1,1,97,0,0.199601," ","integrate(x^3*(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\frac{1}{1920} \, \sqrt{c x^{2} + b x} {\left(2 \, {\left(4 \, {\left(6 \, {\left(8 \, x + \frac{b}{c}\right)} x - \frac{7 \, b^{2}}{c^{2}}\right)} x + \frac{35 \, b^{3}}{c^{3}}\right)} x - \frac{105 \, b^{4}}{c^{4}}\right)} - \frac{7 \, b^{5} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{256 \, c^{\frac{9}{2}}}"," ",0,"1/1920*sqrt(c*x^2 + b*x)*(2*(4*(6*(8*x + b/c)*x - 7*b^2/c^2)*x + 35*b^3/c^3)*x - 105*b^4/c^4) - 7/256*b^5*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(9/2)","A",0
2,1,85,0,0.202216," ","integrate(x^2*(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\frac{1}{192} \, \sqrt{c x^{2} + b x} {\left(2 \, {\left(4 \, {\left(6 \, x + \frac{b}{c}\right)} x - \frac{5 \, b^{2}}{c^{2}}\right)} x + \frac{15 \, b^{3}}{c^{3}}\right)} + \frac{5 \, b^{4} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{128 \, c^{\frac{7}{2}}}"," ",0,"1/192*sqrt(c*x^2 + b*x)*(2*(4*(6*x + b/c)*x - 5*b^2/c^2)*x + 15*b^3/c^3) + 5/128*b^4*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(7/2)","A",0
3,1,73,0,0.195004," ","integrate(x*(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\frac{1}{24} \, \sqrt{c x^{2} + b x} {\left(2 \, {\left(4 \, x + \frac{b}{c}\right)} x - \frac{3 \, b^{2}}{c^{2}}\right)} - \frac{b^{3} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{16 \, c^{\frac{5}{2}}}"," ",0,"1/24*sqrt(c*x^2 + b*x)*(2*(4*x + b/c)*x - 3*b^2/c^2) - 1/16*b^3*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(5/2)","A",0
4,1,61,0,0.204360," ","integrate((c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{c x^{2} + b x} {\left(2 \, x + \frac{b}{c}\right)} + \frac{b^{2} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{8 \, c^{\frac{3}{2}}}"," ",0,"1/4*sqrt(c*x^2 + b*x)*(2*x + b/c) + 1/8*b^2*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(3/2)","A",0
5,1,48,0,0.233875," ","integrate((c*x^2+b*x)^(1/2)/x,x, algorithm=""giac"")","-\frac{b \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{2 \, \sqrt{c}} + \sqrt{c x^{2} + b x}"," ",0,"-1/2*b*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/sqrt(c) + sqrt(c*x^2 + b*x)","A",0
6,1,60,0,0.307393," ","integrate((c*x^2+b*x)^(1/2)/x^2,x, algorithm=""giac"")","-\sqrt{c} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right) + \frac{2 \, b}{\sqrt{c} x - \sqrt{c x^{2} + b x}}"," ",0,"-sqrt(c)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b)) + 2*b/(sqrt(c)*x - sqrt(c*x^2 + b*x))","A",0
7,1,76,0,0.174381," ","integrate((c*x^2+b*x)^(1/2)/x^3,x, algorithm=""giac"")","\frac{2 \, {\left(3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} c + 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} b \sqrt{c} + b^{2}\right)}}{3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3}}"," ",0,"2/3*(3*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*c + 3*(sqrt(c)*x - sqrt(c*x^2 + b*x))*b*sqrt(c) + b^2)/(sqrt(c)*x - sqrt(c*x^2 + b*x))^3","B",0
8,1,107,0,0.226909," ","integrate((c*x^2+b*x)^(1/2)/x^4,x, algorithm=""giac"")","\frac{2 \, {\left(15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} c^{\frac{3}{2}} + 25 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} b c + 15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} b^{2} \sqrt{c} + 3 \, b^{3}\right)}}{15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5}}"," ",0,"2/15*(15*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*c^(3/2) + 25*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*b*c + 15*(sqrt(c)*x - sqrt(c*x^2 + b*x))*b^2*sqrt(c) + 3*b^3)/(sqrt(c)*x - sqrt(c*x^2 + b*x))^5","B",0
9,1,136,0,0.226163," ","integrate((c*x^2+b*x)^(1/2)/x^5,x, algorithm=""giac"")","\frac{2 \, {\left(140 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} c^{2} + 315 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} b c^{\frac{3}{2}} + 273 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} b^{2} c + 105 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} b^{3} \sqrt{c} + 15 \, b^{4}\right)}}{105 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7}}"," ",0,"2/105*(140*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*c^2 + 315*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*b*c^(3/2) + 273*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*b^2*c + 105*(sqrt(c)*x - sqrt(c*x^2 + b*x))*b^3*sqrt(c) + 15*b^4)/(sqrt(c)*x - sqrt(c*x^2 + b*x))^7","B",0
10,1,165,0,0.200147," ","integrate((c*x^2+b*x)^(1/2)/x^6,x, algorithm=""giac"")","\frac{2 \, {\left(630 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} c^{\frac{5}{2}} + 1764 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} b c^{2} + 1995 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} b^{2} c^{\frac{3}{2}} + 1125 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} b^{3} c + 315 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} b^{4} \sqrt{c} + 35 \, b^{5}\right)}}{315 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9}}"," ",0,"2/315*(630*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*c^(5/2) + 1764*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*b*c^2 + 1995*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*b^2*c^(3/2) + 1125*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*b^3*c + 315*(sqrt(c)*x - sqrt(c*x^2 + b*x))*b^4*sqrt(c) + 35*b^5)/(sqrt(c)*x - sqrt(c*x^2 + b*x))^9","A",0
11,1,194,0,0.183847," ","integrate((c*x^2+b*x)^(1/2)/x^7,x, algorithm=""giac"")","\frac{2 \, {\left(11088 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} c^{3} + 36960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} b c^{\frac{5}{2}} + 51480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} b^{2} c^{2} + 38115 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} b^{3} c^{\frac{3}{2}} + 15785 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} b^{4} c + 3465 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} b^{5} \sqrt{c} + 315 \, b^{6}\right)}}{3465 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{11}}"," ",0,"2/3465*(11088*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*c^3 + 36960*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*b*c^(5/2) + 51480*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*b^2*c^2 + 38115*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*b^3*c^(3/2) + 15785*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*b^4*c + 3465*(sqrt(c)*x - sqrt(c*x^2 + b*x))*b^5*sqrt(c) + 315*b^6)/(sqrt(c)*x - sqrt(c*x^2 + b*x))^11","A",0
12,1,108,0,0.233808," ","integrate(x^2*(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","-\frac{7 \, b^{6} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{1024 \, c^{\frac{9}{2}}} + \frac{1}{7680} \, \sqrt{c x^{2} + b x} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(10 \, c x + 13 \, b\right)} x + \frac{3 \, b^{2}}{c}\right)} x - \frac{7 \, b^{3}}{c^{2}}\right)} x + \frac{35 \, b^{4}}{c^{3}}\right)} x - \frac{105 \, b^{5}}{c^{4}}\right)}"," ",0,"-7/1024*b^6*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(9/2) + 1/7680*sqrt(c*x^2 + b*x)*(2*(4*(2*(8*(10*c*x + 13*b)*x + 3*b^2/c)*x - 7*b^3/c^2)*x + 35*b^4/c^3)*x - 105*b^5/c^4)","A",0
13,1,95,0,0.242503," ","integrate(x*(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","\frac{3 \, b^{5} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{256 \, c^{\frac{7}{2}}} + \frac{1}{640} \, \sqrt{c x^{2} + b x} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, c x + 11 \, b\right)} x + \frac{b^{2}}{c}\right)} x - \frac{5 \, b^{3}}{c^{2}}\right)} x + \frac{15 \, b^{4}}{c^{3}}\right)}"," ",0,"3/256*b^5*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(7/2) + 1/640*sqrt(c*x^2 + b*x)*(2*(4*(2*(8*c*x + 11*b)*x + b^2/c)*x - 5*b^3/c^2)*x + 15*b^4/c^3)","A",0
14,1,83,0,0.212460," ","integrate((c*x^2+b*x)^(3/2),x, algorithm=""giac"")","-\frac{3 \, b^{4} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{128 \, c^{\frac{5}{2}}} + \frac{1}{64} \, \sqrt{c x^{2} + b x} {\left(2 \, {\left(4 \, {\left(2 \, c x + 3 \, b\right)} x + \frac{b^{2}}{c}\right)} x - \frac{3 \, b^{3}}{c^{2}}\right)}"," ",0,"-3/128*b^4*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(5/2) + 1/64*sqrt(c*x^2 + b*x)*(2*(4*(2*c*x + 3*b)*x + b^2/c)*x - 3*b^3/c^2)","A",0
15,1,72,0,0.207900," ","integrate((c*x^2+b*x)^(3/2)/x,x, algorithm=""giac"")","\frac{b^{3} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{16 \, c^{\frac{3}{2}}} + \frac{1}{24} \, \sqrt{c x^{2} + b x} {\left(2 \, {\left(4 \, c x + 7 \, b\right)} x + \frac{3 \, b^{2}}{c}\right)}"," ",0,"1/16*b^3*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(3/2) + 1/24*sqrt(c*x^2 + b*x)*(2*(4*c*x + 7*b)*x + 3*b^2/c)","A",0
16,1,60,0,0.202786," ","integrate((c*x^2+b*x)^(3/2)/x^2,x, algorithm=""giac"")","-\frac{3 \, b^{2} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{8 \, \sqrt{c}} + \frac{1}{4} \, \sqrt{c x^{2} + b x} {\left(2 \, c x + 5 \, b\right)}"," ",0,"-3/8*b^2*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/sqrt(c) + 1/4*sqrt(c*x^2 + b*x)*(2*c*x + 5*b)","A",0
17,1,76,0,0.225899," ","integrate((c*x^2+b*x)^(3/2)/x^3,x, algorithm=""giac"")","-\frac{3}{2} \, b \sqrt{c} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right) + \sqrt{c x^{2} + b x} c + \frac{2 \, b^{2}}{\sqrt{c} x - \sqrt{c x^{2} + b x}}"," ",0,"-3/2*b*sqrt(c)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b)) + sqrt(c*x^2 + b*x)*c + 2*b^2/(sqrt(c)*x - sqrt(c*x^2 + b*x))","A",0
18,1,115,0,0.221729," ","integrate((c*x^2+b*x)^(3/2)/x^4,x, algorithm=""giac"")","-c^{\frac{3}{2}} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right) + \frac{2 \, {\left(6 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} b c + 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} b^{2} \sqrt{c} + b^{3}\right)}}{3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3}}"," ",0,"-c^(3/2)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b)) + 2/3*(6*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*b*c + 3*(sqrt(c)*x - sqrt(c*x^2 + b*x))*b^2*sqrt(c) + b^3)/(sqrt(c)*x - sqrt(c*x^2 + b*x))^3","B",0
19,1,134,0,0.222970," ","integrate((c*x^2+b*x)^(3/2)/x^5,x, algorithm=""giac"")","\frac{2 \, {\left(5 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} c^{2} + 10 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} b c^{\frac{3}{2}} + 10 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} b^{2} c + 5 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} b^{3} \sqrt{c} + b^{4}\right)}}{5 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5}}"," ",0,"2/5*(5*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*c^2 + 10*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*b*c^(3/2) + 10*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*b^2*c + 5*(sqrt(c)*x - sqrt(c*x^2 + b*x))*b^3*sqrt(c) + b^4)/(sqrt(c)*x - sqrt(c*x^2 + b*x))^5","B",0
20,1,165,0,0.333665," ","integrate((c*x^2+b*x)^(3/2)/x^6,x, algorithm=""giac"")","\frac{2 \, {\left(35 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} c^{\frac{5}{2}} + 105 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} b c^{2} + 140 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} b^{2} c^{\frac{3}{2}} + 98 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} b^{3} c + 35 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} b^{4} \sqrt{c} + 5 \, b^{5}\right)}}{35 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7}}"," ",0,"2/35*(35*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*c^(5/2) + 105*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*b*c^2 + 140*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*b^2*c^(3/2) + 98*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*b^3*c + 35*(sqrt(c)*x - sqrt(c*x^2 + b*x))*b^4*sqrt(c) + 5*b^5)/(sqrt(c)*x - sqrt(c*x^2 + b*x))^7","B",0
21,1,194,0,0.199277," ","integrate((c*x^2+b*x)^(3/2)/x^7,x, algorithm=""giac"")","\frac{2 \, {\left(420 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} c^{3} + 1575 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} b c^{\frac{5}{2}} + 2583 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} b^{2} c^{2} + 2310 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} b^{3} c^{\frac{3}{2}} + 1170 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} b^{4} c + 315 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} b^{5} \sqrt{c} + 35 \, b^{6}\right)}}{315 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9}}"," ",0,"2/315*(420*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*c^3 + 1575*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*b*c^(5/2) + 2583*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*b^2*c^2 + 2310*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*b^3*c^(3/2) + 1170*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*b^4*c + 315*(sqrt(c)*x - sqrt(c*x^2 + b*x))*b^5*sqrt(c) + 35*b^6)/(sqrt(c)*x - sqrt(c*x^2 + b*x))^9","B",0
22,1,223,0,0.209528," ","integrate((c*x^2+b*x)^(3/2)/x^8,x, algorithm=""giac"")","\frac{2 \, {\left(2310 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} c^{\frac{7}{2}} + 10164 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} b c^{3} + 19635 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} b^{2} c^{\frac{5}{2}} + 21285 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} b^{3} c^{2} + 13860 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} b^{4} c^{\frac{3}{2}} + 5390 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} b^{5} c + 1155 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} b^{6} \sqrt{c} + 105 \, b^{7}\right)}}{1155 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{11}}"," ",0,"2/1155*(2310*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*c^(7/2) + 10164*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*b*c^3 + 19635*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*b^2*c^(5/2) + 21285*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*b^3*c^2 + 13860*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*b^4*c^(3/2) + 5390*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*b^5*c + 1155*(sqrt(c)*x - sqrt(c*x^2 + b*x))*b^6*sqrt(c) + 105*b^7)/(sqrt(c)*x - sqrt(c*x^2 + b*x))^11","B",0
23,1,252,0,0.202662," ","integrate((c*x^2+b*x)^(3/2)/x^9,x, algorithm=""giac"")","\frac{2 \, {\left(48048 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} c^{4} + 240240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} b c^{\frac{7}{2}} + 531960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} b^{2} c^{3} + 675675 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} b^{3} c^{\frac{5}{2}} + 535535 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} b^{4} c^{2} + 270270 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} b^{5} c^{\frac{3}{2}} + 84630 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} b^{6} c + 15015 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} b^{7} \sqrt{c} + 1155 \, b^{8}\right)}}{15015 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{13}}"," ",0,"2/15015*(48048*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*c^4 + 240240*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*b*c^(7/2) + 531960*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*b^2*c^3 + 675675*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*b^3*c^(5/2) + 535535*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*b^4*c^2 + 270270*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*b^5*c^(3/2) + 84630*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*b^6*c + 15015*(sqrt(c)*x - sqrt(c*x^2 + b*x))*b^7*sqrt(c) + 1155*b^8)/(sqrt(c)*x - sqrt(c*x^2 + b*x))^13","B",0
24,1,131,0,0.235321," ","integrate(x^2*(b*x^2+a*x)^(5/2),x, algorithm=""giac"")","\frac{45 \, a^{8} \log\left({\left| -2 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)} \sqrt{b} - a \right|}\right)}{32768 \, b^{\frac{11}{2}}} + \frac{1}{114688} \, \sqrt{b x^{2} + a x} {\left(\frac{315 \, a^{7}}{b^{5}} - 2 \, {\left(\frac{105 \, a^{6}}{b^{4}} - 4 \, {\left(\frac{21 \, a^{5}}{b^{3}} - 2 \, {\left(\frac{9 \, a^{4}}{b^{2}} - 8 \, {\left(\frac{a^{3}}{b} + 2 \, {\left(81 \, a^{2} + 4 \, {\left(14 \, b^{2} x + 33 \, a b\right)} x\right)} x\right)} x\right)} x\right)} x\right)} x\right)}"," ",0,"45/32768*a^8*log(abs(-2*(sqrt(b)*x - sqrt(b*x^2 + a*x))*sqrt(b) - a))/b^(11/2) + 1/114688*sqrt(b*x^2 + a*x)*(315*a^7/b^5 - 2*(105*a^6/b^4 - 4*(21*a^5/b^3 - 2*(9*a^4/b^2 - 8*(a^3/b + 2*(81*a^2 + 4*(14*b^2*x + 33*a*b)*x)*x)*x)*x)*x)*x)","A",0
25,1,120,0,0.235256," ","integrate(x*(b*x^2+a*x)^(5/2),x, algorithm=""giac"")","-\frac{5 \, a^{7} \log\left({\left| -2 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)} \sqrt{b} - a \right|}\right)}{2048 \, b^{\frac{9}{2}}} - \frac{1}{21504} \, \sqrt{b x^{2} + a x} {\left(\frac{105 \, a^{6}}{b^{4}} - 2 \, {\left(\frac{35 \, a^{5}}{b^{3}} - 4 \, {\left(\frac{7 \, a^{4}}{b^{2}} - 2 \, {\left(\frac{3 \, a^{3}}{b} + 8 \, {\left(37 \, a^{2} + 2 \, {\left(12 \, b^{2} x + 29 \, a b\right)} x\right)} x\right)} x\right)} x\right)} x\right)}"," ",0,"-5/2048*a^7*log(abs(-2*(sqrt(b)*x - sqrt(b*x^2 + a*x))*sqrt(b) - a))/b^(9/2) - 1/21504*sqrt(b*x^2 + a*x)*(105*a^6/b^4 - 2*(35*a^5/b^3 - 4*(7*a^4/b^2 - 2*(3*a^3/b + 8*(37*a^2 + 2*(12*b^2*x + 29*a*b)*x)*x)*x)*x)*x)","A",0
26,1,107,0,0.215035," ","integrate((b*x^2+a*x)^(5/2),x, algorithm=""giac"")","\frac{5 \, a^{6} \log\left({\left| -2 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)} \sqrt{b} - a \right|}\right)}{1024 \, b^{\frac{7}{2}}} + \frac{1}{1536} \, \sqrt{b x^{2} + a x} {\left(\frac{15 \, a^{5}}{b^{3}} - 2 \, {\left(\frac{5 \, a^{4}}{b^{2}} - 4 \, {\left(\frac{a^{3}}{b} + 2 \, {\left(27 \, a^{2} + 8 \, {\left(2 \, b^{2} x + 5 \, a b\right)} x\right)} x\right)} x\right)} x\right)}"," ",0,"5/1024*a^6*log(abs(-2*(sqrt(b)*x - sqrt(b*x^2 + a*x))*sqrt(b) - a))/b^(7/2) + 1/1536*sqrt(b*x^2 + a*x)*(15*a^5/b^3 - 2*(5*a^4/b^2 - 4*(a^3/b + 2*(27*a^2 + 8*(2*b^2*x + 5*a*b)*x)*x)*x)*x)","A",0
27,1,96,0,0.216174," ","integrate((b*x^2+a*x)^(5/2)/x,x, algorithm=""giac"")","-\frac{3 \, a^{5} \log\left({\left| -2 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)} \sqrt{b} - a \right|}\right)}{256 \, b^{\frac{5}{2}}} - \frac{1}{640} \, \sqrt{b x^{2} + a x} {\left(\frac{15 \, a^{4}}{b^{2}} - 2 \, {\left(\frac{5 \, a^{3}}{b} + 4 \, {\left(31 \, a^{2} + 2 \, {\left(8 \, b^{2} x + 21 \, a b\right)} x\right)} x\right)} x\right)}"," ",0,"-3/256*a^5*log(abs(-2*(sqrt(b)*x - sqrt(b*x^2 + a*x))*sqrt(b) - a))/b^(5/2) - 1/640*sqrt(b*x^2 + a*x)*(15*a^4/b^2 - 2*(5*a^3/b + 4*(31*a^2 + 2*(8*b^2*x + 21*a*b)*x)*x)*x)","A",0
28,1,84,0,0.213168," ","integrate((b*x^2+a*x)^(5/2)/x^2,x, algorithm=""giac"")","\frac{5 \, a^{4} \log\left({\left| -2 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)} \sqrt{b} - a \right|}\right)}{128 \, b^{\frac{3}{2}}} + \frac{1}{192} \, \sqrt{b x^{2} + a x} {\left(\frac{15 \, a^{3}}{b} + 2 \, {\left(59 \, a^{2} + 4 \, {\left(6 \, b^{2} x + 17 \, a b\right)} x\right)} x\right)}"," ",0,"5/128*a^4*log(abs(-2*(sqrt(b)*x - sqrt(b*x^2 + a*x))*sqrt(b) - a))/b^(3/2) + 1/192*sqrt(b*x^2 + a*x)*(15*a^3/b + 2*(59*a^2 + 4*(6*b^2*x + 17*a*b)*x)*x)","A",0
29,1,72,0,0.216024," ","integrate((b*x^2+a*x)^(5/2)/x^3,x, algorithm=""giac"")","-\frac{5 \, a^{3} \log\left({\left| -2 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)} \sqrt{b} - a \right|}\right)}{16 \, \sqrt{b}} + \frac{1}{24} \, \sqrt{b x^{2} + a x} {\left(33 \, a^{2} + 2 \, {\left(4 \, b^{2} x + 13 \, a b\right)} x\right)}"," ",0,"-5/16*a^3*log(abs(-2*(sqrt(b)*x - sqrt(b*x^2 + a*x))*sqrt(b) - a))/sqrt(b) + 1/24*sqrt(b*x^2 + a*x)*(33*a^2 + 2*(4*b^2*x + 13*a*b)*x)","A",0
30,1,89,0,0.228589," ","integrate((b*x^2+a*x)^(5/2)/x^4,x, algorithm=""giac"")","-\frac{15}{8} \, a^{2} \sqrt{b} \log\left({\left| -2 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)} \sqrt{b} - a \right|}\right) + \frac{2 \, a^{3}}{\sqrt{b} x - \sqrt{b x^{2} + a x}} + \frac{1}{4} \, {\left(2 \, b^{2} x + 9 \, a b\right)} \sqrt{b x^{2} + a x}"," ",0,"-15/8*a^2*sqrt(b)*log(abs(-2*(sqrt(b)*x - sqrt(b*x^2 + a*x))*sqrt(b) - a)) + 2*a^3/(sqrt(b)*x - sqrt(b*x^2 + a*x)) + 1/4*(2*b^2*x + 9*a*b)*sqrt(b*x^2 + a*x)","A",0
31,1,133,0,0.366713," ","integrate((b*x^2+a*x)^(5/2)/x^5,x, algorithm=""giac"")","-\frac{5}{2} \, a b^{\frac{3}{2}} \log\left({\left| -2 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)} \sqrt{b} - a \right|}\right) + \sqrt{b x^{2} + a x} b^{2} + \frac{2 \, {\left(9 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)}^{2} a^{2} b + 3 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)} a^{3} \sqrt{b} + a^{4}\right)}}{3 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)}^{3}}"," ",0,"-5/2*a*b^(3/2)*log(abs(-2*(sqrt(b)*x - sqrt(b*x^2 + a*x))*sqrt(b) - a)) + sqrt(b*x^2 + a*x)*b^2 + 2/3*(9*(sqrt(b)*x - sqrt(b*x^2 + a*x))^2*a^2*b + 3*(sqrt(b)*x - sqrt(b*x^2 + a*x))*a^3*sqrt(b) + a^4)/(sqrt(b)*x - sqrt(b*x^2 + a*x))^3","A",0
32,1,175,0,0.260360," ","integrate((b*x^2+a*x)^(5/2)/x^6,x, algorithm=""giac"")","-b^{\frac{5}{2}} \log\left({\left| -2 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)} \sqrt{b} - a \right|}\right) + \frac{2 \, {\left(45 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)}^{4} a b^{2} + 45 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)}^{3} a^{2} b^{\frac{3}{2}} + 35 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)}^{2} a^{3} b + 15 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)} a^{4} \sqrt{b} + 3 \, a^{5}\right)}}{15 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)}^{5}}"," ",0,"-b^(5/2)*log(abs(-2*(sqrt(b)*x - sqrt(b*x^2 + a*x))*sqrt(b) - a)) + 2/15*(45*(sqrt(b)*x - sqrt(b*x^2 + a*x))^4*a*b^2 + 45*(sqrt(b)*x - sqrt(b*x^2 + a*x))^3*a^2*b^(3/2) + 35*(sqrt(b)*x - sqrt(b*x^2 + a*x))^2*a^3*b + 15*(sqrt(b)*x - sqrt(b*x^2 + a*x))*a^4*sqrt(b) + 3*a^5)/(sqrt(b)*x - sqrt(b*x^2 + a*x))^5","B",0
33,1,192,0,0.214390," ","integrate((b*x^2+a*x)^(5/2)/x^7,x, algorithm=""giac"")","\frac{2 \, {\left(7 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)}^{6} b^{3} + 21 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)}^{5} a b^{\frac{5}{2}} + 35 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)}^{4} a^{2} b^{2} + 35 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)}^{3} a^{3} b^{\frac{3}{2}} + 21 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)}^{2} a^{4} b + 7 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)} a^{5} \sqrt{b} + a^{6}\right)}}{7 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)}^{7}}"," ",0,"2/7*(7*(sqrt(b)*x - sqrt(b*x^2 + a*x))^6*b^3 + 21*(sqrt(b)*x - sqrt(b*x^2 + a*x))^5*a*b^(5/2) + 35*(sqrt(b)*x - sqrt(b*x^2 + a*x))^4*a^2*b^2 + 35*(sqrt(b)*x - sqrt(b*x^2 + a*x))^3*a^3*b^(3/2) + 21*(sqrt(b)*x - sqrt(b*x^2 + a*x))^2*a^4*b + 7*(sqrt(b)*x - sqrt(b*x^2 + a*x))*a^5*sqrt(b) + a^6)/(sqrt(b)*x - sqrt(b*x^2 + a*x))^7","B",0
34,1,223,0,0.211693," ","integrate((b*x^2+a*x)^(5/2)/x^8,x, algorithm=""giac"")","\frac{2 \, {\left(63 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)}^{7} b^{\frac{7}{2}} + 273 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)}^{6} a b^{3} + 567 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)}^{5} a^{2} b^{\frac{5}{2}} + 693 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)}^{4} a^{3} b^{2} + 525 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)}^{3} a^{4} b^{\frac{3}{2}} + 243 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)}^{2} a^{5} b + 63 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)} a^{6} \sqrt{b} + 7 \, a^{7}\right)}}{63 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)}^{9}}"," ",0,"2/63*(63*(sqrt(b)*x - sqrt(b*x^2 + a*x))^7*b^(7/2) + 273*(sqrt(b)*x - sqrt(b*x^2 + a*x))^6*a*b^3 + 567*(sqrt(b)*x - sqrt(b*x^2 + a*x))^5*a^2*b^(5/2) + 693*(sqrt(b)*x - sqrt(b*x^2 + a*x))^4*a^3*b^2 + 525*(sqrt(b)*x - sqrt(b*x^2 + a*x))^3*a^4*b^(3/2) + 243*(sqrt(b)*x - sqrt(b*x^2 + a*x))^2*a^5*b + 63*(sqrt(b)*x - sqrt(b*x^2 + a*x))*a^6*sqrt(b) + 7*a^7)/(sqrt(b)*x - sqrt(b*x^2 + a*x))^9","B",0
35,1,252,0,0.242156," ","integrate((b*x^2+a*x)^(5/2)/x^9,x, algorithm=""giac"")","\frac{2 \, {\left(924 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)}^{8} b^{4} + 4851 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)}^{7} a b^{\frac{7}{2}} + 11781 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)}^{6} a^{2} b^{3} + 16863 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)}^{5} a^{3} b^{\frac{5}{2}} + 15345 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)}^{4} a^{4} b^{2} + 9009 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)}^{3} a^{5} b^{\frac{3}{2}} + 3311 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)}^{2} a^{6} b + 693 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)} a^{7} \sqrt{b} + 63 \, a^{8}\right)}}{693 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)}^{11}}"," ",0,"2/693*(924*(sqrt(b)*x - sqrt(b*x^2 + a*x))^8*b^4 + 4851*(sqrt(b)*x - sqrt(b*x^2 + a*x))^7*a*b^(7/2) + 11781*(sqrt(b)*x - sqrt(b*x^2 + a*x))^6*a^2*b^3 + 16863*(sqrt(b)*x - sqrt(b*x^2 + a*x))^5*a^3*b^(5/2) + 15345*(sqrt(b)*x - sqrt(b*x^2 + a*x))^4*a^4*b^2 + 9009*(sqrt(b)*x - sqrt(b*x^2 + a*x))^3*a^5*b^(3/2) + 3311*(sqrt(b)*x - sqrt(b*x^2 + a*x))^2*a^6*b + 693*(sqrt(b)*x - sqrt(b*x^2 + a*x))*a^7*sqrt(b) + 63*a^8)/(sqrt(b)*x - sqrt(b*x^2 + a*x))^11","B",0
36,1,281,0,0.219409," ","integrate((b*x^2+a*x)^(5/2)/x^10,x, algorithm=""giac"")","\frac{2 \, {\left(6006 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)}^{9} b^{\frac{9}{2}} + 36036 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)}^{8} a b^{4} + 99099 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)}^{7} a^{2} b^{\frac{7}{2}} + 161733 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)}^{6} a^{3} b^{3} + 171171 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)}^{5} a^{4} b^{\frac{5}{2}} + 121121 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)}^{4} a^{5} b^{2} + 57057 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)}^{3} a^{6} b^{\frac{3}{2}} + 17199 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)}^{2} a^{7} b + 3003 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)} a^{8} \sqrt{b} + 231 \, a^{9}\right)}}{3003 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)}^{13}}"," ",0,"2/3003*(6006*(sqrt(b)*x - sqrt(b*x^2 + a*x))^9*b^(9/2) + 36036*(sqrt(b)*x - sqrt(b*x^2 + a*x))^8*a*b^4 + 99099*(sqrt(b)*x - sqrt(b*x^2 + a*x))^7*a^2*b^(7/2) + 161733*(sqrt(b)*x - sqrt(b*x^2 + a*x))^6*a^3*b^3 + 171171*(sqrt(b)*x - sqrt(b*x^2 + a*x))^5*a^4*b^(5/2) + 121121*(sqrt(b)*x - sqrt(b*x^2 + a*x))^4*a^5*b^2 + 57057*(sqrt(b)*x - sqrt(b*x^2 + a*x))^3*a^6*b^(3/2) + 17199*(sqrt(b)*x - sqrt(b*x^2 + a*x))^2*a^7*b + 3003*(sqrt(b)*x - sqrt(b*x^2 + a*x))*a^8*sqrt(b) + 231*a^9)/(sqrt(b)*x - sqrt(b*x^2 + a*x))^13","B",0
37,1,310,0,0.218679," ","integrate((b*x^2+a*x)^(5/2)/x^11,x, algorithm=""giac"")","\frac{2 \, {\left(144144 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)}^{10} b^{5} + 960960 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)}^{9} a b^{\frac{9}{2}} + 2934360 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)}^{8} a^{2} b^{4} + 5360355 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)}^{7} a^{3} b^{\frac{7}{2}} + 6451445 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)}^{6} a^{4} b^{3} + 5324319 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)}^{5} a^{5} b^{\frac{5}{2}} + 3042585 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)}^{4} a^{6} b^{2} + 1186185 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)}^{3} a^{7} b^{\frac{3}{2}} + 301455 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)}^{2} a^{8} b + 45045 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)} a^{9} \sqrt{b} + 3003 \, a^{10}\right)}}{45045 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)}^{15}}"," ",0,"2/45045*(144144*(sqrt(b)*x - sqrt(b*x^2 + a*x))^10*b^5 + 960960*(sqrt(b)*x - sqrt(b*x^2 + a*x))^9*a*b^(9/2) + 2934360*(sqrt(b)*x - sqrt(b*x^2 + a*x))^8*a^2*b^4 + 5360355*(sqrt(b)*x - sqrt(b*x^2 + a*x))^7*a^3*b^(7/2) + 6451445*(sqrt(b)*x - sqrt(b*x^2 + a*x))^6*a^4*b^3 + 5324319*(sqrt(b)*x - sqrt(b*x^2 + a*x))^5*a^5*b^(5/2) + 3042585*(sqrt(b)*x - sqrt(b*x^2 + a*x))^4*a^6*b^2 + 1186185*(sqrt(b)*x - sqrt(b*x^2 + a*x))^3*a^7*b^(3/2) + 301455*(sqrt(b)*x - sqrt(b*x^2 + a*x))^2*a^8*b + 45045*(sqrt(b)*x - sqrt(b*x^2 + a*x))*a^9*sqrt(b) + 3003*a^10)/(sqrt(b)*x - sqrt(b*x^2 + a*x))^15","B",0
38,1,339,0,0.219704," ","integrate((b*x^2+a*x)^(5/2)/x^12,x, algorithm=""giac"")","\frac{2 \, {\left(816816 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)}^{11} b^{\frac{11}{2}} + 5951088 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)}^{10} a b^{5} + 19909890 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)}^{9} a^{2} b^{\frac{9}{2}} + 40160120 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)}^{8} a^{3} b^{4} + 54063009 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)}^{7} a^{4} b^{\frac{7}{2}} + 50860719 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)}^{6} a^{5} b^{3} + 34051017 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)}^{5} a^{6} b^{\frac{5}{2}} + 16198875 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)}^{4} a^{7} b^{2} + 5360355 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)}^{3} a^{8} b^{\frac{3}{2}} + 1174173 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)}^{2} a^{9} b + 153153 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)} a^{10} \sqrt{b} + 9009 \, a^{11}\right)}}{153153 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)}^{17}}"," ",0,"2/153153*(816816*(sqrt(b)*x - sqrt(b*x^2 + a*x))^11*b^(11/2) + 5951088*(sqrt(b)*x - sqrt(b*x^2 + a*x))^10*a*b^5 + 19909890*(sqrt(b)*x - sqrt(b*x^2 + a*x))^9*a^2*b^(9/2) + 40160120*(sqrt(b)*x - sqrt(b*x^2 + a*x))^8*a^3*b^4 + 54063009*(sqrt(b)*x - sqrt(b*x^2 + a*x))^7*a^4*b^(7/2) + 50860719*(sqrt(b)*x - sqrt(b*x^2 + a*x))^6*a^5*b^3 + 34051017*(sqrt(b)*x - sqrt(b*x^2 + a*x))^5*a^6*b^(5/2) + 16198875*(sqrt(b)*x - sqrt(b*x^2 + a*x))^4*a^7*b^2 + 5360355*(sqrt(b)*x - sqrt(b*x^2 + a*x))^3*a^8*b^(3/2) + 1174173*(sqrt(b)*x - sqrt(b*x^2 + a*x))^2*a^9*b + 153153*(sqrt(b)*x - sqrt(b*x^2 + a*x))*a^10*sqrt(b) + 9009*a^11)/(sqrt(b)*x - sqrt(b*x^2 + a*x))^17","B",0
39,1,29,0,0.175409," ","integrate(x*(-x^2+2*x)^(1/2),x, algorithm=""giac"")","\frac{1}{6} \, {\left({\left(2 \, x - 1\right)} x - 3\right)} \sqrt{-x^{2} + 2 \, x} + \frac{1}{2} \, \arcsin\left(x - 1\right)"," ",0,"1/6*((2*x - 1)*x - 3)*sqrt(-x^2 + 2*x) + 1/2*arcsin(x - 1)","A",0
40,1,32,0,0.294064," ","integrate(x*(-4*x^2+3*x)^(1/2),x, algorithm=""giac"")","\frac{1}{384} \, {\left(8 \, {\left(16 \, x - 3\right)} x - 27\right)} \sqrt{-4 \, x^{2} + 3 \, x} + \frac{27}{512} \, \arcsin\left(\frac{8}{3} \, x - 1\right)"," ",0,"1/384*(8*(16*x - 3)*x - 27)*sqrt(-4*x^2 + 3*x) + 27/512*arcsin(8/3*x - 1)","A",0
41,1,38,0,0.199981," ","integrate(x*(x^2+x)^(1/2),x, algorithm=""giac"")","\frac{1}{24} \, {\left(2 \, {\left(4 \, x + 1\right)} x - 3\right)} \sqrt{x^{2} + x} - \frac{1}{16} \, \log\left({\left| -2 \, x + 2 \, \sqrt{x^{2} + x} - 1 \right|}\right)"," ",0,"1/24*(2*(4*x + 1)*x - 3)*sqrt(x^2 + x) - 1/16*log(abs(-2*x + 2*sqrt(x^2 + x) - 1))","A",0
42,1,89,0,0.218263," ","integrate(x^4/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\frac{1}{192} \, \sqrt{c x^{2} + b x} {\left(2 \, {\left(4 \, x {\left(\frac{6 \, x}{c} - \frac{7 \, b}{c^{2}}\right)} + \frac{35 \, b^{2}}{c^{3}}\right)} x - \frac{105 \, b^{3}}{c^{4}}\right)} - \frac{35 \, b^{4} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{128 \, c^{\frac{9}{2}}}"," ",0,"1/192*sqrt(c*x^2 + b*x)*(2*(4*x*(6*x/c - 7*b/c^2) + 35*b^2/c^3)*x - 105*b^3/c^4) - 35/128*b^4*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(9/2)","A",0
43,1,77,0,0.218335," ","integrate(x^3/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\frac{1}{24} \, \sqrt{c x^{2} + b x} {\left(2 \, x {\left(\frac{4 \, x}{c} - \frac{5 \, b}{c^{2}}\right)} + \frac{15 \, b^{2}}{c^{3}}\right)} + \frac{5 \, b^{3} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{16 \, c^{\frac{7}{2}}}"," ",0,"1/24*sqrt(c*x^2 + b*x)*(2*x*(4*x/c - 5*b/c^2) + 15*b^2/c^3) + 5/16*b^3*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(7/2)","A",0
44,1,65,0,0.229375," ","integrate(x^2/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{c x^{2} + b x} {\left(\frac{2 \, x}{c} - \frac{3 \, b}{c^{2}}\right)} - \frac{3 \, b^{2} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{8 \, c^{\frac{5}{2}}}"," ",0,"1/4*sqrt(c*x^2 + b*x)*(2*x/c - 3*b/c^2) - 3/8*b^2*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(5/2)","A",0
45,1,52,0,0.231873," ","integrate(x/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\frac{b \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{2 \, c^{\frac{3}{2}}} + \frac{\sqrt{c x^{2} + b x}}{c}"," ",0,"1/2*b*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(3/2) + sqrt(c*x^2 + b*x)/c","A",0
46,1,35,0,0.198417," ","integrate(1/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","-\frac{\log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{\sqrt{c}}"," ",0,"-log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/sqrt(c)","A",0
47,1,23,0,0.266850," ","integrate(1/x/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\frac{2}{\sqrt{c} x - \sqrt{c x^{2} + b x}}"," ",0,"2/(sqrt(c)*x - sqrt(c*x^2 + b*x))","A",0
48,1,49,0,0.211111," ","integrate(1/x^2/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} + b\right)}}{3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3}}"," ",0,"2/3*(3*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) + b)/(sqrt(c)*x - sqrt(c*x^2 + b*x))^3","A",0
49,1,78,0,0.232333," ","integrate(1/x^3/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(20 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} c + 15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} b \sqrt{c} + 3 \, b^{2}\right)}}{15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5}}"," ",0,"2/15*(20*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*c + 15*(sqrt(c)*x - sqrt(c*x^2 + b*x))*b*sqrt(c) + 3*b^2)/(sqrt(c)*x - sqrt(c*x^2 + b*x))^5","A",0
50,1,107,0,0.213259," ","integrate(1/x^4/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(70 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} c^{\frac{3}{2}} + 84 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} b c + 35 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} b^{2} \sqrt{c} + 5 \, b^{3}\right)}}{35 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7}}"," ",0,"2/35*(70*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*c^(3/2) + 84*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*b*c + 35*(sqrt(c)*x - sqrt(c*x^2 + b*x))*b^2*sqrt(c) + 5*b^3)/(sqrt(c)*x - sqrt(c*x^2 + b*x))^7","A",0
51,1,136,0,0.212242," ","integrate(1/x^5/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(1008 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} c^{2} + 1680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} b c^{\frac{3}{2}} + 1080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} b^{2} c + 315 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} b^{3} \sqrt{c} + 35 \, b^{4}\right)}}{315 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9}}"," ",0,"2/315*(1008*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*c^2 + 1680*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*b*c^(3/2) + 1080*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*b^2*c + 315*(sqrt(c)*x - sqrt(c*x^2 + b*x))*b^3*sqrt(c) + 35*b^4)/(sqrt(c)*x - sqrt(c*x^2 + b*x))^9","A",0
52,1,102,0,0.284906," ","integrate(x^4/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{c x^{2} + b x} {\left(\frac{2 \, x}{c^{2}} - \frac{7 \, b}{c^{3}}\right)} - \frac{15 \, b^{2} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{8 \, c^{\frac{7}{2}}} - \frac{2 \, b^{3}}{{\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} c + b \sqrt{c}\right)} c^{3}}"," ",0,"1/4*sqrt(c*x^2 + b*x)*(2*x/c^2 - 7*b/c^3) - 15/8*b^2*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(7/2) - 2*b^3/(((sqrt(c)*x - sqrt(c*x^2 + b*x))*c + b*sqrt(c))*c^3)","A",0
53,1,89,0,0.252681," ","integrate(x^3/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","\frac{3 \, b \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{2 \, c^{\frac{5}{2}}} + \frac{2 \, b^{2}}{{\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} c + b \sqrt{c}\right)} c^{2}} + \frac{\sqrt{c x^{2} + b x}}{c^{2}}"," ",0,"3/2*b*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(5/2) + 2*b^2/(((sqrt(c)*x - sqrt(c*x^2 + b*x))*c + b*sqrt(c))*c^2) + sqrt(c*x^2 + b*x)/c^2","A",0
54,-2,0,0,0.000000," ","integrate(x^2/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{%%%{1,[1]%%%},[2,2]%%%}+%%%{%%{[-2,0]:[1,0,%%%{-1,[1]%%%}]%%},[1,3]%%%}+%%%{1,[0,4]%%%} / %%%{%%%{1,[2]%%%},[2,0]%%%}+%%%{%%{[%%%{-2,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,1]%%%}+%%%{%%%{1,[1]%%%},[0,2]%%%} Error: Bad Argument Value","F(-2)",0
55,1,32,0,0.231915," ","integrate(x/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","\frac{2}{{\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} + b\right)} \sqrt{c}}"," ",0,"2/(((sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) + b)*sqrt(c))","A",0
56,1,24,0,0.266270," ","integrate(1/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{2 \, c x}{b^{2}} + \frac{1}{b}\right)}}{\sqrt{c x^{2} + b x}}"," ",0,"-2*(2*c*x/b^2 + 1/b)/sqrt(c*x^2 + b*x)","A",0
57,0,0,0,0.000000," ","integrate(1/x/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{2} + b x\right)}^{\frac{3}{2}} x}\,{d x}"," ",0,"integrate(1/((c*x^2 + b*x)^(3/2)*x), x)","F",0
58,0,0,0,0.000000," ","integrate(1/x^2/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{2} + b x\right)}^{\frac{3}{2}} x^{2}}\,{d x}"," ",0,"integrate(1/((c*x^2 + b*x)^(3/2)*x^2), x)","F",0
59,0,0,0,0.000000," ","integrate(1/x^3/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{2} + b x\right)}^{\frac{3}{2}} x^{3}}\,{d x}"," ",0,"integrate(1/((c*x^2 + b*x)^(3/2)*x^3), x)","F",0
60,1,162,0,0.269595," ","integrate(x^6/(b*x^2+a*x)^(5/2),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{b x^{2} + a x} {\left(\frac{2 \, x}{b^{3}} - \frac{11 \, a}{b^{4}}\right)} - \frac{35 \, a^{2} \log\left({\left| -2 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)} \sqrt{b} - a \right|}\right)}{8 \, b^{\frac{9}{2}}} - \frac{2 \, {\left(12 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)}^{2} a^{3} b^{\frac{3}{2}} + 21 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)} a^{4} b + 10 \, a^{5} \sqrt{b}\right)}}{3 \, {\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)} b + a \sqrt{b}\right)}^{3} b^{\frac{7}{2}}}"," ",0,"1/4*sqrt(b*x^2 + a*x)*(2*x/b^3 - 11*a/b^4) - 35/8*a^2*log(abs(-2*(sqrt(b)*x - sqrt(b*x^2 + a*x))*sqrt(b) - a))/b^(9/2) - 2/3*(12*(sqrt(b)*x - sqrt(b*x^2 + a*x))^2*a^3*b^(3/2) + 21*(sqrt(b)*x - sqrt(b*x^2 + a*x))*a^4*b + 10*a^5*sqrt(b))/(((sqrt(b)*x - sqrt(b*x^2 + a*x))*b + a*sqrt(b))^3*b^(7/2))","A",0
61,1,146,0,0.266092," ","integrate(x^5/(b*x^2+a*x)^(5/2),x, algorithm=""giac"")","\frac{5 \, a \log\left({\left| -2 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)} \sqrt{b} - a \right|}\right)}{2 \, b^{\frac{7}{2}}} + \frac{\sqrt{b x^{2} + a x}}{b^{3}} + \frac{2 \, {\left(9 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)}^{2} a^{2} b + 15 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)} a^{3} \sqrt{b} + 7 \, a^{4}\right)}}{3 \, {\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)} b + a \sqrt{b}\right)}^{3} b^{2}}"," ",0,"5/2*a*log(abs(-2*(sqrt(b)*x - sqrt(b*x^2 + a*x))*sqrt(b) - a))/b^(7/2) + sqrt(b*x^2 + a*x)/b^3 + 2/3*(9*(sqrt(b)*x - sqrt(b*x^2 + a*x))^2*a^2*b + 15*(sqrt(b)*x - sqrt(b*x^2 + a*x))*a^3*sqrt(b) + 7*a^4)/(((sqrt(b)*x - sqrt(b*x^2 + a*x))*b + a*sqrt(b))^3*b^2)","A",0
62,-2,0,0,0.000000," ","integrate(x^4/(b*x^2+a*x)^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{%%%{1,[2]%%%},[4,4]%%%}+%%%{%%{[%%%{-4,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,5]%%%}+%%%{%%%{6,[1]%%%},[2,6]%%%}+%%%{%%{[-4,0]:[1,0,%%%{-1,[1]%%%}]%%},[1,7]%%%}+%%%{1,[0,8]%%%} / %%%{%%%{1,[4]%%%},[4,0]%%%}+%%%{%%{[%%%{-4,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,1]%%%}+%%%{%%%{6,[3]%%%},[2,2]%%%}+%%%{%%{[%%%{-4,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,3]%%%}+%%%{%%%{1,[2]%%%},[0,4]%%%} Error: Bad Argument Value","F(-2)",0
63,1,89,0,0.221989," ","integrate(x^3/(b*x^2+a*x)^(5/2),x, algorithm=""giac"")","\frac{2 \, {\left(3 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)}^{2} b^{\frac{3}{2}} + 3 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)} a b + a^{2} \sqrt{b}\right)}}{3 \, {\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)} \sqrt{b} + a\right)}^{3} b^{2}}"," ",0,"2/3*(3*(sqrt(b)*x - sqrt(b*x^2 + a*x))^2*b^(3/2) + 3*(sqrt(b)*x - sqrt(b*x^2 + a*x))*a*b + a^2*sqrt(b))/(((sqrt(b)*x - sqrt(b*x^2 + a*x))*sqrt(b) + a)^3*b^2)","B",0
64,1,61,0,0.227739," ","integrate(x^2/(b*x^2+a*x)^(5/2),x, algorithm=""giac"")","\frac{2 \, {\left(3 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)} b + 2 \, a \sqrt{b}\right)}}{3 \, {\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a x}\right)} \sqrt{b} + a\right)}^{3} b}"," ",0,"2/3*(3*(sqrt(b)*x - sqrt(b*x^2 + a*x))*b + 2*a*sqrt(b))/(((sqrt(b)*x - sqrt(b*x^2 + a*x))*sqrt(b) + a)^3*b)","A",0
65,0,0,0,0.000000," ","integrate(x/(b*x^2+a*x)^(5/2),x, algorithm=""giac"")","\int \frac{x}{{\left(b x^{2} + a x\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(x/(b*x^2 + a*x)^(5/2), x)","F",0
66,1,50,0,0.238151," ","integrate(1/(b*x^2+a*x)^(5/2),x, algorithm=""giac"")","\frac{2 \, {\left(2 \, {\left(4 \, x {\left(\frac{2 \, b^{3} x}{a^{4}} + \frac{3 \, b^{2}}{a^{3}}\right)} + \frac{3 \, b}{a^{2}}\right)} x - \frac{1}{a}\right)}}{3 \, {\left(b x^{2} + a x\right)}^{\frac{3}{2}}}"," ",0,"2/3*(2*(4*x*(2*b^3*x/a^4 + 3*b^2/a^3) + 3*b/a^2)*x - 1/a)/(b*x^2 + a*x)^(3/2)","A",0
67,0,0,0,0.000000," ","integrate(1/x/(b*x^2+a*x)^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{2} + a x\right)}^{\frac{5}{2}} x}\,{d x}"," ",0,"integrate(1/((b*x^2 + a*x)^(5/2)*x), x)","F",0
68,0,0,0,0.000000," ","integrate(1/x^2/(b*x^2+a*x)^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{2} + a x\right)}^{\frac{5}{2}} x^{2}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a*x)^(5/2)*x^2), x)","F",0
69,1,22,0,0.183712," ","integrate(x/(-x^2+4*x)^(1/2),x, algorithm=""giac"")","-\sqrt{-x^{2} + 4 \, x} + 2 \, \arcsin\left(\frac{1}{2} \, x - 1\right)"," ",0,"-sqrt(-x^2 + 4*x) + 2*arcsin(1/2*x - 1)","A",0
70,1,28,0,0.197623," ","integrate(x/(x^2-4*x)^(1/2),x, algorithm=""giac"")","\sqrt{x^{2} - 4 \, x} - 2 \, \log\left({\left| -x + \sqrt{x^{2} - 4 \, x} + 2 \right|}\right)"," ",0,"sqrt(x^2 - 4*x) - 2*log(abs(-x + sqrt(x^2 - 4*x) + 2))","A",0
71,1,23,0,0.197510," ","integrate(x^2/(-x^2+2*x)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{-x^{2} + 2 \, x} {\left(x + 3\right)} + \frac{3}{2} \, \arcsin\left(x - 1\right)"," ",0,"-1/2*sqrt(-x^2 + 2*x)*(x + 3) + 3/2*arcsin(x - 1)","A",0
72,1,70,0,0.176938," ","integrate(x^(7/2)*(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","-\frac{256 \, b^{\frac{11}{2}}}{3465 \, c^{5}} + \frac{2 \, {\left(315 \, {\left(c x + b\right)}^{\frac{11}{2}} - 1540 \, {\left(c x + b\right)}^{\frac{9}{2}} b + 2970 \, {\left(c x + b\right)}^{\frac{7}{2}} b^{2} - 2772 \, {\left(c x + b\right)}^{\frac{5}{2}} b^{3} + 1155 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{4}\right)}}{3465 \, c^{5}}"," ",0,"-256/3465*b^(11/2)/c^5 + 2/3465*(315*(c*x + b)^(11/2) - 1540*(c*x + b)^(9/2)*b + 2970*(c*x + b)^(7/2)*b^2 - 2772*(c*x + b)^(5/2)*b^3 + 1155*(c*x + b)^(3/2)*b^4)/c^5","A",0
73,1,58,0,0.172297," ","integrate(x^(5/2)*(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\frac{32 \, b^{\frac{9}{2}}}{315 \, c^{4}} + \frac{2 \, {\left(35 \, {\left(c x + b\right)}^{\frac{9}{2}} - 135 \, {\left(c x + b\right)}^{\frac{7}{2}} b + 189 \, {\left(c x + b\right)}^{\frac{5}{2}} b^{2} - 105 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{3}\right)}}{315 \, c^{4}}"," ",0,"32/315*b^(9/2)/c^4 + 2/315*(35*(c*x + b)^(9/2) - 135*(c*x + b)^(7/2)*b + 189*(c*x + b)^(5/2)*b^2 - 105*(c*x + b)^(3/2)*b^3)/c^4","A",0
74,1,46,0,0.173764," ","integrate(x^(3/2)*(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","-\frac{16 \, b^{\frac{7}{2}}}{105 \, c^{3}} + \frac{2 \, {\left(15 \, {\left(c x + b\right)}^{\frac{7}{2}} - 42 \, {\left(c x + b\right)}^{\frac{5}{2}} b + 35 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{2}\right)}}{105 \, c^{3}}"," ",0,"-16/105*b^(7/2)/c^3 + 2/105*(15*(c*x + b)^(7/2) - 42*(c*x + b)^(5/2)*b + 35*(c*x + b)^(3/2)*b^2)/c^3","A",0
75,1,34,0,0.162062," ","integrate(x^(1/2)*(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\frac{4 \, b^{\frac{5}{2}}}{15 \, c^{2}} + \frac{2 \, {\left(3 \, {\left(c x + b\right)}^{\frac{5}{2}} - 5 \, {\left(c x + b\right)}^{\frac{3}{2}} b\right)}}{15 \, c^{2}}"," ",0,"4/15*b^(5/2)/c^2 + 2/15*(3*(c*x + b)^(5/2) - 5*(c*x + b)^(3/2)*b)/c^2","A",0
76,1,21,0,0.162517," ","integrate((c*x^2+b*x)^(1/2)/x^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(c x + b\right)}^{\frac{3}{2}}}{3 \, c} - \frac{2 \, b^{\frac{3}{2}}}{3 \, c}"," ",0,"2/3*(c*x + b)^(3/2)/c - 2/3*b^(3/2)/c","A",0
77,1,61,0,0.190946," ","integrate((c*x^2+b*x)^(1/2)/x^(3/2),x, algorithm=""giac"")","\frac{2 \, b \arctan\left(\frac{\sqrt{c x + b}}{\sqrt{-b}}\right)}{\sqrt{-b}} + 2 \, \sqrt{c x + b} - \frac{2 \, {\left(b \arctan\left(\frac{\sqrt{b}}{\sqrt{-b}}\right) + \sqrt{-b} \sqrt{b}\right)}}{\sqrt{-b}}"," ",0,"2*b*arctan(sqrt(c*x + b)/sqrt(-b))/sqrt(-b) + 2*sqrt(c*x + b) - 2*(b*arctan(sqrt(b)/sqrt(-b)) + sqrt(-b)*sqrt(b))/sqrt(-b)","A",0
78,1,41,0,0.209725," ","integrate((c*x^2+b*x)^(1/2)/x^(5/2),x, algorithm=""giac"")","\frac{\frac{c^{2} \arctan\left(\frac{\sqrt{c x + b}}{\sqrt{-b}}\right)}{\sqrt{-b}} - \frac{\sqrt{c x + b} c}{x}}{c}"," ",0,"(c^2*arctan(sqrt(c*x + b)/sqrt(-b))/sqrt(-b) - sqrt(c*x + b)*c/x)/c","A",0
79,1,66,0,0.213624," ","integrate((c*x^2+b*x)^(1/2)/x^(7/2),x, algorithm=""giac"")","-\frac{\frac{c^{3} \arctan\left(\frac{\sqrt{c x + b}}{\sqrt{-b}}\right)}{\sqrt{-b} b} + \frac{{\left(c x + b\right)}^{\frac{3}{2}} c^{3} + \sqrt{c x + b} b c^{3}}{b c^{2} x^{2}}}{4 \, c}"," ",0,"-1/4*(c^3*arctan(sqrt(c*x + b)/sqrt(-b))/(sqrt(-b)*b) + ((c*x + b)^(3/2)*c^3 + sqrt(c*x + b)*b*c^3)/(b*c^2*x^2))/c","A",0
80,1,84,0,0.230090," ","integrate((c*x^2+b*x)^(1/2)/x^(9/2),x, algorithm=""giac"")","\frac{\frac{3 \, c^{4} \arctan\left(\frac{\sqrt{c x + b}}{\sqrt{-b}}\right)}{\sqrt{-b} b^{2}} + \frac{3 \, {\left(c x + b\right)}^{\frac{5}{2}} c^{4} - 8 \, {\left(c x + b\right)}^{\frac{3}{2}} b c^{4} - 3 \, \sqrt{c x + b} b^{2} c^{4}}{b^{2} c^{3} x^{3}}}{24 \, c}"," ",0,"1/24*(3*c^4*arctan(sqrt(c*x + b)/sqrt(-b))/(sqrt(-b)*b^2) + (3*(c*x + b)^(5/2)*c^4 - 8*(c*x + b)^(3/2)*b*c^4 - 3*sqrt(c*x + b)*b^2*c^4)/(b^2*c^3*x^3))/c","A",0
81,1,99,0,0.235429," ","integrate((c*x^2+b*x)^(1/2)/x^(11/2),x, algorithm=""giac"")","-\frac{\frac{15 \, c^{5} \arctan\left(\frac{\sqrt{c x + b}}{\sqrt{-b}}\right)}{\sqrt{-b} b^{3}} + \frac{15 \, {\left(c x + b\right)}^{\frac{7}{2}} c^{5} - 55 \, {\left(c x + b\right)}^{\frac{5}{2}} b c^{5} + 73 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{2} c^{5} + 15 \, \sqrt{c x + b} b^{3} c^{5}}{b^{3} c^{4} x^{4}}}{192 \, c}"," ",0,"-1/192*(15*c^5*arctan(sqrt(c*x + b)/sqrt(-b))/(sqrt(-b)*b^3) + (15*(c*x + b)^(7/2)*c^5 - 55*(c*x + b)^(5/2)*b*c^5 + 73*(c*x + b)^(3/2)*b^2*c^5 + 15*sqrt(c*x + b)*b^3*c^5)/(b^3*c^4*x^4))/c","A",0
82,1,182,0,0.204115," ","integrate(x^(7/2)*(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","-\frac{2}{45045} \, c {\left(\frac{1024 \, b^{\frac{15}{2}}}{c^{7}} - \frac{3003 \, {\left(c x + b\right)}^{\frac{15}{2}} - 20790 \, {\left(c x + b\right)}^{\frac{13}{2}} b + 61425 \, {\left(c x + b\right)}^{\frac{11}{2}} b^{2} - 100100 \, {\left(c x + b\right)}^{\frac{9}{2}} b^{3} + 96525 \, {\left(c x + b\right)}^{\frac{7}{2}} b^{4} - 54054 \, {\left(c x + b\right)}^{\frac{5}{2}} b^{5} + 15015 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{6}}{c^{7}}\right)} + \frac{2}{9009} \, b {\left(\frac{256 \, b^{\frac{13}{2}}}{c^{6}} + \frac{693 \, {\left(c x + b\right)}^{\frac{13}{2}} - 4095 \, {\left(c x + b\right)}^{\frac{11}{2}} b + 10010 \, {\left(c x + b\right)}^{\frac{9}{2}} b^{2} - 12870 \, {\left(c x + b\right)}^{\frac{7}{2}} b^{3} + 9009 \, {\left(c x + b\right)}^{\frac{5}{2}} b^{4} - 3003 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{5}}{c^{6}}\right)}"," ",0,"-2/45045*c*(1024*b^(15/2)/c^7 - (3003*(c*x + b)^(15/2) - 20790*(c*x + b)^(13/2)*b + 61425*(c*x + b)^(11/2)*b^2 - 100100*(c*x + b)^(9/2)*b^3 + 96525*(c*x + b)^(7/2)*b^4 - 54054*(c*x + b)^(5/2)*b^5 + 15015*(c*x + b)^(3/2)*b^6)/c^7) + 2/9009*b*(256*b^(13/2)/c^6 + (693*(c*x + b)^(13/2) - 4095*(c*x + b)^(11/2)*b + 10010*(c*x + b)^(9/2)*b^2 - 12870*(c*x + b)^(7/2)*b^3 + 9009*(c*x + b)^(5/2)*b^4 - 3003*(c*x + b)^(3/2)*b^5)/c^6)","A",0
83,1,158,0,0.199123," ","integrate(x^(5/2)*(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","\frac{2}{9009} \, c {\left(\frac{256 \, b^{\frac{13}{2}}}{c^{6}} + \frac{693 \, {\left(c x + b\right)}^{\frac{13}{2}} - 4095 \, {\left(c x + b\right)}^{\frac{11}{2}} b + 10010 \, {\left(c x + b\right)}^{\frac{9}{2}} b^{2} - 12870 \, {\left(c x + b\right)}^{\frac{7}{2}} b^{3} + 9009 \, {\left(c x + b\right)}^{\frac{5}{2}} b^{4} - 3003 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{5}}{c^{6}}\right)} - \frac{2}{3465} \, b {\left(\frac{128 \, b^{\frac{11}{2}}}{c^{5}} - \frac{315 \, {\left(c x + b\right)}^{\frac{11}{2}} - 1540 \, {\left(c x + b\right)}^{\frac{9}{2}} b + 2970 \, {\left(c x + b\right)}^{\frac{7}{2}} b^{2} - 2772 \, {\left(c x + b\right)}^{\frac{5}{2}} b^{3} + 1155 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{4}}{c^{5}}\right)}"," ",0,"2/9009*c*(256*b^(13/2)/c^6 + (693*(c*x + b)^(13/2) - 4095*(c*x + b)^(11/2)*b + 10010*(c*x + b)^(9/2)*b^2 - 12870*(c*x + b)^(7/2)*b^3 + 9009*(c*x + b)^(5/2)*b^4 - 3003*(c*x + b)^(3/2)*b^5)/c^6) - 2/3465*b*(128*b^(11/2)/c^5 - (315*(c*x + b)^(11/2) - 1540*(c*x + b)^(9/2)*b + 2970*(c*x + b)^(7/2)*b^2 - 2772*(c*x + b)^(5/2)*b^3 + 1155*(c*x + b)^(3/2)*b^4)/c^5)","A",0
84,1,134,0,0.192269," ","integrate(x^(3/2)*(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","-\frac{2}{3465} \, c {\left(\frac{128 \, b^{\frac{11}{2}}}{c^{5}} - \frac{315 \, {\left(c x + b\right)}^{\frac{11}{2}} - 1540 \, {\left(c x + b\right)}^{\frac{9}{2}} b + 2970 \, {\left(c x + b\right)}^{\frac{7}{2}} b^{2} - 2772 \, {\left(c x + b\right)}^{\frac{5}{2}} b^{3} + 1155 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{4}}{c^{5}}\right)} + \frac{2}{315} \, b {\left(\frac{16 \, b^{\frac{9}{2}}}{c^{4}} + \frac{35 \, {\left(c x + b\right)}^{\frac{9}{2}} - 135 \, {\left(c x + b\right)}^{\frac{7}{2}} b + 189 \, {\left(c x + b\right)}^{\frac{5}{2}} b^{2} - 105 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{3}}{c^{4}}\right)}"," ",0,"-2/3465*c*(128*b^(11/2)/c^5 - (315*(c*x + b)^(11/2) - 1540*(c*x + b)^(9/2)*b + 2970*(c*x + b)^(7/2)*b^2 - 2772*(c*x + b)^(5/2)*b^3 + 1155*(c*x + b)^(3/2)*b^4)/c^5) + 2/315*b*(16*b^(9/2)/c^4 + (35*(c*x + b)^(9/2) - 135*(c*x + b)^(7/2)*b + 189*(c*x + b)^(5/2)*b^2 - 105*(c*x + b)^(3/2)*b^3)/c^4)","A",0
85,1,110,0,0.203473," ","integrate(x^(1/2)*(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","\frac{2}{315} \, c {\left(\frac{16 \, b^{\frac{9}{2}}}{c^{4}} + \frac{35 \, {\left(c x + b\right)}^{\frac{9}{2}} - 135 \, {\left(c x + b\right)}^{\frac{7}{2}} b + 189 \, {\left(c x + b\right)}^{\frac{5}{2}} b^{2} - 105 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{3}}{c^{4}}\right)} - \frac{2}{105} \, b {\left(\frac{8 \, b^{\frac{7}{2}}}{c^{3}} - \frac{15 \, {\left(c x + b\right)}^{\frac{7}{2}} - 42 \, {\left(c x + b\right)}^{\frac{5}{2}} b + 35 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{2}}{c^{3}}\right)}"," ",0,"2/315*c*(16*b^(9/2)/c^4 + (35*(c*x + b)^(9/2) - 135*(c*x + b)^(7/2)*b + 189*(c*x + b)^(5/2)*b^2 - 105*(c*x + b)^(3/2)*b^3)/c^4) - 2/105*b*(8*b^(7/2)/c^3 - (15*(c*x + b)^(7/2) - 42*(c*x + b)^(5/2)*b + 35*(c*x + b)^(3/2)*b^2)/c^3)","A",0
86,1,86,0,0.186472," ","integrate((c*x^2+b*x)^(3/2)/x^(1/2),x, algorithm=""giac"")","-\frac{2}{105} \, c {\left(\frac{8 \, b^{\frac{7}{2}}}{c^{3}} - \frac{15 \, {\left(c x + b\right)}^{\frac{7}{2}} - 42 \, {\left(c x + b\right)}^{\frac{5}{2}} b + 35 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{2}}{c^{3}}\right)} + \frac{2}{15} \, b {\left(\frac{2 \, b^{\frac{5}{2}}}{c^{2}} + \frac{3 \, {\left(c x + b\right)}^{\frac{5}{2}} - 5 \, {\left(c x + b\right)}^{\frac{3}{2}} b}{c^{2}}\right)}"," ",0,"-2/105*c*(8*b^(7/2)/c^3 - (15*(c*x + b)^(7/2) - 42*(c*x + b)^(5/2)*b + 35*(c*x + b)^(3/2)*b^2)/c^3) + 2/15*b*(2*b^(5/2)/c^2 + (3*(c*x + b)^(5/2) - 5*(c*x + b)^(3/2)*b)/c^2)","B",0
87,1,60,0,0.185841," ","integrate((c*x^2+b*x)^(3/2)/x^(3/2),x, algorithm=""giac"")","\frac{2}{15} \, c {\left(\frac{2 \, b^{\frac{5}{2}}}{c^{2}} + \frac{3 \, {\left(c x + b\right)}^{\frac{5}{2}} - 5 \, {\left(c x + b\right)}^{\frac{3}{2}} b}{c^{2}}\right)} + \frac{2}{3} \, b {\left(\frac{{\left(c x + b\right)}^{\frac{3}{2}}}{c} - \frac{b^{\frac{3}{2}}}{c}\right)}"," ",0,"2/15*c*(2*b^(5/2)/c^2 + (3*(c*x + b)^(5/2) - 5*(c*x + b)^(3/2)*b)/c^2) + 2/3*b*((c*x + b)^(3/2)/c - b^(3/2)/c)","B",0
88,1,77,0,0.196972," ","integrate((c*x^2+b*x)^(3/2)/x^(5/2),x, algorithm=""giac"")","\frac{2 \, b^{2} \arctan\left(\frac{\sqrt{c x + b}}{\sqrt{-b}}\right)}{\sqrt{-b}} + \frac{2}{3} \, {\left(c x + b\right)}^{\frac{3}{2}} + 2 \, \sqrt{c x + b} b - \frac{2 \, {\left(3 \, b^{2} \arctan\left(\frac{\sqrt{b}}{\sqrt{-b}}\right) + 4 \, \sqrt{-b} b^{\frac{3}{2}}\right)}}{3 \, \sqrt{-b}}"," ",0,"2*b^2*arctan(sqrt(c*x + b)/sqrt(-b))/sqrt(-b) + 2/3*(c*x + b)^(3/2) + 2*sqrt(c*x + b)*b - 2/3*(3*b^2*arctan(sqrt(b)/sqrt(-b)) + 4*sqrt(-b)*b^(3/2))/sqrt(-b)","A",0
89,1,56,0,0.226696," ","integrate((c*x^2+b*x)^(3/2)/x^(7/2),x, algorithm=""giac"")","\frac{\frac{3 \, b c^{2} \arctan\left(\frac{\sqrt{c x + b}}{\sqrt{-b}}\right)}{\sqrt{-b}} + 2 \, \sqrt{c x + b} c^{2} - \frac{\sqrt{c x + b} b c}{x}}{c}"," ",0,"(3*b*c^2*arctan(sqrt(c*x + b)/sqrt(-b))/sqrt(-b) + 2*sqrt(c*x + b)*c^2 - sqrt(c*x + b)*b*c/x)/c","A",0
90,1,64,0,0.238011," ","integrate((c*x^2+b*x)^(3/2)/x^(9/2),x, algorithm=""giac"")","\frac{\frac{3 \, c^{3} \arctan\left(\frac{\sqrt{c x + b}}{\sqrt{-b}}\right)}{\sqrt{-b}} - \frac{5 \, {\left(c x + b\right)}^{\frac{3}{2}} c^{3} - 3 \, \sqrt{c x + b} b c^{3}}{c^{2} x^{2}}}{4 \, c}"," ",0,"1/4*(3*c^3*arctan(sqrt(c*x + b)/sqrt(-b))/sqrt(-b) - (5*(c*x + b)^(3/2)*c^3 - 3*sqrt(c*x + b)*b*c^3)/(c^2*x^2))/c","A",0
91,1,84,0,0.233575," ","integrate((c*x^2+b*x)^(3/2)/x^(11/2),x, algorithm=""giac"")","-\frac{\frac{3 \, c^{4} \arctan\left(\frac{\sqrt{c x + b}}{\sqrt{-b}}\right)}{\sqrt{-b} b} + \frac{3 \, {\left(c x + b\right)}^{\frac{5}{2}} c^{4} + 8 \, {\left(c x + b\right)}^{\frac{3}{2}} b c^{4} - 3 \, \sqrt{c x + b} b^{2} c^{4}}{b c^{3} x^{3}}}{24 \, c}"," ",0,"-1/24*(3*c^4*arctan(sqrt(c*x + b)/sqrt(-b))/(sqrt(-b)*b) + (3*(c*x + b)^(5/2)*c^4 + 8*(c*x + b)^(3/2)*b*c^4 - 3*sqrt(c*x + b)*b^2*c^4)/(b*c^3*x^3))/c","A",0
92,1,99,0,0.291154," ","integrate((c*x^2+b*x)^(3/2)/x^(13/2),x, algorithm=""giac"")","\frac{\frac{3 \, c^{5} \arctan\left(\frac{\sqrt{c x + b}}{\sqrt{-b}}\right)}{\sqrt{-b} b^{2}} + \frac{3 \, {\left(c x + b\right)}^{\frac{7}{2}} c^{5} - 11 \, {\left(c x + b\right)}^{\frac{5}{2}} b c^{5} - 11 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{2} c^{5} + 3 \, \sqrt{c x + b} b^{3} c^{5}}{b^{2} c^{4} x^{4}}}{64 \, c}"," ",0,"1/64*(3*c^5*arctan(sqrt(c*x + b)/sqrt(-b))/(sqrt(-b)*b^2) + (3*(c*x + b)^(7/2)*c^5 - 11*(c*x + b)^(5/2)*b*c^5 - 11*(c*x + b)^(3/2)*b^2*c^5 + 3*sqrt(c*x + b)*b^3*c^5)/(b^2*c^4*x^4))/c","A",0
93,1,114,0,0.269691," ","integrate((c*x^2+b*x)^(3/2)/x^(15/2),x, algorithm=""giac"")","-\frac{\frac{15 \, c^{6} \arctan\left(\frac{\sqrt{c x + b}}{\sqrt{-b}}\right)}{\sqrt{-b} b^{3}} + \frac{15 \, {\left(c x + b\right)}^{\frac{9}{2}} c^{6} - 70 \, {\left(c x + b\right)}^{\frac{7}{2}} b c^{6} + 128 \, {\left(c x + b\right)}^{\frac{5}{2}} b^{2} c^{6} + 70 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{3} c^{6} - 15 \, \sqrt{c x + b} b^{4} c^{6}}{b^{3} c^{5} x^{5}}}{640 \, c}"," ",0,"-1/640*(15*c^6*arctan(sqrt(c*x + b)/sqrt(-b))/(sqrt(-b)*b^3) + (15*(c*x + b)^(9/2)*c^6 - 70*(c*x + b)^(7/2)*b*c^6 + 128*(c*x + b)^(5/2)*b^2*c^6 + 70*(c*x + b)^(3/2)*b^3*c^6 - 15*sqrt(c*x + b)*b^4*c^6)/(b^3*c^5*x^5))/c","A",0
94,1,61,0,0.191183," ","integrate(x^(7/2)/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","-\frac{2 \, \sqrt{c x + b} b^{3}}{c^{4}} + \frac{32 \, b^{\frac{7}{2}}}{35 \, c^{4}} + \frac{2 \, {\left(5 \, {\left(c x + b\right)}^{\frac{7}{2}} - 21 \, {\left(c x + b\right)}^{\frac{5}{2}} b + 35 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{2}\right)}}{35 \, c^{4}}"," ",0,"-2*sqrt(c*x + b)*b^3/c^4 + 32/35*b^(7/2)/c^4 + 2/35*(5*(c*x + b)^(7/2) - 21*(c*x + b)^(5/2)*b + 35*(c*x + b)^(3/2)*b^2)/c^4","A",0
95,1,49,0,0.205563," ","integrate(x^(5/2)/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\frac{2 \, \sqrt{c x + b} b^{2}}{c^{3}} - \frac{16 \, b^{\frac{5}{2}}}{15 \, c^{3}} + \frac{2 \, {\left(3 \, {\left(c x + b\right)}^{\frac{5}{2}} - 10 \, {\left(c x + b\right)}^{\frac{3}{2}} b\right)}}{15 \, c^{3}}"," ",0,"2*sqrt(c*x + b)*b^2/c^3 - 16/15*b^(5/2)/c^3 + 2/15*(3*(c*x + b)^(5/2) - 10*(c*x + b)^(3/2)*b)/c^3","A",0
96,1,34,0,0.172010," ","integrate(x^(3/2)/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(c x + b\right)}^{\frac{3}{2}}}{3 \, c^{2}} - \frac{2 \, \sqrt{c x + b} b}{c^{2}} + \frac{4 \, b^{\frac{3}{2}}}{3 \, c^{2}}"," ",0,"2/3*(c*x + b)^(3/2)/c^2 - 2*sqrt(c*x + b)*b/c^2 + 4/3*b^(3/2)/c^2","A",0
97,1,21,0,0.191974," ","integrate(x^(1/2)/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\frac{2 \, \sqrt{c x + b}}{c} - \frac{2 \, \sqrt{b}}{c}"," ",0,"2*sqrt(c*x + b)/c - 2*sqrt(b)/c","A",0
98,1,39,0,0.209276," ","integrate(1/x^(1/2)/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\frac{2 \, \arctan\left(\frac{\sqrt{c x + b}}{\sqrt{-b}}\right)}{\sqrt{-b}} - \frac{2 \, \arctan\left(\frac{\sqrt{b}}{\sqrt{-b}}\right)}{\sqrt{-b}}"," ",0,"2*arctan(sqrt(c*x + b)/sqrt(-b))/sqrt(-b) - 2*arctan(sqrt(b)/sqrt(-b))/sqrt(-b)","A",0
99,1,47,0,0.205673," ","integrate(1/x^(3/2)/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","-\frac{\frac{c^{2} \arctan\left(\frac{\sqrt{c x + b}}{\sqrt{-b}}\right)}{\sqrt{-b} b} + \frac{\sqrt{c x + b} c}{b x}}{c}"," ",0,"-(c^2*arctan(sqrt(c*x + b)/sqrt(-b))/(sqrt(-b)*b) + sqrt(c*x + b)*c/(b*x))/c","A",0
100,1,69,0,0.219958," ","integrate(1/x^(5/2)/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\frac{\frac{3 \, c^{3} \arctan\left(\frac{\sqrt{c x + b}}{\sqrt{-b}}\right)}{\sqrt{-b} b^{2}} + \frac{3 \, {\left(c x + b\right)}^{\frac{3}{2}} c^{3} - 5 \, \sqrt{c x + b} b c^{3}}{b^{2} c^{2} x^{2}}}{4 \, c}"," ",0,"1/4*(3*c^3*arctan(sqrt(c*x + b)/sqrt(-b))/(sqrt(-b)*b^2) + (3*(c*x + b)^(3/2)*c^3 - 5*sqrt(c*x + b)*b*c^3)/(b^2*c^2*x^2))/c","A",0
101,1,84,0,0.315336," ","integrate(1/x^(7/2)/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","-\frac{\frac{15 \, c^{4} \arctan\left(\frac{\sqrt{c x + b}}{\sqrt{-b}}\right)}{\sqrt{-b} b^{3}} + \frac{15 \, {\left(c x + b\right)}^{\frac{5}{2}} c^{4} - 40 \, {\left(c x + b\right)}^{\frac{3}{2}} b c^{4} + 33 \, \sqrt{c x + b} b^{2} c^{4}}{b^{3} c^{3} x^{3}}}{24 \, c}"," ",0,"-1/24*(15*c^4*arctan(sqrt(c*x + b)/sqrt(-b))/(sqrt(-b)*b^3) + (15*(c*x + b)^(5/2)*c^4 - 40*(c*x + b)^(3/2)*b*c^4 + 33*sqrt(c*x + b)*b^2*c^4)/(b^3*c^3*x^3))/c","A",0
102,1,100,0,0.219364," ","integrate(x^(13/2)/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","-\frac{512 \, b^{\frac{9}{2}}}{63 \, c^{6}} + \frac{2 \, b^{5}}{\sqrt{c x + b} c^{6}} + \frac{2 \, {\left(7 \, {\left(c x + b\right)}^{\frac{9}{2}} c^{48} - 45 \, {\left(c x + b\right)}^{\frac{7}{2}} b c^{48} + 126 \, {\left(c x + b\right)}^{\frac{5}{2}} b^{2} c^{48} - 210 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{3} c^{48} + 315 \, \sqrt{c x + b} b^{4} c^{48}\right)}}{63 \, c^{54}}"," ",0,"-512/63*b^(9/2)/c^6 + 2*b^5/(sqrt(c*x + b)*c^6) + 2/63*(7*(c*x + b)^(9/2)*c^48 - 45*(c*x + b)^(7/2)*b*c^48 + 126*(c*x + b)^(5/2)*b^2*c^48 - 210*(c*x + b)^(3/2)*b^3*c^48 + 315*sqrt(c*x + b)*b^4*c^48)/c^54","A",0
103,1,85,0,0.184752," ","integrate(x^(11/2)/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","\frac{256 \, b^{\frac{7}{2}}}{35 \, c^{5}} - \frac{2 \, b^{4}}{\sqrt{c x + b} c^{5}} + \frac{2 \, {\left(5 \, {\left(c x + b\right)}^{\frac{7}{2}} c^{30} - 28 \, {\left(c x + b\right)}^{\frac{5}{2}} b c^{30} + 70 \, {\left(c x + b\right)}^{\frac{3}{2}} b^{2} c^{30} - 140 \, \sqrt{c x + b} b^{3} c^{30}\right)}}{35 \, c^{35}}"," ",0,"256/35*b^(7/2)/c^5 - 2*b^4/(sqrt(c*x + b)*c^5) + 2/35*(5*(c*x + b)^(7/2)*c^30 - 28*(c*x + b)^(5/2)*b*c^30 + 70*(c*x + b)^(3/2)*b^2*c^30 - 140*sqrt(c*x + b)*b^3*c^30)/c^35","A",0
104,1,69,0,0.182046," ","integrate(x^(9/2)/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","-\frac{32 \, b^{\frac{5}{2}}}{5 \, c^{4}} + \frac{2 \, b^{3}}{\sqrt{c x + b} c^{4}} + \frac{2 \, {\left({\left(c x + b\right)}^{\frac{5}{2}} c^{16} - 5 \, {\left(c x + b\right)}^{\frac{3}{2}} b c^{16} + 15 \, \sqrt{c x + b} b^{2} c^{16}\right)}}{5 \, c^{20}}"," ",0,"-32/5*b^(5/2)/c^4 + 2*b^3/(sqrt(c*x + b)*c^4) + 2/5*((c*x + b)^(5/2)*c^16 - 5*(c*x + b)^(3/2)*b*c^16 + 15*sqrt(c*x + b)*b^2*c^16)/c^20","A",0
105,1,54,0,0.177373," ","integrate(x^(7/2)/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","\frac{16 \, b^{\frac{3}{2}}}{3 \, c^{3}} - \frac{2 \, b^{2}}{\sqrt{c x + b} c^{3}} + \frac{2 \, {\left({\left(c x + b\right)}^{\frac{3}{2}} c^{6} - 6 \, \sqrt{c x + b} b c^{6}\right)}}{3 \, c^{9}}"," ",0,"16/3*b^(3/2)/c^3 - 2*b^2/(sqrt(c*x + b)*c^3) + 2/3*((c*x + b)^(3/2)*c^6 - 6*sqrt(c*x + b)*b*c^6)/c^9","A",0
106,1,38,0,0.171608," ","integrate(x^(5/2)/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{\sqrt{c x + b}}{c} + \frac{b}{\sqrt{c x + b} c}\right)}}{c} - \frac{4 \, \sqrt{b}}{c^{2}}"," ",0,"2*(sqrt(c*x + b)/c + b/(sqrt(c*x + b)*c))/c - 4*sqrt(b)/c^2","A",0
107,1,21,0,0.181553," ","integrate(x^(3/2)/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","-\frac{2}{\sqrt{c x + b} c} + \frac{2}{\sqrt{b} c}"," ",0,"-2/(sqrt(c*x + b)*c) + 2/(sqrt(b)*c)","A",0
108,1,67,0,0.218806," ","integrate(x^(1/2)/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","\frac{2 \, \arctan\left(\frac{\sqrt{c x + b}}{\sqrt{-b}}\right)}{\sqrt{-b} b} - \frac{2 \, {\left(\sqrt{b} \arctan\left(\frac{\sqrt{b}}{\sqrt{-b}}\right) + \sqrt{-b}\right)}}{\sqrt{-b} b^{\frac{3}{2}}} + \frac{2}{\sqrt{c x + b} b}"," ",0,"2*arctan(sqrt(c*x + b)/sqrt(-b))/(sqrt(-b)*b) - 2*(sqrt(b)*arctan(sqrt(b)/sqrt(-b)) + sqrt(-b))/(sqrt(-b)*b^(3/2)) + 2/(sqrt(c*x + b)*b)","A",0
109,1,64,0,0.290843," ","integrate(1/x^(1/2)/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","-\frac{3 \, c \arctan\left(\frac{\sqrt{c x + b}}{\sqrt{-b}}\right)}{\sqrt{-b} b^{2}} - \frac{3 \, {\left(c x + b\right)} c - 2 \, b c}{{\left({\left(c x + b\right)}^{\frac{3}{2}} - \sqrt{c x + b} b\right)} b^{2}}"," ",0,"-3*c*arctan(sqrt(c*x + b)/sqrt(-b))/(sqrt(-b)*b^2) - (3*(c*x + b)*c - 2*b*c)/(((c*x + b)^(3/2) - sqrt(c*x + b)*b)*b^2)","A",0
110,1,80,0,0.247272," ","integrate(1/x^(3/2)/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","\frac{15 \, c^{2} \arctan\left(\frac{\sqrt{c x + b}}{\sqrt{-b}}\right)}{4 \, \sqrt{-b} b^{3}} + \frac{2 \, c^{2}}{\sqrt{c x + b} b^{3}} + \frac{7 \, {\left(c x + b\right)}^{\frac{3}{2}} c^{2} - 9 \, \sqrt{c x + b} b c^{2}}{4 \, b^{3} c^{2} x^{2}}"," ",0,"15/4*c^2*arctan(sqrt(c*x + b)/sqrt(-b))/(sqrt(-b)*b^3) + 2*c^2/(sqrt(c*x + b)*b^3) + 1/4*(7*(c*x + b)^(3/2)*c^2 - 9*sqrt(c*x + b)*b*c^2)/(b^3*c^2*x^2)","A",0
111,1,95,0,0.260715," ","integrate(1/x^(5/2)/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","-\frac{35 \, c^{3} \arctan\left(\frac{\sqrt{c x + b}}{\sqrt{-b}}\right)}{8 \, \sqrt{-b} b^{4}} - \frac{2 \, c^{3}}{\sqrt{c x + b} b^{4}} - \frac{57 \, {\left(c x + b\right)}^{\frac{5}{2}} c^{3} - 136 \, {\left(c x + b\right)}^{\frac{3}{2}} b c^{3} + 87 \, \sqrt{c x + b} b^{2} c^{3}}{24 \, b^{4} c^{3} x^{3}}"," ",0,"-35/8*c^3*arctan(sqrt(c*x + b)/sqrt(-b))/(sqrt(-b)*b^4) - 2*c^3/(sqrt(c*x + b)*b^4) - 1/24*(57*(c*x + b)^(5/2)*c^3 - 136*(c*x + b)^(3/2)*b*c^3 + 87*sqrt(c*x + b)*b^2*c^3)/(b^4*c^3*x^3)","A",0
112,1,264,0,0.196509," ","integrate((d*x)^m*(c*x^2+b*x)^3,x, algorithm=""giac"")","\frac{\left(d x\right)^{m} c^{3} m^{3} x^{7} + 3 \, \left(d x\right)^{m} b c^{2} m^{3} x^{6} + 15 \, \left(d x\right)^{m} c^{3} m^{2} x^{7} + 3 \, \left(d x\right)^{m} b^{2} c m^{3} x^{5} + 48 \, \left(d x\right)^{m} b c^{2} m^{2} x^{6} + 74 \, \left(d x\right)^{m} c^{3} m x^{7} + \left(d x\right)^{m} b^{3} m^{3} x^{4} + 51 \, \left(d x\right)^{m} b^{2} c m^{2} x^{5} + 249 \, \left(d x\right)^{m} b c^{2} m x^{6} + 120 \, \left(d x\right)^{m} c^{3} x^{7} + 18 \, \left(d x\right)^{m} b^{3} m^{2} x^{4} + 282 \, \left(d x\right)^{m} b^{2} c m x^{5} + 420 \, \left(d x\right)^{m} b c^{2} x^{6} + 107 \, \left(d x\right)^{m} b^{3} m x^{4} + 504 \, \left(d x\right)^{m} b^{2} c x^{5} + 210 \, \left(d x\right)^{m} b^{3} x^{4}}{m^{4} + 22 \, m^{3} + 179 \, m^{2} + 638 \, m + 840}"," ",0,"((d*x)^m*c^3*m^3*x^7 + 3*(d*x)^m*b*c^2*m^3*x^6 + 15*(d*x)^m*c^3*m^2*x^7 + 3*(d*x)^m*b^2*c*m^3*x^5 + 48*(d*x)^m*b*c^2*m^2*x^6 + 74*(d*x)^m*c^3*m*x^7 + (d*x)^m*b^3*m^3*x^4 + 51*(d*x)^m*b^2*c*m^2*x^5 + 249*(d*x)^m*b*c^2*m*x^6 + 120*(d*x)^m*c^3*x^7 + 18*(d*x)^m*b^3*m^2*x^4 + 282*(d*x)^m*b^2*c*m*x^5 + 420*(d*x)^m*b*c^2*x^6 + 107*(d*x)^m*b^3*m*x^4 + 504*(d*x)^m*b^2*c*x^5 + 210*(d*x)^m*b^3*x^4)/(m^4 + 22*m^3 + 179*m^2 + 638*m + 840)","B",0
113,1,141,0,0.173106," ","integrate((d*x)^m*(c*x^2+b*x)^2,x, algorithm=""giac"")","\frac{\left(d x\right)^{m} c^{2} m^{2} x^{5} + 2 \, \left(d x\right)^{m} b c m^{2} x^{4} + 7 \, \left(d x\right)^{m} c^{2} m x^{5} + \left(d x\right)^{m} b^{2} m^{2} x^{3} + 16 \, \left(d x\right)^{m} b c m x^{4} + 12 \, \left(d x\right)^{m} c^{2} x^{5} + 9 \, \left(d x\right)^{m} b^{2} m x^{3} + 30 \, \left(d x\right)^{m} b c x^{4} + 20 \, \left(d x\right)^{m} b^{2} x^{3}}{m^{3} + 12 \, m^{2} + 47 \, m + 60}"," ",0,"((d*x)^m*c^2*m^2*x^5 + 2*(d*x)^m*b*c*m^2*x^4 + 7*(d*x)^m*c^2*m*x^5 + (d*x)^m*b^2*m^2*x^3 + 16*(d*x)^m*b*c*m*x^4 + 12*(d*x)^m*c^2*x^5 + 9*(d*x)^m*b^2*m*x^3 + 30*(d*x)^m*b*c*x^4 + 20*(d*x)^m*b^2*x^3)/(m^3 + 12*m^2 + 47*m + 60)","B",0
114,1,56,0,0.153822," ","integrate((d*x)^m*(c*x^2+b*x),x, algorithm=""giac"")","\frac{\left(d x\right)^{m} c m x^{3} + \left(d x\right)^{m} b m x^{2} + 2 \, \left(d x\right)^{m} c x^{3} + 3 \, \left(d x\right)^{m} b x^{2}}{m^{2} + 5 \, m + 6}"," ",0,"((d*x)^m*c*m*x^3 + (d*x)^m*b*m*x^2 + 2*(d*x)^m*c*x^3 + 3*(d*x)^m*b*x^2)/(m^2 + 5*m + 6)","A",0
115,0,0,0,0.000000," ","integrate((d*x)^m/(c*x^2+b*x),x, algorithm=""giac"")","\int \frac{\left(d x\right)^{m}}{c x^{2} + b x}\,{d x}"," ",0,"integrate((d*x)^m/(c*x^2 + b*x), x)","F",0
116,0,0,0,0.000000," ","integrate((d*x)^m/(c*x^2+b*x)^2,x, algorithm=""giac"")","\int \frac{\left(d x\right)^{m}}{{\left(c x^{2} + b x\right)}^{2}}\,{d x}"," ",0,"integrate((d*x)^m/(c*x^2 + b*x)^2, x)","F",0
117,0,0,0,0.000000," ","integrate((d*x)^m/(c*x^2+b*x)^3,x, algorithm=""giac"")","\int \frac{\left(d x\right)^{m}}{{\left(c x^{2} + b x\right)}^{3}}\,{d x}"," ",0,"integrate((d*x)^m/(c*x^2 + b*x)^3, x)","F",0
118,0,0,0,0.000000," ","integrate((d*x)^m*(c*x^2+b*x)^(5/2),x, algorithm=""giac"")","\int {\left(c x^{2} + b x\right)}^{\frac{5}{2}} \left(d x\right)^{m}\,{d x}"," ",0,"integrate((c*x^2 + b*x)^(5/2)*(d*x)^m, x)","F",0
119,0,0,0,0.000000," ","integrate((d*x)^m*(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","\int {\left(c x^{2} + b x\right)}^{\frac{3}{2}} \left(d x\right)^{m}\,{d x}"," ",0,"integrate((c*x^2 + b*x)^(3/2)*(d*x)^m, x)","F",0
120,0,0,0,0.000000," ","integrate((d*x)^m*(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\int \sqrt{c x^{2} + b x} \left(d x\right)^{m}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + b*x)*(d*x)^m, x)","F",0
121,0,0,0,0.000000," ","integrate((d*x)^m/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\int \frac{\left(d x\right)^{m}}{\sqrt{c x^{2} + b x}}\,{d x}"," ",0,"integrate((d*x)^m/sqrt(c*x^2 + b*x), x)","F",0
122,0,0,0,0.000000," ","integrate((d*x)^m/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","\int \frac{\left(d x\right)^{m}}{{\left(c x^{2} + b x\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((d*x)^m/(c*x^2 + b*x)^(3/2), x)","F",0
123,0,0,0,0.000000," ","integrate((d*x)^m/(c*x^2+b*x)^(5/2),x, algorithm=""giac"")","\int \frac{\left(d x\right)^{m}}{{\left(c x^{2} + b x\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((d*x)^m/(c*x^2 + b*x)^(5/2), x)","F",0
124,0,0,0,0.000000," ","integrate((d*x)^m*(c*x^2+b*x)^p,x, algorithm=""giac"")","\int {\left(c x^{2} + b x\right)}^{p} \left(d x\right)^{m}\,{d x}"," ",0,"integrate((c*x^2 + b*x)^p*(d*x)^m, x)","F",0
125,0,0,0,0.000000," ","integrate(x^3*(c*x^2+b*x)^p,x, algorithm=""giac"")","\int {\left(c x^{2} + b x\right)}^{p} x^{3}\,{d x}"," ",0,"integrate((c*x^2 + b*x)^p*x^3, x)","F",0
126,0,0,0,0.000000," ","integrate(x^2*(c*x^2+b*x)^p,x, algorithm=""giac"")","\int {\left(c x^{2} + b x\right)}^{p} x^{2}\,{d x}"," ",0,"integrate((c*x^2 + b*x)^p*x^2, x)","F",0
127,0,0,0,0.000000," ","integrate(x*(c*x^2+b*x)^p,x, algorithm=""giac"")","\int {\left(c x^{2} + b x\right)}^{p} x\,{d x}"," ",0,"integrate((c*x^2 + b*x)^p*x, x)","F",0
128,0,0,0,0.000000," ","integrate((c*x^2+b*x)^p/x,x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x\right)}^{p}}{x}\,{d x}"," ",0,"integrate((c*x^2 + b*x)^p/x, x)","F",0
129,0,0,0,0.000000," ","integrate((c*x^2+b*x)^p/x^2,x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x\right)}^{p}}{x^{2}}\,{d x}"," ",0,"integrate((c*x^2 + b*x)^p/x^2, x)","F",0
130,0,0,0,0.000000," ","integrate((c*x^2+b*x)^p/x^3,x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x\right)}^{p}}{x^{3}}\,{d x}"," ",0,"integrate((c*x^2 + b*x)^p/x^3, x)","F",0
131,0,0,0,0.000000," ","integrate((d*x)^(5/2)*(c*x^2+b*x)^p,x, algorithm=""giac"")","\int \left(d x\right)^{\frac{5}{2}} {\left(c x^{2} + b x\right)}^{p}\,{d x}"," ",0,"integrate((d*x)^(5/2)*(c*x^2 + b*x)^p, x)","F",0
132,0,0,0,0.000000," ","integrate((d*x)^(3/2)*(c*x^2+b*x)^p,x, algorithm=""giac"")","\int \left(d x\right)^{\frac{3}{2}} {\left(c x^{2} + b x\right)}^{p}\,{d x}"," ",0,"integrate((d*x)^(3/2)*(c*x^2 + b*x)^p, x)","F",0
133,0,0,0,0.000000," ","integrate((d*x)^(1/2)*(c*x^2+b*x)^p,x, algorithm=""giac"")","\int \sqrt{d x} {\left(c x^{2} + b x\right)}^{p}\,{d x}"," ",0,"integrate(sqrt(d*x)*(c*x^2 + b*x)^p, x)","F",0
134,0,0,0,0.000000," ","integrate((c*x^2+b*x)^p/(d*x)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x\right)}^{p}}{\sqrt{d x}}\,{d x}"," ",0,"integrate((c*x^2 + b*x)^p/sqrt(d*x), x)","F",0
135,0,0,0,0.000000," ","integrate((c*x^2+b*x)^p/(d*x)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x\right)}^{p}}{\left(d x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c*x^2 + b*x)^p/(d*x)^(3/2), x)","F",0
136,0,0,0,0.000000," ","integrate((c*x^2+b*x)^p/(d*x)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x\right)}^{p}}{\left(d x\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((c*x^2 + b*x)^p/(d*x)^(5/2), x)","F",0
137,1,39,0,0.200137," ","integrate(x^4*((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{6} \, b x^{6} \mathrm{sgn}\left(b x + a\right) + \frac{1}{5} \, a x^{5} \mathrm{sgn}\left(b x + a\right) + \frac{a^{6} \mathrm{sgn}\left(b x + a\right)}{30 \, b^{5}}"," ",0,"1/6*b*x^6*sgn(b*x + a) + 1/5*a*x^5*sgn(b*x + a) + 1/30*a^6*sgn(b*x + a)/b^5","A",0
138,1,39,0,0.162493," ","integrate(x^3*((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{5} \, b x^{5} \mathrm{sgn}\left(b x + a\right) + \frac{1}{4} \, a x^{4} \mathrm{sgn}\left(b x + a\right) - \frac{a^{5} \mathrm{sgn}\left(b x + a\right)}{20 \, b^{4}}"," ",0,"1/5*b*x^5*sgn(b*x + a) + 1/4*a*x^4*sgn(b*x + a) - 1/20*a^5*sgn(b*x + a)/b^4","A",0
139,1,39,0,0.174816," ","integrate(x^2*((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{4} \, b x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{1}{3} \, a x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{a^{4} \mathrm{sgn}\left(b x + a\right)}{12 \, b^{3}}"," ",0,"1/4*b*x^4*sgn(b*x + a) + 1/3*a*x^3*sgn(b*x + a) + 1/12*a^4*sgn(b*x + a)/b^3","A",0
140,1,39,0,0.156504," ","integrate(x*((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{3} \, b x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, a x^{2} \mathrm{sgn}\left(b x + a\right) - \frac{a^{3} \mathrm{sgn}\left(b x + a\right)}{6 \, b^{2}}"," ",0,"1/3*b*x^3*sgn(b*x + a) + 1/2*a*x^2*sgn(b*x + a) - 1/6*a^3*sgn(b*x + a)/b^2","A",0
141,1,33,0,0.168649," ","integrate(((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, {\left(b x^{2} + 2 \, a x\right)} \mathrm{sgn}\left(b x + a\right) + \frac{a^{2} \mathrm{sgn}\left(b x + a\right)}{2 \, b}"," ",0,"1/2*(b*x^2 + 2*a*x)*sgn(b*x + a) + 1/2*a^2*sgn(b*x + a)/b","A",0
142,1,21,0,0.162999," ","integrate(((b*x+a)^2)^(1/2)/x,x, algorithm=""giac"")","b x \mathrm{sgn}\left(b x + a\right) + a \log\left({\left| x \right|}\right) \mathrm{sgn}\left(b x + a\right)"," ",0,"b*x*sgn(b*x + a) + a*log(abs(x))*sgn(b*x + a)","A",0
143,1,24,0,0.199523," ","integrate(((b*x+a)^2)^(1/2)/x^2,x, algorithm=""giac"")","b \log\left({\left| x \right|}\right) \mathrm{sgn}\left(b x + a\right) - \frac{a \mathrm{sgn}\left(b x + a\right)}{x}"," ",0,"b*log(abs(x))*sgn(b*x + a) - a*sgn(b*x + a)/x","A",0
144,1,39,0,0.153727," ","integrate(((b*x+a)^2)^(1/2)/x^3,x, algorithm=""giac"")","-\frac{b^{2} \mathrm{sgn}\left(b x + a\right)}{2 \, a} - \frac{2 \, b x \mathrm{sgn}\left(b x + a\right) + a \mathrm{sgn}\left(b x + a\right)}{2 \, x^{2}}"," ",0,"-1/2*b^2*sgn(b*x + a)/a - 1/2*(2*b*x*sgn(b*x + a) + a*sgn(b*x + a))/x^2","A",0
145,1,40,0,0.169532," ","integrate(((b*x+a)^2)^(1/2)/x^4,x, algorithm=""giac"")","\frac{b^{3} \mathrm{sgn}\left(b x + a\right)}{6 \, a^{2}} - \frac{3 \, b x \mathrm{sgn}\left(b x + a\right) + 2 \, a \mathrm{sgn}\left(b x + a\right)}{6 \, x^{3}}"," ",0,"1/6*b^3*sgn(b*x + a)/a^2 - 1/6*(3*b*x*sgn(b*x + a) + 2*a*sgn(b*x + a))/x^3","A",0
146,1,40,0,0.186770," ","integrate(((b*x+a)^2)^(1/2)/x^5,x, algorithm=""giac"")","-\frac{b^{4} \mathrm{sgn}\left(b x + a\right)}{12 \, a^{3}} - \frac{4 \, b x \mathrm{sgn}\left(b x + a\right) + 3 \, a \mathrm{sgn}\left(b x + a\right)}{12 \, x^{4}}"," ",0,"-1/12*b^4*sgn(b*x + a)/a^3 - 1/12*(4*b*x*sgn(b*x + a) + 3*a*sgn(b*x + a))/x^4","A",0
147,1,40,0,0.166346," ","integrate(((b*x+a)^2)^(1/2)/x^6,x, algorithm=""giac"")","\frac{b^{5} \mathrm{sgn}\left(b x + a\right)}{20 \, a^{4}} - \frac{5 \, b x \mathrm{sgn}\left(b x + a\right) + 4 \, a \mathrm{sgn}\left(b x + a\right)}{20 \, x^{5}}"," ",0,"1/20*b^5*sgn(b*x + a)/a^4 - 1/20*(5*b*x*sgn(b*x + a) + 4*a*sgn(b*x + a))/x^5","A",0
148,1,73,0,0.209576," ","integrate(x^5*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{1}{9} \, b^{3} x^{9} \mathrm{sgn}\left(b x + a\right) + \frac{3}{8} \, a b^{2} x^{8} \mathrm{sgn}\left(b x + a\right) + \frac{3}{7} \, a^{2} b x^{7} \mathrm{sgn}\left(b x + a\right) + \frac{1}{6} \, a^{3} x^{6} \mathrm{sgn}\left(b x + a\right) - \frac{a^{9} \mathrm{sgn}\left(b x + a\right)}{504 \, b^{6}}"," ",0,"1/9*b^3*x^9*sgn(b*x + a) + 3/8*a*b^2*x^8*sgn(b*x + a) + 3/7*a^2*b*x^7*sgn(b*x + a) + 1/6*a^3*x^6*sgn(b*x + a) - 1/504*a^9*sgn(b*x + a)/b^6","A",0
149,1,73,0,0.154683," ","integrate(x^4*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{1}{8} \, b^{3} x^{8} \mathrm{sgn}\left(b x + a\right) + \frac{3}{7} \, a b^{2} x^{7} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, a^{2} b x^{6} \mathrm{sgn}\left(b x + a\right) + \frac{1}{5} \, a^{3} x^{5} \mathrm{sgn}\left(b x + a\right) + \frac{a^{8} \mathrm{sgn}\left(b x + a\right)}{280 \, b^{5}}"," ",0,"1/8*b^3*x^8*sgn(b*x + a) + 3/7*a*b^2*x^7*sgn(b*x + a) + 1/2*a^2*b*x^6*sgn(b*x + a) + 1/5*a^3*x^5*sgn(b*x + a) + 1/280*a^8*sgn(b*x + a)/b^5","A",0
150,1,73,0,0.197742," ","integrate(x^3*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{1}{7} \, b^{3} x^{7} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, a b^{2} x^{6} \mathrm{sgn}\left(b x + a\right) + \frac{3}{5} \, a^{2} b x^{5} \mathrm{sgn}\left(b x + a\right) + \frac{1}{4} \, a^{3} x^{4} \mathrm{sgn}\left(b x + a\right) - \frac{a^{7} \mathrm{sgn}\left(b x + a\right)}{140 \, b^{4}}"," ",0,"1/7*b^3*x^7*sgn(b*x + a) + 1/2*a*b^2*x^6*sgn(b*x + a) + 3/5*a^2*b*x^5*sgn(b*x + a) + 1/4*a^3*x^4*sgn(b*x + a) - 1/140*a^7*sgn(b*x + a)/b^4","A",0
151,1,73,0,0.157632," ","integrate(x^2*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{1}{6} \, b^{3} x^{6} \mathrm{sgn}\left(b x + a\right) + \frac{3}{5} \, a b^{2} x^{5} \mathrm{sgn}\left(b x + a\right) + \frac{3}{4} \, a^{2} b x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{1}{3} \, a^{3} x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{a^{6} \mathrm{sgn}\left(b x + a\right)}{60 \, b^{3}}"," ",0,"1/6*b^3*x^6*sgn(b*x + a) + 3/5*a*b^2*x^5*sgn(b*x + a) + 3/4*a^2*b*x^4*sgn(b*x + a) + 1/3*a^3*x^3*sgn(b*x + a) + 1/60*a^6*sgn(b*x + a)/b^3","A",0
152,1,72,0,0.177276," ","integrate(x*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{1}{5} \, b^{3} x^{5} \mathrm{sgn}\left(b x + a\right) + \frac{3}{4} \, a b^{2} x^{4} \mathrm{sgn}\left(b x + a\right) + a^{2} b x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, a^{3} x^{2} \mathrm{sgn}\left(b x + a\right) - \frac{a^{5} \mathrm{sgn}\left(b x + a\right)}{20 \, b^{2}}"," ",0,"1/5*b^3*x^5*sgn(b*x + a) + 3/4*a*b^2*x^4*sgn(b*x + a) + a^2*b*x^3*sgn(b*x + a) + 1/2*a^3*x^2*sgn(b*x + a) - 1/20*a^5*sgn(b*x + a)/b^2","A",0
153,1,57,0,0.233620," ","integrate((b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{1}{2} \, {\left(b x^{2} + 2 \, a x\right)} a^{2} \mathrm{sgn}\left(b x + a\right) + \frac{a^{4} \mathrm{sgn}\left(b x + a\right)}{4 \, b} + \frac{1}{4} \, {\left(b x^{2} + 2 \, a x\right)}^{2} b \mathrm{sgn}\left(b x + a\right)"," ",0,"1/2*(b*x^2 + 2*a*x)*a^2*sgn(b*x + a) + 1/4*a^4*sgn(b*x + a)/b + 1/4*(b*x^2 + 2*a*x)^2*b*sgn(b*x + a)","B",0
154,1,56,0,0.157484," ","integrate((b^2*x^2+2*a*b*x+a^2)^(3/2)/x,x, algorithm=""giac"")","\frac{1}{3} \, b^{3} x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{3}{2} \, a b^{2} x^{2} \mathrm{sgn}\left(b x + a\right) + 3 \, a^{2} b x \mathrm{sgn}\left(b x + a\right) + a^{3} \log\left({\left| x \right|}\right) \mathrm{sgn}\left(b x + a\right)"," ",0,"1/3*b^3*x^3*sgn(b*x + a) + 3/2*a*b^2*x^2*sgn(b*x + a) + 3*a^2*b*x*sgn(b*x + a) + a^3*log(abs(x))*sgn(b*x + a)","A",0
155,1,57,0,0.214842," ","integrate((b^2*x^2+2*a*b*x+a^2)^(3/2)/x^2,x, algorithm=""giac"")","\frac{1}{2} \, b^{3} x^{2} \mathrm{sgn}\left(b x + a\right) + 3 \, a b^{2} x \mathrm{sgn}\left(b x + a\right) + 3 \, a^{2} b \log\left({\left| x \right|}\right) \mathrm{sgn}\left(b x + a\right) - \frac{a^{3} \mathrm{sgn}\left(b x + a\right)}{x}"," ",0,"1/2*b^3*x^2*sgn(b*x + a) + 3*a*b^2*x*sgn(b*x + a) + 3*a^2*b*log(abs(x))*sgn(b*x + a) - a^3*sgn(b*x + a)/x","A",0
156,1,56,0,0.160912," ","integrate((b^2*x^2+2*a*b*x+a^2)^(3/2)/x^3,x, algorithm=""giac"")","b^{3} x \mathrm{sgn}\left(b x + a\right) + 3 \, a b^{2} \log\left({\left| x \right|}\right) \mathrm{sgn}\left(b x + a\right) - \frac{6 \, a^{2} b x \mathrm{sgn}\left(b x + a\right) + a^{3} \mathrm{sgn}\left(b x + a\right)}{2 \, x^{2}}"," ",0,"b^3*x*sgn(b*x + a) + 3*a*b^2*log(abs(x))*sgn(b*x + a) - 1/2*(6*a^2*b*x*sgn(b*x + a) + a^3*sgn(b*x + a))/x^2","A",0
157,1,59,0,0.157368," ","integrate((b^2*x^2+2*a*b*x+a^2)^(3/2)/x^4,x, algorithm=""giac"")","b^{3} \log\left({\left| x \right|}\right) \mathrm{sgn}\left(b x + a\right) - \frac{18 \, a b^{2} x^{2} \mathrm{sgn}\left(b x + a\right) + 9 \, a^{2} b x \mathrm{sgn}\left(b x + a\right) + 2 \, a^{3} \mathrm{sgn}\left(b x + a\right)}{6 \, x^{3}}"," ",0,"b^3*log(abs(x))*sgn(b*x + a) - 1/6*(18*a*b^2*x^2*sgn(b*x + a) + 9*a^2*b*x*sgn(b*x + a) + 2*a^3*sgn(b*x + a))/x^3","A",0
158,1,73,0,0.239584," ","integrate((b^2*x^2+2*a*b*x+a^2)^(3/2)/x^5,x, algorithm=""giac"")","-\frac{b^{4} \mathrm{sgn}\left(b x + a\right)}{4 \, a} - \frac{4 \, b^{3} x^{3} \mathrm{sgn}\left(b x + a\right) + 6 \, a b^{2} x^{2} \mathrm{sgn}\left(b x + a\right) + 4 \, a^{2} b x \mathrm{sgn}\left(b x + a\right) + a^{3} \mathrm{sgn}\left(b x + a\right)}{4 \, x^{4}}"," ",0,"-1/4*b^4*sgn(b*x + a)/a - 1/4*(4*b^3*x^3*sgn(b*x + a) + 6*a*b^2*x^2*sgn(b*x + a) + 4*a^2*b*x*sgn(b*x + a) + a^3*sgn(b*x + a))/x^4","B",0
159,1,74,0,0.240409," ","integrate((b^2*x^2+2*a*b*x+a^2)^(3/2)/x^6,x, algorithm=""giac"")","\frac{b^{5} \mathrm{sgn}\left(b x + a\right)}{20 \, a^{2}} - \frac{10 \, b^{3} x^{3} \mathrm{sgn}\left(b x + a\right) + 20 \, a b^{2} x^{2} \mathrm{sgn}\left(b x + a\right) + 15 \, a^{2} b x \mathrm{sgn}\left(b x + a\right) + 4 \, a^{3} \mathrm{sgn}\left(b x + a\right)}{20 \, x^{5}}"," ",0,"1/20*b^5*sgn(b*x + a)/a^2 - 1/20*(10*b^3*x^3*sgn(b*x + a) + 20*a*b^2*x^2*sgn(b*x + a) + 15*a^2*b*x*sgn(b*x + a) + 4*a^3*sgn(b*x + a))/x^5","A",0
160,1,74,0,0.162497," ","integrate((b^2*x^2+2*a*b*x+a^2)^(3/2)/x^7,x, algorithm=""giac"")","-\frac{b^{6} \mathrm{sgn}\left(b x + a\right)}{60 \, a^{3}} - \frac{20 \, b^{3} x^{3} \mathrm{sgn}\left(b x + a\right) + 45 \, a b^{2} x^{2} \mathrm{sgn}\left(b x + a\right) + 36 \, a^{2} b x \mathrm{sgn}\left(b x + a\right) + 10 \, a^{3} \mathrm{sgn}\left(b x + a\right)}{60 \, x^{6}}"," ",0,"-1/60*b^6*sgn(b*x + a)/a^3 - 1/60*(20*b^3*x^3*sgn(b*x + a) + 45*a*b^2*x^2*sgn(b*x + a) + 36*a^2*b*x*sgn(b*x + a) + 10*a^3*sgn(b*x + a))/x^6","A",0
161,1,74,0,0.185143," ","integrate((b^2*x^2+2*a*b*x+a^2)^(3/2)/x^8,x, algorithm=""giac"")","\frac{b^{7} \mathrm{sgn}\left(b x + a\right)}{140 \, a^{4}} - \frac{35 \, b^{3} x^{3} \mathrm{sgn}\left(b x + a\right) + 84 \, a b^{2} x^{2} \mathrm{sgn}\left(b x + a\right) + 70 \, a^{2} b x \mathrm{sgn}\left(b x + a\right) + 20 \, a^{3} \mathrm{sgn}\left(b x + a\right)}{140 \, x^{7}}"," ",0,"1/140*b^7*sgn(b*x + a)/a^4 - 1/140*(35*b^3*x^3*sgn(b*x + a) + 84*a*b^2*x^2*sgn(b*x + a) + 70*a^2*b*x*sgn(b*x + a) + 20*a^3*sgn(b*x + a))/x^7","A",0
162,1,74,0,0.179279," ","integrate((b^2*x^2+2*a*b*x+a^2)^(3/2)/x^9,x, algorithm=""giac"")","-\frac{b^{8} \mathrm{sgn}\left(b x + a\right)}{280 \, a^{5}} - \frac{56 \, b^{3} x^{3} \mathrm{sgn}\left(b x + a\right) + 140 \, a b^{2} x^{2} \mathrm{sgn}\left(b x + a\right) + 120 \, a^{2} b x \mathrm{sgn}\left(b x + a\right) + 35 \, a^{3} \mathrm{sgn}\left(b x + a\right)}{280 \, x^{8}}"," ",0,"-1/280*b^8*sgn(b*x + a)/a^5 - 1/280*(56*b^3*x^3*sgn(b*x + a) + 140*a*b^2*x^2*sgn(b*x + a) + 120*a^2*b*x*sgn(b*x + a) + 35*a^3*sgn(b*x + a))/x^8","A",0
163,1,107,0,0.163029," ","integrate(x^5*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{11} \, b^{5} x^{11} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, a b^{4} x^{10} \mathrm{sgn}\left(b x + a\right) + \frac{10}{9} \, a^{2} b^{3} x^{9} \mathrm{sgn}\left(b x + a\right) + \frac{5}{4} \, a^{3} b^{2} x^{8} \mathrm{sgn}\left(b x + a\right) + \frac{5}{7} \, a^{4} b x^{7} \mathrm{sgn}\left(b x + a\right) + \frac{1}{6} \, a^{5} x^{6} \mathrm{sgn}\left(b x + a\right) - \frac{a^{11} \mathrm{sgn}\left(b x + a\right)}{2772 \, b^{6}}"," ",0,"1/11*b^5*x^11*sgn(b*x + a) + 1/2*a*b^4*x^10*sgn(b*x + a) + 10/9*a^2*b^3*x^9*sgn(b*x + a) + 5/4*a^3*b^2*x^8*sgn(b*x + a) + 5/7*a^4*b*x^7*sgn(b*x + a) + 1/6*a^5*x^6*sgn(b*x + a) - 1/2772*a^11*sgn(b*x + a)/b^6","A",0
164,1,107,0,0.164325," ","integrate(x^4*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{10} \, b^{5} x^{10} \mathrm{sgn}\left(b x + a\right) + \frac{5}{9} \, a b^{4} x^{9} \mathrm{sgn}\left(b x + a\right) + \frac{5}{4} \, a^{2} b^{3} x^{8} \mathrm{sgn}\left(b x + a\right) + \frac{10}{7} \, a^{3} b^{2} x^{7} \mathrm{sgn}\left(b x + a\right) + \frac{5}{6} \, a^{4} b x^{6} \mathrm{sgn}\left(b x + a\right) + \frac{1}{5} \, a^{5} x^{5} \mathrm{sgn}\left(b x + a\right) + \frac{a^{10} \mathrm{sgn}\left(b x + a\right)}{1260 \, b^{5}}"," ",0,"1/10*b^5*x^10*sgn(b*x + a) + 5/9*a*b^4*x^9*sgn(b*x + a) + 5/4*a^2*b^3*x^8*sgn(b*x + a) + 10/7*a^3*b^2*x^7*sgn(b*x + a) + 5/6*a^4*b*x^6*sgn(b*x + a) + 1/5*a^5*x^5*sgn(b*x + a) + 1/1260*a^10*sgn(b*x + a)/b^5","A",0
165,1,106,0,0.163651," ","integrate(x^3*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{9} \, b^{5} x^{9} \mathrm{sgn}\left(b x + a\right) + \frac{5}{8} \, a b^{4} x^{8} \mathrm{sgn}\left(b x + a\right) + \frac{10}{7} \, a^{2} b^{3} x^{7} \mathrm{sgn}\left(b x + a\right) + \frac{5}{3} \, a^{3} b^{2} x^{6} \mathrm{sgn}\left(b x + a\right) + a^{4} b x^{5} \mathrm{sgn}\left(b x + a\right) + \frac{1}{4} \, a^{5} x^{4} \mathrm{sgn}\left(b x + a\right) - \frac{a^{9} \mathrm{sgn}\left(b x + a\right)}{504 \, b^{4}}"," ",0,"1/9*b^5*x^9*sgn(b*x + a) + 5/8*a*b^4*x^8*sgn(b*x + a) + 10/7*a^2*b^3*x^7*sgn(b*x + a) + 5/3*a^3*b^2*x^6*sgn(b*x + a) + a^4*b*x^5*sgn(b*x + a) + 1/4*a^5*x^4*sgn(b*x + a) - 1/504*a^9*sgn(b*x + a)/b^4","A",0
166,1,107,0,0.157859," ","integrate(x^2*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{8} \, b^{5} x^{8} \mathrm{sgn}\left(b x + a\right) + \frac{5}{7} \, a b^{4} x^{7} \mathrm{sgn}\left(b x + a\right) + \frac{5}{3} \, a^{2} b^{3} x^{6} \mathrm{sgn}\left(b x + a\right) + 2 \, a^{3} b^{2} x^{5} \mathrm{sgn}\left(b x + a\right) + \frac{5}{4} \, a^{4} b x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{1}{3} \, a^{5} x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{a^{8} \mathrm{sgn}\left(b x + a\right)}{168 \, b^{3}}"," ",0,"1/8*b^5*x^8*sgn(b*x + a) + 5/7*a*b^4*x^7*sgn(b*x + a) + 5/3*a^2*b^3*x^6*sgn(b*x + a) + 2*a^3*b^2*x^5*sgn(b*x + a) + 5/4*a^4*b*x^4*sgn(b*x + a) + 1/3*a^5*x^3*sgn(b*x + a) + 1/168*a^8*sgn(b*x + a)/b^3","A",0
167,1,107,0,0.167918," ","integrate(x*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{7} \, b^{5} x^{7} \mathrm{sgn}\left(b x + a\right) + \frac{5}{6} \, a b^{4} x^{6} \mathrm{sgn}\left(b x + a\right) + 2 \, a^{2} b^{3} x^{5} \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, a^{3} b^{2} x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{5}{3} \, a^{4} b x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, a^{5} x^{2} \mathrm{sgn}\left(b x + a\right) - \frac{a^{7} \mathrm{sgn}\left(b x + a\right)}{42 \, b^{2}}"," ",0,"1/7*b^5*x^7*sgn(b*x + a) + 5/6*a*b^4*x^6*sgn(b*x + a) + 2*a^2*b^3*x^5*sgn(b*x + a) + 5/2*a^3*b^2*x^4*sgn(b*x + a) + 5/3*a^4*b*x^3*sgn(b*x + a) + 1/2*a^5*x^2*sgn(b*x + a) - 1/42*a^7*sgn(b*x + a)/b^2","B",0
168,1,83,0,0.213462," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{2} \, {\left(b x^{2} + 2 \, a x\right)} a^{4} \mathrm{sgn}\left(b x + a\right) + \frac{a^{6} \mathrm{sgn}\left(b x + a\right)}{6 \, b} + \frac{1}{2} \, {\left(b x^{2} + 2 \, a x\right)}^{2} a^{2} b \mathrm{sgn}\left(b x + a\right) + \frac{1}{6} \, {\left(b x^{2} + 2 \, a x\right)}^{3} b^{2} \mathrm{sgn}\left(b x + a\right)"," ",0,"1/2*(b*x^2 + 2*a*x)*a^4*sgn(b*x + a) + 1/6*a^6*sgn(b*x + a)/b + 1/2*(b*x^2 + 2*a*x)^2*a^2*b*sgn(b*x + a) + 1/6*(b*x^2 + 2*a*x)^3*b^2*sgn(b*x + a)","B",0
169,1,90,0,0.158957," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/x,x, algorithm=""giac"")","\frac{1}{5} \, b^{5} x^{5} \mathrm{sgn}\left(b x + a\right) + \frac{5}{4} \, a b^{4} x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{10}{3} \, a^{2} b^{3} x^{3} \mathrm{sgn}\left(b x + a\right) + 5 \, a^{3} b^{2} x^{2} \mathrm{sgn}\left(b x + a\right) + 5 \, a^{4} b x \mathrm{sgn}\left(b x + a\right) + a^{5} \log\left({\left| x \right|}\right) \mathrm{sgn}\left(b x + a\right)"," ",0,"1/5*b^5*x^5*sgn(b*x + a) + 5/4*a*b^4*x^4*sgn(b*x + a) + 10/3*a^2*b^3*x^3*sgn(b*x + a) + 5*a^3*b^2*x^2*sgn(b*x + a) + 5*a^4*b*x*sgn(b*x + a) + a^5*log(abs(x))*sgn(b*x + a)","A",0
170,1,91,0,0.178346," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/x^2,x, algorithm=""giac"")","\frac{1}{4} \, b^{5} x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{5}{3} \, a b^{4} x^{3} \mathrm{sgn}\left(b x + a\right) + 5 \, a^{2} b^{3} x^{2} \mathrm{sgn}\left(b x + a\right) + 10 \, a^{3} b^{2} x \mathrm{sgn}\left(b x + a\right) + 5 \, a^{4} b \log\left({\left| x \right|}\right) \mathrm{sgn}\left(b x + a\right) - \frac{a^{5} \mathrm{sgn}\left(b x + a\right)}{x}"," ",0,"1/4*b^5*x^4*sgn(b*x + a) + 5/3*a*b^4*x^3*sgn(b*x + a) + 5*a^2*b^3*x^2*sgn(b*x + a) + 10*a^3*b^2*x*sgn(b*x + a) + 5*a^4*b*log(abs(x))*sgn(b*x + a) - a^5*sgn(b*x + a)/x","A",0
