frac{\left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{7}{2}}}{4 \left(4 a c -b^{2}\right) \left(x +\frac{b}{2 c}\right)^{2} c^{2} d^{3}}"," ",0,"-1/4/d^3/c^2/(4*a*c-b^2)/(x+1/2*b/c)^2*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(7/2)+1/4/d^3/c/(4*a*c-b^2)*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(5/2)+5/12/d^3/c/(4*a*c-b^2)*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(3/2)*a-5/48/d^3/c^2/(4*a*c-b^2)*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(3/2)*b^2+5/8/d^3/c/(4*a*c-b^2)*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2)*a^2-5/16/d^3/c^2/(4*a*c-b^2)*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2)*a*b^2+5/128/d^3/c^3/(4*a*c-b^2)*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2)*b^4-5/2/d^3/c/(4*a*c-b^2)/((4*a*c-b^2)/c)^(1/2)*ln((1/2*(4*a*c-b^2)/c+1/2*((4*a*c-b^2)/c)^(1/2)*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2))/(x+1/2*b/c))*a^3+15/8/d^3/c^2/(4*a*c-b^2)/((4*a*c-b^2)/c)^(1/2)*ln((1/2*(4*a*c-b^2)/c+1/2*((4*a*c-b^2)/c)^(1/2)*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2))/(x+1/2*b/c))*a^2*b^2-15/32/d^3/c^3/(4*a*c-b^2)/((4*a*c-b^2)/c)^(1/2)*ln((1/2*(4*a*c-b^2)/c+1/2*((4*a*c-b^2)/c)^(1/2)*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2))/(x+1/2*b/c))*a*b^4+5/128/d^3/c^4/(4*a*c-b^2)/((4*a*c-b^2)/c)^(1/2)*ln((1/2*(4*a*c-b^2)/c+1/2*((4*a*c-b^2)/c)^(1/2)*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2))/(x+1/2*b/c))*b^6","B"
1225,1,1022,123,0.067000," ","int((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^4,x)","\frac{5 a^{3} \ln \left(\left(x +\frac{b}{2 c}\right) \sqrt{c}+\sqrt{\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}}\right)}{2 \left(4 a c -b^{2}\right)^{2} \sqrt{c}\, d^{4}}-\frac{15 a^{2} b^{2} \ln \left(\left(x +\frac{b}{2 c}\right) \sqrt{c}+\sqrt{\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}}\right)}{8 \left(4 a c -b^{2}\right)^{2} c^{\frac{3}{2}} d^{4}}+\frac{15 a \,b^{4} \ln \left(\left(x +\frac{b}{2 c}\right) \sqrt{c}+\sqrt{\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}}\right)}{32 \left(4 a c -b^{2}\right)^{2} c^{\frac{5}{2}} d^{4}}-\frac{5 b^{6} \ln \left(\left(x +\frac{b}{2 c}\right) \sqrt{c}+\sqrt{\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}}\right)}{128 \left(4 a c -b^{2}\right)^{2} c^{\frac{7}{2}} d^{4}}+\frac{5 \sqrt{\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}}\, a^{2} x}{2 \left(4 a c -b^{2}\right)^{2} d^{4}}-\frac{5 \sqrt{\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}}\, a \,b^{2} x}{4 \left(4 a c -b^{2}\right)^{2} c \,d^{4}}+\frac{5 \sqrt{\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}}\, b^{4} x}{32 \left(4 a c -b^{2}\right)^{2} c^{2} d^{4}}+\frac{5 \sqrt{\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}}\, a^{2} b}{4 \left(4 a c -b^{2}\right)^{2} c \,d^{4}}-\frac{5 \sqrt{\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}}\, a \,b^{3}}{8 \left(4 a c -b^{2}\right)^{2} c^{2} d^{4}}+\frac{5 \left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{3}{2}} a x}{3 \left(4 a c -b^{2}\right)^{2} d^{4}}+\frac{5 \sqrt{\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}}\, b^{5}}{64 \left(4 a c -b^{2}\right)^{2} c^{3} d^{4}}-\frac{5 \left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{3}{2}} b^{2} x}{12 \left(4 a c -b^{2}\right)^{2} c \,d^{4}}+\frac{5 \left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{3}{2}} a b}{6 \left(4 a c -b^{2}\right)^{2} c \,d^{4}}-\frac{5 \left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{3}{2}} b^{3}}{24 \left(4 a c -b^{2}\right)^{2} c^{2} d^{4}}+\frac{4 \left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{5}{2}} x}{3 \left(4 a c -b^{2}\right)^{2} d^{4}}+\frac{2 \left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{5}{2}} b}{3 \left(4 a c -b^{2}\right)^{2} c \,d^{4}}-\frac{4 \left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{7}{2}}}{3 \left(4 a c -b^{2}\right)^{2} \left(x +\frac{b}{2 c}\right) c \,d^{4}}-\frac{\left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{7}{2}}}{12 \left(4 a c -b^{2}\right) \left(x +\frac{b}{2 c}\right)^{3} c^{3} d^{4}}"," ",0,"-1/12/d^4/c^3/(4*a*c-b^2)/(x+1/2*b/c)^3*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(7/2)-4/3/d^4/c/(4*a*c-b^2)^2/(x+1/2*b/c)*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(7/2)+4/3/d^4/(4*a*c-b^2)^2*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(5/2)*x+2/3/d^4/c/(4*a*c-b^2)^2*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(5/2)*b+5/3/d^4/(4*a*c-b^2)^2*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(3/2)*x*a-5/12/d^4/c/(4*a*c-b^2)^2*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(3/2)*x*b^2+5/6/d^4/c/(4*a*c-b^2)^2*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(3/2)*b*a-5/24/d^4/c^2/(4*a*c-b^2)^2*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(3/2)*b^3+5/2/d^4/(4*a*c-b^2)^2*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(1/2)*x*a^2-5/4/d^4/c/(4*a*c-b^2)^2*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(1/2)*x*a*b^2+5/32/d^4/c^2/(4*a*c-b^2)^2*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(1/2)*x*b^4+5/4/d^4/c/(4*a*c-b^2)^2*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(1/2)*b*a^2-5/8/d^4/c^2/(4*a*c-b^2)^2*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(1/2)*b^3*a+5/64/d^4/c^3/(4*a*c-b^2)^2*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(1/2)*b^5+5/2/d^4/c^(1/2)/(4*a*c-b^2)^2*ln((x+1/2*b/c)*c^(1/2)+((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(1/2))*a^3-15/8/d^4/c^(3/2)/(4*a*c-b^2)^2*ln((x+1/2*b/c)*c^(1/2)+((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(1/2))*b^2*a^2+15/32/d^4/c^(5/2)/(4*a*c-b^2)^2*ln((x+1/2*b/c)*c^(1/2)+((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(1/2))*b^4*a-5/128/d^4/c^(7/2)/(4*a*c-b^2)^2*ln((x+1/2*b/c)*c^(1/2)+((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(1/2))*b^6","B"
1226,1,900,123,0.055000," ","int((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^5,x)","-\frac{15 a^{3} \ln \left(\frac{\frac{4 a c -b^{2}}{2 c}+\frac{\sqrt{\frac{4 a c -b^{2}}{c}}\, \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}}{2}}{x +\frac{b}{2 c}}\right)}{8 \left(4 a c -b^{2}\right)^{2} \sqrt{\frac{4 a c -b^{2}}{c}}\, c \,d^{5}}+\frac{45 a^{2} b^{2} \ln \left(\frac{\frac{4 a c -b^{2}}{2 c}+\frac{\sqrt{\frac{4 a c -b^{2}}{c}}\, \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}}{2}}{x +\frac{b}{2 c}}\right)}{32 \left(4 a c -b^{2}\right)^{2} \sqrt{\frac{4 a c -b^{2}}{c}}\, c^{2} d^{5}}-\frac{45 a \,b^{4} \ln \left(\frac{\frac{4 a c -b^{2}}{2 c}+\frac{\sqrt{\frac{4 a c -b^{2}}{c}}\, \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}}{2}}{x +\frac{b}{2 c}}\right)}{128 \left(4 a c -b^{2}\right)^{2} \sqrt{\frac{4 a c -b^{2}}{c}}\, c^{3} d^{5}}+\frac{15 b^{6} \ln \left(\frac{\frac{4 a c -b^{2}}{2 c}+\frac{\sqrt{\frac{4 a c -b^{2}}{c}}\, \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}}{2}}{x +\frac{b}{2 c}}\right)}{512 \left(4 a c -b^{2}\right)^{2} \sqrt{\frac{4 a c -b^{2}}{c}}\, c^{4} d^{5}}+\frac{15 \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}\, a^{2}}{32 \left(4 a c -b^{2}\right)^{2} c \,d^{5}}-\frac{15 \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}\, a \,b^{2}}{64 \left(4 a c -b^{2}\right)^{2} c^{2} d^{5}}+\frac{15 \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}\, b^{4}}{512 \left(4 a c -b^{2}\right)^{2} c^{3} d^{5}}+\frac{5 \left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{3}{2}} a}{16 \left(4 a c -b^{2}\right)^{2} c \,d^{5}}-\frac{5 \left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{3}{2}} b^{2}}{64 \left(4 a c -b^{2}\right)^{2} c^{2} d^{5}}+\frac{3 \left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{5}{2}}}{16 \left(4 a c -b^{2}\right)^{2} c \,d^{5}}-\frac{3 \left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{7}{2}}}{16 \left(4 a c -b^{2}\right)^{2} \left(x +\frac{b}{2 c}\right)^{2} c^{2} d^{5}}-\frac{\left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{7}{2}}}{32 \left(4 a c -b^{2}\right) \left(x +\frac{b}{2 c}\right)^{4} c^{4} d^{5}}"," ",0,"-1/32/d^5/c^4/(4*a*c-b^2)/(x+1/2*b/c)^4*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(7/2)-3/16/d^5/c^2/(4*a*c-b^2)^2/(x+1/2*b/c)^2*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(7/2)+3/16/d^5/c/(4*a*c-b^2)^2*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(5/2)+5/16/d^5/c/(4*a*c-b^2)^2*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(3/2)*a-5/64/d^5/c^2/(4*a*c-b^2)^2*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(3/2)*b^2+15/32/d^5/c/(4*a*c-b^2)^2*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2)*a^2-15/64/d^5/c^2/(4*a*c-b^2)^2*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2)*a*b^2+15/512/d^5/c^3/(4*a*c-b^2)^2*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2)*b^4-15/8/d^5/c/(4*a*c-b^2)^2/((4*a*c-b^2)/c)^(1/2)*ln((1/2*(4*a*c-b^2)/c+1/2*((4*a*c-b^2)/c)^(1/2)*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2))/(x+1/2*b/c))*a^3+45/32/d^5/c^2/(4*a*c-b^2)^2/((4*a*c-b^2)/c)^(1/2)*ln((1/2*(4*a*c-b^2)/c+1/2*((4*a*c-b^2)/c)^(1/2)*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2))/(x+1/2*b/c))*a^2*b^2-45/128/d^5/c^3/(4*a*c-b^2)^2/((4*a*c-b^2)/c)^(1/2)*ln((1/2*(4*a*c-b^2)/c+1/2*((4*a*c-b^2)/c)^(1/2)*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2))/(x+1/2*b/c))*a*b^4+15/512/d^5/c^4/(4*a*c-b^2)^2/((4*a*c-b^2)/c)^(1/2)*ln((1/2*(4*a*c-b^2)/c+1/2*((4*a*c-b^2)/c)^(1/2)*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2))/(x+1/2*b/c))*b^6","B"
1227,1,1080,117,0.067000," ","int((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^6,x)","\frac{a^{3} \ln \left(\left(x +\frac{b}{2 c}\right) \sqrt{c}+\sqrt{\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}}\right)}{\left(4 a c -b^{2}\right)^{3} \sqrt{c}\, d^{6}}-\frac{3 a^{2} b^{2} \ln \left(\left(x +\frac{b}{2 c}\right) \sqrt{c}+\sqrt{\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}}\right)}{4 \left(4 a c -b^{2}\right)^{3} c^{\frac{3}{2}} d^{6}}+\frac{3 a \,b^{4} \ln \left(\left(x +\frac{b}{2 c}\right) \sqrt{c}+\sqrt{\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}}\right)}{16 \left(4 a c -b^{2}\right)^{3} c^{\frac{5}{2}} d^{6}}-\frac{b^{6} \ln \left(\left(x +\frac{b}{2 c}\right) \sqrt{c}+\sqrt{\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}}\right)}{64 \left(4 a c -b^{2}\right)^{3} c^{\frac{7}{2}} d^{6}}+\frac{\sqrt{\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}}\, a^{2} x}{\left(4 a c -b^{2}\right)^{3} d^{6}}-\frac{\sqrt{\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}}\, a \,b^{2} x}{2 \left(4 a c -b^{2}\right)^{3} c \,d^{6}}+\frac{\sqrt{\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}}\, b^{4} x}{16 \left(4 a c -b^{2}\right)^{3} c^{2} d^{6}}+\frac{\sqrt{\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}}\, a^{2} b}{2 \left(4 a c -b^{2}\right)^{3} c \,d^{6}}-\frac{\sqrt{\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}}\, a \,b^{3}}{4 \left(4 a c -b^{2}\right)^{3} c^{2} d^{6}}+\frac{2 \left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{3}{2}} a x}{3 \left(4 a c -b^{2}\right)^{3} d^{6}}+\frac{\sqrt{\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}}\, b^{5}}{32 \left(4 a c -b^{2}\right)^{3} c^{3} d^{6}}-\frac{\left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{3}{2}} b^{2} x}{6 \left(4 a c -b^{2}\right)^{3} c \,d^{6}}+\frac{\left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{3}{2}} a b}{3 \left(4 a c -b^{2}\right)^{3} c \,d^{6}}-\frac{\left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{3}{2}} b^{3}}{12 \left(4 a c -b^{2}\right)^{3} c^{2} d^{6}}+\frac{8 \left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{5}{2}} x}{15 \left(4 a c -b^{2}\right)^{3} d^{6}}+\frac{4 \left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{5}{2}} b}{15 \left(4 a c -b^{2}\right)^{3} c \,d^{6}}-\frac{8 \left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{7}{2}}}{15 \left(4 a c -b^{2}\right)^{3} \left(x +\frac{b}{2 c}\right) c \,d^{6}}-\frac{\left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{7}{2}}}{30 \left(4 a c -b^{2}\right)^{2} \left(x +\frac{b}{2 c}\right)^{3} c^{3} d^{6}}-\frac{\left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{7}{2}}}{80 \left(4 a c -b^{2}\right) \left(x +\frac{b}{2 c}\right)^{5} c^{5} d^{6}}"," ",0,"-1/80/d^6/c^5/(4*a*c-b^2)/(x+1/2*b/c)^5*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(7/2)-1/30/d^6/c^3/(4*a*c-b^2)^2/(x+1/2*b/c)^3*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(7/2)-8/15/d^6/c/(4*a*c-b^2)^3/(x+1/2*b/c)*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(7/2)+8/15/d^6/(4*a*c-b^2)^3*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(5/2)*x+4/15/d^6/c/(4*a*c-b^2)^3*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(5/2)*b+2/3/d^6/(4*a*c-b^2)^3*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(3/2)*x*a-1/6/d^6/c/(4*a*c-b^2)^3*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(3/2)*x*b^2+1/3/d^6/c/(4*a*c-b^2)^3*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(3/2)*b*a-1/12/d^6/c^2/(4*a*c-b^2)^3*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(3/2)*b^3+1/d^6/(4*a*c-b^2)^3*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(1/2)*x*a^2-1/2/d^6/c/(4*a*c-b^2)^3*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(1/2)*x*a*b^2+1/16/d^6/c^2/(4*a*c-b^2)^3*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(1/2)*x*b^4+1/2/d^6/c/(4*a*c-b^2)^3*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(1/2)*b*a^2-1/4/d^6/c^2/(4*a*c-b^2)^3*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(1/2)*b^3*a+1/32/d^6/c^3/(4*a*c-b^2)^3*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(1/2)*b^5+1/d^6/c^(1/2)/(4*a*c-b^2)^3*ln((x+1/2*b/c)*c^(1/2)+((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(1/2))*a^3-3/4/d^6/c^(3/2)/(4*a*c-b^2)^3*ln((x+1/2*b/c)*c^(1/2)+((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(1/2))*b^2*a^2+3/16/d^6/c^(5/2)/(4*a*c-b^2)^3*ln((x+1/2*b/c)*c^(1/2)+((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(1/2))*b^4*a-1/64/d^6/c^(7/2)/(4*a*c-b^2)^3*ln((x+1/2*b/c)*c^(1/2)+((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(1/2))*b^6","B"
1228,1,960,131,0.063000," ","int((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^7,x)","-\frac{5 a^{3} \ln \left(\frac{\frac{4 a c -b^{2}}{2 c}+\frac{\sqrt{\frac{4 a c -b^{2}}{c}}\, \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}}{2}}{x +\frac{b}{2 c}}\right)}{16 \left(4 a c -b^{2}\right)^{3} \sqrt{\frac{4 a c -b^{2}}{c}}\, c \,d^{7}}+\frac{15 a^{2} b^{2} \ln \left(\frac{\frac{4 a c -b^{2}}{2 c}+\frac{\sqrt{\frac{4 a c -b^{2}}{c}}\, \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}}{2}}{x +\frac{b}{2 c}}\right)}{64 \left(4 a c -b^{2}\right)^{3} \sqrt{\frac{4 a c -b^{2}}{c}}\, c^{2} d^{7}}-\frac{15 a \,b^{4} \ln \left(\frac{\frac{4 a c -b^{2}}{2 c}+\frac{\sqrt{\frac{4 a c -b^{2}}{c}}\, \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}}{2}}{x +\frac{b}{2 c}}\right)}{256 \left(4 a c -b^{2}\right)^{3} \sqrt{\frac{4 a c -b^{2}}{c}}\, c^{3} d^{7}}+\frac{5 b^{6} \ln \left(\frac{\frac{4 a c -b^{2}}{2 c}+\frac{\sqrt{\frac{4 a c -b^{2}}{c}}\, \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}}{2}}{x +\frac{b}{2 c}}\right)}{1024 \left(4 a c -b^{2}\right)^{3} \sqrt{\frac{4 a c -b^{2}}{c}}\, c^{4} d^{7}}+\frac{5 \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}\, a^{2}}{64 \left(4 a c -b^{2}\right)^{3} c \,d^{7}}-\frac{5 \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}\, a \,b^{2}}{128 \left(4 a c -b^{2}\right)^{3} c^{2} d^{7}}+\frac{5 \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}\, b^{4}}{1024 \left(4 a c -b^{2}\right)^{3} c^{3} d^{7}}+\frac{5 \left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{3}{2}} a}{96 \left(4 a c -b^{2}\right)^{3} c \,d^{7}}-\frac{5 \left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{3}{2}} b^{2}}{384 \left(4 a c -b^{2}\right)^{3} c^{2} d^{7}}+\frac{\left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{5}{2}}}{32 \left(4 a c -b^{2}\right)^{3} c \,d^{7}}-\frac{\left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{7}{2}}}{32 \left(4 a c -b^{2}\right)^{3} \left(x +\frac{b}{2 c}\right)^{2} c^{2} d^{7}}-\frac{\left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{7}{2}}}{192 \left(4 a c -b^{2}\right)^{2} \left(x +\frac{b}{2 c}\right)^{4} c^{4} d^{7}}-\frac{\left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{7}{2}}}{192 \left(4 a c -b^{2}\right) \left(x +\frac{b}{2 c}\right)^{6} c^{6} d^{7}}"," ",0,"-1/192/d^7/c^6/(4*a*c-b^2)/(x+1/2*b/c)^6*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(7/2)-1/192/d^7/c^4/(4*a*c-b^2)^2/(x+1/2*b/c)^4*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(7/2)-1/32/d^7/c^2/(4*a*c-b^2)^3/(x+1/2*b/c)^2*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(7/2)+1/32/d^7/c/(4*a*c-b^2)^3*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(5/2)+5/96/d^7/c/(4*a*c-b^2)^3*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(3/2)*a-5/384/d^7/c^2/(4*a*c-b^2)^3*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(3/2)*b^2+5/64/d^7/c/(4*a*c-b^2)^3*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2)*a^2-5/128/d^7/c^2/(4*a*c-b^2)^3*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2)*a*b^2+5/1024/d^7/c^3/(4*a*c-b^2)^3*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2)*b^4-5/16/d^7/c/(4*a*c-b^2)^3/((4*a*c-b^2)/c)^(1/2)*ln((1/2*(4*a*c-b^2)/c+1/2*((4*a*c-b^2)/c)^(1/2)*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2))/(x+1/2*b/c))*a^3+15/64/d^7/c^2/(4*a*c-b^2)^3/((4*a*c-b^2)/c)^(1/2)*ln((1/2*(4*a*c-b^2)/c+1/2*((4*a*c-b^2)/c)^(1/2)*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2))/(x+1/2*b/c))*a^2*b^2-15/256/d^7/c^3/(4*a*c-b^2)^3/((4*a*c-b^2)/c)^(1/2)*ln((1/2*(4*a*c-b^2)/c+1/2*((4*a*c-b^2)/c)^(1/2)*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2))/(x+1/2*b/c))*a*b^4+5/1024/d^7/c^4/(4*a*c-b^2)^3/((4*a*c-b^2)/c)^(1/2)*ln((1/2*(4*a*c-b^2)/c+1/2*((4*a*c-b^2)/c)^(1/2)*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2))/(x+1/2*b/c))*b^6","B"
1229,1,38,35,0.042000," ","int((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^8,x)","-\frac{2 \left(c \,x^{2}+b x +a \right)^{\frac{7}{2}}}{7 \left(2 c x +b \right)^{7} \left(4 a c -b^{2}\right) d^{8}}"," ",0,"-2/7*(c*x^2+b*x+a)^(7/2)/(2*c*x+b)^7/d^8/(4*a*c-b^2)","A"
1230,1,1020,169,0.079000," ","int((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^9,x)","\frac{5 a^{3} \ln \left(\frac{\frac{4 a c -b^{2}}{2 c}+\frac{\sqrt{\frac{4 a c -b^{2}}{c}}\, \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}}{2}}{x +\frac{b}{2 c}}\right)}{128 \left(4 a c -b^{2}\right)^{4} \sqrt{\frac{4 a c -b^{2}}{c}}\, c \,d^{9}}-\frac{15 a^{2} b^{2} \ln \left(\frac{\frac{4 a c -b^{2}}{2 c}+\frac{\sqrt{\frac{4 a c -b^{2}}{c}}\, \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}}{2}}{x +\frac{b}{2 c}}\right)}{512 \left(4 a c -b^{2}\right)^{4} \sqrt{\frac{4 a c -b^{2}}{c}}\, c^{2} d^{9}}+\frac{15 a \,b^{4} \ln \left(\frac{\frac{4 a c -b^{2}}{2 c}+\frac{\sqrt{\frac{4 a c -b^{2}}{c}}\, \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}}{2}}{x +\frac{b}{2 c}}\right)}{2048 \left(4 a c -b^{2}\right)^{4} \sqrt{\frac{4 a c -b^{2}}{c}}\, c^{3} d^{9}}-\frac{5 b^{6} \ln \left(\frac{\frac{4 a c -b^{2}}{2 c}+\frac{\sqrt{\frac{4 a c -b^{2}}{c}}\, \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}}{2}}{x +\frac{b}{2 c}}\right)}{8192 \left(4 a c -b^{2}\right)^{4} \sqrt{\frac{4 a c -b^{2}}{c}}\, c^{4} d^{9}}-\frac{5 \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}\, a^{2}}{512 \left(4 a c -b^{2}\right)^{4} c \,d^{9}}+\frac{5 \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}\, a \,b^{2}}{1024 \left(4 a c -b^{2}\right)^{4} c^{2} d^{9}}-\frac{5 \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}\, b^{4}}{8192 \left(4 a c -b^{2}\right)^{4} c^{3} d^{9}}-\frac{5 \left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{3}{2}} a}{768 \left(4 a c -b^{2}\right)^{4} c \,d^{9}}+\frac{5 \left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{3}{2}} b^{2}}{3072 \left(4 a c -b^{2}\right)^{4} c^{2} d^{9}}-\frac{\left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{5}{2}}}{256 \left(4 a c -b^{2}\right)^{4} c \,d^{9}}+\frac{\left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{7}{2}}}{256 \left(4 a c -b^{2}\right)^{4} \left(x +\frac{b}{2 c}\right)^{2} c^{2} d^{9}}+\frac{\left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{7}{2}}}{1536 \left(4 a c -b^{2}\right)^{3} \left(x +\frac{b}{2 c}\right)^{4} c^{4} d^{9}}+\frac{\left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{7}{2}}}{1536 \left(4 a c -b^{2}\right)^{2} \left(x +\frac{b}{2 c}\right)^{6} c^{6} d^{9}}-\frac{\left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{7}{2}}}{1024 \left(4 a c -b^{2}\right) \left(x +\frac{b}{2 c}\right)^{8} c^{8} d^{9}}"," ",0,"-1/1024/d^9/c^8/(4*a*c-b^2)/(x+1/2*b/c)^8*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(7/2)+1/1536/d^9/c^6/(4*a*c-b^2)^2/(x+1/2*b/c)^6*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(7/2)+1/1536/d^9/c^4/(4*a*c-b^2)^3/(x+1/2*b/c)^4*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(7/2)+1/256/d^9/c^2/(4*a*c-b^2)^4/(x+1/2*b/c)^2*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(7/2)-1/256/d^9/c/(4*a*c-b^2)^4*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(5/2)-5/768/d^9/c/(4*a*c-b^2)^4*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(3/2)*a+5/3072/d^9/c^2/(4*a*c-b^2)^4*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(3/2)*b^2-5/512/d^9/c/(4*a*c-b^2)^4*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2)*a^2+5/1024/d^9/c^2/(4*a*c-b^2)^4*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2)*a*b^2-5/8192/d^9/c^3/(4*a*c-b^2)^4*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2)*b^4+5/128/d^9/c/(4*a*c-b^2)^4/((4*a*c-b^2)/c)^(1/2)*ln((1/2*(4*a*c-b^2)/c+1/2*((4*a*c-b^2)/c)^(1/2)*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2))/(x+1/2*b/c))*a^3-15/512/d^9/c^2/(4*a*c-b^2)^4/((4*a*c-b^2)/c)^(1/2)*ln((1/2*(4*a*c-b^2)/c+1/2*((4*a*c-b^2)/c)^(1/2)*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2))/(x+1/2*b/c))*a^2*b^2+15/2048/d^9/c^3/(4*a*c-b^2)^4/((4*a*c-b^2)/c)^(1/2)*ln((1/2*(4*a*c-b^2)/c+1/2*((4*a*c-b^2)/c)^(1/2)*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2))/(x+1/2*b/c))*a*b^4-5/8192/d^9/c^4/(4*a*c-b^2)^4/((4*a*c-b^2)/c)^(1/2)*ln((1/2*(4*a*c-b^2)/c+1/2*((4*a*c-b^2)/c)^(1/2)*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2))/(x+1/2*b/c))*b^6","B"
1231,1,70,71,0.047000," ","int((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^10,x)","-\frac{2 \left(-8 c^{2} x^{2}-8 b c x +28 a c -9 b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{7}{2}}}{63 \left(2 c x +b \right)^{9} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) d^{10}}"," ",0,"-2/63*(-8*c^2*x^2-8*b*c*x+28*a*c-9*b^2)*(c*x^2+b*x+a)^(7/2)/(2*c*x+b)^9/d^10/(16*a^2*c^2-8*a*b^2*c+b^4)","A"
1232,1,1080,207,0.126000," ","int((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^11,x)","-\frac{3 a^{3} \ln \left(\frac{\frac{4 a c -b^{2}}{2 c}+\frac{\sqrt{\frac{4 a c -b^{2}}{c}}\, \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}}{2}}{x +\frac{b}{2 c}}\right)}{256 \left(4 a c -b^{2}\right)^{5} \sqrt{\frac{4 a c -b^{2}}{c}}\, c \,d^{11}}+\frac{9 a^{2} b^{2} \ln \left(\frac{\frac{4 a c -b^{2}}{2 c}+\frac{\sqrt{\frac{4 a c -b^{2}}{c}}\, \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}}{2}}{x +\frac{b}{2 c}}\right)}{1024 \left(4 a c -b^{2}\right)^{5} \sqrt{\frac{4 a c -b^{2}}{c}}\, c^{2} d^{11}}-\frac{9 a \,b^{4} \ln \left(\frac{\frac{4 a c -b^{2}}{2 c}+\frac{\sqrt{\frac{4 a c -b^{2}}{c}}\, \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}}{2}}{x +\frac{b}{2 c}}\right)}{4096 \left(4 a c -b^{2}\right)^{5} \sqrt{\frac{4 a c -b^{2}}{c}}\, c^{3} d^{11}}+\frac{3 b^{6} \ln \left(\frac{\frac{4 a c -b^{2}}{2 c}+\frac{\sqrt{\frac{4 a c -b^{2}}{c}}\, \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}}{2}}{x +\frac{b}{2 c}}\right)}{16384 \left(4 a c -b^{2}\right)^{5} \sqrt{\frac{4 a c -b^{2}}{c}}\, c^{4} d^{11}}+\frac{3 \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}\, a^{2}}{1024 \left(4 a c -b^{2}\right)^{5} c \,d^{11}}-\frac{3 \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}\, a \,b^{2}}{2048 \left(4 a c -b^{2}\right)^{5} c^{2} d^{11}}+\frac{3 \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}\, b^{4}}{16384 \left(4 a c -b^{2}\right)^{5} c^{3} d^{11}}+\frac{\left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{3}{2}} a}{512 \left(4 a c -b^{2}\right)^{5} c \,d^{11}}-\frac{\left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{3}{2}} b^{2}}{2048 \left(4 a c -b^{2}\right)^{5} c^{2} d^{11}}+\frac{3 \left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{5}{2}}}{2560 \left(4 a c -b^{2}\right)^{5} c \,d^{11}}-\frac{3 \left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{7}{2}}}{2560 \left(4 a c -b^{2}\right)^{5} \left(x +\frac{b}{2 c}\right)^{2} c^{2} d^{11}}-\frac{\left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{7}{2}}}{5120 \left(4 a c -b^{2}\right)^{4} \left(x +\frac{b}{2 c}\right)^{4} c^{4} d^{11}}-\frac{\left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{7}{2}}}{5120 \left(4 a c -b^{2}\right)^{3} \left(x +\frac{b}{2 c}\right)^{6} c^{6} d^{11}}+\frac{3 \left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{7}{2}}}{10240 \left(4 a c -b^{2}\right)^{2} \left(x +\frac{b}{2 c}\right)^{8} c^{8} d^{11}}-\frac{\left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{7}{2}}}{5120 \left(4 a c -b^{2}\right) \left(x +\frac{b}{2 c}\right)^{10} c^{10} d^{11}}"," ",0,"-1/5120/d^11/c^10/(4*a*c-b^2)/(x+1/2*b/c)^10*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(7/2)+3/10240/d^11/c^8/(4*a*c-b^2)^2/(x+1/2*b/c)^8*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(7/2)-1/5120/d^11/c^6/(4*a*c-b^2)^3/(x+1/2*b/c)^6*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(7/2)-1/5120/d^11/c^4/(4*a*c-b^2)^4/(x+1/2*b/c)^4*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(7/2)-3/2560/d^11/c^2/(4*a*c-b^2)^5/(x+1/2*b/c)^2*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(7/2)+3/2560/d^11/c/(4*a*c-b^2)^5*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(5/2)+1/512/d^11/c/(4*a*c-b^2)^5*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(3/2)*a-1/2048/d^11/c^2/(4*a*c-b^2)^5*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(3/2)*b^2+3/1024/d^11/c/(4*a*c-b^2)^5*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2)*a^2-3/2048/d^11/c^2/(4*a*c-b^2)^5*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2)*a*b^2+3/16384/d^11/c^3/(4*a*c-b^2)^5*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2)*b^4-3/256/d^11/c/(4*a*c-b^2)^5/((4*a*c-b^2)/c)^(1/2)*ln((1/2*(4*a*c-b^2)/c+1/2*((4*a*c-b^2)/c)^(1/2)*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2))/(x+1/2*b/c))*a^3+9/1024/d^11/c^2/(4*a*c-b^2)^5/((4*a*c-b^2)/c)^(1/2)*ln((1/2*(4*a*c-b^2)/c+1/2*((4*a*c-b^2)/c)^(1/2)*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2))/(x+1/2*b/c))*a^2*b^2-9/4096/d^11/c^3/(4*a*c-b^2)^5/((4*a*c-b^2)/c)^(1/2)*ln((1/2*(4*a*c-b^2)/c+1/2*((4*a*c-b^2)/c)^(1/2)*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2))/(x+1/2*b/c))*a*b^4+3/16384/d^11/c^4/(4*a*c-b^2)^5/((4*a*c-b^2)/c)^(1/2)*ln((1/2*(4*a*c-b^2)/c+1/2*((4*a*c-b^2)/c)^(1/2)*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2))/(x+1/2*b/c))*b^6","B"
1233,1,133,106,0.050000," ","int((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^12,x)","-\frac{2 \left(128 c^{4} x^{4}+256 b \,c^{3} x^{3}-448 a \,c^{3} x^{2}+304 x^{2} b^{2} c^{2}-448 a b \,c^{2} x +176 x \,b^{3} c +1008 a^{2} c^{2}-616 a \,b^{2} c +99 b^{4}\right) \left(c \,x^{2}+b x +a \right)^{\frac{7}{2}}}{693 \left(2 c x +b \right)^{11} \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) d^{12}}"," ",0,"-2/693*(128*c^4*x^4+256*b*c^3*x^3-448*a*c^3*x^2+304*b^2*c^2*x^2-448*a*b*c^2*x+176*b^3*c*x+1008*a^2*c^2-616*a*b^2*c+99*b^4)*(c*x^2+b*x+a)^(7/2)/(2*c*x+b)^11/d^12/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)","A"
1234,1,242,99,0.054000," ","int((2*c*d*x+b*d)^4/(c*x^2+b*x+a)^(1/2),x)","4 \sqrt{c \,x^{2}+b x +a}\, c^{3} d^{4} x^{3}+6 \sqrt{c \,x^{2}+b x +a}\, b \,c^{2} d^{4} x^{2}+6 a^{2} c^{\frac{3}{2}} d^{4} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)-3 a \,b^{2} \sqrt{c}\, d^{4} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)+\frac{3 b^{4} d^{4} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{8 \sqrt{c}}-6 \sqrt{c \,x^{2}+b x +a}\, a \,c^{2} d^{4} x +\frac{9 \sqrt{c \,x^{2}+b x +a}\, b^{2} c \,d^{4} x}{2}-3 \sqrt{c \,x^{2}+b x +a}\, a b c \,d^{4}+\frac{5 \sqrt{c \,x^{2}+b x +a}\, b^{3} d^{4}}{4}"," ",0,"4*d^4*c^3*x^3*(c*x^2+b*x+a)^(1/2)+6*d^4*c^2*b*x^2*(c*x^2+b*x+a)^(1/2)+9/2*d^4*c*b^2*x*(c*x^2+b*x+a)^(1/2)+5/4*d^4*b^3*(c*x^2+b*x+a)^(1/2)+3/8*d^4*b^4*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))/c^(1/2)-3*d^4*c^(1/2)*b^2*a*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-3*d^4*c*b*a*(c*x^2+b*x+a)^(1/2)-6*d^4*c^2*a*x*(c*x^2+b*x+a)^(1/2)+6*d^4*c^(3/2)*a^2*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))","B"
1235,1,41,51,0.052000," ","int((2*c*d*x+b*d)^3/(c*x^2+b*x+a)^(1/2),x)","-\frac{2 \left(-4 c^{2} x^{2}-4 b c x +8 a c -3 b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, d^{3}}{3}"," ",0,"-2/3*d^3*(-4*c^2*x^2-4*b*c*x+8*a*c-3*b^2)*(c*x^2+b*x+a)^(1/2)","A"
1236,1,108,63,0.053000," ","int((2*c*d*x+b*d)^2/(c*x^2+b*x+a)^(1/2),x)","-2 a \sqrt{c}\, d^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)+\frac{b^{2} d^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{2 \sqrt{c}}+2 \sqrt{c \,x^{2}+b x +a}\, c \,d^{2} x +\sqrt{c \,x^{2}+b x +a}\, b \,d^{2}"," ",0,"2*d^2*c*x*(c*x^2+b*x+a)^(1/2)+d^2*b*(c*x^2+b*x+a)^(1/2)+1/2*d^2*b^2*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))/c^(1/2)-2*d^2*c^(1/2)*a*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))","A"
1237,1,16,15,0.042000," ","int((2*c*d*x+b*d)/(c*x^2+b*x+a)^(1/2),x)","2 \sqrt{c \,x^{2}+b x +a}\, d"," ",0,"2*d*(c*x^2+b*x+a)^(1/2)","A"
1238,1,101,45,0.046000," ","int(1/(2*c*d*x+b*d)/(c*x^2+b*x+a)^(1/2),x)","-\frac{\ln \left(\frac{\frac{4 a c -b^{2}}{2 c}+\frac{\sqrt{\frac{4 a c -b^{2}}{c}}\, \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}}{2}}{x +\frac{b}{2 c}}\right)}{\sqrt{\frac{4 a c -b^{2}}{c}}\, c d}"," ",0,"-1/d/c/((4*a*c-b^2)/c)^(1/2)*ln((1/2*(4*a*c-b^2)/c+1/2*((4*a*c-b^2)/c)^(1/2)*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2))/(x+1/2*b/c))","B"
1239,1,38,35,0.057000," ","int(1/(2*c*d*x+b*d)^2/(c*x^2+b*x+a)^(1/2),x)","-\frac{2 \sqrt{c \,x^{2}+b x +a}}{\left(2 c x +b \right) \left(4 a c -b^{2}\right) d^{2}}"," ",0,"-2*(c*x^2+b*x+a)^(1/2)/(2*c*x+b)/d^2/(4*a*c-b^2)","A"
1240,1,174,81,0.056000," ","int(1/(2*c*d*x+b*d)^3/(c*x^2+b*x+a)^(1/2),x)","\frac{\ln \left(\frac{\frac{4 a c -b^{2}}{2 c}+\frac{\sqrt{\frac{4 a c -b^{2}}{c}}\, \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}}{2}}{x +\frac{b}{2 c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\frac{4 a c -b^{2}}{c}}\, c \,d^{3}}-\frac{\sqrt{\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}}}{4 \left(4 a c -b^{2}\right) \left(x +\frac{b}{2 c}\right)^{2} c^{2} d^{3}}"," ",0,"-1/4/d^3/c^2/(4*a*c-b^2)/(x+1/2*b/c)^2*((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(1/2)+1/2/d^3/c/(4*a*c-b^2)/((4*a*c-b^2)/c)^(1/2)*ln((1/2*(4*a*c-b^2)/c+1/2*((4*a*c-b^2)/c)^(1/2)*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2))/(x+1/2*b/c))","B"
1241,1,70,71,0.043000," ","int(1/(2*c*d*x+b*d)^4/(c*x^2+b*x+a)^(1/2),x)","-\frac{2 \left(-8 c^{2} x^{2}-8 b c x +4 a c -3 b^{2}\right) \sqrt{c \,x^{2}+b x +a}}{3 \left(2 c x +b \right)^{3} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) d^{4}}"," ",0,"-2/3*(-8*c^2*x^2-8*b*c*x+4*a*c-3*b^2)*(c*x^2+b*x+a)^(1/2)/(2*c*x+b)^3/d^4/(16*a^2*c^2-8*a*b^2*c+b^4)","A"
1242,1,340,90,0.062000," ","int((2*c*d*x+b*d)^4/(c*x^2+b*x+a)^(3/2),x)","\frac{24 a \,b^{2} c^{2} d^{4} x}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}}-\frac{6 b^{4} c \,d^{4} x}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}}+\frac{8 c^{3} d^{4} x^{3}}{\sqrt{c \,x^{2}+b x +a}}+\frac{12 a \,b^{3} c \,d^{4}}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}}-\frac{3 b^{5} d^{4}}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}}+\frac{12 b \,c^{2} d^{4} x^{2}}{\sqrt{c \,x^{2}+b x +a}}+\frac{24 a \,c^{2} d^{4} x}{\sqrt{c \,x^{2}+b x +a}}-\frac{6 b^{2} c \,d^{4} x}{\sqrt{c \,x^{2}+b x +a}}-24 a \,c^{\frac{3}{2}} d^{4} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)+6 b^{2} \sqrt{c}\, d^{4} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)+\frac{12 a b c \,d^{4}}{\sqrt{c \,x^{2}+b x +a}}-\frac{5 b^{3} d^{4}}{\sqrt{c \,x^{2}+b x +a}}"," ",0,"-3*d^4*b^5/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)+12*d^4*c^2*b*x^2/(c*x^2+b*x+a)^(1/2)-6*d^4*c*b^2*x/(c*x^2+b*x+a)^(1/2)+6*d^4*c^(1/2)*b^2*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+12*d^4*c*b*a/(c*x^2+b*x+a)^(1/2)+24*d^4*c^2*a*x/(c*x^2+b*x+a)^(1/2)-24*d^4*c^(3/2)*a*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+24*d^4*c^2*b^2*a/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x-6*d^4*c*b^4/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x-5*d^4*b^3/(c*x^2+b*x+a)^(1/2)+8*d^4*c^3*x^3/(c*x^2+b*x+a)^(1/2)+12*d^4*c*b^3*a/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)","B"
1243,1,41,44,0.045000," ","int((2*c*d*x+b*d)^3/(c*x^2+b*x+a)^(3/2),x)","\frac{2 \left(4 c^{2} x^{2}+4 b c x +8 a c -b^{2}\right) d^{3}}{\sqrt{c \,x^{2}+b x +a}}"," ",0,"2*d^3*(4*c^2*x^2+4*b*c*x+8*a*c-b^2)/(c*x^2+b*x+a)^(1/2)","A"
1244,1,72,56,0.049000," ","int((2*c*d*x+b*d)^2/(c*x^2+b*x+a)^(3/2),x)","-\frac{4 c \,d^{2} x}{\sqrt{c \,x^{2}+b x +a}}+4 \sqrt{c}\, d^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)-\frac{2 b \,d^{2}}{\sqrt{c \,x^{2}+b x +a}}"," ",0,"-4*d^2*c*x/(c*x^2+b*x+a)^(1/2)-2*d^2*b/(c*x^2+b*x+a)^(1/2)+4*d^2*c^(1/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))","A"
1245,1,16,15,0.042000," ","int((2*c*d*x+b*d)/(c*x^2+b*x+a)^(3/2),x)","-\frac{2 d}{\sqrt{c \,x^{2}+b x +a}}"," ",0,"-2*d/(c*x^2+b*x+a)^(1/2)","A"
1246,1,158,74,0.050000," ","int(1/(2*c*d*x+b*d)/(c*x^2+b*x+a)^(3/2),x)","-\frac{4 \ln \left(\frac{\frac{4 a c -b^{2}}{2 c}+\frac{\sqrt{\frac{4 a c -b^{2}}{c}}\, \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}}{2}}{x +\frac{b}{2 c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{\frac{4 a c -b^{2}}{c}}\, d}+\frac{2}{\left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}}\, d}"," ",0,"2/d/(4*a*c-b^2)/((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(1/2)-4/d/(4*a*c-b^2)/((4*a*c-b^2)/c)^(1/2)*ln((1/2*(4*a*c-b^2)/c+1/2*((4*a*c-b^2)/c)^(1/2)*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2))/(x+1/2*b/c))","B"
1247,1,68,72,0.044000," ","int(1/(2*c*d*x+b*d)^2/(c*x^2+b*x+a)^(3/2),x)","-\frac{2 \left(8 c^{2} x^{2}+8 b c x +4 a c +b^{2}\right)}{\left(2 c x +b \right) \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{c \,x^{2}+b x +a}\, d^{2}}"," ",0,"-2*(8*c^2*x^2+8*b*c*x+4*a*c+b^2)/(2*c*x+b)/d^2/(16*a^2*c^2-8*a*b^2*c+b^4)/(c*x^2+b*x+a)^(1/2)","A"
1248,1,218,118,0.052000," ","int(1/(2*c*d*x+b*d)^3/(c*x^2+b*x+a)^(3/2),x)","\frac{6 \ln \left(\frac{\frac{4 a c -b^{2}}{2 c}+\frac{\sqrt{\frac{4 a c -b^{2}}{c}}\, \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}}{2}}{x +\frac{b}{2 c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\frac{4 a c -b^{2}}{c}}\, d^{3}}-\frac{3}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}}\, d^{3}}-\frac{1}{4 \left(4 a c -b^{2}\right) \left(x +\frac{b}{2 c}\right)^{2} \sqrt{\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}}\, c^{2} d^{3}}"," ",0,"-1/4/d^3/c^2/(4*a*c-b^2)/(x+1/2*b/c)^2/((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(1/2)-3/d^3/(4*a*c-b^2)^2/((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(1/2)+6/d^3/(4*a*c-b^2)^2/((4*a*c-b^2)/c)^(1/2)*ln((1/2*(4*a*c-b^2)/c+1/2*((4*a*c-b^2)/c)^(1/2)*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2))/(x+1/2*b/c))","A"
1249,1,133,108,0.051000," ","int(1/(2*c*d*x+b*d)^4/(c*x^2+b*x+a)^(3/2),x)","-\frac{2 \left(-128 c^{4} x^{4}-256 b \,c^{3} x^{3}-64 a \,c^{3} x^{2}-176 x^{2} b^{2} c^{2}-64 a b \,c^{2} x -48 x \,b^{3} c +16 a^{2} c^{2}-24 a \,b^{2} c -3 b^{4}\right)}{3 \left(2 c x +b \right)^{3} \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) \sqrt{c \,x^{2}+b x +a}\, d^{4}}"," ",0,"-2/3*(-128*c^4*x^4-256*b*c^3*x^3-64*a*c^3*x^2-176*b^2*c^2*x^2-64*a*b*c^2*x-48*b^3*c*x+16*a^2*c^2-24*a*b^2*c-3*b^4)/(2*c*x+b)^3/d^4/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)/(c*x^2+b*x+a)^(1/2)","A"
1250,1,997,118,0.069000," ","int((2*c*d*x+b*d)^6/(c*x^2+b*x+a)^(5/2),x)","\frac{32 c^{5} d^{6} x^{5}}{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}}}+\frac{1920 a^{2} b^{2} c^{4} d^{6} x}{\left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}}-\frac{960 a \,b^{4} c^{3} d^{6} x}{\left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}}+\frac{120 b^{6} c^{2} d^{6} x}{\left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}}+\frac{80 b \,c^{4} d^{6} x^{4}}{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}}}+\frac{960 a^{2} b^{3} c^{3} d^{6}}{\left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}}+\frac{240 a^{2} b^{2} c^{3} d^{6} x}{\left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}}}-\frac{480 a \,b^{5} c^{2} d^{6}}{\left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}}-\frac{120 a \,b^{4} c^{2} d^{6} x}{\left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}}}+\frac{160 a \,c^{4} d^{6} x^{3}}{3 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}}}+\frac{60 b^{7} c \,d^{6}}{\left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}}+\frac{15 b^{6} c \,d^{6} x}{\left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}}}-\frac{40 b^{2} c^{3} d^{6} x^{3}}{3 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}}}+\frac{120 a^{2} b^{3} c^{2} d^{6}}{\left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}}}-\frac{60 a \,b^{5} c \,d^{6}}{\left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}}}-\frac{160 a \,b^{2} c^{3} d^{6} x}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}}+\frac{240 a b \,c^{3} d^{6} x^{2}}{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}}}+\frac{15 b^{7} d^{6}}{2 \left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}}}+\frac{40 b^{4} c^{2} d^{6} x}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}}-\frac{140 b^{3} c^{2} d^{6} x^{2}}{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}}}-\frac{80 a \,b^{3} c^{2} d^{6}}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}}+\frac{60 a \,b^{2} c^{2} d^{6} x}{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}}}+\frac{20 b^{5} c \,d^{6}}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}}-\frac{65 b^{4} c \,d^{6} x}{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}}}+\frac{160 a^{2} b \,c^{2} d^{6}}{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}}}-\frac{310 a \,b^{3} c \,d^{6}}{3 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}}}+\frac{160 a \,c^{3} d^{6} x}{\sqrt{c \,x^{2}+b x +a}}+\frac{41 b^{5} d^{6}}{6 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}}}-\frac{40 b^{2} c^{2} d^{6} x}{\sqrt{c \,x^{2}+b x +a}}-160 a \,c^{\frac{5}{2}} d^{6} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)+40 b^{2} c^{\frac{3}{2}} d^{6} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)-\frac{80 a b \,c^{2} d^{6}}{\sqrt{c \,x^{2}+b x +a}}+\frac{20 b^{3} c \,d^{6}}{\sqrt{c \,x^{2}+b x +a}}"," ",0,"15*d^6*c*b^6/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)*x-480*d^6*c^2*b^5*a/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)+60*d^6*c^2*b^2*a*x/(c*x^2+b*x+a)^(3/2)+120*d^6*c^2*b^3*a^2/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)+120*d^6*c^2*b^6/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)*x-60*d^6*c*b^5*a/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)+960*d^6*c^3*b^3*a^2/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)+40*d^6*c^2*b^4/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x-80*d^6*c^2*a*b^3/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)+240*d^6*c^3*b*a*x^2/(c*x^2+b*x+a)^(3/2)-40*d^6*c^2*b^2*x/(c*x^2+b*x+a)^(1/2)+32*d^6*c^5*x^5/(c*x^2+b*x+a)^(3/2)-160*d^6*c^(5/2)*a*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+40*d^6*c^(3/2)*b^2*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+15/2*d^6*b^7/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)+20*d^6*c*b^3/(c*x^2+b*x+a)^(1/2)-120*d^6*c^2*b^4*a/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)*x-160*d^6*c^3*a*b^2/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x+240*d^6*c^3*b^2*a^2/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)*x+1920*d^6*c^4*b^2*a^2/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)*x-960*d^6*c^3*b^4*a/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)*x-40/3*d^6*c^3*b^2*x^3/(c*x^2+b*x+a)^(3/2)+160/3*d^6*c^4*a*x^3/(c*x^2+b*x+a)^(3/2)+160*d^6*c^3*a*x/(c*x^2+b*x+a)^(1/2)-80*d^6*c^2*a*b/(c*x^2+b*x+a)^(1/2)+160*d^6*c^2*b*a^2/(c*x^2+b*x+a)^(3/2)+80*d^6*c^4*b*x^4/(c*x^2+b*x+a)^(3/2)+20*d^6*c*b^5/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)-140*d^6*c^2*b^3*x^2/(c*x^2+b*x+a)^(3/2)-65*d^6*c*b^4*x/(c*x^2+b*x+a)^(3/2)+41/6*d^6*b^5/(c*x^2+b*x+a)^(3/2)+60*d^6*c*b^7/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)-310/3*d^6*c*b^3*a/(c*x^2+b*x+a)^(3/2)","B"
1251,1,91,72,0.041000," ","int((2*c*d*x+b*d)^5/(c*x^2+b*x+a)^(5/2),x)","\frac{2 \left(48 c^{4} x^{4}+96 b \,c^{3} x^{3}+192 a \,c^{3} x^{2}+24 x^{2} b^{2} c^{2}+192 a b \,c^{2} x -24 x \,b^{3} c +128 a^{2} c^{2}-16 a \,b^{2} c -b^{4}\right) d^{5}}{3 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}}}"," ",0,"2/3*d^5*(48*c^4*x^4+96*b*c^3*x^3+192*a*c^3*x^2+24*b^2*c^2*x^2+192*a*b*c^2*x-24*b^3*c*x+128*a^2*c^2-16*a*b^2*c-b^4)/(c*x^2+b*x+a)^(3/2)","A"
1252,1,531,82,0.056000," ","int((2*c*d*x+b*d)^4/(c*x^2+b*x+a)^(5/2),x)","-\frac{64 a \,b^{2} c^{3} d^{4} x}{\left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}}+\frac{16 b^{4} c^{2} d^{4} x}{\left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}}-\frac{32 a \,b^{3} c^{2} d^{4}}{\left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}}-\frac{8 a \,b^{2} c^{2} d^{4} x}{\left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}}}+\frac{8 b^{5} c \,d^{4}}{\left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}}+\frac{2 b^{4} c \,d^{4} x}{\left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}}}-\frac{16 c^{3} d^{4} x^{3}}{3 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}}}-\frac{4 a \,b^{3} c \,d^{4}}{\left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}}}+\frac{b^{5} d^{4}}{\left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}}}+\frac{16 b^{2} c^{2} d^{4} x}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}}-\frac{24 b \,c^{2} d^{4} x^{2}}{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}}}+\frac{8 b^{3} c \,d^{4}}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}}-\frac{18 b^{2} c \,d^{4} x}{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}}}-\frac{16 a b c \,d^{4}}{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}}}+\frac{b^{3} d^{4}}{3 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}}}-\frac{16 c^{2} d^{4} x}{\sqrt{c \,x^{2}+b x +a}}+16 c^{\frac{3}{2}} d^{4} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)+\frac{8 b c \,d^{4}}{\sqrt{c \,x^{2}+b x +a}}"," ",0,"-24*d^4*c^2*b*x^2/(c*x^2+b*x+a)^(3/2)-18*d^4*c*b^2*x/(c*x^2+b*x+a)^(3/2)+8*d^4*c*b^5/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)-16*d^4*c*b*a/(c*x^2+b*x+a)^(3/2)+8*d^4*c*b^3/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)-8*d^4*c^2*b^2*a/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)*x-64*d^4*c^3*b^2*a/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)*x-16/3*d^4*c^3*x^3/(c*x^2+b*x+a)^(3/2)+d^4*b^5/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)-16*d^4*c^2*x/(c*x^2+b*x+a)^(1/2)+8*d^4*c*b/(c*x^2+b*x+a)^(1/2)+16*d^4*c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+1/3*d^4*b^3/(c*x^2+b*x+a)^(3/2)-4*d^4*c*b^3*a/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)-32*d^4*c^2*b^3*a/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)+16*d^4*c^2*b^2/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x+2*d^4*c*b^4/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)*x+16*d^4*c^2*b^4/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)*x","B"
1253,1,39,44,0.047000," ","int((2*c*d*x+b*d)^3/(c*x^2+b*x+a)^(5/2),x)","-\frac{2 \left(12 c^{2} x^{2}+12 b c x +8 a c +b^{2}\right) d^{3}}{3 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}}}"," ",0,"-2/3*d^3*(12*c^2*x^2+12*b*c*x+8*a*c+b^2)/(c*x^2+b*x+a)^(3/2)","A"
1254,1,38,35,0.046000," ","int((2*c*d*x+b*d)^2/(c*x^2+b*x+a)^(5/2),x)","\frac{2 \left(2 c x +b \right)^{3} d^{2}}{3 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} \left(4 a c -b^{2}\right)}"," ",0,"2/3*(2*c*x+b)^3*d^2/(c*x^2+b*x+a)^(3/2)/(4*a*c-b^2)","A"
1255,1,16,15,0.045000," ","int((2*c*d*x+b*d)/(c*x^2+b*x+a)^(5/2),x)","-\frac{2 d}{3 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}}}"," ",0,"-2/3*d/(c*x^2+b*x+a)^(3/2)","A"
1256,1,207,102,0.050000," ","int(1/(2*c*d*x+b*d)/(c*x^2+b*x+a)^(5/2),x)","-\frac{16 c \ln \left(\frac{\frac{4 a c -b^{2}}{2 c}+\frac{\sqrt{\frac{4 a c -b^{2}}{c}}\, \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}}{2}}{x +\frac{b}{2 c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\frac{4 a c -b^{2}}{c}}\, d}+\frac{8 c}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}}\, d}+\frac{2}{3 \left(4 a c -b^{2}\right) \left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{3}{2}} d}"," ",0,"2/3/d/(4*a*c-b^2)/((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(3/2)+8*c/d/(4*a*c-b^2)^2/((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(1/2)-16*c/d/(4*a*c-b^2)^2/((4*a*c-b^2)/c)^(1/2)*ln((1/2*(4*a*c-b^2)/c+1/2*((4*a*c-b^2)/c)^(1/2)*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2))/(x+1/2*b/c))","B"
1257,1,133,110,0.051000," ","int(1/(2*c*d*x+b*d)^2/(c*x^2+b*x+a)^(5/2),x)","-\frac{2 \left(128 c^{4} x^{4}+256 b \,c^{3} x^{3}+192 a \,c^{3} x^{2}+144 x^{2} b^{2} c^{2}+192 a b \,c^{2} x +16 x \,b^{3} c +48 a^{2} c^{2}+24 a \,b^{2} c -b^{4}\right)}{3 \left(2 c x +b \right) \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} d^{2}}"," ",0,"-2/3*(128*c^4*x^4+256*b*c^3*x^3+192*a*c^3*x^2+144*b^2*c^2*x^2+192*a*b*c^2*x+16*b^3*c*x+48*a^2*c^2+24*a*b^2*c-b^4)/(2*c*x+b)/d^2/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)/(c*x^2+b*x+a)^(3/2)","A"
1258,1,267,156,0.064000," ","int(1/(2*c*d*x+b*d)^3/(c*x^2+b*x+a)^(5/2),x)","\frac{40 c \ln \left(\frac{\frac{4 a c -b^{2}}{2 c}+\frac{\sqrt{\frac{4 a c -b^{2}}{c}}\, \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}}{2}}{x +\frac{b}{2 c}}\right)}{\left(4 a c -b^{2}\right)^{3} \sqrt{\frac{4 a c -b^{2}}{c}}\, d^{3}}-\frac{20 c}{\left(4 a c -b^{2}\right)^{3} \sqrt{\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}}\, d^{3}}-\frac{5}{3 \left(4 a c -b^{2}\right)^{2} \left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{3}{2}} d^{3}}-\frac{1}{4 \left(4 a c -b^{2}\right) \left(x +\frac{b}{2 c}\right)^{2} \left(\left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{4 c}\right)^{\frac{3}{2}} c^{2} d^{3}}"," ",0,"-1/4/d^3/c^2/(4*a*c-b^2)/(x+1/2*b/c)^2/((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(3/2)-5/3/d^3/(4*a*c-b^2)^2/((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(3/2)-20/d^3*c/(4*a*c-b^2)^3/((x+1/2*b/c)^2*c+1/4*(4*a*c-b^2)/c)^(1/2)+40/d^3*c/(4*a*c-b^2)^3/((4*a*c-b^2)/c)^(1/2)*ln((1/2*(4*a*c-b^2)/c+1/2*((4*a*c-b^2)/c)^(1/2)*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2))/(x+1/2*b/c))","A"
1259,1,218,148,0.052000," ","int(1/(2*c*d*x+b*d)^4/(c*x^2+b*x+a)^(5/2),x)","-\frac{2 \left(-1024 c^{6} x^{6}-3072 b \,c^{5} x^{5}-1536 a \,c^{5} x^{4}-3456 b^{2} c^{4} x^{4}-3072 a b \,c^{4} x^{3}-1792 b^{3} c^{3} x^{3}-384 a^{2} c^{4} x^{2}-2112 a \,b^{2} c^{3} x^{2}-408 b^{4} c^{2} x^{2}-384 a^{2} b \,c^{3} x -576 a \,b^{3} c^{2} x -24 b^{5} c x +64 a^{3} c^{3}-144 a^{2} b^{2} c^{2}-36 a \,b^{4} c +b^{6}\right)}{3 \left(2 c x +b \right)^{3} \left(256 a^{4} c^{4}-256 a^{3} b^{2} c^{3}+96 a^{2} b^{4} c^{2}-16 a \,b^{6} c +b^{8}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} d^{4}}"," ",0,"-2/3*(-1024*c^6*x^6-3072*b*c^5*x^5-1536*a*c^5*x^4-3456*b^2*c^4*x^4-3072*a*b*c^4*x^3-1792*b^3*c^3*x^3-384*a^2*c^4*x^2-2112*a*b^2*c^3*x^2-408*b^4*c^2*x^2-384*a^2*b*c^3*x-576*a*b^3*c^2*x-24*b^5*c*x+64*a^3*c^3-144*a^2*b^2*c^2-36*a*b^4*c+b^6)/(2*c*x+b)^3/d^4/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8)/(c*x^2+b*x+a)^(3/2)","A"
1260,1,24,25,0.046000," ","int(1/(b*x+a)/(b^2*x^2+2*a*b*x+a^2+1)^(1/2),x)","-\frac{\arctanh \left(\frac{1}{\sqrt{\left(x +\frac{a}{b}\right)^{2} b^{2}+1}}\right)}{b}"," ",0,"-1/b*arctanh(1/((x+a/b)^2*b^2+1)^(1/2))","A"
1261,1,46,47,0.036000," ","int((2*c*d*x+b*d)^(5/2)*(c*x^2+b*x+a),x)","\frac{\left(2 c x +b \right) \left(7 c^{2} x^{2}+7 b c x +11 a c -b^{2}\right) \left(2 c d x +b d \right)^{\frac{5}{2}}}{77 c^{2}}"," ",0,"1/77*(2*c*x+b)*(7*c^2*x^2+7*b*c*x+11*a*c-b^2)*(2*c*d*x+b*d)^(5/2)/c^2","A"
1262,1,46,47,0.045000," ","int((2*c*d*x+b*d)^(3/2)*(c*x^2+b*x+a),x)","\frac{\left(2 c x +b \right) \left(5 c^{2} x^{2}+5 b c x +9 a c -b^{2}\right) \left(2 c d x +b d \right)^{\frac{3}{2}}}{45 c^{2}}"," ",0,"1/45*(2*c*x+b)*(5*c^2*x^2+5*b*c*x+9*a*c-b^2)*(2*c*d*x+b*d)^(3/2)/c^2","A"
1263,1,46,47,0.044000," ","int((2*c*d*x+b*d)^(1/2)*(c*x^2+b*x+a),x)","\frac{\left(2 c x +b \right) \left(3 c^{2} x^{2}+3 b c x +7 a c -b^{2}\right) \sqrt{2 c d x +b d}}{21 c^{2}}"," ",0,"1/21*(2*c*x+b)*(3*c^2*x^2+3*b*c*x+7*a*c-b^2)*(2*c*d*x+b*d)^(1/2)/c^2","A"
1264,1,44,47,0.043000," ","int((c*x^2+b*x+a)/(2*c*d*x+b*d)^(1/2),x)","\frac{\left(2 c x +b \right) \left(c^{2} x^{2}+b c x +5 a c -b^{2}\right)}{5 \sqrt{2 c d x +b d}\, c^{2}}"," ",0,"1/5*(2*c*x+b)*(c^2*x^2+b*c*x+5*a*c-b^2)/c^2/(2*c*d*x+b*d)^(1/2)","A"
1265,1,46,47,0.042000," ","int((c*x^2+b*x+a)/(2*c*d*x+b*d)^(3/2),x)","-\frac{\left(2 c x +b \right) \left(-c^{2} x^{2}-b c x +3 a c -b^{2}\right)}{3 \left(2 c d x +b d \right)^{\frac{3}{2}} c^{2}}"," ",0,"-1/3*(2*c*x+b)*(-c^2*x^2-b*c*x+3*a*c-b^2)/c^2/(2*c*d*x+b*d)^(3/2)","A"
1266,1,45,47,0.039000," ","int((c*x^2+b*x+a)/(2*c*d*x+b*d)^(5/2),x)","-\frac{\left(2 c x +b \right) \left(-3 c^{2} x^{2}-3 b c x +a c -b^{2}\right)}{3 \left(2 c d x +b d \right)^{\frac{5}{2}} c^{2}}"," ",0,"-1/3*(2*c*x+b)*(-3*c^2*x^2-3*b*c*x+a*c-b^2)/c^2/(2*c*d*x+b*d)^(5/2)","A"
1267,1,43,47,0.045000," ","int((c*x^2+b*x+a)/(2*c*d*x+b*d)^(7/2),x)","-\frac{\left(2 c x +b \right) \left(5 c^{2} x^{2}+5 b c x +a c +b^{2}\right)}{5 \left(2 c d x +b d \right)^{\frac{7}{2}} c^{2}}"," ",0,"-1/5*(2*c*x+b)*(5*c^2*x^2+5*b*c*x+a*c+b^2)/c^2/(2*c*d*x+b*d)^(7/2)","A"
1268,1,44,47,0.053000," ","int((c*x^2+b*x+a)/(2*c*d*x+b*d)^(9/2),x)","-\frac{\left(2 c x +b \right) \left(7 c^{2} x^{2}+7 b c x +3 a c +b^{2}\right)}{21 \left(2 c d x +b d \right)^{\frac{9}{2}} c^{2}}"," ",0,"-1/21*(2*c*x+b)*(7*c^2*x^2+7*b*c*x+3*a*c+b^2)/c^2/(2*c*d*x+b*d)^(9/2)","A"
1269,1,96,76,0.047000," ","int((2*c*d*x+b*d)^(3/2)*(c*x^2+b*x+a)^2,x)","\frac{\left(2 c x +b \right) \left(45 c^{4} x^{4}+90 b \,c^{3} x^{3}+130 a \,c^{3} x^{2}+35 x^{2} b^{2} c^{2}+130 a b \,c^{2} x -10 x \,b^{3} c +117 a^{2} c^{2}-26 a \,b^{2} c +2 b^{4}\right) \left(2 c d x +b d \right)^{\frac{3}{2}}}{585 c^{3}}"," ",0,"1/585*(2*c*x+b)*(45*c^4*x^4+90*b*c^3*x^3+130*a*c^3*x^2+35*b^2*c^2*x^2+130*a*b*c^2*x-10*b^3*c*x+117*a^2*c^2-26*a*b^2*c+2*b^4)*(2*c*d*x+b*d)^(3/2)/c^3","A"
1270,1,96,76,0.052000," ","int((2*c*d*x+b*d)^(1/2)*(c*x^2+b*x+a)^2,x)","\frac{\left(2 c x +b \right) \left(21 c^{4} x^{4}+42 b \,c^{3} x^{3}+66 a \,c^{3} x^{2}+15 x^{2} b^{2} c^{2}+66 a b \,c^{2} x -6 x \,b^{3} c +77 a^{2} c^{2}-22 a \,b^{2} c +2 b^{4}\right) \sqrt{2 c d x +b d}}{231 c^{3}}"," ",0,"1/231*(2*c*x+b)*(21*c^4*x^4+42*b*c^3*x^3+66*a*c^3*x^2+15*b^2*c^2*x^2+66*a*b*c^2*x-6*b^3*c*x+77*a^2*c^2-22*a*b^2*c+2*b^4)*(2*c*d*x+b*d)^(1/2)/c^3","A"
1271,1,96,76,0.048000," ","int((c*x^2+b*x+a)^2/(2*c*d*x+b*d)^(1/2),x)","\frac{\left(2 c x +b \right) \left(5 c^{4} x^{4}+10 b \,c^{3} x^{3}+18 a \,c^{3} x^{2}+3 x^{2} b^{2} c^{2}+18 a b \,c^{2} x -2 x \,b^{3} c +45 a^{2} c^{2}-18 a \,b^{2} c +2 b^{4}\right)}{45 \sqrt{2 c d x +b d}\, c^{3}}"," ",0,"1/45*(2*c*x+b)*(5*c^4*x^4+10*b*c^3*x^3+18*a*c^3*x^2+3*b^2*c^2*x^2+18*a*b*c^2*x-2*b^3*c*x+45*a^2*c^2-18*a*b^2*c+2*b^4)/c^3/(2*c*d*x+b*d)^(1/2)","A"
1272,1,96,76,0.046000," ","int((c*x^2+b*x+a)^2/(2*c*d*x+b*d)^(3/2),x)","-\frac{\left(2 c x +b \right) \left(-3 c^{4} x^{4}-6 b \,c^{3} x^{3}-14 a \,c^{3} x^{2}-x^{2} b^{2} c^{2}-14 a b \,c^{2} x +2 x \,b^{3} c +21 a^{2} c^{2}-14 a \,b^{2} c +2 b^{4}\right)}{21 \left(2 c d x +b d \right)^{\frac{3}{2}} c^{3}}"," ",0,"-1/21*(2*c*x+b)*(-3*c^4*x^4-6*b*c^3*x^3-14*a*c^3*x^2-b^2*c^2*x^2-14*a*b*c^2*x+2*b^3*c*x+21*a^2*c^2-14*a*b^2*c+2*b^4)/c^3/(2*c*d*x+b*d)^(3/2)","A"
1273,1,96,76,0.046000," ","int((c*x^2+b*x+a)^2/(2*c*d*x+b*d)^(5/2),x)","-\frac{\left(2 c x +b \right) \left(-3 c^{4} x^{4}-6 b \,c^{3} x^{3}-30 a \,c^{3} x^{2}+3 x^{2} b^{2} c^{2}-30 a b \,c^{2} x +6 x \,b^{3} c +5 a^{2} c^{2}-10 a \,b^{2} c +2 b^{4}\right)}{15 \left(2 c d x +b d \right)^{\frac{5}{2}} c^{3}}"," ",0,"-1/15*(2*c*x+b)*(-3*c^4*x^4-6*b*c^3*x^3-30*a*c^3*x^2+3*b^2*c^2*x^2-30*a*b*c^2*x+6*b^3*c*x+5*a^2*c^2-10*a*b^2*c+2*b^4)/c^3/(2*c*d*x+b*d)^(5/2)","A"
1274,1,96,76,0.047000," ","int((c*x^2+b*x+a)^2/(2*c*d*x+b*d)^(7/2),x)","-\frac{\left(2 c x +b \right) \left(-5 c^{4} x^{4}-10 b \,c^{3} x^{3}+30 a \,c^{3} x^{2}-15 x^{2} b^{2} c^{2}+30 a b \,c^{2} x -10 x \,b^{3} c +3 a^{2} c^{2}+6 a \,b^{2} c -2 b^{4}\right)}{15 \left(2 c d x +b d \right)^{\frac{7}{2}} c^{3}}"," ",0,"-1/15*(2*c*x+b)*(-5*c^4*x^4-10*b*c^3*x^3+30*a*c^3*x^2-15*b^2*c^2*x^2+30*a*b*c^2*x-10*b^3*c*x+3*a^2*c^2+6*a*b^2*c-2*b^4)/c^3/(2*c*d*x+b*d)^(7/2)","A"
1275,1,96,76,0.043000," ","int((c*x^2+b*x+a)^2/(2*c*d*x+b*d)^(9/2),x)","-\frac{\left(2 c x +b \right) \left(-21 c^{4} x^{4}-42 b \,c^{3} x^{3}+14 a \,c^{3} x^{2}-35 x^{2} b^{2} c^{2}+14 a b \,c^{2} x -14 x \,b^{3} c +3 a^{2} c^{2}+2 a \,b^{2} c -2 b^{4}\right)}{21 \left(2 c d x +b d \right)^{\frac{9}{2}} c^{3}}"," ",0,"-1/21*(2*c*x+b)*(-21*c^4*x^4-42*b*c^3*x^3+14*a*c^3*x^2-35*b^2*c^2*x^2+14*a*b*c^2*x-14*b^3*c*x+3*a^2*c^2+2*a*b^2*c-2*b^4)/c^3/(2*c*d*x+b*d)^(9/2)","A"
1276,1,96,76,0.045000," ","int((c*x^2+b*x+a)^2/(2*c*d*x+b*d)^(11/2),x)","-\frac{\left(2 c x +b \right) \left(45 c^{4} x^{4}+90 b \,c^{3} x^{3}+18 a \,c^{3} x^{2}+63 x^{2} b^{2} c^{2}+18 a b \,c^{2} x +18 x \,b^{3} c +5 a^{2} c^{2}+2 a \,b^{2} c +2 b^{4}\right)}{45 \left(2 c d x +b d \right)^{\frac{11}{2}} c^{3}}"," ",0,"-1/45*(2*c*x+b)*(45*c^4*x^4+90*b*c^3*x^3+18*a*c^3*x^2+63*b^2*c^2*x^2+18*a*b*c^2*x+18*b^3*c*x+5*a^2*c^2+2*a*b^2*c+2*b^4)/c^3/(2*c*d*x+b*d)^(11/2)","A"
1277,1,174,105,0.048000," ","int((2*c*d*x+b*d)^(1/2)*(c*x^2+b*x+a)^3,x)","\frac{\left(2 c x +b \right) \left(77 c^{6} x^{6}+231 b \,c^{5} x^{5}+315 a \,c^{5} x^{4}+210 b^{2} c^{4} x^{4}+630 a b \,c^{4} x^{3}+35 b^{3} c^{3} x^{3}+495 a^{2} c^{4} x^{2}+225 a \,b^{2} c^{3} x^{2}-15 b^{4} c^{2} x^{2}+495 a^{2} b \,c^{3} x -90 a \,b^{3} c^{2} x +6 b^{5} c x +385 a^{3} c^{3}-165 a^{2} b^{2} c^{2}+30 a \,b^{4} c -2 b^{6}\right) \sqrt{2 c d x +b d}}{1155 c^{4}}"," ",0,"1/1155*(2*c*x+b)*(77*c^6*x^6+231*b*c^5*x^5+315*a*c^5*x^4+210*b^2*c^4*x^4+630*a*b*c^4*x^3+35*b^3*c^3*x^3+495*a^2*c^4*x^2+225*a*b^2*c^3*x^2-15*b^4*c^2*x^2+495*a^2*b*c^3*x-90*a*b^3*c^2*x+6*b^5*c*x+385*a^3*c^3-165*a^2*b^2*c^2+30*a*b^4*c-2*b^6)*(2*c*d*x+b*d)^(1/2)/c^4","A"
1278,1,174,105,0.047000," ","int((c*x^2+b*x+a)^3/(2*c*d*x+b*d)^(1/2),x)","\frac{\left(2 c x +b \right) \left(15 c^{6} x^{6}+45 b \,c^{5} x^{5}+65 a \,c^{5} x^{4}+40 b^{2} c^{4} x^{4}+130 a b \,c^{4} x^{3}+5 b^{3} c^{3} x^{3}+117 a^{2} c^{4} x^{2}+39 a \,b^{2} c^{3} x^{2}-3 b^{4} c^{2} x^{2}+117 a^{2} b \,c^{3} x -26 a \,b^{3} c^{2} x +2 b^{5} c x +195 a^{3} c^{3}-117 a^{2} b^{2} c^{2}+26 a \,b^{4} c -2 b^{6}\right)}{195 \sqrt{2 c d x +b d}\, c^{4}}"," ",0,"1/195*(2*c*x+b)*(15*c^6*x^6+45*b*c^5*x^5+65*a*c^5*x^4+40*b^2*c^4*x^4+130*a*b*c^4*x^3+5*b^3*c^3*x^3+117*a^2*c^4*x^2+39*a*b^2*c^3*x^2-3*b^4*c^2*x^2+117*a^2*b*c^3*x-26*a*b^3*c^2*x+2*b^5*c*x+195*a^3*c^3-117*a^2*b^2*c^2+26*a*b^4*c-2*b^6)/c^4/(2*c*d*x+b*d)^(1/2)","A"
1279,1,173,105,0.048000," ","int((c*x^2+b*x+a)^3/(2*c*d*x+b*d)^(3/2),x)","-\frac{\left(2 c x +b \right) \left(-7 c^{6} x^{6}-21 b \,c^{5} x^{5}-33 a \,c^{5} x^{4}-18 b^{2} c^{4} x^{4}-66 a b \,c^{4} x^{3}-b^{3} c^{3} x^{3}-77 a^{2} c^{4} x^{2}-11 a \,b^{2} c^{3} x^{2}+b^{4} c^{2} x^{2}-77 a^{2} b \,c^{3} x +22 a \,b^{3} c^{2} x -2 b^{5} c x +77 a^{3} c^{3}-77 a^{2} b^{2} c^{2}+22 a \,b^{4} c -2 b^{6}\right)}{77 \left(2 c d x +b d \right)^{\frac{3}{2}} c^{4}}"," ",0,"-1/77*(2*c*x+b)*(-7*c^6*x^6-21*b*c^5*x^5-33*a*c^5*x^4-18*b^2*c^4*x^4-66*a*b*c^4*x^3-b^3*c^3*x^3-77*a^2*c^4*x^2-11*a*b^2*c^3*x^2+b^4*c^2*x^2-77*a^2*b*c^3*x+22*a*b^3*c^2*x-2*b^5*c*x+77*a^3*c^3-77*a^2*b^2*c^2+22*a*b^4*c-2*b^6)/c^4/(2*c*d*x+b*d)^(3/2)","A"
1280,1,173,105,0.047000," ","int((c*x^2+b*x+a)^3/(2*c*d*x+b*d)^(5/2),x)","-\frac{\left(2 c x +b \right) \left(-5 c^{6} x^{6}-15 b \,c^{5} x^{5}-27 a \,c^{5} x^{4}-12 b^{2} c^{4} x^{4}-54 a b \,c^{4} x^{3}+b^{3} c^{3} x^{3}-135 a^{2} c^{4} x^{2}+27 a \,b^{2} c^{3} x^{2}-3 b^{4} c^{2} x^{2}-135 a^{2} b \,c^{3} x +54 a \,b^{3} c^{2} x -6 b^{5} c x +15 a^{3} c^{3}-45 a^{2} b^{2} c^{2}+18 a \,b^{4} c -2 b^{6}\right)}{45 \left(2 c d x +b d \right)^{\frac{5}{2}} c^{4}}"," ",0,"-1/45*(2*c*x+b)*(-5*c^6*x^6-15*b*c^5*x^5-27*a*c^5*x^4-12*b^2*c^4*x^4-54*a*b*c^4*x^3+b^3*c^3*x^3-135*a^2*c^4*x^2+27*a*b^2*c^3*x^2-3*b^4*c^2*x^2-135*a^2*b*c^3*x+54*a*b^3*c^2*x-6*b^5*c*x+15*a^3*c^3-45*a^2*b^2*c^2+18*a*b^4*c-2*b^6)/c^4/(2*c*d*x+b*d)^(5/2)","A"
1281,1,174,105,0.046000," ","int((c*x^2+b*x+a)^3/(2*c*d*x+b*d)^(7/2),x)","-\frac{\left(2 c x +b \right) \left(-5 c^{6} x^{6}-15 b \,c^{5} x^{5}-35 a \,c^{5} x^{4}-10 b^{2} c^{4} x^{4}-70 a b \,c^{4} x^{3}+5 b^{3} c^{3} x^{3}+105 a^{2} c^{4} x^{2}-105 a \,b^{2} c^{3} x^{2}+15 b^{4} c^{2} x^{2}+105 a^{2} b \,c^{3} x -70 a \,b^{3} c^{2} x +10 b^{5} c x +7 a^{3} c^{3}+21 a^{2} b^{2} c^{2}-14 a \,b^{4} c +2 b^{6}\right)}{35 \left(2 c d x +b d \right)^{\frac{7}{2}} c^{4}}"," ",0,"-1/35*(2*c*x+b)*(-5*c^6*x^6-15*b*c^5*x^5-35*a*c^5*x^4-10*b^2*c^4*x^4-70*a*b*c^4*x^3+5*b^3*c^3*x^3+105*a^2*c^4*x^2-105*a*b^2*c^3*x^2+15*b^4*c^2*x^2+105*a^2*b*c^3*x-70*a*b^3*c^2*x+10*b^5*c*x+7*a^3*c^3+21*a^2*b^2*c^2-14*a*b^4*c+2*b^6)/c^4/(2*c*d*x+b*d)^(7/2)","A"
1282,1,163,105,0.047000," ","int((c*x^2+b*x+a)^3/(2*c*d*x+b*d)^(9/2),x)","-\frac{\left(2 c x +b \right) \left(-7 c^{6} x^{6}-21 b \,c^{5} x^{5}-105 a \,c^{5} x^{4}-210 a b \,c^{4} x^{3}+35 b^{3} c^{3} x^{3}+35 a^{2} c^{4} x^{2}-175 a \,b^{2} c^{3} x^{2}+35 b^{4} c^{2} x^{2}+35 a^{2} b \,c^{3} x -70 a \,b^{3} c^{2} x +14 b^{5} c x +5 a^{3} c^{3}+5 a^{2} b^{2} c^{2}-10 a \,b^{4} c +2 b^{6}\right)}{35 \left(2 c d x +b d \right)^{\frac{9}{2}} c^{4}}"," ",0,"-1/35*(2*c*x+b)*(-7*c^6*x^6-21*b*c^5*x^5-105*a*c^5*x^4-210*a*b*c^4*x^3+35*b^3*c^3*x^3+35*a^2*c^4*x^2-175*a*b^2*c^3*x^2+35*b^4*c^2*x^2+35*a^2*b*c^3*x-70*a*b^3*c^2*x+14*b^5*c*x+5*a^3*c^3+5*a^2*b^2*c^2-10*a*b^4*c+2*b^6)/c^4/(2*c*d*x+b*d)^(9/2)","A"
1283,1,174,105,0.044000," ","int((c*x^2+b*x+a)^3/(2*c*d*x+b*d)^(11/2),x)","-\frac{\left(2 c x +b \right) \left(-15 c^{6} x^{6}-45 b \,c^{5} x^{5}+135 a \,c^{5} x^{4}-90 b^{2} c^{4} x^{4}+270 a b \,c^{4} x^{3}-105 b^{3} c^{3} x^{3}+27 a^{2} c^{4} x^{2}+189 a \,b^{2} c^{3} x^{2}-63 b^{4} c^{2} x^{2}+27 a^{2} b \,c^{3} x +54 a \,b^{3} c^{2} x -18 b^{5} c x +5 a^{3} c^{3}+3 a^{2} b^{2} c^{2}+6 a \,b^{4} c -2 b^{6}\right)}{45 \left(2 c d x +b d \right)^{\frac{11}{2}} c^{4}}"," ",0,"-1/45*(2*c*x+b)*(-15*c^6*x^6-45*b*c^5*x^5+135*a*c^5*x^4-90*b^2*c^4*x^4+270*a*b*c^4*x^3-105*b^3*c^3*x^3+27*a^2*c^4*x^2+189*a*b^2*c^3*x^2-63*b^4*c^2*x^2+27*a^2*b*c^3*x+54*a*b^3*c^2*x-18*b^5*c*x+5*a^3*c^3+3*a^2*b^2*c^2+6*a*b^4*c-2*b^6)/c^4/(2*c*d*x+b*d)^(11/2)","A"
1284,1,174,105,0.051000," ","int((c*x^2+b*x+a)^3/(2*c*d*x+b*d)^(13/2),x)","-\frac{\left(2 c x +b \right) \left(-77 c^{6} x^{6}-231 b \,c^{5} x^{5}+77 a \,c^{5} x^{4}-308 b^{2} c^{4} x^{4}+154 a b \,c^{4} x^{3}-231 b^{3} c^{3} x^{3}+33 a^{2} c^{4} x^{2}+99 a \,b^{2} c^{3} x^{2}-99 b^{4} c^{2} x^{2}+33 a^{2} b \,c^{3} x +22 a \,b^{3} c^{2} x -22 b^{5} c x +7 a^{3} c^{3}+3 a^{2} b^{2} c^{2}+2 a \,b^{4} c -2 b^{6}\right)}{77 \left(2 c d x +b d \right)^{\frac{13}{2}} c^{4}}"," ",0,"-1/77*(2*c*x+b)*(-77*c^6*x^6-231*b*c^5*x^5+77*a*c^5*x^4-308*b^2*c^4*x^4+154*a*b*c^4*x^3-231*b^3*c^3*x^3+33*a^2*c^4*x^2+99*a*b^2*c^3*x^2-99*b^4*c^2*x^2+33*a^2*b*c^3*x+22*a*b^3*c^2*x-22*b^5*c*x+7*a^3*c^3+3*a^2*b^2*c^2+2*a*b^4*c-2*b^6)/c^4/(2*c*d*x+b*d)^(13/2)","A"
1285,1,1287,145,0.076000," ","int((2*c*d*x+b*d)^(11/2)/(c*x^2+b*x+a),x)","\frac{64 \sqrt{2}\, a^{3} c^{3} d^{7} \arctan \left(-\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}-\frac{64 \sqrt{2}\, a^{3} c^{3} d^{7} \arctan \left(\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}-\frac{32 \sqrt{2}\, a^{3} c^{3} d^{7} \ln \left(\frac{2 c d x +b d +\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}{2 c d x +b d -\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}-\frac{48 \sqrt{2}\, a^{2} b^{2} c^{2} d^{7} \arctan \left(-\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}+\frac{48 \sqrt{2}\, a^{2} b^{2} c^{2} d^{7} \arctan \left(\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}+\frac{24 \sqrt{2}\, a^{2} b^{2} c^{2} d^{7} \ln \left(\frac{2 c d x +b d +\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}{2 c d x +b d -\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}+\frac{12 \sqrt{2}\, a \,b^{4} c \,d^{7} \arctan \left(-\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}-\frac{12 \sqrt{2}\, a \,b^{4} c \,d^{7} \arctan \left(\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}-\frac{6 \sqrt{2}\, a \,b^{4} c \,d^{7} \ln \left(\frac{2 c d x +b d +\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}{2 c d x +b d -\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}-\frac{\sqrt{2}\, b^{6} d^{7} \arctan \left(-\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}+\frac{\sqrt{2}\, b^{6} d^{7} \arctan \left(\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}+\frac{\sqrt{2}\, b^{6} d^{7} \ln \left(\frac{2 c d x +b d +\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}{2 c d x +b d -\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}\right)}{2 \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}+64 \sqrt{2 c d x +b d}\, a^{2} c^{2} d^{5}-32 \sqrt{2 c d x +b d}\, a \,b^{2} c \,d^{5}+4 \sqrt{2 c d x +b d}\, b^{4} d^{5}-\frac{16 \left(2 c d x +b d \right)^{\frac{5}{2}} a c \,d^{3}}{5}+\frac{4 \left(2 c d x +b d \right)^{\frac{5}{2}} b^{2} d^{3}}{5}+\frac{4 \left(2 c d x +b d \right)^{\frac{9}{2}} d}{9}"," ",0,"4/9*d*(2*c*d*x+b*d)^(9/2)-16/5*(2*c*d*x+b*d)^(5/2)*a*c*d^3+4/5*(2*c*d*x+b*d)^(5/2)*b^2*d^3+64*a^2*c^2*d^5*(2*c*d*x+b*d)^(1/2)-32*a*b^2*c*d^5*(2*c*d*x+b*d)^(1/2)+4*b^4*d^5*(2*c*d*x+b*d)^(1/2)-64*d^7/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*arctan(2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)*a^3*c^3+48*d^7/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*arctan(2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)*a^2*b^2*c^2-12*d^7/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*arctan(2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)*a*b^4*c+d^7/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*arctan(2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)*b^6+64*d^7/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*arctan(-2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)*a^3*c^3-48*d^7/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*arctan(-2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)*a^2*b^2*c^2+12*d^7/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*arctan(-2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)*a*b^4*c-d^7/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*arctan(-2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)*b^6-32*d^7/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*ln((2*c*d*x+b*d+(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2))/(2*c*d*x+b*d-(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2)))*a^3*c^3+24*d^7/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*ln((2*c*d*x+b*d+(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2))/(2*c*d*x+b*d-(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2)))*a^2*b^2*c^2-6*d^7/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*ln((2*c*d*x+b*d+(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2))/(2*c*d*x+b*d-(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2)))*a*b^4*c+1/2*d^7/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*ln((2*c*d*x+b*d+(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2))/(2*c*d*x+b*d-(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2)))*b^6","B"
1286,1,922,119,0.055000," ","int((2*c*d*x+b*d)^(9/2)/(c*x^2+b*x+a),x)","-\frac{16 \sqrt{2}\, a^{2} c^{2} d^{5} \arctan \left(-\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+\frac{16 \sqrt{2}\, a^{2} c^{2} d^{5} \arctan \left(\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+\frac{8 \sqrt{2}\, a^{2} c^{2} d^{5} \ln \left(\frac{2 c d x +b d -\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}{2 c d x +b d +\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+\frac{8 \sqrt{2}\, a \,b^{2} c \,d^{5} \arctan \left(-\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}-\frac{8 \sqrt{2}\, a \,b^{2} c \,d^{5} \arctan \left(\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}-\frac{4 \sqrt{2}\, a \,b^{2} c \,d^{5} \ln \left(\frac{2 c d x +b d -\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}{2 c d x +b d +\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, b^{4} d^{5} \arctan \left(-\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, b^{4} d^{5} \arctan \left(\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, b^{4} d^{5} \ln \left(\frac{2 c d x +b d -\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}{2 c d x +b d +\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}\right)}{2 \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}-\frac{16 \left(2 c d x +b d \right)^{\frac{3}{2}} a c \,d^{3}}{3}+\frac{4 \left(2 c d x +b d \right)^{\frac{3}{2}} b^{2} d^{3}}{3}+\frac{4 \left(2 c d x +b d \right)^{\frac{7}{2}} d}{7}"," ",0,"4/7*d*(2*c*d*x+b*d)^(7/2)-16/3*(2*c*d*x+b*d)^(3/2)*a*c*d^3+4/3*(2*c*d*x+b*d)^(3/2)*b^2*d^3+16*d^5/(4*a*c*d^2-b^2*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)*a^2*c^2-8*d^5/(4*a*c*d^2-b^2*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)*a*b^2*c+d^5/(4*a*c*d^2-b^2*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)*b^4-16*d^5/(4*a*c*d^2-b^2*d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)*a^2*c^2+8*d^5/(4*a*c*d^2-b^2*d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)*a*b^2*c-d^5/(4*a*c*d^2-b^2*d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)*b^4+8*d^5/(4*a*c*d^2-b^2*d^2)^(1/4)*2^(1/2)*ln((2*c*d*x+b*d-(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2))/(2*c*d*x+b*d+(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2)))*a^2*c^2-4*d^5/(4*a*c*d^2-b^2*d^2)^(1/4)*2^(1/2)*ln((2*c*d*x+b*d-(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2))/(2*c*d*x+b*d+(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2)))*a*b^2*c+1/2*d^5/(4*a*c*d^2-b^2*d^2)^(1/4)*2^(1/2)*ln((2*c*d*x+b*d-(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2))/(2*c*d*x+b*d+(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2)))*b^4","B"
1287,1,922,119,0.057000," ","int((2*c*d*x+b*d)^(7/2)/(c*x^2+b*x+a),x)","-\frac{16 \sqrt{2}\, a^{2} c^{2} d^{5} \arctan \left(-\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}+\frac{16 \sqrt{2}\, a^{2} c^{2} d^{5} \arctan \left(\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}+\frac{8 \sqrt{2}\, a^{2} c^{2} d^{5} \ln \left(\frac{2 c d x +b d +\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}{2 c d x +b d -\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}+\frac{8 \sqrt{2}\, a \,b^{2} c \,d^{5} \arctan \left(-\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}-\frac{8 \sqrt{2}\, a \,b^{2} c \,d^{5} \arctan \left(\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}-\frac{4 \sqrt{2}\, a \,b^{2} c \,d^{5} \ln \left(\frac{2 c d x +b d +\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}{2 c d x +b d -\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}-\frac{\sqrt{2}\, b^{4} d^{5} \arctan \left(-\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}+\frac{\sqrt{2}\, b^{4} d^{5} \arctan \left(\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}+\frac{\sqrt{2}\, b^{4} d^{5} \ln \left(\frac{2 c d x +b d +\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}{2 c d x +b d -\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}\right)}{2 \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}-16 \sqrt{2 c d x +b d}\, a c \,d^{3}+4 \sqrt{2 c d x +b d}\, b^{2} d^{3}+\frac{4 \left(2 c d x +b d \right)^{\frac{5}{2}} d}{5}"," ",0,"4/5*d*(2*c*d*x+b*d)^(5/2)-16*a*c*d^3*(2*c*d*x+b*d)^(1/2)+4*b^2*d^3*(2*c*d*x+b*d)^(1/2)-16*d^5/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*arctan(-2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)*a^2*c^2+8*d^5/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*arctan(-2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)*a*b^2*c-d^5/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*arctan(-2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)*b^4+8*d^5/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*ln((2*c*d*x+b*d+(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2))/(2*c*d*x+b*d-(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2)))*a^2*c^2-4*d^5/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*ln((2*c*d*x+b*d+(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2))/(2*c*d*x+b*d-(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2)))*a*b^2*c+1/2*d^5/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*ln((2*c*d*x+b*d+(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2))/(2*c*d*x+b*d-(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2)))*b^4+16*d^5/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*arctan(2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)*a^2*c^2-8*d^5/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*arctan(2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)*a*b^2*c+d^5/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*arctan(2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)*b^4","B"
1288,1,582,95,0.059000," ","int((2*c*d*x+b*d)^(5/2)/(c*x^2+b*x+a),x)","\frac{4 \sqrt{2}\, a c \,d^{3} \arctan \left(-\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}-\frac{4 \sqrt{2}\, a c \,d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}-\frac{2 \sqrt{2}\, a c \,d^{3} \ln \left(\frac{2 c d x +b d -\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}{2 c d x +b d +\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, b^{2} d^{3} \arctan \left(-\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, b^{2} d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, b^{2} d^{3} \ln \left(\frac{2 c d x +b d -\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}{2 c d x +b d +\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}\right)}{2 \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+\frac{4 \left(2 c d x +b d \right)^{\frac{3}{2}} d}{3}"," ",0,"4/3*d*(2*c*d*x+b*d)^(3/2)-4*d^3/(4*a*c*d^2-b^2*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)*a*c+d^3/(4*a*c*d^2-b^2*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)*b^2+4*d^3/(4*a*c*d^2-b^2*d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)*a*c-d^3/(4*a*c*d^2-b^2*d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)*b^2-2*d^3/(4*a*c*d^2-b^2*d^2)^(1/4)*2^(1/2)*ln((2*c*d*x+b*d-(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2))/(2*c*d*x+b*d+(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2)))*a*c+1/2*d^3/(4*a*c*d^2-b^2*d^2)^(1/4)*2^(1/2)*ln((2*c*d*x+b*d-(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2))/(2*c*d*x+b*d+(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2)))*b^2","B"
1289,1,582,95,0.053000," ","int((2*c*d*x+b*d)^(3/2)/(c*x^2+b*x+a),x)","\frac{4 \sqrt{2}\, a c \,d^{3} \arctan \left(-\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}-\frac{4 \sqrt{2}\, a c \,d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}-\frac{2 \sqrt{2}\, a c \,d^{3} \ln \left(\frac{2 c d x +b d +\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}{2 c d x +b d -\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}-\frac{\sqrt{2}\, b^{2} d^{3} \arctan \left(-\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}+\frac{\sqrt{2}\, b^{2} d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}+\frac{\sqrt{2}\, b^{2} d^{3} \ln \left(\frac{2 c d x +b d +\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}{2 c d x +b d -\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}\right)}{2 \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}+4 \sqrt{2 c d x +b d}\, d"," ",0,"4*d*(2*c*d*x+b*d)^(1/2)+4*d^3/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*arctan(-2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)*a*c-d^3/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*arctan(-2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)*b^2-2*d^3/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*ln((2*c*d*x+b*d+(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2))/(2*c*d*x+b*d-(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2)))*a*c+1/2*d^3/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*ln((2*c*d*x+b*d+(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2))/(2*c*d*x+b*d-(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2)))*b^2-4*d^3/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*arctan(2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)*a*c+d^3/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*arctan(2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)*b^2","B"
1290,1,271,81,0.049000," ","int((2*c*d*x+b*d)^(1/2)/(c*x^2+b*x+a),x)","-\frac{\sqrt{2}\, d \arctan \left(-\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, d \arctan \left(\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, d \ln \left(\frac{2 c d x +b d -\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}{2 c d x +b d +\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}\right)}{2 \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}"," ",0,"1/2*d/(4*a*c*d^2-b^2*d^2)^(1/4)*2^(1/2)*ln((2*c*d*x+b*d-(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2))/(2*c*d*x+b*d+(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2)))+d/(4*a*c*d^2-b^2*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)-d/(4*a*c*d^2-b^2*d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)","B"
1291,1,271,81,0.058000," ","int(1/(2*c*d*x+b*d)^(1/2)/(c*x^2+b*x+a),x)","-\frac{\sqrt{2}\, d \arctan \left(-\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}+\frac{\sqrt{2}\, d \arctan \left(\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}+\frac{\sqrt{2}\, d \ln \left(\frac{2 c d x +b d +\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}{2 c d x +b d -\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}\right)}{2 \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}"," ",0,"1/2*d/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*ln((2*c*d*x+b*d+(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2))/(2*c*d*x+b*d-(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2)))+d/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*arctan(2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)-d/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*arctan(-2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)","B"
1292,1,341,107,0.056000," ","int(1/(2*c*d*x+b*d)^(3/2)/(c*x^2+b*x+a),x)","\frac{\sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c -b^{2}\right) \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} d}-\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c -b^{2}\right) \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} d}-\frac{\sqrt{2}\, \ln \left(\frac{2 c d x +b d -\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}{2 c d x +b d +\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}\right)}{2 \left(4 a c -b^{2}\right) \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} d}-\frac{4}{\left(4 a c -b^{2}\right) \sqrt{2 c d x +b d}\, d}"," ",0,"-1/2/d/(4*a*c-b^2)/(4*a*c*d^2-b^2*d^2)^(1/4)*2^(1/2)*ln((2*c*d*x+b*d-(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2))/(2*c*d*x+b*d+(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2)))-1/d/(4*a*c-b^2)/(4*a*c*d^2-b^2*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)+1/d/(4*a*c-b^2)/(4*a*c*d^2-b^2*d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)-4/d/(4*a*c-b^2)/(2*c*d*x+b*d)^(1/2)","B"
1293,1,341,107,0.059000," ","int(1/(2*c*d*x+b*d)^(5/2)/(c*x^2+b*x+a),x)","\frac{\sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c -b^{2}\right) \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}} d}-\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c -b^{2}\right) \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}} d}-\frac{\sqrt{2}\, \ln \left(\frac{2 c d x +b d +\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}{2 c d x +b d -\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}\right)}{2 \left(4 a c -b^{2}\right) \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}} d}-\frac{4}{3 \left(4 a c -b^{2}\right) \left(2 c d x +b d \right)^{\frac{3}{2}} d}"," ",0,"-4/3/d/(4*a*c-b^2)/(2*c*d*x+b*d)^(3/2)-1/2/d/(4*a*c-b^2)/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*ln((2*c*d*x+b*d+(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2))/(2*c*d*x+b*d-(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2)))-1/d/(4*a*c-b^2)/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*arctan(2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)+1/d/(4*a*c-b^2)/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*arctan(-2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)","B"
1294,1,369,133,0.062000," ","int(1/(2*c*d*x+b*d)^(7/2)/(c*x^2+b*x+a),x)","-\frac{4}{5 \left(4 a c -b^{2}\right) \left(2 c d x +b d \right)^{\frac{5}{2}} d}-\frac{\sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c -b^{2}\right)^{2} \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} d^{3}}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c -b^{2}\right)^{2} \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} d^{3}}+\frac{\sqrt{2}\, \ln \left(\frac{2 c d x +b d -\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}{2 c d x +b d +\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}\right)}{2 \left(4 a c -b^{2}\right)^{2} \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} d^{3}}+\frac{4}{\left(4 a c -b^{2}\right)^{2} \sqrt{2 c d x +b d}\, d^{3}}"," ",0,"1/2/d^3/(4*a*c-b^2)^2/(4*a*c*d^2-b^2*d^2)^(1/4)*2^(1/2)*ln((2*c*d*x+b*d-(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2))/(2*c*d*x+b*d+(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2)))+1/d^3/(4*a*c-b^2)^2/(4*a*c*d^2-b^2*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)-1/d^3/(4*a*c-b^2)^2/(4*a*c*d^2-b^2*d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)-4/5/d/(4*a*c-b^2)/(2*c*d*x+b*d)^(5/2)+4/d^3/(4*a*c-b^2)^2/(2*c*d*x+b*d)^(1/2)","B"
1295,1,1512,178,0.062000," ","int((2*c*d*x+b*d)^(15/2)/(c*x^2+b*x+a)^2,x)","\frac{832 \sqrt{2}\, a^{3} c^{4} d^{9} \arctan \left(-\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}-\frac{832 \sqrt{2}\, a^{3} c^{4} d^{9} \arctan \left(\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}-\frac{416 \sqrt{2}\, a^{3} c^{4} d^{9} \ln \left(\frac{2 c d x +b d +\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}{2 c d x +b d -\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}-\frac{624 \sqrt{2}\, a^{2} b^{2} c^{3} d^{9} \arctan \left(-\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}+\frac{624 \sqrt{2}\, a^{2} b^{2} c^{3} d^{9} \arctan \left(\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}+\frac{312 \sqrt{2}\, a^{2} b^{2} c^{3} d^{9} \ln \left(\frac{2 c d x +b d +\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}{2 c d x +b d -\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}+\frac{156 \sqrt{2}\, a \,b^{4} c^{2} d^{9} \arctan \left(-\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}-\frac{156 \sqrt{2}\, a \,b^{4} c^{2} d^{9} \arctan \left(\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}-\frac{78 \sqrt{2}\, a \,b^{4} c^{2} d^{9} \ln \left(\frac{2 c d x +b d +\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}{2 c d x +b d -\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}-\frac{13 \sqrt{2}\, b^{6} c \,d^{9} \arctan \left(-\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}+\frac{13 \sqrt{2}\, b^{6} c \,d^{9} \arctan \left(\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}+\frac{13 \sqrt{2}\, b^{6} c \,d^{9} \ln \left(\frac{2 c d x +b d +\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}{2 c d x +b d -\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}\right)}{2 \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}+\frac{256 \sqrt{2 c d x +b d}\, a^{3} c^{4} d^{9}}{4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}}-\frac{192 \sqrt{2 c d x +b d}\, a^{2} b^{2} c^{3} d^{9}}{4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}}+\frac{48 \sqrt{2 c d x +b d}\, a \,b^{4} c^{2} d^{9}}{4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}}-\frac{4 \sqrt{2 c d x +b d}\, b^{6} c \,d^{9}}{4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}}+768 \sqrt{2 c d x +b d}\, a^{2} c^{3} d^{7}-384 \sqrt{2 c d x +b d}\, a \,b^{2} c^{2} d^{7}+48 \sqrt{2 c d x +b d}\, b^{4} c \,d^{7}-\frac{128 \left(2 c d x +b d \right)^{\frac{5}{2}} a \,c^{2} d^{5}}{5}+\frac{32 \left(2 c d x +b d \right)^{\frac{5}{2}} b^{2} c \,d^{5}}{5}+\frac{16 \left(2 c d x +b d \right)^{\frac{9}{2}} c \,d^{3}}{9}"," ",0,"16/9*c*d^3*(2*c*d*x+b*d)^(9/2)-128/5*c^2*d^5*(2*c*d*x+b*d)^(5/2)*a+32/5*c*d^5*(2*c*d*x+b*d)^(5/2)*b^2+768*c^3*d^7*a^2*(2*c*d*x+b*d)^(1/2)-384*c^2*d^7*a*b^2*(2*c*d*x+b*d)^(1/2)+48*c*d^7*b^4*(2*c*d*x+b*d)^(1/2)+256*c^4*d^9*(2*c*d*x+b*d)^(1/2)/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)*a^3-192*c^3*d^9*(2*c*d*x+b*d)^(1/2)/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)*a^2*b^2+48*c^2*d^9*(2*c*d*x+b*d)^(1/2)/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)*a*b^4-4*c*d^9*(2*c*d*x+b*d)^(1/2)/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)*b^6-832*c^4*d^9/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*arctan(2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)*a^3+624*c^3*d^9/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*arctan(2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)*a^2*b^2-156*c^2*d^9/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*arctan(2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)*a*b^4+13*c*d^9/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*arctan(2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)*b^6+832*c^4*d^9/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*arctan(-2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)*a^3-624*c^3*d^9/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*arctan(-2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)*a^2*b^2+156*c^2*d^9/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*arctan(-2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)*a*b^4-13*c*d^9/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*arctan(-2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)*b^6-416*c^4*d^9/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*ln((2*c*d*x+b*d+(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2))/(2*c*d*x+b*d-(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2)))*a^3+312*c^3*d^9/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*ln((2*c*d*x+b*d+(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2))/(2*c*d*x+b*d-(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2)))*a^2*b^2-78*c^2*d^9/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*ln((2*c*d*x+b*d+(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2))/(2*c*d*x+b*d-(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2)))*a*b^4+13/2*c*d^9/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*ln((2*c*d*x+b*d+(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2))/(2*c*d*x+b*d-(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2)))*b^6","B"
1296,1,1090,151,0.063000," ","int((2*c*d*x+b*d)^(13/2)/(c*x^2+b*x+a)^2,x)","-\frac{176 \sqrt{2}\, a^{2} c^{3} d^{7} \arctan \left(-\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+\frac{176 \sqrt{2}\, a^{2} c^{3} d^{7} \arctan \left(\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+\frac{88 \sqrt{2}\, a^{2} c^{3} d^{7} \ln \left(\frac{2 c d x +b d -\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}{2 c d x +b d +\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+\frac{88 \sqrt{2}\, a \,b^{2} c^{2} d^{7} \arctan \left(-\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}-\frac{88 \sqrt{2}\, a \,b^{2} c^{2} d^{7} \arctan \left(\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}-\frac{44 \sqrt{2}\, a \,b^{2} c^{2} d^{7} \ln \left(\frac{2 c d x +b d -\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}{2 c d x +b d +\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}-\frac{11 \sqrt{2}\, b^{4} c \,d^{7} \arctan \left(-\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+\frac{11 \sqrt{2}\, b^{4} c \,d^{7} \arctan \left(\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+\frac{11 \sqrt{2}\, b^{4} c \,d^{7} \ln \left(\frac{2 c d x +b d -\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}{2 c d x +b d +\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}\right)}{2 \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}-\frac{64 \left(2 c d x +b d \right)^{\frac{3}{2}} a^{2} c^{3} d^{7}}{4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}}+\frac{32 \left(2 c d x +b d \right)^{\frac{3}{2}} a \,b^{2} c^{2} d^{7}}{4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}}-\frac{4 \left(2 c d x +b d \right)^{\frac{3}{2}} b^{4} c \,d^{7}}{4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}}-\frac{128 \left(2 c d x +b d \right)^{\frac{3}{2}} a \,c^{2} d^{5}}{3}+\frac{32 \left(2 c d x +b d \right)^{\frac{3}{2}} b^{2} c \,d^{5}}{3}+\frac{16 \left(2 c d x +b d \right)^{\frac{7}{2}} c \,d^{3}}{7}"," ",0,"16/7*c*d^3*(2*c*d*x+b*d)^(7/2)-128/3*c^2*d^5*(2*c*d*x+b*d)^(3/2)*a+32/3*c*d^5*(2*c*d*x+b*d)^(3/2)*b^2-64*c^3*d^7*(2*c*d*x+b*d)^(3/2)/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)*a^2+32*c^2*d^7*(2*c*d*x+b*d)^(3/2)/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)*a*b^2-4*c*d^7*(2*c*d*x+b*d)^(3/2)/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)*b^4+88*c^3*d^7*2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*a^2*ln((2*c*d*x+b*d-(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2))/(2*c*d*x+b*d+(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2)))+176*c^3*d^7*2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*a^2*arctan(2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)-176*c^3*d^7*2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*a^2*arctan(-2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)-44*c^2*d^7*2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*a*b^2*ln((2*c*d*x+b*d-(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2))/(2*c*d*x+b*d+(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2)))-88*c^2*d^7*2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*a*b^2*arctan(2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)+88*c^2*d^7*2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*a*b^2*arctan(-2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)+11/2*c*d^7*2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*b^4*ln((2*c*d*x+b*d-(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2))/(2*c*d*x+b*d+(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2)))+11*c*d^7*2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*b^4*arctan(2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)-11*c*d^7*2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*b^4*arctan(-2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)","B"
1297,1,1090,151,0.062000," ","int((2*c*d*x+b*d)^(11/2)/(c*x^2+b*x+a)^2,x)","-\frac{144 \sqrt{2}\, a^{2} c^{3} d^{7} \arctan \left(-\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}+\frac{144 \sqrt{2}\, a^{2} c^{3} d^{7} \arctan \left(\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}+\frac{72 \sqrt{2}\, a^{2} c^{3} d^{7} \ln \left(\frac{2 c d x +b d +\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}{2 c d x +b d -\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}+\frac{72 \sqrt{2}\, a \,b^{2} c^{2} d^{7} \arctan \left(-\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}-\frac{72 \sqrt{2}\, a \,b^{2} c^{2} d^{7} \arctan \left(\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}-\frac{36 \sqrt{2}\, a \,b^{2} c^{2} d^{7} \ln \left(\frac{2 c d x +b d +\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}{2 c d x +b d -\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}-\frac{9 \sqrt{2}\, b^{4} c \,d^{7} \arctan \left(-\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}+\frac{9 \sqrt{2}\, b^{4} c \,d^{7} \arctan \left(\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}+\frac{9 \sqrt{2}\, b^{4} c \,d^{7} \ln \left(\frac{2 c d x +b d +\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}{2 c d x +b d -\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}\right)}{2 \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}-\frac{64 \sqrt{2 c d x +b d}\, a^{2} c^{3} d^{7}}{4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}}+\frac{32 \sqrt{2 c d x +b d}\, a \,b^{2} c^{2} d^{7}}{4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}}-\frac{4 \sqrt{2 c d x +b d}\, b^{4} c \,d^{7}}{4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}}-128 \sqrt{2 c d x +b d}\, a \,c^{2} d^{5}+32 \sqrt{2 c d x +b d}\, b^{2} c \,d^{5}+\frac{16 \left(2 c d x +b d \right)^{\frac{5}{2}} c \,d^{3}}{5}"," ",0,"16/5*c*d^3*(2*c*d*x+b*d)^(5/2)-128*c^2*d^5*a*(2*c*d*x+b*d)^(1/2)+32*c*d^5*b^2*(2*c*d*x+b*d)^(1/2)-64*c^3*d^7*(2*c*d*x+b*d)^(1/2)/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)*a^2+32*c^2*d^7*(2*c*d*x+b*d)^(1/2)/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)*a*b^2-4*c*d^7*(2*c*d*x+b*d)^(1/2)/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)*b^4+144*c^3*d^7/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*arctan(2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)*a^2-72*c^2*d^7/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*arctan(2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)*a*b^2+9*c*d^7/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*arctan(2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)*b^4-144*c^3*d^7/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*arctan(-2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)*a^2+72*c^2*d^7/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*arctan(-2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)*a*b^2-9*c*d^7/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*arctan(-2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)*b^4+72*c^3*d^7/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*ln((2*c*d*x+b*d+(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2))/(2*c*d*x+b*d-(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2)))*a^2-36*c^2*d^7/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*ln((2*c*d*x+b*d+(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2))/(2*c*d*x+b*d-(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2)))*a*b^2+9/2*c*d^7/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*ln((2*c*d*x+b*d+(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2))/(2*c*d*x+b*d-(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2)))*b^4","B"
1298,1,693,126,0.065000," ","int((2*c*d*x+b*d)^(9/2)/(c*x^2+b*x+a)^2,x)","\frac{28 \sqrt{2}\, a \,c^{2} d^{5} \arctan \left(-\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}-\frac{28 \sqrt{2}\, a \,c^{2} d^{5} \arctan \left(\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}-\frac{14 \sqrt{2}\, a \,c^{2} d^{5} \ln \left(\frac{2 c d x +b d -\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}{2 c d x +b d +\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}-\frac{7 \sqrt{2}\, b^{2} c \,d^{5} \arctan \left(-\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+\frac{7 \sqrt{2}\, b^{2} c \,d^{5} \arctan \left(\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+\frac{7 \sqrt{2}\, b^{2} c \,d^{5} \ln \left(\frac{2 c d x +b d -\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}{2 c d x +b d +\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}\right)}{2 \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+\frac{16 \left(2 c d x +b d \right)^{\frac{3}{2}} a \,c^{2} d^{5}}{4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}}-\frac{4 \left(2 c d x +b d \right)^{\frac{3}{2}} b^{2} c \,d^{5}}{4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}}+\frac{16 \left(2 c d x +b d \right)^{\frac{3}{2}} c \,d^{3}}{3}"," ",0,"16/3*c*d^3*(2*c*d*x+b*d)^(3/2)+16*c^2*d^5*(2*c*d*x+b*d)^(3/2)/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)*a-4*c*d^5*(2*c*d*x+b*d)^(3/2)/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)*b^2-14*c^2*d^5*2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*a*ln((2*c*d*x+b*d-(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2))/(2*c*d*x+b*d+(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2)))-28*c^2*d^5*2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*a*arctan(2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)+28*c^2*d^5*2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*a*arctan(-2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)+7/2*c*d^5*2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*b^2*ln((2*c*d*x+b*d-(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2))/(2*c*d*x+b*d+(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2)))+7*c*d^5*2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*b^2*arctan(2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)-7*c*d^5*2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*b^2*arctan(-2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)","B"
1299,1,693,126,0.063000," ","int((2*c*d*x+b*d)^(7/2)/(c*x^2+b*x+a)^2,x)","\frac{20 \sqrt{2}\, a \,c^{2} d^{5} \arctan \left(-\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}-\frac{20 \sqrt{2}\, a \,c^{2} d^{5} \arctan \left(\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}-\frac{10 \sqrt{2}\, a \,c^{2} d^{5} \ln \left(\frac{2 c d x +b d +\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}{2 c d x +b d -\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}-\frac{5 \sqrt{2}\, b^{2} c \,d^{5} \arctan \left(-\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}+\frac{5 \sqrt{2}\, b^{2} c \,d^{5} \arctan \left(\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}+\frac{5 \sqrt{2}\, b^{2} c \,d^{5} \ln \left(\frac{2 c d x +b d +\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}{2 c d x +b d -\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}\right)}{2 \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}+\frac{16 \sqrt{2 c d x +b d}\, a \,c^{2} d^{5}}{4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}}-\frac{4 \sqrt{2 c d x +b d}\, b^{2} c \,d^{5}}{4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}}+16 \sqrt{2 c d x +b d}\, c \,d^{3}"," ",0,"16*c*d^3*(2*c*d*x+b*d)^(1/2)+16*c^2*d^5*(2*c*d*x+b*d)^(1/2)/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)*a-4*c*d^5*(2*c*d*x+b*d)^(1/2)/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)*b^2-20*c^2*d^5/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*arctan(2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)*a+5*c*d^5/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*arctan(2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)*b^2+20*c^2*d^5/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*arctan(-2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)*a-5*c*d^5/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*arctan(-2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)*b^2-10*c^2*d^5/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*ln((2*c*d*x+b*d+(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2))/(2*c*d*x+b*d-(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2)))*a+5/2*c*d^5/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*ln((2*c*d*x+b*d+(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2))/(2*c*d*x+b*d-(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2)))*b^2","B"
1300,1,327,109,0.059000," ","int((2*c*d*x+b*d)^(5/2)/(c*x^2+b*x+a)^2,x)","-\frac{3 \sqrt{2}\, c \,d^{3} \arctan \left(-\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+\frac{3 \sqrt{2}\, c \,d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+\frac{3 \sqrt{2}\, c \,d^{3} \ln \left(\frac{2 c d x +b d -\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}{2 c d x +b d +\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}\right)}{2 \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}-\frac{4 \left(2 c d x +b d \right)^{\frac{3}{2}} c \,d^{3}}{4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}}"," ",0,"-4*c*d^3*(2*c*d*x+b*d)^(3/2)/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)+3/2*c*d^3*2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*ln((2*c*d*x+b*d-(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2))/(2*c*d*x+b*d+(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2)))+3*c*d^3*2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*arctan(2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)-3*c*d^3*2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*arctan(-2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)","B"
1301,1,326,109,0.059000," ","int((2*c*d*x+b*d)^(3/2)/(c*x^2+b*x+a)^2,x)","-\frac{\sqrt{2}\, c \,d^{3} \arctan \left(-\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}+\frac{\sqrt{2}\, c \,d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}+\frac{\sqrt{2}\, c \,d^{3} \ln \left(\frac{2 c d x +b d +\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}{2 c d x +b d -\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}\right)}{2 \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}-\frac{4 \sqrt{2 c d x +b d}\, c \,d^{3}}{4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}}"," ",0,"-4*c*d^3*(2*c*d*x+b*d)^(1/2)/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)+1/2*c*d^3/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*ln((2*c*d*x+b*d+(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2))/(2*c*d*x+b*d-(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2)))+c*d^3/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*arctan(2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)-c*d^3/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*arctan(-2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)","B"
1302,1,344,121,0.056000," ","int((2*c*d*x+b*d)^(1/2)/(c*x^2+b*x+a)^2,x)","-\frac{\sqrt{2}\, c \,d^{3} \arctan \left(-\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{5}{4}}}+\frac{\sqrt{2}\, c \,d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{5}{4}}}+\frac{\sqrt{2}\, c \,d^{3} \ln \left(\frac{2 c d x +b d -\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}{2 c d x +b d +\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}\right)}{2 \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{5}{4}}}+\frac{4 \left(2 c d x +b d \right)^{\frac{3}{2}} c \,d^{3}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right) \left(4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}\right)}"," ",0,"4*c*d^3*(2*c*d*x+b*d)^(3/2)/(4*a*c*d^2-b^2*d^2)/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)+1/2*c*d^3/(4*a*c*d^2-b^2*d^2)^(5/4)*2^(1/2)*ln((2*c*d*x+b*d-(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2))/(2*c*d*x+b*d+(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2)))+c*d^3/(4*a*c*d^2-b^2*d^2)^(5/4)*2^(1/2)*arctan(2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)-c*d^3/(4*a*c*d^2-b^2*d^2)^(5/4)*2^(1/2)*arctan(-2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)","B"
1303,1,345,121,0.058000," ","int(1/(2*c*d*x+b*d)^(1/2)/(c*x^2+b*x+a)^2,x)","-\frac{3 \sqrt{2}\, c \,d^{3} \arctan \left(-\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{7}{4}}}+\frac{3 \sqrt{2}\, c \,d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{7}{4}}}+\frac{3 \sqrt{2}\, c \,d^{3} \ln \left(\frac{2 c d x +b d +\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}{2 c d x +b d -\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}\right)}{2 \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{7}{4}}}+\frac{4 \sqrt{2 c d x +b d}\, c \,d^{3}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right) \left(4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}\right)}"," ",0,"4*c*d^3*(2*c*d*x+b*d)^(1/2)/(4*a*c*d^2-b^2*d^2)/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)+3/2*c*d^3/(4*a*c*d^2-b^2*d^2)^(7/4)*2^(1/2)*ln((2*c*d*x+b*d+(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2))/(2*c*d*x+b*d-(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2)))+3*c*d^3/(4*a*c*d^2-b^2*d^2)^(7/4)*2^(1/2)*arctan(2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)-3*c*d^3/(4*a*c*d^2-b^2*d^2)^(7/4)*2^(1/2)*arctan(-2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)","B"
1304,1,404,148,0.068000," ","int(1/(2*c*d*x+b*d)^(3/2)/(c*x^2+b*x+a)^2,x)","\frac{5 \sqrt{2}\, c \arctan \left(-\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c -b^{2}\right)^{2} \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} d}-\frac{5 \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c -b^{2}\right)^{2} \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} d}-\frac{5 \sqrt{2}\, c \ln \left(\frac{2 c d x +b d -\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}{2 c d x +b d +\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}\right)}{2 \left(4 a c -b^{2}\right)^{2} \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} d}-\frac{4 \left(2 c d x +b d \right)^{\frac{3}{2}} c}{\left(4 a c -b^{2}\right)^{2} \left(4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}\right) d}-\frac{16 c}{\left(4 a c -b^{2}\right)^{2} \sqrt{2 c d x +b d}\, d}"," ",0,"-4*c/d/(4*a*c-b^2)^2*(2*c*d*x+b*d)^(3/2)/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)-5/2*c/d/(4*a*c-b^2)^2*2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*ln((2*c*d*x+b*d-(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2))/(2*c*d*x+b*d+(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2)))-5*c/d/(4*a*c-b^2)^2*2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*arctan(2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)+5*c/d/(4*a*c-b^2)^2*2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*arctan(-2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)-16*c/d/(4*a*c-b^2)^2/(2*c*d*x+b*d)^(1/2)","B"
1305,1,404,148,0.065000," ","int(1/(2*c*d*x+b*d)^(5/2)/(c*x^2+b*x+a)^2,x)","\frac{7 \sqrt{2}\, c \arctan \left(-\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c -b^{2}\right)^{2} \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}} d}-\frac{7 \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c -b^{2}\right)^{2} \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}} d}-\frac{7 \sqrt{2}\, c \ln \left(\frac{2 c d x +b d +\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}{2 c d x +b d -\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}\right)}{2 \left(4 a c -b^{2}\right)^{2} \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}} d}-\frac{4 \sqrt{2 c d x +b d}\, c}{\left(4 a c -b^{2}\right)^{2} \left(4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}\right) d}-\frac{16 c}{3 \left(4 a c -b^{2}\right)^{2} \left(2 c d x +b d \right)^{\frac{3}{2}} d}"," ",0,"-4*c/d/(4*a*c-b^2)^2*(2*c*d*x+b*d)^(1/2)/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)-7/2*c/d/(4*a*c-b^2)^2/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*ln((2*c*d*x+b*d+(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2))/(2*c*d*x+b*d-(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2)))-7*c/d/(4*a*c-b^2)^2/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*arctan(2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)+7*c/d/(4*a*c-b^2)^2/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*arctan(-2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)-16/3*c/d/(4*a*c-b^2)^2/(2*c*d*x+b*d)^(3/2)","B"
1306,1,433,175,0.066000," ","int(1/(2*c*d*x+b*d)^(7/2)/(c*x^2+b*x+a)^2,x)","-\frac{16 c}{5 \left(4 a c -b^{2}\right)^{2} \left(2 c d x +b d \right)^{\frac{5}{2}} d}-\frac{9 \sqrt{2}\, c \arctan \left(-\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c -b^{2}\right)^{3} \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} d^{3}}+\frac{9 \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c -b^{2}\right)^{3} \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} d^{3}}+\frac{9 \sqrt{2}\, c \ln \left(\frac{2 c d x +b d -\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}{2 c d x +b d +\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}\right)}{2 \left(4 a c -b^{2}\right)^{3} \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} d^{3}}+\frac{4 \left(2 c d x +b d \right)^{\frac{3}{2}} c}{\left(4 a c -b^{2}\right)^{3} \left(4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}\right) d^{3}}+\frac{32 c}{\left(4 a c -b^{2}\right)^{3} \sqrt{2 c d x +b d}\, d^{3}}"," ",0,"4*c/d^3/(4*a*c-b^2)^3*(2*c*d*x+b*d)^(3/2)/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)+9/2*c/d^3/(4*a*c-b^2)^3*2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*ln((2*c*d*x+b*d-(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2))/(2*c*d*x+b*d+(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2)))+9*c/d^3/(4*a*c-b^2)^3*2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*arctan(2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)-9*c/d^3/(4*a*c-b^2)^3*2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*arctan(-2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)-16/5*c/d/(4*a*c-b^2)^2/(2*c*d*x+b*d)^(5/2)+32*c/d^3/(4*a*c-b^2)^3/(2*c*d*x+b*d)^(1/2)","B"
1307,1,1310,188,0.068000," ","int((2*c*d*x+b*d)^(17/2)/(c*x^2+b*x+a)^3,x)","-\frac{2944 \left(2 c d x +b d \right)^{\frac{3}{2}} a^{3} c^{5} d^{11}}{\left(4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}\right)^{2}}+\frac{2208 \left(2 c d x +b d \right)^{\frac{3}{2}} a^{2} b^{2} c^{4} d^{11}}{\left(4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}\right)^{2}}-\frac{552 \left(2 c d x +b d \right)^{\frac{3}{2}} a \,b^{4} c^{3} d^{11}}{\left(4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}\right)^{2}}+\frac{46 \left(2 c d x +b d \right)^{\frac{3}{2}} b^{6} c^{2} d^{11}}{\left(4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}\right)^{2}}-\frac{1320 \sqrt{2}\, a^{2} c^{4} d^{9} \arctan \left(-\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+\frac{1320 \sqrt{2}\, a^{2} c^{4} d^{9} \arctan \left(\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+\frac{660 \sqrt{2}\, a^{2} c^{4} d^{9} \ln \left(\frac{2 c d x +b d -\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}{2 c d x +b d +\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+\frac{660 \sqrt{2}\, a \,b^{2} c^{3} d^{9} \arctan \left(-\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}-\frac{660 \sqrt{2}\, a \,b^{2} c^{3} d^{9} \arctan \left(\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}-\frac{330 \sqrt{2}\, a \,b^{2} c^{3} d^{9} \ln \left(\frac{2 c d x +b d -\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}{2 c d x +b d +\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}-\frac{165 \sqrt{2}\, b^{4} c^{2} d^{9} \arctan \left(-\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+\frac{165 \sqrt{2}\, b^{4} c^{2} d^{9} \arctan \left(\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+\frac{165 \sqrt{2}\, b^{4} c^{2} d^{9} \ln \left(\frac{2 c d x +b d -\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}{2 c d x +b d +\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}\right)}{4 \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}-\frac{864 \left(2 c d x +b d \right)^{\frac{7}{2}} a^{2} c^{4} d^{9}}{\left(4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}\right)^{2}}+\frac{432 \left(2 c d x +b d \right)^{\frac{7}{2}} a \,b^{2} c^{3} d^{9}}{\left(4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}\right)^{2}}-\frac{54 \left(2 c d x +b d \right)^{\frac{7}{2}} b^{4} c^{2} d^{9}}{\left(4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}\right)^{2}}-256 \left(2 c d x +b d \right)^{\frac{3}{2}} a \,c^{3} d^{7}+64 \left(2 c d x +b d \right)^{\frac{3}{2}} b^{2} c^{2} d^{7}+\frac{64 \left(2 c d x +b d \right)^{\frac{7}{2}} c^{2} d^{5}}{7}"," ",0,"64/7*c^2*d^5*(2*c*d*x+b*d)^(7/2)-256*c^3*d^7*(2*c*d*x+b*d)^(3/2)*a+64*c^2*d^7*(2*c*d*x+b*d)^(3/2)*b^2-864*c^4*d^9/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)^2*(2*c*d*x+b*d)^(7/2)*a^2+432*c^3*d^9/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)^2*(2*c*d*x+b*d)^(7/2)*a*b^2-54*c^2*d^9/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)^2*(2*c*d*x+b*d)^(7/2)*b^4-2944*c^5*d^11/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)^2*(2*c*d*x+b*d)^(3/2)*a^3+2208*c^4*d^11/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)^2*(2*c*d*x+b*d)^(3/2)*a^2*b^2-552*c^3*d^11/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)^2*(2*c*d*x+b*d)^(3/2)*a*b^4+46*c^2*d^11/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)^2*(2*c*d*x+b*d)^(3/2)*b^6+660*c^4*d^9*2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*a^2*ln((2*c*d*x+b*d-(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2))/(2*c*d*x+b*d+(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2)))+1320*c^4*d^9*2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*a^2*arctan(2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)-1320*c^4*d^9*2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*a^2*arctan(-2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)-330*c^3*d^9*2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*a*b^2*ln((2*c*d*x+b*d-(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2))/(2*c*d*x+b*d+(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2)))-660*c^3*d^9*2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*a*b^2*arctan(2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)+660*c^3*d^9*2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*a*b^2*arctan(-2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)+165/4*c^2*d^9*2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*b^4*ln((2*c*d*x+b*d-(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2))/(2*c*d*x+b*d+(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2)))+165/2*c^2*d^9*2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*b^4*arctan(2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)-165/2*c^2*d^9*2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*b^4*arctan(-2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)","B"
1308,1,1310,188,0.069000," ","int((2*c*d*x+b*d)^(15/2)/(c*x^2+b*x+a)^3,x)","-\frac{2688 \sqrt{2 c d x +b d}\, a^{3} c^{5} d^{11}}{\left(4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}\right)^{2}}+\frac{2016 \sqrt{2 c d x +b d}\, a^{2} b^{2} c^{4} d^{11}}{\left(4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}\right)^{2}}-\frac{504 \sqrt{2 c d x +b d}\, a \,b^{4} c^{3} d^{11}}{\left(4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}\right)^{2}}+\frac{42 \sqrt{2 c d x +b d}\, b^{6} c^{2} d^{11}}{\left(4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}\right)^{2}}-\frac{936 \sqrt{2}\, a^{2} c^{4} d^{9} \arctan \left(-\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}+\frac{936 \sqrt{2}\, a^{2} c^{4} d^{9} \arctan \left(\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}+\frac{468 \sqrt{2}\, a^{2} c^{4} d^{9} \ln \left(\frac{2 c d x +b d +\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}{2 c d x +b d -\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}+\frac{468 \sqrt{2}\, a \,b^{2} c^{3} d^{9} \arctan \left(-\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}-\frac{468 \sqrt{2}\, a \,b^{2} c^{3} d^{9} \arctan \left(\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}-\frac{234 \sqrt{2}\, a \,b^{2} c^{3} d^{9} \ln \left(\frac{2 c d x +b d +\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}{2 c d x +b d -\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}-\frac{117 \sqrt{2}\, b^{4} c^{2} d^{9} \arctan \left(-\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}+\frac{117 \sqrt{2}\, b^{4} c^{2} d^{9} \arctan \left(\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}+\frac{117 \sqrt{2}\, b^{4} c^{2} d^{9} \ln \left(\frac{2 c d x +b d +\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}{2 c d x +b d -\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}\right)}{4 \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}-\frac{800 \left(2 c d x +b d \right)^{\frac{5}{2}} a^{2} c^{4} d^{9}}{\left(4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}\right)^{2}}+\frac{400 \left(2 c d x +b d \right)^{\frac{5}{2}} a \,b^{2} c^{3} d^{9}}{\left(4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}\right)^{2}}-\frac{50 \left(2 c d x +b d \right)^{\frac{5}{2}} b^{4} c^{2} d^{9}}{\left(4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}\right)^{2}}-768 \sqrt{2 c d x +b d}\, a \,c^{3} d^{7}+192 \sqrt{2 c d x +b d}\, b^{2} c^{2} d^{7}+\frac{64 \left(2 c d x +b d \right)^{\frac{5}{2}} c^{2} d^{5}}{5}"," ",0,"64/5*c^2*d^5*(2*c*d*x+b*d)^(5/2)-768*c^3*d^7*a*(2*c*d*x+b*d)^(1/2)+192*c^2*d^7*b^2*(2*c*d*x+b*d)^(1/2)-800*c^4*d^9/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)^2*(2*c*d*x+b*d)^(5/2)*a^2+400*c^3*d^9/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)^2*(2*c*d*x+b*d)^(5/2)*a*b^2-50*c^2*d^9/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)^2*(2*c*d*x+b*d)^(5/2)*b^4-2688*c^5*d^11/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)^2*(2*c*d*x+b*d)^(1/2)*a^3+2016*c^4*d^11/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)^2*(2*c*d*x+b*d)^(1/2)*a^2*b^2-504*c^3*d^11/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)^2*(2*c*d*x+b*d)^(1/2)*a*b^4+42*c^2*d^11/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)^2*(2*c*d*x+b*d)^(1/2)*b^6+936*c^4*d^9/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*arctan(2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)*a^2-468*c^3*d^9/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*arctan(2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)*a*b^2+117/2*c^2*d^9/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*arctan(2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)*b^4-936*c^4*d^9/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*arctan(-2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)*a^2+468*c^3*d^9/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*arctan(-2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)*a*b^2-117/2*c^2*d^9/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*arctan(-2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)*b^4+468*c^4*d^9/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*ln((2*c*d*x+b*d+(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2))/(2*c*d*x+b*d-(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2)))*a^2-234*c^3*d^9/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*ln((2*c*d*x+b*d+(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2))/(2*c*d*x+b*d-(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2)))*a*b^2+117/4*c^2*d^9/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*ln((2*c*d*x+b*d+(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2))/(2*c*d*x+b*d-(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2)))*b^4","B"
1309,1,857,161,0.066000," ","int((2*c*d*x+b*d)^(13/2)/(c*x^2+b*x+a)^3,x)","\frac{480 \left(2 c d x +b d \right)^{\frac{3}{2}} a^{2} c^{4} d^{9}}{\left(4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}\right)^{2}}-\frac{240 \left(2 c d x +b d \right)^{\frac{3}{2}} a \,b^{2} c^{3} d^{9}}{\left(4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}\right)^{2}}+\frac{30 \left(2 c d x +b d \right)^{\frac{3}{2}} b^{4} c^{2} d^{9}}{\left(4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}\right)^{2}}+\frac{154 \sqrt{2}\, a \,c^{3} d^{7} \arctan \left(-\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}-\frac{154 \sqrt{2}\, a \,c^{3} d^{7} \arctan \left(\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}-\frac{77 \sqrt{2}\, a \,c^{3} d^{7} \ln \left(\frac{2 c d x +b d -\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}{2 c d x +b d +\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}-\frac{77 \sqrt{2}\, b^{2} c^{2} d^{7} \arctan \left(-\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+\frac{77 \sqrt{2}\, b^{2} c^{2} d^{7} \arctan \left(\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+\frac{77 \sqrt{2}\, b^{2} c^{2} d^{7} \ln \left(\frac{2 c d x +b d -\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}{2 c d x +b d +\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}\right)}{4 \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+\frac{152 \left(2 c d x +b d \right)^{\frac{7}{2}} a \,c^{3} d^{7}}{\left(4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}\right)^{2}}-\frac{38 \left(2 c d x +b d \right)^{\frac{7}{2}} b^{2} c^{2} d^{7}}{\left(4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}\right)^{2}}+\frac{64 \left(2 c d x +b d \right)^{\frac{3}{2}} c^{2} d^{5}}{3}"," ",0,"64/3*c^2*d^5*(2*c*d*x+b*d)^(3/2)+152*c^3*d^7/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)^2*(2*c*d*x+b*d)^(7/2)*a-38*c^2*d^7/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)^2*(2*c*d*x+b*d)^(7/2)*b^2+480*c^4*d^9/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)^2*(2*c*d*x+b*d)^(3/2)*a^2-240*c^3*d^9/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)^2*(2*c*d*x+b*d)^(3/2)*a*b^2+30*c^2*d^9/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)^2*(2*c*d*x+b*d)^(3/2)*b^4-77*c^3*d^7*2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*a*ln((2*c*d*x+b*d-(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2))/(2*c*d*x+b*d+(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2)))-154*c^3*d^7*2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*a*arctan(2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)+154*c^3*d^7*2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*a*arctan(-2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)+77/4*c^2*d^7*2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*b^2*ln((2*c*d*x+b*d-(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2))/(2*c*d*x+b*d+(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2)))+77/2*c^2*d^7*2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*b^2*arctan(2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)-77/2*c^2*d^7*2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*b^2*arctan(-2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)","B"
1310,1,857,161,0.069000," ","int((2*c*d*x+b*d)^(11/2)/(c*x^2+b*x+a)^3,x)","\frac{416 \sqrt{2 c d x +b d}\, a^{2} c^{4} d^{9}}{\left(4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}\right)^{2}}-\frac{208 \sqrt{2 c d x +b d}\, a \,b^{2} c^{3} d^{9}}{\left(4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}\right)^{2}}+\frac{26 \sqrt{2 c d x +b d}\, b^{4} c^{2} d^{9}}{\left(4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}\right)^{2}}+\frac{90 \sqrt{2}\, a \,c^{3} d^{7} \arctan \left(-\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}-\frac{90 \sqrt{2}\, a \,c^{3} d^{7} \arctan \left(\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}-\frac{45 \sqrt{2}\, a \,c^{3} d^{7} \ln \left(\frac{2 c d x +b d +\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}{2 c d x +b d -\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}\right)}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}-\frac{45 \sqrt{2}\, b^{2} c^{2} d^{7} \arctan \left(-\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}+\frac{45 \sqrt{2}\, b^{2} c^{2} d^{7} \arctan \left(\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}+\frac{45 \sqrt{2}\, b^{2} c^{2} d^{7} \ln \left(\frac{2 c d x +b d +\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}{2 c d x +b d -\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}\right)}{4 \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}+\frac{136 \left(2 c d x +b d \right)^{\frac{5}{2}} a \,c^{3} d^{7}}{\left(4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}\right)^{2}}-\frac{34 \left(2 c d x +b d \right)^{\frac{5}{2}} b^{2} c^{2} d^{7}}{\left(4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}\right)^{2}}+64 \sqrt{2 c d x +b d}\, c^{2} d^{5}"," ",0,"64*c^2*d^5*(2*c*d*x+b*d)^(1/2)+136*c^3*d^7/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)^2*(2*c*d*x+b*d)^(5/2)*a-34*c^2*d^7/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)^2*(2*c*d*x+b*d)^(5/2)*b^2+416*c^4*d^9/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)^2*(2*c*d*x+b*d)^(1/2)*a^2-208*c^3*d^9/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)^2*(2*c*d*x+b*d)^(1/2)*a*b^2+26*c^2*d^9/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)^2*(2*c*d*x+b*d)^(1/2)*b^4-90*c^3*d^7/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*arctan(2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)*a+45/2*c^2*d^7/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*arctan(2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)*b^2+90*c^3*d^7/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*arctan(-2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)*a-45/2*c^2*d^7/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*arctan(-2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)*b^2-45*c^3*d^7/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*ln((2*c*d*x+b*d+(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2))/(2*c*d*x+b*d-(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2)))*a+45/4*c^2*d^7/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*ln((2*c*d*x+b*d+(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2))/(2*c*d*x+b*d-(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2)))*b^2","B"
1311,1,435,142,0.067000," ","int((2*c*d*x+b*d)^(9/2)/(c*x^2+b*x+a)^3,x)","-\frac{56 \left(2 c d x +b d \right)^{\frac{3}{2}} a \,c^{3} d^{7}}{\left(4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}\right)^{2}}+\frac{14 \left(2 c d x +b d \right)^{\frac{3}{2}} b^{2} c^{2} d^{7}}{\left(4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}\right)^{2}}-\frac{21 \sqrt{2}\, c^{2} d^{5} \arctan \left(-\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+\frac{21 \sqrt{2}\, c^{2} d^{5} \arctan \left(\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+\frac{21 \sqrt{2}\, c^{2} d^{5} \ln \left(\frac{2 c d x +b d -\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}{2 c d x +b d +\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}\right)}{4 \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}-\frac{22 \left(2 c d x +b d \right)^{\frac{7}{2}} c^{2} d^{5}}{\left(4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}\right)^{2}}"," ",0,"-22*c^2*d^5/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)^2*(2*c*d*x+b*d)^(7/2)-56*c^3*d^7/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)^2*(2*c*d*x+b*d)^(3/2)*a+14*c^2*d^7/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)^2*(2*c*d*x+b*d)^(3/2)*b^2+21/4*c^2*d^5*2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*ln((2*c*d*x+b*d-(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2))/(2*c*d*x+b*d+(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2)))+21/2*c^2*d^5*2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*arctan(2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)-21/2*c^2*d^5*2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*arctan(-2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)","B"
1312,1,435,142,0.059000," ","int((2*c*d*x+b*d)^(7/2)/(c*x^2+b*x+a)^3,x)","-\frac{40 \sqrt{2 c d x +b d}\, a \,c^{3} d^{7}}{\left(4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}\right)^{2}}+\frac{10 \sqrt{2 c d x +b d}\, b^{2} c^{2} d^{7}}{\left(4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}\right)^{2}}-\frac{5 \sqrt{2}\, c^{2} d^{5} \arctan \left(-\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}+\frac{5 \sqrt{2}\, c^{2} d^{5} \arctan \left(\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}+\frac{5 \sqrt{2}\, c^{2} d^{5} \ln \left(\frac{2 c d x +b d +\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}{2 c d x +b d -\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}\right)}{4 \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}-\frac{18 \left(2 c d x +b d \right)^{\frac{5}{2}} c^{2} d^{5}}{\left(4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}\right)^{2}}"," ",0,"-18*c^2*d^5/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)^2*(2*c*d*x+b*d)^(5/2)-40*c^3*d^7/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)^2*(2*c*d*x+b*d)^(1/2)*a+10*c^2*d^7/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)^2*(2*c*d*x+b*d)^(1/2)*b^2+5/4*c^2*d^5/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*ln((2*c*d*x+b*d+(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2))/(2*c*d*x+b*d-(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2)))+5/2*c^2*d^5/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*arctan(2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)-5/2*c^2*d^5/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*arctan(-2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)","B"
1313,1,431,150,0.061000," ","int((2*c*d*x+b*d)^(5/2)/(c*x^2+b*x+a)^3,x)","-\frac{2 \left(2 c d x +b d \right)^{\frac{3}{2}} c^{2} d^{5}}{\left(4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}\right)^{2}}-\frac{3 \sqrt{2}\, c^{2} d^{3} \arctan \left(-\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 \left(4 a c -b^{2}\right) \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+\frac{3 \sqrt{2}\, c^{2} d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 \left(4 a c -b^{2}\right) \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+\frac{3 \sqrt{2}\, c^{2} d^{3} \ln \left(\frac{2 c d x +b d -\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}{2 c d x +b d +\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}\right)}{4 \left(4 a c -b^{2}\right) \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+\frac{6 \left(2 c d x +b d \right)^{\frac{7}{2}} c^{2} d^{3}}{\left(4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}\right)^{2} \left(4 a c -b^{2}\right)}"," ",0,"6*c^2*d^3/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)^2/(4*a*c-b^2)*(2*c*d*x+b*d)^(7/2)-2*c^2*d^5/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)^2*(2*c*d*x+b*d)^(3/2)+3/4*c^2*d^3/(4*a*c-b^2)/(4*a*c*d^2-b^2*d^2)^(1/4)*2^(1/2)*ln((2*c*d*x+b*d-(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2))/(2*c*d*x+b*d+(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2)))+3/2*c^2*d^3/(4*a*c-b^2)/(4*a*c*d^2-b^2*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)-3/2*c^2*d^3/(4*a*c-b^2)/(4*a*c*d^2-b^2*d^2)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)","B"
1314,1,431,150,0.065000," ","int((2*c*d*x+b*d)^(3/2)/(c*x^2+b*x+a)^3,x)","-\frac{6 \sqrt{2 c d x +b d}\, c^{2} d^{5}}{\left(4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}\right)^{2}}-\frac{3 \sqrt{2}\, c^{2} d^{3} \arctan \left(-\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 \left(4 a c -b^{2}\right) \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}+\frac{3 \sqrt{2}\, c^{2} d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 \left(4 a c -b^{2}\right) \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}+\frac{3 \sqrt{2}\, c^{2} d^{3} \ln \left(\frac{2 c d x +b d +\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}{2 c d x +b d -\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}\right)}{4 \left(4 a c -b^{2}\right) \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}}}+\frac{2 \left(2 c d x +b d \right)^{\frac{5}{2}} c^{2} d^{3}}{\left(4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}\right)^{2} \left(4 a c -b^{2}\right)}"," ",0,"2*c^2*d^3/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)^2/(4*a*c-b^2)*(2*c*d*x+b*d)^(5/2)-6*c^2*d^5/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)^2*(2*c*d*x+b*d)^(1/2)+3/4*c^2*d^3/(4*a*c-b^2)/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*ln((2*c*d*x+b*d+(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2))/(2*c*d*x+b*d-(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2)))+3/2*c^2*d^3/(4*a*c-b^2)/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*arctan(2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)-3/2*c^2*d^3/(4*a*c-b^2)/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*arctan(-2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)","B"
1315,1,419,164,0.065000," ","int((2*c*d*x+b*d)^(1/2)/(c*x^2+b*x+a)^3,x)","-\frac{5 \sqrt{2}\, c^{2} d^{5} \arctan \left(-\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{9}{4}}}+\frac{5 \sqrt{2}\, c^{2} d^{5} \arctan \left(\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{9}{4}}}+\frac{5 \sqrt{2}\, c^{2} d^{5} \ln \left(\frac{2 c d x +b d -\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}{2 c d x +b d +\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}\right)}{4 \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{9}{4}}}+\frac{8 \left(2 c d x +b d \right)^{\frac{3}{2}} c^{2} d^{5}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right) \left(4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}\right)^{2}}+\frac{10 \left(2 c d x +b d \right)^{\frac{3}{2}} c^{2} d^{5}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{2} \left(4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}\right)}"," ",0,"8*c^2*d^5*(2*c*d*x+b*d)^(3/2)/(4*a*c*d^2-b^2*d^2)/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)^2+10*c^2*d^5/(4*a*c*d^2-b^2*d^2)^2*(2*c*d*x+b*d)^(3/2)/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)+5/4*c^2*d^5/(4*a*c*d^2-b^2*d^2)^(9/4)*2^(1/2)*ln((2*c*d*x+b*d-(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2))/(2*c*d*x+b*d+(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2)))+5/2*c^2*d^5/(4*a*c*d^2-b^2*d^2)^(9/4)*2^(1/2)*arctan(2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)-5/2*c^2*d^5/(4*a*c*d^2-b^2*d^2)^(9/4)*2^(1/2)*arctan(-2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)","B"
1316,1,419,164,0.056000," ","int(1/(2*c*d*x+b*d)^(1/2)/(c*x^2+b*x+a)^3,x)","-\frac{21 \sqrt{2}\, c^{2} d^{5} \arctan \left(-\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{11}{4}}}+\frac{21 \sqrt{2}\, c^{2} d^{5} \arctan \left(\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{11}{4}}}+\frac{21 \sqrt{2}\, c^{2} d^{5} \ln \left(\frac{2 c d x +b d +\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}{2 c d x +b d -\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}\right)}{4 \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{11}{4}}}+\frac{8 \sqrt{2 c d x +b d}\, c^{2} d^{5}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right) \left(4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}\right)^{2}}+\frac{14 \sqrt{2 c d x +b d}\, c^{2} d^{5}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{2} \left(4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}\right)}"," ",0,"8*c^2*d^5*(2*c*d*x+b*d)^(1/2)/(4*a*c*d^2-b^2*d^2)/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)^2+14*c^2*d^5/(4*a*c*d^2-b^2*d^2)^2*(2*c*d*x+b*d)^(1/2)/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)+21/4*c^2*d^5/(4*a*c*d^2-b^2*d^2)^(11/4)*2^(1/2)*ln((2*c*d*x+b*d+(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2))/(2*c*d*x+b*d-(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2)))+21/2*c^2*d^5/(4*a*c*d^2-b^2*d^2)^(11/4)*2^(1/2)*arctan(2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)-21/2*c^2*d^5/(4*a*c*d^2-b^2*d^2)^(11/4)*2^(1/2)*arctan(-2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)","B"
1317,1,534,193,0.072000," ","int(1/(2*c*d*x+b*d)^(3/2)/(c*x^2+b*x+a)^3,x)","-\frac{136 \left(2 c d x +b d \right)^{\frac{3}{2}} a \,c^{3} d}{\left(4 a c -b^{2}\right)^{3} \left(4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}\right)^{2}}+\frac{34 \left(2 c d x +b d \right)^{\frac{3}{2}} b^{2} c^{2} d}{\left(4 a c -b^{2}\right)^{3} \left(4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}\right)^{2}}+\frac{45 \sqrt{2}\, c^{2} \arctan \left(-\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 \left(4 a c -b^{2}\right)^{3} \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} d}-\frac{45 \sqrt{2}\, c^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 \left(4 a c -b^{2}\right)^{3} \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} d}-\frac{45 \sqrt{2}\, c^{2} \ln \left(\frac{2 c d x +b d -\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}{2 c d x +b d +\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}\right)}{4 \left(4 a c -b^{2}\right)^{3} \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} d}-\frac{26 \left(2 c d x +b d \right)^{\frac{7}{2}} c^{2}}{\left(4 a c -b^{2}\right)^{3} \left(4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}\right)^{2} d}-\frac{64 c^{2}}{\left(4 a c -b^{2}\right)^{3} \sqrt{2 c d x +b d}\, d}"," ",0,"-26*c^2/d/(4*a*c-b^2)^3/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)^2*(2*c*d*x+b*d)^(7/2)-136*c^3*d/(4*a*c-b^2)^3/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)^2*(2*c*d*x+b*d)^(3/2)*a+34*c^2*d/(4*a*c-b^2)^3/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)^2*(2*c*d*x+b*d)^(3/2)*b^2-45/4*c^2/d/(4*a*c-b^2)^3*2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*ln((2*c*d*x+b*d-(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2))/(2*c*d*x+b*d+(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2)))-45/2*c^2/d/(4*a*c-b^2)^3*2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*arctan(2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)+45/2*c^2/d/(4*a*c-b^2)^3*2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*arctan(-2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)-64*c^2/d/(4*a*c-b^2)^3/(2*c*d*x+b*d)^(1/2)","B"
1318,1,534,193,0.076000," ","int(1/(2*c*d*x+b*d)^(5/2)/(c*x^2+b*x+a)^3,x)","-\frac{152 \sqrt{2 c d x +b d}\, a \,c^{3} d}{\left(4 a c -b^{2}\right)^{3} \left(4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}\right)^{2}}+\frac{38 \sqrt{2 c d x +b d}\, b^{2} c^{2} d}{\left(4 a c -b^{2}\right)^{3} \left(4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}\right)^{2}}+\frac{77 \sqrt{2}\, c^{2} \arctan \left(-\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 \left(4 a c -b^{2}\right)^{3} \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}} d}-\frac{77 \sqrt{2}\, c^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 \left(4 a c -b^{2}\right)^{3} \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}} d}-\frac{77 \sqrt{2}\, c^{2} \ln \left(\frac{2 c d x +b d +\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}{2 c d x +b d -\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}\right)}{4 \left(4 a c -b^{2}\right)^{3} \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{3}{4}} d}-\frac{30 \left(2 c d x +b d \right)^{\frac{5}{2}} c^{2}}{\left(4 a c -b^{2}\right)^{3} \left(4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}\right)^{2} d}-\frac{64 c^{2}}{3 \left(4 a c -b^{2}\right)^{3} \left(2 c d x +b d \right)^{\frac{3}{2}} d}"," ",0,"-30*c^2/d/(4*a*c-b^2)^3/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)^2*(2*c*d*x+b*d)^(5/2)-152*c^3*d/(4*a*c-b^2)^3/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)^2*(2*c*d*x+b*d)^(1/2)*a+38*c^2*d/(4*a*c-b^2)^3/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)^2*(2*c*d*x+b*d)^(1/2)*b^2-77/4*c^2/d/(4*a*c-b^2)^3/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*ln((2*c*d*x+b*d+(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2))/(2*c*d*x+b*d-(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2)))-77/2*c^2/d/(4*a*c-b^2)^3/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*arctan(2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)+77/2*c^2/d/(4*a*c-b^2)^3/(4*a*c*d^2-b^2*d^2)^(3/4)*2^(1/2)*arctan(-2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)-64/3*c^2/d/(4*a*c-b^2)^3/(2*c*d*x+b*d)^(3/2)","B"
1319,1,569,222,0.076000," ","int(1/(2*c*d*x+b*d)^(7/2)/(c*x^2+b*x+a)^3,x)","\frac{200 \left(2 c d x +b d \right)^{\frac{3}{2}} a \,c^{3}}{\left(4 a c -b^{2}\right)^{4} \left(4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}\right)^{2} d}-\frac{50 \left(2 c d x +b d \right)^{\frac{3}{2}} b^{2} c^{2}}{\left(4 a c -b^{2}\right)^{4} \left(4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}\right)^{2} d}-\frac{64 c^{2}}{5 \left(4 a c -b^{2}\right)^{3} \left(2 c d x +b d \right)^{\frac{5}{2}} d}-\frac{117 \sqrt{2}\, c^{2} \arctan \left(-\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 \left(4 a c -b^{2}\right)^{4} \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} d^{3}}+\frac{117 \sqrt{2}\, c^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{2 c d x +b d}}{\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}}}+1\right)}{2 \left(4 a c -b^{2}\right)^{4} \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} d^{3}}+\frac{117 \sqrt{2}\, c^{2} \ln \left(\frac{2 c d x +b d -\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}{2 c d x +b d +\left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} \sqrt{2 c d x +b d}\, \sqrt{2}+\sqrt{4 a c \,d^{2}-b^{2} d^{2}}}\right)}{4 \left(4 a c -b^{2}\right)^{4} \left(4 a c \,d^{2}-b^{2} d^{2}\right)^{\frac{1}{4}} d^{3}}+\frac{42 \left(2 c d x +b d \right)^{\frac{7}{2}} c^{2}}{\left(4 a c -b^{2}\right)^{4} \left(4 c^{2} d^{2} x^{2}+4 b c \,d^{2} x +4 a c \,d^{2}\right)^{2} d^{3}}+\frac{192 c^{2}}{\left(4 a c -b^{2}\right)^{4} \sqrt{2 c d x +b d}\, d^{3}}"," ",0,"42*c^2/d^3/(4*a*c-b^2)^4/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)^2*(2*c*d*x+b*d)^(7/2)+200*c^3/d/(4*a*c-b^2)^4/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)^2*(2*c*d*x+b*d)^(3/2)*a-50*c^2/d/(4*a*c-b^2)^4/(4*c^2*d^2*x^2+4*b*c*d^2*x+4*a*c*d^2)^2*(2*c*d*x+b*d)^(3/2)*b^2+117/4*c^2/d^3/(4*a*c-b^2)^4*2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*ln((2*c*d*x+b*d-(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2))/(2*c*d*x+b*d+(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)*2^(1/2)+(4*a*c*d^2-b^2*d^2)^(1/2)))+117/2*c^2/d^3/(4*a*c-b^2)^4*2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*arctan(2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)-117/2*c^2/d^3/(4*a*c-b^2)^4*2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*arctan(-2^(1/2)/(4*a*c*d^2-b^2*d^2)^(1/4)*(2*c*d*x+b*d)^(1/2)+1)-64/5*c^2/d/(4*a*c-b^2)^3/(2*c*d*x+b*d)^(5/2)+192*c^2/d^3/(4*a*c-b^2)^4/(2*c*d*x+b*d)^(1/2)","B"
1320,1,129,134,0.051000," ","int((2*x+1)^(7/2)/(x^2+x+1),x)","3 \,3^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-1+\frac{\sqrt{2}\, \sqrt{2 x +1}\, 3^{\frac{3}{4}}}{3}\right)+3 \,3^{\frac{1}{4}} \sqrt{2}\, \arctan \left(1+\frac{\sqrt{2}\, \sqrt{2 x +1}\, 3^{\frac{3}{4}}}{3}\right)+\frac{3 \,3^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{2 x +1+\sqrt{3}+3^{\frac{1}{4}} \sqrt{2}\, \sqrt{2 x +1}}{2 x +1+\sqrt{3}-3^{\frac{1}{4}} \sqrt{2}\, \sqrt{2 x +1}}\right)}{2}+\frac{4 \left(2 x +1\right)^{\frac{5}{2}}}{5}-12 \sqrt{2 x +1}"," ",0,"4/5*(2*x+1)^(5/2)-12*(2*x+1)^(1/2)+3*3^(1/4)*arctan(1+1/3*2^(1/2)*(2*x+1)^(1/2)*3^(3/4))*2^(1/2)+3*3^(1/4)*arctan(-1+1/3*2^(1/2)*(2*x+1)^(1/2)*3^(3/4))*2^(1/2)+3/2*3^(1/4)*2^(1/2)*ln((1+2*x+3^(1/2)+3^(1/4)*2^(1/2)*(2*x+1)^(1/2))/(1+2*x+3^(1/2)-3^(1/4)*2^(1/2)*(2*x+1)^(1/2)))","A"
1321,1,120,125,0.046000," ","int((2*x+1)^(5/2)/(x^2+x+1),x)","-3^{\frac{3}{4}} \sqrt{2}\, \arctan \left(-1+\frac{\sqrt{2}\, \sqrt{2 x +1}\, 3^{\frac{3}{4}}}{3}\right)-3^{\frac{3}{4}} \sqrt{2}\, \arctan \left(1+\frac{\sqrt{2}\, \sqrt{2 x +1}\, 3^{\frac{3}{4}}}{3}\right)-\frac{\sqrt{2}\, 3^{\frac{3}{4}} \ln \left(\frac{2 x +1+\sqrt{3}-3^{\frac{1}{4}} \sqrt{2}\, \sqrt{2 x +1}}{2 x +1+\sqrt{3}+3^{\frac{1}{4}} \sqrt{2}\, \sqrt{2 x +1}}\right)}{2}+\frac{4 \left(2 x +1\right)^{\frac{3}{2}}}{3}"," ",0,"4/3*(2*x+1)^(3/2)-3^(3/4)*arctan(-1+1/3*2^(1/2)*(2*x+1)^(1/2)*3^(3/4))*2^(1/2)-3^(3/4)*arctan(1+1/3*2^(1/2)*(2*x+1)^(1/2)*3^(3/4))*2^(1/2)-1/2*2^(1/2)*3^(3/4)*ln((2*x+1+3^(1/2)-3^(1/4)*2^(1/2)*(2*x+1)^(1/2))/(2*x+1+3^(1/2)+3^(1/4)*2^(1/2)*(2*x+1)^(1/2)))","A"
1322,1,120,125,0.053000," ","int((2*x+1)^(3/2)/(x^2+x+1),x)","-3^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-1+\frac{\sqrt{2}\, \sqrt{2 x +1}\, 3^{\frac{3}{4}}}{3}\right)-3^{\frac{1}{4}} \sqrt{2}\, \arctan \left(1+\frac{\sqrt{2}\, \sqrt{2 x +1}\, 3^{\frac{3}{4}}}{3}\right)-\frac{3^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{2 x +1+\sqrt{3}+3^{\frac{1}{4}} \sqrt{2}\, \sqrt{2 x +1}}{2 x +1+\sqrt{3}-3^{\frac{1}{4}} \sqrt{2}\, \sqrt{2 x +1}}\right)}{2}+4 \sqrt{2 x +1}"," ",0,"4*(2*x+1)^(1/2)-3^(1/4)*2^(1/2)*arctan(1+1/3*2^(1/2)*(2*x+1)^(1/2)*3^(3/4))-3^(1/4)*2^(1/2)*arctan(-1+1/3*2^(1/2)*(2*x+1)^(1/2)*3^(3/4))-1/2*3^(1/4)*2^(1/2)*ln((2*x+1+3^(1/2)+3^(1/4)*2^(1/2)*(2*x+1)^(1/2))/(2*x+1+3^(1/2)-3^(1/4)*2^(1/2)*(2*x+1)^(1/2)))","A"
1323,1,111,116,0.050000," ","int((2*x+1)^(1/2)/(x^2+x+1),x)","\frac{3^{\frac{3}{4}} \sqrt{2}\, \arctan \left(-1+\frac{\sqrt{2}\, \sqrt{2 x +1}\, 3^{\frac{3}{4}}}{3}\right)}{3}+\frac{3^{\frac{3}{4}} \sqrt{2}\, \arctan \left(1+\frac{\sqrt{2}\, \sqrt{2 x +1}\, 3^{\frac{3}{4}}}{3}\right)}{3}+\frac{\sqrt{2}\, 3^{\frac{3}{4}} \ln \left(\frac{2 x +1+\sqrt{3}-3^{\frac{1}{4}} \sqrt{2}\, \sqrt{2 x +1}}{2 x +1+\sqrt{3}+3^{\frac{1}{4}} \sqrt{2}\, \sqrt{2 x +1}}\right)}{6}"," ",0,"1/3*3^(3/4)*2^(1/2)*arctan(-1+1/3*2^(1/2)*(2*x+1)^(1/2)*3^(3/4))+1/6*2^(1/2)*3^(3/4)*ln((2*x+1+3^(1/2)-3^(1/4)*2^(1/2)*(2*x+1)^(1/2))/(2*x+1+3^(1/2)+3^(1/4)*2^(1/2)*(2*x+1)^(1/2)))+1/3*3^(3/4)*2^(1/2)*arctan(1+1/3*2^(1/2)*(2*x+1)^(1/2)*3^(3/4))","A"
1324,1,111,116,0.044000," ","int(1/(2*x+1)^(1/2)/(x^2+x+1),x)","\frac{3^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-1+\frac{\sqrt{2}\, \sqrt{2 x +1}\, 3^{\frac{3}{4}}}{3}\right)}{3}+\frac{3^{\frac{1}{4}} \sqrt{2}\, \arctan \left(1+\frac{\sqrt{2}\, \sqrt{2 x +1}\, 3^{\frac{3}{4}}}{3}\right)}{3}+\frac{3^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{2 x +1+\sqrt{3}+3^{\frac{1}{4}} \sqrt{2}\, \sqrt{2 x +1}}{2 x +1+\sqrt{3}-3^{\frac{1}{4}} \sqrt{2}\, \sqrt{2 x +1}}\right)}{6}"," ",0,"1/6*3^(1/4)*2^(1/2)*ln((2*x+1+3^(1/2)+3^(1/4)*2^(1/2)*(2*x+1)^(1/2))/(2*x+1+3^(1/2)-3^(1/4)*2^(1/2)*(2*x+1)^(1/2)))+1/3*3^(1/4)*2^(1/2)*arctan(1+1/3*2^(1/2)*(2*x+1)^(1/2)*3^(3/4))+1/3*3^(1/4)*2^(1/2)*arctan(-1+1/3*2^(1/2)*(2*x+1)^(1/2)*3^(3/4))","A"
1325,1,120,125,0.048000," ","int(1/(2*x+1)^(3/2)/(x^2+x+1),x)","-\frac{3^{\frac{3}{4}} \sqrt{2}\, \arctan \left(-1+\frac{\sqrt{2}\, \sqrt{2 x +1}\, 3^{\frac{3}{4}}}{3}\right)}{9}-\frac{3^{\frac{3}{4}} \sqrt{2}\, \arctan \left(1+\frac{\sqrt{2}\, \sqrt{2 x +1}\, 3^{\frac{3}{4}}}{3}\right)}{9}-\frac{\sqrt{2}\, 3^{\frac{3}{4}} \ln \left(\frac{2 x +1+\sqrt{3}-3^{\frac{1}{4}} \sqrt{2}\, \sqrt{2 x +1}}{2 x +1+\sqrt{3}+3^{\frac{1}{4}} \sqrt{2}\, \sqrt{2 x +1}}\right)}{18}-\frac{4}{3 \sqrt{2 x +1}}"," ",0,"-4/3/(2*x+1)^(1/2)-1/9*3^(3/4)*2^(1/2)*arctan(1+1/3*2^(1/2)*(2*x+1)^(1/2)*3^(3/4))-1/9*3^(3/4)*2^(1/2)*arctan(-1+1/3*2^(1/2)*(2*x+1)^(1/2)*3^(3/4))-1/18*2^(1/2)*3^(3/4)*ln((2*x+1+3^(1/2)-3^(1/4)*2^(1/2)*(2*x+1)^(1/2))/(2*x+1+3^(1/2)+3^(1/4)*2^(1/2)*(2*x+1)^(1/2)))","A"
1326,1,120,125,0.051000," ","int(1/(2*x+1)^(5/2)/(x^2+x+1),x)","-\frac{3^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-1+\frac{\sqrt{2}\, \sqrt{2 x +1}\, 3^{\frac{3}{4}}}{3}\right)}{9}-\frac{3^{\frac{1}{4}} \sqrt{2}\, \arctan \left(1+\frac{\sqrt{2}\, \sqrt{2 x +1}\, 3^{\frac{3}{4}}}{3}\right)}{9}-\frac{3^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{2 x +1+\sqrt{3}+3^{\frac{1}{4}} \sqrt{2}\, \sqrt{2 x +1}}{2 x +1+\sqrt{3}-3^{\frac{1}{4}} \sqrt{2}\, \sqrt{2 x +1}}\right)}{18}-\frac{4}{9 \left(2 x +1\right)^{\frac{3}{2}}}"," ",0,"-4/9/(2*x+1)^(3/2)-1/9*3^(1/4)*2^(1/2)*arctan(1+1/3*2^(1/2)*(2*x+1)^(1/2)*3^(3/4))-1/9*3^(1/4)*2^(1/2)*arctan(-1+1/3*2^(1/2)*(2*x+1)^(1/2)*3^(3/4))-1/18*3^(1/4)*2^(1/2)*ln((2*x+1+3^(1/2)+3^(1/4)*2^(1/2)*(2*x+1)^(1/2))/(2*x+1+3^(1/2)-3^(1/4)*2^(1/2)*(2*x+1)^(1/2)))","A"
1327,1,798,193,0.271000," ","int((2*c*d*x+b*d)^(7/2)*(c*x^2+b*x+a)^(1/2),x)","\frac{\sqrt{\left(2 c x +b \right) d}\, \sqrt{c \,x^{2}+b x +a}\, \left(1344 c^{7} x^{7}+4704 b \,c^{6} x^{6}+1728 a \,c^{6} x^{5}+6624 b^{2} c^{5} x^{5}+4320 a b \,c^{5} x^{4}+4800 b^{3} c^{4} x^{4}-256 a^{2} c^{5} x^{3}+4448 a \,b^{2} c^{4} x^{3}+1844 b^{4} c^{3} x^{3}-384 a^{2} b \,c^{4} x^{2}+2352 a \,b^{3} c^{3} x^{2}+318 b^{5} c^{2} x^{2}-640 a^{3} c^{4} x +288 a^{2} b^{2} c^{3} x +516 a \,b^{4} c^{2} x +10 b^{6} c x -320 a^{3} b \,c^{3}+320 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, a^{3} c^{3} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+208 a^{2} b^{3} c^{2}-240 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, a^{2} b^{2} c^{2} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+10 a \,b^{5} c +60 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, a \,b^{4} c \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-5 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, b^{6} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)\right) d^{3}}{462 \left(2 c^{2} x^{3}+3 b c \,x^{2}+2 a c x +b^{2} x +a b \right) c^{2}}"," ",0,"1/462*(d*(2*c*x+b))^(1/2)*(c*x^2+b*x+a)^(1/2)*d^3*(1344*x^7*c^7+4704*x^6*b*c^6+1728*x^5*a*c^6+6624*x^5*b^2*c^5+320*((b+2*c*x+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-b-2*c*x+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((b+2*c*x+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*a^3*c^3-240*((b+2*c*x+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-b-2*c*x+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((b+2*c*x+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*a^2*b^2*c^2+60*((b+2*c*x+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-b-2*c*x+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((b+2*c*x+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*a*b^4*c-5*((b+2*c*x+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-b-2*c*x+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((b+2*c*x+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*b^6+4320*x^4*a*b*c^5+4800*x^4*b^3*c^4-256*x^3*a^2*c^5+4448*x^3*a*b^2*c^4+1844*x^3*b^4*c^3-384*x^2*a^2*b*c^4+2352*x^2*a*b^3*c^3+318*x^2*b^5*c^2-640*x*a^3*c^4+288*x*a^2*b^2*c^3+516*x*a*b^4*c^2+10*x*b^6*c-320*a^3*b*c^3+208*a^2*b^3*c^2+10*a*b^5*c)/c^2/(2*c^2*x^3+3*b*c*x^2+2*a*c*x+b^2*x+a*b)","B"
1328,1,564,152,0.068000," ","int((2*c*d*x+b*d)^(3/2)*(c*x^2+b*x+a)^(1/2),x)","-\frac{\sqrt{\left(2 c x +b \right) d}\, \sqrt{c \,x^{2}+b x +a}\, \left(-48 c^{5} x^{5}-120 b \,c^{4} x^{4}-80 a \,c^{4} x^{3}-100 b^{2} c^{3} x^{3}-120 a b \,c^{3} x^{2}-30 b^{3} c^{2} x^{2}-32 a^{2} c^{3} x -44 a \,b^{2} c^{2} x -2 b^{4} c x -16 a^{2} b \,c^{2}+16 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, a^{2} c^{2} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-2 a \,b^{3} c -8 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, a \,b^{2} c \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, b^{4} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)\right) d}{42 \left(2 c^{2} x^{3}+3 b c \,x^{2}+2 a c x +b^{2} x +a b \right) c^{2}}"," ",0,"-1/42*((2*c*x+b)*d)^(1/2)*(c*x^2+b*x+a)^(1/2)*d*(-48*x^5*c^5+16*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*a^2*c^2-8*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*a*b^2*c+((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*b^4-120*x^4*b*c^4-80*x^3*a*c^4-100*x^3*b^2*c^3-120*x^2*a*b*c^3-30*x^2*b^3*c^2-32*a^2*c^3*x-44*x*a*b^2*c^2-2*x*b^4*c-16*a^2*b*c^2-2*a*b^3*c)/c^2/(2*c^2*x^3+3*b*c*x^2+2*a*c*x+b^2*x+a*b)","B"
1329,1,364,115,0.086000," ","int((c*x^2+b*x+a)^(1/2)/(2*c*d*x+b*d)^(1/2),x)","\frac{\sqrt{c \,x^{2}+b x +a}\, \sqrt{\left(2 c x +b \right) d}\, \left(4 c^{3} x^{3}+6 b \,c^{2} x^{2}+4 a \,c^{2} x +2 b^{2} c x +2 a b c +4 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, a c \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, b^{2} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)\right)}{6 \left(2 c^{2} x^{3}+3 b c \,x^{2}+2 a c x +b^{2} x +a b \right) c^{2} d}"," ",0,"1/6*(c*x^2+b*x+a)^(1/2)*((2*c*x+b)*d)^(1/2)/d*(4*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*a*c-((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*b^2+4*x^3*c^3+6*x^2*b*c^2+4*a*c^2*x+2*b^2*x*c+2*a*b*c)/(2*c^2*x^3+3*b*c*x^2+2*a*c*x+b^2*x+a*b)/c^2","B"
1330,1,319,115,0.141000," ","int((c*x^2+b*x+a)^(1/2)/(2*c*d*x+b*d)^(5/2),x)","\frac{\left(-2 c^{2} x^{2}-2 b c x +2 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, c x \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-2 a c +\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, b \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)\right) \sqrt{\left(2 c x +b \right) d}}{6 \sqrt{c \,x^{2}+b x +a}\, \left(2 c x +b \right)^{2} c^{2} d^{3}}"," ",0,"1/6*(2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*x*c+((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*b-2*c^2*x^2-2*b*c*x-2*a*c)/d^3*((2*c*x+b)*d)^(1/2)/(c*x^2+b*x+a)^(1/2)/(2*c*x+b)^2/c^2","B"
1331,1,659,156,0.105000," ","int((c*x^2+b*x+a)^(1/2)/(2*c*d*x+b*d)^(9/2),x)","-\frac{\left(16 c^{4} x^{4}+32 b \,c^{3} x^{3}+8 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, c^{3} x^{3} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+40 a \,c^{3} x^{2}+14 b^{2} c^{2} x^{2}+12 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, b \,c^{2} x^{2} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+40 a b \,c^{2} x -2 b^{3} c x +6 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, b^{2} c x \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+24 a^{2} c^{2}-2 a \,b^{2} c +\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, b^{3} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)\right) \sqrt{\left(2 c x +b \right) d}}{42 \sqrt{c \,x^{2}+b x +a}\, \left(4 a c -b^{2}\right) \left(2 c x +b \right)^{4} c^{2} d^{5}}"," ",0,"-1/42*(8*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*x^3*c^3+12*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*x^2*b*c^2+6*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*x*b^2*c+((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*b^3+16*c^4*x^4+32*b*c^3*x^3+40*a*c^3*x^2+14*x^2*b^2*c^2+40*a*b*c^2*x-2*x*b^3*c+24*a^2*c^2-2*a*b^2*c)/d^5*((2*c*x+b)*d)^(1/2)/(c*x^2+b*x+a)^(1/2)/(4*a*c-b^2)/(2*c*x+b)^4/c^2","B"
1332,1,1016,197,0.107000," ","int((c*x^2+b*x+a)^(1/2)/(2*c*d*x+b*d)^(13/2),x)","\frac{\left(320 c^{6} x^{6}+960 b \,c^{5} x^{5}+160 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, c^{5} x^{5} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+128 a \,c^{5} x^{4}+1168 b^{2} c^{4} x^{4}+400 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, b \,c^{4} x^{4} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+256 a b \,c^{4} x^{3}+736 b^{3} c^{3} x^{3}+400 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, b^{2} c^{3} x^{3} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-864 a^{2} c^{4} x^{2}+624 a \,b^{2} c^{3} x^{2}+198 b^{4} c^{2} x^{2}+200 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, b^{3} c^{2} x^{2} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-864 a^{2} b \,c^{3} x +496 a \,b^{3} c^{2} x -10 b^{5} c x +50 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, b^{4} c x \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-672 a^{3} c^{3}+288 a^{2} b^{2} c^{2}-10 a \,b^{4} c +5 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, b^{5} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)\right) \sqrt{\left(2 c x +b \right) d}}{462 \sqrt{c \,x^{2}+b x +a}\, \left(4 a c -b^{2}\right)^{2} \left(2 c x +b \right)^{6} c^{2} d^{7}}"," ",0,"1/462*(160*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*x^5*c^5+400*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*x^4*b*c^4+400*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*x^3*b^2*c^3+200*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*x^2*b^3*c^2+320*c^6*x^6+50*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*x*b^4*c+960*b*c^5*x^5+5*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*b^5+128*a*c^5*x^4+1168*b^2*c^4*x^4+256*x^3*a*b*c^4+736*b^3*c^3*x^3-864*a^2*c^4*x^2+624*a*b^2*c^3*x^2+198*b^4*c^2*x^2-864*a^2*b*c^3*x+496*a*b^3*c^2*x-10*b^5*c*x-672*a^3*c^3+288*a^2*b^2*c^2-10*a*b^4*c)/d^7*((2*c*x+b)*d)^(1/2)/(c*x^2+b*x+a)^(1/2)/(4*a*c-b^2)^2/(2*c*x+b)^6/c^2","B"
1333,1,703,235,0.074000," ","int((2*c*d*x+b*d)^(5/2)*(c*x^2+b*x+a)^(1/2),x)","-\frac{\sqrt{\left(2 c x +b \right) d}\, \sqrt{c \,x^{2}+b x +a}\, \left(-160 c^{6} x^{6}-480 b \,c^{5} x^{5}-224 a \,c^{5} x^{4}-544 b^{2} c^{4} x^{4}-448 a b \,c^{4} x^{3}-288 b^{3} c^{3} x^{3}-64 a^{2} c^{4} x^{2}-304 a \,b^{2} c^{3} x^{2}-70 b^{4} c^{2} x^{2}+192 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a^{3} c^{3} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-144 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a^{2} b^{2} c^{2} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-64 a^{2} b \,c^{3} x +36 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a \,b^{4} c \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-80 a \,b^{3} c^{2} x -3 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{6} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-6 b^{5} c x -16 a^{2} b^{2} c^{2}-6 a \,b^{4} c \right) d^{2}}{90 \left(2 c^{2} x^{3}+3 b c \,x^{2}+2 a c x +b^{2} x +a b \right) c^{2}}"," ",0,"-1/90*((2*c*x+b)*d)^(1/2)*(c*x^2+b*x+a)^(1/2)*d^2*(-160*c^6*x^6-480*b*c^5*x^5+192*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*a^3*c^3-144*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*a^2*b^2*c^2+36*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*a*b^4*c-3*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*b^6-224*a*c^5*x^4-544*b^2*c^4*x^4-448*a*b*c^4*x^3-288*b^3*c^3*x^3-64*a^2*c^4*x^2-304*a*b^2*c^3*x^2-70*b^4*c^2*x^2-64*a^2*b*c^3*x-80*a*b^3*c^2*x-6*b^5*c*x-16*a^2*b^2*c^2-6*a*b^4*c)/c^2/(2*c^2*x^3+3*b*c*x^2+2*a*c*x+b^2*x+a*b)","B"
1334,1,492,198,0.069000," ","int((2*c*d*x+b*d)^(1/2)*(c*x^2+b*x+a)^(1/2),x)","\frac{\sqrt{\left(2 c x +b \right) d}\, \sqrt{c \,x^{2}+b x +a}\, \left(8 c^{4} x^{4}+16 b \,c^{3} x^{3}+8 a \,c^{3} x^{2}+10 b^{2} c^{2} x^{2}+16 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a^{2} c^{2} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-8 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a \,b^{2} c \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+8 a b \,c^{2} x +\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{4} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+2 b^{3} c x +2 a \,b^{2} c \right)}{10 \left(2 c^{2} x^{3}+3 b c \,x^{2}+2 a c x +b^{2} x +a b \right) c^{2}}"," ",0,"1/10*((2*c*x+b)*d)^(1/2)*(c*x^2+b*x+a)^(1/2)*(16*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*a^2*c^2-8*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*a*b^2*c+((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*b^4+8*c^4*x^4+16*b*c^3*x^3+8*a*c^3*x^2+10*b^2*c^2*x^2+8*a*b*c^2*x+2*b^3*c*x+2*a*b^2*c)/(2*c^2*x^3+3*b*c*x^2+2*a*c*x+b^2*x+a*b)/c^2","B"
1335,1,325,197,0.139000," ","int((c*x^2+b*x+a)^(1/2)/(2*c*d*x+b*d)^(3/2),x)","\frac{\sqrt{c \,x^{2}+b x +a}\, \sqrt{\left(2 c x +b \right) d}\, \left(-2 c^{2} x^{2}+4 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a c \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{2} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-2 b c x -2 a c \right)}{2 \left(2 c^{2} x^{3}+3 b c \,x^{2}+2 a c x +b^{2} x +a b \right) c^{2} d^{2}}"," ",0,"1/2*(c*x^2+b*x+a)^(1/2)*((2*c*x+b)*d)^(1/2)*(4*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*a*c*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)-EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*b^2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)-2*c^2*x^2-2*b*c*x-2*a*c)/d^2/(2*c^2*x^3+3*b*c*x^2+2*a*c*x+b^2*x+a*b)/c^2","A"
1336,1,874,239,0.114000," ","int((c*x^2+b*x+a)^(1/2)/(2*c*d*x+b*d)^(7/2),x)","\frac{\left(-16 c^{4} x^{4}+16 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a \,c^{3} x^{2} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-4 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{2} c^{2} x^{2} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-32 b \,c^{3} x^{3}+16 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a b \,c^{2} x \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-24 a \,c^{3} x^{2}-4 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{3} c x \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-18 b^{2} c^{2} x^{2}+4 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a \,b^{2} c \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-24 a b \,c^{2} x -\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{4} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-2 b^{3} c x -8 a^{2} c^{2}-2 a \,b^{2} c \right) \sqrt{\left(2 c x +b \right) d}}{10 \sqrt{c \,x^{2}+b x +a}\, \left(4 a c -b^{2}\right) \left(2 c x +b \right)^{3} c^{2} d^{4}}"," ",0,"1/10*(16*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^2*a*c^3*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)-4*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^2*b^2*c^2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)+16*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x*a*b*c^2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)-4*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x*b^3*c*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)+4*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*a*b^2*c-((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*b^4-16*c^4*x^4-32*b*c^3*x^3-24*a*c^3*x^2-18*b^2*c^2*x^2-24*a*b*c^2*x-2*b^3*c*x-8*a^2*c^2-2*a*b^2*c)*((2*c*x+b)*d)^(1/2)/d^4/(c*x^2+b*x+a)^(1/2)/(4*a*c-b^2)/(2*c*x+b)^3/c^2","B"
1337,1,1057,234,0.117000," ","int((2*c*d*x+b*d)^(7/2)*(c*x^2+b*x+a)^(3/2),x)","\frac{\sqrt{\left(2 c x +b \right) d}\, \sqrt{c \,x^{2}+b x +a}\, \left(9856 c^{9} x^{9}+44352 b \,c^{8} x^{8}+25088 a \,c^{8} x^{7}+82432 b^{2} c^{7} x^{7}+87808 a b \,c^{7} x^{6}+81536 b^{3} c^{6} x^{6}+16768 a^{2} c^{7} x^{5}+123328 a \,b^{2} c^{6} x^{5}+45736 b^{4} c^{5} x^{5}+41920 a^{2} b \,c^{6} x^{4}+88800 a \,b^{3} c^{5} x^{4}+13988 b^{5} c^{4} x^{4}-1024 a^{3} c^{6} x^{3}+42688 a^{2} b^{2} c^{5} x^{3}+33728 a \,b^{4} c^{4} x^{3}+1852 b^{6} c^{3} x^{3}-1536 a^{3} b \,c^{5} x^{2}+22112 a^{2} b^{3} c^{4} x^{2}+5696 a \,b^{5} c^{3} x^{2}-10 b^{7} c^{2} x^{2}-2560 a^{4} c^{5} x +1792 a^{3} b^{2} c^{4} x +4856 a^{2} b^{4} c^{3} x +140 a \,b^{6} c^{2} x -10 b^{8} c x -1280 a^{4} b \,c^{4}+1280 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, a^{4} c^{4} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+1152 a^{3} b^{3} c^{3}-1280 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, a^{3} b^{2} c^{3} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+140 a^{2} b^{5} c^{2}+480 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, a^{2} b^{4} c^{2} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-10 a \,b^{7} c -80 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, a \,b^{6} c \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+5 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, b^{8} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)\right) d^{3}}{4620 \left(2 c^{2} x^{3}+3 b c \,x^{2}+2 a c x +b^{2} x +a b \right) c^{3}}"," ",0,"1/4620*((2*c*x+b)*d)^(1/2)*(c*x^2+b*x+a)^(1/2)*d^3*(480*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*a^2*b^4*c^2+44352*x^8*b*c^8+25088*x^7*a*c^8+82432*x^7*b^2*c^7+81536*x^6*b^3*c^6+16768*x^5*a^2*c^7+45736*x^5*b^4*c^5+13988*x^4*b^5*c^4-1024*x^3*a^3*c^6+1852*x^3*b^6*c^3-10*x^2*b^7*c^2-2560*x*a^4*c^5-10*x*b^8*c-80*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*a*b^6*c-1280*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*a^3*b^2*c^3+9856*x^9*c^9+87808*x^6*a*b*c^7+123328*x^5*a*b^2*c^6+41920*x^4*a^2*b*c^6+88800*x^4*a*b^3*c^5+42688*x^3*a^2*b^2*c^5+33728*x^3*a*b^4*c^4-1280*a^4*b*c^4+1152*a^3*b^3*c^3+140*a^2*b^5*c^2-10*a*b^7*c-1536*x^2*a^3*b*c^5+22112*x^2*a^2*b^3*c^4+5696*x^2*a*b^5*c^3+1792*x*a^3*b^2*c^4+4856*x*a^2*b^4*c^3+140*x*a*b^6*c^2+5*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*b^8+1280*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*a^4*c^4)/c^3/(2*c^2*x^3+3*b*c*x^2+2*a*c*x+b^2*x+a*b)","B"
1338,1,796,193,0.163000," ","int((2*c*d*x+b*d)^(3/2)*(c*x^2+b*x+a)^(3/2),x)","-\frac{\sqrt{\left(2 c x +b \right) d}\, \sqrt{c \,x^{2}+b x +a}\, \left(-224 c^{7} x^{7}-784 b \,c^{6} x^{6}-640 a \,c^{6} x^{5}-1016 b^{2} c^{5} x^{5}-1600 a b \,c^{5} x^{4}-580 b^{3} c^{4} x^{4}-544 a^{2} c^{5} x^{3}-1328 a \,b^{2} c^{4} x^{3}-124 b^{4} c^{3} x^{3}-816 a^{2} b \,c^{4} x^{2}-392 a \,b^{3} c^{3} x^{2}+2 b^{5} c^{2} x^{2}-128 a^{3} c^{4} x -312 a^{2} b^{2} c^{3} x -20 a \,b^{4} c^{2} x +2 b^{6} c x -64 a^{3} b \,c^{3}+64 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, a^{3} c^{3} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-20 a^{2} b^{3} c^{2}-48 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, a^{2} b^{2} c^{2} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+2 a \,b^{5} c +12 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, a \,b^{4} c \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, b^{6} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)\right) d}{308 \left(2 c^{2} x^{3}+3 b c \,x^{2}+2 a c x +b^{2} x +a b \right) c^{3}}"," ",0,"-1/308*((2*c*x+b)*d)^(1/2)*(c*x^2+b*x+a)^(1/2)*d*(-224*c^7*x^7-784*b*c^6*x^6-640*a*c^6*x^5-1016*b^2*c^5*x^5+64*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*a^3*c^3-48*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*a^2*b^2*c^2+12*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*a*b^4*c-((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*b^6-1600*a*b*c^5*x^4-580*b^3*c^4*x^4-544*a^2*c^5*x^3-1328*a*b^2*c^4*x^3-124*b^4*c^3*x^3-816*a^2*b*c^4*x^2-392*a*b^3*c^3*x^2+2*b^5*c^2*x^2-128*a^3*c^4*x-312*a^2*b^2*c^3*x-20*a*b^4*c^2*x+2*b^6*c*x-64*a^3*b*c^3-20*a^2*b^3*c^2+2*a*b^5*c)/c^3/(2*c^2*x^3+3*b*c*x^2+2*a*c*x+b^2*x+a*b)","B"
1339,1,566,154,0.082000," ","int((c*x^2+b*x+a)^(3/2)/(2*c*d*x+b*d)^(1/2),x)","\frac{\sqrt{c \,x^{2}+b x +a}\, \sqrt{\left(2 c x +b \right) d}\, \left(8 c^{5} x^{5}+20 b \,c^{4} x^{4}+32 a \,c^{4} x^{3}+12 b^{2} c^{3} x^{3}+48 a b \,c^{3} x^{2}-2 b^{3} c^{2} x^{2}+24 a^{2} c^{3} x +12 a \,b^{2} c^{2} x -2 b^{4} c x +12 a^{2} b \,c^{2}+16 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, a^{2} c^{2} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-2 a \,b^{3} c -8 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, a \,b^{2} c \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, b^{4} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)\right)}{28 \left(2 c^{2} x^{3}+3 b c \,x^{2}+2 a c x +b^{2} x +a b \right) c^{3} d}"," ",0,"1/28*(c*x^2+b*x+a)^(1/2)*((2*c*x+b)*d)^(1/2)/d*(8*x^5*c^5+16*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*a^2*c^2-8*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*a*b^2*c+((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*b^4+20*x^4*b*c^4+32*x^3*a*c^4+12*x^3*b^2*c^3+48*a*b*c^3*x^2-2*b^3*c^2*x^2+24*a^2*c^3*x+12*a*b^2*c^2*x-2*x*b^4*c+12*a^2*b*c^2-2*a*b^3*c)/(2*c^2*x^3+3*b*c*x^2+2*a*c*x+b^2*x+a*b)/c^3","B"
1340,1,626,146,0.074000," ","int((c*x^2+b*x+a)^(3/2)/(2*c*d*x+b*d)^(5/2),x)","\frac{\left(4 c^{4} x^{4}+8 b \,c^{3} x^{3}+6 b^{2} c^{2} x^{2}+8 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, a \,c^{2} x \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+2 b^{3} c x -2 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, b^{2} c x \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-4 a^{2} c^{2}+2 a \,b^{2} c +4 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, a b c \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, b^{3} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)\right) \sqrt{\left(2 c x +b \right) d}}{12 \sqrt{c \,x^{2}+b x +a}\, \left(2 c x +b \right)^{2} c^{3} d^{3}}"," ",0,"1/12*(8*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*x*a*c^2-2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*x*b^2*c+4*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*a*b*c-((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*b^3+4*c^4*x^4+8*b*c^3*x^3+6*b^2*c^2*x^2+2*b^3*c*x-4*a^2*c^2+2*a*b^2*c)/d^3*((2*c*x+b)*d)^(1/2)/(c*x^2+b*x+a)^(1/2)/(2*c*x+b)^2/c^3","B"
1341,1,678,146,0.078000," ","int((c*x^2+b*x+a)^(3/2)/(2*c*d*x+b*d)^(9/2),x)","\frac{\sqrt{c \,x^{2}+b x +a}\, \sqrt{\left(2 c x +b \right) d}\, \left(-12 c^{4} x^{4}-24 b \,c^{3} x^{3}+8 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, c^{3} x^{3} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-16 a \,c^{3} x^{2}-14 b^{2} c^{2} x^{2}+12 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, b \,c^{2} x^{2} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-16 a b \,c^{2} x -2 b^{3} c x +6 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, b^{2} c x \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-4 a^{2} c^{2}-2 a \,b^{2} c +\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, b^{3} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)\right)}{28 \left(2 c^{2} x^{3}+3 b c \,x^{2}+2 a c x +b^{2} x +a b \right) \left(2 c x +b \right)^{3} c^{3} d^{5}}"," ",0,"1/28*(c*x^2+b*x+a)^(1/2)*((2*c*x+b)*d)^(1/2)*(8*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*x^3*c^3+12*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*x^2*b*c^2+6*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*x*b^2*c+((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*b^3-12*c^4*x^4-24*b*c^3*x^3-16*a*c^3*x^2-14*b^2*c^2*x^2-16*a*b*c^2*x-2*b^3*c*x-4*a^2*c^2-2*a*b^2*c)/d^5/(2*c^2*x^3+3*b*c*x^2+2*a*c*x+b^2*x+a*b)/(2*c*x+b)^3/c^3","B"
1342,1,1046,187,0.079000," ","int((c*x^2+b*x+a)^(3/2)/(2*c*d*x+b*d)^(13/2),x)","-\frac{\sqrt{c \,x^{2}+b x +a}\, \sqrt{\left(2 c x +b \right) d}\, \left(64 c^{6} x^{6}+192 b \,c^{5} x^{5}+32 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, c^{5} x^{5} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+272 a \,c^{5} x^{4}+172 b^{2} c^{4} x^{4}+80 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, b \,c^{4} x^{4} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+544 a b \,c^{4} x^{3}+24 b^{3} c^{3} x^{3}+80 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, b^{2} c^{3} x^{3} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+320 a^{2} c^{4} x^{2}+248 a \,b^{2} c^{3} x^{2}-22 b^{4} c^{2} x^{2}+40 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, b^{3} c^{2} x^{2} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+320 a^{2} b \,c^{3} x -24 a \,b^{3} c^{2} x -2 b^{5} c x +10 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, b^{4} c x \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+112 a^{3} c^{3}-4 a^{2} b^{2} c^{2}-2 a \,b^{4} c +\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, b^{5} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)\right)}{308 \left(2 c^{2} x^{3}+3 b c \,x^{2}+2 a c x +b^{2} x +a b \right) \left(2 c x +b \right)^{5} \left(4 a c -b^{2}\right) c^{3} d^{7}}"," ",0,"-1/308*(c*x^2+b*x+a)^(1/2)*((2*c*x+b)*d)^(1/2)*(32*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*x^5*c^5+80*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*x^4*b*c^4+80*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*x^3*b^2*c^3+40*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*x^2*b^3*c^2+64*c^6*x^6+10*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*x*b^4*c+192*b*c^5*x^5+((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*b^5+272*a*c^5*x^4+172*b^2*c^4*x^4+544*a*b*c^4*x^3+24*b^3*c^3*x^3+320*a^2*c^4*x^2+248*a*b^2*c^3*x^2-22*b^4*c^2*x^2+320*a^2*b*c^3*x-24*a*b^3*c^2*x-2*b^5*c*x+112*a^3*c^3-4*a^2*b^2*c^2-2*a*b^4*c)/d^7/(2*c^2*x^3+3*b*c*x^2+2*a*c*x+b^2*x+a*b)/(2*c*x+b)^5/(4*a*c-b^2)/c^3","B"
1343,1,1431,228,0.122000," ","int((c*x^2+b*x+a)^(3/2)/(2*c*d*x+b*d)^(17/2),x)","\frac{\sqrt{c \,x^{2}+b x +a}\, \sqrt{\left(2 c x +b \right) d}\, \left(1280 c^{8} x^{8}+5120 b \,c^{7} x^{7}+640 \sqrt{-4 a c +b^{2}}\, \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, c^{7} x^{7} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+512 a \,c^{7} x^{6}+8832 b^{2} c^{6} x^{6}+2240 \sqrt{-4 a c +b^{2}}\, \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b \,c^{6} x^{6} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+1536 a b \,c^{6} x^{5}+8576 b^{3} c^{5} x^{5}+3360 \sqrt{-4 a c +b^{2}}\, \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{2} c^{5} x^{5} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-8384 a^{2} c^{6} x^{4}+6112 a \,b^{2} c^{5} x^{4}+4596 b^{4} c^{4} x^{4}+2800 \sqrt{-4 a c +b^{2}}\, \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{3} c^{4} x^{4} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-16768 a^{2} b \,c^{5} x^{3}+9664 a \,b^{3} c^{4} x^{3}+872 b^{5} c^{3} x^{3}+1400 \sqrt{-4 a c +b^{2}}\, \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{4} c^{3} x^{3} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-12544 a^{3} c^{5} x^{2}-3168 a^{2} b^{2} c^{4} x^{2}+4416 a \,b^{4} c^{3} x^{2}-150 b^{6} c^{2} x^{2}+420 \sqrt{-4 a c +b^{2}}\, \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{5} c^{2} x^{2} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-12544 a^{3} b \,c^{4} x +5216 a^{2} b^{3} c^{3} x -160 a \,b^{5} c^{2} x -10 b^{7} c x +70 \sqrt{-4 a c +b^{2}}\, \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{6} c x \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-4928 a^{4} c^{4}+1792 a^{3} b^{2} c^{3}-20 a^{2} b^{4} c^{2}-10 a \,b^{6} c +5 \sqrt{-4 a c +b^{2}}\, \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{7} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)\right)}{4620 \left(2 c^{2} x^{3}+3 b c \,x^{2}+2 a c x +b^{2} x +a b \right) \left(2 c x +b \right)^{7} \left(4 a c -b^{2}\right)^{2} c^{3} d^{9}}"," ",0,"1/4620*(c*x^2+b*x+a)^(1/2)*((2*c*x+b)*d)^(1/2)*(5*(-4*a*c+b^2)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*b^7+1792*a^3*b^2*c^3-20*a^2*b^4*c^2-10*a*b^6*c-4928*a^4*c^4+70*(-4*a*c+b^2)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x*b^6*c+1400*(-4*a*c+b^2)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^3*b^4*c^3+420*(-4*a*c+b^2)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^2*b^5*c^2+2240*(-4*a*c+b^2)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^6*b*c^6+3360*(-4*a*c+b^2)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^5*b^2*c^5+2800*(-4*a*c+b^2)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^4*b^3*c^4+8576*x^5*b^3*c^5-150*x^2*b^6*c^2-10*x*b^7*c+8832*x^6*b^2*c^6+5120*x^7*b*c^7+872*x^3*b^5*c^3+4596*x^4*b^4*c^4+512*x^6*a*c^7-8384*x^4*a^2*c^6-12544*x^2*a^3*c^5+1280*x^8*c^8-160*x*a*b^5*c^2+1536*x^5*a*b*c^6+6112*x^4*a*b^2*c^5-16768*x^3*a^2*b*c^5+9664*x^3*a*b^3*c^4-3168*x^2*a^2*b^2*c^4+4416*x^2*a*b^4*c^3-12544*x*a^3*b*c^4+5216*x*a^2*b^3*c^3+640*(-4*a*c+b^2)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^7*c^7)/d^9/(2*c^2*x^3+3*b*c*x^2+2*a*c*x+b^2*x+a*b)/(2*c*x+b)^7/c^3/(4*a*c-b^2)^2","B"
1344,1,938,276,0.080000," ","int((2*c*d*x+b*d)^(5/2)*(c*x^2+b*x+a)^(3/2),x)","-\frac{\sqrt{\left(2 c x +b \right) d}\, \sqrt{c \,x^{2}+b x +a}\, \left(-960 c^{8} x^{8}-3840 b \,c^{7} x^{7}-2560 a \,c^{7} x^{6}-6080 b^{2} c^{6} x^{6}-7680 a b \,c^{6} x^{5}-4800 b^{3} c^{5} x^{5}-1856 a^{2} c^{6} x^{4}-8672 a \,b^{2} c^{5} x^{4}-1916 b^{4} c^{4} x^{4}-3712 a^{2} b \,c^{5} x^{3}-4544 a \,b^{3} c^{4} x^{3}-312 b^{5} c^{3} x^{3}-256 a^{3} c^{5} x^{2}-2592 a^{2} b^{2} c^{4} x^{2}-1056 a \,b^{4} c^{3} x^{2}+10 b^{6} c^{2} x^{2}+768 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a^{4} c^{4} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-768 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a^{3} b^{2} c^{3} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-256 a^{3} b \,c^{4} x +288 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a^{2} b^{4} c^{2} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-736 a^{2} b^{3} c^{3} x -48 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a \,b^{6} c \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-64 a \,b^{5} c^{2} x +3 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{8} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+6 b^{7} c x -64 a^{3} b^{2} c^{3}-68 a^{2} b^{4} c^{2}+6 a \,b^{6} c \right) d^{2}}{780 \left(2 c^{2} x^{3}+3 b c \,x^{2}+2 a c x +b^{2} x +a b \right) c^{3}}"," ",0,"-1/780*((2*c*x+b)*d)^(1/2)*(c*x^2+b*x+a)^(1/2)*d^2*(3*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*b^8+768*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*a^4*c^4-64*a^3*b^2*c^3-68*a^2*b^4*c^2+6*a*b^6*c-4800*b^3*c^5*x^5+10*b^6*c^2*x^2+6*b^7*c*x-6080*b^2*c^6*x^6-3840*b*c^7*x^7-312*b^5*c^3*x^3-1916*b^4*c^4*x^4-2560*a*c^7*x^6-1856*a^2*c^6*x^4-256*a^3*c^5*x^2-960*c^8*x^8-64*a*b^5*c^2*x-7680*a*b*c^6*x^5-8672*a*b^2*c^5*x^4-3712*a^2*b*c^5*x^3-4544*a*b^3*c^4*x^3-2592*a^2*b^2*c^4*x^2-1056*a*b^4*c^3*x^2-256*a^3*b*c^4*x-736*a^2*b^3*c^3*x-48*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*a*b^6*c-768*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*a^3*b^2*c^3+288*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*a^2*b^4*c^2)/c^3/(2*c^2*x^3+3*b*c*x^2+2*a*c*x+b^2*x+a*b)","B"
1345,1,700,237,0.075000," ","int((2*c*d*x+b*d)^(1/2)*(c*x^2+b*x+a)^(3/2),x)","\frac{\sqrt{\left(2 c x +b \right) d}\, \sqrt{c \,x^{2}+b x +a}\, \left(80 c^{6} x^{6}+240 b \,c^{5} x^{5}+256 a \,c^{5} x^{4}+236 b^{2} c^{4} x^{4}+512 a b \,c^{4} x^{3}+72 b^{3} c^{3} x^{3}+176 a^{2} c^{4} x^{2}+296 a \,b^{2} c^{3} x^{2}-10 b^{4} c^{2} x^{2}+192 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a^{3} c^{3} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-144 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a^{2} b^{2} c^{2} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+176 a^{2} b \,c^{3} x +36 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a \,b^{4} c \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+40 a \,b^{3} c^{2} x -3 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{6} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-6 b^{5} c x +44 a^{2} b^{2} c^{2}-6 a \,b^{4} c \right)}{180 \left(2 c^{2} x^{3}+3 b c \,x^{2}+2 a c x +b^{2} x +a b \right) c^{3}}"," ",0,"1/180*((2*c*x+b)*d)^(1/2)*(c*x^2+b*x+a)^(1/2)*(80*c^6*x^6+240*b*c^5*x^5+192*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*a^3*c^3-144*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*a^2*b^2*c^2+36*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*a*b^4*c-3*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*b^6+256*a*c^5*x^4+236*b^2*c^4*x^4+512*a*b*c^4*x^3+72*b^3*c^3*x^3+176*a^2*c^4*x^2+296*a*b^2*c^3*x^2-10*b^4*c^2*x^2+176*a^2*b*c^3*x+40*a*b^3*c^2*x-6*b^5*c*x+44*a^2*b^2*c^2-6*a*b^4*c)/c^3/(2*c^2*x^3+3*b*c*x^2+2*a*c*x+b^2*x+a*b)","B"
1346,1,504,229,0.086000," ","int((c*x^2+b*x+a)^(3/2)/(2*c*d*x+b*d)^(3/2),x)","\frac{\sqrt{c \,x^{2}+b x +a}\, \sqrt{\left(2 c x +b \right) d}\, \left(4 c^{4} x^{4}+8 b \,c^{3} x^{3}-16 a \,c^{3} x^{2}+10 b^{2} c^{2} x^{2}+48 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a^{2} c^{2} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-24 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a \,b^{2} c \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-16 a b \,c^{2} x +3 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{4} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+6 b^{3} c x -20 a^{2} c^{2}+6 a \,b^{2} c \right)}{20 \left(2 c^{2} x^{3}+3 b c \,x^{2}+2 a c x +b^{2} x +a b \right) c^{3} d^{2}}"," ",0,"1/20*(c*x^2+b*x+a)^(1/2)*((2*c*x+b)*d)^(1/2)*(48*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*a^2*c^2-24*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*a*b^2*c+3*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*b^4+4*c^4*x^4+8*b*c^3*x^3-16*a*c^3*x^2+10*b^2*c^2*x^2-16*a*b*c^2*x+6*b^3*c*x-20*a^2*c^2+6*a*b^2*c)/d^2/(2*c^2*x^3+3*b*c*x^2+2*a*c*x+b^2*x+a*b)/c^3","B"
1347,1,893,229,0.086000," ","int((c*x^2+b*x+a)^(3/2)/(2*c*d*x+b*d)^(7/2),x)","\frac{\sqrt{c \,x^{2}+b x +a}\, \sqrt{\left(2 c x +b \right) d}\, \left(-28 c^{4} x^{4}+48 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a \,c^{3} x^{2} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-12 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{2} c^{2} x^{2} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-56 b \,c^{3} x^{3}+48 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a b \,c^{2} x \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-32 a \,c^{3} x^{2}-12 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{3} c x \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-34 b^{2} c^{2} x^{2}+12 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a \,b^{2} c \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-32 a b \,c^{2} x -3 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{4} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-6 b^{3} c x -4 a^{2} c^{2}-6 a \,b^{2} c \right)}{20 \left(2 c^{2} x^{3}+3 b c \,x^{2}+2 a c x +b^{2} x +a b \right) \left(2 c x +b \right)^{2} c^{3} d^{4}}"," ",0,"1/20*(c*x^2+b*x+a)^(1/2)*((2*c*x+b)*d)^(1/2)*(48*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^2*a*c^3*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)-12*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^2*b^2*c^2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)+48*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x*a*b*c^2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)-12*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x*b^3*c*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)+12*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*a*b^2*c-3*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*b^4-28*c^4*x^4-56*b*c^3*x^3-32*a*c^3*x^2-34*b^2*c^2*x^2-32*a*b*c^2*x-6*b^3*c*x-4*a^2*c^2-6*a*b^2*c)/d^4/(2*c^2*x^3+3*b*c*x^2+2*a*c*x+b^2*x+a*b)/(2*c*x+b)^2/c^3","B"
1348,1,1501,270,0.125000," ","int((c*x^2+b*x+a)^(3/2)/(2*c*d*x+b*d)^(11/2),x)","\frac{\sqrt{c \,x^{2}+b x +a}\, \sqrt{\left(2 c x +b \right) d}\, \left(-192 c^{6} x^{6}+192 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a \,c^{5} x^{4} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-48 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{2} c^{4} x^{4} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-576 b \,c^{5} x^{5}+384 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a b \,c^{4} x^{3} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-368 a \,c^{5} x^{4}-96 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{3} c^{3} x^{3} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-628 b^{2} c^{4} x^{4}+288 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a \,b^{2} c^{3} x^{2} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-736 a b \,c^{4} x^{3}-72 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{4} c^{2} x^{2} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-296 b^{3} c^{3} x^{3}-256 a^{2} c^{4} x^{2}+96 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a \,b^{3} c^{2} x \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-424 a \,b^{2} c^{3} x^{2}-24 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{5} c x \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-58 b^{4} c^{2} x^{2}-256 a^{2} b \,c^{3} x +12 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a \,b^{4} c \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-56 a \,b^{3} c^{2} x -3 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{6} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-6 b^{5} c x -80 a^{3} c^{3}-4 a^{2} b^{2} c^{2}-6 a \,b^{4} c \right)}{180 \left(2 c^{2} x^{3}+3 b c \,x^{2}+2 a c x +b^{2} x +a b \right) \left(2 c x +b \right)^{4} \left(4 a c -b^{2}\right) c^{3} d^{6}}"," ",0,"1/180*(c*x^2+b*x+a)^(1/2)*((2*c*x+b)*d)^(1/2)*(-3*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*b^6-424*a*b^2*c^3*x^2-256*a^2*b*c^3*x-576*b*c^5*x^5-56*a*b^3*c^2*x-736*a*b*c^4*x^3+384*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^3*a*b*c^4*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)+288*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^2*a*b^2*c^3*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)-256*a^2*c^4*x^2-58*b^4*c^2*x^2-6*b^5*c*x-6*a*b^4*c-4*a^2*b^2*c^2+192*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^4*a*c^5*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)-48*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^4*b^2*c^4*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)-96*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^3*b^3*c^3*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)-72*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^2*b^4*c^2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)-368*a*c^5*x^4-628*b^2*c^4*x^4-296*b^3*c^3*x^3-192*c^6*x^6+96*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x*a*b^3*c^2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)-80*a^3*c^3-24*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x*b^5*c*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)+12*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*a*b^4*c)/d^6/(2*c^2*x^3+3*b*c*x^2+2*a*c*x+b^2*x+a*b)/(2*c*x+b)^4/(4*a*c-b^2)/c^3","B"
1349,1,1344,275,0.131000," ","int((2*c*d*x+b*d)^(7/2)*(c*x^2+b*x+a)^(5/2),x)","\frac{\sqrt{\left(2 c x +b \right) d}\, \sqrt{c \,x^{2}+b x +a}\, \left(59136 c^{11} x^{11}+325248 b \,c^{10} x^{10}+216832 a \,c^{10} x^{9}+758912 b^{2} c^{9} x^{9}+975744 a b \,c^{9} x^{8}+975744 b^{3} c^{8} x^{8}+277760 a^{2} c^{9} x^{7}+1812608 a \,b^{2} c^{8} x^{7}+749168 b^{4} c^{7} x^{7}+972160 a^{2} b \,c^{8} x^{6}+1790656 a \,b^{3} c^{7} x^{6}+345352 b^{5} c^{6} x^{6}+126208 a^{3} c^{8} x^{5}+1363584 a^{2} b^{2} c^{7} x^{5}+1002096 a \,b^{4} c^{6} x^{5}+89168 b^{6} c^{5} x^{5}+315520 a^{3} b \,c^{7} x^{4}+978560 a^{2} b^{3} c^{6} x^{4}+305336 a \,b^{5} c^{5} x^{4}+10036 b^{7} c^{4} x^{4}-4096 a^{4} c^{7} x^{3}+319616 a^{3} b^{2} c^{6} x^{3}+369424 a^{2} b^{4} c^{5} x^{3}+40208 a \,b^{6} c^{4} x^{3}-4 b^{8} c^{3} x^{3}-6144 a^{4} b \,c^{6} x^{2}+163904 a^{3} b^{3} c^{5} x^{2}+61656 a^{2} b^{5} c^{4} x^{2}-192 a \,b^{7} c^{3} x^{2}+10 b^{9} c^{2} x^{2}-10240 a^{5} c^{6} x +9728 a^{4} b^{2} c^{5} x +36112 a^{3} b^{4} c^{4} x +1248 a^{2} b^{6} c^{3} x -180 a \,b^{8} c^{2} x +10 b^{10} c x -5120 a^{5} b \,c^{5}+5120 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, a^{5} c^{5} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+5888 a^{4} b^{3} c^{4}-6400 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, a^{4} b^{2} c^{4} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+1256 a^{3} b^{5} c^{3}+3200 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, a^{3} b^{4} c^{3} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-180 a^{2} b^{7} c^{2}-800 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, a^{2} b^{6} c^{2} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+10 a \,b^{9} c +100 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, a \,b^{8} c \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-5 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, b^{10} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)\right) d^{3}}{35112 \left(2 c^{2} x^{3}+3 b c \,x^{2}+2 a c x +b^{2} x +a b \right) c^{4}}"," ",0,"1/35112*((2*c*x+b)*d)^(1/2)*(c*x^2+b*x+a)^(1/2)*d^3*(59136*x^11*c^11+216832*x^9*a*c^10+758912*x^9*b^2*c^9+975744*x^8*b^3*c^8-5120*a^5*b*c^5+5888*a^4*b^3*c^4+1256*a^3*b^5*c^3-180*a^2*b^7*c^2+10*a*b^9*c+325248*x^10*b*c^10+305336*x^4*a*b^5*c^5+319616*x^3*a^3*b^2*c^6+369424*x^3*a^2*b^4*c^5+40208*x^3*a*b^6*c^4-6144*x^2*a^4*b*c^6+163904*x^2*a^3*b^3*c^5+61656*x^2*a^2*b^5*c^4-192*x^2*a*b^7*c^3+9728*x*a^4*b^2*c^5+36112*x*a^3*b^4*c^4+1248*x*a^2*b^6*c^3-180*x*a*b^8*c^2+3200*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*a^3*b^4*c^3-800*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*a^2*b^6*c^2+100*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*a*b^8*c+277760*x^7*a^2*c^9+749168*x^7*b^4*c^7+345352*x^6*b^5*c^6+126208*x^5*a^3*c^8+89168*x^5*b^6*c^5+10036*x^4*b^7*c^4-4096*x^3*a^4*c^7-4*x^3*b^8*c^3+10*x^2*b^9*c^2-10240*x*a^5*c^6+10*x*b^10*c+975744*x^8*a*b*c^9+1812608*x^7*a*b^2*c^8+972160*x^6*a^2*b*c^8+1790656*x^6*a*b^3*c^7+1363584*x^5*a^2*b^2*c^7+1002096*x^5*a*b^4*c^6+315520*x^4*a^3*b*c^7+978560*x^4*a^2*b^3*c^6-6400*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*a^4*b^2*c^4+5120*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*a^5*c^5-5*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*b^10)/c^4/(2*c^2*x^3+3*b*c*x^2+2*a*c*x+b^2*x+a*b)","B"
1350,1,1055,234,0.082000," ","int((2*c*d*x+b*d)^(3/2)*(c*x^2+b*x+a)^(5/2),x)","-\frac{\sqrt{\left(2 c x +b \right) d}\, \sqrt{c \,x^{2}+b x +a}\, \left(-4928 c^{9} x^{9}-22176 b \,c^{8} x^{8}-19264 a \,c^{8} x^{7}-39536 b^{2} c^{7} x^{7}-67424 a b \,c^{7} x^{6}-34888 b^{3} c^{6} x^{6}-27584 a^{2} c^{7} x^{5}-87344 a \,b^{2} c^{6} x^{5}-15248 b^{4} c^{5} x^{5}-68960 a^{2} b \,c^{6} x^{4}-49800 a \,b^{3} c^{5} x^{4}-2644 b^{5} c^{4} x^{4}-15808 a^{3} c^{6} x^{3}-57104 a^{2} b^{2} c^{5} x^{3}-10624 a \,b^{4} c^{4} x^{3}+4 b^{6} c^{3} x^{3}-23712 a^{3} b \,c^{5} x^{2}-16696 a^{2} b^{3} c^{4} x^{2}+152 a \,b^{5} c^{3} x^{2}-10 b^{7} c^{2} x^{2}-2560 a^{4} c^{5} x -9296 a^{3} b^{2} c^{4} x -688 a^{2} b^{4} c^{3} x +140 a \,b^{6} c^{2} x -10 b^{8} c x -1280 a^{4} b \,c^{4}+1280 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, a^{4} c^{4} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-696 a^{3} b^{3} c^{3}-1280 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, a^{3} b^{2} c^{3} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+140 a^{2} b^{5} c^{2}+480 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, a^{2} b^{4} c^{2} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-10 a \,b^{7} c -80 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, a \,b^{6} c \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+5 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, b^{8} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)\right) d}{9240 \left(2 c^{2} x^{3}+3 b c \,x^{2}+2 a c x +b^{2} x +a b \right) c^{4}}"," ",0,"-1/9240*((2*c*x+b)*d)^(1/2)*(c*x^2+b*x+a)^(1/2)*d*(-19264*x^7*a*c^8-27584*x^5*a^2*c^7-15248*x^5*b^4*c^5-15808*x^3*a^3*c^6+4*x^3*b^6*c^3-2560*x*a^4*c^5+5*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*b^8-22176*b*c^8*x^8+480*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*a^2*b^4*c^2-80*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*a*b^6*c-1280*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*a^3*b^2*c^3-39536*b^2*c^7*x^7-34888*b^3*c^6*x^6-2644*b^5*c^4*x^4-10*b^7*c^2*x^2-10*b^8*c*x-4928*x^9*c^9-67424*a*b*c^7*x^6-87344*a*b^2*c^6*x^5-57104*a^2*b^2*c^5*x^3-10624*a*b^4*c^4*x^3-68960*x^4*a^2*b*c^6-49800*x^4*a*b^3*c^5-23712*x^2*a^3*b*c^5+152*x^2*a*b^5*c^3-9296*x*a^3*b^2*c^4+140*x*a*b^6*c^2-1280*a^4*b*c^4-696*a^3*b^3*c^3+140*a^2*b^5*c^2-10*a*b^7*c-16696*a^2*b^3*c^4*x^2-688*a^2*b^4*c^3*x+1280*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*a^4*c^4)/c^4/(2*c^2*x^3+3*b*c*x^2+2*a*c*x+b^2*x+a*b)","B"
1351,1,798,195,0.087000," ","int((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^(1/2),x)","\frac{\sqrt{c \,x^{2}+b x +a}\, \sqrt{\left(2 c x +b \right) d}\, \left(112 c^{7} x^{7}+392 b \,c^{6} x^{6}+496 a \,c^{6} x^{5}+464 b^{2} c^{5} x^{5}+1240 a b \,c^{5} x^{4}+180 b^{3} c^{4} x^{4}+976 a^{2} c^{5} x^{3}+752 a \,b^{2} c^{4} x^{3}-4 b^{4} c^{3} x^{3}+1464 a^{2} b \,c^{4} x^{2}-112 a \,b^{3} c^{3} x^{2}+10 b^{5} c^{2} x^{2}+592 a^{3} c^{4} x +288 a^{2} b^{2} c^{3} x -100 a \,b^{4} c^{2} x +10 b^{6} c x +296 a^{3} b \,c^{3}+320 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, a^{3} c^{3} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-100 a^{2} b^{3} c^{2}-240 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, a^{2} b^{2} c^{2} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+10 a \,b^{5} c +60 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, a \,b^{4} c \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-5 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, b^{6} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)\right)}{616 \left(2 c^{2} x^{3}+3 b c \,x^{2}+2 a c x +b^{2} x +a b \right) c^{4} d}"," ",0,"1/616*(c*x^2+b*x+a)^(1/2)*((2*c*x+b)*d)^(1/2)/d*(112*c^7*x^7+392*b*c^6*x^6+496*a*c^6*x^5+464*b^2*c^5*x^5+320*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*a^3*c^3-240*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*a^2*b^2*c^2+60*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*a*b^4*c-5*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*b^6+1240*a*b*c^5*x^4+180*b^3*c^4*x^4+976*a^2*c^5*x^3+752*a*b^2*c^4*x^3-4*b^4*c^3*x^3+1464*a^2*b*c^4*x^2-112*a*b^3*c^3*x^2+10*b^5*c^2*x^2+592*a^3*c^4*x+288*a^2*b^2*c^3*x-100*a*b^4*c^2*x+10*b^6*c*x+296*a^3*b*c^3-100*a^2*b^3*c^2+10*a*b^5*c)/c^4/(2*c^2*x^3+3*b*c*x^2+2*a*c*x+b^2*x+a*b)","B"
1352,1,1000,185,0.086000," ","int((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^(5/2),x)","\frac{\left(24 c^{6} x^{6}+72 b \,c^{5} x^{5}+152 a \,c^{5} x^{4}+52 b^{2} c^{4} x^{4}+304 a b \,c^{4} x^{3}-16 b^{3} c^{3} x^{3}+72 a^{2} c^{4} x^{2}+192 a \,b^{2} c^{3} x^{2}-30 b^{4} c^{2} x^{2}+72 a^{2} b \,c^{3} x +160 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, a^{2} c^{3} x \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+40 a \,b^{3} c^{2} x -80 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, a \,b^{2} c^{2} x \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-10 b^{5} c x +10 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, b^{4} c x \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-56 a^{3} c^{3}+60 a^{2} b^{2} c^{2}+80 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, a^{2} b \,c^{2} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-10 a \,b^{4} c -40 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, a \,b^{3} c \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+5 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, b^{5} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)\right) \sqrt{\left(2 c x +b \right) d}}{168 \sqrt{c \,x^{2}+b x +a}\, \left(2 c x +b \right)^{2} c^{4} d^{3}}"," ",0,"1/168*(24*c^6*x^6+160*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*x*a^2*c^3-80*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*x*a*b^2*c^2+10*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*x*b^4*c+72*b*c^5*x^5+80*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*a^2*b*c^2-40*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*a*b^3*c+5*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*b^5+152*a*c^5*x^4+52*b^2*c^4*x^4+304*a*b*c^4*x^3-16*b^3*c^3*x^3+72*a^2*c^4*x^2+192*a*b^2*c^3*x^2-30*b^4*c^2*x^2+72*a^2*b*c^3*x+40*a*b^3*c^2*x-10*b^5*c*x-56*a^3*c^3+60*a^2*b^2*c^2-10*a*b^4*c)/d^3*((2*c*x+b)*d)^(1/2)/(c*x^2+b*x+a)^(1/2)/(2*c*x+b)^2/c^4","B"
1353,1,1310,177,0.087000," ","int((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^(9/2),x)","\frac{\sqrt{c \,x^{2}+b x +a}\, \sqrt{\left(2 c x +b \right) d}\, \left(56 c^{6} x^{6}+168 b \,c^{5} x^{5}-72 a \,c^{5} x^{4}+228 b^{2} c^{4} x^{4}-144 a b \,c^{4} x^{3}+160 \sqrt{-4 a c +b^{2}}\, \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a \,c^{4} x^{3} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+176 b^{3} c^{3} x^{3}-40 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, b^{2} c^{3} x^{3} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-152 a^{2} c^{4} x^{2}-32 a \,b^{2} c^{3} x^{2}+240 \sqrt{-4 a c +b^{2}}\, \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a b \,c^{3} x^{2} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+70 b^{4} c^{2} x^{2}-60 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, b^{3} c^{2} x^{2} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-152 a^{2} b \,c^{3} x +40 a \,b^{3} c^{2} x +120 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, a \,b^{2} c^{2} x \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+10 b^{5} c x -30 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, b^{4} c x \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-24 a^{3} c^{3}-20 a^{2} b^{2} c^{2}+10 a \,b^{4} c +20 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, a \,b^{3} c \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-5 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, b^{5} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)\right)}{168 \left(2 c^{2} x^{3}+3 b c \,x^{2}+2 a c x +b^{2} x +a b \right) \left(2 c x +b \right)^{3} c^{4} d^{5}}"," ",0,"1/168*(c*x^2+b*x+a)^(1/2)*((2*c*x+b)*d)^(1/2)*(160*(-4*a*c+b^2)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^3*a*c^4-40*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*x^3*b^2*c^3+240*(-4*a*c+b^2)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^2*a*b*c^3-60*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*x^2*b^3*c^2+56*c^6*x^6+120*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*x*a*b^2*c^2-30*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*x*b^4*c+168*b*c^5*x^5+20*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*a*b^3*c-5*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*b^5-72*a*c^5*x^4+228*b^2*c^4*x^4-144*a*b*c^4*x^3+176*b^3*c^3*x^3-152*a^2*c^4*x^2-32*a*b^2*c^3*x^2+70*b^4*c^2*x^2-152*a^2*b*c^3*x+40*a*b^3*c^2*x+10*b^5*c*x-24*a^3*c^3-20*a^2*b^2*c^2+10*a*b^4*c)/d^5/(2*c^2*x^3+3*b*c*x^2+2*a*c*x+b^2*x+a*b)/(2*c*x+b)^3/c^4","B"
1354,1,1035,177,0.087000," ","int((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^(13/2),x)","\frac{\sqrt{c \,x^{2}+b x +a}\, \sqrt{\left(2 c x +b \right) d}\, \left(-296 c^{6} x^{6}-888 b \,c^{5} x^{5}+160 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, c^{5} x^{5} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-488 a \,c^{5} x^{4}-988 b^{2} c^{4} x^{4}+400 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, b \,c^{4} x^{4} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-976 a b \,c^{4} x^{3}-496 b^{3} c^{3} x^{3}+400 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, b^{2} c^{3} x^{3} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-248 a^{2} c^{4} x^{2}-608 a \,b^{2} c^{3} x^{2}-110 b^{4} c^{2} x^{2}+200 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, b^{3} c^{2} x^{2} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-248 a^{2} b \,c^{3} x -120 a \,b^{3} c^{2} x -10 b^{5} c x +50 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, b^{4} c x \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-56 a^{3} c^{3}-20 a^{2} b^{2} c^{2}-10 a \,b^{4} c +5 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, b^{5} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)\right)}{616 \left(2 c^{2} x^{3}+3 b c \,x^{2}+2 a c x +b^{2} x +a b \right) \left(2 c x +b \right)^{5} c^{4} d^{7}}"," ",0,"1/616*(c*x^2+b*x+a)^(1/2)*((2*c*x+b)*d)^(1/2)*(160*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*x^5*c^5+400*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*x^4*b*c^4+400*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*x^3*b^2*c^3+200*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*x^2*b^3*c^2-296*c^6*x^6+50*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*x*b^4*c-888*b*c^5*x^5+5*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*b^5-488*a*c^5*x^4-988*b^2*c^4*x^4-976*a*b*c^4*x^3-496*b^3*c^3*x^3-248*a^2*c^4*x^2-608*a*b^2*c^3*x^2-110*b^4*c^2*x^2-248*a^2*b*c^3*x-120*a*b^3*c^2*x-10*b^5*c*x-56*a^3*c^3-20*a^2*b^2*c^2-10*a*b^4*c)/d^7/(2*c^2*x^3+3*b*c*x^2+2*a*c*x+b^2*x+a*b)/(2*c*x+b)^5/c^4","B"
1355,1,1431,218,0.086000," ","int((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^(17/2),x)","-\frac{\sqrt{c \,x^{2}+b x +a}\, \sqrt{\left(2 c x +b \right) d}\, \left(1280 c^{8} x^{8}+5120 b \,c^{7} x^{7}+640 \sqrt{-4 a c +b^{2}}\, \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, c^{7} x^{7} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+7904 a \,c^{7} x^{6}+6984 b^{2} c^{6} x^{6}+2240 \sqrt{-4 a c +b^{2}}\, \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b \,c^{6} x^{6} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+23712 a b \,c^{6} x^{5}+3032 b^{3} c^{5} x^{5}+3360 \sqrt{-4 a c +b^{2}}\, \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{2} c^{5} x^{5} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+13792 a^{2} c^{6} x^{4}+22744 a \,b^{2} c^{5} x^{4}-948 b^{4} c^{4} x^{4}+2800 \sqrt{-4 a c +b^{2}}\, \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{3} c^{4} x^{4} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+27584 a^{2} b \,c^{5} x^{3}+5968 a \,b^{3} c^{4} x^{3}-976 b^{5} c^{3} x^{3}+1400 \sqrt{-4 a c +b^{2}}\, \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{4} c^{3} x^{3} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+9632 a^{3} c^{5} x^{2}+13464 a^{2} b^{2} c^{4} x^{2}-1128 a \,b^{4} c^{3} x^{2}-150 b^{6} c^{2} x^{2}+420 \sqrt{-4 a c +b^{2}}\, \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{5} c^{2} x^{2} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+9632 a^{3} b \,c^{4} x -328 a^{2} b^{3} c^{3} x -160 a \,b^{5} c^{2} x -10 b^{7} c x +70 \sqrt{-4 a c +b^{2}}\, \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{6} c x \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+2464 a^{4} c^{4}-56 a^{3} b^{2} c^{3}-20 a^{2} b^{4} c^{2}-10 a \,b^{6} c +5 \sqrt{-4 a c +b^{2}}\, \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{7} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)\right)}{9240 \left(2 c^{2} x^{3}+3 b c \,x^{2}+2 a c x +b^{2} x +a b \right) \left(2 c x +b \right)^{7} \left(4 a c -b^{2}\right) c^{4} d^{9}}"," ",0,"-1/9240*(c*x^2+b*x+a)^(1/2)*((2*c*x+b)*d)^(1/2)*(5*(-4*a*c+b^2)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*b^7-56*a^3*b^2*c^3-20*a^2*b^4*c^2-10*a*b^6*c+2464*a^4*c^4+70*(-4*a*c+b^2)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x*b^6*c+1400*(-4*a*c+b^2)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^3*b^4*c^3+420*(-4*a*c+b^2)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^2*b^5*c^2+2240*(-4*a*c+b^2)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^6*b*c^6+3360*(-4*a*c+b^2)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^5*b^2*c^5+2800*(-4*a*c+b^2)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^4*b^3*c^4+3032*b^3*c^5*x^5-150*b^6*c^2*x^2-10*b^7*c*x+6984*b^2*c^6*x^6+5120*b*c^7*x^7-976*b^5*c^3*x^3-948*b^4*c^4*x^4+7904*a*c^7*x^6+13792*a^2*c^6*x^4+9632*a^3*c^5*x^2+1280*c^8*x^8-160*a*b^5*c^2*x+23712*a*b*c^6*x^5+22744*a*b^2*c^5*x^4+27584*a^2*b*c^5*x^3+5968*a*b^3*c^4*x^3+13464*a^2*b^2*c^4*x^2-1128*a*b^4*c^3*x^2+9632*a^3*b*c^4*x-328*a^2*b^3*c^3*x+640*(-4*a*c+b^2)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^7*c^7)/d^9/(2*c^2*x^3+3*b*c*x^2+2*a*c*x+b^2*x+a*b)/(2*c*x+b)^7/(4*a*c-b^2)/c^4","B"
1356,1,1843,259,0.140000," ","int((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^(21/2),x)","\frac{\sqrt{c \,x^{2}+b x +a}\, \sqrt{\left(2 c x +b \right) d}\, \left(5120 c^{10} x^{10}+25600 b \,c^{9} x^{9}+2560 \sqrt{-4 a c +b^{2}}\, \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, c^{9} x^{9} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+2048 a \,c^{9} x^{8}+57088 b^{2} c^{8} x^{8}+11520 \sqrt{-4 a c +b^{2}}\, \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b \,c^{8} x^{8} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+8192 a b \,c^{8} x^{7}+74752 b^{3} c^{7} x^{7}+23040 \sqrt{-4 a c +b^{2}}\, \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{2} c^{7} x^{7} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-63104 a^{2} c^{8} x^{6}+45888 a \,b^{2} c^{7} x^{6}+59672 b^{4} c^{6} x^{6}+26880 \sqrt{-4 a c +b^{2}}\, \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{3} c^{6} x^{6} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-189312 a^{2} b \,c^{7} x^{5}+108992 a \,b^{3} c^{6} x^{5}+24904 b^{5} c^{5} x^{5}+20160 \sqrt{-4 a c +b^{2}}\, \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{4} c^{5} x^{5} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-138880 a^{3} c^{7} x^{4}-132480 a^{2} b^{2} c^{6} x^{4}+101240 a \,b^{4} c^{5} x^{4}+1940 b^{6} c^{4} x^{4}+10080 \sqrt{-4 a c +b^{2}}\, \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{5} c^{4} x^{4} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-277760 a^{3} b \,c^{6} x^{3}+50560 a^{2} b^{3} c^{5} x^{3}+30384 a \,b^{5} c^{4} x^{3}-1616 b^{7} c^{3} x^{3}+3360 \sqrt{-4 a c +b^{2}}\, \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{6} c^{3} x^{3} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-108416 a^{4} c^{6} x^{2}-99904 a^{3} b^{2} c^{5} x^{2}+56424 a^{2} b^{4} c^{4} x^{2}-1808 a \,b^{6} c^{3} x^{2}-190 b^{8} c^{2} x^{2}+720 \sqrt{-4 a c +b^{2}}\, \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{7} c^{2} x^{2} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-108416 a^{4} b \,c^{5} x +38976 a^{3} b^{3} c^{4} x -408 a^{2} b^{5} c^{3} x -200 a \,b^{7} c^{2} x -10 b^{9} c x +90 \sqrt{-4 a c +b^{2}}\, \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{8} c x \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-29568 a^{5} c^{5}+9856 a^{4} b^{2} c^{4}-56 a^{3} b^{4} c^{3}-20 a^{2} b^{6} c^{2}-10 a \,b^{8} c +5 \sqrt{-4 a c +b^{2}}\, \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{9} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)\right)}{35112 \left(2 c^{2} x^{3}+3 b c \,x^{2}+2 a c x +b^{2} x +a b \right) \left(2 c x +b \right)^{9} \left(4 a c -b^{2}\right)^{2} c^{4} d^{11}}"," ",0,"1/35112*(c*x^2+b*x+a)^(1/2)*((2*c*x+b)*d)^(1/2)*(5*(-4*a*c+b^2)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*b^9+5120*x^10*c^10+11520*(-4*a*c+b^2)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^8*b*c^8+23040*(-4*a*c+b^2)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^7*b^2*c^7+26880*(-4*a*c+b^2)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^6*b^3*c^6+9856*a^4*b^2*c^4-56*a^3*b^4*c^3-20*a^2*b^6*c^2-10*a*b^8*c-108416*x^2*a^4*c^6-1808*x^2*a*b^6*c^3-108416*x*a^4*b*c^5+38976*x*a^3*b^3*c^4-408*x*a^2*b^5*c^3-200*x*a*b^7*c^2+8192*x^7*a*b*c^8+45888*x^6*a*b^2*c^7-189312*x^5*a^2*b*c^7+108992*x^5*a*b^3*c^6-132480*x^4*a^2*b^2*c^6+101240*x^4*a*b^4*c^5-29568*a^5*c^5-277760*x^3*a^3*b*c^6+50560*x^3*a^2*b^3*c^5+30384*x^3*a*b^5*c^4-99904*x^2*a^3*b^2*c^5+56424*x^2*a^2*b^4*c^4-1616*x^3*b^7*c^3-10*x*b^9*c+24904*x^5*b^5*c^5+74752*x^7*b^3*c^7+59672*x^6*b^4*c^6+57088*x^8*b^2*c^8+25600*x^9*b*c^9-190*x^2*b^8*c^2+1940*x^4*b^6*c^4+2048*x^8*a*c^9-63104*x^6*a^2*c^8-138880*x^4*a^3*c^7+20160*(-4*a*c+b^2)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^5*b^4*c^5+10080*(-4*a*c+b^2)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^4*b^5*c^4+3360*(-4*a*c+b^2)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^3*b^6*c^3+720*(-4*a*c+b^2)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^2*b^7*c^2+90*(-4*a*c+b^2)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x*b^8*c+2560*(-4*a*c+b^2)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^9*c^9)/d^11/(2*c^2*x^3+3*b*c*x^2+2*a*c*x+b^2*x+a*b)/(2*c*x+b)^9/(4*a*c-b^2)^2/c^4","B"
1357,1,1190,317,0.088000," ","int((2*c*d*x+b*d)^(5/2)*(c*x^2+b*x+a)^(5/2),x)","-\frac{\sqrt{\left(2 c x +b \right) d}\, \sqrt{c \,x^{2}+b x +a}\, \left(-4992 c^{10} x^{10}-24960 b \,c^{9} x^{9}-18816 a \,c^{9} x^{8}-51456 b^{2} c^{8} x^{8}-75264 a b \,c^{8} x^{7}-56064 b^{3} c^{7} x^{7}-25216 a^{2} c^{8} x^{6}-119104 a \,b^{2} c^{7} x^{6}-34168 b^{4} c^{6} x^{6}-75648 a^{2} b \,c^{7} x^{5}-93888 a \,b^{3} c^{6} x^{5}-11112 b^{5} c^{5} x^{5}-12416 a^{3} c^{7} x^{4}-85248 a^{2} b^{2} c^{6} x^{4}-37368 a \,b^{4} c^{5} x^{4}-1516 b^{6} c^{4} x^{4}-24832 a^{3} b \,c^{6} x^{3}-44416 a^{2} b^{3} c^{5} x^{3}-6064 a \,b^{5} c^{4} x^{3}-1024 a^{4} c^{6} x^{2}-17600 a^{3} b^{2} c^{5} x^{2}-10056 a^{2} b^{4} c^{4} x^{2}+160 a \,b^{6} c^{3} x^{2}-10 b^{8} c^{2} x^{2}+3072 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a^{5} c^{5} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-3840 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a^{4} b^{2} c^{4} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-1024 a^{4} b \,c^{5} x +1920 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a^{3} b^{4} c^{3} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-5184 a^{3} b^{3} c^{4} x -480 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a^{2} b^{6} c^{2} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-456 a^{2} b^{5} c^{3} x +60 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a \,b^{8} c \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+88 a \,b^{7} c^{2} x -3 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{10} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-6 b^{9} c x -256 a^{4} b^{2} c^{4}-520 a^{3} b^{4} c^{3}+92 a^{2} b^{6} c^{2}-6 a \,b^{8} c \right) d^{2}}{5304 \left(2 c^{2} x^{3}+3 b c \,x^{2}+2 a c x +b^{2} x +a b \right) c^{4}}"," ",0,"-1/5304*((2*c*x+b)*d)^(1/2)*(c*x^2+b*x+a)^(1/2)*d^2*(-3*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*b^10-4992*c^10*x^10-256*a^4*b^2*c^4-520*a^3*b^4*c^3+92*a^2*b^6*c^2-6*a*b^8*c-1024*a^4*c^6*x^2+160*a*b^6*c^3*x^2-1024*a^4*b*c^5*x-5184*a^3*b^3*c^4*x-456*a^2*b^5*c^3*x+88*a*b^7*c^2*x-75264*a*b*c^8*x^7-119104*a*b^2*c^7*x^6-75648*a^2*b*c^7*x^5-93888*a*b^3*c^6*x^5-85248*a^2*b^2*c^6*x^4-37368*a*b^4*c^5*x^4+3072*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*a^5*c^5-24832*a^3*b*c^6*x^3-44416*a^2*b^3*c^5*x^3-6064*a*b^5*c^4*x^3-17600*a^3*b^2*c^5*x^2-10056*a^2*b^4*c^4*x^2-6*b^9*c*x-11112*b^5*c^5*x^5-56064*b^3*c^7*x^7-34168*b^4*c^6*x^6-51456*b^2*c^8*x^8-24960*b*c^9*x^9-10*b^8*c^2*x^2-1516*b^6*c^4*x^4-18816*a*c^9*x^8-25216*a^2*c^8*x^6-12416*a^3*c^7*x^4-3840*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*a^4*b^2*c^4+1920*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*a^3*b^4*c^3-480*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*a^2*b^6*c^2+60*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*a*b^8*c)/c^4/(2*c^2*x^3+3*b*c*x^2+2*a*c*x+b^2*x+a*b)","B"
1358,1,924,278,0.082000," ","int((2*c*d*x+b*d)^(1/2)*(c*x^2+b*x+a)^(5/2),x)","\frac{\sqrt{\left(2 c x +b \right) d}\, \sqrt{c \,x^{2}+b x +a}\, \left(288 c^{8} x^{8}+1152 b \,c^{7} x^{7}+1184 a \,c^{7} x^{6}+1720 b^{2} c^{6} x^{6}+3552 a b \,c^{6} x^{5}+1128 b^{3} c^{5} x^{5}+1888 a^{2} c^{6} x^{4}+3496 a \,b^{2} c^{5} x^{4}+268 b^{4} c^{4} x^{4}+3776 a^{2} b \,c^{5} x^{3}+1072 a \,b^{3} c^{4} x^{3}+992 a^{3} c^{5} x^{2}+2088 a^{2} b^{2} c^{4} x^{2}-120 a \,b^{4} c^{3} x^{2}+10 b^{6} c^{2} x^{2}+768 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a^{4} c^{4} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-768 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a^{3} b^{2} c^{3} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+992 a^{3} b \,c^{4} x +288 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a^{2} b^{4} c^{2} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+200 a^{2} b^{3} c^{3} x -48 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a \,b^{6} c \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-64 a \,b^{5} c^{2} x +3 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{8} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+6 b^{7} c x +248 a^{3} b^{2} c^{3}-68 a^{2} b^{4} c^{2}+6 a \,b^{6} c \right)}{936 \left(2 c^{2} x^{3}+3 b c \,x^{2}+2 a c x +b^{2} x +a b \right) c^{4}}"," ",0,"1/936*((2*c*x+b)*d)^(1/2)*(c*x^2+b*x+a)^(1/2)*(3*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*b^8+768*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*a^4*c^4+248*a^3*b^2*c^3-68*a^2*b^4*c^2+6*a*b^6*c+1128*b^3*c^5*x^5+10*b^6*c^2*x^2+6*b^7*c*x+1720*b^2*c^6*x^6+1152*b*c^7*x^7+268*b^4*c^4*x^4+1184*a*c^7*x^6+1888*a^2*c^6*x^4+992*a^3*c^5*x^2+288*c^8*x^8-64*a*b^5*c^2*x+3552*a*b*c^6*x^5+3496*a*b^2*c^5*x^4+3776*a^2*b*c^5*x^3+1072*a*b^3*c^4*x^3+2088*a^2*b^2*c^4*x^2-120*a*b^4*c^3*x^2+992*a^3*b*c^4*x+200*a^2*b^3*c^3*x-48*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*a*b^6*c-768*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*a^3*b^2*c^3+288*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*a^2*b^4*c^2)/c^4/(2*c^2*x^3+3*b*c*x^2+2*a*c*x+b^2*x+a*b)","B"
1359,1,700,268,0.097000," ","int((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^(3/2),x)","\frac{\sqrt{c \,x^{2}+b x +a}\, \sqrt{\left(2 c x +b \right) d}\, \left(8 c^{6} x^{6}+24 b \,c^{5} x^{5}+40 a \,c^{5} x^{4}+20 b^{2} c^{4} x^{4}+80 a b \,c^{4} x^{3}-40 a^{2} c^{4} x^{2}+80 a \,b^{2} c^{3} x^{2}-10 b^{4} c^{2} x^{2}+192 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a^{3} c^{3} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-144 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a^{2} b^{2} c^{2} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-40 a^{2} b \,c^{3} x +36 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a \,b^{4} c \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+40 a \,b^{3} c^{2} x -3 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{6} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-6 b^{5} c x -72 a^{3} c^{3}+44 a^{2} b^{2} c^{2}-6 a \,b^{4} c \right)}{72 \left(2 c^{2} x^{3}+3 b c \,x^{2}+2 a c x +b^{2} x +a b \right) c^{4} d^{2}}"," ",0,"1/72*(c*x^2+b*x+a)^(1/2)*((2*c*x+b)*d)^(1/2)*(8*c^6*x^6+24*b*c^5*x^5+192*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*a^3*c^3-144*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*a^2*b^2*c^2+36*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*a*b^4*c-3*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*b^6+40*a*c^5*x^4+20*b^2*c^4*x^4+80*a*b*c^4*x^3-40*a^2*c^4*x^2+80*a*b^2*c^3*x^2-10*b^4*c^2*x^2-40*a^2*b*c^3*x+40*a*b^3*c^2*x-6*b^5*c*x-72*a^3*c^3+44*a^2*b^2*c^2-6*a*b^4*c)/d^2/c^4/(2*c^2*x^3+3*b*c*x^2+2*a*c*x+b^2*x+a*b)","B"
1360,1,1362,260,0.092000," ","int((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^(7/2),x)","\frac{\sqrt{c \,x^{2}+b x +a}\, \sqrt{\left(2 c x +b \right) d}\, \left(8 c^{6} x^{6}+24 b \,c^{5} x^{5}-88 a \,c^{5} x^{4}+52 b^{2} c^{4} x^{4}+192 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a^{2} c^{4} x^{2} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-96 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a \,b^{2} c^{3} x^{2} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-176 a b \,c^{4} x^{3}+12 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{4} c^{2} x^{2} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+64 b^{3} c^{3} x^{3}+192 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a^{2} b \,c^{3} x \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-104 a^{2} c^{4} x^{2}-96 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a \,b^{3} c^{2} x \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-80 a \,b^{2} c^{3} x^{2}+12 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{5} c x \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+34 b^{4} c^{2} x^{2}+48 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a^{2} b^{2} c^{2} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-104 a^{2} b \,c^{3} x -24 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a \,b^{4} c \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+8 a \,b^{3} c^{2} x +3 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{6} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+6 b^{5} c x -8 a^{3} c^{3}-20 a^{2} b^{2} c^{2}+6 a \,b^{4} c \right)}{40 \left(2 c^{2} x^{3}+3 b c \,x^{2}+2 a c x +b^{2} x +a b \right) \left(2 c x +b \right)^{2} c^{4} d^{4}}"," ",0,"1/40*(c*x^2+b*x+a)^(1/2)*((2*c*x+b)*d)^(1/2)*(192*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^2*a^2*c^4*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)-96*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^2*a*b^2*c^3*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)+12*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^2*b^4*c^2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)+8*c^6*x^6+192*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x*a^2*b*c^3*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)-96*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x*a*b^3*c^2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)+12*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x*b^5*c*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)+24*b*c^5*x^5+48*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*a^2*b^2*c^2-24*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*a*b^4*c+3*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*b^6-88*a*c^5*x^4+52*b^2*c^4*x^4-176*a*b*c^4*x^3+64*b^3*c^3*x^3-104*a^2*c^4*x^2-80*a*b^2*c^3*x^2+34*b^4*c^2*x^2-104*a^2*b*c^3*x+8*a*b^3*c^2*x+6*b^5*c*x-8*a^3*c^3-20*a^2*b^2*c^2+6*a*b^4*c)/d^4/(2*c^2*x^3+3*b*c*x^2+2*a*c*x+b^2*x+a*b)/(2*c*x+b)^2/c^4","B"
1361,1,1489,260,0.118000," ","int((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^(11/2),x)","\frac{\sqrt{c \,x^{2}+b x +a}\, \sqrt{\left(2 c x +b \right) d}\, \left(-120 c^{6} x^{6}+192 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a \,c^{5} x^{4} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-48 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{2} c^{4} x^{4} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-360 b \,c^{5} x^{5}+384 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a b \,c^{4} x^{3} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-152 a \,c^{5} x^{4}-96 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{3} c^{3} x^{3} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-412 b^{2} c^{4} x^{4}+288 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a \,b^{2} c^{3} x^{2} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-304 a b \,c^{4} x^{3}-72 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{4} c^{2} x^{2} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-224 b^{3} c^{3} x^{3}-40 a^{2} c^{4} x^{2}+96 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a \,b^{3} c^{2} x \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-208 a \,b^{2} c^{3} x^{2}-24 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{5} c x \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-58 b^{4} c^{2} x^{2}-40 a^{2} b \,c^{3} x +12 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a \,b^{4} c \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-56 a \,b^{3} c^{2} x -3 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{6} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-6 b^{5} c x -8 a^{3} c^{3}-4 a^{2} b^{2} c^{2}-6 a \,b^{4} c \right)}{72 \left(2 c^{2} x^{3}+3 b c \,x^{2}+2 a c x +b^{2} x +a b \right) \left(2 c x +b \right)^{4} c^{4} d^{6}}"," ",0,"1/72*(c*x^2+b*x+a)^(1/2)*((2*c*x+b)*d)^(1/2)*(-3*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*b^6-208*a*b^2*c^3*x^2-40*a^2*b*c^3*x-360*b*c^5*x^5-56*a*b^3*c^2*x-304*a*b*c^4*x^3+384*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^3*a*b*c^4*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)+288*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^2*a*b^2*c^3*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)-40*a^2*c^4*x^2-58*b^4*c^2*x^2-6*b^5*c*x-6*a*b^4*c-4*a^2*b^2*c^2+192*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^4*a*c^5*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)-48*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^4*b^2*c^4*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)-96*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^3*b^3*c^3*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)-72*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^2*b^4*c^2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)-152*a*c^5*x^4-412*b^2*c^4*x^4-224*b^3*c^3*x^3-120*c^6*x^6+96*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x*a*b^3*c^2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)-8*a^3*c^3-24*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x*b^5*c*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)+12*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*a*b^4*c)/d^6/(2*c^2*x^3+3*b*c*x^2+2*a*c*x+b^2*x+a*b)/(2*c*x+b)^4/c^4","B"
1362,1,2125,301,0.243000," ","int((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^(15/2),x)","\frac{\sqrt{c \,x^{2}+b x +a}\, \sqrt{\left(2 c x +b \right) d}\, \left(-768 c^{8} x^{8}+768 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a \,c^{7} x^{6} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-192 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{2} c^{6} x^{6} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-3072 b \,c^{7} x^{7}+2304 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a b \,c^{6} x^{5} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-1760 a \,c^{7} x^{6}-576 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{3} c^{5} x^{5} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-4936 b^{2} c^{6} x^{6}+2880 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a \,b^{2} c^{5} x^{4} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-5280 a b \,c^{6} x^{5}-720 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{4} c^{4} x^{4} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-4056 b^{3} c^{5} x^{5}-1888 a^{2} c^{6} x^{4}+1920 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a \,b^{3} c^{4} x^{3} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-5656 a \,b^{2} c^{5} x^{4}-480 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{5} c^{3} x^{3} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-1828 b^{4} c^{4} x^{4}-3776 a^{2} b \,c^{5} x^{3}+720 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a \,b^{4} c^{3} x^{2} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-2512 a \,b^{3} c^{4} x^{3}-180 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{6} c^{2} x^{2} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-480 b^{5} c^{3} x^{3}-1184 a^{3} c^{5} x^{2}-1944 a^{2} b^{2} c^{4} x^{2}+144 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a \,b^{5} c^{2} x \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-456 a \,b^{4} c^{3} x^{2}-36 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{7} c x \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-82 b^{6} c^{2} x^{2}-1184 a^{3} b \,c^{4} x -56 a^{2} b^{3} c^{3} x +12 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a \,b^{6} c \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-80 a \,b^{5} c^{2} x -3 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{8} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-6 b^{7} c x -288 a^{4} c^{4}-8 a^{3} b^{2} c^{3}-4 a^{2} b^{4} c^{2}-6 a \,b^{6} c \right)}{936 \left(2 c^{2} x^{3}+3 b c \,x^{2}+2 a c x +b^{2} x +a b \right) \left(2 c x +b \right)^{6} \left(4 a c -b^{2}\right) c^{4} d^{8}}"," ",0,"1/936*(c*x^2+b*x+a)^(1/2)*((2*c*x+b)*d)^(1/2)*(-3*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*b^8-8*a^3*b^2*c^3-4*a^2*b^4*c^2-6*a*b^6*c-288*a^4*c^4-4056*b^3*c^5*x^5-82*b^6*c^2*x^2-6*b^7*c*x-4936*b^2*c^6*x^6-3072*b*c^7*x^7-480*b^5*c^3*x^3-1828*b^4*c^4*x^4-1760*a*c^7*x^6-1888*a^2*c^6*x^4-1184*a^3*c^5*x^2-768*c^8*x^8-80*a*b^5*c^2*x-5280*a*b*c^6*x^5-5656*a*b^2*c^5*x^4-3776*a^2*b*c^5*x^3-2512*a*b^3*c^4*x^3-1944*a^2*b^2*c^4*x^2-456*a*b^4*c^3*x^2-1184*a^3*b*c^4*x-56*a^2*b^3*c^3*x+1920*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^3*a*b^3*c^4*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)+720*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^2*a*b^4*c^3*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)+144*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x*a*b^5*c^2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)+2304*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^5*a*b*c^6*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)+2880*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^4*a*b^2*c^5*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)-36*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x*b^7*c*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)+768*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^6*a*c^7*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)-192*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^6*b^2*c^6*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)-576*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^5*b^3*c^5*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)-720*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^4*b^4*c^4*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)-480*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^3*b^5*c^3*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)-180*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^2*b^6*c^2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)+12*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*a*b^6*c)/d^8/(2*c^2*x^3+3*b*c*x^2+2*a*c*x+b^2*x+a*b)/(2*c*x+b)^6/(4*a*c-b^2)/c^4","B"
1363,1,567,146,0.090000," ","int((2*c*d*x+b*d)^(7/2)/(c*x^2+b*x+a)^(1/2),x)","\frac{\sqrt{\left(2 c x +b \right) d}\, \sqrt{c \,x^{2}+b x +a}\, \left(96 c^{5} x^{5}+240 b \,c^{4} x^{4}-64 a \,c^{4} x^{3}+256 b^{2} c^{3} x^{3}-96 a b \,c^{3} x^{2}+144 b^{3} c^{2} x^{2}-160 a^{2} c^{3} x +32 a \,b^{2} c^{2} x +32 b^{4} c x -80 a^{2} b \,c^{2}+80 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, a^{2} c^{2} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+32 a \,b^{3} c -40 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, a \,b^{2} c \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+5 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, b^{4} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)\right) d^{3}}{21 \left(2 c^{2} x^{3}+3 b c \,x^{2}+2 a c x +b^{2} x +a b \right) c}"," ",0,"1/21*((2*c*x+b)*d)^(1/2)*(c*x^2+b*x+a)^(1/2)*d^3*(96*x^5*c^5+80*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*a^2*c^2-40*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*a*b^2*c+5*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*b^4+240*x^4*b*c^4-64*x^3*a*c^4+256*b^2*c^3*x^3-96*x^2*a*b*c^3+144*x^2*b^3*c^2-160*a^2*c^3*x+32*x*a*b^2*c^2+32*x*b^4*c-80*a^2*b*c^2+32*a*b^3*c)/c/(2*c^2*x^3+3*b*c*x^2+2*a*c*x+b^2*x+a*b)","B"
1364,1,362,110,0.083000," ","int((2*c*d*x+b*d)^(3/2)/(c*x^2+b*x+a)^(1/2),x)","-\frac{\sqrt{\left(2 c x +b \right) d}\, \sqrt{c \,x^{2}+b x +a}\, \left(-8 c^{3} x^{3}-12 b \,c^{2} x^{2}-8 a \,c^{2} x -4 b^{2} c x -4 a b c +4 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, a c \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, b^{2} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)\right) d}{3 \left(2 c^{2} x^{3}+3 b c \,x^{2}+2 a c x +b^{2} x +a b \right) c}"," ",0,"-1/3*((2*c*x+b)*d)^(1/2)*(c*x^2+b*x+a)^(1/2)*d*(4*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*a*c-((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*b^2-8*c^3*x^3-12*x^2*b*c^2-8*a*c^2*x-4*b^2*c*x-4*a*b*c)/c/(2*c^2*x^3+3*b*c*x^2+2*a*c*x+b^2*x+a*b)","B"
1365,1,189,83,0.073000," ","int(1/(2*c*d*x+b*d)^(1/2)/(c*x^2+b*x+a)^(1/2),x)","\frac{\sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, \sqrt{\left(2 c x +b \right) d}\, \sqrt{c \,x^{2}+b x +a}\, \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)}{\left(2 c^{2} x^{3}+3 b c \,x^{2}+2 a c x +b^{2} x +a b \right) c d}"," ",0,"EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-4*a*c+b^2)^(1/2)*((2*c*x+b)*d)^(1/2)*(c*x^2+b*x+a)^(1/2)/c/d/(2*c^2*x^3+3*b*c*x^2+2*a*c*x+b^2*x+a*b)","B"
1366,1,362,122,0.076000," ","int(1/(2*c*d*x+b*d)^(5/2)/(c*x^2+b*x+a)^(1/2),x)","-\frac{\sqrt{\left(2 c x +b \right) d}\, \sqrt{c \,x^{2}+b x +a}\, \left(4 c^{2} x^{2}+4 b c x +2 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, c x \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+4 a c +\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, b \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)\right)}{3 \left(2 c^{2} x^{3}+3 b c \,x^{2}+2 a c x +b^{2} x +a b \right) \left(4 a c -b^{2}\right) \left(2 c x +b \right) c \,d^{3}}"," ",0,"-1/3*((2*c*x+b)*d)^(1/2)*(c*x^2+b*x+a)^(1/2)*(2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*x*c+((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*b+4*c^2*x^2+4*b*c*x+4*a*c)/d^3/(2*c^2*x^3+3*b*c*x^2+2*a*c*x+b^2*x+a*b)/(4*a*c-b^2)/(2*c*x+b)/c","B"
1367,1,691,160,0.084000," ","int(1/(2*c*d*x+b*d)^(9/2)/(c*x^2+b*x+a)^(1/2),x)","\frac{\sqrt{\left(2 c x +b \right) d}\, \sqrt{c \,x^{2}+b x +a}\, \left(80 c^{4} x^{4}+160 b \,c^{3} x^{3}+40 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, c^{3} x^{3} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+32 a \,c^{3} x^{2}+112 b^{2} c^{2} x^{2}+60 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, b \,c^{2} x^{2} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+32 a b \,c^{2} x +32 b^{3} c x +30 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, b^{2} c x \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-48 a^{2} c^{2}+32 a \,b^{2} c +5 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, b^{3} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)\right)}{21 \left(2 c^{2} x^{3}+3 b c \,x^{2}+2 a c x +b^{2} x +a b \right) \left(4 a c -b^{2}\right)^{2} \left(2 c x +b \right)^{3} c \,d^{5}}"," ",0,"1/21*((2*c*x+b)*d)^(1/2)*(c*x^2+b*x+a)^(1/2)*(40*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*x^3*c^3+60*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*x^2*b*c^2+30*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*x*b^2*c+5*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*b^3+80*c^4*x^4+160*b*c^3*x^3+32*a*c^3*x^2+112*b^2*c^2*x^2+32*a*b*c^2*x+32*b^3*c*x-48*a^2*c^2+32*a*b^2*c)/d^5/(2*c^2*x^3+3*b*c*x^2+2*a*c*x+b^2*x+a*b)/(4*a*c-b^2)^2/(2*c*x+b)^3/c","B"
1368,1,703,229,0.085000," ","int((2*c*d*x+b*d)^(9/2)/(c*x^2+b*x+a)^(1/2),x)","\frac{\sqrt{\left(2 c x +b \right) d}\, \sqrt{c \,x^{2}+b x +a}\, \left(320 c^{6} x^{6}+960 b \,c^{5} x^{5}-128 a \,c^{5} x^{4}+1232 b^{2} c^{4} x^{4}-256 a b \,c^{4} x^{3}+864 b^{3} c^{3} x^{3}-448 a^{2} c^{4} x^{2}+32 a \,b^{2} c^{3} x^{2}+320 b^{4} c^{2} x^{2}+1344 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a^{3} c^{3} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-1008 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a^{2} b^{2} c^{2} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-448 a^{2} b \,c^{3} x +252 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a \,b^{4} c \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+160 a \,b^{3} c^{2} x -21 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{6} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+48 b^{5} c x -112 a^{2} b^{2} c^{2}+48 a \,b^{4} c \right) d^{4}}{45 \left(2 c^{2} x^{3}+3 b c \,x^{2}+2 a c x +b^{2} x +a b \right) c}"," ",0,"1/45*((2*c*x+b)*d)^(1/2)*(c*x^2+b*x+a)^(1/2)*d^4*(320*c^6*x^6+960*b*c^5*x^5+1344*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*a^3*c^3-1008*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*a^2*b^2*c^2+252*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*a*b^4*c-21*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*b^6-128*a*c^5*x^4+1232*b^2*c^4*x^4-256*a*b*c^4*x^3+864*b^3*c^3*x^3-448*a^2*c^4*x^2+32*a*b^2*c^3*x^2+320*b^4*c^2*x^2-448*a^2*b*c^3*x+160*a*b^3*c^2*x+48*b^5*c*x-112*a^2*b^2*c^2+48*a*b^4*c)/c/(2*c^2*x^3+3*b*c*x^2+2*a*c*x+b^2*x+a*b)","B"
1369,1,496,193,0.064000," ","int((2*c*d*x+b*d)^(5/2)/(c*x^2+b*x+a)^(1/2),x)","-\frac{\sqrt{\left(2 c x +b \right) d}\, \sqrt{c \,x^{2}+b x +a}\, \left(-16 c^{4} x^{4}-32 b \,c^{3} x^{3}-16 a \,c^{3} x^{2}-20 b^{2} c^{2} x^{2}+48 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a^{2} c^{2} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-24 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a \,b^{2} c \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-16 a b \,c^{2} x +3 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{4} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-4 b^{3} c x -4 a \,b^{2} c \right) d^{2}}{5 \left(2 c^{2} x^{3}+3 b c \,x^{2}+2 a c x +b^{2} x +a b \right) c}"," ",0,"-1/5*((2*c*x+b)*d)^(1/2)*(c*x^2+b*x+a)^(1/2)*d^2*(48*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*a^2*c^2-24*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*a*b^2*c+3*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*b^4-16*c^4*x^4-32*b*c^3*x^3-16*a*c^3*x^2-20*b^2*c^2*x^2-16*a*b*c^2*x-4*b^3*c*x-4*a*b^2*c)/c/(2*c^2*x^3+3*b*c*x^2+2*a*c*x+b^2*x+a*b)","B"
1370,1,186,167,0.064000," ","int((2*c*d*x+b*d)^(1/2)/(c*x^2+b*x+a)^(1/2),x)","\frac{\sqrt{\left(2 c x +b \right) d}\, \sqrt{c \,x^{2}+b x +a}\, \left(4 a c -b^{2}\right) \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)}{\left(2 c^{2} x^{3}+3 b c \,x^{2}+2 a c x +b^{2} x +a b \right) c}"," ",0,"((2*c*x+b)*d)^(1/2)*(c*x^2+b*x+a)^(1/2)*(4*a*c-b^2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))/c/(2*c^2*x^3+3*b*c*x^2+2*a*c*x+b^2*x+a*b)","A"
1371,1,336,205,0.086000," ","int(1/(2*c*d*x+b*d)^(3/2)/(c*x^2+b*x+a)^(1/2),x)","\frac{\sqrt{\left(2 c x +b \right) d}\, \sqrt{c \,x^{2}+b x +a}\, \left(-4 c^{2} x^{2}+4 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a c \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{2} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-4 b c x -4 a c \right)}{\left(2 c^{2} x^{3}+3 b c \,x^{2}+2 a c x +b^{2} x +a b \right) \left(4 a c -b^{2}\right) c \,d^{2}}"," ",0,"((2*c*x+b)*d)^(1/2)*(c*x^2+b*x+a)^(1/2)*(4*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*a*c*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)-EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*b^2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)-4*c^2*x^2-4*b*c*x-4*a*c)/c/d^2/(2*c^2*x^3+3*b*c*x^2+2*a*c*x+b^2*x+a*b)/(4*a*c-b^2)","A"
1372,1,874,243,0.095000," ","int(1/(2*c*d*x+b*d)^(7/2)/(c*x^2+b*x+a)^(1/2),x)","-\frac{\left(-48 c^{4} x^{4}+48 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a \,c^{3} x^{2} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-12 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{2} c^{2} x^{2} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-96 b \,c^{3} x^{3}+48 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a b \,c^{2} x \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-32 a \,c^{3} x^{2}-12 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{3} c x \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-64 b^{2} c^{2} x^{2}+12 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a \,b^{2} c \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-32 a b \,c^{2} x -3 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{4} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-16 b^{3} c x +16 a^{2} c^{2}-16 a \,b^{2} c \right) \sqrt{\left(2 c x +b \right) d}}{5 \sqrt{c \,x^{2}+b x +a}\, \left(2 c x +b \right)^{3} \left(4 a c -b^{2}\right)^{2} c \,d^{4}}"," ",0,"-1/5*(48*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^2*a*c^3*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)-12*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^2*b^2*c^2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)+48*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x*a*b*c^2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)-12*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x*b^3*c*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)+12*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*a*b^2*c-3*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*b^4-48*c^4*x^4-96*b*c^3*x^3-32*a*c^3*x^2-64*b^2*c^2*x^2-32*a*b*c^2*x-16*b^3*c*x+16*a^2*c^2-16*a*b^2*c)*((2*c*x+b)*d)^(1/2)/d^4/(c*x^2+b*x+a)^(1/2)/(2*c*x+b)^3/(4*a*c-b^2)^2/c","B"
1373,1,118,62,0.141000," ","int((3-2*x)^(3/2)/(x^2-3*x+1)^(1/2),x)","\frac{\sqrt{-2 x +3}\, \sqrt{x^{2}-3 x +1}\, \left(-8 x^{3}+36 x^{2}-44 x +\sqrt{\left(-2 x +3+\sqrt{5}\right) \sqrt{5}}\, \sqrt{\left(2 x -3\right) \sqrt{5}}\, \sqrt{\left(2 x -3+\sqrt{5}\right) \sqrt{5}}\, \EllipticF \left(\frac{\sqrt{2}\, \sqrt{5}\, \sqrt{\left(-2 x +3+\sqrt{5}\right) \sqrt{5}}}{10}, \sqrt{2}\right)+12\right)}{6 x^{3}-27 x^{2}+33 x -9}"," ",0,"1/3*(3-2*x)^(1/2)*(x^2-3*x+1)^(1/2)*(((-2*x+3+5^(1/2))*5^(1/2))^(1/2)*((2*x-3)*5^(1/2))^(1/2)*((2*x-3+5^(1/2))*5^(1/2))^(1/2)*EllipticF(1/10*2^(1/2)*5^(1/2)*((-2*x+3+5^(1/2))*5^(1/2))^(1/2),2^(1/2))-8*x^3+36*x^2-44*x+12)/(2*x^3-9*x^2+11*x-3)","A"
1374,1,102,42,0.127000," ","int(1/(-2*x+3)^(1/2)/(x^2-3*x+1)^(1/2),x)","\frac{\sqrt{-2 x +3}\, \sqrt{x^{2}-3 x +1}\, \sqrt{\left(-2 x +3+\sqrt{5}\right) \sqrt{5}}\, \sqrt{\left(2 x -3\right) \sqrt{5}}\, \sqrt{\left(2 x -3+\sqrt{5}\right) \sqrt{5}}\, \EllipticF \left(\frac{\sqrt{2}\, \sqrt{5}\, \sqrt{\left(-2 x +3+\sqrt{5}\right) \sqrt{5}}}{10}, \sqrt{2}\right)}{10 x^{3}-45 x^{2}+55 x -15}"," ",0,"1/5*(-2*x+3)^(1/2)*(x^2-3*x+1)^(1/2)*((-2*x+3+5^(1/2))*5^(1/2))^(1/2)*((2*x-3)*5^(1/2))^(1/2)*((2*x-3+5^(1/2))*5^(1/2))^(1/2)*EllipticF(1/10*2^(1/2)*5^(1/2)*((-2*x+3+5^(1/2))*5^(1/2))^(1/2),2^(1/2))/(2*x^3-9*x^2+11*x-3)","B"
1375,1,172,62,0.148000," ","int(1/(-2*x+3)^(5/2)/(x^2-3*x+1)^(1/2),x)","\frac{\left(-20 x^{2}+2 \sqrt{\left(-2 x +3+\sqrt{5}\right) \sqrt{5}}\, \sqrt{\left(2 x -3\right) \sqrt{5}}\, \sqrt{\left(2 x -3+\sqrt{5}\right) \sqrt{5}}\, x \EllipticF \left(\frac{\sqrt{2}\, \sqrt{5}\, \sqrt{\left(-2 x +3+\sqrt{5}\right) \sqrt{5}}}{10}, \sqrt{2}\right)+60 x -3 \sqrt{\left(-2 x +3+\sqrt{5}\right) \sqrt{5}}\, \sqrt{\left(2 x -3\right) \sqrt{5}}\, \sqrt{\left(2 x -3+\sqrt{5}\right) \sqrt{5}}\, \EllipticF \left(\frac{\sqrt{2}\, \sqrt{5}\, \sqrt{\left(-2 x +3+\sqrt{5}\right) \sqrt{5}}}{10}, \sqrt{2}\right)-20\right) \sqrt{-2 x +3}}{75 \sqrt{x^{2}-3 x +1}\, \left(2 x -3\right)^{2}}"," ",0,"1/75*(2*((-2*x+3+5^(1/2))*5^(1/2))^(1/2)*((2*x-3)*5^(1/2))^(1/2)*((2*x-3+5^(1/2))*5^(1/2))^(1/2)*EllipticF(1/10*2^(1/2)*5^(1/2)*((-2*x+3+5^(1/2))*5^(1/2))^(1/2),2^(1/2))*x-3*((-2*x+3+5^(1/2))*5^(1/2))^(1/2)*((2*x-3)*5^(1/2))^(1/2)*((2*x-3+5^(1/2))*5^(1/2))^(1/2)*EllipticF(1/10*2^(1/2)*5^(1/2)*((-2*x+3+5^(1/2))*5^(1/2))^(1/2),2^(1/2))-20*x^2+60*x-20)/(x^2-3*x+1)^(1/2)*(-2*x+3)^(1/2)/(2*x-3)^2","B"
1376,1,127,104,0.193000," ","int((-2*x+3)^(5/2)/(x^2-3*x+1)^(1/2),x)","-\frac{\sqrt{-2 x +3}\, \sqrt{x^{2}-3 x +1}\, \left(-16 x^{4}+96 x^{3}-196 x^{2}+156 x +3 \sqrt{\left(2 x -3\right) \sqrt{5}}\, \sqrt{\left(2 x -3+\sqrt{5}\right) \sqrt{5}}\, \sqrt{\left(-2 x +3+\sqrt{5}\right) \sqrt{5}}\, \sqrt{5}\, \EllipticE \left(\frac{\sqrt{2}\, \sqrt{5}\, \sqrt{\left(-2 x +3+\sqrt{5}\right) \sqrt{5}}}{10}, \sqrt{2}\right)-36\right)}{5 \left(2 x^{3}-9 x^{2}+11 x -3\right)}"," ",0,"-1/5*(-2*x+3)^(1/2)*(x^2-3*x+1)^(1/2)*(3*((2*x-3)*5^(1/2))^(1/2)*((2*x-3+5^(1/2))*5^(1/2))^(1/2)*EllipticE(1/10*2^(1/2)*5^(1/2)*((-2*x+3+5^(1/2))*5^(1/2))^(1/2),2^(1/2))*((-2*x+3+5^(1/2))*5^(1/2))^(1/2)*5^(1/2)-16*x^4+96*x^3-196*x^2+156*x-36)/(2*x^3-9*x^2+11*x-3)","A"
1377,1,105,85,0.059000," ","int((-2*x+3)^(1/2)/(x^2-3*x+1)^(1/2),x)","-\frac{\sqrt{-2 x +3}\, \sqrt{x^{2}-3 x +1}\, \sqrt{\left(-2 x +3+\sqrt{5}\right) \sqrt{5}}\, \sqrt{\left(2 x -3\right) \sqrt{5}}\, \sqrt{\left(2 x -3+\sqrt{5}\right) \sqrt{5}}\, \sqrt{5}\, \EllipticE \left(\frac{\sqrt{2}\, \sqrt{5}\, \sqrt{\left(-2 x +3+\sqrt{5}\right) \sqrt{5}}}{10}, \sqrt{2}\right)}{5 \left(2 x^{3}-9 x^{2}+11 x -3\right)}"," ",0,"-1/5*(-2*x+3)^(1/2)*(x^2-3*x+1)^(1/2)*((-2*x+3+5^(1/2))*5^(1/2))^(1/2)*((2*x-3)*5^(1/2))^(1/2)*((2*x-3+5^(1/2))*5^(1/2))^(1/2)*5^(1/2)*EllipticE(1/10*2^(1/2)*5^(1/2)*((-2*x+3+5^(1/2))*5^(1/2))^(1/2),2^(1/2))/(2*x^3-9*x^2+11*x-3)","A"
1378,1,116,104,0.158000," ","int(1/(-2*x+3)^(3/2)/(x^2-3*x+1)^(1/2),x)","\frac{\sqrt{-2 x +3}\, \sqrt{x^{2}-3 x +1}\, \left(20 x^{2}-60 x +\sqrt{\left(2 x -3\right) \sqrt{5}}\, \sqrt{\left(2 x -3+\sqrt{5}\right) \sqrt{5}}\, \sqrt{\left(-2 x +3+\sqrt{5}\right) \sqrt{5}}\, \sqrt{5}\, \EllipticE \left(\frac{\sqrt{2}\, \sqrt{5}\, \sqrt{\left(-2 x +3+\sqrt{5}\right) \sqrt{5}}}{10}, \sqrt{2}\right)+20\right)}{50 x^{3}-225 x^{2}+275 x -75}"," ",0,"1/25*(-2*x+3)^(1/2)*(x^2-3*x+1)^(1/2)*(((2*x-3)*5^(1/2))^(1/2)*((2*x-3+5^(1/2))*5^(1/2))^(1/2)*EllipticE(1/10*2^(1/2)*5^(1/2)*((-2*x+3+5^(1/2))*5^(1/2))^(1/2),2^(1/2))*((-2*x+3+5^(1/2))*5^(1/2))^(1/2)*5^(1/2)+20*x^2-60*x+20)/(2*x^3-9*x^2+11*x-3)","A"
1379,1,569,173,0.190000," ","int((2*c*d*x+b*d)^(11/2)/(c*x^2+b*x+a)^(3/2),x)","\frac{2 \sqrt{\left(2 c x +b \right) d}\, \sqrt{c \,x^{2}+b x +a}\, \left(64 c^{5} x^{5}+160 b \,c^{4} x^{4}-192 a \,c^{4} x^{3}+208 b^{2} c^{3} x^{3}-288 a b \,c^{3} x^{2}+152 b^{3} c^{2} x^{2}-480 a^{2} c^{3} x +96 a \,b^{2} c^{2} x +26 b^{4} c x -240 a^{2} b \,c^{2}+240 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, a^{2} c^{2} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+96 a \,b^{3} c -120 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, a \,b^{2} c \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-7 b^{5}+15 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, b^{4} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)\right) d^{5}}{7 \left(2 c^{2} x^{3}+3 b c \,x^{2}+2 a c x +b^{2} x +a b \right)}"," ",0,"2/7*((2*c*x+b)*d)^(1/2)*(c*x^2+b*x+a)^(1/2)*d^5*(64*c^5*x^5+240*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*a^2*c^2-120*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*a*b^2*c+15*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*b^4+160*x^4*b*c^4-192*a*c^4*x^3+208*b^2*c^3*x^3-288*x^2*a*b*c^3+152*x^2*b^3*c^2-480*a^2*c^3*x+96*a*b^2*c^2*x+26*b^4*c*x-240*a^2*b*c^2+96*a*b^3*c-7*b^5)/(2*c^2*x^3+3*b*c*x^2+2*a*c*x+b^2*x+a*b)","B"
1380,1,366,136,0.104000," ","int((2*c*d*x+b*d)^(7/2)/(c*x^2+b*x+a)^(3/2),x)","-\frac{2 \sqrt{\left(2 c x +b \right) d}\, \sqrt{c \,x^{2}+b x +a}\, \left(-16 c^{3} x^{3}-24 b \,c^{2} x^{2}-40 a \,c^{2} x -2 b^{2} c x -20 a b c +20 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, a c \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+3 b^{3}-5 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, b^{2} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)\right) d^{3}}{3 \left(2 c^{2} x^{3}+3 b c \,x^{2}+2 a c x +b^{2} x +a b \right)}"," ",0,"-2/3*((2*c*x+b)*d)^(1/2)*(c*x^2+b*x+a)^(1/2)*d^3*(20*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*a*c-5*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*b^2-16*c^3*x^3-24*b*c^2*x^2-40*a*c^2*x-2*b^2*c*x-20*a*b*c+3*b^3)/(2*c^2*x^3+3*b*c*x^2+2*a*c*x+b^2*x+a*b)","B"
1381,1,194,107,0.104000," ","int((2*c*d*x+b*d)^(3/2)/(c*x^2+b*x+a)^(3/2),x)","\frac{2 \sqrt{\left(2 c x +b \right) d}\, \sqrt{c \,x^{2}+b x +a}\, \left(-2 c x -b +\sqrt{-4 a c +b^{2}}\, \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)\right) d}{2 c^{2} x^{3}+3 b c \,x^{2}+2 a c x +b^{2} x +a b}"," ",0,"2*((2*c*x+b)*d)^(1/2)*(c*x^2+b*x+a)^(1/2)*d*(EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)-2*c*x-b)/(2*c^2*x^3+3*b*c*x^2+2*a*c*x+b^2*x+a*b)","A"
1382,1,206,119,0.093000," ","int(1/(2*c*d*x+b*d)^(1/2)/(c*x^2+b*x+a)^(3/2),x)","\frac{2 \left(2 c x +b +\sqrt{-4 a c +b^{2}}\, \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)\right) \sqrt{c \,x^{2}+b x +a}\, \sqrt{\left(2 c x +b \right) d}}{\left(4 a c -b^{2}\right) \left(2 c^{2} x^{3}+3 b c \,x^{2}+2 a c x +b^{2} x +a b \right) d}"," ",0,"2*(EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)+2*c*x+b)*(c*x^2+b*x+a)^(1/2)*((2*c*x+b)*d)^(1/2)/(4*a*c-b^2)/d/(2*c^2*x^3+3*b*c*x^2+2*a*c*x+b^2*x+a*b)","A"
1383,1,365,158,0.091000," ","int(1/(2*c*d*x+b*d)^(5/2)/(c*x^2+b*x+a)^(3/2),x)","-\frac{2 \sqrt{\left(2 c x +b \right) d}\, \sqrt{c \,x^{2}+b x +a}\, \left(20 c^{2} x^{2}+20 b c x +10 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, c x \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+8 a c +3 b^{2}+5 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, b \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)\right)}{3 \left(2 c^{2} x^{3}+3 b c \,x^{2}+2 a c x +b^{2} x +a b \right) \left(4 a c -b^{2}\right)^{2} \left(2 c x +b \right) d^{3}}"," ",0,"-2/3*((2*c*x+b)*d)^(1/2)*(c*x^2+b*x+a)^(1/2)*(10*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*x*c+5*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*b+20*c^2*x^2+20*b*c*x+8*a*c+3*b^2)/d^3/(2*c^2*x^3+3*b*c*x^2+2*a*c*x+b^2*x+a*b)/(4*a*c-b^2)^2/(2*c*x+b)","B"
1384,1,498,216,0.113000," ","int((2*c*d*x+b*d)^(9/2)/(c*x^2+b*x+a)^(3/2),x)","-\frac{2 \left(-32 c^{4} x^{4}-64 b \,c^{3} x^{3}-112 a \,c^{3} x^{2}-20 b^{2} c^{2} x^{2}+336 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a^{2} c^{2} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-168 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a \,b^{2} c \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-112 a b \,c^{2} x +21 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{4} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+12 b^{3} c x -28 a \,b^{2} c +5 b^{4}\right) \sqrt{c \,x^{2}+b x +a}\, \sqrt{\left(2 c x +b \right) d}\, d^{4}}{5 \left(2 c^{2} x^{3}+3 b c \,x^{2}+2 a c x +b^{2} x +a b \right)}"," ",0,"-2/5*d^4*(336*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*a^2*c^2-168*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*a*b^2*c+21*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*b^4-32*c^4*x^4-64*b*c^3*x^3-112*a*c^3*x^2-20*b^2*c^2*x^2-112*a*b*c^2*x+12*b^3*c*x-28*a*b^2*c+5*b^4)*(c*x^2+b*x+a)^(1/2)*((2*c*x+b)*d)^(1/2)/(2*c^2*x^3+3*b*c*x^2+2*a*c*x+b^2*x+a*b)","B"
1385,1,323,187,0.082000," ","int((2*c*d*x+b*d)^(5/2)/(c*x^2+b*x+a)^(3/2),x)","\frac{2 \left(-4 c^{2} x^{2}+12 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a c \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-3 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{2} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-4 b c x -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, \sqrt{\left(2 c x +b \right) d}\, d^{2}}{2 c^{2} x^{3}+3 b c \,x^{2}+2 a c x +b^{2} x +a b}"," ",0,"2*(12*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*a*c*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)-3*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*b^2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)-4*c^2*x^2-4*b*c*x-b^2)*d^2*(c*x^2+b*x+a)^(1/2)*((2*c*x+b)*d)^(1/2)/(2*c^2*x^3+3*b*c*x^2+2*a*c*x+b^2*x+a*b)","A"
1386,1,332,199,0.083000," ","int((2*c*d*x+b*d)^(1/2)/(c*x^2+b*x+a)^(3/2),x)","-\frac{2 \sqrt{\left(2 c x +b \right) d}\, \sqrt{c \,x^{2}+b x +a}\, \left(-4 c^{2} x^{2}+4 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a c \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{2} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-4 b c x -b^{2}\right)}{\left(2 c^{2} x^{3}+3 b c \,x^{2}+2 a c x +b^{2} x +a b \right) \left(4 a c -b^{2}\right)}"," ",0,"-2*((2*c*x+b)*d)^(1/2)*(c*x^2+b*x+a)^(1/2)*(4*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*a*c*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)-EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*b^2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)-4*c^2*x^2-4*b*c*x-b^2)/(2*c^2*x^3+3*b*c*x^2+2*a*c*x+b^2*x+a*b)/(4*a*c-b^2)","A"
1387,1,339,238,0.096000," ","int(1/(2*c*d*x+b*d)^(3/2)/(c*x^2+b*x+a)^(3/2),x)","\frac{2 \sqrt{\left(2 c x +b \right) d}\, \sqrt{c \,x^{2}+b x +a}\, \left(-12 c^{2} x^{2}+12 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a c \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-3 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{2} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-12 b c x -8 a c -b^{2}\right)}{\left(2 c^{2} x^{3}+3 b c \,x^{2}+2 a c x +b^{2} x +a b \right) \left(4 a c -b^{2}\right)^{2} d^{2}}"," ",0,"2*((2*c*x+b)*d)^(1/2)*(c*x^2+b*x+a)^(1/2)*(12*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*a*c*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)-3*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*b^2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)-12*c^2*x^2-12*b*c*x-8*a*c-b^2)/d^2/(2*c^2*x^3+3*b*c*x^2+2*a*c*x+b^2*x+a*b)/(4*a*c-b^2)^2","A"
1388,1,876,277,0.105000," ","int(1/(2*c*d*x+b*d)^(7/2)/(c*x^2+b*x+a)^(3/2),x)","-\frac{2 \left(-336 c^{4} x^{4}+336 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a \,c^{3} x^{2} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-84 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{2} c^{2} x^{2} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-672 b \,c^{3} x^{3}+336 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a b \,c^{2} x \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-224 a \,c^{3} x^{2}-84 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{3} c x \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-448 b^{2} c^{2} x^{2}+84 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a \,b^{2} c \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-224 a b \,c^{2} x -21 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{4} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-112 b^{3} c x +32 a^{2} c^{2}-72 a \,b^{2} c -5 b^{4}\right) \sqrt{\left(2 c x +b \right) d}}{5 \sqrt{c \,x^{2}+b x +a}\, \left(2 c x +b \right)^{3} \left(4 a c -b^{2}\right)^{3} d^{4}}"," ",0,"-2/5*(336*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^2*a*c^3*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)-84*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^2*b^2*c^2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)+336*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x*a*b*c^2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)-84*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x*b^3*c*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)+84*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*a*b^2*c-21*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*b^4-336*c^4*x^4-672*b*c^3*x^3-224*a*c^3*x^2-448*b^2*c^2*x^2-224*a*b*c^2*x-112*b^3*c*x+32*a^2*c^2-72*a*b^2*c-5*b^4)*((2*c*x+b)*d)^(1/2)/d^4/(c*x^2+b*x+a)^(1/2)/(2*c*x+b)^3/(4*a*c-b^2)^3","B"
1389,1,1473,207,0.144000," ","int((2*c*d*x+b*d)^(15/2)/(c*x^2+b*x+a)^(5/2),x)","\frac{2 \left(768 c^{7} x^{7}+2688 b \,c^{6} x^{6}-3328 a \,c^{6} x^{5}+4864 b^{2} c^{5} x^{5}-8320 a b \,c^{5} x^{4}+5440 b^{3} c^{4} x^{4}-17472 a^{2} c^{5} x^{3}+416 a \,b^{2} c^{4} x^{3}+2668 b^{4} c^{3} x^{3}-26208 a^{2} b \,c^{4} x^{2}+6240 \sqrt{-4 a c +b^{2}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, a^{2} c^{4} x^{2} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+8944 a \,b^{3} c^{3} x^{2}-3120 \sqrt{-4 a c +b^{2}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, a \,b^{2} c^{3} x^{2} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-94 b^{5} c^{2} x^{2}+390 \sqrt{-4 a c +b^{2}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, b^{4} c^{2} x^{2} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-12480 a^{3} c^{4} x -3744 a^{2} b^{2} c^{3} x +6240 \sqrt{-4 a c +b^{2}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, a^{2} b \,c^{3} x \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+3172 a \,b^{4} c^{2} x -3120 \sqrt{-4 a c +b^{2}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, a \,b^{3} c^{2} x \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-280 b^{6} c x +390 \sqrt{-4 a c +b^{2}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, b^{5} c x \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-6240 a^{3} b \,c^{3}+6240 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, a^{3} c^{3} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+2496 a^{2} b^{3} c^{2}-3120 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, a^{2} b^{2} c^{2} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-182 a \,b^{5} c +390 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, a \,b^{4} c \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-7 b^{7}\right) \sqrt{\left(2 c x +b \right) d}\, d^{7}}{21 \left(2 c x +b \right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}}}"," ",0,"2/21*(-3120*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*a^2*b^2*c^2-7*b^7-8320*a*b*c^5*x^4+416*a*b^2*c^4*x^3-26208*a^2*b*c^4*x^2+8944*a*b^3*c^3*x^2-3744*a^2*b^2*c^3*x+3172*a*b^4*c^2*x+2688*b*c^6*x^6+390*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*a*b^4*c-3120*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^2*a*b^2*c^3*(-4*a*c+b^2)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)+6240*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x*a^2*b*c^3*(-4*a*c+b^2)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)-3120*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x*a*b^3*c^2*(-4*a*c+b^2)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)+768*c^7*x^7-6240*a^3*b*c^3+2496*a^2*b^3*c^2-182*a*b^5*c-3328*a*c^6*x^5+4864*b^2*c^5*x^5+5440*b^3*c^4*x^4-17472*a^2*c^5*x^3+2668*b^4*c^3*x^3-94*b^5*c^2*x^2-12480*a^3*c^4*x-280*b^6*c*x+6240*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^2*a^2*c^4*(-4*a*c+b^2)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)+390*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^2*b^4*c^2*(-4*a*c+b^2)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)+390*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x*b^5*c*(-4*a*c+b^2)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)+6240*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*a^3*c^3)*d^7*((2*c*x+b)*d)^(1/2)/(2*c*x+b)/(c*x^2+b*x+a)^(3/2)","B"
1390,1,958,168,0.121000," ","int((2*c*d*x+b*d)^(11/2)/(c*x^2+b*x+a)^(5/2),x)","-\frac{2 \left(-64 c^{5} x^{5}-160 b \,c^{4} x^{4}-336 a \,c^{4} x^{3}-76 b^{2} c^{3} x^{3}-504 a b \,c^{3} x^{2}+120 \sqrt{-4 a c +b^{2}}\, \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a \,c^{3} x^{2} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+46 b^{3} c^{2} x^{2}-30 \sqrt{-4 a c +b^{2}}\, \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{2} c^{2} x^{2} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-240 a^{2} c^{3} x -132 a \,b^{2} c^{2} x +120 \sqrt{-4 a c +b^{2}}\, \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a b \,c^{2} x \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+28 b^{4} c x -30 \sqrt{-4 a c +b^{2}}\, \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{3} c x \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-120 a^{2} b \,c^{2}+120 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, a^{2} c^{2} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+18 a \,b^{3} c -30 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, a \,b^{2} c \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+b^{5}\right) \sqrt{\left(2 c x +b \right) d}\, d^{5}}{3 \left(2 c x +b \right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}}}"," ",0,"-2/3*(120*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^2*a*c^3*(-4*a*c+b^2)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)-30*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^2*b^2*c^2*(-4*a*c+b^2)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)+120*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x*a*b*c^2*(-4*a*c+b^2)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)-30*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x*b^3*c*(-4*a*c+b^2)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)-64*c^5*x^5+120*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*a^2*c^2-30*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*a*b^2*c-160*b*c^4*x^4-336*a*c^4*x^3-76*b^2*c^3*x^3-504*a*b*c^3*x^2+46*b^3*c^2*x^2-240*a^2*c^3*x-132*a*b^2*c^2*x+28*b^4*c*x-120*a^2*b*c^2+18*a*b^3*c+b^5)*d^5*((2*c*x+b)*d)^(1/2)/(2*c*x+b)/(c*x^2+b*x+a)^(3/2)","B"
1391,1,479,137,0.126000," ","int((2*c*d*x+b*d)^(7/2)/(c*x^2+b*x+a)^(5/2),x)","\frac{2 \left(-28 c^{3} x^{3}-42 b \,c^{2} x^{2}+10 \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, c^{2} x^{2} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-20 a \,c^{2} x -16 b^{2} c x +10 \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, b c x \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-10 a b c +10 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, a c \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-b^{3}\right) \sqrt{\left(2 c x +b \right) d}\, d^{3}}{3 \left(2 c x +b \right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}}}"," ",0,"2/3*(10*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^2*c^2*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-4*a*c+b^2)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)+10*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x*b*c*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-4*a*c+b^2)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)+10*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*a*c-28*c^3*x^3-42*b*c^2*x^2-20*a*c^2*x-16*b^2*c*x-10*a*b*c-b^3)*d^3*((2*c*x+b)*d)^(1/2)/(2*c*x+b)/(c*x^2+b*x+a)^(3/2)","B"
1392,1,487,145,0.107000," ","int((2*c*d*x+b*d)^(3/2)/(c*x^2+b*x+a)^(5/2),x)","\frac{2 \left(4 c^{3} x^{3}+6 b \,c^{2} x^{2}+2 \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, c^{2} x^{2} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-4 a \,c^{2} x +4 b^{2} c x +2 \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, b c x \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-2 a b c +2 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, a c \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+b^{3}\right) \sqrt{\left(2 c x +b \right) d}\, d}{3 \left(4 a c -b^{2}\right) \left(2 c x +b \right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}}}"," ",0,"2/3*(2*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^2*c^2*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-4*a*c+b^2)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)+2*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x*b*c*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-4*a*c+b^2)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)+2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*a*c+4*c^3*x^3+6*b*c^2*x^2-4*a*c^2*x+4*b^2*c*x-2*a*b*c+b^3)*d*((2*c*x+b)*d)^(1/2)/(4*a*c-b^2)/(2*c*x+b)/(c*x^2+b*x+a)^(3/2)","B"
1393,1,491,159,0.107000," ","int(1/(2*c*d*x+b*d)^(1/2)/(c*x^2+b*x+a)^(5/2),x)","\frac{2 \sqrt{\left(2 c x +b \right) d}\, \left(20 c^{3} x^{3}+30 b \,c^{2} x^{2}+10 \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, c^{2} x^{2} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+28 a \,c^{2} x +8 b^{2} c x +10 \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, b c x \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+14 a b c +10 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, a c \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-b^{3}\right)}{3 \left(2 c x +b \right) \left(4 a c -b^{2}\right)^{2} \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} d}"," ",0,"2/3*((2*c*x+b)*d)^(1/2)*(10*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^2*c^2*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-4*a*c+b^2)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)+10*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x*b*c*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-4*a*c+b^2)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)+10*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*a*c+20*c^3*x^3+30*b*c^2*x^2+28*a*c^2*x+8*b^2*c*x+14*a*b*c-b^3)/d/(2*c*x+b)/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(3/2)","B"
1394,1,797,200,0.103000," ","int(1/(2*c*d*x+b*d)^(5/2)/(c*x^2+b*x+a)^(5/2),x)","-\frac{2 \left(120 c^{4} x^{4}+240 b \,c^{3} x^{3}+60 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, c^{3} x^{3} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+168 a \,c^{3} x^{2}+138 b^{2} c^{2} x^{2}+90 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, b \,c^{2} x^{2} \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+168 a b \,c^{2} x +60 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, a \,c^{2} x \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+18 b^{3} c x +30 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, b^{2} c x \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+32 a^{2} c^{2}+26 a \,b^{2} c +30 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-4 a c +b^{2}}\, a b c \EllipticF \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-b^{4}\right) \sqrt{\left(2 c x +b \right) d}}{3 \left(2 c x +b \right)^{2} \left(4 a c -b^{2}\right)^{3} \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} d^{3}}"," ",0,"-2/3*(60*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*x^3*c^3+90*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*x^2*b*c^2+60*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*x*a*c^2+30*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*x*b^2*c+30*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticF(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*(-4*a*c+b^2)^(1/2)*a*b*c+120*c^4*x^4+240*b*c^3*x^3+168*a*c^3*x^2+138*b^2*c^2*x^2+168*a*b*c^2*x+18*b^3*c*x+32*a^2*c^2+26*a*b^2*c-b^4)*((2*c*x+b)*d)^(1/2)/d^3/(2*c*x+b)^2/(4*a*c-b^2)^3/(c*x^2+b*x+a)^(3/2)","B"
1395,1,1328,249,0.133000," ","int((2*c*d*x+b*d)^(13/2)/(c*x^2+b*x+a)^(5/2),x)","-\frac{2 \sqrt{\left(2 c x +b \right) d}\, \left(-384 c^{6} x^{6}-1152 b \,c^{5} x^{5}-3168 a \,c^{5} x^{4}-648 b^{2} c^{4} x^{4}+7392 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a^{2} c^{4} x^{2} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-3696 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a \,b^{2} c^{3} x^{2} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-6336 a b \,c^{4} x^{3}+462 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{4} c^{2} x^{2} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+624 b^{3} c^{3} x^{3}+7392 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a^{2} b \,c^{3} x \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-2464 a^{2} c^{4} x^{2}-3696 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a \,b^{3} c^{2} x \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-3520 a \,b^{2} c^{3} x^{2}+462 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{5} c x \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)+674 b^{4} c^{2} x^{2}+7392 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a^{3} c^{3} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-3696 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a^{2} b^{2} c^{2} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-2464 a^{2} b \,c^{3} x +462 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a \,b^{4} c \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-352 a \,b^{3} c^{2} x +170 b^{5} c x -616 a^{2} b^{2} c^{2}+110 a \,b^{4} c +5 b^{6}\right) d^{6}}{15 \left(2 c x +b \right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}}}"," ",0,"-2/15*((2*c*x+b)*d)^(1/2)*(7392*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^2*a^2*c^4*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)-3696*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^2*a*b^2*c^3*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)+462*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^2*b^4*c^2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)-384*c^6*x^6+7392*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x*a^2*b*c^3*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)-3696*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x*a*b^3*c^2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)+462*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x*b^5*c*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)-1152*b*c^5*x^5+7392*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*a^3*c^3-3696*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*a^2*b^2*c^2+462*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*a*b^4*c-3168*a*c^5*x^4-648*b^2*c^4*x^4-6336*a*b*c^4*x^3+624*b^3*c^3*x^3-2464*a^2*c^4*x^2-3520*a*b^2*c^3*x^2+674*b^4*c^2*x^2-2464*a^2*b*c^3*x-352*a*b^3*c^2*x+170*b^5*c*x-616*a^2*b^2*c^2+110*a*b^4*c+5*b^6)*d^6/(2*c*x+b)/(c*x^2+b*x+a)^(3/2)","B"
1396,1,859,218,0.097000," ","int((2*c*d*x+b*d)^(9/2)/(c*x^2+b*x+a)^(5/2),x)","\frac{2 \sqrt{\left(2 c x +b \right) d}\, \left(-72 c^{4} x^{4}+168 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a \,c^{3} x^{2} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-42 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{2} c^{2} x^{2} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-144 b \,c^{3} x^{3}+168 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a b \,c^{2} x \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-56 a \,c^{3} x^{2}-42 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{3} c x \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-94 b^{2} c^{2} x^{2}+168 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a^{2} c^{2} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-42 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a \,b^{2} c \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-56 a b \,c^{2} x -22 b^{3} c x -14 a \,b^{2} c -b^{4}\right) d^{4}}{3 \left(2 c x +b \right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}}}"," ",0,"2/3*((2*c*x+b)*d)^(1/2)*(168*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^2*a*c^3*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)-42*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^2*b^2*c^2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)+168*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x*a*b*c^2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)-42*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x*b^3*c*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)+168*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*a^2*c^2-42*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*a*b^2*c-72*c^4*x^4-144*b*c^3*x^3-56*a*c^3*x^2-94*b^2*c^2*x^2-56*a*b*c^2*x-22*b^3*c*x-14*a*b^2*c-b^4)*d^4/(2*c*x+b)/(c*x^2+b*x+a)^(3/2)","B"
1397,1,871,226,0.089000," ","int((2*c*d*x+b*d)^(5/2)/(c*x^2+b*x+a)^(5/2),x)","-\frac{2 \sqrt{\left(2 c x +b \right) d}\, \left(-24 c^{4} x^{4}+24 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a \,c^{3} x^{2} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-6 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{2} c^{2} x^{2} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-48 b \,c^{3} x^{3}+24 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a b \,c^{2} x \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-8 a \,c^{3} x^{2}-6 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{3} c x \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-34 b^{2} c^{2} x^{2}+24 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a^{2} c^{2} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-6 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a \,b^{2} c \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-8 a b \,c^{2} x -10 b^{3} c x -2 a \,b^{2} c -b^{4}\right) d^{2}}{3 \left(2 c x +b \right) \left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}}}"," ",0,"-2/3*((2*c*x+b)*d)^(1/2)*(24*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^2*a*c^3*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)-6*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^2*b^2*c^2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)+24*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x*a*b*c^2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)-6*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x*b^3*c*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)+24*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*a^2*c^2-6*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*a*b^2*c-24*c^4*x^4-48*b*c^3*x^3-8*a*c^3*x^2-34*b^2*c^2*x^2-8*a*b*c^2*x-10*b^3*c*x-2*a*b^2*c-b^4)*d^2/(2*c*x+b)/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)","B"
1398,1,866,240,0.084000," ","int((2*c*d*x+b*d)^(1/2)/(c*x^2+b*x+a)^(5/2),x)","-\frac{2 \left(-24 c^{4} x^{4}+24 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a \,c^{3} x^{2} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-6 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{2} c^{2} x^{2} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-48 b \,c^{3} x^{3}+24 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a b \,c^{2} x \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-40 a \,c^{3} x^{2}-6 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{3} c x \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-26 b^{2} c^{2} x^{2}+24 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a^{2} c^{2} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-6 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a \,b^{2} c \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-40 a b \,c^{2} x -2 b^{3} c x -10 a \,b^{2} c +b^{4}\right) \sqrt{\left(2 c x +b \right) d}}{3 \left(4 a c -b^{2}\right)^{2} \left(2 c x +b \right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}}}"," ",0,"-2/3*(24*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^2*a*c^3*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)-6*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^2*b^2*c^2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)+24*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x*a*b*c^2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)-6*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x*b^3*c*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)+24*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*a^2*c^2-6*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*a*b^2*c-24*c^4*x^4-48*b*c^3*x^3-40*a*c^3*x^2-26*b^2*c^2*x^2-40*a*b*c^2*x-2*b^3*c*x-10*a*b^2*c+b^4)*((2*c*x+b)*d)^(1/2)/(4*a*c-b^2)^2/(2*c*x+b)/(c*x^2+b*x+a)^(3/2)","B"
1399,1,877,281,0.114000," ","int(1/(2*c*d*x+b*d)^(3/2)/(c*x^2+b*x+a)^(5/2),x)","\frac{2 \left(-168 c^{4} x^{4}+168 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a \,c^{3} x^{2} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-42 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{2} c^{2} x^{2} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-336 b \,c^{3} x^{3}+168 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a b \,c^{2} x \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-280 a \,c^{3} x^{2}-42 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, b^{3} c x \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-182 b^{2} c^{2} x^{2}+168 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a^{2} c^{2} \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-42 \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{2 c x +b}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, a \,b^{2} c \EllipticE \left(\frac{\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{2}}{2}, \sqrt{2}\right)-280 a b \,c^{2} x -14 b^{3} c x -96 a^{2} c^{2}-22 a \,b^{2} c +b^{4}\right) \sqrt{\left(2 c x +b \right) d}}{3 \left(4 a c -b^{2}\right)^{3} \left(2 c x +b \right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} d^{2}}"," ",0,"2/3*(168*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^2*a*c^3*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)-42*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x^2*b^2*c^2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)+168*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x*a*b*c^2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)-42*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*x*b^3*c*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)+168*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*a^2*c^2-42*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-(2*c*x+b)/(-4*a*c+b^2)^(1/2))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*EllipticE(1/2*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*2^(1/2),2^(1/2))*a*b^2*c-168*c^4*x^4-336*b*c^3*x^3-280*a*c^3*x^2-182*b^2*c^2*x^2-280*a*b*c^2*x-14*b^3*c*x-96*a^2*c^2-22*a*b^2*c+b^4)*((2*c*x+b)*d)^(1/2)/d^2/(4*a*c-b^2)^3/(2*c*x+b)/(c*x^2+b*x+a)^(3/2)","B"
1400,1,336,144,0.261000," ","int((d*e*x+c*e)^(11/2)/(-d^2*x^2-2*c*d*x-c^2+1)^(1/2),x)","-\frac{\sqrt{\left(d x +c \right) e}\, \sqrt{-d^{2} x^{2}-2 c d x -c^{2}+1}\, \left(42 d^{7} x^{7}+294 c \,d^{6} x^{6}+882 c^{2} d^{5} x^{5}+1470 c^{3} d^{4} x^{4}+1470 c^{4} d^{3} x^{3}+12 d^{5} x^{5}+882 c^{5} d^{2} x^{2}+60 c \,d^{4} x^{4}+294 c^{6} d x +120 c^{2} d^{3} x^{3}+42 c^{7}+120 c^{3} d^{2} x^{2}+60 c^{4} d x +36 d^{3} x^{3}+12 c^{5}+108 c \,d^{2} x^{2}+108 c^{2} d x +36 c^{3}-90 d x -90 c +32 \sqrt{-2 d x -2 c +2}\, \sqrt{d x +c}\, \sqrt{2 d x +2 c +2}\, \EllipticF \left(\frac{\sqrt{-2 d x -2 c +2}}{2}, \sqrt{2}\right)+77 \sqrt{-2 d x -2 c +2}\, \sqrt{2 d x +2 c +2}\, \sqrt{-d x -c}\, \EllipticF \left(\frac{\sqrt{2 d x +2 c +2}}{2}, \sqrt{2}\right)\right) e^{5}}{231 \left(d^{3} x^{3}+3 c \,d^{2} x^{2}+3 c^{2} d x +c^{3}-d x -c \right) d}"," ",0,"-1/231*(e*(d*x+c))^(1/2)*(-d^2*x^2-2*c*d*x-c^2+1)^(1/2)*e^5*(42*x^7*d^7+294*x^6*c*d^6+882*x^5*c^2*d^5+1470*x^4*c^3*d^4+12*x^5*d^5+1470*x^3*c^4*d^3+60*x^4*c*d^4+882*x^2*c^5*d^2+120*x^3*c^2*d^3+294*x*c^6*d+120*x^2*c^3*d^2+42*c^7+36*x^3*d^3+60*x*c^4*d+108*x^2*c*d^2+12*c^5+32*(-2*d*x-2*c+2)^(1/2)*(d*x+c)^(1/2)*(2*d*x+2*c+2)^(1/2)*EllipticF(1/2*(-2*d*x-2*c+2)^(1/2),2^(1/2))+77*(-2*d*x-2*c+2)^(1/2)*(2*d*x+2*c+2)^(1/2)*(-d*x-c)^(1/2)*EllipticF(1/2*(2*d*x+2*c+2)^(1/2),2^(1/2))+108*x*c^2*d+36*c^3-90*d*x-90*c)/d/(d^3*x^3+3*c*d^2*x^2+3*c^2*d*x+c^3-d*x-c)","B"
1401,1,263,104,0.073000," ","int((d*e*x+c*e)^(7/2)/(-d^2*x^2-2*c*d*x-c^2+1)^(1/2),x)","-\frac{\sqrt{\left(d x +c \right) e}\, \sqrt{-d^{2} x^{2}-2 c d x -c^{2}+1}\, \left(6 d^{5} x^{5}+30 c \,d^{4} x^{4}+60 c^{2} d^{3} x^{3}+60 c^{3} d^{2} x^{2}+30 c^{4} d x +4 d^{3} x^{3}+6 c^{5}+12 c \,d^{2} x^{2}+12 c^{2} d x +4 c^{3}-10 d x -10 c +2 \sqrt{-2 d x -2 c +2}\, \sqrt{d x +c}\, \sqrt{2 d x +2 c +2}\, \EllipticF \left(\frac{\sqrt{-2 d x -2 c +2}}{2}, \sqrt{2}\right)+7 \sqrt{-2 d x -2 c +2}\, \sqrt{2 d x +2 c +2}\, \sqrt{-d x -c}\, \EllipticF \left(\frac{\sqrt{2 d x +2 c +2}}{2}, \sqrt{2}\right)\right) e^{3}}{21 \left(d^{3} x^{3}+3 c \,d^{2} x^{2}+3 c^{2} d x +c^{3}-d x -c \right) d}"," ",0,"-1/21*((d*x+c)*e)^(1/2)*(-d^2*x^2-2*c*d*x-c^2+1)^(1/2)*e^3*(6*d^5*x^5+30*c*d^4*x^4+60*c^2*d^3*x^3+60*c^3*d^2*x^2+4*d^3*x^3+30*c^4*d*x+12*c*d^2*x^2+6*c^5+2*(-2*d*x-2*c+2)^(1/2)*(d*x+c)^(1/2)*(2*d*x+2*c+2)^(1/2)*EllipticF(1/2*(-2*d*x-2*c+2)^(1/2),2^(1/2))+7*(-2*d*x-2*c+2)^(1/2)*(2*d*x+2*c+2)^(1/2)*(-d*x-c)^(1/2)*EllipticF(1/2*(2*d*x+2*c+2)^(1/2),2^(1/2))+12*c^2*d*x+4*c^3-10*d*x-10*c)/d/(d^3*x^3+3*c*d^2*x^2+3*c^2*d*x+c^3-d*x-c)","B"
1402,1,161,64,0.070000," ","int((d*e*x+c*e)^(3/2)/(-d^2*x^2-2*c*d*x-c^2+1)^(1/2),x)","-\frac{\sqrt{\left(d x +c \right) e}\, \sqrt{-d^{2} x^{2}-2 c d x -c^{2}+1}\, \left(2 d^{3} x^{3}+6 c \,d^{2} x^{2}+6 c^{2} d x +2 c^{3}-2 d x -2 c +\sqrt{-2 d x -2 c +2}\, \sqrt{2 d x +2 c +2}\, \sqrt{-d x -c}\, \EllipticF \left(\frac{\sqrt{2 d x +2 c +2}}{2}, \sqrt{2}\right)\right) e}{3 \left(d^{3} x^{3}+3 c \,d^{2} x^{2}+3 c^{2} d x +c^{3}-d x -c \right) d}"," ",0,"-1/3*((d*x+c)*e)^(1/2)*(-d^2*x^2-2*c*d*x-c^2+1)^(1/2)*e*(2*d^3*x^3+6*c*d^2*x^2+(-2*d*x-2*c+2)^(1/2)*(2*d*x+2*c+2)^(1/2)*(-d*x-c)^(1/2)*EllipticF(1/2*(2*d*x+2*c+2)^(1/2),2^(1/2))+6*c^2*d*x+2*c^3-2*d*x-2*c)/d/(d^3*x^3+3*c*d^2*x^2+3*c^2*d*x+c^3-d*x-c)","B"
1403,1,153,25,0.101000," ","int(1/(d*e*x+c*e)^(1/2)/(-d^2*x^2-2*c*d*x-c^2+1)^(1/2),x)","-\frac{\sqrt{\left(d x +c \right) e}\, \sqrt{-d^{2} x^{2}-2 c d x -c^{2}+1}\, \sqrt{2 d x +2 c +2}\, \sqrt{-2 d x -2 c +2}\, \left(-2 \sqrt{d x +c}\, \EllipticF \left(\frac{\sqrt{-2 d x -2 c +2}}{2}, \sqrt{2}\right)+\sqrt{-d x -c}\, \EllipticF \left(\frac{\sqrt{2 d x +2 c +2}}{2}, \sqrt{2}\right)\right)}{3 \left(d^{3} x^{3}+3 c \,d^{2} x^{2}+3 c^{2} d x +c^{3}-d x -c \right) d e}"," ",0,"-1/3*((d*x+c)*e)^(1/2)*(-d^2*x^2-2*c*d*x-c^2+1)^(1/2)*(2*d*x+2*c+2)^(1/2)*(-2*d*x-2*c+2)^(1/2)*((-d*x-c)^(1/2)*EllipticF(1/2*(2*d*x+2*c+2)^(1/2),2^(1/2))-2*(d*x+c)^(1/2)*EllipticF(1/2*(-2*d*x-2*c+2)^(1/2),2^(1/2)))/d/e/(d^3*x^3+3*c*d^2*x^2+3*c^2*d*x+c^3-d*x-c)","B"
1404,1,189,66,0.160000," ","int(1/(d*e*x+c*e)^(5/2)/(-d^2*x^2-2*c*d*x-c^2+1)^(1/2),x)","-\frac{\left(2 d^{2} x^{2}+4 c d x +\sqrt{-2 d x -2 c +2}\, \sqrt{2 d x +2 c +2}\, \sqrt{-d x -c}\, d x \EllipticF \left(\frac{\sqrt{2 d x +2 c +2}}{2}, \sqrt{2}\right)+2 c^{2}+\sqrt{-2 d x -2 c +2}\, \sqrt{2 d x +2 c +2}\, \sqrt{-d x -c}\, c \EllipticF \left(\frac{\sqrt{2 d x +2 c +2}}{2}, \sqrt{2}\right)-2\right) \sqrt{-d^{2} x^{2}-2 c d x -c^{2}+1}\, \sqrt{\left(d x +c \right) e}}{3 \left(d x +c \right)^{2} \left(d^{2} x^{2}+2 c d x +c^{2}-1\right) d \,e^{3}}"," ",0,"-1/3*((-2*d*x-2*c+2)^(1/2)*(2*d*x+2*c+2)^(1/2)*(-d*x-c)^(1/2)*EllipticF(1/2*(2*d*x+2*c+2)^(1/2),2^(1/2))*x*d+(-2*d*x-2*c+2)^(1/2)*(2*d*x+2*c+2)^(1/2)*(-d*x-c)^(1/2)*EllipticF(1/2*(2*d*x+2*c+2)^(1/2),2^(1/2))*c+2*d^2*x^2+4*c*d*x+2*c^2-2)/e^3*(-d^2*x^2-2*c*d*x-c^2+1)^(1/2)*((d*x+c)*e)^(1/2)/(d*x+c)^2/(d^2*x^2+2*c*d*x+c^2-1)/d","B"
1405,1,351,106,0.121000," ","int(1/(d*e*x+c*e)^(9/2)/(-d^2*x^2-2*c*d*x-c^2+1)^(1/2),x)","-\frac{\left(10 d^{4} x^{4}+40 c \,d^{3} x^{3}+5 \sqrt{2 d x +2 c +2}\, \sqrt{-d x -c}\, \sqrt{-2 d x -2 c +2}\, d^{3} x^{3} \EllipticF \left(\frac{\sqrt{2 d x +2 c +2}}{2}, \sqrt{2}\right)+60 c^{2} d^{2} x^{2}+15 \sqrt{2 d x +2 c +2}\, \sqrt{-d x -c}\, \sqrt{-2 d x -2 c +2}\, c \,d^{2} x^{2} \EllipticF \left(\frac{\sqrt{2 d x +2 c +2}}{2}, \sqrt{2}\right)+40 c^{3} d x +15 \sqrt{2 d x +2 c +2}\, \sqrt{-d x -c}\, \sqrt{-2 d x -2 c +2}\, c^{2} d x \EllipticF \left(\frac{\sqrt{2 d x +2 c +2}}{2}, \sqrt{2}\right)+10 c^{4}+5 \sqrt{2 d x +2 c +2}\, \sqrt{-d x -c}\, \sqrt{-2 d x -2 c +2}\, c^{3} \EllipticF \left(\frac{\sqrt{2 d x +2 c +2}}{2}, \sqrt{2}\right)-4 d^{2} x^{2}-8 c d x -4 c^{2}-6\right) \sqrt{-d^{2} x^{2}-2 c d x -c^{2}+1}\, \sqrt{\left(d x +c \right) e}}{21 \left(d x +c \right)^{4} \left(d^{2} x^{2}+2 c d x +c^{2}-1\right) d \,e^{5}}"," ",0,"-1/21*(5*(2*d*x+2*c+2)^(1/2)*(-d*x-c)^(1/2)*(-2*d*x-2*c+2)^(1/2)*EllipticF(1/2*(2*d*x+2*c+2)^(1/2),2^(1/2))*x^3*d^3+15*(2*d*x+2*c+2)^(1/2)*(-d*x-c)^(1/2)*(-2*d*x-2*c+2)^(1/2)*EllipticF(1/2*(2*d*x+2*c+2)^(1/2),2^(1/2))*x^2*c*d^2+15*(2*d*x+2*c+2)^(1/2)*(-d*x-c)^(1/2)*(-2*d*x-2*c+2)^(1/2)*EllipticF(1/2*(2*d*x+2*c+2)^(1/2),2^(1/2))*x*c^2*d+10*d^4*x^4+5*(2*d*x+2*c+2)^(1/2)*(-d*x-c)^(1/2)*(-2*d*x-2*c+2)^(1/2)*EllipticF(1/2*(2*d*x+2*c+2)^(1/2),2^(1/2))*c^3+40*x^3*c*d^3+60*c^2*d^2*x^2+40*x*c^3*d-4*d^2*x^2+10*c^4-8*c*d*x-4*c^2-6)/e^5*(-d^2*x^2-2*c*d*x-c^2+1)^(1/2)*((d*x+c)*e)^(1/2)/(d*x+c)^4/(d^2*x^2+2*c*d*x+c^2-1)/d","B"
1406,1,860,146,0.138000," ","int(1/(d*e*x+c*e)^(13/2)/(-d^2*x^2-2*c*d*x-c^2+1)^(1/2),x)","-\frac{\left(90 d^{6} x^{6}+540 c \,d^{5} x^{5}+10 \sqrt{2 d x +2 c +2}\, \sqrt{-2 d x -2 c +2}\, \sqrt{d x +c}\, d^{5} x^{5} \EllipticF \left(\frac{\sqrt{-2 d x -2 c +2}}{2}, \sqrt{2}\right)+55 \sqrt{2 d x +2 c +2}\, \sqrt{-d x -c}\, \sqrt{-2 d x -2 c +2}\, d^{5} x^{5} \EllipticF \left(\frac{\sqrt{2 d x +2 c +2}}{2}, \sqrt{2}\right)+1350 c^{2} d^{4} x^{4}+50 \sqrt{2 d x +2 c +2}\, \sqrt{-2 d x -2 c +2}\, \sqrt{d x +c}\, c \,d^{4} x^{4} \EllipticF \left(\frac{\sqrt{-2 d x -2 c +2}}{2}, \sqrt{2}\right)+275 \sqrt{2 d x +2 c +2}\, \sqrt{-d x -c}\, \sqrt{-2 d x -2 c +2}\, c \,d^{4} x^{4} \EllipticF \left(\frac{\sqrt{2 d x +2 c +2}}{2}, \sqrt{2}\right)+1800 c^{3} d^{3} x^{3}+100 \sqrt{2 d x +2 c +2}\, \sqrt{-2 d x -2 c +2}\, \sqrt{d x +c}\, c^{2} d^{3} x^{3} \EllipticF \left(\frac{\sqrt{-2 d x -2 c +2}}{2}, \sqrt{2}\right)+550 \sqrt{2 d x +2 c +2}\, \sqrt{-d x -c}\, \sqrt{-2 d x -2 c +2}\, c^{2} d^{3} x^{3} \EllipticF \left(\frac{\sqrt{2 d x +2 c +2}}{2}, \sqrt{2}\right)+1350 c^{4} d^{2} x^{2}+100 \sqrt{2 d x +2 c +2}\, \sqrt{-2 d x -2 c +2}\, \sqrt{d x +c}\, c^{3} d^{2} x^{2} \EllipticF \left(\frac{\sqrt{-2 d x -2 c +2}}{2}, \sqrt{2}\right)+550 \sqrt{2 d x +2 c +2}\, \sqrt{-d x -c}\, \sqrt{-2 d x -2 c +2}\, c^{3} d^{2} x^{2} \EllipticF \left(\frac{\sqrt{2 d x +2 c +2}}{2}, \sqrt{2}\right)-36 d^{4} x^{4}+540 c^{5} d x +50 \sqrt{2 d x +2 c +2}\, \sqrt{-2 d x -2 c +2}\, \sqrt{d x +c}\, c^{4} d x \EllipticF \left(\frac{\sqrt{-2 d x -2 c +2}}{2}, \sqrt{2}\right)+275 \sqrt{2 d x +2 c +2}\, \sqrt{-d x -c}\, \sqrt{-2 d x -2 c +2}\, c^{4} d x \EllipticF \left(\frac{\sqrt{2 d x +2 c +2}}{2}, \sqrt{2}\right)-144 c \,d^{3} x^{3}+90 c^{6}+10 \sqrt{2 d x +2 c +2}\, \sqrt{-2 d x -2 c +2}\, \sqrt{d x +c}\, c^{5} \EllipticF \left(\frac{\sqrt{-2 d x -2 c +2}}{2}, \sqrt{2}\right)+55 \sqrt{2 d x +2 c +2}\, \sqrt{-d x -c}\, \sqrt{-2 d x -2 c +2}\, c^{5} \EllipticF \left(\frac{\sqrt{2 d x +2 c +2}}{2}, \sqrt{2}\right)-216 c^{2} d^{2} x^{2}-144 c^{3} d x -36 c^{4}-12 d^{2} x^{2}-24 c d x -12 c^{2}-42\right) \sqrt{-d^{2} x^{2}-2 c d x -c^{2}+1}\, \sqrt{\left(d x +c \right) e}}{231 \left(d x +c \right)^{6} \left(d^{2} x^{2}+2 c d x +c^{2}-1\right) d \,e^{7}}"," ",0,"-1/231*(-42+55*(2*d*x+2*c+2)^(1/2)*(-d*x-c)^(1/2)*(-2*d*x-2*c+2)^(1/2)*EllipticF(1/2*(2*d*x+2*c+2)^(1/2),2^(1/2))*x^5*d^5-36*c^4+55*(2*d*x+2*c+2)^(1/2)*(-d*x-c)^(1/2)*(-2*d*x-2*c+2)^(1/2)*EllipticF(1/2*(2*d*x+2*c+2)^(1/2),2^(1/2))*c^5-12*c^2+10*(2*d*x+2*c+2)^(1/2)*(-2*d*x-2*c+2)^(1/2)*(d*x+c)^(1/2)*EllipticF(1/2*(-2*d*x-2*c+2)^(1/2),2^(1/2))*c^5+90*c^6-12*d^2*x^2-144*c*d^3*x^3-36*d^4*x^4-216*c^2*d^2*x^2+10*(2*d*x+2*c+2)^(1/2)*(-2*d*x-2*c+2)^(1/2)*(d*x+c)^(1/2)*EllipticF(1/2*(-2*d*x-2*c+2)^(1/2),2^(1/2))*x^5*d^5+540*x*c^5*d+1800*x^3*c^3*d^3+1350*x^2*c^4*d^2+1350*x^4*c^2*d^4+540*x^5*c*d^5-144*c^3*d*x+90*d^6*x^6-24*c*d*x+275*(2*d*x+2*c+2)^(1/2)*(-d*x-c)^(1/2)*(-2*d*x-2*c+2)^(1/2)*EllipticF(1/2*(2*d*x+2*c+2)^(1/2),2^(1/2))*x*c^4*d+50*(2*d*x+2*c+2)^(1/2)*(-2*d*x-2*c+2)^(1/2)*(d*x+c)^(1/2)*EllipticF(1/2*(-2*d*x-2*c+2)^(1/2),2^(1/2))*x*c^4*d+275*(2*d*x+2*c+2)^(1/2)*(-d*x-c)^(1/2)*(-2*d*x-2*c+2)^(1/2)*EllipticF(1/2*(2*d*x+2*c+2)^(1/2),2^(1/2))*x^4*c*d^4+50*(2*d*x+2*c+2)^(1/2)*(-2*d*x-2*c+2)^(1/2)*(d*x+c)^(1/2)*EllipticF(1/2*(-2*d*x-2*c+2)^(1/2),2^(1/2))*x^4*c*d^4+550*(2*d*x+2*c+2)^(1/2)*(-d*x-c)^(1/2)*(-2*d*x-2*c+2)^(1/2)*EllipticF(1/2*(2*d*x+2*c+2)^(1/2),2^(1/2))*x^3*c^2*d^3+100*(2*d*x+2*c+2)^(1/2)*(-2*d*x-2*c+2)^(1/2)*(d*x+c)^(1/2)*EllipticF(1/2*(-2*d*x-2*c+2)^(1/2),2^(1/2))*x^3*c^2*d^3+550*(2*d*x+2*c+2)^(1/2)*(-d*x-c)^(1/2)*(-2*d*x-2*c+2)^(1/2)*EllipticF(1/2*(2*d*x+2*c+2)^(1/2),2^(1/2))*x^2*c^3*d^2+100*(2*d*x+2*c+2)^(1/2)*(-2*d*x-2*c+2)^(1/2)*(d*x+c)^(1/2)*EllipticF(1/2*(-2*d*x-2*c+2)^(1/2),2^(1/2))*x^2*c^3*d^2)/e^7*(-d^2*x^2-2*c*d*x-c^2+1)^(1/2)*((d*x+c)*e)^(1/2)/(d*x+c)^6/(d^2*x^2+2*c*d*x+c^2-1)/d","B"
1407,1,296,129,0.077000," ","int((d*e*x+c*e)^(9/2)/(-d^2*x^2-2*c*d*x-c^2+1)^(1/2),x)","-\frac{\sqrt{\left(d x +c \right) e}\, \sqrt{-d^{2} x^{2}-2 c d x -c^{2}+1}\, \left(10 d^{6} x^{6}+60 c \,d^{5} x^{5}+150 c^{2} d^{4} x^{4}+200 c^{3} d^{3} x^{3}+150 c^{4} d^{2} x^{2}+4 d^{4} x^{4}+60 c^{5} d x +16 c \,d^{3} x^{3}+10 c^{6}+24 c^{2} d^{2} x^{2}+16 c^{3} d x +4 c^{4}-14 d^{2} x^{2}-28 c d x -14 c^{2}+24 \sqrt{-2 d x -2 c +2}\, \sqrt{d x +c}\, \sqrt{2 d x +2 c +2}\, \EllipticE \left(\frac{\sqrt{-2 d x -2 c +2}}{2}, \sqrt{2}\right)-45 \sqrt{-2 d x -2 c +2}\, \sqrt{2 d x +2 c +2}\, \sqrt{-d x -c}\, \EllipticE \left(\frac{\sqrt{2 d x +2 c +2}}{2}, \sqrt{2}\right)\right) e^{4}}{45 \left(d^{3} x^{3}+3 c \,d^{2} x^{2}+3 c^{2} d x +c^{3}-d x -c \right) d}"," ",0,"-1/45*((d*x+c)*e)^(1/2)*(-d^2*x^2-2*c*d*x-c^2+1)^(1/2)*e^4*(10*d^6*x^6+60*c*d^5*x^5+150*c^2*d^4*x^4+200*c^3*d^3*x^3+4*d^4*x^4+150*c^4*d^2*x^2+16*c*d^3*x^3+60*c^5*d*x+24*c^2*d^2*x^2+10*c^6+16*c^3*d*x+24*(-2*d*x-2*c+2)^(1/2)*(d*x+c)^(1/2)*(2*d*x+2*c+2)^(1/2)*EllipticE(1/2*(-2*d*x-2*c+2)^(1/2),2^(1/2))-45*(-2*d*x-2*c+2)^(1/2)*(2*d*x+2*c+2)^(1/2)*(-d*x-c)^(1/2)*EllipticE(1/2*(2*d*x+2*c+2)^(1/2),2^(1/2))-14*d^2*x^2+4*c^4-28*c*d*x-14*c^2)/d/(d^3*x^3+3*c*d^2*x^2+3*c^2*d*x+c^3-d*x-c)","B"
1408,1,234,89,0.068000," ","int((d*e*x+c*e)^(5/2)/(-d^2*x^2-2*c*d*x-c^2+1)^(1/2),x)","-\frac{\sqrt{\left(d x +c \right) e}\, \sqrt{-d^{2} x^{2}-2 c d x -c^{2}+1}\, \left(2 d^{4} x^{4}+8 c \,d^{3} x^{3}+12 c^{2} d^{2} x^{2}+8 c^{3} d x +2 c^{4}-2 d^{2} x^{2}-4 c d x -2 c^{2}+2 \sqrt{-2 d x -2 c +2}\, \sqrt{d x +c}\, \sqrt{2 d x +2 c +2}\, \EllipticE \left(\frac{\sqrt{-2 d x -2 c +2}}{2}, \sqrt{2}\right)-5 \sqrt{-2 d x -2 c +2}\, \sqrt{2 d x +2 c +2}\, \sqrt{-d x -c}\, \EllipticE \left(\frac{\sqrt{2 d x +2 c +2}}{2}, \sqrt{2}\right)\right) e^{2}}{5 \left(d^{3} x^{3}+3 c \,d^{2} x^{2}+3 c^{2} d x +c^{3}-d x -c \right) d}"," ",0,"-1/5*((d*x+c)*e)^(1/2)*(-d^2*x^2-2*c*d*x-c^2+1)^(1/2)*e^2*(2*d^4*x^4+8*c*d^3*x^3+12*c^2*d^2*x^2+8*c^3*d*x+2*(-2*d*x-2*c+2)^(1/2)*(d*x+c)^(1/2)*(2*d*x+2*c+2)^(1/2)*EllipticE(1/2*(-2*d*x-2*c+2)^(1/2),2^(1/2))-5*(-2*d*x-2*c+2)^(1/2)*(2*d*x+2*c+2)^(1/2)*(-d*x-c)^(1/2)*EllipticE(1/2*(2*d*x+2*c+2)^(1/2),2^(1/2))-2*d^2*x^2+2*c^4-4*c*d*x-2*c^2)/d/(d^3*x^3+3*c*d^2*x^2+3*c^2*d*x+c^3-d*x-c)","B"
1409,1,121,51,0.068000," ","int((d*e*x+c*e)^(1/2)/(-d^2*x^2-2*c*d*x-c^2+1)^(1/2),x)","\frac{\sqrt{\left(d x +c \right) e}\, \sqrt{-d^{2} x^{2}-2 c d x -c^{2}+1}\, \sqrt{2 d x +2 c +2}\, \sqrt{-d x -c}\, \sqrt{-2 d x -2 c +2}\, \EllipticE \left(\frac{\sqrt{2 d x +2 c +2}}{2}, \sqrt{2}\right)}{\left(d^{3} x^{3}+3 c \,d^{2} x^{2}+3 c^{2} d x +c^{3}-d x -c \right) d}"," ",0,"((d*x+c)*e)^(1/2)*(-d^2*x^2-2*c*d*x-c^2+1)^(1/2)*(2*d*x+2*c+2)^(1/2)*(-d*x-c)^(1/2)*(-2*d*x-2*c+2)^(1/2)*EllipticE(1/2*(2*d*x+2*c+2)^(1/2),2^(1/2))/d/(d^3*x^3+3*c*d^2*x^2+3*c^2*d*x+c^3-d*x-c)","B"
1410,1,193,91,0.207000," ","int(1/(d*e*x+c*e)^(3/2)/(-d^2*x^2-2*c*d*x-c^2+1)^(1/2),x)","\frac{\sqrt{\left(d x +c \right) e}\, \sqrt{-d^{2} x^{2}-2 c d x -c^{2}+1}\, \left(-2 d^{2} x^{2}-4 c d x -2 c^{2}-2 \sqrt{-2 d x -2 c +2}\, \sqrt{d x +c}\, \sqrt{2 d x +2 c +2}\, \EllipticE \left(\frac{\sqrt{-2 d x -2 c +2}}{2}, \sqrt{2}\right)+\sqrt{-2 d x -2 c +2}\, \sqrt{2 d x +2 c +2}\, \sqrt{-d x -c}\, \EllipticE \left(\frac{\sqrt{2 d x +2 c +2}}{2}, \sqrt{2}\right)+2\right)}{\left(d^{3} x^{3}+3 c \,d^{2} x^{2}+3 c^{2} d x +c^{3}-d x -c \right) d \,e^{2}}"," ",0,"((d*x+c)*e)^(1/2)*(-d^2*x^2-2*c*d*x-c^2+1)^(1/2)*((-2*d*x-2*c+2)^(1/2)*(2*d*x+2*c+2)^(1/2)*(-d*x-c)^(1/2)*EllipticE(1/2*(2*d*x+2*c+2)^(1/2),2^(1/2))-2*(-2*d*x-2*c+2)^(1/2)*(d*x+c)^(1/2)*(2*d*x+2*c+2)^(1/2)*EllipticE(1/2*(-2*d*x-2*c+2)^(1/2),2^(1/2))-2*d^2*x^2-4*c*d*x-2*c^2+2)/d/e^2/(d^3*x^3+3*c*d^2*x^2+3*c^2*d*x+c^3-d*x-c)","B"
1411,1,447,131,0.128000," ","int(1/(d*e*x+c*e)^(7/2)/(-d^2*x^2-2*c*d*x-c^2+1)^(1/2),x)","\frac{\left(-6 d^{4} x^{4}-24 c \,d^{3} x^{3}-36 c^{2} d^{2} x^{2}-24 c^{3} d x -10 \sqrt{d x +c}\, \sqrt{2 d x +2 c +2}\, \sqrt{-2 d x -2 c +2}\, d^{2} x^{2} \EllipticE \left(\frac{\sqrt{-2 d x -2 c +2}}{2}, \sqrt{2}\right)+7 \sqrt{2 d x +2 c +2}\, \sqrt{-d x -c}\, \sqrt{-2 d x -2 c +2}\, d^{2} x^{2} \EllipticE \left(\frac{\sqrt{2 d x +2 c +2}}{2}, \sqrt{2}\right)-6 c^{4}-20 \sqrt{d x +c}\, \sqrt{2 d x +2 c +2}\, \sqrt{-2 d x -2 c +2}\, c d x \EllipticE \left(\frac{\sqrt{-2 d x -2 c +2}}{2}, \sqrt{2}\right)+14 \sqrt{2 d x +2 c +2}\, \sqrt{-d x -c}\, \sqrt{-2 d x -2 c +2}\, c d x \EllipticE \left(\frac{\sqrt{2 d x +2 c +2}}{2}, \sqrt{2}\right)+4 d^{2} x^{2}-10 \sqrt{d x +c}\, \sqrt{2 d x +2 c +2}\, \sqrt{-2 d x -2 c +2}\, c^{2} \EllipticE \left(\frac{\sqrt{-2 d x -2 c +2}}{2}, \sqrt{2}\right)+7 \sqrt{2 d x +2 c +2}\, \sqrt{-d x -c}\, \sqrt{-2 d x -2 c +2}\, c^{2} \EllipticE \left(\frac{\sqrt{2 d x +2 c +2}}{2}, \sqrt{2}\right)+8 c d x +4 c^{2}+2\right) \sqrt{-d^{2} x^{2}-2 c d x -c^{2}+1}\, \sqrt{\left(d x +c \right) e}}{5 \left(d x +c \right)^{3} \left(d^{2} x^{2}+2 c d x +c^{2}-1\right) d \,e^{4}}"," ",0,"1/5*(7*EllipticE(1/2*(2*d*x+2*c+2)^(1/2),2^(1/2))*x^2*d^2*(2*d*x+2*c+2)^(1/2)*(-d*x-c)^(1/2)*(-2*d*x-2*c+2)^(1/2)-10*EllipticE(1/2*(-2*d*x-2*c+2)^(1/2),2^(1/2))*x^2*d^2*(d*x+c)^(1/2)*(2*d*x+2*c+2)^(1/2)*(-2*d*x-2*c+2)^(1/2)-6*d^4*x^4+14*EllipticE(1/2*(2*d*x+2*c+2)^(1/2),2^(1/2))*x*c*d*(2*d*x+2*c+2)^(1/2)*(-d*x-c)^(1/2)*(-2*d*x-2*c+2)^(1/2)-20*EllipticE(1/2*(-2*d*x-2*c+2)^(1/2),2^(1/2))*x*c*d*(d*x+c)^(1/2)*(2*d*x+2*c+2)^(1/2)*(-2*d*x-2*c+2)^(1/2)-24*c*d^3*x^3+7*EllipticE(1/2*(2*d*x+2*c+2)^(1/2),2^(1/2))*c^2*(2*d*x+2*c+2)^(1/2)*(-d*x-c)^(1/2)*(-2*d*x-2*c+2)^(1/2)-10*EllipticE(1/2*(-2*d*x-2*c+2)^(1/2),2^(1/2))*c^2*(d*x+c)^(1/2)*(2*d*x+2*c+2)^(1/2)*(-2*d*x-2*c+2)^(1/2)-36*c^2*d^2*x^2-24*c^3*d*x+4*d^2*x^2-6*c^4+8*c*d*x+4*c^2+2)*(-d^2*x^2-2*c*d*x-c^2+1)^(1/2)*((d*x+c)*e)^(1/2)/e^4/(d*x+c)^3/(d^2*x^2+2*c*d*x+c^2-1)/d","B"
1412,0,0,257,1.337000," ","int((c*x^2+b*x+a)^(4/3)/(2*c*d*x+b*d)^(11/3),x)","\int \frac{\left(c \,x^{2}+b x +a \right)^{\frac{4}{3}}}{\left(2 c d x +b d \right)^{\frac{11}{3}}}\, dx"," ",0,"int((c*x^2+b*x+a)^(4/3)/(2*c*d*x+b*d)^(11/3),x)","F"
1413,1,44,38,0.045000," ","int((c*x^2+b*x+a)^(4/3)/(2*c*d*x+b*d)^(17/3),x)","-\frac{3 \left(2 c x +b \right) \left(c \,x^{2}+b x +a \right)^{\frac{7}{3}}}{7 \left(4 a c -b^{2}\right) \left(2 c d x +b d \right)^{\frac{17}{3}}}"," ",0,"-3/7*(2*c*x+b)*(c*x^2+b*x+a)^(7/3)/(4*a*c-b^2)/(2*c*d*x+b*d)^(17/3)","A"
1414,1,76,77,0.044000," ","int((c*x^2+b*x+a)^(4/3)/(2*c*d*x+b*d)^(23/3),x)","-\frac{3 \left(2 c x +b \right) \left(c \,x^{2}+b x +a \right)^{\frac{7}{3}} \left(-6 c^{2} x^{2}-6 b c x +14 a c -5 b^{2}\right)}{35 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \left(2 c d x +b d \right)^{\frac{23}{3}}}"," ",0,"-3/35*(2*c*x+b)*(c*x^2+b*x+a)^(7/3)*(-6*c^2*x^2-6*b*c*x+14*a*c-5*b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)/(2*c*d*x+b*d)^(23/3)","A"
1415,1,139,115,0.046000," ","int((c*x^2+b*x+a)^(4/3)/(2*c*d*x+b*d)^(29/3),x)","-\frac{3 \left(2 c x +b \right) \left(c \,x^{2}+b x +a \right)^{\frac{7}{3}} \left(144 c^{4} x^{4}+288 b \,c^{3} x^{3}-336 a \,c^{3} x^{2}+300 b^{2} c^{2} x^{2}-336 a b \,c^{2} x +156 b^{3} c x +560 a^{2} c^{2}-364 a \,b^{2} c +65 b^{4}\right)}{455 \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) \left(2 c d x +b d \right)^{\frac{29}{3}}}"," ",0,"-3/455*(2*c*x+b)*(c*x^2+b*x+a)^(7/3)*(144*c^4*x^4+288*b*c^3*x^3-336*a*c^3*x^2+300*b^2*c^2*x^2-336*a*b*c^2*x+156*b^3*c*x+560*a^2*c^2-364*a*b^2*c+65*b^4)/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)/(2*c*d*x+b*d)^(29/3)","A"
1416,0,0,656,0.127000," ","int((c*x^2+b*x+a)^(4/3)/(2*c*d*x+b*d)^(2/3),x)","\int \frac{\left(c \,x^{2}+b x +a \right)^{\frac{4}{3}}}{\left(2 c d x +b d \right)^{\frac{2}{3}}}\, dx"," ",0,"int((c*x^2+b*x+a)^(4/3)/(2*c*d*x+b*d)^(2/3),x)","F"
1417,0,0,640,1.001000," ","int((c*x^2+b*x+a)^(4/3)/(2*c*d*x+b*d)^(8/3),x)","\int \frac{\left(c \,x^{2}+b x +a \right)^{\frac{4}{3}}}{\left(2 c d x +b d \right)^{\frac{8}{3}}}\, dx"," ",0,"int((c*x^2+b*x+a)^(4/3)/(2*c*d*x+b*d)^(8/3),x)","F"
1418,0,0,650,1.505000," ","int((c*x^2+b*x+a)^(4/3)/(2*c*d*x+b*d)^(14/3),x)","\int \frac{\left(c \,x^{2}+b x +a \right)^{\frac{4}{3}}}{\left(2 c d x +b d \right)^{\frac{14}{3}}}\, dx"," ",0,"int((c*x^2+b*x+a)^(4/3)/(2*c*d*x+b*d)^(14/3),x)","F"
1419,0,0,690,1.302000," ","int((c*x^2+b*x+a)^(4/3)/(2*c*d*x+b*d)^(20/3),x)","\int \frac{\left(c \,x^{2}+b x +a \right)^{\frac{4}{3}}}{\left(2 c d x +b d \right)^{\frac{20}{3}}}\, dx"," ",0,"int((c*x^2+b*x+a)^(4/3)/(2*c*d*x+b*d)^(20/3),x)","F"
1420,0,0,87,0.602000," ","int((c*x^2+b*x+a)^(4/3)/(2*c*d*x+b*d)^(4/3),x)","\int \frac{\left(c \,x^{2}+b x +a \right)^{\frac{4}{3}}}{\left(2 c d x +b d \right)^{\frac{4}{3}}}\, dx"," ",0,"int((c*x^2+b*x+a)^(4/3)/(2*c*d*x+b*d)^(4/3),x)","F"
1421,0,0,87,1.387000," ","int((c*x^2+b*x+a)^(4/3)/(2*c*d*x+b*d)^(10/3),x)","\int \frac{\left(c \,x^{2}+b x +a \right)^{\frac{4}{3}}}{\left(2 c d x +b d \right)^{\frac{10}{3}}}\, dx"," ",0,"int((c*x^2+b*x+a)^(4/3)/(2*c*d*x+b*d)^(10/3),x)","F"
1422,0,0,87,1.259000," ","int((c*x^2+b*x+a)^(4/3)/(2*c*d*x+b*d)^(16/3),x)","\int \frac{\left(c \,x^{2}+b x +a \right)^{\frac{4}{3}}}{\left(2 c d x +b d \right)^{\frac{16}{3}}}\, dx"," ",0,"int((c*x^2+b*x+a)^(4/3)/(2*c*d*x+b*d)^(16/3),x)","F"
1423,1,653,133,0.049000," ","int((2*c*d*x+b*d)^m*(c*x^2+b*x+a)^3,x)","\frac{\left(4 c^{6} m^{3} x^{6}+12 b \,c^{5} m^{3} x^{5}+36 c^{6} m^{2} x^{6}+12 a \,c^{5} m^{3} x^{4}+12 b^{2} c^{4} m^{3} x^{4}+108 b \,c^{5} m^{2} x^{5}+92 c^{6} m \,x^{6}+24 a b \,c^{4} m^{3} x^{3}+132 a \,c^{5} m^{2} x^{4}+4 b^{3} c^{3} m^{3} x^{3}+102 b^{2} c^{4} m^{2} x^{4}+276 b \,c^{5} m \,x^{5}+60 c^{6} x^{6}+12 a^{2} c^{4} m^{3} x^{2}+12 a \,b^{2} c^{3} m^{3} x^{2}+264 a b \,c^{4} m^{2} x^{3}+372 a \,c^{5} m \,x^{4}+24 b^{3} c^{3} m^{2} x^{3}+252 b^{2} c^{4} m \,x^{4}+180 b \,c^{5} x^{5}+12 a^{2} b \,c^{3} m^{3} x +156 a^{2} c^{4} m^{2} x^{2}+120 a \,b^{2} c^{3} m^{2} x^{2}+744 a b \,c^{4} m \,x^{3}+252 a \,c^{5} x^{4}-6 b^{4} c^{2} m^{2} x^{2}+44 b^{3} c^{3} m \,x^{3}+162 b^{2} c^{4} x^{4}+4 a^{3} c^{3} m^{3}+156 a^{2} b \,c^{3} m^{2} x +564 a^{2} c^{4} m \,x^{2}-12 a \,b^{3} c^{2} m^{2} x +276 a \,b^{2} c^{3} m \,x^{2}+504 a b \,c^{4} x^{3}-18 b^{4} c^{2} m \,x^{2}+24 b^{3} c^{3} x^{3}+60 a^{3} c^{3} m^{2}-6 a^{2} b^{2} c^{2} m^{2}+564 a^{2} b \,c^{3} m x +420 a^{2} c^{4} x^{2}-96 a \,b^{3} c^{2} m x +168 a \,b^{2} c^{3} x^{2}+6 b^{5} c m x -12 b^{4} c^{2} x^{2}+284 a^{3} c^{3} m -72 a^{2} b^{2} c^{2} m +420 a^{2} b \,c^{3} x +6 a \,b^{4} c m -84 a \,b^{3} c^{2} x +6 b^{5} c x +420 a^{3} c^{3}-210 a^{2} b^{2} c^{2}+42 a \,b^{4} c -3 b^{6}\right) \left(2 c x +b \right) \left(2 c d x +b d \right)^{m}}{8 \left(m^{4}+16 m^{3}+86 m^{2}+176 m +105\right) c^{4}}"," ",0,"1/8*(2*c*d*x+b*d)^m*(4*c^6*m^3*x^6+12*b*c^5*m^3*x^5+36*c^6*m^2*x^6+12*a*c^5*m^3*x^4+12*b^2*c^4*m^3*x^4+108*b*c^5*m^2*x^5+92*c^6*m*x^6+24*a*b*c^4*m^3*x^3+132*a*c^5*m^2*x^4+4*b^3*c^3*m^3*x^3+102*b^2*c^4*m^2*x^4+276*b*c^5*m*x^5+60*c^6*x^6+12*a^2*c^4*m^3*x^2+12*a*b^2*c^3*m^3*x^2+264*a*b*c^4*m^2*x^3+372*a*c^5*m*x^4+24*b^3*c^3*m^2*x^3+252*b^2*c^4*m*x^4+180*b*c^5*x^5+12*a^2*b*c^3*m^3*x+156*a^2*c^4*m^2*x^2+120*a*b^2*c^3*m^2*x^2+744*a*b*c^4*m*x^3+252*a*c^5*x^4-6*b^4*c^2*m^2*x^2+44*b^3*c^3*m*x^3+162*b^2*c^4*x^4+4*a^3*c^3*m^3+156*a^2*b*c^3*m^2*x+564*a^2*c^4*m*x^2-12*a*b^3*c^2*m^2*x+276*a*b^2*c^3*m*x^2+504*a*b*c^4*x^3-18*b^4*c^2*m*x^2+24*b^3*c^3*x^3+60*a^3*c^3*m^2-6*a^2*b^2*c^2*m^2+564*a^2*b*c^3*m*x+420*a^2*c^4*x^2-96*a*b^3*c^2*m*x+168*a*b^2*c^3*x^2+6*b^5*c*m*x-12*b^4*c^2*x^2+284*a^3*c^3*m-72*a^2*b^2*c^2*m+420*a^2*b*c^3*x+6*a*b^4*c*m-84*a*b^3*c^2*x+6*b^5*c*x+420*a^3*c^3-210*a^2*b^2*c^2+42*a*b^4*c-3*b^6)*(2*c*x+b)/c^4/(m^4+16*m^3+86*m^2+176*m+105)","B"
1424,1,255,97,0.053000," ","int((2*c*d*x+b*d)^m*(c*x^2+b*x+a)^2,x)","\frac{\left(2 c x +b \right) \left(2 c^{4} m^{2} x^{4}+4 b \,c^{3} m^{2} x^{3}+8 c^{4} m \,x^{4}+4 a \,c^{3} m^{2} x^{2}+2 b^{2} c^{2} m^{2} x^{2}+16 b \,c^{3} m \,x^{3}+6 c^{4} x^{4}+4 a b \,c^{2} m^{2} x +24 a \,c^{3} m \,x^{2}+6 b^{2} c^{2} m \,x^{2}+12 b \,c^{3} x^{3}+2 a^{2} c^{2} m^{2}+24 a b \,c^{2} m x +20 a \,c^{3} x^{2}-2 b^{3} c m x +4 b^{2} c^{2} x^{2}+16 a^{2} c^{2} m -2 a \,b^{2} c m +20 a b \,c^{2} x -2 b^{3} c x +30 a^{2} c^{2}-10 a \,b^{2} c +b^{4}\right) \left(2 c d x +b d \right)^{m}}{4 \left(m^{3}+9 m^{2}+23 m +15\right) c^{3}}"," ",0,"1/4*(2*c*x+b)*(2*c^4*m^2*x^4+4*b*c^3*m^2*x^3+8*c^4*m*x^4+4*a*c^3*m^2*x^2+2*b^2*c^2*m^2*x^2+16*b*c^3*m*x^3+6*c^4*x^4+4*a*b*c^2*m^2*x+24*a*c^3*m*x^2+6*b^2*c^2*m*x^2+12*b*c^3*x^3+2*a^2*c^2*m^2+24*a*b*c^2*m*x+20*a*c^3*x^2-2*b^3*c*m*x+4*b^2*c^2*x^2+16*a^2*c^2*m-2*a*b^2*c*m+20*a*b*c^2*x-2*b^3*c*x+30*a^2*c^2-10*a*b^2*c+b^4)*(2*c*d*x+b*d)^m/c^3/(m^3+9*m^2+23*m+15)","B"
1425,1,76,61,0.043000," ","int((2*c*d*x+b*d)^m*(c*x^2+b*x+a),x)","\frac{\left(2 c^{2} m \,x^{2}+2 b c m x +2 c^{2} x^{2}+2 a c m +2 b c x +6 a c -b^{2}\right) \left(2 c x +b \right) \left(2 c d x +b d \right)^{m}}{4 \left(m^{2}+4 m +3\right) c^{2}}"," ",0,"1/4*(2*c*d*x+b*d)^m*(2*c^2*m*x^2+2*b*c*m*x+2*c^2*x^2+2*a*c*m+2*b*c*x+6*a*c-b^2)*(2*c*x+b)/c^2/(m^2+4*m+3)","A"
1426,0,0,65,1.275000," ","int((2*c*d*x+b*d)^m/(c*x^2+b*x+a),x)","\int \frac{\left(2 c d x +b d \right)^{m}}{c \,x^{2}+b x +a}\, dx"," ",0,"int((2*c*d*x+b*d)^m/(c*x^2+b*x+a),x)","F"
1427,0,0,66,1.465000," ","int((2*c*d*x+b*d)^m/(c*x^2+b*x+a)^2,x)","\int \frac{\left(2 c d x +b d \right)^{m}}{\left(c \,x^{2}+b x +a \right)^{2}}\, dx"," ",0,"int((2*c*d*x+b*d)^m/(c*x^2+b*x+a)^2,x)","F"
1428,0,0,68,1.296000," ","int((2*c*d*x+b*d)^m/(c*x^2+b*x+a)^3,x)","\int \frac{\left(2 c d x +b d \right)^{m}}{\left(c \,x^{2}+b x +a \right)^{3}}\, dx"," ",0,"int((2*c*d*x+b*d)^m/(c*x^2+b*x+a)^3,x)","F"
1429,0,0,78,1.230000," ","int((2*c*d*x+b*d)^m*(c*x^2+b*x+a)^(5/2),x)","\int \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} \left(2 c d x +b d \right)^{m}\, dx"," ",0,"int((2*c*d*x+b*d)^m*(c*x^2+b*x+a)^(5/2),x)","F"
1430,0,0,92,1.354000," ","int((2*c*d*x+b*d)^m*(c*x^2+b*x+a)^(3/2),x)","\int \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} \left(2 c d x +b d \right)^{m}\, dx"," ",0,"int((2*c*d*x+b*d)^m*(c*x^2+b*x+a)^(3/2),x)","F"
1431,0,0,92,1.351000," ","int((2*c*d*x+b*d)^m*(c*x^2+b*x+a)^(1/2),x)","\int \sqrt{c \,x^{2}+b x +a}\, \left(2 c d x +b d \right)^{m}\, dx"," ",0,"int((2*c*d*x+b*d)^m*(c*x^2+b*x+a)^(1/2),x)","F"
1432,0,0,92,1.256000," ","int((2*c*d*x+b*d)^m/(c*x^2+b*x+a)^(1/2),x)","\int \frac{\left(2 c d x +b d \right)^{m}}{\sqrt{c \,x^{2}+b x +a}}\, dx"," ",0,"int((2*c*d*x+b*d)^m/(c*x^2+b*x+a)^(1/2),x)","F"
1433,0,0,90,1.485000," ","int((2*c*d*x+b*d)^m/(c*x^2+b*x+a)^(3/2),x)","\int \frac{\left(2 c d x +b d \right)^{m}}{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}}}\, dx"," ",0,"int((2*c*d*x+b*d)^m/(c*x^2+b*x+a)^(3/2),x)","F"
1434,0,0,92,1.496000," ","int((2*c*d*x+b*d)^m/(c*x^2+b*x+a)^(5/2),x)","\int \frac{\left(2 c d x +b d \right)^{m}}{\left(c \,x^{2}+b x +a \right)^{\frac{5}{2}}}\, dx"," ",0,"int((2*c*d*x+b*d)^m/(c*x^2+b*x+a)^(5/2),x)","F"
1435,0,0,94,1.344000," ","int((2*c*d*x+b*d)^m*(c*x^2+b*x+a)^p,x)","\int \left(2 c d x +b d \right)^{m} \left(c \,x^{2}+b x +a \right)^{p}\, dx"," ",0,"int((2*c*d*x+b*d)^m*(c*x^2+b*x+a)^p,x)","F"
1436,1,233,121,0.047000," ","int((2*c*d*x+b*d)^5*(c*x^2+b*x+a)^p,x)","\frac{\left(16 c^{4} p^{2} x^{4}+32 b \,c^{3} p^{2} x^{3}+48 c^{4} p \,x^{4}+24 b^{2} c^{2} p^{2} x^{2}+96 b \,c^{3} p \,x^{3}+32 c^{4} x^{4}-32 a \,c^{3} p \,x^{2}+8 b^{3} c \,p^{2} x +80 b^{2} c^{2} p \,x^{2}+64 b \,c^{3} x^{3}-32 a b \,c^{2} p x -32 a \,c^{3} x^{2}+b^{4} p^{2}+32 b^{3} c p x +56 b^{2} c^{2} x^{2}-8 a \,b^{2} c p -32 a b \,c^{2} x +5 b^{4} p +24 b^{3} c x +32 a^{2} c^{2}-24 a \,b^{2} c +6 b^{4}\right) d^{5} \left(c \,x^{2}+b x +a \right)^{p +1}}{p^{3}+6 p^{2}+11 p +6}"," ",0,"(c*x^2+b*x+a)^(p+1)*d^5*(16*c^4*p^2*x^4+32*b*c^3*p^2*x^3+48*c^4*p*x^4+24*b^2*c^2*p^2*x^2+96*b*c^3*p*x^3+32*c^4*x^4-32*a*c^3*p*x^2+8*b^3*c*p^2*x+80*b^2*c^2*p*x^2+64*b*c^3*x^3-32*a*b*c^2*p*x-32*a*c^3*x^2+b^4*p^2+32*b^3*c*p*x+56*b^2*c^2*x^2-8*a*b^2*c*p-32*a*b*c^2*x+5*b^4*p+24*b^3*c*x+32*a^2*c^2-24*a*b^2*c+6*b^4)/(p^3+6*p^2+11*p+6)","A"
1437,0,0,77,1.309000," ","int((2*c*d*x+b*d)^4*(c*x^2+b*x+a)^p,x)","\int \left(2 c d x +b d \right)^{4} \left(c \,x^{2}+b x +a \right)^{p}\, dx"," ",0,"int((2*c*d*x+b*d)^4*(c*x^2+b*x+a)^p,x)","F"
1438,1,74,68,0.047000," ","int((2*c*d*x+b*d)^3*(c*x^2+b*x+a)^p,x)","-\frac{\left(-4 c^{2} p \,x^{2}-4 b c p x -4 c^{2} x^{2}-b^{2} p -4 b c x +4 a c -2 b^{2}\right) d^{3} \left(c \,x^{2}+b x +a \right)^{p +1}}{p^{2}+3 p +2}"," ",0,"-(c*x^2+b*x+a)^(p+1)*(-4*c^2*p*x^2-4*b*c*p*x-4*c^2*x^2-b^2*p-4*b*c*x+4*a*c-2*b^2)*d^3/(p^2+3*p+2)","A"
1439,0,0,77,1.257000," ","int((2*c*d*x+b*d)^2*(c*x^2+b*x+a)^p,x)","\int \left(2 c d x +b d \right)^{2} \left(c \,x^{2}+b x +a \right)^{p}\, dx"," ",0,"int((2*c*d*x+b*d)^2*(c*x^2+b*x+a)^p,x)","F"
1440,1,22,21,0.046000," ","int((2*c*d*x+b*d)*(c*x^2+b*x+a)^p,x)","\frac{d \left(c \,x^{2}+b x +a \right)^{p +1}}{p +1}"," ",0,"d*(c*x^2+b*x+a)^(p+1)/(p+1)","A"
1441,0,0,65,1.343000," ","int((c*x^2+b*x+a)^p/(2*c*d*x+b*d),x)","\int \frac{\left(c \,x^{2}+b x +a \right)^{p}}{2 c d x +b d}\, dx"," ",0,"int((c*x^2+b*x+a)^p/(2*c*d*x+b*d),x)","F"
1442,0,0,77,1.273000," ","int((c*x^2+b*x+a)^p/(2*c*d*x+b*d)^2,x)","\int \frac{\left(c \,x^{2}+b x +a \right)^{p}}{\left(2 c d x +b d \right)^{2}}\, dx"," ",0,"int((c*x^2+b*x+a)^p/(2*c*d*x+b*d)^2,x)","F"
1443,0,0,65,1.360000," ","int((c*x^2+b*x+a)^p/(2*c*d*x+b*d)^3,x)","\int \frac{\left(c \,x^{2}+b x +a \right)^{p}}{\left(2 c d x +b d \right)^{3}}\, dx"," ",0,"int((c*x^2+b*x+a)^p/(2*c*d*x+b*d)^3,x)","F"
1444,0,0,77,1.292000," ","int((c*x^2+b*x+a)^p/(2*c*d*x+b*d)^4,x)","\int \frac{\left(c \,x^{2}+b x +a \right)^{p}}{\left(2 c d x +b d \right)^{4}}\, dx"," ",0,"int((c*x^2+b*x+a)^p/(2*c*d*x+b*d)^4,x)","F"
1445,0,0,65,1.335000," ","int((c*x^2+b*x+a)^p/(2*c*d*x+b*d)^5,x)","\int \frac{\left(c \,x^{2}+b x +a \right)^{p}}{\left(2 c d x +b d \right)^{5}}\, dx"," ",0,"int((c*x^2+b*x+a)^p/(2*c*d*x+b*d)^5,x)","F"
1446,0,0,77,1.260000," ","int((c*x^2+b*x+a)^p/(2*c*d*x+b*d)^6,x)","\int \frac{\left(c \,x^{2}+b x +a \right)^{p}}{\left(2 c d x +b d \right)^{6}}\, dx"," ",0,"int((c*x^2+b*x+a)^p/(2*c*d*x+b*d)^6,x)","F"
1447,1,19,12,0.043000," ","int((x+1)/(x^2+2*x-3)^(2/3),x)","\frac{3 \left(x +3\right) \left(x -1\right)}{2 \left(x^{2}+2 x -3\right)^{\frac{2}{3}}}"," ",0,"3/2*(x+3)*(x-1)/(x^2+2*x-3)^(2/3)","A"
1448,1,16,15,0.046000," ","int((c*x+b)/(c*x^2+2*b*x+a)^(3/7),x)","\frac{7 \left(c \,x^{2}+2 b x +a \right)^{\frac{4}{7}}}{8}"," ",0,"7/8*(c*x^2+2*b*x+a)^(4/7)","A"
1449,1,27,26,0.036000," ","int((x+1)^m*(x^2+2*x+1)^n,x)","\frac{\left(x +1\right)^{m +1} \left(x^{2}+2 x +1\right)^{n}}{m +2 n +1}"," ",0,"(x+1)^(m+1)*(x^2+2*x+1)^n/(m+2*n+1)","A"
1450,1,58,46,0.042000," ","int((1/2*b*e/c+e*x)^m*(1/4*b^2/c+b*x+c*x^2)^n,x)","\frac{\left(2 c x +b \right) \left(\frac{4 c^{2} x^{2}+4 b c x +b^{2}}{4 c}\right)^{n} \left(\frac{\left(2 c x +b \right) e}{2 c}\right)^{m}}{2 \left(m +2 n +1\right) c}"," ",0,"1/2*(2*c*x+b)/c/(m+2*n+1)*(1/2*e*(2*c*x+b)/c)^m*(1/4*(4*c^2*x^2+4*b*c*x+b^2)/c)^n","A"
1451,1,163,59,0.042000," ","int((e*x+d)^4*(b^2*x^2+2*a*b*x+a^2),x)","\frac{b^{2} e^{4} x^{7}}{7}+a^{2} d^{4} x +\frac{\left(2 e^{4} a b +4 d \,e^{3} b^{2}\right) x^{6}}{6}+\frac{\left(a^{2} e^{4}+8 d \,e^{3} a b +6 d^{2} e^{2} b^{2}\right) x^{5}}{5}+\frac{\left(4 d \,e^{3} a^{2}+12 d^{2} e^{2} a b +4 d^{3} e \,b^{2}\right) x^{4}}{4}+\frac{\left(6 d^{2} e^{2} a^{2}+8 d^{3} e a b +d^{4} b^{2}\right) x^{3}}{3}+\frac{\left(4 d^{3} e \,a^{2}+2 d^{4} a b \right) x^{2}}{2}"," ",0,"1/7*e^4*b^2*x^7+1/6*(2*a*b*e^4+4*b^2*d*e^3)*x^6+1/5*(a^2*e^4+8*a*b*d*e^3+6*b^2*d^2*e^2)*x^5+1/4*(4*a^2*d*e^3+12*a*b*d^2*e^2+4*b^2*d^3*e)*x^4+1/3*(6*a^2*d^2*e^2+8*a*b*d^3*e+b^2*d^4)*x^3+1/2*(4*a^2*d^3*e+2*a*b*d^4)*x^2+d^4*a^2*x","B"
1452,1,125,59,0.037000," ","int((e*x+d)^3*(b^2*x^2+2*a*b*x+a^2),x)","\frac{b^{2} e^{3} x^{6}}{6}+a^{2} d^{3} x +\frac{\left(2 a b \,e^{3}+3 b^{2} d \,e^{2}\right) x^{5}}{5}+\frac{\left(a^{2} e^{3}+6 d \,e^{2} a b +3 d^{2} e \,b^{2}\right) x^{4}}{4}+\frac{\left(3 d \,e^{2} a^{2}+6 d^{2} e a b +d^{3} b^{2}\right) x^{3}}{3}+\frac{\left(3 d^{2} e \,a^{2}+2 d^{3} a b \right) x^{2}}{2}"," ",0,"1/6*e^3*b^2*x^6+1/5*(2*a*b*e^3+3*b^2*d*e^2)*x^5+1/4*(a^2*e^3+6*a*b*d*e^2+3*b^2*d^2*e)*x^4+1/3*(3*a^2*d*e^2+6*a*b*d^2*e+b^2*d^3)*x^3+1/2*(3*a^2*d^2*e+2*a*b*d^3)*x^2+a^2*d^3*x","B"
1453,1,87,59,0.040000," ","int((e*x+d)^2*(b^2*x^2+2*a*b*x+a^2),x)","\frac{b^{2} e^{2} x^{5}}{5}+a^{2} d^{2} x +\frac{\left(2 e^{2} a b +2 b^{2} d e \right) x^{4}}{4}+\frac{\left(a^{2} e^{2}+4 a b d e +b^{2} d^{2}\right) x^{3}}{3}+\frac{\left(2 d e \,a^{2}+2 d^{2} a b \right) x^{2}}{2}"," ",0,"1/5*b^2*e^2*x^5+1/4*(2*a*b*e^2+2*b^2*d*e)*x^4+1/3*(a^2*e^2+4*a*b*d*e+b^2*d^2)*x^3+1/2*(2*a^2*d*e+2*a*b*d^2)*x^2+a^2*d^2*x","A"
1454,1,49,34,0.039000," ","int((e*x+d)*(b^2*x^2+2*a*b*x+a^2),x)","\frac{b^{2} e \,x^{4}}{4}+a^{2} d x +\frac{\left(2 b e a +b^{2} d \right) x^{3}}{3}+\frac{\left(e \,a^{2}+2 b d a \right) x^{2}}{2}"," ",0,"1/4*e*b^2*x^4+1/3*(2*a*b*e+b^2*d)*x^3+1/2*(a^2*e+2*a*b*d)*x^2+a^2*d*x","A"
1455,1,21,20,0.036000," ","int(b^2*x^2+2*a*b*x+a^2,x)","\frac{1}{3} b^{2} x^{3}+a b \,x^{2}+a^{2} x"," ",0,"a^2*x+a*b*x^2+1/3*b^2*x^3","A"
1456,1,74,48,0.046000," ","int((b^2*x^2+2*a*b*x+a^2)/(e*x+d),x)","\frac{b^{2} x^{2}}{2 e}+\frac{a^{2} \ln \left(e x +d \right)}{e}-\frac{2 a b d \ln \left(e x +d \right)}{e^{2}}+\frac{2 a b x}{e}+\frac{b^{2} d^{2} \ln \left(e x +d \right)}{e^{3}}-\frac{b^{2} d x}{e^{2}}"," ",0,"1/2*b^2/e*x^2+2*b/e*a*x-b^2/e^2*x*d+1/e*ln(e*x+d)*a^2-2/e^2*ln(e*x+d)*a*b*d+1/e^3*ln(e*x+d)*b^2*d^2","A"
1457,1,86,51,0.053000," ","int((b^2*x^2+2*a*b*x+a^2)/(e*x+d)^2,x)","-\frac{a^{2}}{\left(e x +d \right) e}+\frac{2 a b d}{\left(e x +d \right) e^{2}}+\frac{2 a b \ln \left(e x +d \right)}{e^{2}}-\frac{b^{2} d^{2}}{\left(e x +d \right) e^{3}}-\frac{2 b^{2} d \ln \left(e x +d \right)}{e^{3}}+\frac{b^{2} x}{e^{2}}"," ",0,"b^2/e^2*x-1/e/(e*x+d)*a^2+2/e^2/(e*x+d)*a*b*d-1/e^3/(e*x+d)*b^2*d^2+2*b/e^2*ln(e*x+d)*a-2*b^2/e^3*ln(e*x+d)*d","A"
1458,1,92,57,0.052000," ","int((b^2*x^2+2*a*b*x+a^2)/(e*x+d)^3,x)","-\frac{a^{2}}{2 \left(e x +d \right)^{2} e}+\frac{a b d}{\left(e x +d \right)^{2} e^{2}}-\frac{b^{2} d^{2}}{2 \left(e x +d \right)^{2} e^{3}}-\frac{2 a b}{\left(e x +d \right) e^{2}}+\frac{2 b^{2} d}{\left(e x +d \right) e^{3}}+\frac{b^{2} \ln \left(e x +d \right)}{e^{3}}"," ",0,"-2*b/e^2/(e*x+d)*a+2*b^2/e^3/(e*x+d)*d-1/2/e/(e*x+d)^2*a^2+1/e^2/(e*x+d)^2*a*b*d-1/2/e^3/(e*x+d)^2*b^2*d^2+b^2/e^3*ln(e*x+d)","A"
1459,1,71,26,0.050000," ","int((b^2*x^2+2*a*b*x+a^2)/(e*x+d)^4,x)","-\frac{b^{2}}{\left(e x +d \right) e^{3}}-\frac{\left(a e -b d \right) b}{\left(e x +d \right)^{2} e^{3}}-\frac{a^{2} e^{2}-2 a b d e +b^{2} d^{2}}{3 \left(e x +d \right)^{3} e^{3}}"," ",0,"-b^2/e^3/(e*x+d)-b*(a*e-b*d)/e^3/(e*x+d)^2-1/3*(a^2*e^2-2*a*b*d*e+b^2*d^2)/e^3/(e*x+d)^3","B"
1460,1,71,59,0.048000," ","int((b^2*x^2+2*a*b*x+a^2)/(e*x+d)^5,x)","-\frac{b^{2}}{2 \left(e x +d \right)^{2} e^{3}}-\frac{2 \left(a e -b d \right) b}{3 \left(e x +d \right)^{3} e^{3}}-\frac{a^{2} e^{2}-2 a b d e +b^{2} d^{2}}{4 \left(e x +d \right)^{4} e^{3}}"," ",0,"-1/2/(e*x+d)^2*b^2/e^3-1/4*(a^2*e^2-2*a*b*d*e+b^2*d^2)/e^3/(e*x+d)^4-2/3*b*(a*e-b*d)/e^3/(e*x+d)^3","A"
1461,1,71,59,0.053000," ","int((b^2*x^2+2*a*b*x+a^2)/(e*x+d)^6,x)","-\frac{b^{2}}{3 \left(e x +d \right)^{3} e^{3}}-\frac{\left(a e -b d \right) b}{2 \left(e x +d \right)^{4} e^{3}}-\frac{a^{2} e^{2}-2 a b d e +b^{2} d^{2}}{5 \left(e x +d \right)^{5} e^{3}}"," ",0,"-1/2*b*(a*e-b*d)/e^3/(e*x+d)^4-1/3*b^2/e^3/(e*x+d)^3-1/5*(a^2*e^2-2*a*b*d*e+b^2*d^2)/e^3/(e*x+d)^5","A"
1462,1,71,59,0.046000," ","int((b^2*x^2+2*a*b*x+a^2)/(e*x+d)^7,x)","-\frac{b^{2}}{4 \left(e x +d \right)^{4} e^{3}}-\frac{2 \left(a e -b d \right) b}{5 \left(e x +d \right)^{5} e^{3}}-\frac{a^{2} e^{2}-2 a b d e +b^{2} d^{2}}{6 \left(e x +d \right)^{6} e^{3}}"," ",0,"-1/4*b^2/e^3/(e*x+d)^4-1/6*(a^2*e^2-2*a*b*d*e+b^2*d^2)/e^3/(e*x+d)^6-2/5*b*(a*e-b*d)/e^3/(e*x+d)^5","A"
1463,1,427,109,0.042000," ","int((e*x+d)^6*(b^2*x^2+2*a*b*x+a^2)^2,x)","\frac{b^{4} e^{6} x^{11}}{11}+a^{4} d^{6} x +\frac{\left(4 e^{6} a \,b^{3}+6 d \,e^{5} b^{4}\right) x^{10}}{10}+\frac{\left(6 e^{6} b^{2} a^{2}+24 d \,e^{5} a \,b^{3}+15 d^{2} e^{4} b^{4}\right) x^{9}}{9}+\frac{\left(4 e^{6} a^{3} b +36 d \,e^{5} b^{2} a^{2}+60 d^{2} e^{4} a \,b^{3}+20 d^{3} e^{3} b^{4}\right) x^{8}}{8}+\frac{\left(e^{6} a^{4}+24 d \,e^{5} a^{3} b +90 d^{2} e^{4} b^{2} a^{2}+80 d^{3} e^{3} a \,b^{3}+15 d^{4} e^{2} b^{4}\right) x^{7}}{7}+\frac{\left(6 d \,e^{5} a^{4}+60 d^{2} e^{4} a^{3} b +120 d^{3} e^{3} b^{2} a^{2}+60 d^{4} e^{2} a \,b^{3}+6 d^{5} e \,b^{4}\right) x^{6}}{6}+\frac{\left(15 d^{2} e^{4} a^{4}+80 d^{3} e^{3} a^{3} b +90 d^{4} e^{2} b^{2} a^{2}+24 d^{5} e a \,b^{3}+d^{6} b^{4}\right) x^{5}}{5}+\frac{\left(20 d^{3} e^{3} a^{4}+60 d^{4} e^{2} a^{3} b +36 d^{5} e \,b^{2} a^{2}+4 d^{6} a \,b^{3}\right) x^{4}}{4}+\frac{\left(15 d^{4} e^{2} a^{4}+24 d^{5} e \,a^{3} b +6 d^{6} b^{2} a^{2}\right) x^{3}}{3}+\frac{\left(6 d^{5} e \,a^{4}+4 d^{6} a^{3} b \right) x^{2}}{2}"," ",0,"1/11*e^6*b^4*x^11+1/10*(4*a*b^3*e^6+6*b^4*d*e^5)*x^10+1/9*(6*a^2*b^2*e^6+24*a*b^3*d*e^5+15*b^4*d^2*e^4)*x^9+1/8*(4*a^3*b*e^6+36*a^2*b^2*d*e^5+60*a*b^3*d^2*e^4+20*b^4*d^3*e^3)*x^8+1/7*(a^4*e^6+24*a^3*b*d*e^5+90*a^2*b^2*d^2*e^4+80*a*b^3*d^3*e^3+15*b^4*d^4*e^2)*x^7+1/6*(6*a^4*d*e^5+60*a^3*b*d^2*e^4+120*a^2*b^2*d^3*e^3+60*a*b^3*d^4*e^2+6*b^4*d^5*e)*x^6+1/5*(15*a^4*d^2*e^4+80*a^3*b*d^3*e^3+90*a^2*b^2*d^4*e^2+24*a*b^3*d^5*e+b^4*d^6)*x^5+1/4*(20*a^4*d^3*e^3+60*a^3*b*d^4*e^2+36*a^2*b^2*d^5*e+4*a*b^3*d^6)*x^4+1/3*(15*a^4*d^4*e^2+24*a^3*b*d^5*e+6*a^2*b^2*d^6)*x^3+1/2*(6*a^4*d^5*e+4*a^3*b*d^6)*x^2+d^6*a^4*x","B"
1464,1,361,109,0.043000," ","int((e*x+d)^5*(b^2*x^2+2*a*b*x+a^2)^2,x)","\frac{b^{4} e^{5} x^{10}}{10}+a^{4} d^{5} x +\frac{\left(4 a \,b^{3} e^{5}+5 d \,e^{4} b^{4}\right) x^{9}}{9}+\frac{\left(6 e^{5} b^{2} a^{2}+20 d \,e^{4} a \,b^{3}+10 d^{2} e^{3} b^{4}\right) x^{8}}{8}+\frac{\left(4 e^{5} a^{3} b +30 d \,e^{4} b^{2} a^{2}+40 d^{2} e^{3} a \,b^{3}+10 d^{3} e^{2} b^{4}\right) x^{7}}{7}+\frac{\left(e^{5} a^{4}+20 d \,e^{4} a^{3} b +60 d^{2} e^{3} b^{2} a^{2}+40 d^{3} e^{2} a \,b^{3}+5 d^{4} e \,b^{4}\right) x^{6}}{6}+\frac{\left(5 d \,e^{4} a^{4}+40 d^{2} e^{3} a^{3} b +60 d^{3} e^{2} b^{2} a^{2}+20 d^{4} e a \,b^{3}+d^{5} b^{4}\right) x^{5}}{5}+\frac{\left(10 d^{2} e^{3} a^{4}+40 d^{3} e^{2} a^{3} b +30 d^{4} e \,b^{2} a^{2}+4 d^{5} a \,b^{3}\right) x^{4}}{4}+\frac{\left(10 d^{3} e^{2} a^{4}+20 d^{4} e \,a^{3} b +6 d^{5} b^{2} a^{2}\right) x^{3}}{3}+\frac{\left(5 d^{4} e \,a^{4}+4 d^{5} a^{3} b \right) x^{2}}{2}"," ",0,"1/10*e^5*b^4*x^10+1/9*(4*a*b^3*e^5+5*b^4*d*e^4)*x^9+1/8*(6*a^2*b^2*e^5+20*a*b^3*d*e^4+10*b^4*d^2*e^3)*x^8+1/7*(4*a^3*b*e^5+30*a^2*b^2*d*e^4+40*a*b^3*d^2*e^3+10*b^4*d^3*e^2)*x^7+1/6*(a^4*e^5+20*a^3*b*d*e^4+60*a^2*b^2*d^2*e^3+40*a*b^3*d^3*e^2+5*b^4*d^4*e)*x^6+1/5*(5*a^4*d*e^4+40*a^3*b*d^2*e^3+60*a^2*b^2*d^3*e^2+20*a*b^3*d^4*e+b^4*d^5)*x^5+1/4*(10*a^4*d^2*e^3+40*a^3*b*d^3*e^2+30*a^2*b^2*d^4*e+4*a*b^3*d^5)*x^4+1/3*(10*a^4*d^3*e^2+20*a^3*b*d^4*e+6*a^2*b^2*d^5)*x^3+1/2*(5*a^4*d^4*e+4*a^3*b*d^5)*x^2+d^5*a^4*x","B"
1465,1,295,109,0.036000," ","int((e*x+d)^4*(b^2*x^2+2*a*b*x+a^2)^2,x)","\frac{b^{4} e^{4} x^{9}}{9}+a^{4} d^{4} x +\frac{\left(4 e^{4} a \,b^{3}+4 b^{4} d \,e^{3}\right) x^{8}}{8}+\frac{\left(6 e^{4} b^{2} a^{2}+16 d \,e^{3} a \,b^{3}+6 d^{2} e^{2} b^{4}\right) x^{7}}{7}+\frac{\left(4 e^{4} a^{3} b +24 d \,e^{3} b^{2} a^{2}+24 d^{2} e^{2} a \,b^{3}+4 d^{3} e \,b^{4}\right) x^{6}}{6}+\frac{\left(e^{4} a^{4}+16 d \,e^{3} a^{3} b +36 d^{2} e^{2} b^{2} a^{2}+16 d^{3} e a \,b^{3}+d^{4} b^{4}\right) x^{5}}{5}+\frac{\left(4 d \,e^{3} a^{4}+24 d^{2} e^{2} a^{3} b +24 d^{3} e \,b^{2} a^{2}+4 d^{4} a \,b^{3}\right) x^{4}}{4}+\frac{\left(6 d^{2} e^{2} a^{4}+16 d^{3} e \,a^{3} b +6 d^{4} b^{2} a^{2}\right) x^{3}}{3}+\frac{\left(4 d^{3} e \,a^{4}+4 d^{4} a^{3} b \right) x^{2}}{2}"," ",0,"1/9*b^4*e^4*x^9+1/8*(4*a*b^3*e^4+4*b^4*d*e^3)*x^8+1/7*(6*a^2*b^2*e^4+16*a*b^3*d*e^3+6*b^4*d^2*e^2)*x^7+1/6*(4*a^3*b*e^4+24*a^2*b^2*d*e^3+24*a*b^3*d^2*e^2+4*b^4*d^3*e)*x^6+1/5*(a^4*e^4+16*a^3*b*d*e^3+36*a^2*b^2*d^2*e^2+16*a*b^3*d^3*e+b^4*d^4)*x^5+1/4*(4*a^4*d*e^3+24*a^3*b*d^2*e^2+24*a^2*b^2*d^3*e+4*a*b^3*d^4)*x^4+1/3*(6*a^4*d^2*e^2+16*a^3*b*d^3*e+6*a^2*b^2*d^4)*x^3+1/2*(4*a^4*d^3*e+4*a^3*b*d^4)*x^2+a^4*d^4*x","B"
1466,1,229,84,0.037000," ","int((e*x+d)^3*(b^2*x^2+2*a*b*x+a^2)^2,x)","\frac{b^{4} e^{3} x^{8}}{8}+a^{4} d^{3} x +\frac{\left(4 e^{3} a \,b^{3}+3 d \,e^{2} b^{4}\right) x^{7}}{7}+\frac{\left(6 e^{3} b^{2} a^{2}+12 d \,e^{2} a \,b^{3}+3 d^{2} e \,b^{4}\right) x^{6}}{6}+\frac{\left(4 e^{3} a^{3} b +18 d \,e^{2} b^{2} a^{2}+12 d^{2} e a \,b^{3}+d^{3} b^{4}\right) x^{5}}{5}+\frac{\left(e^{3} a^{4}+12 d \,e^{2} a^{3} b +18 d^{2} e \,b^{2} a^{2}+4 d^{3} a \,b^{3}\right) x^{4}}{4}+\frac{\left(3 d \,e^{2} a^{4}+12 d^{2} e \,a^{3} b +6 d^{3} b^{2} a^{2}\right) x^{3}}{3}+\frac{\left(3 d^{2} e \,a^{4}+4 d^{3} a^{3} b \right) x^{2}}{2}"," ",0,"1/8*e^3*b^4*x^8+1/7*(4*a*b^3*e^3+3*b^4*d*e^2)*x^7+1/6*(6*a^2*b^2*e^3+12*a*b^3*d*e^2+3*b^4*d^2*e)*x^6+1/5*(4*a^3*b*e^3+18*a^2*b^2*d*e^2+12*a*b^3*d^2*e+b^4*d^3)*x^5+1/4*(a^4*e^3+12*a^3*b*d*e^2+18*a^2*b^2*d^2*e+4*a*b^3*d^3)*x^4+1/3*(3*a^4*d*e^2+12*a^3*b*d^2*e+6*a^2*b^2*d^3)*x^3+1/2*(3*a^4*d^2*e+4*a^3*b*d^3)*x^2+a^4*d^3*x","B"
1467,1,163,59,0.043000," ","int((e*x+d)^2*(b^2*x^2+2*a*b*x+a^2)^2,x)","\frac{b^{4} e^{2} x^{7}}{7}+a^{4} d^{2} x +\frac{\left(4 e^{2} a \,b^{3}+2 b^{4} d e \right) x^{6}}{6}+\frac{\left(6 a^{2} b^{2} e^{2}+8 d e a \,b^{3}+b^{4} d^{2}\right) x^{5}}{5}+\frac{\left(4 e^{2} a^{3} b +12 d e \,b^{2} a^{2}+4 d^{2} a \,b^{3}\right) x^{4}}{4}+\frac{\left(e^{2} a^{4}+8 d e \,a^{3} b +6 d^{2} b^{2} a^{2}\right) x^{3}}{3}+\frac{\left(2 d e \,a^{4}+4 d^{2} a^{3} b \right) x^{2}}{2}"," ",0,"1/7*e^2*b^4*x^7+1/6*(4*a*b^3*e^2+2*b^4*d*e)*x^6+1/5*(6*a^2*b^2*e^2+8*a*b^3*d*e+b^4*d^2)*x^5+1/4*(4*a^3*b*e^2+12*a^2*b^2*d*e+4*a*b^3*d^2)*x^4+1/3*(a^4*e^2+8*a^3*b*d*e+6*a^2*b^2*d^2)*x^3+1/2*(2*a^4*d*e+4*a^3*b*d^2)*x^2+a^4*d^2*x","B"
1468,1,97,34,0.042000," ","int((e*x+d)*(b^2*x^2+2*a*b*x+a^2)^2,x)","\frac{b^{4} e \,x^{6}}{6}+a^{4} d x +\frac{\left(4 e a \,b^{3}+d \,b^{4}\right) x^{5}}{5}+\frac{\left(6 e \,b^{2} a^{2}+4 d a \,b^{3}\right) x^{4}}{4}+\frac{\left(4 e \,a^{3} b +6 d \,b^{2} a^{2}\right) x^{3}}{3}+\frac{\left(e \,a^{4}+4 d \,a^{3} b \right) x^{2}}{2}"," ",0,"1/6*e*b^4*x^6+1/5*(4*a*b^3*e+b^4*d)*x^5+1/4*(6*a^2*b^2*e+4*a*b^3*d)*x^4+1/3*(4*a^3*b*e+6*a^2*b^2*d)*x^3+1/2*(a^4*e+4*a^3*b*d)*x^2+a^4*d*x","B"
1469,1,43,12,0.039000," ","int((b^2*x^2+2*a*b*x+a^2)^2,x)","\frac{1}{5} b^{4} x^{5}+a \,b^{3} x^{4}+2 a^{2} b^{2} x^{3}+2 a^{3} b \,x^{2}+a^{4} x"," ",0,"1/5*b^4*x^5+a*b^3*x^4+2*b^2*a^2*x^3+2*a^3*b*x^2+a^4*x","B"
1470,1,209,92,0.045000," ","int((b^2*x^2+2*a*b*x+a^2)^2/(e*x+d),x)","\frac{b^{4} x^{4}}{4 e}+\frac{4 a \,b^{3} x^{3}}{3 e}-\frac{b^{4} d \,x^{3}}{3 e^{2}}+\frac{3 a^{2} b^{2} x^{2}}{e}-\frac{2 a \,b^{3} d \,x^{2}}{e^{2}}+\frac{b^{4} d^{2} x^{2}}{2 e^{3}}+\frac{a^{4} \ln \left(e x +d \right)}{e}-\frac{4 a^{3} b d \ln \left(e x +d \right)}{e^{2}}+\frac{4 a^{3} b x}{e}+\frac{6 a^{2} b^{2} d^{2} \ln \left(e x +d \right)}{e^{3}}-\frac{6 a^{2} b^{2} d x}{e^{2}}-\frac{4 a \,b^{3} d^{3} \ln \left(e x +d \right)}{e^{4}}+\frac{4 a \,b^{3} d^{2} x}{e^{3}}+\frac{b^{4} d^{4} \ln \left(e x +d \right)}{e^{5}}-\frac{b^{4} d^{3} x}{e^{4}}"," ",0,"1/4*b^4/e*x^4+4/3*b^3/e*x^3*a-1/3*b^4/e^2*x^3*d+3*b^2/e*x^2*a^2-2*b^3/e^2*x^2*a*d+1/2*b^4/e^3*x^2*d^2+4*b/e*a^3*x-6*b^2/e^2*a^2*d*x+4*b^3/e^3*a*d^2*x-b^4/e^4*d^3*x+1/e*ln(e*x+d)*a^4-4/e^2*ln(e*x+d)*d*a^3*b+6/e^3*ln(e*x+d)*d^2*b^2*a^2-4/e^4*ln(e*x+d)*a*b^3*d^3+1/e^5*ln(e*x+d)*b^4*d^4","B"
1471,1,230,102,0.056000," ","int((b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^2,x)","\frac{b^{4} x^{3}}{3 e^{2}}+\frac{2 a \,b^{3} x^{2}}{e^{2}}-\frac{b^{4} d \,x^{2}}{e^{3}}-\frac{a^{4}}{\left(e x +d \right) e}+\frac{4 a^{3} b d}{\left(e x +d \right) e^{2}}+\frac{4 a^{3} b \ln \left(e x +d \right)}{e^{2}}-\frac{6 a^{2} b^{2} d^{2}}{\left(e x +d \right) e^{3}}-\frac{12 a^{2} b^{2} d \ln \left(e x +d \right)}{e^{3}}+\frac{6 a^{2} b^{2} x}{e^{2}}+\frac{4 a \,b^{3} d^{3}}{\left(e x +d \right) e^{4}}+\frac{12 a \,b^{3} d^{2} \ln \left(e x +d \right)}{e^{4}}-\frac{8 a \,b^{3} d x}{e^{3}}-\frac{b^{4} d^{4}}{\left(e x +d \right) e^{5}}-\frac{4 b^{4} d^{3} \ln \left(e x +d \right)}{e^{5}}+\frac{3 b^{4} d^{2} x}{e^{4}}"," ",0,"1/3*b^4/e^2*x^3+2*b^3/e^2*x^2*a-b^4/e^3*x^2*d+6*b^2/e^2*a^2*x-8*b^3/e^3*a*d*x+3*b^4/e^4*d^2*x-1/e/(e*x+d)*a^4+4/e^2/(e*x+d)*d*a^3*b-6/e^3/(e*x+d)*d^2*b^2*a^2+4/e^4/(e*x+d)*a*b^3*d^3-1/e^5/(e*x+d)*b^4*d^4+4*b/e^2*ln(e*x+d)*a^3-12*b^2/e^3*ln(e*x+d)*a^2*d+12*b^3/e^4*ln(e*x+d)*a*d^2-4*b^4/e^5*ln(e*x+d)*d^3","B"
1472,1,245,99,0.056000," ","int((b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^3,x)","-\frac{a^{4}}{2 \left(e x +d \right)^{2} e}+\frac{2 a^{3} b d}{\left(e x +d \right)^{2} e^{2}}-\frac{3 a^{2} b^{2} d^{2}}{\left(e x +d \right)^{2} e^{3}}+\frac{2 a \,b^{3} d^{3}}{\left(e x +d \right)^{2} e^{4}}-\frac{b^{4} d^{4}}{2 \left(e x +d \right)^{2} e^{5}}+\frac{b^{4} x^{2}}{2 e^{3}}-\frac{4 a^{3} b}{\left(e x +d \right) e^{2}}+\frac{12 a^{2} b^{2} d}{\left(e x +d \right) e^{3}}+\frac{6 a^{2} b^{2} \ln \left(e x +d \right)}{e^{3}}-\frac{12 a \,b^{3} d^{2}}{\left(e x +d \right) e^{4}}-\frac{12 a \,b^{3} d \ln \left(e x +d \right)}{e^{4}}+\frac{4 a \,b^{3} x}{e^{3}}+\frac{4 b^{4} d^{3}}{\left(e x +d \right) e^{5}}+\frac{6 b^{4} d^{2} \ln \left(e x +d \right)}{e^{5}}-\frac{3 b^{4} d x}{e^{4}}"," ",0,"1/2*b^4*x^2/e^3+4*b^3/e^3*a*x-3*b^4/e^4*x*d-4*b/e^2/(e*x+d)*a^3+12*b^2/e^3/(e*x+d)*a^2*d-12*b^3/e^4/(e*x+d)*a*d^2+4*b^4/e^5/(e*x+d)*d^3-1/2/e/(e*x+d)^2*a^4+2/e^2/(e*x+d)^2*d*a^3*b-3/e^3/(e*x+d)^2*d^2*b^2*a^2+2/e^4/(e*x+d)^2*a*b^3*d^3-1/2/e^5/(e*x+d)^2*b^4*d^4+6*b^2/e^3*ln(e*x+d)*a^2-12*b^3/e^4*ln(e*x+d)*a*d+6*b^4/e^5*ln(e*x+d)*d^2","B"
1473,1,255,101,0.053000," ","int((b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^4,x)","-\frac{a^{4}}{3 \left(e x +d \right)^{3} e}+\frac{4 a^{3} b d}{3 \left(e x +d \right)^{3} e^{2}}-\frac{2 a^{2} b^{2} d^{2}}{\left(e x +d \right)^{3} e^{3}}+\frac{4 a \,b^{3} d^{3}}{3 \left(e x +d \right)^{3} e^{4}}-\frac{b^{4} d^{4}}{3 \left(e x +d \right)^{3} e^{5}}-\frac{2 a^{3} b}{\left(e x +d \right)^{2} e^{2}}+\frac{6 a^{2} b^{2} d}{\left(e x +d \right)^{2} e^{3}}-\frac{6 a \,b^{3} d^{2}}{\left(e x +d \right)^{2} e^{4}}+\frac{2 b^{4} d^{3}}{\left(e x +d \right)^{2} e^{5}}-\frac{6 a^{2} b^{2}}{\left(e x +d \right) e^{3}}+\frac{12 a \,b^{3} d}{\left(e x +d \right) e^{4}}+\frac{4 a \,b^{3} \ln \left(e x +d \right)}{e^{4}}-\frac{6 b^{4} d^{2}}{\left(e x +d \right) e^{5}}-\frac{4 b^{4} d \ln \left(e x +d \right)}{e^{5}}+\frac{b^{4} x}{e^{4}}"," ",0,"b^4*x/e^4-6*b^2/e^3/(e*x+d)*a^2+12*b^3/e^4/(e*x+d)*a*d-6*b^4/e^5/(e*x+d)*d^2-2*b/e^2/(e*x+d)^2*a^3+6*b^2/e^3/(e*x+d)^2*a^2*d-6*b^3/e^4/(e*x+d)^2*a*d^2+2*b^4/e^5/(e*x+d)^2*d^3-1/3/e/(e*x+d)^3*a^4+4/3/e^2/(e*x+d)^3*d*a^3*b-2/e^3/(e*x+d)^3*d^2*b^2*a^2+4/3/e^4/(e*x+d)^3*d^3*a*b^3-1/3/e^5/(e*x+d)^3*b^4*d^4+4*b^3/e^4*ln(e*x+d)*a-4*b^4/e^5*ln(e*x+d)*d","B"
1474,1,260,107,0.049000," ","int((b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^5,x)","-\frac{a^{4}}{4 \left(e x +d \right)^{4} e}+\frac{a^{3} b d}{\left(e x +d \right)^{4} e^{2}}-\frac{3 a^{2} b^{2} d^{2}}{2 \left(e x +d \right)^{4} e^{3}}+\frac{a \,b^{3} d^{3}}{\left(e x +d \right)^{4} e^{4}}-\frac{b^{4} d^{4}}{4 \left(e x +d \right)^{4} e^{5}}-\frac{4 a^{3} b}{3 \left(e x +d \right)^{3} e^{2}}+\frac{4 a^{2} b^{2} d}{\left(e x +d \right)^{3} e^{3}}-\frac{4 a \,b^{3} d^{2}}{\left(e x +d \right)^{3} e^{4}}+\frac{4 b^{4} d^{3}}{3 \left(e x +d \right)^{3} e^{5}}-\frac{3 a^{2} b^{2}}{\left(e x +d \right)^{2} e^{3}}+\frac{6 a \,b^{3} d}{\left(e x +d \right)^{2} e^{4}}-\frac{3 b^{4} d^{2}}{\left(e x +d \right)^{2} e^{5}}-\frac{4 a \,b^{3}}{\left(e x +d \right) e^{4}}+\frac{4 b^{4} d}{\left(e x +d \right) e^{5}}+\frac{b^{4} \ln \left(e x +d \right)}{e^{5}}"," ",0,"-4*b^3/e^4/(e*x+d)*a+4*b^4/e^5/(e*x+d)*d-3*b^2/e^3/(e*x+d)^2*a^2+6*b^3/e^4/(e*x+d)^2*a*d-3*b^4/e^5/(e*x+d)^2*d^2-1/4/e/(e*x+d)^4*a^4+1/e^2/(e*x+d)^4*d*a^3*b-3/2/e^3/(e*x+d)^4*d^2*b^2*a^2+1/e^4/(e*x+d)^4*d^3*a*b^3-1/4/e^5/(e*x+d)^4*b^4*d^4-4/3*b/e^2/(e*x+d)^3*a^3+4*b^2/e^3/(e*x+d)^3*a^2*d-4*b^3/e^4/(e*x+d)^3*a*d^2+4/3*b^4/e^5/(e*x+d)^3*d^3+b^4*ln(e*x+d)/e^5","B"
1475,1,186,26,0.049000," ","int((b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^6,x)","-\frac{b^{4}}{\left(e x +d \right) e^{5}}-\frac{2 \left(a e -b d \right) b^{3}}{\left(e x +d \right)^{2} e^{5}}-\frac{2 \left(a^{2} e^{2}-2 a b d e +b^{2} d^{2}\right) b^{2}}{\left(e x +d \right)^{3} e^{5}}-\frac{\left(a^{3} e^{3}-3 a^{2} b d \,e^{2}+3 a \,b^{2} d^{2} e -b^{3} d^{3}\right) b}{\left(e x +d \right)^{4} e^{5}}-\frac{e^{4} a^{4}-4 d \,e^{3} a^{3} b +6 d^{2} e^{2} b^{2} a^{2}-4 d^{3} a \,b^{3} e +b^{4} d^{4}}{5 \left(e x +d \right)^{5} e^{5}}"," ",0,"-b^4/e^5/(e*x+d)-2*b^3*(a*e-b*d)/e^5/(e*x+d)^2-b*(a^3*e^3-3*a^2*b*d*e^2+3*a*b^2*d^2*e-b^3*d^3)/e^5/(e*x+d)^4-2*b^2*(a^2*e^2-2*a*b*d*e+b^2*d^2)/e^5/(e*x+d)^3-1/5*(a^4*e^4-4*a^3*b*d*e^3+6*a^2*b^2*d^2*e^2-4*a*b^3*d^3*e+b^4*d^4)/e^5/(e*x+d)^5","B"
1476,1,186,54,0.049000," ","int((b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^7,x)","-\frac{b^{4}}{2 \left(e x +d \right)^{2} e^{5}}-\frac{4 \left(a e -b d \right) b^{3}}{3 \left(e x +d \right)^{3} e^{5}}-\frac{3 \left(a^{2} e^{2}-2 a b d e +b^{2} d^{2}\right) b^{2}}{2 \left(e x +d \right)^{4} e^{5}}-\frac{4 \left(a^{3} e^{3}-3 a^{2} b d \,e^{2}+3 a \,b^{2} d^{2} e -b^{3} d^{3}\right) b}{5 \left(e x +d \right)^{5} e^{5}}-\frac{e^{4} a^{4}-4 d \,e^{3} a^{3} b +6 d^{2} e^{2} b^{2} a^{2}-4 d^{3} a \,b^{3} e +b^{4} d^{4}}{6 \left(e x +d \right)^{6} e^{5}}"," ",0,"-1/2*b^4/e^5/(e*x+d)^2-3/2*b^2*(a^2*e^2-2*a*b*d*e+b^2*d^2)/e^5/(e*x+d)^4-4/3*b^3*(a*e-b*d)/e^5/(e*x+d)^3-1/6*(a^4*e^4-4*a^3*b*d*e^3+6*a^2*b^2*d^2*e^2-4*a*b^3*d^3*e+b^4*d^4)/e^5/(e*x+d)^6-4/5*b*(a^3*e^3-3*a^2*b*d*e^2+3*a*b^2*d^2*e-b^3*d^3)/e^5/(e*x+d)^5","B"
1477,1,186,83,0.049000," ","int((b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^8,x)","-\frac{b^{4}}{3 \left(e x +d \right)^{3} e^{5}}-\frac{\left(a e -b d \right) b^{3}}{\left(e x +d \right)^{4} e^{5}}-\frac{6 \left(a^{2} e^{2}-2 a b d e +b^{2} d^{2}\right) b^{2}}{5 \left(e x +d \right)^{5} e^{5}}-\frac{2 \left(a^{3} e^{3}-3 a^{2} b d \,e^{2}+3 a \,b^{2} d^{2} e -b^{3} d^{3}\right) b}{3 \left(e x +d \right)^{6} e^{5}}-\frac{e^{4} a^{4}-4 d \,e^{3} a^{3} b +6 d^{2} e^{2} b^{2} a^{2}-4 d^{3} a \,b^{3} e +b^{4} d^{4}}{7 \left(e x +d \right)^{7} e^{5}}"," ",0,"-1/7*(a^4*e^4-4*a^3*b*d*e^3+6*a^2*b^2*d^2*e^2-4*a*b^3*d^3*e+b^4*d^4)/e^5/(e*x+d)^7-b^3*(a*e-b*d)/e^5/(e*x+d)^4-1/3*b^4/e^5/(e*x+d)^3-2/3*b*(a^3*e^3-3*a^2*b*d*e^2+3*a*b^2*d^2*e-b^3*d^3)/e^5/(e*x+d)^6-6/5*b^2*(a^2*e^2-2*a*b*d*e+b^2*d^2)/e^5/(e*x+d)^5","B"
1478,1,186,109,0.047000," ","int((b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^9,x)","-\frac{b^{4}}{4 \left(e x +d \right)^{4} e^{5}}-\frac{4 \left(a e -b d \right) b^{3}}{5 \left(e x +d \right)^{5} e^{5}}-\frac{\left(a^{2} e^{2}-2 a b d e +b^{2} d^{2}\right) b^{2}}{\left(e x +d \right)^{6} e^{5}}-\frac{4 \left(a^{3} e^{3}-3 a^{2} b d \,e^{2}+3 a \,b^{2} d^{2} e -b^{3} d^{3}\right) b}{7 \left(e x +d \right)^{7} e^{5}}-\frac{e^{4} a^{4}-4 d \,e^{3} a^{3} b +6 d^{2} e^{2} b^{2} a^{2}-4 d^{3} a \,b^{3} e +b^{4} d^{4}}{8 \left(e x +d \right)^{8} e^{5}}"," ",0,"-4/7*b*(a^3*e^3-3*a^2*b*d*e^2+3*a*b^2*d^2*e-b^3*d^3)/e^5/(e*x+d)^7-1/4*b^4/e^5/(e*x+d)^4-b^2*(a^2*e^2-2*a*b*d*e+b^2*d^2)/e^5/(e*x+d)^6-4/5*b^3*(a*e-b*d)/e^5/(e*x+d)^5-1/8*(a^4*e^4-4*a^3*b*d*e^3+6*a^2*b^2*d^2*e^2-4*a*b^3*d^3*e+b^4*d^4)/e^5/(e*x+d)^8","A"
1479,1,186,109,0.045000," ","int((b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^10,x)","-\frac{b^{4}}{5 \left(e x +d \right)^{5} e^{5}}-\frac{2 \left(a e -b d \right) b^{3}}{3 \left(e x +d \right)^{6} e^{5}}-\frac{6 \left(a^{2} e^{2}-2 a b d e +b^{2} d^{2}\right) b^{2}}{7 \left(e x +d \right)^{7} e^{5}}-\frac{\left(a^{3} e^{3}-3 a^{2} b d \,e^{2}+3 a \,b^{2} d^{2} e -b^{3} d^{3}\right) b}{2 \left(e x +d \right)^{8} e^{5}}-\frac{e^{4} a^{4}-4 d \,e^{3} a^{3} b +6 d^{2} e^{2} b^{2} a^{2}-4 d^{3} a \,b^{3} e +b^{4} d^{4}}{9 \left(e x +d \right)^{9} e^{5}}"," ",0,"-6/7*b^2*(a^2*e^2-2*a*b*d*e+b^2*d^2)/e^5/(e*x+d)^7-1/9*(a^4*e^4-4*a^3*b*d*e^3+6*a^2*b^2*d^2*e^2-4*a*b^3*d^3*e+b^4*d^4)/e^5/(e*x+d)^9-2/3*b^3*(a*e-b*d)/e^5/(e*x+d)^6-1/5*b^4/e^5/(e*x+d)^5-1/2*b*(a^3*e^3-3*a^2*b*d*e^2+3*a*b^2*d^2*e-b^3*d^3)/e^5/(e*x+d)^8","A"
1480,1,186,109,0.051000," ","int((b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^11,x)","-\frac{b^{4}}{6 \left(e x +d \right)^{6} e^{5}}-\frac{4 \left(a e -b d \right) b^{3}}{7 \left(e x +d \right)^{7} e^{5}}-\frac{3 \left(a^{2} e^{2}-2 a b d e +b^{2} d^{2}\right) b^{2}}{4 \left(e x +d \right)^{8} e^{5}}-\frac{4 \left(a^{3} e^{3}-3 a^{2} b d \,e^{2}+3 a \,b^{2} d^{2} e -b^{3} d^{3}\right) b}{9 \left(e x +d \right)^{9} e^{5}}-\frac{e^{4} a^{4}-4 d \,e^{3} a^{3} b +6 d^{2} e^{2} b^{2} a^{2}-4 d^{3} a \,b^{3} e +b^{4} d^{4}}{10 \left(e x +d \right)^{10} e^{5}}"," ",0,"-1/10*(a^4*e^4-4*a^3*b*d*e^3+6*a^2*b^2*d^2*e^2-4*a*b^3*d^3*e+b^4*d^4)/e^5/(e*x+d)^10-4/7*b^3*(a*e-b*d)/e^5/(e*x+d)^7-4/9*b*(a^3*e^3-3*a^2*b*d*e^2+3*a*b^2*d^2*e-b^3*d^3)/e^5/(e*x+d)^9-1/6*b^4/e^5/(e*x+d)^6-3/4*b^2*(a^2*e^2-2*a*b*d*e+b^2*d^2)/e^5/(e*x+d)^8","A"
1481,1,803,159,0.042000," ","int((e*x+d)^8*(b^2*x^2+2*a*b*x+a^2)^3,x)","\frac{b^{6} e^{8} x^{15}}{15}+a^{6} d^{8} x +\frac{\left(6 e^{8} a \,b^{5}+8 d \,e^{7} b^{6}\right) x^{14}}{14}+\frac{\left(15 e^{8} a^{2} b^{4}+48 d \,e^{7} a \,b^{5}+28 d^{2} e^{6} b^{6}\right) x^{13}}{13}+\frac{\left(20 e^{8} a^{3} b^{3}+120 d \,e^{7} a^{2} b^{4}+168 d^{2} e^{6} a \,b^{5}+56 d^{3} e^{5} b^{6}\right) x^{12}}{12}+\frac{\left(15 e^{8} a^{4} b^{2}+160 d \,e^{7} a^{3} b^{3}+420 d^{2} e^{6} a^{2} b^{4}+336 d^{3} e^{5} a \,b^{5}+70 d^{4} e^{4} b^{6}\right) x^{11}}{11}+\frac{\left(6 e^{8} a^{5} b +120 d \,e^{7} a^{4} b^{2}+560 d^{2} e^{6} a^{3} b^{3}+840 d^{3} e^{5} a^{2} b^{4}+420 d^{4} e^{4} a \,b^{5}+56 d^{5} e^{3} b^{6}\right) x^{10}}{10}+\frac{\left(e^{8} a^{6}+48 d \,e^{7} a^{5} b +420 d^{2} e^{6} a^{4} b^{2}+1120 d^{3} e^{5} a^{3} b^{3}+1050 d^{4} e^{4} a^{2} b^{4}+336 d^{5} e^{3} a \,b^{5}+28 d^{6} e^{2} b^{6}\right) x^{9}}{9}+\frac{\left(8 d \,e^{7} a^{6}+168 d^{2} e^{6} a^{5} b +840 d^{3} e^{5} a^{4} b^{2}+1400 d^{4} e^{4} a^{3} b^{3}+840 d^{5} e^{3} a^{2} b^{4}+168 d^{6} e^{2} a \,b^{5}+8 d^{7} e \,b^{6}\right) x^{8}}{8}+\frac{\left(28 d^{2} e^{6} a^{6}+336 d^{3} e^{5} a^{5} b +1050 d^{4} e^{4} a^{4} b^{2}+1120 d^{5} e^{3} a^{3} b^{3}+420 d^{6} e^{2} a^{2} b^{4}+48 d^{7} e a \,b^{5}+d^{8} b^{6}\right) x^{7}}{7}+\frac{\left(56 d^{3} e^{5} a^{6}+420 d^{4} e^{4} a^{5} b +840 d^{5} e^{3} a^{4} b^{2}+560 d^{6} e^{2} a^{3} b^{3}+120 d^{7} e \,a^{2} b^{4}+6 d^{8} a \,b^{5}\right) x^{6}}{6}+\frac{\left(70 d^{4} e^{4} a^{6}+336 d^{5} e^{3} a^{5} b +420 d^{6} e^{2} a^{4} b^{2}+160 d^{7} e \,a^{3} b^{3}+15 d^{8} a^{2} b^{4}\right) x^{5}}{5}+\frac{\left(56 d^{5} e^{3} a^{6}+168 d^{6} e^{2} a^{5} b +120 d^{7} e \,a^{4} b^{2}+20 d^{8} a^{3} b^{3}\right) x^{4}}{4}+\frac{\left(28 d^{6} e^{2} a^{6}+48 d^{7} e \,a^{5} b +15 d^{8} a^{4} b^{2}\right) x^{3}}{3}+\frac{\left(8 d^{7} e \,a^{6}+6 d^{8} a^{5} b \right) x^{2}}{2}"," ",0,"1/15*e^8*b^6*x^15+1/14*(6*a*b^5*e^8+8*b^6*d*e^7)*x^14+1/13*(15*a^2*b^4*e^8+48*a*b^5*d*e^7+28*b^6*d^2*e^6)*x^13+1/12*(20*a^3*b^3*e^8+120*a^2*b^4*d*e^7+168*a*b^5*d^2*e^6+56*b^6*d^3*e^5)*x^12+1/11*(15*a^4*b^2*e^8+160*a^3*b^3*d*e^7+420*a^2*b^4*d^2*e^6+336*a*b^5*d^3*e^5+70*b^6*d^4*e^4)*x^11+1/10*(6*a^5*b*e^8+120*a^4*b^2*d*e^7+560*a^3*b^3*d^2*e^6+840*a^2*b^4*d^3*e^5+420*a*b^5*d^4*e^4+56*b^6*d^5*e^3)*x^10+1/9*(a^6*e^8+48*a^5*b*d*e^7+420*a^4*b^2*d^2*e^6+1120*a^3*b^3*d^3*e^5+1050*a^2*b^4*d^4*e^4+336*a*b^5*d^5*e^3+28*b^6*d^6*e^2)*x^9+1/8*(8*a^6*d*e^7+168*a^5*b*d^2*e^6+840*a^4*b^2*d^3*e^5+1400*a^3*b^3*d^4*e^4+840*a^2*b^4*d^5*e^3+168*a*b^5*d^6*e^2+8*b^6*d^7*e)*x^8+1/7*(28*a^6*d^2*e^6+336*a^5*b*d^3*e^5+1050*a^4*b^2*d^4*e^4+1120*a^3*b^3*d^5*e^3+420*a^2*b^4*d^6*e^2+48*a*b^5*d^7*e+b^6*d^8)*x^7+1/6*(56*a^6*d^3*e^5+420*a^5*b*d^4*e^4+840*a^4*b^2*d^5*e^3+560*a^3*b^3*d^6*e^2+120*a^2*b^4*d^7*e+6*a*b^5*d^8)*x^6+1/5*(70*a^6*d^4*e^4+336*a^5*b*d^5*e^3+420*a^4*b^2*d^6*e^2+160*a^3*b^3*d^7*e+15*a^2*b^4*d^8)*x^5+1/4*(56*a^6*d^5*e^3+168*a^5*b*d^6*e^2+120*a^4*b^2*d^7*e+20*a^3*b^3*d^8)*x^4+1/3*(28*a^6*d^6*e^2+48*a^5*b*d^7*e+15*a^4*b^2*d^8)*x^3+1/2*(8*a^6*d^7*e+6*a^5*b*d^8)*x^2+d^8*a^6*x","B"
1482,1,709,159,0.038000," ","int((e*x+d)^7*(b^2*x^2+2*a*b*x+a^2)^3,x)","\frac{b^{6} e^{7} x^{14}}{14}+a^{6} d^{7} x +\frac{\left(6 e^{7} a \,b^{5}+7 d \,e^{6} b^{6}\right) x^{13}}{13}+\frac{\left(15 e^{7} a^{2} b^{4}+42 d \,e^{6} a \,b^{5}+21 d^{2} e^{5} b^{6}\right) x^{12}}{12}+\frac{\left(20 e^{7} a^{3} b^{3}+105 d \,e^{6} a^{2} b^{4}+126 d^{2} e^{5} a \,b^{5}+35 d^{3} e^{4} b^{6}\right) x^{11}}{11}+\frac{\left(15 e^{7} a^{4} b^{2}+140 d \,e^{6} a^{3} b^{3}+315 d^{2} e^{5} a^{2} b^{4}+210 d^{3} e^{4} a \,b^{5}+35 d^{4} e^{3} b^{6}\right) x^{10}}{10}+\frac{\left(6 e^{7} a^{5} b +105 d \,e^{6} a^{4} b^{2}+420 d^{2} e^{5} a^{3} b^{3}+525 d^{3} e^{4} a^{2} b^{4}+210 d^{4} e^{3} a \,b^{5}+21 d^{5} e^{2} b^{6}\right) x^{9}}{9}+\frac{\left(e^{7} a^{6}+42 d \,e^{6} a^{5} b +315 d^{2} e^{5} a^{4} b^{2}+700 d^{3} e^{4} a^{3} b^{3}+525 d^{4} e^{3} a^{2} b^{4}+126 d^{5} e^{2} a \,b^{5}+7 d^{6} e \,b^{6}\right) x^{8}}{8}+\frac{\left(7 d \,e^{6} a^{6}+126 d^{2} e^{5} a^{5} b +525 d^{3} e^{4} a^{4} b^{2}+700 d^{4} e^{3} a^{3} b^{3}+315 d^{5} e^{2} a^{2} b^{4}+42 d^{6} e a \,b^{5}+d^{7} b^{6}\right) x^{7}}{7}+\frac{\left(21 d^{2} e^{5} a^{6}+210 d^{3} e^{4} a^{5} b +525 d^{4} e^{3} a^{4} b^{2}+420 d^{5} e^{2} a^{3} b^{3}+105 d^{6} e \,a^{2} b^{4}+6 d^{7} a \,b^{5}\right) x^{6}}{6}+\frac{\left(35 d^{3} e^{4} a^{6}+210 d^{4} e^{3} a^{5} b +315 d^{5} e^{2} a^{4} b^{2}+140 d^{6} e \,a^{3} b^{3}+15 d^{7} a^{2} b^{4}\right) x^{5}}{5}+\frac{\left(35 d^{4} e^{3} a^{6}+126 d^{5} e^{2} a^{5} b +105 d^{6} e \,a^{4} b^{2}+20 d^{7} a^{3} b^{3}\right) x^{4}}{4}+\frac{\left(21 d^{5} e^{2} a^{6}+42 d^{6} e \,a^{5} b +15 d^{7} a^{4} b^{2}\right) x^{3}}{3}+\frac{\left(7 d^{6} e \,a^{6}+6 d^{7} a^{5} b \right) x^{2}}{2}"," ",0,"1/14*e^7*b^6*x^14+1/13*(6*a*b^5*e^7+7*b^6*d*e^6)*x^13+1/12*(15*a^2*b^4*e^7+42*a*b^5*d*e^6+21*b^6*d^2*e^5)*x^12+1/11*(20*a^3*b^3*e^7+105*a^2*b^4*d*e^6+126*a*b^5*d^2*e^5+35*b^6*d^3*e^4)*x^11+1/10*(15*a^4*b^2*e^7+140*a^3*b^3*d*e^6+315*a^2*b^4*d^2*e^5+210*a*b^5*d^3*e^4+35*b^6*d^4*e^3)*x^10+1/9*(6*a^5*b*e^7+105*a^4*b^2*d*e^6+420*a^3*b^3*d^2*e^5+525*a^2*b^4*d^3*e^4+210*a*b^5*d^4*e^3+21*b^6*d^5*e^2)*x^9+1/8*(a^6*e^7+42*a^5*b*d*e^6+315*a^4*b^2*d^2*e^5+700*a^3*b^3*d^3*e^4+525*a^2*b^4*d^4*e^3+126*a*b^5*d^5*e^2+7*b^6*d^6*e)*x^8+1/7*(7*a^6*d*e^6+126*a^5*b*d^2*e^5+525*a^4*b^2*d^3*e^4+700*a^3*b^3*d^4*e^3+315*a^2*b^4*d^5*e^2+42*a*b^5*d^6*e+b^6*d^7)*x^7+1/6*(21*a^6*d^2*e^5+210*a^5*b*d^3*e^4+525*a^4*b^2*d^4*e^3+420*a^3*b^3*d^5*e^2+105*a^2*b^4*d^6*e+6*a*b^5*d^7)*x^6+1/5*(35*a^6*d^3*e^4+210*a^5*b*d^4*e^3+315*a^4*b^2*d^5*e^2+140*a^3*b^3*d^6*e+15*a^2*b^4*d^7)*x^5+1/4*(35*a^6*d^4*e^3+126*a^5*b*d^5*e^2+105*a^4*b^2*d^6*e+20*a^3*b^3*d^7)*x^4+1/3*(21*a^6*d^5*e^2+42*a^5*b*d^6*e+15*a^4*b^2*d^7)*x^3+1/2*(7*a^6*d^6*e+6*a^5*b*d^7)*x^2+d^7*a^6*x","B"
1483,1,615,159,0.040000," ","int((e*x+d)^6*(b^2*x^2+2*a*b*x+a^2)^3,x)","\frac{b^{6} e^{6} x^{13}}{13}+a^{6} d^{6} x +\frac{\left(6 e^{6} a \,b^{5}+6 d \,e^{5} b^{6}\right) x^{12}}{12}+\frac{\left(15 e^{6} a^{2} b^{4}+36 d \,e^{5} a \,b^{5}+15 d^{2} e^{4} b^{6}\right) x^{11}}{11}+\frac{\left(20 e^{6} a^{3} b^{3}+90 d \,e^{5} a^{2} b^{4}+90 d^{2} e^{4} a \,b^{5}+20 d^{3} e^{3} b^{6}\right) x^{10}}{10}+\frac{\left(15 e^{6} a^{4} b^{2}+120 d \,e^{5} a^{3} b^{3}+225 d^{2} e^{4} a^{2} b^{4}+120 d^{3} e^{3} a \,b^{5}+15 d^{4} e^{2} b^{6}\right) x^{9}}{9}+\frac{\left(6 e^{6} a^{5} b +90 d \,e^{5} a^{4} b^{2}+300 d^{2} e^{4} a^{3} b^{3}+300 d^{3} e^{3} a^{2} b^{4}+90 d^{4} e^{2} a \,b^{5}+6 d^{5} e \,b^{6}\right) x^{8}}{8}+\frac{\left(e^{6} a^{6}+36 d \,e^{5} a^{5} b +225 d^{2} e^{4} a^{4} b^{2}+400 d^{3} e^{3} a^{3} b^{3}+225 d^{4} e^{2} a^{2} b^{4}+36 d^{5} e a \,b^{5}+d^{6} b^{6}\right) x^{7}}{7}+\frac{\left(6 d \,e^{5} a^{6}+90 d^{2} e^{4} a^{5} b +300 d^{3} e^{3} a^{4} b^{2}+300 d^{4} e^{2} a^{3} b^{3}+90 d^{5} e \,a^{2} b^{4}+6 d^{6} a \,b^{5}\right) x^{6}}{6}+\frac{\left(15 d^{2} e^{4} a^{6}+120 d^{3} e^{3} a^{5} b +225 d^{4} e^{2} a^{4} b^{2}+120 d^{5} e \,a^{3} b^{3}+15 d^{6} a^{2} b^{4}\right) x^{5}}{5}+\frac{\left(20 d^{3} e^{3} a^{6}+90 d^{4} e^{2} a^{5} b +90 d^{5} e \,a^{4} b^{2}+20 d^{6} a^{3} b^{3}\right) x^{4}}{4}+\frac{\left(15 d^{4} e^{2} a^{6}+36 d^{5} e \,a^{5} b +15 d^{6} a^{4} b^{2}\right) x^{3}}{3}+\frac{\left(6 d^{5} e \,a^{6}+6 d^{6} a^{5} b \right) x^{2}}{2}"," ",0,"1/13*b^6*e^6*x^13+1/12*(6*a*b^5*e^6+6*b^6*d*e^5)*x^12+1/11*(15*a^2*b^4*e^6+36*a*b^5*d*e^5+15*b^6*d^2*e^4)*x^11+1/10*(20*a^3*b^3*e^6+90*a^2*b^4*d*e^5+90*a*b^5*d^2*e^4+20*b^6*d^3*e^3)*x^10+1/9*(15*a^4*b^2*e^6+120*a^3*b^3*d*e^5+225*a^2*b^4*d^2*e^4+120*a*b^5*d^3*e^3+15*b^6*d^4*e^2)*x^9+1/8*(6*a^5*b*e^6+90*a^4*b^2*d*e^5+300*a^3*b^3*d^2*e^4+300*a^2*b^4*d^3*e^3+90*a*b^5*d^4*e^2+6*b^6*d^5*e)*x^8+1/7*(a^6*e^6+36*a^5*b*d*e^5+225*a^4*b^2*d^2*e^4+400*a^3*b^3*d^3*e^3+225*a^2*b^4*d^4*e^2+36*a*b^5*d^5*e+b^6*d^6)*x^7+1/6*(6*a^6*d*e^5+90*a^5*b*d^2*e^4+300*a^4*b^2*d^3*e^3+300*a^3*b^3*d^4*e^2+90*a^2*b^4*d^5*e+6*a*b^5*d^6)*x^6+1/5*(15*a^6*d^2*e^4+120*a^5*b*d^3*e^3+225*a^4*b^2*d^4*e^2+120*a^3*b^3*d^5*e+15*a^2*b^4*d^6)*x^5+1/4*(20*a^6*d^3*e^3+90*a^5*b*d^4*e^2+90*a^4*b^2*d^5*e+20*a^3*b^3*d^6)*x^4+1/3*(15*a^6*d^4*e^2+36*a^5*b*d^5*e+15*a^4*b^2*d^6)*x^3+1/2*(6*a^6*d^5*e+6*a^5*b*d^6)*x^2+d^6*a^6*x","B"
1484,1,521,133,0.052000," ","int((e*x+d)^5*(b^2*x^2+2*a*b*x+a^2)^3,x)","\frac{b^{6} e^{5} x^{12}}{12}+a^{6} d^{5} x +\frac{\left(6 e^{5} a \,b^{5}+5 d \,e^{4} b^{6}\right) x^{11}}{11}+\frac{\left(15 e^{5} a^{2} b^{4}+30 d \,e^{4} a \,b^{5}+10 d^{2} e^{3} b^{6}\right) x^{10}}{10}+\frac{\left(20 e^{5} a^{3} b^{3}+75 d \,e^{4} a^{2} b^{4}+60 d^{2} e^{3} a \,b^{5}+10 d^{3} e^{2} b^{6}\right) x^{9}}{9}+\frac{\left(15 e^{5} a^{4} b^{2}+100 d \,e^{4} a^{3} b^{3}+150 d^{2} e^{3} a^{2} b^{4}+60 d^{3} e^{2} a \,b^{5}+5 d^{4} e \,b^{6}\right) x^{8}}{8}+\frac{\left(6 e^{5} a^{5} b +75 d \,e^{4} a^{4} b^{2}+200 d^{2} e^{3} a^{3} b^{3}+150 d^{3} e^{2} a^{2} b^{4}+30 d^{4} e a \,b^{5}+d^{5} b^{6}\right) x^{7}}{7}+\frac{\left(e^{5} a^{6}+30 d \,e^{4} a^{5} b +150 d^{2} e^{3} a^{4} b^{2}+200 d^{3} e^{2} a^{3} b^{3}+75 d^{4} e \,a^{2} b^{4}+6 d^{5} a \,b^{5}\right) x^{6}}{6}+\frac{\left(5 d \,e^{4} a^{6}+60 d^{2} e^{3} a^{5} b +150 d^{3} e^{2} a^{4} b^{2}+100 d^{4} e \,a^{3} b^{3}+15 d^{5} a^{2} b^{4}\right) x^{5}}{5}+\frac{\left(10 d^{2} e^{3} a^{6}+60 d^{3} e^{2} a^{5} b +75 d^{4} e \,a^{4} b^{2}+20 d^{5} a^{3} b^{3}\right) x^{4}}{4}+\frac{\left(10 d^{3} e^{2} a^{6}+30 d^{4} e \,a^{5} b +15 d^{5} a^{4} b^{2}\right) x^{3}}{3}+\frac{\left(5 d^{4} e \,a^{6}+6 d^{5} a^{5} b \right) x^{2}}{2}"," ",0,"1/12*b^6*e^5*x^12+1/11*(6*a*b^5*e^5+5*b^6*d*e^4)*x^11+1/10*(15*a^2*b^4*e^5+30*a*b^5*d*e^4+10*b^6*d^2*e^3)*x^10+1/9*(20*a^3*b^3*e^5+75*a^2*b^4*d*e^4+60*a*b^5*d^2*e^3+10*b^6*d^3*e^2)*x^9+1/8*(15*a^4*b^2*e^5+100*a^3*b^3*d*e^4+150*a^2*b^4*d^2*e^3+60*a*b^5*d^3*e^2+5*b^6*d^4*e)*x^8+1/7*(6*a^5*b*e^5+75*a^4*b^2*d*e^4+200*a^3*b^3*d^2*e^3+150*a^2*b^4*d^3*e^2+30*a*b^5*d^4*e+b^6*d^5)*x^7+1/6*(a^6*e^5+30*a^5*b*d*e^4+150*a^4*b^2*d^2*e^3+200*a^3*b^3*d^3*e^2+75*a^2*b^4*d^4*e+6*a*b^5*d^5)*x^6+1/5*(5*a^6*d*e^4+60*a^5*b*d^2*e^3+150*a^4*b^2*d^3*e^2+100*a^3*b^3*d^4*e+15*a^2*b^4*d^5)*x^5+1/4*(10*a^6*d^2*e^3+60*a^5*b*d^3*e^2+75*a^4*b^2*d^4*e+20*a^3*b^3*d^5)*x^4+1/3*(10*a^6*d^3*e^2+30*a^5*b*d^4*e+15*a^4*b^2*d^5)*x^3+1/2*(5*a^6*d^4*e+6*a^5*b*d^5)*x^2+d^5*a^6*x","B"
1485,1,427,109,0.044000," ","int((e*x+d)^4*(b^2*x^2+2*a*b*x+a^2)^3,x)","\frac{b^{6} e^{4} x^{11}}{11}+a^{6} d^{4} x +\frac{\left(6 e^{4} a \,b^{5}+4 d \,e^{3} b^{6}\right) x^{10}}{10}+\frac{\left(15 e^{4} a^{2} b^{4}+24 d \,e^{3} a \,b^{5}+6 d^{2} e^{2} b^{6}\right) x^{9}}{9}+\frac{\left(20 e^{4} a^{3} b^{3}+60 d \,e^{3} a^{2} b^{4}+36 d^{2} e^{2} a \,b^{5}+4 d^{3} e \,b^{6}\right) x^{8}}{8}+\frac{\left(15 e^{4} a^{4} b^{2}+80 d \,e^{3} a^{3} b^{3}+90 d^{2} e^{2} a^{2} b^{4}+24 d^{3} e a \,b^{5}+d^{4} b^{6}\right) x^{7}}{7}+\frac{\left(6 e^{4} a^{5} b +60 d \,e^{3} a^{4} b^{2}+120 d^{2} e^{2} a^{3} b^{3}+60 d^{3} e \,a^{2} b^{4}+6 d^{4} a \,b^{5}\right) x^{6}}{6}+\frac{\left(e^{4} a^{6}+24 d \,e^{3} a^{5} b +90 d^{2} e^{2} a^{4} b^{2}+80 d^{3} e \,a^{3} b^{3}+15 d^{4} a^{2} b^{4}\right) x^{5}}{5}+\frac{\left(4 d \,e^{3} a^{6}+36 d^{2} e^{2} a^{5} b +60 d^{3} e \,a^{4} b^{2}+20 d^{4} a^{3} b^{3}\right) x^{4}}{4}+\frac{\left(6 d^{2} e^{2} a^{6}+24 d^{3} e \,a^{5} b +15 d^{4} a^{4} b^{2}\right) x^{3}}{3}+\frac{\left(4 d^{3} e \,a^{6}+6 d^{4} a^{5} b \right) x^{2}}{2}"," ",0,"1/11*e^4*b^6*x^11+1/10*(6*a*b^5*e^4+4*b^6*d*e^3)*x^10+1/9*(15*a^2*b^4*e^4+24*a*b^5*d*e^3+6*b^6*d^2*e^2)*x^9+1/8*(20*a^3*b^3*e^4+60*a^2*b^4*d*e^3+36*a*b^5*d^2*e^2+4*b^6*d^3*e)*x^8+1/7*(15*a^4*b^2*e^4+80*a^3*b^3*d*e^3+90*a^2*b^4*d^2*e^2+24*a*b^5*d^3*e+b^6*d^4)*x^7+1/6*(6*a^5*b*e^4+60*a^4*b^2*d*e^3+120*a^3*b^3*d^2*e^2+60*a^2*b^4*d^3*e+6*a*b^5*d^4)*x^6+1/5*(a^6*e^4+24*a^5*b*d*e^3+90*a^4*b^2*d^2*e^2+80*a^3*b^3*d^3*e+15*a^2*b^4*d^4)*x^5+1/4*(4*a^6*d*e^3+36*a^5*b*d^2*e^2+60*a^4*b^2*d^3*e+20*a^3*b^3*d^4)*x^4+1/3*(6*a^6*d^2*e^2+24*a^5*b*d^3*e+15*a^4*b^2*d^4)*x^3+1/2*(4*a^6*d^3*e+6*a^5*b*d^4)*x^2+d^4*a^6*x","B"
1486,1,333,84,0.041000," ","int((e*x+d)^3*(b^2*x^2+2*a*b*x+a^2)^3,x)","\frac{b^{6} e^{3} x^{10}}{10}+a^{6} d^{3} x +\frac{\left(6 e^{3} a \,b^{5}+3 d \,e^{2} b^{6}\right) x^{9}}{9}+\frac{\left(15 e^{3} a^{2} b^{4}+18 d \,e^{2} a \,b^{5}+3 d^{2} e \,b^{6}\right) x^{8}}{8}+\frac{\left(20 e^{3} a^{3} b^{3}+45 d \,e^{2} a^{2} b^{4}+18 d^{2} e a \,b^{5}+d^{3} b^{6}\right) x^{7}}{7}+\frac{\left(15 e^{3} a^{4} b^{2}+60 d \,e^{2} a^{3} b^{3}+45 d^{2} e \,a^{2} b^{4}+6 d^{3} a \,b^{5}\right) x^{6}}{6}+\frac{\left(6 e^{3} a^{5} b +45 d \,e^{2} a^{4} b^{2}+60 d^{2} e \,a^{3} b^{3}+15 d^{3} a^{2} b^{4}\right) x^{5}}{5}+\frac{\left(e^{3} a^{6}+18 d \,e^{2} a^{5} b +45 d^{2} e \,a^{4} b^{2}+20 d^{3} a^{3} b^{3}\right) x^{4}}{4}+\frac{\left(3 d \,e^{2} a^{6}+18 d^{2} e \,a^{5} b +15 d^{3} a^{4} b^{2}\right) x^{3}}{3}+\frac{\left(3 d^{2} e \,a^{6}+6 d^{3} a^{5} b \right) x^{2}}{2}"," ",0,"1/10*e^3*b^6*x^10+1/9*(6*a*b^5*e^3+3*b^6*d*e^2)*x^9+1/8*(15*a^2*b^4*e^3+18*a*b^5*d*e^2+3*b^6*d^2*e)*x^8+1/7*(20*a^3*b^3*e^3+45*a^2*b^4*d*e^2+18*a*b^5*d^2*e+b^6*d^3)*x^7+1/6*(15*a^4*b^2*e^3+60*a^3*b^3*d*e^2+45*a^2*b^4*d^2*e+6*a*b^5*d^3)*x^6+1/5*(6*a^5*b*e^3+45*a^4*b^2*d*e^2+60*a^3*b^3*d^2*e+15*a^2*b^4*d^3)*x^5+1/4*(a^6*e^3+18*a^5*b*d*e^2+45*a^4*b^2*d^2*e+20*a^3*b^3*d^3)*x^4+1/3*(3*a^6*d*e^2+18*a^5*b*d^2*e+15*a^4*b^2*d^3)*x^3+1/2*(3*a^6*d^2*e+6*a^5*b*d^3)*x^2+d^3*a^6*x","B"
1487,1,239,59,0.043000," ","int((e*x+d)^2*(b^2*x^2+2*a*b*x+a^2)^3,x)","\frac{b^{6} e^{2} x^{9}}{9}+a^{6} d^{2} x +\frac{\left(6 e^{2} a \,b^{5}+2 d e \,b^{6}\right) x^{8}}{8}+\frac{\left(15 e^{2} a^{2} b^{4}+12 d e a \,b^{5}+b^{6} d^{2}\right) x^{7}}{7}+\frac{\left(20 e^{2} a^{3} b^{3}+30 d e \,a^{2} b^{4}+6 d^{2} a \,b^{5}\right) x^{6}}{6}+\frac{\left(15 e^{2} a^{4} b^{2}+40 d e \,a^{3} b^{3}+15 d^{2} a^{2} b^{4}\right) x^{5}}{5}+\frac{\left(6 e^{2} a^{5} b +30 d e \,a^{4} b^{2}+20 d^{2} a^{3} b^{3}\right) x^{4}}{4}+\frac{\left(e^{2} a^{6}+12 d e \,a^{5} b +15 d^{2} a^{4} b^{2}\right) x^{3}}{3}+\frac{\left(2 d e \,a^{6}+6 d^{2} a^{5} b \right) x^{2}}{2}"," ",0,"1/9*e^2*b^6*x^9+1/8*(6*a*b^5*e^2+2*b^6*d*e)*x^8+1/7*(15*a^2*b^4*e^2+12*a*b^5*d*e+b^6*d^2)*x^7+1/6*(20*a^3*b^3*e^2+30*a^2*b^4*d*e+6*a*b^5*d^2)*x^6+1/5*(15*a^4*b^2*e^2+40*a^3*b^3*d*e+15*a^2*b^4*d^2)*x^5+1/4*(6*a^5*b*e^2+30*a^4*b^2*d*e+20*a^3*b^3*d^2)*x^4+1/3*(a^6*e^2+12*a^5*b*d*e+15*a^4*b^2*d^2)*x^3+1/2*(2*a^6*d*e+6*a^5*b*d^2)*x^2+d^2*a^6*x","B"
1488,1,145,34,0.045000," ","int((e*x+d)*(b^2*x^2+2*a*b*x+a^2)^3,x)","\frac{b^{6} e \,x^{8}}{8}+a^{6} d x +\frac{\left(6 e a \,b^{5}+d \,b^{6}\right) x^{7}}{7}+\frac{\left(15 e \,a^{2} b^{4}+6 d a \,b^{5}\right) x^{6}}{6}+\frac{\left(20 e \,a^{3} b^{3}+15 d \,a^{2} b^{4}\right) x^{5}}{5}+\frac{\left(15 e \,a^{4} b^{2}+20 d \,a^{3} b^{3}\right) x^{4}}{4}+\frac{\left(6 e \,a^{5} b +15 d \,a^{4} b^{2}\right) x^{3}}{3}+\frac{\left(e \,a^{6}+6 d \,a^{5} b \right) x^{2}}{2}"," ",0,"1/8*e*b^6*x^8+1/7*(6*a*b^5*e+b^6*d)*x^7+1/6*(15*a^2*b^4*e+6*a*b^5*d)*x^6+1/5*(20*a^3*b^3*e+15*a^2*b^4*d)*x^5+1/4*(15*a^4*b^2*e+20*a^3*b^3*d)*x^4+1/3*(6*a^5*b*e+15*a^4*b^2*d)*x^3+1/2*(a^6*e+6*a^5*b*d)*x^2+d*a^6*x","B"
1489,1,65,12,0.038000," ","int((b^2*x^2+2*a*b*x+a^2)^3,x)","\frac{1}{7} b^{6} x^{7}+a \,b^{5} x^{6}+3 a^{2} b^{4} x^{5}+5 a^{3} b^{3} x^{4}+5 a^{4} b^{2} x^{3}+3 a^{5} b \,x^{2}+a^{6} x"," ",0,"1/7*b^6*x^7+a*b^5*x^6+3*a^2*b^4*x^5+5*a^3*b^3*x^4+5*a^4*b^2*x^3+3*a^5*b*x^2+a^6*x","B"
1490,1,412,136,0.045000," ","int((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d),x)","\frac{b^{6} x^{6}}{6 e}+\frac{6 a \,b^{5} x^{5}}{5 e}-\frac{b^{6} d \,x^{5}}{5 e^{2}}+\frac{15 a^{2} b^{4} x^{4}}{4 e}-\frac{3 a \,b^{5} d \,x^{4}}{2 e^{2}}+\frac{b^{6} d^{2} x^{4}}{4 e^{3}}+\frac{20 a^{3} b^{3} x^{3}}{3 e}-\frac{5 a^{2} b^{4} d \,x^{3}}{e^{2}}+\frac{2 a \,b^{5} d^{2} x^{3}}{e^{3}}-\frac{b^{6} d^{3} x^{3}}{3 e^{4}}+\frac{15 a^{4} b^{2} x^{2}}{2 e}-\frac{10 a^{3} b^{3} d \,x^{2}}{e^{2}}+\frac{15 a^{2} b^{4} d^{2} x^{2}}{2 e^{3}}-\frac{3 a \,b^{5} d^{3} x^{2}}{e^{4}}+\frac{b^{6} d^{4} x^{2}}{2 e^{5}}+\frac{a^{6} \ln \left(e x +d \right)}{e}-\frac{6 a^{5} b d \ln \left(e x +d \right)}{e^{2}}+\frac{6 a^{5} b x}{e}+\frac{15 a^{4} b^{2} d^{2} \ln \left(e x +d \right)}{e^{3}}-\frac{15 a^{4} b^{2} d x}{e^{2}}-\frac{20 a^{3} b^{3} d^{3} \ln \left(e x +d \right)}{e^{4}}+\frac{20 a^{3} b^{3} d^{2} x}{e^{3}}+\frac{15 a^{2} b^{4} d^{4} \ln \left(e x +d \right)}{e^{5}}-\frac{15 a^{2} b^{4} d^{3} x}{e^{4}}-\frac{6 a \,b^{5} d^{5} \ln \left(e x +d \right)}{e^{6}}+\frac{6 a \,b^{5} d^{4} x}{e^{5}}+\frac{b^{6} d^{6} \ln \left(e x +d \right)}{e^{7}}-\frac{b^{6} d^{5} x}{e^{6}}"," ",0,"-3/2*b^5/e^2*x^4*a*d-5*b^4/e^2*x^3*a^2*d+1/e^7*ln(e*x+d)*d^6*b^6+6/5*b^5/e*x^5*a-1/5*b^6/e^2*x^5*d+15/4*b^4/e*x^4*a^2+1/4*b^6/e^3*x^4*d^2+20/3*b^3/e*x^3*a^3-1/3*b^6/e^4*x^3*d^3+15/2*b^2/e*x^2*a^4+1/2*b^6/e^5*x^2*d^4+6*b/e*a^5*x-b^6/e^6*d^5*x+1/6*b^6/e*x^6+1/e*ln(e*x+d)*a^6-15*b^4/e^4*a^2*d^3*x+6*b^5/e^5*a*d^4*x-3*b^5/e^4*x^2*a*d^3-15*b^2/e^2*a^4*d*x-6/e^2*ln(e*x+d)*d*a^5*b+20*b^3/e^3*a^3*d^2*x+15/e^5*ln(e*x+d)*d^4*a^2*b^4-20/e^4*ln(e*x+d)*d^3*a^3*b^3-6/e^6*ln(e*x+d)*d^5*a*b^5+15/e^3*ln(e*x+d)*d^2*a^4*b^2+15/2*b^4/e^3*x^2*a^2*d^2-10*b^3/e^2*x^2*a^3*d+2*b^5/e^3*x^3*a*d^2","B"
1491,1,440,152,0.055000," ","int((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^2,x)","\frac{b^{6} x^{5}}{5 e^{2}}+\frac{3 a \,b^{5} x^{4}}{2 e^{2}}-\frac{b^{6} d \,x^{4}}{2 e^{3}}+\frac{5 a^{2} b^{4} x^{3}}{e^{2}}-\frac{4 a \,b^{5} d \,x^{3}}{e^{3}}+\frac{b^{6} d^{2} x^{3}}{e^{4}}+\frac{10 a^{3} b^{3} x^{2}}{e^{2}}-\frac{15 a^{2} b^{4} d \,x^{2}}{e^{3}}+\frac{9 a \,b^{5} d^{2} x^{2}}{e^{4}}-\frac{2 b^{6} d^{3} x^{2}}{e^{5}}-\frac{a^{6}}{\left(e x +d \right) e}+\frac{6 a^{5} b d}{\left(e x +d \right) e^{2}}+\frac{6 a^{5} b \ln \left(e x +d \right)}{e^{2}}-\frac{15 a^{4} b^{2} d^{2}}{\left(e x +d \right) e^{3}}-\frac{30 a^{4} b^{2} d \ln \left(e x +d \right)}{e^{3}}+\frac{15 a^{4} b^{2} x}{e^{2}}+\frac{20 a^{3} b^{3} d^{3}}{\left(e x +d \right) e^{4}}+\frac{60 a^{3} b^{3} d^{2} \ln \left(e x +d \right)}{e^{4}}-\frac{40 a^{3} b^{3} d x}{e^{3}}-\frac{15 a^{2} b^{4} d^{4}}{\left(e x +d \right) e^{5}}-\frac{60 a^{2} b^{4} d^{3} \ln \left(e x +d \right)}{e^{5}}+\frac{45 a^{2} b^{4} d^{2} x}{e^{4}}+\frac{6 a \,b^{5} d^{5}}{\left(e x +d \right) e^{6}}+\frac{30 a \,b^{5} d^{4} \ln \left(e x +d \right)}{e^{6}}-\frac{24 a \,b^{5} d^{3} x}{e^{5}}-\frac{b^{6} d^{6}}{\left(e x +d \right) e^{7}}-\frac{6 b^{6} d^{5} \ln \left(e x +d \right)}{e^{7}}+\frac{5 b^{6} d^{4} x}{e^{6}}"," ",0,"-60*b^4/e^5*ln(e*x+d)*a^2*d^3+15*b^2/e^2*a^4*x+5*b^6/e^6*d^4*x-1/2*b^6/e^3*x^4*d+5*b^4/e^2*x^3*a^2+b^6/e^4*x^3*d^2+10*b^3/e^2*x^2*a^3-2*b^6/e^5*x^2*d^3-6*b^6/e^7*ln(e*x+d)*d^5-1/e^7/(e*x+d)*d^6*b^6+6*b/e^2*ln(e*x+d)*a^5+3/2*b^5/e^2*x^4*a+1/5*b^6/e^2*x^5-1/e/(e*x+d)*a^6-30*b^2/e^3*ln(e*x+d)*a^4*d+60*b^3/e^4*ln(e*x+d)*a^3*d^2+30*b^5/e^6*ln(e*x+d)*a*d^4+9*b^5/e^4*x^2*a*d^2-40*b^3/e^3*d*a^3*x+45*b^4/e^4*a^2*d^2*x-24*b^5/e^5*a*d^3*x+6/e^2/(e*x+d)*d*a^5*b-15/e^3/(e*x+d)*d^2*a^4*b^2+20/e^4/(e*x+d)*d^3*a^3*b^3-15/e^5/(e*x+d)*d^4*a^2*b^4+6/e^6/(e*x+d)*d^5*a*b^5-4*b^5/e^3*x^3*a*d-15*b^4/e^3*x^2*a^2*d","B"
1492,1,464,152,0.055000," ","int((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^3,x)","\frac{b^{6} x^{4}}{4 e^{3}}+\frac{2 a \,b^{5} x^{3}}{e^{3}}-\frac{b^{6} d \,x^{3}}{e^{4}}-\frac{a^{6}}{2 \left(e x +d \right)^{2} e}+\frac{3 a^{5} b d}{\left(e x +d \right)^{2} e^{2}}-\frac{15 a^{4} b^{2} d^{2}}{2 \left(e x +d \right)^{2} e^{3}}+\frac{10 a^{3} b^{3} d^{3}}{\left(e x +d \right)^{2} e^{4}}-\frac{15 a^{2} b^{4} d^{4}}{2 \left(e x +d \right)^{2} e^{5}}+\frac{15 a^{2} b^{4} x^{2}}{2 e^{3}}+\frac{3 a \,b^{5} d^{5}}{\left(e x +d \right)^{2} e^{6}}-\frac{9 a \,b^{5} d \,x^{2}}{e^{4}}-\frac{b^{6} d^{6}}{2 \left(e x +d \right)^{2} e^{7}}+\frac{3 b^{6} d^{2} x^{2}}{e^{5}}-\frac{6 a^{5} b}{\left(e x +d \right) e^{2}}+\frac{30 a^{4} b^{2} d}{\left(e x +d \right) e^{3}}+\frac{15 a^{4} b^{2} \ln \left(e x +d \right)}{e^{3}}-\frac{60 a^{3} b^{3} d^{2}}{\left(e x +d \right) e^{4}}-\frac{60 a^{3} b^{3} d \ln \left(e x +d \right)}{e^{4}}+\frac{20 a^{3} b^{3} x}{e^{3}}+\frac{60 a^{2} b^{4} d^{3}}{\left(e x +d \right) e^{5}}+\frac{90 a^{2} b^{4} d^{2} \ln \left(e x +d \right)}{e^{5}}-\frac{45 a^{2} b^{4} d x}{e^{4}}-\frac{30 a \,b^{5} d^{4}}{\left(e x +d \right) e^{6}}-\frac{60 a \,b^{5} d^{3} \ln \left(e x +d \right)}{e^{6}}+\frac{36 a \,b^{5} d^{2} x}{e^{5}}+\frac{6 b^{6} d^{5}}{\left(e x +d \right) e^{7}}+\frac{15 b^{6} d^{4} \ln \left(e x +d \right)}{e^{7}}-\frac{10 b^{6} d^{3} x}{e^{6}}"," ",0,"-b^6/e^4*x^3*d+15/2*b^4/e^3*x^2*a^2+3*b^6/e^5*x^2*d^2+20*b^3/e^3*a^3*x-10*b^6/e^6*d^3*x+15*b^2/e^3*ln(e*x+d)*a^4+15*b^6/e^7*ln(e*x+d)*d^4-6*b/e^2/(e*x+d)*a^5+6*b^6/e^7/(e*x+d)*d^5-1/2/e^7/(e*x+d)^2*d^6*b^6+2*b^5/e^3*x^3*a-15/2/e^5/(e*x+d)^2*d^4*a^2*b^4+30*b^2/e^3/(e*x+d)*a^4*d-60*b^3/e^4/(e*x+d)*a^3*d^2+60*b^4/e^5/(e*x+d)*a^2*d^3-30*b^5/e^6/(e*x+d)*a*d^4+3/e^2/(e*x+d)^2*d*a^5*b-15/2/e^3/(e*x+d)^2*d^2*a^4*b^2+10/e^4/(e*x+d)^2*d^3*a^3*b^3+36*b^5/e^5*a*d^2*x-60*b^3/e^4*ln(e*x+d)*d*a^3+90*b^4/e^5*ln(e*x+d)*a^2*d^2-60*b^5/e^6*ln(e*x+d)*a*d^3-9*b^5/e^4*x^2*a*d-45*b^4/e^4*a^2*d*x+3/e^6/(e*x+d)^2*d^5*a*b^5+1/4*b^6/e^3*x^4-1/2/e/(e*x+d)^2*a^6","B"
1493,1,483,152,0.053000," ","int((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^4,x)","-\frac{a^{6}}{3 \left(e x +d \right)^{3} e}+\frac{2 a^{5} b d}{\left(e x +d \right)^{3} e^{2}}-\frac{5 a^{4} b^{2} d^{2}}{\left(e x +d \right)^{3} e^{3}}+\frac{20 a^{3} b^{3} d^{3}}{3 \left(e x +d \right)^{3} e^{4}}-\frac{5 a^{2} b^{4} d^{4}}{\left(e x +d \right)^{3} e^{5}}+\frac{2 a \,b^{5} d^{5}}{\left(e x +d \right)^{3} e^{6}}-\frac{b^{6} d^{6}}{3 \left(e x +d \right)^{3} e^{7}}+\frac{b^{6} x^{3}}{3 e^{4}}-\frac{3 a^{5} b}{\left(e x +d \right)^{2} e^{2}}+\frac{15 a^{4} b^{2} d}{\left(e x +d \right)^{2} e^{3}}-\frac{30 a^{3} b^{3} d^{2}}{\left(e x +d \right)^{2} e^{4}}+\frac{30 a^{2} b^{4} d^{3}}{\left(e x +d \right)^{2} e^{5}}-\frac{15 a \,b^{5} d^{4}}{\left(e x +d \right)^{2} e^{6}}+\frac{3 a \,b^{5} x^{2}}{e^{4}}+\frac{3 b^{6} d^{5}}{\left(e x +d \right)^{2} e^{7}}-\frac{2 b^{6} d \,x^{2}}{e^{5}}-\frac{15 a^{4} b^{2}}{\left(e x +d \right) e^{3}}+\frac{60 a^{3} b^{3} d}{\left(e x +d \right) e^{4}}+\frac{20 a^{3} b^{3} \ln \left(e x +d \right)}{e^{4}}-\frac{90 a^{2} b^{4} d^{2}}{\left(e x +d \right) e^{5}}-\frac{60 a^{2} b^{4} d \ln \left(e x +d \right)}{e^{5}}+\frac{15 a^{2} b^{4} x}{e^{4}}+\frac{60 a \,b^{5} d^{3}}{\left(e x +d \right) e^{6}}+\frac{60 a \,b^{5} d^{2} \ln \left(e x +d \right)}{e^{6}}-\frac{24 a \,b^{5} d x}{e^{5}}-\frac{15 b^{6} d^{4}}{\left(e x +d \right) e^{7}}-\frac{20 b^{6} d^{3} \ln \left(e x +d \right)}{e^{7}}+\frac{10 b^{6} d^{2} x}{e^{6}}"," ",0,"20*b^3/e^4*ln(e*x+d)*a^3-20*b^6/e^7*ln(e*x+d)*d^3-15*b^6/e^7/(e*x+d)*d^4-3*b/e^2/(e*x+d)^2*a^5+3*b^6/e^7/(e*x+d)^2*d^5-1/3/e^7/(e*x+d)^3*d^6*b^6+3*b^5/e^4*x^2*a-2*b^6/e^5*x^2*d+15*b^4/e^4*a^2*x+10*b^6/e^6*d^2*x-15*b^2/e^3/(e*x+d)*a^4+15*b^2/e^3/(e*x+d)^2*a^4*d-30*b^3/e^4/(e*x+d)^2*a^3*d^2+30*b^4/e^5/(e*x+d)^2*a^2*d^3-15*b^5/e^6/(e*x+d)^2*a*d^4+2/e^2/(e*x+d)^3*d*a^5*b-5/e^3/(e*x+d)^3*d^2*a^4*b^2+20/3/e^4/(e*x+d)^3*d^3*a^3*b^3-5/e^5/(e*x+d)^3*d^4*a^2*b^4+2/e^6/(e*x+d)^3*d^5*a*b^5+60*b^3/e^4/(e*x+d)*d*a^3-90*b^4/e^5/(e*x+d)*a^2*d^2+60*b^5/e^6/(e*x+d)*a*d^3-24*b^5/e^5*a*d*x-60*b^4/e^5*ln(e*x+d)*a^2*d-1/3/e/(e*x+d)^3*a^6+1/3*b^6/e^4*x^3+60*b^5/e^6*ln(e*x+d)*a*d^2","B"
1494,1,498,149,0.057000," ","int((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^5,x)","-\frac{a^{6}}{4 \left(e x +d \right)^{4} e}+\frac{3 a^{5} b d}{2 \left(e x +d \right)^{4} e^{2}}-\frac{15 a^{4} b^{2} d^{2}}{4 \left(e x +d \right)^{4} e^{3}}+\frac{5 a^{3} b^{3} d^{3}}{\left(e x +d \right)^{4} e^{4}}-\frac{15 a^{2} b^{4} d^{4}}{4 \left(e x +d \right)^{4} e^{5}}+\frac{3 a \,b^{5} d^{5}}{2 \left(e x +d \right)^{4} e^{6}}-\frac{b^{6} d^{6}}{4 \left(e x +d \right)^{4} e^{7}}-\frac{2 a^{5} b}{\left(e x +d \right)^{3} e^{2}}+\frac{10 a^{4} b^{2} d}{\left(e x +d \right)^{3} e^{3}}-\frac{20 a^{3} b^{3} d^{2}}{\left(e x +d \right)^{3} e^{4}}+\frac{20 a^{2} b^{4} d^{3}}{\left(e x +d \right)^{3} e^{5}}-\frac{10 a \,b^{5} d^{4}}{\left(e x +d \right)^{3} e^{6}}+\frac{2 b^{6} d^{5}}{\left(e x +d \right)^{3} e^{7}}-\frac{15 a^{4} b^{2}}{2 \left(e x +d \right)^{2} e^{3}}+\frac{30 a^{3} b^{3} d}{\left(e x +d \right)^{2} e^{4}}-\frac{45 a^{2} b^{4} d^{2}}{\left(e x +d \right)^{2} e^{5}}+\frac{30 a \,b^{5} d^{3}}{\left(e x +d \right)^{2} e^{6}}-\frac{15 b^{6} d^{4}}{2 \left(e x +d \right)^{2} e^{7}}+\frac{b^{6} x^{2}}{2 e^{5}}-\frac{20 a^{3} b^{3}}{\left(e x +d \right) e^{4}}+\frac{60 a^{2} b^{4} d}{\left(e x +d \right) e^{5}}+\frac{15 a^{2} b^{4} \ln \left(e x +d \right)}{e^{5}}-\frac{60 a \,b^{5} d^{2}}{\left(e x +d \right) e^{6}}-\frac{30 a \,b^{5} d \ln \left(e x +d \right)}{e^{6}}+\frac{6 a \,b^{5} x}{e^{5}}+\frac{20 b^{6} d^{3}}{\left(e x +d \right) e^{7}}+\frac{15 b^{6} d^{2} \ln \left(e x +d \right)}{e^{7}}-\frac{5 b^{6} d x}{e^{6}}"," ",0,"-2*b/e^2/(e*x+d)^3*a^5+2*b^6/e^7/(e*x+d)^3*d^5+6*b^5/e^5*a*x-5*b^6/e^6*x*d-20*b^3/e^4/(e*x+d)*a^3+20*b^6/e^7/(e*x+d)*d^3+15*b^4/e^5*ln(e*x+d)*a^2+15*b^6/e^7*ln(e*x+d)*d^2-15/2*b^2/e^3/(e*x+d)^2*a^4-15/2*b^6/e^7/(e*x+d)^2*d^4-1/4/e^7/(e*x+d)^4*d^6*b^6-1/4/e/(e*x+d)^4*a^6+10*b^2/e^3/(e*x+d)^3*a^4*d-20*b^3/e^4/(e*x+d)^3*a^3*d^2+20*b^4/e^5/(e*x+d)^3*a^2*d^3-10*b^5/e^6/(e*x+d)^3*a*d^4+3/2/e^2/(e*x+d)^4*d*a^5*b-15/4/e^3/(e*x+d)^4*d^2*a^4*b^2+5/e^4/(e*x+d)^4*d^3*a^3*b^3-15/4/e^5/(e*x+d)^4*d^4*a^2*b^4+3/2/e^6/(e*x+d)^4*d^5*a*b^5+30*b^3/e^4/(e*x+d)^2*d*a^3-45*b^4/e^5/(e*x+d)^2*a^2*d^2+30*b^5/e^6/(e*x+d)^2*a*d^3+60*b^4/e^5/(e*x+d)*a^2*d-60*b^5/e^6/(e*x+d)*a*d^2-30*b^5/e^6*ln(e*x+d)*a*d+1/2*b^6*x^2/e^5","B"
1495,1,508,151,0.056000," ","int((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^6,x)","-\frac{a^{6}}{5 \left(e x +d \right)^{5} e}+\frac{6 a^{5} b d}{5 \left(e x +d \right)^{5} e^{2}}-\frac{3 a^{4} b^{2} d^{2}}{\left(e x +d \right)^{5} e^{3}}+\frac{4 a^{3} b^{3} d^{3}}{\left(e x +d \right)^{5} e^{4}}-\frac{3 a^{2} b^{4} d^{4}}{\left(e x +d \right)^{5} e^{5}}+\frac{6 a \,b^{5} d^{5}}{5 \left(e x +d \right)^{5} e^{6}}-\frac{b^{6} d^{6}}{5 \left(e x +d \right)^{5} e^{7}}-\frac{3 a^{5} b}{2 \left(e x +d \right)^{4} e^{2}}+\frac{15 a^{4} b^{2} d}{2 \left(e x +d \right)^{4} e^{3}}-\frac{15 a^{3} b^{3} d^{2}}{\left(e x +d \right)^{4} e^{4}}+\frac{15 a^{2} b^{4} d^{3}}{\left(e x +d \right)^{4} e^{5}}-\frac{15 a \,b^{5} d^{4}}{2 \left(e x +d \right)^{4} e^{6}}+\frac{3 b^{6} d^{5}}{2 \left(e x +d \right)^{4} e^{7}}-\frac{5 a^{4} b^{2}}{\left(e x +d \right)^{3} e^{3}}+\frac{20 a^{3} b^{3} d}{\left(e x +d \right)^{3} e^{4}}-\frac{30 a^{2} b^{4} d^{2}}{\left(e x +d \right)^{3} e^{5}}+\frac{20 a \,b^{5} d^{3}}{\left(e x +d \right)^{3} e^{6}}-\frac{5 b^{6} d^{4}}{\left(e x +d \right)^{3} e^{7}}-\frac{10 a^{3} b^{3}}{\left(e x +d \right)^{2} e^{4}}+\frac{30 a^{2} b^{4} d}{\left(e x +d \right)^{2} e^{5}}-\frac{30 a \,b^{5} d^{2}}{\left(e x +d \right)^{2} e^{6}}+\frac{10 b^{6} d^{3}}{\left(e x +d \right)^{2} e^{7}}-\frac{15 a^{2} b^{4}}{\left(e x +d \right) e^{5}}+\frac{30 a \,b^{5} d}{\left(e x +d \right) e^{6}}+\frac{6 a \,b^{5} \ln \left(e x +d \right)}{e^{6}}-\frac{15 b^{6} d^{2}}{\left(e x +d \right) e^{7}}-\frac{6 b^{6} d \ln \left(e x +d \right)}{e^{7}}+\frac{b^{6} x}{e^{6}}"," ",0,"3/2*b^6/e^7/(e*x+d)^4*d^5-10*b^3/e^4/(e*x+d)^2*a^3+10*b^6/e^7/(e*x+d)^2*d^3-15*b^4/e^5/(e*x+d)*a^2-15*b^6/e^7/(e*x+d)*d^2-1/5/e^7/(e*x+d)^5*b^6*d^6-5*b^6/e^7/(e*x+d)^3*d^4+6*b^5/e^6*ln(e*x+d)*a-6*b^6/e^7*ln(e*x+d)*d-5*b^2/e^3/(e*x+d)^3*a^4-3/2*b/e^2/(e*x+d)^4*a^5+b^6*x/e^6+30*b^5/e^6/(e*x+d)*a*d+20*b^3/e^4/(e*x+d)^3*d*a^3-30*b^4/e^5/(e*x+d)^3*a^2*d^2+20*b^5/e^6/(e*x+d)^3*a*d^3+4/e^4/(e*x+d)^5*d^3*a^3*b^3-3/e^5/(e*x+d)^5*d^4*a^2*b^4+6/5/e^6/(e*x+d)^5*d^5*a*b^5-3/e^3/(e*x+d)^5*d^2*a^4*b^2+15/2*b^2/e^3/(e*x+d)^4*a^4*d+6/5/e^2/(e*x+d)^5*d*a^5*b-15/2*b^5/e^6/(e*x+d)^4*a*d^4+30*b^4/e^5/(e*x+d)^2*a^2*d-30*b^5/e^6/(e*x+d)^2*a*d^2+15*b^4/e^5/(e*x+d)^4*a^2*d^3-15*b^3/e^4/(e*x+d)^4*a^3*d^2-1/5/e/(e*x+d)^5*a^6","B"
1496,1,513,157,0.051000," ","int((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^7,x)","-\frac{a^{6}}{6 \left(e x +d \right)^{6} e}+\frac{a^{5} b d}{\left(e x +d \right)^{6} e^{2}}-\frac{5 a^{4} b^{2} d^{2}}{2 \left(e x +d \right)^{6} e^{3}}+\frac{10 a^{3} b^{3} d^{3}}{3 \left(e x +d \right)^{6} e^{4}}-\frac{5 a^{2} b^{4} d^{4}}{2 \left(e x +d \right)^{6} e^{5}}+\frac{a \,b^{5} d^{5}}{\left(e x +d \right)^{6} e^{6}}-\frac{b^{6} d^{6}}{6 \left(e x +d \right)^{6} e^{7}}-\frac{6 a^{5} b}{5 \left(e x +d \right)^{5} e^{2}}+\frac{6 a^{4} b^{2} d}{\left(e x +d \right)^{5} e^{3}}-\frac{12 a^{3} b^{3} d^{2}}{\left(e x +d \right)^{5} e^{4}}+\frac{12 a^{2} b^{4} d^{3}}{\left(e x +d \right)^{5} e^{5}}-\frac{6 a \,b^{5} d^{4}}{\left(e x +d \right)^{5} e^{6}}+\frac{6 b^{6} d^{5}}{5 \left(e x +d \right)^{5} e^{7}}-\frac{15 a^{4} b^{2}}{4 \left(e x +d \right)^{4} e^{3}}+\frac{15 a^{3} b^{3} d}{\left(e x +d \right)^{4} e^{4}}-\frac{45 a^{2} b^{4} d^{2}}{2 \left(e x +d \right)^{4} e^{5}}+\frac{15 a \,b^{5} d^{3}}{\left(e x +d \right)^{4} e^{6}}-\frac{15 b^{6} d^{4}}{4 \left(e x +d \right)^{4} e^{7}}-\frac{20 a^{3} b^{3}}{3 \left(e x +d \right)^{3} e^{4}}+\frac{20 a^{2} b^{4} d}{\left(e x +d \right)^{3} e^{5}}-\frac{20 a \,b^{5} d^{2}}{\left(e x +d \right)^{3} e^{6}}+\frac{20 b^{6} d^{3}}{3 \left(e x +d \right)^{3} e^{7}}-\frac{15 a^{2} b^{4}}{2 \left(e x +d \right)^{2} e^{5}}+\frac{15 a \,b^{5} d}{\left(e x +d \right)^{2} e^{6}}-\frac{15 b^{6} d^{2}}{2 \left(e x +d \right)^{2} e^{7}}-\frac{6 a \,b^{5}}{\left(e x +d \right) e^{6}}+\frac{6 b^{6} d}{\left(e x +d \right) e^{7}}+\frac{b^{6} \ln \left(e x +d \right)}{e^{7}}"," ",0,"-1/6/e^7/(e*x+d)^6*b^6*d^6-20/3*b^3/e^4/(e*x+d)^3*a^3+20/3*b^6/e^7/(e*x+d)^3*d^3-15/4*b^2/e^3/(e*x+d)^4*a^4-15/4*b^6/e^7/(e*x+d)^4*d^4-15/2*b^4/e^5/(e*x+d)^2*a^2-15/2*b^6/e^7/(e*x+d)^2*d^2-6*b^5/e^6/(e*x+d)*a+6*b^6/e^7/(e*x+d)*d+6/5*b^6/e^7/(e*x+d)^5*d^5-6/5*b/e^2/(e*x+d)^5*a^5+12*b^4/e^5/(e*x+d)^5*a^2*d^3-6*b^5/e^6/(e*x+d)^5*a*d^4+15*b^3/e^4/(e*x+d)^4*d*a^3-1/6/e/(e*x+d)^6*a^6-45/2*b^4/e^5/(e*x+d)^4*a^2*d^2+15*b^5/e^6/(e*x+d)^4*a*d^3+15*b^5/e^6/(e*x+d)^2*a*d+1/e^2/(e*x+d)^6*d*a^5*b+20*b^4/e^5/(e*x+d)^3*a^2*d-20*b^5/e^6/(e*x+d)^3*a*d^2+6*b^2/e^3/(e*x+d)^5*a^4*d-12*b^3/e^4/(e*x+d)^5*a^3*d^2-5/2/e^3/(e*x+d)^6*d^2*a^4*b^2+10/3/e^4/(e*x+d)^6*d^3*a^3*b^3-5/2/e^5/(e*x+d)^6*d^4*a^2*b^4+1/e^6/(e*x+d)^6*d^5*a*b^5+b^6*ln(e*x+d)/e^7","B"
1497,1,357,26,0.048000," ","int((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^8,x)","-\frac{b^{6}}{\left(e x +d \right) e^{7}}-\frac{3 \left(a e -b d \right) b^{5}}{\left(e x +d \right)^{2} e^{7}}-\frac{5 \left(a^{2} e^{2}-2 a b d e +b^{2} d^{2}\right) b^{4}}{\left(e x +d \right)^{3} e^{7}}-\frac{5 \left(a^{3} e^{3}-3 a^{2} b d \,e^{2}+3 a \,b^{2} d^{2} e -b^{3} d^{3}\right) b^{3}}{\left(e x +d \right)^{4} e^{7}}-\frac{3 \left(e^{4} a^{4}-4 d \,e^{3} a^{3} b +6 a^{2} b^{2} d^{2} e^{2}-4 a \,b^{3} d^{3} e +b^{4} d^{4}\right) b^{2}}{\left(e x +d \right)^{5} e^{7}}-\frac{\left(a^{5} e^{5}-5 a^{4} b d \,e^{4}+10 a^{3} b^{2} d^{2} e^{3}-10 a^{2} b^{3} d^{3} e^{2}+5 a \,b^{4} d^{4} e -b^{5} d^{5}\right) b}{\left(e x +d \right)^{6} e^{7}}-\frac{a^{6} e^{6}-6 d \,e^{5} a^{5} b +15 d^{2} e^{4} a^{4} b^{2}-20 d^{3} e^{3} a^{3} b^{3}+15 d^{4} a^{2} b^{4} e^{2}-6 d^{5} e a \,b^{5}+b^{6} d^{6}}{7 \left(e x +d \right)^{7} e^{7}}"," ",0,"-b^6/e^7/(e*x+d)-1/7*(a^6*e^6-6*a^5*b*d*e^5+15*a^4*b^2*d^2*e^4-20*a^3*b^3*d^3*e^3+15*a^2*b^4*d^4*e^2-6*a*b^5*d^5*e+b^6*d^6)/e^7/(e*x+d)^7-3*b^5*(a*e-b*d)/e^7/(e*x+d)^2-5*b^3*(a^3*e^3-3*a^2*b*d*e^2+3*a*b^2*d^2*e-b^3*d^3)/e^7/(e*x+d)^4-5*b^4*(a^2*e^2-2*a*b*d*e+b^2*d^2)/e^7/(e*x+d)^3-b*(a^5*e^5-5*a^4*b*d*e^4+10*a^3*b^2*d^2*e^3-10*a^2*b^3*d^3*e^2+5*a*b^4*d^4*e-b^5*d^5)/e^7/(e*x+d)^6-3*b^2*(a^4*e^4-4*a^3*b*d*e^3+6*a^2*b^2*d^2*e^2-4*a*b^3*d^3*e+b^4*d^4)/e^7/(e*x+d)^5","B"
1498,1,357,54,0.050000," ","int((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^9,x)","-\frac{b^{6}}{2 \left(e x +d \right)^{2} e^{7}}-\frac{2 \left(a e -b d \right) b^{5}}{\left(e x +d \right)^{3} e^{7}}-\frac{15 \left(a^{2} e^{2}-2 a b d e +b^{2} d^{2}\right) b^{4}}{4 \left(e x +d \right)^{4} e^{7}}-\frac{4 \left(a^{3} e^{3}-3 a^{2} b d \,e^{2}+3 a \,b^{2} d^{2} e -b^{3} d^{3}\right) b^{3}}{\left(e x +d \right)^{5} e^{7}}-\frac{5 \left(e^{4} a^{4}-4 d \,e^{3} a^{3} b +6 a^{2} b^{2} d^{2} e^{2}-4 a \,b^{3} d^{3} e +b^{4} d^{4}\right) b^{2}}{2 \left(e x +d \right)^{6} e^{7}}-\frac{6 \left(a^{5} e^{5}-5 a^{4} b d \,e^{4}+10 a^{3} b^{2} d^{2} e^{3}-10 a^{2} b^{3} d^{3} e^{2}+5 a \,b^{4} d^{4} e -b^{5} d^{5}\right) b}{7 \left(e x +d \right)^{7} e^{7}}-\frac{a^{6} e^{6}-6 d \,e^{5} a^{5} b +15 d^{2} e^{4} a^{4} b^{2}-20 d^{3} e^{3} a^{3} b^{3}+15 d^{4} a^{2} b^{4} e^{2}-6 d^{5} e a \,b^{5}+b^{6} d^{6}}{8 \left(e x +d \right)^{8} e^{7}}"," ",0,"-6/7*b*(a^5*e^5-5*a^4*b*d*e^4+10*a^3*b^2*d^2*e^3-10*a^2*b^3*d^3*e^2+5*a*b^4*d^4*e-b^5*d^5)/e^7/(e*x+d)^7-1/2*b^6/e^7/(e*x+d)^2-15/4*b^4*(a^2*e^2-2*a*b*d*e+b^2*d^2)/e^7/(e*x+d)^4-2*b^5*(a*e-b*d)/e^7/(e*x+d)^3-5/2*b^2*(a^4*e^4-4*a^3*b*d*e^3+6*a^2*b^2*d^2*e^2-4*a*b^3*d^3*e+b^4*d^4)/e^7/(e*x+d)^6-4*b^3*(a^3*e^3-3*a^2*b*d*e^2+3*a*b^2*d^2*e-b^3*d^3)/e^7/(e*x+d)^5-1/8*(a^6*e^6-6*a^5*b*d*e^5+15*a^4*b^2*d^2*e^4-20*a^3*b^3*d^3*e^3+15*a^2*b^4*d^4*e^2-6*a*b^5*d^5*e+b^6*d^6)/e^7/(e*x+d)^8","B"
1499,1,357,83,0.052000," ","int((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^10,x)","-\frac{b^{6}}{3 \left(e x +d \right)^{3} e^{7}}-\frac{3 \left(a e -b d \right) b^{5}}{2 \left(e x +d \right)^{4} e^{7}}-\frac{3 \left(a^{2} e^{2}-2 a b d e +b^{2} d^{2}\right) b^{4}}{\left(e x +d \right)^{5} e^{7}}-\frac{10 \left(a^{3} e^{3}-3 a^{2} b d \,e^{2}+3 a \,b^{2} d^{2} e -b^{3} d^{3}\right) b^{3}}{3 \left(e x +d \right)^{6} e^{7}}-\frac{15 \left(e^{4} a^{4}-4 d \,e^{3} a^{3} b +6 a^{2} b^{2} d^{2} e^{2}-4 a \,b^{3} d^{3} e +b^{4} d^{4}\right) b^{2}}{7 \left(e x +d \right)^{7} e^{7}}-\frac{3 \left(a^{5} e^{5}-5 a^{4} b d \,e^{4}+10 a^{3} b^{2} d^{2} e^{3}-10 a^{2} b^{3} d^{3} e^{2}+5 a \,b^{4} d^{4} e -b^{5} d^{5}\right) b}{4 \left(e x +d \right)^{8} e^{7}}-\frac{a^{6} e^{6}-6 d \,e^{5} a^{5} b +15 d^{2} e^{4} a^{4} b^{2}-20 d^{3} e^{3} a^{3} b^{3}+15 d^{4} a^{2} b^{4} e^{2}-6 d^{5} e a \,b^{5}+b^{6} d^{6}}{9 \left(e x +d \right)^{9} e^{7}}"," ",0,"-15/7*b^2*(a^4*e^4-4*a^3*b*d*e^3+6*a^2*b^2*d^2*e^2-4*a*b^3*d^3*e+b^4*d^4)/e^7/(e*x+d)^7-3/2*b^5*(a*e-b*d)/e^7/(e*x+d)^4-1/3*b^6/e^7/(e*x+d)^3-1/9*(a^6*e^6-6*a^5*b*d*e^5+15*a^4*b^2*d^2*e^4-20*a^3*b^3*d^3*e^3+15*a^2*b^4*d^4*e^2-6*a*b^5*d^5*e+b^6*d^6)/e^7/(e*x+d)^9-10/3*b^3*(a^3*e^3-3*a^2*b*d*e^2+3*a*b^2*d^2*e-b^3*d^3)/e^7/(e*x+d)^6-3*b^4*(a^2*e^2-2*a*b*d*e+b^2*d^2)/e^7/(e*x+d)^5-3/4*b*(a^5*e^5-5*a^4*b*d*e^4+10*a^3*b^2*d^2*e^3-10*a^2*b^3*d^3*e^2+5*a*b^4*d^4*e-b^5*d^5)/e^7/(e*x+d)^8","B"
1500,1,357,112,0.049000," ","int((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^11,x)","-\frac{b^{6}}{4 \left(e x +d \right)^{4} e^{7}}-\frac{6 \left(a e -b d \right) b^{5}}{5 \left(e x +d \right)^{5} e^{7}}-\frac{5 \left(a^{2} e^{2}-2 a b d e +b^{2} d^{2}\right) b^{4}}{2 \left(e x +d \right)^{6} e^{7}}-\frac{20 \left(a^{3} e^{3}-3 a^{2} b d \,e^{2}+3 a \,b^{2} d^{2} e -b^{3} d^{3}\right) b^{3}}{7 \left(e x +d \right)^{7} e^{7}}-\frac{15 \left(e^{4} a^{4}-4 d \,e^{3} a^{3} b +6 a^{2} b^{2} d^{2} e^{2}-4 a \,b^{3} d^{3} e +b^{4} d^{4}\right) b^{2}}{8 \left(e x +d \right)^{8} e^{7}}-\frac{2 \left(a^{5} e^{5}-5 a^{4} b d \,e^{4}+10 a^{3} b^{2} d^{2} e^{3}-10 a^{2} b^{3} d^{3} e^{2}+5 a \,b^{4} d^{4} e -b^{5} d^{5}\right) b}{3 \left(e x +d \right)^{9} e^{7}}-\frac{a^{6} e^{6}-6 d \,e^{5} a^{5} b +15 d^{2} e^{4} a^{4} b^{2}-20 d^{3} e^{3} a^{3} b^{3}+15 d^{4} a^{2} b^{4} e^{2}-6 d^{5} e a \,b^{5}+b^{6} d^{6}}{10 \left(e x +d \right)^{10} e^{7}}"," ",0,"-1/10*(a^6*e^6-6*a^5*b*d*e^5+15*a^4*b^2*d^2*e^4-20*a^3*b^3*d^3*e^3+15*a^2*b^4*d^4*e^2-6*a*b^5*d^5*e+b^6*d^6)/e^7/(e*x+d)^10-20/7*b^3*(a^3*e^3-3*a^2*b*d*e^2+3*a*b^2*d^2*e-b^3*d^3)/e^7/(e*x+d)^7-1/4*b^6/e^7/(e*x+d)^4-2/3*b*(a^5*e^5-5*a^4*b*d*e^4+10*a^3*b^2*d^2*e^3-10*a^2*b^3*d^3*e^2+5*a*b^4*d^4*e-b^5*d^5)/e^7/(e*x+d)^9-5/2*b^4*(a^2*e^2-2*a*b*d*e+b^2*d^2)/e^7/(e*x+d)^6-6/5*b^5*(a*e-b*d)/e^7/(e*x+d)^5-15/8*b^2*(a^4*e^4-4*a^3*b*d*e^3+6*a^2*b^2*d^2*e^2-4*a*b^3*d^3*e+b^4*d^4)/e^7/(e*x+d)^8","B"
1501,1,357,158,0.046000," ","int((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^12,x)","-\frac{b^{6}}{5 \left(e x +d \right)^{5} e^{7}}-\frac{\left(a e -b d \right) b^{5}}{\left(e x +d \right)^{6} e^{7}}-\frac{15 \left(a^{2} e^{2}-2 a b d e +b^{2} d^{2}\right) b^{4}}{7 \left(e x +d \right)^{7} e^{7}}-\frac{5 \left(a^{3} e^{3}-3 a^{2} b d \,e^{2}+3 a \,b^{2} d^{2} e -b^{3} d^{3}\right) b^{3}}{2 \left(e x +d \right)^{8} e^{7}}-\frac{5 \left(e^{4} a^{4}-4 d \,e^{3} a^{3} b +6 a^{2} b^{2} d^{2} e^{2}-4 a \,b^{3} d^{3} e +b^{4} d^{4}\right) b^{2}}{3 \left(e x +d \right)^{9} e^{7}}-\frac{3 \left(a^{5} e^{5}-5 a^{4} b d \,e^{4}+10 a^{3} b^{2} d^{2} e^{3}-10 a^{2} b^{3} d^{3} e^{2}+5 a \,b^{4} d^{4} e -b^{5} d^{5}\right) b}{5 \left(e x +d \right)^{10} e^{7}}-\frac{a^{6} e^{6}-6 d \,e^{5} a^{5} b +15 d^{2} e^{4} a^{4} b^{2}-20 d^{3} e^{3} a^{3} b^{3}+15 d^{4} a^{2} b^{4} e^{2}-6 d^{5} e a \,b^{5}+b^{6} d^{6}}{11 \left(e x +d \right)^{11} e^{7}}"," ",0,"-1/11*(a^6*e^6-6*a^5*b*d*e^5+15*a^4*b^2*d^2*e^4-20*a^3*b^3*d^3*e^3+15*a^2*b^4*d^4*e^2-6*a*b^5*d^5*e+b^6*d^6)/e^7/(e*x+d)^11-3/5*b*(a^5*e^5-5*a^4*b*d*e^4+10*a^3*b^2*d^2*e^3-10*a^2*b^3*d^3*e^2+5*a*b^4*d^4*e-b^5*d^5)/e^7/(e*x+d)^10-15/7*b^4*(a^2*e^2-2*a*b*d*e+b^2*d^2)/e^7/(e*x+d)^7-5/3*b^2*(a^4*e^4-4*a^3*b*d*e^3+6*a^2*b^2*d^2*e^2-4*a*b^3*d^3*e+b^4*d^4)/e^7/(e*x+d)^9-b^5*(a*e-b*d)/e^7/(e*x+d)^6-1/5*b^6/e^7/(e*x+d)^5-5/2*b^3*(a^3*e^3-3*a^2*b*d*e^2+3*a*b^2*d^2*e-b^3*d^3)/e^7/(e*x+d)^8","B"
1502,1,357,159,0.050000," ","int((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^13,x)","-\frac{b^{6}}{6 \left(e x +d \right)^{6} e^{7}}-\frac{6 \left(a e -b d \right) b^{5}}{7 \left(e x +d \right)^{7} e^{7}}-\frac{15 \left(a^{2} e^{2}-2 a b d e +b^{2} d^{2}\right) b^{4}}{8 \left(e x +d \right)^{8} e^{7}}-\frac{20 \left(a^{3} e^{3}-3 a^{2} b d \,e^{2}+3 a \,b^{2} d^{2} e -b^{3} d^{3}\right) b^{3}}{9 \left(e x +d \right)^{9} e^{7}}-\frac{3 \left(e^{4} a^{4}-4 d \,e^{3} a^{3} b +6 a^{2} b^{2} d^{2} e^{2}-4 a \,b^{3} d^{3} e +b^{4} d^{4}\right) b^{2}}{2 \left(e x +d \right)^{10} e^{7}}-\frac{6 \left(a^{5} e^{5}-5 a^{4} b d \,e^{4}+10 a^{3} b^{2} d^{2} e^{3}-10 a^{2} b^{3} d^{3} e^{2}+5 a \,b^{4} d^{4} e -b^{5} d^{5}\right) b}{11 \left(e x +d \right)^{11} e^{7}}-\frac{a^{6} e^{6}-6 d \,e^{5} a^{5} b +15 d^{2} e^{4} a^{4} b^{2}-20 d^{3} e^{3} a^{3} b^{3}+15 d^{4} a^{2} b^{4} e^{2}-6 d^{5} e a \,b^{5}+b^{6} d^{6}}{12 \left(e x +d \right)^{12} e^{7}}"," ",0,"-6/11*b*(a^5*e^5-5*a^4*b*d*e^4+10*a^3*b^2*d^2*e^3-10*a^2*b^3*d^3*e^2+5*a*b^4*d^4*e-b^5*d^5)/e^7/(e*x+d)^11-3/2*b^2*(a^4*e^4-4*a^3*b*d*e^3+6*a^2*b^2*d^2*e^2-4*a*b^3*d^3*e+b^4*d^4)/e^7/(e*x+d)^10-6/7*b^5*(a*e-b*d)/e^7/(e*x+d)^7-1/12*(a^6*e^6-6*a^5*b*d*e^5+15*a^4*b^2*d^2*e^4-20*a^3*b^3*d^3*e^3+15*a^2*b^4*d^4*e^2-6*a*b^5*d^5*e+b^6*d^6)/e^7/(e*x+d)^12-20/9*b^3*(a^3*e^3-3*a^2*b*d*e^2+3*a*b^2*d^2*e-b^3*d^3)/e^7/(e*x+d)^9-1/6*b^6/e^7/(e*x+d)^6-15/8*b^4*(a^2*e^2-2*a*b*d*e+b^2*d^2)/e^7/(e*x+d)^8","B"
1503,1,357,159,0.053000," ","int((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^14,x)","-\frac{b^{6}}{7 \left(e x +d \right)^{7} e^{7}}-\frac{3 \left(a e -b d \right) b^{5}}{4 \left(e x +d \right)^{8} e^{7}}-\frac{5 \left(a^{2} e^{2}-2 a b d e +b^{2} d^{2}\right) b^{4}}{3 \left(e x +d \right)^{9} e^{7}}-\frac{2 \left(a^{3} e^{3}-3 a^{2} b d \,e^{2}+3 a \,b^{2} d^{2} e -b^{3} d^{3}\right) b^{3}}{\left(e x +d \right)^{10} e^{7}}-\frac{15 \left(e^{4} a^{4}-4 d \,e^{3} a^{3} b +6 a^{2} b^{2} d^{2} e^{2}-4 a \,b^{3} d^{3} e +b^{4} d^{4}\right) b^{2}}{11 \left(e x +d \right)^{11} e^{7}}-\frac{\left(a^{5} e^{5}-5 a^{4} b d \,e^{4}+10 a^{3} b^{2} d^{2} e^{3}-10 a^{2} b^{3} d^{3} e^{2}+5 a \,b^{4} d^{4} e -b^{5} d^{5}\right) b}{2 \left(e x +d \right)^{12} e^{7}}-\frac{a^{6} e^{6}-6 d \,e^{5} a^{5} b +15 d^{2} e^{4} a^{4} b^{2}-20 d^{3} e^{3} a^{3} b^{3}+15 d^{4} a^{2} b^{4} e^{2}-6 d^{5} e a \,b^{5}+b^{6} d^{6}}{13 \left(e x +d \right)^{13} e^{7}}"," ",0,"-15/11*b^2*(a^4*e^4-4*a^3*b*d*e^3+6*a^2*b^2*d^2*e^2-4*a*b^3*d^3*e+b^4*d^4)/e^7/(e*x+d)^11-2*b^3*(a^3*e^3-3*a^2*b*d*e^2+3*a*b^2*d^2*e-b^3*d^3)/e^7/(e*x+d)^10-1/7*b^6/e^7/(e*x+d)^7-1/2*b*(a^5*e^5-5*a^4*b*d*e^4+10*a^3*b^2*d^2*e^3-10*a^2*b^3*d^3*e^2+5*a*b^4*d^4*e-b^5*d^5)/e^7/(e*x+d)^12-5/3*b^4*(a^2*e^2-2*a*b*d*e+b^2*d^2)/e^7/(e*x+d)^9-1/13*(a^6*e^6-6*a^5*b*d*e^5+15*a^4*b^2*d^2*e^4-20*a^3*b^3*d^3*e^3+15*a^2*b^4*d^4*e^2-6*a*b^5*d^5*e+b^6*d^6)/e^7/(e*x+d)^13-3/4*b^5*(a*e-b*d)/e^7/(e*x+d)^8","B"
1504,1,357,159,0.050000," ","int((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^15,x)","-\frac{b^{6}}{8 \left(e x +d \right)^{8} e^{7}}-\frac{2 \left(a e -b d \right) b^{5}}{3 \left(e x +d \right)^{9} e^{7}}-\frac{3 \left(a^{2} e^{2}-2 a b d e +b^{2} d^{2}\right) b^{4}}{2 \left(e x +d \right)^{10} e^{7}}-\frac{20 \left(a^{3} e^{3}-3 a^{2} b d \,e^{2}+3 a \,b^{2} d^{2} e -b^{3} d^{3}\right) b^{3}}{11 \left(e x +d \right)^{11} e^{7}}-\frac{5 \left(e^{4} a^{4}-4 d \,e^{3} a^{3} b +6 a^{2} b^{2} d^{2} e^{2}-4 a \,b^{3} d^{3} e +b^{4} d^{4}\right) b^{2}}{4 \left(e x +d \right)^{12} e^{7}}-\frac{6 \left(a^{5} e^{5}-5 a^{4} b d \,e^{4}+10 a^{3} b^{2} d^{2} e^{3}-10 a^{2} b^{3} d^{3} e^{2}+5 a \,b^{4} d^{4} e -b^{5} d^{5}\right) b}{13 \left(e x +d \right)^{13} e^{7}}-\frac{a^{6} e^{6}-6 d \,e^{5} a^{5} b +15 d^{2} e^{4} a^{4} b^{2}-20 d^{3} e^{3} a^{3} b^{3}+15 d^{4} a^{2} b^{4} e^{2}-6 d^{5} e a \,b^{5}+b^{6} d^{6}}{14 \left(e x +d \right)^{14} e^{7}}"," ",0,"-20/11*b^3*(a^3*e^3-3*a^2*b*d*e^2+3*a*b^2*d^2*e-b^3*d^3)/e^7/(e*x+d)^11-3/2*b^4*(a^2*e^2-2*a*b*d*e+b^2*d^2)/e^7/(e*x+d)^10-1/14*(a^6*e^6-6*a^5*b*d*e^5+15*a^4*b^2*d^2*e^4-20*a^3*b^3*d^3*e^3+15*a^2*b^4*d^4*e^2-6*a*b^5*d^5*e+b^6*d^6)/e^7/(e*x+d)^14-5/4*b^2*(a^4*e^4-4*a^3*b*d*e^3+6*a^2*b^2*d^2*e^2-4*a*b^3*d^3*e+b^4*d^4)/e^7/(e*x+d)^12-2/3*b^5*(a*e-b*d)/e^7/(e*x+d)^9-6/13*b*(a^5*e^5-5*a^4*b*d*e^4+10*a^3*b^2*d^2*e^3-10*a^2*b^3*d^3*e^2+5*a*b^4*d^4*e-b^5*d^5)/e^7/(e*x+d)^13-1/8*b^6/e^7/(e*x+d)^8","B"
1505,1,326,127,0.052000," ","int((e*x+d)^5/(b^2*x^2+2*a*b*x+a^2),x)","\frac{e^{5} x^{4}}{4 b^{2}}-\frac{2 a \,e^{5} x^{3}}{3 b^{3}}+\frac{5 d \,e^{4} x^{3}}{3 b^{2}}+\frac{3 a^{2} e^{5} x^{2}}{2 b^{4}}-\frac{5 a d \,e^{4} x^{2}}{b^{3}}+\frac{5 d^{2} e^{3} x^{2}}{b^{2}}+\frac{a^{5} e^{5}}{\left(b x +a \right) b^{6}}-\frac{5 a^{4} d \,e^{4}}{\left(b x +a \right) b^{5}}+\frac{5 a^{4} e^{5} \ln \left(b x +a \right)}{b^{6}}+\frac{10 a^{3} d^{2} e^{3}}{\left(b x +a \right) b^{4}}-\frac{20 a^{3} d \,e^{4} \ln \left(b x +a \right)}{b^{5}}-\frac{4 a^{3} e^{5} x}{b^{5}}-\frac{10 a^{2} d^{3} e^{2}}{\left(b x +a \right) b^{3}}+\frac{30 a^{2} d^{2} e^{3} \ln \left(b x +a \right)}{b^{4}}+\frac{15 a^{2} d \,e^{4} x}{b^{4}}+\frac{5 a \,d^{4} e}{\left(b x +a \right) b^{2}}-\frac{20 a \,d^{3} e^{2} \ln \left(b x +a \right)}{b^{3}}-\frac{20 a \,d^{2} e^{3} x}{b^{3}}-\frac{d^{5}}{\left(b x +a \right) b}+\frac{5 d^{4} e \ln \left(b x +a \right)}{b^{2}}+\frac{10 d^{3} e^{2} x}{b^{2}}"," ",0,"1/4*e^5/b^2*x^4-2/3*e^5/b^3*x^3*a+5/3*e^4/b^2*x^3*d+3/2*e^5/b^4*x^2*a^2-5*e^4/b^3*x^2*a*d+5*e^3/b^2*x^2*d^2-4*e^5/b^5*a^3*x+15*e^4/b^4*a^2*d*x-20*e^3/b^3*a*d^2*x+10*e^2/b^2*d^3*x+5/b^6*e^5*ln(b*x+a)*a^4-20/b^5*e^4*ln(b*x+a)*d*a^3+30/b^4*e^3*ln(b*x+a)*a^2*d^2-20/b^3*e^2*ln(b*x+a)*a*d^3+5/b^2*e*ln(b*x+a)*d^4+1/b^6/(b*x+a)*a^5*e^5-5/b^5/(b*x+a)*a^4*d*e^4+10/b^4/(b*x+a)*a^3*d^2*e^3-10/b^3/(b*x+a)*a^2*d^3*e^2+5/b^2/(b*x+a)*a*d^4*e-1/b/(b*x+a)*d^5","B"
1506,1,230,102,0.051000," ","int((e*x+d)^4/(b^2*x^2+2*a*b*x+a^2),x)","\frac{e^{4} x^{3}}{3 b^{2}}-\frac{a \,e^{4} x^{2}}{b^{3}}+\frac{2 d \,e^{3} x^{2}}{b^{2}}-\frac{a^{4} e^{4}}{\left(b x +a \right) b^{5}}+\frac{4 a^{3} d \,e^{3}}{\left(b x +a \right) b^{4}}-\frac{4 a^{3} e^{4} \ln \left(b x +a \right)}{b^{5}}-\frac{6 a^{2} d^{2} e^{2}}{\left(b x +a \right) b^{3}}+\frac{12 a^{2} d \,e^{3} \ln \left(b x +a \right)}{b^{4}}+\frac{3 a^{2} e^{4} x}{b^{4}}+\frac{4 a \,d^{3} e}{\left(b x +a \right) b^{2}}-\frac{12 a \,d^{2} e^{2} \ln \left(b x +a \right)}{b^{3}}-\frac{8 a d \,e^{3} x}{b^{3}}-\frac{d^{4}}{\left(b x +a \right) b}+\frac{4 d^{3} e \ln \left(b x +a \right)}{b^{2}}+\frac{6 d^{2} e^{2} x}{b^{2}}"," ",0,"1/3*e^4/b^2*x^3-e^4/b^3*x^2*a+2*e^3/b^2*x^2*d+3*e^4/b^4*a^2*x-8*e^3/b^3*a*d*x+6*e^2/b^2*d^2*x-4/b^5*e^4*ln(b*x+a)*a^3+12/b^4*e^3*ln(b*x+a)*a^2*d-12/b^3*e^2*ln(b*x+a)*a*d^2+4/b^2*e*ln(b*x+a)*d^3-1/b^5/(b*x+a)*e^4*a^4+4/b^4/(b*x+a)*d*e^3*a^3-6/b^3/(b*x+a)*a^2*d^2*e^2+4/b^2/(b*x+a)*a*d^3*e-1/b/(b*x+a)*d^4","B"
1507,1,149,73,0.049000," ","int((e*x+d)^3/(b^2*x^2+2*a*b*x+a^2),x)","\frac{e^{3} x^{2}}{2 b^{2}}+\frac{a^{3} e^{3}}{\left(b x +a \right) b^{4}}-\frac{3 a^{2} d \,e^{2}}{\left(b x +a \right) b^{3}}+\frac{3 a^{2} e^{3} \ln \left(b x +a \right)}{b^{4}}+\frac{3 a \,d^{2} e}{\left(b x +a \right) b^{2}}-\frac{6 a d \,e^{2} \ln \left(b x +a \right)}{b^{3}}-\frac{2 a \,e^{3} x}{b^{3}}-\frac{d^{3}}{\left(b x +a \right) b}+\frac{3 d^{2} e \ln \left(b x +a \right)}{b^{2}}+\frac{3 d \,e^{2} x}{b^{2}}"," ",0,"1/2*e^3*x^2/b^2-2*e^3/b^3*a*x+3*e^2/b^2*x*d+3/b^4*e^3*ln(b*x+a)*a^2-6/b^3*e^2*ln(b*x+a)*a*d+3/b^2*e*ln(b*x+a)*d^2+1/b^4/(b*x+a)*a^3*e^3-3/b^3/(b*x+a)*a^2*d*e^2+3/b^2/(b*x+a)*a*d^2*e-1/b/(b*x+a)*d^3","B"
1508,1,86,51,0.062000," ","int((e*x+d)^2/(b^2*x^2+2*a*b*x+a^2),x)","-\frac{a^{2} e^{2}}{\left(b x +a \right) b^{3}}+\frac{2 a d e}{\left(b x +a \right) b^{2}}-\frac{2 a \,e^{2} \ln \left(b x +a \right)}{b^{3}}-\frac{d^{2}}{\left(b x +a \right) b}+\frac{2 d e \ln \left(b x +a \right)}{b^{2}}+\frac{e^{2} x}{b^{2}}"," ",0,"e^2*x/b^2-2/b^3*e^2*ln(b*x+a)*a+2/b^2*e*ln(b*x+a)*d-1/b^3/(b*x+a)*a^2*e^2+2/b^2/(b*x+a)*a*d*e-1/b/(b*x+a)*d^2","A"
1509,1,39,31,0.044000," ","int((e*x+d)/(b^2*x^2+2*a*b*x+a^2),x)","\frac{a e}{\left(b x +a \right) b^{2}}-\frac{d}{\left(b x +a \right) b}+\frac{e \ln \left(b x +a \right)}{b^{2}}"," ",0,"e*ln(b*x+a)/b^2+1/b^2/(b*x+a)*a*e-1/b/(b*x+a)*d","A"
1510,1,13,12,0.046000," ","int(1/(b^2*x^2+2*a*b*x+a^2),x)","-\frac{1}{\left(b x +a \right) b}"," ",0,"-1/(b*x+a)/b","A"
1511,1,57,57,0.055000," ","int(1/(e*x+d)/(b^2*x^2+2*a*b*x+a^2),x)","-\frac{e \ln \left(b x +a \right)}{\left(a e -b d \right)^{2}}+\frac{e \ln \left(e x +d \right)}{\left(a e -b d \right)^{2}}+\frac{1}{\left(a e -b d \right) \left(b x +a \right)}"," ",0,"1/(a*e-b*d)/(b*x+a)-e/(a*e-b*d)^2*ln(b*x+a)+e/(a*e-b*d)^2*ln(e*x+d)","A"
1512,1,82,81,0.061000," ","int(1/(e*x+d)^2/(b^2*x^2+2*a*b*x+a^2),x)","\frac{2 b e \ln \left(b x +a \right)}{\left(a e -b d \right)^{3}}-\frac{2 b e \ln \left(e x +d \right)}{\left(a e -b d \right)^{3}}-\frac{b}{\left(a e -b d \right)^{2} \left(b x +a \right)}-\frac{e}{\left(a e -b d \right)^{2} \left(e x +d \right)}"," ",0,"-b/(a*e-b*d)^2/(b*x+a)+2*b/(a*e-b*d)^3*e*ln(b*x+a)-e/(a*e-b*d)^2/(e*x+d)-2*b/(a*e-b*d)^3*e*ln(e*x+d)","A"
1513,1,108,108,0.057000," ","int(1/(e*x+d)^3/(b^2*x^2+2*a*b*x+a^2),x)","-\frac{3 b^{2} e \ln \left(b x +a \right)}{\left(a e -b d \right)^{4}}+\frac{3 b^{2} e \ln \left(e x +d \right)}{\left(a e -b d \right)^{4}}+\frac{b^{2}}{\left(a e -b d \right)^{3} \left(b x +a \right)}+\frac{2 b e}{\left(a e -b d \right)^{3} \left(e x +d \right)}-\frac{e}{2 \left(a e -b d \right)^{2} \left(e x +d \right)^{2}}"," ",0,"b^2/(a*e-b*d)^3/(b*x+a)-3*b^2/(a*e-b*d)^4*e*ln(b*x+a)-1/2*e/(a*e-b*d)^2/(e*x+d)^2+3*b^2/(a*e-b*d)^4*e*ln(e*x+d)+2*e/(a*e-b*d)^3*b/(e*x+d)","A"
1514,1,131,131,0.058000," ","int(1/(e*x+d)^4/(b^2*x^2+2*a*b*x+a^2),x)","\frac{4 b^{3} e \ln \left(b x +a \right)}{\left(a e -b d \right)^{5}}-\frac{4 b^{3} e \ln \left(e x +d \right)}{\left(a e -b d \right)^{5}}-\frac{b^{3}}{\left(a e -b d \right)^{4} \left(b x +a \right)}-\frac{3 b^{2} e}{\left(a e -b d \right)^{4} \left(e x +d \right)}+\frac{b e}{\left(a e -b d \right)^{3} \left(e x +d \right)^{2}}-\frac{e}{3 \left(a e -b d \right)^{2} \left(e x +d \right)^{3}}"," ",0,"-b^3/(a*e-b*d)^4/(b*x+a)+4*b^3/(a*e-b*d)^5*e*ln(b*x+a)-1/3*e/(a*e-b*d)^2/(e*x+d)^3-4*b^3/(a*e-b*d)^5*e*ln(e*x+d)-3*e/(a*e-b*d)^4*b^2/(e*x+d)+e/(a*e-b*d)^3*b/(e*x+d)^2","A"
1515,1,483,152,0.054000," ","int((e*x+d)^6/(b^2*x^2+2*a*b*x+a^2)^2,x)","-\frac{a^{6} e^{6}}{3 \left(b x +a \right)^{3} b^{7}}+\frac{2 a^{5} d \,e^{5}}{\left(b x +a \right)^{3} b^{6}}-\frac{5 a^{4} d^{2} e^{4}}{\left(b x +a \right)^{3} b^{5}}+\frac{20 a^{3} d^{3} e^{3}}{3 \left(b x +a \right)^{3} b^{4}}-\frac{5 a^{2} d^{4} e^{2}}{\left(b x +a \right)^{3} b^{3}}+\frac{2 a \,d^{5} e}{\left(b x +a \right)^{3} b^{2}}-\frac{d^{6}}{3 \left(b x +a \right)^{3} b}+\frac{e^{6} x^{3}}{3 b^{4}}+\frac{3 a^{5} e^{6}}{\left(b x +a \right)^{2} b^{7}}-\frac{15 a^{4} d \,e^{5}}{\left(b x +a \right)^{2} b^{6}}+\frac{30 a^{3} d^{2} e^{4}}{\left(b x +a \right)^{2} b^{5}}-\frac{30 a^{2} d^{3} e^{3}}{\left(b x +a \right)^{2} b^{4}}+\frac{15 a \,d^{4} e^{2}}{\left(b x +a \right)^{2} b^{3}}-\frac{2 a \,e^{6} x^{2}}{b^{5}}-\frac{3 d^{5} e}{\left(b x +a \right)^{2} b^{2}}+\frac{3 d \,e^{5} x^{2}}{b^{4}}-\frac{15 a^{4} e^{6}}{\left(b x +a \right) b^{7}}+\frac{60 a^{3} d \,e^{5}}{\left(b x +a \right) b^{6}}-\frac{20 a^{3} e^{6} \ln \left(b x +a \right)}{b^{7}}-\frac{90 a^{2} d^{2} e^{4}}{\left(b x +a \right) b^{5}}+\frac{60 a^{2} d \,e^{5} \ln \left(b x +a \right)}{b^{6}}+\frac{10 a^{2} e^{6} x}{b^{6}}+\frac{60 a \,d^{3} e^{3}}{\left(b x +a \right) b^{4}}-\frac{60 a \,d^{2} e^{4} \ln \left(b x +a \right)}{b^{5}}-\frac{24 a d \,e^{5} x}{b^{5}}-\frac{15 d^{4} e^{2}}{\left(b x +a \right) b^{3}}+\frac{20 d^{3} e^{3} \ln \left(b x +a \right)}{b^{4}}+\frac{15 d^{2} e^{4} x}{b^{4}}"," ",0,"-15/b^7*e^6/(b*x+a)*a^4-15/b^3*e^2/(b*x+a)*d^4+3/b^7*e^6/(b*x+a)^2*a^5-3/b^2*e/(b*x+a)^2*d^5-1/3/b^7/(b*x+a)^3*a^6*e^6-20/b^7*e^6*ln(b*x+a)*a^3+20/b^4*e^3*ln(b*x+a)*d^3-2*e^6/b^5*x^2*a+3*e^5/b^4*x^2*d+10*e^6/b^6*a^2*x+15*e^4/b^4*d^2*x-30/b^4*e^3/(b*x+a)^2*a^2*d^3+15/b^3*e^2/(b*x+a)^2*a*d^4+60/b^6*e^5/(b*x+a)*d*a^3-90/b^5*e^4/(b*x+a)*a^2*d^2+60/b^4*e^3/(b*x+a)*a*d^3-24*e^5/b^5*a*d*x+2/b^6/(b*x+a)^3*d*e^5*a^5+2/b^2/(b*x+a)^3*d^5*e*a+60/b^6*e^5*ln(b*x+a)*a^2*d+1/3*e^6/b^4*x^3-1/3/b/(b*x+a)^3*d^6-60/b^5*e^4*ln(b*x+a)*a*d^2-5/b^5/(b*x+a)^3*d^2*e^4*a^4+20/3/b^4/(b*x+a)^3*d^3*e^3*a^3-5/b^3/(b*x+a)^3*d^4*a^2*e^2-15/b^6*e^5/(b*x+a)^2*a^4*d+30/b^5*e^4/(b*x+a)^2*a^3*d^2","B"
1516,1,361,123,0.055000," ","int((e*x+d)^5/(b^2*x^2+2*a*b*x+a^2)^2,x)","\frac{a^{5} e^{5}}{3 \left(b x +a \right)^{3} b^{6}}-\frac{5 a^{4} d \,e^{4}}{3 \left(b x +a \right)^{3} b^{5}}+\frac{10 a^{3} d^{2} e^{3}}{3 \left(b x +a \right)^{3} b^{4}}-\frac{10 a^{2} d^{3} e^{2}}{3 \left(b x +a \right)^{3} b^{3}}+\frac{5 a \,d^{4} e}{3 \left(b x +a \right)^{3} b^{2}}-\frac{d^{5}}{3 \left(b x +a \right)^{3} b}-\frac{5 a^{4} e^{5}}{2 \left(b x +a \right)^{2} b^{6}}+\frac{10 a^{3} d \,e^{4}}{\left(b x +a \right)^{2} b^{5}}-\frac{15 a^{2} d^{2} e^{3}}{\left(b x +a \right)^{2} b^{4}}+\frac{10 a \,d^{3} e^{2}}{\left(b x +a \right)^{2} b^{3}}-\frac{5 d^{4} e}{2 \left(b x +a \right)^{2} b^{2}}+\frac{e^{5} x^{2}}{2 b^{4}}+\frac{10 a^{3} e^{5}}{\left(b x +a \right) b^{6}}-\frac{30 a^{2} d \,e^{4}}{\left(b x +a \right) b^{5}}+\frac{10 a^{2} e^{5} \ln \left(b x +a \right)}{b^{6}}+\frac{30 a \,d^{2} e^{3}}{\left(b x +a \right) b^{4}}-\frac{20 a d \,e^{4} \ln \left(b x +a \right)}{b^{5}}-\frac{4 a \,e^{5} x}{b^{5}}-\frac{10 d^{3} e^{2}}{\left(b x +a \right) b^{3}}+\frac{10 d^{2} e^{3} \ln \left(b x +a \right)}{b^{4}}+\frac{5 d \,e^{4} x}{b^{4}}"," ",0,"1/2*e^5*x^2/b^4-4*e^5/b^5*a*x+5*e^4/b^4*x*d+1/3/b^6/(b*x+a)^3*a^5*e^5-5/3/b^5/(b*x+a)^3*a^4*d*e^4+10/3/b^4/(b*x+a)^3*a^3*d^2*e^3-10/3/b^3/(b*x+a)^3*a^2*d^3*e^2+5/3/b^2/(b*x+a)^3*a*d^4*e-1/3/b/(b*x+a)^3*d^5+10/b^6*e^5*ln(b*x+a)*a^2-20/b^5*e^4*ln(b*x+a)*a*d+10/b^4*e^3*ln(b*x+a)*d^2+10/b^6*e^5/(b*x+a)*a^3-30/b^5*e^4/(b*x+a)*a^2*d+30/b^4*e^3/(b*x+a)*a*d^2-10/b^3*e^2/(b*x+a)*d^3-5/2/b^6*e^5/(b*x+a)^2*a^4+10/b^5*e^4/(b*x+a)^2*d*a^3-15/b^4*e^3/(b*x+a)^2*a^2*d^2+10/b^3*e^2/(b*x+a)^2*a*d^3-5/2/b^2*e/(b*x+a)^2*d^4","B"
1517,1,255,101,0.049000," ","int((e*x+d)^4/(b^2*x^2+2*a*b*x+a^2)^2,x)","-\frac{a^{4} e^{4}}{3 \left(b x +a \right)^{3} b^{5}}+\frac{4 a^{3} d \,e^{3}}{3 \left(b x +a \right)^{3} b^{4}}-\frac{2 a^{2} d^{2} e^{2}}{\left(b x +a \right)^{3} b^{3}}+\frac{4 a \,d^{3} e}{3 \left(b x +a \right)^{3} b^{2}}-\frac{d^{4}}{3 \left(b x +a \right)^{3} b}+\frac{2 a^{3} e^{4}}{\left(b x +a \right)^{2} b^{5}}-\frac{6 a^{2} d \,e^{3}}{\left(b x +a \right)^{2} b^{4}}+\frac{6 a \,d^{2} e^{2}}{\left(b x +a \right)^{2} b^{3}}-\frac{2 d^{3} e}{\left(b x +a \right)^{2} b^{2}}-\frac{6 a^{2} e^{4}}{\left(b x +a \right) b^{5}}+\frac{12 a d \,e^{3}}{\left(b x +a \right) b^{4}}-\frac{4 a \,e^{4} \ln \left(b x +a \right)}{b^{5}}-\frac{6 d^{2} e^{2}}{\left(b x +a \right) b^{3}}+\frac{4 d \,e^{3} \ln \left(b x +a \right)}{b^{4}}+\frac{e^{4} x}{b^{4}}"," ",0,"e^4*x/b^4-1/3/b^5/(b*x+a)^3*e^4*a^4+4/3/b^4/(b*x+a)^3*d*e^3*a^3-2/b^3/(b*x+a)^3*a^2*d^2*e^2+4/3/b^2/(b*x+a)^3*a*d^3*e-1/3/b/(b*x+a)^3*d^4-4/b^5*e^4*ln(b*x+a)*a+4/b^4*e^3*ln(b*x+a)*d-6/b^5*e^4/(b*x+a)*a^2+12/b^4*e^3/(b*x+a)*a*d-6/b^3*e^2/(b*x+a)*d^2+2/b^5*e^4/(b*x+a)^2*a^3-6/b^4*e^3/(b*x+a)^2*a^2*d+6/b^3*e^2/(b*x+a)^2*a*d^2-2/b^2*e/(b*x+a)^2*d^3","B"
1518,1,166,82,0.046000," ","int((e*x+d)^3/(b^2*x^2+2*a*b*x+a^2)^2,x)","\frac{a^{3} e^{3}}{3 \left(b x +a \right)^{3} b^{4}}-\frac{a^{2} d \,e^{2}}{\left(b x +a \right)^{3} b^{3}}+\frac{a \,d^{2} e}{\left(b x +a \right)^{3} b^{2}}-\frac{d^{3}}{3 \left(b x +a \right)^{3} b}-\frac{3 a^{2} e^{3}}{2 \left(b x +a \right)^{2} b^{4}}+\frac{3 a d \,e^{2}}{\left(b x +a \right)^{2} b^{3}}-\frac{3 d^{2} e}{2 \left(b x +a \right)^{2} b^{2}}+\frac{3 a \,e^{3}}{\left(b x +a \right) b^{4}}-\frac{3 d \,e^{2}}{\left(b x +a \right) b^{3}}+\frac{e^{3} \ln \left(b x +a \right)}{b^{4}}"," ",0,"1/3/b^4/(b*x+a)^3*a^3*e^3-1/b^3/(b*x+a)^3*a^2*d*e^2+1/b^2/(b*x+a)^3*a*d^2*e-1/3/b/(b*x+a)^3*d^3+e^3*ln(b*x+a)/b^4+3/b^4*e^3/(b*x+a)*a-3/b^3*e^2/(b*x+a)*d-3/2*e^3/b^4/(b*x+a)^2*a^2+3*e^2/b^3/(b*x+a)^2*a*d-3/2*e/b^2/(b*x+a)^2*d^2","B"
1519,1,70,26,0.047000," ","int((e*x+d)^2/(b^2*x^2+2*a*b*x+a^2)^2,x)","-\frac{e^{2}}{\left(b x +a \right) b^{3}}+\frac{\left(a e -b d \right) e}{\left(b x +a \right)^{2} b^{3}}-\frac{a^{2} e^{2}-2 a b d e +b^{2} d^{2}}{3 \left(b x +a \right)^{3} b^{3}}"," ",0,"-1/3*(a^2*e^2-2*a*b*d*e+b^2*d^2)/b^3/(b*x+a)^3-e^2/b^3/(b*x+a)+e*(a*e-b*d)/b^3/(b*x+a)^2","B"
1520,1,35,34,0.051000," ","int((e*x+d)/(b^2*x^2+2*a*b*x+a^2)^2,x)","-\frac{e}{2 \left(b x +a \right)^{2} b^{2}}-\frac{-a e +b d}{3 \left(b x +a \right)^{3} b^{2}}"," ",0,"-1/3*(-a*e+b*d)/b^2/(b*x+a)^3-1/2*e/b^2/(b*x+a)^2","A"
1521,1,13,12,0.040000," ","int(1/(b^2*x^2+2*a*b*x+a^2)^2,x)","-\frac{1}{3 \left(b x +a \right)^{3} b}"," ",0,"-1/3/b/(b*x+a)^3","A"
1522,1,103,103,0.051000," ","int(1/(e*x+d)/(b^2*x^2+2*a*b*x+a^2)^2,x)","-\frac{e^{3} \ln \left(b x +a \right)}{\left(a e -b d \right)^{4}}+\frac{e^{3} \ln \left(e x +d \right)}{\left(a e -b d \right)^{4}}+\frac{e^{2}}{\left(a e -b d \right)^{3} \left(b x +a \right)}+\frac{e}{2 \left(a e -b d \right)^{2} \left(b x +a \right)^{2}}+\frac{1}{3 \left(a e -b d \right) \left(b x +a \right)^{3}}"," ",0,"1/3/(a*e-b*d)/(b*x+a)^3+e^2/(a*e-b*d)^3/(b*x+a)-e^3/(a*e-b*d)^4*ln(b*x+a)+1/2*e/(a*e-b*d)^2/(b*x+a)^2+e^3/(a*e-b*d)^4*ln(e*x+d)","A"
1523,1,132,130,0.061000," ","int(1/(e*x+d)^2/(b^2*x^2+2*a*b*x+a^2)^2,x)","\frac{4 b \,e^{3} \ln \left(b x +a \right)}{\left(a e -b d \right)^{5}}-\frac{4 b \,e^{3} \ln \left(e x +d \right)}{\left(a e -b d \right)^{5}}-\frac{3 b \,e^{2}}{\left(a e -b d \right)^{4} \left(b x +a \right)}-\frac{e^{3}}{\left(a e -b d \right)^{4} \left(e x +d \right)}-\frac{b e}{\left(a e -b d \right)^{3} \left(b x +a \right)^{2}}-\frac{b}{3 \left(a e -b d \right)^{2} \left(b x +a \right)^{3}}"," ",0,"-1/3*b/(a*e-b*d)^2/(b*x+a)^3+4*b/(a*e-b*d)^5*e^3*ln(b*x+a)-3*b/(a*e-b*d)^4*e^2/(b*x+a)-b/(a*e-b*d)^3*e/(b*x+a)^2-e^3/(a*e-b*d)^4/(e*x+d)-4*b/(a*e-b*d)^5*e^3*ln(e*x+d)","A"
1524,1,165,164,0.060000," ","int(1/(e*x+d)^3/(b^2*x^2+2*a*b*x+a^2)^2,x)","-\frac{10 b^{2} e^{3} \ln \left(b x +a \right)}{\left(a e -b d \right)^{6}}+\frac{10 b^{2} e^{3} \ln \left(e x +d \right)}{\left(a e -b d \right)^{6}}+\frac{6 b^{2} e^{2}}{\left(a e -b d \right)^{5} \left(b x +a \right)}+\frac{4 b \,e^{3}}{\left(a e -b d \right)^{5} \left(e x +d \right)}+\frac{3 b^{2} e}{2 \left(a e -b d \right)^{4} \left(b x +a \right)^{2}}-\frac{e^{3}}{2 \left(a e -b d \right)^{4} \left(e x +d \right)^{2}}+\frac{b^{2}}{3 \left(a e -b d \right)^{3} \left(b x +a \right)^{3}}"," ",0,"1/3*b^2/(a*e-b*d)^3/(b*x+a)^3-10*b^2/(a*e-b*d)^6*e^3*ln(b*x+a)+6*b^2/(a*e-b*d)^5*e^2/(b*x+a)+3/2*b^2/(a*e-b*d)^4*e/(b*x+a)^2-1/2*e^3/(a*e-b*d)^4/(e*x+d)^2+10*b^2/(a*e-b*d)^6*e^3*ln(e*x+d)+4*e^3/(a*e-b*d)^5*b/(e*x+d)","A"
1525,1,820,202,0.065000," ","int((e*x+d)^8/(b^2*x^2+2*a*b*x+a^2)^3,x)","-\frac{a^{8} e^{8}}{5 \left(b x +a \right)^{5} b^{9}}+\frac{8 a^{7} d \,e^{7}}{5 \left(b x +a \right)^{5} b^{8}}-\frac{28 a^{6} d^{2} e^{6}}{5 \left(b x +a \right)^{5} b^{7}}+\frac{56 a^{5} d^{3} e^{5}}{5 \left(b x +a \right)^{5} b^{6}}-\frac{14 a^{4} d^{4} e^{4}}{\left(b x +a \right)^{5} b^{5}}+\frac{56 a^{3} d^{5} e^{3}}{5 \left(b x +a \right)^{5} b^{4}}-\frac{28 a^{2} d^{6} e^{2}}{5 \left(b x +a \right)^{5} b^{3}}+\frac{8 a \,d^{7} e}{5 \left(b x +a \right)^{5} b^{2}}-\frac{d^{8}}{5 \left(b x +a \right)^{5} b}+\frac{2 a^{7} e^{8}}{\left(b x +a \right)^{4} b^{9}}-\frac{14 a^{6} d \,e^{7}}{\left(b x +a \right)^{4} b^{8}}+\frac{42 a^{5} d^{2} e^{6}}{\left(b x +a \right)^{4} b^{7}}-\frac{70 a^{4} d^{3} e^{5}}{\left(b x +a \right)^{4} b^{6}}+\frac{70 a^{3} d^{4} e^{4}}{\left(b x +a \right)^{4} b^{5}}-\frac{42 a^{2} d^{5} e^{3}}{\left(b x +a \right)^{4} b^{4}}+\frac{14 a \,d^{6} e^{2}}{\left(b x +a \right)^{4} b^{3}}-\frac{2 d^{7} e}{\left(b x +a \right)^{4} b^{2}}-\frac{28 a^{6} e^{8}}{3 \left(b x +a \right)^{3} b^{9}}+\frac{56 a^{5} d \,e^{7}}{\left(b x +a \right)^{3} b^{8}}-\frac{140 a^{4} d^{2} e^{6}}{\left(b x +a \right)^{3} b^{7}}+\frac{560 a^{3} d^{3} e^{5}}{3 \left(b x +a \right)^{3} b^{6}}-\frac{140 a^{2} d^{4} e^{4}}{\left(b x +a \right)^{3} b^{5}}+\frac{56 a \,d^{5} e^{3}}{\left(b x +a \right)^{3} b^{4}}-\frac{28 d^{6} e^{2}}{3 \left(b x +a \right)^{3} b^{3}}+\frac{e^{8} x^{3}}{3 b^{6}}+\frac{28 a^{5} e^{8}}{\left(b x +a \right)^{2} b^{9}}-\frac{140 a^{4} d \,e^{7}}{\left(b x +a \right)^{2} b^{8}}+\frac{280 a^{3} d^{2} e^{6}}{\left(b x +a \right)^{2} b^{7}}-\frac{280 a^{2} d^{3} e^{5}}{\left(b x +a \right)^{2} b^{6}}+\frac{140 a \,d^{4} e^{4}}{\left(b x +a \right)^{2} b^{5}}-\frac{3 a \,e^{8} x^{2}}{b^{7}}-\frac{28 d^{5} e^{3}}{\left(b x +a \right)^{2} b^{4}}+\frac{4 d \,e^{7} x^{2}}{b^{6}}-\frac{70 a^{4} e^{8}}{\left(b x +a \right) b^{9}}+\frac{280 a^{3} d \,e^{7}}{\left(b x +a \right) b^{8}}-\frac{56 a^{3} e^{8} \ln \left(b x +a \right)}{b^{9}}-\frac{420 a^{2} d^{2} e^{6}}{\left(b x +a \right) b^{7}}+\frac{168 a^{2} d \,e^{7} \ln \left(b x +a \right)}{b^{8}}+\frac{21 a^{2} e^{8} x}{b^{8}}+\frac{280 a \,d^{3} e^{5}}{\left(b x +a \right) b^{6}}-\frac{168 a \,d^{2} e^{6} \ln \left(b x +a \right)}{b^{7}}-\frac{48 a d \,e^{7} x}{b^{7}}-\frac{70 d^{4} e^{4}}{\left(b x +a \right) b^{5}}+\frac{56 d^{3} e^{5} \ln \left(b x +a \right)}{b^{6}}+\frac{28 d^{2} e^{6} x}{b^{6}}"," ",0,"-1/5/b/(b*x+a)^5*d^8+1/3*e^8/b^6*x^3-48*e^7/b^7*a*d*x+8/5/b^8/(b*x+a)^5*a^7*d*e^7+280/b^7*e^6/(b*x+a)^2*a^3*d^2-280/b^6*e^5/(b*x+a)^2*a^2*d^3+140/b^5*e^4/(b*x+a)^2*a*d^4+168/b^8*e^7*ln(b*x+a)*a^2*d-168/b^7*e^6*ln(b*x+a)*a*d^2+280/b^8*e^7/(b*x+a)*d*a^3-420/b^7*e^6/(b*x+a)*a^2*d^2+280/b^6*e^5/(b*x+a)*a*d^3-140/b^8*e^7/(b*x+a)^2*a^4*d-28/3/b^3*e^2/(b*x+a)^3*d^6-1/5/b^9/(b*x+a)^5*a^8*e^8-3*e^8/b^7*x^2*a+4*e^7/b^6*x^2*d+21*e^8/b^8*a^2*x+28*e^6/b^6*d^2*x-56/b^9*e^8*ln(b*x+a)*a^3+56/b^6*e^5*ln(b*x+a)*d^3-70/b^9*e^8/(b*x+a)*a^4-70/b^5*e^4/(b*x+a)*d^4+28/b^9*e^8/(b*x+a)^2*a^5-28/b^4*e^3/(b*x+a)^2*d^5+2/b^9*e^8/(b*x+a)^4*a^7-2/b^2*e/(b*x+a)^4*d^7-28/3/b^9*e^8/(b*x+a)^3*a^6+14/b^3*e^2/(b*x+a)^4*a*d^6+56/b^8*e^7/(b*x+a)^3*d*a^5-140/b^7*e^6/(b*x+a)^3*d^2*a^4+560/3/b^6*e^5/(b*x+a)^3*d^3*a^3-140/b^5*e^4/(b*x+a)^3*d^4*a^2+56/b^4*e^3/(b*x+a)^3*d^5*a-28/5/b^7/(b*x+a)^5*a^6*d^2*e^6+56/5/b^6/(b*x+a)^5*a^5*d^3*e^5-14/b^5/(b*x+a)^5*a^4*d^4*e^4+56/5/b^4/(b*x+a)^5*a^3*d^5*e^3-28/5/b^3/(b*x+a)^5*a^2*d^6*e^2+8/5/b^2/(b*x+a)^5*a*d^7*e-14/b^8*e^7/(b*x+a)^4*a^6*d+42/b^7*e^6/(b*x+a)^4*a^5*d^2-70/b^6*e^5/(b*x+a)^4*a^4*d^3+70/b^5*e^4/(b*x+a)^4*a^3*d^4-42/b^4*e^3/(b*x+a)^4*a^2*d^5","B"
1526,1,656,173,0.058000," ","int((e*x+d)^7/(b^2*x^2+2*a*b*x+a^2)^3,x)","\frac{a^{7} e^{7}}{5 \left(b x +a \right)^{5} b^{8}}-\frac{7 a^{6} d \,e^{6}}{5 \left(b x +a \right)^{5} b^{7}}+\frac{21 a^{5} d^{2} e^{5}}{5 \left(b x +a \right)^{5} b^{6}}-\frac{7 a^{4} d^{3} e^{4}}{\left(b x +a \right)^{5} b^{5}}+\frac{7 a^{3} d^{4} e^{3}}{\left(b x +a \right)^{5} b^{4}}-\frac{21 a^{2} d^{5} e^{2}}{5 \left(b x +a \right)^{5} b^{3}}+\frac{7 a \,d^{6} e}{5 \left(b x +a \right)^{5} b^{2}}-\frac{d^{7}}{5 \left(b x +a \right)^{5} b}-\frac{7 a^{6} e^{7}}{4 \left(b x +a \right)^{4} b^{8}}+\frac{21 a^{5} d \,e^{6}}{2 \left(b x +a \right)^{4} b^{7}}-\frac{105 a^{4} d^{2} e^{5}}{4 \left(b x +a \right)^{4} b^{6}}+\frac{35 a^{3} d^{3} e^{4}}{\left(b x +a \right)^{4} b^{5}}-\frac{105 a^{2} d^{4} e^{3}}{4 \left(b x +a \right)^{4} b^{4}}+\frac{21 a \,d^{5} e^{2}}{2 \left(b x +a \right)^{4} b^{3}}-\frac{7 d^{6} e}{4 \left(b x +a \right)^{4} b^{2}}+\frac{7 a^{5} e^{7}}{\left(b x +a \right)^{3} b^{8}}-\frac{35 a^{4} d \,e^{6}}{\left(b x +a \right)^{3} b^{7}}+\frac{70 a^{3} d^{2} e^{5}}{\left(b x +a \right)^{3} b^{6}}-\frac{70 a^{2} d^{3} e^{4}}{\left(b x +a \right)^{3} b^{5}}+\frac{35 a \,d^{4} e^{3}}{\left(b x +a \right)^{3} b^{4}}-\frac{7 d^{5} e^{2}}{\left(b x +a \right)^{3} b^{3}}-\frac{35 a^{4} e^{7}}{2 \left(b x +a \right)^{2} b^{8}}+\frac{70 a^{3} d \,e^{6}}{\left(b x +a \right)^{2} b^{7}}-\frac{105 a^{2} d^{2} e^{5}}{\left(b x +a \right)^{2} b^{6}}+\frac{70 a \,d^{3} e^{4}}{\left(b x +a \right)^{2} b^{5}}-\frac{35 d^{4} e^{3}}{2 \left(b x +a \right)^{2} b^{4}}+\frac{e^{7} x^{2}}{2 b^{6}}+\frac{35 a^{3} e^{7}}{\left(b x +a \right) b^{8}}-\frac{105 a^{2} d \,e^{6}}{\left(b x +a \right) b^{7}}+\frac{21 a^{2} e^{7} \ln \left(b x +a \right)}{b^{8}}+\frac{105 a \,d^{2} e^{5}}{\left(b x +a \right) b^{6}}-\frac{42 a d \,e^{6} \ln \left(b x +a \right)}{b^{7}}-\frac{6 a \,e^{7} x}{b^{7}}-\frac{35 d^{3} e^{4}}{\left(b x +a \right) b^{5}}+\frac{21 d^{2} e^{5} \ln \left(b x +a \right)}{b^{6}}+\frac{7 d \,e^{6} x}{b^{6}}"," ",0,"-1/5/b/(b*x+a)^5*d^7-7/5/b^7/(b*x+a)^5*a^6*d*e^6+21/5/b^6/(b*x+a)^5*a^5*d^2*e^5-7/b^3*e^2/(b*x+a)^3*d^5-35/2/b^8*e^7/(b*x+a)^2*a^4-35/2/b^4*e^3/(b*x+a)^2*d^4-7/4/b^8*e^7/(b*x+a)^4*a^6-7/4/b^2*e/(b*x+a)^4*d^6+21/b^8*e^7*ln(b*x+a)*a^2+21/b^6*e^5*ln(b*x+a)*d^2+35/b^8*e^7/(b*x+a)*a^3-35/b^5*e^4/(b*x+a)*d^3-6*e^7/b^7*a*x+7*e^6/b^6*x*d+1/5/b^8/(b*x+a)^5*a^7*e^7+7/b^8*e^7/(b*x+a)^3*a^5-105/b^7*e^6/(b*x+a)*a^2*d+105/b^6*e^5/(b*x+a)*a*d^2-42/b^7*e^6*ln(b*x+a)*a*d-35/b^7*e^6/(b*x+a)^3*a^4*d+70/b^6*e^5/(b*x+a)^3*a^3*d^2-70/b^5*e^4/(b*x+a)^3*a^2*d^3+35/b^4*e^3/(b*x+a)^3*a*d^4+21/2/b^7*e^6/(b*x+a)^4*d*a^5-105/4/b^6*e^5/(b*x+a)^4*d^2*a^4+35/b^5*e^4/(b*x+a)^4*d^3*a^3-105/4/b^4*e^3/(b*x+a)^4*d^4*a^2+21/2/b^3*e^2/(b*x+a)^4*d^5*a+1/2*e^7*x^2/b^6+70/b^7*e^6/(b*x+a)^2*d*a^3-7/b^5/(b*x+a)^5*a^4*d^3*e^4+7/b^4/(b*x+a)^5*a^3*d^4*e^3-21/5/b^3/(b*x+a)^5*a^2*d^5*e^2+7/5/b^2/(b*x+a)^5*a*d^6*e-105/b^6*e^5/(b*x+a)^2*a^2*d^2+70/b^5*e^4/(b*x+a)^2*a*d^3","B"
1527,1,508,151,0.058000," ","int((e*x+d)^6/(b^2*x^2+2*a*b*x+a^2)^3,x)","-\frac{a^{6} e^{6}}{5 \left(b x +a \right)^{5} b^{7}}+\frac{6 a^{5} d \,e^{5}}{5 \left(b x +a \right)^{5} b^{6}}-\frac{3 a^{4} d^{2} e^{4}}{\left(b x +a \right)^{5} b^{5}}+\frac{4 a^{3} d^{3} e^{3}}{\left(b x +a \right)^{5} b^{4}}-\frac{3 a^{2} d^{4} e^{2}}{\left(b x +a \right)^{5} b^{3}}+\frac{6 a \,d^{5} e}{5 \left(b x +a \right)^{5} b^{2}}-\frac{d^{6}}{5 \left(b x +a \right)^{5} b}+\frac{3 a^{5} e^{6}}{2 \left(b x +a \right)^{4} b^{7}}-\frac{15 a^{4} d \,e^{5}}{2 \left(b x +a \right)^{4} b^{6}}+\frac{15 a^{3} d^{2} e^{4}}{\left(b x +a \right)^{4} b^{5}}-\frac{15 a^{2} d^{3} e^{3}}{\left(b x +a \right)^{4} b^{4}}+\frac{15 a \,d^{4} e^{2}}{2 \left(b x +a \right)^{4} b^{3}}-\frac{3 d^{5} e}{2 \left(b x +a \right)^{4} b^{2}}-\frac{5 a^{4} e^{6}}{\left(b x +a \right)^{3} b^{7}}+\frac{20 a^{3} d \,e^{5}}{\left(b x +a \right)^{3} b^{6}}-\frac{30 a^{2} d^{2} e^{4}}{\left(b x +a \right)^{3} b^{5}}+\frac{20 a \,d^{3} e^{3}}{\left(b x +a \right)^{3} b^{4}}-\frac{5 d^{4} e^{2}}{\left(b x +a \right)^{3} b^{3}}+\frac{10 a^{3} e^{6}}{\left(b x +a \right)^{2} b^{7}}-\frac{30 a^{2} d \,e^{5}}{\left(b x +a \right)^{2} b^{6}}+\frac{30 a \,d^{2} e^{4}}{\left(b x +a \right)^{2} b^{5}}-\frac{10 d^{3} e^{3}}{\left(b x +a \right)^{2} b^{4}}-\frac{15 a^{2} e^{6}}{\left(b x +a \right) b^{7}}+\frac{30 a d \,e^{5}}{\left(b x +a \right) b^{6}}-\frac{6 a \,e^{6} \ln \left(b x +a \right)}{b^{7}}-\frac{15 d^{2} e^{4}}{\left(b x +a \right) b^{5}}+\frac{6 d \,e^{5} \ln \left(b x +a \right)}{b^{6}}+\frac{e^{6} x}{b^{6}}"," ",0,"-3/b^5/(b*x+a)^5*d^2*e^4*a^4-6/b^7*e^6*ln(b*x+a)*a+6/b^6*e^5*ln(b*x+a)*d+3/2/b^7*e^6/(b*x+a)^4*a^5-3/2/b^2*e/(b*x+a)^4*d^5-15/b^7*e^6/(b*x+a)*a^2-15/b^5*e^4/(b*x+a)*d^2+10/b^7*e^6/(b*x+a)^2*a^3-10/b^4*e^3/(b*x+a)^2*d^3-1/5/b^7/(b*x+a)^5*a^6*e^6-5/b^7*e^6/(b*x+a)^3*a^4-5/b^3*e^2/(b*x+a)^3*d^4+6/5/b^6/(b*x+a)^5*d*e^5*a^5+30/b^5*e^4/(b*x+a)^2*a*d^2+30/b^6*e^5/(b*x+a)*a*d-15/2/b^6*e^5/(b*x+a)^4*a^4*d+15/b^5*e^4/(b*x+a)^4*a^3*d^2-15/b^4*e^3/(b*x+a)^4*a^2*d^3-3/b^3/(b*x+a)^5*d^4*a^2*e^2+6/5/b^2/(b*x+a)^5*d^5*e*a+20/b^6*e^5/(b*x+a)^3*d*a^3-30/b^5*e^4/(b*x+a)^3*a^2*d^2+20/b^4*e^3/(b*x+a)^3*a*d^3+15/2/b^3*e^2/(b*x+a)^4*a*d^4-30/b^6*e^5/(b*x+a)^2*a^2*d+4/b^4/(b*x+a)^5*d^3*e^3*a^3-1/5/b/(b*x+a)^5*d^6+e^6*x/b^6","B"
1528,1,377,132,0.053000," ","int((e*x+d)^5/(b^2*x^2+2*a*b*x+a^2)^3,x)","\frac{a^{5} e^{5}}{5 \left(b x +a \right)^{5} b^{6}}-\frac{a^{4} d \,e^{4}}{\left(b x +a \right)^{5} b^{5}}+\frac{2 a^{3} d^{2} e^{3}}{\left(b x +a \right)^{5} b^{4}}-\frac{2 a^{2} d^{3} e^{2}}{\left(b x +a \right)^{5} b^{3}}+\frac{a \,d^{4} e}{\left(b x +a \right)^{5} b^{2}}-\frac{d^{5}}{5 \left(b x +a \right)^{5} b}-\frac{5 a^{4} e^{5}}{4 \left(b x +a \right)^{4} b^{6}}+\frac{5 a^{3} d \,e^{4}}{\left(b x +a \right)^{4} b^{5}}-\frac{15 a^{2} d^{2} e^{3}}{2 \left(b x +a \right)^{4} b^{4}}+\frac{5 a \,d^{3} e^{2}}{\left(b x +a \right)^{4} b^{3}}-\frac{5 d^{4} e}{4 \left(b x +a \right)^{4} b^{2}}+\frac{10 a^{3} e^{5}}{3 \left(b x +a \right)^{3} b^{6}}-\frac{10 a^{2} d \,e^{4}}{\left(b x +a \right)^{3} b^{5}}+\frac{10 a \,d^{2} e^{3}}{\left(b x +a \right)^{3} b^{4}}-\frac{10 d^{3} e^{2}}{3 \left(b x +a \right)^{3} b^{3}}-\frac{5 a^{2} e^{5}}{\left(b x +a \right)^{2} b^{6}}+\frac{10 a d \,e^{4}}{\left(b x +a \right)^{2} b^{5}}-\frac{5 d^{2} e^{3}}{\left(b x +a \right)^{2} b^{4}}+\frac{5 a \,e^{5}}{\left(b x +a \right) b^{6}}-\frac{5 d \,e^{4}}{\left(b x +a \right) b^{5}}+\frac{e^{5} \ln \left(b x +a \right)}{b^{6}}"," ",0,"1/5/b^6/(b*x+a)^5*a^5*e^5-1/b^5/(b*x+a)^5*a^4*d*e^4+2/b^4/(b*x+a)^5*a^3*d^2*e^3-2/b^3/(b*x+a)^5*a^2*d^3*e^2+1/b^2/(b*x+a)^5*a*d^4*e-1/5/b/(b*x+a)^5*d^5+10/3*e^5/b^6/(b*x+a)^3*a^3-10*e^4/b^5/(b*x+a)^3*a^2*d+10*e^3/b^4/(b*x+a)^3*a*d^2-10/3*e^2/b^3/(b*x+a)^3*d^3+e^5*ln(b*x+a)/b^6-5/4*e^5/b^6/(b*x+a)^4*a^4+5*e^4/b^5/(b*x+a)^4*d*a^3-15/2*e^3/b^4/(b*x+a)^4*a^2*d^2+5*e^2/b^3/(b*x+a)^4*a*d^3-5/4*e/b^2/(b*x+a)^4*d^4+5/b^6*e^5/(b*x+a)*a-5/b^5*e^4/(b*x+a)*d-5*e^5/b^6/(b*x+a)^2*a^2+10*e^4/b^5/(b*x+a)^2*a*d-5*e^3/b^4/(b*x+a)^2*d^2","B"
1529,1,185,26,0.049000," ","int((e*x+d)^4/(b^2*x^2+2*a*b*x+a^2)^3,x)","-\frac{e^{4}}{\left(b x +a \right) b^{5}}+\frac{2 \left(a e -b d \right) e^{3}}{\left(b x +a \right)^{2} b^{5}}-\frac{2 \left(a^{2} e^{2}-2 a b d e +b^{2} d^{2}\right) e^{2}}{\left(b x +a \right)^{3} b^{5}}+\frac{\left(a^{3} e^{3}-3 a^{2} b d \,e^{2}+3 a \,b^{2} d^{2} e -b^{3} d^{3}\right) e}{\left(b x +a \right)^{4} b^{5}}-\frac{e^{4} a^{4}-4 d \,e^{3} a^{3} b +6 d^{2} e^{2} a^{2} b^{2}-4 a \,b^{3} d^{3} e +d^{4} b^{4}}{5 \left(b x +a \right)^{5} b^{5}}"," ",0,"e*(a^3*e^3-3*a^2*b*d*e^2+3*a*b^2*d^2*e-b^3*d^3)/b^5/(b*x+a)^4-1/5*(a^4*e^4-4*a^3*b*d*e^3+6*a^2*b^2*d^2*e^2-4*a*b^3*d^3*e+b^4*d^4)/b^5/(b*x+a)^5-2*e^2*(a^2*e^2-2*a*b*d*e+b^2*d^2)/b^5/(b*x+a)^3-e^4/b^5/(b*x+a)+2*e^3*(a*e-b*d)/b^5/(b*x+a)^2","B"
1530,1,121,54,0.047000," ","int((e*x+d)^3/(b^2*x^2+2*a*b*x+a^2)^3,x)","-\frac{e^{3}}{2 \left(b x +a \right)^{2} b^{4}}+\frac{\left(a e -b d \right) e^{2}}{\left(b x +a \right)^{3} b^{4}}-\frac{3 \left(a^{2} e^{2}-2 a b d e +b^{2} d^{2}\right) e}{4 \left(b x +a \right)^{4} b^{4}}-\frac{-a^{3} e^{3}+3 a^{2} b d \,e^{2}-3 a \,b^{2} d^{2} e +b^{3} d^{3}}{5 \left(b x +a \right)^{5} b^{4}}"," ",0,"-3/4*e*(a^2*e^2-2*a*b*d*e+b^2*d^2)/b^4/(b*x+a)^4-1/5*(-a^3*e^3+3*a^2*b*d*e^2-3*a*b^2*d^2*e+b^3*d^3)/b^4/(b*x+a)^5+e^2*(a*e-b*d)/b^4/(b*x+a)^3-1/2*e^3/b^4/(b*x+a)^2","B"
1531,1,71,59,0.050000," ","int((e*x+d)^2/(b^2*x^2+2*a*b*x+a^2)^3,x)","-\frac{e^{2}}{3 \left(b x +a \right)^{3} b^{3}}+\frac{\left(a e -b d \right) e}{2 \left(b x +a \right)^{4} b^{3}}-\frac{a^{2} e^{2}-2 a b d e +b^{2} d^{2}}{5 \left(b x +a \right)^{5} b^{3}}"," ",0,"-1/5*(a^2*e^2-2*a*b*d*e+b^2*d^2)/b^3/(b*x+a)^5-1/3*e^2/b^3/(b*x+a)^3+1/2*e*(a*e-b*d)/b^3/(b*x+a)^4","A"
1532,1,35,34,0.049000," ","int((e*x+d)/(b^2*x^2+2*a*b*x+a^2)^3,x)","-\frac{e}{4 \left(b x +a \right)^{4} b^{2}}-\frac{-a e +b d}{5 \left(b x +a \right)^{5} b^{2}}"," ",0,"-1/4*e/b^2/(b*x+a)^4-1/5*(-a*e+b*d)/b^2/(b*x+a)^5","A"
1533,1,13,12,0.043000," ","int(1/(b^2*x^2+2*a*b*x+a^2)^3,x)","-\frac{1}{5 \left(b x +a \right)^{5} b}"," ",0,"-1/5/b/(b*x+a)^5","A"
1534,1,147,147,0.056000," ","int(1/(e*x+d)/(b^2*x^2+2*a*b*x+a^2)^3,x)","-\frac{e^{5} \ln \left(b x +a \right)}{\left(a e -b d \right)^{6}}+\frac{e^{5} \ln \left(e x +d \right)}{\left(a e -b d \right)^{6}}+\frac{e^{4}}{\left(a e -b d \right)^{5} \left(b x +a \right)}+\frac{e^{3}}{2 \left(a e -b d \right)^{4} \left(b x +a \right)^{2}}+\frac{e^{2}}{3 \left(a e -b d \right)^{3} \left(b x +a \right)^{3}}+\frac{e}{4 \left(a e -b d \right)^{2} \left(b x +a \right)^{4}}+\frac{1}{5 \left(a e -b d \right) \left(b x +a \right)^{5}}"," ",0,"1/5/(a*e-b*d)/(b*x+a)^5+1/3*e^2/(a*e-b*d)^3/(b*x+a)^3+1/2*e^3/(a*e-b*d)^4/(b*x+a)^2+e^4/(a*e-b*d)^5/(b*x+a)-e^5/(a*e-b*d)^6*ln(b*x+a)+1/4*e/(a*e-b*d)^2/(b*x+a)^4+e^5/(a*e-b*d)^6*ln(e*x+d)","A"
1535,1,178,177,0.061000," ","int(1/(e*x+d)^2/(b^2*x^2+2*a*b*x+a^2)^3,x)","\frac{6 b \,e^{5} \ln \left(b x +a \right)}{\left(a e -b d \right)^{7}}-\frac{6 b \,e^{5} \ln \left(e x +d \right)}{\left(a e -b d \right)^{7}}-\frac{5 b \,e^{4}}{\left(a e -b d \right)^{6} \left(b x +a \right)}-\frac{e^{5}}{\left(a e -b d \right)^{6} \left(e x +d \right)}-\frac{2 b \,e^{3}}{\left(a e -b d \right)^{5} \left(b x +a \right)^{2}}-\frac{b \,e^{2}}{\left(a e -b d \right)^{4} \left(b x +a \right)^{3}}-\frac{b e}{2 \left(a e -b d \right)^{3} \left(b x +a \right)^{4}}-\frac{b}{5 \left(a e -b d \right)^{2} \left(b x +a \right)^{5}}"," ",0,"-1/5*b/(a*e-b*d)^2/(b*x+a)^5+6*b/(a*e-b*d)^7*e^5*ln(b*x+a)-5*b/(a*e-b*d)^6*e^4/(b*x+a)-2*b/(a*e-b*d)^5*e^3/(b*x+a)^2-b/(a*e-b*d)^4*e^2/(b*x+a)^3-1/2*b/(a*e-b*d)^3*e/(b*x+a)^4-e^5/(a*e-b*d)^6/(e*x+d)-6*b/(a*e-b*d)^7*e^5*ln(e*x+d)","A"
1536,1,215,214,0.059000," ","int(1/(e*x+d)^3/(b^2*x^2+2*a*b*x+a^2)^3,x)","-\frac{21 b^{2} e^{5} \ln \left(b x +a \right)}{\left(a e -b d \right)^{8}}+\frac{21 b^{2} e^{5} \ln \left(e x +d \right)}{\left(a e -b d \right)^{8}}+\frac{15 b^{2} e^{4}}{\left(a e -b d \right)^{7} \left(b x +a \right)}+\frac{6 b \,e^{5}}{\left(a e -b d \right)^{7} \left(e x +d \right)}+\frac{5 b^{2} e^{3}}{\left(a e -b d \right)^{6} \left(b x +a \right)^{2}}-\frac{e^{5}}{2 \left(a e -b d \right)^{6} \left(e x +d \right)^{2}}+\frac{2 b^{2} e^{2}}{\left(a e -b d \right)^{5} \left(b x +a \right)^{3}}+\frac{3 b^{2} e}{4 \left(a e -b d \right)^{4} \left(b x +a \right)^{4}}+\frac{b^{2}}{5 \left(a e -b d \right)^{3} \left(b x +a \right)^{5}}"," ",0,"1/5*b^2/(a*e-b*d)^3/(b*x+a)^5-21*b^2/(a*e-b*d)^8*e^5*ln(b*x+a)+15*b^2/(a*e-b*d)^7*e^4/(b*x+a)+5*b^2/(a*e-b*d)^6*e^3/(b*x+a)^2+2*b^2/(a*e-b*d)^5*e^2/(b*x+a)^3+3/4*b^2/(a*e-b*d)^4*e/(b*x+a)^4-1/2*e^5/(a*e-b*d)^6/(e*x+d)^2+21*b^2/(a*e-b*d)^8*e^5*ln(e*x+d)+6*e^5/(a*e-b*d)^7*b/(e*x+d)","A"
1537,1,84,27,0.037000," ","int((e*x+d)*(4*x^2+12*x+9)^3,x)","8 e \,x^{8}+\frac{\left(64 d +576 e \right) x^{7}}{7}+\frac{\left(576 d +2160 e \right) x^{6}}{6}+\frac{\left(2160 d +4320 e \right) x^{5}}{5}+\frac{\left(4320 d +4860 e \right) x^{4}}{4}+\frac{\left(4860 d +2916 e \right) x^{3}}{3}+729 d x +\frac{\left(2916 d +729 e \right) x^{2}}{2}"," ",0,"8*e*x^8+1/7*(64*d+576*e)*x^7+1/6*(576*d+2160*e)*x^6+1/5*(2160*d+4320*e)*x^5+1/4*(4320*d+4860*e)*x^4+1/3*(4860*d+2916*e)*x^3+1/2*(2916*d+729*e)*x^2+729*d*x","B"
1538,1,60,27,0.036000," ","int((e*x+d)*(4*x^2+12*x+9)^2,x)","\frac{8 e \,x^{6}}{3}+\frac{\left(16 d +96 e \right) x^{5}}{5}+\frac{\left(96 d +216 e \right) x^{4}}{4}+\frac{\left(216 d +216 e \right) x^{3}}{3}+81 d x +\frac{\left(216 d +81 e \right) x^{2}}{2}"," ",0,"8/3*e*x^6+1/5*(16*d+96*e)*x^5+1/4*(96*d+216*e)*x^4+1/3*(216*d+216*e)*x^3+1/2*(216*d+81*e)*x^2+81*d*x","B"
1539,1,35,27,0.043000," ","int((e*x+d)*(4*x^2+12*x+9),x)","e \,x^{4}+\frac{\left(4 d +12 e \right) x^{3}}{3}+9 d x +\frac{\left(12 d +9 e \right) x^{2}}{2}"," ",0,"e*x^4+1/3*(4*d+12*e)*x^3+1/2*(12*d+9*e)*x^2+9*d*x","A"
1540,1,31,26,0.051000," ","int((e*x+d)/(4*x^2+12*x+9),x)","\frac{e \ln \left(2 x +3\right)}{4}-\frac{d}{2 \left(2 x +3\right)}+\frac{3 e}{4 \left(2 x +3\right)}"," ",0,"-1/2/(2*x+3)*d+3/4*e/(2*x+3)+1/4*e*ln(2*x+3)","A"
1541,1,28,27,0.044000," ","int((e*x+d)/(4*x^2+12*x+9)^2,x)","-\frac{e}{8 \left(2 x +3\right)^{2}}-\frac{\frac{d}{2}-\frac{3 e}{4}}{3 \left(2 x +3\right)^{3}}"," ",0,"-1/3*(1/2*d-3/4*e)/(2*x+3)^3-1/8*e/(2*x+3)^2","A"
1542,1,28,27,0.046000," ","int((e*x+d)/(4*x^2+12*x+9)^3,x)","-\frac{e}{16 \left(2 x +3\right)^{4}}-\frac{\frac{d}{2}-\frac{3 e}{4}}{5 \left(2 x +3\right)^{5}}"," ",0,"-1/5*(1/2*d-3/4*e)/(2*x+3)^5-1/16*e/(2*x+3)^4","A"
1543,1,114,66,0.041000," ","int((e*x+d)^4*((b*x+a)^2)^(1/2),x)","\frac{\left(5 b \,e^{4} x^{5}+6 x^{4} a \,e^{4}+24 x^{4} b d \,e^{3}+30 x^{3} a d \,e^{3}+45 x^{3} b \,d^{2} e^{2}+60 x^{2} a \,d^{2} e^{2}+40 x^{2} b \,d^{3} e +60 x a \,d^{3} e +15 x b \,d^{4}+30 a \,d^{4}\right) \sqrt{\left(b x +a \right)^{2}}\, x}{30 b x +30 a}"," ",0,"1/30*x*(5*b*e^4*x^5+6*a*e^4*x^4+24*b*d*e^3*x^4+30*a*d*e^3*x^3+45*b*d^2*e^2*x^3+60*a*d^2*e^2*x^2+40*b*d^3*e*x^2+60*a*d^3*e*x+15*b*d^4*x+30*a*d^4)*((b*x+a)^2)^(1/2)/(b*x+a)","A"
1544,1,90,66,0.041000," ","int((e*x+d)^3*((b*x+a)^2)^(1/2),x)","\frac{\left(4 b \,e^{3} x^{4}+5 x^{3} a \,e^{3}+15 x^{3} b d \,e^{2}+20 a d \,e^{2} x^{2}+20 b \,d^{2} e \,x^{2}+30 x a \,d^{2} e +10 x b \,d^{3}+20 a \,d^{3}\right) \sqrt{\left(b x +a \right)^{2}}\, x}{20 b x +20 a}"," ",0,"1/20*x*(4*b*e^3*x^4+5*a*e^3*x^3+15*b*d*e^2*x^3+20*a*d*e^2*x^2+20*b*d^2*e*x^2+30*a*d^2*e*x+10*b*d^3*x+20*a*d^3)*((b*x+a)^2)^(1/2)/(b*x+a)","A"
1545,1,66,66,0.042000," ","int((e*x+d)^2*((b*x+a)^2)^(1/2),x)","\frac{\left(3 b \,e^{2} x^{3}+4 x^{2} a \,e^{2}+8 x^{2} b d e +12 a d e x +6 x b \,d^{2}+12 a \,d^{2}\right) \sqrt{\left(b x +a \right)^{2}}\, x}{12 b x +12 a}"," ",0,"1/12*x*(3*b*e^2*x^3+4*a*e^2*x^2+8*b*d*e*x^2+12*a*d*e*x+6*b*d^2*x+12*a*d^2)*((b*x+a)^2)^(1/2)/(b*x+a)","A"
1546,1,42,52,0.044000," ","int((e*x+d)*((b*x+a)^2)^(1/2),x)","\frac{\left(2 b e \,x^{2}+3 a e x +3 x b d +6 a d \right) \sqrt{\left(b x +a \right)^{2}}\, x}{6 b x +6 a}"," ",0,"1/6*x*(2*b*e*x^2+3*a*e*x+3*b*d*x+6*a*d)*((b*x+a)^2)^(1/2)/(b*x+a)","A"
1547,1,27,19,0.037000," ","int(((b*x+a)^2)^(1/2),x)","\frac{\left(b x +2 a \right) \sqrt{\left(b x +a \right)^{2}}\, x}{2 b x +2 a}"," ",0,"1/2*x*(b*x+2*a)*((b*x+a)^2)^(1/2)/(b*x+a)","A"
1548,1,44,58,0.064000," ","int(((b*x+a)^2)^(1/2)/(e*x+d),x)","\frac{\left(a e \ln \left(b e x +b d \right)-b d \ln \left(b e x +b d \right)+b e x +a e \right) \mathrm{csgn}\left(b x +a \right)}{e^{2}}"," ",0,"csgn(b*x+a)*(ln(b*e*x+b*d)*a*e-ln(b*e*x+b*d)*b*d+b*e*x+a*e)/e^2","C"
1549,1,51,63,0.056000," ","int(((b*x+a)^2)^(1/2)/(e*x+d)^2,x)","\frac{\left(b e x \ln \left(b e x +b d \right)+b d \ln \left(b e x +b d \right)-a e +b d \right) \mathrm{csgn}\left(b x +a \right)}{\left(e x +d \right) e^{2}}"," ",0,"csgn(b*x+a)*(ln(b*e*x+b*d)*x*b*e+b*d*ln(b*e*x+b*d)-a*e+b*d)/e^2/(e*x+d)","C"
1550,1,41,33,0.040000," ","int(((b*x+a)^2)^(1/2)/(e*x+d)^3,x)","-\frac{\left(2 b e x +a e +b d \right) \sqrt{\left(b x +a \right)^{2}}}{2 \left(e x +d \right)^{2} \left(b x +a \right) e^{2}}"," ",0,"-1/2*(2*b*e*x+a*e+b*d)*((b*x+a)^2)^(1/2)/(e*x+d)^2/e^2/(b*x+a)","A"
1551,1,42,66,0.040000," ","int(((b*x+a)^2)^(1/2)/(e*x+d)^4,x)","-\frac{\left(3 b e x +2 a e +b d \right) \sqrt{\left(b x +a \right)^{2}}}{6 \left(e x +d \right)^{3} \left(b x +a \right) e^{2}}"," ",0,"-1/6/e^2*(3*b*e*x+2*a*e+b*d)*((b*x+a)^2)^(1/2)/(e*x+d)^3/(b*x+a)","A"
1552,1,42,66,0.046000," ","int(((b*x+a)^2)^(1/2)/(e*x+d)^5,x)","-\frac{\left(4 b e x +3 a e +b d \right) \sqrt{\left(b x +a \right)^{2}}}{12 \left(e x +d \right)^{4} \left(b x +a \right) e^{2}}"," ",0,"-1/12/e^2*(4*b*e*x+3*a*e+b*d)*((b*x+a)^2)^(1/2)/(e*x+d)^4/(b*x+a)","A"
1553,1,42,66,0.045000," ","int(((b*x+a)^2)^(1/2)/(e*x+d)^6,x)","-\frac{\left(5 b e x +4 a e +b d \right) \sqrt{\left(b x +a \right)^{2}}}{20 \left(e x +d \right)^{5} \left(b x +a \right) e^{2}}"," ",0,"-1/20/e^2*(5*b*e*x+4*a*e+b*d)*((b*x+a)^2)^(1/2)/(e*x+d)^5/(b*x+a)","A"
1554,1,322,148,0.047000," ","int((e*x+d)^5*(b^2*x^2+2*a*b*x+a^2)^(3/2),x)","\frac{\left(56 b^{3} e^{5} x^{8}+189 x^{7} a \,b^{2} e^{5}+315 x^{7} b^{3} d \,e^{4}+216 x^{6} a^{2} b \,e^{5}+1080 x^{6} a \,b^{2} d \,e^{4}+720 x^{6} b^{3} d^{2} e^{3}+84 x^{5} a^{3} e^{5}+1260 x^{5} a^{2} b d \,e^{4}+2520 x^{5} a \,b^{2} d^{2} e^{3}+840 x^{5} b^{3} d^{3} e^{2}+504 a^{3} d \,e^{4} x^{4}+3024 a^{2} b \,d^{2} e^{3} x^{4}+3024 a \,b^{2} d^{3} e^{2} x^{4}+504 b^{3} d^{4} e \,x^{4}+1260 x^{3} a^{3} d^{2} e^{3}+3780 x^{3} a^{2} b \,d^{3} e^{2}+1890 x^{3} a \,b^{2} d^{4} e +126 x^{3} b^{3} d^{5}+1680 x^{2} a^{3} d^{3} e^{2}+2520 x^{2} a^{2} b \,d^{4} e +504 x^{2} a \,b^{2} d^{5}+1260 x \,a^{3} d^{4} e +756 x \,a^{2} b \,d^{5}+504 a^{3} d^{5}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}} x}{504 \left(b x +a \right)^{3}}"," ",0,"1/504*x*(56*b^3*e^5*x^8+189*a*b^2*e^5*x^7+315*b^3*d*e^4*x^7+216*a^2*b*e^5*x^6+1080*a*b^2*d*e^4*x^6+720*b^3*d^2*e^3*x^6+84*a^3*e^5*x^5+1260*a^2*b*d*e^4*x^5+2520*a*b^2*d^2*e^3*x^5+840*b^3*d^3*e^2*x^5+504*a^3*d*e^4*x^4+3024*a^2*b*d^2*e^3*x^4+3024*a*b^2*d^3*e^2*x^4+504*b^3*d^4*e*x^4+1260*a^3*d^2*e^3*x^3+3780*a^2*b*d^3*e^2*x^3+1890*a*b^2*d^4*e*x^3+126*b^3*d^5*x^3+1680*a^3*d^3*e^2*x^2+2520*a^2*b*d^4*e*x^2+504*a*b^2*d^5*x^2+1260*a^3*d^4*e*x+756*a^2*b*d^5*x+504*a^3*d^5)*((b*x+a)^2)^(3/2)/(b*x+a)^3","B"
1555,1,264,148,0.045000," ","int((e*x+d)^4*(b^2*x^2+2*a*b*x+a^2)^(3/2),x)","\frac{\left(35 b^{3} e^{4} x^{7}+120 x^{6} a \,b^{2} e^{4}+160 x^{6} b^{3} d \,e^{3}+140 x^{5} a^{2} b \,e^{4}+560 x^{5} a \,b^{2} d \,e^{3}+280 x^{5} b^{3} d^{2} e^{2}+56 x^{4} a^{3} e^{4}+672 x^{4} a^{2} b d \,e^{3}+1008 x^{4} a \,b^{2} d^{2} e^{2}+224 x^{4} b^{3} d^{3} e +280 x^{3} a^{3} d \,e^{3}+1260 x^{3} a^{2} b \,d^{2} e^{2}+840 x^{3} a \,b^{2} d^{3} e +70 x^{3} b^{3} d^{4}+560 a^{3} d^{2} e^{2} x^{2}+1120 a^{2} b \,d^{3} e \,x^{2}+280 a \,b^{2} d^{4} x^{2}+560 x \,a^{3} d^{3} e +420 x \,a^{2} b \,d^{4}+280 a^{3} d^{4}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}} x}{280 \left(b x +a \right)^{3}}"," ",0,"1/280*x*(35*b^3*e^4*x^7+120*a*b^2*e^4*x^6+160*b^3*d*e^3*x^6+140*a^2*b*e^4*x^5+560*a*b^2*d*e^3*x^5+280*b^3*d^2*e^2*x^5+56*a^3*e^4*x^4+672*a^2*b*d*e^3*x^4+1008*a*b^2*d^2*e^2*x^4+224*b^3*d^3*e*x^4+280*a^3*d*e^3*x^3+1260*a^2*b*d^2*e^2*x^3+840*a*b^2*d^3*e*x^3+70*b^3*d^4*x^3+560*a^3*d^2*e^2*x^2+1120*a^2*b*d^3*e*x^2+280*a*b^2*d^4*x^2+560*a^3*d^3*e*x+420*a^2*b*d^4*x+280*a^3*d^4)*((b*x+a)^2)^(3/2)/(b*x+a)^3","A"
1556,1,206,120,0.047000," ","int((e*x+d)^3*(b^2*x^2+2*a*b*x+a^2)^(3/2),x)","\frac{\left(20 b^{3} e^{3} x^{6}+70 x^{5} a \,b^{2} e^{3}+70 x^{5} b^{3} d \,e^{2}+84 x^{4} a^{2} b \,e^{3}+252 x^{4} a \,b^{2} d \,e^{2}+84 x^{4} b^{3} d^{2} e +35 x^{3} a^{3} e^{3}+315 x^{3} a^{2} b d \,e^{2}+315 x^{3} a \,b^{2} d^{2} e +35 x^{3} b^{3} d^{3}+140 a^{3} d \,e^{2} x^{2}+420 a^{2} b \,d^{2} e \,x^{2}+140 a \,b^{2} d^{3} x^{2}+210 x \,a^{3} d^{2} e +210 x \,a^{2} b \,d^{3}+140 a^{3} d^{3}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}} x}{140 \left(b x +a \right)^{3}}"," ",0,"1/140*x*(20*b^3*e^3*x^6+70*a*b^2*e^3*x^5+70*b^3*d*e^2*x^5+84*a^2*b*e^3*x^4+252*a*b^2*d*e^2*x^4+84*b^3*d^2*e*x^4+35*a^3*e^3*x^3+315*a^2*b*d*e^2*x^3+315*a*b^2*d^2*e*x^3+35*b^3*d^3*x^3+140*a^3*d*e^2*x^2+420*a^2*b*d^2*e*x^2+140*a*b^2*d^3*x^2+210*a^3*d^2*e*x+210*a^2*b*d^3*x+140*a^3*d^3)*((b*x+a)^2)^(3/2)/(b*x+a)^3","A"
1557,1,148,102,0.047000," ","int((e*x+d)^2*(b^2*x^2+2*a*b*x+a^2)^(3/2),x)","\frac{\left(10 b^{3} e^{2} x^{5}+36 x^{4} e^{2} a \,b^{2}+24 x^{4} b^{3} d e +45 x^{3} e^{2} a^{2} b +90 x^{3} d e a \,b^{2}+15 x^{3} d^{2} b^{3}+20 x^{2} a^{3} e^{2}+120 x^{2} d e \,a^{2} b +60 x^{2} a \,b^{2} d^{2}+60 x d e \,a^{3}+90 x \,d^{2} a^{2} b +60 a^{3} d^{2}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}} x}{60 \left(b x +a \right)^{3}}"," ",0,"1/60*x*(10*b^3*e^2*x^5+36*a*b^2*e^2*x^4+24*b^3*d*e*x^4+45*a^2*b*e^2*x^3+90*a*b^2*d*e*x^3+15*b^3*d^2*x^3+20*a^3*e^2*x^2+120*a^2*b*d*e*x^2+60*a*b^2*d^2*x^2+60*a^3*d*e*x+90*a^2*b*d^2*x+60*a^3*d^2)*((b*x+a)^2)^(3/2)/(b*x+a)^3","A"
1558,1,90,61,0.039000," ","int((e*x+d)*(b^2*x^2+2*a*b*x+a^2)^(3/2),x)","\frac{\left(4 e \,b^{3} x^{4}+15 x^{3} e a \,b^{2}+5 x^{3} b^{3} d +20 a^{2} b e \,x^{2}+20 a \,b^{2} d \,x^{2}+10 a^{3} e x +30 x d \,a^{2} b +20 a^{3} d \right) \left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}} x}{20 \left(b x +a \right)^{3}}"," ",0,"1/20*x*(4*b^3*e*x^4+15*a*b^2*e*x^3+5*b^3*d*x^3+20*a^2*b*e*x^2+20*a*b^2*d*x^2+10*a^3*e*x+30*a^2*b*d*x+20*a^3*d)*((b*x+a)^2)^(3/2)/(b*x+a)^3","A"
1559,1,49,28,0.040000," ","int((b^2*x^2+2*a*b*x+a^2)^(3/2),x)","\frac{\left(b^{3} x^{3}+4 a \,b^{2} x^{2}+6 a^{2} b x +4 a^{3}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}} x}{4 \left(b x +a \right)^{3}}"," ",0,"1/4*x*(b^3*x^3+4*a*b^2*x^2+6*a^2*b*x+4*a^3)*((b*x+a)^2)^(3/2)/(b*x+a)^3","A"
1560,1,149,118,0.057000," ","int((b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d),x)","\frac{\left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}} \left(2 b^{3} e^{3} x^{3}+9 a \,b^{2} e^{3} x^{2}-3 b^{3} d \,e^{2} x^{2}+6 a^{3} e^{3} \ln \left(e x +d \right)-18 a^{2} b d \,e^{2} \ln \left(e x +d \right)+18 a^{2} b \,e^{3} x +18 a \,b^{2} d^{2} e \ln \left(e x +d \right)-18 a \,b^{2} d \,e^{2} x -6 b^{3} d^{3} \ln \left(e x +d \right)+6 b^{3} d^{2} e x \right)}{6 \left(b x +a \right)^{3} e^{4}}"," ",0,"1/6*((b*x+a)^2)^(3/2)*(2*x^3*b^3*e^3+9*x^2*a*b^2*e^3-3*x^2*b^3*d*e^2+6*ln(e*x+d)*a^3*e^3-18*ln(e*x+d)*a^2*b*d*e^2+18*ln(e*x+d)*a*b^2*d^2*e-6*ln(e*x+d)*b^3*d^3+18*x*a^2*b*e^3-18*x*a*b^2*d*e^2+6*x*b^3*d^2*e)/(b*x+a)^3/e^4","A"
1561,1,216,137,0.062000," ","int((b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^2,x)","\frac{\left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}} \left(b^{3} e^{3} x^{3}+6 a^{2} b \,e^{3} x \ln \left(e x +d \right)-12 a \,b^{2} d \,e^{2} x \ln \left(e x +d \right)+6 a \,b^{2} e^{3} x^{2}+6 b^{3} d^{2} e x \ln \left(e x +d \right)-3 b^{3} d \,e^{2} x^{2}+6 a^{2} b d \,e^{2} \ln \left(e x +d \right)-12 a \,b^{2} d^{2} e \ln \left(e x +d \right)+6 a \,b^{2} d \,e^{2} x +6 b^{3} d^{3} \ln \left(e x +d \right)-4 b^{3} d^{2} e x -2 a^{3} e^{3}+6 a^{2} b d \,e^{2}-6 a \,b^{2} d^{2} e +2 b^{3} d^{3}\right)}{2 \left(b x +a \right)^{3} \left(e x +d \right) e^{4}}"," ",0,"1/2*((b*x+a)^2)^(3/2)*(b^3*e^3*x^3+6*ln(e*x+d)*x*a^2*b*e^3-12*ln(e*x+d)*x*a*b^2*d*e^2+6*ln(e*x+d)*x*b^3*d^2*e+6*a*b^2*e^3*x^2-3*b^3*d*e^2*x^2+6*a^2*b*d*e^2*ln(e*x+d)-12*a*b^2*d^2*e*ln(e*x+d)+6*b^3*d^3*ln(e*x+d)+6*a*b^2*d*e^2*x-4*b^3*d^2*e*x-2*a^3*e^3+6*a^2*b*d*e^2-6*a*b^2*d^2*e+2*b^3*d^3)/(b*x+a)^3/e^4/(e*x+d)","A"
1562,1,219,140,0.059000," ","int((b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^3,x)","\frac{\left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}} \left(6 a \,b^{2} e^{3} x^{2} \ln \left(e x +d \right)-6 b^{3} d \,e^{2} x^{2} \ln \left(e x +d \right)+2 b^{3} e^{3} x^{3}+12 a \,b^{2} d \,e^{2} x \ln \left(e x +d \right)-12 b^{3} d^{2} e x \ln \left(e x +d \right)+4 b^{3} d \,e^{2} x^{2}-6 a^{2} b \,e^{3} x +6 a \,b^{2} d^{2} e \ln \left(e x +d \right)+12 a \,b^{2} d \,e^{2} x -6 b^{3} d^{3} \ln \left(e x +d \right)-4 b^{3} d^{2} e x -a^{3} e^{3}-3 a^{2} b d \,e^{2}+9 a \,b^{2} d^{2} e -5 b^{3} d^{3}\right)}{2 \left(b x +a \right)^{3} \left(e x +d \right)^{2} e^{4}}"," ",0,"1/2*((b*x+a)^2)^(3/2)*(6*ln(e*x+d)*x^2*a*b^2*e^3-6*ln(e*x+d)*x^2*b^3*d*e^2+2*b^3*e^3*x^3+12*a*b^2*d*e^2*x*ln(e*x+d)-12*b^3*d^2*e*x*ln(e*x+d)+4*b^3*d*e^2*x^2+6*a*b^2*d^2*e*ln(e*x+d)-6*b^3*d^3*ln(e*x+d)-6*a^2*b*e^3*x+12*a*b^2*d*e^2*x-4*b^3*d^2*e*x-a^3*e^3-3*a^2*b*d*e^2+9*a*b^2*d^2*e-5*b^3*d^3)/(b*x+a)^3/e^4/(e*x+d)^2","A"
1563,1,186,146,0.054000," ","int((b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^4,x)","\frac{\left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}} \left(6 b^{3} e^{3} x^{3} \ln \left(e x +d \right)+18 b^{3} d \,e^{2} x^{2} \ln \left(e x +d \right)-18 a \,b^{2} e^{3} x^{2}+18 b^{3} d^{2} e x \ln \left(e x +d \right)+18 b^{3} d \,e^{2} x^{2}-9 a^{2} b \,e^{3} x -18 a \,b^{2} d \,e^{2} x +6 b^{3} d^{3} \ln \left(e x +d \right)+27 b^{3} d^{2} e x -2 a^{3} e^{3}-3 a^{2} b d \,e^{2}-6 a \,b^{2} d^{2} e +11 b^{3} d^{3}\right)}{6 \left(b x +a \right)^{3} \left(e x +d \right)^{3} e^{4}}"," ",0,"1/6*((b*x+a)^2)^(3/2)*(6*ln(e*x+d)*x^3*b^3*e^3+18*b^3*d*e^2*x^2*ln(e*x+d)+18*b^3*d^2*e*x*ln(e*x+d)-18*a*b^2*e^3*x^2+18*b^3*d*e^2*x^2+6*b^3*d^3*ln(e*x+d)-9*a^2*b*e^3*x-18*a*b^2*d*e^2*x+27*b^3*d^2*e*x-2*a^3*e^3-3*a^2*b*d*e^2-6*a*b^2*d^2*e+11*b^3*d^3)/(b*x+a)^3/e^4/(e*x+d)^3","A"
1564,1,128,35,0.048000," ","int((b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^5,x)","-\frac{\left(4 b^{3} e^{3} x^{3}+6 a \,b^{2} e^{3} x^{2}+6 b^{3} d \,e^{2} x^{2}+4 a^{2} b \,e^{3} x +4 a \,b^{2} d \,e^{2} x +4 b^{3} d^{2} e x +a^{3} e^{3}+a^{2} b d \,e^{2}+a \,b^{2} d^{2} e +b^{3} d^{3}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}}}{4 \left(e x +d \right)^{4} \left(b x +a \right)^{3} e^{4}}"," ",0,"-1/4*(4*b^3*e^3*x^3+6*a*b^2*e^3*x^2+6*b^3*d*e^2*x^2+4*a^2*b*e^3*x+4*a*b^2*d*e^2*x+4*b^3*d^2*e*x+a^3*e^3+a^2*b*d*e^2+a*b^2*d^2*e+b^3*d^3)*((b*x+a)^2)^(3/2)/(e*x+d)^4/e^4/(b*x+a)^3","B"
1565,1,131,72,0.049000," ","int((b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^6,x)","-\frac{\left(10 b^{3} e^{3} x^{3}+20 a \,b^{2} e^{3} x^{2}+10 b^{3} d \,e^{2} x^{2}+15 a^{2} b \,e^{3} x +10 a \,b^{2} d \,e^{2} x +5 b^{3} d^{2} e x +4 a^{3} e^{3}+3 a^{2} b d \,e^{2}+2 a \,b^{2} d^{2} e +b^{3} d^{3}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}}}{20 \left(e x +d \right)^{5} \left(b x +a \right)^{3} e^{4}}"," ",0,"-1/20/e^4*(10*b^3*e^3*x^3+20*a*b^2*e^3*x^2+10*b^3*d*e^2*x^2+15*a^2*b*e^3*x+10*a*b^2*d*e^2*x+5*b^3*d^2*e*x+4*a^3*e^3+3*a^2*b*d*e^2+2*a*b^2*d^2*e+b^3*d^3)*((b*x+a)^2)^(3/2)/(e*x+d)^5/(b*x+a)^3","A"
1566,1,131,131,0.048000," ","int((b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^7,x)","-\frac{\left(20 b^{3} e^{3} x^{3}+45 a \,b^{2} e^{3} x^{2}+15 b^{3} d \,e^{2} x^{2}+36 a^{2} b \,e^{3} x +18 a \,b^{2} d \,e^{2} x +6 b^{3} d^{2} e x +10 a^{3} e^{3}+6 a^{2} b d \,e^{2}+3 a \,b^{2} d^{2} e +b^{3} d^{3}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}}}{60 \left(e x +d \right)^{6} \left(b x +a \right)^{3} e^{4}}"," ",0,"-1/60/e^4*(20*b^3*e^3*x^3+45*a*b^2*e^3*x^2+15*b^3*d*e^2*x^2+36*a^2*b*e^3*x+18*a*b^2*d*e^2*x+6*b^3*d^2*e*x+10*a^3*e^3+6*a^2*b*d*e^2+3*a*b^2*d^2*e+b^3*d^3)*((b*x+a)^2)^(3/2)/(e*x+d)^6/(b*x+a)^3","A"
1567,1,131,148,0.045000," ","int((b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^8,x)","-\frac{\left(35 b^{3} e^{3} x^{3}+84 a \,b^{2} e^{3} x^{2}+21 b^{3} d \,e^{2} x^{2}+70 a^{2} b \,e^{3} x +28 a \,b^{2} d \,e^{2} x +7 b^{3} d^{2} e x +20 a^{3} e^{3}+10 a^{2} b d \,e^{2}+4 a \,b^{2} d^{2} e +b^{3} d^{3}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}}}{140 \left(e x +d \right)^{7} \left(b x +a \right)^{3} e^{4}}"," ",0,"-1/140/e^4*(35*b^3*e^3*x^3+84*a*b^2*e^3*x^2+21*b^3*d*e^2*x^2+70*a^2*b*e^3*x+28*a*b^2*d*e^2*x+7*b^3*d^2*e*x+20*a^3*e^3+10*a^2*b*d*e^2+4*a*b^2*d^2*e+b^3*d^3)*((b*x+a)^2)^(3/2)/(e*x+d)^7/(b*x+a)^3","A"
1568,1,131,148,0.052000," ","int((b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^9,x)","-\frac{\left(56 b^{3} e^{3} x^{3}+140 a \,b^{2} e^{3} x^{2}+28 b^{3} d \,e^{2} x^{2}+120 a^{2} b \,e^{3} x +40 a \,b^{2} d \,e^{2} x +8 b^{3} d^{2} e x +35 a^{3} e^{3}+15 a^{2} b d \,e^{2}+5 a \,b^{2} d^{2} e +b^{3} d^{3}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}}}{280 \left(e x +d \right)^{8} \left(b x +a \right)^{3} e^{4}}"," ",0,"-1/280/e^4*(56*b^3*e^3*x^3+140*a*b^2*e^3*x^2+28*b^3*d*e^2*x^2+120*a^2*b*e^3*x+40*a*b^2*d*e^2*x+8*b^3*d^2*e*x+35*a^3*e^3+15*a^2*b*d*e^2+5*a*b^2*d^2*e+b^3*d^3)*((b*x+a)^2)^(3/2)/(e*x+d)^8/(b*x+a)^3","A"
1569,1,506,188,0.049000," ","int((e*x+d)^5*(b^2*x^2+2*a*b*x+a^2)^(5/2),x)","\frac{\left(252 b^{5} e^{5} x^{10}+1386 x^{9} a \,b^{4} e^{5}+1386 x^{9} b^{5} d \,e^{4}+3080 x^{8} a^{2} b^{3} e^{5}+7700 x^{8} a \,b^{4} d \,e^{4}+3080 x^{8} b^{5} d^{2} e^{3}+3465 x^{7} a^{3} b^{2} e^{5}+17325 x^{7} a^{2} b^{3} d \,e^{4}+17325 x^{7} a \,b^{4} d^{2} e^{3}+3465 x^{7} b^{5} d^{3} e^{2}+1980 x^{6} a^{4} b \,e^{5}+19800 x^{6} a^{3} b^{2} d \,e^{4}+39600 x^{6} a^{2} b^{3} d^{2} e^{3}+19800 x^{6} a \,b^{4} d^{3} e^{2}+1980 x^{6} b^{5} d^{4} e +462 x^{5} a^{5} e^{5}+11550 x^{5} a^{4} b d \,e^{4}+46200 x^{5} a^{3} b^{2} d^{2} e^{3}+46200 x^{5} a^{2} b^{3} d^{3} e^{2}+11550 x^{5} a \,b^{4} d^{4} e +462 x^{5} b^{5} d^{5}+2772 a^{5} d \,e^{4} x^{4}+27720 a^{4} b \,d^{2} e^{3} x^{4}+55440 a^{3} b^{2} d^{3} e^{2} x^{4}+27720 a^{2} b^{3} d^{4} e \,x^{4}+2772 a \,b^{4} d^{5} x^{4}+6930 x^{3} a^{5} d^{2} e^{3}+34650 x^{3} a^{4} b \,d^{3} e^{2}+34650 x^{3} a^{3} b^{2} d^{4} e +6930 x^{3} a^{2} b^{3} d^{5}+9240 x^{2} a^{5} d^{3} e^{2}+23100 x^{2} a^{4} b \,d^{4} e +9240 x^{2} a^{3} b^{2} d^{5}+6930 x \,a^{5} d^{4} e +6930 x \,a^{4} b \,d^{5}+2772 a^{5} d^{5}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}} x}{2772 \left(b x +a \right)^{5}}"," ",0,"1/2772*x*(252*b^5*e^5*x^10+1386*a*b^4*e^5*x^9+1386*b^5*d*e^4*x^9+3080*a^2*b^3*e^5*x^8+7700*a*b^4*d*e^4*x^8+3080*b^5*d^2*e^3*x^8+3465*a^3*b^2*e^5*x^7+17325*a^2*b^3*d*e^4*x^7+17325*a*b^4*d^2*e^3*x^7+3465*b^5*d^3*e^2*x^7+1980*a^4*b*e^5*x^6+19800*a^3*b^2*d*e^4*x^6+39600*a^2*b^3*d^2*e^3*x^6+19800*a*b^4*d^3*e^2*x^6+1980*b^5*d^4*e*x^6+462*a^5*e^5*x^5+11550*a^4*b*d*e^4*x^5+46200*a^3*b^2*d^2*e^3*x^5+46200*a^2*b^3*d^3*e^2*x^5+11550*a*b^4*d^4*e*x^5+462*b^5*d^5*x^5+2772*a^5*d*e^4*x^4+27720*a^4*b*d^2*e^3*x^4+55440*a^3*b^2*d^3*e^2*x^4+27720*a^2*b^3*d^4*e*x^4+2772*a*b^4*d^5*x^4+6930*a^5*d^2*e^3*x^3+34650*a^4*b*d^3*e^2*x^3+34650*a^3*b^2*d^4*e*x^3+6930*a^2*b^3*d^5*x^3+9240*a^5*d^3*e^2*x^2+23100*a^4*b*d^4*e*x^2+9240*a^3*b^2*d^5*x^2+6930*a^5*d^4*e*x+6930*a^4*b*d^5*x+2772*a^5*d^5)*((b*x+a)^2)^(5/2)/(b*x+a)^5","B"
1570,1,414,154,0.049000," ","int((e*x+d)^4*(b^2*x^2+2*a*b*x+a^2)^(5/2),x)","\frac{\left(126 e^{4} b^{5} x^{9}+700 x^{8} e^{4} a \,b^{4}+560 x^{8} d \,e^{3} b^{5}+1575 x^{7} e^{4} a^{2} b^{3}+3150 x^{7} d \,e^{3} a \,b^{4}+945 x^{7} d^{2} e^{2} b^{5}+1800 x^{6} e^{4} a^{3} b^{2}+7200 x^{6} d \,e^{3} a^{2} b^{3}+5400 x^{6} d^{2} e^{2} a \,b^{4}+720 x^{6} d^{3} e \,b^{5}+1050 x^{5} e^{4} a^{4} b +8400 x^{5} d \,e^{3} a^{3} b^{2}+12600 x^{5} d^{2} e^{2} a^{2} b^{3}+4200 x^{5} d^{3} e a \,b^{4}+210 x^{5} d^{4} b^{5}+252 x^{4} e^{4} a^{5}+5040 x^{4} d \,e^{3} a^{4} b +15120 x^{4} d^{2} e^{2} a^{3} b^{2}+10080 x^{4} d^{3} e \,a^{2} b^{3}+1260 x^{4} d^{4} a \,b^{4}+1260 x^{3} d \,e^{3} a^{5}+9450 x^{3} d^{2} e^{2} a^{4} b +12600 x^{3} d^{3} e \,a^{3} b^{2}+3150 x^{3} d^{4} a^{2} b^{3}+2520 x^{2} d^{2} e^{2} a^{5}+8400 x^{2} d^{3} e \,a^{4} b +4200 x^{2} d^{4} a^{3} b^{2}+2520 x \,d^{3} e \,a^{5}+3150 x \,d^{4} a^{4} b +1260 d^{4} a^{5}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}} x}{1260 \left(b x +a \right)^{5}}"," ",0,"1/1260*x*(126*b^5*e^4*x^9+700*a*b^4*e^4*x^8+560*b^5*d*e^3*x^8+1575*a^2*b^3*e^4*x^7+3150*a*b^4*d*e^3*x^7+945*b^5*d^2*e^2*x^7+1800*a^3*b^2*e^4*x^6+7200*a^2*b^3*d*e^3*x^6+5400*a*b^4*d^2*e^2*x^6+720*b^5*d^3*e*x^6+1050*a^4*b*e^4*x^5+8400*a^3*b^2*d*e^3*x^5+12600*a^2*b^3*d^2*e^2*x^5+4200*a*b^4*d^3*e*x^5+210*b^5*d^4*x^5+252*a^5*e^4*x^4+5040*a^4*b*d*e^3*x^4+15120*a^3*b^2*d^2*e^2*x^4+10080*a^2*b^3*d^3*e*x^4+1260*a*b^4*d^4*x^4+1260*a^5*d*e^3*x^3+9450*a^4*b*d^2*e^2*x^3+12600*a^3*b^2*d^3*e*x^3+3150*a^2*b^3*d^4*x^3+2520*a^5*d^2*e^2*x^2+8400*a^4*b*d^3*e*x^2+4200*a^3*b^2*d^4*x^2+2520*a^5*d^3*e*x+3150*a^4*b*d^4*x+1260*a^5*d^4)*((b*x+a)^2)^(5/2)/(b*x+a)^5","B"
1571,1,322,120,0.046000," ","int((e*x+d)^3*(b^2*x^2+2*a*b*x+a^2)^(5/2),x)","\frac{\left(56 e^{3} b^{5} x^{8}+315 x^{7} e^{3} a \,b^{4}+189 x^{7} d \,e^{2} b^{5}+720 x^{6} e^{3} a^{2} b^{3}+1080 x^{6} d \,e^{2} a \,b^{4}+216 x^{6} d^{2} e \,b^{5}+840 x^{5} e^{3} a^{3} b^{2}+2520 x^{5} d \,e^{2} a^{2} b^{3}+1260 x^{5} d^{2} e a \,b^{4}+84 x^{5} d^{3} b^{5}+504 a^{4} b \,e^{3} x^{4}+3024 a^{3} b^{2} d \,e^{2} x^{4}+3024 a^{2} b^{3} d^{2} e \,x^{4}+504 a \,b^{4} d^{3} x^{4}+126 x^{3} e^{3} a^{5}+1890 x^{3} d \,e^{2} a^{4} b +3780 x^{3} d^{2} e \,a^{3} b^{2}+1260 x^{3} d^{3} a^{2} b^{3}+504 x^{2} d \,e^{2} a^{5}+2520 x^{2} d^{2} e \,a^{4} b +1680 x^{2} d^{3} a^{3} b^{2}+756 x \,d^{2} e \,a^{5}+1260 x \,d^{3} a^{4} b +504 d^{3} a^{5}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}} x}{504 \left(b x +a \right)^{5}}"," ",0,"1/504*x*(56*b^5*e^3*x^8+315*a*b^4*e^3*x^7+189*b^5*d*e^2*x^7+720*a^2*b^3*e^3*x^6+1080*a*b^4*d*e^2*x^6+216*b^5*d^2*e*x^6+840*a^3*b^2*e^3*x^5+2520*a^2*b^3*d*e^2*x^5+1260*a*b^4*d^2*e*x^5+84*b^5*d^3*x^5+504*a^4*b*e^3*x^4+3024*a^3*b^2*d*e^2*x^4+3024*a^2*b^3*d^2*e*x^4+504*a*b^4*d^3*x^4+126*a^5*e^3*x^3+1890*a^4*b*d*e^2*x^3+3780*a^3*b^2*d^2*e*x^3+1260*a^2*b^3*d^3*x^3+504*a^5*d*e^2*x^2+2520*a^4*b*d^2*e*x^2+1680*a^3*b^2*d^3*x^2+756*a^5*d^2*e*x+1260*a^4*b*d^3*x+504*a^5*d^3)*((b*x+a)^2)^(5/2)/(b*x+a)^5","B"
1572,1,230,86,0.045000," ","int((e*x+d)^2*(b^2*x^2+2*a*b*x+a^2)^(5/2),x)","\frac{\left(21 e^{2} b^{5} x^{7}+120 x^{6} e^{2} a \,b^{4}+48 x^{6} d e \,b^{5}+280 x^{5} e^{2} a^{2} b^{3}+280 x^{5} d e a \,b^{4}+28 x^{5} d^{2} b^{5}+336 a^{3} b^{2} e^{2} x^{4}+672 a^{2} b^{3} d e \,x^{4}+168 a \,b^{4} d^{2} x^{4}+210 x^{3} e^{2} a^{4} b +840 x^{3} d e \,a^{3} b^{2}+420 x^{3} d^{2} a^{2} b^{3}+56 x^{2} e^{2} a^{5}+560 x^{2} d e \,a^{4} b +560 x^{2} d^{2} a^{3} b^{2}+168 x d e \,a^{5}+420 x \,d^{2} a^{4} b +168 d^{2} a^{5}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}} x}{168 \left(b x +a \right)^{5}}"," ",0,"1/168*x*(21*b^5*e^2*x^7+120*a*b^4*e^2*x^6+48*b^5*d*e*x^6+280*a^2*b^3*e^2*x^5+280*a*b^4*d*e*x^5+28*b^5*d^2*x^5+336*a^3*b^2*e^2*x^4+672*a^2*b^3*d*e*x^4+168*a*b^4*d^2*x^4+210*a^4*b*e^2*x^3+840*a^3*b^2*d*e*x^3+420*a^2*b^3*d^2*x^3+56*a^5*e^2*x^2+560*a^4*b*d*e*x^2+560*a^3*b^2*d^2*x^2+168*a^5*d*e*x+420*a^4*b*d^2*x+168*a^5*d^2)*((b*x+a)^2)^(5/2)/(b*x+a)^5","B"
1573,1,138,61,0.054000," ","int((e*x+d)*(b^2*x^2+2*a*b*x+a^2)^(5/2),x)","\frac{\left(6 e \,b^{5} x^{6}+35 x^{5} e a \,b^{4}+7 x^{5} d \,b^{5}+84 a^{2} b^{3} e \,x^{4}+42 a \,b^{4} d \,x^{4}+105 x^{3} e \,a^{3} b^{2}+105 x^{3} d \,a^{2} b^{3}+70 x^{2} e \,a^{4} b +140 x^{2} d \,a^{3} b^{2}+21 x e \,a^{5}+105 x d \,a^{4} b +42 d \,a^{5}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}} x}{42 \left(b x +a \right)^{5}}"," ",0,"1/42*x*(6*b^5*e*x^6+35*a*b^4*e*x^5+7*b^5*d*x^5+84*a^2*b^3*e*x^4+42*a*b^4*d*x^4+105*a^3*b^2*e*x^3+105*a^2*b^3*d*x^3+70*a^4*b*e*x^2+140*a^3*b^2*d*x^2+21*a^5*e*x+105*a^4*b*d*x+42*a^5*d)*((b*x+a)^2)^(5/2)/(b*x+a)^5","B"
1574,1,71,28,0.044000," ","int((b^2*x^2+2*a*b*x+a^2)^(5/2),x)","\frac{\left(b^{5} x^{5}+6 a \,b^{4} x^{4}+15 a^{2} b^{3} x^{3}+20 a^{3} b^{2} x^{2}+15 a^{4} b x +6 a^{5}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}} x}{6 \left(b x +a \right)^{5}}"," ",0,"1/6*x*(b^5*x^5+6*a*b^4*x^4+15*a^2*b^3*x^3+20*a^3*b^2*x^2+15*a^4*b*x+6*a^5)*((b*x+a)^2)^(5/2)/(b*x+a)^5","B"
1575,1,318,180,0.056000," ","int((b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d),x)","\frac{\left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}} \left(12 b^{5} e^{5} x^{5}+75 a \,b^{4} e^{5} x^{4}-15 b^{5} d \,e^{4} x^{4}+200 a^{2} b^{3} e^{5} x^{3}-100 a \,b^{4} d \,e^{4} x^{3}+20 b^{5} d^{2} e^{3} x^{3}+300 a^{3} b^{2} e^{5} x^{2}-300 a^{2} b^{3} d \,e^{4} x^{2}+150 a \,b^{4} d^{2} e^{3} x^{2}-30 b^{5} d^{3} e^{2} x^{2}+60 a^{5} e^{5} \ln \left(e x +d \right)-300 a^{4} b d \,e^{4} \ln \left(e x +d \right)+300 a^{4} b \,e^{5} x +600 a^{3} b^{2} d^{2} e^{3} \ln \left(e x +d \right)-600 a^{3} b^{2} d \,e^{4} x -600 a^{2} b^{3} d^{3} e^{2} \ln \left(e x +d \right)+600 a^{2} b^{3} d^{2} e^{3} x +300 a \,b^{4} d^{4} e \ln \left(e x +d \right)-300 a \,b^{4} d^{3} e^{2} x -60 b^{5} d^{5} \ln \left(e x +d \right)+60 b^{5} d^{4} e x \right)}{60 \left(b x +a \right)^{5} e^{6}}"," ",0,"1/60*((b*x+a)^2)^(5/2)*(12*x^5*b^5*e^5+75*x^4*a*b^4*e^5-15*x^4*b^5*d*e^4+200*x^3*a^2*b^3*e^5-100*x^3*a*b^4*d*e^4+20*x^3*b^5*d^2*e^3+300*x^2*a^3*b^2*e^5-300*x^2*a^2*b^3*d*e^4+150*x^2*a*b^4*d^2*e^3-30*x^2*b^5*d^3*e^2+60*ln(e*x+d)*a^5*e^5-300*ln(e*x+d)*a^4*b*d*e^4+600*ln(e*x+d)*a^3*b^2*d^2*e^3-600*ln(e*x+d)*a^2*b^3*d^3*e^2+300*ln(e*x+d)*a*b^4*d^4*e-60*ln(e*x+d)*b^5*d^5+300*x*a^4*b*e^5-600*x*a^3*b^2*d*e^4+600*x*a^2*b^3*d^2*e^3-300*x*a*b^4*d^3*e^2+60*x*b^5*d^4*e)/(b*x+a)^5/e^6","A"
1576,1,456,222,0.063000," ","int((b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^2,x)","\frac{\left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}} \left(3 b^{5} e^{5} x^{5}+20 a \,b^{4} e^{5} x^{4}-5 b^{5} d \,e^{4} x^{4}+60 a^{2} b^{3} e^{5} x^{3}-40 a \,b^{4} d \,e^{4} x^{3}+10 b^{5} d^{2} e^{3} x^{3}+60 a^{4} b \,e^{5} x \ln \left(e x +d \right)-240 a^{3} b^{2} d \,e^{4} x \ln \left(e x +d \right)+120 a^{3} b^{2} e^{5} x^{2}+360 a^{2} b^{3} d^{2} e^{3} x \ln \left(e x +d \right)-180 a^{2} b^{3} d \,e^{4} x^{2}-240 a \,b^{4} d^{3} e^{2} x \ln \left(e x +d \right)+120 a \,b^{4} d^{2} e^{3} x^{2}+60 b^{5} d^{4} e x \ln \left(e x +d \right)-30 b^{5} d^{3} e^{2} x^{2}+60 a^{4} b d \,e^{4} \ln \left(e x +d \right)-240 a^{3} b^{2} d^{2} e^{3} \ln \left(e x +d \right)+120 a^{3} b^{2} d \,e^{4} x +360 a^{2} b^{3} d^{3} e^{2} \ln \left(e x +d \right)-240 a^{2} b^{3} d^{2} e^{3} x -240 a \,b^{4} d^{4} e \ln \left(e x +d \right)+180 a \,b^{4} d^{3} e^{2} x +60 b^{5} d^{5} \ln \left(e x +d \right)-48 b^{5} d^{4} e x -12 a^{5} e^{5}+60 a^{4} b d \,e^{4}-120 a^{3} b^{2} d^{2} e^{3}+120 a^{2} b^{3} d^{3} e^{2}-60 a \,b^{4} d^{4} e +12 b^{5} d^{5}\right)}{12 \left(b x +a \right)^{5} \left(e x +d \right) e^{6}}"," ",0,"1/12*((b*x+a)^2)^(5/2)*(60*d*e^4*a^4*b-120*a^3*b^2*d^2*e^3+120*a^2*b^3*d^3*e^2-60*a*b^4*d^4*e-240*ln(e*x+d)*x*a*b^4*d^3*e^2-240*ln(e*x+d)*x*a^3*b^2*d*e^4+360*ln(e*x+d)*x*a^2*b^3*d^2*e^3-12*a^5*e^5+360*a^2*b^3*d^3*e^2*ln(e*x+d)+12*b^5*d^5+120*a^3*b^2*e^5*x^2-30*b^5*d^3*e^2*x^2-48*b^5*d^4*e*x+20*a*b^4*e^5*x^4-5*b^5*d*e^4*x^4+60*a^2*b^3*e^5*x^3+10*b^5*d^2*e^3*x^3-240*a*b^4*d^4*e*ln(e*x+d)+120*a^3*b^2*d*e^4*x-240*a^2*b^3*d^2*e^3*x+180*a*b^4*d^3*e^2*x+3*b^5*e^5*x^5+60*b^5*d^5*ln(e*x+d)-180*a^2*b^3*d*e^4*x^2+120*a*b^4*d^2*e^3*x^2+60*a^4*b*d*e^4*ln(e*x+d)-240*a^3*b^2*d^2*e^3*ln(e*x+d)-40*a*b^4*d*e^4*x^3+60*ln(e*x+d)*x*a^4*b*e^5+60*ln(e*x+d)*x*b^5*d^4*e)/(b*x+a)^5/e^6/(e*x+d)","B"
1577,1,502,223,0.068000," ","int((b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^3,x)","\frac{\left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}} \left(2 b^{5} e^{5} x^{5}+15 a \,b^{4} e^{5} x^{4}-5 b^{5} d \,e^{4} x^{4}+60 a^{3} b^{2} e^{5} x^{2} \ln \left(e x +d \right)-180 a^{2} b^{3} d \,e^{4} x^{2} \ln \left(e x +d \right)+60 a^{2} b^{3} e^{5} x^{3}+180 a \,b^{4} d^{2} e^{3} x^{2} \ln \left(e x +d \right)-60 a \,b^{4} d \,e^{4} x^{3}-60 b^{5} d^{3} e^{2} x^{2} \ln \left(e x +d \right)+20 b^{5} d^{2} e^{3} x^{3}+120 a^{3} b^{2} d \,e^{4} x \ln \left(e x +d \right)-360 a^{2} b^{3} d^{2} e^{3} x \ln \left(e x +d \right)+120 a^{2} b^{3} d \,e^{4} x^{2}+360 a \,b^{4} d^{3} e^{2} x \ln \left(e x +d \right)-165 a \,b^{4} d^{2} e^{3} x^{2}-120 b^{5} d^{4} e x \ln \left(e x +d \right)+63 b^{5} d^{3} e^{2} x^{2}-30 a^{4} b \,e^{5} x +60 a^{3} b^{2} d^{2} e^{3} \ln \left(e x +d \right)+120 a^{3} b^{2} d \,e^{4} x -180 a^{2} b^{3} d^{3} e^{2} \ln \left(e x +d \right)-120 a^{2} b^{3} d^{2} e^{3} x +180 a \,b^{4} d^{4} e \ln \left(e x +d \right)+30 a \,b^{4} d^{3} e^{2} x -60 b^{5} d^{5} \ln \left(e x +d \right)+6 b^{5} d^{4} e x -3 a^{5} e^{5}-15 a^{4} b d \,e^{4}+90 a^{3} b^{2} d^{2} e^{3}-150 a^{2} b^{3} d^{3} e^{2}+105 a \,b^{4} d^{4} e -27 b^{5} d^{5}\right)}{6 \left(b x +a \right)^{5} \left(e x +d \right)^{2} e^{6}}"," ",0,"1/6*((b*x+a)^2)^(5/2)*(-15*a^4*b*d*e^4+90*a^3*b^2*d^2*e^3-150*a^2*b^3*d^3*e^2+105*a*b^4*d^4*e-180*ln(e*x+d)*x^2*a^2*b^3*d*e^4+180*ln(e*x+d)*x^2*a*b^4*d^2*e^3+360*a*b^4*d^3*e^2*x*ln(e*x+d)+120*a^3*b^2*d*e^4*x*ln(e*x+d)-360*a^2*b^3*d^2*e^3*x*ln(e*x+d)-3*a^5*e^5-180*a^2*b^3*d^3*e^2*ln(e*x+d)-27*b^5*d^5+63*b^5*d^3*e^2*x^2-30*a^4*b*e^5*x+6*b^5*d^4*e*x+15*a*b^4*e^5*x^4-5*b^5*d*e^4*x^4+60*a^2*b^3*e^5*x^3+20*b^5*d^2*e^3*x^3+60*ln(e*x+d)*x^2*a^3*b^2*e^5-60*ln(e*x+d)*x^2*b^5*d^3*e^2+180*a*b^4*d^4*e*ln(e*x+d)+120*a^3*b^2*d*e^4*x-120*a^2*b^3*d^2*e^3*x+30*a*b^4*d^3*e^2*x+2*b^5*e^5*x^5-60*b^5*d^5*ln(e*x+d)+120*a^2*b^3*d*e^4*x^2-165*a*b^4*d^2*e^3*x^2+60*a^3*b^2*d^2*e^3*ln(e*x+d)-60*a*b^4*d*e^4*x^3-120*b^5*d^4*e*x*ln(e*x+d))/(b*x+a)^5/e^6/(e*x+d)^2","B"
1578,1,502,220,0.063000," ","int((b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^4,x)","\frac{\left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}} \left(3 b^{5} e^{5} x^{5}+60 a^{2} b^{3} e^{5} x^{3} \ln \left(e x +d \right)-120 a \,b^{4} d \,e^{4} x^{3} \ln \left(e x +d \right)+30 a \,b^{4} e^{5} x^{4}+60 b^{5} d^{2} e^{3} x^{3} \ln \left(e x +d \right)-15 b^{5} d \,e^{4} x^{4}+180 a^{2} b^{3} d \,e^{4} x^{2} \ln \left(e x +d \right)-360 a \,b^{4} d^{2} e^{3} x^{2} \ln \left(e x +d \right)+90 a \,b^{4} d \,e^{4} x^{3}+180 b^{5} d^{3} e^{2} x^{2} \ln \left(e x +d \right)-63 b^{5} d^{2} e^{3} x^{3}-60 a^{3} b^{2} e^{5} x^{2}+180 a^{2} b^{3} d^{2} e^{3} x \ln \left(e x +d \right)+180 a^{2} b^{3} d \,e^{4} x^{2}-360 a \,b^{4} d^{3} e^{2} x \ln \left(e x +d \right)-90 a \,b^{4} d^{2} e^{3} x^{2}+180 b^{5} d^{4} e x \ln \left(e x +d \right)-9 b^{5} d^{3} e^{2} x^{2}-15 a^{4} b \,e^{5} x -60 a^{3} b^{2} d \,e^{4} x +60 a^{2} b^{3} d^{3} e^{2} \ln \left(e x +d \right)+270 a^{2} b^{3} d^{2} e^{3} x -120 a \,b^{4} d^{4} e \ln \left(e x +d \right)-270 a \,b^{4} d^{3} e^{2} x +60 b^{5} d^{5} \ln \left(e x +d \right)+81 b^{5} d^{4} e x -2 a^{5} e^{5}-5 a^{4} b d \,e^{4}-20 a^{3} b^{2} d^{2} e^{3}+110 a^{2} b^{3} d^{3} e^{2}-130 a \,b^{4} d^{4} e +47 b^{5} d^{5}\right)}{6 \left(b x +a \right)^{5} \left(e x +d \right)^{3} e^{6}}"," ",0,"1/6*((b*x+a)^2)^(5/2)*(-5*a^4*b*d*e^4-20*a^3*b^2*d^2*e^3+110*a^2*b^3*d^3*e^2-130*a*b^4*d^4*e+60*ln(e*x+d)*x^3*b^5*d^2*e^3-120*ln(e*x+d)*x^3*a*b^4*d*e^4+180*a^2*b^3*d*e^4*x^2*ln(e*x+d)-360*a*b^4*d^2*e^3*x^2*ln(e*x+d)-360*a*b^4*d^3*e^2*x*ln(e*x+d)+180*a^2*b^3*d^2*e^3*x*ln(e*x+d)-2*a^5*e^5+60*a^2*b^3*d^3*e^2*ln(e*x+d)+60*ln(e*x+d)*x^3*a^2*b^3*e^5+47*b^5*d^5-60*a^3*b^2*e^5*x^2-9*b^5*d^3*e^2*x^2-15*a^4*b*e^5*x+81*b^5*d^4*e*x+30*a*b^4*e^5*x^4-15*b^5*d*e^4*x^4-63*b^5*d^2*e^3*x^3+180*b^5*d^3*e^2*x^2*ln(e*x+d)-120*a*b^4*d^4*e*ln(e*x+d)-60*a^3*b^2*d*e^4*x+270*a^2*b^3*d^2*e^3*x-270*a*b^4*d^3*e^2*x+3*b^5*e^5*x^5+60*b^5*d^5*ln(e*x+d)+180*a^2*b^3*d*e^4*x^2-90*a*b^4*d^2*e^3*x^2+90*a*b^4*d*e^4*x^3+180*b^5*d^4*e*x*ln(e*x+d))/(b*x+a)^5/e^6/(e*x+d)^3","B"
1579,1,458,222,0.059000," ","int((b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^5,x)","\frac{\left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}} \left(60 a \,b^{4} e^{5} x^{4} \ln \left(e x +d \right)-60 b^{5} d \,e^{4} x^{4} \ln \left(e x +d \right)+12 b^{5} e^{5} x^{5}+240 a \,b^{4} d \,e^{4} x^{3} \ln \left(e x +d \right)-240 b^{5} d^{2} e^{3} x^{3} \ln \left(e x +d \right)+48 b^{5} d \,e^{4} x^{4}-120 a^{2} b^{3} e^{5} x^{3}+360 a \,b^{4} d^{2} e^{3} x^{2} \ln \left(e x +d \right)+240 a \,b^{4} d \,e^{4} x^{3}-360 b^{5} d^{3} e^{2} x^{2} \ln \left(e x +d \right)-48 b^{5} d^{2} e^{3} x^{3}-60 a^{3} b^{2} e^{5} x^{2}-180 a^{2} b^{3} d \,e^{4} x^{2}+240 a \,b^{4} d^{3} e^{2} x \ln \left(e x +d \right)+540 a \,b^{4} d^{2} e^{3} x^{2}-240 b^{5} d^{4} e x \ln \left(e x +d \right)-252 b^{5} d^{3} e^{2} x^{2}-20 a^{4} b \,e^{5} x -40 a^{3} b^{2} d \,e^{4} x -120 a^{2} b^{3} d^{2} e^{3} x +60 a \,b^{4} d^{4} e \ln \left(e x +d \right)+440 a \,b^{4} d^{3} e^{2} x -60 b^{5} d^{5} \ln \left(e x +d \right)-248 b^{5} d^{4} e x -3 a^{5} e^{5}-5 a^{4} b d \,e^{4}-10 a^{3} b^{2} d^{2} e^{3}-30 a^{2} b^{3} d^{3} e^{2}+125 a \,b^{4} d^{4} e -77 b^{5} d^{5}\right)}{12 \left(b x +a \right)^{5} \left(e x +d \right)^{4} e^{6}}"," ",0,"1/12*((b*x+a)^2)^(5/2)*(-5*a^4*b*d*e^4-10*a^3*b^2*d^2*e^3-30*a^2*b^3*d^3*e^2+125*a*b^4*d^4*e-240*b^5*d^2*e^3*x^3*ln(e*x+d)+240*a*b^4*d*e^4*x^3*ln(e*x+d)+360*a*b^4*d^2*e^3*x^2*ln(e*x+d)+240*a*b^4*d^3*e^2*x*ln(e*x+d)-3*a^5*e^5-60*ln(e*x+d)*x^4*b^5*d*e^4-77*b^5*d^5-60*a^3*b^2*e^5*x^2-252*b^5*d^3*e^2*x^2-20*a^4*b*e^5*x-248*b^5*d^4*e*x+48*b^5*d*e^4*x^4-120*a^2*b^3*e^5*x^3-48*b^5*d^2*e^3*x^3-360*b^5*d^3*e^2*x^2*ln(e*x+d)+60*ln(e*x+d)*x^4*a*b^4*e^5+60*a*b^4*d^4*e*ln(e*x+d)-40*a^3*b^2*d*e^4*x-120*a^2*b^3*d^2*e^3*x+440*a*b^4*d^3*e^2*x+12*b^5*e^5*x^5-60*b^5*d^5*ln(e*x+d)-180*a^2*b^3*d*e^4*x^2+540*a*b^4*d^2*e^3*x^2+240*a*b^4*d*e^4*x^3-240*b^5*d^4*e*x*ln(e*x+d))/(b*x+a)^5/e^6/(e*x+d)^4","B"
1580,1,383,228,0.065000," ","int((b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^6,x)","\frac{\left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}} \left(60 b^{5} e^{5} x^{5} \ln \left(e x +d \right)+300 b^{5} d \,e^{4} x^{4} \ln \left(e x +d \right)-300 a \,b^{4} e^{5} x^{4}+600 b^{5} d^{2} e^{3} x^{3} \ln \left(e x +d \right)+300 b^{5} d \,e^{4} x^{4}-300 a^{2} b^{3} e^{5} x^{3}-600 a \,b^{4} d \,e^{4} x^{3}+600 b^{5} d^{3} e^{2} x^{2} \ln \left(e x +d \right)+900 b^{5} d^{2} e^{3} x^{3}-200 a^{3} b^{2} e^{5} x^{2}-300 a^{2} b^{3} d \,e^{4} x^{2}-600 a \,b^{4} d^{2} e^{3} x^{2}+300 b^{5} d^{4} e x \ln \left(e x +d \right)+1100 b^{5} d^{3} e^{2} x^{2}-75 a^{4} b \,e^{5} x -100 a^{3} b^{2} d \,e^{4} x -150 a^{2} b^{3} d^{2} e^{3} x -300 a \,b^{4} d^{3} e^{2} x +60 b^{5} d^{5} \ln \left(e x +d \right)+625 b^{5} d^{4} e x -12 a^{5} e^{5}-15 a^{4} b d \,e^{4}-20 a^{3} b^{2} d^{2} e^{3}-30 a^{2} b^{3} d^{3} e^{2}-60 a \,b^{4} d^{4} e +137 b^{5} d^{5}\right)}{60 \left(b x +a \right)^{5} \left(e x +d \right)^{5} e^{6}}"," ",0,"1/60*((b*x+a)^2)^(5/2)*(-15*a^4*b*d*e^4-20*a^3*b^2*d^2*e^3-30*a^2*b^3*d^3*e^2-60*a*b^4*d^4*e+600*b^5*d^2*e^3*x^3*ln(e*x+d)-12*a^5*e^5+300*b^5*d*e^4*x^4*ln(e*x+d)+137*b^5*d^5+60*ln(e*x+d)*x^5*b^5*e^5-200*a^3*b^2*e^5*x^2+1100*b^5*d^3*e^2*x^2-75*a^4*b*e^5*x+625*b^5*d^4*e*x-300*a*b^4*e^5*x^4+300*b^5*d*e^4*x^4-300*a^2*b^3*e^5*x^3+900*b^5*d^2*e^3*x^3+600*b^5*d^3*e^2*x^2*ln(e*x+d)-100*a^3*b^2*d*e^4*x-150*a^2*b^3*d^2*e^3*x-300*a*b^4*d^3*e^2*x+60*b^5*d^5*ln(e*x+d)-300*a^2*b^3*d*e^4*x^2-600*a*b^4*d^2*e^3*x^2-600*a*b^4*d*e^4*x^3+300*b^5*d^4*e*x*ln(e*x+d))/(b*x+a)^5/e^6/(e*x+d)^5","A"
1581,1,283,35,0.048000," ","int((b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^7,x)","-\frac{\left(6 b^{5} e^{5} x^{5}+15 a \,b^{4} e^{5} x^{4}+15 b^{5} d \,e^{4} x^{4}+20 a^{2} b^{3} e^{5} x^{3}+20 a \,b^{4} d \,e^{4} x^{3}+20 b^{5} d^{2} e^{3} x^{3}+15 a^{3} b^{2} e^{5} x^{2}+15 a^{2} b^{3} d \,e^{4} x^{2}+15 a \,b^{4} d^{2} e^{3} x^{2}+15 b^{5} d^{3} e^{2} x^{2}+6 a^{4} b \,e^{5} x +6 a^{3} b^{2} d \,e^{4} x +6 a^{2} b^{3} d^{2} e^{3} x +6 a \,b^{4} d^{3} e^{2} x +6 b^{5} d^{4} e x +a^{5} e^{5}+a^{4} b d \,e^{4}+a^{3} b^{2} d^{2} e^{3}+a^{2} b^{3} d^{3} e^{2}+a \,b^{4} d^{4} e +b^{5} d^{5}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}}}{6 \left(e x +d \right)^{6} \left(b x +a \right)^{5} e^{6}}"," ",0,"-1/6*(6*b^5*e^5*x^5+15*a*b^4*e^5*x^4+15*b^5*d*e^4*x^4+20*a^2*b^3*e^5*x^3+20*a*b^4*d*e^4*x^3+20*b^5*d^2*e^3*x^3+15*a^3*b^2*e^5*x^2+15*a^2*b^3*d*e^4*x^2+15*a*b^4*d^2*e^3*x^2+15*b^5*d^3*e^2*x^2+6*a^4*b*e^5*x+6*a^3*b^2*d*e^4*x+6*a^2*b^3*d^2*e^3*x+6*a*b^4*d^3*e^2*x+6*b^5*d^4*e*x+a^5*e^5+a^4*b*d*e^4+a^3*b^2*d^2*e^3+a^2*b^3*d^3*e^2+a*b^4*d^4*e+b^5*d^5)*((b*x+a)^2)^(5/2)/(e*x+d)^6/e^6/(b*x+a)^5","B"
1582,1,288,72,0.049000," ","int((b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^8,x)","-\frac{\left(21 b^{5} e^{5} x^{5}+70 a \,b^{4} e^{5} x^{4}+35 b^{5} d \,e^{4} x^{4}+105 a^{2} b^{3} e^{5} x^{3}+70 a \,b^{4} d \,e^{4} x^{3}+35 b^{5} d^{2} e^{3} x^{3}+84 a^{3} b^{2} e^{5} x^{2}+63 a^{2} b^{3} d \,e^{4} x^{2}+42 a \,b^{4} d^{2} e^{3} x^{2}+21 b^{5} d^{3} e^{2} x^{2}+35 a^{4} b \,e^{5} x +28 a^{3} b^{2} d \,e^{4} x +21 a^{2} b^{3} d^{2} e^{3} x +14 a \,b^{4} d^{3} e^{2} x +7 b^{5} d^{4} e x +6 a^{5} e^{5}+5 a^{4} b d \,e^{4}+4 a^{3} b^{2} d^{2} e^{3}+3 a^{2} b^{3} d^{3} e^{2}+2 a \,b^{4} d^{4} e +b^{5} d^{5}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}}}{42 \left(e x +d \right)^{7} \left(b x +a \right)^{5} e^{6}}"," ",0,"-1/42/e^6*(21*b^5*e^5*x^5+70*a*b^4*e^5*x^4+35*b^5*d*e^4*x^4+105*a^2*b^3*e^5*x^3+70*a*b^4*d*e^4*x^3+35*b^5*d^2*e^3*x^3+84*a^3*b^2*e^5*x^2+63*a^2*b^3*d*e^4*x^2+42*a*b^4*d^2*e^3*x^2+21*b^5*d^3*e^2*x^2+35*a^4*b*e^5*x+28*a^3*b^2*d*e^4*x+21*a^2*b^3*d^2*e^3*x+14*a*b^4*d^3*e^2*x+7*b^5*d^4*e*x+6*a^5*e^5+5*a^4*b*d*e^4+4*a^3*b^2*d^2*e^3+3*a^2*b^3*d^3*e^2+2*a*b^4*d^4*e+b^5*d^5)*((b*x+a)^2)^(5/2)/(e*x+d)^7/(b*x+a)^5","B"
1583,1,288,110,0.050000," ","int((b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^9,x)","-\frac{\left(56 b^{5} e^{5} x^{5}+210 a \,b^{4} e^{5} x^{4}+70 b^{5} d \,e^{4} x^{4}+336 a^{2} b^{3} e^{5} x^{3}+168 a \,b^{4} d \,e^{4} x^{3}+56 b^{5} d^{2} e^{3} x^{3}+280 a^{3} b^{2} e^{5} x^{2}+168 a^{2} b^{3} d \,e^{4} x^{2}+84 a \,b^{4} d^{2} e^{3} x^{2}+28 b^{5} d^{3} e^{2} x^{2}+120 a^{4} b \,e^{5} x +80 a^{3} b^{2} d \,e^{4} x +48 a^{2} b^{3} d^{2} e^{3} x +24 a \,b^{4} d^{3} e^{2} x +8 b^{5} d^{4} e x +21 a^{5} e^{5}+15 a^{4} b d \,e^{4}+10 a^{3} b^{2} d^{2} e^{3}+6 a^{2} b^{3} d^{3} e^{2}+3 a \,b^{4} d^{4} e +b^{5} d^{5}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}}}{168 \left(e x +d \right)^{8} \left(b x +a \right)^{5} e^{6}}"," ",0,"-1/168/e^6*(56*b^5*e^5*x^5+210*a*b^4*e^5*x^4+70*b^5*d*e^4*x^4+336*a^2*b^3*e^5*x^3+168*a*b^4*d*e^4*x^3+56*b^5*d^2*e^3*x^3+280*a^3*b^2*e^5*x^2+168*a^2*b^3*d*e^4*x^2+84*a*b^4*d^2*e^3*x^2+28*b^5*d^3*e^2*x^2+120*a^4*b*e^5*x+80*a^3*b^2*d*e^4*x+48*a^2*b^3*d^2*e^3*x+24*a*b^4*d^3*e^2*x+8*b^5*d^4*e*x+21*a^5*e^5+15*a^4*b*d*e^4+10*a^3*b^2*d^2*e^3+6*a^2*b^3*d^3*e^2+3*a*b^4*d^4*e+b^5*d^5)*((b*x+a)^2)^(5/2)/(e*x+d)^8/(b*x+a)^5","B"
1584,1,288,148,0.053000," ","int((b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^10,x)","-\frac{\left(126 b^{5} e^{5} x^{5}+504 a \,b^{4} e^{5} x^{4}+126 b^{5} d \,e^{4} x^{4}+840 a^{2} b^{3} e^{5} x^{3}+336 a \,b^{4} d \,e^{4} x^{3}+84 b^{5} d^{2} e^{3} x^{3}+720 a^{3} b^{2} e^{5} x^{2}+360 a^{2} b^{3} d \,e^{4} x^{2}+144 a \,b^{4} d^{2} e^{3} x^{2}+36 b^{5} d^{3} e^{2} x^{2}+315 a^{4} b \,e^{5} x +180 a^{3} b^{2} d \,e^{4} x +90 a^{2} b^{3} d^{2} e^{3} x +36 a \,b^{4} d^{3} e^{2} x +9 b^{5} d^{4} e x +56 a^{5} e^{5}+35 a^{4} b d \,e^{4}+20 a^{3} b^{2} d^{2} e^{3}+10 a^{2} b^{3} d^{3} e^{2}+4 a \,b^{4} d^{4} e +b^{5} d^{5}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}}}{504 \left(e x +d \right)^{9} \left(b x +a \right)^{5} e^{6}}"," ",0,"-1/504/e^6*(126*b^5*e^5*x^5+504*a*b^4*e^5*x^4+126*b^5*d*e^4*x^4+840*a^2*b^3*e^5*x^3+336*a*b^4*d*e^4*x^3+84*b^5*d^2*e^3*x^3+720*a^3*b^2*e^5*x^2+360*a^2*b^3*d*e^4*x^2+144*a*b^4*d^2*e^3*x^2+36*b^5*d^3*e^2*x^2+315*a^4*b*e^5*x+180*a^3*b^2*d*e^4*x+90*a^2*b^3*d^2*e^3*x+36*a*b^4*d^3*e^2*x+9*b^5*d^4*e*x+56*a^5*e^5+35*a^4*b*d*e^4+20*a^3*b^2*d^2*e^3+10*a^2*b^3*d^3*e^2+4*a*b^4*d^4*e+b^5*d^5)*((b*x+a)^2)^(5/2)/(e*x+d)^9/(b*x+a)^5","A"
1585,1,288,230,0.052000," ","int((b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^11,x)","-\frac{\left(252 b^{5} e^{5} x^{5}+1050 a \,b^{4} e^{5} x^{4}+210 b^{5} d \,e^{4} x^{4}+1800 a^{2} b^{3} e^{5} x^{3}+600 a \,b^{4} d \,e^{4} x^{3}+120 b^{5} d^{2} e^{3} x^{3}+1575 a^{3} b^{2} e^{5} x^{2}+675 a^{2} b^{3} d \,e^{4} x^{2}+225 a \,b^{4} d^{2} e^{3} x^{2}+45 b^{5} d^{3} e^{2} x^{2}+700 a^{4} b \,e^{5} x +350 a^{3} b^{2} d \,e^{4} x +150 a^{2} b^{3} d^{2} e^{3} x +50 a \,b^{4} d^{3} e^{2} x +10 b^{5} d^{4} e x +126 a^{5} e^{5}+70 a^{4} b d \,e^{4}+35 a^{3} b^{2} d^{2} e^{3}+15 a^{2} b^{3} d^{3} e^{2}+5 a \,b^{4} d^{4} e +b^{5} d^{5}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}}}{1260 \left(e x +d \right)^{10} \left(b x +a \right)^{5} e^{6}}"," ",0,"-1/1260/e^6*(252*b^5*e^5*x^5+1050*a*b^4*e^5*x^4+210*b^5*d*e^4*x^4+1800*a^2*b^3*e^5*x^3+600*a*b^4*d*e^4*x^3+120*b^5*d^2*e^3*x^3+1575*a^3*b^2*e^5*x^2+675*a^2*b^3*d*e^4*x^2+225*a*b^4*d^2*e^3*x^2+45*b^5*d^3*e^2*x^2+700*a^4*b*e^5*x+350*a^3*b^2*d*e^4*x+150*a^2*b^3*d^2*e^3*x+50*a*b^4*d^3*e^2*x+10*b^5*d^4*e*x+126*a^5*e^5+70*a^4*b*d*e^4+35*a^3*b^2*d^2*e^3+15*a^2*b^3*d^3*e^2+5*a*b^4*d^4*e+b^5*d^5)*((b*x+a)^2)^(5/2)/(e*x+d)^10/(b*x+a)^5","A"
1586,1,288,230,0.056000," ","int((b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^12,x)","-\frac{\left(462 b^{5} e^{5} x^{5}+1980 a \,b^{4} e^{5} x^{4}+330 b^{5} d \,e^{4} x^{4}+3465 a^{2} b^{3} e^{5} x^{3}+990 a \,b^{4} d \,e^{4} x^{3}+165 b^{5} d^{2} e^{3} x^{3}+3080 a^{3} b^{2} e^{5} x^{2}+1155 a^{2} b^{3} d \,e^{4} x^{2}+330 a \,b^{4} d^{2} e^{3} x^{2}+55 b^{5} d^{3} e^{2} x^{2}+1386 a^{4} b \,e^{5} x +616 a^{3} b^{2} d \,e^{4} x +231 a^{2} b^{3} d^{2} e^{3} x +66 a \,b^{4} d^{3} e^{2} x +11 b^{5} d^{4} e x +252 a^{5} e^{5}+126 a^{4} b d \,e^{4}+56 a^{3} b^{2} d^{2} e^{3}+21 a^{2} b^{3} d^{3} e^{2}+6 a \,b^{4} d^{4} e +b^{5} d^{5}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}}}{2772 \left(e x +d \right)^{11} \left(b x +a \right)^{5} e^{6}}"," ",0,"-1/2772/e^6*(462*b^5*e^5*x^5+1980*a*b^4*e^5*x^4+330*b^5*d*e^4*x^4+3465*a^2*b^3*e^5*x^3+990*a*b^4*d*e^4*x^3+165*b^5*d^2*e^3*x^3+3080*a^3*b^2*e^5*x^2+1155*a^2*b^3*d*e^4*x^2+330*a*b^4*d^2*e^3*x^2+55*b^5*d^3*e^2*x^2+1386*a^4*b*e^5*x+616*a^3*b^2*d*e^4*x+231*a^2*b^3*d^2*e^3*x+66*a*b^4*d^3*e^2*x+11*b^5*d^4*e*x+252*a^5*e^5+126*a^4*b*d*e^4+56*a^3*b^2*d^2*e^3+21*a^2*b^3*d^3*e^2+6*a*b^4*d^4*e+b^5*d^5)*((b*x+a)^2)^(5/2)/(e*x+d)^11/(b*x+a)^5","A"
1587,1,223,161,0.061000," ","int((e*x+d)^4/((b*x+a)^2)^(1/2),x)","\frac{\left(b x +a \right) \left(3 b^{4} e^{4} x^{4}-4 a \,b^{3} e^{4} x^{3}+16 b^{4} d \,e^{3} x^{3}+6 a^{2} b^{2} e^{4} x^{2}-24 a \,b^{3} d \,e^{3} x^{2}+36 b^{4} d^{2} e^{2} x^{2}+12 a^{4} e^{4} \ln \left(b x +a \right)-48 a^{3} b d \,e^{3} \ln \left(b x +a \right)-12 a^{3} b \,e^{4} x +72 a^{2} b^{2} d^{2} e^{2} \ln \left(b x +a \right)+48 a^{2} b^{2} d \,e^{3} x -48 a \,b^{3} d^{3} e \ln \left(b x +a \right)-72 a \,b^{3} d^{2} e^{2} x +12 b^{4} d^{4} \ln \left(b x +a \right)+48 b^{4} d^{3} e x \right)}{12 \sqrt{\left(b x +a \right)^{2}}\, b^{5}}"," ",0,"1/12*(b*x+a)*(3*x^4*b^4*e^4-4*x^3*a*b^3*e^4+16*x^3*b^4*d*e^3+6*x^2*a^2*b^2*e^4-24*x^2*a*b^3*d*e^3+36*x^2*b^4*d^2*e^2+12*ln(b*x+a)*a^4*e^4-48*ln(b*x+a)*a^3*b*d*e^3+72*ln(b*x+a)*a^2*b^2*d^2*e^2-48*ln(b*x+a)*a*b^3*d^3*e+12*ln(b*x+a)*b^4*d^4-12*x*a^3*b*e^4+48*x*a^2*b^2*d*e^3-72*x*a*b^3*d^2*e^2+48*x*b^4*d^3*e)/((b*x+a)^2)^(1/2)/b^5","A"
1588,1,147,125,0.054000," ","int((e*x+d)^3/((b*x+a)^2)^(1/2),x)","-\frac{\left(b x +a \right) \left(-2 b^{3} e^{3} x^{3}+3 a \,b^{2} e^{3} x^{2}-9 b^{3} d \,e^{2} x^{2}+6 a^{3} e^{3} \ln \left(b x +a \right)-18 a^{2} b d \,e^{2} \ln \left(b x +a \right)-6 a^{2} b \,e^{3} x +18 a \,b^{2} d^{2} e \ln \left(b x +a \right)+18 a \,b^{2} d \,e^{2} x -6 b^{3} d^{3} \ln \left(b x +a \right)-18 b^{3} d^{2} e x \right)}{6 \sqrt{\left(b x +a \right)^{2}}\, b^{4}}"," ",0,"-1/6*(b*x+a)*(-2*b^3*e^3*x^3+3*a*b^2*e^3*x^2-9*b^3*d*e^2*x^2+6*ln(b*x+a)*a^3*e^3-18*ln(b*x+a)*a^2*b*d*e^2+18*ln(b*x+a)*a*b^2*d^2*e-6*ln(b*x+a)*b^3*d^3-6*a^2*b*e^3*x+18*a*b^2*d*e^2*x-18*b^3*d^2*e*x)/((b*x+a)^2)^(1/2)/b^4","A"
1589,1,87,89,0.048000," ","int((e*x+d)^2/((b*x+a)^2)^(1/2),x)","\frac{\left(b x +a \right) \left(b^{2} e^{2} x^{2}+2 a^{2} e^{2} \ln \left(b x +a \right)-4 a b d e \ln \left(b x +a \right)-2 a b \,e^{2} x +2 b^{2} d^{2} \ln \left(b x +a \right)+4 b^{2} d e x \right)}{2 \sqrt{\left(b x +a \right)^{2}}\, b^{3}}"," ",0,"1/2*(b*x+a)*(x^2*b^2*e^2+2*ln(b*x+a)*a^2*e^2-4*ln(b*x+a)*a*b*d*e+2*ln(b*x+a)*b^2*d^2-2*x*a*b*e^2+4*x*b^2*d*e)/((b*x+a)^2)^(1/2)/b^3","A"
1590,1,45,47,0.046000," ","int((e*x+d)/((b*x+a)^2)^(1/2),x)","-\frac{\left(b x +a \right) \left(a e \ln \left(b x +a \right)-b d \ln \left(b x +a \right)-b e x \right)}{\sqrt{\left(b x +a \right)^{2}}\, b^{2}}"," ",0,"-(b*x+a)*(ln(b*x+a)*a*e-ln(b*x+a)*b*d-b*e*x)/((b*x+a)^2)^(1/2)/b^2","A"
1591,1,25,24,0.044000," ","int(1/((b*x+a)^2)^(1/2),x)","\frac{\left(b x +a \right) \ln \left(b x +a \right)}{\sqrt{\left(b x +a \right)^{2}}\, b}"," ",0,"(b*x+a)/((b*x+a)^2)^(1/2)/b*ln(b*x+a)","A"
1592,1,42,64,0.054000," ","int(1/(e*x+d)/((b*x+a)^2)^(1/2),x)","-\frac{\left(b x +a \right) \left(\ln \left(b x +a \right)-\ln \left(e x +d \right)\right)}{\sqrt{\left(b x +a \right)^{2}}\, \left(a e -b d \right)}"," ",0,"-(b*x+a)*(ln(b*x+a)-ln(e*x+d))/((b*x+a)^2)^(1/2)/(a*e-b*d)","A"
1593,1,81,98,0.061000," ","int(1/(e*x+d)^2/((b*x+a)^2)^(1/2),x)","\frac{\left(b x +a \right) \left(b e x \ln \left(b x +a \right)-b e x \ln \left(e x +d \right)+b d \ln \left(b x +a \right)-b d \ln \left(e x +d \right)-a e +b d \right)}{\sqrt{\left(b x +a \right)^{2}}\, \left(a e -b d \right)^{2} \left(e x +d \right)}"," ",0,"(b*x+a)*(ln(b*x+a)*x*b*e-ln(e*x+d)*x*b*e+b*d*ln(b*x+a)-ln(e*x+d)*b*d-a*e+b*d)/((b*x+a)^2)^(1/2)/(a*e-b*d)^2/(e*x+d)","A"
1594,1,162,136,0.058000," ","int(1/(e*x+d)^3/((b*x+a)^2)^(1/2),x)","-\frac{\left(b x +a \right) \left(2 b^{2} e^{2} x^{2} \ln \left(b x +a \right)-2 b^{2} e^{2} x^{2} \ln \left(e x +d \right)+4 b^{2} d e x \ln \left(b x +a \right)-4 b^{2} d e x \ln \left(e x +d \right)-2 a b \,e^{2} x +2 b^{2} d^{2} \ln \left(b x +a \right)-2 b^{2} d^{2} \ln \left(e x +d \right)+2 b^{2} d e x +a^{2} e^{2}-4 a b d e +3 b^{2} d^{2}\right)}{2 \sqrt{\left(b x +a \right)^{2}}\, \left(a e -b d \right)^{3} \left(e x +d \right)^{2}}"," ",0,"-1/2*(b*x+a)*(2*ln(b*x+a)*x^2*b^2*e^2-2*ln(e*x+d)*x^2*b^2*e^2+4*ln(b*x+a)*x*b^2*d*e-4*ln(e*x+d)*x*b^2*d*e+2*b^2*d^2*ln(b*x+a)-2*ln(e*x+d)*b^2*d^2-2*a*b*e^2*x+2*b^2*d*e*x+a^2*e^2-4*a*b*d*e+3*b^2*d^2)/((b*x+a)^2)^(1/2)/(a*e-b*d)^3/(e*x+d)^2","A"
1595,1,256,172,0.064000," ","int(1/(e*x+d)^4/((b*x+a)^2)^(1/2),x)","\frac{\left(b x +a \right) \left(6 b^{3} e^{3} x^{3} \ln \left(b x +a \right)-6 b^{3} e^{3} x^{3} \ln \left(e x +d \right)+18 b^{3} d \,e^{2} x^{2} \ln \left(b x +a \right)-18 b^{3} d \,e^{2} x^{2} \ln \left(e x +d \right)-6 a \,b^{2} e^{3} x^{2}+18 b^{3} d^{2} e x \ln \left(b x +a \right)-18 b^{3} d^{2} e x \ln \left(e x +d \right)+6 b^{3} d \,e^{2} x^{2}+3 a^{2} b \,e^{3} x -18 a \,b^{2} d \,e^{2} x +6 b^{3} d^{3} \ln \left(b x +a \right)-6 b^{3} d^{3} \ln \left(e x +d \right)+15 b^{3} d^{2} e x -2 a^{3} e^{3}+9 a^{2} b d \,e^{2}-18 a \,b^{2} d^{2} e +11 b^{3} d^{3}\right)}{6 \sqrt{\left(b x +a \right)^{2}}\, \left(a e -b d \right)^{4} \left(e x +d \right)^{3}}"," ",0,"1/6*(b*x+a)*(6*ln(b*x+a)*x^3*b^3*e^3-6*b^3*e^3*x^3*ln(e*x+d)+18*ln(b*x+a)*x^2*b^3*d*e^2-18*b^3*d*e^2*x^2*ln(e*x+d)+18*ln(b*x+a)*x*b^3*d^2*e-18*b^3*d^2*e*x*ln(e*x+d)-6*a*b^2*e^3*x^2+6*b^3*d*e^2*x^2+6*b^3*d^3*ln(b*x+a)-6*b^3*d^3*ln(e*x+d)+3*a^2*b*e^3*x-18*a*b^2*d*e^2*x+15*b^3*d^2*e*x-2*a^3*e^3+9*a^2*b*d*e^2-18*a*b^2*d^2*e+11*b^3*d^3)/((b*x+a)^2)^(1/2)/(a*e-b*d)^4/(e*x+d)^3","A"