171,1,91,0,0.186638," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/x^3,x, algorithm=""giac"")","\frac{1}{3} \, b^{5} x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, a b^{4} x^{2} \mathrm{sgn}\left(b x + a\right) + 10 \, a^{2} b^{3} x \mathrm{sgn}\left(b x + a\right) + 10 \, a^{3} b^{2} \log\left({\left| x \right|}\right) \mathrm{sgn}\left(b x + a\right) - \frac{10 \, a^{4} b x \mathrm{sgn}\left(b x + a\right) + a^{5} \mathrm{sgn}\left(b x + a\right)}{2 \, x^{2}}"," ",0,"1/3*b^5*x^3*sgn(b*x + a) + 5/2*a*b^4*x^2*sgn(b*x + a) + 10*a^2*b^3*x*sgn(b*x + a) + 10*a^3*b^2*log(abs(x))*sgn(b*x + a) - 1/2*(10*a^4*b*x*sgn(b*x + a) + a^5*sgn(b*x + a))/x^2","A",0
172,1,92,0,0.181126," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/x^4,x, algorithm=""giac"")","\frac{1}{2} \, b^{5} x^{2} \mathrm{sgn}\left(b x + a\right) + 5 \, a b^{4} x \mathrm{sgn}\left(b x + a\right) + 10 \, a^{2} b^{3} \log\left({\left| x \right|}\right) \mathrm{sgn}\left(b x + a\right) - \frac{60 \, a^{3} b^{2} x^{2} \mathrm{sgn}\left(b x + a\right) + 15 \, a^{4} b x \mathrm{sgn}\left(b x + a\right) + 2 \, a^{5} \mathrm{sgn}\left(b x + a\right)}{6 \, x^{3}}"," ",0,"1/2*b^5*x^2*sgn(b*x + a) + 5*a*b^4*x*sgn(b*x + a) + 10*a^2*b^3*log(abs(x))*sgn(b*x + a) - 1/6*(60*a^3*b^2*x^2*sgn(b*x + a) + 15*a^4*b*x*sgn(b*x + a) + 2*a^5*sgn(b*x + a))/x^3","A",0
173,1,91,0,0.170830," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/x^5,x, algorithm=""giac"")","b^{5} x \mathrm{sgn}\left(b x + a\right) + 5 \, a b^{4} \log\left({\left| x \right|}\right) \mathrm{sgn}\left(b x + a\right) - \frac{120 \, a^{2} b^{3} x^{3} \mathrm{sgn}\left(b x + a\right) + 60 \, a^{3} b^{2} x^{2} \mathrm{sgn}\left(b x + a\right) + 20 \, a^{4} b x \mathrm{sgn}\left(b x + a\right) + 3 \, a^{5} \mathrm{sgn}\left(b x + a\right)}{12 \, x^{4}}"," ",0,"b^5*x*sgn(b*x + a) + 5*a*b^4*log(abs(x))*sgn(b*x + a) - 1/12*(120*a^2*b^3*x^3*sgn(b*x + a) + 60*a^3*b^2*x^2*sgn(b*x + a) + 20*a^4*b*x*sgn(b*x + a) + 3*a^5*sgn(b*x + a))/x^4","A",0
174,1,93,0,0.167973," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/x^6,x, algorithm=""giac"")","b^{5} \log\left({\left| x \right|}\right) \mathrm{sgn}\left(b x + a\right) - \frac{300 \, a b^{4} x^{4} \mathrm{sgn}\left(b x + a\right) + 300 \, a^{2} b^{3} x^{3} \mathrm{sgn}\left(b x + a\right) + 200 \, a^{3} b^{2} x^{2} \mathrm{sgn}\left(b x + a\right) + 75 \, a^{4} b x \mathrm{sgn}\left(b x + a\right) + 12 \, a^{5} \mathrm{sgn}\left(b x + a\right)}{60 \, x^{5}}"," ",0,"b^5*log(abs(x))*sgn(b*x + a) - 1/60*(300*a*b^4*x^4*sgn(b*x + a) + 300*a^2*b^3*x^3*sgn(b*x + a) + 200*a^3*b^2*x^2*sgn(b*x + a) + 75*a^4*b*x*sgn(b*x + a) + 12*a^5*sgn(b*x + a))/x^5","A",0
175,1,107,0,0.163056," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/x^7,x, algorithm=""giac"")","-\frac{b^{6} \mathrm{sgn}\left(b x + a\right)}{6 \, a} - \frac{6 \, b^{5} x^{5} \mathrm{sgn}\left(b x + a\right) + 15 \, a b^{4} x^{4} \mathrm{sgn}\left(b x + a\right) + 20 \, a^{2} b^{3} x^{3} \mathrm{sgn}\left(b x + a\right) + 15 \, a^{3} b^{2} x^{2} \mathrm{sgn}\left(b x + a\right) + 6 \, a^{4} b x \mathrm{sgn}\left(b x + a\right) + a^{5} \mathrm{sgn}\left(b x + a\right)}{6 \, x^{6}}"," ",0,"-1/6*b^6*sgn(b*x + a)/a - 1/6*(6*b^5*x^5*sgn(b*x + a) + 15*a*b^4*x^4*sgn(b*x + a) + 20*a^2*b^3*x^3*sgn(b*x + a) + 15*a^3*b^2*x^2*sgn(b*x + a) + 6*a^4*b*x*sgn(b*x + a) + a^5*sgn(b*x + a))/x^6","B",0
176,1,108,0,0.546081," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/x^8,x, algorithm=""giac"")","\frac{b^{7} \mathrm{sgn}\left(b x + a\right)}{42 \, a^{2}} - \frac{21 \, b^{5} x^{5} \mathrm{sgn}\left(b x + a\right) + 70 \, a b^{4} x^{4} \mathrm{sgn}\left(b x + a\right) + 105 \, a^{2} b^{3} x^{3} \mathrm{sgn}\left(b x + a\right) + 84 \, a^{3} b^{2} x^{2} \mathrm{sgn}\left(b x + a\right) + 35 \, a^{4} b x \mathrm{sgn}\left(b x + a\right) + 6 \, a^{5} \mathrm{sgn}\left(b x + a\right)}{42 \, x^{7}}"," ",0,"1/42*b^7*sgn(b*x + a)/a^2 - 1/42*(21*b^5*x^5*sgn(b*x + a) + 70*a*b^4*x^4*sgn(b*x + a) + 105*a^2*b^3*x^3*sgn(b*x + a) + 84*a^3*b^2*x^2*sgn(b*x + a) + 35*a^4*b*x*sgn(b*x + a) + 6*a^5*sgn(b*x + a))/x^7","B",0
177,1,108,0,0.160328," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/x^9,x, algorithm=""giac"")","-\frac{b^{8} \mathrm{sgn}\left(b x + a\right)}{168 \, a^{3}} - \frac{56 \, b^{5} x^{5} \mathrm{sgn}\left(b x + a\right) + 210 \, a b^{4} x^{4} \mathrm{sgn}\left(b x + a\right) + 336 \, a^{2} b^{3} x^{3} \mathrm{sgn}\left(b x + a\right) + 280 \, a^{3} b^{2} x^{2} \mathrm{sgn}\left(b x + a\right) + 120 \, a^{4} b x \mathrm{sgn}\left(b x + a\right) + 21 \, a^{5} \mathrm{sgn}\left(b x + a\right)}{168 \, x^{8}}"," ",0,"-1/168*b^8*sgn(b*x + a)/a^3 - 1/168*(56*b^5*x^5*sgn(b*x + a) + 210*a*b^4*x^4*sgn(b*x + a) + 336*a^2*b^3*x^3*sgn(b*x + a) + 280*a^3*b^2*x^2*sgn(b*x + a) + 120*a^4*b*x*sgn(b*x + a) + 21*a^5*sgn(b*x + a))/x^8","A",0
178,1,108,0,0.159562," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/x^10,x, algorithm=""giac"")","\frac{b^{9} \mathrm{sgn}\left(b x + a\right)}{504 \, a^{4}} - \frac{126 \, b^{5} x^{5} \mathrm{sgn}\left(b x + a\right) + 504 \, a b^{4} x^{4} \mathrm{sgn}\left(b x + a\right) + 840 \, a^{2} b^{3} x^{3} \mathrm{sgn}\left(b x + a\right) + 720 \, a^{3} b^{2} x^{2} \mathrm{sgn}\left(b x + a\right) + 315 \, a^{4} b x \mathrm{sgn}\left(b x + a\right) + 56 \, a^{5} \mathrm{sgn}\left(b x + a\right)}{504 \, x^{9}}"," ",0,"1/504*b^9*sgn(b*x + a)/a^4 - 1/504*(126*b^5*x^5*sgn(b*x + a) + 504*a*b^4*x^4*sgn(b*x + a) + 840*a^2*b^3*x^3*sgn(b*x + a) + 720*a^3*b^2*x^2*sgn(b*x + a) + 315*a^4*b*x*sgn(b*x + a) + 56*a^5*sgn(b*x + a))/x^9","A",0
179,1,108,0,0.159771," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/x^11,x, algorithm=""giac"")","-\frac{b^{10} \mathrm{sgn}\left(b x + a\right)}{1260 \, a^{5}} - \frac{252 \, b^{5} x^{5} \mathrm{sgn}\left(b x + a\right) + 1050 \, a b^{4} x^{4} \mathrm{sgn}\left(b x + a\right) + 1800 \, a^{2} b^{3} x^{3} \mathrm{sgn}\left(b x + a\right) + 1575 \, a^{3} b^{2} x^{2} \mathrm{sgn}\left(b x + a\right) + 700 \, a^{4} b x \mathrm{sgn}\left(b x + a\right) + 126 \, a^{5} \mathrm{sgn}\left(b x + a\right)}{1260 \, x^{10}}"," ",0,"-1/1260*b^10*sgn(b*x + a)/a^5 - 1/1260*(252*b^5*x^5*sgn(b*x + a) + 1050*a*b^4*x^4*sgn(b*x + a) + 1800*a^2*b^3*x^3*sgn(b*x + a) + 1575*a^3*b^2*x^2*sgn(b*x + a) + 700*a^4*b*x*sgn(b*x + a) + 126*a^5*sgn(b*x + a))/x^10","A",0
180,1,108,0,0.186037," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/x^12,x, algorithm=""giac"")","\frac{b^{11} \mathrm{sgn}\left(b x + a\right)}{2772 \, a^{6}} - \frac{462 \, b^{5} x^{5} \mathrm{sgn}\left(b x + a\right) + 1980 \, a b^{4} x^{4} \mathrm{sgn}\left(b x + a\right) + 3465 \, a^{2} b^{3} x^{3} \mathrm{sgn}\left(b x + a\right) + 3080 \, a^{3} b^{2} x^{2} \mathrm{sgn}\left(b x + a\right) + 1386 \, a^{4} b x \mathrm{sgn}\left(b x + a\right) + 252 \, a^{5} \mathrm{sgn}\left(b x + a\right)}{2772 \, x^{11}}"," ",0,"1/2772*b^11*sgn(b*x + a)/a^6 - 1/2772*(462*b^5*x^5*sgn(b*x + a) + 1980*a*b^4*x^4*sgn(b*x + a) + 3465*a^2*b^3*x^3*sgn(b*x + a) + 3080*a^3*b^2*x^2*sgn(b*x + a) + 1386*a^4*b*x*sgn(b*x + a) + 252*a^5*sgn(b*x + a))/x^11","A",0
181,1,83,0,0.154575," ","integrate(x^4/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{a^{4} \log\left({\left| b x + a \right|}\right) \mathrm{sgn}\left(b x + a\right)}{b^{5}} + \frac{3 \, b^{3} x^{4} \mathrm{sgn}\left(b x + a\right) - 4 \, a b^{2} x^{3} \mathrm{sgn}\left(b x + a\right) + 6 \, a^{2} b x^{2} \mathrm{sgn}\left(b x + a\right) - 12 \, a^{3} x \mathrm{sgn}\left(b x + a\right)}{12 \, b^{4}}"," ",0,"a^4*log(abs(b*x + a))*sgn(b*x + a)/b^5 + 1/12*(3*b^3*x^4*sgn(b*x + a) - 4*a*b^2*x^3*sgn(b*x + a) + 6*a^2*b*x^2*sgn(b*x + a) - 12*a^3*x*sgn(b*x + a))/b^4","A",0
182,1,67,0,0.157347," ","integrate(x^3/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","-\frac{a^{3} \log\left({\left| b x + a \right|}\right) \mathrm{sgn}\left(b x + a\right)}{b^{4}} + \frac{2 \, b^{2} x^{3} \mathrm{sgn}\left(b x + a\right) - 3 \, a b x^{2} \mathrm{sgn}\left(b x + a\right) + 6 \, a^{2} x \mathrm{sgn}\left(b x + a\right)}{6 \, b^{3}}"," ",0,"-a^3*log(abs(b*x + a))*sgn(b*x + a)/b^4 + 1/6*(2*b^2*x^3*sgn(b*x + a) - 3*a*b*x^2*sgn(b*x + a) + 6*a^2*x*sgn(b*x + a))/b^3","A",0
183,1,48,0,0.179584," ","integrate(x^2/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{a^{2} \log\left({\left| b x + a \right|}\right) \mathrm{sgn}\left(b x + a\right)}{b^{3}} + \frac{b x^{2} \mathrm{sgn}\left(b x + a\right) - 2 \, a x \mathrm{sgn}\left(b x + a\right)}{2 \, b^{2}}"," ",0,"a^2*log(abs(b*x + a))*sgn(b*x + a)/b^3 + 1/2*(b*x^2*sgn(b*x + a) - 2*a*x*sgn(b*x + a))/b^2","A",0
184,1,31,0,0.190133," ","integrate(x/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{x \mathrm{sgn}\left(b x + a\right)}{b} - \frac{a \log\left({\left| b x + a \right|}\right) \mathrm{sgn}\left(b x + a\right)}{b^{2}}"," ",0,"x*sgn(b*x + a)/b - a*log(abs(b*x + a))*sgn(b*x + a)/b^2","A",0
185,1,17,0,0.148503," ","integrate(1/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{\log\left({\left| b x + a \right|}\right) \mathrm{sgn}\left(b x + a\right)}{b}"," ",0,"log(abs(b*x + a))*sgn(b*x + a)/b","A",0
186,1,28,0,0.153456," ","integrate(1/x/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","-{\left(\frac{\log\left({\left| b x + a \right|}\right)}{a} - \frac{\log\left({\left| x \right|}\right)}{a}\right)} \mathrm{sgn}\left(b x + a\right)"," ",0,"-(log(abs(b*x + a))/a - log(abs(x))/a)*sgn(b*x + a)","A",0
187,1,37,0,0.155024," ","integrate(1/x^2/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","{\left(\frac{b \log\left({\left| b x + a \right|}\right)}{a^{2}} - \frac{b \log\left({\left| x \right|}\right)}{a^{2}} - \frac{1}{a x}\right)} \mathrm{sgn}\left(b x + a\right)"," ",0,"(b*log(abs(b*x + a))/a^2 - b*log(abs(x))/a^2 - 1/(a*x))*sgn(b*x + a)","A",0
188,1,54,0,0.154223," ","integrate(1/x^3/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \, {\left(\frac{2 \, b^{2} \log\left({\left| b x + a \right|}\right)}{a^{3}} - \frac{2 \, b^{2} \log\left({\left| x \right|}\right)}{a^{3}} - \frac{2 \, a b x - a^{2}}{a^{3} x^{2}}\right)} \mathrm{sgn}\left(b x + a\right)"," ",0,"-1/2*(2*b^2*log(abs(b*x + a))/a^3 - 2*b^2*log(abs(x))/a^3 - (2*a*b*x - a^2)/(a^3*x^2))*sgn(b*x + a)","A",0
189,1,65,0,0.156496," ","integrate(1/x^4/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{6} \, {\left(\frac{6 \, b^{3} \log\left({\left| b x + a \right|}\right)}{a^{4}} - \frac{6 \, b^{3} \log\left({\left| x \right|}\right)}{a^{4}} - \frac{6 \, a b^{2} x^{2} - 3 \, a^{2} b x + 2 \, a^{3}}{a^{4} x^{3}}\right)} \mathrm{sgn}\left(b x + a\right)"," ",0,"1/6*(6*b^3*log(abs(b*x + a))/a^4 - 6*b^3*log(abs(x))/a^4 - (6*a*b^2*x^2 - 3*a^2*b*x + 2*a^3)/(a^4*x^3))*sgn(b*x + a)","A",0
190,0,0,0,0.000000," ","integrate(x^4/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
191,0,0,0,0.000000," ","integrate(x^3/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
192,0,0,0,0.000000," ","integrate(x^2/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
193,0,0,0,0.000000," ","integrate(x/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
194,0,0,0,0.000000," ","integrate(1/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
195,0,0,0,0.000000," ","integrate(1/x/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
196,0,0,0,0.000000," ","integrate(1/x^2/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
197,0,0,0,0.000000," ","integrate(1/x^3/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
198,0,0,0,0.000000," ","integrate(x^6/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
199,0,0,0,0.000000," ","integrate(x^5/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
200,0,0,0,0.000000," ","integrate(x^4/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
201,0,0,0,0.000000," ","integrate(x^3/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
202,0,0,0,0.000000," ","integrate(x^2/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
203,0,0,0,0.000000," ","integrate(x/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
204,0,0,0,0.000000," ","integrate(1/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
205,0,0,0,0.000000," ","integrate(1/x/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
206,0,0,0,0.000000," ","integrate(1/x^2/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
207,0,0,0,0.000000," ","integrate(1/x^3/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
208,1,75,0,0.157261," ","integrate(x*(4*x^2+12*x+9)^(5/2),x, algorithm=""giac"")","\frac{32}{7} \, x^{7} \mathrm{sgn}\left(2 \, x + 3\right) + 40 \, x^{6} \mathrm{sgn}\left(2 \, x + 3\right) + 144 \, x^{5} \mathrm{sgn}\left(2 \, x + 3\right) + 270 \, x^{4} \mathrm{sgn}\left(2 \, x + 3\right) + 270 \, x^{3} \mathrm{sgn}\left(2 \, x + 3\right) + \frac{243}{2} \, x^{2} \mathrm{sgn}\left(2 \, x + 3\right) - \frac{729}{56} \, \mathrm{sgn}\left(2 \, x + 3\right)"," ",0,"32/7*x^7*sgn(2*x + 3) + 40*x^6*sgn(2*x + 3) + 144*x^5*sgn(2*x + 3) + 270*x^4*sgn(2*x + 3) + 270*x^3*sgn(2*x + 3) + 243/2*x^2*sgn(2*x + 3) - 729/56*sgn(2*x + 3)","B",0
209,1,53,0,0.177145," ","integrate(x*(4*x^2+12*x+9)^(3/2),x, algorithm=""giac"")","\frac{8}{5} \, x^{5} \mathrm{sgn}\left(2 \, x + 3\right) + 9 \, x^{4} \mathrm{sgn}\left(2 \, x + 3\right) + 18 \, x^{3} \mathrm{sgn}\left(2 \, x + 3\right) + \frac{27}{2} \, x^{2} \mathrm{sgn}\left(2 \, x + 3\right) - \frac{243}{80} \, \mathrm{sgn}\left(2 \, x + 3\right)"," ",0,"8/5*x^5*sgn(2*x + 3) + 9*x^4*sgn(2*x + 3) + 18*x^3*sgn(2*x + 3) + 27/2*x^2*sgn(2*x + 3) - 243/80*sgn(2*x + 3)","A",0
210,1,31,0,0.158598," ","integrate(x*(4*x^2+12*x+9)^(1/2),x, algorithm=""giac"")","\frac{2}{3} \, x^{3} \mathrm{sgn}\left(2 \, x + 3\right) + \frac{3}{2} \, x^{2} \mathrm{sgn}\left(2 \, x + 3\right) - \frac{9}{8} \, \mathrm{sgn}\left(2 \, x + 3\right)"," ",0,"2/3*x^3*sgn(2*x + 3) + 3/2*x^2*sgn(2*x + 3) - 9/8*sgn(2*x + 3)","A",0
211,1,36,0,0.164712," ","integrate(x/(4*x^2+12*x+9)^(1/2),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{4 \, x^{2} + 12 \, x + 9} + \frac{3}{4} \, \log\left({\left| -2 \, x + \sqrt{4 \, x^{2} + 12 \, x + 9} - 3 \right|}\right)"," ",0,"1/4*sqrt(4*x^2 + 12*x + 9) + 3/4*log(abs(-2*x + sqrt(4*x^2 + 12*x + 9) - 3))","A",0
212,0,0,0,0.000000," ","integrate(x/(4*x^2+12*x+9)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
213,0,0,0,0.000000," ","integrate(x/(4*x^2+12*x+9)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
214,0,0,0,0.000000," ","integrate(x/(4*x^2+12*x+9)^(7/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
215,1,25,0,0.154465," ","integrate(x/((2+3*x)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{3} \, x \mathrm{sgn}\left(3 \, x + 2\right) - \frac{2}{9} \, \log\left({\left| 3 \, x + 2 \right|}\right) \mathrm{sgn}\left(3 \, x + 2\right)"," ",0,"1/3*x*sgn(3*x + 2) - 2/9*log(abs(3*x + 2))*sgn(3*x + 2)","A",0
216,1,25,0,0.173948," ","integrate(x/((-2+3*x)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{3} \, x \mathrm{sgn}\left(3 \, x - 2\right) + \frac{2}{9} \, \log\left({\left| 3 \, x - 2 \right|}\right) \mathrm{sgn}\left(3 \, x - 2\right)"," ",0,"1/3*x*sgn(3*x - 2) + 2/9*log(abs(3*x - 2))*sgn(3*x - 2)","A",0
217,0,0,0,0.000000," ","integrate(x/(-(-2+3*x)^2)^(1/2),x, algorithm=""giac"")","\mathit{undef}"," ",0,"undef","F",0
218,0,0,0,0.000000," ","integrate(x/(-(2+3*x)^2)^(1/2),x, algorithm=""giac"")","\mathit{undef}"," ",0,"undef","F",0
219,1,13,0,0.151684," ","integrate((1+x)/(x^2+2*x),x, algorithm=""giac"")","\frac{1}{2} \, \log\left(2 \, {\left| \frac{1}{2} \, x^{2} + x \right|}\right)"," ",0,"1/2*log(2*abs(1/2*x^2 + x))","A",0
220,1,11,0,0.158830," ","integrate((2*b*x+a)/(b*x^2+a*x),x, algorithm=""giac"")","\log\left({\left| b x^{2} + a x \right|}\right)"," ",0,"log(abs(b*x^2 + a*x))","A",0
221,1,96,0,0.153498," ","integrate((e*x+d)^4*(c*x^2+b*x),x, algorithm=""giac"")","\frac{1}{7} \, c x^{7} e^{4} + \frac{2}{3} \, c d x^{6} e^{3} + \frac{6}{5} \, c d^{2} x^{5} e^{2} + c d^{3} x^{4} e + \frac{1}{3} \, c d^{4} x^{3} + \frac{1}{6} \, b x^{6} e^{4} + \frac{4}{5} \, b d x^{5} e^{3} + \frac{3}{2} \, b d^{2} x^{4} e^{2} + \frac{4}{3} \, b d^{3} x^{3} e + \frac{1}{2} \, b d^{4} x^{2}"," ",0,"1/7*c*x^7*e^4 + 2/3*c*d*x^6*e^3 + 6/5*c*d^2*x^5*e^2 + c*d^3*x^4*e + 1/3*c*d^4*x^3 + 1/6*b*x^6*e^4 + 4/5*b*d*x^5*e^3 + 3/2*b*d^2*x^4*e^2 + 4/3*b*d^3*x^3*e + 1/2*b*d^4*x^2","A",0
222,1,74,0,0.147379," ","integrate((e*x+d)^3*(c*x^2+b*x),x, algorithm=""giac"")","\frac{1}{6} \, c x^{6} e^{3} + \frac{3}{5} \, c d x^{5} e^{2} + \frac{3}{4} \, c d^{2} x^{4} e + \frac{1}{3} \, c d^{3} x^{3} + \frac{1}{5} \, b x^{5} e^{3} + \frac{3}{4} \, b d x^{4} e^{2} + b d^{2} x^{3} e + \frac{1}{2} \, b d^{3} x^{2}"," ",0,"1/6*c*x^6*e^3 + 3/5*c*d*x^5*e^2 + 3/4*c*d^2*x^4*e + 1/3*c*d^3*x^3 + 1/5*b*x^5*e^3 + 3/4*b*d*x^4*e^2 + b*d^2*x^3*e + 1/2*b*d^3*x^2","A",0
223,1,53,0,0.148349," ","integrate((e*x+d)^2*(c*x^2+b*x),x, algorithm=""giac"")","\frac{1}{5} \, c x^{5} e^{2} + \frac{1}{2} \, c d x^{4} e + \frac{1}{3} \, c d^{2} x^{3} + \frac{1}{4} \, b x^{4} e^{2} + \frac{2}{3} \, b d x^{3} e + \frac{1}{2} \, b d^{2} x^{2}"," ",0,"1/5*c*x^5*e^2 + 1/2*c*d*x^4*e + 1/3*c*d^2*x^3 + 1/4*b*x^4*e^2 + 2/3*b*d*x^3*e + 1/2*b*d^2*x^2","A",0
224,1,31,0,0.148858," ","integrate((e*x+d)*(c*x^2+b*x),x, algorithm=""giac"")","\frac{1}{4} \, c x^{4} e + \frac{1}{3} \, c d x^{3} + \frac{1}{3} \, b x^{3} e + \frac{1}{2} \, b d x^{2}"," ",0,"1/4*c*x^4*e + 1/3*c*d*x^3 + 1/3*b*x^3*e + 1/2*b*d*x^2","A",0
225,1,13,0,0.153654," ","integrate(c*x^2+b*x,x, algorithm=""giac"")","\frac{1}{3} \, c x^{3} + \frac{1}{2} \, b x^{2}"," ",0,"1/3*c*x^3 + 1/2*b*x^2","A",0
226,1,47,0,0.189145," ","integrate((c*x^2+b*x)/(e*x+d),x, algorithm=""giac"")","{\left(c d^{2} - b d e\right)} e^{\left(-3\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{2} \, {\left(c x^{2} e - 2 \, c d x + 2 \, b x e\right)} e^{\left(-2\right)}"," ",0,"(c*d^2 - b*d*e)*e^(-3)*log(abs(x*e + d)) + 1/2*(c*x^2*e - 2*c*d*x + 2*b*x*e)*e^(-2)","A",0
227,1,93,0,0.154083," ","integrate((c*x^2+b*x)/(e*x+d)^2,x, algorithm=""giac"")","-{\left(e^{\left(-1\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) - \frac{d e^{\left(-1\right)}}{x e + d}\right)} b e^{\left(-1\right)} + {\left(2 \, d e^{\left(-3\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) + {\left(x e + d\right)} e^{\left(-3\right)} - \frac{d^{2} e^{\left(-3\right)}}{x e + d}\right)} c"," ",0,"-(e^(-1)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) - d*e^(-1)/(x*e + d))*b*e^(-1) + (2*d*e^(-3)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) + (x*e + d)*e^(-3) - d^2*e^(-3)/(x*e + d))*c","A",0
228,1,55,0,0.177925," ","integrate((c*x^2+b*x)/(e*x+d)^3,x, algorithm=""giac"")","c e^{\left(-3\right)} \log\left({\left| x e + d \right|}\right) + \frac{{\left(2 \, {\left(2 \, c d - b e\right)} x + {\left(3 \, c d^{2} - b d e\right)} e^{\left(-1\right)}\right)} e^{\left(-2\right)}}{2 \, {\left(x e + d\right)}^{2}}"," ",0,"c*e^(-3)*log(abs(x*e + d)) + 1/2*(2*(2*c*d - b*e)*x + (3*c*d^2 - b*d*e)*e^(-1))*e^(-2)/(x*e + d)^2","A",0
229,1,45,0,0.154599," ","integrate((c*x^2+b*x)/(e*x+d)^4,x, algorithm=""giac"")","-\frac{{\left(6 \, c x^{2} e^{2} + 6 \, c d x e + 2 \, c d^{2} + 3 \, b x e^{2} + b d e\right)} e^{\left(-3\right)}}{6 \, {\left(x e + d\right)}^{3}}"," ",0,"-1/6*(6*c*x^2*e^2 + 6*c*d*x*e + 2*c*d^2 + 3*b*x*e^2 + b*d*e)*e^(-3)/(x*e + d)^3","A",0
230,1,75,0,0.179689," ","integrate((c*x^2+b*x)/(e*x+d)^5,x, algorithm=""giac"")","-\frac{1}{12} \, {\left(\frac{6 \, c e^{\left(-2\right)}}{{\left(x e + d\right)}^{2}} - \frac{8 \, c d e^{\left(-2\right)}}{{\left(x e + d\right)}^{3}} + \frac{3 \, c d^{2} e^{\left(-2\right)}}{{\left(x e + d\right)}^{4}} + \frac{4 \, b e^{\left(-1\right)}}{{\left(x e + d\right)}^{3}} - \frac{3 \, b d e^{\left(-1\right)}}{{\left(x e + d\right)}^{4}}\right)} e^{\left(-1\right)}"," ",0,"-1/12*(6*c*e^(-2)/(x*e + d)^2 - 8*c*d*e^(-2)/(x*e + d)^3 + 3*c*d^2*e^(-2)/(x*e + d)^4 + 4*b*e^(-1)/(x*e + d)^3 - 3*b*d*e^(-1)/(x*e + d)^4)*e^(-1)","A",0
231,1,169,0,0.153154," ","integrate((e*x+d)^4*(c*x^2+b*x)^2,x, algorithm=""giac"")","\frac{1}{9} \, c^{2} x^{9} e^{4} + \frac{1}{2} \, c^{2} d x^{8} e^{3} + \frac{6}{7} \, c^{2} d^{2} x^{7} e^{2} + \frac{2}{3} \, c^{2} d^{3} x^{6} e + \frac{1}{5} \, c^{2} d^{4} x^{5} + \frac{1}{4} \, b c x^{8} e^{4} + \frac{8}{7} \, b c d x^{7} e^{3} + 2 \, b c d^{2} x^{6} e^{2} + \frac{8}{5} \, b c d^{3} x^{5} e + \frac{1}{2} \, b c d^{4} x^{4} + \frac{1}{7} \, b^{2} x^{7} e^{4} + \frac{2}{3} \, b^{2} d x^{6} e^{3} + \frac{6}{5} \, b^{2} d^{2} x^{5} e^{2} + b^{2} d^{3} x^{4} e + \frac{1}{3} \, b^{2} d^{4} x^{3}"," ",0,"1/9*c^2*x^9*e^4 + 1/2*c^2*d*x^8*e^3 + 6/7*c^2*d^2*x^7*e^2 + 2/3*c^2*d^3*x^6*e + 1/5*c^2*d^4*x^5 + 1/4*b*c*x^8*e^4 + 8/7*b*c*d*x^7*e^3 + 2*b*c*d^2*x^6*e^2 + 8/5*b*c*d^3*x^5*e + 1/2*b*c*d^4*x^4 + 1/7*b^2*x^7*e^4 + 2/3*b^2*d*x^6*e^3 + 6/5*b^2*d^2*x^5*e^2 + b^2*d^3*x^4*e + 1/3*b^2*d^4*x^3","A",0
232,1,131,0,0.151039," ","integrate((e*x+d)^3*(c*x^2+b*x)^2,x, algorithm=""giac"")","\frac{1}{8} \, c^{2} x^{8} e^{3} + \frac{3}{7} \, c^{2} d x^{7} e^{2} + \frac{1}{2} \, c^{2} d^{2} x^{6} e + \frac{1}{5} \, c^{2} d^{3} x^{5} + \frac{2}{7} \, b c x^{7} e^{3} + b c d x^{6} e^{2} + \frac{6}{5} \, b c d^{2} x^{5} e + \frac{1}{2} \, b c d^{3} x^{4} + \frac{1}{6} \, b^{2} x^{6} e^{3} + \frac{3}{5} \, b^{2} d x^{5} e^{2} + \frac{3}{4} \, b^{2} d^{2} x^{4} e + \frac{1}{3} \, b^{2} d^{3} x^{3}"," ",0,"1/8*c^2*x^8*e^3 + 3/7*c^2*d*x^7*e^2 + 1/2*c^2*d^2*x^6*e + 1/5*c^2*d^3*x^5 + 2/7*b*c*x^7*e^3 + b*c*d*x^6*e^2 + 6/5*b*c*d^2*x^5*e + 1/2*b*c*d^3*x^4 + 1/6*b^2*x^6*e^3 + 3/5*b^2*d*x^5*e^2 + 3/4*b^2*d^2*x^4*e + 1/3*b^2*d^3*x^3","A",0
233,1,94,0,0.154421," ","integrate((e*x+d)^2*(c*x^2+b*x)^2,x, algorithm=""giac"")","\frac{1}{7} \, c^{2} x^{7} e^{2} + \frac{1}{3} \, c^{2} d x^{6} e + \frac{1}{5} \, c^{2} d^{2} x^{5} + \frac{1}{3} \, b c x^{6} e^{2} + \frac{4}{5} \, b c d x^{5} e + \frac{1}{2} \, b c d^{2} x^{4} + \frac{1}{5} \, b^{2} x^{5} e^{2} + \frac{1}{2} \, b^{2} d x^{4} e + \frac{1}{3} \, b^{2} d^{2} x^{3}"," ",0,"1/7*c^2*x^7*e^2 + 1/3*c^2*d*x^6*e + 1/5*c^2*d^2*x^5 + 1/3*b*c*x^6*e^2 + 4/5*b*c*d*x^5*e + 1/2*b*c*d^2*x^4 + 1/5*b^2*x^5*e^2 + 1/2*b^2*d*x^4*e + 1/3*b^2*d^2*x^3","A",0
234,1,56,0,0.148081," ","integrate((e*x+d)*(c*x^2+b*x)^2,x, algorithm=""giac"")","\frac{1}{6} \, c^{2} x^{6} e + \frac{1}{5} \, c^{2} d x^{5} + \frac{2}{5} \, b c x^{5} e + \frac{1}{2} \, b c d x^{4} + \frac{1}{4} \, b^{2} x^{4} e + \frac{1}{3} \, b^{2} d x^{3}"," ",0,"1/6*c^2*x^6*e + 1/5*c^2*d*x^5 + 2/5*b*c*x^5*e + 1/2*b*c*d*x^4 + 1/4*b^2*x^4*e + 1/3*b^2*d*x^3","A",0
235,1,24,0,0.172531," ","integrate((c*x^2+b*x)^2,x, algorithm=""giac"")","\frac{1}{5} \, c^{2} x^{5} + \frac{1}{2} \, b c x^{4} + \frac{1}{3} \, b^{2} x^{3}"," ",0,"1/5*c^2*x^5 + 1/2*b*c*x^4 + 1/3*b^2*x^3","A",0
236,1,134,0,0.161592," ","integrate((c*x^2+b*x)^2/(e*x+d),x, algorithm=""giac"")","{\left(c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2}\right)} e^{\left(-5\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{12} \, {\left(3 \, c^{2} x^{4} e^{3} - 4 \, c^{2} d x^{3} e^{2} + 6 \, c^{2} d^{2} x^{2} e - 12 \, c^{2} d^{3} x + 8 \, b c x^{3} e^{3} - 12 \, b c d x^{2} e^{2} + 24 \, b c d^{2} x e + 6 \, b^{2} x^{2} e^{3} - 12 \, b^{2} d x e^{2}\right)} e^{\left(-4\right)}"," ",0,"(c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2)*e^(-5)*log(abs(x*e + d)) + 1/12*(3*c^2*x^4*e^3 - 4*c^2*d*x^3*e^2 + 6*c^2*d^2*x^2*e - 12*c^2*d^3*x + 8*b*c*x^3*e^3 - 12*b*c*d*x^2*e^2 + 24*b*c*d^2*x*e + 6*b^2*x^2*e^3 - 12*b^2*d*x*e^2)*e^(-4)","A",0
237,1,184,0,0.157313," ","integrate((c*x^2+b*x)^2/(e*x+d)^2,x, algorithm=""giac"")","\frac{1}{3} \, {\left(c^{2} - \frac{3 \, {\left(2 \, c^{2} d e - b c e^{2}\right)} e^{\left(-1\right)}}{x e + d} + \frac{3 \, {\left(6 \, c^{2} d^{2} e^{2} - 6 \, b c d e^{3} + b^{2} e^{4}\right)} e^{\left(-2\right)}}{{\left(x e + d\right)}^{2}}\right)} {\left(x e + d\right)}^{3} e^{\left(-5\right)} + 2 \, {\left(2 \, c^{2} d^{3} - 3 \, b c d^{2} e + b^{2} d e^{2}\right)} e^{\left(-5\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) - {\left(\frac{c^{2} d^{4} e^{3}}{x e + d} - \frac{2 \, b c d^{3} e^{4}}{x e + d} + \frac{b^{2} d^{2} e^{5}}{x e + d}\right)} e^{\left(-8\right)}"," ",0,"1/3*(c^2 - 3*(2*c^2*d*e - b*c*e^2)*e^(-1)/(x*e + d) + 3*(6*c^2*d^2*e^2 - 6*b*c*d*e^3 + b^2*e^4)*e^(-2)/(x*e + d)^2)*(x*e + d)^3*e^(-5) + 2*(2*c^2*d^3 - 3*b*c*d^2*e + b^2*d*e^2)*e^(-5)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) - (c^2*d^4*e^3/(x*e + d) - 2*b*c*d^3*e^4/(x*e + d) + b^2*d^2*e^5/(x*e + d))*e^(-8)","A",0
238,1,134,0,0.172625," ","integrate((c*x^2+b*x)^2/(e*x+d)^3,x, algorithm=""giac"")","{\left(6 \, c^{2} d^{2} - 6 \, b c d e + b^{2} e^{2}\right)} e^{\left(-5\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{2} \, {\left(c^{2} x^{2} e^{3} - 6 \, c^{2} d x e^{2} + 4 \, b c x e^{3}\right)} e^{\left(-6\right)} + \frac{{\left(7 \, c^{2} d^{4} - 10 \, b c d^{3} e + 3 \, b^{2} d^{2} e^{2} + 4 \, {\left(2 \, c^{2} d^{3} e - 3 \, b c d^{2} e^{2} + b^{2} d e^{3}\right)} x\right)} e^{\left(-5\right)}}{2 \, {\left(x e + d\right)}^{2}}"," ",0,"(6*c^2*d^2 - 6*b*c*d*e + b^2*e^2)*e^(-5)*log(abs(x*e + d)) + 1/2*(c^2*x^2*e^3 - 6*c^2*d*x*e^2 + 4*b*c*x*e^3)*e^(-6) + 1/2*(7*c^2*d^4 - 10*b*c*d^3*e + 3*b^2*d^2*e^2 + 4*(2*c^2*d^3*e - 3*b*c*d^2*e^2 + b^2*d*e^3)*x)*e^(-5)/(x*e + d)^2","A",0
239,1,131,0,0.193264," ","integrate((c*x^2+b*x)^2/(e*x+d)^4,x, algorithm=""giac"")","c^{2} x e^{\left(-4\right)} - 2 \, {\left(2 \, c^{2} d - b c e\right)} e^{\left(-5\right)} \log\left({\left| x e + d \right|}\right) - \frac{{\left(13 \, c^{2} d^{4} - 11 \, b c d^{3} e + b^{2} d^{2} e^{2} + 3 \, {\left(6 \, c^{2} d^{2} e^{2} - 6 \, b c d e^{3} + b^{2} e^{4}\right)} x^{2} + 3 \, {\left(10 \, c^{2} d^{3} e - 9 \, b c d^{2} e^{2} + b^{2} d e^{3}\right)} x\right)} e^{\left(-5\right)}}{3 \, {\left(x e + d\right)}^{3}}"," ",0,"c^2*x*e^(-4) - 2*(2*c^2*d - b*c*e)*e^(-5)*log(abs(x*e + d)) - 1/3*(13*c^2*d^4 - 11*b*c*d^3*e + b^2*d^2*e^2 + 3*(6*c^2*d^2*e^2 - 6*b*c*d*e^3 + b^2*e^4)*x^2 + 3*(10*c^2*d^3*e - 9*b*c*d^2*e^2 + b^2*d*e^3)*x)*e^(-5)/(x*e + d)^3","A",0
240,1,214,0,0.165161," ","integrate((c*x^2+b*x)^2/(e*x+d)^5,x, algorithm=""giac"")","-c^{2} e^{\left(-5\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) + \frac{1}{12} \, {\left(\frac{48 \, c^{2} d e^{15}}{x e + d} - \frac{36 \, c^{2} d^{2} e^{15}}{{\left(x e + d\right)}^{2}} + \frac{16 \, c^{2} d^{3} e^{15}}{{\left(x e + d\right)}^{3}} - \frac{3 \, c^{2} d^{4} e^{15}}{{\left(x e + d\right)}^{4}} - \frac{24 \, b c e^{16}}{x e + d} + \frac{36 \, b c d e^{16}}{{\left(x e + d\right)}^{2}} - \frac{24 \, b c d^{2} e^{16}}{{\left(x e + d\right)}^{3}} + \frac{6 \, b c d^{3} e^{16}}{{\left(x e + d\right)}^{4}} - \frac{6 \, b^{2} e^{17}}{{\left(x e + d\right)}^{2}} + \frac{8 \, b^{2} d e^{17}}{{\left(x e + d\right)}^{3}} - \frac{3 \, b^{2} d^{2} e^{17}}{{\left(x e + d\right)}^{4}}\right)} e^{\left(-20\right)}"," ",0,"-c^2*e^(-5)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) + 1/12*(48*c^2*d*e^15/(x*e + d) - 36*c^2*d^2*e^15/(x*e + d)^2 + 16*c^2*d^3*e^15/(x*e + d)^3 - 3*c^2*d^4*e^15/(x*e + d)^4 - 24*b*c*e^16/(x*e + d) + 36*b*c*d*e^16/(x*e + d)^2 - 24*b*c*d^2*e^16/(x*e + d)^3 + 6*b*c*d^3*e^16/(x*e + d)^4 - 6*b^2*e^17/(x*e + d)^2 + 8*b^2*d*e^17/(x*e + d)^3 - 3*b^2*d^2*e^17/(x*e + d)^4)*e^(-20)","A",0
241,1,132,0,0.180363," ","integrate((c*x^2+b*x)^2/(e*x+d)^6,x, algorithm=""giac"")","-\frac{{\left(30 \, c^{2} x^{4} e^{4} + 60 \, c^{2} d x^{3} e^{3} + 60 \, c^{2} d^{2} x^{2} e^{2} + 30 \, c^{2} d^{3} x e + 6 \, c^{2} d^{4} + 30 \, b c x^{3} e^{4} + 30 \, b c d x^{2} e^{3} + 15 \, b c d^{2} x e^{2} + 3 \, b c d^{3} e + 10 \, b^{2} x^{2} e^{4} + 5 \, b^{2} d x e^{3} + b^{2} d^{2} e^{2}\right)} e^{\left(-5\right)}}{30 \, {\left(x e + d\right)}^{5}}"," ",0,"-1/30*(30*c^2*x^4*e^4 + 60*c^2*d*x^3*e^3 + 60*c^2*d^2*x^2*e^2 + 30*c^2*d^3*x*e + 6*c^2*d^4 + 30*b*c*x^3*e^4 + 30*b*c*d*x^2*e^3 + 15*b*c*d^2*x*e^2 + 3*b*c*d^3*e + 10*b^2*x^2*e^4 + 5*b^2*d*x*e^3 + b^2*d^2*e^2)*e^(-5)/(x*e + d)^5","A",0
242,1,132,0,0.184917," ","integrate((c*x^2+b*x)^2/(e*x+d)^7,x, algorithm=""giac"")","-\frac{{\left(30 \, c^{2} x^{4} e^{4} + 40 \, c^{2} d x^{3} e^{3} + 30 \, c^{2} d^{2} x^{2} e^{2} + 12 \, c^{2} d^{3} x e + 2 \, c^{2} d^{4} + 40 \, b c x^{3} e^{4} + 30 \, b c d x^{2} e^{3} + 12 \, b c d^{2} x e^{2} + 2 \, b c d^{3} e + 15 \, b^{2} x^{2} e^{4} + 6 \, b^{2} d x e^{3} + b^{2} d^{2} e^{2}\right)} e^{\left(-5\right)}}{60 \, {\left(x e + d\right)}^{6}}"," ",0,"-1/60*(30*c^2*x^4*e^4 + 40*c^2*d*x^3*e^3 + 30*c^2*d^2*x^2*e^2 + 12*c^2*d^3*x*e + 2*c^2*d^4 + 40*b*c*x^3*e^4 + 30*b*c*d*x^2*e^3 + 12*b*c*d^2*x*e^2 + 2*b*c*d^3*e + 15*b^2*x^2*e^4 + 6*b^2*d*x*e^3 + b^2*d^2*e^2)*e^(-5)/(x*e + d)^6","A",0
243,1,133,0,0.152963," ","integrate((c*x^2+b*x)^2/(e*x+d)^8,x, algorithm=""giac"")","-\frac{{\left(70 \, c^{2} x^{4} e^{4} + 70 \, c^{2} d x^{3} e^{3} + 42 \, c^{2} d^{2} x^{2} e^{2} + 14 \, c^{2} d^{3} x e + 2 \, c^{2} d^{4} + 105 \, b c x^{3} e^{4} + 63 \, b c d x^{2} e^{3} + 21 \, b c d^{2} x e^{2} + 3 \, b c d^{3} e + 42 \, b^{2} x^{2} e^{4} + 14 \, b^{2} d x e^{3} + 2 \, b^{2} d^{2} e^{2}\right)} e^{\left(-5\right)}}{210 \, {\left(x e + d\right)}^{7}}"," ",0,"-1/210*(70*c^2*x^4*e^4 + 70*c^2*d*x^3*e^3 + 42*c^2*d^2*x^2*e^2 + 14*c^2*d^3*x*e + 2*c^2*d^4 + 105*b*c*x^3*e^4 + 63*b*c*d*x^2*e^3 + 21*b*c*d^2*x*e^2 + 3*b*c*d^3*e + 42*b^2*x^2*e^4 + 14*b^2*d*x*e^3 + 2*b^2*d^2*e^2)*e^(-5)/(x*e + d)^7","A",0
244,1,242,0,0.169120," ","integrate((e*x+d)^4*(c*x^2+b*x)^3,x, algorithm=""giac"")","\frac{1}{11} \, c^{3} x^{11} e^{4} + \frac{2}{5} \, c^{3} d x^{10} e^{3} + \frac{2}{3} \, c^{3} d^{2} x^{9} e^{2} + \frac{1}{2} \, c^{3} d^{3} x^{8} e + \frac{1}{7} \, c^{3} d^{4} x^{7} + \frac{3}{10} \, b c^{2} x^{10} e^{4} + \frac{4}{3} \, b c^{2} d x^{9} e^{3} + \frac{9}{4} \, b c^{2} d^{2} x^{8} e^{2} + \frac{12}{7} \, b c^{2} d^{3} x^{7} e + \frac{1}{2} \, b c^{2} d^{4} x^{6} + \frac{1}{3} \, b^{2} c x^{9} e^{4} + \frac{3}{2} \, b^{2} c d x^{8} e^{3} + \frac{18}{7} \, b^{2} c d^{2} x^{7} e^{2} + 2 \, b^{2} c d^{3} x^{6} e + \frac{3}{5} \, b^{2} c d^{4} x^{5} + \frac{1}{8} \, b^{3} x^{8} e^{4} + \frac{4}{7} \, b^{3} d x^{7} e^{3} + b^{3} d^{2} x^{6} e^{2} + \frac{4}{5} \, b^{3} d^{3} x^{5} e + \frac{1}{4} \, b^{3} d^{4} x^{4}"," ",0,"1/11*c^3*x^11*e^4 + 2/5*c^3*d*x^10*e^3 + 2/3*c^3*d^2*x^9*e^2 + 1/2*c^3*d^3*x^8*e + 1/7*c^3*d^4*x^7 + 3/10*b*c^2*x^10*e^4 + 4/3*b*c^2*d*x^9*e^3 + 9/4*b*c^2*d^2*x^8*e^2 + 12/7*b*c^2*d^3*x^7*e + 1/2*b*c^2*d^4*x^6 + 1/3*b^2*c*x^9*e^4 + 3/2*b^2*c*d*x^8*e^3 + 18/7*b^2*c*d^2*x^7*e^2 + 2*b^2*c*d^3*x^6*e + 3/5*b^2*c*d^4*x^5 + 1/8*b^3*x^8*e^4 + 4/7*b^3*d*x^7*e^3 + b^3*d^2*x^6*e^2 + 4/5*b^3*d^3*x^5*e + 1/4*b^3*d^4*x^4","A",0
245,1,189,0,0.211150," ","integrate((e*x+d)^3*(c*x^2+b*x)^3,x, algorithm=""giac"")","\frac{1}{10} \, c^{3} x^{10} e^{3} + \frac{1}{3} \, c^{3} d x^{9} e^{2} + \frac{3}{8} \, c^{3} d^{2} x^{8} e + \frac{1}{7} \, c^{3} d^{3} x^{7} + \frac{1}{3} \, b c^{2} x^{9} e^{3} + \frac{9}{8} \, b c^{2} d x^{8} e^{2} + \frac{9}{7} \, b c^{2} d^{2} x^{7} e + \frac{1}{2} \, b c^{2} d^{3} x^{6} + \frac{3}{8} \, b^{2} c x^{8} e^{3} + \frac{9}{7} \, b^{2} c d x^{7} e^{2} + \frac{3}{2} \, b^{2} c d^{2} x^{6} e + \frac{3}{5} \, b^{2} c d^{3} x^{5} + \frac{1}{7} \, b^{3} x^{7} e^{3} + \frac{1}{2} \, b^{3} d x^{6} e^{2} + \frac{3}{5} \, b^{3} d^{2} x^{5} e + \frac{1}{4} \, b^{3} d^{3} x^{4}"," ",0,"1/10*c^3*x^10*e^3 + 1/3*c^3*d*x^9*e^2 + 3/8*c^3*d^2*x^8*e + 1/7*c^3*d^3*x^7 + 1/3*b*c^2*x^9*e^3 + 9/8*b*c^2*d*x^8*e^2 + 9/7*b*c^2*d^2*x^7*e + 1/2*b*c^2*d^3*x^6 + 3/8*b^2*c*x^8*e^3 + 9/7*b^2*c*d*x^7*e^2 + 3/2*b^2*c*d^2*x^6*e + 3/5*b^2*c*d^3*x^5 + 1/7*b^3*x^7*e^3 + 1/2*b^3*d*x^6*e^2 + 3/5*b^3*d^2*x^5*e + 1/4*b^3*d^3*x^4","A",0
246,1,134,0,0.161055," ","integrate((e*x+d)^2*(c*x^2+b*x)^3,x, algorithm=""giac"")","\frac{1}{9} \, c^{3} x^{9} e^{2} + \frac{1}{4} \, c^{3} d x^{8} e + \frac{1}{7} \, c^{3} d^{2} x^{7} + \frac{3}{8} \, b c^{2} x^{8} e^{2} + \frac{6}{7} \, b c^{2} d x^{7} e + \frac{1}{2} \, b c^{2} d^{2} x^{6} + \frac{3}{7} \, b^{2} c x^{7} e^{2} + b^{2} c d x^{6} e + \frac{3}{5} \, b^{2} c d^{2} x^{5} + \frac{1}{6} \, b^{3} x^{6} e^{2} + \frac{2}{5} \, b^{3} d x^{5} e + \frac{1}{4} \, b^{3} d^{2} x^{4}"," ",0,"1/9*c^3*x^9*e^2 + 1/4*c^3*d*x^8*e + 1/7*c^3*d^2*x^7 + 3/8*b*c^2*x^8*e^2 + 6/7*b*c^2*d*x^7*e + 1/2*b*c^2*d^2*x^6 + 3/7*b^2*c*x^7*e^2 + b^2*c*d*x^6*e + 3/5*b^2*c*d^2*x^5 + 1/6*b^3*x^6*e^2 + 2/5*b^3*d*x^5*e + 1/4*b^3*d^2*x^4","A",0
247,1,81,0,0.154451," ","integrate((e*x+d)*(c*x^2+b*x)^3,x, algorithm=""giac"")","\frac{1}{8} \, c^{3} x^{8} e + \frac{1}{7} \, c^{3} d x^{7} + \frac{3}{7} \, b c^{2} x^{7} e + \frac{1}{2} \, b c^{2} d x^{6} + \frac{1}{2} \, b^{2} c x^{6} e + \frac{3}{5} \, b^{2} c d x^{5} + \frac{1}{5} \, b^{3} x^{5} e + \frac{1}{4} \, b^{3} d x^{4}"," ",0,"1/8*c^3*x^8*e + 1/7*c^3*d*x^7 + 3/7*b*c^2*x^7*e + 1/2*b*c^2*d*x^6 + 1/2*b^2*c*x^6*e + 3/5*b^2*c*d*x^5 + 1/5*b^3*x^5*e + 1/4*b^3*d*x^4","A",0
248,1,35,0,0.180339," ","integrate((c*x^2+b*x)^3,x, algorithm=""giac"")","\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,"1/7*c^3*x^7 + 1/2*b*c^2*x^6 + 3/5*b^2*c*x^5 + 1/4*b^3*x^4","A",0
249,1,270,0,0.169685," ","integrate((c*x^2+b*x)^3/(e*x+d),x, algorithm=""giac"")","{\left(c^{3} d^{6} - 3 \, b c^{2} d^{5} e + 3 \, b^{2} c d^{4} e^{2} - b^{3} d^{3} e^{3}\right)} e^{\left(-7\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{60} \, {\left(10 \, c^{3} x^{6} e^{5} - 12 \, c^{3} d x^{5} e^{4} + 15 \, c^{3} d^{2} x^{4} e^{3} - 20 \, c^{3} d^{3} x^{3} e^{2} + 30 \, c^{3} d^{4} x^{2} e - 60 \, c^{3} d^{5} x + 36 \, b c^{2} x^{5} e^{5} - 45 \, b c^{2} d x^{4} e^{4} + 60 \, b c^{2} d^{2} x^{3} e^{3} - 90 \, b c^{2} d^{3} x^{2} e^{2} + 180 \, b c^{2} d^{4} x e + 45 \, b^{2} c x^{4} e^{5} - 60 \, b^{2} c d x^{3} e^{4} + 90 \, b^{2} c d^{2} x^{2} e^{3} - 180 \, b^{2} c d^{3} x e^{2} + 20 \, b^{3} x^{3} e^{5} - 30 \, b^{3} d x^{2} e^{4} + 60 \, b^{3} d^{2} x e^{3}\right)} e^{\left(-6\right)}"," ",0,"(c^3*d^6 - 3*b*c^2*d^5*e + 3*b^2*c*d^4*e^2 - b^3*d^3*e^3)*e^(-7)*log(abs(x*e + d)) + 1/60*(10*c^3*x^6*e^5 - 12*c^3*d*x^5*e^4 + 15*c^3*d^2*x^4*e^3 - 20*c^3*d^3*x^3*e^2 + 30*c^3*d^4*x^2*e - 60*c^3*d^5*x + 36*b*c^2*x^5*e^5 - 45*b*c^2*d*x^4*e^4 + 60*b*c^2*d^2*x^3*e^3 - 90*b*c^2*d^3*x^2*e^2 + 180*b*c^2*d^4*x*e + 45*b^2*c*x^4*e^5 - 60*b^2*c*d*x^3*e^4 + 90*b^2*c*d^2*x^2*e^3 - 180*b^2*c*d^3*x*e^2 + 20*b^3*x^3*e^5 - 30*b^3*d*x^2*e^4 + 60*b^3*d^2*x*e^3)*e^(-6)","A",0
250,1,332,0,0.195704," ","integrate((c*x^2+b*x)^3/(e*x+d)^2,x, algorithm=""giac"")","\frac{1}{20} \, {\left(4 \, c^{3} - \frac{15 \, {\left(2 \, c^{3} d e - b c^{2} e^{2}\right)} e^{\left(-1\right)}}{x e + d} + \frac{20 \, {\left(5 \, c^{3} d^{2} e^{2} - 5 \, b c^{2} d e^{3} + b^{2} c e^{4}\right)} e^{\left(-2\right)}}{{\left(x e + d\right)}^{2}} - \frac{10 \, {\left(20 \, c^{3} d^{3} e^{3} - 30 \, b c^{2} d^{2} e^{4} + 12 \, b^{2} c d e^{5} - b^{3} e^{6}\right)} e^{\left(-3\right)}}{{\left(x e + d\right)}^{3}} + \frac{60 \, {\left(5 \, c^{3} d^{4} e^{4} - 10 \, b c^{2} d^{3} e^{5} + 6 \, b^{2} c d^{2} e^{6} - b^{3} d e^{7}\right)} e^{\left(-4\right)}}{{\left(x e + d\right)}^{4}}\right)} {\left(x e + d\right)}^{5} e^{\left(-7\right)} + 3 \, {\left(2 \, c^{3} d^{5} - 5 \, b c^{2} d^{4} e + 4 \, b^{2} c d^{3} e^{2} - b^{3} d^{2} e^{3}\right)} e^{\left(-7\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) - {\left(\frac{c^{3} d^{6} e^{5}}{x e + d} - \frac{3 \, b c^{2} d^{5} e^{6}}{x e + d} + \frac{3 \, b^{2} c d^{4} e^{7}}{x e + d} - \frac{b^{3} d^{3} e^{8}}{x e + d}\right)} e^{\left(-12\right)}"," ",0,"1/20*(4*c^3 - 15*(2*c^3*d*e - b*c^2*e^2)*e^(-1)/(x*e + d) + 20*(5*c^3*d^2*e^2 - 5*b*c^2*d*e^3 + b^2*c*e^4)*e^(-2)/(x*e + d)^2 - 10*(20*c^3*d^3*e^3 - 30*b*c^2*d^2*e^4 + 12*b^2*c*d*e^5 - b^3*e^6)*e^(-3)/(x*e + d)^3 + 60*(5*c^3*d^4*e^4 - 10*b*c^2*d^3*e^5 + 6*b^2*c*d^2*e^6 - b^3*d*e^7)*e^(-4)/(x*e + d)^4)*(x*e + d)^5*e^(-7) + 3*(2*c^3*d^5 - 5*b*c^2*d^4*e + 4*b^2*c*d^3*e^2 - b^3*d^2*e^3)*e^(-7)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) - (c^3*d^6*e^5/(x*e + d) - 3*b*c^2*d^5*e^6/(x*e + d) + 3*b^2*c*d^4*e^7/(x*e + d) - b^3*d^3*e^8/(x*e + d))*e^(-12)","B",0
251,1,264,0,0.168777," ","integrate((c*x^2+b*x)^3/(e*x+d)^3,x, algorithm=""giac"")","3 \, {\left(5 \, c^{3} d^{4} - 10 \, b c^{2} d^{3} e + 6 \, b^{2} c d^{2} e^{2} - b^{3} d e^{3}\right)} e^{\left(-7\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{4} \, {\left(c^{3} x^{4} e^{9} - 4 \, c^{3} d x^{3} e^{8} + 12 \, c^{3} d^{2} x^{2} e^{7} - 40 \, c^{3} d^{3} x e^{6} + 4 \, b c^{2} x^{3} e^{9} - 18 \, b c^{2} d x^{2} e^{8} + 72 \, b c^{2} d^{2} x e^{7} + 6 \, b^{2} c x^{2} e^{9} - 36 \, b^{2} c d x e^{8} + 4 \, b^{3} x e^{9}\right)} e^{\left(-12\right)} + \frac{{\left(11 \, c^{3} d^{6} - 27 \, b c^{2} d^{5} e + 21 \, b^{2} c d^{4} e^{2} - 5 \, b^{3} d^{3} e^{3} + 6 \, {\left(2 \, c^{3} d^{5} e - 5 \, b c^{2} d^{4} e^{2} + 4 \, b^{2} c d^{3} e^{3} - b^{3} d^{2} e^{4}\right)} x\right)} e^{\left(-7\right)}}{2 \, {\left(x e + d\right)}^{2}}"," ",0,"3*(5*c^3*d^4 - 10*b*c^2*d^3*e + 6*b^2*c*d^2*e^2 - b^3*d*e^3)*e^(-7)*log(abs(x*e + d)) + 1/4*(c^3*x^4*e^9 - 4*c^3*d*x^3*e^8 + 12*c^3*d^2*x^2*e^7 - 40*c^3*d^3*x*e^6 + 4*b*c^2*x^3*e^9 - 18*b*c^2*d*x^2*e^8 + 72*b*c^2*d^2*x*e^7 + 6*b^2*c*x^2*e^9 - 36*b^2*c*d*x*e^8 + 4*b^3*x*e^9)*e^(-12) + 1/2*(11*c^3*d^6 - 27*b*c^2*d^5*e + 21*b^2*c*d^4*e^2 - 5*b^3*d^3*e^3 + 6*(2*c^3*d^5*e - 5*b*c^2*d^4*e^2 + 4*b^2*c*d^3*e^3 - b^3*d^2*e^4)*x)*e^(-7)/(x*e + d)^2","A",0
252,1,261,0,0.182855," ","integrate((c*x^2+b*x)^3/(e*x+d)^4,x, algorithm=""giac"")","-{\left(20 \, c^{3} d^{3} - 30 \, b c^{2} d^{2} e + 12 \, b^{2} c d e^{2} - b^{3} e^{3}\right)} e^{\left(-7\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{6} \, {\left(2 \, c^{3} x^{3} e^{8} - 12 \, c^{3} d x^{2} e^{7} + 60 \, c^{3} d^{2} x e^{6} + 9 \, b c^{2} x^{2} e^{8} - 72 \, b c^{2} d x e^{7} + 18 \, b^{2} c x e^{8}\right)} e^{\left(-12\right)} - \frac{{\left(74 \, c^{3} d^{6} - 141 \, b c^{2} d^{5} e + 78 \, b^{2} c d^{4} e^{2} - 11 \, b^{3} d^{3} e^{3} + 18 \, {\left(5 \, c^{3} d^{4} e^{2} - 10 \, b c^{2} d^{3} e^{3} + 6 \, b^{2} c d^{2} e^{4} - b^{3} d e^{5}\right)} x^{2} + 9 \, {\left(18 \, c^{3} d^{5} e - 35 \, b c^{2} d^{4} e^{2} + 20 \, b^{2} c d^{3} e^{3} - 3 \, b^{3} d^{2} e^{4}\right)} x\right)} e^{\left(-7\right)}}{6 \, {\left(x e + d\right)}^{3}}"," ",0,"-(20*c^3*d^3 - 30*b*c^2*d^2*e + 12*b^2*c*d*e^2 - b^3*e^3)*e^(-7)*log(abs(x*e + d)) + 1/6*(2*c^3*x^3*e^8 - 12*c^3*d*x^2*e^7 + 60*c^3*d^2*x*e^6 + 9*b*c^2*x^2*e^8 - 72*b*c^2*d*x*e^7 + 18*b^2*c*x*e^8)*e^(-12) - 1/6*(74*c^3*d^6 - 141*b*c^2*d^5*e + 78*b^2*c*d^4*e^2 - 11*b^3*d^3*e^3 + 18*(5*c^3*d^4*e^2 - 10*b*c^2*d^3*e^3 + 6*b^2*c*d^2*e^4 - b^3*d*e^5)*x^2 + 9*(18*c^3*d^5*e - 35*b*c^2*d^4*e^2 + 20*b^2*c*d^3*e^3 - 3*b^3*d^2*e^4)*x)*e^(-7)/(x*e + d)^3","A",0
253,1,387,0,0.189803," ","integrate((c*x^2+b*x)^3/(e*x+d)^5,x, algorithm=""giac"")","\frac{1}{2} \, {\left(c^{3} - \frac{6 \, {\left(2 \, c^{3} d e - b c^{2} e^{2}\right)} e^{\left(-1\right)}}{x e + d}\right)} {\left(x e + d\right)}^{2} e^{\left(-7\right)} - 3 \, {\left(5 \, c^{3} d^{2} - 5 \, b c^{2} d e + b^{2} c e^{2}\right)} e^{\left(-7\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) + \frac{1}{4} \, {\left(\frac{80 \, c^{3} d^{3} e^{29}}{x e + d} - \frac{30 \, c^{3} d^{4} e^{29}}{{\left(x e + d\right)}^{2}} + \frac{8 \, c^{3} d^{5} e^{29}}{{\left(x e + d\right)}^{3}} - \frac{c^{3} d^{6} e^{29}}{{\left(x e + d\right)}^{4}} - \frac{120 \, b c^{2} d^{2} e^{30}}{x e + d} + \frac{60 \, b c^{2} d^{3} e^{30}}{{\left(x e + d\right)}^{2}} - \frac{20 \, b c^{2} d^{4} e^{30}}{{\left(x e + d\right)}^{3}} + \frac{3 \, b c^{2} d^{5} e^{30}}{{\left(x e + d\right)}^{4}} + \frac{48 \, b^{2} c d e^{31}}{x e + d} - \frac{36 \, b^{2} c d^{2} e^{31}}{{\left(x e + d\right)}^{2}} + \frac{16 \, b^{2} c d^{3} e^{31}}{{\left(x e + d\right)}^{3}} - \frac{3 \, b^{2} c d^{4} e^{31}}{{\left(x e + d\right)}^{4}} - \frac{4 \, b^{3} e^{32}}{x e + d} + \frac{6 \, b^{3} d e^{32}}{{\left(x e + d\right)}^{2}} - \frac{4 \, b^{3} d^{2} e^{32}}{{\left(x e + d\right)}^{3}} + \frac{b^{3} d^{3} e^{32}}{{\left(x e + d\right)}^{4}}\right)} e^{\left(-36\right)}"," ",0,"1/2*(c^3 - 6*(2*c^3*d*e - b*c^2*e^2)*e^(-1)/(x*e + d))*(x*e + d)^2*e^(-7) - 3*(5*c^3*d^2 - 5*b*c^2*d*e + b^2*c*e^2)*e^(-7)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) + 1/4*(80*c^3*d^3*e^29/(x*e + d) - 30*c^3*d^4*e^29/(x*e + d)^2 + 8*c^3*d^5*e^29/(x*e + d)^3 - c^3*d^6*e^29/(x*e + d)^4 - 120*b*c^2*d^2*e^30/(x*e + d) + 60*b*c^2*d^3*e^30/(x*e + d)^2 - 20*b*c^2*d^4*e^30/(x*e + d)^3 + 3*b*c^2*d^5*e^30/(x*e + d)^4 + 48*b^2*c*d*e^31/(x*e + d) - 36*b^2*c*d^2*e^31/(x*e + d)^2 + 16*b^2*c*d^3*e^31/(x*e + d)^3 - 3*b^2*c*d^4*e^31/(x*e + d)^4 - 4*b^3*e^32/(x*e + d) + 6*b^3*d*e^32/(x*e + d)^2 - 4*b^3*d^2*e^32/(x*e + d)^3 + b^3*d^3*e^32/(x*e + d)^4)*e^(-36)","A",0
254,1,251,0,0.172446," ","integrate((c*x^2+b*x)^3/(e*x+d)^6,x, algorithm=""giac"")","c^{3} x e^{\left(-6\right)} - 3 \, {\left(2 \, c^{3} d - b c^{2} e\right)} e^{\left(-7\right)} \log\left({\left| x e + d \right|}\right) - \frac{{\left(174 \, c^{3} d^{6} - 137 \, b c^{2} d^{5} e + 12 \, b^{2} c d^{4} e^{2} + b^{3} d^{3} e^{3} + 60 \, {\left(5 \, c^{3} d^{2} e^{4} - 5 \, b c^{2} d e^{5} + b^{2} c e^{6}\right)} x^{4} + 10 \, {\left(100 \, c^{3} d^{3} e^{3} - 90 \, b c^{2} d^{2} e^{4} + 12 \, b^{2} c d e^{5} + b^{3} e^{6}\right)} x^{3} + 10 \, {\left(130 \, c^{3} d^{4} e^{2} - 110 \, b c^{2} d^{3} e^{3} + 12 \, b^{2} c d^{2} e^{4} + b^{3} d e^{5}\right)} x^{2} + 5 \, {\left(154 \, c^{3} d^{5} e - 125 \, b c^{2} d^{4} e^{2} + 12 \, b^{2} c d^{3} e^{3} + b^{3} d^{2} e^{4}\right)} x\right)} e^{\left(-7\right)}}{20 \, {\left(x e + d\right)}^{5}}"," ",0,"c^3*x*e^(-6) - 3*(2*c^3*d - b*c^2*e)*e^(-7)*log(abs(x*e + d)) - 1/20*(174*c^3*d^6 - 137*b*c^2*d^5*e + 12*b^2*c*d^4*e^2 + b^3*d^3*e^3 + 60*(5*c^3*d^2*e^4 - 5*b*c^2*d*e^5 + b^2*c*e^6)*x^4 + 10*(100*c^3*d^3*e^3 - 90*b*c^2*d^2*e^4 + 12*b^2*c*d*e^5 + b^3*e^6)*x^3 + 10*(130*c^3*d^4*e^2 - 110*b*c^2*d^3*e^3 + 12*b^2*c*d^2*e^4 + b^3*d*e^5)*x^2 + 5*(154*c^3*d^5*e - 125*b*c^2*d^4*e^2 + 12*b^2*c*d^3*e^3 + b^3*d^2*e^4)*x)*e^(-7)/(x*e + d)^5","A",0
255,1,260,0,0.177178," ","integrate((c*x^2+b*x)^3/(e*x+d)^7,x, algorithm=""giac"")","c^{3} e^{\left(-7\right)} \log\left({\left| x e + d \right|}\right) + \frac{{\left(180 \, {\left(2 \, c^{3} d e^{4} - b c^{2} e^{5}\right)} x^{5} + 90 \, {\left(15 \, c^{3} d^{2} e^{3} - 5 \, b c^{2} d e^{4} - b^{2} c e^{5}\right)} x^{4} + 20 \, {\left(110 \, c^{3} d^{3} e^{2} - 30 \, b c^{2} d^{2} e^{3} - 6 \, b^{2} c d e^{4} - b^{3} e^{5}\right)} x^{3} + 15 \, {\left(125 \, c^{3} d^{4} e - 30 \, b c^{2} d^{3} e^{2} - 6 \, b^{2} c d^{2} e^{3} - b^{3} d e^{4}\right)} x^{2} + 6 \, {\left(137 \, c^{3} d^{5} - 30 \, b c^{2} d^{4} e - 6 \, b^{2} c d^{3} e^{2} - b^{3} d^{2} e^{3}\right)} x + {\left(147 \, c^{3} d^{6} - 30 \, b c^{2} d^{5} e - 6 \, b^{2} c d^{4} e^{2} - b^{3} d^{3} e^{3}\right)} e^{\left(-1\right)}\right)} e^{\left(-6\right)}}{60 \, {\left(x e + d\right)}^{6}}"," ",0,"c^3*e^(-7)*log(abs(x*e + d)) + 1/60*(180*(2*c^3*d*e^4 - b*c^2*e^5)*x^5 + 90*(15*c^3*d^2*e^3 - 5*b*c^2*d*e^4 - b^2*c*e^5)*x^4 + 20*(110*c^3*d^3*e^2 - 30*b*c^2*d^2*e^3 - 6*b^2*c*d*e^4 - b^3*e^5)*x^3 + 15*(125*c^3*d^4*e - 30*b*c^2*d^3*e^2 - 6*b^2*c*d^2*e^3 - b^3*d*e^4)*x^2 + 6*(137*c^3*d^5 - 30*b*c^2*d^4*e - 6*b^2*c*d^3*e^2 - b^3*d^2*e^3)*x + (147*c^3*d^6 - 30*b*c^2*d^5*e - 6*b^2*c*d^4*e^2 - b^3*d^3*e^3)*e^(-1))*e^(-6)/(x*e + d)^6","A",0
256,1,267,0,0.167324," ","integrate((c*x^2+b*x)^3/(e*x+d)^8,x, algorithm=""giac"")","-\frac{{\left(140 \, c^{3} x^{6} e^{6} + 420 \, c^{3} d x^{5} e^{5} + 700 \, c^{3} d^{2} x^{4} e^{4} + 700 \, c^{3} d^{3} x^{3} e^{3} + 420 \, c^{3} d^{4} x^{2} e^{2} + 140 \, c^{3} d^{5} x e + 20 \, c^{3} d^{6} + 210 \, b c^{2} x^{5} e^{6} + 350 \, b c^{2} d x^{4} e^{5} + 350 \, b c^{2} d^{2} x^{3} e^{4} + 210 \, b c^{2} d^{3} x^{2} e^{3} + 70 \, b c^{2} d^{4} x e^{2} + 10 \, b c^{2} d^{5} e + 140 \, b^{2} c x^{4} e^{6} + 140 \, b^{2} c d x^{3} e^{5} + 84 \, b^{2} c d^{2} x^{2} e^{4} + 28 \, b^{2} c d^{3} x e^{3} + 4 \, b^{2} c d^{4} e^{2} + 35 \, b^{3} x^{3} e^{6} + 21 \, b^{3} d x^{2} e^{5} + 7 \, b^{3} d^{2} x e^{4} + b^{3} d^{3} e^{3}\right)} e^{\left(-7\right)}}{140 \, {\left(x e + d\right)}^{7}}"," ",0,"-1/140*(140*c^3*x^6*e^6 + 420*c^3*d*x^5*e^5 + 700*c^3*d^2*x^4*e^4 + 700*c^3*d^3*x^3*e^3 + 420*c^3*d^4*x^2*e^2 + 140*c^3*d^5*x*e + 20*c^3*d^6 + 210*b*c^2*x^5*e^6 + 350*b*c^2*d*x^4*e^5 + 350*b*c^2*d^2*x^3*e^4 + 210*b*c^2*d^3*x^2*e^3 + 70*b*c^2*d^4*x*e^2 + 10*b*c^2*d^5*e + 140*b^2*c*x^4*e^6 + 140*b^2*c*d*x^3*e^5 + 84*b^2*c*d^2*x^2*e^4 + 28*b^2*c*d^3*x*e^3 + 4*b^2*c*d^4*e^2 + 35*b^3*x^3*e^6 + 21*b^3*d*x^2*e^5 + 7*b^3*d^2*x*e^4 + b^3*d^3*e^3)*e^(-7)/(x*e + d)^7","A",0
257,1,267,0,0.158123," ","integrate((c*x^2+b*x)^3/(e*x+d)^9,x, algorithm=""giac"")","-\frac{{\left(140 \, c^{3} x^{6} e^{6} + 280 \, c^{3} d x^{5} e^{5} + 350 \, c^{3} d^{2} x^{4} e^{4} + 280 \, c^{3} d^{3} x^{3} e^{3} + 140 \, c^{3} d^{4} x^{2} e^{2} + 40 \, c^{3} d^{5} x e + 5 \, c^{3} d^{6} + 280 \, b c^{2} x^{5} e^{6} + 350 \, b c^{2} d x^{4} e^{5} + 280 \, b c^{2} d^{2} x^{3} e^{4} + 140 \, b c^{2} d^{3} x^{2} e^{3} + 40 \, b c^{2} d^{4} x e^{2} + 5 \, b c^{2} d^{5} e + 210 \, b^{2} c x^{4} e^{6} + 168 \, b^{2} c d x^{3} e^{5} + 84 \, b^{2} c d^{2} x^{2} e^{4} + 24 \, b^{2} c d^{3} x e^{3} + 3 \, b^{2} c d^{4} e^{2} + 56 \, b^{3} x^{3} e^{6} + 28 \, b^{3} d x^{2} e^{5} + 8 \, b^{3} d^{2} x e^{4} + b^{3} d^{3} e^{3}\right)} e^{\left(-7\right)}}{280 \, {\left(x e + d\right)}^{8}}"," ",0,"-1/280*(140*c^3*x^6*e^6 + 280*c^3*d*x^5*e^5 + 350*c^3*d^2*x^4*e^4 + 280*c^3*d^3*x^3*e^3 + 140*c^3*d^4*x^2*e^2 + 40*c^3*d^5*x*e + 5*c^3*d^6 + 280*b*c^2*x^5*e^6 + 350*b*c^2*d*x^4*e^5 + 280*b*c^2*d^2*x^3*e^4 + 140*b*c^2*d^3*x^2*e^3 + 40*b*c^2*d^4*x*e^2 + 5*b*c^2*d^5*e + 210*b^2*c*x^4*e^6 + 168*b^2*c*d*x^3*e^5 + 84*b^2*c*d^2*x^2*e^4 + 24*b^2*c*d^3*x*e^3 + 3*b^2*c*d^4*e^2 + 56*b^3*x^3*e^6 + 28*b^3*d*x^2*e^5 + 8*b^3*d^2*x*e^4 + b^3*d^3*e^3)*e^(-7)/(x*e + d)^8","A",0
258,1,268,0,0.234764," ","integrate((c*x^2+b*x)^3/(e*x+d)^10,x, algorithm=""giac"")","-\frac{{\left(840 \, c^{3} x^{6} e^{6} + 1260 \, c^{3} d x^{5} e^{5} + 1260 \, c^{3} d^{2} x^{4} e^{4} + 840 \, c^{3} d^{3} x^{3} e^{3} + 360 \, c^{3} d^{4} x^{2} e^{2} + 90 \, c^{3} d^{5} x e + 10 \, c^{3} d^{6} + 1890 \, b c^{2} x^{5} e^{6} + 1890 \, b c^{2} d x^{4} e^{5} + 1260 \, b c^{2} d^{2} x^{3} e^{4} + 540 \, b c^{2} d^{3} x^{2} e^{3} + 135 \, b c^{2} d^{4} x e^{2} + 15 \, b c^{2} d^{5} e + 1512 \, b^{2} c x^{4} e^{6} + 1008 \, b^{2} c d x^{3} e^{5} + 432 \, b^{2} c d^{2} x^{2} e^{4} + 108 \, b^{2} c d^{3} x e^{3} + 12 \, b^{2} c d^{4} e^{2} + 420 \, b^{3} x^{3} e^{6} + 180 \, b^{3} d x^{2} e^{5} + 45 \, b^{3} d^{2} x e^{4} + 5 \, b^{3} d^{3} e^{3}\right)} e^{\left(-7\right)}}{2520 \, {\left(x e + d\right)}^{9}}"," ",0,"-1/2520*(840*c^3*x^6*e^6 + 1260*c^3*d*x^5*e^5 + 1260*c^3*d^2*x^4*e^4 + 840*c^3*d^3*x^3*e^3 + 360*c^3*d^4*x^2*e^2 + 90*c^3*d^5*x*e + 10*c^3*d^6 + 1890*b*c^2*x^5*e^6 + 1890*b*c^2*d*x^4*e^5 + 1260*b*c^2*d^2*x^3*e^4 + 540*b*c^2*d^3*x^2*e^3 + 135*b*c^2*d^4*x*e^2 + 15*b*c^2*d^5*e + 1512*b^2*c*x^4*e^6 + 1008*b^2*c*d*x^3*e^5 + 432*b^2*c*d^2*x^2*e^4 + 108*b^2*c*d^3*x*e^3 + 12*b^2*c*d^4*e^2 + 420*b^3*x^3*e^6 + 180*b^3*d*x^2*e^5 + 45*b^3*d^2*x*e^4 + 5*b^3*d^3*e^3)*e^(-7)/(x*e + d)^9","A",0
259,1,136,0,0.148367," ","integrate((e*x+d)^4/(c*x^2+b*x),x, algorithm=""giac"")","\frac{d^{4} \log\left({\left| x \right|}\right)}{b} + \frac{2 \, c^{2} x^{3} e^{4} + 12 \, c^{2} d x^{2} e^{3} + 36 \, c^{2} d^{2} x e^{2} - 3 \, b c x^{2} e^{4} - 24 \, b c d x e^{3} + 6 \, b^{2} x e^{4}}{6 \, c^{3}} - \frac{{\left(c^{4} d^{4} - 4 \, b c^{3} d^{3} e + 6 \, b^{2} c^{2} d^{2} e^{2} - 4 \, b^{3} c d e^{3} + b^{4} e^{4}\right)} \log\left({\left| c x + b \right|}\right)}{b c^{4}}"," ",0,"d^4*log(abs(x))/b + 1/6*(2*c^2*x^3*e^4 + 12*c^2*d*x^2*e^3 + 36*c^2*d^2*x*e^2 - 3*b*c*x^2*e^4 - 24*b*c*d*x*e^3 + 6*b^2*x*e^4)/c^3 - (c^4*d^4 - 4*b*c^3*d^3*e + 6*b^2*c^2*d^2*e^2 - 4*b^3*c*d*e^3 + b^4*e^4)*log(abs(c*x + b))/(b*c^4)","A",0
260,1,87,0,0.152200," ","integrate((e*x+d)^3/(c*x^2+b*x),x, algorithm=""giac"")","\frac{d^{3} \log\left({\left| x \right|}\right)}{b} + \frac{c x^{2} e^{3} + 6 \, c d x e^{2} - 2 \, b x e^{3}}{2 \, c^{2}} - \frac{{\left(c^{3} d^{3} - 3 \, b c^{2} d^{2} e + 3 \, b^{2} c d e^{2} - b^{3} e^{3}\right)} \log\left({\left| c x + b \right|}\right)}{b c^{3}}"," ",0,"d^3*log(abs(x))/b + 1/2*(c*x^2*e^3 + 6*c*d*x*e^2 - 2*b*x*e^3)/c^2 - (c^3*d^3 - 3*b*c^2*d^2*e + 3*b^2*c*d*e^2 - b^3*e^3)*log(abs(c*x + b))/(b*c^3)","A",0
261,1,54,0,0.149408," ","integrate((e*x+d)^2/(c*x^2+b*x),x, algorithm=""giac"")","\frac{d^{2} \log\left({\left| x \right|}\right)}{b} + \frac{x e^{2}}{c} - \frac{{\left(c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2}\right)} \log\left({\left| c x + b \right|}\right)}{b c^{2}}"," ",0,"d^2*log(abs(x))/b + x*e^2/c - (c^2*d^2 - 2*b*c*d*e + b^2*e^2)*log(abs(c*x + b))/(b*c^2)","A",0
262,1,33,0,0.166938," ","integrate((e*x+d)/(c*x^2+b*x),x, algorithm=""giac"")","\frac{d \log\left({\left| x \right|}\right)}{b} - \frac{{\left(c d - b e\right)} \log\left({\left| c x + b \right|}\right)}{b c}"," ",0,"d*log(abs(x))/b - (c*d - b*e)*log(abs(c*x + b))/(b*c)","A",0
263,1,20,0,0.150302," ","integrate(1/(c*x^2+b*x),x, algorithm=""giac"")","-\frac{\log\left({\left| c x + b \right|}\right)}{b} + \frac{\log\left({\left| x \right|}\right)}{b}"," ",0,"-log(abs(c*x + b))/b + log(abs(x))/b","A",0
264,1,67,0,0.165972," ","integrate(1/(e*x+d)/(c*x^2+b*x),x, algorithm=""giac"")","-\frac{c^{2} \log\left({\left| c x + b \right|}\right)}{b c^{2} d - b^{2} c e} + \frac{e^{2} \log\left({\left| x e + d \right|}\right)}{c d^{2} e - b d e^{2}} + \frac{\log\left({\left| x \right|}\right)}{b d}"," ",0,"-c^2*log(abs(c*x + b))/(b*c^2*d - b^2*c*e) + e^2*log(abs(x*e + d))/(c*d^2*e - b*d*e^2) + log(abs(x))/(b*d)","A",0
265,1,288,0,0.220360," ","integrate(1/(e*x+d)^2/(c*x^2+b*x),x, algorithm=""giac"")","-\frac{{\left(2 \, c^{2} d^{2} e^{2} - 2 \, b c d e^{3} + b^{2} e^{4}\right)} e^{\left(-2\right)} \log\left(\frac{{\left| -2 \, c d e + \frac{2 \, c d^{2} e}{x e + d} + b e^{2} - \frac{2 \, b d e^{2}}{x e + d} - {\left| b \right|} e^{2} \right|}}{{\left| -2 \, c d e + \frac{2 \, c d^{2} e}{x e + d} + b e^{2} - \frac{2 \, b d e^{2}}{x e + d} + {\left| b \right|} e^{2} \right|}}\right)}{2 \, {\left(c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2}\right)} {\left| b \right|}} - \frac{{\left(2 \, c d e - b e^{2}\right)} \log\left({\left| -c + \frac{2 \, c d}{x e + d} - \frac{c d^{2}}{{\left(x e + d\right)}^{2}} - \frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} \right|}\right)}{2 \, {\left(c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2}\right)}} - \frac{e^{3}}{{\left(c d^{2} e^{2} - b d e^{3}\right)} {\left(x e + d\right)}}"," ",0,"-1/2*(2*c^2*d^2*e^2 - 2*b*c*d*e^3 + b^2*e^4)*e^(-2)*log(abs(-2*c*d*e + 2*c*d^2*e/(x*e + d) + b*e^2 - 2*b*d*e^2/(x*e + d) - abs(b)*e^2)/abs(-2*c*d*e + 2*c*d^2*e/(x*e + d) + b*e^2 - 2*b*d*e^2/(x*e + d) + abs(b)*e^2))/((c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2)*abs(b)) - 1/2*(2*c*d*e - b*e^2)*log(abs(-c + 2*c*d/(x*e + d) - c*d^2/(x*e + d)^2 - b*e/(x*e + d) + b*d*e/(x*e + d)^2))/(c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2) - e^3/((c*d^2*e^2 - b*d*e^3)*(x*e + d))","B",0
266,1,227,0,0.157264," ","integrate(1/(e*x+d)^3/(c*x^2+b*x),x, algorithm=""giac"")","-\frac{c^{4} \log\left({\left| c x + b \right|}\right)}{b c^{4} d^{3} - 3 \, b^{2} c^{3} d^{2} e + 3 \, b^{3} c^{2} d e^{2} - b^{4} c e^{3}} + \frac{{\left(3 \, c^{2} d^{2} e^{2} - 3 \, b c d e^{3} + b^{2} e^{4}\right)} \log\left({\left| x e + d \right|}\right)}{c^{3} d^{6} e - 3 \, b c^{2} d^{5} e^{2} + 3 \, b^{2} c d^{4} e^{3} - b^{3} d^{3} e^{4}} + \frac{\log\left({\left| x \right|}\right)}{b d^{3}} - \frac{5 \, c^{2} d^{4} e - 8 \, b c d^{3} e^{2} + 3 \, b^{2} d^{2} e^{3} + 2 \, {\left(2 \, c^{2} d^{3} e^{2} - 3 \, b c d^{2} e^{3} + b^{2} d e^{4}\right)} x}{2 \, {\left(c d - b e\right)}^{3} {\left(x e + d\right)}^{2} d^{3}}"," ",0,"-c^4*log(abs(c*x + b))/(b*c^4*d^3 - 3*b^2*c^3*d^2*e + 3*b^3*c^2*d*e^2 - b^4*c*e^3) + (3*c^2*d^2*e^2 - 3*b*c*d*e^3 + b^2*e^4)*log(abs(x*e + d))/(c^3*d^6*e - 3*b*c^2*d^5*e^2 + 3*b^2*c*d^4*e^3 - b^3*d^3*e^4) + log(abs(x))/(b*d^3) - 1/2*(5*c^2*d^4*e - 8*b*c*d^3*e^2 + 3*b^2*d^2*e^3 + 2*(2*c^2*d^3*e^2 - 3*b*c*d^2*e^3 + b^2*d*e^4)*x)/((c*d - b*e)^3*(x*e + d)^2*d^3)","A",0
267,1,209,0,0.161388," ","integrate((e*x+d)^5/(c*x^2+b*x)^2,x, algorithm=""giac"")","-\frac{{\left(2 \, c d^{5} - 5 \, b d^{4} e\right)} \log\left({\left| x \right|}\right)}{b^{3}} + \frac{c^{2} x^{2} e^{5} + 10 \, c^{2} d x e^{4} - 4 \, b c x e^{5}}{2 \, c^{4}} + \frac{{\left(2 \, c^{5} d^{5} - 5 \, b c^{4} d^{4} e + 10 \, b^{3} c^{2} d^{2} e^{3} - 10 \, b^{4} c d e^{4} + 3 \, b^{5} e^{5}\right)} \log\left({\left| c x + b \right|}\right)}{b^{3} c^{4}} - \frac{b c^{4} d^{5} + {\left(2 \, c^{5} d^{5} - 5 \, b c^{4} d^{4} e + 10 \, b^{2} c^{3} d^{3} e^{2} - 10 \, b^{3} c^{2} d^{2} e^{3} + 5 \, b^{4} c d e^{4} - b^{5} e^{5}\right)} x}{{\left(c x + b\right)} b^{2} c^{4} x}"," ",0,"-(2*c*d^5 - 5*b*d^4*e)*log(abs(x))/b^3 + 1/2*(c^2*x^2*e^5 + 10*c^2*d*x*e^4 - 4*b*c*x*e^5)/c^4 + (2*c^5*d^5 - 5*b*c^4*d^4*e + 10*b^3*c^2*d^2*e^3 - 10*b^4*c*d*e^4 + 3*b^5*e^5)*log(abs(c*x + b))/(b^3*c^4) - (b*c^4*d^5 + (2*c^5*d^5 - 5*b*c^4*d^4*e + 10*b^2*c^3*d^3*e^2 - 10*b^3*c^2*d^2*e^3 + 5*b^4*c*d*e^4 - b^5*e^5)*x)/((c*x + b)*b^2*c^4*x)","A",0
268,1,160,0,0.179001," ","integrate((e*x+d)^4/(c*x^2+b*x)^2,x, algorithm=""giac"")","\frac{x e^{4}}{c^{2}} - \frac{2 \, {\left(c d^{4} - 2 \, b d^{3} e\right)} \log\left({\left| x \right|}\right)}{b^{3}} + \frac{2 \, {\left(c^{4} d^{4} - 2 \, b c^{3} d^{3} e + 2 \, b^{3} c d e^{3} - b^{4} e^{4}\right)} \log\left({\left| c x + b \right|}\right)}{b^{3} c^{3}} - \frac{b c^{2} d^{4} + \frac{{\left(2 \, c^{4} d^{4} - 4 \, b c^{3} d^{3} e + 6 \, b^{2} c^{2} d^{2} e^{2} - 4 \, b^{3} c d e^{3} + b^{4} e^{4}\right)} x}{c}}{{\left(c x + b\right)} b^{2} c^{2} x}"," ",0,"x*e^4/c^2 - 2*(c*d^4 - 2*b*d^3*e)*log(abs(x))/b^3 + 2*(c^4*d^4 - 2*b*c^3*d^3*e + 2*b^3*c*d*e^3 - b^4*e^4)*log(abs(c*x + b))/(b^3*c^3) - (b*c^2*d^4 + (2*c^4*d^4 - 4*b*c^3*d^3*e + 6*b^2*c^2*d^2*e^2 - 4*b^3*c*d*e^3 + b^4*e^4)*x/c)/((c*x + b)*b^2*c^2*x)","A",0
269,1,129,0,0.203434," ","integrate((e*x+d)^3/(c*x^2+b*x)^2,x, algorithm=""giac"")","-\frac{{\left(2 \, c d^{3} - 3 \, b d^{2} e\right)} \log\left({\left| x \right|}\right)}{b^{3}} + \frac{{\left(2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e + b^{3} e^{3}\right)} \log\left({\left| c x + b \right|}\right)}{b^{3} c^{2}} - \frac{b c^{2} d^{3} + {\left(2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e + 3 \, b^{2} c d e^{2} - b^{3} e^{3}\right)} x}{{\left(c x + b\right)} b^{2} c^{2} x}"," ",0,"-(2*c*d^3 - 3*b*d^2*e)*log(abs(x))/b^3 + (2*c^3*d^3 - 3*b*c^2*d^2*e + b^3*e^3)*log(abs(c*x + b))/(b^3*c^2) - (b*c^2*d^3 + (2*c^3*d^3 - 3*b*c^2*d^2*e + 3*b^2*c*d*e^2 - b^3*e^3)*x)/((c*x + b)*b^2*c^2*x)","A",0
270,1,101,0,0.151945," ","integrate((e*x+d)^2/(c*x^2+b*x)^2,x, algorithm=""giac"")","-\frac{2 \, {\left(c d^{2} - b d e\right)} \log\left({\left| x \right|}\right)}{b^{3}} + \frac{2 \, {\left(c^{2} d^{2} - b c d e\right)} \log\left({\left| c x + b \right|}\right)}{b^{3} c} - \frac{2 \, c^{2} d^{2} x - 2 \, b c d x e + b c d^{2} + b^{2} x e^{2}}{{\left(c x^{2} + b x\right)} b^{2} c}"," ",0,"-2*(c*d^2 - b*d*e)*log(abs(x))/b^3 + 2*(c^2*d^2 - b*c*d*e)*log(abs(c*x + b))/(b^3*c) - (2*c^2*d^2*x - 2*b*c*d*x*e + b*c*d^2 + b^2*x*e^2)/((c*x^2 + b*x)*b^2*c)","A",0
271,1,77,0,0.152294," ","integrate((e*x+d)/(c*x^2+b*x)^2,x, algorithm=""giac"")","-\frac{{\left(2 \, c d - b e\right)} \log\left({\left| x \right|}\right)}{b^{3}} - \frac{2 \, c d x - b x e + b d}{{\left(c x^{2} + b x\right)} b^{2}} + \frac{{\left(2 \, c^{2} d - b c e\right)} \log\left({\left| c x + b \right|}\right)}{b^{3} c}"," ",0,"-(2*c*d - b*e)*log(abs(x))/b^3 - (2*c*d*x - b*x*e + b*d)/((c*x^2 + b*x)*b^2) + (2*c^2*d - b*c*e)*log(abs(c*x + b))/(b^3*c)","A",0
272,1,45,0,0.177199," ","integrate(1/(c*x^2+b*x)^2,x, algorithm=""giac"")","\frac{2 \, c \log\left({\left| c x + b \right|}\right)}{b^{3}} - \frac{2 \, c \log\left({\left| x \right|}\right)}{b^{3}} - \frac{2 \, c x + b}{{\left(c x^{2} + b x\right)} b^{2}}"," ",0,"2*c*log(abs(c*x + b))/b^3 - 2*c*log(abs(x))/b^3 - (2*c*x + b)/((c*x^2 + b*x)*b^2)","A",0
273,1,202,0,0.156302," ","integrate(1/(e*x+d)/(c*x^2+b*x)^2,x, algorithm=""giac"")","\frac{{\left(2 \, c^{4} d - 3 \, b c^{3} e\right)} \log\left({\left| c x + b \right|}\right)}{b^{3} c^{3} d^{2} - 2 \, b^{4} c^{2} d e + b^{5} c e^{2}} + \frac{e^{4} \log\left({\left| x e + d \right|}\right)}{c^{2} d^{4} e - 2 \, b c d^{3} e^{2} + b^{2} d^{2} e^{3}} - \frac{{\left(2 \, c d + b e\right)} \log\left({\left| x \right|}\right)}{b^{3} d^{2}} - \frac{b c^{2} d^{3} - 2 \, b^{2} c d^{2} e + b^{3} d e^{2} + {\left(2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e + b^{2} c d e^{2}\right)} x}{{\left(c d - b e\right)}^{2} {\left(c x + b\right)} b^{2} d^{2} x}"," ",0,"(2*c^4*d - 3*b*c^3*e)*log(abs(c*x + b))/(b^3*c^3*d^2 - 2*b^4*c^2*d*e + b^5*c*e^2) + e^4*log(abs(x*e + d))/(c^2*d^4*e - 2*b*c*d^3*e^2 + b^2*d^2*e^3) - (2*c*d + b*e)*log(abs(x))/(b^3*d^2) - (b*c^2*d^3 - 2*b^2*c*d^2*e + b^3*d*e^2 + (2*c^3*d^3 - 3*b*c^2*d^2*e + b^2*c*d*e^2)*x)/((c*d - b*e)^2*(c*x + b)*b^2*d^2*x)","A",0
274,1,555,0,0.248686," ","integrate(1/(e*x+d)^2/(c*x^2+b*x)^2,x, algorithm=""giac"")","\frac{{\left(2 \, c^{4} d^{4} e^{2} - 4 \, b c^{3} d^{3} e^{3} + 2 \, b^{3} c d e^{5} - b^{4} e^{6}\right)} e^{\left(-2\right)} \log\left(\frac{{\left| -2 \, c d e + \frac{2 \, c d^{2} e}{x e + d} + b e^{2} - \frac{2 \, b d e^{2}}{x e + d} - {\left| b \right|} e^{2} \right|}}{{\left| -2 \, c d e + \frac{2 \, c d^{2} e}{x e + d} + b e^{2} - \frac{2 \, b d e^{2}}{x e + d} + {\left| b \right|} e^{2} \right|}}\right)}{{\left(b^{2} c^{3} d^{6} - 3 \, b^{3} c^{2} d^{5} e + 3 \, b^{4} c d^{4} e^{2} - b^{5} d^{3} e^{3}\right)} {\left| b \right|}} - \frac{{\left(2 \, c d e^{3} - b e^{4}\right)} \log\left({\left| -c + \frac{2 \, c d}{x e + d} - \frac{c d^{2}}{{\left(x e + d\right)}^{2}} - \frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} \right|}\right)}{c^{3} d^{6} - 3 \, b c^{2} d^{5} e + 3 \, b^{2} c d^{4} e^{2} - b^{3} d^{3} e^{3}} - \frac{e^{7}}{{\left(c^{2} d^{4} e^{4} - 2 \, b c d^{3} e^{5} + b^{2} d^{2} e^{6}\right)} {\left(x e + d\right)}} - \frac{\frac{2 \, c^{4} d^{3} e - 3 \, b c^{3} d^{2} e^{2} + 3 \, b^{2} c^{2} d e^{3} - b^{3} c e^{4}}{c d^{2} - b d e} - \frac{{\left(2 \, c^{4} d^{4} e^{2} - 4 \, b c^{3} d^{3} e^{3} + 6 \, b^{2} c^{2} d^{2} e^{4} - 4 \, b^{3} c d e^{5} + b^{4} e^{6}\right)} e^{\left(-1\right)}}{{\left(c d^{2} - b d e\right)} {\left(x e + d\right)}}}{{\left(c d - b e\right)}^{2} b^{2} {\left(c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{b e}{x e + d} - \frac{b d e}{{\left(x e + d\right)}^{2}}\right)} d^{2}}"," ",0,"(2*c^4*d^4*e^2 - 4*b*c^3*d^3*e^3 + 2*b^3*c*d*e^5 - b^4*e^6)*e^(-2)*log(abs(-2*c*d*e + 2*c*d^2*e/(x*e + d) + b*e^2 - 2*b*d*e^2/(x*e + d) - abs(b)*e^2)/abs(-2*c*d*e + 2*c*d^2*e/(x*e + d) + b*e^2 - 2*b*d*e^2/(x*e + d) + abs(b)*e^2))/((b^2*c^3*d^6 - 3*b^3*c^2*d^5*e + 3*b^4*c*d^4*e^2 - b^5*d^3*e^3)*abs(b)) - (2*c*d*e^3 - b*e^4)*log(abs(-c + 2*c*d/(x*e + d) - c*d^2/(x*e + d)^2 - b*e/(x*e + d) + b*d*e/(x*e + d)^2))/(c^3*d^6 - 3*b*c^2*d^5*e + 3*b^2*c*d^4*e^2 - b^3*d^3*e^3) - e^7/((c^2*d^4*e^4 - 2*b*c*d^3*e^5 + b^2*d^2*e^6)*(x*e + d)) - ((2*c^4*d^3*e - 3*b*c^3*d^2*e^2 + 3*b^2*c^2*d*e^3 - b^3*c*e^4)/(c*d^2 - b*d*e) - (2*c^4*d^4*e^2 - 4*b*c^3*d^3*e^3 + 6*b^2*c^2*d^2*e^4 - 4*b^3*c*d*e^5 + b^4*e^6)*e^(-1)/((c*d^2 - b*d*e)*(x*e + d)))/((c*d - b*e)^2*b^2*(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + b*e/(x*e + d) - b*d*e/(x*e + d)^2)*d^2)","B",0
275,1,383,0,0.179647," ","integrate((e*x+d)^7/(c*x^2+b*x)^3,x, algorithm=""giac"")","\frac{3 \, {\left(2 \, c^{2} d^{7} - 7 \, b c d^{6} e + 7 \, b^{2} d^{5} e^{2}\right)} \log\left({\left| x \right|}\right)}{b^{5}} + \frac{c^{3} x^{2} e^{7} + 14 \, c^{3} d x e^{6} - 6 \, b c^{2} x e^{7}}{2 \, c^{6}} - \frac{3 \, {\left(2 \, c^{7} d^{7} - 7 \, b c^{6} d^{6} e + 7 \, b^{2} c^{5} d^{5} e^{2} - 7 \, b^{5} c^{2} d^{2} e^{5} + 7 \, b^{6} c d e^{6} - 2 \, b^{7} e^{7}\right)} \log\left({\left| c x + b \right|}\right)}{b^{5} c^{5}} - \frac{b^{3} c^{5} d^{7} - 2 \, {\left(6 \, c^{8} d^{7} - 21 \, b c^{7} d^{6} e + 21 \, b^{2} c^{6} d^{5} e^{2} - 35 \, b^{4} c^{4} d^{3} e^{4} + 42 \, b^{5} c^{3} d^{2} e^{5} - 21 \, b^{6} c^{2} d e^{6} + 4 \, b^{7} c e^{7}\right)} x^{3} - {\left(18 \, b c^{7} d^{7} - 63 \, b^{2} c^{6} d^{6} e + 63 \, b^{3} c^{5} d^{5} e^{2} - 35 \, b^{4} c^{4} d^{4} e^{3} - 35 \, b^{5} c^{3} d^{3} e^{4} + 63 \, b^{6} c^{2} d^{2} e^{5} - 35 \, b^{7} c d e^{6} + 7 \, b^{8} e^{7}\right)} x^{2} - 2 \, {\left(2 \, b^{2} c^{6} d^{7} - 7 \, b^{3} c^{5} d^{6} e\right)} x}{2 \, {\left(c x + b\right)}^{2} b^{4} c^{5} x^{2}}"," ",0,"3*(2*c^2*d^7 - 7*b*c*d^6*e + 7*b^2*d^5*e^2)*log(abs(x))/b^5 + 1/2*(c^3*x^2*e^7 + 14*c^3*d*x*e^6 - 6*b*c^2*x*e^7)/c^6 - 3*(2*c^7*d^7 - 7*b*c^6*d^6*e + 7*b^2*c^5*d^5*e^2 - 7*b^5*c^2*d^2*e^5 + 7*b^6*c*d*e^6 - 2*b^7*e^7)*log(abs(c*x + b))/(b^5*c^5) - 1/2*(b^3*c^5*d^7 - 2*(6*c^8*d^7 - 21*b*c^7*d^6*e + 21*b^2*c^6*d^5*e^2 - 35*b^4*c^4*d^3*e^4 + 42*b^5*c^3*d^2*e^5 - 21*b^6*c^2*d*e^6 + 4*b^7*c*e^7)*x^3 - (18*b*c^7*d^7 - 63*b^2*c^6*d^6*e + 63*b^3*c^5*d^5*e^2 - 35*b^4*c^4*d^4*e^3 - 35*b^5*c^3*d^3*e^4 + 63*b^6*c^2*d^2*e^5 - 35*b^7*c*d*e^6 + 7*b^8*e^7)*x^2 - 2*(2*b^2*c^6*d^7 - 7*b^3*c^5*d^6*e)*x)/((c*x + b)^2*b^4*c^5*x^2)","A",0
276,1,316,0,0.165469," ","integrate((e*x+d)^6/(c*x^2+b*x)^3,x, algorithm=""giac"")","\frac{x e^{6}}{c^{3}} + \frac{3 \, {\left(2 \, c^{2} d^{6} - 6 \, b c d^{5} e + 5 \, b^{2} d^{4} e^{2}\right)} \log\left({\left| x \right|}\right)}{b^{5}} - \frac{3 \, {\left(2 \, c^{6} d^{6} - 6 \, b c^{5} d^{5} e + 5 \, b^{2} c^{4} d^{4} e^{2} - 2 \, b^{5} c d e^{5} + b^{6} e^{6}\right)} \log\left({\left| c x + b \right|}\right)}{b^{5} c^{4}} - \frac{b^{3} c^{4} d^{6} - 6 \, {\left(2 \, c^{7} d^{6} - 6 \, b c^{6} d^{5} e + 5 \, b^{2} c^{5} d^{4} e^{2} - 5 \, b^{4} c^{3} d^{2} e^{4} + 4 \, b^{5} c^{2} d e^{5} - b^{6} c e^{6}\right)} x^{3} - {\left(18 \, b c^{6} d^{6} - 54 \, b^{2} c^{5} d^{5} e + 45 \, b^{3} c^{4} d^{4} e^{2} - 20 \, b^{4} c^{3} d^{3} e^{3} - 15 \, b^{5} c^{2} d^{2} e^{4} + 18 \, b^{6} c d e^{5} - 5 \, b^{7} e^{6}\right)} x^{2} - 4 \, {\left(b^{2} c^{5} d^{6} - 3 \, b^{3} c^{4} d^{5} e\right)} x}{2 \, {\left(c x + b\right)}^{2} b^{4} c^{4} x^{2}}"," ",0,"x*e^6/c^3 + 3*(2*c^2*d^6 - 6*b*c*d^5*e + 5*b^2*d^4*e^2)*log(abs(x))/b^5 - 3*(2*c^6*d^6 - 6*b*c^5*d^5*e + 5*b^2*c^4*d^4*e^2 - 2*b^5*c*d*e^5 + b^6*e^6)*log(abs(c*x + b))/(b^5*c^4) - 1/2*(b^3*c^4*d^6 - 6*(2*c^7*d^6 - 6*b*c^6*d^5*e + 5*b^2*c^5*d^4*e^2 - 5*b^4*c^3*d^2*e^4 + 4*b^5*c^2*d*e^5 - b^6*c*e^6)*x^3 - (18*b*c^6*d^6 - 54*b^2*c^5*d^5*e + 45*b^3*c^4*d^4*e^2 - 20*b^4*c^3*d^3*e^3 - 15*b^5*c^2*d^2*e^4 + 18*b^6*c*d*e^5 - 5*b^7*e^6)*x^2 - 4*(b^2*c^5*d^6 - 3*b^3*c^4*d^5*e)*x)/((c*x + b)^2*b^4*c^4*x^2)","A",0
277,1,275,0,0.195660," ","integrate((e*x+d)^5/(c*x^2+b*x)^3,x, algorithm=""giac"")","\frac{{\left(6 \, c^{2} d^{5} - 15 \, b c d^{4} e + 10 \, b^{2} d^{3} e^{2}\right)} \log\left({\left| x \right|}\right)}{b^{5}} - \frac{{\left(6 \, c^{5} d^{5} - 15 \, b c^{4} d^{4} e + 10 \, b^{2} c^{3} d^{3} e^{2} - b^{5} e^{5}\right)} \log\left({\left| c x + b \right|}\right)}{b^{5} c^{3}} - \frac{b^{3} c^{3} d^{5} - 2 \, {\left(6 \, c^{6} d^{5} - 15 \, b c^{5} d^{4} e + 10 \, b^{2} c^{4} d^{3} e^{2} - 5 \, b^{4} c^{2} d e^{4} + 2 \, b^{5} c e^{5}\right)} x^{3} - {\left(18 \, b c^{5} d^{5} - 45 \, b^{2} c^{4} d^{4} e + 30 \, b^{3} c^{3} d^{3} e^{2} - 10 \, b^{4} c^{2} d^{2} e^{3} - 5 \, b^{5} c d e^{4} + 3 \, b^{6} e^{5}\right)} x^{2} - 2 \, {\left(2 \, b^{2} c^{4} d^{5} - 5 \, b^{3} c^{3} d^{4} e\right)} x}{2 \, {\left(c x + b\right)}^{2} b^{4} c^{3} x^{2}}"," ",0,"(6*c^2*d^5 - 15*b*c*d^4*e + 10*b^2*d^3*e^2)*log(abs(x))/b^5 - (6*c^5*d^5 - 15*b*c^4*d^4*e + 10*b^2*c^3*d^3*e^2 - b^5*e^5)*log(abs(c*x + b))/(b^5*c^3) - 1/2*(b^3*c^3*d^5 - 2*(6*c^6*d^5 - 15*b*c^5*d^4*e + 10*b^2*c^4*d^3*e^2 - 5*b^4*c^2*d*e^4 + 2*b^5*c*e^5)*x^3 - (18*b*c^5*d^5 - 45*b^2*c^4*d^4*e + 30*b^3*c^3*d^3*e^2 - 10*b^4*c^2*d^2*e^3 - 5*b^5*c*d*e^4 + 3*b^6*e^5)*x^2 - 2*(2*b^2*c^4*d^5 - 5*b^3*c^3*d^4*e)*x)/((c*x + b)^2*b^4*c^3*x^2)","A",0
278,1,254,0,0.201998," ","integrate((e*x+d)^4/(c*x^2+b*x)^3,x, algorithm=""giac"")","\frac{6 \, {\left(c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2}\right)} \log\left({\left| x \right|}\right)}{b^{5}} - \frac{6 \, {\left(c^{3} d^{4} - 2 \, b c^{2} d^{3} e + b^{2} c d^{2} e^{2}\right)} \log\left({\left| c x + b \right|}\right)}{b^{5} c} + \frac{12 \, c^{5} d^{4} x^{3} - 24 \, b c^{4} d^{3} x^{3} e + 18 \, b c^{4} d^{4} x^{2} + 12 \, b^{2} c^{3} d^{2} x^{3} e^{2} - 36 \, b^{2} c^{3} d^{3} x^{2} e + 4 \, b^{2} c^{3} d^{4} x + 18 \, b^{3} c^{2} d^{2} x^{2} e^{2} - 8 \, b^{3} c^{2} d^{3} x e - b^{3} c^{2} d^{4} - 2 \, b^{4} c x^{3} e^{4} - 4 \, b^{4} c d x^{2} e^{3} - b^{5} x^{2} e^{4}}{2 \, {\left(c x^{2} + b x\right)}^{2} b^{4} c^{2}}"," ",0,"6*(c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2)*log(abs(x))/b^5 - 6*(c^3*d^4 - 2*b*c^2*d^3*e + b^2*c*d^2*e^2)*log(abs(c*x + b))/(b^5*c) + 1/2*(12*c^5*d^4*x^3 - 24*b*c^4*d^3*x^3*e + 18*b*c^4*d^4*x^2 + 12*b^2*c^3*d^2*x^3*e^2 - 36*b^2*c^3*d^3*x^2*e + 4*b^2*c^3*d^4*x + 18*b^3*c^2*d^2*x^2*e^2 - 8*b^3*c^2*d^3*x*e - b^3*c^2*d^4 - 2*b^4*c*x^3*e^4 - 4*b^4*c*d*x^2*e^3 - b^5*x^2*e^4)/((c*x^2 + b*x)^2*b^4*c^2)","A",0
279,1,219,0,0.160584," ","integrate((e*x+d)^3/(c*x^2+b*x)^3,x, algorithm=""giac"")","\frac{3 \, {\left(2 \, c^{2} d^{3} - 3 \, b c d^{2} e + b^{2} d e^{2}\right)} \log\left({\left| x \right|}\right)}{b^{5}} - \frac{3 \, {\left(2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e + b^{2} c d e^{2}\right)} \log\left({\left| c x + b \right|}\right)}{b^{5} c} + \frac{12 \, c^{4} d^{3} x^{3} - 18 \, b c^{3} d^{2} x^{3} e + 18 \, b c^{3} d^{3} x^{2} + 6 \, b^{2} c^{2} d x^{3} e^{2} - 27 \, b^{2} c^{2} d^{2} x^{2} e + 4 \, b^{2} c^{2} d^{3} x + 9 \, b^{3} c d x^{2} e^{2} - 6 \, b^{3} c d^{2} x e - b^{3} c d^{3} - b^{4} x^{2} e^{3}}{2 \, {\left(c x^{2} + b x\right)}^{2} b^{4} c}"," ",0,"3*(2*c^2*d^3 - 3*b*c*d^2*e + b^2*d*e^2)*log(abs(x))/b^5 - 3*(2*c^3*d^3 - 3*b*c^2*d^2*e + b^2*c*d*e^2)*log(abs(c*x + b))/(b^5*c) + 1/2*(12*c^4*d^3*x^3 - 18*b*c^3*d^2*x^3*e + 18*b*c^3*d^3*x^2 + 6*b^2*c^2*d*x^3*e^2 - 27*b^2*c^2*d^2*x^2*e + 4*b^2*c^2*d^3*x + 9*b^3*c*d*x^2*e^2 - 6*b^3*c*d^2*x*e - b^3*c*d^3 - b^4*x^2*e^3)/((c*x^2 + b*x)^2*b^4*c)","A",0
280,1,182,0,0.177340," ","integrate((e*x+d)^2/(c*x^2+b*x)^3,x, algorithm=""giac"")","\frac{{\left(6 \, c^{2} d^{2} - 6 \, b c d e + b^{2} e^{2}\right)} \log\left({\left| x \right|}\right)}{b^{5}} - \frac{{\left(6 \, c^{3} d^{2} - 6 \, b c^{2} d e + b^{2} c e^{2}\right)} \log\left({\left| c x + b \right|}\right)}{b^{5} c} + \frac{12 \, c^{3} d^{2} x^{3} - 12 \, b c^{2} d x^{3} e + 18 \, b c^{2} d^{2} x^{2} + 2 \, b^{2} c x^{3} e^{2} - 18 \, b^{2} c d x^{2} e + 4 \, b^{2} c d^{2} x + 3 \, b^{3} x^{2} e^{2} - 4 \, b^{3} d x e - b^{3} d^{2}}{2 \, {\left(c x^{2} + b x\right)}^{2} b^{4}}"," ",0,"(6*c^2*d^2 - 6*b*c*d*e + b^2*e^2)*log(abs(x))/b^5 - (6*c^3*d^2 - 6*b*c^2*d*e + b^2*c*e^2)*log(abs(c*x + b))/(b^5*c) + 1/2*(12*c^3*d^2*x^3 - 12*b*c^2*d*x^3*e + 18*b*c^2*d^2*x^2 + 2*b^2*c*x^3*e^2 - 18*b^2*c*d*x^2*e + 4*b^2*c*d^2*x + 3*b^3*x^2*e^2 - 4*b^3*d*x*e - b^3*d^2)/((c*x^2 + b*x)^2*b^4)","A",0
281,1,132,0,0.180358," ","integrate((e*x+d)/(c*x^2+b*x)^3,x, algorithm=""giac"")","\frac{3 \, {\left(2 \, c^{2} d - b c e\right)} \log\left({\left| x \right|}\right)}{b^{5}} - \frac{3 \, {\left(2 \, c^{3} d - b c^{2} e\right)} \log\left({\left| c x + b \right|}\right)}{b^{5} c} + \frac{12 \, c^{3} d x^{3} - 6 \, b c^{2} x^{3} e + 18 \, b c^{2} d x^{2} - 9 \, b^{2} c x^{2} e + 4 \, b^{2} c d x - 2 \, b^{3} x e - b^{3} d}{2 \, {\left(c x^{2} + b x\right)}^{2} b^{4}}"," ",0,"3*(2*c^2*d - b*c*e)*log(abs(x))/b^5 - 3*(2*c^3*d - b*c^2*e)*log(abs(c*x + b))/(b^5*c) + 1/2*(12*c^3*d*x^3 - 6*b*c^2*x^3*e + 18*b*c^2*d*x^2 - 9*b^2*c*x^2*e + 4*b^2*c*d*x - 2*b^3*x*e - b^3*d)/((c*x^2 + b*x)^2*b^4)","A",0
282,1,73,0,0.153361," ","integrate(1/(c*x^2+b*x)^3,x, algorithm=""giac"")","-\frac{6 \, c^{2} \log\left({\left| c x + b \right|}\right)}{b^{5}} + \frac{6 \, c^{2} \log\left({\left| x \right|}\right)}{b^{5}} + \frac{12 \, c^{3} x^{3} + 18 \, b c^{2} x^{2} + 4 \, b^{2} c x - b^{3}}{2 \, {\left(c x^{2} + b x\right)}^{2} b^{4}}"," ",0,"-6*c^2*log(abs(c*x + b))/b^5 + 6*c^2*log(abs(x))/b^5 + 1/2*(12*c^3*x^3 + 18*b*c^2*x^2 + 4*b^2*c*x - b^3)/((c*x^2 + b*x)^2*b^4)","A",0
283,1,414,0,0.176141," ","integrate(1/(e*x+d)/(c*x^2+b*x)^3,x, algorithm=""giac"")","-\frac{{\left(6 \, c^{6} d^{2} - 15 \, b c^{5} d e + 10 \, b^{2} c^{4} e^{2}\right)} \log\left({\left| c x + b \right|}\right)}{b^{5} c^{4} d^{3} - 3 \, b^{6} c^{3} d^{2} e + 3 \, b^{7} c^{2} d e^{2} - b^{8} c e^{3}} + \frac{e^{6} \log\left({\left| x e + d \right|}\right)}{c^{3} d^{6} e - 3 \, b c^{2} d^{5} e^{2} + 3 \, b^{2} c d^{4} e^{3} - b^{3} d^{3} e^{4}} + \frac{{\left(6 \, c^{2} d^{2} + 3 \, b c d e + b^{2} e^{2}\right)} \log\left({\left| x \right|}\right)}{b^{5} d^{3}} - \frac{b^{3} c^{3} d^{5} - 3 \, b^{4} c^{2} d^{4} e + 3 \, b^{5} c d^{3} e^{2} - b^{6} d^{2} e^{3} - 2 \, {\left(6 \, c^{6} d^{5} - 15 \, b c^{5} d^{4} e + 10 \, b^{2} c^{4} d^{3} e^{2} - b^{4} c^{2} d e^{4}\right)} x^{3} - {\left(18 \, b c^{5} d^{5} - 45 \, b^{2} c^{4} d^{4} e + 30 \, b^{3} c^{3} d^{3} e^{2} + b^{4} c^{2} d^{2} e^{3} - 4 \, b^{5} c d e^{4}\right)} x^{2} - 2 \, {\left(2 \, b^{2} c^{4} d^{5} - 5 \, b^{3} c^{3} d^{4} e + 3 \, b^{4} c^{2} d^{3} e^{2} + b^{5} c d^{2} e^{3} - b^{6} d e^{4}\right)} x}{2 \, {\left(c d - b e\right)}^{3} {\left(c x + b\right)}^{2} b^{4} d^{3} x^{2}}"," ",0,"-(6*c^6*d^2 - 15*b*c^5*d*e + 10*b^2*c^4*e^2)*log(abs(c*x + b))/(b^5*c^4*d^3 - 3*b^6*c^3*d^2*e + 3*b^7*c^2*d*e^2 - b^8*c*e^3) + e^6*log(abs(x*e + d))/(c^3*d^6*e - 3*b*c^2*d^5*e^2 + 3*b^2*c*d^4*e^3 - b^3*d^3*e^4) + (6*c^2*d^2 + 3*b*c*d*e + b^2*e^2)*log(abs(x))/(b^5*d^3) - 1/2*(b^3*c^3*d^5 - 3*b^4*c^2*d^4*e + 3*b^5*c*d^3*e^2 - b^6*d^2*e^3 - 2*(6*c^6*d^5 - 15*b*c^5*d^4*e + 10*b^2*c^4*d^3*e^2 - b^4*c^2*d*e^4)*x^3 - (18*b*c^5*d^5 - 45*b^2*c^4*d^4*e + 30*b^3*c^3*d^3*e^2 + b^4*c^2*d^2*e^3 - 4*b^5*c*d*e^4)*x^2 - 2*(2*b^2*c^4*d^5 - 5*b^3*c^3*d^4*e + 3*b^4*c^2*d^3*e^2 + b^5*c*d^2*e^3 - b^6*d*e^4)*x)/((c*d - b*e)^3*(c*x + b)^2*b^4*d^3*x^2)","B",0
284,1,839,0,0.278311," ","integrate(1/(e*x+d)^2/(c*x^2+b*x)^3,x, algorithm=""giac"")","-\frac{3 \, {\left(4 \, c^{6} d^{6} e^{2} - 12 \, b c^{5} d^{5} e^{3} + 10 \, b^{2} c^{4} d^{4} e^{4} - 2 \, b^{5} c d e^{7} + b^{6} e^{8}\right)} e^{\left(-2\right)} \log\left(\frac{{\left| -2 \, c d e + \frac{2 \, c d^{2} e}{x e + d} + b e^{2} - \frac{2 \, b d e^{2}}{x e + d} - {\left| b \right|} e^{2} \right|}}{{\left| -2 \, c d e + \frac{2 \, c d^{2} e}{x e + d} + b e^{2} - \frac{2 \, b d e^{2}}{x e + d} + {\left| b \right|} e^{2} \right|}}\right)}{2 \, {\left(b^{4} c^{4} d^{8} - 4 \, b^{5} c^{3} d^{7} e + 6 \, b^{6} c^{2} d^{6} e^{2} - 4 \, b^{7} c d^{5} e^{3} + b^{8} d^{4} e^{4}\right)} {\left| b \right|}} - \frac{3 \, {\left(2 \, c d e^{5} - b e^{6}\right)} \log\left({\left| -c + \frac{2 \, c d}{x e + d} - \frac{c d^{2}}{{\left(x e + d\right)}^{2}} - \frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} \right|}\right)}{2 \, {\left(c^{4} d^{8} - 4 \, b c^{3} d^{7} e + 6 \, b^{2} c^{2} d^{6} e^{2} - 4 \, b^{3} c d^{5} e^{3} + b^{4} d^{4} e^{4}\right)}} - \frac{e^{11}}{{\left(c^{3} d^{6} e^{6} - 3 \, b c^{2} d^{5} e^{7} + 3 \, b^{2} c d^{4} e^{8} - b^{3} d^{3} e^{9}\right)} {\left(x e + d\right)}} + \frac{12 \, c^{7} d^{5} e - 30 \, b c^{6} d^{4} e^{2} + 16 \, b^{2} c^{5} d^{3} e^{3} + 6 \, b^{3} c^{4} d^{2} e^{4} - 14 \, b^{4} c^{3} d e^{5} + 5 \, b^{5} c^{2} e^{6} - \frac{2 \, {\left(18 \, c^{7} d^{6} e^{2} - 54 \, b c^{6} d^{5} e^{3} + 47 \, b^{2} c^{5} d^{4} e^{4} - 4 \, b^{3} c^{4} d^{3} e^{5} - 29 \, b^{4} c^{3} d^{2} e^{6} + 22 \, b^{5} c^{2} d e^{7} - 5 \, b^{6} c e^{8}\right)} e^{\left(-1\right)}}{x e + d} + \frac{{\left(36 \, c^{7} d^{7} e^{3} - 126 \, b c^{6} d^{6} e^{4} + 144 \, b^{2} c^{5} d^{5} e^{5} - 45 \, b^{3} c^{4} d^{4} e^{6} - 70 \, b^{4} c^{3} d^{3} e^{7} + 87 \, b^{5} c^{2} d^{2} e^{8} - 36 \, b^{6} c d e^{9} + 5 \, b^{7} e^{10}\right)} e^{\left(-2\right)}}{{\left(x e + d\right)}^{2}} - \frac{6 \, {\left(2 \, c^{7} d^{8} e^{4} - 8 \, b c^{6} d^{7} e^{5} + 11 \, b^{2} c^{5} d^{6} e^{6} - 5 \, b^{3} c^{4} d^{5} e^{7} - 5 \, b^{4} c^{3} d^{4} e^{8} + 9 \, b^{5} c^{2} d^{3} e^{9} - 5 \, b^{6} c d^{2} e^{10} + b^{7} d e^{11}\right)} e^{\left(-3\right)}}{{\left(x e + d\right)}^{3}}}{2 \, {\left(c d - b e\right)}^{4} b^{4} {\left(c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{b e}{x e + d} - \frac{b d e}{{\left(x e + d\right)}^{2}}\right)}^{2} d^{4}}"," ",0,"-3/2*(4*c^6*d^6*e^2 - 12*b*c^5*d^5*e^3 + 10*b^2*c^4*d^4*e^4 - 2*b^5*c*d*e^7 + b^6*e^8)*e^(-2)*log(abs(-2*c*d*e + 2*c*d^2*e/(x*e + d) + b*e^2 - 2*b*d*e^2/(x*e + d) - abs(b)*e^2)/abs(-2*c*d*e + 2*c*d^2*e/(x*e + d) + b*e^2 - 2*b*d*e^2/(x*e + d) + abs(b)*e^2))/((b^4*c^4*d^8 - 4*b^5*c^3*d^7*e + 6*b^6*c^2*d^6*e^2 - 4*b^7*c*d^5*e^3 + b^8*d^4*e^4)*abs(b)) - 3/2*(2*c*d*e^5 - b*e^6)*log(abs(-c + 2*c*d/(x*e + d) - c*d^2/(x*e + d)^2 - b*e/(x*e + d) + b*d*e/(x*e + d)^2))/(c^4*d^8 - 4*b*c^3*d^7*e + 6*b^2*c^2*d^6*e^2 - 4*b^3*c*d^5*e^3 + b^4*d^4*e^4) - e^11/((c^3*d^6*e^6 - 3*b*c^2*d^5*e^7 + 3*b^2*c*d^4*e^8 - b^3*d^3*e^9)*(x*e + d)) + 1/2*(12*c^7*d^5*e - 30*b*c^6*d^4*e^2 + 16*b^2*c^5*d^3*e^3 + 6*b^3*c^4*d^2*e^4 - 14*b^4*c^3*d*e^5 + 5*b^5*c^2*e^6 - 2*(18*c^7*d^6*e^2 - 54*b*c^6*d^5*e^3 + 47*b^2*c^5*d^4*e^4 - 4*b^3*c^4*d^3*e^5 - 29*b^4*c^3*d^2*e^6 + 22*b^5*c^2*d*e^7 - 5*b^6*c*e^8)*e^(-1)/(x*e + d) + (36*c^7*d^7*e^3 - 126*b*c^6*d^6*e^4 + 144*b^2*c^5*d^5*e^5 - 45*b^3*c^4*d^4*e^6 - 70*b^4*c^3*d^3*e^7 + 87*b^5*c^2*d^2*e^8 - 36*b^6*c*d*e^9 + 5*b^7*e^10)*e^(-2)/(x*e + d)^2 - 6*(2*c^7*d^8*e^4 - 8*b*c^6*d^7*e^5 + 11*b^2*c^5*d^6*e^6 - 5*b^3*c^4*d^5*e^7 - 5*b^4*c^3*d^4*e^8 + 9*b^5*c^2*d^3*e^9 - 5*b^6*c*d^2*e^10 + b^7*d*e^11)*e^(-3)/(x*e + d)^3)/((c*d - b*e)^4*b^4*(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + b*e/(x*e + d) - b*d*e/(x*e + d)^2)^2*d^4)","B",0
285,1,250,0,0.212855," ","integrate((e*x+d)^3*(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\frac{1}{1920} \, \sqrt{c x^{2} + b x} {\left(2 \, {\left(4 \, {\left(6 \, {\left(8 \, x e^{3} + \frac{30 \, c^{4} d e^{2} + b c^{3} e^{3}}{c^{4}}\right)} x + \frac{240 \, c^{4} d^{2} e + 30 \, b c^{3} d e^{2} - 7 \, b^{2} c^{2} e^{3}}{c^{4}}\right)} x + \frac{5 \, {\left(96 \, c^{4} d^{3} + 48 \, b c^{3} d^{2} e - 30 \, b^{2} c^{2} d e^{2} + 7 \, b^{3} c e^{3}\right)}}{c^{4}}\right)} x + \frac{15 \, {\left(32 \, b c^{3} d^{3} - 48 \, b^{2} c^{2} d^{2} e + 30 \, b^{3} c d e^{2} - 7 \, b^{4} e^{3}\right)}}{c^{4}}\right)} + \frac{{\left(32 \, b^{2} c^{3} d^{3} - 48 \, b^{3} c^{2} d^{2} e + 30 \, b^{4} c d e^{2} - 7 \, b^{5} e^{3}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{256 \, c^{\frac{9}{2}}}"," ",0,"1/1920*sqrt(c*x^2 + b*x)*(2*(4*(6*(8*x*e^3 + (30*c^4*d*e^2 + b*c^3*e^3)/c^4)*x + (240*c^4*d^2*e + 30*b*c^3*d*e^2 - 7*b^2*c^2*e^3)/c^4)*x + 5*(96*c^4*d^3 + 48*b*c^3*d^2*e - 30*b^2*c^2*d*e^2 + 7*b^3*c*e^3)/c^4)*x + 15*(32*b*c^3*d^3 - 48*b^2*c^2*d^2*e + 30*b^3*c*d*e^2 - 7*b^4*e^3)/c^4) + 1/256*(32*b^2*c^3*d^3 - 48*b^3*c^2*d^2*e + 30*b^4*c*d*e^2 - 7*b^5*e^3)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(9/2)","A",0
286,1,172,0,0.241957," ","integrate((e*x+d)^2*(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\frac{1}{192} \, \sqrt{c x^{2} + b x} {\left(2 \, {\left(4 \, {\left(6 \, x e^{2} + \frac{16 \, c^{3} d e + b c^{2} e^{2}}{c^{3}}\right)} x + \frac{48 \, c^{3} d^{2} + 16 \, b c^{2} d e - 5 \, b^{2} c e^{2}}{c^{3}}\right)} x + \frac{3 \, {\left(16 \, b c^{2} d^{2} - 16 \, b^{2} c d e + 5 \, b^{3} e^{2}\right)}}{c^{3}}\right)} + \frac{{\left(16 \, b^{2} c^{2} d^{2} - 16 \, b^{3} c d e + 5 \, b^{4} e^{2}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{128 \, c^{\frac{7}{2}}}"," ",0,"1/192*sqrt(c*x^2 + b*x)*(2*(4*(6*x*e^2 + (16*c^3*d*e + b*c^2*e^2)/c^3)*x + (48*c^3*d^2 + 16*b*c^2*d*e - 5*b^2*c*e^2)/c^3)*x + 3*(16*b*c^2*d^2 - 16*b^2*c*d*e + 5*b^3*e^2)/c^3) + 1/128*(16*b^2*c^2*d^2 - 16*b^3*c*d*e + 5*b^4*e^2)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(7/2)","A",0
287,1,108,0,0.211579," ","integrate((e*x+d)*(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\frac{1}{24} \, \sqrt{c x^{2} + b x} {\left(2 \, {\left(4 \, x e + \frac{6 \, c^{2} d + b c e}{c^{2}}\right)} x + \frac{3 \, {\left(2 \, b c d - b^{2} e\right)}}{c^{2}}\right)} + \frac{{\left(2 \, b^{2} c d - b^{3} e\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{16 \, c^{\frac{5}{2}}}"," ",0,"1/24*sqrt(c*x^2 + b*x)*(2*(4*x*e + (6*c^2*d + b*c*e)/c^2)*x + 3*(2*b*c*d - b^2*e)/c^2) + 1/16*(2*b^2*c*d - b^3*e)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(5/2)","A",0
288,1,61,0,0.169977," ","integrate((c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{c x^{2} + b x} {\left(2 \, x + \frac{b}{c}\right)} + \frac{b^{2} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{8 \, c^{\frac{3}{2}}}"," ",0,"1/4*sqrt(c*x^2 + b*x)*(2*x + b/c) + 1/8*b^2*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(3/2)","A",0
289,-2,0,0,0.000000," ","integrate((c*x^2+b*x)^(1/2)/(e*x+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error: Bad Argument Type","F(-2)",0
290,-2,0,0,0.000000," ","integrate((c*x^2+b*x)^(1/2)/(e*x+d)^2,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]Evaluation time: 0.53Error: Bad Argument Type","F(-2)",0
291,1,409,0,0.274889," ","integrate((c*x^2+b*x)^(1/2)/(e*x+d)^3,x, algorithm=""giac"")","-\frac{b^{2} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} + b d e}}\right)}{4 \, {\left(c d^{2} - b d e\right)} \sqrt{-c d^{2} + b d e}} + \frac{8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} c^{2} d^{2} e + 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} c^{\frac{5}{2}} d^{3} + 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} b c^{2} d^{3} - 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} b c d e^{2} - 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} b^{2} c d^{2} e + 2 \, b^{2} c^{\frac{3}{2}} d^{3} - 5 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} b^{2} \sqrt{c} d e^{2} - b^{3} \sqrt{c} d^{2} e + {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} b^{2} e^{3} - {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} b^{3} d e^{2}}{4 \, {\left(c d^{2} e^{2} - b d e^{3}\right)} {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} e + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} d + b d\right)}^{2}}"," ",0,"-1/4*b^2*arctan(-((sqrt(c)*x - sqrt(c*x^2 + b*x))*e + sqrt(c)*d)/sqrt(-c*d^2 + b*d*e))/((c*d^2 - b*d*e)*sqrt(-c*d^2 + b*d*e)) + 1/4*(8*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*c^2*d^2*e + 8*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*c^(5/2)*d^3 + 8*(sqrt(c)*x - sqrt(c*x^2 + b*x))*b*c^2*d^3 - 8*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*b*c*d*e^2 - 4*(sqrt(c)*x - sqrt(c*x^2 + b*x))*b^2*c*d^2*e + 2*b^2*c^(3/2)*d^3 - 5*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*b^2*sqrt(c)*d*e^2 - b^3*sqrt(c)*d^2*e + (sqrt(c)*x - sqrt(c*x^2 + b*x))^3*b^2*e^3 - (sqrt(c)*x - sqrt(c*x^2 + b*x))*b^3*d*e^2)/((c*d^2*e^2 - b*d*e^3)*((sqrt(c)*x - sqrt(c*x^2 + b*x))^2*e + 2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c)*d + b*d)^2)","B",0
292,1,825,0,0.274037," ","integrate((c*x^2+b*x)^(1/2)/(e*x+d)^4,x, algorithm=""giac"")","\frac{{\left(2 \, b^{2} c d - b^{3} e\right)} \arctan\left(\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} + b d e}}\right)}{8 \, {\left(c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2}\right)} \sqrt{-c d^{2} + b d e}} + \frac{48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} c^{\frac{7}{2}} d^{4} e + 32 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} c^{4} d^{5} + 16 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} b c^{3} d^{4} e + 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} b c^{\frac{7}{2}} d^{5} - 96 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} b c^{\frac{5}{2}} d^{3} e^{2} - 36 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} b^{2} c^{\frac{5}{2}} d^{4} e + 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} b^{2} c^{3} d^{5} - 84 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} b^{2} c^{2} d^{3} e^{2} - 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} b^{3} c^{2} d^{4} e + 4 \, b^{3} c^{\frac{5}{2}} d^{5} + 78 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} b^{2} c^{\frac{3}{2}} d^{2} e^{3} - 6 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} b^{3} c^{\frac{3}{2}} d^{3} e^{2} - 4 \, b^{4} c^{\frac{3}{2}} d^{4} e + 6 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} b^{2} c d e^{4} + 74 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} b^{3} c d^{2} e^{3} + 12 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} b^{4} c d^{3} e^{2} - 15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} b^{3} \sqrt{c} d e^{4} + 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} b^{4} \sqrt{c} d^{2} e^{3} + 3 \, b^{5} \sqrt{c} d^{3} e^{2} - 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} b^{3} e^{5} - 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} b^{4} d e^{4} + 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} b^{5} d^{2} e^{3}}{24 \, {\left(c^{2} d^{4} e^{2} - 2 \, b c d^{3} e^{3} + b^{2} d^{2} e^{4}\right)} {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} e + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} d + b d\right)}^{3}}"," ",0,"1/8*(2*b^2*c*d - b^3*e)*arctan(((sqrt(c)*x - sqrt(c*x^2 + b*x))*e + sqrt(c)*d)/sqrt(-c*d^2 + b*d*e))/((c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2)*sqrt(-c*d^2 + b*d*e)) + 1/24*(48*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*c^(7/2)*d^4*e + 32*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*c^4*d^5 + 16*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*b*c^3*d^4*e + 48*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*b*c^(7/2)*d^5 - 96*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*b*c^(5/2)*d^3*e^2 - 36*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*b^2*c^(5/2)*d^4*e + 24*(sqrt(c)*x - sqrt(c*x^2 + b*x))*b^2*c^3*d^5 - 84*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*b^2*c^2*d^3*e^2 - 24*(sqrt(c)*x - sqrt(c*x^2 + b*x))*b^3*c^2*d^4*e + 4*b^3*c^(5/2)*d^5 + 78*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*b^2*c^(3/2)*d^2*e^3 - 6*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*b^3*c^(3/2)*d^3*e^2 - 4*b^4*c^(3/2)*d^4*e + 6*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*b^2*c*d*e^4 + 74*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*b^3*c*d^2*e^3 + 12*(sqrt(c)*x - sqrt(c*x^2 + b*x))*b^4*c*d^3*e^2 - 15*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*b^3*sqrt(c)*d*e^4 + 24*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*b^4*sqrt(c)*d^2*e^3 + 3*b^5*sqrt(c)*d^3*e^2 - 3*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*b^3*e^5 - 8*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*b^4*d*e^4 + 3*(sqrt(c)*x - sqrt(c*x^2 + b*x))*b^5*d^2*e^3)/((c^2*d^4*e^2 - 2*b*c*d^3*e^3 + b^2*d^2*e^4)*((sqrt(c)*x - sqrt(c*x^2 + b*x))^2*e + 2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c)*d + b*d)^3)","B",0
293,1,1144,0,1.089650," ","integrate((c*x^2+b*x)^(1/2)/(e*x+d)^5,x, algorithm=""giac"")","\frac{1}{384} \, {\left(2 \, \sqrt{c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{b e}{x e + d} - \frac{b d e}{{\left(x e + d\right)}^{2}}} {\left(\frac{2 \, {\left(\frac{4 \, {\left(\frac{2 \, c^{3} d^{5} e^{6} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 5 \, b c^{2} d^{4} e^{7} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 4 \, b^{2} c d^{3} e^{8} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - b^{3} d^{2} e^{9} \mathrm{sgn}\left(\frac{1}{x e + d}\right)}{c^{3} d^{6} e^{8} - 3 \, b c^{2} d^{5} e^{9} + 3 \, b^{2} c d^{4} e^{10} - b^{3} d^{3} e^{11}} - \frac{6 \, {\left(c^{3} d^{6} e^{7} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 3 \, b c^{2} d^{5} e^{8} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 3 \, b^{2} c d^{4} e^{9} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - b^{3} d^{3} e^{10} \mathrm{sgn}\left(\frac{1}{x e + d}\right)\right)} e^{\left(-1\right)}}{{\left(c^{3} d^{6} e^{8} - 3 \, b c^{2} d^{5} e^{9} + 3 \, b^{2} c d^{4} e^{10} - b^{3} d^{3} e^{11}\right)} {\left(x e + d\right)}}\right)} e^{\left(-1\right)}}{x e + d} + \frac{8 \, c^{3} d^{4} e^{5} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 16 \, b c^{2} d^{3} e^{6} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 13 \, b^{2} c d^{2} e^{7} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 5 \, b^{3} d e^{8} \mathrm{sgn}\left(\frac{1}{x e + d}\right)}{c^{3} d^{6} e^{8} - 3 \, b c^{2} d^{5} e^{9} + 3 \, b^{2} c d^{4} e^{10} - b^{3} d^{3} e^{11}}\right)} e^{\left(-1\right)}}{x e + d} + \frac{16 \, c^{3} d^{3} e^{4} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 24 \, b c^{2} d^{2} e^{5} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 38 \, b^{2} c d e^{6} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 15 \, b^{3} e^{7} \mathrm{sgn}\left(\frac{1}{x e + d}\right)}{c^{3} d^{6} e^{8} - 3 \, b c^{2} d^{5} e^{9} + 3 \, b^{2} c d^{4} e^{10} - b^{3} d^{3} e^{11}}\right)} - \frac{{\left(48 \, b^{2} c^{2} d^{2} e^{2} \log\left({\left| 2 \, c d - b e - 2 \, \sqrt{c d^{2} - b d e} \sqrt{c} \right|}\right) + 32 \, \sqrt{c d^{2} - b d e} c^{\frac{7}{2}} d^{3} - 48 \, \sqrt{c d^{2} - b d e} b c^{\frac{5}{2}} d^{2} e - 48 \, b^{3} c d e^{3} \log\left({\left| 2 \, c d - b e - 2 \, \sqrt{c d^{2} - b d e} \sqrt{c} \right|}\right) + 76 \, \sqrt{c d^{2} - b d e} b^{2} c^{\frac{3}{2}} d e^{2} + 15 \, b^{4} e^{4} \log\left({\left| 2 \, c d - b e - 2 \, \sqrt{c d^{2} - b d e} \sqrt{c} \right|}\right) - 30 \, \sqrt{c d^{2} - b d e} b^{3} \sqrt{c} e^{3}\right)} \mathrm{sgn}\left(\frac{1}{x e + d}\right)}{\sqrt{c d^{2} - b d e} c^{3} d^{6} e^{4} - 3 \, \sqrt{c d^{2} - b d e} b c^{2} d^{5} e^{5} + 3 \, \sqrt{c d^{2} - b d e} b^{2} c d^{4} e^{6} - \sqrt{c d^{2} - b d e} b^{3} d^{3} e^{7}} + \frac{3 \, {\left(16 \, b^{2} c^{2} d^{2} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 16 \, b^{3} c d e \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 5 \, b^{4} e^{2} \mathrm{sgn}\left(\frac{1}{x e + d}\right)\right)} \log\left({\left| 2 \, c d - b e - 2 \, \sqrt{c d^{2} - b d e} {\left(\sqrt{c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{b e}{x e + d} - \frac{b d e}{{\left(x e + d\right)}^{2}}} + \frac{\sqrt{c d^{2} e^{2} - b d e^{3}} e^{\left(-1\right)}}{x e + d}\right)} \right|}\right)}{{\left(c^{3} d^{6} e^{2} - 3 \, b c^{2} d^{5} e^{3} + 3 \, b^{2} c d^{4} e^{4} - b^{3} d^{3} e^{5}\right)} \sqrt{c d^{2} - b d e}}\right)} e^{2}"," ",0,"1/384*(2*sqrt(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + b*e/(x*e + d) - b*d*e/(x*e + d)^2)*(2*(4*((2*c^3*d^5*e^6*sgn(1/(x*e + d)) - 5*b*c^2*d^4*e^7*sgn(1/(x*e + d)) + 4*b^2*c*d^3*e^8*sgn(1/(x*e + d)) - b^3*d^2*e^9*sgn(1/(x*e + d)))/(c^3*d^6*e^8 - 3*b*c^2*d^5*e^9 + 3*b^2*c*d^4*e^10 - b^3*d^3*e^11) - 6*(c^3*d^6*e^7*sgn(1/(x*e + d)) - 3*b*c^2*d^5*e^8*sgn(1/(x*e + d)) + 3*b^2*c*d^4*e^9*sgn(1/(x*e + d)) - b^3*d^3*e^10*sgn(1/(x*e + d)))*e^(-1)/((c^3*d^6*e^8 - 3*b*c^2*d^5*e^9 + 3*b^2*c*d^4*e^10 - b^3*d^3*e^11)*(x*e + d)))*e^(-1)/(x*e + d) + (8*c^3*d^4*e^5*sgn(1/(x*e + d)) - 16*b*c^2*d^3*e^6*sgn(1/(x*e + d)) + 13*b^2*c*d^2*e^7*sgn(1/(x*e + d)) - 5*b^3*d*e^8*sgn(1/(x*e + d)))/(c^3*d^6*e^8 - 3*b*c^2*d^5*e^9 + 3*b^2*c*d^4*e^10 - b^3*d^3*e^11))*e^(-1)/(x*e + d) + (16*c^3*d^3*e^4*sgn(1/(x*e + d)) - 24*b*c^2*d^2*e^5*sgn(1/(x*e + d)) + 38*b^2*c*d*e^6*sgn(1/(x*e + d)) - 15*b^3*e^7*sgn(1/(x*e + d)))/(c^3*d^6*e^8 - 3*b*c^2*d^5*e^9 + 3*b^2*c*d^4*e^10 - b^3*d^3*e^11)) - (48*b^2*c^2*d^2*e^2*log(abs(2*c*d - b*e - 2*sqrt(c*d^2 - b*d*e)*sqrt(c))) + 32*sqrt(c*d^2 - b*d*e)*c^(7/2)*d^3 - 48*sqrt(c*d^2 - b*d*e)*b*c^(5/2)*d^2*e - 48*b^3*c*d*e^3*log(abs(2*c*d - b*e - 2*sqrt(c*d^2 - b*d*e)*sqrt(c))) + 76*sqrt(c*d^2 - b*d*e)*b^2*c^(3/2)*d*e^2 + 15*b^4*e^4*log(abs(2*c*d - b*e - 2*sqrt(c*d^2 - b*d*e)*sqrt(c))) - 30*sqrt(c*d^2 - b*d*e)*b^3*sqrt(c)*e^3)*sgn(1/(x*e + d))/(sqrt(c*d^2 - b*d*e)*c^3*d^6*e^4 - 3*sqrt(c*d^2 - b*d*e)*b*c^2*d^5*e^5 + 3*sqrt(c*d^2 - b*d*e)*b^2*c*d^4*e^6 - sqrt(c*d^2 - b*d*e)*b^3*d^3*e^7) + 3*(16*b^2*c^2*d^2*sgn(1/(x*e + d)) - 16*b^3*c*d*e*sgn(1/(x*e + d)) + 5*b^4*e^2*sgn(1/(x*e + d)))*log(abs(2*c*d - b*e - 2*sqrt(c*d^2 - b*d*e)*(sqrt(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + b*e/(x*e + d) - b*d*e/(x*e + d)^2) + sqrt(c*d^2*e^2 - b*d*e^3)*e^(-1)/(x*e + d))))/((c^3*d^6*e^2 - 3*b*c^2*d^5*e^3 + 3*b^2*c*d^4*e^4 - b^3*d^3*e^5)*sqrt(c*d^2 - b*d*e)))*e^2","B",0