1596,1,341,151,0.061000," ","int((e*x+d)^4/(b^2*x^2+2*a*b*x+a^2)^(3/2),x)","\frac{\left(b^{4} e^{4} x^{4}+12 a^{2} b^{2} e^{4} x^{2} \ln \left(b x +a \right)-24 a \,b^{3} d \,e^{3} x^{2} \ln \left(b x +a \right)-4 a \,b^{3} e^{4} x^{3}+12 b^{4} d^{2} e^{2} x^{2} \ln \left(b x +a \right)+8 b^{4} d \,e^{3} x^{3}+24 a^{3} b \,e^{4} x \ln \left(b x +a \right)-48 a^{2} b^{2} d \,e^{3} x \ln \left(b x +a \right)-11 a^{2} b^{2} e^{4} x^{2}+24 a \,b^{3} d^{2} e^{2} x \ln \left(b x +a \right)+16 a \,b^{3} d \,e^{3} x^{2}+12 a^{4} e^{4} \ln \left(b x +a \right)-24 a^{3} b d \,e^{3} \ln \left(b x +a \right)+2 a^{3} b \,e^{4} x +12 a^{2} b^{2} d^{2} e^{2} \ln \left(b x +a \right)-16 a^{2} b^{2} d \,e^{3} x +24 a \,b^{3} d^{2} e^{2} x -8 b^{4} d^{3} e x +7 a^{4} e^{4}-20 a^{3} b d \,e^{3}+18 a^{2} b^{2} d^{2} e^{2}-4 a \,b^{3} d^{3} e -b^{4} d^{4}\right) \left(b x +a \right)}{2 \left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}} b^{5}}"," ",0,"1/2*(b^4*e^4*x^4+12*ln(b*x+a)*x^2*a^2*b^2*e^4-24*ln(b*x+a)*x^2*a*b^3*d*e^3+12*ln(b*x+a)*x^2*b^4*d^2*e^2-4*a*b^3*e^4*x^3+8*b^4*d*e^3*x^3+24*ln(b*x+a)*x*a^3*b*e^4-48*ln(b*x+a)*x*a^2*b^2*d*e^3+24*ln(b*x+a)*x*a*b^3*d^2*e^2-11*a^2*b^2*e^4*x^2+16*a*b^3*d*e^3*x^2+12*a^4*e^4*ln(b*x+a)-24*a^3*b*d*e^3*ln(b*x+a)+12*a^2*b^2*d^2*e^2*ln(b*x+a)+2*a^3*b*e^4*x-16*a^2*b^2*d*e^3*x+24*a*b^3*d^2*e^2*x-8*b^4*d^3*e*x+7*e^4*a^4-20*d*e^3*a^3*b+18*b^2*a^2*d^2*e^2-4*a*b^3*d^3*e-b^4*d^4)*(b*x+a)/b^5/((b*x+a)^2)^(3/2)","B"
1597,1,209,115,0.056000," ","int((e*x+d)^3/(b^2*x^2+2*a*b*x+a^2)^(3/2),x)","-\frac{\left(6 a \,b^{2} e^{3} x^{2} \ln \left(b x +a \right)-6 b^{3} d \,e^{2} x^{2} \ln \left(b x +a \right)-2 b^{3} e^{3} x^{3}+12 a^{2} b \,e^{3} x \ln \left(b x +a \right)-12 a \,b^{2} d \,e^{2} x \ln \left(b x +a \right)-4 a \,b^{2} e^{3} x^{2}+6 a^{3} e^{3} \ln \left(b x +a \right)-6 a^{2} b d \,e^{2} \ln \left(b x +a \right)+4 a^{2} b \,e^{3} x -12 a \,b^{2} d \,e^{2} x +6 b^{3} d^{2} e x +5 a^{3} e^{3}-9 a^{2} b d \,e^{2}+3 a \,b^{2} d^{2} e +b^{3} d^{3}\right) \left(b x +a \right)}{2 \left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}} b^{4}}"," ",0,"-1/2*(6*ln(b*x+a)*x^2*a*b^2*e^3-6*b^3*d*e^2*x^2*ln(b*x+a)-2*b^3*e^3*x^3+12*ln(b*x+a)*x*a^2*b*e^3-12*ln(b*x+a)*x*a*b^2*d*e^2-4*a*b^2*e^3*x^2+6*a^3*e^3*ln(b*x+a)-6*a^2*b*d*e^2*ln(b*x+a)+4*a^2*b*e^3*x-12*a*b^2*d*e^2*x+6*b^3*d^2*e*x+5*a^3*e^3-9*a^2*b*d*e^2+3*a*b^2*d^2*e+b^3*d^3)*(b*x+a)/b^4/((b*x+a)^2)^(3/2)","A"
1598,1,104,82,0.055000," ","int((e*x+d)^2/(b^2*x^2+2*a*b*x+a^2)^(3/2),x)","\frac{\left(2 b^{2} e^{2} x^{2} \ln \left(b x +a \right)+4 a b \,e^{2} x \ln \left(b x +a \right)+2 a^{2} e^{2} \ln \left(b x +a \right)+4 a b \,e^{2} x -4 b^{2} d e x +3 a^{2} e^{2}-2 a b d e -b^{2} d^{2}\right) \left(b x +a \right)}{2 \left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}} b^{3}}"," ",0,"1/2*(2*b^2*e^2*x^2*ln(b*x+a)+4*ln(b*x+a)*x*a*b*e^2+2*a^2*e^2*ln(b*x+a)+4*a*b*e^2*x-4*b^2*d*e*x+3*a^2*e^2-2*a*b*d*e-b^2*d^2)*(b*x+a)/b^3/((b*x+a)^2)^(3/2)","A"
1599,1,32,45,0.047000," ","int((e*x+d)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x)","-\frac{\left(b x +a \right) \left(2 b e x +a e +b d \right)}{2 \left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}} b^{2}}"," ",0,"-1/2*(b*x+a)*(2*b*e*x+a*e+b*d)/b^2/((b*x+a)^2)^(3/2)","A"
1600,1,20,21,0.044000," ","int(1/(b^2*x^2+2*a*b*x+a^2)^(3/2),x)","-\frac{b x +a}{2 \left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}} b}"," ",0,"-1/2*(b*x+a)/b/((b*x+a)^2)^(3/2)","A"
1601,1,156,119,0.066000," ","int(1/(e*x+d)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x)","-\frac{\left(2 b^{2} e^{2} x^{2} \ln \left(b x +a \right)-2 b^{2} e^{2} x^{2} \ln \left(e x +d \right)+4 a b \,e^{2} x \ln \left(b x +a \right)-4 a b \,e^{2} x \ln \left(e x +d \right)+2 a^{2} e^{2} \ln \left(b x +a \right)-2 a^{2} e^{2} \ln \left(e x +d \right)-2 a b \,e^{2} x +2 b^{2} d e x -3 a^{2} e^{2}+4 a b d e -b^{2} d^{2}\right) \left(b x +a \right)}{2 \left(a e -b d \right)^{3} \left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}}}"," ",0,"-1/2*(2*b^2*e^2*x^2*ln(b*x+a)-2*b^2*e^2*x^2*ln(e*x+d)+4*a*b*e^2*x*ln(b*x+a)-4*ln(e*x+d)*x*a*b*e^2+2*a^2*e^2*ln(b*x+a)-2*ln(e*x+d)*a^2*e^2-2*a*b*e^2*x+2*b^2*d*e*x-3*a^2*e^2+4*a*b*d*e-b^2*d^2)*(b*x+a)/(a*e-b*d)^3/((b*x+a)^2)^(3/2)","A"
1602,1,330,160,0.073000," ","int(1/(e*x+d)^2/(b^2*x^2+2*a*b*x+a^2)^(3/2),x)","\frac{\left(6 b^{3} e^{3} x^{3} \ln \left(b x +a \right)-6 b^{3} e^{3} x^{3} \ln \left(e x +d \right)+12 a \,b^{2} e^{3} x^{2} \ln \left(b x +a \right)-12 a \,b^{2} e^{3} x^{2} \ln \left(e x +d \right)+6 b^{3} d \,e^{2} x^{2} \ln \left(b x +a \right)-6 b^{3} d \,e^{2} x^{2} \ln \left(e x +d \right)+6 a^{2} b \,e^{3} x \ln \left(b x +a \right)-6 a^{2} b \,e^{3} x \ln \left(e x +d \right)+12 a \,b^{2} d \,e^{2} x \ln \left(b x +a \right)-12 a \,b^{2} d \,e^{2} x \ln \left(e x +d \right)-6 a \,b^{2} e^{3} x^{2}+6 b^{3} d \,e^{2} x^{2}+6 a^{2} b d \,e^{2} \ln \left(b x +a \right)-6 a^{2} b d \,e^{2} \ln \left(e x +d \right)-9 a^{2} b \,e^{3} x +6 a \,b^{2} d \,e^{2} x +3 b^{3} d^{2} e x -2 a^{3} e^{3}-3 a^{2} b d \,e^{2}+6 a \,b^{2} d^{2} e -b^{3} d^{3}\right) \left(b x +a \right)}{2 \left(e x +d \right) \left(a e -b d \right)^{4} \left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}}}"," ",0,"1/2*(6*b^3*e^3*x^3*ln(b*x+a)-6*b^3*e^3*x^3*ln(e*x+d)+12*a*b^2*e^3*x^2*ln(b*x+a)+6*b^3*d*e^2*x^2*ln(b*x+a)-12*ln(e*x+d)*x^2*a*b^2*e^3-6*b^3*d*e^2*x^2*ln(e*x+d)+6*a^2*b*e^3*x*ln(b*x+a)+12*a*b^2*d*e^2*x*ln(b*x+a)-6*ln(e*x+d)*x*a^2*b*e^3-12*ln(e*x+d)*x*a*b^2*d*e^2-6*a*b^2*e^3*x^2+6*b^3*d*e^2*x^2+6*a^2*b*d*e^2*ln(b*x+a)-6*a^2*b*d*e^2*ln(e*x+d)-9*a^2*b*e^3*x+6*a*b^2*d*e^2*x+3*b^3*d^2*e*x-2*a^3*e^3-3*a^2*b*d*e^2+6*a*b^2*d^2*e-b^3*d^3)*(b*x+a)/(e*x+d)/(a*e-b*d)^4/((b*x+a)^2)^(3/2)","B"
1603,1,508,206,0.068000," ","int(1/(e*x+d)^3/(b^2*x^2+2*a*b*x+a^2)^(3/2),x)","-\frac{\left(12 b^{4} e^{4} x^{4} \ln \left(b x +a \right)-12 b^{4} e^{4} x^{4} \ln \left(e x +d \right)+24 a \,b^{3} e^{4} x^{3} \ln \left(b x +a \right)-24 a \,b^{3} e^{4} x^{3} \ln \left(e x +d \right)+24 b^{4} d \,e^{3} x^{3} \ln \left(b x +a \right)-24 b^{4} d \,e^{3} x^{3} \ln \left(e x +d \right)+12 a^{2} b^{2} e^{4} x^{2} \ln \left(b x +a \right)-12 a^{2} b^{2} e^{4} x^{2} \ln \left(e x +d \right)+48 a \,b^{3} d \,e^{3} x^{2} \ln \left(b x +a \right)-48 a \,b^{3} d \,e^{3} x^{2} \ln \left(e x +d \right)-12 a \,b^{3} e^{4} x^{3}+12 b^{4} d^{2} e^{2} x^{2} \ln \left(b x +a \right)-12 b^{4} d^{2} e^{2} x^{2} \ln \left(e x +d \right)+12 b^{4} d \,e^{3} x^{3}+24 a^{2} b^{2} d \,e^{3} x \ln \left(b x +a \right)-24 a^{2} b^{2} d \,e^{3} x \ln \left(e x +d \right)-18 a^{2} b^{2} e^{4} x^{2}+24 a \,b^{3} d^{2} e^{2} x \ln \left(b x +a \right)-24 a \,b^{3} d^{2} e^{2} x \ln \left(e x +d \right)+18 b^{4} d^{2} e^{2} x^{2}-4 a^{3} b \,e^{4} x +12 a^{2} b^{2} d^{2} e^{2} \ln \left(b x +a \right)-12 a^{2} b^{2} d^{2} e^{2} \ln \left(e x +d \right)-24 a^{2} b^{2} d \,e^{3} x +24 a \,b^{3} d^{2} e^{2} x +4 b^{4} d^{3} e x +a^{4} e^{4}-8 a^{3} b d \,e^{3}+8 a \,b^{3} d^{3} e -b^{4} d^{4}\right) \left(b x +a \right)}{2 \left(e x +d \right)^{2} \left(a e -b d \right)^{5} \left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}}}"," ",0,"-1/2*(8*a*b^3*d^3*e+12*a^2*b^2*e^4*x^2*ln(b*x+a)-24*ln(e*x+d)*x*a^2*b^2*d*e^3-24*ln(e*x+d)*x*a*b^3*d^2*e^2-48*ln(e*x+d)*x^2*a*b^3*d*e^3-18*a^2*b^2*e^4*x^2+18*b^4*d^2*e^2*x^2-4*a^3*b*e^4*x+4*b^4*d^3*e*x-12*a*b^3*e^4*x^3+12*b^4*d*e^3*x^3+24*a*b^3*d^2*e^2*x*ln(b*x+a)+24*a^2*b^2*d*e^3*x*ln(b*x+a)+48*a*b^3*d*e^3*x^2*ln(b*x+a)-8*a^3*b*d*e^3-b^4*d^4+12*b^4*d^2*e^2*x^2*ln(b*x+a)+12*ln(b*x+a)*x^4*b^4*e^4-12*ln(e*x+d)*x^4*b^4*e^4+a^4*e^4+12*a^2*b^2*d^2*e^2*ln(b*x+a)-24*a^2*b^2*d*e^3*x+24*a*b^3*d^2*e^2*x+24*ln(b*x+a)*x^3*a*b^3*e^4+24*ln(b*x+a)*x^3*b^4*d*e^3-24*ln(e*x+d)*x^3*a*b^3*e^4-24*ln(e*x+d)*x^3*b^4*d*e^3-12*ln(e*x+d)*x^2*a^2*b^2*e^4-12*ln(e*x+d)*x^2*b^4*d^2*e^2-12*ln(e*x+d)*a^2*b^2*d^2*e^2)*(b*x+a)/(e*x+d)^2/(a*e-b*d)^5/((b*x+a)^2)^(3/2)","B"
1604,1,661,219,0.067000," ","int((e*x+d)^6/(b^2*x^2+2*a*b*x+a^2)^(5/2),x)","\frac{\left(2 b^{6} e^{6} x^{6}+60 a^{2} b^{4} e^{6} x^{4} \ln \left(b x +a \right)-120 a \,b^{5} d \,e^{5} x^{4} \ln \left(b x +a \right)-12 a \,b^{5} e^{6} x^{5}+60 b^{6} d^{2} e^{4} x^{4} \ln \left(b x +a \right)+24 b^{6} d \,e^{5} x^{5}+240 a^{3} b^{3} e^{6} x^{3} \ln \left(b x +a \right)-480 a^{2} b^{4} d \,e^{5} x^{3} \ln \left(b x +a \right)-68 a^{2} b^{4} e^{6} x^{4}+240 a \,b^{5} d^{2} e^{4} x^{3} \ln \left(b x +a \right)+96 a \,b^{5} d \,e^{5} x^{4}+360 a^{4} b^{2} e^{6} x^{2} \ln \left(b x +a \right)-720 a^{3} b^{3} d \,e^{5} x^{2} \ln \left(b x +a \right)-32 a^{3} b^{3} e^{6} x^{3}+360 a^{2} b^{4} d^{2} e^{4} x^{2} \ln \left(b x +a \right)-96 a^{2} b^{4} d \,e^{5} x^{3}+240 a \,b^{5} d^{2} e^{4} x^{3}-80 b^{6} d^{3} e^{3} x^{3}+240 a^{5} b \,e^{6} x \ln \left(b x +a \right)-480 a^{4} b^{2} d \,e^{5} x \ln \left(b x +a \right)+132 a^{4} b^{2} e^{6} x^{2}+240 a^{3} b^{3} d^{2} e^{4} x \ln \left(b x +a \right)-504 a^{3} b^{3} d \,e^{5} x^{2}+540 a^{2} b^{4} d^{2} e^{4} x^{2}-120 a \,b^{5} d^{3} e^{3} x^{2}-30 b^{6} d^{4} e^{2} x^{2}+60 a^{6} e^{6} \ln \left(b x +a \right)-120 a^{5} b d \,e^{5} \ln \left(b x +a \right)+168 a^{5} b \,e^{6} x +60 a^{4} b^{2} d^{2} e^{4} \ln \left(b x +a \right)-496 a^{4} b^{2} d \,e^{5} x +440 a^{3} b^{3} d^{2} e^{4} x -80 a^{2} b^{4} d^{3} e^{3} x -20 a \,b^{5} d^{4} e^{2} x -8 b^{6} d^{5} e x +57 a^{6} e^{6}-154 a^{5} b d \,e^{5}+125 a^{4} b^{2} d^{2} e^{4}-20 a^{3} b^{3} d^{3} e^{3}-5 a^{2} b^{4} d^{4} e^{2}-2 a \,b^{5} d^{5} e -b^{6} d^{6}\right) \left(b x +a \right)}{4 \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}} b^{7}}"," ",0,"1/4*(-720*ln(b*x+a)*x^2*a^3*b^3*d*e^5+360*ln(b*x+a)*x^2*a^2*b^4*d^2*e^4-480*ln(b*x+a)*x^3*a^2*b^4*d*e^5+240*ln(b*x+a)*x^3*a*b^5*d^2*e^4+240*ln(b*x+a)*x*a^3*b^3*d^2*e^4-120*ln(b*x+a)*x^4*a*b^5*d*e^5-154*a^5*b*d*e^5+125*d^2*e^4*a^4*b^2-480*ln(b*x+a)*x*a^4*b^2*d*e^5-2*d^5*e*a*b^5+57*a^6*e^6-b^6*d^6+2*x^6*b^6*e^6-68*x^4*a^2*b^4*e^6-32*x^3*a^3*b^3*e^6-12*x^5*a*b^5*e^6+24*x^5*b^6*d*e^5-8*x*b^6*d^5*e+132*x^2*a^4*b^2*e^6-30*x^2*b^6*d^4*e^2+168*x*a^5*b*e^6-80*x^3*b^6*d^3*e^3-20*a^3*b^3*d^3*e^3-5*d^4*a^2*b^4*e^2+60*ln(b*x+a)*a^6*e^6+96*x^4*a*b^5*d*e^5-96*x^3*a^2*b^4*d*e^5+60*ln(b*x+a)*x^4*a^2*b^4*e^6+60*ln(b*x+a)*x^4*b^6*d^2*e^4+240*ln(b*x+a)*x^3*a^3*b^3*e^6+360*ln(b*x+a)*x^2*a^4*b^2*e^6+240*ln(b*x+a)*x*a^5*b*e^6-120*ln(b*x+a)*a^5*b*d*e^5+60*ln(b*x+a)*a^4*b^2*d^2*e^4-496*x*a^4*b^2*d*e^5-504*x^2*a^3*b^3*d*e^5+440*x*a^3*b^3*d^2*e^4-80*x*a^2*b^4*d^3*e^3-20*x*a*b^5*d^4*e^2+240*x^3*a*b^5*d^2*e^4+540*x^2*a^2*b^4*d^2*e^4-120*x^2*a*b^5*d^3*e^3)*(b*x+a)/b^7/((b*x+a)^2)^(5/2)","B"
1605,1,449,183,0.067000," ","int((e*x+d)^5/(b^2*x^2+2*a*b*x+a^2)^(5/2),x)","-\frac{\left(60 a \,b^{4} e^{5} x^{4} \ln \left(b x +a \right)-60 b^{5} d \,e^{4} x^{4} \ln \left(b x +a \right)-12 b^{5} e^{5} x^{5}+240 a^{2} b^{3} e^{5} x^{3} \ln \left(b x +a \right)-240 a \,b^{4} d \,e^{4} x^{3} \ln \left(b x +a \right)-48 a \,b^{4} e^{5} x^{4}+360 a^{3} b^{2} e^{5} x^{2} \ln \left(b x +a \right)-360 a^{2} b^{3} d \,e^{4} x^{2} \ln \left(b x +a \right)+48 a^{2} b^{3} e^{5} x^{3}-240 a \,b^{4} d \,e^{4} x^{3}+120 b^{5} d^{2} e^{3} x^{3}+240 a^{4} b \,e^{5} x \ln \left(b x +a \right)-240 a^{3} b^{2} d \,e^{4} x \ln \left(b x +a \right)+252 a^{3} b^{2} e^{5} x^{2}-540 a^{2} b^{3} d \,e^{4} x^{2}+180 a \,b^{4} d^{2} e^{3} x^{2}+60 b^{5} d^{3} e^{2} x^{2}+60 a^{5} e^{5} \ln \left(b x +a \right)-60 a^{4} b d \,e^{4} \ln \left(b x +a \right)+248 a^{4} b \,e^{5} x -440 a^{3} b^{2} d \,e^{4} x +120 a^{2} b^{3} d^{2} e^{3} x +40 a \,b^{4} d^{3} e^{2} x +20 b^{5} d^{4} e x +77 a^{5} e^{5}-125 a^{4} b d \,e^{4}+30 a^{3} b^{2} d^{2} e^{3}+10 a^{2} b^{3} d^{3} e^{2}+5 a \,b^{4} d^{4} e +3 b^{5} d^{5}\right) \left(b x +a \right)}{12 \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}} b^{6}}"," ",0,"-1/12*(-125*a^4*b*d*e^4+30*a^3*b^2*d^2*e^3+10*a^2*b^3*d^3*e^2+5*a*b^4*d^4*e-240*ln(b*x+a)*x*a^3*b^2*d*e^4-240*ln(b*x+a)*x^3*a*b^4*d*e^4-360*ln(b*x+a)*x^2*a^2*b^3*d*e^4+77*a^5*e^5+3*b^5*d^5+60*ln(b*x+a)*a^5*e^5+252*a^3*b^2*e^5*x^2+60*b^5*d^3*e^2*x^2+248*a^4*b*e^5*x+20*b^5*d^4*e*x-48*a*b^4*e^5*x^4+48*a^2*b^3*e^5*x^3+120*b^5*d^2*e^3*x^3-440*a^3*b^2*d*e^4*x+120*a^2*b^3*d^2*e^3*x+40*a*b^4*d^3*e^2*x-12*b^5*e^5*x^5-540*a^2*b^3*d*e^4*x^2+180*a*b^4*d^2*e^3*x^2-240*a*b^4*d*e^4*x^3-60*ln(b*x+a)*x^4*b^5*d*e^4+240*ln(b*x+a)*x^3*a^2*b^3*e^5+360*ln(b*x+a)*x^2*a^3*b^2*e^5+60*ln(b*x+a)*x^4*a*b^4*e^5+240*ln(b*x+a)*x*a^4*b*e^5-60*ln(b*x+a)*a^4*b*d*e^4)*(b*x+a)/b^6/((b*x+a)^2)^(5/2)","B"
1606,1,267,150,0.058000," ","int((e*x+d)^4/(b^2*x^2+2*a*b*x+a^2)^(5/2),x)","\frac{\left(12 b^{4} e^{4} x^{4} \ln \left(b x +a \right)+48 a \,b^{3} e^{4} x^{3} \ln \left(b x +a \right)+72 a^{2} b^{2} e^{4} x^{2} \ln \left(b x +a \right)+48 a \,b^{3} e^{4} x^{3}-48 b^{4} d \,e^{3} x^{3}+48 a^{3} b \,e^{4} x \ln \left(b x +a \right)+108 a^{2} b^{2} e^{4} x^{2}-72 a \,b^{3} d \,e^{3} x^{2}-36 b^{4} d^{2} e^{2} x^{2}+12 a^{4} e^{4} \ln \left(b x +a \right)+88 a^{3} b \,e^{4} x -48 a^{2} b^{2} d \,e^{3} x -24 a \,b^{3} d^{2} e^{2} x -16 b^{4} d^{3} e x +25 a^{4} e^{4}-12 a^{3} b d \,e^{3}-6 a^{2} b^{2} d^{2} e^{2}-4 a \,b^{3} d^{3} e -3 b^{4} d^{4}\right) \left(b x +a \right)}{12 \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}} b^{5}}"," ",0,"1/12*(12*b^4*e^4*x^4*ln(b*x+a)+48*a*b^3*e^4*x^3*ln(b*x+a)+72*a^2*b^2*e^4*x^2*ln(b*x+a)+48*a*b^3*e^4*x^3-48*b^4*d*e^3*x^3+48*a^3*b*e^4*x*ln(b*x+a)+108*a^2*b^2*e^4*x^2-72*a*b^3*d*e^3*x^2-36*b^4*d^2*e^2*x^2+12*a^4*e^4*ln(b*x+a)+88*a^3*b*e^4*x-48*a^2*b^2*d*e^3*x-24*a*b^3*d^2*e^2*x-16*b^4*d^3*e*x+25*a^4*e^4-12*a^3*b*d*e^3-6*a^2*b^2*d^2*e^2-4*a*b^3*d^3*e-3*b^4*d^4)*(b*x+a)/b^5/((b*x+a)^2)^(5/2)","A"
1607,1,119,35,0.053000," ","int((e*x+d)^3/(b^2*x^2+2*a*b*x+a^2)^(5/2),x)","-\frac{\left(b x +a \right) \left(4 b^{3} e^{3} x^{3}+6 a \,b^{2} e^{3} x^{2}+6 b^{3} d \,e^{2} x^{2}+4 a^{2} b \,e^{3} x +4 a \,b^{2} d \,e^{2} x +4 b^{3} d^{2} e x +a^{3} e^{3}+a^{2} b d \,e^{2}+a \,b^{2} d^{2} e +b^{3} d^{3}\right)}{4 \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}} b^{4}}"," ",0,"-1/4*(b*x+a)*(4*b^3*e^3*x^3+6*a*b^2*e^3*x^2+6*b^3*d*e^2*x^2+4*a^2*b*e^3*x+4*a*b^2*d*e^2*x+4*b^3*d^2*e*x+a^3*e^3+a^2*b*d*e^2+a*b^2*d^2*e+b^3*d^3)/b^4/((b*x+a)^2)^(5/2)","B"
1608,1,69,86,0.051000," ","int((e*x+d)^2/(b^2*x^2+2*a*b*x+a^2)^(5/2),x)","-\frac{\left(b x +a \right) \left(6 b^{2} e^{2} x^{2}+4 a b \,e^{2} x +8 b^{2} d e x +a^{2} e^{2}+2 a b d e +3 b^{2} d^{2}\right)}{12 \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}} b^{3}}"," ",0,"-1/12*(b*x+a)/b^3*(6*b^2*e^2*x^2+4*a*b*e^2*x+8*b^2*d*e*x+a^2*e^2+2*a*b*d*e+3*b^2*d^2)/((b*x+a)^2)^(5/2)","A"
1609,1,33,63,0.046000," ","int((e*x+d)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x)","-\frac{\left(b x +a \right) \left(4 b e x +a e +3 b d \right)}{12 \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}} b^{2}}"," ",0,"-1/12*(b*x+a)/b^2*(4*b*e*x+a*e+3*b*d)/((b*x+a)^2)^(5/2)","A"
1610,1,20,30,0.046000," ","int(1/(b^2*x^2+2*a*b*x+a^2)^(5/2),x)","-\frac{b x +a}{4 \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}} b}"," ",0,"-1/4*(b*x+a)/b/((b*x+a)^2)^(5/2)","A"
1611,1,359,181,0.070000," ","int(1/(e*x+d)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x)","-\frac{\left(12 b^{4} e^{4} x^{4} \ln \left(b x +a \right)-12 b^{4} e^{4} x^{4} \ln \left(e x +d \right)+48 a \,b^{3} e^{4} x^{3} \ln \left(b x +a \right)-48 a \,b^{3} e^{4} x^{3} \ln \left(e x +d \right)+72 a^{2} b^{2} e^{4} x^{2} \ln \left(b x +a \right)-72 a^{2} b^{2} e^{4} x^{2} \ln \left(e x +d \right)-12 a \,b^{3} e^{4} x^{3}+12 b^{4} d \,e^{3} x^{3}+48 a^{3} b \,e^{4} x \ln \left(b x +a \right)-48 a^{3} b \,e^{4} x \ln \left(e x +d \right)-42 a^{2} b^{2} e^{4} x^{2}+48 a \,b^{3} d \,e^{3} x^{2}-6 b^{4} d^{2} e^{2} x^{2}+12 a^{4} e^{4} \ln \left(b x +a \right)-12 a^{4} e^{4} \ln \left(e x +d \right)-52 a^{3} b \,e^{4} x +72 a^{2} b^{2} d \,e^{3} x -24 a \,b^{3} d^{2} e^{2} x +4 b^{4} d^{3} e x -25 a^{4} e^{4}+48 a^{3} b d \,e^{3}-36 a^{2} b^{2} d^{2} e^{2}+16 a \,b^{3} d^{3} e -3 b^{4} d^{4}\right) \left(b x +a \right)}{12 \left(a e -b d \right)^{5} \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}}}"," ",0,"-1/12*(12*b^4*e^4*x^4*ln(b*x+a)-12*b^4*e^4*x^4*ln(e*x+d)+48*a*b^3*e^4*x^3*ln(b*x+a)-48*a*b^3*e^4*x^3*ln(e*x+d)+72*a^2*b^2*e^4*x^2*ln(b*x+a)-72*a^2*b^2*e^4*x^2*ln(e*x+d)-12*a*b^3*e^4*x^3+12*b^4*d*e^3*x^3+48*a^3*b*e^4*x*ln(b*x+a)-48*ln(e*x+d)*x*a^3*b*e^4-42*a^2*b^2*e^4*x^2+48*a*b^3*d*e^3*x^2-6*b^4*d^2*e^2*x^2+12*a^4*e^4*ln(b*x+a)-12*ln(e*x+d)*a^4*e^4-52*a^3*b*e^4*x+72*a^2*b^2*d*e^3*x-24*a*b^3*d^2*e^2*x+4*b^4*d^3*e*x-25*a^4*e^4+48*a^3*b*d*e^3-36*a^2*b^2*d^2*e^2+16*a*b^3*d^3*e-3*b^4*d^4)*(b*x+a)/(a*e-b*d)^5/((b*x+a)^2)^(5/2)","A"
1612,1,651,224,0.069000," ","int(1/(e*x+d)^2/(b^2*x^2+2*a*b*x+a^2)^(5/2),x)","\frac{\left(60 b^{5} e^{5} x^{5} \ln \left(b x +a \right)-60 b^{5} e^{5} x^{5} \ln \left(e x +d \right)+240 a \,b^{4} e^{5} x^{4} \ln \left(b x +a \right)-240 a \,b^{4} e^{5} x^{4} \ln \left(e x +d \right)+60 b^{5} d \,e^{4} x^{4} \ln \left(b x +a \right)-60 b^{5} d \,e^{4} x^{4} \ln \left(e x +d \right)+360 a^{2} b^{3} e^{5} x^{3} \ln \left(b x +a \right)-360 a^{2} b^{3} e^{5} x^{3} \ln \left(e x +d \right)+240 a \,b^{4} d \,e^{4} x^{3} \ln \left(b x +a \right)-240 a \,b^{4} d \,e^{4} x^{3} \ln \left(e x +d \right)-60 a \,b^{4} e^{5} x^{4}+60 b^{5} d \,e^{4} x^{4}+240 a^{3} b^{2} e^{5} x^{2} \ln \left(b x +a \right)-240 a^{3} b^{2} e^{5} x^{2} \ln \left(e x +d \right)+360 a^{2} b^{3} d \,e^{4} x^{2} \ln \left(b x +a \right)-360 a^{2} b^{3} d \,e^{4} x^{2} \ln \left(e x +d \right)-210 a^{2} b^{3} e^{5} x^{3}+180 a \,b^{4} d \,e^{4} x^{3}+30 b^{5} d^{2} e^{3} x^{3}+60 a^{4} b \,e^{5} x \ln \left(b x +a \right)-60 a^{4} b \,e^{5} x \ln \left(e x +d \right)+240 a^{3} b^{2} d \,e^{4} x \ln \left(b x +a \right)-240 a^{3} b^{2} d \,e^{4} x \ln \left(e x +d \right)-260 a^{3} b^{2} e^{5} x^{2}+150 a^{2} b^{3} d \,e^{4} x^{2}+120 a \,b^{4} d^{2} e^{3} x^{2}-10 b^{5} d^{3} e^{2} x^{2}+60 a^{4} b d \,e^{4} \ln \left(b x +a \right)-60 a^{4} b d \,e^{4} \ln \left(e x +d \right)-125 a^{4} b \,e^{5} x -20 a^{3} b^{2} d \,e^{4} x +180 a^{2} b^{3} d^{2} e^{3} x -40 a \,b^{4} d^{3} e^{2} x +5 b^{5} d^{4} e x -12 a^{5} e^{5}-65 a^{4} b d \,e^{4}+120 a^{3} b^{2} d^{2} e^{3}-60 a^{2} b^{3} d^{3} e^{2}+20 a \,b^{4} d^{4} e -3 b^{5} d^{5}\right) \left(b x +a \right)}{12 \left(e x +d \right) \left(a e -b d \right)^{6} \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}}}"," ",0,"1/12*(-240*ln(e*x+d)*x*a^3*b^2*d*e^4-65*a^4*b*d*e^4+120*a^3*b^2*d^2*e^3-60*a^2*b^3*d^3*e^2+20*a*b^4*d^4*e-240*a*b^4*d*e^4*x^3*ln(e*x+d)+240*a^3*b^2*d*e^4*x*ln(b*x+a)+240*a*b^4*d*e^4*x^3*ln(b*x+a)-360*a^2*b^3*d*e^4*x^2*ln(e*x+d)+360*a^2*b^3*d*e^4*x^2*ln(b*x+a)-12*a^5*e^5-60*b^5*d*e^4*x^4*ln(e*x+d)-360*a^2*b^3*e^5*x^3*ln(e*x+d)+60*ln(b*x+a)*x^5*b^5*e^5-3*b^5*d^5-60*b^5*e^5*x^5*ln(e*x+d)-260*a^3*b^2*e^5*x^2-10*b^5*d^3*e^2*x^2-125*a^4*b*e^5*x+5*b^5*d^4*e*x-60*a*b^4*e^5*x^4+60*b^5*d*e^4*x^4-210*a^2*b^3*e^5*x^3+30*b^5*d^2*e^3*x^3-240*a^3*b^2*e^5*x^2*ln(e*x+d)-240*a*b^4*e^5*x^4*ln(e*x+d)-20*a^3*b^2*d*e^4*x+180*a^2*b^3*d^2*e^3*x-40*a*b^4*d^3*e^2*x+150*a^2*b^3*d*e^4*x^2+120*a*b^4*d^2*e^3*x^2-60*a^4*b*d*e^4*ln(e*x+d)+180*a*b^4*d*e^4*x^3+60*b^5*d*e^4*x^4*ln(b*x+a)-60*ln(e*x+d)*x*a^4*b*e^5+360*a^2*b^3*e^5*x^3*ln(b*x+a)+240*a^3*b^2*e^5*x^2*ln(b*x+a)+240*a*b^4*e^5*x^4*ln(b*x+a)+60*a^4*b*e^5*x*ln(b*x+a)+60*a^4*b*d*e^4*ln(b*x+a))*(b*x+a)/(e*x+d)/(a*e-b*d)^6/((b*x+a)^2)^(5/2)","B"
1613,1,983,273,0.069000," ","int(1/(e*x+d)^3/(b^2*x^2+2*a*b*x+a^2)^(5/2),x)","-\frac{\left(60 b^{6} e^{6} x^{6} \ln \left(b x +a \right)-60 b^{6} e^{6} x^{6} \ln \left(e x +d \right)+240 a \,b^{5} e^{6} x^{5} \ln \left(b x +a \right)-240 a \,b^{5} e^{6} x^{5} \ln \left(e x +d \right)+120 b^{6} d \,e^{5} x^{5} \ln \left(b x +a \right)-120 b^{6} d \,e^{5} x^{5} \ln \left(e x +d \right)+360 a^{2} b^{4} e^{6} x^{4} \ln \left(b x +a \right)-360 a^{2} b^{4} e^{6} x^{4} \ln \left(e x +d \right)+480 a \,b^{5} d \,e^{5} x^{4} \ln \left(b x +a \right)-480 a \,b^{5} d \,e^{5} x^{4} \ln \left(e x +d \right)-60 a \,b^{5} e^{6} x^{5}+60 b^{6} d^{2} e^{4} x^{4} \ln \left(b x +a \right)-60 b^{6} d^{2} e^{4} x^{4} \ln \left(e x +d \right)+60 b^{6} d \,e^{5} x^{5}+240 a^{3} b^{3} e^{6} x^{3} \ln \left(b x +a \right)-240 a^{3} b^{3} e^{6} x^{3} \ln \left(e x +d \right)+720 a^{2} b^{4} d \,e^{5} x^{3} \ln \left(b x +a \right)-720 a^{2} b^{4} d \,e^{5} x^{3} \ln \left(e x +d \right)-210 a^{2} b^{4} e^{6} x^{4}+240 a \,b^{5} d^{2} e^{4} x^{3} \ln \left(b x +a \right)-240 a \,b^{5} d^{2} e^{4} x^{3} \ln \left(e x +d \right)+120 a \,b^{5} d \,e^{5} x^{4}+90 b^{6} d^{2} e^{4} x^{4}+60 a^{4} b^{2} e^{6} x^{2} \ln \left(b x +a \right)-60 a^{4} b^{2} e^{6} x^{2} \ln \left(e x +d \right)+480 a^{3} b^{3} d \,e^{5} x^{2} \ln \left(b x +a \right)-480 a^{3} b^{3} d \,e^{5} x^{2} \ln \left(e x +d \right)-260 a^{3} b^{3} e^{6} x^{3}+360 a^{2} b^{4} d^{2} e^{4} x^{2} \ln \left(b x +a \right)-360 a^{2} b^{4} d^{2} e^{4} x^{2} \ln \left(e x +d \right)-60 a^{2} b^{4} d \,e^{5} x^{3}+300 a \,b^{5} d^{2} e^{4} x^{3}+20 b^{6} d^{3} e^{3} x^{3}+120 a^{4} b^{2} d \,e^{5} x \ln \left(b x +a \right)-120 a^{4} b^{2} d \,e^{5} x \ln \left(e x +d \right)-125 a^{4} b^{2} e^{6} x^{2}+240 a^{3} b^{3} d^{2} e^{4} x \ln \left(b x +a \right)-240 a^{3} b^{3} d^{2} e^{4} x \ln \left(e x +d \right)-280 a^{3} b^{3} d \,e^{5} x^{2}+330 a^{2} b^{4} d^{2} e^{4} x^{2}+80 a \,b^{5} d^{3} e^{3} x^{2}-5 b^{6} d^{4} e^{2} x^{2}-12 a^{5} b \,e^{6} x +60 a^{4} b^{2} d^{2} e^{4} \ln \left(b x +a \right)-60 a^{4} b^{2} d^{2} e^{4} \ln \left(e x +d \right)-190 a^{4} b^{2} d \,e^{5} x +100 a^{3} b^{3} d^{2} e^{4} x +120 a^{2} b^{4} d^{3} e^{3} x -20 a \,b^{5} d^{4} e^{2} x +2 b^{6} d^{5} e x +2 a^{6} e^{6}-24 a^{5} b d \,e^{5}-35 a^{4} b^{2} d^{2} e^{4}+80 a^{3} b^{3} d^{3} e^{3}-30 a^{2} b^{4} d^{4} e^{2}+8 a \,b^{5} d^{5} e -b^{6} d^{6}\right) \left(b x +a \right)}{4 \left(e x +d \right)^{2} \left(a e -b d \right)^{7} \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}}}"," ",0,"-1/4*(480*a^3*b^3*d*e^5*x^2*ln(b*x+a)+360*a^2*b^4*d^2*e^4*x^2*ln(b*x+a)+720*a^2*b^4*d*e^5*x^3*ln(b*x+a)+240*a*b^5*d^2*e^4*x^3*ln(b*x+a)+240*a^3*b^3*d^2*e^4*x*ln(b*x+a)+480*a*b^5*d*e^5*x^4*ln(b*x+a)-24*a^5*b*d*e^5-35*a^4*b^2*d^2*e^4+120*a^4*b^2*d*e^5*x*ln(b*x+a)+8*a*b^5*d^5*e+2*a^6*e^6-b^6*d^6-210*a^2*b^4*e^6*x^4-260*a^3*b^3*e^6*x^3-60*a*b^5*e^6*x^5+60*b^6*d*e^5*x^5+2*b^6*d^5*e*x-125*a^4*b^2*e^6*x^2-5*b^6*d^4*e^2*x^2-12*a^5*b*e^6*x+20*b^6*d^3*e^3*x^3+80*a^3*b^3*d^3*e^3-30*a^2*b^4*d^4*e^2+90*x^4*b^6*d^2*e^4+60*ln(b*x+a)*x^6*b^6*e^6-60*ln(e*x+d)*x^6*b^6*e^6-240*ln(e*x+d)*x^3*a*b^5*d^2*e^4-480*ln(e*x+d)*x^2*a^3*b^3*d*e^5-360*ln(e*x+d)*x^2*a^2*b^4*d^2*e^4-120*ln(e*x+d)*x*a^4*b^2*d*e^5-240*ln(e*x+d)*x*a^3*b^3*d^2*e^4-480*ln(e*x+d)*x^4*a*b^5*d*e^5-720*ln(e*x+d)*x^3*a^2*b^4*d*e^5+240*ln(b*x+a)*x^5*a*b^5*e^6+120*ln(b*x+a)*x^5*b^6*d*e^5-240*ln(e*x+d)*x^5*a*b^5*e^6-120*ln(e*x+d)*x^5*b^6*d*e^5-360*ln(e*x+d)*x^4*a^2*b^4*e^6-60*ln(e*x+d)*x^4*b^6*d^2*e^4-240*ln(e*x+d)*x^3*a^3*b^3*e^6-60*ln(e*x+d)*x^2*a^4*b^2*e^6-60*ln(e*x+d)*a^4*b^2*d^2*e^4+120*a*b^5*d*e^5*x^4-60*a^2*b^4*d*e^5*x^3+360*a^2*b^4*e^6*x^4*ln(b*x+a)+60*b^6*d^2*e^4*x^4*ln(b*x+a)+240*a^3*b^3*e^6*x^3*ln(b*x+a)+60*a^4*b^2*e^6*x^2*ln(b*x+a)+60*a^4*b^2*d^2*e^4*ln(b*x+a)-190*a^4*b^2*d*e^5*x-280*a^3*b^3*d*e^5*x^2+100*a^3*b^3*d^2*e^4*x+120*a^2*b^4*d^3*e^3*x-20*a*b^5*d^4*e^2*x+300*a*b^5*d^2*e^4*x^3+330*a^2*b^4*d^2*e^4*x^2+80*a*b^5*d^3*e^3*x^2)*(b*x+a)/(e*x+d)^2/(a*e-b*d)^7/((b*x+a)^2)^(5/2)","B"
1614,1,86,42,0.047000," ","int((e*x+d)*(4*x^2+12*x+9)^(5/2),x)","\frac{\left(192 e \,x^{6}+224 x^{5} d +1680 x^{5} e +2016 d \,x^{4}+6048 x^{4} e +7560 d \,x^{3}+11340 x^{3} e +15120 d \,x^{2}+11340 e \,x^{2}+17010 d x +5103 e x +10206 d \right) \left(\left(2 x +3\right)^{2}\right)^{\frac{5}{2}} x}{42 \left(2 x +3\right)^{5}}"," ",0,"1/42*x*(192*e*x^6+224*d*x^5+1680*e*x^5+2016*d*x^4+6048*e*x^4+7560*d*x^3+11340*e*x^3+15120*d*x^2+11340*e*x^2+17010*d*x+5103*e*x+10206*d)*((2*x+3)^2)^(5/2)/(2*x+3)^5","B"
1615,1,62,42,0.043000," ","int((e*x+d)*(4*x^2+12*x+9)^(3/2),x)","\frac{\left(16 x^{4} e +20 d \,x^{3}+90 x^{3} e +120 d \,x^{2}+180 e \,x^{2}+270 d x +135 e x +270 d \right) \left(\left(2 x +3\right)^{2}\right)^{\frac{3}{2}} x}{10 \left(2 x +3\right)^{3}}"," ",0,"1/10*x*(16*e*x^4+20*d*x^3+90*e*x^3+120*d*x^2+180*e*x^2+270*d*x+135*e*x+270*d)*((2*x+3)^2)^(3/2)/(2*x+3)^3","A"
1616,1,38,39,0.044000," ","int((e*x+d)*(4*x^2+12*x+9)^(1/2),x)","\frac{\left(4 e \,x^{2}+6 d x +9 e x +18 d \right) \sqrt{\left(2 x +3\right)^{2}}\, x}{12 x +18}"," ",0,"1/6*x*(4*e*x^2+6*d*x+9*e*x+18*d)*((2*x+3)^2)^(1/2)/(2*x+3)","A"
1617,1,40,42,0.048000," ","int((e*x+d)/(4*x^2+12*x+9)^(1/2),x)","\frac{\left(2 x +3\right) \left(2 d \ln \left(2 x +3\right)+2 e x -3 e \ln \left(2 x +3\right)\right)}{4 \sqrt{\left(2 x +3\right)^{2}}}"," ",0,"1/4*(2*x+3)*(2*ln(2*x+3)*d-3*e*ln(2*x+3)+2*e*x)/((2*x+3)^2)^(1/2)","A"
1618,1,28,38,0.039000," ","int((e*x+d)/(4*x^2+12*x+9)^(3/2),x)","-\frac{\left(2 x +3\right) \left(4 e x +2 d +3 e \right)}{8 \left(\left(2 x +3\right)^{2}\right)^{\frac{3}{2}}}"," ",0,"-1/8*(2*x+3)*(4*e*x+2*d+3*e)/((2*x+3)^2)^(3/2)","A"
1619,1,28,44,0.043000," ","int((e*x+d)/(4*x^2+12*x+9)^(5/2),x)","-\frac{\left(2 x +3\right) \left(8 e x +6 d +3 e \right)}{48 \left(\left(2 x +3\right)^{2}\right)^{\frac{5}{2}}}"," ",0,"-1/48*(2*x+3)*(8*e*x+6*d+3*e)/((2*x+3)^2)^(5/2)","A"
1620,1,28,44,0.044000," ","int((e*x+d)/(4*x^2+12*x+9)^(7/2),x)","-\frac{\left(2 x +3\right) \left(12 e x +10 d +3 e \right)}{120 \left(\left(2 x +3\right)^{2}\right)^{\frac{7}{2}}}"," ",0,"-1/120*(2*x+3)*(12*e*x+10*d+3*e)/((2*x+3)^2)^(7/2)","A"
1621,1,63,59,0.044000," ","int((e*x+d)^(7/2)*(b^2*x^2+2*a*b*x+a^2),x)","\frac{2 \left(e x +d \right)^{\frac{9}{2}} \left(99 b^{2} e^{2} x^{2}+234 a b \,e^{2} x -36 b^{2} d e x +143 a^{2} e^{2}-52 a b d e +8 b^{2} d^{2}\right)}{1287 e^{3}}"," ",0,"2/1287*(e*x+d)^(9/2)*(99*b^2*e^2*x^2+234*a*b*e^2*x-36*b^2*d*e*x+143*a^2*e^2-52*a*b*d*e+8*b^2*d^2)/e^3","A"
1622,1,63,59,0.046000," ","int((e*x+d)^(5/2)*(b^2*x^2+2*a*b*x+a^2),x)","\frac{2 \left(e x +d \right)^{\frac{7}{2}} \left(63 b^{2} e^{2} x^{2}+154 a b \,e^{2} x -28 b^{2} d e x +99 a^{2} e^{2}-44 a b d e +8 b^{2} d^{2}\right)}{693 e^{3}}"," ",0,"2/693*(e*x+d)^(7/2)*(63*b^2*e^2*x^2+154*a*b*e^2*x-28*b^2*d*e*x+99*a^2*e^2-44*a*b*d*e+8*b^2*d^2)/e^3","A"
1623,1,63,59,0.054000," ","int((e*x+d)^(3/2)*(b^2*x^2+2*a*b*x+a^2),x)","\frac{2 \left(e x +d \right)^{\frac{5}{2}} \left(35 b^{2} e^{2} x^{2}+90 a b \,e^{2} x -20 b^{2} d e x +63 a^{2} e^{2}-36 a b d e +8 b^{2} d^{2}\right)}{315 e^{3}}"," ",0,"2/315*(e*x+d)^(5/2)*(35*b^2*e^2*x^2+90*a*b*e^2*x-20*b^2*d*e*x+63*a^2*e^2-36*a*b*d*e+8*b^2*d^2)/e^3","A"
1624,1,63,59,0.046000," ","int((b^2*x^2+2*a*b*x+a^2)*(e*x+d)^(1/2),x)","\frac{2 \left(e x +d \right)^{\frac{3}{2}} \left(15 b^{2} e^{2} x^{2}+42 a b \,e^{2} x -12 b^{2} d e x +35 a^{2} e^{2}-28 a b d e +8 b^{2} d^{2}\right)}{105 e^{3}}"," ",0,"2/105*(e*x+d)^(3/2)*(15*b^2*e^2*x^2+42*a*b*e^2*x-12*b^2*d*e*x+35*a^2*e^2-28*a*b*d*e+8*b^2*d^2)/e^3","A"
1625,1,63,59,0.047000," ","int((b^2*x^2+2*a*b*x+a^2)/(e*x+d)^(1/2),x)","\frac{2 \left(3 b^{2} e^{2} x^{2}+10 a b \,e^{2} x -4 b^{2} d e x +15 a^{2} e^{2}-20 a b d e +8 b^{2} d^{2}\right) \sqrt{e x +d}}{15 e^{3}}"," ",0,"2/15*(3*b^2*e^2*x^2+10*a*b*e^2*x-4*b^2*d*e*x+15*a^2*e^2-20*a*b*d*e+8*b^2*d^2)*(e*x+d)^(1/2)/e^3","A"
1626,1,63,59,0.054000," ","int((b^2*x^2+2*a*b*x+a^2)/(e*x+d)^(3/2),x)","-\frac{2 \left(-b^{2} e^{2} x^{2}-6 a b \,e^{2} x +4 b^{2} d e x +3 a^{2} e^{2}-12 a b d e +8 b^{2} d^{2}\right)}{3 \sqrt{e x +d}\, e^{3}}"," ",0,"-2/3*(-b^2*e^2*x^2-6*a*b*e^2*x+4*b^2*d*e*x+3*a^2*e^2-12*a*b*d*e+8*b^2*d^2)/(e*x+d)^(1/2)/e^3","A"
1627,1,62,59,0.050000," ","int((b^2*x^2+2*a*b*x+a^2)/(e*x+d)^(5/2),x)","-\frac{2 \left(-3 b^{2} e^{2} x^{2}+6 a b \,e^{2} x -12 b^{2} d e x +a^{2} e^{2}+4 a b d e -8 b^{2} d^{2}\right)}{3 \left(e x +d \right)^{\frac{3}{2}} e^{3}}"," ",0,"-2/3*(-3*b^2*e^2*x^2+6*a*b*e^2*x-12*b^2*d*e*x+a^2*e^2+4*a*b*d*e-8*b^2*d^2)/(e*x+d)^(3/2)/e^3","A"
1628,1,63,59,0.121000," ","int((b^2*x^2+2*a*b*x+a^2)/(e*x+d)^(7/2),x)","-\frac{2 \left(15 b^{2} e^{2} x^{2}+10 a b \,e^{2} x +20 b^{2} d e x +3 a^{2} e^{2}+4 a b d e +8 b^{2} d^{2}\right)}{15 \left(e x +d \right)^{\frac{5}{2}} e^{3}}"," ",0,"-2/15*(15*b^2*e^2*x^2+10*a*b*e^2*x+20*b^2*d*e*x+3*a^2*e^2+4*a*b*d*e+8*b^2*d^2)/(e*x+d)^(5/2)/e^3","A"
1629,1,186,109,0.051000," ","int((e*x+d)^(7/2)*(b^2*x^2+2*a*b*x+a^2)^2,x)","\frac{2 \left(e x +d \right)^{\frac{9}{2}} \left(6435 b^{4} e^{4} x^{4}+29172 a \,b^{3} e^{4} x^{3}-3432 b^{4} d \,e^{3} x^{3}+50490 a^{2} b^{2} e^{4} x^{2}-13464 a \,b^{3} d \,e^{3} x^{2}+1584 b^{4} d^{2} e^{2} x^{2}+39780 a^{3} b \,e^{4} x -18360 a^{2} b^{2} d \,e^{3} x +4896 a \,b^{3} d^{2} e^{2} x -576 b^{4} d^{3} e x +12155 a^{4} e^{4}-8840 a^{3} b d \,e^{3}+4080 a^{2} b^{2} d^{2} e^{2}-1088 a \,b^{3} d^{3} e +128 b^{4} d^{4}\right)}{109395 e^{5}}"," ",0,"2/109395*(e*x+d)^(9/2)*(6435*b^4*e^4*x^4+29172*a*b^3*e^4*x^3-3432*b^4*d*e^3*x^3+50490*a^2*b^2*e^4*x^2-13464*a*b^3*d*e^3*x^2+1584*b^4*d^2*e^2*x^2+39780*a^3*b*e^4*x-18360*a^2*b^2*d*e^3*x+4896*a*b^3*d^2*e^2*x-576*b^4*d^3*e*x+12155*a^4*e^4-8840*a^3*b*d*e^3+4080*a^2*b^2*d^2*e^2-1088*a*b^3*d^3*e+128*b^4*d^4)/e^5","A"
1630,1,186,109,0.049000," ","int((e*x+d)^(5/2)*(b^2*x^2+2*a*b*x+a^2)^2,x)","\frac{2 \left(e x +d \right)^{\frac{7}{2}} \left(3003 b^{4} e^{4} x^{4}+13860 a \,b^{3} e^{4} x^{3}-1848 b^{4} d \,e^{3} x^{3}+24570 a^{2} b^{2} e^{4} x^{2}-7560 a \,b^{3} d \,e^{3} x^{2}+1008 b^{4} d^{2} e^{2} x^{2}+20020 a^{3} b \,e^{4} x -10920 a^{2} b^{2} d \,e^{3} x +3360 a \,b^{3} d^{2} e^{2} x -448 b^{4} d^{3} e x +6435 a^{4} e^{4}-5720 a^{3} b d \,e^{3}+3120 a^{2} b^{2} d^{2} e^{2}-960 a \,b^{3} d^{3} e +128 b^{4} d^{4}\right)}{45045 e^{5}}"," ",0,"2/45045*(e*x+d)^(7/2)*(3003*b^4*e^4*x^4+13860*a*b^3*e^4*x^3-1848*b^4*d*e^3*x^3+24570*a^2*b^2*e^4*x^2-7560*a*b^3*d*e^3*x^2+1008*b^4*d^2*e^2*x^2+20020*a^3*b*e^4*x-10920*a^2*b^2*d*e^3*x+3360*a*b^3*d^2*e^2*x-448*b^4*d^3*e*x+6435*a^4*e^4-5720*a^3*b*d*e^3+3120*a^2*b^2*d^2*e^2-960*a*b^3*d^3*e+128*b^4*d^4)/e^5","A"
1631,1,186,109,0.048000," ","int((e*x+d)^(3/2)*(b^2*x^2+2*a*b*x+a^2)^2,x)","\frac{2 \left(e x +d \right)^{\frac{5}{2}} \left(1155 b^{4} e^{4} x^{4}+5460 a \,b^{3} e^{4} x^{3}-840 b^{4} d \,e^{3} x^{3}+10010 a^{2} b^{2} e^{4} x^{2}-3640 a \,b^{3} d \,e^{3} x^{2}+560 b^{4} d^{2} e^{2} x^{2}+8580 a^{3} b \,e^{4} x -5720 a^{2} b^{2} d \,e^{3} x +2080 a \,b^{3} d^{2} e^{2} x -320 b^{4} d^{3} e x +3003 a^{4} e^{4}-3432 a^{3} b d \,e^{3}+2288 a^{2} b^{2} d^{2} e^{2}-832 a \,b^{3} d^{3} e +128 b^{4} d^{4}\right)}{15015 e^{5}}"," ",0,"2/15015*(e*x+d)^(5/2)*(1155*b^4*e^4*x^4+5460*a*b^3*e^4*x^3-840*b^4*d*e^3*x^3+10010*a^2*b^2*e^4*x^2-3640*a*b^3*d*e^3*x^2+560*b^4*d^2*e^2*x^2+8580*a^3*b*e^4*x-5720*a^2*b^2*d*e^3*x+2080*a*b^3*d^2*e^2*x-320*b^4*d^3*e*x+3003*a^4*e^4-3432*a^3*b*d*e^3+2288*a^2*b^2*d^2*e^2-832*a*b^3*d^3*e+128*b^4*d^4)/e^5","A"
1632,1,186,109,0.046000," ","int((b^2*x^2+2*a*b*x+a^2)^2*(e*x+d)^(1/2),x)","\frac{2 \left(e x +d \right)^{\frac{3}{2}} \left(315 b^{4} e^{4} x^{4}+1540 a \,b^{3} e^{4} x^{3}-280 b^{4} d \,e^{3} x^{3}+2970 a^{2} b^{2} e^{4} x^{2}-1320 a \,b^{3} d \,e^{3} x^{2}+240 b^{4} d^{2} e^{2} x^{2}+2772 a^{3} b \,e^{4} x -2376 a^{2} b^{2} d \,e^{3} x +1056 a \,b^{3} d^{2} e^{2} x -192 b^{4} d^{3} e x +1155 a^{4} e^{4}-1848 a^{3} b d \,e^{3}+1584 a^{2} b^{2} d^{2} e^{2}-704 a \,b^{3} d^{3} e +128 b^{4} d^{4}\right)}{3465 e^{5}}"," ",0,"2/3465*(e*x+d)^(3/2)*(315*b^4*e^4*x^4+1540*a*b^3*e^4*x^3-280*b^4*d*e^3*x^3+2970*a^2*b^2*e^4*x^2-1320*a*b^3*d*e^3*x^2+240*b^4*d^2*e^2*x^2+2772*a^3*b*e^4*x-2376*a^2*b^2*d*e^3*x+1056*a*b^3*d^2*e^2*x-192*b^4*d^3*e*x+1155*a^4*e^4-1848*a^3*b*d*e^3+1584*a^2*b^2*d^2*e^2-704*a*b^3*d^3*e+128*b^4*d^4)/e^5","A"
1633,1,186,109,0.048000," ","int((b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^(1/2),x)","\frac{2 \left(35 b^{4} e^{4} x^{4}+180 a \,b^{3} e^{4} x^{3}-40 b^{4} d \,e^{3} x^{3}+378 a^{2} b^{2} e^{4} x^{2}-216 a \,b^{3} d \,e^{3} x^{2}+48 b^{4} d^{2} e^{2} x^{2}+420 a^{3} b \,e^{4} x -504 a^{2} b^{2} d \,e^{3} x +288 a \,b^{3} d^{2} e^{2} x -64 b^{4} d^{3} e x +315 a^{4} e^{4}-840 a^{3} b d \,e^{3}+1008 a^{2} b^{2} d^{2} e^{2}-576 a \,b^{3} d^{3} e +128 b^{4} d^{4}\right) \sqrt{e x +d}}{315 e^{5}}"," ",0,"2/315*(35*b^4*e^4*x^4+180*a*b^3*e^4*x^3-40*b^4*d*e^3*x^3+378*a^2*b^2*e^4*x^2-216*a*b^3*d*e^3*x^2+48*b^4*d^2*e^2*x^2+420*a^3*b*e^4*x-504*a^2*b^2*d*e^3*x+288*a*b^3*d^2*e^2*x-64*b^4*d^3*e*x+315*a^4*e^4-840*a^3*b*d*e^3+1008*a^2*b^2*d^2*e^2-576*a*b^3*d^3*e+128*b^4*d^4)*(e*x+d)^(1/2)/e^5","A"
1634,1,186,109,0.051000," ","int((b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^(3/2),x)","-\frac{2 \left(-5 b^{4} e^{4} x^{4}-28 a \,b^{3} e^{4} x^{3}+8 b^{4} d \,e^{3} x^{3}-70 a^{2} b^{2} e^{4} x^{2}+56 a \,b^{3} d \,e^{3} x^{2}-16 b^{4} d^{2} e^{2} x^{2}-140 a^{3} b \,e^{4} x +280 a^{2} b^{2} d \,e^{3} x -224 a \,b^{3} d^{2} e^{2} x +64 b^{4} d^{3} e x +35 a^{4} e^{4}-280 a^{3} b d \,e^{3}+560 a^{2} b^{2} d^{2} e^{2}-448 a \,b^{3} d^{3} e +128 b^{4} d^{4}\right)}{35 \sqrt{e x +d}\, e^{5}}"," ",0,"-2/35*(-5*b^4*e^4*x^4-28*a*b^3*e^4*x^3+8*b^4*d*e^3*x^3-70*a^2*b^2*e^4*x^2+56*a*b^3*d*e^3*x^2-16*b^4*d^2*e^2*x^2-140*a^3*b*e^4*x+280*a^2*b^2*d*e^3*x-224*a*b^3*d^2*e^2*x+64*b^4*d^3*e*x+35*a^4*e^4-280*a^3*b*d*e^3+560*a^2*b^2*d^2*e^2-448*a*b^3*d^3*e+128*b^4*d^4)/(e*x+d)^(1/2)/e^5","A"
1635,1,186,109,0.047000," ","int((b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^(5/2),x)","-\frac{2 \left(-3 b^{4} e^{4} x^{4}-20 a \,b^{3} e^{4} x^{3}+8 b^{4} d \,e^{3} x^{3}-90 a^{2} b^{2} e^{4} x^{2}+120 a \,b^{3} d \,e^{3} x^{2}-48 b^{4} d^{2} e^{2} x^{2}+60 a^{3} b \,e^{4} x -360 a^{2} b^{2} d \,e^{3} x +480 a \,b^{3} d^{2} e^{2} x -192 b^{4} d^{3} e x +5 a^{4} e^{4}+40 a^{3} b d \,e^{3}-240 a^{2} b^{2} d^{2} e^{2}+320 a \,b^{3} d^{3} e -128 b^{4} d^{4}\right)}{15 \left(e x +d \right)^{\frac{3}{2}} e^{5}}"," ",0,"-2/15*(-3*b^4*e^4*x^4-20*a*b^3*e^4*x^3+8*b^4*d*e^3*x^3-90*a^2*b^2*e^4*x^2+120*a*b^3*d*e^3*x^2-48*b^4*d^2*e^2*x^2+60*a^3*b*e^4*x-360*a^2*b^2*d*e^3*x+480*a*b^3*d^2*e^2*x-192*b^4*d^3*e*x+5*a^4*e^4+40*a^3*b*d*e^3-240*a^2*b^2*d^2*e^2+320*a*b^3*d^3*e-128*b^4*d^4)/(e*x+d)^(3/2)/e^5","A"
1636,1,186,109,0.047000," ","int((b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^(7/2),x)","-\frac{2 \left(-5 b^{4} e^{4} x^{4}-60 a \,b^{3} e^{4} x^{3}+40 b^{4} d \,e^{3} x^{3}+90 a^{2} b^{2} e^{4} x^{2}-360 a \,b^{3} d \,e^{3} x^{2}+240 b^{4} d^{2} e^{2} x^{2}+20 a^{3} b \,e^{4} x +120 a^{2} b^{2} d \,e^{3} x -480 a \,b^{3} d^{2} e^{2} x +320 b^{4} d^{3} e x +3 a^{4} e^{4}+8 a^{3} b d \,e^{3}+48 a^{2} b^{2} d^{2} e^{2}-192 a \,b^{3} d^{3} e +128 b^{4} d^{4}\right)}{15 \left(e x +d \right)^{\frac{5}{2}} e^{5}}"," ",0,"-2/15*(-5*b^4*e^4*x^4-60*a*b^3*e^4*x^3+40*b^4*d*e^3*x^3+90*a^2*b^2*e^4*x^2-360*a*b^3*d*e^3*x^2+240*b^4*d^2*e^2*x^2+20*a^3*b*e^4*x+120*a^2*b^2*d*e^3*x-480*a*b^3*d^2*e^2*x+320*b^4*d^3*e*x+3*a^4*e^4+8*a^3*b*d*e^3+48*a^2*b^2*d^2*e^2-192*a*b^3*d^3*e+128*b^4*d^4)/(e*x+d)^(5/2)/e^5","A"
1637,1,377,159,0.154000," ","int((e*x+d)^(7/2)*(b^2*x^2+2*a*b*x+a^2)^3,x)","\frac{2 \left(e x +d \right)^{\frac{9}{2}} \left(138567 b^{6} e^{6} x^{6}+918918 a \,b^{5} e^{6} x^{5}-87516 b^{6} d \,e^{5} x^{5}+2567565 a^{2} b^{4} e^{6} x^{4}-540540 a \,b^{5} d \,e^{5} x^{4}+51480 b^{6} d^{2} e^{4} x^{4}+3879876 a^{3} b^{3} e^{6} x^{3}-1369368 a^{2} b^{4} d \,e^{5} x^{3}+288288 a \,b^{5} d^{2} e^{4} x^{3}-27456 b^{6} d^{3} e^{3} x^{3}+3357585 a^{4} b^{2} e^{6} x^{2}-1790712 a^{3} b^{3} d \,e^{5} x^{2}+632016 a^{2} b^{4} d^{2} e^{4} x^{2}-133056 a \,b^{5} d^{3} e^{3} x^{2}+12672 b^{6} d^{4} e^{2} x^{2}+1587222 a^{5} b \,e^{6} x -1220940 a^{4} b^{2} d \,e^{5} x +651168 a^{3} b^{3} d^{2} e^{4} x -229824 a^{2} b^{4} d^{3} e^{3} x +48384 a \,b^{5} d^{4} e^{2} x -4608 b^{6} d^{5} e x +323323 a^{6} e^{6}-352716 a^{5} b d \,e^{5}+271320 a^{4} b^{2} d^{2} e^{4}-144704 a^{3} b^{3} d^{3} e^{3}+51072 a^{2} b^{4} d^{4} e^{2}-10752 a \,b^{5} d^{5} e +1024 b^{6} d^{6}\right)}{2909907 e^{7}}"," ",0,"2/2909907*(e*x+d)^(9/2)*(138567*b^6*e^6*x^6+918918*a*b^5*e^6*x^5-87516*b^6*d*e^5*x^5+2567565*a^2*b^4*e^6*x^4-540540*a*b^5*d*e^5*x^4+51480*b^6*d^2*e^4*x^4+3879876*a^3*b^3*e^6*x^3-1369368*a^2*b^4*d*e^5*x^3+288288*a*b^5*d^2*e^4*x^3-27456*b^6*d^3*e^3*x^3+3357585*a^4*b^2*e^6*x^2-1790712*a^3*b^3*d*e^5*x^2+632016*a^2*b^4*d^2*e^4*x^2-133056*a*b^5*d^3*e^3*x^2+12672*b^6*d^4*e^2*x^2+1587222*a^5*b*e^6*x-1220940*a^4*b^2*d*e^5*x+651168*a^3*b^3*d^2*e^4*x-229824*a^2*b^4*d^3*e^3*x+48384*a*b^5*d^4*e^2*x-4608*b^6*d^5*e*x+323323*a^6*e^6-352716*a^5*b*d*e^5+271320*a^4*b^2*d^2*e^4-144704*a^3*b^3*d^3*e^3+51072*a^2*b^4*d^4*e^2-10752*a*b^5*d^5*e+1024*b^6*d^6)/e^7","B"
1638,1,377,159,0.049000," ","int((e*x+d)^(5/2)*(b^2*x^2+2*a*b*x+a^2)^3,x)","\frac{2 \left(e x +d \right)^{\frac{7}{2}} \left(51051 b^{6} e^{6} x^{6}+342342 a \,b^{5} e^{6} x^{5}-36036 b^{6} d \,e^{5} x^{5}+969969 a^{2} b^{4} e^{6} x^{4}-228228 a \,b^{5} d \,e^{5} x^{4}+24024 b^{6} d^{2} e^{4} x^{4}+1492260 a^{3} b^{3} e^{6} x^{3}-596904 a^{2} b^{4} d \,e^{5} x^{3}+140448 a \,b^{5} d^{2} e^{4} x^{3}-14784 b^{6} d^{3} e^{3} x^{3}+1322685 a^{4} b^{2} e^{6} x^{2}-813960 a^{3} b^{3} d \,e^{5} x^{2}+325584 a^{2} b^{4} d^{2} e^{4} x^{2}-76608 a \,b^{5} d^{3} e^{3} x^{2}+8064 b^{6} d^{4} e^{2} x^{2}+646646 a^{5} b \,e^{6} x -587860 a^{4} b^{2} d \,e^{5} x +361760 a^{3} b^{3} d^{2} e^{4} x -144704 a^{2} b^{4} d^{3} e^{3} x +34048 a \,b^{5} d^{4} e^{2} x -3584 b^{6} d^{5} e x +138567 a^{6} e^{6}-184756 a^{5} b d \,e^{5}+167960 a^{4} b^{2} d^{2} e^{4}-103360 a^{3} b^{3} d^{3} e^{3}+41344 a^{2} b^{4} d^{4} e^{2}-9728 a \,b^{5} d^{5} e +1024 b^{6} d^{6}\right)}{969969 e^{7}}"," ",0,"2/969969*(e*x+d)^(7/2)*(51051*b^6*e^6*x^6+342342*a*b^5*e^6*x^5-36036*b^6*d*e^5*x^5+969969*a^2*b^4*e^6*x^4-228228*a*b^5*d*e^5*x^4+24024*b^6*d^2*e^4*x^4+1492260*a^3*b^3*e^6*x^3-596904*a^2*b^4*d*e^5*x^3+140448*a*b^5*d^2*e^4*x^3-14784*b^6*d^3*e^3*x^3+1322685*a^4*b^2*e^6*x^2-813960*a^3*b^3*d*e^5*x^2+325584*a^2*b^4*d^2*e^4*x^2-76608*a*b^5*d^3*e^3*x^2+8064*b^6*d^4*e^2*x^2+646646*a^5*b*e^6*x-587860*a^4*b^2*d*e^5*x+361760*a^3*b^3*d^2*e^4*x-144704*a^2*b^4*d^3*e^3*x+34048*a*b^5*d^4*e^2*x-3584*b^6*d^5*e*x+138567*a^6*e^6-184756*a^5*b*d*e^5+167960*a^4*b^2*d^2*e^4-103360*a^3*b^3*d^3*e^3+41344*a^2*b^4*d^4*e^2-9728*a*b^5*d^5*e+1024*b^6*d^6)/e^7","B"
1639,1,377,159,0.073000," ","int((e*x+d)^(3/2)*(b^2*x^2+2*a*b*x+a^2)^3,x)","\frac{2 \left(e x +d \right)^{\frac{5}{2}} \left(15015 b^{6} e^{6} x^{6}+102102 a \,b^{5} e^{6} x^{5}-12012 b^{6} d \,e^{5} x^{5}+294525 a^{2} b^{4} e^{6} x^{4}-78540 a \,b^{5} d \,e^{5} x^{4}+9240 b^{6} d^{2} e^{4} x^{4}+464100 a^{3} b^{3} e^{6} x^{3}-214200 a^{2} b^{4} d \,e^{5} x^{3}+57120 a \,b^{5} d^{2} e^{4} x^{3}-6720 b^{6} d^{3} e^{3} x^{3}+425425 a^{4} b^{2} e^{6} x^{2}-309400 a^{3} b^{3} d \,e^{5} x^{2}+142800 a^{2} b^{4} d^{2} e^{4} x^{2}-38080 a \,b^{5} d^{3} e^{3} x^{2}+4480 b^{6} d^{4} e^{2} x^{2}+218790 a^{5} b \,e^{6} x -243100 a^{4} b^{2} d \,e^{5} x +176800 a^{3} b^{3} d^{2} e^{4} x -81600 a^{2} b^{4} d^{3} e^{3} x +21760 a \,b^{5} d^{4} e^{2} x -2560 b^{6} d^{5} e x +51051 a^{6} e^{6}-87516 a^{5} b d \,e^{5}+97240 a^{4} b^{2} d^{2} e^{4}-70720 a^{3} b^{3} d^{3} e^{3}+32640 a^{2} b^{4} d^{4} e^{2}-8704 a \,b^{5} d^{5} e +1024 b^{6} d^{6}\right)}{255255 e^{7}}"," ",0,"2/255255*(e*x+d)^(5/2)*(15015*b^6*e^6*x^6+102102*a*b^5*e^6*x^5-12012*b^6*d*e^5*x^5+294525*a^2*b^4*e^6*x^4-78540*a*b^5*d*e^5*x^4+9240*b^6*d^2*e^4*x^4+464100*a^3*b^3*e^6*x^3-214200*a^2*b^4*d*e^5*x^3+57120*a*b^5*d^2*e^4*x^3-6720*b^6*d^3*e^3*x^3+425425*a^4*b^2*e^6*x^2-309400*a^3*b^3*d*e^5*x^2+142800*a^2*b^4*d^2*e^4*x^2-38080*a*b^5*d^3*e^3*x^2+4480*b^6*d^4*e^2*x^2+218790*a^5*b*e^6*x-243100*a^4*b^2*d*e^5*x+176800*a^3*b^3*d^2*e^4*x-81600*a^2*b^4*d^3*e^3*x+21760*a*b^5*d^4*e^2*x-2560*b^6*d^5*e*x+51051*a^6*e^6-87516*a^5*b*d*e^5+97240*a^4*b^2*d^2*e^4-70720*a^3*b^3*d^3*e^3+32640*a^2*b^4*d^4*e^2-8704*a*b^5*d^5*e+1024*b^6*d^6)/e^7","B"
1640,1,377,159,0.050000," ","int((b^2*x^2+2*a*b*x+a^2)^3*(e*x+d)^(1/2),x)","\frac{2 \left(e x +d \right)^{\frac{3}{2}} \left(3003 b^{6} e^{6} x^{6}+20790 a \,b^{5} e^{6} x^{5}-2772 b^{6} d \,e^{5} x^{5}+61425 a^{2} b^{4} e^{6} x^{4}-18900 a \,b^{5} d \,e^{5} x^{4}+2520 b^{6} d^{2} e^{4} x^{4}+100100 a^{3} b^{3} e^{6} x^{3}-54600 a^{2} b^{4} d \,e^{5} x^{3}+16800 a \,b^{5} d^{2} e^{4} x^{3}-2240 b^{6} d^{3} e^{3} x^{3}+96525 a^{4} b^{2} e^{6} x^{2}-85800 a^{3} b^{3} d \,e^{5} x^{2}+46800 a^{2} b^{4} d^{2} e^{4} x^{2}-14400 a \,b^{5} d^{3} e^{3} x^{2}+1920 b^{6} d^{4} e^{2} x^{2}+54054 a^{5} b \,e^{6} x -77220 a^{4} b^{2} d \,e^{5} x +68640 a^{3} b^{3} d^{2} e^{4} x -37440 a^{2} b^{4} d^{3} e^{3} x +11520 a \,b^{5} d^{4} e^{2} x -1536 b^{6} d^{5} e x +15015 a^{6} e^{6}-36036 a^{5} b d \,e^{5}+51480 a^{4} b^{2} d^{2} e^{4}-45760 a^{3} b^{3} d^{3} e^{3}+24960 a^{2} b^{4} d^{4} e^{2}-7680 a \,b^{5} d^{5} e +1024 b^{6} d^{6}\right)}{45045 e^{7}}"," ",0,"2/45045*(e*x+d)^(3/2)*(3003*b^6*e^6*x^6+20790*a*b^5*e^6*x^5-2772*b^6*d*e^5*x^5+61425*a^2*b^4*e^6*x^4-18900*a*b^5*d*e^5*x^4+2520*b^6*d^2*e^4*x^4+100100*a^3*b^3*e^6*x^3-54600*a^2*b^4*d*e^5*x^3+16800*a*b^5*d^2*e^4*x^3-2240*b^6*d^3*e^3*x^3+96525*a^4*b^2*e^6*x^2-85800*a^3*b^3*d*e^5*x^2+46800*a^2*b^4*d^2*e^4*x^2-14400*a*b^5*d^3*e^3*x^2+1920*b^6*d^4*e^2*x^2+54054*a^5*b*e^6*x-77220*a^4*b^2*d*e^5*x+68640*a^3*b^3*d^2*e^4*x-37440*a^2*b^4*d^3*e^3*x+11520*a*b^5*d^4*e^2*x-1536*b^6*d^5*e*x+15015*a^6*e^6-36036*a^5*b*d*e^5+51480*a^4*b^2*d^2*e^4-45760*a^3*b^3*d^3*e^3+24960*a^2*b^4*d^4*e^2-7680*a*b^5*d^5*e+1024*b^6*d^6)/e^7","B"
1641,1,377,159,0.042000," ","int((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^(1/2),x)","\frac{2 \left(231 b^{6} e^{6} x^{6}+1638 a \,b^{5} e^{6} x^{5}-252 b^{6} d \,e^{5} x^{5}+5005 a^{2} b^{4} e^{6} x^{4}-1820 a \,b^{5} d \,e^{5} x^{4}+280 b^{6} d^{2} e^{4} x^{4}+8580 a^{3} b^{3} e^{6} x^{3}-5720 a^{2} b^{4} d \,e^{5} x^{3}+2080 a \,b^{5} d^{2} e^{4} x^{3}-320 b^{6} d^{3} e^{3} x^{3}+9009 a^{4} b^{2} e^{6} x^{2}-10296 a^{3} b^{3} d \,e^{5} x^{2}+6864 a^{2} b^{4} d^{2} e^{4} x^{2}-2496 a \,b^{5} d^{3} e^{3} x^{2}+384 b^{6} d^{4} e^{2} x^{2}+6006 a^{5} b \,e^{6} x -12012 a^{4} b^{2} d \,e^{5} x +13728 a^{3} b^{3} d^{2} e^{4} x -9152 a^{2} b^{4} d^{3} e^{3} x +3328 a \,b^{5} d^{4} e^{2} x -512 b^{6} d^{5} e x +3003 a^{6} e^{6}-12012 a^{5} b d \,e^{5}+24024 a^{4} b^{2} d^{2} e^{4}-27456 a^{3} b^{3} d^{3} e^{3}+18304 a^{2} b^{4} d^{4} e^{2}-6656 a \,b^{5} d^{5} e +1024 b^{6} d^{6}\right) \sqrt{e x +d}}{3003 e^{7}}"," ",0,"2/3003*(231*b^6*e^6*x^6+1638*a*b^5*e^6*x^5-252*b^6*d*e^5*x^5+5005*a^2*b^4*e^6*x^4-1820*a*b^5*d*e^5*x^4+280*b^6*d^2*e^4*x^4+8580*a^3*b^3*e^6*x^3-5720*a^2*b^4*d*e^5*x^3+2080*a*b^5*d^2*e^4*x^3-320*b^6*d^3*e^3*x^3+9009*a^4*b^2*e^6*x^2-10296*a^3*b^3*d*e^5*x^2+6864*a^2*b^4*d^2*e^4*x^2-2496*a*b^5*d^3*e^3*x^2+384*b^6*d^4*e^2*x^2+6006*a^5*b*e^6*x-12012*a^4*b^2*d*e^5*x+13728*a^3*b^3*d^2*e^4*x-9152*a^2*b^4*d^3*e^3*x+3328*a*b^5*d^4*e^2*x-512*b^6*d^5*e*x+3003*a^6*e^6-12012*a^5*b*d*e^5+24024*a^4*b^2*d^2*e^4-27456*a^3*b^3*d^3*e^3+18304*a^2*b^4*d^4*e^2-6656*a*b^5*d^5*e+1024*b^6*d^6)*(e*x+d)^(1/2)/e^7","B"
1642,1,377,159,0.047000," ","int((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^(3/2),x)","-\frac{2 \left(-21 b^{6} e^{6} x^{6}-154 a \,b^{5} e^{6} x^{5}+28 b^{6} d \,e^{5} x^{5}-495 a^{2} b^{4} e^{6} x^{4}+220 a \,b^{5} d \,e^{5} x^{4}-40 b^{6} d^{2} e^{4} x^{4}-924 a^{3} b^{3} e^{6} x^{3}+792 a^{2} b^{4} d \,e^{5} x^{3}-352 a \,b^{5} d^{2} e^{4} x^{3}+64 b^{6} d^{3} e^{3} x^{3}-1155 a^{4} b^{2} e^{6} x^{2}+1848 a^{3} b^{3} d \,e^{5} x^{2}-1584 a^{2} b^{4} d^{2} e^{4} x^{2}+704 a \,b^{5} d^{3} e^{3} x^{2}-128 b^{6} d^{4} e^{2} x^{2}-1386 a^{5} b \,e^{6} x +4620 a^{4} b^{2} d \,e^{5} x -7392 a^{3} b^{3} d^{2} e^{4} x +6336 a^{2} b^{4} d^{3} e^{3} x -2816 a \,b^{5} d^{4} e^{2} x +512 b^{6} d^{5} e x +231 a^{6} e^{6}-2772 a^{5} b d \,e^{5}+9240 a^{4} b^{2} d^{2} e^{4}-14784 a^{3} b^{3} d^{3} e^{3}+12672 a^{2} b^{4} d^{4} e^{2}-5632 a \,b^{5} d^{5} e +1024 b^{6} d^{6}\right)}{231 \sqrt{e x +d}\, e^{7}}"," ",0,"-2/231*(-21*b^6*e^6*x^6-154*a*b^5*e^6*x^5+28*b^6*d*e^5*x^5-495*a^2*b^4*e^6*x^4+220*a*b^5*d*e^5*x^4-40*b^6*d^2*e^4*x^4-924*a^3*b^3*e^6*x^3+792*a^2*b^4*d*e^5*x^3-352*a*b^5*d^2*e^4*x^3+64*b^6*d^3*e^3*x^3-1155*a^4*b^2*e^6*x^2+1848*a^3*b^3*d*e^5*x^2-1584*a^2*b^4*d^2*e^4*x^2+704*a*b^5*d^3*e^3*x^2-128*b^6*d^4*e^2*x^2-1386*a^5*b*e^6*x+4620*a^4*b^2*d*e^5*x-7392*a^3*b^3*d^2*e^4*x+6336*a^2*b^4*d^3*e^3*x-2816*a*b^5*d^4*e^2*x+512*b^6*d^5*e*x+231*a^6*e^6-2772*a^5*b*d*e^5+9240*a^4*b^2*d^2*e^4-14784*a^3*b^3*d^3*e^3+12672*a^2*b^4*d^4*e^2-5632*a*b^5*d^5*e+1024*b^6*d^6)/(e*x+d)^(1/2)/e^7","B"
1643,1,377,159,0.045000," ","int((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^(5/2),x)","-\frac{2 \left(-7 b^{6} e^{6} x^{6}-54 a \,b^{5} e^{6} x^{5}+12 b^{6} d \,e^{5} x^{5}-189 a^{2} b^{4} e^{6} x^{4}+108 a \,b^{5} d \,e^{5} x^{4}-24 b^{6} d^{2} e^{4} x^{4}-420 a^{3} b^{3} e^{6} x^{3}+504 a^{2} b^{4} d \,e^{5} x^{3}-288 a \,b^{5} d^{2} e^{4} x^{3}+64 b^{6} d^{3} e^{3} x^{3}-945 a^{4} b^{2} e^{6} x^{2}+2520 a^{3} b^{3} d \,e^{5} x^{2}-3024 a^{2} b^{4} d^{2} e^{4} x^{2}+1728 a \,b^{5} d^{3} e^{3} x^{2}-384 b^{6} d^{4} e^{2} x^{2}+378 a^{5} b \,e^{6} x -3780 a^{4} b^{2} d \,e^{5} x +10080 a^{3} b^{3} d^{2} e^{4} x -12096 a^{2} b^{4} d^{3} e^{3} x +6912 a \,b^{5} d^{4} e^{2} x -1536 b^{6} d^{5} e x +21 a^{6} e^{6}+252 a^{5} b d \,e^{5}-2520 a^{4} b^{2} d^{2} e^{4}+6720 a^{3} b^{3} d^{3} e^{3}-8064 a^{2} b^{4} d^{4} e^{2}+4608 a \,b^{5} d^{5} e -1024 b^{6} d^{6}\right)}{63 \left(e x +d \right)^{\frac{3}{2}} e^{7}}"," ",0,"-2/63*(-7*b^6*e^6*x^6-54*a*b^5*e^6*x^5+12*b^6*d*e^5*x^5-189*a^2*b^4*e^6*x^4+108*a*b^5*d*e^5*x^4-24*b^6*d^2*e^4*x^4-420*a^3*b^3*e^6*x^3+504*a^2*b^4*d*e^5*x^3-288*a*b^5*d^2*e^4*x^3+64*b^6*d^3*e^3*x^3-945*a^4*b^2*e^6*x^2+2520*a^3*b^3*d*e^5*x^2-3024*a^2*b^4*d^2*e^4*x^2+1728*a*b^5*d^3*e^3*x^2-384*b^6*d^4*e^2*x^2+378*a^5*b*e^6*x-3780*a^4*b^2*d*e^5*x+10080*a^3*b^3*d^2*e^4*x-12096*a^2*b^4*d^3*e^3*x+6912*a*b^5*d^4*e^2*x-1536*b^6*d^5*e*x+21*a^6*e^6+252*a^5*b*d*e^5-2520*a^4*b^2*d^2*e^4+6720*a^3*b^3*d^3*e^3-8064*a^2*b^4*d^4*e^2+4608*a*b^5*d^5*e-1024*b^6*d^6)/(e*x+d)^(3/2)/e^7","B"
1644,1,377,159,0.050000," ","int((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^(7/2),x)","-\frac{2 \left(-5 b^{6} e^{6} x^{6}-42 a \,b^{5} e^{6} x^{5}+12 b^{6} d \,e^{5} x^{5}-175 a^{2} b^{4} e^{6} x^{4}+140 a \,b^{5} d \,e^{5} x^{4}-40 b^{6} d^{2} e^{4} x^{4}-700 a^{3} b^{3} e^{6} x^{3}+1400 a^{2} b^{4} d \,e^{5} x^{3}-1120 a \,b^{5} d^{2} e^{4} x^{3}+320 b^{6} d^{3} e^{3} x^{3}+525 a^{4} b^{2} e^{6} x^{2}-4200 a^{3} b^{3} d \,e^{5} x^{2}+8400 a^{2} b^{4} d^{2} e^{4} x^{2}-6720 a \,b^{5} d^{3} e^{3} x^{2}+1920 b^{6} d^{4} e^{2} x^{2}+70 a^{5} b \,e^{6} x +700 a^{4} b^{2} d \,e^{5} x -5600 a^{3} b^{3} d^{2} e^{4} x +11200 a^{2} b^{4} d^{3} e^{3} x -8960 a \,b^{5} d^{4} e^{2} x +2560 b^{6} d^{5} e x +7 a^{6} e^{6}+28 a^{5} b d \,e^{5}+280 a^{4} b^{2} d^{2} e^{4}-2240 a^{3} b^{3} d^{3} e^{3}+4480 a^{2} b^{4} d^{4} e^{2}-3584 a \,b^{5} d^{5} e +1024 b^{6} d^{6}\right)}{35 \left(e x +d \right)^{\frac{5}{2}} e^{7}}"," ",0,"-2/35*(-5*b^6*e^6*x^6-42*a*b^5*e^6*x^5+12*b^6*d*e^5*x^5-175*a^2*b^4*e^6*x^4+140*a*b^5*d*e^5*x^4-40*b^6*d^2*e^4*x^4-700*a^3*b^3*e^6*x^3+1400*a^2*b^4*d*e^5*x^3-1120*a*b^5*d^2*e^4*x^3+320*b^6*d^3*e^3*x^3+525*a^4*b^2*e^6*x^2-4200*a^3*b^3*d*e^5*x^2+8400*a^2*b^4*d^2*e^4*x^2-6720*a*b^5*d^3*e^3*x^2+1920*b^6*d^4*e^2*x^2+70*a^5*b*e^6*x+700*a^4*b^2*d*e^5*x-5600*a^3*b^3*d^2*e^4*x+11200*a^2*b^4*d^3*e^3*x-8960*a*b^5*d^4*e^2*x+2560*b^6*d^5*e*x+7*a^6*e^6+28*a^5*b*d*e^5+280*a^4*b^2*d^2*e^4-2240*a^3*b^3*d^3*e^3+4480*a^2*b^4*d^4*e^2-3584*a*b^5*d^5*e+1024*b^6*d^6)/(e*x+d)^(5/2)/e^7","B"
1645,1,539,138,0.088000," ","int((e*x+d)^(9/2)/(b^2*x^2+2*a*b*x+a^2),x)","\frac{9 a^{4} e^{5} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)}{\sqrt{\left(a e -b d \right) b}\, b^{5}}-\frac{36 a^{3} d \,e^{4} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)}{\sqrt{\left(a e -b d \right) b}\, b^{4}}+\frac{54 a^{2} d^{2} e^{3} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)}{\sqrt{\left(a e -b d \right) b}\, b^{3}}-\frac{36 a \,d^{3} e^{2} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)}{\sqrt{\left(a e -b d \right) b}\, b^{2}}+\frac{9 d^{4} e \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)}{\sqrt{\left(a e -b d \right) b}\, b}-\frac{\sqrt{e x +d}\, a^{4} e^{5}}{\left(b e x +a e \right) b^{5}}+\frac{4 \sqrt{e x +d}\, a^{3} d \,e^{4}}{\left(b e x +a e \right) b^{4}}-\frac{6 \sqrt{e x +d}\, a^{2} d^{2} e^{3}}{\left(b e x +a e \right) b^{3}}+\frac{4 \sqrt{e x +d}\, a \,d^{3} e^{2}}{\left(b e x +a e \right) b^{2}}-\frac{\sqrt{e x +d}\, d^{4} e}{\left(b e x +a e \right) b}-\frac{8 \sqrt{e x +d}\, a^{3} e^{4}}{b^{5}}+\frac{24 \sqrt{e x +d}\, a^{2} d \,e^{3}}{b^{4}}-\frac{24 \sqrt{e x +d}\, a \,d^{2} e^{2}}{b^{3}}+\frac{8 \sqrt{e x +d}\, d^{3} e}{b^{2}}+\frac{2 \left(e x +d \right)^{\frac{3}{2}} a^{2} e^{3}}{b^{4}}-\frac{4 \left(e x +d \right)^{\frac{3}{2}} a d \,e^{2}}{b^{3}}+\frac{2 \left(e x +d \right)^{\frac{3}{2}} d^{2} e}{b^{2}}-\frac{4 \left(e x +d \right)^{\frac{5}{2}} a \,e^{2}}{5 b^{3}}+\frac{4 \left(e x +d \right)^{\frac{5}{2}} d e}{5 b^{2}}+\frac{2 \left(e x +d \right)^{\frac{7}{2}} e}{7 b^{2}}"," ",0,"2/7*e*(e*x+d)^(7/2)/b^2-4/5/b^3*(e*x+d)^(5/2)*a*e^2+4/5*e/b^2*(e*x+d)^(5/2)*d+2/b^4*(e*x+d)^(3/2)*a^2*e^3-4/b^3*(e*x+d)^(3/2)*a*d*e^2+2*e/b^2*(e*x+d)^(3/2)*d^2-8/b^5*e^4*a^3*(e*x+d)^(1/2)+24/b^4*a^2*d*e^3*(e*x+d)^(1/2)-24/b^3*a*d^2*e^2*(e*x+d)^(1/2)+8*e/b^2*d^3*(e*x+d)^(1/2)-1/b^5*(e*x+d)^(1/2)/(b*e*x+a*e)*a^4*e^5+4/b^4*(e*x+d)^(1/2)/(b*e*x+a*e)*a^3*d*e^4-6/b^3*(e*x+d)^(1/2)/(b*e*x+a*e)*a^2*d^2*e^3+4/b^2*(e*x+d)^(1/2)/(b*e*x+a*e)*a*d^3*e^2-e/b*(e*x+d)^(1/2)/(b*e*x+a*e)*d^4+9/b^5/(b*(a*e-b*d))^(1/2)*arctan((e*x+d)^(1/2)*b/(b*(a*e-b*d))^(1/2))*a^4*e^5-36/b^4/(b*(a*e-b*d))^(1/2)*arctan((e*x+d)^(1/2)*b/(b*(a*e-b*d))^(1/2))*a^3*d*e^4+54/b^3/(b*(a*e-b*d))^(1/2)*arctan((e*x+d)^(1/2)*b/(b*(a*e-b*d))^(1/2))*a^2*d^2*e^3-36/b^2/(b*(a*e-b*d))^(1/2)*arctan((e*x+d)^(1/2)*b/(b*(a*e-b*d))^(1/2))*a*d^3*e^2+9*e/b/(b*(a*e-b*d))^(1/2)*arctan((e*x+d)^(1/2)*b/(b*(a*e-b*d))^(1/2))*d^4","B"
1646,1,387,115,0.068000," ","int((e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2),x)","-\frac{7 a^{3} e^{4} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)}{\sqrt{\left(a e -b d \right) b}\, b^{4}}+\frac{21 a^{2} d \,e^{3} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)}{\sqrt{\left(a e -b d \right) b}\, b^{3}}-\frac{21 a \,d^{2} e^{2} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)}{\sqrt{\left(a e -b d \right) b}\, b^{2}}+\frac{7 d^{3} e \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)}{\sqrt{\left(a e -b d \right) b}\, b}+\frac{\sqrt{e x +d}\, a^{3} e^{4}}{\left(b e x +a e \right) b^{4}}-\frac{3 \sqrt{e x +d}\, a^{2} d \,e^{3}}{\left(b e x +a e \right) b^{3}}+\frac{3 \sqrt{e x +d}\, a \,d^{2} e^{2}}{\left(b e x +a e \right) b^{2}}-\frac{\sqrt{e x +d}\, d^{3} e}{\left(b e x +a e \right) b}+\frac{6 \sqrt{e x +d}\, a^{2} e^{3}}{b^{4}}-\frac{12 \sqrt{e x +d}\, a d \,e^{2}}{b^{3}}+\frac{6 \sqrt{e x +d}\, d^{2} e}{b^{2}}-\frac{4 \left(e x +d \right)^{\frac{3}{2}} a \,e^{2}}{3 b^{3}}+\frac{4 \left(e x +d \right)^{\frac{3}{2}} d e}{3 b^{2}}+\frac{2 \left(e x +d \right)^{\frac{5}{2}} e}{5 b^{2}}"," ",0,"2/5*e*(e*x+d)^(5/2)/b^2-4/3/b^3*(e*x+d)^(3/2)*a*e^2+4/3*e/b^2*(e*x+d)^(3/2)*d+6/b^4*a^2*e^3*(e*x+d)^(1/2)-12/b^3*a*d*e^2*(e*x+d)^(1/2)+6*e/b^2*d^2*(e*x+d)^(1/2)+1/b^4*(e*x+d)^(1/2)/(b*e*x+a*e)*a^3*e^4-3/b^3*(e*x+d)^(1/2)/(b*e*x+a*e)*a^2*d*e^3+3/b^2*(e*x+d)^(1/2)/(b*e*x+a*e)*a*d^2*e^2-e/b*(e*x+d)^(1/2)/(b*e*x+a*e)*d^3-7/b^4/((a*e-b*d)*b)^(1/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*a^3*e^4+21/b^3/((a*e-b*d)*b)^(1/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*a^2*d*e^3-21/b^2/((a*e-b*d)*b)^(1/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*a*d^2*e^2+7*e/b/((a*e-b*d)*b)^(1/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*d^3","B"
1647,1,258,92,0.061000," ","int((e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2),x)","\frac{5 a^{2} e^{3} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)}{\sqrt{\left(a e -b d \right) b}\, b^{3}}-\frac{10 a d \,e^{2} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)}{\sqrt{\left(a e -b d \right) b}\, b^{2}}+\frac{5 d^{2} e \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)}{\sqrt{\left(a e -b d \right) b}\, b}-\frac{\sqrt{e x +d}\, a^{2} e^{3}}{\left(b e x +a e \right) b^{3}}+\frac{2 \sqrt{e x +d}\, a d \,e^{2}}{\left(b e x +a e \right) b^{2}}-\frac{\sqrt{e x +d}\, d^{2} e}{\left(b e x +a e \right) b}-\frac{4 \sqrt{e x +d}\, a \,e^{2}}{b^{3}}+\frac{4 \sqrt{e x +d}\, d e}{b^{2}}+\frac{2 \left(e x +d \right)^{\frac{3}{2}} e}{3 b^{2}}"," ",0,"2/3*e*(e*x+d)^(3/2)/b^2-4/b^3*a*e^2*(e*x+d)^(1/2)+4*e/b^2*(e*x+d)^(1/2)*d-1/b^3*(e*x+d)^(1/2)/(b*e*x+a*e)*a^2*e^3+2/b^2*(e*x+d)^(1/2)/(b*e*x+a*e)*a*d*e^2-e/b*(e*x+d)^(1/2)/(b*e*x+a*e)*d^2+5/b^3/((a*e-b*d)*b)^(1/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*a^2*e^3-10/b^2/((a*e-b*d)*b)^(1/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*a*d*e^2+5*e/b/((a*e-b*d)*b)^(1/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*d^2","B"
1648,1,148,71,0.056000," ","int((e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2),x)","-\frac{3 a \,e^{2} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)}{\sqrt{\left(a e -b d \right) b}\, b^{2}}+\frac{3 d e \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)}{\sqrt{\left(a e -b d \right) b}\, b}+\frac{\sqrt{e x +d}\, a \,e^{2}}{\left(b e x +a e \right) b^{2}}-\frac{\sqrt{e x +d}\, d e}{\left(b e x +a e \right) b}+\frac{2 \sqrt{e x +d}\, e}{b^{2}}"," ",0,"2*e*(e*x+d)^(1/2)/b^2+1/b^2*(e*x+d)^(1/2)/(b*e*x+a*e)*a*e^2-e/b*(e*x+d)^(1/2)/(b*e*x+a*e)*d-3/b^2/((a*e-b*d)*b)^(1/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*a*e^2+3*e/b/((a*e-b*d)*b)^(1/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*d","B"
1649,1,64,58,0.067000," ","int((e*x+d)^(1/2)/(b^2*x^2+2*a*b*x+a^2),x)","\frac{e \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)}{\sqrt{\left(a e -b d \right) b}\, b}-\frac{\sqrt{e x +d}\, e}{\left(b e x +a e \right) b}"," ",0,"-e/b*(e*x+d)^(1/2)/(b*e*x+a*e)+e/b/((a*e-b*d)*b)^(1/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)","A"
1650,1,77,64,0.068000," ","int(1/(e*x+d)^(1/2)/(b^2*x^2+2*a*b*x+a^2),x)","\frac{e \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)}{\left(a e -b d \right) \sqrt{\left(a e -b d \right) b}}+\frac{\sqrt{e x +d}\, e}{\left(a e -b d \right) \left(b e x +a e \right)}"," ",0,"e*(e*x+d)^(1/2)/(a*e-b*d)/(b*e*x+a*e)+e/(a*e-b*d)/((a*e-b*d)*b)^(1/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)","A"
1651,1,101,85,0.069000," ","int(1/(e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2),x)","-\frac{3 b e \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)}{\left(a e -b d \right)^{2} \sqrt{\left(a e -b d \right) b}}-\frac{\sqrt{e x +d}\, b e}{\left(a e -b d \right)^{2} \left(b e x +a e \right)}-\frac{2 e}{\left(a e -b d \right)^{2} \sqrt{e x +d}}"," ",0,"-e*b/(a*e-b*d)^2*(e*x+d)^(1/2)/(b*e*x+a*e)-3*e*b/(a*e-b*d)^2/((a*e-b*d)*b)^(1/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)-2*e/(a*e-b*d)^2/(e*x+d)^(1/2)","A"
1652,1,125,106,0.064000," ","int(1/(e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2),x)","\frac{5 b^{2} e \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)}{\left(a e -b d \right)^{3} \sqrt{\left(a e -b d \right) b}}+\frac{\sqrt{e x +d}\, b^{2} e}{\left(a e -b d \right)^{3} \left(b e x +a e \right)}+\frac{4 b e}{\left(a e -b d \right)^{3} \sqrt{e x +d}}-\frac{2 e}{3 \left(a e -b d \right)^{2} \left(e x +d \right)^{\frac{3}{2}}}"," ",0,"e*b^2/(a*e-b*d)^3*(e*x+d)^(1/2)/(b*e*x+a*e)+5*e*b^2/(a*e-b*d)^3/((a*e-b*d)*b)^(1/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)-2/3*e/(a*e-b*d)^2/(e*x+d)^(3/2)+4*e/(a*e-b*d)^3*b/(e*x+d)^(1/2)","A"
1653,1,149,129,0.059000," ","int(1/(e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2),x)","-\frac{7 b^{3} e \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)}{\left(a e -b d \right)^{4} \sqrt{\left(a e -b d \right) b}}-\frac{\sqrt{e x +d}\, b^{3} e}{\left(a e -b d \right)^{4} \left(b e x +a e \right)}-\frac{6 b^{2} e}{\left(a e -b d \right)^{4} \sqrt{e x +d}}+\frac{4 b e}{3 \left(a e -b d \right)^{3} \left(e x +d \right)^{\frac{3}{2}}}-\frac{2 e}{5 \left(a e -b d \right)^{2} \left(e x +d \right)^{\frac{5}{2}}}"," ",0,"-e*b^3/(a*e-b*d)^4*(e*x+d)^(1/2)/(b*e*x+a*e)-7*e*b^3/(a*e-b*d)^4/((a*e-b*d)*b)^(1/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)-2/5*e/(a*e-b*d)^2/(e*x+d)^(5/2)-6*e/(a*e-b*d)^4*b^2/(e*x+d)^(1/2)+4/3*e/(a*e-b*d)^3*b/(e*x+d)^(3/2)","A"
1654,1,719,165,0.068000," ","int((e*x+d)^(11/2)/(b^2*x^2+2*a*b*x+a^2)^2,x)","\frac{71 \sqrt{e x +d}\, a^{5} e^{8}}{8 \left(b e x +a e \right)^{3} b^{6}}-\frac{355 \sqrt{e x +d}\, a^{4} d \,e^{7}}{8 \left(b e x +a e \right)^{3} b^{5}}+\frac{355 \sqrt{e x +d}\, a^{3} d^{2} e^{6}}{4 \left(b e x +a e \right)^{3} b^{4}}-\frac{355 \sqrt{e x +d}\, a^{2} d^{3} e^{5}}{4 \left(b e x +a e \right)^{3} b^{3}}+\frac{355 \sqrt{e x +d}\, a \,d^{4} e^{4}}{8 \left(b e x +a e \right)^{3} b^{2}}-\frac{71 \sqrt{e x +d}\, d^{5} e^{3}}{8 \left(b e x +a e \right)^{3} b}+\frac{59 \left(e x +d \right)^{\frac{3}{2}} a^{4} e^{7}}{3 \left(b e x +a e \right)^{3} b^{5}}-\frac{236 \left(e x +d \right)^{\frac{3}{2}} a^{3} d \,e^{6}}{3 \left(b e x +a e \right)^{3} b^{4}}+\frac{118 \left(e x +d \right)^{\frac{3}{2}} a^{2} d^{2} e^{5}}{\left(b e x +a e \right)^{3} b^{3}}-\frac{236 \left(e x +d \right)^{\frac{3}{2}} a \,d^{3} e^{4}}{3 \left(b e x +a e \right)^{3} b^{2}}+\frac{59 \left(e x +d \right)^{\frac{3}{2}} d^{4} e^{3}}{3 \left(b e x +a e \right)^{3} b}+\frac{89 \left(e x +d \right)^{\frac{5}{2}} a^{3} e^{6}}{8 \left(b e x +a e \right)^{3} b^{4}}-\frac{267 \left(e x +d \right)^{\frac{5}{2}} a^{2} d \,e^{5}}{8 \left(b e x +a e \right)^{3} b^{3}}+\frac{267 \left(e x +d \right)^{\frac{5}{2}} a \,d^{2} e^{4}}{8 \left(b e x +a e \right)^{3} b^{2}}-\frac{89 \left(e x +d \right)^{\frac{5}{2}} d^{3} e^{3}}{8 \left(b e x +a e \right)^{3} b}-\frac{231 a^{3} e^{6} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)}{8 \sqrt{\left(a e -b d \right) b}\, b^{6}}+\frac{693 a^{2} d \,e^{5} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)}{8 \sqrt{\left(a e -b d \right) b}\, b^{5}}-\frac{693 a \,d^{2} e^{4} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)}{8 \sqrt{\left(a e -b d \right) b}\, b^{4}}+\frac{231 d^{3} e^{3} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)}{8 \sqrt{\left(a e -b d \right) b}\, b^{3}}+\frac{20 \sqrt{e x +d}\, a^{2} e^{5}}{b^{6}}-\frac{40 \sqrt{e x +d}\, a d \,e^{4}}{b^{5}}+\frac{20 \sqrt{e x +d}\, d^{2} e^{3}}{b^{4}}-\frac{8 \left(e x +d \right)^{\frac{3}{2}} a \,e^{4}}{3 b^{5}}+\frac{8 \left(e x +d \right)^{\frac{3}{2}} d \,e^{3}}{3 b^{4}}+\frac{2 \left(e x +d \right)^{\frac{5}{2}} e^{3}}{5 b^{4}}"," ",0,"355/4*e^6/b^4/(b*e*x+a*e)^3*(e*x+d)^(1/2)*a^3*d^2-693/8*e^4/b^4/((a*e-b*d)*b)^(1/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*a*d^2-355/4*e^5/b^3/(b*e*x+a*e)^3*(e*x+d)^(1/2)*a^2*d^3+355/8*e^4/b^2/(b*e*x+a*e)^3*(e*x+d)^(1/2)*a*d^4+693/8*e^5/b^5/((a*e-b*d)*b)^(1/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*a^2*d+118*e^5/b^3/(b*e*x+a*e)^3*(e*x+d)^(3/2)*a^2*d^2+267/8*e^4/b^2/(b*e*x+a*e)^3*(e*x+d)^(5/2)*a*d^2-236/3*e^6/b^4/(b*e*x+a*e)^3*(e*x+d)^(3/2)*a^3*d-267/8*e^5/b^3/(b*e*x+a*e)^3*(e*x+d)^(5/2)*a^2*d-236/3*e^4/b^2/(b*e*x+a*e)^3*(e*x+d)^(3/2)*a*d^3-355/8*e^7/b^5/(b*e*x+a*e)^3*(e*x+d)^(1/2)*a^4*d-8/3*e^4/b^5*(e*x+d)^(3/2)*a+20*e^5/b^6*a^2*(e*x+d)^(1/2)+8/3*e^3/b^4*(e*x+d)^(3/2)*d+20*e^3/b^4*d^2*(e*x+d)^(1/2)+59/3*e^3/b/(b*e*x+a*e)^3*(e*x+d)^(3/2)*d^4-71/8*e^3/b/(b*e*x+a*e)^3*(e*x+d)^(1/2)*d^5+231/8*e^3/b^3/((a*e-b*d)*b)^(1/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*d^3+59/3*e^7/b^5/(b*e*x+a*e)^3*(e*x+d)^(3/2)*a^4+71/8*e^8/b^6/(b*e*x+a*e)^3*(e*x+d)^(1/2)*a^5-231/8*e^6/b^6/((a*e-b*d)*b)^(1/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*a^3+89/8*e^6/b^4/(b*e*x+a*e)^3*(e*x+d)^(5/2)*a^3-40*e^4/b^5*a*d*(e*x+d)^(1/2)-89/8*e^3/b/(b*e*x+a*e)^3*(e*x+d)^(5/2)*d^3+2/5*e^3*(e*x+d)^(5/2)/b^4","B"
1655,1,525,140,0.070000," ","int((e*x+d)^(9/2)/(b^2*x^2+2*a*b*x+a^2)^2,x)","-\frac{41 \sqrt{e x +d}\, a^{4} e^{7}}{8 \left(b e x +a e \right)^{3} b^{5}}+\frac{41 \sqrt{e x +d}\, a^{3} d \,e^{6}}{2 \left(b e x +a e \right)^{3} b^{4}}-\frac{123 \sqrt{e x +d}\, a^{2} d^{2} e^{5}}{4 \left(b e x +a e \right)^{3} b^{3}}+\frac{41 \sqrt{e x +d}\, a \,d^{3} e^{4}}{2 \left(b e x +a e \right)^{3} b^{2}}-\frac{41 \sqrt{e x +d}\, d^{4} e^{3}}{8 \left(b e x +a e \right)^{3} b}-\frac{35 \left(e x +d \right)^{\frac{3}{2}} a^{3} e^{6}}{3 \left(b e x +a e \right)^{3} b^{4}}+\frac{35 \left(e x +d \right)^{\frac{3}{2}} a^{2} d \,e^{5}}{\left(b e x +a e \right)^{3} b^{3}}-\frac{35 \left(e x +d \right)^{\frac{3}{2}} a \,d^{2} e^{4}}{\left(b e x +a e \right)^{3} b^{2}}+\frac{35 \left(e x +d \right)^{\frac{3}{2}} d^{3} e^{3}}{3 \left(b e x +a e \right)^{3} b}-\frac{55 \left(e x +d \right)^{\frac{5}{2}} a^{2} e^{5}}{8 \left(b e x +a e \right)^{3} b^{3}}+\frac{55 \left(e x +d \right)^{\frac{5}{2}} a d \,e^{4}}{4 \left(b e x +a e \right)^{3} b^{2}}-\frac{55 \left(e x +d \right)^{\frac{5}{2}} d^{2} e^{3}}{8 \left(b e x +a e \right)^{3} b}+\frac{105 a^{2} e^{5} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)}{8 \sqrt{\left(a e -b d \right) b}\, b^{5}}-\frac{105 a d \,e^{4} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)}{4 \sqrt{\left(a e -b d \right) b}\, b^{4}}+\frac{105 d^{2} e^{3} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)}{8 \sqrt{\left(a e -b d \right) b}\, b^{3}}-\frac{8 \sqrt{e x +d}\, a \,e^{4}}{b^{5}}+\frac{8 \sqrt{e x +d}\, d \,e^{3}}{b^{4}}+\frac{2 \left(e x +d \right)^{\frac{3}{2}} e^{3}}{3 b^{4}}"," ",0,"2/3*e^3*(e*x+d)^(3/2)/b^4-8*e^4/b^5*a*(e*x+d)^(1/2)+8*e^3/b^4*(e*x+d)^(1/2)*d-55/8*e^5/b^3/(b*e*x+a*e)^3*(e*x+d)^(5/2)*a^2+55/4*e^4/b^2/(b*e*x+a*e)^3*(e*x+d)^(5/2)*a*d-55/8*e^3/b/(b*e*x+a*e)^3*(e*x+d)^(5/2)*d^2-35/3*e^6/b^4/(b*e*x+a*e)^3*(e*x+d)^(3/2)*a^3+35*e^5/b^3/(b*e*x+a*e)^3*(e*x+d)^(3/2)*a^2*d-35*e^4/b^2/(b*e*x+a*e)^3*(e*x+d)^(3/2)*a*d^2+35/3*e^3/b/(b*e*x+a*e)^3*(e*x+d)^(3/2)*d^3-41/8*e^7/b^5/(b*e*x+a*e)^3*(e*x+d)^(1/2)*a^4+41/2*e^6/b^4/(b*e*x+a*e)^3*(e*x+d)^(1/2)*a^3*d-123/4*e^5/b^3/(b*e*x+a*e)^3*(e*x+d)^(1/2)*a^2*d^2+41/2*e^4/b^2/(b*e*x+a*e)^3*(e*x+d)^(1/2)*a*d^3-41/8*e^3/b/(b*e*x+a*e)^3*(e*x+d)^(1/2)*d^4+105/8*e^5/b^5/((a*e-b*d)*b)^(1/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*a^2-105/4*e^4/b^4/((a*e-b*d)*b)^(1/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*a*d+105/8*e^3/b^3/((a*e-b*d)*b)^(1/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*d^2","B"
1656,1,352,117,0.067000," ","int((e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2)^2,x)","\frac{19 \sqrt{e x +d}\, a^{3} e^{6}}{8 \left(b e x +a e \right)^{3} b^{4}}-\frac{57 \sqrt{e x +d}\, a^{2} d \,e^{5}}{8 \left(b e x +a e \right)^{3} b^{3}}+\frac{57 \sqrt{e x +d}\, a \,d^{2} e^{4}}{8 \left(b e x +a e \right)^{3} b^{2}}-\frac{19 \sqrt{e x +d}\, d^{3} e^{3}}{8 \left(b e x +a e \right)^{3} b}+\frac{17 \left(e x +d \right)^{\frac{3}{2}} a^{2} e^{5}}{3 \left(b e x +a e \right)^{3} b^{3}}-\frac{34 \left(e x +d \right)^{\frac{3}{2}} a d \,e^{4}}{3 \left(b e x +a e \right)^{3} b^{2}}+\frac{17 \left(e x +d \right)^{\frac{3}{2}} d^{2} e^{3}}{3 \left(b e x +a e \right)^{3} b}+\frac{29 \left(e x +d \right)^{\frac{5}{2}} a \,e^{4}}{8 \left(b e x +a e \right)^{3} b^{2}}-\frac{29 \left(e x +d \right)^{\frac{5}{2}} d \,e^{3}}{8 \left(b e x +a e \right)^{3} b}-\frac{35 a \,e^{4} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)}{8 \sqrt{\left(a e -b d \right) b}\, b^{4}}+\frac{35 d \,e^{3} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)}{8 \sqrt{\left(a e -b d \right) b}\, b^{3}}+\frac{2 \sqrt{e x +d}\, e^{3}}{b^{4}}"," ",0,"2*e^3*(e*x+d)^(1/2)/b^4+29/8*e^4/b^2/(b*e*x+a*e)^3*(e*x+d)^(5/2)*a-29/8*e^3/b/(b*e*x+a*e)^3*(e*x+d)^(5/2)*d+17/3*e^5/b^3/(b*e*x+a*e)^3*(e*x+d)^(3/2)*a^2-34/3*e^4/b^2/(b*e*x+a*e)^3*(e*x+d)^(3/2)*a*d+17/3*e^3/b/(b*e*x+a*e)^3*(e*x+d)^(3/2)*d^2+19/8*e^6/b^4/(b*e*x+a*e)^3*(e*x+d)^(1/2)*a^3-57/8*e^5/b^3/(b*e*x+a*e)^3*(e*x+d)^(1/2)*a^2*d+57/8*e^4/b^2/(b*e*x+a*e)^3*(e*x+d)^(1/2)*a*d^2-19/8*e^3/b/(b*e*x+a*e)^3*(e*x+d)^(1/2)*d^3-35/8*e^4/b^4/((a*e-b*d)*b)^(1/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*a+35/8*e^3/b^3/((a*e-b*d)*b)^(1/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*d","B"
1657,1,204,102,0.059000," ","int((e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2)^2,x)","-\frac{5 \sqrt{e x +d}\, a^{2} e^{5}}{8 \left(b e x +a e \right)^{3} b^{3}}+\frac{5 \sqrt{e x +d}\, a d \,e^{4}}{4 \left(b e x +a e \right)^{3} b^{2}}-\frac{5 \sqrt{e x +d}\, d^{2} e^{3}}{8 \left(b e x +a e \right)^{3} b}-\frac{5 \left(e x +d \right)^{\frac{3}{2}} a \,e^{4}}{3 \left(b e x +a e \right)^{3} b^{2}}+\frac{5 \left(e x +d \right)^{\frac{3}{2}} d \,e^{3}}{3 \left(b e x +a e \right)^{3} b}-\frac{11 \left(e x +d \right)^{\frac{5}{2}} e^{3}}{8 \left(b e x +a e \right)^{3} b}+\frac{5 e^{3} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)}{8 \sqrt{\left(a e -b d \right) b}\, b^{3}}"," ",0,"-11/8*e^3/(b*e*x+a*e)^3/b*(e*x+d)^(5/2)-5/3*e^4/(b*e*x+a*e)^3/b^2*(e*x+d)^(3/2)*a+5/3*e^3/(b*e*x+a*e)^3/b*(e*x+d)^(3/2)*d-5/8*e^5/(b*e*x+a*e)^3/b^3*(e*x+d)^(1/2)*a^2+5/4*e^4/(b*e*x+a*e)^3/b^2*(e*x+d)^(1/2)*a*d-5/8*e^3/(b*e*x+a*e)^3/b*(e*x+d)^(1/2)*d^2+5/8*e^3/b^3/((a*e-b*d)*b)^(1/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)","A"
1658,1,163,112,0.060000," ","int((e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2)^2,x)","-\frac{\sqrt{e x +d}\, a \,e^{4}}{8 \left(b e x +a e \right)^{3} b^{2}}+\frac{\sqrt{e x +d}\, d \,e^{3}}{8 \left(b e x +a e \right)^{3} b}+\frac{\left(e x +d \right)^{\frac{5}{2}} e^{3}}{8 \left(b e x +a e \right)^{3} \left(a e -b d \right)}-\frac{\left(e x +d \right)^{\frac{3}{2}} e^{3}}{3 \left(b e x +a e \right)^{3} b}+\frac{e^{3} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)}{8 \left(a e -b d \right) \sqrt{\left(a e -b d \right) b}\, b^{2}}"," ",0,"1/8*e^3/(b*e*x+a*e)^3/(a*e-b*d)*(e*x+d)^(5/2)-1/3*e^3/(b*e*x+a*e)^3/b*(e*x+d)^(3/2)-1/8*e^4/(b*e*x+a*e)^3/b^2*(e*x+d)^(1/2)*a+1/8*e^3/(b*e*x+a*e)^3/b*(e*x+d)^(1/2)*d+1/8*e^3/(a*e-b*d)/b^2/((a*e-b*d)*b)^(1/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)","A"
1659,1,170,122,0.062000," ","int((e*x+d)^(1/2)/(b^2*x^2+2*a*b*x+a^2)^2,x)","\frac{\left(e x +d \right)^{\frac{5}{2}} b \,e^{3}}{8 \left(b e x +a e \right)^{3} \left(a^{2} e^{2}-2 a b d e +b^{2} d^{2}\right)}+\frac{e^{3} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)}{8 \left(a^{2} e^{2}-2 a b d e +b^{2} d^{2}\right) \sqrt{\left(a e -b d \right) b}\, b}+\frac{\left(e x +d \right)^{\frac{3}{2}} e^{3}}{3 \left(b e x +a e \right)^{3} \left(a e -b d \right)}-\frac{\sqrt{e x +d}\, e^{3}}{8 \left(b e x +a e \right)^{3} b}"," ",0,"1/8*e^3/(b*e*x+a*e)^3*b/(a^2*e^2-2*a*b*d*e+b^2*d^2)*(e*x+d)^(5/2)+1/3*e^3/(b*e*x+a*e)^3/(a*e-b*d)*(e*x+d)^(3/2)-1/8*e^3/(b*e*x+a*e)^3/b*(e*x+d)^(1/2)+1/8*e^3/b/(a^2*e^2-2*a*b*d*e+b^2*d^2)/((a*e-b*d)*b)^(1/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)","A"
1660,1,147,123,0.151000," ","int(1/(e*x+d)^(1/2)/(b^2*x^2+2*a*b*x+a^2)^2,x)","\frac{5 e^{3} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)}{8 \left(a e -b d \right)^{3} \sqrt{\left(a e -b d \right) b}}+\frac{\sqrt{e x +d}\, e^{3}}{3 \left(a e -b d \right) \left(b e x +a e \right)^{3}}+\frac{5 \sqrt{e x +d}\, e^{3}}{12 \left(a e -b d \right)^{2} \left(b e x +a e \right)^{2}}+\frac{5 \sqrt{e x +d}\, e^{3}}{8 \left(a e -b d \right)^{3} \left(b e x +a e \right)}"," ",0,"1/3*e^3*(e*x+d)^(1/2)/(a*e-b*d)/(b*e*x+a*e)^3+5/12*e^3/(a*e-b*d)^2*(e*x+d)^(1/2)/(b*e*x+a*e)^2+5/8*e^3/(a*e-b*d)^3*(e*x+d)^(1/2)/(b*e*x+a*e)+5/8*e^3/(a*e-b*d)^3/((a*e-b*d)*b)^(1/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)","A"
1661,1,292,145,0.065000," ","int(1/(e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2)^2,x)","-\frac{29 \sqrt{e x +d}\, a^{2} b \,e^{5}}{8 \left(a e -b d \right)^{4} \left(b e x +a e \right)^{3}}+\frac{29 \sqrt{e x +d}\, a \,b^{2} d \,e^{4}}{4 \left(a e -b d \right)^{4} \left(b e x +a e \right)^{3}}-\frac{29 \sqrt{e x +d}\, b^{3} d^{2} e^{3}}{8 \left(a e -b d \right)^{4} \left(b e x +a e \right)^{3}}-\frac{17 \left(e x +d \right)^{\frac{3}{2}} a \,b^{2} e^{4}}{3 \left(a e -b d \right)^{4} \left(b e x +a e \right)^{3}}+\frac{17 \left(e x +d \right)^{\frac{3}{2}} b^{3} d \,e^{3}}{3 \left(a e -b d \right)^{4} \left(b e x +a e \right)^{3}}-\frac{19 \left(e x +d \right)^{\frac{5}{2}} b^{3} e^{3}}{8 \left(a e -b d \right)^{4} \left(b e x +a e \right)^{3}}-\frac{35 b \,e^{3} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)}{8 \left(a e -b d \right)^{4} \sqrt{\left(a e -b d \right) b}}-\frac{2 e^{3}}{\left(a e -b d \right)^{4} \sqrt{e x +d}}"," ",0,"-19/8*e^3/(a*e-b*d)^4*b^3/(b*e*x+a*e)^3*(e*x+d)^(5/2)-17/3*e^4/(a*e-b*d)^4*b^2/(b*e*x+a*e)^3*(e*x+d)^(3/2)*a+17/3*e^3/(a*e-b*d)^4*b^3/(b*e*x+a*e)^3*(e*x+d)^(3/2)*d-29/8*e^5/(a*e-b*d)^4*b/(b*e*x+a*e)^3*(e*x+d)^(1/2)*a^2+29/4*e^4/(a*e-b*d)^4*b^2/(b*e*x+a*e)^3*(e*x+d)^(1/2)*a*d-29/8*e^3/(a*e-b*d)^4*b^3/(b*e*x+a*e)^3*(e*x+d)^(1/2)*d^2-35/8*e^3/(a*e-b*d)^4*b/((a*e-b*d)*b)^(1/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)-2*e^3/(a*e-b*d)^4/(e*x+d)^(1/2)","B"
1662,1,319,168,0.069000," ","int(1/(e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2)^2,x)","\frac{55 \sqrt{e x +d}\, a^{2} b^{2} e^{5}}{8 \left(a e -b d \right)^{5} \left(b e x +a e \right)^{3}}-\frac{55 \sqrt{e x +d}\, a \,b^{3} d \,e^{4}}{4 \left(a e -b d \right)^{5} \left(b e x +a e \right)^{3}}+\frac{55 \sqrt{e x +d}\, b^{4} d^{2} e^{3}}{8 \left(a e -b d \right)^{5} \left(b e x +a e \right)^{3}}+\frac{35 \left(e x +d \right)^{\frac{3}{2}} a \,b^{3} e^{4}}{3 \left(a e -b d \right)^{5} \left(b e x +a e \right)^{3}}-\frac{35 \left(e x +d \right)^{\frac{3}{2}} b^{4} d \,e^{3}}{3 \left(a e -b d \right)^{5} \left(b e x +a e \right)^{3}}+\frac{41 \left(e x +d \right)^{\frac{5}{2}} b^{4} e^{3}}{8 \left(a e -b d \right)^{5} \left(b e x +a e \right)^{3}}+\frac{105 b^{2} e^{3} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)}{8 \left(a e -b d \right)^{5} \sqrt{\left(a e -b d \right) b}}+\frac{8 b \,e^{3}}{\left(a e -b d \right)^{5} \sqrt{e x +d}}-\frac{2 e^{3}}{3 \left(a e -b d \right)^{4} \left(e x +d \right)^{\frac{3}{2}}}"," ",0,"41/8*e^3/(a*e-b*d)^5*b^4/(b*e*x+a*e)^3*(e*x+d)^(5/2)+35/3*e^4/(a*e-b*d)^5*b^3/(b*e*x+a*e)^3*(e*x+d)^(3/2)*a-35/3*e^3/(a*e-b*d)^5*b^4/(b*e*x+a*e)^3*(e*x+d)^(3/2)*d+55/8*e^5/(a*e-b*d)^5*b^2/(b*e*x+a*e)^3*(e*x+d)^(1/2)*a^2-55/4*e^4/(a*e-b*d)^5*b^3/(b*e*x+a*e)^3*(e*x+d)^(1/2)*a*d+55/8*e^3/(a*e-b*d)^5*b^4/(b*e*x+a*e)^3*(e*x+d)^(1/2)*d^2+105/8*e^3/(a*e-b*d)^5*b^2/((a*e-b*d)*b)^(1/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)-2/3*e^3/(a*e-b*d)^4/(e*x+d)^(3/2)+8*e^3/(a*e-b*d)^5*b/(e*x+d)^(1/2)","A"
1663,1,344,193,0.071000," ","int(1/(e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2)^2,x)","-\frac{89 \sqrt{e x +d}\, a^{2} b^{3} e^{5}}{8 \left(a e -b d \right)^{6} \left(b e x +a e \right)^{3}}+\frac{89 \sqrt{e x +d}\, a \,b^{4} d \,e^{4}}{4 \left(a e -b d \right)^{6} \left(b e x +a e \right)^{3}}-\frac{89 \sqrt{e x +d}\, b^{5} d^{2} e^{3}}{8 \left(a e -b d \right)^{6} \left(b e x +a e \right)^{3}}-\frac{59 \left(e x +d \right)^{\frac{3}{2}} a \,b^{4} e^{4}}{3 \left(a e -b d \right)^{6} \left(b e x +a e \right)^{3}}+\frac{59 \left(e x +d \right)^{\frac{3}{2}} b^{5} d \,e^{3}}{3 \left(a e -b d \right)^{6} \left(b e x +a e \right)^{3}}-\frac{71 \left(e x +d \right)^{\frac{5}{2}} b^{5} e^{3}}{8 \left(a e -b d \right)^{6} \left(b e x +a e \right)^{3}}-\frac{231 b^{3} e^{3} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)}{8 \left(a e -b d \right)^{6} \sqrt{\left(a e -b d \right) b}}-\frac{20 b^{2} e^{3}}{\left(a e -b d \right)^{6} \sqrt{e x +d}}+\frac{8 b \,e^{3}}{3 \left(a e -b d \right)^{5} \left(e x +d \right)^{\frac{3}{2}}}-\frac{2 e^{3}}{5 \left(a e -b d \right)^{4} \left(e x +d \right)^{\frac{5}{2}}}"," ",0,"-71/8*e^3/(a*e-b*d)^6*b^5/(b*e*x+a*e)^3*(e*x+d)^(5/2)-59/3*e^4/(a*e-b*d)^6*b^4/(b*e*x+a*e)^3*(e*x+d)^(3/2)*a+59/3*e^3/(a*e-b*d)^6*b^5/(b*e*x+a*e)^3*(e*x+d)^(3/2)*d-89/8*e^5/(a*e-b*d)^6*b^3/(b*e*x+a*e)^3*(e*x+d)^(1/2)*a^2+89/4*e^4/(a*e-b*d)^6*b^4/(b*e*x+a*e)^3*(e*x+d)^(1/2)*a*d-89/8*e^3/(a*e-b*d)^6*b^5/(b*e*x+a*e)^3*(e*x+d)^(1/2)*d^2-231/8*e^3/(a*e-b*d)^6*b^3/((a*e-b*d)*b)^(1/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)-2/5*e^3/(a*e-b*d)^4/(e*x+d)^(5/2)-20*e^3/(a*e-b*d)^6*b^2/(e*x+d)^(1/2)+8/3*e^3/(a*e-b*d)^5*b/(e*x+d)^(3/2)","A"
1664,1,1164,209,0.081000," ","int((e*x+d)^(15/2)/(b^2*x^2+2*a*b*x+a^2)^3,x)","\frac{3633 \sqrt{e x +d}\, a^{7} e^{12}}{128 \left(b e x +a e \right)^{5} b^{8}}-\frac{25431 \sqrt{e x +d}\, a^{6} d \,e^{11}}{128 \left(b e x +a e \right)^{5} b^{7}}+\frac{76293 \sqrt{e x +d}\, a^{5} d^{2} e^{10}}{128 \left(b e x +a e \right)^{5} b^{6}}-\frac{127155 \sqrt{e x +d}\, a^{4} d^{3} e^{9}}{128 \left(b e x +a e \right)^{5} b^{5}}+\frac{127155 \sqrt{e x +d}\, a^{3} d^{4} e^{8}}{128 \left(b e x +a e \right)^{5} b^{4}}-\frac{76293 \sqrt{e x +d}\, a^{2} d^{5} e^{7}}{128 \left(b e x +a e \right)^{5} b^{3}}+\frac{25431 \sqrt{e x +d}\, a \,d^{6} e^{6}}{128 \left(b e x +a e \right)^{5} b^{2}}-\frac{3633 \sqrt{e x +d}\, d^{7} e^{5}}{128 \left(b e x +a e \right)^{5} b}+\frac{7837 \left(e x +d \right)^{\frac{3}{2}} a^{6} e^{11}}{64 \left(b e x +a e \right)^{5} b^{7}}-\frac{23511 \left(e x +d \right)^{\frac{3}{2}} a^{5} d \,e^{10}}{32 \left(b e x +a e \right)^{5} b^{6}}+\frac{117555 \left(e x +d \right)^{\frac{3}{2}} a^{4} d^{2} e^{9}}{64 \left(b e x +a e \right)^{5} b^{5}}-\frac{39185 \left(e x +d \right)^{\frac{3}{2}} a^{3} d^{3} e^{8}}{16 \left(b e x +a e \right)^{5} b^{4}}+\frac{117555 \left(e x +d \right)^{\frac{3}{2}} a^{2} d^{4} e^{7}}{64 \left(b e x +a e \right)^{5} b^{3}}-\frac{23511 \left(e x +d \right)^{\frac{3}{2}} a \,d^{5} e^{6}}{32 \left(b e x +a e \right)^{5} b^{2}}+\frac{7837 \left(e x +d \right)^{\frac{3}{2}} d^{6} e^{5}}{64 \left(b e x +a e \right)^{5} b}+\frac{1001 \left(e x +d \right)^{\frac{5}{2}} a^{5} e^{10}}{5 \left(b e x +a e \right)^{5} b^{6}}-\frac{1001 \left(e x +d \right)^{\frac{5}{2}} a^{4} d \,e^{9}}{\left(b e x +a e \right)^{5} b^{5}}+\frac{2002 \left(e x +d \right)^{\frac{5}{2}} a^{3} d^{2} e^{8}}{\left(b e x +a e \right)^{5} b^{4}}-\frac{2002 \left(e x +d \right)^{\frac{5}{2}} a^{2} d^{3} e^{7}}{\left(b e x +a e \right)^{5} b^{3}}+\frac{1001 \left(e x +d \right)^{\frac{5}{2}} a \,d^{4} e^{6}}{\left(b e x +a e \right)^{5} b^{2}}-\frac{1001 \left(e x +d \right)^{\frac{5}{2}} d^{5} e^{5}}{5 \left(b e x +a e \right)^{5} b}+\frac{9443 \left(e x +d \right)^{\frac{7}{2}} a^{4} e^{9}}{64 \left(b e x +a e \right)^{5} b^{5}}-\frac{9443 \left(e x +d \right)^{\frac{7}{2}} a^{3} d \,e^{8}}{16 \left(b e x +a e \right)^{5} b^{4}}+\frac{28329 \left(e x +d \right)^{\frac{7}{2}} a^{2} d^{2} e^{7}}{32 \left(b e x +a e \right)^{5} b^{3}}-\frac{9443 \left(e x +d \right)^{\frac{7}{2}} a \,d^{3} e^{6}}{16 \left(b e x +a e \right)^{5} b^{2}}+\frac{9443 \left(e x +d \right)^{\frac{7}{2}} d^{4} e^{5}}{64 \left(b e x +a e \right)^{5} b}+\frac{5327 \left(e x +d \right)^{\frac{9}{2}} a^{3} e^{8}}{128 \left(b e x +a e \right)^{5} b^{4}}-\frac{15981 \left(e x +d \right)^{\frac{9}{2}} a^{2} d \,e^{7}}{128 \left(b e x +a e \right)^{5} b^{3}}+\frac{15981 \left(e x +d \right)^{\frac{9}{2}} a \,d^{2} e^{6}}{128 \left(b e x +a e \right)^{5} b^{2}}-\frac{5327 \left(e x +d \right)^{\frac{9}{2}} d^{3} e^{5}}{128 \left(b e x +a e \right)^{5} b}-\frac{9009 a^{3} e^{8} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)}{128 \sqrt{\left(a e -b d \right) b}\, b^{8}}+\frac{27027 a^{2} d \,e^{7} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)}{128 \sqrt{\left(a e -b d \right) b}\, b^{7}}-\frac{27027 a \,d^{2} e^{6} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)}{128 \sqrt{\left(a e -b d \right) b}\, b^{6}}+\frac{9009 d^{3} e^{5} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)}{128 \sqrt{\left(a e -b d \right) b}\, b^{5}}+\frac{42 \sqrt{e x +d}\, a^{2} e^{7}}{b^{8}}-\frac{84 \sqrt{e x +d}\, a d \,e^{6}}{b^{7}}+\frac{42 \sqrt{e x +d}\, d^{2} e^{5}}{b^{6}}-\frac{4 \left(e x +d \right)^{\frac{3}{2}} a \,e^{6}}{b^{7}}+\frac{4 \left(e x +d \right)^{\frac{3}{2}} d \,e^{5}}{b^{6}}+\frac{2 \left(e x +d \right)^{\frac{5}{2}} e^{5}}{5 b^{6}}"," ",0,"2002*e^8/b^4/(b*e*x+a*e)^5*(e*x+d)^(5/2)*a^3*d^2+15981/128*e^6/b^2/(b*e*x+a*e)^5*(e*x+d)^(9/2)*a*d^2-1001*e^9/b^5/(b*e*x+a*e)^5*(e*x+d)^(5/2)*a^4*d-23511/32*e^6/b^2/(b*e*x+a*e)^5*(e*x+d)^(3/2)*a*d^5-25431/128*e^11/b^7/(b*e*x+a*e)^5*(e*x+d)^(1/2)*a^6*d+28329/32*e^7/b^3/(b*e*x+a*e)^5*(e*x+d)^(7/2)*a^2*d^2-9443/16*e^6/b^2/(b*e*x+a*e)^5*(e*x+d)^(7/2)*a*d^3-15981/128*e^7/b^3/(b*e*x+a*e)^5*(e*x+d)^(9/2)*a^2*d-2002*e^7/b^3/(b*e*x+a*e)^5*(e*x+d)^(5/2)*a^2*d^3-9443/16*e^8/b^4/(b*e*x+a*e)^5*(e*x+d)^(7/2)*a^3*d+25431/128*e^6/b^2/(b*e*x+a*e)^5*(e*x+d)^(1/2)*a*d^6+117555/64*e^7/b^3/(b*e*x+a*e)^5*(e*x+d)^(3/2)*a^2*d^4+9443/64*e^9/b^5/(b*e*x+a*e)^5*(e*x+d)^(7/2)*a^4+117555/64*e^9/b^5/(b*e*x+a*e)^5*(e*x+d)^(3/2)*a^4*d^2-39185/16*e^8/b^4/(b*e*x+a*e)^5*(e*x+d)^(3/2)*a^3*d^3-76293/128*e^7/b^3/(b*e*x+a*e)^5*(e*x+d)^(1/2)*a^2*d^5+27027/128*e^7/b^7/((a*e-b*d)*b)^(1/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*a^2*d-27027/128*e^6/b^6/((a*e-b*d)*b)^(1/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*a*d^2-127155/128*e^9/b^5/(b*e*x+a*e)^5*(e*x+d)^(1/2)*a^4*d^3+127155/128*e^8/b^4/(b*e*x+a*e)^5*(e*x+d)^(1/2)*a^3*d^4+76293/128*e^10/b^6/(b*e*x+a*e)^5*(e*x+d)^(1/2)*a^5*d^2+4*e^5/b^6*(e*x+d)^(3/2)*d+42*e^5/b^6*d^2*(e*x+d)^(1/2)-4*e^6/b^7*(e*x+d)^(3/2)*a+42*e^7/b^8*a^2*(e*x+d)^(1/2)+2/5*e^5*(e*x+d)^(5/2)/b^6+1001*e^6/b^2/(b*e*x+a*e)^5*(e*x+d)^(5/2)*a*d^4-23511/32*e^10/b^6/(b*e*x+a*e)^5*(e*x+d)^(3/2)*a^5*d-84*e^6/b^7*a*d*(e*x+d)^(1/2)+9009/128*e^5/b^5/((a*e-b*d)*b)^(1/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*d^3-3633/128*e^5/b/(b*e*x+a*e)^5*(e*x+d)^(1/2)*d^7+9443/64*e^5/b/(b*e*x+a*e)^5*(e*x+d)^(7/2)*d^4-5327/128*e^5/b/(b*e*x+a*e)^5*(e*x+d)^(9/2)*d^3-1001/5*e^5/b/(b*e*x+a*e)^5*(e*x+d)^(5/2)*d^5+7837/64*e^5/b/(b*e*x+a*e)^5*(e*x+d)^(3/2)*d^6-9009/128*e^8/b^8/((a*e-b*d)*b)^(1/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*a^3+3633/128*e^12/b^8/(b*e*x+a*e)^5*(e*x+d)^(1/2)*a^7+5327/128*e^8/b^4/(b*e*x+a*e)^5*(e*x+d)^(9/2)*a^3+1001/5*e^10/b^6/(b*e*x+a*e)^5*(e*x+d)^(5/2)*a^5+7837/64*e^11/b^7/(b*e*x+a*e)^5*(e*x+d)^(3/2)*a^6","B"
1665,1,908,184,0.076000," ","int((e*x+d)^(13/2)/(b^2*x^2+2*a*b*x+a^2)^3,x)","-\frac{1467 \sqrt{e x +d}\, a^{6} e^{11}}{128 \left(b e x +a e \right)^{5} b^{7}}+\frac{4401 \sqrt{e x +d}\, a^{5} d \,e^{10}}{64 \left(b e x +a e \right)^{5} b^{6}}-\frac{22005 \sqrt{e x +d}\, a^{4} d^{2} e^{9}}{128 \left(b e x +a e \right)^{5} b^{5}}+\frac{7335 \sqrt{e x +d}\, a^{3} d^{3} e^{8}}{32 \left(b e x +a e \right)^{5} b^{4}}-\frac{22005 \sqrt{e x +d}\, a^{2} d^{4} e^{7}}{128 \left(b e x +a e \right)^{5} b^{3}}+\frac{4401 \sqrt{e x +d}\, a \,d^{5} e^{6}}{64 \left(b e x +a e \right)^{5} b^{2}}-\frac{1467 \sqrt{e x +d}\, d^{6} e^{5}}{128 \left(b e x +a e \right)^{5} b}-\frac{9629 \left(e x +d \right)^{\frac{3}{2}} a^{5} e^{10}}{192 \left(b e x +a e \right)^{5} b^{6}}+\frac{48145 \left(e x +d \right)^{\frac{3}{2}} a^{4} d \,e^{9}}{192 \left(b e x +a e \right)^{5} b^{5}}-\frac{48145 \left(e x +d \right)^{\frac{3}{2}} a^{3} d^{2} e^{8}}{96 \left(b e x +a e \right)^{5} b^{4}}+\frac{48145 \left(e x +d \right)^{\frac{3}{2}} a^{2} d^{3} e^{7}}{96 \left(b e x +a e \right)^{5} b^{3}}-\frac{48145 \left(e x +d \right)^{\frac{3}{2}} a \,d^{4} e^{6}}{192 \left(b e x +a e \right)^{5} b^{2}}+\frac{9629 \left(e x +d \right)^{\frac{3}{2}} d^{5} e^{5}}{192 \left(b e x +a e \right)^{5} b}-\frac{1253 \left(e x +d \right)^{\frac{5}{2}} a^{4} e^{9}}{15 \left(b e x +a e \right)^{5} b^{5}}+\frac{5012 \left(e x +d \right)^{\frac{5}{2}} a^{3} d \,e^{8}}{15 \left(b e x +a e \right)^{5} b^{4}}-\frac{2506 \left(e x +d \right)^{\frac{5}{2}} a^{2} d^{2} e^{7}}{5 \left(b e x +a e \right)^{5} b^{3}}+\frac{5012 \left(e x +d \right)^{\frac{5}{2}} a \,d^{3} e^{6}}{15 \left(b e x +a e \right)^{5} b^{2}}-\frac{1253 \left(e x +d \right)^{\frac{5}{2}} d^{4} e^{5}}{15 \left(b e x +a e \right)^{5} b}-\frac{12131 \left(e x +d \right)^{\frac{7}{2}} a^{3} e^{8}}{192 \left(b e x +a e \right)^{5} b^{4}}+\frac{12131 \left(e x +d \right)^{\frac{7}{2}} a^{2} d \,e^{7}}{64 \left(b e x +a e \right)^{5} b^{3}}-\frac{12131 \left(e x +d \right)^{\frac{7}{2}} a \,d^{2} e^{6}}{64 \left(b e x +a e \right)^{5} b^{2}}+\frac{12131 \left(e x +d \right)^{\frac{7}{2}} d^{3} e^{5}}{192 \left(b e x +a e \right)^{5} b}-\frac{2373 \left(e x +d \right)^{\frac{9}{2}} a^{2} e^{7}}{128 \left(b e x +a e \right)^{5} b^{3}}+\frac{2373 \left(e x +d \right)^{\frac{9}{2}} a d \,e^{6}}{64 \left(b e x +a e \right)^{5} b^{2}}-\frac{2373 \left(e x +d \right)^{\frac{9}{2}} d^{2} e^{5}}{128 \left(b e x +a e \right)^{5} b}+\frac{3003 a^{2} e^{7} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)}{128 \sqrt{\left(a e -b d \right) b}\, b^{7}}-\frac{3003 a d \,e^{6} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)}{64 \sqrt{\left(a e -b d \right) b}\, b^{6}}+\frac{3003 d^{2} e^{5} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)}{128 \sqrt{\left(a e -b d \right) b}\, b^{5}}-\frac{12 \sqrt{e x +d}\, a \,e^{6}}{b^{7}}+\frac{12 \sqrt{e x +d}\, d \,e^{5}}{b^{6}}+\frac{2 \left(e x +d \right)^{\frac{3}{2}} e^{5}}{3 b^{6}}"," ",0,"-3003/64*e^6/b^6/((a*e-b*d)*b)^(1/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*a*d+48145/192*e^9/b^5/(b*e*x+a*e)^5*(e*x+d)^(3/2)*a^4*d-48145/96*e^8/b^4/(b*e*x+a*e)^5*(e*x+d)^(3/2)*a^3*d^2+48145/96*e^7/b^3/(b*e*x+a*e)^5*(e*x+d)^(3/2)*a^2*d^3-48145/192*e^6/b^2/(b*e*x+a*e)^5*(e*x+d)^(3/2)*d^4*a+4401/64*e^10/b^6/(b*e*x+a*e)^5*(e*x+d)^(1/2)*a^5*d-22005/128*e^9/b^5/(b*e*x+a*e)^5*(e*x+d)^(1/2)*a^4*d^2+7335/32*e^8/b^4/(b*e*x+a*e)^5*(e*x+d)^(1/2)*a^3*d^3+2373/64*e^6/b^2/(b*e*x+a*e)^5*(e*x+d)^(9/2)*a*d+5012/15*e^8/b^4/(b*e*x+a*e)^5*(e*x+d)^(5/2)*a^3*d-22005/128*e^7/b^3/(b*e*x+a*e)^5*(e*x+d)^(1/2)*a^2*d^4+4401/64*e^6/b^2/(b*e*x+a*e)^5*(e*x+d)^(1/2)*a*d^5+12131/64*e^7/b^3/(b*e*x+a*e)^5*(e*x+d)^(7/2)*a^2*d-12131/64*e^6/b^2/(b*e*x+a*e)^5*(e*x+d)^(7/2)*a*d^2-2506/5*e^7/b^3/(b*e*x+a*e)^5*(e*x+d)^(5/2)*d^2*a^2+5012/15*e^6/b^2/(b*e*x+a*e)^5*(e*x+d)^(5/2)*a*d^3-12*e^6/b^7*a*(e*x+d)^(1/2)+12*e^5/b^6*(e*x+d)^(1/2)*d+2/3*e^5*(e*x+d)^(3/2)/b^6+3003/128*e^7/b^7/((a*e-b*d)*b)^(1/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*a^2-2373/128*e^7/b^3/(b*e*x+a*e)^5*(e*x+d)^(9/2)*a^2-1253/15*e^5/b/(b*e*x+a*e)^5*(e*x+d)^(5/2)*d^4+9629/192*e^5/b/(b*e*x+a*e)^5*(e*x+d)^(3/2)*d^5-1467/128*e^5/b/(b*e*x+a*e)^5*(e*x+d)^(1/2)*d^6+12131/192*e^5/b/(b*e*x+a*e)^5*(e*x+d)^(7/2)*d^3-9629/192*e^10/b^6/(b*e*x+a*e)^5*(e*x+d)^(3/2)*a^5-2373/128*e^5/b/(b*e*x+a*e)^5*(e*x+d)^(9/2)*d^2-1253/15*e^9/b^5/(b*e*x+a*e)^5*(e*x+d)^(5/2)*a^4-1467/128*e^11/b^7/(b*e*x+a*e)^5*(e*x+d)^(1/2)*a^6+3003/128*e^5/b^5/((a*e-b*d)*b)^(1/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*d^2-12131/192*e^8/b^4/(b*e*x+a*e)^5*(e*x+d)^(7/2)*a^3","B"
1666,1,673,161,0.072000," ","int((e*x+d)^(11/2)/(b^2*x^2+2*a*b*x+a^2)^3,x)","\frac{437 \sqrt{e x +d}\, a^{5} e^{10}}{128 \left(b e x +a e \right)^{5} b^{6}}-\frac{2185 \sqrt{e x +d}\, a^{4} d \,e^{9}}{128 \left(b e x +a e \right)^{5} b^{5}}+\frac{2185 \sqrt{e x +d}\, a^{3} d^{2} e^{8}}{64 \left(b e x +a e \right)^{5} b^{4}}-\frac{2185 \sqrt{e x +d}\, a^{2} d^{3} e^{7}}{64 \left(b e x +a e \right)^{5} b^{3}}+\frac{2185 \sqrt{e x +d}\, a \,d^{4} e^{6}}{128 \left(b e x +a e \right)^{5} b^{2}}-\frac{437 \sqrt{e x +d}\, d^{5} e^{5}}{128 \left(b e x +a e \right)^{5} b}+\frac{977 \left(e x +d \right)^{\frac{3}{2}} a^{4} e^{9}}{64 \left(b e x +a e \right)^{5} b^{5}}-\frac{977 \left(e x +d \right)^{\frac{3}{2}} a^{3} d \,e^{8}}{16 \left(b e x +a e \right)^{5} b^{4}}+\frac{2931 \left(e x +d \right)^{\frac{3}{2}} a^{2} d^{2} e^{7}}{32 \left(b e x +a e \right)^{5} b^{3}}-\frac{977 \left(e x +d \right)^{\frac{3}{2}} a \,d^{3} e^{6}}{16 \left(b e x +a e \right)^{5} b^{2}}+\frac{977 \left(e x +d \right)^{\frac{3}{2}} d^{4} e^{5}}{64 \left(b e x +a e \right)^{5} b}+\frac{131 \left(e x +d \right)^{\frac{5}{2}} a^{3} e^{8}}{5 \left(b e x +a e \right)^{5} b^{4}}-\frac{393 \left(e x +d \right)^{\frac{5}{2}} a^{2} d \,e^{7}}{5 \left(b e x +a e \right)^{5} b^{3}}+\frac{393 \left(e x +d \right)^{\frac{5}{2}} a \,d^{2} e^{6}}{5 \left(b e x +a e \right)^{5} b^{2}}-\frac{131 \left(e x +d \right)^{\frac{5}{2}} d^{3} e^{5}}{5 \left(b e x +a e \right)^{5} b}+\frac{1327 \left(e x +d \right)^{\frac{7}{2}} a^{2} e^{7}}{64 \left(b e x +a e \right)^{5} b^{3}}-\frac{1327 \left(e x +d \right)^{\frac{7}{2}} a d \,e^{6}}{32 \left(b e x +a e \right)^{5} b^{2}}+\frac{1327 \left(e x +d \right)^{\frac{7}{2}} d^{2} e^{5}}{64 \left(b e x +a e \right)^{5} b}+\frac{843 \left(e x +d \right)^{\frac{9}{2}} a \,e^{6}}{128 \left(b e x +a e \right)^{5} b^{2}}-\frac{843 \left(e x +d \right)^{\frac{9}{2}} d \,e^{5}}{128 \left(b e x +a e \right)^{5} b}-\frac{693 a \,e^{6} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)}{128 \sqrt{\left(a e -b d \right) b}\, b^{6}}+\frac{693 d \,e^{5} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)}{128 \sqrt{\left(a e -b d \right) b}\, b^{5}}+\frac{2 \sqrt{e x +d}\, e^{5}}{b^{6}}"," ",0,"2*e^5*(e*x+d)^(1/2)/b^6+843/128*e^6/b^2/(b*e*x+a*e)^5*(e*x+d)^(9/2)*a-843/128*e^5/b/(b*e*x+a*e)^5*(e*x+d)^(9/2)*d+1327/64*e^7/b^3/(b*e*x+a*e)^5*(e*x+d)^(7/2)*a^2-1327/32*e^6/b^2/(b*e*x+a*e)^5*(e*x+d)^(7/2)*a*d+1327/64*e^5/b/(b*e*x+a*e)^5*(e*x+d)^(7/2)*d^2+131/5*e^8/b^4/(b*e*x+a*e)^5*(e*x+d)^(5/2)*a^3-393/5*e^7/b^3/(b*e*x+a*e)^5*(e*x+d)^(5/2)*a^2*d+393/5*e^6/b^2/(b*e*x+a*e)^5*(e*x+d)^(5/2)*a*d^2-131/5*e^5/b/(b*e*x+a*e)^5*(e*x+d)^(5/2)*d^3+977/64*e^9/b^5/(b*e*x+a*e)^5*(e*x+d)^(3/2)*a^4-977/16*e^8/b^4/(b*e*x+a*e)^5*(e*x+d)^(3/2)*a^3*d+2931/32*e^7/b^3/(b*e*x+a*e)^5*(e*x+d)^(3/2)*d^2*a^2-977/16*e^6/b^2/(b*e*x+a*e)^5*(e*x+d)^(3/2)*a*d^3+977/64*e^5/b/(b*e*x+a*e)^5*(e*x+d)^(3/2)*d^4+437/128*e^10/b^6/(b*e*x+a*e)^5*(e*x+d)^(1/2)*a^5-2185/128*e^9/b^5/(b*e*x+a*e)^5*(e*x+d)^(1/2)*a^4*d+2185/64*e^8/b^4/(b*e*x+a*e)^5*(e*x+d)^(1/2)*a^3*d^2-2185/64*e^7/b^3/(b*e*x+a*e)^5*(e*x+d)^(1/2)*a^2*d^3+2185/128*e^6/b^2/(b*e*x+a*e)^5*(e*x+d)^(1/2)*a*d^4-437/128*e^5/b/(b*e*x+a*e)^5*(e*x+d)^(1/2)*d^5-693/128*e^6/b^6/((a*e-b*d)*b)^(1/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*a+693/128*e^5/b^5/((a*e-b*d)*b)^(1/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*d","B"
1667,1,463,146,0.068000," ","int((e*x+d)^(9/2)/(b^2*x^2+2*a*b*x+a^2)^3,x)","-\frac{63 \sqrt{e x +d}\, a^{4} e^{9}}{128 \left(b e x +a e \right)^{5} b^{5}}+\frac{63 \sqrt{e x +d}\, a^{3} d \,e^{8}}{32 \left(b e x +a e \right)^{5} b^{4}}-\frac{189 \sqrt{e x +d}\, a^{2} d^{2} e^{7}}{64 \left(b e x +a e \right)^{5} b^{3}}+\frac{63 \sqrt{e x +d}\, a \,d^{3} e^{6}}{32 \left(b e x +a e \right)^{5} b^{2}}-\frac{63 \sqrt{e x +d}\, d^{4} e^{5}}{128 \left(b e x +a e \right)^{5} b}-\frac{147 \left(e x +d \right)^{\frac{3}{2}} a^{3} e^{8}}{64 \left(b e x +a e \right)^{5} b^{4}}+\frac{441 \left(e x +d \right)^{\frac{3}{2}} a^{2} d \,e^{7}}{64 \left(b e x +a e \right)^{5} b^{3}}-\frac{441 \left(e x +d \right)^{\frac{3}{2}} a \,d^{2} e^{6}}{64 \left(b e x +a e \right)^{5} b^{2}}+\frac{147 \left(e x +d \right)^{\frac{3}{2}} d^{3} e^{5}}{64 \left(b e x +a e \right)^{5} b}-\frac{21 \left(e x +d \right)^{\frac{5}{2}} a^{2} e^{7}}{5 \left(b e x +a e \right)^{5} b^{3}}+\frac{42 \left(e x +d \right)^{\frac{5}{2}} a d \,e^{6}}{5 \left(b e x +a e \right)^{5} b^{2}}-\frac{21 \left(e x +d \right)^{\frac{5}{2}} d^{2} e^{5}}{5 \left(b e x +a e \right)^{5} b}-\frac{237 \left(e x +d \right)^{\frac{7}{2}} a \,e^{6}}{64 \left(b e x +a e \right)^{5} b^{2}}+\frac{237 \left(e x +d \right)^{\frac{7}{2}} d \,e^{5}}{64 \left(b e x +a e \right)^{5} b}-\frac{193 \left(e x +d \right)^{\frac{9}{2}} e^{5}}{128 \left(b e x +a e \right)^{5} b}+\frac{63 e^{5} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)}{128 \sqrt{\left(a e -b d \right) b}\, b^{5}}"," ",0,"-193/128*e^5/(b*e*x+a*e)^5/b*(e*x+d)^(9/2)-237/64*e^6/(b*e*x+a*e)^5/b^2*(e*x+d)^(7/2)*a+237/64*e^5/(b*e*x+a*e)^5/b*(e*x+d)^(7/2)*d-21/5*e^7/(b*e*x+a*e)^5/b^3*(e*x+d)^(5/2)*a^2+42/5*e^6/(b*e*x+a*e)^5/b^2*(e*x+d)^(5/2)*a*d-21/5*e^5/(b*e*x+a*e)^5/b*(e*x+d)^(5/2)*d^2-147/64*e^8/(b*e*x+a*e)^5/b^4*(e*x+d)^(3/2)*a^3+441/64*e^7/(b*e*x+a*e)^5/b^3*(e*x+d)^(3/2)*a^2*d-441/64*e^6/(b*e*x+a*e)^5/b^2*(e*x+d)^(3/2)*a*d^2+147/64*e^5/(b*e*x+a*e)^5/b*(e*x+d)^(3/2)*d^3-63/128*e^9/(b*e*x+a*e)^5/b^5*(e*x+d)^(1/2)*a^4+63/32*e^8/(b*e*x+a*e)^5/b^4*(e*x+d)^(1/2)*a^3*d-189/64*e^7/(b*e*x+a*e)^5/b^3*(e*x+d)^(1/2)*a^2*d^2+63/32*e^6/(b*e*x+a*e)^5/b^2*(e*x+d)^(1/2)*a*d^3-63/128*e^5/(b*e*x+a*e)^5/b*(e*x+d)^(1/2)*d^4+63/128*e^5/b^5/((a*e-b*d)*b)^(1/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)","B"
1668,1,360,156,0.064000," ","int((e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2)^3,x)","-\frac{7 \sqrt{e x +d}\, a^{3} e^{8}}{128 \left(b e x +a e \right)^{5} b^{4}}+\frac{21 \sqrt{e x +d}\, a^{2} d \,e^{7}}{128 \left(b e x +a e \right)^{5} b^{3}}-\frac{21 \sqrt{e x +d}\, a \,d^{2} e^{6}}{128 \left(b e x +a e \right)^{5} b^{2}}+\frac{7 \sqrt{e x +d}\, d^{3} e^{5}}{128 \left(b e x +a e \right)^{5} b}-\frac{49 \left(e x +d \right)^{\frac{3}{2}} a^{2} e^{7}}{192 \left(b e x +a e \right)^{5} b^{3}}+\frac{49 \left(e x +d \right)^{\frac{3}{2}} a d \,e^{6}}{96 \left(b e x +a e \right)^{5} b^{2}}-\frac{49 \left(e x +d \right)^{\frac{3}{2}} d^{2} e^{5}}{192 \left(b e x +a e \right)^{5} b}-\frac{7 \left(e x +d \right)^{\frac{5}{2}} a \,e^{6}}{15 \left(b e x +a e \right)^{5} b^{2}}+\frac{7 \left(e x +d \right)^{\frac{5}{2}} d \,e^{5}}{15 \left(b e x +a e \right)^{5} b}+\frac{7 \left(e x +d \right)^{\frac{9}{2}} e^{5}}{128 \left(b e x +a e \right)^{5} \left(a e -b d \right)}-\frac{79 \left(e x +d \right)^{\frac{7}{2}} e^{5}}{192 \left(b e x +a e \right)^{5} b}+\frac{7 e^{5} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)}{128 \left(a e -b d \right) \sqrt{\left(a e -b d \right) b}\, b^{4}}"," ",0,"7/128*e^5/(b*e*x+a*e)^5/(a*e-b*d)*(e*x+d)^(9/2)-79/192*e^5/(b*e*x+a*e)^5/b*(e*x+d)^(7/2)-7/15*e^6/(b*e*x+a*e)^5/b^2*(e*x+d)^(5/2)*a+7/15*e^5/(b*e*x+a*e)^5/b*(e*x+d)^(5/2)*d-49/192*e^7/(b*e*x+a*e)^5/b^3*(e*x+d)^(3/2)*a^2+49/96*e^6/(b*e*x+a*e)^5/b^2*(e*x+d)^(3/2)*a*d-49/192*e^5/(b*e*x+a*e)^5/b*(e*x+d)^(3/2)*d^2-7/128*e^8/(b*e*x+a*e)^5/b^4*(e*x+d)^(1/2)*a^3+21/128*e^7/(b*e*x+a*e)^5/b^3*(e*x+d)^(1/2)*a^2*d-21/128*e^6/(b*e*x+a*e)^5/b^2*(e*x+d)^(1/2)*a*d^2+7/128*e^5/(b*e*x+a*e)^5/b*(e*x+d)^(1/2)*d^3+7/128*e^5/(a*e-b*d)/b^4/((a*e-b*d)*b)^(1/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)","B"
1669,1,305,166,0.066000," ","int((e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2)^3,x)","-\frac{3 \sqrt{e x +d}\, a^{2} e^{7}}{128 \left(b e x +a e \right)^{5} b^{3}}+\frac{3 \sqrt{e x +d}\, a d \,e^{6}}{64 \left(b e x +a e \right)^{5} b^{2}}+\frac{3 \left(e x +d \right)^{\frac{9}{2}} b \,e^{5}}{128 \left(b e x +a e \right)^{5} \left(a^{2} e^{2}-2 a b d e +b^{2} d^{2}\right)}-\frac{3 \sqrt{e x +d}\, d^{2} e^{5}}{128 \left(b e x +a e \right)^{5} b}-\frac{7 \left(e x +d \right)^{\frac{3}{2}} a \,e^{6}}{64 \left(b e x +a e \right)^{5} b^{2}}+\frac{7 \left(e x +d \right)^{\frac{3}{2}} d \,e^{5}}{64 \left(b e x +a e \right)^{5} b}+\frac{7 \left(e x +d \right)^{\frac{7}{2}} e^{5}}{64 \left(b e x +a e \right)^{5} \left(a e -b d \right)}-\frac{\left(e x +d \right)^{\frac{5}{2}} e^{5}}{5 \left(b e x +a e \right)^{5} b}+\frac{3 e^{5} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)}{128 \left(a^{2} e^{2}-2 a b d e +b^{2} d^{2}\right) \sqrt{\left(a e -b d \right) b}\, b^{3}}"," ",0,"3/128*e^5/(b*e*x+a*e)^5*b/(a^2*e^2-2*a*b*d*e+b^2*d^2)*(e*x+d)^(9/2)+7/64*e^5/(b*e*x+a*e)^5/(a*e-b*d)*(e*x+d)^(7/2)-1/5*e^5/(b*e*x+a*e)^5/b*(e*x+d)^(5/2)-7/64*e^6/(b*e*x+a*e)^5/b^2*(e*x+d)^(3/2)*a+7/64*e^5/(b*e*x+a*e)^5/b*(e*x+d)^(3/2)*d-3/128*e^7/(b*e*x+a*e)^5/b^3*(e*x+d)^(1/2)*a^2+3/64*e^6/(b*e*x+a*e)^5/b^2*(e*x+d)^(1/2)*a*d-3/128*e^5/(b*e*x+a*e)^5/b*(e*x+d)^(1/2)*d^2+3/128*e^5/b^3/(a^2*e^2-2*a*b*d*e+b^2*d^2)/((a*e-b*d)*b)^(1/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)","A"
1670,1,300,176,0.062000," ","int((e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2)^3,x)","\frac{3 \left(e x +d \right)^{\frac{9}{2}} b^{2} e^{5}}{128 \left(b e x +a e \right)^{5} \left(a^{3} e^{3}-3 a^{2} b d \,e^{2}+3 a \,b^{2} d^{2} e -b^{3} d^{3}\right)}+\frac{7 \left(e x +d \right)^{\frac{7}{2}} b \,e^{5}}{64 \left(b e x +a e \right)^{5} \left(a^{2} e^{2}-2 a b d e +b^{2} d^{2}\right)}-\frac{3 \sqrt{e x +d}\, a \,e^{6}}{128 \left(b e x +a e \right)^{5} b^{2}}+\frac{3 \sqrt{e x +d}\, d \,e^{5}}{128 \left(b e x +a e \right)^{5} b}+\frac{\left(e x +d \right)^{\frac{5}{2}} e^{5}}{5 \left(b e x +a e \right)^{5} \left(a e -b d \right)}-\frac{7 \left(e x +d \right)^{\frac{3}{2}} e^{5}}{64 \left(b e x +a e \right)^{5} b}+\frac{3 e^{5} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)}{128 \left(a^{3} e^{3}-3 a^{2} b d \,e^{2}+3 a \,b^{2} d^{2} e -b^{3} d^{3}\right) \sqrt{\left(a e -b d \right) b}\, b^{2}}"," ",0,"3/128*e^5/(b*e*x+a*e)^5/(a^3*e^3-3*a^2*b*d*e^2+3*a*b^2*d^2*e-b^3*d^3)*b^2*(e*x+d)^(9/2)+7/64*e^5/(b*e*x+a*e)^5*b/(a^2*e^2-2*a*b*d*e+b^2*d^2)*(e*x+d)^(7/2)+1/5*e^5/(b*e*x+a*e)^5/(a*e-b*d)*(e*x+d)^(5/2)-7/64*e^5/(b*e*x+a*e)^5/b*(e*x+d)^(3/2)-3/128*e^6/(b*e*x+a*e)^5/b^2*(e*x+d)^(1/2)*a+3/128*e^5/(b*e*x+a*e)^5/b*(e*x+d)^(1/2)*d+3/128*e^5/(a^3*e^3-3*a^2*b*d*e^2+3*a*b^2*d^2*e-b^3*d^3)/b^2/((a*e-b*d)*b)^(1/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)","A"
1671,1,337,186,0.057000," ","int((e*x+d)^(1/2)/(b^2*x^2+2*a*b*x+a^2)^3,x)","\frac{7 \left(e x +d \right)^{\frac{9}{2}} b^{3} e^{5}}{128 \left(b e x +a e \right)^{5} \left(a^{4} e^{4}-4 a^{3} b d \,e^{3}+6 a^{2} b^{2} d^{2} e^{2}-4 a \,b^{3} d^{3} e +b^{4} d^{4}\right)}+\frac{49 \left(e x +d \right)^{\frac{7}{2}} b^{2} e^{5}}{192 \left(b e x +a e \right)^{5} \left(a^{3} e^{3}-3 a^{2} b d \,e^{2}+3 a \,b^{2} d^{2} e -b^{3} d^{3}\right)}+\frac{7 \left(e x +d \right)^{\frac{5}{2}} b \,e^{5}}{15 \left(b e x +a e \right)^{5} \left(a^{2} e^{2}-2 a b d e +b^{2} d^{2}\right)}+\frac{7 e^{5} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)}{128 \left(a^{4} e^{4}-4 a^{3} b d \,e^{3}+6 a^{2} b^{2} d^{2} e^{2}-4 a \,b^{3} d^{3} e +b^{4} d^{4}\right) \sqrt{\left(a e -b d \right) b}\, b}+\frac{79 \left(e x +d \right)^{\frac{3}{2}} e^{5}}{192 \left(b e x +a e \right)^{5} \left(a e -b d \right)}-\frac{7 \sqrt{e x +d}\, e^{5}}{128 \left(b e x +a e \right)^{5} b}"," ",0,"7/128*e^5/(b*e*x+a*e)^5*b^3/(a^4*e^4-4*a^3*b*d*e^3+6*a^2*b^2*d^2*e^2-4*a*b^3*d^3*e+b^4*d^4)*(e*x+d)^(9/2)+49/192*e^5/(b*e*x+a*e)^5/(a^3*e^3-3*a^2*b*d*e^2+3*a*b^2*d^2*e-b^3*d^3)*b^2*(e*x+d)^(7/2)+7/15*e^5/(b*e*x+a*e)^5*b/(a^2*e^2-2*a*b*d*e+b^2*d^2)*(e*x+d)^(5/2)+79/192*e^5/(b*e*x+a*e)^5/(a*e-b*d)*(e*x+d)^(3/2)-7/128*e^5/(b*e*x+a*e)^5/b*(e*x+d)^(1/2)+7/128*e^5/b/(a^4*e^4-4*a^3*b*d*e^3+6*a^2*b^2*d^2*e^2-4*a*b^3*d^3*e+b^4*d^4)/((a*e-b*d)*b)^(1/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)","A"
1672,1,211,181,0.056000," ","int(1/(e*x+d)^(1/2)/(b^2*x^2+2*a*b*x+a^2)^3,x)","\frac{63 e^{5} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)}{128 \left(a e -b d \right)^{5} \sqrt{\left(a e -b d \right) b}}+\frac{\sqrt{e x +d}\, e^{5}}{5 \left(a e -b d \right) \left(b e x +a e \right)^{5}}+\frac{9 \sqrt{e x +d}\, e^{5}}{40 \left(a e -b d \right)^{2} \left(b e x +a e \right)^{4}}+\frac{21 \sqrt{e x +d}\, e^{5}}{80 \left(a e -b d \right)^{3} \left(b e x +a e \right)^{3}}+\frac{21 \sqrt{e x +d}\, e^{5}}{64 \left(a e -b d \right)^{4} \left(b e x +a e \right)^{2}}+\frac{63 \sqrt{e x +d}\, e^{5}}{128 \left(a e -b d \right)^{5} \left(b e x +a e \right)}"," ",0,"1/5*e^5*(e*x+d)^(1/2)/(a*e-b*d)/(b*e*x+a*e)^5+9/40*e^5/(a*e-b*d)^2*(e*x+d)^(1/2)/(b*e*x+a*e)^4+21/80*e^5/(a*e-b*d)^3*(e*x+d)^(1/2)/(b*e*x+a*e)^3+21/64*e^5/(a*e-b*d)^4*(e*x+d)^(1/2)/(b*e*x+a*e)^2+63/128*e^5/(a*e-b*d)^5*(e*x+d)^(1/2)/(b*e*x+a*e)+63/128*e^5/(a*e-b*d)^5/((a*e-b*d)*b)^(1/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)","A"
1673,1,641,203,0.072000," ","int(1/(e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2)^3,x)","-\frac{843 \sqrt{e x +d}\, a^{4} b \,e^{9}}{128 \left(a e -b d \right)^{6} \left(b e x +a e \right)^{5}}+\frac{843 \sqrt{e x +d}\, a^{3} b^{2} d \,e^{8}}{32 \left(a e -b d \right)^{6} \left(b e x +a e \right)^{5}}-\frac{2529 \sqrt{e x +d}\, a^{2} b^{3} d^{2} e^{7}}{64 \left(a e -b d \right)^{6} \left(b e x +a e \right)^{5}}+\frac{843 \sqrt{e x +d}\, a \,b^{4} d^{3} e^{6}}{32 \left(a e -b d \right)^{6} \left(b e x +a e \right)^{5}}-\frac{843 \sqrt{e x +d}\, b^{5} d^{4} e^{5}}{128 \left(a e -b d \right)^{6} \left(b e x +a e \right)^{5}}-\frac{1327 \left(e x +d \right)^{\frac{3}{2}} a^{3} b^{2} e^{8}}{64 \left(a e -b d \right)^{6} \left(b e x +a e \right)^{5}}+\frac{3981 \left(e x +d \right)^{\frac{3}{2}} a^{2} b^{3} d \,e^{7}}{64 \left(a e -b d \right)^{6} \left(b e x +a e \right)^{5}}-\frac{3981 \left(e x +d \right)^{\frac{3}{2}} a \,b^{4} d^{2} e^{6}}{64 \left(a e -b d \right)^{6} \left(b e x +a e \right)^{5}}+\frac{1327 \left(e x +d \right)^{\frac{3}{2}} b^{5} d^{3} e^{5}}{64 \left(a e -b d \right)^{6} \left(b e x +a e \right)^{5}}-\frac{131 \left(e x +d \right)^{\frac{5}{2}} a^{2} b^{3} e^{7}}{5 \left(a e -b d \right)^{6} \left(b e x +a e \right)^{5}}+\frac{262 \left(e x +d \right)^{\frac{5}{2}} a \,b^{4} d \,e^{6}}{5 \left(a e -b d \right)^{6} \left(b e x +a e \right)^{5}}-\frac{131 \left(e x +d \right)^{\frac{5}{2}} b^{5} d^{2} e^{5}}{5 \left(a e -b d \right)^{6} \left(b e x +a e \right)^{5}}-\frac{977 \left(e x +d \right)^{\frac{7}{2}} a \,b^{4} e^{6}}{64 \left(a e -b d \right)^{6} \left(b e x +a e \right)^{5}}+\frac{977 \left(e x +d \right)^{\frac{7}{2}} b^{5} d \,e^{5}}{64 \left(a e -b d \right)^{6} \left(b e x +a e \right)^{5}}-\frac{437 \left(e x +d \right)^{\frac{9}{2}} b^{5} e^{5}}{128 \left(a e -b d \right)^{6} \left(b e x +a e \right)^{5}}-\frac{693 b \,e^{5} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)}{128 \left(a e -b d \right)^{6} \sqrt{\left(a e -b d \right) b}}-\frac{2 e^{5}}{\left(a e -b d \right)^{6} \sqrt{e x +d}}"," ",0,"-437/128*e^5/(a*e-b*d)^6*b^5/(b*e*x+a*e)^5*(e*x+d)^(9/2)-977/64*e^6/(a*e-b*d)^6*b^4/(b*e*x+a*e)^5*(e*x+d)^(7/2)*a+977/64*e^5/(a*e-b*d)^6*b^5/(b*e*x+a*e)^5*(e*x+d)^(7/2)*d-131/5*e^7/(a*e-b*d)^6*b^3/(b*e*x+a*e)^5*(e*x+d)^(5/2)*a^2+262/5*e^6/(a*e-b*d)^6*b^4/(b*e*x+a*e)^5*(e*x+d)^(5/2)*a*d-131/5*e^5/(a*e-b*d)^6*b^5/(b*e*x+a*e)^5*(e*x+d)^(5/2)*d^2-1327/64*e^8/(a*e-b*d)^6*b^2/(b*e*x+a*e)^5*(e*x+d)^(3/2)*a^3+3981/64*e^7/(a*e-b*d)^6*b^3/(b*e*x+a*e)^5*(e*x+d)^(3/2)*a^2*d-3981/64*e^6/(a*e-b*d)^6*b^4/(b*e*x+a*e)^5*(e*x+d)^(3/2)*a*d^2+1327/64*e^5/(a*e-b*d)^6*b^5/(b*e*x+a*e)^5*(e*x+d)^(3/2)*d^3-843/128*e^9/(a*e-b*d)^6*b/(b*e*x+a*e)^5*(e*x+d)^(1/2)*a^4+843/32*e^8/(a*e-b*d)^6*b^2/(b*e*x+a*e)^5*(e*x+d)^(1/2)*a^3*d-2529/64*e^7/(a*e-b*d)^6*b^3/(b*e*x+a*e)^5*(e*x+d)^(1/2)*a^2*d^2+843/32*e^6/(a*e-b*d)^6*b^4/(b*e*x+a*e)^5*(e*x+d)^(1/2)*a*d^3-843/128*e^5/(a*e-b*d)^6*b^5/(b*e*x+a*e)^5*(e*x+d)^(1/2)*d^4-693/128*e^5/(a*e-b*d)^6*b/((a*e-b*d)*b)^(1/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)-2*e^5/(a*e-b*d)^6/(e*x+d)^(1/2)","B"
1674,1,668,226,0.076000," ","int(1/(e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2)^3,x)","\frac{2373 \sqrt{e x +d}\, a^{4} b^{2} e^{9}}{128 \left(a e -b d \right)^{7} \left(b e x +a e \right)^{5}}-\frac{2373 \sqrt{e x +d}\, a^{3} b^{3} d \,e^{8}}{32 \left(a e -b d \right)^{7} \left(b e x +a e \right)^{5}}+\frac{7119 \sqrt{e x +d}\, a^{2} b^{4} d^{2} e^{7}}{64 \left(a e -b d \right)^{7} \left(b e x +a e \right)^{5}}-\frac{2373 \sqrt{e x +d}\, a \,b^{5} d^{3} e^{6}}{32 \left(a e -b d \right)^{7} \left(b e x +a e \right)^{5}}+\frac{2373 \sqrt{e x +d}\, b^{6} d^{4} e^{5}}{128 \left(a e -b d \right)^{7} \left(b e x +a e \right)^{5}}+\frac{12131 \left(e x +d \right)^{\frac{3}{2}} a^{3} b^{3} e^{8}}{192 \left(a e -b d \right)^{7} \left(b e x +a e \right)^{5}}-\frac{12131 \left(e x +d \right)^{\frac{3}{2}} a^{2} b^{4} d \,e^{7}}{64 \left(a e -b d \right)^{7} \left(b e x +a e \right)^{5}}+\frac{12131 \left(e x +d \right)^{\frac{3}{2}} a \,b^{5} d^{2} e^{6}}{64 \left(a e -b d \right)^{7} \left(b e x +a e \right)^{5}}-\frac{12131 \left(e x +d \right)^{\frac{3}{2}} b^{6} d^{3} e^{5}}{192 \left(a e -b d \right)^{7} \left(b e x +a e \right)^{5}}+\frac{1253 \left(e x +d \right)^{\frac{5}{2}} a^{2} b^{4} e^{7}}{15 \left(a e -b d \right)^{7} \left(b e x +a e \right)^{5}}-\frac{2506 \left(e x +d \right)^{\frac{5}{2}} a \,b^{5} d \,e^{6}}{15 \left(a e -b d \right)^{7} \left(b e x +a e \right)^{5}}+\frac{1253 \left(e x +d \right)^{\frac{5}{2}} b^{6} d^{2} e^{5}}{15 \left(a e -b d \right)^{7} \left(b e x +a e \right)^{5}}+\frac{9629 \left(e x +d \right)^{\frac{7}{2}} a \,b^{5} e^{6}}{192 \left(a e -b d \right)^{7} \left(b e x +a e \right)^{5}}-\frac{9629 \left(e x +d \right)^{\frac{7}{2}} b^{6} d \,e^{5}}{192 \left(a e -b d \right)^{7} \left(b e x +a e \right)^{5}}+\frac{1467 \left(e x +d \right)^{\frac{9}{2}} b^{6} e^{5}}{128 \left(a e -b d \right)^{7} \left(b e x +a e \right)^{5}}+\frac{3003 b^{2} e^{5} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)}{128 \left(a e -b d \right)^{7} \sqrt{\left(a e -b d \right) b}}+\frac{12 b \,e^{5}}{\left(a e -b d \right)^{7} \sqrt{e x +d}}-\frac{2 e^{5}}{3 \left(a e -b d \right)^{6} \left(e x +d \right)^{\frac{3}{2}}}"," ",0,"1467/128*e^5/(a*e-b*d)^7*b^6/(b*e*x+a*e)^5*(e*x+d)^(9/2)+9629/192*e^6/(a*e-b*d)^7*b^5/(b*e*x+a*e)^5*(e*x+d)^(7/2)*a-9629/192*e^5/(a*e-b*d)^7*b^6/(b*e*x+a*e)^5*(e*x+d)^(7/2)*d+1253/15*e^7/(a*e-b*d)^7*b^4/(b*e*x+a*e)^5*(e*x+d)^(5/2)*a^2-2506/15*e^6/(a*e-b*d)^7*b^5/(b*e*x+a*e)^5*(e*x+d)^(5/2)*a*d+1253/15*e^5/(a*e-b*d)^7*b^6/(b*e*x+a*e)^5*(e*x+d)^(5/2)*d^2+12131/192*e^8/(a*e-b*d)^7*b^3/(b*e*x+a*e)^5*(e*x+d)^(3/2)*a^3-12131/64*e^7/(a*e-b*d)^7*b^4/(b*e*x+a*e)^5*(e*x+d)^(3/2)*a^2*d+12131/64*e^6/(a*e-b*d)^7*b^5/(b*e*x+a*e)^5*(e*x+d)^(3/2)*a*d^2-12131/192*e^5/(a*e-b*d)^7*b^6/(b*e*x+a*e)^5*(e*x+d)^(3/2)*d^3+2373/128*e^9/(a*e-b*d)^7*b^2/(b*e*x+a*e)^5*(e*x+d)^(1/2)*a^4-2373/32*e^8/(a*e-b*d)^7*b^3/(b*e*x+a*e)^5*(e*x+d)^(1/2)*a^3*d+7119/64*e^7/(a*e-b*d)^7*b^4/(b*e*x+a*e)^5*(e*x+d)^(1/2)*a^2*d^2-2373/32*e^6/(a*e-b*d)^7*b^5/(b*e*x+a*e)^5*(e*x+d)^(1/2)*a*d^3+2373/128*e^5/(a*e-b*d)^7*b^6/(b*e*x+a*e)^5*(e*x+d)^(1/2)*d^4+3003/128*e^5/(a*e-b*d)^7*b^2/((a*e-b*d)*b)^(1/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)-2/3*e^5/(a*e-b*d)^6/(e*x+d)^(3/2)+12*e^5/(a*e-b*d)^7*b/(e*x+d)^(1/2)","B"
1675,1,693,251,0.074000," ","int(1/(e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2)^3,x)","-\frac{5327 \sqrt{e x +d}\, a^{4} b^{3} e^{9}}{128 \left(a e -b d \right)^{8} \left(b e x +a e \right)^{5}}+\frac{5327 \sqrt{e x +d}\, a^{3} b^{4} d \,e^{8}}{32 \left(a e -b d \right)^{8} \left(b e x +a e \right)^{5}}-\frac{15981 \sqrt{e x +d}\, a^{2} b^{5} d^{2} e^{7}}{64 \left(a e -b d \right)^{8} \left(b e x +a e \right)^{5}}+\frac{5327 \sqrt{e x +d}\, a \,b^{6} d^{3} e^{6}}{32 \left(a e -b d \right)^{8} \left(b e x +a e \right)^{5}}-\frac{5327 \sqrt{e x +d}\, b^{7} d^{4} e^{5}}{128 \left(a e -b d \right)^{8} \left(b e x +a e \right)^{5}}-\frac{9443 \left(e x +d \right)^{\frac{3}{2}} a^{3} b^{4} e^{8}}{64 \left(a e -b d \right)^{8} \left(b e x +a e \right)^{5}}+\frac{28329 \left(e x +d \right)^{\frac{3}{2}} a^{2} b^{5} d \,e^{7}}{64 \left(a e -b d \right)^{8} \left(b e x +a e \right)^{5}}-\frac{28329 \left(e x +d \right)^{\frac{3}{2}} a \,b^{6} d^{2} e^{6}}{64 \left(a e -b d \right)^{8} \left(b e x +a e \right)^{5}}+\frac{9443 \left(e x +d \right)^{\frac{3}{2}} b^{7} d^{3} e^{5}}{64 \left(a e -b d \right)^{8} \left(b e x +a e \right)^{5}}-\frac{1001 \left(e x +d \right)^{\frac{5}{2}} a^{2} b^{5} e^{7}}{5 \left(a e -b d \right)^{8} \left(b e x +a e \right)^{5}}+\frac{2002 \left(e x +d \right)^{\frac{5}{2}} a \,b^{6} d \,e^{6}}{5 \left(a e -b d \right)^{8} \left(b e x +a e \right)^{5}}-\frac{1001 \left(e x +d \right)^{\frac{5}{2}} b^{7} d^{2} e^{5}}{5 \left(a e -b d \right)^{8} \left(b e x +a e \right)^{5}}-\frac{7837 \left(e x +d \right)^{\frac{7}{2}} a \,b^{6} e^{6}}{64 \left(a e -b d \right)^{8} \left(b e x +a e \right)^{5}}+\frac{7837 \left(e x +d \right)^{\frac{7}{2}} b^{7} d \,e^{5}}{64 \left(a e -b d \right)^{8} \left(b e x +a e \right)^{5}}-\frac{3633 \left(e x +d \right)^{\frac{9}{2}} b^{7} e^{5}}{128 \left(a e -b d \right)^{8} \left(b e x +a e \right)^{5}}-\frac{9009 b^{3} e^{5} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)}{128 \left(a e -b d \right)^{8} \sqrt{\left(a e -b d \right) b}}-\frac{42 b^{2} e^{5}}{\left(a e -b d \right)^{8} \sqrt{e x +d}}+\frac{4 b \,e^{5}}{\left(a e -b d \right)^{7} \left(e x +d \right)^{\frac{3}{2}}}-\frac{2 e^{5}}{5 \left(a e -b d \right)^{6} \left(e x +d \right)^{\frac{5}{2}}}"," ",0,"-3633/128*e^5/(a*e-b*d)^8*b^7/(b*e*x+a*e)^5*(e*x+d)^(9/2)-7837/64*e^6/(a*e-b*d)^8*b^6/(b*e*x+a*e)^5*(e*x+d)^(7/2)*a+7837/64*e^5/(a*e-b*d)^8*b^7/(b*e*x+a*e)^5*(e*x+d)^(7/2)*d-1001/5*e^7/(a*e-b*d)^8*b^5/(b*e*x+a*e)^5*(e*x+d)^(5/2)*a^2+2002/5*e^6/(a*e-b*d)^8*b^6/(b*e*x+a*e)^5*(e*x+d)^(5/2)*a*d-1001/5*e^5/(a*e-b*d)^8*b^7/(b*e*x+a*e)^5*(e*x+d)^(5/2)*d^2-9443/64*e^8/(a*e-b*d)^8*b^4/(b*e*x+a*e)^5*(e*x+d)^(3/2)*a^3+28329/64*e^7/(a*e-b*d)^8*b^5/(b*e*x+a*e)^5*(e*x+d)^(3/2)*a^2*d-28329/64*e^6/(a*e-b*d)^8*b^6/(b*e*x+a*e)^5*(e*x+d)^(3/2)*a*d^2+9443/64*e^5/(a*e-b*d)^8*b^7/(b*e*x+a*e)^5*(e*x+d)^(3/2)*d^3-5327/128*e^9/(a*e-b*d)^8*b^3/(b*e*x+a*e)^5*(e*x+d)^(1/2)*a^4+5327/32*e^8/(a*e-b*d)^8*b^4/(b*e*x+a*e)^5*(e*x+d)^(1/2)*a^3*d-15981/64*e^7/(a*e-b*d)^8*b^5/(b*e*x+a*e)^5*(e*x+d)^(1/2)*a^2*d^2+5327/32*e^6/(a*e-b*d)^8*b^6/(b*e*x+a*e)^5*(e*x+d)^(1/2)*a*d^3-5327/128*e^5/(a*e-b*d)^8*b^7/(b*e*x+a*e)^5*(e*x+d)^(1/2)*d^4-9009/128*e^5/(a*e-b*d)^8*b^3/((a*e-b*d)*b)^(1/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)-2/5*e^5/(a*e-b*d)^6/(e*x+d)^(5/2)-42*e^5/(a*e-b*d)^8*b^2/(e*x+d)^(1/2)+4*e^5/(a*e-b*d)^7*b/(e*x+d)^(3/2)","B"
1676,1,43,66,0.043000," ","int((e*x+d)^(5/2)*((b*x+a)^2)^(1/2),x)","\frac{2 \left(e x +d \right)^{\frac{7}{2}} \left(7 b e x +9 a e -2 b d \right) \sqrt{\left(b x +a \right)^{2}}}{63 \left(b x +a \right) e^{2}}"," ",0,"2/63*(e*x+d)^(7/2)*(7*b*e*x+9*a*e-2*b*d)*((b*x+a)^2)^(1/2)/e^2/(b*x+a)","A"
1677,1,43,66,0.043000," ","int((e*x+d)^(3/2)*((b*x+a)^2)^(1/2),x)","\frac{2 \left(e x +d \right)^{\frac{5}{2}} \left(5 b e x +7 a e -2 b d \right) \sqrt{\left(b x +a \right)^{2}}}{35 \left(b x +a \right) e^{2}}"," ",0,"2/35*(e*x+d)^(5/2)*(5*b*e*x+7*a*e-2*b*d)*((b*x+a)^2)^(1/2)/e^2/(b*x+a)","A"
1678,1,43,66,0.045000," ","int((e*x+d)^(1/2)*((b*x+a)^2)^(1/2),x)","\frac{2 \left(e x +d \right)^{\frac{3}{2}} \left(3 b e x +5 a e -2 b d \right) \sqrt{\left(b x +a \right)^{2}}}{15 \left(b x +a \right) e^{2}}"," ",0,"2/15*(e*x+d)^(3/2)*(3*b*e*x+5*a*e-2*b*d)*((b*x+a)^2)^(1/2)/e^2/(b*x+a)","A"
1679,1,42,66,0.045000," ","int(((b*x+a)^2)^(1/2)/(e*x+d)^(1/2),x)","\frac{2 \sqrt{e x +d}\, \left(b e x +3 a e -2 b d \right) \sqrt{\left(b x +a \right)^{2}}}{3 \left(b x +a \right) e^{2}}"," ",0,"2/3*(e*x+d)^(1/2)*(b*e*x+3*a*e-2*b*d)*((b*x+a)^2)^(1/2)/e^2/(b*x+a)","A"
1680,1,42,66,0.061000," ","int(((b*x+a)^2)^(1/2)/(e*x+d)^(3/2),x)","-\frac{2 \left(-b e x +a e -2 b d \right) \sqrt{\left(b x +a \right)^{2}}}{\sqrt{e x +d}\, \left(b x +a \right) e^{2}}"," ",0,"-2/(e*x+d)^(1/2)*(-b*e*x+a*e-2*b*d)*((b*x+a)^2)^(1/2)/e^2/(b*x+a)","A"
1681,1,42,66,0.040000," ","int(((b*x+a)^2)^(1/2)/(e*x+d)^(5/2),x)","-\frac{2 \left(3 b e x +a e +2 b d \right) \sqrt{\left(b x +a \right)^{2}}}{3 \left(e x +d \right)^{\frac{3}{2}} \left(b x +a \right) e^{2}}"," ",0,"-2/3/(e*x+d)^(3/2)*(3*b*e*x+a*e+2*b*d)*((b*x+a)^2)^(1/2)/e^2/(b*x+a)","A"
1682,1,43,66,0.041000," ","int(((b*x+a)^2)^(1/2)/(e*x+d)^(7/2),x)","-\frac{2 \left(5 b e x +3 a e +2 b d \right) \sqrt{\left(b x +a \right)^{2}}}{15 \left(e x +d \right)^{\frac{5}{2}} \left(b x +a \right) e^{2}}"," ",0,"-2/15/(e*x+d)^(5/2)*(5*b*e*x+3*a*e+2*b*d)*((b*x+a)^2)^(1/2)/e^2/(b*x+a)","A"
1683,1,132,148,0.052000," ","int((e*x+d)^(5/2)*(b^2*x^2+2*a*b*x+a^2)^(3/2),x)","\frac{2 \left(e x +d \right)^{\frac{7}{2}} \left(231 b^{3} e^{3} x^{3}+819 a \,b^{2} e^{3} x^{2}-126 b^{3} d \,e^{2} x^{2}+1001 a^{2} b \,e^{3} x -364 a \,b^{2} d \,e^{2} x +56 b^{3} d^{2} e x +429 a^{3} e^{3}-286 a^{2} b d \,e^{2}+104 a \,b^{2} d^{2} e -16 b^{3} d^{3}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}}}{3003 \left(b x +a \right)^{3} e^{4}}"," ",0,"2/3003*(e*x+d)^(7/2)*(231*b^3*e^3*x^3+819*a*b^2*e^3*x^2-126*b^3*d*e^2*x^2+1001*a^2*b*e^3*x-364*a*b^2*d*e^2*x+56*b^3*d^2*e*x+429*a^3*e^3-286*a^2*b*d*e^2+104*a*b^2*d^2*e-16*b^3*d^3)*((b*x+a)^2)^(3/2)/e^4/(b*x+a)^3","A"
1684,1,132,148,0.052000," ","int((e*x+d)^(3/2)*(b^2*x^2+2*a*b*x+a^2)^(3/2),x)","\frac{2 \left(e x +d \right)^{\frac{5}{2}} \left(105 b^{3} e^{3} x^{3}+385 a \,b^{2} e^{3} x^{2}-70 b^{3} d \,e^{2} x^{2}+495 a^{2} b \,e^{3} x -220 a \,b^{2} d \,e^{2} x +40 b^{3} d^{2} e x +231 a^{3} e^{3}-198 a^{2} b d \,e^{2}+88 a \,b^{2} d^{2} e -16 b^{3} d^{3}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}}}{1155 \left(b x +a \right)^{3} e^{4}}"," ",0,"2/1155*(e*x+d)^(5/2)*(105*b^3*e^3*x^3+385*a*b^2*e^3*x^2-70*b^3*d*e^2*x^2+495*a^2*b*e^3*x-220*a*b^2*d*e^2*x+40*b^3*d^2*e*x+231*a^3*e^3-198*a^2*b*d*e^2+88*a*b^2*d^2*e-16*b^3*d^3)*((b*x+a)^2)^(3/2)/e^4/(b*x+a)^3","A"
1685,1,132,148,0.048000," ","int((b^2*x^2+2*a*b*x+a^2)^(3/2)*(e*x+d)^(1/2),x)","\frac{2 \left(e x +d \right)^{\frac{3}{2}} \left(35 b^{3} e^{3} x^{3}+135 a \,b^{2} e^{3} x^{2}-30 b^{3} d \,e^{2} x^{2}+189 a^{2} b \,e^{3} x -108 a \,b^{2} d \,e^{2} x +24 b^{3} d^{2} e x +105 a^{3} e^{3}-126 a^{2} b d \,e^{2}+72 a \,b^{2} d^{2} e -16 b^{3} d^{3}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}}}{315 \left(b x +a \right)^{3} e^{4}}"," ",0,"2/315*(e*x+d)^(3/2)*(35*b^3*e^3*x^3+135*a*b^2*e^3*x^2-30*b^3*d*e^2*x^2+189*a^2*b*e^3*x-108*a*b^2*d*e^2*x+24*b^3*d^2*e*x+105*a^3*e^3-126*a^2*b*d*e^2+72*a*b^2*d^2*e-16*b^3*d^3)*((b*x+a)^2)^(3/2)/e^4/(b*x+a)^3","A"
1686,1,132,148,0.050000," ","int((b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^(1/2),x)","\frac{2 \sqrt{e x +d}\, \left(5 b^{3} e^{3} x^{3}+21 a \,b^{2} e^{3} x^{2}-6 b^{3} d \,e^{2} x^{2}+35 a^{2} b \,e^{3} x -28 a \,b^{2} d \,e^{2} x +8 b^{3} d^{2} e x +35 a^{3} e^{3}-70 a^{2} b d \,e^{2}+56 a \,b^{2} d^{2} e -16 b^{3} d^{3}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}}}{35 \left(b x +a \right)^{3} e^{4}}"," ",0,"2/35*(e*x+d)^(1/2)*(5*b^3*e^3*x^3+21*a*b^2*e^3*x^2-6*b^3*d*e^2*x^2+35*a^2*b*e^3*x-28*a*b^2*d*e^2*x+8*b^3*d^2*e*x+35*a^3*e^3-70*a^2*b*d*e^2+56*a*b^2*d^2*e-16*b^3*d^3)*((b*x+a)^2)^(3/2)/e^4/(b*x+a)^3","A"
1687,1,132,148,0.046000," ","int((b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^(3/2),x)","-\frac{2 \left(-b^{3} e^{3} x^{3}-5 a \,b^{2} e^{3} x^{2}+2 b^{3} d \,e^{2} x^{2}-15 a^{2} b \,e^{3} x +20 a \,b^{2} d \,e^{2} x -8 b^{3} d^{2} e x +5 a^{3} e^{3}-30 a^{2} b d \,e^{2}+40 a \,b^{2} d^{2} e -16 b^{3} d^{3}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}}}{5 \sqrt{e x +d}\, \left(b x +a \right)^{3} e^{4}}"," ",0,"-2/5/(e*x+d)^(1/2)*(-b^3*e^3*x^3-5*a*b^2*e^3*x^2+2*b^3*d*e^2*x^2-15*a^2*b*e^3*x+20*a*b^2*d*e^2*x-8*b^3*d^2*e*x+5*a^3*e^3-30*a^2*b*d*e^2+40*a*b^2*d^2*e-16*b^3*d^3)*((b*x+a)^2)^(3/2)/e^4/(b*x+a)^3","A"
1688,1,131,148,0.046000," ","int((b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^(5/2),x)","-\frac{2 \left(-b^{3} e^{3} x^{3}-9 a \,b^{2} e^{3} x^{2}+6 b^{3} d \,e^{2} x^{2}+9 a^{2} b \,e^{3} x -36 a \,b^{2} d \,e^{2} x +24 b^{3} d^{2} e x +a^{3} e^{3}+6 a^{2} b d \,e^{2}-24 a \,b^{2} d^{2} e +16 b^{3} d^{3}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}}}{3 \left(e x +d \right)^{\frac{3}{2}} \left(b x +a \right)^{3} e^{4}}"," ",0,"-2/3/(e*x+d)^(3/2)*(-b^3*e^3*x^3-9*a*b^2*e^3*x^2+6*b^3*d*e^2*x^2+9*a^2*b*e^3*x-36*a*b^2*d*e^2*x+24*b^3*d^2*e*x+a^3*e^3+6*a^2*b*d*e^2-24*a*b^2*d^2*e+16*b^3*d^3)*((b*x+a)^2)^(3/2)/e^4/(b*x+a)^3","A"
1689,1,131,148,0.050000," ","int((b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^(7/2),x)","-\frac{2 \left(-5 b^{3} e^{3} x^{3}+15 a \,b^{2} e^{3} x^{2}-30 b^{3} d \,e^{2} x^{2}+5 a^{2} b \,e^{3} x +20 a \,b^{2} d \,e^{2} x -40 b^{3} d^{2} e x +a^{3} e^{3}+2 a^{2} b d \,e^{2}+8 a \,b^{2} d^{2} e -16 b^{3} d^{3}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}}}{5 \left(e x +d \right)^{\frac{5}{2}} \left(b x +a \right)^{3} e^{4}}"," ",0,"-2/5/(e*x+d)^(5/2)*(-5*b^3*e^3*x^3+15*a*b^2*e^3*x^2-30*b^3*d*e^2*x^2+5*a^2*b*e^3*x+20*a*b^2*d*e^2*x-40*b^3*d^2*e*x+a^3*e^3+2*a^2*b*d*e^2+8*a*b^2*d^2*e-16*b^3*d^3)*((b*x+a)^2)^(3/2)/e^4/(b*x+a)^3","A"
1690,1,132,148,0.050000," ","int((b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^(9/2),x)","-\frac{2 \left(35 b^{3} e^{3} x^{3}+35 a \,b^{2} e^{3} x^{2}+70 b^{3} d \,e^{2} x^{2}+21 a^{2} b \,e^{3} x +28 a \,b^{2} d \,e^{2} x +56 b^{3} d^{2} e x +5 a^{3} e^{3}+6 a^{2} b d \,e^{2}+8 a \,b^{2} d^{2} e +16 b^{3} d^{3}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}}}{35 \left(e x +d \right)^{\frac{7}{2}} \left(b x +a \right)^{3} e^{4}}"," ",0,"-2/35/(e*x+d)^(7/2)*(35*b^3*e^3*x^3+35*a*b^2*e^3*x^2+70*b^3*d*e^2*x^2+21*a^2*b*e^3*x+28*a*b^2*d*e^2*x+56*b^3*d^2*e*x+5*a^3*e^3+6*a^2*b*d*e^2+8*a*b^2*d^2*e+16*b^3*d^3)*((b*x+a)^2)^(3/2)/e^4/(b*x+a)^3","A"
1691,1,132,148,0.048000," ","int((b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^(11/2),x)","-\frac{2 \left(105 b^{3} e^{3} x^{3}+189 a \,b^{2} e^{3} x^{2}+126 b^{3} d \,e^{2} x^{2}+135 a^{2} b \,e^{3} x +108 a \,b^{2} d \,e^{2} x +72 b^{3} d^{2} e x +35 a^{3} e^{3}+30 a^{2} b d \,e^{2}+24 a \,b^{2} d^{2} e +16 b^{3} d^{3}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}}}{315 \left(e x +d \right)^{\frac{9}{2}} \left(b x +a \right)^{3} e^{4}}"," ",0,"-2/315/(e*x+d)^(9/2)*(105*b^3*e^3*x^3+189*a*b^2*e^3*x^2+126*b^3*d*e^2*x^2+135*a^2*b*e^3*x+108*a*b^2*d*e^2*x+72*b^3*d^2*e*x+35*a^3*e^3+30*a^2*b*d*e^2+24*a*b^2*d^2*e+16*b^3*d^3)*((b*x+a)^2)^(3/2)/e^4/(b*x+a)^3","A"
1692,1,289,230,0.051000," ","int((e*x+d)^(5/2)*(b^2*x^2+2*a*b*x+a^2)^(5/2),x)","\frac{2 \left(e x +d \right)^{\frac{7}{2}} \left(9009 b^{5} e^{5} x^{5}+51051 a \,b^{4} e^{5} x^{4}-6006 b^{5} d \,e^{4} x^{4}+117810 a^{2} b^{3} e^{5} x^{3}-31416 a \,b^{4} d \,e^{4} x^{3}+3696 b^{5} d^{2} e^{3} x^{3}+139230 a^{3} b^{2} e^{5} x^{2}-64260 a^{2} b^{3} d \,e^{4} x^{2}+17136 a \,b^{4} d^{2} e^{3} x^{2}-2016 b^{5} d^{3} e^{2} x^{2}+85085 a^{4} b \,e^{5} x -61880 a^{3} b^{2} d \,e^{4} x +28560 a^{2} b^{3} d^{2} e^{3} x -7616 a \,b^{4} d^{3} e^{2} x +896 b^{5} d^{4} e x +21879 a^{5} e^{5}-24310 a^{4} b d \,e^{4}+17680 a^{3} b^{2} d^{2} e^{3}-8160 a^{2} b^{3} d^{3} e^{2}+2176 a \,b^{4} d^{4} e -256 b^{5} d^{5}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}}}{153153 \left(b x +a \right)^{5} e^{6}}"," ",0,"2/153153*(e*x+d)^(7/2)*(9009*b^5*e^5*x^5+51051*a*b^4*e^5*x^4-6006*b^5*d*e^4*x^4+117810*a^2*b^3*e^5*x^3-31416*a*b^4*d*e^4*x^3+3696*b^5*d^2*e^3*x^3+139230*a^3*b^2*e^5*x^2-64260*a^2*b^3*d*e^4*x^2+17136*a*b^4*d^2*e^3*x^2-2016*b^5*d^3*e^2*x^2+85085*a^4*b*e^5*x-61880*a^3*b^2*d*e^4*x+28560*a^2*b^3*d^2*e^3*x-7616*a*b^4*d^3*e^2*x+896*b^5*d^4*e*x+21879*a^5*e^5-24310*a^4*b*d*e^4+17680*a^3*b^2*d^2*e^3-8160*a^2*b^3*d^3*e^2+2176*a*b^4*d^4*e-256*b^5*d^5)*((b*x+a)^2)^(5/2)/e^6/(b*x+a)^5","A"
1693,1,289,230,0.046000," ","int((e*x+d)^(3/2)*(b^2*x^2+2*a*b*x+a^2)^(5/2),x)","\frac{2 \left(e x +d \right)^{\frac{5}{2}} \left(3003 b^{5} e^{5} x^{5}+17325 a \,b^{4} e^{5} x^{4}-2310 b^{5} d \,e^{4} x^{4}+40950 a^{2} b^{3} e^{5} x^{3}-12600 a \,b^{4} d \,e^{4} x^{3}+1680 b^{5} d^{2} e^{3} x^{3}+50050 a^{3} b^{2} e^{5} x^{2}-27300 a^{2} b^{3} d \,e^{4} x^{2}+8400 a \,b^{4} d^{2} e^{3} x^{2}-1120 b^{5} d^{3} e^{2} x^{2}+32175 a^{4} b \,e^{5} x -28600 a^{3} b^{2} d \,e^{4} x +15600 a^{2} b^{3} d^{2} e^{3} x -4800 a \,b^{4} d^{3} e^{2} x +640 b^{5} d^{4} e x +9009 a^{5} e^{5}-12870 a^{4} b d \,e^{4}+11440 a^{3} b^{2} d^{2} e^{3}-6240 a^{2} b^{3} d^{3} e^{2}+1920 a \,b^{4} d^{4} e -256 b^{5} d^{5}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}}}{45045 \left(b x +a \right)^{5} e^{6}}"," ",0,"2/45045*(e*x+d)^(5/2)*(3003*b^5*e^5*x^5+17325*a*b^4*e^5*x^4-2310*b^5*d*e^4*x^4+40950*a^2*b^3*e^5*x^3-12600*a*b^4*d*e^4*x^3+1680*b^5*d^2*e^3*x^3+50050*a^3*b^2*e^5*x^2-27300*a^2*b^3*d*e^4*x^2+8400*a*b^4*d^2*e^3*x^2-1120*b^5*d^3*e^2*x^2+32175*a^4*b*e^5*x-28600*a^3*b^2*d*e^4*x+15600*a^2*b^3*d^2*e^3*x-4800*a*b^4*d^3*e^2*x+640*b^5*d^4*e*x+9009*a^5*e^5-12870*a^4*b*d*e^4+11440*a^3*b^2*d^2*e^3-6240*a^2*b^3*d^3*e^2+1920*a*b^4*d^4*e-256*b^5*d^5)*((b*x+a)^2)^(5/2)/e^6/(b*x+a)^5","A"
1694,1,289,230,0.044000," ","int((b^2*x^2+2*a*b*x+a^2)^(5/2)*(e*x+d)^(1/2),x)","\frac{2 \left(e x +d \right)^{\frac{3}{2}} \left(693 b^{5} e^{5} x^{5}+4095 a \,b^{4} e^{5} x^{4}-630 b^{5} d \,e^{4} x^{4}+10010 a^{2} b^{3} e^{5} x^{3}-3640 a \,b^{4} d \,e^{4} x^{3}+560 b^{5} d^{2} e^{3} x^{3}+12870 a^{3} b^{2} e^{5} x^{2}-8580 a^{2} b^{3} d \,e^{4} x^{2}+3120 a \,b^{4} d^{2} e^{3} x^{2}-480 b^{5} d^{3} e^{2} x^{2}+9009 a^{4} b \,e^{5} x -10296 a^{3} b^{2} d \,e^{4} x +6864 a^{2} b^{3} d^{2} e^{3} x -2496 a \,b^{4} d^{3} e^{2} x +384 b^{5} d^{4} e x +3003 a^{5} e^{5}-6006 a^{4} b d \,e^{4}+6864 a^{3} b^{2} d^{2} e^{3}-4576 a^{2} b^{3} d^{3} e^{2}+1664 a \,b^{4} d^{4} e -256 b^{5} d^{5}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}}}{9009 \left(b x +a \right)^{5} e^{6}}"," ",0,"2/9009*(e*x+d)^(3/2)*(693*b^5*e^5*x^5+4095*a*b^4*e^5*x^4-630*b^5*d*e^4*x^4+10010*a^2*b^3*e^5*x^3-3640*a*b^4*d*e^4*x^3+560*b^5*d^2*e^3*x^3+12870*a^3*b^2*e^5*x^2-8580*a^2*b^3*d*e^4*x^2+3120*a*b^4*d^2*e^3*x^2-480*b^5*d^3*e^2*x^2+9009*a^4*b*e^5*x-10296*a^3*b^2*d*e^4*x+6864*a^2*b^3*d^2*e^3*x-2496*a*b^4*d^3*e^2*x+384*b^5*d^4*e*x+3003*a^5*e^5-6006*a^4*b*d*e^4+6864*a^3*b^2*d^2*e^3-4576*a^2*b^3*d^3*e^2+1664*a*b^4*d^4*e-256*b^5*d^5)*((b*x+a)^2)^(5/2)/e^6/(b*x+a)^5","A"
1695,1,289,230,0.054000," ","int((b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^(1/2),x)","\frac{2 \sqrt{e x +d}\, \left(63 b^{5} e^{5} x^{5}+385 a \,b^{4} e^{5} x^{4}-70 b^{5} d \,e^{4} x^{4}+990 a^{2} b^{3} e^{5} x^{3}-440 a \,b^{4} d \,e^{4} x^{3}+80 b^{5} d^{2} e^{3} x^{3}+1386 a^{3} b^{2} e^{5} x^{2}-1188 a^{2} b^{3} d \,e^{4} x^{2}+528 a \,b^{4} d^{2} e^{3} x^{2}-96 b^{5} d^{3} e^{2} x^{2}+1155 a^{4} b \,e^{5} x -1848 a^{3} b^{2} d \,e^{4} x +1584 a^{2} b^{3} d^{2} e^{3} x -704 a \,b^{4} d^{3} e^{2} x +128 b^{5} d^{4} e x +693 a^{5} e^{5}-2310 a^{4} b d \,e^{4}+3696 a^{3} b^{2} d^{2} e^{3}-3168 a^{2} b^{3} d^{3} e^{2}+1408 a \,b^{4} d^{4} e -256 b^{5} d^{5}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}}}{693 \left(b x +a \right)^{5} e^{6}}"," ",0,"2/693*(e*x+d)^(1/2)*(63*b^5*e^5*x^5+385*a*b^4*e^5*x^4-70*b^5*d*e^4*x^4+990*a^2*b^3*e^5*x^3-440*a*b^4*d*e^4*x^3+80*b^5*d^2*e^3*x^3+1386*a^3*b^2*e^5*x^2-1188*a^2*b^3*d*e^4*x^2+528*a*b^4*d^2*e^3*x^2-96*b^5*d^3*e^2*x^2+1155*a^4*b*e^5*x-1848*a^3*b^2*d*e^4*x+1584*a^2*b^3*d^2*e^3*x-704*a*b^4*d^3*e^2*x+128*b^5*d^4*e*x+693*a^5*e^5-2310*a^4*b*d*e^4+3696*a^3*b^2*d^2*e^3-3168*a^2*b^3*d^3*e^2+1408*a*b^4*d^4*e-256*b^5*d^5)*((b*x+a)^2)^(5/2)/e^6/(b*x+a)^5","A"
1696,1,289,230,0.050000," ","int((b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^(3/2),x)","-\frac{2 \left(-7 b^{5} e^{5} x^{5}-45 a \,b^{4} e^{5} x^{4}+10 b^{5} d \,e^{4} x^{4}-126 a^{2} b^{3} e^{5} x^{3}+72 a \,b^{4} d \,e^{4} x^{3}-16 b^{5} d^{2} e^{3} x^{3}-210 a^{3} b^{2} e^{5} x^{2}+252 a^{2} b^{3} d \,e^{4} x^{2}-144 a \,b^{4} d^{2} e^{3} x^{2}+32 b^{5} d^{3} e^{2} x^{2}-315 a^{4} b \,e^{5} x +840 a^{3} b^{2} d \,e^{4} x -1008 a^{2} b^{3} d^{2} e^{3} x +576 a \,b^{4} d^{3} e^{2} x -128 b^{5} d^{4} e x +63 a^{5} e^{5}-630 a^{4} b d \,e^{4}+1680 a^{3} b^{2} d^{2} e^{3}-2016 a^{2} b^{3} d^{3} e^{2}+1152 a \,b^{4} d^{4} e -256 b^{5} d^{5}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}}}{63 \sqrt{e x +d}\, \left(b x +a \right)^{5} e^{6}}"," ",0,"-2/63/(e*x+d)^(1/2)*(-7*b^5*e^5*x^5-45*a*b^4*e^5*x^4+10*b^5*d*e^4*x^4-126*a^2*b^3*e^5*x^3+72*a*b^4*d*e^4*x^3-16*b^5*d^2*e^3*x^3-210*a^3*b^2*e^5*x^2+252*a^2*b^3*d*e^4*x^2-144*a*b^4*d^2*e^3*x^2+32*b^5*d^3*e^2*x^2-315*a^4*b*e^5*x+840*a^3*b^2*d*e^4*x-1008*a^2*b^3*d^2*e^3*x+576*a*b^4*d^3*e^2*x-128*b^5*d^4*e*x+63*a^5*e^5-630*a^4*b*d*e^4+1680*a^3*b^2*d^2*e^3-2016*a^2*b^3*d^3*e^2+1152*a*b^4*d^4*e-256*b^5*d^5)*((b*x+a)^2)^(5/2)/e^6/(b*x+a)^5","A"
1697,1,289,230,0.053000," ","int((b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^(5/2),x)","-\frac{2 \left(-3 b^{5} e^{5} x^{5}-21 a \,b^{4} e^{5} x^{4}+6 b^{5} d \,e^{4} x^{4}-70 a^{2} b^{3} e^{5} x^{3}+56 a \,b^{4} d \,e^{4} x^{3}-16 b^{5} d^{2} e^{3} x^{3}-210 a^{3} b^{2} e^{5} x^{2}+420 a^{2} b^{3} d \,e^{4} x^{2}-336 a \,b^{4} d^{2} e^{3} x^{2}+96 b^{5} d^{3} e^{2} x^{2}+105 a^{4} b \,e^{5} x -840 a^{3} b^{2} d \,e^{4} x +1680 a^{2} b^{3} d^{2} e^{3} x -1344 a \,b^{4} d^{3} e^{2} x +384 b^{5} d^{4} e x +7 a^{5} e^{5}+70 a^{4} b d \,e^{4}-560 a^{3} b^{2} d^{2} e^{3}+1120 a^{2} b^{3} d^{3} e^{2}-896 a \,b^{4} d^{4} e +256 b^{5} d^{5}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}}}{21 \left(e x +d \right)^{\frac{3}{2}} \left(b x +a \right)^{5} e^{6}}"," ",0,"-2/21/(e*x+d)^(3/2)*(-3*b^5*e^5*x^5-21*a*b^4*e^5*x^4+6*b^5*d*e^4*x^4-70*a^2*b^3*e^5*x^3+56*a*b^4*d*e^4*x^3-16*b^5*d^2*e^3*x^3-210*a^3*b^2*e^5*x^2+420*a^2*b^3*d*e^4*x^2-336*a*b^4*d^2*e^3*x^2+96*b^5*d^3*e^2*x^2+105*a^4*b*e^5*x-840*a^3*b^2*d*e^4*x+1680*a^2*b^3*d^2*e^3*x-1344*a*b^4*d^3*e^2*x+384*b^5*d^4*e*x+7*a^5*e^5+70*a^4*b*d*e^4-560*a^3*b^2*d^2*e^3+1120*a^2*b^3*d^3*e^2-896*a*b^4*d^4*e+256*b^5*d^5)*((b*x+a)^2)^(5/2)/e^6/(b*x+a)^5","A"
1698,1,289,230,0.054000," ","int((b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^(7/2),x)","-\frac{2 \left(-3 b^{5} e^{5} x^{5}-25 a \,b^{4} e^{5} x^{4}+10 b^{5} d \,e^{4} x^{4}-150 a^{2} b^{3} e^{5} x^{3}+200 a \,b^{4} d \,e^{4} x^{3}-80 b^{5} d^{2} e^{3} x^{3}+150 a^{3} b^{2} e^{5} x^{2}-900 a^{2} b^{3} d \,e^{4} x^{2}+1200 a \,b^{4} d^{2} e^{3} x^{2}-480 b^{5} d^{3} e^{2} x^{2}+25 a^{4} b \,e^{5} x +200 a^{3} b^{2} d \,e^{4} x -1200 a^{2} b^{3} d^{2} e^{3} x +1600 a \,b^{4} d^{3} e^{2} x -640 b^{5} d^{4} e x +3 a^{5} e^{5}+10 a^{4} b d \,e^{4}+80 a^{3} b^{2} d^{2} e^{3}-480 a^{2} b^{3} d^{3} e^{2}+640 a \,b^{4} d^{4} e -256 b^{5} d^{5}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}}}{15 \left(e x +d \right)^{\frac{5}{2}} \left(b x +a \right)^{5} e^{6}}"," ",0,"-2/15/(e*x+d)^(5/2)*(-3*b^5*e^5*x^5-25*a*b^4*e^5*x^4+10*b^5*d*e^4*x^4-150*a^2*b^3*e^5*x^3+200*a*b^4*d*e^4*x^3-80*b^5*d^2*e^3*x^3+150*a^3*b^2*e^5*x^2-900*a^2*b^3*d*e^4*x^2+1200*a*b^4*d^2*e^3*x^2-480*b^5*d^3*e^2*x^2+25*a^4*b*e^5*x+200*a^3*b^2*d*e^4*x-1200*a^2*b^3*d^2*e^3*x+1600*a*b^4*d^3*e^2*x-640*b^5*d^4*e*x+3*a^5*e^5+10*a^4*b*d*e^4+80*a^3*b^2*d^2*e^3-480*a^2*b^3*d^3*e^2+640*a*b^4*d^4*e-256*b^5*d^5)*((b*x+a)^2)^(5/2)/e^6/(b*x+a)^5","A"
1699,1,289,230,0.052000," ","int((b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^(9/2),x)","-\frac{2 \left(-7 b^{5} e^{5} x^{5}-105 a \,b^{4} e^{5} x^{4}+70 b^{5} d \,e^{4} x^{4}+210 a^{2} b^{3} e^{5} x^{3}-840 a \,b^{4} d \,e^{4} x^{3}+560 b^{5} d^{2} e^{3} x^{3}+70 a^{3} b^{2} e^{5} x^{2}+420 a^{2} b^{3} d \,e^{4} x^{2}-1680 a \,b^{4} d^{2} e^{3} x^{2}+1120 b^{5} d^{3} e^{2} x^{2}+21 a^{4} b \,e^{5} x +56 a^{3} b^{2} d \,e^{4} x +336 a^{2} b^{3} d^{2} e^{3} x -1344 a \,b^{4} d^{3} e^{2} x +896 b^{5} d^{4} e x +3 a^{5} e^{5}+6 a^{4} b d \,e^{4}+16 a^{3} b^{2} d^{2} e^{3}+96 a^{2} b^{3} d^{3} e^{2}-384 a \,b^{4} d^{4} e +256 b^{5} d^{5}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}}}{21 \left(e x +d \right)^{\frac{7}{2}} \left(b x +a \right)^{5} e^{6}}"," ",0,"-2/21/(e*x+d)^(7/2)*(-7*b^5*e^5*x^5-105*a*b^4*e^5*x^4+70*b^5*d*e^4*x^4+210*a^2*b^3*e^5*x^3-840*a*b^4*d*e^4*x^3+560*b^5*d^2*e^3*x^3+70*a^3*b^2*e^5*x^2+420*a^2*b^3*d*e^4*x^2-1680*a*b^4*d^2*e^3*x^2+1120*b^5*d^3*e^2*x^2+21*a^4*b*e^5*x+56*a^3*b^2*d*e^4*x+336*a^2*b^3*d^2*e^3*x-1344*a*b^4*d^3*e^2*x+896*b^5*d^4*e*x+3*a^5*e^5+6*a^4*b*d*e^4+16*a^3*b^2*d^2*e^3+96*a^2*b^3*d^3*e^2-384*a*b^4*d^4*e+256*b^5*d^5)*((b*x+a)^2)^(5/2)/e^6/(b*x+a)^5","A"
1700,1,289,230,0.049000," ","int((b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^(11/2),x)","-\frac{2 \left(-63 b^{5} e^{5} x^{5}+315 a \,b^{4} e^{5} x^{4}-630 b^{5} d \,e^{4} x^{4}+210 a^{2} b^{3} e^{5} x^{3}+840 a \,b^{4} d \,e^{4} x^{3}-1680 b^{5} d^{2} e^{3} x^{3}+126 a^{3} b^{2} e^{5} x^{2}+252 a^{2} b^{3} d \,e^{4} x^{2}+1008 a \,b^{4} d^{2} e^{3} x^{2}-2016 b^{5} d^{3} e^{2} x^{2}+45 a^{4} b \,e^{5} x +72 a^{3} b^{2} d \,e^{4} x +144 a^{2} b^{3} d^{2} e^{3} x +576 a \,b^{4} d^{3} e^{2} x -1152 b^{5} d^{4} e x +7 a^{5} e^{5}+10 a^{4} b d \,e^{4}+16 a^{3} b^{2} d^{2} e^{3}+32 a^{2} b^{3} d^{3} e^{2}+128 a \,b^{4} d^{4} e -256 b^{5} d^{5}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}}}{63 \left(e x +d \right)^{\frac{9}{2}} \left(b x +a \right)^{5} e^{6}}"," ",0,"-2/63/(e*x+d)^(9/2)*(-63*b^5*e^5*x^5+315*a*b^4*e^5*x^4-630*b^5*d*e^4*x^4+210*a^2*b^3*e^5*x^3+840*a*b^4*d*e^4*x^3-1680*b^5*d^2*e^3*x^3+126*a^3*b^2*e^5*x^2+252*a^2*b^3*d*e^4*x^2+1008*a*b^4*d^2*e^3*x^2-2016*b^5*d^3*e^2*x^2+45*a^4*b*e^5*x+72*a^3*b^2*d*e^4*x+144*a^2*b^3*d^2*e^3*x+576*a*b^4*d^3*e^2*x-1152*b^5*d^4*e*x+7*a^5*e^5+10*a^4*b*d*e^4+16*a^3*b^2*d^2*e^3+32*a^2*b^3*d^3*e^2+128*a*b^4*d^4*e-256*b^5*d^5)*((b*x+a)^2)^(5/2)/e^6/(b*x+a)^5","A"
1701,1,289,230,0.046000," ","int((b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^(13/2),x)","-\frac{2 \left(693 b^{5} e^{5} x^{5}+1155 a \,b^{4} e^{5} x^{4}+2310 b^{5} d \,e^{4} x^{4}+1386 a^{2} b^{3} e^{5} x^{3}+1848 a \,b^{4} d \,e^{4} x^{3}+3696 b^{5} d^{2} e^{3} x^{3}+990 a^{3} b^{2} e^{5} x^{2}+1188 a^{2} b^{3} d \,e^{4} x^{2}+1584 a \,b^{4} d^{2} e^{3} x^{2}+3168 b^{5} d^{3} e^{2} x^{2}+385 a^{4} b \,e^{5} x +440 a^{3} b^{2} d \,e^{4} x +528 a^{2} b^{3} d^{2} e^{3} x +704 a \,b^{4} d^{3} e^{2} x +1408 b^{5} d^{4} e x +63 a^{5} e^{5}+70 a^{4} b d \,e^{4}+80 a^{3} b^{2} d^{2} e^{3}+96 a^{2} b^{3} d^{3} e^{2}+128 a \,b^{4} d^{4} e +256 b^{5} d^{5}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}}}{693 \left(e x +d \right)^{\frac{11}{2}} \left(b x +a \right)^{5} e^{6}}"," ",0,"-2/693/(e*x+d)^(11/2)*(693*b^5*e^5*x^5+1155*a*b^4*e^5*x^4+2310*b^5*d*e^4*x^4+1386*a^2*b^3*e^5*x^3+1848*a*b^4*d*e^4*x^3+3696*b^5*d^2*e^3*x^3+990*a^3*b^2*e^5*x^2+1188*a^2*b^3*d*e^4*x^2+1584*a*b^4*d^2*e^3*x^2+3168*b^5*d^3*e^2*x^2+385*a^4*b*e^5*x+440*a^3*b^2*d*e^4*x+528*a^2*b^3*d^2*e^3*x+704*a*b^4*d^3*e^2*x+1408*b^5*d^4*e*x+63*a^5*e^5+70*a^4*b*d*e^4+80*a^3*b^2*d^2*e^3+96*a^2*b^3*d^3*e^2+128*a*b^4*d^4*e+256*b^5*d^5)*((b*x+a)^2)^(5/2)/e^6/(b*x+a)^5","A"
1702,1,289,230,0.046000," ","int((b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^(15/2),x)","-\frac{2 \left(3003 b^{5} e^{5} x^{5}+9009 a \,b^{4} e^{5} x^{4}+6006 b^{5} d \,e^{4} x^{4}+12870 a^{2} b^{3} e^{5} x^{3}+10296 a \,b^{4} d \,e^{4} x^{3}+6864 b^{5} d^{2} e^{3} x^{3}+10010 a^{3} b^{2} e^{5} x^{2}+8580 a^{2} b^{3} d \,e^{4} x^{2}+6864 a \,b^{4} d^{2} e^{3} x^{2}+4576 b^{5} d^{3} e^{2} x^{2}+4095 a^{4} b \,e^{5} x +3640 a^{3} b^{2} d \,e^{4} x +3120 a^{2} b^{3} d^{2} e^{3} x +2496 a \,b^{4} d^{3} e^{2} x +1664 b^{5} d^{4} e x +693 a^{5} e^{5}+630 a^{4} b d \,e^{4}+560 a^{3} b^{2} d^{2} e^{3}+480 a^{2} b^{3} d^{3} e^{2}+384 a \,b^{4} d^{4} e +256 b^{5} d^{5}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}}}{9009 \left(e x +d \right)^{\frac{13}{2}} \left(b x +a \right)^{5} e^{6}}"," ",0,"-2/9009/(e*x+d)^(13/2)*(3003*b^5*e^5*x^5+9009*a*b^4*e^5*x^4+6006*b^5*d*e^4*x^4+12870*a^2*b^3*e^5*x^3+10296*a*b^4*d*e^4*x^3+6864*b^5*d^2*e^3*x^3+10010*a^3*b^2*e^5*x^2+8580*a^2*b^3*d*e^4*x^2+6864*a*b^4*d^2*e^3*x^2+4576*b^5*d^3*e^2*x^2+4095*a^4*b*e^5*x+3640*a^3*b^2*d*e^4*x+3120*a^2*b^3*d^2*e^3*x+2496*a*b^4*d^3*e^2*x+1664*b^5*d^4*e*x+693*a^5*e^5+630*a^4*b*d*e^4+560*a^3*b^2*d^2*e^3+480*a^2*b^3*d^3*e^2+384*a*b^4*d^4*e+256*b^5*d^5)*((b*x+a)^2)^(5/2)/e^6/(b*x+a)^5","A"
1703,1,462,184,0.056000," ","int((e*x+d)^(7/2)/((b*x+a)^2)^(1/2),x)","\frac{2 \left(b x +a \right) \left(105 a^{4} e^{4} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)-420 a^{3} b d \,e^{3} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+630 a^{2} b^{2} d^{2} e^{2} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)-420 a \,b^{3} d^{3} e \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+105 b^{4} d^{4} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)-105 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a^{3} e^{3}+315 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a^{2} b d \,e^{2}-315 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a \,b^{2} d^{2} e +105 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, b^{3} d^{3}+35 \left(e x +d \right)^{\frac{3}{2}} \sqrt{\left(a e -b d \right) b}\, a^{2} b \,e^{2}-70 \left(e x +d \right)^{\frac{3}{2}} \sqrt{\left(a e -b d \right) b}\, a \,b^{2} d e +35 \left(e x +d \right)^{\frac{3}{2}} \sqrt{\left(a e -b d \right) b}\, b^{3} d^{2}-21 \left(e x +d \right)^{\frac{5}{2}} \sqrt{\left(a e -b d \right) b}\, a \,b^{2} e +21 \left(e x +d \right)^{\frac{5}{2}} \sqrt{\left(a e -b d \right) b}\, b^{3} d +15 \left(e x +d \right)^{\frac{7}{2}} \sqrt{\left(a e -b d \right) b}\, b^{3}\right)}{105 \sqrt{\left(b x +a \right)^{2}}\, \sqrt{\left(a e -b d \right) b}\, b^{4}}"," ",0,"2/105*(b*x+a)*(15*(e*x+d)^(7/2)*((a*e-b*d)*b)^(1/2)*b^3-21*(e*x+d)^(5/2)*((a*e-b*d)*b)^(1/2)*a*b^2*e+21*(e*x+d)^(5/2)*((a*e-b*d)*b)^(1/2)*b^3*d+35*(e*x+d)^(3/2)*((a*e-b*d)*b)^(1/2)*a^2*b*e^2-70*(e*x+d)^(3/2)*((a*e-b*d)*b)^(1/2)*a*b^2*d*e+35*(e*x+d)^(3/2)*((a*e-b*d)*b)^(1/2)*b^3*d^2+105*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*a^4*e^4-420*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*a^3*b*d*e^3+630*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*a^2*b^2*d^2*e^2-420*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*a*b^3*d^3*e+105*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*b^4*d^4-105*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*a^3*e^3+315*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*a^2*b*d*e^2-315*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*a*b^2*d^2*e+105*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*b^3*d^3)/((b*x+a)^2)^(1/2)/b^4/((a*e-b*d)*b)^(1/2)","B"
1704,1,309,148,0.054000," ","int((e*x+d)^(5/2)/((b*x+a)^2)^(1/2),x)","\frac{2 \left(b x +a \right) \left(-15 a^{3} e^{3} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+45 a^{2} b d \,e^{2} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)-45 a \,b^{2} d^{2} e \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+15 b^{3} d^{3} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+15 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a^{2} e^{2}-30 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a b d e +15 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, b^{2} d^{2}-5 \left(e x +d \right)^{\frac{3}{2}} \sqrt{\left(a e -b d \right) b}\, a b e +5 \left(e x +d \right)^{\frac{3}{2}} \sqrt{\left(a e -b d \right) b}\, b^{2} d +3 \left(e x +d \right)^{\frac{5}{2}} \sqrt{\left(a e -b d \right) b}\, b^{2}\right)}{15 \sqrt{\left(b x +a \right)^{2}}\, \sqrt{\left(a e -b d \right) b}\, b^{3}}"," ",0,"2/15*(b*x+a)*(3*(e*x+d)^(5/2)*((a*e-b*d)*b)^(1/2)*b^2-5*(e*x+d)^(3/2)*((a*e-b*d)*b)^(1/2)*a*b*e+5*(e*x+d)^(3/2)*((a*e-b*d)*b)^(1/2)*b^2*d-15*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*a^3*e^3+45*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*a^2*b*d*e^2-45*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*a*b^2*d^2*e+15*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*b^3*d^3+15*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*a^2*e^2-30*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*a*b*d*e+15*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*b^2*d^2)/((b*x+a)^2)^(1/2)/b^3/((a*e-b*d)*b)^(1/2)","B"
1705,1,188,112,0.053000," ","int((e*x+d)^(3/2)/((b*x+a)^2)^(1/2),x)","\frac{2 \left(b x +a \right) \left(3 a^{2} e^{2} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)-6 a b d e \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+3 b^{2} d^{2} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)-3 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a e +3 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, b d +\left(e x +d \right)^{\frac{3}{2}} \sqrt{\left(a e -b d \right) b}\, b \right)}{3 \sqrt{\left(b x +a \right)^{2}}\, \sqrt{\left(a e -b d \right) b}\, b^{2}}"," ",0,"2/3*(b*x+a)*((e*x+d)^(3/2)*((a*e-b*d)*b)^(1/2)*b+3*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*a^2*e^2-6*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*a*b*d*e+3*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*b^2*d^2-3*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*a*e+3*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*b*d)/((b*x+a)^2)^(1/2)/b^2/((a*e-b*d)*b)^(1/2)","A"
1706,1,104,78,0.050000," ","int((e*x+d)^(1/2)/((b*x+a)^2)^(1/2),x)","\frac{2 \left(b x +a \right) \left(-a e \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+b d \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+\sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\right)}{\sqrt{\left(b x +a \right)^{2}}\, \sqrt{\left(a e -b d \right) b}\, b}"," ",0,"2*(b*x+a)*(-arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*a*e+arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*b*d+(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2))/((b*x+a)^2)^(1/2)/b/((a*e-b*d)*b)^(1/2)","A"
1707,1,51,51,0.054000," ","int(1/(e*x+d)^(1/2)/((b*x+a)^2)^(1/2),x)","\frac{2 \left(b x +a \right) \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)}{\sqrt{\left(b x +a \right)^{2}}\, \sqrt{\left(a e -b d \right) b}}"," ",0,"2/((b*x+a)^2)^(1/2)*(b*x+a)/((a*e-b*d)*b)^(1/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)","A"
1708,1,90,85,0.064000," ","int(1/(e*x+d)^(3/2)/((b*x+a)^2)^(1/2),x)","-\frac{2 \left(b x +a \right) \left(\sqrt{e x +d}\, b \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+\sqrt{\left(a e -b d \right) b}\right)}{\sqrt{\left(b x +a \right)^{2}}\, \left(a e -b d \right) \sqrt{\left(a e -b d \right) b}\, \sqrt{e x +d}}"," ",0,"-2*(b*x+a)*(b*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*(e*x+d)^(1/2)+((a*e-b*d)*b)^(1/2))/((b*x+a)^2)^(1/2)/(a*e-b*d)/((a*e-b*d)*b)^(1/2)/(e*x+d)^(1/2)","A"
1709,1,130,119,0.056000," ","int(1/(e*x+d)^(5/2)/((b*x+a)^2)^(1/2),x)","\frac{2 \left(b x +a \right) \left(3 \left(e x +d \right)^{\frac{3}{2}} b^{2} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+3 \sqrt{\left(a e -b d \right) b}\, b e x -\sqrt{\left(a e -b d \right) b}\, a e +4 \sqrt{\left(a e -b d \right) b}\, b d \right)}{3 \sqrt{\left(b x +a \right)^{2}}\, \left(a e -b d \right)^{2} \sqrt{\left(a e -b d \right) b}\, \left(e x +d \right)^{\frac{3}{2}}}"," ",0,"2/3*(b*x+a)*(3*b^2*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*(e*x+d)^(3/2)+3*((a*e-b*d)*b)^(1/2)*x*b*e-((a*e-b*d)*b)^(1/2)*a*e+4*((a*e-b*d)*b)^(1/2)*b*d)/((b*x+a)^2)^(1/2)/(a*e-b*d)^2/((a*e-b*d)*b)^(1/2)/(e*x+d)^(3/2)","A"
1710,1,202,155,0.066000," ","int(1/(e*x+d)^(7/2)/((b*x+a)^2)^(1/2),x)","-\frac{2 \left(b x +a \right) \left(15 \sqrt{\left(a e -b d \right) b}\, b^{2} e^{2} x^{2}-5 \sqrt{\left(a e -b d \right) b}\, a b \,e^{2} x +35 \sqrt{\left(a e -b d \right) b}\, b^{2} d e x +3 \sqrt{\left(a e -b d \right) b}\, a^{2} e^{2}-11 \sqrt{\left(a e -b d \right) b}\, a b d e +15 \left(e x +d \right)^{\frac{5}{2}} b^{3} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+23 \sqrt{\left(a e -b d \right) b}\, b^{2} d^{2}\right)}{15 \sqrt{\left(b x +a \right)^{2}}\, \left(a e -b d \right)^{3} \sqrt{\left(a e -b d \right) b}\, \left(e x +d \right)^{\frac{5}{2}}}"," ",0,"-2/15*(b*x+a)*(15*b^3*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*(e*x+d)^(5/2)+15*((a*e-b*d)*b)^(1/2)*x^2*b^2*e^2-5*((a*e-b*d)*b)^(1/2)*x*a*b*e^2+35*((a*e-b*d)*b)^(1/2)*x*b^2*d*e+3*((a*e-b*d)*b)^(1/2)*a^2*e^2-11*((a*e-b*d)*b)^(1/2)*a*b*d*e+23*((a*e-b*d)*b)^(1/2)*b^2*d^2)/((b*x+a)^2)^(1/2)/(a*e-b*d)^3/((a*e-b*d)*b)^(1/2)/(e*x+d)^(5/2)","A"
1711,1,1115,210,0.067000," ","int((e*x+d)^(9/2)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x)","\frac{\left(-315 a^{3} b^{2} e^{5} x^{2} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+945 a^{2} b^{3} d \,e^{4} x^{2} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)-945 a \,b^{4} d^{2} e^{3} x^{2} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+315 b^{5} d^{3} e^{2} x^{2} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)-630 a^{4} b \,e^{5} x \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+1890 a^{3} b^{2} d \,e^{4} x \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)-1890 a^{2} b^{3} d^{2} e^{3} x \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+630 a \,b^{4} d^{3} e^{2} x \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)-315 a^{5} e^{5} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+945 a^{4} b d \,e^{4} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)-945 a^{3} b^{2} d^{2} e^{3} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+315 a^{2} b^{3} d^{3} e^{2} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+240 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a^{2} b^{2} e^{4} x^{2}-480 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a \,b^{3} d \,e^{3} x^{2}+240 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, b^{4} d^{2} e^{2} x^{2}+480 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a^{3} b \,e^{4} x -960 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a^{2} b^{2} d \,e^{3} x +480 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a \,b^{3} d^{2} e^{2} x -40 \left(e x +d \right)^{\frac{3}{2}} \sqrt{\left(a e -b d \right) b}\, a \,b^{3} e^{3} x^{2}+40 \left(e x +d \right)^{\frac{3}{2}} \sqrt{\left(a e -b d \right) b}\, b^{4} d \,e^{2} x^{2}+315 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a^{4} e^{4}-780 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a^{3} b d \,e^{3}+690 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a^{2} b^{2} d^{2} e^{2}-80 \left(e x +d \right)^{\frac{3}{2}} \sqrt{\left(a e -b d \right) b}\, a^{2} b^{2} e^{3} x -300 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a \,b^{3} d^{3} e +80 \left(e x +d \right)^{\frac{3}{2}} \sqrt{\left(a e -b d \right) b}\, a \,b^{3} d \,e^{2} x +75 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, b^{4} d^{4}+8 \left(e x +d \right)^{\frac{5}{2}} \sqrt{\left(a e -b d \right) b}\, b^{4} e^{2} x^{2}+45 \left(e x +d \right)^{\frac{3}{2}} \sqrt{\left(a e -b d \right) b}\, a^{3} b \,e^{3}-215 \left(e x +d \right)^{\frac{3}{2}} \sqrt{\left(a e -b d \right) b}\, a^{2} b^{2} d \,e^{2}+255 \left(e x +d \right)^{\frac{3}{2}} \sqrt{\left(a e -b d \right) b}\, a \,b^{3} d^{2} e +16 \left(e x +d \right)^{\frac{5}{2}} \sqrt{\left(a e -b d \right) b}\, a \,b^{3} e^{2} x -85 \left(e x +d \right)^{\frac{3}{2}} \sqrt{\left(a e -b d \right) b}\, b^{4} d^{3}+8 \left(e x +d \right)^{\frac{5}{2}} \sqrt{\left(a e -b d \right) b}\, a^{2} b^{2} e^{2}\right) \left(b x +a \right)}{20 \sqrt{\left(a e -b d \right) b}\, \left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}} b^{5}}"," ",0,"1/20*(480*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*x*a*b^3*d^2*e^2+240*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*x^2*b^4*d^2*e^2+1890*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x*a^3*b^2*d*e^4-1890*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x*a^2*b^3*d^2*e^3+630*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x*a*b^4*d^3*e^2-215*(e*x+d)^(3/2)*((a*e-b*d)*b)^(1/2)*a^2*b^2*d*e^2+255*(e*x+d)^(3/2)*((a*e-b*d)*b)^(1/2)*a*b^3*d^2*e+480*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*x*a^3*b*e^4-780*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*a^3*b*d*e^3+690*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*a^2*b^2*d^2*e^2-300*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*a*b^3*d^3*e+16*(e*x+d)^(5/2)*((a*e-b*d)*b)^(1/2)*x*a*b^3*e^2-40*(e*x+d)^(3/2)*((a*e-b*d)*b)^(1/2)*x^2*a*b^3*e^3+40*(e*x+d)^(3/2)*((a*e-b*d)*b)^(1/2)*x^2*b^4*d*e^2+945*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x^2*a^2*b^3*d*e^4-945*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x^2*a*b^4*d^2*e^3+75*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*b^4*d^4-85*(e*x+d)^(3/2)*((a*e-b*d)*b)^(1/2)*b^4*d^3+315*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*a^4*e^4-80*(e*x+d)^(3/2)*((a*e-b*d)*b)^(1/2)*x*a^2*b^2*e^3+240*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*x^2*a^2*b^2*e^4-315*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*a^5*e^5+80*(e*x+d)^(3/2)*((a*e-b*d)*b)^(1/2)*x*a*b^3*d*e^2-480*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*x^2*a*b^3*d*e^3-960*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*x*a^2*b^2*d*e^3+945*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*a^4*b*d*e^4+315*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x^2*b^5*d^3*e^2+8*(e*x+d)^(5/2)*((a*e-b*d)*b)^(1/2)*a^2*b^2*e^2+8*(e*x+d)^(5/2)*((a*e-b*d)*b)^(1/2)*x^2*b^4*e^2-315*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x^2*a^3*b^2*e^5-630*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x*a^4*b*e^5+45*(e*x+d)^(3/2)*((a*e-b*d)*b)^(1/2)*a^3*b*e^3-945*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*a^3*b^2*d^2*e^3+315*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*a^2*b^3*d^3*e^2)*(b*x+a)/((a*e-b*d)*b)^(1/2)/b^5/((b*x+a)^2)^(3/2)","B"
1712,1,714,171,0.062000," ","int((e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x)","\frac{\left(105 a^{2} b^{2} e^{4} x^{2} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)-210 a \,b^{3} d \,e^{3} x^{2} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+105 b^{4} d^{2} e^{2} x^{2} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+210 a^{3} b \,e^{4} x \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)-420 a^{2} b^{2} d \,e^{3} x \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+210 a \,b^{3} d^{2} e^{2} x \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+105 a^{4} e^{4} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)-210 a^{3} b d \,e^{3} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+105 a^{2} b^{2} d^{2} e^{2} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)-72 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a \,b^{2} e^{3} x^{2}+72 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, b^{3} d \,e^{2} x^{2}-144 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a^{2} b \,e^{3} x +144 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a \,b^{2} d \,e^{2} x +8 \left(e x +d \right)^{\frac{3}{2}} \sqrt{\left(a e -b d \right) b}\, b^{3} e^{2} x^{2}-105 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a^{3} e^{3}+171 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a^{2} b d \,e^{2}-99 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a \,b^{2} d^{2} e +16 \left(e x +d \right)^{\frac{3}{2}} \sqrt{\left(a e -b d \right) b}\, a \,b^{2} e^{2} x +33 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, b^{3} d^{3}-31 \left(e x +d \right)^{\frac{3}{2}} \sqrt{\left(a e -b d \right) b}\, a^{2} b \,e^{2}+78 \left(e x +d \right)^{\frac{3}{2}} \sqrt{\left(a e -b d \right) b}\, a \,b^{2} d e -39 \left(e x +d \right)^{\frac{3}{2}} \sqrt{\left(a e -b d \right) b}\, b^{3} d^{2}\right) \left(b x +a \right)}{12 \sqrt{\left(a e -b d \right) b}\, \left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}} b^{4}}"," ",0,"1/12*(8*(e*x+d)^(3/2)*((a*e-b*d)*b)^(1/2)*x^2*b^3*e^2+105*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x^2*a^2*b^2*e^4-210*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x^2*a*b^3*d*e^3+105*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x^2*b^4*d^2*e^2+16*(e*x+d)^(3/2)*((a*e-b*d)*b)^(1/2)*x*a*b^2*e^2-72*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*x^2*a*b^2*e^3+72*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*x^2*b^3*d*e^2+210*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x*a^3*b*e^4-420*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x*a^2*b^2*d*e^3+210*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x*a*b^3*d^2*e^2-31*(e*x+d)^(3/2)*((a*e-b*d)*b)^(1/2)*a^2*b*e^2+78*(e*x+d)^(3/2)*((a*e-b*d)*b)^(1/2)*a*b^2*d*e-39*(e*x+d)^(3/2)*((a*e-b*d)*b)^(1/2)*b^3*d^2-144*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*x*a^2*b*e^3+144*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*x*a*b^2*d*e^2+105*a^4*e^4*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)-210*a^3*b*d*e^3*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)+105*a^2*b^2*d^2*e^2*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)-105*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*a^3*e^3+171*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*a^2*b*d*e^2-99*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*a*b^2*d^2*e+33*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*b^3*d^3)*(b*x+a)/((a*e-b*d)*b)^(1/2)/b^4/((b*x+a)^2)^(3/2)","B"
1713,1,413,134,0.064000," ","int((e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x)","\frac{\left(-15 a \,b^{2} e^{3} x^{2} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+15 b^{3} d \,e^{2} x^{2} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)-30 a^{2} b \,e^{3} x \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+30 a \,b^{2} d \,e^{2} x \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)-15 a^{3} e^{3} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+15 a^{2} b d \,e^{2} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+8 \sqrt{\left(a e -b d \right) b}\, \sqrt{e x +d}\, b^{2} e^{2} x^{2}+16 \sqrt{\left(a e -b d \right) b}\, \sqrt{e x +d}\, a b \,e^{2} x +15 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a^{2} e^{2}-14 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a b d e +7 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, b^{2} d^{2}+9 \left(e x +d \right)^{\frac{3}{2}} \sqrt{\left(a e -b d \right) b}\, a b e -9 \left(e x +d \right)^{\frac{3}{2}} \sqrt{\left(a e -b d \right) b}\, b^{2} d \right) \left(b x +a \right)}{4 \sqrt{\left(a e -b d \right) b}\, \left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}} b^{3}}"," ",0,"1/4*(-15*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x^2*a*b^2*e^3+15*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x^2*b^3*d*e^2+8*((a*e-b*d)*b)^(1/2)*(e*x+d)^(1/2)*x^2*b^2*e^2-30*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x*a^2*b*e^3+30*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x*a*b^2*d*e^2+9*(e*x+d)^(3/2)*((a*e-b*d)*b)^(1/2)*a*b*e-9*(e*x+d)^(3/2)*((a*e-b*d)*b)^(1/2)*b^2*d+16*((a*e-b*d)*b)^(1/2)*(e*x+d)^(1/2)*x*a*b*e^2-15*a^3*e^3*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)+15*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*a^2*b*d*e^2+15*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*a^2*e^2-14*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*a*b*d*e+7*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*b^2*d^2)*(b*x+a)/((a*e-b*d)*b)^(1/2)/b^3/((b*x+a)^2)^(3/2)","B"
1714,1,194,105,0.063000," ","int((e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x)","-\frac{\left(-3 b^{2} e^{2} x^{2} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)-6 a b \,e^{2} x \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)-3 a^{2} e^{2} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+3 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a e -3 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, b d +5 \left(e x +d \right)^{\frac{3}{2}} \sqrt{\left(a e -b d \right) b}\, b \right) \left(b x +a \right)}{4 \sqrt{\left(a e -b d \right) b}\, \left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}} b^{2}}"," ",0,"-1/4*(-3*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x^2*b^2*e^2-6*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x*a*b*e^2+5*(e*x+d)^(3/2)*((a*e-b*d)*b)^(1/2)*b-3*a^2*e^2*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)+3*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*a*e-3*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*b*d)*(b*x+a)/((a*e-b*d)*b)^(1/2)/b^2/((b*x+a)^2)^(3/2)","A"
1715,1,200,115,0.074000," ","int((e*x+d)^(1/2)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x)","\frac{\left(b^{2} e^{2} x^{2} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+2 a b \,e^{2} x \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+a^{2} e^{2} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)-\sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a e +\sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, b d +\left(e x +d \right)^{\frac{3}{2}} \sqrt{\left(a e -b d \right) b}\, b \right) \left(b x +a \right)}{4 \sqrt{\left(a e -b d \right) b}\, \left(a e -b d \right) \left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}} b}"," ",0,"1/4*(b^2*e^2*x^2*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)+2*a*b*e^2*x*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)+(e*x+d)^(3/2)*((a*e-b*d)*b)^(1/2)*b+a^2*e^2*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)-(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*a*e+(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*b*d)*(b*x+a)/((a*e-b*d)*b)^(1/2)/b/(a*e-b*d)/((b*x+a)^2)^(3/2)","A"
1716,1,203,119,0.089000," ","int(1/(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^(1/2),x)","\frac{\left(3 b^{2} e^{2} x^{2} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+6 a b \,e^{2} x \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+3 a^{2} e^{2} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+3 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, b e x +5 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a e -2 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, b d \right) \left(b x +a \right)}{4 \sqrt{\left(a e -b d \right) b}\, \left(a e -b d \right)^{2} \left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}}}"," ",0,"1/4*(3*b^2*e^2*x^2*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)+6*a*b*e^2*x*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)+3*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*x*b*e+3*a^2*e^2*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)+5*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*a*e-2*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*b*d)*(b*x+a)/((a*e-b*d)*b)^(1/2)/(a*e-b*d)^2/((b*x+a)^2)^(3/2)","A"
1717,1,285,155,0.073000," ","int(1/(e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x)","-\frac{\left(15 \sqrt{e x +d}\, b^{3} e^{2} x^{2} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+30 \sqrt{e x +d}\, a \,b^{2} e^{2} x \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+15 \sqrt{e x +d}\, a^{2} b \,e^{2} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+15 \sqrt{\left(a e -b d \right) b}\, b^{2} e^{2} x^{2}+25 \sqrt{\left(a e -b d \right) b}\, a b \,e^{2} x +5 \sqrt{\left(a e -b d \right) b}\, b^{2} d e x +8 \sqrt{\left(a e -b d \right) b}\, a^{2} e^{2}+9 \sqrt{\left(a e -b d \right) b}\, a b d e -2 \sqrt{\left(a e -b d \right) b}\, b^{2} d^{2}\right) \left(b x +a \right)}{4 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, \left(a e -b d \right)^{3} \left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}}}"," ",0,"-1/4*(15*(e*x+d)^(1/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x^2*b^3*e^2+30*(e*x+d)^(1/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x*a*b^2*e^2+15*(e*x+d)^(1/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*a^2*b*e^2+15*((a*e-b*d)*b)^(1/2)*b^2*e^2*x^2+25*((a*e-b*d)*b)^(1/2)*a*b*e^2*x+5*((a*e-b*d)*b)^(1/2)*b^2*d*e*x+8*((a*e-b*d)*b)^(1/2)*a^2*e^2+9*((a*e-b*d)*b)^(1/2)*a*b*d*e-2*((a*e-b*d)*b)^(1/2)*b^2*d^2)*(b*x+a)/(e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)/(a*e-b*d)^3/((b*x+a)^2)^(3/2)","A"
1718,1,388,192,0.065000," ","int(1/(e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x)","\frac{\left(105 \left(e x +d \right)^{\frac{3}{2}} b^{4} e^{2} x^{2} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+105 \sqrt{\left(a e -b d \right) b}\, b^{3} e^{3} x^{3}+210 \left(e x +d \right)^{\frac{3}{2}} a \,b^{3} e^{2} x \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+175 \sqrt{\left(a e -b d \right) b}\, a \,b^{2} e^{3} x^{2}+140 \sqrt{\left(a e -b d \right) b}\, b^{3} d \,e^{2} x^{2}+105 \left(e x +d \right)^{\frac{3}{2}} a^{2} b^{2} e^{2} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+56 \sqrt{\left(a e -b d \right) b}\, a^{2} b \,e^{3} x +238 \sqrt{\left(a e -b d \right) b}\, a \,b^{2} d \,e^{2} x +21 \sqrt{\left(a e -b d \right) b}\, b^{3} d^{2} e x -8 \sqrt{\left(a e -b d \right) b}\, a^{3} e^{3}+80 \sqrt{\left(a e -b d \right) b}\, a^{2} b d \,e^{2}+39 \sqrt{\left(a e -b d \right) b}\, a \,b^{2} d^{2} e -6 \sqrt{\left(a e -b d \right) b}\, b^{3} d^{3}\right) \left(b x +a \right)}{12 \left(e x +d \right)^{\frac{3}{2}} \sqrt{\left(a e -b d \right) b}\, \left(a e -b d \right)^{4} \left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}}}"," ",0,"1/12*(105*(e*x+d)^(3/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x^2*b^4*e^2+210*(e*x+d)^(3/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x*a*b^3*e^2+105*(e*x+d)^(3/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*a^2*b^2*e^2+105*((a*e-b*d)*b)^(1/2)*x^3*b^3*e^3+175*((a*e-b*d)*b)^(1/2)*x^2*a*b^2*e^3+140*((a*e-b*d)*b)^(1/2)*x^2*b^3*d*e^2+56*((a*e-b*d)*b)^(1/2)*x*a^2*b*e^3+238*((a*e-b*d)*b)^(1/2)*x*a*b^2*d*e^2+21*((a*e-b*d)*b)^(1/2)*x*b^3*d^2*e-8*((a*e-b*d)*b)^(1/2)*a^3*e^3+80*((a*e-b*d)*b)^(1/2)*a^2*b*d*e^2+39*((a*e-b*d)*b)^(1/2)*a*b^2*d^2*e-6*((a*e-b*d)*b)^(1/2)*b^3*d^3)*(b*x+a)/(e*x+d)^(3/2)/((a*e-b*d)*b)^(1/2)/(a*e-b*d)^4/((b*x+a)^2)^(3/2)","B"
1719,1,518,231,0.067000," ","int(1/(e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x)","-\frac{\left(315 \sqrt{\left(a e -b d \right) b}\, b^{4} e^{4} x^{4}+525 \sqrt{\left(a e -b d \right) b}\, a \,b^{3} e^{4} x^{3}+735 \sqrt{\left(a e -b d \right) b}\, b^{4} d \,e^{3} x^{3}+168 \sqrt{\left(a e -b d \right) b}\, a^{2} b^{2} e^{4} x^{2}+1239 \sqrt{\left(a e -b d \right) b}\, a \,b^{3} d \,e^{3} x^{2}+315 \left(e x +d \right)^{\frac{5}{2}} b^{5} e^{2} x^{2} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+483 \sqrt{\left(a e -b d \right) b}\, b^{4} d^{2} e^{2} x^{2}-24 \sqrt{\left(a e -b d \right) b}\, a^{3} b \,e^{4} x +408 \sqrt{\left(a e -b d \right) b}\, a^{2} b^{2} d \,e^{3} x +630 \left(e x +d \right)^{\frac{5}{2}} a \,b^{4} e^{2} x \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+831 \sqrt{\left(a e -b d \right) b}\, a \,b^{3} d^{2} e^{2} x +45 \sqrt{\left(a e -b d \right) b}\, b^{4} d^{3} e x +8 \sqrt{\left(a e -b d \right) b}\, a^{4} e^{4}-56 \sqrt{\left(a e -b d \right) b}\, a^{3} b d \,e^{3}+315 \left(e x +d \right)^{\frac{5}{2}} a^{2} b^{3} e^{2} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+288 \sqrt{\left(a e -b d \right) b}\, a^{2} b^{2} d^{2} e^{2}+85 \sqrt{\left(a e -b d \right) b}\, a \,b^{3} d^{3} e -10 \sqrt{\left(a e -b d \right) b}\, b^{4} d^{4}\right) \left(b x +a \right)}{20 \left(e x +d \right)^{\frac{5}{2}} \sqrt{\left(a e -b d \right) b}\, \left(a e -b d \right)^{5} \left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}}}"," ",0,"-1/20*(315*(e*x+d)^(5/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x^2*b^5*e^2+630*(e*x+d)^(5/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x*a*b^4*e^2+315*(e*x+d)^(5/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*a^2*b^3*e^2+315*((a*e-b*d)*b)^(1/2)*x^4*b^4*e^4+525*((a*e-b*d)*b)^(1/2)*x^3*a*b^3*e^4+735*((a*e-b*d)*b)^(1/2)*x^3*b^4*d*e^3+168*((a*e-b*d)*b)^(1/2)*x^2*a^2*b^2*e^4+1239*((a*e-b*d)*b)^(1/2)*x^2*a*b^3*d*e^3+483*((a*e-b*d)*b)^(1/2)*x^2*b^4*d^2*e^2-24*((a*e-b*d)*b)^(1/2)*x*a^3*b*e^4+408*((a*e-b*d)*b)^(1/2)*x*a^2*b^2*d*e^3+831*((a*e-b*d)*b)^(1/2)*x*a*b^3*d^2*e^2+45*((a*e-b*d)*b)^(1/2)*x*b^4*d^3*e+8*((a*e-b*d)*b)^(1/2)*a^4*e^4-56*((a*e-b*d)*b)^(1/2)*a^3*b*d*e^3+288*((a*e-b*d)*b)^(1/2)*a^2*b^2*d^2*e^2+85*((a*e-b*d)*b)^(1/2)*a*b^3*d^3*e-10*((a*e-b*d)*b)^(1/2)*b^4*d^4)*(b*x+a)/(e*x+d)^(5/2)/((a*e-b*d)*b)^(1/2)/(a*e-b*d)^5/((b*x+a)^2)^(3/2)","B"
1720,1,2192,272,0.075000," ","int((e*x+d)^(13/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x)","\frac{\left(-45045 a^{3} b^{4} e^{7} x^{4} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+135135 a^{2} b^{5} d \,e^{6} x^{4} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)-135135 a \,b^{6} d^{2} e^{5} x^{4} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+45045 b^{7} d^{3} e^{4} x^{4} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)-180180 a^{4} b^{3} e^{7} x^{3} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+540540 a^{3} b^{4} d \,e^{6} x^{3} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)-540540 a^{2} b^{5} d^{2} e^{5} x^{3} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+180180 a \,b^{6} d^{3} e^{4} x^{3} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)-270270 a^{5} b^{2} e^{7} x^{2} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+810810 a^{4} b^{3} d \,e^{6} x^{2} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)-810810 a^{3} b^{4} d^{2} e^{5} x^{2} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+270270 a^{2} b^{5} d^{3} e^{4} x^{2} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)-180180 a^{6} b \,e^{7} x \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+540540 a^{5} b^{2} d \,e^{6} x \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)-540540 a^{4} b^{3} d^{2} e^{5} x \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+180180 a^{3} b^{4} d^{3} e^{4} x \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+28800 \sqrt{\left(a e -b d \right) b}\, \sqrt{e x +d}\, a^{2} b^{4} e^{6} x^{4}-57600 \sqrt{\left(a e -b d \right) b}\, \sqrt{e x +d}\, a \,b^{5} d \,e^{5} x^{4}+28800 \sqrt{\left(a e -b d \right) b}\, \sqrt{e x +d}\, b^{6} d^{2} e^{4} x^{4}-45045 a^{7} e^{7} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+135135 a^{6} b d \,e^{6} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)-135135 a^{5} b^{2} d^{2} e^{5} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+45045 a^{4} b^{3} d^{3} e^{4} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+115200 \sqrt{\left(a e -b d \right) b}\, \sqrt{e x +d}\, a^{3} b^{3} e^{6} x^{3}-230400 \sqrt{\left(a e -b d \right) b}\, \sqrt{e x +d}\, a^{2} b^{4} d \,e^{5} x^{3}+115200 \sqrt{\left(a e -b d \right) b}\, \sqrt{e x +d}\, a \,b^{5} d^{2} e^{4} x^{3}-3200 \sqrt{\left(a e -b d \right) b}\, \left(e x +d \right)^{\frac{3}{2}} a \,b^{5} e^{5} x^{4}+3200 \sqrt{\left(a e -b d \right) b}\, \left(e x +d \right)^{\frac{3}{2}} b^{6} d \,e^{4} x^{4}+172800 \sqrt{\left(a e -b d \right) b}\, \sqrt{e x +d}\, a^{4} b^{2} e^{6} x^{2}-345600 \sqrt{\left(a e -b d \right) b}\, \sqrt{e x +d}\, a^{3} b^{3} d \,e^{5} x^{2}+172800 \sqrt{\left(a e -b d \right) b}\, \sqrt{e x +d}\, a^{2} b^{4} d^{2} e^{4} x^{2}-12800 \sqrt{\left(a e -b d \right) b}\, \left(e x +d \right)^{\frac{3}{2}} a^{2} b^{4} e^{5} x^{3}+12800 \sqrt{\left(a e -b d \right) b}\, \left(e x +d \right)^{\frac{3}{2}} a \,b^{5} d \,e^{4} x^{3}+384 \sqrt{\left(a e -b d \right) b}\, \left(e x +d \right)^{\frac{5}{2}} b^{6} e^{4} x^{4}+115200 \sqrt{\left(a e -b d \right) b}\, \sqrt{e x +d}\, a^{5} b \,e^{6} x -230400 \sqrt{\left(a e -b d \right) b}\, \sqrt{e x +d}\, a^{4} b^{2} d \,e^{5} x +115200 \sqrt{\left(a e -b d \right) b}\, \sqrt{e x +d}\, a^{3} b^{3} d^{2} e^{4} x -19200 \sqrt{\left(a e -b d \right) b}\, \left(e x +d \right)^{\frac{3}{2}} a^{3} b^{3} e^{5} x^{2}+19200 \sqrt{\left(a e -b d \right) b}\, \left(e x +d \right)^{\frac{3}{2}} a^{2} b^{4} d \,e^{4} x^{2}+1536 \sqrt{\left(a e -b d \right) b}\, \left(e x +d \right)^{\frac{5}{2}} a \,b^{5} e^{4} x^{3}+45045 \sqrt{\left(a e -b d \right) b}\, \sqrt{e x +d}\, a^{6} e^{6}-155070 \sqrt{\left(a e -b d \right) b}\, \sqrt{e x +d}\, a^{5} b d \,e^{5}+272475 \sqrt{\left(a e -b d \right) b}\, \sqrt{e x +d}\, a^{4} b^{2} d^{2} e^{4}-12800 \sqrt{\left(a e -b d \right) b}\, \left(e x +d \right)^{\frac{3}{2}} a^{4} b^{2} e^{5} x -324900 \sqrt{\left(a e -b d \right) b}\, \sqrt{e x +d}\, a^{3} b^{3} d^{3} e^{3}+12800 \sqrt{\left(a e -b d \right) b}\, \left(e x +d \right)^{\frac{3}{2}} a^{3} b^{3} d \,e^{4} x +243675 \sqrt{\left(a e -b d \right) b}\, \sqrt{e x +d}\, a^{2} b^{4} d^{4} e^{2}+2304 \sqrt{\left(a e -b d \right) b}\, \left(e x +d \right)^{\frac{5}{2}} a^{2} b^{4} e^{4} x^{2}-97470 \sqrt{\left(a e -b d \right) b}\, \sqrt{e x +d}\, a \,b^{5} d^{5} e +16245 \sqrt{\left(a e -b d \right) b}\, \sqrt{e x +d}\, b^{6} d^{6}+49965 \sqrt{\left(a e -b d \right) b}\, \left(e x +d \right)^{\frac{3}{2}} a^{5} b \,e^{5}-262625 \sqrt{\left(a e -b d \right) b}\, \left(e x +d \right)^{\frac{3}{2}} a^{4} b^{2} d \,e^{4}+531650 \sqrt{\left(a e -b d \right) b}\, \left(e x +d \right)^{\frac{3}{2}} a^{3} b^{3} d^{2} e^{3}+1536 \sqrt{\left(a e -b d \right) b}\, \left(e x +d \right)^{\frac{5}{2}} a^{3} b^{3} e^{4} x -531650 \sqrt{\left(a e -b d \right) b}\, \left(e x +d \right)^{\frac{3}{2}} a^{2} b^{4} d^{3} e^{2}+265825 \sqrt{\left(a e -b d \right) b}\, \left(e x +d \right)^{\frac{3}{2}} a \,b^{5} d^{4} e -53165 \sqrt{\left(a e -b d \right) b}\, \left(e x +d \right)^{\frac{3}{2}} b^{6} d^{5}+59219 \sqrt{\left(a e -b d \right) b}\, \left(e x +d \right)^{\frac{5}{2}} a^{4} b^{2} e^{4}-235340 \sqrt{\left(a e -b d \right) b}\, \left(e x +d \right)^{\frac{5}{2}} a^{3} b^{3} d \,e^{3}+353010 \sqrt{\left(a e -b d \right) b}\, \left(e x +d \right)^{\frac{5}{2}} a^{2} b^{4} d^{2} e^{2}-235340 \sqrt{\left(a e -b d \right) b}\, \left(e x +d \right)^{\frac{5}{2}} a \,b^{5} d^{3} e +58835 \sqrt{\left(a e -b d \right) b}\, \left(e x +d \right)^{\frac{5}{2}} b^{6} d^{4}+22155 \sqrt{\left(a e -b d \right) b}\, \left(e x +d \right)^{\frac{7}{2}} a^{3} b^{3} e^{3}-66465 \sqrt{\left(a e -b d \right) b}\, \left(e x +d \right)^{\frac{7}{2}} a^{2} b^{4} d \,e^{2}+66465 \sqrt{\left(a e -b d \right) b}\, \left(e x +d \right)^{\frac{7}{2}} a \,b^{5} d^{2} e -22155 \sqrt{\left(a e -b d \right) b}\, \left(e x +d \right)^{\frac{7}{2}} b^{6} d^{3}\right) \left(b x +a \right)}{960 \sqrt{\left(a e -b d \right) b}\, \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}} b^{7}}"," ",0,"1/960*(58835*((a*e-b*d)*b)^(1/2)*(e*x+d)^(5/2)*b^6*d^4-53165*((a*e-b*d)*b)^(1/2)*(e*x+d)^(3/2)*b^6*d^5+45045*((a*e-b*d)*b)^(1/2)*(e*x+d)^(1/2)*a^6*e^6+16245*((a*e-b*d)*b)^(1/2)*(e*x+d)^(1/2)*b^6*d^6-22155*((a*e-b*d)*b)^(1/2)*(e*x+d)^(7/2)*b^6*d^3+12800*((a*e-b*d)*b)^(1/2)*(e*x+d)^(3/2)*x*a^3*b^3*d*e^4-345600*((a*e-b*d)*b)^(1/2)*(e*x+d)^(1/2)*x^2*a^3*b^3*d*e^5+172800*((a*e-b*d)*b)^(1/2)*(e*x+d)^(1/2)*x^2*a^2*b^4*d^2*e^4-230400*((a*e-b*d)*b)^(1/2)*(e*x+d)^(1/2)*x*a^4*b^2*d*e^5+115200*((a*e-b*d)*b)^(1/2)*(e*x+d)^(1/2)*x*a^3*b^3*d^2*e^4-135135*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x^4*a*b^6*d^2*e^5+2304*((a*e-b*d)*b)^(1/2)*(e*x+d)^(5/2)*x^2*a^2*b^4*e^4-45045*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*a^7*e^7+115200*((a*e-b*d)*b)^(1/2)*(e*x+d)^(1/2)*x^3*a*b^5*d^2*e^4+12800*((a*e-b*d)*b)^(1/2)*(e*x+d)^(3/2)*x^3*a*b^5*d*e^4-57600*((a*e-b*d)*b)^(1/2)*(e*x+d)^(1/2)*x^4*a*b^5*d*e^5+19200*((a*e-b*d)*b)^(1/2)*(e*x+d)^(3/2)*x^2*a^2*b^4*d*e^4-230400*((a*e-b*d)*b)^(1/2)*(e*x+d)^(1/2)*x^3*a^2*b^4*d*e^5-3200*((a*e-b*d)*b)^(1/2)*(e*x+d)^(3/2)*x^4*a*b^5*e^5+3200*((a*e-b*d)*b)^(1/2)*(e*x+d)^(3/2)*x^4*b^6*d*e^4+45045*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x^4*b^7*d^3*e^4-180180*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x^3*a^4*b^3*e^7+22155*((a*e-b*d)*b)^(1/2)*(e*x+d)^(7/2)*a^3*b^3*e^3-270270*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x^2*a^5*b^2*e^7+59219*((a*e-b*d)*b)^(1/2)*(e*x+d)^(5/2)*a^4*b^2*e^4-180180*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x*a^6*b*e^7+49965*((a*e-b*d)*b)^(1/2)*(e*x+d)^(3/2)*a^5*b*e^5+135135*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*a^6*b*d*e^6-135135*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*a^5*b^2*d^2*e^5+45045*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*a^4*b^3*d^3*e^4+384*((a*e-b*d)*b)^(1/2)*(e*x+d)^(5/2)*x^4*b^6*e^4-45045*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x^4*a^3*b^4*e^7+540540*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x^3*a^3*b^4*d*e^6-531650*((a*e-b*d)*b)^(1/2)*(e*x+d)^(3/2)*a^2*b^4*d^3*e^2-12800*((a*e-b*d)*b)^(1/2)*(e*x+d)^(3/2)*x^3*a^2*b^4*e^5+1536*((a*e-b*d)*b)^(1/2)*(e*x+d)^(5/2)*x^3*a*b^5*e^4+28800*((a*e-b*d)*b)^(1/2)*(e*x+d)^(1/2)*x^4*a^2*b^4*e^6+28800*((a*e-b*d)*b)^(1/2)*(e*x+d)^(1/2)*x^4*b^6*d^2*e^4+810810*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x^2*a^4*b^3*d*e^6-19200*((a*e-b*d)*b)^(1/2)*(e*x+d)^(3/2)*x^2*a^3*b^3*e^5-810810*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x^2*a^3*b^4*d^2*e^5+265825*((a*e-b*d)*b)^(1/2)*(e*x+d)^(3/2)*a*b^5*d^4*e+115200*((a*e-b*d)*b)^(1/2)*(e*x+d)^(1/2)*x*a^5*b*e^6+115200*((a*e-b*d)*b)^(1/2)*(e*x+d)^(1/2)*x^3*a^3*b^3*e^6-540540*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x^3*a^2*b^5*d^2*e^5+135135*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x^4*a^2*b^5*d*e^6+180180*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x^3*a*b^6*d^3*e^4-66465*((a*e-b*d)*b)^(1/2)*(e*x+d)^(7/2)*a^2*b^4*d*e^2+66465*((a*e-b*d)*b)^(1/2)*(e*x+d)^(7/2)*a*b^5*d^2*e+1536*((a*e-b*d)*b)^(1/2)*(e*x+d)^(5/2)*x*a^3*b^3*e^4+270270*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x^2*a^2*b^5*d^3*e^4-235340*((a*e-b*d)*b)^(1/2)*(e*x+d)^(5/2)*a^3*b^3*d*e^3+353010*((a*e-b*d)*b)^(1/2)*(e*x+d)^(5/2)*a^2*b^4*d^2*e^2-235340*((a*e-b*d)*b)^(1/2)*(e*x+d)^(5/2)*a*b^5*d^3*e-12800*((a*e-b*d)*b)^(1/2)*(e*x+d)^(3/2)*x*a^4*b^2*e^5+172800*((a*e-b*d)*b)^(1/2)*(e*x+d)^(1/2)*x^2*a^4*b^2*e^6+540540*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x*a^5*b^2*d*e^6-540540*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x*a^4*b^3*d^2*e^5+180180*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x*a^3*b^4*d^3*e^4-262625*((a*e-b*d)*b)^(1/2)*(e*x+d)^(3/2)*a^4*b^2*d*e^4+531650*((a*e-b*d)*b)^(1/2)*(e*x+d)^(3/2)*a^3*b^3*d^2*e^3-155070*((a*e-b*d)*b)^(1/2)*(e*x+d)^(1/2)*a^5*b*d*e^5+272475*((a*e-b*d)*b)^(1/2)*(e*x+d)^(1/2)*a^4*b^2*d^2*e^4-324900*((a*e-b*d)*b)^(1/2)*(e*x+d)^(1/2)*a^3*b^3*d^3*e^3+243675*((a*e-b*d)*b)^(1/2)*(e*x+d)^(1/2)*a^2*b^4*d^4*e^2-97470*((a*e-b*d)*b)^(1/2)*(e*x+d)^(1/2)*a*b^5*d^5*e)*(b*x+a)/((a*e-b*d)*b)^(1/2)/b^7/((b*x+a)^2)^(5/2)","B"
1721,1,1471,233,0.073000," ","int((e*x+d)^(11/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x)","-\frac{\left(-3465 a^{2} b^{4} e^{6} x^{4} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+6930 a \,b^{5} d \,e^{5} x^{4} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)-3465 b^{6} d^{2} e^{4} x^{4} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)-13860 a^{3} b^{3} e^{6} x^{3} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+27720 a^{2} b^{4} d \,e^{5} x^{3} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)-13860 a \,b^{5} d^{2} e^{4} x^{3} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)-20790 a^{4} b^{2} e^{6} x^{2} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+41580 a^{3} b^{3} d \,e^{5} x^{2} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)-20790 a^{2} b^{4} d^{2} e^{4} x^{2} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)-13860 a^{5} b \,e^{6} x \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+27720 a^{4} b^{2} d \,e^{5} x \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)-13860 a^{3} b^{3} d^{2} e^{4} x \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+1920 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a \,b^{4} e^{5} x^{4}-1920 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, b^{5} d \,e^{4} x^{4}-3465 a^{6} e^{6} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+6930 a^{5} b d \,e^{5} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)-3465 a^{4} b^{2} d^{2} e^{4} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+7680 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a^{2} b^{3} e^{5} x^{3}-7680 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a \,b^{4} d \,e^{4} x^{3}-128 \left(e x +d \right)^{\frac{3}{2}} \sqrt{\left(a e -b d \right) b}\, b^{5} e^{4} x^{4}+11520 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a^{3} b^{2} e^{5} x^{2}-11520 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a^{2} b^{3} d \,e^{4} x^{2}-512 \left(e x +d \right)^{\frac{3}{2}} \sqrt{\left(a e -b d \right) b}\, a \,b^{4} e^{4} x^{3}+7680 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a^{4} b \,e^{5} x -7680 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a^{3} b^{2} d \,e^{4} x -768 \left(e x +d \right)^{\frac{3}{2}} \sqrt{\left(a e -b d \right) b}\, a^{2} b^{3} e^{4} x^{2}+3465 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a^{5} e^{5}-9645 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a^{4} b d \,e^{4}+15450 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a^{3} b^{2} d^{2} e^{3}-512 \left(e x +d \right)^{\frac{3}{2}} \sqrt{\left(a e -b d \right) b}\, a^{3} b^{2} e^{4} x -15450 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a^{2} b^{3} d^{3} e^{2}+7725 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a \,b^{4} d^{4} e -1545 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, b^{5} d^{5}+5025 \left(e x +d \right)^{\frac{3}{2}} \sqrt{\left(a e -b d \right) b}\, a^{4} b \,e^{4}-20612 \left(e x +d \right)^{\frac{3}{2}} \sqrt{\left(a e -b d \right) b}\, a^{3} b^{2} d \,e^{3}+30918 \left(e x +d \right)^{\frac{3}{2}} \sqrt{\left(a e -b d \right) b}\, a^{2} b^{3} d^{2} e^{2}-20612 \left(e x +d \right)^{\frac{3}{2}} \sqrt{\left(a e -b d \right) b}\, a \,b^{4} d^{3} e +5153 \left(e x +d \right)^{\frac{3}{2}} \sqrt{\left(a e -b d \right) b}\, b^{5} d^{4}+5855 \left(e x +d \right)^{\frac{5}{2}} \sqrt{\left(a e -b d \right) b}\, a^{3} b^{2} e^{3}-17565 \left(e x +d \right)^{\frac{5}{2}} \sqrt{\left(a e -b d \right) b}\, a^{2} b^{3} d \,e^{2}+17565 \left(e x +d \right)^{\frac{5}{2}} \sqrt{\left(a e -b d \right) b}\, a \,b^{4} d^{2} e -5855 \left(e x +d \right)^{\frac{5}{2}} \sqrt{\left(a e -b d \right) b}\, b^{5} d^{3}+2295 \left(e x +d \right)^{\frac{7}{2}} \sqrt{\left(a e -b d \right) b}\, a^{2} b^{3} e^{2}-4590 \left(e x +d \right)^{\frac{7}{2}} \sqrt{\left(a e -b d \right) b}\, a \,b^{4} d e +2295 \left(e x +d \right)^{\frac{7}{2}} \sqrt{\left(a e -b d \right) b}\, b^{5} d^{2}\right) \left(b x +a \right)}{192 \sqrt{\left(a e -b d \right) b}\, \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}} b^{6}}"," ",0,"-1/192*(3465*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*a^5*e^5-1545*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*b^5*d^5+2295*(e*x+d)^(7/2)*((a*e-b*d)*b)^(1/2)*b^5*d^2-5855*(e*x+d)^(5/2)*((a*e-b*d)*b)^(1/2)*b^5*d^3+5153*(e*x+d)^(3/2)*((a*e-b*d)*b)^(1/2)*b^5*d^4-11520*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*x^2*a^2*b^3*d*e^4-7680*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*x*a^3*b^2*d*e^4-7680*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*x^3*a*b^4*d*e^4-3465*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*a^6*e^6-128*(e*x+d)^(3/2)*((a*e-b*d)*b)^(1/2)*x^4*b^5*e^4-3465*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x^4*a^2*b^4*e^6-3465*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x^4*b^6*d^2*e^4-13860*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x^3*a^3*b^3*e^6+2295*(e*x+d)^(7/2)*((a*e-b*d)*b)^(1/2)*a^2*b^3*e^2-20790*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x^2*a^4*b^2*e^6+5855*(e*x+d)^(5/2)*((a*e-b*d)*b)^(1/2)*a^3*b^2*e^3-13860*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x*a^5*b*e^6+5025*(e*x+d)^(3/2)*((a*e-b*d)*b)^(1/2)*a^4*b*e^4+6930*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*a^5*b*d*e^5-3465*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*a^4*b^2*d^2*e^4-512*(e*x+d)^(3/2)*((a*e-b*d)*b)^(1/2)*x*a^3*b^2*e^4+11520*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*x^2*a^3*b^2*e^5+27720*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x*a^4*b^2*d*e^5-13860*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x*a^3*b^3*d^2*e^4-20612*(e*x+d)^(3/2)*((a*e-b*d)*b)^(1/2)*a^3*b^2*d*e^3+30918*(e*x+d)^(3/2)*((a*e-b*d)*b)^(1/2)*a^2*b^3*d^2*e^2-20612*(e*x+d)^(3/2)*((a*e-b*d)*b)^(1/2)*a*b^4*d^3*e+7680*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*x*a^4*b*e^5-15450*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*a^2*b^3*d^3*e^2+7725*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*a*b^4*d^4*e-9645*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*a^4*b*d*e^4+15450*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*a^3*b^2*d^2*e^3-512*(e*x+d)^(3/2)*((a*e-b*d)*b)^(1/2)*x^3*a*b^4*e^4+1920*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*x^4*a*b^4*e^5-1920*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*x^4*b^5*d*e^4+27720*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x^3*a^2*b^4*d*e^5+6930*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x^4*a*b^5*d*e^5-13860*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x^3*a*b^5*d^2*e^4-4590*(e*x+d)^(7/2)*((a*e-b*d)*b)^(1/2)*a*b^4*d*e-768*(e*x+d)^(3/2)*((a*e-b*d)*b)^(1/2)*x^2*a^2*b^3*e^4+7680*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*x^3*a^2*b^3*e^5+41580*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x^2*a^3*b^3*d*e^5-20790*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x^2*a^2*b^4*d^2*e^4-17565*(e*x+d)^(5/2)*((a*e-b*d)*b)^(1/2)*a^2*b^3*d*e^2+17565*(e*x+d)^(5/2)*((a*e-b*d)*b)^(1/2)*a*b^4*d^2*e)*(b*x+a)/((a*e-b*d)*b)^(1/2)/b^6/((b*x+a)^2)^(5/2)","B"
1722,1,892,196,0.076000," ","int((e*x+d)^(9/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x)","\frac{\left(-315 a \,b^{4} e^{5} x^{4} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+315 b^{5} d \,e^{4} x^{4} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)-1260 a^{2} b^{3} e^{5} x^{3} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+1260 a \,b^{4} d \,e^{4} x^{3} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)-1890 a^{3} b^{2} e^{5} x^{2} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+1890 a^{2} b^{3} d \,e^{4} x^{2} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)-1260 a^{4} b \,e^{5} x \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+1260 a^{3} b^{2} d \,e^{4} x \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+128 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, b^{4} e^{4} x^{4}-315 a^{5} e^{5} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+315 a^{4} b d \,e^{4} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+512 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a \,b^{3} e^{4} x^{3}+768 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a^{2} b^{2} e^{4} x^{2}+512 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a^{3} b \,e^{4} x +315 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a^{4} e^{4}-748 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a^{3} b d \,e^{3}+1122 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a^{2} b^{2} d^{2} e^{2}-748 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a \,b^{3} d^{3} e +187 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, b^{4} d^{4}+643 \left(e x +d \right)^{\frac{3}{2}} \sqrt{\left(a e -b d \right) b}\, a^{3} b \,e^{3}-1929 \left(e x +d \right)^{\frac{3}{2}} \sqrt{\left(a e -b d \right) b}\, a^{2} b^{2} d \,e^{2}+1929 \left(e x +d \right)^{\frac{3}{2}} \sqrt{\left(a e -b d \right) b}\, a \,b^{3} d^{2} e -643 \left(e x +d \right)^{\frac{3}{2}} \sqrt{\left(a e -b d \right) b}\, b^{4} d^{3}+765 \left(e x +d \right)^{\frac{5}{2}} \sqrt{\left(a e -b d \right) b}\, a^{2} b^{2} e^{2}-1530 \left(e x +d \right)^{\frac{5}{2}} \sqrt{\left(a e -b d \right) b}\, a \,b^{3} d e +765 \left(e x +d \right)^{\frac{5}{2}} \sqrt{\left(a e -b d \right) b}\, b^{4} d^{2}+325 \left(e x +d \right)^{\frac{7}{2}} \sqrt{\left(a e -b d \right) b}\, a \,b^{3} e -325 \left(e x +d \right)^{\frac{7}{2}} \sqrt{\left(a e -b d \right) b}\, b^{4} d \right) \left(b x +a \right)}{64 \sqrt{\left(a e -b d \right) b}\, \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}} b^{5}}"," ",0,"1/64*(-1530*(e*x+d)^(5/2)*((a*e-b*d)*b)^(1/2)*a*b^3*d*e+1260*a^3*b^2*d*e^4*x*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)-1929*(e*x+d)^(3/2)*((a*e-b*d)*b)^(1/2)*a^2*b^2*d*e^2+1929*(e*x+d)^(3/2)*((a*e-b*d)*b)^(1/2)*a*b^3*d^2*e+512*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*a^3*b*e^4*x-748*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*a^3*b*d*e^3+1122*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*a^2*b^2*d^2*e^2-748*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*a*b^3*d^3*e+1890*a^2*b^3*d*e^4*x^2*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)-325*(e*x+d)^(7/2)*((a*e-b*d)*b)^(1/2)*b^4*d+765*(e*x+d)^(5/2)*((a*e-b*d)*b)^(1/2)*b^4*d^2+187*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*b^4*d^4-643*(e*x+d)^(3/2)*((a*e-b*d)*b)^(1/2)*b^4*d^3+315*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*a^4*e^4+768*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*a^2*b^2*e^4*x^2-315*a^5*e^5*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)+315*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x^4*b^5*d*e^4+128*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*x^4*b^4*e^4-1260*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x^3*a^2*b^3*e^5+315*a^4*b*d*e^4*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)+512*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*x^3*a*b^3*e^4+1260*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x^3*a*b^4*d*e^4+765*(e*x+d)^(5/2)*((a*e-b*d)*b)^(1/2)*a^2*b^2*e^2-1890*a^3*b^2*e^5*x^2*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)-1260*a^4*b*e^5*x*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)+643*(e*x+d)^(3/2)*((a*e-b*d)*b)^(1/2)*a^3*b*e^3+325*(e*x+d)^(7/2)*((a*e-b*d)*b)^(1/2)*a*b^3*e-315*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x^4*a*b^4*e^5)*(b*x+a)/((a*e-b*d)*b)^(1/2)/b^5/((b*x+a)^2)^(5/2)","B"
1723,1,467,167,0.063000," ","int((e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x)","-\frac{\left(-105 b^{4} e^{4} x^{4} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)-420 a \,b^{3} e^{4} x^{3} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)-630 a^{2} b^{2} e^{4} x^{2} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)-420 a^{3} b \,e^{4} x \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)-105 a^{4} e^{4} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+105 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a^{3} e^{3}-315 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a^{2} b d \,e^{2}+315 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a \,b^{2} d^{2} e -105 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, b^{3} d^{3}+385 \left(e x +d \right)^{\frac{3}{2}} \sqrt{\left(a e -b d \right) b}\, a^{2} b \,e^{2}-770 \left(e x +d \right)^{\frac{3}{2}} \sqrt{\left(a e -b d \right) b}\, a \,b^{2} d e +385 \left(e x +d \right)^{\frac{3}{2}} \sqrt{\left(a e -b d \right) b}\, b^{3} d^{2}+511 \left(e x +d \right)^{\frac{5}{2}} \sqrt{\left(a e -b d \right) b}\, a \,b^{2} e -511 \left(e x +d \right)^{\frac{5}{2}} \sqrt{\left(a e -b d \right) b}\, b^{3} d +279 \left(e x +d \right)^{\frac{7}{2}} \sqrt{\left(a e -b d \right) b}\, b^{3}\right) \left(b x +a \right)}{192 \sqrt{\left(a e -b d \right) b}\, \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}} b^{4}}"," ",0,"-1/192*(-105*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x^4*b^4*e^4-420*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x^3*a*b^3*e^4+279*(e*x+d)^(7/2)*((a*e-b*d)*b)^(1/2)*b^3-630*a^2*b^2*e^4*x^2*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)+511*(e*x+d)^(5/2)*((a*e-b*d)*b)^(1/2)*a*b^2*e-511*(e*x+d)^(5/2)*((a*e-b*d)*b)^(1/2)*b^3*d-420*a^3*b*e^4*x*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)+385*(e*x+d)^(3/2)*((a*e-b*d)*b)^(1/2)*a^2*b*e^2-770*(e*x+d)^(3/2)*((a*e-b*d)*b)^(1/2)*a*b^2*d*e+385*(e*x+d)^(3/2)*((a*e-b*d)*b)^(1/2)*b^3*d^2-105*a^4*e^4*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)+105*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*a^3*e^3-315*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*a^2*b*d*e^2+315*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*a*b^2*d^2*e-105*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*b^3*d^3)*(b*x+a)/((a*e-b*d)*b)^(1/2)/b^4/((b*x+a)^2)^(5/2)","B"
1724,1,477,177,0.072000," ","int((e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x)","\frac{\left(15 b^{4} e^{4} x^{4} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+60 a \,b^{3} e^{4} x^{3} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+90 a^{2} b^{2} e^{4} x^{2} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+60 a^{3} b \,e^{4} x \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+15 a^{4} e^{4} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)-15 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a^{3} e^{3}+45 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a^{2} b d \,e^{2}-45 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a \,b^{2} d^{2} e +15 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, b^{3} d^{3}-55 \left(e x +d \right)^{\frac{3}{2}} \sqrt{\left(a e -b d \right) b}\, a^{2} b \,e^{2}+110 \left(e x +d \right)^{\frac{3}{2}} \sqrt{\left(a e -b d \right) b}\, a \,b^{2} d e -55 \left(e x +d \right)^{\frac{3}{2}} \sqrt{\left(a e -b d \right) b}\, b^{3} d^{2}-73 \left(e x +d \right)^{\frac{5}{2}} \sqrt{\left(a e -b d \right) b}\, a \,b^{2} e +73 \left(e x +d \right)^{\frac{5}{2}} \sqrt{\left(a e -b d \right) b}\, b^{3} d +15 \left(e x +d \right)^{\frac{7}{2}} \sqrt{\left(a e -b d \right) b}\, b^{3}\right) \left(b x +a \right)}{192 \sqrt{\left(a e -b d \right) b}\, \left(a e -b d \right) \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}} b^{3}}"," ",0,"1/192*(15*b^4*e^4*x^4*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)+60*a*b^3*e^4*x^3*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)+15*(e*x+d)^(7/2)*((a*e-b*d)*b)^(1/2)*b^3+90*a^2*b^2*e^4*x^2*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)-73*(e*x+d)^(5/2)*((a*e-b*d)*b)^(1/2)*a*b^2*e+73*(e*x+d)^(5/2)*((a*e-b*d)*b)^(1/2)*b^3*d+60*a^3*b*e^4*x*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)-55*(e*x+d)^(3/2)*((a*e-b*d)*b)^(1/2)*a^2*b*e^2+110*(e*x+d)^(3/2)*((a*e-b*d)*b)^(1/2)*a*b^2*d*e-55*(e*x+d)^(3/2)*((a*e-b*d)*b)^(1/2)*b^3*d^2+15*a^4*e^4*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)-15*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*a^3*e^3+45*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*a^2*b*d*e^2-45*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*a*b^2*d^2*e+15*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*b^3*d^3)*(b*x+a)/((a*e-b*d)*b)^(1/2)/b^3/(a*e-b*d)/((b*x+a)^2)^(5/2)","B"
1725,1,477,187,0.088000," ","int((e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x)","\frac{\left(b x +a \right) \left(3 b^{4} e^{4} x^{4} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+12 a \,b^{3} e^{4} x^{3} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+18 a^{2} b^{2} e^{4} x^{2} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+12 a^{3} b \,e^{4} x \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+3 a^{4} e^{4} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)-3 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a^{3} e^{3}+9 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a^{2} b d \,e^{2}-9 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a \,b^{2} d^{2} e +3 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, b^{3} d^{3}-11 \left(e x +d \right)^{\frac{3}{2}} \sqrt{\left(a e -b d \right) b}\, a^{2} b \,e^{2}+22 \left(e x +d \right)^{\frac{3}{2}} \sqrt{\left(a e -b d \right) b}\, a \,b^{2} d e -11 \left(e x +d \right)^{\frac{3}{2}} \sqrt{\left(a e -b d \right) b}\, b^{3} d^{2}+11 \left(e x +d \right)^{\frac{5}{2}} \sqrt{\left(a e -b d \right) b}\, a \,b^{2} e -11 \left(e x +d \right)^{\frac{5}{2}} \sqrt{\left(a e -b d \right) b}\, b^{3} d +3 \left(e x +d \right)^{\frac{7}{2}} \sqrt{\left(a e -b d \right) b}\, b^{3}\right)}{64 \sqrt{\left(a e -b d \right) b}\, \left(a e -b d \right)^{2} \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}} b^{2}}"," ",0,"1/64*(b*x+a)*(3*b^4*e^4*x^4*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)+12*a*b^3*e^4*x^3*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)+3*(e*x+d)^(7/2)*((a*e-b*d)*b)^(1/2)*b^3+18*a^2*b^2*e^4*x^2*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)+11*(e*x+d)^(5/2)*((a*e-b*d)*b)^(1/2)*a*b^2*e-11*(e*x+d)^(5/2)*((a*e-b*d)*b)^(1/2)*b^3*d+12*a^3*b*e^4*x*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)-11*(e*x+d)^(3/2)*((a*e-b*d)*b)^(1/2)*a^2*b*e^2+22*(e*x+d)^(3/2)*((a*e-b*d)*b)^(1/2)*a*b^2*d*e-11*(e*x+d)^(3/2)*((a*e-b*d)*b)^(1/2)*b^3*d^2+3*a^4*e^4*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)-3*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*a^3*e^3+9*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*a^2*b*d*e^2-9*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*a*b^2*d^2*e+3*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*b^3*d^3)/((a*e-b*d)*b)^(1/2)/b^2/(a*e-b*d)^2/((b*x+a)^2)^(5/2)","B"
1726,1,500,197,0.101000," ","int((e*x+d)^(1/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x)","\frac{\left(b x +a \right) \left(15 b^{4} e^{4} x^{4} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+60 a \,b^{3} e^{4} x^{3} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+90 a^{2} b^{2} e^{4} x^{2} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+60 a^{3} b \,e^{4} x \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+15 a^{4} e^{4} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)-15 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a^{3} e^{3}+45 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a^{2} b d \,e^{2}-45 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a \,b^{2} d^{2} e +15 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, b^{3} d^{3}+73 \left(e x +d \right)^{\frac{3}{2}} \sqrt{\left(a e -b d \right) b}\, a^{2} b \,e^{2}-146 \left(e x +d \right)^{\frac{3}{2}} \sqrt{\left(a e -b d \right) b}\, a \,b^{2} d e +73 \left(e x +d \right)^{\frac{3}{2}} \sqrt{\left(a e -b d \right) b}\, b^{3} d^{2}+55 \left(e x +d \right)^{\frac{5}{2}} \sqrt{\left(a e -b d \right) b}\, a \,b^{2} e -55 \left(e x +d \right)^{\frac{5}{2}} \sqrt{\left(a e -b d \right) b}\, b^{3} d +15 \left(e x +d \right)^{\frac{7}{2}} \sqrt{\left(a e -b d \right) b}\, b^{3}\right)}{192 \sqrt{\left(a e -b d \right) b}\, \left(a e -b d \right) \left(a^{2} e^{2}-2 a b d e +b^{2} d^{2}\right) \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}} b}"," ",0,"1/192*(b*x+a)*(15*b^4*e^4*x^4*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)+60*a*b^3*e^4*x^3*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)+15*(e*x+d)^(7/2)*((a*e-b*d)*b)^(1/2)*b^3+90*a^2*b^2*e^4*x^2*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)+55*(e*x+d)^(5/2)*((a*e-b*d)*b)^(1/2)*a*b^2*e-55*(e*x+d)^(5/2)*((a*e-b*d)*b)^(1/2)*b^3*d+60*a^3*b*e^4*x*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)+73*(e*x+d)^(3/2)*((a*e-b*d)*b)^(1/2)*a^2*b*e^2-146*(e*x+d)^(3/2)*((a*e-b*d)*b)^(1/2)*a*b^2*d*e+73*(e*x+d)^(3/2)*((a*e-b*d)*b)^(1/2)*b^3*d^2+15*a^4*e^4*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)-15*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*a^3*e^3+45*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*a^2*b*d*e^2-45*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*a*b^2*d^2*e+15*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*b^3*d^3)/((a*e-b*d)*b)^(1/2)/b/(a*e-b*d)/(a^2*e^2-2*a*b*d*e+b^2*d^2)/((b*x+a)^2)^(5/2)","B"
1727,1,497,195,0.070000," ","int(1/(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^(1/2),x)","\frac{\left(105 b^{4} e^{4} x^{4} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+420 a \,b^{3} e^{4} x^{3} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+630 a^{2} b^{2} e^{4} x^{2} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+420 a^{3} b \,e^{4} x \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+105 a^{4} e^{4} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+105 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, b^{3} e^{3} x^{3}+385 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a \,b^{2} e^{3} x^{2}-70 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, b^{3} d \,e^{2} x^{2}+511 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a^{2} b \,e^{3} x -252 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a \,b^{2} d \,e^{2} x +56 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, b^{3} d^{2} e x +279 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a^{3} e^{3}-326 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a^{2} b d \,e^{2}+200 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, a \,b^{2} d^{2} e -48 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, b^{3} d^{3}\right) \left(b x +a \right)}{192 \sqrt{\left(a e -b d \right) b}\, \left(a e -b d \right)^{4} \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}}}"," ",0,"1/192*(105*b^4*e^4*x^4*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)+420*a*b^3*e^4*x^3*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)+105*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*x^3*b^3*e^3+630*a^2*b^2*e^4*x^2*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)+385*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*a*b^2*e^3*x^2-70*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*b^3*d*e^2*x^2+420*a^3*b*e^4*x*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)+511*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*a^2*b*e^3*x-252*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*x*a*b^2*d*e^2+56*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*x*b^3*d^2*e+105*a^4*e^4*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)+279*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*a^3*e^3-326*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*a^2*b*d*e^2+200*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*a*b^2*d^2*e-48*(e*x+d)^(1/2)*((a*e-b*d)*b)^(1/2)*b^3*d^3)*(b*x+a)/((a*e-b*d)*b)^(1/2)/(a*e-b*d)^4/((b*x+a)^2)^(5/2)","B"
1728,1,602,231,0.074000," ","int(1/(e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x)","-\frac{\left(315 \sqrt{e x +d}\, b^{5} e^{4} x^{4} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+1260 \sqrt{e x +d}\, a \,b^{4} e^{4} x^{3} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+1890 \sqrt{e x +d}\, a^{2} b^{3} e^{4} x^{2} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+315 \sqrt{\left(a e -b d \right) b}\, b^{4} e^{4} x^{4}+1260 \sqrt{e x +d}\, a^{3} b^{2} e^{4} x \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+1155 \sqrt{\left(a e -b d \right) b}\, a \,b^{3} e^{4} x^{3}+105 \sqrt{\left(a e -b d \right) b}\, b^{4} d \,e^{3} x^{3}+315 \sqrt{e x +d}\, a^{4} b \,e^{4} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+1533 \sqrt{\left(a e -b d \right) b}\, a^{2} b^{2} e^{4} x^{2}+399 \sqrt{\left(a e -b d \right) b}\, a \,b^{3} d \,e^{3} x^{2}-42 \sqrt{\left(a e -b d \right) b}\, b^{4} d^{2} e^{2} x^{2}+837 \sqrt{\left(a e -b d \right) b}\, a^{3} b \,e^{4} x +555 \sqrt{\left(a e -b d \right) b}\, a^{2} b^{2} d \,e^{3} x -156 \sqrt{\left(a e -b d \right) b}\, a \,b^{3} d^{2} e^{2} x +24 \sqrt{\left(a e -b d \right) b}\, b^{4} d^{3} e x +128 \sqrt{\left(a e -b d \right) b}\, a^{4} e^{4}+325 \sqrt{\left(a e -b d \right) b}\, a^{3} b d \,e^{3}-210 \sqrt{\left(a e -b d \right) b}\, a^{2} b^{2} d^{2} e^{2}+88 \sqrt{\left(a e -b d \right) b}\, a \,b^{3} d^{3} e -16 \sqrt{\left(a e -b d \right) b}\, b^{4} d^{4}\right) \left(b x +a \right)}{64 \sqrt{e x +d}\, \sqrt{\left(a e -b d \right) b}\, \left(a e -b d \right)^{5} \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}}}"," ",0,"-1/64*(315*(e*x+d)^(1/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x^4*b^5*e^4+1260*(e*x+d)^(1/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x^3*a*b^4*e^4+1890*(e*x+d)^(1/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x^2*a^2*b^3*e^4+315*((a*e-b*d)*b)^(1/2)*b^4*e^4*x^4+1260*(e*x+d)^(1/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x*a^3*b^2*e^4+1155*((a*e-b*d)*b)^(1/2)*a*b^3*e^4*x^3+105*((a*e-b*d)*b)^(1/2)*b^4*d*e^3*x^3+315*(e*x+d)^(1/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*a^4*b*e^4+1533*((a*e-b*d)*b)^(1/2)*a^2*b^2*e^4*x^2+399*((a*e-b*d)*b)^(1/2)*a*b^3*d*e^3*x^2-42*((a*e-b*d)*b)^(1/2)*b^4*d^2*e^2*x^2+837*((a*e-b*d)*b)^(1/2)*a^3*b*e^4*x+555*((a*e-b*d)*b)^(1/2)*a^2*b^2*d*e^3*x-156*((a*e-b*d)*b)^(1/2)*a*b^3*d^2*e^2*x+24*((a*e-b*d)*b)^(1/2)*b^4*d^3*e*x+128*((a*e-b*d)*b)^(1/2)*a^4*e^4+325*((a*e-b*d)*b)^(1/2)*a^3*b*d*e^3-210*((a*e-b*d)*b)^(1/2)*a^2*b^2*d^2*e^2+88*((a*e-b*d)*b)^(1/2)*a*b^3*d^3*e-16*((a*e-b*d)*b)^(1/2)*b^4*d^4)*(b*x+a)/(e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)/(a*e-b*d)^5/((b*x+a)^2)^(5/2)","B"
1729,1,763,268,0.084000," ","int(1/(e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x)","\frac{\left(3465 \left(e x +d \right)^{\frac{3}{2}} b^{6} e^{4} x^{4} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+3465 \sqrt{\left(a e -b d \right) b}\, b^{5} e^{5} x^{5}+13860 \left(e x +d \right)^{\frac{3}{2}} a \,b^{5} e^{4} x^{3} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+12705 \sqrt{\left(a e -b d \right) b}\, a \,b^{4} e^{5} x^{4}+4620 \sqrt{\left(a e -b d \right) b}\, b^{5} d \,e^{4} x^{4}+20790 \left(e x +d \right)^{\frac{3}{2}} a^{2} b^{4} e^{4} x^{2} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+16863 \sqrt{\left(a e -b d \right) b}\, a^{2} b^{3} e^{5} x^{3}+17094 \sqrt{\left(a e -b d \right) b}\, a \,b^{4} d \,e^{4} x^{3}+693 \sqrt{\left(a e -b d \right) b}\, b^{5} d^{2} e^{3} x^{3}+13860 \left(e x +d \right)^{\frac{3}{2}} a^{3} b^{3} e^{4} x \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+9207 \sqrt{\left(a e -b d \right) b}\, a^{3} b^{2} e^{5} x^{2}+22968 \sqrt{\left(a e -b d \right) b}\, a^{2} b^{3} d \,e^{4} x^{2}+2673 \sqrt{\left(a e -b d \right) b}\, a \,b^{4} d^{2} e^{3} x^{2}-198 \sqrt{\left(a e -b d \right) b}\, b^{5} d^{3} e^{2} x^{2}+3465 \left(e x +d \right)^{\frac{3}{2}} a^{4} b^{2} e^{4} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+1408 \sqrt{\left(a e -b d \right) b}\, a^{4} b \,e^{5} x +12782 \sqrt{\left(a e -b d \right) b}\, a^{3} b^{2} d \,e^{4} x +3795 \sqrt{\left(a e -b d \right) b}\, a^{2} b^{3} d^{2} e^{3} x -748 \sqrt{\left(a e -b d \right) b}\, a \,b^{4} d^{3} e^{2} x +88 \sqrt{\left(a e -b d \right) b}\, b^{5} d^{4} e x -128 \sqrt{\left(a e -b d \right) b}\, a^{5} e^{5}+2048 \sqrt{\left(a e -b d \right) b}\, a^{4} b d \,e^{4}+2295 \sqrt{\left(a e -b d \right) b}\, a^{3} b^{2} d^{2} e^{3}-1030 \sqrt{\left(a e -b d \right) b}\, a^{2} b^{3} d^{3} e^{2}+328 \sqrt{\left(a e -b d \right) b}\, a \,b^{4} d^{4} e -48 \sqrt{\left(a e -b d \right) b}\, b^{5} d^{5}\right) \left(b x +a \right)}{192 \left(e x +d \right)^{\frac{3}{2}} \sqrt{\left(a e -b d \right) b}\, \left(a e -b d \right)^{6} \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}}}"," ",0,"1/192*(3795*((a*e-b*d)*b)^(1/2)*x*a^2*b^3*d^2*e^3+3465*((a*e-b*d)*b)^(1/2)*x^5*b^5*e^5-128*((a*e-b*d)*b)^(1/2)*a^5*e^5-48*((a*e-b*d)*b)^(1/2)*b^5*d^5+13860*(e*x+d)^(3/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x^3*a*b^5*e^4+20790*(e*x+d)^(3/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x^2*a^2*b^4*e^4+3465*(e*x+d)^(3/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*a^4*b^2*e^4+16863*((a*e-b*d)*b)^(1/2)*x^3*a^2*b^3*e^5+9207*((a*e-b*d)*b)^(1/2)*x^2*a^3*b^2*e^5+1408*((a*e-b*d)*b)^(1/2)*x*a^4*b*e^5+693*((a*e-b*d)*b)^(1/2)*x^3*b^5*d^2*e^3-198*((a*e-b*d)*b)^(1/2)*x^2*b^5*d^3*e^2+88*((a*e-b*d)*b)^(1/2)*x*b^5*d^4*e+3465*(e*x+d)^(3/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x^4*b^6*e^4+12705*((a*e-b*d)*b)^(1/2)*x^4*a*b^4*e^5+4620*((a*e-b*d)*b)^(1/2)*x^4*b^5*d*e^4-1030*((a*e-b*d)*b)^(1/2)*a^2*b^3*d^3*e^2+328*((a*e-b*d)*b)^(1/2)*a*b^4*d^4*e-748*((a*e-b*d)*b)^(1/2)*x*a*b^4*d^3*e^2+2673*((a*e-b*d)*b)^(1/2)*x^2*a*b^4*d^2*e^3+22968*((a*e-b*d)*b)^(1/2)*x^2*a^2*b^3*d*e^4+12782*((a*e-b*d)*b)^(1/2)*x*a^3*b^2*d*e^4+13860*(e*x+d)^(3/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x*a^3*b^3*e^4+17094*((a*e-b*d)*b)^(1/2)*x^3*a*b^4*d*e^4+2048*((a*e-b*d)*b)^(1/2)*a^4*b*d*e^4+2295*((a*e-b*d)*b)^(1/2)*a^3*b^2*d^2*e^3)*(b*x+a)/(e*x+d)^(3/2)/((a*e-b*d)*b)^(1/2)/(a*e-b*d)^6/((b*x+a)^2)^(5/2)","B"
1730,1,951,307,0.096000," ","int(1/(e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x)","-\frac{\left(45045 \sqrt{\left(a e -b d \right) b}\, b^{6} e^{6} x^{6}+165165 \sqrt{\left(a e -b d \right) b}\, a \,b^{5} e^{6} x^{5}+105105 \sqrt{\left(a e -b d \right) b}\, b^{6} d \,e^{5} x^{5}+219219 \sqrt{\left(a e -b d \right) b}\, a^{2} b^{4} e^{6} x^{4}+387387 \sqrt{\left(a e -b d \right) b}\, a \,b^{5} d \,e^{5} x^{4}+45045 \left(e x +d \right)^{\frac{5}{2}} b^{7} e^{4} x^{4} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+69069 \sqrt{\left(a e -b d \right) b}\, b^{6} d^{2} e^{4} x^{4}+119691 \sqrt{\left(a e -b d \right) b}\, a^{3} b^{3} e^{6} x^{3}+517803 \sqrt{\left(a e -b d \right) b}\, a^{2} b^{4} d \,e^{5} x^{3}+180180 \left(e x +d \right)^{\frac{5}{2}} a \,b^{6} e^{4} x^{3} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+256971 \sqrt{\left(a e -b d \right) b}\, a \,b^{5} d^{2} e^{4} x^{3}+6435 \sqrt{\left(a e -b d \right) b}\, b^{6} d^{3} e^{3} x^{3}+18304 \sqrt{\left(a e -b d \right) b}\, a^{4} b^{2} e^{6} x^{2}+285857 \sqrt{\left(a e -b d \right) b}\, a^{3} b^{3} d \,e^{5} x^{2}+270270 \left(e x +d \right)^{\frac{5}{2}} a^{2} b^{5} e^{4} x^{2} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+347919 \sqrt{\left(a e -b d \right) b}\, a^{2} b^{4} d^{2} e^{4} x^{2}+25025 \sqrt{\left(a e -b d \right) b}\, a \,b^{5} d^{3} e^{3} x^{2}-1430 \sqrt{\left(a e -b d \right) b}\, b^{6} d^{4} e^{2} x^{2}-1664 \sqrt{\left(a e -b d \right) b}\, a^{5} b \,e^{6} x +44928 \sqrt{\left(a e -b d \right) b}\, a^{4} b^{2} d \,e^{5} x +180180 \left(e x +d \right)^{\frac{5}{2}} a^{3} b^{4} e^{4} x \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+196001 \sqrt{\left(a e -b d \right) b}\, a^{3} b^{3} d^{2} e^{4} x +35945 \sqrt{\left(a e -b d \right) b}\, a^{2} b^{4} d^{3} e^{3} x -5460 \sqrt{\left(a e -b d \right) b}\, a \,b^{5} d^{4} e^{2} x +520 \sqrt{\left(a e -b d \right) b}\, b^{6} d^{5} e x +384 \sqrt{\left(a e -b d \right) b}\, a^{6} e^{6}-3968 \sqrt{\left(a e -b d \right) b}\, a^{5} b d \,e^{5}+45045 \left(e x +d \right)^{\frac{5}{2}} a^{4} b^{3} e^{4} \arctan \left(\frac{\sqrt{e x +d}\, b}{\sqrt{\left(a e -b d \right) b}}\right)+32384 \sqrt{\left(a e -b d \right) b}\, a^{4} b^{2} d^{2} e^{4}+22155 \sqrt{\left(a e -b d \right) b}\, a^{3} b^{3} d^{3} e^{3}-7630 \sqrt{\left(a e -b d \right) b}\, a^{2} b^{4} d^{4} e^{2}+1960 \sqrt{\left(a e -b d \right) b}\, a \,b^{5} d^{5} e -240 \sqrt{\left(a e -b d \right) b}\, b^{6} d^{6}\right) \left(b x +a \right)}{960 \left(e x +d \right)^{\frac{5}{2}} \sqrt{\left(a e -b d \right) b}\, \left(a e -b d \right)^{7} \left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}}}"," ",0,"-1/960*(44928*((a*e-b*d)*b)^(1/2)*x*a^4*b^2*d*e^5+165165*((a*e-b*d)*b)^(1/2)*x^5*a*b^5*e^6+105105*((a*e-b*d)*b)^(1/2)*x^5*b^6*d*e^5-1664*((a*e-b*d)*b)^(1/2)*x*a^5*b*e^6+45045*(e*x+d)^(5/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*a^4*b^3*e^4+219219*((a*e-b*d)*b)^(1/2)*x^4*a^2*b^4*e^6+69069*((a*e-b*d)*b)^(1/2)*x^4*b^6*d^2*e^4+45045*((a*e-b*d)*b)^(1/2)*x^6*b^6*e^6-240*((a*e-b*d)*b)^(1/2)*b^6*d^6-3968*((a*e-b*d)*b)^(1/2)*a^5*b*d*e^5+32384*((a*e-b*d)*b)^(1/2)*a^4*b^2*d^2*e^4+384*((a*e-b*d)*b)^(1/2)*a^6*e^6+22155*((a*e-b*d)*b)^(1/2)*a^3*b^3*d^3*e^3-7630*((a*e-b*d)*b)^(1/2)*a^2*b^4*d^4*e^2+1960*((a*e-b*d)*b)^(1/2)*a*b^5*d^5*e+180180*(e*x+d)^(5/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x*a^3*b^4*e^4+25025*((a*e-b*d)*b)^(1/2)*x^2*a*b^5*d^3*e^3+119691*((a*e-b*d)*b)^(1/2)*x^3*a^3*b^3*e^6+18304*((a*e-b*d)*b)^(1/2)*x^2*a^4*b^2*e^6+6435*((a*e-b*d)*b)^(1/2)*x^3*b^6*d^3*e^3-1430*((a*e-b*d)*b)^(1/2)*x^2*b^6*d^4*e^2+520*((a*e-b*d)*b)^(1/2)*x*b^6*d^5*e+45045*(e*x+d)^(5/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x^4*b^7*e^4+35945*((a*e-b*d)*b)^(1/2)*x*a^2*b^4*d^3*e^3-5460*((a*e-b*d)*b)^(1/2)*x*a*b^5*d^4*e^2+180180*(e*x+d)^(5/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x^3*a*b^6*e^4+270270*(e*x+d)^(5/2)*arctan((e*x+d)^(1/2)/((a*e-b*d)*b)^(1/2)*b)*x^2*a^2*b^5*e^4+285857*((a*e-b*d)*b)^(1/2)*x^2*a^3*b^3*d*e^5+347919*((a*e-b*d)*b)^(1/2)*x^2*a^2*b^4*d^2*e^4+256971*((a*e-b*d)*b)^(1/2)*x^3*a*b^5*d^2*e^4+387387*((a*e-b*d)*b)^(1/2)*x^4*a*b^5*d*e^5+517803*((a*e-b*d)*b)^(1/2)*x^3*a^2*b^4*d*e^5+196001*((a*e-b*d)*b)^(1/2)*x*a^3*b^3*d^2*e^4)*(b*x+a)/(e*x+d)^(5/2)/((a*e-b*d)*b)^(1/2)/(a*e-b*d)^7/((b*x+a)^2)^(5/2)","B"
1731,1,2157,206,0.077000," ","int((e*x+d)^m*(b^2*x^2+2*a*b*x+a^2)^3,x)","\frac{\left(b^{6} e^{6} m^{6} x^{6}+6 a \,b^{5} e^{6} m^{6} x^{5}+21 b^{6} e^{6} m^{5} x^{6}+15 a^{2} b^{4} e^{6} m^{6} x^{4}+132 a \,b^{5} e^{6} m^{5} x^{5}-6 b^{6} d \,e^{5} m^{5} x^{5}+175 b^{6} e^{6} m^{4} x^{6}+20 a^{3} b^{3} e^{6} m^{6} x^{3}+345 a^{2} b^{4} e^{6} m^{5} x^{4}-30 a \,b^{5} d \,e^{5} m^{5} x^{4}+1140 a \,b^{5} e^{6} m^{4} x^{5}-90 b^{6} d \,e^{5} m^{4} x^{5}+735 b^{6} e^{6} m^{3} x^{6}+15 a^{4} b^{2} e^{6} m^{6} x^{2}+480 a^{3} b^{3} e^{6} m^{5} x^{3}-60 a^{2} b^{4} d \,e^{5} m^{5} x^{3}+3105 a^{2} b^{4} e^{6} m^{4} x^{4}-510 a \,b^{5} d \,e^{5} m^{4} x^{4}+4920 a \,b^{5} e^{6} m^{3} x^{5}+30 b^{6} d^{2} e^{4} m^{4} x^{4}-510 b^{6} d \,e^{5} m^{3} x^{5}+1624 b^{6} e^{6} m^{2} x^{6}+6 a^{5} b \,e^{6} m^{6} x +375 a^{4} b^{2} e^{6} m^{5} x^{2}-60 a^{3} b^{3} d \,e^{5} m^{5} x^{2}+4520 a^{3} b^{3} e^{6} m^{4} x^{3}-1140 a^{2} b^{4} d \,e^{5} m^{4} x^{3}+13875 a^{2} b^{4} e^{6} m^{3} x^{4}+120 a \,b^{5} d^{2} e^{4} m^{4} x^{3}-3150 a \,b^{5} d \,e^{5} m^{3} x^{4}+11094 a \,b^{5} e^{6} m^{2} x^{5}+300 b^{6} d^{2} e^{4} m^{3} x^{4}-1350 b^{6} d \,e^{5} m^{2} x^{5}+1764 b^{6} e^{6} m \,x^{6}+a^{6} e^{6} m^{6}+156 a^{5} b \,e^{6} m^{5} x -30 a^{4} b^{2} d \,e^{5} m^{5} x +3705 a^{4} b^{2} e^{6} m^{4} x^{2}-1260 a^{3} b^{3} d \,e^{5} m^{4} x^{2}+21120 a^{3} b^{3} e^{6} m^{3} x^{3}+180 a^{2} b^{4} d^{2} e^{4} m^{4} x^{2}-7860 a^{2} b^{4} d \,e^{5} m^{3} x^{3}+32160 a^{2} b^{4} e^{6} m^{2} x^{4}+1560 a \,b^{5} d^{2} e^{4} m^{3} x^{3}-8850 a \,b^{5} d \,e^{5} m^{2} x^{4}+12228 a \,b^{5} e^{6} m \,x^{5}-120 b^{6} d^{3} e^{3} m^{3} x^{3}+1050 b^{6} d^{2} e^{4} m^{2} x^{4}-1644 b^{6} d \,e^{5} m \,x^{5}+720 b^{6} e^{6} x^{6}+27 a^{6} e^{6} m^{5}-6 a^{5} b d \,e^{5} m^{5}+1620 a^{5} b \,e^{6} m^{4} x -690 a^{4} b^{2} d \,e^{5} m^{4} x +18285 a^{4} b^{2} e^{6} m^{3} x^{2}+120 a^{3} b^{3} d^{2} e^{4} m^{4} x -9780 a^{3} b^{3} d \,e^{5} m^{3} x^{2}+50900 a^{3} b^{3} e^{6} m^{2} x^{3}+2880 a^{2} b^{4} d^{2} e^{4} m^{3} x^{2}-24060 a^{2} b^{4} d \,e^{5} m^{2} x^{3}+36180 a^{2} b^{4} e^{6} m \,x^{4}-360 a \,b^{5} d^{3} e^{3} m^{3} x^{2}+6360 a \,b^{5} d^{2} e^{4} m^{2} x^{3}-11220 a \,b^{5} d \,e^{5} m \,x^{4}+5040 a \,b^{5} e^{6} x^{5}-720 b^{6} d^{3} e^{3} m^{2} x^{3}+1500 b^{6} d^{2} e^{4} m \,x^{4}-720 b^{6} d \,e^{5} x^{5}+295 a^{6} e^{6} m^{4}-150 a^{5} b d \,e^{5} m^{4}+8520 a^{5} b \,e^{6} m^{3} x +30 a^{4} b^{2} d^{2} e^{4} m^{4}-6030 a^{4} b^{2} d \,e^{5} m^{3} x +46680 a^{4} b^{2} e^{6} m^{2} x^{2}+2280 a^{3} b^{3} d^{2} e^{4} m^{3} x -34020 a^{3} b^{3} d \,e^{5} m^{2} x^{2}+59040 a^{3} b^{3} e^{6} m \,x^{3}-360 a^{2} b^{4} d^{3} e^{3} m^{3} x +14940 a^{2} b^{4} d^{2} e^{4} m^{2} x^{2}-32400 a^{2} b^{4} d \,e^{5} m \,x^{3}+15120 a^{2} b^{4} e^{6} x^{4}-3600 a \,b^{5} d^{3} e^{3} m^{2} x^{2}+9960 a \,b^{5} d^{2} e^{4} m \,x^{3}-5040 a \,b^{5} d \,e^{5} x^{4}+360 b^{6} d^{4} e^{2} m^{2} x^{2}-1320 b^{6} d^{3} e^{3} m \,x^{3}+720 b^{6} d^{2} e^{4} x^{4}+1665 a^{6} e^{6} m^{3}-1470 a^{5} b d \,e^{5} m^{3}+23574 a^{5} b \,e^{6} m^{2} x +660 a^{4} b^{2} d^{2} e^{4} m^{3}-24510 a^{4} b^{2} d \,e^{5} m^{2} x +56940 a^{4} b^{2} e^{6} m \,x^{2}-120 a^{3} b^{3} d^{3} e^{3} m^{3}+15000 a^{3} b^{3} d^{2} e^{4} m^{2} x -50640 a^{3} b^{3} d \,e^{5} m \,x^{2}+25200 a^{3} b^{3} e^{6} x^{3}-5040 a^{2} b^{4} d^{3} e^{3} m^{2} x +27360 a^{2} b^{4} d^{2} e^{4} m \,x^{2}-15120 a^{2} b^{4} d \,e^{5} x^{3}+720 a \,b^{5} d^{4} e^{2} m^{2} x -8280 a \,b^{5} d^{3} e^{3} m \,x^{2}+5040 a \,b^{5} d^{2} e^{4} x^{3}+1080 b^{6} d^{4} e^{2} m \,x^{2}-720 b^{6} d^{3} e^{3} x^{3}+5104 a^{6} e^{6} m^{2}-7050 a^{5} b d \,e^{5} m^{2}+31644 a^{5} b \,e^{6} m x +5370 a^{4} b^{2} d^{2} e^{4} m^{2}-44340 a^{4} b^{2} d \,e^{5} m x +25200 a^{4} b^{2} e^{6} x^{2}-2160 a^{3} b^{3} d^{3} e^{3} m^{2}+38040 a^{3} b^{3} d^{2} e^{4} m x -25200 a^{3} b^{3} d \,e^{5} x^{2}+360 a^{2} b^{4} d^{4} e^{2} m^{2}-19800 a^{2} b^{4} d^{3} e^{3} m x +15120 a^{2} b^{4} d^{2} e^{4} x^{2}+5760 a \,b^{5} d^{4} e^{2} m x -5040 a \,b^{5} d^{3} e^{3} x^{2}-720 b^{6} d^{5} e m x +720 b^{6} d^{4} e^{2} x^{2}+8028 a^{6} e^{6} m -16524 a^{5} b d \,e^{5} m +15120 a^{5} b \,e^{6} x +19140 a^{4} b^{2} d^{2} e^{4} m -25200 a^{4} b^{2} d \,e^{5} x -12840 a^{3} b^{3} d^{3} e^{3} m +25200 a^{3} b^{3} d^{2} e^{4} x +4680 a^{2} b^{4} d^{4} e^{2} m -15120 a^{2} b^{4} d^{3} e^{3} x -720 a \,b^{5} d^{5} e m +5040 a \,b^{5} d^{4} e^{2} x -720 b^{6} d^{5} e x +5040 a^{6} e^{6}-15120 a^{5} b d \,e^{5}+25200 a^{4} b^{2} d^{2} e^{4}-25200 a^{3} b^{3} d^{3} e^{3}+15120 a^{2} b^{4} d^{4} e^{2}-5040 a \,b^{5} d^{5} e +720 b^{6} d^{6}\right) \left(e x +d \right)^{m +1}}{\left(m^{7}+28 m^{6}+322 m^{5}+1960 m^{4}+6769 m^{3}+13132 m^{2}+13068 m +5040\right) e^{7}}"," ",0,"(e*x+d)^(m+1)*(b^6*e^6*m^6*x^6+6*a*b^5*e^6*m^6*x^5+21*b^6*e^6*m^5*x^6+15*a^2*b^4*e^6*m^6*x^4+132*a*b^5*e^6*m^5*x^5-6*b^6*d*e^5*m^5*x^5+175*b^6*e^6*m^4*x^6+20*a^3*b^3*e^6*m^6*x^3+345*a^2*b^4*e^6*m^5*x^4-30*a*b^5*d*e^5*m^5*x^4+1140*a*b^5*e^6*m^4*x^5-90*b^6*d*e^5*m^4*x^5+735*b^6*e^6*m^3*x^6+15*a^4*b^2*e^6*m^6*x^2+480*a^3*b^3*e^6*m^5*x^3-60*a^2*b^4*d*e^5*m^5*x^3+3105*a^2*b^4*e^6*m^4*x^4-510*a*b^5*d*e^5*m^4*x^4+4920*a*b^5*e^6*m^3*x^5+30*b^6*d^2*e^4*m^4*x^4-510*b^6*d*e^5*m^3*x^5+1624*b^6*e^6*m^2*x^6+6*a^5*b*e^6*m^6*x+375*a^4*b^2*e^6*m^5*x^2-60*a^3*b^3*d*e^5*m^5*x^2+4520*a^3*b^3*e^6*m^4*x^3-1140*a^2*b^4*d*e^5*m^4*x^3+13875*a^2*b^4*e^6*m^3*x^4+120*a*b^5*d^2*e^4*m^4*x^3-3150*a*b^5*d*e^5*m^3*x^4+11094*a*b^5*e^6*m^2*x^5+300*b^6*d^2*e^4*m^3*x^4-1350*b^6*d*e^5*m^2*x^5+1764*b^6*e^6*m*x^6+a^6*e^6*m^6+156*a^5*b*e^6*m^5*x-30*a^4*b^2*d*e^5*m^5*x+3705*a^4*b^2*e^6*m^4*x^2-1260*a^3*b^3*d*e^5*m^4*x^2+21120*a^3*b^3*e^6*m^3*x^3+180*a^2*b^4*d^2*e^4*m^4*x^2-7860*a^2*b^4*d*e^5*m^3*x^3+32160*a^2*b^4*e^6*m^2*x^4+1560*a*b^5*d^2*e^4*m^3*x^3-8850*a*b^5*d*e^5*m^2*x^4+12228*a*b^5*e^6*m*x^5-120*b^6*d^3*e^3*m^3*x^3+1050*b^6*d^2*e^4*m^2*x^4-1644*b^6*d*e^5*m*x^5+720*b^6*e^6*x^6+27*a^6*e^6*m^5-6*a^5*b*d*e^5*m^5+1620*a^5*b*e^6*m^4*x-690*a^4*b^2*d*e^5*m^4*x+18285*a^4*b^2*e^6*m^3*x^2+120*a^3*b^3*d^2*e^4*m^4*x-9780*a^3*b^3*d*e^5*m^3*x^2+50900*a^3*b^3*e^6*m^2*x^3+2880*a^2*b^4*d^2*e^4*m^3*x^2-24060*a^2*b^4*d*e^5*m^2*x^3+36180*a^2*b^4*e^6*m*x^4-360*a*b^5*d^3*e^3*m^3*x^2+6360*a*b^5*d^2*e^4*m^2*x^3-11220*a*b^5*d*e^5*m*x^4+5040*a*b^5*e^6*x^5-720*b^6*d^3*e^3*m^2*x^3+1500*b^6*d^2*e^4*m*x^4-720*b^6*d*e^5*x^5+295*a^6*e^6*m^4-150*a^5*b*d*e^5*m^4+8520*a^5*b*e^6*m^3*x+30*a^4*b^2*d^2*e^4*m^4-6030*a^4*b^2*d*e^5*m^3*x+46680*a^4*b^2*e^6*m^2*x^2+2280*a^3*b^3*d^2*e^4*m^3*x-34020*a^3*b^3*d*e^5*m^2*x^2+59040*a^3*b^3*e^6*m*x^3-360*a^2*b^4*d^3*e^3*m^3*x+14940*a^2*b^4*d^2*e^4*m^2*x^2-32400*a^2*b^4*d*e^5*m*x^3+15120*a^2*b^4*e^6*x^4-3600*a*b^5*d^3*e^3*m^2*x^2+9960*a*b^5*d^2*e^4*m*x^3-5040*a*b^5*d*e^5*x^4+360*b^6*d^4*e^2*m^2*x^2-1320*b^6*d^3*e^3*m*x^3+720*b^6*d^2*e^4*x^4+1665*a^6*e^6*m^3-1470*a^5*b*d*e^5*m^3+23574*a^5*b*e^6*m^2*x+660*a^4*b^2*d^2*e^4*m^3-24510*a^4*b^2*d*e^5*m^2*x+56940*a^4*b^2*e^6*m*x^2-120*a^3*b^3*d^3*e^3*m^3+15000*a^3*b^3*d^2*e^4*m^2*x-50640*a^3*b^3*d*e^5*m*x^2+25200*a^3*b^3*e^6*x^3-5040*a^2*b^4*d^3*e^3*m^2*x+27360*a^2*b^4*d^2*e^4*m*x^2-15120*a^2*b^4*d*e^5*x^3+720*a*b^5*d^4*e^2*m^2*x-8280*a*b^5*d^3*e^3*m*x^2+5040*a*b^5*d^2*e^4*x^3+1080*b^6*d^4*e^2*m*x^2-720*b^6*d^3*e^3*x^3+5104*a^6*e^6*m^2-7050*a^5*b*d*e^5*m^2+31644*a^5*b*e^6*m*x+5370*a^4*b^2*d^2*e^4*m^2-44340*a^4*b^2*d*e^5*m*x+25200*a^4*b^2*e^6*x^2-2160*a^3*b^3*d^3*e^3*m^2+38040*a^3*b^3*d^2*e^4*m*x-25200*a^3*b^3*d*e^5*x^2+360*a^2*b^4*d^4*e^2*m^2-19800*a^2*b^4*d^3*e^3*m*x+15120*a^2*b^4*d^2*e^4*x^2+5760*a*b^5*d^4*e^2*m*x-5040*a*b^5*d^3*e^3*x^2-720*b^6*d^5*e*m*x+720*b^6*d^4*e^2*x^2+8028*a^6*e^6*m-16524*a^5*b*d*e^5*m+15120*a^5*b*e^6*x+19140*a^4*b^2*d^2*e^4*m-25200*a^4*b^2*d*e^5*x-12840*a^3*b^3*d^3*e^3*m+25200*a^3*b^3*d^2*e^4*x+4680*a^2*b^4*d^4*e^2*m-15120*a^2*b^4*d^3*e^3*x-720*a*b^5*d^5*e*m+5040*a*b^5*d^4*e^2*x-720*b^6*d^5*e*x+5040*a^6*e^6-15120*a^5*b*d*e^5+25200*a^4*b^2*d^2*e^4-25200*a^3*b^3*d^3*e^3+15120*a^2*b^4*d^4*e^2-5040*a*b^5*d^5*e+720*b^6*d^6)/e^7/(m^7+28*m^6+322*m^5+1960*m^4+6769*m^3+13132*m^2+13068*m+5040)","B"
1732,1,768,142,0.054000," ","int((e*x+d)^m*(b^2*x^2+2*a*b*x+a^2)^2,x)","\frac{\left(b^{4} e^{4} m^{4} x^{4}+4 a \,b^{3} e^{4} m^{4} x^{3}+10 b^{4} e^{4} m^{3} x^{4}+6 a^{2} b^{2} e^{4} m^{4} x^{2}+44 a \,b^{3} e^{4} m^{3} x^{3}-4 b^{4} d \,e^{3} m^{3} x^{3}+35 b^{4} e^{4} m^{2} x^{4}+4 a^{3} b \,e^{4} m^{4} x +72 a^{2} b^{2} e^{4} m^{3} x^{2}-12 a \,b^{3} d \,e^{3} m^{3} x^{2}+164 a \,b^{3} e^{4} m^{2} x^{3}-24 b^{4} d \,e^{3} m^{2} x^{3}+50 b^{4} e^{4} m \,x^{4}+a^{4} e^{4} m^{4}+52 a^{3} b \,e^{4} m^{3} x -12 a^{2} b^{2} d \,e^{3} m^{3} x +294 a^{2} b^{2} e^{4} m^{2} x^{2}-96 a \,b^{3} d \,e^{3} m^{2} x^{2}+244 a \,b^{3} e^{4} m \,x^{3}+12 b^{4} d^{2} e^{2} m^{2} x^{2}-44 b^{4} d \,e^{3} m \,x^{3}+24 b^{4} x^{4} e^{4}+14 a^{4} e^{4} m^{3}-4 a^{3} b d \,e^{3} m^{3}+236 a^{3} b \,e^{4} m^{2} x -120 a^{2} b^{2} d \,e^{3} m^{2} x +468 a^{2} b^{2} e^{4} m \,x^{2}+24 a \,b^{3} d^{2} e^{2} m^{2} x -204 a \,b^{3} d \,e^{3} m \,x^{2}+120 a \,b^{3} e^{4} x^{3}+36 b^{4} d^{2} e^{2} m \,x^{2}-24 b^{4} d \,e^{3} x^{3}+71 a^{4} e^{4} m^{2}-48 a^{3} b d \,e^{3} m^{2}+428 a^{3} b \,e^{4} m x +12 a^{2} b^{2} d^{2} e^{2} m^{2}-348 a^{2} b^{2} d \,e^{3} m x +240 a^{2} b^{2} e^{4} x^{2}+144 a \,b^{3} d^{2} e^{2} m x -120 a \,b^{3} d \,e^{3} x^{2}-24 b^{4} d^{3} e m x +24 b^{4} d^{2} e^{2} x^{2}+154 a^{4} e^{4} m -188 a^{3} b d \,e^{3} m +240 a^{3} b \,e^{4} x +108 a^{2} b^{2} d^{2} e^{2} m -240 a^{2} b^{2} d \,e^{3} x -24 a \,b^{3} d^{3} e m +120 a \,b^{3} d^{2} e^{2} x -24 b^{4} d^{3} e x +120 a^{4} e^{4}-240 a^{3} b d \,e^{3}+240 a^{2} b^{2} d^{2} e^{2}-120 a \,b^{3} d^{3} e +24 b^{4} d^{4}\right) \left(e x +d \right)^{m +1}}{\left(m^{5}+15 m^{4}+85 m^{3}+225 m^{2}+274 m +120\right) e^{5}}"," ",0,"(e*x+d)^(m+1)*(b^4*e^4*m^4*x^4+4*a*b^3*e^4*m^4*x^3+10*b^4*e^4*m^3*x^4+6*a^2*b^2*e^4*m^4*x^2+44*a*b^3*e^4*m^3*x^3-4*b^4*d*e^3*m^3*x^3+35*b^4*e^4*m^2*x^4+4*a^3*b*e^4*m^4*x+72*a^2*b^2*e^4*m^3*x^2-12*a*b^3*d*e^3*m^3*x^2+164*a*b^3*e^4*m^2*x^3-24*b^4*d*e^3*m^2*x^3+50*b^4*e^4*m*x^4+a^4*e^4*m^4+52*a^3*b*e^4*m^3*x-12*a^2*b^2*d*e^3*m^3*x+294*a^2*b^2*e^4*m^2*x^2-96*a*b^3*d*e^3*m^2*x^2+244*a*b^3*e^4*m*x^3+12*b^4*d^2*e^2*m^2*x^2-44*b^4*d*e^3*m*x^3+24*b^4*e^4*x^4+14*a^4*e^4*m^3-4*a^3*b*d*e^3*m^3+236*a^3*b*e^4*m^2*x-120*a^2*b^2*d*e^3*m^2*x+468*a^2*b^2*e^4*m*x^2+24*a*b^3*d^2*e^2*m^2*x-204*a*b^3*d*e^3*m*x^2+120*a*b^3*e^4*x^3+36*b^4*d^2*e^2*m*x^2-24*b^4*d*e^3*x^3+71*a^4*e^4*m^2-48*a^3*b*d*e^3*m^2+428*a^3*b*e^4*m*x+12*a^2*b^2*d^2*e^2*m^2-348*a^2*b^2*d*e^3*m*x+240*a^2*b^2*e^4*x^2+144*a*b^3*d^2*e^2*m*x-120*a*b^3*d*e^3*x^2-24*b^4*d^3*e*m*x+24*b^4*d^2*e^2*x^2+154*a^4*e^4*m-188*a^3*b*d*e^3*m+240*a^3*b*e^4*x+108*a^2*b^2*d^2*e^2*m-240*a^2*b^2*d*e^3*x-24*a*b^3*d^3*e*m+120*a*b^3*d^2*e^2*x-24*b^4*d^3*e*x+120*a^4*e^4-240*a^3*b*d*e^3+240*a^2*b^2*d^2*e^2-120*a*b^3*d^3*e+24*b^4*d^4)/e^5/(m^5+15*m^4+85*m^3+225*m^2+274*m+120)","B"
1733,1,159,78,0.075000," ","int((e*x+d)^m*(b^2*x^2+2*a*b*x+a^2),x)","\frac{\left(b^{2} e^{2} m^{2} x^{2}+2 a b \,e^{2} m^{2} x +3 b^{2} e^{2} m \,x^{2}+a^{2} e^{2} m^{2}+8 a b \,e^{2} m x -2 b^{2} d e m x +2 b^{2} x^{2} e^{2}+5 a^{2} e^{2} m -2 a b d e m +6 a b \,e^{2} x -2 b^{2} d e x +6 a^{2} e^{2}-6 a b d e +2 b^{2} d^{2}\right) \left(e x +d \right)^{m +1}}{\left(m^{3}+6 m^{2}+11 m +6\right) e^{3}}"," ",0,"(e*x+d)^(m+1)*(b^2*e^2*m^2*x^2+2*a*b*e^2*m^2*x+3*b^2*e^2*m*x^2+a^2*e^2*m^2+8*a*b*e^2*m*x-2*b^2*d*e*m*x+2*b^2*e^2*x^2+5*a^2*e^2*m-2*a*b*d*e*m+6*a*b*e^2*x-2*b^2*d*e*x+6*a^2*e^2-6*a*b*d*e+2*b^2*d^2)/e^3/(m^3+6*m^2+11*m+6)","B"
1734,0,0,53,1.436000," ","int((e*x+d)^m/(b^2*x^2+2*a*b*x+a^2),x)","\int \frac{\left(e x +d \right)^{m}}{b^{2} x^{2}+2 a b x +a^{2}}\, dx"," ",0,"int((e*x+d)^m/(b^2*x^2+2*a*b*x+a^2),x)","F"
1735,0,0,55,1.764000," ","int((e*x+d)^m/(b^2*x^2+2*a*b*x+a^2)^2,x)","\int \frac{\left(e x +d \right)^{m}}{\left(b^{2} x^{2}+2 a b x +a^{2}\right)^{2}}\, dx"," ",0,"int((e*x+d)^m/(b^2*x^2+2*a*b*x+a^2)^2,x)","F"
1736,0,0,55,1.658000," ","int((e*x+d)^m/(b^2*x^2+2*a*b*x+a^2)^3,x)","\int \frac{\left(e x +d \right)^{m}}{\left(b^{2} x^{2}+2 a b x +a^{2}\right)^{3}}\, dx"," ",0,"int((e*x+d)^m/(b^2*x^2+2*a*b*x+a^2)^3,x)","F"
1737,1,1361,271,0.066000," ","int((e*x+d)^m*(b^2*x^2+2*a*b*x+a^2)^(5/2),x)","\frac{\left(\left(b x +a \right)^{2}\right)^{\frac{5}{2}} \left(b^{5} e^{5} m^{5} x^{5}+5 a \,b^{4} e^{5} m^{5} x^{4}+15 b^{5} e^{5} m^{4} x^{5}+10 a^{2} b^{3} e^{5} m^{5} x^{3}+80 a \,b^{4} e^{5} m^{4} x^{4}-5 b^{5} d \,e^{4} m^{4} x^{4}+85 b^{5} e^{5} m^{3} x^{5}+10 a^{3} b^{2} e^{5} m^{5} x^{2}+170 a^{2} b^{3} e^{5} m^{4} x^{3}-20 a \,b^{4} d \,e^{4} m^{4} x^{3}+475 a \,b^{4} e^{5} m^{3} x^{4}-50 b^{5} d \,e^{4} m^{3} x^{4}+225 b^{5} e^{5} m^{2} x^{5}+5 a^{4} b \,e^{5} m^{5} x +180 a^{3} b^{2} e^{5} m^{4} x^{2}-30 a^{2} b^{3} d \,e^{4} m^{4} x^{2}+1070 a^{2} b^{3} e^{5} m^{3} x^{3}-240 a \,b^{4} d \,e^{4} m^{3} x^{3}+1300 a \,b^{4} e^{5} m^{2} x^{4}+20 b^{5} d^{2} e^{3} m^{3} x^{3}-175 b^{5} d \,e^{4} m^{2} x^{4}+274 b^{5} e^{5} m \,x^{5}+a^{5} e^{5} m^{5}+95 a^{4} b \,e^{5} m^{4} x -20 a^{3} b^{2} d \,e^{4} m^{4} x +1210 a^{3} b^{2} e^{5} m^{3} x^{2}-420 a^{2} b^{3} d \,e^{4} m^{3} x^{2}+3070 a^{2} b^{3} e^{5} m^{2} x^{3}+60 a \,b^{4} d^{2} e^{3} m^{3} x^{2}-940 a \,b^{4} d \,e^{4} m^{2} x^{3}+1620 a \,b^{4} e^{5} m \,x^{4}+120 b^{5} d^{2} e^{3} m^{2} x^{3}-250 b^{5} d \,e^{4} m \,x^{4}+120 b^{5} x^{5} e^{5}+20 a^{5} e^{5} m^{4}-5 a^{4} b d \,e^{4} m^{4}+685 a^{4} b \,e^{5} m^{3} x -320 a^{3} b^{2} d \,e^{4} m^{3} x +3720 a^{3} b^{2} e^{5} m^{2} x^{2}+60 a^{2} b^{3} d^{2} e^{3} m^{3} x -1950 a^{2} b^{3} d \,e^{4} m^{2} x^{2}+3960 a^{2} b^{3} e^{5} m \,x^{3}+540 a \,b^{4} d^{2} e^{3} m^{2} x^{2}-1440 a \,b^{4} d \,e^{4} m \,x^{3}+720 a \,b^{4} e^{5} x^{4}-60 b^{5} d^{3} e^{2} m^{2} x^{2}+220 b^{5} d^{2} e^{3} m \,x^{3}-120 b^{5} d \,e^{4} x^{4}+155 a^{5} e^{5} m^{3}-90 a^{4} b d \,e^{4} m^{3}+2305 a^{4} b \,e^{5} m^{2} x +20 a^{3} b^{2} d^{2} e^{3} m^{3}-1780 a^{3} b^{2} d \,e^{4} m^{2} x +5080 a^{3} b^{2} e^{5} m \,x^{2}+720 a^{2} b^{3} d^{2} e^{3} m^{2} x -3360 a^{2} b^{3} d \,e^{4} m \,x^{2}+1800 a^{2} b^{3} e^{5} x^{3}-120 a \,b^{4} d^{3} e^{2} m^{2} x +1200 a \,b^{4} d^{2} e^{3} m \,x^{2}-720 a \,b^{4} d \,e^{4} x^{3}-180 b^{5} d^{3} e^{2} m \,x^{2}+120 b^{5} d^{2} e^{3} x^{3}+580 a^{5} e^{5} m^{2}-595 a^{4} b d \,e^{4} m^{2}+3510 a^{4} b \,e^{5} m x +300 a^{3} b^{2} d^{2} e^{3} m^{2}-3880 a^{3} b^{2} d \,e^{4} m x +2400 a^{3} b^{2} e^{5} x^{2}-60 a^{2} b^{3} d^{3} e^{2} m^{2}+2460 a^{2} b^{3} d^{2} e^{3} m x -1800 a^{2} b^{3} d \,e^{4} x^{2}-840 a \,b^{4} d^{3} e^{2} m x +720 a \,b^{4} d^{2} e^{3} x^{2}+120 b^{5} d^{4} e m x -120 b^{5} d^{3} e^{2} x^{2}+1044 a^{5} e^{5} m -1710 a^{4} b d \,e^{4} m +1800 a^{4} b \,e^{5} x +1480 a^{3} b^{2} d^{2} e^{3} m -2400 a^{3} b^{2} d \,e^{4} x -660 a^{2} b^{3} d^{3} e^{2} m +1800 a^{2} b^{3} d^{2} e^{3} x +120 a \,b^{4} d^{4} e m -720 a \,b^{4} d^{3} e^{2} x +120 b^{5} d^{4} e x +720 a^{5} e^{5}-1800 a^{4} b d \,e^{4}+2400 a^{3} b^{2} d^{2} e^{3}-1800 a^{2} b^{3} d^{3} e^{2}+720 a \,b^{4} d^{4} e -120 b^{5} d^{5}\right) \left(e x +d \right)^{m +1}}{\left(b x +a \right)^{5} \left(m^{6}+21 m^{5}+175 m^{4}+735 m^{3}+1624 m^{2}+1764 m +720\right) e^{6}}"," ",0,"((b*x+a)^2)^(5/2)*(e*x+d)^(m+1)*(b^5*e^5*m^5*x^5+5*a*b^4*e^5*m^5*x^4+15*b^5*e^5*m^4*x^5+10*a^2*b^3*e^5*m^5*x^3+80*a*b^4*e^5*m^4*x^4-5*b^5*d*e^4*m^4*x^4+85*b^5*e^5*m^3*x^5+10*a^3*b^2*e^5*m^5*x^2+170*a^2*b^3*e^5*m^4*x^3-20*a*b^4*d*e^4*m^4*x^3+475*a*b^4*e^5*m^3*x^4-50*b^5*d*e^4*m^3*x^4+225*b^5*e^5*m^2*x^5+5*a^4*b*e^5*m^5*x+180*a^3*b^2*e^5*m^4*x^2-30*a^2*b^3*d*e^4*m^4*x^2+1070*a^2*b^3*e^5*m^3*x^3-240*a*b^4*d*e^4*m^3*x^3+1300*a*b^4*e^5*m^2*x^4+20*b^5*d^2*e^3*m^3*x^3-175*b^5*d*e^4*m^2*x^4+274*b^5*e^5*m*x^5+a^5*e^5*m^5+95*a^4*b*e^5*m^4*x-20*a^3*b^2*d*e^4*m^4*x+1210*a^3*b^2*e^5*m^3*x^2-420*a^2*b^3*d*e^4*m^3*x^2+3070*a^2*b^3*e^5*m^2*x^3+60*a*b^4*d^2*e^3*m^3*x^2-940*a*b^4*d*e^4*m^2*x^3+1620*a*b^4*e^5*m*x^4+120*b^5*d^2*e^3*m^2*x^3-250*b^5*d*e^4*m*x^4+120*b^5*e^5*x^5+20*a^5*e^5*m^4-5*a^4*b*d*e^4*m^4+685*a^4*b*e^5*m^3*x-320*a^3*b^2*d*e^4*m^3*x+3720*a^3*b^2*e^5*m^2*x^2+60*a^2*b^3*d^2*e^3*m^3*x-1950*a^2*b^3*d*e^4*m^2*x^2+3960*a^2*b^3*e^5*m*x^3+540*a*b^4*d^2*e^3*m^2*x^2-1440*a*b^4*d*e^4*m*x^3+720*a*b^4*e^5*x^4-60*b^5*d^3*e^2*m^2*x^2+220*b^5*d^2*e^3*m*x^3-120*b^5*d*e^4*x^4+155*a^5*e^5*m^3-90*a^4*b*d*e^4*m^3+2305*a^4*b*e^5*m^2*x+20*a^3*b^2*d^2*e^3*m^3-1780*a^3*b^2*d*e^4*m^2*x+5080*a^3*b^2*e^5*m*x^2+720*a^2*b^3*d^2*e^3*m^2*x-3360*a^2*b^3*d*e^4*m*x^2+1800*a^2*b^3*e^5*x^3-120*a*b^4*d^3*e^2*m^2*x+1200*a*b^4*d^2*e^3*m*x^2-720*a*b^4*d*e^4*x^3-180*b^5*d^3*e^2*m*x^2+120*b^5*d^2*e^3*x^3+580*a^5*e^5*m^2-595*a^4*b*d*e^4*m^2+3510*a^4*b*e^5*m*x+300*a^3*b^2*d^2*e^3*m^2-3880*a^3*b^2*d*e^4*m*x+2400*a^3*b^2*e^5*x^2-60*a^2*b^3*d^3*e^2*m^2+2460*a^2*b^3*d^2*e^3*m*x-1800*a^2*b^3*d*e^4*x^2-840*a*b^4*d^3*e^2*m*x+720*a*b^4*d^2*e^3*x^2+120*b^5*d^4*e*m*x-120*b^5*d^3*e^2*x^2+1044*a^5*e^5*m-1710*a^4*b*d*e^4*m+1800*a^4*b*e^5*x+1480*a^3*b^2*d^2*e^3*m-2400*a^3*b^2*d*e^4*x-660*a^2*b^3*d^3*e^2*m+1800*a^2*b^3*d^2*e^3*x+120*a*b^4*d^4*e*m-720*a*b^4*d^3*e^2*x+120*b^5*d^4*e*x+720*a^5*e^5-1800*a^4*b*d*e^4+2400*a^3*b^2*d^2*e^3-1800*a^2*b^3*d^3*e^2+720*a*b^4*d^4*e-120*b^5*d^5)/(b*x+a)^5/e^6/(m^6+21*m^5+175*m^4+735*m^3+1624*m^2+1764*m+720)","B"
1738,1,402,175,0.056000," ","int((e*x+d)^m*(b^2*x^2+2*a*b*x+a^2)^(3/2),x)","\frac{\left(\left(b x +a \right)^{2}\right)^{\frac{3}{2}} \left(b^{3} e^{3} m^{3} x^{3}+3 a \,b^{2} e^{3} m^{3} x^{2}+6 b^{3} e^{3} m^{2} x^{3}+3 a^{2} b \,e^{3} m^{3} x +21 a \,b^{2} e^{3} m^{2} x^{2}-3 b^{3} d \,e^{2} m^{2} x^{2}+11 b^{3} e^{3} m \,x^{3}+a^{3} e^{3} m^{3}+24 a^{2} b \,e^{3} m^{2} x -6 a \,b^{2} d \,e^{2} m^{2} x +42 a \,b^{2} e^{3} m \,x^{2}-9 b^{3} d \,e^{2} m \,x^{2}+6 b^{3} e^{3} x^{3}+9 a^{3} e^{3} m^{2}-3 a^{2} b d \,e^{2} m^{2}+57 a^{2} b \,e^{3} m x -30 a \,b^{2} d \,e^{2} m x +24 a \,b^{2} e^{3} x^{2}+6 b^{3} d^{2} e m x -6 b^{3} d \,e^{2} x^{2}+26 a^{3} e^{3} m -21 a^{2} b d \,e^{2} m +36 a^{2} b \,e^{3} x +6 a \,b^{2} d^{2} e m -24 a \,b^{2} d \,e^{2} x +6 b^{3} d^{2} e x +24 a^{3} e^{3}-36 a^{2} b d \,e^{2}+24 a \,b^{2} d^{2} e -6 b^{3} d^{3}\right) \left(e x +d \right)^{m +1}}{\left(b x +a \right)^{3} \left(m^{4}+10 m^{3}+35 m^{2}+50 m +24\right) e^{4}}"," ",0,"((b*x+a)^2)^(3/2)*(e*x+d)^(m+1)*(b^3*e^3*m^3*x^3+3*a*b^2*e^3*m^3*x^2+6*b^3*e^3*m^2*x^3+3*a^2*b*e^3*m^3*x+21*a*b^2*e^3*m^2*x^2-3*b^3*d*e^2*m^2*x^2+11*b^3*e^3*m*x^3+a^3*e^3*m^3+24*a^2*b*e^3*m^2*x-6*a*b^2*d*e^2*m^2*x+42*a*b^2*e^3*m*x^2-9*b^3*d*e^2*m*x^2+6*b^3*e^3*x^3+9*a^3*e^3*m^2-3*a^2*b*d*e^2*m^2+57*a^2*b*e^3*m*x-30*a*b^2*d*e^2*m*x+24*a*b^2*e^3*x^2+6*b^3*d^2*e*m*x-6*b^3*d*e^2*x^2+26*a^3*e^3*m-21*a^2*b*d*e^2*m+36*a^2*b*e^3*x+6*a*b^2*d^2*e*m-24*a*b^2*d*e^2*x+6*b^3*d^2*e*x+24*a^3*e^3-36*a^2*b*d*e^2+24*a*b^2*d^2*e-6*b^3*d^3)/(b*x+a)^3/e^4/(m^4+10*m^3+35*m^2+50*m+24)","B"
1739,1,62,79,0.046000," ","int((e*x+d)^m*(b^2*x^2+2*a*b*x+a^2)^(1/2),x)","\frac{\sqrt{\left(b x +a \right)^{2}}\, \left(b e m x +a e m +b e x +2 a e -b d \right) \left(e x +d \right)^{m +1}}{\left(b x +a \right) \left(m^{2}+3 m +2\right) e^{2}}"," ",0,"((b*x+a)^2)^(1/2)*(e*x+d)^(m+1)*(b*e*m*x+a*e*m+b*e*x+2*a*e-b*d)/(b*x+a)/e^2/(m^2+3*m+2)","A"
1740,0,0,67,1.212000," ","int((e*x+d)^m/(b^2*x^2+2*a*b*x+a^2)^(1/2),x)","\int \frac{\left(e x +d \right)^{m}}{\sqrt{b^{2} x^{2}+2 a b x +a^{2}}}\, dx"," ",0,"int((e*x+d)^m/(b^2*x^2+2*a*b*x+a^2)^(1/2),x)","F"
1741,0,0,70,1.142000," ","int((e*x+d)^m/(b^2*x^2+2*a*b*x+a^2)^(3/2),x)","\int \frac{\left(e x +d \right)^{m}}{\left(b^{2} x^{2}+2 a b x +a^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"int((e*x+d)^m/(b^2*x^2+2*a*b*x+a^2)^(3/2),x)","F"
1742,0,0,70,1.206000," ","int((e*x+d)^m/(b^2*x^2+2*a*b*x+a^2)^(5/2),x)","\int \frac{\left(e x +d \right)^{m}}{\left(b^{2} x^{2}+2 a b x +a^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"int((e*x+d)^m/(b^2*x^2+2*a*b*x+a^2)^(5/2),x)","F"
1743,0,0,89,1.339000," ","int((e*x+d)^m*(b^2*x^2+2*a*b*x+a^2)^p,x)","\int \left(e x +d \right)^{m} \left(b^{2} x^{2}+2 a b x +a^{2}\right)^{p}\, dx"," ",0,"int((e*x+d)^m*(b^2*x^2+2*a*b*x+a^2)^p,x)","F"
1744,1,405,177,0.065000," ","int((e*x+d)^3*(b^2*x^2+2*a*b*x+a^2)^p,x)","-\frac{\left(-4 b^{3} e^{3} p^{3} x^{3}-12 b^{3} d \,e^{2} p^{3} x^{2}-12 b^{3} e^{3} p^{2} x^{3}+6 a \,b^{2} e^{3} p^{2} x^{2}-12 b^{3} d^{2} e \,p^{3} x -42 b^{3} d \,e^{2} p^{2} x^{2}-11 b^{3} e^{3} p \,x^{3}+12 a \,b^{2} d \,e^{2} p^{2} x +9 a \,b^{2} e^{3} p \,x^{2}-4 b^{3} d^{3} p^{3}-48 b^{3} d^{2} e \,p^{2} x -42 b^{3} d \,e^{2} p \,x^{2}-3 b^{3} e^{3} x^{3}-6 a^{2} b \,e^{3} p x +6 a \,b^{2} d^{2} e \,p^{2}+30 a \,b^{2} d \,e^{2} p x +3 a \,b^{2} e^{3} x^{2}-18 b^{3} d^{3} p^{2}-57 b^{3} d^{2} e p x -12 b^{3} d \,e^{2} x^{2}-6 a^{2} b d \,e^{2} p -3 a^{2} b \,e^{3} x +21 a \,b^{2} d^{2} e p +12 a \,b^{2} d \,e^{2} x -26 b^{3} d^{3} p -18 b^{3} d^{2} e x +3 a^{3} e^{3}-12 a^{2} b d \,e^{2}+18 a \,b^{2} d^{2} e -12 b^{3} d^{3}\right) \left(b x +a \right) \left(b^{2} x^{2}+2 a b x +a^{2}\right)^{p}}{2 \left(4 p^{4}+20 p^{3}+35 p^{2}+25 p +6\right) b^{4}}"," ",0,"-1/2*(b^2*x^2+2*a*b*x+a^2)^p*(-4*b^3*e^3*p^3*x^3-12*b^3*d*e^2*p^3*x^2-12*b^3*e^3*p^2*x^3+6*a*b^2*e^3*p^2*x^2-12*b^3*d^2*e*p^3*x-42*b^3*d*e^2*p^2*x^2-11*b^3*e^3*p*x^3+12*a*b^2*d*e^2*p^2*x+9*a*b^2*e^3*p*x^2-4*b^3*d^3*p^3-48*b^3*d^2*e*p^2*x-42*b^3*d*e^2*p*x^2-3*b^3*e^3*x^3-6*a^2*b*e^3*p*x+6*a*b^2*d^2*e*p^2+30*a*b^2*d*e^2*p*x+3*a*b^2*e^3*x^2-18*b^3*d^3*p^2-57*b^3*d^2*e*p*x-12*b^3*d*e^2*x^2-6*a^2*b*d*e^2*p-3*a^2*b*e^3*x+21*a*b^2*d^2*e*p+12*a*b^2*d*e^2*x-26*b^3*d^3*p-18*b^3*d^2*e*x+3*a^3*e^3-12*a^2*b*d*e^2+18*a*b^2*d^2*e-12*b^3*d^3)*(b*x+a)/b^4/(4*p^4+20*p^3+35*p^2+25*p+6)","B"
1745,1,175,127,0.056000," ","int((e*x+d)^2*(b^2*x^2+2*a*b*x+a^2)^p,x)","\frac{\left(b x +a \right) \left(2 b^{2} e^{2} p^{2} x^{2}+4 b^{2} d e \,p^{2} x +3 b^{2} e^{2} p \,x^{2}-2 a b \,e^{2} p x +2 b^{2} d^{2} p^{2}+8 b^{2} d e p x +b^{2} x^{2} e^{2}-2 a b d e p -a b \,e^{2} x +5 b^{2} d^{2} p +3 b^{2} d e x +a^{2} e^{2}-3 a b d e +3 b^{2} d^{2}\right) \left(b^{2} x^{2}+2 a b x +a^{2}\right)^{p}}{\left(4 p^{3}+12 p^{2}+11 p +3\right) b^{3}}"," ",0,"(b*x+a)*(2*b^2*e^2*p^2*x^2+4*b^2*d*e*p^2*x+3*b^2*e^2*p*x^2-2*a*b*e^2*p*x+2*b^2*d^2*p^2+8*b^2*d*e*p*x+b^2*e^2*x^2-2*a*b*d*e*p-a*b*e^2*x+5*b^2*d^2*p+3*b^2*d*e*x+a^2*e^2-3*a*b*d*e+3*b^2*d^2)*(b^2*x^2+2*a*b*x+a^2)^p/b^3/(4*p^3+12*p^2+11*p+3)","A"
1746,1,65,74,0.049000," ","int((e*x+d)*(b^2*x^2+2*a*b*x+a^2)^p,x)","-\frac{\left(-2 b e p x -2 b d p -b e x +a e -2 b d \right) \left(b x +a \right) \left(b^{2} x^{2}+2 a b x +a^{2}\right)^{p}}{2 \left(2 p^{2}+3 p +1\right) b^{2}}"," ",0,"-1/2*(b^2*x^2+2*a*b*x+a^2)^p*(-2*b*e*p*x-2*b*d*p-b*e*x+a*e-2*b*d)*(b*x+a)/b^2/(2*p^2+3*p+1)","A"
1747,1,35,34,0.046000," ","int((b^2*x^2+2*a*b*x+a^2)^p,x)","\frac{\left(b x +a \right) \left(b^{2} x^{2}+2 a b x +a^{2}\right)^{p}}{\left(2 p +1\right) b}"," ",0,"(b*x+a)*(b^2*x^2+2*a*b*x+a^2)^p/b/(2*p+1)","A"
1748,0,0,73,1.467000," ","int((b^2*x^2+2*a*b*x+a^2)^p/(e*x+d),x)","\int \frac{\left(b^{2} x^{2}+2 a b x +a^{2}\right)^{p}}{e x +d}\, dx"," ",0,"int((b^2*x^2+2*a*b*x+a^2)^p/(e*x+d),x)","F"
1749,0,0,74,1.363000," ","int((b^2*x^2+2*a*b*x+a^2)^p/(e*x+d)^2,x)","\int \frac{\left(b^{2} x^{2}+2 a b x +a^{2}\right)^{p}}{\left(e x +d \right)^{2}}\, dx"," ",0,"int((b^2*x^2+2*a*b*x+a^2)^p/(e*x+d)^2,x)","F"
1750,0,0,76,1.306000," ","int((b^2*x^2+2*a*b*x+a^2)^p/(e*x+d)^3,x)","\int \frac{\left(b^{2} x^{2}+2 a b x +a^{2}\right)^{p}}{\left(e x +d \right)^{3}}\, dx"," ",0,"int((b^2*x^2+2*a*b*x+a^2)^p/(e*x+d)^3,x)","F"
1751,0,0,79,1.405000," ","int((e*x+d)^(3/2)*(b^2*x^2+2*a*b*x+a^2)^p,x)","\int \left(e x +d \right)^{\frac{3}{2}} \left(b^{2} x^{2}+2 a b x +a^{2}\right)^{p}\, dx"," ",0,"int((e*x+d)^(3/2)*(b^2*x^2+2*a*b*x+a^2)^p,x)","F"
1752,0,0,79,1.951000," ","int((e*x+d)^(1/2)*(b^2*x^2+2*a*b*x+a^2)^p,x)","\int \sqrt{e x +d}\, \left(b^{2} x^{2}+2 a b x +a^{2}\right)^{p}\, dx"," ",0,"int((e*x+d)^(1/2)*(b^2*x^2+2*a*b*x+a^2)^p,x)","F"
1753,0,0,79,1.641000," ","int((b^2*x^2+2*a*b*x+a^2)^p/(e*x+d)^(1/2),x)","\int \frac{\left(b^{2} x^{2}+2 a b x +a^{2}\right)^{p}}{\sqrt{e x +d}}\, dx"," ",0,"int((b^2*x^2+2*a*b*x+a^2)^p/(e*x+d)^(1/2),x)","F"
1754,0,0,79,1.804000," ","int((b^2*x^2+2*a*b*x+a^2)^p/(e*x+d)^(3/2),x)","\int \frac{\left(b^{2} x^{2}+2 a b x +a^{2}\right)^{p}}{\left(e x +d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((b^2*x^2+2*a*b*x+a^2)^p/(e*x+d)^(3/2),x)","F"
1755,0,0,79,1.628000," ","int((b^2*x^2+2*a*b*x+a^2)^p/(e*x+d)^(5/2),x)","\int \frac{\left(b^{2} x^{2}+2 a b x +a^{2}\right)^{p}}{\left(e x +d \right)^{\frac{5}{2}}}\, dx"," ",0,"int((b^2*x^2+2*a*b*x+a^2)^p/(e*x+d)^(5/2),x)","F"
1756,0,0,101,1.346000," ","int((e*x+d)^m*(b^2*x^2+2*a*b*x+a^2)^(5+p),x)","\int \left(e x +d \right)^{m} \left(b^{2} x^{2}+2 a b x +a^{2}\right)^{p +5}\, dx"," ",0,"int((e*x+d)^m*(b^2*x^2+2*a*b*x+a^2)^(5+p),x)","F"
1757,1,139,113,0.051000," ","int((e*x+d)^(-2*p-3)*(b^2*x^2+2*a*b*x+a^2)^p,x)","-\frac{\left(b x +a \right) \left(2 a e p -2 b d p -b e x +a e -2 b d \right) \left(e x +d \right)^{-2 p -2} \left(b^{2} x^{2}+2 a b x +a^{2}\right)^{p}}{2 \left(2 a^{2} e^{2} p^{2}-4 a b d e \,p^{2}+2 b^{2} d^{2} p^{2}+3 a^{2} e^{2} p -6 a b d e p +3 b^{2} d^{2} p +a^{2} e^{2}-2 a b d e +b^{2} d^{2}\right)}"," ",0,"-1/2*(b*x+a)*(e*x+d)^(-2*p-2)*(2*a*e*p-2*b*d*p-b*e*x+a*e-2*b*d)*(b^2*x^2+2*a*b*x+a^2)^p/(2*a^2*e^2*p^2-4*a*b*d*e*p^2+2*b^2*d^2*p^2+3*a^2*e^2*p-6*a*b*d*e*p+3*b^2*d^2*p+a^2*e^2-2*a*b*d*e+b^2*d^2)","A"
1758,1,52,56,0.052000," ","int((e*x+d)*(4*x^2+12*x+9)^p,x)","\frac{\left(4 e p x +4 d p +2 e x +4 d -3 e \right) \left(2 x +3\right) \left(4 x^{2}+12 x +9\right)^{p}}{16 p^{2}+24 p +8}"," ",0,"1/8*(4*x^2+12*x+9)^p*(4*e*p*x+4*d*p+2*e*x+4*d-3*e)*(2*x+3)/(2*p^2+3*p+1)","A"
1759,1,133,34,0.056000," ","int((b*x+a)^3*(a*c+(a*d+b*c)*x+b*d*x^2),x)","\frac{b^{4} d \,x^{6}}{6}+a^{4} c x +\frac{\left(3 a \,b^{3} d +\left(a d +b c \right) b^{3}\right) x^{5}}{5}+\frac{\left(3 a^{2} b^{2} d +a \,b^{3} c +3 \left(a d +b c \right) a \,b^{2}\right) x^{4}}{4}+\frac{\left(a^{3} b d +3 a^{2} b^{2} c +3 \left(a d +b c \right) a^{2} b \right) x^{3}}{3}+\frac{\left(3 a^{3} b c +\left(a d +b c \right) a^{3}\right) x^{2}}{2}"," ",0,"1/6*b^4*d*x^6+1/5*(3*a*b^3*d+b^3*(a*d+b*c))*x^5+1/4*(3*a^2*b^2*d+3*a*b^2*(a*d+b*c)+a*b^3*c)*x^4+1/3*(a^3*b*d+3*a^2*b*(a*d+b*c)+3*a^2*b^2*c)*x^3+1/2*(a^3*(a*d+b*c)+3*a^3*b*c)*x^2+a^4*c*x","B"
1760,1,94,34,0.046000," ","int((b*x+a)^2*(a*c+(a*d+b*c)*x+b*d*x^2),x)","\frac{b^{3} d \,x^{5}}{5}+a^{3} c x +\frac{\left(2 a \,b^{2} d +\left(a d +b c \right) b^{2}\right) x^{4}}{4}+\frac{\left(a^{2} b d +a \,b^{2} c +2 \left(a d +b c \right) a b \right) x^{3}}{3}+\frac{\left(2 a^{2} b c +\left(a d +b c \right) a^{2}\right) x^{2}}{2}"," ",0,"1/5*b^3*d*x^5+1/4*(2*a*b^2*d+b^2*(a*d+b*c))*x^4+1/3*(a^2*b*d+2*a*b*(a*d+b*c)+a*b^2*c)*x^3+1/2*(a^2*(a*d+b*c)+2*a^2*b*c)*x^2+a^3*c*x","B"
1761,1,55,34,0.044000," ","int((b*x+a)*(a*c+(a*d+b*c)*x+b*d*x^2),x)","\frac{b^{2} d \,x^{4}}{4}+a^{2} c x +\frac{\left(a b d +\left(a d +b c \right) b \right) x^{3}}{3}+\frac{\left(a b c +\left(a d +b c \right) a \right) x^{2}}{2}"," ",0,"1/4*b^2*d*x^4+1/3*(b*d*a+b*(a*d+b*c))*x^3+1/2*(a*(a*d+b*c)+a*b*c)*x^2+a^2*c*x","A"
1762,1,25,24,0.046000," ","int(a*c+(a*d+b*c)*x+b*d*x^2,x)","\frac{b d \,x^{3}}{3}+a c x +\frac{\left(a d +b c \right) x^{2}}{2}"," ",0,"a*c*x+1/2*(a*d+b*c)*x^2+1/3*b*d*x^3","A"
1763,1,11,10,0.044000," ","int((a*c+(a*d+b*c)*x+b*d*x^2)/(b*x+a),x)","\frac{1}{2} d \,x^{2}+c x"," ",0,"1/2*d*x^2+c*x","A"
1764,1,32,25,0.063000," ","int((a*c+(a*d+b*c)*x+b*d*x^2)/(b*x+a)^2,x)","-\frac{a d \ln \left(b x +a \right)}{b^{2}}+\frac{c \ln \left(b x +a \right)}{b}+\frac{d x}{b}"," ",0,"1/b*d*x-1/b^2*ln(b*x+a)*a*d+1/b*ln(b*x+a)*c","A"
1765,1,39,31,0.055000," ","int((a*c+(a*d+b*c)*x+b*d*x^2)/(b*x+a)^3,x)","\frac{a d}{\left(b x +a \right) b^{2}}-\frac{c}{\left(b x +a \right) b}+\frac{d \ln \left(b x +a \right)}{b^{2}}"," ",0,"d*ln(b*x+a)/b^2+1/b^2/(b*x+a)*a*d-1/b/(b*x+a)*c","A"
1766,1,35,26,0.046000," ","int((a*c+(a*d+b*c)*x+b*d*x^2)/(b*x+a)^4,x)","-\frac{d}{\left(b x +a \right) b^{2}}-\frac{-a d +b c}{2 \left(b x +a \right)^{2} b^{2}}"," ",0,"-d/b^2/(b*x+a)-1/2*(-a*d+b*c)/b^2/(b*x+a)^2","A"
1767,1,35,34,0.051000," ","int((a*c+(a*d+b*c)*x+b*d*x^2)/(b*x+a)^5,x)","-\frac{d}{2 \left(b x +a \right)^{2} b^{2}}-\frac{-a d +b c}{3 \left(b x +a \right)^{3} b^{2}}"," ",0,"-1/3*(-a*d+b*c)/b^2/(b*x+a)^3-1/2*d/b^2/(b*x+a)^2","A"
1768,1,35,34,0.049000," ","int((a*c+(a*d+b*c)*x+b*d*x^2)/(b*x+a)^6,x)","-\frac{d}{3 \left(b x +a \right)^{3} b^{2}}-\frac{-a d +b c}{4 \left(b x +a \right)^{4} b^{2}}"," ",0,"-1/4*(-a*d+b*c)/b^2/(b*x+a)^4-1/3*d/b^2/(b*x+a)^3","A"
1769,1,315,59,0.048000," ","int((b*x+a)^3*(a*c+(a*d+b*c)*x+b*d*x^2)^2,x)","\frac{b^{5} d^{2} x^{8}}{8}+a^{5} c^{2} x +\frac{\left(3 a \,b^{4} d^{2}+2 \left(a d +b c \right) b^{4} d \right) x^{7}}{7}+\frac{\left(3 a^{2} b^{3} d^{2}+6 \left(a d +b c \right) a \,b^{3} d +\left(2 a b c d +\left(a d +b c \right)^{2}\right) b^{3}\right) x^{6}}{6}+\frac{\left(a^{3} b^{2} d^{2}+6 \left(a d +b c \right) a^{2} b^{2} d +2 \left(a d +b c \right) a \,b^{3} c +3 \left(2 a b c d +\left(a d +b c \right)^{2}\right) a \,b^{2}\right) x^{5}}{5}+\frac{\left(a^{2} b^{3} c^{2}+2 \left(a d +b c \right) a^{3} b d +6 \left(a d +b c \right) a^{2} b^{2} c +3 \left(2 a b c d +\left(a d +b c \right)^{2}\right) a^{2} b \right) x^{4}}{4}+\frac{\left(3 a^{3} b^{2} c^{2}+6 \left(a d +b c \right) a^{3} b c +\left(2 a b c d +\left(a d +b c \right)^{2}\right) a^{3}\right) x^{3}}{3}+\frac{\left(3 a^{4} b \,c^{2}+2 \left(a d +b c \right) a^{4} c \right) x^{2}}{2}"," ",0,"1/8*b^5*d^2*x^8+1/7*(3*a*b^4*d^2+2*b^4*(a*d+b*c)*d)*x^7+1/6*(3*a^2*b^3*d^2+6*a*b^3*(a*d+b*c)*d+b^3*(2*a*b*c*d+(a*d+b*c)^2))*x^6+1/5*(a^3*b^2*d^2+6*a^2*b^2*(a*d+b*c)*d+3*a*b^2*(2*a*b*c*d+(a*d+b*c)^2)+2*b^3*a*c*(a*d+b*c))*x^5+1/4*(2*a^3*(a*d+b*c)*b*d+3*a^2*b*(2*a*b*c*d+(a*d+b*c)^2)+6*a^2*b^2*c*(a*d+b*c)+a^2*b^3*c^2)*x^4+1/3*(a^3*(2*a*b*c*d+(a*d+b*c)^2)+6*a^3*b*c*(a*d+b*c)+3*a^3*b^2*c^2)*x^3+1/2*(2*a^4*c*(a*d+b*c)+3*a^4*b*c^2)*x^2+a^5*c^2*x","B"
1770,1,231,59,0.043000," ","int((b*x+a)^2*(a*c+(a*d+b*c)*x+b*d*x^2)^2,x)","\frac{b^{4} d^{2} x^{7}}{7}+a^{4} c^{2} x +\frac{\left(2 a \,b^{3} d^{2}+2 \left(a d +b c \right) b^{3} d \right) x^{6}}{6}+\frac{\left(a^{2} b^{2} d^{2}+4 \left(a d +b c \right) a \,b^{2} d +\left(2 a b c d +\left(a d +b c \right)^{2}\right) b^{2}\right) x^{5}}{5}+\frac{\left(2 \left(a d +b c \right) a^{2} b d +2 \left(a d +b c \right) a \,b^{2} c +2 \left(2 a b c d +\left(a d +b c \right)^{2}\right) a b \right) x^{4}}{4}+\frac{\left(a^{2} b^{2} c^{2}+4 \left(a d +b c \right) a^{2} b c +\left(2 a b c d +\left(a d +b c \right)^{2}\right) a^{2}\right) x^{3}}{3}+\frac{\left(2 a^{3} b \,c^{2}+2 \left(a d +b c \right) a^{3} c \right) x^{2}}{2}"," ",0,"1/7*b^4*d^2*x^7+1/6*(2*a*b^3*d^2+2*b^3*(a*d+b*c)*d)*x^6+1/5*(a^2*b^2*d^2+4*a*b^2*(a*d+b*c)*d+b^2*(2*a*b*c*d+(a*d+b*c)^2))*x^5+1/4*(2*a^2*(a*d+b*c)*b*d+2*a*b*(2*a*b*c*d+(a*d+b*c)^2)+2*b^2*a*c*(a*d+b*c))*x^4+1/3*(a^2*(2*a*b*c*d+(a*d+b*c)^2)+4*a^2*b*c*(a*d+b*c)+a^2*b^2*c^2)*x^3+1/2*(2*a^3*c*(a*d+b*c)+2*a^3*b*c^2)*x^2+a^4*c^2*x","B"
1771,1,147,59,0.045000," ","int((b*x+a)*(a*c+(a*d+b*c)*x+b*d*x^2)^2,x)","\frac{b^{3} d^{2} x^{6}}{6}+a^{3} c^{2} x +\frac{\left(a \,b^{2} d^{2}+2 \left(a d +b c \right) b^{2} d \right) x^{5}}{5}+\frac{\left(2 \left(a d +b c \right) a b d +\left(2 a b c d +\left(a d +b c \right)^{2}\right) b \right) x^{4}}{4}+\frac{\left(2 \left(a d +b c \right) a b c +\left(2 a b c d +\left(a d +b c \right)^{2}\right) a \right) x^{3}}{3}+\frac{\left(a^{2} b \,c^{2}+2 \left(a d +b c \right) a^{2} c \right) x^{2}}{2}"," ",0,"1/6*b^3*d^2*x^6+1/5*(a*b^2*d^2+2*b^2*(a*d+b*c)*d)*x^5+1/4*(2*a*(a*d+b*c)*b*d+b*(2*a*b*c*d+(a*d+b*c)^2))*x^4+1/3*(a*(2*a*b*c*d+(a*d+b*c)^2)+2*b*a*c*(a*d+b*c))*x^3+1/2*(2*a^2*c*(a*d+b*c)+a^2*b*c^2)*x^2+a^3*c^2*x","B"
1772,1,69,59,0.046000," ","int((a*c+(a*d+b*c)*x+b*d*x^2)^2,x)","\frac{b^{2} d^{2} x^{5}}{5}+\frac{\left(a d +b c \right) b d \,x^{4}}{2}+a^{2} c^{2} x +\left(a d +b c \right) a c \,x^{2}+\frac{\left(2 a b c d +\left(a d +b c \right)^{2}\right) x^{3}}{3}"," ",0,"1/5*b^2*d^2*x^5+1/2*(a*d+b*c)*b*d*x^4+1/3*(2*a*b*c*d+(a*d+b*c)^2)*x^3+a*c*(a*d+b*c)*x^2+a^2*c^2*x","A"
1773,1,55,34,0.039000," ","int((a*c+(a*d+b*c)*x+b*d*x^2)^2/(b*x+a),x)","\frac{b \,d^{2} x^{4}}{4}+a \,c^{2} x +\frac{\left(b c d +\left(a d +b c \right) d \right) x^{3}}{3}+\frac{\left(a c d +\left(a d +b c \right) c \right) x^{2}}{2}"," ",0,"1/4*b*d^2*x^4+1/3*(b*c*d+d*(a*d+b*c))*x^3+1/2*(c*(a*d+b*c)+a*c*d)*x^2+a*c^2*x","A"
1774,1,13,12,0.045000," ","int((a*c+(a*d+b*c)*x+b*d*x^2)^2/(b*x+a)^2,x)","\frac{\left(d x +c \right)^{3}}{3 d}"," ",0,"1/3*(d*x+c)^3/d","A"
1775,1,74,47,0.047000," ","int((a*c+(a*d+b*c)*x+b*d*x^2)^2/(b*x+a)^3,x)","\frac{d^{2} x^{2}}{2 b}+\frac{a^{2} d^{2} \ln \left(b x +a \right)}{b^{3}}-\frac{2 a c d \ln \left(b x +a \right)}{b^{2}}-\frac{a \,d^{2} x}{b^{2}}+\frac{c^{2} \ln \left(b x +a \right)}{b}+\frac{2 c d x}{b}"," ",0,"1/2*d^2/b*x^2-d^2/b^2*a*x+2*d/b*c*x+1/b^3*ln(b*x+a)*a^2*d^2-2/b^2*ln(b*x+a)*a*c*d+1/b*ln(b*x+a)*c^2","A"
1776,1,86,51,0.065000," ","int((a*c+(a*d+b*c)*x+b*d*x^2)^2/(b*x+a)^4,x)","-\frac{a^{2} d^{2}}{\left(b x +a \right) b^{3}}+\frac{2 a c d}{\left(b x +a \right) b^{2}}-\frac{2 a \,d^{2} \ln \left(b x +a \right)}{b^{3}}-\frac{c^{2}}{\left(b x +a \right) b}+\frac{2 c d \ln \left(b x +a \right)}{b^{2}}+\frac{d^{2} x}{b^{2}}"," ",0,"1/b^2*d^2*x-2*d^2/b^3*ln(b*x+a)*a+2*d/b^2*ln(b*x+a)*c-1/b^3/(b*x+a)*a^2*d^2+2/b^2/(b*x+a)*a*c*d-1/b/(b*x+a)*c^2","A"
1777,1,92,57,0.045000," ","int((a*c+(a*d+b*c)*x+b*d*x^2)^2/(b*x+a)^5,x)","-\frac{a^{2} d^{2}}{2 \left(b x +a \right)^{2} b^{3}}+\frac{a c d}{\left(b x +a \right)^{2} b^{2}}-\frac{c^{2}}{2 \left(b x +a \right)^{2} b}+\frac{2 a \,d^{2}}{\left(b x +a \right) b^{3}}-\frac{2 c d}{\left(b x +a \right) b^{2}}+\frac{d^{2} \ln \left(b x +a \right)}{b^{3}}"," ",0,"d^2*ln(b*x+a)/b^3+2*d^2/b^3/(b*x+a)*a-2*d/b^2/(b*x+a)*c-1/2/b^3/(b*x+a)^2*a^2*d^2+1/b^2/(b*x+a)^2*a*c*d-1/2/b/(b*x+a)^2*c^2","A"
1778,1,70,26,0.056000," ","int((a*c+(a*d+b*c)*x+b*d*x^2)^2/(b*x+a)^6,x)","-\frac{d^{2}}{\left(b x +a \right) b^{3}}+\frac{\left(a d -b c \right) d}{\left(b x +a \right)^{2} b^{3}}-\frac{a^{2} d^{2}-2 a b c d +b^{2} c^{2}}{3 \left(b x +a \right)^{3} b^{3}}"," ",0,"-1/3*(a^2*d^2-2*a*b*c*d+b^2*c^2)/b^3/(b*x+a)^3-1/b^3*d^2/(b*x+a)+d*(a*d-b*c)/b^3/(b*x+a)^2","B"
1779,1,71,59,0.049000," ","int((a*c+(a*d+b*c)*x+b*d*x^2)^2/(b*x+a)^7,x)","-\frac{d^{2}}{2 \left(b x +a \right)^{2} b^{3}}+\frac{2 \left(a d -b c \right) d}{3 \left(b x +a \right)^{3} b^{3}}-\frac{a^{2} d^{2}-2 a b c d +b^{2} c^{2}}{4 \left(b x +a \right)^{4} b^{3}}"," ",0,"-1/4*(a^2*d^2-2*a*b*c*d+b^2*c^2)/b^3/(b*x+a)^4+2/3*d*(a*d-b*c)/b^3/(b*x+a)^3-1/2*d^2/b^3/(b*x+a)^2","A"
1780,1,71,59,0.048000," ","int((a*c+(a*d+b*c)*x+b*d*x^2)^2/(b*x+a)^8,x)","-\frac{d^{2}}{3 \left(b x +a \right)^{3} b^{3}}+\frac{\left(a d -b c \right) d}{2 \left(b x +a \right)^{4} b^{3}}-\frac{a^{2} d^{2}-2 a b c d +b^{2} c^{2}}{5 \left(b x +a \right)^{5} b^{3}}"," ",0,"1/2*d*(a*d-b*c)/b^3/(b*x+a)^4-1/5*(a^2*d^2-2*a*b*c*d+b^2*c^2)/b^3/(b*x+a)^5-1/3*d^2/b^3/(b*x+a)^3","A"
1781,1,71,59,0.064000," ","int((a*c+(a*d+b*c)*x+b*d*x^2)^2/(b*x+a)^9,x)","-\frac{d^{2}}{4 \left(b x +a \right)^{4} b^{3}}+\frac{2 \left(a d -b c \right) d}{5 \left(b x +a \right)^{5} b^{3}}-\frac{a^{2} d^{2}-2 a b c d +b^{2} c^{2}}{6 \left(b x +a \right)^{6} b^{3}}"," ",0,"-1/4*d^2/b^3/(b*x+a)^4+2/5*d*(a*d-b*c)/b^3/(b*x+a)^5-1/6*(a^2*d^2-2*a*b*c*d+b^2*c^2)/b^3/(b*x+a)^6","A"
1782,1,71,59,0.049000," ","int((a*c+(a*d+b*c)*x+b*d*x^2)^2/(b*x+a)^10,x)","-\frac{d^{2}}{5 \left(b x +a \right)^{5} b^{3}}+\frac{\left(a d -b c \right) d}{3 \left(b x +a \right)^{6} b^{3}}-\frac{a^{2} d^{2}-2 a b c d +b^{2} c^{2}}{7 \left(b x +a \right)^{7} b^{3}}"," ",0,"-1/5*d^2/b^3/(b*x+a)^5+1/3*d*(a*d-b*c)/b^3/(b*x+a)^6-1/7*(a^2*d^2-2*a*b*c*d+b^2*c^2)/b^3/(b*x+a)^7","A"
1783,1,811,84,0.037000," ","int((b*x+a)^3*(a*c+(a*d+b*c)*x+b*d*x^2)^3,x)","\frac{b^{6} d^{3} x^{10}}{10}+a^{6} c^{3} x +\frac{\left(3 a \,b^{5} d^{3}+3 \left(a d +b c \right) b^{5} d^{2}\right) x^{9}}{9}+\frac{\left(3 a^{2} b^{4} d^{3}+9 \left(a d +b c \right) a \,b^{4} d^{2}+\left(a \,b^{2} c \,d^{2}+2 \left(a d +b c \right)^{2} b d +\left(2 a b c d +\left(a d +b c \right)^{2}\right) b d \right) b^{3}\right) x^{8}}{8}+\frac{\left(a^{3} b^{3} d^{3}+9 \left(a d +b c \right) a^{2} b^{3} d^{2}+3 \left(a \,b^{2} c \,d^{2}+2 \left(a d +b c \right)^{2} b d +\left(2 a b c d +\left(a d +b c \right)^{2}\right) b d \right) a \,b^{2}+\left(4 \left(a d +b c \right) a b c d +\left(a d +b c \right) \left(2 a b c d +\left(a d +b c \right)^{2}\right)\right) b^{3}\right) x^{7}}{7}+\frac{\left(3 \left(a d +b c \right) a^{3} b^{2} d^{2}+3 \left(a \,b^{2} c \,d^{2}+2 \left(a d +b c \right)^{2} b d +\left(2 a b c d +\left(a d +b c \right)^{2}\right) b d \right) a^{2} b +3 \left(4 \left(a d +b c \right) a b c d +\left(a d +b c \right) \left(2 a b c d +\left(a d +b c \right)^{2}\right)\right) a \,b^{2}+\left(a^{2} b \,c^{2} d +\left(2 a b c d +\left(a d +b c \right)^{2}\right) a c +2 \left(a d +b c \right)^{2} a c \right) b^{3}\right) x^{6}}{6}+\frac{\left(3 \left(a d +b c \right) a^{2} b^{3} c^{2}+\left(a \,b^{2} c \,d^{2}+2 \left(a d +b c \right)^{2} b d +\left(2 a b c d +\left(a d +b c \right)^{2}\right) b d \right) a^{3}+3 \left(4 \left(a d +b c \right) a b c d +\left(a d +b c \right) \left(2 a b c d +\left(a d +b c \right)^{2}\right)\right) a^{2} b +3 \left(a^{2} b \,c^{2} d +\left(2 a b c d +\left(a d +b c \right)^{2}\right) a c +2 \left(a d +b c \right)^{2} a c \right) a \,b^{2}\right) x^{5}}{5}+\frac{\left(a^{3} b^{3} c^{3}+9 \left(a d +b c \right) a^{3} b^{2} c^{2}+\left(4 \left(a d +b c \right) a b c d +\left(a d +b c \right) \left(2 a b c d +\left(a d +b c \right)^{2}\right)\right) a^{3}+3 \left(a^{2} b \,c^{2} d +\left(2 a b c d +\left(a d +b c \right)^{2}\right) a c +2 \left(a d +b c \right)^{2} a c \right) a^{2} b \right) x^{4}}{4}+\frac{\left(3 a^{4} b^{2} c^{3}+9 \left(a d +b c \right) a^{4} b \,c^{2}+\left(a^{2} b \,c^{2} d +\left(2 a b c d +\left(a d +b c \right)^{2}\right) a c +2 \left(a d +b c \right)^{2} a c \right) a^{3}\right) x^{3}}{3}+\frac{\left(3 a^{5} b \,c^{3}+3 \left(a d +b c \right) a^{5} c^{2}\right) x^{2}}{2}"," ",0,"1/10*b^6*d^3*x^10+1/9*(3*a*b^5*d^3+3*b^5*(a*d+b*c)*d^2)*x^9+1/8*(3*a^2*b^4*d^3+9*a*b^4*(a*d+b*c)*d^2+b^3*(a*b^2*c*d^2+2*(a*d+b*c)^2*b*d+b*d*(2*a*b*c*d+(a*d+b*c)^2)))*x^8+1/7*(a^3*b^3*d^3+9*a^2*b^3*(a*d+b*c)*d^2+3*a*b^2*(a*b^2*c*d^2+2*(a*d+b*c)^2*b*d+b*d*(2*a*b*c*d+(a*d+b*c)^2))+b^3*(4*a*c*(a*d+b*c)*b*d+(a*d+b*c)*(2*a*b*c*d+(a*d+b*c)^2)))*x^7+1/6*(3*a^3*(a*d+b*c)*b^2*d^2+3*a^2*b*(a*b^2*c*d^2+2*(a*d+b*c)^2*b*d+b*d*(2*a*b*c*d+(a*d+b*c)^2))+3*a*b^2*(4*a*c*(a*d+b*c)*b*d+(a*d+b*c)*(2*a*b*c*d+(a*d+b*c)^2))+b^3*(a*c*(2*a*b*c*d+(a*d+b*c)^2)+2*(a*d+b*c)^2*a*c+b*d*a^2*c^2))*x^6+1/5*(a^3*(a*b^2*c*d^2+2*(a*d+b*c)^2*b*d+b*d*(2*a*b*c*d+(a*d+b*c)^2))+3*a^2*b*(4*a*c*(a*d+b*c)*b*d+(a*d+b*c)*(2*a*b*c*d+(a*d+b*c)^2))+3*a*b^2*(a*c*(2*a*b*c*d+(a*d+b*c)^2)+2*(a*d+b*c)^2*a*c+b*d*a^2*c^2)+3*b^3*a^2*c^2*(a*d+b*c))*x^5+1/4*(a^3*(4*a*c*(a*d+b*c)*b*d+(a*d+b*c)*(2*a*b*c*d+(a*d+b*c)^2))+3*a^2*b*(a*c*(2*a*b*c*d+(a*d+b*c)^2)+2*(a*d+b*c)^2*a*c+b*d*a^2*c^2)+9*a^3*b^2*c^2*(a*d+b*c)+b^3*a^3*c^3)*x^4+1/3*(a^3*(a*c*(2*a*b*c*d+(a*d+b*c)^2)+2*(a*d+b*c)^2*a*c+b*d*a^2*c^2)+9*a^4*b*c^2*(a*d+b*c)+3*a^4*b^2*c^3)*x^3+1/2*(3*a^5*c^2*(a*d+b*c)+3*a^5*b*c^3)*x^2+a^6*c^3*x","B"
1784,1,601,84,0.038000," ","int((b*x+a)^2*(a*c+(a*d+b*c)*x+b*d*x^2)^3,x)","\frac{b^{5} d^{3} x^{9}}{9}+a^{5} c^{3} x +\frac{\left(2 a \,b^{4} d^{3}+3 \left(a d +b c \right) b^{4} d^{2}\right) x^{8}}{8}+\frac{\left(a^{2} b^{3} d^{3}+6 \left(a d +b c \right) a \,b^{3} d^{2}+\left(a \,b^{2} c \,d^{2}+2 \left(a d +b c \right)^{2} b d +\left(2 a b c d +\left(a d +b c \right)^{2}\right) b d \right) b^{2}\right) x^{7}}{7}+\frac{\left(3 \left(a d +b c \right) a^{2} b^{2} d^{2}+2 \left(a \,b^{2} c \,d^{2}+2 \left(a d +b c \right)^{2} b d +\left(2 a b c d +\left(a d +b c \right)^{2}\right) b d \right) a b +\left(4 \left(a d +b c \right) a b c d +\left(a d +b c \right) \left(2 a b c d +\left(a d +b c \right)^{2}\right)\right) b^{2}\right) x^{6}}{6}+\frac{\left(\left(a \,b^{2} c \,d^{2}+2 \left(a d +b c \right)^{2} b d +\left(2 a b c d +\left(a d +b c \right)^{2}\right) b d \right) a^{2}+2 \left(4 \left(a d +b c \right) a b c d +\left(a d +b c \right) \left(2 a b c d +\left(a d +b c \right)^{2}\right)\right) a b +\left(a^{2} b \,c^{2} d +\left(2 a b c d +\left(a d +b c \right)^{2}\right) a c +2 \left(a d +b c \right)^{2} a c \right) b^{2}\right) x^{5}}{5}+\frac{\left(3 \left(a d +b c \right) a^{2} b^{2} c^{2}+\left(4 \left(a d +b c \right) a b c d +\left(a d +b c \right) \left(2 a b c d +\left(a d +b c \right)^{2}\right)\right) a^{2}+2 \left(a^{2} b \,c^{2} d +\left(2 a b c d +\left(a d +b c \right)^{2}\right) a c +2 \left(a d +b c \right)^{2} a c \right) a b \right) x^{4}}{4}+\frac{\left(a^{3} b^{2} c^{3}+6 \left(a d +b c \right) a^{3} b \,c^{2}+\left(a^{2} b \,c^{2} d +\left(2 a b c d +\left(a d +b c \right)^{2}\right) a c +2 \left(a d +b c \right)^{2} a c \right) a^{2}\right) x^{3}}{3}+\frac{\left(2 a^{4} b \,c^{3}+3 \left(a d +b c \right) a^{4} c^{2}\right) x^{2}}{2}"," ",0,"1/9*b^5*d^3*x^9+1/8*(2*a*b^4*d^3+3*b^4*(a*d+b*c)*d^2)*x^8+1/7*(a^2*b^3*d^3+6*a*b^3*(a*d+b*c)*d^2+b^2*(a*b^2*c*d^2+2*(a*d+b*c)^2*b*d+(2*a*b*c*d+(a*d+b*c)^2)*b*d))*x^7+1/6*(3*a^2*(a*d+b*c)*b^2*d^2+2*a*b*(a*b^2*c*d^2+2*(a*d+b*c)^2*b*d+(2*a*b*c*d+(a*d+b*c)^2)*b*d)+b^2*(4*(a*d+b*c)*a*b*c*d+(a*d+b*c)*(2*a*b*c*d+(a*d+b*c)^2)))*x^6+1/5*(a^2*(a*b^2*c*d^2+2*(a*d+b*c)^2*b*d+(2*a*b*c*d+(a*d+b*c)^2)*b*d)+2*a*b*(4*(a*d+b*c)*a*b*c*d+(a*d+b*c)*(2*a*b*c*d+(a*d+b*c)^2))+b^2*(a^2*b*c^2*d+(2*a*b*c*d+(a*d+b*c)^2)*a*c+2*(a*d+b*c)^2*a*c))*x^5+1/4*(a^2*(4*(a*d+b*c)*a*b*c*d+(a*d+b*c)*(2*a*b*c*d+(a*d+b*c)^2))+2*a*b*(a^2*b*c^2*d+(2*a*b*c*d+(a*d+b*c)^2)*a*c+2*(a*d+b*c)^2*a*c)+3*b^2*a^2*c^2*(a*d+b*c))*x^4+1/3*(a^2*(a^2*b*c^2*d+(2*a*b*c*d+(a*d+b*c)^2)*a*c+2*(a*d+b*c)^2*a*c)+6*a^3*b*c^2*(a*d+b*c)+a^3*b^2*c^3)*x^3+1/2*(3*a^4*c^2*(a*d+b*c)+2*a^4*b*c^3)*x^2+a^5*c^3*x","B"
1785,1,391,84,0.043000," ","int((b*x+a)*(a*c+(a*d+b*c)*x+b*d*x^2)^3,x)","\frac{b^{4} d^{3} x^{8}}{8}+a^{4} c^{3} x +\frac{\left(a \,b^{3} d^{3}+3 \left(a d +b c \right) b^{3} d^{2}\right) x^{7}}{7}+\frac{\left(3 \left(a d +b c \right) a \,b^{2} d^{2}+\left(a \,b^{2} c \,d^{2}+2 \left(a d +b c \right)^{2} b d +\left(2 a b c d +\left(a d +b c \right)^{2}\right) b d \right) b \right) x^{6}}{6}+\frac{\left(\left(a \,b^{2} c \,d^{2}+2 \left(a d +b c \right)^{2} b d +\left(2 a b c d +\left(a d +b c \right)^{2}\right) b d \right) a +\left(4 \left(a d +b c \right) a b c d +\left(a d +b c \right) \left(2 a b c d +\left(a d +b c \right)^{2}\right)\right) b \right) x^{5}}{5}+\frac{\left(\left(4 \left(a d +b c \right) a b c d +\left(a d +b c \right) \left(2 a b c d +\left(a d +b c \right)^{2}\right)\right) a +\left(a^{2} b \,c^{2} d +\left(2 a b c d +\left(a d +b c \right)^{2}\right) a c +2 \left(a d +b c \right)^{2} a c \right) b \right) x^{4}}{4}+\frac{\left(3 \left(a d +b c \right) a^{2} b \,c^{2}+\left(a^{2} b \,c^{2} d +\left(2 a b c d +\left(a d +b c \right)^{2}\right) a c +2 \left(a d +b c \right)^{2} a c \right) a \right) x^{3}}{3}+\frac{\left(a^{3} b \,c^{3}+3 \left(a d +b c \right) a^{3} c^{2}\right) x^{2}}{2}"," ",0,"1/8*d^3*b^4*x^8+1/7*(a*b^3*d^3+3*b^3*(a*d+b*c)*d^2)*x^7+1/6*(3*a*(a*d+b*c)*b^2*d^2+b*(a*b^2*c*d^2+2*(a*d+b*c)^2*b*d+(2*a*b*c*d+(a*d+b*c)^2)*b*d))*x^6+1/5*(a*(a*b^2*c*d^2+2*(a*d+b*c)^2*b*d+(2*a*b*c*d+(a*d+b*c)^2)*b*d)+b*(4*(a*d+b*c)*a*b*c*d+(a*d+b*c)*(2*a*b*c*d+(a*d+b*c)^2)))*x^5+1/4*(a*(4*(a*d+b*c)*a*b*c*d+(a*d+b*c)*(2*a*b*c*d+(a*d+b*c)^2))+b*(a^2*b*c^2*d+(2*a*b*c*d+(a*d+b*c)^2)*a*c+2*(a*d+b*c)^2*a*c))*x^4+1/3*(a*(a^2*b*c^2*d+(2*a*b*c*d+(a*d+b*c)^2)*a*c+2*(a*d+b*c)^2*a*c)+3*b*a^2*c^2*(a*d+b*c))*x^3+1/2*(3*a^3*c^2*(a*d+b*c)+a^3*b*c^3)*x^2+a^4*c^3*x","B"
1786,1,194,84,0.049000," ","int((a*c+(a*d+b*c)*x+b*d*x^2)^3,x)","\frac{b^{3} d^{3} x^{7}}{7}+\frac{\left(a d +b c \right) b^{2} d^{2} x^{6}}{2}+a^{3} c^{3} x +\frac{3 \left(a d +b c \right) a^{2} c^{2} x^{2}}{2}+\frac{\left(a \,b^{2} c \,d^{2}+2 \left(a d +b c \right)^{2} b d +\left(2 a b c d +\left(a d +b c \right)^{2}\right) b d \right) x^{5}}{5}+\frac{\left(4 \left(a d +b c \right) a b c d +\left(a d +b c \right) \left(2 a b c d +\left(a d +b c \right)^{2}\right)\right) x^{4}}{4}+\frac{\left(a^{2} b \,c^{2} d +\left(2 a b c d +\left(a d +b c \right)^{2}\right) a c +2 \left(a d +b c \right)^{2} a c \right) x^{3}}{3}"," ",0,"1/7*b^3*d^3*x^7+1/2*(a*d+b*c)*b^2*d^2*x^6+1/5*(a*b^2*c*d^2+2*(a*d+b*c)^2*b*d+(2*a*b*c*d+(a*d+b*c)^2)*b*d)*x^5+1/4*(4*(a*d+b*c)*a*b*c*d+(a*d+b*c)*(2*a*b*c*d+(a*d+b*c)^2))*x^4+1/3*(a^2*b*c^2*d+(2*a*b*c*d+(a*d+b*c)^2)*a*c+2*(a*d+b*c)^2*a*c)*x^3+3/2*a^2*c^2*(a*d+b*c)*x^2+a^3*c^3*x","B"
1787,1,147,59,0.047000," ","int((a*c+(a*d+b*c)*x+b*d*x^2)^3/(b*x+a),x)","\frac{b^{2} d^{3} x^{6}}{6}+a^{2} c^{3} x +\frac{\left(b^{2} c \,d^{2}+2 \left(a d +b c \right) b \,d^{2}\right) x^{5}}{5}+\frac{\left(2 \left(a d +b c \right) b c d +\left(2 a b c d +\left(a d +b c \right)^{2}\right) d \right) x^{4}}{4}+\frac{\left(2 \left(a d +b c \right) a c d +\left(2 a b c d +\left(a d +b c \right)^{2}\right) c \right) x^{3}}{3}+\frac{\left(a^{2} c^{2} d +2 \left(a d +b c \right) a \,c^{2}\right) x^{2}}{2}"," ",0,"1/6*b^2*d^3*x^6+1/5*(c*b^2*d^2+2*d^2*(a*d+b*c)*b)*x^5+1/4*(2*c*(a*d+b*c)*b*d+d*(2*a*b*c*d+(a*d+b*c)^2))*x^4+1/3*(c*(2*a*b*c*d+(a*d+b*c)^2)+2*d*a*c*(a*d+b*c))*x^3+1/2*(2*c^2*a*(a*d+b*c)+d*a^2*c^2)*x^2+a^2*c^3*x","B"
1788,1,94,34,0.040000," ","int((a*c+(a*d+b*c)*x+b*d*x^2)^3/(b*x+a)^2,x)","\frac{b \,d^{3} x^{5}}{5}+a \,c^{3} x +\frac{\left(2 b c \,d^{2}+\left(a d +b c \right) d^{2}\right) x^{4}}{4}+\frac{\left(a c \,d^{2}+b \,c^{2} d +2 \left(a d +b c \right) c d \right) x^{3}}{3}+\frac{\left(2 a \,c^{2} d +\left(a d +b c \right) c^{2}\right) x^{2}}{2}"," ",0,"1/5*b*d^3*x^5+1/4*(2*b*c*d^2+d^2*(a*d+b*c))*x^4+1/3*(b*c^2*d+2*c*d*(a*d+b*c)+a*c*d^2)*x^3+1/2*(c^2*(a*d+b*c)+2*a*c^2*d)*x^2+a*c^3*x","B"
1789,1,13,12,0.043000," ","int((a*c+(a*d+b*c)*x+b*d*x^2)^3/(b*x+a)^3,x)","\frac{\left(d x +c \right)^{4}}{4 d}"," ",0,"1/4*(d*x+c)^4/d","A"
1790,1,133,69,0.055000," ","int((a*c+(a*d+b*c)*x+b*d*x^2)^3/(b*x+a)^4,x)","\frac{d^{3} x^{3}}{3 b}-\frac{a \,d^{3} x^{2}}{2 b^{2}}+\frac{3 c \,d^{2} x^{2}}{2 b}-\frac{a^{3} d^{3} \ln \left(b x +a \right)}{b^{4}}+\frac{3 a^{2} c \,d^{2} \ln \left(b x +a \right)}{b^{3}}+\frac{a^{2} d^{3} x}{b^{3}}-\frac{3 a \,c^{2} d \ln \left(b x +a \right)}{b^{2}}-\frac{3 a c \,d^{2} x}{b^{2}}+\frac{c^{3} \ln \left(b x +a \right)}{b}+\frac{3 c^{2} d x}{b}"," ",0,"1/3*d^3/b*x^3-1/2*d^3/b^2*x^2*a+3/2*d^2/b*x^2*c+d^3/b^3*a^2*x-3*d^2/b^2*a*c*x+3*d/b*c^2*x-1/b^4*ln(b*x+a)*a^3*d^3+3/b^3*ln(b*x+a)*a^2*c*d^2-3/b^2*ln(b*x+a)*a*c^2*d+1/b*ln(b*x+a)*c^3","A"
1791,1,149,73,0.063000," ","int((a*c+(a*d+b*c)*x+b*d*x^2)^3/(b*x+a)^5,x)","\frac{d^{3} x^{2}}{2 b^{2}}+\frac{a^{3} d^{3}}{\left(b x +a \right) b^{4}}-\frac{3 a^{2} c \,d^{2}}{\left(b x +a \right) b^{3}}+\frac{3 a^{2} d^{3} \ln \left(b x +a \right)}{b^{4}}+\frac{3 a \,c^{2} d}{\left(b x +a \right) b^{2}}-\frac{6 a c \,d^{2} \ln \left(b x +a \right)}{b^{3}}-\frac{2 a \,d^{3} x}{b^{3}}-\frac{c^{3}}{\left(b x +a \right) b}+\frac{3 c^{2} d \ln \left(b x +a \right)}{b^{2}}+\frac{3 c \,d^{2} x}{b^{2}}"," ",0,"1/2*d^3*x^2/b^2-2*d^3/b^3*a*x+3*d^2/b^2*c*x+3/b^4*d^3*ln(b*x+a)*a^2-6/b^3*d^2*ln(b*x+a)*a*c+3/b^2*d*ln(b*x+a)*c^2+1/b^4/(b*x+a)*a^3*d^3-3/b^3/(b*x+a)*a^2*c*d^2+3/b^2/(b*x+a)*a*c^2*d-1/b/(b*x+a)*c^3","B"
1792,1,160,76,0.166000," ","int((a*c+(a*d+b*c)*x+b*d*x^2)^3/(b*x+a)^6,x)","\frac{a^{3} d^{3}}{2 \left(b x +a \right)^{2} b^{4}}-\frac{3 a^{2} c \,d^{2}}{2 \left(b x +a \right)^{2} b^{3}}+\frac{3 a \,c^{2} d}{2 \left(b x +a \right)^{2} b^{2}}-\frac{c^{3}}{2 \left(b x +a \right)^{2} b}-\frac{3 a^{2} d^{3}}{\left(b x +a \right) b^{4}}+\frac{6 a c \,d^{2}}{\left(b x +a \right) b^{3}}-\frac{3 a \,d^{3} \ln \left(b x +a \right)}{b^{4}}-\frac{3 c^{2} d}{\left(b x +a \right) b^{2}}+\frac{3 c \,d^{2} \ln \left(b x +a \right)}{b^{3}}+\frac{d^{3} x}{b^{3}}"," ",0,"d^3*x/b^3-3/b^4*d^3*ln(b*x+a)*a+3/b^3*d^2*ln(b*x+a)*c-3/b^4*d^3/(b*x+a)*a^2+6/b^3*d^2/(b*x+a)*a*c-3/b^2*d/(b*x+a)*c^2+1/2/b^4/(b*x+a)^2*a^3*d^3-3/2/b^3/(b*x+a)^2*a^2*c*d^2+3/2/b^2/(b*x+a)^2*a*c^2*d-1/2/b/(b*x+a)^2*c^3","B"
1793,1,166,82,0.062000," ","int((a*c+(a*d+b*c)*x+b*d*x^2)^3/(b*x+a)^7,x)","\frac{a^{3} d^{3}}{3 \left(b x +a \right)^{3} b^{4}}-\frac{a^{2} c \,d^{2}}{\left(b x +a \right)^{3} b^{3}}+\frac{a \,c^{2} d}{\left(b x +a \right)^{3} b^{2}}-\frac{c^{3}}{3 \left(b x +a \right)^{3} b}-\frac{3 a^{2} d^{3}}{2 \left(b x +a \right)^{2} b^{4}}+\frac{3 a c \,d^{2}}{\left(b x +a \right)^{2} b^{3}}-\frac{3 c^{2} d}{2 \left(b x +a \right)^{2} b^{2}}+\frac{3 a \,d^{3}}{\left(b x +a \right) b^{4}}-\frac{3 c \,d^{2}}{\left(b x +a \right) b^{3}}+\frac{d^{3} \ln \left(b x +a \right)}{b^{4}}"," ",0,"1/3/b^4/(b*x+a)^3*a^3*d^3-1/b^3/(b*x+a)^3*a^2*c*d^2+1/b^2/(b*x+a)^3*a*c^2*d-1/3/b/(b*x+a)^3*c^3+d^3*ln(b*x+a)/b^4+3/b^4*d^3/(b*x+a)*a-3/b^3*d^2/(b*x+a)*c-3/2*d^3/b^4/(b*x+a)^2*a^2+3*d^2/b^3/(b*x+a)^2*a*c-3/2*d/b^2/(b*x+a)^2*c^2","B"
1794,1,122,26,0.052000," ","int((a*c+(a*d+b*c)*x+b*d*x^2)^3/(b*x+a)^8,x)","-\frac{d^{3}}{\left(b x +a \right) b^{4}}+\frac{3 \left(a d -b c \right) d^{2}}{2 \left(b x +a \right)^{2} b^{4}}-\frac{\left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right) d}{\left(b x +a \right)^{3} b^{4}}-\frac{-a^{3} d^{3}+3 a^{2} b c \,d^{2}-3 a \,c^{2} d \,b^{2}+c^{3} b^{3}}{4 \left(b x +a \right)^{4} b^{4}}"," ",0,"-1/4*(-a^3*d^3+3*a^2*b*c*d^2-3*a*b^2*c^2*d+b^3*c^3)/b^4/(b*x+a)^4-d*(a^2*d^2-2*a*b*c*d+b^2*c^2)/b^4/(b*x+a)^3-d^3/b^4/(b*x+a)+3/2*d^2*(a*d-b*c)/b^4/(b*x+a)^2","B"
1795,1,121,54,0.052000," ","int((a*c+(a*d+b*c)*x+b*d*x^2)^3/(b*x+a)^9,x)","-\frac{d^{3}}{2 \left(b x +a \right)^{2} b^{4}}+\frac{\left(a d -b c \right) d^{2}}{\left(b x +a \right)^{3} b^{4}}-\frac{3 \left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right) d}{4 \left(b x +a \right)^{4} b^{4}}-\frac{-a^{3} d^{3}+3 a^{2} b c \,d^{2}-3 a \,c^{2} d \,b^{2}+c^{3} b^{3}}{5 \left(b x +a \right)^{5} b^{4}}"," ",0,"-3/4*d*(a^2*d^2-2*a*b*c*d+b^2*c^2)/b^4/(b*x+a)^4-1/5*(-a^3*d^3+3*a^2*b*c*d^2-3*a*b^2*c^2*d+b^3*c^3)/b^4/(b*x+a)^5+d^2*(a*d-b*c)/b^4/(b*x+a)^3-1/2*d^3/b^4/(b*x+a)^2","B"
1796,1,122,84,0.048000," ","int((a*c+(a*d+b*c)*x+b*d*x^2)^3/(b*x+a)^10,x)","-\frac{d^{3}}{3 \left(b x +a \right)^{3} b^{4}}+\frac{3 \left(a d -b c \right) d^{2}}{4 \left(b x +a \right)^{4} b^{4}}-\frac{3 \left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right) d}{5 \left(b x +a \right)^{5} b^{4}}-\frac{-a^{3} d^{3}+3 a^{2} b c \,d^{2}-3 a \,c^{2} d \,b^{2}+c^{3} b^{3}}{6 \left(b x +a \right)^{6} b^{4}}"," ",0,"3/4*d^2*(a*d-b*c)/b^4/(b*x+a)^4-3/5*d*(a^2*d^2-2*a*b*c*d+b^2*c^2)/b^4/(b*x+a)^5-1/3*d^3/b^4/(b*x+a)^3-1/6*(-a^3*d^3+3*a^2*b*c*d^2-3*a*b^2*c^2*d+b^3*c^3)/b^4/(b*x+a)^6","A"
1797,1,122,84,0.054000," ","int((a*c+(a*d+b*c)*x+b*d*x^2)^3/(b*x+a)^11,x)","-\frac{d^{3}}{4 \left(b x +a \right)^{4} b^{4}}+\frac{3 \left(a d -b c \right) d^{2}}{5 \left(b x +a \right)^{5} b^{4}}-\frac{\left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right) d}{2 \left(b x +a \right)^{6} b^{4}}-\frac{-a^{3} d^{3}+3 a^{2} b c \,d^{2}-3 a \,c^{2} d \,b^{2}+c^{3} b^{3}}{7 \left(b x +a \right)^{7} b^{4}}"," ",0,"-1/4*d^3/b^4/(b*x+a)^4+3/5*d^2*(a*d-b*c)/b^4/(b*x+a)^5-1/2*d*(a^2*d^2-2*a*b*c*d+b^2*c^2)/b^4/(b*x+a)^6-1/7*(-a^3*d^3+3*a^2*b*c*d^2-3*a*b^2*c^2*d+b^3*c^3)/b^4/(b*x+a)^7","A"
1798,1,122,84,0.049000," ","int((a*c+(a*d+b*c)*x+b*d*x^2)^3/(b*x+a)^12,x)","-\frac{d^{3}}{5 \left(b x +a \right)^{5} b^{4}}+\frac{\left(a d -b c \right) d^{2}}{2 \left(b x +a \right)^{6} b^{4}}-\frac{3 \left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right) d}{7 \left(b x +a \right)^{7} b^{4}}-\frac{-a^{3} d^{3}+3 a^{2} b c \,d^{2}-3 a \,c^{2} d \,b^{2}+c^{3} b^{3}}{8 \left(b x +a \right)^{8} b^{4}}"," ",0,"-1/8*(-a^3*d^3+3*a^2*b*c*d^2-3*a*b^2*c^2*d+b^3*c^3)/b^4/(b*x+a)^8-1/5*d^3/b^4/(b*x+a)^5+1/2*d^2*(a*d-b*c)/b^4/(b*x+a)^6-3/7*d*(a^2*d^2-2*a*b*c*d+b^2*c^2)/b^4/(b*x+a)^7","A"
1799,1,302,114,0.049000," ","int((b*x+a)^6/(a*c+(a*d+b*c)*x+b*d*x^2),x)","\frac{b^{5} x^{5}}{5 d}+\frac{5 a \,b^{4} x^{4}}{4 d}-\frac{b^{5} c \,x^{4}}{4 d^{2}}+\frac{10 a^{2} b^{3} x^{3}}{3 d}-\frac{5 a \,b^{4} c \,x^{3}}{3 d^{2}}+\frac{b^{5} c^{2} x^{3}}{3 d^{3}}+\frac{5 a^{3} b^{2} x^{2}}{d}-\frac{5 a^{2} b^{3} c \,x^{2}}{d^{2}}+\frac{5 a \,b^{4} c^{2} x^{2}}{2 d^{3}}-\frac{b^{5} c^{3} x^{2}}{2 d^{4}}+\frac{a^{5} \ln \left(d x +c \right)}{d}-\frac{5 a^{4} b c \ln \left(d x +c \right)}{d^{2}}+\frac{5 a^{4} b x}{d}+\frac{10 a^{3} b^{2} c^{2} \ln \left(d x +c \right)}{d^{3}}-\frac{10 a^{3} b^{2} c x}{d^{2}}-\frac{10 a^{2} b^{3} c^{3} \ln \left(d x +c \right)}{d^{4}}+\frac{10 a^{2} b^{3} c^{2} x}{d^{3}}+\frac{5 a \,b^{4} c^{4} \ln \left(d x +c \right)}{d^{5}}-\frac{5 a \,b^{4} c^{3} x}{d^{4}}-\frac{b^{5} c^{5} \ln \left(d x +c \right)}{d^{6}}+\frac{b^{5} c^{4} x}{d^{5}}"," ",0,"1/5*b^5/d*x^5+5/4*b^4/d*x^4*a-1/4*b^5/d^2*x^4*c+10/3*b^3/d*x^3*a^2-5/3*b^4/d^2*x^3*a*c+1/3*b^5/d^3*x^3*c^2+5*b^2/d*x^2*a^3-5*b^3/d^2*x^2*a^2*c+5/2*b^4/d^3*x^2*a*c^2-1/2*b^5/d^4*x^2*c^3+5*b/d*a^4*x-10*b^2/d^2*a^3*c*x+10*b^3/d^3*a^2*c^2*x-5*b^4/d^4*a*c^3*x+b^5/d^5*c^4*x+1/d*ln(d*x+c)*a^5-5/d^2*ln(d*x+c)*a^4*b*c+10/d^3*ln(d*x+c)*a^3*b^2*c^2-10/d^4*ln(d*x+c)*a^2*b^3*c^3+5/d^5*ln(d*x+c)*a*b^4*c^4-1/d^6*ln(d*x+c)*b^5*c^5","B"
1800,1,209,92,0.048000," ","int((b*x+a)^5/(a*c+(a*d+b*c)*x+b*d*x^2),x)","\frac{b^{4} x^{4}}{4 d}+\frac{4 a \,b^{3} x^{3}}{3 d}-\frac{b^{4} c \,x^{3}}{3 d^{2}}+\frac{3 a^{2} b^{2} x^{2}}{d}-\frac{2 a \,b^{3} c \,x^{2}}{d^{2}}+\frac{b^{4} c^{2} x^{2}}{2 d^{3}}+\frac{a^{4} \ln \left(d x +c \right)}{d}-\frac{4 a^{3} b c \ln \left(d x +c \right)}{d^{2}}+\frac{4 a^{3} b x}{d}+\frac{6 a^{2} b^{2} c^{2} \ln \left(d x +c \right)}{d^{3}}-\frac{6 a^{2} b^{2} c x}{d^{2}}-\frac{4 a \,b^{3} c^{3} \ln \left(d x +c \right)}{d^{4}}+\frac{4 a \,b^{3} c^{2} x}{d^{3}}+\frac{b^{4} c^{4} \ln \left(d x +c \right)}{d^{5}}-\frac{b^{4} c^{3} x}{d^{4}}"," ",0,"1/4*b^4/d*x^4+4/3*b^3/d*x^3*a-1/3*b^4/d^2*x^3*c+3*b^2/d*x^2*a^2-2*b^3/d^2*x^2*a*c+1/2*b^4/d^3*x^2*c^2+4*b/d*a^3*x-6*b^2/d^2*a^2*c*x+4*b^3/d^3*a*c^2*x-b^4/d^4*c^3*x+1/d*ln(d*x+c)*a^4-4/d^2*ln(d*x+c)*a^3*b*c+6/d^3*ln(d*x+c)*a^2*b^2*c^2-4/d^4*ln(d*x+c)*a*b^3*c^3+1/d^5*ln(d*x+c)*b^4*c^4","B"
1801,1,133,70,0.049000," ","int((b*x+a)^4/(a*c+(a*d+b*c)*x+b*d*x^2),x)","\frac{b^{3} x^{3}}{3 d}+\frac{3 a \,b^{2} x^{2}}{2 d}-\frac{b^{3} c \,x^{2}}{2 d^{2}}+\frac{a^{3} \ln \left(d x +c \right)}{d}-\frac{3 a^{2} b c \ln \left(d x +c \right)}{d^{2}}+\frac{3 a^{2} b x}{d}+\frac{3 a \,b^{2} c^{2} \ln \left(d x +c \right)}{d^{3}}-\frac{3 a \,b^{2} c x}{d^{2}}-\frac{b^{3} c^{3} \ln \left(d x +c \right)}{d^{4}}+\frac{b^{3} c^{2} x}{d^{3}}"," ",0,"1/3*b^3/d*x^3+3/2*b^2/d*x^2*a-1/2*b^3/d^2*x^2*c+3*b/d*a^2*x-3*b^2/d^2*a*c*x+b^3/d^3*c^2*x+1/d*ln(d*x+c)*a^3-3/d^2*ln(d*x+c)*a^2*b*c+3/d^3*ln(d*x+c)*a*c^2*b^2-1/d^4*ln(d*x+c)*b^3*c^3","A"
1802,1,74,48,0.053000," ","int((b*x+a)^3/(a*c+(a*d+b*c)*x+b*d*x^2),x)","\frac{b^{2} x^{2}}{2 d}+\frac{a^{2} \ln \left(d x +c \right)}{d}-\frac{2 a b c \ln \left(d x +c \right)}{d^{2}}+\frac{2 a b x}{d}+\frac{b^{2} c^{2} \ln \left(d x +c \right)}{d^{3}}-\frac{b^{2} c x}{d^{2}}"," ",0,"1/2*b^2/d*x^2+2*b/d*a*x-b^2/d^2*c*x+1/d*ln(d*x+c)*a^2-2/d^2*ln(d*x+c)*a*b*c+1/d^3*ln(d*x+c)*b^2*c^2","A"
1803,1,32,26,0.144000," ","int((b*x+a)^2/(a*c+(a*d+b*c)*x+b*d*x^2),x)","\frac{a \ln \left(d x +c \right)}{d}-\frac{b c \ln \left(d x +c \right)}{d^{2}}+\frac{b x}{d}"," ",0,"b/d*x+1/d*ln(d*x+c)*a-1/d^2*ln(d*x+c)*b*c","A"
1804,1,11,10,0.042000," ","int((b*x+a)/(a*c+(a*d+b*c)*x+b*d*x^2),x)","\frac{\ln \left(d x +c \right)}{d}"," ",0,"ln(d*x+c)/d","A"
1805,1,37,36,0.049000," ","int(1/(a*c+(a*d+b*c)*x+b*d*x^2),x)","-\frac{\ln \left(b x +a \right)}{a d -b c}+\frac{\ln \left(d x +c \right)}{a d -b c}"," ",0,"1/(a*d-b*c)*ln(d*x+c)-1/(a*d-b*c)*ln(b*x+a)","A"
1806,1,57,57,0.052000," ","int(1/(b*x+a)/(a*c+(a*d+b*c)*x+b*d*x^2),x)","-\frac{d \ln \left(b x +a \right)}{\left(a d -b c \right)^{2}}+\frac{d \ln \left(d x +c \right)}{\left(a d -b c \right)^{2}}+\frac{1}{\left(a d -b c \right) \left(b x +a \right)}"," ",0,"d/(a*d-b*c)^2*ln(d*x+c)+1/(a*d-b*c)/(b*x+a)-d/(a*d-b*c)^2*ln(b*x+a)","A"
1807,1,81,80,0.061000," ","int(1/(b*x+a)^2/(a*c+(a*d+b*c)*x+b*d*x^2),x)","-\frac{d^{2} \ln \left(b x +a \right)}{\left(a d -b c \right)^{3}}+\frac{d^{2} \ln \left(d x +c \right)}{\left(a d -b c \right)^{3}}+\frac{d}{\left(a d -b c \right)^{2} \left(b x +a \right)}+\frac{1}{2 \left(a d -b c \right) \left(b x +a \right)^{2}}"," ",0,"d^2/(a*d-b*c)^3*ln(d*x+c)+1/2/(a*d-b*c)/(b*x+a)^2+d/(a*d-b*c)^2/(b*x+a)-d^2/(a*d-b*c)^3*ln(b*x+a)","A"
1808,1,103,103,0.055000," ","int(1/(b*x+a)^3/(a*c+(a*d+b*c)*x+b*d*x^2),x)","-\frac{d^{3} \ln \left(b x +a \right)}{\left(a d -b c \right)^{4}}+\frac{d^{3} \ln \left(d x +c \right)}{\left(a d -b c \right)^{4}}+\frac{d^{2}}{\left(a d -b c \right)^{3} \left(b x +a \right)}+\frac{d}{2 \left(a d -b c \right)^{2} \left(b x +a \right)^{2}}+\frac{1}{3 \left(a d -b c \right) \left(b x +a \right)^{3}}"," ",0,"d^3/(a*d-b*c)^4*ln(d*x+c)+1/3/(a*d-b*c)/(b*x+a)^3+1/2*d/(a*d-b*c)^2/(b*x+a)^2+d^2/(a*d-b*c)^3/(b*x+a)-d^3/(a*d-b*c)^4*ln(b*x+a)","A"
1809,1,125,124,0.068000," ","int(1/(b*x+a)^4/(a*c+(a*d+b*c)*x+b*d*x^2),x)","-\frac{d^{4} \ln \left(b x +a \right)}{\left(a d -b c \right)^{5}}+\frac{d^{4} \ln \left(d x +c \right)}{\left(a d -b c \right)^{5}}+\frac{d^{3}}{\left(a d -b c \right)^{4} \left(b x +a \right)}+\frac{d^{2}}{2 \left(a d -b c \right)^{3} \left(b x +a \right)^{2}}+\frac{d}{3 \left(a d -b c \right)^{2} \left(b x +a \right)^{3}}+\frac{1}{4 \left(a d -b c \right) \left(b x +a \right)^{4}}"," ",0,"d^4/(a*d-b*c)^5*ln(d*x+c)+1/4/(a*d-b*c)/(b*x+a)^4+1/3*d/(a*d-b*c)^2/(b*x+a)^3+1/2*d^2/(a*d-b*c)^3/(b*x+a)^2+d^3/(a*d-b*c)^4/(b*x+a)-d^4/(a*d-b*c)^5*ln(b*x+a)","A"
1810,1,230,102,0.054000," ","int((b*x+a)^6/(a*c+(a*d+b*c)*x+b*d*x^2)^2,x)","\frac{b^{4} x^{3}}{3 d^{2}}+\frac{2 a \,b^{3} x^{2}}{d^{2}}-\frac{b^{4} c \,x^{2}}{d^{3}}-\frac{a^{4}}{\left(d x +c \right) d}+\frac{4 a^{3} b c}{\left(d x +c \right) d^{2}}+\frac{4 a^{3} b \ln \left(d x +c \right)}{d^{2}}-\frac{6 a^{2} b^{2} c^{2}}{\left(d x +c \right) d^{3}}-\frac{12 a^{2} b^{2} c \ln \left(d x +c \right)}{d^{3}}+\frac{6 a^{2} b^{2} x}{d^{2}}+\frac{4 a \,b^{3} c^{3}}{\left(d x +c \right) d^{4}}+\frac{12 a \,b^{3} c^{2} \ln \left(d x +c \right)}{d^{4}}-\frac{8 a \,b^{3} c x}{d^{3}}-\frac{b^{4} c^{4}}{\left(d x +c \right) d^{5}}-\frac{4 b^{4} c^{3} \ln \left(d x +c \right)}{d^{5}}+\frac{3 b^{4} c^{2} x}{d^{4}}"," ",0,"1/3*b^4/d^2*x^3+2*b^3/d^2*x^2*a-b^4/d^3*x^2*c+6*b^2/d^2*a^2*x-8*b^3/d^3*a*c*x+3*b^4/d^4*c^2*x-1/d/(d*x+c)*a^4+4/d^2/(d*x+c)*c*a^3*b-6/d^3/(d*x+c)*a^2*b^2*c^2+4/d^4/(d*x+c)*a*b^3*c^3-1/d^5/(d*x+c)*b^4*c^4+4*b/d^2*ln(d*x+c)*a^3-12*b^2/d^3*ln(d*x+c)*a^2*c+12*b^3/d^4*ln(d*x+c)*a*c^2-4*b^4/d^5*ln(d*x+c)*c^3","B"
1811,1,149,73,0.046000," ","int((b*x+a)^5/(a*c+(a*d+b*c)*x+b*d*x^2)^2,x)","\frac{b^{3} x^{2}}{2 d^{2}}-\frac{a^{3}}{\left(d x +c \right) d}+\frac{3 a^{2} b c}{\left(d x +c \right) d^{2}}+\frac{3 a^{2} b \ln \left(d x +c \right)}{d^{2}}-\frac{3 a \,b^{2} c^{2}}{\left(d x +c \right) d^{3}}-\frac{6 a \,b^{2} c \ln \left(d x +c \right)}{d^{3}}+\frac{3 a \,b^{2} x}{d^{2}}+\frac{b^{3} c^{3}}{\left(d x +c \right) d^{4}}+\frac{3 b^{3} c^{2} \ln \left(d x +c \right)}{d^{4}}-\frac{2 b^{3} c x}{d^{3}}"," ",0,"1/2*b^3*x^2/d^2+3*b^2/d^2*a*x-2*b^3/d^3*c*x-1/d/(d*x+c)*a^3+3/d^2/(d*x+c)*a^2*b*c-3/d^3/(d*x+c)*a*c^2*b^2+1/d^4/(d*x+c)*b^3*c^3+3*b/d^2*ln(d*x+c)*a^2-6*b^2/d^3*ln(d*x+c)*a*c+3*b^3/d^4*ln(d*x+c)*c^2","B"
1812,1,86,51,0.051000," ","int((b*x+a)^4/(a*c+(a*d+b*c)*x+b*d*x^2)^2,x)","-\frac{a^{2}}{\left(d x +c \right) d}+\frac{2 a b c}{\left(d x +c \right) d^{2}}+\frac{2 a b \ln \left(d x +c \right)}{d^{2}}-\frac{b^{2} c^{2}}{\left(d x +c \right) d^{3}}-\frac{2 b^{2} c \ln \left(d x +c \right)}{d^{3}}+\frac{b^{2} x}{d^{2}}"," ",0,"b^2/d^2*x-1/d/(d*x+c)*a^2+2/d^2/(d*x+c)*a*b*c-1/d^3/(d*x+c)*b^2*c^2+2*b/d^2*ln(d*x+c)*a-2*b^2/d^3*ln(d*x+c)*c","A"
1813,1,39,31,0.050000," ","int((b*x+a)^3/(a*c+(a*d+b*c)*x+b*d*x^2)^2,x)","-\frac{a}{\left(d x +c \right) d}+\frac{b c}{\left(d x +c \right) d^{2}}+\frac{b \ln \left(d x +c \right)}{d^{2}}"," ",0,"-1/d/(d*x+c)*a+1/d^2/(d*x+c)*b*c+b*ln(d*x+c)/d^2","A"
1814,1,13,12,0.043000," ","int((b*x+a)^2/(a*c+(a*d+b*c)*x+b*d*x^2)^2,x)","-\frac{1}{\left(d x +c \right) d}"," ",0,"-1/d/(d*x+c)","A"
1815,1,58,56,0.055000," ","int((b*x+a)/(a*c+(a*d+b*c)*x+b*d*x^2)^2,x)","\frac{b \ln \left(b x +a \right)}{\left(a d -b c \right)^{2}}-\frac{b \ln \left(d x +c \right)}{\left(a d -b c \right)^{2}}-\frac{1}{\left(a d -b c \right) \left(d x +c \right)}"," ",0,"-1/(a*d-b*c)/(d*x+c)-b/(a*d-b*c)^2*ln(d*x+c)+b/(a*d-b*c)^2*ln(b*x+a)","A"
1816,1,82,87,0.058000," ","int(1/(a*c+(a*d+b*c)*x+b*d*x^2)^2,x)","\frac{2 b d \ln \left(b x +a \right)}{\left(a d -b c \right)^{3}}-\frac{2 b d \ln \left(d x +c \right)}{\left(a d -b c \right)^{3}}-\frac{b}{\left(a d -b c \right)^{2} \left(b x +a \right)}-\frac{d}{\left(a d -b c \right)^{2} \left(d x +c \right)}"," ",0,"-d/(a*d-b*c)^2/(d*x+c)-2*d/(a*d-b*c)^3*b*ln(d*x+c)-b/(a*d-b*c)^2/(b*x+a)+2*d/(a*d-b*c)^3*b*ln(b*x+a)","A"
1817,1,109,107,0.059000," ","int(1/(b*x+a)/(a*c+(a*d+b*c)*x+b*d*x^2)^2,x)","\frac{3 b \,d^{2} \ln \left(b x +a \right)}{\left(a d -b c \right)^{4}}-\frac{3 b \,d^{2} \ln \left(d x +c \right)}{\left(a d -b c \right)^{4}}-\frac{2 b d}{\left(a d -b c \right)^{3} \left(b x +a \right)}-\frac{d^{2}}{\left(a d -b c \right)^{3} \left(d x +c \right)}-\frac{b}{2 \left(a d -b c \right)^{2} \left(b x +a \right)^{2}}"," ",0,"-d^2/(a*d-b*c)^3/(d*x+c)-3*d^2/(a*d-b*c)^4*b*ln(d*x+c)-1/2*b/(a*d-b*c)^2/(b*x+a)^2+3*d^2/(a*d-b*c)^4*b*ln(b*x+a)-2*b/(a*d-b*c)^3*d/(b*x+a)","A"
1818,1,346,127,0.061000," ","int((b*x+a)^8/(a*c+(a*d+b*c)*x+b*d*x^2)^3,x)","\frac{b^{5} x^{3}}{3 d^{3}}-\frac{a^{5}}{2 \left(d x +c \right)^{2} d}+\frac{5 a^{4} b c}{2 \left(d x +c \right)^{2} d^{2}}-\frac{5 a^{3} b^{2} c^{2}}{\left(d x +c \right)^{2} d^{3}}+\frac{5 a^{2} b^{3} c^{3}}{\left(d x +c \right)^{2} d^{4}}-\frac{5 a \,b^{4} c^{4}}{2 \left(d x +c \right)^{2} d^{5}}+\frac{5 a \,b^{4} x^{2}}{2 d^{3}}+\frac{b^{5} c^{5}}{2 \left(d x +c \right)^{2} d^{6}}-\frac{3 b^{5} c \,x^{2}}{2 d^{4}}-\frac{5 a^{4} b}{\left(d x +c \right) d^{2}}+\frac{20 a^{3} b^{2} c}{\left(d x +c \right) d^{3}}+\frac{10 a^{3} b^{2} \ln \left(d x +c \right)}{d^{3}}-\frac{30 a^{2} b^{3} c^{2}}{\left(d x +c \right) d^{4}}-\frac{30 a^{2} b^{3} c \ln \left(d x +c \right)}{d^{4}}+\frac{10 a^{2} b^{3} x}{d^{3}}+\frac{20 a \,b^{4} c^{3}}{\left(d x +c \right) d^{5}}+\frac{30 a \,b^{4} c^{2} \ln \left(d x +c \right)}{d^{5}}-\frac{15 a \,b^{4} c x}{d^{4}}-\frac{5 b^{5} c^{4}}{\left(d x +c \right) d^{6}}-\frac{10 b^{5} c^{3} \ln \left(d x +c \right)}{d^{6}}+\frac{6 b^{5} c^{2} x}{d^{5}}"," ",0,"1/3*b^5/d^3*x^3+5/2*b^4/d^3*x^2*a-3/2*b^5/d^4*x^2*c+10*b^3/d^3*a^2*x-15*b^4/d^4*a*c*x+6*b^5/d^5*c^2*x-5*b/d^2/(d*x+c)*a^4+20*b^2/d^3/(d*x+c)*a^3*c-30*b^3/d^4/(d*x+c)*a^2*c^2+20*b^4/d^5/(d*x+c)*a*c^3-5*b^5/d^6/(d*x+c)*c^4+10*b^2/d^3*ln(d*x+c)*a^3-30*b^3/d^4*ln(d*x+c)*a^2*c+30*b^4/d^5*ln(d*x+c)*a*c^2-10*b^5/d^6*ln(d*x+c)*c^3-1/2/d/(d*x+c)^2*a^5+5/2/d^2/(d*x+c)^2*c*a^4*b-5/d^3/(d*x+c)^2*c^2*a^3*b^2+5/d^4/(d*x+c)^2*a^2*b^3*c^3-5/2/d^5/(d*x+c)^2*a*b^4*c^4+1/2/d^6/(d*x+c)^2*b^5*c^5","B"
1819,1,245,99,0.051000," ","int((b*x+a)^7/(a*c+(a*d+b*c)*x+b*d*x^2)^3,x)","-\frac{a^{4}}{2 \left(d x +c \right)^{2} d}+\frac{2 a^{3} b c}{\left(d x +c \right)^{2} d^{2}}-\frac{3 a^{2} b^{2} c^{2}}{\left(d x +c \right)^{2} d^{3}}+\frac{2 a \,b^{3} c^{3}}{\left(d x +c \right)^{2} d^{4}}-\frac{b^{4} c^{4}}{2 \left(d x +c \right)^{2} d^{5}}+\frac{b^{4} x^{2}}{2 d^{3}}-\frac{4 a^{3} b}{\left(d x +c \right) d^{2}}+\frac{12 a^{2} b^{2} c}{\left(d x +c \right) d^{3}}+\frac{6 a^{2} b^{2} \ln \left(d x +c \right)}{d^{3}}-\frac{12 a \,b^{3} c^{2}}{\left(d x +c \right) d^{4}}-\frac{12 a \,b^{3} c \ln \left(d x +c \right)}{d^{4}}+\frac{4 a \,b^{3} x}{d^{3}}+\frac{4 b^{4} c^{3}}{\left(d x +c \right) d^{5}}+\frac{6 b^{4} c^{2} \ln \left(d x +c \right)}{d^{5}}-\frac{3 b^{4} c x}{d^{4}}"," ",0,"1/2*b^4*x^2/d^3+4*b^3/d^3*a*x-3*b^4/d^4*c*x-4*b/d^2/(d*x+c)*a^3+12*b^2/d^3/(d*x+c)*a^2*c-12*b^3/d^4/(d*x+c)*a*c^2+4*b^4/d^5/(d*x+c)*c^3+6*b^2/d^3*ln(d*x+c)*a^2-12*b^3/d^4*ln(d*x+c)*a*c+6*b^4/d^5*ln(d*x+c)*c^2-1/2/d/(d*x+c)^2*a^4+2/d^2/(d*x+c)^2*c*a^3*b-3/d^3/(d*x+c)^2*c^2*a^2*b^2+2/d^4/(d*x+c)^2*a*b^3*c^3-1/2/d^5/(d*x+c)^2*b^4*c^4","B"
1820,1,160,76,0.062000," ","int((b*x+a)^6/(a*c+(a*d+b*c)*x+b*d*x^2)^3,x)","-\frac{a^{3}}{2 \left(d x +c \right)^{2} d}+\frac{3 a^{2} b c}{2 \left(d x +c \right)^{2} d^{2}}-\frac{3 a \,b^{2} c^{2}}{2 \left(d x +c \right)^{2} d^{3}}+\frac{b^{3} c^{3}}{2 \left(d x +c \right)^{2} d^{4}}-\frac{3 a^{2} b}{\left(d x +c \right) d^{2}}+\frac{6 a \,b^{2} c}{\left(d x +c \right) d^{3}}+\frac{3 a \,b^{2} \ln \left(d x +c \right)}{d^{3}}-\frac{3 b^{3} c^{2}}{\left(d x +c \right) d^{4}}-\frac{3 b^{3} c \ln \left(d x +c \right)}{d^{4}}+\frac{b^{3} x}{d^{3}}"," ",0,"b^3*x/d^3-3*b/d^2/(d*x+c)*a^2+6*b^2/d^3/(d*x+c)*a*c-3*b^3/d^4/(d*x+c)*c^2+3*b^2/d^3*ln(d*x+c)*a-3*b^3/d^4*ln(d*x+c)*c-1/2/d/(d*x+c)^2*a^3+3/2/d^2/(d*x+c)^2*a^2*b*c-3/2/d^3/(d*x+c)^2*a*c^2*b^2+1/2/d^4/(d*x+c)^2*b^3*c^3","B"
1821,1,92,57,0.056000," ","int((b*x+a)^5/(a*c+(a*d+b*c)*x+b*d*x^2)^3,x)","-\frac{a^{2}}{2 \left(d x +c \right)^{2} d}+\frac{a b c}{\left(d x +c \right)^{2} d^{2}}-\frac{b^{2} c^{2}}{2 \left(d x +c \right)^{2} d^{3}}-\frac{2 a b}{\left(d x +c \right) d^{2}}+\frac{2 b^{2} c}{\left(d x +c \right) d^{3}}+\frac{b^{2} \ln \left(d x +c \right)}{d^{3}}"," ",0,"-2*b/d^2/(d*x+c)*a+2*b^2/d^3/(d*x+c)*c+b^2*ln(d*x+c)/d^3-1/2/d/(d*x+c)^2*a^2+1/d^2/(d*x+c)^2*a*b*c-1/2/d^3/(d*x+c)^2*b^2*c^2","A"
1822,1,35,26,0.056000," ","int((b*x+a)^4/(a*c+(a*d+b*c)*x+b*d*x^2)^3,x)","-\frac{b}{\left(d x +c \right) d^{2}}-\frac{a d -b c}{2 \left(d x +c \right)^{2} d^{2}}"," ",0,"-b/d^2/(d*x+c)-1/2*(a*d-b*c)/d^2/(d*x+c)^2","A"
1823,1,13,12,0.044000," ","int((b*x+a)^3/(a*c+(a*d+b*c)*x+b*d*x^2)^3,x)","-\frac{1}{2 \left(d x +c \right)^{2} d}"," ",0,"-1/2/d/(d*x+c)^2","A"
1824,1,81,80,0.054000," ","int((b*x+a)^2/(a*c+(a*d+b*c)*x+b*d*x^2)^3,x)","-\frac{b^{2} \ln \left(b x +a \right)}{\left(a d -b c \right)^{3}}+\frac{b^{2} \ln \left(d x +c \right)}{\left(a d -b c \right)^{3}}+\frac{b}{\left(a d -b c \right)^{2} \left(d x +c \right)}-\frac{1}{2 \left(a d -b c \right) \left(d x +c \right)^{2}}"," ",0,"-1/2/(a*d-b*c)/(d*x+c)^2+b^2/(a*d-b*c)^3*ln(d*x+c)+b/(a*d-b*c)^2/(d*x+c)-b^2/(a*d-b*c)^3*ln(b*x+a)","A"
1825,1,108,108,0.058000," ","int((b*x+a)/(a*c+(a*d+b*c)*x+b*d*x^2)^3,x)","-\frac{3 b^{2} d \ln \left(b x +a \right)}{\left(a d -b c \right)^{4}}+\frac{3 b^{2} d \ln \left(d x +c \right)}{\left(a d -b c \right)^{4}}+\frac{b^{2}}{\left(a d -b c \right)^{3} \left(b x +a \right)}+\frac{2 b d}{\left(a d -b c \right)^{3} \left(d x +c \right)}-\frac{d}{2 \left(a d -b c \right)^{2} \left(d x +c \right)^{2}}"," ",0,"-1/2*d/(a*d-b*c)^2/(d*x+c)^2+3*d/(a*d-b*c)^4*b^2*ln(d*x+c)+2*d/(a*d-b*c)^3*b/(d*x+c)+b^2/(a*d-b*c)^3/(b*x+a)-3*d/(a*d-b*c)^4*b^2*ln(b*x+a)","A"
1826,1,140,143,0.057000," ","int(1/(a*c+(a*d+b*c)*x+b*d*x^2)^3,x)","-\frac{6 b^{2} d^{2} \ln \left(b x +a \right)}{\left(a d -b c \right)^{5}}+\frac{6 b^{2} d^{2} \ln \left(d x +c \right)}{\left(a d -b c \right)^{5}}+\frac{3 b^{2} d}{\left(a d -b c \right)^{4} \left(b x +a \right)}+\frac{3 b \,d^{2}}{\left(a d -b c \right)^{4} \left(d x +c \right)}+\frac{b^{2}}{2 \left(a d -b c \right)^{3} \left(b x +a \right)^{2}}-\frac{d^{2}}{2 \left(a d -b c \right)^{3} \left(d x +c \right)^{2}}"," ",0,"-1/2*d^2/(a*d-b*c)^3/(d*x+c)^2+6*d^2/(a*d-b*c)^5*b^2*ln(d*x+c)+3*d^2/(a*d-b*c)^4*b/(d*x+c)+1/2*b^2/(a*d-b*c)^3/(b*x+a)^2-6*d^2/(a*d-b*c)^5*b^2*ln(b*x+a)+3*b^2/(a*d-b*c)^4*d/(b*x+a)","A"
1827,1,165,164,0.062000," ","int(1/(b*x+a)/(a*c+(a*d+b*c)*x+b*d*x^2)^3,x)","-\frac{10 b^{2} d^{3} \ln \left(b x +a \right)}{\left(a d -b c \right)^{6}}+\frac{10 b^{2} d^{3} \ln \left(d x +c \right)}{\left(a d -b c \right)^{6}}+\frac{6 b^{2} d^{2}}{\left(a d -b c \right)^{5} \left(b x +a \right)}+\frac{4 b \,d^{3}}{\left(a d -b c \right)^{5} \left(d x +c \right)}+\frac{3 b^{2} d}{2 \left(a d -b c \right)^{4} \left(b x +a \right)^{2}}-\frac{d^{3}}{2 \left(a d -b c \right)^{4} \left(d x +c \right)^{2}}+\frac{b^{2}}{3 \left(a d -b c \right)^{3} \left(b x +a \right)^{3}}"," ",0,"-1/2*d^3/(a*d-b*c)^4/(d*x+c)^2+10*d^3/(a*d-b*c)^6*b^2*ln(d*x+c)+4*d^3/(a*d-b*c)^5*b/(d*x+c)+1/3*b^2/(a*d-b*c)^3/(b*x+a)^3-10*d^3/(a*d-b*c)^6*b^2*ln(b*x+a)+6*b^2/(a*d-b*c)^5*d^2/(b*x+a)+3/2*b^2/(a*d-b*c)^4*d/(b*x+a)^2","A"
1828,1,198,35,0.048000," ","int((e*x+d)^4*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x)","\frac{c d \,e^{5} x^{7}}{7}+a \,d^{5} e x +\frac{\left(4 c \,d^{2} e^{4}+\left(a \,e^{2}+c \,d^{2}\right) e^{4}\right) x^{6}}{6}+\frac{\left(a d \,e^{5}+6 c \,d^{3} e^{3}+4 \left(a \,e^{2}+c \,d^{2}\right) d \,e^{3}\right) x^{5}}{5}+\frac{\left(4 a \,d^{2} e^{4}+4 c \,d^{4} e^{2}+6 \left(a \,e^{2}+c \,d^{2}\right) d^{2} e^{2}\right) x^{4}}{4}+\frac{\left(6 a \,d^{3} e^{3}+c \,d^{5} e +4 \left(a \,e^{2}+c \,d^{2}\right) d^{3} e \right) x^{3}}{3}+\frac{\left(4 a \,d^{4} e^{2}+\left(a \,e^{2}+c \,d^{2}\right) d^{4}\right) x^{2}}{2}"," ",0,"1/7*d*e^5*c*x^7+1/6*(4*d^2*e^4*c+e^4*(a*e^2+c*d^2))*x^6+1/5*(6*d^3*e^3*c+4*d*e^3*(a*e^2+c*d^2)+e^5*a*d)*x^5+1/4*(4*d^4*e^2*c+6*d^2*e^2*(a*e^2+c*d^2)+4*d^2*e^4*a)*x^4+1/3*(d^5*c*e+4*d^3*e*(a*e^2+c*d^2)+6*d^3*e^3*a)*x^3+1/2*(d^4*(a*e^2+c*d^2)+4*d^4*e^2*a)*x^2+d^5*a*e*x","B"
1829,1,155,35,0.043000," ","int((e*x+d)^3*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x)","\frac{c d \,e^{4} x^{6}}{6}+a \,d^{4} e x +\frac{\left(3 c \,d^{2} e^{3}+\left(a \,e^{2}+c \,d^{2}\right) e^{3}\right) x^{5}}{5}+\frac{\left(a d \,e^{4}+3 c \,d^{3} e^{2}+3 \left(a \,e^{2}+c \,d^{2}\right) d \,e^{2}\right) x^{4}}{4}+\frac{\left(3 a \,d^{2} e^{3}+c \,d^{4} e +3 \left(a \,e^{2}+c \,d^{2}\right) d^{2} e \right) x^{3}}{3}+\frac{\left(3 a \,d^{3} e^{2}+\left(a \,e^{2}+c \,d^{2}\right) d^{3}\right) x^{2}}{2}"," ",0,"1/6*e^4*d*c*x^6+1/5*(3*d^2*e^3*c+e^3*(a*e^2+c*d^2))*x^5+1/4*(3*d^3*e^2*c+3*d*e^2*(a*e^2+c*d^2)+e^4*a*d)*x^4+1/3*(d^4*c*e+3*d^2*e*(a*e^2+c*d^2)+3*d^2*e^3*a)*x^3+1/2*(d^3*(a*e^2+c*d^2)+3*d^3*e^2*a)*x^2+d^4*a*e*x","B"
1830,1,112,35,0.038000," ","int((e*x+d)^2*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x)","\frac{c d \,e^{3} x^{5}}{5}+a \,d^{3} e x +\frac{\left(2 c \,d^{2} e^{2}+\left(a \,e^{2}+c \,d^{2}\right) e^{2}\right) x^{4}}{4}+\frac{\left(a d \,e^{3}+c \,d^{3} e +2 \left(a \,e^{2}+c \,d^{2}\right) d e \right) x^{3}}{3}+\frac{\left(2 a \,d^{2} e^{2}+\left(a \,e^{2}+c \,d^{2}\right) d^{2}\right) x^{2}}{2}"," ",0,"1/5*c*d*e^3*x^5+1/4*(2*d^2*e^2*c+e^2*(a*e^2+c*d^2))*x^4+1/3*(c*d^3*e+2*d*e*(a*e^2+c*d^2)+a*d*e^3)*x^3+1/2*(d^2*(a*e^2+c*d^2)+2*a*d^2*e^2)*x^2+d^3*a*e*x","B"
1831,1,69,35,0.042000," ","int((e*x+d)*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x)","\frac{c d \,e^{2} x^{4}}{4}+a \,d^{2} e x +\frac{\left(c \,d^{2} e +\left(a \,e^{2}+c \,d^{2}\right) e \right) x^{3}}{3}+\frac{\left(a d \,e^{2}+\left(a \,e^{2}+c \,d^{2}\right) d \right) x^{2}}{2}"," ",0,"1/4*d*c*e^2*x^4+1/3*(c*d^2*e+e*(a*e^2+c*d^2))*x^3+1/2*(d*(a*e^2+c*d^2)+a*d*e^2)*x^2+a*d^2*e*x","A"
1832,1,31,30,0.047000," ","int(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2,x)","\frac{c d e \,x^{3}}{3}+a d e x +\frac{\left(a \,e^{2}+c \,d^{2}\right) x^{2}}{2}"," ",0,"a*d*e*x+1/2*(a*e^2+c*d^2)*x^2+1/3*c*d*e*x^3","A"
1833,1,13,12,0.043000," ","int((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)/(e*x+d),x)","\frac{1}{2} c d \,x^{2}+a e x"," ",0,"a*e*x+1/2*c*d*x^2","A"
1834,1,32,26,0.043000," ","int((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)/(e*x+d)^2,x)","a \ln \left(e x +d \right)-\frac{c \,d^{2} \ln \left(e x +d \right)}{e^{2}}+\frac{c d x}{e}"," ",0,"c*d*x/e+ln(e*x+d)*a-1/e^2*ln(e*x+d)*c*d^2","A"
1835,1,39,33,0.053000," ","int((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)/(e*x+d)^3,x)","-\frac{a}{e x +d}+\frac{c \,d^{2}}{\left(e x +d \right) e^{2}}+\frac{c d \ln \left(e x +d \right)}{e^{2}}"," ",0,"-1/(e*x+d)*a+1/e^2/(e*x+d)*c*d^2+c*d*ln(e*x+d)/e^2","A"
1836,1,40,33,0.053000," ","int((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)/(e*x+d)^4,x)","-\frac{c d}{\left(e x +d \right) e^{2}}-\frac{a \,e^{2}-c \,d^{2}}{2 \left(e x +d \right)^{2} e^{2}}"," ",0,"-c*d/e^2/(e*x+d)-1/2*(a*e^2-c*d^2)/e^2/(e*x+d)^2","A"
1837,1,40,36,0.047000," ","int((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)/(e*x+d)^5,x)","-\frac{c d}{2 \left(e x +d \right)^{2} e^{2}}-\frac{a \,e^{2}-c \,d^{2}}{3 \left(e x +d \right)^{3} e^{2}}"," ",0,"-1/2*c*d/e^2/(e*x+d)^2-1/3*(a*e^2-c*d^2)/e^2/(e*x+d)^3","A"
1838,1,40,36,0.053000," ","int((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)/(e*x+d)^6,x)","-\frac{c d}{3 \left(e x +d \right)^{3} e^{2}}-\frac{a \,e^{2}-c \,d^{2}}{4 \left(e x +d \right)^{4} e^{2}}"," ",0,"-1/4*(a*e^2-c*d^2)/e^2/(e*x+d)^4-1/3*c*d/e^2/(e*x+d)^3","A"
1839,1,295,71,0.049000," ","int((e*x+d)^2*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x)","\frac{c^{2} d^{2} e^{4} x^{7}}{7}+a^{2} d^{4} e^{2} x +\frac{\left(2 c^{2} d^{3} e^{3}+2 \left(a \,e^{2}+c \,d^{2}\right) c d \,e^{3}\right) x^{6}}{6}+\frac{\left(c^{2} d^{4} e^{2}+4 \left(a \,e^{2}+c \,d^{2}\right) c \,d^{2} e^{2}+\left(2 a c \,d^{2} e^{2}+\left(a \,e^{2}+c \,d^{2}\right)^{2}\right) e^{2}\right) x^{5}}{5}+\frac{\left(2 \left(a \,e^{2}+c \,d^{2}\right) a d \,e^{3}+2 \left(a \,e^{2}+c \,d^{2}\right) c \,d^{3} e +2 \left(2 a c \,d^{2} e^{2}+\left(a \,e^{2}+c \,d^{2}\right)^{2}\right) d e \right) x^{4}}{4}+\frac{\left(a^{2} d^{2} e^{4}+4 \left(a \,e^{2}+c \,d^{2}\right) a \,d^{2} e^{2}+\left(2 a c \,d^{2} e^{2}+\left(a \,e^{2}+c \,d^{2}\right)^{2}\right) d^{2}\right) x^{3}}{3}+\frac{\left(2 a^{2} d^{3} e^{3}+2 \left(a \,e^{2}+c \,d^{2}\right) a \,d^{3} e \right) x^{2}}{2}"," ",0,"1/7*e^4*d^2*c^2*x^7+1/6*(2*d^3*e^3*c^2+2*e^3*(a*e^2+c*d^2)*d*c)*x^6+1/5*(d^4*c^2*e^2+4*d^2*e^2*(a*e^2+c*d^2)*c+e^2*(2*a*c*d^2*e^2+(a*e^2+c*d^2)^2))*x^5+1/4*(2*d^3*(a*e^2+c*d^2)*c*e+2*d*e*(2*a*c*d^2*e^2+(a*e^2+c*d^2)^2)+2*e^3*a*d*(a*e^2+c*d^2))*x^4+1/3*(d^2*(2*a*c*d^2*e^2+(a*e^2+c*d^2)^2)+4*d^2*e^2*a*(a*e^2+c*d^2)+e^4*a^2*d^2)*x^3+1/2*(2*d^3*a*e*(a*e^2+c*d^2)+2*d^3*e^3*a^2)*x^2+d^4*a^2*e^2*x","B"
1840,1,195,71,0.050000," ","int((e*x+d)*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x)","\frac{c^{2} d^{2} e^{3} x^{6}}{6}+a^{2} d^{3} e^{2} x +\frac{\left(c^{2} d^{3} e^{2}+2 \left(a \,e^{2}+c \,d^{2}\right) c d \,e^{2}\right) x^{5}}{5}+\frac{\left(2 \left(a \,e^{2}+c \,d^{2}\right) c \,d^{2} e +\left(2 a c \,d^{2} e^{2}+\left(a \,e^{2}+c \,d^{2}\right)^{2}\right) e \right) x^{4}}{4}+\frac{\left(2 \left(a \,e^{2}+c \,d^{2}\right) a d \,e^{2}+\left(2 a c \,d^{2} e^{2}+\left(a \,e^{2}+c \,d^{2}\right)^{2}\right) d \right) x^{3}}{3}+\frac{\left(a^{2} d^{2} e^{3}+2 \left(a \,e^{2}+c \,d^{2}\right) a \,d^{2} e \right) x^{2}}{2}"," ",0,"1/6*d^2*c^2*e^3*x^6+1/5*(d^3*c^2*e^2+2*e^2*(a*e^2+c*d^2)*d*c)*x^5+1/4*(2*d^2*(a*e^2+c*d^2)*c*e+e*(2*a*c*d^2*e^2+(a*e^2+c*d^2)^2))*x^4+1/3*(d*(2*a*c*d^2*e^2+(a*e^2+c*d^2)^2)+2*e^2*a*d*(a*e^2+c*d^2))*x^3+1/2*(2*d^2*a*e*(a*e^2+c*d^2)+a^2*d^2*e^3)*x^2+a^2*d^3*e^2*x","B"
1841,1,93,71,0.041000," ","int((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x)","\frac{c^{2} d^{2} e^{2} x^{5}}{5}+a^{2} d^{2} e^{2} x +\frac{\left(a \,e^{2}+c \,d^{2}\right) c d e \,x^{4}}{2}+\left(a \,e^{2}+c \,d^{2}\right) a d e \,x^{2}+\frac{\left(2 a c \,d^{2} e^{2}+\left(a \,e^{2}+c \,d^{2}\right)^{2}\right) x^{3}}{3}"," ",0,"1/5*d^2*c^2*e^2*x^5+1/2*(a*e^2+c*d^2)*d*c*e*x^4+1/3*(2*a*c*d^2*e^2+(a*e^2+c*d^2)^2)*x^3+a*d*e*(a*e^2+c*d^2)*x^2+a^2*d^2*e^2*x","A"
1842,1,77,50,0.053000," ","int((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2/(e*x+d),x)","\frac{c^{2} d^{2} e \,x^{4}}{4}+a^{2} d \,e^{2} x +\frac{\left(a c d \,e^{2}+\left(a \,e^{2}+c \,d^{2}\right) c d \right) x^{3}}{3}+\frac{\left(a c \,d^{2} e +\left(a \,e^{2}+c \,d^{2}\right) a e \right) x^{2}}{2}"," ",0,"1/4*c^2*d^2*e*x^4+1/3*(a*c*d*e^2+c*d*(a*e^2+c*d^2))*x^3+1/2*(a*e*(a*e^2+c*d^2)+c*d^2*a*e)*x^2+a^2*e^2*d*x","A"
1843,1,19,18,0.047000," ","int((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2/(e*x+d)^2,x)","\frac{\left(c d x +a e \right)^{3}}{3 c d}"," ",0,"1/3*(c*d*x+a*e)^3/c/d","A"
1844,1,77,60,0.049000," ","int((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2/(e*x+d)^3,x)","\frac{c^{2} d^{2} x^{2}}{2 e}+a^{2} e \ln \left(e x +d \right)-\frac{2 a c \,d^{2} \ln \left(e x +d \right)}{e}+2 a c d x +\frac{c^{2} d^{4} \ln \left(e x +d \right)}{e^{3}}-\frac{c^{2} d^{3} x}{e^{2}}"," ",0,"1/2*c^2*d^2/e*x^2+2*x*a*c*d-c^2*d^3/e^2*x+e*ln(e*x+d)*a^2-2/e*ln(e*x+d)*a*c*d^2+1/e^3*ln(e*x+d)*c^2*d^4","A"
1845,1,92,63,0.049000," ","int((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2/(e*x+d)^4,x)","-\frac{a^{2} e}{e x +d}+\frac{2 a c \,d^{2}}{\left(e x +d \right) e}+\frac{2 a c d \ln \left(e x +d \right)}{e}-\frac{c^{2} d^{4}}{\left(e x +d \right) e^{3}}-\frac{2 c^{2} d^{3} \ln \left(e x +d \right)}{e^{3}}+\frac{c^{2} d^{2} x}{e^{2}}"," ",0,"c^2*d^2*x/e^2-e/(e*x+d)*a^2+2/e/(e*x+d)*a*c*d^2-1/e^3/(e*x+d)*c^2*d^4+2*d*c/e*ln(e*x+d)*a-2*d^3*c^2/e^3*ln(e*x+d)","A"
1846,1,98,69,0.047000," ","int((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2/(e*x+d)^5,x)","-\frac{a^{2} e}{2 \left(e x +d \right)^{2}}+\frac{a c \,d^{2}}{\left(e x +d \right)^{2} e}-\frac{c^{2} d^{4}}{2 \left(e x +d \right)^{2} e^{3}}-\frac{2 a c d}{\left(e x +d \right) e}+\frac{2 c^{2} d^{3}}{\left(e x +d \right) e^{3}}+\frac{c^{2} d^{2} \ln \left(e x +d \right)}{e^{3}}"," ",0,"-2*d*c/e/(e*x+d)*a+2*d^3*c^2/e^3/(e*x+d)-1/2*e/(e*x+d)^2*a^2+1/e/(e*x+d)^2*a*c*d^2-1/2/e^3/(e*x+d)^2*c^2*d^4+c^2*d^2*ln(e*x+d)/e^3","A"
1847,1,83,33,0.050000," ","int((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2/(e*x+d)^6,x)","-\frac{c^{2} d^{2}}{\left(e x +d \right) e^{3}}-\frac{\left(a \,e^{2}-c \,d^{2}\right) c d}{\left(e x +d \right)^{2} e^{3}}-\frac{a^{2} e^{4}-2 a c \,d^{2} e^{2}+c^{2} d^{4}}{3 \left(e x +d \right)^{3} e^{3}}"," ",0,"-d^2/e^3*c^2/(e*x+d)-c*d*(a*e^2-c*d^2)/e^3/(e*x+d)^2-1/3*(a^2*e^4-2*a*c*d^2*e^2+c^2*d^4)/e^3/(e*x+d)^3","B"
1848,1,83,71,0.051000," ","int((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2/(e*x+d)^7,x)","-\frac{c^{2} d^{2}}{2 \left(e x +d \right)^{2} e^{3}}-\frac{2 \left(a \,e^{2}-c \,d^{2}\right) c d}{3 \left(e x +d \right)^{3} e^{3}}-\frac{a^{2} e^{4}-2 a c \,d^{2} e^{2}+c^{2} d^{4}}{4 \left(e x +d \right)^{4} e^{3}}"," ",0,"-1/2*c^2*d^2/e^3/(e*x+d)^2-1/4*(a^2*e^4-2*a*c*d^2*e^2+c^2*d^4)/e^3/(e*x+d)^4-2/3*c*d*(a*e^2-c*d^2)/e^3/(e*x+d)^3","A"
1849,1,83,71,0.063000," ","int((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2/(e*x+d)^8,x)","-\frac{c^{2} d^{2}}{3 \left(e x +d \right)^{3} e^{3}}-\frac{\left(a \,e^{2}-c \,d^{2}\right) c d}{2 \left(e x +d \right)^{4} e^{3}}-\frac{a^{2} e^{4}-2 a c \,d^{2} e^{2}+c^{2} d^{4}}{5 \left(e x +d \right)^{5} e^{3}}"," ",0,"-1/5*(a^2*e^4-2*a*c*d^2*e^2+c^2*d^4)/e^3/(e*x+d)^5-1/2*c*d*(a*e^2-c*d^2)/e^3/(e*x+d)^4-1/3*c^2*d^2/e^3/(e*x+d)^3","A"
1850,1,83,71,0.051000," ","int((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2/(e*x+d)^9,x)","-\frac{c^{2} d^{2}}{4 \left(e x +d \right)^{4} e^{3}}-\frac{2 \left(a \,e^{2}-c \,d^{2}\right) c d}{5 \left(e x +d \right)^{5} e^{3}}-\frac{a^{2} e^{4}-2 a c \,d^{2} e^{2}+c^{2} d^{4}}{6 \left(e x +d \right)^{6} e^{3}}"," ",0,"-1/6*(a^2*e^4-2*a*c*d^2*e^2+c^2*d^4)/e^3/(e*x+d)^6-2/5*c*d*(a*e^2-c*d^2)/e^3/(e*x+d)^5-1/4*c^2*d^2/e^3/(e*x+d)^4","A"
1851,1,801,103,0.041000," ","int((e*x+d)^2*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x)","\frac{c^{3} d^{3} e^{5} x^{9}}{9}+a^{3} d^{5} e^{3} x +\frac{\left(2 c^{3} d^{4} e^{4}+3 \left(a \,e^{2}+c \,d^{2}\right) c^{2} d^{2} e^{4}\right) x^{8}}{8}+\frac{\left(c^{3} d^{5} e^{3}+6 \left(a \,e^{2}+c \,d^{2}\right) c^{2} d^{3} e^{3}+\left(a \,c^{2} d^{3} e^{3}+2 \left(a \,e^{2}+c \,d^{2}\right)^{2} c d e +\left(2 a c \,d^{2} e^{2}+\left(a \,e^{2}+c \,d^{2}\right)^{2}\right) c d e \right) e^{2}\right) x^{7}}{7}+\frac{\left(3 \left(a \,e^{2}+c \,d^{2}\right) c^{2} d^{4} e^{2}+2 \left(a \,c^{2} d^{3} e^{3}+2 \left(a \,e^{2}+c \,d^{2}\right)^{2} c d e +\left(2 a c \,d^{2} e^{2}+\left(a \,e^{2}+c \,d^{2}\right)^{2}\right) c d e \right) d e +\left(4 \left(a \,e^{2}+c \,d^{2}\right) a c \,d^{2} e^{2}+\left(a \,e^{2}+c \,d^{2}\right) \left(2 a c \,d^{2} e^{2}+\left(a \,e^{2}+c \,d^{2}\right)^{2}\right)\right) e^{2}\right) x^{6}}{6}+\frac{\left(\left(a \,c^{2} d^{3} e^{3}+2 \left(a \,e^{2}+c \,d^{2}\right)^{2} c d e +\left(2 a c \,d^{2} e^{2}+\left(a \,e^{2}+c \,d^{2}\right)^{2}\right) c d e \right) d^{2}+2 \left(4 \left(a \,e^{2}+c \,d^{2}\right) a c \,d^{2} e^{2}+\left(a \,e^{2}+c \,d^{2}\right) \left(2 a c \,d^{2} e^{2}+\left(a \,e^{2}+c \,d^{2}\right)^{2}\right)\right) d e +\left(a^{2} c \,d^{3} e^{3}+\left(2 a c \,d^{2} e^{2}+\left(a \,e^{2}+c \,d^{2}\right)^{2}\right) a d e +2 \left(a \,e^{2}+c \,d^{2}\right)^{2} a d e \right) e^{2}\right) x^{5}}{5}+\frac{\left(3 \left(a \,e^{2}+c \,d^{2}\right) a^{2} d^{2} e^{4}+\left(4 \left(a \,e^{2}+c \,d^{2}\right) a c \,d^{2} e^{2}+\left(a \,e^{2}+c \,d^{2}\right) \left(2 a c \,d^{2} e^{2}+\left(a \,e^{2}+c \,d^{2}\right)^{2}\right)\right) d^{2}+2 \left(a^{2} c \,d^{3} e^{3}+\left(2 a c \,d^{2} e^{2}+\left(a \,e^{2}+c \,d^{2}\right)^{2}\right) a d e +2 \left(a \,e^{2}+c \,d^{2}\right)^{2} a d e \right) d e \right) x^{4}}{4}+\frac{\left(a^{3} d^{3} e^{5}+6 \left(a \,e^{2}+c \,d^{2}\right) a^{2} d^{3} e^{3}+\left(a^{2} c \,d^{3} e^{3}+\left(2 a c \,d^{2} e^{2}+\left(a \,e^{2}+c \,d^{2}\right)^{2}\right) a d e +2 \left(a \,e^{2}+c \,d^{2}\right)^{2} a d e \right) d^{2}\right) x^{3}}{3}+\frac{\left(2 a^{3} d^{4} e^{4}+3 \left(a \,e^{2}+c \,d^{2}\right) a^{2} d^{4} e^{2}\right) x^{2}}{2}"," ",0,"1/9*e^5*d^3*c^3*x^9+1/8*(2*d^4*e^4*c^3+3*e^4*(a*e^2+c*d^2)*d^2*c^2)*x^8+1/7*(d^5*c^3*e^3+6*d^3*e^3*(a*e^2+c*d^2)*c^2+e^2*(a*d^3*e^3*c^2+2*(a*e^2+c*d^2)^2*d*c*e+d*c*e*(2*a*c*d^2*e^2+(a*e^2+c*d^2)^2)))*x^7+1/6*(3*d^4*(a*e^2+c*d^2)*c^2*e^2+2*d*e*(a*d^3*e^3*c^2+2*(a*e^2+c*d^2)^2*d*c*e+d*c*e*(2*a*c*d^2*e^2+(a*e^2+c*d^2)^2))+e^2*(4*a*d^2*e^2*(a*e^2+c*d^2)*c+(a*e^2+c*d^2)*(2*a*c*d^2*e^2+(a*e^2+c*d^2)^2)))*x^6+1/5*(d^2*(a*d^3*e^3*c^2+2*(a*e^2+c*d^2)^2*d*c*e+d*c*e*(2*a*c*d^2*e^2+(a*e^2+c*d^2)^2))+2*d*e*(4*a*d^2*e^2*(a*e^2+c*d^2)*c+(a*e^2+c*d^2)*(2*a*c*d^2*e^2+(a*e^2+c*d^2)^2))+e^2*(a*d*e*(2*a*c*d^2*e^2+(a*e^2+c*d^2)^2)+2*(a*e^2+c*d^2)^2*a*d*e+d^3*c*e^3*a^2))*x^5+1/4*(d^2*(4*a*d^2*e^2*(a*e^2+c*d^2)*c+(a*e^2+c*d^2)*(2*a*c*d^2*e^2+(a*e^2+c*d^2)^2))+2*d*e*(a*d*e*(2*a*c*d^2*e^2+(a*e^2+c*d^2)^2)+2*(a*e^2+c*d^2)^2*a*d*e+d^3*c*e^3*a^2)+3*e^4*a^2*d^2*(a*e^2+c*d^2))*x^4+1/3*(d^2*(a*d*e*(2*a*c*d^2*e^2+(a*e^2+c*d^2)^2)+2*(a*e^2+c*d^2)^2*a*d*e+d^3*c*e^3*a^2)+6*d^3*e^3*a^2*(a*e^2+c*d^2)+e^5*a^3*d^3)*x^3+1/2*(3*d^4*a^2*e^2*(a*e^2+c*d^2)+2*d^4*e^4*a^3)*x^2+d^5*a^3*e^3*x","B"
1852,1,531,103,0.051000," ","int((e*x+d)*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x)","\frac{c^{3} d^{3} e^{4} x^{8}}{8}+a^{3} d^{4} e^{3} x +\frac{\left(c^{3} d^{4} e^{3}+3 \left(a \,e^{2}+c \,d^{2}\right) c^{2} d^{2} e^{3}\right) x^{7}}{7}+\frac{\left(3 \left(a \,e^{2}+c \,d^{2}\right) c^{2} d^{3} e^{2}+\left(a \,c^{2} d^{3} e^{3}+2 \left(a \,e^{2}+c \,d^{2}\right)^{2} c d e +\left(2 a c \,d^{2} e^{2}+\left(a \,e^{2}+c \,d^{2}\right)^{2}\right) c d e \right) e \right) x^{6}}{6}+\frac{\left(\left(a \,c^{2} d^{3} e^{3}+2 \left(a \,e^{2}+c \,d^{2}\right)^{2} c d e +\left(2 a c \,d^{2} e^{2}+\left(a \,e^{2}+c \,d^{2}\right)^{2}\right) c d e \right) d +\left(4 \left(a \,e^{2}+c \,d^{2}\right) a c \,d^{2} e^{2}+\left(a \,e^{2}+c \,d^{2}\right) \left(2 a c \,d^{2} e^{2}+\left(a \,e^{2}+c \,d^{2}\right)^{2}\right)\right) e \right) x^{5}}{5}+\frac{\left(\left(4 \left(a \,e^{2}+c \,d^{2}\right) a c \,d^{2} e^{2}+\left(a \,e^{2}+c \,d^{2}\right) \left(2 a c \,d^{2} e^{2}+\left(a \,e^{2}+c \,d^{2}\right)^{2}\right)\right) d +\left(a^{2} c \,d^{3} e^{3}+\left(2 a c \,d^{2} e^{2}+\left(a \,e^{2}+c \,d^{2}\right)^{2}\right) a d e +2 \left(a \,e^{2}+c \,d^{2}\right)^{2} a d e \right) e \right) x^{4}}{4}+\frac{\left(3 \left(a \,e^{2}+c \,d^{2}\right) a^{2} d^{2} e^{3}+\left(a^{2} c \,d^{3} e^{3}+\left(2 a c \,d^{2} e^{2}+\left(a \,e^{2}+c \,d^{2}\right)^{2}\right) a d e +2 \left(a \,e^{2}+c \,d^{2}\right)^{2} a d e \right) d \right) x^{3}}{3}+\frac{\left(a^{3} d^{3} e^{4}+3 \left(a \,e^{2}+c \,d^{2}\right) a^{2} d^{3} e^{2}\right) x^{2}}{2}"," ",0,"1/8*d^3*c^3*e^4*x^8+1/7*(d^4*c^3*e^3+3*e^3*(a*e^2+c*d^2)*d^2*c^2)*x^7+1/6*(3*d^3*(a*e^2+c*d^2)*c^2*e^2+e*(a*c^2*d^3*e^3+2*(a*e^2+c*d^2)^2*c*d*e+(2*a*c*d^2*e^2+(a*e^2+c*d^2)^2)*c*d*e))*x^6+1/5*(d*(a*c^2*d^3*e^3+2*(a*e^2+c*d^2)^2*c*d*e+(2*a*c*d^2*e^2+(a*e^2+c*d^2)^2)*c*d*e)+e*(4*(a*e^2+c*d^2)*a*c*d^2*e^2+(a*e^2+c*d^2)*(2*a*c*d^2*e^2+(a*e^2+c*d^2)^2)))*x^5+1/4*(d*(4*(a*e^2+c*d^2)*a*c*d^2*e^2+(a*e^2+c*d^2)*(2*a*c*d^2*e^2+(a*e^2+c*d^2)^2))+e*(a^2*c*d^3*e^3+(2*a*c*d^2*e^2+(a*e^2+c*d^2)^2)*a*d*e+2*(a*e^2+c*d^2)^2*a*d*e))*x^4+1/3*(d*(a^2*c*d^3*e^3+(2*a*c*d^2*e^2+(a*e^2+c*d^2)^2)*a*d*e+2*(a*e^2+c*d^2)^2*a*d*e)+3*e^3*a^2*d^2*(a*e^2+c*d^2))*x^3+1/2*(3*d^3*a^2*e^2*(a*e^2+c*d^2)+a^3*d^3*e^4)*x^2+a^3*d^4*e^3*x","B"
1853,1,266,103,0.060000," ","int((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x)","\frac{c^{3} d^{3} e^{3} x^{7}}{7}+\frac{\left(a \,e^{2}+c \,d^{2}\right) c^{2} d^{2} e^{2} x^{6}}{2}+a^{3} d^{3} e^{3} x +\frac{3 \left(a \,e^{2}+c \,d^{2}\right) a^{2} d^{2} e^{2} x^{2}}{2}+\frac{\left(a \,c^{2} d^{3} e^{3}+2 \left(a \,e^{2}+c \,d^{2}\right)^{2} c d e +\left(2 a c \,d^{2} e^{2}+\left(a \,e^{2}+c \,d^{2}\right)^{2}\right) c d e \right) x^{5}}{5}+\frac{\left(4 \left(a \,e^{2}+c \,d^{2}\right) a c \,d^{2} e^{2}+\left(a \,e^{2}+c \,d^{2}\right) \left(2 a c \,d^{2} e^{2}+\left(a \,e^{2}+c \,d^{2}\right)^{2}\right)\right) x^{4}}{4}+\frac{\left(a^{2} c \,d^{3} e^{3}+\left(2 a c \,d^{2} e^{2}+\left(a \,e^{2}+c \,d^{2}\right)^{2}\right) a d e +2 \left(a \,e^{2}+c \,d^{2}\right)^{2} a d e \right) x^{3}}{3}"," ",0,"1/7*d^3*c^3*e^3*x^7+1/2*(a*e^2+c*d^2)*d^2*c^2*e^2*x^6+1/5*(a*c^2*d^3*e^3+2*(a*e^2+c*d^2)^2*c*d*e+(2*a*c*d^2*e^2+(a*e^2+c*d^2)^2)*c*d*e)*x^5+1/4*(4*(a*e^2+c*d^2)*a*c*d^2*e^2+(a*e^2+c*d^2)*(2*a*c*d^2*e^2+(a*e^2+c*d^2)^2))*x^4+1/3*(a^2*c*d^3*e^3+(2*a*c*d^2*e^2+(a*e^2+c*d^2)^2)*a*d*e+2*(a*e^2+c*d^2)^2*a*d*e)*x^3+3/2*a^2*d^2*e^2*(a*e^2+c*d^2)*x^2+a^3*d^3*e^3*x","B"
1854,1,205,85,0.038000," ","int((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3/(e*x+d),x)","\frac{c^{3} d^{3} e^{2} x^{6}}{6}+a^{3} d^{2} e^{3} x +\frac{\left(a \,c^{2} d^{2} e^{3}+2 \left(a \,e^{2}+c \,d^{2}\right) c^{2} d^{2} e \right) x^{5}}{5}+\frac{\left(2 \left(a \,e^{2}+c \,d^{2}\right) a c d \,e^{2}+\left(2 a c \,d^{2} e^{2}+\left(a \,e^{2}+c \,d^{2}\right)^{2}\right) c d \right) x^{4}}{4}+\frac{\left(2 \left(a \,e^{2}+c \,d^{2}\right) a c \,d^{2} e +\left(2 a c \,d^{2} e^{2}+\left(a \,e^{2}+c \,d^{2}\right)^{2}\right) a e \right) x^{3}}{3}+\frac{\left(a^{2} c \,d^{3} e^{2}+2 \left(a \,e^{2}+c \,d^{2}\right) a^{2} d \,e^{2}\right) x^{2}}{2}"," ",0,"1/6*c^3*d^3*e^2*x^6+1/5*(a*e^3*d^2*c^2+2*c^2*d^2*(a*e^2+c*d^2)*e)*x^5+1/4*(2*a*e^2*(a*e^2+c*d^2)*d*c+c*d*(2*a*c*d^2*e^2+(a*e^2+c*d^2)^2))*x^4+1/3*(a*e*(2*a*c*d^2*e^2+(a*e^2+c*d^2)^2)+2*c*d^2*a*e*(a*e^2+c*d^2))*x^3+1/2*(2*a^2*e^2*d*(a*e^2+c*d^2)+c*d^3*a^2*e^2)*x^2+a^3*e^3*d^2*x","B"
1855,1,136,50,0.043000," ","int((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3/(e*x+d)^2,x)","\frac{c^{3} d^{3} e \,x^{5}}{5}+a^{3} d \,e^{3} x +\frac{\left(2 a \,c^{2} d^{2} e^{2}+\left(a \,e^{2}+c \,d^{2}\right) c^{2} d^{2}\right) x^{4}}{4}+\frac{\left(a^{2} c d \,e^{3}+a \,c^{2} d^{3} e +2 \left(a \,e^{2}+c \,d^{2}\right) a c d e \right) x^{3}}{3}+\frac{\left(2 a^{2} c \,d^{2} e^{2}+\left(a \,e^{2}+c \,d^{2}\right) a^{2} e^{2}\right) x^{2}}{2}"," ",0,"1/5*c^3*d^3*e*x^5+1/4*(2*a*c^2*d^2*e^2+c^2*d^2*(a*e^2+c*d^2))*x^4+1/3*(a^2*e^3*d*c+2*a*c*d*e*(a*e^2+c*d^2)+c^2*d^3*a*e)*x^3+1/2*(a^2*e^2*(a*e^2+c*d^2)+2*a^2*c*d^2*e^2)*x^2+a^3*e^3*d*x","B"
1856,1,19,18,0.041000," ","int((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3/(e*x+d)^3,x)","\frac{\left(c d x +a e \right)^{4}}{4 c d}"," ",0,"1/4*(c*d*x+a*e)^4/c/d","A"
1857,1,138,85,0.041000," ","int((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3/(e*x+d)^4,x)","\frac{c^{3} d^{3} x^{3}}{3 e}+\frac{3 a \,c^{2} d^{2} x^{2}}{2}-\frac{c^{3} d^{4} x^{2}}{2 e^{2}}+a^{3} e^{2} \ln \left(e x +d \right)-3 a^{2} c \,d^{2} \ln \left(e x +d \right)+3 a^{2} c d e x +\frac{3 a \,c^{2} d^{4} \ln \left(e x +d \right)}{e^{2}}-\frac{3 a \,c^{2} d^{3} x}{e}-\frac{c^{3} d^{6} \ln \left(e x +d \right)}{e^{4}}+\frac{c^{3} d^{5} x}{e^{3}}"," ",0,"1/3*c^3*d^3/e*x^3+3/2*x^2*a*c^2*d^2-1/2*c^3*d^4/e^2*x^2+3*c*d*e*a^2*x-3*c^2*d^3/e*a*x+c^3*d^5/e^3*x+e^2*ln(e*x+d)*a^3-3*ln(e*x+d)*a^2*c*d^2+3/e^2*ln(e*x+d)*a*c^2*d^4-1/e^4*ln(e*x+d)*c^3*d^6","A"
1858,1,156,92,0.052000," ","int((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3/(e*x+d)^5,x)","\frac{c^{3} d^{3} x^{2}}{2 e^{2}}-\frac{a^{3} e^{2}}{e x +d}+\frac{3 a^{2} c \,d^{2}}{e x +d}+3 a^{2} c d \ln \left(e x +d \right)-\frac{3 a \,c^{2} d^{4}}{\left(e x +d \right) e^{2}}-\frac{6 a \,c^{2} d^{3} \ln \left(e x +d \right)}{e^{2}}+\frac{3 a \,c^{2} d^{2} x}{e}+\frac{c^{3} d^{6}}{\left(e x +d \right) e^{4}}+\frac{3 c^{3} d^{5} \ln \left(e x +d \right)}{e^{4}}-\frac{2 c^{3} d^{4} x}{e^{3}}"," ",0,"1/2*c^3*d^3*x^2/e^2+3*c^2*d^2/e*a*x-2*c^3*d^4/e^3*x-e^2/(e*x+d)*a^3+3/(e*x+d)*a^2*c*d^2-3/e^2/(e*x+d)*a*c^2*d^4+1/e^4/(e*x+d)*c^3*d^6+3*d*c*ln(e*x+d)*a^2-6*d^3*c^2/e^2*ln(e*x+d)*a+3*d^5*c^3/e^4*ln(e*x+d)","A"
1859,1,167,95,0.052000," ","int((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3/(e*x+d)^6,x)","-\frac{a^{3} e^{2}}{2 \left(e x +d \right)^{2}}+\frac{3 a^{2} c \,d^{2}}{2 \left(e x +d \right)^{2}}-\frac{3 a \,c^{2} d^{4}}{2 \left(e x +d \right)^{2} e^{2}}+\frac{c^{3} d^{6}}{2 \left(e x +d \right)^{2} e^{4}}-\frac{3 a^{2} c d}{e x +d}+\frac{6 a \,c^{2} d^{3}}{\left(e x +d \right) e^{2}}+\frac{3 a \,c^{2} d^{2} \ln \left(e x +d \right)}{e^{2}}-\frac{3 c^{3} d^{5}}{\left(e x +d \right) e^{4}}-\frac{3 c^{3} d^{4} \ln \left(e x +d \right)}{e^{4}}+\frac{c^{3} d^{3} x}{e^{3}}"," ",0,"c^3*d^3*x/e^3-3*d*c/(e*x+d)*a^2+6*d^3*c^2/e^2/(e*x+d)*a-3*d^5*c^3/e^4/(e*x+d)-1/2*e^2/(e*x+d)^2*a^3+3/2/(e*x+d)^2*a^2*c*d^2-3/2/e^2/(e*x+d)^2*a*c^2*d^4+1/2/e^4/(e*x+d)^2*c^3*d^6+3*c^2*d^2/e^2*ln(e*x+d)*a-3*c^3*d^4/e^4*ln(e*x+d)","A"
1860,1,173,101,0.047000," ","int((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3/(e*x+d)^7,x)","-\frac{a^{3} e^{2}}{3 \left(e x +d \right)^{3}}+\frac{a^{2} c \,d^{2}}{\left(e x +d \right)^{3}}-\frac{a \,c^{2} d^{4}}{\left(e x +d \right)^{3} e^{2}}+\frac{c^{3} d^{6}}{3 \left(e x +d \right)^{3} e^{4}}-\frac{3 a^{2} c d}{2 \left(e x +d \right)^{2}}+\frac{3 a \,c^{2} d^{3}}{\left(e x +d \right)^{2} e^{2}}-\frac{3 c^{3} d^{5}}{2 \left(e x +d \right)^{2} e^{4}}-\frac{3 a \,c^{2} d^{2}}{\left(e x +d \right) e^{2}}+\frac{3 c^{3} d^{4}}{\left(e x +d \right) e^{4}}+\frac{c^{3} d^{3} \ln \left(e x +d \right)}{e^{4}}"," ",0,"-3*c^2*d^2/e^2/(e*x+d)*a+3*c^3*d^4/e^4/(e*x+d)-3/2*c*d/(e*x+d)^2*a^2+3*c^2*d^3/e^2/(e*x+d)^2*a-3/2*c^3*d^5/e^4/(e*x+d)^2-1/3*e^2/(e*x+d)^3*a^3+1/(e*x+d)^3*a^2*c*d^2-1/e^2/(e*x+d)^3*a*c^2*d^4+1/3/e^4/(e*x+d)^3*c^3*d^6+c^3*d^3*ln(e*x+d)/e^4","A"
1861,1,141,33,0.052000," ","int((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3/(e*x+d)^8,x)","-\frac{c^{3} d^{3}}{\left(e x +d \right) e^{4}}-\frac{3 \left(a \,e^{2}-c \,d^{2}\right) c^{2} d^{2}}{2 \left(e x +d \right)^{2} e^{4}}-\frac{\left(a^{2} e^{4}-2 a c \,d^{2} e^{2}+c^{2} d^{4}\right) c d}{\left(e x +d \right)^{3} e^{4}}-\frac{a^{3} e^{6}-3 a^{2} c \,d^{2} e^{4}+3 a \,c^{2} d^{4} e^{2}-c^{3} d^{6}}{4 \left(e x +d \right)^{4} e^{4}}"," ",0,"-d^3/e^4*c^3/(e*x+d)-3/2*c^2*d^2*(a*e^2-c*d^2)/e^4/(e*x+d)^2-1/4*(a^3*e^6-3*a^2*c*d^2*e^4+3*a*c^2*d^4*e^2-c^3*d^6)/e^4/(e*x+d)^4-c*d*(a^2*e^4-2*a*c*d^2*e^2+c^2*d^4)/e^4/(e*x+d)^3","B"
1862,1,141,69,0.061000," ","int((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3/(e*x+d)^9,x)","-\frac{c^{3} d^{3}}{2 \left(e x +d \right)^{2} e^{4}}-\frac{\left(a \,e^{2}-c \,d^{2}\right) c^{2} d^{2}}{\left(e x +d \right)^{3} e^{4}}-\frac{3 \left(a^{2} e^{4}-2 a c \,d^{2} e^{2}+c^{2} d^{4}\right) c d}{4 \left(e x +d \right)^{4} e^{4}}-\frac{a^{3} e^{6}-3 a^{2} c \,d^{2} e^{4}+3 a \,c^{2} d^{4} e^{2}-c^{3} d^{6}}{5 \left(e x +d \right)^{5} e^{4}}"," ",0,"-1/5*(a^3*e^6-3*a^2*c*d^2*e^4+3*a*c^2*d^4*e^2-c^3*d^6)/e^4/(e*x+d)^5-1/2*d^3/e^4*c^3/(e*x+d)^2-3/4*c*d*(a^2*e^4-2*a*c*d^2*e^2+c^2*d^4)/e^4/(e*x+d)^4-c^2*d^2*(a*e^2-c*d^2)/e^4/(e*x+d)^3","B"
1863,1,141,103,0.048000," ","int((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3/(e*x+d)^10,x)","-\frac{c^{3} d^{3}}{3 \left(e x +d \right)^{3} e^{4}}-\frac{3 \left(a \,e^{2}-c \,d^{2}\right) c^{2} d^{2}}{4 \left(e x +d \right)^{4} e^{4}}-\frac{3 \left(a^{2} e^{4}-2 a c \,d^{2} e^{2}+c^{2} d^{4}\right) c d}{5 \left(e x +d \right)^{5} e^{4}}-\frac{a^{3} e^{6}-3 a^{2} c \,d^{2} e^{4}+3 a \,c^{2} d^{4} e^{2}-c^{3} d^{6}}{6 \left(e x +d \right)^{6} e^{4}}"," ",0,"-1/6*(a^3*e^6-3*a^2*c*d^2*e^4+3*a*c^2*d^4*e^2-c^3*d^6)/e^4/(e*x+d)^6-3/5*c*d*(a^2*e^4-2*a*c*d^2*e^2+c^2*d^4)/e^4/(e*x+d)^5-3/4*c^2*d^2*(a*e^2-c*d^2)/e^4/(e*x+d)^4-1/3*c^3*d^3/e^4/(e*x+d)^3","A"
1864,1,141,103,0.049000," ","int((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3/(e*x+d)^11,x)","-\frac{c^{3} d^{3}}{4 \left(e x +d \right)^{4} e^{4}}-\frac{3 \left(a \,e^{2}-c \,d^{2}\right) c^{2} d^{2}}{5 \left(e x +d \right)^{5} e^{4}}-\frac{\left(a^{2} e^{4}-2 a c \,d^{2} e^{2}+c^{2} d^{4}\right) c d}{2 \left(e x +d \right)^{6} e^{4}}-\frac{a^{3} e^{6}-3 a^{2} c \,d^{2} e^{4}+3 a \,c^{2} d^{4} e^{2}-c^{3} d^{6}}{7 \left(e x +d \right)^{7} e^{4}}"," ",0,"-1/2*c*d*(a^2*e^4-2*a*c*d^2*e^2+c^2*d^4)/e^4/(e*x+d)^6-3/5*c^2*d^2*(a*e^2-c*d^2)/e^4/(e*x+d)^5-1/4*c^3*d^3/e^4/(e*x+d)^4-1/7*(a^3*e^6-3*a^2*c*d^2*e^4+3*a*c^2*d^4*e^2-c^3*d^6)/e^4/(e*x+d)^7","A"
1865,1,239,125,0.055000," ","int((e*x+d)^5/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x)","\frac{e^{4} x^{4}}{4 c d}-\frac{a \,e^{5} x^{3}}{3 c^{2} d^{2}}+\frac{4 e^{3} x^{3}}{3 c}+\frac{a^{2} e^{6} x^{2}}{2 c^{3} d^{3}}-\frac{2 a \,e^{4} x^{2}}{c^{2} d}+\frac{3 d \,e^{2} x^{2}}{c}+\frac{a^{4} e^{8} \ln \left(c d x +a e \right)}{c^{5} d^{5}}-\frac{4 a^{3} e^{6} \ln \left(c d x +a e \right)}{c^{4} d^{3}}-\frac{a^{3} e^{7} x}{c^{4} d^{4}}+\frac{6 a^{2} e^{4} \ln \left(c d x +a e \right)}{c^{3} d}+\frac{4 a^{2} e^{5} x}{c^{3} d^{2}}-\frac{4 a d \,e^{2} \ln \left(c d x +a e \right)}{c^{2}}-\frac{6 a \,e^{3} x}{c^{2}}+\frac{d^{3} \ln \left(c d x +a e \right)}{c}+\frac{4 d^{2} e x}{c}"," ",0,"1/4*e^4/c/d*x^4-1/3*e^5/c^2/d^2*x^3*a+4/3*e^3/c*x^3+1/2*e^6/c^3/d^3*x^2*a^2-2*e^4/c^2/d*x^2*a+3*e^2/c*d*x^2-e^7/c^4/d^4*a^3*x+4*e^5/c^3/d^2*a^2*x-6*e^3/c^2*a*x+4*e/c*d^2*x+1/c^5/d^5*ln(c*d*x+a*e)*a^4*e^8-4/c^4/d^3*ln(c*d*x+a*e)*a^3*e^6+6/c^3/d*ln(c*d*x+a*e)*a^2*e^4-4/c^2*d*ln(c*d*x+a*e)*a*e^2+1/c*d^3*ln(c*d*x+a*e)","A"
1866,1,157,96,0.041000," ","int((e*x+d)^4/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x)","\frac{e^{3} x^{3}}{3 c d}-\frac{a \,e^{4} x^{2}}{2 c^{2} d^{2}}+\frac{3 e^{2} x^{2}}{2 c}-\frac{a^{3} e^{6} \ln \left(c d x +a e \right)}{c^{4} d^{4}}+\frac{3 a^{2} e^{4} \ln \left(c d x +a e \right)}{c^{3} d^{2}}+\frac{a^{2} e^{5} x}{c^{3} d^{3}}-\frac{3 a \,e^{3} x}{c^{2} d}-\frac{3 a \,e^{2} \ln \left(c d x +a e \right)}{c^{2}}+\frac{d^{2} \ln \left(c d x +a e \right)}{c}+\frac{3 d e x}{c}"," ",0,"1/3*e^3/c/d*x^3-1/2*e^4/c^2/d^2*x^2*a+3/2*e^2/c*x^2+e^5/c^3/d^3*a^2*x-3*e^3/c^2/d*a*x+3*e/c*d*x-1/c^4/d^4*ln(c*d*x+a*e)*a^3*e^6+3/c^3/d^2*ln(c*d*x+a*e)*a^2*e^4-3/c^2*ln(c*d*x+a*e)*a*e^2+1/c*d^2*ln(c*d*x+a*e)","A"
1867,1,93,67,0.048000," ","int((e*x+d)^3/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x)","\frac{e^{2} x^{2}}{2 c d}+\frac{a^{2} e^{4} \ln \left(c d x +a e \right)}{c^{3} d^{3}}-\frac{2 a \,e^{2} \ln \left(c d x +a e \right)}{c^{2} d}-\frac{a \,e^{3} x}{c^{2} d^{2}}+\frac{d \ln \left(c d x +a e \right)}{c}+\frac{2 e x}{c}"," ",0,"1/2*e^2/c/d*x^2-e^3/c^2/d^2*a*x+2*e/c*x+1/c^3/d^3*ln(c*d*x+a*e)*a^2*e^4-2/c^2/d*ln(c*d*x+a*e)*a*e^2+1/c*d*ln(c*d*x+a*e)","A"
1868,1,45,38,0.039000," ","int((e*x+d)^2/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x)","-\frac{a \,e^{2} \ln \left(c d x +a e \right)}{c^{2} d^{2}}+\frac{e x}{c d}+\frac{\ln \left(c d x +a e \right)}{c}"," ",0,"e*x/c/d-1/c^2/d^2*ln(c*d*x+a*e)*a*e^2+1/c*ln(c*d*x+a*e)","A"
1869,1,17,16,0.039000," ","int((e*x+d)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x)","\frac{\ln \left(c d x +a e \right)}{c d}"," ",0,"ln(c*d*x+a*e)/c/d","A"
1870,1,48,47,0.053000," ","int(1/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x)","\frac{\ln \left(e x +d \right)}{a \,e^{2}-c \,d^{2}}-\frac{\ln \left(c d x +a e \right)}{a \,e^{2}-c \,d^{2}}"," ",0,"-1/(a*e^2-c*d^2)*ln(c*d*x+a*e)+1/(a*e^2-c*d^2)*ln(e*x+d)","A"
1871,1,75,73,0.053000," ","int(1/(e*x+d)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x)","-\frac{c d \ln \left(e x +d \right)}{\left(a \,e^{2}-c \,d^{2}\right)^{2}}+\frac{c d \ln \left(c d x +a e \right)}{\left(a \,e^{2}-c \,d^{2}\right)^{2}}-\frac{1}{\left(a \,e^{2}-c \,d^{2}\right) \left(e x +d \right)}"," ",0,"c*d/(a*e^2-c*d^2)^2*ln(c*d*x+a*e)-1/(a*e^2-c*d^2)/(e*x+d)-c*d/(a*e^2-c*d^2)^2*ln(e*x+d)","A"
1872,1,107,106,0.047000," ","int(1/(e*x+d)^2/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x)","\frac{c^{2} d^{2} \ln \left(e x +d \right)}{\left(a \,e^{2}-c \,d^{2}\right)^{3}}-\frac{c^{2} d^{2} \ln \left(c d x +a e \right)}{\left(a \,e^{2}-c \,d^{2}\right)^{3}}+\frac{c d}{\left(a \,e^{2}-c \,d^{2}\right)^{2} \left(e x +d \right)}-\frac{1}{2 \left(a \,e^{2}-c \,d^{2}\right) \left(e x +d \right)^{2}}"," ",0,"-c^2*d^2/(a*e^2-c*d^2)^3*ln(c*d*x+a*e)-1/2/(a*e^2-c*d^2)/(e*x+d)^2+c^2*d^2/(a*e^2-c*d^2)^3*ln(e*x+d)+c*d/(a*e^2-c*d^2)^2/(e*x+d)","A"
1873,1,137,135,0.057000," ","int(1/(e*x+d)^3/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x)","-\frac{c^{3} d^{3} \ln \left(e x +d \right)}{\left(a \,e^{2}-c \,d^{2}\right)^{4}}+\frac{c^{3} d^{3} \ln \left(c d x +a e \right)}{\left(a \,e^{2}-c \,d^{2}\right)^{4}}-\frac{c^{2} d^{2}}{\left(a \,e^{2}-c \,d^{2}\right)^{3} \left(e x +d \right)}+\frac{c d}{2 \left(a \,e^{2}-c \,d^{2}\right)^{2} \left(e x +d \right)^{2}}-\frac{1}{3 \left(a \,e^{2}-c \,d^{2}\right) \left(e x +d \right)^{3}}"," ",0,"c^3*d^3/(a*e^2-c*d^2)^4*ln(c*d*x+a*e)-1/3/(a*e^2-c*d^2)/(e*x+d)^3-c^2*d^2/(a*e^2-c*d^2)^3/(e*x+d)+1/2*c*d/(a*e^2-c*d^2)^2/(e*x+d)^2-c^3*d^3/(a*e^2-c*d^2)^4*ln(e*x+d)","A"
1874,1,502,215,0.056000," ","int((e*x+d)^8/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x)","\frac{e^{6} x^{5}}{5 c^{2} d^{2}}-\frac{a \,e^{7} x^{4}}{2 c^{3} d^{3}}+\frac{3 e^{5} x^{4}}{2 c^{2} d}+\frac{a^{2} e^{8} x^{3}}{c^{4} d^{4}}-\frac{4 a \,e^{6} x^{3}}{c^{3} d^{2}}+\frac{5 e^{4} x^{3}}{c^{2}}-\frac{a^{6} e^{12}}{\left(c d x +a e \right) c^{7} d^{7}}+\frac{6 a^{5} e^{10}}{\left(c d x +a e \right) c^{6} d^{5}}-\frac{15 a^{4} e^{8}}{\left(c d x +a e \right) c^{5} d^{3}}+\frac{20 a^{3} e^{6}}{\left(c d x +a e \right) c^{4} d}-\frac{2 a^{3} e^{9} x^{2}}{c^{5} d^{5}}-\frac{15 a^{2} d \,e^{4}}{\left(c d x +a e \right) c^{3}}+\frac{9 a^{2} e^{7} x^{2}}{c^{4} d^{3}}+\frac{6 a \,d^{3} e^{2}}{\left(c d x +a e \right) c^{2}}-\frac{15 a \,e^{5} x^{2}}{c^{3} d}-\frac{d^{5}}{\left(c d x +a e \right) c}+\frac{10 d \,e^{3} x^{2}}{c^{2}}-\frac{6 a^{5} e^{11} \ln \left(c d x +a e \right)}{c^{7} d^{7}}+\frac{30 a^{4} e^{9} \ln \left(c d x +a e \right)}{c^{6} d^{5}}+\frac{5 a^{4} e^{10} x}{c^{6} d^{6}}-\frac{60 a^{3} e^{7} \ln \left(c d x +a e \right)}{c^{5} d^{3}}-\frac{24 a^{3} e^{8} x}{c^{5} d^{4}}+\frac{60 a^{2} e^{5} \ln \left(c d x +a e \right)}{c^{4} d}+\frac{45 a^{2} e^{6} x}{c^{4} d^{2}}-\frac{30 a d \,e^{3} \ln \left(c d x +a e \right)}{c^{3}}-\frac{40 a \,e^{4} x}{c^{3}}+\frac{6 d^{3} e \ln \left(c d x +a e \right)}{c^{2}}+\frac{15 d^{2} e^{2} x}{c^{2}}"," ",0,"e^8/c^4/d^4*x^3*a^2-1/c*d^5/(c*d*x+a*e)+5*e^4/c^2*x^3+3/2*e^5/c^2/d*x^4+10*e^3/c^2*d*x^2-40*e^4/c^3*a*x+15*e^2/c^2*d^2*x+6*d^3/c^2*e*ln(c*d*x+a*e)+1/5*e^6/c^2/d^2*x^5+6/c^6/d^5/(c*d*x+a*e)*a^5*e^10-15/c^5/d^3/(c*d*x+a*e)*a^4*e^8+20/c^4/d/(c*d*x+a*e)*a^3*e^6-15/c^3*d/(c*d*x+a*e)*a^2*e^4+6/c^2*d^3/(c*d*x+a*e)*a*e^2-1/2*e^7/c^3/d^3*x^4*a-6/d^7/c^7*e^11*ln(c*d*x+a*e)*a^5+30/d^5/c^6*e^9*ln(c*d*x+a*e)*a^4-60/d^3/c^5*e^7*ln(c*d*x+a*e)*a^3+60/d/c^4*e^5*ln(c*d*x+a*e)*a^2-30*d/c^3*e^3*ln(c*d*x+a*e)*a-1/c^7/d^7/(c*d*x+a*e)*a^6*e^12-4*e^6/c^3/d^2*x^3*a-2*e^9/c^5/d^5*x^2*a^3+9*e^7/c^4/d^3*x^2*a^2-15*e^5/c^3/d*x^2*a+5*e^10/c^6/d^6*a^4*x-24*e^8/c^5/d^4*a^3*x+45*e^6/c^4/d^2*a^2*x","B"
1875,1,378,180,0.052000," ","int((e*x+d)^7/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x)","\frac{e^{5} x^{4}}{4 c^{2} d^{2}}-\frac{2 a \,e^{6} x^{3}}{3 c^{3} d^{3}}+\frac{5 e^{4} x^{3}}{3 c^{2} d}+\frac{a^{5} e^{10}}{\left(c d x +a e \right) c^{6} d^{6}}-\frac{5 a^{4} e^{8}}{\left(c d x +a e \right) c^{5} d^{4}}+\frac{10 a^{3} e^{6}}{\left(c d x +a e \right) c^{4} d^{2}}-\frac{10 a^{2} e^{4}}{\left(c d x +a e \right) c^{3}}+\frac{3 a^{2} e^{7} x^{2}}{2 c^{4} d^{4}}+\frac{5 a \,d^{2} e^{2}}{\left(c d x +a e \right) c^{2}}-\frac{5 a \,e^{5} x^{2}}{c^{3} d^{2}}-\frac{d^{4}}{\left(c d x +a e \right) c}+\frac{5 e^{3} x^{2}}{c^{2}}+\frac{5 a^{4} e^{9} \ln \left(c d x +a e \right)}{c^{6} d^{6}}-\frac{20 a^{3} e^{7} \ln \left(c d x +a e \right)}{c^{5} d^{4}}-\frac{4 a^{3} e^{8} x}{c^{5} d^{5}}+\frac{30 a^{2} e^{5} \ln \left(c d x +a e \right)}{c^{4} d^{2}}+\frac{15 a^{2} e^{6} x}{c^{4} d^{3}}-\frac{20 a \,e^{4} x}{c^{3} d}-\frac{20 a \,e^{3} \ln \left(c d x +a e \right)}{c^{3}}+\frac{5 d^{2} e \ln \left(c d x +a e \right)}{c^{2}}+\frac{10 d \,e^{2} x}{c^{2}}"," ",0,"1/4*e^5/c^2/d^2*x^4-2/3*e^6/c^3/d^3*x^3*a+5/3*e^4/c^2/d*x^3+3/2*e^7/c^4/d^4*x^2*a^2-5*e^5/c^3/d^2*x^2*a+5*e^3/c^2*x^2-4*e^8/c^5/d^5*a^3*x+15*e^6/c^4/d^3*a^2*x-20*e^4/c^3/d*a*x+10*e^2/c^2*d*x+5/d^6/c^6*e^9*ln(c*d*x+a*e)*a^4-20/d^4/c^5*e^7*ln(c*d*x+a*e)*a^3+30/d^2/c^4*e^5*ln(c*d*x+a*e)*a^2-20/c^3*e^3*ln(c*d*x+a*e)*a+5*d^2/c^2*e*ln(c*d*x+a*e)+1/c^6/d^6/(c*d*x+a*e)*a^5*e^10-5/c^5/d^4/(c*d*x+a*e)*a^4*e^8+10/c^4/d^2/(c*d*x+a*e)*a^3*e^6-10/c^3/(c*d*x+a*e)*a^2*e^4+5/c^2*d^2/(c*d*x+a*e)*a*e^2-1/c*d^4/(c*d*x+a*e)","B"
1876,1,275,143,0.061000," ","int((e*x+d)^6/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x)","\frac{e^{4} x^{3}}{3 c^{2} d^{2}}-\frac{a^{4} e^{8}}{\left(c d x +a e \right) c^{5} d^{5}}+\frac{4 a^{3} e^{6}}{\left(c d x +a e \right) c^{4} d^{3}}-\frac{6 a^{2} e^{4}}{\left(c d x +a e \right) c^{3} d}+\frac{4 a d \,e^{2}}{\left(c d x +a e \right) c^{2}}-\frac{a \,e^{5} x^{2}}{c^{3} d^{3}}-\frac{d^{3}}{\left(c d x +a e \right) c}+\frac{2 e^{3} x^{2}}{c^{2} d}-\frac{4 a^{3} e^{7} \ln \left(c d x +a e \right)}{c^{5} d^{5}}+\frac{12 a^{2} e^{5} \ln \left(c d x +a e \right)}{c^{4} d^{3}}+\frac{3 a^{2} e^{6} x}{c^{4} d^{4}}-\frac{12 a \,e^{3} \ln \left(c d x +a e \right)}{c^{3} d}-\frac{8 a \,e^{4} x}{c^{3} d^{2}}+\frac{4 d e \ln \left(c d x +a e \right)}{c^{2}}+\frac{6 e^{2} x}{c^{2}}"," ",0,"1/3*e^4*x^3/c^2/d^2-e^5/c^3/d^3*x^2*a+2*e^3/c^2/d*x^2+3*e^6/c^4/d^4*a^2*x-8*e^4/c^3/d^2*a*x+6*e^2/c^2*x-4/d^5/c^5*e^7*ln(c*d*x+a*e)*a^3+12/d^3/c^4*e^5*ln(c*d*x+a*e)*a^2-12/d/c^3*e^3*ln(c*d*x+a*e)*a+4*d/c^2*e*ln(c*d*x+a*e)-1/c^5/d^5/(c*d*x+a*e)*a^4*e^8+4/c^4/d^3/(c*d*x+a*e)*a^3*e^6-6/c^3/d/(c*d*x+a*e)*a^2*e^4+4/c^2*d/(c*d*x+a*e)*a*e^2-1/c*d^3/(c*d*x+a*e)","A"
1877,1,184,103,0.052000," ","int((e*x+d)^5/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x)","\frac{a^{3} e^{6}}{\left(c d x +a e \right) c^{4} d^{4}}-\frac{3 a^{2} e^{4}}{\left(c d x +a e \right) c^{3} d^{2}}+\frac{3 a \,e^{2}}{\left(c d x +a e \right) c^{2}}-\frac{d^{2}}{\left(c d x +a e \right) c}+\frac{e^{3} x^{2}}{2 c^{2} d^{2}}+\frac{3 a^{2} e^{5} \ln \left(c d x +a e \right)}{c^{4} d^{4}}-\frac{6 a \,e^{3} \ln \left(c d x +a e \right)}{c^{3} d^{2}}-\frac{2 a \,e^{4} x}{c^{3} d^{3}}+\frac{3 e^{2} x}{c^{2} d}+\frac{3 e \ln \left(c d x +a e \right)}{c^{2}}"," ",0,"1/2*e^3*x^2/c^2/d^2-2*e^4/c^3/d^3*a*x+3*e^2/c^2/d*x+3/d^4/c^4*e^5*ln(c*d*x+a*e)*a^2-6/d^2/c^3*e^3*ln(c*d*x+a*e)*a+3/c^2*e*ln(c*d*x+a*e)+1/c^4/d^4/(c*d*x+a*e)*a^3*e^6-3/c^3/d^2/(c*d*x+a*e)*a^2*e^4+3/c^2/(c*d*x+a*e)*a*e^2-1/c*d^2/(c*d*x+a*e)","A"
1878,1,114,74,0.057000," ","int((e*x+d)^4/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x)","-\frac{a^{2} e^{4}}{\left(c d x +a e \right) c^{3} d^{3}}+\frac{2 a \,e^{2}}{\left(c d x +a e \right) c^{2} d}-\frac{d}{\left(c d x +a e \right) c}-\frac{2 a \,e^{3} \ln \left(c d x +a e \right)}{c^{3} d^{3}}+\frac{2 e \ln \left(c d x +a e \right)}{c^{2} d}+\frac{e^{2} x}{c^{2} d^{2}}"," ",0,"e^2*x/c^2/d^2-2/d^3/c^3*e^3*ln(c*d*x+a*e)*a+2/d/c^2*e*ln(c*d*x+a*e)-1/c^3/d^3/(c*d*x+a*e)*a^2*e^4+2/c^2/d/(c*d*x+a*e)*a*e^2-1/c*d/(c*d*x+a*e)","A"
1879,1,55,47,0.066000," ","int((e*x+d)^3/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x)","\frac{a \,e^{2}}{\left(c d x +a e \right) c^{2} d^{2}}-\frac{1}{\left(c d x +a e \right) c}+\frac{e \ln \left(c d x +a e \right)}{c^{2} d^{2}}"," ",0,"e*ln(c*d*x+a*e)/c^2/d^2+1/c^2/d^2/(c*d*x+a*e)*a*e^2-1/c/(c*d*x+a*e)","A"
1880,1,19,18,0.043000," ","int((e*x+d)^2/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x)","-\frac{1}{\left(c d x +a e \right) c d}"," ",0,"-1/c/d/(c*d*x+a*e)","A"
1881,1,75,75,0.052000," ","int((e*x+d)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x)","\frac{e \ln \left(e x +d \right)}{\left(a \,e^{2}-c \,d^{2}\right)^{2}}-\frac{e \ln \left(c d x +a e \right)}{\left(a \,e^{2}-c \,d^{2}\right)^{2}}+\frac{1}{\left(a \,e^{2}-c \,d^{2}\right) \left(c d x +a e \right)}"," ",0,"1/(a*e^2-c*d^2)/(c*d*x+a*e)-e/(a*e^2-c*d^2)^2*ln(c*d*x+a*e)+e/(a*e^2-c*d^2)^2*ln(e*x+d)","A"
1882,1,107,115,0.051000," ","int(1/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x)","-\frac{2 c d e \ln \left(e x +d \right)}{\left(a \,e^{2}-c \,d^{2}\right)^{3}}+\frac{2 c d e \ln \left(c d x +a e \right)}{\left(a \,e^{2}-c \,d^{2}\right)^{3}}-\frac{c d}{\left(a \,e^{2}-c \,d^{2}\right)^{2} \left(c d x +a e \right)}-\frac{e}{\left(a \,e^{2}-c \,d^{2}\right)^{2} \left(e x +d \right)}"," ",0,"-c*d/(a*e^2-c*d^2)^2/(c*d*x+a*e)+2*c*d/(a*e^2-c*d^2)^3*e*ln(c*d*x+a*e)-e/(a*e^2-c*d^2)^2/(e*x+d)-2*c*d/(a*e^2-c*d^2)^3*e*ln(e*x+d)","A"
1883,1,144,144,0.054000," ","int(1/(e*x+d)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x)","\frac{3 c^{2} d^{2} e \ln \left(e x +d \right)}{\left(a \,e^{2}-c \,d^{2}\right)^{4}}-\frac{3 c^{2} d^{2} e \ln \left(c d x +a e \right)}{\left(a \,e^{2}-c \,d^{2}\right)^{4}}+\frac{c^{2} d^{2}}{\left(a \,e^{2}-c \,d^{2}\right)^{3} \left(c d x +a e \right)}+\frac{2 c d e}{\left(a \,e^{2}-c \,d^{2}\right)^{3} \left(e x +d \right)}-\frac{e}{2 \left(a \,e^{2}-c \,d^{2}\right)^{2} \left(e x +d \right)^{2}}"," ",0,"c^2*d^2/(a*e^2-c*d^2)^3/(c*d*x+a*e)-3*c^2*d^2/(a*e^2-c*d^2)^4*e*ln(c*d*x+a*e)-1/2*e/(a*e^2-c*d^2)^2/(e*x+d)^2+3*c^2*d^2/(a*e^2-c*d^2)^4*e*ln(e*x+d)+2*e/(a*e^2-c*d^2)^3*c*d/(e*x+d)","A"
1884,1,174,174,0.057000," ","int(1/(e*x+d)^2/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x)","-\frac{4 c^{3} d^{3} e \ln \left(e x +d \right)}{\left(a \,e^{2}-c \,d^{2}\right)^{5}}+\frac{4 c^{3} d^{3} e \ln \left(c d x +a e \right)}{\left(a \,e^{2}-c \,d^{2}\right)^{5}}-\frac{c^{3} d^{3}}{\left(a \,e^{2}-c \,d^{2}\right)^{4} \left(c d x +a e \right)}-\frac{3 c^{2} d^{2} e}{\left(a \,e^{2}-c \,d^{2}\right)^{4} \left(e x +d \right)}+\frac{c d e}{\left(a \,e^{2}-c \,d^{2}\right)^{3} \left(e x +d \right)^{2}}-\frac{e}{3 \left(a \,e^{2}-c \,d^{2}\right)^{2} \left(e x +d \right)^{3}}"," ",0,"-c^3*d^3/(a*e^2-c*d^2)^4/(c*d*x+a*e)+4*c^3*d^3/(a*e^2-c*d^2)^5*e*ln(c*d*x+a*e)-1/3*e/(a*e^2-c*d^2)^2/(e*x+d)^3-4*c^3*d^3/(a*e^2-c*d^2)^5*e*ln(e*x+d)-3*e/(a*e^2-c*d^2)^4*c^2*d^2/(e*x+d)+e/(a*e^2-c*d^2)^3*c*d/(e*x+d)^2","A"
1885,1,544,215,0.054000," ","int((e*x+d)^9/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x)","-\frac{a^{6} e^{12}}{2 \left(c d x +a e \right)^{2} c^{7} d^{7}}+\frac{3 a^{5} e^{10}}{\left(c d x +a e \right)^{2} c^{6} d^{5}}-\frac{15 a^{4} e^{8}}{2 \left(c d x +a e \right)^{2} c^{5} d^{3}}+\frac{10 a^{3} e^{6}}{\left(c d x +a e \right)^{2} c^{4} d}-\frac{15 a^{2} d \,e^{4}}{2 \left(c d x +a e \right)^{2} c^{3}}+\frac{3 a \,d^{3} e^{2}}{\left(c d x +a e \right)^{2} c^{2}}-\frac{d^{5}}{2 \left(c d x +a e \right)^{2} c}+\frac{e^{6} x^{4}}{4 c^{3} d^{3}}-\frac{a \,e^{7} x^{3}}{c^{4} d^{4}}+\frac{2 e^{5} x^{3}}{c^{3} d^{2}}+\frac{6 a^{5} e^{11}}{\left(c d x +a e \right) c^{7} d^{7}}-\frac{30 a^{4} e^{9}}{\left(c d x +a e \right) c^{6} d^{5}}+\frac{60 a^{3} e^{7}}{\left(c d x +a e \right) c^{5} d^{3}}-\frac{60 a^{2} e^{5}}{\left(c d x +a e \right) c^{4} d}+\frac{3 a^{2} e^{8} x^{2}}{c^{5} d^{5}}+\frac{30 a d \,e^{3}}{\left(c d x +a e \right) c^{3}}-\frac{9 a \,e^{6} x^{2}}{c^{4} d^{3}}-\frac{6 d^{3} e}{\left(c d x +a e \right) c^{2}}+\frac{15 e^{4} x^{2}}{2 c^{3} d}+\frac{15 a^{4} e^{10} \ln \left(c d x +a e \right)}{c^{7} d^{7}}-\frac{60 a^{3} e^{8} \ln \left(c d x +a e \right)}{c^{6} d^{5}}-\frac{10 a^{3} e^{9} x}{c^{6} d^{6}}+\frac{90 a^{2} e^{6} \ln \left(c d x +a e \right)}{c^{5} d^{3}}+\frac{36 a^{2} e^{7} x}{c^{5} d^{4}}-\frac{60 a \,e^{4} \ln \left(c d x +a e \right)}{c^{4} d}-\frac{45 a \,e^{5} x}{c^{4} d^{2}}+\frac{15 d \,e^{2} \ln \left(c d x +a e \right)}{c^{3}}+\frac{20 e^{3} x}{c^{3}}"," ",0,"-e^7/c^4/d^4*x^3*a+3*e^8/c^5/d^5*x^2*a^2-9*e^6/c^4/d^3*x^2*a+6/d^7/c^7*e^11/(c*d*x+a*e)*a^5-30/d^5/c^6*e^9/(c*d*x+a*e)*a^4+20*e^3/c^3*x-1/2/c*d^5/(c*d*x+a*e)^2+15/c^3*d*e^2*ln(c*d*x+a*e)-6*d^3/c^2*e/(c*d*x+a*e)+1/4*e^6/c^3/d^3*x^4+2*e^5/c^3/d^2*x^3+15/2*e^4/c^3/d*x^2+15/c^7/d^7*e^10*ln(c*d*x+a*e)*a^4-60/c^6/d^5*e^8*ln(c*d*x+a*e)*a^3+60/d^3/c^5*e^7/(c*d*x+a*e)*a^3-60/d/c^4*e^5/(c*d*x+a*e)*a^2+30*d/c^3*e^3/(c*d*x+a*e)*a+90/c^5/d^3*e^6*ln(c*d*x+a*e)*a^2-60/c^4/d*e^4*ln(c*d*x+a*e)*a-10*e^9/c^6/d^6*a^3*x+36*e^7/c^5/d^4*a^2*x-45*e^5/c^4/d^2*a*x-1/2/c^7/d^7/(c*d*x+a*e)^2*a^6*e^12+3/c^6/d^5/(c*d*x+a*e)^2*a^5*e^10-15/2/c^5/d^3/(c*d*x+a*e)^2*a^4*e^8+10/c^4/d/(c*d*x+a*e)^2*a^3*e^6-15/2/c^3*d/(c*d*x+a*e)^2*a^2*e^4+3/c^2*d^3/(c*d*x+a*e)^2*a*e^2","B"
1886,1,412,179,0.053000," ","int((e*x+d)^8/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x)","\frac{a^{5} e^{10}}{2 \left(c d x +a e \right)^{2} c^{6} d^{6}}-\frac{5 a^{4} e^{8}}{2 \left(c d x +a e \right)^{2} c^{5} d^{4}}+\frac{5 a^{3} e^{6}}{\left(c d x +a e \right)^{2} c^{4} d^{2}}-\frac{5 a^{2} e^{4}}{\left(c d x +a e \right)^{2} c^{3}}+\frac{5 a \,d^{2} e^{2}}{2 \left(c d x +a e \right)^{2} c^{2}}-\frac{d^{4}}{2 \left(c d x +a e \right)^{2} c}+\frac{e^{5} x^{3}}{3 c^{3} d^{3}}-\frac{5 a^{4} e^{9}}{\left(c d x +a e \right) c^{6} d^{6}}+\frac{20 a^{3} e^{7}}{\left(c d x +a e \right) c^{5} d^{4}}-\frac{30 a^{2} e^{5}}{\left(c d x +a e \right) c^{4} d^{2}}+\frac{20 a \,e^{3}}{\left(c d x +a e \right) c^{3}}-\frac{3 a \,e^{6} x^{2}}{2 c^{4} d^{4}}-\frac{5 d^{2} e}{\left(c d x +a e \right) c^{2}}+\frac{5 e^{4} x^{2}}{2 c^{3} d^{2}}-\frac{10 a^{3} e^{8} \ln \left(c d x +a e \right)}{c^{6} d^{6}}+\frac{30 a^{2} e^{6} \ln \left(c d x +a e \right)}{c^{5} d^{4}}+\frac{6 a^{2} e^{7} x}{c^{5} d^{5}}-\frac{30 a \,e^{4} \ln \left(c d x +a e \right)}{c^{4} d^{2}}-\frac{15 a \,e^{5} x}{c^{4} d^{3}}+\frac{10 e^{3} x}{c^{3} d}+\frac{10 e^{2} \ln \left(c d x +a e \right)}{c^{3}}"," ",0,"1/3*e^5*x^3/c^3/d^3-3/2*e^6/c^4/d^4*x^2*a+5/2*e^4/c^3/d^2*x^2+6*e^7/c^5/d^5*a^2*x-15*e^5/c^4/d^3*a*x+10*e^3/c^3/d*x+1/2/c^6/d^6/(c*d*x+a*e)^2*a^5*e^10-5/2/c^5/d^4/(c*d*x+a*e)^2*a^4*e^8+5/c^4/d^2/(c*d*x+a*e)^2*a^3*e^6-5/c^3/(c*d*x+a*e)^2*a^2*e^4+5/2/c^2*d^2/(c*d*x+a*e)^2*a*e^2-1/2/c*d^4/(c*d*x+a*e)^2-10/c^6/d^6*e^8*ln(c*d*x+a*e)*a^3+30/c^5/d^4*e^6*ln(c*d*x+a*e)*a^2-30/c^4/d^2*e^4*ln(c*d*x+a*e)*a+10/c^3*e^2*ln(c*d*x+a*e)-5/d^6/c^6*e^9/(c*d*x+a*e)*a^4+20/d^4/c^5*e^7/(c*d*x+a*e)*a^3-30/d^2/c^4*e^5/(c*d*x+a*e)*a^2+20/c^3*e^3/(c*d*x+a*e)*a-5*d^2/c^2*e/(c*d*x+a*e)","B"
1887,1,302,138,0.054000," ","int((e*x+d)^7/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x)","-\frac{a^{4} e^{8}}{2 \left(c d x +a e \right)^{2} c^{5} d^{5}}+\frac{2 a^{3} e^{6}}{\left(c d x +a e \right)^{2} c^{4} d^{3}}-\frac{3 a^{2} e^{4}}{\left(c d x +a e \right)^{2} c^{3} d}+\frac{2 a d \,e^{2}}{\left(c d x +a e \right)^{2} c^{2}}-\frac{d^{3}}{2 \left(c d x +a e \right)^{2} c}+\frac{4 a^{3} e^{7}}{\left(c d x +a e \right) c^{5} d^{5}}-\frac{12 a^{2} e^{5}}{\left(c d x +a e \right) c^{4} d^{3}}+\frac{12 a \,e^{3}}{\left(c d x +a e \right) c^{3} d}-\frac{4 d e}{\left(c d x +a e \right) c^{2}}+\frac{e^{4} x^{2}}{2 c^{3} d^{3}}+\frac{6 a^{2} e^{6} \ln \left(c d x +a e \right)}{c^{5} d^{5}}-\frac{12 a \,e^{4} \ln \left(c d x +a e \right)}{c^{4} d^{3}}-\frac{3 a \,e^{5} x}{c^{4} d^{4}}+\frac{6 e^{2} \ln \left(c d x +a e \right)}{c^{3} d}+\frac{4 e^{3} x}{c^{3} d^{2}}"," ",0,"1/2*e^4*x^2/c^3/d^3-3*e^5/c^4/d^4*a*x+4*e^3/c^3/d^2*x-1/2/c^5/d^5/(c*d*x+a*e)^2*a^4*e^8+2/c^4/d^3/(c*d*x+a*e)^2*a^3*e^6-3/c^3/d/(c*d*x+a*e)^2*a^2*e^4+2/c^2*d/(c*d*x+a*e)^2*a*e^2-1/2/c*d^3/(c*d*x+a*e)^2+6/c^5/d^5*e^6*ln(c*d*x+a*e)*a^2-12/c^4/d^3*e^4*ln(c*d*x+a*e)*a+6/c^3/d*e^2*ln(c*d*x+a*e)+4/d^5/c^5*e^7/(c*d*x+a*e)*a^3-12/d^3/c^4*e^5/(c*d*x+a*e)*a^2+12/d/c^3*e^3/(c*d*x+a*e)*a-4*d/c^2*e/(c*d*x+a*e)","B"
1888,1,201,109,0.056000," ","int((e*x+d)^6/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x)","\frac{a^{3} e^{6}}{2 \left(c d x +a e \right)^{2} c^{4} d^{4}}-\frac{3 a^{2} e^{4}}{2 \left(c d x +a e \right)^{2} c^{3} d^{2}}+\frac{3 a \,e^{2}}{2 \left(c d x +a e \right)^{2} c^{2}}-\frac{d^{2}}{2 \left(c d x +a e \right)^{2} c}-\frac{3 a^{2} e^{5}}{\left(c d x +a e \right) c^{4} d^{4}}+\frac{6 a \,e^{3}}{\left(c d x +a e \right) c^{3} d^{2}}-\frac{3 e}{\left(c d x +a e \right) c^{2}}-\frac{3 a \,e^{4} \ln \left(c d x +a e \right)}{c^{4} d^{4}}+\frac{3 e^{2} \ln \left(c d x +a e \right)}{c^{3} d^{2}}+\frac{e^{3} x}{c^{3} d^{3}}"," ",0,"e^3*x/c^3/d^3+1/2/c^4/d^4/(c*d*x+a*e)^2*a^3*e^6-3/2/c^3/d^2/(c*d*x+a*e)^2*a^2*e^4+3/2/c^2/(c*d*x+a*e)^2*a*e^2-1/2/c*d^2/(c*d*x+a*e)^2-3/c^4/d^4*e^4*ln(c*d*x+a*e)*a+3/c^3/d^2*e^2*ln(c*d*x+a*e)-3/d^4/c^4*e^5/(c*d*x+a*e)*a^2+6/d^2/c^3*e^3/(c*d*x+a*e)*a-3/c^2*e/(c*d*x+a*e)","A"
1889,1,123,83,0.053000," ","int((e*x+d)^5/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x)","-\frac{a^{2} e^{4}}{2 \left(c d x +a e \right)^{2} c^{3} d^{3}}+\frac{a \,e^{2}}{\left(c d x +a e \right)^{2} c^{2} d}-\frac{d}{2 \left(c d x +a e \right)^{2} c}+\frac{2 a \,e^{3}}{\left(c d x +a e \right) c^{3} d^{3}}-\frac{2 e}{\left(c d x +a e \right) c^{2} d}+\frac{e^{2} \ln \left(c d x +a e \right)}{c^{3} d^{3}}"," ",0,"-1/2/c^3/d^3/(c*d*x+a*e)^2*a^2*e^4+1/c^2/d/(c*d*x+a*e)^2*a*e^2-1/2/c*d/(c*d*x+a*e)^2+e^2*ln(c*d*x+a*e)/c^3/d^3+2/d^3/c^3*e^3/(c*d*x+a*e)*a-2/d/c^2*e/(c*d*x+a*e)","A"
1890,1,51,33,0.056000," ","int((e*x+d)^4/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x)","-\frac{e}{\left(c d x +a e \right) c^{2} d^{2}}-\frac{-a \,e^{2}+c \,d^{2}}{2 \left(c d x +a e \right)^{2} c^{2} d^{2}}"," ",0,"-1/2*(-a*e^2+c*d^2)/c^2/d^2/(c*d*x+a*e)^2-1/d^2/c^2*e/(c*d*x+a*e)","A"
1891,1,19,18,0.043000," ","int((e*x+d)^3/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x)","-\frac{1}{2 \left(c d x +a e \right)^{2} c d}"," ",0,"-1/2/c/d/(c*d*x+a*e)^2","A"
1892,1,106,105,0.058000," ","int((e*x+d)^2/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x)","\frac{e^{2} \ln \left(e x +d \right)}{\left(a \,e^{2}-c \,d^{2}\right)^{3}}-\frac{e^{2} \ln \left(c d x +a e \right)}{\left(a \,e^{2}-c \,d^{2}\right)^{3}}+\frac{e}{\left(a \,e^{2}-c \,d^{2}\right)^{2} \left(c d x +a e \right)}+\frac{1}{2 \left(a \,e^{2}-c \,d^{2}\right) \left(c d x +a e \right)^{2}}"," ",0,"1/2/(a*e^2-c*d^2)/(c*d*x+a*e)^2+e/(a*e^2-c*d^2)^2/(c*d*x+a*e)-e^2/(a*e^2-c*d^2)^3*ln(c*d*x+a*e)+e^2/(a*e^2-c*d^2)^3*ln(e*x+d)","A"
1893,1,142,140,0.057000," ","int((e*x+d)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x)","-\frac{3 c d \,e^{2} \ln \left(e x +d \right)}{\left(a \,e^{2}-c \,d^{2}\right)^{4}}+\frac{3 c d \,e^{2} \ln \left(c d x +a e \right)}{\left(a \,e^{2}-c \,d^{2}\right)^{4}}-\frac{2 c d e}{\left(a \,e^{2}-c \,d^{2}\right)^{3} \left(c d x +a e \right)}-\frac{c d}{2 \left(a \,e^{2}-c \,d^{2}\right)^{2} \left(c d x +a e \right)^{2}}-\frac{e^{2}}{\left(a \,e^{2}-c \,d^{2}\right)^{3} \left(e x +d \right)}"," ",0,"-1/2*c*d/(a*e^2-c*d^2)^2/(c*d*x+a*e)^2+3*c*d/(a*e^2-c*d^2)^4*e^2*ln(c*d*x+a*e)-2*c*d/(a*e^2-c*d^2)^3*e/(c*d*x+a*e)-e^2/(a*e^2-c*d^2)^3/(e*x+d)-3*c*d/(a*e^2-c*d^2)^4*e^2*ln(e*x+d)","A"
1894,1,186,191,0.055000," ","int(1/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x)","\frac{6 c^{2} d^{2} e^{2} \ln \left(e x +d \right)}{\left(a \,e^{2}-c \,d^{2}\right)^{5}}-\frac{6 c^{2} d^{2} e^{2} \ln \left(c d x +a e \right)}{\left(a \,e^{2}-c \,d^{2}\right)^{5}}+\frac{3 c^{2} d^{2} e}{\left(a \,e^{2}-c \,d^{2}\right)^{4} \left(c d x +a e \right)}+\frac{c^{2} d^{2}}{2 \left(a \,e^{2}-c \,d^{2}\right)^{3} \left(c d x +a e \right)^{2}}+\frac{3 c d \,e^{2}}{\left(a \,e^{2}-c \,d^{2}\right)^{4} \left(e x +d \right)}-\frac{e^{2}}{2 \left(a \,e^{2}-c \,d^{2}\right)^{3} \left(e x +d \right)^{2}}"," ",0,"1/2*c^2*d^2/(a*e^2-c*d^2)^3/(c*d*x+a*e)^2-6*c^2*d^2/(a*e^2-c*d^2)^5*e^2*ln(c*d*x+a*e)+3*c^2*d^2/(a*e^2-c*d^2)^4*e/(c*d*x+a*e)-1/2*e^2/(a*e^2-c*d^2)^3/(e*x+d)^2+6*c^2*d^2/(a*e^2-c*d^2)^5*e^2*ln(e*x+d)+3*e^2/(a*e^2-c*d^2)^4*c*d/(e*x+d)","A"
1895,1,218,217,0.065000," ","int(1/(e*x+d)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x)","-\frac{10 c^{3} d^{3} e^{2} \ln \left(e x +d \right)}{\left(a \,e^{2}-c \,d^{2}\right)^{6}}+\frac{10 c^{3} d^{3} e^{2} \ln \left(c d x +a e \right)}{\left(a \,e^{2}-c \,d^{2}\right)^{6}}-\frac{4 c^{3} d^{3} e}{\left(a \,e^{2}-c \,d^{2}\right)^{5} \left(c d x +a e \right)}-\frac{c^{3} d^{3}}{2 \left(a \,e^{2}-c \,d^{2}\right)^{4} \left(c d x +a e \right)^{2}}-\frac{6 c^{2} d^{2} e^{2}}{\left(a \,e^{2}-c \,d^{2}\right)^{5} \left(e x +d \right)}+\frac{3 c d \,e^{2}}{2 \left(a \,e^{2}-c \,d^{2}\right)^{4} \left(e x +d \right)^{2}}-\frac{e^{2}}{3 \left(a \,e^{2}-c \,d^{2}\right)^{3} \left(e x +d \right)^{3}}"," ",0,"-1/2*c^3*d^3/(a*e^2-c*d^2)^4/(c*d*x+a*e)^2+10*c^3*d^3/(a*e^2-c*d^2)^6*e^2*ln(c*d*x+a*e)-4*c^3*d^3/(a*e^2-c*d^2)^5*e/(c*d*x+a*e)-1/3*e^2/(a*e^2-c*d^2)^3/(e*x+d)^3-10*c^3*d^3/(a*e^2-c*d^2)^6*e^2*ln(e*x+d)-6*e^2/(a*e^2-c*d^2)^5*c^2*d^2/(e*x+d)+3/2*e^2/(a*e^2-c*d^2)^4*c*d/(e*x+d)^2","A"
1896,1,578,213,0.056000," ","int((e*x+d)^10/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^4,x)","-\frac{a^{6} e^{12}}{3 \left(c d x +a e \right)^{3} c^{7} d^{7}}+\frac{2 a^{5} e^{10}}{\left(c d x +a e \right)^{3} c^{6} d^{5}}-\frac{5 a^{4} e^{8}}{\left(c d x +a e \right)^{3} c^{5} d^{3}}+\frac{20 a^{3} e^{6}}{3 \left(c d x +a e \right)^{3} c^{4} d}-\frac{5 a^{2} d \,e^{4}}{\left(c d x +a e \right)^{3} c^{3}}+\frac{2 a \,d^{3} e^{2}}{\left(c d x +a e \right)^{3} c^{2}}-\frac{d^{5}}{3 \left(c d x +a e \right)^{3} c}+\frac{3 a^{5} e^{11}}{\left(c d x +a e \right)^{2} c^{7} d^{7}}-\frac{15 a^{4} e^{9}}{\left(c d x +a e \right)^{2} c^{6} d^{5}}+\frac{30 a^{3} e^{7}}{\left(c d x +a e \right)^{2} c^{5} d^{3}}-\frac{30 a^{2} e^{5}}{\left(c d x +a e \right)^{2} c^{4} d}+\frac{15 a d \,e^{3}}{\left(c d x +a e \right)^{2} c^{3}}-\frac{3 d^{3} e}{\left(c d x +a e \right)^{2} c^{2}}+\frac{e^{6} x^{3}}{3 c^{4} d^{4}}-\frac{15 a^{4} e^{10}}{\left(c d x +a e \right) c^{7} d^{7}}+\frac{60 a^{3} e^{8}}{\left(c d x +a e \right) c^{6} d^{5}}-\frac{90 a^{2} e^{6}}{\left(c d x +a e \right) c^{5} d^{3}}+\frac{60 a \,e^{4}}{\left(c d x +a e \right) c^{4} d}-\frac{2 a \,e^{7} x^{2}}{c^{5} d^{5}}-\frac{15 d \,e^{2}}{\left(c d x +a e \right) c^{3}}+\frac{3 e^{5} x^{2}}{c^{4} d^{3}}-\frac{20 a^{3} e^{9} \ln \left(c d x +a e \right)}{c^{7} d^{7}}+\frac{60 a^{2} e^{7} \ln \left(c d x +a e \right)}{c^{6} d^{5}}+\frac{10 a^{2} e^{8} x}{c^{6} d^{6}}-\frac{60 a \,e^{5} \ln \left(c d x +a e \right)}{c^{5} d^{3}}-\frac{24 a \,e^{6} x}{c^{5} d^{4}}+\frac{20 e^{3} \ln \left(c d x +a e \right)}{c^{4} d}+\frac{15 e^{4} x}{c^{4} d^{2}}"," ",0,"-5/c^5/d^3/(c*d*x+a*e)^3*a^4*e^8+20/3/c^4/d/(c*d*x+a*e)^3*a^3*e^6+20/c^4/d*e^3*ln(c*d*x+a*e)-15/c^3*d*e^2/(c*d*x+a*e)+3*e^5/c^4/d^3*x^2+15*e^4/c^4/d^2*x-3*d^3/c^2*e/(c*d*x+a*e)^2-1/3/c^7/d^7/(c*d*x+a*e)^3*a^6*e^12+2/c^6/d^5/(c*d*x+a*e)^3*a^5*e^10-2*e^7/c^5/d^5*x^2*a-1/3/c*d^5/(c*d*x+a*e)^3+60/c^4/d*e^4/(c*d*x+a*e)*a+60/c^6/d^5*e^7*ln(c*d*x+a*e)*a^2-60/c^5/d^3*e^5*ln(c*d*x+a*e)*a-15/c^7/d^7*e^10/(c*d*x+a*e)*a^4+60/c^6/d^5*e^8/(c*d*x+a*e)*a^3-90/c^5/d^3*e^6/(c*d*x+a*e)*a^2-5/c^3*d/(c*d*x+a*e)^3*a^2*e^4+2/c^2*d^3/(c*d*x+a*e)^3*a*e^2+3/d^7/c^7*e^11/(c*d*x+a*e)^2*a^5-15/d^5/c^6*e^9/(c*d*x+a*e)^2*a^4+30/d^3/c^5*e^7/(c*d*x+a*e)^2*a^3-30/d/c^4*e^5/(c*d*x+a*e)^2*a^2+15*d/c^3*e^3/(c*d*x+a*e)^2*a-24*e^6/c^5/d^4*a*x+10*e^8/c^6/d^6*a^2*x-20/c^7/d^7*e^9*ln(c*d*x+a*e)*a^3+1/3*e^6*x^3/c^4/d^4","B"
1897,1,436,173,0.054000," ","int((e*x+d)^9/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^4,x)","\frac{a^{5} e^{10}}{3 \left(c d x +a e \right)^{3} c^{6} d^{6}}-\frac{5 a^{4} e^{8}}{3 \left(c d x +a e \right)^{3} c^{5} d^{4}}+\frac{10 a^{3} e^{6}}{3 \left(c d x +a e \right)^{3} c^{4} d^{2}}-\frac{10 a^{2} e^{4}}{3 \left(c d x +a e \right)^{3} c^{3}}+\frac{5 a \,d^{2} e^{2}}{3 \left(c d x +a e \right)^{3} c^{2}}-\frac{d^{4}}{3 \left(c d x +a e \right)^{3} c}-\frac{5 a^{4} e^{9}}{2 \left(c d x +a e \right)^{2} c^{6} d^{6}}+\frac{10 a^{3} e^{7}}{\left(c d x +a e \right)^{2} c^{5} d^{4}}-\frac{15 a^{2} e^{5}}{\left(c d x +a e \right)^{2} c^{4} d^{2}}+\frac{10 a \,e^{3}}{\left(c d x +a e \right)^{2} c^{3}}-\frac{5 d^{2} e}{2 \left(c d x +a e \right)^{2} c^{2}}+\frac{10 a^{3} e^{8}}{\left(c d x +a e \right) c^{6} d^{6}}-\frac{30 a^{2} e^{6}}{\left(c d x +a e \right) c^{5} d^{4}}+\frac{30 a \,e^{4}}{\left(c d x +a e \right) c^{4} d^{2}}-\frac{10 e^{2}}{\left(c d x +a e \right) c^{3}}+\frac{e^{5} x^{2}}{2 c^{4} d^{4}}+\frac{10 a^{2} e^{7} \ln \left(c d x +a e \right)}{c^{6} d^{6}}-\frac{20 a \,e^{5} \ln \left(c d x +a e \right)}{c^{5} d^{4}}-\frac{4 a \,e^{6} x}{c^{5} d^{5}}+\frac{10 e^{3} \ln \left(c d x +a e \right)}{c^{4} d^{2}}+\frac{5 e^{4} x}{c^{4} d^{3}}"," ",0,"1/2*e^5*x^2/c^4/d^4-4*e^6/c^5/d^5*a*x+5*e^4/c^4/d^3*x+1/3/c^6/d^6/(c*d*x+a*e)^3*a^5*e^10-5/3/c^5/d^4/(c*d*x+a*e)^3*a^4*e^8+10/3/c^4/d^2/(c*d*x+a*e)^3*a^3*e^6-10/3/c^3/(c*d*x+a*e)^3*a^2*e^4+5/3/c^2*d^2/(c*d*x+a*e)^3*a*e^2-1/3/c*d^4/(c*d*x+a*e)^3-5/2/d^6/c^6*e^9/(c*d*x+a*e)^2*a^4+10/d^4/c^5*e^7/(c*d*x+a*e)^2*a^3-15/d^2/c^4*e^5/(c*d*x+a*e)^2*a^2+10/c^3*e^3/(c*d*x+a*e)^2*a-5/2*d^2/c^2*e/(c*d*x+a*e)^2+10/c^6/d^6*e^7*ln(c*d*x+a*e)*a^2-20/c^5/d^4*e^5*ln(c*d*x+a*e)*a+10/c^4/d^2*e^3*ln(c*d*x+a*e)+10/c^6/d^6*e^8/(c*d*x+a*e)*a^3-30/c^5/d^4*e^6/(c*d*x+a*e)*a^2+30/c^4/d^2*e^4/(c*d*x+a*e)*a-10/c^3*e^2/(c*d*x+a*e)","B"
1898,1,318,144,0.052000," ","int((e*x+d)^8/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^4,x)","-\frac{a^{4} e^{8}}{3 \left(c d x +a e \right)^{3} c^{5} d^{5}}+\frac{4 a^{3} e^{6}}{3 \left(c d x +a e \right)^{3} c^{4} d^{3}}-\frac{2 a^{2} e^{4}}{\left(c d x +a e \right)^{3} c^{3} d}+\frac{4 a d \,e^{2}}{3 \left(c d x +a e \right)^{3} c^{2}}-\frac{d^{3}}{3 \left(c d x +a e \right)^{3} c}+\frac{2 a^{3} e^{7}}{\left(c d x +a e \right)^{2} c^{5} d^{5}}-\frac{6 a^{2} e^{5}}{\left(c d x +a e \right)^{2} c^{4} d^{3}}+\frac{6 a \,e^{3}}{\left(c d x +a e \right)^{2} c^{3} d}-\frac{2 d e}{\left(c d x +a e \right)^{2} c^{2}}-\frac{6 a^{2} e^{6}}{\left(c d x +a e \right) c^{5} d^{5}}+\frac{12 a \,e^{4}}{\left(c d x +a e \right) c^{4} d^{3}}-\frac{6 e^{2}}{\left(c d x +a e \right) c^{3} d}-\frac{4 a \,e^{5} \ln \left(c d x +a e \right)}{c^{5} d^{5}}+\frac{4 e^{3} \ln \left(c d x +a e \right)}{c^{4} d^{3}}+\frac{e^{4} x}{c^{4} d^{4}}"," ",0,"e^4*x/c^4/d^4-1/3/c^5/d^5/(c*d*x+a*e)^3*a^4*e^8+4/3/c^4/d^3/(c*d*x+a*e)^3*a^3*e^6-2/c^3/d/(c*d*x+a*e)^3*a^2*e^4+4/3/c^2*d/(c*d*x+a*e)^3*a*e^2-1/3/c*d^3/(c*d*x+a*e)^3+2/d^5/c^5*e^7/(c*d*x+a*e)^2*a^3-6/d^3/c^4*e^5/(c*d*x+a*e)^2*a^2+6/d/c^3*e^3/(c*d*x+a*e)^2*a-2*d/c^2*e/(c*d*x+a*e)^2-4/c^5/d^5*e^5*ln(c*d*x+a*e)*a+4/c^4/d^3*e^3*ln(c*d*x+a*e)-6/c^5/d^5*e^6/(c*d*x+a*e)*a^2+12/c^4/d^3*e^4/(c*d*x+a*e)*a-6/c^3/d*e^2/(c*d*x+a*e)","B"
1899,1,210,118,0.050000," ","int((e*x+d)^7/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^4,x)","\frac{a^{3} e^{6}}{3 \left(c d x +a e \right)^{3} c^{4} d^{4}}-\frac{a^{2} e^{4}}{\left(c d x +a e \right)^{3} c^{3} d^{2}}+\frac{a \,e^{2}}{\left(c d x +a e \right)^{3} c^{2}}-\frac{d^{2}}{3 \left(c d x +a e \right)^{3} c}-\frac{3 a^{2} e^{5}}{2 \left(c d x +a e \right)^{2} c^{4} d^{4}}+\frac{3 a \,e^{3}}{\left(c d x +a e \right)^{2} c^{3} d^{2}}-\frac{3 e}{2 \left(c d x +a e \right)^{2} c^{2}}+\frac{3 a \,e^{4}}{\left(c d x +a e \right) c^{4} d^{4}}-\frac{3 e^{2}}{\left(c d x +a e \right) c^{3} d^{2}}+\frac{e^{3} \ln \left(c d x +a e \right)}{c^{4} d^{4}}"," ",0,"1/3/c^4/d^4/(c*d*x+a*e)^3*a^3*e^6-1/c^3/d^2/(c*d*x+a*e)^3*a^2*e^4+1/c^2/(c*d*x+a*e)^3*a*e^2-1/3/c*d^2/(c*d*x+a*e)^3-3/2*e^5/c^4/d^4/(c*d*x+a*e)^2*a^2+3*e^3/c^3/d^2/(c*d*x+a*e)^2*a-3/2*e/c^2/(c*d*x+a*e)^2+e^3*ln(c*d*x+a*e)/c^4/d^4+3/c^4/d^4*e^4/(c*d*x+a*e)*a-3/c^3/d^2*e^2/(c*d*x+a*e)","A"
1900,1,96,33,0.047000," ","int((e*x+d)^6/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^4,x)","-\frac{e^{2}}{\left(c d x +a e \right) c^{3} d^{3}}+\frac{\left(a \,e^{2}-c \,d^{2}\right) e}{\left(c d x +a e \right)^{2} c^{3} d^{3}}-\frac{a^{2} e^{4}-2 a c \,d^{2} e^{2}+c^{2} d^{4}}{3 \left(c d x +a e \right)^{3} c^{3} d^{3}}"," ",0,"-1/3*(a^2*e^4-2*a*c*d^2*e^2+c^2*d^4)/c^3/d^3/(c*d*x+a*e)^3+e*(a*e^2-c*d^2)/c^3/d^3/(c*d*x+a*e)^2-e^2/c^3/d^3/(c*d*x+a*e)","B"
1901,1,51,50,0.055000," ","int((e*x+d)^5/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^4,x)","-\frac{e}{2 \left(c d x +a e \right)^{2} c^{2} d^{2}}-\frac{-a \,e^{2}+c \,d^{2}}{3 \left(c d x +a e \right)^{3} c^{2} d^{2}}"," ",0,"-1/3*(-a*e^2+c*d^2)/c^2/d^2/(c*d*x+a*e)^3-1/2*e/c^2/d^2/(c*d*x+a*e)^2","A"
1902,1,19,18,0.051000," ","int((e*x+d)^4/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^4,x)","-\frac{1}{3 \left(c d x +a e \right)^{3} c d}"," ",0,"-1/3/c/d/(c*d*x+a*e)^3","A"
1903,1,135,135,0.052000," ","int((e*x+d)^3/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^4,x)","\frac{e^{3} \ln \left(e x +d \right)}{\left(a \,e^{2}-c \,d^{2}\right)^{4}}-\frac{e^{3} \ln \left(c d x +a e \right)}{\left(a \,e^{2}-c \,d^{2}\right)^{4}}+\frac{e^{2}}{\left(a \,e^{2}-c \,d^{2}\right)^{3} \left(c d x +a e \right)}+\frac{e}{2 \left(a \,e^{2}-c \,d^{2}\right)^{2} \left(c d x +a e \right)^{2}}+\frac{1}{3 \left(a \,e^{2}-c \,d^{2}\right) \left(c d x +a e \right)^{3}}"," ",0,"1/3/(a*e^2-c*d^2)/(c*d*x+a*e)^3+1/2*e/(a*e^2-c*d^2)^2/(c*d*x+a*e)^2+e^2/(a*e^2-c*d^2)^3/(c*d*x+a*e)-e^3/(a*e^2-c*d^2)^4*ln(c*d*x+a*e)+e^3/(a*e^2-c*d^2)^4*ln(e*x+d)","A"
1904,1,173,171,0.059000," ","int((e*x+d)^2/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^4,x)","-\frac{4 c d \,e^{3} \ln \left(e x +d \right)}{\left(a \,e^{2}-c \,d^{2}\right)^{5}}+\frac{4 c d \,e^{3} \ln \left(c d x +a e \right)}{\left(a \,e^{2}-c \,d^{2}\right)^{5}}-\frac{3 c d \,e^{2}}{\left(a \,e^{2}-c \,d^{2}\right)^{4} \left(c d x +a e \right)}-\frac{c d e}{\left(a \,e^{2}-c \,d^{2}\right)^{3} \left(c d x +a e \right)^{2}}-\frac{e^{3}}{\left(a \,e^{2}-c \,d^{2}\right)^{4} \left(e x +d \right)}-\frac{c d}{3 \left(a \,e^{2}-c \,d^{2}\right)^{2} \left(c d x +a e \right)^{3}}"," ",0,"-1/3*c*d/(a*e^2-c*d^2)^2/(c*d*x+a*e)^3+4*c*d/(a*e^2-c*d^2)^5*e^3*ln(c*d*x+a*e)-3*c*d/(a*e^2-c*d^2)^4*e^2/(c*d*x+a*e)-c*d/(a*e^2-c*d^2)^3*e/(c*d*x+a*e)^2-e^3/(a*e^2-c*d^2)^4/(e*x+d)-4*c*d/(a*e^2-c*d^2)^5*e^3*ln(e*x+d)","A"
1905,1,221,220,0.062000," ","int((e*x+d)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^4,x)","\frac{10 c^{2} d^{2} e^{3} \ln \left(e x +d \right)}{\left(a \,e^{2}-c \,d^{2}\right)^{6}}-\frac{10 c^{2} d^{2} e^{3} \ln \left(c d x +a e \right)}{\left(a \,e^{2}-c \,d^{2}\right)^{6}}+\frac{6 c^{2} d^{2} e^{2}}{\left(a \,e^{2}-c \,d^{2}\right)^{5} \left(c d x +a e \right)}+\frac{3 c^{2} d^{2} e}{2 \left(a \,e^{2}-c \,d^{2}\right)^{4} \left(c d x +a e \right)^{2}}+\frac{4 c d \,e^{3}}{\left(a \,e^{2}-c \,d^{2}\right)^{5} \left(e x +d \right)}+\frac{c^{2} d^{2}}{3 \left(a \,e^{2}-c \,d^{2}\right)^{3} \left(c d x +a e \right)^{3}}-\frac{e^{3}}{2 \left(a \,e^{2}-c \,d^{2}\right)^{4} \left(e x +d \right)^{2}}"," ",0,"1/3*c^2*d^2/(a*e^2-c*d^2)^3/(c*d*x+a*e)^3-10*c^2*d^2/(a*e^2-c*d^2)^6*e^3*ln(c*d*x+a*e)+6*c^2*d^2/(a*e^2-c*d^2)^5*e^2/(c*d*x+a*e)+3/2*c^2*d^2/(a*e^2-c*d^2)^4*e/(c*d*x+a*e)^2-1/2*e^3/(a*e^2-c*d^2)^4/(e*x+d)^2+10*c^2*d^2/(a*e^2-c*d^2)^6*e^3*ln(e*x+d)+4*e^3/(a*e^2-c*d^2)^5*c*d/(e*x+d)","A"
1906,1,253,260,0.054000," ","int(1/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^4,x)","-\frac{20 c^{3} d^{3} e^{3} \ln \left(e x +d \right)}{\left(a \,e^{2}-c \,d^{2}\right)^{7}}+\frac{20 c^{3} d^{3} e^{3} \ln \left(c d x +a e \right)}{\left(a \,e^{2}-c \,d^{2}\right)^{7}}-\frac{10 c^{3} d^{3} e^{2}}{\left(a \,e^{2}-c \,d^{2}\right)^{6} \left(c d x +a e \right)}-\frac{2 c^{3} d^{3} e}{\left(a \,e^{2}-c \,d^{2}\right)^{5} \left(c d x +a e \right)^{2}}-\frac{10 c^{2} d^{2} e^{3}}{\left(a \,e^{2}-c \,d^{2}\right)^{6} \left(e x +d \right)}-\frac{c^{3} d^{3}}{3 \left(a \,e^{2}-c \,d^{2}\right)^{4} \left(c d x +a e \right)^{3}}+\frac{2 c d \,e^{3}}{\left(a \,e^{2}-c \,d^{2}\right)^{5} \left(e x +d \right)^{2}}-\frac{e^{3}}{3 \left(a \,e^{2}-c \,d^{2}\right)^{4} \left(e x +d \right)^{3}}"," ",0,"-1/3*c^3*d^3/(a*e^2-c*d^2)^4/(c*d*x+a*e)^3+20*c^3*d^3/(a*e^2-c*d^2)^7*e^3*ln(c*d*x+a*e)-10*c^3*d^3/(a*e^2-c*d^2)^6*e^2/(c*d*x+a*e)-2*c^3*d^3/(a*e^2-c*d^2)^5*e/(c*d*x+a*e)^2-1/3*e^3/(a*e^2-c*d^2)^4/(e*x+d)^3-20*c^3*d^3/(a*e^2-c*d^2)^7*e^3*ln(e*x+d)-10*e^3/(a*e^2-c*d^2)^6*c^2*d^2/(e*x+d)+2*e^3/(a*e^2-c*d^2)^5*c*d/(e*x+d)^2","A"
1907,1,1327,350,0.115000," ","int((e*x+d)^4*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x)","-\frac{21 a^{6} e^{11} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{1024 \sqrt{c d e}\, c^{5} d^{5}}+\frac{63 a^{5} e^{9} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{512 \sqrt{c d e}\, c^{4} d^{3}}-\frac{315 a^{4} e^{7} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{1024 \sqrt{c d e}\, c^{3} d}+\frac{105 a^{3} d \,e^{5} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{256 \sqrt{c d e}\, c^{2}}-\frac{315 a^{2} d^{3} e^{3} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{1024 \sqrt{c d e}\, c}+\frac{63 a \,d^{5} e \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{512 \sqrt{c d e}}-\frac{21 c \,d^{7} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{1024 \sqrt{c d e}\, e}+\frac{21 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{4} e^{8} x}{256 c^{4} d^{4}}-\frac{21 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{3} e^{6} x}{64 c^{3} d^{2}}+\frac{63 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{2} e^{4} x}{128 c^{2}}-\frac{21 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a \,d^{2} e^{2} x}{64 c}+\frac{21 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, d^{4} x}{256}+\frac{21 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{5} e^{9}}{512 c^{5} d^{5}}-\frac{63 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{4} e^{7}}{512 c^{4} d^{3}}+\frac{21 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{3} e^{5}}{256 c^{3} d}+\frac{21 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{2} d \,e^{3}}{256 c^{2}}-\frac{63 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a \,d^{3} e}{512 c}+\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} e^{3} x^{3}}{6 c d}+\frac{21 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, d^{5}}{512 e}-\frac{3 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a \,e^{4} x^{2}}{20 c^{2} d^{2}}+\frac{13 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} e^{2} x^{2}}{20 c}+\frac{21 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a^{2} e^{5} x}{160 c^{3} d^{3}}-\frac{9 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a \,e^{3} x}{16 c^{2} d}+\frac{149 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} d e x}{160 c}-\frac{7 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a^{3} e^{6}}{64 c^{4} d^{4}}+\frac{147 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a^{2} e^{4}}{320 c^{3} d^{2}}-\frac{237 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a \,e^{2}}{320 c^{2}}+\frac{107 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} d^{2}}{192 c}"," ",0,"107/192*d^2/c*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)+21/256*d^4*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)*x+21/512/e*d^5*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)+21/512*e^9/d^5/c^5*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)*a^5-63/512*e*d^3/c*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)*a+21/256*e^5/d/c^3*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)*a^3+21/256*e^3*d/c^2*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)*a^2+63/512*e*d^5*ln((1/2*a*e^2+1/2*c*d^2+c*d*e*x)/(d*c*e)^(1/2)+(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2))/(d*c*e)^(1/2)*a+63/128*e^4/c^2*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)*x*a^2-63/512*e^7/d^3/c^4*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)*a^4+149/160*e*d/c*x*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)-237/320*e^2/c^2*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)*a+13/20*e^2/c*x^2*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)+1/6*e^3*x^3*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)/d/c+21/160*e^5/d^3/c^3*x*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)*a^2+147/320*e^4/d^2/c^3*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)*a^2-7/64*e^6/d^4/c^4*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)*a^3-21/1024/e*d^7*c*ln((1/2*a*e^2+1/2*c*d^2+c*d*e*x)/(d*c*e)^(1/2)+(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2))/(d*c*e)^(1/2)-21/64*e^2*d^2/c*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)*x*a-3/20*e^4/d^2/c^2*x^2*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)*a+105/256*e^5*d/c^2*ln((1/2*a*e^2+1/2*c*d^2+c*d*e*x)/(d*c*e)^(1/2)+(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2))/(d*c*e)^(1/2)*a^3-21/64*e^6/d^2/c^3*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)*x*a^3-21/1024*e^11/d^5/c^5*ln((1/2*a*e^2+1/2*c*d^2+c*d*e*x)/(d*c*e)^(1/2)+(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2))/(d*c*e)^(1/2)*a^6+63/512*e^9/d^3/c^4*ln((1/2*a*e^2+1/2*c*d^2+c*d*e*x)/(d*c*e)^(1/2)+(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2))/(d*c*e)^(1/2)*a^5-315/1024*e^7/d/c^3*ln((1/2*a*e^2+1/2*c*d^2+c*d*e*x)/(d*c*e)^(1/2)+(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2))/(d*c*e)^(1/2)*a^4+21/256*e^8/d^4/c^4*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)*x*a^4-315/1024*e^3*d^3/c*ln((1/2*a*e^2+1/2*c*d^2+c*d*e*x)/(d*c*e)^(1/2)+(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2))/(d*c*e)^(1/2)*a^2-9/16*e^3/d/c^2*x*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)*a","B"
1908,1,968,294,0.094000," ","int((e*x+d)^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","\frac{7 a^{5} e^{9} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{256 \sqrt{c d e}\, c^{4} d^{4}}-\frac{35 a^{4} e^{7} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{256 \sqrt{c d e}\, c^{3} d^{2}}+\frac{35 a^{3} e^{5} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{128 \sqrt{c d e}\, c^{2}}-\frac{35 a^{2} d^{2} e^{3} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{128 \sqrt{c d e}\, c}+\frac{35 a \,d^{4} e \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{256 \sqrt{c d e}}-\frac{7 c \,d^{6} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{256 \sqrt{c d e}\, e}-\frac{7 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{3} e^{6} x}{64 c^{3} d^{3}}+\frac{21 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{2} e^{4} x}{64 c^{2} d}-\frac{21 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a d \,e^{2} x}{64 c}+\frac{7 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, d^{3} x}{64}-\frac{7 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{4} e^{7}}{128 c^{4} d^{4}}+\frac{7 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{3} e^{5}}{64 c^{3} d^{2}}-\frac{7 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a \,d^{2} e}{64 c}+\frac{7 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, d^{4}}{128 e}+\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} e^{2} x^{2}}{5 c d}-\frac{7 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a \,e^{3} x}{40 c^{2} d^{2}}+\frac{23 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} e x}{40 c}+\frac{7 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a^{2} e^{4}}{48 c^{3} d^{3}}-\frac{7 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a \,e^{2}}{15 c^{2} d}+\frac{25 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} d}{48 c}"," ",0,"7/128/e*d^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+25/48/c*d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)+7/64*d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x+23/40*e/c*x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)+35/128*e^5/c^2*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^3+1/5*e^2*x^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)/d/c+21/64*e^4/c^2/d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^2-7/64*e^6/c^3/d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^3-21/64*e^2/c*d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a+7/256*e^9/c^4/d^4*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^5-7/15*e^2/c^2/d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a-7/128*e^7/c^4/d^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^4-35/256*e^7/c^3/d^2*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^4-7/40*e^3/c^2/d^2*x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a-35/128*e^3/c*d^2*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^2+35/256*e*d^4*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a+7/64*e^5/c^3/d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^3-7/64*e/c*d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a-7/256/e*c*d^6*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)+7/48*e^4/c^3/d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a^2","B"
1909,1,730,238,0.057000," ","int((e*x+d)^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","-\frac{5 a^{4} e^{7} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{128 \sqrt{c d e}\, c^{3} d^{3}}+\frac{5 a^{3} e^{5} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{32 \sqrt{c d e}\, c^{2} d}-\frac{15 a^{2} d \,e^{3} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{64 \sqrt{c d e}\, c}+\frac{5 a \,d^{3} e \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{32 \sqrt{c d e}}-\frac{5 c \,d^{5} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{128 \sqrt{c d e}\, e}+\frac{5 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{2} e^{4} x}{32 c^{2} d^{2}}-\frac{5 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a \,e^{2} x}{16 c}+\frac{5 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, d^{2} x}{32}+\frac{5 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{3} e^{5}}{64 c^{3} d^{3}}-\frac{5 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{2} e^{3}}{64 c^{2} d}-\frac{5 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a d e}{64 c}+\frac{5 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, d^{3}}{64 e}+\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} e x}{4 c d}-\frac{5 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a \,e^{2}}{24 c^{2} d^{2}}+\frac{11 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}}}{24 c}"," ",0,"5/32*e^5*a^3/c^2/d*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)-15/64*e^3/c*d*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^2-5/128*e^7/c^3/d^3*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^4+5/32*e^4/c^2/d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^2+1/4*e*x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)/d/c-5/24*e^2/c^2/d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a-5/16*e^2/c*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a+5/64*e^5/c^3/d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^3-5/64*e^3/c^2/d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^2-5/64*e/c*d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a-5/128/e*c*d^5*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)+5/32*e*a*d^3*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)+11/24/c*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)+5/32*d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x+5/64/e*d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)","B"
1910,1,465,184,0.075000," ","int((e*x+d)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","\frac{a^{3} e^{5} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{16 \sqrt{c d e}\, c^{2} d^{2}}-\frac{3 a^{2} e^{3} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{16 \sqrt{c d e}\, c}+\frac{3 a \,d^{2} e \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{16 \sqrt{c d e}}-\frac{c \,d^{4} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{16 \sqrt{c d e}\, e}-\frac{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a \,e^{2} x}{4 c d}+\frac{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, d x}{4}-\frac{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{2} e^{3}}{8 c^{2} d^{2}}+\frac{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, d^{2}}{8 e}+\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}}}{3 c d}"," ",0,"1/3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)/c/d-1/4/c/d*e^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a+1/4*d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x-1/8/c^2/d^2*e^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^2+1/8*d^2/e*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+1/16/c^2/d^2*e^5*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^3-3/16/c*e^3*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^2+3/16*e*d^2*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a-1/16*c*d^4/e*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)","B"
1911,1,265,137,0.043000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","-\frac{a^{2} e^{3} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{8 \sqrt{c d e}\, c d}+\frac{a d e \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{4 \sqrt{c d e}}-\frac{c \,d^{3} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{8 \sqrt{c d e}\, e}+\frac{\left(2 c d e x +a \,e^{2}+c \,d^{2}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{4 c d e}"," ",0,"1/4*(2*c*d*e*x+a*e^2+c*d^2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)/c/d/e-1/8/d/c*e^3*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^2+1/4*d*e*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a-1/8*d^3*c/e*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)","A"
1912,1,205,111,0.049000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)/(e*x+d),x)","\frac{a e \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{2 \sqrt{c d e}}-\frac{c \,d^{2} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{2 \sqrt{c d e}\, e}+\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}}{e}"," ",0,"1/e*(c*d*e*(x+d/e)^2+(a*e^2-c*d^2)*(x+d/e))^(1/2)+1/2*e*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+(c*d*e*(x+d/e)^2+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)*a-1/2/e*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+(c*d*e*(x+d/e)^2+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)*c*d^2","A"
1913,1,317,106,0.053000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)/(e*x+d)^2,x)","\frac{a c d e \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{\left(a \,e^{2}-c \,d^{2}\right) \sqrt{c d e}}-\frac{c^{2} d^{3} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{\left(a \,e^{2}-c \,d^{2}\right) \sqrt{c d e}\, e}+\frac{2 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, c d}{\left(a \,e^{2}-c \,d^{2}\right) e}-\frac{2 \left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}}}{\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)^{2} e^{2}}"," ",0,"-2/e^2/(a*e^2-c*d^2)/(x+d/e)^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)+2/e*c*d/(a*e^2-c*d^2)*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)+e*c*d/(a*e^2-c*d^2)*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)*a-1/e*c^2*d^3/(a*e^2-c*d^2)*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)","B"
1914,1,58,50,0.048000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)/(e*x+d)^3,x)","-\frac{2 \left(c d x +a e \right) \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}}{3 \left(e x +d \right)^{2} \left(a \,e^{2}-c \,d^{2}\right)}"," ",0,"-2/3*(c*d*x+a*e)/(e*x+d)^2/(a*e^2-c*d^2)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)","A"
1915,1,90,103,0.043000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)/(e*x+d)^4,x)","-\frac{2 \left(c d x +a e \right) \left(-2 c d e x +3 a \,e^{2}-5 c \,d^{2}\right) \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}}{15 \left(e x +d \right)^{3} \left(a^{2} e^{4}-2 a c \,d^{2} e^{2}+c^{2} d^{4}\right)}"," ",0,"-2/15*(c*d*x+a*e)*(-2*c*d*e*x+3*a*e^2-5*c*d^2)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)/(e*x+d)^3/(a^2*e^4-2*a*c*d^2*e^2+c^2*d^4)","A"
1916,1,146,159,0.061000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)/(e*x+d)^5,x)","-\frac{2 \left(c d x +a e \right) \left(8 c^{2} d^{2} e^{2} x^{2}-12 a c d \,e^{3} x +28 c^{2} d^{3} e x +15 a^{2} e^{4}-42 a c \,d^{2} e^{2}+35 c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}}{105 \left(e x +d \right)^{4} \left(a^{3} e^{6}-3 a^{2} c \,d^{2} e^{4}+3 a \,c^{2} d^{4} e^{2}-c^{3} d^{6}\right)}"," ",0,"-2/105*(c*d*x+a*e)*(8*c^2*d^2*e^2*x^2-12*a*c*d*e^3*x+28*c^2*d^3*e*x+15*a^2*e^4-42*a*c*d^2*e^2+35*c^2*d^4)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)/(e*x+d)^4/(a^3*e^6-3*a^2*c*d^2*e^4+3*a*c^2*d^4*e^2-c^3*d^6)","A"
1917,1,217,215,0.044000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)/(e*x+d)^6,x)","-\frac{2 \left(c d x +a e \right) \left(-16 c^{3} d^{3} e^{3} x^{3}+24 a \,c^{2} d^{2} e^{4} x^{2}-72 c^{3} d^{4} e^{2} x^{2}-30 a^{2} c d \,e^{5} x +108 a \,c^{2} d^{3} e^{3} x -126 c^{3} d^{5} e x +35 a^{3} e^{6}-135 a^{2} c \,d^{2} e^{4}+189 a \,c^{2} d^{4} e^{2}-105 c^{3} d^{6}\right) \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}}{315 \left(e x +d \right)^{5} \left(a^{4} e^{8}-4 a^{3} c \,d^{2} e^{6}+6 a^{2} c^{2} d^{4} e^{4}-4 a \,c^{3} d^{6} e^{2}+c^{4} d^{8}\right)}"," ",0,"-2/315*(c*d*x+a*e)*(-16*c^3*d^3*e^3*x^3+24*a*c^2*d^2*e^4*x^2-72*c^3*d^4*e^2*x^2-30*a^2*c*d*e^5*x+108*a*c^2*d^3*e^3*x-126*c^3*d^5*e*x+35*a^3*e^6-135*a^2*c*d^2*e^4+189*a*c^2*d^4*e^2-105*c^3*d^6)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)/(e*x+d)^5/(a^4*e^8-4*a^3*c*d^2*e^6+6*a^2*c^2*d^4*e^4-4*a*c^3*d^6*e^2+c^4*d^8)","A"
1918,1,2065,419,0.076000," ","int((e*x+d)^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2),x)","\frac{99 a^{8} e^{14} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{32768 \sqrt{c d e}\, c^{6} d^{6}}-\frac{99 a^{7} e^{12} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{4096 \sqrt{c d e}\, c^{5} d^{4}}+\frac{693 a^{6} e^{10} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{8192 \sqrt{c d e}\, c^{4} d^{2}}-\frac{693 a^{5} e^{8} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{4096 \sqrt{c d e}\, c^{3}}+\frac{3465 a^{4} d^{2} e^{6} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{16384 \sqrt{c d e}\, c^{2}}-\frac{693 a^{3} d^{4} e^{4} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{4096 \sqrt{c d e}\, c}+\frac{693 a^{2} d^{6} e^{2} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{8192 \sqrt{c d e}}-\frac{99 a c \,d^{8} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{4096 \sqrt{c d e}}+\frac{99 c^{2} d^{10} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{32768 \sqrt{c d e}\, e^{2}}-\frac{99 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{6} e^{11} x}{8192 c^{5} d^{5}}+\frac{297 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{5} e^{9} x}{4096 c^{4} d^{3}}-\frac{1485 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{4} e^{7} x}{8192 c^{3} d}+\frac{495 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{3} d \,e^{5} x}{2048 c^{2}}-\frac{1485 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{2} d^{3} e^{3} x}{8192 c}+\frac{297 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a \,d^{5} e x}{4096}-\frac{99 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c \,d^{7} x}{8192 e}-\frac{99 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{7} e^{12}}{16384 c^{6} d^{6}}+\frac{495 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{6} e^{10}}{16384 c^{5} d^{4}}-\frac{891 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{5} e^{8}}{16384 c^{4} d^{2}}+\frac{495 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{4} e^{6}}{16384 c^{3}}+\frac{495 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{3} d^{2} e^{4}}{16384 c^{2}}-\frac{891 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{2} d^{4} e^{2}}{16384 c}+\frac{495 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a \,d^{6}}{16384}-\frac{99 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c \,d^{8}}{16384 e^{2}}+\frac{33 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a^{4} e^{8} x}{1024 c^{4} d^{4}}-\frac{33 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a^{3} e^{6} x}{256 c^{3} d^{2}}+\frac{99 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a^{2} e^{4} x}{512 c^{2}}-\frac{33 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a \,d^{2} e^{2} x}{256 c}+\frac{33 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} d^{4} x}{1024}+\frac{33 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a^{5} e^{9}}{2048 c^{5} d^{5}}-\frac{99 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a^{4} e^{7}}{2048 c^{4} d^{3}}+\frac{33 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a^{3} e^{5}}{1024 c^{3} d}+\frac{33 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a^{2} d \,e^{3}}{1024 c^{2}}-\frac{99 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a \,d^{3} e}{2048 c}+\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} e^{3} x^{3}}{8 c d}+\frac{33 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} d^{5}}{2048 e}-\frac{11 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} a \,e^{4} x^{2}}{112 c^{2} d^{2}}+\frac{53 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} e^{2} x^{2}}{112 c}+\frac{33 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} a^{2} e^{5} x}{448 c^{3} d^{3}}-\frac{11 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} a \,e^{3} x}{32 c^{2} d}+\frac{289 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} d e x}{448 c}-\frac{33 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} a^{3} e^{6}}{640 c^{4} d^{4}}+\frac{1023 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} a^{2} e^{4}}{4480 c^{3} d^{2}}-\frac{1793 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} a \,e^{2}}{4480 c^{2}}+\frac{223 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} d^{2}}{640 c}"," ",0,"297/4096*e*d^5*a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x+33/2048/e*d^5*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)+33/1024*d^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x+223/640/c*d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)+495/16384*d^6*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a+99/512*e^4/c^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*a^2-99/16384/e^2*c*d^8*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)-1793/4480*e^2/c^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*a+495/16384*e^6/c^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^4+53/112*e^2/c*x^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)-693/4096*e^8/c^3*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^5+693/8192*e^2*d^6*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^2+33/1024*e^5/c^3/d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a^3-33/640*e^6/c^4/d^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*a^3+99/32768/e^2*c^2*d^10*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)+1/8*e^3*x^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/c/d-99/2048*e/c*d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a-891/16384*e^2/c*d^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^2-99/4096*c*d^8*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a+289/448*e/c*d*x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)+495/16384*e^4/c^2*d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^3+33/2048*e^9/c^5/d^5*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a^5-99/2048*e^7/c^4/d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a^4+1023/4480*e^4/c^3/d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*a^2+33/1024*e^3/c^2*d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a^2-99/8192/e*c*d^7*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x-99/16384*e^12/c^6/d^6*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^7+495/16384*e^10/c^5/d^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^6-891/16384*e^8/c^4/d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^5+33/448*e^5/c^3/d^3*x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*a^2-11/112*e^4/c^2/d^2*x^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*a-99/4096*e^12/c^5/d^4*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^7-1485/8192*e^7/c^3/d*a^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x-1485/8192*e^3/c*d^3*a^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x+693/8192*e^10/c^4/d^2*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^6-33/256*e^6/c^3/d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*a^3+3465/16384*e^6/c^2*d^2*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^4+33/1024*e^8/c^4/d^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*a^4+297/4096*e^9/c^4/d^3*a^5*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x+99/32768*e^14/c^6/d^6*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^8+495/2048*e^5/c^2*d*a^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x-693/4096*e^4/c*d^4*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^3-99/8192*e^11/c^5/d^5*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^6-33/256*e^2/c*d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*a-11/32*e^3/c^2/d*x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*a","B"
1919,1,1586,363,0.061000," ","int((e*x+d)^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2),x)","-\frac{9 a^{7} e^{12} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{2048 \sqrt{c d e}\, c^{5} d^{5}}+\frac{63 a^{6} e^{10} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{2048 \sqrt{c d e}\, c^{4} d^{3}}-\frac{189 a^{5} e^{8} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{2048 \sqrt{c d e}\, c^{3} d}+\frac{315 a^{4} d \,e^{6} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{2048 \sqrt{c d e}\, c^{2}}-\frac{315 a^{3} d^{3} e^{4} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{2048 \sqrt{c d e}\, c}+\frac{189 a^{2} d^{5} e^{2} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{2048 \sqrt{c d e}}-\frac{63 a c \,d^{7} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{2048 \sqrt{c d e}}+\frac{9 c^{2} d^{9} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{2048 \sqrt{c d e}\, e^{2}}+\frac{9 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{5} e^{9} x}{512 c^{4} d^{4}}-\frac{45 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{4} e^{7} x}{512 c^{3} d^{2}}+\frac{45 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{3} e^{5} x}{256 c^{2}}-\frac{45 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{2} d^{2} e^{3} x}{256 c}+\frac{45 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a \,d^{4} e x}{512}-\frac{9 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c \,d^{6} x}{512 e}+\frac{9 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{6} e^{10}}{1024 c^{5} d^{5}}-\frac{9 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{5} e^{8}}{256 c^{4} d^{3}}+\frac{45 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{4} e^{6}}{1024 c^{3} d}-\frac{45 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{2} d^{3} e^{2}}{1024 c}+\frac{9 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a \,d^{5}}{256}-\frac{9 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c \,d^{7}}{1024 e^{2}}-\frac{3 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a^{3} e^{6} x}{64 c^{3} d^{3}}+\frac{9 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a^{2} e^{4} x}{64 c^{2} d}-\frac{9 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a d \,e^{2} x}{64 c}+\frac{3 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} d^{3} x}{64}-\frac{3 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a^{4} e^{7}}{128 c^{4} d^{4}}+\frac{3 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a^{3} e^{5}}{64 c^{3} d^{2}}-\frac{3 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a \,d^{2} e}{64 c}+\frac{3 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} d^{4}}{128 e}+\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} e^{2} x^{2}}{7 c d}-\frac{3 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} a \,e^{3} x}{28 c^{2} d^{2}}+\frac{11 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} e x}{28 c}+\frac{3 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} a^{2} e^{4}}{40 c^{3} d^{3}}-\frac{9 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} a \,e^{2}}{35 c^{2} d}+\frac{13 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} d}{40 c}"," ",0,"-9/1024/e^2*c*d^7*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+11/28*e/c*x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)-45/1024*e^2/c*d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^2-3/64*e/c*d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a+3/128/e*d^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)+13/40/c*d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)+3/64*d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x+9/256*d^5*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a-9/512/e*c*d^6*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x-9/35*e^2/c^2/d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*a+45/1024*e^6/c^3/d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^4-3/128*e^7/c^4/d^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a^4-63/2048*c*d^7*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a+1/7*e^2*x^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/c/d+189/2048*e^2*d^5*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^2+3/64*e^5/c^3/d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a^3+3/40*e^4/c^3/d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*a^2+9/2048/e^2*c^2*d^9*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)+45/256*e^5/c^2*a^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x+45/512*e*d^4*a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x+9/1024*e^10/c^5/d^5*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^6-9/256*e^8/c^4/d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^5-315/2048*e^4/c*d^3*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^3-45/512*e^7/c^3/d^2*a^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x+9/64*e^4/c^2/d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*a^2-9/2048*e^12/c^5/d^5*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^7+63/2048*e^10/c^4/d^3*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^6+9/512*e^9/c^4/d^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^5+315/2048*e^6/c^2*d*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^4-189/2048*e^8/c^3/d*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^5-9/64*e^2/c*d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*a-3/64*e^6/c^3/d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*a^3-3/28*e^3/c^2/d^2*x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*a-45/256*e^3/c*d^2*a^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x","B"
1920,1,1302,307,0.059000," ","int((e*x+d)^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2),x)","\frac{7 a^{6} e^{10} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{1024 \sqrt{c d e}\, c^{4} d^{4}}-\frac{21 a^{5} e^{8} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{512 \sqrt{c d e}\, c^{3} d^{2}}+\frac{105 a^{4} e^{6} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{1024 \sqrt{c d e}\, c^{2}}-\frac{35 a^{3} d^{2} e^{4} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{256 \sqrt{c d e}\, c}+\frac{105 a^{2} d^{4} e^{2} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{1024 \sqrt{c d e}}-\frac{21 a c \,d^{6} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{512 \sqrt{c d e}}+\frac{7 c^{2} d^{8} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{1024 \sqrt{c d e}\, e^{2}}-\frac{7 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{4} e^{7} x}{256 c^{3} d^{3}}+\frac{7 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{3} e^{5} x}{64 c^{2} d}-\frac{21 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{2} d \,e^{3} x}{128 c}+\frac{7 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a \,d^{3} e x}{64}-\frac{7 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c \,d^{5} x}{256 e}-\frac{7 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{5} e^{8}}{512 c^{4} d^{4}}+\frac{21 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{4} e^{6}}{512 c^{3} d^{2}}-\frac{7 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{3} e^{4}}{256 c^{2}}-\frac{7 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{2} d^{2} e^{2}}{256 c}+\frac{21 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a \,d^{4}}{512}-\frac{7 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c \,d^{6}}{512 e^{2}}+\frac{7 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a^{2} e^{4} x}{96 c^{2} d^{2}}-\frac{7 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a \,e^{2} x}{48 c}+\frac{7 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} d^{2} x}{96}+\frac{7 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a^{3} e^{5}}{192 c^{3} d^{3}}-\frac{7 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a^{2} e^{3}}{192 c^{2} d}-\frac{7 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a d e}{192 c}+\frac{7 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} d^{3}}{192 e}+\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} e x}{6 c d}-\frac{7 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} a \,e^{2}}{60 c^{2} d^{2}}+\frac{17 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}}}{60 c}"," ",0,"-7/256*e^2/c*d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^2+7/64*e*a*d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x+7/192*e^5/c^3/d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a^3-7/192*e^3/c^2/d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a^2-7/192*e/c*d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a-7/512*e^8/c^4/d^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^5+105/1024*e^2*d^4*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^2+1/6*e*x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/c/d+21/512*e^6/c^3/d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^4-7/60*e^2/c^2/d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*a-21/128*e^3/c*d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^2+7/1024*e^10/c^4/d^4*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^6-35/256*e^4/c*d^2*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^3-7/512/e^2*c*d^6*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)-7/256*e^4/c^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^3+17/60/c*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)-7/256/e*c*d^5*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x+7/64*e^5*a^3/c^2/d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x-7/48*e^2/c*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*a+7/96*d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x+21/512*d^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a+7/192/e*d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)-21/512*e^8/c^3/d^2*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^5+7/96*e^4/c^2/d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*a^2-7/256*e^7/c^3/d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^4+7/1024/e^2*c^2*d^8*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)-21/512*c*d^6*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a+105/1024*e^6/c^2*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^4","B"
1921,1,917,253,0.051000," ","int((e*x+d)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2),x)","-\frac{3 a^{5} e^{8} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{256 \sqrt{c d e}\, c^{3} d^{3}}+\frac{15 a^{4} e^{6} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{256 \sqrt{c d e}\, c^{2} d}-\frac{15 a^{3} d \,e^{4} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{128 \sqrt{c d e}\, c}+\frac{15 a^{2} d^{3} e^{2} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{128 \sqrt{c d e}}-\frac{15 a c \,d^{5} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{256 \sqrt{c d e}}+\frac{3 c^{2} d^{7} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{256 \sqrt{c d e}\, e^{2}}+\frac{3 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{3} e^{5} x}{64 c^{2} d^{2}}-\frac{9 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{2} e^{3} x}{64 c}+\frac{9 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a \,d^{2} e x}{64}-\frac{3 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c \,d^{4} x}{64 e}+\frac{3 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{4} e^{6}}{128 c^{3} d^{3}}-\frac{3 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{3} e^{4}}{64 c^{2} d}+\frac{3 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a \,d^{3}}{64}-\frac{3 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c \,d^{5}}{128 e^{2}}-\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a \,e^{2} x}{8 c d}+\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} d x}{8}-\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a^{2} e^{3}}{16 c^{2} d^{2}}+\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} d^{2}}{16 e}+\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}}}{5 c d}"," ",0,"-1/8/c/d*e^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*a-3/256/c^3/d^3*e^8*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^5+15/256/c^2/d*e^6*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^4-15/128/c*d*e^4*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^3+3/64/c^2/d^2*e^5*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^3+3/64*d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a-9/64/c*e^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^2+9/64*e*d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a+15/128*d^3*e^2*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^2-1/16/c^2/d^2*e^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a^2-3/64*c*d^4/e*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x-3/128*c*d^5/e^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+1/16*d^2/e*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)+1/5*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/c/d+1/8*d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x+3/256*c^2*d^7/e^2*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)+3/128/c^3/d^3*e^6*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^4-15/256*c*d^5*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a-3/64/c^2/d*e^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^3","B"
1922,1,671,206,0.048000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2),x)","\frac{3 a^{4} e^{6} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{128 \sqrt{c d e}\, c^{2} d^{2}}-\frac{3 a^{3} e^{4} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{32 \sqrt{c d e}\, c}+\frac{9 a^{2} d^{2} e^{2} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{64 \sqrt{c d e}}-\frac{3 a c \,d^{4} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{32 \sqrt{c d e}}+\frac{3 c^{2} d^{6} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{128 \sqrt{c d e}\, e^{2}}-\frac{3 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{2} e^{3} x}{32 c d}+\frac{3 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a d e x}{16}-\frac{3 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c \,d^{3} x}{32 e}-\frac{3 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{3} e^{4}}{64 c^{2} d^{2}}+\frac{3 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{2} e^{2}}{64 c}+\frac{3 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a \,d^{2}}{64}-\frac{3 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c \,d^{4}}{64 e^{2}}+\frac{\left(2 c d e x +a \,e^{2}+c \,d^{2}\right) \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}}}{8 c d e}"," ",0,"1/8*(2*c*d*e*x+a*e^2+c*d^2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)/c/d/e-3/32/c/d*e^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^2+3/16*d*e*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a-3/32*c*d^3/e*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x-3/64/c^2/d^2*e^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^3+3/64/c*e^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^2+3/64*d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a-3/64*c*d^4/e^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+3/128/c^2/d^2*e^6*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^4-3/32/c*e^4*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^3+9/64*d^2*e^2*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^2-3/32*c*d^4*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a+3/128*c^2*d^6/e^2*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)","B"
1923,1,566,175,0.050000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)/(e*x+d),x)","-\frac{a^{3} e^{4} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{16 \sqrt{c d e}\, c d}+\frac{3 a^{2} d \,e^{2} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{16 \sqrt{c d e}}-\frac{3 a c \,d^{3} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{16 \sqrt{c d e}}+\frac{c^{2} d^{5} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{16 \sqrt{c d e}\, e^{2}}+\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a e x}{4}-\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, c \,d^{2} x}{4 e}+\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{2} e^{2}}{8 c d}-\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, c \,d^{3}}{8 e^{2}}+\frac{\left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}}}{3 e}"," ",0,"1/3/e*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)+1/4*e*a*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x+1/8*e^2*a^2/c/d*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)-1/16*e^4*a^3/c/d*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+3/16*e^2*a^2*d*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-3/16*a*c*d^3*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-1/4/e*c*d^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x-1/8/e^2*c*d^3*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)+1/16/e^2*c^2*d^5*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)","B"
1924,1,757,161,0.049000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)/(e*x+d)^2,x)","\frac{3 a^{3} e^{4} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{8 \left(a \,e^{2}-c \,d^{2}\right) \sqrt{c d e}}-\frac{9 a^{2} c \,d^{2} e^{2} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{8 \left(a \,e^{2}-c \,d^{2}\right) \sqrt{c d e}}+\frac{9 a \,c^{2} d^{4} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{8 \left(a \,e^{2}-c \,d^{2}\right) \sqrt{c d e}}-\frac{3 c^{3} d^{6} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{8 \left(a \,e^{2}-c \,d^{2}\right) \sqrt{c d e}\, e^{2}}-\frac{3 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a c d e x}{2 \left(a \,e^{2}-c \,d^{2}\right)}+\frac{3 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, c^{2} d^{3} x}{2 \left(a \,e^{2}-c \,d^{2}\right) e}-\frac{3 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{2} e^{2}}{4 \left(a \,e^{2}-c \,d^{2}\right)}+\frac{3 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, c^{2} d^{4}}{4 \left(a \,e^{2}-c \,d^{2}\right) e^{2}}-\frac{2 \left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}} c d}{\left(a \,e^{2}-c \,d^{2}\right) e}+\frac{2 \left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{5}{2}}}{\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)^{2} e^{2}}"," ",0,"2/e^2/(a*e^2-c*d^2)/(x+d/e)^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(5/2)-2/e*c*d/(a*e^2-c*d^2)*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)-3/2*e*c*d/(a*e^2-c*d^2)*a*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x-3/4*e^2/(a*e^2-c*d^2)*a^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)+3/8*e^4/(a*e^2-c*d^2)*a^3*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-9/8*e^2*c*d^2/(a*e^2-c*d^2)*a^2*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+9/8*c^2*d^4/(a*e^2-c*d^2)*a*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+3/2/e*c^2*d^3/(a*e^2-c*d^2)*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x+3/4/e^2*c^2*d^4/(a*e^2-c*d^2)*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)-3/8/e^2*c^3*d^6/(a*e^2-c*d^2)*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)","B"
1925,1,837,153,0.064000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)/(e*x+d)^3,x)","\frac{3 a^{3} c d \,e^{4} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{2 \left(a \,e^{2}-c \,d^{2}\right)^{2} \sqrt{c d e}}-\frac{9 a^{2} c^{2} d^{3} e^{2} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{2 \left(a \,e^{2}-c \,d^{2}\right)^{2} \sqrt{c d e}}+\frac{9 a \,c^{3} d^{5} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{2 \left(a \,e^{2}-c \,d^{2}\right)^{2} \sqrt{c d e}}-\frac{3 c^{4} d^{7} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{2 \left(a \,e^{2}-c \,d^{2}\right)^{2} \sqrt{c d e}\, e^{2}}-\frac{6 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a \,c^{2} d^{2} e x}{\left(a \,e^{2}-c \,d^{2}\right)^{2}}+\frac{6 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, c^{3} d^{4} x}{\left(a \,e^{2}-c \,d^{2}\right)^{2} e}-\frac{3 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{2} c d \,e^{2}}{\left(a \,e^{2}-c \,d^{2}\right)^{2}}+\frac{3 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, c^{3} d^{5}}{\left(a \,e^{2}-c \,d^{2}\right)^{2} e^{2}}-\frac{8 \left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}} c^{2} d^{2}}{\left(a \,e^{2}-c \,d^{2}\right)^{2} e}+\frac{8 \left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{5}{2}} c d}{\left(a \,e^{2}-c \,d^{2}\right)^{2} \left(x +\frac{d}{e}\right)^{2} e^{2}}-\frac{2 \left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{5}{2}}}{\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)^{3} e^{3}}"," ",0,"-2/e^3/(a*e^2-c*d^2)/(x+d/e)^3*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(5/2)+8/e^2*c*d/(a*e^2-c*d^2)^2/(x+d/e)^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(5/2)-8/e*c^2*d^2/(a*e^2-c*d^2)^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)-6*e*c^2*d^2/(a*e^2-c*d^2)^2*a*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x-3*e^2*c*d/(a*e^2-c*d^2)^2*a^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)+3/2*e^4*c*d/(a*e^2-c*d^2)^2*a^3*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-9/2*e^2*c^2*d^3/(a*e^2-c*d^2)^2*a^2*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+9/2*c^3*d^5/(a*e^2-c*d^2)^2*a*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+6/e*c^3*d^4/(a*e^2-c*d^2)^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x+3/e^2*c^3*d^5/(a*e^2-c*d^2)^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)-3/2/e^2*c^4*d^7/(a*e^2-c*d^2)^2*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)","B"
1926,1,914,147,0.053000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)/(e*x+d)^4,x)","\frac{a^{3} c^{2} d^{2} e^{4} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{\left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{c d e}}-\frac{3 a^{2} c^{3} d^{4} e^{2} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{\left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{c d e}}+\frac{3 a \,c^{4} d^{6} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{\left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{c d e}}-\frac{c^{5} d^{8} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{\left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{c d e}\, e^{2}}-\frac{4 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a \,c^{3} d^{3} e x}{\left(a \,e^{2}-c \,d^{2}\right)^{3}}+\frac{4 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, c^{4} d^{5} x}{\left(a \,e^{2}-c \,d^{2}\right)^{3} e}-\frac{2 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{2} c^{2} d^{2} e^{2}}{\left(a \,e^{2}-c \,d^{2}\right)^{3}}+\frac{2 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, c^{4} d^{6}}{\left(a \,e^{2}-c \,d^{2}\right)^{3} e^{2}}-\frac{16 \left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}} c^{3} d^{3}}{3 \left(a \,e^{2}-c \,d^{2}\right)^{3} e}+\frac{16 \left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{5}{2}} c^{2} d^{2}}{3 \left(a \,e^{2}-c \,d^{2}\right)^{3} \left(x +\frac{d}{e}\right)^{2} e^{2}}-\frac{4 \left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{5}{2}} c d}{3 \left(a \,e^{2}-c \,d^{2}\right)^{2} \left(x +\frac{d}{e}\right)^{3} e^{3}}-\frac{2 \left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{5}{2}}}{3 \left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)^{4} e^{4}}"," ",0,"-2/3/e^4/(a*e^2-c*d^2)/(x+d/e)^4*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(5/2)-4/3/e^3*c*d/(a*e^2-c*d^2)^2/(x+d/e)^3*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(5/2)+16/3/e^2*c^2*d^2/(a*e^2-c*d^2)^3/(x+d/e)^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(5/2)-16/3/e*c^3*d^3/(a*e^2-c*d^2)^3*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)-4*e*c^3*d^3/(a*e^2-c*d^2)^3*a*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x-2*e^2*c^2*d^2/(a*e^2-c*d^2)^3*a^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)+e^4*c^2*d^2/(a*e^2-c*d^2)^3*a^3*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-3*e^2*c^3*d^4/(a*e^2-c*d^2)^3*a^2*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+3*c^4*d^6/(a*e^2-c*d^2)^3*a*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+4/e*c^4*d^5/(a*e^2-c*d^2)^3*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x+2/e^2*c^4*d^6/(a*e^2-c*d^2)^3*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)-1/e^2*c^5*d^8/(a*e^2-c*d^2)^3*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)","B"
1927,1,58,50,0.046000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)/(e*x+d)^5,x)","-\frac{2 \left(c d x +a e \right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{3}{2}}}{5 \left(e x +d \right)^{4} \left(a \,e^{2}-c \,d^{2}\right)}"," ",0,"-2/5*(c*d*x+a*e)/(e*x+d)^4/(a*e^2-c*d^2)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(3/2)","A"
1928,1,90,103,0.050000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)/(e*x+d)^6,x)","-\frac{2 \left(c d x +a e \right) \left(-2 c d e x +5 a \,e^{2}-7 c \,d^{2}\right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{3}{2}}}{35 \left(e x +d \right)^{5} \left(a^{2} e^{4}-2 a c \,d^{2} e^{2}+c^{2} d^{4}\right)}"," ",0,"-2/35*(c*d*x+a*e)*(-2*c*d*e*x+5*a*e^2-7*c*d^2)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(3/2)/(e*x+d)^5/(a^2*e^4-2*a*c*d^2*e^2+c^2*d^4)","A"
1929,1,146,159,0.051000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)/(e*x+d)^7,x)","-\frac{2 \left(c d x +a e \right) \left(8 c^{2} d^{2} e^{2} x^{2}-20 a c d \,e^{3} x +36 c^{2} d^{3} e x +35 a^{2} e^{4}-90 a c \,d^{2} e^{2}+63 c^{2} d^{4}\right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{3}{2}}}{315 \left(e x +d \right)^{6} \left(a^{3} e^{6}-3 a^{2} c \,d^{2} e^{4}+3 a \,c^{2} d^{4} e^{2}-c^{3} d^{6}\right)}"," ",0,"-2/315*(c*d*x+a*e)*(8*c^2*d^2*e^2*x^2-20*a*c*d*e^3*x+36*c^2*d^3*e*x+35*a^2*e^4-90*a*c*d^2*e^2+63*c^2*d^4)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(3/2)/(e*x+d)^6/(a^3*e^6-3*a^2*c*d^2*e^4+3*a*c^2*d^4*e^2-c^3*d^6)","A"
1930,1,217,215,0.052000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)/(e*x+d)^8,x)","-\frac{2 \left(c d x +a e \right) \left(-16 c^{3} d^{3} e^{3} x^{3}+40 a \,c^{2} d^{2} e^{4} x^{2}-88 c^{3} d^{4} e^{2} x^{2}-70 a^{2} c d \,e^{5} x +220 a \,c^{2} d^{3} e^{3} x -198 c^{3} d^{5} e x +105 a^{3} e^{6}-385 a^{2} c \,d^{2} e^{4}+495 a \,c^{2} d^{4} e^{2}-231 c^{3} d^{6}\right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{3}{2}}}{1155 \left(e x +d \right)^{7} \left(a^{4} e^{8}-4 a^{3} c \,d^{2} e^{6}+6 a^{2} c^{2} d^{4} e^{4}-4 a \,c^{3} d^{6} e^{2}+c^{4} d^{8}\right)}"," ",0,"-2/1155*(c*d*x+a*e)*(-16*c^3*d^3*e^3*x^3+40*a*c^2*d^2*e^4*x^2-88*c^3*d^4*e^2*x^2-70*a^2*c*d*e^5*x+220*a*c^2*d^3*e^3*x-198*c^3*d^5*e*x+105*a^3*e^6-385*a^2*c*d^2*e^4+495*a*c^2*d^4*e^2-231*c^3*d^6)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(3/2)/(e*x+d)^7/(a^4*e^8-4*a^3*c*d^2*e^6+6*a^2*c^2*d^4*e^4-4*a*c^3*d^6*e^2+c^4*d^8)","A"
1931,1,2973,488,0.076000," ","int((e*x+d)^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2),x)","\text{output too large to display}"," ",0,"1137/4480/c*d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)+143/7680*d^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*x+715/49152*d^6*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a+143/15360/e*d^5*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)+1/10*e^3*x^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)/c/d-1001/131072/e*c*d^9*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a+715/32768*e*d^7*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^2+143/131072/e^3*c^2*d^11*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)-143/49152/e^2*c*d^8*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)+67/180*e^2/c*x^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)-10777/40320*e^2/c^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)*a+715/49152*e^6/c^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a^4-143/262144/e^3*c^3*d^13*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)-1001/131072*e^13/c^6/d^5*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^8+715/32768*e^11/c^5/d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^7+143/7680*e^3/c^2*d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*a^2-143/5120*e/c*d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*a-429/16384*e^2/c*d^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a^2+143/4096*e*d^5*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*a-143/8192*c*d^8*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a-1001/32768*e^3/c*d^5*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^3+143/7680*e^5/c^3/d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*a^3-1001/32768*e^9/c^4/d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^6+1001/65536*e^7/c^3*d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^5-143/4480*e^6/c^4/d^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)*a^3+5863/40320*e^4/c^3/d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)*a^2+1423/2880*e/c*d*x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)+143/131072*e^15/c^7/d^7*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^9+1001/65536*e^5/c^2*d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^4-143/49152*e^12/c^6/d^6*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a^7+715/49152*e^10/c^5/d^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a^6-429/16384*e^8/c^4/d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a^5-143/24576/e*c*d^7*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x+143/65536/e^2*c^2*d^10*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x+715/49152*e^4/c^2*d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a^3+143/15360*e^9/c^5/d^5*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*a^5-143/5120*e^7/c^4/d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*a^4-1001/8192*e^8/c^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^5+1001/16384*e^2*d^6*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^2+143/1280*e^4/c^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*x*a^2+2145/32768*e^3*d^7*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^3-15015/131072*e^5/c*d^5*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^4-13/180*e^4/c^2/d^2*x^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)*a+715/131072/e*c^2*d^11*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a+1001/16384*e^10/c^4/d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^6+5005/32768*e^6/c^2*d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^4-1001/8192*e^4/c*d^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^3-15015/131072*e^9/c^3*d*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^6+9009/65536*e^7/c^2*d^3*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^5-6435/262144*e^13/c^5/d^3*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^8-143/24576*e^11/c^5/d^5*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*a^6+143/4096*e^9/c^4/d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*a^5-715/8192*e^7/c^3/d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*a^4-143/262144*e^17/c^7/d^7*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^10+715/131072*e^15/c^6/d^5*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^9+143/2880*e^5/c^3/d^3*x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)*a^2+715/6144*e^5/c^2*d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*a^3+143/7680*e^8/c^4/d^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*x*a^4-143/1920*e^6/c^3/d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*x*a^3-6435/262144*e*c*d^9*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^2+143/65536*e^14/c^6/d^6*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^8-143/8192*e^12/c^5/d^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^7-39/160*e^3/c^2/d*x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)*a-143/1920*e^2/c*d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*x*a-715/8192*e^3/c*d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*a^2+2145/32768*e^11/c^4/d*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^7","B"
1932,1,2368,432,0.063000," ","int((e*x+d)^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2),x)","\frac{55 a^{9} e^{15} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{65536 \sqrt{c d e}\, c^{6} d^{6}}-\frac{495 a^{8} e^{13} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{65536 \sqrt{c d e}\, c^{5} d^{4}}+\frac{495 a^{7} e^{11} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{16384 \sqrt{c d e}\, c^{4} d^{2}}-\frac{1155 a^{6} e^{9} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{16384 \sqrt{c d e}\, c^{3}}+\frac{3465 a^{5} d^{2} e^{7} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{32768 \sqrt{c d e}\, c^{2}}-\frac{3465 a^{4} d^{4} e^{5} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{32768 \sqrt{c d e}\, c}+\frac{1155 a^{3} d^{6} e^{3} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{16384 \sqrt{c d e}}-\frac{495 a^{2} c \,d^{8} e \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{16384 \sqrt{c d e}}+\frac{495 a \,c^{2} d^{10} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{65536 \sqrt{c d e}\, e}-\frac{55 c^{3} d^{12} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{65536 \sqrt{c d e}\, e^{3}}-\frac{55 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{7} e^{12} x}{16384 c^{5} d^{5}}+\frac{385 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{6} e^{10} x}{16384 c^{4} d^{3}}-\frac{1155 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{5} e^{8} x}{16384 c^{3} d}+\frac{1925 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{4} d \,e^{6} x}{16384 c^{2}}-\frac{1925 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{3} d^{3} e^{4} x}{16384 c}+\frac{1155 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{2} d^{5} e^{2} x}{16384}-\frac{385 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a c \,d^{7} x}{16384}+\frac{55 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2} d^{9} x}{16384 e^{2}}-\frac{55 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{8} e^{13}}{32768 c^{6} d^{6}}+\frac{165 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{7} e^{11}}{16384 c^{5} d^{4}}-\frac{385 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{6} e^{9}}{16384 c^{4} d^{2}}+\frac{385 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{5} e^{7}}{16384 c^{3}}-\frac{385 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{3} d^{4} e^{3}}{16384 c}+\frac{385 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{2} d^{6} e}{16384}-\frac{165 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a c \,d^{8}}{16384 e}+\frac{55 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2} d^{10}}{32768 e^{3}}+\frac{55 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a^{5} e^{9} x}{6144 c^{4} d^{4}}-\frac{275 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a^{4} e^{7} x}{6144 c^{3} d^{2}}+\frac{275 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a^{3} e^{5} x}{3072 c^{2}}-\frac{275 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a^{2} d^{2} e^{3} x}{3072 c}+\frac{275 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a \,d^{4} e x}{6144}-\frac{55 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c \,d^{6} x}{6144 e}+\frac{55 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a^{6} e^{10}}{12288 c^{5} d^{5}}-\frac{55 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a^{5} e^{8}}{3072 c^{4} d^{3}}+\frac{275 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a^{4} e^{6}}{12288 c^{3} d}-\frac{275 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a^{2} d^{3} e^{2}}{12288 c}+\frac{55 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a \,d^{5}}{3072}-\frac{55 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c \,d^{7}}{12288 e^{2}}-\frac{11 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} a^{3} e^{6} x}{384 c^{3} d^{3}}+\frac{11 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} a^{2} e^{4} x}{128 c^{2} d}-\frac{11 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} a d \,e^{2} x}{128 c}+\frac{11 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} d^{3} x}{384}-\frac{11 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} a^{4} e^{7}}{768 c^{4} d^{4}}+\frac{11 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} a^{3} e^{5}}{384 c^{3} d^{2}}-\frac{11 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} a \,d^{2} e}{384 c}+\frac{11 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} d^{4}}{768 e}+\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{7}{2}} e^{2} x^{2}}{9 c d}-\frac{11 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{7}{2}} a \,e^{3} x}{144 c^{2} d^{2}}+\frac{43 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{7}{2}} e x}{144 c}+\frac{11 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{7}{2}} a^{2} e^{4}}{224 c^{3} d^{3}}-\frac{11 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{7}{2}} a \,e^{2}}{63 c^{2} d}+\frac{53 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{7}{2}} d}{224 c}"," ",0,"11/224*e^4/c^3/d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)*a^2+55/12288*e^10/c^5/d^5*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a^6+53/224/c*d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)+11/384*d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*x+55/3072*d^5*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a+11/768/e*d^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)-55/12288/e^2*c*d^7*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)+55/32768/e^3*c^2*d^10*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+385/16384*e^7/c^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^5+43/144*e/c*x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)+385/16384*e*d^6*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^2-55/3072*e^8/c^4/d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a^5+275/12288*e^6/c^3/d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a^4+1/9*e^2*x^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)/c/d+1155/16384*e^3*d^6*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^3+275/3072*e^5/c^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*a^3+495/65536/e*c^2*d^10*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a-3465/32768*e^5/c*d^4*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^4+385/16384*e^10/c^4/d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^6-11/144*e^3/c^2/d^2*x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)*a-11/384*e^6/c^3/d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*x*a^3+3465/32768*e^7/c^2*d^2*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^5+11/128*e^4/c^2/d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*x*a^2-275/6144*e^7/c^3/d^2*a^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x+55/6144*e^9/c^4/d^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*a^5-495/65536*e^13/c^5/d^4*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^8+55/65536*e^15/c^6/d^6*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^9+495/16384*e^11/c^4/d^2*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^7-1925/16384*e^4/c*d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^3-55/16384*e^12/c^5/d^5*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^7-1155/16384*e^8/c^3/d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^5-11/128*e^2/c*d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*x*a+1925/16384*e^6/c^2*d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^4-495/16384*e*c*d^8*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^2+275/6144*e*d^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*a-1155/16384*e^9/c^3*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^6+1155/16384*e^2*d^5*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^2-11/768*e^7/c^4/d^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*a^4+11/384*e^5/c^3/d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*a^3-165/16384/e*c*d^8*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a-55/65536/e^3*c^3*d^12*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)-55/32768*e^13/c^6/d^6*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^8+165/16384*e^11/c^5/d^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^7-385/16384*c*d^7*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a+55/16384/e^2*c^2*d^9*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x-275/12288*e^2/c*d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a^2-385/16384*e^3/c*d^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^3-11/384*e/c*d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*a-11/63*e^2/c^2/d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)*a-55/6144/e*c*d^6*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x-385/16384*e^9/c^4/d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^6-275/3072*e^3/c*d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*a^2","B"
1933,1,2044,376,0.057000," ","int((e*x+d)^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2),x)","-\frac{45 a^{8} e^{13} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{32768 \sqrt{c d e}\, c^{5} d^{5}}+\frac{45 a^{7} e^{11} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{4096 \sqrt{c d e}\, c^{4} d^{3}}-\frac{315 a^{6} e^{9} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{8192 \sqrt{c d e}\, c^{3} d}+\frac{315 a^{5} d \,e^{7} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{4096 \sqrt{c d e}\, c^{2}}-\frac{1575 a^{4} d^{3} e^{5} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{16384 \sqrt{c d e}\, c}+\frac{315 a^{3} d^{5} e^{3} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{4096 \sqrt{c d e}}-\frac{315 a^{2} c \,d^{7} e \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{8192 \sqrt{c d e}}+\frac{45 a \,c^{2} d^{9} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{4096 \sqrt{c d e}\, e}-\frac{45 c^{3} d^{11} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{32768 \sqrt{c d e}\, e^{3}}+\frac{45 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{6} e^{10} x}{8192 c^{4} d^{4}}-\frac{135 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{5} e^{8} x}{4096 c^{3} d^{2}}+\frac{675 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{4} e^{6} x}{8192 c^{2}}-\frac{225 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{3} d^{2} e^{4} x}{2048 c}+\frac{675 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{2} d^{4} e^{2} x}{8192}-\frac{135 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a c \,d^{6} x}{4096}+\frac{45 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2} d^{8} x}{8192 e^{2}}+\frac{45 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{7} e^{11}}{16384 c^{5} d^{5}}-\frac{225 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{6} e^{9}}{16384 c^{4} d^{3}}+\frac{405 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{5} e^{7}}{16384 c^{3} d}-\frac{225 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{4} d \,e^{5}}{16384 c^{2}}-\frac{225 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{3} d^{3} e^{3}}{16384 c}+\frac{405 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{2} d^{5} e}{16384}-\frac{225 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a c \,d^{7}}{16384 e}+\frac{45 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2} d^{9}}{16384 e^{3}}-\frac{15 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a^{4} e^{7} x}{1024 c^{3} d^{3}}+\frac{15 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a^{3} e^{5} x}{256 c^{2} d}-\frac{45 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a^{2} d \,e^{3} x}{512 c}+\frac{15 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a \,d^{3} e x}{256}-\frac{15 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c \,d^{5} x}{1024 e}-\frac{15 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a^{5} e^{8}}{2048 c^{4} d^{4}}+\frac{45 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a^{4} e^{6}}{2048 c^{3} d^{2}}-\frac{15 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a^{3} e^{4}}{1024 c^{2}}-\frac{15 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a^{2} d^{2} e^{2}}{1024 c}+\frac{45 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a \,d^{4}}{2048}-\frac{15 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c \,d^{6}}{2048 e^{2}}+\frac{3 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} a^{2} e^{4} x}{64 c^{2} d^{2}}-\frac{3 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} a \,e^{2} x}{32 c}+\frac{3 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} d^{2} x}{64}+\frac{3 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} a^{3} e^{5}}{128 c^{3} d^{3}}-\frac{3 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} a^{2} e^{3}}{128 c^{2} d}-\frac{3 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} a d e}{128 c}+\frac{3 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} d^{3}}{128 e}+\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{7}{2}} e x}{8 c d}-\frac{9 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{7}{2}} a \,e^{2}}{112 c^{2} d^{2}}+\frac{23 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{7}{2}}}{112 c}"," ",0,"45/2048*d^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a+3/64*d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*x-15/1024*e^2/c*d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a^2-3/32*e^2/c*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*x*a+405/16384*e^7/c^3/d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^5-3/128*e/c*d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*a-225/16384*e^3/c*d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^3+3/128*e^5/c^3/d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*a^3+45/2048*e^6/c^3/d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a^4+45/16384*e^11/c^5/d^5*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^7-225/16384/e*c*d^7*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a+15/256*e*a*d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x+45/16384/e^3*c^2*d^9*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)-15/1024*e^4/c^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a^3+405/16384*e*d^5*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^2-15/2048/e^2*c*d^6*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)+315/4096*e^3*d^5*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^3+675/8192*e^2*d^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^2+23/112/c*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)+3/128/e*d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)-45/32768/e^3*c^3*d^11*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)-15/1024/e*c*d^5*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x-9/112*e^2/c^2/d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)*a+45/8192/e^2*c^2*d^8*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x-225/16384*e^5/c^2*d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^4+675/8192*e^6/c^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^4-135/4096*c*d^6*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a-15/2048*e^8/c^4/d^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a^5+1/8*e*x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)/c/d-225/16384*e^9/c^4/d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^6-3/128*e^3/c^2/d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*a^2+45/4096*e^11/c^4/d^3*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^7+45/8192*e^10/c^4/d^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^6-45/32768*e^13/c^5/d^5*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^8-315/8192*e*c*d^7*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^2-45/512*e^3/c*d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*a^2+45/4096/e*c^2*d^9*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a+15/256*e^5*a^3/c^2/d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x-135/4096*e^8/c^3/d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^5-225/2048*e^4/c*d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^3+3/64*e^4/c^2/d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*x*a^2-315/8192*e^9/c^3/d*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^6+315/4096*e^7/c^2*d*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^5-1575/16384*e^5/c*d^3*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^4-15/1024*e^7/c^3/d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*a^4","B"
1934,1,1533,322,0.053000," ","int((e*x+d)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2),x)","\frac{5 a^{7} e^{11} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{2048 \sqrt{c d e}\, c^{4} d^{4}}-\frac{35 a^{6} e^{9} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{2048 \sqrt{c d e}\, c^{3} d^{2}}+\frac{105 a^{5} e^{7} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{2048 \sqrt{c d e}\, c^{2}}-\frac{175 a^{4} d^{2} e^{5} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{2048 \sqrt{c d e}\, c}+\frac{175 a^{3} d^{4} e^{3} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{2048 \sqrt{c d e}}-\frac{105 a^{2} c \,d^{6} e \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{2048 \sqrt{c d e}}+\frac{35 a \,c^{2} d^{8} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{2048 \sqrt{c d e}\, e}-\frac{5 c^{3} d^{10} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{2048 \sqrt{c d e}\, e^{3}}-\frac{5 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{5} e^{8} x}{512 c^{3} d^{3}}+\frac{25 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{4} e^{6} x}{512 c^{2} d}-\frac{25 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{3} d \,e^{4} x}{256 c}+\frac{25 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{2} d^{3} e^{2} x}{256}-\frac{25 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a c \,d^{5} x}{512}+\frac{5 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2} d^{7} x}{512 e^{2}}-\frac{5 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{6} e^{9}}{1024 c^{4} d^{4}}+\frac{5 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{5} e^{7}}{256 c^{3} d^{2}}-\frac{25 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{4} e^{5}}{1024 c^{2}}+\frac{25 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{2} d^{4} e}{1024}-\frac{5 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a c \,d^{6}}{256 e}+\frac{5 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2} d^{8}}{1024 e^{3}}+\frac{5 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a^{3} e^{5} x}{192 c^{2} d^{2}}-\frac{5 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a^{2} e^{3} x}{64 c}+\frac{5 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a \,d^{2} e x}{64}-\frac{5 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c \,d^{4} x}{192 e}+\frac{5 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a^{4} e^{6}}{384 c^{3} d^{3}}-\frac{5 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a^{3} e^{4}}{192 c^{2} d}+\frac{5 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a \,d^{3}}{192}-\frac{5 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c \,d^{5}}{384 e^{2}}-\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} a \,e^{2} x}{12 c d}+\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} d x}{12}-\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} a^{2} e^{3}}{24 c^{2} d^{2}}+\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} d^{2}}{24 e}+\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{7}{2}}}{7 c d}"," ",0,"-1/12/c/d*e^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*x*a-105/2048*e*c*d^6*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^2-35/2048/c^3/d^2*e^9*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^6+1/7*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)/c/d-25/1024/c^2*e^5*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^4+25/1024*e*d^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^2+5/1024*c^2*d^8/e^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)-5/384*c*d^5/e^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)+5/192*d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a+1/24*d^2/e*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)+1/12*d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*x-25/512*c*d^5*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a-5/192/c^2/d*e^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a^3+5/512*c^2*d^7/e^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x+5/64*e*d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*a+25/256*d^3*e^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^2+105/2048/c^2*e^7*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^5-5/256*c*d^6/e*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a-5/192*c*d^4/e*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x-1/24/c^2/d^2*e^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*a^2+5/256/c^3/d^2*e^7*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^5+175/2048*d^4*e^3*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^3-5/64/c*e^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*a^2-5/2048*c^3*d^10/e^3*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)+5/384/c^3/d^3*e^6*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a^4-5/1024/c^4/d^4*e^9*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^6+25/512/c^2/d*e^6*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^4-25/256/c*d*e^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^3-175/2048/c*d^2*e^5*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^4+35/2048*c^2*d^8/e*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a+5/192/c^2/d^2*e^5*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*a^3-5/512/c^3/d^3*e^8*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^5+5/2048/c^4/d^4*e^11*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^7","B"
1935,1,1247,275,0.059000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2),x)","-\frac{5 a^{6} e^{9} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{1024 \sqrt{c d e}\, c^{3} d^{3}}+\frac{15 a^{5} e^{7} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{512 \sqrt{c d e}\, c^{2} d}-\frac{75 a^{4} d \,e^{5} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{1024 \sqrt{c d e}\, c}+\frac{25 a^{3} d^{3} e^{3} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{256 \sqrt{c d e}}-\frac{75 a^{2} c \,d^{5} e \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{1024 \sqrt{c d e}}+\frac{15 a \,c^{2} d^{7} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{512 \sqrt{c d e}\, e}-\frac{5 c^{3} d^{9} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{1024 \sqrt{c d e}\, e^{3}}+\frac{5 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{4} e^{6} x}{256 c^{2} d^{2}}-\frac{5 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{3} e^{4} x}{64 c}+\frac{15 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{2} d^{2} e^{2} x}{128}-\frac{5 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a c \,d^{4} x}{64}+\frac{5 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2} d^{6} x}{256 e^{2}}+\frac{5 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{5} e^{7}}{512 c^{3} d^{3}}-\frac{15 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{4} e^{5}}{512 c^{2} d}+\frac{5 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{3} d \,e^{3}}{256 c}+\frac{5 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{2} d^{3} e}{256}-\frac{15 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a c \,d^{5}}{512 e}+\frac{5 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2} d^{7}}{512 e^{3}}-\frac{5 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a^{2} e^{3} x}{96 c d}+\frac{5 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a d e x}{48}-\frac{5 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c \,d^{3} x}{96 e}-\frac{5 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a^{3} e^{4}}{192 c^{2} d^{2}}+\frac{5 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a^{2} e^{2}}{192 c}+\frac{5 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a \,d^{2}}{192}-\frac{5 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c \,d^{4}}{192 e^{2}}+\frac{\left(2 c d e x +a \,e^{2}+c \,d^{2}\right) \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}}}{12 c d e}"," ",0,"15/128*d^2*e^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^2-15/512/c^2/d*e^5*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^4-5/64/c*e^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^3+5/256/c^2/d^2*e^6*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^4-5/96/c/d*e^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*a^2-5/1024/c^3/d^3*e^9*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^6-75/1024/c*d*e^5*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^4+15/512*c^2*d^7/e*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a-75/1024*c*d^5*e*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^2+15/512/c^2/d*e^7*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^5-5/192*c*d^4/e^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)+5/512*c^2*d^7/e^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+5/192/c*e^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a^2+5/256*d^3*e*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^2+5/192*d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a+5/48*d*e*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*a-5/192/c^2/d^2*e^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a^3-15/512*c*d^5/e*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a-5/96*c*d^3/e*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x-5/1024*c^3*d^9/e^3*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)+5/256/c*d*e^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^3+5/512/c^3/d^3*e^7*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^5+5/256*c^2*d^6/e^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x+25/256*d^3*e^3*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^3-5/64*c*d^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a+1/12*(2*c*d*e*x+a*e^2+c*d^2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/c/d/e","B"
1936,1,1123,244,0.055000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/(e*x+d),x)","\frac{3 a^{5} e^{7} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{256 \sqrt{c d e}\, c^{2} d^{2}}-\frac{15 a^{4} e^{5} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{256 \sqrt{c d e}\, c}+\frac{15 a^{3} d^{2} e^{3} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{128 \sqrt{c d e}}-\frac{15 a^{2} c \,d^{4} e \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{128 \sqrt{c d e}}+\frac{15 a \,c^{2} d^{6} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{256 \sqrt{c d e}\, e}-\frac{3 c^{3} d^{8} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{256 \sqrt{c d e}\, e^{3}}-\frac{3 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{3} e^{4} x}{64 c d}+\frac{9 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{2} d \,e^{2} x}{64}-\frac{9 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a c \,d^{3} x}{64}+\frac{3 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, c^{2} d^{5} x}{64 e^{2}}-\frac{3 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{4} e^{5}}{128 c^{2} d^{2}}+\frac{3 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{3} e^{3}}{64 c}-\frac{3 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a c \,d^{4}}{64 e}+\frac{3 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, c^{2} d^{6}}{128 e^{3}}+\frac{\left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}} a e x}{8}-\frac{\left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}} c \,d^{2} x}{8 e}+\frac{\left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}} a^{2} e^{2}}{16 c d}-\frac{\left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}} c \,d^{3}}{16 e^{2}}+\frac{\left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{5}{2}}}{5 e}"," ",0,"1/5/e*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(5/2)-1/16/e^2*c*d^3*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)+3/128/e^3*c^2*d^6*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)-1/8/e*c*d^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)*x-15/128*e*a^2*c*d^4*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+15/256/e*a*c^2*d^6*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-3/64*e^4*a^3/c/d*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x-9/64*a*c*d^3*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x+3/256*e^7*a^5/c^2/d^2*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+3/64*e^3*a^3/c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)+1/8*e*a*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)*x+1/16*e^2*a^2/c/d*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)+15/128*e^3*a^3*d^2*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+3/64/e^2*c^2*d^5*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x-15/256*e^5*a^4/c*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+9/64*e^2*a^2*d*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x-3/128*e^5*a^4/c^2/d^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)-3/64/e*a*c*d^4*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)-3/256/e^3*c^3*d^8*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)","B"
1937,1,1455,231,0.064000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/(e*x+d)^2,x)","-\frac{5 a^{5} e^{7} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{128 \left(a \,e^{2}-c \,d^{2}\right) \sqrt{c d e}\, c d}+\frac{25 a^{4} d \,e^{5} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{128 \left(a \,e^{2}-c \,d^{2}\right) \sqrt{c d e}}-\frac{25 a^{3} c \,d^{3} e^{3} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{64 \left(a \,e^{2}-c \,d^{2}\right) \sqrt{c d e}}+\frac{25 a^{2} c^{2} d^{5} e \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{64 \left(a \,e^{2}-c \,d^{2}\right) \sqrt{c d e}}-\frac{25 a \,c^{3} d^{7} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{128 \left(a \,e^{2}-c \,d^{2}\right) \sqrt{c d e}\, e}+\frac{5 c^{4} d^{9} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{128 \left(a \,e^{2}-c \,d^{2}\right) \sqrt{c d e}\, e^{3}}+\frac{5 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{3} e^{4} x}{32 \left(a \,e^{2}-c \,d^{2}\right)}-\frac{15 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{2} c \,d^{2} e^{2} x}{32 \left(a \,e^{2}-c \,d^{2}\right)}+\frac{15 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a \,c^{2} d^{4} x}{32 \left(a \,e^{2}-c \,d^{2}\right)}-\frac{5 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, c^{3} d^{6} x}{32 \left(a \,e^{2}-c \,d^{2}\right) e^{2}}+\frac{5 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{4} e^{5}}{64 \left(a \,e^{2}-c \,d^{2}\right) c d}-\frac{5 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{3} d \,e^{3}}{32 \left(a \,e^{2}-c \,d^{2}\right)}+\frac{5 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a \,c^{2} d^{5}}{32 \left(a \,e^{2}-c \,d^{2}\right) e}-\frac{5 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, c^{3} d^{7}}{64 \left(a \,e^{2}-c \,d^{2}\right) e^{3}}-\frac{5 \left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}} a c d e x}{12 \left(a \,e^{2}-c \,d^{2}\right)}+\frac{5 \left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}} c^{2} d^{3} x}{12 \left(a \,e^{2}-c \,d^{2}\right) e}-\frac{5 \left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}} a^{2} e^{2}}{24 \left(a \,e^{2}-c \,d^{2}\right)}+\frac{5 \left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}} c^{2} d^{4}}{24 \left(a \,e^{2}-c \,d^{2}\right) e^{2}}-\frac{2 \left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{5}{2}} c d}{3 \left(a \,e^{2}-c \,d^{2}\right) e}+\frac{2 \left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{7}{2}}}{3 \left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)^{2} e^{2}}"," ",0,"2/3/e^2/(a*e^2-c*d^2)/(x+d/e)^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(7/2)-2/3/e*c*d/(a*e^2-c*d^2)*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(5/2)-5/64/e^3*c^3*d^7/(a*e^2-c*d^2)*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)+5/12/e*c^2*d^3/(a*e^2-c*d^2)*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)*x+5/24/e^2*c^2*d^4/(a*e^2-c*d^2)*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)-5/12*e*c*d/(a*e^2-c*d^2)*a*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)*x-5/32*e^3*d/(a*e^2-c*d^2)*a^3*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)-25/128/e*c^3*d^7/(a*e^2-c*d^2)*a*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+5/32*e^4/(a*e^2-c*d^2)*a^3*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x+15/32*c^2*d^4/(a*e^2-c*d^2)*a*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x-5/128*e^7/c/d/(a*e^2-c*d^2)*a^5*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+25/64*e*c^2*d^5/(a*e^2-c*d^2)*a^2*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+25/128*e^5*d/(a*e^2-c*d^2)*a^4*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-25/64*e^3*c*d^3/(a*e^2-c*d^2)*a^3*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-5/24*e^2/(a*e^2-c*d^2)*a^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)-15/32*e^2*c*d^2/(a*e^2-c*d^2)*a^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x+5/64*e^5/c/d/(a*e^2-c*d^2)*a^4*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)+5/32/e*c^2*d^5/(a*e^2-c*d^2)*a*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)-5/32/e^2*c^3*d^6/(a*e^2-c*d^2)*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x+5/128/e^3*c^4*d^9/(a*e^2-c*d^2)*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)","B"
1938,1,1531,216,0.057000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/(e*x+d)^3,x)","\frac{5 a^{5} e^{7} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{16 \left(a \,e^{2}-c \,d^{2}\right)^{2} \sqrt{c d e}}-\frac{25 a^{4} c \,d^{2} e^{5} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{16 \left(a \,e^{2}-c \,d^{2}\right)^{2} \sqrt{c d e}}+\frac{25 a^{3} c^{2} d^{4} e^{3} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{8 \left(a \,e^{2}-c \,d^{2}\right)^{2} \sqrt{c d e}}-\frac{25 a^{2} c^{3} d^{6} e \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{8 \left(a \,e^{2}-c \,d^{2}\right)^{2} \sqrt{c d e}}+\frac{25 a \,c^{4} d^{8} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{16 \left(a \,e^{2}-c \,d^{2}\right)^{2} \sqrt{c d e}\, e}-\frac{5 c^{5} d^{10} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{16 \left(a \,e^{2}-c \,d^{2}\right)^{2} \sqrt{c d e}\, e^{3}}-\frac{5 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{3} c d \,e^{4} x}{4 \left(a \,e^{2}-c \,d^{2}\right)^{2}}+\frac{15 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{2} c^{2} d^{3} e^{2} x}{4 \left(a \,e^{2}-c \,d^{2}\right)^{2}}-\frac{15 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a \,c^{3} d^{5} x}{4 \left(a \,e^{2}-c \,d^{2}\right)^{2}}+\frac{5 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, c^{4} d^{7} x}{4 \left(a \,e^{2}-c \,d^{2}\right)^{2} e^{2}}-\frac{5 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{4} e^{5}}{8 \left(a \,e^{2}-c \,d^{2}\right)^{2}}+\frac{5 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{3} c \,d^{2} e^{3}}{4 \left(a \,e^{2}-c \,d^{2}\right)^{2}}-\frac{5 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a \,c^{3} d^{6}}{4 \left(a \,e^{2}-c \,d^{2}\right)^{2} e}+\frac{5 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, c^{4} d^{8}}{8 \left(a \,e^{2}-c \,d^{2}\right)^{2} e^{3}}+\frac{10 \left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}} a \,c^{2} d^{2} e x}{3 \left(a \,e^{2}-c \,d^{2}\right)^{2}}-\frac{10 \left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}} c^{3} d^{4} x}{3 \left(a \,e^{2}-c \,d^{2}\right)^{2} e}+\frac{5 \left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}} a^{2} c d \,e^{2}}{3 \left(a \,e^{2}-c \,d^{2}\right)^{2}}-\frac{5 \left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}} c^{3} d^{5}}{3 \left(a \,e^{2}-c \,d^{2}\right)^{2} e^{2}}+\frac{16 \left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{5}{2}} c^{2} d^{2}}{3 \left(a \,e^{2}-c \,d^{2}\right)^{2} e}-\frac{16 \left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{7}{2}} c d}{3 \left(a \,e^{2}-c \,d^{2}\right)^{2} \left(x +\frac{d}{e}\right)^{2} e^{2}}+\frac{2 \left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{7}{2}}}{\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)^{3} e^{3}}"," ",0,"2/e^3/(a*e^2-c*d^2)/(x+d/e)^3*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(7/2)-16/3/e^2*c*d/(a*e^2-c*d^2)^2/(x+d/e)^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(7/2)+16/3/e*c^2*d^2/(a*e^2-c*d^2)^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(5/2)-25/8*e*c^3*d^6/(a*e^2-c*d^2)^2*a^2*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+25/16/e*c^4*d^8/(a*e^2-c*d^2)^2*a*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-5/4*e^4*c*d/(a*e^2-c*d^2)^2*a^3*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x-15/4*c^3*d^5/(a*e^2-c*d^2)^2*a*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x+5/16*e^7/(a*e^2-c*d^2)^2*a^5*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+5/8/e^3*c^4*d^8/(a*e^2-c*d^2)^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)-5/3/e^2*c^3*d^5/(a*e^2-c*d^2)^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)-10/3/e*c^3*d^4/(a*e^2-c*d^2)^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)*x+5/4*e^3*c*d^2/(a*e^2-c*d^2)^2*a^3*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)+10/3*e*c^2*d^2/(a*e^2-c*d^2)^2*a*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)*x+5/3*e^2*c*d/(a*e^2-c*d^2)^2*a^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)+15/4*e^2*c^2*d^3/(a*e^2-c*d^2)^2*a^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x-5/8*e^5/(a*e^2-c*d^2)^2*a^4*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)+5/4/e^2*c^4*d^7/(a*e^2-c*d^2)^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x-5/16/e^3*c^5*d^10/(a*e^2-c*d^2)^2*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+25/8*e^3*c^2*d^4/(a*e^2-c*d^2)^2*a^3*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-5/4/e*c^3*d^6/(a*e^2-c*d^2)^2*a*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)-25/16*e^5*c*d^2/(a*e^2-c*d^2)^2*a^4*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)","B"
1939,1,1617,207,0.057000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/(e*x+d)^4,x)","\frac{15 a^{5} c d \,e^{7} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{8 \left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{c d e}}-\frac{75 a^{4} c^{2} d^{3} e^{5} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{8 \left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{c d e}}+\frac{75 a^{3} c^{3} d^{5} e^{3} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{4 \left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{c d e}}-\frac{75 a^{2} c^{4} d^{7} e \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{4 \left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{c d e}}+\frac{75 a \,c^{5} d^{9} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{8 \left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{c d e}\, e}-\frac{15 c^{6} d^{11} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{8 \left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{c d e}\, e^{3}}-\frac{15 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{3} c^{2} d^{2} e^{4} x}{2 \left(a \,e^{2}-c \,d^{2}\right)^{3}}+\frac{45 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{2} c^{3} d^{4} e^{2} x}{2 \left(a \,e^{2}-c \,d^{2}\right)^{3}}-\frac{45 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a \,c^{4} d^{6} x}{2 \left(a \,e^{2}-c \,d^{2}\right)^{3}}+\frac{15 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, c^{5} d^{8} x}{2 \left(a \,e^{2}-c \,d^{2}\right)^{3} e^{2}}-\frac{15 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{4} c d \,e^{5}}{4 \left(a \,e^{2}-c \,d^{2}\right)^{3}}+\frac{15 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{3} c^{2} d^{3} e^{3}}{2 \left(a \,e^{2}-c \,d^{2}\right)^{3}}-\frac{15 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a \,c^{4} d^{7}}{2 \left(a \,e^{2}-c \,d^{2}\right)^{3} e}+\frac{15 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, c^{5} d^{9}}{4 \left(a \,e^{2}-c \,d^{2}\right)^{3} e^{3}}+\frac{20 \left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}} a \,c^{3} d^{3} e x}{\left(a \,e^{2}-c \,d^{2}\right)^{3}}-\frac{20 \left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}} c^{4} d^{5} x}{\left(a \,e^{2}-c \,d^{2}\right)^{3} e}+\frac{10 \left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}} a^{2} c^{2} d^{2} e^{2}}{\left(a \,e^{2}-c \,d^{2}\right)^{3}}-\frac{10 \left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}} c^{4} d^{6}}{\left(a \,e^{2}-c \,d^{2}\right)^{3} e^{2}}+\frac{32 \left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{5}{2}} c^{3} d^{3}}{\left(a \,e^{2}-c \,d^{2}\right)^{3} e}-\frac{32 \left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{7}{2}} c^{2} d^{2}}{\left(a \,e^{2}-c \,d^{2}\right)^{3} \left(x +\frac{d}{e}\right)^{2} e^{2}}+\frac{12 \left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{7}{2}} c d}{\left(a \,e^{2}-c \,d^{2}\right)^{2} \left(x +\frac{d}{e}\right)^{3} e^{3}}-\frac{2 \left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{7}{2}}}{\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)^{4} e^{4}}"," ",0,"-2/e^4/(a*e^2-c*d^2)/(x+d/e)^4*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(7/2)+12/e^3*c*d/(a*e^2-c*d^2)^2/(x+d/e)^3*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(7/2)-32/e^2*c^2*d^2/(a*e^2-c*d^2)^3/(x+d/e)^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(7/2)+32/e*c^3*d^3/(a*e^2-c*d^2)^3*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(5/2)+15/4/e^3*c^5*d^9/(a*e^2-c*d^2)^3*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)-20/e*c^4*d^5/(a*e^2-c*d^2)^3*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)*x-10/e^2*c^4*d^6/(a*e^2-c*d^2)^3*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)+20*e*c^3*d^3/(a*e^2-c*d^2)^3*a*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)*x+15/2*e^3*c^2*d^3/(a*e^2-c*d^2)^3*a^3*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)+75/8/e*c^5*d^9/(a*e^2-c*d^2)^3*a*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-45/2*c^4*d^6/(a*e^2-c*d^2)^3*a*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x+15/8*e^7*c*d/(a*e^2-c*d^2)^3*a^5*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-75/4*e*c^4*d^7/(a*e^2-c*d^2)^3*a^2*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-15/2*e^4*c^2*d^2/(a*e^2-c*d^2)^3*a^3*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x+10*e^2*c^2*d^2/(a*e^2-c*d^2)^3*a^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)+45/2*e^2*c^3*d^4/(a*e^2-c*d^2)^3*a^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x-15/4*e^5*c*d/(a*e^2-c*d^2)^3*a^4*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)-15/2/e*c^4*d^7/(a*e^2-c*d^2)^3*a*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)-15/8/e^3*c^6*d^11/(a*e^2-c*d^2)^3*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+15/2/e^2*c^5*d^8/(a*e^2-c*d^2)^3*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x-75/8*e^5*c^2*d^3/(a*e^2-c*d^2)^3*a^4*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+75/4*e^3*c^3*d^5/(a*e^2-c*d^2)^3*a^3*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)","B"
1940,1,1695,198,0.059000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/(e*x+d)^5,x)","\frac{5 a^{5} c^{2} d^{2} e^{7} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{2 \left(a \,e^{2}-c \,d^{2}\right)^{4} \sqrt{c d e}}-\frac{25 a^{4} c^{3} d^{4} e^{5} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{2 \left(a \,e^{2}-c \,d^{2}\right)^{4} \sqrt{c d e}}+\frac{25 a^{3} c^{4} d^{6} e^{3} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{\left(a \,e^{2}-c \,d^{2}\right)^{4} \sqrt{c d e}}-\frac{25 a^{2} c^{5} d^{8} e \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{\left(a \,e^{2}-c \,d^{2}\right)^{4} \sqrt{c d e}}+\frac{25 a \,c^{6} d^{10} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{2 \left(a \,e^{2}-c \,d^{2}\right)^{4} \sqrt{c d e}\, e}-\frac{5 c^{7} d^{12} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{2 \left(a \,e^{2}-c \,d^{2}\right)^{4} \sqrt{c d e}\, e^{3}}-\frac{10 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{3} c^{3} d^{3} e^{4} x}{\left(a \,e^{2}-c \,d^{2}\right)^{4}}+\frac{30 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{2} c^{4} d^{5} e^{2} x}{\left(a \,e^{2}-c \,d^{2}\right)^{4}}-\frac{30 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a \,c^{5} d^{7} x}{\left(a \,e^{2}-c \,d^{2}\right)^{4}}+\frac{10 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, c^{6} d^{9} x}{\left(a \,e^{2}-c \,d^{2}\right)^{4} e^{2}}-\frac{5 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{4} c^{2} d^{2} e^{5}}{\left(a \,e^{2}-c \,d^{2}\right)^{4}}+\frac{10 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{3} c^{3} d^{4} e^{3}}{\left(a \,e^{2}-c \,d^{2}\right)^{4}}-\frac{10 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a \,c^{5} d^{8}}{\left(a \,e^{2}-c \,d^{2}\right)^{4} e}+\frac{5 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, c^{6} d^{10}}{\left(a \,e^{2}-c \,d^{2}\right)^{4} e^{3}}+\frac{80 \left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}} a \,c^{4} d^{4} e x}{3 \left(a \,e^{2}-c \,d^{2}\right)^{4}}-\frac{80 \left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}} c^{5} d^{6} x}{3 \left(a \,e^{2}-c \,d^{2}\right)^{4} e}+\frac{40 \left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}} a^{2} c^{3} d^{3} e^{2}}{3 \left(a \,e^{2}-c \,d^{2}\right)^{4}}-\frac{40 \left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}} c^{5} d^{7}}{3 \left(a \,e^{2}-c \,d^{2}\right)^{4} e^{2}}+\frac{128 \left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{5}{2}} c^{4} d^{4}}{3 \left(a \,e^{2}-c \,d^{2}\right)^{4} e}-\frac{128 \left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{7}{2}} c^{3} d^{3}}{3 \left(a \,e^{2}-c \,d^{2}\right)^{4} \left(x +\frac{d}{e}\right)^{2} e^{2}}+\frac{16 \left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{7}{2}} c^{2} d^{2}}{\left(a \,e^{2}-c \,d^{2}\right)^{3} \left(x +\frac{d}{e}\right)^{3} e^{3}}-\frac{8 \left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{7}{2}} c d}{3 \left(a \,e^{2}-c \,d^{2}\right)^{2} \left(x +\frac{d}{e}\right)^{4} e^{4}}-\frac{2 \left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{7}{2}}}{3 \left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)^{5} e^{5}}"," ",0,"-2/3/e^5/(a*e^2-c*d^2)/(x+d/e)^5*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(7/2)-8/3/e^4*c*d/(a*e^2-c*d^2)^2/(x+d/e)^4*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(7/2)+16/e^3*c^2*d^2/(a*e^2-c*d^2)^3/(x+d/e)^3*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(7/2)-128/3/e^2*c^3*d^3/(a*e^2-c*d^2)^4/(x+d/e)^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(7/2)+128/3/e*c^4*d^4/(a*e^2-c*d^2)^4*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(5/2)+5/e^3*c^6*d^10/(a*e^2-c*d^2)^4*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)-80/3/e*c^5*d^6/(a*e^2-c*d^2)^4*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)*x-40/3/e^2*c^5*d^7/(a*e^2-c*d^2)^4*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)+80/3*e*c^4*d^4/(a*e^2-c*d^2)^4*a*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)*x+10*e^3*c^3*d^4/(a*e^2-c*d^2)^4*a^3*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)-25*e*c^5*d^8/(a*e^2-c*d^2)^4*a^2*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+25/2/e*c^6*d^10/(a*e^2-c*d^2)^4*a*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-10*e^4*c^3*d^3/(a*e^2-c*d^2)^4*a^3*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x-30*c^5*d^7/(a*e^2-c*d^2)^4*a*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x+5/2*e^7*c^2*d^2/(a*e^2-c*d^2)^4*a^5*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-5/2/e^3*c^7*d^12/(a*e^2-c*d^2)^4*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-25/2*e^5*c^3*d^4/(a*e^2-c*d^2)^4*a^4*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+25*e^3*c^4*d^6/(a*e^2-c*d^2)^4*a^3*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+10/e^2*c^6*d^9/(a*e^2-c*d^2)^4*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x+40/3*e^2*c^3*d^3/(a*e^2-c*d^2)^4*a^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)+30*e^2*c^4*d^5/(a*e^2-c*d^2)^4*a^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x-5*e^5*c^2*d^2/(a*e^2-c*d^2)^4*a^4*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)-10/e*c^5*d^8/(a*e^2-c*d^2)^4*a*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)","B"
1941,1,1764,192,0.062000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/(e*x+d)^6,x)","\frac{a^{5} c^{3} d^{3} e^{7} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{\left(a \,e^{2}-c \,d^{2}\right)^{5} \sqrt{c d e}}-\frac{5 a^{4} c^{4} d^{5} e^{5} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{\left(a \,e^{2}-c \,d^{2}\right)^{5} \sqrt{c d e}}+\frac{10 a^{3} c^{5} d^{7} e^{3} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{\left(a \,e^{2}-c \,d^{2}\right)^{5} \sqrt{c d e}}-\frac{10 a^{2} c^{6} d^{9} e \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{\left(a \,e^{2}-c \,d^{2}\right)^{5} \sqrt{c d e}}+\frac{5 a \,c^{7} d^{11} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{\left(a \,e^{2}-c \,d^{2}\right)^{5} \sqrt{c d e}\, e}-\frac{c^{8} d^{13} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{\left(a \,e^{2}-c \,d^{2}\right)^{5} \sqrt{c d e}\, e^{3}}-\frac{4 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{3} c^{4} d^{4} e^{4} x}{\left(a \,e^{2}-c \,d^{2}\right)^{5}}+\frac{12 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{2} c^{5} d^{6} e^{2} x}{\left(a \,e^{2}-c \,d^{2}\right)^{5}}-\frac{12 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a \,c^{6} d^{8} x}{\left(a \,e^{2}-c \,d^{2}\right)^{5}}+\frac{4 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, c^{7} d^{10} x}{\left(a \,e^{2}-c \,d^{2}\right)^{5} e^{2}}-\frac{2 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{4} c^{3} d^{3} e^{5}}{\left(a \,e^{2}-c \,d^{2}\right)^{5}}+\frac{4 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{3} c^{4} d^{5} e^{3}}{\left(a \,e^{2}-c \,d^{2}\right)^{5}}-\frac{4 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a \,c^{6} d^{9}}{\left(a \,e^{2}-c \,d^{2}\right)^{5} e}+\frac{2 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, c^{7} d^{11}}{\left(a \,e^{2}-c \,d^{2}\right)^{5} e^{3}}+\frac{32 \left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}} a \,c^{5} d^{5} e x}{3 \left(a \,e^{2}-c \,d^{2}\right)^{5}}-\frac{32 \left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}} c^{6} d^{7} x}{3 \left(a \,e^{2}-c \,d^{2}\right)^{5} e}+\frac{16 \left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}} a^{2} c^{4} d^{4} e^{2}}{3 \left(a \,e^{2}-c \,d^{2}\right)^{5}}-\frac{16 \left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}} c^{6} d^{8}}{3 \left(a \,e^{2}-c \,d^{2}\right)^{5} e^{2}}+\frac{256 \left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{5}{2}} c^{5} d^{5}}{15 \left(a \,e^{2}-c \,d^{2}\right)^{5} e}-\frac{256 \left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{7}{2}} c^{4} d^{4}}{15 \left(a \,e^{2}-c \,d^{2}\right)^{5} \left(x +\frac{d}{e}\right)^{2} e^{2}}+\frac{32 \left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{7}{2}} c^{3} d^{3}}{5 \left(a \,e^{2}-c \,d^{2}\right)^{4} \left(x +\frac{d}{e}\right)^{3} e^{3}}-\frac{16 \left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{7}{2}} c^{2} d^{2}}{15 \left(a \,e^{2}-c \,d^{2}\right)^{3} \left(x +\frac{d}{e}\right)^{4} e^{4}}-\frac{4 \left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{7}{2}} c d}{15 \left(a \,e^{2}-c \,d^{2}\right)^{2} \left(x +\frac{d}{e}\right)^{5} e^{5}}-\frac{2 \left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{7}{2}}}{5 \left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)^{6} e^{6}}"," ",0,"-2/5/e^6/(a*e^2-c*d^2)/(x+d/e)^6*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(7/2)-4/15/e^5*c*d/(a*e^2-c*d^2)^2/(x+d/e)^5*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(7/2)-16/15/e^4*c^2*d^2/(a*e^2-c*d^2)^3/(x+d/e)^4*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(7/2)+32/5/e^3*c^3*d^3/(a*e^2-c*d^2)^4/(x+d/e)^3*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(7/2)-256/15/e^2*c^4*d^4/(a*e^2-c*d^2)^5/(x+d/e)^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(7/2)+256/15/e*c^5*d^5/(a*e^2-c*d^2)^5*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(5/2)+2/e^3*c^7*d^11/(a*e^2-c*d^2)^5*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)-32/3/e*c^6*d^7/(a*e^2-c*d^2)^5*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)*x-16/3/e^2*c^6*d^8/(a*e^2-c*d^2)^5*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)+4*e^3*c^4*d^5/(a*e^2-c*d^2)^5*a^3*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)+32/3*e*c^5*d^5/(a*e^2-c*d^2)^5*a*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)*x+5/e*c^7*d^11/(a*e^2-c*d^2)^5*a*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-10*e*c^6*d^9/(a*e^2-c*d^2)^5*a^2*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+e^7*c^3*d^3/(a*e^2-c*d^2)^5*a^5*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-12*c^6*d^8/(a*e^2-c*d^2)^5*a*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x-4*e^4*c^4*d^4/(a*e^2-c*d^2)^5*a^3*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x+16/3*e^2*c^4*d^4/(a*e^2-c*d^2)^5*a^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)+12*e^2*c^5*d^6/(a*e^2-c*d^2)^5*a^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x-2*e^5*c^3*d^3/(a*e^2-c*d^2)^5*a^4*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)+4/e^2*c^7*d^10/(a*e^2-c*d^2)^5*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x-1/e^3*c^8*d^13/(a*e^2-c*d^2)^5*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-4/e*c^6*d^9/(a*e^2-c*d^2)^5*a*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)-5*e^5*c^4*d^5/(a*e^2-c*d^2)^5*a^4*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+10*e^3*c^5*d^7/(a*e^2-c*d^2)^5*a^3*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)","B"