294,1,2101,0,0.437119," ","integrate((c*x^2+b*x)^(1/2)/(e*x+d)^6,x, algorithm=""giac"")","\frac{{\left(32 \, b^{2} c^{3} d^{3} - 48 \, b^{3} c^{2} d^{2} e + 30 \, b^{4} c d e^{2} - 7 \, b^{5} e^{3}\right)} \arctan\left(\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} + b d e}}\right)}{128 \, {\left(c^{4} d^{8} - 4 \, b c^{3} d^{7} e + 6 \, b^{2} c^{2} d^{6} e^{2} - 4 \, b^{3} c d^{5} e^{3} + b^{4} d^{4} e^{4}\right)} \sqrt{-c d^{2} + b d e}} + \frac{7680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} c^{\frac{13}{2}} d^{8} e + 3072 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} c^{7} d^{9} + 9216 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} b c^{6} d^{8} e + 7680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} b c^{\frac{13}{2}} d^{9} - 30720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} b c^{\frac{11}{2}} d^{7} e^{2} - 3840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} b^{2} c^{\frac{11}{2}} d^{8} e + 7680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} b^{2} c^{6} d^{9} - 50048 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} b^{2} c^{5} d^{7} e^{2} - 11520 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} b^{3} c^{5} d^{8} e + 3840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} b^{3} c^{\frac{11}{2}} d^{9} + 70720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} b^{2} c^{\frac{9}{2}} d^{6} e^{3} - 17600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} b^{3} c^{\frac{9}{2}} d^{7} e^{2} - 7200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} b^{4} c^{\frac{9}{2}} d^{8} e + 960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} b^{4} c^{5} d^{9} + 15040 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} b^{2} c^{4} d^{5} e^{4} + 129280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} b^{3} c^{4} d^{6} e^{3} + 14080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} b^{4} c^{4} d^{7} e^{2} - 1920 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} b^{5} c^{4} d^{8} e + 96 \, b^{5} c^{\frac{9}{2}} d^{9} + 4320 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} b^{2} c^{\frac{7}{2}} d^{4} e^{5} - 52000 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} b^{3} c^{\frac{7}{2}} d^{5} e^{4} + 81920 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} b^{4} c^{\frac{7}{2}} d^{6} e^{3} + 13760 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} b^{5} c^{\frac{7}{2}} d^{7} e^{2} - 192 \, b^{6} c^{\frac{7}{2}} d^{8} e + 480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} b^{2} c^{3} d^{3} e^{6} - 20320 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} b^{3} c^{3} d^{4} e^{5} - 120680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} b^{4} c^{3} d^{5} e^{4} + 14080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} b^{5} c^{3} d^{6} e^{3} + 4280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} b^{6} c^{3} d^{7} e^{2} - 6480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} b^{3} c^{\frac{5}{2}} d^{3} e^{6} + 7260 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} b^{4} c^{\frac{5}{2}} d^{4} e^{5} - 85780 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} b^{5} c^{\frac{5}{2}} d^{5} e^{4} - 6340 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} b^{6} c^{\frac{5}{2}} d^{6} e^{3} + 476 \, b^{7} c^{\frac{5}{2}} d^{7} e^{2} - 720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} b^{3} c^{2} d^{2} e^{7} + 10740 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} b^{4} c^{2} d^{3} e^{6} + 47944 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} b^{5} c^{2} d^{4} e^{5} - 25220 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} b^{6} c^{2} d^{5} e^{4} - 3080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} b^{7} c^{2} d^{6} e^{3} + 4050 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} b^{4} c^{\frac{3}{2}} d^{2} e^{7} + 9310 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} b^{5} c^{\frac{3}{2}} d^{3} e^{6} + 35330 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} b^{6} c^{\frac{3}{2}} d^{4} e^{5} - 1750 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} b^{7} c^{\frac{3}{2}} d^{5} e^{4} - 380 \, b^{8} c^{\frac{3}{2}} d^{6} e^{3} + 450 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} b^{4} c d e^{8} - 1190 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} b^{5} c d^{2} e^{7} - 4658 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} b^{6} c d^{3} e^{6} + 10510 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} b^{7} c d^{4} e^{5} + 600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} b^{8} c d^{5} e^{4} - 945 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{8} b^{5} \sqrt{c} d e^{8} - 3430 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{6} b^{6} \sqrt{c} d^{2} e^{7} - 4480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{4} b^{7} \sqrt{c} d^{3} e^{6} + 1470 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} b^{8} \sqrt{c} d^{4} e^{5} + 105 \, b^{9} \sqrt{c} d^{5} e^{4} - 105 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{9} b^{5} e^{9} - 490 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{7} b^{6} d e^{8} - 896 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{5} b^{7} d^{2} e^{7} - 790 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} b^{8} d^{3} e^{6} + 105 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} b^{9} d^{4} e^{5}}{1920 \, {\left(c^{4} d^{8} e^{2} - 4 \, b c^{3} d^{7} e^{3} + 6 \, b^{2} c^{2} d^{6} e^{4} - 4 \, b^{3} c d^{5} e^{5} + b^{4} d^{4} e^{6}\right)} {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} e + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} d + b d\right)}^{5}}"," ",0,"1/128*(32*b^2*c^3*d^3 - 48*b^3*c^2*d^2*e + 30*b^4*c*d*e^2 - 7*b^5*e^3)*arctan(((sqrt(c)*x - sqrt(c*x^2 + b*x))*e + sqrt(c)*d)/sqrt(-c*d^2 + b*d*e))/((c^4*d^8 - 4*b*c^3*d^7*e + 6*b^2*c^2*d^6*e^2 - 4*b^3*c*d^5*e^3 + b^4*d^4*e^4)*sqrt(-c*d^2 + b*d*e)) + 1/1920*(7680*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*c^(13/2)*d^8*e + 3072*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*c^7*d^9 + 9216*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*b*c^6*d^8*e + 7680*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*b*c^(13/2)*d^9 - 30720*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*b*c^(11/2)*d^7*e^2 - 3840*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*b^2*c^(11/2)*d^8*e + 7680*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*b^2*c^6*d^9 - 50048*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*b^2*c^5*d^7*e^2 - 11520*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*b^3*c^5*d^8*e + 3840*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*b^3*c^(11/2)*d^9 + 70720*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*b^2*c^(9/2)*d^6*e^3 - 17600*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*b^3*c^(9/2)*d^7*e^2 - 7200*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*b^4*c^(9/2)*d^8*e + 960*(sqrt(c)*x - sqrt(c*x^2 + b*x))*b^4*c^5*d^9 + 15040*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*b^2*c^4*d^5*e^4 + 129280*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*b^3*c^4*d^6*e^3 + 14080*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*b^4*c^4*d^7*e^2 - 1920*(sqrt(c)*x - sqrt(c*x^2 + b*x))*b^5*c^4*d^8*e + 96*b^5*c^(9/2)*d^9 + 4320*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*b^2*c^(7/2)*d^4*e^5 - 52000*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*b^3*c^(7/2)*d^5*e^4 + 81920*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*b^4*c^(7/2)*d^6*e^3 + 13760*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*b^5*c^(7/2)*d^7*e^2 - 192*b^6*c^(7/2)*d^8*e + 480*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*b^2*c^3*d^3*e^6 - 20320*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*b^3*c^3*d^4*e^5 - 120680*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*b^4*c^3*d^5*e^4 + 14080*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*b^5*c^3*d^6*e^3 + 4280*(sqrt(c)*x - sqrt(c*x^2 + b*x))*b^6*c^3*d^7*e^2 - 6480*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*b^3*c^(5/2)*d^3*e^6 + 7260*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*b^4*c^(5/2)*d^4*e^5 - 85780*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*b^5*c^(5/2)*d^5*e^4 - 6340*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*b^6*c^(5/2)*d^6*e^3 + 476*b^7*c^(5/2)*d^7*e^2 - 720*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*b^3*c^2*d^2*e^7 + 10740*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*b^4*c^2*d^3*e^6 + 47944*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*b^5*c^2*d^4*e^5 - 25220*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*b^6*c^2*d^5*e^4 - 3080*(sqrt(c)*x - sqrt(c*x^2 + b*x))*b^7*c^2*d^6*e^3 + 4050*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*b^4*c^(3/2)*d^2*e^7 + 9310*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*b^5*c^(3/2)*d^3*e^6 + 35330*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*b^6*c^(3/2)*d^4*e^5 - 1750*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*b^7*c^(3/2)*d^5*e^4 - 380*b^8*c^(3/2)*d^6*e^3 + 450*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*b^4*c*d*e^8 - 1190*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*b^5*c*d^2*e^7 - 4658*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*b^6*c*d^3*e^6 + 10510*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*b^7*c*d^4*e^5 + 600*(sqrt(c)*x - sqrt(c*x^2 + b*x))*b^8*c*d^5*e^4 - 945*(sqrt(c)*x - sqrt(c*x^2 + b*x))^8*b^5*sqrt(c)*d*e^8 - 3430*(sqrt(c)*x - sqrt(c*x^2 + b*x))^6*b^6*sqrt(c)*d^2*e^7 - 4480*(sqrt(c)*x - sqrt(c*x^2 + b*x))^4*b^7*sqrt(c)*d^3*e^6 + 1470*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*b^8*sqrt(c)*d^4*e^5 + 105*b^9*sqrt(c)*d^5*e^4 - 105*(sqrt(c)*x - sqrt(c*x^2 + b*x))^9*b^5*e^9 - 490*(sqrt(c)*x - sqrt(c*x^2 + b*x))^7*b^6*d*e^8 - 896*(sqrt(c)*x - sqrt(c*x^2 + b*x))^5*b^7*d^2*e^7 - 790*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*b^8*d^3*e^6 + 105*(sqrt(c)*x - sqrt(c*x^2 + b*x))*b^9*d^4*e^5)/((c^4*d^8*e^2 - 4*b*c^3*d^7*e^3 + 6*b^2*c^2*d^6*e^4 - 4*b^3*c*d^5*e^5 + b^4*d^4*e^6)*((sqrt(c)*x - sqrt(c*x^2 + b*x))^2*e + 2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c)*d + b*d)^5)","B",0
295,1,365,0,0.242579," ","integrate((e*x+d)^3*(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","\frac{1}{35840} \, \sqrt{c x^{2} + b x} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(10 \, {\left(4 \, c x e^{3} + \frac{14 \, c^{7} d e^{2} + 5 \, b c^{6} e^{3}}{c^{6}}\right)} x + \frac{168 \, c^{7} d^{2} e + 182 \, b c^{6} d e^{2} + b^{2} c^{5} e^{3}}{c^{6}}\right)} x + \frac{560 \, c^{7} d^{3} + 1848 \, b c^{6} d^{2} e + 42 \, b^{2} c^{5} d e^{2} - 9 \, b^{3} c^{4} e^{3}}{c^{6}}\right)} x + \frac{7 \, {\left(240 \, b c^{6} d^{3} + 24 \, b^{2} c^{5} d^{2} e - 14 \, b^{3} c^{4} d e^{2} + 3 \, b^{4} c^{3} e^{3}\right)}}{c^{6}}\right)} x + \frac{35 \, {\left(16 \, b^{2} c^{5} d^{3} - 24 \, b^{3} c^{4} d^{2} e + 14 \, b^{4} c^{3} d e^{2} - 3 \, b^{5} c^{2} e^{3}\right)}}{c^{6}}\right)} x - \frac{105 \, {\left(16 \, b^{3} c^{4} d^{3} - 24 \, b^{4} c^{3} d^{2} e + 14 \, b^{5} c^{2} d e^{2} - 3 \, b^{6} c e^{3}\right)}}{c^{6}}\right)} - \frac{3 \, {\left(16 \, b^{4} c^{3} d^{3} - 24 \, b^{5} c^{2} d^{2} e + 14 \, b^{6} c d e^{2} - 3 \, b^{7} e^{3}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{2048 \, c^{\frac{11}{2}}}"," ",0,"1/35840*sqrt(c*x^2 + b*x)*(2*(4*(2*(8*(10*(4*c*x*e^3 + (14*c^7*d*e^2 + 5*b*c^6*e^3)/c^6)*x + (168*c^7*d^2*e + 182*b*c^6*d*e^2 + b^2*c^5*e^3)/c^6)*x + (560*c^7*d^3 + 1848*b*c^6*d^2*e + 42*b^2*c^5*d*e^2 - 9*b^3*c^4*e^3)/c^6)*x + 7*(240*b*c^6*d^3 + 24*b^2*c^5*d^2*e - 14*b^3*c^4*d*e^2 + 3*b^4*c^3*e^3)/c^6)*x + 35*(16*b^2*c^5*d^3 - 24*b^3*c^4*d^2*e + 14*b^4*c^3*d*e^2 - 3*b^5*c^2*e^3)/c^6)*x - 105*(16*b^3*c^4*d^3 - 24*b^4*c^3*d^2*e + 14*b^5*c^2*d*e^2 - 3*b^6*c*e^3)/c^6) - 3/2048*(16*b^4*c^3*d^3 - 24*b^5*c^2*d^2*e + 14*b^6*c*d*e^2 - 3*b^7*e^3)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(11/2)","A",0
296,1,262,0,0.282671," ","integrate((e*x+d)^2*(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","\frac{1}{7680} \, \sqrt{c x^{2} + b x} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(10 \, c x e^{2} + \frac{24 \, c^{6} d e + 13 \, b c^{5} e^{2}}{c^{5}}\right)} x + \frac{3 \, {\left(40 \, c^{6} d^{2} + 88 \, b c^{5} d e + b^{2} c^{4} e^{2}\right)}}{c^{5}}\right)} x + \frac{360 \, b c^{5} d^{2} + 24 \, b^{2} c^{4} d e - 7 \, b^{3} c^{3} e^{2}}{c^{5}}\right)} x + \frac{5 \, {\left(24 \, b^{2} c^{4} d^{2} - 24 \, b^{3} c^{3} d e + 7 \, b^{4} c^{2} e^{2}\right)}}{c^{5}}\right)} x - \frac{15 \, {\left(24 \, b^{3} c^{3} d^{2} - 24 \, b^{4} c^{2} d e + 7 \, b^{5} c e^{2}\right)}}{c^{5}}\right)} - \frac{{\left(24 \, b^{4} c^{2} d^{2} - 24 \, b^{5} c d e + 7 \, b^{6} e^{2}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{1024 \, c^{\frac{9}{2}}}"," ",0,"1/7680*sqrt(c*x^2 + b*x)*(2*(4*(2*(8*(10*c*x*e^2 + (24*c^6*d*e + 13*b*c^5*e^2)/c^5)*x + 3*(40*c^6*d^2 + 88*b*c^5*d*e + b^2*c^4*e^2)/c^5)*x + (360*b*c^5*d^2 + 24*b^2*c^4*d*e - 7*b^3*c^3*e^2)/c^5)*x + 5*(24*b^2*c^4*d^2 - 24*b^3*c^3*d*e + 7*b^4*c^2*e^2)/c^5)*x - 15*(24*b^3*c^3*d^2 - 24*b^4*c^2*d*e + 7*b^5*c*e^2)/c^5) - 1/1024*(24*b^4*c^2*d^2 - 24*b^5*c*d*e + 7*b^6*e^2)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(9/2)","A",0
297,1,171,0,0.220697," ","integrate((e*x+d)*(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","\frac{1}{640} \, \sqrt{c x^{2} + b x} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, c x e + \frac{10 \, c^{5} d + 11 \, b c^{4} e}{c^{4}}\right)} x + \frac{30 \, b c^{4} d + b^{2} c^{3} e}{c^{4}}\right)} x + \frac{5 \, {\left(2 \, b^{2} c^{3} d - b^{3} c^{2} e\right)}}{c^{4}}\right)} x - \frac{15 \, {\left(2 \, b^{3} c^{2} d - b^{4} c e\right)}}{c^{4}}\right)} - \frac{3 \, {\left(2 \, b^{4} c d - b^{5} e\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{256 \, c^{\frac{7}{2}}}"," ",0,"1/640*sqrt(c*x^2 + b*x)*(2*(4*(2*(8*c*x*e + (10*c^5*d + 11*b*c^4*e)/c^4)*x + (30*b*c^4*d + b^2*c^3*e)/c^4)*x + 5*(2*b^2*c^3*d - b^3*c^2*e)/c^4)*x - 15*(2*b^3*c^2*d - b^4*c*e)/c^4) - 3/256*(2*b^4*c*d - b^5*e)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(7/2)","A",0
298,1,83,0,0.218341," ","integrate((c*x^2+b*x)^(3/2),x, algorithm=""giac"")","-\frac{3 \, b^{4} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{128 \, c^{\frac{5}{2}}} + \frac{1}{64} \, \sqrt{c x^{2} + b x} {\left(2 \, {\left(4 \, {\left(2 \, c x + 3 \, b\right)} x + \frac{b^{2}}{c}\right)} x - \frac{3 \, b^{3}}{c^{2}}\right)}"," ",0,"-3/128*b^4*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(5/2) + 1/64*sqrt(c*x^2 + b*x)*(2*(4*(2*c*x + 3*b)*x + b^2/c)*x - 3*b^3/c^2)","A",0
299,-2,0,0,0.000000," ","integrate((c*x^2+b*x)^(3/2)/(e*x+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error: Bad Argument Type","F(-2)",0
300,-1,0,0,0.000000," ","integrate((c*x^2+b*x)^(3/2)/(e*x+d)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
301,1,500,0,0.414460," ","integrate((c*x^2+b*x)^(3/2)/(e*x+d)^3,x, algorithm=""giac"")","\sqrt{c x^{2} + b x} c e^{\left(-3\right)} + \frac{3 \, {\left(8 \, c^{2} d^{2} - 8 \, b c d e + b^{2} e^{2}\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} + b d e}}\right) e^{\left(-4\right)}}{4 \, \sqrt{-c d^{2} + b d e}} + \frac{3 \, {\left(2 \, c^{2} d - b c e\right)} e^{\left(-4\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{2 \, \sqrt{c}} + \frac{{\left(24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} c^{2} d^{2} e + 40 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} c^{\frac{5}{2}} d^{3} - 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} b c^{\frac{3}{2}} d^{2} e + 40 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} b c^{2} d^{3} - 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} b c d e^{2} - 28 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} b^{2} c d^{2} e + 10 \, b^{2} c^{\frac{3}{2}} d^{3} - {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} b^{2} \sqrt{c} d e^{2} - 5 \, b^{3} \sqrt{c} d^{2} e + 5 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} b^{2} e^{3} + 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} b^{3} d e^{2}\right)} e^{\left(-4\right)}}{4 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} e + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} d + b d\right)}^{2}}"," ",0,"sqrt(c*x^2 + b*x)*c*e^(-3) + 3/4*(8*c^2*d^2 - 8*b*c*d*e + b^2*e^2)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + b*x))*e + sqrt(c)*d)/sqrt(-c*d^2 + b*d*e))*e^(-4)/sqrt(-c*d^2 + b*d*e) + 3/2*(2*c^2*d - b*c*e)*e^(-4)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/sqrt(c) + 1/4*(24*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*c^2*d^2*e + 40*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*c^(5/2)*d^3 - 24*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*b*c^(3/2)*d^2*e + 40*(sqrt(c)*x - sqrt(c*x^2 + b*x))*b*c^2*d^3 - 24*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*b*c*d*e^2 - 28*(sqrt(c)*x - sqrt(c*x^2 + b*x))*b^2*c*d^2*e + 10*b^2*c^(3/2)*d^3 - (sqrt(c)*x - sqrt(c*x^2 + b*x))^2*b^2*sqrt(c)*d*e^2 - 5*b^3*sqrt(c)*d^2*e + 5*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*b^2*e^3 + 3*(sqrt(c)*x - sqrt(c*x^2 + b*x))*b^3*d*e^2)*e^(-4)/((sqrt(c)*x - sqrt(c*x^2 + b*x))^2*e + 2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c)*d + b*d)^2","B",0
302,1,480,0,0.300956," ","integrate((e*x+d)^3*(c*x^2+b*x)^(5/2),x, algorithm=""giac"")","\frac{1}{2064384} \, \sqrt{c x^{2} + b x} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(2 \, {\left(4 \, {\left(14 \, {\left(16 \, c^{2} x e^{3} + \frac{54 \, c^{10} d e^{2} + 37 \, b c^{9} e^{3}}{c^{8}}\right)} x + \frac{3 \, {\left(288 \, c^{10} d^{2} e + 594 \, b c^{9} d e^{2} + 103 \, b^{2} c^{8} e^{3}\right)}}{c^{8}}\right)} x + \frac{1344 \, c^{10} d^{3} + 8352 \, b c^{9} d^{2} e + 4374 \, b^{2} c^{8} d e^{2} + 5 \, b^{3} c^{7} e^{3}}{c^{8}}\right)} x + \frac{6720 \, b c^{9} d^{3} + 10656 \, b^{2} c^{8} d^{2} e + 54 \, b^{3} c^{7} d e^{2} - 11 \, b^{4} c^{6} e^{3}}{c^{8}}\right)} x + \frac{9 \, {\left(4032 \, b^{2} c^{8} d^{3} + 96 \, b^{3} c^{7} d^{2} e - 54 \, b^{4} c^{6} d e^{2} + 11 \, b^{5} c^{5} e^{3}\right)}}{c^{8}}\right)} x + \frac{21 \, {\left(64 \, b^{3} c^{7} d^{3} - 96 \, b^{4} c^{6} d^{2} e + 54 \, b^{5} c^{5} d e^{2} - 11 \, b^{6} c^{4} e^{3}\right)}}{c^{8}}\right)} x - \frac{105 \, {\left(64 \, b^{4} c^{6} d^{3} - 96 \, b^{5} c^{5} d^{2} e + 54 \, b^{6} c^{4} d e^{2} - 11 \, b^{7} c^{3} e^{3}\right)}}{c^{8}}\right)} x + \frac{315 \, {\left(64 \, b^{5} c^{5} d^{3} - 96 \, b^{6} c^{4} d^{2} e + 54 \, b^{7} c^{3} d e^{2} - 11 \, b^{8} c^{2} e^{3}\right)}}{c^{8}}\right)} + \frac{5 \, {\left(64 \, b^{6} c^{3} d^{3} - 96 \, b^{7} c^{2} d^{2} e + 54 \, b^{8} c d e^{2} - 11 \, b^{9} e^{3}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{65536 \, c^{\frac{13}{2}}}"," ",0,"1/2064384*sqrt(c*x^2 + b*x)*(2*(4*(2*(8*(2*(4*(14*(16*c^2*x*e^3 + (54*c^10*d*e^2 + 37*b*c^9*e^3)/c^8)*x + 3*(288*c^10*d^2*e + 594*b*c^9*d*e^2 + 103*b^2*c^8*e^3)/c^8)*x + (1344*c^10*d^3 + 8352*b*c^9*d^2*e + 4374*b^2*c^8*d*e^2 + 5*b^3*c^7*e^3)/c^8)*x + (6720*b*c^9*d^3 + 10656*b^2*c^8*d^2*e + 54*b^3*c^7*d*e^2 - 11*b^4*c^6*e^3)/c^8)*x + 9*(4032*b^2*c^8*d^3 + 96*b^3*c^7*d^2*e - 54*b^4*c^6*d*e^2 + 11*b^5*c^5*e^3)/c^8)*x + 21*(64*b^3*c^7*d^3 - 96*b^4*c^6*d^2*e + 54*b^5*c^5*d*e^2 - 11*b^6*c^4*e^3)/c^8)*x - 105*(64*b^4*c^6*d^3 - 96*b^5*c^5*d^2*e + 54*b^6*c^4*d*e^2 - 11*b^7*c^3*e^3)/c^8)*x + 315*(64*b^5*c^5*d^3 - 96*b^6*c^4*d^2*e + 54*b^7*c^3*d*e^2 - 11*b^8*c^2*e^3)/c^8) + 5/65536*(64*b^6*c^3*d^3 - 96*b^7*c^2*d^2*e + 54*b^8*c*d*e^2 - 11*b^9*e^3)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(13/2)","A",0
303,1,350,0,0.287670," ","integrate((e*x+d)^2*(c*x^2+b*x)^(5/2),x, algorithm=""giac"")","\frac{1}{344064} \, \sqrt{c x^{2} + b x} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(2 \, {\left(12 \, {\left(14 \, c^{2} x e^{2} + \frac{32 \, c^{9} d e + 33 \, b c^{8} e^{2}}{c^{7}}\right)} x + \frac{224 \, c^{9} d^{2} + 928 \, b c^{8} d e + 243 \, b^{2} c^{7} e^{2}}{c^{7}}\right)} x + \frac{1120 \, b c^{8} d^{2} + 1184 \, b^{2} c^{7} d e + 3 \, b^{3} c^{6} e^{2}}{c^{7}}\right)} x + \frac{3 \, {\left(2016 \, b^{2} c^{7} d^{2} + 32 \, b^{3} c^{6} d e - 9 \, b^{4} c^{5} e^{2}\right)}}{c^{7}}\right)} x + \frac{7 \, {\left(32 \, b^{3} c^{6} d^{2} - 32 \, b^{4} c^{5} d e + 9 \, b^{5} c^{4} e^{2}\right)}}{c^{7}}\right)} x - \frac{35 \, {\left(32 \, b^{4} c^{5} d^{2} - 32 \, b^{5} c^{4} d e + 9 \, b^{6} c^{3} e^{2}\right)}}{c^{7}}\right)} x + \frac{105 \, {\left(32 \, b^{5} c^{4} d^{2} - 32 \, b^{6} c^{3} d e + 9 \, b^{7} c^{2} e^{2}\right)}}{c^{7}}\right)} + \frac{5 \, {\left(32 \, b^{6} c^{2} d^{2} - 32 \, b^{7} c d e + 9 \, b^{8} e^{2}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{32768 \, c^{\frac{11}{2}}}"," ",0,"1/344064*sqrt(c*x^2 + b*x)*(2*(4*(2*(8*(2*(12*(14*c^2*x*e^2 + (32*c^9*d*e + 33*b*c^8*e^2)/c^7)*x + (224*c^9*d^2 + 928*b*c^8*d*e + 243*b^2*c^7*e^2)/c^7)*x + (1120*b*c^8*d^2 + 1184*b^2*c^7*d*e + 3*b^3*c^6*e^2)/c^7)*x + 3*(2016*b^2*c^7*d^2 + 32*b^3*c^6*d*e - 9*b^4*c^5*e^2)/c^7)*x + 7*(32*b^3*c^6*d^2 - 32*b^4*c^5*d*e + 9*b^5*c^4*e^2)/c^7)*x - 35*(32*b^4*c^5*d^2 - 32*b^5*c^4*d*e + 9*b^6*c^3*e^2)/c^7)*x + 105*(32*b^5*c^4*d^2 - 32*b^6*c^3*d*e + 9*b^7*c^2*e^2)/c^7) + 5/32768*(32*b^6*c^2*d^2 - 32*b^7*c*d*e + 9*b^8*e^2)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(11/2)","A",0
304,1,233,0,0.302899," ","integrate((e*x+d)*(c*x^2+b*x)^(5/2),x, algorithm=""giac"")","\frac{1}{21504} \, \sqrt{c x^{2} + b x} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(2 \, {\left(12 \, c^{2} x e + \frac{14 \, c^{8} d + 29 \, b c^{7} e}{c^{6}}\right)} x + \frac{70 \, b c^{7} d + 37 \, b^{2} c^{6} e}{c^{6}}\right)} x + \frac{3 \, {\left(126 \, b^{2} c^{6} d + b^{3} c^{5} e\right)}}{c^{6}}\right)} x + \frac{7 \, {\left(2 \, b^{3} c^{5} d - b^{4} c^{4} e\right)}}{c^{6}}\right)} x - \frac{35 \, {\left(2 \, b^{4} c^{4} d - b^{5} c^{3} e\right)}}{c^{6}}\right)} x + \frac{105 \, {\left(2 \, b^{5} c^{3} d - b^{6} c^{2} e\right)}}{c^{6}}\right)} + \frac{5 \, {\left(2 \, b^{6} c d - b^{7} e\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{2048 \, c^{\frac{9}{2}}}"," ",0,"1/21504*sqrt(c*x^2 + b*x)*(2*(4*(2*(8*(2*(12*c^2*x*e + (14*c^8*d + 29*b*c^7*e)/c^6)*x + (70*b*c^7*d + 37*b^2*c^6*e)/c^6)*x + 3*(126*b^2*c^6*d + b^3*c^5*e)/c^6)*x + 7*(2*b^3*c^5*d - b^4*c^4*e)/c^6)*x - 35*(2*b^4*c^4*d - b^5*c^3*e)/c^6)*x + 105*(2*b^5*c^3*d - b^6*c^2*e)/c^6) + 5/2048*(2*b^6*c*d - b^7*e)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(9/2)","A",0
305,1,107,0,0.244560," ","integrate((c*x^2+b*x)^(5/2),x, algorithm=""giac"")","\frac{5 \, b^{6} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{1024 \, c^{\frac{7}{2}}} + \frac{1}{1536} \, \sqrt{c x^{2} + b x} {\left(\frac{15 \, b^{5}}{c^{3}} - 2 \, {\left(\frac{5 \, b^{4}}{c^{2}} - 4 \, {\left(\frac{b^{3}}{c} + 2 \, {\left(27 \, b^{2} + 8 \, {\left(2 \, c^{2} x + 5 \, b c\right)} x\right)} x\right)} x\right)} x\right)}"," ",0,"5/1024*b^6*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(7/2) + 1/1536*sqrt(c*x^2 + b*x)*(15*b^5/c^3 - 2*(5*b^4/c^2 - 4*(b^3/c + 2*(27*b^2 + 8*(2*c^2*x + 5*b*c)*x)*x)*x)*x)","A",0
306,-2,0,0,0.000000," ","integrate((c*x^2+b*x)^(5/2)/(e*x+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error: Bad Argument Type","F(-2)",0
307,-1,0,0,0.000000," ","integrate((c*x^2+b*x)^(5/2)/(e*x+d)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
308,1,732,0,0.498413," ","integrate((c*x^2+b*x)^(5/2)/(e*x+d)^3,x, algorithm=""giac"")","\frac{5 \, {\left(16 \, c^{3} d^{4} - 32 \, b c^{2} d^{3} e + 19 \, b^{2} c d^{2} e^{2} - 3 \, b^{3} d e^{3}\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} + b d e}}\right) e^{\left(-6\right)}}{4 \, \sqrt{-c d^{2} + b d e}} + \frac{5 \, {\left(32 \, c^{3} d^{3} - 48 \, b c^{2} d^{2} e + 18 \, b^{2} c d e^{2} - b^{3} e^{3}\right)} e^{\left(-6\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{16 \, \sqrt{c}} + \frac{1}{24} \, \sqrt{c x^{2} + b x} {\left(2 \, {\left(4 \, c^{2} x e^{\left(-3\right)} - \frac{{\left(18 \, c^{4} d e^{14} - 13 \, b c^{3} e^{15}\right)} e^{\left(-18\right)}}{c^{2}}\right)} x + \frac{3 \, {\left(48 \, c^{4} d^{2} e^{13} - 54 \, b c^{3} d e^{14} + 11 \, b^{2} c^{2} e^{15}\right)} e^{\left(-18\right)}}{c^{2}}\right)} + \frac{{\left(40 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} c^{3} d^{4} e + 72 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} c^{\frac{7}{2}} d^{5} - 120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} b c^{\frac{5}{2}} d^{4} e + 72 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} b c^{3} d^{5} - 80 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} b c^{2} d^{3} e^{2} - 124 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} b^{2} c^{2} d^{4} e + 18 \, b^{2} c^{\frac{5}{2}} d^{5} + 51 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} b^{2} c^{\frac{3}{2}} d^{3} e^{2} - 27 \, b^{3} c^{\frac{3}{2}} d^{4} e + 49 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} b^{2} c d^{2} e^{3} + 59 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} b^{3} c d^{3} e^{2} - 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} b^{3} \sqrt{c} d^{2} e^{3} + 9 \, b^{4} \sqrt{c} d^{3} e^{2} - 9 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} b^{3} d e^{4} - 7 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} b^{4} d^{2} e^{3}\right)} e^{\left(-6\right)}}{4 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} e + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} d + b d\right)}^{2}}"," ",0,"5/4*(16*c^3*d^4 - 32*b*c^2*d^3*e + 19*b^2*c*d^2*e^2 - 3*b^3*d*e^3)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + b*x))*e + sqrt(c)*d)/sqrt(-c*d^2 + b*d*e))*e^(-6)/sqrt(-c*d^2 + b*d*e) + 5/16*(32*c^3*d^3 - 48*b*c^2*d^2*e + 18*b^2*c*d*e^2 - b^3*e^3)*e^(-6)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/sqrt(c) + 1/24*sqrt(c*x^2 + b*x)*(2*(4*c^2*x*e^(-3) - (18*c^4*d*e^14 - 13*b*c^3*e^15)*e^(-18)/c^2)*x + 3*(48*c^4*d^2*e^13 - 54*b*c^3*d*e^14 + 11*b^2*c^2*e^15)*e^(-18)/c^2) + 1/4*(40*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*c^3*d^4*e + 72*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*c^(7/2)*d^5 - 120*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*b*c^(5/2)*d^4*e + 72*(sqrt(c)*x - sqrt(c*x^2 + b*x))*b*c^3*d^5 - 80*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*b*c^2*d^3*e^2 - 124*(sqrt(c)*x - sqrt(c*x^2 + b*x))*b^2*c^2*d^4*e + 18*b^2*c^(5/2)*d^5 + 51*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*b^2*c^(3/2)*d^3*e^2 - 27*b^3*c^(3/2)*d^4*e + 49*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*b^2*c*d^2*e^3 + 59*(sqrt(c)*x - sqrt(c*x^2 + b*x))*b^3*c*d^3*e^2 - 3*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*b^3*sqrt(c)*d^2*e^3 + 9*b^4*sqrt(c)*d^3*e^2 - 9*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*b^3*d*e^4 - 7*(sqrt(c)*x - sqrt(c*x^2 + b*x))*b^4*d^2*e^3)*e^(-6)/((sqrt(c)*x - sqrt(c*x^2 + b*x))^2*e + 2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c)*d + b*d)^2","B",0
309,1,27,0,0.211508," ","integrate((x^2+2*x)^(1/2)/(1+x),x, algorithm=""giac"")","\sqrt{x^{2} + 2 \, x} - 2 \, \arctan\left(-x + \sqrt{x^{2} + 2 \, x} - 1\right)"," ",0,"sqrt(x^2 + 2*x) - 2*arctan(-x + sqrt(x^2 + 2*x) - 1)","A",0
310,1,47,0,0.192659," ","integrate((-x^2+2*x)^(3/2)/(2-2*x),x, algorithm=""giac"")","\frac{1}{6} \, {\left({\left(x - 2\right)} x - 3\right)} \sqrt{-x^{2} + 2 \, x} - \frac{1}{2} \, \log\left(-\frac{2 \, {\left(\sqrt{-x^{2} + 2 \, x} - 1\right)}}{{\left| -2 \, x + 2 \right|}}\right)"," ",0,"1/6*((x - 2)*x - 3)*sqrt(-x^2 + 2*x) - 1/2*log(-2*(sqrt(-x^2 + 2*x) - 1)/abs(-2*x + 2))","A",0
311,1,40,0,0.192326," ","integrate((-x^2+2*x)^(1/2)/(2-2*x),x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{-x^{2} + 2 \, x} - \frac{1}{2} \, \log\left(-\frac{2 \, {\left(\sqrt{-x^{2} + 2 \, x} - 1\right)}}{{\left| -2 \, x + 2 \right|}}\right)"," ",0,"-1/2*sqrt(-x^2 + 2*x) - 1/2*log(-2*(sqrt(-x^2 + 2*x) - 1)/abs(-2*x + 2))","A",0
312,1,26,0,0.199682," ","integrate(1/(2-2*x)/(-x^2+2*x)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \, \log\left(-\frac{2 \, {\left(\sqrt{-x^{2} + 2 \, x} - 1\right)}}{{\left| -2 \, x + 2 \right|}}\right)"," ",0,"-1/2*log(-2*(sqrt(-x^2 + 2*x) - 1)/abs(-2*x + 2))","A",0
313,1,49,0,0.220805," ","integrate(1/(2-2*x)/(-x^2+2*x)^(3/2),x, algorithm=""giac"")","\frac{\sqrt{-x^{2} + 2 \, x}}{2 \, {\left(x^{2} - 2 \, x\right)}} - \frac{1}{2} \, \log\left(-\frac{2 \, {\left(\sqrt{-x^{2} + 2 \, x} - 1\right)}}{{\left| -2 \, x + 2 \right|}}\right)"," ",0,"1/2*sqrt(-x^2 + 2*x)/(x^2 - 2*x) - 1/2*log(-2*(sqrt(-x^2 + 2*x) - 1)/abs(-2*x + 2))","A",0
314,1,57,0,0.249305," ","integrate(1/(2-2*x)/(-x^2+2*x)^(5/2),x, algorithm=""giac"")","\frac{{\left(3 \, {\left(x - 2\right)} x - 1\right)} \sqrt{-x^{2} + 2 \, x}}{6 \, {\left(x^{2} - 2 \, x\right)}^{2}} - \frac{1}{2} \, \log\left(-\frac{2 \, {\left(\sqrt{-x^{2} + 2 \, x} - 1\right)}}{{\left| -2 \, x + 2 \right|}}\right)"," ",0,"1/6*(3*(x - 2)*x - 1)*sqrt(-x^2 + 2*x)/(x^2 - 2*x)^2 - 1/2*log(-2*(sqrt(-x^2 + 2*x) - 1)/abs(-2*x + 2))","A",0
315,1,147,0,0.267601," ","integrate((e*x+d)^3/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\frac{1}{24} \, \sqrt{c x^{2} + b x} {\left(2 \, x {\left(\frac{4 \, x e^{3}}{c} + \frac{18 \, c^{2} d e^{2} - 5 \, b c e^{3}}{c^{3}}\right)} + \frac{3 \, {\left(24 \, c^{2} d^{2} e - 18 \, b c d e^{2} + 5 \, b^{2} e^{3}\right)}}{c^{3}}\right)} - \frac{{\left(16 \, c^{3} d^{3} - 24 \, b c^{2} d^{2} e + 18 \, b^{2} c d e^{2} - 5 \, b^{3} e^{3}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{16 \, c^{\frac{7}{2}}}"," ",0,"1/24*sqrt(c*x^2 + b*x)*(2*x*(4*x*e^3/c + (18*c^2*d*e^2 - 5*b*c*e^3)/c^3) + 3*(24*c^2*d^2*e - 18*b*c*d*e^2 + 5*b^2*e^3)/c^3) - 1/16*(16*c^3*d^3 - 24*b*c^2*d^2*e + 18*b^2*c*d*e^2 - 5*b^3*e^3)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(7/2)","A",0
316,1,97,0,0.306045," ","integrate((e*x+d)^2/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{c x^{2} + b x} {\left(\frac{2 \, x e^{2}}{c} + \frac{8 \, c d e - 3 \, b e^{2}}{c^{2}}\right)} - \frac{{\left(8 \, c^{2} d^{2} - 8 \, b c d e + 3 \, b^{2} e^{2}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{8 \, c^{\frac{5}{2}}}"," ",0,"1/4*sqrt(c*x^2 + b*x)*(2*x*e^2/c + (8*c*d*e - 3*b*e^2)/c^2) - 1/8*(8*c^2*d^2 - 8*b*c*d*e + 3*b^2*e^2)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(5/2)","A",0
317,1,63,0,0.263894," ","integrate((e*x+d)/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\frac{\sqrt{c x^{2} + b x} e}{c} - \frac{{\left(2 \, c d - b e\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{2 \, c^{\frac{3}{2}}}"," ",0,"sqrt(c*x^2 + b*x)*e/c - 1/2*(2*c*d - b*e)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(3/2)","A",0
318,1,35,0,0.258519," ","integrate(1/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","-\frac{\log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{\sqrt{c}}"," ",0,"-log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/sqrt(c)","A",0
319,1,61,0,0.257604," ","integrate(1/(e*x+d)/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\frac{2 \, \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} + b d e}}\right)}{\sqrt{-c d^{2} + b d e}}"," ",0,"2*arctan(-((sqrt(c)*x - sqrt(c*x^2 + b*x))*e + sqrt(c)*d)/sqrt(-c*d^2 + b*d*e))/sqrt(-c*d^2 + b*d*e)","A",0
320,1,400,0,1.347550," ","integrate(1/(e*x+d)^2/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\frac{{\left(2 \, c d \log\left({\left| 2 \, c d - b e - 2 \, \sqrt{c d^{2} - b d e} \sqrt{c} \right|}\right) - b e \log\left({\left| 2 \, c d - b e - 2 \, \sqrt{c d^{2} - b d e} \sqrt{c} \right|}\right) + 2 \, \sqrt{c d^{2} - b d e} \sqrt{c}\right)} \mathrm{sgn}\left(\frac{1}{x e + d}\right)}{2 \, {\left(\sqrt{c d^{2} - b d e} c d^{2} - \sqrt{c d^{2} - b d e} b d e\right)}} - \frac{\sqrt{c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{b e}{x e + d} - \frac{b d e}{{\left(x e + d\right)}^{2}}}}{c d^{2} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - b d e \mathrm{sgn}\left(\frac{1}{x e + d}\right)} - \frac{{\left(2 \, c d e - b e^{2}\right)} \log\left({\left| 2 \, c d - b e - 2 \, \sqrt{c d^{2} - b d e} {\left(\sqrt{c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{b e}{x e + d} - \frac{b d e}{{\left(x e + d\right)}^{2}}} + \frac{\sqrt{c d^{2} e^{2} - b d e^{3}} e^{\left(-1\right)}}{x e + d}\right)} \right|}\right)}{2 \, {\left(c d^{2} e - b d e^{2}\right)} \sqrt{c d^{2} - b d e} \mathrm{sgn}\left(\frac{1}{x e + d}\right)}"," ",0,"1/2*(2*c*d*log(abs(2*c*d - b*e - 2*sqrt(c*d^2 - b*d*e)*sqrt(c))) - b*e*log(abs(2*c*d - b*e - 2*sqrt(c*d^2 - b*d*e)*sqrt(c))) + 2*sqrt(c*d^2 - b*d*e)*sqrt(c))*sgn(1/(x*e + d))/(sqrt(c*d^2 - b*d*e)*c*d^2 - sqrt(c*d^2 - b*d*e)*b*d*e) - sqrt(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + b*e/(x*e + d) - b*d*e/(x*e + d)^2)/(c*d^2*sgn(1/(x*e + d)) - b*d*e*sgn(1/(x*e + d))) - 1/2*(2*c*d*e - b*e^2)*log(abs(2*c*d - b*e - 2*sqrt(c*d^2 - b*d*e)*(sqrt(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + b*e/(x*e + d) - b*d*e/(x*e + d)^2) + sqrt(c*d^2*e^2 - b*d*e^3)*e^(-1)/(x*e + d))))/((c*d^2*e - b*d*e^2)*sqrt(c*d^2 - b*d*e)*sgn(1/(x*e + d)))","B",0
321,1,487,0,0.295485," ","integrate(1/(e*x+d)^3/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","-\frac{{\left(8 \, c^{2} d^{2} - 8 \, b c d e + 3 \, b^{2} e^{2}\right)} \arctan\left(\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} + b d e}}\right)}{4 \, {\left(c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2}\right)} \sqrt{-c d^{2} + b d e}} - \frac{8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} c^{2} d^{2} e + 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} c^{\frac{5}{2}} d^{3} - 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} b c^{\frac{3}{2}} d^{2} e + 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} b c^{2} d^{3} - 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} b c d e^{2} - 20 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} b^{2} c d^{2} e + 6 \, b^{2} c^{\frac{3}{2}} d^{3} + 9 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} b^{2} \sqrt{c} d e^{2} - 3 \, b^{3} \sqrt{c} d^{2} e + 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} b^{2} e^{3} + 5 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} b^{3} d e^{2}}{4 \, {\left(c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2}\right)} {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} e + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} d + b d\right)}^{2}}"," ",0,"-1/4*(8*c^2*d^2 - 8*b*c*d*e + 3*b^2*e^2)*arctan(((sqrt(c)*x - sqrt(c*x^2 + b*x))*e + sqrt(c)*d)/sqrt(-c*d^2 + b*d*e))/((c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2)*sqrt(-c*d^2 + b*d*e)) - 1/4*(8*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*c^2*d^2*e + 24*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*c^(5/2)*d^3 - 24*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*b*c^(3/2)*d^2*e + 24*(sqrt(c)*x - sqrt(c*x^2 + b*x))*b*c^2*d^3 - 8*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*b*c*d*e^2 - 20*(sqrt(c)*x - sqrt(c*x^2 + b*x))*b^2*c*d^2*e + 6*b^2*c^(3/2)*d^3 + 9*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*b^2*sqrt(c)*d*e^2 - 3*b^3*sqrt(c)*d^2*e + 3*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*b^2*e^3 + 5*(sqrt(c)*x - sqrt(c*x^2 + b*x))*b^3*d*e^2)/((c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2)*((sqrt(c)*x - sqrt(c*x^2 + b*x))^2*e + 2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c)*d + b*d)^2)","B",0
322,1,125,0,0.266470," ","integrate((e*x+d)^3/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","-\frac{\frac{2 \, d^{3}}{b} - x {\left(\frac{x e^{3}}{c} - \frac{4 \, c^{3} d^{3} - 6 \, b c^{2} d^{2} e + 6 \, b^{2} c d e^{2} - 3 \, b^{3} e^{3}}{b^{2} c^{2}}\right)}}{\sqrt{c x^{2} + b x}} - \frac{3 \, {\left(2 \, c d e^{2} - b e^{3}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{2 \, c^{\frac{5}{2}}}"," ",0,"-(2*d^3/b - x*(x*e^3/c - (4*c^3*d^3 - 6*b*c^2*d^2*e + 6*b^2*c*d*e^2 - 3*b^3*e^3)/(b^2*c^2)))/sqrt(c*x^2 + b*x) - 3/2*(2*c*d*e^2 - b*e^3)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(5/2)","A",0
323,1,89,0,0.395328," ","integrate((e*x+d)^2/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{d^{2}}{b} + \frac{{\left(2 \, c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2}\right)} x}{b^{2} c}\right)}}{\sqrt{c x^{2} + b x}} - \frac{e^{2} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{c^{\frac{3}{2}}}"," ",0,"-2*(d^2/b + (2*c^2*d^2 - 2*b*c*d*e + b^2*e^2)*x/(b^2*c))/sqrt(c*x^2 + b*x) - e^2*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(3/2)","A",0
324,1,34,0,0.223722," ","integrate((e*x+d)/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{d}{b} + \frac{{\left(2 \, c d - b e\right)} x}{b^{2}}\right)}}{\sqrt{c x^{2} + b x}}"," ",0,"-2*(d/b + (2*c*d - b*e)*x/b^2)/sqrt(c*x^2 + b*x)","A",0
325,1,24,0,0.218540," ","integrate(1/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{2 \, c x}{b^{2}} + \frac{1}{b}\right)}}{\sqrt{c x^{2} + b x}}"," ",0,"-2*(2*c*x/b^2 + 1/b)/sqrt(c*x^2 + b*x)","A",0
326,1,167,0,0.243235," ","integrate(1/(e*x+d)/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{{\left(2 \, c^{2} d^{2} - b c d e\right)} x}{b^{2} c d^{3} - b^{3} d^{2} e} + \frac{b c d^{2} - b^{2} d e}{b^{2} c d^{3} - b^{3} d^{2} e}\right)}}{\sqrt{c x^{2} + b x}} - \frac{2 \, \arctan\left(\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} + b d e}}\right) e^{2}}{{\left(c d^{2} - b d e\right)} \sqrt{-c d^{2} + b d e}}"," ",0,"-2*((2*c^2*d^2 - b*c*d*e)*x/(b^2*c*d^3 - b^3*d^2*e) + (b*c*d^2 - b^2*d*e)/(b^2*c*d^3 - b^3*d^2*e))/sqrt(c*x^2 + b*x) - 2*arctan(((sqrt(c)*x - sqrt(c*x^2 + b*x))*e + sqrt(c)*d)/sqrt(-c*d^2 + b*d*e))*e^2/((c*d^2 - b*d*e)*sqrt(-c*d^2 + b*d*e))","A",0
327,1,776,0,1.175071," ","integrate(1/(e*x+d)^2/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","\frac{1}{2} \, {\left(\frac{{\left(8 \, \sqrt{c d^{2} - b d e} c^{\frac{5}{2}} d^{2} e^{2} + 6 \, b^{2} c d e^{4} \log\left({\left| 2 \, c d - b e - 2 \, \sqrt{c d^{2} - b d e} \sqrt{c} \right|}\right) - 8 \, \sqrt{c d^{2} - b d e} b c^{\frac{3}{2}} d e^{3} - 3 \, b^{3} e^{5} \log\left({\left| 2 \, c d - b e - 2 \, \sqrt{c d^{2} - b d e} \sqrt{c} \right|}\right) + 6 \, \sqrt{c d^{2} - b d e} b^{2} \sqrt{c} e^{4}\right)} \mathrm{sgn}\left(\frac{1}{x e + d}\right)}{\sqrt{c d^{2} - b d e} b^{2} c^{2} d^{4} - 2 \, \sqrt{c d^{2} - b d e} b^{3} c d^{3} e + \sqrt{c d^{2} - b d e} b^{4} d^{2} e^{2}} + \frac{2 \, {\left(\frac{{\left(\frac{4 \, c^{3} d^{3} e^{8} - 6 \, b c^{2} d^{2} e^{9} + 8 \, b^{2} c d e^{10} - 3 \, b^{3} e^{11}}{b^{2} c^{2} d^{4} e^{5} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 2 \, b^{3} c d^{3} e^{6} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + b^{4} d^{2} e^{7} \mathrm{sgn}\left(\frac{1}{x e + d}\right)} - \frac{{\left(b^{2} c d^{2} e^{11} - b^{3} d e^{12}\right)} e^{\left(-1\right)}}{{\left(b^{2} c^{2} d^{4} e^{5} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 2 \, b^{3} c d^{3} e^{6} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + b^{4} d^{2} e^{7} \mathrm{sgn}\left(\frac{1}{x e + d}\right)\right)} {\left(x e + d\right)}}\right)} e^{\left(-1\right)}}{x e + d} - \frac{4 \, c^{3} d^{2} e^{7} - 4 \, b c^{2} d e^{8} + 3 \, b^{2} c e^{9}}{b^{2} c^{2} d^{4} e^{5} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 2 \, b^{3} c d^{3} e^{6} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + b^{4} d^{2} e^{7} \mathrm{sgn}\left(\frac{1}{x e + d}\right)}\right)}}{\sqrt{c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{b e}{x e + d} - \frac{b d e}{{\left(x e + d\right)}^{2}}}} - \frac{3 \, {\left(2 \, c d e^{5} - b e^{6}\right)} \log\left({\left| 2 \, c d - b e - 2 \, \sqrt{c d^{2} - b d e} {\left(\sqrt{c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{b e}{x e + d} - \frac{b d e}{{\left(x e + d\right)}^{2}}} + \frac{\sqrt{c d^{2} e^{2} - b d e^{3}} e^{\left(-1\right)}}{x e + d}\right)} \right|}\right)}{{\left(c^{2} d^{4} e - 2 \, b c d^{3} e^{2} + b^{2} d^{2} e^{3}\right)} \sqrt{c d^{2} - b d e} \mathrm{sgn}\left(\frac{1}{x e + d}\right)}\right)} e^{\left(-2\right)}"," ",0,"1/2*((8*sqrt(c*d^2 - b*d*e)*c^(5/2)*d^2*e^2 + 6*b^2*c*d*e^4*log(abs(2*c*d - b*e - 2*sqrt(c*d^2 - b*d*e)*sqrt(c))) - 8*sqrt(c*d^2 - b*d*e)*b*c^(3/2)*d*e^3 - 3*b^3*e^5*log(abs(2*c*d - b*e - 2*sqrt(c*d^2 - b*d*e)*sqrt(c))) + 6*sqrt(c*d^2 - b*d*e)*b^2*sqrt(c)*e^4)*sgn(1/(x*e + d))/(sqrt(c*d^2 - b*d*e)*b^2*c^2*d^4 - 2*sqrt(c*d^2 - b*d*e)*b^3*c*d^3*e + sqrt(c*d^2 - b*d*e)*b^4*d^2*e^2) + 2*(((4*c^3*d^3*e^8 - 6*b*c^2*d^2*e^9 + 8*b^2*c*d*e^10 - 3*b^3*e^11)/(b^2*c^2*d^4*e^5*sgn(1/(x*e + d)) - 2*b^3*c*d^3*e^6*sgn(1/(x*e + d)) + b^4*d^2*e^7*sgn(1/(x*e + d))) - (b^2*c*d^2*e^11 - b^3*d*e^12)*e^(-1)/((b^2*c^2*d^4*e^5*sgn(1/(x*e + d)) - 2*b^3*c*d^3*e^6*sgn(1/(x*e + d)) + b^4*d^2*e^7*sgn(1/(x*e + d)))*(x*e + d)))*e^(-1)/(x*e + d) - (4*c^3*d^2*e^7 - 4*b*c^2*d*e^8 + 3*b^2*c*e^9)/(b^2*c^2*d^4*e^5*sgn(1/(x*e + d)) - 2*b^3*c*d^3*e^6*sgn(1/(x*e + d)) + b^4*d^2*e^7*sgn(1/(x*e + d))))/sqrt(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + b*e/(x*e + d) - b*d*e/(x*e + d)^2) - 3*(2*c*d*e^5 - b*e^6)*log(abs(2*c*d - b*e - 2*sqrt(c*d^2 - b*d*e)*(sqrt(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + b*e/(x*e + d) - b*d*e/(x*e + d)^2) + sqrt(c*d^2*e^2 - b*d*e^3)*e^(-1)/(x*e + d))))/((c^2*d^4*e - 2*b*c*d^3*e^2 + b^2*d^2*e^3)*sqrt(c*d^2 - b*d*e)*sgn(1/(x*e + d))))*e^(-2)","B",0
328,1,722,0,0.352885," ","integrate(1/(e*x+d)^3/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{{\left(2 \, c^{4} d^{6} - 3 \, b c^{3} d^{5} e + 3 \, b^{2} c^{2} d^{4} e^{2} - b^{3} c d^{3} e^{3}\right)} x}{b^{2} c^{3} d^{9} - 3 \, b^{3} c^{2} d^{8} e + 3 \, b^{4} c d^{7} e^{2} - b^{5} d^{6} e^{3}} + \frac{b c^{3} d^{6} - 3 \, b^{2} c^{2} d^{5} e + 3 \, b^{3} c d^{4} e^{2} - b^{4} d^{3} e^{3}}{b^{2} c^{3} d^{9} - 3 \, b^{3} c^{2} d^{8} e + 3 \, b^{4} c d^{7} e^{2} - b^{5} d^{6} e^{3}}\right)}}{\sqrt{c x^{2} + b x}} + \frac{3 \, {\left(16 \, c^{2} d^{2} e^{2} - 16 \, b c d e^{3} + 5 \, b^{2} e^{4}\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} + b d e}}\right)}{4 \, {\left(c^{3} d^{6} - 3 \, b c^{2} d^{5} e + 3 \, b^{2} c d^{4} e^{2} - b^{3} d^{3} e^{3}\right)} \sqrt{-c d^{2} + b d e}} - \frac{56 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} c^{\frac{5}{2}} d^{3} e^{2} + 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} c^{2} d^{2} e^{3} + 56 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} b c^{2} d^{3} e^{2} - 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} b c^{\frac{3}{2}} d^{2} e^{3} + 14 \, b^{2} c^{\frac{3}{2}} d^{3} e^{2} - 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} b c d e^{4} - 44 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} b^{2} c d^{2} e^{3} + 13 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} b^{2} \sqrt{c} d e^{4} - 7 \, b^{3} \sqrt{c} d^{2} e^{3} + 7 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{3} b^{2} e^{5} + 9 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} b^{3} d e^{4}}{4 \, {\left(c^{3} d^{6} - 3 \, b c^{2} d^{5} e + 3 \, b^{2} c d^{4} e^{2} - b^{3} d^{3} e^{3}\right)} {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)}^{2} e + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} d + b d\right)}^{2}}"," ",0,"-2*((2*c^4*d^6 - 3*b*c^3*d^5*e + 3*b^2*c^2*d^4*e^2 - b^3*c*d^3*e^3)*x/(b^2*c^3*d^9 - 3*b^3*c^2*d^8*e + 3*b^4*c*d^7*e^2 - b^5*d^6*e^3) + (b*c^3*d^6 - 3*b^2*c^2*d^5*e + 3*b^3*c*d^4*e^2 - b^4*d^3*e^3)/(b^2*c^3*d^9 - 3*b^3*c^2*d^8*e + 3*b^4*c*d^7*e^2 - b^5*d^6*e^3))/sqrt(c*x^2 + b*x) + 3/4*(16*c^2*d^2*e^2 - 16*b*c*d*e^3 + 5*b^2*e^4)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + b*x))*e + sqrt(c)*d)/sqrt(-c*d^2 + b*d*e))/((c^3*d^6 - 3*b*c^2*d^5*e + 3*b^2*c*d^4*e^2 - b^3*d^3*e^3)*sqrt(-c*d^2 + b*d*e)) - 1/4*(56*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*c^(5/2)*d^3*e^2 + 24*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*c^2*d^2*e^3 + 56*(sqrt(c)*x - sqrt(c*x^2 + b*x))*b*c^2*d^3*e^2 - 48*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*b*c^(3/2)*d^2*e^3 + 14*b^2*c^(3/2)*d^3*e^2 - 24*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*b*c*d*e^4 - 44*(sqrt(c)*x - sqrt(c*x^2 + b*x))*b^2*c*d^2*e^3 + 13*(sqrt(c)*x - sqrt(c*x^2 + b*x))^2*b^2*sqrt(c)*d*e^4 - 7*b^3*sqrt(c)*d^2*e^3 + 7*(sqrt(c)*x - sqrt(c*x^2 + b*x))^3*b^2*e^5 + 9*(sqrt(c)*x - sqrt(c*x^2 + b*x))*b^3*d*e^4)/((c^3*d^6 - 3*b*c^2*d^5*e + 3*b^2*c*d^4*e^2 - b^3*d^3*e^3)*((sqrt(c)*x - sqrt(c*x^2 + b*x))^2*e + 2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c)*d + b*d)^2)","B",0
329,1,209,0,0.357854," ","integrate((e*x+d)^4/(c*x^2+b*x)^(5/2),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{d^{4}}{b} - {\left(x {\left(\frac{4 \, {\left(4 \, c^{5} d^{4} - 8 \, b c^{4} d^{3} e + 3 \, b^{2} c^{3} d^{2} e^{2} + b^{3} c^{2} d e^{3} - b^{4} c e^{4}\right)} x}{b^{4} c^{2}} + \frac{3 \, {\left(8 \, b c^{4} d^{4} - 16 \, b^{2} c^{3} d^{3} e + 6 \, b^{3} c^{2} d^{2} e^{2} - b^{5} e^{4}\right)}}{b^{4} c^{2}}\right)} + \frac{6 \, {\left(b^{2} c^{3} d^{4} - 2 \, b^{3} c^{2} d^{3} e\right)}}{b^{4} c^{2}}\right)} x\right)}}{3 \, {\left(c x^{2} + b x\right)}^{\frac{3}{2}}} - \frac{e^{4} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} \sqrt{c} - b \right|}\right)}{c^{\frac{5}{2}}}"," ",0,"-2/3*(d^4/b - (x*(4*(4*c^5*d^4 - 8*b*c^4*d^3*e + 3*b^2*c^3*d^2*e^2 + b^3*c^2*d*e^3 - b^4*c*e^4)*x/(b^4*c^2) + 3*(8*b*c^4*d^4 - 16*b^2*c^3*d^3*e + 6*b^3*c^2*d^2*e^2 - b^5*e^4)/(b^4*c^2)) + 6*(b^2*c^3*d^4 - 2*b^3*c^2*d^3*e)/(b^4*c^2))*x)/(c*x^2 + b*x)^(3/2) - e^4*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x))*sqrt(c) - b))/c^(5/2)","A",0
330,1,127,0,0.245583," ","integrate((e*x+d)^3/(c*x^2+b*x)^(5/2),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{d^{3}}{b} - {\left(x {\left(\frac{{\left(16 \, c^{3} d^{3} - 24 \, b c^{2} d^{2} e + 6 \, b^{2} c d e^{2} + b^{3} e^{3}\right)} x}{b^{4}} + \frac{3 \, {\left(8 \, b c^{2} d^{3} - 12 \, b^{2} c d^{2} e + 3 \, b^{3} d e^{2}\right)}}{b^{4}}\right)} + \frac{3 \, {\left(2 \, b^{2} c d^{3} - 3 \, b^{3} d^{2} e\right)}}{b^{4}}\right)} x\right)}}{3 \, {\left(c x^{2} + b x\right)}^{\frac{3}{2}}}"," ",0,"-2/3*(d^3/b - (x*((16*c^3*d^3 - 24*b*c^2*d^2*e + 6*b^2*c*d*e^2 + b^3*e^3)*x/b^4 + 3*(8*b*c^2*d^3 - 12*b^2*c*d^2*e + 3*b^3*d*e^2)/b^4) + 3*(2*b^2*c*d^3 - 3*b^3*d^2*e)/b^4)*x)/(c*x^2 + b*x)^(3/2)","A",0
331,1,111,0,0.270633," ","integrate((e*x+d)^2/(c*x^2+b*x)^(5/2),x, algorithm=""giac"")","\frac{2 \, {\left({\left(x {\left(\frac{2 \, {\left(8 \, c^{3} d^{2} - 8 \, b c^{2} d e + b^{2} c e^{2}\right)} x}{b^{4}} + \frac{3 \, {\left(8 \, b c^{2} d^{2} - 8 \, b^{2} c d e + b^{3} e^{2}\right)}}{b^{4}}\right)} + \frac{6 \, {\left(b^{2} c d^{2} - b^{3} d e\right)}}{b^{4}}\right)} x - \frac{d^{2}}{b}\right)}}{3 \, {\left(c x^{2} + b x\right)}^{\frac{3}{2}}}"," ",0,"2/3*((x*(2*(8*c^3*d^2 - 8*b*c^2*d*e + b^2*c*e^2)*x/b^4 + 3*(8*b*c^2*d^2 - 8*b^2*c*d*e + b^3*e^2)/b^4) + 6*(b^2*c*d^2 - b^3*d*e)/b^4)*x - d^2/b)/(c*x^2 + b*x)^(3/2)","A",0
332,1,89,0,0.245217," ","integrate((e*x+d)/(c*x^2+b*x)^(5/2),x, algorithm=""giac"")","\frac{2 \, {\left({\left(4 \, x {\left(\frac{2 \, {\left(2 \, c^{3} d - b c^{2} e\right)} x}{b^{4}} + \frac{3 \, {\left(2 \, b c^{2} d - b^{2} c e\right)}}{b^{4}}\right)} + \frac{3 \, {\left(2 \, b^{2} c d - b^{3} e\right)}}{b^{4}}\right)} x - \frac{d}{b}\right)}}{3 \, {\left(c x^{2} + b x\right)}^{\frac{3}{2}}}"," ",0,"2/3*((4*x*(2*(2*c^3*d - b*c^2*e)*x/b^4 + 3*(2*b*c^2*d - b^2*c*e)/b^4) + 3*(2*b^2*c*d - b^3*e)/b^4)*x - d/b)/(c*x^2 + b*x)^(3/2)","A",0
333,1,50,0,0.219684," ","integrate(1/(c*x^2+b*x)^(5/2),x, algorithm=""giac"")","\frac{2 \, {\left(2 \, {\left(4 \, x {\left(\frac{2 \, c^{3} x}{b^{4}} + \frac{3 \, c^{2}}{b^{3}}\right)} + \frac{3 \, c}{b^{2}}\right)} x - \frac{1}{b}\right)}}{3 \, {\left(c x^{2} + b x\right)}^{\frac{3}{2}}}"," ",0,"2/3*(2*(4*x*(2*c^3*x/b^4 + 3*c^2/b^3) + 3*c/b^2)*x - 1/b)/(c*x^2 + b*x)^(3/2)","A",0
334,1,628,0,0.299434," ","integrate(1/(e*x+d)/(c*x^2+b*x)^(5/2),x, algorithm=""giac"")","-\frac{2 \, \arctan\left(\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + b x}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} + b d e}}\right) e^{4}}{{\left(c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2}\right)} \sqrt{-c d^{2} + b d e}} + \frac{2 \, {\left({\left({\left(\frac{{\left(16 \, c^{7} d^{10} - 56 \, b c^{6} d^{9} e + 66 \, b^{2} c^{5} d^{8} e^{2} - 25 \, b^{3} c^{4} d^{7} e^{3} - 4 \, b^{4} c^{3} d^{6} e^{4} + 3 \, b^{5} c^{2} d^{5} e^{5}\right)} x}{b^{4} c^{4} d^{11} - 4 \, b^{5} c^{3} d^{10} e + 6 \, b^{6} c^{2} d^{9} e^{2} - 4 \, b^{7} c d^{8} e^{3} + b^{8} d^{7} e^{4}} + \frac{3 \, {\left(8 \, b c^{6} d^{10} - 28 \, b^{2} c^{5} d^{9} e + 33 \, b^{3} c^{4} d^{8} e^{2} - 12 \, b^{4} c^{3} d^{7} e^{3} - 3 \, b^{5} c^{2} d^{6} e^{4} + 2 \, b^{6} c d^{5} e^{5}\right)}}{b^{4} c^{4} d^{11} - 4 \, b^{5} c^{3} d^{10} e + 6 \, b^{6} c^{2} d^{9} e^{2} - 4 \, b^{7} c d^{8} e^{3} + b^{8} d^{7} e^{4}}\right)} x + \frac{3 \, {\left(2 \, b^{2} c^{5} d^{10} - 7 \, b^{3} c^{4} d^{9} e + 8 \, b^{4} c^{3} d^{8} e^{2} - 2 \, b^{5} c^{2} d^{7} e^{3} - 2 \, b^{6} c d^{6} e^{4} + b^{7} d^{5} e^{5}\right)}}{b^{4} c^{4} d^{11} - 4 \, b^{5} c^{3} d^{10} e + 6 \, b^{6} c^{2} d^{9} e^{2} - 4 \, b^{7} c d^{8} e^{3} + b^{8} d^{7} e^{4}}\right)} x - \frac{b^{3} c^{4} d^{10} - 4 \, b^{4} c^{3} d^{9} e + 6 \, b^{5} c^{2} d^{8} e^{2} - 4 \, b^{6} c d^{7} e^{3} + b^{7} d^{6} e^{4}}{b^{4} c^{4} d^{11} - 4 \, b^{5} c^{3} d^{10} e + 6 \, b^{6} c^{2} d^{9} e^{2} - 4 \, b^{7} c d^{8} e^{3} + b^{8} d^{7} e^{4}}\right)}}{3 \, {\left(c x^{2} + b x\right)}^{\frac{3}{2}}}"," ",0,"-2*arctan(((sqrt(c)*x - sqrt(c*x^2 + b*x))*e + sqrt(c)*d)/sqrt(-c*d^2 + b*d*e))*e^4/((c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2)*sqrt(-c*d^2 + b*d*e)) + 2/3*((((16*c^7*d^10 - 56*b*c^6*d^9*e + 66*b^2*c^5*d^8*e^2 - 25*b^3*c^4*d^7*e^3 - 4*b^4*c^3*d^6*e^4 + 3*b^5*c^2*d^5*e^5)*x/(b^4*c^4*d^11 - 4*b^5*c^3*d^10*e + 6*b^6*c^2*d^9*e^2 - 4*b^7*c*d^8*e^3 + b^8*d^7*e^4) + 3*(8*b*c^6*d^10 - 28*b^2*c^5*d^9*e + 33*b^3*c^4*d^8*e^2 - 12*b^4*c^3*d^7*e^3 - 3*b^5*c^2*d^6*e^4 + 2*b^6*c*d^5*e^5)/(b^4*c^4*d^11 - 4*b^5*c^3*d^10*e + 6*b^6*c^2*d^9*e^2 - 4*b^7*c*d^8*e^3 + b^8*d^7*e^4))*x + 3*(2*b^2*c^5*d^10 - 7*b^3*c^4*d^9*e + 8*b^4*c^3*d^8*e^2 - 2*b^5*c^2*d^7*e^3 - 2*b^6*c*d^6*e^4 + b^7*d^5*e^5)/(b^4*c^4*d^11 - 4*b^5*c^3*d^10*e + 6*b^6*c^2*d^9*e^2 - 4*b^7*c*d^8*e^3 + b^8*d^7*e^4))*x - (b^3*c^4*d^10 - 4*b^4*c^3*d^9*e + 6*b^5*c^2*d^8*e^2 - 4*b^6*c*d^7*e^3 + b^7*d^6*e^4)/(b^4*c^4*d^11 - 4*b^5*c^3*d^10*e + 6*b^6*c^2*d^9*e^2 - 4*b^7*c*d^8*e^3 + b^8*d^7*e^4))/(c*x^2 + b*x)^(3/2)","B",0
335,1,1363,0,1.582126," ","integrate(1/(e*x+d)^2/(c*x^2+b*x)^(5/2),x, algorithm=""giac"")","-\frac{1}{6} \, {\left(\frac{{\left(64 \, \sqrt{c d^{2} - b d e} c^{5} d^{4} e^{2} - 128 \, \sqrt{c d^{2} - b d e} b c^{4} d^{3} e^{3} + 24 \, \sqrt{c d^{2} - b d e} b^{2} c^{3} d^{2} e^{4} - 30 \, b^{4} c^{\frac{3}{2}} d e^{6} \log\left({\left| 2 \, c d - b e - 2 \, \sqrt{c d^{2} - b d e} \sqrt{c} \right|}\right) + 40 \, \sqrt{c d^{2} - b d e} b^{3} c^{2} d e^{5} + 15 \, b^{5} \sqrt{c} e^{7} \log\left({\left| 2 \, c d - b e - 2 \, \sqrt{c d^{2} - b d e} \sqrt{c} \right|}\right) - 30 \, \sqrt{c d^{2} - b d e} b^{4} c e^{6}\right)} \mathrm{sgn}\left(\frac{1}{x e + d}\right)}{\sqrt{c d^{2} - b d e} b^{4} c^{\frac{7}{2}} d^{6} - 3 \, \sqrt{c d^{2} - b d e} b^{5} c^{\frac{5}{2}} d^{5} e + 3 \, \sqrt{c d^{2} - b d e} b^{6} c^{\frac{3}{2}} d^{4} e^{2} - \sqrt{c d^{2} - b d e} b^{7} \sqrt{c} d^{3} e^{3}} + \frac{2 \, {\left(\frac{{\left(\frac{{\left(\frac{{\left(\frac{4 \, {\left(8 \, c^{6} d^{7} e^{16} - 28 \, b c^{5} d^{6} e^{17} + 30 \, b^{2} c^{4} d^{5} e^{18} - 5 \, b^{3} c^{3} d^{4} e^{19} - 18 \, b^{4} c^{2} d^{3} e^{20} + 18 \, b^{5} c d^{2} e^{21} - 5 \, b^{6} d e^{22}\right)}}{b^{4} c^{3} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 3 \, b^{5} c^{2} d^{5} e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 3 \, b^{6} c d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - b^{7} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right)} + \frac{3 \, {\left(b^{4} c^{2} d^{4} e^{21} - 2 \, b^{5} c d^{3} e^{22} + b^{6} d^{2} e^{23}\right)} e^{\left(-1\right)}}{{\left(b^{4} c^{3} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 3 \, b^{5} c^{2} d^{5} e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 3 \, b^{6} c d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - b^{7} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right)\right)} {\left(x e + d\right)}}\right)} e^{\left(-1\right)}}{x e + d} - \frac{3 \, {\left(32 \, c^{6} d^{6} e^{15} - 96 \, b c^{5} d^{5} e^{16} + 80 \, b^{2} c^{4} d^{4} e^{17} - 46 \, b^{4} c^{2} d^{2} e^{19} + 30 \, b^{5} c d e^{20} - 5 \, b^{6} e^{21}\right)}}{b^{4} c^{3} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 3 \, b^{5} c^{2} d^{5} e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 3 \, b^{6} c d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - b^{7} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right)}\right)} e^{\left(-1\right)}}{x e + d} + \frac{6 \, {\left(16 \, c^{6} d^{5} e^{14} - 40 \, b c^{5} d^{4} e^{15} + 22 \, b^{2} c^{4} d^{3} e^{16} + 7 \, b^{3} c^{3} d^{2} e^{17} - 15 \, b^{4} c^{2} d e^{18} + 5 \, b^{5} c e^{19}\right)}}{b^{4} c^{3} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 3 \, b^{5} c^{2} d^{5} e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 3 \, b^{6} c d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - b^{7} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right)}\right)} e^{\left(-1\right)}}{x e + d} - \frac{32 \, c^{6} d^{4} e^{13} - 64 \, b c^{5} d^{3} e^{14} + 12 \, b^{2} c^{4} d^{2} e^{15} + 20 \, b^{3} c^{3} d e^{16} - 15 \, b^{4} c^{2} e^{17}}{b^{4} c^{3} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 3 \, b^{5} c^{2} d^{5} e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 3 \, b^{6} c d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - b^{7} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right)}\right)}}{{\left(c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{b e}{x e + d} - \frac{b d e}{{\left(x e + d\right)}^{2}}\right)}^{\frac{3}{2}}} + \frac{15 \, {\left(2 \, c d e^{7} - b e^{8}\right)} \log\left({\left| 2 \, c d - b e - 2 \, \sqrt{c d^{2} - b d e} {\left(\sqrt{c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{b e}{x e + d} - \frac{b d e}{{\left(x e + d\right)}^{2}}} + \frac{\sqrt{c d^{2} e^{2} - b d e^{3}} e^{\left(-1\right)}}{x e + d}\right)} \right|}\right)}{{\left(c^{3} d^{6} e - 3 \, b c^{2} d^{5} e^{2} + 3 \, b^{2} c d^{4} e^{3} - b^{3} d^{3} e^{4}\right)} \sqrt{c d^{2} - b d e} \mathrm{sgn}\left(\frac{1}{x e + d}\right)}\right)} e^{\left(-2\right)}"," ",0,"-1/6*((64*sqrt(c*d^2 - b*d*e)*c^5*d^4*e^2 - 128*sqrt(c*d^2 - b*d*e)*b*c^4*d^3*e^3 + 24*sqrt(c*d^2 - b*d*e)*b^2*c^3*d^2*e^4 - 30*b^4*c^(3/2)*d*e^6*log(abs(2*c*d - b*e - 2*sqrt(c*d^2 - b*d*e)*sqrt(c))) + 40*sqrt(c*d^2 - b*d*e)*b^3*c^2*d*e^5 + 15*b^5*sqrt(c)*e^7*log(abs(2*c*d - b*e - 2*sqrt(c*d^2 - b*d*e)*sqrt(c))) - 30*sqrt(c*d^2 - b*d*e)*b^4*c*e^6)*sgn(1/(x*e + d))/(sqrt(c*d^2 - b*d*e)*b^4*c^(7/2)*d^6 - 3*sqrt(c*d^2 - b*d*e)*b^5*c^(5/2)*d^5*e + 3*sqrt(c*d^2 - b*d*e)*b^6*c^(3/2)*d^4*e^2 - sqrt(c*d^2 - b*d*e)*b^7*sqrt(c)*d^3*e^3) + 2*((((4*(8*c^6*d^7*e^16 - 28*b*c^5*d^6*e^17 + 30*b^2*c^4*d^5*e^18 - 5*b^3*c^3*d^4*e^19 - 18*b^4*c^2*d^3*e^20 + 18*b^5*c*d^2*e^21 - 5*b^6*d*e^22)/(b^4*c^3*d^6*e^11*sgn(1/(x*e + d)) - 3*b^5*c^2*d^5*e^12*sgn(1/(x*e + d)) + 3*b^6*c*d^4*e^13*sgn(1/(x*e + d)) - b^7*d^3*e^14*sgn(1/(x*e + d))) + 3*(b^4*c^2*d^4*e^21 - 2*b^5*c*d^3*e^22 + b^6*d^2*e^23)*e^(-1)/((b^4*c^3*d^6*e^11*sgn(1/(x*e + d)) - 3*b^5*c^2*d^5*e^12*sgn(1/(x*e + d)) + 3*b^6*c*d^4*e^13*sgn(1/(x*e + d)) - b^7*d^3*e^14*sgn(1/(x*e + d)))*(x*e + d)))*e^(-1)/(x*e + d) - 3*(32*c^6*d^6*e^15 - 96*b*c^5*d^5*e^16 + 80*b^2*c^4*d^4*e^17 - 46*b^4*c^2*d^2*e^19 + 30*b^5*c*d*e^20 - 5*b^6*e^21)/(b^4*c^3*d^6*e^11*sgn(1/(x*e + d)) - 3*b^5*c^2*d^5*e^12*sgn(1/(x*e + d)) + 3*b^6*c*d^4*e^13*sgn(1/(x*e + d)) - b^7*d^3*e^14*sgn(1/(x*e + d))))*e^(-1)/(x*e + d) + 6*(16*c^6*d^5*e^14 - 40*b*c^5*d^4*e^15 + 22*b^2*c^4*d^3*e^16 + 7*b^3*c^3*d^2*e^17 - 15*b^4*c^2*d*e^18 + 5*b^5*c*e^19)/(b^4*c^3*d^6*e^11*sgn(1/(x*e + d)) - 3*b^5*c^2*d^5*e^12*sgn(1/(x*e + d)) + 3*b^6*c*d^4*e^13*sgn(1/(x*e + d)) - b^7*d^3*e^14*sgn(1/(x*e + d))))*e^(-1)/(x*e + d) - (32*c^6*d^4*e^13 - 64*b*c^5*d^3*e^14 + 12*b^2*c^4*d^2*e^15 + 20*b^3*c^3*d*e^16 - 15*b^4*c^2*e^17)/(b^4*c^3*d^6*e^11*sgn(1/(x*e + d)) - 3*b^5*c^2*d^5*e^12*sgn(1/(x*e + d)) + 3*b^6*c*d^4*e^13*sgn(1/(x*e + d)) - b^7*d^3*e^14*sgn(1/(x*e + d))))/(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + b*e/(x*e + d) - b*d*e/(x*e + d)^2)^(3/2) + 15*(2*c*d*e^7 - b*e^8)*log(abs(2*c*d - b*e - 2*sqrt(c*d^2 - b*d*e)*(sqrt(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + b*e/(x*e + d) - b*d*e/(x*e + d)^2) + sqrt(c*d^2*e^2 - b*d*e^3)*e^(-1)/(x*e + d))))/((c^3*d^6*e - 3*b*c^2*d^5*e^2 + 3*b^2*c*d^4*e^3 - b^3*d^3*e^4)*sqrt(c*d^2 - b*d*e)*sgn(1/(x*e + d))))*e^(-2)","B",0
336,1,18,0,0.188122," ","integrate(1/(2+x)/(x^2+2*x)^(1/2),x, algorithm=""giac"")","\frac{2}{x - \sqrt{x^{2} + 2 \, x} + 2}"," ",0,"2/(x - sqrt(x^2 + 2*x) + 2)","A",0
337,1,618,0,0.199381," ","integrate((e*x+d)^(7/2)*(c*x^2+b*x),x, algorithm=""giac"")","\frac{2}{45045} \, {\left(15015 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} b d^{4} e^{\left(-1\right)} + 3003 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} c d^{4} e^{\left(-2\right)} + 12012 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} b d^{3} e^{\left(-1\right)} + 5148 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} c d^{3} e^{\left(-2\right)} + 7722 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b d^{2} e^{\left(-1\right)} + 858 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} c d^{2} e^{\left(-2\right)} + 572 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b d e^{\left(-1\right)} + 260 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} c d e^{\left(-2\right)} + 65 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b e^{\left(-1\right)} + 15 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} c e^{\left(-2\right)}\right)} e^{\left(-1\right)}"," ",0,"2/45045*(15015*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*b*d^4*e^(-1) + 3003*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*c*d^4*e^(-2) + 12012*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*b*d^3*e^(-1) + 5148*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*c*d^3*e^(-2) + 7722*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b*d^2*e^(-1) + 858*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*c*d^2*e^(-2) + 572*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b*d*e^(-1) + 260*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*c*d*e^(-2) + 65*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b*e^(-1) + 15*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*c*e^(-2))*e^(-1)","B",0
338,1,441,0,0.186173," ","integrate((e*x+d)^(5/2)*(c*x^2+b*x),x, algorithm=""giac"")","\frac{2}{3465} \, {\left(1155 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} b d^{3} e^{\left(-1\right)} + 231 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} c d^{3} e^{\left(-2\right)} + 693 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} b d^{2} e^{\left(-1\right)} + 297 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} c d^{2} e^{\left(-2\right)} + 297 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b d e^{\left(-1\right)} + 33 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} c d e^{\left(-2\right)} + 11 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b e^{\left(-1\right)} + 5 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} c e^{\left(-2\right)}\right)} e^{\left(-1\right)}"," ",0,"2/3465*(1155*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*b*d^3*e^(-1) + 231*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*c*d^3*e^(-2) + 693*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*b*d^2*e^(-1) + 297*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*c*d^2*e^(-2) + 297*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b*d*e^(-1) + 33*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*c*d*e^(-2) + 11*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b*e^(-1) + 5*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*c*e^(-2))*e^(-1)","B",0
339,1,289,0,0.166448," ","integrate((e*x+d)^(3/2)*(c*x^2+b*x),x, algorithm=""giac"")","\frac{2}{315} \, {\left(105 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} b d^{2} e^{\left(-1\right)} + 21 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} c d^{2} e^{\left(-2\right)} + 42 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} b d e^{\left(-1\right)} + 18 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} c d e^{\left(-2\right)} + 9 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b e^{\left(-1\right)} + {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} c e^{\left(-2\right)}\right)} e^{\left(-1\right)}"," ",0,"2/315*(105*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*b*d^2*e^(-1) + 21*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*c*d^2*e^(-2) + 42*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*b*d*e^(-1) + 18*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*c*d*e^(-2) + 9*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b*e^(-1) + (35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*c*e^(-2))*e^(-1)","B",0
340,1,165,0,0.183298," ","integrate((e*x+d)^(1/2)*(c*x^2+b*x),x, algorithm=""giac"")","\frac{2}{105} \, {\left(35 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} b d e^{\left(-1\right)} + 7 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} c d e^{\left(-2\right)} + 7 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} b e^{\left(-1\right)} + 3 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} c e^{\left(-2\right)}\right)} e^{\left(-1\right)}"," ",0,"2/105*(35*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*b*d*e^(-1) + 7*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*c*d*e^(-2) + 7*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*b*e^(-1) + 3*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*c*e^(-2))*e^(-1)","B",0
341,1,69,0,0.158781," ","integrate((c*x^2+b*x)/(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{15} \, {\left(5 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} b e^{\left(-1\right)} + {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} c e^{\left(-2\right)}\right)} e^{\left(-1\right)}"," ",0,"2/15*(5*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*b*e^(-1) + (3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*c*e^(-2))*e^(-1)","A",0
342,1,69,0,0.162150," ","integrate((c*x^2+b*x)/(e*x+d)^(3/2),x, algorithm=""giac"")","\frac{2}{3} \, {\left({\left(x e + d\right)}^{\frac{3}{2}} c e^{6} - 6 \, \sqrt{x e + d} c d e^{6} + 3 \, \sqrt{x e + d} b e^{7}\right)} e^{\left(-9\right)} - \frac{2 \, {\left(c d^{2} - b d e\right)} e^{\left(-3\right)}}{\sqrt{x e + d}}"," ",0,"2/3*((x*e + d)^(3/2)*c*e^6 - 6*sqrt(x*e + d)*c*d*e^6 + 3*sqrt(x*e + d)*b*e^7)*e^(-9) - 2*(c*d^2 - b*d*e)*e^(-3)/sqrt(x*e + d)","A",0
343,1,59,0,0.180849," ","integrate((c*x^2+b*x)/(e*x+d)^(5/2),x, algorithm=""giac"")","2 \, \sqrt{x e + d} c e^{\left(-3\right)} + \frac{2 \, {\left(6 \, {\left(x e + d\right)} c d - c d^{2} - 3 \, {\left(x e + d\right)} b e + b d e\right)} e^{\left(-3\right)}}{3 \, {\left(x e + d\right)}^{\frac{3}{2}}}"," ",0,"2*sqrt(x*e + d)*c*e^(-3) + 2/3*(6*(x*e + d)*c*d - c*d^2 - 3*(x*e + d)*b*e + b*d*e)*e^(-3)/(x*e + d)^(3/2)","A",0
344,1,57,0,0.171364," ","integrate((c*x^2+b*x)/(e*x+d)^(7/2),x, algorithm=""giac"")","-\frac{2 \, {\left(15 \, {\left(x e + d\right)}^{2} c - 10 \, {\left(x e + d\right)} c d + 3 \, c d^{2} + 5 \, {\left(x e + d\right)} b e - 3 \, b d e\right)} e^{\left(-3\right)}}{15 \, {\left(x e + d\right)}^{\frac{5}{2}}}"," ",0,"-2/15*(15*(x*e + d)^2*c - 10*(x*e + d)*c*d + 3*c*d^2 + 5*(x*e + d)*b*e - 3*b*d*e)*e^(-3)/(x*e + d)^(5/2)","A",0
345,1,1245,0,0.254728," ","integrate((e*x+d)^(7/2)*(c*x^2+b*x)^2,x, algorithm=""giac"")","\frac{2}{765765} \, {\left(51051 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} b^{2} d^{4} e^{\left(-2\right)} + 43758 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b c d^{4} e^{\left(-3\right)} + 2431 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} c^{2} d^{4} e^{\left(-4\right)} + 87516 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b^{2} d^{3} e^{\left(-2\right)} + 19448 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b c d^{3} e^{\left(-3\right)} + 4420 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} c^{2} d^{3} e^{\left(-4\right)} + 14586 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b^{2} d^{2} e^{\left(-2\right)} + 13260 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b c d^{2} e^{\left(-3\right)} + 1530 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} c^{2} d^{2} e^{\left(-4\right)} + 4420 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b^{2} d e^{\left(-2\right)} + 2040 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} b c d e^{\left(-3\right)} + 476 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} c^{2} d e^{\left(-4\right)} + 255 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} b^{2} e^{\left(-2\right)} + 238 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} b c e^{\left(-3\right)} + 7 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} c^{2} e^{\left(-4\right)}\right)} e^{\left(-1\right)}"," ",0,"2/765765*(51051*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*b^2*d^4*e^(-2) + 43758*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b*c*d^4*e^(-3) + 2431*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*c^2*d^4*e^(-4) + 87516*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b^2*d^3*e^(-2) + 19448*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b*c*d^3*e^(-3) + 4420*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*c^2*d^3*e^(-4) + 14586*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b^2*d^2*e^(-2) + 13260*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b*c*d^2*e^(-3) + 1530*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*c^2*d^2*e^(-4) + 4420*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b^2*d*e^(-2) + 2040*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*b*c*d*e^(-3) + 476*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*c^2*d*e^(-4) + 255*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*b^2*e^(-2) + 238*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*b*c*e^(-3) + 7*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*c^2*e^(-4))*e^(-1)","B",0
346,1,916,0,0.580859," ","integrate((e*x+d)^(5/2)*(c*x^2+b*x)^2,x, algorithm=""giac"")","\frac{2}{45045} \, {\left(3003 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} b^{2} d^{3} e^{\left(-2\right)} + 2574 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b c d^{3} e^{\left(-3\right)} + 143 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} c^{2} d^{3} e^{\left(-4\right)} + 3861 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b^{2} d^{2} e^{\left(-2\right)} + 858 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b c d^{2} e^{\left(-3\right)} + 195 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} c^{2} d^{2} e^{\left(-4\right)} + 429 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b^{2} d e^{\left(-2\right)} + 390 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b c d e^{\left(-3\right)} + 45 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} c^{2} d e^{\left(-4\right)} + 65 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b^{2} e^{\left(-2\right)} + 30 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} b c e^{\left(-3\right)} + 7 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} c^{2} e^{\left(-4\right)}\right)} e^{\left(-1\right)}"," ",0,"2/45045*(3003*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*b^2*d^3*e^(-2) + 2574*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b*c*d^3*e^(-3) + 143*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*c^2*d^3*e^(-4) + 3861*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b^2*d^2*e^(-2) + 858*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b*c*d^2*e^(-3) + 195*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*c^2*d^2*e^(-4) + 429*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b^2*d*e^(-2) + 390*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b*c*d*e^(-3) + 45*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*c^2*d*e^(-4) + 65*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b^2*e^(-2) + 30*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*b*c*e^(-3) + 7*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*c^2*e^(-4))*e^(-1)","B",0
347,1,626,0,0.188048," ","integrate((e*x+d)^(3/2)*(c*x^2+b*x)^2,x, algorithm=""giac"")","\frac{2}{45045} \, {\left(3003 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} b^{2} d^{2} e^{\left(-2\right)} + 2574 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b c d^{2} e^{\left(-3\right)} + 143 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} c^{2} d^{2} e^{\left(-4\right)} + 2574 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b^{2} d e^{\left(-2\right)} + 572 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b c d e^{\left(-3\right)} + 130 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} c^{2} d e^{\left(-4\right)} + 143 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b^{2} e^{\left(-2\right)} + 130 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b c e^{\left(-3\right)} + 15 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} c^{2} e^{\left(-4\right)}\right)} e^{\left(-1\right)}"," ",0,"2/45045*(3003*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*b^2*d^2*e^(-2) + 2574*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b*c*d^2*e^(-3) + 143*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*c^2*d^2*e^(-4) + 2574*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b^2*d*e^(-2) + 572*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b*c*d*e^(-3) + 130*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*c^2*d*e^(-4) + 143*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b^2*e^(-2) + 130*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b*c*e^(-3) + 15*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*c^2*e^(-4))*e^(-1)","B",0
348,1,375,0,0.169255," ","integrate((e*x+d)^(1/2)*(c*x^2+b*x)^2,x, algorithm=""giac"")","\frac{2}{3465} \, {\left(231 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} b^{2} d e^{\left(-2\right)} + 198 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b c d e^{\left(-3\right)} + 11 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} c^{2} d e^{\left(-4\right)} + 99 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b^{2} e^{\left(-2\right)} + 22 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b c e^{\left(-3\right)} + 5 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} c^{2} e^{\left(-4\right)}\right)} e^{\left(-1\right)}"," ",0,"2/3465*(231*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*b^2*d*e^(-2) + 198*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b*c*d*e^(-3) + 11*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*c^2*d*e^(-4) + 99*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b^2*e^(-2) + 22*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b*c*e^(-3) + 5*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*c^2*e^(-4))*e^(-1)","B",0
349,1,168,0,0.189893," ","integrate((c*x^2+b*x)^2/(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{315} \, {\left(21 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} b^{2} e^{\left(-2\right)} + 18 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b c e^{\left(-3\right)} + {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} c^{2} e^{\left(-4\right)}\right)} e^{\left(-1\right)}"," ",0,"2/315*(21*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*b^2*e^(-2) + 18*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b*c*e^(-3) + (35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*c^2*e^(-4))*e^(-1)","A",0
350,1,188,0,0.210483," ","integrate((c*x^2+b*x)^2/(e*x+d)^(3/2),x, algorithm=""giac"")","\frac{2}{105} \, {\left(15 \, {\left(x e + d\right)}^{\frac{7}{2}} c^{2} e^{30} - 84 \, {\left(x e + d\right)}^{\frac{5}{2}} c^{2} d e^{30} + 210 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{2} d^{2} e^{30} - 420 \, \sqrt{x e + d} c^{2} d^{3} e^{30} + 42 \, {\left(x e + d\right)}^{\frac{5}{2}} b c e^{31} - 210 \, {\left(x e + d\right)}^{\frac{3}{2}} b c d e^{31} + 630 \, \sqrt{x e + d} b c d^{2} e^{31} + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{2} e^{32} - 210 \, \sqrt{x e + d} b^{2} d e^{32}\right)} e^{\left(-35\right)} - \frac{2 \, {\left(c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2}\right)} e^{\left(-5\right)}}{\sqrt{x e + d}}"," ",0,"2/105*(15*(x*e + d)^(7/2)*c^2*e^30 - 84*(x*e + d)^(5/2)*c^2*d*e^30 + 210*(x*e + d)^(3/2)*c^2*d^2*e^30 - 420*sqrt(x*e + d)*c^2*d^3*e^30 + 42*(x*e + d)^(5/2)*b*c*e^31 - 210*(x*e + d)^(3/2)*b*c*d*e^31 + 630*sqrt(x*e + d)*b*c*d^2*e^31 + 35*(x*e + d)^(3/2)*b^2*e^32 - 210*sqrt(x*e + d)*b^2*d*e^32)*e^(-35) - 2*(c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2)*e^(-5)/sqrt(x*e + d)","A",0
351,1,182,0,0.175817," ","integrate((c*x^2+b*x)^2/(e*x+d)^(5/2),x, algorithm=""giac"")","\frac{2}{15} \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} c^{2} e^{20} - 20 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{2} d e^{20} + 90 \, \sqrt{x e + d} c^{2} d^{2} e^{20} + 10 \, {\left(x e + d\right)}^{\frac{3}{2}} b c e^{21} - 90 \, \sqrt{x e + d} b c d e^{21} + 15 \, \sqrt{x e + d} b^{2} e^{22}\right)} e^{\left(-25\right)} + \frac{2 \, {\left(12 \, {\left(x e + d\right)} c^{2} d^{3} - c^{2} d^{4} - 18 \, {\left(x e + d\right)} b c d^{2} e + 2 \, b c d^{3} e + 6 \, {\left(x e + d\right)} b^{2} d e^{2} - b^{2} d^{2} e^{2}\right)} e^{\left(-5\right)}}{3 \, {\left(x e + d\right)}^{\frac{3}{2}}}"," ",0,"2/15*(3*(x*e + d)^(5/2)*c^2*e^20 - 20*(x*e + d)^(3/2)*c^2*d*e^20 + 90*sqrt(x*e + d)*c^2*d^2*e^20 + 10*(x*e + d)^(3/2)*b*c*e^21 - 90*sqrt(x*e + d)*b*c*d*e^21 + 15*sqrt(x*e + d)*b^2*e^22)*e^(-25) + 2/3*(12*(x*e + d)*c^2*d^3 - c^2*d^4 - 18*(x*e + d)*b*c*d^2*e + 2*b*c*d^3*e + 6*(x*e + d)*b^2*d*e^2 - b^2*d^2*e^2)*e^(-5)/(x*e + d)^(3/2)","A",0
352,1,179,0,0.183460," ","integrate((c*x^2+b*x)^2/(e*x+d)^(7/2),x, algorithm=""giac"")","\frac{2}{3} \, {\left({\left(x e + d\right)}^{\frac{3}{2}} c^{2} e^{10} - 12 \, \sqrt{x e + d} c^{2} d e^{10} + 6 \, \sqrt{x e + d} b c e^{11}\right)} e^{\left(-15\right)} - \frac{2 \, {\left(90 \, {\left(x e + d\right)}^{2} c^{2} d^{2} - 20 \, {\left(x e + d\right)} c^{2} d^{3} + 3 \, c^{2} d^{4} - 90 \, {\left(x e + d\right)}^{2} b c d e + 30 \, {\left(x e + d\right)} b c d^{2} e - 6 \, b c d^{3} e + 15 \, {\left(x e + d\right)}^{2} b^{2} e^{2} - 10 \, {\left(x e + d\right)} b^{2} d e^{2} + 3 \, b^{2} d^{2} e^{2}\right)} e^{\left(-5\right)}}{15 \, {\left(x e + d\right)}^{\frac{5}{2}}}"," ",0,"2/3*((x*e + d)^(3/2)*c^2*e^10 - 12*sqrt(x*e + d)*c^2*d*e^10 + 6*sqrt(x*e + d)*b*c*e^11)*e^(-15) - 2/15*(90*(x*e + d)^2*c^2*d^2 - 20*(x*e + d)*c^2*d^3 + 3*c^2*d^4 - 90*(x*e + d)^2*b*c*d*e + 30*(x*e + d)*b*c*d^2*e - 6*b*c*d^3*e + 15*(x*e + d)^2*b^2*e^2 - 10*(x*e + d)*b^2*d*e^2 + 3*b^2*d^2*e^2)*e^(-5)/(x*e + d)^(5/2)","A",0
353,1,2065,0,0.309659," ","integrate((e*x+d)^(7/2)*(c*x^2+b*x)^3,x, algorithm=""giac"")","\frac{2}{14549535} \, {\left(415701 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b^{3} d^{4} e^{\left(-3\right)} + 138567 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b^{2} c d^{4} e^{\left(-4\right)} + 62985 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b c^{2} d^{4} e^{\left(-5\right)} + 4845 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} c^{3} d^{4} e^{\left(-6\right)} + 184756 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b^{3} d^{3} e^{\left(-3\right)} + 251940 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b^{2} c d^{3} e^{\left(-4\right)} + 58140 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} b c^{2} d^{3} e^{\left(-5\right)} + 9044 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} c^{3} d^{3} e^{\left(-6\right)} + 125970 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b^{3} d^{2} e^{\left(-3\right)} + 87210 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} b^{2} c d^{2} e^{\left(-4\right)} + 40698 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} b c^{2} d^{2} e^{\left(-5\right)} + 798 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} c^{3} d^{2} e^{\left(-6\right)} + 19380 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} b^{3} d e^{\left(-3\right)} + 27132 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} b^{2} c d e^{\left(-4\right)} + 1596 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} b c^{2} d e^{\left(-5\right)} + 252 \, {\left(12155 \, {\left(x e + d\right)}^{\frac{19}{2}} - 122265 \, {\left(x e + d\right)}^{\frac{17}{2}} d + 554268 \, {\left(x e + d\right)}^{\frac{15}{2}} d^{2} - 1492260 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{3} + 2645370 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{4} - 3233230 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{5} + 2771340 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{6} - 1662804 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{7} + 692835 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{8} - 230945 \, \sqrt{x e + d} d^{9}\right)} c^{3} d e^{\left(-6\right)} + 2261 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} b^{3} e^{\left(-3\right)} + 399 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} b^{2} c e^{\left(-4\right)} + 189 \, {\left(12155 \, {\left(x e + d\right)}^{\frac{19}{2}} - 122265 \, {\left(x e + d\right)}^{\frac{17}{2}} d + 554268 \, {\left(x e + d\right)}^{\frac{15}{2}} d^{2} - 1492260 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{3} + 2645370 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{4} - 3233230 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{5} + 2771340 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{6} - 1662804 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{7} + 692835 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{8} - 230945 \, \sqrt{x e + d} d^{9}\right)} b c^{2} e^{\left(-5\right)} + 15 \, {\left(46189 \, {\left(x e + d\right)}^{\frac{21}{2}} - 510510 \, {\left(x e + d\right)}^{\frac{19}{2}} d + 2567565 \, {\left(x e + d\right)}^{\frac{17}{2}} d^{2} - 7759752 \, {\left(x e + d\right)}^{\frac{15}{2}} d^{3} + 15668730 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{4} - 22221108 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{5} + 22632610 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{6} - 16628040 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{7} + 8729721 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{8} - 3233230 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{9} + 969969 \, \sqrt{x e + d} d^{10}\right)} c^{3} e^{\left(-6\right)}\right)} e^{\left(-1\right)}"," ",0,"2/14549535*(415701*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b^3*d^4*e^(-3) + 138567*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b^2*c*d^4*e^(-4) + 62985*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b*c^2*d^4*e^(-5) + 4845*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*c^3*d^4*e^(-6) + 184756*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b^3*d^3*e^(-3) + 251940*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b^2*c*d^3*e^(-4) + 58140*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*b*c^2*d^3*e^(-5) + 9044*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*c^3*d^3*e^(-6) + 125970*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b^3*d^2*e^(-3) + 87210*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*b^2*c*d^2*e^(-4) + 40698*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*b*c^2*d^2*e^(-5) + 798*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*c^3*d^2*e^(-6) + 19380*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*b^3*d*e^(-3) + 27132*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*b^2*c*d*e^(-4) + 1596*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*b*c^2*d*e^(-5) + 252*(12155*(x*e + d)^(19/2) - 122265*(x*e + d)^(17/2)*d + 554268*(x*e + d)^(15/2)*d^2 - 1492260*(x*e + d)^(13/2)*d^3 + 2645370*(x*e + d)^(11/2)*d^4 - 3233230*(x*e + d)^(9/2)*d^5 + 2771340*(x*e + d)^(7/2)*d^6 - 1662804*(x*e + d)^(5/2)*d^7 + 692835*(x*e + d)^(3/2)*d^8 - 230945*sqrt(x*e + d)*d^9)*c^3*d*e^(-6) + 2261*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*b^3*e^(-3) + 399*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*b^2*c*e^(-4) + 189*(12155*(x*e + d)^(19/2) - 122265*(x*e + d)^(17/2)*d + 554268*(x*e + d)^(15/2)*d^2 - 1492260*(x*e + d)^(13/2)*d^3 + 2645370*(x*e + d)^(11/2)*d^4 - 3233230*(x*e + d)^(9/2)*d^5 + 2771340*(x*e + d)^(7/2)*d^6 - 1662804*(x*e + d)^(5/2)*d^7 + 692835*(x*e + d)^(3/2)*d^8 - 230945*sqrt(x*e + d)*d^9)*b*c^2*e^(-5) + 15*(46189*(x*e + d)^(21/2) - 510510*(x*e + d)^(19/2)*d + 2567565*(x*e + d)^(17/2)*d^2 - 7759752*(x*e + d)^(15/2)*d^3 + 15668730*(x*e + d)^(13/2)*d^4 - 22221108*(x*e + d)^(11/2)*d^5 + 22632610*(x*e + d)^(9/2)*d^6 - 16628040*(x*e + d)^(7/2)*d^7 + 8729721*(x*e + d)^(5/2)*d^8 - 3233230*(x*e + d)^(3/2)*d^9 + 969969*sqrt(x*e + d)*d^10)*c^3*e^(-6))*e^(-1)","B",0
354,1,1545,0,0.255839," ","integrate((e*x+d)^(5/2)*(c*x^2+b*x)^3,x, algorithm=""giac"")","\frac{2}{4849845} \, {\left(138567 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b^{3} d^{3} e^{\left(-3\right)} + 46189 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b^{2} c d^{3} e^{\left(-4\right)} + 20995 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b c^{2} d^{3} e^{\left(-5\right)} + 1615 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} c^{3} d^{3} e^{\left(-6\right)} + 46189 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b^{3} d^{2} e^{\left(-3\right)} + 62985 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b^{2} c d^{2} e^{\left(-4\right)} + 14535 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} b c^{2} d^{2} e^{\left(-5\right)} + 2261 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} c^{3} d^{2} e^{\left(-6\right)} + 20995 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b^{3} d e^{\left(-3\right)} + 14535 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} b^{2} c d e^{\left(-4\right)} + 6783 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} b c^{2} d e^{\left(-5\right)} + 133 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} c^{3} d e^{\left(-6\right)} + 1615 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} b^{3} e^{\left(-3\right)} + 2261 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} b^{2} c e^{\left(-4\right)} + 133 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} b c^{2} e^{\left(-5\right)} + 21 \, {\left(12155 \, {\left(x e + d\right)}^{\frac{19}{2}} - 122265 \, {\left(x e + d\right)}^{\frac{17}{2}} d + 554268 \, {\left(x e + d\right)}^{\frac{15}{2}} d^{2} - 1492260 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{3} + 2645370 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{4} - 3233230 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{5} + 2771340 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{6} - 1662804 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{7} + 692835 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{8} - 230945 \, \sqrt{x e + d} d^{9}\right)} c^{3} e^{\left(-6\right)}\right)} e^{\left(-1\right)}"," ",0,"2/4849845*(138567*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b^3*d^3*e^(-3) + 46189*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b^2*c*d^3*e^(-4) + 20995*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b*c^2*d^3*e^(-5) + 1615*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*c^3*d^3*e^(-6) + 46189*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b^3*d^2*e^(-3) + 62985*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b^2*c*d^2*e^(-4) + 14535*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*b*c^2*d^2*e^(-5) + 2261*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*c^3*d^2*e^(-6) + 20995*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b^3*d*e^(-3) + 14535*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*b^2*c*d*e^(-4) + 6783*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*b*c^2*d*e^(-5) + 133*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*c^3*d*e^(-6) + 1615*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*b^3*e^(-3) + 2261*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*b^2*c*e^(-4) + 133*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*b*c^2*e^(-5) + 21*(12155*(x*e + d)^(19/2) - 122265*(x*e + d)^(17/2)*d + 554268*(x*e + d)^(15/2)*d^2 - 1492260*(x*e + d)^(13/2)*d^3 + 2645370*(x*e + d)^(11/2)*d^4 - 3233230*(x*e + d)^(9/2)*d^5 + 2771340*(x*e + d)^(7/2)*d^6 - 1662804*(x*e + d)^(5/2)*d^7 + 692835*(x*e + d)^(3/2)*d^8 - 230945*sqrt(x*e + d)*d^9)*c^3*e^(-6))*e^(-1)","B",0
355,1,1077,0,0.217575," ","integrate((e*x+d)^(3/2)*(c*x^2+b*x)^3,x, algorithm=""giac"")","\frac{2}{765765} \, {\left(21879 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b^{3} d^{2} e^{\left(-3\right)} + 7293 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b^{2} c d^{2} e^{\left(-4\right)} + 3315 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b c^{2} d^{2} e^{\left(-5\right)} + 255 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} c^{3} d^{2} e^{\left(-6\right)} + 4862 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b^{3} d e^{\left(-3\right)} + 6630 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b^{2} c d e^{\left(-4\right)} + 1530 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} b c^{2} d e^{\left(-5\right)} + 238 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} c^{3} d e^{\left(-6\right)} + 1105 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b^{3} e^{\left(-3\right)} + 765 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} b^{2} c e^{\left(-4\right)} + 357 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} b c^{2} e^{\left(-5\right)} + 7 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} c^{3} e^{\left(-6\right)}\right)} e^{\left(-1\right)}"," ",0,"2/765765*(21879*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b^3*d^2*e^(-3) + 7293*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b^2*c*d^2*e^(-4) + 3315*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b*c^2*d^2*e^(-5) + 255*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*c^3*d^2*e^(-6) + 4862*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b^3*d*e^(-3) + 6630*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b^2*c*d*e^(-4) + 1530*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*b*c^2*d*e^(-5) + 238*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*c^3*d*e^(-6) + 1105*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b^3*e^(-3) + 765*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*b^2*c*e^(-4) + 357*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*b*c^2*e^(-5) + 7*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*c^3*e^(-6))*e^(-1)","B",0