1942,1,58,50,0.045000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/(e*x+d)^7,x)","-\frac{2 \left(c d x +a e \right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{5}{2}}}{7 \left(e x +d \right)^{6} \left(a \,e^{2}-c \,d^{2}\right)}"," ",0,"-2/7*(c*d*x+a*e)/(e*x+d)^6/(a*e^2-c*d^2)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(5/2)","A"
1943,1,90,103,0.052000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/(e*x+d)^8,x)","-\frac{2 \left(c d x +a e \right) \left(-2 c d e x +7 a \,e^{2}-9 c \,d^{2}\right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{5}{2}}}{63 \left(e x +d \right)^{7} \left(a^{2} e^{4}-2 a c \,d^{2} e^{2}+c^{2} d^{4}\right)}"," ",0,"-2/63*(c*d*x+a*e)*(-2*c*d*e*x+7*a*e^2-9*c*d^2)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(5/2)/(e*x+d)^7/(a^2*e^4-2*a*c*d^2*e^2+c^2*d^4)","A"
1944,1,146,159,0.060000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/(e*x+d)^9,x)","-\frac{2 \left(c d x +a e \right) \left(8 c^{2} d^{2} e^{2} x^{2}-28 a c d \,e^{3} x +44 c^{2} d^{3} e x +63 a^{2} e^{4}-154 a c \,d^{2} e^{2}+99 c^{2} d^{4}\right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{5}{2}}}{693 \left(e x +d \right)^{8} \left(a^{3} e^{6}-3 a^{2} c \,d^{2} e^{4}+3 a \,c^{2} d^{4} e^{2}-c^{3} d^{6}\right)}"," ",0,"-2/693*(c*d*x+a*e)*(8*c^2*d^2*e^2*x^2-28*a*c*d*e^3*x+44*c^2*d^3*e*x+63*a^2*e^4-154*a*c*d^2*e^2+99*c^2*d^4)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(5/2)/(e*x+d)^8/(a^3*e^6-3*a^2*c*d^2*e^4+3*a*c^2*d^4*e^2-c^3*d^6)","A"
1945,1,217,215,0.057000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/(e*x+d)^10,x)","-\frac{2 \left(c d x +a e \right) \left(-16 c^{3} d^{3} e^{3} x^{3}+56 a \,c^{2} d^{2} e^{4} x^{2}-104 c^{3} d^{4} e^{2} x^{2}-126 a^{2} c d \,e^{5} x +364 a \,c^{2} d^{3} e^{3} x -286 c^{3} d^{5} e x +231 a^{3} e^{6}-819 a^{2} c \,d^{2} e^{4}+1001 a \,c^{2} d^{4} e^{2}-429 c^{3} d^{6}\right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{5}{2}}}{3003 \left(e x +d \right)^{9} \left(a^{4} e^{8}-4 a^{3} c \,d^{2} e^{6}+6 a^{2} c^{2} d^{4} e^{4}-4 a \,c^{3} d^{6} e^{2}+c^{4} d^{8}\right)}"," ",0,"-2/3003*(c*d*x+a*e)*(-16*c^3*d^3*e^3*x^3+56*a*c^2*d^2*e^4*x^2-104*c^3*d^4*e^2*x^2-126*a^2*c*d*e^5*x+364*a*c^2*d^3*e^3*x-286*c^3*d^5*e*x+231*a^3*e^6-819*a^2*c*d^2*e^4+1001*a*c^2*d^4*e^2-429*c^3*d^6)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(5/2)/(e*x+d)^9/(a^4*e^8-4*a^3*c*d^2*e^6+6*a^2*c^2*d^4*e^4-4*a*c^3*d^6*e^2+c^4*d^8)","A"
1946,1,513,225,0.066000," ","int((e*x+d)^3/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","-\frac{5 a^{3} e^{6} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{16 \sqrt{c d e}\, c^{3} d^{3}}+\frac{15 a^{2} e^{4} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{16 \sqrt{c d e}\, c^{2} d}-\frac{15 a d \,e^{2} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{16 \sqrt{c d e}\, c}+\frac{5 d^{3} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{16 \sqrt{c d e}}+\frac{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, e^{2} x^{2}}{3 c d}-\frac{5 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a \,e^{3} x}{12 c^{2} d^{2}}+\frac{13 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, e x}{12 c}+\frac{5 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{2} e^{4}}{8 c^{3} d^{3}}-\frac{5 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a \,e^{2}}{3 c^{2} d}+\frac{11 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, d}{8 c}"," ",0,"1/3*e^2*x^2/c/d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)-5/12*e^3/c^2/d^2*x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a+13/12*e/c*x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+5/8*e^4/c^3/d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^2-5/3*e^2/c^2/d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a+11/8/c*d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)-5/16*e^6/c^3/d^3*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^3+15/16*e^4/c^2/d*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^2-15/16*e^2/c*d*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a+5/16*d^3*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)","B"
1947,1,318,169,0.052000," ","int((e*x+d)^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","\frac{3 a^{2} e^{4} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{8 \sqrt{c d e}\, c^{2} d^{2}}-\frac{3 a \,e^{2} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{4 \sqrt{c d e}\, c}+\frac{3 d^{2} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{8 \sqrt{c d e}}+\frac{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, e x}{2 c d}-\frac{3 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a \,e^{2}}{4 c^{2} d^{2}}+\frac{5 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{4 c}"," ",0,"1/2*e*x/c/d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)-3/4*e^2/c^2/d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a+5/4/c*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+3/8*e^4/c^2/d^2*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^2-3/4*e^2/c*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a+3/8*d^2*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)","A"
1948,1,171,114,0.057000," ","int((e*x+d)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","-\frac{a \,e^{2} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{2 \sqrt{c d e}\, c d}+\frac{d \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{2 \sqrt{c d e}}+\frac{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{c d}"," ",0,"(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)/c/d-1/2/c/d*e^2*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a+1/2*d*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)","A"
1949,1,62,66,0.048000," ","int(1/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","\frac{\ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{\sqrt{c d e}}"," ",0,"ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)","A"
1950,1,51,50,0.049000," ","int(1/(e*x+d)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","-\frac{2 \left(c d x +a e \right)}{\left(a \,e^{2}-c \,d^{2}\right) \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}}"," ",0,"-2*(c*d*x+a*e)/(a*e^2-c*d^2)/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)","A"
1951,1,89,103,0.049000," ","int(1/(e*x+d)^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","-\frac{2 \left(c d x +a e \right) \left(-2 c d e x +a \,e^{2}-3 c \,d^{2}\right)}{3 \left(e x +d \right) \left(a^{2} e^{4}-2 a c \,d^{2} e^{2}+c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}}"," ",0,"-2/3*(c*d*x+a*e)*(-2*c*d*e*x+a*e^2-3*c*d^2)/(e*x+d)/(a^2*e^4-2*a*c*d^2*e^2+c^2*d^4)/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)","A"
1952,1,146,159,0.051000," ","int(1/(e*x+d)^3/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","-\frac{2 \left(c d x +a e \right) \left(8 c^{2} d^{2} e^{2} x^{2}-4 a c d \,e^{3} x +20 c^{2} d^{3} e x +3 a^{2} e^{4}-10 a c \,d^{2} e^{2}+15 c^{2} d^{4}\right)}{15 \left(e x +d \right)^{2} \left(a^{3} e^{6}-3 a^{2} c \,d^{2} e^{4}+3 a \,c^{2} d^{4} e^{2}-c^{3} d^{6}\right) \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}}"," ",0,"-2/15*(c*d*x+a*e)*(8*c^2*d^2*e^2*x^2-4*a*c*d*e^3*x+20*c^2*d^3*e*x+3*a^2*e^4-10*a*c*d^2*e^2+15*c^2*d^4)/(e*x+d)^2/(a^3*e^6-3*a^2*c*d^2*e^4+3*a*c^2*d^4*e^2-c^3*d^6)/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)","A"
1953,1,217,215,0.057000," ","int(1/(e*x+d)^4/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","-\frac{2 \left(c d x +a e \right) \left(-16 c^{3} d^{3} e^{3} x^{3}+8 a \,c^{2} d^{2} e^{4} x^{2}-56 c^{3} d^{4} e^{2} x^{2}-6 a^{2} c d \,e^{5} x +28 a \,c^{2} d^{3} e^{3} x -70 c^{3} d^{5} e x +5 a^{3} e^{6}-21 a^{2} c \,d^{2} e^{4}+35 a \,c^{2} d^{4} e^{2}-35 c^{3} d^{6}\right)}{35 \left(e x +d \right)^{3} \left(a^{4} e^{8}-4 a^{3} c \,d^{2} e^{6}+6 a^{2} c^{2} d^{4} e^{4}-4 a \,c^{3} d^{6} e^{2}+c^{4} d^{8}\right) \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}}"," ",0,"-2/35*(c*d*x+a*e)*(-16*c^3*d^3*e^3*x^3+8*a*c^2*d^2*e^4*x^2-56*c^3*d^4*e^2*x^2-6*a^2*c*d*e^5*x+28*a*c^2*d^3*e^3*x-70*c^3*d^5*e*x+5*a^3*e^6-21*a^2*c*d^2*e^4+35*a*c^2*d^4*e^2-35*c^3*d^6)/(e*x+d)^3/(a^4*e^8-4*a^3*c*d^2*e^6+6*a^2*c^2*d^4*e^4-4*a*c^3*d^6*e^2+c^4*d^8)/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)","A"
1954,1,1850,270,0.071000," ","int((e*x+d)^5/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2),x)","-\frac{35 a^{5} e^{11} x}{16 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{4} d^{4}}+\frac{385 a^{4} e^{9} x}{48 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{3} d^{2}}-\frac{203 a^{3} e^{7} x}{24 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2}}-\frac{53 a^{2} d^{2} e^{5} x}{24 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c}+\frac{415 a \,d^{4} e^{3} x}{48 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}-\frac{125 c \,d^{6} e x}{16 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}-\frac{35 a^{6} e^{12}}{32 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{5} d^{5}}+\frac{35 a^{5} e^{10}}{12 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{4} d^{3}}-\frac{7 a^{4} e^{8}}{32 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{3} d}-\frac{16 a^{3} d \,e^{6}}{3 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2}}+\frac{103 a^{2} d^{3} e^{4}}{32 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c}+\frac{5 a \,d^{5} e^{2}}{12 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}-\frac{125 c \,d^{7}}{32 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}+\frac{e^{4} x^{4}}{3 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c d}-\frac{7 a \,e^{5} x^{3}}{12 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2} d^{2}}+\frac{23 e^{3} x^{3}}{12 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c}+\frac{2 \left(2 c d e x +a \,e^{2}+c \,d^{2}\right) d^{5}}{\left(4 a c \,d^{2} e^{2}-\left(a \,e^{2}+c \,d^{2}\right)^{2}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}+\frac{35 a^{2} e^{6} x^{2}}{24 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{3} d^{3}}-\frac{14 a \,e^{4} x^{2}}{3 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2} d}+\frac{125 d \,e^{2} x^{2}}{24 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c}+\frac{35 a^{3} e^{7} x}{16 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{4} d^{4}}-\frac{35 a^{3} e^{7} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{16 \sqrt{c d e}\, c^{4} d^{4}}-\frac{105 a^{2} e^{5} x}{16 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{3} d^{2}}+\frac{105 a^{2} e^{5} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{16 \sqrt{c d e}\, c^{3} d^{2}}+\frac{105 a \,e^{3} x}{16 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2}}-\frac{105 a \,e^{3} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{16 \sqrt{c d e}\, c^{2}}-\frac{35 d^{2} e x}{16 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c}+\frac{35 d^{2} e \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{16 \sqrt{c d e}\, c}-\frac{35 a^{4} e^{8}}{32 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{5} d^{5}}+\frac{245 a^{3} e^{6}}{48 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{4} d^{3}}-\frac{28 a^{2} e^{4}}{3 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{3} d}+\frac{395 a d \,e^{2}}{48 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2}}-\frac{125 d^{3}}{32 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c}"," ",0,"35/16*e/c*d^2*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)-105/16*e^3/c^2*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a-125/32/c*d^3/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+2*d^5*(2*c*d*e*x+a*e^2+c*d^2)/(4*a*c*d^2*e^2-(a*e^2+c*d^2)^2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+23/12*e^3/c*x^3/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)-125/32*c*d^7/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+5/12*e^2*d^5/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a+105/16*e^3/c^2*x/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a+245/48*e^6/c^4/d^3/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^3-35/16*e/c*d^2*x/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+1/3*e^4*x^4/c/d/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)-28/3*e^4/c^3/d/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^2+125/24*e^2/c*d*x^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+395/48*e^2/c^2*d/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a-35/32*e^8/c^5/d^5/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^4-35/16*e^11/c^4/d^4/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^5+385/48*e^9/c^3/d^2/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^4-53/24*e^5/c*d^2/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^2-35/32*e^12/c^5/d^5/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^6+103/32*e^4/c*d^3/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^2-14/3*e^4/c^2/d*x^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a+415/48*e^3*d^4/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a-105/16*e^5/c^3/d^2*x/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^2-203/24*e^7/c^2/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^3+105/16*e^5/c^3/d^2*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^2+35/12*e^10/c^4/d^3/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^5-7/32*e^8/c^3/d/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^4-125/16*e*c*d^6/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x-16/3*e^6/c^2*d/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^3+35/24*e^6/c^3/d^3*x^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^2-35/16*e^7/c^4/d^4*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^3+35/16*e^7/c^4/d^4*x/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^3-7/12*e^5/c^2/d^2*x^3/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a","B"
1955,1,1428,213,0.068000," ","int((e*x+d)^4/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2),x)","\frac{15 a^{4} e^{9} x}{8 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{3} d^{3}}-\frac{5 a^{3} e^{7} x}{\left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2} d}+\frac{9 a^{2} d \,e^{5} x}{4 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c}+\frac{3 a \,d^{3} e^{3} x}{\left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}-\frac{49 c \,d^{5} e x}{8 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}+\frac{15 a^{5} e^{10}}{16 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{4} d^{4}}-\frac{25 a^{4} e^{8}}{16 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{3} d^{2}}-\frac{11 a^{3} e^{6}}{8 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2}}+\frac{21 a^{2} d^{2} e^{4}}{8 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c}-\frac{25 a \,d^{4} e^{2}}{16 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}-\frac{49 c \,d^{6}}{16 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}+\frac{e^{3} x^{3}}{2 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c d}+\frac{2 \left(2 c d e x +a \,e^{2}+c \,d^{2}\right) d^{4}}{\left(4 a c \,d^{2} e^{2}-\left(a \,e^{2}+c \,d^{2}\right)^{2}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}-\frac{5 a \,e^{4} x^{2}}{4 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2} d^{2}}+\frac{11 e^{2} x^{2}}{4 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c}-\frac{15 a^{2} e^{5} x}{8 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{3} d^{3}}+\frac{15 a^{2} e^{5} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{8 \sqrt{c d e}\, c^{3} d^{3}}+\frac{15 a \,e^{3} x}{4 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2} d}-\frac{15 a \,e^{3} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{4 \sqrt{c d e}\, c^{2} d}-\frac{15 d e x}{8 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c}+\frac{15 d e \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{8 \sqrt{c d e}\, c}+\frac{15 a^{3} e^{6}}{16 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{4} d^{4}}-\frac{55 a^{2} e^{4}}{16 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{3} d^{2}}+\frac{73 a \,e^{2}}{16 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2}}-\frac{49 d^{2}}{16 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c}"," ",0,"-49/16*c*d^6/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+11/4*e^2/c*x^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+73/16*e^2/c^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a+2*d^4*(2*c*d*e*x+a*e^2+c*d^2)/(4*a*c*d^2*e^2-(a*e^2+c*d^2)^2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+15/16*e^6/c^4/d^4/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^3-11/8*e^6/c^2/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^3-49/16/c*d^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+9/4*e^5/c*d/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^2+15/8*e^9/c^3/d^3/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^4-5*e^7/c^2/d/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^3-55/16*e^4/c^3/d^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^2+1/2*e^3*x^3/c/d/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)-25/16*e^2*d^4/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a-15/8*e/c*d*x/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+15/8*e/c*d*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)-15/8*e^5/c^3/d^3*x/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^2+21/8*e^4/c*d^2/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^2-5/4*e^4/c^2/d^2*x^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a+3*e^3*d^3/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a-49/8*e*c*d^5/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x+15/16*e^10/c^4/d^4/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^5-25/16*e^8/c^3/d^2/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^4+15/4*e^3/c^2/d*x/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a-15/4*e^3/c^2/d*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a+15/8*e^5/c^3/d^3*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^2","B"
1956,1,1047,158,0.063000," ","int((e*x+d)^3/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2),x)","-\frac{3 a^{3} e^{7} x}{2 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2} d^{2}}+\frac{5 a^{2} e^{5} x}{2 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c}-\frac{a \,d^{2} e^{3} x}{2 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}-\frac{9 c \,d^{4} e x}{2 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}-\frac{3 a^{4} e^{8}}{4 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{3} d^{3}}+\frac{a^{3} e^{6}}{2 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2} d}+\frac{a^{2} d \,e^{4}}{\left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c}-\frac{5 a \,d^{3} e^{2}}{2 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}-\frac{9 c \,d^{5}}{4 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}+\frac{2 \left(2 c d e x +a \,e^{2}+c \,d^{2}\right) d^{3}}{\left(4 a c \,d^{2} e^{2}-\left(a \,e^{2}+c \,d^{2}\right)^{2}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}+\frac{e^{2} x^{2}}{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c d}+\frac{3 a \,e^{3} x}{2 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2} d^{2}}-\frac{3 a \,e^{3} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{2 \sqrt{c d e}\, c^{2} d^{2}}-\frac{3 e x}{2 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c}+\frac{3 e \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{2 \sqrt{c d e}\, c}-\frac{3 a^{2} e^{4}}{4 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{3} d^{3}}+\frac{2 a \,e^{2}}{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2} d}-\frac{9 d}{4 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c}"," ",0,"e^4/c*d/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^2-3/2*e^3/c^2/d^2*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a-9/2*e*c*d^4/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x-3/4*e^8/c^3/d^3/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^4+1/2*e^6/c^2/d/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^3-1/2*e^3*d^2/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a+3/2*e^3/c^2/d^2*x/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a+5/2*e^5/c/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^2-3/2*e^7/c^2/d^2/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^3+e^2*x^2/c/d/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)-3/4*e^4/c^3/d^3/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^2+2*e^2/c^2/d/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a-5/2*e^2*d^3/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a-3/2*e/c*x/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)-9/4*c*d^5/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+3/2*e/c*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)+2*d^3*(2*c*d*e*x+a*e^2+c*d^2)/(4*a*c*d^2*e^2-(a*e^2+c*d^2)^2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)-9/4/c*d/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)","B"
1957,1,717,107,0.061000," ","int((e*x+d)^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2),x)","\frac{a^{2} e^{5} x}{\left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c d}-\frac{2 a d \,e^{3} x}{\left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}-\frac{3 c \,d^{3} e x}{\left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}+\frac{a^{3} e^{6}}{2 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2} d^{2}}-\frac{a^{2} e^{4}}{2 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c}-\frac{5 a \,d^{2} e^{2}}{2 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}-\frac{3 c \,d^{4}}{2 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}+\frac{2 \left(2 c d e x +a \,e^{2}+c \,d^{2}\right) d^{2}}{\left(4 a c \,d^{2} e^{2}-\left(a \,e^{2}+c \,d^{2}\right)^{2}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}-\frac{e x}{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c d}+\frac{e \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{\sqrt{c d e}\, c d}+\frac{a \,e^{2}}{2 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2} d^{2}}-\frac{3}{2 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c}"," ",0,"-e*x/c/d/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+1/2*e^2/c^2/d^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a-3/2/c/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+e^5/c/d/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^2-2*e^3*d/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a-3*e*c*d^3/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x+1/2*e^6/c^2/d^2/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^3-1/2*e^4/c/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^2-5/2*e^2*d^2/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a-3/2*c*d^4/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+e/c/d*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)+2*d^2*(2*c*d*e*x+a*e^2+c*d^2)/(4*a*c*d^2*e^2-(a*e^2+c*d^2)^2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)","B"
1958,1,58,48,0.050000," ","int((e*x+d)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2),x)","\frac{2 \left(c d x +a e \right) \left(e x +d \right)^{2}}{\left(a \,e^{2}-c \,d^{2}\right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{3}{2}}}"," ",0,"2*(c*d*x+a*e)*(e*x+d)^2/(a*e^2-c*d^2)/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(3/2)","A"
1959,1,86,60,0.049000," ","int(1/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2),x)","-\frac{2 \left(c d x +a e \right) \left(e x +d \right) \left(2 c d e x +a \,e^{2}+c \,d^{2}\right)}{\left(a^{2} e^{4}-2 a c \,d^{2} e^{2}+c^{2} d^{4}\right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{3}{2}}}"," ",0,"-2*(c*d*x+a*e)*(e*x+d)*(2*c*d*e*x+a*e^2+c*d^2)/(a^2*e^4-2*a*c*d^2*e^2+c^2*d^4)/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(3/2)","A"
1960,1,138,113,0.053000," ","int(1/(e*x+d)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2),x)","-\frac{2 \left(c d x +a e \right) \left(-8 c^{2} d^{2} e^{2} x^{2}-4 a c d \,e^{3} x -12 c^{2} d^{3} e x +a^{2} e^{4}-6 a c \,d^{2} e^{2}-3 c^{2} d^{4}\right)}{3 \left(a^{3} e^{6}-3 a^{2} c \,d^{2} e^{4}+3 a \,c^{2} d^{4} e^{2}-c^{3} d^{6}\right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{3}{2}}}"," ",0,"-2/3*(c*d*x+a*e)*(-8*c^2*d^2*e^2*x^2-4*a*c*d*e^3*x-12*c^2*d^3*e*x+a^2*e^4-6*a*c*d^2*e^2-3*c^2*d^4)/(a^3*e^6-3*a^2*c*d^2*e^4+3*a*c^2*d^4*e^2-c^3*d^6)/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(3/2)","A"
1961,1,216,169,0.056000," ","int(1/(e*x+d)^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2),x)","-\frac{2 \left(c d x +a e \right) \left(16 c^{3} d^{3} e^{3} x^{3}+8 a \,c^{2} d^{2} e^{4} x^{2}+40 c^{3} d^{4} e^{2} x^{2}-2 a^{2} c d \,e^{5} x +20 a \,c^{2} d^{3} e^{3} x +30 c^{3} d^{5} e x +a^{3} e^{6}-5 a^{2} c \,d^{2} e^{4}+15 a \,c^{2} d^{4} e^{2}+5 c^{3} d^{6}\right)}{5 \left(e x +d \right) \left(a^{4} e^{8}-4 a^{3} c \,d^{2} e^{6}+6 a^{2} c^{2} d^{4} e^{4}-4 a \,c^{3} d^{6} e^{2}+c^{4} d^{8}\right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{3}{2}}}"," ",0,"-2/5*(c*d*x+a*e)*(16*c^3*d^3*e^3*x^3+8*a*c^2*d^2*e^4*x^2+40*c^3*d^4*e^2*x^2-2*a^2*c*d*e^5*x+20*a*c^2*d^3*e^3*x+30*c^3*d^5*e*x+a^3*e^6-5*a^2*c*d^2*e^4+15*a*c^2*d^4*e^2+5*c^3*d^6)/(e*x+d)/(a^4*e^8-4*a^3*c*d^2*e^6+6*a^2*c^2*d^4*e^4-4*a*c^3*d^6*e^2+c^4*d^8)/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(3/2)","A"
1962,1,307,225,0.065000," ","int(1/(e*x+d)^3/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2),x)","-\frac{2 \left(c d x +a e \right) \left(-128 c^{4} d^{4} e^{4} x^{4}-64 a \,c^{3} d^{3} e^{5} x^{3}-448 c^{4} d^{5} e^{3} x^{3}+16 a^{2} c^{2} d^{2} e^{6} x^{2}-224 a \,c^{3} d^{4} e^{4} x^{2}-560 c^{4} d^{6} e^{2} x^{2}-8 a^{3} c d \,e^{7} x +56 a^{2} c^{2} d^{3} e^{5} x -280 a \,c^{3} d^{5} e^{3} x -280 c^{4} d^{7} e x +5 a^{4} e^{8}-28 a^{3} c \,d^{2} e^{6}+70 a^{2} c^{2} d^{4} e^{4}-140 a \,c^{3} d^{6} e^{2}-35 c^{4} d^{8}\right)}{35 \left(e x +d \right)^{2} \left(a^{5} e^{10}-5 a^{4} c \,d^{2} e^{8}+10 a^{3} c^{2} d^{4} e^{6}-10 a^{2} c^{3} d^{6} e^{4}+5 a \,c^{4} d^{8} e^{2}-c^{5} d^{10}\right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{3}{2}}}"," ",0,"-2/35*(c*d*x+a*e)*(-128*c^4*d^4*e^4*x^4-64*a*c^3*d^3*e^5*x^3-448*c^4*d^5*e^3*x^3+16*a^2*c^2*d^2*e^6*x^2-224*a*c^3*d^4*e^4*x^2-560*c^4*d^6*e^2*x^2-8*a^3*c*d*e^7*x+56*a^2*c^2*d^3*e^5*x-280*a*c^3*d^5*e^3*x-280*c^4*d^7*e*x+5*a^4*e^8-28*a^3*c*d^2*e^6+70*a^2*c^2*d^4*e^4-140*a*c^3*d^6*e^2-35*c^4*d^8)/(e*x+d)^2/(a^5*e^10-5*a^4*c*d^2*e^8+10*a^3*c^2*d^4*e^6-10*a^2*c^3*d^6*e^4+5*a*c^4*d^8*e^2-c^5*d^10)/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(3/2)","A"
1963,1,412,281,0.056000," ","int(1/(e*x+d)^4/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2),x)","-\frac{2 \left(c d x +a e \right) \left(256 c^{5} d^{5} e^{5} x^{5}+128 a \,c^{4} d^{4} e^{6} x^{4}+1152 c^{5} d^{6} e^{4} x^{4}-32 a^{2} c^{3} d^{3} e^{7} x^{3}+576 a \,c^{4} d^{5} e^{5} x^{3}+2016 c^{5} d^{7} e^{3} x^{3}+16 a^{3} c^{2} d^{2} e^{8} x^{2}-144 a^{2} c^{3} d^{4} e^{6} x^{2}+1008 a \,c^{4} d^{6} e^{4} x^{2}+1680 c^{5} d^{8} e^{2} x^{2}-10 a^{4} c d \,e^{9} x +72 a^{3} c^{2} d^{3} e^{7} x -252 a^{2} c^{3} d^{5} e^{5} x +840 a \,c^{4} d^{7} e^{3} x +630 c^{5} d^{9} e x +7 a^{5} e^{10}-45 a^{4} c \,d^{2} e^{8}+126 a^{3} c^{2} d^{4} e^{6}-210 a^{2} c^{3} d^{6} e^{4}+315 a \,c^{4} d^{8} e^{2}+63 c^{5} d^{10}\right)}{63 \left(e x +d \right)^{3} \left(a^{6} e^{12}-6 a^{5} c \,d^{2} e^{10}+15 a^{4} c^{2} d^{4} e^{8}-20 a^{3} c^{3} d^{6} e^{6}+15 a^{2} c^{4} d^{8} e^{4}-6 a \,c^{5} d^{10} e^{2}+c^{6} d^{12}\right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{3}{2}}}"," ",0,"-2/63*(c*d*x+a*e)*(256*c^5*d^5*e^5*x^5+128*a*c^4*d^4*e^6*x^4+1152*c^5*d^6*e^4*x^4-32*a^2*c^3*d^3*e^7*x^3+576*a*c^4*d^5*e^5*x^3+2016*c^5*d^7*e^3*x^3+16*a^3*c^2*d^2*e^8*x^2-144*a^2*c^3*d^4*e^6*x^2+1008*a*c^4*d^6*e^4*x^2+1680*c^5*d^8*e^2*x^2-10*a^4*c*d*e^9*x+72*a^3*c^2*d^3*e^7*x-252*a^2*c^3*d^5*e^5*x+840*a*c^4*d^7*e^3*x+630*c^5*d^9*e*x+7*a^5*e^10-45*a^4*c*d^2*e^8+126*a^3*c^2*d^4*e^6-210*a^2*c^3*d^6*e^4+315*a*c^4*d^8*e^2+63*c^5*d^10)/(e*x+d)^3/(a^6*e^12-6*a^5*c*d^2*e^10+15*a^4*c^2*d^4*e^8-20*a^3*c^3*d^6*e^6+15*a^2*c^4*d^8*e^4-6*a*c^5*d^10*e^2+c^6*d^12)/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(3/2)","A"
1964,1,4008,260,0.137000," ","int((e*x+d)^6/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2),x)","\text{output too large to display}"," 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a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^5+35/16*e^9/c^4/d^3/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^4-35/8*e^6/c^4/d^4*x/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^2+35/8*e^6/c^4/d^4*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^2-185/48*e^9/c^2*d/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^4+1255/48*e^7/c*d^3/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^3+35/16*e^8/c^4/d^4*x^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a^3+253/24*e^2*c^2*d^8/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x+253/192*e*c*d^7/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x","B"
1965,1,3215,203,0.074000," ","int((e*x+d)^5/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2),x)","\text{output too large to display}"," ",0,"5/4*e/c^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)-15/32/c*d^3/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)+1/12*e^2*d^5/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a+5/2*e^2*d^3/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x+5/4*e*d^4/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)-5/6*e^3/c*x^3/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)+19/96*c*d^7/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)+19/12*e*c^2*d^8/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)-5/2*e^2/c^2/d*x/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+73/12*e^9/c^2/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^4-97/12*e^5*d^4/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^2+11/4*e^4/c^3/d/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a^2+5/2*e^2/c^2/d*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)-71/16*e^2/c^2*d/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a+5/96*e^8/c^5/d^5/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a^4-43/48*e^6/c^4/d^3/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a^3-115/16*e/c*d^2*x/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)-35/4*e^2/c*d*x^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)+e^4*x^4/c/d/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)-5/4*e^5/c^4/d^4/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^2-19/16*e^3/c^2*x/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a-5/2*e^6/c^2/d/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^2+5/48*e^11/c^4/d^4/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*a^5-61/48*e^9/c^3/d^2/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*a^4+5/6*e^12/c^3/d^3/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^5-61/6*e^10/c^2/d/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^4-43/24*e^5/c*d^2/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*a^2+5/2*e^4/c*d/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a+67/3*e^8/c*d/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^3-11/6*e^4*c*d^5/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a-5/2*e^8/c^3/d^3/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^3+11/16*e^5/c^3/d^2*x/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a^2+5/12*e^13/c^4/d^4/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^6+19/6*e^2*c^2*d^7/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x-7/12*e^10/c^4/d^3/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a^5+73/96*e^8/c^3/d/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a^4+19/48*e*c*d^6/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x+5/6*e^5/c^2/d^2*x^3/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a+2/3*e^3*c*d^6/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a+5/2*e^4/c^3/d^3*x/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a-5/2*e^4/c^3/d^3*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a-5/4*e^9/c^4/d^4/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^4-97/96*e^4/c*d^3/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a^2+5/96*e^12/c^5/d^5/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a^6-5/4*e^6/c^3/d^3*x^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a^2-5/16*e^7/c^4/d^4*x/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a^3+4*e^4/c^2/d*x^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a+67/24*e^7/c^2/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*a^3-43/3*e^6*d^3/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^2-11/48*e^3*d^4/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*a+5/2*e^3/c*d^2/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a-5/2*e^7/c^3/d^2/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^3+1/2*e^6/c^2*d/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a^3+4*e^7/c*d^2/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^3-14/3*e^11/c^3/d^2/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^5","B"
1966,1,2538,150,0.075000," ","int((e*x+d)^4/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2),x)","-\frac{a^{4} e^{10} x}{3 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right)^{2} \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2} d^{2}}+\frac{16 a^{3} e^{8} x}{3 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right)^{2} \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c}-\frac{10 a^{2} d^{2} e^{6} x}{\left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right)^{2} \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}+\frac{16 a c \,d^{4} e^{4} x}{3 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right)^{2} \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}-\frac{c^{2} d^{6} e^{2} x}{3 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right)^{2} \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}-\frac{a^{5} e^{11}}{6 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right)^{2} \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{3} d^{3}}+\frac{5 a^{4} e^{9}}{2 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right)^{2} \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2} d}-\frac{7 a^{3} d \,e^{7}}{3 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right)^{2} \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c}-\frac{7 a^{2} d^{3} e^{5}}{3 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right)^{2} \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}+\frac{5 a c \,d^{5} e^{3}}{2 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right)^{2} \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}-\frac{c^{2} d^{7} e}{6 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right)^{2} \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}-\frac{a^{4} e^{9} x}{24 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c^{3} d^{3}}+\frac{2 a^{3} e^{7} x}{3 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c^{2} d}-\frac{5 a^{2} d \,e^{5} x}{4 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c}+\frac{2 a \,d^{3} e^{3} x}{3 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}}}-\frac{c \,d^{5} e x}{24 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}}}-\frac{a^{5} e^{10}}{48 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c^{4} d^{4}}+\frac{5 a^{4} e^{8}}{16 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c^{3} d^{2}}-\frac{7 a^{3} e^{6}}{24 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c^{2}}-\frac{7 a^{2} d^{2} e^{4}}{24 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c}+\frac{5 a \,d^{4} e^{2}}{16 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}}}-\frac{c \,d^{6}}{48 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}}}+\frac{a^{2} e^{6} x}{\left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2} d^{2}}+\frac{2 a \,e^{4} x}{\left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c}+\frac{d^{2} e^{2} x}{\left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}+\frac{a^{3} e^{7}}{2 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{3} d^{3}}+\frac{3 a^{2} e^{5}}{2 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2} d}+\frac{3 a d \,e^{3}}{2 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c}-\frac{e^{3} x^{3}}{3 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c d}+\frac{d^{3} e}{2 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}+\frac{a \,e^{4} x^{2}}{2 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c^{2} d^{2}}-\frac{7 e^{2} x^{2}}{2 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c}+\frac{a^{2} e^{5} x}{8 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c^{3} d^{3}}-\frac{3 a \,e^{3} x}{4 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c^{2} d}-\frac{31 d e x}{8 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c}-\frac{a^{3} e^{6}}{48 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c^{4} d^{4}}+\frac{7 a^{2} e^{4}}{16 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c^{3} d^{2}}-\frac{25 a \,e^{2}}{16 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c^{2}}-\frac{11 d^{2}}{16 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c}-\frac{e^{2} x}{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2} d^{2}}+\frac{e^{2} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{\sqrt{c d e}\, c^{2} d^{2}}+\frac{a \,e^{3}}{2 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{3} d^{3}}+\frac{e}{2 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2} d}"," ",0,"1/2*e/c^2/d/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+1/2*e*d^3/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)-25/16*e^2/c^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a-7/2*e^2/c*x^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)-1/48*c*d^6/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)-11/16/c*d^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)-7/3*e^5*d^3/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^2+7/16*e^4/c^3/d^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a^2-1/24*e*c*d^5/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x-1/3*e^3*x^3/c/d/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)+e^2*d^2/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x-7/24*e^6/c^2/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a^3+5/16*e^2*d^4/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a-1/6*e*c^2*d^7/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)-1/48*e^6/c^4/d^4/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a^3+e^2/c^2/d^2*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)-e^2/c^2/d^2*x/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+1/2*e^3/c^3/d^3/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a-31/8*e/c*d*x/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)+e^6/c^2/d^2/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^2+2/3*e^7/c^2/d/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*a^3+16/3*e^4*c*d^4/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a-1/3*e^10/c^2/d^2/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^4-5/4*e^5/c*d/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*a^2-1/24*e^9/c^3/d^3/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*a^4+5/2*e^3*c*d^5/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a+1/2*e^4/c^2/d^2*x^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a+1/8*e^5/c^3/d^3*x/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a^2-7/3*e^7/c*d/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^3-1/3*e^2*c^2*d^6/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x-1/48*e^10/c^4/d^4/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a^5+2*e^4/c/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a+1/2*e^7/c^3/d^3/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^3+3/2*e^5/c^2/d/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^2-10*e^6*d^2/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^2+16/3*e^8/c/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^3+2/3*e^3*d^3/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*a+3/2*e^3/c*d/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a+5/16*e^8/c^3/d^2/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a^4-1/6*e^11/c^3/d^3/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^5+5/2*e^9/c^2/d/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^4-7/24*e^4/c*d^2/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a^2-3/4*e^3/c^2/d*x/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a","B"
1967,1,58,50,0.064000," ","int((e*x+d)^3/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2),x)","\frac{2 \left(c d x +a e \right) \left(e x +d \right)^{4}}{3 \left(a \,e^{2}-c \,d^{2}\right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{5}{2}}}"," ",0,"2/3*(c*d*x+a*e)*(e*x+d)^4/(a*e^2-c*d^2)/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(5/2)","A"
1968,1,90,108,0.050000," ","int((e*x+d)^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2),x)","\frac{2 \left(c d x +a e \right) \left(e x +d \right)^{3} \left(2 c d e x +3 a \,e^{2}-c \,d^{2}\right)}{3 \left(a^{2} e^{4}-2 a c \,d^{2} e^{2}+c^{2} d^{4}\right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{5}{2}}}"," ",0,"2/3*(c*d*x+a*e)*(e*x+d)^3*(2*c*d*e*x+3*a*e^2-c*d^2)/(a^2*e^4-2*a*c*d^2*e^2+c^2*d^4)/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(5/2)","A"
1969,1,146,110,0.055000," ","int((e*x+d)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2),x)","-\frac{2 \left(c d x +a e \right) \left(e x +d \right)^{2} \left(8 c^{2} d^{2} e^{2} x^{2}+12 a c d \,e^{3} x +4 c^{2} d^{3} e x +3 a^{2} e^{4}+6 a c \,d^{2} e^{2}-c^{2} d^{4}\right)}{3 \left(a^{3} e^{6}-3 a^{2} c \,d^{2} e^{4}+3 a \,c^{2} d^{4} e^{2}-c^{3} d^{6}\right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{5}{2}}}"," ",0,"-2/3*(c*d*x+a*e)*(e*x+d)^2*(8*c^2*d^2*e^2*x^2+12*a*c*d*e^3*x+4*c^2*d^3*e*x+3*a^2*e^4+6*a*c*d^2*e^2-c^2*d^4)/(a^3*e^6-3*a^2*c*d^2*e^4+3*a*c^2*d^4*e^2-c^3*d^6)/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(5/2)","A"
1970,1,213,124,0.060000," ","int(1/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2),x)","-\frac{2 \left(c d x +a e \right) \left(e x +d \right) \left(-16 c^{3} d^{3} e^{3} x^{3}-24 a \,c^{2} d^{2} e^{4} x^{2}-24 c^{3} d^{4} e^{2} x^{2}-6 a^{2} c d \,e^{5} x -36 a \,c^{2} d^{3} e^{3} x -6 c^{3} d^{5} e x +a^{3} e^{6}-9 a^{2} c \,d^{2} e^{4}-9 a \,c^{2} d^{4} e^{2}+c^{3} d^{6}\right)}{3 \left(a^{4} e^{8}-4 a^{3} c \,d^{2} e^{6}+6 a^{2} c^{2} d^{4} e^{4}-4 a \,c^{3} d^{6} e^{2}+c^{4} d^{8}\right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{5}{2}}}"," ",0,"-2/3*(c*d*x+a*e)*(e*x+d)*(-16*c^3*d^3*e^3*x^3-24*a*c^2*d^2*e^4*x^2-24*c^3*d^4*e^2*x^2-6*a^2*c*d*e^5*x-36*a*c^2*d^3*e^3*x-6*c^3*d^5*e*x+a^3*e^6-9*a^2*c*d^2*e^4-9*a*c^2*d^4*e^2+c^3*d^6)/(a^4*e^8-4*a^3*c*d^2*e^6+6*a^2*c^2*d^4*e^4-4*a*c^3*d^6*e^2+c^4*d^8)/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(5/2)","A"
1971,1,300,180,0.053000," ","int(1/(e*x+d)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2),x)","-\frac{2 \left(c d x +a e \right) \left(128 c^{4} d^{4} e^{4} x^{4}+192 a \,c^{3} d^{3} e^{5} x^{3}+320 c^{4} d^{5} e^{3} x^{3}+48 a^{2} c^{2} d^{2} e^{6} x^{2}+480 a \,c^{3} d^{4} e^{4} x^{2}+240 c^{4} d^{6} e^{2} x^{2}-8 a^{3} c d \,e^{7} x +120 a^{2} c^{2} d^{3} e^{5} x +360 a \,c^{3} d^{5} e^{3} x +40 c^{4} d^{7} e x +3 a^{4} e^{8}-20 a^{3} c \,d^{2} e^{6}+90 a^{2} c^{2} d^{4} e^{4}+60 a \,c^{3} d^{6} e^{2}-5 c^{4} d^{8}\right)}{15 \left(a^{5} e^{10}-5 a^{4} c \,d^{2} e^{8}+10 a^{3} c^{2} d^{4} e^{6}-10 a^{2} c^{3} d^{6} e^{4}+5 a \,c^{4} d^{8} e^{2}-c^{5} d^{10}\right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{5}{2}}}"," ",0,"-2/15*(c*d*x+a*e)*(128*c^4*d^4*e^4*x^4+192*a*c^3*d^3*e^5*x^3+320*c^4*d^5*e^3*x^3+48*a^2*c^2*d^2*e^6*x^2+480*a*c^3*d^4*e^4*x^2+240*c^4*d^6*e^2*x^2-8*a^3*c*d*e^7*x+120*a^2*c^2*d^3*e^5*x+360*a*c^3*d^5*e^3*x+40*c^4*d^7*e*x+3*a^4*e^8-20*a^3*c*d^2*e^6+90*a^2*c^2*d^4*e^4+60*a*c^3*d^6*e^2-5*c^4*d^8)/(a^5*e^10-5*a^4*c*d^2*e^8+10*a^3*c^2*d^4*e^6-10*a^2*c^3*d^6*e^4+5*a*c^4*d^8*e^2-c^5*d^10)/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(5/2)","A"
1972,1,412,236,0.063000," ","int(1/(e*x+d)^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2),x)","-\frac{2 \left(c d x +a e \right) \left(-256 c^{5} d^{5} e^{5} x^{5}-384 a \,c^{4} d^{4} e^{6} x^{4}-896 c^{5} d^{6} e^{4} x^{4}-96 a^{2} c^{3} d^{3} e^{7} x^{3}-1344 a \,c^{4} d^{5} e^{5} x^{3}-1120 c^{5} d^{7} e^{3} x^{3}+16 a^{3} c^{2} d^{2} e^{8} x^{2}-336 a^{2} c^{3} d^{4} e^{6} x^{2}-1680 a \,c^{4} d^{6} e^{4} x^{2}-560 c^{5} d^{8} e^{2} x^{2}-6 a^{4} c d \,e^{9} x +56 a^{3} c^{2} d^{3} e^{7} x -420 a^{2} c^{3} d^{5} e^{5} x -840 a \,c^{4} d^{7} e^{3} x -70 c^{5} d^{9} e x +3 a^{5} e^{10}-21 a^{4} c \,d^{2} e^{8}+70 a^{3} c^{2} d^{4} e^{6}-210 a^{2} c^{3} d^{6} e^{4}-105 a \,c^{4} d^{8} e^{2}+7 c^{5} d^{10}\right)}{21 \left(e x +d \right) \left(a^{6} e^{12}-6 a^{5} c \,d^{2} e^{10}+15 a^{4} c^{2} d^{4} e^{8}-20 a^{3} c^{3} d^{6} e^{6}+15 a^{2} c^{4} d^{8} e^{4}-6 a \,c^{5} d^{10} e^{2}+c^{6} d^{12}\right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{5}{2}}}"," ",0,"-2/21*(c*d*x+a*e)*(-256*c^5*d^5*e^5*x^5-384*a*c^4*d^4*e^6*x^4-896*c^5*d^6*e^4*x^4-96*a^2*c^3*d^3*e^7*x^3-1344*a*c^4*d^5*e^5*x^3-1120*c^5*d^7*e^3*x^3+16*a^3*c^2*d^2*e^8*x^2-336*a^2*c^3*d^4*e^6*x^2-1680*a*c^4*d^6*e^4*x^2-560*c^5*d^8*e^2*x^2-6*a^4*c*d*e^9*x+56*a^3*c^2*d^3*e^7*x-420*a^2*c^3*d^5*e^5*x-840*a*c^4*d^7*e^3*x-70*c^5*d^9*e*x+3*a^5*e^10-21*a^4*c*d^2*e^8+70*a^3*c^2*d^4*e^6-210*a^2*c^3*d^6*e^4-105*a*c^4*d^8*e^2+7*c^5*d^10)/(e*x+d)/(a^6*e^12-6*a^5*c*d^2*e^10+15*a^4*c^2*d^4*e^8-20*a^3*c^3*d^6*e^6+15*a^2*c^4*d^8*e^4-6*a*c^5*d^10*e^2+c^6*d^12)/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(5/2)","A"
1973,1,536,292,0.057000," ","int(1/(e*x+d)^3/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2),x)","-\frac{2 \left(c d x +a e \right) \left(1024 c^{6} d^{6} e^{6} x^{6}+1536 a \,c^{5} d^{5} e^{7} x^{5}+4608 c^{6} d^{7} e^{5} x^{5}+384 a^{2} c^{4} d^{4} e^{8} x^{4}+6912 a \,c^{5} d^{6} e^{6} x^{4}+8064 c^{6} d^{8} e^{4} x^{4}-64 a^{3} c^{3} d^{3} e^{9} x^{3}+1728 a^{2} c^{4} d^{5} e^{7} x^{3}+12096 a \,c^{5} d^{7} e^{5} x^{3}+6720 c^{6} d^{9} e^{3} x^{3}+24 a^{4} c^{2} d^{2} e^{10} x^{2}-288 a^{3} c^{3} d^{4} e^{8} x^{2}+3024 a^{2} c^{4} d^{6} e^{6} x^{2}+10080 a \,c^{5} d^{8} e^{4} x^{2}+2520 c^{6} d^{10} e^{2} x^{2}-12 a^{5} c d \,e^{11} x +108 a^{4} c^{2} d^{3} e^{9} x -504 a^{3} c^{3} d^{5} e^{7} x +2520 a^{2} c^{4} d^{7} e^{5} x +3780 a \,c^{5} d^{9} e^{3} x +252 c^{6} d^{11} e x +7 a^{6} e^{12}-54 a^{5} c \,d^{2} e^{10}+189 a^{4} c^{2} d^{4} e^{8}-420 a^{3} c^{3} d^{6} e^{6}+945 a^{2} c^{4} d^{8} e^{4}+378 a \,c^{5} d^{10} e^{2}-21 c^{6} d^{12}\right)}{63 \left(e x +d \right)^{2} \left(a^{7} e^{14}-7 a^{6} c \,d^{2} e^{12}+21 a^{5} c^{2} d^{4} e^{10}-35 a^{4} c^{3} d^{6} e^{8}+35 a^{3} c^{4} d^{8} e^{6}-21 a^{2} c^{5} d^{10} e^{4}+7 a \,c^{6} d^{12} e^{2}-c^{7} d^{14}\right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{5}{2}}}"," ",0,"-2/63*(c*d*x+a*e)*(1024*c^6*d^6*e^6*x^6+1536*a*c^5*d^5*e^7*x^5+4608*c^6*d^7*e^5*x^5+384*a^2*c^4*d^4*e^8*x^4+6912*a*c^5*d^6*e^6*x^4+8064*c^6*d^8*e^4*x^4-64*a^3*c^3*d^3*e^9*x^3+1728*a^2*c^4*d^5*e^7*x^3+12096*a*c^5*d^7*e^5*x^3+6720*c^6*d^9*e^3*x^3+24*a^4*c^2*d^2*e^10*x^2-288*a^3*c^3*d^4*e^8*x^2+3024*a^2*c^4*d^6*e^6*x^2+10080*a*c^5*d^8*e^4*x^2+2520*c^6*d^10*e^2*x^2-12*a^5*c*d*e^11*x+108*a^4*c^2*d^3*e^9*x-504*a^3*c^3*d^5*e^7*x+2520*a^2*c^4*d^7*e^5*x+3780*a*c^5*d^9*e^3*x+252*c^6*d^11*e*x+7*a^6*e^12-54*a^5*c*d^2*e^10+189*a^4*c^2*d^4*e^8-420*a^3*c^3*d^6*e^6+945*a^2*c^4*d^8*e^4+378*a*c^5*d^10*e^2-21*c^6*d^12)/(e*x+d)^2/(a^7*e^14-7*a^6*c*d^2*e^12+21*a^5*c^2*d^4*e^10-35*a^4*c^3*d^6*e^8+35*a^3*c^4*d^8*e^6-21*a^2*c^5*d^10*e^4+7*a*c^6*d^12*e^2-c^7*d^14)/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(5/2)","A"
1974,0,0,1196,1.317000," ","int((e*x+d)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/3),x)","\int \frac{e x +d}{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{1}{3}}}\, dx"," ",0,"int((e*x+d)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/3),x)","F"
1975,0,0,1148,1.933000," ","int(1/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/3),x)","\int \frac{1}{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{1}{3}}}\, dx"," ",0,"int(1/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/3),x)","F"
1976,1,32,35,0.042000," ","int((e*x+d)^(3/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x),x)","\frac{2 \left(e x +d \right)^{\frac{7}{2}} \left(7 c d e x +9 a \,e^{2}-2 c \,d^{2}\right)}{63 e^{2}}"," ",0,"2/63*(e*x+d)^(7/2)*(7*c*d*e*x+9*a*e^2-2*c*d^2)/e^2","A"
1977,1,32,35,0.047000," ","int((e*x+d)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x),x)","\frac{2 \left(e x +d \right)^{\frac{5}{2}} \left(5 c d e x +7 a \,e^{2}-2 c \,d^{2}\right)}{35 e^{2}}"," ",0,"2/35*(e*x+d)^(5/2)*(5*c*d*e*x+7*a*e^2-2*c*d^2)/e^2","A"
1978,1,32,35,0.051000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)/(e*x+d)^(1/2),x)","\frac{2 \left(e x +d \right)^{\frac{3}{2}} \left(3 c d e x +5 a \,e^{2}-2 c \,d^{2}\right)}{15 e^{2}}"," ",0,"2/15*(e*x+d)^(3/2)*(3*c*d*e*x+5*a*e^2-2*c*d^2)/e^2","A"
1979,1,31,35,0.043000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)/(e*x+d)^(3/2),x)","\frac{2 \sqrt{e x +d}\, \left(c d e x +3 a \,e^{2}-2 c \,d^{2}\right)}{3 e^{2}}"," ",0,"2/3*(e*x+d)^(1/2)*(c*d*e*x+3*a*e^2-2*c*d^2)/e^2","A"
1980,1,31,35,0.042000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)/(e*x+d)^(5/2),x)","-\frac{2 \left(-c d e x +a \,e^{2}-2 c \,d^{2}\right)}{\sqrt{e x +d}\, e^{2}}"," ",0,"-2/(e*x+d)^(1/2)*(-c*d*e*x+a*e^2-2*c*d^2)/e^2","A"
1981,1,31,35,0.043000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)/(e*x+d)^(7/2),x)","-\frac{2 \left(3 c d e x +a \,e^{2}+2 c \,d^{2}\right)}{3 \left(e x +d \right)^{\frac{3}{2}} e^{2}}"," ",0,"-2/3/(e*x+d)^(3/2)*(3*c*d*e*x+a*e^2+2*c*d^2)/e^2","A"
1982,1,32,35,0.051000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)/(e*x+d)^(9/2),x)","-\frac{2 \left(5 c d e x +3 a \,e^{2}+2 c \,d^{2}\right)}{15 \left(e x +d \right)^{\frac{5}{2}} e^{2}}"," ",0,"-2/15/(e*x+d)^(5/2)*(5*c*d*e*x+3*a*e^2+2*c*d^2)/e^2","A"
1983,1,32,35,0.046000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)/(e*x+d)^(11/2),x)","-\frac{2 \left(7 c d e x +5 a \,e^{2}+2 c \,d^{2}\right)}{35 \left(e x +d \right)^{\frac{7}{2}} e^{2}}"," ",0,"-2/35/(e*x+d)^(7/2)*(7*c*d*e*x+5*a*e^2+2*c*d^2)/e^2","A"
1984,1,73,71,0.051000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^2*(e*x+d)^(1/2),x)","\frac{2 \left(e x +d \right)^{\frac{7}{2}} \left(63 c^{2} d^{2} e^{2} x^{2}+154 a c d \,e^{3} x -28 c^{2} d^{3} e x +99 a^{2} e^{4}-44 a c \,d^{2} e^{2}+8 c^{2} d^{4}\right)}{693 e^{3}}"," ",0,"2/693*(e*x+d)^(7/2)*(63*c^2*d^2*e^2*x^2+154*a*c*d*e^3*x-28*c^2*d^3*e*x+99*a^2*e^4-44*a*c*d^2*e^2+8*c^2*d^4)/e^3","A"
1985,1,73,71,0.048000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^2/(e*x+d)^(1/2),x)","\frac{2 \left(e x +d \right)^{\frac{5}{2}} \left(35 c^{2} d^{2} e^{2} x^{2}+90 a c d \,e^{3} x -20 c^{2} d^{3} e x +63 a^{2} e^{4}-36 a c \,d^{2} e^{2}+8 c^{2} d^{4}\right)}{315 e^{3}}"," ",0,"2/315*(e*x+d)^(5/2)*(35*c^2*d^2*e^2*x^2+90*a*c*d*e^3*x-20*c^2*d^3*e*x+63*a^2*e^4-36*a*c*d^2*e^2+8*c^2*d^4)/e^3","A"
1986,1,73,71,0.054000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^2/(e*x+d)^(3/2),x)","\frac{2 \left(e x +d \right)^{\frac{3}{2}} \left(15 c^{2} d^{2} e^{2} x^{2}+42 a c d \,e^{3} x -12 c^{2} d^{3} e x +35 a^{2} e^{4}-28 a c \,d^{2} e^{2}+8 c^{2} d^{4}\right)}{105 e^{3}}"," ",0,"2/105*(e*x+d)^(3/2)*(15*c^2*d^2*e^2*x^2+42*a*c*d*e^3*x-12*c^2*d^3*e*x+35*a^2*e^4-28*a*c*d^2*e^2+8*c^2*d^4)/e^3","A"
1987,1,73,71,0.044000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^2/(e*x+d)^(5/2),x)","\frac{2 \sqrt{e x +d}\, \left(3 c^{2} d^{2} e^{2} x^{2}+10 a c d \,e^{3} x -4 c^{2} d^{3} e x +15 a^{2} e^{4}-20 a c \,d^{2} e^{2}+8 c^{2} d^{4}\right)}{15 e^{3}}"," ",0,"2/15*(e*x+d)^(1/2)*(3*c^2*d^2*e^2*x^2+10*a*c*d*e^3*x-4*c^2*d^3*e*x+15*a^2*e^4-20*a*c*d^2*e^2+8*c^2*d^4)/e^3","A"
1988,1,73,71,0.047000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^2/(e*x+d)^(7/2),x)","-\frac{2 \left(-c^{2} d^{2} e^{2} x^{2}-6 a c d \,e^{3} x +4 c^{2} d^{3} e x +3 a^{2} e^{4}-12 a c \,d^{2} e^{2}+8 c^{2} d^{4}\right)}{3 \sqrt{e x +d}\, e^{3}}"," ",0,"-2/3/(e*x+d)^(1/2)*(-c^2*d^2*e^2*x^2-6*a*c*d*e^3*x+4*c^2*d^3*e*x+3*a^2*e^4-12*a*c*d^2*e^2+8*c^2*d^4)/e^3","A"
1989,1,72,71,0.048000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^2/(e*x+d)^(9/2),x)","-\frac{2 \left(-3 c^{2} d^{2} e^{2} x^{2}+6 a c d \,e^{3} x -12 c^{2} d^{3} e x +a^{2} e^{4}+4 a c \,d^{2} e^{2}-8 c^{2} d^{4}\right)}{3 \left(e x +d \right)^{\frac{3}{2}} e^{3}}"," ",0,"-2/3/(e*x+d)^(3/2)*(-3*c^2*d^2*e^2*x^2+6*a*c*d*e^3*x-12*c^2*d^3*e*x+a^2*e^4+4*a*c*d^2*e^2-8*c^2*d^4)/e^3","A"
1990,1,73,71,0.050000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^2/(e*x+d)^(11/2),x)","-\frac{2 \left(15 c^{2} d^{2} e^{2} x^{2}+10 a c d \,e^{3} x +20 c^{2} d^{3} e x +3 a^{2} e^{4}+4 a c \,d^{2} e^{2}+8 c^{2} d^{4}\right)}{15 \left(e x +d \right)^{\frac{5}{2}} e^{3}}"," ",0,"-2/15/(e*x+d)^(5/2)*(15*c^2*d^2*e^2*x^2+10*a*c*d*e^3*x+20*c^2*d^3*e*x+3*a^2*e^4+4*a*c*d^2*e^2+8*c^2*d^4)/e^3","A"
1991,1,73,71,0.049000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^2/(e*x+d)^(13/2),x)","-\frac{2 \left(35 c^{2} d^{2} e^{2} x^{2}+42 a c d \,e^{3} x +28 c^{2} d^{3} e x +15 a^{2} e^{4}+12 a c \,d^{2} e^{2}+8 c^{2} d^{4}\right)}{105 \left(e x +d \right)^{\frac{7}{2}} e^{3}}"," ",0,"-2/105/(e*x+d)^(7/2)*(35*c^2*d^2*e^2*x^2+42*a*c*d*e^3*x+28*c^2*d^3*e*x+15*a^2*e^4+12*a*c*d^2*e^2+8*c^2*d^4)/e^3","A"
1992,1,131,103,0.046000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^3*(e*x+d)^(1/2),x)","\frac{2 \left(e x +d \right)^{\frac{9}{2}} \left(429 c^{3} d^{3} e^{3} x^{3}+1485 a \,c^{2} d^{2} e^{4} x^{2}-198 c^{3} d^{4} e^{2} x^{2}+1755 a^{2} c d \,e^{5} x -540 a \,c^{2} d^{3} e^{3} x +72 c^{3} d^{5} e x +715 a^{3} e^{6}-390 a^{2} c \,d^{2} e^{4}+120 a \,c^{2} d^{4} e^{2}-16 c^{3} d^{6}\right)}{6435 e^{4}}"," ",0,"2/6435*(e*x+d)^(9/2)*(429*c^3*d^3*e^3*x^3+1485*a*c^2*d^2*e^4*x^2-198*c^3*d^4*e^2*x^2+1755*a^2*c*d*e^5*x-540*a*c^2*d^3*e^3*x+72*c^3*d^5*e*x+715*a^3*e^6-390*a^2*c*d^2*e^4+120*a*c^2*d^4*e^2-16*c^3*d^6)/e^4","A"
1993,1,131,103,0.046000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^3/(e*x+d)^(1/2),x)","\frac{2 \left(e x +d \right)^{\frac{7}{2}} \left(231 c^{3} d^{3} e^{3} x^{3}+819 a \,c^{2} d^{2} e^{4} x^{2}-126 c^{3} d^{4} e^{2} x^{2}+1001 a^{2} c d \,e^{5} x -364 a \,c^{2} d^{3} e^{3} x +56 c^{3} d^{5} e x +429 a^{3} e^{6}-286 a^{2} c \,d^{2} e^{4}+104 a \,c^{2} d^{4} e^{2}-16 c^{3} d^{6}\right)}{3003 e^{4}}"," ",0,"2/3003*(e*x+d)^(7/2)*(231*c^3*d^3*e^3*x^3+819*a*c^2*d^2*e^4*x^2-126*c^3*d^4*e^2*x^2+1001*a^2*c*d*e^5*x-364*a*c^2*d^3*e^3*x+56*c^3*d^5*e*x+429*a^3*e^6-286*a^2*c*d^2*e^4+104*a*c^2*d^4*e^2-16*c^3*d^6)/e^4","A"
1994,1,131,103,0.066000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^3/(e*x+d)^(3/2),x)","\frac{2 \left(e x +d \right)^{\frac{5}{2}} \left(105 c^{3} d^{3} e^{3} x^{3}+385 a \,c^{2} d^{2} e^{4} x^{2}-70 c^{3} d^{4} e^{2} x^{2}+495 a^{2} c d \,e^{5} x -220 a \,c^{2} d^{3} e^{3} x +40 c^{3} d^{5} e x +231 a^{3} e^{6}-198 a^{2} c \,d^{2} e^{4}+88 a \,c^{2} d^{4} e^{2}-16 c^{3} d^{6}\right)}{1155 e^{4}}"," ",0,"2/1155*(e*x+d)^(5/2)*(105*c^3*d^3*e^3*x^3+385*a*c^2*d^2*e^4*x^2-70*c^3*d^4*e^2*x^2+495*a^2*c*d*e^5*x-220*a*c^2*d^3*e^3*x+40*c^3*d^5*e*x+231*a^3*e^6-198*a^2*c*d^2*e^4+88*a*c^2*d^4*e^2-16*c^3*d^6)/e^4","A"
1995,1,131,103,0.046000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^3/(e*x+d)^(5/2),x)","\frac{2 \left(e x +d \right)^{\frac{3}{2}} \left(35 c^{3} d^{3} e^{3} x^{3}+135 a \,c^{2} d^{2} e^{4} x^{2}-30 c^{3} d^{4} e^{2} x^{2}+189 a^{2} c d \,e^{5} x -108 a \,c^{2} d^{3} e^{3} x +24 c^{3} d^{5} e x +105 a^{3} e^{6}-126 a^{2} c \,d^{2} e^{4}+72 a \,c^{2} d^{4} e^{2}-16 c^{3} d^{6}\right)}{315 e^{4}}"," ",0,"2/315*(e*x+d)^(3/2)*(35*c^3*d^3*e^3*x^3+135*a*c^2*d^2*e^4*x^2-30*c^3*d^4*e^2*x^2+189*a^2*c*d*e^5*x-108*a*c^2*d^3*e^3*x+24*c^3*d^5*e*x+105*a^3*e^6-126*a^2*c*d^2*e^4+72*a*c^2*d^4*e^2-16*c^3*d^6)/e^4","A"
1996,1,131,103,0.056000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^3/(e*x+d)^(7/2),x)","\frac{2 \sqrt{e x +d}\, \left(5 c^{3} d^{3} e^{3} x^{3}+21 a \,c^{2} d^{2} e^{4} x^{2}-6 c^{3} d^{4} e^{2} x^{2}+35 a^{2} c d \,e^{5} x -28 a \,c^{2} d^{3} e^{3} x +8 c^{3} d^{5} e x +35 a^{3} e^{6}-70 a^{2} c \,d^{2} e^{4}+56 a \,c^{2} d^{4} e^{2}-16 c^{3} d^{6}\right)}{35 e^{4}}"," ",0,"2/35*(e*x+d)^(1/2)*(5*c^3*d^3*e^3*x^3+21*a*c^2*d^2*e^4*x^2-6*c^3*d^4*e^2*x^2+35*a^2*c*d*e^5*x-28*a*c^2*d^3*e^3*x+8*c^3*d^5*e*x+35*a^3*e^6-70*a^2*c*d^2*e^4+56*a*c^2*d^4*e^2-16*c^3*d^6)/e^4","A"
1997,1,131,103,0.045000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^3/(e*x+d)^(9/2),x)","-\frac{2 \left(-c^{3} d^{3} e^{3} x^{3}-5 a \,c^{2} d^{2} e^{4} x^{2}+2 c^{3} d^{4} e^{2} x^{2}-15 a^{2} c d \,e^{5} x +20 a \,c^{2} d^{3} e^{3} x -8 c^{3} d^{5} e x +5 a^{3} e^{6}-30 a^{2} c \,d^{2} e^{4}+40 a \,c^{2} d^{4} e^{2}-16 c^{3} d^{6}\right)}{5 \sqrt{e x +d}\, e^{4}}"," ",0,"-2/5/(e*x+d)^(1/2)*(-c^3*d^3*e^3*x^3-5*a*c^2*d^2*e^4*x^2+2*c^3*d^4*e^2*x^2-15*a^2*c*d*e^5*x+20*a*c^2*d^3*e^3*x-8*c^3*d^5*e*x+5*a^3*e^6-30*a^2*c*d^2*e^4+40*a*c^2*d^4*e^2-16*c^3*d^6)/e^4","A"
1998,1,130,103,0.047000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^3/(e*x+d)^(11/2),x)","-\frac{2 \left(-c^{3} d^{3} e^{3} x^{3}-9 a \,c^{2} d^{2} e^{4} x^{2}+6 c^{3} d^{4} e^{2} x^{2}+9 a^{2} c d \,e^{5} x -36 a \,c^{2} d^{3} e^{3} x +24 c^{3} d^{5} e x +a^{3} e^{6}+6 a^{2} c \,d^{2} e^{4}-24 a \,c^{2} d^{4} e^{2}+16 c^{3} d^{6}\right)}{3 \left(e x +d \right)^{\frac{3}{2}} e^{4}}"," ",0,"-2/3/(e*x+d)^(3/2)*(-c^3*d^3*e^3*x^3-9*a*c^2*d^2*e^4*x^2+6*c^3*d^4*e^2*x^2+9*a^2*c*d*e^5*x-36*a*c^2*d^3*e^3*x+24*c^3*d^5*e*x+a^3*e^6+6*a^2*c*d^2*e^4-24*a*c^2*d^4*e^2+16*c^3*d^6)/e^4","A"
1999,1,130,103,0.048000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^3/(e*x+d)^(13/2),x)","-\frac{2 \left(-5 c^{3} d^{3} e^{3} x^{3}+15 a \,c^{2} d^{2} e^{4} x^{2}-30 c^{3} d^{4} e^{2} x^{2}+5 a^{2} c d \,e^{5} x +20 a \,c^{2} d^{3} e^{3} x -40 c^{3} d^{5} e x +a^{3} e^{6}+2 a^{2} c \,d^{2} e^{4}+8 a \,c^{2} d^{4} e^{2}-16 c^{3} d^{6}\right)}{5 \left(e x +d \right)^{\frac{5}{2}} e^{4}}"," ",0,"-2/5/(e*x+d)^(5/2)*(-5*c^3*d^3*e^3*x^3+15*a*c^2*d^2*e^4*x^2-30*c^3*d^4*e^2*x^2+5*a^2*c*d*e^5*x+20*a*c^2*d^3*e^3*x-40*c^3*d^5*e*x+a^3*e^6+2*a^2*c*d^2*e^4+8*a*c^2*d^4*e^2-16*c^3*d^6)/e^4","A"
2000,1,455,152,0.078000," ","int((e*x+d)^(9/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x),x)","\frac{2 a^{4} e^{8} \arctan \left(\frac{\sqrt{e x +d}\, c d}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}\right)}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}\, c^{4} d^{4}}-\frac{8 a^{3} e^{6} \arctan \left(\frac{\sqrt{e x +d}\, c d}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}\right)}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}\, c^{3} d^{2}}+\frac{12 a^{2} e^{4} \arctan \left(\frac{\sqrt{e x +d}\, c d}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}\right)}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}\, c^{2}}-\frac{8 a \,d^{2} e^{2} \arctan \left(\frac{\sqrt{e x +d}\, c d}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}\right)}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}\, c}+\frac{2 d^{4} \arctan \left(\frac{\sqrt{e x +d}\, c d}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}\right)}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}-\frac{2 \sqrt{e x +d}\, a^{3} e^{6}}{c^{4} d^{4}}+\frac{6 \sqrt{e x +d}\, a^{2} e^{4}}{c^{3} d^{2}}-\frac{6 \sqrt{e x +d}\, a \,e^{2}}{c^{2}}+\frac{2 \sqrt{e x +d}\, d^{2}}{c}+\frac{2 \left(e x +d \right)^{\frac{3}{2}} a^{2} e^{4}}{3 c^{3} d^{3}}-\frac{4 \left(e x +d \right)^{\frac{3}{2}} a \,e^{2}}{3 c^{2} d}+\frac{2 \left(e x +d \right)^{\frac{3}{2}} d}{3 c}-\frac{2 \left(e x +d \right)^{\frac{5}{2}} a \,e^{2}}{5 c^{2} d^{2}}+\frac{2 \left(e x +d \right)^{\frac{5}{2}}}{5 c}+\frac{2 \left(e x +d \right)^{\frac{7}{2}}}{7 c d}"," ",0,"2/7*(e*x+d)^(7/2)/c/d-2/5/c^2/d^2*(e*x+d)^(5/2)*a*e^2+2/5/c*(e*x+d)^(5/2)+2/3/c^3/d^3*(e*x+d)^(3/2)*a^2*e^4-4/3/c^2/d*(e*x+d)^(3/2)*a*e^2+2/3/c*d*(e*x+d)^(3/2)-2/c^4/d^4*a^3*e^6*(e*x+d)^(1/2)+6/c^3/d^2*a^2*e^4*(e*x+d)^(1/2)-6/c^2*a*e^2*(e*x+d)^(1/2)+2/c*d^2*(e*x+d)^(1/2)+2/c^4/d^4/((a*e^2-c*d^2)*c*d)^(1/2)*arctan((e*x+d)^(1/2)*c*d/((a*e^2-c*d^2)*c*d)^(1/2))*a^4*e^8-8/c^3/d^2/((a*e^2-c*d^2)*c*d)^(1/2)*arctan((e*x+d)^(1/2)*c*d/((a*e^2-c*d^2)*c*d)^(1/2))*a^3*e^6+12/c^2/((a*e^2-c*d^2)*c*d)^(1/2)*arctan((e*x+d)^(1/2)*c*d/((a*e^2-c*d^2)*c*d)^(1/2))*a^2*e^4-8/c*d^2/((a*e^2-c*d^2)*c*d)^(1/2)*arctan((e*x+d)^(1/2)*c*d/((a*e^2-c*d^2)*c*d)^(1/2))*a*e^2+2*d^4/((a*e^2-c*d^2)*c*d)^(1/2)*arctan((e*x+d)^(1/2)*c*d/((a*e^2-c*d^2)*c*d)^(1/2))","B"
2001,1,324,123,0.056000," ","int((e*x+d)^(7/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x),x)","-\frac{2 a^{3} e^{6} \arctan \left(\frac{\sqrt{e x +d}\, c d}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}\right)}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}\, c^{3} d^{3}}+\frac{6 a^{2} e^{4} \arctan \left(\frac{\sqrt{e x +d}\, c d}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}\right)}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}\, c^{2} d}-\frac{6 a d \,e^{2} \arctan \left(\frac{\sqrt{e x +d}\, c d}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}\right)}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}\, c}+\frac{2 d^{3} \arctan \left(\frac{\sqrt{e x +d}\, c d}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}\right)}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}+\frac{2 \sqrt{e x +d}\, a^{2} e^{4}}{c^{3} d^{3}}-\frac{4 \sqrt{e x +d}\, a \,e^{2}}{c^{2} d}+\frac{2 \sqrt{e x +d}\, d}{c}-\frac{2 \left(e x +d \right)^{\frac{3}{2}} a \,e^{2}}{3 c^{2} d^{2}}+\frac{2 \left(e x +d \right)^{\frac{3}{2}}}{3 c}+\frac{2 \left(e x +d \right)^{\frac{5}{2}}}{5 c d}"," ",0,"2/5*(e*x+d)^(5/2)/c/d-2/3/c^2/d^2*(e*x+d)^(3/2)*a*e^2+2/3/c*(e*x+d)^(3/2)+2/c^3/d^3*a^2*e^4*(e*x+d)^(1/2)-4/c^2/d*a*e^2*(e*x+d)^(1/2)+2/c*d*(e*x+d)^(1/2)-2/c^3/d^3/((a*e^2-c*d^2)*c*d)^(1/2)*arctan((e*x+d)^(1/2)/((a*e^2-c*d^2)*c*d)^(1/2)*c*d)*a^3*e^6+6/c^2/d/((a*e^2-c*d^2)*c*d)^(1/2)*arctan((e*x+d)^(1/2)/((a*e^2-c*d^2)*c*d)^(1/2)*c*d)*a^2*e^4-6/c*d/((a*e^2-c*d^2)*c*d)^(1/2)*arctan((e*x+d)^(1/2)/((a*e^2-c*d^2)*c*d)^(1/2)*c*d)*a*e^2+2*d^3/((a*e^2-c*d^2)*c*d)^(1/2)*arctan((e*x+d)^(1/2)/((a*e^2-c*d^2)*c*d)^(1/2)*c*d)","B"
2002,1,211,94,0.054000," ","int((e*x+d)^(5/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x),x)","\frac{2 a^{2} e^{4} \arctan \left(\frac{\sqrt{e x +d}\, c d}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}\right)}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}\, c^{2} d^{2}}-\frac{4 a \,e^{2} \arctan \left(\frac{\sqrt{e x +d}\, c d}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}\right)}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}\, c}+\frac{2 d^{2} \arctan \left(\frac{\sqrt{e x +d}\, c d}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}\right)}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}-\frac{2 \sqrt{e x +d}\, a \,e^{2}}{c^{2} d^{2}}+\frac{2 \sqrt{e x +d}}{c}+\frac{2 \left(e x +d \right)^{\frac{3}{2}}}{3 c d}"," ",0,"2/3*(e*x+d)^(3/2)/c/d-2/c^2/d^2*a*e^2*(e*x+d)^(1/2)+2/c*(e*x+d)^(1/2)+2/c^2/d^2/((a*e^2-c*d^2)*c*d)^(1/2)*arctan((e*x+d)^(1/2)/((a*e^2-c*d^2)*c*d)^(1/2)*c*d)*a^2*e^4-4/c/((a*e^2-c*d^2)*c*d)^(1/2)*arctan((e*x+d)^(1/2)/((a*e^2-c*d^2)*c*d)^(1/2)*c*d)*a*e^2+2*d^2/((a*e^2-c*d^2)*c*d)^(1/2)*arctan((e*x+d)^(1/2)/((a*e^2-c*d^2)*c*d)^(1/2)*c*d)","B"
2003,1,122,67,0.048000," ","int((e*x+d)^(3/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x),x)","-\frac{2 a \,e^{2} \arctan \left(\frac{\sqrt{e x +d}\, c d}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}\right)}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}\, c d}+\frac{2 d \arctan \left(\frac{\sqrt{e x +d}\, c d}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}\right)}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}+\frac{2 \sqrt{e x +d}}{c d}"," ",0,"2*(e*x+d)^(1/2)/c/d-2/c/d/((a*e^2-c*d^2)*c*d)^(1/2)*arctan((e*x+d)^(1/2)/((a*e^2-c*d^2)*c*d)^(1/2)*c*d)*a*e^2+2*d/((a*e^2-c*d^2)*c*d)^(1/2)*arctan((e*x+d)^(1/2)/((a*e^2-c*d^2)*c*d)^(1/2)*c*d)","A"
2004,1,48,51,0.052000," ","int((e*x+d)^(1/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x),x)","\frac{2 \arctan \left(\frac{\sqrt{e x +d}\, c d}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}\right)}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}"," ",0,"2/((a*e^2-c*d^2)*c*d)^(1/2)*arctan((e*x+d)^(1/2)/((a*e^2-c*d^2)*c*d)^(1/2)*c*d)","A"
2005,1,88,75,0.053000," ","int(1/(e*x+d)^(1/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x),x)","-\frac{2 c d \arctan \left(\frac{\sqrt{e x +d}\, c d}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}\right)}{\left(a \,e^{2}-c \,d^{2}\right) \sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}-\frac{2}{\left(a \,e^{2}-c \,d^{2}\right) \sqrt{e x +d}}"," ",0,"-2*c*d/(a*e^2-c*d^2)/((a*e^2-c*d^2)*c*d)^(1/2)*arctan((e*x+d)^(1/2)/((a*e^2-c*d^2)*c*d)^(1/2)*c*d)-2/(a*e^2-c*d^2)/(e*x+d)^(1/2)","A"
2006,1,117,100,0.061000," ","int(1/(e*x+d)^(3/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x),x)","\frac{2 c^{2} d^{2} \arctan \left(\frac{\sqrt{e x +d}\, c d}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}\right)}{\left(a \,e^{2}-c \,d^{2}\right)^{2} \sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}+\frac{2 c d}{\left(a \,e^{2}-c \,d^{2}\right)^{2} \sqrt{e x +d}}-\frac{2}{3 \left(a \,e^{2}-c \,d^{2}\right) \left(e x +d \right)^{\frac{3}{2}}}"," ",0,"2*c^2*d^2/(a*e^2-c*d^2)^2/((a*e^2-c*d^2)*c*d)^(1/2)*arctan((e*x+d)^(1/2)/((a*e^2-c*d^2)*c*d)^(1/2)*c*d)-2/3/(a*e^2-c*d^2)/(e*x+d)^(3/2)+2*c*d/(a*e^2-c*d^2)^2/(e*x+d)^(1/2)","A"
2007,1,146,129,0.063000," ","int(1/(e*x+d)^(5/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x),x)","-\frac{2 c^{3} d^{3} \arctan \left(\frac{\sqrt{e x +d}\, c d}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}\right)}{\left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}-\frac{2 c^{2} d^{2}}{\left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{e x +d}}+\frac{2 c d}{3 \left(a \,e^{2}-c \,d^{2}\right)^{2} \left(e x +d \right)^{\frac{3}{2}}}-\frac{2}{5 \left(a \,e^{2}-c \,d^{2}\right) \left(e x +d \right)^{\frac{5}{2}}}"," ",0,"-2*c^3*d^3/(a*e^2-c*d^2)^3/((a*e^2-c*d^2)*c*d)^(1/2)*arctan((e*x+d)^(1/2)/((a*e^2-c*d^2)*c*d)^(1/2)*c*d)-2/5/(a*e^2-c*d^2)/(e*x+d)^(5/2)-2*c^2*d^2/(a*e^2-c*d^2)^3/(e*x+d)^(1/2)+2/3*c*d/(a*e^2-c*d^2)^2/(e*x+d)^(3/2)","A"
2008,1,175,158,0.065000," ","int(1/(e*x+d)^(7/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x),x)","\frac{2 c^{4} d^{4} \arctan \left(\frac{\sqrt{e x +d}\, c d}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}\right)}{\left(a \,e^{2}-c \,d^{2}\right)^{4} \sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}+\frac{2 c^{3} d^{3}}{\left(a \,e^{2}-c \,d^{2}\right)^{4} \sqrt{e x +d}}-\frac{2 c^{2} d^{2}}{3 \left(a \,e^{2}-c \,d^{2}\right)^{3} \left(e x +d \right)^{\frac{3}{2}}}+\frac{2 c d}{5 \left(a \,e^{2}-c \,d^{2}\right)^{2} \left(e x +d \right)^{\frac{5}{2}}}-\frac{2}{7 \left(a \,e^{2}-c \,d^{2}\right) \left(e x +d \right)^{\frac{7}{2}}}"," ",0,"2*c^4*d^4/(a*e^2-c*d^2)^4/((a*e^2-c*d^2)*c*d)^(1/2)*arctan((e*x+d)^(1/2)/((a*e^2-c*d^2)*c*d)^(1/2)*c*d)-2/7/(a*e^2-c*d^2)/(e*x+d)^(7/2)-2/3*c^2*d^2/(a*e^2-c*d^2)^3/(e*x+d)^(3/2)+2/5*c*d/(a*e^2-c*d^2)^2/(e*x+d)^(5/2)+2*c^3*d^3/(a*e^2-c*d^2)^4/(e*x+d)^(1/2)","A"
2009,1,628,182,0.065000," ","int((e*x+d)^(13/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^2,x)","\frac{9 a^{4} e^{9} \arctan \left(\frac{\sqrt{e x +d}\, c d}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}\right)}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}\, c^{5} d^{5}}-\frac{36 a^{3} e^{7} \arctan \left(\frac{\sqrt{e x +d}\, c d}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}\right)}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}\, c^{4} d^{3}}+\frac{54 a^{2} e^{5} \arctan \left(\frac{\sqrt{e x +d}\, c d}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}\right)}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}\, c^{3} d}-\frac{36 a d \,e^{3} \arctan \left(\frac{\sqrt{e x +d}\, c d}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}\right)}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}\, c^{2}}+\frac{9 d^{3} e \arctan \left(\frac{\sqrt{e x +d}\, c d}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}\right)}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}\, c}-\frac{\sqrt{e x +d}\, a^{4} e^{9}}{\left(c d e x +a \,e^{2}\right) c^{5} d^{5}}+\frac{4 \sqrt{e x +d}\, a^{3} e^{7}}{\left(c d e x +a \,e^{2}\right) c^{4} d^{3}}-\frac{6 \sqrt{e x +d}\, a^{2} e^{5}}{\left(c d e x +a \,e^{2}\right) c^{3} d}+\frac{4 \sqrt{e x +d}\, a d \,e^{3}}{\left(c d e x +a \,e^{2}\right) c^{2}}-\frac{\sqrt{e x +d}\, d^{3} e}{\left(c d e x +a \,e^{2}\right) c}-\frac{8 \sqrt{e x +d}\, a^{3} e^{7}}{c^{5} d^{5}}+\frac{24 \sqrt{e x +d}\, a^{2} e^{5}}{c^{4} d^{3}}-\frac{24 \sqrt{e x +d}\, a \,e^{3}}{c^{3} d}+\frac{8 \sqrt{e x +d}\, d e}{c^{2}}+\frac{2 \left(e x +d \right)^{\frac{3}{2}} a^{2} e^{5}}{c^{4} d^{4}}-\frac{4 \left(e x +d \right)^{\frac{3}{2}} a \,e^{3}}{c^{3} d^{2}}+\frac{2 \left(e x +d \right)^{\frac{3}{2}} e}{c^{2}}-\frac{4 \left(e x +d \right)^{\frac{5}{2}} a \,e^{3}}{5 c^{3} d^{3}}+\frac{4 \left(e x +d \right)^{\frac{5}{2}} e}{5 c^{2} d}+\frac{2 \left(e x +d \right)^{\frac{7}{2}} e}{7 c^{2} d^{2}}"," ",0,"2/7*e*(e*x+d)^(7/2)/c^2/d^2-4/5/c^3/d^3*(e*x+d)^(5/2)*a*e^3+4/5*e/c^2/d*(e*x+d)^(5/2)+2/c^4/d^4*(e*x+d)^(3/2)*a^2*e^5-4/c^3/d^2*(e*x+d)^(3/2)*a*e^3+2*e/c^2*(e*x+d)^(3/2)-8/c^5/d^5*a^3*e^7*(e*x+d)^(1/2)+24/c^4/d^3*a^2*e^5*(e*x+d)^(1/2)-24/c^3/d*a*e^3*(e*x+d)^(1/2)+8*e/c^2*d*(e*x+d)^(1/2)-1/c^5/d^5*(e*x+d)^(1/2)/(c*d*e*x+a*e^2)*a^4*e^9+4/c^4/d^3*(e*x+d)^(1/2)/(c*d*e*x+a*e^2)*a^3*e^7-6/c^3/d*(e*x+d)^(1/2)/(c*d*e*x+a*e^2)*a^2*e^5+4/c^2*d*(e*x+d)^(1/2)/(c*d*e*x+a*e^2)*a*e^3-e/c*d^3*(e*x+d)^(1/2)/(c*d*e*x+a*e^2)+9/c^5/d^5/((a*e^2-c*d^2)*c*d)^(1/2)*arctan((e*x+d)^(1/2)/((a*e^2-c*d^2)*c*d)^(1/2)*c*d)*a^4*e^9-36/c^4/d^3/((a*e^2-c*d^2)*c*d)^(1/2)*arctan((e*x+d)^(1/2)/((a*e^2-c*d^2)*c*d)^(1/2)*c*d)*a^3*e^7+54/c^3/d/((a*e^2-c*d^2)*c*d)^(1/2)*arctan((e*x+d)^(1/2)/((a*e^2-c*d^2)*c*d)^(1/2)*c*d)*a^2*e^5-36/c^2*d/((a*e^2-c*d^2)*c*d)^(1/2)*arctan((e*x+d)^(1/2)/((a*e^2-c*d^2)*c*d)^(1/2)*c*d)*a*e^3+9*e/c*d^3/((a*e^2-c*d^2)*c*d)^(1/2)*arctan((e*x+d)^(1/2)/((a*e^2-c*d^2)*c*d)^(1/2)*c*d)","B"
2010,1,457,152,0.073000," ","int((e*x+d)^(11/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^2,x)","-\frac{7 a^{3} e^{7} \arctan \left(\frac{\sqrt{e x +d}\, c d}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}\right)}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}\, c^{4} d^{4}}+\frac{21 a^{2} e^{5} \arctan \left(\frac{\sqrt{e x +d}\, c d}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}\right)}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}\, c^{3} d^{2}}-\frac{21 a \,e^{3} \arctan \left(\frac{\sqrt{e x +d}\, c d}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}\right)}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}\, c^{2}}+\frac{7 d^{2} e \arctan \left(\frac{\sqrt{e x +d}\, c d}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}\right)}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}\, c}+\frac{\sqrt{e x +d}\, a^{3} e^{7}}{\left(c d e x +a \,e^{2}\right) c^{4} d^{4}}-\frac{3 \sqrt{e x +d}\, a^{2} e^{5}}{\left(c d e x +a \,e^{2}\right) c^{3} d^{2}}+\frac{3 \sqrt{e x +d}\, a \,e^{3}}{\left(c d e x +a \,e^{2}\right) c^{2}}-\frac{\sqrt{e x +d}\, d^{2} e}{\left(c d e x +a \,e^{2}\right) c}+\frac{6 \sqrt{e x +d}\, a^{2} e^{5}}{c^{4} d^{4}}-\frac{12 \sqrt{e x +d}\, a \,e^{3}}{c^{3} d^{2}}+\frac{6 \sqrt{e x +d}\, e}{c^{2}}-\frac{4 \left(e x +d \right)^{\frac{3}{2}} a \,e^{3}}{3 c^{3} d^{3}}+\frac{4 \left(e x +d \right)^{\frac{3}{2}} e}{3 c^{2} d}+\frac{2 \left(e x +d \right)^{\frac{5}{2}} e}{5 c^{2} d^{2}}"," ",0,"2/5*e*(e*x+d)^(5/2)/c^2/d^2-4/3/c^3/d^3*(e*x+d)^(3/2)*a*e^3+4/3*e/c^2/d*(e*x+d)^(3/2)+6/c^4/d^4*a^2*e^5*(e*x+d)^(1/2)-12/c^3/d^2*a*e^3*(e*x+d)^(1/2)+6*e/c^2*(e*x+d)^(1/2)+1/c^4/d^4*(e*x+d)^(1/2)/(c*d*e*x+a*e^2)*a^3*e^7-3/c^3/d^2*(e*x+d)^(1/2)/(c*d*e*x+a*e^2)*a^2*e^5+3/c^2*(e*x+d)^(1/2)/(c*d*e*x+a*e^2)*a*e^3-e/c*d^2*(e*x+d)^(1/2)/(c*d*e*x+a*e^2)-7/c^4/d^4/((a*e^2-c*d^2)*c*d)^(1/2)*arctan((e*x+d)^(1/2)/((a*e^2-c*d^2)*c*d)^(1/2)*c*d)*a^3*e^7+21/c^3/d^2/((a*e^2-c*d^2)*c*d)^(1/2)*arctan((e*x+d)^(1/2)/((a*e^2-c*d^2)*c*d)^(1/2)*c*d)*a^2*e^5-21/c^2/((a*e^2-c*d^2)*c*d)^(1/2)*arctan((e*x+d)^(1/2)/((a*e^2-c*d^2)*c*d)^(1/2)*c*d)*a*e^3+7*e/c*d^2/((a*e^2-c*d^2)*c*d)^(1/2)*arctan((e*x+d)^(1/2)/((a*e^2-c*d^2)*c*d)^(1/2)*c*d)","B"
2011,1,314,122,0.083000," ","int((e*x+d)^(9/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^2,x)","\frac{5 a^{2} e^{5} \arctan \left(\frac{\sqrt{e x +d}\, c d}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}\right)}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}\, c^{3} d^{3}}-\frac{10 a \,e^{3} \arctan \left(\frac{\sqrt{e x +d}\, c d}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}\right)}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}\, c^{2} d}+\frac{5 d e \arctan \left(\frac{\sqrt{e x +d}\, c d}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}\right)}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}\, c}-\frac{\sqrt{e x +d}\, a^{2} e^{5}}{\left(c d e x +a \,e^{2}\right) c^{3} d^{3}}+\frac{2 \sqrt{e x +d}\, a \,e^{3}}{\left(c d e x +a \,e^{2}\right) c^{2} d}-\frac{\sqrt{e x +d}\, d e}{\left(c d e x +a \,e^{2}\right) c}-\frac{4 \sqrt{e x +d}\, a \,e^{3}}{c^{3} d^{3}}+\frac{4 \sqrt{e x +d}\, e}{c^{2} d}+\frac{2 \left(e x +d \right)^{\frac{3}{2}} e}{3 c^{2} d^{2}}"," ",0,"2/3*e*(e*x+d)^(3/2)/c^2/d^2-4/c^3/d^3*a*e^3*(e*x+d)^(1/2)+4*e/c^2/d*(e*x+d)^(1/2)-1/c^3/d^3*(e*x+d)^(1/2)/(c*d*e*x+a*e^2)*a^2*e^5+2/c^2/d*(e*x+d)^(1/2)/(c*d*e*x+a*e^2)*a*e^3-e/c*d*(e*x+d)^(1/2)/(c*d*e*x+a*e^2)+5/c^3/d^3/((a*e^2-c*d^2)*c*d)^(1/2)*arctan((e*x+d)^(1/2)/((a*e^2-c*d^2)*c*d)^(1/2)*c*d)*a^2*e^5-10/c^2/d/((a*e^2-c*d^2)*c*d)^(1/2)*arctan((e*x+d)^(1/2)/((a*e^2-c*d^2)*c*d)^(1/2)*c*d)*a*e^3+5*e/c*d/((a*e^2-c*d^2)*c*d)^(1/2)*arctan((e*x+d)^(1/2)/((a*e^2-c*d^2)*c*d)^(1/2)*c*d)","B"
2012,1,183,94,0.074000," ","int((e*x+d)^(7/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^2,x)","-\frac{3 a \,e^{3} \arctan \left(\frac{\sqrt{e x +d}\, c d}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}\right)}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}\, c^{2} d^{2}}+\frac{3 e \arctan \left(\frac{\sqrt{e x +d}\, c d}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}\right)}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}\, c}+\frac{\sqrt{e x +d}\, a \,e^{3}}{\left(c d e x +a \,e^{2}\right) c^{2} d^{2}}-\frac{\sqrt{e x +d}\, e}{\left(c d e x +a \,e^{2}\right) c}+\frac{2 \sqrt{e x +d}\, e}{c^{2} d^{2}}"," ",0,"2*e*(e*x+d)^(1/2)/c^2/d^2+1/c^2/d^2*(e*x+d)^(1/2)/(c*d*e*x+a*e^2)*a*e^3-e/c*(e*x+d)^(1/2)/(c*d*e*x+a*e^2)-3/c^2/d^2/((a*e^2-c*d^2)*c*d)^(1/2)*arctan((e*x+d)^(1/2)/((a*e^2-c*d^2)*c*d)^(1/2)*c*d)*a*e^3+3*e/c/((a*e^2-c*d^2)*c*d)^(1/2)*arctan((e*x+d)^(1/2)/((a*e^2-c*d^2)*c*d)^(1/2)*c*d)","A"
2013,1,84,78,0.055000," ","int((e*x+d)^(5/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^2,x)","\frac{e \arctan \left(\frac{\sqrt{e x +d}\, c d}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}\right)}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}\, c d}-\frac{\sqrt{e x +d}\, e}{\left(c d e x +a \,e^{2}\right) c d}"," ",0,"-e/c/d*(e*x+d)^(1/2)/(c*d*e*x+a*e^2)+e/c/d/((a*e^2-c*d^2)*c*d)^(1/2)*arctan((e*x+d)^(1/2)/((a*e^2-c*d^2)*c*d)^(1/2)*c*d)","A"
2014,1,99,85,0.059000," ","int((e*x+d)^(3/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^2,x)","\frac{e \arctan \left(\frac{\sqrt{e x +d}\, c d}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}\right)}{\left(a \,e^{2}-c \,d^{2}\right) \sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}+\frac{\sqrt{e x +d}\, e}{\left(a \,e^{2}-c \,d^{2}\right) \left(c d e x +a \,e^{2}\right)}"," ",0,"e*(e*x+d)^(1/2)/(a*e^2-c*d^2)/(c*d*e*x+a*e^2)+e/(a*e^2-c*d^2)/((a*e^2-c*d^2)*c*d)^(1/2)*arctan((e*x+d)^(1/2)/((a*e^2-c*d^2)*c*d)^(1/2)*c*d)","A"
2015,1,129,110,0.062000," ","int((e*x+d)^(1/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^2,x)","-\frac{3 c d e \arctan \left(\frac{\sqrt{e x +d}\, c d}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}\right)}{\left(a \,e^{2}-c \,d^{2}\right)^{2} \sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}-\frac{\sqrt{e x +d}\, c d e}{\left(a \,e^{2}-c \,d^{2}\right)^{2} \left(c d e x +a \,e^{2}\right)}-\frac{2 e}{\left(a \,e^{2}-c \,d^{2}\right)^{2} \sqrt{e x +d}}"," ",0,"-e*c*d/(a*e^2-c*d^2)^2*(e*x+d)^(1/2)/(c*d*e*x+a*e^2)-3*e*c*d/(a*e^2-c*d^2)^2/((a*e^2-c*d^2)*c*d)^(1/2)*arctan((e*x+d)^(1/2)/((a*e^2-c*d^2)*c*d)^(1/2)*c*d)-2*e/(a*e^2-c*d^2)^2/(e*x+d)^(1/2)","A"
2016,1,162,136,0.062000," ","int(1/(e*x+d)^(1/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^2,x)","\frac{5 c^{2} d^{2} e \arctan \left(\frac{\sqrt{e x +d}\, c d}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}\right)}{\left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}+\frac{\sqrt{e x +d}\, c^{2} d^{2} e}{\left(a \,e^{2}-c \,d^{2}\right)^{3} \left(c d e x +a \,e^{2}\right)}+\frac{4 c d e}{\left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{e x +d}}-\frac{2 e}{3 \left(a \,e^{2}-c \,d^{2}\right)^{2} \left(e x +d \right)^{\frac{3}{2}}}"," ",0,"e*c^2*d^2/(a*e^2-c*d^2)^3*(e*x+d)^(1/2)/(c*d*e*x+a*e^2)+5*e*c^2*d^2/(a*e^2-c*d^2)^3/((a*e^2-c*d^2)*c*d)^(1/2)*arctan((e*x+d)^(1/2)/((a*e^2-c*d^2)*c*d)^(1/2)*c*d)-2/3*e/(a*e^2-c*d^2)^2/(e*x+d)^(3/2)+4*e/(a*e^2-c*d^2)^3*c*d/(e*x+d)^(1/2)","A"
2017,1,193,166,0.072000," ","int(1/(e*x+d)^(3/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^2,x)","-\frac{7 c^{3} d^{3} e \arctan \left(\frac{\sqrt{e x +d}\, c d}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}\right)}{\left(a \,e^{2}-c \,d^{2}\right)^{4} \sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}-\frac{\sqrt{e x +d}\, c^{3} d^{3} e}{\left(a \,e^{2}-c \,d^{2}\right)^{4} \left(c d e x +a \,e^{2}\right)}-\frac{6 c^{2} d^{2} e}{\left(a \,e^{2}-c \,d^{2}\right)^{4} \sqrt{e x +d}}+\frac{4 c d e}{3 \left(a \,e^{2}-c \,d^{2}\right)^{3} \left(e x +d \right)^{\frac{3}{2}}}-\frac{2 e}{5 \left(a \,e^{2}-c \,d^{2}\right)^{2} \left(e x +d \right)^{\frac{5}{2}}}"," ",0,"-e*c^3*d^3/(a*e^2-c*d^2)^4*(e*x+d)^(1/2)/(c*d*e*x+a*e^2)-7*e*c^3*d^3/(a*e^2-c*d^2)^4/((a*e^2-c*d^2)*c*d)^(1/2)*arctan((e*x+d)^(1/2)/((a*e^2-c*d^2)*c*d)^(1/2)*c*d)-2/5*e/(a*e^2-c*d^2)^2/(e*x+d)^(5/2)-6*e/(a*e^2-c*d^2)^4*c^2*d^2/(e*x+d)^(1/2)+4/3*e/(a*e^2-c*d^2)^3*c*d/(e*x+d)^(3/2)","A"
2018,1,635,186,0.078000," ","int((e*x+d)^(15/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^3,x)","\frac{15 \sqrt{e x +d}\, a^{4} e^{10}}{4 \left(c d e x +a \,e^{2}\right)^{2} c^{5} d^{5}}-\frac{15 \sqrt{e x +d}\, a^{3} e^{8}}{\left(c d e x +a \,e^{2}\right)^{2} c^{4} d^{3}}+\frac{45 \sqrt{e x +d}\, a^{2} e^{6}}{2 \left(c d e x +a \,e^{2}\right)^{2} c^{3} d}-\frac{15 \sqrt{e x +d}\, a d \,e^{4}}{\left(c d e x +a \,e^{2}\right)^{2} c^{2}}+\frac{15 \sqrt{e x +d}\, d^{3} e^{2}}{4 \left(c d e x +a \,e^{2}\right)^{2} c}+\frac{17 \left(e x +d \right)^{\frac{3}{2}} a^{3} e^{8}}{4 \left(c d e x +a \,e^{2}\right)^{2} c^{4} d^{4}}-\frac{51 \left(e x +d \right)^{\frac{3}{2}} a^{2} e^{6}}{4 \left(c d e x +a \,e^{2}\right)^{2} c^{3} d^{2}}+\frac{51 \left(e x +d \right)^{\frac{3}{2}} a \,e^{4}}{4 \left(c d e x +a \,e^{2}\right)^{2} c^{2}}-\frac{17 \left(e x +d \right)^{\frac{3}{2}} d^{2} e^{2}}{4 \left(c d e x +a \,e^{2}\right)^{2} c}-\frac{63 a^{3} e^{8} \arctan \left(\frac{\sqrt{e x +d}\, c d}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}\right)}{4 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}\, c^{5} d^{5}}+\frac{189 a^{2} e^{6} \arctan \left(\frac{\sqrt{e x +d}\, c d}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}\right)}{4 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}\, c^{4} d^{3}}-\frac{189 a \,e^{4} \arctan \left(\frac{\sqrt{e x +d}\, c d}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}\right)}{4 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}\, c^{3} d}+\frac{63 d \,e^{2} \arctan \left(\frac{\sqrt{e x +d}\, c d}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}\right)}{4 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}\, c^{2}}+\frac{12 \sqrt{e x +d}\, a^{2} e^{6}}{c^{5} d^{5}}-\frac{24 \sqrt{e x +d}\, a \,e^{4}}{c^{4} d^{3}}+\frac{12 \sqrt{e x +d}\, e^{2}}{c^{3} d}-\frac{2 \left(e x +d \right)^{\frac{3}{2}} a \,e^{4}}{c^{4} d^{4}}+\frac{2 \left(e x +d \right)^{\frac{3}{2}} e^{2}}{c^{3} d^{2}}+\frac{2 \left(e x +d \right)^{\frac{5}{2}} e^{2}}{5 c^{3} d^{3}}"," ",0,"2/5*e^2*(e*x+d)^(5/2)/c^3/d^3-2*e^4/c^4/d^4*(e*x+d)^(3/2)*a+2*e^2/c^3/d^2*(e*x+d)^(3/2)+12*e^6/c^5/d^5*a^2*(e*x+d)^(1/2)-24*e^4/c^4/d^3*a*(e*x+d)^(1/2)+12*e^2/c^3/d*(e*x+d)^(1/2)+17/4*e^8/c^4/d^4/(c*d*e*x+a*e^2)^2*(e*x+d)^(3/2)*a^3-51/4*e^6/c^3/d^2/(c*d*e*x+a*e^2)^2*(e*x+d)^(3/2)*a^2+51/4*e^4/c^2/(c*d*e*x+a*e^2)^2*(e*x+d)^(3/2)*a-17/4*e^2/c*d^2/(c*d*e*x+a*e^2)^2*(e*x+d)^(3/2)+15/4*e^10/c^5/d^5/(c*d*e*x+a*e^2)^2*(e*x+d)^(1/2)*a^4-15*e^8/c^4/d^3/(c*d*e*x+a*e^2)^2*(e*x+d)^(1/2)*a^3+45/2*e^6/c^3/d/(c*d*e*x+a*e^2)^2*(e*x+d)^(1/2)*a^2-15*e^4/c^2*d/(c*d*e*x+a*e^2)^2*(e*x+d)^(1/2)*a+15/4*e^2/c*d^3/(c*d*e*x+a*e^2)^2*(e*x+d)^(1/2)-63/4*e^8/c^5/d^5/((a*e^2-c*d^2)*c*d)^(1/2)*arctan((e*x+d)^(1/2)/((a*e^2-c*d^2)*c*d)^(1/2)*c*d)*a^3+189/4*e^6/c^4/d^3/((a*e^2-c*d^2)*c*d)^(1/2)*arctan((e*x+d)^(1/2)/((a*e^2-c*d^2)*c*d)^(1/2)*c*d)*a^2-189/4*e^4/c^3/d/((a*e^2-c*d^2)*c*d)^(1/2)*arctan((e*x+d)^(1/2)/((a*e^2-c*d^2)*c*d)^(1/2)*c*d)*a+63/4*e^2/c^2*d/((a*e^2-c*d^2)*c*d)^(1/2)*arctan((e*x+d)^(1/2)/((a*e^2-c*d^2)*c*d)^(1/2)*c*d)","B"
2019,1,449,154,0.062000," ","int((e*x+d)^(13/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^3,x)","-\frac{11 \sqrt{e x +d}\, a^{3} e^{8}}{4 \left(c d e x +a \,e^{2}\right)^{2} c^{4} d^{4}}+\frac{33 \sqrt{e x +d}\, a^{2} e^{6}}{4 \left(c d e x +a \,e^{2}\right)^{2} c^{3} d^{2}}-\frac{33 \sqrt{e x +d}\, a \,e^{4}}{4 \left(c d e x +a \,e^{2}\right)^{2} c^{2}}+\frac{11 \sqrt{e x +d}\, d^{2} e^{2}}{4 \left(c d e x +a \,e^{2}\right)^{2} c}-\frac{13 \left(e x +d \right)^{\frac{3}{2}} a^{2} e^{6}}{4 \left(c d e x +a \,e^{2}\right)^{2} c^{3} d^{3}}+\frac{13 \left(e x +d \right)^{\frac{3}{2}} a \,e^{4}}{2 \left(c d e x +a \,e^{2}\right)^{2} c^{2} d}-\frac{13 \left(e x +d \right)^{\frac{3}{2}} d \,e^{2}}{4 \left(c d e x +a \,e^{2}\right)^{2} c}+\frac{35 a^{2} e^{6} \arctan \left(\frac{\sqrt{e x +d}\, c d}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}\right)}{4 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}\, c^{4} d^{4}}-\frac{35 a \,e^{4} \arctan \left(\frac{\sqrt{e x +d}\, c d}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}\right)}{2 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}\, c^{3} d^{2}}+\frac{35 e^{2} \arctan \left(\frac{\sqrt{e x +d}\, c d}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}\right)}{4 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}\, c^{2}}-\frac{6 \sqrt{e x +d}\, a \,e^{4}}{c^{4} d^{4}}+\frac{6 \sqrt{e x +d}\, e^{2}}{c^{3} d^{2}}+\frac{2 \left(e x +d \right)^{\frac{3}{2}} e^{2}}{3 c^{3} d^{3}}"," ",0,"2/3*e^2*(e*x+d)^(3/2)/c^3/d^3-6*e^4/c^4/d^4*a*(e*x+d)^(1/2)+6*e^2/c^3/d^2*(e*x+d)^(1/2)-13/4*e^6/c^3/d^3/(c*d*e*x+a*e^2)^2*(e*x+d)^(3/2)*a^2+13/2*e^4/c^2/d/(c*d*e*x+a*e^2)^2*(e*x+d)^(3/2)*a-13/4*e^2/c*d/(c*d*e*x+a*e^2)^2*(e*x+d)^(3/2)-11/4*e^8/c^4/d^4/(c*d*e*x+a*e^2)^2*(e*x+d)^(1/2)*a^3+33/4*e^6/c^3/d^2/(c*d*e*x+a*e^2)^2*(e*x+d)^(1/2)*a^2-33/4*e^4/c^2/(c*d*e*x+a*e^2)^2*(e*x+d)^(1/2)*a+11/4*e^2/c*d^2/(c*d*e*x+a*e^2)^2*(e*x+d)^(1/2)+35/4*e^6/c^4/d^4/((a*e^2-c*d^2)*c*d)^(1/2)*arctan((e*x+d)^(1/2)/((a*e^2-c*d^2)*c*d)^(1/2)*c*d)*a^2-35/2*e^4/c^3/d^2/((a*e^2-c*d^2)*c*d)^(1/2)*arctan((e*x+d)^(1/2)/((a*e^2-c*d^2)*c*d)^(1/2)*c*d)*a+35/4*e^2/c^2/((a*e^2-c*d^2)*c*d)^(1/2)*arctan((e*x+d)^(1/2)/((a*e^2-c*d^2)*c*d)^(1/2)*c*d)","B"
2020,1,288,124,0.067000," ","int((e*x+d)^(11/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^3,x)","\frac{7 \sqrt{e x +d}\, a^{2} e^{6}}{4 \left(c d e x +a \,e^{2}\right)^{2} c^{3} d^{3}}-\frac{7 \sqrt{e x +d}\, a \,e^{4}}{2 \left(c d e x +a \,e^{2}\right)^{2} c^{2} d}+\frac{7 \sqrt{e x +d}\, d \,e^{2}}{4 \left(c d e x +a \,e^{2}\right)^{2} c}+\frac{9 \left(e x +d \right)^{\frac{3}{2}} a \,e^{4}}{4 \left(c d e x +a \,e^{2}\right)^{2} c^{2} d^{2}}-\frac{9 \left(e x +d \right)^{\frac{3}{2}} e^{2}}{4 \left(c d e x +a \,e^{2}\right)^{2} c}-\frac{15 a \,e^{4} \arctan \left(\frac{\sqrt{e x +d}\, c d}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}\right)}{4 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}\, c^{3} d^{3}}+\frac{15 e^{2} \arctan \left(\frac{\sqrt{e x +d}\, c d}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}\right)}{4 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}\, c^{2} d}+\frac{2 \sqrt{e x +d}\, e^{2}}{c^{3} d^{3}}"," ",0,"2*e^2*(e*x+d)^(1/2)/c^3/d^3+9/4*e^4/c^2/d^2/(c*d*e*x+a*e^2)^2*(e*x+d)^(3/2)*a-9/4*e^2/c/(c*d*e*x+a*e^2)^2*(e*x+d)^(3/2)+7/4*e^6/c^3/d^3/(c*d*e*x+a*e^2)^2*(e*x+d)^(1/2)*a^2-7/2*e^4/c^2/d/(c*d*e*x+a*e^2)^2*(e*x+d)^(1/2)*a+7/4*e^2/c*d/(c*d*e*x+a*e^2)^2*(e*x+d)^(1/2)-15/4*e^4/c^3/d^3/((a*e^2-c*d^2)*c*d)^(1/2)*arctan((e*x+d)^(1/2)/((a*e^2-c*d^2)*c*d)^(1/2)*c*d)*a+15/4*e^2/c^2/d/((a*e^2-c*d^2)*c*d)^(1/2)*arctan((e*x+d)^(1/2)/((a*e^2-c*d^2)*c*d)^(1/2)*c*d)","B"
2021,1,149,106,0.058000," ","int((e*x+d)^(9/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^3,x)","-\frac{3 \sqrt{e x +d}\, a \,e^{4}}{4 \left(c d e x +a \,e^{2}\right)^{2} c^{2} d^{2}}+\frac{3 \sqrt{e x +d}\, e^{2}}{4 \left(c d e x +a \,e^{2}\right)^{2} c}-\frac{5 \left(e x +d \right)^{\frac{3}{2}} e^{2}}{4 \left(c d e x +a \,e^{2}\right)^{2} c d}+\frac{3 e^{2} \arctan \left(\frac{\sqrt{e x +d}\, c d}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}\right)}{4 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}\, c^{2} d^{2}}"," ",0,"-5/4*e^2/(c*d*e*x+a*e^2)^2/c/d*(e*x+d)^(3/2)-3/4*e^4/(c*d*e*x+a*e^2)^2/c^2/d^2*(e*x+d)^(1/2)*a+3/4*e^2/(c*d*e*x+a*e^2)^2/c*(e*x+d)^(1/2)+3/4*e^2/c^2/d^2/((a*e^2-c*d^2)*c*d)^(1/2)*arctan((e*x+d)^(1/2)/((a*e^2-c*d^2)*c*d)^(1/2)*c*d)","A"
2022,1,142,120,0.066000," ","int((e*x+d)^(7/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^3,x)","\frac{\left(e x +d \right)^{\frac{3}{2}} e^{2}}{4 \left(c d e x +a \,e^{2}\right)^{2} \left(a \,e^{2}-c \,d^{2}\right)}+\frac{e^{2} \arctan \left(\frac{\sqrt{e x +d}\, c d}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}\right)}{4 \left(a \,e^{2}-c \,d^{2}\right) \sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}\, c d}-\frac{\sqrt{e x +d}\, e^{2}}{4 \left(c d e x +a \,e^{2}\right)^{2} c d}"," ",0,"1/4*e^2/(c*d*e*x+a*e^2)^2/(a*e^2-c*d^2)*(e*x+d)^(3/2)-1/4*e^2/(c*d*e*x+a*e^2)^2/c/d*(e*x+d)^(1/2)+1/4*e^2/(a*e^2-c*d^2)/c/d/((a*e^2-c*d^2)*c*d)^(1/2)*arctan((e*x+d)^(1/2)/((a*e^2-c*d^2)*c*d)^(1/2)*c*d)","A"
2023,1,144,122,0.066000," ","int((e*x+d)^(5/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^3,x)","\frac{3 e^{2} \arctan \left(\frac{\sqrt{e x +d}\, c d}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}\right)}{4 \left(a \,e^{2}-c \,d^{2}\right)^{2} \sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}+\frac{\sqrt{e x +d}\, e^{2}}{2 \left(a \,e^{2}-c \,d^{2}\right) \left(c d e x +a \,e^{2}\right)^{2}}+\frac{3 \sqrt{e x +d}\, e^{2}}{4 \left(a \,e^{2}-c \,d^{2}\right)^{2} \left(c d e x +a \,e^{2}\right)}"," ",0,"1/2*e^2*(e*x+d)^(1/2)/(a*e^2-c*d^2)/(c*d*e*x+a*e^2)^2+3/4*e^2/(a*e^2-c*d^2)^2*(e*x+d)^(1/2)/(c*d*e*x+a*e^2)+3/4*e^2/(a*e^2-c*d^2)^2/((a*e^2-c*d^2)*c*d)^(1/2)*arctan((e*x+d)^(1/2)/((a*e^2-c*d^2)*c*d)^(1/2)*c*d)","A"
2024,1,226,148,0.073000," ","int((e*x+d)^(3/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^3,x)","-\frac{9 \sqrt{e x +d}\, a c d \,e^{4}}{4 \left(a \,e^{2}-c \,d^{2}\right)^{3} \left(c d e x +a \,e^{2}\right)^{2}}+\frac{9 \sqrt{e x +d}\, c^{2} d^{3} e^{2}}{4 \left(a \,e^{2}-c \,d^{2}\right)^{3} \left(c d e x +a \,e^{2}\right)^{2}}-\frac{7 \left(e x +d \right)^{\frac{3}{2}} c^{2} d^{2} e^{2}}{4 \left(a \,e^{2}-c \,d^{2}\right)^{3} \left(c d e x +a \,e^{2}\right)^{2}}-\frac{15 c d \,e^{2} \arctan \left(\frac{\sqrt{e x +d}\, c d}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}\right)}{4 \left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}-\frac{2 e^{2}}{\left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{e x +d}}"," ",0,"-7/4*e^2/(a*e^2-c*d^2)^3*c^2*d^2/(c*d*e*x+a*e^2)^2*(e*x+d)^(3/2)-9/4*e^4/(a*e^2-c*d^2)^3*c*d/(c*d*e*x+a*e^2)^2*(e*x+d)^(1/2)*a+9/4*e^2/(a*e^2-c*d^2)^3*c^2*d^3/(c*d*e*x+a*e^2)^2*(e*x+d)^(1/2)-15/4*e^2/(a*e^2-c*d^2)^3*c*d/((a*e^2-c*d^2)*c*d)^(1/2)*arctan((e*x+d)^(1/2)/((a*e^2-c*d^2)*c*d)^(1/2)*c*d)-2*e^2/(a*e^2-c*d^2)^3/(e*x+d)^(1/2)","A"
2025,1,262,176,0.069000," ","int((e*x+d)^(1/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^3,x)","\frac{13 \sqrt{e x +d}\, a \,c^{2} d^{2} e^{4}}{4 \left(a \,e^{2}-c \,d^{2}\right)^{4} \left(c d e x +a \,e^{2}\right)^{2}}-\frac{13 \sqrt{e x +d}\, c^{3} d^{4} e^{2}}{4 \left(a \,e^{2}-c \,d^{2}\right)^{4} \left(c d e x +a \,e^{2}\right)^{2}}+\frac{11 \left(e x +d \right)^{\frac{3}{2}} c^{3} d^{3} e^{2}}{4 \left(a \,e^{2}-c \,d^{2}\right)^{4} \left(c d e x +a \,e^{2}\right)^{2}}+\frac{35 c^{2} d^{2} e^{2} \arctan \left(\frac{\sqrt{e x +d}\, c d}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}\right)}{4 \left(a \,e^{2}-c \,d^{2}\right)^{4} \sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}+\frac{6 c d \,e^{2}}{\left(a \,e^{2}-c \,d^{2}\right)^{4} \sqrt{e x +d}}-\frac{2 e^{2}}{3 \left(a \,e^{2}-c \,d^{2}\right)^{3} \left(e x +d \right)^{\frac{3}{2}}}"," ",0,"11/4*e^2/(a*e^2-c*d^2)^4*c^3*d^3/(c*d*e*x+a*e^2)^2*(e*x+d)^(3/2)+13/4*e^4/(a*e^2-c*d^2)^4*c^2*d^2/(c*d*e*x+a*e^2)^2*(e*x+d)^(1/2)*a-13/4*e^2/(a*e^2-c*d^2)^4*c^3*d^4/(c*d*e*x+a*e^2)^2*(e*x+d)^(1/2)+35/4*e^2/(a*e^2-c*d^2)^4*c^2*d^2/((a*e^2-c*d^2)*c*d)^(1/2)*arctan((e*x+d)^(1/2)/((a*e^2-c*d^2)*c*d)^(1/2)*c*d)-2/3*e^2/(a*e^2-c*d^2)^3/(e*x+d)^(3/2)+6*e^2/(a*e^2-c*d^2)^4*c*d/(e*x+d)^(1/2)","A"
2026,1,294,208,0.064000," ","int(1/(e*x+d)^(1/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^3,x)","-\frac{17 \sqrt{e x +d}\, a \,c^{3} d^{3} e^{4}}{4 \left(a \,e^{2}-c \,d^{2}\right)^{5} \left(c d e x +a \,e^{2}\right)^{2}}+\frac{17 \sqrt{e x +d}\, c^{4} d^{5} e^{2}}{4 \left(a \,e^{2}-c \,d^{2}\right)^{5} \left(c d e x +a \,e^{2}\right)^{2}}-\frac{15 \left(e x +d \right)^{\frac{3}{2}} c^{4} d^{4} e^{2}}{4 \left(a \,e^{2}-c \,d^{2}\right)^{5} \left(c d e x +a \,e^{2}\right)^{2}}-\frac{63 c^{3} d^{3} e^{2} \arctan \left(\frac{\sqrt{e x +d}\, c d}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}\right)}{4 \left(a \,e^{2}-c \,d^{2}\right)^{5} \sqrt{\left(a \,e^{2}-c \,d^{2}\right) c d}}-\frac{12 c^{2} d^{2} e^{2}}{\left(a \,e^{2}-c \,d^{2}\right)^{5} \sqrt{e x +d}}+\frac{2 c d \,e^{2}}{\left(a \,e^{2}-c \,d^{2}\right)^{4} \left(e x +d \right)^{\frac{3}{2}}}-\frac{2 e^{2}}{5 \left(a \,e^{2}-c \,d^{2}\right)^{3} \left(e x +d \right)^{\frac{5}{2}}}"," ",0,"-15/4*e^2/(a*e^2-c*d^2)^5*c^4*d^4/(c*d*e*x+a*e^2)^2*(e*x+d)^(3/2)-17/4*e^4/(a*e^2-c*d^2)^5*c^3*d^3/(c*d*e*x+a*e^2)^2*(e*x+d)^(1/2)*a+17/4*e^2/(a*e^2-c*d^2)^5*c^4*d^5/(c*d*e*x+a*e^2)^2*(e*x+d)^(1/2)-63/4*e^2/(a*e^2-c*d^2)^5*c^3*d^3/((a*e^2-c*d^2)*c*d)^(1/2)*arctan((e*x+d)^(1/2)/((a*e^2-c*d^2)*c*d)^(1/2)*c*d)-2/5*e^2/(a*e^2-c*d^2)^3/(e*x+d)^(5/2)-12*e^2/(a*e^2-c*d^2)^5*c^2*d^2/(e*x+d)^(1/2)+2*e^2/(a*e^2-c*d^2)^4*c*d/(e*x+d)^(3/2)","A"
2027,1,243,265,0.044000," ","int((e*x+d)^(7/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","\frac{2 \left(c d x +a e \right) \left(315 c^{4} d^{4} e^{4} x^{4}-280 a \,c^{3} d^{3} e^{5} x^{3}+1540 c^{4} d^{5} e^{3} x^{3}+240 a^{2} c^{2} d^{2} e^{6} x^{2}-1320 a \,c^{3} d^{4} e^{4} x^{2}+2970 c^{4} d^{6} e^{2} x^{2}-192 a^{3} c d \,e^{7} x +1056 a^{2} c^{2} d^{3} e^{5} x -2376 a \,c^{3} d^{5} e^{3} x +2772 c^{4} d^{7} e x +128 a^{4} e^{8}-704 a^{3} c \,d^{2} e^{6}+1584 a^{2} c^{2} d^{4} e^{4}-1848 a \,c^{3} d^{6} e^{2}+1155 c^{4} d^{8}\right) \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}}{3465 \sqrt{e x +d}\, c^{5} d^{5}}"," ",0,"2/3465*(c*d*x+a*e)*(315*c^4*d^4*e^4*x^4-280*a*c^3*d^3*e^5*x^3+1540*c^4*d^5*e^3*x^3+240*a^2*c^2*d^2*e^6*x^2-1320*a*c^3*d^4*e^4*x^2+2970*c^4*d^6*e^2*x^2-192*a^3*c*d*e^7*x+1056*a^2*c^2*d^3*e^5*x-2376*a*c^3*d^5*e^3*x+2772*c^4*d^7*e*x+128*a^4*e^8-704*a^3*c*d^2*e^6+1584*a^2*c^2*d^4*e^4-1848*a*c^3*d^6*e^2+1155*c^4*d^8)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)/c^5/d^5/(e*x+d)^(1/2)","A"
2028,1,168,209,0.055000," ","int((e*x+d)^(5/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","-\frac{2 \left(c d x +a e \right) \left(-35 c^{3} d^{3} e^{3} x^{3}+30 a \,c^{2} d^{2} e^{4} x^{2}-135 c^{3} d^{4} e^{2} x^{2}-24 a^{2} c d \,e^{5} x +108 a \,c^{2} d^{3} e^{3} x -189 c^{3} d^{5} e x +16 a^{3} e^{6}-72 a^{2} c \,d^{2} e^{4}+126 a \,c^{2} d^{4} e^{2}-105 c^{3} d^{6}\right) \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}}{315 \sqrt{e x +d}\, c^{4} d^{4}}"," ",0,"-2/315*(c*d*x+a*e)*(-35*c^3*d^3*e^3*x^3+30*a*c^2*d^2*e^4*x^2-135*c^3*d^4*e^2*x^2-24*a^2*c*d*e^5*x+108*a*c^2*d^3*e^3*x-189*c^3*d^5*e*x+16*a^3*e^6-72*a^2*c*d^2*e^4+126*a*c^2*d^4*e^2-105*c^3*d^6)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)/c^4/d^4/(e*x+d)^(1/2)","A"
2029,1,110,153,0.050000," ","int((e*x+d)^(3/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","\frac{2 \left(c d x +a e \right) \left(15 c^{2} d^{2} e^{2} x^{2}-12 a c d \,e^{3} x +42 c^{2} d^{3} e x +8 a^{2} e^{4}-28 a c \,d^{2} e^{2}+35 c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}}{105 \sqrt{e x +d}\, c^{3} d^{3}}"," ",0,"2/105*(c*d*x+a*e)*(15*c^2*d^2*e^2*x^2-12*a*c*d*e^3*x+42*c^2*d^3*e*x+8*a^2*e^4-28*a*c*d^2*e^2+35*c^2*d^4)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)/c^3/d^3/(e*x+d)^(1/2)","A"
2030,1,69,97,0.046000," ","int((e*x+d)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","-\frac{2 \left(c d x +a e \right) \left(-3 c d e x +2 a \,e^{2}-5 c \,d^{2}\right) \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}}{15 \sqrt{e x +d}\, c^{2} d^{2}}"," ",0,"-2/15*(c*d*x+a*e)*(-3*c*d*e*x+2*a*e^2-5*c*d^2)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)/c^2/d^2/(e*x+d)^(1/2)","A"
2031,1,50,42,0.051000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)/(e*x+d)^(1/2),x)","\frac{2 \left(c d x +a e \right) \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}}{3 \sqrt{e x +d}\, c d}"," ",0,"2/3*(c*d*x+a*e)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)/c/d/(e*x+d)^(1/2)","A"
2032,1,163,112,0.087000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)/(e*x+d)^(3/2),x)","-\frac{2 \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(a \,e^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)-c \,d^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)-\sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\right)}{\sqrt{e x +d}\, \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, e}"," ",0,"-2*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)/(e*x+d)^(1/2)*(arctanh(e*(c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2))*a*e^2-arctanh(e*(c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2))*c*d^2-(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2))/(c*d*x+a*e)^(1/2)/e/((a*e^2-c*d^2)*e)^(1/2)","A"
2033,1,163,113,0.075000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)/(e*x+d)^(5/2),x)","\frac{\left(-c d e x \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)-c \,d^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)-\sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\right) \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}}{\left(e x +d \right)^{\frac{3}{2}} \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, e}"," ",0,"(-arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x*c*d*e-arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*c*d^2-(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2))*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)/(e*x+d)^(3/2)/(c*d*x+a*e)^(1/2)/e/((a*e^2-c*d^2)*e)^(1/2)","A"
2034,1,292,173,0.086000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)/(e*x+d)^(7/2),x)","\frac{\sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(c^{2} d^{2} e^{2} x^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+2 c^{2} d^{3} e x \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+c^{2} d^{4} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)-\sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c d e x -2 \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a \,e^{2}+\sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c \,d^{2}\right)}{4 \left(e x +d \right)^{\frac{5}{2}} \sqrt{c d x +a e}\, \left(a \,e^{2}-c \,d^{2}\right) \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, e}"," ",0,"1/4*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x^2*c^2*d^2*e^2+2*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x*c^2*d^3*e+arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*c^2*d^4-x*c*d*e*(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)-2*(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)*a*e^2+(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)*c*d^2)/(e*x+d)^(5/2)/(c*d*x+a*e)^(1/2)/(a*e^2-c*d^2)/e/((a*e^2-c*d^2)*e)^(1/2)","A"
2035,1,457,232,0.076000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)/(e*x+d)^(9/2),x)","-\frac{\sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(3 c^{3} d^{3} e^{3} x^{3} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+9 c^{3} d^{4} e^{2} x^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+9 c^{3} d^{5} e x \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+3 c^{3} d^{6} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)-3 \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{2} d^{2} e^{2} x^{2}+2 \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a c d \,e^{3} x -8 \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{2} d^{3} e x +8 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, \sqrt{c d x +a e}\, a^{2} e^{4}-14 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, \sqrt{c d x +a e}\, a c \,d^{2} e^{2}+3 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, \sqrt{c d x +a e}\, c^{2} d^{4}\right)}{24 \left(e x +d \right)^{\frac{7}{2}} \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, \left(a \,e^{2}-c \,d^{2}\right)^{2} \sqrt{c d x +a e}\, e}"," ",0,"-1/24*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(3*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x^3*c^3*d^3*e^3+9*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x^2*c^3*d^4*e^2+9*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x*c^3*d^5*e+3*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*c^3*d^6-3*x^2*c^2*d^2*e^2*(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)+2*x*a*c*d*e^3*(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)-8*x*c^2*d^3*e*(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)+8*((a*e^2-c*d^2)*e)^(1/2)*(c*d*x+a*e)^(1/2)*a^2*e^4-14*((a*e^2-c*d^2)*e)^(1/2)*(c*d*x+a*e)^(1/2)*a*c*d^2*e^2+3*((a*e^2-c*d^2)*e)^(1/2)*(c*d*x+a*e)^(1/2)*c^2*d^4)/(e*x+d)^(7/2)/((a*e^2-c*d^2)*e)^(1/2)/e/(a*e^2-c*d^2)^2/(c*d*x+a*e)^(1/2)","A"
2036,1,243,265,0.049000," ","int((e*x+d)^(5/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2),x)","\frac{2 \left(c d x +a e \right) \left(1155 c^{4} d^{4} e^{4} x^{4}-840 a \,c^{3} d^{3} e^{5} x^{3}+5460 c^{4} d^{5} e^{3} x^{3}+560 a^{2} c^{2} d^{2} e^{6} x^{2}-3640 a \,c^{3} d^{4} e^{4} x^{2}+10010 c^{4} d^{6} e^{2} x^{2}-320 a^{3} c d \,e^{7} x +2080 a^{2} c^{2} d^{3} e^{5} x -5720 a \,c^{3} d^{5} e^{3} x +8580 c^{4} d^{7} e x +128 a^{4} e^{8}-832 a^{3} c \,d^{2} e^{6}+2288 a^{2} c^{2} d^{4} e^{4}-3432 a \,c^{3} d^{6} e^{2}+3003 c^{4} d^{8}\right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{3}{2}}}{15015 \left(e x +d \right)^{\frac{3}{2}} c^{5} d^{5}}"," ",0,"2/15015*(c*d*x+a*e)*(1155*c^4*d^4*e^4*x^4-840*a*c^3*d^3*e^5*x^3+5460*c^4*d^5*e^3*x^3+560*a^2*c^2*d^2*e^6*x^2-3640*a*c^3*d^4*e^4*x^2+10010*c^4*d^6*e^2*x^2-320*a^3*c*d*e^7*x+2080*a^2*c^2*d^3*e^5*x-5720*a*c^3*d^5*e^3*x+8580*c^4*d^7*e*x+128*a^4*e^8-832*a^3*c*d^2*e^6+2288*a^2*c^2*d^4*e^4-3432*a*c^3*d^6*e^2+3003*c^4*d^8)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(3/2)/c^5/d^5/(e*x+d)^(3/2)","A"
2037,1,168,209,0.052000," ","int((e*x+d)^(3/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2),x)","-\frac{2 \left(c d x +a e \right) \left(-105 c^{3} d^{3} e^{3} x^{3}+70 a \,c^{2} d^{2} e^{4} x^{2}-385 c^{3} d^{4} e^{2} x^{2}-40 a^{2} c d \,e^{5} x +220 a \,c^{2} d^{3} e^{3} x -495 c^{3} d^{5} e x +16 a^{3} e^{6}-88 a^{2} c \,d^{2} e^{4}+198 a \,c^{2} d^{4} e^{2}-231 c^{3} d^{6}\right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{3}{2}}}{1155 \left(e x +d \right)^{\frac{3}{2}} c^{4} d^{4}}"," ",0,"-2/1155*(c*d*x+a*e)*(-105*c^3*d^3*e^3*x^3+70*a*c^2*d^2*e^4*x^2-385*c^3*d^4*e^2*x^2-40*a^2*c*d*e^5*x+220*a*c^2*d^3*e^3*x-495*c^3*d^5*e*x+16*a^3*e^6-88*a^2*c*d^2*e^4+198*a*c^2*d^4*e^2-231*c^3*d^6)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(3/2)/c^4/d^4/(e*x+d)^(3/2)","A"
2038,1,110,153,0.052000," ","int((e*x+d)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2),x)","\frac{2 \left(c d x +a e \right) \left(35 c^{2} d^{2} e^{2} x^{2}-20 a c d \,e^{3} x +90 c^{2} d^{3} e x +8 a^{2} e^{4}-36 a c \,d^{2} e^{2}+63 c^{2} d^{4}\right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{3}{2}}}{315 \left(e x +d \right)^{\frac{3}{2}} c^{3} d^{3}}"," ",0,"2/315*(c*d*x+a*e)*(35*c^2*d^2*e^2*x^2-20*a*c*d*e^3*x+90*c^2*d^3*e*x+8*a^2*e^4-36*a*c*d^2*e^2+63*c^2*d^4)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(3/2)/c^3/d^3/(e*x+d)^(3/2)","A"
2039,1,69,97,0.046000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)/(e*x+d)^(1/2),x)","-\frac{2 \left(c d x +a e \right) \left(-5 c d e x +2 a \,e^{2}-7 c \,d^{2}\right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{3}{2}}}{35 \left(e x +d \right)^{\frac{3}{2}} c^{2} d^{2}}"," ",0,"-2/35*(c*d*x+a*e)*(-5*c*d*e*x+2*a*e^2-7*c*d^2)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(3/2)/c^2/d^2/(e*x+d)^(3/2)","A"
2040,1,50,42,0.053000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)/(e*x+d)^(3/2),x)","\frac{2 \left(c d x +a e \right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{3}{2}}}{5 \left(e x +d \right)^{\frac{3}{2}} c d}"," ",0,"2/5*(c*d*x+a*e)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(3/2)/c/d/(e*x+d)^(3/2)","A"
2041,1,275,159,0.062000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)/(e*x+d)^(5/2),x)","-\frac{2 \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(3 a^{2} e^{4} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)-6 a c \,d^{2} e^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+3 c^{2} d^{4} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)-\sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c d e x -4 \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a \,e^{2}+3 \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c \,d^{2}\right)}{3 \sqrt{e x +d}\, \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, e^{2}}"," ",0,"-2/3*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(3*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*a^2*e^4-6*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*a*c*d^2*e^2+3*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*c^2*d^4-(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)*c*d*e*x-4*(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)*a*e^2+3*(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)*c*d^2)/(e*x+d)^(1/2)/(c*d*x+a*e)^(1/2)/e^2/((a*e^2-c*d^2)*e)^(1/2)","A"
2042,1,314,155,0.079000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)/(e*x+d)^(7/2),x)","\frac{\sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(-3 a c d \,e^{3} x \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+3 c^{2} d^{3} e x \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)-3 a c \,d^{2} e^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+3 c^{2} d^{4} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+2 \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c d e x -\sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a \,e^{2}+3 \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c \,d^{2}\right)}{\left(e x +d \right)^{\frac{3}{2}} \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, e^{2}}"," ",0,"(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)/(e*x+d)^(3/2)*(-3*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x*a*c*d*e^3+3*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x*c^2*d^3*e-3*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*a*c*d^2*e^2+3*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*c^2*d^4+2*(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)*c*d*e*x-(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)*a*e^2+3*(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)*c*d^2)/(c*d*x+a*e)^(1/2)/e^2/((a*e^2-c*d^2)*e)^(1/2)","B"
2043,1,281,159,0.087000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)/(e*x+d)^(9/2),x)","-\frac{\sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(3 c^{2} d^{2} e^{2} x^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+6 c^{2} d^{3} e x \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+3 c^{2} d^{4} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+5 \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c d e x +2 \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a \,e^{2}+3 \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c \,d^{2}\right)}{4 \left(e x +d \right)^{\frac{5}{2}} \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, e^{2}}"," ",0,"-1/4*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(3*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x^2*c^2*d^2*e^2+6*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x*c^2*d^3*e+3*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*c^2*d^4+5*(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)*c*d*e*x+2*(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)*a*e^2+3*(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)*c*d^2)/(e*x+d)^(5/2)/(c*d*x+a*e)^(1/2)/e^2/((a*e^2-c*d^2)*e)^(1/2)","A"
2044,1,457,218,0.091000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)/(e*x+d)^(11/2),x)","\frac{\sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(3 c^{3} d^{3} e^{3} x^{3} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+9 c^{3} d^{4} e^{2} x^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+9 c^{3} d^{5} e x \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+3 c^{3} d^{6} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)-3 \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{2} d^{2} e^{2} x^{2}-14 \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a c d \,e^{3} x +8 \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{2} d^{3} e x -8 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, \sqrt{c d x +a e}\, a^{2} e^{4}+2 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, \sqrt{c d x +a e}\, a c \,d^{2} e^{2}+3 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, \sqrt{c d x +a e}\, c^{2} d^{4}\right)}{24 \left(e x +d \right)^{\frac{7}{2}} \sqrt{c d x +a e}\, \left(a \,e^{2}-c \,d^{2}\right) \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, e^{2}}"," ",0,"1/24*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(3*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x^3*c^3*d^3*e^3+9*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x^2*c^3*d^4*e^2+9*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x*c^3*d^5*e+3*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*c^3*d^6-3*(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)*c^2*d^2*e^2*x^2-14*(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)*a*c*d*e^3*x+8*(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)*c^2*d^3*e*x-8*((a*e^2-c*d^2)*e)^(1/2)*(c*d*x+a*e)^(1/2)*a^2*e^4+2*((a*e^2-c*d^2)*e)^(1/2)*(c*d*x+a*e)^(1/2)*a*c*d^2*e^2+3*((a*e^2-c*d^2)*e)^(1/2)*(c*d*x+a*e)^(1/2)*c^2*d^4)/(e*x+d)^(7/2)/(c*d*x+a*e)^(1/2)/(a*e^2-c*d^2)/e^2/((a*e^2-c*d^2)*e)^(1/2)","B"
2045,1,662,277,0.086000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)/(e*x+d)^(13/2),x)","-\frac{\sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(3 c^{4} d^{4} e^{4} x^{4} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+12 c^{4} d^{5} e^{3} x^{3} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+18 c^{4} d^{6} e^{2} x^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+12 c^{4} d^{7} e x \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+3 c^{4} d^{8} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)-3 \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{3} d^{3} e^{3} x^{3}+2 \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a \,c^{2} d^{2} e^{4} x^{2}-11 \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{3} d^{4} e^{2} x^{2}+24 \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a^{2} c d \,e^{5} x -44 \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a \,c^{2} d^{3} e^{3} x +11 \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{3} d^{5} e x +16 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, \sqrt{c d x +a e}\, a^{3} e^{6}-24 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, \sqrt{c d x +a e}\, a^{2} c \,d^{2} e^{4}+2 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, \sqrt{c d x +a e}\, a \,c^{2} d^{4} e^{2}+3 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, \sqrt{c d x +a e}\, c^{3} d^{6}\right)}{64 \left(e x +d \right)^{\frac{9}{2}} \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, \left(a \,e^{2}-c \,d^{2}\right)^{2} \sqrt{c d x +a e}\, e^{2}}"," ",0,"-1/64*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(3*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x^4*c^4*d^4*e^4+12*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x^3*c^4*d^5*e^3+18*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x^2*c^4*d^6*e^2+12*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x*c^4*d^7*e-3*x^3*c^3*d^3*e^3*(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)+3*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*c^4*d^8+2*x^2*a*c^2*d^2*e^4*(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)-11*x^2*c^3*d^4*e^2*(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)+24*x*a^2*c*d*e^5*(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)-44*x*a*c^2*d^3*e^3*(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)+11*x*c^3*d^5*e*(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)+16*((a*e^2-c*d^2)*e)^(1/2)*(c*d*x+a*e)^(1/2)*a^3*e^6-24*((a*e^2-c*d^2)*e)^(1/2)*(c*d*x+a*e)^(1/2)*a^2*c*d^2*e^4+2*((a*e^2-c*d^2)*e)^(1/2)*(c*d*x+a*e)^(1/2)*a*c^2*d^4*e^2+3*((a*e^2-c*d^2)*e)^(1/2)*(c*d*x+a*e)^(1/2)*c^3*d^6)/(e*x+d)^(9/2)/((a*e^2-c*d^2)*e)^(1/2)/e^2/(a*e^2-c*d^2)^2/(c*d*x+a*e)^(1/2)","B"
2046,1,243,265,0.064000," ","int((e*x+d)^(3/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2),x)","\frac{2 \left(c d x +a e \right) \left(3003 c^{4} d^{4} e^{4} x^{4}-1848 a \,c^{3} d^{3} e^{5} x^{3}+13860 c^{4} d^{5} e^{3} x^{3}+1008 a^{2} c^{2} d^{2} e^{6} x^{2}-7560 a \,c^{3} d^{4} e^{4} x^{2}+24570 c^{4} d^{6} e^{2} x^{2}-448 a^{3} c d \,e^{7} x +3360 a^{2} c^{2} d^{3} e^{5} x -10920 a \,c^{3} d^{5} e^{3} x +20020 c^{4} d^{7} e x +128 a^{4} e^{8}-960 a^{3} c \,d^{2} e^{6}+3120 a^{2} c^{2} d^{4} e^{4}-5720 a \,c^{3} d^{6} e^{2}+6435 c^{4} d^{8}\right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{5}{2}}}{45045 \left(e x +d \right)^{\frac{5}{2}} c^{5} d^{5}}"," ",0,"2/45045*(c*d*x+a*e)*(3003*c^4*d^4*e^4*x^4-1848*a*c^3*d^3*e^5*x^3+13860*c^4*d^5*e^3*x^3+1008*a^2*c^2*d^2*e^6*x^2-7560*a*c^3*d^4*e^4*x^2+24570*c^4*d^6*e^2*x^2-448*a^3*c*d*e^7*x+3360*a^2*c^2*d^3*e^5*x-10920*a*c^3*d^5*e^3*x+20020*c^4*d^7*e*x+128*a^4*e^8-960*a^3*c*d^2*e^6+3120*a^2*c^2*d^4*e^4-5720*a*c^3*d^6*e^2+6435*c^4*d^8)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(5/2)/c^5/d^5/(e*x+d)^(5/2)","A"
2047,1,168,209,0.056000," ","int((e*x+d)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2),x)","-\frac{2 \left(c d x +a e \right) \left(-231 c^{3} d^{3} e^{3} x^{3}+126 a \,c^{2} d^{2} e^{4} x^{2}-819 c^{3} d^{4} e^{2} x^{2}-56 a^{2} c d \,e^{5} x +364 a \,c^{2} d^{3} e^{3} x -1001 c^{3} d^{5} e x +16 a^{3} e^{6}-104 a^{2} c \,d^{2} e^{4}+286 a \,c^{2} d^{4} e^{2}-429 c^{3} d^{6}\right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{5}{2}}}{3003 \left(e x +d \right)^{\frac{5}{2}} c^{4} d^{4}}"," ",0,"-2/3003*(c*d*x+a*e)*(-231*c^3*d^3*e^3*x^3+126*a*c^2*d^2*e^4*x^2-819*c^3*d^4*e^2*x^2-56*a^2*c*d*e^5*x+364*a*c^2*d^3*e^3*x-1001*c^3*d^5*e*x+16*a^3*e^6-104*a^2*c*d^2*e^4+286*a*c^2*d^4*e^2-429*c^3*d^6)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(5/2)/c^4/d^4/(e*x+d)^(5/2)","A"
2048,1,110,153,0.046000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/(e*x+d)^(1/2),x)","\frac{2 \left(c d x +a e \right) \left(63 c^{2} d^{2} e^{2} x^{2}-28 a c d \,e^{3} x +154 c^{2} d^{3} e x +8 a^{2} e^{4}-44 a c \,d^{2} e^{2}+99 c^{2} d^{4}\right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{5}{2}}}{693 \left(e x +d \right)^{\frac{5}{2}} c^{3} d^{3}}"," ",0,"2/693*(c*d*x+a*e)*(63*c^2*d^2*e^2*x^2-28*a*c*d*e^3*x+154*c^2*d^3*e*x+8*a^2*e^4-44*a*c*d^2*e^2+99*c^2*d^4)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(5/2)/c^3/d^3/(e*x+d)^(5/2)","A"
2049,1,69,97,0.052000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/(e*x+d)^(3/2),x)","-\frac{2 \left(c d x +a e \right) \left(-7 c d e x +2 a \,e^{2}-9 c \,d^{2}\right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{5}{2}}}{63 \left(e x +d \right)^{\frac{5}{2}} c^{2} d^{2}}"," ",0,"-2/63*(c*d*x+a*e)*(-7*c*d*e*x+2*a*e^2-9*c*d^2)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(5/2)/c^2/d^2/(e*x+d)^(5/2)","A"
2050,1,50,42,0.042000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/(e*x+d)^(5/2),x)","\frac{2 \left(c d x +a e \right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{5}{2}}}{7 \left(e x +d \right)^{\frac{5}{2}} c d}"," ",0,"2/7*(c*d*x+a*e)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(5/2)/c/d/(e*x+d)^(5/2)","A"
2051,1,437,212,0.067000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/(e*x+d)^(7/2),x)","-\frac{2 \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(15 a^{3} e^{6} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)-45 a^{2} c \,d^{2} e^{4} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+45 a \,c^{2} d^{4} e^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)-15 c^{3} d^{6} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)-3 \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{2} d^{2} e^{2} x^{2}-11 \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a c d \,e^{3} x +5 \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{2} d^{3} e x -23 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, \sqrt{c d x +a e}\, a^{2} e^{4}+35 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, \sqrt{c d x +a e}\, a c \,d^{2} e^{2}-15 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, \sqrt{c d x +a e}\, c^{2} d^{4}\right)}{15 \sqrt{e x +d}\, \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, e^{3}}"," ",0,"-2/15*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(15*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*a^3*e^6-45*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*a^2*c*d^2*e^4+45*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*a*c^2*d^4*e^2-15*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*c^3*d^6-3*(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)*c^2*d^2*e^2*x^2-11*(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)*a*c*d*e^3*x+5*(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)*c^2*d^3*e*x-23*((a*e^2-c*d^2)*e)^(1/2)*(c*d*x+a*e)^(1/2)*a^2*e^4+35*((a*e^2-c*d^2)*e)^(1/2)*(c*d*x+a*e)^(1/2)*a*c*d^2*e^2-15*((a*e^2-c*d^2)*e)^(1/2)*(c*d*x+a*e)^(1/2)*c^2*d^4)/(e*x+d)^(1/2)/(c*d*x+a*e)^(1/2)/e^3/((a*e^2-c*d^2)*e)^(1/2)","B"
2052,1,521,207,0.079000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/(e*x+d)^(9/2),x)","-\frac{\sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(15 a^{2} c d \,e^{5} x \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)-30 a \,c^{2} d^{3} e^{3} x \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+15 c^{3} d^{5} e x \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+15 a^{2} c \,d^{2} e^{4} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)-30 a \,c^{2} d^{4} e^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+15 c^{3} d^{6} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)-2 \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{2} d^{2} e^{2} x^{2}-14 \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a c d \,e^{3} x +10 \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{2} d^{3} e x +3 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, \sqrt{c d x +a e}\, a^{2} e^{4}-20 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, \sqrt{c d x +a e}\, a c \,d^{2} e^{2}+15 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, \sqrt{c d x +a e}\, c^{2} d^{4}\right)}{3 \left(e x +d \right)^{\frac{3}{2}} \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, e^{3}}"," ",0,"-1/3*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(15*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x*a^2*c*d*e^5-30*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x*a*c^2*d^3*e^3+15*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x*c^3*d^5*e+15*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*a^2*c*d^2*e^4-30*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*a*c^2*d^4*e^2+15*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*c^3*d^6-2*(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)*c^2*d^2*e^2*x^2-14*(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)*a*c*d*e^3*x+10*(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)*c^2*d^3*e*x+3*((a*e^2-c*d^2)*e)^(1/2)*(c*d*x+a*e)^(1/2)*a^2*e^4-20*((a*e^2-c*d^2)*e)^(1/2)*(c*d*x+a*e)^(1/2)*a*c*d^2*e^2+15*((a*e^2-c*d^2)*e)^(1/2)*(c*d*x+a*e)^(1/2)*c^2*d^4)/(e*x+d)^(3/2)/(c*d*x+a*e)^(1/2)/e^3/((a*e^2-c*d^2)*e)^(1/2)","B"
2053,1,527,204,0.077000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/(e*x+d)^(11/2),x)","-\frac{\sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(15 a \,c^{2} d^{2} e^{4} x^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)-15 c^{3} d^{4} e^{2} x^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+30 a \,c^{2} d^{3} e^{3} x \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)-30 c^{3} d^{5} e x \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+15 a \,c^{2} d^{4} e^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)-15 c^{3} d^{6} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)-8 \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{2} d^{2} e^{2} x^{2}+9 \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a c d \,e^{3} x -25 \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{2} d^{3} e x +2 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, \sqrt{c d x +a e}\, a^{2} e^{4}+5 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, \sqrt{c d x +a e}\, a c \,d^{2} e^{2}-15 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, \sqrt{c d x +a e}\, c^{2} d^{4}\right)}{4 \left(e x +d \right)^{\frac{5}{2}} \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, e^{3}}"," ",0,"-1/4*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(15*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x^2*a*c^2*d^2*e^4-15*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x^2*c^3*d^4*e^2+30*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x*a*c^2*d^3*e^3-30*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x*c^3*d^5*e+15*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*a*c^2*d^4*e^2-15*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*c^3*d^6-8*(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)*c^2*d^2*e^2*x^2+9*(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)*a*c*d*e^3*x-25*(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)*c^2*d^3*e*x+2*((a*e^2-c*d^2)*e)^(1/2)*(c*d*x+a*e)^(1/2)*a^2*e^4+5*((a*e^2-c*d^2)*e)^(1/2)*(c*d*x+a*e)^(1/2)*a*c*d^2*e^2-15*((a*e^2-c*d^2)*e)^(1/2)*(c*d*x+a*e)^(1/2)*c^2*d^4)/(e*x+d)^(5/2)/(c*d*x+a*e)^(1/2)/e^3/((a*e^2-c*d^2)*e)^(1/2)","B"
2054,1,443,204,0.081000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/(e*x+d)^(13/2),x)","-\frac{\sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(15 c^{3} d^{3} e^{3} x^{3} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+45 c^{3} d^{4} e^{2} x^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+45 c^{3} d^{5} e x \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+15 c^{3} d^{6} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+33 \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{2} d^{2} e^{2} x^{2}+26 \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a c d \,e^{3} x +40 \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{2} d^{3} e x +8 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, \sqrt{c d x +a e}\, a^{2} e^{4}+10 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, \sqrt{c d x +a e}\, a c \,d^{2} e^{2}+15 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, \sqrt{c d x +a e}\, c^{2} d^{4}\right)}{24 \left(e x +d \right)^{\frac{7}{2}} \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, e^{3}}"," ",0,"-1/24*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(15*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x^3*c^3*d^3*e^3+45*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x^2*c^3*d^4*e^2+45*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x*c^3*d^5*e+15*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*c^3*d^6+33*(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)*c^2*d^2*e^2*x^2+26*(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)*a*c*d*e^3*x+40*(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)*c^2*d^3*e*x+8*((a*e^2-c*d^2)*e)^(1/2)*(c*d*x+a*e)^(1/2)*a^2*e^4+10*((a*e^2-c*d^2)*e)^(1/2)*(c*d*x+a*e)^(1/2)*a*c*d^2*e^2+15*((a*e^2-c*d^2)*e)^(1/2)*(c*d*x+a*e)^(1/2)*c^2*d^4)/(e*x+d)^(7/2)/(c*d*x+a*e)^(1/2)/e^3/((a*e^2-c*d^2)*e)^(1/2)","B"
2055,1,662,263,0.080000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/(e*x+d)^(15/2),x)","\frac{\sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(15 c^{4} d^{4} e^{4} x^{4} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+60 c^{4} d^{5} e^{3} x^{3} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+90 c^{4} d^{6} e^{2} x^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+60 c^{4} d^{7} e x \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+15 c^{4} d^{8} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)-15 \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{3} d^{3} e^{3} x^{3}-118 \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a \,c^{2} d^{2} e^{4} x^{2}+73 \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{3} d^{4} e^{2} x^{2}-136 \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a^{2} c d \,e^{5} x +36 \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a \,c^{2} d^{3} e^{3} x +55 \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{3} d^{5} e x -48 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, \sqrt{c d x +a e}\, a^{3} e^{6}+8 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, \sqrt{c d x +a e}\, a^{2} c \,d^{2} e^{4}+10 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, \sqrt{c d x +a e}\, a \,c^{2} d^{4} e^{2}+15 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, \sqrt{c d x +a e}\, c^{3} d^{6}\right)}{192 \left(e x +d \right)^{\frac{9}{2}} \sqrt{c d x +a e}\, \left(a \,e^{2}-c \,d^{2}\right) \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, e^{3}}"," ",0,"1/192*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(15*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x^4*c^4*d^4*e^4+60*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x^3*c^4*d^5*e^3+90*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x^2*c^4*d^6*e^2+60*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x*c^4*d^7*e-15*(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)*c^3*d^3*e^3*x^3+15*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*c^4*d^8-118*(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)*a*c^2*d^2*e^4*x^2+73*(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)*c^3*d^4*e^2*x^2-136*(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)*a^2*c*d*e^5*x+36*(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)*a*c^2*d^3*e^3*x+55*(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)*c^3*d^5*e*x-48*((a*e^2-c*d^2)*e)^(1/2)*(c*d*x+a*e)^(1/2)*a^3*e^6+8*((a*e^2-c*d^2)*e)^(1/2)*(c*d*x+a*e)^(1/2)*a^2*c*d^2*e^4+10*((a*e^2-c*d^2)*e)^(1/2)*(c*d*x+a*e)^(1/2)*a*c^2*d^4*e^2+15*((a*e^2-c*d^2)*e)^(1/2)*(c*d*x+a*e)^(1/2)*c^3*d^6)/(e*x+d)^(9/2)/(c*d*x+a*e)^(1/2)/e^3/(a*e^2-c*d^2)/((a*e^2-c*d^2)*e)^(1/2)","B"
2056,1,910,322,0.087000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/(e*x+d)^(17/2),x)","-\frac{\sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(15 c^{5} d^{5} e^{5} x^{5} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+75 c^{5} d^{6} e^{4} x^{4} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+150 c^{5} d^{7} e^{3} x^{3} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+150 c^{5} d^{8} e^{2} x^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+75 c^{5} d^{9} e x \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+15 c^{5} d^{10} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)-15 \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{4} d^{4} e^{4} x^{4}+10 \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a \,c^{3} d^{3} e^{5} x^{3}-70 \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{4} d^{5} e^{3} x^{3}+248 \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a^{2} c^{2} d^{2} e^{6} x^{2}-466 \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a \,c^{3} d^{4} e^{4} x^{2}+128 \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{4} d^{6} e^{2} x^{2}+336 \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a^{3} c d \,e^{7} x -512 \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a^{2} c^{2} d^{3} e^{5} x +46 \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a \,c^{3} d^{5} e^{3} x +70 \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{4} d^{7} e x +128 \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a^{4} e^{8}-176 \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a^{3} c \,d^{2} e^{6}+8 \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a^{2} c^{2} d^{4} e^{4}+10 \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a \,c^{3} d^{6} e^{2}+15 \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{4} d^{8}\right)}{640 \left(e x +d \right)^{\frac{11}{2}} \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, \left(a \,e^{2}-c \,d^{2}\right)^{2} \sqrt{c d x +a e}\, e^{3}}"," ",0,"-1/640*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(15*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x^5*c^5*d^5*e^5+75*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x^4*c^5*d^6*e^4+150*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x^3*c^5*d^7*e^3+150*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x^2*c^5*d^8*e^2-15*x^4*c^4*d^4*e^4*(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)+75*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x*c^5*d^9*e+10*x^3*a*c^3*d^3*e^5*(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)-70*x^3*c^4*d^5*e^3*(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)+15*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*c^5*d^10+248*x^2*a^2*c^2*d^2*e^6*(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)-466*x^2*a*c^3*d^4*e^4*(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)+128*x^2*c^4*d^6*e^2*(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)+336*x*a^3*c*d*e^7*(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)-512*x*a^2*c^2*d^3*e^5*(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)+46*x*a*c^3*d^5*e^3*(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)+70*x*c^4*d^7*e*(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)+128*(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)*a^4*e^8-176*(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)*a^3*c*d^2*e^6+8*(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)*a^2*c^2*d^4*e^4+10*(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)*a*c^3*d^6*e^2+15*(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)*c^4*d^8)/(e*x+d)^(11/2)/((a*e^2-c*d^2)*e)^(1/2)/e^3/(a*e^2-c*d^2)^2/(c*d*x+a*e)^(1/2)","B"
2057,1,168,209,0.051000," ","int((e*x+d)^(7/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","-\frac{2 \left(c d x +a e \right) \left(-5 c^{3} d^{3} e^{3} x^{3}+6 a \,c^{2} d^{2} e^{4} x^{2}-21 c^{3} d^{4} e^{2} x^{2}-8 a^{2} c d \,e^{5} x +28 a \,c^{2} d^{3} e^{3} x -35 c^{3} d^{5} e x +16 a^{3} e^{6}-56 a^{2} c \,d^{2} e^{4}+70 a \,c^{2} d^{4} e^{2}-35 c^{3} d^{6}\right) \sqrt{e x +d}}{35 \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, c^{4} d^{4}}"," ",0,"-2/35*(c*d*x+a*e)*(-5*c^3*d^3*e^3*x^3+6*a*c^2*d^2*e^4*x^2-21*c^3*d^4*e^2*x^2-8*a^2*c*d*e^5*x+28*a*c^2*d^3*e^3*x-35*c^3*d^5*e*x+16*a^3*e^6-56*a^2*c*d^2*e^4+70*a*c^2*d^4*e^2-35*c^3*d^6)*(e*x+d)^(1/2)/c^4/d^4/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)","A"
2058,1,110,153,0.046000," ","int((e*x+d)^(5/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","\frac{2 \left(c d x +a e \right) \left(3 c^{2} d^{2} e^{2} x^{2}-4 a c d \,e^{3} x +10 c^{2} d^{3} e x +8 a^{2} e^{4}-20 a c \,d^{2} e^{2}+15 c^{2} d^{4}\right) \sqrt{e x +d}}{15 \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, c^{3} d^{3}}"," ",0,"2/15*(c*d*x+a*e)*(3*c^2*d^2*e^2*x^2-4*a*c*d*e^3*x+10*c^2*d^3*e*x+8*a^2*e^4-20*a*c*d^2*e^2+15*c^2*d^4)*(e*x+d)^(1/2)/c^3/d^3/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)","A"
2059,1,69,97,0.049000," ","int((e*x+d)^(3/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","-\frac{2 \left(c d x +a e \right) \left(-c d e x +2 a \,e^{2}-3 c \,d^{2}\right) \sqrt{e x +d}}{3 \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, c^{2} d^{2}}"," ",0,"-2/3*(c*d*x+a*e)*(-c*d*e*x+2*a*e^2-3*c*d^2)*(e*x+d)^(1/2)/c^2/d^2/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)","A"
2060,1,50,42,0.041000," ","int((e*x+d)^(1/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","\frac{2 \left(c d x +a e \right) \sqrt{e x +d}}{\sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, c d}"," ",0,"2*(c*d*x+a*e)*(e*x+d)^(1/2)/c/d/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)","A"
2061,1,91,72,0.089000," ","int(1/(e*x+d)^(1/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","-\frac{2 \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)}{\sqrt{e x +d}\, \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}"," ",0,"-2/(e*x+d)^(1/2)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)/(c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)","A"
2062,1,172,123,0.068000," ","int(1/(e*x+d)^(3/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","\frac{\sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(c d e x \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+c \,d^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)-\sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\right)}{\left(e x +d \right)^{\frac{3}{2}} \sqrt{c d x +a e}\, \left(a \,e^{2}-c \,d^{2}\right) \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}"," ",0,"(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x*c*d*e+arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*c*d^2-(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2))/(e*x+d)^(3/2)/(c*d*x+a*e)^(1/2)/(a*e^2-c*d^2)/((a*e^2-c*d^2)*e)^(1/2)","A"
2063,1,292,181,0.075000," ","int(1/(e*x+d)^(5/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","-\frac{\sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(3 c^{2} d^{2} e^{2} x^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+6 c^{2} d^{3} e x \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+3 c^{2} d^{4} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)-3 \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c d e x +2 \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a \,e^{2}-5 \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c \,d^{2}\right)}{4 \left(e x +d \right)^{\frac{5}{2}} \sqrt{c d x +a e}\, \left(a \,e^{2}-c \,d^{2}\right)^{2} \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}"," ",0,"-1/4*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(3*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x^2*c^2*d^2*e^2+6*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x*c^2*d^3*e+3*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*c^2*d^4-3*(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)*c*d*e*x+2*(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)*a*e^2-5*(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)*c*d^2)/(e*x+d)^(5/2)/(c*d*x+a*e)^(1/2)/(a*e^2-c*d^2)^2/((a*e^2-c*d^2)*e)^(1/2)","A"
2064,1,454,237,0.068000," ","int(1/(e*x+d)^(7/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","\frac{\sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(15 c^{3} d^{3} e^{3} x^{3} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+45 c^{3} d^{4} e^{2} x^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+45 c^{3} d^{5} e x \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+15 c^{3} d^{6} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)-15 \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{2} d^{2} e^{2} x^{2}+10 \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a c d \,e^{3} x -40 \sqrt{c d x +a e}\, \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{2} d^{3} e x -8 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, \sqrt{c d x +a e}\, a^{2} e^{4}+26 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, \sqrt{c d x +a e}\, a c \,d^{2} e^{2}-33 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, \sqrt{c d x +a e}\, c^{2} d^{4}\right)}{24 \left(e x +d \right)^{\frac{7}{2}} \sqrt{c d x +a e}\, \left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}"," ",0,"1/24*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(15*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x^3*c^3*d^3*e^3+45*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x^2*c^3*d^4*e^2+45*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x*c^3*d^5*e+15*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*c^3*d^6-15*(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)*c^2*d^2*e^2*x^2+10*(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)*a*c*d*e^3*x-40*(c*d*x+a*e)^(1/2)*((a*e^2-c*d^2)*e)^(1/2)*c^2*d^3*e*x-8*((a*e^2-c*d^2)*e)^(1/2)*(c*d*x+a*e)^(1/2)*a^2*e^4+26*((a*e^2-c*d^2)*e)^(1/2)*(c*d*x+a*e)^(1/2)*a*c*d^2*e^2-33*((a*e^2-c*d^2)*e)^(1/2)*(c*d*x+a*e)^(1/2)*c^2*d^4)/(e*x+d)^(7/2)/(c*d*x+a*e)^(1/2)/(a*e^2-c*d^2)^3/((a*e^2-c*d^2)*e)^(1/2)","A"
2065,1,110,153,0.054000," ","int((e*x+d)^(7/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2),x)","-\frac{2 \left(c d x +a e \right) \left(-c^{2} d^{2} e^{2} x^{2}+4 a c d \,e^{3} x -6 c^{2} d^{3} e x +8 a^{2} e^{4}-12 a c \,d^{2} e^{2}+3 c^{2} d^{4}\right) \left(e x +d \right)^{\frac{3}{2}}}{3 \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{3}{2}} c^{3} d^{3}}"," ",0,"-2/3*(c*d*x+a*e)*(-c^2*d^2*e^2*x^2+4*a*c*d*e^3*x-6*c^2*d^3*e*x+8*a^2*e^4-12*a*c*d^2*e^2+3*c^2*d^4)*(e*x+d)^(3/2)/c^3/d^3/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(3/2)","A"
2066,1,68,97,0.046000," ","int((e*x+d)^(5/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2),x)","\frac{2 \left(c d x +a e \right) \left(c d e x +2 a \,e^{2}-c \,d^{2}\right) \left(e x +d \right)^{\frac{3}{2}}}{\left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{3}{2}} c^{2} d^{2}}"," ",0,"2*(c*d*x+a*e)*(c*d*e*x+2*a*e^2-c*d^2)*(e*x+d)^(3/2)/c^2/d^2/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(3/2)","A"
2067,1,50,42,0.052000," ","int((e*x+d)^(3/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2),x)","-\frac{2 \left(c d x +a e \right) \left(e x +d \right)^{\frac{3}{2}}}{\left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{3}{2}} c d}"," ",0,"-2*(c*d*x+a*e)*(e*x+d)^(3/2)/c/d/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(3/2)","A"
2068,1,136,123,0.070000," ","int((e*x+d)^(1/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2),x)","-\frac{2 \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(\sqrt{c d x +a e}\, e \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)-\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\right)}{\sqrt{e x +d}\, \left(c d x +a e \right) \left(a \,e^{2}-c \,d^{2}\right) \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}"," ",0,"-2*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(e*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*(c*d*x+a*e)^(1/2)-((a*e^2-c*d^2)*e)^(1/2))/(e*x+d)^(1/2)/(c*d*x+a*e)/(a*e^2-c*d^2)/((a*e^2-c*d^2)*e)^(1/2)","A"
2069,1,235,176,0.083000," ","int(1/(e*x+d)^(1/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2),x)","\frac{\sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(3 \sqrt{c d x +a e}\, c d \,e^{2} x \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+3 \sqrt{c d x +a e}\, c \,d^{2} e \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)-3 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c d e x -\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a \,e^{2}-2 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c \,d^{2}\right)}{\left(e x +d \right)^{\frac{3}{2}} \left(c d x +a e \right) \left(a \,e^{2}-c \,d^{2}\right)^{2} \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}"," ",0,"(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(3*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*(c*d*x+a*e)^(1/2)*x*c*d*e^2+3*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*(c*d*x+a*e)^(1/2)*c*d^2*e-3*((a*e^2-c*d^2)*e)^(1/2)*x*c*d*e-((a*e^2-c*d^2)*e)^(1/2)*a*e^2-2*((a*e^2-c*d^2)*e)^(1/2)*c*d^2)/(e*x+d)^(3/2)/(c*d*x+a*e)/(a*e^2-c*d^2)^2/((a*e^2-c*d^2)*e)^(1/2)","A"
2070,1,384,237,0.079000," ","int(1/(e*x+d)^(3/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2),x)","-\frac{\sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(15 \sqrt{c d x +a e}\, c^{2} d^{2} e^{3} x^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+30 \sqrt{c d x +a e}\, c^{2} d^{3} e^{2} x \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+15 \sqrt{c d x +a e}\, c^{2} d^{4} e \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)-15 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{2} d^{2} e^{2} x^{2}-5 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a c d \,e^{3} x -25 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{2} d^{3} e x +2 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a^{2} e^{4}-9 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a c \,d^{2} e^{2}-8 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{2} d^{4}\right)}{4 \left(e x +d \right)^{\frac{5}{2}} \left(c d x +a e \right) \left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}"," ",0,"-1/4/(e*x+d)^(5/2)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(15*(c*d*x+a*e)^(1/2)*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x^2*c^2*d^2*e^3+30*(c*d*x+a*e)^(1/2)*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x*c^2*d^3*e^2+15*(c*d*x+a*e)^(1/2)*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*c^2*d^4*e-15*((a*e^2-c*d^2)*e)^(1/2)*x^2*c^2*d^2*e^2-5*((a*e^2-c*d^2)*e)^(1/2)*x*a*c*d*e^3-25*((a*e^2-c*d^2)*e)^(1/2)*x*c^2*d^3*e+2*((a*e^2-c*d^2)*e)^(1/2)*a^2*e^4-9*((a*e^2-c*d^2)*e)^(1/2)*a*c*d^2*e^2-8*((a*e^2-c*d^2)*e)^(1/2)*c^2*d^4)/(c*d*x+a*e)/(a*e^2-c*d^2)^3/((a*e^2-c*d^2)*e)^(1/2)","A"
2071,1,559,293,0.089000," ","int(1/(e*x+d)^(5/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2),x)","\frac{\sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(105 \sqrt{c d x +a e}\, c^{3} d^{3} e^{4} x^{3} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+315 \sqrt{c d x +a e}\, c^{3} d^{4} e^{3} x^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+315 \sqrt{c d x +a e}\, c^{3} d^{5} e^{2} x \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)-105 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{3} d^{3} e^{3} x^{3}-35 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a \,c^{2} d^{2} e^{4} x^{2}+105 \sqrt{c d x +a e}\, c^{3} d^{6} e \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)-280 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{3} d^{4} e^{2} x^{2}+14 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a^{2} c d \,e^{5} x -98 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a \,c^{2} d^{3} e^{3} x -231 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{3} d^{5} e x -8 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a^{3} e^{6}+38 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a^{2} c \,d^{2} e^{4}-87 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a \,c^{2} d^{4} e^{2}-48 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{3} d^{6}\right)}{24 \left(e x +d \right)^{\frac{7}{2}} \left(c d x +a e \right) \left(a \,e^{2}-c \,d^{2}\right)^{4} \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}"," ",0,"1/24*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(105*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*(c*d*x+a*e)^(1/2)*x^3*c^3*d^3*e^4+315*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*(c*d*x+a*e)^(1/2)*x^2*c^3*d^4*e^3+315*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*(c*d*x+a*e)^(1/2)*x*c^3*d^5*e^2-105*((a*e^2-c*d^2)*e)^(1/2)*x^3*c^3*d^3*e^3+105*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*(c*d*x+a*e)^(1/2)*c^3*d^6*e-35*((a*e^2-c*d^2)*e)^(1/2)*x^2*a*c^2*d^2*e^4-280*((a*e^2-c*d^2)*e)^(1/2)*x^2*c^3*d^4*e^2+14*((a*e^2-c*d^2)*e)^(1/2)*x*a^2*c*d*e^5-98*((a*e^2-c*d^2)*e)^(1/2)*x*a*c^2*d^3*e^3-231*((a*e^2-c*d^2)*e)^(1/2)*x*c^3*d^5*e-8*((a*e^2-c*d^2)*e)^(1/2)*a^3*e^6+38*((a*e^2-c*d^2)*e)^(1/2)*a^2*c*d^2*e^4-87*((a*e^2-c*d^2)*e)^(1/2)*a*c^2*d^4*e^2-48*((a*e^2-c*d^2)*e)^(1/2)*c^3*d^6)/(e*x+d)^(7/2)/(c*d*x+a*e)/(a*e^2-c*d^2)^4/((a*e^2-c*d^2)*e)^(1/2)","A"
2072,1,767,349,0.090000," ","int(1/(e*x+d)^(7/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2),x)","-\frac{\sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(315 \sqrt{c d x +a e}\, c^{4} d^{4} e^{5} x^{4} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+1260 \sqrt{c d x +a e}\, c^{4} d^{5} e^{4} x^{3} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+1890 \sqrt{c d x +a e}\, c^{4} d^{6} e^{3} x^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)-315 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{4} d^{4} e^{4} x^{4}-105 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a \,c^{3} d^{3} e^{5} x^{3}+1260 \sqrt{c d x +a e}\, c^{4} d^{7} e^{2} x \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)-1155 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{4} d^{5} e^{3} x^{3}+42 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a^{2} c^{2} d^{2} e^{6} x^{2}-399 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a \,c^{3} d^{4} e^{4} x^{2}+315 \sqrt{c d x +a e}\, c^{4} d^{8} e \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)-1533 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{4} d^{6} e^{2} x^{2}-24 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a^{3} c d \,e^{7} x +156 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a^{2} c^{2} d^{3} e^{5} x -555 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a \,c^{3} d^{5} e^{3} x -837 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{4} d^{7} e x +16 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a^{4} e^{8}-88 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a^{3} c \,d^{2} e^{6}+210 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a^{2} c^{2} d^{4} e^{4}-325 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a \,c^{3} d^{6} e^{2}-128 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{4} d^{8}\right)}{64 \left(e x +d \right)^{\frac{9}{2}} \left(c d x +a e \right) \left(a \,e^{2}-c \,d^{2}\right)^{5} \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}"," ",0,"-1/64*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(315*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*(c*d*x+a*e)^(1/2)*x^4*c^4*d^4*e^5+1260*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*(c*d*x+a*e)^(1/2)*x^3*c^4*d^5*e^4+1890*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*(c*d*x+a*e)^(1/2)*x^2*c^4*d^6*e^3-315*((a*e^2-c*d^2)*e)^(1/2)*x^4*c^4*d^4*e^4+1260*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*(c*d*x+a*e)^(1/2)*x*c^4*d^7*e^2-105*((a*e^2-c*d^2)*e)^(1/2)*x^3*a*c^3*d^3*e^5-1155*((a*e^2-c*d^2)*e)^(1/2)*x^3*c^4*d^5*e^3+315*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*(c*d*x+a*e)^(1/2)*c^4*d^8*e+42*((a*e^2-c*d^2)*e)^(1/2)*x^2*a^2*c^2*d^2*e^6-399*((a*e^2-c*d^2)*e)^(1/2)*x^2*a*c^3*d^4*e^4-1533*((a*e^2-c*d^2)*e)^(1/2)*x^2*c^4*d^6*e^2-24*((a*e^2-c*d^2)*e)^(1/2)*x*a^3*c*d*e^7+156*((a*e^2-c*d^2)*e)^(1/2)*x*a^2*c^2*d^3*e^5-555*((a*e^2-c*d^2)*e)^(1/2)*x*a*c^3*d^5*e^3-837*((a*e^2-c*d^2)*e)^(1/2)*x*c^4*d^7*e+16*((a*e^2-c*d^2)*e)^(1/2)*a^4*e^8-88*((a*e^2-c*d^2)*e)^(1/2)*a^3*c*d^2*e^6+210*((a*e^2-c*d^2)*e)^(1/2)*a^2*c^2*d^4*e^4-325*((a*e^2-c*d^2)*e)^(1/2)*a*c^3*d^6*e^2-128*((a*e^2-c*d^2)*e)^(1/2)*c^4*d^8)/(e*x+d)^(9/2)/(c*d*x+a*e)/(a*e^2-c*d^2)^5/((a*e^2-c*d^2)*e)^(1/2)","B"
2073,1,68,97,0.046000," ","int((e*x+d)^(7/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2),x)","-\frac{2 \left(c d x +a e \right) \left(3 c d e x +2 a \,e^{2}+c \,d^{2}\right) \left(e x +d \right)^{\frac{5}{2}}}{3 \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{5}{2}} c^{2} d^{2}}"," ",0,"-2/3*(c*d*x+a*e)*(3*c*d*e*x+2*a*e^2+c*d^2)*(e*x+d)^(5/2)/c^2/d^2/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(5/2)","A"
2074,1,50,42,0.051000," ","int((e*x+d)^(5/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2),x)","-\frac{2 \left(c d x +a e \right) \left(e x +d \right)^{\frac{5}{2}}}{3 \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{5}{2}} c d}"," ",0,"-2/3*(c*d*x+a*e)*(e*x+d)^(5/2)/c/d/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(5/2)","A"
2075,1,234,223,0.080000," ","int((e*x+d)^(3/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2),x)","-\frac{2 \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(3 \sqrt{c d x +a e}\, c d \,e^{2} x \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+3 \sqrt{c d x +a e}\, a \,e^{3} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)-3 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c d e x -4 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a \,e^{2}+\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c \,d^{2}\right)}{3 \sqrt{e x +d}\, \left(c d x +a e \right)^{2} \left(a \,e^{2}-c \,d^{2}\right)^{2} \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}"," ",0,"-2/3*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(3*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*(c*d*x+a*e)^(1/2)*x*c*d*e^2+3*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*a*e^3*(c*d*x+a*e)^(1/2)-3*((a*e^2-c*d^2)*e)^(1/2)*c*d*e*x-4*((a*e^2-c*d^2)*e)^(1/2)*a*e^2+((a*e^2-c*d^2)*e)^(1/2)*c*d^2)/(e*x+d)^(1/2)/(c*d*x+a*e)^2/(a*e^2-c*d^2)^2/((a*e^2-c*d^2)*e)^(1/2)","A"
2076,1,433,229,0.082000," ","int((e*x+d)^(1/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2),x)","\frac{\sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(15 \sqrt{c d x +a e}\, c^{2} d^{2} e^{3} x^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+15 \sqrt{c d x +a e}\, a c d \,e^{4} x \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+15 \sqrt{c d x +a e}\, c^{2} d^{3} e^{2} x \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+15 \sqrt{c d x +a e}\, a c \,d^{2} e^{3} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)-15 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{2} d^{2} e^{2} x^{2}-20 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a c d \,e^{3} x -10 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{2} d^{3} e x -3 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a^{2} e^{4}-14 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a c \,d^{2} e^{2}+2 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{2} d^{4}\right)}{3 \left(e x +d \right)^{\frac{3}{2}} \left(c d x +a e \right)^{2} \left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}"," ",0,"1/3*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(15*(c*d*x+a*e)^(1/2)*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x^2*c^2*d^2*e^3+15*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x*a*c*d*e^4*(c*d*x+a*e)^(1/2)+15*(c*d*x+a*e)^(1/2)*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x*c^2*d^3*e^2+15*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*a*c*d^2*e^3*(c*d*x+a*e)^(1/2)-15*((a*e^2-c*d^2)*e)^(1/2)*c^2*d^2*e^2*x^2-20*((a*e^2-c*d^2)*e)^(1/2)*a*c*d*e^3*x-10*((a*e^2-c*d^2)*e)^(1/2)*c^2*d^3*e*x-3*((a*e^2-c*d^2)*e)^(1/2)*a^2*e^4-14*((a*e^2-c*d^2)*e)^(1/2)*a*c*d^2*e^2+2*((a*e^2-c*d^2)*e)^(1/2)*c^2*d^4)/(e*x+d)^(3/2)/(c*d*x+a*e)^2/(a*e^2-c*d^2)^3/((a*e^2-c*d^2)*e)^(1/2)","A"
2077,1,668,291,0.092000," ","int(1/(e*x+d)^(1/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2),x)","-\frac{\sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(105 \sqrt{c d x +a e}\, c^{3} d^{3} e^{4} x^{3} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+105 \sqrt{c d x +a e}\, a \,c^{2} d^{2} e^{5} x^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+210 \sqrt{c d x +a e}\, c^{3} d^{4} e^{3} x^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+210 \sqrt{c d x +a e}\, a \,c^{2} d^{3} e^{4} x \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+105 \sqrt{c d x +a e}\, c^{3} d^{5} e^{2} x \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)-105 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{3} d^{3} e^{3} x^{3}+105 \sqrt{c d x +a e}\, a \,c^{2} d^{4} e^{3} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)-140 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a \,c^{2} d^{2} e^{4} x^{2}-175 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{3} d^{4} e^{2} x^{2}-21 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a^{2} c d \,e^{5} x -238 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a \,c^{2} d^{3} e^{3} x -56 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{3} d^{5} e x +6 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a^{3} e^{6}-39 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a^{2} c \,d^{2} e^{4}-80 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a \,c^{2} d^{4} e^{2}+8 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{3} d^{6}\right)}{12 \left(e x +d \right)^{\frac{5}{2}} \left(c d x +a e \right)^{2} \left(a \,e^{2}-c \,d^{2}\right)^{4} \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}"," ",0,"-1/12*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(105*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*(c*d*x+a*e)^(1/2)*x^3*c^3*d^3*e^4+105*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x^2*a*c^2*d^2*e^5*(c*d*x+a*e)^(1/2)+210*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*(c*d*x+a*e)^(1/2)*x^2*c^3*d^4*e^3+210*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x*a*c^2*d^3*e^4*(c*d*x+a*e)^(1/2)+105*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*(c*d*x+a*e)^(1/2)*x*c^3*d^5*e^2-105*((a*e^2-c*d^2)*e)^(1/2)*c^3*d^3*e^3*x^3+105*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*a*c^2*d^4*e^3*(c*d*x+a*e)^(1/2)-140*((a*e^2-c*d^2)*e)^(1/2)*a*c^2*d^2*e^4*x^2-175*((a*e^2-c*d^2)*e)^(1/2)*c^3*d^4*e^2*x^2-21*((a*e^2-c*d^2)*e)^(1/2)*a^2*c*d*e^5*x-238*((a*e^2-c*d^2)*e)^(1/2)*a*c^2*d^3*e^3*x-56*((a*e^2-c*d^2)*e)^(1/2)*c^3*d^5*e*x+6*((a*e^2-c*d^2)*e)^(1/2)*a^3*e^6-39*((a*e^2-c*d^2)*e)^(1/2)*a^2*c*d^2*e^4-80*((a*e^2-c*d^2)*e)^(1/2)*a*c^2*d^4*e^2+8*((a*e^2-c*d^2)*e)^(1/2)*c^3*d^6)/(e*x+d)^(5/2)/(c*d*x+a*e)^2/(a*e^2-c*d^2)^4/((a*e^2-c*d^2)*e)^(1/2)","B"
2078,1,930,351,0.088000," ","int(1/(e*x+d)^(3/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2),x)","\frac{\sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(315 \sqrt{c d x +a e}\, c^{4} d^{4} e^{5} x^{4} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+315 \sqrt{c d x +a e}\, a \,c^{3} d^{3} e^{6} x^{3} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+945 \sqrt{c d x +a e}\, c^{4} d^{5} e^{4} x^{3} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+945 \sqrt{c d x +a e}\, a \,c^{3} d^{4} e^{5} x^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+945 \sqrt{c d x +a e}\, c^{4} d^{6} e^{3} x^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)-315 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{4} d^{4} e^{4} x^{4}+945 \sqrt{c d x +a e}\, a \,c^{3} d^{5} e^{4} x \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)-420 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a \,c^{3} d^{3} e^{5} x^{3}+315 \sqrt{c d x +a e}\, c^{4} d^{7} e^{2} x \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)-840 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{4} d^{5} e^{3} x^{3}-63 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a^{2} c^{2} d^{2} e^{6} x^{2}+315 \sqrt{c d x +a e}\, a \,c^{3} d^{6} e^{3} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)-1134 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a \,c^{3} d^{4} e^{4} x^{2}-693 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{4} d^{6} e^{2} x^{2}+18 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a^{3} c d \,e^{7} x -180 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a^{2} c^{2} d^{3} e^{5} x -954 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a \,c^{3} d^{5} e^{3} x -144 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{4} d^{7} e x -8 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a^{4} e^{8}+50 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a^{3} c \,d^{2} e^{6}-165 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a^{2} c^{2} d^{4} e^{4}-208 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a \,c^{3} d^{6} e^{2}+16 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{4} d^{8}\right)}{24 \left(e x +d \right)^{\frac{7}{2}} \left(c d x +a e \right)^{2} \left(a \,e^{2}-c \,d^{2}\right)^{5} \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}"," ",0,"1/24*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(315*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*(c*d*x+a*e)^(1/2)*x^4*c^4*d^4*e^5+315*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x^3*a*c^3*d^3*e^6*(c*d*x+a*e)^(1/2)+945*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*(c*d*x+a*e)^(1/2)*x^3*c^4*d^5*e^4+945*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x^2*a*c^3*d^4*e^5*(c*d*x+a*e)^(1/2)+945*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*(c*d*x+a*e)^(1/2)*x^2*c^4*d^6*e^3-315*((a*e^2-c*d^2)*e)^(1/2)*c^4*d^4*e^4*x^4+945*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x*a*c^3*d^5*e^4*(c*d*x+a*e)^(1/2)+315*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*(c*d*x+a*e)^(1/2)*x*c^4*d^7*e^2-420*((a*e^2-c*d^2)*e)^(1/2)*a*c^3*d^3*e^5*x^3-840*((a*e^2-c*d^2)*e)^(1/2)*c^4*d^5*e^3*x^3+315*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*a*c^3*d^6*e^3*(c*d*x+a*e)^(1/2)-63*((a*e^2-c*d^2)*e)^(1/2)*a^2*c^2*d^2*e^6*x^2-1134*((a*e^2-c*d^2)*e)^(1/2)*a*c^3*d^4*e^4*x^2-693*((a*e^2-c*d^2)*e)^(1/2)*c^4*d^6*e^2*x^2+18*((a*e^2-c*d^2)*e)^(1/2)*a^3*c*d*e^7*x-180*((a*e^2-c*d^2)*e)^(1/2)*a^2*c^2*d^3*e^5*x-954*((a*e^2-c*d^2)*e)^(1/2)*a*c^3*d^5*e^3*x-144*((a*e^2-c*d^2)*e)^(1/2)*c^4*d^7*e*x-8*((a*e^2-c*d^2)*e)^(1/2)*a^4*e^8+50*((a*e^2-c*d^2)*e)^(1/2)*a^3*c*d^2*e^6-165*((a*e^2-c*d^2)*e)^(1/2)*a^2*c^2*d^4*e^4-208*((a*e^2-c*d^2)*e)^(1/2)*a*c^3*d^6*e^2+16*((a*e^2-c*d^2)*e)^(1/2)*c^4*d^8)/(e*x+d)^(7/2)/(c*d*x+a*e)^2/(a*e^2-c*d^2)^5/((a*e^2-c*d^2)*e)^(1/2)","B"
2079,1,1225,407,0.089000," ","int(1/(e*x+d)^(5/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2),x)","-\frac{\sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(3465 \sqrt{c d x +a e}\, c^{5} d^{5} e^{6} x^{5} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+3465 \sqrt{c d x +a e}\, a \,c^{4} d^{4} e^{7} x^{4} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+13860 \sqrt{c d x +a e}\, c^{5} d^{6} e^{5} x^{4} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+13860 \sqrt{c d x +a e}\, a \,c^{4} d^{5} e^{6} x^{3} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+20790 \sqrt{c d x +a e}\, c^{5} d^{7} e^{4} x^{3} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)-3465 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{5} d^{5} e^{5} x^{5}+20790 \sqrt{c d x +a e}\, a \,c^{4} d^{6} e^{5} x^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)-4620 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a \,c^{4} d^{4} e^{6} x^{4}+13860 \sqrt{c d x +a e}\, c^{5} d^{8} e^{3} x^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)-12705 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{5} d^{6} e^{4} x^{4}-693 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a^{2} c^{3} d^{3} e^{7} x^{3}+13860 \sqrt{c d x +a e}\, a \,c^{4} d^{7} e^{4} x \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)-17094 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a \,c^{4} d^{5} e^{5} x^{3}+3465 \sqrt{c d x +a e}\, c^{5} d^{9} e^{2} x \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)-16863 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{5} d^{7} e^{3} x^{3}+198 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a^{3} c^{2} d^{2} e^{8} x^{2}-2673 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a^{2} c^{3} d^{4} e^{6} x^{2}+3465 \sqrt{c d x +a e}\, a \,c^{4} d^{8} e^{3} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)-22968 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a \,c^{4} d^{6} e^{4} x^{2}-9207 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{5} d^{8} e^{2} x^{2}-88 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a^{4} c d \,e^{9} x +748 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a^{3} c^{2} d^{3} e^{7} x -3795 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a^{2} c^{3} d^{5} e^{5} x -12782 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a \,c^{4} d^{7} e^{3} x -1408 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{5} d^{9} e x +48 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a^{5} e^{10}-328 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a^{4} c \,d^{2} e^{8}+1030 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a^{3} c^{2} d^{4} e^{6}-2295 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a^{2} c^{3} d^{6} e^{4}-2048 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a \,c^{4} d^{8} e^{2}+128 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{5} d^{10}\right)}{192 \left(e x +d \right)^{\frac{9}{2}} \left(c d x +a e \right)^{2} \left(a \,e^{2}-c \,d^{2}\right)^{6} \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}"," ",0,"-1/192*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(-12705*((a*e^2-c*d^2)*e)^(1/2)*x^4*c^5*d^6*e^4-16863*((a*e^2-c*d^2)*e)^(1/2)*x^3*c^5*d^7*e^3-9207*((a*e^2-c*d^2)*e)^(1/2)*x^2*c^5*d^8*e^2-1408*((a*e^2-c*d^2)*e)^(1/2)*x*c^5*d^9*e-3465*((a*e^2-c*d^2)*e)^(1/2)*x^5*c^5*d^5*e^5+128*((a*e^2-c*d^2)*e)^(1/2)*c^5*d^10+48*((a*e^2-c*d^2)*e)^(1/2)*a^5*e^10-328*((a*e^2-c*d^2)*e)^(1/2)*a^4*c*d^2*e^8+1030*((a*e^2-c*d^2)*e)^(1/2)*a^3*c^2*d^4*e^6-2295*((a*e^2-c*d^2)*e)^(1/2)*a^2*c^3*d^6*e^4-2048*((a*e^2-c*d^2)*e)^(1/2)*a*c^4*d^8*e^2+20790*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x^2*a*c^4*d^6*e^5*(c*d*x+a*e)^(1/2)+13860*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x*a*c^4*d^7*e^4*(c*d*x+a*e)^(1/2)+3465*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x^4*a*c^4*d^4*e^7*(c*d*x+a*e)^(1/2)+13860*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x^3*a*c^4*d^5*e^6*(c*d*x+a*e)^(1/2)-88*((a*e^2-c*d^2)*e)^(1/2)*x*a^4*c*d*e^9+748*((a*e^2-c*d^2)*e)^(1/2)*x*a^3*c^2*d^3*e^7-3795*((a*e^2-c*d^2)*e)^(1/2)*x*a^2*c^3*d^5*e^5-2673*((a*e^2-c*d^2)*e)^(1/2)*x^2*a^2*c^3*d^4*e^6-693*((a*e^2-c*d^2)*e)^(1/2)*x^3*a^2*c^3*d^3*e^7+198*((a*e^2-c*d^2)*e)^(1/2)*x^2*a^3*c^2*d^2*e^8-4620*((a*e^2-c*d^2)*e)^(1/2)*x^4*a*c^4*d^4*e^6-17094*((a*e^2-c*d^2)*e)^(1/2)*x^3*a*c^4*d^5*e^5-22968*((a*e^2-c*d^2)*e)^(1/2)*x^2*a*c^4*d^6*e^4-12782*((a*e^2-c*d^2)*e)^(1/2)*x*a*c^4*d^7*e^3+3465*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x^5*c^5*d^5*e^6*(c*d*x+a*e)^(1/2)+13860*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x^4*c^5*d^6*e^5*(c*d*x+a*e)^(1/2)+20790*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x^3*c^5*d^7*e^4*(c*d*x+a*e)^(1/2)+13860*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x^2*c^5*d^8*e^3*(c*d*x+a*e)^(1/2)+3465*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x*c^5*d^9*e^2*(c*d*x+a*e)^(1/2)+3465*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*a*c^4*d^8*e^3*(c*d*x+a*e)^(1/2))/(e*x+d)^(9/2)/(c*d*x+a*e)^2/(a*e^2-c*d^2)^6/((a*e^2-c*d^2)*e)^(1/2)","B"
2080,1,1553,463,0.111000," ","int(1/(e*x+d)^(7/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2),x)","\frac{\sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(45045 \sqrt{c d x +a e}\, c^{6} d^{6} e^{7} x^{6} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+45045 \sqrt{c d x +a e}\, a \,c^{5} d^{5} e^{8} x^{5} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+225225 \sqrt{c d x +a e}\, c^{6} d^{7} e^{6} x^{5} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+225225 \sqrt{c d x +a e}\, a \,c^{5} d^{6} e^{7} x^{4} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)+450450 \sqrt{c d x +a e}\, c^{6} d^{8} e^{5} x^{4} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)-45045 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{6} d^{6} e^{6} x^{6}+450450 \sqrt{c d x +a e}\, a \,c^{5} d^{7} e^{6} x^{3} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)-60060 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a \,c^{5} d^{5} e^{7} x^{5}+450450 \sqrt{c d x +a e}\, c^{6} d^{9} e^{4} x^{3} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)-210210 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{6} d^{7} e^{5} x^{5}-9009 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a^{2} c^{4} d^{4} e^{8} x^{4}+450450 \sqrt{c d x +a e}\, a \,c^{5} d^{8} e^{5} x^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)-282282 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a \,c^{5} d^{6} e^{6} x^{4}+225225 \sqrt{c d x +a e}\, c^{6} d^{10} e^{3} x^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)-384384 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{6} d^{8} e^{4} x^{4}+2574 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a^{3} c^{3} d^{3} e^{9} x^{3}-43758 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a^{2} c^{4} d^{5} e^{7} x^{3}+225225 \sqrt{c d x +a e}\, a \,c^{5} d^{9} e^{4} x \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)-520806 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a \,c^{5} d^{7} e^{5} x^{3}+45045 \sqrt{c d x +a e}\, c^{6} d^{11} e^{2} x \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)-338910 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{6} d^{9} e^{3} x^{3}-1144 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a^{4} c^{2} d^{2} e^{10} x^{2}+12298 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a^{3} c^{3} d^{4} e^{8} x^{2}-84084 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a^{2} c^{4} d^{6} e^{6} x^{2}+45045 \sqrt{c d x +a e}\, a \,c^{5} d^{10} e^{3} \arctanh \left(\frac{\sqrt{c d x +a e}\, e}{\sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}\right)-464750 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a \,c^{5} d^{8} e^{4} x^{2}-137995 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{6} d^{10} e^{2} x^{2}+624 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a^{5} c d \,e^{11} x -5408 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a^{4} c^{2} d^{3} e^{9} x +23114 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a^{3} c^{3} d^{5} e^{7} x -79170 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a^{2} c^{4} d^{7} e^{5} x -192790 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a \,c^{5} d^{9} e^{3} x -16640 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{6} d^{11} e x -384 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a^{6} e^{12}+2928 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a^{5} c \,d^{2} e^{10}-10024 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a^{4} c^{2} d^{4} e^{8}+21070 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a^{3} c^{3} d^{6} e^{6}-35595 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a^{2} c^{4} d^{8} e^{4}-24320 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, a \,c^{5} d^{10} e^{2}+1280 \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}\, c^{6} d^{12}\right)}{1920 \left(e x +d \right)^{\frac{11}{2}} \left(c d x +a e \right)^{2} \left(a \,e^{2}-c \,d^{2}\right)^{7} \sqrt{\left(a \,e^{2}-c \,d^{2}\right) e}}"," ",0,"1/1920*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(-137995*((a*e^2-c*d^2)*e)^(1/2)*x^2*c^6*d^10*e^2+1280*((a*e^2-c*d^2)*e)^(1/2)*c^6*d^12-384*((a*e^2-c*d^2)*e)^(1/2)*a^6*e^12+2928*((a*e^2-c*d^2)*e)^(1/2)*a^5*c*d^2*e^10-10024*((a*e^2-c*d^2)*e)^(1/2)*a^4*c^2*d^4*e^8+21070*((a*e^2-c*d^2)*e)^(1/2)*a^3*c^3*d^6*e^6-35595*((a*e^2-c*d^2)*e)^(1/2)*a^2*c^4*d^8*e^4-24320*((a*e^2-c*d^2)*e)^(1/2)*a*c^5*d^10*e^2-16640*((a*e^2-c*d^2)*e)^(1/2)*x*c^6*d^11*e-45045*((a*e^2-c*d^2)*e)^(1/2)*x^6*c^6*d^6*e^6-210210*((a*e^2-c*d^2)*e)^(1/2)*x^5*c^6*d^7*e^5-384384*((a*e^2-c*d^2)*e)^(1/2)*x^4*c^6*d^8*e^4-338910*((a*e^2-c*d^2)*e)^(1/2)*x^3*c^6*d^9*e^3+45045*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x^5*a*c^5*d^5*e^8*(c*d*x+a*e)^(1/2)+225225*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x^4*a*c^5*d^6*e^7*(c*d*x+a*e)^(1/2)+450450*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x^3*a*c^5*d^7*e^6*(c*d*x+a*e)^(1/2)+450450*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x^2*a*c^5*d^8*e^5*(c*d*x+a*e)^(1/2)+225225*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x*a*c^5*d^9*e^4*(c*d*x+a*e)^(1/2)-60060*((a*e^2-c*d^2)*e)^(1/2)*x^5*a*c^5*d^5*e^7-282282*((a*e^2-c*d^2)*e)^(1/2)*x^4*a*c^5*d^6*e^6-464750*((a*e^2-c*d^2)*e)^(1/2)*x^2*a*c^5*d^8*e^4+624*((a*e^2-c*d^2)*e)^(1/2)*x*a^5*c*d*e^11-5408*((a*e^2-c*d^2)*e)^(1/2)*x*a^4*c^2*d^3*e^9-9009*((a*e^2-c*d^2)*e)^(1/2)*x^4*a^2*c^4*d^4*e^8-84084*((a*e^2-c*d^2)*e)^(1/2)*x^2*a^2*c^4*d^6*e^6+45045*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x^6*c^6*d^6*e^7*(c*d*x+a*e)^(1/2)+225225*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x^5*c^6*d^7*e^6*(c*d*x+a*e)^(1/2)+450450*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x^4*c^6*d^8*e^5*(c*d*x+a*e)^(1/2)+450450*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x^3*c^6*d^9*e^4*(c*d*x+a*e)^(1/2)+225225*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x^2*c^6*d^10*e^3*(c*d*x+a*e)^(1/2)+45045*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*x*c^6*d^11*e^2*(c*d*x+a*e)^(1/2)+45045*arctanh((c*d*x+a*e)^(1/2)/((a*e^2-c*d^2)*e)^(1/2)*e)*a*c^5*d^10*e^3*(c*d*x+a*e)^(1/2)+23114*((a*e^2-c*d^2)*e)^(1/2)*x*a^3*c^3*d^5*e^7+2574*((a*e^2-c*d^2)*e)^(1/2)*x^3*a^3*c^3*d^3*e^9-43758*((a*e^2-c*d^2)*e)^(1/2)*x^3*a^2*c^4*d^5*e^7-79170*((a*e^2-c*d^2)*e)^(1/2)*x*a^2*c^4*d^7*e^5-520806*((a*e^2-c*d^2)*e)^(1/2)*x^3*a*c^5*d^7*e^5-192790*((a*e^2-c*d^2)*e)^(1/2)*x*a*c^5*d^9*e^3-1144*((a*e^2-c*d^2)*e)^(1/2)*x^2*a^4*c^2*d^2*e^10+12298*((a*e^2-c*d^2)*e)^(1/2)*x^2*a^3*c^3*d^4*e^8)/(e*x+d)^(11/2)/(c*d*x+a*e)^2/(a*e^2-c*d^2)^7/((a*e^2-c*d^2)*e)^(1/2)","B"
2081,1,58,41,0.058000," ","int(1/(e*x+d)^(1/2)/(-e^2*x^2+d^2)^(1/2),x)","-\frac{\sqrt{-e^{2} x^{2}+d^{2}}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{-e x +d}\, \sqrt{2}}{2 \sqrt{d}}\right)}{\sqrt{e x +d}\, \sqrt{-e x +d}\, \sqrt{d}\, e}"," ",0,"-1/(e*x+d)^(1/2)*(-e^2*x^2+d^2)^(1/2)/(-e*x+d)^(1/2)/e*2^(1/2)/d^(1/2)*arctanh(1/2*(-e*x+d)^(1/2)*2^(1/2)/d^(1/2))","A"
2082,1,63,42,0.057000," ","int(1/(e*x-d)^(1/2)/(-e^2*x^2+d^2)^(1/2),x)","\frac{\sqrt{-e^{2} x^{2}+d^{2}}\, \sqrt{2}\, \arctan \left(\frac{\sqrt{-e x -d}\, \sqrt{2}}{2 \sqrt{d}}\right)}{\sqrt{e x -d}\, \sqrt{-e x -d}\, \sqrt{d}\, e}"," ",0,"1/(e*x-d)^(1/2)*(-e^2*x^2+d^2)^(1/2)/(-e*x-d)^(1/2)/e*2^(1/2)/d^(1/2)*arctan(1/2*(-e*x-d)^(1/2)*2^(1/2)/d^(1/2))","A"
2083,0,0,635,0.317000," ","int((e*x+d)^(2/3)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","\int \frac{\left(e x +d \right)^{\frac{2}{3}}}{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}\, dx"," ",0,"int((e*x+d)^(2/3)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","F"
2084,1,436,130,0.053000," ","int((e*x+d)^m*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^3,x)","\frac{\left(c^{3} d^{3} e^{3} m^{3} x^{3}+3 a \,c^{2} d^{2} e^{4} m^{3} x^{2}+15 c^{3} d^{3} e^{3} m^{2} x^{3}+3 a^{2} c d \,e^{5} m^{3} x +48 a \,c^{2} d^{2} e^{4} m^{2} x^{2}-3 c^{3} d^{4} e^{2} m^{2} x^{2}+74 c^{3} d^{3} e^{3} m \,x^{3}+a^{3} e^{6} m^{3}+51 a^{2} c d \,e^{5} m^{2} x -6 a \,c^{2} d^{3} e^{3} m^{2} x +249 a \,c^{2} d^{2} e^{4} m \,x^{2}-27 c^{3} d^{4} e^{2} m \,x^{2}+120 c^{3} d^{3} e^{3} x^{3}+18 a^{3} e^{6} m^{2}-3 a^{2} c \,d^{2} e^{4} m^{2}+282 a^{2} c d \,e^{5} m x -66 a \,c^{2} d^{3} e^{3} m x +420 a \,c^{2} d^{2} e^{4} x^{2}+6 c^{3} d^{5} e m x -60 c^{3} d^{4} e^{2} x^{2}+107 a^{3} e^{6} m -39 a^{2} c \,d^{2} e^{4} m +504 a^{2} c d \,e^{5} x +6 a \,c^{2} d^{4} e^{2} m -168 a \,c^{2} d^{3} e^{3} x +24 c^{3} d^{5} e x +210 a^{3} e^{6}-126 a^{2} c \,d^{2} e^{4}+42 a \,c^{2} d^{4} e^{2}-6 c^{3} d^{6}\right) \left(e x +d \right)^{m +4}}{\left(m^{4}+22 m^{3}+179 m^{2}+638 m +840\right) e^{4}}"," ",0,"(e*x+d)^(m+4)*(c^3*d^3*e^3*m^3*x^3+3*a*c^2*d^2*e^4*m^3*x^2+15*c^3*d^3*e^3*m^2*x^3+3*a^2*c*d*e^5*m^3*x+48*a*c^2*d^2*e^4*m^2*x^2-3*c^3*d^4*e^2*m^2*x^2+74*c^3*d^3*e^3*m*x^3+a^3*e^6*m^3+51*a^2*c*d*e^5*m^2*x-6*a*c^2*d^3*e^3*m^2*x+249*a*c^2*d^2*e^4*m*x^2-27*c^3*d^4*e^2*m*x^2+120*c^3*d^3*e^3*x^3+18*a^3*e^6*m^2-3*a^2*c*d^2*e^4*m^2+282*a^2*c*d*e^5*m*x-66*a*c^2*d^3*e^3*m*x+420*a*c^2*d^2*e^4*x^2+6*c^3*d^5*e*m*x-60*c^3*d^4*e^2*x^2+107*a^3*e^6*m-39*a^2*c*d^2*e^4*m+504*a^2*c*d*e^5*x+6*a*c^2*d^4*e^2*m-168*a*c^2*d^3*e^3*x+24*c^3*d^5*e*x+210*a^3*e^6-126*a^2*c*d^2*e^4+42*a*c^2*d^4*e^2-6*c^3*d^6)/e^4/(m^4+22*m^3+179*m^2+638*m+840)","B"
2085,1,183,90,0.047000," ","int((e*x+d)^m*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^2,x)","\frac{\left(c^{2} d^{2} e^{2} m^{2} x^{2}+2 a c d \,e^{3} m^{2} x +7 c^{2} d^{2} e^{2} m \,x^{2}+a^{2} e^{4} m^{2}+16 a c d \,e^{3} m x -2 c^{2} d^{3} e m x +12 c^{2} d^{2} e^{2} x^{2}+9 a^{2} e^{4} m -2 a c \,d^{2} e^{2} m +30 a c d \,e^{3} x -6 c^{2} d^{3} e x +20 a^{2} e^{4}-10 a c \,d^{2} e^{2}+2 c^{2} d^{4}\right) \left(e x +d \right)^{m +3}}{\left(m^{3}+12 m^{2}+47 m +60\right) e^{3}}"," ",0,"(e*x+d)^(m+3)*(c^2*d^2*e^2*m^2*x^2+2*a*c*d*e^3*m^2*x+7*c^2*d^2*e^2*m*x^2+a^2*e^4*m^2+16*a*c*d*e^3*m*x-2*c^2*d^3*e*m*x+12*c^2*d^2*e^2*x^2+9*a^2*e^4*m-2*a*c*d^2*e^2*m+30*a*c*d*e^3*x-6*c^2*d^3*e*x+20*a^2*e^4-10*a*c*d^2*e^2+2*c^2*d^4)/e^3/(m^3+12*m^2+47*m+60)","B"
2086,1,55,52,0.048000," ","int((e*x+d)^m*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x),x)","\frac{\left(c d e m x +a \,e^{2} m +2 c d e x +3 a \,e^{2}-c \,d^{2}\right) \left(e x +d \right)^{m +2}}{\left(m^{2}+5 m +6\right) e^{2}}"," ",0,"(e*x+d)^(m+2)*(c*d*e*m*x+a*e^2*m+2*c*d*e*x+3*a*e^2-c*d^2)/e^2/(m^2+5*m+6)","A"
2087,0,0,56,2.068000," ","int((e*x+d)^m/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x),x)","\int \frac{\left(e x +d \right)^{m}}{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, dx"," ",0,"int((e*x+d)^m/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x),x)","F"
2088,0,0,63,1.696000," ","int((e*x+d)^m/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^2,x)","\int \frac{\left(e x +d \right)^{m}}{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{2}}\, dx"," ",0,"int((e*x+d)^m/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^2,x)","F"
2089,0,0,66,1.854000," ","int((e*x+d)^m/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^3,x)","\int \frac{\left(e x +d \right)^{m}}{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{3}}\, dx"," ",0,"int((e*x+d)^m/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^3,x)","F"
2090,0,0,67,1.703000," ","int((e*x+d)^m/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^4,x)","\int \frac{\left(e x +d \right)^{m}}{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{4}}\, dx"," ",0,"int((e*x+d)^m/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^4,x)","F"
2091,0,0,102,1.585000," ","int((e*x+d)^m*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^p,x)","\int \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{p} \left(e x +d \right)^{m}\, dx"," ",0,"int((e*x+d)^m*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^p,x)","F"
2092,0,0,97,1.615000," ","int((e*x+d)^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^p,x)","\int \left(e x +d \right)^{3} \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{p}\, dx"," ",0,"int((e*x+d)^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^p,x)","F"
2093,0,0,97,1.414000," ","int((e*x+d)^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^p,x)","\int \left(e x +d \right)^{2} \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{p}\, dx"," ",0,"int((e*x+d)^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^p,x)","F"
2094,0,0,97,1.490000," ","int((e*x+d)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^p,x)","\int \left(e x +d \right) \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{p}\, dx"," ",0,"int((e*x+d)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^p,x)","F"
2095,0,0,115,1.291000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^p,x)","\int \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{p}\, dx"," ",0,"int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^p,x)","F"
2096,0,0,95,1.568000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^p/(e*x+d),x)","\int \frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{p}}{e x +d}\, dx"," ",0,"int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^p/(e*x+d),x)","F"
2097,0,0,94,1.448000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^p/(e*x+d)^2,x)","\int \frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{p}}{\left(e x +d \right)^{2}}\, dx"," ",0,"int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^p/(e*x+d)^2,x)","F"
2098,0,0,98,1.597000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^p/(e*x+d)^3,x)","\int \frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{p}}{\left(e x +d \right)^{3}}\, dx"," ",0,"int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^p/(e*x+d)^3,x)","F"
2099,0,0,117,1.559000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^p/((e*x+d)^(2*p)),x)","\int \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{p} \left(e x +d \right)^{-2 p}\, dx"," ",0,"int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^p/((e*x+d)^(2*p)),x)","F"
2100,0,0,111,1.661000," ","int((e*x+d)^(-2*p-1)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^p,x)","\int \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{p} \left(e x +d \right)^{-2 p -1}\, dx"," ",0,"int((e*x+d)^(-2*p-1)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^p,x)","F"
2101,1,75,62,0.046000," ","int((e*x+d)^(-2*p-2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^p,x)","-\frac{\left(c d x +a e \right) \left(e x +d \right)^{-2 p -1} \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{p}}{a \,e^{2} p -c \,d^{2} p +a \,e^{2}-c \,d^{2}}"," ",0,"-(c*d*x+a*e)*(e*x+d)^(-2*p-1)/(a*e^2*p-c*d^2*p+a*e^2-c*d^2)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^p","A"
2102,1,170,130,0.048000," ","int((e*x+d)^(-2*p-3)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^p,x)","-\frac{\left(c d x +a e \right) \left(a \,e^{2} p -c \,d^{2} p -c d e x +a \,e^{2}-2 c \,d^{2}\right) \left(e x +d \right)^{-2 p -2} \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{p}}{a^{2} e^{4} p^{2}-2 a c \,d^{2} e^{2} p^{2}+c^{2} d^{4} p^{2}+3 a^{2} e^{4} p -6 a c \,d^{2} e^{2} p +3 c^{2} d^{4} p +2 a^{2} e^{4}-4 a c \,d^{2} e^{2}+2 c^{2} d^{4}}"," ",0,"-(c*d*x+a*e)*(e*x+d)^(-2*p-2)*(a*e^2*p-c*d^2*p-c*d*e*x+a*e^2-2*c*d^2)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^p/(a^2*e^4*p^2-2*a*c*d^2*e^2*p^2+c^2*d^4*p^2+3*a^2*e^4*p-6*a*c*d^2*e^2*p+3*c^2*d^4*p+2*a^2*e^4-4*a*c*d^2*e^2+2*c^2*d^4)","A"
2103,1,381,210,0.066000," ","int((e*x+d)^(-2*p-4)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^p,x)","-\frac{\left(c d x +a e \right) \left(a^{2} e^{4} p^{2}-2 a c \,d^{2} e^{2} p^{2}-2 a c d \,e^{3} p x +c^{2} d^{4} p^{2}+2 c^{2} d^{3} e p x +2 c^{2} d^{2} e^{2} x^{2}+3 a^{2} e^{4} p -8 a c \,d^{2} e^{2} p -2 a c d \,e^{3} x +5 c^{2} d^{4} p +6 c^{2} d^{3} e x +2 a^{2} e^{4}-6 a c \,d^{2} e^{2}+6 c^{2} d^{4}\right) \left(e x +d \right)^{-2 p -3} \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{p}}{a^{3} e^{6} p^{3}-3 a^{2} c \,d^{2} e^{4} p^{3}+3 a \,c^{2} d^{4} e^{2} p^{3}-c^{3} d^{6} p^{3}+6 a^{3} e^{6} p^{2}-18 a^{2} c \,d^{2} e^{4} p^{2}+18 a \,c^{2} d^{4} e^{2} p^{2}-6 c^{3} d^{6} p^{2}+11 a^{3} e^{6} p -33 a^{2} c \,d^{2} e^{4} p +33 a \,c^{2} d^{4} e^{2} p -11 c^{3} d^{6} p +6 a^{3} e^{6}-18 a^{2} c \,d^{2} e^{4}+18 a \,c^{2} d^{4} e^{2}-6 c^{3} d^{6}}"," ",0,"-(c*d*x+a*e)*(e*x+d)^(-2*p-3)*(a^2*e^4*p^2-2*a*c*d^2*e^2*p^2-2*a*c*d*e^3*p*x+c^2*d^4*p^2+2*c^2*d^3*e*p*x+2*c^2*d^2*e^2*x^2+3*a^2*e^4*p-8*a*c*d^2*e^2*p-2*a*c*d*e^3*x+5*c^2*d^4*p+6*c^2*d^3*e*x+2*a^2*e^4-6*a*c*d^2*e^2+6*c^2*d^4)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^p/(a^3*e^6*p^3-3*a^2*c*d^2*e^4*p^3+3*a*c^2*d^4*e^2*p^3-c^3*d^6*p^3+6*a^3*e^6*p^2-18*a^2*c*d^2*e^4*p^2+18*a*c^2*d^4*e^2*p^2-6*c^3*d^6*p^2+11*a^3*e^6*p-33*a^2*c*d^2*e^4*p+33*a*c^2*d^4*e^2*p-11*c^3*d^6*p+6*a^3*e^6-18*a^2*c*d^2*e^4+18*a*c^2*d^4*e^2-6*c^3*d^6)","A"
2104,1,745,292,0.057000," ","int((e*x+d)^(-2*p-5)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^p,x)","-\frac{\left(c d x +a e \right) \left(a^{3} e^{6} p^{3}-3 a^{2} c \,d^{2} e^{4} p^{3}-3 a^{2} c d \,e^{5} p^{2} x +3 a \,c^{2} d^{4} e^{2} p^{3}+6 a \,c^{2} d^{3} e^{3} p^{2} x +6 a \,c^{2} d^{2} e^{4} p \,x^{2}-c^{3} d^{6} p^{3}-3 c^{3} d^{5} e \,p^{2} x -6 c^{3} d^{4} e^{2} p \,x^{2}-6 c^{3} d^{3} e^{3} x^{3}+6 a^{3} e^{6} p^{2}-21 a^{2} c \,d^{2} e^{4} p^{2}-9 a^{2} c d \,e^{5} p x +24 a \,c^{2} d^{4} e^{2} p^{2}+30 a \,c^{2} d^{3} e^{3} p x +6 a \,c^{2} d^{2} e^{4} x^{2}-9 c^{3} d^{6} p^{2}-21 c^{3} d^{5} e p x -24 c^{3} d^{4} e^{2} x^{2}+11 a^{3} e^{6} p -42 a^{2} c \,d^{2} e^{4} p -6 a^{2} c d \,e^{5} x +57 a \,c^{2} d^{4} e^{2} p +24 a \,c^{2} d^{3} e^{3} x -26 c^{3} d^{6} p -36 c^{3} d^{5} e x +6 a^{3} e^{6}-24 a^{2} c \,d^{2} e^{4}+36 a \,c^{2} d^{4} e^{2}-24 c^{3} d^{6}\right) \left(e x +d \right)^{-2 p -4} \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{p}}{a^{4} e^{8} p^{4}-4 a^{3} c \,d^{2} e^{6} p^{4}+6 a^{2} c^{2} d^{4} e^{4} p^{4}-4 a \,c^{3} d^{6} e^{2} p^{4}+c^{4} d^{8} p^{4}+10 a^{4} e^{8} p^{3}-40 a^{3} c \,d^{2} e^{6} p^{3}+60 a^{2} c^{2} d^{4} e^{4} p^{3}-40 a \,c^{3} d^{6} e^{2} p^{3}+10 c^{4} d^{8} p^{3}+35 a^{4} e^{8} p^{2}-140 a^{3} c \,d^{2} e^{6} p^{2}+210 a^{2} c^{2} d^{4} e^{4} p^{2}-140 a \,c^{3} d^{6} e^{2} p^{2}+35 c^{4} d^{8} p^{2}+50 a^{4} e^{8} p -200 a^{3} c \,d^{2} e^{6} p +300 a^{2} c^{2} d^{4} e^{4} p -200 a \,c^{3} d^{6} e^{2} p +50 c^{4} d^{8} p +24 a^{4} e^{8}-96 a^{3} c \,d^{2} e^{6}+144 a^{2} c^{2} d^{4} e^{4}-96 a \,c^{3} d^{6} e^{2}+24 c^{4} d^{8}}"," ",0,"-(c*d*x+a*e)*(e*x+d)^(-2*p-4)*(a^3*e^6*p^3-3*a^2*c*d^2*e^4*p^3-3*a^2*c*d*e^5*p^2*x+3*a*c^2*d^4*e^2*p^3+6*a*c^2*d^3*e^3*p^2*x+6*a*c^2*d^2*e^4*p*x^2-c^3*d^6*p^3-3*c^3*d^5*e*p^2*x-6*c^3*d^4*e^2*p*x^2-6*c^3*d^3*e^3*x^3+6*a^3*e^6*p^2-21*a^2*c*d^2*e^4*p^2-9*a^2*c*d*e^5*p*x+24*a*c^2*d^4*e^2*p^2+30*a*c^2*d^3*e^3*p*x+6*a*c^2*d^2*e^4*x^2-9*c^3*d^6*p^2-21*c^3*d^5*e*p*x-24*c^3*d^4*e^2*x^2+11*a^3*e^6*p-42*a^2*c*d^2*e^4*p-6*a^2*c*d*e^5*x+57*a*c^2*d^4*e^2*p+24*a*c^2*d^3*e^3*x-26*c^3*d^6*p-36*c^3*d^5*e*x+6*a^3*e^6-24*a^2*c*d^2*e^4+36*a*c^2*d^4*e^2-24*c^3*d^6)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^p/(a^4*e^8*p^4-4*a^3*c*d^2*e^6*p^4+6*a^2*c^2*d^4*e^4*p^4-4*a*c^3*d^6*e^2*p^4+c^4*d^8*p^4+10*a^4*e^8*p^3-40*a^3*c*d^2*e^6*p^3+60*a^2*c^2*d^4*e^4*p^3-40*a*c^3*d^6*e^2*p^3+10*c^4*d^8*p^3+35*a^4*e^8*p^2-140*a^3*c*d^2*e^6*p^2+210*a^2*c^2*d^4*e^4*p^2-140*a*c^3*d^6*e^2*p^2+35*c^4*d^8*p^2+50*a^4*e^8*p-200*a^3*c*d^2*e^6*p+300*a^2*c^2*d^4*e^4*p-200*a*c^3*d^6*e^2*p+50*c^4*d^8*p+24*a^4*e^8-96*a^3*c*d^2*e^6+144*a^2*c^2*d^4*e^4-96*a*c^3*d^6*e^2+24*c^4*d^8)","B"
2105,1,57,54,0.039000," ","int((e*x+d)^m/((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^m),x)","-\frac{\left(c d x +a e \right) \left(e x +d \right)^{m} \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{-m}}{\left(m -1\right) c d}"," ",0,"-(c*d*x+a*e)/c/d/(m-1)*(e*x+d)^m/((c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^m)","A"
2106,1,56,52,0.049000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^p/((e*x+d)^p),x)","\frac{\left(c d x +a e \right) \left(e x +d \right)^{-p} \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{p}}{\left(p +1\right) c d}"," ",0,"(c*d*x+a*e)/c/d/(p+1)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^p/((e*x+d)^p)","A"
2107,1,136,63,0.042000," ","int((e*x+d)^4*(c*x^2+b*x+a),x)","\frac{c \,e^{4} x^{7}}{7}+a \,d^{4} x +\frac{\left(e^{4} b +4 c d \,e^{3}\right) x^{6}}{6}+\frac{\left(e^{4} a +4 d \,e^{3} b +6 c \,d^{2} e^{2}\right) x^{5}}{5}+\frac{\left(4 a d \,e^{3}+6 d^{2} e^{2} b +4 c \,d^{3} e \right) x^{4}}{4}+\frac{\left(6 a \,d^{2} e^{2}+4 d^{3} e b +c \,d^{4}\right) x^{3}}{3}+\frac{\left(4 d^{3} e a +b \,d^{4}\right) x^{2}}{2}"," ",0,"1/7*e^4*c*x^7+1/6*(b*e^4+4*c*d*e^3)*x^6+1/5*(a*e^4+4*b*d*e^3+6*c*d^2*e^2)*x^5+1/4*(4*a*d*e^3+6*b*d^2*e^2+4*c*d^3*e)*x^4+1/3*(6*a*d^2*e^2+4*b*d^3*e+c*d^4)*x^3+1/2*(4*a*d^3*e+b*d^4)*x^2+d^4*a*x","B"
2108,1,103,63,0.080000," ","int((e*x+d)^3*(c*x^2+b*x+a),x)","\frac{c \,e^{3} x^{6}}{6}+a \,d^{3} x +\frac{\left(e^{3} b +3 d \,e^{2} c \right) x^{5}}{5}+\frac{\left(a \,e^{3}+3 d \,e^{2} b +3 c \,d^{2} e \right) x^{4}}{4}+\frac{\left(3 a d \,e^{2}+3 d^{2} e b +c \,d^{3}\right) x^{3}}{3}+\frac{\left(3 d^{2} e a +b \,d^{3}\right) x^{2}}{2}"," ",0,"1/6*e^3*c*x^6+1/5*(b*e^3+3*c*d*e^2)*x^5+1/4*(a*e^3+3*b*d*e^2+3*c*d^2*e)*x^4+1/3*(3*a*d*e^2+3*b*d^2*e+c*d^3)*x^3+1/2*(3*a*d^2*e+b*d^3)*x^2+d^3*a*x","A"
2109,1,70,63,0.046000," ","int((e*x+d)^2*(c*x^2+b*x+a),x)","\frac{c \,e^{2} x^{5}}{5}+a \,d^{2} x +\frac{\left(b \,e^{2}+2 c d e \right) x^{4}}{4}+\frac{\left(a \,e^{2}+2 b d e +c \,d^{2}\right) x^{3}}{3}+\frac{\left(2 a d e +d^{2} b \right) x^{2}}{2}"," ",0,"1/5*c*e^2*x^5+1/4*(b*e^2+2*c*d*e)*x^4+1/3*(a*e^2+2*b*d*e+c*d^2)*x^3+1/2*(2*a*d*e+b*d^2)*x^2+a*d^2*x","A"
2110,1,37,36,0.042000," ","int((e*x+d)*(c*x^2+b*x+a),x)","\frac{c e \,x^{4}}{4}+a d x +\frac{\left(b e +c d \right) x^{3}}{3}+\frac{\left(a e +b d \right) x^{2}}{2}"," ",0,"a*d*x+1/2*(a*e+b*d)*x^2+1/3*(b*e+c*d)*x^3+1/4*c*e*x^4","A"
2111,1,17,16,0.038000," ","int(c*x^2+b*x+a,x)","\frac{1}{3} c \,x^{3}+\frac{1}{2} b \,x^{2}+a x"," ",0,"a*x+1/2*b*x^2+1/3*c*x^3","A"
2112,1,63,50,0.041000," ","int((c*x^2+b*x+a)/(e*x+d),x)","\frac{c \,x^{2}}{2 e}+\frac{a \ln \left(e x +d \right)}{e}-\frac{b d \ln \left(e x +d \right)}{e^{2}}+\frac{b x}{e}+\frac{c \,d^{2} \ln \left(e x +d \right)}{e^{3}}-\frac{c d x}{e^{2}}"," ",0,"1/2*c/e*x^2+1/e*x*b-c*d/e^2*x+1/e*ln(e*x+d)*a-1/e^2*ln(e*x+d)*b*d+1/e^3*ln(e*x+d)*c*d^2","A"
2113,1,74,55,0.048000," ","int((c*x^2+b*x+a)/(e*x+d)^2,x)","-\frac{a}{\left(e x +d \right) e}+\frac{b d}{\left(e x +d \right) e^{2}}+\frac{b \ln \left(e x +d \right)}{e^{2}}-\frac{c \,d^{2}}{\left(e x +d \right) e^{3}}-\frac{2 c d \ln \left(e x +d \right)}{e^{3}}+\frac{c x}{e^{2}}"," ",0,"c/e^2*x-1/e/(e*x+d)*a+1/e^2/(e*x+d)*b*d-1/e^3/(e*x+d)*c*d^2+1/e^2*ln(e*x+d)*b-2*c*d/e^3*ln(e*x+d)","A"
2114,1,83,61,0.049000," ","int((c*x^2+b*x+a)/(e*x+d)^3,x)","-\frac{a}{2 \left(e x +d \right)^{2} e}+\frac{b d}{2 \left(e x +d \right)^{2} e^{2}}-\frac{c \,d^{2}}{2 \left(e x +d \right)^{2} e^{3}}-\frac{b}{\left(e x +d \right) e^{2}}+\frac{2 c d}{\left(e x +d \right) e^{3}}+\frac{c \ln \left(e x +d \right)}{e^{3}}"," ",0,"-1/e^2/(e*x+d)*b+2/(e*x+d)*c*d/e^3-1/2/e/(e*x+d)^2*a+1/2/e^2/(e*x+d)^2*b*d-1/2/e^3/(e*x+d)^2*c*d^2+c/e^3*ln(e*x+d)","A"
2115,1,63,64,0.043000," ","int((c*x^2+b*x+a)/(e*x+d)^4,x)","-\frac{c}{\left(e x +d \right) e^{3}}-\frac{b e -2 c d}{2 \left(e x +d \right)^{2} e^{3}}-\frac{a \,e^{2}-b d e +c \,d^{2}}{3 \left(e x +d \right)^{3} e^{3}}"," ",0,"-1/(e*x+d)*c/e^3-1/2*(b*e-2*c*d)/e^3/(e*x+d)^2-1/3*(a*e^2-b*d*e+c*d^2)/e^3/(e*x+d)^3","A"
2116,1,63,64,0.049000," ","int((c*x^2+b*x+a)/(e*x+d)^5,x)","-\frac{c}{2 \left(e x +d \right)^{2} e^{3}}-\frac{b e -2 c d}{3 \left(e x +d \right)^{3} e^{3}}-\frac{a \,e^{2}-b d e +c \,d^{2}}{4 \left(e x +d \right)^{4} e^{3}}"," ",0,"-1/2/(e*x+d)^2*c/e^3-1/3*(b*e-2*c*d)/e^3/(e*x+d)^3-1/4*(a*e^2-b*d*e+c*d^2)/e^3/(e*x+d)^4","A"
2117,1,63,64,0.046000," ","int((c*x^2+b*x+a)/(e*x+d)^6,x)","-\frac{c}{3 \left(e x +d \right)^{3} e^{3}}-\frac{a \,e^{2}-b d e +c \,d^{2}}{5 \left(e x +d \right)^{5} e^{3}}-\frac{b e -2 c d}{4 \left(e x +d \right)^{4} e^{3}}"," ",0,"-1/5*(a*e^2-b*d*e+c*d^2)/e^3/(e*x+d)^5-1/3*c/e^3/(e*x+d)^3-1/4*(b*e-2*c*d)/e^3/(e*x+d)^4","A"
2118,1,283,146,0.046000," ","int((e*x+d)^4*(c*x^2+b*x+a)^2,x)","\frac{c^{2} e^{4} x^{9}}{9}+\frac{\left(2 e^{4} b c +4 d \,e^{3} c^{2}\right) x^{8}}{8}+a^{2} d^{4} x +\frac{\left(8 b c d \,e^{3}+6 c^{2} d^{2} e^{2}+\left(2 a c +b^{2}\right) e^{4}\right) x^{7}}{7}+\frac{\left(2 a b \,e^{4}+12 b c \,d^{2} e^{2}+4 c^{2} d^{3} e +4 \left(2 a c +b^{2}\right) d \,e^{3}\right) x^{6}}{6}+\frac{\left(a^{2} e^{4}+8 a b d \,e^{3}+8 b c \,d^{3} e +c^{2} d^{4}+6 \left(2 a c +b^{2}\right) d^{2} e^{2}\right) x^{5}}{5}+\frac{\left(4 a^{2} d \,e^{3}+12 a b \,d^{2} e^{2}+2 b c \,d^{4}+4 \left(2 a c +b^{2}\right) d^{3} e \right) x^{4}}{4}+\frac{\left(6 a^{2} d^{2} e^{2}+8 a b \,d^{3} e +\left(2 a c +b^{2}\right) d^{4}\right) x^{3}}{3}+\frac{\left(4 d^{3} e \,a^{2}+2 d^{4} a b \right) x^{2}}{2}"," ",0,"1/9*e^4*c^2*x^9+1/8*(2*b*c*e^4+4*c^2*d*e^3)*x^8+1/7*(6*d^2*e^2*c^2+8*d*e^3*b*c+e^4*(2*a*c+b^2))*x^7+1/6*(4*d^3*e*c^2+12*d^2*e^2*b*c+4*d*e^3*(2*a*c+b^2)+2*e^4*a*b)*x^6+1/5*(c^2*d^4+8*d^3*e*b*c+6*d^2*e^2*(2*a*c+b^2)+8*d*e^3*a*b+a^2*e^4)*x^5+1/4*(2*d^4*b*c+4*d^3*e*(2*a*c+b^2)+12*d^2*e^2*a*b+4*d*e^3*a^2)*x^4+1/3*(d^4*(2*a*c+b^2)+8*d^3*e*a*b+6*d^2*e^2*a^2)*x^3+1/2*(4*a^2*d^3*e+2*a*b*d^4)*x^2+d^4*a^2*x","A"
2119,1,219,146,0.041000," ","int((e*x+d)^3*(c*x^2+b*x+a)^2,x)","\frac{c^{2} e^{3} x^{8}}{8}+\frac{\left(2 e^{3} b c +3 d \,e^{2} c^{2}\right) x^{7}}{7}+a^{2} d^{3} x +\frac{\left(6 b c d \,e^{2}+3 c^{2} d^{2} e +\left(2 a c +b^{2}\right) e^{3}\right) x^{6}}{6}+\frac{\left(2 a b \,e^{3}+6 b c \,d^{2} e +c^{2} d^{3}+3 \left(2 a c +b^{2}\right) d \,e^{2}\right) x^{5}}{5}+\frac{\left(a^{2} e^{3}+6 a b d \,e^{2}+2 b c \,d^{3}+3 \left(2 a c +b^{2}\right) d^{2} e \right) x^{4}}{4}+\frac{\left(3 a^{2} d \,e^{2}+6 a b \,d^{2} e +\left(2 a c +b^{2}\right) d^{3}\right) x^{3}}{3}+\frac{\left(3 d^{2} e \,a^{2}+2 d^{3} a b \right) x^{2}}{2}"," ",0,"1/8*c^2*e^3*x^8+1/7*(2*b*c*e^3+3*c^2*d*e^2)*x^7+1/6*(3*d^2*e*c^2+6*d*e^2*b*c+e^3*(2*a*c+b^2))*x^6+1/5*(c^2*d^3+6*b*c*d^2*e+3*d*e^2*(2*a*c+b^2)+2*a*b*e^3)*x^5+1/4*(2*b*c*d^3+3*d^2*e*(2*a*c+b^2)+6*d*e^2*a*b+a^2*e^3)*x^4+1/3*(d^3*(2*a*c+b^2)+6*d^2*e*a*b+3*d*e^2*a^2)*x^3+1/2*(3*a^2*d^2*e+2*a*b*d^3)*x^2+a^2*d^3*x","A"
2120,1,155,146,0.050000," ","int((e*x+d)^2*(c*x^2+b*x+a)^2,x)","\frac{c^{2} e^{2} x^{7}}{7}+\frac{\left(2 e^{2} b c +2 c^{2} d e \right) x^{6}}{6}+a^{2} d^{2} x +\frac{\left(4 b c d e +c^{2} d^{2}+\left(2 a c +b^{2}\right) e^{2}\right) x^{5}}{5}+\frac{\left(2 a b \,e^{2}+2 b c \,d^{2}+2 \left(2 a c +b^{2}\right) d e \right) x^{4}}{4}+\frac{\left(a^{2} e^{2}+4 a b d e +\left(2 a c +b^{2}\right) d^{2}\right) x^{3}}{3}+\frac{\left(2 d e \,a^{2}+2 d^{2} a b \right) x^{2}}{2}"," ",0,"1/7*c^2*e^2*x^7+1/6*(2*b*c*e^2+2*c^2*d*e)*x^6+1/5*(c^2*d^2+4*b*c*d*e+e^2*(2*a*c+b^2))*x^5+1/4*(2*b*c*d^2+2*d*e*(2*a*c+b^2)+2*e^2*a*b)*x^4+1/3*(d^2*(2*a*c+b^2)+4*a*b*d*e+a^2*e^2)*x^3+1/2*(2*a^2*d*e+2*a*b*d^2)*x^2+a^2*d^2*x","A"
2121,1,91,86,0.046000," ","int((e*x+d)*(c*x^2+b*x+a)^2,x)","\frac{c^{2} e \,x^{6}}{6}+\frac{\left(2 b c e +c^{2} d \right) x^{5}}{5}+a^{2} d x +\frac{\left(2 b c d +\left(2 a c +b^{2}\right) e \right) x^{4}}{4}+\frac{\left(2 a b e +\left(2 a c +b^{2}\right) d \right) x^{3}}{3}+\frac{\left(e \,a^{2}+2 a b d \right) x^{2}}{2}"," ",0,"1/6*c^2*e*x^6+1/5*(2*b*c*e+c^2*d)*x^5+1/4*(2*b*c*d+e*(2*a*c+b^2))*x^4+1/3*((2*a*c+b^2)*d+2*b*e*a)*x^3+1/2*(a^2*e+2*a*b*d)*x^2+a^2*d*x","A"
2122,1,41,40,0.057000," ","int((c*x^2+b*x+a)^2,x)","\frac{c^{2} x^{5}}{5}+\frac{b c \,x^{4}}{2}+a b \,x^{2}+a^{2} x +\frac{\left(2 a c +b^{2}\right) x^{3}}{3}"," ",0,"a^2*x+a*b*x^2+1/3*(2*a*c+b^2)*x^3+1/2*b*c*x^4+1/5*c^2*x^5","A"
2123,1,221,123,0.046000," ","int((c*x^2+b*x+a)^2/(e*x+d),x)","\frac{c^{2} x^{4}}{4 e}+\frac{2 b c \,x^{3}}{3 e}-\frac{c^{2} d \,x^{3}}{3 e^{2}}+\frac{a c \,x^{2}}{e}+\frac{b^{2} x^{2}}{2 e}-\frac{b c d \,x^{2}}{e^{2}}+\frac{c^{2} d^{2} x^{2}}{2 e^{3}}+\frac{a^{2} \ln \left(e x +d \right)}{e}-\frac{2 a b d \ln \left(e x +d \right)}{e^{2}}+\frac{2 a b x}{e}+\frac{2 a c \,d^{2} \ln \left(e x +d \right)}{e^{3}}-\frac{2 a c d x}{e^{2}}+\frac{b^{2} d^{2} \ln \left(e x +d \right)}{e^{3}}-\frac{b^{2} d x}{e^{2}}-\frac{2 b c \,d^{3} \ln \left(e x +d \right)}{e^{4}}+\frac{2 b c \,d^{2} x}{e^{3}}+\frac{c^{2} d^{4} \ln \left(e x +d \right)}{e^{5}}-\frac{c^{2} d^{3} x}{e^{4}}"," ",0,"1/4*c^2/e*x^4+2/3/e*x^3*b*c-1/3*c^2*d/e^2*x^3+1/e*x^2*a*c+1/2/e*x^2*b^2-1/e^2*x^2*b*c*d+1/2/e^3*x^2*c^2*d^2+2/e*x*a*b-2/e^2*x*a*c*d-1/e^2*x*b^2*d+2/e^3*x*b*c*d^2-1/e^4*x*c^2*d^3+1/e*ln(e*x+d)*a^2-2/e^2*ln(e*x+d)*a*b*d+2/e^3*ln(e*x+d)*a*c*d^2+1/e^3*ln(e*x+d)*b^2*d^2-2/e^4*ln(e*x+d)*b*c*d^3+1/e^5*ln(e*x+d)*c^2*d^4","A"
2124,1,246,129,0.057000," ","int((c*x^2+b*x+a)^2/(e*x+d)^2,x)","\frac{c^{2} x^{3}}{3 e^{2}}+\frac{b c \,x^{2}}{e^{2}}-\frac{c^{2} d \,x^{2}}{e^{3}}-\frac{a^{2}}{\left(e x +d \right) e}+\frac{2 a b d}{\left(e x +d \right) e^{2}}+\frac{2 a b \ln \left(e x +d \right)}{e^{2}}-\frac{2 a c \,d^{2}}{\left(e x +d \right) e^{3}}-\frac{4 a c d \ln \left(e x +d \right)}{e^{3}}+\frac{2 a c x}{e^{2}}-\frac{b^{2} d^{2}}{\left(e x +d \right) e^{3}}-\frac{2 b^{2} d \ln \left(e x +d \right)}{e^{3}}+\frac{b^{2} x}{e^{2}}+\frac{2 b c \,d^{3}}{\left(e x +d \right) e^{4}}+\frac{6 b c \,d^{2} \ln \left(e x +d \right)}{e^{4}}-\frac{4 b c d x}{e^{3}}-\frac{c^{2} d^{4}}{\left(e x +d \right) e^{5}}-\frac{4 c^{2} d^{3} \ln \left(e x +d \right)}{e^{5}}+\frac{3 c^{2} d^{2} x}{e^{4}}"," ",0,"1/3*c^2/e^2*x^3+1/e^2*x^2*b*c-c^2*d/e^3*x^2+2/e^2*a*c*x+b^2/e^2*x-4/e^3*b*c*d*x+3/e^4*c^2*d^2*x-1/e/(e*x+d)*a^2+2/e^2/(e*x+d)*a*b*d-2/e^3/(e*x+d)*a*c*d^2-1/e^3/(e*x+d)*b^2*d^2+2/e^4/(e*x+d)*b*c*d^3-1/e^5/(e*x+d)*c^2*d^4+2/e^2*ln(e*x+d)*a*b-4/e^3*ln(e*x+d)*a*c*d-2/e^3*ln(e*x+d)*b^2*d+6/e^4*ln(e*x+d)*b*c*d^2-4/e^5*ln(e*x+d)*c^2*d^3","A"
2125,1,266,134,0.053000," ","int((c*x^2+b*x+a)^2/(e*x+d)^3,x)","-\frac{a^{2}}{2 \left(e x +d \right)^{2} e}+\frac{a b d}{\left(e x +d \right)^{2} e^{2}}-\frac{a c \,d^{2}}{\left(e x +d \right)^{2} e^{3}}-\frac{b^{2} d^{2}}{2 \left(e x +d \right)^{2} e^{3}}+\frac{b c \,d^{3}}{\left(e x +d \right)^{2} e^{4}}-\frac{c^{2} d^{4}}{2 \left(e x +d \right)^{2} e^{5}}+\frac{c^{2} x^{2}}{2 e^{3}}-\frac{2 a b}{\left(e x +d \right) e^{2}}+\frac{4 a c d}{\left(e x +d \right) e^{3}}+\frac{2 a c \ln \left(e x +d \right)}{e^{3}}+\frac{2 b^{2} d}{\left(e x +d \right) e^{3}}+\frac{b^{2} \ln \left(e x +d \right)}{e^{3}}-\frac{6 b c \,d^{2}}{\left(e x +d \right) e^{4}}-\frac{6 b c d \ln \left(e x +d \right)}{e^{4}}+\frac{2 b c x}{e^{3}}+\frac{4 c^{2} d^{3}}{\left(e x +d \right) e^{5}}+\frac{6 c^{2} d^{2} \ln \left(e x +d \right)}{e^{5}}-\frac{3 c^{2} d x}{e^{4}}"," ",0,"1/2*c^2/e^3*x^2+2*c/e^3*x*b-3*c^2*d/e^4*x-2/e^2/(e*x+d)*a*b+4/e^3/(e*x+d)*a*c*d+2/e^3/(e*x+d)*b^2*d-6/e^4/(e*x+d)*b*c*d^2+4/e^5/(e*x+d)*c^2*d^3-1/2/e/(e*x+d)^2*a^2+1/e^2/(e*x+d)^2*a*b*d-1/e^3/(e*x+d)^2*a*c*d^2-1/2/e^3/(e*x+d)^2*d^2*b^2+1/e^4/(e*x+d)^2*b*c*d^3-1/2/e^5/(e*x+d)^2*c^2*d^4+2/e^3*ln(e*x+d)*a*c+b^2/e^3*ln(e*x+d)-6/e^4*ln(e*x+d)*b*c*d+6/e^5*ln(e*x+d)*c^2*d^2","A"
2126,1,279,137,0.059000," ","int((c*x^2+b*x+a)^2/(e*x+d)^4,x)","-\frac{a^{2}}{3 \left(e x +d \right)^{3} e}+\frac{2 a b d}{3 \left(e x +d \right)^{3} e^{2}}-\frac{2 a c \,d^{2}}{3 \left(e x +d \right)^{3} e^{3}}-\frac{b^{2} d^{2}}{3 \left(e x +d \right)^{3} e^{3}}+\frac{2 b c \,d^{3}}{3 \left(e x +d \right)^{3} e^{4}}-\frac{c^{2} d^{4}}{3 \left(e x +d \right)^{3} e^{5}}-\frac{a b}{\left(e x +d \right)^{2} e^{2}}+\frac{2 a c d}{\left(e x +d \right)^{2} e^{3}}+\frac{b^{2} d}{\left(e x +d \right)^{2} e^{3}}-\frac{3 b c \,d^{2}}{\left(e x +d \right)^{2} e^{4}}+\frac{2 c^{2} d^{3}}{\left(e x +d \right)^{2} e^{5}}-\frac{2 a c}{\left(e x +d \right) e^{3}}-\frac{b^{2}}{\left(e x +d \right) e^{3}}+\frac{6 b c d}{\left(e x +d \right) e^{4}}+\frac{2 b c \ln \left(e x +d \right)}{e^{4}}-\frac{6 c^{2} d^{2}}{\left(e x +d \right) e^{5}}-\frac{4 c^{2} d \ln \left(e x +d \right)}{e^{5}}+\frac{c^{2} x}{e^{4}}"," ",0,"c^2/e^4*x-2/e^3/(e*x+d)*a*c-1/e^3/(e*x+d)*b^2+6/e^4/(e*x+d)*b*c*d-6/e^5/(e*x+d)*c^2*d^2-1/e^2/(e*x+d)^2*a*b+2/e^3/(e*x+d)^2*a*c*d+1/e^3/(e*x+d)^2*b^2*d-3/e^4/(e*x+d)^2*b*c*d^2+2/e^5/(e*x+d)^2*c^2*d^3-1/3/e/(e*x+d)^3*a^2+2/3/e^2/(e*x+d)^3*a*b*d-2/3/e^3/(e*x+d)^3*a*c*d^2-1/3/e^3/(e*x+d)^3*d^2*b^2+2/3/e^4/(e*x+d)^3*b*c*d^3-1/3/e^5/(e*x+d)^3*c^2*d^4+2*c/e^4*ln(e*x+d)*b-4*c^2*d/e^5*ln(e*x+d)","B"
2127,1,287,145,0.081000," ","int((c*x^2+b*x+a)^2/(e*x+d)^5,x)","-\frac{a^{2}}{4 \left(e x +d \right)^{4} e}+\frac{a b d}{2 \left(e x +d \right)^{4} e^{2}}-\frac{a c \,d^{2}}{2 \left(e x +d \right)^{4} e^{3}}-\frac{b^{2} d^{2}}{4 \left(e x +d \right)^{4} e^{3}}+\frac{b c \,d^{3}}{2 \left(e x +d \right)^{4} e^{4}}-\frac{c^{2} d^{4}}{4 \left(e x +d \right)^{4} e^{5}}-\frac{2 a b}{3 \left(e x +d \right)^{3} e^{2}}+\frac{4 a c d}{3 \left(e x +d \right)^{3} e^{3}}+\frac{2 b^{2} d}{3 \left(e x +d \right)^{3} e^{3}}-\frac{2 b c \,d^{2}}{\left(e x +d \right)^{3} e^{4}}+\frac{4 c^{2} d^{3}}{3 \left(e x +d \right)^{3} e^{5}}-\frac{a c}{\left(e x +d \right)^{2} e^{3}}-\frac{b^{2}}{2 \left(e x +d \right)^{2} e^{3}}+\frac{3 b c d}{\left(e x +d \right)^{2} e^{4}}-\frac{3 c^{2} d^{2}}{\left(e x +d \right)^{2} e^{5}}-\frac{2 b c}{\left(e x +d \right) e^{4}}+\frac{4 c^{2} d}{\left(e x +d \right) e^{5}}+\frac{c^{2} \ln \left(e x +d \right)}{e^{5}}"," ",0,"-2*c/e^4/(e*x+d)*b+4/(e*x+d)*c^2*d/e^5-1/(e*x+d)^2*a*c/e^3-1/2/(e*x+d)^2*b^2/e^3+3/e^4/(e*x+d)^2*b*c*d-3/(e*x+d)^2*c^2*d^2/e^5-2/3/e^2/(e*x+d)^3*a*b+4/3/(e*x+d)^3*a*c*d/e^3+2/3/e^3/(e*x+d)^3*b^2*d-2/e^4/(e*x+d)^3*b*c*d^2+4/3/(e*x+d)^3*c^2*d^3/e^5-1/4/(e*x+d)^4*a^2/e+1/2/e^2/(e*x+d)^4*a*b*d-1/2/(e*x+d)^4*a*c*d^2/e^3-1/4/e^3/(e*x+d)^4*b^2*d^2+1/2/e^4/(e*x+d)^4*b*c*d^3-1/4/(e*x+d)^4*c^2*d^4/e^5+c^2/e^5*ln(e*x+d)","A"
2128,1,195,146,0.051000," ","int((c*x^2+b*x+a)^2/(e*x+d)^6,x)","-\frac{c^{2}}{\left(e x +d \right) e^{5}}-\frac{\left(b e -2 c d \right) c}{\left(e x +d \right)^{2} e^{5}}-\frac{a^{2} e^{4}-2 a b d \,e^{3}+2 a c \,d^{2} e^{2}+b^{2} d^{2} e^{2}-2 b c \,d^{3} e +c^{2} d^{4}}{5 \left(e x +d \right)^{5} e^{5}}-\frac{2 a c \,e^{2}+b^{2} e^{2}-6 b c d e +6 c^{2} d^{2}}{3 \left(e x +d \right)^{3} e^{5}}-\frac{2 a b \,e^{3}-4 a c d \,e^{2}-2 b^{2} d \,e^{2}+6 b c \,d^{2} e -4 c^{2} d^{3}}{4 \left(e x +d \right)^{4} e^{5}}"," ",0,"-1/(e*x+d)*c^2/e^5-1/5*(a^2*e^4-2*a*b*d*e^3+2*a*c*d^2*e^2+b^2*d^2*e^2-2*b*c*d^3*e+c^2*d^4)/e^5/(e*x+d)^5-c*(b*e-2*c*d)/e^5/(e*x+d)^2-1/3*(2*a*c*e^2+b^2*e^2-6*b*c*d*e+6*c^2*d^2)/e^5/(e*x+d)^3-1/4*(2*a*b*e^3-4*a*c*d*e^2-2*b^2*d*e^2+6*b*c*d^2*e-4*c^2*d^3)/e^5/(e*x+d)^4","A"
2129,1,195,147,0.054000," ","int((c*x^2+b*x+a)^2/(e*x+d)^7,x)","-\frac{c^{2}}{2 \left(e x +d \right)^{2} e^{5}}-\frac{2 \left(b e -2 c d \right) c}{3 \left(e x +d \right)^{3} e^{5}}-\frac{2 a b \,e^{3}-4 a c d \,e^{2}-2 b^{2} d \,e^{2}+6 b c \,d^{2} e -4 c^{2} d^{3}}{5 \left(e x +d \right)^{5} e^{5}}-\frac{a^{2} e^{4}-2 a b d \,e^{3}+2 a c \,d^{2} e^{2}+b^{2} d^{2} e^{2}-2 b c \,d^{3} e +c^{2} d^{4}}{6 \left(e x +d \right)^{6} e^{5}}-\frac{2 a c \,e^{2}+b^{2} e^{2}-6 b c d e +6 c^{2} d^{2}}{4 \left(e x +d \right)^{4} e^{5}}"," ",0,"-1/5*(2*a*b*e^3-4*a*c*d*e^2-2*b^2*d*e^2+6*b*c*d^2*e-4*c^2*d^3)/e^5/(e*x+d)^5-1/6*(a^2*e^4-2*a*b*d*e^3+2*a*c*d^2*e^2+b^2*d^2*e^2-2*b*c*d^3*e+c^2*d^4)/e^5/(e*x+d)^6-1/2/(e*x+d)^2*c^2/e^5-2/3*c*(b*e-2*c*d)/e^5/(e*x+d)^3-1/4*(2*a*c*e^2+b^2*e^2-6*b*c*d*e+6*c^2*d^2)/e^5/(e*x+d)^4","A"
2130,1,195,147,0.059000," ","int((c*x^2+b*x+a)^2/(e*x+d)^8,x)","-\frac{c^{2}}{3 \left(e x +d \right)^{3} e^{5}}-\frac{\left(b e -2 c d \right) c}{2 \left(e x +d \right)^{4} e^{5}}-\frac{a^{2} e^{4}-2 a b d \,e^{3}+2 a c \,d^{2} e^{2}+b^{2} d^{2} e^{2}-2 b c \,d^{3} e +c^{2} d^{4}}{7 \left(e x +d \right)^{7} e^{5}}-\frac{2 a c \,e^{2}+b^{2} e^{2}-6 b c d e +6 c^{2} d^{2}}{5 \left(e x +d \right)^{5} e^{5}}-\frac{2 a b \,e^{3}-4 a c d \,e^{2}-2 b^{2} d \,e^{2}+6 b c \,d^{2} e -4 c^{2} d^{3}}{6 \left(e x +d \right)^{6} e^{5}}"," ",0,"-1/7*(a^2*e^4-2*a*b*d*e^3+2*a*c*d^2*e^2+b^2*d^2*e^2-2*b*c*d^3*e+c^2*d^4)/e^5/(e*x+d)^7-1/5*(2*a*c*e^2+b^2*e^2-6*b*c*d*e+6*c^2*d^2)/e^5/(e*x+d)^5-1/6*(2*a*b*e^3-4*a*c*d*e^2-2*b^2*d*e^2+6*b*c*d^2*e-4*c^2*d^3)/e^5/(e*x+d)^6-1/3/(e*x+d)^3*c^2/e^5-1/2*c*(b*e-2*c*d)/e^5/(e*x+d)^4","A"
2131,1,631,258,0.042000," ","int((e*x+d)^4*(c*x^2+b*x+a)^3,x)","\frac{c^{3} e^{4} x^{11}}{11}+\frac{\left(3 e^{4} b \,c^{2}+4 d \,e^{3} c^{3}\right) x^{10}}{10}+\frac{\left(12 b \,c^{2} d \,e^{3}+6 c^{3} d^{2} e^{2}+\left(a \,c^{2}+2 b^{2} c +\left(2 a c +b^{2}\right) c \right) e^{4}\right) x^{9}}{9}+a^{3} d^{4} x +\frac{\left(18 b \,c^{2} d^{2} e^{2}+4 c^{3} d^{3} e +4 \left(a \,c^{2}+2 b^{2} c +\left(2 a c +b^{2}\right) c \right) d \,e^{3}+\left(4 a b c +\left(2 a c +b^{2}\right) b \right) e^{4}\right) x^{8}}{8}+\frac{\left(12 b \,c^{2} d^{3} e +c^{3} d^{4}+6 \left(a \,c^{2}+2 b^{2} c +\left(2 a c +b^{2}\right) c \right) d^{2} e^{2}+4 \left(4 a b c +\left(2 a c +b^{2}\right) b \right) d \,e^{3}+\left(a^{2} c +2 a \,b^{2}+\left(2 a c +b^{2}\right) a \right) e^{4}\right) x^{7}}{7}+\frac{\left(3 a^{2} b \,e^{4}+3 b \,c^{2} d^{4}+4 \left(a \,c^{2}+2 b^{2} c +\left(2 a c +b^{2}\right) c \right) d^{3} e +6 \left(4 a b c +\left(2 a c +b^{2}\right) b \right) d^{2} e^{2}+4 \left(a^{2} c +2 a \,b^{2}+\left(2 a c +b^{2}\right) a \right) d \,e^{3}\right) x^{6}}{6}+\frac{\left(a^{3} e^{4}+12 a^{2} b d \,e^{3}+\left(a \,c^{2}+2 b^{2} c +\left(2 a c +b^{2}\right) c \right) d^{4}+4 \left(4 a b c +\left(2 a c +b^{2}\right) b \right) d^{3} e +6 \left(a^{2} c +2 a \,b^{2}+\left(2 a c +b^{2}\right) a \right) d^{2} e^{2}\right) x^{5}}{5}+\frac{\left(4 a^{3} d \,e^{3}+18 a^{2} b \,d^{2} e^{2}+\left(4 a b c +\left(2 a c +b^{2}\right) b \right) d^{4}+4 \left(a^{2} c +2 a \,b^{2}+\left(2 a c +b^{2}\right) a \right) d^{3} e \right) x^{4}}{4}+\frac{\left(6 a^{3} d^{2} e^{2}+12 a^{2} b \,d^{3} e +\left(a^{2} c +2 a \,b^{2}+\left(2 a c +b^{2}\right) a \right) d^{4}\right) x^{3}}{3}+\frac{\left(4 d^{3} e \,a^{3}+3 d^{4} a^{2} b \right) x^{2}}{2}"," ",0,"1/11*c^3*e^4*x^11+1/10*(3*b*c^2*e^4+4*c^3*d*e^3)*x^10+1/9*(6*d^2*e^2*c^3+12*d*e^3*b*c^2+e^4*(a*c^2+2*b^2*c+c*(2*a*c+b^2)))*x^9+1/8*(4*d^3*e*c^3+18*d^2*e^2*b*c^2+4*d*e^3*(a*c^2+2*b^2*c+c*(2*a*c+b^2))+e^4*(4*a*b*c+b*(2*a*c+b^2)))*x^8+1/7*(d^4*c^3+12*d^3*e*b*c^2+6*d^2*e^2*(a*c^2+2*b^2*c+c*(2*a*c+b^2))+4*d*e^3*(4*a*b*c+b*(2*a*c+b^2))+e^4*(a*(2*a*c+b^2)+2*a*b^2+c*a^2))*x^7+1/6*(3*d^4*b*c^2+4*d^3*e*(a*c^2+2*b^2*c+c*(2*a*c+b^2))+6*d^2*e^2*(4*a*b*c+b*(2*a*c+b^2))+4*d*e^3*(a*(2*a*c+b^2)+2*a*b^2+c*a^2)+3*e^4*a^2*b)*x^6+1/5*(d^4*(a*c^2+2*b^2*c+c*(2*a*c+b^2))+4*d^3*e*(4*a*b*c+b*(2*a*c+b^2))+6*d^2*e^2*(a*(2*a*c+b^2)+2*a*b^2+c*a^2)+12*d*e^3*a^2*b+e^4*a^3)*x^5+1/4*(d^4*(4*a*b*c+b*(2*a*c+b^2))+4*d^3*e*(a*(2*a*c+b^2)+2*a*b^2+c*a^2)+18*d^2*e^2*a^2*b+4*d*e^3*a^3)*x^4+1/3*(d^4*(a*(2*a*c+b^2)+2*a*b^2+c*a^2)+12*d^3*e*a^2*b+6*d^2*e^2*a^3)*x^3+1/2*(4*a^3*d^3*e+3*a^2*b*d^4)*x^2+d^4*a^3*x","B"
2132,1,495,258,0.043000," ","int((e*x+d)^3*(c*x^2+b*x+a)^3,x)","\frac{c^{3} e^{3} x^{10}}{10}+\frac{\left(3 e^{3} b \,c^{2}+3 d \,e^{2} c^{3}\right) x^{9}}{9}+\frac{\left(9 b \,c^{2} d \,e^{2}+3 c^{3} d^{2} e +\left(a \,c^{2}+2 b^{2} c +\left(2 a c +b^{2}\right) c \right) e^{3}\right) x^{8}}{8}+a^{3} d^{3} x +\frac{\left(9 b \,c^{2} d^{2} e +c^{3} d^{3}+3 \left(a \,c^{2}+2 b^{2} c +\left(2 a c +b^{2}\right) c \right) d \,e^{2}+\left(4 a b c +\left(2 a c +b^{2}\right) b \right) e^{3}\right) x^{7}}{7}+\frac{\left(3 b \,c^{2} d^{3}+3 \left(a \,c^{2}+2 b^{2} c +\left(2 a c +b^{2}\right) c \right) d^{2} e +3 \left(4 a b c +\left(2 a c +b^{2}\right) b \right) d \,e^{2}+\left(a^{2} c +2 a \,b^{2}+\left(2 a c +b^{2}\right) a \right) e^{3}\right) x^{6}}{6}+\frac{\left(3 a^{2} b \,e^{3}+\left(a \,c^{2}+2 b^{2} c +\left(2 a c +b^{2}\right) c \right) d^{3}+3 \left(4 a b c +\left(2 a c +b^{2}\right) b \right) d^{2} e +3 \left(a^{2} c +2 a \,b^{2}+\left(2 a c +b^{2}\right) a \right) d \,e^{2}\right) x^{5}}{5}+\frac{\left(a^{3} e^{3}+9 a^{2} b d \,e^{2}+\left(4 a b c +\left(2 a c +b^{2}\right) b \right) d^{3}+3 \left(a^{2} c +2 a \,b^{2}+\left(2 a c +b^{2}\right) a \right) d^{2} e \right) x^{4}}{4}+\frac{\left(3 a^{3} d \,e^{2}+9 a^{2} b \,d^{2} e +\left(a^{2} c +2 a \,b^{2}+\left(2 a c +b^{2}\right) a \right) d^{3}\right) x^{3}}{3}+\frac{\left(3 d^{2} e \,a^{3}+3 d^{3} a^{2} b \right) x^{2}}{2}"," ",0,"1/10*c^3*e^3*x^10+1/9*(3*b*c^2*e^3+3*c^3*d*e^2)*x^9+1/8*(3*d^2*e*c^3+9*d*e^2*b*c^2+e^3*(a*c^2+2*b^2*c+(2*a*c+b^2)*c))*x^8+1/7*(c^3*d^3+9*b*c^2*d^2*e+3*d*e^2*(a*c^2+2*b^2*c+(2*a*c+b^2)*c)+e^3*(4*a*b*c+(2*a*c+b^2)*b))*x^7+1/6*(3*d^3*b*c^2+3*d^2*e*(a*c^2+2*b^2*c+(2*a*c+b^2)*c)+3*d*e^2*(4*a*b*c+(2*a*c+b^2)*b)+e^3*(a^2*c+2*a*b^2+(2*a*c+b^2)*a))*x^6+1/5*(d^3*(a*c^2+2*b^2*c+(2*a*c+b^2)*c)+3*d^2*e*(4*a*b*c+(2*a*c+b^2)*b)+3*d*e^2*(a^2*c+2*a*b^2+(2*a*c+b^2)*a)+3*e^3*a^2*b)*x^5+1/4*(d^3*(4*a*b*c+(2*a*c+b^2)*b)+3*d^2*e*(a^2*c+2*a*b^2+(2*a*c+b^2)*a)+9*a^2*b*d*e^2+a^3*e^3)*x^4+1/3*(d^3*(a^2*c+2*a*b^2+(2*a*c+b^2)*a)+9*d^2*e*a^2*b+3*d*e^2*a^3)*x^3+1/2*(3*a^3*d^2*e+3*a^2*b*d^3)*x^2+a^3*d^3*x","A"
2133,1,359,258,0.048000," ","int((e*x+d)^2*(c*x^2+b*x+a)^3,x)","\frac{c^{3} e^{2} x^{9}}{9}+\frac{\left(3 e^{2} b \,c^{2}+2 d e \,c^{3}\right) x^{8}}{8}+\frac{\left(6 b \,c^{2} d e +c^{3} d^{2}+\left(a \,c^{2}+2 b^{2} c +\left(2 a c +b^{2}\right) c \right) e^{2}\right) x^{7}}{7}+a^{3} d^{2} x +\frac{\left(3 b \,c^{2} d^{2}+2 \left(a \,c^{2}+2 b^{2} c +\left(2 a c +b^{2}\right) c \right) d e +\left(4 a b c +\left(2 a c +b^{2}\right) b \right) e^{2}\right) x^{6}}{6}+\frac{\left(\left(a \,c^{2}+2 b^{2} c +\left(2 a c +b^{2}\right) c \right) d^{2}+2 \left(4 a b c +\left(2 a c +b^{2}\right) b \right) d e +\left(a^{2} c +2 a \,b^{2}+\left(2 a c +b^{2}\right) a \right) e^{2}\right) x^{5}}{5}+\frac{\left(3 a^{2} b \,e^{2}+\left(4 a b c +\left(2 a c +b^{2}\right) b \right) d^{2}+2 \left(a^{2} c +2 a \,b^{2}+\left(2 a c +b^{2}\right) a \right) d e \right) x^{4}}{4}+\frac{\left(a^{3} e^{2}+6 a^{2} b d e +\left(a^{2} c +2 a \,b^{2}+\left(2 a c +b^{2}\right) a \right) d^{2}\right) x^{3}}{3}+\frac{\left(2 d e \,a^{3}+3 d^{2} a^{2} b \right) x^{2}}{2}"," ",0,"1/9*c^3*e^2*x^9+1/8*(3*b*c^2*e^2+2*c^3*d*e)*x^8+1/7*(c^3*d^2+6*d*e*b*c^2+e^2*(a*c^2+2*b^2*c+(2*a*c+b^2)*c))*x^7+1/6*(3*b*c^2*d^2+2*d*e*(a*c^2+2*b^2*c+(2*a*c+b^2)*c)+e^2*(4*a*b*c+(2*a*c+b^2)*b))*x^6+1/5*(d^2*(a*c^2+2*b^2*c+(2*a*c+b^2)*c)+2*d*e*(4*a*b*c+(2*a*c+b^2)*b)+e^2*(a^2*c+2*a*b^2+(2*a*c+b^2)*a))*x^5+1/4*(d^2*(4*a*b*c+(2*a*c+b^2)*b)+2*d*e*(a^2*c+2*a*b^2+(2*a*c+b^2)*a)+3*a^2*b*e^2)*x^4+1/3*(d^2*(a^2*c+2*a*b^2+(2*a*c+b^2)*a)+6*d*e*a^2*b+a^3*e^2)*x^3+1/2*(2*a^3*d*e+3*a^2*b*d^2)*x^2+a^3*d^2*x","A"
2134,1,223,149,0.042000," ","int((e*x+d)*(c*x^2+b*x+a)^3,x)","\frac{c^{3} e \,x^{8}}{8}+\frac{\left(3 e b \,c^{2}+c^{3} d \right) x^{7}}{7}+\frac{\left(3 b \,c^{2} d +\left(a \,c^{2}+2 b^{2} c +\left(2 a c +b^{2}\right) c \right) e \right) x^{6}}{6}+a^{3} d x +\frac{\left(\left(a \,c^{2}+2 b^{2} c +\left(2 a c +b^{2}\right) c \right) d +\left(4 a b c +\left(2 a c +b^{2}\right) b \right) e \right) x^{5}}{5}+\frac{\left(\left(4 a b c +\left(2 a c +b^{2}\right) b \right) d +\left(a^{2} c +2 a \,b^{2}+\left(2 a c +b^{2}\right) a \right) e \right) x^{4}}{4}+\frac{\left(3 a^{2} b e +\left(a^{2} c +2 a \,b^{2}+\left(2 a c +b^{2}\right) a \right) d \right) x^{3}}{3}+\frac{\left(a^{3} e +3 a^{2} b d \right) x^{2}}{2}"," ",0,"1/8*c^3*e*x^8+1/7*(3*b*c^2*e+c^3*d)*x^7+1/6*(3*b*c^2*d+e*(a*c^2+2*b^2*c+(2*a*c+b^2)*c))*x^6+1/5*(d*(a*c^2+2*b^2*c+(2*a*c+b^2)*c)+e*(4*a*b*c+(2*a*c+b^2)*b))*x^5+1/4*(d*(4*a*b*c+(2*a*c+b^2)*b)+e*(a^2*c+2*a*b^2+(2*a*c+b^2)*a))*x^4+1/3*(d*(a^2*c+2*a*b^2+(2*a*c+b^2)*a)+3*e*a^2*b)*x^3+1/2*(a^3*e+3*a^2*b*d)*x^2+a^3*d*x","A"
2135,1,108,71,0.045000," ","int((c*x^2+b*x+a)^3,x)","\frac{c^{3} x^{7}}{7}+\frac{b \,c^{2} x^{6}}{2}+\frac{3 a^{2} b \,x^{2}}{2}+\frac{\left(a \,c^{2}+2 b^{2} c +\left(2 a c +b^{2}\right) c \right) x^{5}}{5}+a^{3} x +\frac{\left(4 a b c +\left(2 a c +b^{2}\right) b \right) x^{4}}{4}+\frac{\left(a^{2} c +2 a \,b^{2}+\left(2 a c +b^{2}\right) a \right) x^{3}}{3}"," ",0,"1/7*c^3*x^7+1/2*b*c^2*x^6+1/5*(a*c^2+2*b^2*c+(2*a*c+b^2)*c)*x^5+1/4*(4*a*b*c+(2*a*c+b^2)*b)*x^4+1/3*(a^2*c+2*a*b^2+(2*a*c+b^2)*a)*x^3+3/2*a^2*b*x^2+a^3*x","A"
2136,1,546,250,0.044000," ","int((c*x^2+b*x+a)^3/(e*x+d),x)","\frac{c^{3} x^{6}}{6 e}+\frac{3 b \,c^{2} x^{5}}{5 e}-\frac{c^{3} d \,x^{5}}{5 e^{2}}+\frac{3 a \,c^{2} x^{4}}{4 e}+\frac{3 b^{2} c \,x^{4}}{4 e}-\frac{3 b \,c^{2} d \,x^{4}}{4 e^{2}}+\frac{c^{3} d^{2} x^{4}}{4 e^{3}}+\frac{2 a b c \,x^{3}}{e}-\frac{a \,c^{2} d \,x^{3}}{e^{2}}+\frac{b^{3} x^{3}}{3 e}-\frac{b^{2} c d \,x^{3}}{e^{2}}+\frac{b \,c^{2} d^{2} x^{3}}{e^{3}}-\frac{c^{3} d^{3} x^{3}}{3 e^{4}}+\frac{3 a^{2} c \,x^{2}}{2 e}+\frac{3 a \,b^{2} x^{2}}{2 e}-\frac{3 a b c d \,x^{2}}{e^{2}}+\frac{3 a \,c^{2} d^{2} x^{2}}{2 e^{3}}-\frac{b^{3} d \,x^{2}}{2 e^{2}}+\frac{3 b^{2} c \,d^{2} x^{2}}{2 e^{3}}-\frac{3 b \,c^{2} d^{3} x^{2}}{2 e^{4}}+\frac{c^{3} d^{4} x^{2}}{2 e^{5}}+\frac{a^{3} \ln \left(e x +d \right)}{e}-\frac{3 a^{2} b d \ln \left(e x +d \right)}{e^{2}}+\frac{3 a^{2} b x}{e}+\frac{3 a^{2} c \,d^{2} \ln \left(e x +d \right)}{e^{3}}-\frac{3 a^{2} c d x}{e^{2}}+\frac{3 a \,b^{2} d^{2} \ln \left(e x +d \right)}{e^{3}}-\frac{3 a \,b^{2} d x}{e^{2}}-\frac{6 a b c \,d^{3} \ln \left(e x +d \right)}{e^{4}}+\frac{6 a b c \,d^{2} x}{e^{3}}+\frac{3 a \,c^{2} d^{4} \ln \left(e x +d \right)}{e^{5}}-\frac{3 a \,c^{2} d^{3} x}{e^{4}}-\frac{b^{3} d^{3} \ln \left(e x +d \right)}{e^{4}}+\frac{b^{3} d^{2} x}{e^{3}}+\frac{3 b^{2} c \,d^{4} \ln \left(e x +d \right)}{e^{5}}-\frac{3 b^{2} c \,d^{3} x}{e^{4}}-\frac{3 b \,c^{2} d^{5} \ln \left(e x +d \right)}{e^{6}}+\frac{3 b \,c^{2} d^{4} x}{e^{5}}+\frac{c^{3} d^{6} \ln \left(e x +d \right)}{e^{7}}-\frac{c^{3} d^{5} x}{e^{6}}"," ",0,"2/e*x^3*a*b*c-1/e^2*x^3*a*c^2*d-3/e^2*x^2*a*b*c*d-6/e^4*ln(e*x+d)*a*b*c*d^3+6/e^3*x*a*b*c*d^2+1/2/e^5*x^2*c^3*d^4-1/2/e^2*x^2*b^3*d+3/2/e*x^2*a*b^2-1/3/e^4*x^3*c^3*d^3+3/2/e*x^2*a^2*c+3/5/e*x^5*b*c^2+3/4/e*x^4*a*c^2+3/e*x*a^2*b+1/e^3*x*b^3*d^2-1/e^6*x*c^3*d^5+3/4/e*x^4*b^2*c+1/4/e^3*x^4*c^3*d^2-1/e^4*ln(e*x+d)*b^3*d^3+1/e^7*ln(e*x+d)*c^3*d^6-3/e^4*x*a*c^2*d^3-3/e^4*x*b^2*c*d^3+1/e*ln(e*x+d)*a^3+1/3/e*x^3*b^3+3/e^3*ln(e*x+d)*a*b^2*d^2-3/e^6*ln(e*x+d)*b*c^2*d^5+3/e^5*x*b*c^2*d^4+3/e^3*ln(e*x+d)*a^2*c*d^2+3/2/e^3*x^2*b^2*c*d^2-3/2/e^4*x^2*b*c^2*d^3+1/e^3*x^3*b*c^2*d^2-3/4/e^2*x^4*b*c^2*d-3/e^2*x*a^2*c*d+3/e^5*ln(e*x+d)*a*c^2*d^4-3/e^2*x*a*b^2*d+3/e^5*ln(e*x+d)*b^2*c*d^4-3/e^2*ln(e*x+d)*a^2*b*d-1/e^2*x^3*b^2*c*d+3/2/e^3*x^2*a*c^2*d^2+1/6*c^3/e*x^6-1/5*c^3*d/e^2*x^5","B"
2137,1,585,250,0.070000," ","int((c*x^2+b*x+a)^3/(e*x+d)^2,x)","\frac{c^{3} x^{5}}{5 e^{2}}+\frac{3 b \,c^{2} x^{4}}{4 e^{2}}-\frac{c^{3} d \,x^{4}}{2 e^{3}}+\frac{a \,c^{2} x^{3}}{e^{2}}+\frac{b^{2} c \,x^{3}}{e^{2}}-\frac{2 b \,c^{2} d \,x^{3}}{e^{3}}+\frac{c^{3} d^{2} x^{3}}{e^{4}}+\frac{3 a b c \,x^{2}}{e^{2}}-\frac{3 a \,c^{2} d \,x^{2}}{e^{3}}+\frac{b^{3} x^{2}}{2 e^{2}}-\frac{3 b^{2} c d \,x^{2}}{e^{3}}+\frac{9 b \,c^{2} d^{2} x^{2}}{2 e^{4}}-\frac{2 c^{3} d^{3} x^{2}}{e^{5}}-\frac{a^{3}}{\left(e x +d \right) e}+\frac{3 a^{2} b d}{\left(e x +d \right) e^{2}}+\frac{3 a^{2} b \ln \left(e x +d \right)}{e^{2}}-\frac{3 a^{2} c \,d^{2}}{\left(e x +d \right) e^{3}}-\frac{6 a^{2} c d \ln \left(e x +d \right)}{e^{3}}+\frac{3 a^{2} c x}{e^{2}}-\frac{3 a \,b^{2} d^{2}}{\left(e x +d \right) e^{3}}-\frac{6 a \,b^{2} d \ln \left(e x +d \right)}{e^{3}}+\frac{3 a \,b^{2} x}{e^{2}}+\frac{6 a b c \,d^{3}}{\left(e x +d \right) e^{4}}+\frac{18 a b c \,d^{2} \ln \left(e x +d \right)}{e^{4}}-\frac{12 a b c d x}{e^{3}}-\frac{3 a \,c^{2} d^{4}}{\left(e x +d \right) e^{5}}-\frac{12 a \,c^{2} d^{3} \ln \left(e x +d \right)}{e^{5}}+\frac{9 a \,c^{2} d^{2} x}{e^{4}}+\frac{b^{3} d^{3}}{\left(e x +d \right) e^{4}}+\frac{3 b^{3} d^{2} \ln \left(e x +d \right)}{e^{4}}-\frac{2 b^{3} d x}{e^{3}}-\frac{3 b^{2} c \,d^{4}}{\left(e x +d \right) e^{5}}-\frac{12 b^{2} c \,d^{3} \ln \left(e x +d \right)}{e^{5}}+\frac{9 b^{2} c \,d^{2} x}{e^{4}}+\frac{3 b \,c^{2} d^{5}}{\left(e x +d \right) e^{6}}+\frac{15 b \,c^{2} d^{4} \ln \left(e x +d \right)}{e^{6}}-\frac{12 b \,c^{2} d^{3} x}{e^{5}}-\frac{c^{3} d^{6}}{\left(e x +d \right) e^{7}}-\frac{6 c^{3} d^{5} \ln \left(e x +d \right)}{e^{7}}+\frac{5 c^{3} d^{4} x}{e^{6}}"," ",0,"6/e^4/(e*x+d)*a*b*c*d^3-12/e^3*a*b*c*d*x+18/e^4*ln(e*x+d)*a*b*c*d^2+1/e^2*x^3*a*c^2+3/e^2*ln(e*x+d)*a^2*b+3/e^2*a^2*c*x+3/e^2*a*b^2*x-1/(e*x+d)*c^3*d^6/e^7+3*b^3*d^2/e^4*ln(e*x+d)-6*c^3*d^5/e^7*ln(e*x+d)+b^2*c/e^2*x^3+c^3*d^2/e^4*x^3-2*c^3*d^3/e^5*x^2-2*b^3*d/e^3*x+5*c^3*d^4/e^6*x+1/(e*x+d)*b^3*d^3/e^4+3/4*b*c^2/e^2*x^4+1/2*b^3/e^2*x^2-1/e/(e*x+d)*a^3+3/e^2*x^2*a*b*c-6/e^3*ln(e*x+d)*a*b^2*d-12/e^5*ln(e*x+d)*a*c^2*d^3-3/e^3*x^2*a*c^2*d-2*b*c^2*d/e^3*x^3-3*b^2*c*d/e^3*x^2+9/2*b*c^2*d^2/e^4*x^2+9*b^2*c*d^2/e^4*x-12*b*c^2*d^3/e^5*x-3/(e*x+d)*b^2*c*d^4/e^5+3/(e*x+d)*b*c^2*d^5/e^6-12*b^2*c*d^3/e^5*ln(e*x+d)+15*b*c^2*d^4/e^6*ln(e*x+d)+9/e^4*a*c^2*d^2*x-6/e^3*ln(e*x+d)*a^2*c*d-3/e^5/(e*x+d)*a*c^2*d^4+3/e^2/(e*x+d)*d*a^2*b-3/e^3/(e*x+d)*a^2*c*d^2-3/e^3/(e*x+d)*a*b^2*d^2+1/5*c^3/e^2*x^5-1/2*c^3*d/e^3*x^4","B"
2138,1,624,249,0.057000," ","int((c*x^2+b*x+a)^3/(e*x+d)^3,x)","\frac{c^{3} x^{4}}{4 e^{3}}+\frac{b \,c^{2} x^{3}}{e^{3}}-\frac{c^{3} d \,x^{3}}{e^{4}}-\frac{a^{3}}{2 \left(e x +d \right)^{2} e}+\frac{3 a^{2} b d}{2 \left(e x +d \right)^{2} e^{2}}-\frac{3 a^{2} c \,d^{2}}{2 \left(e x +d \right)^{2} e^{3}}-\frac{3 a \,b^{2} d^{2}}{2 \left(e x +d \right)^{2} e^{3}}+\frac{3 a b c \,d^{3}}{\left(e x +d \right)^{2} e^{4}}-\frac{3 a \,c^{2} d^{4}}{2 \left(e x +d \right)^{2} e^{5}}+\frac{3 a \,c^{2} x^{2}}{2 e^{3}}+\frac{b^{3} d^{3}}{2 \left(e x +d \right)^{2} e^{4}}-\frac{3 b^{2} c \,d^{4}}{2 \left(e x +d \right)^{2} e^{5}}+\frac{3 b^{2} c \,x^{2}}{2 e^{3}}+\frac{3 b \,c^{2} d^{5}}{2 \left(e x +d \right)^{2} e^{6}}-\frac{9 b \,c^{2} d \,x^{2}}{2 e^{4}}-\frac{c^{3} d^{6}}{2 \left(e x +d \right)^{2} e^{7}}+\frac{3 c^{3} d^{2} x^{2}}{e^{5}}-\frac{3 a^{2} b}{\left(e x +d \right) e^{2}}+\frac{6 a^{2} c d}{\left(e x +d \right) e^{3}}+\frac{3 a^{2} c \ln \left(e x +d \right)}{e^{3}}+\frac{6 a \,b^{2} d}{\left(e x +d \right) e^{3}}+\frac{3 a \,b^{2} \ln \left(e x +d \right)}{e^{3}}-\frac{18 a b c \,d^{2}}{\left(e x +d \right) e^{4}}-\frac{18 a b c d \ln \left(e x +d \right)}{e^{4}}+\frac{6 a b c x}{e^{3}}+\frac{12 a \,c^{2} d^{3}}{\left(e x +d \right) e^{5}}+\frac{18 a \,c^{2} d^{2} \ln \left(e x +d \right)}{e^{5}}-\frac{9 a \,c^{2} d x}{e^{4}}-\frac{3 b^{3} d^{2}}{\left(e x +d \right) e^{4}}-\frac{3 b^{3} d \ln \left(e x +d \right)}{e^{4}}+\frac{b^{3} x}{e^{3}}+\frac{12 b^{2} c \,d^{3}}{\left(e x +d \right) e^{5}}+\frac{18 b^{2} c \,d^{2} \ln \left(e x +d \right)}{e^{5}}-\frac{9 b^{2} c d x}{e^{4}}-\frac{15 b \,c^{2} d^{4}}{\left(e x +d \right) e^{6}}-\frac{30 b \,c^{2} d^{3} \ln \left(e x +d \right)}{e^{6}}+\frac{18 b \,c^{2} d^{2} x}{e^{5}}+\frac{6 c^{3} d^{5}}{\left(e x +d \right) e^{7}}+\frac{15 c^{3} d^{4} \ln \left(e x +d \right)}{e^{7}}-\frac{10 c^{3} d^{3} x}{e^{6}}"," ",0,"3/e^4/(e*x+d)^2*a*b*c*d^3-18/e^4*ln(e*x+d)*a*b*c*d-18/e^4/(e*x+d)*a*b*c*d^2+3/e^3*ln(e*x+d)*a*b^2-3/e^4*ln(e*x+d)*b^3*d+15/e^7*ln(e*x+d)*c^3*d^4-10/e^6*c^3*d^3*x-3/e^2/(e*x+d)*a^2*b-3/e^4/(e*x+d)*b^3*d^2+6/e^7/(e*x+d)*c^3*d^5+1/2/e^4/(e*x+d)^2*b^3*d^3-1/2/e^7/(e*x+d)^2*c^3*d^6+1/e^3*x^3*b*c^2+3/2/e^3*x^2*a*c^2+3/2/e^3*x^2*b^2*c+3/e^5*x^2*c^3*d^2+3/e^3*ln(e*x+d)*a^2*c-9/2/e^4*x^2*b*c^2*d+1/e^3*b^3*x-1/2/e/(e*x+d)^2*a^3+6/e^3*a*b*c*x-9/e^4*c^2*a*d*x-9/e^4*b^2*c*d*x+18/e^5*b*c^2*d^2*x+6/e^3/(e*x+d)*a^2*c*d+6/e^3/(e*x+d)*a*b^2*d+12/e^5/(e*x+d)*a*c^2*d^3-30/e^6*ln(e*x+d)*b*c^2*d^3+12/e^5/(e*x+d)*b^2*c*d^3-15/e^6/(e*x+d)*b*c^2*d^4+3/2/e^2/(e*x+d)^2*d*a^2*b-3/2/e^3/(e*x+d)^2*a^2*c*d^2-3/2/e^3/(e*x+d)^2*d^2*a*b^2-3/2/e^5/(e*x+d)^2*a*c^2*d^4-3/2/e^5/(e*x+d)^2*b^2*c*d^4+3/2/e^6/(e*x+d)^2*b*c^2*d^5+18/e^5*ln(e*x+d)*a*c^2*d^2+18/e^5*ln(e*x+d)*b^2*c*d^2+1/4*c^3/e^3*x^4-c^3*d/e^4*x^3","B"
2139,1,653,243,0.065000," ","int((c*x^2+b*x+a)^3/(e*x+d)^4,x)","-\frac{a^{3}}{3 \left(e x +d \right)^{3} e}+\frac{a^{2} b d}{\left(e x +d \right)^{3} e^{2}}-\frac{a^{2} c \,d^{2}}{\left(e x +d \right)^{3} e^{3}}-\frac{a \,b^{2} d^{2}}{\left(e x +d \right)^{3} e^{3}}+\frac{2 a b c \,d^{3}}{\left(e x +d \right)^{3} e^{4}}-\frac{a \,c^{2} d^{4}}{\left(e x +d \right)^{3} e^{5}}+\frac{b^{3} d^{3}}{3 \left(e x +d \right)^{3} e^{4}}-\frac{b^{2} c \,d^{4}}{\left(e x +d \right)^{3} e^{5}}+\frac{b \,c^{2} d^{5}}{\left(e x +d \right)^{3} e^{6}}-\frac{c^{3} d^{6}}{3 \left(e x +d \right)^{3} e^{7}}+\frac{c^{3} x^{3}}{3 e^{4}}-\frac{3 a^{2} b}{2 \left(e x +d \right)^{2} e^{2}}+\frac{3 a^{2} c d}{\left(e x +d \right)^{2} e^{3}}+\frac{3 a \,b^{2} d}{\left(e x +d \right)^{2} e^{3}}-\frac{9 a b c \,d^{2}}{\left(e x +d \right)^{2} e^{4}}+\frac{6 a \,c^{2} d^{3}}{\left(e x +d \right)^{2} e^{5}}-\frac{3 b^{3} d^{2}}{2 \left(e x +d \right)^{2} e^{4}}+\frac{6 b^{2} c \,d^{3}}{\left(e x +d \right)^{2} e^{5}}-\frac{15 b \,c^{2} d^{4}}{2 \left(e x +d \right)^{2} e^{6}}+\frac{3 b \,c^{2} x^{2}}{2 e^{4}}+\frac{3 c^{3} d^{5}}{\left(e x +d \right)^{2} e^{7}}-\frac{2 c^{3} d \,x^{2}}{e^{5}}-\frac{3 a^{2} c}{\left(e x +d \right) e^{3}}-\frac{3 a \,b^{2}}{\left(e x +d \right) e^{3}}+\frac{18 a b c d}{\left(e x +d \right) e^{4}}+\frac{6 a b c \ln \left(e x +d \right)}{e^{4}}-\frac{18 a \,c^{2} d^{2}}{\left(e x +d \right) e^{5}}-\frac{12 a \,c^{2} d \ln \left(e x +d \right)}{e^{5}}+\frac{3 a \,c^{2} x}{e^{4}}+\frac{3 b^{3} d}{\left(e x +d \right) e^{4}}+\frac{b^{3} \ln \left(e x +d \right)}{e^{4}}-\frac{18 b^{2} c \,d^{2}}{\left(e x +d \right) e^{5}}-\frac{12 b^{2} c d \ln \left(e x +d \right)}{e^{5}}+\frac{3 b^{2} c x}{e^{4}}+\frac{30 b \,c^{2} d^{3}}{\left(e x +d \right) e^{6}}+\frac{30 b \,c^{2} d^{2} \ln \left(e x +d \right)}{e^{6}}-\frac{12 b \,c^{2} d x}{e^{5}}-\frac{15 c^{3} d^{4}}{\left(e x +d \right) e^{7}}-\frac{20 c^{3} d^{3} \ln \left(e x +d \right)}{e^{7}}+\frac{10 c^{3} d^{2} x}{e^{6}}"," ",0,"-12/e^5*ln(e*x+d)*b^2*c*d+30/e^6*ln(e*x+d)*b*c^2*d^2-12*c^2/e^5*b*d*x+3/e^3/(e*x+d)^2*a^2*c*d+3/e^3/(e*x+d)^2*a*b^2*d+6/e^5/(e*x+d)^2*a*c^2*d^3+6/e^5/(e*x+d)^2*b^2*c*d^3-15/2/e^6/(e*x+d)^2*b*c^2*d^4+1/e^2/(e*x+d)^3*d*a^2*b-1/e^3/(e*x+d)^3*a^2*c*d^2-1/e^3/(e*x+d)^3*d^2*a*b^2-1/e^5/(e*x+d)^3*a*c^2*d^4-1/e^5/(e*x+d)^3*b^2*c*d^4+18/e^4/(e*x+d)*a*b*c*d-9/e^4/(e*x+d)^2*a*b*c*d^2+2/e^4/(e*x+d)^3*d^3*a*b*c-12/e^5*ln(e*x+d)*c^2*a*d-15/e^7/(e*x+d)*c^3*d^4+10*c^3/e^6*d^2*x-3/e^3/(e*x+d)*a^2*c-3/e^3/(e*x+d)*a*b^2+3/e^4/(e*x+d)*b^3*d-3/2/e^2/(e*x+d)^2*a^2*b-3/2/e^4/(e*x+d)^2*b^3*d^2+3/e^7/(e*x+d)^2*c^3*d^5+1/3/e^4/(e*x+d)^3*d^3*b^3-1/3/e^7/(e*x+d)^3*c^3*d^6+3/2*c^2/e^4*x^2*b+3*c^2/e^4*a*x+3*c/e^4*b^2*x-20/e^7*ln(e*x+d)*c^3*d^3+1/e^6/(e*x+d)^3*b*c^2*d^5-18/e^5/(e*x+d)*a*c^2*d^2-18/e^5/(e*x+d)*b^2*c*d^2+30/e^6/(e*x+d)*b*c^2*d^3-1/3/e/(e*x+d)^3*a^3+1/e^4*ln(e*x+d)*b^3+6/e^4*ln(e*x+d)*a*b*c+1/3*c^3/e^4*x^3-2*c^3*d/e^5*x^2","B"
2140,1,678,245,0.052000," ","int((c*x^2+b*x+a)^3/(e*x+d)^5,x)","-\frac{a^{3}}{4 \left(e x +d \right)^{4} e}+\frac{3 a^{2} b d}{4 \left(e x +d \right)^{4} e^{2}}-\frac{3 a^{2} c \,d^{2}}{4 \left(e x +d \right)^{4} e^{3}}-\frac{3 a \,b^{2} d^{2}}{4 \left(e x +d \right)^{4} e^{3}}+\frac{3 a b c \,d^{3}}{2 \left(e x +d \right)^{4} e^{4}}-\frac{3 a \,c^{2} d^{4}}{4 \left(e x +d \right)^{4} e^{5}}+\frac{b^{3} d^{3}}{4 \left(e x +d \right)^{4} e^{4}}-\frac{3 b^{2} c \,d^{4}}{4 \left(e x +d \right)^{4} e^{5}}+\frac{3 b \,c^{2} d^{5}}{4 \left(e x +d \right)^{4} e^{6}}-\frac{c^{3} d^{6}}{4 \left(e x +d \right)^{4} e^{7}}-\frac{a^{2} b}{\left(e x +d \right)^{3} e^{2}}+\frac{2 a^{2} c d}{\left(e x +d \right)^{3} e^{3}}+\frac{2 a \,b^{2} d}{\left(e x +d \right)^{3} e^{3}}-\frac{6 a b c \,d^{2}}{\left(e x +d \right)^{3} e^{4}}+\frac{4 a \,c^{2} d^{3}}{\left(e x +d \right)^{3} e^{5}}-\frac{b^{3} d^{2}}{\left(e x +d \right)^{3} e^{4}}+\frac{4 b^{2} c \,d^{3}}{\left(e x +d \right)^{3} e^{5}}-\frac{5 b \,c^{2} d^{4}}{\left(e x +d \right)^{3} e^{6}}+\frac{2 c^{3} d^{5}}{\left(e x +d \right)^{3} e^{7}}-\frac{3 a^{2} c}{2 \left(e x +d \right)^{2} e^{3}}-\frac{3 a \,b^{2}}{2 \left(e x +d \right)^{2} e^{3}}+\frac{9 a b c d}{\left(e x +d \right)^{2} e^{4}}-\frac{9 a \,c^{2} d^{2}}{\left(e x +d \right)^{2} e^{5}}+\frac{3 b^{3} d}{2 \left(e x +d \right)^{2} e^{4}}-\frac{9 b^{2} c \,d^{2}}{\left(e x +d \right)^{2} e^{5}}+\frac{15 b \,c^{2} d^{3}}{\left(e x +d \right)^{2} e^{6}}-\frac{15 c^{3} d^{4}}{2 \left(e x +d \right)^{2} e^{7}}+\frac{c^{3} x^{2}}{2 e^{5}}-\frac{6 a b c}{\left(e x +d \right) e^{4}}+\frac{12 a \,c^{2} d}{\left(e x +d \right) e^{5}}+\frac{3 a \,c^{2} \ln \left(e x +d \right)}{e^{5}}-\frac{b^{3}}{\left(e x +d \right) e^{4}}+\frac{12 b^{2} c d}{\left(e x +d \right) e^{5}}+\frac{3 b^{2} c \ln \left(e x +d \right)}{e^{5}}-\frac{30 b \,c^{2} d^{2}}{\left(e x +d \right) e^{6}}-\frac{15 b \,c^{2} d \ln \left(e x +d \right)}{e^{6}}+\frac{3 b \,c^{2} x}{e^{5}}+\frac{20 c^{3} d^{3}}{\left(e x +d \right) e^{7}}+\frac{15 c^{3} d^{2} \ln \left(e x +d \right)}{e^{7}}-\frac{5 c^{3} d x}{e^{6}}"," ",0,"-3/4/e^5/(e*x+d)^4*d^4*b^2*c+3/4/e^6/(e*x+d)^4*b*c^2*d^5+12/e^5/(e*x+d)*b^2*c*d-30/e^6/(e*x+d)*b*c^2*d^2-6/e^4/(e*x+d)^3*a*b*c*d^2+3/2/e^4/(e*x+d)^4*d^3*a*b*c+9/e^4/(e*x+d)^2*a*b*c*d-6/e^4/(e*x+d)*a*b*c+12/e^5/(e*x+d)*c^2*a*d-15*c^2/e^6*ln(e*x+d)*b*d+4/e^5/(e*x+d)^3*b^2*c*d^3+3*c/e^5*ln(e*x+d)*b^2+3*c^2/e^5*ln(e*x+d)*a-3/2/e^3/(e*x+d)^2*a*b^2+3/2/e^4/(e*x+d)^2*b^3*d-15/2/e^7/(e*x+d)^2*c^3*d^4+3*c^2/e^5*x*b+20/e^7/(e*x+d)*c^3*d^3+15*c^3/e^7*ln(e*x+d)*d^2+1/4/e^4/(e*x+d)^4*d^3*b^3-1/4/e^7/(e*x+d)^4*c^3*d^6-1/e^2/(e*x+d)^3*a^2*b-1/e^4/(e*x+d)^3*b^3*d^2+2/e^7/(e*x+d)^3*c^3*d^5-3/2/e^3/(e*x+d)^2*a^2*c-5/e^6/(e*x+d)^3*b*c^2*d^4+3/4/e^2/(e*x+d)^4*d*a^2*b-3/4/e^3/(e*x+d)^4*a^2*c*d^2-1/4/e/(e*x+d)^4*a^3-1/e^4/(e*x+d)*b^3+1/2*c^3/e^5*x^2+2/e^3/(e*x+d)^3*a^2*c*d+2/e^3/(e*x+d)^3*a*b^2*d+4/e^5/(e*x+d)^3*a*c^2*d^3-3/4/e^3/(e*x+d)^4*d^2*a*b^2-3/4/e^5/(e*x+d)^4*a*c^2*d^4-9/e^5/(e*x+d)^2*a*c^2*d^2-9/e^5/(e*x+d)^2*b^2*c*d^2+15/e^6/(e*x+d)^2*b*c^2*d^3-5*c^3*d/e^6*x","B"
2141,1,688,250,0.059000," ","int((c*x^2+b*x+a)^3/(e*x+d)^6,x)","-\frac{a^{3}}{5 \left(e x +d \right)^{5} e}+\frac{3 a^{2} b d}{5 \left(e x +d \right)^{5} e^{2}}-\frac{3 a^{2} c \,d^{2}}{5 \left(e x +d \right)^{5} e^{3}}-\frac{3 a \,b^{2} d^{2}}{5 \left(e x +d \right)^{5} e^{3}}+\frac{6 a b c \,d^{3}}{5 \left(e x +d \right)^{5} e^{4}}-\frac{3 a \,c^{2} d^{4}}{5 \left(e x +d \right)^{5} e^{5}}+\frac{b^{3} d^{3}}{5 \left(e x +d \right)^{5} e^{4}}-\frac{3 b^{2} c \,d^{4}}{5 \left(e x +d \right)^{5} e^{5}}+\frac{3 b \,c^{2} d^{5}}{5 \left(e x +d \right)^{5} e^{6}}-\frac{c^{3} d^{6}}{5 \left(e x +d \right)^{5} e^{7}}-\frac{3 a^{2} b}{4 \left(e x +d \right)^{4} e^{2}}+\frac{3 a^{2} c d}{2 \left(e x +d \right)^{4} e^{3}}+\frac{3 a \,b^{2} d}{2 \left(e x +d \right)^{4} e^{3}}-\frac{9 a b c \,d^{2}}{2 \left(e x +d \right)^{4} e^{4}}+\frac{3 a \,c^{2} d^{3}}{\left(e x +d \right)^{4} e^{5}}-\frac{3 b^{3} d^{2}}{4 \left(e x +d \right)^{4} e^{4}}+\frac{3 b^{2} c \,d^{3}}{\left(e x +d \right)^{4} e^{5}}-\frac{15 b \,c^{2} d^{4}}{4 \left(e x +d \right)^{4} e^{6}}+\frac{3 c^{3} d^{5}}{2 \left(e x +d \right)^{4} e^{7}}-\frac{a^{2} c}{\left(e x +d \right)^{3} e^{3}}-\frac{a \,b^{2}}{\left(e x +d \right)^{3} e^{3}}+\frac{6 a b c d}{\left(e x +d \right)^{3} e^{4}}-\frac{6 a \,c^{2} d^{2}}{\left(e x +d \right)^{3} e^{5}}+\frac{b^{3} d}{\left(e x +d \right)^{3} e^{4}}-\frac{6 b^{2} c \,d^{2}}{\left(e x +d \right)^{3} e^{5}}+\frac{10 b \,c^{2} d^{3}}{\left(e x +d \right)^{3} e^{6}}-\frac{5 c^{3} d^{4}}{\left(e x +d \right)^{3} e^{7}}-\frac{3 a b c}{\left(e x +d \right)^{2} e^{4}}+\frac{6 a \,c^{2} d}{\left(e x +d \right)^{2} e^{5}}-\frac{b^{3}}{2 \left(e x +d \right)^{2} e^{4}}+\frac{6 b^{2} c d}{\left(e x +d \right)^{2} e^{5}}-\frac{15 b \,c^{2} d^{2}}{\left(e x +d \right)^{2} e^{6}}+\frac{10 c^{3} d^{3}}{\left(e x +d \right)^{2} e^{7}}-\frac{3 a \,c^{2}}{\left(e x +d \right) e^{5}}-\frac{3 b^{2} c}{\left(e x +d \right) e^{5}}+\frac{15 b \,c^{2} d}{\left(e x +d \right) e^{6}}+\frac{3 b \,c^{2} \ln \left(e x +d \right)}{e^{6}}-\frac{15 c^{3} d^{2}}{\left(e x +d \right) e^{7}}-\frac{6 c^{3} d \ln \left(e x +d \right)}{e^{7}}+\frac{c^{3} x}{e^{6}}"," ",0,"-5/e^7/(e*x+d)^3*c^3*d^4-1/e^3/(e*x+d)^3*a^2*c-1/e^3/(e*x+d)^3*a*b^2+1/e^4/(e*x+d)^3*b^3*d-3*c/e^5/(e*x+d)*b^2-15*c^3/e^7/(e*x+d)*d^2+1/5/e^4/(e*x+d)^5*d^3*b^3+3/2/e^7/(e*x+d)^4*c^3*d^5-3/4/e^4/(e*x+d)^4*b^3*d^2+3*c^2/e^6*ln(e*x+d)*b-3/4/e^2/(e*x+d)^4*a^2*b-3/5/e^3/(e*x+d)^5*a^2*c*d^2-6/e^5/(e*x+d)^3*b^2*c*d^2+10/e^6/(e*x+d)^3*b*c^2*d^3+3/2/e^3/(e*x+d)^4*a^2*c*d+3/2/e^3/(e*x+d)^4*a*b^2*d+3/e^5/(e*x+d)^4*a*c^2*d^3+3/e^5/(e*x+d)^4*b^2*c*d^3+6/5/e^4/(e*x+d)^5*d^3*a*b*c+6/e^4/(e*x+d)^3*a*b*c*d-9/2/e^4/(e*x+d)^4*a*b*c*d^2-15/4/e^6/(e*x+d)^4*b*c^2*d^4+6/e^5/(e*x+d)^2*b^2*c*d-15/e^6/(e*x+d)^2*b*c^2*d^2-6/e^5/(e*x+d)^3*a*c^2*d^2-3/5/e^3/(e*x+d)^5*d^2*a*b^2-3/5/e^5/(e*x+d)^5*a*c^2*d^4-3/5/e^5/(e*x+d)^5*d^4*b^2*c-1/2/e^4/(e*x+d)^2*b^3-1/5/e/(e*x+d)^5*a^3+c^3/e^6*x-1/5/e^7/(e*x+d)^5*c^3*d^6+10/e^7/(e*x+d)^2*c^3*d^3-3*c^2/e^5/(e*x+d)*a+15*c^2/e^6/(e*x+d)*b*d+3/5/e^2/(e*x+d)^5*d*a^2*b+3/5/e^6/(e*x+d)^5*d^5*b*c^2-3/e^4/(e*x+d)^2*a*b*c+6/e^5/(e*x+d)^2*c^2*a*d-6*c^3*d/e^7*ln(e*x+d)","B"
2142,1,695,256,0.059000," ","int((c*x^2+b*x+a)^3/(e*x+d)^7,x)","-\frac{a^{3}}{6 \left(e x +d \right)^{6} e}+\frac{a^{2} b d}{2 \left(e x +d \right)^{6} e^{2}}-\frac{a^{2} c \,d^{2}}{2 \left(e x +d \right)^{6} e^{3}}-\frac{a \,b^{2} d^{2}}{2 \left(e x +d \right)^{6} e^{3}}+\frac{a b c \,d^{3}}{\left(e x +d \right)^{6} e^{4}}-\frac{a \,c^{2} d^{4}}{2 \left(e x +d \right)^{6} e^{5}}+\frac{b^{3} d^{3}}{6 \left(e x +d \right)^{6} e^{4}}-\frac{b^{2} c \,d^{4}}{2 \left(e x +d \right)^{6} e^{5}}+\frac{b \,c^{2} d^{5}}{2 \left(e x +d \right)^{6} e^{6}}-\frac{c^{3} d^{6}}{6 \left(e x +d \right)^{6} e^{7}}-\frac{3 a^{2} b}{5 \left(e x +d \right)^{5} e^{2}}+\frac{6 a^{2} c d}{5 \left(e x +d \right)^{5} e^{3}}+\frac{6 a \,b^{2} d}{5 \left(e x +d \right)^{5} e^{3}}-\frac{18 a b c \,d^{2}}{5 \left(e x +d \right)^{5} e^{4}}+\frac{12 a \,c^{2} d^{3}}{5 \left(e x +d \right)^{5} e^{5}}-\frac{3 b^{3} d^{2}}{5 \left(e x +d \right)^{5} e^{4}}+\frac{12 b^{2} c \,d^{3}}{5 \left(e x +d \right)^{5} e^{5}}-\frac{3 b \,c^{2} d^{4}}{\left(e x +d \right)^{5} e^{6}}+\frac{6 c^{3} d^{5}}{5 \left(e x +d \right)^{5} e^{7}}-\frac{3 a^{2} c}{4 \left(e x +d \right)^{4} e^{3}}-\frac{3 a \,b^{2}}{4 \left(e x +d \right)^{4} e^{3}}+\frac{9 a b c d}{2 \left(e x +d \right)^{4} e^{4}}-\frac{9 a \,c^{2} d^{2}}{2 \left(e x +d \right)^{4} e^{5}}+\frac{3 b^{3} d}{4 \left(e x +d \right)^{4} e^{4}}-\frac{9 b^{2} c \,d^{2}}{2 \left(e x +d \right)^{4} e^{5}}+\frac{15 b \,c^{2} d^{3}}{2 \left(e x +d \right)^{4} e^{6}}-\frac{15 c^{3} d^{4}}{4 \left(e x +d \right)^{4} e^{7}}-\frac{2 a b c}{\left(e x +d \right)^{3} e^{4}}+\frac{4 a \,c^{2} d}{\left(e x +d \right)^{3} e^{5}}-\frac{b^{3}}{3 \left(e x +d \right)^{3} e^{4}}+\frac{4 b^{2} c d}{\left(e x +d \right)^{3} e^{5}}-\frac{10 b \,c^{2} d^{2}}{\left(e x +d \right)^{3} e^{6}}+\frac{20 c^{3} d^{3}}{3 \left(e x +d \right)^{3} e^{7}}-\frac{3 a \,c^{2}}{2 \left(e x +d \right)^{2} e^{5}}-\frac{3 b^{2} c}{2 \left(e x +d \right)^{2} e^{5}}+\frac{15 b \,c^{2} d}{2 \left(e x +d \right)^{2} e^{6}}-\frac{15 c^{3} d^{2}}{2 \left(e x +d \right)^{2} e^{7}}-\frac{3 b \,c^{2}}{\left(e x +d \right) e^{6}}+\frac{6 c^{3} d}{\left(e x +d \right) e^{7}}+\frac{c^{3} \ln \left(e x +d \right)}{e^{7}}"," ",0,"3/4/e^4/(e*x+d)^4*b^3*d-15/4/e^7/(e*x+d)^4*c^3*d^4-3/4/e^3/(e*x+d)^4*a^2*c-3/4/e^3/(e*x+d)^4*a*b^2+9/2/e^4/(e*x+d)^4*a*b*c*d+1/e^4/(e*x+d)^6*d^3*a*c*b-18/5/e^4/(e*x+d)^5*d^2*a*c*b+4/e^5/(e*x+d)^3*c^2*a*d-15/2*c^3/e^7/(e*x+d)^2*d^2+1/6/e^4/(e*x+d)^6*b^3*d^3-1/6/e^7/(e*x+d)^6*c^3*d^6-3*c^2/e^6/(e*x+d)*b-3/5/e^2/(e*x+d)^5*a^2*b-3/5/e^4/(e*x+d)^5*b^3*d^2+6/5/e^7/(e*x+d)^5*c^3*d^5+20/3/e^7/(e*x+d)^3*c^3*d^3-3/2*c^2/e^5/(e*x+d)^2*a-3/2*c/e^5/(e*x+d)^2*b^2-1/6/e/(e*x+d)^6*a^3-1/3/e^4/(e*x+d)^3*b^3+15/2*c^2/e^6/(e*x+d)^2*b*d-2/e^4/(e*x+d)^3*a*b*c-9/2/e^5/(e*x+d)^4*a*c^2*d^2-9/2/e^5/(e*x+d)^4*d^2*b^2*c+15/2/e^6/(e*x+d)^4*b*c^2*d^3+1/2/e^2/(e*x+d)^6*a^2*b*d-1/2/e^3/(e*x+d)^6*a^2*c*d^2-1/2/e^3/(e*x+d)^6*a*b^2*d^2-1/2/e^5/(e*x+d)^6*a*c^2*d^4-1/2/e^5/(e*x+d)^6*d^4*b^2*c+1/2/e^6/(e*x+d)^6*d^5*b*c^2+6/5/e^3/(e*x+d)^5*a^2*c*d-10/e^6/(e*x+d)^3*b*c^2*d^2+6/5/e^3/(e*x+d)^5*d*a*b^2+12/5/e^5/(e*x+d)^5*a*c^2*d^3+12/5/e^5/(e*x+d)^5*d^3*b^2*c-3/e^6/(e*x+d)^5*b*c^2*d^4+4/e^5/(e*x+d)^3*b^2*c*d+c^3/e^7*ln(e*x+d)+6/(e*x+d)*c^3*d/e^7","B"
2143,1,461,258,0.052000," ","int((c*x^2+b*x+a)^3/(e*x+d)^8,x)","-\frac{c^{3}}{\left(e x +d \right) e^{7}}-\frac{3 \left(b e -2 c d \right) c^{2}}{2 \left(e x +d \right)^{2} e^{7}}-\frac{\left(a c \,e^{2}+b^{2} e^{2}-5 b c d e +5 c^{2} d^{2}\right) c}{\left(e x +d \right)^{3} e^{7}}-\frac{a^{3} e^{6}-3 a^{2} b d \,e^{5}+3 a^{2} c \,d^{2} e^{4}+3 a \,b^{2} d^{2} e^{4}-6 d^{3} a c b \,e^{3}+3 a \,c^{2} d^{4} e^{2}-b^{3} d^{3} e^{3}+3 d^{4} b^{2} c \,e^{2}-3 b \,c^{2} d^{5} e +c^{3} d^{6}}{7 \left(e x +d \right)^{7} e^{7}}-\frac{3 a^{2} c \,e^{4}+3 a \,b^{2} e^{4}-18 a b c d \,e^{3}+18 a \,c^{2} d^{2} e^{2}-3 b^{3} d \,e^{3}+18 d^{2} b^{2} c \,e^{2}-30 b \,c^{2} d^{3} e +15 c^{3} d^{4}}{5 \left(e x +d \right)^{5} e^{7}}-\frac{3 a^{2} b \,e^{5}-6 a^{2} c d \,e^{4}-6 d a \,b^{2} e^{4}+18 d^{2} a c b \,e^{3}-12 a \,c^{2} d^{3} e^{2}+3 b^{3} d^{2} e^{3}-12 d^{3} b^{2} c \,e^{2}+15 b \,c^{2} d^{4} e -6 c^{3} d^{5}}{6 \left(e x +d \right)^{6} e^{7}}-\frac{6 a b c \,e^{3}-12 c^{2} a d \,e^{2}+b^{3} e^{3}-12 b^{2} c d \,e^{2}+30 b \,c^{2} d^{2} e -20 c^{3} d^{3}}{4 \left(e x +d \right)^{4} e^{7}}"," ",0,"-1/(e*x+d)*c^3/e^7-1/7*(a^3*e^6-3*a^2*b*d*e^5+3*a^2*c*d^2*e^4+3*a*b^2*d^2*e^4-6*a*b*c*d^3*e^3+3*a*c^2*d^4*e^2-b^3*d^3*e^3+3*b^2*c*d^4*e^2-3*b*c^2*d^5*e+c^3*d^6)/e^7/(e*x+d)^7-1/5*(3*a^2*c*e^4+3*a*b^2*e^4-18*a*b*c*d*e^3+18*a*c^2*d^2*e^2-3*b^3*d*e^3+18*b^2*c*d^2*e^2-30*b*c^2*d^3*e+15*c^3*d^4)/e^7/(e*x+d)^5-1/6*(3*a^2*b*e^5-6*a^2*c*d*e^4-6*a*b^2*d*e^4+18*a*b*c*d^2*e^3-12*a*c^2*d^3*e^2+3*b^3*d^2*e^3-12*b^2*c*d^3*e^2+15*b*c^2*d^4*e-6*c^3*d^5)/e^7/(e*x+d)^6-3/2*c^2*(b*e-2*c*d)/e^7/(e*x+d)^2-c*(a*c*e^2+b^2*e^2-5*b*c*d*e+5*c^2*d^2)/e^7/(e*x+d)^3-1/4*(6*a*b*c*e^3-12*a*c^2*d*e^2+b^3*e^3-12*b^2*c*d*e^2+30*b*c^2*d^2*e-20*c^3*d^3)/e^7/(e*x+d)^4","A"
2144,1,461,257,0.054000," ","int((c*x^2+b*x+a)^3/(e*x+d)^9,x)","-\frac{c^{3}}{2 \left(e x +d \right)^{2} e^{7}}-\frac{\left(b e -2 c d \right) c^{2}}{\left(e x +d \right)^{3} e^{7}}-\frac{3 \left(a c \,e^{2}+b^{2} e^{2}-5 b c d e +5 c^{2} d^{2}\right) c}{4 \left(e x +d \right)^{4} e^{7}}-\frac{3 a^{2} b \,e^{5}-6 a^{2} c d \,e^{4}-6 d a \,b^{2} e^{4}+18 d^{2} a c b \,e^{3}-12 a \,c^{2} d^{3} e^{2}+3 b^{3} d^{2} e^{3}-12 d^{3} b^{2} c \,e^{2}+15 b \,c^{2} d^{4} e -6 c^{3} d^{5}}{7 \left(e x +d \right)^{7} e^{7}}-\frac{6 a b c \,e^{3}-12 c^{2} a d \,e^{2}+b^{3} e^{3}-12 b^{2} c d \,e^{2}+30 b \,c^{2} d^{2} e -20 c^{3} d^{3}}{5 \left(e x +d \right)^{5} e^{7}}-\frac{3 a^{2} c \,e^{4}+3 a \,b^{2} e^{4}-18 a b c d \,e^{3}+18 a \,c^{2} d^{2} e^{2}-3 b^{3} d \,e^{3}+18 d^{2} b^{2} c \,e^{2}-30 b \,c^{2} d^{3} e +15 c^{3} d^{4}}{6 \left(e x +d \right)^{6} e^{7}}-\frac{a^{3} e^{6}-3 a^{2} b d \,e^{5}+3 a^{2} c \,d^{2} e^{4}+3 a \,b^{2} d^{2} e^{4}-6 d^{3} a c b \,e^{3}+3 a \,c^{2} d^{4} e^{2}-b^{3} d^{3} e^{3}+3 d^{4} b^{2} c \,e^{2}-3 b \,c^{2} d^{5} e +c^{3} d^{6}}{8 \left(e x +d \right)^{8} e^{7}}"," ",0,"-1/7*(3*a^2*b*e^5-6*a^2*c*d*e^4-6*a*b^2*d*e^4+18*a*b*c*d^2*e^3-12*a*c^2*d^3*e^2+3*b^3*d^2*e^3-12*b^2*c*d^3*e^2+15*b*c^2*d^4*e-6*c^3*d^5)/e^7/(e*x+d)^7-1/5*(6*a*b*c*e^3-12*a*c^2*d*e^2+b^3*e^3-12*b^2*c*d*e^2+30*b*c^2*d^2*e-20*c^3*d^3)/e^7/(e*x+d)^5-1/6*(3*a^2*c*e^4+3*a*b^2*e^4-18*a*b*c*d*e^3+18*a*c^2*d^2*e^2-3*b^3*d*e^3+18*b^2*c*d^2*e^2-30*b*c^2*d^3*e+15*c^3*d^4)/e^7/(e*x+d)^6-1/2/(e*x+d)^2*c^3/e^7-c^2*(b*e-2*c*d)/e^7/(e*x+d)^3-3/4*c*(a*c*e^2+b^2*e^2-5*b*c*d*e+5*c^2*d^2)/e^7/(e*x+d)^4-1/8*(a^3*e^6-3*a^2*b*d*e^5+3*a^2*c*d^2*e^4+3*a*b^2*d^2*e^4-6*a*b*c*d^3*e^3+3*a*c^2*d^4*e^2-b^3*d^3*e^3+3*b^2*c*d^4*e^2-3*b*c^2*d^5*e+c^3*d^6)/e^7/(e*x+d)^8","A"
2145,1,461,258,0.052000," ","int((c*x^2+b*x+a)^3/(e*x+d)^10,x)","-\frac{c^{3}}{3 \left(e x +d \right)^{3} e^{7}}-\frac{3 \left(b e -2 c d \right) c^{2}}{4 \left(e x +d \right)^{4} e^{7}}-\frac{3 \left(a c \,e^{2}+b^{2} e^{2}-5 b c d e +5 c^{2} d^{2}\right) c}{5 \left(e x +d \right)^{5} e^{7}}-\frac{3 a^{2} c \,e^{4}+3 a \,b^{2} e^{4}-18 a b c d \,e^{3}+18 a \,c^{2} d^{2} e^{2}-3 b^{3} d \,e^{3}+18 d^{2} b^{2} c \,e^{2}-30 b \,c^{2} d^{3} e +15 c^{3} d^{4}}{7 \left(e x +d \right)^{7} e^{7}}-\frac{a^{3} e^{6}-3 a^{2} b d \,e^{5}+3 a^{2} c \,d^{2} e^{4}+3 a \,b^{2} d^{2} e^{4}-6 d^{3} a c b \,e^{3}+3 a \,c^{2} d^{4} e^{2}-b^{3} d^{3} e^{3}+3 d^{4} b^{2} c \,e^{2}-3 b \,c^{2} d^{5} e +c^{3} d^{6}}{9 \left(e x +d \right)^{9} e^{7}}-\frac{3 a^{2} b \,e^{5}-6 a^{2} c d \,e^{4}-6 d a \,b^{2} e^{4}+18 d^{2} a c b \,e^{3}-12 a \,c^{2} d^{3} e^{2}+3 b^{3} d^{2} e^{3}-12 d^{3} b^{2} c \,e^{2}+15 b \,c^{2} d^{4} e -6 c^{3} d^{5}}{8 \left(e x +d \right)^{8} e^{7}}-\frac{6 a b c \,e^{3}-12 c^{2} a d \,e^{2}+b^{3} e^{3}-12 b^{2} c d \,e^{2}+30 b \,c^{2} d^{2} e -20 c^{3} d^{3}}{6 \left(e x +d \right)^{6} e^{7}}"," ",0,"-1/7*(3*a^2*c*e^4+3*a*b^2*e^4-18*a*b*c*d*e^3+18*a*c^2*d^2*e^2-3*b^3*d*e^3+18*b^2*c*d^2*e^2-30*b*c^2*d^3*e+15*c^3*d^4)/e^7/(e*x+d)^7-3/5*c*(a*c*e^2+b^2*e^2-5*b*c*d*e+5*c^2*d^2)/e^7/(e*x+d)^5-1/3/(e*x+d)^3*c^3/e^7-3/4*c^2*(b*e-2*c*d)/e^7/(e*x+d)^4-1/9*(a^3*e^6-3*a^2*b*d*e^5+3*a^2*c*d^2*e^4+3*a*b^2*d^2*e^4-6*a*b*c*d^3*e^3+3*a*c^2*d^4*e^2-b^3*d^3*e^3+3*b^2*c*d^4*e^2-3*b*c^2*d^5*e+c^3*d^6)/e^7/(e*x+d)^9-1/8*(3*a^2*b*e^5-6*a^2*c*d*e^4-6*a*b^2*d*e^4+18*a*b*c*d^2*e^3-12*a*c^2*d^3*e^2+3*b^3*d^2*e^3-12*b^2*c*d^3*e^2+15*b*c^2*d^4*e-6*c^3*d^5)/e^7/(e*x+d)^8-1/6*(6*a*b*c*e^3-12*a*c^2*d*e^2+b^3*e^3-12*b^2*c*d*e^2+30*b*c^2*d^2*e-20*c^3*d^3)/e^7/(e*x+d)^6","A"
2146,1,949,425,0.041000," ","int((e*x+d)^4*(c*x^2+b*x+a)^4,x)","\frac{c^{4} e^{4} x^{13}}{13}+\frac{\left(4 e^{4} b \,c^{3}+4 d \,e^{3} c^{4}\right) x^{12}}{12}+\frac{\left(16 b \,c^{3} d \,e^{3}+6 c^{4} d^{2} e^{2}+\left(4 b^{2} c^{2}+2 \left(2 a c +b^{2}\right) c^{2}\right) e^{4}\right) x^{11}}{11}+\frac{\left(24 b \,c^{3} d^{2} e^{2}+4 c^{4} d^{3} e +4 \left(4 b^{2} c^{2}+2 \left(2 a c +b^{2}\right) c^{2}\right) d \,e^{3}+\left(4 a b \,c^{2}+4 \left(2 a c +b^{2}\right) b c \right) e^{4}\right) x^{10}}{10}+a^{4} d^{4} x +\frac{\left(16 b \,c^{3} d^{3} e +c^{4} d^{4}+6 \left(4 b^{2} c^{2}+2 \left(2 a c +b^{2}\right) c^{2}\right) d^{2} e^{2}+4 \left(4 a b \,c^{2}+4 \left(2 a c +b^{2}\right) b c \right) d \,e^{3}+\left(2 a^{2} c^{2}+8 a \,b^{2} c +\left(2 a c +b^{2}\right)^{2}\right) e^{4}\right) x^{9}}{9}+\frac{\left(4 b \,c^{3} d^{4}+4 \left(4 b^{2} c^{2}+2 \left(2 a c +b^{2}\right) c^{2}\right) d^{3} e +6 \left(4 a b \,c^{2}+4 \left(2 a c +b^{2}\right) b c \right) d^{2} e^{2}+4 \left(2 a^{2} c^{2}+8 a \,b^{2} c +\left(2 a c +b^{2}\right)^{2}\right) d \,e^{3}+\left(4 a^{2} b c +4 \left(2 a c +b^{2}\right) a b \right) e^{4}\right) x^{8}}{8}+\frac{\left(\left(4 b^{2} c^{2}+2 \left(2 a c +b^{2}\right) c^{2}\right) d^{4}+4 \left(4 a b \,c^{2}+4 \left(2 a c +b^{2}\right) b c \right) d^{3} e +6 \left(2 a^{2} c^{2}+8 a \,b^{2} c +\left(2 a c +b^{2}\right)^{2}\right) d^{2} e^{2}+4 \left(4 a^{2} b c +4 \left(2 a c +b^{2}\right) a b \right) d \,e^{3}+\left(4 a^{2} b^{2}+2 \left(2 a c +b^{2}\right) a^{2}\right) e^{4}\right) x^{7}}{7}+\frac{\left(4 a^{3} b \,e^{4}+\left(4 a b \,c^{2}+4 \left(2 a c +b^{2}\right) b c \right) d^{4}+4 \left(2 a^{2} c^{2}+8 a \,b^{2} c +\left(2 a c +b^{2}\right)^{2}\right) d^{3} e +6 \left(4 a^{2} b c +4 \left(2 a c +b^{2}\right) a b \right) d^{2} e^{2}+4 \left(4 a^{2} b^{2}+2 \left(2 a c +b^{2}\right) a^{2}\right) d \,e^{3}\right) x^{6}}{6}+\frac{\left(a^{4} e^{4}+16 a^{3} b d \,e^{3}+\left(2 a^{2} c^{2}+8 a \,b^{2} c +\left(2 a c +b^{2}\right)^{2}\right) d^{4}+4 \left(4 a^{2} b c +4 \left(2 a c +b^{2}\right) a b \right) d^{3} e +6 \left(4 a^{2} b^{2}+2 \left(2 a c +b^{2}\right) a^{2}\right) d^{2} e^{2}\right) x^{5}}{5}+\frac{\left(4 a^{4} d \,e^{3}+24 a^{3} b \,d^{2} e^{2}+\left(4 a^{2} b c +4 \left(2 a c +b^{2}\right) a b \right) d^{4}+4 \left(4 a^{2} b^{2}+2 \left(2 a c +b^{2}\right) a^{2}\right) d^{3} e \right) x^{4}}{4}+\frac{\left(6 a^{4} d^{2} e^{2}+16 a^{3} b \,d^{3} e +\left(4 a^{2} b^{2}+2 \left(2 a c +b^{2}\right) a^{2}\right) d^{4}\right) x^{3}}{3}+\frac{\left(4 d^{3} e \,a^{4}+4 d^{4} a^{3} b \right) x^{2}}{2}"," ",0,"1/13*c^4*e^4*x^13+1/12*(4*b*c^3*e^4+4*c^4*d*e^3)*x^12+1/11*(6*d^2*e^2*c^4+16*d*e^3*b*c^3+e^4*(2*(2*a*c+b^2)*c^2+4*b^2*c^2))*x^11+1/10*(4*d^3*e*c^4+24*d^2*e^2*b*c^3+4*d*e^3*(2*(2*a*c+b^2)*c^2+4*b^2*c^2)+e^4*(4*b*a*c^2+4*(2*a*c+b^2)*b*c))*x^10+1/9*(c^4*d^4+16*b*c^3*d^3*e+6*d^2*e^2*(2*(2*a*c+b^2)*c^2+4*b^2*c^2)+4*d*e^3*(4*b*a*c^2+4*(2*a*c+b^2)*b*c)+e^4*(2*a^2*c^2+8*a*b^2*c+(2*a*c+b^2)^2))*x^9+1/8*(4*d^4*b*c^3+4*d^3*e*(2*(2*a*c+b^2)*c^2+4*b^2*c^2)+6*d^2*e^2*(4*b*a*c^2+4*(2*a*c+b^2)*b*c)+4*d*e^3*(2*a^2*c^2+8*a*b^2*c+(2*a*c+b^2)^2)+e^4*(4*a^2*b*c+4*a*b*(2*a*c+b^2)))*x^8+1/7*(d^4*(2*(2*a*c+b^2)*c^2+4*b^2*c^2)+4*d^3*e*(4*b*a*c^2+4*(2*a*c+b^2)*b*c)+6*d^2*e^2*(2*a^2*c^2+8*a*b^2*c+(2*a*c+b^2)^2)+4*d*e^3*(4*a^2*b*c+4*a*b*(2*a*c+b^2))+e^4*(2*a^2*(2*a*c+b^2)+4*b^2*a^2))*x^7+1/6*(d^4*(4*b*a*c^2+4*(2*a*c+b^2)*b*c)+4*d^3*e*(2*a^2*c^2+8*a*b^2*c+(2*a*c+b^2)^2)+6*d^2*e^2*(4*a^2*b*c+4*a*b*(2*a*c+b^2))+4*d*e^3*(2*a^2*(2*a*c+b^2)+4*b^2*a^2)+4*e^4*a^3*b)*x^6+1/5*(d^4*(2*a^2*c^2+8*a*b^2*c+(2*a*c+b^2)^2)+4*d^3*e*(4*a^2*b*c+4*a*b*(2*a*c+b^2))+6*d^2*e^2*(2*a^2*(2*a*c+b^2)+4*b^2*a^2)+16*a^3*b*d*e^3+a^4*e^4)*x^5+1/4*(d^4*(4*a^2*b*c+4*a*b*(2*a*c+b^2))+4*d^3*e*(2*a^2*(2*a*c+b^2)+4*b^2*a^2)+24*d^2*e^2*a^3*b+4*d*e^3*a^4)*x^4+1/3*(d^4*(2*a^2*(2*a*c+b^2)+4*b^2*a^2)+16*d^3*e*a^3*b+6*d^2*e^2*a^4)*x^3+1/2*(4*a^4*d^3*e+4*a^3*b*d^4)*x^2+a^4*d^4*x","B"
2147,1,747,425,0.043000," ","int((e*x+d)^3*(c*x^2+b*x+a)^4,x)","\frac{c^{4} e^{3} x^{12}}{12}+\frac{\left(4 e^{3} b \,c^{3}+3 d \,e^{2} c^{4}\right) x^{11}}{11}+\frac{\left(12 b \,c^{3} d \,e^{2}+3 c^{4} d^{2} e +\left(4 b^{2} c^{2}+2 \left(2 a c +b^{2}\right) c^{2}\right) e^{3}\right) x^{10}}{10}+\frac{\left(12 b \,c^{3} d^{2} e +c^{4} d^{3}+3 \left(4 b^{2} c^{2}+2 \left(2 a c +b^{2}\right) c^{2}\right) d \,e^{2}+\left(4 a b \,c^{2}+4 \left(2 a c +b^{2}\right) b c \right) e^{3}\right) x^{9}}{9}+a^{4} d^{3} x +\frac{\left(4 b \,c^{3} d^{3}+3 \left(4 b^{2} c^{2}+2 \left(2 a c +b^{2}\right) c^{2}\right) d^{2} e +3 \left(4 a b \,c^{2}+4 \left(2 a c +b^{2}\right) b c \right) d \,e^{2}+\left(2 a^{2} c^{2}+8 a \,b^{2} c +\left(2 a c +b^{2}\right)^{2}\right) e^{3}\right) x^{8}}{8}+\frac{\left(\left(4 b^{2} c^{2}+2 \left(2 a c +b^{2}\right) c^{2}\right) d^{3}+3 \left(4 a b \,c^{2}+4 \left(2 a c +b^{2}\right) b c \right) d^{2} e +3 \left(2 a^{2} c^{2}+8 a \,b^{2} c +\left(2 a c +b^{2}\right)^{2}\right) d \,e^{2}+\left(4 a^{2} b c +4 \left(2 a c +b^{2}\right) a b \right) e^{3}\right) x^{7}}{7}+\frac{\left(\left(4 a b \,c^{2}+4 \left(2 a c +b^{2}\right) b c \right) d^{3}+3 \left(2 a^{2} c^{2}+8 a \,b^{2} c +\left(2 a c +b^{2}\right)^{2}\right) d^{2} e +3 \left(4 a^{2} b c +4 \left(2 a c +b^{2}\right) a b \right) d \,e^{2}+\left(4 a^{2} b^{2}+2 \left(2 a c +b^{2}\right) a^{2}\right) e^{3}\right) x^{6}}{6}+\frac{\left(4 a^{3} b \,e^{3}+\left(2 a^{2} c^{2}+8 a \,b^{2} c +\left(2 a c +b^{2}\right)^{2}\right) d^{3}+3 \left(4 a^{2} b c +4 \left(2 a c +b^{2}\right) a b \right) d^{2} e +3 \left(4 a^{2} b^{2}+2 \left(2 a c +b^{2}\right) a^{2}\right) d \,e^{2}\right) x^{5}}{5}+\frac{\left(a^{4} e^{3}+12 a^{3} b d \,e^{2}+\left(4 a^{2} b c +4 \left(2 a c +b^{2}\right) a b \right) d^{3}+3 \left(4 a^{2} b^{2}+2 \left(2 a c +b^{2}\right) a^{2}\right) d^{2} e \right) x^{4}}{4}+\frac{\left(3 a^{4} d \,e^{2}+12 a^{3} b \,d^{2} e +\left(4 a^{2} b^{2}+2 \left(2 a c +b^{2}\right) a^{2}\right) d^{3}\right) x^{3}}{3}+\frac{\left(3 d^{2} e \,a^{4}+4 d^{3} a^{3} b \right) x^{2}}{2}"," ",0,"1/12*c^4*e^3*x^12+1/11*(4*b*c^3*e^3+3*c^4*d*e^2)*x^11+1/10*(3*d^2*e*c^4+12*d*e^2*b*c^3+e^3*(4*b^2*c^2+2*(2*a*c+b^2)*c^2))*x^10+1/9*(d^3*c^4+12*d^2*e*b*c^3+3*d*e^2*(4*b^2*c^2+2*(2*a*c+b^2)*c^2)+e^3*(4*a*b*c^2+4*(2*a*c+b^2)*b*c))*x^9+1/8*(4*d^3*b*c^3+3*d^2*e*(4*b^2*c^2+2*(2*a*c+b^2)*c^2)+3*d*e^2*(4*a*b*c^2+4*(2*a*c+b^2)*b*c)+e^3*(2*a^2*c^2+8*a*b^2*c+(2*a*c+b^2)^2))*x^8+1/7*(d^3*(4*b^2*c^2+2*(2*a*c+b^2)*c^2)+3*d^2*e*(4*a*b*c^2+4*(2*a*c+b^2)*b*c)+3*d*e^2*(2*a^2*c^2+8*a*b^2*c+(2*a*c+b^2)^2)+e^3*(4*a^2*b*c+4*(2*a*c+b^2)*a*b))*x^7+1/6*(d^3*(4*a*b*c^2+4*(2*a*c+b^2)*b*c)+3*d^2*e*(2*a^2*c^2+8*a*b^2*c+(2*a*c+b^2)^2)+3*d*e^2*(4*a^2*b*c+4*(2*a*c+b^2)*a*b)+e^3*(4*a^2*b^2+2*(2*a*c+b^2)*a^2))*x^6+1/5*(d^3*(2*a^2*c^2+8*a*b^2*c+(2*a*c+b^2)^2)+3*d^2*e*(4*a^2*b*c+4*(2*a*c+b^2)*a*b)+3*d*e^2*(4*a^2*b^2+2*(2*a*c+b^2)*a^2)+4*a^3*b*e^3)*x^5+1/4*(d^3*(4*a^2*b*c+4*(2*a*c+b^2)*a*b)+3*d^2*e*(4*a^2*b^2+2*(2*a*c+b^2)*a^2)+12*d*e^2*a^3*b+e^3*a^4)*x^4+1/3*(d^3*(4*a^2*b^2+2*(2*a*c+b^2)*a^2)+12*d^2*e*a^3*b+3*d*e^2*a^4)*x^3+1/2*(3*a^4*d^2*e+4*a^3*b*d^3)*x^2+a^4*d^3*x","A"
2148,1,545,425,0.035000," ","int((e*x+d)^2*(c*x^2+b*x+a)^4,x)","\frac{c^{4} e^{2} x^{11}}{11}+\frac{\left(4 e^{2} b \,c^{3}+2 d e \,c^{4}\right) x^{10}}{10}+\frac{\left(8 b \,c^{3} d e +c^{4} d^{2}+\left(4 b^{2} c^{2}+2 \left(2 a c +b^{2}\right) c^{2}\right) e^{2}\right) x^{9}}{9}+\frac{\left(4 b \,c^{3} d^{2}+2 \left(4 b^{2} c^{2}+2 \left(2 a c +b^{2}\right) c^{2}\right) d e +\left(4 a b \,c^{2}+4 \left(2 a c +b^{2}\right) b c \right) e^{2}\right) x^{8}}{8}+a^{4} d^{2} x +\frac{\left(\left(4 b^{2} c^{2}+2 \left(2 a c +b^{2}\right) c^{2}\right) d^{2}+2 \left(4 a b \,c^{2}+4 \left(2 a c +b^{2}\right) b c \right) d e +\left(2 a^{2} c^{2}+8 a \,b^{2} c +\left(2 a c +b^{2}\right)^{2}\right) e^{2}\right) x^{7}}{7}+\frac{\left(\left(4 a b \,c^{2}+4 \left(2 a c +b^{2}\right) b c \right) d^{2}+2 \left(2 a^{2} c^{2}+8 a \,b^{2} c +\left(2 a c +b^{2}\right)^{2}\right) d e +\left(4 a^{2} b c +4 \left(2 a c +b^{2}\right) a b \right) e^{2}\right) x^{6}}{6}+\frac{\left(\left(2 a^{2} c^{2}+8 a \,b^{2} c +\left(2 a c +b^{2}\right)^{2}\right) d^{2}+2 \left(4 a^{2} b c +4 \left(2 a c +b^{2}\right) a b \right) d e +\left(4 a^{2} b^{2}+2 \left(2 a c +b^{2}\right) a^{2}\right) e^{2}\right) x^{5}}{5}+\frac{\left(4 a^{3} b \,e^{2}+\left(4 a^{2} b c +4 \left(2 a c +b^{2}\right) a b \right) d^{2}+2 \left(4 a^{2} b^{2}+2 \left(2 a c +b^{2}\right) a^{2}\right) d e \right) x^{4}}{4}+\frac{\left(a^{4} e^{2}+8 a^{3} b d e +\left(4 a^{2} b^{2}+2 \left(2 a c +b^{2}\right) a^{2}\right) d^{2}\right) x^{3}}{3}+\frac{\left(2 d e \,a^{4}+4 d^{2} a^{3} b \right) x^{2}}{2}"," ",0,"1/11*c^4*e^2*x^11+1/10*(4*b*c^3*e^2+2*c^4*d*e)*x^10+1/9*(c^4*d^2+8*d*e*b*c^3+e^2*(4*b^2*c^2+2*(2*a*c+b^2)*c^2))*x^9+1/8*(4*d^2*b*c^3+2*d*e*(4*b^2*c^2+2*(2*a*c+b^2)*c^2)+e^2*(4*a*b*c^2+4*(2*a*c+b^2)*b*c))*x^8+1/7*(d^2*(4*b^2*c^2+2*(2*a*c+b^2)*c^2)+2*d*e*(4*a*b*c^2+4*(2*a*c+b^2)*b*c)+e^2*(2*a^2*c^2+8*a*b^2*c+(2*a*c+b^2)^2))*x^7+1/6*(d^2*(4*a*b*c^2+4*(2*a*c+b^2)*b*c)+2*d*e*(2*a^2*c^2+8*a*b^2*c+(2*a*c+b^2)^2)+e^2*(4*a^2*b*c+4*(2*a*c+b^2)*a*b))*x^6+1/5*(d^2*(2*a^2*c^2+8*a*b^2*c+(2*a*c+b^2)^2)+2*d*e*(4*a^2*b*c+4*(2*a*c+b^2)*a*b)+e^2*(4*a^2*b^2+2*(2*a*c+b^2)*a^2))*x^5+1/4*(d^2*(4*a^2*b*c+4*(2*a*c+b^2)*a*b)+2*d*e*(4*a^2*b^2+2*(2*a*c+b^2)*a^2)+4*e^2*a^3*b)*x^4+1/3*(d^2*(4*a^2*b^2+2*(2*a*c+b^2)*a^2)+8*d*e*a^3*b+e^2*a^4)*x^3+1/2*(2*a^4*d*e+4*a^3*b*d^2)*x^2+a^4*d^2*x","A"
2149,1,343,250,0.043000," ","int((e*x+d)*(c*x^2+b*x+a)^4,x)","\frac{c^{4} e \,x^{10}}{10}+\frac{\left(4 e b \,c^{3}+d \,c^{4}\right) x^{9}}{9}+\frac{\left(4 b \,c^{3} d +\left(4 b^{2} c^{2}+2 \left(2 a c +b^{2}\right) c^{2}\right) e \right) x^{8}}{8}+\frac{\left(\left(4 b^{2} c^{2}+2 \left(2 a c +b^{2}\right) c^{2}\right) d +\left(4 a b \,c^{2}+4 \left(2 a c +b^{2}\right) b c \right) e \right) x^{7}}{7}+a^{4} d x +\frac{\left(\left(4 a b \,c^{2}+4 \left(2 a c +b^{2}\right) b c \right) d +\left(2 a^{2} c^{2}+8 a \,b^{2} c +\left(2 a c +b^{2}\right)^{2}\right) e \right) x^{6}}{6}+\frac{\left(\left(2 a^{2} c^{2}+8 a \,b^{2} c +\left(2 a c +b^{2}\right)^{2}\right) d +\left(4 a^{2} b c +4 \left(2 a c +b^{2}\right) a b \right) e \right) x^{5}}{5}+\frac{\left(\left(4 a^{2} b c +4 \left(2 a c +b^{2}\right) a b \right) d +\left(4 a^{2} b^{2}+2 \left(2 a c +b^{2}\right) a^{2}\right) e \right) x^{4}}{4}+\frac{\left(4 a^{3} b e +\left(4 a^{2} b^{2}+2 \left(2 a c +b^{2}\right) a^{2}\right) d \right) x^{3}}{3}+\frac{\left(e \,a^{4}+4 d \,a^{3} b \right) x^{2}}{2}"," ",0,"1/10*c^4*e*x^10+1/9*(4*b*c^3*e+c^4*d)*x^9+1/8*(4*c^3*d*b+e*(4*b^2*c^2+2*(2*a*c+b^2)*c^2))*x^8+1/7*(d*(4*b^2*c^2+2*(2*a*c+b^2)*c^2)+e*(4*a*b*c^2+4*(2*a*c+b^2)*b*c))*x^7+1/6*(d*(4*a*b*c^2+4*(2*a*c+b^2)*b*c)+e*(2*a^2*c^2+8*a*b^2*c+(2*a*c+b^2)^2))*x^6+1/5*(d*(2*a^2*c^2+8*a*b^2*c+(2*a*c+b^2)^2)+e*(4*a^2*b*c+4*(2*a*c+b^2)*a*b))*x^5+1/4*(d*(4*a^2*b*c+4*(2*a*c+b^2)*a*b)+e*(4*a^2*b^2+2*(2*a*c+b^2)*a^2))*x^4+1/3*(d*(4*a^2*b^2+2*(2*a*c+b^2)*a^2)+4*e*a^3*b)*x^3+1/2*(a^4*e+4*a^3*b*d)*x^2+a^4*d*x","A"
2150,1,168,121,0.047000," ","int((c*x^2+b*x+a)^4,x)","\frac{c^{4} x^{9}}{9}+\frac{b \,c^{3} x^{8}}{2}+\frac{\left(4 b^{2} c^{2}+2 \left(2 a c +b^{2}\right) c^{2}\right) x^{7}}{7}+2 a^{3} b \,x^{2}+\frac{\left(4 a b \,c^{2}+4 \left(2 a c +b^{2}\right) b c \right) x^{6}}{6}+a^{4} x +\frac{\left(2 a^{2} c^{2}+8 a \,b^{2} c +\left(2 a c +b^{2}\right)^{2}\right) x^{5}}{5}+\frac{\left(4 a^{2} b c +4 \left(2 a c +b^{2}\right) a b \right) x^{4}}{4}+\frac{\left(4 a^{2} b^{2}+2 \left(2 a c +b^{2}\right) a^{2}\right) x^{3}}{3}"," ",0,"1/9*c^4*x^9+1/2*b*c^3*x^8+1/7*(4*b^2*c^2+2*(2*a*c+b^2)*c^2)*x^7+1/6*(4*a*b*c^2+4*(2*a*c+b^2)*b*c)*x^6+1/5*(2*a^2*c^2+8*a*b^2*c+(2*a*c+b^2)^2)*x^5+1/4*(4*a^2*b*c+4*(2*a*c+b^2)*a*b)*x^4+1/3*(4*a^2*b^2+2*(2*a*c+b^2)*a^2)*x^3+2*a^3*b*x^2+a^4*x","A"
2151,1,1096,416,0.050000," ","int((c*x^2+b*x+a)^4/(e*x+d),x)","\frac{c^{4} x^{8}}{8 e}+\frac{4 b \,c^{3} x^{7}}{7 e}-\frac{c^{4} d \,x^{7}}{7 e^{2}}+\frac{2 a \,c^{3} x^{6}}{3 e}+\frac{b^{2} c^{2} x^{6}}{e}-\frac{2 b \,c^{3} d \,x^{6}}{3 e^{2}}+\frac{c^{4} d^{2} x^{6}}{6 e^{3}}+\frac{12 a b \,c^{2} x^{5}}{5 e}-\frac{4 a \,c^{3} d \,x^{5}}{5 e^{2}}+\frac{4 b^{3} c \,x^{5}}{5 e}-\frac{6 b^{2} c^{2} d \,x^{5}}{5 e^{2}}+\frac{4 b \,c^{3} d^{2} x^{5}}{5 e^{3}}-\frac{c^{4} d^{3} x^{5}}{5 e^{4}}+\frac{3 a^{2} c^{2} x^{4}}{2 e}+\frac{3 a \,b^{2} c \,x^{4}}{e}-\frac{3 a b \,c^{2} d \,x^{4}}{e^{2}}+\frac{a \,c^{3} d^{2} x^{4}}{e^{3}}+\frac{b^{4} x^{4}}{4 e}-\frac{b^{3} c d \,x^{4}}{e^{2}}+\frac{3 b^{2} c^{2} d^{2} x^{4}}{2 e^{3}}-\frac{b \,c^{3} d^{3} x^{4}}{e^{4}}+\frac{c^{4} d^{4} x^{4}}{4 e^{5}}+\frac{4 a^{2} b c \,x^{3}}{e}-\frac{2 a^{2} c^{2} d \,x^{3}}{e^{2}}+\frac{4 a \,b^{3} x^{3}}{3 e}-\frac{4 a \,b^{2} c d \,x^{3}}{e^{2}}+\frac{4 a b \,c^{2} d^{2} x^{3}}{e^{3}}-\frac{4 a \,c^{3} d^{3} x^{3}}{3 e^{4}}-\frac{b^{4} d \,x^{3}}{3 e^{2}}+\frac{4 b^{3} c \,d^{2} x^{3}}{3 e^{3}}-\frac{2 b^{2} c^{2} d^{3} x^{3}}{e^{4}}+\frac{4 b \,c^{3} d^{4} x^{3}}{3 e^{5}}-\frac{c^{4} d^{5} x^{3}}{3 e^{6}}+\frac{2 a^{3} c \,x^{2}}{e}+\frac{3 a^{2} b^{2} x^{2}}{e}-\frac{6 a^{2} b c d \,x^{2}}{e^{2}}+\frac{3 a^{2} c^{2} d^{2} x^{2}}{e^{3}}-\frac{2 a \,b^{3} d \,x^{2}}{e^{2}}+\frac{6 a \,b^{2} c \,d^{2} x^{2}}{e^{3}}-\frac{6 a b \,c^{2} d^{3} x^{2}}{e^{4}}+\frac{2 a \,c^{3} d^{4} x^{2}}{e^{5}}+\frac{b^{4} d^{2} x^{2}}{2 e^{3}}-\frac{2 b^{3} c \,d^{3} x^{2}}{e^{4}}+\frac{3 b^{2} c^{2} d^{4} x^{2}}{e^{5}}-\frac{2 b \,c^{3} d^{5} x^{2}}{e^{6}}+\frac{c^{4} d^{6} x^{2}}{2 e^{7}}+\frac{a^{4} \ln \left(e x +d \right)}{e}-\frac{4 a^{3} b d \ln \left(e x +d \right)}{e^{2}}+\frac{4 a^{3} b x}{e}+\frac{4 a^{3} c \,d^{2} \ln \left(e x +d \right)}{e^{3}}-\frac{4 a^{3} c d x}{e^{2}}+\frac{6 a^{2} b^{2} d^{2} \ln \left(e x +d \right)}{e^{3}}-\frac{6 a^{2} b^{2} d x}{e^{2}}-\frac{12 a^{2} b c \,d^{3} \ln \left(e x +d \right)}{e^{4}}+\frac{12 a^{2} b c \,d^{2} x}{e^{3}}+\frac{6 a^{2} c^{2} d^{4} \ln \left(e x +d \right)}{e^{5}}-\frac{6 a^{2} c^{2} d^{3} x}{e^{4}}-\frac{4 a \,b^{3} d^{3} \ln \left(e x +d \right)}{e^{4}}+\frac{4 a \,b^{3} d^{2} x}{e^{3}}+\frac{12 a \,b^{2} c \,d^{4} \ln \left(e x +d \right)}{e^{5}}-\frac{12 a \,b^{2} c \,d^{3} x}{e^{4}}-\frac{12 a b \,c^{2} d^{5} \ln \left(e x +d \right)}{e^{6}}+\frac{12 a b \,c^{2} d^{4} x}{e^{5}}+\frac{4 a \,c^{3} d^{6} \ln \left(e x +d \right)}{e^{7}}-\frac{4 a \,c^{3} d^{5} x}{e^{6}}+\frac{b^{4} d^{4} \ln \left(e x +d \right)}{e^{5}}-\frac{b^{4} d^{3} x}{e^{4}}-\frac{4 b^{3} c \,d^{5} \ln \left(e x +d \right)}{e^{6}}+\frac{4 b^{3} c \,d^{4} x}{e^{5}}+\frac{6 b^{2} c^{2} d^{6} \ln \left(e x +d \right)}{e^{7}}-\frac{6 b^{2} c^{2} d^{5} x}{e^{6}}-\frac{4 b \,c^{3} d^{7} \ln \left(e x +d \right)}{e^{8}}+\frac{4 b \,c^{3} d^{6} x}{e^{7}}+\frac{c^{4} d^{8} \ln \left(e x +d \right)}{e^{9}}-\frac{c^{4} d^{7} x}{e^{8}}"," ",0,"-6/e^4*x^2*a*b*c^2*d^3-6/e^2*x^2*a^2*b*c*d-4/e^2*x^3*a*b^2*c*d+4/e^3*x^3*a*b*c^2*d^2-3/e^2*x^4*a*b*c^2*d-12/e^4*x*a*b^2*c*d^3+12/e^5*x*a*b*c^2*d^4+12/e^3*x*a^2*b*c*d^2-12/e^6*ln(e*x+d)*a*b*c^2*d^5-12/e^4*ln(e*x+d)*a^2*b*c*d^3+12/e^5*ln(e*x+d)*a*b^2*c*d^4+6/e^3*x^2*a*b^2*c*d^2+1/2/e^7*x^2*c^4*d^6+1/2/e^3*x^2*b^4*d^2-1/5/e^4*x^5*c^4*d^3-1/e^4*x*b^4*d^3+1/e*x^6*b^2*c^2-1/e^8*x*c^4*d^7+2/3/e*x^6*a*c^3+4/7/e*x^7*b*c^3+3/e*x^2*a^2*b^2-1/3/e^6*x^3*c^4*d^5+2/e*x^2*a^3*c+4/5/e*x^5*b^3*c+1/6/e^3*x^6*c^4*d^2+4/3/e*x^3*a*b^3-1/7/e^2*x^7*c^4*d+4/e*x*a^3*b-1/3/e^2*x^3*b^4*d+3/2/e*x^4*a^2*c^2+1/4/e^5*x^4*c^4*d^4+1/e^5*ln(e*x+d)*b^4*d^4+1/e^9*ln(e*x+d)*c^4*d^8+1/4/e*x^4*b^4+1/8/e*c^4*x^8+1/e*ln(e*x+d)*a^4+4/e*x^3*a^2*b*c+4/5/e^3*x^5*b*c^3*d^2-1/e^2*x^4*b^3*c*d+3/2/e^3*x^4*b^2*c^2*d^2-2/e^2*x^3*a^2*c^2*d-4/3/e^4*x^3*a*c^3*d^3-2/3/e^2*x^6*b*c^3*d-2/e^4*x^2*b^3*c*d^3-4/5/e^2*x^5*a*c^3*d+4/3/e^5*x^3*b*c^3*d^4+4/3/e^3*x^3*b^3*c*d^2-2/e^4*x^3*b^2*c^2*d^3-6/5/e^2*x^5*b^2*c^2*d-1/e^4*x^4*b*c^3*d^3+3/e*x^4*a*b^2*c+12/5/e*x^5*a*b*c^2+4/e^7*x*b*c^3*d^6-4/e^2*ln(e*x+d)*a^3*b*d+4/e^3*ln(e*x+d)*a^3*c*d^2-6/e^4*x*a^2*c^2*d^3+4/e^3*x*a*b^3*d^2-4/e^8*ln(e*x+d)*b*c^3*d^7+6/e^3*ln(e*x+d)*a^2*b^2*d^2+3/e^5*x^2*b^2*c^2*d^4-2/e^6*x^2*b*c^3*d^5+1/e^3*x^4*a*c^3*d^2-6/e^2*x*a^2*b^2*d+6/e^5*ln(e*x+d)*a^2*c^2*d^4-4/e^4*ln(e*x+d)*a*b^3*d^3+4/e^7*ln(e*x+d)*a*c^3*d^6-4/e^6*ln(e*x+d)*b^3*c*d^5+6/e^7*ln(e*x+d)*b^2*c^2*d^6-6/e^6*x*b^2*c^2*d^5-4/e^2*x*a^3*c*d+3/e^3*x^2*a^2*c^2*d^2-2/e^2*x^2*a*b^3*d+2/e^5*x^2*a*c^3*d^4-4/e^6*x*a*c^3*d^5+4/e^5*x*b^3*c*d^4","B"
2152,1,1159,418,0.064000," ","int((c*x^2+b*x+a)^4/(e*x+d)^2,x)","\frac{c^{4} x^{7}}{7 e^{2}}+\frac{2 b \,c^{3} x^{6}}{3 e^{2}}-\frac{c^{4} d \,x^{6}}{3 e^{3}}+\frac{4 a \,c^{3} x^{5}}{5 e^{2}}+\frac{6 b^{2} c^{2} x^{5}}{5 e^{2}}-\frac{8 b \,c^{3} d \,x^{5}}{5 e^{3}}+\frac{3 c^{4} d^{2} x^{5}}{5 e^{4}}+\frac{3 a b \,c^{2} x^{4}}{e^{2}}-\frac{2 a \,c^{3} d \,x^{4}}{e^{3}}+\frac{b^{3} c \,x^{4}}{e^{2}}-\frac{3 b^{2} c^{2} d \,x^{4}}{e^{3}}+\frac{3 b \,c^{3} d^{2} x^{4}}{e^{4}}-\frac{c^{4} d^{3} x^{4}}{e^{5}}+\frac{2 a^{2} c^{2} x^{3}}{e^{2}}+\frac{4 a \,b^{2} c \,x^{3}}{e^{2}}-\frac{8 a b \,c^{2} d \,x^{3}}{e^{3}}+\frac{4 a \,c^{3} d^{2} x^{3}}{e^{4}}+\frac{b^{4} x^{3}}{3 e^{2}}-\frac{8 b^{3} c d \,x^{3}}{3 e^{3}}+\frac{6 b^{2} c^{2} d^{2} x^{3}}{e^{4}}-\frac{16 b \,c^{3} d^{3} x^{3}}{3 e^{5}}+\frac{5 c^{4} d^{4} x^{3}}{3 e^{6}}+\frac{6 a^{2} b c \,x^{2}}{e^{2}}-\frac{6 a^{2} c^{2} d \,x^{2}}{e^{3}}+\frac{2 a \,b^{3} x^{2}}{e^{2}}-\frac{12 a \,b^{2} c d \,x^{2}}{e^{3}}+\frac{18 a b \,c^{2} d^{2} x^{2}}{e^{4}}-\frac{8 a \,c^{3} d^{3} x^{2}}{e^{5}}-\frac{b^{4} d \,x^{2}}{e^{3}}+\frac{6 b^{3} c \,d^{2} x^{2}}{e^{4}}-\frac{12 b^{2} c^{2} d^{3} x^{2}}{e^{5}}+\frac{10 b \,c^{3} d^{4} x^{2}}{e^{6}}-\frac{3 c^{4} d^{5} x^{2}}{e^{7}}-\frac{a^{4}}{\left(e x +d \right) e}+\frac{4 a^{3} b d}{\left(e x +d \right) e^{2}}+\frac{4 a^{3} b \ln \left(e x +d \right)}{e^{2}}-\frac{4 a^{3} c \,d^{2}}{\left(e x +d \right) e^{3}}-\frac{8 a^{3} c d \ln \left(e x +d \right)}{e^{3}}+\frac{4 a^{3} c x}{e^{2}}-\frac{6 a^{2} b^{2} d^{2}}{\left(e x +d \right) e^{3}}-\frac{12 a^{2} b^{2} d \ln \left(e x +d \right)}{e^{3}}+\frac{6 a^{2} b^{2} x}{e^{2}}+\frac{12 a^{2} b c \,d^{3}}{\left(e x +d \right) e^{4}}+\frac{36 a^{2} b c \,d^{2} \ln \left(e x +d \right)}{e^{4}}-\frac{24 a^{2} b c d x}{e^{3}}-\frac{6 a^{2} c^{2} d^{4}}{\left(e x +d \right) e^{5}}-\frac{24 a^{2} c^{2} d^{3} \ln \left(e x +d \right)}{e^{5}}+\frac{18 a^{2} c^{2} d^{2} x}{e^{4}}+\frac{4 a \,b^{3} d^{3}}{\left(e x +d \right) e^{4}}+\frac{12 a \,b^{3} d^{2} \ln \left(e x +d \right)}{e^{4}}-\frac{8 a \,b^{3} d x}{e^{3}}-\frac{12 a \,b^{2} c \,d^{4}}{\left(e x +d \right) e^{5}}-\frac{48 a \,b^{2} c \,d^{3} \ln \left(e x +d \right)}{e^{5}}+\frac{36 a \,b^{2} c \,d^{2} x}{e^{4}}+\frac{12 a b \,c^{2} d^{5}}{\left(e x +d \right) e^{6}}+\frac{60 a b \,c^{2} d^{4} \ln \left(e x +d \right)}{e^{6}}-\frac{48 a b \,c^{2} d^{3} x}{e^{5}}-\frac{4 a \,c^{3} d^{6}}{\left(e x +d \right) e^{7}}-\frac{24 a \,c^{3} d^{5} \ln \left(e x +d \right)}{e^{7}}+\frac{20 a \,c^{3} d^{4} x}{e^{6}}-\frac{b^{4} d^{4}}{\left(e x +d \right) e^{5}}-\frac{4 b^{4} d^{3} \ln \left(e x +d \right)}{e^{5}}+\frac{3 b^{4} d^{2} x}{e^{4}}+\frac{4 b^{3} c \,d^{5}}{\left(e x +d \right) e^{6}}+\frac{20 b^{3} c \,d^{4} \ln \left(e x +d \right)}{e^{6}}-\frac{16 b^{3} c \,d^{3} x}{e^{5}}-\frac{6 b^{2} c^{2} d^{6}}{\left(e x +d \right) e^{7}}-\frac{36 b^{2} c^{2} d^{5} \ln \left(e x +d \right)}{e^{7}}+\frac{30 b^{2} c^{2} d^{4} x}{e^{6}}+\frac{4 b \,c^{3} d^{7}}{\left(e x +d \right) e^{8}}+\frac{28 b \,c^{3} d^{6} \ln \left(e x +d \right)}{e^{8}}-\frac{24 b \,c^{3} d^{5} x}{e^{7}}-\frac{c^{4} d^{8}}{\left(e x +d \right) e^{9}}-\frac{8 c^{4} d^{7} \ln \left(e x +d \right)}{e^{9}}+\frac{7 c^{4} d^{6} x}{e^{8}}"," ",0,"10/e^6*x^2*b*c^3*d^4+12/e^4*ln(e*x+d)*a*b^3*d^2+1/e^2*x^4*b^3*c+4/e^2*ln(e*x+d)*a^3*b-4/e^5*ln(e*x+d)*b^4*d^3-8/e^9*ln(e*x+d)*c^4*d^7+2/e^2*x^3*a^2*c^2+2/3/e^2*x^6*b*c^3+4/5/e^2*x^5*a*c^3-1/e^5/(e*x+d)*b^4*d^4-1/e^9/(e*x+d)*c^4*d^8+7/e^8*c^4*d^6*x-3/e^7*x^2*c^4*d^5+4/e^2*a^3*c*x+6/e^2*a^2*b^2*x+3/e^4*b^4*d^2*x+5/3/e^6*x^3*c^4*d^4+2/e^2*x^2*a*b^3-1/e^3*x^2*b^4*d+6/5/e^2*x^5*b^2*c^2+3/5/e^4*x^5*c^4*d^2-1/e^5*x^4*c^4*d^3-24/e^7*ln(e*x+d)*a*c^3*d^5+20/e^6*ln(e*x+d)*b^3*c*d^4+12/e^4/(e*x+d)*a^2*b*c*d^3-12/e^5/(e*x+d)*a*b^2*c*d^4+12/e^6/(e*x+d)*a*b*c^2*d^5+36/e^4*ln(e*x+d)*a^2*b*c*d^2-48/e^5*ln(e*x+d)*a*b^2*c*d^3+60/e^6*ln(e*x+d)*a*b*c^2*d^4+1/3/e^2*x^3*b^4-1/e/(e*x+d)*a^4-24/e^3*a^2*b*c*d*x+36/e^4*a*b^2*c*d^2*x-48/e^5*a*b*c^2*d^3*x-12/e^3*x^2*a*b^2*c*d+18/e^4*x^2*a*b*c^2*d^2-8/e^3*x^3*a*b*c^2*d-12/e^5*x^2*b^2*c^2*d^3-16/3/e^5*x^3*b*c^3*d^3+4/e^2/(e*x+d)*d*a^3*b-4/e^3/(e*x+d)*a^3*c*d^2-6/e^3/(e*x+d)*a^2*b^2*d^2-6/e^5/(e*x+d)*a^2*c^2*d^4+4/e^4/(e*x+d)*a*b^3*d^3-4/e^7/(e*x+d)*a*c^3*d^6+4/e^6/(e*x+d)*b^3*c*d^5-6/e^7/(e*x+d)*b^2*c^2*d^6+4/e^8/(e*x+d)*b*c^3*d^7+1/7*c^4/e^2*x^7-36/e^7*ln(e*x+d)*b^2*c^2*d^5+28/e^8*ln(e*x+d)*b*c^3*d^6-8/e^3*ln(e*x+d)*a^3*c*d-12/e^3*ln(e*x+d)*a^2*b^2*d-24/e^5*ln(e*x+d)*a^2*c^2*d^3+6/e^4*x^3*b^2*c^2*d^2-8/5/e^3*x^5*b*c^3*d+3/e^2*x^4*a*b*c^2-2/e^3*x^4*a*c^3*d-3/e^3*x^4*b^2*c^2*d+4/e^4*x^3*a*c^3*d^2+3/e^4*x^4*b*c^3*d^2-8/e^3*a*b^3*d*x+20/e^6*a*c^3*d^4*x-16/e^5*b^3*c*d^3*x+30/e^6*b^2*c^2*d^4*x-24/e^7*b*c^3*d^5*x+18/e^4*a^2*c^2*d^2*x+4/e^2*x^3*a*b^2*c-8/3/e^3*x^3*b^3*c*d+6/e^2*x^2*a^2*b*c-6/e^3*x^2*a^2*c^2*d-8/e^5*x^2*a*c^3*d^3+6/e^4*x^2*b^3*c*d^2-1/3*c^4*d/e^3*x^6","B"
2153,1,1216,418,0.068000," ","int((c*x^2+b*x+a)^4/(e*x+d)^3,x)","\frac{c^{4} x^{6}}{6 e^{3}}+\frac{4 b \,c^{3} x^{5}}{5 e^{3}}-\frac{3 c^{4} d \,x^{5}}{5 e^{4}}+\frac{a \,c^{3} x^{4}}{e^{3}}+\frac{3 b^{2} c^{2} x^{4}}{2 e^{3}}-\frac{3 b \,c^{3} d \,x^{4}}{e^{4}}+\frac{3 c^{4} d^{2} x^{4}}{2 e^{5}}+\frac{4 a b \,c^{2} x^{3}}{e^{3}}-\frac{4 a \,c^{3} d \,x^{3}}{e^{4}}+\frac{4 b^{3} c \,x^{3}}{3 e^{3}}-\frac{6 b^{2} c^{2} d \,x^{3}}{e^{4}}+\frac{8 b \,c^{3} d^{2} x^{3}}{e^{5}}-\frac{10 c^{4} d^{3} x^{3}}{3 e^{6}}-\frac{a^{4}}{2 \left(e x +d \right)^{2} e}+\frac{2 a^{3} b d}{\left(e x +d \right)^{2} e^{2}}-\frac{2 a^{3} c \,d^{2}}{\left(e x +d \right)^{2} e^{3}}-\frac{3 a^{2} b^{2} d^{2}}{\left(e x +d \right)^{2} e^{3}}+\frac{6 a^{2} b c \,d^{3}}{\left(e x +d \right)^{2} e^{4}}-\frac{3 a^{2} c^{2} d^{4}}{\left(e x +d \right)^{2} e^{5}}+\frac{3 a^{2} c^{2} x^{2}}{e^{3}}+\frac{2 a \,b^{3} d^{3}}{\left(e x +d \right)^{2} e^{4}}-\frac{6 a \,b^{2} c \,d^{4}}{\left(e x +d \right)^{2} e^{5}}+\frac{6 a \,b^{2} c \,x^{2}}{e^{3}}+\frac{6 a b \,c^{2} d^{5}}{\left(e x +d \right)^{2} e^{6}}-\frac{18 a b \,c^{2} d \,x^{2}}{e^{4}}-\frac{2 a \,c^{3} d^{6}}{\left(e x +d \right)^{2} e^{7}}+\frac{12 a \,c^{3} d^{2} x^{2}}{e^{5}}-\frac{b^{4} d^{4}}{2 \left(e x +d \right)^{2} e^{5}}+\frac{b^{4} x^{2}}{2 e^{3}}+\frac{2 b^{3} c \,d^{5}}{\left(e x +d \right)^{2} e^{6}}-\frac{6 b^{3} c d \,x^{2}}{e^{4}}-\frac{3 b^{2} c^{2} d^{6}}{\left(e x +d \right)^{2} e^{7}}+\frac{18 b^{2} c^{2} d^{2} x^{2}}{e^{5}}+\frac{2 b \,c^{3} d^{7}}{\left(e x +d \right)^{2} e^{8}}-\frac{20 b \,c^{3} d^{3} x^{2}}{e^{6}}-\frac{c^{4} d^{8}}{2 \left(e x +d \right)^{2} e^{9}}+\frac{15 c^{4} d^{4} x^{2}}{2 e^{7}}-\frac{4 a^{3} b}{\left(e x +d \right) e^{2}}+\frac{8 a^{3} c d}{\left(e x +d \right) e^{3}}+\frac{4 a^{3} c \ln \left(e x +d \right)}{e^{3}}+\frac{12 a^{2} b^{2} d}{\left(e x +d \right) e^{3}}+\frac{6 a^{2} b^{2} \ln \left(e x +d \right)}{e^{3}}-\frac{36 a^{2} b c \,d^{2}}{\left(e x +d \right) e^{4}}-\frac{36 a^{2} b c d \ln \left(e x +d \right)}{e^{4}}+\frac{12 a^{2} b c x}{e^{3}}+\frac{24 a^{2} c^{2} d^{3}}{\left(e x +d \right) e^{5}}+\frac{36 a^{2} c^{2} d^{2} \ln \left(e x +d \right)}{e^{5}}-\frac{18 a^{2} c^{2} d x}{e^{4}}-\frac{12 a \,b^{3} d^{2}}{\left(e x +d \right) e^{4}}-\frac{12 a \,b^{3} d \ln \left(e x +d \right)}{e^{4}}+\frac{4 a \,b^{3} x}{e^{3}}+\frac{48 a \,b^{2} c \,d^{3}}{\left(e x +d \right) e^{5}}+\frac{72 a \,b^{2} c \,d^{2} \ln \left(e x +d \right)}{e^{5}}-\frac{36 a \,b^{2} c d x}{e^{4}}-\frac{60 a b \,c^{2} d^{4}}{\left(e x +d \right) e^{6}}-\frac{120 a b \,c^{2} d^{3} \ln \left(e x +d \right)}{e^{6}}+\frac{72 a b \,c^{2} d^{2} x}{e^{5}}+\frac{24 a \,c^{3} d^{5}}{\left(e x +d \right) e^{7}}+\frac{60 a \,c^{3} d^{4} \ln \left(e x +d \right)}{e^{7}}-\frac{40 a \,c^{3} d^{3} x}{e^{6}}+\frac{4 b^{4} d^{3}}{\left(e x +d \right) e^{5}}+\frac{6 b^{4} d^{2} \ln \left(e x +d \right)}{e^{5}}-\frac{3 b^{4} d x}{e^{4}}-\frac{20 b^{3} c \,d^{4}}{\left(e x +d \right) e^{6}}-\frac{40 b^{3} c \,d^{3} \ln \left(e x +d \right)}{e^{6}}+\frac{24 b^{3} c \,d^{2} x}{e^{5}}+\frac{36 b^{2} c^{2} d^{5}}{\left(e x +d \right) e^{7}}+\frac{90 b^{2} c^{2} d^{4} \ln \left(e x +d \right)}{e^{7}}-\frac{60 b^{2} c^{2} d^{3} x}{e^{6}}-\frac{28 b \,c^{3} d^{6}}{\left(e x +d \right) e^{8}}-\frac{84 b \,c^{3} d^{5} \ln \left(e x +d \right)}{e^{8}}+\frac{60 b \,c^{3} d^{4} x}{e^{7}}+\frac{8 c^{4} d^{7}}{\left(e x +d \right) e^{9}}+\frac{28 c^{4} d^{6} \ln \left(e x +d \right)}{e^{9}}-\frac{21 c^{4} d^{5} x}{e^{8}}"," ",0,"-18/e^4*x^2*a*b*c^2*d-36/e^4/(e*x+d)*a^2*b*c*d^2+48/e^5/(e*x+d)*a*b^2*c*d^3-60/e^6/(e*x+d)*a*b*c^2*d^4+6/e^4/(e*x+d)^2*a^2*b*c*d^3-6/e^5/(e*x+d)^2*a*b^2*c*d^4+6/e^6/(e*x+d)^2*a*b*c^2*d^5-36/e^4*a*b^2*c*d*x+72/e^5*ln(e*x+d)*a*b^2*c*d^2-120/e^6*ln(e*x+d)*a*b*c^2*d^3+72/e^5*a*b*c^2*d^2*x-36/e^4*ln(e*x+d)*a^2*b*c*d-10/3/e^6*x^3*c^4*d^3+3/e^3*x^2*a^2*c^2+4/5/e^3*x^5*b*c^3-3/5/e^4*x^5*c^4*d-4/e^2/(e*x+d)*a^3*b+4/e^5/(e*x+d)*b^4*d^3+8/e^9/(e*x+d)*c^4*d^7-1/2/e^5/(e*x+d)^2*b^4*d^4-1/2/e^9/(e*x+d)^2*c^4*d^8+4/e^3*ln(e*x+d)*a^3*c+6/e^3*ln(e*x+d)*a^2*b^2+6/e^5*ln(e*x+d)*b^4*d^2+28/e^9*ln(e*x+d)*c^4*d^6+1/e^3*x^4*a*c^3+15/2/e^7*x^2*c^4*d^4+4/e^3*a*b^3*x-3/e^4*b^4*d*x+3/2/e^3*x^4*b^2*c^2+3/2/e^5*x^4*c^4*d^2+4/3/e^3*x^3*b^3*c-21/e^8*c^4*d^5*x-1/2/e/(e*x+d)^2*a^4+1/6/e^3*c^4*x^6+1/2*b^4/e^3*x^2-84/e^8*ln(e*x+d)*b*c^3*d^5-28/e^8/(e*x+d)*b*c^3*d^6+2/e^2/(e*x+d)^2*d*a^3*b-40/e^6*ln(e*x+d)*b^3*c*d^3+90/e^7*ln(e*x+d)*b^2*c^2*d^4-60/e^6*b^2*c^2*d^3*x+60/e^7*b*c^3*d^4*x+8/e^3/(e*x+d)*a^3*c*d+12/e^3/(e*x+d)*a^2*b^2*d+24/e^5/(e*x+d)*a^2*c^2*d^3-12/e^4/(e*x+d)*a*b^3*d^2+24/e^7/(e*x+d)*a*c^3*d^5-20/e^6/(e*x+d)*b^3*c*d^4+36/e^7/(e*x+d)*b^2*c^2*d^5-2/e^3/(e*x+d)^2*a^3*c*d^2-3/e^3/(e*x+d)^2*d^2*a^2*b^2-3/e^5/(e*x+d)^2*a^2*c^2*d^4+2/e^4/(e*x+d)^2*a*b^3*d^3-2/e^7/(e*x+d)^2*a*c^3*d^6+2/e^6/(e*x+d)^2*b^3*c*d^5-3/e^7/(e*x+d)^2*b^2*c^2*d^6+2/e^8/(e*x+d)^2*b*c^3*d^7+36/e^5*ln(e*x+d)*a^2*c^2*d^2-12/e^4*ln(e*x+d)*a*b^3*d+60/e^7*ln(e*x+d)*a*c^3*d^4+6/e^3*x^2*a*b^2*c+12/e^5*x^2*a*c^3*d^2-6/e^4*x^2*b^3*c*d+18/e^5*x^2*b^2*c^2*d^2-20/e^6*x^2*b*c^3*d^3+12/e^3*a^2*b*c*x-18/e^4*a^2*c^2*d*x-40/e^6*a*c^3*d^3*x+24/e^5*b^3*c*d^2*x-3/e^4*x^4*b*c^3*d+4/e^3*x^3*a*b*c^2-4/e^4*x^3*a*c^3*d-6/e^4*x^3*b^2*c^2*d+8/e^5*x^3*b*c^3*d^2","B"
2154,1,1265,411,0.060000," ","int((c*x^2+b*x+a)^4/(e*x+d)^4,x)","\frac{c^{4} x^{5}}{5 e^{4}}+\frac{b \,c^{3} x^{4}}{e^{4}}-\frac{c^{4} d \,x^{4}}{e^{5}}-\frac{a^{4}}{3 \left(e x +d \right)^{3} e}+\frac{4 a^{3} b d}{3 \left(e x +d \right)^{3} e^{2}}-\frac{4 a^{3} c \,d^{2}}{3 \left(e x +d \right)^{3} e^{3}}-\frac{2 a^{2} b^{2} d^{2}}{\left(e x +d \right)^{3} e^{3}}+\frac{4 a^{2} b c \,d^{3}}{\left(e x +d \right)^{3} e^{4}}-\frac{2 a^{2} c^{2} d^{4}}{\left(e x +d \right)^{3} e^{5}}+\frac{4 a \,b^{3} d^{3}}{3 \left(e x +d \right)^{3} e^{4}}-\frac{4 a \,b^{2} c \,d^{4}}{\left(e x +d \right)^{3} e^{5}}+\frac{4 a b \,c^{2} d^{5}}{\left(e x +d \right)^{3} e^{6}}-\frac{4 a \,c^{3} d^{6}}{3 \left(e x +d \right)^{3} e^{7}}+\frac{4 a \,c^{3} x^{3}}{3 e^{4}}-\frac{b^{4} d^{4}}{3 \left(e x +d \right)^{3} e^{5}}+\frac{4 b^{3} c \,d^{5}}{3 \left(e x +d \right)^{3} e^{6}}-\frac{2 b^{2} c^{2} d^{6}}{\left(e x +d \right)^{3} e^{7}}+\frac{2 b^{2} c^{2} x^{3}}{e^{4}}+\frac{4 b \,c^{3} d^{7}}{3 \left(e x +d \right)^{3} e^{8}}-\frac{16 b \,c^{3} d \,x^{3}}{3 e^{5}}-\frac{c^{4} d^{8}}{3 \left(e x +d \right)^{3} e^{9}}+\frac{10 c^{4} d^{2} x^{3}}{3 e^{6}}-\frac{2 a^{3} b}{\left(e x +d \right)^{2} e^{2}}+\frac{4 a^{3} c d}{\left(e x +d \right)^{2} e^{3}}+\frac{6 a^{2} b^{2} d}{\left(e x +d \right)^{2} e^{3}}-\frac{18 a^{2} b c \,d^{2}}{\left(e x +d \right)^{2} e^{4}}+\frac{12 a^{2} c^{2} d^{3}}{\left(e x +d \right)^{2} e^{5}}-\frac{6 a \,b^{3} d^{2}}{\left(e x +d \right)^{2} e^{4}}+\frac{24 a \,b^{2} c \,d^{3}}{\left(e x +d \right)^{2} e^{5}}-\frac{30 a b \,c^{2} d^{4}}{\left(e x +d \right)^{2} e^{6}}+\frac{6 a b \,c^{2} x^{2}}{e^{4}}+\frac{12 a \,c^{3} d^{5}}{\left(e x +d \right)^{2} e^{7}}-\frac{8 a \,c^{3} d \,x^{2}}{e^{5}}+\frac{2 b^{4} d^{3}}{\left(e x +d \right)^{2} e^{5}}-\frac{10 b^{3} c \,d^{4}}{\left(e x +d \right)^{2} e^{6}}+\frac{2 b^{3} c \,x^{2}}{e^{4}}+\frac{18 b^{2} c^{2} d^{5}}{\left(e x +d \right)^{2} e^{7}}-\frac{12 b^{2} c^{2} d \,x^{2}}{e^{5}}-\frac{14 b \,c^{3} d^{6}}{\left(e x +d \right)^{2} e^{8}}+\frac{20 b \,c^{3} d^{2} x^{2}}{e^{6}}+\frac{4 c^{4} d^{7}}{\left(e x +d \right)^{2} e^{9}}-\frac{10 c^{4} d^{3} x^{2}}{e^{7}}-\frac{4 a^{3} c}{\left(e x +d \right) e^{3}}-\frac{6 a^{2} b^{2}}{\left(e x +d \right) e^{3}}+\frac{36 a^{2} b c d}{\left(e x +d \right) e^{4}}+\frac{12 a^{2} b c \ln \left(e x +d \right)}{e^{4}}-\frac{36 a^{2} c^{2} d^{2}}{\left(e x +d \right) e^{5}}-\frac{24 a^{2} c^{2} d \ln \left(e x +d \right)}{e^{5}}+\frac{6 a^{2} c^{2} x}{e^{4}}+\frac{12 a \,b^{3} d}{\left(e x +d \right) e^{4}}+\frac{4 a \,b^{3} \ln \left(e x +d \right)}{e^{4}}-\frac{72 a \,b^{2} c \,d^{2}}{\left(e x +d \right) e^{5}}-\frac{48 a \,b^{2} c d \ln \left(e x +d \right)}{e^{5}}+\frac{12 a \,b^{2} c x}{e^{4}}+\frac{120 a b \,c^{2} d^{3}}{\left(e x +d \right) e^{6}}+\frac{120 a b \,c^{2} d^{2} \ln \left(e x +d \right)}{e^{6}}-\frac{48 a b \,c^{2} d x}{e^{5}}-\frac{60 a \,c^{3} d^{4}}{\left(e x +d \right) e^{7}}-\frac{80 a \,c^{3} d^{3} \ln \left(e x +d \right)}{e^{7}}+\frac{40 a \,c^{3} d^{2} x}{e^{6}}-\frac{6 b^{4} d^{2}}{\left(e x +d \right) e^{5}}-\frac{4 b^{4} d \ln \left(e x +d \right)}{e^{5}}+\frac{b^{4} x}{e^{4}}+\frac{40 b^{3} c \,d^{3}}{\left(e x +d \right) e^{6}}+\frac{40 b^{3} c \,d^{2} \ln \left(e x +d \right)}{e^{6}}-\frac{16 b^{3} c d x}{e^{5}}-\frac{90 b^{2} c^{2} d^{4}}{\left(e x +d \right) e^{7}}-\frac{120 b^{2} c^{2} d^{3} \ln \left(e x +d \right)}{e^{7}}+\frac{60 b^{2} c^{2} d^{2} x}{e^{6}}+\frac{84 b \,c^{3} d^{5}}{\left(e x +d \right) e^{8}}+\frac{140 b \,c^{3} d^{4} \ln \left(e x +d \right)}{e^{8}}-\frac{80 b \,c^{3} d^{3} x}{e^{7}}-\frac{28 c^{4} d^{6}}{\left(e x +d \right) e^{9}}-\frac{56 c^{4} d^{5} \ln \left(e x +d \right)}{e^{9}}+\frac{35 c^{4} d^{4} x}{e^{8}}"," ",0,"-36/e^5/(e*x+d)*a^2*c^2*d^2+12/e^4/(e*x+d)*a*b^3*d-16/3/e^5*x^3*b*c^3*d+6/e^4*x^2*a*b*c^2+1/5*c^4*x^5/e^4-1/3/e/(e*x+d)^3*a^4+1/e^4*x^4*b*c^3-1/e^5*x^4*c^4*d+4/3/e^4*x^3*a*c^3+2/e^4*x^3*b^2*c^2+10/3/e^6*x^3*c^4*d^2+2/e^4*x^2*b^3*c-10/e^7*x^2*c^4*d^3+6/e^4*c^2*a^2*x+35/e^8*c^4*d^4*x-4/e^3/(e*x+d)*a^3*c-6/e^3/(e*x+d)*a^2*b^2-6/e^5/(e*x+d)*b^4*d^2-28/e^9/(e*x+d)*c^4*d^6-2/e^2/(e*x+d)^2*a^3*b+4/e^6/(e*x+d)^3*a*b*c^2*d^5-48/e^5*ln(e*x+d)*a*b^2*c*d+120/e^6*ln(e*x+d)*a*b*c^2*d^2-48/e^5*a*b*c^2*d*x+36/e^4/(e*x+d)*a^2*b*c*d-72/e^5/(e*x+d)*a*b^2*c*d^2+120/e^6/(e*x+d)*a*b*c^2*d^3-18/e^4/(e*x+d)^2*a^2*b*c*d^2+24/e^5/(e*x+d)^2*a*b^2*c*d^3-30/e^6/(e*x+d)^2*a*b*c^2*d^4+4/e^4/(e*x+d)^3*d^3*a^2*b*c-4/e^5/(e*x+d)^3*a*b^2*c*d^4+b^4/e^4*x+4/e^4*ln(e*x+d)*a*b^3-4/e^5*ln(e*x+d)*b^4*d-56/e^9*ln(e*x+d)*c^4*d^5+4/e^9/(e*x+d)^2*c^4*d^7-1/3/e^5/(e*x+d)^3*b^4*d^4-1/3/e^9/(e*x+d)^3*c^4*d^8+2/e^5/(e*x+d)^2*b^4*d^3-90/e^7/(e*x+d)*b^2*c^2*d^4+84/e^8/(e*x+d)*b*c^3*d^5+4/e^3/(e*x+d)^2*a^3*c*d+6/e^3/(e*x+d)^2*a^2*b^2*d+12/e^5/(e*x+d)^2*a^2*c^2*d^3-6/e^4/(e*x+d)^2*a*b^3*d^2+12/e^7/(e*x+d)^2*a*c^3*d^5-10/e^6/(e*x+d)^2*b^3*c*d^4+18/e^7/(e*x+d)^2*b^2*c^2*d^5-14/e^8/(e*x+d)^2*b*c^3*d^6+4/3/e^2/(e*x+d)^3*d*a^3*b-4/3/e^3/(e*x+d)^3*a^3*c*d^2-2/e^3/(e*x+d)^3*d^2*a^2*b^2-2/e^5/(e*x+d)^3*a^2*c^2*d^4+4/3/e^4/(e*x+d)^3*d^3*a*b^3-4/3/e^7/(e*x+d)^3*a*c^3*d^6+4/3/e^6/(e*x+d)^3*b^3*c*d^5-2/e^7/(e*x+d)^3*b^2*c^2*d^6+4/3/e^8/(e*x+d)^3*b*c^3*d^7+12/e^4*ln(e*x+d)*a^2*b*c-24/e^5*ln(e*x+d)*a^2*c^2*d-80/e^7*ln(e*x+d)*a*c^3*d^3+40/e^6*ln(e*x+d)*b^3*c*d^2-120/e^7*ln(e*x+d)*b^2*c^2*d^3+140/e^8*ln(e*x+d)*b*c^3*d^4-8/e^5*x^2*a*c^3*d-12/e^5*x^2*b^2*c^2*d+20/e^6*x^2*b*c^3*d^2+12/e^4*a*b^2*c*x+40/e^6*a*c^3*d^2*x-16/e^5*b^3*c*d*x+60/e^6*b^2*c^2*d^2*x-80/e^7*b*c^3*d^3*x-60/e^7/(e*x+d)*a*c^3*d^4+40/e^6/(e*x+d)*b^3*c*d^3","B"
2155,1,1306,416,0.070000," ","int((c*x^2+b*x+a)^4/(e*x+d)^5,x)","-\frac{a^{4}}{4 \left(e x +d \right)^{4} e}+\frac{a^{3} b d}{\left(e x +d \right)^{4} e^{2}}-\frac{a^{3} c \,d^{2}}{\left(e x +d \right)^{4} e^{3}}-\frac{3 a^{2} b^{2} d^{2}}{2 \left(e x +d \right)^{4} e^{3}}+\frac{3 a^{2} b c \,d^{3}}{\left(e x +d \right)^{4} e^{4}}-\frac{3 a^{2} c^{2} d^{4}}{2 \left(e x +d \right)^{4} e^{5}}+\frac{a \,b^{3} d^{3}}{\left(e x +d \right)^{4} e^{4}}-\frac{3 a \,b^{2} c \,d^{4}}{\left(e x +d \right)^{4} e^{5}}+\frac{3 a b \,c^{2} d^{5}}{\left(e x +d \right)^{4} e^{6}}-\frac{a \,c^{3} d^{6}}{\left(e x +d \right)^{4} e^{7}}-\frac{b^{4} d^{4}}{4 \left(e x +d \right)^{4} e^{5}}+\frac{b^{3} c \,d^{5}}{\left(e x +d \right)^{4} e^{6}}-\frac{3 b^{2} c^{2} d^{6}}{2 \left(e x +d \right)^{4} e^{7}}+\frac{b \,c^{3} d^{7}}{\left(e x +d \right)^{4} e^{8}}-\frac{c^{4} d^{8}}{4 \left(e x +d \right)^{4} e^{9}}+\frac{c^{4} x^{4}}{4 e^{5}}-\frac{4 a^{3} b}{3 \left(e x +d \right)^{3} e^{2}}+\frac{8 a^{3} c d}{3 \left(e x +d \right)^{3} e^{3}}+\frac{4 a^{2} b^{2} d}{\left(e x +d \right)^{3} e^{3}}-\frac{12 a^{2} b c \,d^{2}}{\left(e x +d \right)^{3} e^{4}}+\frac{8 a^{2} c^{2} d^{3}}{\left(e x +d \right)^{3} e^{5}}-\frac{4 a \,b^{3} d^{2}}{\left(e x +d \right)^{3} e^{4}}+\frac{16 a \,b^{2} c \,d^{3}}{\left(e x +d \right)^{3} e^{5}}-\frac{20 a b \,c^{2} d^{4}}{\left(e x +d \right)^{3} e^{6}}+\frac{8 a \,c^{3} d^{5}}{\left(e x +d \right)^{3} e^{7}}+\frac{4 b^{4} d^{3}}{3 \left(e x +d \right)^{3} e^{5}}-\frac{20 b^{3} c \,d^{4}}{3 \left(e x +d \right)^{3} e^{6}}+\frac{12 b^{2} c^{2} d^{5}}{\left(e x +d \right)^{3} e^{7}}-\frac{28 b \,c^{3} d^{6}}{3 \left(e x +d \right)^{3} e^{8}}+\frac{4 b \,c^{3} x^{3}}{3 e^{5}}+\frac{8 c^{4} d^{7}}{3 \left(e x +d \right)^{3} e^{9}}-\frac{5 c^{4} d \,x^{3}}{3 e^{6}}-\frac{2 a^{3} c}{\left(e x +d \right)^{2} e^{3}}-\frac{3 a^{2} b^{2}}{\left(e x +d \right)^{2} e^{3}}+\frac{18 a^{2} b c d}{\left(e x +d \right)^{2} e^{4}}-\frac{18 a^{2} c^{2} d^{2}}{\left(e x +d \right)^{2} e^{5}}+\frac{6 a \,b^{3} d}{\left(e x +d \right)^{2} e^{4}}-\frac{36 a \,b^{2} c \,d^{2}}{\left(e x +d \right)^{2} e^{5}}+\frac{60 a b \,c^{2} d^{3}}{\left(e x +d \right)^{2} e^{6}}-\frac{30 a \,c^{3} d^{4}}{\left(e x +d \right)^{2} e^{7}}+\frac{2 a \,c^{3} x^{2}}{e^{5}}-\frac{3 b^{4} d^{2}}{\left(e x +d \right)^{2} e^{5}}+\frac{20 b^{3} c \,d^{3}}{\left(e x +d \right)^{2} e^{6}}-\frac{45 b^{2} c^{2} d^{4}}{\left(e x +d \right)^{2} e^{7}}+\frac{3 b^{2} c^{2} x^{2}}{e^{5}}+\frac{42 b \,c^{3} d^{5}}{\left(e x +d \right)^{2} e^{8}}-\frac{10 b \,c^{3} d \,x^{2}}{e^{6}}-\frac{14 c^{4} d^{6}}{\left(e x +d \right)^{2} e^{9}}+\frac{15 c^{4} d^{2} x^{2}}{2 e^{7}}-\frac{12 a^{2} b c}{\left(e x +d \right) e^{4}}+\frac{24 a^{2} c^{2} d}{\left(e x +d \right) e^{5}}+\frac{6 a^{2} c^{2} \ln \left(e x +d \right)}{e^{5}}-\frac{4 a \,b^{3}}{\left(e x +d \right) e^{4}}+\frac{48 a \,b^{2} c d}{\left(e x +d \right) e^{5}}+\frac{12 a \,b^{2} c \ln \left(e x +d \right)}{e^{5}}-\frac{120 a b \,c^{2} d^{2}}{\left(e x +d \right) e^{6}}-\frac{60 a b \,c^{2} d \ln \left(e x +d \right)}{e^{6}}+\frac{12 a b \,c^{2} x}{e^{5}}+\frac{80 a \,c^{3} d^{3}}{\left(e x +d \right) e^{7}}+\frac{60 a \,c^{3} d^{2} \ln \left(e x +d \right)}{e^{7}}-\frac{20 a \,c^{3} d x}{e^{6}}+\frac{4 b^{4} d}{\left(e x +d \right) e^{5}}+\frac{b^{4} \ln \left(e x +d \right)}{e^{5}}-\frac{40 b^{3} c \,d^{2}}{\left(e x +d \right) e^{6}}-\frac{20 b^{3} c d \ln \left(e x +d \right)}{e^{6}}+\frac{4 b^{3} c x}{e^{5}}+\frac{120 b^{2} c^{2} d^{3}}{\left(e x +d \right) e^{7}}+\frac{90 b^{2} c^{2} d^{2} \ln \left(e x +d \right)}{e^{7}}-\frac{30 b^{2} c^{2} d x}{e^{6}}-\frac{140 b \,c^{3} d^{4}}{\left(e x +d \right) e^{8}}-\frac{140 b \,c^{3} d^{3} \ln \left(e x +d \right)}{e^{8}}+\frac{60 b \,c^{3} d^{2} x}{e^{7}}+\frac{56 c^{4} d^{5}}{\left(e x +d \right) e^{9}}+\frac{70 c^{4} d^{4} \ln \left(e x +d \right)}{e^{9}}-\frac{35 c^{4} d^{3} x}{e^{8}}"," ",0,"48/e^5/(e*x+d)*a*b^2*c*d-120/e^6/(e*x+d)*a*b*c^2*d^2+18/e^4/(e*x+d)^2*a^2*b*c*d-36/e^5/(e*x+d)^2*a*b^2*c*d^2+15/2*c^4/e^7*x^2*d^2+4*c/e^5*b^3*x-35*c^4/e^8*d^3*x-4/e^4/(e*x+d)*a*b^3+4/e^5/(e*x+d)*b^4*d+56/e^9/(e*x+d)*c^4*d^5-2/e^3/(e*x+d)^2*a^3*c-3/e^3/(e*x+d)^2*a^2*b^2-3/e^5/(e*x+d)^2*b^4*d^2-14/e^9/(e*x+d)^2*c^4*d^6+4/3*c^3/e^5*x^3*b-5/3*c^4/e^6*x^3*d+2*c^3/e^5*x^2*a+3*c^2/e^5*x^2*b^2-4/3/e^2/(e*x+d)^3*a^3*b-1/4/e^5/(e*x+d)^4*d^4*b^4-1/4/e^9/(e*x+d)^4*c^4*d^8+6/e^5*ln(e*x+d)*c^2*a^2+70/e^9*ln(e*x+d)*c^4*d^4+4/3/e^5/(e*x+d)^3*b^4*d^3+8/3/e^9/(e*x+d)^3*c^4*d^7-10*c^3/e^6*x^2*b*d+12/e^7/(e*x+d)^3*b^2*c^2*d^5+3/e^6/(e*x+d)^4*a*b*c^2*d^5+3/e^4/(e*x+d)^4*d^3*a^2*b*c-60/e^6*ln(e*x+d)*a*b*c^2*d+60/e^6/(e*x+d)^2*a*b*c^2*d^3-12/e^4/(e*x+d)^3*a^2*b*c*d^2+16/e^5/(e*x+d)^3*a*b^2*c*d^3-20/e^6/(e*x+d)^3*a*b*c^2*d^4-1/4/e/(e*x+d)^4*a^4-45/e^7/(e*x+d)^2*b^2*c^2*d^4+42/e^8/(e*x+d)^2*b*c^3*d^5+8/3/e^3/(e*x+d)^3*a^3*c*d+4/e^3/(e*x+d)^3*a^2*b^2*d+8/e^5/(e*x+d)^3*a^2*c^2*d^3-4/e^4/(e*x+d)^3*a*b^3*d^2+8/e^7/(e*x+d)^3*a*c^3*d^5-20/3/e^6/(e*x+d)^3*b^3*c*d^4-20*c^3/e^6*a*d*x+12*c^2/e^5*a*b*x-3/e^5/(e*x+d)^4*d^4*a*b^2*c+b^4/e^5*ln(e*x+d)+1/4*c^4*x^4/e^5-28/3/e^8/(e*x+d)^3*b*c^3*d^6+1/e^2/(e*x+d)^4*d*a^3*b-1/e^3/(e*x+d)^4*a^3*c*d^2-3/2/e^3/(e*x+d)^4*d^2*a^2*b^2-3/2/e^5/(e*x+d)^4*a^2*c^2*d^4+1/e^4/(e*x+d)^4*d^3*a*b^3-1/e^7/(e*x+d)^4*a*c^3*d^6+1/e^6/(e*x+d)^4*b^3*c*d^5-3/2/e^7/(e*x+d)^4*b^2*c^2*d^6+1/e^8/(e*x+d)^4*b*c^3*d^7-30*c^2/e^6*b^2*d*x+60*c^3/e^7*b*d^2*x-12/e^4/(e*x+d)*a^2*b*c+24/e^5/(e*x+d)*a^2*c^2*d+80/e^7/(e*x+d)*a*c^3*d^3-40/e^6/(e*x+d)*b^3*c*d^2+120/e^7/(e*x+d)*b^2*c^2*d^3-140/e^8/(e*x+d)*b*c^3*d^4-18/e^5/(e*x+d)^2*a^2*c^2*d^2+6/e^4/(e*x+d)^2*a*b^3*d-30/e^7/(e*x+d)^2*a*c^3*d^4+20/e^6/(e*x+d)^2*b^3*c*d^3+12/e^5*ln(e*x+d)*a*b^2*c+60/e^7*ln(e*x+d)*a*c^3*d^2-20/e^6*ln(e*x+d)*b^3*c*d+90/e^7*ln(e*x+d)*b^2*c^2*d^2-140/e^8*ln(e*x+d)*b*c^3*d^3","B"
2156,1,1341,408,0.066000," ","int((c*x^2+b*x+a)^4/(e*x+d)^6,x)","-\frac{a^{4}}{5 \left(e x +d \right)^{5} e}+\frac{4 a^{3} b d}{5 \left(e x +d \right)^{5} e^{2}}-\frac{4 a^{3} c \,d^{2}}{5 \left(e x +d \right)^{5} e^{3}}-\frac{6 a^{2} b^{2} d^{2}}{5 \left(e x +d \right)^{5} e^{3}}+\frac{12 a^{2} b c \,d^{3}}{5 \left(e x +d \right)^{5} e^{4}}-\frac{6 a^{2} c^{2} d^{4}}{5 \left(e x +d \right)^{5} e^{5}}+\frac{4 a \,b^{3} d^{3}}{5 \left(e x +d \right)^{5} e^{4}}-\frac{12 a \,b^{2} c \,d^{4}}{5 \left(e x +d \right)^{5} e^{5}}+\frac{12 a b \,c^{2} d^{5}}{5 \left(e x +d \right)^{5} e^{6}}-\frac{4 a \,c^{3} d^{6}}{5 \left(e x +d \right)^{5} e^{7}}-\frac{b^{4} d^{4}}{5 \left(e x +d \right)^{5} e^{5}}+\frac{4 b^{3} c \,d^{5}}{5 \left(e x +d \right)^{5} e^{6}}-\frac{6 b^{2} c^{2} d^{6}}{5 \left(e x +d \right)^{5} e^{7}}+\frac{4 b \,c^{3} d^{7}}{5 \left(e x +d \right)^{5} e^{8}}-\frac{c^{4} d^{8}}{5 \left(e x +d \right)^{5} e^{9}}-\frac{a^{3} b}{\left(e x +d \right)^{4} e^{2}}+\frac{2 a^{3} c d}{\left(e x +d \right)^{4} e^{3}}+\frac{3 a^{2} b^{2} d}{\left(e x +d \right)^{4} e^{3}}-\frac{9 a^{2} b c \,d^{2}}{\left(e x +d \right)^{4} e^{4}}+\frac{6 a^{2} c^{2} d^{3}}{\left(e x +d \right)^{4} e^{5}}-\frac{3 a \,b^{3} d^{2}}{\left(e x +d \right)^{4} e^{4}}+\frac{12 a \,b^{2} c \,d^{3}}{\left(e x +d \right)^{4} e^{5}}-\frac{15 a b \,c^{2} d^{4}}{\left(e x +d \right)^{4} e^{6}}+\frac{6 a \,c^{3} d^{5}}{\left(e x +d \right)^{4} e^{7}}+\frac{b^{4} d^{3}}{\left(e x +d \right)^{4} e^{5}}-\frac{5 b^{3} c \,d^{4}}{\left(e x +d \right)^{4} e^{6}}+\frac{9 b^{2} c^{2} d^{5}}{\left(e x +d \right)^{4} e^{7}}-\frac{7 b \,c^{3} d^{6}}{\left(e x +d \right)^{4} e^{8}}+\frac{2 c^{4} d^{7}}{\left(e x +d \right)^{4} e^{9}}-\frac{4 a^{3} c}{3 \left(e x +d \right)^{3} e^{3}}-\frac{2 a^{2} b^{2}}{\left(e x +d \right)^{3} e^{3}}+\frac{12 a^{2} b c d}{\left(e x +d \right)^{3} e^{4}}-\frac{12 a^{2} c^{2} d^{2}}{\left(e x +d \right)^{3} e^{5}}+\frac{4 a \,b^{3} d}{\left(e x +d \right)^{3} e^{4}}-\frac{24 a \,b^{2} c \,d^{2}}{\left(e x +d \right)^{3} e^{5}}+\frac{40 a b \,c^{2} d^{3}}{\left(e x +d \right)^{3} e^{6}}-\frac{20 a \,c^{3} d^{4}}{\left(e x +d \right)^{3} e^{7}}-\frac{2 b^{4} d^{2}}{\left(e x +d \right)^{3} e^{5}}+\frac{40 b^{3} c \,d^{3}}{3 \left(e x +d \right)^{3} e^{6}}-\frac{30 b^{2} c^{2} d^{4}}{\left(e x +d \right)^{3} e^{7}}+\frac{28 b \,c^{3} d^{5}}{\left(e x +d \right)^{3} e^{8}}-\frac{28 c^{4} d^{6}}{3 \left(e x +d \right)^{3} e^{9}}+\frac{c^{4} x^{3}}{3 e^{6}}-\frac{6 a^{2} b c}{\left(e x +d \right)^{2} e^{4}}+\frac{12 a^{2} c^{2} d}{\left(e x +d \right)^{2} e^{5}}-\frac{2 a \,b^{3}}{\left(e x +d \right)^{2} e^{4}}+\frac{24 a \,b^{2} c d}{\left(e x +d \right)^{2} e^{5}}-\frac{60 a b \,c^{2} d^{2}}{\left(e x +d \right)^{2} e^{6}}+\frac{40 a \,c^{3} d^{3}}{\left(e x +d \right)^{2} e^{7}}+\frac{2 b^{4} d}{\left(e x +d \right)^{2} e^{5}}-\frac{20 b^{3} c \,d^{2}}{\left(e x +d \right)^{2} e^{6}}+\frac{60 b^{2} c^{2} d^{3}}{\left(e x +d \right)^{2} e^{7}}-\frac{70 b \,c^{3} d^{4}}{\left(e x +d \right)^{2} e^{8}}+\frac{2 b \,c^{3} x^{2}}{e^{6}}+\frac{28 c^{4} d^{5}}{\left(e x +d \right)^{2} e^{9}}-\frac{3 c^{4} d \,x^{2}}{e^{7}}-\frac{6 a^{2} c^{2}}{\left(e x +d \right) e^{5}}-\frac{12 a \,b^{2} c}{\left(e x +d \right) e^{5}}+\frac{60 a b \,c^{2} d}{\left(e x +d \right) e^{6}}+\frac{12 a b \,c^{2} \ln \left(e x +d \right)}{e^{6}}-\frac{60 a \,c^{3} d^{2}}{\left(e x +d \right) e^{7}}-\frac{24 a \,c^{3} d \ln \left(e x +d \right)}{e^{7}}+\frac{4 a \,c^{3} x}{e^{6}}-\frac{b^{4}}{\left(e x +d \right) e^{5}}+\frac{20 b^{3} c d}{\left(e x +d \right) e^{6}}+\frac{4 b^{3} c \ln \left(e x +d \right)}{e^{6}}-\frac{90 b^{2} c^{2} d^{2}}{\left(e x +d \right) e^{7}}-\frac{36 b^{2} c^{2} d \ln \left(e x +d \right)}{e^{7}}+\frac{6 b^{2} c^{2} x}{e^{6}}+\frac{140 b \,c^{3} d^{3}}{\left(e x +d \right) e^{8}}+\frac{84 b \,c^{3} d^{2} \ln \left(e x +d \right)}{e^{8}}-\frac{24 b \,c^{3} d x}{e^{7}}-\frac{70 c^{4} d^{4}}{\left(e x +d \right) e^{9}}-\frac{56 c^{4} d^{3} \ln \left(e x +d \right)}{e^{9}}+\frac{21 c^{4} d^{2} x}{e^{8}}"," ",0,"12/e^5/(e*x+d)^4*a*b^2*c*d^3+60/e^6/(e*x+d)*a*b*c^2*d-24/e^5/(e*x+d)^3*a*b^2*c*d^2+40/e^6/(e*x+d)^3*a*b*c^2*d^3-9/e^4/(e*x+d)^4*a^2*b*c*d^2+4*c^3/e^6*a*x+6*c^2/e^6*b^2*x+21*c^4/e^8*d^2*x+12/e^5/(e*x+d)^2*a^2*c^2*d+40/e^7/(e*x+d)^2*a*c^3*d^3-20/e^6/(e*x+d)^2*b^3*c*d^2+60/e^7/(e*x+d)^2*b^2*c^2*d^3-24*c^3/e^7*b*d*x+12*c^2/e^6*ln(e*x+d)*a*b-24*c^3/e^7*ln(e*x+d)*a*d-36*c^2/e^7*ln(e*x+d)*b^2*d+84*c^3/e^8*ln(e*x+d)*b*d^2-3/e^4/(e*x+d)^4*a*b^3*d^2+6/e^7/(e*x+d)^4*a*c^3*d^5+28/e^8/(e*x+d)^3*b*c^3*d^5+2/e^3/(e*x+d)^4*a^3*c*d+3/e^3/(e*x+d)^4*a^2*b^2*d+6/e^5/(e*x+d)^4*a^2*c^2*d^3-1/e^5/(e*x+d)*b^4-1/5/e/(e*x+d)^5*a^4-12/5/e^5/(e*x+d)^5*d^4*a*b^2*c+12/5/e^6/(e*x+d)^5*d^5*a*b*c^2+24/e^5/(e*x+d)^2*a*b^2*c*d-60/e^6/(e*x+d)^2*a*b*c^2*d^2+12/e^4/(e*x+d)^3*a^2*b*c*d-15/e^6/(e*x+d)^4*a*b*c^2*d^4+12/5/e^4/(e*x+d)^5*d^3*a^2*b*c-2/e^5/(e*x+d)^3*b^4*d^2+4*c/e^6*ln(e*x+d)*b^3-56*c^4/e^9*ln(e*x+d)*d^3+2*c^3/e^6*x^2*b-3*c^4/e^7*x^2*d-28/3/e^9/(e*x+d)^3*c^4*d^6-1/e^2/(e*x+d)^4*a^3*b+1/e^5/(e*x+d)^4*b^4*d^3+2/e^9/(e*x+d)^4*c^4*d^7-6/e^5/(e*x+d)*c^2*a^2-70/e^9/(e*x+d)*c^4*d^4-1/5/e^5/(e*x+d)^5*d^4*b^4-1/5/e^9/(e*x+d)^5*c^4*d^8-2/e^4/(e*x+d)^2*a*b^3+2/e^5/(e*x+d)^2*b^4*d+28/e^9/(e*x+d)^2*c^4*d^5-4/3/e^3/(e*x+d)^3*a^3*c-2/e^3/(e*x+d)^3*a^2*b^2+1/3*c^4*x^3/e^6-70/e^8/(e*x+d)^2*b*c^3*d^4-12/e^5/(e*x+d)^3*a^2*c^2*d^2-30/e^7/(e*x+d)^3*b^2*c^2*d^4-5/e^6/(e*x+d)^4*b^3*c*d^4+9/e^7/(e*x+d)^4*b^2*c^2*d^5-7/e^8/(e*x+d)^4*b*c^3*d^6-12/e^5/(e*x+d)*a*b^2*c-60/e^7/(e*x+d)*a*c^3*d^2+20/e^6/(e*x+d)*b^3*c*d-90/e^7/(e*x+d)*b^2*c^2*d^2+140/e^8/(e*x+d)*b*c^3*d^3+4/5/e^2/(e*x+d)^5*d*a^3*b-4/5/e^3/(e*x+d)^5*a^3*c*d^2-6/5/e^3/(e*x+d)^5*d^2*a^2*b^2-6/5/e^5/(e*x+d)^5*a^2*c^2*d^4+4/5/e^4/(e*x+d)^5*d^3*a*b^3-4/5/e^7/(e*x+d)^5*a*c^3*d^6+4/5/e^6/(e*x+d)^5*d^5*b^3*c-6/5/e^7/(e*x+d)^5*b^2*c^2*d^6+4/5/e^8/(e*x+d)^5*b*c^3*d^7-6/e^4/(e*x+d)^2*a^2*b*c+4/e^4/(e*x+d)^3*a*b^3*d-20/e^7/(e*x+d)^3*a*c^3*d^4+40/3/e^6/(e*x+d)^3*b^3*c*d^3","B"
2157,1,1364,415,0.069000," ","int((c*x^2+b*x+a)^4/(e*x+d)^7,x)","-\frac{a^{4}}{6 \left(e x +d \right)^{6} e}+\frac{2 a^{3} b d}{3 \left(e x +d \right)^{6} e^{2}}-\frac{2 a^{3} c \,d^{2}}{3 \left(e x +d \right)^{6} e^{3}}-\frac{a^{2} b^{2} d^{2}}{\left(e x +d \right)^{6} e^{3}}+\frac{2 a^{2} b c \,d^{3}}{\left(e x +d \right)^{6} e^{4}}-\frac{a^{2} c^{2} d^{4}}{\left(e x +d \right)^{6} e^{5}}+\frac{2 a \,b^{3} d^{3}}{3 \left(e x +d \right)^{6} e^{4}}-\frac{2 a \,b^{2} c \,d^{4}}{\left(e x +d \right)^{6} e^{5}}+\frac{2 a b \,c^{2} d^{5}}{\left(e x +d \right)^{6} e^{6}}-\frac{2 a \,c^{3} d^{6}}{3 \left(e x +d \right)^{6} e^{7}}-\frac{b^{4} d^{4}}{6 \left(e x +d \right)^{6} e^{5}}+\frac{2 b^{3} c \,d^{5}}{3 \left(e x +d \right)^{6} e^{6}}-\frac{b^{2} c^{2} d^{6}}{\left(e x +d \right)^{6} e^{7}}+\frac{2 b \,c^{3} d^{7}}{3 \left(e x +d \right)^{6} e^{8}}-\frac{c^{4} d^{8}}{6 \left(e x +d \right)^{6} e^{9}}-\frac{4 a^{3} b}{5 \left(e x +d \right)^{5} e^{2}}+\frac{8 a^{3} c d}{5 \left(e x +d \right)^{5} e^{3}}+\frac{12 a^{2} b^{2} d}{5 \left(e x +d \right)^{5} e^{3}}-\frac{36 a^{2} b c \,d^{2}}{5 \left(e x +d \right)^{5} e^{4}}+\frac{24 a^{2} c^{2} d^{3}}{5 \left(e x +d \right)^{5} e^{5}}-\frac{12 a \,b^{3} d^{2}}{5 \left(e x +d \right)^{5} e^{4}}+\frac{48 a \,b^{2} c \,d^{3}}{5 \left(e x +d \right)^{5} e^{5}}-\frac{12 a b \,c^{2} d^{4}}{\left(e x +d \right)^{5} e^{6}}+\frac{24 a \,c^{3} d^{5}}{5 \left(e x +d \right)^{5} e^{7}}+\frac{4 b^{4} d^{3}}{5 \left(e x +d \right)^{5} e^{5}}-\frac{4 b^{3} c \,d^{4}}{\left(e x +d \right)^{5} e^{6}}+\frac{36 b^{2} c^{2} d^{5}}{5 \left(e x +d \right)^{5} e^{7}}-\frac{28 b \,c^{3} d^{6}}{5 \left(e x +d \right)^{5} e^{8}}+\frac{8 c^{4} d^{7}}{5 \left(e x +d \right)^{5} e^{9}}-\frac{a^{3} c}{\left(e x +d \right)^{4} e^{3}}-\frac{3 a^{2} b^{2}}{2 \left(e x +d \right)^{4} e^{3}}+\frac{9 a^{2} b c d}{\left(e x +d \right)^{4} e^{4}}-\frac{9 a^{2} c^{2} d^{2}}{\left(e x +d \right)^{4} e^{5}}+\frac{3 a \,b^{3} d}{\left(e x +d \right)^{4} e^{4}}-\frac{18 a \,b^{2} c \,d^{2}}{\left(e x +d \right)^{4} e^{5}}+\frac{30 a b \,c^{2} d^{3}}{\left(e x +d \right)^{4} e^{6}}-\frac{15 a \,c^{3} d^{4}}{\left(e x +d \right)^{4} e^{7}}-\frac{3 b^{4} d^{2}}{2 \left(e x +d \right)^{4} e^{5}}+\frac{10 b^{3} c \,d^{3}}{\left(e x +d \right)^{4} e^{6}}-\frac{45 b^{2} c^{2} d^{4}}{2 \left(e x +d \right)^{4} e^{7}}+\frac{21 b \,c^{3} d^{5}}{\left(e x +d \right)^{4} e^{8}}-\frac{7 c^{4} d^{6}}{\left(e x +d \right)^{4} e^{9}}-\frac{4 a^{2} b c}{\left(e x +d \right)^{3} e^{4}}+\frac{8 a^{2} c^{2} d}{\left(e x +d \right)^{3} e^{5}}-\frac{4 a \,b^{3}}{3 \left(e x +d \right)^{3} e^{4}}+\frac{16 a \,b^{2} c d}{\left(e x +d \right)^{3} e^{5}}-\frac{40 a b \,c^{2} d^{2}}{\left(e x +d \right)^{3} e^{6}}+\frac{80 a \,c^{3} d^{3}}{3 \left(e x +d \right)^{3} e^{7}}+\frac{4 b^{4} d}{3 \left(e x +d \right)^{3} e^{5}}-\frac{40 b^{3} c \,d^{2}}{3 \left(e x +d \right)^{3} e^{6}}+\frac{40 b^{2} c^{2} d^{3}}{\left(e x +d \right)^{3} e^{7}}-\frac{140 b \,c^{3} d^{4}}{3 \left(e x +d \right)^{3} e^{8}}+\frac{56 c^{4} d^{5}}{3 \left(e x +d \right)^{3} e^{9}}-\frac{3 a^{2} c^{2}}{\left(e x +d \right)^{2} e^{5}}-\frac{6 a \,b^{2} c}{\left(e x +d \right)^{2} e^{5}}+\frac{30 a b \,c^{2} d}{\left(e x +d \right)^{2} e^{6}}-\frac{30 a \,c^{3} d^{2}}{\left(e x +d \right)^{2} e^{7}}-\frac{b^{4}}{2 \left(e x +d \right)^{2} e^{5}}+\frac{10 b^{3} c d}{\left(e x +d \right)^{2} e^{6}}-\frac{45 b^{2} c^{2} d^{2}}{\left(e x +d \right)^{2} e^{7}}+\frac{70 b \,c^{3} d^{3}}{\left(e x +d \right)^{2} e^{8}}-\frac{35 c^{4} d^{4}}{\left(e x +d \right)^{2} e^{9}}+\frac{c^{4} x^{2}}{2 e^{7}}-\frac{12 a b \,c^{2}}{\left(e x +d \right) e^{6}}+\frac{24 a \,c^{3} d}{\left(e x +d \right) e^{7}}+\frac{4 a \,c^{3} \ln \left(e x +d \right)}{e^{7}}-\frac{4 b^{3} c}{\left(e x +d \right) e^{6}}+\frac{36 b^{2} c^{2} d}{\left(e x +d \right) e^{7}}+\frac{6 b^{2} c^{2} \ln \left(e x +d \right)}{e^{7}}-\frac{84 b \,c^{3} d^{2}}{\left(e x +d \right) e^{8}}-\frac{28 b \,c^{3} d \ln \left(e x +d \right)}{e^{8}}+\frac{4 b \,c^{3} x}{e^{7}}+\frac{56 c^{4} d^{3}}{\left(e x +d \right) e^{9}}+\frac{28 c^{4} d^{2} \ln \left(e x +d \right)}{e^{9}}-\frac{7 c^{4} d x}{e^{8}}"," ",0,"-18/e^5/(e*x+d)^4*a*b^2*c*d^2+30/e^6/(e*x+d)^4*a*b*c^2*d^3-4/5/e^2/(e*x+d)^5*a^3*b+4/5/e^5/(e*x+d)^5*b^4*d^3+8/5/e^9/(e*x+d)^5*c^4*d^7-3/e^5/(e*x+d)^2*c^2*a^2-35/e^9/(e*x+d)^2*c^4*d^4-4/3/e^4/(e*x+d)^3*a*b^3+4/3/e^5/(e*x+d)^3*b^4*d+56/3/e^9/(e*x+d)^3*c^4*d^5-4*c/e^6/(e*x+d)*b^3+56*c^4/e^9/(e*x+d)*d^3-1/6/e^5/(e*x+d)^6*d^4*b^4-1/6/e^9/(e*x+d)^6*c^4*d^8+4*c^3/e^7*x*b-7*c^4/e^8*x*d+6*c^2/e^7*ln(e*x+d)*b^2+28*c^4/e^9*ln(e*x+d)*d^2-1/e^3/(e*x+d)^4*a^3*c-3/2/e^3/(e*x+d)^4*a^2*b^2-3/2/e^5/(e*x+d)^4*b^4*d^2-7/e^9/(e*x+d)^4*c^4*d^6+4*c^3/e^7*ln(e*x+d)*a+8/5/e^3/(e*x+d)^5*a^3*c*d+12/5/e^3/(e*x+d)^5*a^2*b^2*d-2/3/e^7/(e*x+d)^6*a*c^3*d^6+2/3/e^6/(e*x+d)^6*d^5*b^3*c-1/e^7/(e*x+d)^6*d^6*b^2*c^2+2/3/e^8/(e*x+d)^6*b*c^3*d^7-1/6/e/(e*x+d)^6*a^4-1/2/e^5/(e*x+d)^2*b^4-40/e^6/(e*x+d)^3*a*b*c^2*d^2+9/e^4/(e*x+d)^4*a^2*b*c*d+2/e^4/(e*x+d)^6*d^3*a^2*b*c-2/e^5/(e*x+d)^6*d^4*a*b^2*c+2/e^6/(e*x+d)^6*d^5*a*b*c^2-36/5/e^4/(e*x+d)^5*a^2*b*c*d^2+48/5/e^5/(e*x+d)^5*a*b^2*c*d^3-12/e^6/(e*x+d)^5*a*b*c^2*d^4+30/e^6/(e*x+d)^2*a*b*c^2*d+16/e^5/(e*x+d)^3*a*b^2*c*d-28*c^3/e^8*ln(e*x+d)*b*d+24/5/e^5/(e*x+d)^5*a^2*c^2*d^3+1/2*c^4*x^2/e^7+36/5/e^7/(e*x+d)^5*b^2*c^2*d^5-28/5/e^8/(e*x+d)^5*b*c^3*d^6-6/e^5/(e*x+d)^2*a*b^2*c-30/e^7/(e*x+d)^2*a*c^3*d^2+10/e^6/(e*x+d)^2*b^3*c*d-45/e^7/(e*x+d)^2*b^2*c^2*d^2+70/e^8/(e*x+d)^2*b*c^3*d^3-4/e^4/(e*x+d)^3*a^2*b*c+8/e^5/(e*x+d)^3*a^2*c^2*d+80/3/e^7/(e*x+d)^3*a*c^3*d^3-40/3/e^6/(e*x+d)^3*b^3*c*d^2+40/e^7/(e*x+d)^3*b^2*c^2*d^3-140/3/e^8/(e*x+d)^3*b*c^3*d^4-9/e^5/(e*x+d)^4*a^2*c^2*d^2+3/e^4/(e*x+d)^4*a*b^3*d-15/e^7/(e*x+d)^4*a*c^3*d^4+10/e^6/(e*x+d)^4*b^3*c*d^3-45/2/e^7/(e*x+d)^4*b^2*c^2*d^4+21/e^8/(e*x+d)^4*b*c^3*d^5-12*c^2/e^6/(e*x+d)*a*b+24*c^3/e^7/(e*x+d)*a*d+36*c^2/e^7/(e*x+d)*b^2*d-84*c^3/e^8/(e*x+d)*b*d^2-12/5/e^4/(e*x+d)^5*a*b^3*d^2+2/3/e^2/(e*x+d)^6*d*a^3*b-2/3/e^3/(e*x+d)^6*a^3*c*d^2-1/e^3/(e*x+d)^6*d^2*a^2*b^2-1/e^5/(e*x+d)^6*a^2*c^2*d^4+2/3/e^4/(e*x+d)^6*d^3*a*b^3+24/5/e^7/(e*x+d)^5*a*c^3*d^5-4/e^6/(e*x+d)^5*b^3*c*d^4","B"
2158,1,1374,417,0.062000," ","int((c*x^2+b*x+a)^4/(e*x+d)^8,x)","-\frac{a^{4}}{7 \left(e x +d \right)^{7} e}+\frac{4 a^{3} b d}{7 \left(e x +d \right)^{7} e^{2}}-\frac{4 a^{3} c \,d^{2}}{7 \left(e x +d \right)^{7} e^{3}}-\frac{6 a^{2} b^{2} d^{2}}{7 \left(e x +d \right)^{7} e^{3}}+\frac{12 a^{2} b c \,d^{3}}{7 \left(e x +d \right)^{7} e^{4}}-\frac{6 a^{2} c^{2} d^{4}}{7 \left(e x +d \right)^{7} e^{5}}+\frac{4 a \,b^{3} d^{3}}{7 \left(e x +d \right)^{7} e^{4}}-\frac{12 a \,b^{2} c \,d^{4}}{7 \left(e x +d \right)^{7} e^{5}}+\frac{12 a b \,c^{2} d^{5}}{7 \left(e x +d \right)^{7} e^{6}}-\frac{4 a \,c^{3} d^{6}}{7 \left(e x +d \right)^{7} e^{7}}-\frac{b^{4} d^{4}}{7 \left(e x +d \right)^{7} e^{5}}+\frac{4 b^{3} c \,d^{5}}{7 \left(e x +d \right)^{7} e^{6}}-\frac{6 b^{2} c^{2} d^{6}}{7 \left(e x +d \right)^{7} e^{7}}+\frac{4 b \,c^{3} d^{7}}{7 \left(e x +d \right)^{7} e^{8}}-\frac{c^{4} d^{8}}{7 \left(e x +d \right)^{7} e^{9}}-\frac{2 a^{3} b}{3 \left(e x +d \right)^{6} e^{2}}+\frac{4 a^{3} c d}{3 \left(e x +d \right)^{6} e^{3}}+\frac{2 a^{2} b^{2} d}{\left(e x +d \right)^{6} e^{3}}-\frac{6 a^{2} b c \,d^{2}}{\left(e x +d \right)^{6} e^{4}}+\frac{4 a^{2} c^{2} d^{3}}{\left(e x +d \right)^{6} e^{5}}-\frac{2 a \,b^{3} d^{2}}{\left(e x +d \right)^{6} e^{4}}+\frac{8 a \,b^{2} c \,d^{3}}{\left(e x +d \right)^{6} e^{5}}-\frac{10 a b \,c^{2} d^{4}}{\left(e x +d \right)^{6} e^{6}}+\frac{4 a \,c^{3} d^{5}}{\left(e x +d \right)^{6} e^{7}}+\frac{2 b^{4} d^{3}}{3 \left(e x +d \right)^{6} e^{5}}-\frac{10 b^{3} c \,d^{4}}{3 \left(e x +d \right)^{6} e^{6}}+\frac{6 b^{2} c^{2} d^{5}}{\left(e x +d \right)^{6} e^{7}}-\frac{14 b \,c^{3} d^{6}}{3 \left(e x +d \right)^{6} e^{8}}+\frac{4 c^{4} d^{7}}{3 \left(e x +d \right)^{6} e^{9}}-\frac{4 a^{3} c}{5 \left(e x +d \right)^{5} e^{3}}-\frac{6 a^{2} b^{2}}{5 \left(e x +d \right)^{5} e^{3}}+\frac{36 a^{2} b c d}{5 \left(e x +d \right)^{5} e^{4}}-\frac{36 a^{2} c^{2} d^{2}}{5 \left(e x +d \right)^{5} e^{5}}+\frac{12 a \,b^{3} d}{5 \left(e x +d \right)^{5} e^{4}}-\frac{72 a \,b^{2} c \,d^{2}}{5 \left(e x +d \right)^{5} e^{5}}+\frac{24 a b \,c^{2} d^{3}}{\left(e x +d \right)^{5} e^{6}}-\frac{12 a \,c^{3} d^{4}}{\left(e x +d \right)^{5} e^{7}}-\frac{6 b^{4} d^{2}}{5 \left(e x +d \right)^{5} e^{5}}+\frac{8 b^{3} c \,d^{3}}{\left(e x +d \right)^{5} e^{6}}-\frac{18 b^{2} c^{2} d^{4}}{\left(e x +d \right)^{5} e^{7}}+\frac{84 b \,c^{3} d^{5}}{5 \left(e x +d \right)^{5} e^{8}}-\frac{28 c^{4} d^{6}}{5 \left(e x +d \right)^{5} e^{9}}-\frac{3 a^{2} b c}{\left(e x +d \right)^{4} e^{4}}+\frac{6 a^{2} c^{2} d}{\left(e x +d \right)^{4} e^{5}}-\frac{a \,b^{3}}{\left(e x +d \right)^{4} e^{4}}+\frac{12 a \,b^{2} c d}{\left(e x +d \right)^{4} e^{5}}-\frac{30 a b \,c^{2} d^{2}}{\left(e x +d \right)^{4} e^{6}}+\frac{20 a \,c^{3} d^{3}}{\left(e x +d \right)^{4} e^{7}}+\frac{b^{4} d}{\left(e x +d \right)^{4} e^{5}}-\frac{10 b^{3} c \,d^{2}}{\left(e x +d \right)^{4} e^{6}}+\frac{30 b^{2} c^{2} d^{3}}{\left(e x +d \right)^{4} e^{7}}-\frac{35 b \,c^{3} d^{4}}{\left(e x +d \right)^{4} e^{8}}+\frac{14 c^{4} d^{5}}{\left(e x +d \right)^{4} e^{9}}-\frac{2 a^{2} c^{2}}{\left(e x +d \right)^{3} e^{5}}-\frac{4 a \,b^{2} c}{\left(e x +d \right)^{3} e^{5}}+\frac{20 a b \,c^{2} d}{\left(e x +d \right)^{3} e^{6}}-\frac{20 a \,c^{3} d^{2}}{\left(e x +d \right)^{3} e^{7}}-\frac{b^{4}}{3 \left(e x +d \right)^{3} e^{5}}+\frac{20 b^{3} c d}{3 \left(e x +d \right)^{3} e^{6}}-\frac{30 b^{2} c^{2} d^{2}}{\left(e x +d \right)^{3} e^{7}}+\frac{140 b \,c^{3} d^{3}}{3 \left(e x +d \right)^{3} e^{8}}-\frac{70 c^{4} d^{4}}{3 \left(e x +d \right)^{3} e^{9}}-\frac{6 a b \,c^{2}}{\left(e x +d \right)^{2} e^{6}}+\frac{12 a \,c^{3} d}{\left(e x +d \right)^{2} e^{7}}-\frac{2 b^{3} c}{\left(e x +d \right)^{2} e^{6}}+\frac{18 b^{2} c^{2} d}{\left(e x +d \right)^{2} e^{7}}-\frac{42 b \,c^{3} d^{2}}{\left(e x +d \right)^{2} e^{8}}+\frac{28 c^{4} d^{3}}{\left(e x +d \right)^{2} e^{9}}-\frac{4 a \,c^{3}}{\left(e x +d \right) e^{7}}-\frac{6 b^{2} c^{2}}{\left(e x +d \right) e^{7}}+\frac{28 b \,c^{3} d}{\left(e x +d \right) e^{8}}+\frac{4 b \,c^{3} \ln \left(e x +d \right)}{e^{8}}-\frac{28 c^{4} d^{2}}{\left(e x +d \right) e^{9}}-\frac{8 c^{4} d \ln \left(e x +d \right)}{e^{9}}+\frac{c^{4} x}{e^{8}}"," ",0,"-6/e^4/(e*x+d)^6*a^2*b*c*d^2+12/7/e^4/(e*x+d)^7*d^3*a^2*b*c-12/7/e^5/(e*x+d)^7*d^4*a*b^2*c+20/e^6/(e*x+d)^3*a*b*c^2*d+12/e^5/(e*x+d)^4*a*b^2*c*d-30/e^6/(e*x+d)^4*a*b*c^2*d^2+8/e^5/(e*x+d)^6*a*b^2*c*d^3-10/e^6/(e*x+d)^6*a*b*c^2*d^4+36/5/e^4/(e*x+d)^5*a^2*b*c*d-72/5/e^5/(e*x+d)^5*a*b^2*c*d^2+24/e^6/(e*x+d)^5*a*b*c^2*d^3+12/7/e^6/(e*x+d)^7*d^5*a*b*c^2-28*c^4/e^9/(e*x+d)*d^2-1/7/e^5/(e*x+d)^7*d^4*b^4-1/7/e^9/(e*x+d)^7*c^4*d^8+4*c^3/e^8*ln(e*x+d)*b-8*c^4/e^9*ln(e*x+d)*d-1/e^4/(e*x+d)^4*a*b^3+1/e^5/(e*x+d)^4*b^4*d+14/e^9/(e*x+d)^4*c^4*d^5-4/5/e^3/(e*x+d)^5*a^3*c-6/5/e^3/(e*x+d)^5*a^2*b^2-6/5/e^5/(e*x+d)^5*b^4*d^2-28/5/e^9/(e*x+d)^5*c^4*d^6-2*c/e^6/(e*x+d)^2*b^3+28*c^4/e^9/(e*x+d)^2*d^3-2/e^5/(e*x+d)^3*c^2*a^2-70/3/e^9/(e*x+d)^3*c^4*d^4+4/3/e^9/(e*x+d)^6*c^4*d^7-2/3/e^2/(e*x+d)^6*a^3*b+2/3/e^5/(e*x+d)^6*b^4*d^3-4*c^3/e^7/(e*x+d)*a-6*c^2/e^7/(e*x+d)*b^2-6/7/e^5/(e*x+d)^7*a^2*c^2*d^4+4/7/e^4/(e*x+d)^7*d^3*a*b^3-4/7/e^7/(e*x+d)^7*a*c^3*d^6+4/7/e^6/(e*x+d)^7*d^5*b^3*c-6/7/e^7/(e*x+d)^7*d^6*b^2*c^2-36/5/e^5/(e*x+d)^5*a^2*c^2*d^2+12/5/e^4/(e*x+d)^5*a*b^3*d-12/e^7/(e*x+d)^5*a*c^3*d^4-1/3/(e*x+d)^3*b^4/e^5-35/e^8/(e*x+d)^4*b*c^3*d^4+4/7/e^8/(e*x+d)^7*d^7*b*c^3+4/3/e^3/(e*x+d)^6*a^3*c*d+2/e^3/(e*x+d)^6*a^2*b^2*d+4/e^5/(e*x+d)^6*a^2*c^2*d^3+4/e^7/(e*x+d)^6*a*c^3*d^5+28*c^3/e^8/(e*x+d)*b*d+4/7/e^2/(e*x+d)^7*d*a^3*b-4/7/e^3/(e*x+d)^7*a^3*c*d^2-6/7/e^3/(e*x+d)^7*d^2*a^2*b^2-1/7/e/(e*x+d)^7*a^4-6*c^2/e^6/(e*x+d)^2*a*b+12*c^3/e^7/(e*x+d)^2*a*d+18*c^2/e^7/(e*x+d)^2*b^2*d-42*c^3/e^8/(e*x+d)^2*b*d^2-4/e^5/(e*x+d)^3*a*b^2*c-20/e^7/(e*x+d)^3*a*c^3*d^2-2/e^4/(e*x+d)^6*a*b^3*d^2+20/3/e^6/(e*x+d)^3*b^3*c*d-30/e^7/(e*x+d)^3*b^2*c^2*d^2-10/3/e^6/(e*x+d)^6*b^3*c*d^4+6/e^7/(e*x+d)^6*b^2*c^2*d^5+140/3/e^8/(e*x+d)^3*b*c^3*d^3-3/e^4/(e*x+d)^4*a^2*b*c+6/e^5/(e*x+d)^4*a^2*c^2*d+20/e^7/(e*x+d)^4*a*c^3*d^3-10/e^6/(e*x+d)^4*b^3*c*d^2+30/e^7/(e*x+d)^4*b^2*c^2*d^3+8/e^6/(e*x+d)^5*b^3*c*d^3-18/e^7/(e*x+d)^5*b^2*c^2*d^4+84/5/e^8/(e*x+d)^5*b*c^3*d^5-14/3/e^8/(e*x+d)^6*b*c^3*d^6+c^4*x/e^8","B"
2159,1,1382,424,0.066000," ","int((c*x^2+b*x+a)^4/(e*x+d)^9,x)","-\frac{a^{4}}{8 \left(e x +d \right)^{8} e}+\frac{a^{3} b d}{2 \left(e x +d \right)^{8} e^{2}}-\frac{a^{3} c \,d^{2}}{2 \left(e x +d \right)^{8} e^{3}}-\frac{3 a^{2} b^{2} d^{2}}{4 \left(e x +d \right)^{8} e^{3}}+\frac{3 a^{2} b c \,d^{3}}{2 \left(e x +d \right)^{8} e^{4}}-\frac{3 a^{2} c^{2} d^{4}}{4 \left(e x +d \right)^{8} e^{5}}+\frac{a \,b^{3} d^{3}}{2 \left(e x +d \right)^{8} e^{4}}-\frac{3 a \,b^{2} c \,d^{4}}{2 \left(e x +d \right)^{8} e^{5}}+\frac{3 a b \,c^{2} d^{5}}{2 \left(e x +d \right)^{8} e^{6}}-\frac{a \,c^{3} d^{6}}{2 \left(e x +d \right)^{8} e^{7}}-\frac{b^{4} d^{4}}{8 \left(e x +d \right)^{8} e^{5}}+\frac{b^{3} c \,d^{5}}{2 \left(e x +d \right)^{8} e^{6}}-\frac{3 b^{2} c^{2} d^{6}}{4 \left(e x +d \right)^{8} e^{7}}+\frac{b \,c^{3} d^{7}}{2 \left(e x +d \right)^{8} e^{8}}-\frac{c^{4} d^{8}}{8 \left(e x +d \right)^{8} e^{9}}-\frac{4 a^{3} b}{7 \left(e x +d \right)^{7} e^{2}}+\frac{8 a^{3} c d}{7 \left(e x +d \right)^{7} e^{3}}+\frac{12 a^{2} b^{2} d}{7 \left(e x +d \right)^{7} e^{3}}-\frac{36 a^{2} b c \,d^{2}}{7 \left(e x +d \right)^{7} e^{4}}+\frac{24 a^{2} c^{2} d^{3}}{7 \left(e x +d \right)^{7} e^{5}}-\frac{12 a \,b^{3} d^{2}}{7 \left(e x +d \right)^{7} e^{4}}+\frac{48 a \,b^{2} c \,d^{3}}{7 \left(e x +d \right)^{7} e^{5}}-\frac{60 a b \,c^{2} d^{4}}{7 \left(e x +d \right)^{7} e^{6}}+\frac{24 a \,c^{3} d^{5}}{7 \left(e x +d \right)^{7} e^{7}}+\frac{4 b^{4} d^{3}}{7 \left(e x +d \right)^{7} e^{5}}-\frac{20 b^{3} c \,d^{4}}{7 \left(e x +d \right)^{7} e^{6}}+\frac{36 b^{2} c^{2} d^{5}}{7 \left(e x +d \right)^{7} e^{7}}-\frac{4 b \,c^{3} d^{6}}{\left(e x +d \right)^{7} e^{8}}+\frac{8 c^{4} d^{7}}{7 \left(e x +d \right)^{7} e^{9}}-\frac{2 a^{3} c}{3 \left(e x +d \right)^{6} e^{3}}-\frac{a^{2} b^{2}}{\left(e x +d \right)^{6} e^{3}}+\frac{6 a^{2} b c d}{\left(e x +d \right)^{6} e^{4}}-\frac{6 a^{2} c^{2} d^{2}}{\left(e x +d \right)^{6} e^{5}}+\frac{2 a \,b^{3} d}{\left(e x +d \right)^{6} e^{4}}-\frac{12 a \,b^{2} c \,d^{2}}{\left(e x +d \right)^{6} e^{5}}+\frac{20 a b \,c^{2} d^{3}}{\left(e x +d \right)^{6} e^{6}}-\frac{10 a \,c^{3} d^{4}}{\left(e x +d \right)^{6} e^{7}}-\frac{b^{4} d^{2}}{\left(e x +d \right)^{6} e^{5}}+\frac{20 b^{3} c \,d^{3}}{3 \left(e x +d \right)^{6} e^{6}}-\frac{15 b^{2} c^{2} d^{4}}{\left(e x +d \right)^{6} e^{7}}+\frac{14 b \,c^{3} d^{5}}{\left(e x +d \right)^{6} e^{8}}-\frac{14 c^{4} d^{6}}{3 \left(e x +d \right)^{6} e^{9}}-\frac{12 a^{2} b c}{5 \left(e x +d \right)^{5} e^{4}}+\frac{24 a^{2} c^{2} d}{5 \left(e x +d \right)^{5} e^{5}}-\frac{4 a \,b^{3}}{5 \left(e x +d \right)^{5} e^{4}}+\frac{48 a \,b^{2} c d}{5 \left(e x +d \right)^{5} e^{5}}-\frac{24 a b \,c^{2} d^{2}}{\left(e x +d \right)^{5} e^{6}}+\frac{16 a \,c^{3} d^{3}}{\left(e x +d \right)^{5} e^{7}}+\frac{4 b^{4} d}{5 \left(e x +d \right)^{5} e^{5}}-\frac{8 b^{3} c \,d^{2}}{\left(e x +d \right)^{5} e^{6}}+\frac{24 b^{2} c^{2} d^{3}}{\left(e x +d \right)^{5} e^{7}}-\frac{28 b \,c^{3} d^{4}}{\left(e x +d \right)^{5} e^{8}}+\frac{56 c^{4} d^{5}}{5 \left(e x +d \right)^{5} e^{9}}-\frac{3 a^{2} c^{2}}{2 \left(e x +d \right)^{4} e^{5}}-\frac{3 a \,b^{2} c}{\left(e x +d \right)^{4} e^{5}}+\frac{15 a b \,c^{2} d}{\left(e x +d \right)^{4} e^{6}}-\frac{15 a \,c^{3} d^{2}}{\left(e x +d \right)^{4} e^{7}}-\frac{b^{4}}{4 \left(e x +d \right)^{4} e^{5}}+\frac{5 b^{3} c d}{\left(e x +d \right)^{4} e^{6}}-\frac{45 b^{2} c^{2} d^{2}}{2 \left(e x +d \right)^{4} e^{7}}+\frac{35 b \,c^{3} d^{3}}{\left(e x +d \right)^{4} e^{8}}-\frac{35 c^{4} d^{4}}{2 \left(e x +d \right)^{4} e^{9}}-\frac{4 a b \,c^{2}}{\left(e x +d \right)^{3} e^{6}}+\frac{8 a \,c^{3} d}{\left(e x +d \right)^{3} e^{7}}-\frac{4 b^{3} c}{3 \left(e x +d \right)^{3} e^{6}}+\frac{12 b^{2} c^{2} d}{\left(e x +d \right)^{3} e^{7}}-\frac{28 b \,c^{3} d^{2}}{\left(e x +d \right)^{3} e^{8}}+\frac{56 c^{4} d^{3}}{3 \left(e x +d \right)^{3} e^{9}}-\frac{2 a \,c^{3}}{\left(e x +d \right)^{2} e^{7}}-\frac{3 b^{2} c^{2}}{\left(e x +d \right)^{2} e^{7}}+\frac{14 b \,c^{3} d}{\left(e x +d \right)^{2} e^{8}}-\frac{14 c^{4} d^{2}}{\left(e x +d \right)^{2} e^{9}}-\frac{4 b \,c^{3}}{\left(e x +d \right) e^{8}}+\frac{8 c^{4} d}{\left(e x +d \right) e^{9}}+\frac{c^{4} \ln \left(e x +d \right)}{e^{9}}"," ",0,"6/e^4/(e*x+d)^6*d*a^2*b*c-60/7/e^6/(e*x+d)^7*d^4*a*b*c^2+48/7/e^5/(e*x+d)^7*d^3*a*b^2*c-36/7/e^4/(e*x+d)^7*a^2*b*c*d^2+48/5/e^5/(e*x+d)^5*a*b^2*c*d-12/e^5/(e*x+d)^6*a*b^2*c*d^2+20/e^6/(e*x+d)^6*d^3*a*b*c^2+15/e^6/(e*x+d)^4*a*b*c^2*d-24/e^6/(e*x+d)^5*d^2*a*b*c^2+3/2/e^4/(e*x+d)^8*d^3*a^2*b*c-3/2/e^5/(e*x+d)^8*d^4*a*b^2*c+3/2/e^6/(e*x+d)^8*d^5*a*b*c^2-1/8/e/(e*x+d)^8*a^4+4/5/e^5/(e*x+d)^5*b^4*d+56/5/e^9/(e*x+d)^5*c^4*d^5-4*c^3/e^8/(e*x+d)*b+8*c^4/e^9/(e*x+d)*d-4/7/e^2/(e*x+d)^7*a^3*b+4/7/e^5/(e*x+d)^7*d^3*b^4-3/2/e^5/(e*x+d)^4*c^2*a^2-35/2/e^9/(e*x+d)^4*c^4*d^4+8/7/e^9/(e*x+d)^7*c^4*d^7-2/3/e^3/(e*x+d)^6*a^3*c-1/e^3/(e*x+d)^6*a^2*b^2-1/e^5/(e*x+d)^6*b^4*d^2-14/3/e^9/(e*x+d)^6*c^4*d^6-4/5/e^4/(e*x+d)^5*a*b^3-1/8/e^5/(e*x+d)^8*b^4*d^4-1/8/e^9/(e*x+d)^8*c^4*d^8-2*c^3/e^7/(e*x+d)^2*a-3*c^2/e^7/(e*x+d)^2*b^2-14*c^4/e^9/(e*x+d)^2*d^2-4/3*c/e^6/(e*x+d)^3*b^3+56/3*c^4/e^9/(e*x+d)^3*d^3-8/e^6/(e*x+d)^5*d^2*b^3*c-10/e^7/(e*x+d)^6*a*c^3*d^4-4*c^2/e^6/(e*x+d)^3*a*b+8*c^3/e^7/(e*x+d)^3*a*d+1/2/e^4/(e*x+d)^8*d^3*a*b^3-1/2/e^7/(e*x+d)^8*a*c^3*d^6+1/2/e^6/(e*x+d)^8*d^5*b^3*c-1/4/(e*x+d)^4*b^4/e^5+12*c^2/e^7/(e*x+d)^3*b^2*d-1/2/e^3/(e*x+d)^8*a^3*c*d^2+24/5/e^5/(e*x+d)^5*d*a^2*c^2+14/e^8/(e*x+d)^6*d^5*b*c^3-12/5/e^4/(e*x+d)^5*a^2*b*c+20/3/e^6/(e*x+d)^6*d^3*b^3*c-15/e^7/(e*x+d)^6*d^4*b^2*c^2-45/2/e^7/(e*x+d)^4*b^2*c^2*d^2+35/e^8/(e*x+d)^4*b*c^3*d^3+1/2/e^2/(e*x+d)^8*d*a^3*b-3/4/e^7/(e*x+d)^8*d^6*b^2*c^2-3/4/e^3/(e*x+d)^8*d^2*a^2*b^2-3/4/e^5/(e*x+d)^8*a^2*c^2*d^4+24/7/e^5/(e*x+d)^7*a^2*c^2*d^3-12/7/e^4/(e*x+d)^7*d^2*a*b^3+24/7/e^7/(e*x+d)^7*a*c^3*d^5-20/7/e^6/(e*x+d)^7*d^4*b^3*c+36/7/e^7/(e*x+d)^7*d^5*b^2*c^2-4/e^8/(e*x+d)^7*d^6*b*c^3-6/e^5/(e*x+d)^6*a^2*c^2*d^2+2/e^4/(e*x+d)^6*d*a*b^3+24/e^7/(e*x+d)^5*d^3*b^2*c^2-28/e^8/(e*x+d)^5*b*c^3*d^4+14*c^3/e^8/(e*x+d)^2*b*d+8/7/e^3/(e*x+d)^7*a^3*c*d+12/7/e^3/(e*x+d)^7*d*a^2*b^2-28*c^3/e^8/(e*x+d)^3*b*d^2-3/e^5/(e*x+d)^4*a*b^2*c-15/e^7/(e*x+d)^4*a*c^3*d^2+5/e^6/(e*x+d)^4*b^3*c*d+1/2/e^8/(e*x+d)^8*d^7*b*c^3+16/e^7/(e*x+d)^5*d^3*a*c^3+c^4*ln(e*x+d)/e^9","B"
2160,1,914,425,0.056000," ","int((c*x^2+b*x+a)^4/(e*x+d)^10,x)","-\frac{c^{4}}{\left(e x +d \right) e^{9}}-\frac{2 \left(b e -2 c d \right) c^{3}}{\left(e x +d \right)^{2} e^{9}}-\frac{2 \left(2 a c \,e^{2}+3 b^{2} e^{2}-14 b c d e +14 c^{2} d^{2}\right) c^{2}}{3 \left(e x +d \right)^{3} e^{9}}-\frac{\left(3 a b c \,e^{3}-6 c^{2} a d \,e^{2}+b^{3} e^{3}-9 b^{2} c d \,e^{2}+21 b \,c^{2} d^{2} e -14 c^{3} d^{3}\right) c}{\left(e x +d \right)^{4} e^{9}}-\frac{4 e^{6} a^{3} c +6 a^{2} b^{2} e^{6}-36 d \,a^{2} b c \,e^{5}+36 a^{2} c^{2} d^{2} e^{4}-12 d a \,b^{3} e^{5}+72 a \,b^{2} c \,d^{2} e^{4}-120 d^{3} a b \,c^{2} e^{3}+60 a \,c^{3} d^{4} e^{2}+6 b^{4} d^{2} e^{4}-40 d^{3} b^{3} c \,e^{3}+90 d^{4} b^{2} c^{2} e^{2}-84 b \,c^{3} d^{5} e +28 c^{4} d^{6}}{7 \left(e x +d \right)^{7} e^{9}}-\frac{12 a^{2} b c \,e^{5}-24 d \,a^{2} c^{2} e^{4}+4 a \,b^{3} e^{5}-48 a \,b^{2} c d \,e^{4}+120 d^{2} a b \,c^{2} e^{3}-80 d^{3} a \,c^{3} e^{2}-4 b^{4} d \,e^{4}+40 d^{2} b^{3} c \,e^{3}-120 d^{3} b^{2} c^{2} e^{2}+140 b \,c^{3} d^{4} e -56 c^{4} d^{5}}{6 \left(e x +d \right)^{6} e^{9}}-\frac{6 c^{2} a^{2} e^{4}+12 a \,b^{2} c \,e^{4}-60 a b \,c^{2} d \,e^{3}+60 a \,c^{3} d^{2} e^{2}+b^{4} e^{4}-20 b^{3} c d \,e^{3}+90 b^{2} c^{2} d^{2} e^{2}-140 b \,c^{3} d^{3} e +70 c^{4} d^{4}}{5 \left(e x +d \right)^{5} e^{9}}-\frac{a^{4} e^{8}-4 d \,a^{3} b \,e^{7}+4 a^{3} c \,d^{2} e^{6}+6 d^{2} a^{2} b^{2} e^{6}-12 d^{3} a^{2} b c \,e^{5}+6 a^{2} c^{2} d^{4} e^{4}-4 d^{3} a \,b^{3} e^{5}+12 d^{4} a \,b^{2} c \,e^{4}-12 d^{5} a b \,c^{2} e^{3}+4 a \,c^{3} d^{6} e^{2}+b^{4} d^{4} e^{4}-4 d^{5} b^{3} c \,e^{3}+6 d^{6} b^{2} c^{2} e^{2}-4 b \,c^{3} d^{7} e +c^{4} d^{8}}{9 \left(e x +d \right)^{9} e^{9}}-\frac{4 a^{3} b \,e^{7}-8 a^{3} c d \,e^{6}-12 d \,a^{2} b^{2} e^{6}+36 a^{2} b c \,d^{2} e^{5}-24 a^{2} c^{2} d^{3} e^{4}+12 d^{2} a \,b^{3} e^{5}-48 d^{3} a \,b^{2} c \,e^{4}+60 d^{4} a b \,c^{2} e^{3}-24 a \,c^{3} d^{5} e^{2}-4 d^{3} b^{4} e^{4}+20 d^{4} b^{3} c \,e^{3}-36 d^{5} b^{2} c^{2} e^{2}+28 b \,c^{3} d^{6} e -8 c^{4} d^{7}}{8 \left(e x +d \right)^{8} e^{9}}"," ",0,"-c^4/e^9/(e*x+d)-1/7*(4*a^3*c*e^6+6*a^2*b^2*e^6-36*a^2*b*c*d*e^5+36*a^2*c^2*d^2*e^4-12*a*b^3*d*e^5+72*a*b^2*c*d^2*e^4-120*a*b*c^2*d^3*e^3+60*a*c^3*d^4*e^2+6*b^4*d^2*e^4-40*b^3*c*d^3*e^3+90*b^2*c^2*d^4*e^2-84*b*c^3*d^5*e+28*c^4*d^6)/e^9/(e*x+d)^7-1/6*(12*a^2*b*c*e^5-24*a^2*c^2*d*e^4+4*a*b^3*e^5-48*a*b^2*c*d*e^4+120*a*b*c^2*d^2*e^3-80*a*c^3*d^3*e^2-4*b^4*d*e^4+40*b^3*c*d^2*e^3-120*b^2*c^2*d^3*e^2+140*b*c^3*d^4*e-56*c^4*d^5)/e^9/(e*x+d)^6-1/5*(6*a^2*c^2*e^4+12*a*b^2*c*e^4-60*a*b*c^2*d*e^3+60*a*c^3*d^2*e^2+b^4*e^4-20*b^3*c*d*e^3+90*b^2*c^2*d^2*e^2-140*b*c^3*d^3*e+70*c^4*d^4)/e^9/(e*x+d)^5-2*c^3*(b*e-2*c*d)/e^9/(e*x+d)^2-2/3*c^2*(2*a*c*e^2+3*b^2*e^2-14*b*c*d*e+14*c^2*d^2)/e^9/(e*x+d)^3-c*(3*a*b*c*e^3-6*a*c^2*d*e^2+b^3*e^3-9*b^2*c*d*e^2+21*b*c^2*d^2*e-14*c^3*d^3)/e^9/(e*x+d)^4-1/9*(a^4*e^8-4*a^3*b*d*e^7+4*a^3*c*d^2*e^6+6*a^2*b^2*d^2*e^6-12*a^2*b*c*d^3*e^5+6*a^2*c^2*d^4*e^4-4*a*b^3*d^3*e^5+12*a*b^2*c*d^4*e^4-12*a*b*c^2*d^5*e^3+4*a*c^3*d^6*e^2+b^4*d^4*e^4-4*b^3*c*d^5*e^3+6*b^2*c^2*d^6*e^2-4*b*c^3*d^7*e+c^4*d^8)/e^9/(e*x+d)^9-1/8*(4*a^3*b*e^7-8*a^3*c*d*e^6-12*a^2*b^2*d*e^6+36*a^2*b*c*d^2*e^5-24*a^2*c^2*d^3*e^4+12*a*b^3*d^2*e^5-48*a*b^2*c*d^3*e^4+60*a*b*c^2*d^4*e^3-24*a*c^3*d^5*e^2-4*b^4*d^3*e^4+20*b^3*c*d^4*e^3-36*b^2*c^2*d^5*e^2+28*b*c^3*d^6*e-8*c^4*d^7)/e^9/(e*x+d)^8","B"
2161,1,914,426,0.090000," ","int((c*x^2+b*x+a)^4/(e*x+d)^11,x)","-\frac{c^{4}}{2 \left(e x +d \right)^{2} e^{9}}-\frac{4 \left(b e -2 c d \right) c^{3}}{3 \left(e x +d \right)^{3} e^{9}}-\frac{\left(2 a c \,e^{2}+3 b^{2} e^{2}-14 b c d e +14 c^{2} d^{2}\right) c^{2}}{2 \left(e x +d \right)^{4} e^{9}}-\frac{4 \left(3 a b c \,e^{3}-6 c^{2} a d \,e^{2}+b^{3} e^{3}-9 b^{2} c d \,e^{2}+21 b \,c^{2} d^{2} e -14 c^{3} d^{3}\right) c}{5 \left(e x +d \right)^{5} e^{9}}-\frac{a^{4} e^{8}-4 d \,a^{3} b \,e^{7}+4 a^{3} c \,d^{2} e^{6}+6 d^{2} a^{2} b^{2} e^{6}-12 d^{3} a^{2} b c \,e^{5}+6 a^{2} c^{2} d^{4} e^{4}-4 d^{3} a \,b^{3} e^{5}+12 d^{4} a \,b^{2} c \,e^{4}-12 d^{5} a b \,c^{2} e^{3}+4 a \,c^{3} d^{6} e^{2}+b^{4} d^{4} e^{4}-4 d^{5} b^{3} c \,e^{3}+6 d^{6} b^{2} c^{2} e^{2}-4 b \,c^{3} d^{7} e +c^{4} d^{8}}{10 \left(e x +d \right)^{10} e^{9}}-\frac{12 a^{2} b c \,e^{5}-24 d \,a^{2} c^{2} e^{4}+4 a \,b^{3} e^{5}-48 a \,b^{2} c d \,e^{4}+120 d^{2} a b \,c^{2} e^{3}-80 d^{3} a \,c^{3} e^{2}-4 b^{4} d \,e^{4}+40 d^{2} b^{3} c \,e^{3}-120 d^{3} b^{2} c^{2} e^{2}+140 b \,c^{3} d^{4} e -56 c^{4} d^{5}}{7 \left(e x +d \right)^{7} e^{9}}-\frac{6 c^{2} a^{2} e^{4}+12 a \,b^{2} c \,e^{4}-60 a b \,c^{2} d \,e^{3}+60 a \,c^{3} d^{2} e^{2}+b^{4} e^{4}-20 b^{3} c d \,e^{3}+90 b^{2} c^{2} d^{2} e^{2}-140 b \,c^{3} d^{3} e +70 c^{4} d^{4}}{6 \left(e x +d \right)^{6} e^{9}}-\frac{4 a^{3} b \,e^{7}-8 a^{3} c d \,e^{6}-12 d \,a^{2} b^{2} e^{6}+36 a^{2} b c \,d^{2} e^{5}-24 a^{2} c^{2} d^{3} e^{4}+12 d^{2} a \,b^{3} e^{5}-48 d^{3} a \,b^{2} c \,e^{4}+60 d^{4} a b \,c^{2} e^{3}-24 a \,c^{3} d^{5} e^{2}-4 d^{3} b^{4} e^{4}+20 d^{4} b^{3} c \,e^{3}-36 d^{5} b^{2} c^{2} e^{2}+28 b \,c^{3} d^{6} e -8 c^{4} d^{7}}{9 \left(e x +d \right)^{9} e^{9}}-\frac{4 e^{6} a^{3} c +6 a^{2} b^{2} e^{6}-36 d \,a^{2} b c \,e^{5}+36 a^{2} c^{2} d^{2} e^{4}-12 d a \,b^{3} e^{5}+72 a \,b^{2} c \,d^{2} e^{4}-120 d^{3} a b \,c^{2} e^{3}+60 a \,c^{3} d^{4} e^{2}+6 b^{4} d^{2} e^{4}-40 d^{3} b^{3} c \,e^{3}+90 d^{4} b^{2} c^{2} e^{2}-84 b \,c^{3} d^{5} e +28 c^{4} d^{6}}{8 \left(e x +d \right)^{8} e^{9}}"," ",0,"-1/10*(a^4*e^8-4*a^3*b*d*e^7+4*a^3*c*d^2*e^6+6*a^2*b^2*d^2*e^6-12*a^2*b*c*d^3*e^5+6*a^2*c^2*d^4*e^4-4*a*b^3*d^3*e^5+12*a*b^2*c*d^4*e^4-12*a*b*c^2*d^5*e^3+4*a*c^3*d^6*e^2+b^4*d^4*e^4-4*b^3*c*d^5*e^3+6*b^2*c^2*d^6*e^2-4*b*c^3*d^7*e+c^4*d^8)/e^9/(e*x+d)^10-1/7*(12*a^2*b*c*e^5-24*a^2*c^2*d*e^4+4*a*b^3*e^5-48*a*b^2*c*d*e^4+120*a*b*c^2*d^2*e^3-80*a*c^3*d^3*e^2-4*b^4*d*e^4+40*b^3*c*d^2*e^3-120*b^2*c^2*d^3*e^2+140*b*c^3*d^4*e-56*c^4*d^5)/e^9/(e*x+d)^7-1/6*(6*a^2*c^2*e^4+12*a*b^2*c*e^4-60*a*b*c^2*d*e^3+60*a*c^3*d^2*e^2+b^4*e^4-20*b^3*c*d*e^3+90*b^2*c^2*d^2*e^2-140*b*c^3*d^3*e+70*c^4*d^4)/e^9/(e*x+d)^6-4/5*c*(3*a*b*c*e^3-6*a*c^2*d*e^2+b^3*e^3-9*b^2*c*d*e^2+21*b*c^2*d^2*e-14*c^3*d^3)/e^9/(e*x+d)^5-1/2*c^4/e^9/(e*x+d)^2-4/3*c^3*(b*e-2*c*d)/e^9/(e*x+d)^3-1/2*c^2*(2*a*c*e^2+3*b^2*e^2-14*b*c*d*e+14*c^2*d^2)/e^9/(e*x+d)^4-1/9*(4*a^3*b*e^7-8*a^3*c*d*e^6-12*a^2*b^2*d*e^6+36*a^2*b*c*d^2*e^5-24*a^2*c^2*d^3*e^4+12*a*b^3*d^2*e^5-48*a*b^2*c*d^3*e^4+60*a*b*c^2*d^4*e^3-24*a*c^3*d^5*e^2-4*b^4*d^3*e^4+20*b^3*c*d^4*e^3-36*b^2*c^2*d^5*e^2+28*b*c^3*d^6*e-8*c^4*d^7)/e^9/(e*x+d)^9-1/8*(4*a^3*c*e^6+6*a^2*b^2*e^6-36*a^2*b*c*d*e^5+36*a^2*c^2*d^2*e^4-12*a*b^3*d*e^5+72*a*b^2*c*d^2*e^4-120*a*b*c^2*d^3*e^3+60*a*c^3*d^4*e^2+6*b^4*d^2*e^4-40*b^3*c*d^3*e^3+90*b^2*c^2*d^4*e^2-84*b*c^3*d^5*e+28*c^4*d^6)/e^9/(e*x+d)^8","B"
2162,1,914,425,0.049000," ","int((c*x^2+b*x+a)^4/(e*x+d)^12,x)","-\frac{c^{4}}{3 \left(e x +d \right)^{3} e^{9}}-\frac{\left(b e -2 c d \right) c^{3}}{\left(e x +d \right)^{4} e^{9}}-\frac{2 \left(2 a c \,e^{2}+3 b^{2} e^{2}-14 b c d e +14 c^{2} d^{2}\right) c^{2}}{5 \left(e x +d \right)^{5} e^{9}}-\frac{2 \left(3 a b c \,e^{3}-6 c^{2} a d \,e^{2}+b^{3} e^{3}-9 b^{2} c d \,e^{2}+21 b \,c^{2} d^{2} e -14 c^{3} d^{3}\right) c}{3 \left(e x +d \right)^{6} e^{9}}-\frac{4 a^{3} b \,e^{7}-8 a^{3} c d \,e^{6}-12 d \,a^{2} b^{2} e^{6}+36 a^{2} b c \,d^{2} e^{5}-24 a^{2} c^{2} d^{3} e^{4}+12 d^{2} a \,b^{3} e^{5}-48 d^{3} a \,b^{2} c \,e^{4}+60 d^{4} a b \,c^{2} e^{3}-24 a \,c^{3} d^{5} e^{2}-4 d^{3} b^{4} e^{4}+20 d^{4} b^{3} c \,e^{3}-36 d^{5} b^{2} c^{2} e^{2}+28 b \,c^{3} d^{6} e -8 c^{4} d^{7}}{10 \left(e x +d \right)^{10} e^{9}}-\frac{6 c^{2} a^{2} e^{4}+12 a \,b^{2} c \,e^{4}-60 a b \,c^{2} d \,e^{3}+60 a \,c^{3} d^{2} e^{2}+b^{4} e^{4}-20 b^{3} c d \,e^{3}+90 b^{2} c^{2} d^{2} e^{2}-140 b \,c^{3} d^{3} e +70 c^{4} d^{4}}{7 \left(e x +d \right)^{7} e^{9}}-\frac{4 e^{6} a^{3} c +6 a^{2} b^{2} e^{6}-36 d \,a^{2} b c \,e^{5}+36 a^{2} c^{2} d^{2} e^{4}-12 d a \,b^{3} e^{5}+72 a \,b^{2} c \,d^{2} e^{4}-120 d^{3} a b \,c^{2} e^{3}+60 a \,c^{3} d^{4} e^{2}+6 b^{4} d^{2} e^{4}-40 d^{3} b^{3} c \,e^{3}+90 d^{4} b^{2} c^{2} e^{2}-84 b \,c^{3} d^{5} e +28 c^{4} d^{6}}{9 \left(e x +d \right)^{9} e^{9}}-\frac{12 a^{2} b c \,e^{5}-24 d \,a^{2} c^{2} e^{4}+4 a \,b^{3} e^{5}-48 a \,b^{2} c d \,e^{4}+120 d^{2} a b \,c^{2} e^{3}-80 d^{3} a \,c^{3} e^{2}-4 b^{4} d \,e^{4}+40 d^{2} b^{3} c \,e^{3}-120 d^{3} b^{2} c^{2} e^{2}+140 b \,c^{3} d^{4} e -56 c^{4} d^{5}}{8 \left(e x +d \right)^{8} e^{9}}-\frac{a^{4} e^{8}-4 d \,a^{3} b \,e^{7}+4 a^{3} c \,d^{2} e^{6}+6 d^{2} a^{2} b^{2} e^{6}-12 d^{3} a^{2} b c \,e^{5}+6 a^{2} c^{2} d^{4} e^{4}-4 d^{3} a \,b^{3} e^{5}+12 d^{4} a \,b^{2} c \,e^{4}-12 d^{5} a b \,c^{2} e^{3}+4 a \,c^{3} d^{6} e^{2}+b^{4} d^{4} e^{4}-4 d^{5} b^{3} c \,e^{3}+6 d^{6} b^{2} c^{2} e^{2}-4 b \,c^{3} d^{7} e +c^{4} d^{8}}{11 \left(e x +d \right)^{11} e^{9}}"," ",0,"-1/10*(4*a^3*b*e^7-8*a^3*c*d*e^6-12*a^2*b^2*d*e^6+36*a^2*b*c*d^2*e^5-24*a^2*c^2*d^3*e^4+12*a*b^3*d^2*e^5-48*a*b^2*c*d^3*e^4+60*a*b*c^2*d^4*e^3-24*a*c^3*d^5*e^2-4*b^4*d^3*e^4+20*b^3*c*d^4*e^3-36*b^2*c^2*d^5*e^2+28*b*c^3*d^6*e-8*c^4*d^7)/e^9/(e*x+d)^10-1/7*(6*a^2*c^2*e^4+12*a*b^2*c*e^4-60*a*b*c^2*d*e^3+60*a*c^3*d^2*e^2+b^4*e^4-20*b^3*c*d*e^3+90*b^2*c^2*d^2*e^2-140*b*c^3*d^3*e+70*c^4*d^4)/e^9/(e*x+d)^7-2/3*c*(3*a*b*c*e^3-6*a*c^2*d*e^2+b^3*e^3-9*b^2*c*d*e^2+21*b*c^2*d^2*e-14*c^3*d^3)/e^9/(e*x+d)^6-2/5*c^2*(2*a*c*e^2+3*b^2*e^2-14*b*c*d*e+14*c^2*d^2)/e^9/(e*x+d)^5-1/3*c^4/e^9/(e*x+d)^3-c^3*(b*e-2*c*d)/e^9/(e*x+d)^4-1/9*(4*a^3*c*e^6+6*a^2*b^2*e^6-36*a^2*b*c*d*e^5+36*a^2*c^2*d^2*e^4-12*a*b^3*d*e^5+72*a*b^2*c*d^2*e^4-120*a*b*c^2*d^3*e^3+60*a*c^3*d^4*e^2+6*b^4*d^2*e^4-40*b^3*c*d^3*e^3+90*b^2*c^2*d^4*e^2-84*b*c^3*d^5*e+28*c^4*d^6)/e^9/(e*x+d)^9-1/8*(12*a^2*b*c*e^5-24*a^2*c^2*d*e^4+4*a*b^3*e^5-48*a*b^2*c*d*e^4+120*a*b*c^2*d^2*e^3-80*a*c^3*d^3*e^2-4*b^4*d*e^4+40*b^3*c*d^2*e^3-120*b^2*c^2*d^3*e^2+140*b*c^3*d^4*e-56*c^4*d^5)/e^9/(e*x+d)^8-1/11*(a^4*e^8-4*a^3*b*d*e^7+4*a^3*c*d^2*e^6+6*a^2*b^2*d^2*e^6-12*a^2*b*c*d^3*e^5+6*a^2*c^2*d^4*e^4-4*a*b^3*d^3*e^5+12*a*b^2*c*d^4*e^4-12*a*b*c^2*d^5*e^3+4*a*c^3*d^6*e^2+b^4*d^4*e^4-4*b^3*c*d^5*e^3+6*b^2*c^2*d^6*e^2-4*b*c^3*d^7*e+c^4*d^8)/e^9/(e*x+d)^11","B"
2163,1,27,26,0.043000," ","int(x^4*(x^2-4*x+3)^2,x)","\frac{1}{9} x^{9}-x^{8}+\frac{22}{7} x^{7}-4 x^{6}+\frac{9}{5} x^{5}"," ",0,"9/5*x^5-4*x^6+22/7*x^7-x^8+1/9*x^9","A"
2164,1,27,26,0.043000," ","int(x^3*(x^2-4*x+3)^2,x)","\frac{1}{8} x^{8}-\frac{8}{7} x^{7}+\frac{11}{3} x^{6}-\frac{24}{5} x^{5}+\frac{9}{4} x^{4}"," ",0,"9/4*x^4-24/5*x^5+11/3*x^6-8/7*x^7+1/8*x^8","A"
2165,1,27,26,0.038000," ","int(x^2*(x^2-4*x+3)^2,x)","\frac{1}{7} x^{7}-\frac{4}{3} x^{6}+\frac{22}{5} x^{5}-6 x^{4}+3 x^{3}"," ",0,"3*x^3-6*x^4+22/5*x^5-4/3*x^6+1/7*x^7","A"
2166,1,27,26,0.046000," ","int(x*(x^2-4*x+3)^2,x)","\frac{1}{6} x^{6}-\frac{8}{5} x^{5}+\frac{11}{2} x^{4}-8 x^{3}+\frac{9}{2} x^{2}"," ",0,"9/2*x^2-8*x^3+11/2*x^4-8/5*x^5+1/6*x^6","A"
2167,1,25,24,0.040000," ","int((x^2-4*x+3)^2,x)","\frac{1}{5} x^{5}-2 x^{4}+\frac{22}{3} x^{3}-12 x^{2}+9 x"," ",0,"1/5*x^5-2*x^4+22/3*x^3-12*x^2+9*x","A"
2168,1,24,23,0.040000," ","int((x^2-4*x+3)^2/x,x)","\frac{x^{4}}{4}-\frac{8 x^{3}}{3}+11 x^{2}-24 x +9 \ln \left(x \right)"," ",0,"-24*x+11*x^2-8/3*x^3+1/4*x^4+9*ln(x)","A"
2169,1,24,23,0.051000," ","int((x^2-4*x+3)^2/x^2,x)","\frac{x^{3}}{3}-4 x^{2}+22 x -24 \ln \left(x \right)-\frac{9}{x}"," ",0,"-9/x+22*x-4*x^2+1/3*x^3-24*ln(x)","A"
2170,1,24,23,0.048000," ","int((x^2-4*x+3)^2/x^3,x)","\frac{x^{2}}{2}-8 x +22 \ln \left(x \right)+\frac{24}{x}-\frac{9}{2 x^{2}}"," ",0,"-9/2/x^2+24/x-8*x+1/2*x^2+22*ln(x)","A"
2171,1,22,21,0.052000," ","int((x^2-4*x+3)^2/x^4,x)","x -8 \ln \left(x \right)-\frac{22}{x}+\frac{12}{x^{2}}-\frac{3}{x^{3}}"," ",0,"-3/x^3+12/x^2-22/x+x-8*ln(x)","A"
2172,1,24,23,0.052000," ","int((x^2-4*x+3)^2/x^5,x)","\ln \left(x \right)+\frac{8}{x}-\frac{11}{x^{2}}+\frac{8}{x^{3}}-\frac{9}{4 x^{4}}"," ",0,"-9/4/x^4+8/x^3-11/x^2+8/x+ln(x)","A"
2173,1,27,26,0.052000," ","int((x^2-4*x+3)^2/x^6,x)","-\frac{1}{x}+\frac{4}{x^{2}}-\frac{22}{3 x^{3}}+\frac{6}{x^{4}}-\frac{9}{5 x^{5}}"," ",0,"-9/5/x^5+6/x^4-22/3/x^3+4/x^2-1/x","A"
2174,1,27,26,0.048000," ","int((x^2-4*x+3)^2/x^7,x)","-\frac{1}{2 x^{2}}+\frac{8}{3 x^{3}}-\frac{11}{2 x^{4}}+\frac{24}{5 x^{5}}-\frac{3}{2 x^{6}}"," ",0,"-3/2/x^6+24/5/x^5-11/2/x^4+8/3/x^3-1/2/x^2","A"
2175,1,13,12,0.044000," ","int((x^2+2*x+2)/(x+2),x)","\frac{x^{2}}{2}+2 \ln \left(x +2\right)"," ",0,"1/2*x^2+2*ln(x+2)","A"
2176,1,16,17,0.047000," ","int((x^2+4*x+5)/(x-2),x)","\frac{x^{2}}{2}+6 x +17 \ln \left(x -2\right)"," ",0,"1/2*x^2+6*x+17*ln(x-2)","A"
2177,1,13,12,0.062000," ","int((x^2+2*x+2)/(x+1)^3,x)","\ln \left(x +1\right)-\frac{1}{2 \left(x +1\right)^{2}}"," ",0,"-1/2/(x+1)^2+ln(x+1)","A"
2178,1,20,19,0.056000," ","int((2*x^2+3*x+3)/(x+1)^3,x)","2 \ln \left(x +1\right)-\frac{1}{\left(x +1\right)^{2}}+\frac{1}{x +1}"," ",0,"-1/(x+1)^2+1/(x+1)+2*ln(x+1)","A"
2179,1,10,9,0.046000," ","int((x^2+x+1)/x,x)","\frac{x^{2}}{2}+x +\ln \left(x \right)"," ",0,"x+1/2*x^2+ln(x)","A"
2180,1,12,11,0.066000," ","int((x^2+6*x+9)/x^2,x)","x +6 \ln \left(x \right)-\frac{9}{x}"," ",0,"-9/x+x+6*ln(x)","A"
2181,1,17,16,0.053000," ","int((x^2+2*x+1)/x^4,x)","-\frac{1}{x}-\frac{1}{x^{2}}-\frac{1}{3 x^{3}}"," ",0,"-1/3/x^3-1/x^2-1/x","A"
2182,1,595,233,0.055000," ","int((e*x+d)^4/(c*x^2+b*x+a),x)","\frac{e^{4} x^{3}}{3 c}+\frac{2 a^{2} e^{4} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, c^{2}}-\frac{4 a \,b^{2} e^{4} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, c^{3}}+\frac{12 a b d \,e^{3} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, c^{2}}-\frac{12 a \,d^{2} e^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, c}+\frac{b^{4} e^{4} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, c^{4}}-\frac{4 b^{3} d \,e^{3} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, c^{3}}+\frac{6 b^{2} d^{2} e^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, c^{2}}-\frac{4 b \,d^{3} e \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, c}-\frac{b \,e^{4} x^{2}}{2 c^{2}}+\frac{2 d \,e^{3} x^{2}}{c}+\frac{2 d^{4} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}}+\frac{a b \,e^{4} \ln \left(c \,x^{2}+b x +a \right)}{c^{3}}-\frac{2 a d \,e^{3} \ln \left(c \,x^{2}+b x +a \right)}{c^{2}}-\frac{a \,e^{4} x}{c^{2}}-\frac{b^{3} e^{4} \ln \left(c \,x^{2}+b x +a \right)}{2 c^{4}}+\frac{2 b^{2} d \,e^{3} \ln \left(c \,x^{2}+b x +a \right)}{c^{3}}+\frac{b^{2} e^{4} x}{c^{3}}-\frac{3 b \,d^{2} e^{2} \ln \left(c \,x^{2}+b x +a \right)}{c^{2}}-\frac{4 b d \,e^{3} x}{c^{2}}+\frac{2 d^{3} e \ln \left(c \,x^{2}+b x +a \right)}{c}+\frac{6 d^{2} e^{2} x}{c}"," ",0,"1/3/c*e^4*x^3-1/2*e^4/c^2*x^2*b+2/c*d*e^3*x^2-e^4/c^2*a*x+e^4/c^3*b^2*x-4*e^3/c^2*b*d*x+6*e^2/c*d^2*x+1/c^3*ln(c*x^2+b*x+a)*a*b*e^4-2/c^2*ln(c*x^2+b*x+a)*a*d*e^3-1/2/c^4*ln(c*x^2+b*x+a)*b^3*e^4+2/c^3*ln(c*x^2+b*x+a)*b^2*d*e^3-3/c^2*ln(c*x^2+b*x+a)*b*d^2*e^2+2/c*ln(c*x^2+b*x+a)*d^3*e+2/c^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a^2*e^4-4/c^3/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*b^2*e^4+12/c^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*b*d*e^3-12/c/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*d^2*e^2+2/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*d^4+1/c^4/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^4*e^4-4/c^3/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^3*d*e^3+6/c^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*d^2*b^2*e^2-4/c/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b*d^3*e","B"
2183,1,366,143,0.052000," ","int((e*x+d)^3/(c*x^2+b*x+a),x)","\frac{3 a b \,e^{3} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, c^{2}}-\frac{6 a d \,e^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, c}-\frac{b^{3} e^{3} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, c^{3}}+\frac{3 b^{2} d \,e^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, c^{2}}-\frac{3 b \,d^{2} e \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, c}+\frac{e^{3} x^{2}}{2 c}+\frac{2 d^{3} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}}-\frac{a \,e^{3} \ln \left(c \,x^{2}+b x +a \right)}{2 c^{2}}+\frac{b^{2} e^{3} \ln \left(c \,x^{2}+b x +a \right)}{2 c^{3}}-\frac{3 b d \,e^{2} \ln \left(c \,x^{2}+b x +a \right)}{2 c^{2}}-\frac{b \,e^{3} x}{c^{2}}+\frac{3 d^{2} e \ln \left(c \,x^{2}+b x +a \right)}{2 c}+\frac{3 d \,e^{2} x}{c}"," ",0,"1/2/c*e^3*x^2-e^3/c^2*x*b+3/c*d*e^2*x-1/2/c^2*ln(c*x^2+b*x+a)*a*e^3+1/2/c^3*ln(c*x^2+b*x+a)*b^2*e^3-3/2/c^2*ln(c*x^2+b*x+a)*b*d*e^2+3/2/c*ln(c*x^2+b*x+a)*d^2*e+3/c^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*b*e^3-6/c/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*d*e^2+2/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*d^3-1/c^3/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^3*e^3+3/c^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^2*d*e^2-3/c/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b*d^2*e","B"
2184,1,207,95,0.052000," ","int((e*x+d)^2/(c*x^2+b*x+a),x)","-\frac{2 a \,e^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, c}+\frac{b^{2} e^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, c^{2}}-\frac{2 b d e \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, c}+\frac{2 d^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}}-\frac{b \,e^{2} \ln \left(c \,x^{2}+b x +a \right)}{2 c^{2}}+\frac{d e \ln \left(c \,x^{2}+b x +a \right)}{c}+\frac{e^{2} x}{c}"," ",0,"1/c*e^2*x-1/2/c^2*ln(c*x^2+b*x+a)*b*e^2+1/c*ln(c*x^2+b*x+a)*d*e-2/c/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*e^2+2/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*d^2+1/c^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^2*e^2-2/c/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b*d*e","B"
2185,1,93,60,0.052000," ","int((e*x+d)/(c*x^2+b*x+a),x)","-\frac{b e \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, c}+\frac{2 d \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}}+\frac{e \ln \left(c \,x^{2}+b x +a \right)}{2 c}"," ",0,"1/2*e*ln(c*x^2+b*x+a)/c+2/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*d-1/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b*e/c","A"
2186,1,35,30,0.040000," ","int(1/(c*x^2+b*x+a),x)","\frac{2 \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}}"," ",0,"2/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))","A"
2187,1,168,116,0.059000," ","int(1/(e*x+d)/(c*x^2+b*x+a),x)","-\frac{b e \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \sqrt{4 a c -b^{2}}}+\frac{2 c d \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \sqrt{4 a c -b^{2}}}+\frac{e \ln \left(e x +d \right)}{a \,e^{2}-b d e +c \,d^{2}}-\frac{e \ln \left(c \,x^{2}+b x +a \right)}{2 \left(a \,e^{2}-b d e +c \,d^{2}\right)}"," ",0,"e*ln(e*x+d)/(a*e^2-b*d*e+c*d^2)-1/2*e*ln(c*x^2+b*x+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+b)/(4*a*c-b^2)^(1/2))*b*e+2/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*c*d","A"
2188,1,386,180,0.053000," ","int(1/(e*x+d)^2/(c*x^2+b*x+a),x)","-\frac{2 a c \,e^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \sqrt{4 a c -b^{2}}}+\frac{b^{2} e^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \sqrt{4 a c -b^{2}}}-\frac{2 b c d e \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \sqrt{4 a c -b^{2}}}+\frac{2 c^{2} d^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \sqrt{4 a c -b^{2}}}-\frac{b \,e^{2} \ln \left(e x +d \right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2}}+\frac{b \,e^{2} \ln \left(c \,x^{2}+b x +a \right)}{2 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{2}}+\frac{2 c d e \ln \left(e x +d \right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2}}-\frac{c d e \ln \left(c \,x^{2}+b x +a \right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2}}-\frac{e}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \left(e x +d \right)}"," ",0,"-e/(a*e^2-b*d*e+c*d^2)/(e*x+d)-e^2/(a*e^2-b*d*e+c*d^2)^2*ln(e*x+d)*b+2*e/(a*e^2-b*d*e+c*d^2)^2*ln(e*x+d)*c*d+1/2/(a*e^2-b*d*e+c*d^2)^2*ln(c*x^2+b*x+a)*b*e^2-1/(a*e^2-b*d*e+c*d^2)^2*c*ln(c*x^2+b*x+a)*d*e-2/(a*e^2-b*d*e+c*d^2)^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*c*e^2+1/(a*e^2-b*d*e+c*d^2)^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^2*e^2-2/(a*e^2-b*d*e+c*d^2)^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b*c*d*e+2/(a*e^2-b*d*e+c*d^2)^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*c^2*d^2","B"
2189,1,719,264,0.075000," ","int(1/(e*x+d)^3/(c*x^2+b*x+a),x)","\frac{3 a b c \,e^{3} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \sqrt{4 a c -b^{2}}}-\frac{6 a \,c^{2} d \,e^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \sqrt{4 a c -b^{2}}}-\frac{b^{3} e^{3} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \sqrt{4 a c -b^{2}}}+\frac{3 b^{2} c d \,e^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \sqrt{4 a c -b^{2}}}-\frac{3 b \,c^{2} d^{2} e \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \sqrt{4 a c -b^{2}}}+\frac{2 c^{3} d^{3} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \sqrt{4 a c -b^{2}}}-\frac{a c \,e^{3} \ln \left(e x +d \right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{3}}+\frac{a c \,e^{3} \ln \left(c \,x^{2}+b x +a \right)}{2 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{3}}+\frac{b^{2} e^{3} \ln \left(e x +d \right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{3}}-\frac{b^{2} e^{3} \ln \left(c \,x^{2}+b x +a \right)}{2 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{3}}-\frac{3 b c d \,e^{2} \ln \left(e x +d \right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{3}}+\frac{3 b c d \,e^{2} \ln \left(c \,x^{2}+b x +a \right)}{2 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{3}}+\frac{3 c^{2} d^{2} e \ln \left(e x +d \right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{3}}-\frac{3 c^{2} d^{2} e \ln \left(c \,x^{2}+b x +a \right)}{2 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{3}}+\frac{b \,e^{2}}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(e x +d \right)}-\frac{2 c d e}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(e x +d \right)}-\frac{e}{2 \left(a \,e^{2}-b d e +c \,d^{2}\right) \left(e x +d \right)^{2}}"," ",0,"-1/2*e/(a*e^2-b*d*e+c*d^2)/(e*x+d)^2+e^2/(a*e^2-b*d*e+c*d^2)^2/(e*x+d)*b-2*e/(a*e^2-b*d*e+c*d^2)^2/(e*x+d)*c*d-e^3/(a*e^2-b*d*e+c*d^2)^3*ln(e*x+d)*a*c+e^3/(a*e^2-b*d*e+c*d^2)^3*ln(e*x+d)*b^2-3*e^2/(a*e^2-b*d*e+c*d^2)^3*ln(e*x+d)*b*c*d+3*e/(a*e^2-b*d*e+c*d^2)^3*ln(e*x+d)*c^2*d^2+1/2/(a*e^2-b*d*e+c*d^2)^3*c*ln(c*x^2+b*x+a)*a*e^3-1/2/(a*e^2-b*d*e+c*d^2)^3*ln(c*x^2+b*x+a)*b^2*e^3+3/2/(a*e^2-b*d*e+c*d^2)^3*c*ln(c*x^2+b*x+a)*b*d*e^2-3/2/(a*e^2-b*d*e+c*d^2)^3*c^2*ln(c*x^2+b*x+a)*d^2*e+3/(a*e^2-b*d*e+c*d^2)^3/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*b*c*e^3-6/(a*e^2-b*d*e+c*d^2)^3/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*c^2*a*d*e^2-1/(a*e^2-b*d*e+c*d^2)^3/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^3*e^3+3/(a*e^2-b*d*e+c*d^2)^3/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^2*c*d*e^2-3/(a*e^2-b*d*e+c*d^2)^3/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b*c^2*d^2*e+2/(a*e^2-b*d*e+c*d^2)^3/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*c^3*d^3","B"
2190,1,1542,366,0.063000," ","int((e*x+d)^5/(c*x^2+b*x+a)^2,x)","-\frac{5 a^{2} b \,e^{5} x}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) c^{2}}+\frac{30 a^{2} b \,e^{5} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} c^{2}}+\frac{10 a^{2} d \,e^{4} x}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) c}-\frac{60 a^{2} d \,e^{4} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} c}+\frac{5 a \,b^{3} e^{5} x}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) c^{3}}-\frac{20 a \,b^{3} e^{5} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} c^{3}}-\frac{20 a \,b^{2} d \,e^{4} x}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) c^{2}}+\frac{60 a \,b^{2} d \,e^{4} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} c^{2}}+\frac{30 a b \,d^{2} e^{3} x}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) c}-\frac{60 a b \,d^{2} e^{3} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} c}-\frac{20 a \,d^{3} e^{2} x}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}+\frac{40 a \,d^{3} e^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}}}-\frac{b^{5} e^{5} x}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) c^{4}}+\frac{3 b^{5} e^{5} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} c^{4}}+\frac{5 b^{4} d \,e^{4} x}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) c^{3}}-\frac{10 b^{4} d \,e^{4} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} c^{3}}-\frac{10 b^{3} d^{2} e^{3} x}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) c^{2}}+\frac{10 b^{3} d^{2} e^{3} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} c^{2}}+\frac{10 b^{2} d^{3} e^{2} x}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) c}-\frac{5 b \,d^{4} e x}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}-\frac{10 b \,d^{4} e \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}}}+\frac{2 c \,d^{5} x}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}+\frac{4 c \,d^{5} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}}}-\frac{2 a^{3} e^{5}}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) c^{2}}+\frac{4 a^{2} b^{2} e^{5}}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) c^{3}}-\frac{15 a^{2} b d \,e^{4}}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) c^{2}}+\frac{20 a^{2} d^{2} e^{3}}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) c}-\frac{4 a^{2} e^{5} \ln \left(c \,x^{2}+b x +a \right)}{\left(4 a c -b^{2}\right) c^{2}}-\frac{a \,b^{4} e^{5}}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) c^{4}}+\frac{5 a \,b^{3} d \,e^{4}}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) c^{3}}-\frac{10 a \,b^{2} d^{2} e^{3}}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) c^{2}}+\frac{7 a \,b^{2} e^{5} \ln \left(c \,x^{2}+b x +a \right)}{\left(4 a c -b^{2}\right) c^{3}}+\frac{10 a b \,d^{3} e^{2}}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) c}-\frac{20 a b d \,e^{4} \ln \left(c \,x^{2}+b x +a \right)}{\left(4 a c -b^{2}\right) c^{2}}+\frac{20 a \,d^{2} e^{3} \ln \left(c \,x^{2}+b x +a \right)}{\left(4 a c -b^{2}\right) c}-\frac{10 a \,d^{4} e}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}-\frac{3 b^{4} e^{5} \ln \left(c \,x^{2}+b x +a \right)}{2 \left(4 a c -b^{2}\right) c^{4}}+\frac{5 b^{3} d \,e^{4} \ln \left(c \,x^{2}+b x +a \right)}{\left(4 a c -b^{2}\right) c^{3}}-\frac{5 b^{2} d^{2} e^{3} \ln \left(c \,x^{2}+b x +a \right)}{\left(4 a c -b^{2}\right) c^{2}}+\frac{b \,d^{5}}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}+\frac{e^{5} x^{2}}{2 c^{2}}-\frac{2 b \,e^{5} x}{c^{3}}+\frac{5 d \,e^{4} x}{c^{2}}"," ",0,"10/c/(c*x^2+b*x+a)/(4*a*c-b^2)*a*b*d^3*e^2-5/c^2/(c*x^2+b*x+a)/(4*a*c-b^2)*x*a^2*b*e^5+10/c/(c*x^2+b*x+a)/(4*a*c-b^2)*x*a^2*d*e^4-10/c^2/(c*x^2+b*x+a)/(4*a*c-b^2)*x*b^3*d^2*e^3+5/c^3/(c*x^2+b*x+a)/(4*a*c-b^2)*x*a*b^3*e^5+5/c^3/(c*x^2+b*x+a)/(4*a*c-b^2)*a*b^3*d*e^4-20/c^2/(4*a*c-b^2)*ln(c*x^2+b*x+a)*a*b*d*e^4+60/c^2/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*b^2*d*e^4-60/c/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*d^2*a*b*e^3+10/c^2/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*d^2*b^3*e^3+30/c^2/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a^2*b*e^5-20/c^3/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*b^3*e^5+7/c^3/(4*a*c-b^2)*ln(c*x^2+b*x+a)*a*b^2*e^5-5/c^2/(4*a*c-b^2)*ln(c*x^2+b*x+a)*b^2*d^2*e^3-10/c^3/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^4*d*e^4+20/c/(4*a*c-b^2)*ln(c*x^2+b*x+a)*a*d^2*e^3-20/c^2/(c*x^2+b*x+a)/(4*a*c-b^2)*x*a*b^2*d*e^4+30/c/(c*x^2+b*x+a)/(4*a*c-b^2)*x*a*b*d^2*e^3+4*c/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*d^5-2*e^5/c^3*x*b+5*e^4/c^2*x*d+1/(c*x^2+b*x+a)/(4*a*c-b^2)*b*d^5+5/c^3/(c*x^2+b*x+a)/(4*a*c-b^2)*x*b^4*d*e^4+10/c/(c*x^2+b*x+a)/(4*a*c-b^2)*x*b^2*d^3*e^2-15/c^2/(c*x^2+b*x+a)/(4*a*c-b^2)*a^2*b*d*e^4-10/c^2/(c*x^2+b*x+a)/(4*a*c-b^2)*a*b^2*d^2*e^3-5/(c*x^2+b*x+a)/(4*a*c-b^2)*x*b*d^4*e-20/(c*x^2+b*x+a)/(4*a*c-b^2)*x*a*d^3*e^2+4/c^3/(c*x^2+b*x+a)/(4*a*c-b^2)*a^2*b^2*e^5-1/c^4/(c*x^2+b*x+a)/(4*a*c-b^2)*x*b^5*e^5+20/c/(c*x^2+b*x+a)/(4*a*c-b^2)*a^2*d^2*e^3-1/c^4/(c*x^2+b*x+a)/(4*a*c-b^2)*a*b^4*e^5-60/c/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*d*a^2*e^4+5/c^3/(4*a*c-b^2)*ln(c*x^2+b*x+a)*b^3*d*e^4+1/2/c^2*e^5*x^2-10/(c*x^2+b*x+a)/(4*a*c-b^2)*a*d^4*e+2*c/(c*x^2+b*x+a)/(4*a*c-b^2)*x*d^5-2/c^2/(c*x^2+b*x+a)/(4*a*c-b^2)*a^3*e^5+40/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*d^3*a*e^2-10/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b*d^4*e-4/c^2/(4*a*c-b^2)*ln(c*x^2+b*x+a)*a^2*e^5-3/2/c^4/(4*a*c-b^2)*ln(c*x^2+b*x+a)*b^4*e^5+3/c^4/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^5*e^5","B"
2191,1,1037,256,0.061000," ","int((e*x+d)^4/(c*x^2+b*x+a)^2,x)","\frac{2 a^{2} e^{4} x}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) c}-\frac{12 a^{2} e^{4} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} c}-\frac{4 a \,b^{2} e^{4} x}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) c^{2}}+\frac{12 a \,b^{2} e^{4} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} c^{2}}+\frac{12 a b d \,e^{3} x}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) c}-\frac{24 a b d \,e^{3} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} c}-\frac{12 a \,d^{2} e^{2} x}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}+\frac{24 a \,d^{2} e^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}}}+\frac{b^{4} e^{4} x}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) c^{3}}-\frac{2 b^{4} e^{4} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} c^{3}}-\frac{4 b^{3} d \,e^{3} x}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) c^{2}}+\frac{4 b^{3} d \,e^{3} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} c^{2}}+\frac{6 b^{2} d^{2} e^{2} x}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) c}-\frac{4 b \,d^{3} e x}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}-\frac{8 b \,d^{3} e \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}}}+\frac{2 c \,d^{4} x}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}+\frac{4 c \,d^{4} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}}}-\frac{3 a^{2} b \,e^{4}}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) c^{2}}+\frac{8 a^{2} d \,e^{3}}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) c}+\frac{a \,b^{3} e^{4}}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) c^{3}}-\frac{4 a \,b^{2} d \,e^{3}}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) c^{2}}+\frac{6 a b \,d^{2} e^{2}}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) c}-\frac{4 a b \,e^{4} \ln \left(c \,x^{2}+b x +a \right)}{\left(4 a c -b^{2}\right) c^{2}}+\frac{8 a d \,e^{3} \ln \left(c \,x^{2}+b x +a \right)}{\left(4 a c -b^{2}\right) c}-\frac{8 a \,d^{3} e}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}+\frac{b^{3} e^{4} \ln \left(c \,x^{2}+b x +a \right)}{\left(4 a c -b^{2}\right) c^{3}}-\frac{2 b^{2} d \,e^{3} \ln \left(c \,x^{2}+b x +a \right)}{\left(4 a c -b^{2}\right) c^{2}}+\frac{b \,d^{4}}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}+\frac{e^{4} x}{c^{2}}"," ",0,"-4/c^2/(4*a*c-b^2)*ln(c*x^2+b*x+a)*a*b*e^4+12/c^2/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*b^2*e^4+4/c^2/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^3*d*e^3-2/c^2/(4*a*c-b^2)*ln(c*x^2+b*x+a)*b^2*d*e^3+4*c/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*d^4+1/(c*x^2+b*x+a)/(4*a*c-b^2)*b*d^4+12/c/(c*x^2+b*x+a)/(4*a*c-b^2)*x*a*b*d*e^3+1/c^2*e^4*x-24/c/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*b*d*e^3+6/c/(c*x^2+b*x+a)/(4*a*c-b^2)*x*b^2*d^2*e^2-4/c^2/(c*x^2+b*x+a)/(4*a*c-b^2)*x*b^3*d*e^3-4/c^2/(c*x^2+b*x+a)/(4*a*c-b^2)*a*b^2*d*e^3-4/c^2/(c*x^2+b*x+a)/(4*a*c-b^2)*x*a*b^2*e^4+6/c/(c*x^2+b*x+a)/(4*a*c-b^2)*a*b*d^2*e^2+24/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*d^2*e^2-4/(c*x^2+b*x+a)/(4*a*c-b^2)*x*b*d^3*e-12/(c*x^2+b*x+a)/(4*a*c-b^2)*x*a*d^2*e^2-3/c^2/(c*x^2+b*x+a)/(4*a*c-b^2)*a^2*b*e^4+2/c/(c*x^2+b*x+a)/(4*a*c-b^2)*x*a^2*e^4+1/c^3/(c*x^2+b*x+a)/(4*a*c-b^2)*x*b^4*e^4+8/c/(c*x^2+b*x+a)/(4*a*c-b^2)*a^2*d*e^3+1/c^3/(c*x^2+b*x+a)/(4*a*c-b^2)*a*b^3*e^4+8/c/(4*a*c-b^2)*ln(c*x^2+b*x+a)*a*d*e^3+2*c/(c*x^2+b*x+a)/(4*a*c-b^2)*x*d^4-2/c^3/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^4*e^4-12/c/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a^2*e^4+1/c^3/(4*a*c-b^2)*ln(c*x^2+b*x+a)*b^3*e^4-8/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b*d^3*e-8/(c*x^2+b*x+a)/(4*a*c-b^2)*a*d^3*e","B"
2192,1,416,167,0.062000," ","int((e*x+d)^3/(c*x^2+b*x+a)^2,x)","-\frac{6 a b \,e^{3} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} c}+\frac{12 a d \,e^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}}}+\frac{b^{3} e^{3} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} c^{2}}-\frac{6 b \,d^{2} e \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}}}+\frac{4 c \,d^{3} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}}}+\frac{2 a \,e^{3} \ln \left(c \,x^{2}+b x +a \right)}{\left(4 a c -b^{2}\right) c}-\frac{b^{2} e^{3} \ln \left(c \,x^{2}+b x +a \right)}{2 \left(4 a c -b^{2}\right) c^{2}}+\frac{\frac{\left(3 a b c \,e^{3}-6 c^{2} a d \,e^{2}-b^{3} e^{3}+3 b^{2} c d \,e^{2}-3 b \,c^{2} d^{2} e +2 c^{3} d^{3}\right) x}{\left(4 a c -b^{2}\right) c^{2}}+\frac{2 a^{2} c \,e^{3}-a \,b^{2} e^{3}+3 a b c d \,e^{2}-6 a \,c^{2} d^{2} e +b \,c^{2} d^{3}}{\left(4 a c -b^{2}\right) c^{2}}}{c \,x^{2}+b x +a}"," ",0,"((3*a*b*c*e^3-6*a*c^2*d*e^2-b^3*e^3+3*b^2*c*d*e^2-3*b*c^2*d^2*e+2*c^3*d^3)/c^2/(4*a*c-b^2)*x+(2*a^2*c*e^3-a*b^2*e^3+3*a*b*c*d*e^2-6*a*c^2*d^2*e+b*c^2*d^3)/c^2/(4*a*c-b^2))/(c*x^2+b*x+a)+2/c/(4*a*c-b^2)*ln(c*x^2+b*x+a)*a*e^3-1/2/c^2/(4*a*c-b^2)*ln(c*x^2+b*x+a)*b^2*e^3-6/c/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*b*e^3+12/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*d*e^2-6/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b*d^2*e+4*c/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*d^3+1/c^2/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^3*e^3","B"
2193,1,212,95,0.048000," ","int((e*x+d)^2/(c*x^2+b*x+a)^2,x)","\frac{4 a \,e^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}}}-\frac{4 b d e \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}}}+\frac{4 c \,d^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}}}+\frac{-\frac{\left(2 a c \,e^{2}-b^{2} e^{2}+2 b c d e -2 c^{2} d^{2}\right) x}{\left(4 a c -b^{2}\right) c}+\frac{a b \,e^{2}-4 a c d e +b c \,d^{2}}{\left(4 a c -b^{2}\right) c}}{c \,x^{2}+b x +a}"," ",0,"(-(2*a*c*e^2-b^2*e^2+2*b*c*d*e-2*c^2*d^2)/c/(4*a*c-b^2)*x+1/c*(a*b*e^2-4*a*c*d*e+b*c*d^2)/(4*a*c-b^2))/(c*x^2+b*x+a)+4/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*e^2-4/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b*d*e+4/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*c*d^2","B"
2194,1,118,84,0.049000," ","int((e*x+d)/(c*x^2+b*x+a)^2,x)","-\frac{2 b e \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}}}+\frac{4 c d \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}}}+\frac{-2 a e +b d +\left(-b e +2 c d \right) x}{\left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)}"," ",0,"(b*d-2*a*e+(-b*e+2*c*d)*x)/(4*a*c-b^2)/(c*x^2+b*x+a)-2/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b*e+4/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*c*d","A"
2195,1,68,63,0.066000," ","int(1/(c*x^2+b*x+a)^2,x)","\frac{4 c \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}}}+\frac{2 c x +b}{\left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)}"," ",0,"(2*c*x+b)/(4*a*c-b^2)/(c*x^2+b*x+a)+4*c/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))","A"
2196,1,1037,218,0.067000," ","int(1/(e*x+d)/(c*x^2+b*x+a)^2,x)","-\frac{a b c \,e^{3} x}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}-\frac{6 a b c \,e^{3} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(4 a c -b^{2}\right)^{\frac{3}{2}}}+\frac{2 a \,c^{2} d \,e^{2} x}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}+\frac{12 a \,c^{2} d \,e^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(4 a c -b^{2}\right)^{\frac{3}{2}}}+\frac{b^{3} e^{3} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(4 a c -b^{2}\right)^{\frac{3}{2}}}+\frac{b^{2} c d \,e^{2} x}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}-\frac{3 b \,c^{2} d^{2} e x}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}-\frac{6 b \,c^{2} d^{2} e \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(4 a c -b^{2}\right)^{\frac{3}{2}}}+\frac{2 c^{3} d^{3} x}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}+\frac{4 c^{3} d^{3} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(4 a c -b^{2}\right)^{\frac{3}{2}}}+\frac{2 a^{2} c \,e^{3}}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}-\frac{a \,b^{2} e^{3}}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}-\frac{a b c d \,e^{2}}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}+\frac{2 a \,c^{2} d^{2} e}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}-\frac{2 a c \,e^{3} \ln \left(c \,x^{2}+b x +a \right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(4 a c -b^{2}\right)}+\frac{b^{3} d \,e^{2}}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}-\frac{2 b^{2} c \,d^{2} e}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}+\frac{b^{2} e^{3} \ln \left(c \,x^{2}+b x +a \right)}{2 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(4 a c -b^{2}\right)}+\frac{b \,c^{2} d^{3}}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}+\frac{e^{3} \ln \left(e x +d \right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2}}"," ",0,"e^3*ln(e*x+d)/(a*e^2-b*d*e+c*d^2)^2-1/(a*e^2-b*d*e+c*d^2)^2/(c*x^2+b*x+a)*c/(4*a*c-b^2)*x*a*b*e^3+2/(a*e^2-b*d*e+c*d^2)^2/(c*x^2+b*x+a)*c^2/(4*a*c-b^2)*x*a*d*e^2+1/(a*e^2-b*d*e+c*d^2)^2/(c*x^2+b*x+a)*c/(4*a*c-b^2)*x*b^2*d*e^2-3/(a*e^2-b*d*e+c*d^2)^2/(c*x^2+b*x+a)*c^2/(4*a*c-b^2)*x*b*d^2*e+2/(a*e^2-b*d*e+c*d^2)^2/(c*x^2+b*x+a)*c^3/(4*a*c-b^2)*x*d^3+2/(a*e^2-b*d*e+c*d^2)^2/(c*x^2+b*x+a)/(4*a*c-b^2)*a^2*c*e^3-1/(a*e^2-b*d*e+c*d^2)^2/(c*x^2+b*x+a)/(4*a*c-b^2)*a*b^2*e^3-1/(a*e^2-b*d*e+c*d^2)^2/(c*x^2+b*x+a)/(4*a*c-b^2)*a*b*c*d*e^2+2/(a*e^2-b*d*e+c*d^2)^2/(c*x^2+b*x+a)/(4*a*c-b^2)*a*c^2*d^2*e+1/(a*e^2-b*d*e+c*d^2)^2/(c*x^2+b*x+a)/(4*a*c-b^2)*b^3*d*e^2-2/(a*e^2-b*d*e+c*d^2)^2/(c*x^2+b*x+a)/(4*a*c-b^2)*b^2*c*d^2*e+1/(a*e^2-b*d*e+c*d^2)^2/(c*x^2+b*x+a)/(4*a*c-b^2)*b*c^2*d^3-2/(a*e^2-b*d*e+c*d^2)^2/(4*a*c-b^2)*c*ln(c*x^2+b*x+a)*a*e^3+1/2/(a*e^2-b*d*e+c*d^2)^2/(4*a*c-b^2)*ln(c*x^2+b*x+a)*b^2*e^3-6/(a*e^2-b*d*e+c*d^2)^2/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*b*c*e^3+12/(a*e^2-b*d*e+c*d^2)^2/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*c^2*a*d*e^2+1/(a*e^2-b*d*e+c*d^2)^2/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^3*e^3-6/(a*e^2-b*d*e+c*d^2)^2/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b*c^2*d^2*e+4/(a*e^2-b*d*e+c*d^2)^2/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*c^3*d^3","B"
2197,1,1617,340,0.079000," ","int(1/(e*x+d)^2/(c*x^2+b*x+a)^2,x)","-\frac{2 a^{2} c^{2} e^{4} x}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}-\frac{12 a^{2} c^{2} e^{4} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \left(4 a c -b^{2}\right)^{\frac{3}{2}}}+\frac{a \,b^{2} c \,e^{4} x}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}+\frac{12 a \,b^{2} c \,e^{4} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \left(4 a c -b^{2}\right)^{\frac{3}{2}}}-\frac{24 a b \,c^{2} d \,e^{3} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \left(4 a c -b^{2}\right)^{\frac{3}{2}}}+\frac{24 a \,c^{3} d^{2} e^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \left(4 a c -b^{2}\right)^{\frac{3}{2}}}-\frac{2 b^{4} e^{4} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \left(4 a c -b^{2}\right)^{\frac{3}{2}}}-\frac{b^{3} c d \,e^{3} x}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}+\frac{4 b^{3} c d \,e^{3} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \left(4 a c -b^{2}\right)^{\frac{3}{2}}}+\frac{3 b^{2} c^{2} d^{2} e^{2} x}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}-\frac{4 b \,c^{3} d^{3} e x}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}-\frac{8 b \,c^{3} d^{3} e \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \left(4 a c -b^{2}\right)^{\frac{3}{2}}}+\frac{2 c^{4} d^{4} x}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}+\frac{4 c^{4} d^{4} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \left(4 a c -b^{2}\right)^{\frac{3}{2}}}-\frac{3 a^{2} b c \,e^{4}}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}+\frac{4 a^{2} c^{2} d \,e^{3}}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}+\frac{a \,b^{3} e^{4}}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}+\frac{a \,b^{2} c d \,e^{3}}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}-\frac{6 a b \,c^{2} d^{2} e^{2}}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}+\frac{4 a b c \,e^{4} \ln \left(c \,x^{2}+b x +a \right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \left(4 a c -b^{2}\right)}+\frac{4 a \,c^{3} d^{3} e}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}-\frac{8 a \,c^{2} d \,e^{3} \ln \left(c \,x^{2}+b x +a \right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \left(4 a c -b^{2}\right)}-\frac{b^{4} d \,e^{3}}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}+\frac{3 b^{3} c \,d^{2} e^{2}}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}-\frac{b^{3} e^{4} \ln \left(c \,x^{2}+b x +a \right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \left(4 a c -b^{2}\right)}-\frac{3 b^{2} c^{2} d^{3} e}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}+\frac{2 b^{2} c d \,e^{3} \ln \left(c \,x^{2}+b x +a \right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \left(4 a c -b^{2}\right)}+\frac{b \,c^{3} d^{4}}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}-\frac{2 b \,e^{4} \ln \left(e x +d \right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{3}}+\frac{4 c d \,e^{3} \ln \left(e x +d \right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{3}}-\frac{e^{3}}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(e x +d \right)}"," ",0,"-4/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)*c^3/(4*a*c-b^2)*x*b*d^3*e-24/(a*e^2-b*d*e+c*d^2)^3/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*b*c^2*d*e^3-2*e^4/(a*e^2-b*d*e+c*d^2)^3*ln(e*x+d)*b-6/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)/(4*a*c-b^2)*a*b*c^2*d^2*e^2+1/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)/(4*a*c-b^2)*a*b^2*c*d*e^3+3/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)*c^2/(4*a*c-b^2)*x*d^2*b^2*e^2+1/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)*c/(4*a*c-b^2)*x*a*b^2*e^4-1/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)*c/(4*a*c-b^2)*x*b^3*d*e^3-e^3/(a*e^2-b*d*e+c*d^2)^2/(e*x+d)-2/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)*c^2/(4*a*c-b^2)*x*a^2*e^4-3/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)/(4*a*c-b^2)*a^2*b*c*e^4+4/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)/(4*a*c-b^2)*a^2*c^2*d*e^3+4/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)/(4*a*c-b^2)*a*c^3*d^3*e+4/(a*e^2-b*d*e+c*d^2)^3/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^3*c*d*e^3+4/(a*e^2-b*d*e+c*d^2)^3/(4*a*c-b^2)*c*ln(c*x^2+b*x+a)*a*b*e^4-8/(a*e^2-b*d*e+c*d^2)^3/(4*a*c-b^2)*c^2*ln(c*x^2+b*x+a)*a*d*e^3+2/(a*e^2-b*d*e+c*d^2)^3/(4*a*c-b^2)*c*ln(c*x^2+b*x+a)*b^2*d*e^3-8/(a*e^2-b*d*e+c*d^2)^3/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b*c^3*d^3*e-1/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)/(4*a*c-b^2)*b^4*d*e^3+1/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)/(4*a*c-b^2)*b*c^3*d^4+2/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)*c^4/(4*a*c-b^2)*x*d^4+1/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)/(4*a*c-b^2)*a*b^3*e^4-12/(a*e^2-b*d*e+c*d^2)^3/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*c^2*a^2*e^4+12/(a*e^2-b*d*e+c*d^2)^3/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*b^2*c*e^4+24/(a*e^2-b*d*e+c*d^2)^3/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*c^3*d^2*e^2+3/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)/(4*a*c-b^2)*b^3*c*d^2*e^2-3/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)/(4*a*c-b^2)*b^2*c^2*d^3*e-2/(a*e^2-b*d*e+c*d^2)^3/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^4*e^4+4/(a*e^2-b*d*e+c*d^2)^3/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*c^4*d^4+4*e^3/(a*e^2-b*d*e+c*d^2)^3*ln(e*x+d)*c*d-1/(a*e^2-b*d*e+c*d^2)^3/(4*a*c-b^2)*ln(c*x^2+b*x+a)*b^3*e^4","B"
2198,1,2554,477,0.081000," ","int(1/(e*x+d)^3/(c*x^2+b*x+a)^2,x)","\frac{3 a^{2} b \,c^{2} e^{5} x}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{4} \left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}+\frac{30 a^{2} b \,c^{2} e^{5} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{4} \left(4 a c -b^{2}\right)^{\frac{3}{2}}}-\frac{6 a^{2} c^{3} d \,e^{4} x}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{4} \left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}-\frac{60 a^{2} c^{3} d \,e^{4} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{4} \left(4 a c -b^{2}\right)^{\frac{3}{2}}}-\frac{a \,b^{3} c \,e^{5} x}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{4} \left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}-\frac{20 a \,b^{3} c \,e^{5} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{4} \left(4 a c -b^{2}\right)^{\frac{3}{2}}}+\frac{60 a \,b^{2} c^{2} d \,e^{4} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{4} \left(4 a c -b^{2}\right)^{\frac{3}{2}}}+\frac{6 a b \,c^{3} d^{2} e^{3} x}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{4} \left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}-\frac{60 a b \,c^{3} d^{2} e^{3} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{4} \left(4 a c -b^{2}\right)^{\frac{3}{2}}}-\frac{4 a \,c^{4} d^{3} e^{2} x}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{4} \left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}+\frac{40 a \,c^{4} d^{3} e^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{4} \left(4 a c -b^{2}\right)^{\frac{3}{2}}}+\frac{3 b^{5} e^{5} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{4} \left(4 a c -b^{2}\right)^{\frac{3}{2}}}+\frac{b^{4} c d \,e^{4} x}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{4} \left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}-\frac{10 b^{4} c d \,e^{4} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{4} \left(4 a c -b^{2}\right)^{\frac{3}{2}}}-\frac{4 b^{3} c^{2} d^{2} e^{3} x}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{4} \left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}+\frac{10 b^{3} c^{2} d^{2} e^{3} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{4} \left(4 a c -b^{2}\right)^{\frac{3}{2}}}+\frac{6 b^{2} c^{3} d^{3} e^{2} x}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{4} \left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}-\frac{5 b \,c^{4} d^{4} e x}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{4} \left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}-\frac{10 b \,c^{4} d^{4} e \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{4} \left(4 a c -b^{2}\right)^{\frac{3}{2}}}+\frac{2 c^{5} d^{5} x}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{4} \left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}+\frac{4 c^{5} d^{5} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{4} \left(4 a c -b^{2}\right)^{\frac{3}{2}}}-\frac{2 a^{3} c^{2} e^{5}}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{4} \left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}+\frac{4 a^{2} b^{2} c \,e^{5}}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{4} \left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}-\frac{7 a^{2} b \,c^{2} d \,e^{4}}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{4} \left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}+\frac{4 a^{2} c^{3} d^{2} e^{3}}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{4} \left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}+\frac{4 a^{2} c^{2} e^{5} \ln \left(c \,x^{2}+b x +a \right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{4} \left(4 a c -b^{2}\right)}-\frac{a \,b^{4} e^{5}}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{4} \left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}-\frac{a \,b^{3} c d \,e^{4}}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{4} \left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}+\frac{10 a \,b^{2} c^{2} d^{2} e^{3}}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{4} \left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}-\frac{7 a \,b^{2} c \,e^{5} \ln \left(c \,x^{2}+b x +a \right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{4} \left(4 a c -b^{2}\right)}-\frac{14 a b \,c^{3} d^{3} e^{2}}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{4} \left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}+\frac{20 a b \,c^{2} d \,e^{4} \ln \left(c \,x^{2}+b x +a \right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{4} \left(4 a c -b^{2}\right)}+\frac{6 a \,c^{4} d^{4} e}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{4} \left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}-\frac{20 a \,c^{3} d^{2} e^{3} \ln \left(c \,x^{2}+b x +a \right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{4} \left(4 a c -b^{2}\right)}+\frac{b^{5} d \,e^{4}}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{4} \left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}-\frac{4 b^{4} c \,d^{2} e^{3}}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{4} \left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}+\frac{3 b^{4} e^{5} \ln \left(c \,x^{2}+b x +a \right)}{2 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{4} \left(4 a c -b^{2}\right)}+\frac{6 b^{3} c^{2} d^{3} e^{2}}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{4} \left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}-\frac{5 b^{3} c d \,e^{4} \ln \left(c \,x^{2}+b x +a \right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{4} \left(4 a c -b^{2}\right)}-\frac{4 b^{2} c^{3} d^{4} e}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{4} \left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}+\frac{5 b^{2} c^{2} d^{2} e^{3} \ln \left(c \,x^{2}+b x +a \right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{4} \left(4 a c -b^{2}\right)}+\frac{b \,c^{4} d^{5}}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{4} \left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}-\frac{2 a c \,e^{5} \ln \left(e x +d \right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{4}}+\frac{3 b^{2} e^{5} \ln \left(e x +d \right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{4}}-\frac{10 b c d \,e^{4} \ln \left(e x +d \right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{4}}+\frac{10 c^{2} d^{2} e^{3} \ln \left(e x +d \right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{4}}+\frac{2 b \,e^{4}}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \left(e x +d \right)}-\frac{4 c d \,e^{3}}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \left(e x +d \right)}-\frac{e^{3}}{2 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(e x +d \right)^{2}}"," ",0,"6/(a*e^2-b*d*e+c*d^2)^4/(c*x^2+b*x+a)*c^3/(4*a*c-b^2)*x*d^3*b^2*e^2-60/(a*e^2-b*d*e+c*d^2)^4/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*b*c^3*d^2*e^3+60/(a*e^2-b*d*e+c*d^2)^4/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*b^2*c^2*d*e^4+3/(a*e^2-b*d*e+c*d^2)^4/(c*x^2+b*x+a)*c^2/(4*a*c-b^2)*x*a^2*b*e^5-4/(a*e^2-b*d*e+c*d^2)^4/(c*x^2+b*x+a)*c^4/(4*a*c-b^2)*x*d^3*a*e^2+1/(a*e^2-b*d*e+c*d^2)^4/(c*x^2+b*x+a)*c/(4*a*c-b^2)*x*b^4*d*e^4+6/(a*e^2-b*d*e+c*d^2)^4/(c*x^2+b*x+a)*c^3/(4*a*c-b^2)*x*d^2*a*b*e^3+2*e^4/(a*e^2-b*d*e+c*d^2)^3/(e*x+d)*b+3*e^5/(a*e^2-b*d*e+c*d^2)^4*ln(e*x+d)*b^2-4/(a*e^2-b*d*e+c*d^2)^4/(c*x^2+b*x+a)*c^2/(4*a*c-b^2)*x*d^2*b^3*e^3+20/(a*e^2-b*d*e+c*d^2)^4/(4*a*c-b^2)*c^2*ln(c*x^2+b*x+a)*a*b*d*e^4+4/(a*e^2-b*d*e+c*d^2)^4/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*c^5*d^5+3/2/(a*e^2-b*d*e+c*d^2)^4/(4*a*c-b^2)*ln(c*x^2+b*x+a)*b^4*e^5+3/(a*e^2-b*d*e+c*d^2)^4/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^5*e^5-4*e^3/(a*e^2-b*d*e+c*d^2)^3/(e*x+d)*c*d-2*e^5/(a*e^2-b*d*e+c*d^2)^4*ln(e*x+d)*a*c+10*e^3/(a*e^2-b*d*e+c*d^2)^4*ln(e*x+d)*c^2*d^2-1/2*e^3/(a*e^2-b*d*e+c*d^2)^2/(e*x+d)^2-5/(a*e^2-b*d*e+c*d^2)^4/(c*x^2+b*x+a)*c^4/(4*a*c-b^2)*x*b*d^4*e-7/(a*e^2-b*d*e+c*d^2)^4/(c*x^2+b*x+a)/(4*a*c-b^2)*a^2*b*c^2*d*e^4-1/(a*e^2-b*d*e+c*d^2)^4/(c*x^2+b*x+a)/(4*a*c-b^2)*a*b^3*c*d*e^4+10/(a*e^2-b*d*e+c*d^2)^4/(c*x^2+b*x+a)/(4*a*c-b^2)*a*b^2*c^2*d^2*e^3-14/(a*e^2-b*d*e+c*d^2)^4/(c*x^2+b*x+a)/(4*a*c-b^2)*a*b*c^3*d^3*e^2-1/(a*e^2-b*d*e+c*d^2)^4/(c*x^2+b*x+a)*c/(4*a*c-b^2)*x*a*b^3*e^5-6/(a*e^2-b*d*e+c*d^2)^4/(c*x^2+b*x+a)*c^3/(4*a*c-b^2)*x*d*a^2*e^4-10*e^4/(a*e^2-b*d*e+c*d^2)^4*ln(e*x+d)*b*c*d+2/(a*e^2-b*d*e+c*d^2)^4/(c*x^2+b*x+a)*c^5/(4*a*c-b^2)*x*d^5-2/(a*e^2-b*d*e+c*d^2)^4/(c*x^2+b*x+a)/(4*a*c-b^2)*a^3*c^2*e^5-1/(a*e^2-b*d*e+c*d^2)^4/(c*x^2+b*x+a)/(4*a*c-b^2)*a*b^4*e^5+1/(a*e^2-b*d*e+c*d^2)^4/(c*x^2+b*x+a)/(4*a*c-b^2)*b^5*d*e^4+1/(a*e^2-b*d*e+c*d^2)^4/(c*x^2+b*x+a)/(4*a*c-b^2)*b*c^4*d^5+4/(a*e^2-b*d*e+c*d^2)^4/(4*a*c-b^2)*c^2*ln(c*x^2+b*x+a)*a^2*e^5-10/(a*e^2-b*d*e+c*d^2)^4/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b*c^4*d^4*e+30/(a*e^2-b*d*e+c*d^2)^4/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a^2*b*c^2*e^5-60/(a*e^2-b*d*e+c*d^2)^4/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a^2*c^3*d*e^4+4/(a*e^2-b*d*e+c*d^2)^4/(c*x^2+b*x+a)/(4*a*c-b^2)*a^2*b^2*c*e^5+4/(a*e^2-b*d*e+c*d^2)^4/(c*x^2+b*x+a)/(4*a*c-b^2)*a^2*c^3*d^2*e^3+6/(a*e^2-b*d*e+c*d^2)^4/(c*x^2+b*x+a)/(4*a*c-b^2)*a*c^4*d^4*e-4/(a*e^2-b*d*e+c*d^2)^4/(c*x^2+b*x+a)/(4*a*c-b^2)*b^4*c*d^2*e^3+6/(a*e^2-b*d*e+c*d^2)^4/(c*x^2+b*x+a)/(4*a*c-b^2)*b^3*c^2*d^3*e^2-4/(a*e^2-b*d*e+c*d^2)^4/(c*x^2+b*x+a)/(4*a*c-b^2)*b^2*c^3*d^4*e-7/(a*e^2-b*d*e+c*d^2)^4/(4*a*c-b^2)*c*ln(c*x^2+b*x+a)*a*b^2*e^5-20/(a*e^2-b*d*e+c*d^2)^4/(4*a*c-b^2)*c^3*ln(c*x^2+b*x+a)*a*d^2*e^3-5/(a*e^2-b*d*e+c*d^2)^4/(4*a*c-b^2)*c*ln(c*x^2+b*x+a)*b^3*d*e^4+5/(a*e^2-b*d*e+c*d^2)^4/(4*a*c-b^2)*c^2*ln(c*x^2+b*x+a)*b^2*d^2*e^3-20/(a*e^2-b*d*e+c*d^2)^4/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*b^3*c*e^5+40/(a*e^2-b*d*e+c*d^2)^4/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*c^4*d^3*e^2-10/(a*e^2-b*d*e+c*d^2)^4/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^4*c*d*e^4+10/(a*e^2-b*d*e+c*d^2)^4/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^3*c^2*d^2*e^3","B"
2199,1,1187,282,0.077000," ","int(x^7/(c*x^2+b*x+a)^3,x)","-\frac{63 a^{3} b \,x^{3}}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c}+\frac{91 a^{2} b^{3} x^{3}}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{2}}-\frac{35 a \,b^{5} x^{3}}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{3}}+\frac{4 b^{7} x^{3}}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{4}}-\frac{24 a^{4} x^{2}}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c}+\frac{27 a^{3} b^{2} x^{2}}{2 \left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{2}}+\frac{47 a^{2} b^{4} x^{2}}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{3}}-\frac{53 a \,b^{6} x^{2}}{2 \left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{4}}+\frac{7 b^{8} x^{2}}{2 \left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{5}}-\frac{73 a^{4} b x}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{2}}+\frac{136 a^{3} b^{3} x}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{3}}-\frac{58 a^{2} b^{5} x}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{4}}+\frac{7 a \,b^{7} x}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{5}}-\frac{20 a^{5}}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{2}}+\frac{115 a^{4} b^{2}}{2 \left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{3}}-\frac{55 a^{3} b^{4}}{2 \left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{4}}+\frac{210 a^{3} b \arctan \left(\frac{2 c x +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{7 a^{2} b^{6}}{2 \left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{5}}-\frac{210 a^{2} b^{3} \arctan \left(\frac{2 c x +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{63 a \,b^{5} \arctan \left(\frac{2 c x +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^{4}}-\frac{6 b^{7} \arctan \left(\frac{2 c x +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^{5}}-\frac{24 a^{3} \ln \left(c \,x^{2}+b x +a \right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{2}}+\frac{60 a^{2} b^{2} \ln \left(c \,x^{2}+b x +a \right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{3}}-\frac{51 a \,b^{4} \ln \left(c \,x^{2}+b x +a \right)}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{4}}+\frac{3 b^{6} \ln \left(c \,x^{2}+b x +a \right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{5}}+\frac{x^{2}}{2 c^{3}}-\frac{3 b x}{c^{4}}"," ",0,"-73/c^2/(c*x^2+b*x+a)^2*a^4*b/(16*a^2*c^2-8*a*b^2*c+b^4)*x+1/2/c^3*x^2-3/c^4*x*b-20/c^2/(c*x^2+b*x+a)^2*a^5/(16*a^2*c^2-8*a*b^2*c+b^4)-24/c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*ln(c*x^2+b*x+a)*a^3+3/c^5/(16*a^2*c^2-8*a*b^2*c+b^4)*ln(c*x^2+b*x+a)*b^6+115/2/c^3/(c*x^2+b*x+a)^2*a^4/(16*a^2*c^2-8*a*b^2*c+b^4)*b^2+7/2/c^5/(c*x^2+b*x+a)^2*a^2/(16*a^2*c^2-8*a*b^2*c+b^4)*b^6+60/c^3/(16*a^2*c^2-8*a*b^2*c+b^4)*ln(c*x^2+b*x+a)*a^2*b^2-51/2/c^4/(16*a^2*c^2-8*a*b^2*c+b^4)*ln(c*x^2+b*x+a)*a*b^4-24/c/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*a^4+27/2/c^2/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*a^3*b^2+47/c^3/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*a^2*b^4-55/2/c^4/(c*x^2+b*x+a)^2*a^3/(16*a^2*c^2-8*a*b^2*c+b^4)*b^4-6/c^5/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^7-35/c^3/(c*x^2+b*x+a)^2*b^5/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3*a+4/c^4/(c*x^2+b*x+a)^2*b^7/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3+7/2/c^5/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*b^8+136/c^3/(c*x^2+b*x+a)^2*a^3*b^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x+7/c^5/(c*x^2+b*x+a)^2*a*b^7/(16*a^2*c^2-8*a*b^2*c+b^4)*x-58/c^4/(c*x^2+b*x+a)^2*a^2*b^5/(16*a^2*c^2-8*a*b^2*c+b^4)*x+63/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+b)/(4*a*c-b^2)^(1/2))*a*b^5-210/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+b)/(4*a*c-b^2)^(1/2))*a^2*b^3+210/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+b)/(4*a*c-b^2)^(1/2))*a^3*b-63/c/(c*x^2+b*x+a)^2*b/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3*a^3+91/c^2/(c*x^2+b*x+a)^2*b^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3*a^2-53/2/c^4/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*a*b^6","B"
2200,1,1040,228,0.098000," ","int(x^6/(c*x^2+b*x+a)^3,x)","\frac{18 a^{3} x^{3}}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}-\frac{51 a^{2} b^{2} x^{3}}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c}+\frac{24 a \,b^{4} x^{3}}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{2}}-\frac{3 b^{6} x^{3}}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{3}}-\frac{21 a^{3} b \,x^{2}}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c}-\frac{41 a^{2} b^{3} x^{2}}{2 \left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{2}}+\frac{17 a \,b^{5} x^{2}}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{3}}-\frac{5 b^{7} x^{2}}{2 \left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{4}}+\frac{14 a^{4} x}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c}-\frac{71 a^{3} b^{2} x}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{2}}+\frac{38 a^{2} b^{4} x}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{3}}-\frac{5 a \,b^{6} x}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{4}}-\frac{29 a^{4} b}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{2}}+\frac{18 a^{3} b^{3}}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{3}}-\frac{60 a^{3} \arctan \left(\frac{2 c x +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^{2} b^{5}}{2 \left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{4}}+\frac{90 a^{2} b^{2} \arctan \left(\frac{2 c x +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{30 a \,b^{4} \arctan \left(\frac{2 c x +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^{6} \arctan \left(\frac{2 c x +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^{4}}-\frac{24 a^{2} b \ln \left(c \,x^{2}+b x +a \right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{2}}+\frac{12 a \,b^{3} \ln \left(c \,x^{2}+b x +a \right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{3}}-\frac{3 b^{5} \ln \left(c \,x^{2}+b x +a \right)}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{4}}+\frac{x}{c^{3}}"," ",0,"1/c^3*x+18/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3*a^3-51/c/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3*a^2*b^2+24/c^2/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3*a*b^4-3/c^3/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3*b^6-21/c/(c*x^2+b*x+a)^2*b/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*a^3-41/2/c^2/(c*x^2+b*x+a)^2*b^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*a^2+17/c^3/(c*x^2+b*x+a)^2*b^5/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*a-5/2/c^4/(c*x^2+b*x+a)^2*b^7/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2+14/c/(c*x^2+b*x+a)^2*a^4/(16*a^2*c^2-8*a*b^2*c+b^4)*x-71/c^2/(c*x^2+b*x+a)^2*a^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x*b^2+38/c^3/(c*x^2+b*x+a)^2*a^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x*b^4-5/c^4/(c*x^2+b*x+a)^2*a/(16*a^2*c^2-8*a*b^2*c+b^4)*x*b^6-29/c^2/(c*x^2+b*x+a)^2*b*a^4/(16*a^2*c^2-8*a*b^2*c+b^4)+18/c^3/(c*x^2+b*x+a)^2*b^3*a^3/(16*a^2*c^2-8*a*b^2*c+b^4)-5/2/c^4/(c*x^2+b*x+a)^2*b^5*a^2/(16*a^2*c^2-8*a*b^2*c+b^4)-24/c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*ln(c*x^2+b*x+a)*a^2*b+12/c^3/(16*a^2*c^2-8*a*b^2*c+b^4)*ln(c*x^2+b*x+a)*a*b^3-3/2/c^4/(16*a^2*c^2-8*a*b^2*c+b^4)*ln(c*x^2+b*x+a)*b^5-60/c/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a^3+90/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+b)/(4*a*c-b^2)^(1/2))*a^2*b^2-30/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+b)/(4*a*c-b^2)^(1/2))*a*b^4+3/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+b)/(4*a*c-b^2)^(1/2))*b^6","B"
2201,1,1444,378,0.091000," ","int((e*x+d)^5/(c*x^2+b*x+a)^3,x)","-\frac{30 a^{2} b \,e^{5} \arctan \left(\frac{2 c x +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{60 a^{2} d \,e^{4} \arctan \left(\frac{2 c x +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{10 a \,b^{3} e^{5} \arctan \left(\frac{2 c x +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{60 a b \,d^{2} e^{3} \arctan \left(\frac{2 c x +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{40 a c \,d^{3} e^{2} \arctan \left(\frac{2 c x +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^{5} e^{5} \arctan \left(\frac{2 c x +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{20 b^{2} d^{3} e^{2} \arctan \left(\frac{2 c x +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{30 b c \,d^{4} e \arctan \left(\frac{2 c x +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{12 c^{2} d^{5} \arctan \left(\frac{2 c x +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{8 a^{2} e^{5} \ln \left(c \,x^{2}+b x +a \right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c}-\frac{4 a \,b^{2} e^{5} \ln \left(c \,x^{2}+b x +a \right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{2}}+\frac{b^{4} e^{5} \ln \left(c \,x^{2}+b x +a \right)}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{3}}+\frac{\frac{\left(25 a^{2} b \,c^{2} e^{5}-50 a^{2} c^{3} d \,e^{4}-15 a \,b^{3} c \,e^{5}+40 a \,b^{2} c^{2} d \,e^{4}-30 a b \,c^{3} d^{2} e^{3}+20 a \,c^{4} d^{3} e^{2}+2 b^{5} e^{5}-5 b^{4} c d \,e^{4}+10 b^{2} c^{3} d^{3} e^{2}-15 b \,c^{4} d^{4} e +6 c^{5} d^{5}\right) x^{3}}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{2}}+\frac{\left(32 a^{3} c^{3} e^{5}+11 a^{2} b^{2} c^{2} e^{5}+10 a^{2} b \,c^{3} d \,e^{4}-160 a^{2} c^{4} d^{2} e^{3}-19 a \,b^{4} c \,e^{5}+40 a \,b^{3} c^{2} d \,e^{4}-10 a \,b^{2} c^{3} d^{2} e^{3}+60 a b \,c^{4} d^{3} e^{2}+3 b^{6} e^{5}-5 b^{5} c d \,e^{4}-10 b^{4} c^{2} d^{2} e^{3}+30 b^{3} c^{3} d^{3} e^{2}-45 b^{2} c^{4} d^{4} e +18 b \,c^{5} d^{5}\right) x^{2}}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{3}}+\frac{\left(31 a^{3} b \,c^{2} e^{5}-30 a^{3} c^{3} d \,e^{4}-22 a^{2} b^{3} c \,e^{5}+50 a^{2} b^{2} c^{2} d \,e^{4}-50 a^{2} b \,c^{3} d^{2} e^{3}-20 a^{2} c^{4} d^{3} e^{2}+3 a \,b^{5} e^{5}-5 a \,b^{4} c d \,e^{4}-10 a \,b^{3} c^{2} d^{2} e^{3}+50 a \,b^{2} c^{3} d^{3} e^{2}-25 a b \,c^{4} d^{4} e +10 a \,c^{5} d^{5}-5 b^{3} c^{3} d^{4} e +2 b^{2} c^{4} d^{5}\right) x}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{3}}+\frac{24 a^{4} c^{2} e^{5}-21 a^{3} b^{2} c \,e^{5}+50 a^{3} b \,c^{2} d \,e^{4}-80 a^{3} c^{3} d^{2} e^{3}+3 a^{2} b^{4} e^{5}-5 a^{2} b^{3} c d \,e^{4}-10 a^{2} b^{2} c^{2} d^{2} e^{3}+60 a^{2} b \,c^{3} d^{3} e^{2}-40 a^{2} c^{4} d^{4} e -5 a \,b^{2} c^{3} d^{4} e +10 a b \,c^{4} d^{5}-b^{3} c^{3} d^{5}}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{3}}}{\left(c \,x^{2}+b x +a \right)^{2}}"," ",0,"((25*a^2*b*c^2*e^5-50*a^2*c^3*d*e^4-15*a*b^3*c*e^5+40*a*b^2*c^2*d*e^4-30*a*b*c^3*d^2*e^3+20*a*c^4*d^3*e^2+2*b^5*e^5-5*b^4*c*d*e^4+10*b^2*c^3*d^3*e^2-15*b*c^4*d^4*e+6*c^5*d^5)/c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3+1/2*(32*a^3*c^3*e^5+11*a^2*b^2*c^2*e^5+10*a^2*b*c^3*d*e^4-160*a^2*c^4*d^2*e^3-19*a*b^4*c*e^5+40*a*b^3*c^2*d*e^4-10*a*b^2*c^3*d^2*e^3+60*a*b*c^4*d^3*e^2+3*b^6*e^5-5*b^5*c*d*e^4-10*b^4*c^2*d^2*e^3+30*b^3*c^3*d^3*e^2-45*b^2*c^4*d^4*e+18*b*c^5*d^5)/(16*a^2*c^2-8*a*b^2*c+b^4)/c^3*x^2+(31*a^3*b*c^2*e^5-30*a^3*c^3*d*e^4-22*a^2*b^3*c*e^5+50*a^2*b^2*c^2*d*e^4-50*a^2*b*c^3*d^2*e^3-20*a^2*c^4*d^3*e^2+3*a*b^5*e^5-5*a*b^4*c*d*e^4-10*a*b^3*c^2*d^2*e^3+50*a*b^2*c^3*d^3*e^2-25*a*b*c^4*d^4*e+10*a*c^5*d^5-5*b^3*c^3*d^4*e+2*b^2*c^4*d^5)/(16*a^2*c^2-8*a*b^2*c+b^4)/c^3*x+1/2/c^3*(24*a^4*c^2*e^5-21*a^3*b^2*c*e^5+50*a^3*b*c^2*d*e^4-80*a^3*c^3*d^2*e^3+3*a^2*b^4*e^5-5*a^2*b^3*c*d*e^4-10*a^2*b^2*c^2*d^2*e^3+60*a^2*b*c^3*d^3*e^2-40*a^2*c^4*d^4*e-5*a*b^2*c^3*d^4*e+10*a*b*c^4*d^5-b^3*c^3*d^5)/(16*a^2*c^2-8*a*b^2*c+b^4))/(c*x^2+b*x+a)^2+8/c/(16*a^2*c^2-8*a*b^2*c+b^4)*ln(c*x^2+b*x+a)*a^2*e^5-4/c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*ln(c*x^2+b*x+a)*a*b^2*e^5+1/2/c^3/(16*a^2*c^2-8*a*b^2*c+b^4)*ln(c*x^2+b*x+a)*b^4*e^5-30/c/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a^2*b*e^5+60/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*d*a^2*e^4+10/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+b)/(4*a*c-b^2)^(1/2))*a*b^3*e^5-60/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*d^2*a*b*e^3+40*c/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*d^3*a*e^2+20/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*d^3*b^2*e^2-30*c/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b*d^4*e+12*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+b)/(4*a*c-b^2)^(1/2))*d^5-1/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+b)/(4*a*c-b^2)^(1/2))*b^5*e^5","B"
2202,1,932,163,0.060000," ","int((e*x+d)^4/(c*x^2+b*x+a)^3,x)","\frac{12 a^{2} e^{4} \arctan \left(\frac{2 c x +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{24 a b d \,e^{3} \arctan \left(\frac{2 c x +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{24 a c \,d^{2} e^{2} \arctan \left(\frac{2 c x +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{12 b^{2} d^{2} e^{2} \arctan \left(\frac{2 c x +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{24 b c \,d^{3} e \arctan \left(\frac{2 c x +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{12 c^{2} d^{4} \arctan \left(\frac{2 c x +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(10 c^{2} a^{2} e^{4}-8 a \,b^{2} c \,e^{4}+12 a b \,c^{2} d \,e^{3}-12 a \,c^{3} d^{2} e^{2}+b^{4} e^{4}-6 b^{2} c^{2} d^{2} e^{2}+12 b \,c^{3} d^{3} e -6 c^{4} d^{4}\right) x^{3}}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c}+\frac{\left(2 a^{2} b \,c^{2} e^{4}-64 a^{2} c^{3} d \,e^{3}+8 a \,b^{3} c \,e^{4}-4 a \,b^{2} c^{2} d \,e^{3}+36 a b \,c^{3} d^{2} e^{2}-b^{5} e^{4}-4 b^{4} c d \,e^{3}+18 b^{3} c^{2} d^{2} e^{2}-36 b^{2} c^{3} d^{3} e +18 b \,c^{4} d^{4}\right) x^{2}}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{2}}-\frac{\left(6 a^{3} c^{2} e^{4}-10 a^{2} b^{2} c \,e^{4}+20 a^{2} b \,c^{2} d \,e^{3}+12 a^{2} c^{3} d^{2} e^{2}+a \,b^{4} e^{4}+4 a \,b^{3} c d \,e^{3}-30 a \,b^{2} c^{2} d^{2} e^{2}+20 a b \,c^{3} d^{3} e -10 a \,c^{4} d^{4}+4 b^{3} c^{2} d^{3} e -2 b^{2} c^{3} d^{4}\right) x}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{2}}+\frac{10 a^{3} b c \,e^{4}-32 a^{3} c^{2} d \,e^{3}-a^{2} b^{3} e^{4}-4 a^{2} b^{2} c d \,e^{3}+36 a^{2} b \,c^{2} d^{2} e^{2}-32 a^{2} c^{3} d^{3} e -4 a \,b^{2} c^{2} d^{3} e +10 a b \,c^{3} d^{4}-b^{3} c^{2} d^{4}}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{2}}}{\left(c \,x^{2}+b x +a \right)^{2}}"," ",0,"(-(10*a^2*c^2*e^4-8*a*b^2*c*e^4+12*a*b*c^2*d*e^3-12*a*c^3*d^2*e^2+b^4*e^4-6*b^2*c^2*d^2*e^2+12*b*c^3*d^3*e-6*c^4*d^4)/c/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3+1/2*(2*a^2*b*c^2*e^4-64*a^2*c^3*d*e^3+8*a*b^3*c*e^4-4*a*b^2*c^2*d*e^3+36*a*b*c^3*d^2*e^2-b^5*e^4-4*b^4*c*d*e^3+18*b^3*c^2*d^2*e^2-36*b^2*c^3*d^3*e+18*b*c^4*d^4)/c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2-(6*a^3*c^2*e^4-10*a^2*b^2*c*e^4+20*a^2*b*c^2*d*e^3+12*a^2*c^3*d^2*e^2+a*b^4*e^4+4*a*b^3*c*d*e^3-30*a*b^2*c^2*d^2*e^2+20*a*b*c^3*d^3*e-10*a*c^4*d^4+4*b^3*c^2*d^3*e-2*b^2*c^3*d^4)/(16*a^2*c^2-8*a*b^2*c+b^4)/c^2*x+1/2/c^2*(10*a^3*b*c*e^4-32*a^3*c^2*d*e^3-a^2*b^3*e^4-4*a^2*b^2*c*d*e^3+36*a^2*b*c^2*d^2*e^2-32*a^2*c^3*d^3*e-4*a*b^2*c^2*d^3*e+10*a*b*c^3*d^4-b^3*c^2*d^4)/(16*a^2*c^2-8*a*b^2*c+b^4))/(c*x^2+b*x+a)^2+12/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a^2*e^4-24/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*b*d*e^3+24/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*c*d^2*e^2+12/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^2*d^2*e^2-24/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b*c*d^3*e+12/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*c^2*d^4","B"
2203,1,695,150,0.058000," ","int((e*x+d)^3/(c*x^2+b*x+a)^3,x)","-\frac{6 a b \,e^{3} \arctan \left(\frac{2 c x +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{12 a c d \,e^{2} \arctan \left(\frac{2 c x +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^{2} d \,e^{2} \arctan \left(\frac{2 c x +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{18 b c \,d^{2} e \arctan \left(\frac{2 c x +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{12 c^{2} d^{3} \arctan \left(\frac{2 c x +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{3 \left(a b \,e^{3}-2 a c d \,e^{2}-b^{2} d \,e^{2}+3 b c \,d^{2} e -2 c^{2} d^{3}\right) c \,x^{3}}{16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}}-\frac{\left(16 a^{2} c^{2} e^{3}+a \,b^{2} c \,e^{3}-18 a b \,c^{2} d \,e^{2}+b^{4} e^{3}-9 b^{3} c d \,e^{2}+27 b^{2} c^{2} d^{2} e -18 b \,c^{3} d^{3}\right) x^{2}}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c}-\frac{\left(5 a^{2} b c \,e^{3}+6 a^{2} c^{2} d \,e^{2}+a \,b^{3} e^{3}-15 a \,b^{2} c d \,e^{2}+15 a b \,c^{2} d^{2} e -10 a \,c^{3} d^{3}+3 b^{3} c \,d^{2} e -2 b^{2} c^{2} d^{3}\right) x}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c}-\frac{8 a^{3} c \,e^{3}+a^{2} b^{2} e^{3}-18 a^{2} b c d \,e^{2}+24 a^{2} c^{2} d^{2} e +3 a \,b^{2} c \,d^{2} e -10 a b \,c^{2} d^{3}+b^{3} c \,d^{3}}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c}}{\left(c \,x^{2}+b x +a \right)^{2}}"," ",0,"(-3*c*(a*b*e^3-2*a*c*d*e^2-b^2*d*e^2+3*b*c*d^2*e-2*c^2*d^3)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3-1/2*(16*a^2*c^2*e^3+a*b^2*c*e^3-18*a*b*c^2*d*e^2+b^4*e^3-9*b^3*c*d*e^2+27*b^2*c^2*d^2*e-18*b*c^3*d^3)/c/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2-1/c*(5*a^2*b*c*e^3+6*a^2*c^2*d*e^2+a*b^3*e^3-15*a*b^2*c*d*e^2+15*a*b*c^2*d^2*e-10*a*c^3*d^3+3*b^3*c*d^2*e-2*b^2*c^2*d^3)/(16*a^2*c^2-8*a*b^2*c+b^4)*x-1/2/c*(8*a^3*c*e^3+a^2*b^2*e^3-18*a^2*b*c*d*e^2+24*a^2*c^2*d^2*e+3*a*b^2*c*d^2*e-10*a*b*c^2*d^3+b^3*c*d^3)/(16*a^2*c^2-8*a*b^2*c+b^4))/(c*x^2+b*x+a)^2-6/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*b*e^3+12/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*c*d*e^2+6/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^2*d*e^2-18/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b*c*d^2*e+12/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*c^2*d^3","B"
2204,1,508,190,0.056000," ","int((e*x+d)^2/(c*x^2+b*x+a)^3,x)","\frac{4 a c \,e^{2} \arctan \left(\frac{2 c x +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^{2} e^{2} \arctan \left(\frac{2 c x +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{12 b c d e \arctan \left(\frac{2 c x +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{12 c^{2} d^{2} \arctan \left(\frac{2 c x +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 c \,e^{2}+b^{2} e^{2}-6 b c d e +6 c^{2} d^{2}\right) c \,x^{3}}{16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}}+\frac{3 \left(2 a c \,e^{2}+b^{2} e^{2}-6 b c d e +6 c^{2} d^{2}\right) b \,x^{2}}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}-\frac{\left(2 a^{2} c \,e^{2}-5 a \,b^{2} e^{2}+10 a b c d e -10 a \,c^{2} d^{2}+2 b^{3} d e -2 b^{2} c \,d^{2}\right) x}{16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}}+\frac{6 a^{2} b \,e^{2}-16 a^{2} c d e -2 a \,b^{2} d e +10 a b c \,d^{2}-b^{3} d^{2}}{32 a^{2} c^{2}-16 a \,b^{2} c +2 b^{4}}}{\left(c \,x^{2}+b x +a \right)^{2}}"," ",0,"(c*(2*a*c*e^2+b^2*e^2-6*b*c*d*e+6*c^2*d^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3+3/2*b*(2*a*c*e^2+b^2*e^2-6*b*c*d*e+6*c^2*d^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2-(2*a^2*c*e^2-5*a*b^2*e^2+10*a*b*c*d*e-10*a*c^2*d^2+2*b^3*d*e-2*b^2*c*d^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*x+1/2*(6*a^2*b*e^2-16*a^2*c*d*e-2*a*b^2*d*e+10*a*b*c*d^2-b^3*d^2)/(16*a^2*c^2-8*a*b^2*c+b^4))/(c*x^2+b*x+a)^2+4/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*c*e^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+b)/(4*a*c-b^2)^(1/2))*b^2*e^2-12/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b*c*d*e+12/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*c^2*d^2","B"
2205,1,242,125,0.051000," ","int((e*x+d)/(c*x^2+b*x+a)^3,x)","-\frac{3 b c e x}{\left(4 a c -b^{2}\right)^{2} \left(c \,x^{2}+b x +a \right)}-\frac{6 b c e \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{5}{2}}}+\frac{6 c^{2} d x}{\left(4 a c -b^{2}\right)^{2} \left(c \,x^{2}+b x +a \right)}+\frac{12 c^{2} d \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{5}{2}}}-\frac{3 b^{2} e}{2 \left(4 a c -b^{2}\right)^{2} \left(c \,x^{2}+b x +a \right)}+\frac{3 b c d}{\left(4 a c -b^{2}\right)^{2} \left(c \,x^{2}+b x +a \right)}+\frac{-2 a e +b d +\left(-b e +2 c d \right) x}{2 \left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{2}}"," ",0,"1/2*(-2*a*e+b*d+(-b*e+2*c*d)*x)/(4*a*c-b^2)/(c*x^2+b*x+a)^2-3/(4*a*c-b^2)^2/(c*x^2+b*x+a)*c*x*b*e+6/(4*a*c-b^2)^2/(c*x^2+b*x+a)*c^2*x*d-3/2/(4*a*c-b^2)^2/(c*x^2+b*x+a)*b^2*e+3/(4*a*c-b^2)^2/(c*x^2+b*x+a)*b*c*d-6/(4*a*c-b^2)^(5/2)*c*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b*e+12/(4*a*c-b^2)^(5/2)*c^2*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*d","A"
2206,1,129,97,0.051000," ","int(1/(c*x^2+b*x+a)^3,x)","\frac{6 c^{2} x}{\left(4 a c -b^{2}\right)^{2} \left(c \,x^{2}+b x +a \right)}+\frac{12 c^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{5}{2}}}+\frac{3 b c}{\left(4 a c -b^{2}\right)^{2} \left(c \,x^{2}+b x +a \right)}+\frac{2 c x +b}{2 \left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{2}}"," ",0,"1/2*(2*c*x+b)/(4*a*c-b^2)/(c*x^2+b*x+a)^2+6*c^2/(4*a*c-b^2)^2/(c*x^2+b*x+a)*x+3*c/(4*a*c-b^2)^2/(c*x^2+b*x+a)*b+12*c^2/(4*a*c-b^2)^(5/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))","A"
2207,1,4701,419,0.112000," ","int(1/(e*x+d)/(c*x^2+b*x+a)^3,x)","\text{output too large to display}"," ",0,"-30/(a*e^2-b*d*e+c*d^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+b)/(4*a*c-b^2)^(1/2))*b*c^4*d^4*e+40/(a*e^2-b*d*e+c*d^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+b)/(4*a*c-b^2)^(1/2))*a*c^4*d^3*e^2+20/(a*e^2-b*d*e+c*d^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+b)/(4*a*c-b^2)^(1/2))*b^2*c^3*d^3*e^2+8/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)^2*c^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3*a*b^2*d*e^4-30/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)^2*c^4/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3*d^2*a*b*e^3+13/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)^2*c^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*a^2*b*d*e^4+16/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)^2*c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*a*b^3*d*e^4-49/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)^2*c^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*a*b^2*d^2*e^3+30/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)^2*c^4/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*a*b*d^3*e^2+10/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x*a^2*b^2*c^2*d*e^4-34/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x*a^2*b*c^3*d^2*e^3+6/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x*a*b^4*c*d*e^4-18/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x*a*b^3*c^2*d^2*e^3-60/(a*e^2-b*d*e+c*d^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+b)/(4*a*c-b^2)^(1/2))*a*b*c^3*d^2*e^3+26/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x*a*b^2*c^3*d^3*e^2-25/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x*a*b*c^4*d^4*e-15/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)^2*c^5/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3*b*d^4*e-25/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*a^2*b^2*c^2*d^2*e^3+10/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)^2*c^4/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3*d^3*b^2*e^2-29/2/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)^2*c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*a^2*b^2*e^5+8/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)^2*c^4/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*a^2*d^2*e^3+2/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)^2*c/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*a*b^4*e^5-29/2/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*a*b^2*c^3*d^4*e+27/2/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*a^2*b^3*c*d*e^4-7/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)^2*c^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3*a^2*b*e^5+14/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)^2*c^4/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3*d*a^2*e^4+1/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)^2*c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3*a*b^3*e^5-1/2/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*a*b^4*c*d^2*e^3-30/(a*e^2-b*d*e+c*d^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+b)/(4*a*c-b^2)^(1/2))*a^2*b*c^2*e^5+60/(a*e^2-b*d*e+c*d^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+b)/(4*a*c-b^2)^(1/2))*a^2*c^3*d*e^4+10/(a*e^2-b*d*e+c*d^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+b)/(4*a*c-b^2)^(1/2))*a*b^3*c*e^5-2/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)^2*c/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*b^5*d*e^4+6/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*a^2*b*c^3*d^3*e^2-1/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x*a^3*b*c^2*e^5+18/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x*a^3*c^3*d*e^4-7/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*a^3*b*c^2*d*e^4+20/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)^2*c^5/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3*d^3*a*e^2-1/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)^2*c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3*b^4*d*e^4+12/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*a*b^3*c^2*d^3*e^2-6/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x*a^2*b^3*c*e^5+28/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x*a^2*c^4*d^3*e^2+1/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x*b^5*c*d^2*e^3+3/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x*b^4*c^2*d^3*e^2-5/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x*b^3*c^3*d^4*e+1/2/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)^2*c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*b^4*d^2*e^3+15/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)^2*c^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*b^3*d^3*e^2-45/2/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)^2*c^4/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*b^2*d^4*e+12/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*a^4*c^2*e^5+3/2/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*a^2*b^4*e^5+1/2/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*b^6*d^2*e^3-1/2/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*b^3*c^3*d^5+6/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)^2*c^6/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3*d^5-1/(a*e^2-b*d*e+c*d^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+b)/(4*a*c-b^2)^(1/2))*b^5*e^5+12/(a*e^2-b*d*e+c*d^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+b)/(4*a*c-b^2)^(1/2))*c^5*d^5-8/(a*e^2-b*d*e+c*d^2)^3/(16*a^2*c^2-8*a*b^2*c+b^4)*c^2*ln(c*x^2+b*x+a)*a^2*e^5-1/2/(a*e^2-b*d*e+c*d^2)^3/(16*a^2*c^2-8*a*b^2*c+b^4)*ln(c*x^2+b*x+a)*b^4*e^5+e^5*ln(e*x+d)/(a*e^2-b*d*e+c*d^2)^3+5/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*a*b*c^4*d^5+4/(a*e^2-b*d*e+c*d^2)^3/(16*a^2*c^2-8*a*b^2*c+b^4)*c*ln(c*x^2+b*x+a)*a*b^2*e^5-3/2/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*b^5*c*d^3*e^2+3/2/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*b^4*c^2*d^4*e+8/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)^2*c^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*a^3*e^5+9/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)^2*c^5/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*b*d^5+1/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x*a*b^5*e^5+10/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x*a*c^5*d^5-1/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x*b^6*d*e^4+2/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x*b^2*c^4*d^5-21/2/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*a^3*b^2*c*e^5+16/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*a^3*c^3*d^2*e^3+4/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*a^2*c^4*d^4*e-2/(a*e^2-b*d*e+c*d^2)^3/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*a*b^5*d*e^4","B"
2208,1,954,229,0.077000," ","int(1/x^2/(c*x^2+b*x+a)^3,x)","-\frac{14 c^{4} x^{3}}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}+\frac{13 b^{2} c^{3} x^{3}}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}-\frac{2 b^{4} c^{2} x^{3}}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{3}}-\frac{37 b \,c^{3} x^{2}}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}+\frac{55 b^{3} c^{2} x^{2}}{2 \left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}-\frac{4 b^{5} c \,x^{2}}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{3}}-\frac{7 b^{2} c^{2} x}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}+\frac{12 b^{4} c x}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}-\frac{2 b^{6} x}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{3}}-\frac{18 c^{3} x}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}+\frac{18 b^{3} c}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}-\frac{60 c^{3} \arctan \left(\frac{2 c x +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^{5}}{2 \left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}+\frac{90 b^{2} c^{2} \arctan \left(\frac{2 c x +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{30 b^{4} c \arctan \left(\frac{2 c x +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 b^{6} \arctan \left(\frac{2 c x +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^{4}}-\frac{29 b \,c^{2}}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}+\frac{24 b \,c^{2} \ln \left(c \,x^{2}+b x +a \right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}-\frac{12 b^{3} c \ln \left(c \,x^{2}+b x +a \right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{3}}+\frac{3 b^{5} \ln \left(c \,x^{2}+b x +a \right)}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{4}}-\frac{3 b \ln \left(x \right)}{a^{4}}-\frac{1}{a^{3} x}"," ",0,"-14/a/(c*x^2+b*x+a)^2*c^4/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3+13/a^2/(c*x^2+b*x+a)^2*c^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3*b^2-2/a^3/(c*x^2+b*x+a)^2*c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3*b^4-37/a/(c*x^2+b*x+a)^2*b*c^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2+55/2/a^2/(c*x^2+b*x+a)^2*b^3*c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2-4/a^3/(c*x^2+b*x+a)^2*b^5*c/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2-18/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x*c^3-7/a/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x*b^2*c^2+12/a^2/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x*b^4*c-2/a^3/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x*b^6-29/(c*x^2+b*x+a)^2*b/(16*a^2*c^2-8*a*b^2*c+b^4)*c^2+18/a/(c*x^2+b*x+a)^2*b^3/(16*a^2*c^2-8*a*b^2*c+b^4)*c-5/2/a^2/(c*x^2+b*x+a)^2*b^5/(16*a^2*c^2-8*a*b^2*c+b^4)+24/a^2/(16*a^2*c^2-8*a*b^2*c+b^4)*c^2*ln(c*x^2+b*x+a)*b-12/a^3/(16*a^2*c^2-8*a*b^2*c+b^4)*c*ln(c*x^2+b*x+a)*b^3+3/2/a^4/(16*a^2*c^2-8*a*b^2*c+b^4)*ln(c*x^2+b*x+a)*b^5-60/a/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*c^3+90/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+b)/(4*a*c-b^2)^(1/2))*b^2*c^2-30/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+b)/(4*a*c-b^2)^(1/2))*b^4*c+3/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+b)/(4*a*c-b^2)^(1/2))*b^6-1/a^3/x-3/a^4*b*ln(x)","B"
2209,1,1110,294,0.072000," ","int(1/x^3/(c*x^2+b*x+a)^3,x)","\frac{33 b \,c^{4} x^{3}}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}-\frac{21 b^{3} c^{3} x^{3}}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{3}}+\frac{3 b^{5} c^{2} x^{3}}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{4}}-\frac{16 c^{4} x^{2}}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}+\frac{163 b^{2} c^{3} x^{2}}{2 \left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}-\frac{89 b^{4} c^{2} x^{2}}{2 \left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{3}}+\frac{6 b^{6} c \,x^{2}}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{4}}+\frac{23 b \,c^{3} x}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}+\frac{24 b^{3} c^{2} x}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}-\frac{20 b^{5} c x}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{3}}+\frac{3 b^{7} x}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{4}}+\frac{115 b^{2} c^{2}}{2 \left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}-\frac{55 b^{4} c}{2 \left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}+\frac{210 b \,c^{3} \arctan \left(\frac{2 c x +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{7 b^{6}}{2 \left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{3}}-\frac{210 b^{3} c^{2} \arctan \left(\frac{2 c x +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{63 b^{5} c \arctan \left(\frac{2 c x +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^{4}}-\frac{6 b^{7} \arctan \left(\frac{2 c x +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^{5}}-\frac{20 c^{3}}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}+\frac{24 c^{3} \ln \left(c \,x^{2}+b x +a \right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}-\frac{60 b^{2} c^{2} \ln \left(c \,x^{2}+b x +a \right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{3}}+\frac{51 b^{4} c \ln \left(c \,x^{2}+b x +a \right)}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{4}}-\frac{3 b^{6} \ln \left(c \,x^{2}+b x +a \right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{5}}-\frac{3 c \ln \left(x \right)}{a^{4}}+\frac{6 b^{2} \ln \left(x \right)}{a^{5}}+\frac{3 b}{a^{4} x}-\frac{1}{2 a^{3} x^{2}}"," ",0,"-6/a^5/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^7-16/a/(c*x^2+b*x+a)^2*c^4/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2+3/a^4/(c*x^2+b*x+a)^2*b^7/(16*a^2*c^2-8*a*b^2*c+b^4)*x+115/2/a/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*b^2*c^2-55/2/a^2/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*b^4*c-60/a^3/(16*a^2*c^2-8*a*b^2*c+b^4)*c^2*ln(c*x^2+b*x+a)*b^2+51/2/a^4/(16*a^2*c^2-8*a*b^2*c+b^4)*c*ln(c*x^2+b*x+a)*b^4+6/a^5*b^2*ln(x)+24/a^2/(c*x^2+b*x+a)^2*b^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x*c^2-20/a^3/(c*x^2+b*x+a)^2*b^5/(16*a^2*c^2-8*a*b^2*c+b^4)*x*c+210/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+b)/(4*a*c-b^2)^(1/2))*b*c^3-210/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+b)/(4*a*c-b^2)^(1/2))*b^3*c^2+63/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+b)/(4*a*c-b^2)^(1/2))*b^5*c+33/a^2/(c*x^2+b*x+a)^2*b*c^4/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3-21/a^3/(c*x^2+b*x+a)^2*b^3*c^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3+3/a^4/(c*x^2+b*x+a)^2*b^5*c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3+163/2/a^2/(c*x^2+b*x+a)^2*c^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*b^2-89/2/a^3/(c*x^2+b*x+a)^2*c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*b^4+7/2/a^3/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*b^6+24/a^2/(16*a^2*c^2-8*a*b^2*c+b^4)*c^3*ln(c*x^2+b*x+a)-3/a^5/(16*a^2*c^2-8*a*b^2*c+b^4)*ln(c*x^2+b*x+a)*b^6+6/a^4/(c*x^2+b*x+a)^2*c/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*b^6+23/a/(c*x^2+b*x+a)^2*b/(16*a^2*c^2-8*a*b^2*c+b^4)*x*c^3-3/a^4*c*ln(x)-1/2/a^3/x^2-20/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*c^3+3/a^4*b/x","B"
2210,1,2336,339,0.092000," ","int(x^8/(c*x^2+b*x+a)^4,x)","\frac{116 a^{4} c \,x^{5}}{\left(c \,x^{2}+b x +a \right)^{3} \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right)}-\frac{424 a^{3} b^{2} x^{5}}{\left(c \,x^{2}+b x +a \right)^{3} \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right)}+\frac{292 a^{2} b^{4} x^{5}}{\left(c \,x^{2}+b x +a \right)^{3} \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) c}-\frac{72 a \,b^{6} x^{5}}{\left(c \,x^{2}+b x +a \right)^{3} \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) c^{2}}+\frac{6 b^{8} x^{5}}{\left(c \,x^{2}+b x +a \right)^{3} \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) c^{3}}-\frac{94 a^{4} b \,x^{4}}{\left(c \,x^{2}+b x +a \right)^{3} \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right)}-\frac{452 a^{3} b^{3} x^{4}}{\left(c \,x^{2}+b x +a \right)^{3} \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) c}+\frac{418 a^{2} b^{5} x^{4}}{\left(c \,x^{2}+b x +a \right)^{3} \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) c^{2}}-\frac{114 a \,b^{7} x^{4}}{\left(c \,x^{2}+b x +a \right)^{3} \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) c^{3}}+\frac{10 b^{9} x^{4}}{\left(c \,x^{2}+b x +a \right)^{3} \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) c^{4}}+\frac{544 a^{5} x^{3}}{3 \left(c \,x^{2}+b x +a \right)^{3} \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right)}-\frac{1078 a^{4} b^{2} x^{3}}{\left(c \,x^{2}+b x +a \right)^{3} \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) c}+\frac{596 a^{3} b^{4} x^{3}}{\left(c \,x^{2}+b x +a \right)^{3} \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) c^{2}}-\frac{68 a^{2} b^{6} x^{3}}{3 \left(c \,x^{2}+b x +a \right)^{3} \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) c^{3}}-\frac{32 a \,b^{8} x^{3}}{\left(c \,x^{2}+b x +a \right)^{3} \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) c^{4}}+\frac{13 b^{10} x^{3}}{3 \left(c \,x^{2}+b x +a \right)^{3} \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) c^{5}}-\frac{304 a^{5} b \,x^{2}}{\left(c \,x^{2}+b x +a \right)^{3} \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) c}-\frac{387 a^{4} b^{3} x^{2}}{\left(c \,x^{2}+b x +a \right)^{3} \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) c^{2}}+\frac{486 a^{3} b^{5} x^{2}}{\left(c \,x^{2}+b x +a \right)^{3} \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) c^{3}}-\frac{143 a^{2} b^{7} x^{2}}{\left(c \,x^{2}+b x +a \right)^{3} \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) c^{4}}+\frac{13 a \,b^{9} x^{2}}{\left(c \,x^{2}+b x +a \right)^{3} \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) c^{5}}+\frac{76 a^{6} x}{\left(c \,x^{2}+b x +a \right)^{3} \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) c}-\frac{694 a^{5} b^{2} x}{\left(c \,x^{2}+b x +a \right)^{3} \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) c^{2}}+\frac{567 a^{4} b^{4} x}{\left(c \,x^{2}+b x +a \right)^{3} \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) c^{3}}-\frac{150 a^{3} b^{6} x}{\left(c \,x^{2}+b x +a \right)^{3} \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) c^{4}}+\frac{13 a^{2} b^{8} x}{\left(c \,x^{2}+b x +a \right)^{3} \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) c^{5}}-\frac{590 a^{6} b}{3 \left(c \,x^{2}+b x +a \right)^{3} \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) c^{2}}+\frac{535 a^{5} b^{3}}{3 \left(c \,x^{2}+b x +a \right)^{3} \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) c^{3}}-\frac{49 a^{4} b^{5}}{\left(c \,x^{2}+b x +a \right)^{3} \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) c^{4}}+\frac{13 a^{3} b^{7}}{3 \left(c \,x^{2}+b x +a \right)^{3} \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) c^{5}}-\frac{280 a^{4} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) \sqrt{4 a c -b^{2}}\, c}+\frac{560 a^{3} b^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) \sqrt{4 a c -b^{2}}\, c^{2}}-\frac{280 a^{2} b^{4} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) \sqrt{4 a c -b^{2}}\, c^{3}}+\frac{56 a \,b^{6} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) \sqrt{4 a c -b^{2}}\, c^{4}}-\frac{4 b^{8} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) \sqrt{4 a c -b^{2}}\, c^{5}}-\frac{128 a^{3} b \ln \left(c \,x^{2}+b x +a \right)}{\left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) c^{2}}+\frac{96 a^{2} b^{3} \ln \left(c \,x^{2}+b x +a \right)}{\left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) c^{3}}-\frac{24 a \,b^{5} \ln \left(c \,x^{2}+b x +a \right)}{\left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) c^{4}}+\frac{2 b^{7} \ln \left(c \,x^{2}+b x +a \right)}{\left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) c^{5}}+\frac{x}{c^{4}}"," ",0,"116*c/(c*x^2+b*x+a)^3/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x^5*a^4+6/c^3/(c*x^2+b*x+a)^3/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x^5*b^8+13/3/c^5/(c*x^2+b*x+a)^3/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x^3*b^10+76/c/(c*x^2+b*x+a)^3*a^6/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x-68/3/c^3/(c*x^2+b*x+a)^3/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x^3*a^2*b^6-694/c^2/(c*x^2+b*x+a)^3*a^5/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x*b^2+567/c^3/(c*x^2+b*x+a)^3*a^4/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x*b^4-304/c/(c*x^2+b*x+a)^3*a^5*b/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x^2-387/c^2/(c*x^2+b*x+a)^3*a^4*b^3/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x^2+486/c^3/(c*x^2+b*x+a)^3*a^3*b^5/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x^2+2/c^5/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*ln(c*x^2+b*x+a)*b^7+544/3/(c*x^2+b*x+a)^3/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x^3*a^5+292/c/(c*x^2+b*x+a)^3/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x^5*a^2*b^4+13/c^5/(c*x^2+b*x+a)^3*a*b^9/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x^2-114/c^3/(c*x^2+b*x+a)^3*b^7/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x^4*a-1078/c/(c*x^2+b*x+a)^3/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x^3*a^4*b^2+596/c^2/(c*x^2+b*x+a)^3/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x^3*a^3*b^4-150/c^4/(c*x^2+b*x+a)^3*a^3/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x*b^6-143/c^4/(c*x^2+b*x+a)^3*a^2*b^7/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x^2+1/c^4*x-49/c^4/(c*x^2+b*x+a)^3*a^4*b^5/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)-72/c^2/(c*x^2+b*x+a)^3/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x^5*a*b^6-452/c/(c*x^2+b*x+a)^3*b^3/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x^4*a^3-94/(c*x^2+b*x+a)^3*b/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x^4*a^4-424/(c*x^2+b*x+a)^3/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x^5*a^3*b^2-280/c/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a^4+10/c^4/(c*x^2+b*x+a)^3*b^9/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x^4-32/c^4/(c*x^2+b*x+a)^3/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x^3*a*b^8+418/c^2/(c*x^2+b*x+a)^3*b^5/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x^4*a^2+13/c^5/(c*x^2+b*x+a)^3*a^2/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x*b^8+560/c^2/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a^3*b^2-280/c^3/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a^2*b^4+56/c^4/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*b^6-590/3/c^2/(c*x^2+b*x+a)^3*a^6*b/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)+535/3/c^3/(c*x^2+b*x+a)^3*a^5*b^3/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)+13/3/c^5/(c*x^2+b*x+a)^3*a^3*b^7/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)-4/c^5/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^8+96/c^3/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*ln(c*x^2+b*x+a)*a^2*b^3-128/c^2/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*ln(c*x^2+b*x+a)*a^3*b-24/c^4/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*ln(c*x^2+b*x+a)*a*b^5","B"
2211,1,1013,279,0.072000," ","int(x^7/(c*x^2+b*x+a)^4,x)","-\frac{140 a^{3} b \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) \sqrt{4 a c -b^{2}}\, c}+\frac{70 a^{2} b^{3} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) \sqrt{4 a c -b^{2}}\, c^{2}}-\frac{14 a \,b^{5} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) \sqrt{4 a c -b^{2}}\, c^{3}}+\frac{b^{7} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) \sqrt{4 a c -b^{2}}\, c^{4}}+\frac{32 a^{3} \ln \left(c \,x^{2}+b x +a \right)}{\left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) c}-\frac{24 a^{2} b^{2} \ln \left(c \,x^{2}+b x +a \right)}{\left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) c^{2}}+\frac{6 a \,b^{4} \ln \left(c \,x^{2}+b x +a \right)}{\left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) c^{3}}-\frac{b^{6} \ln \left(c \,x^{2}+b x +a \right)}{2 \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) c^{4}}+\frac{\frac{\left(154 a^{3} c^{3}-133 a^{2} b^{2} c^{2}+35 a \,b^{4} c -3 b^{6}\right) b \,x^{5}}{\left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) c^{2}}+\frac{\left(192 a^{4} c^{4}+242 a^{3} b^{2} c^{3}-341 a^{2} b^{4} c^{2}+100 a \,b^{6} c -9 b^{8}\right) x^{4}}{2 \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) c^{3}}+\frac{\left(428 a^{3} c^{3}-460 a^{2} b^{2} c^{2}+126 a \,b^{4} c -11 b^{6}\right) a^{2} b x}{2 \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) c^{4}}+\frac{\left(2272 a^{4} c^{4}-1698 a^{3} b^{2} c^{3}+117 a^{2} b^{4} c^{2}+76 a \,b^{6} c -11 b^{8}\right) b \,x^{3}}{6 \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) c^{4}}+\frac{\left(352 a^{3} c^{3}-438 a^{2} b^{2} c^{2}+124 a \,b^{4} c -11 b^{6}\right) a^{3}}{6 \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) c^{4}}+\frac{\left(288 a^{4} c^{4}+152 a^{3} b^{2} c^{3}-381 a^{2} b^{4} c^{2}+119 a \,b^{6} c -11 b^{8}\right) a \,x^{2}}{2 \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) c^{4}}}{\left(c \,x^{2}+b x +a \right)^{3}}"," ",0,"((154*a^3*c^3-133*a^2*b^2*c^2+35*a*b^4*c-3*b^6)*b/c^2/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x^5+1/2*(192*a^4*c^4+242*a^3*b^2*c^3-341*a^2*b^4*c^2+100*a*b^6*c-9*b^8)/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)/c^3*x^4+1/6*b/c^4*(2272*a^4*c^4-1698*a^3*b^2*c^3+117*a^2*b^4*c^2+76*a*b^6*c-11*b^8)/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x^3+1/2/c^4*a*(288*a^4*c^4+152*a^3*b^2*c^3-381*a^2*b^4*c^2+119*a*b^6*c-11*b^8)/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x^2+1/2*a^2*b*(428*a^3*c^3-460*a^2*b^2*c^2+126*a*b^4*c-11*b^6)/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)/c^4*x+1/6*(352*a^3*c^3-438*a^2*b^2*c^2+124*a*b^4*c-11*b^6)*a^3/c^4/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6))/(c*x^2+b*x+a)^3+32/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)/c*ln(c*x^2+b*x+a)*a^3-24/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)/c^2*ln(c*x^2+b*x+a)*a^2*b^2+6/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)/c^3*ln(c*x^2+b*x+a)*a*b^4-1/2/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)/c^4*ln(c*x^2+b*x+a)*b^6-140/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)/c/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a^3*b+70/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)/c^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a^2*b^3-14/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)/c^3/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*b^5+1/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)/c^4/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^7","B"
2212,1,531,138,0.063000," ","int(x^6/(c*x^2+b*x+a)^4,x)","\frac{40 a^{3} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) \sqrt{4 a c -b^{2}}}+\frac{-\frac{\left(44 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) x^{5}}{\left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) c}-\frac{\left(14 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) b \,x^{4}}{\left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) c^{2}}+\frac{\left(66 a^{2} c^{2}-13 a \,b^{2} c +b^{4}\right) a^{3} b}{3 \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) c^{3}}+\frac{\left(16 a^{3} c^{3}+53 a^{2} b^{2} c^{2}-12 a \,b^{4} c +b^{6}\right) a b \,x^{2}}{\left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) c^{3}}-\frac{\left(20 a^{3} c^{3}-66 a^{2} b^{2} c^{2}+13 a \,b^{4} c -b^{6}\right) a^{2} x}{\left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) c^{3}}-\frac{\left(160 a^{4} c^{4}-286 a^{3} b^{2} c^{3}+12 a^{2} b^{4} c^{2}+7 a \,b^{6} c -b^{8}\right) x^{3}}{3 \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) c^{3}}}{\left(c \,x^{2}+b x +a \right)^{3}}"," ",0,"(-(44*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)/c/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x^5-b*(14*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)/c^2*x^4-1/3/c^3*(160*a^4*c^4-286*a^3*b^2*c^3+12*a^2*b^4*c^2+7*a*b^6*c-b^8)/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x^3+b/c^3*a*(16*a^3*c^3+53*a^2*b^2*c^2-12*a*b^4*c+b^6)/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x^2-a^2*(20*a^3*c^3-66*a^2*b^2*c^2+13*a*b^4*c-b^6)/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)/c^3*x+1/3*(66*a^2*c^2-13*a*b^2*c+b^4)*a^3*b/c^3/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6))/(c*x^2+b*x+a)^3+40*a^3/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))","B"
2213,1,486,137,0.067000," ","int(x^5/(c*x^2+b*x+a)^4,x)","-\frac{20 a^{2} b \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) \sqrt{4 a c -b^{2}}}+\frac{-\frac{10 a^{2} b \,c^{2} x^{5}}{64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}}-\frac{\left(64 a^{3} c^{3}+2 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) x^{4}}{2 \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) c}-\frac{\left(44 a^{2} c^{2}+18 a \,b^{2} c -b^{4}\right) a^{2} b x}{2 \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) c^{2}}-\frac{\left(224 a^{3} c^{3}+62 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) b \,x^{3}}{6 \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) c^{2}}-\frac{\left(64 a^{2} c^{2}+18 a \,b^{2} c -b^{4}\right) a^{3}}{6 \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) c^{2}}-\frac{\left(64 a^{3} c^{3}+32 a^{2} b^{2} c^{2}+17 a \,b^{4} c -b^{6}\right) a \,x^{2}}{2 \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) c^{2}}}{\left(c \,x^{2}+b x +a \right)^{3}}"," ",0,"(-10*a^2*b/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*c^2*x^5-1/2*(64*a^3*c^3+2*a^2*b^2*c^2+12*a*b^4*c-b^6)/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)/c*x^4-1/6*b*(224*a^3*c^3+62*a^2*b^2*c^2+12*a*b^4*c-b^6)/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)/c^2*x^3-1/2*a*(64*a^3*c^3+32*a^2*b^2*c^2+17*a*b^4*c-b^6)/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)/c^2*x^2-1/2*a^2*b*(44*a^2*c^2+18*a*b^2*c-b^4)/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)/c^2*x-1/6*a^3*(64*a^2*c^2+18*a*b^2*c-b^4)/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)/c^2)/(c*x^2+b*x+a)^3-20*a^2*b/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))","B"
2214,1,1666,251,0.069000," ","int((e*x+d)^4/(c*x^2+b*x+a)^4,x)","\frac{8 a^{2} c \,e^{4} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) \sqrt{4 a c -b^{2}}}+\frac{8 a \,b^{2} e^{4} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) \sqrt{4 a c -b^{2}}}-\frac{48 a b c d \,e^{3} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) \sqrt{4 a c -b^{2}}}+\frac{48 a \,c^{2} d^{2} e^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) \sqrt{4 a c -b^{2}}}-\frac{8 b^{3} d \,e^{3} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) \sqrt{4 a c -b^{2}}}+\frac{48 b^{2} c \,d^{2} e^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) \sqrt{4 a c -b^{2}}}-\frac{80 b \,c^{2} d^{3} e \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) \sqrt{4 a c -b^{2}}}+\frac{40 c^{3} d^{4} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) \sqrt{4 a c -b^{2}}}+\frac{\frac{4 \left(a^{2} c \,e^{4}+a \,b^{2} e^{4}-6 a b c d \,e^{3}+6 a \,c^{2} d^{2} e^{2}-b^{3} d \,e^{3}+6 d^{2} b^{2} c \,e^{2}-10 b \,c^{2} d^{3} e +5 c^{3} d^{4}\right) c^{2} x^{5}}{64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}}+\frac{10 \left(a^{2} c \,e^{4}+a \,b^{2} e^{4}-6 a b c d \,e^{3}+6 a \,c^{2} d^{2} e^{2}-b^{3} d \,e^{3}+6 d^{2} b^{2} c \,e^{2}-10 b \,c^{2} d^{3} e +5 c^{3} d^{4}\right) b c \,x^{4}}{64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}}-\frac{\left(32 a^{3} c^{3} e^{4}-102 a^{2} b^{2} c^{2} e^{4}+192 a^{2} b \,c^{3} d \,e^{3}-192 a^{2} c^{4} d^{2} e^{2}-10 a \,b^{4} c \,e^{4}+164 a \,b^{3} c^{2} d \,e^{3}-324 a \,b^{2} c^{3} d^{2} e^{2}+320 a b \,c^{4} d^{3} e -160 a \,c^{5} d^{4}-b^{6} e^{4}+22 b^{5} c d \,e^{3}-132 b^{4} c^{2} d^{2} e^{2}+220 b^{3} c^{3} d^{3} e -110 b^{2} c^{4} d^{4}\right) x^{3}}{3 \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) c}+\frac{\left(16 a^{3} b \,c^{2} e^{4}-64 a^{3} c^{3} d \,e^{3}+17 a^{2} b^{3} c \,e^{4}-48 a^{2} b^{2} c^{2} d \,e^{3}+96 a^{2} b \,c^{3} d^{2} e^{2}+a \,b^{5} e^{4}-34 a \,b^{4} c d \,e^{3}+102 a \,b^{3} c^{2} d^{2} e^{2}-160 a \,b^{2} c^{3} d^{3} e +80 a b \,c^{4} d^{4}+6 b^{5} c \,d^{2} e^{2}-10 b^{4} c^{2} d^{3} e +5 b^{3} c^{3} d^{4}\right) x^{2}}{\left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) c}-\frac{\left(4 a^{4} c^{2} e^{4}-22 a^{3} b^{2} c \,e^{4}+40 a^{3} b \,c^{2} d \,e^{3}+24 a^{3} c^{3} d^{2} e^{2}-a^{2} b^{4} e^{4}+40 a^{2} b^{3} c d \,e^{3}-132 a^{2} b^{2} c^{2} d^{2} e^{2}+88 a^{2} b \,c^{3} d^{3} e -44 a^{2} c^{4} d^{4}-6 a \,b^{4} c \,d^{2} e^{2}+36 a \,b^{3} c^{2} d^{3} e -18 a \,b^{2} c^{3} d^{4}-2 b^{5} c \,d^{3} e +b^{4} c^{2} d^{4}\right) x}{\left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) c}+\frac{26 a^{4} b c \,e^{4}-64 a^{4} c^{2} d \,e^{3}+a^{3} b^{3} e^{4}-44 a^{3} b^{2} c d \,e^{3}+156 a^{3} b \,c^{2} d^{2} e^{2}-128 a^{3} c^{3} d^{3} e +6 a^{2} b^{3} c \,d^{2} e^{2}-36 a^{2} b^{2} c^{2} d^{3} e +66 a^{2} b \,c^{3} d^{4}+2 a \,b^{4} c \,d^{3} e -13 a \,b^{3} c^{2} d^{4}+b^{5} c \,d^{4}}{3 \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) c}}{\left(c \,x^{2}+b x +a \right)^{3}}"," ",0,"(4*(a^2*c*e^4+a*b^2*e^4-6*a*b*c*d*e^3+6*a*c^2*d^2*e^2-b^3*d*e^3+6*b^2*c*d^2*e^2-10*b*c^2*d^3*e+5*c^3*d^4)/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*c^2*x^5+10*(a^2*c*e^4+a*b^2*e^4-6*a*b*c*d*e^3+6*a*c^2*d^2*e^2-b^3*d*e^3+6*b^2*c*d^2*e^2-10*b*c^2*d^3*e+5*c^3*d^4)/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*b*c*x^4-1/3*(32*a^3*c^3*e^4-102*a^2*b^2*c^2*e^4+192*a^2*b*c^3*d*e^3-192*a^2*c^4*d^2*e^2-10*a*b^4*c*e^4+164*a*b^3*c^2*d*e^3-324*a*b^2*c^3*d^2*e^2+320*a*b*c^4*d^3*e-160*a*c^5*d^4-b^6*e^4+22*b^5*c*d*e^3-132*b^4*c^2*d^2*e^2+220*b^3*c^3*d^3*e-110*b^2*c^4*d^4)/c/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x^3+(16*a^3*b*c^2*e^4-64*a^3*c^3*d*e^3+17*a^2*b^3*c*e^4-48*a^2*b^2*c^2*d*e^3+96*a^2*b*c^3*d^2*e^2+a*b^5*e^4-34*a*b^4*c*d*e^3+102*a*b^3*c^2*d^2*e^2-160*a*b^2*c^3*d^3*e+80*a*b*c^4*d^4+6*b^5*c*d^2*e^2-10*b^4*c^2*d^3*e+5*b^3*c^3*d^4)/c/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x^2-(4*a^4*c^2*e^4-22*a^3*b^2*c*e^4+40*a^3*b*c^2*d*e^3+24*a^3*c^3*d^2*e^2-a^2*b^4*e^4+40*a^2*b^3*c*d*e^3-132*a^2*b^2*c^2*d^2*e^2+88*a^2*b*c^3*d^3*e-44*a^2*c^4*d^4-6*a*b^4*c*d^2*e^2+36*a*b^3*c^2*d^3*e-18*a*b^2*c^3*d^4-2*b^5*c*d^3*e+b^4*c^2*d^4)/c/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x+1/3*(26*a^4*b*c*e^4-64*a^4*c^2*d*e^3+a^3*b^3*e^4-44*a^3*b^2*c*d*e^3+156*a^3*b*c^2*d^2*e^2-128*a^3*c^3*d^3*e+6*a^2*b^3*c*d^2*e^2-36*a^2*b^2*c^2*d^3*e+66*a^2*b*c^3*d^4+2*a*b^4*c*d^3*e-13*a*b^3*c^2*d^4+b^5*c*d^4)/c/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6))/(c*x^2+b*x+a)^3+8/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a^2*c*e^4+8/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*b^2*e^4-48/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*b*c*d*e^3+48/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*c^2*d^2*e^2-8/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^3*d*e^3+48/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*d^2*b^2*c*e^2-80/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b*c^2*d^3*e+40/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*c^3*d^4","B"
2215,1,1213,295,0.070000," ","int((e*x+d)^3/(c*x^2+b*x+a)^4,x)","-\frac{12 a b c \,e^{3} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) \sqrt{4 a c -b^{2}}}+\frac{24 a \,c^{2} d \,e^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) \sqrt{4 a c -b^{2}}}-\frac{2 b^{3} e^{3} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) \sqrt{4 a c -b^{2}}}+\frac{24 b^{2} c d \,e^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) \sqrt{4 a c -b^{2}}}-\frac{60 b \,c^{2} d^{2} e \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) \sqrt{4 a c -b^{2}}}+\frac{40 c^{3} d^{3} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) \sqrt{4 a c -b^{2}}}+\frac{-\frac{\left(6 a b c \,e^{3}-12 c^{2} a d \,e^{2}+b^{3} e^{3}-12 b^{2} c d \,e^{2}+30 b \,c^{2} d^{2} e -20 c^{3} d^{3}\right) c^{2} x^{5}}{64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}}-\frac{5 \left(6 a b c \,e^{3}-12 c^{2} a d \,e^{2}+b^{3} e^{3}-12 b^{2} c d \,e^{2}+30 b \,c^{2} d^{2} e -20 c^{3} d^{3}\right) b c \,x^{4}}{2 \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right)}-\frac{\left(16 a c +11 b^{2}\right) \left(6 a b c \,e^{3}-12 c^{2} a d \,e^{2}+b^{3} e^{3}-12 b^{2} c d \,e^{2}+30 b \,c^{2} d^{2} e -20 c^{3} d^{3}\right) x^{3}}{6 \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right)}-\frac{\left(32 a^{3} c^{2} e^{3}+24 a^{2} b^{2} c \,e^{3}-96 a^{2} b \,c^{2} d \,e^{2}+17 a \,b^{4} e^{3}-102 a \,b^{3} c d \,e^{2}+240 a \,b^{2} c^{2} d^{2} e -160 a b \,c^{3} d^{3}-6 b^{5} d \,e^{2}+15 b^{4} c \,d^{2} e -10 b^{3} c^{2} d^{3}\right) x^{2}}{2 \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right)}-\frac{\left(20 a^{3} b c \,e^{3}+24 a^{3} c^{2} d \,e^{2}+20 a^{2} b^{3} e^{3}-132 a^{2} b^{2} c d \,e^{2}+132 a^{2} b \,c^{2} d^{2} e -88 a^{2} c^{3} d^{3}-6 a \,b^{4} d \,e^{2}+54 a \,b^{3} c \,d^{2} e -36 a \,b^{2} c^{2} d^{3}-3 b^{5} d^{2} e +2 b^{4} c \,d^{3}\right) x}{2 \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right)}-\frac{32 a^{4} c \,e^{3}+22 a^{3} b^{2} e^{3}-156 a^{3} b c d \,e^{2}+192 a^{3} c^{2} d^{2} e -6 a^{2} b^{3} d \,e^{2}+54 a^{2} b^{2} c \,d^{2} e -132 a^{2} b \,c^{2} d^{3}-3 a \,b^{4} d^{2} e +26 a \,b^{3} c \,d^{3}-2 b^{5} d^{3}}{6 \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right)}}{\left(c \,x^{2}+b x +a \right)^{3}}"," ",0,"(-(6*a*b*c*e^3-12*a*c^2*d*e^2+b^3*e^3-12*b^2*c*d*e^2+30*b*c^2*d^2*e-20*c^3*d^3)/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*c^2*x^5-5/2*(6*a*b*c*e^3-12*a*c^2*d*e^2+b^3*e^3-12*b^2*c*d*e^2+30*b*c^2*d^2*e-20*c^3*d^3)/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*b*c*x^4-1/6*(16*a*c+11*b^2)*(6*a*b*c*e^3-12*a*c^2*d*e^2+b^3*e^3-12*b^2*c*d*e^2+30*b*c^2*d^2*e-20*c^3*d^3)/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x^3-1/2*(32*a^3*c^2*e^3+24*a^2*b^2*c*e^3-96*a^2*b*c^2*d*e^2+17*a*b^4*e^3-102*a*b^3*c*d*e^2+240*a*b^2*c^2*d^2*e-160*a*b*c^3*d^3-6*b^5*d*e^2+15*b^4*c*d^2*e-10*b^3*c^2*d^3)/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x^2-1/2*(20*a^3*b*c*e^3+24*a^3*c^2*d*e^2+20*a^2*b^3*e^3-132*a^2*b^2*c*d*e^2+132*a^2*b*c^2*d^2*e-88*a^2*c^3*d^3-6*a*b^4*d*e^2+54*a*b^3*c*d^2*e-36*a*b^2*c^2*d^3-3*b^5*d^2*e+2*b^4*c*d^3)/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x-1/6*(32*a^4*c*e^3+22*a^3*b^2*e^3-156*a^3*b*c*d*e^2+192*a^3*c^2*d^2*e-6*a^2*b^3*d*e^2+54*a^2*b^2*c*d^2*e-132*a^2*b*c^2*d^3-3*a*b^4*d^2*e+26*a*b^3*c*d^3-2*b^5*d^3)/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6))/(c*x^2+b*x+a)^3-12/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*b*c*e^3+24/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*c^2*a*d*e^2-2/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^3*e^3+24/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^2*c*d*e^2-60/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b*c^2*d^2*e+40/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*c^3*d^3","B"
2216,1,850,252,0.063000," ","int((e*x+d)^2/(c*x^2+b*x+a)^4,x)","\frac{8 a \,c^{2} e^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) \sqrt{4 a c -b^{2}}}+\frac{8 b^{2} c \,e^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) \sqrt{4 a c -b^{2}}}-\frac{40 b \,c^{2} d e \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) \sqrt{4 a c -b^{2}}}+\frac{40 c^{3} d^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) \sqrt{4 a c -b^{2}}}+\frac{\frac{4 \left(a c \,e^{2}+b^{2} e^{2}-5 b c d e +5 c^{2} d^{2}\right) c^{3} x^{5}}{64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}}+\frac{10 \left(a c \,e^{2}+b^{2} e^{2}-5 b c d e +5 c^{2} d^{2}\right) b \,c^{2} x^{4}}{64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}}+\frac{2 \left(16 a c +11 b^{2}\right) \left(a c \,e^{2}+b^{2} e^{2}-5 b c d e +5 c^{2} d^{2}\right) c \,x^{3}}{3 \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right)}+\frac{\left(16 a c +b^{2}\right) \left(a c \,e^{2}+b^{2} e^{2}-5 b c d e +5 c^{2} d^{2}\right) b \,x^{2}}{64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}}-\frac{\left(4 a^{3} c^{2} e^{2}-22 a^{2} b^{2} c \,e^{2}+44 a^{2} b \,c^{2} d e -44 a^{2} c^{3} d^{2}-a \,b^{4} e^{2}+18 a \,b^{3} c d e -18 a \,b^{2} c^{2} d^{2}-b^{5} d e +b^{4} c \,d^{2}\right) x}{64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}}+\frac{26 a^{3} b c \,e^{2}-64 a^{3} c^{2} d e +a^{2} b^{3} e^{2}-18 a^{2} b^{2} c d e +66 a^{2} b \,c^{2} d^{2}+a \,b^{4} d e -13 a \,b^{3} c \,d^{2}+b^{5} d^{2}}{192 a^{3} c^{3}-144 a^{2} b^{2} c^{2}+36 a \,b^{4} c -3 b^{6}}}{\left(c \,x^{2}+b x +a \right)^{3}}"," ",0,"(4*c^3*(a*c*e^2+b^2*e^2-5*b*c*d*e+5*c^2*d^2)/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x^5+10*c^2*(a*c*e^2+b^2*e^2-5*b*c*d*e+5*c^2*d^2)/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*b*x^4+2/3*(16*a*c+11*b^2)*c*(a*c*e^2+b^2*e^2-5*b*c*d*e+5*c^2*d^2)/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x^3+b*(16*a*c+b^2)*(a*c*e^2+b^2*e^2-5*b*c*d*e+5*c^2*d^2)/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x^2-(4*a^3*c^2*e^2-22*a^2*b^2*c*e^2+44*a^2*b*c^2*d*e-44*a^2*c^3*d^2-a*b^4*e^2+18*a*b^3*c*d*e-18*a*b^2*c^2*d^2-b^5*d*e+b^4*c*d^2)/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x+1/3*(26*a^3*b*c*e^2-64*a^3*c^2*d*e+a^2*b^3*e^2-18*a^2*b^2*c*d*e+66*a^2*b*c^2*d^2+a*b^4*d*e-13*a*b^3*c*d^2+b^5*d^2)/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6))/(c*x^2+b*x+a)^3+8*c^2/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*e^2+8*c/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^2*e^2-40*c^2/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b*d*e+40*c^3/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*d^2","B"
2217,1,369,167,0.052000," ","int((e*x+d)/(c*x^2+b*x+a)^4,x)","-\frac{10 b \,c^{2} e x}{\left(4 a c -b^{2}\right)^{3} \left(c \,x^{2}+b x +a \right)}-\frac{20 b \,c^{2} e \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{7}{2}}}+\frac{20 c^{3} d x}{\left(4 a c -b^{2}\right)^{3} \left(c \,x^{2}+b x +a \right)}+\frac{40 c^{3} d \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{7}{2}}}-\frac{5 b^{2} c e}{\left(4 a c -b^{2}\right)^{3} \left(c \,x^{2}+b x +a \right)}+\frac{10 b \,c^{2} d}{\left(4 a c -b^{2}\right)^{3} \left(c \,x^{2}+b x +a \right)}-\frac{5 b c e x}{3 \left(4 a c -b^{2}\right)^{2} \left(c \,x^{2}+b x +a \right)^{2}}+\frac{10 c^{2} d x}{3 \left(4 a c -b^{2}\right)^{2} \left(c \,x^{2}+b x +a \right)^{2}}-\frac{5 b^{2} e}{6 \left(4 a c -b^{2}\right)^{2} \left(c \,x^{2}+b x +a \right)^{2}}+\frac{5 b c d}{3 \left(4 a c -b^{2}\right)^{2} \left(c \,x^{2}+b x +a \right)^{2}}+\frac{-2 a e +b d +\left(-b e +2 c d \right) x}{3 \left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{3}}"," ",0,"1/3*(-2*a*e+b*d+(-b*e+2*c*d)*x)/(4*a*c-b^2)/(c*x^2+b*x+a)^3-5/3/(4*a*c-b^2)^2/(c*x^2+b*x+a)^2*c*x*b*e+10/3/(4*a*c-b^2)^2/(c*x^2+b*x+a)^2*c^2*x*d-5/6/(4*a*c-b^2)^2/(c*x^2+b*x+a)^2*b^2*e+5/3/(4*a*c-b^2)^2/(c*x^2+b*x+a)^2*b*c*d-10/(4*a*c-b^2)^3*c^2/(c*x^2+b*x+a)*x*b*e+20/(4*a*c-b^2)^3*c^3/(c*x^2+b*x+a)*x*d-5/(4*a*c-b^2)^3*c/(c*x^2+b*x+a)*b^2*e+10/(4*a*c-b^2)^3*c^2/(c*x^2+b*x+a)*b*d-20/(4*a*c-b^2)^(7/2)*c^2*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b*e+40/(4*a*c-b^2)^(7/2)*c^3*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*d","B"
2218,1,189,130,0.055000," ","int(1/(c*x^2+b*x+a)^4,x)","\frac{20 c^{3} x}{\left(4 a c -b^{2}\right)^{3} \left(c \,x^{2}+b x +a \right)}+\frac{40 c^{3} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{7}{2}}}+\frac{10 b \,c^{2}}{\left(4 a c -b^{2}\right)^{3} \left(c \,x^{2}+b x +a \right)}+\frac{10 c^{2} x}{3 \left(4 a c -b^{2}\right)^{2} \left(c \,x^{2}+b x +a \right)^{2}}+\frac{5 b c}{3 \left(4 a c -b^{2}\right)^{2} \left(c \,x^{2}+b x +a \right)^{2}}+\frac{2 c x +b}{3 \left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{3}}"," ",0,"1/3*(2*c*x+b)/(4*a*c-b^2)/(c*x^2+b*x+a)^3+10/3*c^2/(4*a*c-b^2)^2/(c*x^2+b*x+a)^2*x+5/3*c/(4*a*c-b^2)^2/(c*x^2+b*x+a)^2*b+20*c^3/(4*a*c-b^2)^3/(c*x^2+b*x+a)*x+10*c^2/(4*a*c-b^2)^3/(c*x^2+b*x+a)*b+40*c^3/(4*a*c-b^2)^(7/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))","A"
2219,1,14396,758,0.104000," ","int(1/(e*x+d)/(c*x^2+b*x+a)^4,x)","\text{output too large to display}"," ",0,"result too large to display","B"
2220,1,2162,341,0.089000," ","int(1/x^2/(c*x^2+b*x+a)^4,x)","-\frac{76 c^{6} x^{5}}{\left(c \,x^{2}+b x +a \right)^{3} \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) a}+\frac{104 b^{2} c^{5} x^{5}}{\left(c \,x^{2}+b x +a \right)^{3} \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) a^{2}}-\frac{32 b^{4} c^{4} x^{5}}{\left(c \,x^{2}+b x +a \right)^{3} \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) a^{3}}+\frac{3 b^{6} c^{3} x^{5}}{\left(c \,x^{2}+b x +a \right)^{3} \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) a^{4}}-\frac{286 b \,c^{5} x^{4}}{\left(c \,x^{2}+b x +a \right)^{3} \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) a}+\frac{332 b^{3} c^{4} x^{4}}{\left(c \,x^{2}+b x +a \right)^{3} \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) a^{2}}-\frac{98 b^{5} c^{3} x^{4}}{\left(c \,x^{2}+b x +a \right)^{3} \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) a^{3}}+\frac{9 b^{7} c^{2} x^{4}}{\left(c \,x^{2}+b x +a \right)^{3} \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) a^{4}}-\frac{102 b^{2} c^{4} x^{3}}{\left(c \,x^{2}+b x +a \right)^{3} \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) a}+\frac{832 b^{4} c^{3} x^{3}}{3 \left(c \,x^{2}+b x +a \right)^{3} \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) a^{2}}-\frac{93 b^{6} c^{2} x^{3}}{\left(c \,x^{2}+b x +a \right)^{3} \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) a^{3}}+\frac{9 b^{8} c \,x^{3}}{\left(c \,x^{2}+b x +a \right)^{3} \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) a^{4}}-\frac{544 c^{5} x^{3}}{3 \left(c \,x^{2}+b x +a \right)^{3} \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right)}+\frac{397 b^{3} c^{3} x^{2}}{\left(c \,x^{2}+b x +a \right)^{3} \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) a}-\frac{30 b^{5} c^{2} x^{2}}{\left(c \,x^{2}+b x +a \right)^{3} \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) a^{2}}-\frac{20 b^{7} c \,x^{2}}{\left(c \,x^{2}+b x +a \right)^{3} \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) a^{3}}+\frac{3 b^{9} x^{2}}{\left(c \,x^{2}+b x +a \right)^{3} \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) a^{4}}-\frac{496 b \,c^{4} x^{2}}{\left(c \,x^{2}+b x +a \right)^{3} \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right)}-\frac{116 a \,c^{4} x}{\left(c \,x^{2}+b x +a \right)^{3} \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right)}+\frac{243 b^{4} c^{2} x}{\left(c \,x^{2}+b x +a \right)^{3} \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) a}-\frac{75 b^{6} c x}{\left(c \,x^{2}+b x +a \right)^{3} \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) a^{2}}+\frac{7 b^{8} x}{\left(c \,x^{2}+b x +a \right)^{3} \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) a^{3}}-\frac{166 b^{2} c^{3} x}{\left(c \,x^{2}+b x +a \right)^{3} \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right)}-\frac{590 a b \,c^{3}}{3 \left(c \,x^{2}+b x +a \right)^{3} \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right)}-\frac{49 b^{5} c}{\left(c \,x^{2}+b x +a \right)^{3} \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) a}+\frac{13 b^{7}}{3 \left(c \,x^{2}+b x +a \right)^{3} \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) a^{2}}+\frac{535 b^{3} c^{2}}{3 \left(c \,x^{2}+b x +a \right)^{3} \left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right)}-\frac{280 c^{4} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) \sqrt{4 a c -b^{2}}\, a}+\frac{560 b^{2} c^{3} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) \sqrt{4 a c -b^{2}}\, a^{2}}-\frac{280 b^{4} c^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) \sqrt{4 a c -b^{2}}\, a^{3}}+\frac{56 b^{6} c \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) \sqrt{4 a c -b^{2}}\, a^{4}}-\frac{4 b^{8} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) \sqrt{4 a c -b^{2}}\, a^{5}}+\frac{128 b \,c^{3} \ln \left(c \,x^{2}+b x +a \right)}{\left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) a^{2}}-\frac{96 b^{3} c^{2} \ln \left(c \,x^{2}+b x +a \right)}{\left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) a^{3}}+\frac{24 b^{5} c \ln \left(c \,x^{2}+b x +a \right)}{\left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) a^{4}}-\frac{2 b^{7} \ln \left(c \,x^{2}+b x +a \right)}{\left(64 a^{3} c^{3}-48 a^{2} b^{2} c^{2}+12 a \,b^{4} c -b^{6}\right) a^{5}}-\frac{4 b \ln \left(x \right)}{a^{5}}-\frac{1}{a^{4} x}"," ",0,"13/3/a^2/(c*x^2+b*x+a)^3*b^7/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)-2/a^5/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*ln(c*x^2+b*x+a)*b^7+535/3/(c*x^2+b*x+a)^3*b^3/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*c^2-544/3/(c*x^2+b*x+a)^3*c^5/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x^3+332/a^2/(c*x^2+b*x+a)^3*b^3*c^4/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x^4-98/a^3/(c*x^2+b*x+a)^3*b^5*c^3/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x^4+9/a^4/(c*x^2+b*x+a)^3*b^7*c^2/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x^4-93/a^3/(c*x^2+b*x+a)^3*c^2/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x^3*b^6+3/a^4/(c*x^2+b*x+a)^3*c^3/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x^5*b^6+56/a^4/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^6*c+560/a^2/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^2*c^3-280/a^3/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^4*c^2-75/a^2/(c*x^2+b*x+a)^3/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x*b^6*c-96/a^3/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*c^2*ln(c*x^2+b*x+a)*b^3-1/a^4/x-166/(c*x^2+b*x+a)^3/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x*b^2*c^3+128/a^2/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*c^3*ln(c*x^2+b*x+a)*b-286/a/(c*x^2+b*x+a)^3*b*c^5/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x^4+9/a^4/(c*x^2+b*x+a)^3*c/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x^3*b^8+397/a/(c*x^2+b*x+a)^3*b^3/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x^2*c^3-30/a^2/(c*x^2+b*x+a)^3*b^5/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x^2*c^2-20/a^3/(c*x^2+b*x+a)^3*b^7/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x^2*c+243/a/(c*x^2+b*x+a)^3/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x*b^4*c^2-102/a/(c*x^2+b*x+a)^3*c^4/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x^3*b^2+832/3/a^2/(c*x^2+b*x+a)^3*c^3/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x^3*b^4+104/a^2/(c*x^2+b*x+a)^3*c^5/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x^5*b^2-32/a^3/(c*x^2+b*x+a)^3*c^4/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x^5*b^4+24/a^4/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*c*ln(c*x^2+b*x+a)*b^5+7/a^3/(c*x^2+b*x+a)^3/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x*b^8+3/a^4/(c*x^2+b*x+a)^3*b^9/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x^2-49/a/(c*x^2+b*x+a)^3*b^5/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*c-116*a/(c*x^2+b*x+a)^3/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x*c^4-76/a/(c*x^2+b*x+a)^3*c^6/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x^5-590/3*a/(c*x^2+b*x+a)^3*b/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*c^3-496/(c*x^2+b*x+a)^3*b/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)*x^2*c^4-280/a/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*c^4-4/a^5/(64*a^3*c^3-48*a^2*b^2*c^2+12*a*b^4*c-b^6)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^8-4*b*ln(x)/a^5","B"
2221,1,3092,376,0.074000," ","int((e*x+d)^5/(c*x^2+b*x+a)^5,x)","\text{output too large to display}"," ",0,"(-5*(3*a^2*b*c*e^5-6*a^2*c^2*d*e^4+a*b^3*e^5-12*a*b^2*c*d*e^4+30*a*b*c^2*d^2*e^3-20*a*c^3*d^3*e^2-b^4*d*e^4+10*b^3*c*d^2*e^3-30*b^2*c^2*d^3*e^2+35*b*c^3*d^4*e-14*c^4*d^5)/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8)*c^3*x^7-35/2*(3*a^2*b*c*e^5-6*a^2*c^2*d*e^4+a*b^3*e^5-12*a*b^2*c*d*e^4+30*a*b*c^2*d^2*e^3-20*a*c^3*d^3*e^2-b^4*d*e^4+10*b^3*c*d^2*e^3-30*b^2*c^2*d^3*e^2+35*b*c^3*d^4*e-14*c^4*d^5)/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8)*b*c^2*x^6-5/3*c*(11*a*c+13*b^2)*(3*a^2*b*c*e^5-6*a^2*c^2*d*e^4+a*b^3*e^5-12*a*b^2*c*d*e^4+30*a*b*c^2*d^2*e^3-20*a*c^3*d^3*e^2-b^4*d*e^4+10*b^3*c*d^2*e^3-30*b^2*c^2*d^3*e^2+35*b*c^3*d^4*e-14*c^4*d^5)/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8)*x^5-1/12*(768*a^4*c^4*e^5+882*a^3*b^2*c^3*e^5-3300*a^3*b*c^4*d*e^4+1213*a^2*b^4*c^2*e^5-7350*a^2*b^3*c^3*d*e^4+16500*a^2*b^2*c^4*d^2*e^3-11000*a^2*b*c^5*d^3*e^2+77*a*b^6*c*e^5-2050*a*b^5*c^2*d*e^4+9250*a*b^4*c^3*d^2*e^3-19000*a*b^3*c^4*d^3*e^2+19250*a*b^2*c^5*d^4*e-7700*a*b*c^6*d^5+3*b^8*e^5-125*b^7*c*d*e^4+1250*b^6*c^2*d^2*e^3-3750*b^5*c^3*d^3*e^2+4375*b^4*c^4*d^4*e-1750*b^3*c^5*d^5)/c/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8)*x^4-1/3*(219*a^4*b*c^3*e^5+330*a^4*c^4*d*e^4+376*a^3*b^3*c^2*e^5-2250*a^3*b^2*c^3*d*e^4+2190*a^3*b*c^4*d^2*e^3-1460*a^3*c^5*d^3*e^2+110*a^2*b^5*c*e^5-1015*a^2*b^4*c^2*d*e^4+3760*a^2*b^3*c^3*d^2*e^3-4210*a^2*b^2*c^4*d^3*e^2+2555*a^2*b*c^5*d^4*e-1022*a^2*c^6*d^5+3*a*b^7*e^5-185*a*b^6*c*d*e^4+1100*a*b^5*c^2*d^2*e^3-3090*a*b^4*c^3*d^3*e^2+3535*a*b^3*c^4*d^4*e-1414*a*b^2*c^5*d^5+30*b^7*c*d^2*e^3-90*b^6*c^2*d^3*e^2+105*b^5*c^3*d^4*e-42*b^4*c^4*d^5)/c/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8)*x^3-1/6*(256*a^5*c^3*e^5+401*a^4*b^2*c^2*e^5-1570*a^4*b*c^3*d*e^4+2560*a^4*c^4*d^2*e^3+399*a^3*b^4*c*e^5-2540*a^3*b^3*c^2*d*e^4+4010*a^3*b^2*c^3*d^2*e^3-4380*a^3*b*c^4*d^3*e^2+9*a^2*b^6*e^5-645*a^2*b^5*c*d*e^4+3990*a^2*b^4*c^2*d^2*e^3-7130*a^2*b^3*c^3*d^3*e^2+7665*a^2*b^2*c^4*d^4*e-3066*a^2*b*c^5*d^5+90*a*b^6*c*d^2*e^3-820*a*b^5*c^2*d^3*e^2+980*a*b^4*c^3*d^4*e-392*a*b^3*c^4*d^5+30*b^7*c*d^3*e^2-35*b^6*c^2*d^4*e+14*b^5*c^3*d^5)/c/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8)*x^2-1/3*(83*a^5*b*c^2*e^5+90*a^5*c^3*d*e^4+151*a^4*b^3*c*e^5-920*a^4*b^2*c^2*d*e^4+830*a^4*b*c^3*d^2*e^3+300*a^4*c^4*d^3*e^2+3*a^3*b^5*e^5-235*a^3*b^4*c*d*e^4+1510*a^3*b^3*c^2*d^2*e^3-2790*a^3*b^2*c^3*d^3*e^2+1395*a^3*b*c^4*d^4*e-558*a^3*c^5*d^5+30*a^2*b^5*c*d^2*e^3-280*a^2*b^4*c^2*d^3*e^2+870*a^2*b^3*c^3*d^4*e-348*a^2*b^2*c^4*d^5+10*a*b^6*c*d^3*e^2-95*a*b^5*c^2*d^4*e+38*a*b^4*c^3*d^5+5*b^7*c*d^4*e-2*b^6*c^2*d^5)/c/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8)*x-1/12*(128*a^6*c^2*e^5+166*a^5*b^2*c*e^5-1100*a^5*b*c^2*d*e^4+1280*a^5*c^3*d^2*e^3+3*a^4*b^4*e^5-250*a^4*b^3*c*d*e^4+1660*a^4*b^2*c^2*d^2*e^3-3240*a^4*b*c^3*d^3*e^2+1920*a^4*c^4*d^4*e+30*a^3*b^4*c*d^2*e^3-280*a^3*b^3*c^2*d^3*e^2+870*a^3*b^2*c^3*d^4*e-1116*a^3*b*c^4*d^5+10*a^2*b^5*c*d^3*e^2-95*a^2*b^4*c^2*d^4*e+326*a^2*b^3*c^3*d^5+5*a*b^6*c*d^4*e-50*a*b^5*c^2*d^5+3*b^7*c*d^5)/c/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8))/(c*x^2+b*x+a)^4-30/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a^2*b*c*e^5+60/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*d*a^2*c^2*e^4-10/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*b^3*e^5+120/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*b^2*c*d*e^4-300/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*d^2*a*b*c^2*e^3+200/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*d^3*a*c^3*e^2+10/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^4*d*e^4-100/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*d^2*b^3*c*e^3+300/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*d^3*b^2*c^2*e^2-350/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b*c^3*d^4*e+140/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*c^4*d^5","B"
2222,1,2430,532,0.083000," ","int((e*x+d)^4/(c*x^2+b*x+a)^5,x)","\frac{12 a^{2} c^{2} e^{4} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(256 a^{4} c^{4}-256 a^{3} b^{2} c^{3}+96 a^{2} b^{4} c^{2}-16 a \,b^{6} c +b^{8}\right) \sqrt{4 a c -b^{2}}}+\frac{24 a \,b^{2} c \,e^{4} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(256 a^{4} c^{4}-256 a^{3} b^{2} c^{3}+96 a^{2} b^{4} c^{2}-16 a \,b^{6} c +b^{8}\right) \sqrt{4 a c -b^{2}}}-\frac{120 a b \,c^{2} d \,e^{3} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(256 a^{4} c^{4}-256 a^{3} b^{2} c^{3}+96 a^{2} b^{4} c^{2}-16 a \,b^{6} c +b^{8}\right) \sqrt{4 a c -b^{2}}}+\frac{120 a \,c^{3} d^{2} e^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(256 a^{4} c^{4}-256 a^{3} b^{2} c^{3}+96 a^{2} b^{4} c^{2}-16 a \,b^{6} c +b^{8}\right) \sqrt{4 a c -b^{2}}}+\frac{2 b^{4} e^{4} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(256 a^{4} c^{4}-256 a^{3} b^{2} c^{3}+96 a^{2} b^{4} c^{2}-16 a \,b^{6} c +b^{8}\right) \sqrt{4 a c -b^{2}}}-\frac{40 b^{3} c d \,e^{3} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(256 a^{4} c^{4}-256 a^{3} b^{2} c^{3}+96 a^{2} b^{4} c^{2}-16 a \,b^{6} c +b^{8}\right) \sqrt{4 a c -b^{2}}}+\frac{180 b^{2} c^{2} d^{2} e^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(256 a^{4} c^{4}-256 a^{3} b^{2} c^{3}+96 a^{2} b^{4} c^{2}-16 a \,b^{6} c +b^{8}\right) \sqrt{4 a c -b^{2}}}-\frac{280 b \,c^{3} d^{3} e \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(256 a^{4} c^{4}-256 a^{3} b^{2} c^{3}+96 a^{2} b^{4} c^{2}-16 a \,b^{6} c +b^{8}\right) \sqrt{4 a c -b^{2}}}+\frac{140 c^{4} d^{4} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(256 a^{4} c^{4}-256 a^{3} b^{2} c^{3}+96 a^{2} b^{4} c^{2}-16 a \,b^{6} c +b^{8}\right) \sqrt{4 a c -b^{2}}}+\frac{\frac{\left(6 c^{2} a^{2} e^{4}+12 a \,b^{2} c \,e^{4}-60 a b \,c^{2} d \,e^{3}+60 a \,c^{3} d^{2} e^{2}+b^{4} e^{4}-20 b^{3} c d \,e^{3}+90 b^{2} c^{2} d^{2} e^{2}-140 b \,c^{3} d^{3} e +70 c^{4} d^{4}\right) c^{3} x^{7}}{256 a^{4} c^{4}-256 a^{3} b^{2} c^{3}+96 a^{2} b^{4} c^{2}-16 a \,b^{6} c +b^{8}}+\frac{7 \left(6 c^{2} a^{2} e^{4}+12 a \,b^{2} c \,e^{4}-60 a b \,c^{2} d \,e^{3}+60 a \,c^{3} d^{2} e^{2}+b^{4} e^{4}-20 b^{3} c d \,e^{3}+90 b^{2} c^{2} d^{2} e^{2}-140 b \,c^{3} d^{3} e +70 c^{4} d^{4}\right) b \,c^{2} x^{6}}{2 \left(256 a^{4} c^{4}-256 a^{3} b^{2} c^{3}+96 a^{2} b^{4} c^{2}-16 a \,b^{6} c +b^{8}\right)}+\frac{\left(11 a c +13 b^{2}\right) \left(6 c^{2} a^{2} e^{4}+12 a \,b^{2} c \,e^{4}-60 a b \,c^{2} d \,e^{3}+60 a \,c^{3} d^{2} e^{2}+b^{4} e^{4}-20 b^{3} c d \,e^{3}+90 b^{2} c^{2} d^{2} e^{2}-140 b \,c^{3} d^{3} e +70 c^{4} d^{4}\right) c \,x^{5}}{768 a^{4} c^{4}-768 a^{3} b^{2} c^{3}+288 a^{2} b^{4} c^{2}-48 a \,b^{6} c +3 b^{8}}+\frac{5 \left(22 a c +5 b^{2}\right) \left(6 c^{2} a^{2} e^{4}+12 a \,b^{2} c \,e^{4}-60 a b \,c^{2} d \,e^{3}+60 a \,c^{3} d^{2} e^{2}+b^{4} e^{4}-20 b^{3} c d \,e^{3}+90 b^{2} c^{2} d^{2} e^{2}-140 b \,c^{3} d^{3} e +70 c^{4} d^{4}\right) b \,x^{4}}{12 \left(256 a^{4} c^{4}-256 a^{3} b^{2} c^{3}+96 a^{2} b^{4} c^{2}-16 a \,b^{6} c +b^{8}\right)}-\frac{\left(66 a^{4} c^{3} e^{4}-450 a^{3} b^{2} c^{2} e^{4}+876 a^{3} b \,c^{3} d \,e^{3}-876 a^{3} c^{4} d^{2} e^{2}-203 a^{2} b^{4} c \,e^{4}+1504 a^{2} b^{3} c^{2} d \,e^{3}-2526 a^{2} b^{2} c^{3} d^{2} e^{2}+2044 a^{2} b \,c^{4} d^{3} e -1022 a^{2} c^{5} d^{4}-37 a \,b^{6} e^{4}+440 a \,b^{5} c d \,e^{3}-1854 a \,b^{4} c^{2} d^{2} e^{2}+2828 a \,b^{3} c^{3} d^{3} e -1414 a \,b^{2} c^{4} d^{4}+12 b^{7} d \,e^{3}-54 b^{6} c \,d^{2} e^{2}+84 b^{5} c^{2} d^{3} e -42 b^{4} c^{3} d^{4}\right) x^{3}}{3 \left(256 a^{4} c^{4}-256 a^{3} b^{2} c^{3}+96 a^{2} b^{4} c^{2}-16 a \,b^{6} c +b^{8}\right)}+\frac{\left(314 a^{4} b \,c^{2} e^{4}-1024 a^{4} c^{3} d \,e^{3}+508 a^{3} b^{3} c \,e^{4}-1604 a^{3} b^{2} c^{2} d \,e^{3}+2628 a^{3} b \,c^{3} d^{2} e^{2}+129 a^{2} b^{5} e^{4}-1596 a^{2} b^{4} c d \,e^{3}+4278 a^{2} b^{3} c^{2} d^{2} e^{2}-6132 a^{2} b^{2} c^{3} d^{3} e +3066 a^{2} b \,c^{4} d^{4}-36 a \,b^{6} d \,e^{3}+492 a \,b^{5} c \,d^{2} e^{2}-784 a \,b^{4} c^{2} d^{3} e +392 a \,b^{3} c^{3} d^{4}-18 b^{7} d^{2} e^{2}+28 b^{6} c \,d^{3} e -14 b^{5} c^{2} d^{4}\right) x^{2}}{1536 a^{4} c^{4}-1536 a^{3} b^{2} c^{3}+576 a^{2} b^{4} c^{2}-96 a \,b^{6} c +6 b^{8}}-\frac{\left(18 a^{5} c^{2} e^{4}-184 a^{4} b^{2} c \,e^{4}+332 a^{4} b \,c^{2} d \,e^{3}+180 a^{4} c^{3} d^{2} e^{2}-47 a^{3} b^{4} e^{4}+604 a^{3} b^{3} c d \,e^{3}-1674 a^{3} b^{2} c^{2} d^{2} e^{2}+1116 a^{3} b \,c^{3} d^{3} e -558 a^{3} c^{4} d^{4}+12 a^{2} b^{5} d \,e^{3}-168 a^{2} b^{4} c \,d^{2} e^{2}+696 a^{2} b^{3} c^{2} d^{3} e -348 a^{2} b^{2} c^{3} d^{4}+6 a \,b^{6} d^{2} e^{2}-76 a \,b^{5} c \,d^{3} e +38 a \,b^{4} c^{2} d^{4}+4 b^{7} d^{3} e -2 b^{6} c \,d^{4}\right) x}{3 \left(256 a^{4} c^{4}-256 a^{3} b^{2} c^{3}+96 a^{2} b^{4} c^{2}-16 a \,b^{6} c +b^{8}\right)}+\frac{220 a^{5} b c \,e^{4}-512 a^{5} c^{2} d \,e^{3}+50 a^{4} b^{3} e^{4}-664 a^{4} b^{2} c d \,e^{3}+1944 a^{4} b \,c^{2} d^{2} e^{2}-1536 a^{4} c^{3} d^{3} e -12 a^{3} b^{4} d \,e^{3}+168 a^{3} b^{3} c \,d^{2} e^{2}-696 a^{3} b^{2} c^{2} d^{3} e +1116 a^{3} b \,c^{3} d^{4}-6 a^{2} b^{5} d^{2} e^{2}+76 a^{2} b^{4} c \,d^{3} e -326 a^{2} b^{3} c^{2} d^{4}-4 a \,b^{6} d^{3} e +50 a \,b^{5} c \,d^{4}-3 b^{7} d^{4}}{3072 a^{4} c^{4}-3072 a^{3} b^{2} c^{3}+1152 a^{2} b^{4} c^{2}-192 a \,b^{6} c +12 b^{8}}}{\left(c \,x^{2}+b x +a \right)^{4}}"," ",0,"((6*a^2*c^2*e^4+12*a*b^2*c*e^4-60*a*b*c^2*d*e^3+60*a*c^3*d^2*e^2+b^4*e^4-20*b^3*c*d*e^3+90*b^2*c^2*d^2*e^2-140*b*c^3*d^3*e+70*c^4*d^4)/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8)*c^3*x^7+7/2*(6*a^2*c^2*e^4+12*a*b^2*c*e^4-60*a*b*c^2*d*e^3+60*a*c^3*d^2*e^2+b^4*e^4-20*b^3*c*d*e^3+90*b^2*c^2*d^2*e^2-140*b*c^3*d^3*e+70*c^4*d^4)/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8)*b*c^2*x^6+1/3*c*(11*a*c+13*b^2)*(6*a^2*c^2*e^4+12*a*b^2*c*e^4-60*a*b*c^2*d*e^3+60*a*c^3*d^2*e^2+b^4*e^4-20*b^3*c*d*e^3+90*b^2*c^2*d^2*e^2-140*b*c^3*d^3*e+70*c^4*d^4)/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8)*x^5+5/12*b*(22*a*c+5*b^2)*(6*a^2*c^2*e^4+12*a*b^2*c*e^4-60*a*b*c^2*d*e^3+60*a*c^3*d^2*e^2+b^4*e^4-20*b^3*c*d*e^3+90*b^2*c^2*d^2*e^2-140*b*c^3*d^3*e+70*c^4*d^4)/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8)*x^4-1/3*(66*a^4*c^3*e^4-450*a^3*b^2*c^2*e^4+876*a^3*b*c^3*d*e^3-876*a^3*c^4*d^2*e^2-203*a^2*b^4*c*e^4+1504*a^2*b^3*c^2*d*e^3-2526*a^2*b^2*c^3*d^2*e^2+2044*a^2*b*c^4*d^3*e-1022*a^2*c^5*d^4-37*a*b^6*e^4+440*a*b^5*c*d*e^3-1854*a*b^4*c^2*d^2*e^2+2828*a*b^3*c^3*d^3*e-1414*a*b^2*c^4*d^4+12*b^7*d*e^3-54*b^6*c*d^2*e^2+84*b^5*c^2*d^3*e-42*b^4*c^3*d^4)/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8)*x^3+1/6*(314*a^4*b*c^2*e^4-1024*a^4*c^3*d*e^3+508*a^3*b^3*c*e^4-1604*a^3*b^2*c^2*d*e^3+2628*a^3*b*c^3*d^2*e^2+129*a^2*b^5*e^4-1596*a^2*b^4*c*d*e^3+4278*a^2*b^3*c^2*d^2*e^2-6132*a^2*b^2*c^3*d^3*e+3066*a^2*b*c^4*d^4-36*a*b^6*d*e^3+492*a*b^5*c*d^2*e^2-784*a*b^4*c^2*d^3*e+392*a*b^3*c^3*d^4-18*b^7*d^2*e^2+28*b^6*c*d^3*e-14*b^5*c^2*d^4)/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8)*x^2-1/3*(18*a^5*c^2*e^4-184*a^4*b^2*c*e^4+332*a^4*b*c^2*d*e^3+180*a^4*c^3*d^2*e^2-47*a^3*b^4*e^4+604*a^3*b^3*c*d*e^3-1674*a^3*b^2*c^2*d^2*e^2+1116*a^3*b*c^3*d^3*e-558*a^3*c^4*d^4+12*a^2*b^5*d*e^3-168*a^2*b^4*c*d^2*e^2+696*a^2*b^3*c^2*d^3*e-348*a^2*b^2*c^3*d^4+6*a*b^6*d^2*e^2-76*a*b^5*c*d^3*e+38*a*b^4*c^2*d^4+4*b^7*d^3*e-2*b^6*c*d^4)/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8)*x+1/12*(220*a^5*b*c*e^4-512*a^5*c^2*d*e^3+50*a^4*b^3*e^4-664*a^4*b^2*c*d*e^3+1944*a^4*b*c^2*d^2*e^2-1536*a^4*c^3*d^3*e-12*a^3*b^4*d*e^3+168*a^3*b^3*c*d^2*e^2-696*a^3*b^2*c^2*d^3*e+1116*a^3*b*c^3*d^4-6*a^2*b^5*d^2*e^2+76*a^2*b^4*c*d^3*e-326*a^2*b^3*c^2*d^4-4*a*b^6*d^3*e+50*a*b^5*c*d^4-3*b^7*d^4)/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8))/(c*x^2+b*x+a)^4+12/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*c^2*a^2*e^4+24/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*b^2*c*e^4-120/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*b*c^2*d*e^3+120/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*c^3*d^2*e^2+2/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^4*e^4-40/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^3*c*d*e^3+180/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^2*c^2*d^2*e^2-280/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b*c^3*d^3*e+140/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*c^4*d^4","B"
2223,1,1742,365,0.071000," ","int((e*x+d)^3/(c*x^2+b*x+a)^5,x)","-\frac{30 a b \,c^{2} e^{3} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(256 a^{4} c^{4}-256 a^{3} b^{2} c^{3}+96 a^{2} b^{4} c^{2}-16 a \,b^{6} c +b^{8}\right) \sqrt{4 a c -b^{2}}}+\frac{60 a \,c^{3} d \,e^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(256 a^{4} c^{4}-256 a^{3} b^{2} c^{3}+96 a^{2} b^{4} c^{2}-16 a \,b^{6} c +b^{8}\right) \sqrt{4 a c -b^{2}}}-\frac{10 b^{3} c \,e^{3} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(256 a^{4} c^{4}-256 a^{3} b^{2} c^{3}+96 a^{2} b^{4} c^{2}-16 a \,b^{6} c +b^{8}\right) \sqrt{4 a c -b^{2}}}+\frac{90 b^{2} c^{2} d \,e^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(256 a^{4} c^{4}-256 a^{3} b^{2} c^{3}+96 a^{2} b^{4} c^{2}-16 a \,b^{6} c +b^{8}\right) \sqrt{4 a c -b^{2}}}-\frac{210 b \,c^{3} d^{2} e \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(256 a^{4} c^{4}-256 a^{3} b^{2} c^{3}+96 a^{2} b^{4} c^{2}-16 a \,b^{6} c +b^{8}\right) \sqrt{4 a c -b^{2}}}+\frac{140 c^{4} d^{3} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(256 a^{4} c^{4}-256 a^{3} b^{2} c^{3}+96 a^{2} b^{4} c^{2}-16 a \,b^{6} c +b^{8}\right) \sqrt{4 a c -b^{2}}}+\frac{-\frac{5 \left(3 a b c \,e^{3}-6 c^{2} a d \,e^{2}+b^{3} e^{3}-9 b^{2} c d \,e^{2}+21 b \,c^{2} d^{2} e -14 c^{3} d^{3}\right) c^{4} x^{7}}{256 a^{4} c^{4}-256 a^{3} b^{2} c^{3}+96 a^{2} b^{4} c^{2}-16 a \,b^{6} c +b^{8}}-\frac{35 \left(3 a b c \,e^{3}-6 c^{2} a d \,e^{2}+b^{3} e^{3}-9 b^{2} c d \,e^{2}+21 b \,c^{2} d^{2} e -14 c^{3} d^{3}\right) b \,c^{3} x^{6}}{2 \left(256 a^{4} c^{4}-256 a^{3} b^{2} c^{3}+96 a^{2} b^{4} c^{2}-16 a \,b^{6} c +b^{8}\right)}-\frac{5 \left(11 a c +13 b^{2}\right) \left(3 a b c \,e^{3}-6 c^{2} a d \,e^{2}+b^{3} e^{3}-9 b^{2} c d \,e^{2}+21 b \,c^{2} d^{2} e -14 c^{3} d^{3}\right) c^{2} x^{5}}{3 \left(256 a^{4} c^{4}-256 a^{3} b^{2} c^{3}+96 a^{2} b^{4} c^{2}-16 a \,b^{6} c +b^{8}\right)}-\frac{25 \left(22 a c +5 b^{2}\right) \left(3 a b c \,e^{3}-6 c^{2} a d \,e^{2}+b^{3} e^{3}-9 b^{2} c d \,e^{2}+21 b \,c^{2} d^{2} e -14 c^{3} d^{3}\right) b c \,x^{4}}{12 \left(256 a^{4} c^{4}-256 a^{3} b^{2} c^{3}+96 a^{2} b^{4} c^{2}-16 a \,b^{6} c +b^{8}\right)}-\frac{\left(73 a^{2} c^{2}+101 a \,b^{2} c +3 b^{4}\right) \left(3 a b c \,e^{3}-6 c^{2} a d \,e^{2}+b^{3} e^{3}-9 b^{2} c d \,e^{2}+21 b \,c^{2} d^{2} e -14 c^{3} d^{3}\right) x^{3}}{3 \left(256 a^{4} c^{4}-256 a^{3} b^{2} c^{3}+96 a^{2} b^{4} c^{2}-16 a \,b^{6} c +b^{8}\right)}-\frac{\left(256 a^{4} c^{3} e^{3}+401 a^{3} b^{2} c^{2} e^{3}-1314 a^{3} b \,c^{3} d \,e^{2}+399 a^{2} b^{4} c \,e^{3}-2139 a^{2} b^{3} c^{2} d \,e^{2}+4599 a^{2} b^{2} c^{3} d^{2} e -3066 a^{2} b \,c^{4} d^{3}+9 a \,b^{6} e^{3}-246 a \,b^{5} c d \,e^{2}+588 a \,b^{4} c^{2} d^{2} e -392 a \,b^{3} c^{3} d^{3}+9 b^{7} d \,e^{2}-21 b^{6} c \,d^{2} e +14 b^{5} c^{2} d^{3}\right) x^{2}}{6 \left(256 a^{4} c^{4}-256 a^{3} b^{2} c^{3}+96 a^{2} b^{4} c^{2}-16 a \,b^{6} c +b^{8}\right)}-\frac{\left(83 a^{4} b \,c^{2} e^{3}+90 a^{4} c^{3} d \,e^{2}+151 a^{3} b^{3} c \,e^{3}-837 a^{3} b^{2} c^{2} d \,e^{2}+837 a^{3} b \,c^{3} d^{2} e -558 a^{3} c^{4} d^{3}+3 a^{2} b^{5} e^{3}-84 a^{2} b^{4} c d \,e^{2}+522 a^{2} b^{3} c^{2} d^{2} e -348 a^{2} b^{2} c^{3} d^{3}+3 a \,b^{6} d \,e^{2}-57 a \,b^{5} c \,d^{2} e +38 a \,b^{4} c^{2} d^{3}+3 b^{7} d^{2} e -2 b^{6} c \,d^{3}\right) x}{3 \left(256 a^{4} c^{4}-256 a^{3} b^{2} c^{3}+96 a^{2} b^{4} c^{2}-16 a \,b^{6} c +b^{8}\right)}-\frac{128 a^{5} c^{2} e^{3}+166 a^{4} b^{2} c \,e^{3}-972 a^{4} b \,c^{2} d \,e^{2}+1152 a^{4} c^{3} d^{2} e +3 a^{3} b^{4} e^{3}-84 a^{3} b^{3} c d \,e^{2}+522 a^{3} b^{2} c^{2} d^{2} e -1116 a^{3} b \,c^{3} d^{3}+3 a^{2} b^{5} d \,e^{2}-57 a^{2} b^{4} c \,d^{2} e +326 a^{2} b^{3} c^{2} d^{3}+3 a \,b^{6} d^{2} e -50 a \,b^{5} c \,d^{3}+3 b^{7} d^{3}}{12 \left(256 a^{4} c^{4}-256 a^{3} b^{2} c^{3}+96 a^{2} b^{4} c^{2}-16 a \,b^{6} c +b^{8}\right)}}{\left(c \,x^{2}+b x +a \right)^{4}}"," ",0,"(-5*c^4*(3*a*b*c*e^3-6*a*c^2*d*e^2+b^3*e^3-9*b^2*c*d*e^2+21*b*c^2*d^2*e-14*c^3*d^3)/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8)*x^7-35/2*c^3*(3*a*b*c*e^3-6*a*c^2*d*e^2+b^3*e^3-9*b^2*c*d*e^2+21*b*c^2*d^2*e-14*c^3*d^3)/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8)*b*x^6-5/3*c^2*(11*a*c+13*b^2)*(3*a*b*c*e^3-6*a*c^2*d*e^2+b^3*e^3-9*b^2*c*d*e^2+21*b*c^2*d^2*e-14*c^3*d^3)/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8)*x^5-25/12*b*(22*a*c+5*b^2)*c*(3*a*b*c*e^3-6*a*c^2*d*e^2+b^3*e^3-9*b^2*c*d*e^2+21*b*c^2*d^2*e-14*c^3*d^3)/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8)*x^4-1/3*(73*a^2*c^2+101*a*b^2*c+3*b^4)*(3*a*b*c*e^3-6*a*c^2*d*e^2+b^3*e^3-9*b^2*c*d*e^2+21*b*c^2*d^2*e-14*c^3*d^3)/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8)*x^3-1/6*(256*a^4*c^3*e^3+401*a^3*b^2*c^2*e^3-1314*a^3*b*c^3*d*e^2+399*a^2*b^4*c*e^3-2139*a^2*b^3*c^2*d*e^2+4599*a^2*b^2*c^3*d^2*e-3066*a^2*b*c^4*d^3+9*a*b^6*e^3-246*a*b^5*c*d*e^2+588*a*b^4*c^2*d^2*e-392*a*b^3*c^3*d^3+9*b^7*d*e^2-21*b^6*c*d^2*e+14*b^5*c^2*d^3)/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8)*x^2-1/3*(83*a^4*b*c^2*e^3+90*a^4*c^3*d*e^2+151*a^3*b^3*c*e^3-837*a^3*b^2*c^2*d*e^2+837*a^3*b*c^3*d^2*e-558*a^3*c^4*d^3+3*a^2*b^5*e^3-84*a^2*b^4*c*d*e^2+522*a^2*b^3*c^2*d^2*e-348*a^2*b^2*c^3*d^3+3*a*b^6*d*e^2-57*a*b^5*c*d^2*e+38*a*b^4*c^2*d^3+3*b^7*d^2*e-2*b^6*c*d^3)/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8)*x-1/12*(128*a^5*c^2*e^3+166*a^4*b^2*c*e^3-972*a^4*b*c^2*d*e^2+1152*a^4*c^3*d^2*e+3*a^3*b^4*e^3-84*a^3*b^3*c*d*e^2+522*a^3*b^2*c^2*d^2*e-1116*a^3*b*c^3*d^3+3*a^2*b^5*d*e^2-57*a^2*b^4*c*d^2*e+326*a^2*b^3*c^2*d^3+3*a*b^6*d^2*e-50*a*b^5*c*d^3+3*b^7*d^3)/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8))/(c*x^2+b*x+a)^4-30*c^2/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*b*e^3+60*c^3/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*d*e^2-10*c/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^3*e^3+90*c^2/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^2*d*e^2-210*c^3/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b*d^2*e+140*c^4/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*d^3","B"