356,1,661,0,0.227831," ","integrate((e*x+d)^(1/2)*(c*x^2+b*x)^3,x, algorithm=""giac"")","\frac{2}{45045} \, {\left(1287 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b^{3} d e^{\left(-3\right)} + 429 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b^{2} c d e^{\left(-4\right)} + 195 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b c^{2} d e^{\left(-5\right)} + 15 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} c^{3} d e^{\left(-6\right)} + 143 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b^{3} e^{\left(-3\right)} + 195 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b^{2} c e^{\left(-4\right)} + 45 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} b c^{2} e^{\left(-5\right)} + 7 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} c^{3} e^{\left(-6\right)}\right)} e^{\left(-1\right)}"," ",0,"2/45045*(1287*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b^3*d*e^(-3) + 429*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b^2*c*d*e^(-4) + 195*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b*c^2*d*e^(-5) + 15*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*c^3*d*e^(-6) + 143*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b^3*e^(-3) + 195*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b^2*c*e^(-4) + 45*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*b*c^2*e^(-5) + 7*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*c^3*e^(-6))*e^(-1)","B",0
357,1,305,0,0.172619," ","integrate((c*x^2+b*x)^3/(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{15015} \, {\left(429 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b^{3} e^{\left(-3\right)} + 143 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b^{2} c e^{\left(-4\right)} + 65 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b c^{2} e^{\left(-5\right)} + 5 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} c^{3} e^{\left(-6\right)}\right)} e^{\left(-1\right)}"," ",0,"2/15015*(429*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b^3*e^(-3) + 143*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b^2*c*e^(-4) + 65*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b*c^2*e^(-5) + 5*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*c^3*e^(-6))*e^(-1)","A",0
358,1,371,0,0.190748," ","integrate((c*x^2+b*x)^3/(e*x+d)^(3/2),x, algorithm=""giac"")","\frac{2}{1155} \, {\left(105 \, {\left(x e + d\right)}^{\frac{11}{2}} c^{3} e^{70} - 770 \, {\left(x e + d\right)}^{\frac{9}{2}} c^{3} d e^{70} + 2475 \, {\left(x e + d\right)}^{\frac{7}{2}} c^{3} d^{2} e^{70} - 4620 \, {\left(x e + d\right)}^{\frac{5}{2}} c^{3} d^{3} e^{70} + 5775 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{3} d^{4} e^{70} - 6930 \, \sqrt{x e + d} c^{3} d^{5} e^{70} + 385 \, {\left(x e + d\right)}^{\frac{9}{2}} b c^{2} e^{71} - 2475 \, {\left(x e + d\right)}^{\frac{7}{2}} b c^{2} d e^{71} + 6930 \, {\left(x e + d\right)}^{\frac{5}{2}} b c^{2} d^{2} e^{71} - 11550 \, {\left(x e + d\right)}^{\frac{3}{2}} b c^{2} d^{3} e^{71} + 17325 \, \sqrt{x e + d} b c^{2} d^{4} e^{71} + 495 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{2} c e^{72} - 2772 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{2} c d e^{72} + 6930 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{2} c d^{2} e^{72} - 13860 \, \sqrt{x e + d} b^{2} c d^{3} e^{72} + 231 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{3} e^{73} - 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{3} d e^{73} + 3465 \, \sqrt{x e + d} b^{3} d^{2} e^{73}\right)} e^{\left(-77\right)} - \frac{2 \, {\left(c^{3} d^{6} - 3 \, b c^{2} d^{5} e + 3 \, b^{2} c d^{4} e^{2} - b^{3} d^{3} e^{3}\right)} e^{\left(-7\right)}}{\sqrt{x e + d}}"," ",0,"2/1155*(105*(x*e + d)^(11/2)*c^3*e^70 - 770*(x*e + d)^(9/2)*c^3*d*e^70 + 2475*(x*e + d)^(7/2)*c^3*d^2*e^70 - 4620*(x*e + d)^(5/2)*c^3*d^3*e^70 + 5775*(x*e + d)^(3/2)*c^3*d^4*e^70 - 6930*sqrt(x*e + d)*c^3*d^5*e^70 + 385*(x*e + d)^(9/2)*b*c^2*e^71 - 2475*(x*e + d)^(7/2)*b*c^2*d*e^71 + 6930*(x*e + d)^(5/2)*b*c^2*d^2*e^71 - 11550*(x*e + d)^(3/2)*b*c^2*d^3*e^71 + 17325*sqrt(x*e + d)*b*c^2*d^4*e^71 + 495*(x*e + d)^(7/2)*b^2*c*e^72 - 2772*(x*e + d)^(5/2)*b^2*c*d*e^72 + 6930*(x*e + d)^(3/2)*b^2*c*d^2*e^72 - 13860*sqrt(x*e + d)*b^2*c*d^3*e^72 + 231*(x*e + d)^(5/2)*b^3*e^73 - 1155*(x*e + d)^(3/2)*b^3*d*e^73 + 3465*sqrt(x*e + d)*b^3*d^2*e^73)*e^(-77) - 2*(c^3*d^6 - 3*b*c^2*d^5*e + 3*b^2*c*d^4*e^2 - b^3*d^3*e^3)*e^(-7)/sqrt(x*e + d)","A",0
359,1,361,0,0.195834," ","integrate((c*x^2+b*x)^3/(e*x+d)^(5/2),x, algorithm=""giac"")","\frac{2}{315} \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} c^{3} e^{56} - 270 \, {\left(x e + d\right)}^{\frac{7}{2}} c^{3} d e^{56} + 945 \, {\left(x e + d\right)}^{\frac{5}{2}} c^{3} d^{2} e^{56} - 2100 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{3} d^{3} e^{56} + 4725 \, \sqrt{x e + d} c^{3} d^{4} e^{56} + 135 \, {\left(x e + d\right)}^{\frac{7}{2}} b c^{2} e^{57} - 945 \, {\left(x e + d\right)}^{\frac{5}{2}} b c^{2} d e^{57} + 3150 \, {\left(x e + d\right)}^{\frac{3}{2}} b c^{2} d^{2} e^{57} - 9450 \, \sqrt{x e + d} b c^{2} d^{3} e^{57} + 189 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{2} c e^{58} - 1260 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{2} c d e^{58} + 5670 \, \sqrt{x e + d} b^{2} c d^{2} e^{58} + 105 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{3} e^{59} - 945 \, \sqrt{x e + d} b^{3} d e^{59}\right)} e^{\left(-63\right)} + \frac{2 \, {\left(18 \, {\left(x e + d\right)} c^{3} d^{5} - c^{3} d^{6} - 45 \, {\left(x e + d\right)} b c^{2} d^{4} e + 3 \, b c^{2} d^{5} e + 36 \, {\left(x e + d\right)} b^{2} c d^{3} e^{2} - 3 \, b^{2} c d^{4} e^{2} - 9 \, {\left(x e + d\right)} b^{3} d^{2} e^{3} + b^{3} d^{3} e^{3}\right)} e^{\left(-7\right)}}{3 \, {\left(x e + d\right)}^{\frac{3}{2}}}"," ",0,"2/315*(35*(x*e + d)^(9/2)*c^3*e^56 - 270*(x*e + d)^(7/2)*c^3*d*e^56 + 945*(x*e + d)^(5/2)*c^3*d^2*e^56 - 2100*(x*e + d)^(3/2)*c^3*d^3*e^56 + 4725*sqrt(x*e + d)*c^3*d^4*e^56 + 135*(x*e + d)^(7/2)*b*c^2*e^57 - 945*(x*e + d)^(5/2)*b*c^2*d*e^57 + 3150*(x*e + d)^(3/2)*b*c^2*d^2*e^57 - 9450*sqrt(x*e + d)*b*c^2*d^3*e^57 + 189*(x*e + d)^(5/2)*b^2*c*e^58 - 1260*(x*e + d)^(3/2)*b^2*c*d*e^58 + 5670*sqrt(x*e + d)*b^2*c*d^2*e^58 + 105*(x*e + d)^(3/2)*b^3*e^59 - 945*sqrt(x*e + d)*b^3*d*e^59)*e^(-63) + 2/3*(18*(x*e + d)*c^3*d^5 - c^3*d^6 - 45*(x*e + d)*b*c^2*d^4*e + 3*b*c^2*d^5*e + 36*(x*e + d)*b^2*c*d^3*e^2 - 3*b^2*c*d^4*e^2 - 9*(x*e + d)*b^3*d^2*e^3 + b^3*d^3*e^3)*e^(-7)/(x*e + d)^(3/2)","A",0
360,1,359,0,0.206825," ","integrate((c*x^2+b*x)^3/(e*x+d)^(7/2),x, algorithm=""giac"")","\frac{2}{35} \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} c^{3} e^{42} - 42 \, {\left(x e + d\right)}^{\frac{5}{2}} c^{3} d e^{42} + 175 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{3} d^{2} e^{42} - 700 \, \sqrt{x e + d} c^{3} d^{3} e^{42} + 21 \, {\left(x e + d\right)}^{\frac{5}{2}} b c^{2} e^{43} - 175 \, {\left(x e + d\right)}^{\frac{3}{2}} b c^{2} d e^{43} + 1050 \, \sqrt{x e + d} b c^{2} d^{2} e^{43} + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{2} c e^{44} - 420 \, \sqrt{x e + d} b^{2} c d e^{44} + 35 \, \sqrt{x e + d} b^{3} e^{45}\right)} e^{\left(-49\right)} - \frac{2 \, {\left(75 \, {\left(x e + d\right)}^{2} c^{3} d^{4} - 10 \, {\left(x e + d\right)} c^{3} d^{5} + c^{3} d^{6} - 150 \, {\left(x e + d\right)}^{2} b c^{2} d^{3} e + 25 \, {\left(x e + d\right)} b c^{2} d^{4} e - 3 \, b c^{2} d^{5} e + 90 \, {\left(x e + d\right)}^{2} b^{2} c d^{2} e^{2} - 20 \, {\left(x e + d\right)} b^{2} c d^{3} e^{2} + 3 \, b^{2} c d^{4} e^{2} - 15 \, {\left(x e + d\right)}^{2} b^{3} d e^{3} + 5 \, {\left(x e + d\right)} b^{3} d^{2} e^{3} - b^{3} d^{3} e^{3}\right)} e^{\left(-7\right)}}{5 \, {\left(x e + d\right)}^{\frac{5}{2}}}"," ",0,"2/35*(5*(x*e + d)^(7/2)*c^3*e^42 - 42*(x*e + d)^(5/2)*c^3*d*e^42 + 175*(x*e + d)^(3/2)*c^3*d^2*e^42 - 700*sqrt(x*e + d)*c^3*d^3*e^42 + 21*(x*e + d)^(5/2)*b*c^2*e^43 - 175*(x*e + d)^(3/2)*b*c^2*d*e^43 + 1050*sqrt(x*e + d)*b*c^2*d^2*e^43 + 35*(x*e + d)^(3/2)*b^2*c*e^44 - 420*sqrt(x*e + d)*b^2*c*d*e^44 + 35*sqrt(x*e + d)*b^3*e^45)*e^(-49) - 2/5*(75*(x*e + d)^2*c^3*d^4 - 10*(x*e + d)*c^3*d^5 + c^3*d^6 - 150*(x*e + d)^2*b*c^2*d^3*e + 25*(x*e + d)*b*c^2*d^4*e - 3*b*c^2*d^5*e + 90*(x*e + d)^2*b^2*c*d^2*e^2 - 20*(x*e + d)*b^2*c*d^3*e^2 + 3*b^2*c*d^4*e^2 - 15*(x*e + d)^2*b^3*d*e^3 + 5*(x*e + d)*b^3*d^2*e^3 - b^3*d^3*e^3)*e^(-7)/(x*e + d)^(5/2)","A",0
361,1,229,0,0.230864," ","integrate((e*x+d)^(7/2)/(c*x^2+b*x),x, algorithm=""giac"")","\frac{2 \, d^{4} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-d}}\right)}{b \sqrt{-d}} - \frac{2 \, {\left(c^{4} d^{4} - 4 \, b c^{3} d^{3} e + 6 \, b^{2} c^{2} d^{2} e^{2} - 4 \, b^{3} c d e^{3} + b^{4} e^{4}\right)} \arctan\left(\frac{\sqrt{x e + d} c}{\sqrt{-c^{2} d + b c e}}\right)}{\sqrt{-c^{2} d + b c e} b c^{3}} + \frac{2 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} c^{4} e + 10 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{4} d e + 45 \, \sqrt{x e + d} c^{4} d^{2} e - 5 \, {\left(x e + d\right)}^{\frac{3}{2}} b c^{3} e^{2} - 45 \, \sqrt{x e + d} b c^{3} d e^{2} + 15 \, \sqrt{x e + d} b^{2} c^{2} e^{3}\right)}}{15 \, c^{5}}"," ",0,"2*d^4*arctan(sqrt(x*e + d)/sqrt(-d))/(b*sqrt(-d)) - 2*(c^4*d^4 - 4*b*c^3*d^3*e + 6*b^2*c^2*d^2*e^2 - 4*b^3*c*d*e^3 + b^4*e^4)*arctan(sqrt(x*e + d)*c/sqrt(-c^2*d + b*c*e))/(sqrt(-c^2*d + b*c*e)*b*c^3) + 2/15*(3*(x*e + d)^(5/2)*c^4*e + 10*(x*e + d)^(3/2)*c^4*d*e + 45*sqrt(x*e + d)*c^4*d^2*e - 5*(x*e + d)^(3/2)*b*c^3*e^2 - 45*sqrt(x*e + d)*b*c^3*d*e^2 + 15*sqrt(x*e + d)*b^2*c^2*e^3)/c^5","A",0
362,1,161,0,0.240235," ","integrate((e*x+d)^(5/2)/(c*x^2+b*x),x, algorithm=""giac"")","\frac{2 \, d^{3} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-d}}\right)}{b \sqrt{-d}} - \frac{2 \, {\left(c^{3} d^{3} - 3 \, b c^{2} d^{2} e + 3 \, b^{2} c d e^{2} - b^{3} e^{3}\right)} \arctan\left(\frac{\sqrt{x e + d} c}{\sqrt{-c^{2} d + b c e}}\right)}{\sqrt{-c^{2} d + b c e} b c^{2}} + \frac{2 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} c^{2} e + 6 \, \sqrt{x e + d} c^{2} d e - 3 \, \sqrt{x e + d} b c e^{2}\right)}}{3 \, c^{3}}"," ",0,"2*d^3*arctan(sqrt(x*e + d)/sqrt(-d))/(b*sqrt(-d)) - 2*(c^3*d^3 - 3*b*c^2*d^2*e + 3*b^2*c*d*e^2 - b^3*e^3)*arctan(sqrt(x*e + d)*c/sqrt(-c^2*d + b*c*e))/(sqrt(-c^2*d + b*c*e)*b*c^2) + 2/3*((x*e + d)^(3/2)*c^2*e + 6*sqrt(x*e + d)*c^2*d*e - 3*sqrt(x*e + d)*b*c*e^2)/c^3","A",0
363,1,112,0,0.187480," ","integrate((e*x+d)^(3/2)/(c*x^2+b*x),x, algorithm=""giac"")","\frac{2 \, d^{2} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-d}}\right)}{b \sqrt{-d}} + \frac{2 \, \sqrt{x e + d} e}{c} - \frac{2 \, {\left(c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2}\right)} \arctan\left(\frac{\sqrt{x e + d} c}{\sqrt{-c^{2} d + b c e}}\right)}{\sqrt{-c^{2} d + b c e} b c}"," ",0,"2*d^2*arctan(sqrt(x*e + d)/sqrt(-d))/(b*sqrt(-d)) + 2*sqrt(x*e + d)*e/c - 2*(c^2*d^2 - 2*b*c*d*e + b^2*e^2)*arctan(sqrt(x*e + d)*c/sqrt(-c^2*d + b*c*e))/(sqrt(-c^2*d + b*c*e)*b*c)","A",0
364,1,80,0,0.178502," ","integrate((e*x+d)^(1/2)/(c*x^2+b*x),x, algorithm=""giac"")","-\frac{2 \, {\left(c d - b e\right)} \arctan\left(\frac{\sqrt{x e + d} c}{\sqrt{-c^{2} d + b c e}}\right)}{\sqrt{-c^{2} d + b c e} b} + \frac{2 \, d \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-d}}\right)}{b \sqrt{-d}}"," ",0,"-2*(c*d - b*e)*arctan(sqrt(x*e + d)*c/sqrt(-c^2*d + b*c*e))/(sqrt(-c^2*d + b*c*e)*b) + 2*d*arctan(sqrt(x*e + d)/sqrt(-d))/(b*sqrt(-d))","A",0
365,1,71,0,0.167182," ","integrate(1/(e*x+d)^(1/2)/(c*x^2+b*x),x, algorithm=""giac"")","-\frac{2 \, c \arctan\left(\frac{\sqrt{x e + d} c}{\sqrt{-c^{2} d + b c e}}\right)}{\sqrt{-c^{2} d + b c e} b} + \frac{2 \, \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-d}}\right)}{b \sqrt{-d}}"," ",0,"-2*c*arctan(sqrt(x*e + d)*c/sqrt(-c^2*d + b*c*e))/(sqrt(-c^2*d + b*c*e)*b) + 2*arctan(sqrt(x*e + d)/sqrt(-d))/(b*sqrt(-d))","A",0
366,1,113,0,0.188118," ","integrate(1/(e*x+d)^(3/2)/(c*x^2+b*x),x, algorithm=""giac"")","-\frac{2 \, c^{2} \arctan\left(\frac{\sqrt{x e + d} c}{\sqrt{-c^{2} d + b c e}}\right)}{{\left(b c d - b^{2} e\right)} \sqrt{-c^{2} d + b c e}} - \frac{2 \, e}{{\left(c d^{2} - b d e\right)} \sqrt{x e + d}} + \frac{2 \, \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-d}}\right)}{b \sqrt{-d} d}"," ",0,"-2*c^2*arctan(sqrt(x*e + d)*c/sqrt(-c^2*d + b*c*e))/((b*c*d - b^2*e)*sqrt(-c^2*d + b*c*e)) - 2*e/((c*d^2 - b*d*e)*sqrt(x*e + d)) + 2*arctan(sqrt(x*e + d)/sqrt(-d))/(b*sqrt(-d)*d)","A",0
367,1,174,0,0.188248," ","integrate(1/(e*x+d)^(5/2)/(c*x^2+b*x),x, algorithm=""giac"")","-\frac{2 \, c^{3} \arctan\left(\frac{\sqrt{x e + d} c}{\sqrt{-c^{2} d + b c e}}\right)}{{\left(b c^{2} d^{2} - 2 \, b^{2} c d e + b^{3} e^{2}\right)} \sqrt{-c^{2} d + b c e}} - \frac{2 \, {\left(6 \, {\left(x e + d\right)} c d e + c d^{2} e - 3 \, {\left(x e + d\right)} b e^{2} - b d e^{2}\right)}}{3 \, {\left(c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2}\right)} {\left(x e + d\right)}^{\frac{3}{2}}} + \frac{2 \, \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-d}}\right)}{b \sqrt{-d} d^{2}}"," ",0,"-2*c^3*arctan(sqrt(x*e + d)*c/sqrt(-c^2*d + b*c*e))/((b*c^2*d^2 - 2*b^2*c*d*e + b^3*e^2)*sqrt(-c^2*d + b*c*e)) - 2/3*(6*(x*e + d)*c*d*e + c*d^2*e - 3*(x*e + d)*b*e^2 - b*d*e^2)/((c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2)*(x*e + d)^(3/2)) + 2*arctan(sqrt(x*e + d)/sqrt(-d))/(b*sqrt(-d)*d^2)","A",0
368,1,288,0,0.204891," ","integrate(1/(e*x+d)^(7/2)/(c*x^2+b*x),x, algorithm=""giac"")","-\frac{2 \, c^{4} \arctan\left(\frac{\sqrt{x e + d} c}{\sqrt{-c^{2} d + b c e}}\right)}{{\left(b c^{3} d^{3} - 3 \, b^{2} c^{2} d^{2} e + 3 \, b^{3} c d e^{2} - b^{4} e^{3}\right)} \sqrt{-c^{2} d + b c e}} - \frac{2 \, {\left(45 \, {\left(x e + d\right)}^{2} c^{2} d^{2} e + 10 \, {\left(x e + d\right)} c^{2} d^{3} e + 3 \, c^{2} d^{4} e - 45 \, {\left(x e + d\right)}^{2} b c d e^{2} - 15 \, {\left(x e + d\right)} b c d^{2} e^{2} - 6 \, b c d^{3} e^{2} + 15 \, {\left(x e + d\right)}^{2} b^{2} e^{3} + 5 \, {\left(x e + d\right)} b^{2} d e^{3} + 3 \, b^{2} d^{2} e^{3}\right)}}{15 \, {\left(c^{3} d^{6} - 3 \, b c^{2} d^{5} e + 3 \, b^{2} c d^{4} e^{2} - b^{3} d^{3} e^{3}\right)} {\left(x e + d\right)}^{\frac{5}{2}}} + \frac{2 \, \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-d}}\right)}{b \sqrt{-d} d^{3}}"," ",0,"-2*c^4*arctan(sqrt(x*e + d)*c/sqrt(-c^2*d + b*c*e))/((b*c^3*d^3 - 3*b^2*c^2*d^2*e + 3*b^3*c*d*e^2 - b^4*e^3)*sqrt(-c^2*d + b*c*e)) - 2/15*(45*(x*e + d)^2*c^2*d^2*e + 10*(x*e + d)*c^2*d^3*e + 3*c^2*d^4*e - 45*(x*e + d)^2*b*c*d*e^2 - 15*(x*e + d)*b*c*d^2*e^2 - 6*b*c*d^3*e^2 + 15*(x*e + d)^2*b^2*e^3 + 5*(x*e + d)*b^2*d*e^3 + 3*b^2*d^2*e^3)/((c^3*d^6 - 3*b*c^2*d^5*e + 3*b^2*c*d^4*e^2 - b^3*d^3*e^3)*(x*e + d)^(5/2)) + 2*arctan(sqrt(x*e + d)/sqrt(-d))/(b*sqrt(-d)*d^3)","A",0
369,1,436,0,0.275633," ","integrate((e*x+d)^(9/2)/(c*x^2+b*x)^2,x, algorithm=""giac"")","-\frac{{\left(4 \, c d^{5} - 9 \, b d^{4} e\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-d}}\right)}{b^{3} \sqrt{-d}} + \frac{{\left(4 \, c^{5} d^{5} - 11 \, b c^{4} d^{4} e + 4 \, b^{2} c^{3} d^{3} e^{2} + 14 \, b^{3} c^{2} d^{2} e^{3} - 16 \, b^{4} c d e^{4} + 5 \, b^{5} e^{5}\right)} \arctan\left(\frac{\sqrt{x e + d} c}{\sqrt{-c^{2} d + b c e}}\right)}{\sqrt{-c^{2} d + b c e} b^{3} c^{3}} + \frac{2 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} c^{4} e^{3} + 12 \, \sqrt{x e + d} c^{4} d e^{3} - 6 \, \sqrt{x e + d} b c^{3} e^{4}\right)}}{3 \, c^{6}} - \frac{2 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{4} d^{4} e - 2 \, \sqrt{x e + d} c^{4} d^{5} e - 4 \, {\left(x e + d\right)}^{\frac{3}{2}} b c^{3} d^{3} e^{2} + 5 \, \sqrt{x e + d} b c^{3} d^{4} e^{2} + 6 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{2} c^{2} d^{2} e^{3} - 6 \, \sqrt{x e + d} b^{2} c^{2} d^{3} e^{3} - 4 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{3} c d e^{4} + 4 \, \sqrt{x e + d} b^{3} c d^{2} e^{4} + {\left(x e + d\right)}^{\frac{3}{2}} b^{4} e^{5} - \sqrt{x e + d} b^{4} d e^{5}}{{\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + {\left(x e + d\right)} b e - b d e\right)} b^{2} c^{3}}"," ",0,"-(4*c*d^5 - 9*b*d^4*e)*arctan(sqrt(x*e + d)/sqrt(-d))/(b^3*sqrt(-d)) + (4*c^5*d^5 - 11*b*c^4*d^4*e + 4*b^2*c^3*d^3*e^2 + 14*b^3*c^2*d^2*e^3 - 16*b^4*c*d*e^4 + 5*b^5*e^5)*arctan(sqrt(x*e + d)*c/sqrt(-c^2*d + b*c*e))/(sqrt(-c^2*d + b*c*e)*b^3*c^3) + 2/3*((x*e + d)^(3/2)*c^4*e^3 + 12*sqrt(x*e + d)*c^4*d*e^3 - 6*sqrt(x*e + d)*b*c^3*e^4)/c^6 - (2*(x*e + d)^(3/2)*c^4*d^4*e - 2*sqrt(x*e + d)*c^4*d^5*e - 4*(x*e + d)^(3/2)*b*c^3*d^3*e^2 + 5*sqrt(x*e + d)*b*c^3*d^4*e^2 + 6*(x*e + d)^(3/2)*b^2*c^2*d^2*e^3 - 6*sqrt(x*e + d)*b^2*c^2*d^3*e^3 - 4*(x*e + d)^(3/2)*b^3*c*d*e^4 + 4*sqrt(x*e + d)*b^3*c*d^2*e^4 + (x*e + d)^(3/2)*b^4*e^5 - sqrt(x*e + d)*b^4*d*e^5)/(((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + (x*e + d)*b*e - b*d*e)*b^2*c^3)","A",0
370,1,344,0,0.229206," ","integrate((e*x+d)^(7/2)/(c*x^2+b*x)^2,x, algorithm=""giac"")","\frac{2 \, \sqrt{x e + d} e^{3}}{c^{2}} - \frac{{\left(4 \, c d^{4} - 7 \, b d^{3} e\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-d}}\right)}{b^{3} \sqrt{-d}} + \frac{{\left(4 \, c^{4} d^{4} - 9 \, b c^{3} d^{3} e + 3 \, b^{2} c^{2} d^{2} e^{2} + 5 \, b^{3} c d e^{3} - 3 \, b^{4} e^{4}\right)} \arctan\left(\frac{\sqrt{x e + d} c}{\sqrt{-c^{2} d + b c e}}\right)}{\sqrt{-c^{2} d + b c e} b^{3} c^{2}} - \frac{2 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{3} d^{3} e - 2 \, \sqrt{x e + d} c^{3} d^{4} e - 3 \, {\left(x e + d\right)}^{\frac{3}{2}} b c^{2} d^{2} e^{2} + 4 \, \sqrt{x e + d} b c^{2} d^{3} e^{2} + 3 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{2} c d e^{3} - 3 \, \sqrt{x e + d} b^{2} c d^{2} e^{3} - {\left(x e + d\right)}^{\frac{3}{2}} b^{3} e^{4} + \sqrt{x e + d} b^{3} d e^{4}}{{\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + {\left(x e + d\right)} b e - b d e\right)} b^{2} c^{2}}"," ",0,"2*sqrt(x*e + d)*e^3/c^2 - (4*c*d^4 - 7*b*d^3*e)*arctan(sqrt(x*e + d)/sqrt(-d))/(b^3*sqrt(-d)) + (4*c^4*d^4 - 9*b*c^3*d^3*e + 3*b^2*c^2*d^2*e^2 + 5*b^3*c*d*e^3 - 3*b^4*e^4)*arctan(sqrt(x*e + d)*c/sqrt(-c^2*d + b*c*e))/(sqrt(-c^2*d + b*c*e)*b^3*c^2) - (2*(x*e + d)^(3/2)*c^3*d^3*e - 2*sqrt(x*e + d)*c^3*d^4*e - 3*(x*e + d)^(3/2)*b*c^2*d^2*e^2 + 4*sqrt(x*e + d)*b*c^2*d^3*e^2 + 3*(x*e + d)^(3/2)*b^2*c*d*e^3 - 3*sqrt(x*e + d)*b^2*c*d^2*e^3 - (x*e + d)^(3/2)*b^3*e^4 + sqrt(x*e + d)*b^3*d*e^4)/(((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + (x*e + d)*b*e - b*d*e)*b^2*c^2)","A",0
371,1,273,0,0.202443," ","integrate((e*x+d)^(5/2)/(c*x^2+b*x)^2,x, algorithm=""giac"")","-\frac{{\left(4 \, c d^{3} - 5 \, b d^{2} e\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-d}}\right)}{b^{3} \sqrt{-d}} + \frac{{\left(4 \, c^{3} d^{3} - 7 \, b c^{2} d^{2} e + 2 \, b^{2} c d e^{2} + b^{3} e^{3}\right)} \arctan\left(\frac{\sqrt{x e + d} c}{\sqrt{-c^{2} d + b c e}}\right)}{\sqrt{-c^{2} d + b c e} b^{3} c} - \frac{2 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{2} d^{2} e - 2 \, \sqrt{x e + d} c^{2} d^{3} e - 2 \, {\left(x e + d\right)}^{\frac{3}{2}} b c d e^{2} + 3 \, \sqrt{x e + d} b c d^{2} e^{2} + {\left(x e + d\right)}^{\frac{3}{2}} b^{2} e^{3} - \sqrt{x e + d} b^{2} d e^{3}}{{\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + {\left(x e + d\right)} b e - b d e\right)} b^{2} c}"," ",0,"-(4*c*d^3 - 5*b*d^2*e)*arctan(sqrt(x*e + d)/sqrt(-d))/(b^3*sqrt(-d)) + (4*c^3*d^3 - 7*b*c^2*d^2*e + 2*b^2*c*d*e^2 + b^3*e^3)*arctan(sqrt(x*e + d)*c/sqrt(-c^2*d + b*c*e))/(sqrt(-c^2*d + b*c*e)*b^3*c) - (2*(x*e + d)^(3/2)*c^2*d^2*e - 2*sqrt(x*e + d)*c^2*d^3*e - 2*(x*e + d)^(3/2)*b*c*d*e^2 + 3*sqrt(x*e + d)*b*c*d^2*e^2 + (x*e + d)^(3/2)*b^2*e^3 - sqrt(x*e + d)*b^2*d*e^3)/(((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + (x*e + d)*b*e - b*d*e)*b^2*c)","A",0
372,1,211,0,0.196354," ","integrate((e*x+d)^(3/2)/(c*x^2+b*x)^2,x, algorithm=""giac"")","\frac{{\left(4 \, c^{2} d^{2} - 5 \, b c d e + b^{2} e^{2}\right)} \arctan\left(\frac{\sqrt{x e + d} c}{\sqrt{-c^{2} d + b c e}}\right)}{\sqrt{-c^{2} d + b c e} b^{3}} - \frac{{\left(4 \, c d^{2} - 3 \, b d e\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-d}}\right)}{b^{3} \sqrt{-d}} - \frac{2 \, {\left(x e + d\right)}^{\frac{3}{2}} c d e - 2 \, \sqrt{x e + d} c d^{2} e - {\left(x e + d\right)}^{\frac{3}{2}} b e^{2} + 2 \, \sqrt{x e + d} b d e^{2}}{{\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + {\left(x e + d\right)} b e - b d e\right)} b^{2}}"," ",0,"(4*c^2*d^2 - 5*b*c*d*e + b^2*e^2)*arctan(sqrt(x*e + d)*c/sqrt(-c^2*d + b*c*e))/(sqrt(-c^2*d + b*c*e)*b^3) - (4*c*d^2 - 3*b*d*e)*arctan(sqrt(x*e + d)/sqrt(-d))/(b^3*sqrt(-d)) - (2*(x*e + d)^(3/2)*c*d*e - 2*sqrt(x*e + d)*c*d^2*e - (x*e + d)^(3/2)*b*e^2 + 2*sqrt(x*e + d)*b*d*e^2)/(((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + (x*e + d)*b*e - b*d*e)*b^2)","A",0
373,1,181,0,0.196470," ","integrate((e*x+d)^(1/2)/(c*x^2+b*x)^2,x, algorithm=""giac"")","\frac{{\left(4 \, c^{2} d - 3 \, b c e\right)} \arctan\left(\frac{\sqrt{x e + d} c}{\sqrt{-c^{2} d + b c e}}\right)}{\sqrt{-c^{2} d + b c e} b^{3}} - \frac{{\left(4 \, c d - b e\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-d}}\right)}{b^{3} \sqrt{-d}} - \frac{2 \, {\left(x e + d\right)}^{\frac{3}{2}} c e - 2 \, \sqrt{x e + d} c d e + \sqrt{x e + d} b e^{2}}{{\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + {\left(x e + d\right)} b e - b d e\right)} b^{2}}"," ",0,"(4*c^2*d - 3*b*c*e)*arctan(sqrt(x*e + d)*c/sqrt(-c^2*d + b*c*e))/(sqrt(-c^2*d + b*c*e)*b^3) - (4*c*d - b*e)*arctan(sqrt(x*e + d)/sqrt(-d))/(b^3*sqrt(-d)) - (2*(x*e + d)^(3/2)*c*e - 2*sqrt(x*e + d)*c*d*e + sqrt(x*e + d)*b*e^2)/(((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + (x*e + d)*b*e - b*d*e)*b^2)","A",0
374,1,253,0,0.178841," ","integrate(1/(e*x+d)^(1/2)/(c*x^2+b*x)^2,x, algorithm=""giac"")","\frac{{\left(4 \, c^{3} d - 5 \, b c^{2} e\right)} \arctan\left(\frac{\sqrt{x e + d} c}{\sqrt{-c^{2} d + b c e}}\right)}{{\left(b^{3} c d - b^{4} e\right)} \sqrt{-c^{2} d + b c e}} - \frac{2 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{2} d e - 2 \, \sqrt{x e + d} c^{2} d^{2} e - {\left(x e + d\right)}^{\frac{3}{2}} b c e^{2} + 2 \, \sqrt{x e + d} b c d e^{2} - \sqrt{x e + d} b^{2} e^{3}}{{\left(b^{2} c d^{2} - b^{3} d e\right)} {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + {\left(x e + d\right)} b e - b d e\right)}} - \frac{{\left(4 \, c d + b e\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-d}}\right)}{b^{3} \sqrt{-d} d}"," ",0,"(4*c^3*d - 5*b*c^2*e)*arctan(sqrt(x*e + d)*c/sqrt(-c^2*d + b*c*e))/((b^3*c*d - b^4*e)*sqrt(-c^2*d + b*c*e)) - (2*(x*e + d)^(3/2)*c^2*d*e - 2*sqrt(x*e + d)*c^2*d^2*e - (x*e + d)^(3/2)*b*c*e^2 + 2*sqrt(x*e + d)*b*c*d*e^2 - sqrt(x*e + d)*b^2*e^3)/((b^2*c*d^2 - b^3*d*e)*((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + (x*e + d)*b*e - b*d*e)) - (4*c*d + b*e)*arctan(sqrt(x*e + d)/sqrt(-d))/(b^3*sqrt(-d)*d)","A",0
375,1,353,0,0.215182," ","integrate(1/(e*x+d)^(3/2)/(c*x^2+b*x)^2,x, algorithm=""giac"")","\frac{{\left(4 \, c^{4} d - 7 \, b c^{3} e\right)} \arctan\left(\frac{\sqrt{x e + d} c}{\sqrt{-c^{2} d + b c e}}\right)}{{\left(b^{3} c^{2} d^{2} - 2 \, b^{4} c d e + b^{5} e^{2}\right)} \sqrt{-c^{2} d + b c e}} - \frac{2 \, {\left(x e + d\right)}^{2} c^{3} d^{2} e - 2 \, {\left(x e + d\right)} c^{3} d^{3} e - 2 \, {\left(x e + d\right)}^{2} b c^{2} d e^{2} + 3 \, {\left(x e + d\right)} b c^{2} d^{2} e^{2} + 3 \, {\left(x e + d\right)}^{2} b^{2} c e^{3} - 7 \, {\left(x e + d\right)} b^{2} c d e^{3} + 2 \, b^{2} c d^{2} e^{3} + 3 \, {\left(x e + d\right)} b^{3} e^{4} - 2 \, b^{3} d e^{4}}{{\left(b^{2} c^{2} d^{4} - 2 \, b^{3} c d^{3} e + b^{4} d^{2} e^{2}\right)} {\left({\left(x e + d\right)}^{\frac{5}{2}} c - 2 \, {\left(x e + d\right)}^{\frac{3}{2}} c d + \sqrt{x e + d} c d^{2} + {\left(x e + d\right)}^{\frac{3}{2}} b e - \sqrt{x e + d} b d e\right)}} - \frac{{\left(4 \, c d + 3 \, b e\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-d}}\right)}{b^{3} \sqrt{-d} d^{2}}"," ",0,"(4*c^4*d - 7*b*c^3*e)*arctan(sqrt(x*e + d)*c/sqrt(-c^2*d + b*c*e))/((b^3*c^2*d^2 - 2*b^4*c*d*e + b^5*e^2)*sqrt(-c^2*d + b*c*e)) - (2*(x*e + d)^2*c^3*d^2*e - 2*(x*e + d)*c^3*d^3*e - 2*(x*e + d)^2*b*c^2*d*e^2 + 3*(x*e + d)*b*c^2*d^2*e^2 + 3*(x*e + d)^2*b^2*c*e^3 - 7*(x*e + d)*b^2*c*d*e^3 + 2*b^2*c*d^2*e^3 + 3*(x*e + d)*b^3*e^4 - 2*b^3*d*e^4)/((b^2*c^2*d^4 - 2*b^3*c*d^3*e + b^4*d^2*e^2)*((x*e + d)^(5/2)*c - 2*(x*e + d)^(3/2)*c*d + sqrt(x*e + d)*c*d^2 + (x*e + d)^(3/2)*b*e - sqrt(x*e + d)*b*d*e)) - (4*c*d + 3*b*e)*arctan(sqrt(x*e + d)/sqrt(-d))/(b^3*sqrt(-d)*d^2)","A",0
376,1,481,0,0.269925," ","integrate(1/(e*x+d)^(5/2)/(c*x^2+b*x)^2,x, algorithm=""giac"")","\frac{{\left(4 \, c^{5} d - 9 \, b c^{4} e\right)} \arctan\left(\frac{\sqrt{x e + d} c}{\sqrt{-c^{2} d + b c e}}\right)}{{\left(b^{3} c^{3} d^{3} - 3 \, b^{4} c^{2} d^{2} e + 3 \, b^{5} c d e^{2} - b^{6} e^{3}\right)} \sqrt{-c^{2} d + b c e}} - \frac{2 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{4} d^{3} e - 2 \, \sqrt{x e + d} c^{4} d^{4} e - 3 \, {\left(x e + d\right)}^{\frac{3}{2}} b c^{3} d^{2} e^{2} + 4 \, \sqrt{x e + d} b c^{3} d^{3} e^{2} + 3 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{2} c^{2} d e^{3} - 6 \, \sqrt{x e + d} b^{2} c^{2} d^{2} e^{3} - {\left(x e + d\right)}^{\frac{3}{2}} b^{3} c e^{4} + 4 \, \sqrt{x e + d} b^{3} c d e^{4} - \sqrt{x e + d} b^{4} e^{5}}{{\left(b^{2} c^{3} d^{6} - 3 \, b^{3} c^{2} d^{5} e + 3 \, b^{4} c d^{4} e^{2} - b^{5} d^{3} e^{3}\right)} {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + {\left(x e + d\right)} b e - b d e\right)}} - \frac{2 \, {\left(12 \, {\left(x e + d\right)} c d e^{3} + c d^{2} e^{3} - 6 \, {\left(x e + d\right)} b e^{4} - b d e^{4}\right)}}{3 \, {\left(c^{3} d^{6} - 3 \, b c^{2} d^{5} e + 3 \, b^{2} c d^{4} e^{2} - b^{3} d^{3} e^{3}\right)} {\left(x e + d\right)}^{\frac{3}{2}}} - \frac{{\left(4 \, c d + 5 \, b e\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-d}}\right)}{b^{3} \sqrt{-d} d^{3}}"," ",0,"(4*c^5*d - 9*b*c^4*e)*arctan(sqrt(x*e + d)*c/sqrt(-c^2*d + b*c*e))/((b^3*c^3*d^3 - 3*b^4*c^2*d^2*e + 3*b^5*c*d*e^2 - b^6*e^3)*sqrt(-c^2*d + b*c*e)) - (2*(x*e + d)^(3/2)*c^4*d^3*e - 2*sqrt(x*e + d)*c^4*d^4*e - 3*(x*e + d)^(3/2)*b*c^3*d^2*e^2 + 4*sqrt(x*e + d)*b*c^3*d^3*e^2 + 3*(x*e + d)^(3/2)*b^2*c^2*d*e^3 - 6*sqrt(x*e + d)*b^2*c^2*d^2*e^3 - (x*e + d)^(3/2)*b^3*c*e^4 + 4*sqrt(x*e + d)*b^3*c*d*e^4 - sqrt(x*e + d)*b^4*e^5)/((b^2*c^3*d^6 - 3*b^3*c^2*d^5*e + 3*b^4*c*d^4*e^2 - b^5*d^3*e^3)*((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + (x*e + d)*b*e - b*d*e)) - 2/3*(12*(x*e + d)*c*d*e^3 + c*d^2*e^3 - 6*(x*e + d)*b*e^4 - b*d*e^4)/((c^3*d^6 - 3*b*c^2*d^5*e + 3*b^2*c*d^4*e^2 - b^3*d^3*e^3)*(x*e + d)^(3/2)) - (4*c*d + 5*b*e)*arctan(sqrt(x*e + d)/sqrt(-d))/(b^3*sqrt(-d)*d^3)","A",0
377,1,643,0,0.305561," ","integrate(1/(e*x+d)^(7/2)/(c*x^2+b*x)^2,x, algorithm=""giac"")","\frac{{\left(4 \, c^{6} d - 11 \, b c^{5} e\right)} \arctan\left(\frac{\sqrt{x e + d} c}{\sqrt{-c^{2} d + b c e}}\right)}{{\left(b^{3} c^{4} d^{4} - 4 \, b^{4} c^{3} d^{3} e + 6 \, b^{5} c^{2} d^{2} e^{2} - 4 \, b^{6} c d e^{3} + b^{7} e^{4}\right)} \sqrt{-c^{2} d + b c e}} - \frac{2 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{5} d^{4} e - 2 \, \sqrt{x e + d} c^{5} d^{5} e - 4 \, {\left(x e + d\right)}^{\frac{3}{2}} b c^{4} d^{3} e^{2} + 5 \, \sqrt{x e + d} b c^{4} d^{4} e^{2} + 6 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{2} c^{3} d^{2} e^{3} - 10 \, \sqrt{x e + d} b^{2} c^{3} d^{3} e^{3} - 4 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{3} c^{2} d e^{4} + 10 \, \sqrt{x e + d} b^{3} c^{2} d^{2} e^{4} + {\left(x e + d\right)}^{\frac{3}{2}} b^{4} c e^{5} - 5 \, \sqrt{x e + d} b^{4} c d e^{5} + \sqrt{x e + d} b^{5} e^{6}}{{\left(b^{2} c^{4} d^{8} - 4 \, b^{3} c^{3} d^{7} e + 6 \, b^{4} c^{2} d^{6} e^{2} - 4 \, b^{5} c d^{5} e^{3} + b^{6} d^{4} e^{4}\right)} {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + {\left(x e + d\right)} b e - b d e\right)}} - \frac{2 \, {\left(150 \, {\left(x e + d\right)}^{2} c^{2} d^{2} e^{3} + 20 \, {\left(x e + d\right)} c^{2} d^{3} e^{3} + 3 \, c^{2} d^{4} e^{3} - 150 \, {\left(x e + d\right)}^{2} b c d e^{4} - 30 \, {\left(x e + d\right)} b c d^{2} e^{4} - 6 \, b c d^{3} e^{4} + 45 \, {\left(x e + d\right)}^{2} b^{2} e^{5} + 10 \, {\left(x e + d\right)} b^{2} d e^{5} + 3 \, b^{2} d^{2} e^{5}\right)}}{15 \, {\left(c^{4} d^{8} - 4 \, b c^{3} d^{7} e + 6 \, b^{2} c^{2} d^{6} e^{2} - 4 \, b^{3} c d^{5} e^{3} + b^{4} d^{4} e^{4}\right)} {\left(x e + d\right)}^{\frac{5}{2}}} - \frac{{\left(4 \, c d + 7 \, b e\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-d}}\right)}{b^{3} \sqrt{-d} d^{4}}"," ",0,"(4*c^6*d - 11*b*c^5*e)*arctan(sqrt(x*e + d)*c/sqrt(-c^2*d + b*c*e))/((b^3*c^4*d^4 - 4*b^4*c^3*d^3*e + 6*b^5*c^2*d^2*e^2 - 4*b^6*c*d*e^3 + b^7*e^4)*sqrt(-c^2*d + b*c*e)) - (2*(x*e + d)^(3/2)*c^5*d^4*e - 2*sqrt(x*e + d)*c^5*d^5*e - 4*(x*e + d)^(3/2)*b*c^4*d^3*e^2 + 5*sqrt(x*e + d)*b*c^4*d^4*e^2 + 6*(x*e + d)^(3/2)*b^2*c^3*d^2*e^3 - 10*sqrt(x*e + d)*b^2*c^3*d^3*e^3 - 4*(x*e + d)^(3/2)*b^3*c^2*d*e^4 + 10*sqrt(x*e + d)*b^3*c^2*d^2*e^4 + (x*e + d)^(3/2)*b^4*c*e^5 - 5*sqrt(x*e + d)*b^4*c*d*e^5 + sqrt(x*e + d)*b^5*e^6)/((b^2*c^4*d^8 - 4*b^3*c^3*d^7*e + 6*b^4*c^2*d^6*e^2 - 4*b^5*c*d^5*e^3 + b^6*d^4*e^4)*((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + (x*e + d)*b*e - b*d*e)) - 2/15*(150*(x*e + d)^2*c^2*d^2*e^3 + 20*(x*e + d)*c^2*d^3*e^3 + 3*c^2*d^4*e^3 - 150*(x*e + d)^2*b*c*d*e^4 - 30*(x*e + d)*b*c*d^2*e^4 - 6*b*c*d^3*e^4 + 45*(x*e + d)^2*b^2*e^5 + 10*(x*e + d)*b^2*d*e^5 + 3*b^2*d^2*e^5)/((c^4*d^8 - 4*b*c^3*d^7*e + 6*b^2*c^2*d^6*e^2 - 4*b^3*c*d^5*e^3 + b^4*d^4*e^4)*(x*e + d)^(5/2)) - (4*c*d + 7*b*e)*arctan(sqrt(x*e + d)/sqrt(-d))/(b^3*sqrt(-d)*d^4)","B",0
378,1,631,0,0.281748," ","integrate((e*x+d)^(9/2)/(c*x^2+b*x)^3,x, algorithm=""giac"")","\frac{3 \, {\left(16 \, c^{2} d^{5} - 36 \, b c d^{4} e + 21 \, b^{2} d^{3} e^{2}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-d}}\right)}{4 \, b^{5} \sqrt{-d}} - \frac{3 \, {\left(16 \, c^{5} d^{5} - 44 \, b c^{4} d^{4} e + 37 \, b^{2} c^{3} d^{3} e^{2} - 7 \, b^{3} c^{2} d^{2} e^{3} - b^{4} c d e^{4} - b^{5} e^{5}\right)} \arctan\left(\frac{\sqrt{x e + d} c}{\sqrt{-c^{2} d + b c e}}\right)}{4 \, \sqrt{-c^{2} d + b c e} b^{5} c^{2}} + \frac{24 \, {\left(x e + d\right)}^{\frac{7}{2}} c^{5} d^{4} e - 72 \, {\left(x e + d\right)}^{\frac{5}{2}} c^{5} d^{5} e + 72 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{5} d^{6} e - 24 \, \sqrt{x e + d} c^{5} d^{7} e - 48 \, {\left(x e + d\right)}^{\frac{7}{2}} b c^{4} d^{3} e^{2} + 180 \, {\left(x e + d\right)}^{\frac{5}{2}} b c^{4} d^{4} e^{2} - 216 \, {\left(x e + d\right)}^{\frac{3}{2}} b c^{4} d^{5} e^{2} + 84 \, \sqrt{x e + d} b c^{4} d^{6} e^{2} + 21 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{2} c^{3} d^{2} e^{3} - 136 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{2} c^{3} d^{3} e^{3} + 217 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{2} c^{3} d^{4} e^{3} - 102 \, \sqrt{x e + d} b^{2} c^{3} d^{5} e^{3} + 3 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{3} c^{2} d e^{4} + 24 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{3} c^{2} d^{2} e^{4} - 74 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{3} c^{2} d^{3} e^{4} + 45 \, \sqrt{x e + d} b^{3} c^{2} d^{4} e^{4} - 5 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{4} c e^{5} + 10 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{4} c d e^{5} - 5 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{4} c d^{2} e^{5} - 3 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{5} e^{6} + 6 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{5} d e^{6} - 3 \, \sqrt{x e + d} b^{5} d^{2} e^{6}}{4 \, {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + {\left(x e + d\right)} b e - b d e\right)}^{2} b^{4} c^{2}}"," ",0,"3/4*(16*c^2*d^5 - 36*b*c*d^4*e + 21*b^2*d^3*e^2)*arctan(sqrt(x*e + d)/sqrt(-d))/(b^5*sqrt(-d)) - 3/4*(16*c^5*d^5 - 44*b*c^4*d^4*e + 37*b^2*c^3*d^3*e^2 - 7*b^3*c^2*d^2*e^3 - b^4*c*d*e^4 - b^5*e^5)*arctan(sqrt(x*e + d)*c/sqrt(-c^2*d + b*c*e))/(sqrt(-c^2*d + b*c*e)*b^5*c^2) + 1/4*(24*(x*e + d)^(7/2)*c^5*d^4*e - 72*(x*e + d)^(5/2)*c^5*d^5*e + 72*(x*e + d)^(3/2)*c^5*d^6*e - 24*sqrt(x*e + d)*c^5*d^7*e - 48*(x*e + d)^(7/2)*b*c^4*d^3*e^2 + 180*(x*e + d)^(5/2)*b*c^4*d^4*e^2 - 216*(x*e + d)^(3/2)*b*c^4*d^5*e^2 + 84*sqrt(x*e + d)*b*c^4*d^6*e^2 + 21*(x*e + d)^(7/2)*b^2*c^3*d^2*e^3 - 136*(x*e + d)^(5/2)*b^2*c^3*d^3*e^3 + 217*(x*e + d)^(3/2)*b^2*c^3*d^4*e^3 - 102*sqrt(x*e + d)*b^2*c^3*d^5*e^3 + 3*(x*e + d)^(7/2)*b^3*c^2*d*e^4 + 24*(x*e + d)^(5/2)*b^3*c^2*d^2*e^4 - 74*(x*e + d)^(3/2)*b^3*c^2*d^3*e^4 + 45*sqrt(x*e + d)*b^3*c^2*d^4*e^4 - 5*(x*e + d)^(7/2)*b^4*c*e^5 + 10*(x*e + d)^(5/2)*b^4*c*d*e^5 - 5*(x*e + d)^(3/2)*b^4*c*d^2*e^5 - 3*(x*e + d)^(5/2)*b^5*e^6 + 6*(x*e + d)^(3/2)*b^5*d*e^6 - 3*sqrt(x*e + d)*b^5*d^2*e^6)/(((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + (x*e + d)*b*e - b*d*e)^2*b^4*c^2)","B",0
379,1,552,0,0.282993," ","integrate((e*x+d)^(7/2)/(c*x^2+b*x)^3,x, algorithm=""giac"")","\frac{{\left(48 \, c^{2} d^{4} - 84 \, b c d^{3} e + 35 \, b^{2} d^{2} e^{2}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-d}}\right)}{4 \, b^{5} \sqrt{-d}} - \frac{{\left(48 \, c^{4} d^{4} - 108 \, b c^{3} d^{3} e + 71 \, b^{2} c^{2} d^{2} e^{2} - 10 \, b^{3} c d e^{3} - b^{4} e^{4}\right)} \arctan\left(\frac{\sqrt{x e + d} c}{\sqrt{-c^{2} d + b c e}}\right)}{4 \, \sqrt{-c^{2} d + b c e} b^{5} c} + \frac{24 \, {\left(x e + d\right)}^{\frac{7}{2}} c^{4} d^{3} e - 72 \, {\left(x e + d\right)}^{\frac{5}{2}} c^{4} d^{4} e + 72 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{4} d^{5} e - 24 \, \sqrt{x e + d} c^{4} d^{6} e - 36 \, {\left(x e + d\right)}^{\frac{7}{2}} b c^{3} d^{2} e^{2} + 144 \, {\left(x e + d\right)}^{\frac{5}{2}} b c^{3} d^{3} e^{2} - 180 \, {\left(x e + d\right)}^{\frac{3}{2}} b c^{3} d^{4} e^{2} + 72 \, \sqrt{x e + d} b c^{3} d^{5} e^{2} + 10 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{2} c^{2} d e^{3} - 85 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{2} c^{2} d^{2} e^{3} + 148 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{2} c^{2} d^{3} e^{3} - 73 \, \sqrt{x e + d} b^{2} c^{2} d^{4} e^{3} + {\left(x e + d\right)}^{\frac{7}{2}} b^{3} c e^{4} + 13 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{3} c d e^{4} - 42 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{3} c d^{2} e^{4} + 26 \, \sqrt{x e + d} b^{3} c d^{3} e^{4} - {\left(x e + d\right)}^{\frac{5}{2}} b^{4} e^{5} + 2 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{4} d e^{5} - \sqrt{x e + d} b^{4} d^{2} e^{5}}{4 \, {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + {\left(x e + d\right)} b e - b d e\right)}^{2} b^{4} c}"," ",0,"1/4*(48*c^2*d^4 - 84*b*c*d^3*e + 35*b^2*d^2*e^2)*arctan(sqrt(x*e + d)/sqrt(-d))/(b^5*sqrt(-d)) - 1/4*(48*c^4*d^4 - 108*b*c^3*d^3*e + 71*b^2*c^2*d^2*e^2 - 10*b^3*c*d*e^3 - b^4*e^4)*arctan(sqrt(x*e + d)*c/sqrt(-c^2*d + b*c*e))/(sqrt(-c^2*d + b*c*e)*b^5*c) + 1/4*(24*(x*e + d)^(7/2)*c^4*d^3*e - 72*(x*e + d)^(5/2)*c^4*d^4*e + 72*(x*e + d)^(3/2)*c^4*d^5*e - 24*sqrt(x*e + d)*c^4*d^6*e - 36*(x*e + d)^(7/2)*b*c^3*d^2*e^2 + 144*(x*e + d)^(5/2)*b*c^3*d^3*e^2 - 180*(x*e + d)^(3/2)*b*c^3*d^4*e^2 + 72*sqrt(x*e + d)*b*c^3*d^5*e^2 + 10*(x*e + d)^(7/2)*b^2*c^2*d*e^3 - 85*(x*e + d)^(5/2)*b^2*c^2*d^2*e^3 + 148*(x*e + d)^(3/2)*b^2*c^2*d^3*e^3 - 73*sqrt(x*e + d)*b^2*c^2*d^4*e^3 + (x*e + d)^(7/2)*b^3*c*e^4 + 13*(x*e + d)^(5/2)*b^3*c*d*e^4 - 42*(x*e + d)^(3/2)*b^3*c*d^2*e^4 + 26*sqrt(x*e + d)*b^3*c*d^3*e^4 - (x*e + d)^(5/2)*b^4*e^5 + 2*(x*e + d)^(3/2)*b^4*d*e^5 - sqrt(x*e + d)*b^4*d^2*e^5)/(((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + (x*e + d)*b*e - b*d*e)^2*b^4*c)","B",0
380,1,448,0,0.252517," ","integrate((e*x+d)^(5/2)/(c*x^2+b*x)^3,x, algorithm=""giac"")","-\frac{3 \, {\left(16 \, c^{3} d^{3} - 28 \, b c^{2} d^{2} e + 13 \, b^{2} c d e^{2} - b^{3} e^{3}\right)} \arctan\left(\frac{\sqrt{x e + d} c}{\sqrt{-c^{2} d + b c e}}\right)}{4 \, \sqrt{-c^{2} d + b c e} b^{5}} + \frac{3 \, {\left(16 \, c^{2} d^{3} - 20 \, b c d^{2} e + 5 \, b^{2} d e^{2}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-d}}\right)}{4 \, b^{5} \sqrt{-d}} + \frac{24 \, {\left(x e + d\right)}^{\frac{7}{2}} c^{3} d^{2} e - 72 \, {\left(x e + d\right)}^{\frac{5}{2}} c^{3} d^{3} e + 72 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{3} d^{4} e - 24 \, \sqrt{x e + d} c^{3} d^{5} e - 24 \, {\left(x e + d\right)}^{\frac{7}{2}} b c^{2} d e^{2} + 108 \, {\left(x e + d\right)}^{\frac{5}{2}} b c^{2} d^{2} e^{2} - 144 \, {\left(x e + d\right)}^{\frac{3}{2}} b c^{2} d^{3} e^{2} + 60 \, \sqrt{x e + d} b c^{2} d^{4} e^{2} + 3 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{2} c e^{3} - 46 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{2} c d e^{3} + 91 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{2} c d^{2} e^{3} - 48 \, \sqrt{x e + d} b^{2} c d^{3} e^{3} + 5 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{3} e^{4} - 19 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{3} d e^{4} + 12 \, \sqrt{x e + d} b^{3} d^{2} e^{4}}{4 \, {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + {\left(x e + d\right)} b e - b d e\right)}^{2} b^{4}}"," ",0,"-3/4*(16*c^3*d^3 - 28*b*c^2*d^2*e + 13*b^2*c*d*e^2 - b^3*e^3)*arctan(sqrt(x*e + d)*c/sqrt(-c^2*d + b*c*e))/(sqrt(-c^2*d + b*c*e)*b^5) + 3/4*(16*c^2*d^3 - 20*b*c*d^2*e + 5*b^2*d*e^2)*arctan(sqrt(x*e + d)/sqrt(-d))/(b^5*sqrt(-d)) + 1/4*(24*(x*e + d)^(7/2)*c^3*d^2*e - 72*(x*e + d)^(5/2)*c^3*d^3*e + 72*(x*e + d)^(3/2)*c^3*d^4*e - 24*sqrt(x*e + d)*c^3*d^5*e - 24*(x*e + d)^(7/2)*b*c^2*d*e^2 + 108*(x*e + d)^(5/2)*b*c^2*d^2*e^2 - 144*(x*e + d)^(3/2)*b*c^2*d^3*e^2 + 60*sqrt(x*e + d)*b*c^2*d^4*e^2 + 3*(x*e + d)^(7/2)*b^2*c*e^3 - 46*(x*e + d)^(5/2)*b^2*c*d*e^3 + 91*(x*e + d)^(3/2)*b^2*c*d^2*e^3 - 48*sqrt(x*e + d)*b^2*c*d^3*e^3 + 5*(x*e + d)^(5/2)*b^3*e^4 - 19*(x*e + d)^(3/2)*b^3*d*e^4 + 12*sqrt(x*e + d)*b^3*d^2*e^4)/(((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + (x*e + d)*b*e - b*d*e)^2*b^4)","B",0
381,1,392,0,0.232838," ","integrate((e*x+d)^(3/2)/(c*x^2+b*x)^3,x, algorithm=""giac"")","-\frac{3 \, {\left(16 \, c^{3} d^{2} - 20 \, b c^{2} d e + 5 \, b^{2} c e^{2}\right)} \arctan\left(\frac{\sqrt{x e + d} c}{\sqrt{-c^{2} d + b c e}}\right)}{4 \, \sqrt{-c^{2} d + b c e} b^{5}} + \frac{3 \, {\left(16 \, c^{2} d^{2} - 12 \, b c d e + b^{2} e^{2}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-d}}\right)}{4 \, b^{5} \sqrt{-d}} + \frac{24 \, {\left(x e + d\right)}^{\frac{7}{2}} c^{3} d e - 72 \, {\left(x e + d\right)}^{\frac{5}{2}} c^{3} d^{2} e + 72 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{3} d^{3} e - 24 \, \sqrt{x e + d} c^{3} d^{4} e - 12 \, {\left(x e + d\right)}^{\frac{7}{2}} b c^{2} e^{2} + 72 \, {\left(x e + d\right)}^{\frac{5}{2}} b c^{2} d e^{2} - 108 \, {\left(x e + d\right)}^{\frac{3}{2}} b c^{2} d^{2} e^{2} + 48 \, \sqrt{x e + d} b c^{2} d^{3} e^{2} - 19 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{2} c e^{3} + 46 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{2} c d e^{3} - 27 \, \sqrt{x e + d} b^{2} c d^{2} e^{3} - 5 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{3} e^{4} + 3 \, \sqrt{x e + d} b^{3} d e^{4}}{4 \, {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + {\left(x e + d\right)} b e - b d e\right)}^{2} b^{4}}"," ",0,"-3/4*(16*c^3*d^2 - 20*b*c^2*d*e + 5*b^2*c*e^2)*arctan(sqrt(x*e + d)*c/sqrt(-c^2*d + b*c*e))/(sqrt(-c^2*d + b*c*e)*b^5) + 3/4*(16*c^2*d^2 - 12*b*c*d*e + b^2*e^2)*arctan(sqrt(x*e + d)/sqrt(-d))/(b^5*sqrt(-d)) + 1/4*(24*(x*e + d)^(7/2)*c^3*d*e - 72*(x*e + d)^(5/2)*c^3*d^2*e + 72*(x*e + d)^(3/2)*c^3*d^3*e - 24*sqrt(x*e + d)*c^3*d^4*e - 12*(x*e + d)^(7/2)*b*c^2*e^2 + 72*(x*e + d)^(5/2)*b*c^2*d*e^2 - 108*(x*e + d)^(3/2)*b*c^2*d^2*e^2 + 48*sqrt(x*e + d)*b*c^2*d^3*e^2 - 19*(x*e + d)^(5/2)*b^2*c*e^3 + 46*(x*e + d)^(3/2)*b^2*c*d*e^3 - 27*sqrt(x*e + d)*b^2*c*d^2*e^3 - 5*(x*e + d)^(3/2)*b^3*e^4 + 3*sqrt(x*e + d)*b^3*d*e^4)/(((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + (x*e + d)*b*e - b*d*e)^2*b^4)","A",0
382,1,508,0,0.245468," ","integrate((e*x+d)^(1/2)/(c*x^2+b*x)^3,x, algorithm=""giac"")","-\frac{{\left(48 \, c^{4} d^{2} - 84 \, b c^{3} d e + 35 \, b^{2} c^{2} e^{2}\right)} \arctan\left(\frac{\sqrt{x e + d} c}{\sqrt{-c^{2} d + b c e}}\right)}{4 \, {\left(b^{5} c d - b^{6} e\right)} \sqrt{-c^{2} d + b c e}} + \frac{24 \, {\left(x e + d\right)}^{\frac{7}{2}} c^{4} d^{2} e - 72 \, {\left(x e + d\right)}^{\frac{5}{2}} c^{4} d^{3} e + 72 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{4} d^{4} e - 24 \, \sqrt{x e + d} c^{4} d^{5} e - 24 \, {\left(x e + d\right)}^{\frac{7}{2}} b c^{3} d e^{2} + 108 \, {\left(x e + d\right)}^{\frac{5}{2}} b c^{3} d^{2} e^{2} - 144 \, {\left(x e + d\right)}^{\frac{3}{2}} b c^{3} d^{3} e^{2} + 60 \, \sqrt{x e + d} b c^{3} d^{4} e^{2} + {\left(x e + d\right)}^{\frac{7}{2}} b^{2} c^{2} e^{3} - 40 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{2} c^{2} d e^{3} + 85 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{2} c^{2} d^{2} e^{3} - 46 \, \sqrt{x e + d} b^{2} c^{2} d^{3} e^{3} + 2 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{3} c e^{4} - 13 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{3} c d e^{4} + 9 \, \sqrt{x e + d} b^{3} c d^{2} e^{4} + {\left(x e + d\right)}^{\frac{3}{2}} b^{4} e^{5} + \sqrt{x e + d} b^{4} d e^{5}}{4 \, {\left(b^{4} c d^{2} - b^{5} d e\right)} {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + {\left(x e + d\right)} b e - b d e\right)}^{2}} + \frac{{\left(48 \, c^{2} d^{2} - 12 \, b c d e - b^{2} e^{2}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-d}}\right)}{4 \, b^{5} \sqrt{-d} d}"," ",0,"-1/4*(48*c^4*d^2 - 84*b*c^3*d*e + 35*b^2*c^2*e^2)*arctan(sqrt(x*e + d)*c/sqrt(-c^2*d + b*c*e))/((b^5*c*d - b^6*e)*sqrt(-c^2*d + b*c*e)) + 1/4*(24*(x*e + d)^(7/2)*c^4*d^2*e - 72*(x*e + d)^(5/2)*c^4*d^3*e + 72*(x*e + d)^(3/2)*c^4*d^4*e - 24*sqrt(x*e + d)*c^4*d^5*e - 24*(x*e + d)^(7/2)*b*c^3*d*e^2 + 108*(x*e + d)^(5/2)*b*c^3*d^2*e^2 - 144*(x*e + d)^(3/2)*b*c^3*d^3*e^2 + 60*sqrt(x*e + d)*b*c^3*d^4*e^2 + (x*e + d)^(7/2)*b^2*c^2*e^3 - 40*(x*e + d)^(5/2)*b^2*c^2*d*e^3 + 85*(x*e + d)^(3/2)*b^2*c^2*d^2*e^3 - 46*sqrt(x*e + d)*b^2*c^2*d^3*e^3 + 2*(x*e + d)^(5/2)*b^3*c*e^4 - 13*(x*e + d)^(3/2)*b^3*c*d*e^4 + 9*sqrt(x*e + d)*b^3*c*d^2*e^4 + (x*e + d)^(3/2)*b^4*e^5 + sqrt(x*e + d)*b^4*d*e^5)/((b^4*c*d^2 - b^5*d*e)*((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + (x*e + d)*b*e - b*d*e)^2) + 1/4*(48*c^2*d^2 - 12*b*c*d*e - b^2*e^2)*arctan(sqrt(x*e + d)/sqrt(-d))/(b^5*sqrt(-d)*d)","B",0
383,1,619,0,0.221134," ","integrate(1/(e*x+d)^(1/2)/(c*x^2+b*x)^3,x, algorithm=""giac"")","-\frac{3 \, {\left(16 \, c^{5} d^{2} - 36 \, b c^{4} d e + 21 \, b^{2} c^{3} e^{2}\right)} \arctan\left(\frac{\sqrt{x e + d} c}{\sqrt{-c^{2} d + b c e}}\right)}{4 \, {\left(b^{5} c^{2} d^{2} - 2 \, b^{6} c d e + b^{7} e^{2}\right)} \sqrt{-c^{2} d + b c e}} + \frac{24 \, {\left(x e + d\right)}^{\frac{7}{2}} c^{5} d^{3} e - 72 \, {\left(x e + d\right)}^{\frac{5}{2}} c^{5} d^{4} e + 72 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{5} d^{5} e - 24 \, \sqrt{x e + d} c^{5} d^{6} e - 36 \, {\left(x e + d\right)}^{\frac{7}{2}} b c^{4} d^{2} e^{2} + 144 \, {\left(x e + d\right)}^{\frac{5}{2}} b c^{4} d^{3} e^{2} - 180 \, {\left(x e + d\right)}^{\frac{3}{2}} b c^{4} d^{4} e^{2} + 72 \, \sqrt{x e + d} b c^{4} d^{5} e^{2} + 6 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{2} c^{3} d e^{3} - 73 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{2} c^{3} d^{2} e^{3} + 136 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{2} c^{3} d^{3} e^{3} - 69 \, \sqrt{x e + d} b^{2} c^{3} d^{4} e^{3} + 3 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{3} c^{2} e^{4} + {\left(x e + d\right)}^{\frac{5}{2}} b^{3} c^{2} d e^{4} - 24 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{3} c^{2} d^{2} e^{4} + 18 \, \sqrt{x e + d} b^{3} c^{2} d^{3} e^{4} + 6 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{4} c e^{5} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{4} c d e^{5} + 8 \, \sqrt{x e + d} b^{4} c d^{2} e^{5} + 3 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{5} e^{6} - 5 \, \sqrt{x e + d} b^{5} d e^{6}}{4 \, {\left(b^{4} c^{2} d^{4} - 2 \, b^{5} c d^{3} e + b^{6} d^{2} e^{2}\right)} {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + {\left(x e + d\right)} b e - b d e\right)}^{2}} + \frac{3 \, {\left(16 \, c^{2} d^{2} + 4 \, b c d e + b^{2} e^{2}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-d}}\right)}{4 \, b^{5} \sqrt{-d} d^{2}}"," ",0,"-3/4*(16*c^5*d^2 - 36*b*c^4*d*e + 21*b^2*c^3*e^2)*arctan(sqrt(x*e + d)*c/sqrt(-c^2*d + b*c*e))/((b^5*c^2*d^2 - 2*b^6*c*d*e + b^7*e^2)*sqrt(-c^2*d + b*c*e)) + 1/4*(24*(x*e + d)^(7/2)*c^5*d^3*e - 72*(x*e + d)^(5/2)*c^5*d^4*e + 72*(x*e + d)^(3/2)*c^5*d^5*e - 24*sqrt(x*e + d)*c^5*d^6*e - 36*(x*e + d)^(7/2)*b*c^4*d^2*e^2 + 144*(x*e + d)^(5/2)*b*c^4*d^3*e^2 - 180*(x*e + d)^(3/2)*b*c^4*d^4*e^2 + 72*sqrt(x*e + d)*b*c^4*d^5*e^2 + 6*(x*e + d)^(7/2)*b^2*c^3*d*e^3 - 73*(x*e + d)^(5/2)*b^2*c^3*d^2*e^3 + 136*(x*e + d)^(3/2)*b^2*c^3*d^3*e^3 - 69*sqrt(x*e + d)*b^2*c^3*d^4*e^3 + 3*(x*e + d)^(7/2)*b^3*c^2*e^4 + (x*e + d)^(5/2)*b^3*c^2*d*e^4 - 24*(x*e + d)^(3/2)*b^3*c^2*d^2*e^4 + 18*sqrt(x*e + d)*b^3*c^2*d^3*e^4 + 6*(x*e + d)^(5/2)*b^4*c*e^5 - 10*(x*e + d)^(3/2)*b^4*c*d*e^5 + 8*sqrt(x*e + d)*b^4*c*d^2*e^5 + 3*(x*e + d)^(3/2)*b^5*e^6 - 5*sqrt(x*e + d)*b^5*d*e^6)/((b^4*c^2*d^4 - 2*b^5*c*d^3*e + b^6*d^2*e^2)*((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + (x*e + d)*b*e - b*d*e)^2) + 3/4*(16*c^2*d^2 + 4*b*c*d*e + b^2*e^2)*arctan(sqrt(x*e + d)/sqrt(-d))/(b^5*sqrt(-d)*d^2)","B",0
384,1,787,0,0.279627," ","integrate(1/(e*x+d)^(3/2)/(c*x^2+b*x)^3,x, algorithm=""giac"")","-\frac{3 \, {\left(16 \, c^{6} d^{2} - 44 \, b c^{5} d e + 33 \, b^{2} c^{4} e^{2}\right)} \arctan\left(\frac{\sqrt{x e + d} c}{\sqrt{-c^{2} d + b c e}}\right)}{4 \, {\left(b^{5} c^{3} d^{3} - 3 \, b^{6} c^{2} d^{2} e + 3 \, b^{7} c d e^{2} - b^{8} e^{3}\right)} \sqrt{-c^{2} d + b c e}} - \frac{2 \, e^{5}}{{\left(c^{3} d^{6} - 3 \, b c^{2} d^{5} e + 3 \, b^{2} c d^{4} e^{2} - b^{3} d^{3} e^{3}\right)} \sqrt{x e + d}} + \frac{24 \, {\left(x e + d\right)}^{\frac{7}{2}} c^{6} d^{4} e - 72 \, {\left(x e + d\right)}^{\frac{5}{2}} c^{6} d^{5} e + 72 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{6} d^{6} e - 24 \, \sqrt{x e + d} c^{6} d^{7} e - 48 \, {\left(x e + d\right)}^{\frac{7}{2}} b c^{5} d^{3} e^{2} + 180 \, {\left(x e + d\right)}^{\frac{5}{2}} b c^{5} d^{4} e^{2} - 216 \, {\left(x e + d\right)}^{\frac{3}{2}} b c^{5} d^{5} e^{2} + 84 \, \sqrt{x e + d} b c^{5} d^{6} e^{2} + 15 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{2} c^{4} d^{2} e^{3} - 118 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{2} c^{4} d^{3} e^{3} + 199 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{2} c^{4} d^{4} e^{3} - 96 \, \sqrt{x e + d} b^{2} c^{4} d^{5} e^{3} + 9 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{3} c^{3} d e^{4} - 3 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{3} c^{3} d^{2} e^{4} - 38 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{3} c^{3} d^{3} e^{4} + 30 \, \sqrt{x e + d} b^{3} c^{3} d^{4} e^{4} - 7 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{4} c^{2} e^{5} + 41 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{4} c^{2} d e^{5} - 58 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{4} c^{2} d^{2} e^{5} + 30 \, \sqrt{x e + d} b^{4} c^{2} d^{3} e^{5} - 14 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{5} c e^{6} + 41 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{5} c d e^{6} - 33 \, \sqrt{x e + d} b^{5} c d^{2} e^{6} - 7 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{6} e^{7} + 9 \, \sqrt{x e + d} b^{6} d e^{7}}{4 \, {\left(b^{4} c^{3} d^{6} - 3 \, b^{5} c^{2} d^{5} e + 3 \, b^{6} c d^{4} e^{2} - b^{7} d^{3} e^{3}\right)} {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + {\left(x e + d\right)} b e - b d e\right)}^{2}} + \frac{3 \, {\left(16 \, c^{2} d^{2} + 12 \, b c d e + 5 \, b^{2} e^{2}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-d}}\right)}{4 \, b^{5} \sqrt{-d} d^{3}}"," ",0,"-3/4*(16*c^6*d^2 - 44*b*c^5*d*e + 33*b^2*c^4*e^2)*arctan(sqrt(x*e + d)*c/sqrt(-c^2*d + b*c*e))/((b^5*c^3*d^3 - 3*b^6*c^2*d^2*e + 3*b^7*c*d*e^2 - b^8*e^3)*sqrt(-c^2*d + b*c*e)) - 2*e^5/((c^3*d^6 - 3*b*c^2*d^5*e + 3*b^2*c*d^4*e^2 - b^3*d^3*e^3)*sqrt(x*e + d)) + 1/4*(24*(x*e + d)^(7/2)*c^6*d^4*e - 72*(x*e + d)^(5/2)*c^6*d^5*e + 72*(x*e + d)^(3/2)*c^6*d^6*e - 24*sqrt(x*e + d)*c^6*d^7*e - 48*(x*e + d)^(7/2)*b*c^5*d^3*e^2 + 180*(x*e + d)^(5/2)*b*c^5*d^4*e^2 - 216*(x*e + d)^(3/2)*b*c^5*d^5*e^2 + 84*sqrt(x*e + d)*b*c^5*d^6*e^2 + 15*(x*e + d)^(7/2)*b^2*c^4*d^2*e^3 - 118*(x*e + d)^(5/2)*b^2*c^4*d^3*e^3 + 199*(x*e + d)^(3/2)*b^2*c^4*d^4*e^3 - 96*sqrt(x*e + d)*b^2*c^4*d^5*e^3 + 9*(x*e + d)^(7/2)*b^3*c^3*d*e^4 - 3*(x*e + d)^(5/2)*b^3*c^3*d^2*e^4 - 38*(x*e + d)^(3/2)*b^3*c^3*d^3*e^4 + 30*sqrt(x*e + d)*b^3*c^3*d^4*e^4 - 7*(x*e + d)^(7/2)*b^4*c^2*e^5 + 41*(x*e + d)^(5/2)*b^4*c^2*d*e^5 - 58*(x*e + d)^(3/2)*b^4*c^2*d^2*e^5 + 30*sqrt(x*e + d)*b^4*c^2*d^3*e^5 - 14*(x*e + d)^(5/2)*b^5*c*e^6 + 41*(x*e + d)^(3/2)*b^5*c*d*e^6 - 33*sqrt(x*e + d)*b^5*c*d^2*e^6 - 7*(x*e + d)^(3/2)*b^6*e^7 + 9*sqrt(x*e + d)*b^6*d*e^7)/((b^4*c^3*d^6 - 3*b^5*c^2*d^5*e + 3*b^6*c*d^4*e^2 - b^7*d^3*e^3)*((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + (x*e + d)*b*e - b*d*e)^2) + 3/4*(16*c^2*d^2 + 12*b*c*d*e + 5*b^2*e^2)*arctan(sqrt(x*e + d)/sqrt(-d))/(b^5*sqrt(-d)*d^3)","B",0
385,1,942,0,0.733735," ","integrate(1/(e*x+d)^(5/2)/(c*x^2+b*x)^3,x, algorithm=""giac"")","-\frac{{\left(48 \, c^{7} d^{2} - 156 \, b c^{6} d e + 143 \, b^{2} c^{5} e^{2}\right)} \arctan\left(\frac{\sqrt{x e + d} c}{\sqrt{-c^{2} d + b c e}}\right)}{4 \, {\left(b^{5} c^{4} d^{4} - 4 \, b^{6} c^{3} d^{3} e + 6 \, b^{7} c^{2} d^{2} e^{2} - 4 \, b^{8} c d e^{3} + b^{9} e^{4}\right)} \sqrt{-c^{2} d + b c e}} - \frac{2 \, {\left(18 \, {\left(x e + d\right)} c d e^{5} + c d^{2} e^{5} - 9 \, {\left(x e + d\right)} b e^{6} - b d e^{6}\right)}}{3 \, {\left(c^{4} d^{8} - 4 \, b c^{3} d^{7} e + 6 \, b^{2} c^{2} d^{6} e^{2} - 4 \, b^{3} c d^{5} e^{3} + b^{4} d^{4} e^{4}\right)} {\left(x e + d\right)}^{\frac{3}{2}}} + \frac{24 \, {\left(x e + d\right)}^{\frac{7}{2}} c^{7} d^{5} e - 72 \, {\left(x e + d\right)}^{\frac{5}{2}} c^{7} d^{6} e + 72 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{7} d^{7} e - 24 \, \sqrt{x e + d} c^{7} d^{8} e - 60 \, {\left(x e + d\right)}^{\frac{7}{2}} b c^{6} d^{4} e^{2} + 216 \, {\left(x e + d\right)}^{\frac{5}{2}} b c^{6} d^{5} e^{2} - 252 \, {\left(x e + d\right)}^{\frac{3}{2}} b c^{6} d^{6} e^{2} + 96 \, \sqrt{x e + d} b c^{6} d^{7} e^{2} + 28 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{2} c^{5} d^{3} e^{3} - 175 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{2} c^{5} d^{4} e^{3} + 274 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{2} c^{5} d^{5} e^{3} - 127 \, \sqrt{x e + d} b^{2} c^{5} d^{6} e^{3} + 18 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{3} c^{4} d^{2} e^{4} - 10 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{3} c^{4} d^{3} e^{4} - 55 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{3} c^{4} d^{4} e^{4} + 45 \, \sqrt{x e + d} b^{3} c^{4} d^{5} e^{4} - 32 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{4} c^{3} d e^{5} + 140 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{4} c^{3} d^{2} e^{5} - 180 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{4} c^{3} d^{3} e^{5} + 80 \, \sqrt{x e + d} b^{4} c^{3} d^{4} e^{5} + 11 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{5} c^{2} e^{6} - 99 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{5} c^{2} d e^{6} + 199 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{5} c^{2} d^{2} e^{6} - 123 \, \sqrt{x e + d} b^{5} c^{2} d^{3} e^{6} + 22 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{6} c e^{7} - 80 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{6} c d e^{7} + 66 \, \sqrt{x e + d} b^{6} c d^{2} e^{7} + 11 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{7} e^{8} - 13 \, \sqrt{x e + d} b^{7} d e^{8}}{4 \, {\left(b^{4} c^{4} d^{8} - 4 \, b^{5} c^{3} d^{7} e + 6 \, b^{6} c^{2} d^{6} e^{2} - 4 \, b^{7} c d^{5} e^{3} + b^{8} d^{4} e^{4}\right)} {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + {\left(x e + d\right)} b e - b d e\right)}^{2}} + \frac{{\left(48 \, c^{2} d^{2} + 60 \, b c d e + 35 \, b^{2} e^{2}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-d}}\right)}{4 \, b^{5} \sqrt{-d} d^{4}}"," ",0,"-1/4*(48*c^7*d^2 - 156*b*c^6*d*e + 143*b^2*c^5*e^2)*arctan(sqrt(x*e + d)*c/sqrt(-c^2*d + b*c*e))/((b^5*c^4*d^4 - 4*b^6*c^3*d^3*e + 6*b^7*c^2*d^2*e^2 - 4*b^8*c*d*e^3 + b^9*e^4)*sqrt(-c^2*d + b*c*e)) - 2/3*(18*(x*e + d)*c*d*e^5 + c*d^2*e^5 - 9*(x*e + d)*b*e^6 - b*d*e^6)/((c^4*d^8 - 4*b*c^3*d^7*e + 6*b^2*c^2*d^6*e^2 - 4*b^3*c*d^5*e^3 + b^4*d^4*e^4)*(x*e + d)^(3/2)) + 1/4*(24*(x*e + d)^(7/2)*c^7*d^5*e - 72*(x*e + d)^(5/2)*c^7*d^6*e + 72*(x*e + d)^(3/2)*c^7*d^7*e - 24*sqrt(x*e + d)*c^7*d^8*e - 60*(x*e + d)^(7/2)*b*c^6*d^4*e^2 + 216*(x*e + d)^(5/2)*b*c^6*d^5*e^2 - 252*(x*e + d)^(3/2)*b*c^6*d^6*e^2 + 96*sqrt(x*e + d)*b*c^6*d^7*e^2 + 28*(x*e + d)^(7/2)*b^2*c^5*d^3*e^3 - 175*(x*e + d)^(5/2)*b^2*c^5*d^4*e^3 + 274*(x*e + d)^(3/2)*b^2*c^5*d^5*e^3 - 127*sqrt(x*e + d)*b^2*c^5*d^6*e^3 + 18*(x*e + d)^(7/2)*b^3*c^4*d^2*e^4 - 10*(x*e + d)^(5/2)*b^3*c^4*d^3*e^4 - 55*(x*e + d)^(3/2)*b^3*c^4*d^4*e^4 + 45*sqrt(x*e + d)*b^3*c^4*d^5*e^4 - 32*(x*e + d)^(7/2)*b^4*c^3*d*e^5 + 140*(x*e + d)^(5/2)*b^4*c^3*d^2*e^5 - 180*(x*e + d)^(3/2)*b^4*c^3*d^3*e^5 + 80*sqrt(x*e + d)*b^4*c^3*d^4*e^5 + 11*(x*e + d)^(7/2)*b^5*c^2*e^6 - 99*(x*e + d)^(5/2)*b^5*c^2*d*e^6 + 199*(x*e + d)^(3/2)*b^5*c^2*d^2*e^6 - 123*sqrt(x*e + d)*b^5*c^2*d^3*e^6 + 22*(x*e + d)^(5/2)*b^6*c*e^7 - 80*(x*e + d)^(3/2)*b^6*c*d*e^7 + 66*sqrt(x*e + d)*b^6*c*d^2*e^7 + 11*(x*e + d)^(3/2)*b^7*e^8 - 13*sqrt(x*e + d)*b^7*d*e^8)/((b^4*c^4*d^8 - 4*b^5*c^3*d^7*e + 6*b^6*c^2*d^6*e^2 - 4*b^7*c*d^5*e^3 + b^8*d^4*e^4)*((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + (x*e + d)*b*e - b*d*e)^2) + 1/4*(48*c^2*d^2 + 60*b*c*d*e + 35*b^2*e^2)*arctan(sqrt(x*e + d)/sqrt(-d))/(b^5*sqrt(-d)*d^4)","B",0
386,0,0,0,0.000000," ","integrate((e*x+d)^(3/2)*(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\int \sqrt{c x^{2} + b x} {\left(e x + d\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + b*x)*(e*x + d)^(3/2), x)","F",0
387,0,0,0,0.000000," ","integrate((e*x+d)^(1/2)*(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\int \sqrt{c x^{2} + b x} \sqrt{e x + d}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + b*x)*sqrt(e*x + d), x)","F",0
388,0,0,0,0.000000," ","integrate((c*x^2+b*x)^(1/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{c x^{2} + b x}}{\sqrt{e x + d}}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + b*x)/sqrt(e*x + d), x)","F",0
389,0,0,0,0.000000," ","integrate((c*x^2+b*x)^(1/2)/(e*x+d)^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{c x^{2} + b x}}{{\left(e x + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + b*x)/(e*x + d)^(3/2), x)","F",0
390,0,0,0,0.000000," ","integrate((c*x^2+b*x)^(1/2)/(e*x+d)^(5/2),x, algorithm=""giac"")","\int \frac{\sqrt{c x^{2} + b x}}{{\left(e x + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + b*x)/(e*x + d)^(5/2), x)","F",0
391,0,0,0,0.000000," ","integrate((c*x^2+b*x)^(1/2)/(e*x+d)^(7/2),x, algorithm=""giac"")","\int \frac{\sqrt{c x^{2} + b x}}{{\left(e x + d\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + b*x)/(e*x + d)^(7/2), x)","F",0
392,0,0,0,0.000000," ","integrate((e*x+d)^(3/2)*(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","\int {\left(c x^{2} + b x\right)}^{\frac{3}{2}} {\left(e x + d\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((c*x^2 + b*x)^(3/2)*(e*x + d)^(3/2), x)","F",0
393,0,0,0,0.000000," ","integrate((c*x^2+b*x)^(3/2)*(e*x+d)^(1/2),x, algorithm=""giac"")","\int {\left(c x^{2} + b x\right)}^{\frac{3}{2}} \sqrt{e x + d}\,{d x}"," ",0,"integrate((c*x^2 + b*x)^(3/2)*sqrt(e*x + d), x)","F",0
394,0,0,0,0.000000," ","integrate((c*x^2+b*x)^(3/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x\right)}^{\frac{3}{2}}}{\sqrt{e x + d}}\,{d x}"," ",0,"integrate((c*x^2 + b*x)^(3/2)/sqrt(e*x + d), x)","F",0
395,0,0,0,0.000000," ","integrate((c*x^2+b*x)^(3/2)/(e*x+d)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x\right)}^{\frac{3}{2}}}{{\left(e x + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c*x^2 + b*x)^(3/2)/(e*x + d)^(3/2), x)","F",0
396,0,0,0,0.000000," ","integrate((c*x^2+b*x)^(3/2)/(e*x+d)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x\right)}^{\frac{3}{2}}}{{\left(e x + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((c*x^2 + b*x)^(3/2)/(e*x + d)^(5/2), x)","F",0
397,-2,0,0,0.000000," ","integrate((c*x^2+b*x)^(3/2)/(e*x+d)^(7/2),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(d*exp(1)+x*exp(1)^2)]Evaluation time: 2.84Unable to transpose Error: Bad Argument Value","F(-2)",0
398,0,0,0,0.000000," ","integrate((c*x^2+b*x)^(3/2)/(e*x+d)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x\right)}^{\frac{3}{2}}}{{\left(e x + d\right)}^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((c*x^2 + b*x)^(3/2)/(e*x + d)^(9/2), x)","F",0
399,0,0,0,0.000000," ","integrate((c*x^2+b*x)^(5/2)*(e*x+d)^(1/2),x, algorithm=""giac"")","\int {\left(c x^{2} + b x\right)}^{\frac{5}{2}} \sqrt{e x + d}\,{d x}"," ",0,"integrate((c*x^2 + b*x)^(5/2)*sqrt(e*x + d), x)","F",0
400,0,0,0,0.000000," ","integrate((c*x^2+b*x)^(5/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x\right)}^{\frac{5}{2}}}{\sqrt{e x + d}}\,{d x}"," ",0,"integrate((c*x^2 + b*x)^(5/2)/sqrt(e*x + d), x)","F",0
401,0,0,0,0.000000," ","integrate((c*x^2+b*x)^(5/2)/(e*x+d)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x\right)}^{\frac{5}{2}}}{{\left(e x + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c*x^2 + b*x)^(5/2)/(e*x + d)^(3/2), x)","F",0
402,0,0,0,0.000000," ","integrate((c*x^2+b*x)^(5/2)/(e*x+d)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x\right)}^{\frac{5}{2}}}{{\left(e x + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((c*x^2 + b*x)^(5/2)/(e*x + d)^(5/2), x)","F",0
403,0,0,0,0.000000," ","integrate((c*x^2+b*x)^(5/2)/(e*x+d)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x\right)}^{\frac{5}{2}}}{{\left(e x + d\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((c*x^2 + b*x)^(5/2)/(e*x + d)^(7/2), x)","F",0
404,0,0,0,0.000000," ","integrate((c*x^2+b*x)^(5/2)/(e*x+d)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x\right)}^{\frac{5}{2}}}{{\left(e x + d\right)}^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((c*x^2 + b*x)^(5/2)/(e*x + d)^(9/2), x)","F",0
405,-2,0,0,0.000000," ","integrate((c*x^2+b*x)^(5/2)/(e*x+d)^(11/2),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(d*exp(1)+x*exp(1)^2)]Evaluation time: 5.12Unable to transpose Error: Bad Argument Value","F(-2)",0
406,0,0,0,0.000000," ","integrate((e*x+d)^(7/2)/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{\frac{7}{2}}}{\sqrt{c x^{2} + b x}}\,{d x}"," ",0,"integrate((e*x + d)^(7/2)/sqrt(c*x^2 + b*x), x)","F",0
407,0,0,0,0.000000," ","integrate((e*x+d)^(5/2)/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{\frac{5}{2}}}{\sqrt{c x^{2} + b x}}\,{d x}"," ",0,"integrate((e*x + d)^(5/2)/sqrt(c*x^2 + b*x), x)","F",0
408,0,0,0,0.000000," ","integrate((e*x+d)^(3/2)/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{\frac{3}{2}}}{\sqrt{c x^{2} + b x}}\,{d x}"," ",0,"integrate((e*x + d)^(3/2)/sqrt(c*x^2 + b*x), x)","F",0
409,0,0,0,0.000000," ","integrate((e*x+d)^(1/2)/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{e x + d}}{\sqrt{c x^{2} + b x}}\,{d x}"," ",0,"integrate(sqrt(e*x + d)/sqrt(c*x^2 + b*x), x)","F",0
410,0,0,0,0.000000," ","integrate(1/(e*x+d)^(1/2)/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{c x^{2} + b x} \sqrt{e x + d}}\,{d x}"," ",0,"integrate(1/(sqrt(c*x^2 + b*x)*sqrt(e*x + d)), x)","F",0
411,0,0,0,0.000000," ","integrate(1/(e*x+d)^(3/2)/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{c x^{2} + b x} {\left(e x + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(c*x^2 + b*x)*(e*x + d)^(3/2)), x)","F",0
412,0,0,0,0.000000," ","integrate(1/(e*x+d)^(5/2)/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{c x^{2} + b x} {\left(e x + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(c*x^2 + b*x)*(e*x + d)^(5/2)), x)","F",0
413,0,0,0,0.000000," ","integrate(1/(e*x+d)^(7/2)/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{c x^{2} + b x} {\left(e x + d\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(c*x^2 + b*x)*(e*x + d)^(7/2)), x)","F",0
414,0,0,0,0.000000," ","integrate((e*x+d)^(7/2)/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{\frac{7}{2}}}{{\left(c x^{2} + b x\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((e*x + d)^(7/2)/(c*x^2 + b*x)^(3/2), x)","F",0
415,0,0,0,0.000000," ","integrate((e*x+d)^(5/2)/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{\frac{5}{2}}}{{\left(c x^{2} + b x\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((e*x + d)^(5/2)/(c*x^2 + b*x)^(3/2), x)","F",0
416,0,0,0,0.000000," ","integrate((e*x+d)^(3/2)/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{\frac{3}{2}}}{{\left(c x^{2} + b x\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((e*x + d)^(3/2)/(c*x^2 + b*x)^(3/2), x)","F",0
417,0,0,0,0.000000," ","integrate((e*x+d)^(1/2)/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{e x + d}}{{\left(c x^{2} + b x\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(e*x + d)/(c*x^2 + b*x)^(3/2), x)","F",0
418,0,0,0,0.000000," ","integrate(1/(c*x^2+b*x)^(3/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{2} + b x\right)}^{\frac{3}{2}} \sqrt{e x + d}}\,{d x}"," ",0,"integrate(1/((c*x^2 + b*x)^(3/2)*sqrt(e*x + d)), x)","F",0
419,-2,0,0,0.000000," ","integrate(1/(e*x+d)^(3/2)/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Evaluation time: 1.17Unable to transpose Error: Bad Argument Value","F(-2)",0
420,-2,0,0,0.000000," ","integrate(1/(e*x+d)^(5/2)/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Evaluation time: 3.26Unable to transpose Error: Bad Argument Value","F(-2)",0
421,0,0,0,0.000000," ","integrate((e*x+d)^(9/2)/(c*x^2+b*x)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{\frac{9}{2}}}{{\left(c x^{2} + b x\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((e*x + d)^(9/2)/(c*x^2 + b*x)^(5/2), x)","F",0
422,0,0,0,0.000000," ","integrate((e*x+d)^(7/2)/(c*x^2+b*x)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{\frac{7}{2}}}{{\left(c x^{2} + b x\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((e*x + d)^(7/2)/(c*x^2 + b*x)^(5/2), x)","F",0
423,0,0,0,0.000000," ","integrate((e*x+d)^(5/2)/(c*x^2+b*x)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{\frac{5}{2}}}{{\left(c x^{2} + b x\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((e*x + d)^(5/2)/(c*x^2 + b*x)^(5/2), x)","F",0
424,0,0,0,0.000000," ","integrate((e*x+d)^(3/2)/(c*x^2+b*x)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{\frac{3}{2}}}{{\left(c x^{2} + b x\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((e*x + d)^(3/2)/(c*x^2 + b*x)^(5/2), x)","F",0
425,0,0,0,0.000000," ","integrate((e*x+d)^(1/2)/(c*x^2+b*x)^(5/2),x, algorithm=""giac"")","\int \frac{\sqrt{e x + d}}{{\left(c x^{2} + b x\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(e*x + d)/(c*x^2 + b*x)^(5/2), x)","F",0
426,0,0,0,0.000000," ","integrate(1/(c*x^2+b*x)^(5/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{2} + b x\right)}^{\frac{5}{2}} \sqrt{e x + d}}\,{d x}"," ",0,"integrate(1/((c*x^2 + b*x)^(5/2)*sqrt(e*x + d)), x)","F",0
427,-2,0,0,0.000000," ","integrate(1/(e*x+d)^(3/2)/(c*x^2+b*x)^(5/2),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Evaluation time: 2.52Unable to transpose Error: Bad Argument Value","F(-2)",0
428,0,0,0,0.000000," ","integrate((e*x+d)^(1/2)/(-3*x^2+2*x)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{e x + d}}{\sqrt{-3 \, x^{2} + 2 \, x}}\,{d x}"," ",0,"integrate(sqrt(e*x + d)/sqrt(-3*x^2 + 2*x), x)","F",0
429,0,0,0,0.000000," ","integrate(1/(e*x+d)^(1/2)/(-3*x^2+2*x)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{e x + d} \sqrt{-3 \, x^{2} + 2 \, x}}\,{d x}"," ",0,"integrate(1/(sqrt(e*x + d)*sqrt(-3*x^2 + 2*x)), x)","F",0
430,0,0,0,0.000000," ","integrate((e*x+d)^(1/2)/(-3*x^2-2*x)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{e x + d}}{\sqrt{-3 \, x^{2} - 2 \, x}}\,{d x}"," ",0,"integrate(sqrt(e*x + d)/sqrt(-3*x^2 - 2*x), x)","F",0
431,0,0,0,0.000000," ","integrate(1/(e*x+d)^(1/2)/(-3*x^2-2*x)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{e x + d} \sqrt{-3 \, x^{2} - 2 \, x}}\,{d x}"," ",0,"integrate(1/(sqrt(e*x + d)*sqrt(-3*x^2 - 2*x)), x)","F",0
432,0,0,0,0.000000," ","integrate((1-x)^(1/2)/(-x)^(1/2)/(1+x)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-x + 1}}{\sqrt{-x} \sqrt{x + 1}}\,{d x}"," ",0,"integrate(sqrt(-x + 1)/(sqrt(-x)*sqrt(x + 1)), x)","F",0
433,0,0,0,0.000000," ","integrate((1-x)^(1/2)/(-x^2-x)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-x + 1}}{\sqrt{-x^{2} - x}}\,{d x}"," ",0,"integrate(sqrt(-x + 1)/sqrt(-x^2 - x), x)","F",0
434,1,528,0,0.208226," ","integrate((e*x+d)^m*(c*e*x^2+c*d*x)^3,x, algorithm=""giac"")","\frac{{\left(x e + d\right)}^{m} c^{3} m^{3} x^{7} e^{7} + 4 \, {\left(x e + d\right)}^{m} c^{3} d m^{3} x^{6} e^{6} + 6 \, {\left(x e + d\right)}^{m} c^{3} d^{2} m^{3} x^{5} e^{5} + 4 \, {\left(x e + d\right)}^{m} c^{3} d^{3} m^{3} x^{4} e^{4} + {\left(x e + d\right)}^{m} c^{3} d^{4} m^{3} x^{3} e^{3} + 15 \, {\left(x e + d\right)}^{m} c^{3} m^{2} x^{7} e^{7} + 57 \, {\left(x e + d\right)}^{m} c^{3} d m^{2} x^{6} e^{6} + 78 \, {\left(x e + d\right)}^{m} c^{3} d^{2} m^{2} x^{5} e^{5} + 42 \, {\left(x e + d\right)}^{m} c^{3} d^{3} m^{2} x^{4} e^{4} + 3 \, {\left(x e + d\right)}^{m} c^{3} d^{4} m^{2} x^{3} e^{3} - 3 \, {\left(x e + d\right)}^{m} c^{3} d^{5} m^{2} x^{2} e^{2} + 74 \, {\left(x e + d\right)}^{m} c^{3} m x^{7} e^{7} + 269 \, {\left(x e + d\right)}^{m} c^{3} d m x^{6} e^{6} + 342 \, {\left(x e + d\right)}^{m} c^{3} d^{2} m x^{5} e^{5} + 158 \, {\left(x e + d\right)}^{m} c^{3} d^{3} m x^{4} e^{4} + 2 \, {\left(x e + d\right)}^{m} c^{3} d^{4} m x^{3} e^{3} - 3 \, {\left(x e + d\right)}^{m} c^{3} d^{5} m x^{2} e^{2} + 6 \, {\left(x e + d\right)}^{m} c^{3} d^{6} m x e + 120 \, {\left(x e + d\right)}^{m} c^{3} x^{7} e^{7} + 420 \, {\left(x e + d\right)}^{m} c^{3} d x^{6} e^{6} + 504 \, {\left(x e + d\right)}^{m} c^{3} d^{2} x^{5} e^{5} + 210 \, {\left(x e + d\right)}^{m} c^{3} d^{3} x^{4} e^{4} - 6 \, {\left(x e + d\right)}^{m} c^{3} d^{7}}{m^{4} e^{4} + 22 \, m^{3} e^{4} + 179 \, m^{2} e^{4} + 638 \, m e^{4} + 840 \, e^{4}}"," ",0,"((x*e + d)^m*c^3*m^3*x^7*e^7 + 4*(x*e + d)^m*c^3*d*m^3*x^6*e^6 + 6*(x*e + d)^m*c^3*d^2*m^3*x^5*e^5 + 4*(x*e + d)^m*c^3*d^3*m^3*x^4*e^4 + (x*e + d)^m*c^3*d^4*m^3*x^3*e^3 + 15*(x*e + d)^m*c^3*m^2*x^7*e^7 + 57*(x*e + d)^m*c^3*d*m^2*x^6*e^6 + 78*(x*e + d)^m*c^3*d^2*m^2*x^5*e^5 + 42*(x*e + d)^m*c^3*d^3*m^2*x^4*e^4 + 3*(x*e + d)^m*c^3*d^4*m^2*x^3*e^3 - 3*(x*e + d)^m*c^3*d^5*m^2*x^2*e^2 + 74*(x*e + d)^m*c^3*m*x^7*e^7 + 269*(x*e + d)^m*c^3*d*m*x^6*e^6 + 342*(x*e + d)^m*c^3*d^2*m*x^5*e^5 + 158*(x*e + d)^m*c^3*d^3*m*x^4*e^4 + 2*(x*e + d)^m*c^3*d^4*m*x^3*e^3 - 3*(x*e + d)^m*c^3*d^5*m*x^2*e^2 + 6*(x*e + d)^m*c^3*d^6*m*x*e + 120*(x*e + d)^m*c^3*x^7*e^7 + 420*(x*e + d)^m*c^3*d*x^6*e^6 + 504*(x*e + d)^m*c^3*d^2*x^5*e^5 + 210*(x*e + d)^m*c^3*d^3*x^4*e^4 - 6*(x*e + d)^m*c^3*d^7)/(m^4*e^4 + 22*m^3*e^4 + 179*m^2*e^4 + 638*m*e^4 + 840*e^4)","B",0
435,1,292,0,0.215571," ","integrate((e*x+d)^m*(c*e*x^2+c*d*x)^2,x, algorithm=""giac"")","\frac{{\left(x e + d\right)}^{m} c^{2} m^{2} x^{5} e^{5} + 3 \, {\left(x e + d\right)}^{m} c^{2} d m^{2} x^{4} e^{4} + 3 \, {\left(x e + d\right)}^{m} c^{2} d^{2} m^{2} x^{3} e^{3} + {\left(x e + d\right)}^{m} c^{2} d^{3} m^{2} x^{2} e^{2} + 7 \, {\left(x e + d\right)}^{m} c^{2} m x^{5} e^{5} + 19 \, {\left(x e + d\right)}^{m} c^{2} d m x^{4} e^{4} + 15 \, {\left(x e + d\right)}^{m} c^{2} d^{2} m x^{3} e^{3} + {\left(x e + d\right)}^{m} c^{2} d^{3} m x^{2} e^{2} - 2 \, {\left(x e + d\right)}^{m} c^{2} d^{4} m x e + 12 \, {\left(x e + d\right)}^{m} c^{2} x^{5} e^{5} + 30 \, {\left(x e + d\right)}^{m} c^{2} d x^{4} e^{4} + 20 \, {\left(x e + d\right)}^{m} c^{2} d^{2} x^{3} e^{3} + 2 \, {\left(x e + d\right)}^{m} c^{2} d^{5}}{m^{3} e^{3} + 12 \, m^{2} e^{3} + 47 \, m e^{3} + 60 \, e^{3}}"," ",0,"((x*e + d)^m*c^2*m^2*x^5*e^5 + 3*(x*e + d)^m*c^2*d*m^2*x^4*e^4 + 3*(x*e + d)^m*c^2*d^2*m^2*x^3*e^3 + (x*e + d)^m*c^2*d^3*m^2*x^2*e^2 + 7*(x*e + d)^m*c^2*m*x^5*e^5 + 19*(x*e + d)^m*c^2*d*m*x^4*e^4 + 15*(x*e + d)^m*c^2*d^2*m*x^3*e^3 + (x*e + d)^m*c^2*d^3*m*x^2*e^2 - 2*(x*e + d)^m*c^2*d^4*m*x*e + 12*(x*e + d)^m*c^2*x^5*e^5 + 30*(x*e + d)^m*c^2*d*x^4*e^4 + 20*(x*e + d)^m*c^2*d^2*x^3*e^3 + 2*(x*e + d)^m*c^2*d^5)/(m^3*e^3 + 12*m^2*e^3 + 47*m*e^3 + 60*e^3)","B",0
436,1,118,0,0.175664," ","integrate((e*x+d)^m*(c*e*x^2+c*d*x),x, algorithm=""giac"")","\frac{{\left(x e + d\right)}^{m} c m x^{3} e^{3} + 2 \, {\left(x e + d\right)}^{m} c d m x^{2} e^{2} + {\left(x e + d\right)}^{m} c d^{2} m x e + 2 \, {\left(x e + d\right)}^{m} c x^{3} e^{3} + 3 \, {\left(x e + d\right)}^{m} c d x^{2} e^{2} - {\left(x e + d\right)}^{m} c d^{3}}{m^{2} e^{2} + 5 \, m e^{2} + 6 \, e^{2}}"," ",0,"((x*e + d)^m*c*m*x^3*e^3 + 2*(x*e + d)^m*c*d*m*x^2*e^2 + (x*e + d)^m*c*d^2*m*x*e + 2*(x*e + d)^m*c*x^3*e^3 + 3*(x*e + d)^m*c*d*x^2*e^2 - (x*e + d)^m*c*d^3)/(m^2*e^2 + 5*m*e^2 + 6*e^2)","B",0
437,1,18,0,0.152244," ","integrate((e*x+d)^m,x, algorithm=""giac"")","\frac{{\left(x e + d\right)}^{m + 1} e^{\left(-1\right)}}{m + 1}"," ",0,"(x*e + d)^(m + 1)*e^(-1)/(m + 1)","A",0
438,0,0,0,0.000000," ","integrate((e*x+d)^m/(c*e*x^2+c*d*x),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{m}}{c e x^{2} + c d x}\,{d x}"," ",0,"integrate((e*x + d)^m/(c*e*x^2 + c*d*x), x)","F",0
439,0,0,0,0.000000," ","integrate((e*x+d)^m/(c*e*x^2+c*d*x)^2,x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{m}}{{\left(c e x^{2} + c d x\right)}^{2}}\,{d x}"," ",0,"integrate((e*x + d)^m/(c*e*x^2 + c*d*x)^2, x)","F",0
440,1,2538,0,0.269982," ","integrate((e*x+d)^m*(c*x^2+b*x)^3,x, algorithm=""giac"")","\frac{{\left(x e + d\right)}^{m} c^{3} m^{6} x^{7} e^{7} + {\left(x e + d\right)}^{m} c^{3} d m^{6} x^{6} e^{6} + 3 \, {\left(x e + d\right)}^{m} b c^{2} m^{6} x^{6} e^{7} + 21 \, {\left(x e + d\right)}^{m} c^{3} m^{5} x^{7} e^{7} + 3 \, {\left(x e + d\right)}^{m} b c^{2} d m^{6} x^{5} e^{6} + 15 \, {\left(x e + d\right)}^{m} c^{3} d m^{5} x^{6} e^{6} - 6 \, {\left(x e + d\right)}^{m} c^{3} d^{2} m^{5} x^{5} e^{5} + 3 \, {\left(x e + d\right)}^{m} b^{2} c m^{6} x^{5} e^{7} + 66 \, {\left(x e + d\right)}^{m} b c^{2} m^{5} x^{6} e^{7} + 175 \, {\left(x e + d\right)}^{m} c^{3} m^{4} x^{7} e^{7} + 3 \, {\left(x e + d\right)}^{m} b^{2} c d m^{6} x^{4} e^{6} + 51 \, {\left(x e + d\right)}^{m} b c^{2} d m^{5} x^{5} e^{6} + 85 \, {\left(x e + d\right)}^{m} c^{3} d m^{4} x^{6} e^{6} - 15 \, {\left(x e + d\right)}^{m} b c^{2} d^{2} m^{5} x^{4} e^{5} - 60 \, {\left(x e + d\right)}^{m} c^{3} d^{2} m^{4} x^{5} e^{5} + 30 \, {\left(x e + d\right)}^{m} c^{3} d^{3} m^{4} x^{4} e^{4} + {\left(x e + d\right)}^{m} b^{3} m^{6} x^{4} e^{7} + 69 \, {\left(x e + d\right)}^{m} b^{2} c m^{5} x^{5} e^{7} + 570 \, {\left(x e + d\right)}^{m} b c^{2} m^{4} x^{6} e^{7} + 735 \, {\left(x e + d\right)}^{m} c^{3} m^{3} x^{7} e^{7} + {\left(x e + d\right)}^{m} b^{3} d m^{6} x^{3} e^{6} + 57 \, {\left(x e + d\right)}^{m} b^{2} c d m^{5} x^{4} e^{6} + 315 \, {\left(x e + d\right)}^{m} b c^{2} d m^{4} x^{5} e^{6} + 225 \, {\left(x e + d\right)}^{m} c^{3} d m^{3} x^{6} e^{6} - 12 \, {\left(x e + d\right)}^{m} b^{2} c d^{2} m^{5} x^{3} e^{5} - 195 \, {\left(x e + d\right)}^{m} b c^{2} d^{2} m^{4} x^{4} e^{5} - 210 \, {\left(x e + d\right)}^{m} c^{3} d^{2} m^{3} x^{5} e^{5} + 60 \, {\left(x e + d\right)}^{m} b c^{2} d^{3} m^{4} x^{3} e^{4} + 180 \, {\left(x e + d\right)}^{m} c^{3} d^{3} m^{3} x^{4} e^{4} - 120 \, {\left(x e + d\right)}^{m} c^{3} d^{4} m^{3} x^{3} e^{3} + 24 \, {\left(x e + d\right)}^{m} b^{3} m^{5} x^{4} e^{7} + 621 \, {\left(x e + d\right)}^{m} b^{2} c m^{4} x^{5} e^{7} + 2460 \, {\left(x e + d\right)}^{m} b c^{2} m^{3} x^{6} e^{7} + 1624 \, {\left(x e + d\right)}^{m} c^{3} m^{2} x^{7} e^{7} + 21 \, {\left(x e + d\right)}^{m} b^{3} d m^{5} x^{3} e^{6} + 393 \, {\left(x e + d\right)}^{m} b^{2} c d m^{4} x^{4} e^{6} + 885 \, {\left(x e + d\right)}^{m} b c^{2} d m^{3} x^{5} e^{6} + 274 \, {\left(x e + d\right)}^{m} c^{3} d m^{2} x^{6} e^{6} - 3 \, {\left(x e + d\right)}^{m} b^{3} d^{2} m^{5} x^{2} e^{5} - 192 \, {\left(x e + d\right)}^{m} b^{2} c d^{2} m^{4} x^{3} e^{5} - 795 \, {\left(x e + d\right)}^{m} b c^{2} d^{2} m^{3} x^{4} e^{5} - 300 \, {\left(x e + d\right)}^{m} c^{3} d^{2} m^{2} x^{5} e^{5} + 36 \, {\left(x e + d\right)}^{m} b^{2} c d^{3} m^{4} x^{2} e^{4} + 600 \, {\left(x e + d\right)}^{m} b c^{2} d^{3} m^{3} x^{3} e^{4} + 330 \, {\left(x e + d\right)}^{m} c^{3} d^{3} m^{2} x^{4} e^{4} - 180 \, {\left(x e + d\right)}^{m} b c^{2} d^{4} m^{3} x^{2} e^{3} - 360 \, {\left(x e + d\right)}^{m} c^{3} d^{4} m^{2} x^{3} e^{3} + 360 \, {\left(x e + d\right)}^{m} c^{3} d^{5} m^{2} x^{2} e^{2} + 226 \, {\left(x e + d\right)}^{m} b^{3} m^{4} x^{4} e^{7} + 2775 \, {\left(x e + d\right)}^{m} b^{2} c m^{3} x^{5} e^{7} + 5547 \, {\left(x e + d\right)}^{m} b c^{2} m^{2} x^{6} e^{7} + 1764 \, {\left(x e + d\right)}^{m} c^{3} m x^{7} e^{7} + 163 \, {\left(x e + d\right)}^{m} b^{3} d m^{4} x^{3} e^{6} + 1203 \, {\left(x e + d\right)}^{m} b^{2} c d m^{3} x^{4} e^{6} + 1122 \, {\left(x e + d\right)}^{m} b c^{2} d m^{2} x^{5} e^{6} + 120 \, {\left(x e + d\right)}^{m} c^{3} d m x^{6} e^{6} - 57 \, {\left(x e + d\right)}^{m} b^{3} d^{2} m^{4} x^{2} e^{5} - 996 \, {\left(x e + d\right)}^{m} b^{2} c d^{2} m^{3} x^{3} e^{5} - 1245 \, {\left(x e + d\right)}^{m} b c^{2} d^{2} m^{2} x^{4} e^{5} - 144 \, {\left(x e + d\right)}^{m} c^{3} d^{2} m x^{5} e^{5} + 6 \, {\left(x e + d\right)}^{m} b^{3} d^{3} m^{4} x e^{4} + 504 \, {\left(x e + d\right)}^{m} b^{2} c d^{3} m^{3} x^{2} e^{4} + 1380 \, {\left(x e + d\right)}^{m} b c^{2} d^{3} m^{2} x^{3} e^{4} + 180 \, {\left(x e + d\right)}^{m} c^{3} d^{3} m x^{4} e^{4} - 72 \, {\left(x e + d\right)}^{m} b^{2} c d^{4} m^{3} x e^{3} - 1440 \, {\left(x e + d\right)}^{m} b c^{2} d^{4} m^{2} x^{2} e^{3} - 240 \, {\left(x e + d\right)}^{m} c^{3} d^{4} m x^{3} e^{3} + 360 \, {\left(x e + d\right)}^{m} b c^{2} d^{5} m^{2} x e^{2} + 360 \, {\left(x e + d\right)}^{m} c^{3} d^{5} m x^{2} e^{2} - 720 \, {\left(x e + d\right)}^{m} c^{3} d^{6} m x e + 1056 \, {\left(x e + d\right)}^{m} b^{3} m^{3} x^{4} e^{7} + 6432 \, {\left(x e + d\right)}^{m} b^{2} c m^{2} x^{5} e^{7} + 6114 \, {\left(x e + d\right)}^{m} b c^{2} m x^{6} e^{7} + 720 \, {\left(x e + d\right)}^{m} c^{3} x^{7} e^{7} + 567 \, {\left(x e + d\right)}^{m} b^{3} d m^{3} x^{3} e^{6} + 1620 \, {\left(x e + d\right)}^{m} b^{2} c d m^{2} x^{4} e^{6} + 504 \, {\left(x e + d\right)}^{m} b c^{2} d m x^{5} e^{6} - 375 \, {\left(x e + d\right)}^{m} b^{3} d^{2} m^{3} x^{2} e^{5} - 1824 \, {\left(x e + d\right)}^{m} b^{2} c d^{2} m^{2} x^{3} e^{5} - 630 \, {\left(x e + d\right)}^{m} b c^{2} d^{2} m x^{4} e^{5} + 108 \, {\left(x e + d\right)}^{m} b^{3} d^{3} m^{3} x e^{4} + 1980 \, {\left(x e + d\right)}^{m} b^{2} c d^{3} m^{2} x^{2} e^{4} + 840 \, {\left(x e + d\right)}^{m} b c^{2} d^{3} m x^{3} e^{4} - 6 \, {\left(x e + d\right)}^{m} b^{3} d^{4} m^{3} e^{3} - 936 \, {\left(x e + d\right)}^{m} b^{2} c d^{4} m^{2} x e^{3} - 1260 \, {\left(x e + d\right)}^{m} b c^{2} d^{4} m x^{2} e^{3} + 72 \, {\left(x e + d\right)}^{m} b^{2} c d^{5} m^{2} e^{2} + 2520 \, {\left(x e + d\right)}^{m} b c^{2} d^{5} m x e^{2} - 360 \, {\left(x e + d\right)}^{m} b c^{2} d^{6} m e + 720 \, {\left(x e + d\right)}^{m} c^{3} d^{7} + 2545 \, {\left(x e + d\right)}^{m} b^{3} m^{2} x^{4} e^{7} + 7236 \, {\left(x e + d\right)}^{m} b^{2} c m x^{5} e^{7} + 2520 \, {\left(x e + d\right)}^{m} b c^{2} x^{6} e^{7} + 844 \, {\left(x e + d\right)}^{m} b^{3} d m^{2} x^{3} e^{6} + 756 \, {\left(x e + d\right)}^{m} b^{2} c d m x^{4} e^{6} - 951 \, {\left(x e + d\right)}^{m} b^{3} d^{2} m^{2} x^{2} e^{5} - 1008 \, {\left(x e + d\right)}^{m} b^{2} c d^{2} m x^{3} e^{5} + 642 \, {\left(x e + d\right)}^{m} b^{3} d^{3} m^{2} x e^{4} + 1512 \, {\left(x e + d\right)}^{m} b^{2} c d^{3} m x^{2} e^{4} - 108 \, {\left(x e + d\right)}^{m} b^{3} d^{4} m^{2} e^{3} - 3024 \, {\left(x e + d\right)}^{m} b^{2} c d^{4} m x e^{3} + 936 \, {\left(x e + d\right)}^{m} b^{2} c d^{5} m e^{2} - 2520 \, {\left(x e + d\right)}^{m} b c^{2} d^{6} e + 2952 \, {\left(x e + d\right)}^{m} b^{3} m x^{4} e^{7} + 3024 \, {\left(x e + d\right)}^{m} b^{2} c x^{5} e^{7} + 420 \, {\left(x e + d\right)}^{m} b^{3} d m x^{3} e^{6} - 630 \, {\left(x e + d\right)}^{m} b^{3} d^{2} m x^{2} e^{5} + 1260 \, {\left(x e + d\right)}^{m} b^{3} d^{3} m x e^{4} - 642 \, {\left(x e + d\right)}^{m} b^{3} d^{4} m e^{3} + 3024 \, {\left(x e + d\right)}^{m} b^{2} c d^{5} e^{2} + 1260 \, {\left(x e + d\right)}^{m} b^{3} x^{4} e^{7} - 1260 \, {\left(x e + d\right)}^{m} b^{3} d^{4} e^{3}}{m^{7} e^{7} + 28 \, m^{6} e^{7} + 322 \, m^{5} e^{7} + 1960 \, m^{4} e^{7} + 6769 \, m^{3} e^{7} + 13132 \, m^{2} e^{7} + 13068 \, m e^{7} + 5040 \, e^{7}}"," ",0,"((x*e + d)^m*c^3*m^6*x^7*e^7 + (x*e + d)^m*c^3*d*m^6*x^6*e^6 + 3*(x*e + d)^m*b*c^2*m^6*x^6*e^7 + 21*(x*e + d)^m*c^3*m^5*x^7*e^7 + 3*(x*e + d)^m*b*c^2*d*m^6*x^5*e^6 + 15*(x*e + d)^m*c^3*d*m^5*x^6*e^6 - 6*(x*e + d)^m*c^3*d^2*m^5*x^5*e^5 + 3*(x*e + d)^m*b^2*c*m^6*x^5*e^7 + 66*(x*e + d)^m*b*c^2*m^5*x^6*e^7 + 175*(x*e + d)^m*c^3*m^4*x^7*e^7 + 3*(x*e + d)^m*b^2*c*d*m^6*x^4*e^6 + 51*(x*e + d)^m*b*c^2*d*m^5*x^5*e^6 + 85*(x*e + d)^m*c^3*d*m^4*x^6*e^6 - 15*(x*e + d)^m*b*c^2*d^2*m^5*x^4*e^5 - 60*(x*e + d)^m*c^3*d^2*m^4*x^5*e^5 + 30*(x*e + d)^m*c^3*d^3*m^4*x^4*e^4 + (x*e + d)^m*b^3*m^6*x^4*e^7 + 69*(x*e + d)^m*b^2*c*m^5*x^5*e^7 + 570*(x*e + d)^m*b*c^2*m^4*x^6*e^7 + 735*(x*e + d)^m*c^3*m^3*x^7*e^7 + (x*e + d)^m*b^3*d*m^6*x^3*e^6 + 57*(x*e + d)^m*b^2*c*d*m^5*x^4*e^6 + 315*(x*e + d)^m*b*c^2*d*m^4*x^5*e^6 + 225*(x*e + d)^m*c^3*d*m^3*x^6*e^6 - 12*(x*e + d)^m*b^2*c*d^2*m^5*x^3*e^5 - 195*(x*e + d)^m*b*c^2*d^2*m^4*x^4*e^5 - 210*(x*e + d)^m*c^3*d^2*m^3*x^5*e^5 + 60*(x*e + d)^m*b*c^2*d^3*m^4*x^3*e^4 + 180*(x*e + d)^m*c^3*d^3*m^3*x^4*e^4 - 120*(x*e + d)^m*c^3*d^4*m^3*x^3*e^3 + 24*(x*e + d)^m*b^3*m^5*x^4*e^7 + 621*(x*e + d)^m*b^2*c*m^4*x^5*e^7 + 2460*(x*e + d)^m*b*c^2*m^3*x^6*e^7 + 1624*(x*e + d)^m*c^3*m^2*x^7*e^7 + 21*(x*e + d)^m*b^3*d*m^5*x^3*e^6 + 393*(x*e + d)^m*b^2*c*d*m^4*x^4*e^6 + 885*(x*e + d)^m*b*c^2*d*m^3*x^5*e^6 + 274*(x*e + d)^m*c^3*d*m^2*x^6*e^6 - 3*(x*e + d)^m*b^3*d^2*m^5*x^2*e^5 - 192*(x*e + d)^m*b^2*c*d^2*m^4*x^3*e^5 - 795*(x*e + d)^m*b*c^2*d^2*m^3*x^4*e^5 - 300*(x*e + d)^m*c^3*d^2*m^2*x^5*e^5 + 36*(x*e + d)^m*b^2*c*d^3*m^4*x^2*e^4 + 600*(x*e + d)^m*b*c^2*d^3*m^3*x^3*e^4 + 330*(x*e + d)^m*c^3*d^3*m^2*x^4*e^4 - 180*(x*e + d)^m*b*c^2*d^4*m^3*x^2*e^3 - 360*(x*e + d)^m*c^3*d^4*m^2*x^3*e^3 + 360*(x*e + d)^m*c^3*d^5*m^2*x^2*e^2 + 226*(x*e + d)^m*b^3*m^4*x^4*e^7 + 2775*(x*e + d)^m*b^2*c*m^3*x^5*e^7 + 5547*(x*e + d)^m*b*c^2*m^2*x^6*e^7 + 1764*(x*e + d)^m*c^3*m*x^7*e^7 + 163*(x*e + d)^m*b^3*d*m^4*x^3*e^6 + 1203*(x*e + d)^m*b^2*c*d*m^3*x^4*e^6 + 1122*(x*e + d)^m*b*c^2*d*m^2*x^5*e^6 + 120*(x*e + d)^m*c^3*d*m*x^6*e^6 - 57*(x*e + d)^m*b^3*d^2*m^4*x^2*e^5 - 996*(x*e + d)^m*b^2*c*d^2*m^3*x^3*e^5 - 1245*(x*e + d)^m*b*c^2*d^2*m^2*x^4*e^5 - 144*(x*e + d)^m*c^3*d^2*m*x^5*e^5 + 6*(x*e + d)^m*b^3*d^3*m^4*x*e^4 + 504*(x*e + d)^m*b^2*c*d^3*m^3*x^2*e^4 + 1380*(x*e + d)^m*b*c^2*d^3*m^2*x^3*e^4 + 180*(x*e + d)^m*c^3*d^3*m*x^4*e^4 - 72*(x*e + d)^m*b^2*c*d^4*m^3*x*e^3 - 1440*(x*e + d)^m*b*c^2*d^4*m^2*x^2*e^3 - 240*(x*e + d)^m*c^3*d^4*m*x^3*e^3 + 360*(x*e + d)^m*b*c^2*d^5*m^2*x*e^2 + 360*(x*e + d)^m*c^3*d^5*m*x^2*e^2 - 720*(x*e + d)^m*c^3*d^6*m*x*e + 1056*(x*e + d)^m*b^3*m^3*x^4*e^7 + 6432*(x*e + d)^m*b^2*c*m^2*x^5*e^7 + 6114*(x*e + d)^m*b*c^2*m*x^6*e^7 + 720*(x*e + d)^m*c^3*x^7*e^7 + 567*(x*e + d)^m*b^3*d*m^3*x^3*e^6 + 1620*(x*e + d)^m*b^2*c*d*m^2*x^4*e^6 + 504*(x*e + d)^m*b*c^2*d*m*x^5*e^6 - 375*(x*e + d)^m*b^3*d^2*m^3*x^2*e^5 - 1824*(x*e + d)^m*b^2*c*d^2*m^2*x^3*e^5 - 630*(x*e + d)^m*b*c^2*d^2*m*x^4*e^5 + 108*(x*e + d)^m*b^3*d^3*m^3*x*e^4 + 1980*(x*e + d)^m*b^2*c*d^3*m^2*x^2*e^4 + 840*(x*e + d)^m*b*c^2*d^3*m*x^3*e^4 - 6*(x*e + d)^m*b^3*d^4*m^3*e^3 - 936*(x*e + d)^m*b^2*c*d^4*m^2*x*e^3 - 1260*(x*e + d)^m*b*c^2*d^4*m*x^2*e^3 + 72*(x*e + d)^m*b^2*c*d^5*m^2*e^2 + 2520*(x*e + d)^m*b*c^2*d^5*m*x*e^2 - 360*(x*e + d)^m*b*c^2*d^6*m*e + 720*(x*e + d)^m*c^3*d^7 + 2545*(x*e + d)^m*b^3*m^2*x^4*e^7 + 7236*(x*e + d)^m*b^2*c*m*x^5*e^7 + 2520*(x*e + d)^m*b*c^2*x^6*e^7 + 844*(x*e + d)^m*b^3*d*m^2*x^3*e^6 + 756*(x*e + d)^m*b^2*c*d*m*x^4*e^6 - 951*(x*e + d)^m*b^3*d^2*m^2*x^2*e^5 - 1008*(x*e + d)^m*b^2*c*d^2*m*x^3*e^5 + 642*(x*e + d)^m*b^3*d^3*m^2*x*e^4 + 1512*(x*e + d)^m*b^2*c*d^3*m*x^2*e^4 - 108*(x*e + d)^m*b^3*d^4*m^2*e^3 - 3024*(x*e + d)^m*b^2*c*d^4*m*x*e^3 + 936*(x*e + d)^m*b^2*c*d^5*m*e^2 - 2520*(x*e + d)^m*b*c^2*d^6*e + 2952*(x*e + d)^m*b^3*m*x^4*e^7 + 3024*(x*e + d)^m*b^2*c*x^5*e^7 + 420*(x*e + d)^m*b^3*d*m*x^3*e^6 - 630*(x*e + d)^m*b^3*d^2*m*x^2*e^5 + 1260*(x*e + d)^m*b^3*d^3*m*x*e^4 - 642*(x*e + d)^m*b^3*d^4*m*e^3 + 3024*(x*e + d)^m*b^2*c*d^5*e^2 + 1260*(x*e + d)^m*b^3*x^4*e^7 - 1260*(x*e + d)^m*b^3*d^4*e^3)/(m^7*e^7 + 28*m^6*e^7 + 322*m^5*e^7 + 1960*m^4*e^7 + 6769*m^3*e^7 + 13132*m^2*e^7 + 13068*m*e^7 + 5040*e^7)","B",0
441,1,1002,0,0.192531," ","integrate((e*x+d)^m*(c*x^2+b*x)^2,x, algorithm=""giac"")","\frac{{\left(x e + d\right)}^{m} c^{2} m^{4} x^{5} e^{5} + {\left(x e + d\right)}^{m} c^{2} d m^{4} x^{4} e^{4} + 2 \, {\left(x e + d\right)}^{m} b c m^{4} x^{4} e^{5} + 10 \, {\left(x e + d\right)}^{m} c^{2} m^{3} x^{5} e^{5} + 2 \, {\left(x e + d\right)}^{m} b c d m^{4} x^{3} e^{4} + 6 \, {\left(x e + d\right)}^{m} c^{2} d m^{3} x^{4} e^{4} - 4 \, {\left(x e + d\right)}^{m} c^{2} d^{2} m^{3} x^{3} e^{3} + {\left(x e + d\right)}^{m} b^{2} m^{4} x^{3} e^{5} + 22 \, {\left(x e + d\right)}^{m} b c m^{3} x^{4} e^{5} + 35 \, {\left(x e + d\right)}^{m} c^{2} m^{2} x^{5} e^{5} + {\left(x e + d\right)}^{m} b^{2} d m^{4} x^{2} e^{4} + 16 \, {\left(x e + d\right)}^{m} b c d m^{3} x^{3} e^{4} + 11 \, {\left(x e + d\right)}^{m} c^{2} d m^{2} x^{4} e^{4} - 6 \, {\left(x e + d\right)}^{m} b c d^{2} m^{3} x^{2} e^{3} - 12 \, {\left(x e + d\right)}^{m} c^{2} d^{2} m^{2} x^{3} e^{3} + 12 \, {\left(x e + d\right)}^{m} c^{2} d^{3} m^{2} x^{2} e^{2} + 12 \, {\left(x e + d\right)}^{m} b^{2} m^{3} x^{3} e^{5} + 82 \, {\left(x e + d\right)}^{m} b c m^{2} x^{4} e^{5} + 50 \, {\left(x e + d\right)}^{m} c^{2} m x^{5} e^{5} + 10 \, {\left(x e + d\right)}^{m} b^{2} d m^{3} x^{2} e^{4} + 34 \, {\left(x e + d\right)}^{m} b c d m^{2} x^{3} e^{4} + 6 \, {\left(x e + d\right)}^{m} c^{2} d m x^{4} e^{4} - 2 \, {\left(x e + d\right)}^{m} b^{2} d^{2} m^{3} x e^{3} - 36 \, {\left(x e + d\right)}^{m} b c d^{2} m^{2} x^{2} e^{3} - 8 \, {\left(x e + d\right)}^{m} c^{2} d^{2} m x^{3} e^{3} + 12 \, {\left(x e + d\right)}^{m} b c d^{3} m^{2} x e^{2} + 12 \, {\left(x e + d\right)}^{m} c^{2} d^{3} m x^{2} e^{2} - 24 \, {\left(x e + d\right)}^{m} c^{2} d^{4} m x e + 49 \, {\left(x e + d\right)}^{m} b^{2} m^{2} x^{3} e^{5} + 122 \, {\left(x e + d\right)}^{m} b c m x^{4} e^{5} + 24 \, {\left(x e + d\right)}^{m} c^{2} x^{5} e^{5} + 29 \, {\left(x e + d\right)}^{m} b^{2} d m^{2} x^{2} e^{4} + 20 \, {\left(x e + d\right)}^{m} b c d m x^{3} e^{4} - 18 \, {\left(x e + d\right)}^{m} b^{2} d^{2} m^{2} x e^{3} - 30 \, {\left(x e + d\right)}^{m} b c d^{2} m x^{2} e^{3} + 2 \, {\left(x e + d\right)}^{m} b^{2} d^{3} m^{2} e^{2} + 60 \, {\left(x e + d\right)}^{m} b c d^{3} m x e^{2} - 12 \, {\left(x e + d\right)}^{m} b c d^{4} m e + 24 \, {\left(x e + d\right)}^{m} c^{2} d^{5} + 78 \, {\left(x e + d\right)}^{m} b^{2} m x^{3} e^{5} + 60 \, {\left(x e + d\right)}^{m} b c x^{4} e^{5} + 20 \, {\left(x e + d\right)}^{m} b^{2} d m x^{2} e^{4} - 40 \, {\left(x e + d\right)}^{m} b^{2} d^{2} m x e^{3} + 18 \, {\left(x e + d\right)}^{m} b^{2} d^{3} m e^{2} - 60 \, {\left(x e + d\right)}^{m} b c d^{4} e + 40 \, {\left(x e + d\right)}^{m} b^{2} x^{3} e^{5} + 40 \, {\left(x e + d\right)}^{m} b^{2} d^{3} e^{2}}{m^{5} e^{5} + 15 \, m^{4} e^{5} + 85 \, m^{3} e^{5} + 225 \, m^{2} e^{5} + 274 \, m e^{5} + 120 \, e^{5}}"," ",0,"((x*e + d)^m*c^2*m^4*x^5*e^5 + (x*e + d)^m*c^2*d*m^4*x^4*e^4 + 2*(x*e + d)^m*b*c*m^4*x^4*e^5 + 10*(x*e + d)^m*c^2*m^3*x^5*e^5 + 2*(x*e + d)^m*b*c*d*m^4*x^3*e^4 + 6*(x*e + d)^m*c^2*d*m^3*x^4*e^4 - 4*(x*e + d)^m*c^2*d^2*m^3*x^3*e^3 + (x*e + d)^m*b^2*m^4*x^3*e^5 + 22*(x*e + d)^m*b*c*m^3*x^4*e^5 + 35*(x*e + d)^m*c^2*m^2*x^5*e^5 + (x*e + d)^m*b^2*d*m^4*x^2*e^4 + 16*(x*e + d)^m*b*c*d*m^3*x^3*e^4 + 11*(x*e + d)^m*c^2*d*m^2*x^4*e^4 - 6*(x*e + d)^m*b*c*d^2*m^3*x^2*e^3 - 12*(x*e + d)^m*c^2*d^2*m^2*x^3*e^3 + 12*(x*e + d)^m*c^2*d^3*m^2*x^2*e^2 + 12*(x*e + d)^m*b^2*m^3*x^3*e^5 + 82*(x*e + d)^m*b*c*m^2*x^4*e^5 + 50*(x*e + d)^m*c^2*m*x^5*e^5 + 10*(x*e + d)^m*b^2*d*m^3*x^2*e^4 + 34*(x*e + d)^m*b*c*d*m^2*x^3*e^4 + 6*(x*e + d)^m*c^2*d*m*x^4*e^4 - 2*(x*e + d)^m*b^2*d^2*m^3*x*e^3 - 36*(x*e + d)^m*b*c*d^2*m^2*x^2*e^3 - 8*(x*e + d)^m*c^2*d^2*m*x^3*e^3 + 12*(x*e + d)^m*b*c*d^3*m^2*x*e^2 + 12*(x*e + d)^m*c^2*d^3*m*x^2*e^2 - 24*(x*e + d)^m*c^2*d^4*m*x*e + 49*(x*e + d)^m*b^2*m^2*x^3*e^5 + 122*(x*e + d)^m*b*c*m*x^4*e^5 + 24*(x*e + d)^m*c^2*x^5*e^5 + 29*(x*e + d)^m*b^2*d*m^2*x^2*e^4 + 20*(x*e + d)^m*b*c*d*m*x^3*e^4 - 18*(x*e + d)^m*b^2*d^2*m^2*x*e^3 - 30*(x*e + d)^m*b*c*d^2*m*x^2*e^3 + 2*(x*e + d)^m*b^2*d^3*m^2*e^2 + 60*(x*e + d)^m*b*c*d^3*m*x*e^2 - 12*(x*e + d)^m*b*c*d^4*m*e + 24*(x*e + d)^m*c^2*d^5 + 78*(x*e + d)^m*b^2*m*x^3*e^5 + 60*(x*e + d)^m*b*c*x^4*e^5 + 20*(x*e + d)^m*b^2*d*m*x^2*e^4 - 40*(x*e + d)^m*b^2*d^2*m*x*e^3 + 18*(x*e + d)^m*b^2*d^3*m*e^2 - 60*(x*e + d)^m*b*c*d^4*e + 40*(x*e + d)^m*b^2*x^3*e^5 + 40*(x*e + d)^m*b^2*d^3*e^2)/(m^5*e^5 + 15*m^4*e^5 + 85*m^3*e^5 + 225*m^2*e^5 + 274*m*e^5 + 120*e^5)","B",0
442,1,263,0,0.176123," ","integrate((e*x+d)^m*(c*x^2+b*x),x, algorithm=""giac"")","\frac{{\left(x e + d\right)}^{m} c m^{2} x^{3} e^{3} + {\left(x e + d\right)}^{m} c d m^{2} x^{2} e^{2} + {\left(x e + d\right)}^{m} b m^{2} x^{2} e^{3} + 3 \, {\left(x e + d\right)}^{m} c m x^{3} e^{3} + {\left(x e + d\right)}^{m} b d m^{2} x e^{2} + {\left(x e + d\right)}^{m} c d m x^{2} e^{2} - 2 \, {\left(x e + d\right)}^{m} c d^{2} m x e + 4 \, {\left(x e + d\right)}^{m} b m x^{2} e^{3} + 2 \, {\left(x e + d\right)}^{m} c x^{3} e^{3} + 3 \, {\left(x e + d\right)}^{m} b d m x e^{2} - {\left(x e + d\right)}^{m} b d^{2} m e + 2 \, {\left(x e + d\right)}^{m} c d^{3} + 3 \, {\left(x e + d\right)}^{m} b x^{2} e^{3} - 3 \, {\left(x e + d\right)}^{m} b d^{2} e}{m^{3} e^{3} + 6 \, m^{2} e^{3} + 11 \, m e^{3} + 6 \, e^{3}}"," ",0,"((x*e + d)^m*c*m^2*x^3*e^3 + (x*e + d)^m*c*d*m^2*x^2*e^2 + (x*e + d)^m*b*m^2*x^2*e^3 + 3*(x*e + d)^m*c*m*x^3*e^3 + (x*e + d)^m*b*d*m^2*x*e^2 + (x*e + d)^m*c*d*m*x^2*e^2 - 2*(x*e + d)^m*c*d^2*m*x*e + 4*(x*e + d)^m*b*m*x^2*e^3 + 2*(x*e + d)^m*c*x^3*e^3 + 3*(x*e + d)^m*b*d*m*x*e^2 - (x*e + d)^m*b*d^2*m*e + 2*(x*e + d)^m*c*d^3 + 3*(x*e + d)^m*b*x^2*e^3 - 3*(x*e + d)^m*b*d^2*e)/(m^3*e^3 + 6*m^2*e^3 + 11*m*e^3 + 6*e^3)","B",0
443,0,0,0,0.000000," ","integrate((e*x+d)^m/(c*x^2+b*x),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{m}}{c x^{2} + b x}\,{d x}"," ",0,"integrate((e*x + d)^m/(c*x^2 + b*x), x)","F",0
444,0,0,0,0.000000," ","integrate((e*x+d)^m/(c*x^2+b*x)^2,x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{m}}{{\left(c x^{2} + b x\right)}^{2}}\,{d x}"," ",0,"integrate((e*x + d)^m/(c*x^2 + b*x)^2, x)","F",0
445,0,0,0,0.000000," ","integrate((e*x+d)^m/(c*x^2+b*x)^3,x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{m}}{{\left(c x^{2} + b x\right)}^{3}}\,{d x}"," ",0,"integrate((e*x + d)^m/(c*x^2 + b*x)^3, x)","F",0
446,0,0,0,0.000000," ","integrate((e*x+d)^m*(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","\int {\left(c x^{2} + b x\right)}^{\frac{3}{2}} {\left(e x + d\right)}^{m}\,{d x}"," ",0,"integrate((c*x^2 + b*x)^(3/2)*(e*x + d)^m, x)","F",0
447,0,0,0,0.000000," ","integrate((e*x+d)^m*(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\int \sqrt{c x^{2} + b x} {\left(e x + d\right)}^{m}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + b*x)*(e*x + d)^m, x)","F",0
448,0,0,0,0.000000," ","integrate((e*x+d)^m/(c*x^2+b*x)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{m}}{\sqrt{c x^{2} + b x}}\,{d x}"," ",0,"integrate((e*x + d)^m/sqrt(c*x^2 + b*x), x)","F",0
449,0,0,0,0.000000," ","integrate((e*x+d)^m/(c*x^2+b*x)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{m}}{{\left(c x^{2} + b x\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((e*x + d)^m/(c*x^2 + b*x)^(3/2), x)","F",0
450,0,0,0,0.000000," ","integrate((e*x+d)^m*(c*x^2+b*x)^p,x, algorithm=""giac"")","\int {\left(c x^{2} + b x\right)}^{p} {\left(e x + d\right)}^{m}\,{d x}"," ",0,"integrate((c*x^2 + b*x)^p*(e*x + d)^m, x)","F",0
451,1,92,0,0.149674," ","integrate((e*x+d)^4*(c*x^2+a),x, algorithm=""giac"")","\frac{1}{7} \, c x^{7} e^{4} + \frac{2}{3} \, c d x^{6} e^{3} + \frac{6}{5} \, c d^{2} x^{5} e^{2} + c d^{3} x^{4} e + \frac{1}{3} \, c d^{4} x^{3} + \frac{1}{5} \, a x^{5} e^{4} + a d x^{4} e^{3} + 2 \, a d^{2} x^{3} e^{2} + 2 \, a d^{3} x^{2} e + a d^{4} x"," ",0,"1/7*c*x^7*e^4 + 2/3*c*d*x^6*e^3 + 6/5*c*d^2*x^5*e^2 + c*d^3*x^4*e + 1/3*c*d^4*x^3 + 1/5*a*x^5*e^4 + a*d*x^4*e^3 + 2*a*d^2*x^3*e^2 + 2*a*d^3*x^2*e + a*d^4*x","A",0
452,1,71,0,0.169542," ","integrate((e*x+d)^3*(c*x^2+a),x, algorithm=""giac"")","\frac{1}{6} \, c x^{6} e^{3} + \frac{3}{5} \, c d x^{5} e^{2} + \frac{3}{4} \, c d^{2} x^{4} e + \frac{1}{3} \, c d^{3} x^{3} + \frac{1}{4} \, a x^{4} e^{3} + a d x^{3} e^{2} + \frac{3}{2} \, a d^{2} x^{2} e + a d^{3} x"," ",0,"1/6*c*x^6*e^3 + 3/5*c*d*x^5*e^2 + 3/4*c*d^2*x^4*e + 1/3*c*d^3*x^3 + 1/4*a*x^4*e^3 + a*d*x^3*e^2 + 3/2*a*d^2*x^2*e + a*d^3*x","A",0
453,1,49,0,0.148905," ","integrate((e*x+d)^2*(c*x^2+a),x, algorithm=""giac"")","\frac{1}{5} \, c x^{5} e^{2} + \frac{1}{2} \, c d x^{4} e + \frac{1}{3} \, c d^{2} x^{3} + \frac{1}{3} \, a x^{3} e^{2} + a d x^{2} e + a d^{2} x"," ",0,"1/5*c*x^5*e^2 + 1/2*c*d*x^4*e + 1/3*c*d^2*x^3 + 1/3*a*x^3*e^2 + a*d*x^2*e + a*d^2*x","A",0
454,1,28,0,0.150995," ","integrate((e*x+d)*(c*x^2+a),x, algorithm=""giac"")","\frac{1}{4} \, c x^{4} e + \frac{1}{3} \, c d x^{3} + \frac{1}{2} \, a x^{2} e + a d x"," ",0,"1/4*c*x^4*e + 1/3*c*d*x^3 + 1/2*a*x^2*e + a*d*x","A",0
455,1,39,0,0.154100," ","integrate((c*x^2+a)/(e*x+d),x, algorithm=""giac"")","{\left(c d^{2} + a e^{2}\right)} e^{\left(-3\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{2} \, {\left(c x^{2} e - 2 \, c d x\right)} e^{\left(-2\right)}"," ",0,"(c*d^2 + a*e^2)*e^(-3)*log(abs(x*e + d)) + 1/2*(c*x^2*e - 2*c*d*x)*e^(-2)","A",0
456,1,65,0,0.152968," ","integrate((c*x^2+a)/(e*x+d)^2,x, algorithm=""giac"")","{\left(2 \, d e^{\left(-3\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) + {\left(x e + d\right)} e^{\left(-3\right)} - \frac{d^{2} e^{\left(-3\right)}}{x e + d}\right)} c - \frac{a e^{\left(-1\right)}}{x e + d}"," ",0,"(2*d*e^(-3)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) + (x*e + d)*e^(-3) - d^2*e^(-3)/(x*e + d))*c - a*e^(-1)/(x*e + d)","A",0
457,1,46,0,0.156296," ","integrate((c*x^2+a)/(e*x+d)^3,x, algorithm=""giac"")","c e^{\left(-3\right)} \log\left({\left| x e + d \right|}\right) + \frac{{\left(4 \, c d x + {\left(3 \, c d^{2} - a e^{2}\right)} e^{\left(-1\right)}\right)} e^{\left(-2\right)}}{2 \, {\left(x e + d\right)}^{2}}"," ",0,"c*e^(-3)*log(abs(x*e + d)) + 1/2*(4*c*d*x + (3*c*d^2 - a*e^2)*e^(-1))*e^(-2)/(x*e + d)^2","A",0
458,1,37,0,0.175279," ","integrate((c*x^2+a)/(e*x+d)^4,x, algorithm=""giac"")","-\frac{{\left(3 \, c x^{2} e^{2} + 3 \, c d x e + c d^{2} + a e^{2}\right)} e^{\left(-3\right)}}{3 \, {\left(x e + d\right)}^{3}}"," ",0,"-1/3*(3*c*x^2*e^2 + 3*c*d*x*e + c*d^2 + a*e^2)*e^(-3)/(x*e + d)^3","A",0
459,1,59,0,0.154554," ","integrate((c*x^2+a)/(e*x+d)^5,x, algorithm=""giac"")","-\frac{1}{12} \, {\left(\frac{6 \, c e^{\left(-2\right)}}{{\left(x e + d\right)}^{2}} - \frac{8 \, c d e^{\left(-2\right)}}{{\left(x e + d\right)}^{3}} + \frac{3 \, c d^{2} e^{\left(-2\right)}}{{\left(x e + d\right)}^{4}} + \frac{3 \, a}{{\left(x e + d\right)}^{4}}\right)} e^{\left(-1\right)}"," ",0,"-1/12*(6*c*e^(-2)/(x*e + d)^2 - 8*c*d*e^(-2)/(x*e + d)^3 + 3*c*d^2*e^(-2)/(x*e + d)^4 + 3*a/(x*e + d)^4)*e^(-1)","A",0
460,1,166,0,0.153042," ","integrate((e*x+d)^4*(c*x^2+a)^2,x, algorithm=""giac"")","\frac{1}{9} \, c^{2} x^{9} e^{4} + \frac{1}{2} \, c^{2} d x^{8} e^{3} + \frac{6}{7} \, c^{2} d^{2} x^{7} e^{2} + \frac{2}{3} \, c^{2} d^{3} x^{6} e + \frac{1}{5} \, c^{2} d^{4} x^{5} + \frac{2}{7} \, a c x^{7} e^{4} + \frac{4}{3} \, a c d x^{6} e^{3} + \frac{12}{5} \, a c d^{2} x^{5} e^{2} + 2 \, a c d^{3} x^{4} e + \frac{2}{3} \, a c d^{4} x^{3} + \frac{1}{5} \, a^{2} x^{5} e^{4} + a^{2} d x^{4} e^{3} + 2 \, a^{2} d^{2} x^{3} e^{2} + 2 \, a^{2} d^{3} x^{2} e + a^{2} d^{4} x"," ",0,"1/9*c^2*x^9*e^4 + 1/2*c^2*d*x^8*e^3 + 6/7*c^2*d^2*x^7*e^2 + 2/3*c^2*d^3*x^6*e + 1/5*c^2*d^4*x^5 + 2/7*a*c*x^7*e^4 + 4/3*a*c*d*x^6*e^3 + 12/5*a*c*d^2*x^5*e^2 + 2*a*c*d^3*x^4*e + 2/3*a*c*d^4*x^3 + 1/5*a^2*x^5*e^4 + a^2*d*x^4*e^3 + 2*a^2*d^2*x^3*e^2 + 2*a^2*d^3*x^2*e + a^2*d^4*x","A",0
461,1,128,0,0.161399," ","integrate((e*x+d)^3*(c*x^2+a)^2,x, algorithm=""giac"")","\frac{1}{8} \, c^{2} x^{8} e^{3} + \frac{3}{7} \, c^{2} d x^{7} e^{2} + \frac{1}{2} \, c^{2} d^{2} x^{6} e + \frac{1}{5} \, c^{2} d^{3} x^{5} + \frac{1}{3} \, a c x^{6} e^{3} + \frac{6}{5} \, a c d x^{5} e^{2} + \frac{3}{2} \, a c d^{2} x^{4} e + \frac{2}{3} \, a c d^{3} x^{3} + \frac{1}{4} \, a^{2} x^{4} e^{3} + a^{2} d x^{3} e^{2} + \frac{3}{2} \, a^{2} d^{2} x^{2} e + a^{2} d^{3} x"," ",0,"1/8*c^2*x^8*e^3 + 3/7*c^2*d*x^7*e^2 + 1/2*c^2*d^2*x^6*e + 1/5*c^2*d^3*x^5 + 1/3*a*c*x^6*e^3 + 6/5*a*c*d*x^5*e^2 + 3/2*a*c*d^2*x^4*e + 2/3*a*c*d^3*x^3 + 1/4*a^2*x^4*e^3 + a^2*d*x^3*e^2 + 3/2*a^2*d^2*x^2*e + a^2*d^3*x","A",0
462,1,89,0,0.193601," ","integrate((e*x+d)^2*(c*x^2+a)^2,x, algorithm=""giac"")","\frac{1}{7} \, c^{2} x^{7} e^{2} + \frac{1}{3} \, c^{2} d x^{6} e + \frac{1}{5} \, c^{2} d^{2} x^{5} + \frac{2}{5} \, a c x^{5} e^{2} + a c d x^{4} e + \frac{2}{3} \, a c d^{2} x^{3} + \frac{1}{3} \, a^{2} x^{3} e^{2} + a^{2} d x^{2} e + a^{2} d^{2} x"," ",0,"1/7*c^2*x^7*e^2 + 1/3*c^2*d*x^6*e + 1/5*c^2*d^2*x^5 + 2/5*a*c*x^5*e^2 + a*c*d*x^4*e + 2/3*a*c*d^2*x^3 + 1/3*a^2*x^3*e^2 + a^2*d*x^2*e + a^2*d^2*x","A",0
463,1,53,0,0.193726," ","integrate((e*x+d)*(c*x^2+a)^2,x, algorithm=""giac"")","\frac{1}{6} \, c^{2} x^{6} e + \frac{1}{5} \, c^{2} d x^{5} + \frac{1}{2} \, a c x^{4} e + \frac{2}{3} \, a c d x^{3} + \frac{1}{2} \, a^{2} x^{2} e + a^{2} d x"," ",0,"1/6*c^2*x^6*e + 1/5*c^2*d*x^5 + 1/2*a*c*x^4*e + 2/3*a*c*d*x^3 + 1/2*a^2*x^2*e + a^2*d*x","A",0
464,1,100,0,0.171112," ","integrate((c*x^2+a)^2/(e*x+d),x, algorithm=""giac"")","{\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} e^{\left(-5\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{12} \, {\left(3 \, c^{2} x^{4} e^{3} - 4 \, c^{2} d x^{3} e^{2} + 6 \, c^{2} d^{2} x^{2} e - 12 \, c^{2} d^{3} x + 12 \, a c x^{2} e^{3} - 24 \, a c d x e^{2}\right)} e^{\left(-4\right)}"," ",0,"(c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4)*e^(-5)*log(abs(x*e + d)) + 1/12*(3*c^2*x^4*e^3 - 4*c^2*d*x^3*e^2 + 6*c^2*d^2*x^2*e - 12*c^2*d^3*x + 12*a*c*x^2*e^3 - 24*a*c*d*x*e^2)*e^(-4)","A",0
465,1,149,0,0.175949," ","integrate((c*x^2+a)^2/(e*x+d)^2,x, algorithm=""giac"")","\frac{1}{3} \, {\left(c^{2} - \frac{6 \, c^{2} d}{x e + d} + \frac{6 \, {\left(3 \, c^{2} d^{2} e^{2} + a c e^{4}\right)} e^{\left(-2\right)}}{{\left(x e + d\right)}^{2}}\right)} {\left(x e + d\right)}^{3} e^{\left(-5\right)} + 4 \, {\left(c^{2} d^{3} + a c d e^{2}\right)} e^{\left(-5\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) - {\left(\frac{c^{2} d^{4} e^{3}}{x e + d} + \frac{2 \, a c d^{2} e^{5}}{x e + d} + \frac{a^{2} e^{7}}{x e + d}\right)} e^{\left(-8\right)}"," ",0,"1/3*(c^2 - 6*c^2*d/(x*e + d) + 6*(3*c^2*d^2*e^2 + a*c*e^4)*e^(-2)/(x*e + d)^2)*(x*e + d)^3*e^(-5) + 4*(c^2*d^3 + a*c*d*e^2)*e^(-5)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) - (c^2*d^4*e^3/(x*e + d) + 2*a*c*d^2*e^5/(x*e + d) + a^2*e^7/(x*e + d))*e^(-8)","A",0
466,1,106,0,0.173354," ","integrate((c*x^2+a)^2/(e*x+d)^3,x, algorithm=""giac"")","2 \, {\left(3 \, c^{2} d^{2} + a c e^{2}\right)} e^{\left(-5\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{2} \, {\left(c^{2} x^{2} e^{3} - 6 \, c^{2} d x e^{2}\right)} e^{\left(-6\right)} + \frac{{\left(7 \, c^{2} d^{4} + 6 \, a c d^{2} e^{2} - a^{2} e^{4} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)} e^{\left(-5\right)}}{2 \, {\left(x e + d\right)}^{2}}"," ",0,"2*(3*c^2*d^2 + a*c*e^2)*e^(-5)*log(abs(x*e + d)) + 1/2*(c^2*x^2*e^3 - 6*c^2*d*x*e^2)*e^(-6) + 1/2*(7*c^2*d^4 + 6*a*c*d^2*e^2 - a^2*e^4 + 8*(c^2*d^3*e + a*c*d*e^3)*x)*e^(-5)/(x*e + d)^2","A",0
467,1,101,0,0.157113," ","integrate((c*x^2+a)^2/(e*x+d)^4,x, algorithm=""giac"")","-4 \, c^{2} d e^{\left(-5\right)} \log\left({\left| x e + d \right|}\right) + c^{2} x e^{\left(-4\right)} - \frac{{\left(13 \, c^{2} d^{4} + 2 \, a c d^{2} e^{2} + 6 \, {\left(3 \, c^{2} d^{2} e^{2} + a c e^{4}\right)} x^{2} + a^{2} e^{4} + 6 \, {\left(5 \, c^{2} d^{3} e + a c d e^{3}\right)} x\right)} e^{\left(-5\right)}}{3 \, {\left(x e + d\right)}^{3}}"," ",0,"-4*c^2*d*e^(-5)*log(abs(x*e + d)) + c^2*x*e^(-4) - 1/3*(13*c^2*d^4 + 2*a*c*d^2*e^2 + 6*(3*c^2*d^2*e^2 + a*c*e^4)*x^2 + a^2*e^4 + 6*(5*c^2*d^3*e + a*c*d*e^3)*x)*e^(-5)/(x*e + d)^3","A",0
468,1,163,0,0.180576," ","integrate((c*x^2+a)^2/(e*x+d)^5,x, algorithm=""giac"")","-c^{2} e^{\left(-5\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) + \frac{1}{12} \, {\left(\frac{48 \, c^{2} d e^{15}}{x e + d} - \frac{36 \, c^{2} d^{2} e^{15}}{{\left(x e + d\right)}^{2}} + \frac{16 \, c^{2} d^{3} e^{15}}{{\left(x e + d\right)}^{3}} - \frac{3 \, c^{2} d^{4} e^{15}}{{\left(x e + d\right)}^{4}} - \frac{12 \, a c e^{17}}{{\left(x e + d\right)}^{2}} + \frac{16 \, a c d e^{17}}{{\left(x e + d\right)}^{3}} - \frac{6 \, a c d^{2} e^{17}}{{\left(x e + d\right)}^{4}} - \frac{3 \, a^{2} e^{19}}{{\left(x e + d\right)}^{4}}\right)} e^{\left(-20\right)}"," ",0,"-c^2*e^(-5)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) + 1/12*(48*c^2*d*e^15/(x*e + d) - 36*c^2*d^2*e^15/(x*e + d)^2 + 16*c^2*d^3*e^15/(x*e + d)^3 - 3*c^2*d^4*e^15/(x*e + d)^4 - 12*a*c*e^17/(x*e + d)^2 + 16*a*c*d*e^17/(x*e + d)^3 - 6*a*c*d^2*e^17/(x*e + d)^4 - 3*a^2*e^19/(x*e + d)^4)*e^(-20)","A",0
469,1,98,0,0.157815," ","integrate((c*x^2+a)^2/(e*x+d)^6,x, algorithm=""giac"")","-\frac{{\left(15 \, c^{2} x^{4} e^{4} + 30 \, c^{2} d x^{3} e^{3} + 30 \, c^{2} d^{2} x^{2} e^{2} + 15 \, c^{2} d^{3} x e + 3 \, c^{2} d^{4} + 10 \, a c x^{2} e^{4} + 5 \, a c d x e^{3} + a c d^{2} e^{2} + 3 \, a^{2} e^{4}\right)} e^{\left(-5\right)}}{15 \, {\left(x e + d\right)}^{5}}"," ",0,"-1/15*(15*c^2*x^4*e^4 + 30*c^2*d*x^3*e^3 + 30*c^2*d^2*x^2*e^2 + 15*c^2*d^3*x*e + 3*c^2*d^4 + 10*a*c*x^2*e^4 + 5*a*c*d*x*e^3 + a*c*d^2*e^2 + 3*a^2*e^4)*e^(-5)/(x*e + d)^5","A",0
470,1,97,0,0.154904," ","integrate((c*x^2+a)^2/(e*x+d)^7,x, algorithm=""giac"")","-\frac{{\left(15 \, c^{2} x^{4} e^{4} + 20 \, c^{2} d x^{3} e^{3} + 15 \, c^{2} d^{2} x^{2} e^{2} + 6 \, c^{2} d^{3} x e + c^{2} d^{4} + 15 \, a c x^{2} e^{4} + 6 \, a c d x e^{3} + a c d^{2} e^{2} + 5 \, a^{2} e^{4}\right)} e^{\left(-5\right)}}{30 \, {\left(x e + d\right)}^{6}}"," ",0,"-1/30*(15*c^2*x^4*e^4 + 20*c^2*d*x^3*e^3 + 15*c^2*d^2*x^2*e^2 + 6*c^2*d^3*x*e + c^2*d^4 + 15*a*c*x^2*e^4 + 6*a*c*d*x*e^3 + a*c*d^2*e^2 + 5*a^2*e^4)*e^(-5)/(x*e + d)^6","A",0
471,1,98,0,0.191179," ","integrate((c*x^2+a)^2/(e*x+d)^8,x, algorithm=""giac"")","-\frac{{\left(35 \, c^{2} x^{4} e^{4} + 35 \, c^{2} d x^{3} e^{3} + 21 \, c^{2} d^{2} x^{2} e^{2} + 7 \, c^{2} d^{3} x e + c^{2} d^{4} + 42 \, a c x^{2} e^{4} + 14 \, a c d x e^{3} + 2 \, a c d^{2} e^{2} + 15 \, a^{2} e^{4}\right)} e^{\left(-5\right)}}{105 \, {\left(x e + d\right)}^{7}}"," ",0,"-1/105*(35*c^2*x^4*e^4 + 35*c^2*d*x^3*e^3 + 21*c^2*d^2*x^2*e^2 + 7*c^2*d^3*x*e + c^2*d^4 + 42*a*c*x^2*e^4 + 14*a*c*d*x*e^3 + 2*a*c*d^2*e^2 + 15*a^2*e^4)*e^(-5)/(x*e + d)^7","A",0
472,1,346,0,0.179267," ","integrate((e*x+d)^6*(c*x^2+a)^3,x, algorithm=""giac"")","\frac{1}{13} \, c^{3} x^{13} e^{6} + \frac{1}{2} \, c^{3} d x^{12} e^{5} + \frac{15}{11} \, c^{3} d^{2} x^{11} e^{4} + 2 \, c^{3} d^{3} x^{10} e^{3} + \frac{5}{3} \, c^{3} d^{4} x^{9} e^{2} + \frac{3}{4} \, c^{3} d^{5} x^{8} e + \frac{1}{7} \, c^{3} d^{6} x^{7} + \frac{3}{11} \, a c^{2} x^{11} e^{6} + \frac{9}{5} \, a c^{2} d x^{10} e^{5} + 5 \, a c^{2} d^{2} x^{9} e^{4} + \frac{15}{2} \, a c^{2} d^{3} x^{8} e^{3} + \frac{45}{7} \, a c^{2} d^{4} x^{7} e^{2} + 3 \, a c^{2} d^{5} x^{6} e + \frac{3}{5} \, a c^{2} d^{6} x^{5} + \frac{1}{3} \, a^{2} c x^{9} e^{6} + \frac{9}{4} \, a^{2} c d x^{8} e^{5} + \frac{45}{7} \, a^{2} c d^{2} x^{7} e^{4} + 10 \, a^{2} c d^{3} x^{6} e^{3} + 9 \, a^{2} c d^{4} x^{5} e^{2} + \frac{9}{2} \, a^{2} c d^{5} x^{4} e + a^{2} c d^{6} x^{3} + \frac{1}{7} \, a^{3} x^{7} e^{6} + a^{3} d x^{6} e^{5} + 3 \, a^{3} d^{2} x^{5} e^{4} + 5 \, a^{3} d^{3} x^{4} e^{3} + 5 \, a^{3} d^{4} x^{3} e^{2} + 3 \, a^{3} d^{5} x^{2} e + a^{3} d^{6} x"," ",0,"1/13*c^3*x^13*e^6 + 1/2*c^3*d*x^12*e^5 + 15/11*c^3*d^2*x^11*e^4 + 2*c^3*d^3*x^10*e^3 + 5/3*c^3*d^4*x^9*e^2 + 3/4*c^3*d^5*x^8*e + 1/7*c^3*d^6*x^7 + 3/11*a*c^2*x^11*e^6 + 9/5*a*c^2*d*x^10*e^5 + 5*a*c^2*d^2*x^9*e^4 + 15/2*a*c^2*d^3*x^8*e^3 + 45/7*a*c^2*d^4*x^7*e^2 + 3*a*c^2*d^5*x^6*e + 3/5*a*c^2*d^6*x^5 + 1/3*a^2*c*x^9*e^6 + 9/4*a^2*c*d*x^8*e^5 + 45/7*a^2*c*d^2*x^7*e^4 + 10*a^2*c*d^3*x^6*e^3 + 9*a^2*c*d^4*x^5*e^2 + 9/2*a^2*c*d^5*x^4*e + a^2*c*d^6*x^3 + 1/7*a^3*x^7*e^6 + a^3*d*x^6*e^5 + 3*a^3*d^2*x^5*e^4 + 5*a^3*d^3*x^4*e^3 + 5*a^3*d^4*x^3*e^2 + 3*a^3*d^5*x^2*e + a^3*d^6*x","A",0
473,1,291,0,0.168628," ","integrate((e*x+d)^5*(c*x^2+a)^3,x, algorithm=""giac"")","\frac{1}{12} \, c^{3} x^{12} e^{5} + \frac{5}{11} \, c^{3} d x^{11} e^{4} + c^{3} d^{2} x^{10} e^{3} + \frac{10}{9} \, c^{3} d^{3} x^{9} e^{2} + \frac{5}{8} \, c^{3} d^{4} x^{8} e + \frac{1}{7} \, c^{3} d^{5} x^{7} + \frac{3}{10} \, a c^{2} x^{10} e^{5} + \frac{5}{3} \, a c^{2} d x^{9} e^{4} + \frac{15}{4} \, a c^{2} d^{2} x^{8} e^{3} + \frac{30}{7} \, a c^{2} d^{3} x^{7} e^{2} + \frac{5}{2} \, a c^{2} d^{4} x^{6} e + \frac{3}{5} \, a c^{2} d^{5} x^{5} + \frac{3}{8} \, a^{2} c x^{8} e^{5} + \frac{15}{7} \, a^{2} c d x^{7} e^{4} + 5 \, a^{2} c d^{2} x^{6} e^{3} + 6 \, a^{2} c d^{3} x^{5} e^{2} + \frac{15}{4} \, a^{2} c d^{4} x^{4} e + a^{2} c d^{5} x^{3} + \frac{1}{6} \, a^{3} x^{6} e^{5} + a^{3} d x^{5} e^{4} + \frac{5}{2} \, a^{3} d^{2} x^{4} e^{3} + \frac{10}{3} \, a^{3} d^{3} x^{3} e^{2} + \frac{5}{2} \, a^{3} d^{4} x^{2} e + a^{3} d^{5} x"," ",0,"1/12*c^3*x^12*e^5 + 5/11*c^3*d*x^11*e^4 + c^3*d^2*x^10*e^3 + 10/9*c^3*d^3*x^9*e^2 + 5/8*c^3*d^4*x^8*e + 1/7*c^3*d^5*x^7 + 3/10*a*c^2*x^10*e^5 + 5/3*a*c^2*d*x^9*e^4 + 15/4*a*c^2*d^2*x^8*e^3 + 30/7*a*c^2*d^3*x^7*e^2 + 5/2*a*c^2*d^4*x^6*e + 3/5*a*c^2*d^5*x^5 + 3/8*a^2*c*x^8*e^5 + 15/7*a^2*c*d*x^7*e^4 + 5*a^2*c*d^2*x^6*e^3 + 6*a^2*c*d^3*x^5*e^2 + 15/4*a^2*c*d^4*x^4*e + a^2*c*d^5*x^3 + 1/6*a^3*x^6*e^5 + a^3*d*x^5*e^4 + 5/2*a^3*d^2*x^4*e^3 + 10/3*a^3*d^3*x^3*e^2 + 5/2*a^3*d^4*x^2*e + a^3*d^5*x","A",0
474,1,238,0,0.159331," ","integrate((e*x+d)^4*(c*x^2+a)^3,x, algorithm=""giac"")","\frac{1}{11} \, c^{3} x^{11} e^{4} + \frac{2}{5} \, c^{3} d x^{10} e^{3} + \frac{2}{3} \, c^{3} d^{2} x^{9} e^{2} + \frac{1}{2} \, c^{3} d^{3} x^{8} e + \frac{1}{7} \, c^{3} d^{4} x^{7} + \frac{1}{3} \, a c^{2} x^{9} e^{4} + \frac{3}{2} \, a c^{2} d x^{8} e^{3} + \frac{18}{7} \, a c^{2} d^{2} x^{7} e^{2} + 2 \, a c^{2} d^{3} x^{6} e + \frac{3}{5} \, a c^{2} d^{4} x^{5} + \frac{3}{7} \, a^{2} c x^{7} e^{4} + 2 \, a^{2} c d x^{6} e^{3} + \frac{18}{5} \, a^{2} c d^{2} x^{5} e^{2} + 3 \, a^{2} c d^{3} x^{4} e + a^{2} c d^{4} x^{3} + \frac{1}{5} \, a^{3} x^{5} e^{4} + a^{3} d x^{4} e^{3} + 2 \, a^{3} d^{2} x^{3} e^{2} + 2 \, a^{3} d^{3} x^{2} e + a^{3} d^{4} x"," ",0,"1/11*c^3*x^11*e^4 + 2/5*c^3*d*x^10*e^3 + 2/3*c^3*d^2*x^9*e^2 + 1/2*c^3*d^3*x^8*e + 1/7*c^3*d^4*x^7 + 1/3*a*c^2*x^9*e^4 + 3/2*a*c^2*d*x^8*e^3 + 18/7*a*c^2*d^2*x^7*e^2 + 2*a*c^2*d^3*x^6*e + 3/5*a*c^2*d^4*x^5 + 3/7*a^2*c*x^7*e^4 + 2*a^2*c*d*x^6*e^3 + 18/5*a^2*c*d^2*x^5*e^2 + 3*a^2*c*d^3*x^4*e + a^2*c*d^4*x^3 + 1/5*a^3*x^5*e^4 + a^3*d*x^4*e^3 + 2*a^3*d^2*x^3*e^2 + 2*a^3*d^3*x^2*e + a^3*d^4*x","A",0
475,1,184,0,0.195894," ","integrate((e*x+d)^3*(c*x^2+a)^3,x, algorithm=""giac"")","\frac{1}{10} \, c^{3} x^{10} e^{3} + \frac{1}{3} \, c^{3} d x^{9} e^{2} + \frac{3}{8} \, c^{3} d^{2} x^{8} e + \frac{1}{7} \, c^{3} d^{3} x^{7} + \frac{3}{8} \, a c^{2} x^{8} e^{3} + \frac{9}{7} \, a c^{2} d x^{7} e^{2} + \frac{3}{2} \, a c^{2} d^{2} x^{6} e + \frac{3}{5} \, a c^{2} d^{3} x^{5} + \frac{1}{2} \, a^{2} c x^{6} e^{3} + \frac{9}{5} \, a^{2} c d x^{5} e^{2} + \frac{9}{4} \, a^{2} c d^{2} x^{4} e + a^{2} c d^{3} x^{3} + \frac{1}{4} \, a^{3} x^{4} e^{3} + a^{3} d x^{3} e^{2} + \frac{3}{2} \, a^{3} d^{2} x^{2} e + a^{3} d^{3} x"," ",0,"1/10*c^3*x^10*e^3 + 1/3*c^3*d*x^9*e^2 + 3/8*c^3*d^2*x^8*e + 1/7*c^3*d^3*x^7 + 3/8*a*c^2*x^8*e^3 + 9/7*a*c^2*d*x^7*e^2 + 3/2*a*c^2*d^2*x^6*e + 3/5*a*c^2*d^3*x^5 + 1/2*a^2*c*x^6*e^3 + 9/5*a^2*c*d*x^5*e^2 + 9/4*a^2*c*d^2*x^4*e + a^2*c*d^3*x^3 + 1/4*a^3*x^4*e^3 + a^3*d*x^3*e^2 + 3/2*a^3*d^2*x^2*e + a^3*d^3*x","A",0
476,1,129,0,0.150291," ","integrate((e*x+d)^2*(c*x^2+a)^3,x, algorithm=""giac"")","\frac{1}{9} \, c^{3} x^{9} e^{2} + \frac{1}{4} \, c^{3} d x^{8} e + \frac{1}{7} \, c^{3} d^{2} x^{7} + \frac{3}{7} \, a c^{2} x^{7} e^{2} + a c^{2} d x^{6} e + \frac{3}{5} \, a c^{2} d^{2} x^{5} + \frac{3}{5} \, a^{2} c x^{5} e^{2} + \frac{3}{2} \, a^{2} c d x^{4} e + a^{2} c d^{2} x^{3} + \frac{1}{3} \, a^{3} x^{3} e^{2} + a^{3} d x^{2} e + a^{3} d^{2} x"," ",0,"1/9*c^3*x^9*e^2 + 1/4*c^3*d*x^8*e + 1/7*c^3*d^2*x^7 + 3/7*a*c^2*x^7*e^2 + a*c^2*d*x^6*e + 3/5*a*c^2*d^2*x^5 + 3/5*a^2*c*x^5*e^2 + 3/2*a^2*c*d*x^4*e + a^2*c*d^2*x^3 + 1/3*a^3*x^3*e^2 + a^3*d*x^2*e + a^3*d^2*x","A",0
477,1,77,0,0.154426," ","integrate((e*x+d)*(c*x^2+a)^3,x, algorithm=""giac"")","\frac{1}{8} \, c^{3} x^{8} e + \frac{1}{7} \, c^{3} d x^{7} + \frac{1}{2} \, a c^{2} x^{6} e + \frac{3}{5} \, a c^{2} d x^{5} + \frac{3}{4} \, a^{2} c x^{4} e + a^{2} c d x^{3} + \frac{1}{2} \, a^{3} x^{2} e + a^{3} d x"," ",0,"1/8*c^3*x^8*e + 1/7*c^3*d*x^7 + 1/2*a*c^2*x^6*e + 3/5*a*c^2*d*x^5 + 3/4*a^2*c*x^4*e + a^2*c*d*x^3 + 1/2*a^3*x^2*e + a^3*d*x","A",0
478,1,192,0,0.153945," ","integrate((c*x^2+a)^3/(e*x+d),x, algorithm=""giac"")","{\left(c^{3} d^{6} + 3 \, a c^{2} d^{4} e^{2} + 3 \, a^{2} c d^{2} e^{4} + a^{3} e^{6}\right)} e^{\left(-7\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{60} \, {\left(10 \, c^{3} x^{6} e^{5} - 12 \, c^{3} d x^{5} e^{4} + 15 \, c^{3} d^{2} x^{4} e^{3} - 20 \, c^{3} d^{3} x^{3} e^{2} + 30 \, c^{3} d^{4} x^{2} e - 60 \, c^{3} d^{5} x + 45 \, a c^{2} x^{4} e^{5} - 60 \, a c^{2} d x^{3} e^{4} + 90 \, a c^{2} d^{2} x^{2} e^{3} - 180 \, a c^{2} d^{3} x e^{2} + 90 \, a^{2} c x^{2} e^{5} - 180 \, a^{2} c d x e^{4}\right)} e^{\left(-6\right)}"," ",0,"(c^3*d^6 + 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4 + a^3*e^6)*e^(-7)*log(abs(x*e + d)) + 1/60*(10*c^3*x^6*e^5 - 12*c^3*d*x^5*e^4 + 15*c^3*d^2*x^4*e^3 - 20*c^3*d^3*x^3*e^2 + 30*c^3*d^4*x^2*e - 60*c^3*d^5*x + 45*a*c^2*x^4*e^5 - 60*a*c^2*d*x^3*e^4 + 90*a*c^2*d^2*x^2*e^3 - 180*a*c^2*d^3*x*e^2 + 90*a^2*c*x^2*e^5 - 180*a^2*c*d*x*e^4)*e^(-6)","A",0
479,1,260,0,0.164683," ","integrate((c*x^2+a)^3/(e*x+d)^2,x, algorithm=""giac"")","\frac{1}{10} \, {\left(2 \, c^{3} - \frac{15 \, c^{3} d}{x e + d} + \frac{10 \, {\left(5 \, c^{3} d^{2} e^{2} + a c^{2} e^{4}\right)} e^{\left(-2\right)}}{{\left(x e + d\right)}^{2}} - \frac{20 \, {\left(5 \, c^{3} d^{3} e^{3} + 3 \, a c^{2} d e^{5}\right)} e^{\left(-3\right)}}{{\left(x e + d\right)}^{3}} + \frac{30 \, {\left(5 \, c^{3} d^{4} e^{4} + 6 \, a c^{2} d^{2} e^{6} + a^{2} c e^{8}\right)} e^{\left(-4\right)}}{{\left(x e + d\right)}^{4}}\right)} {\left(x e + d\right)}^{5} e^{\left(-7\right)} + 6 \, {\left(c^{3} d^{5} + 2 \, a c^{2} d^{3} e^{2} + a^{2} c d e^{4}\right)} e^{\left(-7\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) - {\left(\frac{c^{3} d^{6} e^{5}}{x e + d} + \frac{3 \, a c^{2} d^{4} e^{7}}{x e + d} + \frac{3 \, a^{2} c d^{2} e^{9}}{x e + d} + \frac{a^{3} e^{11}}{x e + d}\right)} e^{\left(-12\right)}"," ",0,"1/10*(2*c^3 - 15*c^3*d/(x*e + d) + 10*(5*c^3*d^2*e^2 + a*c^2*e^4)*e^(-2)/(x*e + d)^2 - 20*(5*c^3*d^3*e^3 + 3*a*c^2*d*e^5)*e^(-3)/(x*e + d)^3 + 30*(5*c^3*d^4*e^4 + 6*a*c^2*d^2*e^6 + a^2*c*e^8)*e^(-4)/(x*e + d)^4)*(x*e + d)^5*e^(-7) + 6*(c^3*d^5 + 2*a*c^2*d^3*e^2 + a^2*c*d*e^4)*e^(-7)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) - (c^3*d^6*e^5/(x*e + d) + 3*a*c^2*d^4*e^7/(x*e + d) + 3*a^2*c*d^2*e^9/(x*e + d) + a^3*e^11/(x*e + d))*e^(-12)","A",0
480,1,192,0,0.162689," ","integrate((c*x^2+a)^3/(e*x+d)^3,x, algorithm=""giac"")","3 \, {\left(5 \, c^{3} d^{4} + 6 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}\right)} e^{\left(-7\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{4} \, {\left(c^{3} x^{4} e^{9} - 4 \, c^{3} d x^{3} e^{8} + 12 \, c^{3} d^{2} x^{2} e^{7} - 40 \, c^{3} d^{3} x e^{6} + 6 \, a c^{2} x^{2} e^{9} - 36 \, a c^{2} d x e^{8}\right)} e^{\left(-12\right)} + \frac{{\left(11 \, c^{3} d^{6} + 21 \, a c^{2} d^{4} e^{2} + 9 \, a^{2} c d^{2} e^{4} - a^{3} e^{6} + 12 \, {\left(c^{3} d^{5} e + 2 \, a c^{2} d^{3} e^{3} + a^{2} c d e^{5}\right)} x\right)} e^{\left(-7\right)}}{2 \, {\left(x e + d\right)}^{2}}"," ",0,"3*(5*c^3*d^4 + 6*a*c^2*d^2*e^2 + a^2*c*e^4)*e^(-7)*log(abs(x*e + d)) + 1/4*(c^3*x^4*e^9 - 4*c^3*d*x^3*e^8 + 12*c^3*d^2*x^2*e^7 - 40*c^3*d^3*x*e^6 + 6*a*c^2*x^2*e^9 - 36*a*c^2*d*x*e^8)*e^(-12) + 1/2*(11*c^3*d^6 + 21*a*c^2*d^4*e^2 + 9*a^2*c*d^2*e^4 - a^3*e^6 + 12*(c^3*d^5*e + 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)*x)*e^(-7)/(x*e + d)^2","A",0
481,1,192,0,0.164608," ","integrate((c*x^2+a)^3/(e*x+d)^4,x, algorithm=""giac"")","-4 \, {\left(5 \, c^{3} d^{3} + 3 \, a c^{2} d e^{2}\right)} e^{\left(-7\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{3} \, {\left(c^{3} x^{3} e^{8} - 6 \, c^{3} d x^{2} e^{7} + 30 \, c^{3} d^{2} x e^{6} + 9 \, a c^{2} x e^{8}\right)} e^{\left(-12\right)} - \frac{{\left(37 \, c^{3} d^{6} + 39 \, a c^{2} d^{4} e^{2} + 3 \, a^{2} c d^{2} e^{4} + a^{3} e^{6} + 9 \, {\left(5 \, c^{3} d^{4} e^{2} + 6 \, a c^{2} d^{2} e^{4} + a^{2} c e^{6}\right)} x^{2} + 9 \, {\left(9 \, c^{3} d^{5} e + 10 \, a c^{2} d^{3} e^{3} + a^{2} c d e^{5}\right)} x\right)} e^{\left(-7\right)}}{3 \, {\left(x e + d\right)}^{3}}"," ",0,"-4*(5*c^3*d^3 + 3*a*c^2*d*e^2)*e^(-7)*log(abs(x*e + d)) + 1/3*(c^3*x^3*e^8 - 6*c^3*d*x^2*e^7 + 30*c^3*d^2*x*e^6 + 9*a*c^2*x*e^8)*e^(-12) - 1/3*(37*c^3*d^6 + 39*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4 + a^3*e^6 + 9*(5*c^3*d^4*e^2 + 6*a*c^2*d^2*e^4 + a^2*c*e^6)*x^2 + 9*(9*c^3*d^5*e + 10*a*c^2*d^3*e^3 + a^2*c*d*e^5)*x)*e^(-7)/(x*e + d)^3","A",0
482,1,288,0,0.181334," ","integrate((c*x^2+a)^3/(e*x+d)^5,x, algorithm=""giac"")","\frac{1}{2} \, {\left(c^{3} - \frac{12 \, c^{3} d}{x e + d}\right)} {\left(x e + d\right)}^{2} e^{\left(-7\right)} - 3 \, {\left(5 \, c^{3} d^{2} + a c^{2} e^{2}\right)} e^{\left(-7\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) + \frac{1}{4} \, {\left(\frac{80 \, c^{3} d^{3} e^{29}}{x e + d} - \frac{30 \, c^{3} d^{4} e^{29}}{{\left(x e + d\right)}^{2}} + \frac{8 \, c^{3} d^{5} e^{29}}{{\left(x e + d\right)}^{3}} - \frac{c^{3} d^{6} e^{29}}{{\left(x e + d\right)}^{4}} + \frac{48 \, a c^{2} d e^{31}}{x e + d} - \frac{36 \, a c^{2} d^{2} e^{31}}{{\left(x e + d\right)}^{2}} + \frac{16 \, a c^{2} d^{3} e^{31}}{{\left(x e + d\right)}^{3}} - \frac{3 \, a c^{2} d^{4} e^{31}}{{\left(x e + d\right)}^{4}} - \frac{6 \, a^{2} c e^{33}}{{\left(x e + d\right)}^{2}} + \frac{8 \, a^{2} c d e^{33}}{{\left(x e + d\right)}^{3}} - \frac{3 \, a^{2} c d^{2} e^{33}}{{\left(x e + d\right)}^{4}} - \frac{a^{3} e^{35}}{{\left(x e + d\right)}^{4}}\right)} e^{\left(-36\right)}"," ",0,"1/2*(c^3 - 12*c^3*d/(x*e + d))*(x*e + d)^2*e^(-7) - 3*(5*c^3*d^2 + a*c^2*e^2)*e^(-7)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) + 1/4*(80*c^3*d^3*e^29/(x*e + d) - 30*c^3*d^4*e^29/(x*e + d)^2 + 8*c^3*d^5*e^29/(x*e + d)^3 - c^3*d^6*e^29/(x*e + d)^4 + 48*a*c^2*d*e^31/(x*e + d) - 36*a*c^2*d^2*e^31/(x*e + d)^2 + 16*a*c^2*d^3*e^31/(x*e + d)^3 - 3*a*c^2*d^4*e^31/(x*e + d)^4 - 6*a^2*c*e^33/(x*e + d)^2 + 8*a^2*c*d*e^33/(x*e + d)^3 - 3*a^2*c*d^2*e^33/(x*e + d)^4 - a^3*e^35/(x*e + d)^4)*e^(-36)","A",0
483,1,188,0,0.157665," ","integrate((c*x^2+a)^3/(e*x+d)^6,x, algorithm=""giac"")","-6 \, c^{3} d e^{\left(-7\right)} \log\left({\left| x e + d \right|}\right) + c^{3} x e^{\left(-6\right)} - \frac{{\left(87 \, c^{3} d^{6} + 6 \, a c^{2} d^{4} e^{2} + a^{2} c d^{2} e^{4} + 30 \, {\left(5 \, c^{3} d^{2} e^{4} + a c^{2} e^{6}\right)} x^{4} + 20 \, {\left(25 \, c^{3} d^{3} e^{3} + 3 \, a c^{2} d e^{5}\right)} x^{3} + 2 \, a^{3} e^{6} + 10 \, {\left(65 \, c^{3} d^{4} e^{2} + 6 \, a c^{2} d^{2} e^{4} + a^{2} c e^{6}\right)} x^{2} + 5 \, {\left(77 \, c^{3} d^{5} e + 6 \, a c^{2} d^{3} e^{3} + a^{2} c d e^{5}\right)} x\right)} e^{\left(-7\right)}}{10 \, {\left(x e + d\right)}^{5}}"," ",0,"-6*c^3*d*e^(-7)*log(abs(x*e + d)) + c^3*x*e^(-6) - 1/10*(87*c^3*d^6 + 6*a*c^2*d^4*e^2 + a^2*c*d^2*e^4 + 30*(5*c^3*d^2*e^4 + a*c^2*e^6)*x^4 + 20*(25*c^3*d^3*e^3 + 3*a*c^2*d*e^5)*x^3 + 2*a^3*e^6 + 10*(65*c^3*d^4*e^2 + 6*a*c^2*d^2*e^4 + a^2*c*e^6)*x^2 + 5*(77*c^3*d^5*e + 6*a*c^2*d^3*e^3 + a^2*c*d*e^5)*x)*e^(-7)/(x*e + d)^5","A",0
484,1,196,0,0.165909," ","integrate((c*x^2+a)^3/(e*x+d)^7,x, algorithm=""giac"")","c^{3} e^{\left(-7\right)} \log\left({\left| x e + d \right|}\right) + \frac{{\left(360 \, c^{3} d x^{5} e^{4} + 90 \, {\left(15 \, c^{3} d^{2} e^{3} - a c^{2} e^{5}\right)} x^{4} + 40 \, {\left(55 \, c^{3} d^{3} e^{2} - 3 \, a c^{2} d e^{4}\right)} x^{3} + 15 \, {\left(125 \, c^{3} d^{4} e - 6 \, a c^{2} d^{2} e^{3} - 3 \, a^{2} c e^{5}\right)} x^{2} + 6 \, {\left(137 \, c^{3} d^{5} - 6 \, a c^{2} d^{3} e^{2} - 3 \, a^{2} c d e^{4}\right)} x + {\left(147 \, c^{3} d^{6} - 6 \, a c^{2} d^{4} e^{2} - 3 \, a^{2} c d^{2} e^{4} - 10 \, a^{3} e^{6}\right)} e^{\left(-1\right)}\right)} e^{\left(-6\right)}}{60 \, {\left(x e + d\right)}^{6}}"," ",0,"c^3*e^(-7)*log(abs(x*e + d)) + 1/60*(360*c^3*d*x^5*e^4 + 90*(15*c^3*d^2*e^3 - a*c^2*e^5)*x^4 + 40*(55*c^3*d^3*e^2 - 3*a*c^2*d*e^4)*x^3 + 15*(125*c^3*d^4*e - 6*a*c^2*d^2*e^3 - 3*a^2*c*e^5)*x^2 + 6*(137*c^3*d^5 - 6*a*c^2*d^3*e^2 - 3*a^2*c*d*e^4)*x + (147*c^3*d^6 - 6*a*c^2*d^4*e^2 - 3*a^2*c*d^2*e^4 - 10*a^3*e^6)*e^(-1))*e^(-6)/(x*e + d)^6","A",0
485,1,189,0,0.173775," ","integrate((c*x^2+a)^3/(e*x+d)^8,x, algorithm=""giac"")","-\frac{{\left(35 \, c^{3} x^{6} e^{6} + 105 \, c^{3} d x^{5} e^{5} + 175 \, c^{3} d^{2} x^{4} e^{4} + 175 \, c^{3} d^{3} x^{3} e^{3} + 105 \, c^{3} d^{4} x^{2} e^{2} + 35 \, c^{3} d^{5} x e + 5 \, c^{3} d^{6} + 35 \, a c^{2} x^{4} e^{6} + 35 \, a c^{2} d x^{3} e^{5} + 21 \, a c^{2} d^{2} x^{2} e^{4} + 7 \, a c^{2} d^{3} x e^{3} + a c^{2} d^{4} e^{2} + 21 \, a^{2} c x^{2} e^{6} + 7 \, a^{2} c d x e^{5} + a^{2} c d^{2} e^{4} + 5 \, a^{3} e^{6}\right)} e^{\left(-7\right)}}{35 \, {\left(x e + d\right)}^{7}}"," ",0,"-1/35*(35*c^3*x^6*e^6 + 105*c^3*d*x^5*e^5 + 175*c^3*d^2*x^4*e^4 + 175*c^3*d^3*x^3*e^3 + 105*c^3*d^4*x^2*e^2 + 35*c^3*d^5*x*e + 5*c^3*d^6 + 35*a*c^2*x^4*e^6 + 35*a*c^2*d*x^3*e^5 + 21*a*c^2*d^2*x^2*e^4 + 7*a*c^2*d^3*x*e^3 + a*c^2*d^4*e^2 + 21*a^2*c*x^2*e^6 + 7*a^2*c*d*x*e^5 + a^2*c*d^2*e^4 + 5*a^3*e^6)*e^(-7)/(x*e + d)^7","A",0
486,1,191,0,0.223326," ","integrate((c*x^2+a)^3/(e*x+d)^9,x, algorithm=""giac"")","-\frac{{\left(140 \, c^{3} x^{6} e^{6} + 280 \, c^{3} d x^{5} e^{5} + 350 \, c^{3} d^{2} x^{4} e^{4} + 280 \, c^{3} d^{3} x^{3} e^{3} + 140 \, c^{3} d^{4} x^{2} e^{2} + 40 \, c^{3} d^{5} x e + 5 \, c^{3} d^{6} + 210 \, a c^{2} x^{4} e^{6} + 168 \, a c^{2} d x^{3} e^{5} + 84 \, a c^{2} d^{2} x^{2} e^{4} + 24 \, a c^{2} d^{3} x e^{3} + 3 \, a c^{2} d^{4} e^{2} + 140 \, a^{2} c x^{2} e^{6} + 40 \, a^{2} c d x e^{5} + 5 \, a^{2} c d^{2} e^{4} + 35 \, a^{3} e^{6}\right)} e^{\left(-7\right)}}{280 \, {\left(x e + d\right)}^{8}}"," ",0,"-1/280*(140*c^3*x^6*e^6 + 280*c^3*d*x^5*e^5 + 350*c^3*d^2*x^4*e^4 + 280*c^3*d^3*x^3*e^3 + 140*c^3*d^4*x^2*e^2 + 40*c^3*d^5*x*e + 5*c^3*d^6 + 210*a*c^2*x^4*e^6 + 168*a*c^2*d*x^3*e^5 + 84*a*c^2*d^2*x^2*e^4 + 24*a*c^2*d^3*x*e^3 + 3*a*c^2*d^4*e^2 + 140*a^2*c*x^2*e^6 + 40*a^2*c*d*x*e^5 + 5*a^2*c*d^2*e^4 + 35*a^3*e^6)*e^(-7)/(x*e + d)^8","A",0
487,1,191,0,0.155969," ","integrate((c*x^2+a)^3/(e*x+d)^10,x, algorithm=""giac"")","-\frac{{\left(420 \, c^{3} x^{6} e^{6} + 630 \, c^{3} d x^{5} e^{5} + 630 \, c^{3} d^{2} x^{4} e^{4} + 420 \, c^{3} d^{3} x^{3} e^{3} + 180 \, c^{3} d^{4} x^{2} e^{2} + 45 \, c^{3} d^{5} x e + 5 \, c^{3} d^{6} + 756 \, a c^{2} x^{4} e^{6} + 504 \, a c^{2} d x^{3} e^{5} + 216 \, a c^{2} d^{2} x^{2} e^{4} + 54 \, a c^{2} d^{3} x e^{3} + 6 \, a c^{2} d^{4} e^{2} + 540 \, a^{2} c x^{2} e^{6} + 135 \, a^{2} c d x e^{5} + 15 \, a^{2} c d^{2} e^{4} + 140 \, a^{3} e^{6}\right)} e^{\left(-7\right)}}{1260 \, {\left(x e + d\right)}^{9}}"," ",0,"-1/1260*(420*c^3*x^6*e^6 + 630*c^3*d*x^5*e^5 + 630*c^3*d^2*x^4*e^4 + 420*c^3*d^3*x^3*e^3 + 180*c^3*d^4*x^2*e^2 + 45*c^3*d^5*x*e + 5*c^3*d^6 + 756*a*c^2*x^4*e^6 + 504*a*c^2*d*x^3*e^5 + 216*a*c^2*d^2*x^2*e^4 + 54*a*c^2*d^3*x*e^3 + 6*a*c^2*d^4*e^2 + 540*a^2*c*x^2*e^6 + 135*a^2*c*d*x*e^5 + 15*a^2*c*d^2*e^4 + 140*a^3*e^6)*e^(-7)/(x*e + d)^9","A",0
488,1,522,0,0.224440," ","integrate((e*x+d)^7*(c*x^2+a)^4,x, algorithm=""giac"")","\frac{1}{16} \, c^{4} x^{16} e^{7} + \frac{7}{15} \, c^{4} d x^{15} e^{6} + \frac{3}{2} \, c^{4} d^{2} x^{14} e^{5} + \frac{35}{13} \, c^{4} d^{3} x^{13} e^{4} + \frac{35}{12} \, c^{4} d^{4} x^{12} e^{3} + \frac{21}{11} \, c^{4} d^{5} x^{11} e^{2} + \frac{7}{10} \, c^{4} d^{6} x^{10} e + \frac{1}{9} \, c^{4} d^{7} x^{9} + \frac{2}{7} \, a c^{3} x^{14} e^{7} + \frac{28}{13} \, a c^{3} d x^{13} e^{6} + 7 \, a c^{3} d^{2} x^{12} e^{5} + \frac{140}{11} \, a c^{3} d^{3} x^{11} e^{4} + 14 \, a c^{3} d^{4} x^{10} e^{3} + \frac{28}{3} \, a c^{3} d^{5} x^{9} e^{2} + \frac{7}{2} \, a c^{3} d^{6} x^{8} e + \frac{4}{7} \, a c^{3} d^{7} x^{7} + \frac{1}{2} \, a^{2} c^{2} x^{12} e^{7} + \frac{42}{11} \, a^{2} c^{2} d x^{11} e^{6} + \frac{63}{5} \, a^{2} c^{2} d^{2} x^{10} e^{5} + \frac{70}{3} \, a^{2} c^{2} d^{3} x^{9} e^{4} + \frac{105}{4} \, a^{2} c^{2} d^{4} x^{8} e^{3} + 18 \, a^{2} c^{2} d^{5} x^{7} e^{2} + 7 \, a^{2} c^{2} d^{6} x^{6} e + \frac{6}{5} \, a^{2} c^{2} d^{7} x^{5} + \frac{2}{5} \, a^{3} c x^{10} e^{7} + \frac{28}{9} \, a^{3} c d x^{9} e^{6} + \frac{21}{2} \, a^{3} c d^{2} x^{8} e^{5} + 20 \, a^{3} c d^{3} x^{7} e^{4} + \frac{70}{3} \, a^{3} c d^{4} x^{6} e^{3} + \frac{84}{5} \, a^{3} c d^{5} x^{5} e^{2} + 7 \, a^{3} c d^{6} x^{4} e + \frac{4}{3} \, a^{3} c d^{7} x^{3} + \frac{1}{8} \, a^{4} x^{8} e^{7} + a^{4} d x^{7} e^{6} + \frac{7}{2} \, a^{4} d^{2} x^{6} e^{5} + 7 \, a^{4} d^{3} x^{5} e^{4} + \frac{35}{4} \, a^{4} d^{4} x^{4} e^{3} + 7 \, a^{4} d^{5} x^{3} e^{2} + \frac{7}{2} \, a^{4} d^{6} x^{2} e + a^{4} d^{7} x"," ",0,"1/16*c^4*x^16*e^7 + 7/15*c^4*d*x^15*e^6 + 3/2*c^4*d^2*x^14*e^5 + 35/13*c^4*d^3*x^13*e^4 + 35/12*c^4*d^4*x^12*e^3 + 21/11*c^4*d^5*x^11*e^2 + 7/10*c^4*d^6*x^10*e + 1/9*c^4*d^7*x^9 + 2/7*a*c^3*x^14*e^7 + 28/13*a*c^3*d*x^13*e^6 + 7*a*c^3*d^2*x^12*e^5 + 140/11*a*c^3*d^3*x^11*e^4 + 14*a*c^3*d^4*x^10*e^3 + 28/3*a*c^3*d^5*x^9*e^2 + 7/2*a*c^3*d^6*x^8*e + 4/7*a*c^3*d^7*x^7 + 1/2*a^2*c^2*x^12*e^7 + 42/11*a^2*c^2*d*x^11*e^6 + 63/5*a^2*c^2*d^2*x^10*e^5 + 70/3*a^2*c^2*d^3*x^9*e^4 + 105/4*a^2*c^2*d^4*x^8*e^3 + 18*a^2*c^2*d^5*x^7*e^2 + 7*a^2*c^2*d^6*x^6*e + 6/5*a^2*c^2*d^7*x^5 + 2/5*a^3*c*x^10*e^7 + 28/9*a^3*c*d*x^9*e^6 + 21/2*a^3*c*d^2*x^8*e^5 + 20*a^3*c*d^3*x^7*e^4 + 70/3*a^3*c*d^4*x^6*e^3 + 84/5*a^3*c*d^5*x^5*e^2 + 7*a^3*c*d^6*x^4*e + 4/3*a^3*c*d^7*x^3 + 1/8*a^4*x^8*e^7 + a^4*d*x^7*e^6 + 7/2*a^4*d^2*x^6*e^5 + 7*a^4*d^3*x^5*e^4 + 35/4*a^4*d^4*x^4*e^3 + 7*a^4*d^5*x^3*e^2 + 7/2*a^4*d^6*x^2*e + a^4*d^7*x","B",0
489,1,452,0,0.156883," ","integrate((e*x+d)^6*(c*x^2+a)^4,x, algorithm=""giac"")","\frac{1}{15} \, c^{4} x^{15} e^{6} + \frac{3}{7} \, c^{4} d x^{14} e^{5} + \frac{15}{13} \, c^{4} d^{2} x^{13} e^{4} + \frac{5}{3} \, c^{4} d^{3} x^{12} e^{3} + \frac{15}{11} \, c^{4} d^{4} x^{11} e^{2} + \frac{3}{5} \, c^{4} d^{5} x^{10} e + \frac{1}{9} \, c^{4} d^{6} x^{9} + \frac{4}{13} \, a c^{3} x^{13} e^{6} + 2 \, a c^{3} d x^{12} e^{5} + \frac{60}{11} \, a c^{3} d^{2} x^{11} e^{4} + 8 \, a c^{3} d^{3} x^{10} e^{3} + \frac{20}{3} \, a c^{3} d^{4} x^{9} e^{2} + 3 \, a c^{3} d^{5} x^{8} e + \frac{4}{7} \, a c^{3} d^{6} x^{7} + \frac{6}{11} \, a^{2} c^{2} x^{11} e^{6} + \frac{18}{5} \, a^{2} c^{2} d x^{10} e^{5} + 10 \, a^{2} c^{2} d^{2} x^{9} e^{4} + 15 \, a^{2} c^{2} d^{3} x^{8} e^{3} + \frac{90}{7} \, a^{2} c^{2} d^{4} x^{7} e^{2} + 6 \, a^{2} c^{2} d^{5} x^{6} e + \frac{6}{5} \, a^{2} c^{2} d^{6} x^{5} + \frac{4}{9} \, a^{3} c x^{9} e^{6} + 3 \, a^{3} c d x^{8} e^{5} + \frac{60}{7} \, a^{3} c d^{2} x^{7} e^{4} + \frac{40}{3} \, a^{3} c d^{3} x^{6} e^{3} + 12 \, a^{3} c d^{4} x^{5} e^{2} + 6 \, a^{3} c d^{5} x^{4} e + \frac{4}{3} \, a^{3} c d^{6} x^{3} + \frac{1}{7} \, a^{4} x^{7} e^{6} + a^{4} d x^{6} e^{5} + 3 \, a^{4} d^{2} x^{5} e^{4} + 5 \, a^{4} d^{3} x^{4} e^{3} + 5 \, a^{4} d^{4} x^{3} e^{2} + 3 \, a^{4} d^{5} x^{2} e + a^{4} d^{6} x"," ",0,"1/15*c^4*x^15*e^6 + 3/7*c^4*d*x^14*e^5 + 15/13*c^4*d^2*x^13*e^4 + 5/3*c^4*d^3*x^12*e^3 + 15/11*c^4*d^4*x^11*e^2 + 3/5*c^4*d^5*x^10*e + 1/9*c^4*d^6*x^9 + 4/13*a*c^3*x^13*e^6 + 2*a*c^3*d*x^12*e^5 + 60/11*a*c^3*d^2*x^11*e^4 + 8*a*c^3*d^3*x^10*e^3 + 20/3*a*c^3*d^4*x^9*e^2 + 3*a*c^3*d^5*x^8*e + 4/7*a*c^3*d^6*x^7 + 6/11*a^2*c^2*x^11*e^6 + 18/5*a^2*c^2*d*x^10*e^5 + 10*a^2*c^2*d^2*x^9*e^4 + 15*a^2*c^2*d^3*x^8*e^3 + 90/7*a^2*c^2*d^4*x^7*e^2 + 6*a^2*c^2*d^5*x^6*e + 6/5*a^2*c^2*d^6*x^5 + 4/9*a^3*c*x^9*e^6 + 3*a^3*c*d*x^8*e^5 + 60/7*a^3*c*d^2*x^7*e^4 + 40/3*a^3*c*d^3*x^6*e^3 + 12*a^3*c*d^4*x^5*e^2 + 6*a^3*c*d^5*x^4*e + 4/3*a^3*c*d^6*x^3 + 1/7*a^4*x^7*e^6 + a^4*d*x^6*e^5 + 3*a^4*d^2*x^5*e^4 + 5*a^4*d^3*x^4*e^3 + 5*a^4*d^4*x^3*e^2 + 3*a^4*d^5*x^2*e + a^4*d^6*x","A",0
490,1,382,0,0.158892," ","integrate((e*x+d)^5*(c*x^2+a)^4,x, algorithm=""giac"")","\frac{1}{14} \, c^{4} x^{14} e^{5} + \frac{5}{13} \, c^{4} d x^{13} e^{4} + \frac{5}{6} \, c^{4} d^{2} x^{12} e^{3} + \frac{10}{11} \, c^{4} d^{3} x^{11} e^{2} + \frac{1}{2} \, c^{4} d^{4} x^{10} e + \frac{1}{9} \, c^{4} d^{5} x^{9} + \frac{1}{3} \, a c^{3} x^{12} e^{5} + \frac{20}{11} \, a c^{3} d x^{11} e^{4} + 4 \, a c^{3} d^{2} x^{10} e^{3} + \frac{40}{9} \, a c^{3} d^{3} x^{9} e^{2} + \frac{5}{2} \, a c^{3} d^{4} x^{8} e + \frac{4}{7} \, a c^{3} d^{5} x^{7} + \frac{3}{5} \, a^{2} c^{2} x^{10} e^{5} + \frac{10}{3} \, a^{2} c^{2} d x^{9} e^{4} + \frac{15}{2} \, a^{2} c^{2} d^{2} x^{8} e^{3} + \frac{60}{7} \, a^{2} c^{2} d^{3} x^{7} e^{2} + 5 \, a^{2} c^{2} d^{4} x^{6} e + \frac{6}{5} \, a^{2} c^{2} d^{5} x^{5} + \frac{1}{2} \, a^{3} c x^{8} e^{5} + \frac{20}{7} \, a^{3} c d x^{7} e^{4} + \frac{20}{3} \, a^{3} c d^{2} x^{6} e^{3} + 8 \, a^{3} c d^{3} x^{5} e^{2} + 5 \, a^{3} c d^{4} x^{4} e + \frac{4}{3} \, a^{3} c d^{5} x^{3} + \frac{1}{6} \, a^{4} x^{6} e^{5} + a^{4} d x^{5} e^{4} + \frac{5}{2} \, a^{4} d^{2} x^{4} e^{3} + \frac{10}{3} \, a^{4} d^{3} x^{3} e^{2} + \frac{5}{2} \, a^{4} d^{4} x^{2} e + a^{4} d^{5} x"," ",0,"1/14*c^4*x^14*e^5 + 5/13*c^4*d*x^13*e^4 + 5/6*c^4*d^2*x^12*e^3 + 10/11*c^4*d^3*x^11*e^2 + 1/2*c^4*d^4*x^10*e + 1/9*c^4*d^5*x^9 + 1/3*a*c^3*x^12*e^5 + 20/11*a*c^3*d*x^11*e^4 + 4*a*c^3*d^2*x^10*e^3 + 40/9*a*c^3*d^3*x^9*e^2 + 5/2*a*c^3*d^4*x^8*e + 4/7*a*c^3*d^5*x^7 + 3/5*a^2*c^2*x^10*e^5 + 10/3*a^2*c^2*d*x^9*e^4 + 15/2*a^2*c^2*d^2*x^8*e^3 + 60/7*a^2*c^2*d^3*x^7*e^2 + 5*a^2*c^2*d^4*x^6*e + 6/5*a^2*c^2*d^5*x^5 + 1/2*a^3*c*x^8*e^5 + 20/7*a^3*c*d*x^7*e^4 + 20/3*a^3*c*d^2*x^6*e^3 + 8*a^3*c*d^3*x^5*e^2 + 5*a^3*c*d^4*x^4*e + 4/3*a^3*c*d^5*x^3 + 1/6*a^4*x^6*e^5 + a^4*d*x^5*e^4 + 5/2*a^4*d^2*x^4*e^3 + 10/3*a^4*d^3*x^3*e^2 + 5/2*a^4*d^4*x^2*e + a^4*d^5*x","A",0
491,1,312,0,0.199534," ","integrate((e*x+d)^4*(c*x^2+a)^4,x, algorithm=""giac"")","\frac{1}{13} \, c^{4} x^{13} e^{4} + \frac{1}{3} \, c^{4} d x^{12} e^{3} + \frac{6}{11} \, c^{4} d^{2} x^{11} e^{2} + \frac{2}{5} \, c^{4} d^{3} x^{10} e + \frac{1}{9} \, c^{4} d^{4} x^{9} + \frac{4}{11} \, a c^{3} x^{11} e^{4} + \frac{8}{5} \, a c^{3} d x^{10} e^{3} + \frac{8}{3} \, a c^{3} d^{2} x^{9} e^{2} + 2 \, a c^{3} d^{3} x^{8} e + \frac{4}{7} \, a c^{3} d^{4} x^{7} + \frac{2}{3} \, a^{2} c^{2} x^{9} e^{4} + 3 \, a^{2} c^{2} d x^{8} e^{3} + \frac{36}{7} \, a^{2} c^{2} d^{2} x^{7} e^{2} + 4 \, a^{2} c^{2} d^{3} x^{6} e + \frac{6}{5} \, a^{2} c^{2} d^{4} x^{5} + \frac{4}{7} \, a^{3} c x^{7} e^{4} + \frac{8}{3} \, a^{3} c d x^{6} e^{3} + \frac{24}{5} \, a^{3} c d^{2} x^{5} e^{2} + 4 \, a^{3} c d^{3} x^{4} e + \frac{4}{3} \, a^{3} c d^{4} x^{3} + \frac{1}{5} \, a^{4} x^{5} e^{4} + a^{4} d x^{4} e^{3} + 2 \, a^{4} d^{2} x^{3} e^{2} + 2 \, a^{4} d^{3} x^{2} e + a^{4} d^{4} x"," ",0,"1/13*c^4*x^13*e^4 + 1/3*c^4*d*x^12*e^3 + 6/11*c^4*d^2*x^11*e^2 + 2/5*c^4*d^3*x^10*e + 1/9*c^4*d^4*x^9 + 4/11*a*c^3*x^11*e^4 + 8/5*a*c^3*d*x^10*e^3 + 8/3*a*c^3*d^2*x^9*e^2 + 2*a*c^3*d^3*x^8*e + 4/7*a*c^3*d^4*x^7 + 2/3*a^2*c^2*x^9*e^4 + 3*a^2*c^2*d*x^8*e^3 + 36/7*a^2*c^2*d^2*x^7*e^2 + 4*a^2*c^2*d^3*x^6*e + 6/5*a^2*c^2*d^4*x^5 + 4/7*a^3*c*x^7*e^4 + 8/3*a^3*c*d*x^6*e^3 + 24/5*a^3*c*d^2*x^5*e^2 + 4*a^3*c*d^3*x^4*e + 4/3*a^3*c*d^4*x^3 + 1/5*a^4*x^5*e^4 + a^4*d*x^4*e^3 + 2*a^4*d^2*x^3*e^2 + 2*a^4*d^3*x^2*e + a^4*d^4*x","A",0
492,1,242,0,0.170685," ","integrate((e*x+d)^3*(c*x^2+a)^4,x, algorithm=""giac"")","\frac{1}{12} \, c^{4} x^{12} e^{3} + \frac{3}{11} \, c^{4} d x^{11} e^{2} + \frac{3}{10} \, c^{4} d^{2} x^{10} e + \frac{1}{9} \, c^{4} d^{3} x^{9} + \frac{2}{5} \, a c^{3} x^{10} e^{3} + \frac{4}{3} \, a c^{3} d x^{9} e^{2} + \frac{3}{2} \, a c^{3} d^{2} x^{8} e + \frac{4}{7} \, a c^{3} d^{3} x^{7} + \frac{3}{4} \, a^{2} c^{2} x^{8} e^{3} + \frac{18}{7} \, a^{2} c^{2} d x^{7} e^{2} + 3 \, a^{2} c^{2} d^{2} x^{6} e + \frac{6}{5} \, a^{2} c^{2} d^{3} x^{5} + \frac{2}{3} \, a^{3} c x^{6} e^{3} + \frac{12}{5} \, a^{3} c d x^{5} e^{2} + 3 \, a^{3} c d^{2} x^{4} e + \frac{4}{3} \, a^{3} c d^{3} x^{3} + \frac{1}{4} \, a^{4} x^{4} e^{3} + a^{4} d x^{3} e^{2} + \frac{3}{2} \, a^{4} d^{2} x^{2} e + a^{4} d^{3} x"," ",0,"1/12*c^4*x^12*e^3 + 3/11*c^4*d*x^11*e^2 + 3/10*c^4*d^2*x^10*e + 1/9*c^4*d^3*x^9 + 2/5*a*c^3*x^10*e^3 + 4/3*a*c^3*d*x^9*e^2 + 3/2*a*c^3*d^2*x^8*e + 4/7*a*c^3*d^3*x^7 + 3/4*a^2*c^2*x^8*e^3 + 18/7*a^2*c^2*d*x^7*e^2 + 3*a^2*c^2*d^2*x^6*e + 6/5*a^2*c^2*d^3*x^5 + 2/3*a^3*c*x^6*e^3 + 12/5*a^3*c*d*x^5*e^2 + 3*a^3*c*d^2*x^4*e + 4/3*a^3*c*d^3*x^3 + 1/4*a^4*x^4*e^3 + a^4*d*x^3*e^2 + 3/2*a^4*d^2*x^2*e + a^4*d^3*x","A",0
493,1,171,0,0.153728," ","integrate((e*x+d)^2*(c*x^2+a)^4,x, algorithm=""giac"")","\frac{1}{11} \, c^{4} x^{11} e^{2} + \frac{1}{5} \, c^{4} d x^{10} e + \frac{1}{9} \, c^{4} d^{2} x^{9} + \frac{4}{9} \, a c^{3} x^{9} e^{2} + a c^{3} d x^{8} e + \frac{4}{7} \, a c^{3} d^{2} x^{7} + \frac{6}{7} \, a^{2} c^{2} x^{7} e^{2} + 2 \, a^{2} c^{2} d x^{6} e + \frac{6}{5} \, a^{2} c^{2} d^{2} x^{5} + \frac{4}{5} \, a^{3} c x^{5} e^{2} + 2 \, a^{3} c d x^{4} e + \frac{4}{3} \, a^{3} c d^{2} x^{3} + \frac{1}{3} \, a^{4} x^{3} e^{2} + a^{4} d x^{2} e + a^{4} d^{2} x"," ",0,"1/11*c^4*x^11*e^2 + 1/5*c^4*d*x^10*e + 1/9*c^4*d^2*x^9 + 4/9*a*c^3*x^9*e^2 + a*c^3*d*x^8*e + 4/7*a*c^3*d^2*x^7 + 6/7*a^2*c^2*x^7*e^2 + 2*a^2*c^2*d*x^6*e + 6/5*a^2*c^2*d^2*x^5 + 4/5*a^3*c*x^5*e^2 + 2*a^3*c*d*x^4*e + 4/3*a^3*c*d^2*x^3 + 1/3*a^4*x^3*e^2 + a^4*d*x^2*e + a^4*d^2*x","A",0
494,1,101,0,0.175141," ","integrate((e*x+d)*(c*x^2+a)^4,x, algorithm=""giac"")","\frac{1}{10} \, c^{4} x^{10} e + \frac{1}{9} \, c^{4} d x^{9} + \frac{1}{2} \, a c^{3} x^{8} e + \frac{4}{7} \, a c^{3} d x^{7} + a^{2} c^{2} x^{6} e + \frac{6}{5} \, a^{2} c^{2} d x^{5} + a^{3} c x^{4} e + \frac{4}{3} \, a^{3} c d x^{3} + \frac{1}{2} \, a^{4} x^{2} e + a^{4} d x"," ",0,"1/10*c^4*x^10*e + 1/9*c^4*d*x^9 + 1/2*a*c^3*x^8*e + 4/7*a*c^3*d*x^7 + a^2*c^2*x^6*e + 6/5*a^2*c^2*d*x^5 + a^3*c*x^4*e + 4/3*a^3*c*d*x^3 + 1/2*a^4*x^2*e + a^4*d*x","A",0
495,1,316,0,0.155344," ","integrate((c*x^2+a)^4/(e*x+d),x, algorithm=""giac"")","{\left(c^{4} d^{8} + 4 \, a c^{3} d^{6} e^{2} + 6 \, a^{2} c^{2} d^{4} e^{4} + 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}\right)} e^{\left(-9\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{840} \, {\left(105 \, c^{4} x^{8} e^{7} - 120 \, c^{4} d x^{7} e^{6} + 140 \, c^{4} d^{2} x^{6} e^{5} - 168 \, c^{4} d^{3} x^{5} e^{4} + 210 \, c^{4} d^{4} x^{4} e^{3} - 280 \, c^{4} d^{5} x^{3} e^{2} + 420 \, c^{4} d^{6} x^{2} e - 840 \, c^{4} d^{7} x + 560 \, a c^{3} x^{6} e^{7} - 672 \, a c^{3} d x^{5} e^{6} + 840 \, a c^{3} d^{2} x^{4} e^{5} - 1120 \, a c^{3} d^{3} x^{3} e^{4} + 1680 \, a c^{3} d^{4} x^{2} e^{3} - 3360 \, a c^{3} d^{5} x e^{2} + 1260 \, a^{2} c^{2} x^{4} e^{7} - 1680 \, a^{2} c^{2} d x^{3} e^{6} + 2520 \, a^{2} c^{2} d^{2} x^{2} e^{5} - 5040 \, a^{2} c^{2} d^{3} x e^{4} + 1680 \, a^{3} c x^{2} e^{7} - 3360 \, a^{3} c d x e^{6}\right)} e^{\left(-8\right)}"," ",0,"(c^4*d^8 + 4*a*c^3*d^6*e^2 + 6*a^2*c^2*d^4*e^4 + 4*a^3*c*d^2*e^6 + a^4*e^8)*e^(-9)*log(abs(x*e + d)) + 1/840*(105*c^4*x^8*e^7 - 120*c^4*d*x^7*e^6 + 140*c^4*d^2*x^6*e^5 - 168*c^4*d^3*x^5*e^4 + 210*c^4*d^4*x^4*e^3 - 280*c^4*d^5*x^3*e^2 + 420*c^4*d^6*x^2*e - 840*c^4*d^7*x + 560*a*c^3*x^6*e^7 - 672*a*c^3*d*x^5*e^6 + 840*a*c^3*d^2*x^4*e^5 - 1120*a*c^3*d^3*x^3*e^4 + 1680*a*c^3*d^4*x^2*e^3 - 3360*a*c^3*d^5*x*e^2 + 1260*a^2*c^2*x^4*e^7 - 1680*a^2*c^2*d*x^3*e^6 + 2520*a^2*c^2*d^2*x^2*e^5 - 5040*a^2*c^2*d^3*x*e^4 + 1680*a^3*c*x^2*e^7 - 3360*a^3*c*d*x*e^6)*e^(-8)","A",0
496,1,396,0,0.165780," ","integrate((c*x^2+a)^4/(e*x+d)^2,x, algorithm=""giac"")","\frac{1}{105} \, {\left(15 \, c^{4} - \frac{140 \, c^{4} d}{x e + d} + \frac{84 \, {\left(7 \, c^{4} d^{2} e^{2} + a c^{3} e^{4}\right)} e^{\left(-2\right)}}{{\left(x e + d\right)}^{2}} - \frac{210 \, {\left(7 \, c^{4} d^{3} e^{3} + 3 \, a c^{3} d e^{5}\right)} e^{\left(-3\right)}}{{\left(x e + d\right)}^{3}} + \frac{70 \, {\left(35 \, c^{4} d^{4} e^{4} + 30 \, a c^{3} d^{2} e^{6} + 3 \, a^{2} c^{2} e^{8}\right)} e^{\left(-4\right)}}{{\left(x e + d\right)}^{4}} - \frac{420 \, {\left(7 \, c^{4} d^{5} e^{5} + 10 \, a c^{3} d^{3} e^{7} + 3 \, a^{2} c^{2} d e^{9}\right)} e^{\left(-5\right)}}{{\left(x e + d\right)}^{5}} + \frac{420 \, {\left(7 \, c^{4} d^{6} e^{6} + 15 \, a c^{3} d^{4} e^{8} + 9 \, a^{2} c^{2} d^{2} e^{10} + a^{3} c e^{12}\right)} e^{\left(-6\right)}}{{\left(x e + d\right)}^{6}}\right)} {\left(x e + d\right)}^{7} e^{\left(-9\right)} + 8 \, {\left(c^{4} d^{7} + 3 \, a c^{3} d^{5} e^{2} + 3 \, a^{2} c^{2} d^{3} e^{4} + a^{3} c d e^{6}\right)} e^{\left(-9\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) - {\left(\frac{c^{4} d^{8} e^{7}}{x e + d} + \frac{4 \, a c^{3} d^{6} e^{9}}{x e + d} + \frac{6 \, a^{2} c^{2} d^{4} e^{11}}{x e + d} + \frac{4 \, a^{3} c d^{2} e^{13}}{x e + d} + \frac{a^{4} e^{15}}{x e + d}\right)} e^{\left(-16\right)}"," ",0,"1/105*(15*c^4 - 140*c^4*d/(x*e + d) + 84*(7*c^4*d^2*e^2 + a*c^3*e^4)*e^(-2)/(x*e + d)^2 - 210*(7*c^4*d^3*e^3 + 3*a*c^3*d*e^5)*e^(-3)/(x*e + d)^3 + 70*(35*c^4*d^4*e^4 + 30*a*c^3*d^2*e^6 + 3*a^2*c^2*e^8)*e^(-4)/(x*e + d)^4 - 420*(7*c^4*d^5*e^5 + 10*a*c^3*d^3*e^7 + 3*a^2*c^2*d*e^9)*e^(-5)/(x*e + d)^5 + 420*(7*c^4*d^6*e^6 + 15*a*c^3*d^4*e^8 + 9*a^2*c^2*d^2*e^10 + a^3*c*e^12)*e^(-6)/(x*e + d)^6)*(x*e + d)^7*e^(-9) + 8*(c^4*d^7 + 3*a*c^3*d^5*e^2 + 3*a^2*c^2*d^3*e^4 + a^3*c*d*e^6)*e^(-9)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) - (c^4*d^8*e^7/(x*e + d) + 4*a*c^3*d^6*e^9/(x*e + d) + 6*a^2*c^2*d^4*e^11/(x*e + d) + 4*a^3*c*d^2*e^13/(x*e + d) + a^4*e^15/(x*e + d))*e^(-16)","A",0
497,1,96,0,0.161345," ","integrate((d*x+c)*(b*x^2+a)^4,x, algorithm=""giac"")","\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*b^4*d*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",0
498,1,113,0,0.180956," ","integrate((e*x+d)^4/(c*x^2+a),x, algorithm=""giac"")","\frac{2 \, {\left(c d^{3} e - a d e^{3}\right)} \log\left(c x^{2} + a\right)}{c^{2}} + \frac{{\left(c^{2} d^{4} - 6 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{\sqrt{a c} c^{2}} + \frac{c^{2} x^{3} e^{4} + 6 \, c^{2} d x^{2} e^{3} + 18 \, c^{2} d^{2} x e^{2} - 3 \, a c x e^{4}}{3 \, c^{3}}"," ",0,"2*(c*d^3*e - a*d*e^3)*log(c*x^2 + a)/c^2 + (c^2*d^4 - 6*a*c*d^2*e^2 + a^2*e^4)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*c^2) + 1/3*(c^2*x^3*e^4 + 6*c^2*d*x^2*e^3 + 18*c^2*d^2*x*e^2 - 3*a*c*x*e^4)/c^3","A",0
499,1,78,0,0.154299," ","integrate((e*x+d)^3/(c*x^2+a),x, algorithm=""giac"")","\frac{{\left(c d^{3} - 3 \, a d e^{2}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{\sqrt{a c} c} + \frac{{\left(3 \, c d^{2} e - a e^{3}\right)} \log\left(c x^{2} + a\right)}{2 \, c^{2}} + \frac{c x^{2} e^{3} + 6 \, c d x e^{2}}{2 \, c^{2}}"," ",0,"(c*d^3 - 3*a*d*e^2)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*c) + 1/2*(3*c*d^2*e - a*e^3)*log(c*x^2 + a)/c^2 + 1/2*(c*x^2*e^3 + 6*c*d*x*e^2)/c^2","A",0
500,1,52,0,0.152512," ","integrate((e*x+d)^2/(c*x^2+a),x, algorithm=""giac"")","\frac{d e \log\left(c x^{2} + a\right)}{c} + \frac{x e^{2}}{c} + \frac{{\left(c d^{2} - a e^{2}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{\sqrt{a c} c}"," ",0,"d*e*log(c*x^2 + a)/c + x*e^2/c + (c*d^2 - a*e^2)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*c)","A",0
501,1,32,0,0.175045," ","integrate((e*x+d)/(c*x^2+a),x, algorithm=""giac"")","\frac{d \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{\sqrt{a c}} + \frac{e \log\left(c x^{2} + a\right)}{2 \, c}"," ",0,"d*arctan(c*x/sqrt(a*c))/sqrt(a*c) + 1/2*e*log(c*x^2 + a)/c","A",0
502,1,79,0,0.172343," ","integrate(1/(e*x+d)/(c*x^2+a),x, algorithm=""giac"")","\frac{c d \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{{\left(c d^{2} + a e^{2}\right)} \sqrt{a c}} - \frac{e \log\left(c x^{2} + a\right)}{2 \, {\left(c d^{2} + a e^{2}\right)}} + \frac{e^{2} \log\left({\left| x e + d \right|}\right)}{c d^{2} e + a e^{3}}"," ",0,"c*d*arctan(c*x/sqrt(a*c))/((c*d^2 + a*e^2)*sqrt(a*c)) - 1/2*e*log(c*x^2 + a)/(c*d^2 + a*e^2) + e^2*log(abs(x*e + d))/(c*d^2*e + a*e^3)","A",0
503,1,187,0,0.160468," ","integrate(1/(e*x+d)^2/(c*x^2+a),x, algorithm=""giac"")","-\frac{c d e \log\left(c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right)}{c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}} + \frac{{\left(c^{2} d^{2} e^{2} - a c e^{4}\right)} \arctan\left(\frac{{\left(c d - \frac{c d^{2}}{x e + d} - \frac{a e^{2}}{x e + d}\right)} e^{\left(-1\right)}}{\sqrt{a c}}\right) e^{\left(-2\right)}}{{\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} \sqrt{a c}} - \frac{e^{3}}{{\left(c d^{2} e^{2} + a e^{4}\right)} {\left(x e + d\right)}}"," ",0,"-c*d*e*log(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + a*e^2/(x*e + d)^2)/(c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4) + (c^2*d^2*e^2 - a*c*e^4)*arctan((c*d - c*d^2/(x*e + d) - a*e^2/(x*e + d))*e^(-1)/sqrt(a*c))*e^(-2)/((c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(a*c)) - e^3/((c*d^2*e^2 + a*e^4)*(x*e + d))","A",0
504,1,269,0,0.198248," ","integrate(1/(e*x+d)^3/(c*x^2+a),x, algorithm=""giac"")","-\frac{{\left(3 \, c^{2} d^{2} e - a c e^{3}\right)} \log\left(c x^{2} + a\right)}{2 \, {\left(c^{3} d^{6} + 3 \, a c^{2} d^{4} e^{2} + 3 \, a^{2} c d^{2} e^{4} + a^{3} e^{6}\right)}} + \frac{{\left(3 \, c^{2} d^{2} e^{2} - a c e^{4}\right)} \log\left({\left| x e + d \right|}\right)}{c^{3} d^{6} e + 3 \, a c^{2} d^{4} e^{3} + 3 \, a^{2} c d^{2} e^{5} + a^{3} e^{7}} + \frac{{\left(c^{3} d^{3} - 3 \, a c^{2} d e^{2}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{{\left(c^{3} d^{6} + 3 \, a c^{2} d^{4} e^{2} + 3 \, a^{2} c d^{2} e^{4} + a^{3} e^{6}\right)} \sqrt{a c}} - \frac{5 \, c^{2} d^{4} e + 6 \, a c d^{2} e^{3} + a^{2} e^{5} + 4 \, {\left(c^{2} d^{3} e^{2} + a c d e^{4}\right)} x}{2 \, {\left(c d^{2} + a e^{2}\right)}^{3} {\left(x e + d\right)}^{2}}"," ",0,"-1/2*(3*c^2*d^2*e - a*c*e^3)*log(c*x^2 + a)/(c^3*d^6 + 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4 + a^3*e^6) + (3*c^2*d^2*e^2 - a*c*e^4)*log(abs(x*e + d))/(c^3*d^6*e + 3*a*c^2*d^4*e^3 + 3*a^2*c*d^2*e^5 + a^3*e^7) + (c^3*d^3 - 3*a*c^2*d*e^2)*arctan(c*x/sqrt(a*c))/((c^3*d^6 + 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4 + a^3*e^6)*sqrt(a*c)) - 1/2*(5*c^2*d^4*e + 6*a*c*d^2*e^3 + a^2*e^5 + 4*(c^2*d^3*e^2 + a*c*d*e^4)*x)/((c*d^2 + a*e^2)^3*(x*e + d)^2)","A",0
505,1,175,0,0.167168," ","integrate((e*x+d)^5/(c*x^2+a)^2,x, algorithm=""giac"")","\frac{{\left(5 \, c d^{2} e^{3} - a e^{5}\right)} \log\left(c x^{2} + a\right)}{c^{3}} + \frac{{\left(c^{2} d^{5} + 10 \, a c d^{3} e^{2} - 15 \, a^{2} d e^{4}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{2 \, \sqrt{a c} a c^{2}} + \frac{c^{2} x^{2} e^{5} + 10 \, c^{2} d x e^{4}}{2 \, c^{4}} - \frac{5 \, a c^{2} d^{4} e - 10 \, a^{2} c d^{2} e^{3} + a^{3} e^{5} - {\left(c^{3} d^{5} - 10 \, a c^{2} d^{3} e^{2} + 5 \, a^{2} c d e^{4}\right)} x}{2 \, {\left(c x^{2} + a\right)} a c^{3}}"," ",0,"(5*c*d^2*e^3 - a*e^5)*log(c*x^2 + a)/c^3 + 1/2*(c^2*d^5 + 10*a*c*d^3*e^2 - 15*a^2*d*e^4)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*a*c^2) + 1/2*(c^2*x^2*e^5 + 10*c^2*d*x*e^4)/c^4 - 1/2*(5*a*c^2*d^4*e - 10*a^2*c*d^2*e^3 + a^3*e^5 - (c^3*d^5 - 10*a*c^2*d^3*e^2 + 5*a^2*c*d*e^4)*x)/((c*x^2 + a)*a*c^3)","A",0
506,1,131,0,0.156992," ","integrate((e*x+d)^4/(c*x^2+a)^2,x, algorithm=""giac"")","\frac{2 \, d e^{3} \log\left(c x^{2} + a\right)}{c^{2}} + \frac{x e^{4}}{c^{2}} + \frac{{\left(c^{2} d^{4} + 6 \, a c d^{2} e^{2} - 3 \, a^{2} e^{4}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{2 \, \sqrt{a c} a c^{2}} - \frac{4 \, a c d^{3} e - 4 \, a^{2} d e^{3} - {\left(c^{2} d^{4} - 6 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} x}{2 \, {\left(c x^{2} + a\right)} a c^{2}}"," ",0,"2*d*e^3*log(c*x^2 + a)/c^2 + x*e^4/c^2 + 1/2*(c^2*d^4 + 6*a*c*d^2*e^2 - 3*a^2*e^4)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*a*c^2) - 1/2*(4*a*c*d^3*e - 4*a^2*d*e^3 - (c^2*d^4 - 6*a*c*d^2*e^2 + a^2*e^4)*x)/((c*x^2 + a)*a*c^2)","A",0
507,1,104,0,0.158766," ","integrate((e*x+d)^3/(c*x^2+a)^2,x, algorithm=""giac"")","\frac{e^{3} \log\left(c x^{2} + a\right)}{2 \, c^{2}} + \frac{{\left(c d^{3} + 3 \, a d e^{2}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{2 \, \sqrt{a c} a c} + \frac{{\left(c d^{3} - 3 \, a d e^{2}\right)} x - \frac{3 \, a c d^{2} e - a^{2} e^{3}}{c}}{2 \, {\left(c x^{2} + a\right)} a c}"," ",0,"1/2*e^3*log(c*x^2 + a)/c^2 + 1/2*(c*d^3 + 3*a*d*e^2)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*a*c) + 1/2*((c*d^3 - 3*a*d*e^2)*x - (3*a*c*d^2*e - a^2*e^3)/c)/((c*x^2 + a)*a*c)","A",0
508,1,69,0,0.175571," ","integrate((e*x+d)^2/(c*x^2+a)^2,x, algorithm=""giac"")","\frac{{\left(c d^{2} + a e^{2}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{2 \, \sqrt{a c} a c} + \frac{c d^{2} x - a x e^{2} - 2 \, a d e}{2 \, {\left(c x^{2} + a\right)} a c}"," ",0,"1/2*(c*d^2 + a*e^2)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*a*c) + 1/2*(c*d^2*x - a*x*e^2 - 2*a*d*e)/((c*x^2 + a)*a*c)","A",0
509,1,48,0,0.152569," ","integrate((e*x+d)/(c*x^2+a)^2,x, algorithm=""giac"")","\frac{d \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{2 \, \sqrt{a c} a} + \frac{c d x - a e}{2 \, {\left(c x^{2} + a\right)} a c}"," ",0,"1/2*d*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*a) + 1/2*(c*d*x - a*e)/((c*x^2 + a)*a*c)","A",0
510,1,192,0,0.158992," ","integrate(1/(e*x+d)/(c*x^2+a)^2,x, algorithm=""giac"")","-\frac{e^{3} \log\left(c x^{2} + a\right)}{2 \, {\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)}} + \frac{e^{4} \log\left({\left| x e + d \right|}\right)}{c^{2} d^{4} e + 2 \, a c d^{2} e^{3} + a^{2} e^{5}} + \frac{{\left(c^{2} d^{3} + 3 \, a c d e^{2}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{2 \, {\left(a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} \sqrt{a c}} + \frac{a c d^{2} e + a^{2} e^{3} + {\left(c^{2} d^{3} + a c d e^{2}\right)} x}{2 \, {\left(c d^{2} + a e^{2}\right)}^{2} {\left(c x^{2} + a\right)} a}"," ",0,"-1/2*e^3*log(c*x^2 + a)/(c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4) + e^4*log(abs(x*e + d))/(c^2*d^4*e + 2*a*c*d^2*e^3 + a^2*e^5) + 1/2*(c^2*d^3 + 3*a*c*d*e^2)*arctan(c*x/sqrt(a*c))/((a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4)*sqrt(a*c)) + 1/2*(a*c*d^2*e + a^2*e^3 + (c^2*d^3 + a*c*d*e^2)*x)/((c*d^2 + a*e^2)^2*(c*x^2 + a)*a)","A",0
511,1,386,0,0.165986," ","integrate(1/(e*x+d)^2/(c*x^2+a)^2,x, algorithm=""giac"")","-\frac{2 \, c d e^{3} \log\left(c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right)}{c^{3} d^{6} + 3 \, a c^{2} d^{4} e^{2} + 3 \, a^{2} c d^{2} e^{4} + a^{3} e^{6}} + \frac{{\left(c^{3} d^{4} e^{2} + 6 \, a c^{2} d^{2} e^{4} - 3 \, a^{2} c e^{6}\right)} \arctan\left(\frac{{\left(c d - \frac{c d^{2}}{x e + d} - \frac{a e^{2}}{x e + d}\right)} e^{\left(-1\right)}}{\sqrt{a c}}\right) e^{\left(-2\right)}}{2 \, {\left(a c^{3} d^{6} + 3 \, a^{2} c^{2} d^{4} e^{2} + 3 \, a^{3} c d^{2} e^{4} + a^{4} e^{6}\right)} \sqrt{a c}} - \frac{e^{7}}{{\left(c^{2} d^{4} e^{4} + 2 \, a c d^{2} e^{6} + a^{2} e^{8}\right)} {\left(x e + d\right)}} + \frac{\frac{c^{3} d^{3} e - 3 \, a c^{2} d e^{3}}{c d^{2} + a e^{2}} - \frac{{\left(c^{3} d^{4} e^{2} - 6 \, a c^{2} d^{2} e^{4} + a^{2} c e^{6}\right)} e^{\left(-1\right)}}{{\left(c d^{2} + a e^{2}\right)} {\left(x e + d\right)}}}{2 \, {\left(c d^{2} + a e^{2}\right)}^{2} a {\left(c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right)}}"," ",0,"-2*c*d*e^3*log(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + a*e^2/(x*e + d)^2)/(c^3*d^6 + 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4 + a^3*e^6) + 1/2*(c^3*d^4*e^2 + 6*a*c^2*d^2*e^4 - 3*a^2*c*e^6)*arctan((c*d - c*d^2/(x*e + d) - a*e^2/(x*e + d))*e^(-1)/sqrt(a*c))*e^(-2)/((a*c^3*d^6 + 3*a^2*c^2*d^4*e^2 + 3*a^3*c*d^2*e^4 + a^4*e^6)*sqrt(a*c)) - e^7/((c^2*d^4*e^4 + 2*a*c*d^2*e^6 + a^2*e^8)*(x*e + d)) + 1/2*((c^3*d^3*e - 3*a*c^2*d*e^3)/(c*d^2 + a*e^2) - (c^3*d^4*e^2 - 6*a*c^2*d^2*e^4 + a^2*c*e^6)*e^(-1)/((c*d^2 + a*e^2)*(x*e + d)))/((c*d^2 + a*e^2)^2*a*(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + a*e^2/(x*e + d)^2))","B",0
512,1,207,0,0.174176," ","integrate((e*x+d)^5/(c*x^2+a)^3,x, algorithm=""giac"")","\frac{e^{5} \log\left(c x^{2} + a\right)}{2 \, c^{3}} + \frac{{\left(3 \, c^{2} d^{5} + 10 \, a c d^{3} e^{2} + 15 \, a^{2} d e^{4}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{8 \, \sqrt{a c} a^{2} c^{2}} + \frac{{\left(3 \, c^{3} d^{5} + 10 \, a c^{2} d^{3} e^{2} - 25 \, a^{2} c d e^{4}\right)} x^{3} - 8 \, {\left(5 \, a^{2} c d^{2} e^{3} - a^{3} e^{5}\right)} x^{2} + 5 \, {\left(a c^{2} d^{5} - 2 \, a^{2} c d^{3} e^{2} - 3 \, a^{3} d e^{4}\right)} x - \frac{2 \, {\left(5 \, a^{2} c^{2} d^{4} e + 10 \, a^{3} c d^{2} e^{3} - 3 \, a^{4} e^{5}\right)}}{c}}{8 \, {\left(c x^{2} + a\right)}^{2} a^{2} c^{2}}"," ",0,"1/2*e^5*log(c*x^2 + a)/c^3 + 1/8*(3*c^2*d^5 + 10*a*c*d^3*e^2 + 15*a^2*d*e^4)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*a^2*c^2) + 1/8*((3*c^3*d^5 + 10*a*c^2*d^3*e^2 - 25*a^2*c*d*e^4)*x^3 - 8*(5*a^2*c*d^2*e^3 - a^3*e^5)*x^2 + 5*(a*c^2*d^5 - 2*a^2*c*d^3*e^2 - 3*a^3*d*e^4)*x - 2*(5*a^2*c^2*d^4*e + 10*a^3*c*d^2*e^3 - 3*a^4*e^5)/c)/((c*x^2 + a)^2*a^2*c^2)","A",0
513,1,161,0,0.190084," ","integrate((e*x+d)^4/(c*x^2+a)^3,x, algorithm=""giac"")","\frac{3 \, {\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{8 \, \sqrt{a c} a^{2} c^{2}} + \frac{3 \, c^{3} d^{4} x^{3} + 6 \, a c^{2} d^{2} x^{3} e^{2} + 5 \, a c^{2} d^{4} x - 5 \, a^{2} c x^{3} e^{4} - 16 \, a^{2} c d x^{2} e^{3} - 6 \, a^{2} c d^{2} x e^{2} - 8 \, a^{2} c d^{3} e - 3 \, a^{3} x e^{4} - 8 \, a^{3} d e^{3}}{8 \, {\left(c x^{2} + a\right)}^{2} a^{2} c^{2}}"," ",0,"3/8*(c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*a^2*c^2) + 1/8*(3*c^3*d^4*x^3 + 6*a*c^2*d^2*x^3*e^2 + 5*a*c^2*d^4*x - 5*a^2*c*x^3*e^4 - 16*a^2*c*d*x^2*e^3 - 6*a^2*c*d^2*x*e^2 - 8*a^2*c*d^3*e - 3*a^3*x*e^4 - 8*a^3*d*e^3)/((c*x^2 + a)^2*a^2*c^2)","A",0
514,1,124,0,0.177833," ","integrate((e*x+d)^3/(c*x^2+a)^3,x, algorithm=""giac"")","\frac{3 \, {\left(c d^{3} + a d e^{2}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{8 \, \sqrt{a c} a^{2} c} + \frac{3 \, c^{3} d^{3} x^{3} + 3 \, a c^{2} d x^{3} e^{2} + 5 \, a c^{2} d^{3} x - 4 \, a^{2} c x^{2} e^{3} - 3 \, a^{2} c d x e^{2} - 6 \, a^{2} c d^{2} e - 2 \, a^{3} e^{3}}{8 \, {\left(c x^{2} + a\right)}^{2} a^{2} c^{2}}"," ",0,"3/8*(c*d^3 + a*d*e^2)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*a^2*c) + 1/8*(3*c^3*d^3*x^3 + 3*a*c^2*d*x^3*e^2 + 5*a*c^2*d^3*x - 4*a^2*c*x^2*e^3 - 3*a^2*c*d*x*e^2 - 6*a^2*c*d^2*e - 2*a^3*e^3)/((c*x^2 + a)^2*a^2*c^2)","A",0
515,1,95,0,0.172363," ","integrate((e*x+d)^2/(c*x^2+a)^3,x, algorithm=""giac"")","\frac{{\left(3 \, c d^{2} + a e^{2}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{8 \, \sqrt{a c} a^{2} c} + \frac{3 \, c^{2} d^{2} x^{3} + a c x^{3} e^{2} + 5 \, a c d^{2} x - a^{2} x e^{2} - 4 \, a^{2} d e}{8 \, {\left(c x^{2} + a\right)}^{2} a^{2} c}"," ",0,"1/8*(3*c*d^2 + a*e^2)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*a^2*c) + 1/8*(3*c^2*d^2*x^3 + a*c*x^3*e^2 + 5*a*c*d^2*x - a^2*x*e^2 - 4*a^2*d*e)/((c*x^2 + a)^2*a^2*c)","A",0
516,1,61,0,0.155704," ","integrate((e*x+d)/(c*x^2+a)^3,x, algorithm=""giac"")","\frac{3 \, d \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{8 \, \sqrt{a c} a^{2}} + \frac{3 \, c^{2} d x^{3} + 5 \, a c d x - 2 \, a^{2} e}{8 \, {\left(c x^{2} + a\right)}^{2} a^{2} c}"," ",0,"3/8*d*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*a^2) + 1/8*(3*c^2*d*x^3 + 5*a*c*d*x - 2*a^2*e)/((c*x^2 + a)^2*a^2*c)","A",0
517,1,342,0,0.166563," ","integrate(1/(e*x+d)/(c*x^2+a)^3,x, algorithm=""giac"")","-\frac{e^{5} \log\left(c x^{2} + a\right)}{2 \, {\left(c^{3} d^{6} + 3 \, a c^{2} d^{4} e^{2} + 3 \, a^{2} c d^{2} e^{4} + a^{3} e^{6}\right)}} + \frac{e^{6} \log\left({\left| x e + d \right|}\right)}{c^{3} d^{6} e + 3 \, a c^{2} d^{4} e^{3} + 3 \, a^{2} c d^{2} e^{5} + a^{3} e^{7}} + \frac{{\left(3 \, c^{3} d^{5} + 10 \, a c^{2} d^{3} e^{2} + 15 \, a^{2} c d e^{4}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{8 \, {\left(a^{2} c^{3} d^{6} + 3 \, a^{3} c^{2} d^{4} e^{2} + 3 \, a^{4} c d^{2} e^{4} + a^{5} e^{6}\right)} \sqrt{a c}} + \frac{2 \, a^{2} c^{2} d^{4} e + 8 \, a^{3} c d^{2} e^{3} + 6 \, a^{4} e^{5} + {\left(3 \, c^{4} d^{5} + 10 \, a c^{3} d^{3} e^{2} + 7 \, a^{2} c^{2} d e^{4}\right)} x^{3} + 4 \, {\left(a^{2} c^{2} d^{2} e^{3} + a^{3} c e^{5}\right)} x^{2} + {\left(5 \, a c^{3} d^{5} + 14 \, a^{2} c^{2} d^{3} e^{2} + 9 \, a^{3} c d e^{4}\right)} x}{8 \, {\left(c d^{2} + a e^{2}\right)}^{3} {\left(c x^{2} + a\right)}^{2} a^{2}}"," ",0,"-1/2*e^5*log(c*x^2 + a)/(c^3*d^6 + 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4 + a^3*e^6) + e^6*log(abs(x*e + d))/(c^3*d^6*e + 3*a*c^2*d^4*e^3 + 3*a^2*c*d^2*e^5 + a^3*e^7) + 1/8*(3*c^3*d^5 + 10*a*c^2*d^3*e^2 + 15*a^2*c*d*e^4)*arctan(c*x/sqrt(a*c))/((a^2*c^3*d^6 + 3*a^3*c^2*d^4*e^2 + 3*a^4*c*d^2*e^4 + a^5*e^6)*sqrt(a*c)) + 1/8*(2*a^2*c^2*d^4*e + 8*a^3*c*d^2*e^3 + 6*a^4*e^5 + (3*c^4*d^5 + 10*a*c^3*d^3*e^2 + 7*a^2*c^2*d*e^4)*x^3 + 4*(a^2*c^2*d^2*e^3 + a^3*c*e^5)*x^2 + (5*a*c^3*d^5 + 14*a^2*c^2*d^3*e^2 + 9*a^3*c*d*e^4)*x)/((c*d^2 + a*e^2)^3*(c*x^2 + a)^2*a^2)","A",0
518,1,569,0,0.190316," ","integrate(1/(e*x+d)^2/(c*x^2+a)^3,x, algorithm=""giac"")","-\frac{3 \, c d e^{5} \log\left(c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right)}{c^{4} d^{8} + 4 \, a c^{3} d^{6} e^{2} + 6 \, a^{2} c^{2} d^{4} e^{4} + 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}} + \frac{3 \, {\left(c^{4} d^{6} e^{2} + 5 \, a c^{3} d^{4} e^{4} + 15 \, a^{2} c^{2} d^{2} e^{6} - 5 \, a^{3} c e^{8}\right)} \arctan\left(\frac{{\left(c d - \frac{c d^{2}}{x e + d} - \frac{a e^{2}}{x e + d}\right)} e^{\left(-1\right)}}{\sqrt{a c}}\right) e^{\left(-2\right)}}{8 \, {\left(a^{2} c^{4} d^{8} + 4 \, a^{3} c^{3} d^{6} e^{2} + 6 \, a^{4} c^{2} d^{4} e^{4} + 4 \, a^{5} c d^{2} e^{6} + a^{6} e^{8}\right)} \sqrt{a c}} - \frac{e^{11}}{{\left(c^{3} d^{6} e^{6} + 3 \, a c^{2} d^{4} e^{8} + 3 \, a^{2} c d^{2} e^{10} + a^{3} e^{12}\right)} {\left(x e + d\right)}} + \frac{3 \, c^{5} d^{5} e + 14 \, a c^{4} d^{3} e^{3} - 29 \, a^{2} c^{3} d e^{5} - \frac{{\left(9 \, c^{5} d^{6} e^{2} + 41 \, a c^{4} d^{4} e^{4} - 121 \, a^{2} c^{3} d^{2} e^{6} + 7 \, a^{3} c^{2} e^{8}\right)} e^{\left(-1\right)}}{x e + d} + \frac{{\left(9 \, c^{5} d^{7} e^{3} + 45 \, a c^{4} d^{5} e^{5} - 145 \, a^{2} c^{3} d^{3} e^{7} - 21 \, a^{3} c^{2} d e^{9}\right)} e^{\left(-2\right)}}{{\left(x e + d\right)}^{2}} - \frac{3 \, {\left(c^{5} d^{8} e^{4} + 6 \, a c^{4} d^{6} e^{6} - 20 \, a^{2} c^{3} d^{4} e^{8} - 22 \, a^{3} c^{2} d^{2} e^{10} + 3 \, a^{4} c e^{12}\right)} e^{\left(-3\right)}}{{\left(x e + d\right)}^{3}}}{8 \, {\left(c d^{2} + a e^{2}\right)}^{4} a^{2} {\left(c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right)}^{2}}"," ",0,"-3*c*d*e^5*log(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + a*e^2/(x*e + d)^2)/(c^4*d^8 + 4*a*c^3*d^6*e^2 + 6*a^2*c^2*d^4*e^4 + 4*a^3*c*d^2*e^6 + a^4*e^8) + 3/8*(c^4*d^6*e^2 + 5*a*c^3*d^4*e^4 + 15*a^2*c^2*d^2*e^6 - 5*a^3*c*e^8)*arctan((c*d - c*d^2/(x*e + d) - a*e^2/(x*e + d))*e^(-1)/sqrt(a*c))*e^(-2)/((a^2*c^4*d^8 + 4*a^3*c^3*d^6*e^2 + 6*a^4*c^2*d^4*e^4 + 4*a^5*c*d^2*e^6 + a^6*e^8)*sqrt(a*c)) - e^11/((c^3*d^6*e^6 + 3*a*c^2*d^4*e^8 + 3*a^2*c*d^2*e^10 + a^3*e^12)*(x*e + d)) + 1/8*(3*c^5*d^5*e + 14*a*c^4*d^3*e^3 - 29*a^2*c^3*d*e^5 - (9*c^5*d^6*e^2 + 41*a*c^4*d^4*e^4 - 121*a^2*c^3*d^2*e^6 + 7*a^3*c^2*e^8)*e^(-1)/(x*e + d) + (9*c^5*d^7*e^3 + 45*a*c^4*d^5*e^5 - 145*a^2*c^3*d^3*e^7 - 21*a^3*c^2*d*e^9)*e^(-2)/(x*e + d)^2 - 3*(c^5*d^8*e^4 + 6*a*c^4*d^6*e^6 - 20*a^2*c^3*d^4*e^8 - 22*a^3*c^2*d^2*e^10 + 3*a^4*c*e^12)*e^(-3)/(x*e + d)^3)/((c*d^2 + a*e^2)^4*a^2*(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + a*e^2/(x*e + d)^2)^2)","A",0
519,1,205,0,0.204331," ","integrate((e*x+d)^4/(c*x^2+a)^4,x, algorithm=""giac"")","\frac{{\left(5 \, c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{16 \, \sqrt{a c} a^{3} c^{2}} + \frac{15 \, c^{4} d^{4} x^{5} + 18 \, a c^{3} d^{2} x^{5} e^{2} + 40 \, a c^{3} d^{4} x^{3} + 3 \, a^{2} c^{2} x^{5} e^{4} + 48 \, a^{2} c^{2} d^{2} x^{3} e^{2} + 33 \, a^{2} c^{2} d^{4} x - 8 \, a^{3} c x^{3} e^{4} - 48 \, a^{3} c d x^{2} e^{3} - 18 \, a^{3} c d^{2} x e^{2} - 32 \, a^{3} c d^{3} e - 3 \, a^{4} x e^{4} - 16 \, a^{4} d e^{3}}{48 \, {\left(c x^{2} + a\right)}^{3} a^{3} c^{2}}"," ",0,"1/16*(5*c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*a^3*c^2) + 1/48*(15*c^4*d^4*x^5 + 18*a*c^3*d^2*x^5*e^2 + 40*a*c^3*d^4*x^3 + 3*a^2*c^2*x^5*e^4 + 48*a^2*c^2*d^2*x^3*e^2 + 33*a^2*c^2*d^4*x - 8*a^3*c*x^3*e^4 - 48*a^3*c*d*x^2*e^3 - 18*a^3*c*d^2*x*e^2 - 32*a^3*c*d^3*e - 3*a^4*x*e^4 - 16*a^4*d*e^3)/((c*x^2 + a)^3*a^3*c^2)","A",0
520,1,154,0,0.157725," ","integrate((e*x+d)^3/(c*x^2+a)^4,x, algorithm=""giac"")","\frac{{\left(5 \, c d^{3} + 3 \, a d e^{2}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{16 \, \sqrt{a c} a^{3} c} + \frac{15 \, c^{4} d^{3} x^{5} + 9 \, a c^{3} d x^{5} e^{2} + 40 \, a c^{3} d^{3} x^{3} + 24 \, a^{2} c^{2} d x^{3} e^{2} + 33 \, a^{2} c^{2} d^{3} x - 12 \, a^{3} c x^{2} e^{3} - 9 \, a^{3} c d x e^{2} - 24 \, a^{3} c d^{2} e - 4 \, a^{4} e^{3}}{48 \, {\left(c x^{2} + a\right)}^{3} a^{3} c^{2}}"," ",0,"1/16*(5*c*d^3 + 3*a*d*e^2)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*a^3*c) + 1/48*(15*c^4*d^3*x^5 + 9*a*c^3*d*x^5*e^2 + 40*a*c^3*d^3*x^3 + 24*a^2*c^2*d*x^3*e^2 + 33*a^2*c^2*d^3*x - 12*a^3*c*x^2*e^3 - 9*a^3*c*d*x*e^2 - 24*a^3*c*d^2*e - 4*a^4*e^3)/((c*x^2 + a)^3*a^3*c^2)","A",0
521,1,123,0,0.174682," ","integrate((e*x+d)^2/(c*x^2+a)^4,x, algorithm=""giac"")","\frac{{\left(5 \, c d^{2} + a e^{2}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{16 \, \sqrt{a c} a^{3} c} + \frac{15 \, c^{3} d^{2} x^{5} + 3 \, a c^{2} x^{5} e^{2} + 40 \, a c^{2} d^{2} x^{3} + 8 \, a^{2} c x^{3} e^{2} + 33 \, a^{2} c d^{2} x - 3 \, a^{3} x e^{2} - 16 \, a^{3} d e}{48 \, {\left(c x^{2} + a\right)}^{3} a^{3} c}"," ",0,"1/16*(5*c*d^2 + a*e^2)*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*a^3*c) + 1/48*(15*c^3*d^2*x^5 + 3*a*c^2*x^5*e^2 + 40*a*c^2*d^2*x^3 + 8*a^2*c*x^3*e^2 + 33*a^2*c*d^2*x - 3*a^3*x*e^2 - 16*a^3*d*e)/((c*x^2 + a)^3*a^3*c)","A",0
522,1,73,0,0.162407," ","integrate((e*x+d)/(c*x^2+a)^4,x, algorithm=""giac"")","\frac{5 \, d \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{16 \, \sqrt{a c} a^{3}} + \frac{15 \, c^{3} d x^{5} + 40 \, a c^{2} d x^{3} + 33 \, a^{2} c d x - 8 \, a^{3} e}{48 \, {\left(c x^{2} + a\right)}^{3} a^{3} c}"," ",0,"5/16*d*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*a^3) + 1/48*(15*c^3*d*x^5 + 40*a*c^2*d*x^3 + 33*a^2*c*d*x - 8*a^3*e)/((c*x^2 + a)^3*a^3*c)","A",0
523,1,530,0,0.166313," ","integrate(1/(e*x+d)/(c*x^2+a)^4,x, algorithm=""giac"")","-\frac{e^{7} \log\left(c x^{2} + a\right)}{2 \, {\left(c^{4} d^{8} + 4 \, a c^{3} d^{6} e^{2} + 6 \, a^{2} c^{2} d^{4} e^{4} + 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}\right)}} + \frac{e^{8} \log\left({\left| x e + d \right|}\right)}{c^{4} d^{8} e + 4 \, a c^{3} d^{6} e^{3} + 6 \, a^{2} c^{2} d^{4} e^{5} + 4 \, a^{3} c d^{2} e^{7} + a^{4} e^{9}} + \frac{{\left(5 \, c^{4} d^{7} + 21 \, a c^{3} d^{5} e^{2} + 35 \, a^{2} c^{2} d^{3} e^{4} + 35 \, a^{3} c d e^{6}\right)} \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{16 \, {\left(a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}\right)} \sqrt{a c}} + \frac{8 \, a^{3} c^{3} d^{6} e + 36 \, a^{4} c^{2} d^{4} e^{3} + 72 \, a^{5} c d^{2} e^{5} + 44 \, a^{6} e^{7} + 3 \, {\left(5 \, c^{6} d^{7} + 21 \, a c^{5} d^{5} e^{2} + 35 \, a^{2} c^{4} d^{3} e^{4} + 19 \, a^{3} c^{3} d e^{6}\right)} x^{5} + 24 \, {\left(a^{3} c^{3} d^{2} e^{5} + a^{4} c^{2} e^{7}\right)} x^{4} + 8 \, {\left(5 \, a c^{5} d^{7} + 21 \, a^{2} c^{4} d^{5} e^{2} + 33 \, a^{3} c^{3} d^{3} e^{4} + 17 \, a^{4} c^{2} d e^{6}\right)} x^{3} + 12 \, {\left(a^{3} c^{3} d^{4} e^{3} + 6 \, a^{4} c^{2} d^{2} e^{5} + 5 \, a^{5} c e^{7}\right)} x^{2} + 3 \, {\left(11 \, a^{2} c^{4} d^{7} + 43 \, a^{3} c^{3} d^{5} e^{2} + 61 \, a^{4} c^{2} d^{3} e^{4} + 29 \, a^{5} c d e^{6}\right)} x}{48 \, {\left(c d^{2} + a e^{2}\right)}^{4} {\left(c x^{2} + a\right)}^{3} a^{3}}"," ",0,"-1/2*e^7*log(c*x^2 + a)/(c^4*d^8 + 4*a*c^3*d^6*e^2 + 6*a^2*c^2*d^4*e^4 + 4*a^3*c*d^2*e^6 + a^4*e^8) + e^8*log(abs(x*e + d))/(c^4*d^8*e + 4*a*c^3*d^6*e^3 + 6*a^2*c^2*d^4*e^5 + 4*a^3*c*d^2*e^7 + a^4*e^9) + 1/16*(5*c^4*d^7 + 21*a*c^3*d^5*e^2 + 35*a^2*c^2*d^3*e^4 + 35*a^3*c*d*e^6)*arctan(c*x/sqrt(a*c))/((a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)*sqrt(a*c)) + 1/48*(8*a^3*c^3*d^6*e + 36*a^4*c^2*d^4*e^3 + 72*a^5*c*d^2*e^5 + 44*a^6*e^7 + 3*(5*c^6*d^7 + 21*a*c^5*d^5*e^2 + 35*a^2*c^4*d^3*e^4 + 19*a^3*c^3*d*e^6)*x^5 + 24*(a^3*c^3*d^2*e^5 + a^4*c^2*e^7)*x^4 + 8*(5*a*c^5*d^7 + 21*a^2*c^4*d^5*e^2 + 33*a^3*c^3*d^3*e^4 + 17*a^4*c^2*d*e^6)*x^3 + 12*(a^3*c^3*d^4*e^3 + 6*a^4*c^2*d^2*e^5 + 5*a^5*c*e^7)*x^2 + 3*(11*a^2*c^4*d^7 + 43*a^3*c^3*d^5*e^2 + 61*a^4*c^2*d^3*e^4 + 29*a^5*c*d*e^6)*x)/((c*d^2 + a*e^2)^4*(c*x^2 + a)^3*a^3)","A",0
524,1,856,0,0.201995," ","integrate(1/(e*x+d)^2/(c*x^2+a)^4,x, algorithm=""giac"")","-\frac{4 \, c d e^{7} \log\left(c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right)}{c^{5} d^{10} + 5 \, a c^{4} d^{8} e^{2} + 10 \, a^{2} c^{3} d^{6} e^{4} + 10 \, a^{3} c^{2} d^{4} e^{6} + 5 \, a^{4} c d^{2} e^{8} + a^{5} e^{10}} + \frac{{\left(5 \, c^{5} d^{8} e^{2} + 28 \, a c^{4} d^{6} e^{4} + 70 \, a^{2} c^{3} d^{4} e^{6} + 140 \, a^{3} c^{2} d^{2} e^{8} - 35 \, a^{4} c e^{10}\right)} \arctan\left(\frac{{\left(c d - \frac{c d^{2}}{x e + d} - \frac{a e^{2}}{x e + d}\right)} e^{\left(-1\right)}}{\sqrt{a c}}\right) e^{\left(-2\right)}}{16 \, {\left(a^{3} c^{5} d^{10} + 5 \, a^{4} c^{4} d^{8} e^{2} + 10 \, a^{5} c^{3} d^{6} e^{4} + 10 \, a^{6} c^{2} d^{4} e^{6} + 5 \, a^{7} c d^{2} e^{8} + a^{8} e^{10}\right)} \sqrt{a c}} - \frac{e^{15}}{{\left(c^{4} d^{8} e^{8} + 4 \, a c^{3} d^{6} e^{10} + 6 \, a^{2} c^{2} d^{4} e^{12} + 4 \, a^{3} c d^{2} e^{14} + a^{4} e^{16}\right)} {\left(x e + d\right)}} + \frac{15 \, c^{7} d^{7} e + 79 \, a c^{6} d^{5} e^{3} + 185 \, a^{2} c^{5} d^{3} e^{5} - 295 \, a^{3} c^{4} d e^{7} - \frac{3 \, {\left(25 \, c^{7} d^{8} e^{2} + 130 \, a c^{6} d^{6} e^{4} + 300 \, a^{2} c^{5} d^{4} e^{6} - 618 \, a^{3} c^{4} d^{2} e^{8} + 19 \, a^{4} c^{3} e^{10}\right)} e^{\left(-1\right)}}{x e + d} + \frac{6 \, {\left(25 \, c^{7} d^{9} e^{3} + 135 \, a c^{6} d^{7} e^{5} + 327 \, a^{2} c^{5} d^{5} e^{7} - 691 \, a^{3} c^{4} d^{3} e^{9} - 76 \, a^{4} c^{3} d e^{11}\right)} e^{\left(-2\right)}}{{\left(x e + d\right)}^{2}} - \frac{2 \, {\left(75 \, c^{7} d^{10} e^{4} + 440 \, a c^{6} d^{8} e^{6} + 1162 \, a^{2} c^{5} d^{6} e^{8} - 2212 \, a^{3} c^{4} d^{4} e^{10} - 1277 \, a^{4} c^{3} d^{2} e^{12} + 68 \, a^{5} c^{2} e^{14}\right)} e^{\left(-3\right)}}{{\left(x e + d\right)}^{3}} + \frac{3 \, {\left(25 \, c^{7} d^{11} e^{5} + 165 \, a c^{6} d^{9} e^{7} + 490 \, a^{2} c^{5} d^{7} e^{9} - 742 \, a^{3} c^{4} d^{5} e^{11} - 1139 \, a^{4} c^{3} d^{3} e^{13} - 47 \, a^{5} c^{2} d e^{15}\right)} e^{\left(-4\right)}}{{\left(x e + d\right)}^{4}} - \frac{3 \, {\left(5 \, c^{7} d^{12} e^{6} + 38 \, a c^{6} d^{10} e^{8} + 131 \, a^{2} c^{5} d^{8} e^{10} - 140 \, a^{3} c^{4} d^{6} e^{12} - 517 \, a^{4} c^{3} d^{4} e^{14} - 250 \, a^{5} c^{2} d^{2} e^{16} + 29 \, a^{6} c e^{18}\right)} e^{\left(-5\right)}}{{\left(x e + d\right)}^{5}}}{48 \, {\left(c d^{2} + a e^{2}\right)}^{5} a^{3} {\left(c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right)}^{3}}"," ",0,"-4*c*d*e^7*log(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + a*e^2/(x*e + d)^2)/(c^5*d^10 + 5*a*c^4*d^8*e^2 + 10*a^2*c^3*d^6*e^4 + 10*a^3*c^2*d^4*e^6 + 5*a^4*c*d^2*e^8 + a^5*e^10) + 1/16*(5*c^5*d^8*e^2 + 28*a*c^4*d^6*e^4 + 70*a^2*c^3*d^4*e^6 + 140*a^3*c^2*d^2*e^8 - 35*a^4*c*e^10)*arctan((c*d - c*d^2/(x*e + d) - a*e^2/(x*e + d))*e^(-1)/sqrt(a*c))*e^(-2)/((a^3*c^5*d^10 + 5*a^4*c^4*d^8*e^2 + 10*a^5*c^3*d^6*e^4 + 10*a^6*c^2*d^4*e^6 + 5*a^7*c*d^2*e^8 + a^8*e^10)*sqrt(a*c)) - e^15/((c^4*d^8*e^8 + 4*a*c^3*d^6*e^10 + 6*a^2*c^2*d^4*e^12 + 4*a^3*c*d^2*e^14 + a^4*e^16)*(x*e + d)) + 1/48*(15*c^7*d^7*e + 79*a*c^6*d^5*e^3 + 185*a^2*c^5*d^3*e^5 - 295*a^3*c^4*d*e^7 - 3*(25*c^7*d^8*e^2 + 130*a*c^6*d^6*e^4 + 300*a^2*c^5*d^4*e^6 - 618*a^3*c^4*d^2*e^8 + 19*a^4*c^3*e^10)*e^(-1)/(x*e + d) + 6*(25*c^7*d^9*e^3 + 135*a*c^6*d^7*e^5 + 327*a^2*c^5*d^5*e^7 - 691*a^3*c^4*d^3*e^9 - 76*a^4*c^3*d*e^11)*e^(-2)/(x*e + d)^2 - 2*(75*c^7*d^10*e^4 + 440*a*c^6*d^8*e^6 + 1162*a^2*c^5*d^6*e^8 - 2212*a^3*c^4*d^4*e^10 - 1277*a^4*c^3*d^2*e^12 + 68*a^5*c^2*e^14)*e^(-3)/(x*e + d)^3 + 3*(25*c^7*d^11*e^5 + 165*a*c^6*d^9*e^7 + 490*a^2*c^5*d^7*e^9 - 742*a^3*c^4*d^5*e^11 - 1139*a^4*c^3*d^3*e^13 - 47*a^5*c^2*d*e^15)*e^(-4)/(x*e + d)^4 - 3*(5*c^7*d^12*e^6 + 38*a*c^6*d^10*e^8 + 131*a^2*c^5*d^8*e^10 - 140*a^3*c^4*d^6*e^12 - 517*a^4*c^3*d^4*e^14 - 250*a^5*c^2*d^2*e^16 + 29*a^6*c*e^18)*e^(-5)/(x*e + d)^5)/((c*d^2 + a*e^2)^5*a^3*(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + a*e^2/(x*e + d)^2)^3)","B",0
525,1,197,0,0.241326," ","integrate((e*x+d)^4*(c*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{1}{240} \, \sqrt{c x^{2} + a} {\left({\left(2 \, {\left({\left(4 \, {\left(5 \, x e^{4} + 24 \, d e^{3}\right)} x + \frac{5 \, {\left(36 \, c^{4} d^{2} e^{2} + a c^{3} e^{4}\right)}}{c^{4}}\right)} x + \frac{32 \, {\left(5 \, c^{4} d^{3} e + a c^{3} d e^{3}\right)}}{c^{4}}\right)} x + \frac{15 \, {\left(8 \, c^{4} d^{4} + 12 \, a c^{3} d^{2} e^{2} - a^{2} c^{2} e^{4}\right)}}{c^{4}}\right)} x + \frac{64 \, {\left(5 \, a c^{3} d^{3} e - 2 \, a^{2} c^{2} d e^{3}\right)}}{c^{4}}\right)} - \frac{{\left(8 \, a c^{2} d^{4} - 12 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{16 \, c^{\frac{5}{2}}}"," ",0,"1/240*sqrt(c*x^2 + a)*((2*((4*(5*x*e^4 + 24*d*e^3)*x + 5*(36*c^4*d^2*e^2 + a*c^3*e^4)/c^4)*x + 32*(5*c^4*d^3*e + a*c^3*d*e^3)/c^4)*x + 15*(8*c^4*d^4 + 12*a*c^3*d^2*e^2 - a^2*c^2*e^4)/c^4)*x + 64*(5*a*c^3*d^3*e - 2*a^2*c^2*d*e^3)/c^4) - 1/16*(8*a*c^2*d^4 - 12*a^2*c*d^2*e^2 + a^3*e^4)*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/c^(5/2)","A",0
526,1,144,0,0.330540," ","integrate((e*x+d)^3*(c*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{1}{120} \, \sqrt{c x^{2} + a} {\left({\left(2 \, {\left(3 \, {\left(4 \, x e^{3} + 15 \, d e^{2}\right)} x + \frac{4 \, {\left(15 \, c^{3} d^{2} e + a c^{2} e^{3}\right)}}{c^{3}}\right)} x + \frac{15 \, {\left(4 \, c^{3} d^{3} + 3 \, a c^{2} d e^{2}\right)}}{c^{3}}\right)} x + \frac{8 \, {\left(15 \, a c^{2} d^{2} e - 2 \, a^{2} c e^{3}\right)}}{c^{3}}\right)} - \frac{{\left(4 \, a c d^{3} - 3 \, a^{2} d e^{2}\right)} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{8 \, c^{\frac{3}{2}}}"," ",0,"1/120*sqrt(c*x^2 + a)*((2*(3*(4*x*e^3 + 15*d*e^2)*x + 4*(15*c^3*d^2*e + a*c^2*e^3)/c^3)*x + 15*(4*c^3*d^3 + 3*a*c^2*d*e^2)/c^3)*x + 8*(15*a*c^2*d^2*e - 2*a^2*c*e^3)/c^3) - 1/8*(4*a*c*d^3 - 3*a^2*d*e^2)*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/c^(3/2)","A",0
527,1,96,0,0.200175," ","integrate((e*x+d)^2*(c*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{1}{24} \, \sqrt{c x^{2} + a} {\left({\left(2 \, {\left(3 \, x e^{2} + 8 \, d e\right)} x + \frac{3 \, {\left(4 \, c^{2} d^{2} + a c e^{2}\right)}}{c^{2}}\right)} x + \frac{16 \, a d e}{c}\right)} - \frac{{\left(4 \, a c d^{2} - a^{2} e^{2}\right)} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{8 \, c^{\frac{3}{2}}}"," ",0,"1/24*sqrt(c*x^2 + a)*((2*(3*x*e^2 + 8*d*e)*x + 3*(4*c^2*d^2 + a*c*e^2)/c^2)*x + 16*a*d*e/c) - 1/8*(4*a*c*d^2 - a^2*e^2)*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/c^(3/2)","A",0
528,1,57,0,0.191724," ","integrate((e*x+d)*(c*x^2+a)^(1/2),x, algorithm=""giac"")","-\frac{a d \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{2 \, \sqrt{c}} + \frac{1}{6} \, \sqrt{c x^{2} + a} {\left({\left(2 \, x e + 3 \, d\right)} x + \frac{2 \, a e}{c}\right)}"," ",0,"-1/2*a*d*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/sqrt(c) + 1/6*sqrt(c*x^2 + a)*((2*x*e + 3*d)*x + 2*a*e/c)","A",0
529,1,109,0,0.206837," ","integrate((c*x^2+a)^(1/2)/(e*x+d),x, algorithm=""giac"")","\sqrt{c} d e^{\left(-2\right)} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right) + \frac{2 \, {\left(c d^{2} + a e^{2}\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} - a e^{2}}}\right) e^{\left(-2\right)}}{\sqrt{-c d^{2} - a e^{2}}} + \sqrt{c x^{2} + a} e^{\left(-1\right)}"," ",0,"sqrt(c)*d*e^(-2)*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a))) + 2*(c*d^2 + a*e^2)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + a))*e + sqrt(c)*d)/sqrt(-c*d^2 - a*e^2))*e^(-2)/sqrt(-c*d^2 - a*e^2) + sqrt(c*x^2 + a)*e^(-1)","A",0
530,-2,0,0,0.000000," ","integrate((c*x^2+a)^(1/2)/(e*x+d)^2,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]Error: Bad Argument Type","F(-2)",0
531,1,312,0,0.239883," ","integrate((c*x^2+a)^(1/2)/(e*x+d)^3,x, algorithm=""giac"")","-\frac{a c \arctan\left(\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} - a e^{2}}}\right)}{{\left(c d^{2} + a e^{2}\right)} \sqrt{-c d^{2} - a e^{2}}} + \frac{2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} c^{2} d^{2} e + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} c^{\frac{5}{2}} d^{3} - 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a c^{2} d^{2} e - {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a c^{\frac{3}{2}} d e^{2} + {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a c e^{3} + a^{2} c^{\frac{3}{2}} d e^{2} + {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{2} c e^{3}}{{\left(c d^{2} e^{2} + a e^{4}\right)} {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} e + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} \sqrt{c} d - a e\right)}^{2}}"," ",0,"-a*c*arctan(((sqrt(c)*x - sqrt(c*x^2 + a))*e + sqrt(c)*d)/sqrt(-c*d^2 - a*e^2))/((c*d^2 + a*e^2)*sqrt(-c*d^2 - a*e^2)) + (2*(sqrt(c)*x - sqrt(c*x^2 + a))^3*c^2*d^2*e + 2*(sqrt(c)*x - sqrt(c*x^2 + a))^2*c^(5/2)*d^3 - 2*(sqrt(c)*x - sqrt(c*x^2 + a))*a*c^2*d^2*e - (sqrt(c)*x - sqrt(c*x^2 + a))^2*a*c^(3/2)*d*e^2 + (sqrt(c)*x - sqrt(c*x^2 + a))^3*a*c*e^3 + a^2*c^(3/2)*d*e^2 + (sqrt(c)*x - sqrt(c*x^2 + a))*a^2*c*e^3)/((c*d^2*e^2 + a*e^4)*((sqrt(c)*x - sqrt(c*x^2 + a))^2*e + 2*(sqrt(c)*x - sqrt(c*x^2 + a))*sqrt(c)*d - a*e)^2)","B",0
532,1,518,0,0.255032," ","integrate((c*x^2+a)^(1/2)/(e*x+d)^4,x, algorithm=""giac"")","-\frac{a c^{2} d \arctan\left(\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} - a e^{2}}}\right)}{{\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} \sqrt{-c d^{2} - a e^{2}}} + \frac{6 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} c^{\frac{7}{2}} d^{4} e + 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} c^{4} d^{5} - 6 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a c^{\frac{7}{2}} d^{4} e - 14 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a c^{3} d^{3} e^{2} - 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a c^{\frac{5}{2}} d^{2} e^{3} - 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a c^{2} d e^{4} + 6 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{2} c^{3} d^{3} e^{2} + 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{2} c^{\frac{5}{2}} d^{2} e^{3} + 12 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{2} c^{2} d e^{4} + 6 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{2} c^{\frac{3}{2}} e^{5} - a^{3} c^{\frac{5}{2}} d^{2} e^{3} - 9 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{3} c^{2} d e^{4} + 2 \, a^{4} c^{\frac{3}{2}} e^{5}}{3 \, {\left(c^{2} d^{4} e^{2} + 2 \, a c d^{2} e^{4} + a^{2} e^{6}\right)} {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} e + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} \sqrt{c} d - a e\right)}^{3}}"," ",0,"-a*c^2*d*arctan(((sqrt(c)*x - sqrt(c*x^2 + a))*e + sqrt(c)*d)/sqrt(-c*d^2 - a*e^2))/((c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-c*d^2 - a*e^2)) + 1/3*(6*(sqrt(c)*x - sqrt(c*x^2 + a))^4*c^(7/2)*d^4*e + 4*(sqrt(c)*x - sqrt(c*x^2 + a))^3*c^4*d^5 - 6*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a*c^(7/2)*d^4*e - 14*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a*c^3*d^3*e^2 - 3*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a*c^(5/2)*d^2*e^3 - 3*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a*c^2*d*e^4 + 6*(sqrt(c)*x - sqrt(c*x^2 + a))*a^2*c^3*d^3*e^2 + 24*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^2*c^(5/2)*d^2*e^3 + 12*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^2*c^2*d*e^4 + 6*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^2*c^(3/2)*e^5 - a^3*c^(5/2)*d^2*e^3 - 9*(sqrt(c)*x - sqrt(c*x^2 + a))*a^3*c^2*d*e^4 + 2*a^4*c^(3/2)*e^5)/((c^2*d^4*e^2 + 2*a*c*d^2*e^4 + a^2*e^6)*((sqrt(c)*x - sqrt(c*x^2 + a))^2*e + 2*(sqrt(c)*x - sqrt(c*x^2 + a))*sqrt(c)*d - a*e)^3)","B",0
533,-1,0,0,0.000000," ","integrate((c*x^2+a)^(1/2)/(e*x+d)^5,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
534,1,277,0,0.240506," ","integrate((e*x+d)^4*(c*x^2+a)^(3/2),x, algorithm=""giac"")","\frac{1}{4480} \, \sqrt{c x^{2} + a} {\left({\left(2 \, {\left({\left(4 \, {\left(5 \, {\left(2 \, {\left(7 \, c x e^{4} + 32 \, c d e^{3}\right)} x + \frac{7 \, {\left(16 \, c^{7} d^{2} e^{2} + 3 \, a c^{6} e^{4}\right)}}{c^{6}}\right)} x + \frac{64 \, {\left(7 \, c^{7} d^{3} e + 8 \, a c^{6} d e^{3}\right)}}{c^{6}}\right)} x + \frac{35 \, {\left(16 \, c^{7} d^{4} + 112 \, a c^{6} d^{2} e^{2} + a^{2} c^{5} e^{4}\right)}}{c^{6}}\right)} x + \frac{256 \, {\left(14 \, a c^{6} d^{3} e + a^{2} c^{5} d e^{3}\right)}}{c^{6}}\right)} x + \frac{35 \, {\left(80 \, a c^{6} d^{4} + 48 \, a^{2} c^{5} d^{2} e^{2} - 3 \, a^{3} c^{4} e^{4}\right)}}{c^{6}}\right)} x + \frac{512 \, {\left(7 \, a^{2} c^{5} d^{3} e - 2 \, a^{3} c^{4} d e^{3}\right)}}{c^{6}}\right)} - \frac{3 \, {\left(16 \, a^{2} c^{2} d^{4} - 16 \, a^{3} c d^{2} e^{2} + a^{4} e^{4}\right)} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{128 \, c^{\frac{5}{2}}}"," ",0,"1/4480*sqrt(c*x^2 + a)*((2*((4*(5*(2*(7*c*x*e^4 + 32*c*d*e^3)*x + 7*(16*c^7*d^2*e^2 + 3*a*c^6*e^4)/c^6)*x + 64*(7*c^7*d^3*e + 8*a*c^6*d*e^3)/c^6)*x + 35*(16*c^7*d^4 + 112*a*c^6*d^2*e^2 + a^2*c^5*e^4)/c^6)*x + 256*(14*a*c^6*d^3*e + a^2*c^5*d*e^3)/c^6)*x + 35*(80*a*c^6*d^4 + 48*a^2*c^5*d^2*e^2 - 3*a^3*c^4*e^4)/c^6)*x + 512*(7*a^2*c^5*d^3*e - 2*a^3*c^4*d*e^3)/c^6) - 3/128*(16*a^2*c^2*d^4 - 16*a^3*c*d^2*e^2 + a^4*e^4)*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/c^(5/2)","A",0
535,1,212,0,0.256733," ","integrate((e*x+d)^3*(c*x^2+a)^(3/2),x, algorithm=""giac"")","\frac{1}{560} \, \sqrt{c x^{2} + a} {\left({\left(2 \, {\left({\left(4 \, {\left(5 \, {\left(2 \, c x e^{3} + 7 \, c d e^{2}\right)} x + \frac{2 \, {\left(21 \, c^{6} d^{2} e + 8 \, a c^{5} e^{3}\right)}}{c^{5}}\right)} x + \frac{35 \, {\left(2 \, c^{6} d^{3} + 7 \, a c^{5} d e^{2}\right)}}{c^{5}}\right)} x + \frac{8 \, {\left(42 \, a c^{5} d^{2} e + a^{2} c^{4} e^{3}\right)}}{c^{5}}\right)} x + \frac{35 \, {\left(10 \, a c^{5} d^{3} + 3 \, a^{2} c^{4} d e^{2}\right)}}{c^{5}}\right)} x + \frac{16 \, {\left(21 \, a^{2} c^{4} d^{2} e - 2 \, a^{3} c^{3} e^{3}\right)}}{c^{5}}\right)} - \frac{3 \, {\left(2 \, a^{2} c d^{3} - a^{3} d e^{2}\right)} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{16 \, c^{\frac{3}{2}}}"," ",0,"1/560*sqrt(c*x^2 + a)*((2*((4*(5*(2*c*x*e^3 + 7*c*d*e^2)*x + 2*(21*c^6*d^2*e + 8*a*c^5*e^3)/c^5)*x + 35*(2*c^6*d^3 + 7*a*c^5*d*e^2)/c^5)*x + 8*(42*a*c^5*d^2*e + a^2*c^4*e^3)/c^5)*x + 35*(10*a*c^5*d^3 + 3*a^2*c^4*d*e^2)/c^5)*x + 16*(21*a^2*c^4*d^2*e - 2*a^3*c^3*e^3)/c^5) - 3/16*(2*a^2*c*d^3 - a^3*d*e^2)*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/c^(3/2)","A",0
536,1,142,0,0.227838," ","integrate((e*x+d)^2*(c*x^2+a)^(3/2),x, algorithm=""giac"")","\frac{1}{240} \, \sqrt{c x^{2} + a} {\left(\frac{96 \, a^{2} d e}{c} + {\left(2 \, {\left(96 \, a d e + {\left(4 \, {\left(5 \, c x e^{2} + 12 \, c d e\right)} x + \frac{5 \, {\left(6 \, c^{5} d^{2} + 7 \, a c^{4} e^{2}\right)}}{c^{4}}\right)} x\right)} x + \frac{15 \, {\left(10 \, a c^{4} d^{2} + a^{2} c^{3} e^{2}\right)}}{c^{4}}\right)} x\right)} - \frac{{\left(6 \, a^{2} c d^{2} - a^{3} e^{2}\right)} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{16 \, c^{\frac{3}{2}}}"," ",0,"1/240*sqrt(c*x^2 + a)*(96*a^2*d*e/c + (2*(96*a*d*e + (4*(5*c*x*e^2 + 12*c*d*e)*x + 5*(6*c^5*d^2 + 7*a*c^4*e^2)/c^4)*x)*x + 15*(10*a*c^4*d^2 + a^2*c^3*e^2)/c^4)*x) - 1/16*(6*a^2*c*d^2 - a^3*e^2)*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/c^(3/2)","A",0
537,1,79,0,0.236431," ","integrate((e*x+d)*(c*x^2+a)^(3/2),x, algorithm=""giac"")","-\frac{3 \, a^{2} d \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{8 \, \sqrt{c}} + \frac{1}{40} \, \sqrt{c x^{2} + a} {\left({\left(25 \, a d + 2 \, {\left({\left(4 \, c x e + 5 \, c d\right)} x + 8 \, a e\right)} x\right)} x + \frac{8 \, a^{2} e}{c}\right)}"," ",0,"-3/8*a^2*d*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/sqrt(c) + 1/40*sqrt(c*x^2 + a)*((25*a*d + 2*((4*c*x*e + 5*c*d)*x + 8*a*e)*x)*x + 8*a^2*e/c)","A",0
538,1,176,0,0.270743," ","integrate((c*x^2+a)^(3/2)/(e*x+d),x, algorithm=""giac"")","\frac{1}{2} \, {\left(2 \, c^{\frac{3}{2}} d^{3} + 3 \, a \sqrt{c} d e^{2}\right)} e^{\left(-4\right)} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right) + \frac{2 \, {\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} - a e^{2}}}\right) e^{\left(-4\right)}}{\sqrt{-c d^{2} - a e^{2}}} + \frac{1}{6} \, \sqrt{c x^{2} + a} {\left({\left(2 \, c x e^{\left(-1\right)} - 3 \, c d e^{\left(-2\right)}\right)} x + \frac{2 \, {\left(3 \, c^{2} d^{2} e^{7} + 4 \, a c e^{9}\right)} e^{\left(-10\right)}}{c}\right)}"," ",0,"1/2*(2*c^(3/2)*d^3 + 3*a*sqrt(c)*d*e^2)*e^(-4)*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a))) + 2*(c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + a))*e + sqrt(c)*d)/sqrt(-c*d^2 - a*e^2))*e^(-4)/sqrt(-c*d^2 - a*e^2) + 1/6*sqrt(c*x^2 + a)*((2*c*x*e^(-1) - 3*c*d*e^(-2))*x + 2*(3*c^2*d^2*e^7 + 4*a*c*e^9)*e^(-10)/c)","A",0
539,-1,0,0,0.000000," ","integrate((c*x^2+a)^(3/2)/(e*x+d)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
540,-2,0,0,0.000000," ","integrate((c*x^2+a)^(3/2)/(e*x+d)^3,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{-1,[6,0,7,0]%%%}+%%%{%%{[6,0]:[1,0,%%%{-1,[1]%%%}]%%},[5,1,6,0]%%%}+%%%{%%%{-12,[1]%%%},[4,2,5,0]%%%}+%%%{3,[4,0,7,1]%%%}+%%%{%%{[%%%{8,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,3,4,0]%%%}+%%%{%%{[-12,0]:[1,0,%%%{-1,[1]%%%}]%%},[3,1,6,1]%%%}+%%%{%%%{12,[1]%%%},[2,2,5,1]%%%}+%%%{-3,[2,0,7,2]%%%}+%%%{%%{[6,0]:[1,0,%%%{-1,[1]%%%}]%%},[1,1,6,2]%%%}+%%%{1,[0,0,7,3]%%%} / %%%{%%{poly1[%%%{1,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[6,0,3,0]%%%}+%%%{%%%{-6,[2]%%%},[5,1,2,0]%%%}+%%%{%%{[%%%{12,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,2,1,0]%%%}+%%%{%%{poly1[%%%{-3,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,3,1]%%%}+%%%{%%%{-8,[3]%%%},[3,3,0,0]%%%}+%%%{%%%{12,[2]%%%},[3,1,2,1]%%%}+%%%{%%{[%%%{-12,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,2,1,1]%%%}+%%%{%%{poly1[%%%{3,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,3,2]%%%}+%%%{%%%{-6,[2]%%%},[1,1,2,2]%%%}+%%%{%%{poly1[%%%{-1,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,3,3]%%%} Error: Bad Argument Value","F(-2)",0
541,1,589,0,0.414921," ","integrate((c*x^2+a)^(3/2)/(e*x+d)^4,x, algorithm=""giac"")","-c^{\frac{3}{2}} e^{\left(-4\right)} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right) + \frac{{\left(2 \, c^{3} d^{3} + 3 \, a c^{2} d e^{2}\right)} \arctan\left(\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} - a e^{2}}}\right)}{{\left(c d^{2} e^{4} + a e^{6}\right)} \sqrt{-c d^{2} - a e^{2}}} - \frac{54 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} c^{\frac{7}{2}} d^{4} e + 44 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} c^{4} d^{5} + 18 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} c^{3} d^{3} e^{2} - 78 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a c^{\frac{7}{2}} d^{4} e - 34 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a c^{3} d^{3} e^{2} + 27 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a c^{\frac{5}{2}} d^{2} e^{3} + 15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a c^{2} d e^{4} + 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{2} c^{3} d^{3} e^{2} - 36 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{2} c^{\frac{5}{2}} d^{2} e^{3} - 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{2} c^{2} d e^{4} - 12 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{2} c^{\frac{3}{2}} e^{5} - 11 \, a^{3} c^{\frac{5}{2}} d^{2} e^{3} + 33 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{3} c^{2} d e^{4} + 12 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{3} c^{\frac{3}{2}} e^{5} - 8 \, a^{4} c^{\frac{3}{2}} e^{5}}{3 \, {\left(c d^{2} e^{4} + a e^{6}\right)} {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} e + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} \sqrt{c} d - a e\right)}^{3}}"," ",0,"-c^(3/2)*e^(-4)*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a))) + (2*c^3*d^3 + 3*a*c^2*d*e^2)*arctan(((sqrt(c)*x - sqrt(c*x^2 + a))*e + sqrt(c)*d)/sqrt(-c*d^2 - a*e^2))/((c*d^2*e^4 + a*e^6)*sqrt(-c*d^2 - a*e^2)) - 1/3*(54*(sqrt(c)*x - sqrt(c*x^2 + a))^4*c^(7/2)*d^4*e + 44*(sqrt(c)*x - sqrt(c*x^2 + a))^3*c^4*d^5 + 18*(sqrt(c)*x - sqrt(c*x^2 + a))^5*c^3*d^3*e^2 - 78*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a*c^(7/2)*d^4*e - 34*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a*c^3*d^3*e^2 + 27*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a*c^(5/2)*d^2*e^3 + 15*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a*c^2*d*e^4 + 48*(sqrt(c)*x - sqrt(c*x^2 + a))*a^2*c^3*d^3*e^2 - 36*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^2*c^(5/2)*d^2*e^3 - 48*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^2*c^2*d*e^4 - 12*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^2*c^(3/2)*e^5 - 11*a^3*c^(5/2)*d^2*e^3 + 33*(sqrt(c)*x - sqrt(c*x^2 + a))*a^3*c^2*d*e^4 + 12*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^3*c^(3/2)*e^5 - 8*a^4*c^(3/2)*e^5)/((c*d^2*e^4 + a*e^6)*((sqrt(c)*x - sqrt(c*x^2 + a))^2*e + 2*(sqrt(c)*x - sqrt(c*x^2 + a))*sqrt(c)*d - a*e)^3)","B",0