2224,1,1243,317,0.070000," ","int((e*x+d)^2/(c*x^2+b*x+a)^5,x)","\frac{20 a \,c^{3} e^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(256 a^{4} c^{4}-256 a^{3} b^{2} c^{3}+96 a^{2} b^{4} c^{2}-16 a \,b^{6} c +b^{8}\right) \sqrt{4 a c -b^{2}}}+\frac{30 b^{2} c^{2} e^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(256 a^{4} c^{4}-256 a^{3} b^{2} c^{3}+96 a^{2} b^{4} c^{2}-16 a \,b^{6} c +b^{8}\right) \sqrt{4 a c -b^{2}}}-\frac{140 b \,c^{3} d e \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(256 a^{4} c^{4}-256 a^{3} b^{2} c^{3}+96 a^{2} b^{4} c^{2}-16 a \,b^{6} c +b^{8}\right) \sqrt{4 a c -b^{2}}}+\frac{140 c^{4} d^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(256 a^{4} c^{4}-256 a^{3} b^{2} c^{3}+96 a^{2} b^{4} c^{2}-16 a \,b^{6} c +b^{8}\right) \sqrt{4 a c -b^{2}}}+\frac{\frac{5 \left(2 a c \,e^{2}+3 b^{2} e^{2}-14 b c d e +14 c^{2} d^{2}\right) c^{5} x^{7}}{256 a^{4} c^{4}-256 a^{3} b^{2} c^{3}+96 a^{2} b^{4} c^{2}-16 a \,b^{6} c +b^{8}}+\frac{35 \left(2 a c \,e^{2}+3 b^{2} e^{2}-14 b c d e +14 c^{2} d^{2}\right) b \,c^{4} x^{6}}{2 \left(256 a^{4} c^{4}-256 a^{3} b^{2} c^{3}+96 a^{2} b^{4} c^{2}-16 a \,b^{6} c +b^{8}\right)}+\frac{5 \left(11 a c +13 b^{2}\right) \left(2 a c \,e^{2}+3 b^{2} e^{2}-14 b c d e +14 c^{2} d^{2}\right) c^{3} x^{5}}{3 \left(256 a^{4} c^{4}-256 a^{3} b^{2} c^{3}+96 a^{2} b^{4} c^{2}-16 a \,b^{6} c +b^{8}\right)}+\frac{25 \left(22 a c +5 b^{2}\right) \left(2 a c \,e^{2}+3 b^{2} e^{2}-14 b c d e +14 c^{2} d^{2}\right) b \,c^{2} x^{4}}{12 \left(256 a^{4} c^{4}-256 a^{3} b^{2} c^{3}+96 a^{2} b^{4} c^{2}-16 a \,b^{6} c +b^{8}\right)}+\frac{\left(73 a^{2} c^{2}+101 a \,b^{2} c +3 b^{4}\right) \left(2 a c \,e^{2}+3 b^{2} e^{2}-14 b c d e +14 c^{2} d^{2}\right) c \,x^{3}}{768 a^{4} c^{4}-768 a^{3} b^{2} c^{3}+288 a^{2} b^{4} c^{2}-48 a \,b^{6} c +3 b^{8}}+\frac{\left(219 a^{2} c^{2}+28 a \,b^{2} c -b^{4}\right) \left(2 a c \,e^{2}+3 b^{2} e^{2}-14 b c d e +14 c^{2} d^{2}\right) b \,x^{2}}{1536 a^{4} c^{4}-1536 a^{3} b^{2} c^{3}+576 a^{2} b^{4} c^{2}-96 a \,b^{6} c +6 b^{8}}-\frac{\left(30 a^{4} c^{3} e^{2}-279 a^{3} b^{2} c^{2} e^{2}+558 a^{3} b \,c^{3} d e -558 a^{3} c^{4} d^{2}-28 a^{2} b^{4} c \,e^{2}+348 a^{2} b^{3} c^{2} d e -348 a^{2} b^{2} c^{3} d^{2}+a \,b^{6} e^{2}-38 a \,b^{5} c d e +38 a \,b^{4} c^{2} d^{2}+2 b^{7} d e -2 b^{6} c \,d^{2}\right) x}{3 \left(256 a^{4} c^{4}-256 a^{3} b^{2} c^{3}+96 a^{2} b^{4} c^{2}-16 a \,b^{6} c +b^{8}\right)}+\frac{324 a^{4} b \,c^{2} e^{2}-768 a^{4} c^{3} d e +28 a^{3} b^{3} c \,e^{2}-348 a^{3} b^{2} c^{2} d e +1116 a^{3} b \,c^{3} d^{2}-a^{2} b^{5} e^{2}+38 a^{2} b^{4} c d e -326 a^{2} b^{3} c^{2} d^{2}-2 a \,b^{6} d e +50 a \,b^{5} c \,d^{2}-3 b^{7} d^{2}}{3072 a^{4} c^{4}-3072 a^{3} b^{2} c^{3}+1152 a^{2} b^{4} c^{2}-192 a \,b^{6} c +12 b^{8}}}{\left(c \,x^{2}+b x +a \right)^{4}}"," ",0,"(5*c^5*(2*a*c*e^2+3*b^2*e^2-14*b*c*d*e+14*c^2*d^2)/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8)*x^7+35/2*c^4*(2*a*c*e^2+3*b^2*e^2-14*b*c*d*e+14*c^2*d^2)/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8)*b*x^6+5/3*c^3*(11*a*c+13*b^2)*(2*a*c*e^2+3*b^2*e^2-14*b*c*d*e+14*c^2*d^2)/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8)*x^5+25/12*b*(22*a*c+5*b^2)*c^2*(2*a*c*e^2+3*b^2*e^2-14*b*c*d*e+14*c^2*d^2)/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8)*x^4+1/3*(73*a^2*c^2+101*a*b^2*c+3*b^4)*c*(2*a*c*e^2+3*b^2*e^2-14*b*c*d*e+14*c^2*d^2)/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8)*x^3+1/6*b*(219*a^2*c^2+28*a*b^2*c-b^4)*(2*a*c*e^2+3*b^2*e^2-14*b*c*d*e+14*c^2*d^2)/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8)*x^2-1/3*(30*a^4*c^3*e^2-279*a^3*b^2*c^2*e^2+558*a^3*b*c^3*d*e-558*a^3*c^4*d^2-28*a^2*b^4*c*e^2+348*a^2*b^3*c^2*d*e-348*a^2*b^2*c^3*d^2+a*b^6*e^2-38*a*b^5*c*d*e+38*a*b^4*c^2*d^2+2*b^7*d*e-2*b^6*c*d^2)/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8)*x+1/12*(324*a^4*b*c^2*e^2-768*a^4*c^3*d*e+28*a^3*b^3*c*e^2-348*a^3*b^2*c^2*d*e+1116*a^3*b*c^3*d^2-a^2*b^5*e^2+38*a^2*b^4*c*d*e-326*a^2*b^3*c^2*d^2-2*a*b^6*d*e+50*a*b^5*c*d^2-3*b^7*d^2)/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8))/(c*x^2+b*x+a)^4+20*c^3/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*e^2+30*c^2/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^2*e^2-140*c^3/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b*d*e+140*c^4/(256*a^4*c^4-256*a^3*b^2*c^3+96*a^2*b^4*c^2-16*a*b^6*c+b^8)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*d^2","B"
2225,1,496,209,0.056000," ","int((e*x+d)/(c*x^2+b*x+a)^5,x)","-\frac{35 b \,c^{3} e x}{\left(4 a c -b^{2}\right)^{4} \left(c \,x^{2}+b x +a \right)}-\frac{70 b \,c^{3} e \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{9}{2}}}+\frac{70 c^{4} d x}{\left(4 a c -b^{2}\right)^{4} \left(c \,x^{2}+b x +a \right)}+\frac{140 c^{4} d \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{9}{2}}}-\frac{35 b^{2} c^{2} e}{2 \left(4 a c -b^{2}\right)^{4} \left(c \,x^{2}+b x +a \right)}+\frac{35 b \,c^{3} d}{\left(4 a c -b^{2}\right)^{4} \left(c \,x^{2}+b x +a \right)}-\frac{35 b \,c^{2} e x}{6 \left(4 a c -b^{2}\right)^{3} \left(c \,x^{2}+b x +a \right)^{2}}+\frac{35 c^{3} d x}{3 \left(4 a c -b^{2}\right)^{3} \left(c \,x^{2}+b x +a \right)^{2}}-\frac{35 b^{2} c e}{12 \left(4 a c -b^{2}\right)^{3} \left(c \,x^{2}+b x +a \right)^{2}}+\frac{35 b \,c^{2} d}{6 \left(4 a c -b^{2}\right)^{3} \left(c \,x^{2}+b x +a \right)^{2}}-\frac{7 b c e x}{6 \left(4 a c -b^{2}\right)^{2} \left(c \,x^{2}+b x +a \right)^{3}}+\frac{7 c^{2} d x}{3 \left(4 a c -b^{2}\right)^{2} \left(c \,x^{2}+b x +a \right)^{3}}-\frac{7 b^{2} e}{12 \left(4 a c -b^{2}\right)^{2} \left(c \,x^{2}+b x +a \right)^{3}}+\frac{7 b c d}{6 \left(4 a c -b^{2}\right)^{2} \left(c \,x^{2}+b x +a \right)^{3}}+\frac{-2 a e +b d +\left(-b e +2 c d \right) x}{4 \left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{4}}"," ",0,"1/4*(-2*a*e+b*d+(-b*e+2*c*d)*x)/(4*a*c-b^2)/(c*x^2+b*x+a)^4-7/6/(4*a*c-b^2)^2/(c*x^2+b*x+a)^3*c*x*b*e+7/3/(4*a*c-b^2)^2/(c*x^2+b*x+a)^3*c^2*x*d-7/12/(4*a*c-b^2)^2/(c*x^2+b*x+a)^3*b^2*e+7/6/(4*a*c-b^2)^2/(c*x^2+b*x+a)^3*b*c*d-35/6/(4*a*c-b^2)^3*c^2/(c*x^2+b*x+a)^2*x*b*e+35/3/(4*a*c-b^2)^3*c^3/(c*x^2+b*x+a)^2*x*d-35/12/(4*a*c-b^2)^3*c/(c*x^2+b*x+a)^2*b^2*e+35/6/(4*a*c-b^2)^3*c^2/(c*x^2+b*x+a)^2*b*d-35/(4*a*c-b^2)^4*c^3/(c*x^2+b*x+a)*x*b*e+70/(4*a*c-b^2)^4*c^4/(c*x^2+b*x+a)*x*d-35/2/(4*a*c-b^2)^4*c^2/(c*x^2+b*x+a)*b^2*e+35/(4*a*c-b^2)^4*c^3/(c*x^2+b*x+a)*b*d-70/(4*a*c-b^2)^(9/2)*c^3*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b*e+140/(4*a*c-b^2)^(9/2)*c^4*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*d","B"
2226,1,249,163,0.057000," ","int(1/(c*x^2+b*x+a)^5,x)","\frac{70 c^{4} x}{\left(4 a c -b^{2}\right)^{4} \left(c \,x^{2}+b x +a \right)}+\frac{140 c^{4} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{9}{2}}}+\frac{35 b \,c^{3}}{\left(4 a c -b^{2}\right)^{4} \left(c \,x^{2}+b x +a \right)}+\frac{35 c^{3} x}{3 \left(4 a c -b^{2}\right)^{3} \left(c \,x^{2}+b x +a \right)^{2}}+\frac{35 b \,c^{2}}{6 \left(4 a c -b^{2}\right)^{3} \left(c \,x^{2}+b x +a \right)^{2}}+\frac{7 c^{2} x}{3 \left(4 a c -b^{2}\right)^{2} \left(c \,x^{2}+b x +a \right)^{3}}+\frac{7 b c}{6 \left(4 a c -b^{2}\right)^{2} \left(c \,x^{2}+b x +a \right)^{3}}+\frac{2 c x +b}{4 \left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{4}}"," ",0,"1/4*(2*c*x+b)/(4*a*c-b^2)/(c*x^2+b*x+a)^4+7/3*c^2/(4*a*c-b^2)^2/(c*x^2+b*x+a)^3*x+7/6*c/(4*a*c-b^2)^2/(c*x^2+b*x+a)^3*b+35/3*c^3/(4*a*c-b^2)^3/(c*x^2+b*x+a)^2*x+35/6*c^2/(4*a*c-b^2)^3/(c*x^2+b*x+a)^2*b+70*c^4/(4*a*c-b^2)^4/(c*x^2+b*x+a)*x+35*c^3/(4*a*c-b^2)^4/(c*x^2+b*x+a)*b+140*c^4/(4*a*c-b^2)^(9/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))","A"
2227,1,32834,1310,0.146000," ","int(1/(e*x+d)/(c*x^2+b*x+a)^5,x)","\text{output too large to display}"," ",0,"result too large to display","B"
2228,1,39599,1746,0.145000," ","int(1/(e*x+d)^2/(c*x^2+b*x+a)^5,x)","\text{output too large to display}"," ",0,"result too large to display","B"
2229,1,68,76,0.060000," ","int(1/(2*x+1)/(5*x^2+3*x+2)^3,x)","\frac{125624 \sqrt{31}\, \arctan \left(\frac{\left(10 x +3\right) \sqrt{31}}{31}\right)}{10218313}+\frac{32 \ln \left(2 x +1\right)}{343}-\frac{16 \ln \left(5 x^{2}+3 x +2\right)}{343}-\frac{25 \left(-\frac{6412}{961} x^{3}-\frac{55762}{4805} x^{2}-\frac{188888}{24025} x -\frac{202307}{48050}\right)}{343 \left(5 x^{2}+3 x +2\right)^{2}}"," ",0,"32/343*ln(2*x+1)-25/343*(-6412/961*x^3-55762/4805*x^2-188888/24025*x-202307/48050)/(5*x^2+3*x+2)^2-16/343*ln(5*x^2+3*x+2)+125624/10218313*arctan(1/31*(3+10*x)*31^(1/2))*31^(1/2)","A"
2230,1,77,99,0.059000," ","int(1/(2*x+1)^2/(5*x^2+3*x+2)^3,x)","-\frac{1065012 \sqrt{31}\, \arctan \left(\frac{\left(10 x +3\right) \sqrt{31}}{31}\right)}{71528191}+\frac{384 \ln \left(2 x +1\right)}{2401}-\frac{192 \ln \left(5 x^{2}+3 x +2\right)}{2401}-\frac{32}{343 \left(2 x +1\right)}-\frac{25 \left(\frac{72674}{961} x^{3}+\frac{111769}{4805} x^{2}+\frac{613046}{24025} x -\frac{490329}{48050}\right)}{2401 \left(5 x^{2}+3 x +2\right)^{2}}"," ",0,"-32/343/(2*x+1)+384/2401*ln(2*x+1)-25/2401*(72674/961*x^3+111769/4805*x^2+613046/24025*x-490329/48050)/(5*x^2+3*x+2)^2-192/2401*ln(5*x^2+3*x+2)-1065012/71528191*31^(1/2)*arctan(1/31*(10*x+3)*31^(1/2))","A"
2231,1,78,95,0.064000," ","int(1/(2*x+1)/(5*x^2+3*x+2)^4,x)","\frac{19007376 \sqrt{31}\, \arctan \left(\frac{\left(10 x +3\right) \sqrt{31}}{31}\right)}{2217373921}+\frac{128 \ln \left(2 x +1\right)}{2401}-\frac{64 \ln \left(5 x^{2}+3 x +2\right)}{2401}-\frac{125 \left(-\frac{1138088}{29791} x^{5}-\frac{11872252}{148955} x^{4}-\frac{200767868}{2234325} x^{3}-\frac{245601636}{3723875} x^{2}-\frac{104844096}{3723875} x -\frac{19363631}{2234325}\right)}{2401 \left(5 x^{2}+3 x +2\right)^{3}}"," ",0,"128/2401*ln(2*x+1)-125/2401*(-1138088/29791*x^5-11872252/148955*x^4-200767868/2234325*x^3-245601636/3723875*x^2-104844096/3723875*x-19363631/2234325)/(5*x^2+3*x+2)^3-64/2401*ln(5*x^2+3*x+2)+19007376/2217373921*31^(1/2)*arctan(1/31*(10*x+3)*31^(1/2))","A"
2232,1,87,125,0.063000," ","int(1/(2*x+1)^2/(5*x^2+3*x+2)^4,x)","-\frac{116056984 \sqrt{31}\, \arctan \left(\frac{\left(10 x +3\right) \sqrt{31}}{31}\right)}{15521617447}+\frac{2048 \ln \left(2 x +1\right)}{16807}-\frac{1024 \ln \left(5 x^{2}+3 x +2\right)}{16807}-\frac{128}{2401 \left(2 x +1\right)}-\frac{125 \left(\frac{10461724}{29791} x^{5}+\frac{38423826}{148955} x^{4}+\frac{199128958}{744775} x^{3}-\frac{6944987}{3723875} x^{2}-\frac{410739}{744775} x -\frac{371196343}{11171625}\right)}{16807 \left(5 x^{2}+3 x +2\right)^{3}}"," ",0,"-128/2401/(2*x+1)+2048/16807*ln(2*x+1)-125/16807*(10461724/29791*x^5+38423826/148955*x^4+199128958/744775*x^3-6944987/3723875*x^2-410739/744775*x-371196343/11171625)/(5*x^2+3*x+2)^3-1024/16807*ln(5*x^2+3*x+2)-116056984/15521617447*31^(1/2)*arctan(1/31*(10*x+3)*31^(1/2))","A"
2233,1,29,35,0.052000," ","int((7-3*x)/(x^2+2*x-5),x)","-\frac{5 \sqrt{6}\, \arctanh \left(\frac{\left(2 x +2\right) \sqrt{6}}{12}\right)}{3}-\frac{3 \ln \left(x^{2}+2 x -5\right)}{2}"," ",0,"-3/2*ln(x^2+2*x-5)-5/3*6^(1/2)*arctanh(1/12*(2*x+2)*6^(1/2))","A"
2234,1,33,34,0.056000," ","int(1/(x-1)/(x^2+x+1),x)","-\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x +1\right) \sqrt{3}}{3}\right)}{3}+\frac{\ln \left(x -1\right)}{3}-\frac{\ln \left(x^{2}+x +1\right)}{6}"," ",0,"1/3*ln(x-1)-1/6*ln(x^2+x+1)-1/3*3^(1/2)*arctan(1/3*(2*x+1)*3^(1/2))","A"
2235,1,311,114,0.533000," ","int(2*((a/b)^(1/n)-x*cos(Pi*(2*k-1)/n))/((a/b)^(2/n)+x^2-2*(a/b)^(1/n)*x*cos(Pi*(2*k-1)/n)),x)","\frac{2 \left(\frac{a}{b}\right)^{\frac{1}{n}} \arctan \left(\frac{2 \left(\frac{a}{b}\right)^{\frac{1}{n}} \cos \left(\frac{\pi  \left(2 k -1\right)}{n}\right)-2 x}{2 \sqrt{-\left(\frac{a}{b}\right)^{\frac{2}{n}} \left(\cos^{2}\left(\frac{\pi  \left(2 k -1\right)}{n}\right)\right)+\left(\frac{a}{b}\right)^{\frac{2}{n}}}}\right) \left(\cos^{2}\left(\frac{\pi  \left(2 k -1\right)}{n}\right)\right)}{\sqrt{-\left(\frac{a}{b}\right)^{\frac{2}{n}} \left(\cos^{2}\left(\frac{\pi  \left(2 k -1\right)}{n}\right)\right)+\left(\frac{a}{b}\right)^{\frac{2}{n}}}}-\frac{2 \left(\frac{a}{b}\right)^{\frac{1}{n}} \arctan \left(\frac{2 \left(\frac{a}{b}\right)^{\frac{1}{n}} \cos \left(\frac{\pi  \left(2 k -1\right)}{n}\right)-2 x}{2 \sqrt{-\left(\frac{a}{b}\right)^{\frac{2}{n}} \left(\cos^{2}\left(\frac{\pi  \left(2 k -1\right)}{n}\right)\right)+\left(\frac{a}{b}\right)^{\frac{2}{n}}}}\right)}{\sqrt{-\left(\frac{a}{b}\right)^{\frac{2}{n}} \left(\cos^{2}\left(\frac{\pi  \left(2 k -1\right)}{n}\right)\right)+\left(\frac{a}{b}\right)^{\frac{2}{n}}}}-\cos \left(\frac{\pi  \left(2 k -1\right)}{n}\right) \ln \left(2 x \left(\frac{a}{b}\right)^{\frac{1}{n}} \cos \left(\frac{\pi  \left(2 k -1\right)}{n}\right)-x^{2}-\left(\frac{a}{b}\right)^{\frac{2}{n}}\right)"," ",0,"-cos(Pi*(2*k-1)/n)*ln(2*(a/b)^(1/n)*x*cos(Pi*(2*k-1)/n)-x^2-(a/b)^(2/n))+2/((a/b)^(2/n)-cos(Pi*(2*k-1)/n)^2*((a/b)^(1/n))^2)^(1/2)*arctan(1/2*(2*(a/b)^(1/n)*cos(Pi*(2*k-1)/n)-2*x)/((a/b)^(2/n)-cos(Pi*(2*k-1)/n)^2*((a/b)^(1/n))^2)^(1/2))*cos(Pi*(2*k-1)/n)^2*(a/b)^(1/n)-2/((a/b)^(2/n)-cos(Pi*(2*k-1)/n)^2*((a/b)^(1/n))^2)^(1/2)*arctan(1/2*(2*(a/b)^(1/n)*cos(Pi*(2*k-1)/n)-2*x)/((a/b)^(2/n)-cos(Pi*(2*k-1)/n)^2*((a/b)^(1/n))^2)^(1/2))*(a/b)^(1/n)","B"
2236,1,31,30,0.056000," ","int(x^4/(15*x^2+13*x+2),x)","\frac{x^{3}}{45}-\frac{13 x^{2}}{450}+\frac{139 x}{3375}+\frac{\ln \left(5 x +1\right)}{4375}-\frac{16 \ln \left(3 x +2\right)}{567}"," ",0,"139/3375*x-13/450*x^2+1/45*x^3-16/567*ln(3*x+2)+1/4375*ln(1+5*x)","A"
2237,1,26,25,0.051000," ","int(x^3/(15*x^2+13*x+2),x)","\frac{x^{2}}{30}-\frac{13 x}{225}-\frac{\ln \left(5 x +1\right)}{875}+\frac{8 \ln \left(3 x +2\right)}{189}"," ",0,"-13/225*x+1/30*x^2+8/189*ln(3*x+2)-1/875*ln(5*x+1)","A"
2238,1,21,20,0.057000," ","int(x^2/(15*x^2+13*x+2),x)","\frac{x}{15}+\frac{\ln \left(5 x +1\right)}{175}-\frac{4 \ln \left(3 x +2\right)}{63}"," ",0,"1/15*x-4/63*ln(3*x+2)+1/175*ln(5*x+1)","A"
2239,1,18,17,0.050000," ","int(x/(15*x^2+13*x+2),x)","-\frac{\ln \left(5 x +1\right)}{35}+\frac{2 \ln \left(3 x +2\right)}{21}"," ",0,"2/21*ln(3*x+2)-1/35*ln(5*x+1)","A"
2240,1,18,17,0.053000," ","int(1/(15*x^2+13*x+2),x)","\frac{\ln \left(5 x +1\right)}{7}-\frac{\ln \left(3 x +2\right)}{7}"," ",0,"-1/7*ln(3*x+2)+1/7*ln(5*x+1)","A"
2241,1,22,21,0.059000," ","int(1/x/(15*x^2+13*x+2),x)","\frac{\ln \left(x \right)}{2}-\frac{5 \ln \left(5 x +1\right)}{7}+\frac{3 \ln \left(3 x +2\right)}{14}"," ",0,"1/2*ln(x)+3/14*ln(3*x+2)-5/7*ln(5*x+1)","A"
2242,1,27,26,0.062000," ","int(1/x^2/(15*x^2+13*x+2),x)","-\frac{13 \ln \left(x \right)}{4}+\frac{25 \ln \left(5 x +1\right)}{7}-\frac{9 \ln \left(3 x +2\right)}{28}-\frac{1}{2 x}"," ",0,"-1/2/x-13/4*ln(x)-9/28*ln(3*x+2)+25/7*ln(5*x+1)","A"
2243,1,32,31,0.058000," ","int(1/x^3/(15*x^2+13*x+2),x)","\frac{139 \ln \left(x \right)}{8}-\frac{125 \ln \left(5 x +1\right)}{7}+\frac{27 \ln \left(3 x +2\right)}{56}+\frac{13}{4 x}-\frac{1}{4 x^{2}}"," ",0,"-1/4/x^2+13/4/x+139/8*ln(x)+27/56*ln(3*x+2)-125/7*ln(5*x+1)","A"
2244,1,37,36,0.061000," ","int(1/x^4/(15*x^2+13*x+2),x)","-\frac{1417 \ln \left(x \right)}{16}+\frac{625 \ln \left(5 x +1\right)}{7}-\frac{81 \ln \left(3 x +2\right)}{112}-\frac{139}{8 x}+\frac{13}{8 x^{2}}-\frac{1}{6 x^{3}}"," ",0,"-1/6/x^3+13/8/x^2-139/8/x-1417/16*ln(x)-81/112*ln(3*x+2)+625/7*ln(5*x+1)","A"
2245,1,31,30,0.047000," ","int(x^5/(15*x^3+13*x^2+2*x),x)","\frac{x^{3}}{45}-\frac{13 x^{2}}{450}+\frac{139 x}{3375}+\frac{\ln \left(5 x +1\right)}{4375}-\frac{16 \ln \left(3 x +2\right)}{567}"," ",0,"1/45*x^3-13/450*x^2+139/3375*x+1/4375*ln(5*x+1)-16/567*ln(3*x+2)","A"
2246,1,26,25,0.068000," ","int(x^4/(15*x^3+13*x^2+2*x),x)","\frac{x^{2}}{30}-\frac{13 x}{225}-\frac{\ln \left(5 x +1\right)}{875}+\frac{8 \ln \left(3 x +2\right)}{189}"," ",0,"1/30*x^2-13/225*x-1/875*ln(5*x+1)+8/189*ln(3*x+2)","A"
2247,1,21,20,0.050000," ","int(x^3/(15*x^3+13*x^2+2*x),x)","\frac{x}{15}+\frac{\ln \left(5 x +1\right)}{175}-\frac{4 \ln \left(3 x +2\right)}{63}"," ",0,"1/15*x+1/175*ln(5*x+1)-4/63*ln(3*x+2)","A"
2248,1,18,17,0.051000," ","int(x^2/(15*x^3+13*x^2+2*x),x)","-\frac{\ln \left(5 x +1\right)}{35}+\frac{2 \ln \left(3 x +2\right)}{21}"," ",0,"-1/35*ln(5*x+1)+2/21*ln(3*x+2)","A"
2249,1,18,17,0.044000," ","int(x/(15*x^3+13*x^2+2*x),x)","\frac{\ln \left(5 x +1\right)}{7}-\frac{\ln \left(3 x +2\right)}{7}"," ",0,"1/7*ln(5*x+1)-1/7*ln(3*x+2)","A"
2250,1,22,21,0.053000," ","int(1/(15*x^3+13*x^2+2*x),x)","\frac{\ln \left(x \right)}{2}-\frac{5 \ln \left(5 x +1\right)}{7}+\frac{3 \ln \left(3 x +2\right)}{14}"," ",0,"1/2*ln(x)-5/7*ln(5*x+1)+3/14*ln(3*x+2)","A"
2251,1,27,26,0.057000," ","int(1/x/(15*x^3+13*x^2+2*x),x)","-\frac{13 \ln \left(x \right)}{4}+\frac{25 \ln \left(5 x +1\right)}{7}-\frac{9 \ln \left(3 x +2\right)}{28}-\frac{1}{2 x}"," ",0,"-13/4*ln(x)+25/7*ln(5*x+1)-9/28*ln(3*x+2)-1/2/x","A"
2252,1,32,31,0.053000," ","int(1/x^2/(15*x^3+13*x^2+2*x),x)","\frac{139 \ln \left(x \right)}{8}-\frac{125 \ln \left(5 x +1\right)}{7}+\frac{27 \ln \left(3 x +2\right)}{56}+\frac{13}{4 x}-\frac{1}{4 x^{2}}"," ",0,"139/8*ln(x)-125/7*ln(5*x+1)+27/56*ln(3*x+2)+13/4/x-1/4/x^2","A"
2253,1,37,36,0.050000," ","int(1/x^3/(15*x^3+13*x^2+2*x),x)","-\frac{1417 \ln \left(x \right)}{16}+\frac{625 \ln \left(5 x +1\right)}{7}-\frac{81 \ln \left(3 x +2\right)}{112}-\frac{139}{8 x}+\frac{13}{8 x^{2}}-\frac{1}{6 x^{3}}"," ",0,"-1417/16*ln(x)+625/7*ln(5*x+1)-81/112*ln(3*x+2)-139/8/x+13/8/x^2-1/6/x^3","A"
2254,1,13,12,0.049000," ","int(x/(x^2+4*x+4),x)","\ln \left(x +2\right)+\frac{2}{x +2}"," ",0,"2/(x+2)+ln(x+2)","A"
2255,1,21,20,0.070000," ","int(x/(x^2+2*x+5),x)","-\frac{\arctan \left(\frac{x}{2}+\frac{1}{2}\right)}{2}+\frac{\ln \left(x^{2}+2 x +5\right)}{2}"," ",0,"-1/2*arctan(1/2*x+1/2)+1/2*ln(x^2+2*x+5)","A"
2256,1,14,17,0.061000," ","int(x/(x^2-5*x+6),x)","3 \ln \left(x -3\right)-2 \ln \left(x -2\right)"," ",0,"-2*ln(x-2)+3*ln(x-3)","A"
2257,1,25,24,0.043000," ","int(x/(x^2+2*x+2)^2,x)","-\frac{\arctan \left(x +1\right)}{2}+\frac{-2 x -4}{4 x^{2}+8 x +8}"," ",0,"1/4*(-2*x-4)/(x^2+2*x+2)-1/2*arctan(x+1)","A"
2258,1,48,47,0.049000," ","int(x/(x^2+x+1)^3,x)","-\frac{2 \sqrt{3}\, \arctan \left(\frac{\left(2 x +1\right) \sqrt{3}}{3}\right)}{9}+\frac{-x -2}{6 \left(x^{2}+x +1\right)^{2}}-\frac{2 x +1}{6 \left(x^{2}+x +1\right)}"," ",0,"1/6*(-x-2)/(x^2+x+1)^2-1/6*(2*x+1)/(x^2+x+1)-2/9*3^(1/2)*arctan(1/3*(2*x+1)*3^(1/2))","A"
2259,1,28,27,0.043000," ","int(x^2/(x^2+x+1),x)","x -\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x +1\right) \sqrt{3}}{3}\right)}{3}-\frac{\ln \left(x^{2}+x +1\right)}{2}"," ",0,"x-1/2*ln(x^2+x+1)-1/3*3^(1/2)*arctan(1/3*(2*x+1)*3^(1/2))","A"
2260,1,15,18,0.057000," ","int(x^2/(x^2-3*x+2),x)","x +4 \ln \left(x -2\right)-\ln \left(x -1\right)"," ",0,"x-ln(x-1)+4*ln(x-2)","A"
2261,1,15,16,0.064000," ","int(x^2/(x^2+x-6),x)","x -\frac{9 \ln \left(x +3\right)}{5}+\frac{4 \ln \left(x -2\right)}{5}"," ",0,"x+4/5*ln(x-2)-9/5*ln(x+3)","A"
2262,1,16,15,0.048000," ","int(x^2/(x^2+2*x+2)^2,x)","\arctan \left(x +1\right)+\frac{1}{x^{2}+2 x +2}"," ",0,"1/(x^2+2*x+2)+arctan(x+1)","A"
2263,1,22,25,0.055000," ","int(x^3/(x^2-3*x+2),x)","\frac{x^{2}}{2}+3 x +8 \ln \left(x -2\right)-\ln \left(x -1\right)"," ",0,"1/2*x^2+3*x-ln(x-1)+8*ln(x-2)","A"
2264,1,21,20,0.052000," ","int(x^3/(x^2+2*x+1),x)","\frac{x^{2}}{2}-2 x +3 \ln \left(x +1\right)+\frac{1}{x +1}"," ",0,"-2*x+1/2*x^2+1/(x+1)+3*ln(x+1)","A"
2265,1,23,24,0.077000," ","int(x^3/(x^2-2*x+1),x)","\frac{x^{2}}{2}+2 x +3 \ln \left(x -1\right)-\frac{1}{x -1}"," ",0,"1/2*x^2+2*x+3*ln(x-1)-1/(x-1)","A"
2266,1,28,27,0.049000," ","int(x^4/(x^2+4*x+4),x)","\frac{x^{3}}{3}-2 x^{2}+12 x -32 \ln \left(x +2\right)-\frac{16}{x +2}"," ",0,"12*x-2*x^2+1/3*x^3-16/(x+2)-32*ln(x+2)","A"
2267,1,29,28,0.060000," ","int(1/x/(x^2+x+1),x)","-\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x +1\right) \sqrt{3}}{3}\right)}{3}+\ln \left(x \right)-\frac{\ln \left(x^{2}+x +1\right)}{2}"," ",0,"ln(x)-1/2*ln(x^2+x+1)-1/3*3^(1/2)*arctan(1/3*(2*x+1)*3^(1/2))","A"
2268,1,53,63,0.044000," ","int((e*x+d)^(5/2)*(c*x^2+b*x+a),x)","\frac{2 \left(e x +d \right)^{\frac{7}{2}} \left(63 c \,e^{2} x^{2}+77 b \,e^{2} x -28 c d e x +99 a \,e^{2}-22 b d e +8 c \,d^{2}\right)}{693 e^{3}}"," ",0,"2/693*(e*x+d)^(7/2)*(63*c*e^2*x^2+77*b*e^2*x-28*c*d*e*x+99*a*e^2-22*b*d*e+8*c*d^2)/e^3","A"
2269,1,53,63,0.054000," ","int((e*x+d)^(3/2)*(c*x^2+b*x+a),x)","\frac{2 \left(e x +d \right)^{\frac{5}{2}} \left(35 c \,e^{2} x^{2}+45 b \,e^{2} x -20 c d e x +63 a \,e^{2}-18 b d e +8 c \,d^{2}\right)}{315 e^{3}}"," ",0,"2/315*(e*x+d)^(5/2)*(35*c*e^2*x^2+45*b*e^2*x-20*c*d*e*x+63*a*e^2-18*b*d*e+8*c*d^2)/e^3","A"
2270,1,53,63,0.049000," ","int((c*x^2+b*x+a)*(e*x+d)^(1/2),x)","\frac{2 \left(e x +d \right)^{\frac{3}{2}} \left(15 c \,e^{2} x^{2}+21 b \,e^{2} x -12 c d e x +35 a \,e^{2}-14 b d e +8 c \,d^{2}\right)}{105 e^{3}}"," ",0,"2/105*(e*x+d)^(3/2)*(15*c*e^2*x^2+21*b*e^2*x-12*c*d*e*x+35*a*e^2-14*b*d*e+8*c*d^2)/e^3","A"
2271,1,53,63,0.046000," ","int((c*x^2+b*x+a)/(e*x+d)^(1/2),x)","\frac{2 \sqrt{e x +d}\, \left(3 c \,e^{2} x^{2}+5 b \,e^{2} x -4 c d e x +15 a \,e^{2}-10 b d e +8 c \,d^{2}\right)}{15 e^{3}}"," ",0,"2/15*(e*x+d)^(1/2)*(3*c*e^2*x^2+5*b*e^2*x-4*c*d*e*x+15*a*e^2-10*b*d*e+8*c*d^2)/e^3","A"
2272,1,53,63,0.047000," ","int((c*x^2+b*x+a)/(e*x+d)^(3/2),x)","-\frac{2 \left(-c \,e^{2} x^{2}-3 b \,e^{2} x +4 c d e x +3 a \,e^{2}-6 b d e +8 c \,d^{2}\right)}{3 \sqrt{e x +d}\, e^{3}}"," ",0,"-2/3/(e*x+d)^(1/2)*(-c*e^2*x^2-3*b*e^2*x+4*c*d*e*x+3*a*e^2-6*b*d*e+8*c*d^2)/e^3","A"
2273,1,52,63,0.055000," ","int((c*x^2+b*x+a)/(e*x+d)^(5/2),x)","-\frac{2 \left(-3 c \,e^{2} x^{2}+3 b \,e^{2} x -12 c d e x +a \,e^{2}+2 b d e -8 c \,d^{2}\right)}{3 \left(e x +d \right)^{\frac{3}{2}} e^{3}}"," ",0,"-2/3/(e*x+d)^(3/2)*(-3*c*e^2*x^2+3*b*e^2*x-12*c*d*e*x+a*e^2+2*b*d*e-8*c*d^2)/e^3","A"
2274,1,53,63,0.046000," ","int((c*x^2+b*x+a)/(e*x+d)^(7/2),x)","-\frac{2 \left(15 c \,e^{2} x^{2}+5 b \,e^{2} x +20 c d e x +3 a \,e^{2}+2 b d e +8 c \,d^{2}\right)}{15 \left(e x +d \right)^{\frac{5}{2}} e^{3}}"," ",0,"-2/15/(e*x+d)^(5/2)*(15*c*e^2*x^2+5*b*e^2*x+20*c*d*e*x+3*a*e^2+2*b*d*e+8*c*d^2)/e^3","A"
2275,1,194,146,0.053000," ","int((e*x+d)^(5/2)*(c*x^2+b*x+a)^2,x)","\frac{2 \left(e x +d \right)^{\frac{7}{2}} \left(3003 c^{2} x^{4} e^{4}+6930 b c \,e^{4} x^{3}-1848 c^{2} d \,e^{3} x^{3}+8190 a c \,e^{4} x^{2}+4095 b^{2} e^{4} x^{2}-3780 b c d \,e^{3} x^{2}+1008 c^{2} d^{2} e^{2} x^{2}+10010 a b \,e^{4} x -3640 a c d \,e^{3} x -1820 b^{2} d \,e^{3} x +1680 b c \,d^{2} e^{2} x -448 c^{2} d^{3} e x +6435 a^{2} e^{4}-2860 a b d \,e^{3}+1040 a c \,d^{2} e^{2}+520 b^{2} d^{2} e^{2}-480 b c \,d^{3} e +128 c^{2} d^{4}\right)}{45045 e^{5}}"," ",0,"2/45045*(e*x+d)^(7/2)*(3003*c^2*e^4*x^4+6930*b*c*e^4*x^3-1848*c^2*d*e^3*x^3+8190*a*c*e^4*x^2+4095*b^2*e^4*x^2-3780*b*c*d*e^3*x^2+1008*c^2*d^2*e^2*x^2+10010*a*b*e^4*x-3640*a*c*d*e^3*x-1820*b^2*d*e^3*x+1680*b*c*d^2*e^2*x-448*c^2*d^3*e*x+6435*a^2*e^4-2860*a*b*d*e^3+1040*a*c*d^2*e^2+520*b^2*d^2*e^2-480*b*c*d^3*e+128*c^2*d^4)/e^5","A"
2276,1,194,146,0.053000," ","int((e*x+d)^(3/2)*(c*x^2+b*x+a)^2,x)","\frac{2 \left(e x +d \right)^{\frac{5}{2}} \left(3465 c^{2} x^{4} e^{4}+8190 b c \,e^{4} x^{3}-2520 c^{2} d \,e^{3} x^{3}+10010 a c \,e^{4} x^{2}+5005 b^{2} e^{4} x^{2}-5460 b c d \,e^{3} x^{2}+1680 c^{2} d^{2} e^{2} x^{2}+12870 a b \,e^{4} x -5720 a c d \,e^{3} x -2860 b^{2} d \,e^{3} x +3120 b c \,d^{2} e^{2} x -960 c^{2} d^{3} e x +9009 a^{2} e^{4}-5148 a b d \,e^{3}+2288 a c \,d^{2} e^{2}+1144 b^{2} d^{2} e^{2}-1248 b c \,d^{3} e +384 c^{2} d^{4}\right)}{45045 e^{5}}"," ",0,"2/45045*(e*x+d)^(5/2)*(3465*c^2*e^4*x^4+8190*b*c*e^4*x^3-2520*c^2*d*e^3*x^3+10010*a*c*e^4*x^2+5005*b^2*e^4*x^2-5460*b*c*d*e^3*x^2+1680*c^2*d^2*e^2*x^2+12870*a*b*e^4*x-5720*a*c*d*e^3*x-2860*b^2*d*e^3*x+3120*b*c*d^2*e^2*x-960*c^2*d^3*e*x+9009*a^2*e^4-5148*a*b*d*e^3+2288*a*c*d^2*e^2+1144*b^2*d^2*e^2-1248*b*c*d^3*e+384*c^2*d^4)/e^5","A"
2277,1,194,146,0.056000," ","int((c*x^2+b*x+a)^2*(e*x+d)^(1/2),x)","\frac{2 \left(e x +d \right)^{\frac{3}{2}} \left(315 c^{2} x^{4} e^{4}+770 b c \,e^{4} x^{3}-280 c^{2} d \,e^{3} x^{3}+990 a c \,e^{4} x^{2}+495 b^{2} e^{4} x^{2}-660 b c d \,e^{3} x^{2}+240 c^{2} d^{2} e^{2} x^{2}+1386 a b \,e^{4} x -792 a c d \,e^{3} x -396 b^{2} d \,e^{3} x +528 b c \,d^{2} e^{2} x -192 c^{2} d^{3} e x +1155 a^{2} e^{4}-924 a b d \,e^{3}+528 a c \,d^{2} e^{2}+264 b^{2} d^{2} e^{2}-352 b c \,d^{3} e +128 c^{2} d^{4}\right)}{3465 e^{5}}"," ",0,"2/3465*(e*x+d)^(3/2)*(315*c^2*e^4*x^4+770*b*c*e^4*x^3-280*c^2*d*e^3*x^3+990*a*c*e^4*x^2+495*b^2*e^4*x^2-660*b*c*d*e^3*x^2+240*c^2*d^2*e^2*x^2+1386*a*b*e^4*x-792*a*c*d*e^3*x-396*b^2*d*e^3*x+528*b*c*d^2*e^2*x-192*c^2*d^3*e*x+1155*a^2*e^4-924*a*b*d*e^3+528*a*c*d^2*e^2+264*b^2*d^2*e^2-352*b*c*d^3*e+128*c^2*d^4)/e^5","A"
2278,1,194,146,0.049000," ","int((c*x^2+b*x+a)^2/(e*x+d)^(1/2),x)","\frac{2 \sqrt{e x +d}\, \left(35 c^{2} x^{4} e^{4}+90 b c \,e^{4} x^{3}-40 c^{2} d \,e^{3} x^{3}+126 a c \,e^{4} x^{2}+63 b^{2} e^{4} x^{2}-108 b c d \,e^{3} x^{2}+48 c^{2} d^{2} e^{2} x^{2}+210 a b \,e^{4} x -168 a c d \,e^{3} x -84 b^{2} d \,e^{3} x +144 b c \,d^{2} e^{2} x -64 c^{2} d^{3} e x +315 a^{2} e^{4}-420 a b d \,e^{3}+336 a c \,d^{2} e^{2}+168 b^{2} d^{2} e^{2}-288 b c \,d^{3} e +128 c^{2} d^{4}\right)}{315 e^{5}}"," ",0,"2/315*(e*x+d)^(1/2)*(35*c^2*e^4*x^4+90*b*c*e^4*x^3-40*c^2*d*e^3*x^3+126*a*c*e^4*x^2+63*b^2*e^4*x^2-108*b*c*d*e^3*x^2+48*c^2*d^2*e^2*x^2+210*a*b*e^4*x-168*a*c*d*e^3*x-84*b^2*d*e^3*x+144*b*c*d^2*e^2*x-64*c^2*d^3*e*x+315*a^2*e^4-420*a*b*d*e^3+336*a*c*d^2*e^2+168*b^2*d^2*e^2-288*b*c*d^3*e+128*c^2*d^4)/e^5","A"
2279,1,194,146,0.053000," ","int((c*x^2+b*x+a)^2/(e*x+d)^(3/2),x)","-\frac{2 \left(-15 c^{2} x^{4} e^{4}-42 b c \,e^{4} x^{3}+24 c^{2} d \,e^{3} x^{3}-70 a c \,e^{4} x^{2}-35 b^{2} e^{4} x^{2}+84 b c d \,e^{3} x^{2}-48 c^{2} d^{2} e^{2} x^{2}-210 a b \,e^{4} x +280 a c d \,e^{3} x +140 b^{2} d \,e^{3} x -336 b c \,d^{2} e^{2} x +192 c^{2} d^{3} e x +105 a^{2} e^{4}-420 a b d \,e^{3}+560 a c \,d^{2} e^{2}+280 b^{2} d^{2} e^{2}-672 b c \,d^{3} e +384 c^{2} d^{4}\right)}{105 \sqrt{e x +d}\, e^{5}}"," ",0,"-2/105/(e*x+d)^(1/2)*(-15*c^2*e^4*x^4-42*b*c*e^4*x^3+24*c^2*d*e^3*x^3-70*a*c*e^4*x^2-35*b^2*e^4*x^2+84*b*c*d*e^3*x^2-48*c^2*d^2*e^2*x^2-210*a*b*e^4*x+280*a*c*d*e^3*x+140*b^2*d*e^3*x-336*b*c*d^2*e^2*x+192*c^2*d^3*e*x+105*a^2*e^4-420*a*b*d*e^3+560*a*c*d^2*e^2+280*b^2*d^2*e^2-672*b*c*d^3*e+384*c^2*d^4)/e^5","A"
2280,1,194,146,0.052000," ","int((c*x^2+b*x+a)^2/(e*x+d)^(5/2),x)","-\frac{2 \left(-3 c^{2} x^{4} e^{4}-10 b c \,e^{4} x^{3}+8 c^{2} d \,e^{3} x^{3}-30 a c \,e^{4} x^{2}-15 b^{2} e^{4} x^{2}+60 b c d \,e^{3} x^{2}-48 c^{2} d^{2} e^{2} x^{2}+30 a b \,e^{4} x -120 a c d \,e^{3} x -60 b^{2} d \,e^{3} x +240 b c \,d^{2} e^{2} x -192 c^{2} d^{3} e x +5 a^{2} e^{4}+20 a b d \,e^{3}-80 a c \,d^{2} e^{2}-40 b^{2} d^{2} e^{2}+160 b c \,d^{3} e -128 c^{2} d^{4}\right)}{15 \left(e x +d \right)^{\frac{3}{2}} e^{5}}"," ",0,"-2/15/(e*x+d)^(3/2)*(-3*c^2*e^4*x^4-10*b*c*e^4*x^3+8*c^2*d*e^3*x^3-30*a*c*e^4*x^2-15*b^2*e^4*x^2+60*b*c*d*e^3*x^2-48*c^2*d^2*e^2*x^2+30*a*b*e^4*x-120*a*c*d*e^3*x-60*b^2*d*e^3*x+240*b*c*d^2*e^2*x-192*c^2*d^3*e*x+5*a^2*e^4+20*a*b*d*e^3-80*a*c*d^2*e^2-40*b^2*d^2*e^2+160*b*c*d^3*e-128*c^2*d^4)/e^5","A"
2281,1,194,146,0.052000," ","int((c*x^2+b*x+a)^2/(e*x+d)^(7/2),x)","-\frac{2 \left(-5 c^{2} x^{4} e^{4}-30 b c \,e^{4} x^{3}+40 c^{2} d \,e^{3} x^{3}+30 a c \,e^{4} x^{2}+15 b^{2} e^{4} x^{2}-180 b c d \,e^{3} x^{2}+240 c^{2} d^{2} e^{2} x^{2}+10 a b \,e^{4} x +40 a c d \,e^{3} x +20 b^{2} d \,e^{3} x -240 b c \,d^{2} e^{2} x +320 c^{2} d^{3} e x +3 a^{2} e^{4}+4 a b d \,e^{3}+16 a c \,d^{2} e^{2}+8 b^{2} d^{2} e^{2}-96 b c \,d^{3} e +128 c^{2} d^{4}\right)}{15 \left(e x +d \right)^{\frac{5}{2}} e^{5}}"," ",0,"-2/15/(e*x+d)^(5/2)*(-5*c^2*e^4*x^4-30*b*c*e^4*x^3+40*c^2*d*e^3*x^3+30*a*c*e^4*x^2+15*b^2*e^4*x^2-180*b*c*d*e^3*x^2+240*c^2*d^2*e^2*x^2+10*a*b*e^4*x+40*a*c*d*e^3*x+20*b^2*d*e^3*x-240*b*c*d^2*e^2*x+320*c^2*d^3*e*x+3*a^2*e^4+4*a*b*d*e^3+16*a*c*d^2*e^2+8*b^2*d^2*e^2-96*b*c*d^3*e+128*c^2*d^4)/e^5","A"
2282,1,495,258,0.052000," ","int((e*x+d)^(5/2)*(c*x^2+b*x+a)^3,x)","\frac{2 \left(e x +d \right)^{\frac{7}{2}} \left(255255 c^{3} x^{6} e^{6}+855855 b \,c^{2} e^{6} x^{5}-180180 c^{3} d \,e^{5} x^{5}+969969 a \,c^{2} e^{6} x^{4}+969969 b^{2} c \,e^{6} x^{4}-570570 b \,c^{2} d \,e^{5} x^{4}+120120 c^{3} d^{2} e^{4} x^{4}+2238390 a b c \,e^{6} x^{3}-596904 a \,c^{2} d \,e^{5} x^{3}+373065 b^{3} e^{6} x^{3}-596904 b^{2} c d \,e^{5} x^{3}+351120 b \,c^{2} d^{2} e^{4} x^{3}-73920 c^{3} d^{3} e^{3} x^{3}+1322685 a^{2} c \,e^{6} x^{2}+1322685 a \,b^{2} e^{6} x^{2}-1220940 a b c d \,e^{5} x^{2}+325584 a \,c^{2} d^{2} e^{4} x^{2}-203490 b^{3} d \,e^{5} x^{2}+325584 b^{2} c \,d^{2} e^{4} x^{2}-191520 b \,c^{2} d^{3} e^{3} x^{2}+40320 c^{3} d^{4} e^{2} x^{2}+1616615 a^{2} b \,e^{6} x -587860 a^{2} c d \,e^{5} x -587860 a \,b^{2} d \,e^{5} x +542640 a b c \,d^{2} e^{4} x -144704 a \,c^{2} d^{3} e^{3} x +90440 b^{3} d^{2} e^{4} x -144704 b^{2} c \,d^{3} e^{3} x +85120 b \,c^{2} d^{4} e^{2} x -17920 c^{3} d^{5} e x +692835 a^{3} e^{6}-461890 a^{2} b d \,e^{5}+167960 a^{2} c \,d^{2} e^{4}+167960 a \,b^{2} d^{2} e^{4}-155040 a b c \,d^{3} e^{3}+41344 a \,c^{2} d^{4} e^{2}-25840 b^{3} d^{3} e^{3}+41344 b^{2} c \,d^{4} e^{2}-24320 b \,c^{2} d^{5} e +5120 c^{3} d^{6}\right)}{4849845 e^{7}}"," ",0,"2/4849845*(e*x+d)^(7/2)*(255255*c^3*e^6*x^6+855855*b*c^2*e^6*x^5-180180*c^3*d*e^5*x^5+969969*a*c^2*e^6*x^4+969969*b^2*c*e^6*x^4-570570*b*c^2*d*e^5*x^4+120120*c^3*d^2*e^4*x^4+2238390*a*b*c*e^6*x^3-596904*a*c^2*d*e^5*x^3+373065*b^3*e^6*x^3-596904*b^2*c*d*e^5*x^3+351120*b*c^2*d^2*e^4*x^3-73920*c^3*d^3*e^3*x^3+1322685*a^2*c*e^6*x^2+1322685*a*b^2*e^6*x^2-1220940*a*b*c*d*e^5*x^2+325584*a*c^2*d^2*e^4*x^2-203490*b^3*d*e^5*x^2+325584*b^2*c*d^2*e^4*x^2-191520*b*c^2*d^3*e^3*x^2+40320*c^3*d^4*e^2*x^2+1616615*a^2*b*e^6*x-587860*a^2*c*d*e^5*x-587860*a*b^2*d*e^5*x+542640*a*b*c*d^2*e^4*x-144704*a*c^2*d^3*e^3*x+90440*b^3*d^2*e^4*x-144704*b^2*c*d^3*e^3*x+85120*b*c^2*d^4*e^2*x-17920*c^3*d^5*e*x+692835*a^3*e^6-461890*a^2*b*d*e^5+167960*a^2*c*d^2*e^4+167960*a*b^2*d^2*e^4-155040*a*b*c*d^3*e^3+41344*a*c^2*d^4*e^2-25840*b^3*d^3*e^3+41344*b^2*c*d^4*e^2-24320*b*c^2*d^5*e+5120*c^3*d^6)/e^7","A"
2283,1,495,258,0.049000," ","int((e*x+d)^(3/2)*(c*x^2+b*x+a)^3,x)","\frac{2 \left(e x +d \right)^{\frac{5}{2}} \left(15015 c^{3} x^{6} e^{6}+51051 b \,c^{2} e^{6} x^{5}-12012 c^{3} d \,e^{5} x^{5}+58905 a \,c^{2} e^{6} x^{4}+58905 b^{2} c \,e^{6} x^{4}-39270 b \,c^{2} d \,e^{5} x^{4}+9240 c^{3} d^{2} e^{4} x^{4}+139230 a b c \,e^{6} x^{3}-42840 a \,c^{2} d \,e^{5} x^{3}+23205 b^{3} e^{6} x^{3}-42840 b^{2} c d \,e^{5} x^{3}+28560 b \,c^{2} d^{2} e^{4} x^{3}-6720 c^{3} d^{3} e^{3} x^{3}+85085 a^{2} c \,e^{6} x^{2}+85085 a \,b^{2} e^{6} x^{2}-92820 a b c d \,e^{5} x^{2}+28560 a \,c^{2} d^{2} e^{4} x^{2}-15470 b^{3} d \,e^{5} x^{2}+28560 b^{2} c \,d^{2} e^{4} x^{2}-19040 b \,c^{2} d^{3} e^{3} x^{2}+4480 c^{3} d^{4} e^{2} x^{2}+109395 a^{2} b \,e^{6} x -48620 a^{2} c d \,e^{5} x -48620 a \,b^{2} d \,e^{5} x +53040 a b c \,d^{2} e^{4} x -16320 a \,c^{2} d^{3} e^{3} x +8840 b^{3} d^{2} e^{4} x -16320 b^{2} c \,d^{3} e^{3} x +10880 b \,c^{2} d^{4} e^{2} x -2560 c^{3} d^{5} e x +51051 a^{3} e^{6}-43758 a^{2} b d \,e^{5}+19448 a^{2} c \,d^{2} e^{4}+19448 a \,b^{2} d^{2} e^{4}-21216 a b c \,d^{3} e^{3}+6528 a \,c^{2} d^{4} e^{2}-3536 b^{3} d^{3} e^{3}+6528 b^{2} c \,d^{4} e^{2}-4352 b \,c^{2} d^{5} e +1024 c^{3} d^{6}\right)}{255255 e^{7}}"," ",0,"2/255255*(e*x+d)^(5/2)*(15015*c^3*e^6*x^6+51051*b*c^2*e^6*x^5-12012*c^3*d*e^5*x^5+58905*a*c^2*e^6*x^4+58905*b^2*c*e^6*x^4-39270*b*c^2*d*e^5*x^4+9240*c^3*d^2*e^4*x^4+139230*a*b*c*e^6*x^3-42840*a*c^2*d*e^5*x^3+23205*b^3*e^6*x^3-42840*b^2*c*d*e^5*x^3+28560*b*c^2*d^2*e^4*x^3-6720*c^3*d^3*e^3*x^3+85085*a^2*c*e^6*x^2+85085*a*b^2*e^6*x^2-92820*a*b*c*d*e^5*x^2+28560*a*c^2*d^2*e^4*x^2-15470*b^3*d*e^5*x^2+28560*b^2*c*d^2*e^4*x^2-19040*b*c^2*d^3*e^3*x^2+4480*c^3*d^4*e^2*x^2+109395*a^2*b*e^6*x-48620*a^2*c*d*e^5*x-48620*a*b^2*d*e^5*x+53040*a*b*c*d^2*e^4*x-16320*a*c^2*d^3*e^3*x+8840*b^3*d^2*e^4*x-16320*b^2*c*d^3*e^3*x+10880*b*c^2*d^4*e^2*x-2560*c^3*d^5*e*x+51051*a^3*e^6-43758*a^2*b*d*e^5+19448*a^2*c*d^2*e^4+19448*a*b^2*d^2*e^4-21216*a*b*c*d^3*e^3+6528*a*c^2*d^4*e^2-3536*b^3*d^3*e^3+6528*b^2*c*d^4*e^2-4352*b*c^2*d^5*e+1024*c^3*d^6)/e^7","A"
2284,1,495,258,0.051000," ","int((c*x^2+b*x+a)^3*(e*x+d)^(1/2),x)","\frac{2 \left(e x +d \right)^{\frac{3}{2}} \left(3003 c^{3} x^{6} e^{6}+10395 b \,c^{2} e^{6} x^{5}-2772 c^{3} d \,e^{5} x^{5}+12285 a \,c^{2} e^{6} x^{4}+12285 b^{2} c \,e^{6} x^{4}-9450 b \,c^{2} d \,e^{5} x^{4}+2520 c^{3} d^{2} e^{4} x^{4}+30030 a b c \,e^{6} x^{3}-10920 a \,c^{2} d \,e^{5} x^{3}+5005 b^{3} e^{6} x^{3}-10920 b^{2} c d \,e^{5} x^{3}+8400 b \,c^{2} d^{2} e^{4} x^{3}-2240 c^{3} d^{3} e^{3} x^{3}+19305 a^{2} c \,e^{6} x^{2}+19305 a \,b^{2} e^{6} x^{2}-25740 a b c d \,e^{5} x^{2}+9360 a \,c^{2} d^{2} e^{4} x^{2}-4290 b^{3} d \,e^{5} x^{2}+9360 b^{2} c \,d^{2} e^{4} x^{2}-7200 b \,c^{2} d^{3} e^{3} x^{2}+1920 c^{3} d^{4} e^{2} x^{2}+27027 a^{2} b \,e^{6} x -15444 a^{2} c d \,e^{5} x -15444 a \,b^{2} d \,e^{5} x +20592 a b c \,d^{2} e^{4} x -7488 a \,c^{2} d^{3} e^{3} x +3432 b^{3} d^{2} e^{4} x -7488 b^{2} c \,d^{3} e^{3} x +5760 b \,c^{2} d^{4} e^{2} x -1536 c^{3} d^{5} e x +15015 a^{3} e^{6}-18018 a^{2} b d \,e^{5}+10296 a^{2} c \,d^{2} e^{4}+10296 a \,b^{2} d^{2} e^{4}-13728 a b c \,d^{3} e^{3}+4992 a \,c^{2} d^{4} e^{2}-2288 b^{3} d^{3} e^{3}+4992 b^{2} c \,d^{4} e^{2}-3840 b \,c^{2} d^{5} e +1024 c^{3} d^{6}\right)}{45045 e^{7}}"," ",0,"2/45045*(e*x+d)^(3/2)*(3003*c^3*e^6*x^6+10395*b*c^2*e^6*x^5-2772*c^3*d*e^5*x^5+12285*a*c^2*e^6*x^4+12285*b^2*c*e^6*x^4-9450*b*c^2*d*e^5*x^4+2520*c^3*d^2*e^4*x^4+30030*a*b*c*e^6*x^3-10920*a*c^2*d*e^5*x^3+5005*b^3*e^6*x^3-10920*b^2*c*d*e^5*x^3+8400*b*c^2*d^2*e^4*x^3-2240*c^3*d^3*e^3*x^3+19305*a^2*c*e^6*x^2+19305*a*b^2*e^6*x^2-25740*a*b*c*d*e^5*x^2+9360*a*c^2*d^2*e^4*x^2-4290*b^3*d*e^5*x^2+9360*b^2*c*d^2*e^4*x^2-7200*b*c^2*d^3*e^3*x^2+1920*c^3*d^4*e^2*x^2+27027*a^2*b*e^6*x-15444*a^2*c*d*e^5*x-15444*a*b^2*d*e^5*x+20592*a*b*c*d^2*e^4*x-7488*a*c^2*d^3*e^3*x+3432*b^3*d^2*e^4*x-7488*b^2*c*d^3*e^3*x+5760*b*c^2*d^4*e^2*x-1536*c^3*d^5*e*x+15015*a^3*e^6-18018*a^2*b*d*e^5+10296*a^2*c*d^2*e^4+10296*a*b^2*d^2*e^4-13728*a*b*c*d^3*e^3+4992*a*c^2*d^4*e^2-2288*b^3*d^3*e^3+4992*b^2*c*d^4*e^2-3840*b*c^2*d^5*e+1024*c^3*d^6)/e^7","A"
2285,1,495,258,0.049000," ","int((c*x^2+b*x+a)^3/(e*x+d)^(1/2),x)","\frac{2 \sqrt{e x +d}\, \left(1155 c^{3} x^{6} e^{6}+4095 b \,c^{2} e^{6} x^{5}-1260 c^{3} d \,e^{5} x^{5}+5005 a \,c^{2} e^{6} x^{4}+5005 b^{2} c \,e^{6} x^{4}-4550 b \,c^{2} d \,e^{5} x^{4}+1400 c^{3} d^{2} e^{4} x^{4}+12870 a b c \,e^{6} x^{3}-5720 a \,c^{2} d \,e^{5} x^{3}+2145 b^{3} e^{6} x^{3}-5720 b^{2} c d \,e^{5} x^{3}+5200 b \,c^{2} d^{2} e^{4} x^{3}-1600 c^{3} d^{3} e^{3} x^{3}+9009 a^{2} c \,e^{6} x^{2}+9009 a \,b^{2} e^{6} x^{2}-15444 a b c d \,e^{5} x^{2}+6864 a \,c^{2} d^{2} e^{4} x^{2}-2574 b^{3} d \,e^{5} x^{2}+6864 b^{2} c \,d^{2} e^{4} x^{2}-6240 b \,c^{2} d^{3} e^{3} x^{2}+1920 c^{3} d^{4} e^{2} x^{2}+15015 a^{2} b \,e^{6} x -12012 a^{2} c d \,e^{5} x -12012 a \,b^{2} d \,e^{5} x +20592 a b c \,d^{2} e^{4} x -9152 a \,c^{2} d^{3} e^{3} x +3432 b^{3} d^{2} e^{4} x -9152 b^{2} c \,d^{3} e^{3} x +8320 b \,c^{2} d^{4} e^{2} x -2560 c^{3} d^{5} e x +15015 a^{3} e^{6}-30030 a^{2} b d \,e^{5}+24024 a^{2} c \,d^{2} e^{4}+24024 a \,b^{2} d^{2} e^{4}-41184 a b c \,d^{3} e^{3}+18304 a \,c^{2} d^{4} e^{2}-6864 b^{3} d^{3} e^{3}+18304 b^{2} c \,d^{4} e^{2}-16640 b \,c^{2} d^{5} e +5120 c^{3} d^{6}\right)}{15015 e^{7}}"," ",0,"2/15015*(e*x+d)^(1/2)*(1155*c^3*e^6*x^6+4095*b*c^2*e^6*x^5-1260*c^3*d*e^5*x^5+5005*a*c^2*e^6*x^4+5005*b^2*c*e^6*x^4-4550*b*c^2*d*e^5*x^4+1400*c^3*d^2*e^4*x^4+12870*a*b*c*e^6*x^3-5720*a*c^2*d*e^5*x^3+2145*b^3*e^6*x^3-5720*b^2*c*d*e^5*x^3+5200*b*c^2*d^2*e^4*x^3-1600*c^3*d^3*e^3*x^3+9009*a^2*c*e^6*x^2+9009*a*b^2*e^6*x^2-15444*a*b*c*d*e^5*x^2+6864*a*c^2*d^2*e^4*x^2-2574*b^3*d*e^5*x^2+6864*b^2*c*d^2*e^4*x^2-6240*b*c^2*d^3*e^3*x^2+1920*c^3*d^4*e^2*x^2+15015*a^2*b*e^6*x-12012*a^2*c*d*e^5*x-12012*a*b^2*d*e^5*x+20592*a*b*c*d^2*e^4*x-9152*a*c^2*d^3*e^3*x+3432*b^3*d^2*e^4*x-9152*b^2*c*d^3*e^3*x+8320*b*c^2*d^4*e^2*x-2560*c^3*d^5*e*x+15015*a^3*e^6-30030*a^2*b*d*e^5+24024*a^2*c*d^2*e^4+24024*a*b^2*d^2*e^4-41184*a*b*c*d^3*e^3+18304*a*c^2*d^4*e^2-6864*b^3*d^3*e^3+18304*b^2*c*d^4*e^2-16640*b*c^2*d^5*e+5120*c^3*d^6)/e^7","A"
2286,1,495,258,0.050000," ","int((c*x^2+b*x+a)^3/(e*x+d)^(3/2),x)","-\frac{2 \left(-105 c^{3} x^{6} e^{6}-385 b \,c^{2} e^{6} x^{5}+140 c^{3} d \,e^{5} x^{5}-495 a \,c^{2} e^{6} x^{4}-495 b^{2} c \,e^{6} x^{4}+550 b \,c^{2} d \,e^{5} x^{4}-200 c^{3} d^{2} e^{4} x^{4}-1386 a b c \,e^{6} x^{3}+792 a \,c^{2} d \,e^{5} x^{3}-231 b^{3} e^{6} x^{3}+792 b^{2} c d \,e^{5} x^{3}-880 b \,c^{2} d^{2} e^{4} x^{3}+320 c^{3} d^{3} e^{3} x^{3}-1155 a^{2} c \,e^{6} x^{2}-1155 a \,b^{2} e^{6} x^{2}+2772 a b c d \,e^{5} x^{2}-1584 a \,c^{2} d^{2} e^{4} x^{2}+462 b^{3} d \,e^{5} x^{2}-1584 b^{2} c \,d^{2} e^{4} x^{2}+1760 b \,c^{2} d^{3} e^{3} x^{2}-640 c^{3} d^{4} e^{2} x^{2}-3465 a^{2} b \,e^{6} x +4620 a^{2} c d \,e^{5} x +4620 a \,b^{2} d \,e^{5} x -11088 a b c \,d^{2} e^{4} x +6336 a \,c^{2} d^{3} e^{3} x -1848 b^{3} d^{2} e^{4} x +6336 b^{2} c \,d^{3} e^{3} x -7040 b \,c^{2} d^{4} e^{2} x +2560 c^{3} d^{5} e x +1155 a^{3} e^{6}-6930 a^{2} b d \,e^{5}+9240 a^{2} c \,d^{2} e^{4}+9240 a \,b^{2} d^{2} e^{4}-22176 a b c \,d^{3} e^{3}+12672 a \,c^{2} d^{4} e^{2}-3696 b^{3} d^{3} e^{3}+12672 b^{2} c \,d^{4} e^{2}-14080 b \,c^{2} d^{5} e +5120 c^{3} d^{6}\right)}{1155 \sqrt{e x +d}\, e^{7}}"," ",0,"-2/1155/(e*x+d)^(1/2)*(-105*c^3*e^6*x^6-385*b*c^2*e^6*x^5+140*c^3*d*e^5*x^5-495*a*c^2*e^6*x^4-495*b^2*c*e^6*x^4+550*b*c^2*d*e^5*x^4-200*c^3*d^2*e^4*x^4-1386*a*b*c*e^6*x^3+792*a*c^2*d*e^5*x^3-231*b^3*e^6*x^3+792*b^2*c*d*e^5*x^3-880*b*c^2*d^2*e^4*x^3+320*c^3*d^3*e^3*x^3-1155*a^2*c*e^6*x^2-1155*a*b^2*e^6*x^2+2772*a*b*c*d*e^5*x^2-1584*a*c^2*d^2*e^4*x^2+462*b^3*d*e^5*x^2-1584*b^2*c*d^2*e^4*x^2+1760*b*c^2*d^3*e^3*x^2-640*c^3*d^4*e^2*x^2-3465*a^2*b*e^6*x+4620*a^2*c*d*e^5*x+4620*a*b^2*d*e^5*x-11088*a*b*c*d^2*e^4*x+6336*a*c^2*d^3*e^3*x-1848*b^3*d^2*e^4*x+6336*b^2*c*d^3*e^3*x-7040*b*c^2*d^4*e^2*x+2560*c^3*d^5*e*x+1155*a^3*e^6-6930*a^2*b*d*e^5+9240*a^2*c*d^2*e^4+9240*a*b^2*d^2*e^4-22176*a*b*c*d^3*e^3+12672*a*c^2*d^4*e^2-3696*b^3*d^3*e^3+12672*b^2*c*d^4*e^2-14080*b*c^2*d^5*e+5120*c^3*d^6)/e^7","A"
2287,1,495,258,0.048000," ","int((c*x^2+b*x+a)^3/(e*x+d)^(5/2),x)","-\frac{2 \left(-35 c^{3} x^{6} e^{6}-135 b \,c^{2} e^{6} x^{5}+60 c^{3} d \,e^{5} x^{5}-189 a \,c^{2} e^{6} x^{4}-189 b^{2} c \,e^{6} x^{4}+270 b \,c^{2} d \,e^{5} x^{4}-120 c^{3} d^{2} e^{4} x^{4}-630 a b c \,e^{6} x^{3}+504 a \,c^{2} d \,e^{5} x^{3}-105 b^{3} e^{6} x^{3}+504 b^{2} c d \,e^{5} x^{3}-720 b \,c^{2} d^{2} e^{4} x^{3}+320 c^{3} d^{3} e^{3} x^{3}-945 a^{2} c \,e^{6} x^{2}-945 a \,b^{2} e^{6} x^{2}+3780 a b c d \,e^{5} x^{2}-3024 a \,c^{2} d^{2} e^{4} x^{2}+630 b^{3} d \,e^{5} x^{2}-3024 b^{2} c \,d^{2} e^{4} x^{2}+4320 b \,c^{2} d^{3} e^{3} x^{2}-1920 c^{3} d^{4} e^{2} x^{2}+945 a^{2} b \,e^{6} x -3780 a^{2} c d \,e^{5} x -3780 a \,b^{2} d \,e^{5} x +15120 a b c \,d^{2} e^{4} x -12096 a \,c^{2} d^{3} e^{3} x +2520 b^{3} d^{2} e^{4} x -12096 b^{2} c \,d^{3} e^{3} x +17280 b \,c^{2} d^{4} e^{2} x -7680 c^{3} d^{5} e x +105 a^{3} e^{6}+630 a^{2} b d \,e^{5}-2520 a^{2} c \,d^{2} e^{4}-2520 a \,b^{2} d^{2} e^{4}+10080 a b c \,d^{3} e^{3}-8064 a \,c^{2} d^{4} e^{2}+1680 b^{3} d^{3} e^{3}-8064 b^{2} c \,d^{4} e^{2}+11520 b \,c^{2} d^{5} e -5120 c^{3} d^{6}\right)}{315 \left(e x +d \right)^{\frac{3}{2}} e^{7}}"," ",0,"-2/315/(e*x+d)^(3/2)*(-35*c^3*e^6*x^6-135*b*c^2*e^6*x^5+60*c^3*d*e^5*x^5-189*a*c^2*e^6*x^4-189*b^2*c*e^6*x^4+270*b*c^2*d*e^5*x^4-120*c^3*d^2*e^4*x^4-630*a*b*c*e^6*x^3+504*a*c^2*d*e^5*x^3-105*b^3*e^6*x^3+504*b^2*c*d*e^5*x^3-720*b*c^2*d^2*e^4*x^3+320*c^3*d^3*e^3*x^3-945*a^2*c*e^6*x^2-945*a*b^2*e^6*x^2+3780*a*b*c*d*e^5*x^2-3024*a*c^2*d^2*e^4*x^2+630*b^3*d*e^5*x^2-3024*b^2*c*d^2*e^4*x^2+4320*b*c^2*d^3*e^3*x^2-1920*c^3*d^4*e^2*x^2+945*a^2*b*e^6*x-3780*a^2*c*d*e^5*x-3780*a*b^2*d*e^5*x+15120*a*b*c*d^2*e^4*x-12096*a*c^2*d^3*e^3*x+2520*b^3*d^2*e^4*x-12096*b^2*c*d^3*e^3*x+17280*b*c^2*d^4*e^2*x-7680*c^3*d^5*e*x+105*a^3*e^6+630*a^2*b*d*e^5-2520*a^2*c*d^2*e^4-2520*a*b^2*d^2*e^4+10080*a*b*c*d^3*e^3-8064*a*c^2*d^4*e^2+1680*b^3*d^3*e^3-8064*b^2*c*d^4*e^2+11520*b*c^2*d^5*e-5120*c^3*d^6)/e^7","A"
2288,1,495,258,0.061000," ","int((c*x^2+b*x+a)^3/(e*x+d)^(7/2),x)","-\frac{2 \left(-5 c^{3} x^{6} e^{6}-21 b \,c^{2} e^{6} x^{5}+12 c^{3} d \,e^{5} x^{5}-35 a \,c^{2} e^{6} x^{4}-35 b^{2} c \,e^{6} x^{4}+70 b \,c^{2} d \,e^{5} x^{4}-40 c^{3} d^{2} e^{4} x^{4}-210 a b c \,e^{6} x^{3}+280 a \,c^{2} d \,e^{5} x^{3}-35 b^{3} e^{6} x^{3}+280 b^{2} c d \,e^{5} x^{3}-560 b \,c^{2} d^{2} e^{4} x^{3}+320 c^{3} d^{3} e^{3} x^{3}+105 a^{2} c \,e^{6} x^{2}+105 a \,b^{2} e^{6} x^{2}-1260 a b c d \,e^{5} x^{2}+1680 a \,c^{2} d^{2} e^{4} x^{2}-210 b^{3} d \,e^{5} x^{2}+1680 b^{2} c \,d^{2} e^{4} x^{2}-3360 b \,c^{2} d^{3} e^{3} x^{2}+1920 c^{3} d^{4} e^{2} x^{2}+35 a^{2} b \,e^{6} x +140 a^{2} c d \,e^{5} x +140 a \,b^{2} d \,e^{5} x -1680 a b c \,d^{2} e^{4} x +2240 a \,c^{2} d^{3} e^{3} x -280 b^{3} d^{2} e^{4} x +2240 b^{2} c \,d^{3} e^{3} x -4480 b \,c^{2} d^{4} e^{2} x +2560 c^{3} d^{5} e x +7 a^{3} e^{6}+14 a^{2} b d \,e^{5}+56 a^{2} c \,d^{2} e^{4}+56 a \,b^{2} d^{2} e^{4}-672 a b c \,d^{3} e^{3}+896 a \,c^{2} d^{4} e^{2}-112 b^{3} d^{3} e^{3}+896 b^{2} c \,d^{4} e^{2}-1792 b \,c^{2} d^{5} e +1024 c^{3} d^{6}\right)}{35 \left(e x +d \right)^{\frac{5}{2}} e^{7}}"," ",0,"-2/35/(e*x+d)^(5/2)*(-5*c^3*e^6*x^6-21*b*c^2*e^6*x^5+12*c^3*d*e^5*x^5-35*a*c^2*e^6*x^4-35*b^2*c*e^6*x^4+70*b*c^2*d*e^5*x^4-40*c^3*d^2*e^4*x^4-210*a*b*c*e^6*x^3+280*a*c^2*d*e^5*x^3-35*b^3*e^6*x^3+280*b^2*c*d*e^5*x^3-560*b*c^2*d^2*e^4*x^3+320*c^3*d^3*e^3*x^3+105*a^2*c*e^6*x^2+105*a*b^2*e^6*x^2-1260*a*b*c*d*e^5*x^2+1680*a*c^2*d^2*e^4*x^2-210*b^3*d*e^5*x^2+1680*b^2*c*d^2*e^4*x^2-3360*b*c^2*d^3*e^3*x^2+1920*c^3*d^4*e^2*x^2+35*a^2*b*e^6*x+140*a^2*c*d*e^5*x+140*a*b^2*d*e^5*x-1680*a*b*c*d^2*e^4*x+2240*a*c^2*d^3*e^3*x-280*b^3*d^2*e^4*x+2240*b^2*c*d^3*e^3*x-4480*b*c^2*d^4*e^2*x+2560*c^3*d^5*e*x+7*a^3*e^6+14*a^2*b*d*e^5+56*a^2*c*d^2*e^4+56*a*b^2*d^2*e^4-672*a*b*c*d^3*e^3+896*a*c^2*d^4*e^2-112*b^3*d^3*e^3+896*b^2*c*d^4*e^2-1792*b*c^2*d^5*e+1024*c^3*d^6)/e^7","A"
2289,1,1929,397,0.210000," ","int((e*x+d)^(5/2)/(c*x^2+b*x+a),x)","-\frac{3 \sqrt{2}\, a b \,e^{4} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c}-\frac{3 \sqrt{2}\, a b \,e^{4} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c}+\frac{6 \sqrt{2}\, a d \,e^{3} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{6 \sqrt{2}\, a d \,e^{3} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{\sqrt{2}\, b^{3} e^{4} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c^{2}}+\frac{\sqrt{2}\, b^{3} e^{4} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c^{2}}-\frac{3 \sqrt{2}\, b^{2} d \,e^{3} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c}-\frac{3 \sqrt{2}\, b^{2} d \,e^{3} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c}+\frac{3 \sqrt{2}\, b \,d^{2} e^{2} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{3 \sqrt{2}\, b \,d^{2} e^{2} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{2 \sqrt{2}\, c \,d^{3} e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{2 \sqrt{2}\, c \,d^{3} e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{\sqrt{2}\, a \,e^{3} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c}-\frac{\sqrt{2}\, a \,e^{3} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c}-\frac{\sqrt{2}\, b^{2} e^{3} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c^{2}}+\frac{\sqrt{2}\, b^{2} e^{3} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c^{2}}+\frac{3 \sqrt{2}\, b d \,e^{2} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c}-\frac{3 \sqrt{2}\, b d \,e^{2} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c}-\frac{3 \sqrt{2}\, d^{2} e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{3 \sqrt{2}\, d^{2} e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{2 \sqrt{e x +d}\, b \,e^{2}}{c^{2}}+\frac{4 \sqrt{e x +d}\, d e}{c}+\frac{2 \left(e x +d \right)^{\frac{3}{2}} e}{3 c}"," ",0,"2/3*(e*x+d)^(3/2)/c*e-2/c^2*(e*x+d)^(1/2)*b*e^2+4*(e*x+d)^(1/2)/c*d*e-3/c/(-e^2*(4*a*c-b^2))^(1/2)*2^(1/2)/((-b*e+2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2)*arctanh(c*(e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2))*a*b*e^4+6/(-e^2*(4*a*c-b^2))^(1/2)*2^(1/2)/((-b*e+2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2)*arctanh(c*(e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2))*a*d*e^3+1/c^2/(-e^2*(4*a*c-b^2))^(1/2)*2^(1/2)/((-b*e+2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2)*arctanh(c*(e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2))*b^3*e^4-3/c/(-e^2*(4*a*c-b^2))^(1/2)*2^(1/2)/((-b*e+2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2)*arctanh(c*(e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2))*b^2*d*e^3+3/(-e^2*(4*a*c-b^2))^(1/2)*2^(1/2)/((-b*e+2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2)*arctanh(c*(e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2))*b*d^2*e^2-2*e*c/(-e^2*(4*a*c-b^2))^(1/2)*2^(1/2)/((-b*e+2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2)*arctanh(c*(e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2))*d^3+1/c*2^(1/2)/((-b*e+2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2)*arctanh(c*(e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2))*a*e^3-1/c^2*2^(1/2)/((-b*e+2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2)*arctanh(c*(e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2))*b^2*e^3+3/c*2^(1/2)/((-b*e+2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2)*arctanh(c*(e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2))*b*d*e^2-3*e*2^(1/2)/((-b*e+2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2)*arctanh(c*(e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2))*d^2-3/c/(-e^2*(4*a*c-b^2))^(1/2)*2^(1/2)/((b*e-2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2)*arctan(c*(e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2))*a*b*e^4+6/(-e^2*(4*a*c-b^2))^(1/2)*2^(1/2)/((b*e-2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2)*arctan(c*(e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2))*a*d*e^3+1/c^2/(-e^2*(4*a*c-b^2))^(1/2)*2^(1/2)/((b*e-2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2)*arctan(c*(e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2))*b^3*e^4-3/c/(-e^2*(4*a*c-b^2))^(1/2)*2^(1/2)/((b*e-2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2)*arctan(c*(e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2))*b^2*d*e^3+3/(-e^2*(4*a*c-b^2))^(1/2)*2^(1/2)/((b*e-2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2)*arctan(c*(e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2))*b*d^2*e^2-2*e*c/(-e^2*(4*a*c-b^2))^(1/2)*2^(1/2)/((b*e-2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2)*arctan(c*(e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2))*d^3-1/c*2^(1/2)/((b*e-2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2)*arctan(c*(e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2))*a*e^3+1/c^2*2^(1/2)/((b*e-2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2)*arctan(c*(e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2))*b^2*e^3-3/c*2^(1/2)/((b*e-2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2)*arctan(c*(e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2))*b*d*e^2+3*e*2^(1/2)/((b*e-2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2)*arctan(c*(e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2))*d^2","B"
2290,1,1138,272,0.140000," ","int((e*x+d)^(3/2)/(c*x^2+b*x+a),x)","\frac{2 \sqrt{2}\, a \,e^{3} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{2 \sqrt{2}\, a \,e^{3} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{\sqrt{2}\, b^{2} e^{3} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c}-\frac{\sqrt{2}\, b^{2} e^{3} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c}+\frac{2 \sqrt{2}\, b d \,e^{2} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{2 \sqrt{2}\, b d \,e^{2} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{2 \sqrt{2}\, c \,d^{2} e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{2 \sqrt{2}\, c \,d^{2} e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{\sqrt{2}\, b \,e^{2} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c}-\frac{\sqrt{2}\, b \,e^{2} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c}-\frac{2 \sqrt{2}\, d e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{2 \sqrt{2}\, d e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{2 \sqrt{e x +d}\, e}{c}"," ",0,"2*(e*x+d)^(1/2)/c*e+2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*e^3-1/c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2*e^3+2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*d*e^2-2*e*c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d^2+1/c*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*e^2-2*e*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d+2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*e^3-1/c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2*e^3+2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*d*e^2-2*e*c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d^2-1/c*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*e^2+2*e*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d","B"
2291,1,545,158,0.153000," ","int((e*x+d)^(1/2)/(c*x^2+b*x+a),x)","\frac{\sqrt{2}\, b \,e^{2} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{\sqrt{2}\, b \,e^{2} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{2 \sqrt{2}\, c d e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{2 \sqrt{2}\, c d e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{\sqrt{2}\, e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{\sqrt{2}\, e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}"," ",0,"e^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b-2*c*e/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d-e*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)+e^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b-2*c*e/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d+e*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)","B"
2292,1,194,159,0.118000," ","int(1/(e*x+d)^(1/2)/(c*x^2+b*x+a),x)","-\frac{2 \sqrt{2}\, c e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{2 \sqrt{2}\, c e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}"," ",0,"-2*c*e/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)-2*c*e/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)","A"
2293,1,689,264,0.089000," ","int(1/(e*x+d)^(3/2)/(c*x^2+b*x+a),x)","\frac{\sqrt{2}\, b c \,e^{2} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{\sqrt{2}\, b c \,e^{2} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{2 \sqrt{2}\, c^{2} d e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{2 \sqrt{2}\, c^{2} d e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{\sqrt{2}\, c e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{\sqrt{2}\, c e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{2 e}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \sqrt{e x +d}}"," ",0,"c/(a*e^2-b*d*e+c*d^2)/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*e^2-2*e*c^2/(a*e^2-b*d*e+c*d^2)/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d+e*c/(a*e^2-b*d*e+c*d^2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)+c/(a*e^2-b*d*e+c*d^2)/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*e^2-2*e*c^2/(a*e^2-b*d*e+c*d^2)/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d-e*c/(a*e^2-b*d*e+c*d^2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)-2*e/(a*e^2-b*d*e+c*d^2)/(e*x+d)^(1/2)","B"
2294,1,1444,360,0.136000," ","int(1/(e*x+d)^(5/2)/(c*x^2+b*x+a),x)","\frac{2 \sqrt{2}\, a \,c^{2} e^{3} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{2 \sqrt{2}\, a \,c^{2} e^{3} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{\sqrt{2}\, b^{2} c \,e^{3} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{\sqrt{2}\, b^{2} c \,e^{3} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{2 \sqrt{2}\, b \,c^{2} d \,e^{2} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{2 \sqrt{2}\, b \,c^{2} d \,e^{2} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{2 \sqrt{2}\, c^{3} d^{2} e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{2 \sqrt{2}\, c^{3} d^{2} e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{\sqrt{2}\, b c \,e^{2} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{\sqrt{2}\, b c \,e^{2} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{2 \sqrt{2}\, c^{2} d e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{2 \sqrt{2}\, c^{2} d e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{2 b \,e^{2}}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \sqrt{e x +d}}-\frac{4 c d e}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \sqrt{e x +d}}-\frac{2 e}{3 \left(a \,e^{2}-b d e +c \,d^{2}\right) \left(e x +d \right)^{\frac{3}{2}}}"," ",0,"2/(a*e^2-b*d*e+c*d^2)^2*c^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*e^3-1/(a*e^2-b*d*e+c*d^2)^2*c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2*e^3+2/(a*e^2-b*d*e+c*d^2)^2*c^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*d*e^2-2*e/(a*e^2-b*d*e+c*d^2)^2*c^3/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d^2-1/(a*e^2-b*d*e+c*d^2)^2*c*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*e^2+2*e/(a*e^2-b*d*e+c*d^2)^2*c^2*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d+2/(a*e^2-b*d*e+c*d^2)^2*c^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*e^3-1/(a*e^2-b*d*e+c*d^2)^2*c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2*e^3+2/(a*e^2-b*d*e+c*d^2)^2*c^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*d*e^2-2*e/(a*e^2-b*d*e+c*d^2)^2*c^3/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d^2+1/(a*e^2-b*d*e+c*d^2)^2*c*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*e^2-2*e/(a*e^2-b*d*e+c*d^2)^2*c^2*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d-2/3*e/(a*e^2-b*d*e+c*d^2)/(e*x+d)^(3/2)+2/(a*e^2-b*d*e+c*d^2)^2/(e*x+d)^(1/2)*b*e^2-4*e/(a*e^2-b*d*e+c*d^2)^2/(e*x+d)^(1/2)*c*d","B"
2295,1,3838,622,0.315000," ","int((e*x+d)^(7/2)/(c*x^2+b*x+a)^2,x)","\text{output too large to display}"," ",0,"-18*e^3*c/(4*a*c-b^2)/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*d^2-18*e^3*c/(4*a*c-b^2)/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*d^2+18*e^4/(4*a*c-b^2)/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*b*d+18*e^4/(4*a*c-b^2)/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*b*d+8*e^2*c/(4*a*c-b^2)/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*d^3-5/2*e^4/c/(4*a*c-b^2)/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^3*d+8*e^2*c/(4*a*c-b^2)/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*d^3-19/2*e^5/c/(4*a*c-b^2)/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*b^2-19/2*e^5/c/(4*a*c-b^2)/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*b^2-5/2*e^4/c/(4*a*c-b^2)/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^3*d-e^4/c^2/(c*e^2*x^2+b*e^2*x+a*e^2)/(4*a*c-b^2)*(e*x+d)^(3/2)*b^3-6*e^3/(c*e^2*x^2+b*e^2*x+a*e^2)/(4*a*c-b^2)*(e*x+d)^(3/2)*a*d+2*e*c/(c*e^2*x^2+b*e^2*x+a*e^2)/(4*a*c-b^2)*(e*x+d)^(3/2)*d^3+2*e^5/c/(c*e^2*x^2+b*e^2*x+a*e^2)/(4*a*c-b^2)*(e*x+d)^(1/2)*a^2-2*e*c/(c*e^2*x^2+b*e^2*x+a*e^2)/(4*a*c-b^2)*(e*x+d)^(1/2)*d^4-3*e^2/(c*e^2*x^2+b*e^2*x+a*e^2)/(4*a*c-b^2)*(e*x+d)^(3/2)*b*d^2+4*e^2/(c*e^2*x^2+b*e^2*x+a*e^2)/(4*a*c-b^2)*(e*x+d)^(1/2)*b*d^3+3/2*e^5/c^2/(4*a*c-b^2)/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^4+3/2*e^5/c^2/(4*a*c-b^2)/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^4-4*e*c^2/(4*a*c-b^2)/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d^4-13/2*e^4/c/(4*a*c-b^2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*b+13/2*e^4/c/(4*a*c-b^2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*b-3/2*e^3/(4*a*c-b^2)/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2*d^2-3/2*e^3/(4*a*c-b^2)/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2*d^2-5/2*e^3/c/(4*a*c-b^2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2*d+5/2*e^3/c/(4*a*c-b^2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2*d-4*e*c^2/(4*a*c-b^2)/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d^4+2*e^3/c^2*(e*x+d)^(1/2)+e^4/c^2/(c*e^2*x^2+b*e^2*x+a*e^2)/(4*a*c-b^2)*(e*x+d)^(1/2)*b^3*d+13*e^3/(4*a*c-b^2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*d-13*e^3/(4*a*c-b^2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*d+3*e^4/c/(c*e^2*x^2+b*e^2*x+a*e^2)/(4*a*c-b^2)*(e*x+d)^(3/2)*a*b-e*c/(4*a*c-b^2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d^3+e*c/(4*a*c-b^2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d^3-3/2*e^4/c^2/(4*a*c-b^2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^3+3/2*e^4/c^2/(4*a*c-b^2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^3+10*e^5/(4*a*c-b^2)/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a^2+10*e^5/(4*a*c-b^2)/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a^2-3/2*e^2/(4*a*c-b^2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*d^2+3/2*e^2/(4*a*c-b^2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*d^2+3*e^3/c/(c*e^2*x^2+b*e^2*x+a*e^2)/(4*a*c-b^2)*(e*x+d)^(3/2)*b^2*d-3*e^3/c/(c*e^2*x^2+b*e^2*x+a*e^2)/(4*a*c-b^2)*(e*x+d)^(1/2)*b^2*d^2-e^5/c^2/(c*e^2*x^2+b*e^2*x+a*e^2)/(4*a*c-b^2)*(e*x+d)^(1/2)*a*b^2","B"
2296,1,2557,445,0.135000," ","int((e*x+d)^(5/2)/(c*x^2+b*x+a)^2,x)","\frac{4 \sqrt{2}\, a b \,e^{4} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{4 \sqrt{2}\, a b \,e^{4} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{8 \sqrt{2}\, a c d \,e^{3} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{8 \sqrt{2}\, a c d \,e^{3} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{\sqrt{2}\, b^{3} e^{4} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c}-\frac{\sqrt{2}\, b^{3} e^{4} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c}-\frac{\sqrt{2}\, b^{2} d \,e^{3} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{\sqrt{2}\, b^{2} d \,e^{3} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{6 \sqrt{2}\, b c \,d^{2} e^{2} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{6 \sqrt{2}\, b c \,d^{2} e^{2} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{4 \sqrt{2}\, c^{2} d^{3} e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{4 \sqrt{2}\, c^{2} d^{3} e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{\sqrt{e x +d}\, a b \,e^{4}}{\left(c \,e^{2} x^{2}+b \,e^{2} x +a \,e^{2}\right) \left(4 a c -b^{2}\right) c}-\frac{2 \sqrt{e x +d}\, a d \,e^{3}}{\left(c \,e^{2} x^{2}+b \,e^{2} x +a \,e^{2}\right) \left(4 a c -b^{2}\right)}-\frac{3 \sqrt{2}\, a \,e^{3} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{3 \sqrt{2}\, a \,e^{3} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{\sqrt{e x +d}\, b^{2} d \,e^{3}}{\left(c \,e^{2} x^{2}+b \,e^{2} x +a \,e^{2}\right) \left(4 a c -b^{2}\right) c}+\frac{\sqrt{2}\, b^{2} e^{3} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c}-\frac{\sqrt{2}\, b^{2} e^{3} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c}+\frac{3 \sqrt{e x +d}\, b \,d^{2} e^{2}}{\left(c \,e^{2} x^{2}+b \,e^{2} x +a \,e^{2}\right) \left(4 a c -b^{2}\right)}+\frac{\sqrt{2}\, b d \,e^{2} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{\sqrt{2}\, b d \,e^{2} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{2 \sqrt{e x +d}\, c \,d^{3} e}{\left(c \,e^{2} x^{2}+b \,e^{2} x +a \,e^{2}\right) \left(4 a c -b^{2}\right)}-\frac{\sqrt{2}\, c \,d^{2} e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{\sqrt{2}\, c \,d^{2} e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{2 \left(e x +d \right)^{\frac{3}{2}} a \,e^{3}}{\left(c \,e^{2} x^{2}+b \,e^{2} x +a \,e^{2}\right) \left(4 a c -b^{2}\right)}+\frac{\left(e x +d \right)^{\frac{3}{2}} b^{2} e^{3}}{\left(c \,e^{2} x^{2}+b \,e^{2} x +a \,e^{2}\right) \left(4 a c -b^{2}\right) c}-\frac{2 \left(e x +d \right)^{\frac{3}{2}} b d \,e^{2}}{\left(c \,e^{2} x^{2}+b \,e^{2} x +a \,e^{2}\right) \left(4 a c -b^{2}\right)}+\frac{2 \left(e x +d \right)^{\frac{3}{2}} c \,d^{2} e}{\left(c \,e^{2} x^{2}+b \,e^{2} x +a \,e^{2}\right) \left(4 a c -b^{2}\right)}"," ",0,"-4*e/(4*a*c-b^2)*c^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d^3-4*e/(4*a*c-b^2)*c^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d^3+4*e^4/(4*a*c-b^2)/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*b-1/2*e^4/(4*a*c-b^2)/c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^3+4*e^4/(4*a*c-b^2)/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*b-8*e^3/(4*a*c-b^2)*c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*d+6*e^2/(4*a*c-b^2)*c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*d^2-8*e^3/(4*a*c-b^2)*c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*d+6*e^2/(4*a*c-b^2)*c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*d^2-e^3/(4*a*c-b^2)/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2*d-1/2*e^4/(4*a*c-b^2)/c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^3-e^3/(4*a*c-b^2)/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2*d+e^4/(c*e^2*x^2+b*e^2*x+a*e^2)/c/(4*a*c-b^2)*(e*x+d)^(1/2)*a*b-2*e^2/(c*e^2*x^2+b*e^2*x+a*e^2)/(4*a*c-b^2)*(e*x+d)^(3/2)*b*d+2*e/(c*e^2*x^2+b*e^2*x+a*e^2)*c/(4*a*c-b^2)*(e*x+d)^(3/2)*d^2-2*e^3/(c*e^2*x^2+b*e^2*x+a*e^2)/(4*a*c-b^2)*(e*x+d)^(1/2)*a*d+3*e^2/(c*e^2*x^2+b*e^2*x+a*e^2)/(4*a*c-b^2)*(e*x+d)^(1/2)*b*d^2-2*e/(c*e^2*x^2+b*e^2*x+a*e^2)*c/(4*a*c-b^2)*(e*x+d)^(1/2)*d^3+e^3/(c*e^2*x^2+b*e^2*x+a*e^2)/c/(4*a*c-b^2)*(e*x+d)^(3/2)*b^2-3*e^3/(4*a*c-b^2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a+3*e^3/(4*a*c-b^2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a-2*e^3/(c*e^2*x^2+b*e^2*x+a*e^2)/(4*a*c-b^2)*(e*x+d)^(3/2)*a-1/2*e^3/(4*a*c-b^2)/c*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2-e^2/(4*a*c-b^2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*d-e/(4*a*c-b^2)*c*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d^2+e/(4*a*c-b^2)*c*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d^2-e^3/(c*e^2*x^2+b*e^2*x+a*e^2)/c/(4*a*c-b^2)*(e*x+d)^(1/2)*b^2*d+1/2*e^3/(4*a*c-b^2)/c*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2+e^2/(4*a*c-b^2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*d","B"
2297,1,1503,314,0.126000," ","int((e*x+d)^(3/2)/(c*x^2+b*x+a)^2,x)","-\frac{2 \sqrt{2}\, a c \,e^{3} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{2 \sqrt{2}\, a c \,e^{3} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{\sqrt{2}\, b^{2} e^{3} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{\sqrt{2}\, b^{2} e^{3} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{4 \sqrt{2}\, b c d \,e^{2} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{4 \sqrt{2}\, b c d \,e^{2} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{4 \sqrt{2}\, c^{2} d^{2} e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{4 \sqrt{2}\, c^{2} d^{2} e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{2 \sqrt{e x +d}\, a \,e^{3}}{\left(c \,e^{2} x^{2}+b \,e^{2} x +a \,e^{2}\right) \left(4 a c -b^{2}\right)}+\frac{2 \sqrt{e x +d}\, b d \,e^{2}}{\left(c \,e^{2} x^{2}+b \,e^{2} x +a \,e^{2}\right) \left(4 a c -b^{2}\right)}+\frac{\sqrt{2}\, b \,e^{2} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{\sqrt{2}\, b \,e^{2} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{2 \sqrt{e x +d}\, c \,d^{2} e}{\left(c \,e^{2} x^{2}+b \,e^{2} x +a \,e^{2}\right) \left(4 a c -b^{2}\right)}-\frac{\sqrt{2}\, c d e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{\sqrt{2}\, c d e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{\left(e x +d \right)^{\frac{3}{2}} b \,e^{2}}{\left(c \,e^{2} x^{2}+b \,e^{2} x +a \,e^{2}\right) \left(4 a c -b^{2}\right)}+\frac{2 \left(e x +d \right)^{\frac{3}{2}} c d e}{\left(c \,e^{2} x^{2}+b \,e^{2} x +a \,e^{2}\right) \left(4 a c -b^{2}\right)}"," ",0,"-e^2/(c*e^2*x^2+b*e^2*x+a*e^2)/(4*a*c-b^2)*(e*x+d)^(3/2)*b+2*e/(c*e^2*x^2+b*e^2*x+a*e^2)/(4*a*c-b^2)*(e*x+d)^(3/2)*c*d-2*e^3/(c*e^2*x^2+b*e^2*x+a*e^2)/(4*a*c-b^2)*(e*x+d)^(1/2)*a+2*e^2/(c*e^2*x^2+b*e^2*x+a*e^2)/(4*a*c-b^2)*(e*x+d)^(1/2)*b*d-2*e/(c*e^2*x^2+b*e^2*x+a*e^2)/(4*a*c-b^2)*(e*x+d)^(1/2)*c*d^2-2*e^3/(4*a*c-b^2)*c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a-1/2*e^3/(4*a*c-b^2)/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2+4*e^2/(4*a*c-b^2)*c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*d-4*e/(4*a*c-b^2)*c^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d^2+1/2*e^2/(4*a*c-b^2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b-e/(4*a*c-b^2)*c*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d-2*e^3/(4*a*c-b^2)*c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a-1/2*e^3/(4*a*c-b^2)/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2+4*e^2/(4*a*c-b^2)*c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*d-4*e/(4*a*c-b^2)*c^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d^2-1/2*e^2/(4*a*c-b^2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b+e/(4*a*c-b^2)*c*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d","B"
2298,1,869,241,0.344000," ","int((e*x+d)^(1/2)/(c*x^2+b*x+a)^2,x)","\frac{2 \sqrt{2}\, b c \,e^{2} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{2 \sqrt{2}\, b c \,e^{2} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{4 \sqrt{2}\, c^{2} d e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{4 \sqrt{2}\, c^{2} d e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{\sqrt{2}\, \sqrt{-4 a c \,e^{2}+b^{2} e^{2}}\, c e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{\sqrt{2}\, \sqrt{-4 a c \,e^{2}+b^{2} e^{2}}\, c e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{\sqrt{-4 a c \,e^{2}+b^{2} e^{2}}\, \sqrt{e x +d}\, e}{\left(4 a c -b^{2}\right) \sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \left(e x +\frac{b e}{2 c}-\frac{\sqrt{\left(-4 a c +b^{2}\right) e^{2}}}{2 c}\right)}+\frac{\sqrt{-4 a c \,e^{2}+b^{2} e^{2}}\, \sqrt{e x +d}\, e}{\left(4 a c -b^{2}\right) \sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \left(e x +\frac{b e}{2 c}+\frac{\sqrt{\left(-4 a c +b^{2}\right) e^{2}}}{2 c}\right)}"," ",0,"e/(4*a*c-b^2)/(-(4*a*c-b^2)*e^2)^(1/2)*(-4*a*c*e^2+b^2*e^2)^(1/2)*(e*x+d)^(1/2)/(e*x+1/2*b*e/c-1/2/c*((-4*a*c+b^2)*e^2)^(1/2))+2*e^2*c/(4*a*c-b^2)/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b-4*e*c^2/(4*a*c-b^2)/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d-e*c/(4*a*c-b^2)/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*(-4*a*c*e^2+b^2*e^2)^(1/2)+e/(4*a*c-b^2)/(-(4*a*c-b^2)*e^2)^(1/2)*(-4*a*c*e^2+b^2*e^2)^(1/2)*(e*x+d)^(1/2)/(e*x+1/2*b*e/c+1/2/c*((-4*a*c+b^2)*e^2)^(1/2))+2*e^2*c/(4*a*c-b^2)/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b-4*e*c^2/(4*a*c-b^2)/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d+e*c/(4*a*c-b^2)/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*(-4*a*c*e^2+b^2*e^2)^(1/2)","B"
2299,1,1120,379,0.437000," ","int(1/(e*x+d)^(1/2)/(c*x^2+b*x+a)^2,x)","\frac{8 \sqrt{2}\, b \,c^{2} e^{2} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \left(4 a c -b^{2}\right) \left(-2 b e +4 c d +2 \sqrt{-4 a c \,e^{2}+b^{2} e^{2}}\right) \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{8 \sqrt{2}\, b \,c^{2} e^{2} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \left(4 a c -b^{2}\right) \left(2 b e -4 c d +2 \sqrt{-4 a c \,e^{2}+b^{2} e^{2}}\right) \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{16 \sqrt{2}\, c^{3} d e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \left(4 a c -b^{2}\right) \left(-2 b e +4 c d +2 \sqrt{-4 a c \,e^{2}+b^{2} e^{2}}\right) \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{16 \sqrt{2}\, c^{3} d e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \left(4 a c -b^{2}\right) \left(2 b e -4 c d +2 \sqrt{-4 a c \,e^{2}+b^{2} e^{2}}\right) \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{12 \sqrt{2}\, \sqrt{-4 a c \,e^{2}+b^{2} e^{2}}\, c^{2} e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \left(4 a c -b^{2}\right) \left(-2 b e +4 c d +2 \sqrt{-4 a c \,e^{2}+b^{2} e^{2}}\right) \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{12 \sqrt{2}\, \sqrt{-4 a c \,e^{2}+b^{2} e^{2}}\, c^{2} e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \left(4 a c -b^{2}\right) \left(2 b e -4 c d +2 \sqrt{-4 a c \,e^{2}+b^{2} e^{2}}\right) \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{2 \sqrt{-4 a c \,e^{2}+b^{2} e^{2}}\, \sqrt{e x +d}\, c e}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \left(4 a c -b^{2}\right) \left(-b e +2 c d +\sqrt{-4 a c \,e^{2}+b^{2} e^{2}}\right) \left(e x +\frac{b e}{2 c}-\frac{\sqrt{\left(-4 a c +b^{2}\right) e^{2}}}{2 c}\right)}+\frac{2 \sqrt{-4 a c \,e^{2}+b^{2} e^{2}}\, \sqrt{e x +d}\, c e}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \left(4 a c -b^{2}\right) \left(-b e +2 c d -\sqrt{-4 a c \,e^{2}+b^{2} e^{2}}\right) \left(e x +\frac{b e}{2 c}+\frac{\sqrt{\left(-4 a c +b^{2}\right) e^{2}}}{2 c}\right)}"," ",0,"2*e*c/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)/(-b*e+2*c*d+(-4*a*c*e^2+b^2*e^2)^(1/2))*(-4*a*c*e^2+b^2*e^2)^(1/2)*(e*x+d)^(1/2)/(e*x+1/2*b/c*e-1/2*((-4*a*c+b^2)*e^2)^(1/2)/c)+8*e^2*c^2/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)/(-2*b*e+4*c*d+2*(-4*a*c*e^2+b^2*e^2)^(1/2))*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b-16*e*c^3/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)/(-2*b*e+4*c*d+2*(-4*a*c*e^2+b^2*e^2)^(1/2))*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d-12*e*c^2/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)/(-2*b*e+4*c*d+2*(-4*a*c*e^2+b^2*e^2)^(1/2))*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*(-4*a*c*e^2+b^2*e^2)^(1/2)+2*e*c/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)/(-b*e+2*c*d-(-4*a*c*e^2+b^2*e^2)^(1/2))*(-4*a*c*e^2+b^2*e^2)^(1/2)*(e*x+d)^(1/2)/(e*x+1/2*b/c*e+1/2*((-4*a*c+b^2)*e^2)^(1/2)/c)-8*e^2*c^2/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)/(2*b*e-4*c*d+2*(-4*a*c*e^2+b^2*e^2)^(1/2))*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b+16*e*c^3/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)/(2*b*e-4*c*d+2*(-4*a*c*e^2+b^2*e^2)^(1/2))*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d-12*e*c^2/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)/(2*b*e-4*c*d+2*(-4*a*c*e^2+b^2*e^2)^(1/2))*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*(-4*a*c*e^2+b^2*e^2)^(1/2)","B"
2300,1,3212,545,0.154000," ","int(1/(e*x+d)^(3/2)/(c*x^2+b*x+a)^2,x)","\text{output too large to display}"," ",0,"-3/2*e^4/(a*e^2-b*d*e+c*d^2)^2/(4*a*c-b^2)*c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^3+8*e^4/(a*e^2-b*d*e+c*d^2)^2/(4*a*c-b^2)*c^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*b-16*e^3/(a*e^2-b*d*e+c*d^2)^2/(4*a*c-b^2)*c^3/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*d-4*e/(a*e^2-b*d*e+c*d^2)^2/(4*a*c-b^2)*c^4/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d^3-e^2/(a*e^2-b*d*e+c*d^2)^2/(4*a*c-b^2)*c^2*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*d-3/2*e^4/(a*e^2-b*d*e+c*d^2)^2/(4*a*c-b^2)*c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^3+e^2/(a*e^2-b*d*e+c*d^2)^2/(4*a*c-b^2)*c^2*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*d-4*e/(a*e^2-b*d*e+c*d^2)^2/(4*a*c-b^2)*c^4/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d^3-16*e^3/(a*e^2-b*d*e+c*d^2)^2/(4*a*c-b^2)*c^3/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*d+e^3/(a*e^2-b*d*e+c*d^2)^2/(4*a*c-b^2)*c^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2*d+e^3/(a*e^2-b*d*e+c*d^2)^2/(4*a*c-b^2)*c^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2*d+6*e^2/(a*e^2-b*d*e+c*d^2)^2/(4*a*c-b^2)*c^3/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*d^2+8*e^4/(a*e^2-b*d*e+c*d^2)^2/(4*a*c-b^2)*c^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*b+6*e^2/(a*e^2-b*d*e+c*d^2)^2/(4*a*c-b^2)*c^3/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*d^2-2*e^3/(a*e^2-b*d*e+c*d^2)^2/(e*x+d)^(1/2)+3*e^2/(a*e^2-b*d*e+c*d^2)^2/(c*e^2*x^2+b*e^2*x+a*e^2)/(4*a*c-b^2)*(e*x+d)^(1/2)*b*c^2*d^2-e/(a*e^2-b*d*e+c*d^2)^2/(4*a*c-b^2)*c^3*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d^2+6*e^3/(a*e^2-b*d*e+c*d^2)^2/(c*e^2*x^2+b*e^2*x+a*e^2)/(4*a*c-b^2)*(e*x+d)^(1/2)*c^2*a*d+e/(a*e^2-b*d*e+c*d^2)^2/(4*a*c-b^2)*c^3*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d^2-3*e^3/(a*e^2-b*d*e+c*d^2)^2/(c*e^2*x^2+b*e^2*x+a*e^2)/(4*a*c-b^2)*(e*x+d)^(1/2)*b^2*c*d-5*e^3/(a*e^2-b*d*e+c*d^2)^2/(4*a*c-b^2)*c^2*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a-2*e^2/(a*e^2-b*d*e+c*d^2)^2/(c*e^2*x^2+b*e^2*x+a*e^2)*c^2/(4*a*c-b^2)*(e*x+d)^(3/2)*b*d-3*e^4/(a*e^2-b*d*e+c*d^2)^2/(c*e^2*x^2+b*e^2*x+a*e^2)/(4*a*c-b^2)*(e*x+d)^(1/2)*a*b*c-3/2*e^3/(a*e^2-b*d*e+c*d^2)^2/(4*a*c-b^2)*c*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2+3/2*e^3/(a*e^2-b*d*e+c*d^2)^2/(4*a*c-b^2)*c*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2+5*e^3/(a*e^2-b*d*e+c*d^2)^2/(4*a*c-b^2)*c^2*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a+e^4/(a*e^2-b*d*e+c*d^2)^2/(c*e^2*x^2+b*e^2*x+a*e^2)/(4*a*c-b^2)*(e*x+d)^(1/2)*b^3-2*e^3/(a*e^2-b*d*e+c*d^2)^2/(c*e^2*x^2+b*e^2*x+a*e^2)*c^2/(4*a*c-b^2)*(e*x+d)^(3/2)*a+e^3/(a*e^2-b*d*e+c*d^2)^2/(c*e^2*x^2+b*e^2*x+a*e^2)*c/(4*a*c-b^2)*(e*x+d)^(3/2)*b^2+2*e/(a*e^2-b*d*e+c*d^2)^2/(c*e^2*x^2+b*e^2*x+a*e^2)*c^3/(4*a*c-b^2)*(e*x+d)^(3/2)*d^2-2*e/(a*e^2-b*d*e+c*d^2)^2/(c*e^2*x^2+b*e^2*x+a*e^2)/(4*a*c-b^2)*(e*x+d)^(1/2)*c^3*d^3","B"
2301,1,929,309,0.130000," ","int(1/x^(5/2)/(c*x^2+b*x+a)^2,x)","\frac{14 \sqrt{2}\, c^{3} \arctanh \left(\frac{\sqrt{2}\, c \sqrt{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{14 \sqrt{2}\, c^{3} \arctan \left(\frac{\sqrt{2}\, c \sqrt{x}}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{29 \sqrt{2}\, b^{2} c^{2} \arctanh \left(\frac{\sqrt{2}\, c \sqrt{x}}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}-\frac{29 \sqrt{2}\, b^{2} c^{2} \arctan \left(\frac{\sqrt{2}\, c \sqrt{x}}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}+\frac{5 \sqrt{2}\, b^{4} c \arctanh \left(\frac{\sqrt{2}\, c \sqrt{x}}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{3}}+\frac{5 \sqrt{2}\, b^{4} c \arctan \left(\frac{\sqrt{2}\, c \sqrt{x}}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{3}}+\frac{3 b \,c^{2} x^{\frac{3}{2}}}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) a^{2}}-\frac{b^{3} c \,x^{\frac{3}{2}}}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) a^{3}}-\frac{19 \sqrt{2}\, b \,c^{2} \arctanh \left(\frac{\sqrt{2}\, c \sqrt{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^{2}}+\frac{19 \sqrt{2}\, b \,c^{2} \arctan \left(\frac{\sqrt{2}\, c \sqrt{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^{2}}+\frac{5 \sqrt{2}\, b^{3} c \arctanh \left(\frac{\sqrt{2}\, c \sqrt{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^{3}}-\frac{5 \sqrt{2}\, b^{3} c \arctan \left(\frac{\sqrt{2}\, c \sqrt{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^{3}}-\frac{2 c^{2} \sqrt{x}}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) a}+\frac{4 b^{2} c \sqrt{x}}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) a^{2}}-\frac{b^{4} \sqrt{x}}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) a^{3}}+\frac{4 b}{a^{3} \sqrt{x}}-\frac{2}{3 a^{2} x^{\frac{3}{2}}}"," ",0,"3/a^2/(c*x^2+b*x+a)*b*c^2/(4*a*c-b^2)*x^(3/2)-1/a^3/(c*x^2+b*x+a)*b^3*c/(4*a*c-b^2)*x^(3/2)-2/a/(c*x^2+b*x+a)/(4*a*c-b^2)*x^(1/2)*c^2+4/a^2/(c*x^2+b*x+a)/(4*a*c-b^2)*x^(1/2)*b^2*c-1/a^3/(c*x^2+b*x+a)/(4*a*c-b^2)*x^(1/2)*b^4+19/2/a^2/(4*a*c-b^2)*c^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(c*x^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2))*b-5/2/a^3/(4*a*c-b^2)*c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(c*x^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2))*b^3+14/a/(4*a*c-b^2)*c^3/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(c*x^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2))-29/2/a^2/(4*a*c-b^2)*c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(c*x^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2))*b^2+5/2/a^3/(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(c*x^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2))*b^4-19/2/a^2/(4*a*c-b^2)*c^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(c*x^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2))*b+5/2/a^3/(4*a*c-b^2)*c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(c*x^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2))*b^3+14/a/(4*a*c-b^2)*c^3/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(c*x^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2))-29/2/a^2/(4*a*c-b^2)*c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(c*x^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2))*b^2+5/2/a^3/(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(c*x^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2))*b^4-2/3/a^2/x^(3/2)+4/a^3*b/x^(1/2)","B"
2302,1,5849,675,0.199000," ","int((e*x+d)^(7/2)/(c*x^2+b*x+a)^3,x)","\text{output too large to display}"," ",0,"result too large to display","B"
2303,1,3925,509,0.122000," ","int((e*x+d)^(5/2)/(c*x^2+b*x+a)^3,x)","\text{output too large to display}"," ",0,"-19/4*e^4/(c*e^2*x^2+b*e^2*x+a*e^2)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*(e*x+d)^(3/2)*b^3*d-e^5/(c*e^2*x^2+b*e^2*x+a*e^2)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*(e*x+d)^(3/2)*a^2*c+19/4*e^5/(c*e^2*x^2+b*e^2*x+a*e^2)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*(e*x+d)^(3/2)*a*b^2+9/2*e^4/(16*a^2*c^2-8*a*b^2*c+b^4)*c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*b-9*e^3/(16*a^2*c^2-8*a*b^2*c+b^4)*c^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*d-27/4*e^3/(16*a^2*c^2-8*a*b^2*c+b^4)*c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2*d+18*e^2/(16*a^2*c^2-8*a*b^2*c+b^4)*c^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*d^2+9/2*e^4/(16*a^2*c^2-8*a*b^2*c+b^4)*c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*b-9*e^3/(16*a^2*c^2-8*a*b^2*c+b^4)*c^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*d-27/4*e^3/(16*a^2*c^2-8*a*b^2*c+b^4)*c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2*d+18*e^2/(16*a^2*c^2-8*a*b^2*c+b^4)*c^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*d^2-3/8*e^3/(16*a^2*c^2-8*a*b^2*c+b^4)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2+3/8*e^3/(16*a^2*c^2-8*a*b^2*c+b^4)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2+18*e/(c*e^2*x^2+b*e^2*x+a*e^2)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*(e*x+d)^(3/2)*c^3*d^4+3*e^6/(c*e^2*x^2+b*e^2*x+a*e^2)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*(e*x+d)^(1/2)*a^2*b+3*e^4/(c*e^2*x^2+b*e^2*x+a*e^2)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*(e*x+d)^(1/2)*b^3*d^2-6*e/(c*e^2*x^2+b*e^2*x+a*e^2)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*(e*x+d)^(1/2)*c^3*d^5+3*e^3/(c*e^2*x^2+b*e^2*x+a*e^2)^2*c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*(e*x+d)^(7/2)*a+3/4*e^3/(c*e^2*x^2+b*e^2*x+a*e^2)^2*c/(16*a^2*c^2-8*a*b^2*c+b^4)*(e*x+d)^(7/2)*b^2+6*e/(c*e^2*x^2+b*e^2*x+a*e^2)^2*c^3/(16*a^2*c^2-8*a*b^2*c+b^4)*(e*x+d)^(7/2)*d^2-18*e/(c*e^2*x^2+b*e^2*x+a*e^2)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*(e*x+d)^(5/2)*c^3*d^3-3*e^2/(16*a^2*c^2-8*a*b^2*c+b^4)*c*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*d+18*e^4/(c*e^2*x^2+b*e^2*x+a*e^2)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*(e*x+d)^(1/2)*a*b*c*d^2-17*e^4/(c*e^2*x^2+b*e^2*x+a*e^2)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*(e*x+d)^(3/2)*a*b*c*d-12*e/(16*a^2*c^2-8*a*b^2*c+b^4)*c^3/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d^3+3*e^2/(16*a^2*c^2-8*a*b^2*c+b^4)*c*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*d-12*e/(16*a^2*c^2-8*a*b^2*c+b^4)*c^3/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d^3+5/4*e^4/(c*e^2*x^2+b*e^2*x+a*e^2)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*(e*x+d)^(5/2)*b^3-36*e^2/(c*e^2*x^2+b*e^2*x+a*e^2)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*(e*x+d)^(3/2)*b*c^2*d^3-12*e^3/(c*e^2*x^2+b*e^2*x+a*e^2)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*(e*x+d)^(1/2)*a*c^2*d^3-12*e^3/(c*e^2*x^2+b*e^2*x+a*e^2)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*(e*x+d)^(1/2)*b^2*c*d^3+15*e^2/(c*e^2*x^2+b*e^2*x+a*e^2)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*(e*x+d)^(1/2)*b*c^2*d^4-23/2*e^3/(c*e^2*x^2+b*e^2*x+a*e^2)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*(e*x+d)^(5/2)*b^2*c*d+27*e^2/(c*e^2*x^2+b*e^2*x+a*e^2)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*(e*x+d)^(5/2)*b*c^2*d^2+17*e^3/(c*e^2*x^2+b*e^2*x+a*e^2)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*(e*x+d)^(3/2)*a*c^2*d^2+91/4*e^3/(c*e^2*x^2+b*e^2*x+a*e^2)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*(e*x+d)^(3/2)*b^2*c*d^2-3/2*e^3/(16*a^2*c^2-8*a*b^2*c+b^4)*c*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a-3*e/(16*a^2*c^2-8*a*b^2*c+b^4)*c^2*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d^2+3/2*e^3/(16*a^2*c^2-8*a*b^2*c+b^4)*c*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a+3*e/(16*a^2*c^2-8*a*b^2*c+b^4)*c^2*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d^2+3/8*e^4/(16*a^2*c^2-8*a*b^2*c+b^4)/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^3+3/8*e^4/(16*a^2*c^2-8*a*b^2*c+b^4)/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^3-6*e^5/(c*e^2*x^2+b*e^2*x+a*e^2)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*(e*x+d)^(1/2)*a^2*c*d-6*e^5/(c*e^2*x^2+b*e^2*x+a*e^2)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*(e*x+d)^(1/2)*a*b^2*d-6*e^2/(c*e^2*x^2+b*e^2*x+a*e^2)^2*c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*(e*x+d)^(7/2)*b*d+4*e^4/(c*e^2*x^2+b*e^2*x+a*e^2)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*(e*x+d)^(5/2)*a*b*c-8*e^3/(c*e^2*x^2+b*e^2*x+a*e^2)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*(e*x+d)^(5/2)*c^2*a*d","B"
2304,1,2582,381,0.115000," ","int((e*x+d)^(3/2)/(c*x^2+b*x+a)^3,x)","-\frac{3 \sqrt{e x +d}\, a^{2} c \,e^{5}}{\left(c \,e^{2} x^{2}+b \,e^{2} x +a \,e^{2}\right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}-\frac{3 \sqrt{e x +d}\, a \,b^{2} e^{5}}{4 \left(c \,e^{2} x^{2}+b \,e^{2} x +a \,e^{2}\right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}+\frac{9 \sqrt{e x +d}\, a b c d \,e^{4}}{\left(c \,e^{2} x^{2}+b \,e^{2} x +a \,e^{2}\right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}-\frac{9 \sqrt{e x +d}\, a \,c^{2} d^{2} e^{3}}{\left(c \,e^{2} x^{2}+b \,e^{2} x +a \,e^{2}\right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}+\frac{3 \sqrt{e x +d}\, b^{3} d \,e^{4}}{4 \left(c \,e^{2} x^{2}+b \,e^{2} x +a \,e^{2}\right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}-\frac{27 \sqrt{e x +d}\, b^{2} c \,d^{2} e^{3}}{4 \left(c \,e^{2} x^{2}+b \,e^{2} x +a \,e^{2}\right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}+\frac{12 \sqrt{e x +d}\, b \,c^{2} d^{3} e^{2}}{\left(c \,e^{2} x^{2}+b \,e^{2} x +a \,e^{2}\right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}-\frac{6 \sqrt{e x +d}\, c^{3} d^{4} e}{\left(c \,e^{2} x^{2}+b \,e^{2} x +a \,e^{2}\right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}-\frac{4 \left(e x +d \right)^{\frac{3}{2}} a b c \,e^{4}}{\left(c \,e^{2} x^{2}+b \,e^{2} x +a \,e^{2}\right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}+\frac{8 \left(e x +d \right)^{\frac{3}{2}} a \,c^{2} d \,e^{3}}{\left(c \,e^{2} x^{2}+b \,e^{2} x +a \,e^{2}\right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}-\frac{3 \sqrt{2}\, a \,c^{2} e^{3} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{3 \sqrt{2}\, a \,c^{2} e^{3} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{5 \left(e x +d \right)^{\frac{3}{2}} b^{3} e^{4}}{4 \left(c \,e^{2} x^{2}+b \,e^{2} x +a \,e^{2}\right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}+\frac{23 \left(e x +d \right)^{\frac{3}{2}} b^{2} c d \,e^{3}}{2 \left(c \,e^{2} x^{2}+b \,e^{2} x +a \,e^{2}\right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}-\frac{9 \sqrt{2}\, b^{2} c \,e^{3} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{4 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{9 \sqrt{2}\, b^{2} c \,e^{3} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{4 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{27 \left(e x +d \right)^{\frac{3}{2}} b \,c^{2} d^{2} e^{2}}{\left(c \,e^{2} x^{2}+b \,e^{2} x +a \,e^{2}\right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}+\frac{12 \sqrt{2}\, b \,c^{2} d \,e^{2} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{12 \sqrt{2}\, b \,c^{2} d \,e^{2} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{18 \left(e x +d \right)^{\frac{3}{2}} c^{3} d^{3} e}{\left(c \,e^{2} x^{2}+b \,e^{2} x +a \,e^{2}\right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}-\frac{12 \sqrt{2}\, c^{3} d^{2} e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{12 \sqrt{2}\, c^{3} d^{2} e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{\left(e x +d \right)^{\frac{5}{2}} a \,c^{2} e^{3}}{\left(c \,e^{2} x^{2}+b \,e^{2} x +a \,e^{2}\right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}-\frac{19 \left(e x +d \right)^{\frac{5}{2}} b^{2} c \,e^{3}}{4 \left(c \,e^{2} x^{2}+b \,e^{2} x +a \,e^{2}\right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}+\frac{18 \left(e x +d \right)^{\frac{5}{2}} b \,c^{2} d \,e^{2}}{\left(c \,e^{2} x^{2}+b \,e^{2} x +a \,e^{2}\right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}-\frac{18 \left(e x +d \right)^{\frac{5}{2}} c^{3} d^{2} e}{\left(c \,e^{2} x^{2}+b \,e^{2} x +a \,e^{2}\right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}-\frac{3 \left(e x +d \right)^{\frac{7}{2}} b \,c^{2} e^{2}}{\left(c \,e^{2} x^{2}+b \,e^{2} x +a \,e^{2}\right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}+\frac{3 \sqrt{2}\, b c \,e^{2} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{3 \sqrt{2}\, b c \,e^{2} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{6 \left(e x +d \right)^{\frac{7}{2}} c^{3} d e}{\left(c \,e^{2} x^{2}+b \,e^{2} x +a \,e^{2}\right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}-\frac{3 \sqrt{2}\, c^{2} d e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{3 \sqrt{2}\, c^{2} d e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}"," ",0,"12*e^2/(16*a^2*c^2-8*a*b^2*c+b^4)*c^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*d+12*e^2/(16*a^2*c^2-8*a*b^2*c+b^4)*c^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*d-3*e^2/(c*e^2*x^2+b*e^2*x+a*e^2)^2*c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*(e*x+d)^(7/2)*b+6*e/(c*e^2*x^2+b*e^2*x+a*e^2)^2*c^3/(16*a^2*c^2-8*a*b^2*c+b^4)*(e*x+d)^(7/2)*d+e^3/(c*e^2*x^2+b*e^2*x+a*e^2)^2*c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*(e*x+d)^(5/2)*a-19/4*e^3/(c*e^2*x^2+b*e^2*x+a*e^2)^2*c/(16*a^2*c^2-8*a*b^2*c+b^4)*(e*x+d)^(5/2)*b^2-18*e/(c*e^2*x^2+b*e^2*x+a*e^2)^2*c^3/(16*a^2*c^2-8*a*b^2*c+b^4)*(e*x+d)^(5/2)*d^2+18*e/(c*e^2*x^2+b*e^2*x+a*e^2)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*(e*x+d)^(3/2)*c^3*d^3+3/4*e^4/(c*e^2*x^2+b*e^2*x+a*e^2)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*(e*x+d)^(1/2)*b^3*d-6*e/(c*e^2*x^2+b*e^2*x+a*e^2)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*(e*x+d)^(1/2)*c^3*d^4-3*e^5/(c*e^2*x^2+b*e^2*x+a*e^2)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*(e*x+d)^(1/2)*a^2*c-9/4*e^3/(16*a^2*c^2-8*a*b^2*c+b^4)*c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2-12*e/(16*a^2*c^2-8*a*b^2*c+b^4)*c^3/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d^2-3*e^3/(16*a^2*c^2-8*a*b^2*c+b^4)*c^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a-9/4*e^3/(16*a^2*c^2-8*a*b^2*c+b^4)*c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2+9*e^4/(c*e^2*x^2+b*e^2*x+a*e^2)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*(e*x+d)^(1/2)*a*b*c*d-12*e/(16*a^2*c^2-8*a*b^2*c+b^4)*c^3/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d^2-3*e^3/(16*a^2*c^2-8*a*b^2*c+b^4)*c^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a-3/4*e^5/(c*e^2*x^2+b*e^2*x+a*e^2)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*(e*x+d)^(1/2)*a*b^2+12*e^2/(c*e^2*x^2+b*e^2*x+a*e^2)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*(e*x+d)^(1/2)*b*c^2*d^3+18*e^2/(c*e^2*x^2+b*e^2*x+a*e^2)^2*c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*(e*x+d)^(5/2)*b*d-4*e^4/(c*e^2*x^2+b*e^2*x+a*e^2)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*(e*x+d)^(3/2)*a*b*c-3*e/(16*a^2*c^2-8*a*b^2*c+b^4)*c^2*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d-3/2*e^2/(16*a^2*c^2-8*a*b^2*c+b^4)*c*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b+8*e^3/(c*e^2*x^2+b*e^2*x+a*e^2)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*(e*x+d)^(3/2)*c^2*a*d+23/2*e^3/(c*e^2*x^2+b*e^2*x+a*e^2)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*(e*x+d)^(3/2)*b^2*c*d-27*e^2/(c*e^2*x^2+b*e^2*x+a*e^2)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*(e*x+d)^(3/2)*b*c^2*d^2-9*e^3/(c*e^2*x^2+b*e^2*x+a*e^2)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*(e*x+d)^(1/2)*a*c^2*d^2-5/4*e^4/(c*e^2*x^2+b*e^2*x+a*e^2)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*(e*x+d)^(3/2)*b^3+3*e/(16*a^2*c^2-8*a*b^2*c+b^4)*c^2*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d-27/4*e^3/(c*e^2*x^2+b*e^2*x+a*e^2)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*(e*x+d)^(1/2)*b^2*c*d^2+3/2*e^2/(16*a^2*c^2-8*a*b^2*c+b^4)*c*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b","B"
2305,1,3360,566,0.985000," ","int((e*x+d)^(1/2)/(c*x^2+b*x+a)^3,x)","\text{output too large to display}"," ",0,"6*e*c^2/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)^2/(e*x+1/2*b/c*e-1/2*((-4*a*c+b^2)*e^2)^(1/2)/c)^2*(-4*a*c*e^2+b^2*e^2)^(1/2)/(-b*e+2*c*d+(-4*a*c*e^2+b^2*e^2)^(1/2))*(e*x+d)^(3/2)*d-3*e^2*c/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)^2/(e*x+1/2*b/c*e-1/2*((-4*a*c+b^2)*e^2)^(1/2)/c)^2*(-4*a*c*e^2+b^2*e^2)^(1/2)/(-b*e+2*c*d+(-4*a*c*e^2+b^2*e^2)^(1/2))*(e*x+d)^(3/2)*b+7/4*e^3/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)^2/(e*x+1/2*b/c*e+1/2*((-4*a*c+b^2)*e^2)^(1/2)/c)^2*(e*x+d)^(1/2)*b^2+40*e^3*c^3/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)^2/(-4*b*e+8*c*d+4*(-4*a*c*e^2+b^2*e^2)^(1/2))*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a-34*e^3*c^2/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)^2/(-4*b*e+8*c*d+4*(-4*a*c*e^2+b^2*e^2)^(1/2))*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2-96*e*c^4/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)^2/(-4*b*e+8*c*d+4*(-4*a*c*e^2+b^2*e^2)^(1/2))*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d^2-3*e^2*c/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)^2/(e*x+1/2*b/c*e+1/2*((-4*a*c+b^2)*e^2)^(1/2)/c)^2*(-4*a*c*e^2+b^2*e^2)^(1/2)/(-b*e+2*c*d-(-4*a*c*e^2+b^2*e^2)^(1/2))*(e*x+d)^(3/2)*b+6*e*c^2/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)^2/(e*x+1/2*b/c*e+1/2*((-4*a*c+b^2)*e^2)^(1/2)/c)^2*(-4*a*c*e^2+b^2*e^2)^(1/2)/(-b*e+2*c*d-(-4*a*c*e^2+b^2*e^2)^(1/2))*(e*x+d)^(3/2)*d-40*e^3*c^3/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)^2/(4*b*e-8*c*d+4*(-4*a*c*e^2+b^2*e^2)^(1/2))*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a+34*e^3*c^2/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)^2/(4*b*e-8*c*d+4*(-4*a*c*e^2+b^2*e^2)^(1/2))*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2+96*e*c^4/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)^2/(4*b*e-8*c*d+4*(-4*a*c*e^2+b^2*e^2)^(1/2))*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d^2-10*e^3*c^2/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)^2/(e*x+1/2*b/c*e-1/2*((-4*a*c+b^2)*e^2)^(1/2)/c)^2/(-b*e+2*c*d+(-4*a*c*e^2+b^2*e^2)^(1/2))*(e*x+d)^(3/2)*a+5/2*e^3*c/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)^2/(e*x+1/2*b/c*e-1/2*((-4*a*c+b^2)*e^2)^(1/2)/c)^2/(-b*e+2*c*d+(-4*a*c*e^2+b^2*e^2)^(1/2))*(e*x+d)^(3/2)*b^2+10*e^3*c^2/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)^2/(e*x+1/2*b/c*e+1/2*((-4*a*c+b^2)*e^2)^(1/2)/c)^2/(-b*e+2*c*d-(-4*a*c*e^2+b^2*e^2)^(1/2))*(e*x+d)^(3/2)*a-5/2*e^3*c/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)^2/(e*x+1/2*b/c*e+1/2*((-4*a*c+b^2)*e^2)^(1/2)/c)^2/(-b*e+2*c*d-(-4*a*c*e^2+b^2*e^2)^(1/2))*(e*x+d)^(3/2)*b^2-3*e*c/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)^2/(e*x+1/2*b/c*e-1/2*((-4*a*c+b^2)*e^2)^(1/2)/c)^2*(-4*a*c*e^2+b^2*e^2)^(1/2)*(e*x+d)^(1/2)*d-3*e*c/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)^2/(e*x+1/2*b/c*e+1/2*((-4*a*c+b^2)*e^2)^(1/2)/c)^2*(-4*a*c*e^2+b^2*e^2)^(1/2)*(e*x+d)^(1/2)*d+36*e^2*c^2/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)^2/(-4*b*e+8*c*d+4*(-4*a*c*e^2+b^2*e^2)^(1/2))*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*(-4*a*c*e^2+b^2*e^2)^(1/2)-72*e*c^3/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)^2/(-4*b*e+8*c*d+4*(-4*a*c*e^2+b^2*e^2)^(1/2))*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d*(-4*a*c*e^2+b^2*e^2)^(1/2)-96*e^2*c^3/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)^2/(4*b*e-8*c*d+4*(-4*a*c*e^2+b^2*e^2)^(1/2))*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*d+36*e^2*c^2/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)^2/(4*b*e-8*c*d+4*(-4*a*c*e^2+b^2*e^2)^(1/2))*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*(-4*a*c*e^2+b^2*e^2)^(1/2)-72*e*c^3/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)^2/(4*b*e-8*c*d+4*(-4*a*c*e^2+b^2*e^2)^(1/2))*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d*(-4*a*c*e^2+b^2*e^2)^(1/2)+96*e^2*c^3/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)^2/(-4*b*e+8*c*d+4*(-4*a*c*e^2+b^2*e^2)^(1/2))*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*d-7/4*e^3/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)^2/(e*x+1/2*b/c*e-1/2*((-4*a*c+b^2)*e^2)^(1/2)/c)^2*(e*x+d)^(1/2)*b^2+3/2*e^2/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)^2/(e*x+1/2*b/c*e+1/2*((-4*a*c+b^2)*e^2)^(1/2)/c)^2*(-4*a*c*e^2+b^2*e^2)^(1/2)*(e*x+d)^(1/2)*b+3/2*e^2/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)^2/(e*x+1/2*b/c*e-1/2*((-4*a*c+b^2)*e^2)^(1/2)/c)^2*(-4*a*c*e^2+b^2*e^2)^(1/2)*(e*x+d)^(1/2)*b+7*e^3*c/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)^2/(e*x+1/2*b/c*e-1/2*((-4*a*c+b^2)*e^2)^(1/2)/c)^2*(e*x+d)^(1/2)*a-7*e^3*c/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)^2/(e*x+1/2*b/c*e+1/2*((-4*a*c+b^2)*e^2)^(1/2)/c)^2*(e*x+d)^(1/2)*a","B"
2306,1,4488,758,0.698000," ","int(1/(e*x+d)^(1/2)/(c*x^2+b*x+a)^3,x)","\text{output too large to display}"," ",0,"-3*e^2*c^2/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)^2/(e*x+1/2*b/c*e-1/2*((-4*a*c+b^2)*e^2)^(1/2)/c)^2*(-4*a*c*e^2+b^2*e^2)^(1/2)/(-2*a*c*e^2+b^2*e^2-2*b*c*d*e+2*c^2*d^2-b*e*(-4*a*c*e^2+b^2*e^2)^(1/2)+2*d*(-4*a*c*e^2+b^2*e^2)^(1/2)*c)*(e*x+d)^(3/2)*b+3*e^2*c/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)^2/(e*x+1/2*b/c*e-1/2*((-4*a*c+b^2)*e^2)^(1/2)/c)^2*(-4*a*c*e^2+b^2*e^2)^(1/2)/(-b*e+2*c*d+(-4*a*c*e^2+b^2*e^2)^(1/2))*(e*x+d)^(1/2)*b-6*e*c^2/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)^2/(e*x+1/2*b/c*e-1/2*((-4*a*c+b^2)*e^2)^(1/2)/c)^2*(-4*a*c*e^2+b^2*e^2)^(1/2)/(-b*e+2*c*d+(-4*a*c*e^2+b^2*e^2)^(1/2))*(e*x+d)^(1/2)*d-168*e^3*c^4/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)^2/(8*a*c*e^2-4*b^2*e^2+8*b*c*d*e-8*c^2*d^2+4*b*e*(-4*a*c*e^2+b^2*e^2)^(1/2)-8*d*(-4*a*c*e^2+b^2*e^2)^(1/2)*c)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a+96*e*c^5/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)^2/(8*a*c*e^2-4*b^2*e^2+8*b*c*d*e-8*c^2*d^2+4*b*e*(-4*a*c*e^2+b^2*e^2)^(1/2)-8*d*(-4*a*c*e^2+b^2*e^2)^(1/2)*c)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d^2-3*e^2*c^2/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)^2/(e*x+1/2*b/c*e+1/2*((-4*a*c+b^2)*e^2)^(1/2)/c)^2*(-4*a*c*e^2+b^2*e^2)^(1/2)/(-2*a*c*e^2+b^2*e^2-2*b*c*d*e+2*c^2*d^2+b*e*(-4*a*c*e^2+b^2*e^2)^(1/2)-2*d*(-4*a*c*e^2+b^2*e^2)^(1/2)*c)*(e*x+d)^(3/2)*b+3*e^2*c/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)^2/(e*x+1/2*b/c*e+1/2*((-4*a*c+b^2)*e^2)^(1/2)/c)^2*(-4*a*c*e^2+b^2*e^2)^(1/2)/(-b*e+2*c*d-(-4*a*c*e^2+b^2*e^2)^(1/2))*(e*x+d)^(1/2)*b+96*e^2*c^4/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)^2/(-8*a*c*e^2+4*b^2*e^2-8*b*c*d*e+8*c^2*d^2+4*b*e*(-4*a*c*e^2+b^2*e^2)^(1/2)-8*d*(-4*a*c*e^2+b^2*e^2)^(1/2)*c)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*d-60*e^2*c^3/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)^2/(8*a*c*e^2-4*b^2*e^2+8*b*c*d*e-8*c^2*d^2+4*b*e*(-4*a*c*e^2+b^2*e^2)^(1/2)-8*d*(-4*a*c*e^2+b^2*e^2)^(1/2)*c)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*(-4*a*c*e^2+b^2*e^2)^(1/2)-60*e^2*c^3/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)^2/(-8*a*c*e^2+4*b^2*e^2-8*b*c*d*e+8*c^2*d^2+4*b*e*(-4*a*c*e^2+b^2*e^2)^(1/2)-8*d*(-4*a*c*e^2+b^2*e^2)^(1/2)*c)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*(-4*a*c*e^2+b^2*e^2)^(1/2)-18*e^3*c^3/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)^2/(e*x+1/2*b/c*e-1/2*((-4*a*c+b^2)*e^2)^(1/2)/c)^2/(-2*a*c*e^2+b^2*e^2-2*b*c*d*e+2*c^2*d^2-b*e*(-4*a*c*e^2+b^2*e^2)^(1/2)+2*d*(-4*a*c*e^2+b^2*e^2)^(1/2)*c)*(e*x+d)^(3/2)*a+9/2*e^3*c^2/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)^2/(e*x+1/2*b/c*e-1/2*((-4*a*c+b^2)*e^2)^(1/2)/c)^2/(-2*a*c*e^2+b^2*e^2-2*b*c*d*e+2*c^2*d^2-b*e*(-4*a*c*e^2+b^2*e^2)^(1/2)+2*d*(-4*a*c*e^2+b^2*e^2)^(1/2)*c)*(e*x+d)^(3/2)*b^2+22*e^3*c^2/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)^2/(e*x+1/2*b/c*e-1/2*((-4*a*c+b^2)*e^2)^(1/2)/c)^2/(-b*e+2*c*d+(-4*a*c*e^2+b^2*e^2)^(1/2))*(e*x+d)^(1/2)*a-11/2*e^3*c/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)^2/(e*x+1/2*b/c*e-1/2*((-4*a*c+b^2)*e^2)^(1/2)/c)^2/(-b*e+2*c*d+(-4*a*c*e^2+b^2*e^2)^(1/2))*(e*x+d)^(1/2)*b^2+18*e^3*c^3/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)^2/(e*x+1/2*b/c*e+1/2*((-4*a*c+b^2)*e^2)^(1/2)/c)^2/(-2*a*c*e^2+b^2*e^2-2*b*c*d*e+2*c^2*d^2+b*e*(-4*a*c*e^2+b^2*e^2)^(1/2)-2*d*(-4*a*c*e^2+b^2*e^2)^(1/2)*c)*(e*x+d)^(3/2)*a-9/2*e^3*c^2/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)^2/(e*x+1/2*b/c*e+1/2*((-4*a*c+b^2)*e^2)^(1/2)/c)^2/(-2*a*c*e^2+b^2*e^2-2*b*c*d*e+2*c^2*d^2+b*e*(-4*a*c*e^2+b^2*e^2)^(1/2)-2*d*(-4*a*c*e^2+b^2*e^2)^(1/2)*c)*(e*x+d)^(3/2)*b^2-22*e^3*c^2/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)^2/(e*x+1/2*b/c*e+1/2*((-4*a*c+b^2)*e^2)^(1/2)/c)^2/(-b*e+2*c*d-(-4*a*c*e^2+b^2*e^2)^(1/2))*(e*x+d)^(1/2)*a+11/2*e^3*c/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)^2/(e*x+1/2*b/c*e+1/2*((-4*a*c+b^2)*e^2)^(1/2)/c)^2/(-b*e+2*c*d-(-4*a*c*e^2+b^2*e^2)^(1/2))*(e*x+d)^(1/2)*b^2-6*e*c^2/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)^2/(e*x+1/2*b/c*e+1/2*((-4*a*c+b^2)*e^2)^(1/2)/c)^2*(-4*a*c*e^2+b^2*e^2)^(1/2)/(-b*e+2*c*d-(-4*a*c*e^2+b^2*e^2)^(1/2))*(e*x+d)^(1/2)*d+168*e^3*c^4/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)^2/(-8*a*c*e^2+4*b^2*e^2-8*b*c*d*e+8*c^2*d^2+4*b*e*(-4*a*c*e^2+b^2*e^2)^(1/2)-8*d*(-4*a*c*e^2+b^2*e^2)^(1/2)*c)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a-96*e*c^5/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)^2/(-8*a*c*e^2+4*b^2*e^2-8*b*c*d*e+8*c^2*d^2+4*b*e*(-4*a*c*e^2+b^2*e^2)^(1/2)-8*d*(-4*a*c*e^2+b^2*e^2)^(1/2)*c)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d^2+6*e*c^3/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)^2/(e*x+1/2*b/c*e+1/2*((-4*a*c+b^2)*e^2)^(1/2)/c)^2*(-4*a*c*e^2+b^2*e^2)^(1/2)/(-2*a*c*e^2+b^2*e^2-2*b*c*d*e+2*c^2*d^2+b*e*(-4*a*c*e^2+b^2*e^2)^(1/2)-2*d*(-4*a*c*e^2+b^2*e^2)^(1/2)*c)*(e*x+d)^(3/2)*d-66*e^3*c^3/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)^2/(-8*a*c*e^2+4*b^2*e^2-8*b*c*d*e+8*c^2*d^2+4*b*e*(-4*a*c*e^2+b^2*e^2)^(1/2)-8*d*(-4*a*c*e^2+b^2*e^2)^(1/2)*c)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2+66*e^3*c^3/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)^2/(8*a*c*e^2-4*b^2*e^2+8*b*c*d*e-8*c^2*d^2+4*b*e*(-4*a*c*e^2+b^2*e^2)^(1/2)-8*d*(-4*a*c*e^2+b^2*e^2)^(1/2)*c)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2+6*e*c^3/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)^2/(e*x+1/2*b/c*e-1/2*((-4*a*c+b^2)*e^2)^(1/2)/c)^2*(-4*a*c*e^2+b^2*e^2)^(1/2)/(-2*a*c*e^2+b^2*e^2-2*b*c*d*e+2*c^2*d^2-b*e*(-4*a*c*e^2+b^2*e^2)^(1/2)+2*d*(-4*a*c*e^2+b^2*e^2)^(1/2)*c)*(e*x+d)^(3/2)*d+120*e*c^4/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)^2/(-8*a*c*e^2+4*b^2*e^2-8*b*c*d*e+8*c^2*d^2+4*b*e*(-4*a*c*e^2+b^2*e^2)^(1/2)-8*d*(-4*a*c*e^2+b^2*e^2)^(1/2)*c)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d*(-4*a*c*e^2+b^2*e^2)^(1/2)+120*e*c^4/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)^2/(8*a*c*e^2-4*b^2*e^2+8*b*c*d*e-8*c^2*d^2+4*b*e*(-4*a*c*e^2+b^2*e^2)^(1/2)-8*d*(-4*a*c*e^2+b^2*e^2)^(1/2)*c)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d*(-4*a*c*e^2+b^2*e^2)^(1/2)-96*e^2*c^4/(-(4*a*c-b^2)*e^2)^(1/2)/(4*a*c-b^2)^2/(8*a*c*e^2-4*b^2*e^2+8*b*c*d*e-8*c^2*d^2+4*b*e*(-4*a*c*e^2+b^2*e^2)^(1/2)-8*d*(-4*a*c*e^2+b^2*e^2)^(1/2)*c)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*d","B"
2307,1,609,515,0.627000," ","int((e*x+d)^(1/2)/(a+I*b*x+c*x^2),x)","\frac{e \arctan \left(\frac{2 \sqrt{e x +d}\, \sqrt{c}-\sqrt{-i b e +2 c d +2 \sqrt{-\left(i b d e -a \,e^{2}-c \,d^{2}\right) c}}}{\sqrt{i b e -2 c d +4 \sqrt{-i b d e +a \,e^{2}+c \,d^{2}}\, \sqrt{c}-2 \sqrt{-\left(i b d e -a \,e^{2}-c \,d^{2}\right) c}}}\right)}{\sqrt{i b e -2 c d +4 \sqrt{-i b d e +a \,e^{2}+c \,d^{2}}\, \sqrt{c}-2 \sqrt{-\left(i b d e -a \,e^{2}-c \,d^{2}\right) c}}\, \sqrt{c}}+\frac{e \arctan \left(\frac{2 \sqrt{e x +d}\, \sqrt{c}+\sqrt{-i b e +2 c d +2 \sqrt{-\left(i b d e -a \,e^{2}-c \,d^{2}\right) c}}}{\sqrt{i b e -2 c d +4 \sqrt{-i b d e +a \,e^{2}+c \,d^{2}}\, \sqrt{c}-2 \sqrt{-\left(i b d e -a \,e^{2}-c \,d^{2}\right) c}}}\right)}{\sqrt{i b e -2 c d +4 \sqrt{-i b d e +a \,e^{2}+c \,d^{2}}\, \sqrt{c}-2 \sqrt{-\left(i b d e -a \,e^{2}-c \,d^{2}\right) c}}\, \sqrt{c}}+\frac{e \ln \left(\left(e x +d \right) \sqrt{c}-\sqrt{e x +d}\, \sqrt{-i b e +2 c d +2 \sqrt{-\left(i b d e -a \,e^{2}-c \,d^{2}\right) c}}+\sqrt{-i b d e +a \,e^{2}+c \,d^{2}}\right)}{2 \sqrt{-i b e +2 c d +2 \sqrt{-\left(i b d e -a \,e^{2}-c \,d^{2}\right) c}}\, \sqrt{c}}-\frac{e \ln \left(\left(e x +d \right) \sqrt{c}+\sqrt{e x +d}\, \sqrt{-i b e +2 c d +2 \sqrt{-\left(i b d e -a \,e^{2}-c \,d^{2}\right) c}}+\sqrt{-i b d e +a \,e^{2}+c \,d^{2}}\right)}{2 \sqrt{-i b e +2 c d +2 \sqrt{-\left(i b d e -a \,e^{2}-c \,d^{2}\right) c}}\, \sqrt{c}}"," ",0,"-1/2*e/(2*(-c*(I*b*d*e-a*e^2-c*d^2))^(1/2)-I*b*e+2*c*d)^(1/2)/c^(1/2)*ln((e*x+d)*c^(1/2)+(e*x+d)^(1/2)*(2*(-c*(I*b*d*e-a*e^2-c*d^2))^(1/2)-I*b*e+2*c*d)^(1/2)+(-I*b*d*e+a*e^2+c*d^2)^(1/2))+e/c^(1/2)/(4*c^(1/2)*(-I*b*d*e+a*e^2+c*d^2)^(1/2)-2*(-c*(I*b*d*e-a*e^2-c*d^2))^(1/2)+I*b*e-2*c*d)^(1/2)*arctan((2*(e*x+d)^(1/2)*c^(1/2)+(2*(-c*(I*b*d*e-a*e^2-c*d^2))^(1/2)-I*b*e+2*c*d)^(1/2))/(4*c^(1/2)*(-I*b*d*e+a*e^2+c*d^2)^(1/2)-2*(-c*(I*b*d*e-a*e^2-c*d^2))^(1/2)+I*b*e-2*c*d)^(1/2))+1/2*e/(2*(-c*(I*b*d*e-a*e^2-c*d^2))^(1/2)-I*b*e+2*c*d)^(1/2)/c^(1/2)*ln((e*x+d)*c^(1/2)-(e*x+d)^(1/2)*(2*(-c*(I*b*d*e-a*e^2-c*d^2))^(1/2)-I*b*e+2*c*d)^(1/2)+(-I*b*d*e+a*e^2+c*d^2)^(1/2))+e/c^(1/2)/(4*c^(1/2)*(-I*b*d*e+a*e^2+c*d^2)^(1/2)-2*(-c*(I*b*d*e-a*e^2-c*d^2))^(1/2)+I*b*e-2*c*d)^(1/2)*arctan((2*(e*x+d)^(1/2)*c^(1/2)-(2*(-c*(I*b*d*e-a*e^2-c*d^2))^(1/2)-I*b*e+2*c*d)^(1/2))/(4*c^(1/2)*(-I*b*d*e+a*e^2+c*d^2)^(1/2)-2*(-c*(I*b*d*e-a*e^2-c*d^2))^(1/2)+I*b*e-2*c*d)^(1/2))","A"
2308,1,673,587,0.389000," ","int(1/(e*x+d)^(1/2)/(a+I*b*x+c*x^2),x)","\frac{e \arctan \left(\frac{2 \sqrt{e x +d}\, \sqrt{c}-\sqrt{-i b e +2 c d +2 \sqrt{-\left(i b d e -a \,e^{2}-c \,d^{2}\right) c}}}{\sqrt{i b e -2 c d +4 \sqrt{-i b d e +a \,e^{2}+c \,d^{2}}\, \sqrt{c}-2 \sqrt{-\left(i b d e -a \,e^{2}-c \,d^{2}\right) c}}}\right)}{\sqrt{-i b d e +a \,e^{2}+c \,d^{2}}\, \sqrt{i b e -2 c d +4 \sqrt{-i b d e +a \,e^{2}+c \,d^{2}}\, \sqrt{c}-2 \sqrt{-\left(i b d e -a \,e^{2}-c \,d^{2}\right) c}}}+\frac{e \arctan \left(\frac{2 \sqrt{e x +d}\, \sqrt{c}+\sqrt{-i b e +2 c d +2 \sqrt{-\left(i b d e -a \,e^{2}-c \,d^{2}\right) c}}}{\sqrt{i b e -2 c d +4 \sqrt{-i b d e +a \,e^{2}+c \,d^{2}}\, \sqrt{c}-2 \sqrt{-\left(i b d e -a \,e^{2}-c \,d^{2}\right) c}}}\right)}{\sqrt{-i b d e +a \,e^{2}+c \,d^{2}}\, \sqrt{i b e -2 c d +4 \sqrt{-i b d e +a \,e^{2}+c \,d^{2}}\, \sqrt{c}-2 \sqrt{-\left(i b d e -a \,e^{2}-c \,d^{2}\right) c}}}-\frac{e \ln \left(\left(e x +d \right) \sqrt{c}-\sqrt{e x +d}\, \sqrt{-i b e +2 c d +2 \sqrt{-\left(i b d e -a \,e^{2}-c \,d^{2}\right) c}}+\sqrt{-i b d e +a \,e^{2}+c \,d^{2}}\right)}{2 \sqrt{-i b e +2 c d +2 \sqrt{-\left(i b d e -a \,e^{2}-c \,d^{2}\right) c}}\, \sqrt{-i b d e +a \,e^{2}+c \,d^{2}}}+\frac{e \ln \left(\left(e x +d \right) \sqrt{c}+\sqrt{e x +d}\, \sqrt{-i b e +2 c d +2 \sqrt{-\left(i b d e -a \,e^{2}-c \,d^{2}\right) c}}+\sqrt{-i b d e +a \,e^{2}+c \,d^{2}}\right)}{2 \sqrt{-i b e +2 c d +2 \sqrt{-\left(i b d e -a \,e^{2}-c \,d^{2}\right) c}}\, \sqrt{-i b d e +a \,e^{2}+c \,d^{2}}}"," ",0,"1/2*e/(-I*b*e+2*c*d+2*(-(-a*e^2+I*b*d*e-c*d^2)*c)^(1/2))^(1/2)/(a*e^2-I*b*d*e+c*d^2)^(1/2)*ln((e*x+d)*c^(1/2)+(e*x+d)^(1/2)*(-I*b*e+2*c*d+2*(-(-a*e^2+I*b*d*e-c*d^2)*c)^(1/2))^(1/2)+(a*e^2-I*b*d*e+c*d^2)^(1/2))+e/(a*e^2-I*b*d*e+c*d^2)^(1/2)/(I*b*e-2*c*d+4*(a*e^2-I*b*d*e+c*d^2)^(1/2)*c^(1/2)-2*(-(-a*e^2+I*b*d*e-c*d^2)*c)^(1/2))^(1/2)*arctan((2*(e*x+d)^(1/2)*c^(1/2)+(-I*b*e+2*c*d+2*(-(-a*e^2+I*b*d*e-c*d^2)*c)^(1/2))^(1/2))/(I*b*e-2*c*d+4*(a*e^2-I*b*d*e+c*d^2)^(1/2)*c^(1/2)-2*(-(-a*e^2+I*b*d*e-c*d^2)*c)^(1/2))^(1/2))-1/2*e/(-I*b*e+2*c*d+2*(-(-a*e^2+I*b*d*e-c*d^2)*c)^(1/2))^(1/2)/(a*e^2-I*b*d*e+c*d^2)^(1/2)*ln((e*x+d)*c^(1/2)-(e*x+d)^(1/2)*(-I*b*e+2*c*d+2*(-(-a*e^2+I*b*d*e-c*d^2)*c)^(1/2))^(1/2)+(a*e^2-I*b*d*e+c*d^2)^(1/2))+e/(a*e^2-I*b*d*e+c*d^2)^(1/2)/(I*b*e-2*c*d+4*(a*e^2-I*b*d*e+c*d^2)^(1/2)*c^(1/2)-2*(-(-a*e^2+I*b*d*e-c*d^2)*c)^(1/2))^(1/2)*arctan((2*(e*x+d)^(1/2)*c^(1/2)-(-I*b*e+2*c*d+2*(-(-a*e^2+I*b*d*e-c*d^2)*c)^(1/2))^(1/2))/(I*b*e-2*c*d+4*(a*e^2-I*b*d*e+c*d^2)^(1/2)*c^(1/2)-2*(-(-a*e^2+I*b*d*e-c*d^2)*c)^(1/2))^(1/2))","A"
2309,1,634,185,1.992000," ","int((2*x+1)^(7/2)/(5*x^2+3*x+2),x)","-\frac{178 \sqrt{5}\, \left(2 \sqrt{5}\, \sqrt{7}+4\right) \sqrt{7}\, \arctan \left(\frac{-\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{3875 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}-\frac{233 \left(2 \sqrt{5}\, \sqrt{7}+4\right) \arctan \left(\frac{-\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{3875 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}+\frac{76 \sqrt{5}\, \sqrt{7}\, \arctan \left(\frac{-\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{125 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}-\frac{178 \sqrt{5}\, \left(2 \sqrt{5}\, \sqrt{7}+4\right) \sqrt{7}\, \arctan \left(\frac{\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{3875 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}-\frac{233 \left(2 \sqrt{5}\, \sqrt{7}+4\right) \arctan \left(\frac{\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{3875 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}+\frac{76 \sqrt{5}\, \sqrt{7}\, \arctan \left(\frac{\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{125 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}-\frac{89 \sqrt{7}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}-\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{3875}-\frac{233 \sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}-\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{38750}+\frac{89 \sqrt{7}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}+\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{3875}+\frac{233 \sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}+\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{38750}+\frac{4 \left(2 x +1\right)^{\frac{5}{2}}}{25}+\frac{16 \left(2 x +1\right)^{\frac{3}{2}}}{75}-\frac{76 \sqrt{2 x +1}}{125}"," ",0,"4/25*(2*x+1)^(5/2)+16/75*(2*x+1)^(3/2)-76/125*(2*x+1)^(1/2)+89/3875*ln(5^(1/2)*7^(1/2)+(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+10*x+5)*7^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+233/38750*ln(5^(1/2)*7^(1/2)+(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+10*x+5)*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)-178/3875/(10*5^(1/2)*7^(1/2)-20)^(1/2)*arctan((5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)*7^(1/2)-233/3875/(10*5^(1/2)*7^(1/2)-20)^(1/2)*arctan((5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))*(2*5^(1/2)*7^(1/2)+4)+76/125/(10*5^(1/2)*7^(1/2)-20)^(1/2)*arctan((5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))*5^(1/2)*7^(1/2)-89/3875*ln(5^(1/2)*7^(1/2)-(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+10*x+5)*7^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)-233/38750*ln(5^(1/2)*7^(1/2)-(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+10*x+5)*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)-178/3875/(10*5^(1/2)*7^(1/2)-20)^(1/2)*arctan((-5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)*7^(1/2)-233/3875/(10*5^(1/2)*7^(1/2)-20)^(1/2)*arctan((-5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))*(2*5^(1/2)*7^(1/2)+4)+76/125/(10*5^(1/2)*7^(1/2)-20)^(1/2)*arctan((-5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))*5^(1/2)*7^(1/2)","B"
2310,1,625,176,0.317000," ","int((2*x+1)^(5/2)/(5*x^2+3*x+2),x)","\frac{178 \left(2 \sqrt{5}\, \sqrt{7}+4\right) \arctan \left(\frac{-\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{775 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}-\frac{27 \sqrt{5}\, \left(2 \sqrt{5}\, \sqrt{7}+4\right) \sqrt{7}\, \arctan \left(\frac{-\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{775 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}-\frac{16 \sqrt{5}\, \sqrt{7}\, \arctan \left(\frac{-\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{25 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}+\frac{178 \left(2 \sqrt{5}\, \sqrt{7}+4\right) \arctan \left(\frac{\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{775 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}-\frac{27 \sqrt{5}\, \left(2 \sqrt{5}\, \sqrt{7}+4\right) \sqrt{7}\, \arctan \left(\frac{\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{775 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}-\frac{16 \sqrt{5}\, \sqrt{7}\, \arctan \left(\frac{\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{25 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}+\frac{89 \sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}-\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{3875}-\frac{27 \sqrt{7}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}-\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{1550}-\frac{89 \sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}+\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{3875}+\frac{27 \sqrt{7}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}+\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{1550}+\frac{4 \left(2 x +1\right)^{\frac{3}{2}}}{15}+\frac{16 \sqrt{2 x +1}}{25}"," ",0,"4/15*(2*x+1)^(3/2)+16/25*(2*x+1)^(1/2)-89/3875*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)+(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)+27/1550*7^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)+(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)+178/775/(10*5^(1/2)*7^(1/2)-20)^(1/2)*(2*5^(1/2)*7^(1/2)+4)*arctan((5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))-27/775/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)*7^(1/2)*arctan((5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))-16/25/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*7^(1/2)*arctan((5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))+89/3875*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)-(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)-27/1550*7^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)-(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)+178/775/(10*5^(1/2)*7^(1/2)-20)^(1/2)*(2*5^(1/2)*7^(1/2)+4)*arctan((-5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))-27/775/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)*7^(1/2)*arctan((-5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))-16/25/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*7^(1/2)*arctan((-5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))","B"
2311,1,616,167,0.142000," ","int((2*x+1)^(3/2)/(5*x^2+3*x+2),x)","\frac{27 \left(2 \sqrt{5}\, \sqrt{7}+4\right) \arctan \left(\frac{-\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{155 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}+\frac{2 \sqrt{5}\, \left(2 \sqrt{5}\, \sqrt{7}+4\right) \sqrt{7}\, \arctan \left(\frac{-\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{155 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}-\frac{4 \sqrt{5}\, \sqrt{7}\, \arctan \left(\frac{-\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{5 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}+\frac{27 \left(2 \sqrt{5}\, \sqrt{7}+4\right) \arctan \left(\frac{\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{155 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}+\frac{2 \sqrt{5}\, \left(2 \sqrt{5}\, \sqrt{7}+4\right) \sqrt{7}\, \arctan \left(\frac{\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{155 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}-\frac{4 \sqrt{5}\, \sqrt{7}\, \arctan \left(\frac{\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{5 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}+\frac{27 \sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}-\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{1550}+\frac{\sqrt{7}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}-\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{155}-\frac{27 \sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}+\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{1550}-\frac{\sqrt{7}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}+\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{155}+\frac{4 \sqrt{2 x +1}}{5}"," ",0,"4/5*(2*x+1)^(1/2)-27/1550*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)+(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)-1/155*7^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)+(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)+27/155/(10*5^(1/2)*7^(1/2)-20)^(1/2)*(2*5^(1/2)*7^(1/2)+4)*arctan((5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))+2/155/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)*7^(1/2)*arctan((5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))-4/5/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*7^(1/2)*arctan((5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))+27/1550*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)-(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)+1/155*7^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)-(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)+27/155/(10*5^(1/2)*7^(1/2)-20)^(1/2)*(2*5^(1/2)*7^(1/2)+4)*arctan((-5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))+2/155/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)*7^(1/2)*arctan((-5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))-4/5/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*7^(1/2)*arctan((-5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))","B"
2312,1,486,159,0.376000," ","int((2*x+1)^(1/2)/(5*x^2+3*x+2),x)","-\frac{2 \left(2 \sqrt{5}\, \sqrt{7}+4\right) \arctan \left(\frac{-\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{31 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}+\frac{\sqrt{5}\, \left(2 \sqrt{5}\, \sqrt{7}+4\right) \sqrt{7}\, \arctan \left(\frac{-\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{31 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}-\frac{2 \left(2 \sqrt{5}\, \sqrt{7}+4\right) \arctan \left(\frac{\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{31 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}+\frac{\sqrt{5}\, \left(2 \sqrt{5}\, \sqrt{7}+4\right) \sqrt{7}\, \arctan \left(\frac{\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{31 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}-\frac{\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}-\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{155}+\frac{\sqrt{7}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}-\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{62}+\frac{\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}+\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{155}-\frac{\sqrt{7}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}+\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{62}"," ",0,"1/155*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)+(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)-2/31/(10*5^(1/2)*7^(1/2)-20)^(1/2)*(2*5^(1/2)*7^(1/2)+4)*arctan((5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))-1/62*7^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)+(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)+1/31/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)*7^(1/2)*arctan((5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))-1/155*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)-(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)-2/31/(10*5^(1/2)*7^(1/2)-20)^(1/2)*(2*5^(1/2)*7^(1/2)+4)*arctan((-5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))+1/62*7^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)-(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)+1/31/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)*7^(1/2)*arctan((-5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))","B"
2313,1,607,157,0.342000," ","int(1/(2*x+1)^(1/2)/(5*x^2+3*x+2),x)","-\frac{5 \left(2 \sqrt{5}\, \sqrt{7}+4\right) \arctan \left(\frac{-\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{31 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}+\frac{2 \sqrt{5}\, \left(2 \sqrt{5}\, \sqrt{7}+4\right) \sqrt{7}\, \arctan \left(\frac{-\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{217 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}+\frac{4 \sqrt{5}\, \sqrt{7}\, \arctan \left(\frac{-\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{7 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}-\frac{5 \left(2 \sqrt{5}\, \sqrt{7}+4\right) \arctan \left(\frac{\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{31 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}+\frac{2 \sqrt{5}\, \left(2 \sqrt{5}\, \sqrt{7}+4\right) \sqrt{7}\, \arctan \left(\frac{\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{217 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}+\frac{4 \sqrt{5}\, \sqrt{7}\, \arctan \left(\frac{\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{7 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}-\frac{\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}-\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{62}+\frac{\sqrt{7}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}-\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{217}+\frac{\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}+\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{62}-\frac{\sqrt{7}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}+\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{217}"," ",0,"1/62*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)+(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)-1/217*7^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)+(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)-5/31/(10*5^(1/2)*7^(1/2)-20)^(1/2)*(2*5^(1/2)*7^(1/2)+4)*arctan((5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))+2/217/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)*7^(1/2)*arctan((5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))+4/7/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*7^(1/2)*arctan((5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))-1/62*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)-(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)+1/217*7^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)-(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)-5/31/(10*5^(1/2)*7^(1/2)-20)^(1/2)*(2*5^(1/2)*7^(1/2)+4)*arctan((-5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))+2/217/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)*7^(1/2)*arctan((-5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))+4/7/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*7^(1/2)*arctan((-5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))","B"
2314,1,616,167,0.326000," ","int(1/(2*x+1)^(3/2)/(5*x^2+3*x+2),x)","-\frac{10 \left(2 \sqrt{5}\, \sqrt{7}+4\right) \arctan \left(\frac{-\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{217 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}-\frac{27 \sqrt{5}\, \left(2 \sqrt{5}\, \sqrt{7}+4\right) \sqrt{7}\, \arctan \left(\frac{-\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{1519 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}+\frac{16 \sqrt{5}\, \sqrt{7}\, \arctan \left(\frac{-\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{49 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}-\frac{10 \left(2 \sqrt{5}\, \sqrt{7}+4\right) \arctan \left(\frac{\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{217 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}-\frac{27 \sqrt{5}\, \left(2 \sqrt{5}\, \sqrt{7}+4\right) \sqrt{7}\, \arctan \left(\frac{\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{1519 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}+\frac{16 \sqrt{5}\, \sqrt{7}\, \arctan \left(\frac{\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{49 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}-\frac{\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}-\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{217}-\frac{27 \sqrt{7}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}-\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{3038}+\frac{\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}+\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{217}+\frac{27 \sqrt{7}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}+\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{3038}-\frac{4}{7 \sqrt{2 x +1}}"," ",0,"1/217*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)+(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)+27/3038*7^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)+(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)-10/217/(10*5^(1/2)*7^(1/2)-20)^(1/2)*(2*5^(1/2)*7^(1/2)+4)*arctan((5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))-27/1519/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)*7^(1/2)*arctan((5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))+16/49/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*7^(1/2)*arctan((5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))-1/217*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)-(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)-27/3038*7^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)-(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)-10/217/(10*5^(1/2)*7^(1/2)-20)^(1/2)*(2*5^(1/2)*7^(1/2)+4)*arctan((-5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))-27/1519/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)*7^(1/2)*arctan((-5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))+16/49/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*7^(1/2)*arctan((-5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))-4/7/(2*x+1)^(1/2)","B"
2315,1,625,176,0.159000," ","int(1/(2*x+1)^(5/2)/(5*x^2+3*x+2),x)","\frac{135 \left(2 \sqrt{5}\, \sqrt{7}+4\right) \arctan \left(\frac{-\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{1519 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}-\frac{178 \sqrt{5}\, \left(2 \sqrt{5}\, \sqrt{7}+4\right) \sqrt{7}\, \arctan \left(\frac{-\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{10633 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}-\frac{76 \sqrt{5}\, \sqrt{7}\, \arctan \left(\frac{-\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{343 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}+\frac{135 \left(2 \sqrt{5}\, \sqrt{7}+4\right) \arctan \left(\frac{\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{1519 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}-\frac{178 \sqrt{5}\, \left(2 \sqrt{5}\, \sqrt{7}+4\right) \sqrt{7}\, \arctan \left(\frac{\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{10633 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}-\frac{76 \sqrt{5}\, \sqrt{7}\, \arctan \left(\frac{\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{343 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}+\frac{27 \sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}-\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{3038}-\frac{89 \sqrt{7}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}-\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{10633}-\frac{27 \sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}+\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{3038}+\frac{89 \sqrt{7}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}+\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{10633}-\frac{4}{21 \left(2 x +1\right)^{\frac{3}{2}}}-\frac{16}{49 \sqrt{2 x +1}}"," ",0,"-27/3038*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)+(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)+89/10633*7^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)+(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)+135/1519/(10*5^(1/2)*7^(1/2)-20)^(1/2)*(2*5^(1/2)*7^(1/2)+4)*arctan((5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))-178/10633/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)*7^(1/2)*arctan((5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))-76/343/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*7^(1/2)*arctan((5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))+27/3038*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)-(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)-89/10633*7^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)-(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)+135/1519/(10*5^(1/2)*7^(1/2)-20)^(1/2)*(2*5^(1/2)*7^(1/2)+4)*arctan((-5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))-178/10633/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)*7^(1/2)*arctan((-5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))-76/343/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*7^(1/2)*arctan((-5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))-4/21/(2*x+1)^(3/2)-16/49/(2*x+1)^(1/2)","B"
2316,1,651,202,0.367000," ","int((2*x+1)^(7/2)/(5*x^2+3*x+2)^2,x)","\frac{3657 \left(2 \sqrt{5}\, \sqrt{7}+4\right) \arctan \left(\frac{-\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{24025 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}+\frac{512 \sqrt{5}\, \left(2 \sqrt{5}\, \sqrt{7}+4\right) \sqrt{7}\, \arctan \left(\frac{-\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{24025 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}-\frac{604 \sqrt{5}\, \sqrt{7}\, \arctan \left(\frac{-\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{775 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}+\frac{3657 \left(2 \sqrt{5}\, \sqrt{7}+4\right) \arctan \left(\frac{\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{24025 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}+\frac{512 \sqrt{5}\, \left(2 \sqrt{5}\, \sqrt{7}+4\right) \sqrt{7}\, \arctan \left(\frac{\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{24025 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}-\frac{604 \sqrt{5}\, \sqrt{7}\, \arctan \left(\frac{\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{775 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}+\frac{3657 \sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}-\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{240250}+\frac{256 \sqrt{7}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}-\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{24025}-\frac{3657 \sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}+\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{240250}-\frac{256 \sqrt{7}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}+\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{24025}+\frac{16 \sqrt{2 x +1}}{25}+\frac{-\frac{712 \left(2 x +1\right)^{\frac{3}{2}}}{3875}+\frac{756 \sqrt{2 x +1}}{3875}}{-\frac{8 x}{5}+\left(2 x +1\right)^{2}+\frac{3}{5}}"," ",0,"16/25*(2*x+1)^(1/2)+16/25*(-89/310*(2*x+1)^(3/2)+189/620*(2*x+1)^(1/2))/((2*x+1)^2-8/5*x+3/5)-3657/240250*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)+(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)-256/24025*7^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)+(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)+3657/24025/(10*5^(1/2)*7^(1/2)-20)^(1/2)*(2*5^(1/2)*7^(1/2)+4)*arctan((5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))+512/24025/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)*7^(1/2)*arctan((5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))-604/775/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*7^(1/2)*arctan((5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))+3657/240250*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)-(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)+256/24025*7^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)-(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)+3657/24025/(10*5^(1/2)*7^(1/2)-20)^(1/2)*(2*5^(1/2)*7^(1/2)+4)*arctan((-5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))+512/24025/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)*7^(1/2)*arctan((-5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))-604/775/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*7^(1/2)*arctan((-5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))","B"
2317,1,642,193,0.157000," ","int((2*x+1)^(5/2)/(5*x^2+3*x+2)^2,x)","-\frac{264 \left(2 \sqrt{5}\, \sqrt{7}+4\right) \arctan \left(\frac{-\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{4805 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}+\frac{101 \sqrt{5}\, \left(2 \sqrt{5}\, \sqrt{7}+4\right) \sqrt{7}\, \arctan \left(\frac{-\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{4805 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}+\frac{8 \sqrt{5}\, \sqrt{7}\, \arctan \left(\frac{-\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{155 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}-\frac{264 \left(2 \sqrt{5}\, \sqrt{7}+4\right) \arctan \left(\frac{\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{4805 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}+\frac{101 \sqrt{5}\, \left(2 \sqrt{5}\, \sqrt{7}+4\right) \sqrt{7}\, \arctan \left(\frac{\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{4805 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}+\frac{8 \sqrt{5}\, \sqrt{7}\, \arctan \left(\frac{\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{155 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}-\frac{132 \sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}-\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{24025}+\frac{101 \sqrt{7}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}-\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{9610}+\frac{132 \sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}+\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{24025}-\frac{101 \sqrt{7}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}+\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{9610}+\frac{-\frac{108 \left(2 x +1\right)^{\frac{3}{2}}}{775}-\frac{56 \sqrt{2 x +1}}{775}}{-\frac{8 x}{5}+\left(2 x +1\right)^{2}+\frac{3}{5}}"," ",0,"16*(-27/3100*(2*x+1)^(3/2)-7/1550*(2*x+1)^(1/2))/(-8/5*x+(2*x+1)^2+3/5)+132/24025*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)+(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)-101/9610*7^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)+(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)-264/4805/(10*5^(1/2)*7^(1/2)-20)^(1/2)*(2*5^(1/2)*7^(1/2)+4)*arctan((5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))+101/4805/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)*7^(1/2)*arctan((5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))+8/155/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*7^(1/2)*arctan((5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))-132/24025*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)-(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)+101/9610*7^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)-(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)-264/4805/(10*5^(1/2)*7^(1/2)-20)^(1/2)*(2*5^(1/2)*7^(1/2)+4)*arctan((-5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))+101/4805/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)*7^(1/2)*arctan((-5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))+8/155/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*7^(1/2)*arctan((-5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))","B"
2318,1,642,184,0.288000," ","int((2*x+1)^(3/2)/(5*x^2+3*x+2)^2,x)","-\frac{39 \left(2 \sqrt{5}\, \sqrt{7}+4\right) \arctan \left(\frac{-\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{961 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}+\frac{4 \sqrt{5}\, \left(2 \sqrt{5}\, \sqrt{7}+4\right) \sqrt{7}\, \arctan \left(\frac{-\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{961 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}+\frac{4 \sqrt{5}\, \sqrt{7}\, \arctan \left(\frac{-\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{31 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}-\frac{39 \left(2 \sqrt{5}\, \sqrt{7}+4\right) \arctan \left(\frac{\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{961 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}+\frac{4 \sqrt{5}\, \left(2 \sqrt{5}\, \sqrt{7}+4\right) \sqrt{7}\, \arctan \left(\frac{\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{961 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}+\frac{4 \sqrt{5}\, \sqrt{7}\, \arctan \left(\frac{\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{31 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}-\frac{39 \sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}-\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{9610}+\frac{2 \sqrt{7}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}-\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{961}+\frac{39 \sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}+\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{9610}-\frac{2 \sqrt{7}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}+\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{961}+\frac{\frac{8 \left(2 x +1\right)^{\frac{3}{2}}}{155}-\frac{28 \sqrt{2 x +1}}{155}}{-\frac{8 x}{5}+\left(2 x +1\right)^{2}+\frac{3}{5}}"," ",0,"16*(1/310*(2*x+1)^(3/2)-7/620*(2*x+1)^(1/2))/(-8/5*x+(2*x+1)^2+3/5)+39/9610*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)+(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)-2/961*7^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)+(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)-39/961/(10*5^(1/2)*7^(1/2)-20)^(1/2)*(2*5^(1/2)*7^(1/2)+4)*arctan((5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))+4/961/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)*7^(1/2)*arctan((5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))+4/31/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*7^(1/2)*arctan((5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))-39/9610*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)-(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)+2/961*7^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)-(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)-39/961/(10*5^(1/2)*7^(1/2)-20)^(1/2)*(2*5^(1/2)*7^(1/2)+4)*arctan((-5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))+4/961/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)*7^(1/2)*arctan((-5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))+4/31/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*7^(1/2)*arctan((-5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))","B"
2319,1,972,184,1.941000," ","int((2*x+1)^(1/2)/(5*x^2+3*x+2)^2,x)","\frac{218 \sqrt{20+10 \sqrt{35}}\, \sqrt{2 \sqrt{35}+4}\, \sqrt{35}\, \arctan \left(\frac{-\sqrt{20+10 \sqrt{35}}+10 \sqrt{2 x +1}}{\sqrt{-20+10 \sqrt{35}}}\right)}{6727 \left(2 \sqrt{5}-5 \sqrt{7}\right) \sqrt{-20+10 \sqrt{35}}}-\frac{235 \sqrt{20+10 \sqrt{35}}\, \sqrt{2 \sqrt{35}+4}\, \arctan \left(\frac{-\sqrt{20+10 \sqrt{35}}+10 \sqrt{2 x +1}}{\sqrt{-20+10 \sqrt{35}}}\right)}{961 \left(2 \sqrt{5}-5 \sqrt{7}\right) \sqrt{-20+10 \sqrt{35}}}-\frac{40 \sqrt{5}\, \arctan \left(\frac{-\sqrt{20+10 \sqrt{35}}+10 \sqrt{2 x +1}}{\sqrt{-20+10 \sqrt{35}}}\right)}{31 \left(2 \sqrt{5}-5 \sqrt{7}\right) \sqrt{-20+10 \sqrt{35}}}+\frac{80 \sqrt{7}\, \arctan \left(\frac{-\sqrt{20+10 \sqrt{35}}+10 \sqrt{2 x +1}}{\sqrt{-20+10 \sqrt{35}}}\right)}{217 \left(2 \sqrt{5}-5 \sqrt{7}\right) \sqrt{-20+10 \sqrt{35}}}+\frac{218 \sqrt{20+10 \sqrt{35}}\, \sqrt{2 \sqrt{35}+4}\, \sqrt{35}\, \arctan \left(\frac{10 \sqrt{2 x +1}+\sqrt{20+10 \sqrt{35}}}{\sqrt{-20+10 \sqrt{35}}}\right)}{6727 \left(2 \sqrt{5}-5 \sqrt{7}\right) \sqrt{-20+10 \sqrt{35}}}-\frac{235 \sqrt{20+10 \sqrt{35}}\, \sqrt{2 \sqrt{35}+4}\, \arctan \left(\frac{10 \sqrt{2 x +1}+\sqrt{20+10 \sqrt{35}}}{\sqrt{-20+10 \sqrt{35}}}\right)}{961 \left(2 \sqrt{5}-5 \sqrt{7}\right) \sqrt{-20+10 \sqrt{35}}}-\frac{40 \sqrt{5}\, \arctan \left(\frac{10 \sqrt{2 x +1}+\sqrt{20+10 \sqrt{35}}}{\sqrt{-20+10 \sqrt{35}}}\right)}{31 \left(2 \sqrt{5}-5 \sqrt{7}\right) \sqrt{-20+10 \sqrt{35}}}+\frac{80 \sqrt{7}\, \arctan \left(\frac{10 \sqrt{2 x +1}+\sqrt{20+10 \sqrt{35}}}{\sqrt{-20+10 \sqrt{35}}}\right)}{217 \left(2 \sqrt{5}-5 \sqrt{7}\right) \sqrt{-20+10 \sqrt{35}}}+\frac{109 \sqrt{2 \sqrt{35}+4}\, \sqrt{35}\, \ln \left(10 x +5+\sqrt{35}-\sqrt{2 x +1}\, \sqrt{20+10 \sqrt{35}}\right)}{6727 \left(2 \sqrt{5}-5 \sqrt{7}\right)}-\frac{235 \sqrt{2 \sqrt{35}+4}\, \ln \left(10 x +5+\sqrt{35}-\sqrt{2 x +1}\, \sqrt{20+10 \sqrt{35}}\right)}{1922 \left(2 \sqrt{5}-5 \sqrt{7}\right)}-\frac{109 \sqrt{2 \sqrt{35}+4}\, \sqrt{35}\, \ln \left(10 x +5+\sqrt{35}+\sqrt{2 x +1}\, \sqrt{20+10 \sqrt{35}}\right)}{6727 \left(2 \sqrt{5}-5 \sqrt{7}\right)}+\frac{235 \sqrt{2 \sqrt{35}+4}\, \ln \left(10 x +5+\sqrt{35}+\sqrt{2 x +1}\, \sqrt{20+10 \sqrt{35}}\right)}{1922 \left(2 \sqrt{5}-5 \sqrt{7}\right)}+\frac{\frac{2 \left(-5425 \sqrt{7}+2170 \sqrt{5}\right) \sqrt{2 x +1}}{33635 \left(2 \sqrt{5}-5 \sqrt{7}\right)}+\frac{5 \sqrt{7}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \left(-1085 \sqrt{5}+310 \sqrt{7}\right)}{6727 \left(50 \sqrt{5}-125 \sqrt{7}\right)}}{2 x +\frac{\sqrt{5}\, \sqrt{7}}{5}+\frac{\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}}{5}+1}-\frac{5 \left(-\frac{2 \left(-5425 \sqrt{7}+2170 \sqrt{5}\right) \sqrt{2 x +1}}{25 \left(2 \sqrt{5}-5 \sqrt{7}\right)}+\frac{\sqrt{7}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \left(-1085 \sqrt{5}+310 \sqrt{7}\right)}{50 \sqrt{5}-125 \sqrt{7}}\right)}{6727 \left(2 x +\frac{\sqrt{5}\, \sqrt{7}}{5}-\frac{\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}}{5}+1\right)}"," ",0,"5/6727*(2/25*(-5425*7^(1/2)+2170*5^(1/2))/(2*5^(1/2)-5*7^(1/2))*(2*x+1)^(1/2)+1/25*7^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*(-1085*5^(1/2)+310*7^(1/2))/(2*5^(1/2)-5*7^(1/2)))/(1/5*5^(1/2)*7^(1/2)+1/5*(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+2*x+1)-109/6727/(2*5^(1/2)-5*7^(1/2))*ln(10*x+5+35^(1/2)+(2*x+1)^(1/2)*(20+10*35^(1/2))^(1/2))*(2*35^(1/2)+4)^(1/2)*35^(1/2)+235/1922/(2*5^(1/2)-5*7^(1/2))*ln(10*x+5+35^(1/2)+(2*x+1)^(1/2)*(20+10*35^(1/2))^(1/2))*(2*35^(1/2)+4)^(1/2)+218/6727/(2*5^(1/2)-5*7^(1/2))/(-20+10*35^(1/2))^(1/2)*arctan((10*(2*x+1)^(1/2)+(20+10*35^(1/2))^(1/2))/(-20+10*35^(1/2))^(1/2))*(20+10*35^(1/2))^(1/2)*(2*35^(1/2)+4)^(1/2)*35^(1/2)-235/961/(2*5^(1/2)-5*7^(1/2))/(-20+10*35^(1/2))^(1/2)*arctan((10*(2*x+1)^(1/2)+(20+10*35^(1/2))^(1/2))/(-20+10*35^(1/2))^(1/2))*(20+10*35^(1/2))^(1/2)*(2*35^(1/2)+4)^(1/2)-40/31/(2*5^(1/2)-5*7^(1/2))/(-20+10*35^(1/2))^(1/2)*arctan((10*(2*x+1)^(1/2)+(20+10*35^(1/2))^(1/2))/(-20+10*35^(1/2))^(1/2))*5^(1/2)+80/217/(2*5^(1/2)-5*7^(1/2))/(-20+10*35^(1/2))^(1/2)*arctan((10*(2*x+1)^(1/2)+(20+10*35^(1/2))^(1/2))/(-20+10*35^(1/2))^(1/2))*7^(1/2)-5/6727*(-2/25*(-5425*7^(1/2)+2170*5^(1/2))/(2*5^(1/2)-5*7^(1/2))*(2*x+1)^(1/2)+1/25*7^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*(-1085*5^(1/2)+310*7^(1/2))/(2*5^(1/2)-5*7^(1/2)))/(1/5*5^(1/2)*7^(1/2)-1/5*(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+2*x+1)+109/6727/(2*5^(1/2)-5*7^(1/2))*ln(10*x+5+35^(1/2)-(2*x+1)^(1/2)*(20+10*35^(1/2))^(1/2))*(2*35^(1/2)+4)^(1/2)*35^(1/2)-235/1922/(2*5^(1/2)-5*7^(1/2))*ln(10*x+5+35^(1/2)-(2*x+1)^(1/2)*(20+10*35^(1/2))^(1/2))*(2*35^(1/2)+4)^(1/2)+218/6727/(2*5^(1/2)-5*7^(1/2))/(-20+10*35^(1/2))^(1/2)*arctan((-(20+10*35^(1/2))^(1/2)+10*(2*x+1)^(1/2))/(-20+10*35^(1/2))^(1/2))*(20+10*35^(1/2))^(1/2)*(2*35^(1/2)+4)^(1/2)*35^(1/2)-235/961/(2*5^(1/2)-5*7^(1/2))/(-20+10*35^(1/2))^(1/2)*arctan((-(20+10*35^(1/2))^(1/2)+10*(2*x+1)^(1/2))/(-20+10*35^(1/2))^(1/2))*(20+10*35^(1/2))^(1/2)*(2*35^(1/2)+4)^(1/2)-40/31/(2*5^(1/2)-5*7^(1/2))/(-20+10*35^(1/2))^(1/2)*arctan((-(20+10*35^(1/2))^(1/2)+10*(2*x+1)^(1/2))/(-20+10*35^(1/2))^(1/2))*5^(1/2)+80/217/(2*5^(1/2)-5*7^(1/2))/(-20+10*35^(1/2))^(1/2)*arctan((-(20+10*35^(1/2))^(1/2)+10*(2*x+1)^(1/2))/(-20+10*35^(1/2))^(1/2))*7^(1/2)","B"
2320,1,968,184,0.934000," ","int(1/(2*x+1)^(1/2)/(5*x^2+3*x+2)^2,x)","\frac{4063 \sqrt{20+10 \sqrt{35}}\, \sqrt{2 \sqrt{35}+4}\, \sqrt{35}\, \arctan \left(\frac{-\sqrt{20+10 \sqrt{35}}+10 \sqrt{2 x +1}}{\sqrt{-20+10 \sqrt{35}}}\right)}{47089 \left(2 \sqrt{5}-5 \sqrt{7}\right) \sqrt{-20+10 \sqrt{35}}}-\frac{2330 \sqrt{20+10 \sqrt{35}}\, \sqrt{2 \sqrt{35}+4}\, \arctan \left(\frac{-\sqrt{20+10 \sqrt{35}}+10 \sqrt{2 x +1}}{\sqrt{-20+10 \sqrt{35}}}\right)}{6727 \left(2 \sqrt{5}-5 \sqrt{7}\right) \sqrt{-20+10 \sqrt{35}}}-\frac{1940 \sqrt{5}\, \arctan \left(\frac{-\sqrt{20+10 \sqrt{35}}+10 \sqrt{2 x +1}}{\sqrt{-20+10 \sqrt{35}}}\right)}{217 \left(2 \sqrt{5}-5 \sqrt{7}\right) \sqrt{-20+10 \sqrt{35}}}+\frac{3880 \sqrt{7}\, \arctan \left(\frac{-\sqrt{20+10 \sqrt{35}}+10 \sqrt{2 x +1}}{\sqrt{-20+10 \sqrt{35}}}\right)}{1519 \left(2 \sqrt{5}-5 \sqrt{7}\right) \sqrt{-20+10 \sqrt{35}}}+\frac{4063 \sqrt{20+10 \sqrt{35}}\, \sqrt{2 \sqrt{35}+4}\, \sqrt{35}\, \arctan \left(\frac{10 \sqrt{2 x +1}+\sqrt{20+10 \sqrt{35}}}{\sqrt{-20+10 \sqrt{35}}}\right)}{47089 \left(2 \sqrt{5}-5 \sqrt{7}\right) \sqrt{-20+10 \sqrt{35}}}-\frac{2330 \sqrt{20+10 \sqrt{35}}\, \sqrt{2 \sqrt{35}+4}\, \arctan \left(\frac{10 \sqrt{2 x +1}+\sqrt{20+10 \sqrt{35}}}{\sqrt{-20+10 \sqrt{35}}}\right)}{6727 \left(2 \sqrt{5}-5 \sqrt{7}\right) \sqrt{-20+10 \sqrt{35}}}-\frac{1940 \sqrt{5}\, \arctan \left(\frac{10 \sqrt{2 x +1}+\sqrt{20+10 \sqrt{35}}}{\sqrt{-20+10 \sqrt{35}}}\right)}{217 \left(2 \sqrt{5}-5 \sqrt{7}\right) \sqrt{-20+10 \sqrt{35}}}+\frac{3880 \sqrt{7}\, \arctan \left(\frac{10 \sqrt{2 x +1}+\sqrt{20+10 \sqrt{35}}}{\sqrt{-20+10 \sqrt{35}}}\right)}{1519 \left(2 \sqrt{5}-5 \sqrt{7}\right) \sqrt{-20+10 \sqrt{35}}}+\frac{4063 \sqrt{2 \sqrt{35}+4}\, \sqrt{35}\, \ln \left(10 x +5+\sqrt{35}-\sqrt{2 x +1}\, \sqrt{20+10 \sqrt{35}}\right)}{94178 \left(2 \sqrt{5}-5 \sqrt{7}\right)}-\frac{1165 \sqrt{2 \sqrt{35}+4}\, \ln \left(10 x +5+\sqrt{35}-\sqrt{2 x +1}\, \sqrt{20+10 \sqrt{35}}\right)}{6727 \left(2 \sqrt{5}-5 \sqrt{7}\right)}-\frac{4063 \sqrt{2 \sqrt{35}+4}\, \sqrt{35}\, \ln \left(10 x +5+\sqrt{35}+\sqrt{2 x +1}\, \sqrt{20+10 \sqrt{35}}\right)}{94178 \left(2 \sqrt{5}-5 \sqrt{7}\right)}+\frac{1165 \sqrt{2 \sqrt{35}+4}\, \ln \left(10 x +5+\sqrt{35}+\sqrt{2 x +1}\, \sqrt{20+10 \sqrt{35}}\right)}{6727 \left(2 \sqrt{5}-5 \sqrt{7}\right)}+\frac{-\frac{2 \left(-6488300+3244150 \sqrt{5}\, \sqrt{7}\right) \sqrt{5}\, \sqrt{2 x +1}}{351990275 \left(2 \sqrt{5}-5 \sqrt{7}\right)}-\frac{\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \left(-13949845+1946490 \sqrt{5}\, \sqrt{7}\right)}{70398055 \left(2 \sqrt{5}-5 \sqrt{7}\right)}}{2 x +\frac{\sqrt{5}\, \sqrt{7}}{5}+\frac{\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}}{5}+1}-\frac{5 \left(\frac{2 \left(-6488300+3244150 \sqrt{5}\, \sqrt{7}\right) \sqrt{5}\, \sqrt{2 x +1}}{37375 \left(2 \sqrt{5}-5 \sqrt{7}\right)}-\frac{\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \left(-13949845+1946490 \sqrt{5}\, \sqrt{7}\right)}{7475 \left(2 \sqrt{5}-5 \sqrt{7}\right)}\right)}{47089 \left(2 x +\frac{\sqrt{5}\, \sqrt{7}}{5}-\frac{\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}}{5}+1\right)}"," ",0,"5/47089*(-2/37375*(-6488300+3244150*5^(1/2)*7^(1/2))/(2*5^(1/2)-5*7^(1/2))*5^(1/2)*(2*x+1)^(1/2)-1/7475/(2*5^(1/2)-5*7^(1/2))*(2*5^(1/2)*7^(1/2)+4)^(1/2)*(-13949845+1946490*5^(1/2)*7^(1/2)))/(2*x+1/5*5^(1/2)*7^(1/2)+1/5*(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+1)-4063/94178/(2*5^(1/2)-5*7^(1/2))*(2*35^(1/2)+4)^(1/2)*35^(1/2)*ln(10*x+5+35^(1/2)+(2*x+1)^(1/2)*(20+10*35^(1/2))^(1/2))+1165/6727/(2*5^(1/2)-5*7^(1/2))*(2*35^(1/2)+4)^(1/2)*ln(10*x+5+35^(1/2)+(2*x+1)^(1/2)*(20+10*35^(1/2))^(1/2))+4063/47089/(2*5^(1/2)-5*7^(1/2))/(-20+10*35^(1/2))^(1/2)*(20+10*35^(1/2))^(1/2)*(2*35^(1/2)+4)^(1/2)*35^(1/2)*arctan((10*(2*x+1)^(1/2)+(20+10*35^(1/2))^(1/2))/(-20+10*35^(1/2))^(1/2))-2330/6727/(2*5^(1/2)-5*7^(1/2))/(-20+10*35^(1/2))^(1/2)*(20+10*35^(1/2))^(1/2)*(2*35^(1/2)+4)^(1/2)*arctan((10*(2*x+1)^(1/2)+(20+10*35^(1/2))^(1/2))/(-20+10*35^(1/2))^(1/2))-1940/217/(2*5^(1/2)-5*7^(1/2))/(-20+10*35^(1/2))^(1/2)*5^(1/2)*arctan((10*(2*x+1)^(1/2)+(20+10*35^(1/2))^(1/2))/(-20+10*35^(1/2))^(1/2))+3880/1519/(2*5^(1/2)-5*7^(1/2))/(-20+10*35^(1/2))^(1/2)*7^(1/2)*arctan((10*(2*x+1)^(1/2)+(20+10*35^(1/2))^(1/2))/(-20+10*35^(1/2))^(1/2))-5/47089*(2/37375*(-6488300+3244150*5^(1/2)*7^(1/2))/(2*5^(1/2)-5*7^(1/2))*5^(1/2)*(2*x+1)^(1/2)-1/7475/(2*5^(1/2)-5*7^(1/2))*(2*5^(1/2)*7^(1/2)+4)^(1/2)*(-13949845+1946490*5^(1/2)*7^(1/2)))/(2*x+1/5*5^(1/2)*7^(1/2)-1/5*(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+1)+4063/94178/(2*5^(1/2)-5*7^(1/2))*(2*35^(1/2)+4)^(1/2)*35^(1/2)*ln(10*x+5+35^(1/2)-(2*x+1)^(1/2)*(20+10*35^(1/2))^(1/2))-1165/6727/(2*5^(1/2)-5*7^(1/2))*(2*35^(1/2)+4)^(1/2)*ln(10*x+5+35^(1/2)-(2*x+1)^(1/2)*(20+10*35^(1/2))^(1/2))+4063/47089/(2*5^(1/2)-5*7^(1/2))/(-20+10*35^(1/2))^(1/2)*(20+10*35^(1/2))^(1/2)*(2*35^(1/2)+4)^(1/2)*35^(1/2)*arctan((-(20+10*35^(1/2))^(1/2)+10*(2*x+1)^(1/2))/(-20+10*35^(1/2))^(1/2))-2330/6727/(2*5^(1/2)-5*7^(1/2))/(-20+10*35^(1/2))^(1/2)*(20+10*35^(1/2))^(1/2)*(2*35^(1/2)+4)^(1/2)*arctan((-(20+10*35^(1/2))^(1/2)+10*(2*x+1)^(1/2))/(-20+10*35^(1/2))^(1/2))-1940/217/(2*5^(1/2)-5*7^(1/2))/(-20+10*35^(1/2))^(1/2)*5^(1/2)*arctan((-(20+10*35^(1/2))^(1/2)+10*(2*x+1)^(1/2))/(-20+10*35^(1/2))^(1/2))+3880/1519/(2*5^(1/2)-5*7^(1/2))/(-20+10*35^(1/2))^(1/2)*7^(1/2)*arctan((-(20+10*35^(1/2))^(1/2)+10*(2*x+1)^(1/2))/(-20+10*35^(1/2))^(1/2))","B"
2321,1,651,193,0.174000," ","int(1/(2*x+1)^(3/2)/(5*x^2+3*x+2)^2,x)","-\frac{2560 \left(2 \sqrt{5}\, \sqrt{7}+4\right) \arctan \left(\frac{-\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{47089 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}-\frac{3657 \sqrt{5}\, \left(2 \sqrt{5}\, \sqrt{7}+4\right) \sqrt{7}\, \arctan \left(\frac{-\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{329623 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}+\frac{3256 \sqrt{5}\, \sqrt{7}\, \arctan \left(\frac{-\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{10633 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}-\frac{2560 \left(2 \sqrt{5}\, \sqrt{7}+4\right) \arctan \left(\frac{\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{47089 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}-\frac{3657 \sqrt{5}\, \left(2 \sqrt{5}\, \sqrt{7}+4\right) \sqrt{7}\, \arctan \left(\frac{\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{329623 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}+\frac{3256 \sqrt{5}\, \sqrt{7}\, \arctan \left(\frac{\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{10633 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}-\frac{256 \sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}-\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{47089}-\frac{3657 \sqrt{7}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}-\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{659246}+\frac{256 \sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}+\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{47089}+\frac{3657 \sqrt{7}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}+\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{659246}-\frac{16 \left(\frac{27 \left(2 x +1\right)^{\frac{3}{2}}}{124}-\frac{89 \sqrt{2 x +1}}{310}\right)}{49 \left(-\frac{8 x}{5}+\left(2 x +1\right)^{2}+\frac{3}{5}\right)}-\frac{16}{49 \sqrt{2 x +1}}"," ",0,"-16/49*(27/124*(2*x+1)^(3/2)-89/310*(2*x+1)^(1/2))/(-8/5*x+(2*x+1)^2+3/5)+256/47089*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)+(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)+3657/659246*7^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)+(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)-2560/47089/(10*5^(1/2)*7^(1/2)-20)^(1/2)*(2*5^(1/2)*7^(1/2)+4)*arctan((5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))-3657/329623/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)*7^(1/2)*arctan((5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))+3256/10633/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*7^(1/2)*arctan((5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))-256/47089*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)-(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)-3657/659246*7^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)-(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)-2560/47089/(10*5^(1/2)*7^(1/2)-20)^(1/2)*(2*5^(1/2)*7^(1/2)+4)*arctan((-5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))-3657/329623/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)*7^(1/2)*arctan((-5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))+3256/10633/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*7^(1/2)*arctan((-5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))-16/49/(2*x+1)^(1/2)","B"
2322,1,660,202,0.363000," ","int(1/(2*x+1)^(5/2)/(5*x^2+3*x+2)^2,x)","\frac{24175 \left(2 \sqrt{5}\, \sqrt{7}+4\right) \arctan \left(\frac{-\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{329623 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}-\frac{45940 \sqrt{5}\, \left(2 \sqrt{5}\, \sqrt{7}+4\right) \sqrt{7}\, \arctan \left(\frac{-\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{2307361 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}-\frac{9980 \sqrt{5}\, \sqrt{7}\, \arctan \left(\frac{-\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{74431 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}+\frac{24175 \left(2 \sqrt{5}\, \sqrt{7}+4\right) \arctan \left(\frac{\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{329623 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}-\frac{45940 \sqrt{5}\, \left(2 \sqrt{5}\, \sqrt{7}+4\right) \sqrt{7}\, \arctan \left(\frac{\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{2307361 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}-\frac{9980 \sqrt{5}\, \sqrt{7}\, \arctan \left(\frac{\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{74431 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}+\frac{4835 \sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}-\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{659246}-\frac{22970 \sqrt{7}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}-\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{2307361}-\frac{4835 \sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}+\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{659246}+\frac{22970 \sqrt{7}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}+\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{2307361}-\frac{16 \left(\frac{89 \left(2 x +1\right)^{\frac{3}{2}}}{62}+\frac{233 \sqrt{2 x +1}}{620}\right)}{343 \left(-\frac{8 x}{5}+\left(2 x +1\right)^{2}+\frac{3}{5}\right)}-\frac{16}{147 \left(2 x +1\right)^{\frac{3}{2}}}-\frac{128}{343 \sqrt{2 x +1}}"," ",0,"-16/343*(89/62*(2*x+1)^(3/2)+233/620*(2*x+1)^(1/2))/(-8/5*x+(2*x+1)^2+3/5)-4835/659246*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)+(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)+22970/2307361*7^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)+(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)+24175/329623/(10*5^(1/2)*7^(1/2)-20)^(1/2)*(2*5^(1/2)*7^(1/2)+4)*arctan((5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))-45940/2307361/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)*7^(1/2)*arctan((5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))-9980/74431/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*7^(1/2)*arctan((5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))+4835/659246*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)-(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)-22970/2307361*7^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)-(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)+24175/329623/(10*5^(1/2)*7^(1/2)-20)^(1/2)*(2*5^(1/2)*7^(1/2)+4)*arctan((-5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))-45940/2307361/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)*7^(1/2)*arctan((-5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))-9980/74431/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*7^(1/2)*arctan((-5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))-16/147/(2*x+1)^(3/2)-128/343/(2*x+1)^(1/2)","B"
2323,1,662,219,0.254000," ","int((2*x+1)^(9/2)/(5*x^2+3*x+2)^3,x)","-\frac{35997 \left(2 \sqrt{5}\, \sqrt{7}+4\right) \arctan \left(\frac{-\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{744775 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}+\frac{23721 \sqrt{5}\, \left(2 \sqrt{5}\, \sqrt{7}+4\right) \sqrt{7}\, \arctan \left(\frac{-\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{1489550 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}+\frac{1584 \sqrt{5}\, \sqrt{7}\, \arctan \left(\frac{-\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{24025 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}-\frac{35997 \left(2 \sqrt{5}\, \sqrt{7}+4\right) \arctan \left(\frac{\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{744775 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}+\frac{23721 \sqrt{5}\, \left(2 \sqrt{5}\, \sqrt{7}+4\right) \sqrt{7}\, \arctan \left(\frac{\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{1489550 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}+\frac{1584 \sqrt{5}\, \sqrt{7}\, \arctan \left(\frac{\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{24025 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}-\frac{35997 \sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}-\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{7447750}+\frac{23721 \sqrt{7}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}-\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{2979100}+\frac{35997 \sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}+\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{7447750}-\frac{23721 \sqrt{7}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}+\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{2979100}+\frac{-\frac{3446 \left(2 x +1\right)^{\frac{7}{2}}}{961}-\frac{30664 \left(2 x +1\right)^{\frac{5}{2}}}{24025}-\frac{29386 \left(2 x +1\right)^{\frac{3}{2}}}{24025}-\frac{77616 \sqrt{2 x +1}}{24025}}{\left(-8 x +5 \left(2 x +1\right)^{2}+3\right)^{2}}"," ",0,"1600*(-1723/768800*(2*x+1)^(7/2)-3833/4805000*(2*x+1)^(5/2)-14693/19220000*(2*x+1)^(3/2)-4851/2402500*(2*x+1)^(1/2))/(5*(2*x+1)^2-8*x+3)^2+35997/7447750*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)+(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)-23721/2979100*7^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)+(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)-35997/744775/(10*5^(1/2)*7^(1/2)-20)^(1/2)*(2*5^(1/2)*7^(1/2)+4)*arctan((5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))+23721/1489550/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)*7^(1/2)*arctan((5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))+1584/24025/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*7^(1/2)*arctan((5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))-35997/7447750*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)-(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)+23721/2979100*7^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)-(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)-35997/744775/(10*5^(1/2)*7^(1/2)-20)^(1/2)*(2*5^(1/2)*7^(1/2)+4)*arctan((-5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))+23721/1489550/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)*7^(1/2)*arctan((-5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))+1584/24025/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*7^(1/2)*arctan((-5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))","B"
2324,1,662,210,0.153000," ","int((2*x+1)^(7/2)/(5*x^2+3*x+2)^3,x)","-\frac{7353 \left(2 \sqrt{5}\, \sqrt{7}+4\right) \arctan \left(\frac{-\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{297910 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}+\frac{451 \sqrt{5}\, \left(2 \sqrt{5}\, \sqrt{7}+4\right) \sqrt{7}\, \arctan \left(\frac{-\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{148955 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}+\frac{358 \sqrt{5}\, \sqrt{7}\, \arctan \left(\frac{-\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{4805 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}-\frac{7353 \left(2 \sqrt{5}\, \sqrt{7}+4\right) \arctan \left(\frac{\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{297910 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}+\frac{451 \sqrt{5}\, \left(2 \sqrt{5}\, \sqrt{7}+4\right) \sqrt{7}\, \arctan \left(\frac{\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{148955 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}+\frac{358 \sqrt{5}\, \sqrt{7}\, \arctan \left(\frac{\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{4805 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}-\frac{7353 \sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}-\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{2979100}+\frac{451 \sqrt{7}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}-\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{297910}+\frac{7353 \sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}+\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{2979100}-\frac{451 \sqrt{7}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}+\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{297910}+\frac{\frac{1088 \left(2 x +1\right)^{\frac{7}{2}}}{961}-\frac{23578 \left(2 x +1\right)^{\frac{5}{2}}}{4805}+\frac{14168 \left(2 x +1\right)^{\frac{3}{2}}}{4805}-\frac{17542 \sqrt{2 x +1}}{4805}}{\left(-8 x +5 \left(2 x +1\right)^{2}+3\right)^{2}}"," ",0,"1600*(17/24025*(2*x+1)^(7/2)-11789/3844000*(2*x+1)^(5/2)+1771/961000*(2*x+1)^(3/2)-8771/3844000*(2*x+1)^(1/2))/(-8*x+5*(2*x+1)^2+3)^2+7353/2979100*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)+(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)-451/297910*7^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)+(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)-7353/297910/(10*5^(1/2)*7^(1/2)-20)^(1/2)*(2*5^(1/2)*7^(1/2)+4)*arctan((5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))+451/148955/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)*7^(1/2)*arctan((5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))+358/4805/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*7^(1/2)*arctan((5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))-7353/2979100*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)-(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)+451/297910*7^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)-(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)-7353/297910/(10*5^(1/2)*7^(1/2)-20)^(1/2)*(2*5^(1/2)*7^(1/2)+4)*arctan((-5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))+451/148955/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)*7^(1/2)*arctan((-5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))+358/4805/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*7^(1/2)*arctan((-5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))","B"
2325,1,662,210,0.188000," ","int((2*x+1)^(5/2)/(5*x^2+3*x+2)^3,x)","-\frac{327 \left(2 \sqrt{5}\, \sqrt{7}+4\right) \arctan \left(\frac{-\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{29791 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}+\frac{141 \sqrt{5}\, \left(2 \sqrt{5}\, \sqrt{7}+4\right) \sqrt{7}\, \arctan \left(\frac{-\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{59582 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}+\frac{24 \sqrt{5}\, \sqrt{7}\, \arctan \left(\frac{-\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{961 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}-\frac{327 \left(2 \sqrt{5}\, \sqrt{7}+4\right) \arctan \left(\frac{\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{29791 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}+\frac{141 \sqrt{5}\, \left(2 \sqrt{5}\, \sqrt{7}+4\right) \sqrt{7}\, \arctan \left(\frac{\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{59582 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}+\frac{24 \sqrt{5}\, \sqrt{7}\, \arctan \left(\frac{\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{961 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}-\frac{327 \sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}-\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{297910}+\frac{141 \sqrt{7}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}-\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{119164}+\frac{327 \sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}+\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{297910}-\frac{141 \sqrt{7}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}+\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{119164}+\frac{\frac{1170 \left(2 x +1\right)^{\frac{7}{2}}}{961}-\frac{1280 \left(2 x +1\right)^{\frac{5}{2}}}{961}+\frac{574 \left(2 x +1\right)^{\frac{3}{2}}}{961}-\frac{1176 \sqrt{2 x +1}}{961}}{\left(-8 x +5 \left(2 x +1\right)^{2}+3\right)^{2}}"," ",0,"1600*(117/153760*(2*x+1)^(7/2)-4/4805*(2*x+1)^(5/2)+287/768800*(2*x+1)^(3/2)-147/192200*(2*x+1)^(1/2))/(-8*x+5*(2*x+1)^2+3)^2+327/297910*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)+(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)-141/119164*7^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)+(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)-327/29791/(10*5^(1/2)*7^(1/2)-20)^(1/2)*(2*5^(1/2)*7^(1/2)+4)*arctan((5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))+141/59582/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)*7^(1/2)*arctan((5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))+24/961/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*7^(1/2)*arctan((5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))-327/297910*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)-(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)+141/119164*7^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)-(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)-327/29791/(10*5^(1/2)*7^(1/2)-20)^(1/2)*(2*5^(1/2)*7^(1/2)+4)*arctan((-5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))+141/59582/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)*7^(1/2)*arctan((-5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))+24/961/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*7^(1/2)*arctan((-5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))","B"
2326,1,662,210,0.311000," ","int((2*x+1)^(3/2)/(5*x^2+3*x+2)^3,x)","-\frac{705 \left(2 \sqrt{5}\, \sqrt{7}+4\right) \arctan \left(\frac{-\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{59582 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}+\frac{327 \sqrt{5}\, \left(2 \sqrt{5}\, \sqrt{7}+4\right) \sqrt{7}\, \arctan \left(\frac{-\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{208537 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}+\frac{234 \sqrt{5}\, \sqrt{7}\, \arctan \left(\frac{-\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{6727 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}-\frac{705 \left(2 \sqrt{5}\, \sqrt{7}+4\right) \arctan \left(\frac{\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{59582 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}+\frac{327 \sqrt{5}\, \left(2 \sqrt{5}\, \sqrt{7}+4\right) \sqrt{7}\, \arctan \left(\frac{\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{208537 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}+\frac{234 \sqrt{5}\, \sqrt{7}\, \arctan \left(\frac{\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{6727 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}-\frac{141 \sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}-\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{119164}+\frac{327 \sqrt{7}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}-\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{417074}+\frac{141 \sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}+\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{119164}-\frac{327 \sqrt{7}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}+\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{417074}+\frac{\frac{600 \left(2 x +1\right)^{\frac{7}{2}}}{961}-\frac{410 \left(2 x +1\right)^{\frac{5}{2}}}{961}+\frac{1280 \left(2 x +1\right)^{\frac{3}{2}}}{961}-\frac{1638 \sqrt{2 x +1}}{961}}{\left(-8 x +5 \left(2 x +1\right)^{2}+3\right)^{2}}"," ",0,"1600*(3/7688*(2*x+1)^(7/2)-41/153760*(2*x+1)^(5/2)+4/4805*(2*x+1)^(3/2)-819/768800*(2*x+1)^(1/2))/(-8*x+5*(2*x+1)^2+3)^2+141/119164*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)+(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)-327/417074*7^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)+(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)-705/59582/(10*5^(1/2)*7^(1/2)-20)^(1/2)*(2*5^(1/2)*7^(1/2)+4)*arctan((5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))+327/208537/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)*7^(1/2)*arctan((5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))+234/6727/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*7^(1/2)*arctan((5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))-141/119164*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)-(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)+327/417074*7^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)-(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)-705/59582/(10*5^(1/2)*7^(1/2)-20)^(1/2)*(2*5^(1/2)*7^(1/2)+4)*arctan((-5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))+327/208537/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)*7^(1/2)*arctan((-5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))+234/6727/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*7^(1/2)*arctan((-5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))","B"
2327,1,1108,210,1.451000," ","int((2*x+1)^(1/2)/(5*x^2+3*x+2)^3,x)","\frac{161475 \sqrt{20+10 \sqrt{35}}\, \sqrt{5}\, \sqrt{2 \sqrt{35}+4}\, \arctan \left(\frac{-\sqrt{20+10 \sqrt{35}}+10 \sqrt{2 x +1}}{\sqrt{-20+10 \sqrt{35}}}\right)}{208537 \left(20 \sqrt{5}\, \sqrt{7}-195\right) \sqrt{-20+10 \sqrt{35}}}-\frac{2065235 \sqrt{20+10 \sqrt{35}}\, \sqrt{2 \sqrt{35}+4}\, \sqrt{7}\, \arctan \left(\frac{-\sqrt{20+10 \sqrt{35}}+10 \sqrt{2 x +1}}{\sqrt{-20+10 \sqrt{35}}}\right)}{2919518 \left(20 \sqrt{5}\, \sqrt{7}-195\right) \sqrt{-20+10 \sqrt{35}}}-\frac{212160 \sqrt{35}\, \arctan \left(\frac{-\sqrt{20+10 \sqrt{35}}+10 \sqrt{2 x +1}}{\sqrt{-20+10 \sqrt{35}}}\right)}{47089 \left(20 \sqrt{5}\, \sqrt{7}-195\right) \sqrt{-20+10 \sqrt{35}}}+\frac{108800 \arctan \left(\frac{-\sqrt{20+10 \sqrt{35}}+10 \sqrt{2 x +1}}{\sqrt{-20+10 \sqrt{35}}}\right)}{6727 \left(20 \sqrt{5}\, \sqrt{7}-195\right) \sqrt{-20+10 \sqrt{35}}}+\frac{161475 \sqrt{20+10 \sqrt{35}}\, \sqrt{5}\, \sqrt{2 \sqrt{35}+4}\, \arctan \left(\frac{10 \sqrt{2 x +1}+\sqrt{20+10 \sqrt{35}}}{\sqrt{-20+10 \sqrt{35}}}\right)}{208537 \left(20 \sqrt{5}\, \sqrt{7}-195\right) \sqrt{-20+10 \sqrt{35}}}-\frac{2065235 \sqrt{20+10 \sqrt{35}}\, \sqrt{2 \sqrt{35}+4}\, \sqrt{7}\, \arctan \left(\frac{10 \sqrt{2 x +1}+\sqrt{20+10 \sqrt{35}}}{\sqrt{-20+10 \sqrt{35}}}\right)}{2919518 \left(20 \sqrt{5}\, \sqrt{7}-195\right) \sqrt{-20+10 \sqrt{35}}}-\frac{212160 \sqrt{35}\, \arctan \left(\frac{10 \sqrt{2 x +1}+\sqrt{20+10 \sqrt{35}}}{\sqrt{-20+10 \sqrt{35}}}\right)}{47089 \left(20 \sqrt{5}\, \sqrt{7}-195\right) \sqrt{-20+10 \sqrt{35}}}+\frac{108800 \arctan \left(\frac{10 \sqrt{2 x +1}+\sqrt{20+10 \sqrt{35}}}{\sqrt{-20+10 \sqrt{35}}}\right)}{6727 \left(20 \sqrt{5}\, \sqrt{7}-195\right) \sqrt{-20+10 \sqrt{35}}}+\frac{161475 \sqrt{5}\, \sqrt{2 \sqrt{35}+4}\, \ln \left(10 x +5+\sqrt{35}-\sqrt{2 x +1}\, \sqrt{20+10 \sqrt{35}}\right)}{417074 \left(20 \sqrt{5}\, \sqrt{7}-195\right)}-\frac{2065235 \sqrt{2 \sqrt{35}+4}\, \sqrt{7}\, \ln \left(10 x +5+\sqrt{35}-\sqrt{2 x +1}\, \sqrt{20+10 \sqrt{35}}\right)}{5839036 \left(20 \sqrt{5}\, \sqrt{7}-195\right)}-\frac{161475 \sqrt{5}\, \sqrt{2 \sqrt{35}+4}\, \ln \left(10 x +5+\sqrt{35}+\sqrt{2 x +1}\, \sqrt{20+10 \sqrt{35}}\right)}{417074 \left(20 \sqrt{5}\, \sqrt{7}-195\right)}+\frac{2065235 \sqrt{2 \sqrt{35}+4}\, \sqrt{7}\, \ln \left(10 x +5+\sqrt{35}+\sqrt{2 x +1}\, \sqrt{20+10 \sqrt{35}}\right)}{5839036 \left(20 \sqrt{5}\, \sqrt{7}-195\right)}+\frac{\frac{\sqrt{5}\, \left(-13012793430 \sqrt{5}+6673227400 \sqrt{7}\right) \left(2 x +1\right)^{\frac{3}{2}}}{6269664905 \left(-390+40 \sqrt{5}\, \sqrt{7}\right)}+\frac{5 \left(-214587133600 \sqrt{5}+114637845000 \sqrt{7}\right) \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \left(2 x +1\right)}{2919518 \left(-41876250+4295000 \sqrt{5}\, \sqrt{7}\right)}+\frac{\left(-141628999400 \sqrt{5}\, \sqrt{7}+440433008400\right) \sqrt{2 x +1}}{31348324525 \left(-390+40 \sqrt{5}\, \sqrt{7}\right)}+\frac{5 \left(-76332028500 \sqrt{7}+54802482000 \sqrt{5}\right) \sqrt{2 \sqrt{5}\, \sqrt{7}+4}}{2919518 \left(-41876250+4295000 \sqrt{5}\, \sqrt{7}\right)}}{\left(2 x +\frac{\sqrt{5}\, \sqrt{7}}{5}+\frac{\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}}{5}+1\right)^{2}}+\frac{\frac{\sqrt{5}\, \left(-13012793430 \sqrt{5}+6673227400 \sqrt{7}\right) \left(2 x +1\right)^{\frac{3}{2}}}{6269664905 \left(-390+40 \sqrt{5}\, \sqrt{7}\right)}-\frac{\left(-214587133600 \sqrt{5}+114637845000 \sqrt{7}\right) \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \left(2 x +1\right)}{62696649050 \left(-390+40 \sqrt{5}\, \sqrt{7}\right)}+\frac{\left(-141628999400 \sqrt{5}\, \sqrt{7}+440433008400\right) \sqrt{2 x +1}}{31348324525 \left(-390+40 \sqrt{5}\, \sqrt{7}\right)}-\frac{\left(-76332028500 \sqrt{7}+54802482000 \sqrt{5}\right) \sqrt{2 \sqrt{5}\, \sqrt{7}+4}}{62696649050 \left(-390+40 \sqrt{5}\, \sqrt{7}\right)}}{\left(2 x +\frac{\sqrt{5}\, \sqrt{7}}{5}-\frac{\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}}{5}+1\right)^{2}}"," ",0,"5/2919518*(2/21475*5^(1/2)*(-13012793430*5^(1/2)+6673227400*7^(1/2))/(-390+40*5^(1/2)*7^(1/2))*(2*x+1)^(3/2)+1/107375/(-390+40*5^(1/2)*7^(1/2))*(-214587133600*5^(1/2)+114637845000*7^(1/2))*(2*5^(1/2)*7^(1/2)+4)^(1/2)*(2*x+1)+2/107375*(-141628999400*5^(1/2)*7^(1/2)+440433008400)/(-390+40*5^(1/2)*7^(1/2))*(2*x+1)^(1/2)+1/107375*(-76332028500*7^(1/2)+54802482000*5^(1/2))*(2*5^(1/2)*7^(1/2)+4)^(1/2)/(-390+40*5^(1/2)*7^(1/2)))/(2*x+1/5*5^(1/2)*7^(1/2)+1/5*(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+1)^2-161475/417074/(20*5^(1/2)*7^(1/2)-195)*ln(10*x+5+35^(1/2)+(2*x+1)^(1/2)*(20+10*35^(1/2))^(1/2))*5^(1/2)*(2*35^(1/2)+4)^(1/2)+2065235/5839036/(20*5^(1/2)*7^(1/2)-195)*ln(10*x+5+35^(1/2)+(2*x+1)^(1/2)*(20+10*35^(1/2))^(1/2))*(2*35^(1/2)+4)^(1/2)*7^(1/2)+161475/208537/(20*5^(1/2)*7^(1/2)-195)/(-20+10*35^(1/2))^(1/2)*arctan((10*(2*x+1)^(1/2)+(20+10*35^(1/2))^(1/2))/(-20+10*35^(1/2))^(1/2))*(20+10*35^(1/2))^(1/2)*5^(1/2)*(2*35^(1/2)+4)^(1/2)-2065235/2919518/(20*5^(1/2)*7^(1/2)-195)/(-20+10*35^(1/2))^(1/2)*arctan((10*(2*x+1)^(1/2)+(20+10*35^(1/2))^(1/2))/(-20+10*35^(1/2))^(1/2))*(20+10*35^(1/2))^(1/2)*(2*35^(1/2)+4)^(1/2)*7^(1/2)-212160/47089/(20*5^(1/2)*7^(1/2)-195)/(-20+10*35^(1/2))^(1/2)*arctan((10*(2*x+1)^(1/2)+(20+10*35^(1/2))^(1/2))/(-20+10*35^(1/2))^(1/2))*35^(1/2)+108800/6727/(20*5^(1/2)*7^(1/2)-195)/(-20+10*35^(1/2))^(1/2)*arctan((10*(2*x+1)^(1/2)+(20+10*35^(1/2))^(1/2))/(-20+10*35^(1/2))^(1/2))+5/2919518*(2/21475*5^(1/2)*(-13012793430*5^(1/2)+6673227400*7^(1/2))/(-390+40*5^(1/2)*7^(1/2))*(2*x+1)^(3/2)-1/107375/(-390+40*5^(1/2)*7^(1/2))*(-214587133600*5^(1/2)+114637845000*7^(1/2))*(2*5^(1/2)*7^(1/2)+4)^(1/2)*(2*x+1)+2/107375*(-141628999400*5^(1/2)*7^(1/2)+440433008400)/(-390+40*5^(1/2)*7^(1/2))*(2*x+1)^(1/2)-1/107375*(-76332028500*7^(1/2)+54802482000*5^(1/2))*(2*5^(1/2)*7^(1/2)+4)^(1/2)/(-390+40*5^(1/2)*7^(1/2)))/(2*x+1/5*5^(1/2)*7^(1/2)-1/5*(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+1)^2+161475/417074/(20*5^(1/2)*7^(1/2)-195)*ln(10*x+5+35^(1/2)-(2*x+1)^(1/2)*(20+10*35^(1/2))^(1/2))*5^(1/2)*(2*35^(1/2)+4)^(1/2)-2065235/5839036/(20*5^(1/2)*7^(1/2)-195)*ln(10*x+5+35^(1/2)-(2*x+1)^(1/2)*(20+10*35^(1/2))^(1/2))*(2*35^(1/2)+4)^(1/2)*7^(1/2)+161475/208537/(20*5^(1/2)*7^(1/2)-195)/(-20+10*35^(1/2))^(1/2)*arctan((-(20+10*35^(1/2))^(1/2)+10*(2*x+1)^(1/2))/(-20+10*35^(1/2))^(1/2))*(20+10*35^(1/2))^(1/2)*5^(1/2)*(2*35^(1/2)+4)^(1/2)-2065235/2919518/(20*5^(1/2)*7^(1/2)-195)/(-20+10*35^(1/2))^(1/2)*arctan((-(20+10*35^(1/2))^(1/2)+10*(2*x+1)^(1/2))/(-20+10*35^(1/2))^(1/2))*(20+10*35^(1/2))^(1/2)*(2*35^(1/2)+4)^(1/2)*7^(1/2)-212160/47089/(20*5^(1/2)*7^(1/2)-195)/(-20+10*35^(1/2))^(1/2)*arctan((-(20+10*35^(1/2))^(1/2)+10*(2*x+1)^(1/2))/(-20+10*35^(1/2))^(1/2))*35^(1/2)+108800/6727/(20*5^(1/2)*7^(1/2)-195)/(-20+10*35^(1/2))^(1/2)*arctan((-(20+10*35^(1/2))^(1/2)+10*(2*x+1)^(1/2))/(-20+10*35^(1/2))^(1/2))","B"
2328,1,1100,224,1.681000," ","int(1/(2*x+1)^(1/2)/(5*x^2+3*x+2)^3,x)","\frac{6065475 \sqrt{20+10 \sqrt{35}}\, \sqrt{5}\, \sqrt{2 \sqrt{35}+4}\, \arctan \left(\frac{-\sqrt{20+10 \sqrt{35}}+10 \sqrt{2 x +1}}{\sqrt{-20+10 \sqrt{35}}}\right)}{2919518 \left(20 \sqrt{5}\, \sqrt{7}-195\right) \sqrt{-20+10 \sqrt{35}}}-\frac{15321765 \sqrt{20+10 \sqrt{35}}\, \sqrt{2 \sqrt{35}+4}\, \sqrt{7}\, \arctan \left(\frac{-\sqrt{20+10 \sqrt{35}}+10 \sqrt{2 x +1}}{\sqrt{-20+10 \sqrt{35}}}\right)}{10218313 \left(20 \sqrt{5}\, \sqrt{7}-195\right) \sqrt{-20+10 \sqrt{35}}}-\frac{8633430 \sqrt{35}\, \arctan \left(\frac{-\sqrt{20+10 \sqrt{35}}+10 \sqrt{2 x +1}}{\sqrt{-20+10 \sqrt{35}}}\right)}{329623 \left(20 \sqrt{5}\, \sqrt{7}-195\right) \sqrt{-20+10 \sqrt{35}}}+\frac{4427400 \arctan \left(\frac{-\sqrt{20+10 \sqrt{35}}+10 \sqrt{2 x +1}}{\sqrt{-20+10 \sqrt{35}}}\right)}{47089 \left(20 \sqrt{5}\, \sqrt{7}-195\right) \sqrt{-20+10 \sqrt{35}}}+\frac{6065475 \sqrt{20+10 \sqrt{35}}\, \sqrt{5}\, \sqrt{2 \sqrt{35}+4}\, \arctan \left(\frac{10 \sqrt{2 x +1}+\sqrt{20+10 \sqrt{35}}}{\sqrt{-20+10 \sqrt{35}}}\right)}{2919518 \left(20 \sqrt{5}\, \sqrt{7}-195\right) \sqrt{-20+10 \sqrt{35}}}-\frac{15321765 \sqrt{20+10 \sqrt{35}}\, \sqrt{2 \sqrt{35}+4}\, \sqrt{7}\, \arctan \left(\frac{10 \sqrt{2 x +1}+\sqrt{20+10 \sqrt{35}}}{\sqrt{-20+10 \sqrt{35}}}\right)}{10218313 \left(20 \sqrt{5}\, \sqrt{7}-195\right) \sqrt{-20+10 \sqrt{35}}}-\frac{8633430 \sqrt{35}\, \arctan \left(\frac{10 \sqrt{2 x +1}+\sqrt{20+10 \sqrt{35}}}{\sqrt{-20+10 \sqrt{35}}}\right)}{329623 \left(20 \sqrt{5}\, \sqrt{7}-195\right) \sqrt{-20+10 \sqrt{35}}}+\frac{4427400 \arctan \left(\frac{10 \sqrt{2 x +1}+\sqrt{20+10 \sqrt{35}}}{\sqrt{-20+10 \sqrt{35}}}\right)}{47089 \left(20 \sqrt{5}\, \sqrt{7}-195\right) \sqrt{-20+10 \sqrt{35}}}+\frac{6065475 \sqrt{5}\, \sqrt{2 \sqrt{35}+4}\, \ln \left(10 x +5+\sqrt{35}-\sqrt{2 x +1}\, \sqrt{20+10 \sqrt{35}}\right)}{5839036 \left(20 \sqrt{5}\, \sqrt{7}-195\right)}-\frac{15321765 \sqrt{2 \sqrt{35}+4}\, \sqrt{7}\, \ln \left(10 x +5+\sqrt{35}-\sqrt{2 x +1}\, \sqrt{20+10 \sqrt{35}}\right)}{20436626 \left(20 \sqrt{5}\, \sqrt{7}-195\right)}-\frac{6065475 \sqrt{5}\, \sqrt{2 \sqrt{35}+4}\, \ln \left(10 x +5+\sqrt{35}+\sqrt{2 x +1}\, \sqrt{20+10 \sqrt{35}}\right)}{5839036 \left(20 \sqrt{5}\, \sqrt{7}-195\right)}+\frac{15321765 \sqrt{2 \sqrt{35}+4}\, \sqrt{7}\, \ln \left(10 x +5+\sqrt{35}+\sqrt{2 x +1}\, \sqrt{20+10 \sqrt{35}}\right)}{20436626 \left(20 \sqrt{5}\, \sqrt{7}-195\right)}+\frac{\frac{3 \left(-6045943503600+620096769600 \sqrt{5}\, \sqrt{7}\right) \left(2 x +1\right)^{\frac{3}{2}}}{2765126589365 \left(-390+40 \sqrt{5}\, \sqrt{7}\right)}+\frac{5 \left(-91048526818200 \sqrt{5}+65791327714000 \sqrt{7}\right) \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \left(2 x +1\right)}{20436626 \left(-2638398750+270605000 \sqrt{5}\, \sqrt{7}\right)}+\frac{\left(-59423591568600 \sqrt{5}\, \sqrt{7}+320925328420550\right) \sqrt{2 x +1}}{13825632946825 \left(-390+40 \sqrt{5}\, \sqrt{7}\right)}+\frac{5 \left(-123371070933600 \sqrt{7}+152992435939000 \sqrt{5}\right) \sqrt{2 \sqrt{5}\, \sqrt{7}+4}}{20436626 \left(-5276797500+541210000 \sqrt{5}\, \sqrt{7}\right)}}{\left(2 x +\frac{\sqrt{5}\, \sqrt{7}}{5}+\frac{\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}}{5}+1\right)^{2}}-\frac{5 \left(-\frac{6 \left(-6045943503600+620096769600 \sqrt{5}\, \sqrt{7}\right) \left(2 x +1\right)^{\frac{3}{2}}}{1353025 \left(-390+40 \sqrt{5}\, \sqrt{7}\right)}+\frac{\left(-91048526818200 \sqrt{5}+65791327714000 \sqrt{7}\right) \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \left(2 x +1\right)}{-2638398750+270605000 \sqrt{5}\, \sqrt{7}}-\frac{2 \left(-59423591568600 \sqrt{5}\, \sqrt{7}+320925328420550\right) \sqrt{2 x +1}}{6765125 \left(-390+40 \sqrt{5}\, \sqrt{7}\right)}+\frac{\left(-123371070933600 \sqrt{7}+152992435939000 \sqrt{5}\right) \sqrt{2 \sqrt{5}\, \sqrt{7}+4}}{-5276797500+541210000 \sqrt{5}\, \sqrt{7}}\right)}{20436626 \left(2 x +\frac{\sqrt{5}\, \sqrt{7}}{5}-\frac{\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}}{5}+1\right)^{2}}"," ",0,"5/20436626*(6/1353025*(-6045943503600+620096769600*5^(1/2)*7^(1/2))/(-390+40*5^(1/2)*7^(1/2))*(2*x+1)^(3/2)+1/6765125/(-390+40*5^(1/2)*7^(1/2))*(-91048526818200*5^(1/2)+65791327714000*7^(1/2))*(2*5^(1/2)*7^(1/2)+4)^(1/2)*(2*x+1)+2/6765125*(-59423591568600*5^(1/2)*7^(1/2)+320925328420550)/(-390+40*5^(1/2)*7^(1/2))*(2*x+1)^(1/2)+1/13530250*(-123371070933600*7^(1/2)+152992435939000*5^(1/2))*(2*5^(1/2)*7^(1/2)+4)^(1/2)/(-390+40*5^(1/2)*7^(1/2)))/(2*x+1/5*5^(1/2)*7^(1/2)+1/5*(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+1)^2-6065475/5839036/(20*5^(1/2)*7^(1/2)-195)*5^(1/2)*(2*35^(1/2)+4)^(1/2)*ln(10*x+5+35^(1/2)+(2*x+1)^(1/2)*(20+10*35^(1/2))^(1/2))+15321765/20436626/(20*5^(1/2)*7^(1/2)-195)*(2*35^(1/2)+4)^(1/2)*7^(1/2)*ln(10*x+5+35^(1/2)+(2*x+1)^(1/2)*(20+10*35^(1/2))^(1/2))+6065475/2919518/(20*5^(1/2)*7^(1/2)-195)/(-20+10*35^(1/2))^(1/2)*(20+10*35^(1/2))^(1/2)*5^(1/2)*(2*35^(1/2)+4)^(1/2)*arctan((10*(2*x+1)^(1/2)+(20+10*35^(1/2))^(1/2))/(-20+10*35^(1/2))^(1/2))-15321765/10218313/(20*5^(1/2)*7^(1/2)-195)/(-20+10*35^(1/2))^(1/2)*(20+10*35^(1/2))^(1/2)*(2*35^(1/2)+4)^(1/2)*7^(1/2)*arctan((10*(2*x+1)^(1/2)+(20+10*35^(1/2))^(1/2))/(-20+10*35^(1/2))^(1/2))-8633430/329623/(20*5^(1/2)*7^(1/2)-195)/(-20+10*35^(1/2))^(1/2)*35^(1/2)*arctan((10*(2*x+1)^(1/2)+(20+10*35^(1/2))^(1/2))/(-20+10*35^(1/2))^(1/2))+4427400/47089/(20*5^(1/2)*7^(1/2)-195)/(-20+10*35^(1/2))^(1/2)*arctan((10*(2*x+1)^(1/2)+(20+10*35^(1/2))^(1/2))/(-20+10*35^(1/2))^(1/2))-5/20436626*(-6/1353025*(-6045943503600+620096769600*5^(1/2)*7^(1/2))/(-390+40*5^(1/2)*7^(1/2))*(2*x+1)^(3/2)+1/6765125/(-390+40*5^(1/2)*7^(1/2))*(-91048526818200*5^(1/2)+65791327714000*7^(1/2))*(2*5^(1/2)*7^(1/2)+4)^(1/2)*(2*x+1)-2/6765125*(-59423591568600*5^(1/2)*7^(1/2)+320925328420550)/(-390+40*5^(1/2)*7^(1/2))*(2*x+1)^(1/2)+1/13530250*(-123371070933600*7^(1/2)+152992435939000*5^(1/2))*(2*5^(1/2)*7^(1/2)+4)^(1/2)/(-390+40*5^(1/2)*7^(1/2)))/(2*x+1/5*5^(1/2)*7^(1/2)-1/5*(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+1)^2+6065475/5839036/(20*5^(1/2)*7^(1/2)-195)*5^(1/2)*(2*35^(1/2)+4)^(1/2)*ln(10*x+5+35^(1/2)-(2*x+1)^(1/2)*(20+10*35^(1/2))^(1/2))-15321765/20436626/(20*5^(1/2)*7^(1/2)-195)*(2*35^(1/2)+4)^(1/2)*7^(1/2)*ln(10*x+5+35^(1/2)-(2*x+1)^(1/2)*(20+10*35^(1/2))^(1/2))+6065475/2919518/(20*5^(1/2)*7^(1/2)-195)/(-20+10*35^(1/2))^(1/2)*(20+10*35^(1/2))^(1/2)*5^(1/2)*(2*35^(1/2)+4)^(1/2)*arctan((-(20+10*35^(1/2))^(1/2)+10*(2*x+1)^(1/2))/(-20+10*35^(1/2))^(1/2))-15321765/10218313/(20*5^(1/2)*7^(1/2)-195)/(-20+10*35^(1/2))^(1/2)*(20+10*35^(1/2))^(1/2)*(2*35^(1/2)+4)^(1/2)*7^(1/2)*arctan((-(20+10*35^(1/2))^(1/2)+10*(2*x+1)^(1/2))/(-20+10*35^(1/2))^(1/2))-8633430/329623/(20*5^(1/2)*7^(1/2)-195)/(-20+10*35^(1/2))^(1/2)*35^(1/2)*arctan((-(20+10*35^(1/2))^(1/2)+10*(2*x+1)^(1/2))/(-20+10*35^(1/2))^(1/2))+4427400/47089/(20*5^(1/2)*7^(1/2)-195)/(-20+10*35^(1/2))^(1/2)*arctan((-(20+10*35^(1/2))^(1/2)+10*(2*x+1)^(1/2))/(-20+10*35^(1/2))^(1/2))","B"
2329,1,671,219,0.161000," ","int(1/(2*x+1)^(3/2)/(5*x^2+3*x+2)^3,x)","-\frac{475725 \left(2 \sqrt{5}\, \sqrt{7}+4\right) \arctan \left(\frac{-\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{10218313 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}-\frac{876315 \sqrt{5}\, \left(2 \sqrt{5}\, \sqrt{7}+4\right) \sqrt{7}\, \arctan \left(\frac{-\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{143056382 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}+\frac{542760 \sqrt{5}\, \sqrt{7}\, \arctan \left(\frac{-\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{2307361 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}-\frac{475725 \left(2 \sqrt{5}\, \sqrt{7}+4\right) \arctan \left(\frac{\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{10218313 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}-\frac{876315 \sqrt{5}\, \left(2 \sqrt{5}\, \sqrt{7}+4\right) \sqrt{7}\, \arctan \left(\frac{\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{143056382 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}+\frac{542760 \sqrt{5}\, \sqrt{7}\, \arctan \left(\frac{\sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}+10 \sqrt{2 x +1}}{\sqrt{10 \sqrt{5}\, \sqrt{7}-20}}\right)}{2307361 \sqrt{10 \sqrt{5}\, \sqrt{7}-20}}-\frac{95145 \sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}-\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{20436626}-\frac{876315 \sqrt{7}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}-\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{286112764}+\frac{95145 \sqrt{5}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}+\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{20436626}+\frac{876315 \sqrt{7}\, \sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \ln \left(10 x +\sqrt{5}\, \sqrt{7}+\sqrt{2 \sqrt{5}\, \sqrt{7}+4}\, \sqrt{5}\, \sqrt{2 x +1}+5\right)}{286112764}-\frac{1600 \left(\frac{9793 \left(2 x +1\right)^{\frac{7}{2}}}{30752}-\frac{14343 \left(2 x +1\right)^{\frac{5}{2}}}{19220}+\frac{762223 \left(2 x +1\right)^{\frac{3}{2}}}{768800}-\frac{170877 \sqrt{2 x +1}}{192200}\right)}{343 \left(-8 x +5 \left(2 x +1\right)^{2}+3\right)^{2}}-\frac{64}{343 \sqrt{2 x +1}}"," ",0,"-1600/343*(9793/30752*(2*x+1)^(7/2)-14343/19220*(2*x+1)^(5/2)+762223/768800*(2*x+1)^(3/2)-170877/192200*(2*x+1)^(1/2))/(-8*x+5*(2*x+1)^2+3)^2+95145/20436626*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)+(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)+876315/286112764*7^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)+(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)-475725/10218313/(10*5^(1/2)*7^(1/2)-20)^(1/2)*(2*5^(1/2)*7^(1/2)+4)*arctan((5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))-876315/143056382/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)*7^(1/2)*arctan((5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))+542760/2307361/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*7^(1/2)*arctan((5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))-95145/20436626*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)-(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)-876315/286112764*7^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)*ln(10*x+5^(1/2)*7^(1/2)-(2*5^(1/2)*7^(1/2)+4)^(1/2)*5^(1/2)*(2*x+1)^(1/2)+5)-475725/10218313/(10*5^(1/2)*7^(1/2)-20)^(1/2)*(2*5^(1/2)*7^(1/2)+4)*arctan((-5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))-876315/143056382/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*(2*5^(1/2)*7^(1/2)+4)*7^(1/2)*arctan((-5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))+542760/2307361/(10*5^(1/2)*7^(1/2)-20)^(1/2)*5^(1/2)*7^(1/2)*arctan((-5^(1/2)*(2*5^(1/2)*7^(1/2)+4)^(1/2)+10*(2*x+1)^(1/2))/(10*5^(1/2)*7^(1/2)-20)^(1/2))-64/343/(2*x+1)^(1/2)","B"
2330,1,1166,334,0.154000," ","int(x^(9/2)/(c*x^2+b*x+a)^3,x)","\frac{33 \sqrt{2}\, a^{2} b \arctanh \left(\frac{\sqrt{2}\, c \sqrt{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{33 \sqrt{2}\, a^{2} b \arctan \left(\frac{\sqrt{2}\, c \sqrt{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{33 \sqrt{2}\, a \,b^{3} \arctanh \left(\frac{\sqrt{2}\, c \sqrt{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}\, c}-\frac{33 \sqrt{2}\, a \,b^{3} \arctan \left(\frac{\sqrt{2}\, c \sqrt{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}\, c}+\frac{3 \sqrt{2}\, b^{5} \arctanh \left(\frac{\sqrt{2}\, c \sqrt{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}\, c^{2}}+\frac{3 \sqrt{2}\, b^{5} \arctan \left(\frac{\sqrt{2}\, c \sqrt{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}\, c^{2}}-\frac{21 \sqrt{2}\, a^{2} \arctanh \left(\frac{\sqrt{2}\, c \sqrt{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{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{21 \sqrt{2}\, a^{2} \arctan \left(\frac{\sqrt{2}\, c \sqrt{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{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{27 \sqrt{2}\, a \,b^{2} \arctanh \left(\frac{\sqrt{2}\, c \sqrt{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{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{27 \sqrt{2}\, a \,b^{2} \arctan \left(\frac{\sqrt{2}\, c \sqrt{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{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{3 \sqrt{2}\, b^{4} \arctanh \left(\frac{\sqrt{2}\, c \sqrt{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{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}+\frac{3 \sqrt{2}\, b^{4} \arctan \left(\frac{\sqrt{2}\, c \sqrt{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{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}+\frac{-\frac{\left(44 a^{2} c^{2}-37 a \,b^{2} c +5 b^{4}\right) x^{\frac{7}{2}}}{4 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c}+\frac{3 \left(8 a c -b^{2}\right) a^{2} b \sqrt{x}}{4 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{2}}+\frac{\left(4 a^{2} c^{2}+20 a \,b^{2} c -3 b^{4}\right) b \,x^{\frac{5}{2}}}{4 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{2}}-\frac{\left(28 a^{2} c^{2}-49 a \,b^{2} c +6 b^{4}\right) a \,x^{\frac{3}{2}}}{4 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{2}}}{\left(c \,x^{2}+b x +a \right)^{2}}"," ",0,"2*(-1/8*(44*a^2*c^2-37*a*b^2*c+5*b^4)/(16*a^2*c^2-8*a*b^2*c+b^4)/c*x^(7/2)+1/8*b*(4*a^2*c^2+20*a*b^2*c-3*b^4)/c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^(5/2)-1/8*a/c^2*(28*a^2*c^2-49*a*b^2*c+6*b^4)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^(3/2)+3/8*a^2*b*(8*a*c-b^2)/c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^(1/2))/(c*x^2+b*x+a)^2+21/2/(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^(1/2))*a^2-27/8/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^(1/2))*a*b^2+3/8/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^(1/2))*b^4+33/2/(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^(1/2))*a^2*b-33/8/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^(1/2))*a*b^3+3/8/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^(1/2))*b^5-21/2/(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^(1/2))*a^2+27/8/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^(1/2))*a*b^2-3/8/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^(1/2))*b^4+33/2/(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^(1/2))*a^2*b-33/8/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^(1/2))*a*b^3+3/8/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^(1/2))*b^5","B"
2331,1,1571,394,0.193000," ","int(1/x^(3/2)/(c*x^2+b*x+a)^3,x)","-\frac{13 c^{4} x^{\frac{7}{2}}}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}+\frac{47 b^{2} c^{3} x^{\frac{7}{2}}}{4 \left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}-\frac{7 b^{4} c^{2} x^{\frac{7}{2}}}{4 \left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{3}}-\frac{34 b \,c^{3} x^{\frac{5}{2}}}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}+\frac{99 b^{3} c^{2} x^{\frac{5}{2}}}{4 \left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}-\frac{7 b^{5} c \,x^{\frac{5}{2}}}{2 \left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{3}}-\frac{25 b^{2} c^{2} x^{\frac{3}{2}}}{4 \left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}+\frac{43 b^{4} c \,x^{\frac{3}{2}}}{4 \left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}-\frac{7 b^{6} x^{\frac{3}{2}}}{4 \left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{3}}-\frac{17 c^{3} x^{\frac{3}{2}}}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}+\frac{93 \sqrt{2}\, b \,c^{3} \arctanh \left(\frac{\sqrt{2}\, c \sqrt{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}\, a}+\frac{93 \sqrt{2}\, b \,c^{3} \arctan \left(\frac{\sqrt{2}\, c \sqrt{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}\, a}-\frac{141 \sqrt{2}\, b^{3} c^{2} \arctanh \left(\frac{\sqrt{2}\, c \sqrt{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}\, a^{2}}-\frac{141 \sqrt{2}\, b^{3} c^{2} \arctan \left(\frac{\sqrt{2}\, c \sqrt{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}\, a^{2}}+\frac{15 \sqrt{2}\, b^{5} c \arctanh \left(\frac{\sqrt{2}\, c \sqrt{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}\, a^{3}}+\frac{15 \sqrt{2}\, b^{5} c \arctan \left(\frac{\sqrt{2}\, c \sqrt{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}\, a^{3}}+\frac{33 b^{3} c \sqrt{x}}{2 \left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}-\frac{9 b^{5} \sqrt{x}}{4 \left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}-\frac{27 b \,c^{2} \sqrt{x}}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}+\frac{45 \sqrt{2}\, c^{3} \arctanh \left(\frac{\sqrt{2}\, c \sqrt{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{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{45 \sqrt{2}\, c^{3} \arctan \left(\frac{\sqrt{2}\, c \sqrt{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{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{111 \sqrt{2}\, b^{2} c^{2} \arctanh \left(\frac{\sqrt{2}\, c \sqrt{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{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}+\frac{111 \sqrt{2}\, b^{2} c^{2} \arctan \left(\frac{\sqrt{2}\, c \sqrt{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{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}+\frac{15 \sqrt{2}\, b^{4} c \arctanh \left(\frac{\sqrt{2}\, c \sqrt{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{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{3}}-\frac{15 \sqrt{2}\, b^{4} c \arctan \left(\frac{\sqrt{2}\, c \sqrt{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{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{3}}-\frac{2}{a^{3} \sqrt{x}}"," ",0,"43/4/a^2/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^(3/2)*b^4*c+33/2/a/(c*x^2+b*x+a)^2*b^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x^(1/2)*c-7/2/a^3/(c*x^2+b*x+a)^2*c*b^5/(16*a^2*c^2-8*a*b^2*c+b^4)*x^(5/2)+47/4/a^2/(c*x^2+b*x+a)^2*c^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x^(7/2)*b^2-34/a/(c*x^2+b*x+a)^2*c^3*b/(16*a^2*c^2-8*a*b^2*c+b^4)*x^(5/2)+99/4/a^2/(c*x^2+b*x+a)^2*c^2*b^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x^(5/2)-2/a^3/x^(1/2)-45/2/a/(16*a^2*c^2-8*a*b^2*c+b^4)*c^3*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x^(1/2))+45/2/a/(16*a^2*c^2-8*a*b^2*c+b^4)*c^3*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x^(1/2))-25/4/a/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^(3/2)*b^2*c^2-7/4/a^3/(c*x^2+b*x+a)^2*c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^(7/2)*b^4-17/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^(3/2)*c^3+15/8/a^3/(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^(1/2))*b^5-141/8/a^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^(1/2))*b^3-141/8/a^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^(1/2))*b^3+15/8/a^3/(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^(1/2))*b^5+93/2/a/(16*a^2*c^2-8*a*b^2*c+b^4)*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^(1/2))*b+93/2/a/(16*a^2*c^2-8*a*b^2*c+b^4)*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^(1/2))*b-27/(c*x^2+b*x+a)^2*b/(16*a^2*c^2-8*a*b^2*c+b^4)*x^(1/2)*c^2-7/4/a^3/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^(3/2)*b^6-13/a/(c*x^2+b*x+a)^2*c^4/(16*a^2*c^2-8*a*b^2*c+b^4)*x^(7/2)-9/4/a^2/(c*x^2+b*x+a)^2*b^5/(16*a^2*c^2-8*a*b^2*c+b^4)*x^(1/2)-15/8/a^3/(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^(1/2))*b^4+15/8/a^3/(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^(1/2))*b^4-111/8/a^2/(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^(1/2))*b^2+111/8/a^2/(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^(1/2))*b^2","B"
2332,1,16,16,0.046000," ","int((x^2-x+3)/x^(1/3),x)","\frac{3 \left(5 x^{2}-8 x +60\right) x^{\frac{2}{3}}}{40}"," ",0,"3/40*x^(2/3)*(5*x^2-8*x+60)","A"
2333,1,795,226,0.105000," ","int((e*x+d)^3*(c*x^2+b*x+a)^(1/2),x)","\frac{3 a^{2} b \,e^{3} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{16 c^{\frac{5}{2}}}-\frac{3 a^{2} d \,e^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{8 c^{\frac{3}{2}}}-\frac{5 a \,b^{3} e^{3} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{32 c^{\frac{7}{2}}}+\frac{9 a \,b^{2} d \,e^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{16 c^{\frac{5}{2}}}-\frac{3 a b \,d^{2} e \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{4 c^{\frac{3}{2}}}+\frac{a \,d^{3} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{2 \sqrt{c}}+\frac{7 b^{5} e^{3} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{256 c^{\frac{9}{2}}}-\frac{15 b^{4} d \,e^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{128 c^{\frac{7}{2}}}+\frac{3 b^{3} d^{2} e \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{16 c^{\frac{5}{2}}}-\frac{b^{2} d^{3} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{8 c^{\frac{3}{2}}}+\frac{3 \sqrt{c \,x^{2}+b x +a}\, a b \,e^{3} x}{16 c^{2}}-\frac{3 \sqrt{c \,x^{2}+b x +a}\, a d \,e^{2} x}{8 c}-\frac{7 \sqrt{c \,x^{2}+b x +a}\, b^{3} e^{3} x}{64 c^{3}}+\frac{15 \sqrt{c \,x^{2}+b x +a}\, b^{2} d \,e^{2} x}{32 c^{2}}-\frac{3 \sqrt{c \,x^{2}+b x +a}\, b \,d^{2} e x}{4 c}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} e^{3} x^{2}}{5 c}+\frac{\sqrt{c \,x^{2}+b x +a}\, d^{3} x}{2}+\frac{3 \sqrt{c \,x^{2}+b x +a}\, a \,b^{2} e^{3}}{32 c^{3}}-\frac{3 \sqrt{c \,x^{2}+b x +a}\, a b d \,e^{2}}{16 c^{2}}-\frac{7 \sqrt{c \,x^{2}+b x +a}\, b^{4} e^{3}}{128 c^{4}}+\frac{15 \sqrt{c \,x^{2}+b x +a}\, b^{3} d \,e^{2}}{64 c^{3}}-\frac{3 \sqrt{c \,x^{2}+b x +a}\, b^{2} d^{2} e}{8 c^{2}}+\frac{\sqrt{c \,x^{2}+b x +a}\, b \,d^{3}}{4 c}-\frac{7 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b \,e^{3} x}{40 c^{2}}+\frac{3 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} d \,e^{2} x}{4 c}-\frac{2 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a \,e^{3}}{15 c^{2}}+\frac{7 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{2} e^{3}}{48 c^{3}}-\frac{5 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b d \,e^{2}}{8 c^{2}}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} d^{2} e}{c}"," ",0,"-7/40*e^3*b/c^2*x*(c*x^2+b*x+a)^(3/2)-3/8*d^2*e*b^2/c^2*(c*x^2+b*x+a)^(1/2)+3/16*d^2*e*b^3/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+7/256*e^3*b^5/c^(9/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-2/15*e^3*a/c^2*(c*x^2+b*x+a)^(3/2)+1/5*e^3*x^2*(c*x^2+b*x+a)^(3/2)/c+7/48*e^3*b^2/c^3*(c*x^2+b*x+a)^(3/2)+1/2*d^3/c^(1/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a+d^2*e*(c*x^2+b*x+a)^(3/2)/c-7/128*e^3*b^4/c^4*(c*x^2+b*x+a)^(1/2)-1/8*d^3/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*b^2+1/4*d^3/c*(c*x^2+b*x+a)^(1/2)*b+15/32*d*e^2*b^2/c^2*x*(c*x^2+b*x+a)^(1/2)+9/16*d*e^2*b^2/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a+3/16*e^3*b/c^2*a*x*(c*x^2+b*x+a)^(1/2)-3/4*d^2*e*b/c*x*(c*x^2+b*x+a)^(1/2)-3/4*d^2*e*b/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a-3/16*d*e^2*a/c^2*(c*x^2+b*x+a)^(1/2)*b-3/8*d*e^2*a/c*x*(c*x^2+b*x+a)^(1/2)+1/2*d^3*x*(c*x^2+b*x+a)^(1/2)-7/64*e^3*b^3/c^3*x*(c*x^2+b*x+a)^(1/2)-5/32*e^3*b^3/c^(7/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a+3/16*e^3*b/c^(5/2)*a^2*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+3/4*d*e^2*x*(c*x^2+b*x+a)^(3/2)/c-5/8*d*e^2*b/c^2*(c*x^2+b*x+a)^(3/2)+3/32*e^3*b^2/c^3*a*(c*x^2+b*x+a)^(1/2)+15/64*d*e^2*b^3/c^3*(c*x^2+b*x+a)^(1/2)-15/128*d*e^2*b^4/c^(7/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-3/8*d*e^2*a^2/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))","B"
2334,1,484,169,0.090000," ","int((e*x+d)^2*(c*x^2+b*x+a)^(1/2),x)","-\frac{a^{2} e^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{8 c^{\frac{3}{2}}}+\frac{3 a \,b^{2} e^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{16 c^{\frac{5}{2}}}-\frac{a b d e \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{2 c^{\frac{3}{2}}}+\frac{a \,d^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{2 \sqrt{c}}-\frac{5 b^{4} e^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{128 c^{\frac{7}{2}}}+\frac{b^{3} d e \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{8 c^{\frac{5}{2}}}-\frac{b^{2} d^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{8 c^{\frac{3}{2}}}-\frac{\sqrt{c \,x^{2}+b x +a}\, a \,e^{2} x}{8 c}+\frac{5 \sqrt{c \,x^{2}+b x +a}\, b^{2} e^{2} x}{32 c^{2}}-\frac{\sqrt{c \,x^{2}+b x +a}\, b d e x}{2 c}+\frac{\sqrt{c \,x^{2}+b x +a}\, d^{2} x}{2}-\frac{\sqrt{c \,x^{2}+b x +a}\, a b \,e^{2}}{16 c^{2}}+\frac{5 \sqrt{c \,x^{2}+b x +a}\, b^{3} e^{2}}{64 c^{3}}-\frac{\sqrt{c \,x^{2}+b x +a}\, b^{2} d e}{4 c^{2}}+\frac{\sqrt{c \,x^{2}+b x +a}\, b \,d^{2}}{4 c}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} e^{2} x}{4 c}-\frac{5 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b \,e^{2}}{24 c^{2}}+\frac{2 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} d e}{3 c}"," ",0,"1/4*e^2*x*(c*x^2+b*x+a)^(3/2)/c-5/24*e^2*b/c^2*(c*x^2+b*x+a)^(3/2)+5/32*e^2*b^2/c^2*x*(c*x^2+b*x+a)^(1/2)+5/64*e^2*b^3/c^3*(c*x^2+b*x+a)^(1/2)+3/16*e^2*b^2/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a-5/128*e^2*b^4/c^(7/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-1/8*e^2*a/c*x*(c*x^2+b*x+a)^(1/2)-1/16*e^2*a/c^2*(c*x^2+b*x+a)^(1/2)*b-1/8*e^2*a^2/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+2/3*d*e*(c*x^2+b*x+a)^(3/2)/c-1/2*d*e*b/c*x*(c*x^2+b*x+a)^(1/2)-1/4*d*e*b^2/c^2*(c*x^2+b*x+a)^(1/2)-1/2*d*e*b/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a+1/8*d*e*b^3/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+1/2*d^2*x*(c*x^2+b*x+a)^(1/2)+1/4*d^2/c*(c*x^2+b*x+a)^(1/2)*b+1/2*d^2/c^(1/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a-1/8*d^2/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*b^2","B"
2335,1,229,97,0.054000," ","int((e*x+d)*(c*x^2+b*x+a)^(1/2),x)","-\frac{a b e \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{4 c^{\frac{3}{2}}}+\frac{a d \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{2 \sqrt{c}}+\frac{b^{3} e \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{16 c^{\frac{5}{2}}}-\frac{b^{2} d \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{8 c^{\frac{3}{2}}}-\frac{\sqrt{c \,x^{2}+b x +a}\, b e x}{4 c}+\frac{\sqrt{c \,x^{2}+b x +a}\, d x}{2}-\frac{\sqrt{c \,x^{2}+b x +a}\, b^{2} e}{8 c^{2}}+\frac{\sqrt{c \,x^{2}+b x +a}\, b d}{4 c}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} e}{3 c}"," ",0,"1/3*e*(c*x^2+b*x+a)^(3/2)/c-1/4*e*b/c*x*(c*x^2+b*x+a)^(1/2)-1/8*e*b^2/c^2*(c*x^2+b*x+a)^(1/2)-1/4*e*b/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a+1/16*e*b^3/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+1/2*d*x*(c*x^2+b*x+a)^(1/2)+1/4*d/c*(c*x^2+b*x+a)^(1/2)*b+1/2*d/c^(1/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a-1/8*d/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*b^2","B"
2336,1,89,61,0.058000," ","int((c*x^2+b*x+a)^(1/2),x)","\frac{a \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{2 \sqrt{c}}-\frac{b^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{8 c^{\frac{3}{2}}}+\frac{\left(2 c x +b \right) \sqrt{c \,x^{2}+b x +a}}{4 c}"," ",0,"1/4*(2*c*x+b)*(c*x^2+b*x+a)^(1/2)/c+1/2/c^(1/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a-1/8/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*b^2","A"
2337,1,715,132,0.082000," ","int((c*x^2+b*x+a)^(1/2)/(e*x+d),x)","-\frac{a \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e}+\frac{b d \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e^{2}}-\frac{c \,d^{2} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e^{3}}+\frac{b \ln \left(\frac{\left(x +\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\right)}{2 \sqrt{c}\, e}-\frac{\sqrt{c}\, d \ln \left(\frac{\left(x +\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\right)}{e^{2}}+\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{e}"," ",0,"1/e*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)+1/2/e*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/c^(1/2)*b-1/e^2*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*c^(1/2)*d-1/e/((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)*(x+d/e)/e+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*a+1/e^2/((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)*(x+d/e)/e+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*b*d-1/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)*(x+d/e)/e+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*c*d^2","B"
2338,1,1519,140,0.076000," ","int((c*x^2+b*x+a)^(1/2)/(e*x+d)^2,x)","-\frac{a b \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{2 \left(a \,e^{2}-b d e +c \,d^{2}\right) \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}+\frac{a c d \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e}+\frac{b^{2} d \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{2 \left(a \,e^{2}-b d e +c \,d^{2}\right) \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e}-\frac{3 b c \,d^{2} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{2 \left(a \,e^{2}-b d e +c \,d^{2}\right) \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e^{2}}+\frac{c^{2} d^{3} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e^{3}}+\frac{a \sqrt{c}\, \ln \left(\frac{\left(x +\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\right)}{a \,e^{2}-b d e +c \,d^{2}}-\frac{b \sqrt{c}\, d \ln \left(\frac{\left(x +\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right) e}+\frac{c^{\frac{3}{2}} d^{2} \ln \left(\frac{\left(x +\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right) e^{2}}+\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, c x}{a \,e^{2}-b d e +c \,d^{2}}+\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, b}{a \,e^{2}-b d e +c \,d^{2}}-\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, c d}{\left(a \,e^{2}-b d e +c \,d^{2}\right) e}-\frac{\left(\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}\right)^{\frac{3}{2}}}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \left(x +\frac{d}{e}\right)}"," ",0,"-1/(a*e^2-b*d*e+c*d^2)/(x+d/e)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(3/2)+1/(a*e^2-b*d*e+c*d^2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b-1/e/(a*e^2-b*d*e+c*d^2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*c*d-1/e/(a*e^2-b*d*e+c*d^2)*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*c^(1/2)*d*b+1/e^2/(a*e^2-b*d*e+c*d^2)*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*c^(3/2)*d^2-1/2/(a*e^2-b*d*e+c*d^2)/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*a*b+1/e/(a*e^2-b*d*e+c*d^2)/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*a*c*d+1/2/e/(a*e^2-b*d*e+c*d^2)/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*b^2*d-3/2/e^2/(a*e^2-b*d*e+c*d^2)/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*b*d^2*c+1/e^3/(a*e^2-b*d*e+c*d^2)/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*c^2*d^3+c/(a*e^2-b*d*e+c*d^2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x+c^(1/2)/(a*e^2-b*d*e+c*d^2)*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*a","B"
2339,1,3269,139,0.063000," ","int((c*x^2+b*x+a)^(1/2)/(e*x+d)^3,x)","\text{output too large to display}"," ",0,"-3/4/e/(a*e^2-b*d*e+c*d^2)^2*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*c^(3/2)*d^2*b+1/8*e/(a*e^2-b*d*e+c*d^2)^2/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*a*b^2+1/2/e^3/(a*e^2-b*d*e+c*d^2)^2/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*c^3*d^4-1/4*e/(a*e^2-b*d*e+c*d^2)^2*c^(1/2)*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*a*b-1/2/e*c/(a*e^2-b*d*e+c*d^2)/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*a-1/2/e^3*c^2/(a*e^2-b*d*e+c*d^2)/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*d^2-1/4*e/(a*e^2-b*d*e+c*d^2)^2*c*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*b-1/2/e/(a*e^2-b*d*e+c*d^2)/(x+d/e)^2*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(3/2)+1/2/e*c/(a*e^2-b*d*e+c*d^2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)-1/4*e/(a*e^2-b*d*e+c*d^2)^2*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b^2+5/8/e/(a*e^2-b*d*e+c*d^2)^2/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*b^2*d^2*c-1/e^2/(a*e^2-b*d*e+c*d^2)^2/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*b*d^3*c^2-1/2/(a*e^2-b*d*e+c*d^2)^2/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*a*b*c*d-1/2/(a*e^2-b*d*e+c*d^2)^2/(x+d/e)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(3/2)*c*d-1/2/e^2*c^(3/2)/(a*e^2-b*d*e+c*d^2)*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*d+1/2/e^2/(a*e^2-b*d*e+c*d^2)^2*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*c^(5/2)*d^3+1/4*e/(a*e^2-b*d*e+c*d^2)^2/(x+d/e)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(3/2)*b-1/2/e/(a*e^2-b*d*e+c*d^2)^2*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*c^2*d^2+1/2/e^2*c/(a*e^2-b*d*e+c*d^2)/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*b*d+1/2/e/(a*e^2-b*d*e+c*d^2)^2/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*a*c^2*d^2+3/4/(a*e^2-b*d*e+c*d^2)^2*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b*c*d-1/8/(a*e^2-b*d*e+c*d^2)^2/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*b^3*d+1/4/(a*e^2-b*d*e+c*d^2)^2*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*c^(1/2)*d*b^2+1/2/(a*e^2-b*d*e+c*d^2)^2*c^2*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*d+1/2/(a*e^2-b*d*e+c*d^2)^2*c^(3/2)*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*a*d+1/4/e*c^(1/2)/(a*e^2-b*d*e+c*d^2)*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*b","B"
2340,1,4844,197,0.062000," ","int((c*x^2+b*x+a)^(1/2)/(e*x+d)^4,x)","\text{output too large to display}"," ",0,"1/2/e/(a*e^2-b*d*e+c*d^2)^2*c^(3/2)*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*d*b+1/8*e^2/(a*e^2-b*d*e+c*d^2)^3*c^(1/2)*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*a*b^2+1/16*e/(a*e^2-b*d*e+c*d^2)^3/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*b^4*d-1/2/e/(a*e^2-b*d*e+c*d^2)^2/(x+d/e)^2*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(3/2)*c*d-5/8*e/(a*e^2-b*d*e+c*d^2)^3*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b^2*c*d+1/8*e^2/(a*e^2-b*d*e+c*d^2)^3*c*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*b^2-1/2/e^3/(a*e^2-b*d*e+c*d^2)^2*c^3/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*d^3+3/8*e/(a*e^2-b*d*e+c*d^2)^3/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*a*b^2*c*d-1/8/(a*e^2-b*d*e+c*d^2)^2*c^(1/2)*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*b^2+1/8*e^2/(a*e^2-b*d*e+c*d^2)^3*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b^3-1/3/e^2/(a*e^2-b*d*e+c*d^2)/(x+d/e)^3*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(3/2)+1/4/(a*e^2-b*d*e+c*d^2)^2/(x+d/e)^2*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(3/2)*b-1/4/(a*e^2-b*d*e+c*d^2)^2*c*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b+1/2/e/(a*e^2-b*d*e+c*d^2)^3/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*a*c^3*d^3+9/8/e/(a*e^2-b*d*e+c*d^2)^3/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*b^2*d^3*c^2-1/4/e/(a*e^2-b*d*e+c*d^2)^2*c/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*b^2*d-5/4/e^2/(a*e^2-b*d*e+c*d^2)^3/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*c^3*d^4*b-1/2*e/(a*e^2-b*d*e+c*d^2)^3*c^2*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*b*d-1/2*e/(a*e^2-b*d*e+c*d^2)^3*c^(3/2)*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*a*d*b+1/2*e/(a*e^2-b*d*e+c*d^2)^3/(x+d/e)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(3/2)*c*d*b-3/4/(a*e^2-b*d*e+c*d^2)^3/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*a*b*c^2*d^2-1/2/e/(a*e^2-b*d*e+c*d^2)^2*c^2/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*a*d-1/2/(a*e^2-b*d*e+c*d^2)^3/(x+d/e)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(3/2)*c^2*d^2+1/(a*e^2-b*d*e+c*d^2)^3*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b*c^2*d^2+1/2/e/(a*e^2-b*d*e+c*d^2)^2*c^2*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*d-1/8*e^2/(a*e^2-b*d*e+c*d^2)^3/(x+d/e)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(3/2)*b^2+5/8/(a*e^2-b*d*e+c*d^2)^3*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*c^(3/2)*d^2*b^2+1/2/(a*e^2-b*d*e+c*d^2)^3*c^3*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*d^2+1/2/(a*e^2-b*d*e+c*d^2)^3*c^(5/2)*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*a*d^2+1/2/e^3/(a*e^2-b*d*e+c*d^2)^3/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*c^4*d^5-1/8*e/(a*e^2-b*d*e+c*d^2)^3*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*c^(1/2)*d*b^3-1/e/(a*e^2-b*d*e+c*d^2)^3*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*c^(5/2)*d^3*b+1/4/(a*e^2-b*d*e+c*d^2)^2*c/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*a*b-7/16/(a*e^2-b*d*e+c*d^2)^3/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*b^3*d^2*c-1/16*e^2/(a*e^2-b*d*e+c*d^2)^3/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*a*b^3+1/2/e^2/(a*e^2-b*d*e+c*d^2)^3*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*c^(7/2)*d^4-1/2/e^2/(a*e^2-b*d*e+c*d^2)^2*c^(5/2)*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*d^2-1/2/e/(a*e^2-b*d*e+c*d^2)^3*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*c^3*d^3+3/4/e^2/(a*e^2-b*d*e+c*d^2)^2*c^2/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*d^2*b","B"
2341,1,7991,286,0.147000," ","int((c*x^2+b*x+a)^(1/2)/(e*x+d)^5,x)","\text{output too large to display}"," ",0,"result too large to display","B"
2342,1,10791,376,0.141000," ","int((c*x^2+b*x+a)^(1/2)/(e*x+d)^6,x)","\text{output too large to display}"," ",0,"result too large to display","B"
2343,1,1437,295,0.070000," ","int((e*x+d)^3*(c*x^2+b*x+a)^(3/2),x)","\frac{3 a^{3} b \,e^{3} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{32 c^{\frac{5}{2}}}-\frac{3 a^{3} d \,e^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{16 c^{\frac{3}{2}}}-\frac{15 a^{2} b^{3} e^{3} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{128 c^{\frac{7}{2}}}+\frac{27 a^{2} b^{2} d \,e^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{64 c^{\frac{5}{2}}}-\frac{9 a^{2} b \,d^{2} e \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{16 c^{\frac{3}{2}}}+\frac{3 a^{2} d^{3} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{8 \sqrt{c}}+\frac{21 a \,b^{5} e^{3} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{512 c^{\frac{9}{2}}}-\frac{45 a \,b^{4} d \,e^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{256 c^{\frac{7}{2}}}+\frac{9 a \,b^{3} d^{2} e \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{32 c^{\frac{5}{2}}}-\frac{3 a \,b^{2} d^{3} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{16 c^{\frac{3}{2}}}-\frac{9 b^{7} e^{3} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{2048 c^{\frac{11}{2}}}+\frac{21 b^{6} d \,e^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{1024 c^{\frac{9}{2}}}-\frac{9 b^{5} d^{2} e \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{256 c^{\frac{7}{2}}}+\frac{3 b^{4} d^{3} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{128 c^{\frac{5}{2}}}+\frac{3 \sqrt{c \,x^{2}+b x +a}\, a^{2} b \,e^{3} x}{32 c^{2}}-\frac{3 \sqrt{c \,x^{2}+b x +a}\, a^{2} d \,e^{2} x}{16 c}-\frac{3 \sqrt{c \,x^{2}+b x +a}\, a \,b^{3} e^{3} x}{32 c^{3}}+\frac{3 \sqrt{c \,x^{2}+b x +a}\, a \,b^{2} d \,e^{2} x}{8 c^{2}}-\frac{9 \sqrt{c \,x^{2}+b x +a}\, a b \,d^{2} e x}{16 c}+\frac{3 \sqrt{c \,x^{2}+b x +a}\, a \,d^{3} x}{8}+\frac{9 \sqrt{c \,x^{2}+b x +a}\, b^{5} e^{3} x}{512 c^{4}}-\frac{21 \sqrt{c \,x^{2}+b x +a}\, b^{4} d \,e^{2} x}{256 c^{3}}+\frac{9 \sqrt{c \,x^{2}+b x +a}\, b^{3} d^{2} e x}{64 c^{2}}-\frac{3 \sqrt{c \,x^{2}+b x +a}\, b^{2} d^{3} x}{32 c}+\frac{3 \sqrt{c \,x^{2}+b x +a}\, a^{2} b^{2} e^{3}}{64 c^{3}}-\frac{3 \sqrt{c \,x^{2}+b x +a}\, a^{2} b d \,e^{2}}{32 c^{2}}-\frac{3 \sqrt{c \,x^{2}+b x +a}\, a \,b^{4} e^{3}}{64 c^{4}}+\frac{3 \sqrt{c \,x^{2}+b x +a}\, a \,b^{3} d \,e^{2}}{16 c^{3}}-\frac{9 \sqrt{c \,x^{2}+b x +a}\, a \,b^{2} d^{2} e}{32 c^{2}}+\frac{3 \sqrt{c \,x^{2}+b x +a}\, a b \,d^{3}}{16 c}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a b \,e^{3} x}{16 c^{2}}-\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a d \,e^{2} x}{8 c}+\frac{9 \sqrt{c \,x^{2}+b x +a}\, b^{6} e^{3}}{1024 c^{5}}-\frac{21 \sqrt{c \,x^{2}+b x +a}\, b^{5} d \,e^{2}}{512 c^{4}}+\frac{9 \sqrt{c \,x^{2}+b x +a}\, b^{4} d^{2} e}{128 c^{3}}-\frac{3 \sqrt{c \,x^{2}+b x +a}\, b^{3} d^{3}}{64 c^{2}}-\frac{3 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{3} e^{3} x}{64 c^{3}}+\frac{7 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{2} d \,e^{2} x}{32 c^{2}}-\frac{3 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b \,d^{2} e x}{8 c}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} e^{3} x^{2}}{7 c}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} d^{3} x}{4}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a \,b^{2} e^{3}}{32 c^{3}}-\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a b d \,e^{2}}{16 c^{2}}-\frac{3 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{4} e^{3}}{128 c^{4}}+\frac{7 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{3} d \,e^{2}}{64 c^{3}}-\frac{3 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{2} d^{2} e}{16 c^{2}}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b \,d^{3}}{8 c}-\frac{3 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} b \,e^{3} x}{28 c^{2}}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} d \,e^{2} x}{2 c}-\frac{2 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} a \,e^{3}}{35 c^{2}}+\frac{3 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} b^{2} e^{3}}{40 c^{3}}-\frac{7 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} b d \,e^{2}}{20 c^{2}}+\frac{3 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} d^{2} e}{5 c}"," ",0,"-9/16*d^2*e*b/c*(c*x^2+b*x+a)^(1/2)*x*a+3/8*d*e^2*b^2/c^2*(c*x^2+b*x+a)^(1/2)*x*a+7/32*d*e^2*b^2/c^2*x*(c*x^2+b*x+a)^(3/2)+3/32*e^3*b/c^2*a^2*(c*x^2+b*x+a)^(1/2)*x+1/16*e^3*b/c^2*a*x*(c*x^2+b*x+a)^(3/2)-3/32*e^3*b^3/c^3*(c*x^2+b*x+a)^(1/2)*x*a-3/16*d*e^2*a^2/c*(c*x^2+b*x+a)^(1/2)*x-1/8*d*e^2*a/c*x*(c*x^2+b*x+a)^(3/2)+27/64*d*e^2*b^2/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a^2-45/256*d*e^2*b^4/c^(7/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a+3/16*d*e^2*b^3/c^3*(c*x^2+b*x+a)^(1/2)*a-21/256*d*e^2*b^4/c^3*(c*x^2+b*x+a)^(1/2)*x-3/8*d^2*e*b/c*x*(c*x^2+b*x+a)^(3/2)+9/64*d^2*e*b^3/c^2*(c*x^2+b*x+a)^(1/2)*x-3/32*d*e^2*a^2/c^2*(c*x^2+b*x+a)^(1/2)*b-1/16*d*e^2*a/c^2*(c*x^2+b*x+a)^(3/2)*b+9/32*d^2*e*b^3/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a-9/32*d^2*e*b^2/c^2*(c*x^2+b*x+a)^(1/2)*a-9/16*d^2*e*b/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a^2-3/28*e^3*b/c^2*x*(c*x^2+b*x+a)^(5/2)-3/64*e^3*b^3/c^3*x*(c*x^2+b*x+a)^(3/2)-3/16*d^2*e*b^2/c^2*(c*x^2+b*x+a)^(3/2)+3/40*e^3*b^2/c^3*(c*x^2+b*x+a)^(5/2)-3/128*e^3*b^4/c^4*(c*x^2+b*x+a)^(3/2)+9/1024*e^3*b^6/c^5*(c*x^2+b*x+a)^(1/2)-9/2048*e^3*b^7/c^(11/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+1/7*e^3*x^2*(c*x^2+b*x+a)^(5/2)/c-2/35*e^3*a/c^2*(c*x^2+b*x+a)^(5/2)+3/128*d^3/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*b^4+1/8*d^3/c*(c*x^2+b*x+a)^(3/2)*b+3/8*d^3*(c*x^2+b*x+a)^(1/2)*x*a-3/64*d^3/c^2*(c*x^2+b*x+a)^(1/2)*b^3+3/8*d^3/c^(1/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a^2+3/5*d^2*e*(c*x^2+b*x+a)^(5/2)/c+3/32*e^3*b/c^(5/2)*a^3*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+9/128*d^2*e*b^4/c^3*(c*x^2+b*x+a)^(1/2)-9/256*d^2*e*b^5/c^(7/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+21/1024*d*e^2*b^6/c^(9/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-3/16*d*e^2*a^3/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-3/16*d^3/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*b^2*a+9/512*e^3*b^5/c^4*(c*x^2+b*x+a)^(1/2)*x-3/64*e^3*b^4/c^4*(c*x^2+b*x+a)^(1/2)*a+1/32*e^3*b^2/c^3*a*(c*x^2+b*x+a)^(3/2)+1/4*d^3*x*(c*x^2+b*x+a)^(3/2)-21/512*d*e^2*b^5/c^4*(c*x^2+b*x+a)^(1/2)-3/32*d^3/c*(c*x^2+b*x+a)^(1/2)*x*b^2+3/16*d^3/c*(c*x^2+b*x+a)^(1/2)*b*a+3/64*e^3*b^2/c^3*a^2*(c*x^2+b*x+a)^(1/2)-15/128*e^3*b^3/c^(7/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a^2+21/512*e^3*b^5/c^(9/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a+1/2*d*e^2*x*(c*x^2+b*x+a)^(5/2)/c-7/20*d*e^2*b/c^2*(c*x^2+b*x+a)^(5/2)+7/64*d*e^2*b^3/c^3*(c*x^2+b*x+a)^(3/2)","B"