542,-1,0,0,0.000000," ","integrate((c*x^2+a)^(3/2)/(e*x+d)^5,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
543,1,1246,0,0.467251," ","integrate((c*x^2+a)^(3/2)/(e*x+d)^6,x, algorithm=""giac"")","-\frac{3 \, a^{2} c^{3} d \arctan\left(\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} - a e^{2}}}\right)}{4 \, {\left(c^{3} d^{6} + 3 \, a c^{2} d^{4} e^{2} + 3 \, a^{2} c d^{2} e^{4} + a^{3} e^{6}\right)} \sqrt{-c d^{2} - a e^{2}}} + \frac{80 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} c^{\frac{13}{2}} d^{8} e + 32 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} c^{7} d^{9} + 80 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} c^{6} d^{7} e^{2} + 40 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} c^{\frac{11}{2}} d^{6} e^{3} - 80 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a c^{\frac{13}{2}} d^{8} e - 16 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a c^{6} d^{7} e^{2} + 240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a c^{\frac{11}{2}} d^{6} e^{3} + 240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a c^{5} d^{5} e^{4} + 80 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{2} c^{6} d^{7} e^{2} + 120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a c^{\frac{9}{2}} d^{4} e^{5} - 240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{2} c^{\frac{11}{2}} d^{6} e^{3} - 788 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{2} c^{5} d^{5} e^{4} - 530 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{2} c^{\frac{9}{2}} d^{4} e^{5} - 40 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{3} c^{\frac{11}{2}} d^{6} e^{3} - 230 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{2} c^{4} d^{3} e^{6} + 400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{3} c^{5} d^{5} e^{4} - 15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{2} c^{\frac{7}{2}} d^{2} e^{7} + 1170 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{3} c^{\frac{9}{2}} d^{4} e^{5} - 15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a^{2} c^{3} d e^{8} + 910 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{3} c^{4} d^{3} e^{6} + 20 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{4} c^{5} d^{5} e^{4} + 570 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{3} c^{\frac{7}{2}} d^{2} e^{7} - 230 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{4} c^{\frac{9}{2}} d^{4} e^{5} + 150 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{3} c^{3} d e^{8} - 770 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{4} c^{4} d^{3} e^{6} + 40 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{3} c^{\frac{5}{2}} e^{9} - 480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{4} c^{\frac{7}{2}} d^{2} e^{7} - 2 \, a^{5} c^{\frac{9}{2}} d^{4} e^{5} - 240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{4} c^{3} d e^{8} + 90 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{5} c^{4} d^{3} e^{6} + 350 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{5} c^{\frac{7}{2}} d^{2} e^{7} + 170 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{5} c^{3} d e^{8} + 80 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{5} c^{\frac{5}{2}} e^{9} - 9 \, a^{6} c^{\frac{7}{2}} d^{2} e^{7} - 65 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{6} c^{3} d e^{8} + 8 \, a^{7} c^{\frac{5}{2}} e^{9}}{20 \, {\left(c^{3} d^{6} e^{4} + 3 \, a c^{2} d^{4} e^{6} + 3 \, a^{2} c d^{2} e^{8} + a^{3} e^{10}\right)} {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} e + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} \sqrt{c} d - a e\right)}^{5}}"," ",0,"-3/4*a^2*c^3*d*arctan(((sqrt(c)*x - sqrt(c*x^2 + a))*e + sqrt(c)*d)/sqrt(-c*d^2 - a*e^2))/((c^3*d^6 + 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4 + a^3*e^6)*sqrt(-c*d^2 - a*e^2)) + 1/20*(80*(sqrt(c)*x - sqrt(c*x^2 + a))^6*c^(13/2)*d^8*e + 32*(sqrt(c)*x - sqrt(c*x^2 + a))^5*c^7*d^9 + 80*(sqrt(c)*x - sqrt(c*x^2 + a))^7*c^6*d^7*e^2 + 40*(sqrt(c)*x - sqrt(c*x^2 + a))^8*c^(11/2)*d^6*e^3 - 80*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a*c^(13/2)*d^8*e - 16*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a*c^6*d^7*e^2 + 240*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a*c^(11/2)*d^6*e^3 + 240*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a*c^5*d^5*e^4 + 80*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^2*c^6*d^7*e^2 + 120*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a*c^(9/2)*d^4*e^5 - 240*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^2*c^(11/2)*d^6*e^3 - 788*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^2*c^5*d^5*e^4 - 530*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^2*c^(9/2)*d^4*e^5 - 40*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^3*c^(11/2)*d^6*e^3 - 230*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^2*c^4*d^3*e^6 + 400*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^3*c^5*d^5*e^4 - 15*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^2*c^(7/2)*d^2*e^7 + 1170*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^3*c^(9/2)*d^4*e^5 - 15*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a^2*c^3*d*e^8 + 910*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^3*c^4*d^3*e^6 + 20*(sqrt(c)*x - sqrt(c*x^2 + a))*a^4*c^5*d^5*e^4 + 570*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^3*c^(7/2)*d^2*e^7 - 230*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^4*c^(9/2)*d^4*e^5 + 150*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^3*c^3*d*e^8 - 770*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^4*c^4*d^3*e^6 + 40*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^3*c^(5/2)*e^9 - 480*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^4*c^(7/2)*d^2*e^7 - 2*a^5*c^(9/2)*d^4*e^5 - 240*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^4*c^3*d*e^8 + 90*(sqrt(c)*x - sqrt(c*x^2 + a))*a^5*c^4*d^3*e^6 + 350*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^5*c^(7/2)*d^2*e^7 + 170*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^5*c^3*d*e^8 + 80*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^5*c^(5/2)*e^9 - 9*a^6*c^(7/2)*d^2*e^7 - 65*(sqrt(c)*x - sqrt(c*x^2 + a))*a^6*c^3*d*e^8 + 8*a^7*c^(5/2)*e^9)/((c^3*d^6*e^4 + 3*a*c^2*d^4*e^6 + 3*a^2*c*d^2*e^8 + a^3*e^10)*((sqrt(c)*x - sqrt(c*x^2 + a))^2*e + 2*(sqrt(c)*x - sqrt(c*x^2 + a))*sqrt(c)*d - a*e)^5)","B",0
544,1,1818,0,0.512144," ","integrate((c*x^2+a)^(3/2)/(e*x+d)^7,x, algorithm=""giac"")","-\frac{{\left(6 \, a^{2} c^{4} d^{2} - a^{3} c^{3} e^{2}\right)} \arctan\left(\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} - a e^{2}}}\right)}{8 \, {\left(c^{4} d^{8} + 4 \, a c^{3} d^{6} e^{2} + 6 \, a^{2} c^{2} d^{4} e^{4} + 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}\right)} \sqrt{-c d^{2} - a e^{2}}} + \frac{384 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} c^{8} d^{10} e + 128 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} c^{\frac{17}{2}} d^{11} + 480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} c^{\frac{15}{2}} d^{9} e^{2} + 320 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} c^{7} d^{8} e^{3} - 384 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a c^{8} d^{10} e - 64 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a c^{\frac{15}{2}} d^{9} e^{2} + 1728 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a c^{7} d^{8} e^{3} + 1920 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a c^{\frac{13}{2}} d^{7} e^{4} + 480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{2} c^{\frac{15}{2}} d^{9} e^{2} + 1280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a c^{6} d^{6} e^{5} - 1728 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{2} c^{7} d^{8} e^{3} - 8592 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{2} c^{\frac{13}{2}} d^{7} e^{4} - 9456 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{2} c^{6} d^{6} e^{5} - 320 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{3} c^{7} d^{8} e^{3} - 7380 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{2} c^{\frac{11}{2}} d^{5} e^{6} + 3840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{3} c^{\frac{13}{2}} d^{7} e^{4} - 2520 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a^{2} c^{5} d^{4} e^{7} + 19056 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{3} c^{6} d^{6} e^{5} - 990 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{10} a^{2} c^{\frac{9}{2}} d^{3} e^{8} + 24440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{3} c^{\frac{11}{2}} d^{5} e^{6} + 240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{4} c^{\frac{13}{2}} d^{7} e^{4} - 90 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{11} a^{2} c^{4} d^{2} e^{9} + 20760 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{3} c^{5} d^{4} e^{7} - 2960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{4} c^{6} d^{6} e^{5} + 8220 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{3} c^{\frac{9}{2}} d^{3} e^{8} - 18720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{4} c^{\frac{11}{2}} d^{5} e^{6} + 2530 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a^{3} c^{4} d^{2} e^{9} - 21480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{4} c^{5} d^{4} e^{7} - 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{5} c^{6} d^{6} e^{5} + 165 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{10} a^{3} c^{\frac{7}{2}} d e^{10} - 14860 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{4} c^{\frac{9}{2}} d^{3} e^{8} + 1656 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{5} c^{\frac{11}{2}} d^{5} e^{6} + 15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{11} a^{3} c^{3} e^{11} - 2700 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{4} c^{4} d^{2} e^{9} + 12120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{5} c^{5} d^{4} e^{7} - 285 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{4} c^{\frac{7}{2}} d e^{10} + 11640 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{5} c^{\frac{9}{2}} d^{3} e^{8} + 4 \, a^{6} c^{\frac{11}{2}} d^{5} e^{6} + 235 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a^{4} c^{3} e^{11} + 7020 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{5} c^{4} d^{2} e^{9} - 336 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{6} c^{5} d^{4} e^{7} + 810 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{5} c^{\frac{7}{2}} d e^{10} - 4038 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{6} c^{\frac{9}{2}} d^{3} e^{8} + 390 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{5} c^{3} e^{11} - 2330 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{6} c^{4} d^{2} e^{9} - 930 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{6} c^{\frac{7}{2}} d e^{10} + 28 \, a^{7} c^{\frac{9}{2}} d^{3} e^{8} + 390 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{6} c^{3} e^{11} + 882 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{7} c^{4} d^{2} e^{9} + 321 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{7} c^{\frac{7}{2}} d e^{10} + 235 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{7} c^{3} e^{11} - 81 \, a^{8} c^{\frac{7}{2}} d e^{10} + 15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{8} c^{3} e^{11}}{120 \, {\left(c^{4} d^{8} e^{4} + 4 \, a c^{3} d^{6} e^{6} + 6 \, a^{2} c^{2} d^{4} e^{8} + 4 \, a^{3} c d^{2} e^{10} + a^{4} e^{12}\right)} {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} e + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} \sqrt{c} d - a e\right)}^{6}}"," ",0,"-1/8*(6*a^2*c^4*d^2 - a^3*c^3*e^2)*arctan(((sqrt(c)*x - sqrt(c*x^2 + a))*e + sqrt(c)*d)/sqrt(-c*d^2 - a*e^2))/((c^4*d^8 + 4*a*c^3*d^6*e^2 + 6*a^2*c^2*d^4*e^4 + 4*a^3*c*d^2*e^6 + a^4*e^8)*sqrt(-c*d^2 - a*e^2)) + 1/120*(384*(sqrt(c)*x - sqrt(c*x^2 + a))^7*c^8*d^10*e + 128*(sqrt(c)*x - sqrt(c*x^2 + a))^6*c^(17/2)*d^11 + 480*(sqrt(c)*x - sqrt(c*x^2 + a))^8*c^(15/2)*d^9*e^2 + 320*(sqrt(c)*x - sqrt(c*x^2 + a))^9*c^7*d^8*e^3 - 384*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a*c^8*d^10*e - 64*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a*c^(15/2)*d^9*e^2 + 1728*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a*c^7*d^8*e^3 + 1920*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a*c^(13/2)*d^7*e^4 + 480*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^2*c^(15/2)*d^9*e^2 + 1280*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a*c^6*d^6*e^5 - 1728*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^2*c^7*d^8*e^3 - 8592*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^2*c^(13/2)*d^7*e^4 - 9456*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^2*c^6*d^6*e^5 - 320*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^3*c^7*d^8*e^3 - 7380*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^2*c^(11/2)*d^5*e^6 + 3840*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^3*c^(13/2)*d^7*e^4 - 2520*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a^2*c^5*d^4*e^7 + 19056*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^3*c^6*d^6*e^5 - 990*(sqrt(c)*x - sqrt(c*x^2 + a))^10*a^2*c^(9/2)*d^3*e^8 + 24440*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^3*c^(11/2)*d^5*e^6 + 240*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^4*c^(13/2)*d^7*e^4 - 90*(sqrt(c)*x - sqrt(c*x^2 + a))^11*a^2*c^4*d^2*e^9 + 20760*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^3*c^5*d^4*e^7 - 2960*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^4*c^6*d^6*e^5 + 8220*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^3*c^(9/2)*d^3*e^8 - 18720*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^4*c^(11/2)*d^5*e^6 + 2530*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a^3*c^4*d^2*e^9 - 21480*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^4*c^5*d^4*e^7 - 48*(sqrt(c)*x - sqrt(c*x^2 + a))*a^5*c^6*d^6*e^5 + 165*(sqrt(c)*x - sqrt(c*x^2 + a))^10*a^3*c^(7/2)*d*e^10 - 14860*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^4*c^(9/2)*d^3*e^8 + 1656*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^5*c^(11/2)*d^5*e^6 + 15*(sqrt(c)*x - sqrt(c*x^2 + a))^11*a^3*c^3*e^11 - 2700*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^4*c^4*d^2*e^9 + 12120*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^5*c^5*d^4*e^7 - 285*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^4*c^(7/2)*d*e^10 + 11640*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^5*c^(9/2)*d^3*e^8 + 4*a^6*c^(11/2)*d^5*e^6 + 235*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a^4*c^3*e^11 + 7020*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^5*c^4*d^2*e^9 - 336*(sqrt(c)*x - sqrt(c*x^2 + a))*a^6*c^5*d^4*e^7 + 810*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^5*c^(7/2)*d*e^10 - 4038*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^6*c^(9/2)*d^3*e^8 + 390*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^5*c^3*e^11 - 2330*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^6*c^4*d^2*e^9 - 930*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^6*c^(7/2)*d*e^10 + 28*a^7*c^(9/2)*d^3*e^8 + 390*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^6*c^3*e^11 + 882*(sqrt(c)*x - sqrt(c*x^2 + a))*a^7*c^4*d^2*e^9 + 321*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^7*c^(7/2)*d*e^10 + 235*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^7*c^3*e^11 - 81*a^8*c^(7/2)*d*e^10 + 15*(sqrt(c)*x - sqrt(c*x^2 + a))*a^8*c^3*e^11)/((c^4*d^8*e^4 + 4*a*c^3*d^6*e^6 + 6*a^2*c^2*d^4*e^8 + 4*a^3*c*d^2*e^10 + a^4*e^12)*((sqrt(c)*x - sqrt(c*x^2 + a))^2*e + 2*(sqrt(c)*x - sqrt(c*x^2 + a))*sqrt(c)*d - a*e)^6)","B",0
545,1,360,0,0.291631," ","integrate((e*x+d)^4*(c*x^2+a)^(5/2),x, algorithm=""giac"")","\frac{1}{80640} \, \sqrt{c x^{2} + a} {\left({\left(2 \, {\left({\left(4 \, {\left({\left(2 \, {\left(7 \, {\left(8 \, {\left(9 \, c^{2} x e^{4} + 40 \, c^{2} d e^{3}\right)} x + \frac{27 \, {\left(20 \, c^{10} d^{2} e^{2} + 7 \, a c^{9} e^{4}\right)}}{c^{8}}\right)} x + \frac{320 \, {\left(9 \, c^{10} d^{3} e + 19 \, a c^{9} d e^{3}\right)}}{c^{8}}\right)} x + \frac{21 \, {\left(80 \, c^{10} d^{4} + 1020 \, a c^{9} d^{2} e^{2} + 93 \, a^{2} c^{8} e^{4}\right)}}{c^{8}}\right)} x + \frac{1920 \, {\left(9 \, a c^{9} d^{3} e + 5 \, a^{2} c^{8} d e^{3}\right)}}{c^{8}}\right)} x + \frac{105 \, {\left(208 \, a c^{9} d^{4} + 708 \, a^{2} c^{8} d^{2} e^{2} + 3 \, a^{3} c^{7} e^{4}\right)}}{c^{8}}\right)} x + \frac{2560 \, {\left(27 \, a^{2} c^{8} d^{3} e + a^{3} c^{7} d e^{3}\right)}}{c^{8}}\right)} x + \frac{315 \, {\left(176 \, a^{2} c^{8} d^{4} + 60 \, a^{3} c^{7} d^{2} e^{2} - 3 \, a^{4} c^{6} e^{4}\right)}}{c^{8}}\right)} x + \frac{5120 \, {\left(9 \, a^{3} c^{7} d^{3} e - 2 \, a^{4} c^{6} d e^{3}\right)}}{c^{8}}\right)} - \frac{{\left(80 \, a^{3} c^{2} d^{4} - 60 \, a^{4} c d^{2} e^{2} + 3 \, a^{5} e^{4}\right)} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{256 \, c^{\frac{5}{2}}}"," ",0,"1/80640*sqrt(c*x^2 + a)*((2*((4*((2*(7*(8*(9*c^2*x*e^4 + 40*c^2*d*e^3)*x + 27*(20*c^10*d^2*e^2 + 7*a*c^9*e^4)/c^8)*x + 320*(9*c^10*d^3*e + 19*a*c^9*d*e^3)/c^8)*x + 21*(80*c^10*d^4 + 1020*a*c^9*d^2*e^2 + 93*a^2*c^8*e^4)/c^8)*x + 1920*(9*a*c^9*d^3*e + 5*a^2*c^8*d*e^3)/c^8)*x + 105*(208*a*c^9*d^4 + 708*a^2*c^8*d^2*e^2 + 3*a^3*c^7*e^4)/c^8)*x + 2560*(27*a^2*c^8*d^3*e + a^3*c^7*d*e^3)/c^8)*x + 315*(176*a^2*c^8*d^4 + 60*a^3*c^7*d^2*e^2 - 3*a^4*c^6*e^4)/c^8)*x + 5120*(9*a^3*c^7*d^3*e - 2*a^4*c^6*d*e^3)/c^8) - 1/256*(80*a^3*c^2*d^4 - 60*a^4*c*d^2*e^2 + 3*a^5*e^4)*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/c^(5/2)","A",0
546,1,280,0,0.252444," ","integrate((e*x+d)^3*(c*x^2+a)^(5/2),x, algorithm=""giac"")","\frac{1}{8064} \, \sqrt{c x^{2} + a} {\left({\left(2 \, {\left({\left(4 \, {\left({\left(2 \, {\left(7 \, {\left(8 \, c^{2} x e^{3} + 27 \, c^{2} d e^{2}\right)} x + \frac{8 \, {\left(27 \, c^{9} d^{2} e + 19 \, a c^{8} e^{3}\right)}}{c^{7}}\right)} x + \frac{21 \, {\left(8 \, c^{9} d^{3} + 51 \, a c^{8} d e^{2}\right)}}{c^{7}}\right)} x + \frac{48 \, {\left(27 \, a c^{8} d^{2} e + 5 \, a^{2} c^{7} e^{3}\right)}}{c^{7}}\right)} x + \frac{21 \, {\left(104 \, a c^{8} d^{3} + 177 \, a^{2} c^{7} d e^{2}\right)}}{c^{7}}\right)} x + \frac{64 \, {\left(81 \, a^{2} c^{7} d^{2} e + a^{3} c^{6} e^{3}\right)}}{c^{7}}\right)} x + \frac{63 \, {\left(88 \, a^{2} c^{7} d^{3} + 15 \, a^{3} c^{6} d e^{2}\right)}}{c^{7}}\right)} x + \frac{128 \, {\left(27 \, a^{3} c^{6} d^{2} e - 2 \, a^{4} c^{5} e^{3}\right)}}{c^{7}}\right)} - \frac{5 \, {\left(8 \, a^{3} c d^{3} - 3 \, a^{4} d e^{2}\right)} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{128 \, c^{\frac{3}{2}}}"," ",0,"1/8064*sqrt(c*x^2 + a)*((2*((4*((2*(7*(8*c^2*x*e^3 + 27*c^2*d*e^2)*x + 8*(27*c^9*d^2*e + 19*a*c^8*e^3)/c^7)*x + 21*(8*c^9*d^3 + 51*a*c^8*d*e^2)/c^7)*x + 48*(27*a*c^8*d^2*e + 5*a^2*c^7*e^3)/c^7)*x + 21*(104*a*c^8*d^3 + 177*a^2*c^7*d*e^2)/c^7)*x + 64*(81*a^2*c^7*d^2*e + a^3*c^6*e^3)/c^7)*x + 63*(88*a^2*c^7*d^3 + 15*a^3*c^6*d*e^2)/c^7)*x + 128*(27*a^3*c^6*d^2*e - 2*a^4*c^5*e^3)/c^7) - 5/128*(8*a^3*c*d^3 - 3*a^4*d*e^2)*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/c^(3/2)","A",0
547,1,190,0,0.253626," ","integrate((e*x+d)^2*(c*x^2+a)^(5/2),x, algorithm=""giac"")","\frac{1}{2688} \, {\left(\frac{768 \, a^{3} d e}{c} + {\left(2 \, {\left(1152 \, a^{2} d e + {\left(4 \, {\left(288 \, a c d e + {\left(6 \, {\left(7 \, c^{2} x e^{2} + 16 \, c^{2} d e\right)} x + \frac{7 \, {\left(8 \, c^{8} d^{2} + 17 \, a c^{7} e^{2}\right)}}{c^{6}}\right)} x\right)} x + \frac{7 \, {\left(104 \, a c^{7} d^{2} + 59 \, a^{2} c^{6} e^{2}\right)}}{c^{6}}\right)} x\right)} x + \frac{21 \, {\left(88 \, a^{2} c^{6} d^{2} + 5 \, a^{3} c^{5} e^{2}\right)}}{c^{6}}\right)} x\right)} \sqrt{c x^{2} + a} - \frac{5 \, {\left(8 \, a^{3} c d^{2} - a^{4} e^{2}\right)} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{128 \, c^{\frac{3}{2}}}"," ",0,"1/2688*(768*a^3*d*e/c + (2*(1152*a^2*d*e + (4*(288*a*c*d*e + (6*(7*c^2*x*e^2 + 16*c^2*d*e)*x + 7*(8*c^8*d^2 + 17*a*c^7*e^2)/c^6)*x)*x + 7*(104*a*c^7*d^2 + 59*a^2*c^6*e^2)/c^6)*x)*x + 21*(88*a^2*c^6*d^2 + 5*a^3*c^5*e^2)/c^6)*x)*sqrt(c*x^2 + a) - 5/128*(8*a^3*c*d^2 - a^4*e^2)*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/c^(3/2)","A",0
548,1,105,0,0.199404," ","integrate((e*x+d)*(c*x^2+a)^(5/2),x, algorithm=""giac"")","-\frac{5 \, a^{3} d \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{16 \, \sqrt{c}} + \frac{1}{336} \, \sqrt{c x^{2} + a} {\left(\frac{48 \, a^{3} e}{c} + {\left(231 \, a^{2} d + 2 \, {\left(72 \, a^{2} e + {\left(91 \, a c d + 4 \, {\left(18 \, a c e + {\left(6 \, c^{2} x e + 7 \, c^{2} d\right)} x\right)} x\right)} x\right)} x\right)} x\right)}"," ",0,"-5/16*a^3*d*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/sqrt(c) + 1/336*sqrt(c*x^2 + a)*(48*a^3*e/c + (231*a^2*d + 2*(72*a^2*e + (91*a*c*d + 4*(18*a*c*e + (6*c^2*x*e + 7*c^2*d)*x)*x)*x)*x)*x)","A",0
549,1,282,0,0.254206," ","integrate((c*x^2+a)^(5/2)/(e*x+d),x, algorithm=""giac"")","\frac{1}{8} \, {\left(8 \, c^{\frac{5}{2}} d^{5} + 20 \, a c^{\frac{3}{2}} d^{3} e^{2} + 15 \, a^{2} \sqrt{c} d e^{4}\right)} e^{\left(-6\right)} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right) + \frac{2 \, {\left(c^{3} d^{6} + 3 \, a c^{2} d^{4} e^{2} + 3 \, a^{2} c d^{2} e^{4} + a^{3} e^{6}\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} - a e^{2}}}\right) e^{\left(-6\right)}}{\sqrt{-c d^{2} - a e^{2}}} + \frac{1}{120} \, \sqrt{c x^{2} + a} {\left({\left(2 \, {\left(3 \, {\left(4 \, c^{2} x e^{\left(-1\right)} - 5 \, c^{2} d e^{\left(-2\right)}\right)} x + \frac{4 \, {\left(5 \, c^{5} d^{2} e^{18} + 11 \, a c^{4} e^{20}\right)} e^{\left(-21\right)}}{c^{3}}\right)} x - \frac{15 \, {\left(4 \, c^{5} d^{3} e^{17} + 9 \, a c^{4} d e^{19}\right)} e^{\left(-21\right)}}{c^{3}}\right)} x + \frac{8 \, {\left(15 \, c^{5} d^{4} e^{16} + 35 \, a c^{4} d^{2} e^{18} + 23 \, a^{2} c^{3} e^{20}\right)} e^{\left(-21\right)}}{c^{3}}\right)}"," ",0,"1/8*(8*c^(5/2)*d^5 + 20*a*c^(3/2)*d^3*e^2 + 15*a^2*sqrt(c)*d*e^4)*e^(-6)*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a))) + 2*(c^3*d^6 + 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4 + a^3*e^6)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + a))*e + sqrt(c)*d)/sqrt(-c*d^2 - a*e^2))*e^(-6)/sqrt(-c*d^2 - a*e^2) + 1/120*sqrt(c*x^2 + a)*((2*(3*(4*c^2*x*e^(-1) - 5*c^2*d*e^(-2))*x + 4*(5*c^5*d^2*e^18 + 11*a*c^4*e^20)*e^(-21)/c^3)*x - 15*(4*c^5*d^3*e^17 + 9*a*c^4*d*e^19)*e^(-21)/c^3)*x + 8*(15*c^5*d^4*e^16 + 35*a*c^4*d^2*e^18 + 23*a^2*c^3*e^20)*e^(-21)/c^3)","A",0
550,-1,0,0,0.000000," ","integrate((c*x^2+a)^(5/2)/(e*x+d)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
551,1,521,0,0.377681," ","integrate((c*x^2+a)^(5/2)/(e*x+d)^3,x, algorithm=""giac"")","\frac{5}{2} \, {\left(4 \, c^{\frac{5}{2}} d^{3} + 3 \, a c^{\frac{3}{2}} d e^{2}\right)} e^{\left(-6\right)} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right) + \frac{5 \, {\left(4 \, c^{3} d^{4} + 5 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} - a e^{2}}}\right) e^{\left(-6\right)}}{\sqrt{-c d^{2} - a e^{2}}} + \frac{1}{6} \, \sqrt{c x^{2} + a} {\left({\left(2 \, c^{2} x e^{\left(-3\right)} - 9 \, c^{2} d e^{\left(-4\right)}\right)} x + \frac{2 \, {\left(18 \, c^{3} d^{2} e^{13} + 7 \, a c^{2} e^{15}\right)} e^{\left(-18\right)}}{c}\right)} + \frac{{\left(10 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} c^{3} d^{4} e + 18 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} c^{\frac{7}{2}} d^{5} - 26 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a c^{3} d^{4} e + 9 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a c^{\frac{5}{2}} d^{3} e^{2} + 11 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a c^{2} d^{2} e^{3} + 9 \, a^{2} c^{\frac{5}{2}} d^{3} e^{2} - 25 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{2} c^{2} d^{2} e^{3} - 9 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{2} c^{\frac{3}{2}} d e^{4} + {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{2} c e^{5} + 9 \, a^{3} c^{\frac{3}{2}} d e^{4} + {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{3} c e^{5}\right)} e^{\left(-6\right)}}{{\left({\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} e + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} \sqrt{c} d - a e\right)}^{2}}"," ",0,"5/2*(4*c^(5/2)*d^3 + 3*a*c^(3/2)*d*e^2)*e^(-6)*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a))) + 5*(4*c^3*d^4 + 5*a*c^2*d^2*e^2 + a^2*c*e^4)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + a))*e + sqrt(c)*d)/sqrt(-c*d^2 - a*e^2))*e^(-6)/sqrt(-c*d^2 - a*e^2) + 1/6*sqrt(c*x^2 + a)*((2*c^2*x*e^(-3) - 9*c^2*d*e^(-4))*x + 2*(18*c^3*d^2*e^13 + 7*a*c^2*e^15)*e^(-18)/c) + (10*(sqrt(c)*x - sqrt(c*x^2 + a))^3*c^3*d^4*e + 18*(sqrt(c)*x - sqrt(c*x^2 + a))^2*c^(7/2)*d^5 - 26*(sqrt(c)*x - sqrt(c*x^2 + a))*a*c^3*d^4*e + 9*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a*c^(5/2)*d^3*e^2 + 11*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a*c^2*d^2*e^3 + 9*a^2*c^(5/2)*d^3*e^2 - 25*(sqrt(c)*x - sqrt(c*x^2 + a))*a^2*c^2*d^2*e^3 - 9*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^2*c^(3/2)*d*e^4 + (sqrt(c)*x - sqrt(c*x^2 + a))^3*a^2*c*e^5 + 9*a^3*c^(3/2)*d*e^4 + (sqrt(c)*x - sqrt(c*x^2 + a))*a^3*c*e^5)*e^(-6)/((sqrt(c)*x - sqrt(c*x^2 + a))^2*e + 2*(sqrt(c)*x - sqrt(c*x^2 + a))*sqrt(c)*d - a*e)^2","B",0
552,1,575,0,0.498769," ","integrate((c*x^2+a)^(5/2)/(e*x+d)^4,x, algorithm=""giac"")","-\frac{5}{2} \, {\left(4 \, c^{\frac{5}{2}} d^{2} + a c^{\frac{3}{2}} e^{2}\right)} e^{\left(-6\right)} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right) - \frac{5 \, {\left(4 \, c^{3} d^{3} + 3 \, a c^{2} d e^{2}\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} - a e^{2}}}\right) e^{\left(-6\right)}}{\sqrt{-c d^{2} - a e^{2}}} + \frac{1}{2} \, {\left(c^{2} x e^{\left(-4\right)} - 8 \, c^{2} d e^{\left(-5\right)}\right)} \sqrt{c x^{2} + a} - \frac{{\left(210 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} c^{\frac{7}{2}} d^{4} e + 188 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} c^{4} d^{5} + 60 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} c^{3} d^{3} e^{2} - 354 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a c^{\frac{7}{2}} d^{4} e - 226 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a c^{3} d^{3} e^{2} + 27 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a c^{\frac{5}{2}} d^{2} e^{3} + 27 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a c^{2} d e^{4} + 222 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{2} c^{3} d^{3} e^{2} - 84 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{2} c^{2} d e^{4} - 18 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{2} c^{\frac{3}{2}} e^{5} - 47 \, a^{3} c^{\frac{5}{2}} d^{2} e^{3} + 57 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{3} c^{2} d e^{4} + 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{3} c^{\frac{3}{2}} e^{5} - 14 \, a^{4} c^{\frac{3}{2}} e^{5}\right)} e^{\left(-6\right)}}{3 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} e + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} \sqrt{c} d - a e\right)}^{3}}"," ",0,"-5/2*(4*c^(5/2)*d^2 + a*c^(3/2)*e^2)*e^(-6)*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a))) - 5*(4*c^3*d^3 + 3*a*c^2*d*e^2)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + a))*e + sqrt(c)*d)/sqrt(-c*d^2 - a*e^2))*e^(-6)/sqrt(-c*d^2 - a*e^2) + 1/2*(c^2*x*e^(-4) - 8*c^2*d*e^(-5))*sqrt(c*x^2 + a) - 1/3*(210*(sqrt(c)*x - sqrt(c*x^2 + a))^4*c^(7/2)*d^4*e + 188*(sqrt(c)*x - sqrt(c*x^2 + a))^3*c^4*d^5 + 60*(sqrt(c)*x - sqrt(c*x^2 + a))^5*c^3*d^3*e^2 - 354*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a*c^(7/2)*d^4*e - 226*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a*c^3*d^3*e^2 + 27*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a*c^(5/2)*d^2*e^3 + 27*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a*c^2*d*e^4 + 222*(sqrt(c)*x - sqrt(c*x^2 + a))*a^2*c^3*d^3*e^2 - 84*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^2*c^2*d*e^4 - 18*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^2*c^(3/2)*e^5 - 47*a^3*c^(5/2)*d^2*e^3 + 57*(sqrt(c)*x - sqrt(c*x^2 + a))*a^3*c^2*d*e^4 + 24*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^3*c^(3/2)*e^5 - 14*a^4*c^(3/2)*e^5)*e^(-6)/((sqrt(c)*x - sqrt(c*x^2 + a))^2*e + 2*(sqrt(c)*x - sqrt(c*x^2 + a))*sqrt(c)*d - a*e)^3","B",0
553,-2,0,0,0.000000," ","integrate((c*x^2+a)^(5/2)/(e*x+d)^5,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]Unable to divide, perhaps due to rounding error%%%{%%%{1,[0,8,0,0]%%%},[4,0]%%%}+%%%{%%%{-2,[0,8,1,0]%%%},[2,0]%%%}+%%%{%%%{1,[0,8,2,0]%%%},[0,0]%%%} / %%%{%%%{1,[1,2,0,0]%%%}+%%%{1,[0,0,1,2]%%%},[4,0]%%%}+%%%{%%%{-2,[1,2,1,0]%%%}+%%%{-2,[0,0,2,2]%%%},[2,0]%%%}+%%%{%%%{1,[1,2,2,0]%%%}+%%%{1,[0,0,3,2]%%%},[0,0]%%%} Error: Bad Argument Value","F(-2)",0
554,1,1389,0,1.023345," ","integrate((c*x^2+a)^(5/2)/(e*x+d)^6,x, algorithm=""giac"")","-c^{\frac{5}{2}} e^{\left(-6\right)} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right) - \frac{{\left(8 \, c^{5} d^{5} + 20 \, a c^{4} d^{3} e^{2} + 15 \, a^{2} c^{3} d e^{4}\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} - a e^{2}}}\right)}{4 \, {\left(c^{2} d^{4} e^{6} + 2 \, a c d^{2} e^{8} + a^{2} e^{10}\right)} \sqrt{-c d^{2} - a e^{2}}} - \frac{10000 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} c^{\frac{13}{2}} d^{8} e + 4384 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} c^{7} d^{9} + 8800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} c^{6} d^{7} e^{2} + 3600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} c^{\frac{11}{2}} d^{6} e^{3} - 11920 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a c^{\frac{13}{2}} d^{8} e + 600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} c^{5} d^{5} e^{4} - 13872 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a c^{6} d^{7} e^{2} + 3800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a c^{\frac{11}{2}} d^{6} e^{3} + 12200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a c^{5} d^{5} e^{4} + 13120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{2} c^{6} d^{7} e^{2} + 6300 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a c^{\frac{9}{2}} d^{4} e^{5} - 3560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{2} c^{\frac{11}{2}} d^{6} e^{3} + 1140 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a c^{4} d^{3} e^{6} - 29076 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{2} c^{5} d^{5} e^{4} - 18950 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{2} c^{\frac{9}{2}} d^{4} e^{5} - 7360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{3} c^{\frac{11}{2}} d^{6} e^{3} - 1250 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{2} c^{4} d^{3} e^{6} + 17080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{3} c^{5} d^{5} e^{4} + 1935 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{2} c^{\frac{7}{2}} d^{2} e^{7} + 23950 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{3} c^{\frac{9}{2}} d^{4} e^{5} + 495 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a^{2} c^{3} d e^{8} + 370 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{3} c^{4} d^{3} e^{6} + 2140 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{4} c^{5} d^{5} e^{4} - 8250 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{3} c^{\frac{7}{2}} d^{2} e^{7} - 12450 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{4} c^{\frac{9}{2}} d^{4} e^{5} - 3030 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{3} c^{3} d e^{8} - 4150 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{4} c^{4} d^{3} e^{6} - 360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{3} c^{\frac{5}{2}} e^{9} + 8800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{4} c^{\frac{7}{2}} d^{2} e^{7} - 274 \, a^{5} c^{\frac{9}{2}} d^{4} e^{5} + 5520 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{4} c^{3} d e^{8} + 3890 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{5} c^{4} d^{3} e^{6} + 720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{4} c^{\frac{5}{2}} e^{9} - 2910 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{5} c^{\frac{7}{2}} d^{2} e^{7} - 4330 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{5} c^{3} d e^{8} - 1120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{5} c^{\frac{5}{2}} e^{9} - 503 \, a^{6} c^{\frac{7}{2}} d^{2} e^{7} + 1345 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{6} c^{3} d e^{8} + 560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{6} c^{\frac{5}{2}} e^{9} - 184 \, a^{7} c^{\frac{5}{2}} e^{9}}{60 \, {\left(c^{2} d^{4} e^{6} + 2 \, a c d^{2} e^{8} + a^{2} e^{10}\right)} {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} e + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} \sqrt{c} d - a e\right)}^{5}}"," ",0,"-c^(5/2)*e^(-6)*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a))) - 1/4*(8*c^5*d^5 + 20*a*c^4*d^3*e^2 + 15*a^2*c^3*d*e^4)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + a))*e + sqrt(c)*d)/sqrt(-c*d^2 - a*e^2))/((c^2*d^4*e^6 + 2*a*c*d^2*e^8 + a^2*e^10)*sqrt(-c*d^2 - a*e^2)) - 1/60*(10000*(sqrt(c)*x - sqrt(c*x^2 + a))^6*c^(13/2)*d^8*e + 4384*(sqrt(c)*x - sqrt(c*x^2 + a))^5*c^7*d^9 + 8800*(sqrt(c)*x - sqrt(c*x^2 + a))^7*c^6*d^7*e^2 + 3600*(sqrt(c)*x - sqrt(c*x^2 + a))^8*c^(11/2)*d^6*e^3 - 11920*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a*c^(13/2)*d^8*e + 600*(sqrt(c)*x - sqrt(c*x^2 + a))^9*c^5*d^5*e^4 - 13872*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a*c^6*d^7*e^2 + 3800*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a*c^(11/2)*d^6*e^3 + 12200*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a*c^5*d^5*e^4 + 13120*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^2*c^6*d^7*e^2 + 6300*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a*c^(9/2)*d^4*e^5 - 3560*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^2*c^(11/2)*d^6*e^3 + 1140*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a*c^4*d^3*e^6 - 29076*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^2*c^5*d^5*e^4 - 18950*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^2*c^(9/2)*d^4*e^5 - 7360*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^3*c^(11/2)*d^6*e^3 - 1250*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^2*c^4*d^3*e^6 + 17080*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^3*c^5*d^5*e^4 + 1935*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^2*c^(7/2)*d^2*e^7 + 23950*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^3*c^(9/2)*d^4*e^5 + 495*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a^2*c^3*d*e^8 + 370*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^3*c^4*d^3*e^6 + 2140*(sqrt(c)*x - sqrt(c*x^2 + a))*a^4*c^5*d^5*e^4 - 8250*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^3*c^(7/2)*d^2*e^7 - 12450*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^4*c^(9/2)*d^4*e^5 - 3030*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^3*c^3*d*e^8 - 4150*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^4*c^4*d^3*e^6 - 360*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^3*c^(5/2)*e^9 + 8800*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^4*c^(7/2)*d^2*e^7 - 274*a^5*c^(9/2)*d^4*e^5 + 5520*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^4*c^3*d*e^8 + 3890*(sqrt(c)*x - sqrt(c*x^2 + a))*a^5*c^4*d^3*e^6 + 720*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^4*c^(5/2)*e^9 - 2910*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^5*c^(7/2)*d^2*e^7 - 4330*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^5*c^3*d*e^8 - 1120*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^5*c^(5/2)*e^9 - 503*a^6*c^(7/2)*d^2*e^7 + 1345*(sqrt(c)*x - sqrt(c*x^2 + a))*a^6*c^3*d*e^8 + 560*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^6*c^(5/2)*e^9 - 184*a^7*c^(5/2)*e^9)/((c^2*d^4*e^6 + 2*a*c*d^2*e^8 + a^2*e^10)*((sqrt(c)*x - sqrt(c*x^2 + a))^2*e + 2*(sqrt(c)*x - sqrt(c*x^2 + a))*sqrt(c)*d - a*e)^5)","B",0
555,1,1895,0,0.557980," ","integrate((c*x^2+a)^(5/2)/(e*x+d)^7,x, algorithm=""giac"")","\frac{5 \, a^{3} c^{3} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} - a e^{2}}}\right)}{8 \, {\left(c^{3} d^{6} + 3 \, a c^{2} d^{4} e^{2} + 3 \, a^{2} c d^{2} e^{4} + a^{3} e^{6}\right)} \sqrt{-c d^{2} - a e^{2}}} + \frac{768 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} c^{8} d^{10} e + 256 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} c^{\frac{17}{2}} d^{11} + 960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} c^{\frac{15}{2}} d^{9} e^{2} + 640 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} c^{7} d^{8} e^{3} - 768 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a c^{8} d^{10} e + 240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{10} c^{\frac{13}{2}} d^{7} e^{4} - 1088 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a c^{\frac{15}{2}} d^{9} e^{2} + 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{11} c^{6} d^{6} e^{5} + 576 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a c^{7} d^{8} e^{3} + 2160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a c^{\frac{13}{2}} d^{7} e^{4} + 960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{2} c^{\frac{15}{2}} d^{9} e^{2} + 1840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a c^{6} d^{6} e^{5} - 576 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{2} c^{7} d^{8} e^{3} + 720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{10} a c^{\frac{11}{2}} d^{5} e^{6} - 3744 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{2} c^{\frac{13}{2}} d^{7} e^{4} + 144 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{11} a c^{5} d^{4} e^{7} - 2592 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{2} c^{6} d^{6} e^{5} - 640 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{3} c^{7} d^{8} e^{3} + 720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{2} c^{\frac{11}{2}} d^{5} e^{6} + 2160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{3} c^{\frac{13}{2}} d^{7} e^{4} + 1680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a^{2} c^{5} d^{4} e^{7} + 2592 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{3} c^{6} d^{6} e^{5} + 720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{10} a^{2} c^{\frac{9}{2}} d^{3} e^{8} - 3320 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{3} c^{\frac{11}{2}} d^{5} e^{6} + 240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{4} c^{\frac{13}{2}} d^{7} e^{4} + 144 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{11} a^{2} c^{4} d^{2} e^{9} - 5640 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{3} c^{5} d^{4} e^{7} - 1840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{4} c^{6} d^{6} e^{5} - 2910 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{3} c^{\frac{9}{2}} d^{3} e^{8} + 1080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{4} c^{\frac{11}{2}} d^{5} e^{6} - 340 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a^{3} c^{4} d^{2} e^{9} + 7080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{4} c^{5} d^{4} e^{7} - 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{5} c^{6} d^{6} e^{5} + 75 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{10} a^{3} c^{\frac{7}{2}} d e^{10} + 5680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{4} c^{\frac{9}{2}} d^{3} e^{8} + 792 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{5} c^{\frac{11}{2}} d^{5} e^{6} + 33 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{11} a^{3} c^{3} e^{11} + 1800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{4} c^{4} d^{2} e^{9} - 2040 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{5} c^{5} d^{4} e^{7} + 45 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{4} c^{\frac{7}{2}} d e^{10} - 4620 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{5} c^{\frac{9}{2}} d^{3} e^{8} + 8 \, a^{6} c^{\frac{11}{2}} d^{5} e^{6} + 5 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a^{4} c^{3} e^{11} - 2160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{5} c^{4} d^{2} e^{9} - 168 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{6} c^{5} d^{4} e^{7} - 330 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{5} c^{\frac{7}{2}} d e^{10} + 1104 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{6} c^{\frac{9}{2}} d^{3} e^{8} + 90 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{5} c^{3} e^{11} + 1640 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{6} c^{4} d^{2} e^{9} + 450 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{6} c^{\frac{7}{2}} d e^{10} + 26 \, a^{7} c^{\frac{9}{2}} d^{3} e^{8} + 90 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{6} c^{3} e^{11} - 252 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{7} c^{4} d^{2} e^{9} - 273 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{7} c^{\frac{7}{2}} d e^{10} + 5 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{7} c^{3} e^{11} + 33 \, a^{8} c^{\frac{7}{2}} d e^{10} + 33 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{8} c^{3} e^{11}}{24 \, {\left(c^{3} d^{6} e^{6} + 3 \, a c^{2} d^{4} e^{8} + 3 \, a^{2} c d^{2} e^{10} + a^{3} e^{12}\right)} {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} e + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} \sqrt{c} d - a e\right)}^{6}}"," ",0,"5/8*a^3*c^3*arctan(-((sqrt(c)*x - sqrt(c*x^2 + a))*e + sqrt(c)*d)/sqrt(-c*d^2 - a*e^2))/((c^3*d^6 + 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4 + a^3*e^6)*sqrt(-c*d^2 - a*e^2)) + 1/24*(768*(sqrt(c)*x - sqrt(c*x^2 + a))^7*c^8*d^10*e + 256*(sqrt(c)*x - sqrt(c*x^2 + a))^6*c^(17/2)*d^11 + 960*(sqrt(c)*x - sqrt(c*x^2 + a))^8*c^(15/2)*d^9*e^2 + 640*(sqrt(c)*x - sqrt(c*x^2 + a))^9*c^7*d^8*e^3 - 768*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a*c^8*d^10*e + 240*(sqrt(c)*x - sqrt(c*x^2 + a))^10*c^(13/2)*d^7*e^4 - 1088*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a*c^(15/2)*d^9*e^2 + 48*(sqrt(c)*x - sqrt(c*x^2 + a))^11*c^6*d^6*e^5 + 576*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a*c^7*d^8*e^3 + 2160*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a*c^(13/2)*d^7*e^4 + 960*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^2*c^(15/2)*d^9*e^2 + 1840*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a*c^6*d^6*e^5 - 576*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^2*c^7*d^8*e^3 + 720*(sqrt(c)*x - sqrt(c*x^2 + a))^10*a*c^(11/2)*d^5*e^6 - 3744*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^2*c^(13/2)*d^7*e^4 + 144*(sqrt(c)*x - sqrt(c*x^2 + a))^11*a*c^5*d^4*e^7 - 2592*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^2*c^6*d^6*e^5 - 640*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^3*c^7*d^8*e^3 + 720*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^2*c^(11/2)*d^5*e^6 + 2160*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^3*c^(13/2)*d^7*e^4 + 1680*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a^2*c^5*d^4*e^7 + 2592*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^3*c^6*d^6*e^5 + 720*(sqrt(c)*x - sqrt(c*x^2 + a))^10*a^2*c^(9/2)*d^3*e^8 - 3320*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^3*c^(11/2)*d^5*e^6 + 240*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^4*c^(13/2)*d^7*e^4 + 144*(sqrt(c)*x - sqrt(c*x^2 + a))^11*a^2*c^4*d^2*e^9 - 5640*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^3*c^5*d^4*e^7 - 1840*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^4*c^6*d^6*e^5 - 2910*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^3*c^(9/2)*d^3*e^8 + 1080*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^4*c^(11/2)*d^5*e^6 - 340*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a^3*c^4*d^2*e^9 + 7080*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^4*c^5*d^4*e^7 - 48*(sqrt(c)*x - sqrt(c*x^2 + a))*a^5*c^6*d^6*e^5 + 75*(sqrt(c)*x - sqrt(c*x^2 + a))^10*a^3*c^(7/2)*d*e^10 + 5680*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^4*c^(9/2)*d^3*e^8 + 792*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^5*c^(11/2)*d^5*e^6 + 33*(sqrt(c)*x - sqrt(c*x^2 + a))^11*a^3*c^3*e^11 + 1800*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^4*c^4*d^2*e^9 - 2040*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^5*c^5*d^4*e^7 + 45*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^4*c^(7/2)*d*e^10 - 4620*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^5*c^(9/2)*d^3*e^8 + 8*a^6*c^(11/2)*d^5*e^6 + 5*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a^4*c^3*e^11 - 2160*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^5*c^4*d^2*e^9 - 168*(sqrt(c)*x - sqrt(c*x^2 + a))*a^6*c^5*d^4*e^7 - 330*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^5*c^(7/2)*d*e^10 + 1104*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^6*c^(9/2)*d^3*e^8 + 90*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^5*c^3*e^11 + 1640*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^6*c^4*d^2*e^9 + 450*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^6*c^(7/2)*d*e^10 + 26*a^7*c^(9/2)*d^3*e^8 + 90*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^6*c^3*e^11 - 252*(sqrt(c)*x - sqrt(c*x^2 + a))*a^7*c^4*d^2*e^9 - 273*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^7*c^(7/2)*d*e^10 + 5*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^7*c^3*e^11 + 33*a^8*c^(7/2)*d*e^10 + 33*(sqrt(c)*x - sqrt(c*x^2 + a))*a^8*c^3*e^11)/((c^3*d^6*e^6 + 3*a*c^2*d^4*e^8 + 3*a^2*c*d^2*e^10 + a^3*e^12)*((sqrt(c)*x - sqrt(c*x^2 + a))^2*e + 2*(sqrt(c)*x - sqrt(c*x^2 + a))*sqrt(c)*d - a*e)^6)","B",0
556,1,2354,0,0.683784," ","integrate((c*x^2+a)^(5/2)/(e*x+d)^8,x, algorithm=""giac"")","-\frac{5 \, a^{3} c^{4} d \arctan\left(\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} - a e^{2}}}\right)}{8 \, {\left(c^{4} d^{8} + 4 \, a c^{3} d^{6} e^{2} + 6 \, a^{2} c^{2} d^{4} e^{4} + 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}\right)} \sqrt{-c d^{2} - a e^{2}}} + \frac{1792 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} c^{\frac{19}{2}} d^{12} e + 512 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} c^{10} d^{13} + 2688 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} c^{9} d^{11} e^{2} + 2240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{10} c^{\frac{17}{2}} d^{10} e^{3} - 1792 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a c^{\frac{19}{2}} d^{12} e + 1120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{11} c^{8} d^{9} e^{4} - 2944 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a c^{9} d^{11} e^{2} + 336 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{12} c^{\frac{15}{2}} d^{8} e^{5} + 1792 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a c^{\frac{17}{2}} d^{10} e^{3} + 8288 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a c^{8} d^{9} e^{4} + 2688 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{2} c^{9} d^{11} e^{2} + 8960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{10} a c^{\frac{15}{2}} d^{8} e^{5} - 1792 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{2} c^{\frac{17}{2}} d^{10} e^{3} + 4480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{11} a c^{7} d^{7} e^{6} - 13248 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{2} c^{8} d^{9} e^{4} + 1344 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{12} a c^{\frac{13}{2}} d^{6} e^{7} - 9072 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{2} c^{\frac{15}{2}} d^{8} e^{5} - 2240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{3} c^{\frac{17}{2}} d^{10} e^{3} + 6272 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a^{2} c^{7} d^{7} e^{6} + 8288 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{3} c^{8} d^{9} e^{4} + 13440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{10} a^{2} c^{\frac{13}{2}} d^{6} e^{7} + 9072 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{3} c^{\frac{15}{2}} d^{8} e^{5} + 6720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{11} a^{2} c^{6} d^{5} e^{8} - 30736 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{3} c^{7} d^{7} e^{6} + 1120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{4} c^{8} d^{9} e^{4} + 2016 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{12} a^{2} c^{\frac{11}{2}} d^{4} e^{9} - 55832 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{3} c^{\frac{13}{2}} d^{6} e^{7} - 8960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{4} c^{\frac{15}{2}} d^{8} e^{5} - 42588 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a^{3} c^{6} d^{5} e^{8} + 11312 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{4} c^{7} d^{7} e^{6} - 13370 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{10} a^{3} c^{\frac{11}{2}} d^{4} e^{9} + 80192 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{4} c^{\frac{13}{2}} d^{6} e^{7} - 336 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{5} c^{\frac{15}{2}} d^{8} e^{5} - 3010 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{11} a^{3} c^{5} d^{3} e^{10} + 100016 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{4} c^{6} d^{5} e^{8} + 5488 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{5} c^{7} d^{7} e^{6} - 21 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{12} a^{3} c^{\frac{9}{2}} d^{2} e^{11} + 70210 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{4} c^{\frac{11}{2}} d^{4} e^{9} - 19488 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{5} c^{\frac{13}{2}} d^{6} e^{7} - 105 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{13} a^{3} c^{4} d e^{12} + 27370 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a^{4} c^{5} d^{3} e^{10} - 79128 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{5} c^{6} d^{5} e^{8} + 112 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{6} c^{7} d^{7} e^{6} + 9940 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{10} a^{4} c^{\frac{9}{2}} d^{2} e^{11} - 82180 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{5} c^{\frac{11}{2}} d^{4} e^{9} - 1792 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{6} c^{\frac{13}{2}} d^{6} e^{7} + 1820 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{11} a^{4} c^{4} d e^{12} - 52500 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{5} c^{5} d^{3} e^{10} + 14448 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{6} c^{6} d^{5} e^{8} + 336 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{12} a^{4} c^{\frac{7}{2}} e^{13} - 16485 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{5} c^{\frac{9}{2}} d^{2} e^{11} + 49252 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{6} c^{\frac{11}{2}} d^{4} e^{9} - 8 \, a^{7} c^{\frac{13}{2}} d^{6} e^{7} - 4445 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a^{5} c^{4} d e^{12} + 44660 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{6} c^{5} d^{3} e^{10} + 532 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{7} c^{6} d^{5} e^{8} + 26880 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{6} c^{\frac{9}{2}} d^{2} e^{11} - 5026 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{7} c^{\frac{11}{2}} d^{4} e^{9} + 6720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{6} c^{4} d e^{12} - 17738 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{7} c^{5} d^{3} e^{10} + 1680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{6} c^{\frac{7}{2}} e^{13} - 12047 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{7} c^{\frac{9}{2}} d^{2} e^{11} - 38 \, a^{8} c^{\frac{11}{2}} d^{4} e^{9} - 5635 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{7} c^{4} d e^{12} + 1218 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{8} c^{5} d^{3} e^{10} + 4620 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{8} c^{\frac{9}{2}} d^{2} e^{11} + 2212 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{8} c^{4} d e^{12} + 1008 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{8} c^{\frac{7}{2}} e^{13} - 87 \, a^{9} c^{\frac{9}{2}} d^{2} e^{11} - 567 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{9} c^{4} d e^{12} + 48 \, a^{10} c^{\frac{7}{2}} e^{13}}{168 \, {\left(c^{4} d^{8} e^{6} + 4 \, a c^{3} d^{6} e^{8} + 6 \, a^{2} c^{2} d^{4} e^{10} + 4 \, a^{3} c d^{2} e^{12} + a^{4} e^{14}\right)} {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} e + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} \sqrt{c} d - a e\right)}^{7}}"," ",0,"-5/8*a^3*c^4*d*arctan(((sqrt(c)*x - sqrt(c*x^2 + a))*e + sqrt(c)*d)/sqrt(-c*d^2 - a*e^2))/((c^4*d^8 + 4*a*c^3*d^6*e^2 + 6*a^2*c^2*d^4*e^4 + 4*a^3*c*d^2*e^6 + a^4*e^8)*sqrt(-c*d^2 - a*e^2)) + 1/168*(1792*(sqrt(c)*x - sqrt(c*x^2 + a))^8*c^(19/2)*d^12*e + 512*(sqrt(c)*x - sqrt(c*x^2 + a))^7*c^10*d^13 + 2688*(sqrt(c)*x - sqrt(c*x^2 + a))^9*c^9*d^11*e^2 + 2240*(sqrt(c)*x - sqrt(c*x^2 + a))^10*c^(17/2)*d^10*e^3 - 1792*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a*c^(19/2)*d^12*e + 1120*(sqrt(c)*x - sqrt(c*x^2 + a))^11*c^8*d^9*e^4 - 2944*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a*c^9*d^11*e^2 + 336*(sqrt(c)*x - sqrt(c*x^2 + a))^12*c^(15/2)*d^8*e^5 + 1792*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a*c^(17/2)*d^10*e^3 + 8288*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a*c^8*d^9*e^4 + 2688*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^2*c^9*d^11*e^2 + 8960*(sqrt(c)*x - sqrt(c*x^2 + a))^10*a*c^(15/2)*d^8*e^5 - 1792*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^2*c^(17/2)*d^10*e^3 + 4480*(sqrt(c)*x - sqrt(c*x^2 + a))^11*a*c^7*d^7*e^6 - 13248*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^2*c^8*d^9*e^4 + 1344*(sqrt(c)*x - sqrt(c*x^2 + a))^12*a*c^(13/2)*d^6*e^7 - 9072*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^2*c^(15/2)*d^8*e^5 - 2240*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^3*c^(17/2)*d^10*e^3 + 6272*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a^2*c^7*d^7*e^6 + 8288*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^3*c^8*d^9*e^4 + 13440*(sqrt(c)*x - sqrt(c*x^2 + a))^10*a^2*c^(13/2)*d^6*e^7 + 9072*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^3*c^(15/2)*d^8*e^5 + 6720*(sqrt(c)*x - sqrt(c*x^2 + a))^11*a^2*c^6*d^5*e^8 - 30736*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^3*c^7*d^7*e^6 + 1120*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^4*c^8*d^9*e^4 + 2016*(sqrt(c)*x - sqrt(c*x^2 + a))^12*a^2*c^(11/2)*d^4*e^9 - 55832*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^3*c^(13/2)*d^6*e^7 - 8960*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^4*c^(15/2)*d^8*e^5 - 42588*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a^3*c^6*d^5*e^8 + 11312*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^4*c^7*d^7*e^6 - 13370*(sqrt(c)*x - sqrt(c*x^2 + a))^10*a^3*c^(11/2)*d^4*e^9 + 80192*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^4*c^(13/2)*d^6*e^7 - 336*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^5*c^(15/2)*d^8*e^5 - 3010*(sqrt(c)*x - sqrt(c*x^2 + a))^11*a^3*c^5*d^3*e^10 + 100016*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^4*c^6*d^5*e^8 + 5488*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^5*c^7*d^7*e^6 - 21*(sqrt(c)*x - sqrt(c*x^2 + a))^12*a^3*c^(9/2)*d^2*e^11 + 70210*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^4*c^(11/2)*d^4*e^9 - 19488*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^5*c^(13/2)*d^6*e^7 - 105*(sqrt(c)*x - sqrt(c*x^2 + a))^13*a^3*c^4*d*e^12 + 27370*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a^4*c^5*d^3*e^10 - 79128*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^5*c^6*d^5*e^8 + 112*(sqrt(c)*x - sqrt(c*x^2 + a))*a^6*c^7*d^7*e^6 + 9940*(sqrt(c)*x - sqrt(c*x^2 + a))^10*a^4*c^(9/2)*d^2*e^11 - 82180*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^5*c^(11/2)*d^4*e^9 - 1792*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^6*c^(13/2)*d^6*e^7 + 1820*(sqrt(c)*x - sqrt(c*x^2 + a))^11*a^4*c^4*d*e^12 - 52500*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^5*c^5*d^3*e^10 + 14448*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^6*c^6*d^5*e^8 + 336*(sqrt(c)*x - sqrt(c*x^2 + a))^12*a^4*c^(7/2)*e^13 - 16485*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^5*c^(9/2)*d^2*e^11 + 49252*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^6*c^(11/2)*d^4*e^9 - 8*a^7*c^(13/2)*d^6*e^7 - 4445*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a^5*c^4*d*e^12 + 44660*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^6*c^5*d^3*e^10 + 532*(sqrt(c)*x - sqrt(c*x^2 + a))*a^7*c^6*d^5*e^8 + 26880*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^6*c^(9/2)*d^2*e^11 - 5026*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^7*c^(11/2)*d^4*e^9 + 6720*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^6*c^4*d*e^12 - 17738*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^7*c^5*d^3*e^10 + 1680*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^6*c^(7/2)*e^13 - 12047*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^7*c^(9/2)*d^2*e^11 - 38*a^8*c^(11/2)*d^4*e^9 - 5635*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^7*c^4*d*e^12 + 1218*(sqrt(c)*x - sqrt(c*x^2 + a))*a^8*c^5*d^3*e^10 + 4620*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^8*c^(9/2)*d^2*e^11 + 2212*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^8*c^4*d*e^12 + 1008*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^8*c^(7/2)*e^13 - 87*a^9*c^(9/2)*d^2*e^11 - 567*(sqrt(c)*x - sqrt(c*x^2 + a))*a^9*c^4*d*e^12 + 48*a^10*c^(7/2)*e^13)/((c^4*d^8*e^6 + 4*a*c^3*d^6*e^8 + 6*a^2*c^2*d^4*e^10 + 4*a^3*c*d^2*e^12 + a^4*e^14)*((sqrt(c)*x - sqrt(c*x^2 + a))^2*e + 2*(sqrt(c)*x - sqrt(c*x^2 + a))*sqrt(c)*d - a*e)^7)","B",0
557,1,3116,0,0.892790," ","integrate((c*x^2+a)^(5/2)/(e*x+d)^9,x, algorithm=""giac"")","\frac{5 \, {\left(8 \, a^{3} c^{5} d^{2} - a^{4} c^{4} e^{2}\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} - a e^{2}}}\right)}{64 \, {\left(c^{5} d^{10} + 5 \, a c^{4} d^{8} e^{2} + 10 \, a^{2} c^{3} d^{6} e^{4} + 10 \, a^{3} c^{2} d^{4} e^{6} + 5 \, a^{4} c d^{2} e^{8} + a^{5} e^{10}\right)} \sqrt{-c d^{2} - a e^{2}}} + \frac{8192 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} c^{11} d^{14} e + 2048 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} c^{\frac{23}{2}} d^{15} + 14336 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{10} c^{\frac{21}{2}} d^{13} e^{2} + 14336 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{11} c^{10} d^{12} e^{3} - 8192 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a c^{11} d^{14} e + 8960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{12} c^{\frac{19}{2}} d^{11} e^{4} - 15360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a c^{\frac{21}{2}} d^{13} e^{2} + 3584 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{13} c^{9} d^{10} e^{5} + 10240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a c^{10} d^{12} e^{3} + 57344 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{10} a c^{\frac{19}{2}} d^{11} e^{4} + 14336 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{2} c^{\frac{21}{2}} d^{13} e^{2} + 75264 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{11} a c^{9} d^{10} e^{5} - 10240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{2} c^{10} d^{12} e^{3} + 44800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{12} a c^{\frac{17}{2}} d^{9} e^{6} - 85248 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{2} c^{\frac{19}{2}} d^{11} e^{4} + 17920 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{13} a c^{8} d^{8} e^{7} - 54272 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a^{2} c^{9} d^{10} e^{5} - 14336 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{3} c^{10} d^{12} e^{3} + 71680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{10} a^{2} c^{\frac{17}{2}} d^{9} e^{6} + 57344 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{3} c^{\frac{19}{2}} d^{11} e^{4} + 161280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{11} a^{2} c^{8} d^{8} e^{7} + 54272 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{3} c^{9} d^{10} e^{5} + 89600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{12} a^{2} c^{\frac{15}{2}} d^{7} e^{8} - 416384 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{3} c^{\frac{17}{2}} d^{9} e^{6} + 8960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{4} c^{\frac{19}{2}} d^{11} e^{4} + 35840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{13} a^{2} c^{7} d^{6} e^{9} - 877056 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a^{3} c^{8} d^{8} e^{7} - 75264 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{4} c^{9} d^{10} e^{5} - 916608 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{10} a^{3} c^{\frac{15}{2}} d^{7} e^{8} + 152320 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{4} c^{\frac{17}{2}} d^{9} e^{6} - 486528 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{11} a^{3} c^{7} d^{6} e^{9} + 1334016 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{4} c^{8} d^{8} e^{7} - 3584 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{5} c^{9} d^{10} e^{5} - 208880 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{12} a^{3} c^{\frac{13}{2}} d^{5} e^{10} + 2315376 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{4} c^{\frac{15}{2}} d^{7} e^{8} + 60928 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{5} c^{\frac{17}{2}} d^{9} e^{6} - 45920 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{13} a^{3} c^{6} d^{4} e^{11} + 2366784 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a^{4} c^{7} d^{6} e^{9} - 274176 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{5} c^{8} d^{8} e^{7} - 12600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{14} a^{3} c^{\frac{11}{2}} d^{3} e^{12} + 1412880 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{10} a^{4} c^{\frac{13}{2}} d^{5} e^{10} - 1755264 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{5} c^{\frac{15}{2}} d^{7} e^{8} + 1792 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{6} c^{\frac{17}{2}} d^{9} e^{6} - 840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{15} a^{3} c^{5} d^{2} e^{13} + 650160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{11} a^{4} c^{6} d^{4} e^{11} - 2796864 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{5} c^{7} d^{6} e^{9} - 26880 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{6} c^{8} d^{8} e^{7} + 165830 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{12} a^{4} c^{\frac{11}{2}} d^{3} e^{12} - 2638440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{5} c^{\frac{13}{2}} d^{5} e^{10} + 255360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{6} c^{\frac{15}{2}} d^{7} e^{8} + 34580 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{13} a^{4} c^{5} d^{2} e^{13} - 1325520 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a^{5} c^{6} d^{4} e^{11} + 1495424 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{6} c^{7} d^{6} e^{9} - 256 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{7} c^{8} d^{8} e^{7} + 1575 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{14} a^{4} c^{\frac{9}{2}} d e^{14} - 464520 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{10} a^{5} c^{\frac{11}{2}} d^{3} e^{12} + 2173136 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{6} c^{\frac{13}{2}} d^{5} e^{10} + 11520 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{7} c^{\frac{15}{2}} d^{7} e^{8} + 105 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{15} a^{4} c^{4} e^{15} - 46620 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{11} a^{5} c^{5} d^{2} e^{13} + 1851920 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{6} c^{6} d^{4} e^{11} - 118272 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{7} c^{7} d^{6} e^{9} - 1505 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{12} a^{5} c^{\frac{9}{2}} d e^{14} + 755510 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{6} c^{\frac{11}{2}} d^{3} e^{12} - 779408 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{7} c^{\frac{13}{2}} d^{5} e^{10} + 16 \, a^{8} c^{\frac{15}{2}} d^{7} e^{8} + 2779 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{13} a^{5} c^{4} e^{15} + 229040 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a^{6} c^{5} d^{2} e^{13} - 959280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{7} c^{6} d^{4} e^{11} - 1664 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{8} c^{7} d^{6} e^{9} + 15155 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{10} a^{6} c^{\frac{9}{2}} d e^{14} - 670040 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{7} c^{\frac{11}{2}} d^{3} e^{12} + 40608 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{8} c^{\frac{13}{2}} d^{5} e^{10} + 6265 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{11} a^{6} c^{4} e^{15} - 142240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{7} c^{5} d^{2} e^{13} + 292544 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{8} c^{6} d^{4} e^{11} - 23205 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{8} a^{7} c^{\frac{9}{2}} d e^{14} + 290066 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{8} c^{\frac{11}{2}} d^{3} e^{12} + 104 \, a^{9} c^{\frac{13}{2}} d^{5} e^{10} + 12355 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{9} a^{7} c^{4} e^{15} + 176148 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{8} c^{5} d^{2} e^{13} - 5920 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{9} c^{6} d^{4} e^{11} + 21973 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{6} a^{8} c^{\frac{9}{2}} d e^{14} - 64616 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{9} c^{\frac{11}{2}} d^{3} e^{12} + 12355 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{7} a^{8} c^{4} e^{15} - 39676 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{9} c^{5} d^{2} e^{13} - 17059 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{9} c^{\frac{9}{2}} d e^{14} + 370 \, a^{10} c^{\frac{11}{2}} d^{3} e^{12} + 6265 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a^{9} c^{4} e^{15} + 9768 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{10} c^{5} d^{2} e^{13} + 3729 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{10} c^{\frac{9}{2}} d e^{14} + 2779 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{10} c^{4} e^{15} - 663 \, a^{11} c^{\frac{9}{2}} d e^{14} + 105 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{11} c^{4} e^{15}}{1344 \, {\left(c^{5} d^{10} e^{6} + 5 \, a c^{4} d^{8} e^{8} + 10 \, a^{2} c^{3} d^{6} e^{10} + 10 \, a^{3} c^{2} d^{4} e^{12} + 5 \, a^{4} c d^{2} e^{14} + a^{5} e^{16}\right)} {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} e + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} \sqrt{c} d - a e\right)}^{8}}"," ",0,"5/64*(8*a^3*c^5*d^2 - a^4*c^4*e^2)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + a))*e + sqrt(c)*d)/sqrt(-c*d^2 - a*e^2))/((c^5*d^10 + 5*a*c^4*d^8*e^2 + 10*a^2*c^3*d^6*e^4 + 10*a^3*c^2*d^4*e^6 + 5*a^4*c*d^2*e^8 + a^5*e^10)*sqrt(-c*d^2 - a*e^2)) + 1/1344*(8192*(sqrt(c)*x - sqrt(c*x^2 + a))^9*c^11*d^14*e + 2048*(sqrt(c)*x - sqrt(c*x^2 + a))^8*c^(23/2)*d^15 + 14336*(sqrt(c)*x - sqrt(c*x^2 + a))^10*c^(21/2)*d^13*e^2 + 14336*(sqrt(c)*x - sqrt(c*x^2 + a))^11*c^10*d^12*e^3 - 8192*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a*c^11*d^14*e + 8960*(sqrt(c)*x - sqrt(c*x^2 + a))^12*c^(19/2)*d^11*e^4 - 15360*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a*c^(21/2)*d^13*e^2 + 3584*(sqrt(c)*x - sqrt(c*x^2 + a))^13*c^9*d^10*e^5 + 10240*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a*c^10*d^12*e^3 + 57344*(sqrt(c)*x - sqrt(c*x^2 + a))^10*a*c^(19/2)*d^11*e^4 + 14336*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^2*c^(21/2)*d^13*e^2 + 75264*(sqrt(c)*x - sqrt(c*x^2 + a))^11*a*c^9*d^10*e^5 - 10240*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^2*c^10*d^12*e^3 + 44800*(sqrt(c)*x - sqrt(c*x^2 + a))^12*a*c^(17/2)*d^9*e^6 - 85248*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^2*c^(19/2)*d^11*e^4 + 17920*(sqrt(c)*x - sqrt(c*x^2 + a))^13*a*c^8*d^8*e^7 - 54272*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a^2*c^9*d^10*e^5 - 14336*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^3*c^10*d^12*e^3 + 71680*(sqrt(c)*x - sqrt(c*x^2 + a))^10*a^2*c^(17/2)*d^9*e^6 + 57344*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^3*c^(19/2)*d^11*e^4 + 161280*(sqrt(c)*x - sqrt(c*x^2 + a))^11*a^2*c^8*d^8*e^7 + 54272*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^3*c^9*d^10*e^5 + 89600*(sqrt(c)*x - sqrt(c*x^2 + a))^12*a^2*c^(15/2)*d^7*e^8 - 416384*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^3*c^(17/2)*d^9*e^6 + 8960*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^4*c^(19/2)*d^11*e^4 + 35840*(sqrt(c)*x - sqrt(c*x^2 + a))^13*a^2*c^7*d^6*e^9 - 877056*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a^3*c^8*d^8*e^7 - 75264*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^4*c^9*d^10*e^5 - 916608*(sqrt(c)*x - sqrt(c*x^2 + a))^10*a^3*c^(15/2)*d^7*e^8 + 152320*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^4*c^(17/2)*d^9*e^6 - 486528*(sqrt(c)*x - sqrt(c*x^2 + a))^11*a^3*c^7*d^6*e^9 + 1334016*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^4*c^8*d^8*e^7 - 3584*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^5*c^9*d^10*e^5 - 208880*(sqrt(c)*x - sqrt(c*x^2 + a))^12*a^3*c^(13/2)*d^5*e^10 + 2315376*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^4*c^(15/2)*d^7*e^8 + 60928*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^5*c^(17/2)*d^9*e^6 - 45920*(sqrt(c)*x - sqrt(c*x^2 + a))^13*a^3*c^6*d^4*e^11 + 2366784*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a^4*c^7*d^6*e^9 - 274176*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^5*c^8*d^8*e^7 - 12600*(sqrt(c)*x - sqrt(c*x^2 + a))^14*a^3*c^(11/2)*d^3*e^12 + 1412880*(sqrt(c)*x - sqrt(c*x^2 + a))^10*a^4*c^(13/2)*d^5*e^10 - 1755264*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^5*c^(15/2)*d^7*e^8 + 1792*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^6*c^(17/2)*d^9*e^6 - 840*(sqrt(c)*x - sqrt(c*x^2 + a))^15*a^3*c^5*d^2*e^13 + 650160*(sqrt(c)*x - sqrt(c*x^2 + a))^11*a^4*c^6*d^4*e^11 - 2796864*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^5*c^7*d^6*e^9 - 26880*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^6*c^8*d^8*e^7 + 165830*(sqrt(c)*x - sqrt(c*x^2 + a))^12*a^4*c^(11/2)*d^3*e^12 - 2638440*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^5*c^(13/2)*d^5*e^10 + 255360*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^6*c^(15/2)*d^7*e^8 + 34580*(sqrt(c)*x - sqrt(c*x^2 + a))^13*a^4*c^5*d^2*e^13 - 1325520*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a^5*c^6*d^4*e^11 + 1495424*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^6*c^7*d^6*e^9 - 256*(sqrt(c)*x - sqrt(c*x^2 + a))*a^7*c^8*d^8*e^7 + 1575*(sqrt(c)*x - sqrt(c*x^2 + a))^14*a^4*c^(9/2)*d*e^14 - 464520*(sqrt(c)*x - sqrt(c*x^2 + a))^10*a^5*c^(11/2)*d^3*e^12 + 2173136*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^6*c^(13/2)*d^5*e^10 + 11520*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^7*c^(15/2)*d^7*e^8 + 105*(sqrt(c)*x - sqrt(c*x^2 + a))^15*a^4*c^4*e^15 - 46620*(sqrt(c)*x - sqrt(c*x^2 + a))^11*a^5*c^5*d^2*e^13 + 1851920*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^6*c^6*d^4*e^11 - 118272*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^7*c^7*d^6*e^9 - 1505*(sqrt(c)*x - sqrt(c*x^2 + a))^12*a^5*c^(9/2)*d*e^14 + 755510*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^6*c^(11/2)*d^3*e^12 - 779408*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^7*c^(13/2)*d^5*e^10 + 16*a^8*c^(15/2)*d^7*e^8 + 2779*(sqrt(c)*x - sqrt(c*x^2 + a))^13*a^5*c^4*e^15 + 229040*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a^6*c^5*d^2*e^13 - 959280*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^7*c^6*d^4*e^11 - 1664*(sqrt(c)*x - sqrt(c*x^2 + a))*a^8*c^7*d^6*e^9 + 15155*(sqrt(c)*x - sqrt(c*x^2 + a))^10*a^6*c^(9/2)*d*e^14 - 670040*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^7*c^(11/2)*d^3*e^12 + 40608*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^8*c^(13/2)*d^5*e^10 + 6265*(sqrt(c)*x - sqrt(c*x^2 + a))^11*a^6*c^4*e^15 - 142240*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^7*c^5*d^2*e^13 + 292544*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^8*c^6*d^4*e^11 - 23205*(sqrt(c)*x - sqrt(c*x^2 + a))^8*a^7*c^(9/2)*d*e^14 + 290066*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^8*c^(11/2)*d^3*e^12 + 104*a^9*c^(13/2)*d^5*e^10 + 12355*(sqrt(c)*x - sqrt(c*x^2 + a))^9*a^7*c^4*e^15 + 176148*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^8*c^5*d^2*e^13 - 5920*(sqrt(c)*x - sqrt(c*x^2 + a))*a^9*c^6*d^4*e^11 + 21973*(sqrt(c)*x - sqrt(c*x^2 + a))^6*a^8*c^(9/2)*d*e^14 - 64616*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^9*c^(11/2)*d^3*e^12 + 12355*(sqrt(c)*x - sqrt(c*x^2 + a))^7*a^8*c^4*e^15 - 39676*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^9*c^5*d^2*e^13 - 17059*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^9*c^(9/2)*d*e^14 + 370*a^10*c^(11/2)*d^3*e^12 + 6265*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a^9*c^4*e^15 + 9768*(sqrt(c)*x - sqrt(c*x^2 + a))*a^10*c^5*d^2*e^13 + 3729*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^10*c^(9/2)*d*e^14 + 2779*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^10*c^4*e^15 - 663*a^11*c^(9/2)*d*e^14 + 105*(sqrt(c)*x - sqrt(c*x^2 + a))*a^11*c^4*e^15)/((c^5*d^10*e^6 + 5*a*c^4*d^8*e^8 + 10*a^2*c^3*d^6*e^10 + 10*a^3*c^2*d^4*e^12 + 5*a^4*c*d^2*e^14 + a^5*e^16)*((sqrt(c)*x - sqrt(c*x^2 + a))^2*e + 2*(sqrt(c)*x - sqrt(c*x^2 + a))*sqrt(c)*d - a*e)^8)","B",0
558,1,71,0,0.250865," ","integrate((x^2+2)^(1/2)/(1+4*x),x, algorithm=""giac"")","\frac{1}{16} \, \sqrt{33} \log\left(\frac{{\left| -4 \, x - \sqrt{33} + 4 \, \sqrt{x^{2} + 2} - 1 \right|}}{{\left| -4 \, x + \sqrt{33} + 4 \, \sqrt{x^{2} + 2} - 1 \right|}}\right) + \frac{1}{4} \, \sqrt{x^{2} + 2} + \frac{1}{16} \, \log\left(-x + \sqrt{x^{2} + 2}\right)"," ",0,"1/16*sqrt(33)*log(abs(-4*x - sqrt(33) + 4*sqrt(x^2 + 2) - 1)/abs(-4*x + sqrt(33) + 4*sqrt(x^2 + 2) - 1)) + 1/4*sqrt(x^2 + 2) + 1/16*log(-x + sqrt(x^2 + 2))","A",0
559,1,105,0,0.300918," ","integrate((4*x^2+2)^(1/2)/(5+4*x),x, algorithm=""giac"")","\frac{1}{16} \, \sqrt{2} {\left(5 \, \sqrt{2} \log\left(-\sqrt{2} x + \sqrt{2 \, x^{2} + 1}\right) + \sqrt{66} \log\left(-\frac{{\left| -4 \, \sqrt{2} x - \sqrt{66} - 5 \, \sqrt{2} + 4 \, \sqrt{2 \, x^{2} + 1} \right|}}{4 \, \sqrt{2} x - \sqrt{66} + 5 \, \sqrt{2} - 4 \, \sqrt{2 \, x^{2} + 1}}\right) + 4 \, \sqrt{2 \, x^{2} + 1}\right)}"," ",0,"1/16*sqrt(2)*(5*sqrt(2)*log(-sqrt(2)*x + sqrt(2*x^2 + 1)) + sqrt(66)*log(-abs(-4*sqrt(2)*x - sqrt(66) - 5*sqrt(2) + 4*sqrt(2*x^2 + 1))/(4*sqrt(2)*x - sqrt(66) + 5*sqrt(2) - 4*sqrt(2*x^2 + 1))) + 4*sqrt(2*x^2 + 1))","B",0
560,1,43,0,0.212962," ","integrate((2+3*x)*(7*x^2-5)^(1/2),x, algorithm=""giac"")","\frac{1}{7} \, {\left(7 \, {\left(x + 1\right)} x - 5\right)} \sqrt{7 \, x^{2} - 5} + \frac{5}{7} \, \sqrt{7} \log\left({\left| -\sqrt{7} x + \sqrt{7 \, x^{2} - 5} \right|}\right)"," ",0,"1/7*(7*(x + 1)*x - 5)*sqrt(7*x^2 - 5) + 5/7*sqrt(7)*log(abs(-sqrt(7)*x + sqrt(7*x^2 - 5)))","A",0
561,1,133,0,0.275256," ","integrate((e*x+d)^4/(c*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{1}{24} \, \sqrt{c x^{2} + a} {\left({\left(2 \, x {\left(\frac{3 \, x e^{4}}{c} + \frac{16 \, d e^{3}}{c}\right)} + \frac{9 \, {\left(8 \, c^{3} d^{2} e^{2} - a c^{2} e^{4}\right)}}{c^{4}}\right)} x + \frac{32 \, {\left(3 \, c^{3} d^{3} e - 2 \, a c^{2} d e^{3}\right)}}{c^{4}}\right)} - \frac{{\left(8 \, c^{2} d^{4} - 24 \, a c d^{2} e^{2} + 3 \, a^{2} e^{4}\right)} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{8 \, c^{\frac{5}{2}}}"," ",0,"1/24*sqrt(c*x^2 + a)*((2*x*(3*x*e^4/c + 16*d*e^3/c) + 9*(8*c^3*d^2*e^2 - a*c^2*e^4)/c^4)*x + 32*(3*c^3*d^3*e - 2*a*c^2*d*e^3)/c^4) - 1/8*(8*c^2*d^4 - 24*a*c*d^2*e^2 + 3*a^2*e^4)*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/c^(5/2)","A",0
562,1,90,0,0.259252," ","integrate((e*x+d)^3/(c*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{1}{6} \, \sqrt{c x^{2} + a} {\left(x {\left(\frac{2 \, x e^{3}}{c} + \frac{9 \, d e^{2}}{c}\right)} + \frac{2 \, {\left(9 \, c^{2} d^{2} e - 2 \, a c e^{3}\right)}}{c^{3}}\right)} - \frac{{\left(2 \, c d^{3} - 3 \, a d e^{2}\right)} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{2 \, c^{\frac{3}{2}}}"," ",0,"1/6*sqrt(c*x^2 + a)*(x*(2*x*e^3/c + 9*d*e^2/c) + 2*(9*c^2*d^2*e - 2*a*c*e^3)/c^3) - 1/2*(2*c*d^3 - 3*a*d*e^2)*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/c^(3/2)","A",0
563,1,63,0,0.254486," ","integrate((e*x+d)^2/(c*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{c x^{2} + a} {\left(\frac{x e^{2}}{c} + \frac{4 \, d e}{c}\right)} - \frac{{\left(2 \, c d^{2} - a e^{2}\right)} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{2 \, c^{\frac{3}{2}}}"," ",0,"1/2*sqrt(c*x^2 + a)*(x*e^2/c + 4*d*e/c) - 1/2*(2*c*d^2 - a*e^2)*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/c^(3/2)","A",0
564,1,40,0,0.242271," ","integrate((e*x+d)/(c*x^2+a)^(1/2),x, algorithm=""giac"")","-\frac{d \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{\sqrt{c}} + \frac{\sqrt{c x^{2} + a} e}{c}"," ",0,"-d*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/sqrt(c) + sqrt(c*x^2 + a)*e/c","A",0
565,1,59,0,0.241683," ","integrate(1/(e*x+d)/(c*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{2 \, \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} - a e^{2}}}\right)}{\sqrt{-c d^{2} - a e^{2}}}"," ",0,"2*arctan(-((sqrt(c)*x - sqrt(c*x^2 + a))*e + sqrt(c)*d)/sqrt(-c*d^2 - a*e^2))/sqrt(-c*d^2 - a*e^2)","A",0
566,-1,0,0,0.000000," ","integrate(1/(e*x+d)^2/(c*x^2+a)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
567,1,345,0,0.281668," ","integrate(1/(e*x+d)^3/(c*x^2+a)^(1/2),x, algorithm=""giac"")","-c {\left(\frac{{\left(2 \, c d^{2} - a e^{2}\right)} \arctan\left(\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} - a e^{2}}}\right)}{{\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} \sqrt{-c d^{2} - a e^{2}}} + \frac{2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} c d^{2} e + 6 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} c^{\frac{3}{2}} d^{3} - 10 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a c d^{2} e - 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a \sqrt{c} d e^{2} - {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a e^{3} + 3 \, a^{2} \sqrt{c} d e^{2} - {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{2} e^{3}}{{\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} e + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} \sqrt{c} d - a e\right)}^{2}}\right)}"," ",0,"-c*((2*c*d^2 - a*e^2)*arctan(((sqrt(c)*x - sqrt(c*x^2 + a))*e + sqrt(c)*d)/sqrt(-c*d^2 - a*e^2))/((c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-c*d^2 - a*e^2)) + (2*(sqrt(c)*x - sqrt(c*x^2 + a))^3*c*d^2*e + 6*(sqrt(c)*x - sqrt(c*x^2 + a))^2*c^(3/2)*d^3 - 10*(sqrt(c)*x - sqrt(c*x^2 + a))*a*c*d^2*e - 3*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a*sqrt(c)*d*e^2 - (sqrt(c)*x - sqrt(c*x^2 + a))^3*a*e^3 + 3*a^2*sqrt(c)*d*e^2 - (sqrt(c)*x - sqrt(c*x^2 + a))*a^2*e^3)/((c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4)*((sqrt(c)*x - sqrt(c*x^2 + a))^2*e + 2*(sqrt(c)*x - sqrt(c*x^2 + a))*sqrt(c)*d - a*e)^2))","B",0
568,1,578,0,0.291086," ","integrate(1/(e*x+d)^4/(c*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{1}{3} \, c^{\frac{3}{2}} {\left(\frac{3 \, {\left(2 \, c^{\frac{3}{2}} d^{3} - 3 \, a \sqrt{c} d e^{2}\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} - a e^{2}}}\right)}{{\left(c^{3} d^{6} + 3 \, a c^{2} d^{4} e^{2} + 3 \, a^{2} c d^{2} e^{4} + a^{3} e^{6}\right)} \sqrt{-c d^{2} - a e^{2}}} - \frac{30 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} c^{2} d^{4} e + 44 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} c^{\frac{5}{2}} d^{5} + 6 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} c^{\frac{3}{2}} d^{3} e^{2} - 102 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a c^{2} d^{4} e - 82 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a c^{\frac{3}{2}} d^{3} e^{2} - 45 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a c d^{2} e^{3} - 9 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a \sqrt{c} d e^{4} + 60 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{2} c^{\frac{3}{2}} d^{3} e^{2} + 36 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{2} c d^{2} e^{3} + 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{2} \sqrt{c} d e^{4} - 11 \, a^{3} c d^{2} e^{3} - 15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{3} \sqrt{c} d e^{4} - 12 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{3} e^{5} + 4 \, a^{4} e^{5}}{{\left(c^{3} d^{6} + 3 \, a c^{2} d^{4} e^{2} + 3 \, a^{2} c d^{2} e^{4} + a^{3} e^{6}\right)} {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} e + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} \sqrt{c} d - a e\right)}^{3}}\right)}"," ",0,"1/3*c^(3/2)*(3*(2*c^(3/2)*d^3 - 3*a*sqrt(c)*d*e^2)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + a))*e + sqrt(c)*d)/sqrt(-c*d^2 - a*e^2))/((c^3*d^6 + 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4 + a^3*e^6)*sqrt(-c*d^2 - a*e^2)) - (30*(sqrt(c)*x - sqrt(c*x^2 + a))^4*c^2*d^4*e + 44*(sqrt(c)*x - sqrt(c*x^2 + a))^3*c^(5/2)*d^5 + 6*(sqrt(c)*x - sqrt(c*x^2 + a))^5*c^(3/2)*d^3*e^2 - 102*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a*c^2*d^4*e - 82*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a*c^(3/2)*d^3*e^2 - 45*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a*c*d^2*e^3 - 9*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a*sqrt(c)*d*e^4 + 60*(sqrt(c)*x - sqrt(c*x^2 + a))*a^2*c^(3/2)*d^3*e^2 + 36*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^2*c*d^2*e^3 + 24*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^2*sqrt(c)*d*e^4 - 11*a^3*c*d^2*e^3 - 15*(sqrt(c)*x - sqrt(c*x^2 + a))*a^3*sqrt(c)*d*e^4 - 12*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^3*e^5 + 4*a^4*e^5)/((c^3*d^6 + 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4 + a^3*e^6)*((sqrt(c)*x - sqrt(c*x^2 + a))^2*e + 2*(sqrt(c)*x - sqrt(c*x^2 + a))*sqrt(c)*d - a*e)^3))","B",0
569,1,138,0,0.278195," ","integrate((e*x+d)^4/(c*x^2+a)^(3/2),x, algorithm=""giac"")","\frac{{\left(x {\left(\frac{x e^{4}}{c} + \frac{8 \, d e^{3}}{c}\right)} + \frac{2 \, c^{4} d^{4} - 12 \, a c^{3} d^{2} e^{2} + 3 \, a^{2} c^{2} e^{4}}{a c^{4}}\right)} x - \frac{8 \, {\left(a c^{3} d^{3} e - 2 \, a^{2} c^{2} d e^{3}\right)}}{a c^{4}}}{2 \, \sqrt{c x^{2} + a}} - \frac{3 \, {\left(4 \, c d^{2} e^{2} - a e^{4}\right)} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{2 \, c^{\frac{5}{2}}}"," ",0,"1/2*((x*(x*e^4/c + 8*d*e^3/c) + (2*c^4*d^4 - 12*a*c^3*d^2*e^2 + 3*a^2*c^2*e^4)/(a*c^4))*x - 8*(a*c^3*d^3*e - 2*a^2*c^2*d*e^3)/(a*c^4))/sqrt(c*x^2 + a) - 3/2*(4*c*d^2*e^2 - a*e^4)*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/c^(5/2)","A",0
570,1,100,0,0.266754," ","integrate((e*x+d)^3/(c*x^2+a)^(3/2),x, algorithm=""giac"")","-\frac{3 \, d e^{2} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{c^{\frac{3}{2}}} + \frac{x {\left(\frac{x e^{3}}{c} + \frac{c^{3} d^{3} - 3 \, a c^{2} d e^{2}}{a c^{3}}\right)} - \frac{3 \, a c^{2} d^{2} e - 2 \, a^{2} c e^{3}}{a c^{3}}}{\sqrt{c x^{2} + a}}"," ",0,"-3*d*e^2*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/c^(3/2) + (x*(x*e^3/c + (c^3*d^3 - 3*a*c^2*d*e^2)/(a*c^3)) - (3*a*c^2*d^2*e - 2*a^2*c*e^3)/(a*c^3))/sqrt(c*x^2 + a)","A",0
571,1,69,0,0.223450," ","integrate((e*x+d)^2/(c*x^2+a)^(3/2),x, algorithm=""giac"")","-\frac{\frac{2 \, d e}{c} - \frac{{\left(c^{2} d^{2} - a c e^{2}\right)} x}{a c^{2}}}{\sqrt{c x^{2} + a}} - \frac{e^{2} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{c^{\frac{3}{2}}}"," ",0,"-(2*d*e/c - (c^2*d^2 - a*c*e^2)*x/(a*c^2))/sqrt(c*x^2 + a) - e^2*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/c^(3/2)","A",0
572,1,24,0,0.248011," ","integrate((e*x+d)/(c*x^2+a)^(3/2),x, algorithm=""giac"")","\frac{\frac{d x}{a} - \frac{e}{c}}{\sqrt{c x^{2} + a}}"," ",0,"(d*x/a - e/c)/sqrt(c*x^2 + a)","A",0
573,1,172,0,0.238754," ","integrate(1/(e*x+d)/(c*x^2+a)^(3/2),x, algorithm=""giac"")","\frac{\frac{{\left(c^{2} d^{3} + a c d e^{2}\right)} x}{a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}} + \frac{a c d^{2} e + a^{2} e^{3}}{a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}}}{\sqrt{c x^{2} + a}} - \frac{2 \, \arctan\left(\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} - a e^{2}}}\right) e^{2}}{{\left(c d^{2} + a e^{2}\right)} \sqrt{-c d^{2} - a e^{2}}}"," ",0,"((c^2*d^3 + a*c*d*e^2)*x/(a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4) + (a*c*d^2*e + a^2*e^3)/(a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4))/sqrt(c*x^2 + a) - 2*arctan(((sqrt(c)*x - sqrt(c*x^2 + a))*e + sqrt(c)*d)/sqrt(-c*d^2 - a*e^2))*e^2/((c*d^2 + a*e^2)*sqrt(-c*d^2 - a*e^2))","A",0
574,-1,0,0,0.000000," ","integrate(1/(e*x+d)^2/(c*x^2+a)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
575,1,649,0,0.330884," ","integrate(1/(e*x+d)^3/(c*x^2+a)^(3/2),x, algorithm=""giac"")","\frac{\frac{{\left(c^{6} d^{9} - 6 \, a^{2} c^{4} d^{5} e^{4} - 8 \, a^{3} c^{3} d^{3} e^{6} - 3 \, a^{4} c^{2} d e^{8}\right)} x}{a c^{6} d^{12} + 6 \, a^{2} c^{5} d^{10} e^{2} + 15 \, a^{3} c^{4} d^{8} e^{4} + 20 \, a^{4} c^{3} d^{6} e^{6} + 15 \, a^{5} c^{2} d^{4} e^{8} + 6 \, a^{6} c d^{2} e^{10} + a^{7} e^{12}} + \frac{3 \, a c^{5} d^{8} e + 8 \, a^{2} c^{4} d^{6} e^{3} + 6 \, a^{3} c^{3} d^{4} e^{5} - a^{5} c e^{9}}{a c^{6} d^{12} + 6 \, a^{2} c^{5} d^{10} e^{2} + 15 \, a^{3} c^{4} d^{8} e^{4} + 20 \, a^{4} c^{3} d^{6} e^{6} + 15 \, a^{5} c^{2} d^{4} e^{8} + 6 \, a^{6} c d^{2} e^{10} + a^{7} e^{12}}}{\sqrt{c x^{2} + a}} + \frac{3 \, {\left(4 \, c^{2} d^{2} e^{2} - a c e^{4}\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} - a e^{2}}}\right)}{{\left(c^{3} d^{6} + 3 \, a c^{2} d^{4} e^{2} + 3 \, a^{2} c d^{2} e^{4} + a^{3} e^{6}\right)} \sqrt{-c d^{2} - a e^{2}}} - \frac{14 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} c^{\frac{5}{2}} d^{3} e^{2} + 6 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} c^{2} d^{2} e^{3} - 22 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a c^{2} d^{2} e^{3} - 7 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a c^{\frac{3}{2}} d e^{4} - {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a c e^{5} + 7 \, a^{2} c^{\frac{3}{2}} d e^{4} - {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{2} c e^{5}}{{\left(c^{3} d^{6} + 3 \, a c^{2} d^{4} e^{2} + 3 \, a^{2} c d^{2} e^{4} + a^{3} e^{6}\right)} {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} e + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} \sqrt{c} d - a e\right)}^{2}}"," ",0,"((c^6*d^9 - 6*a^2*c^4*d^5*e^4 - 8*a^3*c^3*d^3*e^6 - 3*a^4*c^2*d*e^8)*x/(a*c^6*d^12 + 6*a^2*c^5*d^10*e^2 + 15*a^3*c^4*d^8*e^4 + 20*a^4*c^3*d^6*e^6 + 15*a^5*c^2*d^4*e^8 + 6*a^6*c*d^2*e^10 + a^7*e^12) + (3*a*c^5*d^8*e + 8*a^2*c^4*d^6*e^3 + 6*a^3*c^3*d^4*e^5 - a^5*c*e^9)/(a*c^6*d^12 + 6*a^2*c^5*d^10*e^2 + 15*a^3*c^4*d^8*e^4 + 20*a^4*c^3*d^6*e^6 + 15*a^5*c^2*d^4*e^8 + 6*a^6*c*d^2*e^10 + a^7*e^12))/sqrt(c*x^2 + a) + 3*(4*c^2*d^2*e^2 - a*c*e^4)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + a))*e + sqrt(c)*d)/sqrt(-c*d^2 - a*e^2))/((c^3*d^6 + 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4 + a^3*e^6)*sqrt(-c*d^2 - a*e^2)) - (14*(sqrt(c)*x - sqrt(c*x^2 + a))^2*c^(5/2)*d^3*e^2 + 6*(sqrt(c)*x - sqrt(c*x^2 + a))^3*c^2*d^2*e^3 - 22*(sqrt(c)*x - sqrt(c*x^2 + a))*a*c^2*d^2*e^3 - 7*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a*c^(3/2)*d*e^4 - (sqrt(c)*x - sqrt(c*x^2 + a))^3*a*c*e^5 + 7*a^2*c^(3/2)*d*e^4 - (sqrt(c)*x - sqrt(c*x^2 + a))*a^2*c*e^5)/((c^3*d^6 + 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4 + a^3*e^6)*((sqrt(c)*x - sqrt(c*x^2 + a))^2*e + 2*(sqrt(c)*x - sqrt(c*x^2 + a))*sqrt(c)*d - a*e)^2)","B",0
576,1,1025,0,0.520633," ","integrate(1/(e*x+d)^4/(c*x^2+a)^(3/2),x, algorithm=""giac"")","\frac{\frac{{\left(c^{8} d^{12} - 2 \, a c^{7} d^{10} e^{2} - 17 \, a^{2} c^{6} d^{8} e^{4} - 28 \, a^{3} c^{5} d^{6} e^{6} - 17 \, a^{4} c^{4} d^{4} e^{8} - 2 \, a^{5} c^{3} d^{2} e^{10} + a^{6} c^{2} e^{12}\right)} x}{a c^{8} d^{16} + 8 \, a^{2} c^{7} d^{14} e^{2} + 28 \, a^{3} c^{6} d^{12} e^{4} + 56 \, a^{4} c^{5} d^{10} e^{6} + 70 \, a^{5} c^{4} d^{8} e^{8} + 56 \, a^{6} c^{3} d^{6} e^{10} + 28 \, a^{7} c^{2} d^{4} e^{12} + 8 \, a^{8} c d^{2} e^{14} + a^{9} e^{16}} + \frac{4 \, {\left(a c^{7} d^{11} e + 3 \, a^{2} c^{6} d^{9} e^{3} + 2 \, a^{3} c^{5} d^{7} e^{5} - 2 \, a^{4} c^{4} d^{5} e^{7} - 3 \, a^{5} c^{3} d^{3} e^{9} - a^{6} c^{2} d e^{11}\right)}}{a c^{8} d^{16} + 8 \, a^{2} c^{7} d^{14} e^{2} + 28 \, a^{3} c^{6} d^{12} e^{4} + 56 \, a^{4} c^{5} d^{10} e^{6} + 70 \, a^{5} c^{4} d^{8} e^{8} + 56 \, a^{6} c^{3} d^{6} e^{10} + 28 \, a^{7} c^{2} d^{4} e^{12} + 8 \, a^{8} c d^{2} e^{14} + a^{9} e^{16}}}{\sqrt{c x^{2} + a}} + \frac{5 \, {\left(4 \, c^{3} d^{3} e^{2} - 3 \, a c^{2} d e^{4}\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} - a e^{2}}}\right)}{{\left(c^{4} d^{8} + 4 \, a c^{3} d^{6} e^{2} + 6 \, a^{2} c^{2} d^{4} e^{4} + 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}\right)} \sqrt{-c d^{2} - a e^{2}}} - \frac{188 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} c^{4} d^{5} e^{2} + 162 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} c^{\frac{7}{2}} d^{4} e^{3} + 36 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} c^{3} d^{3} e^{4} - 402 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a c^{\frac{7}{2}} d^{4} e^{3} - 322 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a c^{3} d^{3} e^{4} - 117 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a c^{\frac{5}{2}} d^{2} e^{5} - 21 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{5} a c^{2} d e^{6} + 246 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{2} c^{3} d^{3} e^{4} + 144 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{2} c^{\frac{5}{2}} d^{2} e^{5} + 60 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a^{2} c^{2} d e^{6} + 6 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{4} a^{2} c^{\frac{3}{2}} e^{7} - 47 \, a^{3} c^{\frac{5}{2}} d^{2} e^{5} - 39 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{3} c^{2} d e^{6} - 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a^{3} c^{\frac{3}{2}} e^{7} + 10 \, a^{4} c^{\frac{3}{2}} e^{7}}{3 \, {\left(c^{4} d^{8} + 4 \, a c^{3} d^{6} e^{2} + 6 \, a^{2} c^{2} d^{4} e^{4} + 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}\right)} {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} e + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} \sqrt{c} d - a e\right)}^{3}}"," ",0,"((c^8*d^12 - 2*a*c^7*d^10*e^2 - 17*a^2*c^6*d^8*e^4 - 28*a^3*c^5*d^6*e^6 - 17*a^4*c^4*d^4*e^8 - 2*a^5*c^3*d^2*e^10 + a^6*c^2*e^12)*x/(a*c^8*d^16 + 8*a^2*c^7*d^14*e^2 + 28*a^3*c^6*d^12*e^4 + 56*a^4*c^5*d^10*e^6 + 70*a^5*c^4*d^8*e^8 + 56*a^6*c^3*d^6*e^10 + 28*a^7*c^2*d^4*e^12 + 8*a^8*c*d^2*e^14 + a^9*e^16) + 4*(a*c^7*d^11*e + 3*a^2*c^6*d^9*e^3 + 2*a^3*c^5*d^7*e^5 - 2*a^4*c^4*d^5*e^7 - 3*a^5*c^3*d^3*e^9 - a^6*c^2*d*e^11)/(a*c^8*d^16 + 8*a^2*c^7*d^14*e^2 + 28*a^3*c^6*d^12*e^4 + 56*a^4*c^5*d^10*e^6 + 70*a^5*c^4*d^8*e^8 + 56*a^6*c^3*d^6*e^10 + 28*a^7*c^2*d^4*e^12 + 8*a^8*c*d^2*e^14 + a^9*e^16))/sqrt(c*x^2 + a) + 5*(4*c^3*d^3*e^2 - 3*a*c^2*d*e^4)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + a))*e + sqrt(c)*d)/sqrt(-c*d^2 - a*e^2))/((c^4*d^8 + 4*a*c^3*d^6*e^2 + 6*a^2*c^2*d^4*e^4 + 4*a^3*c*d^2*e^6 + a^4*e^8)*sqrt(-c*d^2 - a*e^2)) - 1/3*(188*(sqrt(c)*x - sqrt(c*x^2 + a))^3*c^4*d^5*e^2 + 162*(sqrt(c)*x - sqrt(c*x^2 + a))^4*c^(7/2)*d^4*e^3 + 36*(sqrt(c)*x - sqrt(c*x^2 + a))^5*c^3*d^3*e^4 - 402*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a*c^(7/2)*d^4*e^3 - 322*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a*c^3*d^3*e^4 - 117*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a*c^(5/2)*d^2*e^5 - 21*(sqrt(c)*x - sqrt(c*x^2 + a))^5*a*c^2*d*e^6 + 246*(sqrt(c)*x - sqrt(c*x^2 + a))*a^2*c^3*d^3*e^4 + 144*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^2*c^(5/2)*d^2*e^5 + 60*(sqrt(c)*x - sqrt(c*x^2 + a))^3*a^2*c^2*d*e^6 + 6*(sqrt(c)*x - sqrt(c*x^2 + a))^4*a^2*c^(3/2)*e^7 - 47*a^3*c^(5/2)*d^2*e^5 - 39*(sqrt(c)*x - sqrt(c*x^2 + a))*a^3*c^2*d*e^6 - 24*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a^3*c^(3/2)*e^7 + 10*a^4*c^(3/2)*e^7)/((c^4*d^8 + 4*a*c^3*d^6*e^2 + 6*a^2*c^2*d^4*e^4 + 4*a^3*c*d^2*e^6 + a^4*e^8)*((sqrt(c)*x - sqrt(c*x^2 + a))^2*e + 2*(sqrt(c)*x - sqrt(c*x^2 + a))*sqrt(c)*d - a*e)^3)","B",0
577,1,199,0,0.265446," ","integrate((e*x+d)^5/(c*x^2+a)^(5/2),x, algorithm=""giac"")","-\frac{5 \, d e^{4} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{c^{\frac{5}{2}}} + \frac{{\left({\left(x {\left(\frac{3 \, x e^{5}}{c} + \frac{2 \, {\left(c^{6} d^{5} + 5 \, a c^{5} d^{3} e^{2} - 10 \, a^{2} c^{4} d e^{4}\right)}}{a^{2} c^{5}}\right)} - \frac{6 \, {\left(5 \, a^{2} c^{4} d^{2} e^{3} - 2 \, a^{3} c^{3} e^{5}\right)}}{a^{2} c^{5}}\right)} x + \frac{3 \, {\left(a c^{5} d^{5} - 5 \, a^{3} c^{3} d e^{4}\right)}}{a^{2} c^{5}}\right)} x - \frac{5 \, a^{2} c^{4} d^{4} e + 20 \, a^{3} c^{3} d^{2} e^{3} - 8 \, a^{4} c^{2} e^{5}}{a^{2} c^{5}}}{3 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}}}"," ",0,"-5*d*e^4*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/c^(5/2) + 1/3*(((x*(3*x*e^5/c + 2*(c^6*d^5 + 5*a*c^5*d^3*e^2 - 10*a^2*c^4*d*e^4)/(a^2*c^5)) - 6*(5*a^2*c^4*d^2*e^3 - 2*a^3*c^3*e^5)/(a^2*c^5))*x + 3*(a*c^5*d^5 - 5*a^3*c^3*d*e^4)/(a^2*c^5))*x - (5*a^2*c^4*d^4*e + 20*a^3*c^3*d^2*e^3 - 8*a^4*c^2*e^5)/(a^2*c^5))/(c*x^2 + a)^(3/2)","A",0
578,1,150,0,0.256583," ","integrate((e*x+d)^4/(c*x^2+a)^(5/2),x, algorithm=""giac"")","-\frac{{\left(2 \, x {\left(\frac{6 \, d e^{3}}{c} - \frac{{\left(c^{5} d^{4} + 3 \, a c^{4} d^{2} e^{2} - 2 \, a^{2} c^{3} e^{4}\right)} x}{a^{2} c^{4}}\right)} - \frac{3 \, {\left(a c^{4} d^{4} - a^{3} c^{2} e^{4}\right)}}{a^{2} c^{4}}\right)} x + \frac{4 \, {\left(a^{2} c^{3} d^{3} e + 2 \, a^{3} c^{2} d e^{3}\right)}}{a^{2} c^{4}}}{3 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}}} - \frac{e^{4} \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + a} \right|}\right)}{c^{\frac{5}{2}}}"," ",0,"-1/3*((2*x*(6*d*e^3/c - (c^5*d^4 + 3*a*c^4*d^2*e^2 - 2*a^2*c^3*e^4)*x/(a^2*c^4)) - 3*(a*c^4*d^4 - a^3*c^2*e^4)/(a^2*c^4))*x + 4*(a^2*c^3*d^3*e + 2*a^3*c^2*d*e^3)/(a^2*c^4))/(c*x^2 + a)^(3/2) - e^4*log(abs(-sqrt(c)*x + sqrt(c*x^2 + a)))/c^(5/2)","A",0
579,1,88,0,0.249562," ","integrate((e*x+d)^3/(c*x^2+a)^(5/2),x, algorithm=""giac"")","\frac{{\left(\frac{3 \, d^{3}}{a} - x {\left(\frac{3 \, e^{3}}{c} - \frac{{\left(2 \, c^{3} d^{3} + 3 \, a c^{2} d e^{2}\right)} x}{a^{2} c^{2}}\right)}\right)} x - \frac{3 \, a^{2} c d^{2} e + 2 \, a^{3} e^{3}}{a^{2} c^{2}}}{3 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}}}"," ",0,"1/3*((3*d^3/a - x*(3*e^3/c - (2*c^3*d^3 + 3*a*c^2*d*e^2)*x/(a^2*c^2)))*x - (3*a^2*c*d^2*e + 2*a^3*e^3)/(a^2*c^2))/(c*x^2 + a)^(3/2)","A",0
580,1,55,0,0.237261," ","integrate((e*x+d)^2/(c*x^2+a)^(5/2),x, algorithm=""giac"")","\frac{{\left(\frac{3 \, d^{2}}{a} + \frac{{\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2}}{a^{2} c}\right)} x - \frac{2 \, d e}{c}}{3 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}}}"," ",0,"1/3*((3*d^2/a + (2*c^2*d^2 + a*c*e^2)*x^2/(a^2*c))*x - 2*d*e/c)/(c*x^2 + a)^(3/2)","A",0
581,1,38,0,0.231212," ","integrate((e*x+d)/(c*x^2+a)^(5/2),x, algorithm=""giac"")","\frac{{\left(\frac{2 \, c d x^{2}}{a^{2}} + \frac{3 \, d}{a}\right)} x - \frac{e}{c}}{3 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}}}"," ",0,"1/3*((2*c*d*x^2/a^2 + 3*d/a)*x - e/c)/(c*x^2 + a)^(3/2)","A",0
582,1,935,0,0.345634," ","integrate(1/(e*x+d)/(c*x^2+a)^(5/2),x, algorithm=""giac"")","-\frac{2 \, \arctan\left(\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} - a e^{2}}}\right) e^{4}}{{\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} \sqrt{-c d^{2} - a e^{2}}} + \frac{{\left({\left(\frac{{\left(2 \, c^{10} d^{15} + 17 \, a c^{9} d^{13} e^{2} + 60 \, a^{2} c^{8} d^{11} e^{4} + 115 \, a^{3} c^{7} d^{9} e^{6} + 130 \, a^{4} c^{6} d^{7} e^{8} + 87 \, a^{5} c^{5} d^{5} e^{10} + 32 \, a^{6} c^{4} d^{3} e^{12} + 5 \, a^{7} c^{3} d e^{14}\right)} x}{a^{2} c^{9} d^{16} + 8 \, a^{3} c^{8} d^{14} e^{2} + 28 \, a^{4} c^{7} d^{12} e^{4} + 56 \, a^{5} c^{6} d^{10} e^{6} + 70 \, a^{6} c^{5} d^{8} e^{8} + 56 \, a^{7} c^{4} d^{6} e^{10} + 28 \, a^{8} c^{3} d^{4} e^{12} + 8 \, a^{9} c^{2} d^{2} e^{14} + a^{10} c e^{16}} + \frac{3 \, {\left(a^{2} c^{8} d^{12} e^{3} + 6 \, a^{3} c^{7} d^{10} e^{5} + 15 \, a^{4} c^{6} d^{8} e^{7} + 20 \, a^{5} c^{5} d^{6} e^{9} + 15 \, a^{6} c^{4} d^{4} e^{11} + 6 \, a^{7} c^{3} d^{2} e^{13} + a^{8} c^{2} e^{15}\right)}}{a^{2} c^{9} d^{16} + 8 \, a^{3} c^{8} d^{14} e^{2} + 28 \, a^{4} c^{7} d^{12} e^{4} + 56 \, a^{5} c^{6} d^{10} e^{6} + 70 \, a^{6} c^{5} d^{8} e^{8} + 56 \, a^{7} c^{4} d^{6} e^{10} + 28 \, a^{8} c^{3} d^{4} e^{12} + 8 \, a^{9} c^{2} d^{2} e^{14} + a^{10} c e^{16}}\right)} x + \frac{3 \, {\left(a c^{9} d^{15} + 8 \, a^{2} c^{8} d^{13} e^{2} + 27 \, a^{3} c^{7} d^{11} e^{4} + 50 \, a^{4} c^{6} d^{9} e^{6} + 55 \, a^{5} c^{5} d^{7} e^{8} + 36 \, a^{6} c^{4} d^{5} e^{10} + 13 \, a^{7} c^{3} d^{3} e^{12} + 2 \, a^{8} c^{2} d e^{14}\right)}}{a^{2} c^{9} d^{16} + 8 \, a^{3} c^{8} d^{14} e^{2} + 28 \, a^{4} c^{7} d^{12} e^{4} + 56 \, a^{5} c^{6} d^{10} e^{6} + 70 \, a^{6} c^{5} d^{8} e^{8} + 56 \, a^{7} c^{4} d^{6} e^{10} + 28 \, a^{8} c^{3} d^{4} e^{12} + 8 \, a^{9} c^{2} d^{2} e^{14} + a^{10} c e^{16}}\right)} x + \frac{a^{2} c^{8} d^{14} e + 10 \, a^{3} c^{7} d^{12} e^{3} + 39 \, a^{4} c^{6} d^{10} e^{5} + 80 \, a^{5} c^{5} d^{8} e^{7} + 95 \, a^{6} c^{4} d^{6} e^{9} + 66 \, a^{7} c^{3} d^{4} e^{11} + 25 \, a^{8} c^{2} d^{2} e^{13} + 4 \, a^{9} c e^{15}}{a^{2} c^{9} d^{16} + 8 \, a^{3} c^{8} d^{14} e^{2} + 28 \, a^{4} c^{7} d^{12} e^{4} + 56 \, a^{5} c^{6} d^{10} e^{6} + 70 \, a^{6} c^{5} d^{8} e^{8} + 56 \, a^{7} c^{4} d^{6} e^{10} + 28 \, a^{8} c^{3} d^{4} e^{12} + 8 \, a^{9} c^{2} d^{2} e^{14} + a^{10} c e^{16}}}{3 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}}}"," ",0,"-2*arctan(((sqrt(c)*x - sqrt(c*x^2 + a))*e + sqrt(c)*d)/sqrt(-c*d^2 - a*e^2))*e^4/((c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-c*d^2 - a*e^2)) + 1/3*((((2*c^10*d^15 + 17*a*c^9*d^13*e^2 + 60*a^2*c^8*d^11*e^4 + 115*a^3*c^7*d^9*e^6 + 130*a^4*c^6*d^7*e^8 + 87*a^5*c^5*d^5*e^10 + 32*a^6*c^4*d^3*e^12 + 5*a^7*c^3*d*e^14)*x/(a^2*c^9*d^16 + 8*a^3*c^8*d^14*e^2 + 28*a^4*c^7*d^12*e^4 + 56*a^5*c^6*d^10*e^6 + 70*a^6*c^5*d^8*e^8 + 56*a^7*c^4*d^6*e^10 + 28*a^8*c^3*d^4*e^12 + 8*a^9*c^2*d^2*e^14 + a^10*c*e^16) + 3*(a^2*c^8*d^12*e^3 + 6*a^3*c^7*d^10*e^5 + 15*a^4*c^6*d^8*e^7 + 20*a^5*c^5*d^6*e^9 + 15*a^6*c^4*d^4*e^11 + 6*a^7*c^3*d^2*e^13 + a^8*c^2*e^15)/(a^2*c^9*d^16 + 8*a^3*c^8*d^14*e^2 + 28*a^4*c^7*d^12*e^4 + 56*a^5*c^6*d^10*e^6 + 70*a^6*c^5*d^8*e^8 + 56*a^7*c^4*d^6*e^10 + 28*a^8*c^3*d^4*e^12 + 8*a^9*c^2*d^2*e^14 + a^10*c*e^16))*x + 3*(a*c^9*d^15 + 8*a^2*c^8*d^13*e^2 + 27*a^3*c^7*d^11*e^4 + 50*a^4*c^6*d^9*e^6 + 55*a^5*c^5*d^7*e^8 + 36*a^6*c^4*d^5*e^10 + 13*a^7*c^3*d^3*e^12 + 2*a^8*c^2*d*e^14)/(a^2*c^9*d^16 + 8*a^3*c^8*d^14*e^2 + 28*a^4*c^7*d^12*e^4 + 56*a^5*c^6*d^10*e^6 + 70*a^6*c^5*d^8*e^8 + 56*a^7*c^4*d^6*e^10 + 28*a^8*c^3*d^4*e^12 + 8*a^9*c^2*d^2*e^14 + a^10*c*e^16))*x + (a^2*c^8*d^14*e + 10*a^3*c^7*d^12*e^3 + 39*a^4*c^6*d^10*e^5 + 80*a^5*c^5*d^8*e^7 + 95*a^6*c^4*d^6*e^9 + 66*a^7*c^3*d^4*e^11 + 25*a^8*c^2*d^2*e^13 + 4*a^9*c*e^15)/(a^2*c^9*d^16 + 8*a^3*c^8*d^14*e^2 + 28*a^4*c^7*d^12*e^4 + 56*a^5*c^6*d^10*e^6 + 70*a^6*c^5*d^8*e^8 + 56*a^7*c^4*d^6*e^10 + 28*a^8*c^3*d^4*e^12 + 8*a^9*c^2*d^2*e^14 + a^10*c*e^16))/(c*x^2 + a)^(3/2)","B",0
583,1,1073,0,0.949656," ","integrate(1/(e*x+d)^2/(c*x^2+a)^(5/2),x, algorithm=""giac"")","-\frac{1}{3} \, {\left(\frac{15 \, c d e^{7} \log\left({\left| -c d + \sqrt{c d^{2} + a e^{2}} {\left(\sqrt{c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{a e^{2}}{{\left(x e + d\right)}^{2}}} + \frac{\sqrt{c d^{2} e^{2} + a e^{4}} e^{\left(-1\right)}}{x e + d}\right)} \right|}\right)}{{\left(c^{3} d^{6} e + 3 \, a c^{2} d^{4} e^{3} + 3 \, a^{2} c d^{2} e^{5} + a^{3} e^{7}\right)} \sqrt{c d^{2} + a e^{2}} \mathrm{sgn}\left(\frac{1}{x e + d}\right)} + \frac{{\left(2 \, \sqrt{c d^{2} + a e^{2}} c^{3} d^{4} e^{2} + 9 \, \sqrt{c d^{2} + a e^{2}} a c^{2} d^{2} e^{4} - 15 \, a^{2} c^{\frac{3}{2}} d e^{6} \log\left({\left| -c d + \sqrt{c d^{2} + a e^{2}} \sqrt{c} \right|}\right) - 8 \, \sqrt{c d^{2} + a e^{2}} a^{2} c e^{6}\right)} \mathrm{sgn}\left(\frac{1}{x e + d}\right)}{\sqrt{c d^{2} + a e^{2}} a^{2} c^{\frac{7}{2}} d^{6} + 3 \, \sqrt{c d^{2} + a e^{2}} a^{3} c^{\frac{5}{2}} d^{4} e^{2} + 3 \, \sqrt{c d^{2} + a e^{2}} a^{4} c^{\frac{3}{2}} d^{2} e^{4} + \sqrt{c d^{2} + a e^{2}} a^{5} \sqrt{c} e^{6}} + \frac{\frac{{\left(\frac{{\left(\frac{{\left(\frac{2 \, {\left(c^{5} d^{7} e^{16} + 6 \, a c^{4} d^{5} e^{18} - 11 \, a^{2} c^{3} d^{3} e^{20} - 16 \, a^{3} c^{2} d e^{22}\right)}}{a^{2} c^{4} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 3 \, a^{3} c^{3} d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 3 \, a^{4} c^{2} d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + a^{5} c e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right)} + \frac{3 \, {\left(a^{2} c^{3} d^{4} e^{21} + 2 \, a^{3} c^{2} d^{2} e^{23} + a^{4} c e^{25}\right)} e^{\left(-1\right)}}{{\left(a^{2} c^{4} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 3 \, a^{3} c^{3} d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 3 \, a^{4} c^{2} d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + a^{5} c e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right)\right)} {\left(x e + d\right)}}\right)} e^{\left(-1\right)}}{x e + d} - \frac{6 \, {\left(c^{5} d^{6} e^{15} + 5 \, a c^{4} d^{4} e^{17} - 8 \, a^{2} c^{3} d^{2} e^{19} - 2 \, a^{3} c^{2} e^{21}\right)}}{a^{2} c^{4} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 3 \, a^{3} c^{3} d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 3 \, a^{4} c^{2} d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + a^{5} c e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right)}\right)} e^{\left(-1\right)}}{x e + d} + \frac{3 \, {\left(2 \, c^{5} d^{5} e^{14} + 9 \, a c^{4} d^{3} e^{16} - 13 \, a^{2} c^{3} d e^{18}\right)}}{a^{2} c^{4} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 3 \, a^{3} c^{3} d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 3 \, a^{4} c^{2} d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + a^{5} c e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right)}\right)} e^{\left(-1\right)}}{x e + d} - \frac{2 \, c^{5} d^{4} e^{13} + 9 \, a c^{4} d^{2} e^{15} - 8 \, a^{2} c^{3} e^{17}}{a^{2} c^{4} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 3 \, a^{3} c^{3} d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 3 \, a^{4} c^{2} d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + a^{5} c e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right)}}{{\left(c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right)}^{\frac{3}{2}}}\right)} e^{\left(-2\right)}"," ",0,"-1/3*(15*c*d*e^7*log(abs(-c*d + sqrt(c*d^2 + a*e^2)*(sqrt(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + a*e^2/(x*e + d)^2) + sqrt(c*d^2*e^2 + a*e^4)*e^(-1)/(x*e + d))))/((c^3*d^6*e + 3*a*c^2*d^4*e^3 + 3*a^2*c*d^2*e^5 + a^3*e^7)*sqrt(c*d^2 + a*e^2)*sgn(1/(x*e + d))) + (2*sqrt(c*d^2 + a*e^2)*c^3*d^4*e^2 + 9*sqrt(c*d^2 + a*e^2)*a*c^2*d^2*e^4 - 15*a^2*c^(3/2)*d*e^6*log(abs(-c*d + sqrt(c*d^2 + a*e^2)*sqrt(c))) - 8*sqrt(c*d^2 + a*e^2)*a^2*c*e^6)*sgn(1/(x*e + d))/(sqrt(c*d^2 + a*e^2)*a^2*c^(7/2)*d^6 + 3*sqrt(c*d^2 + a*e^2)*a^3*c^(5/2)*d^4*e^2 + 3*sqrt(c*d^2 + a*e^2)*a^4*c^(3/2)*d^2*e^4 + sqrt(c*d^2 + a*e^2)*a^5*sqrt(c)*e^6) + ((((2*(c^5*d^7*e^16 + 6*a*c^4*d^5*e^18 - 11*a^2*c^3*d^3*e^20 - 16*a^3*c^2*d*e^22)/(a^2*c^4*d^6*e^11*sgn(1/(x*e + d)) + 3*a^3*c^3*d^4*e^13*sgn(1/(x*e + d)) + 3*a^4*c^2*d^2*e^15*sgn(1/(x*e + d)) + a^5*c*e^17*sgn(1/(x*e + d))) + 3*(a^2*c^3*d^4*e^21 + 2*a^3*c^2*d^2*e^23 + a^4*c*e^25)*e^(-1)/((a^2*c^4*d^6*e^11*sgn(1/(x*e + d)) + 3*a^3*c^3*d^4*e^13*sgn(1/(x*e + d)) + 3*a^4*c^2*d^2*e^15*sgn(1/(x*e + d)) + a^5*c*e^17*sgn(1/(x*e + d)))*(x*e + d)))*e^(-1)/(x*e + d) - 6*(c^5*d^6*e^15 + 5*a*c^4*d^4*e^17 - 8*a^2*c^3*d^2*e^19 - 2*a^3*c^2*e^21)/(a^2*c^4*d^6*e^11*sgn(1/(x*e + d)) + 3*a^3*c^3*d^4*e^13*sgn(1/(x*e + d)) + 3*a^4*c^2*d^2*e^15*sgn(1/(x*e + d)) + a^5*c*e^17*sgn(1/(x*e + d))))*e^(-1)/(x*e + d) + 3*(2*c^5*d^5*e^14 + 9*a*c^4*d^3*e^16 - 13*a^2*c^3*d*e^18)/(a^2*c^4*d^6*e^11*sgn(1/(x*e + d)) + 3*a^3*c^3*d^4*e^13*sgn(1/(x*e + d)) + 3*a^4*c^2*d^2*e^15*sgn(1/(x*e + d)) + a^5*c*e^17*sgn(1/(x*e + d))))*e^(-1)/(x*e + d) - (2*c^5*d^4*e^13 + 9*a*c^4*d^2*e^15 - 8*a^2*c^3*e^17)/(a^2*c^4*d^6*e^11*sgn(1/(x*e + d)) + 3*a^3*c^3*d^4*e^13*sgn(1/(x*e + d)) + 3*a^4*c^2*d^2*e^15*sgn(1/(x*e + d)) + a^5*c*e^17*sgn(1/(x*e + d))))/(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + a*e^2/(x*e + d)^2)^(3/2))*e^(-2)","B",0
584,1,2044,0,0.638958," ","integrate(1/(e*x+d)^3/(c*x^2+a)^(5/2),x, algorithm=""giac"")","\frac{5 \, {\left(6 \, c^{2} d^{2} e^{4} - a c e^{6}\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} - a e^{2}}}\right)}{{\left(c^{4} d^{8} + 4 \, a c^{3} d^{6} e^{2} + 6 \, a^{2} c^{2} d^{4} e^{4} + 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}\right)} \sqrt{-c d^{2} - a e^{2}}} + \frac{{\left(2 \, {\left(\frac{{\left(c^{18} d^{29} + 19 \, a c^{17} d^{27} e^{2} + 138 \, a^{2} c^{16} d^{25} e^{4} + 538 \, a^{3} c^{15} d^{23} e^{6} + 1243 \, a^{4} c^{14} d^{21} e^{8} + 1617 \, a^{5} c^{13} d^{19} e^{10} + 528 \, a^{6} c^{12} d^{17} e^{12} - 2244 \, a^{7} c^{11} d^{15} e^{14} - 5049 \, a^{8} c^{10} d^{13} e^{16} - 5819 \, a^{9} c^{9} d^{11} e^{18} - 4334 \, a^{10} c^{8} d^{9} e^{20} - 2166 \, a^{11} c^{7} d^{7} e^{22} - 707 \, a^{12} c^{6} d^{5} e^{24} - 137 \, a^{13} c^{5} d^{3} e^{26} - 12 \, a^{14} c^{4} d e^{28}\right)} x}{a^{2} c^{17} d^{32} + 16 \, a^{3} c^{16} d^{30} e^{2} + 120 \, a^{4} c^{15} d^{28} e^{4} + 560 \, a^{5} c^{14} d^{26} e^{6} + 1820 \, a^{6} c^{13} d^{24} e^{8} + 4368 \, a^{7} c^{12} d^{22} e^{10} + 8008 \, a^{8} c^{11} d^{20} e^{12} + 11440 \, a^{9} c^{10} d^{18} e^{14} + 12870 \, a^{10} c^{9} d^{16} e^{16} + 11440 \, a^{11} c^{8} d^{14} e^{18} + 8008 \, a^{12} c^{7} d^{12} e^{20} + 4368 \, a^{13} c^{6} d^{10} e^{22} + 1820 \, a^{14} c^{5} d^{8} e^{24} + 560 \, a^{15} c^{4} d^{6} e^{26} + 120 \, a^{16} c^{3} d^{4} e^{28} + 16 \, a^{17} c^{2} d^{2} e^{30} + a^{18} c e^{32}} + \frac{3 \, {\left(5 \, a^{2} c^{16} d^{26} e^{3} + 59 \, a^{3} c^{15} d^{24} e^{5} + 318 \, a^{4} c^{14} d^{22} e^{7} + 1034 \, a^{5} c^{13} d^{20} e^{9} + 2255 \, a^{6} c^{12} d^{18} e^{11} + 3465 \, a^{7} c^{11} d^{16} e^{13} + 3828 \, a^{8} c^{10} d^{14} e^{15} + 3036 \, a^{9} c^{9} d^{12} e^{17} + 1683 \, a^{10} c^{8} d^{10} e^{19} + 605 \, a^{11} c^{7} d^{8} e^{21} + 110 \, a^{12} c^{6} d^{6} e^{23} - 6 \, a^{13} c^{5} d^{4} e^{25} - 7 \, a^{14} c^{4} d^{2} e^{27} - a^{15} c^{3} e^{29}\right)}}{a^{2} c^{17} d^{32} + 16 \, a^{3} c^{16} d^{30} e^{2} + 120 \, a^{4} c^{15} d^{28} e^{4} + 560 \, a^{5} c^{14} d^{26} e^{6} + 1820 \, a^{6} c^{13} d^{24} e^{8} + 4368 \, a^{7} c^{12} d^{22} e^{10} + 8008 \, a^{8} c^{11} d^{20} e^{12} + 11440 \, a^{9} c^{10} d^{18} e^{14} + 12870 \, a^{10} c^{9} d^{16} e^{16} + 11440 \, a^{11} c^{8} d^{14} e^{18} + 8008 \, a^{12} c^{7} d^{12} e^{20} + 4368 \, a^{13} c^{6} d^{10} e^{22} + 1820 \, a^{14} c^{5} d^{8} e^{24} + 560 \, a^{15} c^{4} d^{6} e^{26} + 120 \, a^{16} c^{3} d^{4} e^{28} + 16 \, a^{17} c^{2} d^{2} e^{30} + a^{18} c e^{32}}\right)} x + \frac{3 \, {\left(a c^{17} d^{29} + 16 \, a^{2} c^{16} d^{27} e^{2} + 105 \, a^{3} c^{15} d^{25} e^{4} + 376 \, a^{4} c^{14} d^{23} e^{6} + 781 \, a^{5} c^{13} d^{21} e^{8} + 792 \, a^{6} c^{12} d^{19} e^{10} - 363 \, a^{7} c^{11} d^{17} e^{12} - 2640 \, a^{8} c^{10} d^{15} e^{14} - 4653 \, a^{9} c^{9} d^{13} e^{16} - 4928 \, a^{10} c^{8} d^{11} e^{18} - 3509 \, a^{11} c^{7} d^{9} e^{20} - 1704 \, a^{12} c^{6} d^{7} e^{22} - 545 \, a^{13} c^{5} d^{5} e^{24} - 104 \, a^{14} c^{4} d^{3} e^{26} - 9 \, a^{15} c^{3} d e^{28}\right)}}{a^{2} c^{17} d^{32} + 16 \, a^{3} c^{16} d^{30} e^{2} + 120 \, a^{4} c^{15} d^{28} e^{4} + 560 \, a^{5} c^{14} d^{26} e^{6} + 1820 \, a^{6} c^{13} d^{24} e^{8} + 4368 \, a^{7} c^{12} d^{22} e^{10} + 8008 \, a^{8} c^{11} d^{20} e^{12} + 11440 \, a^{9} c^{10} d^{18} e^{14} + 12870 \, a^{10} c^{9} d^{16} e^{16} + 11440 \, a^{11} c^{8} d^{14} e^{18} + 8008 \, a^{12} c^{7} d^{12} e^{20} + 4368 \, a^{13} c^{6} d^{10} e^{22} + 1820 \, a^{14} c^{5} d^{8} e^{24} + 560 \, a^{15} c^{4} d^{6} e^{26} + 120 \, a^{16} c^{3} d^{4} e^{28} + 16 \, a^{17} c^{2} d^{2} e^{30} + a^{18} c e^{32}}\right)} x + \frac{3 \, a^{2} c^{16} d^{28} e + 68 \, a^{3} c^{15} d^{26} e^{3} + 575 \, a^{4} c^{14} d^{24} e^{5} + 2688 \, a^{5} c^{13} d^{22} e^{7} + 8063 \, a^{6} c^{12} d^{20} e^{9} + 16676 \, a^{7} c^{11} d^{18} e^{11} + 24651 \, a^{8} c^{10} d^{16} e^{13} + 26400 \, a^{9} c^{9} d^{14} e^{15} + 20361 \, a^{10} c^{8} d^{12} e^{17} + 10956 \, a^{11} c^{7} d^{10} e^{19} + 3773 \, a^{12} c^{6} d^{8} e^{21} + 608 \, a^{13} c^{5} d^{6} e^{23} - 75 \, a^{14} c^{4} d^{4} e^{25} - 52 \, a^{15} c^{3} d^{2} e^{27} - 7 \, a^{16} c^{2} e^{29}}{a^{2} c^{17} d^{32} + 16 \, a^{3} c^{16} d^{30} e^{2} + 120 \, a^{4} c^{15} d^{28} e^{4} + 560 \, a^{5} c^{14} d^{26} e^{6} + 1820 \, a^{6} c^{13} d^{24} e^{8} + 4368 \, a^{7} c^{12} d^{22} e^{10} + 8008 \, a^{8} c^{11} d^{20} e^{12} + 11440 \, a^{9} c^{10} d^{18} e^{14} + 12870 \, a^{10} c^{9} d^{16} e^{16} + 11440 \, a^{11} c^{8} d^{14} e^{18} + 8008 \, a^{12} c^{7} d^{12} e^{20} + 4368 \, a^{13} c^{6} d^{10} e^{22} + 1820 \, a^{14} c^{5} d^{8} e^{24} + 560 \, a^{15} c^{4} d^{6} e^{26} + 120 \, a^{16} c^{3} d^{4} e^{28} + 16 \, a^{17} c^{2} d^{2} e^{30} + a^{18} c e^{32}}}{3 \, {\left(c x^{2} + a\right)}^{\frac{3}{2}}} - \frac{22 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} c^{\frac{5}{2}} d^{3} e^{4} + 10 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} c^{2} d^{2} e^{5} - 34 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a c^{2} d^{2} e^{5} - 11 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} a c^{\frac{3}{2}} d e^{6} - {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{3} a c e^{7} + 11 \, a^{2} c^{\frac{3}{2}} d e^{6} - {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} a^{2} c e^{7}}{{\left(c^{4} d^{8} + 4 \, a c^{3} d^{6} e^{2} + 6 \, a^{2} c^{2} d^{4} e^{4} + 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}\right)} {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)}^{2} e + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + a}\right)} \sqrt{c} d - a e\right)}^{2}}"," ",0,"5*(6*c^2*d^2*e^4 - a*c*e^6)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + a))*e + sqrt(c)*d)/sqrt(-c*d^2 - a*e^2))/((c^4*d^8 + 4*a*c^3*d^6*e^2 + 6*a^2*c^2*d^4*e^4 + 4*a^3*c*d^2*e^6 + a^4*e^8)*sqrt(-c*d^2 - a*e^2)) + 1/3*((2*((c^18*d^29 + 19*a*c^17*d^27*e^2 + 138*a^2*c^16*d^25*e^4 + 538*a^3*c^15*d^23*e^6 + 1243*a^4*c^14*d^21*e^8 + 1617*a^5*c^13*d^19*e^10 + 528*a^6*c^12*d^17*e^12 - 2244*a^7*c^11*d^15*e^14 - 5049*a^8*c^10*d^13*e^16 - 5819*a^9*c^9*d^11*e^18 - 4334*a^10*c^8*d^9*e^20 - 2166*a^11*c^7*d^7*e^22 - 707*a^12*c^6*d^5*e^24 - 137*a^13*c^5*d^3*e^26 - 12*a^14*c^4*d*e^28)*x/(a^2*c^17*d^32 + 16*a^3*c^16*d^30*e^2 + 120*a^4*c^15*d^28*e^4 + 560*a^5*c^14*d^26*e^6 + 1820*a^6*c^13*d^24*e^8 + 4368*a^7*c^12*d^22*e^10 + 8008*a^8*c^11*d^20*e^12 + 11440*a^9*c^10*d^18*e^14 + 12870*a^10*c^9*d^16*e^16 + 11440*a^11*c^8*d^14*e^18 + 8008*a^12*c^7*d^12*e^20 + 4368*a^13*c^6*d^10*e^22 + 1820*a^14*c^5*d^8*e^24 + 560*a^15*c^4*d^6*e^26 + 120*a^16*c^3*d^4*e^28 + 16*a^17*c^2*d^2*e^30 + a^18*c*e^32) + 3*(5*a^2*c^16*d^26*e^3 + 59*a^3*c^15*d^24*e^5 + 318*a^4*c^14*d^22*e^7 + 1034*a^5*c^13*d^20*e^9 + 2255*a^6*c^12*d^18*e^11 + 3465*a^7*c^11*d^16*e^13 + 3828*a^8*c^10*d^14*e^15 + 3036*a^9*c^9*d^12*e^17 + 1683*a^10*c^8*d^10*e^19 + 605*a^11*c^7*d^8*e^21 + 110*a^12*c^6*d^6*e^23 - 6*a^13*c^5*d^4*e^25 - 7*a^14*c^4*d^2*e^27 - a^15*c^3*e^29)/(a^2*c^17*d^32 + 16*a^3*c^16*d^30*e^2 + 120*a^4*c^15*d^28*e^4 + 560*a^5*c^14*d^26*e^6 + 1820*a^6*c^13*d^24*e^8 + 4368*a^7*c^12*d^22*e^10 + 8008*a^8*c^11*d^20*e^12 + 11440*a^9*c^10*d^18*e^14 + 12870*a^10*c^9*d^16*e^16 + 11440*a^11*c^8*d^14*e^18 + 8008*a^12*c^7*d^12*e^20 + 4368*a^13*c^6*d^10*e^22 + 1820*a^14*c^5*d^8*e^24 + 560*a^15*c^4*d^6*e^26 + 120*a^16*c^3*d^4*e^28 + 16*a^17*c^2*d^2*e^30 + a^18*c*e^32))*x + 3*(a*c^17*d^29 + 16*a^2*c^16*d^27*e^2 + 105*a^3*c^15*d^25*e^4 + 376*a^4*c^14*d^23*e^6 + 781*a^5*c^13*d^21*e^8 + 792*a^6*c^12*d^19*e^10 - 363*a^7*c^11*d^17*e^12 - 2640*a^8*c^10*d^15*e^14 - 4653*a^9*c^9*d^13*e^16 - 4928*a^10*c^8*d^11*e^18 - 3509*a^11*c^7*d^9*e^20 - 1704*a^12*c^6*d^7*e^22 - 545*a^13*c^5*d^5*e^24 - 104*a^14*c^4*d^3*e^26 - 9*a^15*c^3*d*e^28)/(a^2*c^17*d^32 + 16*a^3*c^16*d^30*e^2 + 120*a^4*c^15*d^28*e^4 + 560*a^5*c^14*d^26*e^6 + 1820*a^6*c^13*d^24*e^8 + 4368*a^7*c^12*d^22*e^10 + 8008*a^8*c^11*d^20*e^12 + 11440*a^9*c^10*d^18*e^14 + 12870*a^10*c^9*d^16*e^16 + 11440*a^11*c^8*d^14*e^18 + 8008*a^12*c^7*d^12*e^20 + 4368*a^13*c^6*d^10*e^22 + 1820*a^14*c^5*d^8*e^24 + 560*a^15*c^4*d^6*e^26 + 120*a^16*c^3*d^4*e^28 + 16*a^17*c^2*d^2*e^30 + a^18*c*e^32))*x + (3*a^2*c^16*d^28*e + 68*a^3*c^15*d^26*e^3 + 575*a^4*c^14*d^24*e^5 + 2688*a^5*c^13*d^22*e^7 + 8063*a^6*c^12*d^20*e^9 + 16676*a^7*c^11*d^18*e^11 + 24651*a^8*c^10*d^16*e^13 + 26400*a^9*c^9*d^14*e^15 + 20361*a^10*c^8*d^12*e^17 + 10956*a^11*c^7*d^10*e^19 + 3773*a^12*c^6*d^8*e^21 + 608*a^13*c^5*d^6*e^23 - 75*a^14*c^4*d^4*e^25 - 52*a^15*c^3*d^2*e^27 - 7*a^16*c^2*e^29)/(a^2*c^17*d^32 + 16*a^3*c^16*d^30*e^2 + 120*a^4*c^15*d^28*e^4 + 560*a^5*c^14*d^26*e^6 + 1820*a^6*c^13*d^24*e^8 + 4368*a^7*c^12*d^22*e^10 + 8008*a^8*c^11*d^20*e^12 + 11440*a^9*c^10*d^18*e^14 + 12870*a^10*c^9*d^16*e^16 + 11440*a^11*c^8*d^14*e^18 + 8008*a^12*c^7*d^12*e^20 + 4368*a^13*c^6*d^10*e^22 + 1820*a^14*c^5*d^8*e^24 + 560*a^15*c^4*d^6*e^26 + 120*a^16*c^3*d^4*e^28 + 16*a^17*c^2*d^2*e^30 + a^18*c*e^32))/(c*x^2 + a)^(3/2) - (22*(sqrt(c)*x - sqrt(c*x^2 + a))^2*c^(5/2)*d^3*e^4 + 10*(sqrt(c)*x - sqrt(c*x^2 + a))^3*c^2*d^2*e^5 - 34*(sqrt(c)*x - sqrt(c*x^2 + a))*a*c^2*d^2*e^5 - 11*(sqrt(c)*x - sqrt(c*x^2 + a))^2*a*c^(3/2)*d*e^6 - (sqrt(c)*x - sqrt(c*x^2 + a))^3*a*c*e^7 + 11*a^2*c^(3/2)*d*e^6 - (sqrt(c)*x - sqrt(c*x^2 + a))*a^2*c*e^7)/((c^4*d^8 + 4*a*c^3*d^6*e^2 + 6*a^2*c^2*d^4*e^4 + 4*a^3*c*d^2*e^6 + a^4*e^8)*((sqrt(c)*x - sqrt(c*x^2 + a))^2*e + 2*(sqrt(c)*x - sqrt(c*x^2 + a))*sqrt(c)*d - a*e)^2)","B",0
585,1,16,0,0.224894," ","integrate((3+x)/(-x^2+1)^(1/2),x, algorithm=""giac"")","-\sqrt{-x^{2} + 1} + 3 \, \arcsin\left(x\right)"," ",0,"-sqrt(-x^2 + 1) + 3*arcsin(x)","A",0
586,1,16,0,0.212785," ","integrate((1+x)/(-x^2+4)^(1/2),x, algorithm=""giac"")","-\sqrt{-x^{2} + 4} + \arcsin\left(\frac{1}{2} \, x\right)"," ",0,"-sqrt(-x^2 + 4) + arcsin(1/2*x)","A",0
587,1,22,0,0.206260," ","integrate((2+x)/(x^2+9)^(1/2),x, algorithm=""giac"")","\sqrt{x^{2} + 9} - 2 \, \log\left(-x + \sqrt{x^{2} + 9}\right)"," ",0,"sqrt(x^2 + 9) - 2*log(-x + sqrt(x^2 + 9))","A",0
588,1,35,0,0.205771," ","integrate((b*x+a)^2/(-x^2+1)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, {\left(2 \, a^{2} + b^{2}\right)} \arcsin\left(x\right) - \frac{1}{2} \, {\left(b^{2} x + 4 \, a b\right)} \sqrt{-x^{2} + 1}"," ",0,"1/2*(2*a^2 + b^2)*arcsin(x) - 1/2*(b^2*x + 4*a*b)*sqrt(-x^2 + 1)","A",0
589,1,45,0,0.198817," ","integrate((b*x+a)^2/(x^2+1)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \, {\left(2 \, a^{2} - b^{2}\right)} \log\left(-x + \sqrt{x^{2} + 1}\right) + \frac{1}{2} \, {\left(b^{2} x + 4 \, a b\right)} \sqrt{x^{2} + 1}"," ",0,"-1/2*(2*a^2 - b^2)*log(-x + sqrt(x^2 + 1)) + 1/2*(b^2*x + 4*a*b)*sqrt(x^2 + 1)","A",0
590,1,12,0,0.190332," ","integrate((2+3*x)/(x^2+4)^(3/2),x, algorithm=""giac"")","\frac{x - 6}{2 \, \sqrt{x^{2} + 4}}"," ",0,"1/2*(x - 6)/sqrt(x^2 + 4)","A",0
591,1,380,0,0.224023," ","integrate((e*x+d)^(5/2)*(c*x^2+a),x, algorithm=""giac"")","\frac{2}{3465} \, {\left(231 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} c d^{3} e^{\left(-2\right)} + 297 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} c d^{2} e^{\left(-2\right)} + 3465 \, \sqrt{x e + d} a d^{3} + 3465 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a d^{2} + 33 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} c d e^{\left(-2\right)} + 693 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a d + 5 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} c e^{\left(-2\right)} + 99 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a\right)} e^{\left(-1\right)}"," ",0,"2/3465*(231*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*c*d^3*e^(-2) + 297*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*c*d^2*e^(-2) + 3465*sqrt(x*e + d)*a*d^3 + 3465*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a*d^2 + 33*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*c*d*e^(-2) + 693*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a*d + 5*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*c*e^(-2) + 99*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a)*e^(-1)","B",0
592,1,243,0,0.173539," ","integrate((e*x+d)^(3/2)*(c*x^2+a),x, algorithm=""giac"")","\frac{2}{315} \, {\left(21 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} c d^{2} e^{\left(-2\right)} + 18 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} c d e^{\left(-2\right)} + 315 \, \sqrt{x e + d} a d^{2} + 210 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a d + {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} c e^{\left(-2\right)} + 21 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a\right)} e^{\left(-1\right)}"," ",0,"2/315*(21*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*c*d^2*e^(-2) + 18*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*c*d*e^(-2) + 315*sqrt(x*e + d)*a*d^2 + 210*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a*d + (35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*c*e^(-2) + 21*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a)*e^(-1)","B",0
593,1,134,0,0.179985," ","integrate((c*x^2+a)*(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{105} \, {\left(7 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} c d e^{\left(-2\right)} + 3 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} c e^{\left(-2\right)} + 105 \, \sqrt{x e + d} a d + 35 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a\right)} e^{\left(-1\right)}"," ",0,"2/105*(7*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*c*d*e^(-2) + 3*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*c*e^(-2) + 105*sqrt(x*e + d)*a*d + 35*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a)*e^(-1)","B",0
594,1,55,0,0.205488," ","integrate((c*x^2+a)/(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{15} \, {\left({\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} c e^{\left(-2\right)} + 15 \, \sqrt{x e + d} a\right)} e^{\left(-1\right)}"," ",0,"2/15*((3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*c*e^(-2) + 15*sqrt(x*e + d)*a)*e^(-1)","A",0
595,1,54,0,0.184651," ","integrate((c*x^2+a)/(e*x+d)^(3/2),x, algorithm=""giac"")","\frac{2}{3} \, {\left({\left(x e + d\right)}^{\frac{3}{2}} c e^{6} - 6 \, \sqrt{x e + d} c d e^{6}\right)} e^{\left(-9\right)} - \frac{2 \, {\left(c d^{2} + a e^{2}\right)} e^{\left(-3\right)}}{\sqrt{x e + d}}"," ",0,"2/3*((x*e + d)^(3/2)*c*e^6 - 6*sqrt(x*e + d)*c*d*e^6)*e^(-9) - 2*(c*d^2 + a*e^2)*e^(-3)/sqrt(x*e + d)","A",0
596,1,48,0,0.183075," ","integrate((c*x^2+a)/(e*x+d)^(5/2),x, algorithm=""giac"")","2 \, \sqrt{x e + d} c e^{\left(-3\right)} + \frac{2 \, {\left(6 \, {\left(x e + d\right)} c d - c d^{2} - a e^{2}\right)} e^{\left(-3\right)}}{3 \, {\left(x e + d\right)}^{\frac{3}{2}}}"," ",0,"2*sqrt(x*e + d)*c*e^(-3) + 2/3*(6*(x*e + d)*c*d - c*d^2 - a*e^2)*e^(-3)/(x*e + d)^(3/2)","A",0
597,1,45,0,0.208186," ","integrate((c*x^2+a)/(e*x+d)^(7/2),x, algorithm=""giac"")","-\frac{2 \, {\left(15 \, {\left(x e + d\right)}^{2} c - 10 \, {\left(x e + d\right)} c d + 3 \, c d^{2} + 3 \, a e^{2}\right)} e^{\left(-3\right)}}{15 \, {\left(x e + d\right)}^{\frac{5}{2}}}"," ",0,"-2/15*(15*(x*e + d)^2*c - 10*(x*e + d)*c*d + 3*c*d^2 + 3*a*e^2)*e^(-3)/(x*e + d)^(5/2)","A",0
598,1,749,0,0.241413," ","integrate((e*x+d)^(5/2)*(c*x^2+a)^2,x, algorithm=""giac"")","\frac{2}{45045} \, {\left(6006 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a c d^{3} e^{\left(-2\right)} + 143 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} c^{2} d^{3} e^{\left(-4\right)} + 7722 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a c d^{2} e^{\left(-2\right)} + 195 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} c^{2} d^{2} e^{\left(-4\right)} + 45045 \, \sqrt{x e + d} a^{2} d^{3} + 45045 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{2} d^{2} + 858 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a c d e^{\left(-2\right)} + 45 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} c^{2} d e^{\left(-4\right)} + 9009 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{2} d + 130 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a c e^{\left(-2\right)} + 7 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} c^{2} e^{\left(-4\right)} + 1287 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{2}\right)} e^{\left(-1\right)}"," ",0,"2/45045*(6006*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a*c*d^3*e^(-2) + 143*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*c^2*d^3*e^(-4) + 7722*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*c*d^2*e^(-2) + 195*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*c^2*d^2*e^(-4) + 45045*sqrt(x*e + d)*a^2*d^3 + 45045*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^2*d^2 + 858*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*c*d*e^(-2) + 45*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*c^2*d*e^(-4) + 9009*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^2*d + 130*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a*c*e^(-2) + 7*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*c^2*e^(-4) + 1287*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^2)*e^(-1)","B",0
599,1,500,0,0.203995," ","integrate((e*x+d)^(3/2)*(c*x^2+a)^2,x, algorithm=""giac"")","\frac{2}{45045} \, {\left(6006 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a c d^{2} e^{\left(-2\right)} + 143 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} c^{2} d^{2} e^{\left(-4\right)} + 5148 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a c d e^{\left(-2\right)} + 130 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} c^{2} d e^{\left(-4\right)} + 45045 \, \sqrt{x e + d} a^{2} d^{2} + 30030 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{2} d + 286 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a c e^{\left(-2\right)} + 15 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} c^{2} e^{\left(-4\right)} + 3003 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{2}\right)} e^{\left(-1\right)}"," ",0,"2/45045*(6006*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a*c*d^2*e^(-2) + 143*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*c^2*d^2*e^(-4) + 5148*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*c*d*e^(-2) + 130*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*c^2*d*e^(-4) + 45045*sqrt(x*e + d)*a^2*d^2 + 30030*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^2*d + 286*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*c*e^(-2) + 15*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*c^2*e^(-4) + 3003*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^2)*e^(-1)","B",0
600,1,290,0,0.197545," ","integrate((c*x^2+a)^2*(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{3465} \, {\left(462 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a c d e^{\left(-2\right)} + 11 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} c^{2} d e^{\left(-4\right)} + 198 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a c e^{\left(-2\right)} + 5 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} c^{2} e^{\left(-4\right)} + 3465 \, \sqrt{x e + d} a^{2} d + 1155 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{2}\right)} e^{\left(-1\right)}"," ",0,"2/3465*(462*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a*c*d*e^(-2) + 11*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*c^2*d*e^(-4) + 198*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*c*e^(-2) + 5*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*c^2*e^(-4) + 3465*sqrt(x*e + d)*a^2*d + 1155*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^2)*e^(-1)","B",0
601,1,126,0,0.193210," ","integrate((c*x^2+a)^2/(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{315} \, {\left(42 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a c e^{\left(-2\right)} + {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} c^{2} e^{\left(-4\right)} + 315 \, \sqrt{x e + d} a^{2}\right)} e^{\left(-1\right)}"," ",0,"2/315*(42*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a*c*e^(-2) + (35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*c^2*e^(-4) + 315*sqrt(x*e + d)*a^2)*e^(-1)","A",0
602,1,137,0,0.202965," ","integrate((c*x^2+a)^2/(e*x+d)^(3/2),x, algorithm=""giac"")","\frac{2}{105} \, {\left(15 \, {\left(x e + d\right)}^{\frac{7}{2}} c^{2} e^{30} - 84 \, {\left(x e + d\right)}^{\frac{5}{2}} c^{2} d e^{30} + 210 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{2} d^{2} e^{30} - 420 \, \sqrt{x e + d} c^{2} d^{3} e^{30} + 70 \, {\left(x e + d\right)}^{\frac{3}{2}} a c e^{32} - 420 \, \sqrt{x e + d} a c d e^{32}\right)} e^{\left(-35\right)} - \frac{2 \, {\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} e^{\left(-5\right)}}{\sqrt{x e + d}}"," ",0,"2/105*(15*(x*e + d)^(7/2)*c^2*e^30 - 84*(x*e + d)^(5/2)*c^2*d*e^30 + 210*(x*e + d)^(3/2)*c^2*d^2*e^30 - 420*sqrt(x*e + d)*c^2*d^3*e^30 + 70*(x*e + d)^(3/2)*a*c*e^32 - 420*sqrt(x*e + d)*a*c*d*e^32)*e^(-35) - 2*(c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4)*e^(-5)/sqrt(x*e + d)","A",0
603,1,133,0,0.202132," ","integrate((c*x^2+a)^2/(e*x+d)^(5/2),x, algorithm=""giac"")","\frac{2}{15} \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} c^{2} e^{20} - 20 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{2} d e^{20} + 90 \, \sqrt{x e + d} c^{2} d^{2} e^{20} + 30 \, \sqrt{x e + d} a c e^{22}\right)} e^{\left(-25\right)} + \frac{2 \, {\left(12 \, {\left(x e + d\right)} c^{2} d^{3} - c^{2} d^{4} + 12 \, {\left(x e + d\right)} a c d e^{2} - 2 \, a c d^{2} e^{2} - a^{2} e^{4}\right)} e^{\left(-5\right)}}{3 \, {\left(x e + d\right)}^{\frac{3}{2}}}"," ",0,"2/15*(3*(x*e + d)^(5/2)*c^2*e^20 - 20*(x*e + d)^(3/2)*c^2*d*e^20 + 90*sqrt(x*e + d)*c^2*d^2*e^20 + 30*sqrt(x*e + d)*a*c*e^22)*e^(-25) + 2/3*(12*(x*e + d)*c^2*d^3 - c^2*d^4 + 12*(x*e + d)*a*c*d*e^2 - 2*a*c*d^2*e^2 - a^2*e^4)*e^(-5)/(x*e + d)^(3/2)","A",0
604,1,130,0,0.205747," ","integrate((c*x^2+a)^2/(e*x+d)^(7/2),x, algorithm=""giac"")","\frac{2}{3} \, {\left({\left(x e + d\right)}^{\frac{3}{2}} c^{2} e^{10} - 12 \, \sqrt{x e + d} c^{2} d e^{10}\right)} e^{\left(-15\right)} - \frac{2 \, {\left(90 \, {\left(x e + d\right)}^{2} c^{2} d^{2} - 20 \, {\left(x e + d\right)} c^{2} d^{3} + 3 \, c^{2} d^{4} + 30 \, {\left(x e + d\right)}^{2} a c e^{2} - 20 \, {\left(x e + d\right)} a c d e^{2} + 6 \, a c d^{2} e^{2} + 3 \, a^{2} e^{4}\right)} e^{\left(-5\right)}}{15 \, {\left(x e + d\right)}^{\frac{5}{2}}}"," ",0,"2/3*((x*e + d)^(3/2)*c^2*e^10 - 12*sqrt(x*e + d)*c^2*d*e^10)*e^(-15) - 2/15*(90*(x*e + d)^2*c^2*d^2 - 20*(x*e + d)*c^2*d^3 + 3*c^2*d^4 + 30*(x*e + d)^2*a*c*e^2 - 20*(x*e + d)*a*c*d*e^2 + 6*a*c*d^2*e^2 + 3*a^2*e^4)*e^(-5)/(x*e + d)^(5/2)","A",0
605,1,1222,0,0.262166," ","integrate((e*x+d)^(5/2)*(c*x^2+a)^3,x, algorithm=""giac"")","\frac{2}{4849845} \, {\left(969969 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{2} c d^{3} e^{\left(-2\right)} + 46189 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a c^{2} d^{3} e^{\left(-4\right)} + 1615 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} c^{3} d^{3} e^{\left(-6\right)} + 1247103 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{2} c d^{2} e^{\left(-2\right)} + 62985 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a c^{2} d^{2} e^{\left(-4\right)} + 2261 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} c^{3} d^{2} e^{\left(-6\right)} + 4849845 \, \sqrt{x e + d} a^{3} d^{3} + 4849845 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{3} d^{2} + 138567 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{2} c d e^{\left(-2\right)} + 14535 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} a c^{2} d e^{\left(-4\right)} + 133 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} c^{3} d e^{\left(-6\right)} + 969969 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{3} d + 20995 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a^{2} c e^{\left(-2\right)} + 2261 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} a c^{2} e^{\left(-4\right)} + 21 \, {\left(12155 \, {\left(x e + d\right)}^{\frac{19}{2}} - 122265 \, {\left(x e + d\right)}^{\frac{17}{2}} d + 554268 \, {\left(x e + d\right)}^{\frac{15}{2}} d^{2} - 1492260 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{3} + 2645370 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{4} - 3233230 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{5} + 2771340 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{6} - 1662804 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{7} + 692835 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{8} - 230945 \, \sqrt{x e + d} d^{9}\right)} c^{3} e^{\left(-6\right)} + 138567 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{3}\right)} e^{\left(-1\right)}"," ",0,"2/4849845*(969969*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^2*c*d^3*e^(-2) + 46189*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*c^2*d^3*e^(-4) + 1615*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*c^3*d^3*e^(-6) + 1247103*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^2*c*d^2*e^(-2) + 62985*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a*c^2*d^2*e^(-4) + 2261*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*c^3*d^2*e^(-6) + 4849845*sqrt(x*e + d)*a^3*d^3 + 4849845*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^3*d^2 + 138567*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^2*c*d*e^(-2) + 14535*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*a*c^2*d*e^(-4) + 133*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*c^3*d*e^(-6) + 969969*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^3*d + 20995*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a^2*c*e^(-2) + 2261*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*a*c^2*e^(-4) + 21*(12155*(x*e + d)^(19/2) - 122265*(x*e + d)^(17/2)*d + 554268*(x*e + d)^(15/2)*d^2 - 1492260*(x*e + d)^(13/2)*d^3 + 2645370*(x*e + d)^(11/2)*d^4 - 3233230*(x*e + d)^(9/2)*d^5 + 2771340*(x*e + d)^(7/2)*d^6 - 1662804*(x*e + d)^(5/2)*d^7 + 692835*(x*e + d)^(3/2)*d^8 - 230945*sqrt(x*e + d)*d^9)*c^3*e^(-6) + 138567*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^3)*e^(-1)","B",0
606,1,834,0,0.237030," ","integrate((e*x+d)^(3/2)*(c*x^2+a)^3,x, algorithm=""giac"")","\frac{2}{765765} \, {\left(153153 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{2} c d^{2} e^{\left(-2\right)} + 7293 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a c^{2} d^{2} e^{\left(-4\right)} + 255 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} c^{3} d^{2} e^{\left(-6\right)} + 131274 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{2} c d e^{\left(-2\right)} + 6630 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a c^{2} d e^{\left(-4\right)} + 238 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} c^{3} d e^{\left(-6\right)} + 765765 \, \sqrt{x e + d} a^{3} d^{2} + 510510 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{3} d + 7293 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{2} c e^{\left(-2\right)} + 765 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} a c^{2} e^{\left(-4\right)} + 7 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} c^{3} e^{\left(-6\right)} + 51051 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{3}\right)} e^{\left(-1\right)}"," ",0,"2/765765*(153153*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^2*c*d^2*e^(-2) + 7293*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*c^2*d^2*e^(-4) + 255*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*c^3*d^2*e^(-6) + 131274*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^2*c*d*e^(-2) + 6630*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a*c^2*d*e^(-4) + 238*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*c^3*d*e^(-6) + 765765*sqrt(x*e + d)*a^3*d^2 + 510510*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^3*d + 7293*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^2*c*e^(-2) + 765*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*a*c^2*e^(-4) + 7*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*c^3*e^(-6) + 51051*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^3)*e^(-1)","B",0
607,1,498,0,0.242715," ","integrate((c*x^2+a)^3*(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{45045} \, {\left(9009 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{2} c d e^{\left(-2\right)} + 429 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a c^{2} d e^{\left(-4\right)} + 15 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} c^{3} d e^{\left(-6\right)} + 3861 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{2} c e^{\left(-2\right)} + 195 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a c^{2} e^{\left(-4\right)} + 7 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} c^{3} e^{\left(-6\right)} + 45045 \, \sqrt{x e + d} a^{3} d + 15015 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{3}\right)} e^{\left(-1\right)}"," ",0,"2/45045*(9009*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^2*c*d*e^(-2) + 429*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*c^2*d*e^(-4) + 15*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*c^3*d*e^(-6) + 3861*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^2*c*e^(-2) + 195*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a*c^2*e^(-4) + 7*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*c^3*e^(-6) + 45045*sqrt(x*e + d)*a^3*d + 15015*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^3)*e^(-1)","B",0
608,1,224,0,0.173326," ","integrate((c*x^2+a)^3/(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{15015} \, {\left(3003 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{2} c e^{\left(-2\right)} + 143 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a c^{2} e^{\left(-4\right)} + 5 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} c^{3} e^{\left(-6\right)} + 15015 \, \sqrt{x e + d} a^{3}\right)} e^{\left(-1\right)}"," ",0,"2/15015*(3003*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^2*c*e^(-2) + 143*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*c^2*e^(-4) + 5*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*c^3*e^(-6) + 15015*sqrt(x*e + d)*a^3)*e^(-1)","A",0
609,1,261,0,0.178503," ","integrate((c*x^2+a)^3/(e*x+d)^(3/2),x, algorithm=""giac"")","\frac{2}{1155} \, {\left(105 \, {\left(x e + d\right)}^{\frac{11}{2}} c^{3} e^{70} - 770 \, {\left(x e + d\right)}^{\frac{9}{2}} c^{3} d e^{70} + 2475 \, {\left(x e + d\right)}^{\frac{7}{2}} c^{3} d^{2} e^{70} - 4620 \, {\left(x e + d\right)}^{\frac{5}{2}} c^{3} d^{3} e^{70} + 5775 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{3} d^{4} e^{70} - 6930 \, \sqrt{x e + d} c^{3} d^{5} e^{70} + 495 \, {\left(x e + d\right)}^{\frac{7}{2}} a c^{2} e^{72} - 2772 \, {\left(x e + d\right)}^{\frac{5}{2}} a c^{2} d e^{72} + 6930 \, {\left(x e + d\right)}^{\frac{3}{2}} a c^{2} d^{2} e^{72} - 13860 \, \sqrt{x e + d} a c^{2} d^{3} e^{72} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} c e^{74} - 6930 \, \sqrt{x e + d} a^{2} c d e^{74}\right)} e^{\left(-77\right)} - \frac{2 \, {\left(c^{3} d^{6} + 3 \, a c^{2} d^{4} e^{2} + 3 \, a^{2} c d^{2} e^{4} + a^{3} e^{6}\right)} e^{\left(-7\right)}}{\sqrt{x e + d}}"," ",0,"2/1155*(105*(x*e + d)^(11/2)*c^3*e^70 - 770*(x*e + d)^(9/2)*c^3*d*e^70 + 2475*(x*e + d)^(7/2)*c^3*d^2*e^70 - 4620*(x*e + d)^(5/2)*c^3*d^3*e^70 + 5775*(x*e + d)^(3/2)*c^3*d^4*e^70 - 6930*sqrt(x*e + d)*c^3*d^5*e^70 + 495*(x*e + d)^(7/2)*a*c^2*e^72 - 2772*(x*e + d)^(5/2)*a*c^2*d*e^72 + 6930*(x*e + d)^(3/2)*a*c^2*d^2*e^72 - 13860*sqrt(x*e + d)*a*c^2*d^3*e^72 + 1155*(x*e + d)^(3/2)*a^2*c*e^74 - 6930*sqrt(x*e + d)*a^2*c*d*e^74)*e^(-77) - 2*(c^3*d^6 + 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4 + a^3*e^6)*e^(-7)/sqrt(x*e + d)","A",0
610,1,255,0,0.214917," ","integrate((c*x^2+a)^3/(e*x+d)^(5/2),x, algorithm=""giac"")","\frac{2}{315} \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} c^{3} e^{56} - 270 \, {\left(x e + d\right)}^{\frac{7}{2}} c^{3} d e^{56} + 945 \, {\left(x e + d\right)}^{\frac{5}{2}} c^{3} d^{2} e^{56} - 2100 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{3} d^{3} e^{56} + 4725 \, \sqrt{x e + d} c^{3} d^{4} e^{56} + 189 \, {\left(x e + d\right)}^{\frac{5}{2}} a c^{2} e^{58} - 1260 \, {\left(x e + d\right)}^{\frac{3}{2}} a c^{2} d e^{58} + 5670 \, \sqrt{x e + d} a c^{2} d^{2} e^{58} + 945 \, \sqrt{x e + d} a^{2} c e^{60}\right)} e^{\left(-63\right)} + \frac{2 \, {\left(18 \, {\left(x e + d\right)} c^{3} d^{5} - c^{3} d^{6} + 36 \, {\left(x e + d\right)} a c^{2} d^{3} e^{2} - 3 \, a c^{2} d^{4} e^{2} + 18 \, {\left(x e + d\right)} a^{2} c d e^{4} - 3 \, a^{2} c d^{2} e^{4} - a^{3} e^{6}\right)} e^{\left(-7\right)}}{3 \, {\left(x e + d\right)}^{\frac{3}{2}}}"," ",0,"2/315*(35*(x*e + d)^(9/2)*c^3*e^56 - 270*(x*e + d)^(7/2)*c^3*d*e^56 + 945*(x*e + d)^(5/2)*c^3*d^2*e^56 - 2100*(x*e + d)^(3/2)*c^3*d^3*e^56 + 4725*sqrt(x*e + d)*c^3*d^4*e^56 + 189*(x*e + d)^(5/2)*a*c^2*e^58 - 1260*(x*e + d)^(3/2)*a*c^2*d*e^58 + 5670*sqrt(x*e + d)*a*c^2*d^2*e^58 + 945*sqrt(x*e + d)*a^2*c*e^60)*e^(-63) + 2/3*(18*(x*e + d)*c^3*d^5 - c^3*d^6 + 36*(x*e + d)*a*c^2*d^3*e^2 - 3*a*c^2*d^4*e^2 + 18*(x*e + d)*a^2*c*d*e^4 - 3*a^2*c*d^2*e^4 - a^3*e^6)*e^(-7)/(x*e + d)^(3/2)","A",0
611,1,251,0,0.275881," ","integrate((c*x^2+a)^3/(e*x+d)^(7/2),x, algorithm=""giac"")","\frac{2}{35} \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} c^{3} e^{42} - 42 \, {\left(x e + d\right)}^{\frac{5}{2}} c^{3} d e^{42} + 175 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{3} d^{2} e^{42} - 700 \, \sqrt{x e + d} c^{3} d^{3} e^{42} + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} a c^{2} e^{44} - 420 \, \sqrt{x e + d} a c^{2} d e^{44}\right)} e^{\left(-49\right)} - \frac{2 \, {\left(75 \, {\left(x e + d\right)}^{2} c^{3} d^{4} - 10 \, {\left(x e + d\right)} c^{3} d^{5} + c^{3} d^{6} + 90 \, {\left(x e + d\right)}^{2} a c^{2} d^{2} e^{2} - 20 \, {\left(x e + d\right)} a c^{2} d^{3} e^{2} + 3 \, a c^{2} d^{4} e^{2} + 15 \, {\left(x e + d\right)}^{2} a^{2} c e^{4} - 10 \, {\left(x e + d\right)} a^{2} c d e^{4} + 3 \, a^{2} c d^{2} e^{4} + a^{3} e^{6}\right)} e^{\left(-7\right)}}{5 \, {\left(x e + d\right)}^{\frac{5}{2}}}"," ",0,"2/35*(5*(x*e + d)^(7/2)*c^3*e^42 - 42*(x*e + d)^(5/2)*c^3*d*e^42 + 175*(x*e + d)^(3/2)*c^3*d^2*e^42 - 700*sqrt(x*e + d)*c^3*d^3*e^42 + 35*(x*e + d)^(3/2)*a*c^2*e^44 - 420*sqrt(x*e + d)*a*c^2*d*e^44)*e^(-49) - 2/5*(75*(x*e + d)^2*c^3*d^4 - 10*(x*e + d)*c^3*d^5 + c^3*d^6 + 90*(x*e + d)^2*a*c^2*d^2*e^2 - 20*(x*e + d)*a*c^2*d^3*e^2 + 3*a*c^2*d^4*e^2 + 15*(x*e + d)^2*a^2*c*e^4 - 10*(x*e + d)*a^2*c*d*e^4 + 3*a^2*c*d^2*e^4 + a^3*e^6)*e^(-7)/(x*e + d)^(5/2)","A",0
612,1,402,0,0.326033," ","integrate((e*x+d)^(5/2)/(-c*x^2+a),x, algorithm=""giac"")","-\frac{{\left(\sqrt{a c} c^{4} d^{4} + 3 \, \sqrt{a c} a c^{3} d^{2} e^{2} - {\left(3 \, \sqrt{a c} a c d^{2} e^{2} + \sqrt{a c} a^{2} e^{4}\right)} c^{2} + 2 \, {\left(a c^{3} d^{3} e - a^{2} c^{2} d e^{3}\right)} {\left| c \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{c^{4} d + \sqrt{c^{8} d^{2} - {\left(c^{4} d^{2} - a c^{3} e^{2}\right)} c^{4}}}{c^{4}}}}\right)}{{\left(a c^{4} d - \sqrt{a c} a c^{3} e\right)} \sqrt{-c^{2} d - \sqrt{a c} c e}} + \frac{{\left(\sqrt{a c} c^{4} d^{4} + 3 \, \sqrt{a c} a c^{3} d^{2} e^{2} - {\left(3 \, \sqrt{a c} a c d^{2} e^{2} + \sqrt{a c} a^{2} e^{4}\right)} c^{2} - 2 \, {\left(a c^{3} d^{3} e - a^{2} c^{2} d e^{3}\right)} {\left| c \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{c^{4} d - \sqrt{c^{8} d^{2} - {\left(c^{4} d^{2} - a c^{3} e^{2}\right)} c^{4}}}{c^{4}}}}\right)}{{\left(a c^{4} d + \sqrt{a c} a c^{3} e\right)} \sqrt{-c^{2} d + \sqrt{a c} c e}} - \frac{2 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} c^{2} e + 6 \, \sqrt{x e + d} c^{2} d e\right)}}{3 \, c^{3}}"," ",0,"-(sqrt(a*c)*c^4*d^4 + 3*sqrt(a*c)*a*c^3*d^2*e^2 - (3*sqrt(a*c)*a*c*d^2*e^2 + sqrt(a*c)*a^2*e^4)*c^2 + 2*(a*c^3*d^3*e - a^2*c^2*d*e^3)*abs(c))*arctan(sqrt(x*e + d)/sqrt(-(c^4*d + sqrt(c^8*d^2 - (c^4*d^2 - a*c^3*e^2)*c^4))/c^4))/((a*c^4*d - sqrt(a*c)*a*c^3*e)*sqrt(-c^2*d - sqrt(a*c)*c*e)) + (sqrt(a*c)*c^4*d^4 + 3*sqrt(a*c)*a*c^3*d^2*e^2 - (3*sqrt(a*c)*a*c*d^2*e^2 + sqrt(a*c)*a^2*e^4)*c^2 - 2*(a*c^3*d^3*e - a^2*c^2*d*e^3)*abs(c))*arctan(sqrt(x*e + d)/sqrt(-(c^4*d - sqrt(c^8*d^2 - (c^4*d^2 - a*c^3*e^2)*c^4))/c^4))/((a*c^4*d + sqrt(a*c)*a*c^3*e)*sqrt(-c^2*d + sqrt(a*c)*c*e)) - 2/3*((x*e + d)^(3/2)*c^2*e + 6*sqrt(x*e + d)*c^2*d*e)/c^3","B",0
613,1,304,0,0.295311," ","integrate((e*x+d)^(3/2)/(-c*x^2+a),x, algorithm=""giac"")","-\frac{{\left(\sqrt{a c} c^{3} d^{3} - \sqrt{a c} a c^{2} d e^{2} + {\left(a c^{2} d^{2} e - a^{2} c e^{3}\right)} {\left| c \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{c^{2} d + \sqrt{c^{4} d^{2} - {\left(c^{2} d^{2} - a c e^{2}\right)} c^{2}}}{c^{2}}}}\right)}{{\left(a c^{3} d - \sqrt{a c} a c^{2} e\right)} \sqrt{-c^{2} d - \sqrt{a c} c e}} + \frac{{\left(\sqrt{a c} c^{3} d^{3} - \sqrt{a c} a c^{2} d e^{2} - {\left(a c^{2} d^{2} e - a^{2} c e^{3}\right)} {\left| c \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{c^{2} d - \sqrt{c^{4} d^{2} - {\left(c^{2} d^{2} - a c e^{2}\right)} c^{2}}}{c^{2}}}}\right)}{{\left(a c^{3} d + \sqrt{a c} a c^{2} e\right)} \sqrt{-c^{2} d + \sqrt{a c} c e}} - \frac{2 \, \sqrt{x e + d} e}{c}"," ",0,"-(sqrt(a*c)*c^3*d^3 - sqrt(a*c)*a*c^2*d*e^2 + (a*c^2*d^2*e - a^2*c*e^3)*abs(c))*arctan(sqrt(x*e + d)/sqrt(-(c^2*d + sqrt(c^4*d^2 - (c^2*d^2 - a*c*e^2)*c^2))/c^2))/((a*c^3*d - sqrt(a*c)*a*c^2*e)*sqrt(-c^2*d - sqrt(a*c)*c*e)) + (sqrt(a*c)*c^3*d^3 - sqrt(a*c)*a*c^2*d*e^2 - (a*c^2*d^2*e - a^2*c*e^3)*abs(c))*arctan(sqrt(x*e + d)/sqrt(-(c^2*d - sqrt(c^4*d^2 - (c^2*d^2 - a*c*e^2)*c^2))/c^2))/((a*c^3*d + sqrt(a*c)*a*c^2*e)*sqrt(-c^2*d + sqrt(a*c)*c*e)) - 2*sqrt(x*e + d)*e/c","B",0
614,1,153,0,0.244084," ","integrate((e*x+d)^(1/2)/(-c*x^2+a),x, algorithm=""giac"")","\frac{\sqrt{-c^{2} d - \sqrt{a c} c e} {\left| c \right|} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{c d + \sqrt{c^{2} d^{2} - {\left(c d^{2} - a e^{2}\right)} c}}{c}}}\right)}{\sqrt{a c} c^{2}} - \frac{\sqrt{-c^{2} d + \sqrt{a c} c e} {\left| c \right|} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{c d - \sqrt{c^{2} d^{2} - {\left(c d^{2} - a e^{2}\right)} c}}{c}}}\right)}{\sqrt{a c} c^{2}}"," ",0,"sqrt(-c^2*d - sqrt(a*c)*c*e)*abs(c)*arctan(sqrt(x*e + d)/sqrt(-(c*d + sqrt(c^2*d^2 - (c*d^2 - a*e^2)*c))/c))/(sqrt(a*c)*c^2) - sqrt(-c^2*d + sqrt(a*c)*c*e)*abs(c)*arctan(sqrt(x*e + d)/sqrt(-(c*d - sqrt(c^2*d^2 - (c*d^2 - a*e^2)*c))/c))/(sqrt(a*c)*c^2)","A",0
615,1,159,0,0.221743," ","integrate(1/(-c*x^2+a)/(e*x+d)^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{a c} {\left| c \right|} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{c d + \sqrt{c^{2} d^{2} - {\left(c d^{2} - a e^{2}\right)} c}}{c}}}\right)}{\sqrt{-c^{2} d - \sqrt{a c} c e} a c} + \frac{\sqrt{a c} {\left| c \right|} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{c d - \sqrt{c^{2} d^{2} - {\left(c d^{2} - a e^{2}\right)} c}}{c}}}\right)}{\sqrt{-c^{2} d + \sqrt{a c} c e} a c}"," ",0,"-sqrt(a*c)*abs(c)*arctan(sqrt(x*e + d)/sqrt(-(c*d + sqrt(c^2*d^2 - (c*d^2 - a*e^2)*c))/c))/(sqrt(-c^2*d - sqrt(a*c)*c*e)*a*c) + sqrt(a*c)*abs(c)*arctan(sqrt(x*e + d)/sqrt(-(c*d - sqrt(c^2*d^2 - (c*d^2 - a*e^2)*c))/c))/(sqrt(-c^2*d + sqrt(a*c)*c*e)*a*c)","A",0
616,1,686,0,0.718474," ","integrate(1/(e*x+d)^(3/2)/(-c*x^2+a),x, algorithm=""giac"")","-\frac{{\left({\left(c d^{2} e - a e^{3}\right)}^{2} \sqrt{a c} a {\left| c \right|} e - 2 \, {\left(a c^{2} d^{3} e - a^{2} c d e^{3}\right)} {\left| c d^{2} e - a e^{3} \right|} {\left| c \right|} + {\left(\sqrt{a c} c^{3} d^{6} e - 2 \, \sqrt{a c} a c^{2} d^{4} e^{3} + \sqrt{a c} a^{2} c d^{2} e^{5}\right)} {\left| c \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{c^{2} d^{3} - a c d e^{2} + \sqrt{{\left(c^{2} d^{3} - a c d e^{2}\right)}^{2} - {\left(c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} {\left(c^{2} d^{2} - a c e^{2}\right)}}}{c^{2} d^{2} - a c e^{2}}}}\right)}{{\left(a c^{3} d^{5} - \sqrt{a c} a c^{2} d^{4} e - 2 \, a^{2} c^{2} d^{3} e^{2} + 2 \, \sqrt{a c} a^{2} c d^{2} e^{3} + a^{3} c d e^{4} - \sqrt{a c} a^{3} e^{5}\right)} \sqrt{-c^{2} d - \sqrt{a c} c e} {\left| c d^{2} e - a e^{3} \right|}} + \frac{{\left({\left(c d^{2} e - a e^{3}\right)}^{2} \sqrt{a c} a {\left| c \right|} e + 2 \, {\left(a c^{2} d^{3} e - a^{2} c d e^{3}\right)} {\left| c d^{2} e - a e^{3} \right|} {\left| c \right|} + {\left(\sqrt{a c} c^{3} d^{6} e - 2 \, \sqrt{a c} a c^{2} d^{4} e^{3} + \sqrt{a c} a^{2} c d^{2} e^{5}\right)} {\left| c \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{c^{2} d^{3} - a c d e^{2} - \sqrt{{\left(c^{2} d^{3} - a c d e^{2}\right)}^{2} - {\left(c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} {\left(c^{2} d^{2} - a c e^{2}\right)}}}{c^{2} d^{2} - a c e^{2}}}}\right)}{{\left(a c^{3} d^{5} + \sqrt{a c} a c^{2} d^{4} e - 2 \, a^{2} c^{2} d^{3} e^{2} - 2 \, \sqrt{a c} a^{2} c d^{2} e^{3} + a^{3} c d e^{4} + \sqrt{a c} a^{3} e^{5}\right)} \sqrt{-c^{2} d + \sqrt{a c} c e} {\left| c d^{2} e - a e^{3} \right|}} + \frac{2 \, e}{{\left(c d^{2} - a e^{2}\right)} \sqrt{x e + d}}"," ",0,"-((c*d^2*e - a*e^3)^2*sqrt(a*c)*a*abs(c)*e - 2*(a*c^2*d^3*e - a^2*c*d*e^3)*abs(c*d^2*e - a*e^3)*abs(c) + (sqrt(a*c)*c^3*d^6*e - 2*sqrt(a*c)*a*c^2*d^4*e^3 + sqrt(a*c)*a^2*c*d^2*e^5)*abs(c))*arctan(sqrt(x*e + d)/sqrt(-(c^2*d^3 - a*c*d*e^2 + sqrt((c^2*d^3 - a*c*d*e^2)^2 - (c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*(c^2*d^2 - a*c*e^2)))/(c^2*d^2 - a*c*e^2)))/((a*c^3*d^5 - sqrt(a*c)*a*c^2*d^4*e - 2*a^2*c^2*d^3*e^2 + 2*sqrt(a*c)*a^2*c*d^2*e^3 + a^3*c*d*e^4 - sqrt(a*c)*a^3*e^5)*sqrt(-c^2*d - sqrt(a*c)*c*e)*abs(c*d^2*e - a*e^3)) + ((c*d^2*e - a*e^3)^2*sqrt(a*c)*a*abs(c)*e + 2*(a*c^2*d^3*e - a^2*c*d*e^3)*abs(c*d^2*e - a*e^3)*abs(c) + (sqrt(a*c)*c^3*d^6*e - 2*sqrt(a*c)*a*c^2*d^4*e^3 + sqrt(a*c)*a^2*c*d^2*e^5)*abs(c))*arctan(sqrt(x*e + d)/sqrt(-(c^2*d^3 - a*c*d*e^2 - sqrt((c^2*d^3 - a*c*d*e^2)^2 - (c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*(c^2*d^2 - a*c*e^2)))/(c^2*d^2 - a*c*e^2)))/((a*c^3*d^5 + sqrt(a*c)*a*c^2*d^4*e - 2*a^2*c^2*d^3*e^2 - 2*sqrt(a*c)*a^2*c*d^2*e^3 + a^3*c*d*e^4 + sqrt(a*c)*a^3*e^5)*sqrt(-c^2*d + sqrt(a*c)*c*e)*abs(c*d^2*e - a*e^3)) + 2*e/((c*d^2 - a*e^2)*sqrt(x*e + d))","B",0
617,1,529,0,0.534968," ","integrate(1/(e*x+d)^(5/2)/(-c*x^2+a),x, algorithm=""giac"")","\frac{\sqrt{-c^{2} d - \sqrt{a c} c e} {\left| c \right|} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{c^{3} d^{5} - 2 \, a c^{2} d^{3} e^{2} + a^{2} c d e^{4} + \sqrt{{\left(c^{3} d^{5} - 2 \, a c^{2} d^{3} e^{2} + a^{2} c d e^{4}\right)}^{2} - {\left(c^{3} d^{6} - 3 \, a c^{2} d^{4} e^{2} + 3 \, a^{2} c d^{2} e^{4} - a^{3} e^{6}\right)} {\left(c^{3} d^{4} - 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}\right)}}}{c^{3} d^{4} - 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}}}\right)}{3 \, a c^{2} d^{2} e + \sqrt{a c} c^{2} d^{3} + 3 \, \sqrt{a c} a c d e^{2} + a^{2} c e^{3}} + \frac{\sqrt{-c^{2} d + \sqrt{a c} c e} {\left| c \right|} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{c^{3} d^{5} - 2 \, a c^{2} d^{3} e^{2} + a^{2} c d e^{4} - \sqrt{{\left(c^{3} d^{5} - 2 \, a c^{2} d^{3} e^{2} + a^{2} c d e^{4}\right)}^{2} - {\left(c^{3} d^{6} - 3 \, a c^{2} d^{4} e^{2} + 3 \, a^{2} c d^{2} e^{4} - a^{3} e^{6}\right)} {\left(c^{3} d^{4} - 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}\right)}}}{c^{3} d^{4} - 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}}}\right)}{3 \, a c^{2} d^{2} e - \sqrt{a c} c^{2} d^{3} - 3 \, \sqrt{a c} a c d e^{2} + a^{2} c e^{3}} + \frac{2 \, {\left(6 \, {\left(x e + d\right)} c d e + c d^{2} e - a e^{3}\right)}}{3 \, {\left(c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} {\left(x e + d\right)}^{\frac{3}{2}}}"," ",0,"sqrt(-c^2*d - sqrt(a*c)*c*e)*abs(c)*arctan(sqrt(x*e + d)/sqrt(-(c^3*d^5 - 2*a*c^2*d^3*e^2 + a^2*c*d*e^4 + sqrt((c^3*d^5 - 2*a*c^2*d^3*e^2 + a^2*c*d*e^4)^2 - (c^3*d^6 - 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4 - a^3*e^6)*(c^3*d^4 - 2*a*c^2*d^2*e^2 + a^2*c*e^4)))/(c^3*d^4 - 2*a*c^2*d^2*e^2 + a^2*c*e^4)))/(3*a*c^2*d^2*e + sqrt(a*c)*c^2*d^3 + 3*sqrt(a*c)*a*c*d*e^2 + a^2*c*e^3) + sqrt(-c^2*d + sqrt(a*c)*c*e)*abs(c)*arctan(sqrt(x*e + d)/sqrt(-(c^3*d^5 - 2*a*c^2*d^3*e^2 + a^2*c*d*e^4 - sqrt((c^3*d^5 - 2*a*c^2*d^3*e^2 + a^2*c*d*e^4)^2 - (c^3*d^6 - 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4 - a^3*e^6)*(c^3*d^4 - 2*a*c^2*d^2*e^2 + a^2*c*e^4)))/(c^3*d^4 - 2*a*c^2*d^2*e^2 + a^2*c*e^4)))/(3*a*c^2*d^2*e - sqrt(a*c)*c^2*d^3 - 3*sqrt(a*c)*a*c*d*e^2 + a^2*c*e^3) + 2/3*(6*(x*e + d)*c*d*e + c*d^2*e - a*e^3)/((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*(x*e + d)^(3/2))","B",0
618,0,0,0,0.000000," ","integrate((e*x+d)^(5/2)/(c*x^2+a),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
619,-1,0,0,0.000000," ","integrate((e*x+d)^(3/2)/(c*x^2+a),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
620,0,0,0,0.000000," ","integrate((e*x+d)^(1/2)/(c*x^2+a),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
621,0,0,0,0.000000," ","integrate(1/(c*x^2+a)/(e*x+d)^(1/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
622,1,646,0,0.402569," ","integrate(1/(e*x+d)^(3/2)/(c*x^2+a),x, algorithm=""giac"")","\frac{{\left({\left(c d^{2} e + a e^{3}\right)}^{2} a {\left| c \right|} e + 2 \, {\left(\sqrt{-a c} c d^{3} e + \sqrt{-a c} a d e^{3}\right)} {\left| -c d^{2} e - a e^{3} \right|} {\left| c \right|} - {\left(c^{3} d^{6} e + 2 \, a c^{2} d^{4} e^{3} + a^{2} c d^{2} e^{5}\right)} {\left| c \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{c^{2} d^{3} + a c d e^{2} + \sqrt{{\left(c^{2} d^{3} + a c d e^{2}\right)}^{2} - {\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} {\left(c^{2} d^{2} + a c e^{2}\right)}}}{c^{2} d^{2} + a c e^{2}}}}\right)}{{\left(a c^{2} d^{4} e - \sqrt{-a c} c^{2} d^{5} - 2 \, \sqrt{-a c} a c d^{3} e^{2} + 2 \, a^{2} c d^{2} e^{3} - \sqrt{-a c} a^{2} d e^{4} + a^{3} e^{5}\right)} \sqrt{-c^{2} d + \sqrt{-a c} c e} {\left| -c d^{2} e - a e^{3} \right|}} + \frac{{\left({\left(c d^{2} e + a e^{3}\right)}^{2} a {\left| c \right|} e - 2 \, {\left(\sqrt{-a c} c d^{3} e + \sqrt{-a c} a d e^{3}\right)} {\left| -c d^{2} e - a e^{3} \right|} {\left| c \right|} - {\left(c^{3} d^{6} e + 2 \, a c^{2} d^{4} e^{3} + a^{2} c d^{2} e^{5}\right)} {\left| c \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{c^{2} d^{3} + a c d e^{2} - \sqrt{{\left(c^{2} d^{3} + a c d e^{2}\right)}^{2} - {\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} {\left(c^{2} d^{2} + a c e^{2}\right)}}}{c^{2} d^{2} + a c e^{2}}}}\right)}{{\left(a c^{2} d^{4} e + \sqrt{-a c} c^{2} d^{5} + 2 \, \sqrt{-a c} a c d^{3} e^{2} + 2 \, a^{2} c d^{2} e^{3} + \sqrt{-a c} a^{2} d e^{4} + a^{3} e^{5}\right)} \sqrt{-c^{2} d - \sqrt{-a c} c e} {\left| -c d^{2} e - a e^{3} \right|}} - \frac{2 \, e}{{\left(c d^{2} + a e^{2}\right)} \sqrt{x e + d}}"," ",0,"((c*d^2*e + a*e^3)^2*a*abs(c)*e + 2*(sqrt(-a*c)*c*d^3*e + sqrt(-a*c)*a*d*e^3)*abs(-c*d^2*e - a*e^3)*abs(c) - (c^3*d^6*e + 2*a*c^2*d^4*e^3 + a^2*c*d^2*e^5)*abs(c))*arctan(sqrt(x*e + d)/sqrt(-(c^2*d^3 + a*c*d*e^2 + sqrt((c^2*d^3 + a*c*d*e^2)^2 - (c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4)*(c^2*d^2 + a*c*e^2)))/(c^2*d^2 + a*c*e^2)))/((a*c^2*d^4*e - sqrt(-a*c)*c^2*d^5 - 2*sqrt(-a*c)*a*c*d^3*e^2 + 2*a^2*c*d^2*e^3 - sqrt(-a*c)*a^2*d*e^4 + a^3*e^5)*sqrt(-c^2*d + sqrt(-a*c)*c*e)*abs(-c*d^2*e - a*e^3)) + ((c*d^2*e + a*e^3)^2*a*abs(c)*e - 2*(sqrt(-a*c)*c*d^3*e + sqrt(-a*c)*a*d*e^3)*abs(-c*d^2*e - a*e^3)*abs(c) - (c^3*d^6*e + 2*a*c^2*d^4*e^3 + a^2*c*d^2*e^5)*abs(c))*arctan(sqrt(x*e + d)/sqrt(-(c^2*d^3 + a*c*d*e^2 - sqrt((c^2*d^3 + a*c*d*e^2)^2 - (c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4)*(c^2*d^2 + a*c*e^2)))/(c^2*d^2 + a*c*e^2)))/((a*c^2*d^4*e + sqrt(-a*c)*c^2*d^5 + 2*sqrt(-a*c)*a*c*d^3*e^2 + 2*a^2*c*d^2*e^3 + sqrt(-a*c)*a^2*d*e^4 + a^3*e^5)*sqrt(-c^2*d - sqrt(-a*c)*c*e)*abs(-c*d^2*e - a*e^3)) - 2*e/((c*d^2 + a*e^2)*sqrt(x*e + d))","A",0
623,1,506,0,0.533975," ","integrate(1/(e*x+d)^(5/2)/(c*x^2+a),x, algorithm=""giac"")","-\frac{\sqrt{-a c} {\left| c \right|} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{c^{3} d^{5} + 2 \, a c^{2} d^{3} e^{2} + a^{2} c d e^{4} + \sqrt{{\left(c^{3} d^{5} + 2 \, a c^{2} d^{3} e^{2} + a^{2} c d e^{4}\right)}^{2} - {\left(c^{3} d^{6} + 3 \, a c^{2} d^{4} e^{2} + 3 \, a^{2} c d^{2} e^{4} + a^{3} e^{6}\right)} {\left(c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}\right)}}}{c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}}}\right)}{{\left(a c d^{2} + 2 \, \sqrt{-a c} a d e - a^{2} e^{2}\right)} \sqrt{-c^{2} d - \sqrt{-a c} c e}} + \frac{\sqrt{-a c} {\left| c \right|} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{c^{3} d^{5} + 2 \, a c^{2} d^{3} e^{2} + a^{2} c d e^{4} - \sqrt{{\left(c^{3} d^{5} + 2 \, a c^{2} d^{3} e^{2} + a^{2} c d e^{4}\right)}^{2} - {\left(c^{3} d^{6} + 3 \, a c^{2} d^{4} e^{2} + 3 \, a^{2} c d^{2} e^{4} + a^{3} e^{6}\right)} {\left(c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}\right)}}}{c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}}}\right)}{{\left(a c d^{2} - 2 \, \sqrt{-a c} a d e - a^{2} e^{2}\right)} \sqrt{-c^{2} d + \sqrt{-a c} c e}} - \frac{2 \, {\left(6 \, {\left(x e + d\right)} c d e + c d^{2} e + a e^{3}\right)}}{3 \, {\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} {\left(x e + d\right)}^{\frac{3}{2}}}"," ",0,"-sqrt(-a*c)*abs(c)*arctan(sqrt(x*e + d)/sqrt(-(c^3*d^5 + 2*a*c^2*d^3*e^2 + a^2*c*d*e^4 + sqrt((c^3*d^5 + 2*a*c^2*d^3*e^2 + a^2*c*d*e^4)^2 - (c^3*d^6 + 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4 + a^3*e^6)*(c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4)))/(c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4)))/((a*c*d^2 + 2*sqrt(-a*c)*a*d*e - a^2*e^2)*sqrt(-c^2*d - sqrt(-a*c)*c*e)) + sqrt(-a*c)*abs(c)*arctan(sqrt(x*e + d)/sqrt(-(c^3*d^5 + 2*a*c^2*d^3*e^2 + a^2*c*d*e^4 - sqrt((c^3*d^5 + 2*a*c^2*d^3*e^2 + a^2*c*d*e^4)^2 - (c^3*d^6 + 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4 + a^3*e^6)*(c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4)))/(c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4)))/((a*c*d^2 - 2*sqrt(-a*c)*a*d*e - a^2*e^2)*sqrt(-c^2*d + sqrt(-a*c)*c*e)) - 2/3*(6*(x*e + d)*c*d*e + c*d^2*e + a*e^3)/((c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4)*(x*e + d)^(3/2))","A",0
624,1,572,0,0.658929," ","integrate((e*x+d)^(7/2)/(-c*x^2+a)^2,x, algorithm=""giac"")","-\frac{{\left({\left(c^{2} d^{3} e^{2} - 13 \, a c d e^{4}\right)} a^{2} {\left| c \right|} + {\left(\sqrt{a c} c^{2} d^{4} e + 4 \, \sqrt{a c} a c d^{2} e^{3} - 5 \, \sqrt{a c} a^{2} e^{5}\right)} {\left| a \right|} {\left| c \right|} - {\left(2 \, a c^{3} d^{5} - 9 \, a^{2} c^{2} d^{3} e^{2} - 5 \, a^{3} c d e^{4}\right)} {\left| c \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a c^{3} d + \sqrt{a^{2} c^{6} d^{2} - {\left(a c^{3} d^{2} - a^{2} c^{2} e^{2}\right)} a c^{3}}}{a c^{3}}}}\right)}{4 \, {\left(a^{2} c^{3} e - \sqrt{a c} a c^{3} d\right)} \sqrt{-c^{2} d - \sqrt{a c} c e} {\left| a \right|}} - \frac{{\left({\left(\sqrt{a c} c d^{3} e^{2} - 13 \, \sqrt{a c} a d e^{4}\right)} a^{2} {\left| c \right|} - {\left(a c^{2} d^{4} e + 4 \, a^{2} c d^{2} e^{3} - 5 \, a^{3} e^{5}\right)} {\left| a \right|} {\left| c \right|} - {\left(2 \, \sqrt{a c} a c^{2} d^{5} - 9 \, \sqrt{a c} a^{2} c d^{3} e^{2} - 5 \, \sqrt{a c} a^{3} d e^{4}\right)} {\left| c \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a c^{3} d - \sqrt{a^{2} c^{6} d^{2} - {\left(a c^{3} d^{2} - a^{2} c^{2} e^{2}\right)} a c^{3}}}{a c^{3}}}}\right)}{4 \, {\left(a^{2} c^{3} d + \sqrt{a c} a^{2} c^{2} e\right)} \sqrt{-c^{2} d + \sqrt{a c} c e} {\left| a \right|}} + \frac{2 \, \sqrt{x e + d} e^{3}}{c^{2}} - \frac{{\left(x e + d\right)}^{\frac{3}{2}} c^{2} d^{3} e - \sqrt{x e + d} c^{2} d^{4} e + 3 \, {\left(x e + d\right)}^{\frac{3}{2}} a c d e^{3} + \sqrt{x e + d} a^{2} e^{5}}{2 \, {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} - a e^{2}\right)} a c^{2}}"," ",0,"-1/4*((c^2*d^3*e^2 - 13*a*c*d*e^4)*a^2*abs(c) + (sqrt(a*c)*c^2*d^4*e + 4*sqrt(a*c)*a*c*d^2*e^3 - 5*sqrt(a*c)*a^2*e^5)*abs(a)*abs(c) - (2*a*c^3*d^5 - 9*a^2*c^2*d^3*e^2 - 5*a^3*c*d*e^4)*abs(c))*arctan(sqrt(x*e + d)/sqrt(-(a*c^3*d + sqrt(a^2*c^6*d^2 - (a*c^3*d^2 - a^2*c^2*e^2)*a*c^3))/(a*c^3)))/((a^2*c^3*e - sqrt(a*c)*a*c^3*d)*sqrt(-c^2*d - sqrt(a*c)*c*e)*abs(a)) - 1/4*((sqrt(a*c)*c*d^3*e^2 - 13*sqrt(a*c)*a*d*e^4)*a^2*abs(c) - (a*c^2*d^4*e + 4*a^2*c*d^2*e^3 - 5*a^3*e^5)*abs(a)*abs(c) - (2*sqrt(a*c)*a*c^2*d^5 - 9*sqrt(a*c)*a^2*c*d^3*e^2 - 5*sqrt(a*c)*a^3*d*e^4)*abs(c))*arctan(sqrt(x*e + d)/sqrt(-(a*c^3*d - sqrt(a^2*c^6*d^2 - (a*c^3*d^2 - a^2*c^2*e^2)*a*c^3))/(a*c^3)))/((a^2*c^3*d + sqrt(a*c)*a^2*c^2*e)*sqrt(-c^2*d + sqrt(a*c)*c*e)*abs(a)) + 2*sqrt(x*e + d)*e^3/c^2 - 1/2*((x*e + d)^(3/2)*c^2*d^3*e - sqrt(x*e + d)*c^2*d^4*e + 3*(x*e + d)^(3/2)*a*c*d*e^3 + sqrt(x*e + d)*a^2*e^5)/(((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 - a*e^2)*a*c^2)","B",0
625,1,493,0,0.627936," ","integrate((e*x+d)^(5/2)/(-c*x^2+a)^2,x, algorithm=""giac"")","\frac{{\left(2 \, a c^{4} d^{4} - 4 \, a^{2} c^{3} d^{2} e^{2} - {\left(c d^{2} e^{2} - 3 \, a e^{4}\right)} a^{2} c^{2} - {\left(\sqrt{a c} c^{2} d^{3} e - \sqrt{a c} a c d e^{3}\right)} {\left| a \right|} {\left| c \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a c^{2} d + \sqrt{a^{2} c^{4} d^{2} - {\left(a c^{2} d^{2} - a^{2} c e^{2}\right)} a c^{2}}}{a c^{2}}}}\right)}{4 \, {\left(a^{2} c^{3} e - \sqrt{a c} a c^{3} d\right)} \sqrt{-c^{2} d - \sqrt{a c} c e} {\left| a \right|}} + \frac{{\left(2 \, \sqrt{a c} a c^{4} d^{4} - 4 \, \sqrt{a c} a^{2} c^{3} d^{2} e^{2} - {\left(\sqrt{a c} c d^{2} e^{2} - 3 \, \sqrt{a c} a e^{4}\right)} a^{2} c^{2} + {\left(a c^{3} d^{3} e - a^{2} c^{2} d e^{3}\right)} {\left| a \right|} {\left| c \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a c^{2} d - \sqrt{a^{2} c^{4} d^{2} - {\left(a c^{2} d^{2} - a^{2} c e^{2}\right)} a c^{2}}}{a c^{2}}}}\right)}{4 \, {\left(a^{2} c^{4} d + \sqrt{a c} a^{2} c^{3} e\right)} \sqrt{-c^{2} d + \sqrt{a c} c e} {\left| a \right|}} - \frac{{\left(x e + d\right)}^{\frac{3}{2}} c d^{2} e - \sqrt{x e + d} c d^{3} e + {\left(x e + d\right)}^{\frac{3}{2}} a e^{3} + \sqrt{x e + d} a d e^{3}}{2 \, {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} - a e^{2}\right)} a c}"," ",0,"1/4*(2*a*c^4*d^4 - 4*a^2*c^3*d^2*e^2 - (c*d^2*e^2 - 3*a*e^4)*a^2*c^2 - (sqrt(a*c)*c^2*d^3*e - sqrt(a*c)*a*c*d*e^3)*abs(a)*abs(c))*arctan(sqrt(x*e + d)/sqrt(-(a*c^2*d + sqrt(a^2*c^4*d^2 - (a*c^2*d^2 - a^2*c*e^2)*a*c^2))/(a*c^2)))/((a^2*c^3*e - sqrt(a*c)*a*c^3*d)*sqrt(-c^2*d - sqrt(a*c)*c*e)*abs(a)) + 1/4*(2*sqrt(a*c)*a*c^4*d^4 - 4*sqrt(a*c)*a^2*c^3*d^2*e^2 - (sqrt(a*c)*c*d^2*e^2 - 3*sqrt(a*c)*a*e^4)*a^2*c^2 + (a*c^3*d^3*e - a^2*c^2*d*e^3)*abs(a)*abs(c))*arctan(sqrt(x*e + d)/sqrt(-(a*c^2*d - sqrt(a^2*c^4*d^2 - (a*c^2*d^2 - a^2*c*e^2)*a*c^2))/(a*c^2)))/((a^2*c^4*d + sqrt(a*c)*a^2*c^3*e)*sqrt(-c^2*d + sqrt(a*c)*c*e)*abs(a)) - 1/2*((x*e + d)^(3/2)*c*d^2*e - sqrt(x*e + d)*c*d^3*e + (x*e + d)^(3/2)*a*e^3 + sqrt(x*e + d)*a*d*e^3)/(((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 - a*e^2)*a*c)","B",0
626,1,423,0,0.536072," ","integrate((e*x+d)^(3/2)/(-c*x^2+a)^2,x, algorithm=""giac"")","-\frac{{\left(2 \, \sqrt{a c} a c^{3} d^{3} - 2 \, \sqrt{a c} a^{2} c^{2} d e^{2} - {\left(a c^{2} d^{2} e - a^{2} c e^{3}\right)} {\left| a \right|} {\left| c \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a c^{2} d + \sqrt{a^{2} c^{4} d^{2} - {\left(a c^{2} d^{2} - a^{2} c e^{2}\right)} a c^{2}}}{a c^{2}}}}\right)}{4 \, {\left(a^{2} c^{3} d - \sqrt{a c} a^{2} c^{2} e\right)} \sqrt{-c^{2} d - \sqrt{a c} c e} {\left| a \right|}} + \frac{{\left(2 \, \sqrt{a c} a c^{3} d^{3} - 2 \, \sqrt{a c} a^{2} c^{2} d e^{2} + {\left(a c^{2} d^{2} e - a^{2} c e^{3}\right)} {\left| a \right|} {\left| c \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a c^{2} d - \sqrt{a^{2} c^{4} d^{2} - {\left(a c^{2} d^{2} - a^{2} c e^{2}\right)} a c^{2}}}{a c^{2}}}}\right)}{4 \, {\left(a^{2} c^{3} d + \sqrt{a c} a^{2} c^{2} e\right)} \sqrt{-c^{2} d + \sqrt{a c} c e} {\left| a \right|}} - \frac{{\left(x e + d\right)}^{\frac{3}{2}} c d e - \sqrt{x e + d} c d^{2} e + \sqrt{x e + d} a e^{3}}{2 \, {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} - a e^{2}\right)} a c}"," ",0,"-1/4*(2*sqrt(a*c)*a*c^3*d^3 - 2*sqrt(a*c)*a^2*c^2*d*e^2 - (a*c^2*d^2*e - a^2*c*e^3)*abs(a)*abs(c))*arctan(sqrt(x*e + d)/sqrt(-(a*c^2*d + sqrt(a^2*c^4*d^2 - (a*c^2*d^2 - a^2*c*e^2)*a*c^2))/(a*c^2)))/((a^2*c^3*d - sqrt(a*c)*a^2*c^2*e)*sqrt(-c^2*d - sqrt(a*c)*c*e)*abs(a)) + 1/4*(2*sqrt(a*c)*a*c^3*d^3 - 2*sqrt(a*c)*a^2*c^2*d*e^2 + (a*c^2*d^2*e - a^2*c*e^3)*abs(a)*abs(c))*arctan(sqrt(x*e + d)/sqrt(-(a*c^2*d - sqrt(a^2*c^4*d^2 - (a*c^2*d^2 - a^2*c*e^2)*a*c^2))/(a*c^2)))/((a^2*c^3*d + sqrt(a*c)*a^2*c^2*e)*sqrt(-c^2*d + sqrt(a*c)*c*e)*abs(a)) - 1/2*((x*e + d)^(3/2)*c*d*e - sqrt(x*e + d)*c*d^2*e + sqrt(x*e + d)*a*e^3)/(((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 - a*e^2)*a*c)","B",0
627,1,342,0,0.526021," ","integrate((e*x+d)^(1/2)/(-c*x^2+a)^2,x, algorithm=""giac"")","\frac{{\left(2 \, a c d^{2} {\left| c \right|} - \sqrt{a c} d {\left| a \right|} {\left| c \right|} e - a^{2} {\left| c \right|} e^{2}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a c d + \sqrt{a^{2} c^{2} d^{2} - {\left(a c d^{2} - a^{2} e^{2}\right)} a c}}{a c}}}\right)}{4 \, {\left(a^{2} c e - \sqrt{a c} a c d\right)} \sqrt{-c^{2} d - \sqrt{a c} c e} {\left| a \right|}} + \frac{{\left(a c d {\left| a \right|} {\left| c \right|} e + 2 \, \sqrt{a c} a c d^{2} {\left| c \right|} - \sqrt{a c} a^{2} {\left| c \right|} e^{2}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a c d - \sqrt{a^{2} c^{2} d^{2} - {\left(a c d^{2} - a^{2} e^{2}\right)} a c}}{a c}}}\right)}{4 \, {\left(a^{2} c^{2} d + \sqrt{a c} a^{2} c e\right)} \sqrt{-c^{2} d + \sqrt{a c} c e} {\left| a \right|}} - \frac{{\left(x e + d\right)}^{\frac{3}{2}} e - \sqrt{x e + d} d e}{2 \, {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} - a e^{2}\right)} a}"," ",0,"1/4*(2*a*c*d^2*abs(c) - sqrt(a*c)*d*abs(a)*abs(c)*e - a^2*abs(c)*e^2)*arctan(sqrt(x*e + d)/sqrt(-(a*c*d + sqrt(a^2*c^2*d^2 - (a*c*d^2 - a^2*e^2)*a*c))/(a*c)))/((a^2*c*e - sqrt(a*c)*a*c*d)*sqrt(-c^2*d - sqrt(a*c)*c*e)*abs(a)) + 1/4*(a*c*d*abs(a)*abs(c)*e + 2*sqrt(a*c)*a*c*d^2*abs(c) - sqrt(a*c)*a^2*abs(c)*e^2)*arctan(sqrt(x*e + d)/sqrt(-(a*c*d - sqrt(a^2*c^2*d^2 - (a*c*d^2 - a^2*e^2)*a*c))/(a*c)))/((a^2*c^2*d + sqrt(a*c)*a^2*c*e)*sqrt(-c^2*d + sqrt(a*c)*c*e)*abs(a)) - 1/2*((x*e + d)^(3/2)*e - sqrt(x*e + d)*d*e)/(((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 - a*e^2)*a)","B",0
628,1,859,0,0.529080," ","integrate(1/(-c*x^2+a)^2/(e*x+d)^(1/2),x, algorithm=""giac"")","-\frac{{\left({\left(a c d^{2} e - a^{2} e^{3}\right)}^{2} c d {\left| c \right|} e + {\left(\sqrt{a c} c^{2} d^{4} e - 4 \, \sqrt{a c} a c d^{2} e^{3} + 3 \, \sqrt{a c} a^{2} e^{5}\right)} {\left| a c d^{2} e - a^{2} e^{3} \right|} {\left| c \right|} - {\left(2 \, a c^{4} d^{7} e - 7 \, a^{2} c^{3} d^{5} e^{3} + 8 \, a^{3} c^{2} d^{3} e^{5} - 3 \, a^{4} c d e^{7}\right)} {\left| c \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a c^{2} d^{3} - a^{2} c d e^{2} + \sqrt{{\left(a c^{2} d^{3} - a^{2} c d e^{2}\right)}^{2} - {\left(a c^{2} d^{4} - 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} {\left(a c^{2} d^{2} - a^{2} c e^{2}\right)}}}{a c^{2} d^{2} - a^{2} c e^{2}}}}\right)}{4 \, {\left(a^{2} c^{3} d^{4} e - \sqrt{a c} a c^{3} d^{5} + 2 \, \sqrt{a c} a^{2} c^{2} d^{3} e^{2} - 2 \, a^{3} c^{2} d^{2} e^{3} - \sqrt{a c} a^{3} c d e^{4} + a^{4} c e^{5}\right)} \sqrt{-c^{2} d - \sqrt{a c} c e} {\left| a c d^{2} e - a^{2} e^{3} \right|}} - \frac{{\left({\left(a c d^{2} e - a^{2} e^{3}\right)}^{2} \sqrt{a c} d {\left| c \right|} e - {\left(a c^{2} d^{4} e - 4 \, a^{2} c d^{2} e^{3} + 3 \, a^{3} e^{5}\right)} {\left| a c d^{2} e - a^{2} e^{3} \right|} {\left| c \right|} - {\left(2 \, \sqrt{a c} a c^{3} d^{7} e - 7 \, \sqrt{a c} a^{2} c^{2} d^{5} e^{3} + 8 \, \sqrt{a c} a^{3} c d^{3} e^{5} - 3 \, \sqrt{a c} a^{4} d e^{7}\right)} {\left| c \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a c^{2} d^{3} - a^{2} c d e^{2} - \sqrt{{\left(a c^{2} d^{3} - a^{2} c d e^{2}\right)}^{2} - {\left(a c^{2} d^{4} - 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} {\left(a c^{2} d^{2} - a^{2} c e^{2}\right)}}}{a c^{2} d^{2} - a^{2} c e^{2}}}}\right)}{4 \, {\left(a^{2} c^{3} d^{5} + \sqrt{a c} a^{2} c^{2} d^{4} e - 2 \, a^{3} c^{2} d^{3} e^{2} - 2 \, \sqrt{a c} a^{3} c d^{2} e^{3} + a^{4} c d e^{4} + \sqrt{a c} a^{4} e^{5}\right)} \sqrt{-c^{2} d + \sqrt{a c} c e} {\left| a c d^{2} e - a^{2} e^{3} \right|}} - \frac{{\left(x e + d\right)}^{\frac{3}{2}} c d e - \sqrt{x e + d} c d^{2} e - \sqrt{x e + d} a e^{3}}{2 \, {\left(a c d^{2} - a^{2} e^{2}\right)} {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} - a e^{2}\right)}}"," ",0,"-1/4*((a*c*d^2*e - a^2*e^3)^2*c*d*abs(c)*e + (sqrt(a*c)*c^2*d^4*e - 4*sqrt(a*c)*a*c*d^2*e^3 + 3*sqrt(a*c)*a^2*e^5)*abs(a*c*d^2*e - a^2*e^3)*abs(c) - (2*a*c^4*d^7*e - 7*a^2*c^3*d^5*e^3 + 8*a^3*c^2*d^3*e^5 - 3*a^4*c*d*e^7)*abs(c))*arctan(sqrt(x*e + d)/sqrt(-(a*c^2*d^3 - a^2*c*d*e^2 + sqrt((a*c^2*d^3 - a^2*c*d*e^2)^2 - (a*c^2*d^4 - 2*a^2*c*d^2*e^2 + a^3*e^4)*(a*c^2*d^2 - a^2*c*e^2)))/(a*c^2*d^2 - a^2*c*e^2)))/((a^2*c^3*d^4*e - sqrt(a*c)*a*c^3*d^5 + 2*sqrt(a*c)*a^2*c^2*d^3*e^2 - 2*a^3*c^2*d^2*e^3 - sqrt(a*c)*a^3*c*d*e^4 + a^4*c*e^5)*sqrt(-c^2*d - sqrt(a*c)*c*e)*abs(a*c*d^2*e - a^2*e^3)) - 1/4*((a*c*d^2*e - a^2*e^3)^2*sqrt(a*c)*d*abs(c)*e - (a*c^2*d^4*e - 4*a^2*c*d^2*e^3 + 3*a^3*e^5)*abs(a*c*d^2*e - a^2*e^3)*abs(c) - (2*sqrt(a*c)*a*c^3*d^7*e - 7*sqrt(a*c)*a^2*c^2*d^5*e^3 + 8*sqrt(a*c)*a^3*c*d^3*e^5 - 3*sqrt(a*c)*a^4*d*e^7)*abs(c))*arctan(sqrt(x*e + d)/sqrt(-(a*c^2*d^3 - a^2*c*d*e^2 - sqrt((a*c^2*d^3 - a^2*c*d*e^2)^2 - (a*c^2*d^4 - 2*a^2*c*d^2*e^2 + a^3*e^4)*(a*c^2*d^2 - a^2*c*e^2)))/(a*c^2*d^2 - a^2*c*e^2)))/((a^2*c^3*d^5 + sqrt(a*c)*a^2*c^2*d^4*e - 2*a^3*c^2*d^3*e^2 - 2*sqrt(a*c)*a^3*c*d^2*e^3 + a^4*c*d*e^4 + sqrt(a*c)*a^4*e^5)*sqrt(-c^2*d + sqrt(a*c)*c*e)*abs(a*c*d^2*e - a^2*e^3)) - 1/2*((x*e + d)^(3/2)*c*d*e - sqrt(x*e + d)*c*d^2*e - sqrt(x*e + d)*a*e^3)/((a*c*d^2 - a^2*e^2)*((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 - a*e^2))","B",0
629,1,1333,0,0.948853," ","integrate(1/(e*x+d)^(3/2)/(-c*x^2+a)^2,x, algorithm=""giac"")","-\frac{{\left({\left(a c^{2} d^{4} e - 2 \, a^{2} c d^{2} e^{3} + a^{3} e^{5}\right)}^{2} {\left(c d^{2} e + 5 \, a e^{3}\right)} {\left| c \right|} + {\left(\sqrt{a c} c^{3} d^{7} e - 15 \, \sqrt{a c} a c^{2} d^{5} e^{3} + 27 \, \sqrt{a c} a^{2} c d^{3} e^{5} - 13 \, \sqrt{a c} a^{3} d e^{7}\right)} {\left| a c^{2} d^{4} e - 2 \, a^{2} c d^{2} e^{3} + a^{3} e^{5} \right|} {\left| c \right|} - 2 \, {\left(a c^{6} d^{12} e - 8 \, a^{2} c^{5} d^{10} e^{3} + 22 \, a^{3} c^{4} d^{8} e^{5} - 28 \, a^{4} c^{3} d^{6} e^{7} + 17 \, a^{5} c^{2} d^{4} e^{9} - 4 \, a^{6} c d^{2} e^{11}\right)} {\left| c \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a c^{3} d^{5} - 2 \, a^{2} c^{2} d^{3} e^{2} + a^{3} c d e^{4} + \sqrt{{\left(a c^{3} d^{5} - 2 \, a^{2} c^{2} d^{3} e^{2} + a^{3} c d e^{4}\right)}^{2} - {\left(a c^{3} d^{6} - 3 \, a^{2} c^{2} d^{4} e^{2} + 3 \, a^{3} c d^{2} e^{4} - a^{4} e^{6}\right)} {\left(a c^{3} d^{4} - 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)}}}{a c^{3} d^{4} - 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}}}}\right)}{4 \, {\left(a^{2} c^{4} d^{8} e - \sqrt{a c} a c^{4} d^{9} + 4 \, \sqrt{a c} a^{2} c^{3} d^{7} e^{2} - 4 \, a^{3} c^{3} d^{6} e^{3} - 6 \, \sqrt{a c} a^{3} c^{2} d^{5} e^{4} + 6 \, a^{4} c^{2} d^{4} e^{5} + 4 \, \sqrt{a c} a^{4} c d^{3} e^{6} - 4 \, a^{5} c d^{2} e^{7} - \sqrt{a c} a^{5} d e^{8} + a^{6} e^{9}\right)} \sqrt{-c^{2} d - \sqrt{a c} c e} {\left| a c^{2} d^{4} e - 2 \, a^{2} c d^{2} e^{3} + a^{3} e^{5} \right|}} - \frac{{\left({\left(a c^{2} d^{4} e - 2 \, a^{2} c d^{2} e^{3} + a^{3} e^{5}\right)}^{2} {\left(c d^{2} e + 5 \, a e^{3}\right)} {\left| c \right|} - {\left(\sqrt{a c} c^{3} d^{7} e - 15 \, \sqrt{a c} a c^{2} d^{5} e^{3} + 27 \, \sqrt{a c} a^{2} c d^{3} e^{5} - 13 \, \sqrt{a c} a^{3} d e^{7}\right)} {\left| a c^{2} d^{4} e - 2 \, a^{2} c d^{2} e^{3} + a^{3} e^{5} \right|} {\left| c \right|} - 2 \, {\left(a c^{6} d^{12} e - 8 \, a^{2} c^{5} d^{10} e^{3} + 22 \, a^{3} c^{4} d^{8} e^{5} - 28 \, a^{4} c^{3} d^{6} e^{7} + 17 \, a^{5} c^{2} d^{4} e^{9} - 4 \, a^{6} c d^{2} e^{11}\right)} {\left| c \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a c^{3} d^{5} - 2 \, a^{2} c^{2} d^{3} e^{2} + a^{3} c d e^{4} - \sqrt{{\left(a c^{3} d^{5} - 2 \, a^{2} c^{2} d^{3} e^{2} + a^{3} c d e^{4}\right)}^{2} - {\left(a c^{3} d^{6} - 3 \, a^{2} c^{2} d^{4} e^{2} + 3 \, a^{3} c d^{2} e^{4} - a^{4} e^{6}\right)} {\left(a c^{3} d^{4} - 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)}}}{a c^{3} d^{4} - 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}}}}\right)}{4 \, {\left(a^{2} c^{4} d^{8} e + \sqrt{a c} a c^{4} d^{9} - 4 \, \sqrt{a c} a^{2} c^{3} d^{7} e^{2} - 4 \, a^{3} c^{3} d^{6} e^{3} + 6 \, \sqrt{a c} a^{3} c^{2} d^{5} e^{4} + 6 \, a^{4} c^{2} d^{4} e^{5} - 4 \, \sqrt{a c} a^{4} c d^{3} e^{6} - 4 \, a^{5} c d^{2} e^{7} + \sqrt{a c} a^{5} d e^{8} + a^{6} e^{9}\right)} \sqrt{-c^{2} d + \sqrt{a c} c e} {\left| a c^{2} d^{4} e - 2 \, a^{2} c d^{2} e^{3} + a^{3} e^{5} \right|}} - \frac{{\left(x e + d\right)}^{2} c^{2} d^{2} e - {\left(x e + d\right)} c^{2} d^{3} e + 5 \, {\left(x e + d\right)}^{2} a c e^{3} - 11 \, {\left(x e + d\right)} a c d e^{3} + 4 \, a c d^{2} e^{3} - 4 \, a^{2} e^{5}}{2 \, {\left(a c^{2} d^{4} - 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} {\left({\left(x e + d\right)}^{\frac{5}{2}} c - 2 \, {\left(x e + d\right)}^{\frac{3}{2}} c d + \sqrt{x e + d} c d^{2} - \sqrt{x e + d} a e^{2}\right)}}"," ",0,"-1/4*((a*c^2*d^4*e - 2*a^2*c*d^2*e^3 + a^3*e^5)^2*(c*d^2*e + 5*a*e^3)*abs(c) + (sqrt(a*c)*c^3*d^7*e - 15*sqrt(a*c)*a*c^2*d^5*e^3 + 27*sqrt(a*c)*a^2*c*d^3*e^5 - 13*sqrt(a*c)*a^3*d*e^7)*abs(a*c^2*d^4*e - 2*a^2*c*d^2*e^3 + a^3*e^5)*abs(c) - 2*(a*c^6*d^12*e - 8*a^2*c^5*d^10*e^3 + 22*a^3*c^4*d^8*e^5 - 28*a^4*c^3*d^6*e^7 + 17*a^5*c^2*d^4*e^9 - 4*a^6*c*d^2*e^11)*abs(c))*arctan(sqrt(x*e + d)/sqrt(-(a*c^3*d^5 - 2*a^2*c^2*d^3*e^2 + a^3*c*d*e^4 + sqrt((a*c^3*d^5 - 2*a^2*c^2*d^3*e^2 + a^3*c*d*e^4)^2 - (a*c^3*d^6 - 3*a^2*c^2*d^4*e^2 + 3*a^3*c*d^2*e^4 - a^4*e^6)*(a*c^3*d^4 - 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)))/(a*c^3*d^4 - 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)))/((a^2*c^4*d^8*e - sqrt(a*c)*a*c^4*d^9 + 4*sqrt(a*c)*a^2*c^3*d^7*e^2 - 4*a^3*c^3*d^6*e^3 - 6*sqrt(a*c)*a^3*c^2*d^5*e^4 + 6*a^4*c^2*d^4*e^5 + 4*sqrt(a*c)*a^4*c*d^3*e^6 - 4*a^5*c*d^2*e^7 - sqrt(a*c)*a^5*d*e^8 + a^6*e^9)*sqrt(-c^2*d - sqrt(a*c)*c*e)*abs(a*c^2*d^4*e - 2*a^2*c*d^2*e^3 + a^3*e^5)) - 1/4*((a*c^2*d^4*e - 2*a^2*c*d^2*e^3 + a^3*e^5)^2*(c*d^2*e + 5*a*e^3)*abs(c) - (sqrt(a*c)*c^3*d^7*e - 15*sqrt(a*c)*a*c^2*d^5*e^3 + 27*sqrt(a*c)*a^2*c*d^3*e^5 - 13*sqrt(a*c)*a^3*d*e^7)*abs(a*c^2*d^4*e - 2*a^2*c*d^2*e^3 + a^3*e^5)*abs(c) - 2*(a*c^6*d^12*e - 8*a^2*c^5*d^10*e^3 + 22*a^3*c^4*d^8*e^5 - 28*a^4*c^3*d^6*e^7 + 17*a^5*c^2*d^4*e^9 - 4*a^6*c*d^2*e^11)*abs(c))*arctan(sqrt(x*e + d)/sqrt(-(a*c^3*d^5 - 2*a^2*c^2*d^3*e^2 + a^3*c*d*e^4 - sqrt((a*c^3*d^5 - 2*a^2*c^2*d^3*e^2 + a^3*c*d*e^4)^2 - (a*c^3*d^6 - 3*a^2*c^2*d^4*e^2 + 3*a^3*c*d^2*e^4 - a^4*e^6)*(a*c^3*d^4 - 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)))/(a*c^3*d^4 - 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)))/((a^2*c^4*d^8*e + sqrt(a*c)*a*c^4*d^9 - 4*sqrt(a*c)*a^2*c^3*d^7*e^2 - 4*a^3*c^3*d^6*e^3 + 6*sqrt(a*c)*a^3*c^2*d^5*e^4 + 6*a^4*c^2*d^4*e^5 - 4*sqrt(a*c)*a^4*c*d^3*e^6 - 4*a^5*c*d^2*e^7 + sqrt(a*c)*a^5*d*e^8 + a^6*e^9)*sqrt(-c^2*d + sqrt(a*c)*c*e)*abs(a*c^2*d^4*e - 2*a^2*c*d^2*e^3 + a^3*e^5)) - 1/2*((x*e + d)^2*c^2*d^2*e - (x*e + d)*c^2*d^3*e + 5*(x*e + d)^2*a*c*e^3 - 11*(x*e + d)*a*c*d*e^3 + 4*a*c*d^2*e^3 - 4*a^2*e^5)/((a*c^2*d^4 - 2*a^2*c*d^2*e^2 + a^3*e^4)*((x*e + d)^(5/2)*c - 2*(x*e + d)^(3/2)*c*d + sqrt(x*e + d)*c*d^2 - sqrt(x*e + d)*a*e^2))","B",0