2344,1,922,231,0.064000," ","int((e*x+d)^2*(c*x^2+b*x+a)^(3/2),x)","-\frac{a^{3} e^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{16 c^{\frac{3}{2}}}+\frac{9 a^{2} b^{2} e^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{64 c^{\frac{5}{2}}}-\frac{3 a^{2} b d e \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{8 c^{\frac{3}{2}}}+\frac{3 a^{2} d^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{8 \sqrt{c}}-\frac{15 a \,b^{4} e^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{256 c^{\frac{7}{2}}}+\frac{3 a \,b^{3} d e \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{16 c^{\frac{5}{2}}}-\frac{3 a \,b^{2} d^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{16 c^{\frac{3}{2}}}+\frac{7 b^{6} e^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{1024 c^{\frac{9}{2}}}-\frac{3 b^{5} d e \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{128 c^{\frac{7}{2}}}+\frac{3 b^{4} d^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{128 c^{\frac{5}{2}}}-\frac{\sqrt{c \,x^{2}+b x +a}\, a^{2} e^{2} x}{16 c}+\frac{\sqrt{c \,x^{2}+b x +a}\, a \,b^{2} e^{2} x}{8 c^{2}}-\frac{3 \sqrt{c \,x^{2}+b x +a}\, a b d e x}{8 c}+\frac{3 \sqrt{c \,x^{2}+b x +a}\, a \,d^{2} x}{8}-\frac{7 \sqrt{c \,x^{2}+b x +a}\, b^{4} e^{2} x}{256 c^{3}}+\frac{3 \sqrt{c \,x^{2}+b x +a}\, b^{3} d e x}{32 c^{2}}-\frac{3 \sqrt{c \,x^{2}+b x +a}\, b^{2} d^{2} x}{32 c}-\frac{\sqrt{c \,x^{2}+b x +a}\, a^{2} b \,e^{2}}{32 c^{2}}+\frac{\sqrt{c \,x^{2}+b x +a}\, a \,b^{3} e^{2}}{16 c^{3}}-\frac{3 \sqrt{c \,x^{2}+b x +a}\, a \,b^{2} d e}{16 c^{2}}+\frac{3 \sqrt{c \,x^{2}+b x +a}\, a b \,d^{2}}{16 c}-\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a \,e^{2} x}{24 c}-\frac{7 \sqrt{c \,x^{2}+b x +a}\, b^{5} e^{2}}{512 c^{4}}+\frac{3 \sqrt{c \,x^{2}+b x +a}\, b^{4} d e}{64 c^{3}}-\frac{3 \sqrt{c \,x^{2}+b x +a}\, b^{3} d^{2}}{64 c^{2}}+\frac{7 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{2} e^{2} x}{96 c^{2}}-\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b d e x}{4 c}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} d^{2} x}{4}-\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a b \,e^{2}}{48 c^{2}}+\frac{7 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{3} e^{2}}{192 c^{3}}-\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{2} d e}{8 c^{2}}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b \,d^{2}}{8 c}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} e^{2} x}{6 c}-\frac{7 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} b \,e^{2}}{60 c^{2}}+\frac{2 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} d e}{5 c}"," ",0,"-15/256*e^2*b^4/c^(7/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a-1/24*e^2*a/c*x*(c*x^2+b*x+a)^(3/2)-3/8*d*e*b/c*(c*x^2+b*x+a)^(1/2)*x*a+1/6*e^2*x*(c*x^2+b*x+a)^(5/2)/c-7/60*e^2*b/c^2*(c*x^2+b*x+a)^(5/2)+7/1024*e^2*b^6/c^(9/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+7/192*e^2*b^3/c^3*(c*x^2+b*x+a)^(3/2)+1/8*d^2/c*(c*x^2+b*x+a)^(3/2)*b+2/5*d*e*(c*x^2+b*x+a)^(5/2)/c-1/16*e^2*a^3/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-7/512*e^2*b^5/c^4*(c*x^2+b*x+a)^(1/2)+3/128*d^2/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*b^4+3/8*d^2*(c*x^2+b*x+a)^(1/2)*x*a-3/64*d^2/c^2*(c*x^2+b*x+a)^(1/2)*b^3+3/8*d^2/c^(1/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a^2+1/8*e^2*b^2/c^2*(c*x^2+b*x+a)^(1/2)*x*a+3/16*d*e*b^3/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a-1/4*d*e*b/c*x*(c*x^2+b*x+a)^(3/2)+3/32*d*e*b^3/c^2*(c*x^2+b*x+a)^(1/2)*x-3/16*d*e*b^2/c^2*(c*x^2+b*x+a)^(1/2)*a-3/8*d*e*b/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a^2+1/4*d^2*x*(c*x^2+b*x+a)^(3/2)-3/32*d^2/c*(c*x^2+b*x+a)^(1/2)*x*b^2+3/16*d^2/c*(c*x^2+b*x+a)^(1/2)*b*a+7/96*e^2*b^2/c^2*x*(c*x^2+b*x+a)^(3/2)-7/256*e^2*b^4/c^3*(c*x^2+b*x+a)^(1/2)*x-1/8*d*e*b^2/c^2*(c*x^2+b*x+a)^(3/2)+3/64*d*e*b^4/c^3*(c*x^2+b*x+a)^(1/2)-3/16*d^2/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*b^2*a+1/16*e^2*b^3/c^3*(c*x^2+b*x+a)^(1/2)*a-1/48*e^2*a/c^2*(c*x^2+b*x+a)^(3/2)*b+9/64*e^2*b^2/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a^2-3/128*d*e*b^5/c^(7/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-1/16*e^2*a^2/c*(c*x^2+b*x+a)^(1/2)*x-1/32*e^2*a^2/c^2*(c*x^2+b*x+a)^(1/2)*b","B"
2345,1,469,139,0.062000," ","int((e*x+d)*(c*x^2+b*x+a)^(3/2),x)","-\frac{3 a^{2} b e \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{16 c^{\frac{3}{2}}}+\frac{3 a^{2} d \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{8 \sqrt{c}}+\frac{3 a \,b^{3} e \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{32 c^{\frac{5}{2}}}-\frac{3 a \,b^{2} d \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{16 c^{\frac{3}{2}}}-\frac{3 b^{5} e \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{256 c^{\frac{7}{2}}}+\frac{3 b^{4} d \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{128 c^{\frac{5}{2}}}-\frac{3 \sqrt{c \,x^{2}+b x +a}\, a b e x}{16 c}+\frac{3 \sqrt{c \,x^{2}+b x +a}\, a d x}{8}+\frac{3 \sqrt{c \,x^{2}+b x +a}\, b^{3} e x}{64 c^{2}}-\frac{3 \sqrt{c \,x^{2}+b x +a}\, b^{2} d x}{32 c}-\frac{3 \sqrt{c \,x^{2}+b x +a}\, a \,b^{2} e}{32 c^{2}}+\frac{3 \sqrt{c \,x^{2}+b x +a}\, a b d}{16 c}+\frac{3 \sqrt{c \,x^{2}+b x +a}\, b^{4} e}{128 c^{3}}-\frac{3 \sqrt{c \,x^{2}+b x +a}\, b^{3} d}{64 c^{2}}-\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b e x}{8 c}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} d x}{4}-\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{2} e}{16 c^{2}}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b d}{8 c}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} e}{5 c}"," ",0,"1/5*e*(c*x^2+b*x+a)^(5/2)/c-1/8*e*b/c*x*(c*x^2+b*x+a)^(3/2)-1/16*e*b^2/c^2*(c*x^2+b*x+a)^(3/2)-3/16*e*b/c*(c*x^2+b*x+a)^(1/2)*x*a+3/64*e*b^3/c^2*(c*x^2+b*x+a)^(1/2)*x-3/32*e*b^2/c^2*(c*x^2+b*x+a)^(1/2)*a+3/128*e*b^4/c^3*(c*x^2+b*x+a)^(1/2)-3/16*e*b/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a^2+3/32*e*b^3/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a-3/256*e*b^5/c^(7/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+1/4*d*x*(c*x^2+b*x+a)^(3/2)+1/8*d/c*(c*x^2+b*x+a)^(3/2)*b+3/8*d*(c*x^2+b*x+a)^(1/2)*x*a-3/32*d/c*(c*x^2+b*x+a)^(1/2)*x*b^2+3/16*d/c*(c*x^2+b*x+a)^(1/2)*b*a-3/64*d/c^2*(c*x^2+b*x+a)^(1/2)*b^3+3/8*d/c^(1/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a^2-3/16*d/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*b^2*a+3/128*d/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*b^4","B"
2346,1,201,94,0.052000," ","int((c*x^2+b*x+a)^(3/2),x)","\frac{3 a^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{8 \sqrt{c}}-\frac{3 a \,b^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{16 c^{\frac{3}{2}}}+\frac{3 b^{4} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{128 c^{\frac{5}{2}}}+\frac{3 \sqrt{c \,x^{2}+b x +a}\, a x}{8}-\frac{3 \sqrt{c \,x^{2}+b x +a}\, b^{2} x}{32 c}+\frac{3 \sqrt{c \,x^{2}+b x +a}\, a b}{16 c}-\frac{3 \sqrt{c \,x^{2}+b x +a}\, b^{3}}{64 c^{2}}+\frac{\left(2 c x +b \right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}}}{8 c}"," ",0,"1/8*(2*c*x+b)*(c*x^2+b*x+a)^(3/2)/c+3/8*(c*x^2+b*x+a)^(1/2)*x*a-3/32/c*(c*x^2+b*x+a)^(1/2)*x*b^2+3/16/c*(c*x^2+b*x+a)^(1/2)*b*a-3/64/c^2*(c*x^2+b*x+a)^(1/2)*b^3+3/8/c^(1/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a^2-3/16/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a*b^2+3/128/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*b^4","B"
2347,1,1946,226,0.061000," ","int((c*x^2+b*x+a)^(3/2)/(e*x+d),x)","-\frac{a^{2} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e}+\frac{2 a b d \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e^{2}}-\frac{2 a c \,d^{2} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-b d e +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 +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e^{3}}+\frac{2 b c \,d^{3} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e^{4}}-\frac{c^{2} d^{4} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e^{5}}+\frac{3 a b \ln \left(\frac{\left(x +\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\right)}{4 \sqrt{c}\, e}-\frac{3 a \sqrt{c}\, d \ln \left(\frac{\left(x +\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\right)}{2 e^{2}}-\frac{b^{3} \ln \left(\frac{\left(x +\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\right)}{16 c^{\frac{3}{2}} e}-\frac{3 b^{2} d \ln \left(\frac{\left(x +\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\right)}{8 \sqrt{c}\, e^{2}}+\frac{3 b \sqrt{c}\, d^{2} \ln \left(\frac{\left(x +\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\right)}{2 e^{3}}-\frac{c^{\frac{3}{2}} d^{3} \ln \left(\frac{\left(x +\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\right)}{e^{4}}+\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, b x}{4 e}-\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, c d x}{2 e^{2}}+\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, a}{e}+\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, b^{2}}{8 c e}-\frac{5 \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, b d}{4 e^{2}}+\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, c \,d^{2}}{e^{3}}+\frac{\left(\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}\right)^{\frac{3}{2}}}{3 e}"," ",0,"1/3/e*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(3/2)+1/4/e*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*b-1/2/e^2*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*c*d+1/8/e/c*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b^2-5/4/e^2*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b*d+3/4/e/c^(1/2)*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*a*b-3/2/e^2*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*c^(1/2)*d*a-1/16/e/c^(3/2)*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*b^3-3/8/e^2*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/c^(1/2)*b^2*d+1/e*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*a+1/e^3*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*c*d^2+3/2/e^3*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*c^(1/2)*d^2*b-1/e^4*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*c^(3/2)*d^3-1/e/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*a^2+2/e^2/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*a*b*d-2/e^3/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*a*c*d^2-1/e^3/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*b^2*d^2+2/e^4/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*b*d^3*c-1/e^5/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*c^2*d^4","B"
2348,1,3450,201,0.112000," ","int((c*x^2+b*x+a)^(3/2)/(e*x+d)^2,x)","\text{output too large to display}"," ",0,"c/(a*e^2-b*d*e+c*d^2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(3/2)*x+3/2*c^(1/2)/(a*e^2-b*d*e+c*d^2)*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*a^2+9/4/(a*e^2-b*d*e+c*d^2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*a*b-3/e/(a*e^2-b*d*e+c*d^2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*a*c*d-6/e^3/(a*e^2-b*d*e+c*d^2)*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*c^(3/2)*d^3*b+9/2/e^2/(a*e^2-b*d*e+c*d^2)*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*c^(3/2)*d^2*a+3/e^5/(a*e^2-b*d*e+c*d^2)/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*c^3*d^5+3/2*c/(a*e^2-b*d*e+c*d^2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*a+1/(a*e^2-b*d*e+c*d^2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(3/2)*b-1/(a*e^2-b*d*e+c*d^2)/(x+d/e)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(5/2)-9/e^2/(a*e^2-b*d*e+c*d^2)/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*a*b*d^2*c+6/e^3/(a*e^2-b*d*e+c*d^2)/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*b^2*d^3*c-3/2/e/(a*e^2-b*d*e+c*d^2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*b*c*d-9/2/e/(a*e^2-b*d*e+c*d^2)*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*c^(1/2)*d*a*b+3/e/(a*e^2-b*d*e+c*d^2)/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*a^2*c*d-15/2/e^4/(a*e^2-b*d*e+c*d^2)/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*b*d^4*c^2+6/e^3/(a*e^2-b*d*e+c*d^2)/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*a*c^2*d^3+3/e/(a*e^2-b*d*e+c*d^2)/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*a*b^2*d+21/4/e^2/(a*e^2-b*d*e+c*d^2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b*d^2*c-3/2/e^2/(a*e^2-b*d*e+c*d^2)/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*b^3*d^2-3/8/e/(a*e^2-b*d*e+c*d^2)*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/c^(1/2)*b^3*d+3/8/(a*e^2-b*d*e+c*d^2)/c^(1/2)*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*a*b^2-9/4/e/(a*e^2-b*d*e+c*d^2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b^2*d-1/e/(a*e^2-b*d*e+c*d^2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(3/2)*c*d+3/e^4/(a*e^2-b*d*e+c*d^2)*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*c^(5/2)*d^4-3/e^3/(a*e^2-b*d*e+c*d^2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*c^2*d^3-3/2/(a*e^2-b*d*e+c*d^2)/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*a^2*b+3/2/e^2/(a*e^2-b*d*e+c*d^2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*c^2*d^2+27/8/e^2/(a*e^2-b*d*e+c*d^2)*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*c^(1/2)*d^2*b^2","B"
2349,1,7299,208,0.061000," ","int((c*x^2+b*x+a)^(3/2)/(e*x+d)^3,x)","\text{output too large to display}"," ",0,"result too large to display","B"
2350,1,10401,281,0.158000," ","int((c*x^2+b*x+a)^(3/2)/(e*x+d)^4,x)","\text{output too large to display}"," ",0,"result too large to display","B"
2351,1,15932,207,0.068000," ","int((c*x^2+b*x+a)^(3/2)/(e*x+d)^5,x)","\text{output too large to display}"," ",0,"result too large to display","B"
2352,1,20477,274,0.079000," ","int((c*x^2+b*x+a)^(3/2)/(e*x+d)^6,x)","\text{output too large to display}"," ",0,"result too large to display","B"
2353,1,28629,383,0.539000," ","int((c*x^2+b*x+a)^(3/2)/(e*x+d)^7,x)","\text{output too large to display}"," ",0,"result too large to display","B"
2354,1,35234,480,1.099000," ","int((c*x^2+b*x+a)^(3/2)/(e*x+d)^8,x)","\text{output too large to display}"," ",0,"result too large to display","B"
2355,1,2294,370,0.060000," ","int((e*x+d)^3*(c*x^2+b*x+a)^(5/2),x)","\frac{15 a^{4} b \,e^{3} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{256 c^{\frac{5}{2}}}-\frac{15 a^{4} d \,e^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{128 c^{\frac{3}{2}}}-\frac{25 a^{3} b^{3} e^{3} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{256 c^{\frac{7}{2}}}+\frac{45 a^{3} b^{2} d \,e^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{128 c^{\frac{5}{2}}}-\frac{15 a^{3} b \,d^{2} e \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{32 c^{\frac{3}{2}}}+\frac{5 a^{3} d^{3} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{16 \sqrt{c}}+\frac{105 a^{2} b^{5} e^{3} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{2048 c^{\frac{9}{2}}}-\frac{225 a^{2} b^{4} d \,e^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{1024 c^{\frac{7}{2}}}+\frac{45 a^{2} b^{3} d^{2} e \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{128 c^{\frac{5}{2}}}-\frac{15 a^{2} b^{2} d^{3} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{64 c^{\frac{3}{2}}}-\frac{45 a \,b^{7} e^{3} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{4096 c^{\frac{11}{2}}}+\frac{105 a \,b^{6} d \,e^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{2048 c^{\frac{9}{2}}}-\frac{45 a \,b^{5} d^{2} e \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{512 c^{\frac{7}{2}}}+\frac{15 a \,b^{4} d^{3} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{256 c^{\frac{5}{2}}}+\frac{55 b^{9} e^{3} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{65536 c^{\frac{13}{2}}}-\frac{135 b^{8} d \,e^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{32768 c^{\frac{11}{2}}}+\frac{15 b^{7} d^{2} e \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{2048 c^{\frac{9}{2}}}-\frac{5 b^{6} d^{3} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{1024 c^{\frac{7}{2}}}+\frac{15 \sqrt{c \,x^{2}+b x +a}\, a^{3} b \,e^{3} x}{256 c^{2}}-\frac{15 \sqrt{c \,x^{2}+b x +a}\, a^{3} d \,e^{2} x}{128 c}-\frac{85 \sqrt{c \,x^{2}+b x +a}\, a^{2} b^{3} e^{3} x}{1024 c^{3}}+\frac{165 \sqrt{c \,x^{2}+b x +a}\, a^{2} b^{2} d \,e^{2} x}{512 c^{2}}-\frac{15 \sqrt{c \,x^{2}+b x +a}\, a^{2} b \,d^{2} e x}{32 c}+\frac{5 \sqrt{c \,x^{2}+b x +a}\, a^{2} d^{3} x}{16}+\frac{125 \sqrt{c \,x^{2}+b x +a}\, a \,b^{5} e^{3} x}{4096 c^{4}}-\frac{285 \sqrt{c \,x^{2}+b x +a}\, a \,b^{4} d \,e^{2} x}{2048 c^{3}}+\frac{15 \sqrt{c \,x^{2}+b x +a}\, a \,b^{3} d^{2} e x}{64 c^{2}}-\frac{5 \sqrt{c \,x^{2}+b x +a}\, a \,b^{2} d^{3} x}{32 c}-\frac{55 \sqrt{c \,x^{2}+b x +a}\, b^{7} e^{3} x}{16384 c^{5}}+\frac{135 \sqrt{c \,x^{2}+b x +a}\, b^{6} d \,e^{2} x}{8192 c^{4}}-\frac{15 \sqrt{c \,x^{2}+b x +a}\, b^{5} d^{2} e x}{512 c^{3}}+\frac{5 \sqrt{c \,x^{2}+b x +a}\, b^{4} d^{3} x}{256 c^{2}}+\frac{15 \sqrt{c \,x^{2}+b x +a}\, a^{3} b^{2} e^{3}}{512 c^{3}}-\frac{15 \sqrt{c \,x^{2}+b x +a}\, a^{3} b d \,e^{2}}{256 c^{2}}-\frac{85 \sqrt{c \,x^{2}+b x +a}\, a^{2} b^{4} e^{3}}{2048 c^{4}}+\frac{165 \sqrt{c \,x^{2}+b x +a}\, a^{2} b^{3} d \,e^{2}}{1024 c^{3}}-\frac{15 \sqrt{c \,x^{2}+b x +a}\, a^{2} b^{2} d^{2} e}{64 c^{2}}+\frac{5 \sqrt{c \,x^{2}+b x +a}\, a^{2} b \,d^{3}}{32 c}+\frac{5 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a^{2} b \,e^{3} x}{128 c^{2}}-\frac{5 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a^{2} d \,e^{2} x}{64 c}+\frac{125 \sqrt{c \,x^{2}+b x +a}\, a \,b^{6} e^{3}}{8192 c^{5}}-\frac{285 \sqrt{c \,x^{2}+b x +a}\, a \,b^{5} d \,e^{2}}{4096 c^{4}}+\frac{15 \sqrt{c \,x^{2}+b x +a}\, a \,b^{4} d^{2} e}{128 c^{3}}-\frac{5 \sqrt{c \,x^{2}+b x +a}\, a \,b^{3} d^{3}}{64 c^{2}}-\frac{35 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a \,b^{3} e^{3} x}{768 c^{3}}+\frac{25 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a \,b^{2} d \,e^{2} x}{128 c^{2}}-\frac{5 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a b \,d^{2} e x}{16 c}+\frac{5 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a \,d^{3} x}{24}-\frac{55 \sqrt{c \,x^{2}+b x +a}\, b^{8} e^{3}}{32768 c^{6}}+\frac{135 \sqrt{c \,x^{2}+b x +a}\, b^{7} d \,e^{2}}{16384 c^{5}}-\frac{15 \sqrt{c \,x^{2}+b x +a}\, b^{6} d^{2} e}{1024 c^{4}}+\frac{5 \sqrt{c \,x^{2}+b x +a}\, b^{5} d^{3}}{512 c^{3}}+\frac{55 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{5} e^{3} x}{6144 c^{4}}-\frac{45 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{4} d \,e^{2} x}{1024 c^{3}}+\frac{5 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{3} d^{2} e x}{64 c^{2}}-\frac{5 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{2} d^{3} x}{96 c}+\frac{5 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a^{2} b^{2} e^{3}}{256 c^{3}}-\frac{5 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a^{2} b d \,e^{2}}{128 c^{2}}-\frac{35 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a \,b^{4} e^{3}}{1536 c^{4}}+\frac{25 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a \,b^{3} d \,e^{2}}{256 c^{3}}-\frac{5 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a \,b^{2} d^{2} e}{32 c^{2}}+\frac{5 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a b \,d^{3}}{48 c}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} a b \,e^{3} x}{32 c^{2}}-\frac{\left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} a d \,e^{2} x}{16 c}+\frac{55 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{6} e^{3}}{12288 c^{5}}-\frac{45 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{5} d \,e^{2}}{2048 c^{4}}+\frac{5 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{4} d^{2} e}{128 c^{3}}-\frac{5 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{3} d^{3}}{192 c^{2}}-\frac{11 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} b^{3} e^{3} x}{384 c^{3}}+\frac{9 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} b^{2} d \,e^{2} x}{64 c^{2}}-\frac{\left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} b \,d^{2} e x}{4 c}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{7}{2}} e^{3} x^{2}}{9 c}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} d^{3} x}{6}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} a \,b^{2} e^{3}}{64 c^{3}}-\frac{\left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} a b d \,e^{2}}{32 c^{2}}-\frac{11 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} b^{4} e^{3}}{768 c^{4}}+\frac{9 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} b^{3} d \,e^{2}}{128 c^{3}}-\frac{\left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} b^{2} d^{2} e}{8 c^{2}}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} b \,d^{3}}{12 c}-\frac{11 \left(c \,x^{2}+b x +a \right)^{\frac{7}{2}} b \,e^{3} x}{144 c^{2}}+\frac{3 \left(c \,x^{2}+b x +a \right)^{\frac{7}{2}} d \,e^{2} x}{8 c}-\frac{2 \left(c \,x^{2}+b x +a \right)^{\frac{7}{2}} a \,e^{3}}{63 c^{2}}+\frac{11 \left(c \,x^{2}+b x +a \right)^{\frac{7}{2}} b^{2} e^{3}}{224 c^{3}}-\frac{27 \left(c \,x^{2}+b x +a \right)^{\frac{7}{2}} b d \,e^{2}}{112 c^{2}}+\frac{3 \left(c \,x^{2}+b x +a \right)^{\frac{7}{2}} d^{2} e}{7 c}"," ",0,"105/2048*d*e^2*b^6/c^(9/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a+45/128*d*e^2*b^2/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a^3-285/4096*d*e^2*b^5/c^4*(c*x^2+b*x+a)^(1/2)*a-5/32*d^2*e*b^2/c^2*(c*x^2+b*x+a)^(3/2)*a-15/512*d^2*e*b^5/c^3*(c*x^2+b*x+a)^(1/2)*x-15/64*d^2*e*b^2/c^2*(c*x^2+b*x+a)^(1/2)*a^2+15/128*d^2*e*b^4/c^3*(c*x^2+b*x+a)^(1/2)*a-15/32*d^2*e*b/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a^3-1/4*d^2*e*b/c*x*(c*x^2+b*x+a)^(5/2)+5/64*d^2*e*b^3/c^2*(c*x^2+b*x+a)^(3/2)*x-225/1024*d*e^2*b^4/c^(7/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a^2-5/64*d*e^2*a^2/c*(c*x^2+b*x+a)^(3/2)*x-1/32*d*e^2*a/c^2*(c*x^2+b*x+a)^(5/2)*b+45/128*d^2*e*b^3/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a^2-45/512*d^2*e*b^5/c^(7/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a-5/32*d^3/c*(c*x^2+b*x+a)^(1/2)*x*a*b^2-15/64*d^3/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*b^2*a^2+15/256*d^3/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*b^4*a-1/8*d^2*e*b^2/c^2*(c*x^2+b*x+a)^(5/2)+5/128*d^2*e*b^4/c^3*(c*x^2+b*x+a)^(3/2)-15/1024*d^2*e*b^6/c^4*(c*x^2+b*x+a)^(1/2)+15/2048*d^2*e*b^7/c^(9/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-5/96*d^3/c*(c*x^2+b*x+a)^(3/2)*x*b^2+5/48*d^3/c*(c*x^2+b*x+a)^(3/2)*b*a+5/256*d^3/c^2*(c*x^2+b*x+a)^(1/2)*x*b^4-11/144*e^3*b/c^2*x*(c*x^2+b*x+a)^(7/2)+105/2048*e^3*b^5/c^(9/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a^2-45/4096*e^3*b^7/c^(11/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a-15/32*d^2*e*b/c*(c*x^2+b*x+a)^(1/2)*x*a^2+15/64*d^2*e*b^3/c^2*(c*x^2+b*x+a)^(1/2)*x*a+25/128*d*e^2*b^2/c^2*(c*x^2+b*x+a)^(3/2)*x*a+1/6*d^3*x*(c*x^2+b*x+a)^(5/2)-45/2048*d*e^2*b^5/c^4*(c*x^2+b*x+a)^(3/2)-15/128*d*e^2*a^4/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-135/32768*d*e^2*b^8/c^(11/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+5/32*d^3/c*(c*x^2+b*x+a)^(1/2)*b*a^2-5/64*d^3/c^2*(c*x^2+b*x+a)^(1/2)*b^3*a+15/256*e^3*b/c^(5/2)*a^4*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-25/256*e^3*b^3/c^(7/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a^3+135/16384*d*e^2*b^7/c^5*(c*x^2+b*x+a)^(1/2)-27/112*d*e^2*b/c^2*(c*x^2+b*x+a)^(7/2)+5/256*e^3*b^2/c^3*a^2*(c*x^2+b*x+a)^(3/2)+15/512*e^3*b^2/c^3*a^3*(c*x^2+b*x+a)^(1/2)-11/384*e^3*b^3/c^3*x*(c*x^2+b*x+a)^(5/2)+55/6144*e^3*b^5/c^4*(c*x^2+b*x+a)^(3/2)*x+1/64*e^3*b^2/c^3*a*(c*x^2+b*x+a)^(5/2)+125/8192*e^3*b^6/c^5*(c*x^2+b*x+a)^(1/2)*a-35/1536*e^3*b^4/c^4*(c*x^2+b*x+a)^(3/2)*a-55/16384*e^3*b^7/c^5*(c*x^2+b*x+a)^(1/2)*x-85/2048*e^3*b^4/c^4*(c*x^2+b*x+a)^(1/2)*a^2-5/192*d^3/c^2*(c*x^2+b*x+a)^(3/2)*b^3+5/16*d^3*(c*x^2+b*x+a)^(1/2)*x*a^2+5/512*d^3/c^3*(c*x^2+b*x+a)^(1/2)*b^5+5/16*d^3/c^(1/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a^3-5/1024*d^3/c^(7/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*b^6+3/7*d^2*e*(c*x^2+b*x+a)^(7/2)/c+1/9*e^3*x^2*(c*x^2+b*x+a)^(7/2)/c-11/768*e^3*b^4/c^4*(c*x^2+b*x+a)^(5/2)+55/12288*e^3*b^6/c^5*(c*x^2+b*x+a)^(3/2)-55/32768*e^3*b^8/c^6*(c*x^2+b*x+a)^(1/2)+11/224*e^3*b^2/c^3*(c*x^2+b*x+a)^(7/2)-2/63*e^3*a/c^2*(c*x^2+b*x+a)^(7/2)+55/65536*e^3*b^9/c^(13/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+1/12*d^3/c*(c*x^2+b*x+a)^(5/2)*b+5/24*d^3*(c*x^2+b*x+a)^(3/2)*x*a-1/16*d*e^2*a/c*x*(c*x^2+b*x+a)^(5/2)+9/64*d*e^2*b^2/c^2*x*(c*x^2+b*x+a)^(5/2)-45/1024*d*e^2*b^4/c^3*(c*x^2+b*x+a)^(3/2)*x+25/256*d*e^2*b^3/c^3*(c*x^2+b*x+a)^(3/2)*a+135/8192*d*e^2*b^6/c^4*(c*x^2+b*x+a)^(1/2)*x+165/1024*d*e^2*b^3/c^3*(c*x^2+b*x+a)^(1/2)*a^2-15/256*d*e^2*a^3/c^2*(c*x^2+b*x+a)^(1/2)*b-5/128*d*e^2*a^2/c^2*(c*x^2+b*x+a)^(3/2)*b-15/128*d*e^2*a^3/c*(c*x^2+b*x+a)^(1/2)*x+125/4096*e^3*b^5/c^4*(c*x^2+b*x+a)^(1/2)*x*a+5/128*e^3*b/c^2*a^2*(c*x^2+b*x+a)^(3/2)*x-85/1024*e^3*b^3/c^3*(c*x^2+b*x+a)^(1/2)*x*a^2+9/128*d*e^2*b^3/c^3*(c*x^2+b*x+a)^(5/2)+3/8*d*e^2*x*(c*x^2+b*x+a)^(7/2)/c-5/16*d^2*e*b/c*(c*x^2+b*x+a)^(3/2)*x*a+165/512*d*e^2*b^2/c^2*(c*x^2+b*x+a)^(1/2)*x*a^2-285/2048*d*e^2*b^4/c^3*(c*x^2+b*x+a)^(1/2)*x*a-35/768*e^3*b^3/c^3*(c*x^2+b*x+a)^(3/2)*x*a+15/256*e^3*b/c^2*a^3*(c*x^2+b*x+a)^(1/2)*x+1/32*e^3*b/c^2*a*x*(c*x^2+b*x+a)^(5/2)","B"
2356,1,1517,293,0.060000," ","int((e*x+d)^2*(c*x^2+b*x+a)^(5/2),x)","-\frac{5 a^{4} e^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{128 c^{\frac{3}{2}}}+\frac{15 a^{3} b^{2} e^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{128 c^{\frac{5}{2}}}-\frac{5 a^{3} b d e \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{16 c^{\frac{3}{2}}}+\frac{5 a^{3} d^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{16 \sqrt{c}}-\frac{75 a^{2} b^{4} e^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{1024 c^{\frac{7}{2}}}+\frac{15 a^{2} b^{3} d e \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{64 c^{\frac{5}{2}}}-\frac{15 a^{2} b^{2} d^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{64 c^{\frac{3}{2}}}+\frac{35 a \,b^{6} e^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{2048 c^{\frac{9}{2}}}-\frac{15 a \,b^{5} d e \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{256 c^{\frac{7}{2}}}+\frac{15 a \,b^{4} d^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{256 c^{\frac{5}{2}}}-\frac{45 b^{8} e^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{32768 c^{\frac{11}{2}}}+\frac{5 b^{7} d e \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{1024 c^{\frac{9}{2}}}-\frac{5 b^{6} d^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{1024 c^{\frac{7}{2}}}-\frac{5 \sqrt{c \,x^{2}+b x +a}\, a^{3} e^{2} x}{128 c}+\frac{55 \sqrt{c \,x^{2}+b x +a}\, a^{2} b^{2} e^{2} x}{512 c^{2}}-\frac{5 \sqrt{c \,x^{2}+b x +a}\, a^{2} b d e x}{16 c}+\frac{5 \sqrt{c \,x^{2}+b x +a}\, a^{2} d^{2} x}{16}-\frac{95 \sqrt{c \,x^{2}+b x +a}\, a \,b^{4} e^{2} x}{2048 c^{3}}+\frac{5 \sqrt{c \,x^{2}+b x +a}\, a \,b^{3} d e x}{32 c^{2}}-\frac{5 \sqrt{c \,x^{2}+b x +a}\, a \,b^{2} d^{2} x}{32 c}+\frac{45 \sqrt{c \,x^{2}+b x +a}\, b^{6} e^{2} x}{8192 c^{4}}-\frac{5 \sqrt{c \,x^{2}+b x +a}\, b^{5} d e x}{256 c^{3}}+\frac{5 \sqrt{c \,x^{2}+b x +a}\, b^{4} d^{2} x}{256 c^{2}}-\frac{5 \sqrt{c \,x^{2}+b x +a}\, a^{3} b \,e^{2}}{256 c^{2}}+\frac{55 \sqrt{c \,x^{2}+b x +a}\, a^{2} b^{3} e^{2}}{1024 c^{3}}-\frac{5 \sqrt{c \,x^{2}+b x +a}\, a^{2} b^{2} d e}{32 c^{2}}+\frac{5 \sqrt{c \,x^{2}+b x +a}\, a^{2} b \,d^{2}}{32 c}-\frac{5 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a^{2} e^{2} x}{192 c}-\frac{95 \sqrt{c \,x^{2}+b x +a}\, a \,b^{5} e^{2}}{4096 c^{4}}+\frac{5 \sqrt{c \,x^{2}+b x +a}\, a \,b^{4} d e}{64 c^{3}}-\frac{5 \sqrt{c \,x^{2}+b x +a}\, a \,b^{3} d^{2}}{64 c^{2}}+\frac{25 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a \,b^{2} e^{2} x}{384 c^{2}}-\frac{5 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a b d e x}{24 c}+\frac{5 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a \,d^{2} x}{24}+\frac{45 \sqrt{c \,x^{2}+b x +a}\, b^{7} e^{2}}{16384 c^{5}}-\frac{5 \sqrt{c \,x^{2}+b x +a}\, b^{6} d e}{512 c^{4}}+\frac{5 \sqrt{c \,x^{2}+b x +a}\, b^{5} d^{2}}{512 c^{3}}-\frac{15 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{4} e^{2} x}{1024 c^{3}}+\frac{5 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{3} d e x}{96 c^{2}}-\frac{5 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{2} d^{2} x}{96 c}-\frac{5 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a^{2} b \,e^{2}}{384 c^{2}}+\frac{25 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a \,b^{3} e^{2}}{768 c^{3}}-\frac{5 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a \,b^{2} d e}{48 c^{2}}+\frac{5 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a b \,d^{2}}{48 c}-\frac{\left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} a \,e^{2} x}{48 c}-\frac{15 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{5} e^{2}}{2048 c^{4}}+\frac{5 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{4} d e}{192 c^{3}}-\frac{5 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{3} d^{2}}{192 c^{2}}+\frac{3 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} b^{2} e^{2} x}{64 c^{2}}-\frac{\left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} b d e x}{6 c}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} d^{2} x}{6}-\frac{\left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} a b \,e^{2}}{96 c^{2}}+\frac{3 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} b^{3} e^{2}}{128 c^{3}}-\frac{\left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} b^{2} d e}{12 c^{2}}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} b \,d^{2}}{12 c}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{7}{2}} e^{2} x}{8 c}-\frac{9 \left(c \,x^{2}+b x +a \right)^{\frac{7}{2}} b \,e^{2}}{112 c^{2}}+\frac{2 \left(c \,x^{2}+b x +a \right)^{\frac{7}{2}} d e}{7 c}"," ",0,"55/512*e^2*b^2/c^2*(c*x^2+b*x+a)^(1/2)*x*a^2-95/2048*e^2*b^4/c^3*(c*x^2+b*x+a)^(1/2)*x*a+25/384*e^2*b^2/c^2*(c*x^2+b*x+a)^(3/2)*x*a-5/48*d*e*b^2/c^2*(c*x^2+b*x+a)^(3/2)*a-1/6*d*e*b/c*x*(c*x^2+b*x+a)^(5/2)+5/96*d*e*b^3/c^2*(c*x^2+b*x+a)^(3/2)*x-5/16*d*e*b/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a^3+15/64*d*e*b^3/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a^2-15/256*d*e*b^5/c^(7/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a-5/32*d^2/c*(c*x^2+b*x+a)^(1/2)*x*a*b^2-5/256*d*e*b^5/c^3*(c*x^2+b*x+a)^(1/2)*x-5/32*d*e*b^2/c^2*(c*x^2+b*x+a)^(1/2)*a^2+5/64*d*e*b^4/c^3*(c*x^2+b*x+a)^(1/2)*a+5/32*d*e*b^3/c^2*(c*x^2+b*x+a)^(1/2)*x*a-5/128*e^2*a^3/c*(c*x^2+b*x+a)^(1/2)*x-5/256*e^2*a^3/c^2*(c*x^2+b*x+a)^(1/2)*b-5/192*e^2*a^2/c*(c*x^2+b*x+a)^(3/2)*x-5/384*e^2*a^2/c^2*(c*x^2+b*x+a)^(3/2)*b-1/48*e^2*a/c*x*(c*x^2+b*x+a)^(5/2)-1/96*e^2*a/c^2*(c*x^2+b*x+a)^(5/2)*b+55/1024*e^2*b^3/c^3*(c*x^2+b*x+a)^(1/2)*a^2+15/256*d^2/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*b^4*a-5/96*d^2/c*(c*x^2+b*x+a)^(3/2)*x*b^2+5/48*d^2/c*(c*x^2+b*x+a)^(3/2)*b*a+5/256*d^2/c^2*(c*x^2+b*x+a)^(1/2)*x*b^4+5/32*d^2/c*(c*x^2+b*x+a)^(1/2)*b*a^2-5/64*d^2/c^2*(c*x^2+b*x+a)^(1/2)*b^3*a-15/64*d^2/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*b^2*a^2+2/7*d*e*(c*x^2+b*x+a)^(7/2)/c-9/112*e^2*b/c^2*(c*x^2+b*x+a)^(7/2)+1/12*d^2/c*(c*x^2+b*x+a)^(5/2)*b+5/24*d^2*(c*x^2+b*x+a)^(3/2)*x*a-5/192*d^2/c^2*(c*x^2+b*x+a)^(3/2)*b^3+5/16*d^2*(c*x^2+b*x+a)^(1/2)*x*a^2+5/512*d^2/c^3*(c*x^2+b*x+a)^(1/2)*b^5+5/16*d^2/c^(1/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a^3-5/1024*d^2/c^(7/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*b^6+45/16384*e^2*b^7/c^5*(c*x^2+b*x+a)^(1/2)+1/8*e^2*x*(c*x^2+b*x+a)^(7/2)/c-15/2048*e^2*b^5/c^4*(c*x^2+b*x+a)^(3/2)-5/128*e^2*a^4/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-45/32768*e^2*b^8/c^(11/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+3/128*e^2*b^3/c^3*(c*x^2+b*x+a)^(5/2)-5/24*d*e*b/c*(c*x^2+b*x+a)^(3/2)*x*a-5/16*d*e*b/c*(c*x^2+b*x+a)^(1/2)*x*a^2-95/4096*e^2*b^5/c^4*(c*x^2+b*x+a)^(1/2)*a+3/64*e^2*b^2/c^2*x*(c*x^2+b*x+a)^(5/2)+5/1024*d*e*b^7/c^(9/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-1/12*d*e*b^2/c^2*(c*x^2+b*x+a)^(5/2)+45/8192*e^2*b^6/c^4*(c*x^2+b*x+a)^(1/2)*x+25/768*e^2*b^3/c^3*(c*x^2+b*x+a)^(3/2)*a+15/128*e^2*b^2/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a^3-75/1024*e^2*b^4/c^(7/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a^2+35/2048*e^2*b^6/c^(9/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a-15/1024*e^2*b^4/c^3*(c*x^2+b*x+a)^(3/2)*x+5/192*d*e*b^4/c^3*(c*x^2+b*x+a)^(3/2)-5/512*d*e*b^6/c^4*(c*x^2+b*x+a)^(1/2)+1/6*d^2*x*(c*x^2+b*x+a)^(5/2)","B"
2357,1,807,181,0.052000," ","int((e*x+d)*(c*x^2+b*x+a)^(5/2),x)","-\frac{5 a^{3} b e \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{32 c^{\frac{3}{2}}}+\frac{5 a^{3} d \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{16 \sqrt{c}}+\frac{15 a^{2} b^{3} e \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{128 c^{\frac{5}{2}}}-\frac{15 a^{2} b^{2} d \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{64 c^{\frac{3}{2}}}-\frac{15 a \,b^{5} e \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{512 c^{\frac{7}{2}}}+\frac{15 a \,b^{4} d \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{256 c^{\frac{5}{2}}}+\frac{5 b^{7} e \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{2048 c^{\frac{9}{2}}}-\frac{5 b^{6} d \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{1024 c^{\frac{7}{2}}}-\frac{5 \sqrt{c \,x^{2}+b x +a}\, a^{2} b e x}{32 c}+\frac{5 \sqrt{c \,x^{2}+b x +a}\, a^{2} d x}{16}+\frac{5 \sqrt{c \,x^{2}+b x +a}\, a \,b^{3} e x}{64 c^{2}}-\frac{5 \sqrt{c \,x^{2}+b x +a}\, a \,b^{2} d x}{32 c}-\frac{5 \sqrt{c \,x^{2}+b x +a}\, b^{5} e x}{512 c^{3}}+\frac{5 \sqrt{c \,x^{2}+b x +a}\, b^{4} d x}{256 c^{2}}-\frac{5 \sqrt{c \,x^{2}+b x +a}\, a^{2} b^{2} e}{64 c^{2}}+\frac{5 \sqrt{c \,x^{2}+b x +a}\, a^{2} b d}{32 c}+\frac{5 \sqrt{c \,x^{2}+b x +a}\, a \,b^{4} e}{128 c^{3}}-\frac{5 \sqrt{c \,x^{2}+b x +a}\, a \,b^{3} d}{64 c^{2}}-\frac{5 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a b e x}{48 c}+\frac{5 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a d x}{24}-\frac{5 \sqrt{c \,x^{2}+b x +a}\, b^{6} e}{1024 c^{4}}+\frac{5 \sqrt{c \,x^{2}+b x +a}\, b^{5} d}{512 c^{3}}+\frac{5 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{3} e x}{192 c^{2}}-\frac{5 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{2} d x}{96 c}-\frac{5 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a \,b^{2} e}{96 c^{2}}+\frac{5 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a b d}{48 c}+\frac{5 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{4} e}{384 c^{3}}-\frac{5 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{3} d}{192 c^{2}}-\frac{\left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} b e x}{12 c}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} d x}{6}-\frac{\left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} b^{2} e}{24 c^{2}}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} b d}{12 c}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{7}{2}} e}{7 c}"," ",0,"-1/24*e*b^2/c^2*(c*x^2+b*x+a)^(5/2)+5/384*e*b^4/c^3*(c*x^2+b*x+a)^(3/2)+5/2048*e*b^7/c^(9/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+5/16*d*(c*x^2+b*x+a)^(1/2)*x*a^2-5/1024*e*b^6/c^4*(c*x^2+b*x+a)^(1/2)-5/192*d/c^2*(c*x^2+b*x+a)^(3/2)*b^3+5/24*d*(c*x^2+b*x+a)^(3/2)*x*a+1/12*d/c*(c*x^2+b*x+a)^(5/2)*b+5/16*d/c^(1/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a^3-5/1024*d/c^(7/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*b^6+5/512*d/c^3*(c*x^2+b*x+a)^(1/2)*b^5-5/48*e*b/c*(c*x^2+b*x+a)^(3/2)*x*a-5/32*e*b/c*(c*x^2+b*x+a)^(1/2)*x*a^2-5/32*d/c*(c*x^2+b*x+a)^(1/2)*x*a*b^2+5/64*e*b^3/c^2*(c*x^2+b*x+a)^(1/2)*x*a-5/96*e*b^2/c^2*(c*x^2+b*x+a)^(3/2)*a+15/256*d/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*b^4*a-1/12*e*b/c*x*(c*x^2+b*x+a)^(5/2)+5/192*e*b^3/c^2*(c*x^2+b*x+a)^(3/2)*x+1/6*d*x*(c*x^2+b*x+a)^(5/2)+15/128*e*b^3/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a^2-15/512*e*b^5/c^(7/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a-15/64*d/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*b^2*a^2-5/32*e*b/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a^3+5/256*d/c^2*(c*x^2+b*x+a)^(1/2)*x*b^4+5/32*d/c*(c*x^2+b*x+a)^(1/2)*b*a^2-5/64*d/c^2*(c*x^2+b*x+a)^(1/2)*b^3*a+5/48*d/c*(c*x^2+b*x+a)^(3/2)*b*a-5/96*d/c*(c*x^2+b*x+a)^(3/2)*x*b^2-5/512*e*b^5/c^3*(c*x^2+b*x+a)^(1/2)*x-5/64*e*b^2/c^2*(c*x^2+b*x+a)^(1/2)*a^2+5/128*e*b^4/c^3*(c*x^2+b*x+a)^(1/2)*a+1/7*e*(c*x^2+b*x+a)^(7/2)/c","B"
2358,1,360,127,0.048000," ","int((c*x^2+b*x+a)^(5/2),x)","\frac{5 a^{3} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{16 \sqrt{c}}-\frac{15 a^{2} b^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{64 c^{\frac{3}{2}}}+\frac{15 a \,b^{4} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{256 c^{\frac{5}{2}}}-\frac{5 b^{6} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{1024 c^{\frac{7}{2}}}+\frac{5 \sqrt{c \,x^{2}+b x +a}\, a^{2} x}{16}-\frac{5 \sqrt{c \,x^{2}+b x +a}\, a \,b^{2} x}{32 c}+\frac{5 \sqrt{c \,x^{2}+b x +a}\, b^{4} x}{256 c^{2}}+\frac{5 \sqrt{c \,x^{2}+b x +a}\, a^{2} b}{32 c}-\frac{5 \sqrt{c \,x^{2}+b x +a}\, a \,b^{3}}{64 c^{2}}+\frac{5 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a x}{24}+\frac{5 \sqrt{c \,x^{2}+b x +a}\, b^{5}}{512 c^{3}}-\frac{5 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{2} x}{96 c}+\frac{5 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a b}{48 c}-\frac{5 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{3}}{192 c^{2}}+\frac{\left(2 c x +b \right) \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}}}{12 c}"," ",0,"1/12*(2*c*x+b)*(c*x^2+b*x+a)^(5/2)/c+5/24*(c*x^2+b*x+a)^(3/2)*x*a-5/96/c*(c*x^2+b*x+a)^(3/2)*x*b^2+5/48/c*(c*x^2+b*x+a)^(3/2)*b*a-5/192/c^2*(c*x^2+b*x+a)^(3/2)*b^3+5/16*(c*x^2+b*x+a)^(1/2)*x*a^2-5/32/c*(c*x^2+b*x+a)^(1/2)*x*a*b^2+5/256/c^2*(c*x^2+b*x+a)^(1/2)*x*b^4+5/32/c*(c*x^2+b*x+a)^(1/2)*b*a^2-5/64/c^2*(c*x^2+b*x+a)^(1/2)*b^3*a+5/512/c^3*(c*x^2+b*x+a)^(1/2)*b^5+5/16/c^(1/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a^3-15/64/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a^2*b^2+15/256/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*b^4*a-5/1024/c^(7/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*b^6","B"
2359,1,4126,429,0.055000," ","int((c*x^2+b*x+a)^(5/2)/(e*x+d),x)","\text{output too large to display}"," ",0,"3/4/e^3*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*b*c*d^2-3/e^3/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*a^2*c*d^2+15/4/e^3*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*c^(1/2)*d^2*a*b-15/16/e^2/c^(1/2)*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*a*b^2*d+3/e^6/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*b*d^5*c^2-3/e^5/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*a*c^2*d^4-3/e^5/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*b^2*d^4*c+3/e^2/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*a^2*b*d-3/e^3/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*a*b^2*d^2-7/8/e^2*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*a*c*d-11/24/e^2*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(3/2)*b*d+1/8/e*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(3/2)*x*b-3/128/e/c^2*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b^4+3/256/e/c^(5/2)*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*b^5+1/16/e/c*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(3/2)*b^2-1/e/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*a^3+1/e^5*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*c^2*d^4+11/8/e^3*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b^2*d^2-1/e^6*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*c^(5/2)*d^5+1/3/e^3*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(3/2)*c*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+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*b^3*d^3-5/64/e^2/c*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b^3*d+15/16/e/c^(1/2)*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*a^2*b-5/32/e/c^(3/2)*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*b^3*a-1/2/e^4*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*c^2*d^3-9/4/e^4*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b*d^3*c+2/e^3*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*a*c*d^2-1/e^7/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*c^3*d^6-39/16/e^2*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b*a*d+1/3/e*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(3/2)*a+1/e*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*a^2-15/8/e^4*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*c^(1/2)*d^3*b^2-15/8/e^2*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*c^(1/2)*d*a^2+5/128/e^2/c^(3/2)*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*b^4*d-5/2/e^4*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*c^(3/2)*d^3*a+5/2/e^5*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*c^(3/2)*d^4*b-1/4/e^2*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(3/2)*x*c*d+7/16/e*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*a*b-3/64/e/c*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*b^3-5/32/e^2*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*b^2*d+7/32/e/c*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b^2*a+1/5/e*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(5/2)+5/16/e^3*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/c^(1/2)*b^3*d^2+6/e^4/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*a*b*d^3*c","B"
2360,1,6711,358,0.105000," ","int((c*x^2+b*x+a)^(5/2)/(e*x+d)^2,x)","\text{output too large to display}"," ",0,"result too large to display","B"
2361,1,14002,299,0.062000," ","int((c*x^2+b*x+a)^(5/2)/(e*x+d)^3,x)","\text{output too large to display}"," ",0,"result too large to display","B"
2362,1,18718,305,0.099000," ","int((c*x^2+b*x+a)^(5/2)/(e*x+d)^4,x)","\text{output too large to display}"," ",0,"result too large to display","B"
2363,1,28635,460,0.337000," ","int((c*x^2+b*x+a)^(5/2)/(e*x+d)^5,x)","\text{output too large to display}"," ",0,"result too large to display","B"
2364,1,71,68,0.054000," ","int((5*x^2-3*x-2)^(1/2)/x,x)","-\sqrt{2}\, \arctan \left(\frac{\left(-3 x -4\right) \sqrt{2}}{4 \sqrt{5 x^{2}-3 x -2}}\right)-\frac{3 \sqrt{5}\, \ln \left(\frac{\left(5 x -\frac{3}{2}\right) \sqrt{5}}{5}+\sqrt{5 x^{2}-3 x -2}\right)}{10}+\sqrt{5 x^{2}-3 x -2}"," ",0,"(5*x^2-3*x-2)^(1/2)-3/10*ln(1/5*(-3/2+5*x)*5^(1/2)+(5*x^2-3*x-2)^(1/2))*5^(1/2)-2^(1/2)*arctan(1/4*(-3*x-4)*2^(1/2)/(5*x^2-3*x-2)^(1/2))","A"
2365,1,88,54,0.056000," ","int((-x^2-x+2)^(1/2)/x^2,x)","\frac{\sqrt{2}\, \arctanh \left(\frac{\left(-x +4\right) \sqrt{2}}{4 \sqrt{-x^{2}-x +2}}\right)}{4}-\arcsin \left(\frac{2 x}{3}+\frac{1}{3}\right)-\frac{\left(-x^{2}-x +2\right)^{\frac{3}{2}}}{2 x}-\frac{\sqrt{-x^{2}-x +2}}{4}+\frac{\left(-2 x -1\right) \sqrt{-x^{2}-x +2}}{4}"," ",0,"-1/2/x*(-x^2-x+2)^(3/2)-1/4*(-x^2-x+2)^(1/2)-arcsin(1/3+2/3*x)+1/4*arctanh(1/4*(4-x)*2^(1/2)/(-x^2-x+2)^(1/2))*2^(1/2)+1/4*(-1-2*x)*(-x^2-x+2)^(1/2)","A"
2366,1,23,30,0.054000," ","int((x+1)^3*(x^2+2*x+2)^(1/2),x)","\frac{\left(x^{2}+2 x +2\right)^{\frac{3}{2}} \left(3 x^{2}+6 x +1\right)}{15}"," ",0,"1/15*(x^2+2*x+2)^(3/2)*(3*x^2+6*x+1)","A"
2367,1,43,42,0.051000," ","int((3*x-2)*(9*x^2+12*x+8)^(1/2),x)","-\frac{8 \arcsinh \left(\frac{3 x}{2}+1\right)}{3}+\frac{\left(9 x^{2}+12 x +8\right)^{\frac{3}{2}}}{9}-\frac{\left(18 x +12\right) \sqrt{9 x^{2}+12 x +8}}{9}"," ",0,"1/9*(9*x^2+12*x+8)^(3/2)-1/9*(18*x+12)*(9*x^2+12*x+8)^(1/2)-8/3*arcsinh(1+3/2*x)","A"
2368,1,43,42,0.056000," ","int((7-2*x)*(-4*x^2+16*x+9)^(1/2),x)","\frac{75 \arcsin \left(\frac{2 x}{5}-\frac{4}{5}\right)}{4}-\frac{3 \left(-8 x +16\right) \sqrt{-4 x^{2}+16 x +9}}{16}+\frac{\left(-4 x^{2}+16 x +9\right)^{\frac{3}{2}}}{6}"," ",0,"-3/16*(-8*x+16)*(-4*x^2+16*x+9)^(1/2)+75/4*arcsin(-4/5+2/5*x)+1/6*(-4*x^2+16*x+9)^(3/2)","A"
2369,1,54,49,0.054000," ","int((x^2-x-1)^(1/2)/(x+1),x)","-\arctanh \left(\frac{-3 x -1}{2 \sqrt{-3 x +\left(x +1\right)^{2}-2}}\right)-\frac{3 \ln \left(x -\frac{1}{2}+\sqrt{-3 x +\left(x +1\right)^{2}-2}\right)}{2}+\sqrt{-3 x +\left(x +1\right)^{2}-2}"," ",0,"((x+1)^2-3*x-2)^(1/2)-3/2*ln(x-1/2+((x+1)^2-3*x-2)^(1/2))-arctanh(1/2*(-3*x-1)/((x+1)^2-3*x-2)^(1/2))","A"
2370,1,46,53,0.053000," ","int((x^2-x-1)^(1/2)/(-x+1),x)","\arctan \left(\frac{x -3}{2 \sqrt{x +\left(x -1\right)^{2}-2}}\right)-\frac{\ln \left(x -\frac{1}{2}+\sqrt{x +\left(x -1\right)^{2}-2}\right)}{2}-\sqrt{x +\left(x -1\right)^{2}-2}"," ",0,"-((x-1)^2+x-2)^(1/2)-1/2*ln(-1/2+x+((x-1)^2+x-2)^(1/2))+arctan(1/2*(x-3)/((x-1)^2+x-2)^(1/2))","A"
2371,1,394,231,0.092000," ","int(x^6/(c*x^2+b*x+a)^(1/2),x)","\frac{\sqrt{c \,x^{2}+b x +a}\, x^{5}}{6 c}-\frac{11 \sqrt{c \,x^{2}+b x +a}\, b \,x^{4}}{60 c^{2}}-\frac{5 \sqrt{c \,x^{2}+b x +a}\, a \,x^{3}}{24 c^{2}}+\frac{33 \sqrt{c \,x^{2}+b x +a}\, b^{2} x^{3}}{160 c^{3}}+\frac{39 \sqrt{c \,x^{2}+b x +a}\, a b \,x^{2}}{80 c^{3}}-\frac{77 \sqrt{c \,x^{2}+b x +a}\, b^{3} x^{2}}{320 c^{4}}-\frac{5 a^{3} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{16 c^{\frac{7}{2}}}+\frac{105 a^{2} b^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{64 c^{\frac{9}{2}}}-\frac{315 a \,b^{4} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{256 c^{\frac{11}{2}}}+\frac{231 b^{6} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{1024 c^{\frac{13}{2}}}+\frac{5 \sqrt{c \,x^{2}+b x +a}\, a^{2} x}{16 c^{3}}-\frac{147 \sqrt{c \,x^{2}+b x +a}\, a \,b^{2} x}{160 c^{4}}+\frac{77 \sqrt{c \,x^{2}+b x +a}\, b^{4} x}{256 c^{5}}-\frac{231 \sqrt{c \,x^{2}+b x +a}\, a^{2} b}{160 c^{4}}+\frac{119 \sqrt{c \,x^{2}+b x +a}\, a \,b^{3}}{64 c^{5}}-\frac{231 \sqrt{c \,x^{2}+b x +a}\, b^{5}}{512 c^{6}}"," ",0,"1/6*x^5*(c*x^2+b*x+a)^(1/2)/c-11/60*b*x^4*(c*x^2+b*x+a)^(1/2)/c^2+33/160*b^2/c^3*x^3*(c*x^2+b*x+a)^(1/2)-77/320*b^3/c^4*x^2*(c*x^2+b*x+a)^(1/2)+77/256*b^4/c^5*x*(c*x^2+b*x+a)^(1/2)-231/512*b^5/c^6*(c*x^2+b*x+a)^(1/2)+231/1024*b^6/c^(13/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-315/256*b^4/c^(11/2)*a*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+119/64*b^3/c^5*a*(c*x^2+b*x+a)^(1/2)-147/160*b^2/c^4*a*x*(c*x^2+b*x+a)^(1/2)+105/64*b^2/c^(9/2)*a^2*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+39/80*b/c^3*a*x^2*(c*x^2+b*x+a)^(1/2)-231/160*b/c^4*a^2*(c*x^2+b*x+a)^(1/2)-5/24*a/c^2*x^3*(c*x^2+b*x+a)^(1/2)+5/16*a^2/c^3*x*(c*x^2+b*x+a)^(1/2)-5/16*a^3/c^(7/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))","A"
2372,1,290,176,0.062000," ","int(x^5/(c*x^2+b*x+a)^(1/2),x)","\frac{\sqrt{c \,x^{2}+b x +a}\, x^{4}}{5 c}-\frac{9 \sqrt{c \,x^{2}+b x +a}\, b \,x^{3}}{40 c^{2}}-\frac{4 \sqrt{c \,x^{2}+b x +a}\, a \,x^{2}}{15 c^{2}}+\frac{21 \sqrt{c \,x^{2}+b x +a}\, b^{2} x^{2}}{80 c^{3}}-\frac{15 a^{2} b \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{16 c^{\frac{7}{2}}}+\frac{35 a \,b^{3} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{32 c^{\frac{9}{2}}}-\frac{63 b^{5} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{256 c^{\frac{11}{2}}}+\frac{161 \sqrt{c \,x^{2}+b x +a}\, a b x}{240 c^{3}}-\frac{21 \sqrt{c \,x^{2}+b x +a}\, b^{3} x}{64 c^{4}}+\frac{8 \sqrt{c \,x^{2}+b x +a}\, a^{2}}{15 c^{3}}-\frac{49 \sqrt{c \,x^{2}+b x +a}\, a \,b^{2}}{32 c^{4}}+\frac{63 \sqrt{c \,x^{2}+b x +a}\, b^{4}}{128 c^{5}}"," ",0,"1/5*x^4*(c*x^2+b*x+a)^(1/2)/c-9/40*b*x^3*(c*x^2+b*x+a)^(1/2)/c^2+21/80*b^2/c^3*x^2*(c*x^2+b*x+a)^(1/2)-21/64*b^3/c^4*x*(c*x^2+b*x+a)^(1/2)+63/128*b^4/c^5*(c*x^2+b*x+a)^(1/2)-63/256*b^5/c^(11/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+35/32*b^3/c^(9/2)*a*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-49/32*b^2/c^4*a*(c*x^2+b*x+a)^(1/2)+161/240*b/c^3*a*x*(c*x^2+b*x+a)^(1/2)-15/16*b/c^(7/2)*a^2*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-4/15*a/c^2*x^2*(c*x^2+b*x+a)^(1/2)+8/15*a^2/c^3*(c*x^2+b*x+a)^(1/2)","A"
2373,1,627,274,0.064000," ","int((e*x+d)^4/(c*x^2+b*x+a)^(1/2),x)","\frac{\sqrt{c \,x^{2}+b x +a}\, e^{4} x^{3}}{4 c}-\frac{7 \sqrt{c \,x^{2}+b x +a}\, b \,e^{4} x^{2}}{24 c^{2}}+\frac{4 \sqrt{c \,x^{2}+b x +a}\, d \,e^{3} x^{2}}{3 c}+\frac{3 a^{2} e^{4} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{8 c^{\frac{5}{2}}}-\frac{15 a \,b^{2} e^{4} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{16 c^{\frac{7}{2}}}+\frac{3 a b d \,e^{3} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{c^{\frac{5}{2}}}-\frac{3 a \,d^{2} e^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{c^{\frac{3}{2}}}+\frac{35 b^{4} e^{4} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{128 c^{\frac{9}{2}}}-\frac{5 b^{3} d \,e^{3} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{4 c^{\frac{7}{2}}}+\frac{9 b^{2} d^{2} e^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{4 c^{\frac{5}{2}}}-\frac{2 b \,d^{3} e \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{c^{\frac{3}{2}}}+\frac{d^{4} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{\sqrt{c}}-\frac{3 \sqrt{c \,x^{2}+b x +a}\, a \,e^{4} x}{8 c^{2}}+\frac{35 \sqrt{c \,x^{2}+b x +a}\, b^{2} e^{4} x}{96 c^{3}}-\frac{5 \sqrt{c \,x^{2}+b x +a}\, b d \,e^{3} x}{3 c^{2}}+\frac{3 \sqrt{c \,x^{2}+b x +a}\, d^{2} e^{2} x}{c}+\frac{55 \sqrt{c \,x^{2}+b x +a}\, a b \,e^{4}}{48 c^{3}}-\frac{8 \sqrt{c \,x^{2}+b x +a}\, a d \,e^{3}}{3 c^{2}}-\frac{35 \sqrt{c \,x^{2}+b x +a}\, b^{3} e^{4}}{64 c^{4}}+\frac{5 \sqrt{c \,x^{2}+b x +a}\, b^{2} d \,e^{3}}{2 c^{3}}-\frac{9 \sqrt{c \,x^{2}+b x +a}\, b \,d^{2} e^{2}}{2 c^{2}}+\frac{4 \sqrt{c \,x^{2}+b x +a}\, d^{3} e}{c}"," ",0,"1/4*e^4*x^3/c*(c*x^2+b*x+a)^(1/2)-7/24*e^4*b/c^2*x^2*(c*x^2+b*x+a)^(1/2)+35/96*e^4*b^2/c^3*x*(c*x^2+b*x+a)^(1/2)-35/64*e^4*b^3/c^4*(c*x^2+b*x+a)^(1/2)+35/128*e^4*b^4/c^(9/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-15/16*e^4*b^2/c^(7/2)*a*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+55/48*e^4*b/c^3*a*(c*x^2+b*x+a)^(1/2)-3/8*e^4*a/c^2*x*(c*x^2+b*x+a)^(1/2)+3/8*e^4*a^2/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+4/3*d*e^3*x^2/c*(c*x^2+b*x+a)^(1/2)-5/3*d*e^3*b/c^2*x*(c*x^2+b*x+a)^(1/2)+5/2*d*e^3*b^2/c^3*(c*x^2+b*x+a)^(1/2)-5/4*d*e^3*b^3/c^(7/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+3*d*e^3*b/c^(5/2)*a*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-8/3*d*e^3*a/c^2*(c*x^2+b*x+a)^(1/2)+3*d^2*e^2*x/c*(c*x^2+b*x+a)^(1/2)-9/2*d^2*e^2*b/c^2*(c*x^2+b*x+a)^(1/2)+9/4*d^2*e^2*b^2/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-3*d^2*e^2*a/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+4*d^3*e/c*(c*x^2+b*x+a)^(1/2)-2*d^3*e*b/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+d^4*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))/c^(1/2)","B"
2374,1,366,156,0.062000," ","int((e*x+d)^3/(c*x^2+b*x+a)^(1/2),x)","\frac{\sqrt{c \,x^{2}+b x +a}\, e^{3} x^{2}}{3 c}+\frac{3 a b \,e^{3} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{4 c^{\frac{5}{2}}}-\frac{3 a d \,e^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{2 c^{\frac{3}{2}}}-\frac{5 b^{3} e^{3} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{16 c^{\frac{7}{2}}}+\frac{9 b^{2} d \,e^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{8 c^{\frac{5}{2}}}-\frac{3 b \,d^{2} e \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{2 c^{\frac{3}{2}}}+\frac{d^{3} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{\sqrt{c}}-\frac{5 \sqrt{c \,x^{2}+b x +a}\, b \,e^{3} x}{12 c^{2}}+\frac{3 \sqrt{c \,x^{2}+b x +a}\, d \,e^{2} x}{2 c}-\frac{2 \sqrt{c \,x^{2}+b x +a}\, a \,e^{3}}{3 c^{2}}+\frac{5 \sqrt{c \,x^{2}+b x +a}\, b^{2} e^{3}}{8 c^{3}}-\frac{9 \sqrt{c \,x^{2}+b x +a}\, b d \,e^{2}}{4 c^{2}}+\frac{3 \sqrt{c \,x^{2}+b x +a}\, d^{2} e}{c}"," ",0,"1/3*e^3*x^2/c*(c*x^2+b*x+a)^(1/2)-5/12*e^3*b/c^2*x*(c*x^2+b*x+a)^(1/2)+5/8*e^3*b^2/c^3*(c*x^2+b*x+a)^(1/2)-5/16*e^3*b^3/c^(7/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+3/4*e^3*b/c^(5/2)*a*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-2/3*e^3*a/c^2*(c*x^2+b*x+a)^(1/2)+3/2*d*e^2*x/c*(c*x^2+b*x+a)^(1/2)-9/4*d*e^2*b/c^2*(c*x^2+b*x+a)^(1/2)+9/8*d*e^2*b^2/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-3/2*d*e^2*a/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+3*d^2*e/c*(c*x^2+b*x+a)^(1/2)-3/2*d^2*e*b/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+d^3*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))/c^(1/2)","B"
2375,1,198,109,0.066000," ","int((e*x+d)^2/(c*x^2+b*x+a)^(1/2),x)","-\frac{a \,e^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{2 c^{\frac{3}{2}}}+\frac{3 b^{2} e^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{8 c^{\frac{5}{2}}}-\frac{b d e \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{c^{\frac{3}{2}}}+\frac{d^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{\sqrt{c}}+\frac{\sqrt{c \,x^{2}+b x +a}\, e^{2} x}{2 c}-\frac{3 \sqrt{c \,x^{2}+b x +a}\, b \,e^{2}}{4 c^{2}}+\frac{2 \sqrt{c \,x^{2}+b x +a}\, d e}{c}"," ",0,"1/2*e^2*x/c*(c*x^2+b*x+a)^(1/2)-3/4*e^2*b/c^2*(c*x^2+b*x+a)^(1/2)+3/8*e^2*b^2/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-1/2*e^2*a/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+2*d*e/c*(c*x^2+b*x+a)^(1/2)-d*e*b/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+d^2*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))/c^(1/2)","A"
2376,1,81,56,0.052000," ","int((e*x+d)/(c*x^2+b*x+a)^(1/2),x)","-\frac{b e \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{2 c^{\frac{3}{2}}}+\frac{d \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{\sqrt{c}}+\frac{\sqrt{c \,x^{2}+b x +a}\, e}{c}"," ",0,"e*(c*x^2+b*x+a)^(1/2)/c-1/2*e*b/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+d*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))/c^(1/2)","A"
2377,1,30,28,0.051000," ","int(1/(c*x^2+b*x+a)^(1/2),x)","\frac{\ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{\sqrt{c}}"," ",0,"ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))/c^(1/2)","A"
2378,1,157,71,0.062000," ","int(1/(e*x+d)/(c*x^2+b*x+a)^(1/2),x)","-\frac{\ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e}"," ",0,"-1/e/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))","B"
2379,1,432,122,0.058000," ","int(1/(e*x+d)^2/(c*x^2+b*x+a)^(1/2),x)","\frac{b \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{2 \left(a \,e^{2}-b d e +c \,d^{2}\right) \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}-\frac{c d \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e}-\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \left(x +\frac{d}{e}\right)}"," ",0,"-1/(a*e^2-b*d*e+c*d^2)/(x+d/e)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)+1/2/(a*e^2-b*d*e+c*d^2)/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*b-1/e/(a*e^2-b*d*e+c*d^2)/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*c*d","B"
2380,1,959,191,0.089000," ","int(1/(e*x+d)^3/(c*x^2+b*x+a)^(1/2),x)","-\frac{3 b^{2} e \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{8 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}+\frac{3 b c d \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{2 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}-\frac{3 c^{2} d^{2} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{2 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e}+\frac{3 \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, b e}{4 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(x +\frac{d}{e}\right)}-\frac{3 \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, c d}{2 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(x +\frac{d}{e}\right)}+\frac{c \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{2 \left(a \,e^{2}-b d e +c \,d^{2}\right) \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e}-\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{2 \left(a \,e^{2}-b d e +c \,d^{2}\right) \left(x +\frac{d}{e}\right)^{2} e}"," ",0,"-1/2/e/(a*e^2-b*d*e+c*d^2)/(x+d/e)^2*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)+3/4*e/(a*e^2-b*d*e+c*d^2)^2/(x+d/e)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b-3/2/(a*e^2-b*d*e+c*d^2)^2/(x+d/e)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*c*d-3/8*e/(a*e^2-b*d*e+c*d^2)^2/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*b^2+3/2/(a*e^2-b*d*e+c*d^2)^2/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*b*c*d-3/2/e/(a*e^2-b*d*e+c*d^2)^2/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*c^2*d^2+1/2/e*c/(a*e^2-b*d*e+c*d^2)/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))","B"
2381,1,1665,271,0.089000," ","int(1/(e*x+d)^4/(c*x^2+b*x+a)^(1/2),x)","\frac{5 b^{3} e^{2} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{16 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}-\frac{15 b^{2} c d e \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{8 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}+\frac{15 b \,c^{2} d^{2} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{4 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}-\frac{5 c^{3} d^{3} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{2 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e}-\frac{5 \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, b^{2} e^{2}}{8 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \left(x +\frac{d}{e}\right)}+\frac{5 \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, b c d e}{2 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \left(x +\frac{d}{e}\right)}-\frac{5 \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, c^{2} d^{2}}{2 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \left(x +\frac{d}{e}\right)}-\frac{3 b c \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{4 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}+\frac{3 c^{2} d \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{2 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e}+\frac{5 \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, b}{12 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(x +\frac{d}{e}\right)^{2}}-\frac{5 \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, c d}{6 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(x +\frac{d}{e}\right)^{2} e}+\frac{2 \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, c}{3 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(x +\frac{d}{e}\right)}-\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{3 \left(a \,e^{2}-b d e +c \,d^{2}\right) \left(x +\frac{d}{e}\right)^{3} e^{2}}"," ",0,"-1/3/e^2/(a*e^2-b*d*e+c*d^2)/(x+d/e)^3*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)+5/12/(a*e^2-b*d*e+c*d^2)^2/(x+d/e)^2*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b-5/6/e/(a*e^2-b*d*e+c*d^2)^2/(x+d/e)^2*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*c*d-5/8*e^2/(a*e^2-b*d*e+c*d^2)^3/(x+d/e)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b^2+5/2*e/(a*e^2-b*d*e+c*d^2)^3/(x+d/e)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b*c*d-5/2/(a*e^2-b*d*e+c*d^2)^3/(x+d/e)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*c^2*d^2+5/16*e^2/(a*e^2-b*d*e+c*d^2)^3/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*b^3-15/8*e/(a*e^2-b*d*e+c*d^2)^3/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*b^2*c*d+15/4/(a*e^2-b*d*e+c*d^2)^3/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*b*c^2*d^2-5/2/e/(a*e^2-b*d*e+c*d^2)^3/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*c^3*d^3-3/4/(a*e^2-b*d*e+c*d^2)^2*c/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*b+3/2/e/(a*e^2-b*d*e+c*d^2)^2*c^2/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*d+2/3*c/(a*e^2-b*d*e+c*d^2)^2/(x+d/e)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)","B"
2382,1,913,268,0.069000," ","int((e*x+d)^4/(c*x^2+b*x+a)^(3/2),x)","-\frac{13 a \,b^{2} e^{4} x}{2 \left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, c^{2}}+\frac{16 a b d \,e^{3} x}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, c}+\frac{15 b^{4} e^{4} x}{8 \left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, c^{3}}-\frac{6 b^{3} d \,e^{3} x}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, c^{2}}+\frac{6 b^{2} d^{2} e^{2} x}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, c}-\frac{8 b \,d^{3} e x}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}}+\frac{e^{4} x^{3}}{2 \sqrt{c \,x^{2}+b x +a}\, c}-\frac{13 a \,b^{3} e^{4}}{4 \left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, c^{3}}+\frac{8 a \,b^{2} d \,e^{3}}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, c^{2}}+\frac{15 b^{5} e^{4}}{16 \left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, c^{4}}-\frac{3 b^{4} d \,e^{3}}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, c^{3}}+\frac{3 b^{3} d^{2} e^{2}}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, c^{2}}-\frac{4 b^{2} d^{3} e}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, c}-\frac{5 b \,e^{4} x^{2}}{4 \sqrt{c \,x^{2}+b x +a}\, c^{2}}+\frac{4 d \,e^{3} x^{2}}{\sqrt{c \,x^{2}+b x +a}\, c}+\frac{3 a \,e^{4} x}{2 \sqrt{c \,x^{2}+b x +a}\, c^{2}}-\frac{15 b^{2} e^{4} x}{8 \sqrt{c \,x^{2}+b x +a}\, c^{3}}+\frac{6 b d \,e^{3} x}{\sqrt{c \,x^{2}+b x +a}\, c^{2}}-\frac{6 d^{2} e^{2} x}{\sqrt{c \,x^{2}+b x +a}\, c}+\frac{2 \left(2 c x +b \right) d^{4}}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}}-\frac{3 a \,e^{4} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{2 c^{\frac{5}{2}}}+\frac{15 b^{2} e^{4} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{8 c^{\frac{7}{2}}}-\frac{6 b d \,e^{3} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{c^{\frac{5}{2}}}+\frac{6 d^{2} e^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{c^{\frac{3}{2}}}-\frac{13 a b \,e^{4}}{4 \sqrt{c \,x^{2}+b x +a}\, c^{3}}+\frac{8 a d \,e^{3}}{\sqrt{c \,x^{2}+b x +a}\, c^{2}}+\frac{15 b^{3} e^{4}}{16 \sqrt{c \,x^{2}+b x +a}\, c^{4}}-\frac{3 b^{2} d \,e^{3}}{\sqrt{c \,x^{2}+b x +a}\, c^{3}}+\frac{3 b \,d^{2} e^{2}}{\sqrt{c \,x^{2}+b x +a}\, c^{2}}-\frac{4 d^{3} e}{\sqrt{c \,x^{2}+b x +a}\, c}"," ",0,"-4*d^3*e/c/(c*x^2+b*x+a)^(1/2)+6*d^2*e^2/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+1/2*e^4*x^3/c/(c*x^2+b*x+a)^(1/2)+15/16*e^4*b^3/c^4/(c*x^2+b*x+a)^(1/2)+15/8*e^4*b^2/c^(7/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-3/2*e^4*a/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+2*d^4*(2*c*x+b)/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)+15/8*e^4*b^4/c^3/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x-13/4*e^4*b^3/c^3*a/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)+3*d^2*e^2*b^3/c^2/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)+6*d*e^3*b/c^2*x/(c*x^2+b*x+a)^(1/2)-3*d*e^3*b^4/c^3/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)-8*d^3*e*b/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x-4*d^3*e*b^2/c/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)-13/2*e^4*b^2/c^2*a/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x+6*d^2*e^2*b^2/c/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x+16*d*e^3*a/c*b/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x-13/4*e^4*b/c^3*a/(c*x^2+b*x+a)^(1/2)+3/2*e^4*a/c^2*x/(c*x^2+b*x+a)^(1/2)-5/4*e^4*b/c^2*x^2/(c*x^2+b*x+a)^(1/2)-15/8*e^4*b^2/c^3*x/(c*x^2+b*x+a)^(1/2)+15/16*e^4*b^5/c^4/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)-6*d*e^3*b^3/c^2/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x-6*d*e^3*b/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+8*d*e^3*a/c^2/(c*x^2+b*x+a)^(1/2)-3*d*e^3*b^2/c^3/(c*x^2+b*x+a)^(1/2)+4*d*e^3*x^2/c/(c*x^2+b*x+a)^(1/2)+8*d*e^3*a/c^2*b^2/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)+3*d^2*e^2*b/c^2/(c*x^2+b*x+a)^(1/2)-6*d^2*e^2*x/c/(c*x^2+b*x+a)^(1/2)","B"
2383,1,541,163,0.089000," ","int((e*x+d)^3/(c*x^2+b*x+a)^(3/2),x)","\frac{4 a b \,e^{3} x}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, c}-\frac{3 b^{3} e^{3} x}{2 \left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, c^{2}}+\frac{3 b^{2} d \,e^{2} x}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, c}-\frac{6 b \,d^{2} e x}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}}+\frac{2 a \,b^{2} e^{3}}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, c^{2}}-\frac{3 b^{4} e^{3}}{4 \left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, c^{3}}+\frac{3 b^{3} d \,e^{2}}{2 \left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, c^{2}}-\frac{3 b^{2} d^{2} e}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, c}+\frac{e^{3} x^{2}}{\sqrt{c \,x^{2}+b x +a}\, c}+\frac{3 b \,e^{3} x}{2 \sqrt{c \,x^{2}+b x +a}\, c^{2}}-\frac{3 d \,e^{2} x}{\sqrt{c \,x^{2}+b x +a}\, c}+\frac{2 \left(2 c x +b \right) d^{3}}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}}-\frac{3 b \,e^{3} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{2 c^{\frac{5}{2}}}+\frac{3 d \,e^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{c^{\frac{3}{2}}}+\frac{2 a \,e^{3}}{\sqrt{c \,x^{2}+b x +a}\, c^{2}}-\frac{3 b^{2} e^{3}}{4 \sqrt{c \,x^{2}+b x +a}\, c^{3}}+\frac{3 b d \,e^{2}}{2 \sqrt{c \,x^{2}+b x +a}\, c^{2}}-\frac{3 d^{2} e}{\sqrt{c \,x^{2}+b x +a}\, c}"," ",0,"e^3*x^2/c/(c*x^2+b*x+a)^(1/2)+3/2*e^3*b/c^2*x/(c*x^2+b*x+a)^(1/2)-3/4*e^3*b^2/c^3/(c*x^2+b*x+a)^(1/2)-3/2*e^3*b^3/c^2/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x-3/4*e^3*b^4/c^3/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)-3/2*e^3*b/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+2*e^3*a/c^2/(c*x^2+b*x+a)^(1/2)+4*e^3*a/c*b/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x+2*e^3*a/c^2*b^2/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)-3*d*e^2*x/c/(c*x^2+b*x+a)^(1/2)+3/2*d*e^2*b/c^2/(c*x^2+b*x+a)^(1/2)+3*d*e^2*b^2/c/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x+3/2*d*e^2*b^3/c^2/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)+3*d*e^2/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-3*d^2*e/c/(c*x^2+b*x+a)^(1/2)-6*d^2*e*b/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x-3*d^2*e*b^2/c/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)+2*d^3*(2*c*x+b)/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)","B"
2384,1,264,117,0.065000," ","int((e*x+d)^2/(c*x^2+b*x+a)^(3/2),x)","\frac{b^{2} e^{2} x}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, c}-\frac{4 b d e x}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}}+\frac{b^{3} e^{2}}{2 \left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, c^{2}}-\frac{2 b^{2} d e}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, c}-\frac{e^{2} x}{\sqrt{c \,x^{2}+b x +a}\, c}+\frac{2 \left(2 c x +b \right) d^{2}}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}}+\frac{e^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{c^{\frac{3}{2}}}+\frac{b \,e^{2}}{2 \sqrt{c \,x^{2}+b x +a}\, c^{2}}-\frac{2 d e}{\sqrt{c \,x^{2}+b x +a}\, c}"," ",0,"-e^2*x/c/(c*x^2+b*x+a)^(1/2)+1/2*e^2*b/c^2/(c*x^2+b*x+a)^(1/2)+e^2*b^2/c/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x+1/2*e^2*b^3/c^2/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)+e^2/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-2*d*e/c/(c*x^2+b*x+a)^(1/2)-4*d*e*b/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x-2*d*e*b^2/c/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)+2*d^2*(2*c*x+b)/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)","B"
2385,1,45,43,0.057000," ","int((e*x+d)/(c*x^2+b*x+a)^(3/2),x)","-\frac{2 \left(b e x -2 c d x +2 a e -b d \right)}{\sqrt{c \,x^{2}+b x +a}\, \left(4 a c -b^{2}\right)}"," ",0,"-2/(c*x^2+b*x+a)^(1/2)*(b*e*x-2*c*d*x+2*a*e-b*d)/(4*a*c-b^2)","A"
2386,1,33,30,0.056000," ","int(1/(c*x^2+b*x+a)^(3/2),x)","\frac{4 c x +2 b}{\sqrt{c \,x^{2}+b x +a}\, \left(4 a c -b^{2}\right)}"," ",0,"2*(2*c*x+b)/(c*x^2+b*x+a)^(1/2)/(4*a*c-b^2)","A"
2387,1,603,145,0.059000," ","int(1/(e*x+d)/(c*x^2+b*x+a)^(3/2),x)","-\frac{2 b c e x}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}+\frac{4 c^{2} d x}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}-\frac{b^{2} e}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}+\frac{2 b c d}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}-\frac{e \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}+\frac{e}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}"," ",0,"e/(a*e^2-b*d*e+c*d^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)-2*e/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*b*c+4/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*c^2*d-e/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b^2+2/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b*c*d-e/(a*e^2-b*d*e+c*d^2)/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))","B"
2388,1,1313,241,0.086000," ","int(1/(e*x+d)^2/(c*x^2+b*x+a)^(3/2),x)","\frac{3 b^{2} c \,e^{2} x}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}-\frac{12 b \,c^{2} d e x}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}+\frac{12 c^{3} d^{2} x}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}+\frac{3 b^{3} e^{2}}{2 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}-\frac{6 b^{2} c d e}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}+\frac{6 b \,c^{2} d^{2}}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}+\frac{3 b \,e^{2} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{2 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}-\frac{3 c d e \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}-\frac{3 b \,e^{2}}{2 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}-\frac{8 c^{2} x}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}+\frac{3 c d e}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}-\frac{4 b c}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}-\frac{1}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \left(x +\frac{d}{e}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}"," ",0,"-1/(a*e^2-b*d*e+c*d^2)/(x+d/e)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)-3/2*e^2/(a*e^2-b*d*e+c*d^2)^2/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b+3*e/(a*e^2-b*d*e+c*d^2)^2/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*c*d+3*e^2/(a*e^2-b*d*e+c*d^2)^2/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*b^2*c-12*e/(a*e^2-b*d*e+c*d^2)^2/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*b*c^2*d+12/(a*e^2-b*d*e+c*d^2)^2/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*c^3*d^2+3/2*e^2/(a*e^2-b*d*e+c*d^2)^2/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b^3-6*e/(a*e^2-b*d*e+c*d^2)^2/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b^2*c*d+6/(a*e^2-b*d*e+c*d^2)^2/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b*c^2*d^2+3/2*e^2/(a*e^2-b*d*e+c*d^2)^2/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*b-3*e/(a*e^2-b*d*e+c*d^2)^2/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*c*d-8*c^2/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x-4*c/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b","B"
2389,1,2380,351,0.096000," ","int(1/(e*x+d)^3/(c*x^2+b*x+a)^(3/2),x)","-\frac{15 b^{3} c \,e^{3} x}{4 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}+\frac{45 b^{2} c^{2} d \,e^{2} x}{2 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}-\frac{45 b \,c^{3} d^{2} e x}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}+\frac{30 c^{4} d^{3} x}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}-\frac{15 b^{4} e^{3}}{8 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}+\frac{45 b^{3} c d \,e^{2}}{4 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}-\frac{45 b^{2} c^{2} d^{2} e}{2 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}+\frac{15 b \,c^{3} d^{3}}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}-\frac{15 b^{2} e^{3} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{8 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}+\frac{15 b c d \,e^{2} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{2 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}-\frac{15 c^{2} d^{2} e \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{2 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}+\frac{15 b^{2} e^{3}}{8 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}+\frac{13 b \,c^{2} e x}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}-\frac{15 b c d \,e^{2}}{2 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}-\frac{26 c^{3} d x}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}+\frac{15 c^{2} d^{2} e}{2 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}+\frac{13 b^{2} c e}{2 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}-\frac{13 b \,c^{2} d}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}+\frac{3 c e \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{2 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}+\frac{5 b e}{4 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(x +\frac{d}{e}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}-\frac{5 c d}{2 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(x +\frac{d}{e}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}-\frac{3 c e}{2 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}-\frac{1}{2 \left(a \,e^{2}-b d e +c \,d^{2}\right) \left(x +\frac{d}{e}\right)^{2} \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e}"," ",0,"-5/2/(a*e^2-b*d*e+c*d^2)^2/(x+d/e)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*c*d-15/2*e/(a*e^2-b*d*e+c*d^2)^3/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*c^2*d^2+13/2*e/(a*e^2-b*d*e+c*d^2)^2*c/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b^2-15/2*e^2/(a*e^2-b*d*e+c*d^2)^3/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b*c*d-45*e/(a*e^2-b*d*e+c*d^2)^3/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*b*c^3*d^2+45/2*e^2/(a*e^2-b*d*e+c*d^2)^3/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*b^2*c^2*d-3/2*e*c/(a*e^2-b*d*e+c*d^2)^2/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)+15/8*e^3/(a*e^2-b*d*e+c*d^2)^3/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b^2-1/2/e/(a*e^2-b*d*e+c*d^2)/(x+d/e)^2/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)-15/4*e^3/(a*e^2-b*d*e+c*d^2)^3/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*b^3*c+30/(a*e^2-b*d*e+c*d^2)^3/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*c^4*d^3+45/4*e^2/(a*e^2-b*d*e+c*d^2)^3/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b^3*c*d-45/2*e/(a*e^2-b*d*e+c*d^2)^3/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b^2*c^2*d^2+15/(a*e^2-b*d*e+c*d^2)^3/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b*c^3*d^3+15/2*e^2/(a*e^2-b*d*e+c*d^2)^3/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*b*c*d+13*e/(a*e^2-b*d*e+c*d^2)^2*c^2/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*b-26/(a*e^2-b*d*e+c*d^2)^2*c^3/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*d-13/(a*e^2-b*d*e+c*d^2)^2*c^2/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b*d+5/4*e/(a*e^2-b*d*e+c*d^2)^2/(x+d/e)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b+15/2*e/(a*e^2-b*d*e+c*d^2)^3/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*c^2*d^2-15/8*e^3/(a*e^2-b*d*e+c*d^2)^3/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b^4-15/8*e^3/(a*e^2-b*d*e+c*d^2)^3/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*b^2+3/2*e*c/(a*e^2-b*d*e+c*d^2)^2/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))","B"
2390,1,3823,495,0.124000," ","int(1/(e*x+d)^4/(c*x^2+b*x+a)^(3/2),x)","\text{output too large to display}"," ",0,"-115/12*e^2/(a*e^2-b*d*e+c*d^2)^3*c/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b^3+105/8*e^3/(a*e^2-b*d*e+c*d^2)^4/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b^2*c*d-105/4*e^2/(a*e^2-b*d*e+c*d^2)^4/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b*c^2*d^2+70/(a*e^2-b*d*e+c*d^2)^4/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*c^5*d^4-7/6/e/(a*e^2-b*d*e+c*d^2)^2/(x+d/e)^2/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*c*d-15/4*e^2/(a*e^2-b*d*e+c*d^2)^3*c/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*b+15/2*e/(a*e^2-b*d*e+c*d^2)^3*c^2/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*d-35/2*e/(a*e^2-b*d*e+c*d^2)^4/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*c^3*d^3-1/3/e^2/(a*e^2-b*d*e+c*d^2)/(x+d/e)^3/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)-35/16*e^4/(a*e^2-b*d*e+c*d^2)^4/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b^3+4/3*c/(a*e^2-b*d*e+c*d^2)^2/(x+d/e)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)+7/12/(a*e^2-b*d*e+c*d^2)^2/(x+d/e)^2/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b-35*e^3/(a*e^2-b*d*e+c*d^2)^4/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*b^3*c^2*d+105*e^2/(a*e^2-b*d*e+c*d^2)^4/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*b^2*c^3*d^2+230/3*e/(a*e^2-b*d*e+c*d^2)^3*c^3/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*b*d-140*e/(a*e^2-b*d*e+c*d^2)^4/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*b*c^4*d^3+15/4*e^2/(a*e^2-b*d*e+c*d^2)^3*c/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b+35/16*e^4/(a*e^2-b*d*e+c*d^2)^4/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*b^3-35/24*e^2/(a*e^2-b*d*e+c*d^2)^3/(x+d/e)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b^2-35/6/(a*e^2-b*d*e+c*d^2)^3/(x+d/e)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*c^2*d^2+16/3*c^2/(a*e^2-b*d*e+c*d^2)^2/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b+32/3*c^3/(a*e^2-b*d*e+c*d^2)^2/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x+35/2*e/(a*e^2-b*d*e+c*d^2)^4/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*c^3*d^3+35/16*e^4/(a*e^2-b*d*e+c*d^2)^4/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b^5-115/3/(a*e^2-b*d*e+c*d^2)^3*c^3/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b*d^2+35/(a*e^2-b*d*e+c*d^2)^4/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b*c^4*d^4-230/3/(a*e^2-b*d*e+c*d^2)^3*c^4/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*d^2-15/2*e/(a*e^2-b*d*e+c*d^2)^3*c^2/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*d+35/6*e/(a*e^2-b*d*e+c*d^2)^3/(x+d/e)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*c*d*b+105/2*e^2/(a*e^2-b*d*e+c*d^2)^4/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b^3*c^2*d^2-70*e/(a*e^2-b*d*e+c*d^2)^4/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b^2*c^3*d^3+35/8*e^4/(a*e^2-b*d*e+c*d^2)^4/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*b^4*c-105/8*e^3/(a*e^2-b*d*e+c*d^2)^4/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*b^2*c*d-115/6*e^2/(a*e^2-b*d*e+c*d^2)^3*c^2/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*b^2-35/2*e^3/(a*e^2-b*d*e+c*d^2)^4/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b^4*c*d+105/4*e^2/(a*e^2-b*d*e+c*d^2)^4/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*c^2*d^2*b+115/3*e/(a*e^2-b*d*e+c*d^2)^3*c^2/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b^2*d","B"
2391,1,2395,367,0.094000," ","int((e*x+d)^5/(c*x^2+b*x+a)^(5/2),x)","\frac{32 a^{2} b \,e^{5} x}{\left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}\, c}-\frac{38 a \,b^{3} e^{5} x}{3 \left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}\, c^{2}}+\frac{20 a \,b^{2} d \,e^{4} x}{\left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}\, c}-\frac{80 a b \,d^{2} e^{3} x}{\left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}}+\frac{160 a c \,d^{3} e^{2} x}{3 \left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}}+\frac{5 b^{5} e^{5} x}{6 \left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}\, c^{3}}-\frac{5 b^{4} d \,e^{4} x}{3 \left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}\, c^{2}}+\frac{20 b^{3} d^{2} e^{3} x}{3 \left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}\, c}+\frac{40 b^{2} d^{3} e^{2} x}{3 \left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}}-\frac{80 b c \,d^{4} e x}{3 \left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}}+\frac{32 c^{2} d^{5} x}{3 \left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}}+\frac{e^{5} x^{4}}{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c}+\frac{16 a^{2} b^{2} e^{5}}{\left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}\, c^{2}}+\frac{4 a^{2} b \,e^{5} x}{\left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{2}}-\frac{19 a \,b^{4} e^{5}}{3 \left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}\, c^{3}}+\frac{10 a \,b^{3} d \,e^{4}}{\left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}\, c^{2}}-\frac{19 a \,b^{3} e^{5} x}{12 \left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{3}}-\frac{40 a \,b^{2} d^{2} e^{3}}{\left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}\, c}+\frac{5 a \,b^{2} d \,e^{4} x}{2 \left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{2}}-\frac{10 a b \,d^{2} e^{3} x}{\left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c}+\frac{80 a b \,d^{3} e^{2}}{3 \left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}}+\frac{20 a \,d^{3} e^{2} x}{3 \left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}}}+\frac{5 b^{6} e^{5}}{12 \left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}\, c^{4}}-\frac{5 b^{5} d \,e^{4}}{6 \left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}\, c^{3}}+\frac{5 b^{5} e^{5} x}{48 \left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{4}}+\frac{10 b^{4} d^{2} e^{3}}{3 \left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}\, c^{2}}-\frac{5 b^{4} d \,e^{4} x}{24 \left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{3}}+\frac{20 b^{3} d^{3} e^{2}}{3 \left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}\, c}+\frac{5 b^{3} d^{2} e^{3} x}{6 \left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{2}}+\frac{5 b^{2} d^{3} e^{2} x}{3 \left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c}-\frac{40 b^{2} d^{4} e}{3 \left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}}+\frac{16 b c \,d^{5}}{3 \left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}}+\frac{5 b \,e^{5} x^{3}}{6 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{2}}-\frac{10 b \,d^{4} e x}{3 \left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}}}+\frac{4 c \,d^{5} x}{3 \left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}}}-\frac{5 d \,e^{4} x^{3}}{3 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c}+\frac{2 a^{2} b^{2} e^{5}}{\left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{3}}-\frac{19 a \,b^{4} e^{5}}{24 \left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{4}}+\frac{5 a \,b^{3} d \,e^{4}}{4 \left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{3}}-\frac{5 a \,b^{2} d^{2} e^{3}}{\left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{2}}+\frac{10 a b \,d^{3} e^{2}}{3 \left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c}+\frac{4 a \,e^{5} x^{2}}{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{2}}+\frac{5 b^{6} e^{5}}{96 \left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{5}}-\frac{5 b^{5} d \,e^{4}}{48 \left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{4}}+\frac{5 b^{4} d^{2} e^{3}}{12 \left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{3}}+\frac{5 b^{3} d^{3} e^{2}}{6 \left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{2}}-\frac{5 b^{3} e^{5} x}{2 \left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, c^{3}}-\frac{5 b^{2} d^{4} e}{3 \left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c}+\frac{5 b^{2} d \,e^{4} x}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, c^{2}}-\frac{5 b^{2} e^{5} x^{2}}{4 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{3}}+\frac{5 b d \,e^{4} x^{2}}{2 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{2}}+\frac{2 b \,d^{5}}{3 \left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}}}-\frac{10 d^{2} e^{3} x^{2}}{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c}+\frac{a b \,e^{5} x}{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{3}}-\frac{5 b^{4} e^{5}}{4 \left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, c^{4}}+\frac{5 b^{3} d \,e^{4}}{2 \left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, c^{3}}-\frac{5 b^{3} e^{5} x}{16 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{4}}+\frac{5 b^{2} d \,e^{4} x}{8 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{3}}-\frac{5 b \,d^{2} e^{3} x}{2 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{2}}-\frac{5 d^{3} e^{2} x}{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c}+\frac{8 a^{2} e^{5}}{3 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{3}}-\frac{a \,b^{2} e^{5}}{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{4}}+\frac{5 a b d \,e^{4}}{3 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{3}}-\frac{20 a \,d^{2} e^{3}}{3 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{2}}+\frac{5 b^{4} e^{5}}{96 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{5}}-\frac{5 b^{3} d \,e^{4}}{48 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{4}}+\frac{5 b^{2} d^{2} e^{3}}{12 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{3}}+\frac{5 b \,d^{3} e^{2}}{6 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{2}}+\frac{5 b \,e^{5} x}{2 \sqrt{c \,x^{2}+b x +a}\, c^{3}}-\frac{5 d^{4} e}{3 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c}-\frac{5 d \,e^{4} x}{\sqrt{c \,x^{2}+b x +a}\, c^{2}}-\frac{5 b \,e^{5} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{2 c^{\frac{7}{2}}}+\frac{5 d \,e^{4} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{c^{\frac{5}{2}}}-\frac{5 b^{2} e^{5}}{4 \sqrt{c \,x^{2}+b x +a}\, c^{4}}+\frac{5 b d \,e^{4}}{2 \sqrt{c \,x^{2}+b x +a}\, c^{3}}"," ",0,"10/3*d^2*e^3*b^4/c^2/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)+5/6*d^3*e^2*b^3/c^2/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)+5/8*d*e^4*b^2/c^3*x/(c*x^2+b*x+a)^(3/2)-5/48*d*e^4*b^5/c^4/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)-5/6*d*e^4*b^5/c^3/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)+5/3*d*e^4*b/c^3*a/(c*x^2+b*x+a)^(3/2)+5/2*d*e^4/c^3*b^3/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)-19/3*e^5*b^4/c^3*a/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)-5/2*e^5*b^3/c^3/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x+e^5*a/c^3*b*x/(c*x^2+b*x+a)^(3/2)+2*e^5*a^2/c^3*b^2/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)-5/3*d^4*e*b^2/c/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)-5/2*d^2*e^3*b/c^2*x/(c*x^2+b*x+a)^(3/2)+5/12*d^2*e^3*b^4/c^3/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)+20/3*d^3*e^2*a/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)*x+80/3*d^3*e^2*a/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)*b-10/3*d^4*e*b/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)*x+20/3*d^3*e^2*b^3/c/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)+20*d*e^4*b^2/c*a/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)*x-10*d^2*e^3*b/c*a/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)*x+5/2*d*e^4*b^2/c^2*a/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)*x+5*d*e^4/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+5/96*e^5*b^4/c^5/(c*x^2+b*x+a)^(3/2)-5/4*e^5*b^2/c^4/(c*x^2+b*x+a)^(1/2)+8/3*e^5*a^2/c^3/(c*x^2+b*x+a)^(3/2)+e^5*x^4/c/(c*x^2+b*x+a)^(3/2)-5/2*e^5*b/c^(7/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+2/3*d^5/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)*b-5/3*d^4*e/c/(c*x^2+b*x+a)^(3/2)+16*e^5*a^2/c^2*b^2/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)+5/48*e^5*b^5/c^4/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)*x+5/6*e^5*b^5/c^3/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)*x-19/24*e^5*b^4/c^4*a/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)+40/3*d^3*e^2*b^2/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)*x+32*e^5*a^2/c*b/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)*x-19/12*e^5*b^3/c^3*a/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)*x-38/3*e^5*b^3/c^2*a/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)*x+4*e^5*a^2/c^2*b/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)*x-80/3*d^4*e*b*c/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)*x-5/24*d*e^4*b^4/c^3/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)*x-5/3*d*e^4*b^4/c^2/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)*x+5/4*d*e^4*b^3/c^3*a/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)+5/3*d^3*e^2*b^2/c/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)*x+10/3*d^3*e^2*a/c/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)*b+160/3*d^3*e^2*a*c/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)*x+10*d*e^4*b^3/c^2*a/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)+5*d*e^4/c^2*b^2/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x+5/6*d^2*e^3*b^3/c^2/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)*x+20/3*d^2*e^3*b^3/c/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)*x-5*d^2*e^3*b^2/c^2*a/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)-80*d^2*e^3*b*a/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)*x-40*d^2*e^3*b^2/c*a/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)-5/4*e^5*b^2/c^3*x^2/(c*x^2+b*x+a)^(3/2)-5/16*e^5*b^3/c^4*x/(c*x^2+b*x+a)^(3/2)+5/12*e^5*b^6/c^4/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)-e^5*b^2/c^4*a/(c*x^2+b*x+a)^(3/2)+5/2*e^5*b/c^3*x/(c*x^2+b*x+a)^(1/2)-5*d^3*e^2*x/c/(c*x^2+b*x+a)^(3/2)+5/2*d*e^4*b/c^2*x^2/(c*x^2+b*x+a)^(3/2)-10*d^2*e^3*x^2/c/(c*x^2+b*x+a)^(3/2)+5/12*d^2*e^3*b^2/c^3/(c*x^2+b*x+a)^(3/2)+5/6*d^3*e^2*b/c^2/(c*x^2+b*x+a)^(3/2)-5/3*d*e^4*x^3/c/(c*x^2+b*x+a)^(3/2)-20/3*d^2*e^3*a/c^2/(c*x^2+b*x+a)^(3/2)-5/4*e^5*b^4/c^4/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)+5/96*e^5*b^6/c^5/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)+4*e^5*a/c^2*x^2/(c*x^2+b*x+a)^(3/2)+5/6*e^5*b/c^2*x^3/(c*x^2+b*x+a)^(3/2)-5/48*d*e^4*b^3/c^4/(c*x^2+b*x+a)^(3/2)-5*d*e^4/c^2*x/(c*x^2+b*x+a)^(1/2)+5/2*d*e^4/c^3*b/(c*x^2+b*x+a)^(1/2)-40/3*d^4*e*b^2/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)+4/3*d^5/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)*c*x+32/3*d^5*c^2/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)*x+16/3*d^5*c/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)*b","B"
2392,1,1550,275,0.099000," ","int((e*x+d)^4/(c*x^2+b*x+a)^(5/2),x)","\frac{4 a \,b^{2} e^{4} x}{\left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}\, c}-\frac{32 a b d \,e^{3} x}{\left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}}+\frac{32 a c \,d^{2} e^{2} x}{\left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}}-\frac{b^{4} e^{4} x}{3 \left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}\, c^{2}}+\frac{8 b^{3} d \,e^{3} x}{3 \left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}\, c}+\frac{8 b^{2} d^{2} e^{2} x}{\left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}}-\frac{64 b c \,d^{3} e x}{3 \left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}}+\frac{32 c^{2} d^{4} x}{3 \left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}}+\frac{2 a \,b^{3} e^{4}}{\left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}\, c^{2}}-\frac{16 a \,b^{2} d \,e^{3}}{\left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}\, c}+\frac{a \,b^{2} e^{4} x}{2 \left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a 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-b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}}-\frac{8 b \,d^{3} e x}{3 \left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}}}+\frac{4 c \,d^{4} x}{3 \left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}}}-\frac{e^{4} x^{3}}{3 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c}+\frac{a \,b^{3} e^{4}}{4 \left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{3}}-\frac{2 a \,b^{2} d \,e^{3}}{\left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{2}}+\frac{2 a b \,d^{2} e^{2}}{\left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c}-\frac{b^{5} e^{4}}{48 \left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{4}}+\frac{b^{4} d \,e^{3}}{6 \left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{3}}+\frac{b^{3} d^{2} e^{2}}{2 \left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{2}}-\frac{4 b^{2} d^{3} e}{3 \left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c}+\frac{b^{2} e^{4} x}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, c^{2}}+\frac{b \,e^{4} x^{2}}{2 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{2}}+\frac{2 b \,d^{4}}{3 \left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}}}-\frac{4 d \,e^{3} x^{2}}{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c}+\frac{b^{3} e^{4}}{2 \left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, c^{3}}+\frac{b^{2} e^{4} x}{8 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{3}}-\frac{b d \,e^{3} x}{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{2}}-\frac{3 d^{2} e^{2} x}{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c}+\frac{a b \,e^{4}}{3 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{3}}-\frac{8 a d \,e^{3}}{3 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{2}}-\frac{b^{3} e^{4}}{48 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{4}}+\frac{b^{2} d \,e^{3}}{6 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{3}}+\frac{b \,d^{2} e^{2}}{2 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{2}}-\frac{4 d^{3} e}{3 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c}-\frac{e^{4} x}{\sqrt{c \,x^{2}+b x +a}\, c^{2}}+\frac{e^{4} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{c^{\frac{5}{2}}}+\frac{b \,e^{4}}{2 \sqrt{c \,x^{2}+b x +a}\, c^{3}}"," ",0,"-4/3*d^3*e*b^2/c/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)+1/2*d^2*e^2*b^3/c^2/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)+8*d^2*e^2*b^2/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)*x+4*d^2*e^2*b^3/c/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)-d*e^3*b/c^2*x/(c*x^2+b*x+a)^(3/2)+1/6*d*e^3*b^4/c^3/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)+4/3*d*e^3*b^4/c^2/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)+16*d^2*e^2*a/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)*b-8/3*d^3*e*b/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)*x+4*d^2*e^2*a/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)*x+2*d^2*e^2*a/c/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)*b+1/2*e^4*b^2/c^2*a/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)*x+32*d^2*e^2*a*c/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)*x-16*d*e^3*b^2/c*a/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)+d^2*e^2*b^2/c/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)*x+1/3*d*e^3*b^3/c^2/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)*x+e^4/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-4*d*e^3*b/c*a/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)*x-8/3*d*e^3*a/c^2/(c*x^2+b*x+a)^(3/2)-32/3*d^3*e*b^2/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)+4/3*d^4/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)*c*x+32/3*d^4*c^2/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)*x+16/3*d^4*c/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)*b+1/2*e^4/c^3*b/(c*x^2+b*x+a)^(1/2)-4/3*d^3*e/c/(c*x^2+b*x+a)^(3/2)+2/3*d^4/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)*b-1/3*e^4*x^3/c/(c*x^2+b*x+a)^(3/2)-1/48*e^4*b^3/c^4/(c*x^2+b*x+a)^(3/2)-e^4/c^2*x/(c*x^2+b*x+a)^(1/2)-4*d*e^3*x^2/c/(c*x^2+b*x+a)^(3/2)+e^4/c^2*b^2/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x+2*e^4*b^3/c^2*a/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)-1/3*e^4*b^4/c^2/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)*x+1/4*e^4*b^3/c^3*a/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)-1/24*e^4*b^4/c^3/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)*x-2*d*e^3*b^2/c^2*a/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)-32*d*e^3*b*a/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)*x+4*e^4*b^2/c*a/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)*x+8/3*d*e^3*b^3/c/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)*x+1/6*d*e^3*b^2/c^3/(c*x^2+b*x+a)^(3/2)-64/3*d^3*e*b*c/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)*x+1/8*e^4*b^2/c^3*x/(c*x^2+b*x+a)^(3/2)-1/48*e^4*b^5/c^4/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)-1/6*e^4*b^5/c^3/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)+1/3*e^4*b/c^3*a/(c*x^2+b*x+a)^(3/2)+1/2*e^4/c^3*b^3/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)+1/2*d^2*e^2*b/c^2/(c*x^2+b*x+a)^(3/2)-3*d^2*e^2*x/c/(c*x^2+b*x+a)^(3/2)+1/2*e^4*b/c^2*x^2/(c*x^2+b*x+a)^(3/2)","B"
2393,1,296,110,0.112000," ","int((e*x+d)^3/(c*x^2+b*x+a)^(5/2),x)","-\frac{2 \left(12 a b c \,e^{3} x^{3}-24 a \,c^{2} d \,e^{2} x^{3}-b^{3} e^{3} x^{3}-6 b^{2} c d \,e^{2} x^{3}+24 b \,c^{2} d^{2} e \,x^{3}-16 c^{3} d^{3} x^{3}+24 a^{2} c \,e^{3} x^{2}+6 a \,b^{2} e^{3} x^{2}-36 a b c d \,e^{2} x^{2}-9 b^{3} d \,e^{2} x^{2}+36 b^{2} c \,d^{2} e \,x^{2}-24 b \,c^{2} d^{3} x^{2}+24 a^{2} b \,e^{3} x -36 a \,b^{2} d \,e^{2} x +36 a b c \,d^{2} e x -24 a \,c^{2} d^{3} x +9 b^{3} d^{2} e x -6 b^{2} c \,d^{3} x +16 a^{3} e^{3}-24 a^{2} b d \,e^{2}+24 a^{2} c \,d^{2} e +6 a \,b^{2} d^{2} e -12 a b c \,d^{3}+b^{3} d^{3}\right)}{3 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}"," ",0,"-2/3/(c*x^2+b*x+a)^(3/2)*(12*a*b*c*e^3*x^3-24*a*c^2*d*e^2*x^3-b^3*e^3*x^3-6*b^2*c*d*e^2*x^3+24*b*c^2*d^2*e*x^3-16*c^3*d^3*x^3+24*a^2*c*e^3*x^2+6*a*b^2*e^3*x^2-36*a*b*c*d*e^2*x^2-9*b^3*d*e^2*x^2+36*b^2*c*d^2*e*x^2-24*b*c^2*d^3*x^2+24*a^2*b*e^3*x-36*a*b^2*d*e^2*x+36*a*b*c*d^2*e*x-24*a*c^2*d^3*x+9*b^3*d^2*e*x-6*b^2*c*d^3*x+16*a^3*e^3-24*a^2*b*d*e^2+24*a^2*c*d^2*e+6*a*b^2*d^2*e-12*a*b*c*d^3+b^3*d^3)/(16*a^2*c^2-8*a*b^2*c+b^4)","B"
2394,1,215,90,0.058000," ","int((e*x+d)^2/(c*x^2+b*x+a)^(5/2),x)","\frac{\frac{16}{3} a \,c^{2} e^{2} x^{3}+\frac{4}{3} b^{2} c \,e^{2} x^{3}-\frac{32}{3} b \,c^{2} d e \,x^{3}+\frac{32}{3} c^{3} d^{2} x^{3}+8 a b c \,e^{2} x^{2}+2 b^{3} e^{2} x^{2}-16 b^{2} c d e \,x^{2}+16 b \,c^{2} d^{2} x^{2}+8 a \,b^{2} e^{2} x -16 a b c d e x +16 a \,c^{2} d^{2} x -4 b^{3} d e x +4 b^{2} c \,d^{2} x +\frac{16}{3} a^{2} b \,e^{2}-\frac{32}{3} a^{2} c d e -\frac{8}{3} a \,b^{2} d e +8 a b c \,d^{2}-\frac{2}{3} b^{3} d^{2}}{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}"," ",0,"2/3/(c*x^2+b*x+a)^(3/2)*(8*a*c^2*e^2*x^3+2*b^2*c*e^2*x^3-16*b*c^2*d*e*x^3+16*c^3*d^2*x^3+12*a*b*c*e^2*x^2+3*b^3*e^2*x^2-24*b^2*c*d*e*x^2+24*b*c^2*d^2*x^2+12*a*b^2*e^2*x-24*a*b*c*d*e*x+24*a*c^2*d^2*x-6*b^3*d*e*x+6*b^2*c*d^2*x+8*a^2*b*e^2-16*a^2*c*d*e-4*a*b^2*d*e+12*a*b*c*d^2-b^3*d^2)/(16*a^2*c^2-8*a*b^2*c+b^4)","B"
2395,1,131,83,0.045000," ","int((e*x+d)/(c*x^2+b*x+a)^(5/2),x)","-\frac{2 \left(8 b \,c^{2} e \,x^{3}-16 c^{3} d \,x^{3}+12 b^{2} c e \,x^{2}-24 b \,c^{2} d \,x^{2}+12 a b c e x -24 a \,c^{2} d x +3 b^{3} e x -6 b^{2} c d x +8 a^{2} c e +2 a \,b^{2} e -12 a b c d +b^{3} d \right)}{3 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}"," ",0,"-2/3/(c*x^2+b*x+a)^(3/2)*(8*b*c^2*e*x^3-16*c^3*d*x^3+12*b^2*c*e*x^2-24*b*c^2*d*x^2+12*a*b*c*e*x-24*a*c^2*d*x+3*b^3*e*x-6*b^2*c*d*x+8*a^2*c*e+2*a*b^2*e-12*a*b*c*d+b^3*d)/(16*a^2*c^2-8*a*b^2*c+b^4)","A"
2396,1,78,62,0.062000," ","int(1/(c*x^2+b*x+a)^(5/2),x)","\frac{\frac{32}{3} c^{3} x^{3}+16 b \,c^{2} x^{2}+16 a \,c^{2} x +4 b^{2} c x +8 a b c -\frac{2}{3} b^{3}}{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}"," ",0,"2/3/(c*x^2+b*x+a)^(3/2)*(16*c^3*x^3+24*b*c^2*x^2+24*a*c^2*x+6*b^2*c*x+12*a*b*c-b^3)/(16*a^2*c^2-8*a*b^2*c+b^4)","A"
2397,1,1408,294,0.072000," ","int(1/(e*x+d)/(c*x^2+b*x+a)^(5/2),x)","-\frac{2 b c \,e^{3} x}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}+\frac{4 c^{2} d \,e^{2} x}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}-\frac{b^{2} e^{3}}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}-\frac{16 b \,c^{2} e x}{3 \left(a \,e^{2}-b d e +c \,d^{2}\right) \left(4 a c -b^{2}\right)^{2} \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}+\frac{2 b c d \,e^{2}}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}+\frac{32 c^{3} d x}{3 \left(a \,e^{2}-b d e +c \,d^{2}\right) \left(4 a c -b^{2}\right)^{2} \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}-\frac{8 b^{2} c e}{3 \left(a \,e^{2}-b d e +c \,d^{2}\right) \left(4 a c -b^{2}\right)^{2} \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}+\frac{16 b \,c^{2} d}{3 \left(a \,e^{2}-b d e +c \,d^{2}\right) \left(4 a c -b^{2}\right)^{2} \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}-\frac{2 b c e x}{3 \left(a \,e^{2}-b d e +c \,d^{2}\right) \left(4 a c -b^{2}\right) \left(\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}\right)^{\frac{3}{2}}}+\frac{4 c^{2} d x}{3 \left(a \,e^{2}-b d e +c \,d^{2}\right) \left(4 a c -b^{2}\right) \left(\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}\right)^{\frac{3}{2}}}-\frac{e^{3} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}-\frac{b^{2} e}{3 \left(a \,e^{2}-b d e +c \,d^{2}\right) \left(4 a c -b^{2}\right) \left(\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}\right)^{\frac{3}{2}}}+\frac{2 b c d}{3 \left(a \,e^{2}-b d e +c \,d^{2}\right) \left(4 a c -b^{2}\right) \left(\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}\right)^{\frac{3}{2}}}+\frac{e^{3}}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}+\frac{e}{3 \left(a \,e^{2}-b d e +c \,d^{2}\right) \left(\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}\right)^{\frac{3}{2}}}"," ",0,"1/3*e/(a*e^2-b*d*e+c*d^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(3/2)-2/3*e/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(3/2)*c*x*b+4/3/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(3/2)*c^2*x*d-1/3*e/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(3/2)*b^2+2/3/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(3/2)*b*c*d-16/3*e/(a*e^2-b*d*e+c*d^2)*c^2/(4*a*c-b^2)^2/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*b+32/3/(a*e^2-b*d*e+c*d^2)*c^3/(4*a*c-b^2)^2/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*d-8/3*e/(a*e^2-b*d*e+c*d^2)*c/(4*a*c-b^2)^2/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b^2+16/3/(a*e^2-b*d*e+c*d^2)*c^2/(4*a*c-b^2)^2/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b*d+e^3/(a*e^2-b*d*e+c*d^2)^2/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)-2*e^3/(a*e^2-b*d*e+c*d^2)^2/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*b*c+4*e^2/(a*e^2-b*d*e+c*d^2)^2/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*c^2*d-e^3/(a*e^2-b*d*e+c*d^2)^2/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b^2+2*e^2/(a*e^2-b*d*e+c*d^2)^2/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b*c*d-e^3/(a*e^2-b*d*e+c*d^2)^2/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))","B"
2398,1,2765,451,0.081000," ","int(1/(e*x+d)^2/(c*x^2+b*x+a)^(5/2),x)","-\frac{20 b \,c^{2} d e x}{3 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(4 a c -b^{2}\right) \left(\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}\right)^{\frac{3}{2}}}-\frac{5 b \,e^{2}}{6 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}\right)^{\frac{3}{2}}}-\frac{5 b \,e^{4}}{2 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}-\frac{20 b \,c^{2} d \,e^{3} x}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}-\frac{160 b \,c^{3} d e x}{3 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(4 a c -b^{2}\right)^{2} \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}-\frac{1}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \left(x +\frac{d}{e}\right) \left(\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}\right)^{\frac{3}{2}}}-\frac{5 c d \,e^{3} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}+\frac{20 b^{3} c \,e^{2}}{3 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(4 a c -b^{2}\right)^{2} \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}+\frac{160 c^{4} d^{2} x}{3 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(4 a c -b^{2}\right)^{2} \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}+\frac{80 b \,c^{3} d^{2}}{3 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(4 a c -b^{2}\right)^{2} \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}+\frac{20 c^{3} d^{2} x}{3 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(4 a c -b^{2}\right) \left(\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}\right)^{\frac{3}{2}}}+\frac{10 b \,c^{2} d^{2}}{3 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(4 a c -b^{2}\right) \left(\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}\right)^{\frac{3}{2}}}-\frac{128 c^{3} x}{3 \left(a \,e^{2}-b d e +c \,d^{2}\right) \left(4 a c -b^{2}\right)^{2} \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}+\frac{5 b \,e^{4} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{2 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}-\frac{64 b \,c^{2}}{3 \left(a \,e^{2}-b d e +c \,d^{2}\right) \left(4 a c -b^{2}\right)^{2} \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}-\frac{16 c^{2} x}{3 \left(a \,e^{2}-b d e +c \,d^{2}\right) \left(4 a c -b^{2}\right) \left(\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}\right)^{\frac{3}{2}}}-\frac{8 b c}{3 \left(a \,e^{2}-b d e +c \,d^{2}\right) \left(4 a c -b^{2}\right) \left(\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}\right)^{\frac{3}{2}}}+\frac{5 c d e}{3 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}\right)^{\frac{3}{2}}}+\frac{5 b^{3} e^{2}}{6 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(4 a c -b^{2}\right) \left(\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}\right)^{\frac{3}{2}}}+\frac{5 c d \,e^{3}}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}+\frac{5 b^{3} e^{4}}{2 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}-\frac{80 b^{2} c^{2} d e}{3 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(4 a c -b^{2}\right)^{2} \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}+\frac{5 b^{2} c \,e^{4} x}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}+\frac{20 c^{3} d^{2} e^{2} x}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}-\frac{10 b^{2} c d \,e^{3}}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}+\frac{10 b \,c^{2} d^{2} e^{2}}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{3} \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}+\frac{5 b^{2} c \,e^{2} x}{3 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(4 a c -b^{2}\right) \left(\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}\right)^{\frac{3}{2}}}-\frac{10 b^{2} c d e}{3 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(4 a c -b^{2}\right) \left(\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}\right)^{\frac{3}{2}}}+\frac{40 b^{2} c^{2} e^{2} x}{3 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(4 a c -b^{2}\right)^{2} \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}"," 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2399,1,4942,595,0.072000," ","int(1/(e*x+d)^3/(c*x^2+b*x+a)^(5/2),x)","\text{output too large to display}"," ",0,"5/2*e^3*c/(a*e^2-b*d*e+c*d^2)^3/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b^2-35/3*e^3/(a*e^2-b*d*e+c*d^2)^3*c/(4*a*c-b^2)^2/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b^4-35/2*e^3/(a*e^2-b*d*e+c*d^2)^4/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*c^2*d^2+11/2*e/(a*e^2-b*d*e+c*d^2)^2*c/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(3/2)*b^2-35/6*e^2/(a*e^2-b*d*e+c*d^2)^3/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(3/2)*b*c*d+44*e/(a*e^2-b*d*e+c*d^2)^2*c^2/(4*a*c-b^2)^2/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b^2-35/2*e^4/(a*e^2-b*d*e+c*d^2)^4/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*c*d*b-22/(a*e^2-b*d*e+c*d^2)^2*c^3/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(3/2)*x*d-11/(a*e^2-b*d*e+c*d^2)^2*c^2/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(3/2)*b*d+280/3/(a*e^2-b*d*e+c*d^2)^3*c^4/(4*a*c-b^2)^2/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b*d^3+70/3/(a*e^2-b*d*e+c*d^2)^3/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(3/2)*c^4*x*d^3-88/(a*e^2-b*d*e+c*d^2)^2*c^3/(4*a*c-b^2)^2/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b*d+35/3/(a*e^2-b*d*e+c*d^2)^3/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(3/2)*b*c^3*d^3-176/(a*e^2-b*d*e+c*d^2)^2*c^4/(4*a*c-b^2)^2/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*d+560/3/(a*e^2-b*d*e+c*d^2)^3*c^5/(4*a*c-b^2)^2/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*d^3-280*e/(a*e^2-b*d*e+c*d^2)^3*c^4/(4*a*c-b^2)^2/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*b*d^2+35/2*e^2/(a*e^2-b*d*e+c*d^2)^3/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(3/2)*c^2*x*b^2*d+105/2*e^4/(a*e^2-b*d*e+c*d^2)^4/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*b^2*c^2*d-105*e^3/(a*e^2-b*d*e+c*d^2)^4/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*b*c^3*d^2-35*e/(a*e^2-b*d*e+c*d^2)^3/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(3/2)*c^3*x*b*d^2+140*e^2/(a*e^2-b*d*e+c*d^2)^3*c^3/(4*a*c-b^2)^2/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*b^2*d+35/8*e^5/(a*e^2-b*d*e+c*d^2)^4/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b^2-5/6*e*c/(a*e^2-b*d*e+c*d^2)^2/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(3/2)-5/2*e^3*c/(a*e^2-b*d*e+c*d^2)^3/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)-1/2/e/(a*e^2-b*d*e+c*d^2)/(x+d/e)^2/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(3/2)+7/4*e/(a*e^2-b*d*e+c*d^2)^2/(x+d/e)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(3/2)*b+35/6*e/(a*e^2-b*d*e+c*d^2)^3/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(3/2)*c^2*d^2-35/24*e^3/(a*e^2-b*d*e+c*d^2)^3/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(3/2)*b^4+35/2*e^3/(a*e^2-b*d*e+c*d^2)^4/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*c^2*d^2-35/8*e^5/(a*e^2-b*d*e+c*d^2)^4/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b^4-35/8*e^5/(a*e^2-b*d*e+c*d^2)^4/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*b^2+5/2*e^3*c/(a*e^2-b*d*e+c*d^2)^3/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))-7/2/(a*e^2-b*d*e+c*d^2)^2/(x+d/e)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(3/2)*c*d+35/24*e^3/(a*e^2-b*d*e+c*d^2)^3/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(3/2)*b^2-35/2*e/(a*e^2-b*d*e+c*d^2)^3/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(3/2)*b^2*c^2*d^2-70/3*e^3/(a*e^2-b*d*e+c*d^2)^3*c^2/(4*a*c-b^2)^2/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*b^3+11*e/(a*e^2-b*d*e+c*d^2)^2*c^2/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(3/2)*x*b+88*e/(a*e^2-b*d*e+c*d^2)^2*c^3/(4*a*c-b^2)^2/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*b+70*e^2/(a*e^2-b*d*e+c*d^2)^4/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*c^4*d^3-35/12*e^3/(a*e^2-b*d*e+c*d^2)^3/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(3/2)*c*x*b^3-105/2*e^3/(a*e^2-b*d*e+c*d^2)^4/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b^2*c^2*d^2+35*e^2/(a*e^2-b*d*e+c*d^2)^4/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b*c^3*d^3+35/4*e^2/(a*e^2-b*d*e+c*d^2)^3/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(3/2)*b^3*c*d+5*e^3*c^2/(a*e^2-b*d*e+c*d^2)^3/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*b-10*e^2*c^3/(a*e^2-b*d*e+c*d^2)^3/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*d-5*e^2*c^2/(a*e^2-b*d*e+c*d^2)^3/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b*d-140*e/(a*e^2-b*d*e+c*d^2)^3*c^3/(4*a*c-b^2)^2/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b^2*d^2+105/4*e^4/(a*e^2-b*d*e+c*d^2)^4/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b^3*c*d+35/2*e^4/(a*e^2-b*d*e+c*d^2)^4/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+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+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*b*c*d+70*e^2/(a*e^2-b*d*e+c*d^2)^3*c^2/(4*a*c-b^2)^2/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b^3*d-35/4*e^5/(a*e^2-b*d*e+c*d^2)^4/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*b^3*c","B"
2400,1,22,21,0.059000," ","int((x+3)/(-x^2-4*x+5)^(1/2),x)","\arcsin \left(\frac{x}{3}+\frac{2}{3}\right)-\sqrt{-x^{2}-4 x +5}"," ",0,"arcsin(1/3*x+2/3)-(-x^2-4*x+5)^(1/2)","A"
2401,1,24,23,0.062000," ","int(1/2*(5-4*x)/(-x^2+3*x-2)^(1/2),x)","-\frac{\arcsin \left(2 x -3\right)}{2}+2 \sqrt{-x^{2}+3 x -2}"," ",0,"-1/2*arcsin(2*x-3)+2*(-x^2+3*x-2)^(1/2)","A"
2402,1,20,19,0.065000," ","int((2*x+3)/(x^2+2*x+5)^(1/2),x)","\arcsinh \left(\frac{x}{2}+\frac{1}{2}\right)+2 \sqrt{x^{2}+2 x +5}"," ",0,"arcsinh(1/2*x+1/2)+2*(x^2+2*x+5)^(1/2)","A"
2403,1,26,30,0.053000," ","int((x-1)/(x^2-4*x+3)^(1/2),x)","\ln \left(x -2+\sqrt{x^{2}-4 x +3}\right)+\sqrt{x^{2}-4 x +3}"," ",0,"(x^2-4*x+3)^(1/2)+ln(x-2+(x^2-4*x+3)^(1/2))","A"
2404,1,23,17,0.064000," ","int(1/(-x+1)/(x^2+2*x-4)^(1/2),x)","-\arctan \left(\frac{4 x -6}{2 \sqrt{4 x +\left(x -1\right)^{2}-5}}\right)"," ",0,"-arctan(1/2*(-6+4*x)/((x-1)^2+4*x-5)^(1/2))","A"
2405,1,13,11,0.060000," ","int(1/(x-2)/(x^2-4*x+3)^(1/2),x)","-\arctan \left(\frac{1}{\sqrt{\left(x -2\right)^{2}-1}}\right)"," ",0,"-arctan(1/((x-2)^2-1)^(1/2))","A"
2406,1,21,15,0.050000," ","int((x+1)/(x^2+3*x+2)^(3/2),x)","\frac{2 \left(x +1\right)^{2} \left(x +2\right)}{\left(x^{2}+3 x +2\right)^{\frac{3}{2}}}"," ",0,"2*(x+1)^2*(x+2)/(x^2+3*x+2)^(3/2)","A"
2407,1,58,92,0.167000," ","int(2/(e*x+d)/(b^2/c+4*b*x+4*c*x^2)^(1/2),x)","\frac{2 \left(2 c x +b \right) \left(-\ln \left(2 c x +b \right)+\ln \left(e x +d \right)\right)}{\sqrt{\frac{4 c^{2} x^{2}+4 b c x +b^{2}}{c}}\, \left(b e -2 c d \right)}"," ",0,"2*(2*c*x+b)*(ln(e*x+d)-ln(2*c*x+b))/((4*c^2*x^2+4*b*c*x+b^2)/c)^(1/2)/(b*e-2*c*d)","A"
2408,1,98,46,0.106000," ","int(1/(1/2*b/c*e+e*x)/(c*x^2+b*x+a)^(1/2),x)","-\frac{2 \ln \left(\frac{\frac{4 a c -b^{2}}{2 c}+\frac{\sqrt{\frac{4 a c -b^{2}}{c}}\, \sqrt{4 \left(x +\frac{b}{2 c}\right)^{2} c +\frac{4 a c -b^{2}}{c}}}{2}}{x +\frac{b}{2 c}}\right)}{\sqrt{\frac{4 a c -b^{2}}{c}}\, e}"," ",0,"-2/e/((4*a*c-b^2)/c)^(1/2)*ln((1/2*(4*a*c-b^2)/c+1/2*((4*a*c-b^2)/c)^(1/2)*(4*(x+1/2*b/c)^2*c+(4*a*c-b^2)/c)^(1/2))/(x+1/2*b/c))","B"
2409,1,59,46,0.050000," ","int(1/(e*x+d)/((b*d*e-c*d^2)/e^2+b*x+c*x^2)^(1/2),x)","-\frac{2 \left(c e x +b e -c d \right)}{\left(b e -2 c d \right) \sqrt{\frac{c \,e^{2} x^{2}+b \,e^{2} x +b d e -c \,d^{2}}{e^{2}}}\, e}"," ",0,"-2*(c*e*x+b*e-c*d)/e/(b*e-2*c*d)/((c*e^2*x^2+b*e^2*x+b*d*e-c*d^2)/e^2)^(1/2)","A"
2410,1,29,25,0.052000," ","int(2/(1/2*b/c*e+e*x)/(b^2/c+4*b*x+4*c*x^2)^(1/2),x)","-\frac{2}{\sqrt{\frac{4 c^{2} x^{2}+4 b c x +b^{2}}{c}}\, e}"," ",0,"-2/((4*c^2*x^2+4*b*c*x+b^2)/c)^(1/2)/e","A"
2411,1,30,31,0.057000," ","int(x/(3*x^2+4*x+2)^(1/2),x)","-\frac{2 \sqrt{3}\, \arcsinh \left(\frac{3 \sqrt{2}\, \left(x +\frac{2}{3}\right)}{2}\right)}{9}+\frac{\sqrt{3 x^{2}+4 x +2}}{3}"," ",0,"1/3*(3*x^2+4*x+2)^(1/2)-2/9*3^(1/2)*arcsinh(3/2*2^(1/2)*(x+2/3))","A"
2412,1,30,31,0.050000," ","int(x/(-3*x^2+4*x+2)^(1/2),x)","\frac{2 \sqrt{3}\, \arcsin \left(\frac{3 \sqrt{10}\, \left(x -\frac{2}{3}\right)}{10}\right)}{9}-\frac{\sqrt{-3 x^{2}+4 x +2}}{3}"," ",0,"-1/3*(-3*x^2+4*x+2)^(1/2)+2/9*3^(1/2)*arcsin(3/10*10^(1/2)*(x-2/3))","A"
2413,1,45,43,0.054000," ","int(x/(3*x^2+5*x+2)^(1/2),x)","-\frac{5 \sqrt{3}\, \ln \left(\frac{\left(3 x +\frac{5}{2}\right) \sqrt{3}}{3}+\sqrt{3 x^{2}+5 x +2}\right)}{18}+\frac{\sqrt{3 x^{2}+5 x +2}}{3}"," ",0,"1/3*(3*x^2+5*x+2)^(1/2)-5/18*ln(1/3*(5/2+3*x)*3^(1/2)+(3*x^2+5*x+2)^(1/2))*3^(1/2)","A"
2414,1,27,26,0.046000," ","int(x/(-3*x^2+5*x+2)^(1/2),x)","\frac{5 \sqrt{3}\, \arcsin \left(\frac{6 x}{7}-\frac{5}{7}\right)}{18}-\frac{\sqrt{-3 x^{2}+5 x +2}}{3}"," ",0,"5/18*3^(1/2)*arcsin(6/7*x-5/7)-1/3*(-3*x^2+5*x+2)^(1/2)","A"
2415,1,45,43,0.055000," ","int(x/(3*x^2+4*x-2)^(1/2),x)","-\frac{2 \sqrt{3}\, \ln \left(\frac{\left(3 x +2\right) \sqrt{3}}{3}+\sqrt{3 x^{2}+4 x -2}\right)}{9}+\frac{\sqrt{3 x^{2}+4 x -2}}{3}"," ",0,"1/3*(3*x^2+4*x-2)^(1/2)-2/9*ln(1/3*(3*x+2)*3^(1/2)+(3*x^2+4*x-2)^(1/2))*3^(1/2)","A"
2416,1,41,43,0.059000," ","int(x/(-3*x^2+4*x-2)^(1/2),x)","\frac{2 \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(x -\frac{2}{3}\right)}{\sqrt{-3 x^{2}+4 x -2}}\right)}{9}-\frac{\sqrt{-3 x^{2}+4 x -2}}{3}"," ",0,"-1/3*(-3*x^2+4*x-2)^(1/2)+2/9*3^(1/2)*arctan(3^(1/2)*(x-2/3)/(-3*x^2+4*x-2)^(1/2))","A"
2417,1,45,43,0.054000," ","int(x/(3*x^2+5*x-2)^(1/2),x)","-\frac{5 \sqrt{3}\, \ln \left(\frac{\left(3 x +\frac{5}{2}\right) \sqrt{3}}{3}+\sqrt{3 x^{2}+5 x -2}\right)}{18}+\frac{\sqrt{3 x^{2}+5 x -2}}{3}"," ",0,"1/3*(3*x^2+5*x-2)^(1/2)-5/18*ln(1/3*(3*x+5/2)*3^(1/2)+(3*x^2+5*x-2)^(1/2))*3^(1/2)","A"
2418,1,27,26,0.050000," ","int(x/(-3*x^2+5*x-2)^(1/2),x)","\frac{5 \sqrt{3}\, \arcsin \left(6 x -5\right)}{18}-\frac{\sqrt{-3 x^{2}+5 x -2}}{3}"," ",0,"5/18*3^(1/2)*arcsin(6*x-5)-1/3*(-3*x^2+5*x-2)^(1/2)","A"
2419,1,28,22,0.056000," ","int(1/x/((3*x+2)^2)^(1/2),x)","-\frac{\left(3 x +2\right) \left(-\ln \left(x \right)+\ln \left(3 x +2\right)\right)}{2 \sqrt{\left(3 x +2\right)^{2}}}"," ",0,"-1/2*(3*x+2)*(ln(3*x+2)-ln(x))/((3*x+2)^2)^(1/2)","A"
2420,1,28,21,0.061000," ","int(1/x/((3*x-2)^2)^(1/2),x)","\frac{\left(3 x -2\right) \left(-\ln \left(x \right)+\ln \left(3 x -2\right)\right)}{2 \sqrt{\left(3 x -2\right)^{2}}}"," ",0,"1/2*(3*x-2)*(ln(3*x-2)-ln(x))/((3*x-2)^2)^(1/2)","A"
2421,1,30,23,0.091000," ","int(1/x/(-(3*x-2)^2)^(1/2),x)","\frac{\left(3 x -2\right) \left(-\ln \left(x \right)+\ln \left(3 x -2\right)\right)}{2 \sqrt{-\left(3 x -2\right)^{2}}}"," ",0,"1/2*(3*x-2)*(-ln(x)+ln(3*x-2))/(-(3*x-2)^2)^(1/2)","A"
2422,1,30,24,0.051000," ","int(1/x/(-(3*x+2)^2)^(1/2),x)","-\frac{\left(3 x +2\right) \left(-\ln \left(x \right)+\ln \left(3 x +2\right)\right)}{2 \sqrt{-\left(3 x +2\right)^{2}}}"," ",0,"-1/2*(3*x+2)*(-ln(x)+ln(3*x+2))/(-(3*x+2)^2)^(1/2)","A"
2423,1,31,46,0.061000," ","int(1/x/((b*x+a)^2)^(1/2),x)","-\frac{\left(b x +a \right) \left(-\ln \left(x \right)+\ln \left(b x +a \right)\right)}{\sqrt{\left(b x +a \right)^{2}}\, a}"," ",0,"-(b*x+a)*(ln(b*x+a)-ln(x))/((b*x+a)^2)^(1/2)/a","A"
2424,1,36,53,0.161000," ","int(1/x/((b*x-a)^2)^(1/2),x)","\frac{\left(b x -a \right) \left(-\ln \left(x \right)+\ln \left(b x -a \right)\right)}{\sqrt{\left(b x -a \right)^{2}}\, a}"," ",0,"(b*x-a)*(ln(b*x-a)-ln(x))/((b*x-a)^2)^(1/2)/a","A"
2425,1,38,57,0.053000," ","int(1/x/(-(b*x-a)^2)^(1/2),x)","\frac{\left(b x -a \right) \left(-\ln \left(x \right)+\ln \left(b x -a \right)\right)}{\sqrt{-\left(b x -a \right)^{2}}\, a}"," ",0,"(b*x-a)*(-ln(x)+ln(b*x-a))/(-(b*x-a)^2)^(1/2)/a","A"
2426,1,33,50,0.061000," ","int(1/x/(-(b*x+a)^2)^(1/2),x)","-\frac{\left(b x +a \right) \left(-\ln \left(x \right)+\ln \left(b x +a \right)\right)}{\sqrt{-\left(b x +a \right)^{2}}\, a}"," ",0,"-(b*x+a)*(-ln(x)+ln(b*x+a))/(-(b*x+a)^2)^(1/2)/a","A"
2427,1,43,40,0.044000," ","int(x*(-x^2-2*x+3)^(1/2),x)","-2 \arcsin \left(\frac{x}{2}+\frac{1}{2}\right)-\frac{\left(-x^{2}-2 x +3\right)^{\frac{3}{2}}}{3}+\frac{\left(-2 x -2\right) \sqrt{-x^{2}-2 x +3}}{4}"," ",0,"-1/3*(-x^2-2*x+3)^(3/2)+1/4*(-2-2*x)*(-x^2-2*x+3)^(1/2)-2*arcsin(1/2*x+1/2)","A"
2428,1,43,42,0.056000," ","int(x*(-x^2+2*x+8)^(1/2),x)","\frac{9 \arcsin \left(\frac{x}{3}-\frac{1}{3}\right)}{2}-\frac{\left(-x^{2}+2 x +8\right)^{\frac{3}{2}}}{3}-\frac{\left(-2 x +2\right) \sqrt{-x^{2}+2 x +8}}{4}"," ",0,"-1/3*(-x^2+2*x+8)^(3/2)-1/4*(-2*x+2)*(-x^2+2*x+8)^(1/2)+9/2*arcsin(-1/3+1/3*x)","A"
2429,1,42,39,0.046000," ","int(x*(x^2+2*x+4)^(1/2),x)","-\frac{3 \arcsinh \left(\frac{\left(x +1\right) \sqrt{3}}{3}\right)}{2}+\frac{\left(x^{2}+2 x +4\right)^{\frac{3}{2}}}{3}-\frac{\left(2 x +2\right) \sqrt{x^{2}+2 x +4}}{4}"," ",0,"1/3*(x^2+2*x+4)^(3/2)-1/4*(2*x+2)*(x^2+2*x+4)^(1/2)-3/2*arcsinh(1/3*(x+1)*3^(1/2))","A"
2430,1,29,25,0.050000," ","int(1/x/(3*x^2+4*x+2)^(1/2),x)","-\frac{\sqrt{2}\, \arctanh \left(\frac{\left(4 x +4\right) \sqrt{2}}{4 \sqrt{3 x^{2}+4 x +2}}\right)}{2}"," ",0,"-1/2*2^(1/2)*arctanh(1/4*(4+4*x)*2^(1/2)/(3*x^2+4*x+2)^(1/2))","A"
2431,1,29,25,0.043000," ","int(1/x/(-3*x^2+4*x+2)^(1/2),x)","-\frac{\sqrt{2}\, \arctanh \left(\frac{\left(4 x +4\right) \sqrt{2}}{4 \sqrt{-3 x^{2}+4 x +2}}\right)}{2}"," ",0,"-1/2*2^(1/2)*arctanh(1/4*(4*x+4)*2^(1/2)/(-3*x^2+4*x+2)^(1/2))","A"
2432,1,29,28,0.049000," ","int(1/x/(3*x^2+5*x+2)^(1/2),x)","-\frac{\sqrt{2}\, \arctanh \left(\frac{\left(5 x +4\right) \sqrt{2}}{4 \sqrt{3 x^{2}+5 x +2}}\right)}{2}"," ",0,"-1/2*arctanh(1/4*(4+5*x)*2^(1/2)/(3*x^2+5*x+2)^(1/2))*2^(1/2)","A"
2433,1,29,28,0.050000," ","int(1/x/(-3*x^2+5*x+2)^(1/2),x)","-\frac{\sqrt{2}\, \arctanh \left(\frac{\left(5 x +4\right) \sqrt{2}}{4 \sqrt{-3 x^{2}+5 x +2}}\right)}{2}"," ",0,"-1/2*arctanh(1/4*(5*x+4)*2^(1/2)/(-3*x^2+5*x+2)^(1/2))*2^(1/2)","A"
2434,1,29,27,0.047000," ","int(1/x/(3*x^2+4*x-2)^(1/2),x)","\frac{\sqrt{2}\, \arctan \left(\frac{\left(4 x -4\right) \sqrt{2}}{4 \sqrt{3 x^{2}+4 x -2}}\right)}{2}"," ",0,"1/2*2^(1/2)*arctan(1/4*(-4+4*x)*2^(1/2)/(3*x^2+4*x-2)^(1/2))","A"
2435,1,29,27,0.050000," ","int(1/x/(-3*x^2+4*x-2)^(1/2),x)","\frac{\sqrt{2}\, \arctan \left(\frac{\left(4 x -4\right) \sqrt{2}}{4 \sqrt{-3 x^{2}+4 x -2}}\right)}{2}"," ",0,"1/2*2^(1/2)*arctan(1/4*(4*x-4)*2^(1/2)/(-3*x^2+4*x-2)^(1/2))","A"
2436,1,29,28,0.054000," ","int(1/x/(3*x^2+5*x-2)^(1/2),x)","\frac{\sqrt{2}\, \arctan \left(\frac{\left(5 x -4\right) \sqrt{2}}{4 \sqrt{3 x^{2}+5 x -2}}\right)}{2}"," ",0,"1/2*2^(1/2)*arctan(1/4*(5*x-4)*2^(1/2)/(3*x^2+5*x-2)^(1/2))","A"
2437,1,29,28,0.044000," ","int(1/x/(-3*x^2+5*x-2)^(1/2),x)","\frac{\sqrt{2}\, \arctan \left(\frac{\left(5 x -4\right) \sqrt{2}}{4 \sqrt{-3 x^{2}+5 x -2}}\right)}{2}"," ",0,"1/2*2^(1/2)*arctan(1/4*(5*x-4)*2^(1/2)/(-3*x^2+5*x-2)^(1/2))","A"
2438,1,44,43,0.054000," ","int(1/x^3/(x^2+x+1)^(1/2),x)","\frac{\arctanh \left(\frac{x +2}{2 \sqrt{x^{2}+x +1}}\right)}{8}+\frac{3 \sqrt{x^{2}+x +1}}{4 x}-\frac{\sqrt{x^{2}+x +1}}{2 x^{2}}"," ",0,"1/8*arctanh(1/2*(x+2)/(x^2+x+1)^(1/2))-1/2*(x^2+x+1)^(1/2)/x^2+3/4*(x^2+x+1)^(1/2)/x","A"
2439,1,24,21,0.044000," ","int(1/x-1/x/(c*x^2+b*x+1)^(1/2),x)","\arctanh \left(\frac{b x +2}{2 \sqrt{c \,x^{2}+b x +1}}\right)+\ln \left(x \right)"," ",0,"arctanh(1/2*(b*x+2)/(c*x^2+b*x+1)^(1/2))+ln(x)","A"
2440,1,2062,476,0.148000," ","int((d*x)^(5/2)*(c*x^2+b*x+a)^(1/2),x)","\frac{\sqrt{d x}\, \left(70 c^{6} x^{6}+80 b \,c^{5} x^{5}+98 a \,c^{5} x^{4}-2 b^{2} c^{4} x^{4}-16 a b \,c^{4} x^{3}+4 b^{3} c^{3} x^{3}+28 a^{2} c^{4} x^{2}-66 a \,b^{2} c^{3} x^{2}+16 b^{4} c^{2} x^{2}-168 \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{c x}{b +\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{b +\sqrt{-4 a c +b^{2}}}}\, a^{3} c^{3} \EllipticE \left(\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{b +\sqrt{-4 a c +b^{2}}}}, \frac{\sqrt{2}\, \sqrt{\frac{b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}}{2}\right)+84 \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{c x}{b +\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{b +\sqrt{-4 a c +b^{2}}}}\, a^{3} c^{3} \EllipticF \left(\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{b +\sqrt{-4 a c +b^{2}}}}, \frac{\sqrt{2}\, \sqrt{\frac{b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}}{2}\right)+330 \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{c x}{b +\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{b +\sqrt{-4 a c +b^{2}}}}\, a^{2} b^{2} c^{2} \EllipticE \left(\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{b +\sqrt{-4 a c +b^{2}}}}, \frac{\sqrt{2}\, \sqrt{\frac{b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}}{2}\right)-117 \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{c x}{b +\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{b +\sqrt{-4 a c +b^{2}}}}\, a^{2} b^{2} c^{2} \EllipticF \left(\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{b +\sqrt{-4 a c +b^{2}}}}, \frac{\sqrt{2}\, \sqrt{\frac{b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}}{2}\right)-54 a^{2} b \,c^{3} x -136 \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{c x}{b +\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{b +\sqrt{-4 a c +b^{2}}}}\, a \,b^{4} c \EllipticE \left(\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{b +\sqrt{-4 a c +b^{2}}}}, \frac{\sqrt{2}\, \sqrt{\frac{b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}}{2}\right)+24 \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{c x}{b +\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{b +\sqrt{-4 a c +b^{2}}}}\, a \,b^{4} c \EllipticF \left(\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{b +\sqrt{-4 a c +b^{2}}}}, \frac{\sqrt{2}\, \sqrt{\frac{b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}}{2}\right)+16 a \,b^{3} c^{2} x +16 \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{c x}{b +\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{b +\sqrt{-4 a c +b^{2}}}}\, b^{6} \EllipticE \left(\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{b +\sqrt{-4 a c +b^{2}}}}, \frac{\sqrt{2}\, \sqrt{\frac{b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}}{2}\right)+42 \sqrt{-4 a c +b^{2}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{c x}{b +\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{b +\sqrt{-4 a c +b^{2}}}}\, a^{2} b \,c^{2} \EllipticE \left(\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{b +\sqrt{-4 a c +b^{2}}}}, \frac{\sqrt{2}\, \sqrt{\frac{b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}}{2}\right)+27 \sqrt{-4 a c +b^{2}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{c x}{b +\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{b +\sqrt{-4 a c +b^{2}}}}\, a^{2} b \,c^{2} \EllipticF \left(\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{b +\sqrt{-4 a c +b^{2}}}}, \frac{\sqrt{2}\, \sqrt{\frac{b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}}{2}\right)-72 \sqrt{-4 a c +b^{2}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{c x}{b +\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{b +\sqrt{-4 a c +b^{2}}}}\, a \,b^{3} c \EllipticE \left(\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{b +\sqrt{-4 a c +b^{2}}}}, \frac{\sqrt{2}\, \sqrt{\frac{b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}}{2}\right)-8 \sqrt{-4 a c +b^{2}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{c x}{b +\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{b +\sqrt{-4 a c +b^{2}}}}\, a \,b^{3} c \EllipticF \left(\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{b +\sqrt{-4 a c +b^{2}}}}, \frac{\sqrt{2}\, \sqrt{\frac{b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}}{2}\right)+16 \sqrt{-4 a c +b^{2}}\, \sqrt{\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}\, \sqrt{-\frac{c x}{b +\sqrt{-4 a c +b^{2}}}}\, \sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{b +\sqrt{-4 a c +b^{2}}}}\, b^{5} \EllipticE \left(\sqrt{\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{b +\sqrt{-4 a c +b^{2}}}}, \frac{\sqrt{2}\, \sqrt{\frac{b +\sqrt{-4 a c +b^{2}}}{\sqrt{-4 a c +b^{2}}}}}{2}\right)\right) d^{2}}{315 \sqrt{c \,x^{2}+b x +a}\, c^{5} x}"," ",0,"1/315*d^2*(d*x)^(1/2)*(70*c^6*x^6+80*b*c^5*x^5+84*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-c*x/(b+(-4*a*c+b^2)^(1/2)))^(1/2)*EllipticF(((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b+(-4*a*c+b^2)^(1/2)))^(1/2),1/2*2^(1/2)*((b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2))*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b+(-4*a*c+b^2)^(1/2)))^(1/2)*a^3*c^3-117*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-c*x/(b+(-4*a*c+b^2)^(1/2)))^(1/2)*EllipticF(((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b+(-4*a*c+b^2)^(1/2)))^(1/2),1/2*2^(1/2)*((b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2))*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b+(-4*a*c+b^2)^(1/2)))^(1/2)*a^2*b^2*c^2+27*(-4*a*c+b^2)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-c*x/(b+(-4*a*c+b^2)^(1/2)))^(1/2)*EllipticF(((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b+(-4*a*c+b^2)^(1/2)))^(1/2),1/2*2^(1/2)*((b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2))*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b+(-4*a*c+b^2)^(1/2)))^(1/2)*a^2*b*c^2+24*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-c*x/(b+(-4*a*c+b^2)^(1/2)))^(1/2)*EllipticF(((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b+(-4*a*c+b^2)^(1/2)))^(1/2),1/2*2^(1/2)*((b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2))*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b+(-4*a*c+b^2)^(1/2)))^(1/2)*a*b^4*c-8*(-4*a*c+b^2)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-c*x/(b+(-4*a*c+b^2)^(1/2)))^(1/2)*EllipticF(((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b+(-4*a*c+b^2)^(1/2)))^(1/2),1/2*2^(1/2)*((b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2))*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b+(-4*a*c+b^2)^(1/2)))^(1/2)*a*b^3*c-168*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-c*x/(b+(-4*a*c+b^2)^(1/2)))^(1/2)*EllipticE(((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b+(-4*a*c+b^2)^(1/2)))^(1/2),1/2*2^(1/2)*((b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2))*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b+(-4*a*c+b^2)^(1/2)))^(1/2)*a^3*c^3+330*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-c*x/(b+(-4*a*c+b^2)^(1/2)))^(1/2)*EllipticE(((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b+(-4*a*c+b^2)^(1/2)))^(1/2),1/2*2^(1/2)*((b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2))*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b+(-4*a*c+b^2)^(1/2)))^(1/2)*a^2*b^2*c^2+42*(-4*a*c+b^2)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-c*x/(b+(-4*a*c+b^2)^(1/2)))^(1/2)*EllipticE(((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b+(-4*a*c+b^2)^(1/2)))^(1/2),1/2*2^(1/2)*((b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2))*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b+(-4*a*c+b^2)^(1/2)))^(1/2)*a^2*b*c^2-136*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-c*x/(b+(-4*a*c+b^2)^(1/2)))^(1/2)*EllipticE(((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b+(-4*a*c+b^2)^(1/2)))^(1/2),1/2*2^(1/2)*((b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2))*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b+(-4*a*c+b^2)^(1/2)))^(1/2)*a*b^4*c-72*(-4*a*c+b^2)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-c*x/(b+(-4*a*c+b^2)^(1/2)))^(1/2)*EllipticE(((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b+(-4*a*c+b^2)^(1/2)))^(1/2),1/2*2^(1/2)*((b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2))*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b+(-4*a*c+b^2)^(1/2)))^(1/2)*a*b^3*c+16*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-c*x/(b+(-4*a*c+b^2)^(1/2)))^(1/2)*EllipticE(((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b+(-4*a*c+b^2)^(1/2)))^(1/2),1/2*2^(1/2)*((b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2))*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b+(-4*a*c+b^2)^(1/2)))^(1/2)*b^6+16*(-4*a*c+b^2)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-c*x/(b+(-4*a*c+b^2)^(1/2)))^(1/2)*EllipticE(((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b+(-4*a*c+b^2)^(1/2)))^(1/2),1/2*2^(1/2)*((b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2))*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b+(-4*a*c+b^2)^(1/2)))^(1/2)*b^5+98*a*c^5*x^4-2*b^2*c^4*x^4-16*a*b*c^4*x^3+4*b^3*c^3*x^3+28*a^2*c^4*x^2-66*a*b^2*c^3*x^2+16*b^4*c^2*x^2-54*a^2*b*c^3*x+16*a*b^3*c^2*x)/x/(c*x^2+b*x+a)^(1/2)/c^5","B"
2441,1,6516,517,0.214000," ","int((e*x+d)^(3/2)*(c*x^2+b*x+a)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
2442,1,4356,449,0.099000," ","int((e*x+d)^(1/2)*(c*x^2+b*x+a)^(1/2),x)","\text{output too large to display}"," ",0,"-1/15*(e*x+d)^(1/2)*(c*x^2+b*x+a)^(1/2)*(-2*a*b*c*d*e^3-2*x*a*b*c*e^4-8*2^(1/2)*(-(e*x+d)*c/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2)*(e*(-2*c*x-b+(-4*a*c+b^2)^(1/2))/(2*c*d-b*e+e*(-4*a*c+b^2)^(1/2)))^(1/2)*(e*(2*c*x+b+(-4*a*c+b^2)^(1/2))/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)*c/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2),(-(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d)/(2*c*d-b*e+e*(-4*a*c+b^2)^(1/2)))^(1/2))*b^2*c*d^2*e^2+8*2^(1/2)*(-(e*x+d)*c/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2)*(e*(-2*c*x-b+(-4*a*c+b^2)^(1/2))/(2*c*d-b*e+e*(-4*a*c+b^2)^(1/2)))^(1/2)*(e*(2*c*x+b+(-4*a*c+b^2)^(1/2))/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)*c/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2),(-(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d)/(2*c*d-b*e+e*(-4*a*c+b^2)^(1/2)))^(1/2))*b*c^2*d^3*e-8*x*a*c^2*d*e^3-2*x*b^2*c*d*e^3-10*x^2*b*c^2*d*e^3-2*x*b*c^2*d^2*e^2-6*x^4*c^3*e^4-8*x^3*b*c^2*e^4-8*x^3*c^3*d*e^3-6*x^2*a*c^2*e^4+2*2^(1/2)*(-(e*x+d)*c/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2)*(e*(-2*c*x-b+(-4*a*c+b^2)^(1/2))/(2*c*d-b*e+e*(-4*a*c+b^2)^(1/2)))^(1/2)*(e*(2*c*x+b+(-4*a*c+b^2)^(1/2))/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)*c/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2),(-(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d)/(2*c*d-b*e+e*(-4*a*c+b^2)^(1/2)))^(1/2))*(-4*a*c+b^2)^(1/2)*a*c*d*e^3-3*2^(1/2)*(-(e*x+d)*c/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2)*(e*(-2*c*x-b+(-4*a*c+b^2)^(1/2))/(2*c*d-b*e+e*(-4*a*c+b^2)^(1/2)))^(1/2)*(e*(2*c*x+b+(-4*a*c+b^2)^(1/2))/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)*c/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2),(-(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d)/(2*c*d-b*e+e*(-4*a*c+b^2)^(1/2)))^(1/2))*(-4*a*c+b^2)^(1/2)*b*c*d^2*e^2+12*2^(1/2)*(-(e*x+d)*c/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2)*(e*(-2*c*x-b+(-4*a*c+b^2)^(1/2))/(2*c*d-b*e+e*(-4*a*c+b^2)^(1/2)))^(1/2)*(e*(2*c*x+b+(-4*a*c+b^2)^(1/2))/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)*c/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2),(-(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d)/(2*c*d-b*e+e*(-4*a*c+b^2)^(1/2)))^(1/2))*a*b*c*d*e^3-8*2^(1/2)*(-(e*x+d)*c/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2)*(e*(-2*c*x-b+(-4*a*c+b^2)^(1/2))/(2*c*d-b*e+e*(-4*a*c+b^2)^(1/2)))^(1/2)*(e*(2*c*x+b+(-4*a*c+b^2)^(1/2))/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)*c/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2),(-(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d)/(2*c*d-b*e+e*(-4*a*c+b^2)^(1/2)))^(1/2))*a*b*c*d*e^3+8*2^(1/2)*(-(e*x+d)*c/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2)*(e*(-2*c*x-b+(-4*a*c+b^2)^(1/2))/(2*c*d-b*e+e*(-4*a*c+b^2)^(1/2)))^(1/2)*(e*(2*c*x+b+(-4*a*c+b^2)^(1/2))/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)*c/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2),(-(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d)/(2*c*d-b*e+e*(-4*a*c+b^2)^(1/2)))^(1/2))*a*c^2*d^2*e^2+3*2^(1/2)*(-(e*x+d)*c/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2)*(e*(-2*c*x-b+(-4*a*c+b^2)^(1/2))/(2*c*d-b*e+e*(-4*a*c+b^2)^(1/2)))^(1/2)*(e*(2*c*x+b+(-4*a*c+b^2)^(1/2))/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)*c/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2),(-(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d)/(2*c*d-b*e+e*(-4*a*c+b^2)^(1/2)))^(1/2))*b^2*c*d^2*e^2-12*2^(1/2)*(-(e*x+d)*c/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2)*(e*(-2*c*x-b+(-4*a*c+b^2)^(1/2))/(2*c*d-b*e+e*(-4*a*c+b^2)^(1/2)))^(1/2)*(e*(2*c*x+b+(-4*a*c+b^2)^(1/2))/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)*c/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2),(-(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d)/(2*c*d-b*e+e*(-4*a*c+b^2)^(1/2)))^(1/2))*a*c^2*d^2*e^2+2^(1/2)*(-(e*x+d)*c/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2)*(e*(-2*c*x-b+(-4*a*c+b^2)^(1/2))/(2*c*d-b*e+e*(-4*a*c+b^2)^(1/2)))^(1/2)*(e*(2*c*x+b+(-4*a*c+b^2)^(1/2))/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)*c/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2),(-(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d)/(2*c*d-b*e+e*(-4*a*c+b^2)^(1/2)))^(1/2))*(-4*a*c+b^2)^(1/2)*b^2*d*e^3+2*2^(1/2)*(-(e*x+d)*c/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2)*(e*(-2*c*x-b+(-4*a*c+b^2)^(1/2))/(2*c*d-b*e+e*(-4*a*c+b^2)^(1/2)))^(1/2)*(e*(2*c*x+b+(-4*a*c+b^2)^(1/2))/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)*c/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2),(-(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d)/(2*c*d-b*e+e*(-4*a*c+b^2)^(1/2)))^(1/2))*(-4*a*c+b^2)^(1/2)*c^2*d^3*e-2^(1/2)*(-(e*x+d)*c/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2)*(e*(-2*c*x-b+(-4*a*c+b^2)^(1/2))/(2*c*d-b*e+e*(-4*a*c+b^2)^(1/2)))^(1/2)*(e*(2*c*x+b+(-4*a*c+b^2)^(1/2))/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)*c/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2),(-(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d)/(2*c*d-b*e+e*(-4*a*c+b^2)^(1/2)))^(1/2))*(-4*a*c+b^2)^(1/2)*a*b*e^4-4*2^(1/2)*(-(e*x+d)*c/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2)*(e*(-2*c*x-b+(-4*a*c+b^2)^(1/2))/(2*c*d-b*e+e*(-4*a*c+b^2)^(1/2)))^(1/2)*(e*(2*c*x+b+(-4*a*c+b^2)^(1/2))/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)*c/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2),(-(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d)/(2*c*d-b*e+e*(-4*a*c+b^2)^(1/2)))^(1/2))*a*b^2*e^4-2*x^2*b^2*c*e^4-2*x^2*c^3*d^2*e^2-2*a*c^2*d^2*e^2+4*2^(1/2)*(-(e*x+d)*c/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2)*(e*(-2*c*x-b+(-4*a*c+b^2)^(1/2))/(2*c*d-b*e+e*(-4*a*c+b^2)^(1/2)))^(1/2)*(e*(2*c*x+b+(-4*a*c+b^2)^(1/2))/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)*c/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2),(-(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d)/(2*c*d-b*e+e*(-4*a*c+b^2)^(1/2)))^(1/2))*b^3*d*e^3-12*2^(1/2)*(-(e*x+d)*c/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2)*(e*(-2*c*x-b+(-4*a*c+b^2)^(1/2))/(2*c*d-b*e+e*(-4*a*c+b^2)^(1/2)))^(1/2)*(e*(2*c*x+b+(-4*a*c+b^2)^(1/2))/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)*c/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2),(-(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d)/(2*c*d-b*e+e*(-4*a*c+b^2)^(1/2)))^(1/2))*a^2*c*e^4+3*2^(1/2)*(-(e*x+d)*c/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2)*(e*(-2*c*x-b+(-4*a*c+b^2)^(1/2))/(2*c*d-b*e+e*(-4*a*c+b^2)^(1/2)))^(1/2)*(e*(2*c*x+b+(-4*a*c+b^2)^(1/2))/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)*c/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2),(-(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d)/(2*c*d-b*e+e*(-4*a*c+b^2)^(1/2)))^(1/2))*a*b^2*e^4-3*2^(1/2)*(-(e*x+d)*c/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2)*(e*(-2*c*x-b+(-4*a*c+b^2)^(1/2))/(2*c*d-b*e+e*(-4*a*c+b^2)^(1/2)))^(1/2)*(e*(2*c*x+b+(-4*a*c+b^2)^(1/2))/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)*c/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2),(-(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d)/(2*c*d-b*e+e*(-4*a*c+b^2)^(1/2)))^(1/2))*b^3*d*e^3+12*2^(1/2)*(-(e*x+d)*c/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2)*(e*(-2*c*x-b+(-4*a*c+b^2)^(1/2))/(2*c*d-b*e+e*(-4*a*c+b^2)^(1/2)))^(1/2)*(e*(2*c*x+b+(-4*a*c+b^2)^(1/2))/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)*c/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2),(-(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d)/(2*c*d-b*e+e*(-4*a*c+b^2)^(1/2)))^(1/2))*a^2*c*e^4-4*2^(1/2)*(-(e*x+d)*c/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2)*(e*(-2*c*x-b+(-4*a*c+b^2)^(1/2))/(2*c*d-b*e+e*(-4*a*c+b^2)^(1/2)))^(1/2)*(e*(2*c*x+b+(-4*a*c+b^2)^(1/2))/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)*c/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2),(-(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d)/(2*c*d-b*e+e*(-4*a*c+b^2)^(1/2)))^(1/2))*c^3*d^4)/c^2/(c*e*x^3+b*e*x^2+c*d*x^2+a*e*x+b*d*x+a*d)/e^3","B"
2443,1,1854,386,0.211000," ","int((c*x^2+b*x+a)^(1/2)/(e*x+d)^(1/2),x)","-\frac{2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{e x +d}\, \left(-c^{2} e^{3} x^{3}-b c \,e^{3} x^{2}-c^{2} d \,e^{2} x^{2}+\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) e}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, a b \,e^{3} \EllipticE \left(\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}, \sqrt{-\frac{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\right)-2 \sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) e}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, a c d \,e^{2} \EllipticE \left(\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}, \sqrt{-\frac{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\right)-a c \,e^{3} x -\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) e}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, b^{2} d \,e^{2} \EllipticE \left(\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}, \sqrt{-\frac{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\right)+3 \sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) e}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, b c \,d^{2} e \EllipticE \left(\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}, \sqrt{-\frac{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\right)-b c d \,e^{2} x -2 \sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) e}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, c^{2} d^{3} \EllipticE \left(\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}, \sqrt{-\frac{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\right)-a c d \,e^{2}+\sqrt{-4 a c +b^{2}}\, \sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) e}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, a \,e^{3} \EllipticF \left(\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}, \sqrt{-\frac{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\right)-\sqrt{-4 a c +b^{2}}\, \sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) e}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, b d \,e^{2} \EllipticF \left(\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}, \sqrt{-\frac{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\right)+\sqrt{-4 a c +b^{2}}\, \sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) e}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, c \,d^{2} e \EllipticF \left(\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}, \sqrt{-\frac{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\right)\right)}{3 \left(c e \,x^{3}+b e \,x^{2}+c d \,x^{2}+a e x +b d x +a d \right) c \,e^{3}}"," ",0,"-2/3*(c*x^2+b*x+a)^(1/2)*(e*x+d)^(1/2)/c*((-4*a*c+b^2)^(1/2)*2^(1/2)*(-(e*x+d)*c/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2)*(e*(-2*c*x-b+(-4*a*c+b^2)^(1/2))/(2*c*d-b*e+e*(-4*a*c+b^2)^(1/2)))^(1/2)*(e*(2*c*x+b+(-4*a*c+b^2)^(1/2))/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)*c/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2),(-(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d)/(2*c*d-b*e+e*(-4*a*c+b^2)^(1/2)))^(1/2))*a*e^3-(-4*a*c+b^2)^(1/2)*2^(1/2)*(-(e*x+d)*c/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2)*(e*(-2*c*x-b+(-4*a*c+b^2)^(1/2))/(2*c*d-b*e+e*(-4*a*c+b^2)^(1/2)))^(1/2)*(e*(2*c*x+b+(-4*a*c+b^2)^(1/2))/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)*c/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2),(-(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d)/(2*c*d-b*e+e*(-4*a*c+b^2)^(1/2)))^(1/2))*b*d*e^2+(-4*a*c+b^2)^(1/2)*2^(1/2)*(-(e*x+d)*c/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2)*(e*(-2*c*x-b+(-4*a*c+b^2)^(1/2))/(2*c*d-b*e+e*(-4*a*c+b^2)^(1/2)))^(1/2)*(e*(2*c*x+b+(-4*a*c+b^2)^(1/2))/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)*c/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2),(-(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d)/(2*c*d-b*e+e*(-4*a*c+b^2)^(1/2)))^(1/2))*c*d^2*e+2^(1/2)*(-(e*x+d)*c/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2)*(e*(-2*c*x-b+(-4*a*c+b^2)^(1/2))/(2*c*d-b*e+e*(-4*a*c+b^2)^(1/2)))^(1/2)*(e*(2*c*x+b+(-4*a*c+b^2)^(1/2))/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)*c/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2),(-(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d)/(2*c*d-b*e+e*(-4*a*c+b^2)^(1/2)))^(1/2))*a*b*e^3-2*2^(1/2)*(-(e*x+d)*c/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2)*(e*(-2*c*x-b+(-4*a*c+b^2)^(1/2))/(2*c*d-b*e+e*(-4*a*c+b^2)^(1/2)))^(1/2)*(e*(2*c*x+b+(-4*a*c+b^2)^(1/2))/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)*c/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2),(-(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d)/(2*c*d-b*e+e*(-4*a*c+b^2)^(1/2)))^(1/2))*a*c*d*e^2-2^(1/2)*(-(e*x+d)*c/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2)*(e*(-2*c*x-b+(-4*a*c+b^2)^(1/2))/(2*c*d-b*e+e*(-4*a*c+b^2)^(1/2)))^(1/2)*(e*(2*c*x+b+(-4*a*c+b^2)^(1/2))/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)*c/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2),(-(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d)/(2*c*d-b*e+e*(-4*a*c+b^2)^(1/2)))^(1/2))*b^2*d*e^2+3*2^(1/2)*(-(e*x+d)*c/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2)*(e*(-2*c*x-b+(-4*a*c+b^2)^(1/2))/(2*c*d-b*e+e*(-4*a*c+b^2)^(1/2)))^(1/2)*(e*(2*c*x+b+(-4*a*c+b^2)^(1/2))/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)*c/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2),(-(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d)/(2*c*d-b*e+e*(-4*a*c+b^2)^(1/2)))^(1/2))*b*c*d^2*e-2*2^(1/2)*(-(e*x+d)*c/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2)*(e*(-2*c*x-b+(-4*a*c+b^2)^(1/2))/(2*c*d-b*e+e*(-4*a*c+b^2)^(1/2)))^(1/2)*(e*(2*c*x+b+(-4*a*c+b^2)^(1/2))/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)*c/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2),(-(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d)/(2*c*d-b*e+e*(-4*a*c+b^2)^(1/2)))^(1/2))*c^2*d^3-x^3*c^2*e^3-x^2*b*c*e^3-x^2*c^2*d*e^2-a*c*e^3*x-x*b*c*d*e^2-a*c*d*e^2)/(c*e*x^3+b*e*x^2+c*d*x^2+a*e*x+b*d*x+a*d)/e^3","B"
2444,1,1595,367,0.244000," ","int((c*x^2+b*x+a)^(1/2)/(e*x+d)^(3/2),x)","\frac{\sqrt{c \,x^{2}+b x +a}\, \sqrt{e x +d}\, \left(-2 c^{2} e^{2} x^{2}-4 \sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) e}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, a c \,e^{2} \EllipticE \left(\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}, \sqrt{-\frac{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\right)+4 \sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) e}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, a c \,e^{2} \EllipticF \left(\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}, \sqrt{-\frac{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\right)-\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) e}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, b^{2} e^{2} \EllipticF \left(\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}, \sqrt{-\frac{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\right)+4 \sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) e}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, b c d e \EllipticE \left(\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}, \sqrt{-\frac{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\right)-2 b c \,e^{2} x -4 \sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) e}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, c^{2} d^{2} \EllipticE \left(\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}, \sqrt{-\frac{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\right)-2 a c \,e^{2}-\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) e}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{-4 a c +b^{2}}\, b \,e^{2} \EllipticF \left(\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}, \sqrt{-\frac{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\right)+2 \sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) e}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{-4 a c +b^{2}}\, c d e \EllipticF \left(\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}, \sqrt{-\frac{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\right)\right)}{\left(c e \,x^{3}+b e \,x^{2}+c d \,x^{2}+a e x +b d x +a d \right) c \,e^{3}}"," ",0,"(c*x^2+b*x+a)^(1/2)*(e*x+d)^(1/2)*(4*2^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*a*c*e^2*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)-2^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*b^2*e^2*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)-2^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*b*e^2*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*(-4*a*c+b^2)^(1/2)+2*2^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*c*d*e*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*(-4*a*c+b^2)^(1/2)-4*2^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*a*c*e^2*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)+4*2^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*b*c*d*e*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)-4*2^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*c^2*d^2*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)-2*c^2*e^2*x^2-2*b*c*e^2*x-2*a*c*e^2)/c/(c*e*x^3+b*e*x^2+c*d*x^2+a*e*x+b*d*x+a*d)/e^3","B"
2445,1,3645,433,0.142000," ","int((c*x^2+b*x+a)^(1/2)/(e*x+d)^(5/2),x)","\text{output too large to display}"," ",0,"-2/3*(a^2*e^4-2*x^2*b*c*d*e^3-2*2^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*a*c*d^2*e^2*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)+3*2^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*b*c*d^3*e*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)+2^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*a*d*e^3*(-4*a*c+b^2)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)-2^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*b*d^2*e^2*(-4*a*c+b^2)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)+2^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*c*d^3*e*(-4*a*c+b^2)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)+2^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*x*a*b*e^4*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)-2^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*x*b^2*d*e^3*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)-2*2^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*x*c^2*d^3*e*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)+2^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*x*a*e^4*(-4*a*c+b^2)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)+2^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*a*b*d*e^3*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)-2^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*b^2*d^2*e^2*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)+3*2^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*x*b*c*d^2*e^2*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)-2^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*x*b*d*e^3*(-4*a*c+b^2)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)+2^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*x*c*d^2*e^2*(-4*a*c+b^2)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)-2*2^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*x*a*c*d*e^3*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)+x^3*b*c*e^4-2*x^3*c^2*d*e^3+x^2*a*c*e^4-x^2*c^2*d^2*e^2+2*x*a*b*e^4+x^2*b^2*e^4-2*x*a*c*d*e^3-x*b*c*d^2*e^2-2*2^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*c^2*d^4*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)-a*c*d^2*e^2)/(c*x^2+b*x+a)^(1/2)/(a*e^2-b*d*e+c*d^2)/e^3/(e*x+d)^(3/2)","B"
2446,1,12980,547,0.179000," ","int((c*x^2+b*x+a)^(1/2)/(e*x+d)^(7/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
2447,1,11933,746,0.157000," ","int((e*x+d)^(3/2)*(c*x^2+b*x+a)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
2448,1,9177,642,0.112000," ","int((e*x+d)^(1/2)*(c*x^2+b*x+a)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
2449,1,6516,515,0.122000," ","int((c*x^2+b*x+a)^(3/2)/(e*x+d)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
2450,1,4365,453,0.184000," ","int((c*x^2+b*x+a)^(3/2)/(e*x+d)^(3/2),x)","\text{output too large to display}"," ",0,"-2/5*(c*x^2+b*x+a)^(1/2)*(e*x+d)^(1/2)*(-7*a*b*c*d*e^3+3*x*a*b*c*e^4+17*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*b^2*c*d^2*e^2-32*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*b*c^2*d^3*e+2*x*a*c^2*d*e^3-7*x*b^2*c*d*e^3-5*x^2*b*c^2*d*e^3+8*x*b*c^2*d^2*e^2-x^4*c^3*e^4-3*x^3*b*c^2*e^4+2*x^3*c^3*d*e^3+4*x^2*a*c^2*e^4-8*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*(-4*a*c+b^2)^(1/2)*a*c*d*e^3+12*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*(-4*a*c+b^2)^(1/2)*b*c*d^2*e^2+12*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*a*b*c*d*e^3-28*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*a*b*c*d*e^3+28*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*a*c^2*d^2*e^2+3*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*b^2*c*d^2*e^2-12*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*a*c^2*d^2*e^2-4*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*(-4*a*c+b^2)^(1/2)*b^2*d*e^3-8*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*(-4*a*c+b^2)^(1/2)*c^2*d^3*e+4*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*(-4*a*c+b^2)^(1/2)*a*b*e^4+2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*a*b^2*e^4-2*x^2*b^2*c*e^4+8*x^2*c^3*d^2*e^2+8*a*c^2*d^2*e^2+5*a^2*c*e^4-2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*b^3*d*e^3-12*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*a^2*c*e^4+3*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*a*b^2*e^4-3*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*b^3*d*e^3+12*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*a^2*c*e^4+16*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*c^3*d^4)/c/(c*e*x^3+b*e*x^2+c*d*x^2+a*e*x+b*d*x+a*d)/e^5","B"
2451,1,5874,435,0.192000," ","int((c*x^2+b*x+a)^(3/2)/(e*x+d)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
2452,1,12944,514,0.257000," ","int((c*x^2+b*x+a)^(3/2)/(e*x+d)^(7/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
2453,1,25722,651,0.335000," ","int((c*x^2+b*x+a)^(3/2)/(e*x+d)^(9/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
2454,1,2810,579,0.209000," ","int((d*x)^(1/2)*(c*x^2+b*x+a)^(5/2),x)","\text{output too large to display}"," ",0,"-1/9009*(d*x)^(1/2)*(-48*x*a*b^5*c^2-13856*x^5*a*b*c^6-8692*x^4*a*b^2*c^5-12332*x^3*a^2*b*c^5-7392*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b+(-4*a*c+b^2)^(1/2)))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-1/(b+(-4*a*c+b^2)^(1/2))*c*x)^(1/2)*EllipticE(((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b+(-4*a*c+b^2)^(1/2)))^(1/2),1/2*2^(1/2)*((b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2))*a^4*c^4-2256*x^5*b^3*c^5-48*x^2*b^6*c^2-5628*x^6*b^2*c^6-4788*x^7*b*c^7-12*x^3*b^5*c^3+6*x^4*b^4*c^4-5698*x^6*a*c^7-9086*x^4*a^2*c^6-4774*x^2*a^3*c^5+24*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b+(-4*a*c+b^2)^(1/2)))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-1/(b+(-4*a*c+b^2)^(1/2))*c*x)^(1/2)*EllipticF(((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b+(-4*a*c+b^2)^(1/2)))^(1/2),1/2*2^(1/2)*((b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2))*(-4*a*c+b^2)^(1/2)*a*b^5*c+1848*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b+(-4*a*c+b^2)^(1/2)))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-1/(b+(-4*a*c+b^2)^(1/2))*c*x)^(1/2)*EllipticE(((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b+(-4*a*c+b^2)^(1/2)))^(1/2),1/2*2^(1/2)*((b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2))*(-4*a*c+b^2)^(1/2)*a^3*b*c^3+3696*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b+(-4*a*c+b^2)^(1/2)))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-1/(b+(-4*a*c+b^2)^(1/2))*c*x)^(1/2)*EllipticF(((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b+(-4*a*c+b^2)^(1/2)))^(1/2),1/2*2^(1/2)*((b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2))*a^4*c^4-48*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b+(-4*a*c+b^2)^(1/2)))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-1/(b+(-4*a*c+b^2)^(1/2))*c*x)^(1/2)*EllipticE(((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b+(-4*a*c+b^2)^(1/2)))^(1/2),1/2*2^(1/2)*((b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2))*(-4*a*c+b^2)^(1/2)*b^7-1902*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b+(-4*a*c+b^2)^(1/2)))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-1/(b+(-4*a*c+b^2)^(1/2))*c*x)^(1/2)*EllipticE(((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b+(-4*a*c+b^2)^(1/2)))^(1/2),1/2*2^(1/2)*((b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2))*(-4*a*c+b^2)^(1/2)*a^2*b^3*c^2+536*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b+(-4*a*c+b^2)^(1/2)))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-1/(b+(-4*a*c+b^2)^(1/2))*c*x)^(1/2)*EllipticE(((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b+(-4*a*c+b^2)^(1/2)))^(1/2),1/2*2^(1/2)*((b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2))*(-4*a*c+b^2)^(1/2)*a*b^5*c+708*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b+(-4*a*c+b^2)^(1/2)))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-1/(b+(-4*a*c+b^2)^(1/2))*c*x)^(1/2)*EllipticF(((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b+(-4*a*c+b^2)^(1/2)))^(1/2),1/2*2^(1/2)*((b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2))*(-4*a*c+b^2)^(1/2)*a^3*b*c^3-241*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b+(-4*a*c+b^2)^(1/2)))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-1/(b+(-4*a*c+b^2)^(1/2))*c*x)^(1/2)*EllipticF(((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b+(-4*a*c+b^2)^(1/2)))^(1/2),1/2*2^(1/2)*((b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2))*(-4*a*c+b^2)^(1/2)*a^2*b^3*c^2-1386*x^8*c^8+128*x^3*a*b^3*c^4-1740*x^2*a^2*b^2*c^4+518*x^2*a*b^4*c^3-1416*x*a^3*b*c^4+482*x*a^2*b^3*c^3-48*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b+(-4*a*c+b^2)^(1/2)))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-1/(b+(-4*a*c+b^2)^(1/2))*c*x)^(1/2)*EllipticE(((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b+(-4*a*c+b^2)^(1/2)))^(1/2),1/2*2^(1/2)*((b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2))*b^8+831*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b+(-4*a*c+b^2)^(1/2)))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-1/(b+(-4*a*c+b^2)^(1/2))*c*x)^(1/2)*EllipticF(((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b+(-4*a*c+b^2)^(1/2)))^(1/2),1/2*2^(1/2)*((b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2))*a^2*b^4*c^2-72*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b+(-4*a*c+b^2)^(1/2)))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-1/(b+(-4*a*c+b^2)^(1/2))*c*x)^(1/2)*EllipticF(((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b+(-4*a*c+b^2)^(1/2)))^(1/2),1/2*2^(1/2)*((b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2))*a*b^6*c+9456*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b+(-4*a*c+b^2)^(1/2)))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-1/(b+(-4*a*c+b^2)^(1/2))*c*x)^(1/2)*EllipticE(((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b+(-4*a*c+b^2)^(1/2)))^(1/2),1/2*2^(1/2)*((b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2))*a^3*b^2*c^3-4046*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b+(-4*a*c+b^2)^(1/2)))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-1/(b+(-4*a*c+b^2)^(1/2))*c*x)^(1/2)*EllipticE(((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b+(-4*a*c+b^2)^(1/2)))^(1/2),1/2*2^(1/2)*((b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2))*a^2*b^4*c^2+728*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b+(-4*a*c+b^2)^(1/2)))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-1/(b+(-4*a*c+b^2)^(1/2))*c*x)^(1/2)*EllipticE(((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b+(-4*a*c+b^2)^(1/2)))^(1/2),1/2*2^(1/2)*((b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2))*a*b^6*c-3096*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b+(-4*a*c+b^2)^(1/2)))^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2)*(-1/(b+(-4*a*c+b^2)^(1/2))*c*x)^(1/2)*EllipticF(((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b+(-4*a*c+b^2)^(1/2)))^(1/2),1/2*2^(1/2)*((b+(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(1/2))^(1/2))*a^3*b^2*c^3)/(c*x^2+b*x+a)^(1/2)/c^5/x","B"
2455,1,12153,777,0.150000," ","int((c*x^2+b*x+a)^(5/2)/(e*x+d)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
2456,1,9187,648,0.329000," ","int((c*x^2+b*x+a)^(5/2)/(e*x+d)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
2457,1,12847,552,0.257000," ","int((c*x^2+b*x+a)^(5/2)/(e*x+d)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
2458,1,14453,533,0.194000," ","int((c*x^2+b*x+a)^(5/2)/(e*x+d)^(7/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
2459,1,25728,661,0.237000," ","int((c*x^2+b*x+a)^(5/2)/(e*x+d)^(9/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
2460,1,44994,853,0.346000," ","int((c*x^2+b*x+a)^(5/2)/(e*x+d)^(11/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
2461,1,6947,530,0.132000," ","int((e*x+d)^(7/2)/(c*x^2+b*x+a)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
2462,1,4787,445,0.155000," ","int((e*x+d)^(5/2)/(c*x^2+b*x+a)^(1/2),x)","\text{output too large to display}"," ",0,"2/15*(e*x+d)^(1/2)*(c*x^2+b*x+a)^(1/2)*(-4*a*b*c*d*e^3-4*x*a*b*c*e^4-31*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*b^2*c*d^2*e^2+46*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*b*c^2*d^3*e+14*x*a*c^2*d*e^3-4*x*b^2*c*d*e^3+10*x^2*b*c^2*d*e^3+11*x*b*c^2*d^2*e^2+3*x^4*c^3*e^4-x^3*b*c^2*e^4+14*x^3*c^3*d*e^3+3*x^2*a*c^2*e^4+4*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*(-4*a*c+b^2)^(1/2)*a*c*d*e^3-6*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*(-4*a*c+b^2)^(1/2)*b*c*d^2*e^2-6*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*a*b*c*d*e^3+14*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*a*b*c*d*e^3-14*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*a*c^2*d^2*e^2+21*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*b^2*c*d^2*e^2+6*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*a*c^2*d^2*e^2+2*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*(-4*a*c+b^2)^(1/2)*b^2*d*e^3+4*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*(-4*a*c+b^2)^(1/2)*c^2*d^3*e-2*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*(-4*a*c+b^2)^(1/2)*a*b*e^4-8*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*a*b^2*e^4-4*x^2*b^2*c*e^4+11*x^2*c^3*d^2*e^2+11*a*c^2*d^2*e^2-30*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*b*c^2*d^3*e+8*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*b^3*d*e^3-9*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*a^2*c*e^4+6*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*a*b^2*e^4-6*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*b^3*d*e^3+9*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*a^2*c*e^4+15*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*c^3*d^4-23*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*c^3*d^4)/c^3/e/(c*e*x^3+b*e*x^2+c*d*x^2+a*e*x+b*d*x+a*d)","B"
2463,1,2926,381,0.161000," ","int((e*x+d)^(3/2)/(c*x^2+b*x+a)^(1/2),x)","\text{output too large to display}"," ",0,"-1/3*(e*x+d)^(1/2)*(c*x^2+b*x+a)^(1/2)*(3*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*a*b*e^3-6*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*a*c*d*e^2-(-4*a*c+b^2)^(1/2)*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*a*e^3-3*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*b^2*d*e^2+9*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*b*c*d^2*e+(-4*a*c+b^2)^(1/2)*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*b*d*e^2-6*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*c^2*d^3-(-4*a*c+b^2)^(1/2)*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*c*d^2*e-4*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*a*b*e^3+8*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*a*c*d*e^2+4*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*b^2*d*e^2-12*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*b*c*d^2*e+8*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*c^2*d^3-2*c^2*e^3*x^3-2*b*c*e^3*x^2-2*c^2*d*e^2*x^2-2*a*c*e^3*x-2*b*c*d*e^2*x-2*a*c*d*e^2)/c^2/e/(c*e*x^3+b*e*x^2+c*d*x^2+a*e*x+b*d*x+a*d)","B"
2464,1,747,164,0.188000," ","int((e*x+d)^(1/2)/(c*x^2+b*x+a)^(1/2),x)","\frac{\sqrt{e x +d}\, \sqrt{c \,x^{2}+b x +a}\, \left(b e -2 c d +\sqrt{-4 a c +b^{2}}\, e \right) \sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) e}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \left(-b e \EllipticE \left(\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}, \sqrt{-\frac{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\right)+b e \EllipticF \left(\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}, \sqrt{-\frac{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\right)+2 c d \EllipticE \left(\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}, \sqrt{-\frac{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\right)-2 c d \EllipticF \left(\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}, \sqrt{-\frac{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\right)+\sqrt{-4 a c +b^{2}}\, e \EllipticE \left(\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}, \sqrt{-\frac{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\right)-\sqrt{-4 a c +b^{2}}\, e \EllipticF \left(\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}, \sqrt{-\frac{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\right)\right)}{2 \left(c e \,x^{3}+b e \,x^{2}+c d \,x^{2}+a e x +b d x +a d \right) c^{2} e}"," ",0,"1/2*(e*x+d)^(1/2)*(c*x^2+b*x+a)^(1/2)*(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*(EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*e*b-2*d*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*c-EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*e*(-4*a*c+b^2)^(1/2)-EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*b*e+2*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*c*d+(-4*a*c+b^2)^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*e)/e/(c*e*x^3+b*e*x^2+c*d*x^2+a*e*x+b*d*x+a*d)/c^2","B"
2465,1,287,165,0.191000," ","int(1/(e*x+d)^(1/2)/(c*x^2+b*x+a)^(1/2),x)","\frac{\left(-b e +2 c d -\sqrt{-4 a c +b^{2}}\, e \right) \sqrt{\frac{\left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) e}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{e x +d}\, \sqrt{c \,x^{2}+b x +a}\, \EllipticF \left(\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}, \sqrt{-\frac{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\right)}{\left(c e \,x^{3}+b e \,x^{2}+c d \,x^{2}+a e x +b d x +a d \right) c e}"," ",0,"(-(-4*a*c+b^2)^(1/2)*e-b*e+2*c*d)/c*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)/e*(e*x+d)^(1/2)*(c*x^2+b*x+a)^(1/2)/(c*e*x^3+b*e*x^2+c*d*x^2+a*e*x+b*d*x+a*d)","A"
2466,1,1365,220,0.201000," ","int(1/(e*x+d)^(3/2)/(c*x^2+b*x+a)^(1/2),x)","\frac{2 \left(-c \,e^{2} x^{2}-\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) e}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, a \,e^{2} \EllipticE \left(\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}, \sqrt{-\frac{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\right)+\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) e}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, a \,e^{2} \EllipticF \left(\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}, \sqrt{-\frac{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\right)+\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) e}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, b d e \EllipticE \left(\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}, \sqrt{-\frac{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\right)-\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) e}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, b d e \EllipticF \left(\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}, \sqrt{-\frac{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\right)-b \,e^{2} x -\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) e}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, c \,d^{2} \EllipticE \left(\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}, \sqrt{-\frac{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\right)+\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) e}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, c \,d^{2} \EllipticF \left(\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}, \sqrt{-\frac{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\right)-a \,e^{2}\right) \sqrt{c \,x^{2}+b x +a}\, \sqrt{e x +d}}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \left(c e \,x^{3}+b e \,x^{2}+c d \,x^{2}+a e x +b d x +a d \right) e}"," ",0,"2*(2^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*a*e^2*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)-2^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*b*d*e*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)+2^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*c*d^2*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)-2^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*a*e^2*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)+2^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*b*d*e*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)-2^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*c*d^2*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)-c*e^2*x^2-b*e^2*x-a*e^2)*(c*x^2+b*x+a)^(1/2)*(e*x+d)^(1/2)/e/(a*e^2-b*d*e+c*d^2)/(c*e*x^3+b*e*x^2+c*d*x^2+a*e*x+b*d*x+a*d)","B"
2467,1,5822,459,0.218000," ","int(1/(e*x+d)^(5/2)/(c*x^2+b*x+a)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
2468,1,14312,559,0.216000," ","int(1/(e*x+d)^(7/2)/(c*x^2+b*x+a)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
2469,1,6486,575,0.358000," ","int((e*x+d)^(7/2)/(c*x^2+b*x+a)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
2470,1,4352,477,0.217000," ","int((e*x+d)^(5/2)/(c*x^2+b*x+a)^(3/2),x)","\text{output too large to display}"," ",0,"(e*x+d)^(1/2)*(c*x^2+b*x+a)^(1/2)*(2*a*b*c*d*e^3+2*b*c^2*d^3*e+2*x*a*b*c*e^4+8*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*b^2*c*d^2*e^2-8*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*b*c^2*d^3*e-12*x*a*c^2*d*e^3+2*x*b^2*c*d*e^3-4*x^2*b*c^2*d*e^3-2*x*b*c^2*d^2*e^2-4*x^2*a*c^2*e^4-2*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*(-4*a*c+b^2)^(1/2)*a*c*d*e^3+3*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*(-4*a*c+b^2)^(1/2)*b*c*d^2*e^2-12*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*a*b*c*d*e^3+8*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*a*b*c*d*e^3-8*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*a*c^2*d^2*e^2-3*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*b^2*c*d^2*e^2+12*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*a*c^2*d^2*e^2-2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*(-4*a*c+b^2)^(1/2)*b^2*d*e^3-2*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*(-4*a*c+b^2)^(1/2)*c^2*d^3*e+2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*(-4*a*c+b^2)^(1/2)*a*b*e^4+4*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*a*b^2*e^4+2*x^2*b^2*c*e^4+4*x^2*c^3*d^2*e^2-8*a*c^2*d^2*e^2+4*x*c^3*d^3*e-4*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*b^3*d*e^3+12*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*a^2*c*e^4-3*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*a*b^2*e^4+3*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*b^3*d*e^3-12*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*a^2*c*e^4+4*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*c^3*d^4)/c^2/e/(c*e*x^3+b*e*x^2+c*d*x^2+a*e*x+b*d*x+a*d)/(4*a*c-b^2)","B"
2471,1,1863,405,0.129000," ","int((e*x+d)^(3/2)/(c*x^2+b*x+a)^(3/2),x)","-\frac{2 \sqrt{e x +d}\, \sqrt{c \,x^{2}+b x +a}\, \left(b c \,e^{3} x^{2}-2 c^{2} d \,e^{2} x^{2}+\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) e}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, a b \,e^{3} \EllipticE \left(\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}, \sqrt{-\frac{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\right)-2 \sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) e}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, a c d \,e^{2} \EllipticE \left(\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}, \sqrt{-\frac{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\right)+2 a c \,e^{3} x -\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) e}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, b^{2} d \,e^{2} \EllipticE \left(\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}, \sqrt{-\frac{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\right)+3 \sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) e}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, b c \,d^{2} e \EllipticE \left(\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}, \sqrt{-\frac{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\right)-2 \sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) e}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, c^{2} d^{3} \EllipticE \left(\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}, \sqrt{-\frac{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\right)-2 c^{2} d^{2} e x +2 a c d \,e^{2}+\sqrt{-4 a c +b^{2}}\, \sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) e}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, a \,e^{3} \EllipticF \left(\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}, \sqrt{-\frac{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\right)-b c \,d^{2} e -\sqrt{-4 a c +b^{2}}\, \sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) e}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, b d \,e^{2} \EllipticF \left(\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}, \sqrt{-\frac{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\right)+\sqrt{-4 a c +b^{2}}\, \sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) e}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, c \,d^{2} e \EllipticF \left(\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}, \sqrt{-\frac{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\right)\right)}{\left(c e \,x^{3}+b e \,x^{2}+c d \,x^{2}+a e x +b d x +a d \right) \left(4 a c -b^{2}\right) c e}"," ",0,"-2*(e*x+d)^(1/2)*(c*x^2+b*x+a)^(1/2)*((-4*a*c+b^2)^(1/2)*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*a*e^3-(-4*a*c+b^2)^(1/2)*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*b*d*e^2+(-4*a*c+b^2)^(1/2)*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*c*d^2*e+2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*a*b*e^3-2*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*a*c*d*e^2-2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*b^2*d*e^2+3*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*b*c*d^2*e-2*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*c^2*d^3+b*c*e^3*x^2-2*c^2*d*e^2*x^2+2*a*c*e^3*x-2*x*c^2*d^2*e+2*a*c*d*e^2-b*c*d^2*e)/c/e/(c*e*x^3+b*e*x^2+c*d*x^2+a*e*x+b*d*x+a*d)/(4*a*c-b^2)","B"
2472,1,1612,374,0.167000," ","int((e*x+d)^(1/2)/(c*x^2+b*x+a)^(3/2),x)","\frac{\left(4 c^{2} e^{2} x^{2}+4 \sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) e}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, a c \,e^{2} \EllipticE \left(\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}, \sqrt{-\frac{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\right)-4 \sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) e}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, a c \,e^{2} \EllipticF \left(\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}, \sqrt{-\frac{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\right)+\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) e}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, b^{2} e^{2} \EllipticF \left(\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}, \sqrt{-\frac{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\right)-4 \sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) e}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, b c d e \EllipticE \left(\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}, \sqrt{-\frac{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\right)+2 b c \,e^{2} x +4 \sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) e}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, c^{2} d^{2} \EllipticE \left(\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}, \sqrt{-\frac{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\right)+4 c^{2} d e x +2 b c d e +\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) e}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{-4 a c +b^{2}}\, b \,e^{2} \EllipticF \left(\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}, \sqrt{-\frac{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\right)-2 \sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) e}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{-4 a c +b^{2}}\, c d e \EllipticF \left(\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}, \sqrt{-\frac{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\right)\right) \sqrt{e x +d}\, \sqrt{c \,x^{2}+b x +a}}{\left(c e \,x^{3}+b e \,x^{2}+c d \,x^{2}+a e x +b d x +a d \right) \left(4 a c -b^{2}\right) c e}"," ",0,"(-4*2^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*a*c*e^2*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)+2^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*b^2*e^2*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)+2^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*b*e^2*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*(-4*a*c+b^2)^(1/2)-2*2^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*c*d*e*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*(-4*a*c+b^2)^(1/2)+4*2^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*a*c*e^2*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)-4*2^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*b*c*d*e*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)+4*2^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*c^2*d^2*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)+4*c^2*e^2*x^2+2*b*c*e^2*x+4*x*c^2*d*e+2*b*c*d*e)*(e*x+d)^(1/2)*(c*x^2+b*x+a)^(1/2)/c/e/(c*e*x^3+b*e*x^2+c*d*x^2+a*e*x+b*d*x+a*d)/(4*a*c-b^2)","B"
2473,1,1894,428,0.163000," ","int(1/(e*x+d)^(1/2)/(c*x^2+b*x+a)^(3/2),x)","-\frac{2 \left(b c \,e^{3} x^{2}-2 c^{2} d \,e^{2} x^{2}+\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) e}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, a b \,e^{3} \EllipticE \left(\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}, \sqrt{-\frac{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\right)-2 \sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) e}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, a c d \,e^{2} \EllipticE \left(\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}, \sqrt{-\frac{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\right)-2 a c \,e^{3} x -\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) e}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, b^{2} d \,e^{2} \EllipticE \left(\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}, \sqrt{-\frac{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\right)+b^{2} e^{3} x +3 \sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) e}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, b c \,d^{2} e \EllipticE \left(\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}, \sqrt{-\frac{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\right)-2 \sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) e}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, c^{2} d^{3} \EllipticE \left(\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}, \sqrt{-\frac{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\right)-2 c^{2} d^{2} e x -2 a c d \,e^{2}+\sqrt{-4 a c +b^{2}}\, \sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) e}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, a \,e^{3} \EllipticF \left(\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}, \sqrt{-\frac{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\right)+b^{2} d \,e^{2}-b c \,d^{2} e -\sqrt{-4 a c +b^{2}}\, \sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) e}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, b d \,e^{2} \EllipticF \left(\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}, \sqrt{-\frac{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\right)+\sqrt{-4 a c +b^{2}}\, \sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, \sqrt{\frac{\left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) e}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}\, c \,d^{2} e \EllipticF \left(\sqrt{2}\, \sqrt{-\frac{\left(e x +d \right) c}{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}}, \sqrt{-\frac{b e -2 c d +\sqrt{-4 a c +b^{2}}\, e}{-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e}}\right)\right) \sqrt{c \,x^{2}+b x +a}\, \sqrt{e x +d}}{\left(4 a c -b^{2}\right) \left(a \,e^{2}-b d e +c \,d^{2}\right) \left(c e \,x^{3}+b e \,x^{2}+c d \,x^{2}+a e x +b d x +a d \right) e}"," ",0,"-2*(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*a*b*e^3-2*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*a*c*d*e^2-2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*b^2*d*e^2+3*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*b*c*d^2*e-2*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*c^2*d^3+(-4*a*c+b^2)^(1/2)*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*a*e^3-(-4*a*c+b^2)^(1/2)*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*b*d*e^2+(-4*a*c+b^2)^(1/2)*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*c*d^2*e+b*c*e^3*x^2-2*c^2*d*e^2*x^2-2*a*c*e^3*x+x*b^2*e^3-2*c^2*d^2*e*x-2*a*c*d*e^2+b^2*d*e^2-b*c*d^2*e)*(c*x^2+b*x+a)^(1/2)*(e*x+d)^(1/2)/e/(4*a*c-b^2)/(a*e^2-b*d*e+c*d^2)/(c*e*x^3+b*e*x^2+c*d*x^2+a*e*x+b*d*x+a*d)","B"
2474,1,4415,551,0.214000," ","int(1/(e*x+d)^(3/2)/(c*x^2+b*x+a)^(3/2),x)","\text{output too large to display}"," ",0,"(-6*a*b*c*d*e^3+2*b*c^2*d^3*e-14*x*a*b*c*e^4+8*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*b^2*c*d^2*e^2-8*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*b*c^2*d^3*e+4*x*a*c^2*d*e^3-2*x*b^2*c*d*e^3-4*x^2*b*c^2*d*e^3-2*x*b*c^2*d^2*e^2+2*b^3*d*e^3-4*b^2*c*d^2*e^2-12*x^2*a*c^2*e^4-2*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*(-4*a*c+b^2)^(1/2)*a*c*d*e^3+3*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*(-4*a*c+b^2)^(1/2)*b*c*d^2*e^2-12*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*a*b*c*d*e^3+8*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*a*b*c*d*e^3-8*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*a*c^2*d^2*e^2-3*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*b^2*c*d^2*e^2+12*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*a*c^2*d^2*e^2-2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*(-4*a*c+b^2)^(1/2)*b^2*d*e^3-2*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*(-4*a*c+b^2)^(1/2)*c^2*d^3*e+2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*(-4*a*c+b^2)^(1/2)*a*b*e^4+2*a*b^2*e^4+4*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*a*b^2*e^4+4*x^2*b^2*c*e^4+4*x^2*c^3*d^2*e^2+8*a*c^2*d^2*e^2+4*x*c^3*d^3*e-8*a^2*c*e^4-4*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*b^3*d*e^3+12*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*a^2*c*e^4-3*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*a*b^2*e^4+3*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticF(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*b^3*d*e^3-12*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*a^2*c*e^4+4*x*b^3*e^4+4*2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*e)^(1/2)*EllipticE(2^(1/2)*(-(e*x+d)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*c)^(1/2),(-(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))^(1/2))*c^3*d^4)*(c*x^2+b*x+a)^(1/2)*(e*x+d)^(1/2)/e/(4*a*c-b^2)/(a*e^2-b*d*e+c*d^2)^2/(c*e*x^3+b*e*x^2+c*d*x^2+a*e*x+b*d*x+a*d)","B"
2475,1,12894,676,0.451000," ","int(1/(e*x+d)^(5/2)/(c*x^2+b*x+a)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
2476,1,19258,595,0.368000," ","int((e*x+d)^(7/2)/(c*x^2+b*x+a)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
2477,1,12990,526,0.283000," ","int((e*x+d)^(5/2)/(c*x^2+b*x+a)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
2478,1,8889,478,0.216000," ","int((e*x+d)^(3/2)/(c*x^2+b*x+a)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
2479,1,13069,541,0.190000," ","int((e*x+d)^(1/2)/(c*x^2+b*x+a)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
2480,1,19400,661,0.385000," ","int(1/(e*x+d)^(1/2)/(c*x^2+b*x+a)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
2481,1,27157,848,0.530000," ","int(1/(e*x+d)^(3/2)/(c*x^2+b*x+a)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
2482,1,77,23,0.098000," ","int((5*x+3)^(1/2)/(-12*x^2+5*x+2)^(1/2),x)","-\frac{\left(-\EllipticE \left(\frac{\sqrt{285 x +171}}{19}, \frac{2 \sqrt{399}}{21}\right)+\EllipticF \left(\frac{\sqrt{285 x +171}}{19}, \frac{2 \sqrt{399}}{21}\right)\right) \sqrt{-285 x +190}\, \sqrt{-140 x -35}\, \sqrt{57}\, \sqrt{-12 x^{2}+5 x +2}}{570 \left(12 x^{2}-5 x -2\right)}"," ",0,"-1/570*(EllipticF(1/19*(285*x+171)^(1/2),2/21*399^(1/2))-EllipticE(1/19*(285*x+171)^(1/2),2/21*399^(1/2)))*(-285*x+190)^(1/2)*(-140*x-35)^(1/2)*57^(1/2)*(-12*x^2+5*x+2)^(1/2)/(12*x^2-5*x-2)","B"
2483,0,0,535,1.668000," ","int((e*x+d)^2*(c*x^2+b*x+a)^(4/3),x)","\int \left(e x +d \right)^{2} \left(c \,x^{2}+b x +a \right)^{\frac{4}{3}}\, dx"," ",0,"int((e*x+d)^2*(c*x^2+b*x+a)^(4/3),x)","F"
2484,0,0,440,1.422000," ","int((e*x+d)*(c*x^2+b*x+a)^(4/3),x)","\int \left(e x +d \right) \left(c \,x^{2}+b x +a \right)^{\frac{4}{3}}\, dx"," ",0,"int((e*x+d)*(c*x^2+b*x+a)^(4/3),x)","F"
2485,0,0,395,2.507000," ","int((c*x^2+b*x+a)^(4/3),x)","\int \left(c \,x^{2}+b x +a \right)^{\frac{4}{3}}\, dx"," ",0,"int((c*x^2+b*x+a)^(4/3),x)","F"
2486,0,0,152,1.884000," ","int((c*x^2+b*x+a)^(4/3)/(e*x+d),x)","\int \frac{\left(c \,x^{2}+b x +a \right)^{\frac{4}{3}}}{e x +d}\, dx"," ",0,"int((c*x^2+b*x+a)^(4/3)/(e*x+d),x)","F"
2487,0,0,159,2.480000," ","int((c*x^2+b*x+a)^(4/3)/(e*x+d)^2,x)","\int \frac{\left(c \,x^{2}+b x +a \right)^{\frac{4}{3}}}{\left(e x +d \right)^{2}}\, dx"," ",0,"int((c*x^2+b*x+a)^(4/3)/(e*x+d)^2,x)","F"
2488,0,0,159,1.663000," ","int((c*x^2+b*x+a)^(4/3)/(e*x+d)^3,x)","\int \frac{\left(c \,x^{2}+b x +a \right)^{\frac{4}{3}}}{\left(e x +d \right)^{3}}\, dx"," ",0,"int((c*x^2+b*x+a)^(4/3)/(e*x+d)^3,x)","F"
2489,0,0,1022,2.014000," ","int((e*x+d)^3/(c*x^2+b*x+a)^(7/3),x)","\int \frac{\left(e x +d \right)^{3}}{\left(c \,x^{2}+b x +a \right)^{\frac{7}{3}}}\, dx"," ",0,"int((e*x+d)^3/(c*x^2+b*x+a)^(7/3),x)","F"
2490,0,0,951,2.059000," ","int((e*x+d)^2/(c*x^2+b*x+a)^(7/3),x)","\int \frac{\left(e x +d \right)^{2}}{\left(c \,x^{2}+b x +a \right)^{\frac{7}{3}}}\, dx"," ",0,"int((e*x+d)^2/(c*x^2+b*x+a)^(7/3),x)","F"
2491,0,0,841,1.451000," ","int((e*x+d)/(c*x^2+b*x+a)^(7/3),x)","\int \frac{e x +d}{\left(c \,x^{2}+b x +a \right)^{\frac{7}{3}}}\, dx"," ",0,"int((e*x+d)/(c*x^2+b*x+a)^(7/3),x)","F"
2492,0,0,793,2.595000," ","int(1/(c*x^2+b*x+a)^(7/3),x)","\int \frac{1}{\left(c \,x^{2}+b x +a \right)^{\frac{7}{3}}}\, dx"," ",0,"int(1/(c*x^2+b*x+a)^(7/3),x)","F"
2493,0,0,152,1.569000," ","int(1/(e*x+d)/(c*x^2+b*x+a)^(7/3),x)","\int \frac{1}{\left(e x +d \right) \left(c \,x^{2}+b x +a \right)^{\frac{7}{3}}}\, dx"," ",0,"int(1/(e*x+d)/(c*x^2+b*x+a)^(7/3),x)","F"
2494,0,0,159,1.961000," ","int(1/(e*x+d)^2/(c*x^2+b*x+a)^(7/3),x)","\int \frac{1}{\left(e x +d \right)^{2} \left(c \,x^{2}+b x +a \right)^{\frac{7}{3}}}\, dx"," ",0,"int(1/(e*x+d)^2/(c*x^2+b*x+a)^(7/3),x)","F"
2495,0,0,159,1.815000," ","int(1/(e*x+d)^3/(c*x^2+b*x+a)^(7/3),x)","\int \frac{1}{\left(e x +d \right)^{3} \left(c \,x^{2}+b x +a \right)^{\frac{7}{3}}}\, dx"," ",0,"int(1/(e*x+d)^3/(c*x^2+b*x+a)^(7/3),x)","F"
2496,0,0,220,2.561000," ","int(1/(e*x+d)/(3*c^2*e^2*x^2+3*b*c*e^2*x+b^2*e^2-b*c*d*e+c^2*d^2)^(1/3),x)","\int \frac{1}{\left(e x +d \right) \left(3 c^{2} e^{2} x^{2}+3 b c \,e^{2} x +b^{2} e^{2}-b c d e +c^{2} d^{2}\right)^{\frac{1}{3}}}\, dx"," ",0,"int(1/(e*x+d)/(3*c^2*e^2*x^2+3*b*c*e^2*x+b^2*e^2-b*c*d*e+c^2*d^2)^(1/3),x)","F"
2497,0,0,479,3.501000," ","int((3*x+2)^3/(27*x^2-54*x+52)^(1/3),x)","\int \frac{\left(3 x +2\right)^{3}}{\left(27 x^{2}-54 x +52\right)^{\frac{1}{3}}}\, dx"," ",0,"int((3*x+2)^3/(27*x^2-54*x+52)^(1/3),x)","F"
2498,0,0,472,2.211000," ","int((3*x+2)^2/(27*x^2-54*x+52)^(1/3),x)","\int \frac{\left(3 x +2\right)^{2}}{\left(27 x^{2}-54 x +52\right)^{\frac{1}{3}}}\, dx"," ",0,"int((3*x+2)^2/(27*x^2-54*x+52)^(1/3),x)","F"
2499,0,0,453,2.623000," ","int((3*x+2)/(27*x^2-54*x+52)^(1/3),x)","\int \frac{3 x +2}{\left(27 x^{2}-54 x +52\right)^{\frac{1}{3}}}\, dx"," ",0,"int((3*x+2)/(27*x^2-54*x+52)^(1/3),x)","F"
2500,1,2201,83,25.948000," ","int(1/(3*x+2)/(27*x^2-54*x+52)^(1/3),x)","\text{Expression too large to display}"," ",0,"1/3*RootOf(RootOf(_Z^3-10)^2+30*_Z*RootOf(_Z^3-10)+900*_Z^2)*ln(-(321317013531015450*RootOf(RootOf(_Z^3-10)^2+30*_Z*RootOf(_Z^3-10)+900*_Z^2)^2*RootOf(_Z^3-10)^2*x^3+1201310549293725*RootOf(RootOf(_Z^3-10)^2+30*_Z*RootOf(_Z^3-10)+900*_Z^2)*RootOf(_Z^3-10)^3*x^3+593200640364951600*RootOf(RootOf(_Z^3-10)^2+30*_Z*RootOf(_Z^3-10)+900*_Z^2)^2*RootOf(_Z^3-10)^2*x^2+2217804091003800*RootOf(RootOf(_Z^3-10)^2+30*_Z*RootOf(_Z^3-10)+900*_Z^2)*RootOf(_Z^3-10)^3*x^2+35356252380606720*(27*x^2-54*x+52)^(2/3)*RootOf(RootOf(_Z^3-10)^2+30*_Z*RootOf(_Z^3-10)+900*_Z^2)*RootOf(_Z^3-10)^2*x+527289458102179200*RootOf(RootOf(_Z^3-10)^2+30*_Z*RootOf(_Z^3-10)+900*_Z^2)^2*RootOf(_Z^3-10)^2*x+1971381414225600*RootOf(RootOf(_Z^3-10)^2+30*_Z*RootOf(_Z^3-10)+900*_Z^2)*RootOf(_Z^3-10)^3*x-94283339681617920*(27*x^2-54*x+52)^(2/3)*RootOf(RootOf(_Z^3-10)^2+30*_Z*RootOf(_Z^3-10)+900*_Z^2)*RootOf(_Z^3-10)^2-106068757141820160*(27*x^2-54*x+52)^(1/3)*RootOf(RootOf(_Z^3-10)^2+30*_Z*RootOf(_Z^3-10)+900*_Z^2)*RootOf(_Z^3-10)*x^2-380074665718431*(27*x^2-54*x+52)^(1/3)*RootOf(_Z^3-10)^2*x^2+565700038089707520*(27*x^2-54*x+52)^(1/3)*RootOf(RootOf(_Z^3-10)^2+30*_Z*RootOf(_Z^3-10)+900*_Z^2)*RootOf(_Z^3-10)*x+212563562797440990*RootOf(RootOf(_Z^3-10)^2+30*_Z*RootOf(_Z^3-10)+900*_Z^2)*x^3+2027064883831632*(27*x^2-54*x+52)^(1/3)*RootOf(_Z^3-10)^2*x+794713132609695*RootOf(_Z^3-10)*x^3-754266717452943360*(27*x^2-54*x+52)^(1/3)*RootOf(RootOf(_Z^3-10)^2+30*_Z*RootOf(_Z^3-10)+900*_Z^2)*RootOf(_Z^3-10)-2771565214149579420*RootOf(RootOf(_Z^3-10)^2+30*_Z*RootOf(_Z^3-10)+900*_Z^2)*x^2-2702753178442176*(27*x^2-54*x+52)^(1/3)*RootOf(_Z^3-10)^2-10362073558523310*RootOf(_Z^3-10)*x^2+1266915552394770*(27*x^2-54*x+52)^(2/3)*x+6676802763218844120*RootOf(RootOf(_Z^3-10)^2+30*_Z*RootOf(_Z^3-10)+900*_Z^2)*x+24962617157631660*RootOf(_Z^3-10)*x-3378441473052720*(27*x^2-54*x+52)^(2/3)-6093610857938239440*RootOf(RootOf(_Z^3-10)^2+30*_Z*RootOf(_Z^3-10)+900*_Z^2)-22782232806434920*RootOf(_Z^3-10))/(3*x+2)^3)-1/90*ln(-(321317013531015450*RootOf(RootOf(_Z^3-10)^2+30*_Z*RootOf(_Z^3-10)+900*_Z^2)^2*RootOf(_Z^3-10)^2*x^3+9509256568406790*RootOf(RootOf(_Z^3-10)^2+30*_Z*RootOf(_Z^3-10)+900*_Z^2)*RootOf(_Z^3-10)^3*x^3+593200640364951600*RootOf(RootOf(_Z^3-10)^2+30*_Z*RootOf(_Z^3-10)+900*_Z^2)^2*RootOf(_Z^3-10)^2*x^2+17555550587827920*RootOf(RootOf(_Z^3-10)^2+30*_Z*RootOf(_Z^3-10)+900*_Z^2)*RootOf(_Z^3-10)^3*x^2-35356252380606720*(27*x^2-54*x+52)^(2/3)*RootOf(RootOf(_Z^3-10)^2+30*_Z*RootOf(_Z^3-10)+900*_Z^2)*RootOf(_Z^3-10)^2*x+527289458102179200*RootOf(RootOf(_Z^3-10)^2+30*_Z*RootOf(_Z^3-10)+900*_Z^2)^2*RootOf(_Z^3-10)^2*x+15604933855847040*RootOf(RootOf(_Z^3-10)^2+30*_Z*RootOf(_Z^3-10)+900*_Z^2)*RootOf(_Z^3-10)^3*x+94283339681617920*(27*x^2-54*x+52)^(2/3)*RootOf(RootOf(_Z^3-10)^2+30*_Z*RootOf(_Z^3-10)+900*_Z^2)*RootOf(_Z^3-10)^2+106068757141820160*(27*x^2-54*x+52)^(1/3)*RootOf(RootOf(_Z^3-10)^2+30*_Z*RootOf(_Z^3-10)+900*_Z^2)*RootOf(_Z^3-10)*x^2+3155550572342241*(27*x^2-54*x+52)^(1/3)*RootOf(_Z^3-10)^2*x^2-565700038089707520*(27*x^2-54*x+52)^(1/3)*RootOf(RootOf(_Z^3-10)^2+30*_Z*RootOf(_Z^3-10)+900*_Z^2)*RootOf(_Z^3-10)*x-105457891620435840*RootOf(RootOf(_Z^3-10)^2+30*_Z*RootOf(_Z^3-10)+900*_Z^2)*x^3-16829603052491952*(27*x^2-54*x+52)^(1/3)*RootOf(_Z^3-10)^2*x-3120986771169408*RootOf(_Z^3-10)*x^3+754266717452943360*(27*x^2-54*x+52)^(1/3)*RootOf(RootOf(_Z^3-10)^2+30*_Z*RootOf(_Z^3-10)+900*_Z^2)*RootOf(_Z^3-10)+2969298760937896620*RootOf(RootOf(_Z^3-10)^2+30*_Z*RootOf(_Z^3-10)+900*_Z^2)*x^2+22439470736655936*(27*x^2-54*x+52)^(1/3)*RootOf(_Z^3-10)^2+87875283775738644*RootOf(_Z^3-10)*x^2-10518501907807470*(27*x^2-54*x+52)^(2/3)*x-6501039610518117720*RootOf(RootOf(_Z^3-10)^2+30*_Z*RootOf(_Z^3-10)+900*_Z^2)*x-192395830331047464*RootOf(_Z^3-10)*x+28049338420819920*(27*x^2-54*x+52)^(2/3)+6093610857938239440*RootOf(RootOf(_Z^3-10)^2+30*_Z*RootOf(_Z^3-10)+900*_Z^2)+180338129124839728*RootOf(_Z^3-10))/(3*x+2)^3)*RootOf(_Z^3-10)-1/3*ln(-(321317013531015450*RootOf(RootOf(_Z^3-10)^2+30*_Z*RootOf(_Z^3-10)+900*_Z^2)^2*RootOf(_Z^3-10)^2*x^3+9509256568406790*RootOf(RootOf(_Z^3-10)^2+30*_Z*RootOf(_Z^3-10)+900*_Z^2)*RootOf(_Z^3-10)^3*x^3+593200640364951600*RootOf(RootOf(_Z^3-10)^2+30*_Z*RootOf(_Z^3-10)+900*_Z^2)^2*RootOf(_Z^3-10)^2*x^2+17555550587827920*RootOf(RootOf(_Z^3-10)^2+30*_Z*RootOf(_Z^3-10)+900*_Z^2)*RootOf(_Z^3-10)^3*x^2-35356252380606720*(27*x^2-54*x+52)^(2/3)*RootOf(RootOf(_Z^3-10)^2+30*_Z*RootOf(_Z^3-10)+900*_Z^2)*RootOf(_Z^3-10)^2*x+527289458102179200*RootOf(RootOf(_Z^3-10)^2+30*_Z*RootOf(_Z^3-10)+900*_Z^2)^2*RootOf(_Z^3-10)^2*x+15604933855847040*RootOf(RootOf(_Z^3-10)^2+30*_Z*RootOf(_Z^3-10)+900*_Z^2)*RootOf(_Z^3-10)^3*x+94283339681617920*(27*x^2-54*x+52)^(2/3)*RootOf(RootOf(_Z^3-10)^2+30*_Z*RootOf(_Z^3-10)+900*_Z^2)*RootOf(_Z^3-10)^2+106068757141820160*(27*x^2-54*x+52)^(1/3)*RootOf(RootOf(_Z^3-10)^2+30*_Z*RootOf(_Z^3-10)+900*_Z^2)*RootOf(_Z^3-10)*x^2+3155550572342241*(27*x^2-54*x+52)^(1/3)*RootOf(_Z^3-10)^2*x^2-565700038089707520*(27*x^2-54*x+52)^(1/3)*RootOf(RootOf(_Z^3-10)^2+30*_Z*RootOf(_Z^3-10)+900*_Z^2)*RootOf(_Z^3-10)*x-105457891620435840*RootOf(RootOf(_Z^3-10)^2+30*_Z*RootOf(_Z^3-10)+900*_Z^2)*x^3-16829603052491952*(27*x^2-54*x+52)^(1/3)*RootOf(_Z^3-10)^2*x-3120986771169408*RootOf(_Z^3-10)*x^3+754266717452943360*(27*x^2-54*x+52)^(1/3)*RootOf(RootOf(_Z^3-10)^2+30*_Z*RootOf(_Z^3-10)+900*_Z^2)*RootOf(_Z^3-10)+2969298760937896620*RootOf(RootOf(_Z^3-10)^2+30*_Z*RootOf(_Z^3-10)+900*_Z^2)*x^2+22439470736655936*(27*x^2-54*x+52)^(1/3)*RootOf(_Z^3-10)^2+87875283775738644*RootOf(_Z^3-10)*x^2-10518501907807470*(27*x^2-54*x+52)^(2/3)*x-6501039610518117720*RootOf(RootOf(_Z^3-10)^2+30*_Z*RootOf(_Z^3-10)+900*_Z^2)*x-192395830331047464*RootOf(_Z^3-10)*x+28049338420819920*(27*x^2-54*x+52)^(2/3)+6093610857938239440*RootOf(RootOf(_Z^3-10)^2+30*_Z*RootOf(_Z^3-10)+900*_Z^2)+180338129124839728*RootOf(_Z^3-10))/(3*x+2)^3)*RootOf(RootOf(_Z^3-10)^2+30*_Z*RootOf(_Z^3-10)+900*_Z^2)","C"
2501,0,0,542,2.229000," ","int(1/(3*x+2)^2/(27*x^2-54*x+52)^(1/3),x)","\int \frac{1}{\left(3 x +2\right)^{2} \left(27 x^{2}-54 x +52\right)^{\frac{1}{3}}}\, dx"," ",0,"int(1/(3*x+2)^2/(27*x^2-54*x+52)^(1/3),x)","F"
2502,0,0,563,2.046000," ","int(1/(3*x+2)^3/(27*x^2-54*x+52)^(1/3),x)","\int \frac{1}{\left(3 x +2\right)^{3} \left(27 x^{2}-54 x +52\right)^{\frac{1}{3}}}\, dx"," ",0,"int(1/(3*x+2)^3/(27*x^2-54*x+52)^(1/3),x)","F"
2503,0,0,448,3.111000," ","int((3*x+2)^3/(27*x^2+54*x+28)^(1/3),x)","\int \frac{\left(3 x +2\right)^{3}}{\left(27 x^{2}+54 x +28\right)^{\frac{1}{3}}}\, dx"," ",0,"int((3*x+2)^3/(27*x^2+54*x+28)^(1/3),x)","F"
2504,0,0,450,3.206000," ","int((3*x+2)^2/(27*x^2+54*x+28)^(1/3),x)","\int \frac{\left(3 x +2\right)^{2}}{\left(27 x^{2}+54 x +28\right)^{\frac{1}{3}}}\, dx"," ",0,"int((3*x+2)^2/(27*x^2+54*x+28)^(1/3),x)","F"
2505,0,0,431,1.724000," ","int((3*x+2)/(27*x^2+54*x+28)^(1/3),x)","\int \frac{3 x +2}{\left(27 x^{2}+54 x +28\right)^{\frac{1}{3}}}\, dx"," ",0,"int((3*x+2)/(27*x^2+54*x+28)^(1/3),x)","F"
2506,0,0,80,4.723000," ","int(1/(3*x+2)/(27*x^2+54*x+28)^(1/3),x)","\int \frac{1}{\left(3 x +2\right) \left(27 x^{2}+54 x +28\right)^{\frac{1}{3}}}\, dx"," ",0,"int(1/(3*x+2)/(27*x^2+54*x+28)^(1/3),x)","F"
2507,0,0,517,1.974000," ","int(1/(3*x+2)^2/(27*x^2+54*x+28)^(1/3),x)","\int \frac{1}{\left(3 x +2\right)^{2} \left(27 x^{2}+54 x +28\right)^{\frac{1}{3}}}\, dx"," ",0,"int(1/(3*x+2)^2/(27*x^2+54*x+28)^(1/3),x)","F"
2508,0,0,538,2.151000," ","int(1/(3*x+2)^3/(27*x^2+54*x+28)^(1/3),x)","\int \frac{1}{\left(3 x +2\right)^{3} \left(27 x^{2}+54 x +28\right)^{\frac{1}{3}}}\, dx"," ",0,"int(1/(3*x+2)^3/(27*x^2+54*x+28)^(1/3),x)","F"
2509,0,0,487,1.714000," ","int(1/(e*x+d)/(9*c^2*e^2*x^2+9*b*c*e^2*x+2*b^2*e^2+b*c*d*e-c^2*d^2)^(1/3),x)","\int \frac{1}{\left(e x +d \right) \left(9 c^{2} e^{2} x^{2}+9 b c \,e^{2} x +2 b^{2} e^{2}+b c d e -c^{2} d^{2}\right)^{\frac{1}{3}}}\, dx"," ",0,"int(1/(e*x+d)/(9*c^2*e^2*x^2+9*b*c*e^2*x+2*b^2*e^2+b*c*d*e-c^2*d^2)^(1/3),x)","F"
2510,0,0,407,1.971000," ","int((e*x+d)^3*(c*x^2+b*x+a)^(1/4),x)","\int \left(e x +d \right)^{3} \left(c \,x^{2}+b x +a \right)^{\frac{1}{4}}\, dx"," ",0,"int((e*x+d)^3*(c*x^2+b*x+a)^(1/4),x)","F"
2511,0,0,352,1.186000," ","int((e*x+d)^2*(c*x^2+b*x+a)^(1/4),x)","\int \left(e x +d \right)^{2} \left(c \,x^{2}+b x +a \right)^{\frac{1}{4}}\, dx"," ",0,"int((e*x+d)^2*(c*x^2+b*x+a)^(1/4),x)","F"
2512,0,0,278,2.295000," ","int((e*x+d)*(c*x^2+b*x+a)^(1/4),x)","\int \left(e x +d \right) \left(c \,x^{2}+b x +a \right)^{\frac{1}{4}}\, dx"," ",0,"int((e*x+d)*(c*x^2+b*x+a)^(1/4),x)","F"
2513,0,0,242,1.989000," ","int((c*x^2+b*x+a)^(1/4),x)","\int \left(c \,x^{2}+b x +a \right)^{\frac{1}{4}}\, dx"," ",0,"int((c*x^2+b*x+a)^(1/4),x)","F"
2514,0,0,844,2.224000," ","int((c*x^2+b*x+a)^(1/4)/(e*x+d),x)","\int \frac{\left(c \,x^{2}+b x +a \right)^{\frac{1}{4}}}{e x +d}\, dx"," ",0,"int((c*x^2+b*x+a)^(1/4)/(e*x+d),x)","F"
2515,0,0,900,1.562000," ","int((c*x^2+b*x+a)^(1/4)/(e*x+d)^2,x)","\int \frac{\left(c \,x^{2}+b x +a \right)^{\frac{1}{4}}}{\left(e x +d \right)^{2}}\, dx"," ",0,"int((c*x^2+b*x+a)^(1/4)/(e*x+d)^2,x)","F"
2516,0,0,767,1.950000," ","int((e*x+d)^3*(c*x^2+b*x+a)^(3/4),x)","\int \left(e x +d \right)^{3} \left(c \,x^{2}+b x +a \right)^{\frac{3}{4}}\, dx"," ",0,"int((e*x+d)^3*(c*x^2+b*x+a)^(3/4),x)","F"
2517,0,0,694,1.411000," ","int((e*x+d)^2*(c*x^2+b*x+a)^(3/4),x)","\int \left(e x +d \right)^{2} \left(c \,x^{2}+b x +a \right)^{\frac{3}{4}}\, dx"," ",0,"int((e*x+d)^2*(c*x^2+b*x+a)^(3/4),x)","F"
2518,0,0,578,1.664000," ","int((e*x+d)*(c*x^2+b*x+a)^(3/4),x)","\int \left(e x +d \right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{4}}\, dx"," ",0,"int((e*x+d)*(c*x^2+b*x+a)^(3/4),x)","F"
2519,0,0,524,2.484000," ","int((c*x^2+b*x+a)^(3/4),x)","\int \left(c \,x^{2}+b x +a \right)^{\frac{3}{4}}\, dx"," ",0,"int((c*x^2+b*x+a)^(3/4),x)","F"
2520,0,0,1193,2.177000," ","int((c*x^2+b*x+a)^(3/4)/(e*x+d),x)","\int \frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{4}}}{e x +d}\, dx"," ",0,"int((c*x^2+b*x+a)^(3/4)/(e*x+d),x)","F"
2521,0,0,1196,1.607000," ","int((c*x^2+b*x+a)^(3/4)/(e*x+d)^2,x)","\int \frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{4}}}{\left(e x +d \right)^{2}}\, dx"," ",0,"int((c*x^2+b*x+a)^(3/4)/(e*x+d)^2,x)","F"
2522,0,0,477,1.608000," ","int((e*x+d)^3*(c*x^2+b*x+a)^(5/4),x)","\int \left(e x +d \right)^{3} \left(c \,x^{2}+b x +a \right)^{\frac{5}{4}}\, dx"," ",0,"int((e*x+d)^3*(c*x^2+b*x+a)^(5/4),x)","F"
2523,0,0,413,1.517000," ","int((e*x+d)^2*(c*x^2+b*x+a)^(5/4),x)","\int \left(e x +d \right)^{2} \left(c \,x^{2}+b x +a \right)^{\frac{5}{4}}\, dx"," ",0,"int((e*x+d)^2*(c*x^2+b*x+a)^(5/4),x)","F"
2524,0,0,318,1.762000," ","int((e*x+d)*(c*x^2+b*x+a)^(5/4),x)","\int \left(e x +d \right) \left(c \,x^{2}+b x +a \right)^{\frac{5}{4}}\, dx"," ",0,"int((e*x+d)*(c*x^2+b*x+a)^(5/4),x)","F"
2525,0,0,273,2.320000," ","int((c*x^2+b*x+a)^(5/4),x)","\int \left(c \,x^{2}+b x +a \right)^{\frac{5}{4}}\, dx"," ",0,"int((c*x^2+b*x+a)^(5/4),x)","F"
2526,0,0,969,2.697000," ","int((c*x^2+b*x+a)^(5/4)/(e*x+d),x)","\int \frac{\left(c \,x^{2}+b x +a \right)^{\frac{5}{4}}}{e x +d}\, dx"," ",0,"int((c*x^2+b*x+a)^(5/4)/(e*x+d),x)","F"
2527,0,0,924,1.790000," ","int((c*x^2+b*x+a)^(5/4)/(e*x+d)^2,x)","\int \frac{\left(c \,x^{2}+b x +a \right)^{\frac{5}{4}}}{\left(e x +d \right)^{2}}\, dx"," ",0,"int((c*x^2+b*x+a)^(5/4)/(e*x+d)^2,x)","F"
2528,0,0,705,2.226000," ","int((e*x+d)^3/(c*x^2+b*x+a)^(1/4),x)","\int \frac{\left(e x +d \right)^{3}}{\left(c \,x^{2}+b x +a \right)^{\frac{1}{4}}}\, dx"," ",0,"int((e*x+d)^3/(c*x^2+b*x+a)^(1/4),x)","F"
2529,0,0,641,1.160000," ","int((e*x+d)^2/(c*x^2+b*x+a)^(1/4),x)","\int \frac{\left(e x +d \right)^{2}}{\left(c \,x^{2}+b x +a \right)^{\frac{1}{4}}}\, dx"," ",0,"int((e*x+d)^2/(c*x^2+b*x+a)^(1/4),x)","F"
2530,0,0,545,1.273000," ","int((e*x+d)/(c*x^2+b*x+a)^(1/4),x)","\int \frac{e x +d}{\left(c \,x^{2}+b x +a \right)^{\frac{1}{4}}}\, dx"," ",0,"int((e*x+d)/(c*x^2+b*x+a)^(1/4),x)","F"
2531,0,0,501,2.118000," ","int(1/(c*x^2+b*x+a)^(1/4),x)","\int \frac{1}{\left(c \,x^{2}+b x +a \right)^{\frac{1}{4}}}\, dx"," ",0,"int(1/(c*x^2+b*x+a)^(1/4),x)","F"
2532,0,0,640,1.432000," ","int(1/(e*x+d)/(c*x^2+b*x+a)^(1/4),x)","\int \frac{1}{\left(e x +d \right) \left(c \,x^{2}+b x +a \right)^{\frac{1}{4}}}\, dx"," ",0,"int(1/(e*x+d)/(c*x^2+b*x+a)^(1/4),x)","F"
2533,0,0,1256,1.454000," ","int(1/(e*x+d)^2/(c*x^2+b*x+a)^(1/4),x)","\int \frac{1}{\left(e x +d \right)^{2} \left(c \,x^{2}+b x +a \right)^{\frac{1}{4}}}\, dx"," ",0,"int(1/(e*x+d)^2/(c*x^2+b*x+a)^(1/4),x)","F"
2534,0,0,1431,1.385000," ","int(1/(e*x+d)^3/(c*x^2+b*x+a)^(1/4),x)","\int \frac{1}{\left(e x +d \right)^{3} \left(c \,x^{2}+b x +a \right)^{\frac{1}{4}}}\, dx"," ",0,"int(1/(e*x+d)^3/(c*x^2+b*x+a)^(1/4),x)","F"
2535,0,0,344,1.306000," ","int((e*x+d)^3/(c*x^2+b*x+a)^(3/4),x)","\int \frac{\left(e x +d \right)^{3}}{\left(c \,x^{2}+b x +a \right)^{\frac{3}{4}}}\, dx"," ",0,"int((e*x+d)^3/(c*x^2+b*x+a)^(3/4),x)","F"
2536,0,0,299,1.820000," ","int((e*x+d)^2/(c*x^2+b*x+a)^(3/4),x)","\int \frac{\left(e x +d \right)^{2}}{\left(c \,x^{2}+b x +a \right)^{\frac{3}{4}}}\, dx"," ",0,"int((e*x+d)^2/(c*x^2+b*x+a)^(3/4),x)","F"
2537,0,0,246,1.227000," ","int((e*x+d)/(c*x^2+b*x+a)^(3/4),x)","\int \frac{e x +d}{\left(c \,x^{2}+b x +a \right)^{\frac{3}{4}}}\, dx"," ",0,"int((e*x+d)/(c*x^2+b*x+a)^(3/4),x)","F"
2538,0,0,217,2.949000," ","int(1/(c*x^2+b*x+a)^(3/4),x)","\int \frac{1}{\left(c \,x^{2}+b x +a \right)^{\frac{3}{4}}}\, dx"," ",0,"int(1/(c*x^2+b*x+a)^(3/4),x)","F"
2539,0,0,627,1.719000," ","int(1/(e*x+d)/(c*x^2+b*x+a)^(3/4),x)","\int \frac{1}{\left(e x +d \right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{4}}}\, dx"," ",0,"int(1/(e*x+d)/(c*x^2+b*x+a)^(3/4),x)","F"
2540,0,0,925,1.869000," ","int(1/(e*x+d)^2/(c*x^2+b*x+a)^(3/4),x)","\int \frac{1}{\left(e x +d \right)^{2} \left(c \,x^{2}+b x +a \right)^{\frac{3}{4}}}\, dx"," ",0,"int(1/(e*x+d)^2/(c*x^2+b*x+a)^(3/4),x)","F"
2541,0,0,1081,1.741000," ","int(1/(e*x+d)^3/(c*x^2+b*x+a)^(3/4),x)","\int \frac{1}{\left(e x +d \right)^{3} \left(c \,x^{2}+b x +a \right)^{\frac{3}{4}}}\, dx"," ",0,"int(1/(e*x+d)^3/(c*x^2+b*x+a)^(3/4),x)","F"
2542,0,0,736,2.889000," ","int((e*x+d)^3/(c*x^2+b*x+a)^(5/4),x)","\int \frac{\left(e x +d \right)^{3}}{\left(c \,x^{2}+b x +a \right)^{\frac{5}{4}}}\, dx"," ",0,"int((e*x+d)^3/(c*x^2+b*x+a)^(5/4),x)","F"
2543,0,0,673,1.678000," ","int((e*x+d)^2/(c*x^2+b*x+a)^(5/4),x)","\int \frac{\left(e x +d \right)^{2}}{\left(c \,x^{2}+b x +a \right)^{\frac{5}{4}}}\, dx"," ",0,"int((e*x+d)^2/(c*x^2+b*x+a)^(5/4),x)","F"
2544,0,0,570,1.875000," ","int((e*x+d)/(c*x^2+b*x+a)^(5/4),x)","\int \frac{e x +d}{\left(c \,x^{2}+b x +a \right)^{\frac{5}{4}}}\, dx"," ",0,"int((e*x+d)/(c*x^2+b*x+a)^(5/4),x)","F"
2545,0,0,531,2.792000," ","int(1/(c*x^2+b*x+a)^(5/4),x)","\int \frac{1}{\left(c \,x^{2}+b x +a \right)^{\frac{5}{4}}}\, dx"," ",0,"int(1/(c*x^2+b*x+a)^(5/4),x)","F"
2546,0,0,1286,2.010000," ","int(1/(e*x+d)/(c*x^2+b*x+a)^(5/4),x)","\int \frac{1}{\left(e x +d \right) \left(c \,x^{2}+b x +a \right)^{\frac{5}{4}}}\, dx"," ",0,"int(1/(e*x+d)/(c*x^2+b*x+a)^(5/4),x)","F"
2547,0,0,1459,1.852000," ","int(1/(e*x+d)^2/(c*x^2+b*x+a)^(5/4),x)","\int \frac{1}{\left(e x +d \right)^{2} \left(c \,x^{2}+b x +a \right)^{\frac{5}{4}}}\, dx"," ",0,"int(1/(e*x+d)^2/(c*x^2+b*x+a)^(5/4),x)","F"
2548,0,0,211,2.240000," ","int(1/(e*x+d)^(3/2)/(c*x^2+b*x+a)^(1/4),x)","\int \frac{1}{\left(e x +d \right)^{\frac{3}{2}} \left(c \,x^{2}+b x +a \right)^{\frac{1}{4}}}\, dx"," ",0,"int(1/(e*x+d)^(3/2)/(c*x^2+b*x+a)^(1/4),x)","F"
2549,1,7696,485,0.105000," ","int((e*x+d)^m*(c*x^2+b*x+a)^4,x)","\text{output too large to display}"," ",0,"result too large to display","B"
2550,1,2927,305,0.079000," ","int((e*x+d)^m*(c*x^2+b*x+a)^3,x)","\text{output too large to display}"," ",0,"(e*x+d)^(m+1)*(c^3*e^6*m^6*x^6+3*b*c^2*e^6*m^6*x^5+21*c^3*e^6*m^5*x^6+3*a*c^2*e^6*m^6*x^4+3*b^2*c*e^6*m^6*x^4+66*b*c^2*e^6*m^5*x^5-6*c^3*d*e^5*m^5*x^5+175*c^3*e^6*m^4*x^6+6*a*b*c*e^6*m^6*x^3+69*a*c^2*e^6*m^5*x^4+b^3*e^6*m^6*x^3+69*b^2*c*e^6*m^5*x^4-15*b*c^2*d*e^5*m^5*x^4+570*b*c^2*e^6*m^4*x^5-90*c^3*d*e^5*m^4*x^5+735*c^3*e^6*m^3*x^6+3*a^2*c*e^6*m^6*x^2+3*a*b^2*e^6*m^6*x^2+144*a*b*c*e^6*m^5*x^3-12*a*c^2*d*e^5*m^5*x^3+621*a*c^2*e^6*m^4*x^4+24*b^3*e^6*m^5*x^3-12*b^2*c*d*e^5*m^5*x^3+621*b^2*c*e^6*m^4*x^4-255*b*c^2*d*e^5*m^4*x^4+2460*b*c^2*e^6*m^3*x^5+30*c^3*d^2*e^4*m^4*x^4-510*c^3*d*e^5*m^3*x^5+1624*c^3*e^6*m^2*x^6+3*a^2*b*e^6*m^6*x+75*a^2*c*e^6*m^5*x^2+75*a*b^2*e^6*m^5*x^2-18*a*b*c*d*e^5*m^5*x^2+1356*a*b*c*e^6*m^4*x^3-228*a*c^2*d*e^5*m^4*x^3+2775*a*c^2*e^6*m^3*x^4-3*b^3*d*e^5*m^5*x^2+226*b^3*e^6*m^4*x^3-228*b^2*c*d*e^5*m^4*x^3+2775*b^2*c*e^6*m^3*x^4+60*b*c^2*d^2*e^4*m^4*x^3-1575*b*c^2*d*e^5*m^3*x^4+5547*b*c^2*e^6*m^2*x^5+300*c^3*d^2*e^4*m^3*x^4-1350*c^3*d*e^5*m^2*x^5+1764*c^3*e^6*m*x^6+a^3*e^6*m^6+78*a^2*b*e^6*m^5*x-6*a^2*c*d*e^5*m^5*x+741*a^2*c*e^6*m^4*x^2-6*a*b^2*d*e^5*m^5*x+741*a*b^2*e^6*m^4*x^2-378*a*b*c*d*e^5*m^4*x^2+6336*a*b*c*e^6*m^3*x^3+36*a*c^2*d^2*e^4*m^4*x^2-1572*a*c^2*d*e^5*m^3*x^3+6432*a*c^2*e^6*m^2*x^4-63*b^3*d*e^5*m^4*x^2+1056*b^3*e^6*m^3*x^3+36*b^2*c*d^2*e^4*m^4*x^2-1572*b^2*c*d*e^5*m^3*x^3+6432*b^2*c*e^6*m^2*x^4+780*b*c^2*d^2*e^4*m^3*x^3-4425*b*c^2*d*e^5*m^2*x^4+6114*b*c^2*e^6*m*x^5-120*c^3*d^3*e^3*m^3*x^3+1050*c^3*d^2*e^4*m^2*x^4-1644*c^3*d*e^5*m*x^5+720*c^3*e^6*x^6+27*a^3*e^6*m^5-3*a^2*b*d*e^5*m^5+810*a^2*b*e^6*m^4*x-138*a^2*c*d*e^5*m^4*x+3657*a^2*c*e^6*m^3*x^2-138*a*b^2*d*e^5*m^4*x+3657*a*b^2*e^6*m^3*x^2+36*a*b*c*d^2*e^4*m^4*x-2934*a*b*c*d*e^5*m^3*x^2+15270*a*b*c*e^6*m^2*x^3+576*a*c^2*d^2*e^4*m^3*x^2-4812*a*c^2*d*e^5*m^2*x^3+7236*a*c^2*e^6*m*x^4+6*b^3*d^2*e^4*m^4*x-489*b^3*d*e^5*m^3*x^2+2545*b^3*e^6*m^2*x^3+576*b^2*c*d^2*e^4*m^3*x^2-4812*b^2*c*d*e^5*m^2*x^3+7236*b^2*c*e^6*m*x^4-180*b*c^2*d^3*e^3*m^3*x^2+3180*b*c^2*d^2*e^4*m^2*x^3-5610*b*c^2*d*e^5*m*x^4+2520*b*c^2*e^6*x^5-720*c^3*d^3*e^3*m^2*x^3+1500*c^3*d^2*e^4*m*x^4-720*c^3*d*e^5*x^5+295*a^3*e^6*m^4-75*a^2*b*d*e^5*m^4+4260*a^2*b*e^6*m^3*x+6*a^2*c*d^2*e^4*m^4-1206*a^2*c*d*e^5*m^3*x+9336*a^2*c*e^6*m^2*x^2+6*a*b^2*d^2*e^4*m^4-1206*a*b^2*d*e^5*m^3*x+9336*a*b^2*e^6*m^2*x^2+684*a*b*c*d^2*e^4*m^3*x-10206*a*b*c*d*e^5*m^2*x^2+17712*a*b*c*e^6*m*x^3-72*a*c^2*d^3*e^3*m^3*x+2988*a*c^2*d^2*e^4*m^2*x^2-6480*a*c^2*d*e^5*m*x^3+3024*a*c^2*e^6*x^4+114*b^3*d^2*e^4*m^3*x-1701*b^3*d*e^5*m^2*x^2+2952*b^3*e^6*m*x^3-72*b^2*c*d^3*e^3*m^3*x+2988*b^2*c*d^2*e^4*m^2*x^2-6480*b^2*c*d*e^5*m*x^3+3024*b^2*c*e^6*x^4-1800*b*c^2*d^3*e^3*m^2*x^2+4980*b*c^2*d^2*e^4*m*x^3-2520*b*c^2*d*e^5*x^4+360*c^3*d^4*e^2*m^2*x^2-1320*c^3*d^3*e^3*m*x^3+720*c^3*d^2*e^4*x^4+1665*a^3*e^6*m^3-735*a^2*b*d*e^5*m^3+11787*a^2*b*e^6*m^2*x+132*a^2*c*d^2*e^4*m^3-4902*a^2*c*d*e^5*m^2*x+11388*a^2*c*e^6*m*x^2+132*a*b^2*d^2*e^4*m^3-4902*a*b^2*d*e^5*m^2*x+11388*a*b^2*e^6*m*x^2-36*a*b*c*d^3*e^3*m^3+4500*a*b*c*d^2*e^4*m^2*x-15192*a*b*c*d*e^5*m*x^2+7560*a*b*c*e^6*x^3-1008*a*c^2*d^3*e^3*m^2*x+5472*a*c^2*d^2*e^4*m*x^2-3024*a*c^2*d*e^5*x^3-6*b^3*d^3*e^3*m^3+750*b^3*d^2*e^4*m^2*x-2532*b^3*d*e^5*m*x^2+1260*b^3*e^6*x^3-1008*b^2*c*d^3*e^3*m^2*x+5472*b^2*c*d^2*e^4*m*x^2-3024*b^2*c*d*e^5*x^3+360*b*c^2*d^4*e^2*m^2*x-4140*b*c^2*d^3*e^3*m*x^2+2520*b*c^2*d^2*e^4*x^3+1080*c^3*d^4*e^2*m*x^2-720*c^3*d^3*e^3*x^3+5104*a^3*e^6*m^2-3525*a^2*b*d*e^5*m^2+15822*a^2*b*e^6*m*x+1074*a^2*c*d^2*e^4*m^2-8868*a^2*c*d*e^5*m*x+5040*a^2*c*e^6*x^2+1074*a*b^2*d^2*e^4*m^2-8868*a*b^2*d*e^5*m*x+5040*a*b^2*e^6*x^2-648*a*b*c*d^3*e^3*m^2+11412*a*b*c*d^2*e^4*m*x-7560*a*b*c*d*e^5*x^2+72*a*c^2*d^4*e^2*m^2-3960*a*c^2*d^3*e^3*m*x+3024*a*c^2*d^2*e^4*x^2-108*b^3*d^3*e^3*m^2+1902*b^3*d^2*e^4*m*x-1260*b^3*d*e^5*x^2+72*b^2*c*d^4*e^2*m^2-3960*b^2*c*d^3*e^3*m*x+3024*b^2*c*d^2*e^4*x^2+2880*b*c^2*d^4*e^2*m*x-2520*b*c^2*d^3*e^3*x^2-720*c^3*d^5*e*m*x+720*c^3*d^4*e^2*x^2+8028*a^3*e^6*m-8262*a^2*b*d*e^5*m+7560*a^2*b*e^6*x+3828*a^2*c*d^2*e^4*m-5040*a^2*c*d*e^5*x+3828*a*b^2*d^2*e^4*m-5040*a*b^2*d*e^5*x-3852*a*b*c*d^3*e^3*m+7560*a*b*c*d^2*e^4*x+936*a*c^2*d^4*e^2*m-3024*a*c^2*d^3*e^3*x-642*b^3*d^3*e^3*m+1260*b^3*d^2*e^4*x+936*b^2*c*d^4*e^2*m-3024*b^2*c*d^3*e^3*x-360*b*c^2*d^5*e*m+2520*b*c^2*d^4*e^2*x-720*c^3*d^5*e*x+5040*a^3*e^6-7560*a^2*b*d*e^5+5040*a^2*c*d^2*e^4+5040*a*b^2*d^2*e^4-7560*a*b*c*d^3*e^3+3024*a*c^2*d^4*e^2-1260*b^3*d^3*e^3+3024*b^2*c*d^4*e^2-2520*b*c^2*d^5*e+720*c^3*d^6)/e^7/(m^7+28*m^6+322*m^5+1960*m^4+6769*m^3+13132*m^2+13068*m+5040)","B"
2551,1,822,178,0.060000," ","int((e*x+d)^m*(c*x^2+b*x+a)^2,x)","\frac{\left(c^{2} e^{4} m^{4} x^{4}+2 b c \,e^{4} m^{4} x^{3}+10 c^{2} e^{4} m^{3} x^{4}+2 a c \,e^{4} m^{4} x^{2}+b^{2} e^{4} m^{4} x^{2}+22 b c \,e^{4} m^{3} x^{3}-4 c^{2} d \,e^{3} m^{3} x^{3}+35 c^{2} e^{4} m^{2} x^{4}+2 a b \,e^{4} m^{4} x +24 a c \,e^{4} m^{3} x^{2}+12 b^{2} e^{4} m^{3} x^{2}-6 b c d \,e^{3} m^{3} x^{2}+82 b c \,e^{4} m^{2} x^{3}-24 c^{2} d \,e^{3} m^{2} x^{3}+50 c^{2} e^{4} m \,x^{4}+a^{2} e^{4} m^{4}+26 a b \,e^{4} m^{3} x -4 a c d \,e^{3} m^{3} x +98 a c \,e^{4} m^{2} x^{2}-2 b^{2} d \,e^{3} m^{3} x +49 b^{2} e^{4} m^{2} x^{2}-48 b c d \,e^{3} m^{2} x^{2}+122 b c \,e^{4} m \,x^{3}+12 c^{2} d^{2} e^{2} m^{2} x^{2}-44 c^{2} d \,e^{3} m \,x^{3}+24 c^{2} x^{4} e^{4}+14 a^{2} e^{4} m^{3}-2 a b d \,e^{3} m^{3}+118 a b \,e^{4} m^{2} x -40 a c d \,e^{3} m^{2} x +156 a c \,e^{4} m \,x^{2}-20 b^{2} d \,e^{3} m^{2} x +78 b^{2} e^{4} m \,x^{2}+12 b c \,d^{2} e^{2} m^{2} x -102 b c d \,e^{3} m \,x^{2}+60 b c \,e^{4} x^{3}+36 c^{2} d^{2} e^{2} m \,x^{2}-24 c^{2} d \,e^{3} x^{3}+71 a^{2} e^{4} m^{2}-24 a b d \,e^{3} m^{2}+214 a b \,e^{4} m x +4 a c \,d^{2} e^{2} m^{2}-116 a c d \,e^{3} m x +80 a c \,e^{4} x^{2}+2 b^{2} d^{2} e^{2} m^{2}-58 b^{2} d \,e^{3} m x +40 b^{2} e^{4} x^{2}+72 b c \,d^{2} e^{2} m x -60 b c d \,e^{3} x^{2}-24 c^{2} d^{3} e m x +24 c^{2} d^{2} e^{2} x^{2}+154 a^{2} e^{4} m -94 a b d \,e^{3} m +120 a b x \,e^{4}+36 a c \,d^{2} e^{2} m -80 a c d \,e^{3} x +18 b^{2} d^{2} e^{2} m -40 b^{2} d \,e^{3} x -12 b c \,d^{3} e m +60 b c \,d^{2} e^{2} x -24 c^{2} d^{3} x e +120 a^{2} e^{4}-120 a b d \,e^{3}+80 a c \,d^{2} e^{2}+40 b^{2} d^{2} e^{2}-60 b c \,d^{3} e +24 c^{2} d^{4}\right) \left(e x +d \right)^{m +1}}{\left(m^{5}+15 m^{4}+85 m^{3}+225 m^{2}+274 m +120\right) e^{5}}"," ",0,"(e*x+d)^(m+1)*(c^2*e^4*m^4*x^4+2*b*c*e^4*m^4*x^3+10*c^2*e^4*m^3*x^4+2*a*c*e^4*m^4*x^2+b^2*e^4*m^4*x^2+22*b*c*e^4*m^3*x^3-4*c^2*d*e^3*m^3*x^3+35*c^2*e^4*m^2*x^4+2*a*b*e^4*m^4*x+24*a*c*e^4*m^3*x^2+12*b^2*e^4*m^3*x^2-6*b*c*d*e^3*m^3*x^2+82*b*c*e^4*m^2*x^3-24*c^2*d*e^3*m^2*x^3+50*c^2*e^4*m*x^4+a^2*e^4*m^4+26*a*b*e^4*m^3*x-4*a*c*d*e^3*m^3*x+98*a*c*e^4*m^2*x^2-2*b^2*d*e^3*m^3*x+49*b^2*e^4*m^2*x^2-48*b*c*d*e^3*m^2*x^2+122*b*c*e^4*m*x^3+12*c^2*d^2*e^2*m^2*x^2-44*c^2*d*e^3*m*x^3+24*c^2*e^4*x^4+14*a^2*e^4*m^3-2*a*b*d*e^3*m^3+118*a*b*e^4*m^2*x-40*a*c*d*e^3*m^2*x+156*a*c*e^4*m*x^2-20*b^2*d*e^3*m^2*x+78*b^2*e^4*m*x^2+12*b*c*d^2*e^2*m^2*x-102*b*c*d*e^3*m*x^2+60*b*c*e^4*x^3+36*c^2*d^2*e^2*m*x^2-24*c^2*d*e^3*x^3+71*a^2*e^4*m^2-24*a*b*d*e^3*m^2+214*a*b*e^4*m*x+4*a*c*d^2*e^2*m^2-116*a*c*d*e^3*m*x+80*a*c*e^4*x^2+2*b^2*d^2*e^2*m^2-58*b^2*d*e^3*m*x+40*b^2*e^4*x^2+72*b*c*d^2*e^2*m*x-60*b*c*d*e^3*x^2-24*c^2*d^3*e*m*x+24*c^2*d^2*e^2*x^2+154*a^2*e^4*m-94*a*b*d*e^3*m+120*a*b*e^4*x+36*a*c*d^2*e^2*m-80*a*c*d*e^3*x+18*b^2*d^2*e^2*m-40*b^2*d*e^3*x-12*b*c*d^3*e*m+60*b*c*d^2*e^2*x-24*c^2*d^3*e*x+120*a^2*e^4-120*a*b*d*e^3+80*a*c*d^2*e^2+40*b^2*d^2*e^2-60*b*c*d^3*e+24*c^2*d^4)/e^5/(m^5+15*m^4+85*m^3+225*m^2+274*m+120)","B"
2552,1,135,82,0.048000," ","int((e*x+d)^m*(c*x^2+b*x+a),x)","\frac{\left(c \,e^{2} m^{2} x^{2}+b \,e^{2} m^{2} x +3 c \,e^{2} m \,x^{2}+a \,e^{2} m^{2}+4 b \,e^{2} m x -2 c d e m x +2 c \,e^{2} x^{2}+5 a \,e^{2} m -b d e m +3 b \,e^{2} x -2 c d e x +6 a \,e^{2}-3 b d e +2 c \,d^{2}\right) \left(e x +d \right)^{m +1}}{\left(m^{3}+6 m^{2}+11 m +6\right) e^{3}}"," ",0,"(e*x+d)^(m+1)*(c*e^2*m^2*x^2+b*e^2*m^2*x+3*c*e^2*m*x^2+a*e^2*m^2+4*b*e^2*m*x-2*c*d*e*m*x+2*c*e^2*x^2+5*a*e^2*m-b*d*e*m+3*b*e^2*x-2*c*d*e*x+6*a*e^2-3*b*d*e+2*c*d^2)/e^3/(m^3+6*m^2+11*m+6)","A"
2553,0,0,183,1.398000," ","int((e*x+d)^m/(c*x^2+b*x+a),x)","\int \frac{\left(e x +d \right)^{m}}{c \,x^{2}+b x +a}\, dx"," ",0,"int((e*x+d)^m/(c*x^2+b*x+a),x)","F"
2554,0,0,413,1.435000," ","int((e*x+d)^m/(c*x^2+b*x+a)^2,x)","\int \frac{\left(e x +d \right)^{m}}{\left(c \,x^{2}+b x +a \right)^{2}}\, dx"," ",0,"int((e*x+d)^m/(c*x^2+b*x+a)^2,x)","F"
2555,0,0,171,1.592000," ","int((e*x+d)^m*(c*x^2+b*x+a)^(5/2),x)","\int \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} \left(e x +d \right)^{m}\, dx"," ",0,"int((e*x+d)^m*(c*x^2+b*x+a)^(5/2),x)","F"
2556,0,0,171,1.453000," ","int((e*x+d)^m*(c*x^2+b*x+a)^(3/2),x)","\int \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} \left(e x +d \right)^{m}\, dx"," ",0,"int((e*x+d)^m*(c*x^2+b*x+a)^(3/2),x)","F"
2557,0,0,171,1.379000," ","int((e*x+d)^m*(c*x^2+b*x+a)^(1/2),x)","\int \sqrt{c \,x^{2}+b x +a}\, \left(e x +d \right)^{m}\, dx"," ",0,"int((e*x+d)^m*(c*x^2+b*x+a)^(1/2),x)","F"
2558,0,0,171,1.789000," ","int((e*x+d)^m/(c*x^2+b*x+a)^(1/2),x)","\int \frac{\left(e x +d \right)^{m}}{\sqrt{c \,x^{2}+b x +a}}\, dx"," ",0,"int((e*x+d)^m/(c*x^2+b*x+a)^(1/2),x)","F"
2559,0,0,171,11.988000," ","int((e*x+d)^m/(c*x^2+b*x+a)^(3/2),x)","\int \frac{\left(e x +d \right)^{m}}{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}}}\, dx"," ",0,"int((e*x+d)^m/(c*x^2+b*x+a)^(3/2),x)","F"
2560,0,0,171,1.512000," ","int((e*x+d)^m/(c*x^2+b*x+a)^(5/2),x)","\int \frac{\left(e x +d \right)^{m}}{\left(c \,x^{2}+b x +a \right)^{\frac{5}{2}}}\, dx"," ",0,"int((e*x+d)^m/(c*x^2+b*x+a)^(5/2),x)","F"
2561,0,0,129,1.483000," ","int((d*x)^m*(c*x^2+b*x+a)^p,x)","\int \left(d x \right)^{m} \left(c \,x^{2}+b x +a \right)^{p}\, dx"," ",0,"int((d*x)^m*(c*x^2+b*x+a)^p,x)","F"
2562,0,0,179,1.473000," ","int((e*x+d)^m*(c*x^2+b*x+a)^p,x)","\int \left(e x +d \right)^{m} \left(c \,x^{2}+b x +a \right)^{p}\, dx"," ",0,"int((e*x+d)^m*(c*x^2+b*x+a)^p,x)","F"
2563,0,0,312,1.469000," ","int((e*x+d)^3*(c*x^2+b*x+a)^p,x)","\int \left(e x +d \right)^{3} \left(c \,x^{2}+b x +a \right)^{p}\, dx"," ",0,"int((e*x+d)^3*(c*x^2+b*x+a)^p,x)","F"
2564,0,0,235,1.796000," ","int((e*x+d)^2*(c*x^2+b*x+a)^p,x)","\int \left(e x +d \right)^{2} \left(c \,x^{2}+b x +a \right)^{p}\, dx"," ",0,"int((e*x+d)^2*(c*x^2+b*x+a)^p,x)","F"
2565,0,0,147,1.315000," ","int((e*x+d)*(c*x^2+b*x+a)^p,x)","\int \left(e x +d \right) \left(c \,x^{2}+b x +a \right)^{p}\, dx"," ",0,"int((e*x+d)*(c*x^2+b*x+a)^p,x)","F"
2566,0,0,111,0.079000," ","int((c*x^2+b*x+a)^p,x)","\int \left(c \,x^{2}+b x +a \right)^{p}\, dx"," ",0,"int((c*x^2+b*x+a)^p,x)","F"
2567,0,0,172,1.584000," ","int((c*x^2+b*x+a)^p/(e*x+d),x)","\int \frac{\left(c \,x^{2}+b x +a \right)^{p}}{e x +d}\, dx"," ",0,"int((c*x^2+b*x+a)^p/(e*x+d),x)","F"
2568,0,0,182,1.602000," ","int((c*x^2+b*x+a)^p/(e*x+d)^2,x)","\int \frac{\left(c \,x^{2}+b x +a \right)^{p}}{\left(e x +d \right)^{2}}\, dx"," ",0,"int((c*x^2+b*x+a)^p/(e*x+d)^2,x)","F"
2569,0,0,186,1.447000," ","int((c*x^2+b*x+a)^p/(e*x+d)^3,x)","\int \frac{\left(c \,x^{2}+b x +a \right)^{p}}{\left(e x +d \right)^{3}}\, dx"," ",0,"int((c*x^2+b*x+a)^p/(e*x+d)^3,x)","F"
2570,0,0,169,1.567000," ","int((e*x+d)^(3/2)*(c*x^2+b*x+a)^p,x)","\int \left(e x +d \right)^{\frac{3}{2}} \left(c \,x^{2}+b x +a \right)^{p}\, dx"," ",0,"int((e*x+d)^(3/2)*(c*x^2+b*x+a)^p,x)","F"
2571,0,0,169,3.030000," ","int((e*x+d)^(1/2)*(c*x^2+b*x+a)^p,x)","\int \sqrt{e x +d}\, \left(c \,x^{2}+b x +a \right)^{p}\, dx"," ",0,"int((e*x+d)^(1/2)*(c*x^2+b*x+a)^p,x)","F"
2572,0,0,169,3.100000," ","int((c*x^2+b*x+a)^p/(e*x+d)^(1/2),x)","\int \frac{\left(c \,x^{2}+b x +a \right)^{p}}{\sqrt{e x +d}}\, dx"," ",0,"int((c*x^2+b*x+a)^p/(e*x+d)^(1/2),x)","F"
2573,0,0,169,1.970000," ","int((c*x^2+b*x+a)^p/(e*x+d)^(3/2),x)","\int \frac{\left(c \,x^{2}+b x +a \right)^{p}}{\left(e x +d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((c*x^2+b*x+a)^p/(e*x+d)^(3/2),x)","F"
2574,0,0,187,1.541000," ","int((c*x^2+b*x+a)^p/((e*x+d)^(2*p)),x)","\int \left(e x +d \right)^{-2 p} \left(c \,x^{2}+b x +a \right)^{p}\, dx"," ",0,"int((c*x^2+b*x+a)^p/((e*x+d)^(2*p)),x)","F"
2575,0,0,182,2.047000," ","int((e*x+d)^(-2*p-1)*(c*x^2+b*x+a)^p,x)","\int \left(e x +d \right)^{-2 p -1} \left(c \,x^{2}+b x +a \right)^{p}\, dx"," ",0,"int((e*x+d)^(-2*p-1)*(c*x^2+b*x+a)^p,x)","F"
2576,0,0,232,1.379000," ","int((e*x+d)^(-2*p-2)*(c*x^2+b*x+a)^p,x)","\int \left(e x +d \right)^{-2 p -2} \left(c \,x^{2}+b x +a \right)^{p}\, dx"," ",0,"int((e*x+d)^(-2*p-2)*(c*x^2+b*x+a)^p,x)","F"
2577,0,0,314,1.873000," ","int((e*x+d)^(-2*p-3)*(c*x^2+b*x+a)^p,x)","\int \left(e x +d \right)^{-2 p -3} \left(c \,x^{2}+b x +a \right)^{p}\, dx"," ",0,"int((e*x+d)^(-2*p-3)*(c*x^2+b*x+a)^p,x)","F"
2578,0,0,424,1.525000," ","int((e*x+d)^(-2*p-4)*(c*x^2+b*x+a)^p,x)","\int \left(e x +d \right)^{-2 p -4} \left(c \,x^{2}+b x +a \right)^{p}\, dx"," ",0,"int((e*x+d)^(-2*p-4)*(c*x^2+b*x+a)^p,x)","F"
2579,0,0,557,1.864000," ","int((e*x+d)^(-2*p-5)*(c*x^2+b*x+a)^p,x)","\int \left(e x +d \right)^{-2 p -5} \left(c \,x^{2}+b x +a \right)^{p}\, dx"," ",0,"int((e*x+d)^(-2*p-5)*(c*x^2+b*x+a)^p,x)","F"
2580,0,0,789,1.829000," ","int((e*x+d)^(-2*p-6)*(c*x^2+b*x+a)^p,x)","\int \left(e x +d \right)^{-2 p -6} \left(c \,x^{2}+b x +a \right)^{p}\, dx"," ",0,"int((e*x+d)^(-2*p-6)*(c*x^2+b*x+a)^p,x)","F"
2581,0,0,410,1.909000," ","int((e*x+d)^m*(c*x^2+b*x+a)^(-2-1/2*m),x)","\int \left(e x +d \right)^{m} \left(c \,x^{2}+b x +a \right)^{-\frac{m}{2}-2}\, dx"," ",0,"int((e*x+d)^m*(c*x^2+b*x+a)^(-2-1/2*m),x)","F"
2582,0,0,82,3.846000," ","int(1/(x+1)^(1/3)/(x^2-x+1)^(1/3),x)","\int \frac{1}{\left(x +1\right)^{\frac{1}{3}} \left(x^{2}-x +1\right)^{\frac{1}{3}}}\, dx"," ",0,"int(1/(x+1)^(1/3)/(x^2-x+1)^(1/3),x)","F"
2583,0,0,35,2.391000," ","int(1/(x+1)^(2/3)/(x^2-x+1)^(2/3),x)","\int \frac{1}{\left(x +1\right)^{\frac{2}{3}} \left(x^{2}-x +1\right)^{\frac{2}{3}}}\, dx"," ",0,"int(1/(x+1)^(2/3)/(x^2-x+1)^(2/3),x)","F"
2584,0,0,39,1.972000," ","int((x+1)^p*(x^2-x+1)^p,x)","\int \left(x +1\right)^{p} \left(x^{2}-x +1\right)^{p}\, dx"," ",0,"int((x+1)^p*(x^2-x+1)^p,x)","F"
2585,0,0,88,2.882000," ","int(1/(-x+1)^(1/3)/(x^2+x+1)^(1/3),x)","\int \frac{1}{\left(-x +1\right)^{\frac{1}{3}} \left(x^{2}+x +1\right)^{\frac{1}{3}}}\, dx"," ",0,"int(1/(-x+1)^(1/3)/(x^2+x+1)^(1/3),x)","F"
2586,0,0,35,2.133000," ","int(1/(-x+1)^(2/3)/(x^2+x+1)^(2/3),x)","\int \frac{1}{\left(-x +1\right)^{\frac{2}{3}} \left(x^{2}+x +1\right)^{\frac{2}{3}}}\, dx"," ",0,"int(1/(-x+1)^(2/3)/(x^2+x+1)^(2/3),x)","F"
2587,0,0,39,2.736000," ","int((-x+1)^p*(x^2+x+1)^p,x)","\int \left(-x +1\right)^{p} \left(x^{2}+x +1\right)^{p}\, dx"," ",0,"int((-x+1)^p*(x^2+x+1)^p,x)","F"
2588,0,0,167,2.196000," ","int(1/(-c*e*x+b*e)^(1/3)/(c^2*x^2+b*c*x+b^2)^(1/3),x)","\int \frac{1}{\left(-c e x +b e \right)^{\frac{1}{3}} \left(c^{2} x^{2}+b c x +b^{2}\right)^{\frac{1}{3}}}\, dx"," ",0,"int(1/(-c*e*x+b*e)^(1/3)/(c^2*x^2+b*c*x+b^2)^(1/3),x)","F"
2589,0,0,61,3.095000," ","int(1/(-c*e*x+b*e)^(2/3)/(c^2*x^2+b*c*x+b^2)^(2/3),x)","\int \frac{1}{\left(-c e x +b e \right)^{\frac{2}{3}} \left(c^{2} x^{2}+b c x +b^{2}\right)^{\frac{2}{3}}}\, dx"," ",0,"int(1/(-c*e*x+b*e)^(2/3)/(c^2*x^2+b*c*x+b^2)^(2/3),x)","F"
2590,0,0,65,2.122000," ","int((-c*e*x+b*e)^p*(c^2*x^2+b*c*x+b^2)^p,x)","\int \left(-c e x +b e \right)^{p} \left(c^{2} x^{2}+b c x +b^{2}\right)^{p}\, dx"," ",0,"int((-c*e*x+b*e)^p*(c^2*x^2+b*c*x+b^2)^p,x)","F"