630,1,1872,0,1.314498," ","integrate(1/(e*x+d)^(5/2)/(-c*x^2+a)^2,x, algorithm=""giac"")","\frac{{\left({\left(a c^{3} d^{6} e - 3 \, a^{2} c^{2} d^{4} e^{3} + 3 \, a^{3} c d^{2} e^{5} - a^{4} e^{7}\right)}^{2} {\left(\sqrt{a c} c d^{3} e + 19 \, \sqrt{a c} a d e^{3}\right)} \sqrt{-c^{2} d + \sqrt{a c} c e} {\left| c \right|} - {\left(a c^{5} d^{10} e - 37 \, a^{2} c^{4} d^{8} e^{3} + 98 \, a^{3} c^{3} d^{6} e^{5} - 82 \, a^{4} c^{2} d^{4} e^{7} + 13 \, a^{5} c d^{2} e^{9} + 7 \, a^{6} e^{11}\right)} \sqrt{-c^{2} d + \sqrt{a c} c e} {\left| a c^{3} d^{6} e - 3 \, a^{2} c^{2} d^{4} e^{3} + 3 \, a^{3} c d^{2} e^{5} - a^{4} e^{7} \right|} {\left| c \right|} - {\left(2 \, \sqrt{a c} a c^{8} d^{17} e - 27 \, \sqrt{a c} a^{2} c^{7} d^{15} e^{3} + 113 \, \sqrt{a c} a^{3} c^{6} d^{13} e^{5} - 223 \, \sqrt{a c} a^{4} c^{5} d^{11} e^{7} + 225 \, \sqrt{a c} a^{5} c^{4} d^{9} e^{9} - 97 \, \sqrt{a c} a^{6} c^{3} d^{7} e^{11} - 13 \, \sqrt{a c} a^{7} c^{2} d^{5} e^{13} + 27 \, \sqrt{a c} a^{8} c d^{3} e^{15} - 7 \, \sqrt{a c} a^{9} d e^{17}\right)} \sqrt{-c^{2} d + \sqrt{a c} c e} {\left| c \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a c^{4} d^{7} - 3 \, a^{2} c^{3} d^{5} e^{2} + 3 \, a^{3} c^{2} d^{3} e^{4} - a^{4} c d e^{6} - \sqrt{{\left(a c^{4} d^{7} - 3 \, a^{2} c^{3} d^{5} e^{2} + 3 \, a^{3} c^{2} d^{3} e^{4} - a^{4} c d e^{6}\right)}^{2} - {\left(a c^{4} d^{8} - 4 \, a^{2} c^{3} d^{6} e^{2} + 6 \, a^{3} c^{2} d^{4} e^{4} - 4 \, a^{4} c d^{2} e^{6} + a^{5} e^{8}\right)} {\left(a c^{4} d^{6} - 3 \, a^{2} c^{3} d^{4} e^{2} + 3 \, a^{3} c^{2} d^{2} e^{4} - a^{4} c e^{6}\right)}}}{a c^{4} d^{6} - 3 \, a^{2} c^{3} d^{4} e^{2} + 3 \, a^{3} c^{2} d^{2} e^{4} - a^{4} c e^{6}}}}\right)}{4 \, {\left(a^{2} c^{8} d^{14} - 7 \, a^{3} c^{7} d^{12} e^{2} + 21 \, a^{4} c^{6} d^{10} e^{4} - 35 \, a^{5} c^{5} d^{8} e^{6} + 35 \, a^{6} c^{4} d^{6} e^{8} - 21 \, a^{7} c^{3} d^{4} e^{10} + 7 \, a^{8} c^{2} d^{2} e^{12} - a^{9} c e^{14}\right)} {\left| a c^{3} d^{6} e - 3 \, a^{2} c^{2} d^{4} e^{3} + 3 \, a^{3} c d^{2} e^{5} - a^{4} e^{7} \right|}} - \frac{{\left({\left(a c^{3} d^{6} e - 3 \, a^{2} c^{2} d^{4} e^{3} + 3 \, a^{3} c d^{2} e^{5} - a^{4} e^{7}\right)}^{2} {\left(c^{2} d^{3} e + 19 \, a c d e^{3}\right)} {\left| c \right|} + {\left(\sqrt{a c} c^{5} d^{10} e - 37 \, \sqrt{a c} a c^{4} d^{8} e^{3} + 98 \, \sqrt{a c} a^{2} c^{3} d^{6} e^{5} - 82 \, \sqrt{a c} a^{3} c^{2} d^{4} e^{7} + 13 \, \sqrt{a c} a^{4} c d^{2} e^{9} + 7 \, \sqrt{a c} a^{5} e^{11}\right)} {\left| a c^{3} d^{6} e - 3 \, a^{2} c^{2} d^{4} e^{3} + 3 \, a^{3} c d^{2} e^{5} - a^{4} e^{7} \right|} {\left| c \right|} - {\left(2 \, a c^{9} d^{17} e - 27 \, a^{2} c^{8} d^{15} e^{3} + 113 \, a^{3} c^{7} d^{13} e^{5} - 223 \, a^{4} c^{6} d^{11} e^{7} + 225 \, a^{5} c^{5} d^{9} e^{9} - 97 \, a^{6} c^{4} d^{7} e^{11} - 13 \, a^{7} c^{3} d^{5} e^{13} + 27 \, a^{8} c^{2} d^{3} e^{15} - 7 \, a^{9} c d e^{17}\right)} {\left| c \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a c^{4} d^{7} - 3 \, a^{2} c^{3} d^{5} e^{2} + 3 \, a^{3} c^{2} d^{3} e^{4} - a^{4} c d e^{6} + \sqrt{{\left(a c^{4} d^{7} - 3 \, a^{2} c^{3} d^{5} e^{2} + 3 \, a^{3} c^{2} d^{3} e^{4} - a^{4} c d e^{6}\right)}^{2} - {\left(a c^{4} d^{8} - 4 \, a^{2} c^{3} d^{6} e^{2} + 6 \, a^{3} c^{2} d^{4} e^{4} - 4 \, a^{4} c d^{2} e^{6} + a^{5} e^{8}\right)} {\left(a c^{4} d^{6} - 3 \, a^{2} c^{3} d^{4} e^{2} + 3 \, a^{3} c^{2} d^{2} e^{4} - a^{4} c e^{6}\right)}}}{a c^{4} d^{6} - 3 \, a^{2} c^{3} d^{4} e^{2} + 3 \, a^{3} c^{2} d^{2} e^{4} - a^{4} c e^{6}}}}\right)}{4 \, {\left(a^{2} c^{6} d^{12} e - \sqrt{a c} a c^{6} d^{13} + 6 \, \sqrt{a c} a^{2} c^{5} d^{11} e^{2} - 6 \, a^{3} c^{5} d^{10} e^{3} - 15 \, \sqrt{a c} a^{3} c^{4} d^{9} e^{4} + 15 \, a^{4} c^{4} d^{8} e^{5} + 20 \, \sqrt{a c} a^{4} c^{3} d^{7} e^{6} - 20 \, a^{5} c^{3} d^{6} e^{7} - 15 \, \sqrt{a c} a^{5} c^{2} d^{5} e^{8} + 15 \, a^{6} c^{2} d^{4} e^{9} + 6 \, \sqrt{a c} a^{6} c d^{3} e^{10} - 6 \, a^{7} c d^{2} e^{11} - \sqrt{a c} a^{7} d e^{12} + a^{8} e^{13}\right)} \sqrt{-c^{2} d - \sqrt{a c} c e} {\left| a c^{3} d^{6} e - 3 \, a^{2} c^{2} d^{4} e^{3} + 3 \, a^{3} c d^{2} e^{5} - a^{4} e^{7} \right|}} - \frac{{\left(x e + d\right)}^{\frac{3}{2}} c^{3} d^{3} e - \sqrt{x e + d} c^{3} d^{4} e + 3 \, {\left(x e + d\right)}^{\frac{3}{2}} a c^{2} d e^{3} - 6 \, \sqrt{x e + d} a c^{2} d^{2} e^{3} - \sqrt{x e + d} a^{2} c e^{5}}{2 \, {\left(a c^{3} d^{6} - 3 \, a^{2} c^{2} d^{4} e^{2} + 3 \, a^{3} c d^{2} e^{4} - a^{4} e^{6}\right)} {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} - a e^{2}\right)}} - \frac{2 \, {\left(12 \, {\left(x e + d\right)} c d e^{3} + c d^{2} e^{3} - a e^{5}\right)}}{3 \, {\left(c^{3} d^{6} - 3 \, a c^{2} d^{4} e^{2} + 3 \, a^{2} c d^{2} e^{4} - a^{3} e^{6}\right)} {\left(x e + d\right)}^{\frac{3}{2}}}"," ",0,"1/4*((a*c^3*d^6*e - 3*a^2*c^2*d^4*e^3 + 3*a^3*c*d^2*e^5 - a^4*e^7)^2*(sqrt(a*c)*c*d^3*e + 19*sqrt(a*c)*a*d*e^3)*sqrt(-c^2*d + sqrt(a*c)*c*e)*abs(c) - (a*c^5*d^10*e - 37*a^2*c^4*d^8*e^3 + 98*a^3*c^3*d^6*e^5 - 82*a^4*c^2*d^4*e^7 + 13*a^5*c*d^2*e^9 + 7*a^6*e^11)*sqrt(-c^2*d + sqrt(a*c)*c*e)*abs(a*c^3*d^6*e - 3*a^2*c^2*d^4*e^3 + 3*a^3*c*d^2*e^5 - a^4*e^7)*abs(c) - (2*sqrt(a*c)*a*c^8*d^17*e - 27*sqrt(a*c)*a^2*c^7*d^15*e^3 + 113*sqrt(a*c)*a^3*c^6*d^13*e^5 - 223*sqrt(a*c)*a^4*c^5*d^11*e^7 + 225*sqrt(a*c)*a^5*c^4*d^9*e^9 - 97*sqrt(a*c)*a^6*c^3*d^7*e^11 - 13*sqrt(a*c)*a^7*c^2*d^5*e^13 + 27*sqrt(a*c)*a^8*c*d^3*e^15 - 7*sqrt(a*c)*a^9*d*e^17)*sqrt(-c^2*d + sqrt(a*c)*c*e)*abs(c))*arctan(sqrt(x*e + d)/sqrt(-(a*c^4*d^7 - 3*a^2*c^3*d^5*e^2 + 3*a^3*c^2*d^3*e^4 - a^4*c*d*e^6 - sqrt((a*c^4*d^7 - 3*a^2*c^3*d^5*e^2 + 3*a^3*c^2*d^3*e^4 - a^4*c*d*e^6)^2 - (a*c^4*d^8 - 4*a^2*c^3*d^6*e^2 + 6*a^3*c^2*d^4*e^4 - 4*a^4*c*d^2*e^6 + a^5*e^8)*(a*c^4*d^6 - 3*a^2*c^3*d^4*e^2 + 3*a^3*c^2*d^2*e^4 - a^4*c*e^6)))/(a*c^4*d^6 - 3*a^2*c^3*d^4*e^2 + 3*a^3*c^2*d^2*e^4 - a^4*c*e^6)))/((a^2*c^8*d^14 - 7*a^3*c^7*d^12*e^2 + 21*a^4*c^6*d^10*e^4 - 35*a^5*c^5*d^8*e^6 + 35*a^6*c^4*d^6*e^8 - 21*a^7*c^3*d^4*e^10 + 7*a^8*c^2*d^2*e^12 - a^9*c*e^14)*abs(a*c^3*d^6*e - 3*a^2*c^2*d^4*e^3 + 3*a^3*c*d^2*e^5 - a^4*e^7)) - 1/4*((a*c^3*d^6*e - 3*a^2*c^2*d^4*e^3 + 3*a^3*c*d^2*e^5 - a^4*e^7)^2*(c^2*d^3*e + 19*a*c*d*e^3)*abs(c) + (sqrt(a*c)*c^5*d^10*e - 37*sqrt(a*c)*a*c^4*d^8*e^3 + 98*sqrt(a*c)*a^2*c^3*d^6*e^5 - 82*sqrt(a*c)*a^3*c^2*d^4*e^7 + 13*sqrt(a*c)*a^4*c*d^2*e^9 + 7*sqrt(a*c)*a^5*e^11)*abs(a*c^3*d^6*e - 3*a^2*c^2*d^4*e^3 + 3*a^3*c*d^2*e^5 - a^4*e^7)*abs(c) - (2*a*c^9*d^17*e - 27*a^2*c^8*d^15*e^3 + 113*a^3*c^7*d^13*e^5 - 223*a^4*c^6*d^11*e^7 + 225*a^5*c^5*d^9*e^9 - 97*a^6*c^4*d^7*e^11 - 13*a^7*c^3*d^5*e^13 + 27*a^8*c^2*d^3*e^15 - 7*a^9*c*d*e^17)*abs(c))*arctan(sqrt(x*e + d)/sqrt(-(a*c^4*d^7 - 3*a^2*c^3*d^5*e^2 + 3*a^3*c^2*d^3*e^4 - a^4*c*d*e^6 + sqrt((a*c^4*d^7 - 3*a^2*c^3*d^5*e^2 + 3*a^3*c^2*d^3*e^4 - a^4*c*d*e^6)^2 - (a*c^4*d^8 - 4*a^2*c^3*d^6*e^2 + 6*a^3*c^2*d^4*e^4 - 4*a^4*c*d^2*e^6 + a^5*e^8)*(a*c^4*d^6 - 3*a^2*c^3*d^4*e^2 + 3*a^3*c^2*d^2*e^4 - a^4*c*e^6)))/(a*c^4*d^6 - 3*a^2*c^3*d^4*e^2 + 3*a^3*c^2*d^2*e^4 - a^4*c*e^6)))/((a^2*c^6*d^12*e - sqrt(a*c)*a*c^6*d^13 + 6*sqrt(a*c)*a^2*c^5*d^11*e^2 - 6*a^3*c^5*d^10*e^3 - 15*sqrt(a*c)*a^3*c^4*d^9*e^4 + 15*a^4*c^4*d^8*e^5 + 20*sqrt(a*c)*a^4*c^3*d^7*e^6 - 20*a^5*c^3*d^6*e^7 - 15*sqrt(a*c)*a^5*c^2*d^5*e^8 + 15*a^6*c^2*d^4*e^9 + 6*sqrt(a*c)*a^6*c*d^3*e^10 - 6*a^7*c*d^2*e^11 - sqrt(a*c)*a^7*d*e^12 + a^8*e^13)*sqrt(-c^2*d - sqrt(a*c)*c*e)*abs(a*c^3*d^6*e - 3*a^2*c^2*d^4*e^3 + 3*a^3*c*d^2*e^5 - a^4*e^7)) - 1/2*((x*e + d)^(3/2)*c^3*d^3*e - sqrt(x*e + d)*c^3*d^4*e + 3*(x*e + d)^(3/2)*a*c^2*d*e^3 - 6*sqrt(x*e + d)*a*c^2*d^2*e^3 - sqrt(x*e + d)*a^2*c*e^5)/((a*c^3*d^6 - 3*a^2*c^2*d^4*e^2 + 3*a^3*c*d^2*e^4 - a^4*e^6)*((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 - a*e^2)) - 2/3*(12*(x*e + d)*c*d*e^3 + c*d^2*e^3 - a*e^5)/((c^3*d^6 - 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4 - a^3*e^6)*(x*e + d)^(3/2))","B",0
631,1,581,0,0.669134," ","integrate((e*x+d)^(7/2)/(c*x^2+a)^2,x, algorithm=""giac"")","-\frac{{\left({\left(c^{2} d^{3} e^{2} + 13 \, a c d e^{4}\right)} a^{2} {\left| c \right|} - {\left(\sqrt{-a c} c^{2} d^{4} e - 4 \, \sqrt{-a c} a c d^{2} e^{3} - 5 \, \sqrt{-a c} a^{2} e^{5}\right)} {\left| a \right|} {\left| c \right|} + {\left(2 \, a c^{3} d^{5} + 9 \, a^{2} c^{2} d^{3} e^{2} - 5 \, a^{3} c d e^{4}\right)} {\left| c \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a c^{3} d + \sqrt{a^{2} c^{6} d^{2} - {\left(a c^{3} d^{2} + a^{2} c^{2} e^{2}\right)} a c^{3}}}{a c^{3}}}}\right)}{4 \, {\left(a^{2} c^{3} e - \sqrt{-a c} a c^{3} d\right)} \sqrt{-c^{2} d + \sqrt{-a c} c e} {\left| a \right|}} + \frac{{\left({\left(\sqrt{-a c} c d^{3} e^{2} + 13 \, \sqrt{-a c} a d e^{4}\right)} a^{2} {\left| c \right|} - {\left(a c^{2} d^{4} e - 4 \, a^{2} c d^{2} e^{3} - 5 \, a^{3} e^{5}\right)} {\left| a \right|} {\left| c \right|} + {\left(2 \, \sqrt{-a c} a c^{2} d^{5} + 9 \, \sqrt{-a c} a^{2} c d^{3} e^{2} - 5 \, \sqrt{-a c} a^{3} d e^{4}\right)} {\left| c \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a c^{3} d - \sqrt{a^{2} c^{6} d^{2} - {\left(a c^{3} d^{2} + a^{2} c^{2} e^{2}\right)} a c^{3}}}{a c^{3}}}}\right)}{4 \, {\left(a^{2} c^{3} d - \sqrt{-a c} a^{2} c^{2} e\right)} \sqrt{-c^{2} d - \sqrt{-a c} c e} {\left| a \right|}} + \frac{2 \, \sqrt{x e + d} e^{3}}{c^{2}} + \frac{{\left(x e + d\right)}^{\frac{3}{2}} c^{2} d^{3} e - \sqrt{x e + d} c^{2} d^{4} e - 3 \, {\left(x e + d\right)}^{\frac{3}{2}} a c d e^{3} + \sqrt{x e + d} a^{2} e^{5}}{2 \, {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + a e^{2}\right)} a c^{2}}"," ",0,"-1/4*((c^2*d^3*e^2 + 13*a*c*d*e^4)*a^2*abs(c) - (sqrt(-a*c)*c^2*d^4*e - 4*sqrt(-a*c)*a*c*d^2*e^3 - 5*sqrt(-a*c)*a^2*e^5)*abs(a)*abs(c) + (2*a*c^3*d^5 + 9*a^2*c^2*d^3*e^2 - 5*a^3*c*d*e^4)*abs(c))*arctan(sqrt(x*e + d)/sqrt(-(a*c^3*d + sqrt(a^2*c^6*d^2 - (a*c^3*d^2 + a^2*c^2*e^2)*a*c^3))/(a*c^3)))/((a^2*c^3*e - sqrt(-a*c)*a*c^3*d)*sqrt(-c^2*d + sqrt(-a*c)*c*e)*abs(a)) + 1/4*((sqrt(-a*c)*c*d^3*e^2 + 13*sqrt(-a*c)*a*d*e^4)*a^2*abs(c) - (a*c^2*d^4*e - 4*a^2*c*d^2*e^3 - 5*a^3*e^5)*abs(a)*abs(c) + (2*sqrt(-a*c)*a*c^2*d^5 + 9*sqrt(-a*c)*a^2*c*d^3*e^2 - 5*sqrt(-a*c)*a^3*d*e^4)*abs(c))*arctan(sqrt(x*e + d)/sqrt(-(a*c^3*d - sqrt(a^2*c^6*d^2 - (a*c^3*d^2 + a^2*c^2*e^2)*a*c^3))/(a*c^3)))/((a^2*c^3*d - sqrt(-a*c)*a^2*c^2*e)*sqrt(-c^2*d - sqrt(-a*c)*c*e)*abs(a)) + 2*sqrt(x*e + d)*e^3/c^2 + 1/2*((x*e + d)^(3/2)*c^2*d^3*e - sqrt(x*e + d)*c^2*d^4*e - 3*(x*e + d)^(3/2)*a*c*d*e^3 + sqrt(x*e + d)*a^2*e^5)/(((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + a*e^2)*a*c^2)","A",0
632,1,479,0,0.581809," ","integrate((e*x+d)^(5/2)/(c*x^2+a)^2,x, algorithm=""giac"")","-\frac{{\left(2 \, a c^{4} d^{4} + 4 \, a^{2} c^{3} d^{2} e^{2} + {\left(c d^{2} e^{2} + 3 \, a e^{4}\right)} a^{2} c^{2} - {\left(\sqrt{-a c} c^{2} d^{3} e + \sqrt{-a c} a c d e^{3}\right)} {\left| a \right|} {\left| c \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a c^{2} d + \sqrt{a^{2} c^{4} d^{2} - {\left(a c^{2} d^{2} + a^{2} c e^{2}\right)} a c^{2}}}{a c^{2}}}}\right)}{4 \, {\left(a^{2} c^{3} e - \sqrt{-a c} a c^{3} d\right)} \sqrt{-c^{2} d + \sqrt{-a c} c e} {\left| a \right|}} - \frac{{\left(2 \, a c^{4} d^{4} + 4 \, a^{2} c^{3} d^{2} e^{2} + {\left(c d^{2} e^{2} + 3 \, a e^{4}\right)} a^{2} c^{2} + {\left(\sqrt{-a c} c^{2} d^{3} e + \sqrt{-a c} a c d e^{3}\right)} {\left| a \right|} {\left| c \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a c^{2} d - \sqrt{a^{2} c^{4} d^{2} - {\left(a c^{2} d^{2} + a^{2} c e^{2}\right)} a c^{2}}}{a c^{2}}}}\right)}{4 \, {\left(a^{2} c^{3} e + \sqrt{-a c} a c^{3} d\right)} \sqrt{-c^{2} d - \sqrt{-a c} c e} {\left| a \right|}} + \frac{{\left(x e + d\right)}^{\frac{3}{2}} c d^{2} e - \sqrt{x e + d} c d^{3} e - {\left(x e + d\right)}^{\frac{3}{2}} a e^{3} - \sqrt{x e + d} a d e^{3}}{2 \, {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + a e^{2}\right)} a c}"," ",0,"-1/4*(2*a*c^4*d^4 + 4*a^2*c^3*d^2*e^2 + (c*d^2*e^2 + 3*a*e^4)*a^2*c^2 - (sqrt(-a*c)*c^2*d^3*e + sqrt(-a*c)*a*c*d*e^3)*abs(a)*abs(c))*arctan(sqrt(x*e + d)/sqrt(-(a*c^2*d + sqrt(a^2*c^4*d^2 - (a*c^2*d^2 + a^2*c*e^2)*a*c^2))/(a*c^2)))/((a^2*c^3*e - sqrt(-a*c)*a*c^3*d)*sqrt(-c^2*d + sqrt(-a*c)*c*e)*abs(a)) - 1/4*(2*a*c^4*d^4 + 4*a^2*c^3*d^2*e^2 + (c*d^2*e^2 + 3*a*e^4)*a^2*c^2 + (sqrt(-a*c)*c^2*d^3*e + sqrt(-a*c)*a*c*d*e^3)*abs(a)*abs(c))*arctan(sqrt(x*e + d)/sqrt(-(a*c^2*d - sqrt(a^2*c^4*d^2 - (a*c^2*d^2 + a^2*c*e^2)*a*c^2))/(a*c^2)))/((a^2*c^3*e + sqrt(-a*c)*a*c^3*d)*sqrt(-c^2*d - sqrt(-a*c)*c*e)*abs(a)) + 1/2*((x*e + d)^(3/2)*c*d^2*e - sqrt(x*e + d)*c*d^3*e - (x*e + d)^(3/2)*a*e^3 - sqrt(x*e + d)*a*d*e^3)/(((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + a*e^2)*a*c)","A",0
633,1,411,0,0.560119," ","integrate((e*x+d)^(3/2)/(c*x^2+a)^2,x, algorithm=""giac"")","-\frac{{\left(2 \, a c^{3} d^{3} + 2 \, a^{2} c^{2} d e^{2} - {\left(\sqrt{-a c} c d^{2} e + \sqrt{-a c} a e^{3}\right)} {\left| a \right|} {\left| c \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a c^{2} d + \sqrt{a^{2} c^{4} d^{2} - {\left(a c^{2} d^{2} + a^{2} c e^{2}\right)} a c^{2}}}{a c^{2}}}}\right)}{4 \, {\left(a^{2} c^{2} e - \sqrt{-a c} a c^{2} d\right)} \sqrt{-c^{2} d + \sqrt{-a c} c e} {\left| a \right|}} - \frac{{\left(2 \, a c^{3} d^{3} + 2 \, a^{2} c^{2} d e^{2} + {\left(\sqrt{-a c} c d^{2} e + \sqrt{-a c} a e^{3}\right)} {\left| a \right|} {\left| c \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a c^{2} d - \sqrt{a^{2} c^{4} d^{2} - {\left(a c^{2} d^{2} + a^{2} c e^{2}\right)} a c^{2}}}{a c^{2}}}}\right)}{4 \, {\left(a^{2} c^{2} e + \sqrt{-a c} a c^{2} d\right)} \sqrt{-c^{2} d - \sqrt{-a c} c e} {\left| a \right|}} + \frac{{\left(x e + d\right)}^{\frac{3}{2}} c d e - \sqrt{x e + d} c d^{2} e - \sqrt{x e + d} a e^{3}}{2 \, {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + a e^{2}\right)} a c}"," ",0,"-1/4*(2*a*c^3*d^3 + 2*a^2*c^2*d*e^2 - (sqrt(-a*c)*c*d^2*e + sqrt(-a*c)*a*e^3)*abs(a)*abs(c))*arctan(sqrt(x*e + d)/sqrt(-(a*c^2*d + sqrt(a^2*c^4*d^2 - (a*c^2*d^2 + a^2*c*e^2)*a*c^2))/(a*c^2)))/((a^2*c^2*e - sqrt(-a*c)*a*c^2*d)*sqrt(-c^2*d + sqrt(-a*c)*c*e)*abs(a)) - 1/4*(2*a*c^3*d^3 + 2*a^2*c^2*d*e^2 + (sqrt(-a*c)*c*d^2*e + sqrt(-a*c)*a*e^3)*abs(a)*abs(c))*arctan(sqrt(x*e + d)/sqrt(-(a*c^2*d - sqrt(a^2*c^4*d^2 - (a*c^2*d^2 + a^2*c*e^2)*a*c^2))/(a*c^2)))/((a^2*c^2*e + sqrt(-a*c)*a*c^2*d)*sqrt(-c^2*d - sqrt(-a*c)*c*e)*abs(a)) + 1/2*((x*e + d)^(3/2)*c*d*e - sqrt(x*e + d)*c*d^2*e - sqrt(x*e + d)*a*e^3)/(((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + a*e^2)*a*c)","A",0
634,1,332,0,0.494404," ","integrate((e*x+d)^(1/2)/(c*x^2+a)^2,x, algorithm=""giac"")","-\frac{{\left(2 \, a c d^{2} {\left| c \right|} - \sqrt{-a c} d {\left| a \right|} {\left| c \right|} e + a^{2} {\left| c \right|} e^{2}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a c d + \sqrt{a^{2} c^{2} d^{2} - {\left(a c d^{2} + a^{2} e^{2}\right)} a c}}{a c}}}\right)}{4 \, {\left(a^{2} c e - \sqrt{-a c} a c d\right)} \sqrt{-c^{2} d + \sqrt{-a c} c e} {\left| a \right|}} - \frac{{\left(2 \, a c d^{2} {\left| c \right|} + \sqrt{-a c} d {\left| a \right|} {\left| c \right|} e + a^{2} {\left| c \right|} e^{2}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a c d - \sqrt{a^{2} c^{2} d^{2} - {\left(a c d^{2} + a^{2} e^{2}\right)} a c}}{a c}}}\right)}{4 \, {\left(a^{2} c e + \sqrt{-a c} a c d\right)} \sqrt{-c^{2} d - \sqrt{-a c} c e} {\left| a \right|}} + \frac{{\left(x e + d\right)}^{\frac{3}{2}} e - \sqrt{x e + d} d e}{2 \, {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + a e^{2}\right)} a}"," ",0,"-1/4*(2*a*c*d^2*abs(c) - sqrt(-a*c)*d*abs(a)*abs(c)*e + a^2*abs(c)*e^2)*arctan(sqrt(x*e + d)/sqrt(-(a*c*d + sqrt(a^2*c^2*d^2 - (a*c*d^2 + a^2*e^2)*a*c))/(a*c)))/((a^2*c*e - sqrt(-a*c)*a*c*d)*sqrt(-c^2*d + sqrt(-a*c)*c*e)*abs(a)) - 1/4*(2*a*c*d^2*abs(c) + sqrt(-a*c)*d*abs(a)*abs(c)*e + a^2*abs(c)*e^2)*arctan(sqrt(x*e + d)/sqrt(-(a*c*d - sqrt(a^2*c^2*d^2 - (a*c*d^2 + a^2*e^2)*a*c))/(a*c)))/((a^2*c*e + sqrt(-a*c)*a*c*d)*sqrt(-c^2*d - sqrt(-a*c)*c*e)*abs(a)) + 1/2*((x*e + d)^(3/2)*e - sqrt(x*e + d)*d*e)/(((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + a*e^2)*a)","A",0
635,1,861,0,0.950721," ","integrate(1/(c*x^2+a)^2/(e*x+d)^(1/2),x, algorithm=""giac"")","-\frac{{\left({\left(a c d^{2} e + a^{2} e^{3}\right)}^{2} \sqrt{-a c} d {\left| c \right|} e + {\left(a c^{2} d^{4} e + 4 \, a^{2} c d^{2} e^{3} + 3 \, a^{3} e^{5}\right)} {\left| -a c d^{2} e - a^{2} e^{3} \right|} {\left| c \right|} + {\left(2 \, \sqrt{-a c} a c^{3} d^{7} e + 7 \, \sqrt{-a c} a^{2} c^{2} d^{5} e^{3} + 8 \, \sqrt{-a c} a^{3} c d^{3} e^{5} + 3 \, \sqrt{-a c} a^{4} d e^{7}\right)} {\left| c \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a c^{2} d^{3} + a^{2} c d e^{2} + \sqrt{{\left(a c^{2} d^{3} + a^{2} c d e^{2}\right)}^{2} - {\left(a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} {\left(a c^{2} d^{2} + a^{2} c e^{2}\right)}}}{a c^{2} d^{2} + a^{2} c e^{2}}}}\right)}{4 \, {\left(a^{2} c^{3} d^{5} + \sqrt{-a c} a^{2} c^{2} d^{4} e + 2 \, a^{3} c^{2} d^{3} e^{2} + 2 \, \sqrt{-a c} a^{3} c d^{2} e^{3} + a^{4} c d e^{4} + \sqrt{-a c} a^{4} e^{5}\right)} \sqrt{-c^{2} d + \sqrt{-a c} c e} {\left| -a c d^{2} e - a^{2} e^{3} \right|}} - \frac{{\left({\left(a c d^{2} e + a^{2} e^{3}\right)}^{2} c d {\left| c \right|} e + {\left(\sqrt{-a c} c^{2} d^{4} e + 4 \, \sqrt{-a c} a c d^{2} e^{3} + 3 \, \sqrt{-a c} a^{2} e^{5}\right)} {\left| -a c d^{2} e - a^{2} e^{3} \right|} {\left| c \right|} + {\left(2 \, a c^{4} d^{7} e + 7 \, a^{2} c^{3} d^{5} e^{3} + 8 \, a^{3} c^{2} d^{3} e^{5} + 3 \, a^{4} c d e^{7}\right)} {\left| c \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a c^{2} d^{3} + a^{2} c d e^{2} - \sqrt{{\left(a c^{2} d^{3} + a^{2} c d e^{2}\right)}^{2} - {\left(a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} {\left(a c^{2} d^{2} + a^{2} c e^{2}\right)}}}{a c^{2} d^{2} + a^{2} c e^{2}}}}\right)}{4 \, {\left(a^{2} c^{3} d^{4} e + \sqrt{-a c} a c^{3} d^{5} + 2 \, \sqrt{-a c} a^{2} c^{2} d^{3} e^{2} + 2 \, a^{3} c^{2} d^{2} e^{3} + \sqrt{-a c} a^{3} c d e^{4} + a^{4} c e^{5}\right)} \sqrt{-c^{2} d - \sqrt{-a c} c e} {\left| -a c d^{2} e - a^{2} e^{3} \right|}} + \frac{{\left(x e + d\right)}^{\frac{3}{2}} c d e - \sqrt{x e + d} c d^{2} e + \sqrt{x e + d} a e^{3}}{2 \, {\left(a c d^{2} + a^{2} e^{2}\right)} {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + a e^{2}\right)}}"," ",0,"-1/4*((a*c*d^2*e + a^2*e^3)^2*sqrt(-a*c)*d*abs(c)*e + (a*c^2*d^4*e + 4*a^2*c*d^2*e^3 + 3*a^3*e^5)*abs(-a*c*d^2*e - a^2*e^3)*abs(c) + (2*sqrt(-a*c)*a*c^3*d^7*e + 7*sqrt(-a*c)*a^2*c^2*d^5*e^3 + 8*sqrt(-a*c)*a^3*c*d^3*e^5 + 3*sqrt(-a*c)*a^4*d*e^7)*abs(c))*arctan(sqrt(x*e + d)/sqrt(-(a*c^2*d^3 + a^2*c*d*e^2 + sqrt((a*c^2*d^3 + a^2*c*d*e^2)^2 - (a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4)*(a*c^2*d^2 + a^2*c*e^2)))/(a*c^2*d^2 + a^2*c*e^2)))/((a^2*c^3*d^5 + sqrt(-a*c)*a^2*c^2*d^4*e + 2*a^3*c^2*d^3*e^2 + 2*sqrt(-a*c)*a^3*c*d^2*e^3 + a^4*c*d*e^4 + sqrt(-a*c)*a^4*e^5)*sqrt(-c^2*d + sqrt(-a*c)*c*e)*abs(-a*c*d^2*e - a^2*e^3)) - 1/4*((a*c*d^2*e + a^2*e^3)^2*c*d*abs(c)*e + (sqrt(-a*c)*c^2*d^4*e + 4*sqrt(-a*c)*a*c*d^2*e^3 + 3*sqrt(-a*c)*a^2*e^5)*abs(-a*c*d^2*e - a^2*e^3)*abs(c) + (2*a*c^4*d^7*e + 7*a^2*c^3*d^5*e^3 + 8*a^3*c^2*d^3*e^5 + 3*a^4*c*d*e^7)*abs(c))*arctan(sqrt(x*e + d)/sqrt(-(a*c^2*d^3 + a^2*c*d*e^2 - sqrt((a*c^2*d^3 + a^2*c*d*e^2)^2 - (a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4)*(a*c^2*d^2 + a^2*c*e^2)))/(a*c^2*d^2 + a^2*c*e^2)))/((a^2*c^3*d^4*e + sqrt(-a*c)*a*c^3*d^5 + 2*sqrt(-a*c)*a^2*c^2*d^3*e^2 + 2*a^3*c^2*d^2*e^3 + sqrt(-a*c)*a^3*c*d*e^4 + a^4*c*e^5)*sqrt(-c^2*d - sqrt(-a*c)*c*e)*abs(-a*c*d^2*e - a^2*e^3)) + 1/2*((x*e + d)^(3/2)*c*d*e - sqrt(x*e + d)*c*d^2*e + sqrt(x*e + d)*a*e^3)/((a*c*d^2 + a^2*e^2)*((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + a*e^2))","A",0
636,1,1350,0,0.961470," ","integrate(1/(e*x+d)^(3/2)/(c*x^2+a)^2,x, algorithm=""giac"")","\frac{{\left({\left(a c^{2} d^{4} e + 2 \, a^{2} c d^{2} e^{3} + a^{3} e^{5}\right)}^{2} {\left(c d^{2} e - 5 \, a e^{3}\right)} {\left| c \right|} - {\left(\sqrt{-a c} c^{3} d^{7} e + 15 \, \sqrt{-a c} a c^{2} d^{5} e^{3} + 27 \, \sqrt{-a c} a^{2} c d^{3} e^{5} + 13 \, \sqrt{-a c} a^{3} d e^{7}\right)} {\left| a c^{2} d^{4} e + 2 \, a^{2} c d^{2} e^{3} + a^{3} e^{5} \right|} {\left| c \right|} + 2 \, {\left(a c^{6} d^{12} e + 8 \, a^{2} c^{5} d^{10} e^{3} + 22 \, a^{3} c^{4} d^{8} e^{5} + 28 \, a^{4} c^{3} d^{6} e^{7} + 17 \, a^{5} c^{2} d^{4} e^{9} + 4 \, a^{6} c d^{2} e^{11}\right)} {\left| c \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a c^{3} d^{5} + 2 \, a^{2} c^{2} d^{3} e^{2} + a^{3} c d e^{4} + \sqrt{{\left(a c^{3} d^{5} + 2 \, a^{2} c^{2} d^{3} e^{2} + a^{3} c d e^{4}\right)}^{2} - {\left(a c^{3} d^{6} + 3 \, a^{2} c^{2} d^{4} e^{2} + 3 \, a^{3} c d^{2} e^{4} + a^{4} e^{6}\right)} {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)}}}{a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}}}}\right)}{4 \, {\left(a^{2} c^{4} d^{8} e + \sqrt{-a c} a c^{4} d^{9} + 4 \, \sqrt{-a c} a^{2} c^{3} d^{7} e^{2} + 4 \, a^{3} c^{3} d^{6} e^{3} + 6 \, \sqrt{-a c} a^{3} c^{2} d^{5} e^{4} + 6 \, a^{4} c^{2} d^{4} e^{5} + 4 \, \sqrt{-a c} a^{4} c d^{3} e^{6} + 4 \, a^{5} c d^{2} e^{7} + \sqrt{-a c} a^{5} d e^{8} + a^{6} e^{9}\right)} \sqrt{-c^{2} d - \sqrt{-a c} c e} {\left| a c^{2} d^{4} e + 2 \, a^{2} c d^{2} e^{3} + a^{3} e^{5} \right|}} + \frac{{\left({\left(a c^{2} d^{4} e + 2 \, a^{2} c d^{2} e^{3} + a^{3} e^{5}\right)}^{2} {\left(c d^{2} e - 5 \, a e^{3}\right)} {\left| c \right|} + {\left(\sqrt{-a c} c^{3} d^{7} e + 15 \, \sqrt{-a c} a c^{2} d^{5} e^{3} + 27 \, \sqrt{-a c} a^{2} c d^{3} e^{5} + 13 \, \sqrt{-a c} a^{3} d e^{7}\right)} {\left| a c^{2} d^{4} e + 2 \, a^{2} c d^{2} e^{3} + a^{3} e^{5} \right|} {\left| c \right|} + 2 \, {\left(a c^{6} d^{12} e + 8 \, a^{2} c^{5} d^{10} e^{3} + 22 \, a^{3} c^{4} d^{8} e^{5} + 28 \, a^{4} c^{3} d^{6} e^{7} + 17 \, a^{5} c^{2} d^{4} e^{9} + 4 \, a^{6} c d^{2} e^{11}\right)} {\left| c \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a c^{3} d^{5} + 2 \, a^{2} c^{2} d^{3} e^{2} + a^{3} c d e^{4} - \sqrt{{\left(a c^{3} d^{5} + 2 \, a^{2} c^{2} d^{3} e^{2} + a^{3} c d e^{4}\right)}^{2} - {\left(a c^{3} d^{6} + 3 \, a^{2} c^{2} d^{4} e^{2} + 3 \, a^{3} c d^{2} e^{4} + a^{4} e^{6}\right)} {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)}}}{a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}}}}\right)}{4 \, {\left(a^{2} c^{4} d^{8} e - \sqrt{-a c} a c^{4} d^{9} - 4 \, \sqrt{-a c} a^{2} c^{3} d^{7} e^{2} + 4 \, a^{3} c^{3} d^{6} e^{3} - 6 \, \sqrt{-a c} a^{3} c^{2} d^{5} e^{4} + 6 \, a^{4} c^{2} d^{4} e^{5} - 4 \, \sqrt{-a c} a^{4} c d^{3} e^{6} + 4 \, a^{5} c d^{2} e^{7} - \sqrt{-a c} a^{5} d e^{8} + a^{6} e^{9}\right)} \sqrt{-c^{2} d + \sqrt{-a c} c e} {\left| a c^{2} d^{4} e + 2 \, a^{2} c d^{2} e^{3} + a^{3} e^{5} \right|}} + \frac{{\left(x e + d\right)}^{2} c^{2} d^{2} e - {\left(x e + d\right)} c^{2} d^{3} e - 5 \, {\left(x e + d\right)}^{2} a c e^{3} + 11 \, {\left(x e + d\right)} a c d e^{3} - 4 \, a c d^{2} e^{3} - 4 \, a^{2} e^{5}}{2 \, {\left(a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} {\left({\left(x e + d\right)}^{\frac{5}{2}} c - 2 \, {\left(x e + d\right)}^{\frac{3}{2}} c d + \sqrt{x e + d} c d^{2} + \sqrt{x e + d} a e^{2}\right)}}"," ",0,"1/4*((a*c^2*d^4*e + 2*a^2*c*d^2*e^3 + a^3*e^5)^2*(c*d^2*e - 5*a*e^3)*abs(c) - (sqrt(-a*c)*c^3*d^7*e + 15*sqrt(-a*c)*a*c^2*d^5*e^3 + 27*sqrt(-a*c)*a^2*c*d^3*e^5 + 13*sqrt(-a*c)*a^3*d*e^7)*abs(a*c^2*d^4*e + 2*a^2*c*d^2*e^3 + a^3*e^5)*abs(c) + 2*(a*c^6*d^12*e + 8*a^2*c^5*d^10*e^3 + 22*a^3*c^4*d^8*e^5 + 28*a^4*c^3*d^6*e^7 + 17*a^5*c^2*d^4*e^9 + 4*a^6*c*d^2*e^11)*abs(c))*arctan(sqrt(x*e + d)/sqrt(-(a*c^3*d^5 + 2*a^2*c^2*d^3*e^2 + a^3*c*d*e^4 + sqrt((a*c^3*d^5 + 2*a^2*c^2*d^3*e^2 + a^3*c*d*e^4)^2 - (a*c^3*d^6 + 3*a^2*c^2*d^4*e^2 + 3*a^3*c*d^2*e^4 + a^4*e^6)*(a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)))/(a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)))/((a^2*c^4*d^8*e + sqrt(-a*c)*a*c^4*d^9 + 4*sqrt(-a*c)*a^2*c^3*d^7*e^2 + 4*a^3*c^3*d^6*e^3 + 6*sqrt(-a*c)*a^3*c^2*d^5*e^4 + 6*a^4*c^2*d^4*e^5 + 4*sqrt(-a*c)*a^4*c*d^3*e^6 + 4*a^5*c*d^2*e^7 + sqrt(-a*c)*a^5*d*e^8 + a^6*e^9)*sqrt(-c^2*d - sqrt(-a*c)*c*e)*abs(a*c^2*d^4*e + 2*a^2*c*d^2*e^3 + a^3*e^5)) + 1/4*((a*c^2*d^4*e + 2*a^2*c*d^2*e^3 + a^3*e^5)^2*(c*d^2*e - 5*a*e^3)*abs(c) + (sqrt(-a*c)*c^3*d^7*e + 15*sqrt(-a*c)*a*c^2*d^5*e^3 + 27*sqrt(-a*c)*a^2*c*d^3*e^5 + 13*sqrt(-a*c)*a^3*d*e^7)*abs(a*c^2*d^4*e + 2*a^2*c*d^2*e^3 + a^3*e^5)*abs(c) + 2*(a*c^6*d^12*e + 8*a^2*c^5*d^10*e^3 + 22*a^3*c^4*d^8*e^5 + 28*a^4*c^3*d^6*e^7 + 17*a^5*c^2*d^4*e^9 + 4*a^6*c*d^2*e^11)*abs(c))*arctan(sqrt(x*e + d)/sqrt(-(a*c^3*d^5 + 2*a^2*c^2*d^3*e^2 + a^3*c*d*e^4 - sqrt((a*c^3*d^5 + 2*a^2*c^2*d^3*e^2 + a^3*c*d*e^4)^2 - (a*c^3*d^6 + 3*a^2*c^2*d^4*e^2 + 3*a^3*c*d^2*e^4 + a^4*e^6)*(a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)))/(a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)))/((a^2*c^4*d^8*e - sqrt(-a*c)*a*c^4*d^9 - 4*sqrt(-a*c)*a^2*c^3*d^7*e^2 + 4*a^3*c^3*d^6*e^3 - 6*sqrt(-a*c)*a^3*c^2*d^5*e^4 + 6*a^4*c^2*d^4*e^5 - 4*sqrt(-a*c)*a^4*c*d^3*e^6 + 4*a^5*c*d^2*e^7 - sqrt(-a*c)*a^5*d*e^8 + a^6*e^9)*sqrt(-c^2*d + sqrt(-a*c)*c*e)*abs(a*c^2*d^4*e + 2*a^2*c*d^2*e^3 + a^3*e^5)) + 1/2*((x*e + d)^2*c^2*d^2*e - (x*e + d)*c^2*d^3*e - 5*(x*e + d)^2*a*c*e^3 + 11*(x*e + d)*a*c*d*e^3 - 4*a*c*d^2*e^3 - 4*a^2*e^5)/((a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4)*((x*e + d)^(5/2)*c - 2*(x*e + d)^(3/2)*c*d + sqrt(x*e + d)*c*d^2 + sqrt(x*e + d)*a*e^2))","A",0
637,1,1928,0,1.417449," ","integrate(1/(e*x+d)^(5/2)/(c*x^2+a)^2,x, algorithm=""giac"")","-\frac{{\left({\left(a c^{3} d^{6} e + 3 \, a^{2} c^{2} d^{4} e^{3} + 3 \, a^{3} c d^{2} e^{5} + a^{4} e^{7}\right)}^{2} {\left(c^{2} d^{3} e - 19 \, a c d e^{3}\right)} {\left| c \right|} - {\left(\sqrt{-a c} c^{5} d^{10} e + 37 \, \sqrt{-a c} a c^{4} d^{8} e^{3} + 98 \, \sqrt{-a c} a^{2} c^{3} d^{6} e^{5} + 82 \, \sqrt{-a c} a^{3} c^{2} d^{4} e^{7} + 13 \, \sqrt{-a c} a^{4} c d^{2} e^{9} - 7 \, \sqrt{-a c} a^{5} e^{11}\right)} {\left| -a c^{3} d^{6} e - 3 \, a^{2} c^{2} d^{4} e^{3} - 3 \, a^{3} c d^{2} e^{5} - a^{4} e^{7} \right|} {\left| c \right|} + {\left(2 \, a c^{9} d^{17} e + 27 \, a^{2} c^{8} d^{15} e^{3} + 113 \, a^{3} c^{7} d^{13} e^{5} + 223 \, a^{4} c^{6} d^{11} e^{7} + 225 \, a^{5} c^{5} d^{9} e^{9} + 97 \, a^{6} c^{4} d^{7} e^{11} - 13 \, a^{7} c^{3} d^{5} e^{13} - 27 \, a^{8} c^{2} d^{3} e^{15} - 7 \, a^{9} c d e^{17}\right)} {\left| c \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a c^{4} d^{7} + 3 \, a^{2} c^{3} d^{5} e^{2} + 3 \, a^{3} c^{2} d^{3} e^{4} + a^{4} c d e^{6} + \sqrt{{\left(a c^{4} d^{7} + 3 \, a^{2} c^{3} d^{5} e^{2} + 3 \, a^{3} c^{2} d^{3} e^{4} + a^{4} c d e^{6}\right)}^{2} - {\left(a c^{4} d^{8} + 4 \, a^{2} c^{3} d^{6} e^{2} + 6 \, a^{3} c^{2} d^{4} e^{4} + 4 \, a^{4} c d^{2} e^{6} + a^{5} e^{8}\right)} {\left(a c^{4} d^{6} + 3 \, a^{2} c^{3} d^{4} e^{2} + 3 \, a^{3} c^{2} d^{2} e^{4} + a^{4} c e^{6}\right)}}}{a c^{4} d^{6} + 3 \, a^{2} c^{3} d^{4} e^{2} + 3 \, a^{3} c^{2} d^{2} e^{4} + a^{4} c e^{6}}}}\right)}{4 \, {\left(a^{2} c^{6} d^{12} e - \sqrt{-a c} a c^{6} d^{13} - 6 \, \sqrt{-a c} a^{2} c^{5} d^{11} e^{2} + 6 \, a^{3} c^{5} d^{10} e^{3} - 15 \, \sqrt{-a c} a^{3} c^{4} d^{9} e^{4} + 15 \, a^{4} c^{4} d^{8} e^{5} - 20 \, \sqrt{-a c} a^{4} c^{3} d^{7} e^{6} + 20 \, a^{5} c^{3} d^{6} e^{7} - 15 \, \sqrt{-a c} a^{5} c^{2} d^{5} e^{8} + 15 \, a^{6} c^{2} d^{4} e^{9} - 6 \, \sqrt{-a c} a^{6} c d^{3} e^{10} + 6 \, a^{7} c d^{2} e^{11} - \sqrt{-a c} a^{7} d e^{12} + a^{8} e^{13}\right)} \sqrt{-c^{2} d + \sqrt{-a c} c e} {\left| -a c^{3} d^{6} e - 3 \, a^{2} c^{2} d^{4} e^{3} - 3 \, a^{3} c d^{2} e^{5} - a^{4} e^{7} \right|}} - \frac{{\left({\left(a c^{3} d^{6} e + 3 \, a^{2} c^{2} d^{4} e^{3} + 3 \, a^{3} c d^{2} e^{5} + a^{4} e^{7}\right)}^{2} {\left(c^{2} d^{3} e - 19 \, a c d e^{3}\right)} {\left| c \right|} + {\left(\sqrt{-a c} c^{5} d^{10} e + 37 \, \sqrt{-a c} a c^{4} d^{8} e^{3} + 98 \, \sqrt{-a c} a^{2} c^{3} d^{6} e^{5} + 82 \, \sqrt{-a c} a^{3} c^{2} d^{4} e^{7} + 13 \, \sqrt{-a c} a^{4} c d^{2} e^{9} - 7 \, \sqrt{-a c} a^{5} e^{11}\right)} {\left| -a c^{3} d^{6} e - 3 \, a^{2} c^{2} d^{4} e^{3} - 3 \, a^{3} c d^{2} e^{5} - a^{4} e^{7} \right|} {\left| c \right|} + {\left(2 \, a c^{9} d^{17} e + 27 \, a^{2} c^{8} d^{15} e^{3} + 113 \, a^{3} c^{7} d^{13} e^{5} + 223 \, a^{4} c^{6} d^{11} e^{7} + 225 \, a^{5} c^{5} d^{9} e^{9} + 97 \, a^{6} c^{4} d^{7} e^{11} - 13 \, a^{7} c^{3} d^{5} e^{13} - 27 \, a^{8} c^{2} d^{3} e^{15} - 7 \, a^{9} c d e^{17}\right)} {\left| c \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a c^{4} d^{7} + 3 \, a^{2} c^{3} d^{5} e^{2} + 3 \, a^{3} c^{2} d^{3} e^{4} + a^{4} c d e^{6} - \sqrt{{\left(a c^{4} d^{7} + 3 \, a^{2} c^{3} d^{5} e^{2} + 3 \, a^{3} c^{2} d^{3} e^{4} + a^{4} c d e^{6}\right)}^{2} - {\left(a c^{4} d^{8} + 4 \, a^{2} c^{3} d^{6} e^{2} + 6 \, a^{3} c^{2} d^{4} e^{4} + 4 \, a^{4} c d^{2} e^{6} + a^{5} e^{8}\right)} {\left(a c^{4} d^{6} + 3 \, a^{2} c^{3} d^{4} e^{2} + 3 \, a^{3} c^{2} d^{2} e^{4} + a^{4} c e^{6}\right)}}}{a c^{4} d^{6} + 3 \, a^{2} c^{3} d^{4} e^{2} + 3 \, a^{3} c^{2} d^{2} e^{4} + a^{4} c e^{6}}}}\right)}{4 \, {\left(a^{2} c^{6} d^{12} e + \sqrt{-a c} a c^{6} d^{13} + 6 \, \sqrt{-a c} a^{2} c^{5} d^{11} e^{2} + 6 \, a^{3} c^{5} d^{10} e^{3} + 15 \, \sqrt{-a c} a^{3} c^{4} d^{9} e^{4} + 15 \, a^{4} c^{4} d^{8} e^{5} + 20 \, \sqrt{-a c} a^{4} c^{3} d^{7} e^{6} + 20 \, a^{5} c^{3} d^{6} e^{7} + 15 \, \sqrt{-a c} a^{5} c^{2} d^{5} e^{8} + 15 \, a^{6} c^{2} d^{4} e^{9} + 6 \, \sqrt{-a c} a^{6} c d^{3} e^{10} + 6 \, a^{7} c d^{2} e^{11} + \sqrt{-a c} a^{7} d e^{12} + a^{8} e^{13}\right)} \sqrt{-c^{2} d - \sqrt{-a c} c e} {\left| -a c^{3} d^{6} e - 3 \, a^{2} c^{2} d^{4} e^{3} - 3 \, a^{3} c d^{2} e^{5} - a^{4} e^{7} \right|}} + \frac{{\left(x e + d\right)}^{\frac{3}{2}} c^{3} d^{3} e - \sqrt{x e + d} c^{3} d^{4} e - 3 \, {\left(x e + d\right)}^{\frac{3}{2}} a c^{2} d e^{3} + 6 \, \sqrt{x e + d} a c^{2} d^{2} e^{3} - \sqrt{x e + d} a^{2} c e^{5}}{2 \, {\left(a c^{3} d^{6} + 3 \, a^{2} c^{2} d^{4} e^{2} + 3 \, a^{3} c d^{2} e^{4} + a^{4} e^{6}\right)} {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + a e^{2}\right)}} - \frac{2 \, {\left(12 \, {\left(x e + d\right)} c d e^{3} + c d^{2} e^{3} + a e^{5}\right)}}{3 \, {\left(c^{3} d^{6} + 3 \, a c^{2} d^{4} e^{2} + 3 \, a^{2} c d^{2} e^{4} + a^{3} e^{6}\right)} {\left(x e + d\right)}^{\frac{3}{2}}}"," ",0,"-1/4*((a*c^3*d^6*e + 3*a^2*c^2*d^4*e^3 + 3*a^3*c*d^2*e^5 + a^4*e^7)^2*(c^2*d^3*e - 19*a*c*d*e^3)*abs(c) - (sqrt(-a*c)*c^5*d^10*e + 37*sqrt(-a*c)*a*c^4*d^8*e^3 + 98*sqrt(-a*c)*a^2*c^3*d^6*e^5 + 82*sqrt(-a*c)*a^3*c^2*d^4*e^7 + 13*sqrt(-a*c)*a^4*c*d^2*e^9 - 7*sqrt(-a*c)*a^5*e^11)*abs(-a*c^3*d^6*e - 3*a^2*c^2*d^4*e^3 - 3*a^3*c*d^2*e^5 - a^4*e^7)*abs(c) + (2*a*c^9*d^17*e + 27*a^2*c^8*d^15*e^3 + 113*a^3*c^7*d^13*e^5 + 223*a^4*c^6*d^11*e^7 + 225*a^5*c^5*d^9*e^9 + 97*a^6*c^4*d^7*e^11 - 13*a^7*c^3*d^5*e^13 - 27*a^8*c^2*d^3*e^15 - 7*a^9*c*d*e^17)*abs(c))*arctan(sqrt(x*e + d)/sqrt(-(a*c^4*d^7 + 3*a^2*c^3*d^5*e^2 + 3*a^3*c^2*d^3*e^4 + a^4*c*d*e^6 + sqrt((a*c^4*d^7 + 3*a^2*c^3*d^5*e^2 + 3*a^3*c^2*d^3*e^4 + a^4*c*d*e^6)^2 - (a*c^4*d^8 + 4*a^2*c^3*d^6*e^2 + 6*a^3*c^2*d^4*e^4 + 4*a^4*c*d^2*e^6 + a^5*e^8)*(a*c^4*d^6 + 3*a^2*c^3*d^4*e^2 + 3*a^3*c^2*d^2*e^4 + a^4*c*e^6)))/(a*c^4*d^6 + 3*a^2*c^3*d^4*e^2 + 3*a^3*c^2*d^2*e^4 + a^4*c*e^6)))/((a^2*c^6*d^12*e - sqrt(-a*c)*a*c^6*d^13 - 6*sqrt(-a*c)*a^2*c^5*d^11*e^2 + 6*a^3*c^5*d^10*e^3 - 15*sqrt(-a*c)*a^3*c^4*d^9*e^4 + 15*a^4*c^4*d^8*e^5 - 20*sqrt(-a*c)*a^4*c^3*d^7*e^6 + 20*a^5*c^3*d^6*e^7 - 15*sqrt(-a*c)*a^5*c^2*d^5*e^8 + 15*a^6*c^2*d^4*e^9 - 6*sqrt(-a*c)*a^6*c*d^3*e^10 + 6*a^7*c*d^2*e^11 - sqrt(-a*c)*a^7*d*e^12 + a^8*e^13)*sqrt(-c^2*d + sqrt(-a*c)*c*e)*abs(-a*c^3*d^6*e - 3*a^2*c^2*d^4*e^3 - 3*a^3*c*d^2*e^5 - a^4*e^7)) - 1/4*((a*c^3*d^6*e + 3*a^2*c^2*d^4*e^3 + 3*a^3*c*d^2*e^5 + a^4*e^7)^2*(c^2*d^3*e - 19*a*c*d*e^3)*abs(c) + (sqrt(-a*c)*c^5*d^10*e + 37*sqrt(-a*c)*a*c^4*d^8*e^3 + 98*sqrt(-a*c)*a^2*c^3*d^6*e^5 + 82*sqrt(-a*c)*a^3*c^2*d^4*e^7 + 13*sqrt(-a*c)*a^4*c*d^2*e^9 - 7*sqrt(-a*c)*a^5*e^11)*abs(-a*c^3*d^6*e - 3*a^2*c^2*d^4*e^3 - 3*a^3*c*d^2*e^5 - a^4*e^7)*abs(c) + (2*a*c^9*d^17*e + 27*a^2*c^8*d^15*e^3 + 113*a^3*c^7*d^13*e^5 + 223*a^4*c^6*d^11*e^7 + 225*a^5*c^5*d^9*e^9 + 97*a^6*c^4*d^7*e^11 - 13*a^7*c^3*d^5*e^13 - 27*a^8*c^2*d^3*e^15 - 7*a^9*c*d*e^17)*abs(c))*arctan(sqrt(x*e + d)/sqrt(-(a*c^4*d^7 + 3*a^2*c^3*d^5*e^2 + 3*a^3*c^2*d^3*e^4 + a^4*c*d*e^6 - sqrt((a*c^4*d^7 + 3*a^2*c^3*d^5*e^2 + 3*a^3*c^2*d^3*e^4 + a^4*c*d*e^6)^2 - (a*c^4*d^8 + 4*a^2*c^3*d^6*e^2 + 6*a^3*c^2*d^4*e^4 + 4*a^4*c*d^2*e^6 + a^5*e^8)*(a*c^4*d^6 + 3*a^2*c^3*d^4*e^2 + 3*a^3*c^2*d^2*e^4 + a^4*c*e^6)))/(a*c^4*d^6 + 3*a^2*c^3*d^4*e^2 + 3*a^3*c^2*d^2*e^4 + a^4*c*e^6)))/((a^2*c^6*d^12*e + sqrt(-a*c)*a*c^6*d^13 + 6*sqrt(-a*c)*a^2*c^5*d^11*e^2 + 6*a^3*c^5*d^10*e^3 + 15*sqrt(-a*c)*a^3*c^4*d^9*e^4 + 15*a^4*c^4*d^8*e^5 + 20*sqrt(-a*c)*a^4*c^3*d^7*e^6 + 20*a^5*c^3*d^6*e^7 + 15*sqrt(-a*c)*a^5*c^2*d^5*e^8 + 15*a^6*c^2*d^4*e^9 + 6*sqrt(-a*c)*a^6*c*d^3*e^10 + 6*a^7*c*d^2*e^11 + sqrt(-a*c)*a^7*d*e^12 + a^8*e^13)*sqrt(-c^2*d - sqrt(-a*c)*c*e)*abs(-a*c^3*d^6*e - 3*a^2*c^2*d^4*e^3 - 3*a^3*c*d^2*e^5 - a^4*e^7)) + 1/2*((x*e + d)^(3/2)*c^3*d^3*e - sqrt(x*e + d)*c^3*d^4*e - 3*(x*e + d)^(3/2)*a*c^2*d*e^3 + 6*sqrt(x*e + d)*a*c^2*d^2*e^3 - sqrt(x*e + d)*a^2*c*e^5)/((a*c^3*d^6 + 3*a^2*c^2*d^4*e^2 + 3*a^3*c*d^2*e^4 + a^4*e^6)*((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + a*e^2)) - 2/3*(12*(x*e + d)*c*d*e^3 + c*d^2*e^3 + a*e^5)/((c^3*d^6 + 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4 + a^3*e^6)*(x*e + d)^(3/2))","B",0
638,1,535,0,0.564115," ","integrate((e*x+d)^(7/2)/(-c*x^2+a)^3,x, algorithm=""giac"")","-\frac{{\left(6 \, a c d^{2} e - 12 \, \sqrt{a c} c d^{3} + 13 \, \sqrt{a c} a d e^{2} - 5 \, a^{2} e^{3}\right)} \sqrt{-c^{2} d - \sqrt{a c} c e} {\left| c \right|} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a^{2} c^{3} d + \sqrt{a^{4} c^{6} d^{2} - {\left(a^{2} c^{3} d^{2} - a^{3} c^{2} e^{2}\right)} a^{2} c^{3}}}{a^{2} c^{3}}}}\right)}{32 \, a^{3} c^{4}} - \frac{{\left(6 \, a c d^{2} e + 12 \, \sqrt{a c} c d^{3} - 13 \, \sqrt{a c} a d e^{2} - 5 \, a^{2} e^{3}\right)} \sqrt{-c^{2} d + \sqrt{a c} c e} {\left| c \right|} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a^{2} c^{3} d - \sqrt{a^{4} c^{6} d^{2} - {\left(a^{2} c^{3} d^{2} - a^{3} c^{2} e^{2}\right)} a^{2} c^{3}}}{a^{2} c^{3}}}}\right)}{32 \, a^{3} c^{4}} - \frac{6 \, {\left(x e + d\right)}^{\frac{7}{2}} c^{3} d^{3} e - 18 \, {\left(x e + d\right)}^{\frac{5}{2}} c^{3} d^{4} e + 18 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{3} d^{5} e - 6 \, \sqrt{x e + d} c^{3} d^{6} e - 8 \, {\left(x e + d\right)}^{\frac{7}{2}} a c^{2} d e^{3} + 23 \, {\left(x e + d\right)}^{\frac{5}{2}} a c^{2} d^{2} e^{3} - 32 \, {\left(x e + d\right)}^{\frac{3}{2}} a c^{2} d^{3} e^{3} + 17 \, \sqrt{x e + d} a c^{2} d^{4} e^{3} - 9 \, {\left(x e + d\right)}^{\frac{5}{2}} a^{2} c e^{5} + 14 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} c d e^{5} - 16 \, \sqrt{x e + d} a^{2} c d^{2} e^{5} + 5 \, \sqrt{x e + d} a^{3} e^{7}}{16 \, {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} - a e^{2}\right)}^{2} a^{2} c^{2}}"," ",0,"-1/32*(6*a*c*d^2*e - 12*sqrt(a*c)*c*d^3 + 13*sqrt(a*c)*a*d*e^2 - 5*a^2*e^3)*sqrt(-c^2*d - sqrt(a*c)*c*e)*abs(c)*arctan(sqrt(x*e + d)/sqrt(-(a^2*c^3*d + sqrt(a^4*c^6*d^2 - (a^2*c^3*d^2 - a^3*c^2*e^2)*a^2*c^3))/(a^2*c^3)))/(a^3*c^4) - 1/32*(6*a*c*d^2*e + 12*sqrt(a*c)*c*d^3 - 13*sqrt(a*c)*a*d*e^2 - 5*a^2*e^3)*sqrt(-c^2*d + sqrt(a*c)*c*e)*abs(c)*arctan(sqrt(x*e + d)/sqrt(-(a^2*c^3*d - sqrt(a^4*c^6*d^2 - (a^2*c^3*d^2 - a^3*c^2*e^2)*a^2*c^3))/(a^2*c^3)))/(a^3*c^4) - 1/16*(6*(x*e + d)^(7/2)*c^3*d^3*e - 18*(x*e + d)^(5/2)*c^3*d^4*e + 18*(x*e + d)^(3/2)*c^3*d^5*e - 6*sqrt(x*e + d)*c^3*d^6*e - 8*(x*e + d)^(7/2)*a*c^2*d*e^3 + 23*(x*e + d)^(5/2)*a*c^2*d^2*e^3 - 32*(x*e + d)^(3/2)*a*c^2*d^3*e^3 + 17*sqrt(x*e + d)*a*c^2*d^4*e^3 - 9*(x*e + d)^(5/2)*a^2*c*e^5 + 14*(x*e + d)^(3/2)*a^2*c*d*e^5 - 16*sqrt(x*e + d)*a^2*c*d^2*e^5 + 5*sqrt(x*e + d)*a^3*e^7)/(((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 - a*e^2)^2*a^2*c^2)","B",0
639,1,617,0,0.644534," ","integrate((e*x+d)^(5/2)/(-c*x^2+a)^3,x, algorithm=""giac"")","-\frac{3 \, {\left(4 \, \sqrt{a c} c^{4} d^{4} - 3 \, \sqrt{a c} a c^{3} d^{2} e^{2} - {\left(2 \, \sqrt{a c} a c d^{2} e^{2} - \sqrt{a c} a^{2} e^{4}\right)} c^{2} - 2 \, {\left(a c^{3} d^{3} e - a^{2} c^{2} d e^{3}\right)} {\left| c \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a^{2} c^{2} d + \sqrt{a^{4} c^{4} d^{2} - {\left(a^{2} c^{2} d^{2} - a^{3} c e^{2}\right)} a^{2} c^{2}}}{a^{2} c^{2}}}}\right)}{32 \, {\left(a^{3} c^{4} d - \sqrt{a c} a^{3} c^{3} e\right)} \sqrt{-c^{2} d - \sqrt{a c} c e}} + \frac{3 \, {\left(4 \, \sqrt{a c} c^{4} d^{4} - 3 \, \sqrt{a c} a c^{3} d^{2} e^{2} - {\left(2 \, \sqrt{a c} a c d^{2} e^{2} - \sqrt{a c} a^{2} e^{4}\right)} c^{2} + 2 \, {\left(a c^{3} d^{3} e - a^{2} c^{2} d e^{3}\right)} {\left| c \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a^{2} c^{2} d - \sqrt{a^{4} c^{4} d^{2} - {\left(a^{2} c^{2} d^{2} - a^{3} c e^{2}\right)} a^{2} c^{2}}}{a^{2} c^{2}}}}\right)}{32 \, {\left(a^{3} c^{4} d + \sqrt{a c} a^{3} c^{3} e\right)} \sqrt{-c^{2} d + \sqrt{a c} c e}} - \frac{6 \, {\left(x e + d\right)}^{\frac{7}{2}} c^{2} d^{2} e - 18 \, {\left(x e + d\right)}^{\frac{5}{2}} c^{2} d^{3} e + 18 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{2} d^{4} e - 6 \, \sqrt{x e + d} c^{2} d^{5} e - 3 \, {\left(x e + d\right)}^{\frac{7}{2}} a c e^{3} + 8 \, {\left(x e + d\right)}^{\frac{5}{2}} a c d e^{3} - 17 \, {\left(x e + d\right)}^{\frac{3}{2}} a c d^{2} e^{3} + 12 \, \sqrt{x e + d} a c d^{3} e^{3} - {\left(x e + d\right)}^{\frac{3}{2}} a^{2} e^{5} - 6 \, \sqrt{x e + d} a^{2} d e^{5}}{16 \, {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} - a e^{2}\right)}^{2} a^{2} c}"," ",0,"-3/32*(4*sqrt(a*c)*c^4*d^4 - 3*sqrt(a*c)*a*c^3*d^2*e^2 - (2*sqrt(a*c)*a*c*d^2*e^2 - sqrt(a*c)*a^2*e^4)*c^2 - 2*(a*c^3*d^3*e - a^2*c^2*d*e^3)*abs(c))*arctan(sqrt(x*e + d)/sqrt(-(a^2*c^2*d + sqrt(a^4*c^4*d^2 - (a^2*c^2*d^2 - a^3*c*e^2)*a^2*c^2))/(a^2*c^2)))/((a^3*c^4*d - sqrt(a*c)*a^3*c^3*e)*sqrt(-c^2*d - sqrt(a*c)*c*e)) + 3/32*(4*sqrt(a*c)*c^4*d^4 - 3*sqrt(a*c)*a*c^3*d^2*e^2 - (2*sqrt(a*c)*a*c*d^2*e^2 - sqrt(a*c)*a^2*e^4)*c^2 + 2*(a*c^3*d^3*e - a^2*c^2*d*e^3)*abs(c))*arctan(sqrt(x*e + d)/sqrt(-(a^2*c^2*d - sqrt(a^4*c^4*d^2 - (a^2*c^2*d^2 - a^3*c*e^2)*a^2*c^2))/(a^2*c^2)))/((a^3*c^4*d + sqrt(a*c)*a^3*c^3*e)*sqrt(-c^2*d + sqrt(a*c)*c*e)) - 1/16*(6*(x*e + d)^(7/2)*c^2*d^2*e - 18*(x*e + d)^(5/2)*c^2*d^3*e + 18*(x*e + d)^(3/2)*c^2*d^4*e - 6*sqrt(x*e + d)*c^2*d^5*e - 3*(x*e + d)^(7/2)*a*c*e^3 + 8*(x*e + d)^(5/2)*a*c*d*e^3 - 17*(x*e + d)^(3/2)*a*c*d^2*e^3 + 12*sqrt(x*e + d)*a*c*d^3*e^3 - (x*e + d)^(3/2)*a^2*e^5 - 6*sqrt(x*e + d)*a^2*d*e^5)/(((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 - a*e^2)^2*a^2*c)","B",0
640,1,509,0,0.617199," ","integrate((e*x+d)^(3/2)/(-c*x^2+a)^3,x, algorithm=""giac"")","-\frac{3 \, {\left(4 \, \sqrt{a c} c^{3} d^{3} - 3 \, \sqrt{a c} a c^{2} d e^{2} - {\left(2 \, a c^{2} d^{2} e - a^{2} c e^{3}\right)} {\left| c \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a^{2} c^{2} d + \sqrt{a^{4} c^{4} d^{2} - {\left(a^{2} c^{2} d^{2} - a^{3} c e^{2}\right)} a^{2} c^{2}}}{a^{2} c^{2}}}}\right)}{32 \, {\left(a^{3} c^{3} d - \sqrt{a c} a^{3} c^{2} e\right)} \sqrt{-c^{2} d - \sqrt{a c} c e}} + \frac{3 \, {\left(4 \, \sqrt{a c} c^{3} d^{3} - 3 \, \sqrt{a c} a c^{2} d e^{2} + {\left(2 \, a c^{2} d^{2} e - a^{2} c e^{3}\right)} {\left| c \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a^{2} c^{2} d - \sqrt{a^{4} c^{4} d^{2} - {\left(a^{2} c^{2} d^{2} - a^{3} c e^{2}\right)} a^{2} c^{2}}}{a^{2} c^{2}}}}\right)}{32 \, {\left(a^{3} c^{3} d + \sqrt{a c} a^{3} c^{2} e\right)} \sqrt{-c^{2} d + \sqrt{a c} c e}} - \frac{6 \, {\left(x e + d\right)}^{\frac{7}{2}} c^{2} d e - 18 \, {\left(x e + d\right)}^{\frac{5}{2}} c^{2} d^{2} e + 18 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{2} d^{3} e - 6 \, \sqrt{x e + d} c^{2} d^{4} e - {\left(x e + d\right)}^{\frac{5}{2}} a c e^{3} - 8 \, {\left(x e + d\right)}^{\frac{3}{2}} a c d e^{3} + 9 \, \sqrt{x e + d} a c d^{2} e^{3} - 3 \, \sqrt{x e + d} a^{2} e^{5}}{16 \, {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} - a e^{2}\right)}^{2} a^{2} c}"," ",0,"-3/32*(4*sqrt(a*c)*c^3*d^3 - 3*sqrt(a*c)*a*c^2*d*e^2 - (2*a*c^2*d^2*e - a^2*c*e^3)*abs(c))*arctan(sqrt(x*e + d)/sqrt(-(a^2*c^2*d + sqrt(a^4*c^4*d^2 - (a^2*c^2*d^2 - a^3*c*e^2)*a^2*c^2))/(a^2*c^2)))/((a^3*c^3*d - sqrt(a*c)*a^3*c^2*e)*sqrt(-c^2*d - sqrt(a*c)*c*e)) + 3/32*(4*sqrt(a*c)*c^3*d^3 - 3*sqrt(a*c)*a*c^2*d*e^2 + (2*a*c^2*d^2*e - a^2*c*e^3)*abs(c))*arctan(sqrt(x*e + d)/sqrt(-(a^2*c^2*d - sqrt(a^4*c^4*d^2 - (a^2*c^2*d^2 - a^3*c*e^2)*a^2*c^2))/(a^2*c^2)))/((a^3*c^3*d + sqrt(a*c)*a^3*c^2*e)*sqrt(-c^2*d + sqrt(a*c)*c*e)) - 1/16*(6*(x*e + d)^(7/2)*c^2*d*e - 18*(x*e + d)^(5/2)*c^2*d^2*e + 18*(x*e + d)^(3/2)*c^2*d^3*e - 6*sqrt(x*e + d)*c^2*d^4*e - (x*e + d)^(5/2)*a*c*e^3 - 8*(x*e + d)^(3/2)*a*c*d*e^3 + 9*sqrt(x*e + d)*a*c*d^2*e^3 - 3*sqrt(x*e + d)*a^2*e^5)/(((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 - a*e^2)^2*a^2*c)","B",0
641,1,1074,0,0.878974," ","integrate((e*x+d)^(1/2)/(-c*x^2+a)^3,x, algorithm=""giac"")","-\frac{{\left({\left(a^{2} c d^{2} e - a^{3} e^{3}\right)}^{2} {\left(6 \, c d^{2} e - 5 \, a e^{3}\right)} {\left| c \right|} + 2 \, {\left(3 \, \sqrt{a c} a c^{2} d^{5} e - 7 \, \sqrt{a c} a^{2} c d^{3} e^{3} + 4 \, \sqrt{a c} a^{3} d e^{5}\right)} {\left| a^{2} c d^{2} e - a^{3} e^{3} \right|} {\left| c \right|} - {\left(12 \, a^{3} c^{4} d^{8} e - 37 \, a^{4} c^{3} d^{6} e^{3} + 38 \, a^{5} c^{2} d^{4} e^{5} - 13 \, a^{6} c d^{2} e^{7}\right)} {\left| c \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a^{2} c^{2} d^{3} - a^{3} c d e^{2} + \sqrt{{\left(a^{2} c^{2} d^{3} - a^{3} c d e^{2}\right)}^{2} - {\left(a^{2} c^{2} d^{4} - 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4}\right)} {\left(a^{2} c^{2} d^{2} - a^{3} c e^{2}\right)}}}{a^{2} c^{2} d^{2} - a^{3} c e^{2}}}}\right)}{32 \, {\left(a^{4} c^{3} d^{4} e - \sqrt{a c} a^{3} c^{3} d^{5} + 2 \, \sqrt{a c} a^{4} c^{2} d^{3} e^{2} - 2 \, a^{5} c^{2} d^{2} e^{3} - \sqrt{a c} a^{5} c d e^{4} + a^{6} c e^{5}\right)} \sqrt{-c^{2} d - \sqrt{a c} c e} {\left| a^{2} c d^{2} e - a^{3} e^{3} \right|}} - \frac{{\left({\left(a^{2} c d^{2} e - a^{3} e^{3}\right)}^{2} {\left(6 \, \sqrt{a c} c d^{2} e - 5 \, \sqrt{a c} a e^{3}\right)} {\left| c \right|} - 2 \, {\left(3 \, a^{2} c^{3} d^{5} e - 7 \, a^{3} c^{2} d^{3} e^{3} + 4 \, a^{4} c d e^{5}\right)} {\left| a^{2} c d^{2} e - a^{3} e^{3} \right|} {\left| c \right|} - {\left(12 \, \sqrt{a c} a^{3} c^{4} d^{8} e - 37 \, \sqrt{a c} a^{4} c^{3} d^{6} e^{3} + 38 \, \sqrt{a c} a^{5} c^{2} d^{4} e^{5} - 13 \, \sqrt{a c} a^{6} c d^{2} e^{7}\right)} {\left| c \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a^{2} c^{2} d^{3} - a^{3} c d e^{2} - \sqrt{{\left(a^{2} c^{2} d^{3} - a^{3} c d e^{2}\right)}^{2} - {\left(a^{2} c^{2} d^{4} - 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4}\right)} {\left(a^{2} c^{2} d^{2} - a^{3} c e^{2}\right)}}}{a^{2} c^{2} d^{2} - a^{3} c e^{2}}}}\right)}{32 \, {\left(a^{4} c^{4} d^{5} + \sqrt{a c} a^{4} c^{3} d^{4} e - 2 \, a^{5} c^{3} d^{3} e^{2} - 2 \, \sqrt{a c} a^{5} c^{2} d^{2} e^{3} + a^{6} c^{2} d e^{4} + \sqrt{a c} a^{6} c e^{5}\right)} \sqrt{-c^{2} d + \sqrt{a c} c e} {\left| a^{2} c d^{2} e - a^{3} e^{3} \right|}} - \frac{6 \, {\left(x e + d\right)}^{\frac{7}{2}} c^{2} d^{2} e - 18 \, {\left(x e + d\right)}^{\frac{5}{2}} c^{2} d^{3} e + 18 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{2} d^{4} e - 6 \, \sqrt{x e + d} c^{2} d^{5} e - 5 \, {\left(x e + d\right)}^{\frac{7}{2}} a c e^{3} + 14 \, {\left(x e + d\right)}^{\frac{5}{2}} a c d e^{3} - 23 \, {\left(x e + d\right)}^{\frac{3}{2}} a c d^{2} e^{3} + 14 \, \sqrt{x e + d} a c d^{3} e^{3} + 9 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} e^{5} - 8 \, \sqrt{x e + d} a^{2} d e^{5}}{16 \, {\left(a^{2} c d^{2} - a^{3} e^{2}\right)} {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} - a e^{2}\right)}^{2}}"," ",0,"-1/32*((a^2*c*d^2*e - a^3*e^3)^2*(6*c*d^2*e - 5*a*e^3)*abs(c) + 2*(3*sqrt(a*c)*a*c^2*d^5*e - 7*sqrt(a*c)*a^2*c*d^3*e^3 + 4*sqrt(a*c)*a^3*d*e^5)*abs(a^2*c*d^2*e - a^3*e^3)*abs(c) - (12*a^3*c^4*d^8*e - 37*a^4*c^3*d^6*e^3 + 38*a^5*c^2*d^4*e^5 - 13*a^6*c*d^2*e^7)*abs(c))*arctan(sqrt(x*e + d)/sqrt(-(a^2*c^2*d^3 - a^3*c*d*e^2 + sqrt((a^2*c^2*d^3 - a^3*c*d*e^2)^2 - (a^2*c^2*d^4 - 2*a^3*c*d^2*e^2 + a^4*e^4)*(a^2*c^2*d^2 - a^3*c*e^2)))/(a^2*c^2*d^2 - a^3*c*e^2)))/((a^4*c^3*d^4*e - sqrt(a*c)*a^3*c^3*d^5 + 2*sqrt(a*c)*a^4*c^2*d^3*e^2 - 2*a^5*c^2*d^2*e^3 - sqrt(a*c)*a^5*c*d*e^4 + a^6*c*e^5)*sqrt(-c^2*d - sqrt(a*c)*c*e)*abs(a^2*c*d^2*e - a^3*e^3)) - 1/32*((a^2*c*d^2*e - a^3*e^3)^2*(6*sqrt(a*c)*c*d^2*e - 5*sqrt(a*c)*a*e^3)*abs(c) - 2*(3*a^2*c^3*d^5*e - 7*a^3*c^2*d^3*e^3 + 4*a^4*c*d*e^5)*abs(a^2*c*d^2*e - a^3*e^3)*abs(c) - (12*sqrt(a*c)*a^3*c^4*d^8*e - 37*sqrt(a*c)*a^4*c^3*d^6*e^3 + 38*sqrt(a*c)*a^5*c^2*d^4*e^5 - 13*sqrt(a*c)*a^6*c*d^2*e^7)*abs(c))*arctan(sqrt(x*e + d)/sqrt(-(a^2*c^2*d^3 - a^3*c*d*e^2 - sqrt((a^2*c^2*d^3 - a^3*c*d*e^2)^2 - (a^2*c^2*d^4 - 2*a^3*c*d^2*e^2 + a^4*e^4)*(a^2*c^2*d^2 - a^3*c*e^2)))/(a^2*c^2*d^2 - a^3*c*e^2)))/((a^4*c^4*d^5 + sqrt(a*c)*a^4*c^3*d^4*e - 2*a^5*c^3*d^3*e^2 - 2*sqrt(a*c)*a^5*c^2*d^2*e^3 + a^6*c^2*d*e^4 + sqrt(a*c)*a^6*c*e^5)*sqrt(-c^2*d + sqrt(a*c)*c*e)*abs(a^2*c*d^2*e - a^3*e^3)) - 1/16*(6*(x*e + d)^(7/2)*c^2*d^2*e - 18*(x*e + d)^(5/2)*c^2*d^3*e + 18*(x*e + d)^(3/2)*c^2*d^4*e - 6*sqrt(x*e + d)*c^2*d^5*e - 5*(x*e + d)^(7/2)*a*c*e^3 + 14*(x*e + d)^(5/2)*a*c*d*e^3 - 23*(x*e + d)^(3/2)*a*c*d^2*e^3 + 14*sqrt(x*e + d)*a*c*d^3*e^3 + 9*(x*e + d)^(3/2)*a^2*e^5 - 8*sqrt(x*e + d)*a^2*d*e^5)/((a^2*c*d^2 - a^3*e^2)*((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 - a*e^2)^2)","B",0
642,1,827,0,0.783491," ","integrate(1/(-c*x^2+a)^3/(e*x+d)^(1/2),x, algorithm=""giac"")","-\frac{3 \, {\left(4 \, c d^{2} + 10 \, \sqrt{a c} d e + 7 \, a e^{2}\right)} {\left| c \right|} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a^{2} c^{3} d^{5} - 2 \, a^{3} c^{2} d^{3} e^{2} + a^{4} c d e^{4} + \sqrt{{\left(a^{2} c^{3} d^{5} - 2 \, a^{3} c^{2} d^{3} e^{2} + a^{4} c d e^{4}\right)}^{2} - {\left(a^{2} c^{3} d^{6} - 3 \, a^{3} c^{2} d^{4} e^{2} + 3 \, a^{4} c d^{2} e^{4} - a^{5} e^{6}\right)} {\left(a^{2} c^{3} d^{4} - 2 \, a^{3} c^{2} d^{2} e^{2} + a^{4} c e^{4}\right)}}}{a^{2} c^{3} d^{4} - 2 \, a^{3} c^{2} d^{2} e^{2} + a^{4} c e^{4}}}}\right)}{32 \, {\left(2 \, a^{3} c d e + \sqrt{a c} a^{2} c d^{2} + \sqrt{a c} a^{3} e^{2}\right)} \sqrt{-c^{2} d - \sqrt{a c} c e}} - \frac{3 \, {\left(4 \, c d^{2} - 10 \, \sqrt{a c} d e + 7 \, a e^{2}\right)} {\left| c \right|} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a^{2} c^{3} d^{5} - 2 \, a^{3} c^{2} d^{3} e^{2} + a^{4} c d e^{4} - \sqrt{{\left(a^{2} c^{3} d^{5} - 2 \, a^{3} c^{2} d^{3} e^{2} + a^{4} c d e^{4}\right)}^{2} - {\left(a^{2} c^{3} d^{6} - 3 \, a^{3} c^{2} d^{4} e^{2} + 3 \, a^{4} c d^{2} e^{4} - a^{5} e^{6}\right)} {\left(a^{2} c^{3} d^{4} - 2 \, a^{3} c^{2} d^{2} e^{2} + a^{4} c e^{4}\right)}}}{a^{2} c^{3} d^{4} - 2 \, a^{3} c^{2} d^{2} e^{2} + a^{4} c e^{4}}}}\right)}{32 \, {\left(2 \, a^{3} c d e - \sqrt{a c} a^{2} c d^{2} - \sqrt{a c} a^{3} e^{2}\right)} \sqrt{-c^{2} d + \sqrt{a c} c e}} - \frac{6 \, {\left(x e + d\right)}^{\frac{7}{2}} c^{3} d^{3} e - 18 \, {\left(x e + d\right)}^{\frac{5}{2}} c^{3} d^{4} e + 18 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{3} d^{5} e - 6 \, \sqrt{x e + d} c^{3} d^{6} e - 12 \, {\left(x e + d\right)}^{\frac{7}{2}} a c^{2} d e^{3} + 35 \, {\left(x e + d\right)}^{\frac{5}{2}} a c^{2} d^{2} e^{3} - 44 \, {\left(x e + d\right)}^{\frac{3}{2}} a c^{2} d^{3} e^{3} + 21 \, \sqrt{x e + d} a c^{2} d^{4} e^{3} + 7 \, {\left(x e + d\right)}^{\frac{5}{2}} a^{2} c e^{5} + 2 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} c d e^{5} - 4 \, \sqrt{x e + d} a^{2} c d^{2} e^{5} - 11 \, \sqrt{x e + d} a^{3} e^{7}}{16 \, {\left(a^{2} c^{2} d^{4} - 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4}\right)} {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} - a e^{2}\right)}^{2}}"," ",0,"-3/32*(4*c*d^2 + 10*sqrt(a*c)*d*e + 7*a*e^2)*abs(c)*arctan(sqrt(x*e + d)/sqrt(-(a^2*c^3*d^5 - 2*a^3*c^2*d^3*e^2 + a^4*c*d*e^4 + sqrt((a^2*c^3*d^5 - 2*a^3*c^2*d^3*e^2 + a^4*c*d*e^4)^2 - (a^2*c^3*d^6 - 3*a^3*c^2*d^4*e^2 + 3*a^4*c*d^2*e^4 - a^5*e^6)*(a^2*c^3*d^4 - 2*a^3*c^2*d^2*e^2 + a^4*c*e^4)))/(a^2*c^3*d^4 - 2*a^3*c^2*d^2*e^2 + a^4*c*e^4)))/((2*a^3*c*d*e + sqrt(a*c)*a^2*c*d^2 + sqrt(a*c)*a^3*e^2)*sqrt(-c^2*d - sqrt(a*c)*c*e)) - 3/32*(4*c*d^2 - 10*sqrt(a*c)*d*e + 7*a*e^2)*abs(c)*arctan(sqrt(x*e + d)/sqrt(-(a^2*c^3*d^5 - 2*a^3*c^2*d^3*e^2 + a^4*c*d*e^4 - sqrt((a^2*c^3*d^5 - 2*a^3*c^2*d^3*e^2 + a^4*c*d*e^4)^2 - (a^2*c^3*d^6 - 3*a^3*c^2*d^4*e^2 + 3*a^4*c*d^2*e^4 - a^5*e^6)*(a^2*c^3*d^4 - 2*a^3*c^2*d^2*e^2 + a^4*c*e^4)))/(a^2*c^3*d^4 - 2*a^3*c^2*d^2*e^2 + a^4*c*e^4)))/((2*a^3*c*d*e - sqrt(a*c)*a^2*c*d^2 - sqrt(a*c)*a^3*e^2)*sqrt(-c^2*d + sqrt(a*c)*c*e)) - 1/16*(6*(x*e + d)^(7/2)*c^3*d^3*e - 18*(x*e + d)^(5/2)*c^3*d^4*e + 18*(x*e + d)^(3/2)*c^3*d^5*e - 6*sqrt(x*e + d)*c^3*d^6*e - 12*(x*e + d)^(7/2)*a*c^2*d*e^3 + 35*(x*e + d)^(5/2)*a*c^2*d^2*e^3 - 44*(x*e + d)^(3/2)*a*c^2*d^3*e^3 + 21*sqrt(x*e + d)*a*c^2*d^4*e^3 + 7*(x*e + d)^(5/2)*a^2*c*e^5 + 2*(x*e + d)^(3/2)*a^2*c*d*e^5 - 4*sqrt(x*e + d)*a^2*c*d^2*e^5 - 11*sqrt(x*e + d)*a^3*e^7)/((a^2*c^2*d^4 - 2*a^3*c*d^2*e^2 + a^4*e^4)*((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 - a*e^2)^2)","B",0
643,1,550,0,0.557989," ","integrate((e*x+d)^(7/2)/(c*x^2+a)^3,x, algorithm=""giac"")","-\frac{{\left(12 \, c^{2} d^{3} - 6 \, \sqrt{-a c} c d^{2} e + 13 \, a c d e^{2} - 5 \, \sqrt{-a c} a e^{3}\right)} \sqrt{-c^{2} d - \sqrt{-a c} c e} {\left| c \right|} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a^{2} c^{3} d + \sqrt{a^{4} c^{6} d^{2} - {\left(a^{2} c^{3} d^{2} + a^{3} c^{2} e^{2}\right)} a^{2} c^{3}}}{a^{2} c^{3}}}}\right)}{32 \, \sqrt{-a c} a^{2} c^{4}} + \frac{{\left(12 \, c^{2} d^{3} + 6 \, \sqrt{-a c} c d^{2} e + 13 \, a c d e^{2} + 5 \, \sqrt{-a c} a e^{3}\right)} \sqrt{-c^{2} d + \sqrt{-a c} c e} {\left| c \right|} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a^{2} c^{3} d - \sqrt{a^{4} c^{6} d^{2} - {\left(a^{2} c^{3} d^{2} + a^{3} c^{2} e^{2}\right)} a^{2} c^{3}}}{a^{2} c^{3}}}}\right)}{32 \, \sqrt{-a c} a^{2} c^{4}} + \frac{6 \, {\left(x e + d\right)}^{\frac{7}{2}} c^{3} d^{3} e - 18 \, {\left(x e + d\right)}^{\frac{5}{2}} c^{3} d^{4} e + 18 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{3} d^{5} e - 6 \, \sqrt{x e + d} c^{3} d^{6} e + 8 \, {\left(x e + d\right)}^{\frac{7}{2}} a c^{2} d e^{3} - 23 \, {\left(x e + d\right)}^{\frac{5}{2}} a c^{2} d^{2} e^{3} + 32 \, {\left(x e + d\right)}^{\frac{3}{2}} a c^{2} d^{3} e^{3} - 17 \, \sqrt{x e + d} a c^{2} d^{4} e^{3} - 9 \, {\left(x e + d\right)}^{\frac{5}{2}} a^{2} c e^{5} + 14 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} c d e^{5} - 16 \, \sqrt{x e + d} a^{2} c d^{2} e^{5} - 5 \, \sqrt{x e + d} a^{3} e^{7}}{16 \, {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + a e^{2}\right)}^{2} a^{2} c^{2}}"," ",0,"-1/32*(12*c^2*d^3 - 6*sqrt(-a*c)*c*d^2*e + 13*a*c*d*e^2 - 5*sqrt(-a*c)*a*e^3)*sqrt(-c^2*d - sqrt(-a*c)*c*e)*abs(c)*arctan(sqrt(x*e + d)/sqrt(-(a^2*c^3*d + sqrt(a^4*c^6*d^2 - (a^2*c^3*d^2 + a^3*c^2*e^2)*a^2*c^3))/(a^2*c^3)))/(sqrt(-a*c)*a^2*c^4) + 1/32*(12*c^2*d^3 + 6*sqrt(-a*c)*c*d^2*e + 13*a*c*d*e^2 + 5*sqrt(-a*c)*a*e^3)*sqrt(-c^2*d + sqrt(-a*c)*c*e)*abs(c)*arctan(sqrt(x*e + d)/sqrt(-(a^2*c^3*d - sqrt(a^4*c^6*d^2 - (a^2*c^3*d^2 + a^3*c^2*e^2)*a^2*c^3))/(a^2*c^3)))/(sqrt(-a*c)*a^2*c^4) + 1/16*(6*(x*e + d)^(7/2)*c^3*d^3*e - 18*(x*e + d)^(5/2)*c^3*d^4*e + 18*(x*e + d)^(3/2)*c^3*d^5*e - 6*sqrt(x*e + d)*c^3*d^6*e + 8*(x*e + d)^(7/2)*a*c^2*d*e^3 - 23*(x*e + d)^(5/2)*a*c^2*d^2*e^3 + 32*(x*e + d)^(3/2)*a*c^2*d^3*e^3 - 17*sqrt(x*e + d)*a*c^2*d^4*e^3 - 9*(x*e + d)^(5/2)*a^2*c*e^5 + 14*(x*e + d)^(3/2)*a^2*c*d*e^5 - 16*sqrt(x*e + d)*a^2*c*d^2*e^5 - 5*sqrt(x*e + d)*a^3*e^7)/(((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + a*e^2)^2*a^2*c^2)","A",0
644,1,586,0,0.644665," ","integrate((e*x+d)^(5/2)/(c*x^2+a)^3,x, algorithm=""giac"")","-\frac{3 \, {\left(4 \, c^{4} d^{4} + 3 \, a c^{3} d^{2} e^{2} + {\left(2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} c^{2} - 2 \, {\left(\sqrt{-a c} c^{2} d^{3} e + \sqrt{-a c} a c d e^{3}\right)} {\left| c \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a^{2} c^{2} d + \sqrt{a^{4} c^{4} d^{2} - {\left(a^{2} c^{2} d^{2} + a^{3} c e^{2}\right)} a^{2} c^{2}}}{a^{2} c^{2}}}}\right)}{32 \, {\left(a^{3} c^{3} e - \sqrt{-a c} a^{2} c^{3} d\right)} \sqrt{-c^{2} d + \sqrt{-a c} c e}} - \frac{3 \, {\left(4 \, c^{4} d^{4} + 3 \, a c^{3} d^{2} e^{2} + {\left(2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} c^{2} + 2 \, {\left(\sqrt{-a c} c^{2} d^{3} e + \sqrt{-a c} a c d e^{3}\right)} {\left| c \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a^{2} c^{2} d - \sqrt{a^{4} c^{4} d^{2} - {\left(a^{2} c^{2} d^{2} + a^{3} c e^{2}\right)} a^{2} c^{2}}}{a^{2} c^{2}}}}\right)}{32 \, {\left(a^{3} c^{3} e + \sqrt{-a c} a^{2} c^{3} d\right)} \sqrt{-c^{2} d - \sqrt{-a c} c e}} + \frac{6 \, {\left(x e + d\right)}^{\frac{7}{2}} c^{2} d^{2} e - 18 \, {\left(x e + d\right)}^{\frac{5}{2}} c^{2} d^{3} e + 18 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{2} d^{4} e - 6 \, \sqrt{x e + d} c^{2} d^{5} e + 3 \, {\left(x e + d\right)}^{\frac{7}{2}} a c e^{3} - 8 \, {\left(x e + d\right)}^{\frac{5}{2}} a c d e^{3} + 17 \, {\left(x e + d\right)}^{\frac{3}{2}} a c d^{2} e^{3} - 12 \, \sqrt{x e + d} a c d^{3} e^{3} - {\left(x e + d\right)}^{\frac{3}{2}} a^{2} e^{5} - 6 \, \sqrt{x e + d} a^{2} d e^{5}}{16 \, {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + a e^{2}\right)}^{2} a^{2} c}"," ",0,"-3/32*(4*c^4*d^4 + 3*a*c^3*d^2*e^2 + (2*a*c*d^2*e^2 + a^2*e^4)*c^2 - 2*(sqrt(-a*c)*c^2*d^3*e + sqrt(-a*c)*a*c*d*e^3)*abs(c))*arctan(sqrt(x*e + d)/sqrt(-(a^2*c^2*d + sqrt(a^4*c^4*d^2 - (a^2*c^2*d^2 + a^3*c*e^2)*a^2*c^2))/(a^2*c^2)))/((a^3*c^3*e - sqrt(-a*c)*a^2*c^3*d)*sqrt(-c^2*d + sqrt(-a*c)*c*e)) - 3/32*(4*c^4*d^4 + 3*a*c^3*d^2*e^2 + (2*a*c*d^2*e^2 + a^2*e^4)*c^2 + 2*(sqrt(-a*c)*c^2*d^3*e + sqrt(-a*c)*a*c*d*e^3)*abs(c))*arctan(sqrt(x*e + d)/sqrt(-(a^2*c^2*d - sqrt(a^4*c^4*d^2 - (a^2*c^2*d^2 + a^3*c*e^2)*a^2*c^2))/(a^2*c^2)))/((a^3*c^3*e + sqrt(-a*c)*a^2*c^3*d)*sqrt(-c^2*d - sqrt(-a*c)*c*e)) + 1/16*(6*(x*e + d)^(7/2)*c^2*d^2*e - 18*(x*e + d)^(5/2)*c^2*d^3*e + 18*(x*e + d)^(3/2)*c^2*d^4*e - 6*sqrt(x*e + d)*c^2*d^5*e + 3*(x*e + d)^(7/2)*a*c*e^3 - 8*(x*e + d)^(5/2)*a*c*d*e^3 + 17*(x*e + d)^(3/2)*a*c*d^2*e^3 - 12*sqrt(x*e + d)*a*c*d^3*e^3 - (x*e + d)^(3/2)*a^2*e^5 - 6*sqrt(x*e + d)*a^2*d*e^5)/(((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + a*e^2)^2*a^2*c)","A",0
645,1,499,0,0.609864," ","integrate((e*x+d)^(3/2)/(c*x^2+a)^3,x, algorithm=""giac"")","-\frac{3 \, {\left(4 \, c^{3} d^{3} + 3 \, a c^{2} d e^{2} - {\left(2 \, \sqrt{-a c} c d^{2} e + \sqrt{-a c} a e^{3}\right)} {\left| c \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a^{2} c^{2} d + \sqrt{a^{4} c^{4} d^{2} - {\left(a^{2} c^{2} d^{2} + a^{3} c e^{2}\right)} a^{2} c^{2}}}{a^{2} c^{2}}}}\right)}{32 \, {\left(a^{3} c^{2} e - \sqrt{-a c} a^{2} c^{2} d\right)} \sqrt{-c^{2} d + \sqrt{-a c} c e}} - \frac{3 \, {\left(4 \, c^{3} d^{3} + 3 \, a c^{2} d e^{2} + {\left(2 \, \sqrt{-a c} c d^{2} e + \sqrt{-a c} a e^{3}\right)} {\left| c \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a^{2} c^{2} d - \sqrt{a^{4} c^{4} d^{2} - {\left(a^{2} c^{2} d^{2} + a^{3} c e^{2}\right)} a^{2} c^{2}}}{a^{2} c^{2}}}}\right)}{32 \, {\left(a^{3} c^{2} e + \sqrt{-a c} a^{2} c^{2} d\right)} \sqrt{-c^{2} d - \sqrt{-a c} c e}} + \frac{6 \, {\left(x e + d\right)}^{\frac{7}{2}} c^{2} d e - 18 \, {\left(x e + d\right)}^{\frac{5}{2}} c^{2} d^{2} e + 18 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{2} d^{3} e - 6 \, \sqrt{x e + d} c^{2} d^{4} e + {\left(x e + d\right)}^{\frac{5}{2}} a c e^{3} + 8 \, {\left(x e + d\right)}^{\frac{3}{2}} a c d e^{3} - 9 \, \sqrt{x e + d} a c d^{2} e^{3} - 3 \, \sqrt{x e + d} a^{2} e^{5}}{16 \, {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + a e^{2}\right)}^{2} a^{2} c}"," ",0,"-3/32*(4*c^3*d^3 + 3*a*c^2*d*e^2 - (2*sqrt(-a*c)*c*d^2*e + sqrt(-a*c)*a*e^3)*abs(c))*arctan(sqrt(x*e + d)/sqrt(-(a^2*c^2*d + sqrt(a^4*c^4*d^2 - (a^2*c^2*d^2 + a^3*c*e^2)*a^2*c^2))/(a^2*c^2)))/((a^3*c^2*e - sqrt(-a*c)*a^2*c^2*d)*sqrt(-c^2*d + sqrt(-a*c)*c*e)) - 3/32*(4*c^3*d^3 + 3*a*c^2*d*e^2 + (2*sqrt(-a*c)*c*d^2*e + sqrt(-a*c)*a*e^3)*abs(c))*arctan(sqrt(x*e + d)/sqrt(-(a^2*c^2*d - sqrt(a^4*c^4*d^2 - (a^2*c^2*d^2 + a^3*c*e^2)*a^2*c^2))/(a^2*c^2)))/((a^3*c^2*e + sqrt(-a*c)*a^2*c^2*d)*sqrt(-c^2*d - sqrt(-a*c)*c*e)) + 1/16*(6*(x*e + d)^(7/2)*c^2*d*e - 18*(x*e + d)^(5/2)*c^2*d^2*e + 18*(x*e + d)^(3/2)*c^2*d^3*e - 6*sqrt(x*e + d)*c^2*d^4*e + (x*e + d)^(5/2)*a*c*e^3 + 8*(x*e + d)^(3/2)*a*c*d*e^3 - 9*sqrt(x*e + d)*a*c*d^2*e^3 - 3*sqrt(x*e + d)*a^2*e^5)/(((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + a*e^2)^2*a^2*c)","A",0
646,1,1056,0,0.844934," ","integrate((e*x+d)^(1/2)/(c*x^2+a)^3,x, algorithm=""giac"")","-\frac{{\left({\left(a^{2} c d^{2} e + a^{3} e^{3}\right)}^{2} {\left(6 \, c d^{2} e + 5 \, a e^{3}\right)} {\left| c \right|} - 2 \, {\left(3 \, \sqrt{-a c} a c^{2} d^{5} e + 7 \, \sqrt{-a c} a^{2} c d^{3} e^{3} + 4 \, \sqrt{-a c} a^{3} d e^{5}\right)} {\left| -a^{2} c d^{2} e - a^{3} e^{3} \right|} {\left| c \right|} + {\left(12 \, a^{3} c^{4} d^{8} e + 37 \, a^{4} c^{3} d^{6} e^{3} + 38 \, a^{5} c^{2} d^{4} e^{5} + 13 \, a^{6} c d^{2} e^{7}\right)} {\left| c \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a^{2} c^{2} d^{3} + a^{3} c d e^{2} + \sqrt{{\left(a^{2} c^{2} d^{3} + a^{3} c d e^{2}\right)}^{2} - {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4}\right)} {\left(a^{2} c^{2} d^{2} + a^{3} c e^{2}\right)}}}{a^{2} c^{2} d^{2} + a^{3} c e^{2}}}}\right)}{32 \, {\left(a^{4} c^{3} d^{4} e - \sqrt{-a c} a^{3} c^{3} d^{5} - 2 \, \sqrt{-a c} a^{4} c^{2} d^{3} e^{2} + 2 \, a^{5} c^{2} d^{2} e^{3} - \sqrt{-a c} a^{5} c d e^{4} + a^{6} c e^{5}\right)} \sqrt{-c^{2} d + \sqrt{-a c} c e} {\left| -a^{2} c d^{2} e - a^{3} e^{3} \right|}} - \frac{{\left({\left(a^{2} c d^{2} e + a^{3} e^{3}\right)}^{2} {\left(6 \, c d^{2} e + 5 \, a e^{3}\right)} {\left| c \right|} + 2 \, {\left(3 \, \sqrt{-a c} a c^{2} d^{5} e + 7 \, \sqrt{-a c} a^{2} c d^{3} e^{3} + 4 \, \sqrt{-a c} a^{3} d e^{5}\right)} {\left| -a^{2} c d^{2} e - a^{3} e^{3} \right|} {\left| c \right|} + {\left(12 \, a^{3} c^{4} d^{8} e + 37 \, a^{4} c^{3} d^{6} e^{3} + 38 \, a^{5} c^{2} d^{4} e^{5} + 13 \, a^{6} c d^{2} e^{7}\right)} {\left| c \right|}\right)} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a^{2} c^{2} d^{3} + a^{3} c d e^{2} - \sqrt{{\left(a^{2} c^{2} d^{3} + a^{3} c d e^{2}\right)}^{2} - {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4}\right)} {\left(a^{2} c^{2} d^{2} + a^{3} c e^{2}\right)}}}{a^{2} c^{2} d^{2} + a^{3} c e^{2}}}}\right)}{32 \, {\left(a^{4} c^{3} d^{4} e + \sqrt{-a c} a^{3} c^{3} d^{5} + 2 \, \sqrt{-a c} a^{4} c^{2} d^{3} e^{2} + 2 \, a^{5} c^{2} d^{2} e^{3} + \sqrt{-a c} a^{5} c d e^{4} + a^{6} c e^{5}\right)} \sqrt{-c^{2} d - \sqrt{-a c} c e} {\left| -a^{2} c d^{2} e - a^{3} e^{3} \right|}} + \frac{6 \, {\left(x e + d\right)}^{\frac{7}{2}} c^{2} d^{2} e - 18 \, {\left(x e + d\right)}^{\frac{5}{2}} c^{2} d^{3} e + 18 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{2} d^{4} e - 6 \, \sqrt{x e + d} c^{2} d^{5} e + 5 \, {\left(x e + d\right)}^{\frac{7}{2}} a c e^{3} - 14 \, {\left(x e + d\right)}^{\frac{5}{2}} a c d e^{3} + 23 \, {\left(x e + d\right)}^{\frac{3}{2}} a c d^{2} e^{3} - 14 \, \sqrt{x e + d} a c d^{3} e^{3} + 9 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} e^{5} - 8 \, \sqrt{x e + d} a^{2} d e^{5}}{16 \, {\left(a^{2} c d^{2} + a^{3} e^{2}\right)} {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + a e^{2}\right)}^{2}}"," ",0,"-1/32*((a^2*c*d^2*e + a^3*e^3)^2*(6*c*d^2*e + 5*a*e^3)*abs(c) - 2*(3*sqrt(-a*c)*a*c^2*d^5*e + 7*sqrt(-a*c)*a^2*c*d^3*e^3 + 4*sqrt(-a*c)*a^3*d*e^5)*abs(-a^2*c*d^2*e - a^3*e^3)*abs(c) + (12*a^3*c^4*d^8*e + 37*a^4*c^3*d^6*e^3 + 38*a^5*c^2*d^4*e^5 + 13*a^6*c*d^2*e^7)*abs(c))*arctan(sqrt(x*e + d)/sqrt(-(a^2*c^2*d^3 + a^3*c*d*e^2 + sqrt((a^2*c^2*d^3 + a^3*c*d*e^2)^2 - (a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4)*(a^2*c^2*d^2 + a^3*c*e^2)))/(a^2*c^2*d^2 + a^3*c*e^2)))/((a^4*c^3*d^4*e - sqrt(-a*c)*a^3*c^3*d^5 - 2*sqrt(-a*c)*a^4*c^2*d^3*e^2 + 2*a^5*c^2*d^2*e^3 - sqrt(-a*c)*a^5*c*d*e^4 + a^6*c*e^5)*sqrt(-c^2*d + sqrt(-a*c)*c*e)*abs(-a^2*c*d^2*e - a^3*e^3)) - 1/32*((a^2*c*d^2*e + a^3*e^3)^2*(6*c*d^2*e + 5*a*e^3)*abs(c) + 2*(3*sqrt(-a*c)*a*c^2*d^5*e + 7*sqrt(-a*c)*a^2*c*d^3*e^3 + 4*sqrt(-a*c)*a^3*d*e^5)*abs(-a^2*c*d^2*e - a^3*e^3)*abs(c) + (12*a^3*c^4*d^8*e + 37*a^4*c^3*d^6*e^3 + 38*a^5*c^2*d^4*e^5 + 13*a^6*c*d^2*e^7)*abs(c))*arctan(sqrt(x*e + d)/sqrt(-(a^2*c^2*d^3 + a^3*c*d*e^2 - sqrt((a^2*c^2*d^3 + a^3*c*d*e^2)^2 - (a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4)*(a^2*c^2*d^2 + a^3*c*e^2)))/(a^2*c^2*d^2 + a^3*c*e^2)))/((a^4*c^3*d^4*e + sqrt(-a*c)*a^3*c^3*d^5 + 2*sqrt(-a*c)*a^4*c^2*d^3*e^2 + 2*a^5*c^2*d^2*e^3 + sqrt(-a*c)*a^5*c*d*e^4 + a^6*c*e^5)*sqrt(-c^2*d - sqrt(-a*c)*c*e)*abs(-a^2*c*d^2*e - a^3*e^3)) + 1/16*(6*(x*e + d)^(7/2)*c^2*d^2*e - 18*(x*e + d)^(5/2)*c^2*d^3*e + 18*(x*e + d)^(3/2)*c^2*d^4*e - 6*sqrt(x*e + d)*c^2*d^5*e + 5*(x*e + d)^(7/2)*a*c*e^3 - 14*(x*e + d)^(5/2)*a*c*d*e^3 + 23*(x*e + d)^(3/2)*a*c*d^2*e^3 - 14*sqrt(x*e + d)*a*c*d^3*e^3 + 9*(x*e + d)^(3/2)*a^2*e^5 - 8*sqrt(x*e + d)*a^2*d*e^5)/((a^2*c*d^2 + a^3*e^2)*((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + a*e^2)^2)","A",0
647,1,832,0,0.764982," ","integrate(1/(c*x^2+a)^3/(e*x+d)^(1/2),x, algorithm=""giac"")","-\frac{3 \, {\left(4 \, c d^{2} + 10 \, \sqrt{-a c} d e - 7 \, a e^{2}\right)} {\left| c \right|} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a^{2} c^{3} d^{5} + 2 \, a^{3} c^{2} d^{3} e^{2} + a^{4} c d e^{4} + \sqrt{{\left(a^{2} c^{3} d^{5} + 2 \, a^{3} c^{2} d^{3} e^{2} + a^{4} c d e^{4}\right)}^{2} - {\left(a^{2} c^{3} d^{6} + 3 \, a^{3} c^{2} d^{4} e^{2} + 3 \, a^{4} c d^{2} e^{4} + a^{5} e^{6}\right)} {\left(a^{2} c^{3} d^{4} + 2 \, a^{3} c^{2} d^{2} e^{2} + a^{4} c e^{4}\right)}}}{a^{2} c^{3} d^{4} + 2 \, a^{3} c^{2} d^{2} e^{2} + a^{4} c e^{4}}}}\right)}{32 \, {\left(2 \, a^{3} c d e - \sqrt{-a c} a^{2} c d^{2} + \sqrt{-a c} a^{3} e^{2}\right)} \sqrt{-c^{2} d - \sqrt{-a c} c e}} - \frac{3 \, {\left(4 \, c d^{2} - 10 \, \sqrt{-a c} d e - 7 \, a e^{2}\right)} {\left| c \right|} \arctan\left(\frac{\sqrt{x e + d}}{\sqrt{-\frac{a^{2} c^{3} d^{5} + 2 \, a^{3} c^{2} d^{3} e^{2} + a^{4} c d e^{4} - \sqrt{{\left(a^{2} c^{3} d^{5} + 2 \, a^{3} c^{2} d^{3} e^{2} + a^{4} c d e^{4}\right)}^{2} - {\left(a^{2} c^{3} d^{6} + 3 \, a^{3} c^{2} d^{4} e^{2} + 3 \, a^{4} c d^{2} e^{4} + a^{5} e^{6}\right)} {\left(a^{2} c^{3} d^{4} + 2 \, a^{3} c^{2} d^{2} e^{2} + a^{4} c e^{4}\right)}}}{a^{2} c^{3} d^{4} + 2 \, a^{3} c^{2} d^{2} e^{2} + a^{4} c e^{4}}}}\right)}{32 \, {\left(2 \, a^{3} c d e + \sqrt{-a c} a^{2} c d^{2} - \sqrt{-a c} a^{3} e^{2}\right)} \sqrt{-c^{2} d + \sqrt{-a c} c e}} + \frac{6 \, {\left(x e + d\right)}^{\frac{7}{2}} c^{3} d^{3} e - 18 \, {\left(x e + d\right)}^{\frac{5}{2}} c^{3} d^{4} e + 18 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{3} d^{5} e - 6 \, \sqrt{x e + d} c^{3} d^{6} e + 12 \, {\left(x e + d\right)}^{\frac{7}{2}} a c^{2} d e^{3} - 35 \, {\left(x e + d\right)}^{\frac{5}{2}} a c^{2} d^{2} e^{3} + 44 \, {\left(x e + d\right)}^{\frac{3}{2}} a c^{2} d^{3} e^{3} - 21 \, \sqrt{x e + d} a c^{2} d^{4} e^{3} + 7 \, {\left(x e + d\right)}^{\frac{5}{2}} a^{2} c e^{5} + 2 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} c d e^{5} - 4 \, \sqrt{x e + d} a^{2} c d^{2} e^{5} + 11 \, \sqrt{x e + d} a^{3} e^{7}}{16 \, {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4}\right)} {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + a e^{2}\right)}^{2}}"," ",0,"-3/32*(4*c*d^2 + 10*sqrt(-a*c)*d*e - 7*a*e^2)*abs(c)*arctan(sqrt(x*e + d)/sqrt(-(a^2*c^3*d^5 + 2*a^3*c^2*d^3*e^2 + a^4*c*d*e^4 + sqrt((a^2*c^3*d^5 + 2*a^3*c^2*d^3*e^2 + a^4*c*d*e^4)^2 - (a^2*c^3*d^6 + 3*a^3*c^2*d^4*e^2 + 3*a^4*c*d^2*e^4 + a^5*e^6)*(a^2*c^3*d^4 + 2*a^3*c^2*d^2*e^2 + a^4*c*e^4)))/(a^2*c^3*d^4 + 2*a^3*c^2*d^2*e^2 + a^4*c*e^4)))/((2*a^3*c*d*e - sqrt(-a*c)*a^2*c*d^2 + sqrt(-a*c)*a^3*e^2)*sqrt(-c^2*d - sqrt(-a*c)*c*e)) - 3/32*(4*c*d^2 - 10*sqrt(-a*c)*d*e - 7*a*e^2)*abs(c)*arctan(sqrt(x*e + d)/sqrt(-(a^2*c^3*d^5 + 2*a^3*c^2*d^3*e^2 + a^4*c*d*e^4 - sqrt((a^2*c^3*d^5 + 2*a^3*c^2*d^3*e^2 + a^4*c*d*e^4)^2 - (a^2*c^3*d^6 + 3*a^3*c^2*d^4*e^2 + 3*a^4*c*d^2*e^4 + a^5*e^6)*(a^2*c^3*d^4 + 2*a^3*c^2*d^2*e^2 + a^4*c*e^4)))/(a^2*c^3*d^4 + 2*a^3*c^2*d^2*e^2 + a^4*c*e^4)))/((2*a^3*c*d*e + sqrt(-a*c)*a^2*c*d^2 - sqrt(-a*c)*a^3*e^2)*sqrt(-c^2*d + sqrt(-a*c)*c*e)) + 1/16*(6*(x*e + d)^(7/2)*c^3*d^3*e - 18*(x*e + d)^(5/2)*c^3*d^4*e + 18*(x*e + d)^(3/2)*c^3*d^5*e - 6*sqrt(x*e + d)*c^3*d^6*e + 12*(x*e + d)^(7/2)*a*c^2*d*e^3 - 35*(x*e + d)^(5/2)*a*c^2*d^2*e^3 + 44*(x*e + d)^(3/2)*a*c^2*d^3*e^3 - 21*sqrt(x*e + d)*a*c^2*d^4*e^3 + 7*(x*e + d)^(5/2)*a^2*c*e^5 + 2*(x*e + d)^(3/2)*a^2*c*d*e^5 - 4*sqrt(x*e + d)*a^2*c*d^2*e^5 + 11*sqrt(x*e + d)*a^3*e^7)/((a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4)*((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + a*e^2)^2)","A",0
648,1,179,0,1.103280," ","integrate((2+3*x)^(1/2)/(x^2+1),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{2 \, \sqrt{13} + 4} \arctan\left(\frac{13^{\frac{3}{4}} {\left(13^{\frac{1}{4}} \sqrt{\frac{1}{13} \, \sqrt{13} + \frac{1}{2}} + \sqrt{3 \, x + 2}\right)}}{13 \, \sqrt{-\frac{1}{13} \, \sqrt{13} + \frac{1}{2}}}\right) + \frac{1}{2} \, \sqrt{2 \, \sqrt{13} + 4} \arctan\left(-\frac{13^{\frac{3}{4}} {\left(13^{\frac{1}{4}} \sqrt{\frac{1}{13} \, \sqrt{13} + \frac{1}{2}} - \sqrt{3 \, x + 2}\right)}}{13 \, \sqrt{-\frac{1}{13} \, \sqrt{13} + \frac{1}{2}}}\right) - \frac{1}{4} \, \sqrt{2 \, \sqrt{13} - 4} \log\left(2 \cdot 13^{\frac{1}{4}} \sqrt{3 \, x + 2} \sqrt{\frac{1}{13} \, \sqrt{13} + \frac{1}{2}} + 3 \, x + \sqrt{13} + 2\right) + \frac{1}{4} \, \sqrt{2 \, \sqrt{13} - 4} \log\left(-2 \cdot 13^{\frac{1}{4}} \sqrt{3 \, x + 2} \sqrt{\frac{1}{13} \, \sqrt{13} + \frac{1}{2}} + 3 \, x + \sqrt{13} + 2\right)"," ",0,"1/2*sqrt(2*sqrt(13) + 4)*arctan(1/13*13^(3/4)*(13^(1/4)*sqrt(1/13*sqrt(13) + 1/2) + sqrt(3*x + 2))/sqrt(-1/13*sqrt(13) + 1/2)) + 1/2*sqrt(2*sqrt(13) + 4)*arctan(-1/13*13^(3/4)*(13^(1/4)*sqrt(1/13*sqrt(13) + 1/2) - sqrt(3*x + 2))/sqrt(-1/13*sqrt(13) + 1/2)) - 1/4*sqrt(2*sqrt(13) - 4)*log(2*13^(1/4)*sqrt(3*x + 2)*sqrt(1/13*sqrt(13) + 1/2) + 3*x + sqrt(13) + 2) + 1/4*sqrt(2*sqrt(13) - 4)*log(-2*13^(1/4)*sqrt(3*x + 2)*sqrt(1/13*sqrt(13) + 1/2) + 3*x + sqrt(13) + 2)","A",0
649,-1,0,0,0.000000," ","integrate((d*x+c)^(1/2)/(x^2+1),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
650,1,48,0,0.217795," ","integrate((2+3*x)^(1/2)/(-x^2+1),x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{5} \log\left(\frac{{\left| -2 \, \sqrt{5} + 2 \, \sqrt{3 \, x + 2} \right|}}{2 \, {\left(\sqrt{5} + \sqrt{3 \, x + 2}\right)}}\right) - \arctan\left(\sqrt{3 \, x + 2}\right)"," ",0,"-1/2*sqrt(5)*log(1/2*abs(-2*sqrt(5) + 2*sqrt(3*x + 2))/(sqrt(5) + sqrt(3*x + 2))) - arctan(sqrt(3*x + 2))","A",0
651,1,54,0,0.197678," ","integrate((d*x+c)^(1/2)/(-x^2+1),x, algorithm=""giac"")","-\sqrt{-c + d} \arctan\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,"-sqrt(-c + d)*arctan(sqrt(d*x + c)/sqrt(-c + d)) + sqrt(-c - d)*arctan(sqrt(d*x + c)/sqrt(-c - d))","A",0
652,1,234,0,0.412884," ","integrate((2+3*x)^(1/2)/(b*x^2+a),x, algorithm=""giac"")","\frac{{\left(4 \, \sqrt{-a b} \sqrt{-2 \, b^{2} - 3 \, \sqrt{-a b} b} a - 17 \, \sqrt{-a b} \sqrt{-2 \, b^{2} - 3 \, \sqrt{-a b} b} b\right)} {\left| b \right|} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{3 \, x + 2}}{\sqrt{-\frac{4 \, b + \sqrt{-4 \, {\left(9 \, a + 4 \, b\right)} b + 16 \, b^{2}}}{b}}}\right)}{4 \, a^{2} b^{3} - 17 \, a b^{4}} - \frac{{\left(4 \, \sqrt{-a b} \sqrt{-2 \, b^{2} + 3 \, \sqrt{-a b} b} a - 17 \, \sqrt{-a b} \sqrt{-2 \, b^{2} + 3 \, \sqrt{-a b} b} b\right)} {\left| b \right|} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{3 \, x + 2}}{\sqrt{-\frac{4 \, b - \sqrt{-4 \, {\left(9 \, a + 4 \, b\right)} b + 16 \, b^{2}}}{b}}}\right)}{4 \, a^{2} b^{3} - 17 \, a b^{4}}"," ",0,"(4*sqrt(-a*b)*sqrt(-2*b^2 - 3*sqrt(-a*b)*b)*a - 17*sqrt(-a*b)*sqrt(-2*b^2 - 3*sqrt(-a*b)*b)*b)*abs(b)*arctan(2*sqrt(1/2)*sqrt(3*x + 2)/sqrt(-(4*b + sqrt(-4*(9*a + 4*b)*b + 16*b^2))/b))/(4*a^2*b^3 - 17*a*b^4) - (4*sqrt(-a*b)*sqrt(-2*b^2 + 3*sqrt(-a*b)*b)*a - 17*sqrt(-a*b)*sqrt(-2*b^2 + 3*sqrt(-a*b)*b)*b)*abs(b)*arctan(2*sqrt(1/2)*sqrt(3*x + 2)/sqrt(-(4*b - sqrt(-4*(9*a + 4*b)*b + 16*b^2))/b))/(4*a^2*b^3 - 17*a*b^4)","A",0
653,1,216,0,0.406389," ","integrate((2+3*x)^(1/2)/(-b*x^2+a),x, algorithm=""giac"")","\frac{{\left(4 \, \sqrt{a b} \sqrt{-2 \, b^{2} - 3 \, \sqrt{a b} b} a + 17 \, \sqrt{a b} \sqrt{-2 \, b^{2} - 3 \, \sqrt{a b} b} b\right)} {\left| b \right|} \arctan\left(\frac{\sqrt{3 \, x + 2}}{\sqrt{-\frac{2 \, b + \sqrt{{\left(9 \, a - 4 \, b\right)} b + 4 \, b^{2}}}{b}}}\right)}{4 \, a^{2} b^{3} + 17 \, a b^{4}} - \frac{{\left(4 \, \sqrt{a b} \sqrt{-2 \, b^{2} + 3 \, \sqrt{a b} b} a + 17 \, \sqrt{a b} \sqrt{-2 \, b^{2} + 3 \, \sqrt{a b} b} b\right)} {\left| b \right|} \arctan\left(\frac{\sqrt{3 \, x + 2}}{\sqrt{-\frac{2 \, b - \sqrt{{\left(9 \, a - 4 \, b\right)} b + 4 \, b^{2}}}{b}}}\right)}{4 \, a^{2} b^{3} + 17 \, a b^{4}}"," ",0,"(4*sqrt(a*b)*sqrt(-2*b^2 - 3*sqrt(a*b)*b)*a + 17*sqrt(a*b)*sqrt(-2*b^2 - 3*sqrt(a*b)*b)*b)*abs(b)*arctan(sqrt(3*x + 2)/sqrt(-(2*b + sqrt((9*a - 4*b)*b + 4*b^2))/b))/(4*a^2*b^3 + 17*a*b^4) - (4*sqrt(a*b)*sqrt(-2*b^2 + 3*sqrt(a*b)*b)*a + 17*sqrt(a*b)*sqrt(-2*b^2 + 3*sqrt(a*b)*b)*b)*abs(b)*arctan(sqrt(3*x + 2)/sqrt(-(2*b - sqrt((9*a - 4*b)*b + 4*b^2))/b))/(4*a^2*b^3 + 17*a*b^4)","B",0
654,1,160,0,0.938995," ","integrate((1+x)^(1/2)/(x^2+1),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{2 \, \sqrt{2} + 2} \arctan\left(\frac{2^{\frac{3}{4}} {\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} + 2 \, \sqrt{x + 1}\right)}}{2 \, \sqrt{-\sqrt{2} + 2}}\right) + \frac{1}{2} \, \sqrt{2 \, \sqrt{2} + 2} \arctan\left(-\frac{2^{\frac{3}{4}} {\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} - 2 \, \sqrt{x + 1}\right)}}{2 \, \sqrt{-\sqrt{2} + 2}}\right) - \frac{1}{4} \, \sqrt{2 \, \sqrt{2} - 2} \log\left(2^{\frac{1}{4}} \sqrt{x + 1} \sqrt{\sqrt{2} + 2} + x + \sqrt{2} + 1\right) + \frac{1}{4} \, \sqrt{2 \, \sqrt{2} - 2} \log\left(-2^{\frac{1}{4}} \sqrt{x + 1} \sqrt{\sqrt{2} + 2} + x + \sqrt{2} + 1\right)"," ",0,"1/2*sqrt(2*sqrt(2) + 2)*arctan(1/2*2^(3/4)*(2^(1/4)*sqrt(sqrt(2) + 2) + 2*sqrt(x + 1))/sqrt(-sqrt(2) + 2)) + 1/2*sqrt(2*sqrt(2) + 2)*arctan(-1/2*2^(3/4)*(2^(1/4)*sqrt(sqrt(2) + 2) - 2*sqrt(x + 1))/sqrt(-sqrt(2) + 2)) - 1/4*sqrt(2*sqrt(2) - 2)*log(2^(1/4)*sqrt(x + 1)*sqrt(sqrt(2) + 2) + x + sqrt(2) + 1) + 1/4*sqrt(2*sqrt(2) - 2)*log(-2^(1/4)*sqrt(x + 1)*sqrt(sqrt(2) + 2) + x + sqrt(2) + 1)","A",0
655,1,152,0,0.542444," ","integrate(1/(x^2+1)/(1+x)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{\sqrt{2} + 1} \arctan\left(\frac{2^{\frac{3}{4}} {\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} + 2 \, \sqrt{x + 1}\right)}}{2 \, \sqrt{-\sqrt{2} + 2}}\right) + \frac{1}{2} \, \sqrt{\sqrt{2} + 1} \arctan\left(-\frac{2^{\frac{3}{4}} {\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} - 2 \, \sqrt{x + 1}\right)}}{2 \, \sqrt{-\sqrt{2} + 2}}\right) + \frac{1}{4} \, \sqrt{\sqrt{2} - 1} \log\left(2^{\frac{1}{4}} \sqrt{x + 1} \sqrt{\sqrt{2} + 2} + x + \sqrt{2} + 1\right) - \frac{1}{4} \, \sqrt{\sqrt{2} - 1} \log\left(-2^{\frac{1}{4}} \sqrt{x + 1} \sqrt{\sqrt{2} + 2} + x + \sqrt{2} + 1\right)"," ",0,"1/2*sqrt(sqrt(2) + 1)*arctan(1/2*2^(3/4)*(2^(1/4)*sqrt(sqrt(2) + 2) + 2*sqrt(x + 1))/sqrt(-sqrt(2) + 2)) + 1/2*sqrt(sqrt(2) + 1)*arctan(-1/2*2^(3/4)*(2^(1/4)*sqrt(sqrt(2) + 2) - 2*sqrt(x + 1))/sqrt(-sqrt(2) + 2)) + 1/4*sqrt(sqrt(2) - 1)*log(2^(1/4)*sqrt(x + 1)*sqrt(sqrt(2) + 2) + x + sqrt(2) + 1) - 1/4*sqrt(sqrt(2) - 1)*log(-2^(1/4)*sqrt(x + 1)*sqrt(sqrt(2) + 2) + x + sqrt(2) + 1)","A",0
656,1,206,0,0.985507," ","integrate((-1+x)^(1/2)/(x^2+1)^3,x, algorithm=""giac"")","\frac{1}{128} \, \sqrt{746 \, \sqrt{2} - 1054} \arctan\left(\frac{2^{\frac{3}{4}} {\left(2^{\frac{1}{4}} \sqrt{-\sqrt{2} + 2} + 2 \, \sqrt{x - 1}\right)}}{2 \, \sqrt{\sqrt{2} + 2}}\right) + \frac{1}{128} \, \sqrt{746 \, \sqrt{2} - 1054} \arctan\left(-\frac{2^{\frac{3}{4}} {\left(2^{\frac{1}{4}} \sqrt{-\sqrt{2} + 2} - 2 \, \sqrt{x - 1}\right)}}{2 \, \sqrt{\sqrt{2} + 2}}\right) - \frac{1}{256} \, \sqrt{746 \, \sqrt{2} + 1054} \log\left(2^{\frac{1}{4}} \sqrt{x - 1} \sqrt{-\sqrt{2} + 2} + x + \sqrt{2} - 1\right) + \frac{1}{256} \, \sqrt{746 \, \sqrt{2} + 1054} \log\left(-2^{\frac{1}{4}} \sqrt{x - 1} \sqrt{-\sqrt{2} + 2} + x + \sqrt{2} - 1\right) + \frac{11 \, {\left(x - 1\right)}^{\frac{7}{2}} + 32 \, {\left(x - 1\right)}^{\frac{5}{2}} + 50 \, {\left(x - 1\right)}^{\frac{3}{2}} + 28 \, \sqrt{x - 1}}{32 \, {\left({\left(x - 1\right)}^{2} + 2 \, x\right)}^{2}}"," ",0,"1/128*sqrt(746*sqrt(2) - 1054)*arctan(1/2*2^(3/4)*(2^(1/4)*sqrt(-sqrt(2) + 2) + 2*sqrt(x - 1))/sqrt(sqrt(2) + 2)) + 1/128*sqrt(746*sqrt(2) - 1054)*arctan(-1/2*2^(3/4)*(2^(1/4)*sqrt(-sqrt(2) + 2) - 2*sqrt(x - 1))/sqrt(sqrt(2) + 2)) - 1/256*sqrt(746*sqrt(2) + 1054)*log(2^(1/4)*sqrt(x - 1)*sqrt(-sqrt(2) + 2) + x + sqrt(2) - 1) + 1/256*sqrt(746*sqrt(2) + 1054)*log(-2^(1/4)*sqrt(x - 1)*sqrt(-sqrt(2) + 2) + x + sqrt(2) - 1) + 1/32*(11*(x - 1)^(7/2) + 32*(x - 1)^(5/2) + 50*(x - 1)^(3/2) + 28*sqrt(x - 1))/((x - 1)^2 + 2*x)^2","A",0
657,0,0,0,0.000000," ","integrate((e*x+d)^(3/2)*(c*x^2+a)^(1/2),x, algorithm=""giac"")","\int \sqrt{c x^{2} + a} {\left(e x + d\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + a)*(e*x + d)^(3/2), x)","F",0
658,0,0,0,0.000000," ","integrate((e*x+d)^(1/2)*(c*x^2+a)^(1/2),x, algorithm=""giac"")","\int \sqrt{c x^{2} + a} \sqrt{e x + d}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + a)*sqrt(e*x + d), x)","F",0
659,0,0,0,0.000000," ","integrate((c*x^2+a)^(1/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{c x^{2} + a}}{\sqrt{e x + d}}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + a)/sqrt(e*x + d), x)","F",0
660,0,0,0,0.000000," ","integrate((c*x^2+a)^(1/2)/(e*x+d)^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{c x^{2} + a}}{{\left(e x + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + a)/(e*x + d)^(3/2), x)","F",0
661,0,0,0,0.000000," ","integrate((c*x^2+a)^(1/2)/(e*x+d)^(5/2),x, algorithm=""giac"")","\int \frac{\sqrt{c x^{2} + a}}{{\left(e x + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + a)/(e*x + d)^(5/2), x)","F",0
662,0,0,0,0.000000," ","integrate((c*x^2+a)^(1/2)/(e*x+d)^(7/2),x, algorithm=""giac"")","\int \frac{\sqrt{c x^{2} + a}}{{\left(e x + d\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + a)/(e*x + d)^(7/2), x)","F",0
663,0,0,0,0.000000," ","integrate((e*x+d)^(3/2)*(c*x^2+a)^(3/2),x, algorithm=""giac"")","\int {\left(c x^{2} + a\right)}^{\frac{3}{2}} {\left(e x + d\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((c*x^2 + a)^(3/2)*(e*x + d)^(3/2), x)","F",0
664,0,0,0,0.000000," ","integrate((c*x^2+a)^(3/2)*(e*x+d)^(1/2),x, algorithm=""giac"")","\int {\left(c x^{2} + a\right)}^{\frac{3}{2}} \sqrt{e x + d}\,{d x}"," ",0,"integrate((c*x^2 + a)^(3/2)*sqrt(e*x + d), x)","F",0
665,0,0,0,0.000000," ","integrate((c*x^2+a)^(3/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}}}{\sqrt{e x + d}}\,{d x}"," ",0,"integrate((c*x^2 + a)^(3/2)/sqrt(e*x + d), x)","F",0
666,0,0,0,0.000000," ","integrate((c*x^2+a)^(3/2)/(e*x+d)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}}}{{\left(e x + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c*x^2 + a)^(3/2)/(e*x + d)^(3/2), x)","F",0
667,0,0,0,0.000000," ","integrate((c*x^2+a)^(3/2)/(e*x+d)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}}}{{\left(e x + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((c*x^2 + a)^(3/2)/(e*x + d)^(5/2), x)","F",0
668,-2,0,0,0.000000," ","integrate((c*x^2+a)^(3/2)/(e*x+d)^(7/2),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(d*exp(1)+x*exp(1)^2)]integrate()  Bad Argument Typeintegrate()  Bad Argument TypeEvaluation time: 1.68Unable to transpose Error: Bad Argument Value","F(-2)",0
669,0,0,0,0.000000," ","integrate((c*x^2+a)^(3/2)/(e*x+d)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}}}{{\left(e x + d\right)}^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((c*x^2 + a)^(3/2)/(e*x + d)^(9/2), x)","F",0
670,0,0,0,0.000000," ","integrate((c*x^2+a)^(5/2)*(e*x+d)^(1/2),x, algorithm=""giac"")","\int {\left(c x^{2} + a\right)}^{\frac{5}{2}} \sqrt{e x + d}\,{d x}"," ",0,"integrate((c*x^2 + a)^(5/2)*sqrt(e*x + d), x)","F",0
671,0,0,0,0.000000," ","integrate((c*x^2+a)^(5/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}}}{\sqrt{e x + d}}\,{d x}"," ",0,"integrate((c*x^2 + a)^(5/2)/sqrt(e*x + d), x)","F",0
672,0,0,0,0.000000," ","integrate((c*x^2+a)^(5/2)/(e*x+d)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}}}{{\left(e x + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c*x^2 + a)^(5/2)/(e*x + d)^(3/2), x)","F",0
673,0,0,0,0.000000," ","integrate((c*x^2+a)^(5/2)/(e*x+d)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}}}{{\left(e x + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((c*x^2 + a)^(5/2)/(e*x + d)^(5/2), x)","F",0
674,0,0,0,0.000000," ","integrate((c*x^2+a)^(5/2)/(e*x+d)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}}}{{\left(e x + d\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((c*x^2 + a)^(5/2)/(e*x + d)^(7/2), x)","F",0
675,0,0,0,0.000000," ","integrate((c*x^2+a)^(5/2)/(e*x+d)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + a\right)}^{\frac{5}{2}}}{{\left(e x + d\right)}^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((c*x^2 + a)^(5/2)/(e*x + d)^(9/2), x)","F",0
676,-2,0,0,0.000000," ","integrate((c*x^2+a)^(5/2)/(e*x+d)^(11/2),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(d*exp(1)+x*exp(1)^2)]integrate()  Bad Argument Typeintegrate()  Bad Argument TypeEvaluation time: 4.27Unable to transpose Error: Bad Argument Value","F(-2)",0
677,0,0,0,0.000000," ","integrate((e*x+d)^(7/2)/(c*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{\frac{7}{2}}}{\sqrt{c x^{2} + a}}\,{d x}"," ",0,"integrate((e*x + d)^(7/2)/sqrt(c*x^2 + a), x)","F",0
678,0,0,0,0.000000," ","integrate((e*x+d)^(5/2)/(c*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{\frac{5}{2}}}{\sqrt{c x^{2} + a}}\,{d x}"," ",0,"integrate((e*x + d)^(5/2)/sqrt(c*x^2 + a), x)","F",0
679,0,0,0,0.000000," ","integrate((e*x+d)^(3/2)/(c*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{\frac{3}{2}}}{\sqrt{c x^{2} + a}}\,{d x}"," ",0,"integrate((e*x + d)^(3/2)/sqrt(c*x^2 + a), x)","F",0
680,0,0,0,0.000000," ","integrate((e*x+d)^(1/2)/(c*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{e x + d}}{\sqrt{c x^{2} + a}}\,{d x}"," ",0,"integrate(sqrt(e*x + d)/sqrt(c*x^2 + a), x)","F",0
681,0,0,0,0.000000," ","integrate(1/(e*x+d)^(1/2)/(c*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{c x^{2} + a} \sqrt{e x + d}}\,{d x}"," ",0,"integrate(1/(sqrt(c*x^2 + a)*sqrt(e*x + d)), x)","F",0
682,0,0,0,0.000000," ","integrate(1/(e*x+d)^(3/2)/(c*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{c x^{2} + a} {\left(e x + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(c*x^2 + a)*(e*x + d)^(3/2)), x)","F",0
683,0,0,0,0.000000," ","integrate(1/(e*x+d)^(5/2)/(c*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{c x^{2} + a} {\left(e x + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(c*x^2 + a)*(e*x + d)^(5/2)), x)","F",0
684,0,0,0,0.000000," ","integrate(1/(e*x+d)^(7/2)/(c*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{c x^{2} + a} {\left(e x + d\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(c*x^2 + a)*(e*x + d)^(7/2)), x)","F",0
685,0,0,0,0.000000," ","integrate((e*x+d)^(7/2)/(c*x^2+a)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{\frac{7}{2}}}{{\left(c x^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((e*x + d)^(7/2)/(c*x^2 + a)^(3/2), x)","F",0
686,0,0,0,0.000000," ","integrate((e*x+d)^(5/2)/(c*x^2+a)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{\frac{5}{2}}}{{\left(c x^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((e*x + d)^(5/2)/(c*x^2 + a)^(3/2), x)","F",0
687,0,0,0,0.000000," ","integrate((e*x+d)^(3/2)/(c*x^2+a)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{\frac{3}{2}}}{{\left(c x^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((e*x + d)^(3/2)/(c*x^2 + a)^(3/2), x)","F",0
688,0,0,0,0.000000," ","integrate((e*x+d)^(1/2)/(c*x^2+a)^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{e x + d}}{{\left(c x^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(e*x + d)/(c*x^2 + a)^(3/2), x)","F",0
689,0,0,0,0.000000," ","integrate(1/(c*x^2+a)^(3/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{2} + a\right)}^{\frac{3}{2}} \sqrt{e x + d}}\,{d x}"," ",0,"integrate(1/((c*x^2 + a)^(3/2)*sqrt(e*x + d)), x)","F",0
690,-2,0,0,0.000000," ","integrate(1/(e*x+d)^(3/2)/(c*x^2+a)^(3/2),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:integrate()  Bad Argument Typeintegrate()  Bad Argument TypeEvaluation time: 5.52Unable to transpose Error: Bad Argument Value","F(-2)",0
691,-1,0,0,0.000000," ","integrate(1/(e*x+d)^(5/2)/(c*x^2+a)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
692,0,0,0,0.000000," ","integrate((e*x+d)^(9/2)/(c*x^2+a)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{\frac{9}{2}}}{{\left(c x^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((e*x + d)^(9/2)/(c*x^2 + a)^(5/2), x)","F",0
693,0,0,0,0.000000," ","integrate((e*x+d)^(7/2)/(c*x^2+a)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{\frac{7}{2}}}{{\left(c x^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((e*x + d)^(7/2)/(c*x^2 + a)^(5/2), x)","F",0
694,0,0,0,0.000000," ","integrate((e*x+d)^(5/2)/(c*x^2+a)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{\frac{5}{2}}}{{\left(c x^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((e*x + d)^(5/2)/(c*x^2 + a)^(5/2), x)","F",0
695,0,0,0,0.000000," ","integrate((e*x+d)^(3/2)/(c*x^2+a)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{\frac{3}{2}}}{{\left(c x^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((e*x + d)^(3/2)/(c*x^2 + a)^(5/2), x)","F",0
696,0,0,0,0.000000," ","integrate((e*x+d)^(1/2)/(c*x^2+a)^(5/2),x, algorithm=""giac"")","\int \frac{\sqrt{e x + d}}{{\left(c x^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(e*x + d)/(c*x^2 + a)^(5/2), x)","F",0
697,0,0,0,0.000000," ","integrate(1/(c*x^2+a)^(5/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{2} + a\right)}^{\frac{5}{2}} \sqrt{e x + d}}\,{d x}"," ",0,"integrate(1/((c*x^2 + a)^(5/2)*sqrt(e*x + d)), x)","F",0
698,-2,0,0,0.000000," ","integrate(1/(e*x+d)^(3/2)/(c*x^2+a)^(5/2),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Evaluation time: 1.61Unable to transpose Error: Bad Argument Value","F(-2)",0
699,0,0,0,0.000000," ","integrate(1/(e*x+d)/(3*e^2*x^2+d^2)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(3 \, e^{2} x^{2} + d^{2}\right)}^{\frac{1}{3}} {\left(e x + d\right)}}\,{d x}"," ",0,"integrate(1/((3*e^2*x^2 + d^2)^(1/3)*(e*x + d)), x)","F",0
700,0,0,0,0.000000," ","integrate((2+3*x)^3/(27*x^2+4)^(1/3),x, algorithm=""giac"")","\int \frac{{\left(3 \, x + 2\right)}^{3}}{{\left(27 \, x^{2} + 4\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((3*x + 2)^3/(27*x^2 + 4)^(1/3), x)","F",0
701,0,0,0,0.000000," ","integrate((2+3*x)^2/(27*x^2+4)^(1/3),x, algorithm=""giac"")","\int \frac{{\left(3 \, x + 2\right)}^{2}}{{\left(27 \, x^{2} + 4\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((3*x + 2)^2/(27*x^2 + 4)^(1/3), x)","F",0
702,0,0,0,0.000000," ","integrate((2+3*x)/(27*x^2+4)^(1/3),x, algorithm=""giac"")","\int \frac{3 \, x + 2}{{\left(27 \, x^{2} + 4\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((3*x + 2)/(27*x^2 + 4)^(1/3), x)","F",0
703,0,0,0,0.000000," ","integrate(1/(2+3*x)/(27*x^2+4)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(27 \, x^{2} + 4\right)}^{\frac{1}{3}} {\left(3 \, x + 2\right)}}\,{d x}"," ",0,"integrate(1/((27*x^2 + 4)^(1/3)*(3*x + 2)), x)","F",0
704,0,0,0,0.000000," ","integrate(1/(2+3*x)^2/(27*x^2+4)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(27 \, x^{2} + 4\right)}^{\frac{1}{3}} {\left(3 \, x + 2\right)}^{2}}\,{d x}"," ",0,"integrate(1/((27*x^2 + 4)^(1/3)*(3*x + 2)^2), x)","F",0
705,0,0,0,0.000000," ","integrate(1/(2+3*x)^3/(27*x^2+4)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(27 \, x^{2} + 4\right)}^{\frac{1}{3}} {\left(3 \, x + 2\right)}^{3}}\,{d x}"," ",0,"integrate(1/((27*x^2 + 4)^(1/3)*(3*x + 2)^3), x)","F",0
706,0,0,0,0.000000," ","integrate((2+3*I*x)^3/(-27*x^2+4)^(1/3),x, algorithm=""giac"")","\int \frac{{\left(3 i \, x + 2\right)}^{3}}{{\left(-27 \, x^{2} + 4\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((3*I*x + 2)^3/(-27*x^2 + 4)^(1/3), x)","F",0
707,0,0,0,0.000000," ","integrate((2+3*I*x)^2/(-27*x^2+4)^(1/3),x, algorithm=""giac"")","\int \frac{{\left(3 i \, x + 2\right)}^{2}}{{\left(-27 \, x^{2} + 4\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((3*I*x + 2)^2/(-27*x^2 + 4)^(1/3), x)","F",0
708,0,0,0,0.000000," ","integrate((2+3*I*x)/(-27*x^2+4)^(1/3),x, algorithm=""giac"")","\int \frac{3 i \, x + 2}{{\left(-27 \, x^{2} + 4\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((3*I*x + 2)/(-27*x^2 + 4)^(1/3), x)","F",0
709,0,0,0,0.000000," ","integrate(1/(2+3*I*x)/(-27*x^2+4)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(-27 \, x^{2} + 4\right)}^{\frac{1}{3}} {\left(3 i \, x + 2\right)}}\,{d x}"," ",0,"integrate(1/((-27*x^2 + 4)^(1/3)*(3*I*x + 2)), x)","F",0
710,0,0,0,0.000000," ","integrate(1/(2+3*I*x)^2/(-27*x^2+4)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(-27 \, x^{2} + 4\right)}^{\frac{1}{3}} {\left(3 i \, x + 2\right)}^{2}}\,{d x}"," ",0,"integrate(1/((-27*x^2 + 4)^(1/3)*(3*I*x + 2)^2), x)","F",0
711,0,0,0,0.000000," ","integrate(1/(2+3*I*x)^3/(-27*x^2+4)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(-27 \, x^{2} + 4\right)}^{\frac{1}{3}} {\left(3 i \, x + 2\right)}^{3}}\,{d x}"," ",0,"integrate(1/((-27*x^2 + 4)^(1/3)*(3*I*x + 2)^3), x)","F",0
712,0,0,0,0.000000," ","integrate(1/(x^2+1)^(1/3)/(x+3^(1/2)),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{2} + 1\right)}^{\frac{1}{3}} {\left(x + \sqrt{3}\right)}}\,{d x}"," ",0,"integrate(1/((x^2 + 1)^(1/3)*(x + sqrt(3))), x)","F",0
713,0,0,0,0.000000," ","integrate(1/(x^2+1)^(1/3)/(-x+3^(1/2)),x, algorithm=""giac"")","\int -\frac{1}{{\left(x^{2} + 1\right)}^{\frac{1}{3}} {\left(x - \sqrt{3}\right)}}\,{d x}"," ",0,"integrate(-1/((x^2 + 1)^(1/3)*(x - sqrt(3))), x)","F",0
714,0,0,0,0.000000," ","integrate(1/(3-x)/(-x^2+1)^(1/3),x, algorithm=""giac"")","\int -\frac{1}{{\left(-x^{2} + 1\right)}^{\frac{1}{3}} {\left(x - 3\right)}}\,{d x}"," ",0,"integrate(-1/((-x^2 + 1)^(1/3)*(x - 3)), x)","F",0
715,0,0,0,0.000000," ","integrate(1/(3+x)/(-x^2+1)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(-x^{2} + 1\right)}^{\frac{1}{3}} {\left(x + 3\right)}}\,{d x}"," ",0,"integrate(1/((-x^2 + 1)^(1/3)*(x + 3)), x)","F",0
716,0,0,0,0.000000," ","integrate(1/(e*x+d)/(-9*e^2*x^2+d^2)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(-9 \, e^{2} x^{2} + d^{2}\right)}^{\frac{1}{3}} {\left(e x + d\right)}}\,{d x}"," ",0,"integrate(1/((-9*e^2*x^2 + d^2)^(1/3)*(e*x + d)), x)","F",0
717,0,0,0,0.000000," ","integrate(1/(b*x+a)/(d*x^2+c)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(d x^{2} + c\right)}^{\frac{1}{4}} {\left(b x + a\right)}}\,{d x}"," ",0,"integrate(1/((d*x^2 + c)^(1/4)*(b*x + a)), x)","F",0
718,0,0,0,0.000000," ","integrate(1/(b*x+a)/(d*x^2+c)^(3/4),x, algorithm=""giac"")","\int \frac{1}{{\left(d x^{2} + c\right)}^{\frac{3}{4}} {\left(b x + a\right)}}\,{d x}"," ",0,"integrate(1/((d*x^2 + c)^(3/4)*(b*x + a)), x)","F",0
719,0,0,0,0.000000," ","integrate(1/(e*x+d)^(3/2)/(c*x^2+a)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{2} + a\right)}^{\frac{1}{4}} {\left(e x + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((c*x^2 + a)^(1/4)*(e*x + d)^(3/2)), x)","F",0
720,0,0,0,0.000000," ","integrate(1/(1+x)/(x^2+1)^(1/6),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{2} + 1\right)}^{\frac{1}{6}} {\left(x + 1\right)}}\,{d x}"," ",0,"integrate(1/((x^2 + 1)^(1/6)*(x + 1)), x)","F",0
721,1,2080,0,0.247485," ","integrate((e*x+d)^m*(c*x^2+a)^3,x, algorithm=""giac"")","\frac{{\left(x e + d\right)}^{m} c^{3} m^{6} x^{7} e^{7} + {\left(x e + d\right)}^{m} c^{3} d m^{6} x^{6} e^{6} + 21 \, {\left(x e + d\right)}^{m} c^{3} m^{5} x^{7} e^{7} + 15 \, {\left(x e + d\right)}^{m} c^{3} d m^{5} x^{6} e^{6} - 6 \, {\left(x e + d\right)}^{m} c^{3} d^{2} m^{5} x^{5} e^{5} + 3 \, {\left(x e + d\right)}^{m} a c^{2} m^{6} x^{5} e^{7} + 175 \, {\left(x e + d\right)}^{m} c^{3} m^{4} x^{7} e^{7} + 3 \, {\left(x e + d\right)}^{m} a c^{2} d m^{6} x^{4} e^{6} + 85 \, {\left(x e + d\right)}^{m} c^{3} d m^{4} x^{6} e^{6} - 60 \, {\left(x e + d\right)}^{m} c^{3} d^{2} m^{4} x^{5} e^{5} + 30 \, {\left(x e + d\right)}^{m} c^{3} d^{3} m^{4} x^{4} e^{4} + 69 \, {\left(x e + d\right)}^{m} a c^{2} m^{5} x^{5} e^{7} + 735 \, {\left(x e + d\right)}^{m} c^{3} m^{3} x^{7} e^{7} + 57 \, {\left(x e + d\right)}^{m} a c^{2} d m^{5} x^{4} e^{6} + 225 \, {\left(x e + d\right)}^{m} c^{3} d m^{3} x^{6} e^{6} - 12 \, {\left(x e + d\right)}^{m} a c^{2} d^{2} m^{5} x^{3} e^{5} - 210 \, {\left(x e + d\right)}^{m} c^{3} d^{2} m^{3} x^{5} e^{5} + 180 \, {\left(x e + d\right)}^{m} c^{3} d^{3} m^{3} x^{4} e^{4} - 120 \, {\left(x e + d\right)}^{m} c^{3} d^{4} m^{3} x^{3} e^{3} + 3 \, {\left(x e + d\right)}^{m} a^{2} c m^{6} x^{3} e^{7} + 621 \, {\left(x e + d\right)}^{m} a c^{2} m^{4} x^{5} e^{7} + 1624 \, {\left(x e + d\right)}^{m} c^{3} m^{2} x^{7} e^{7} + 3 \, {\left(x e + d\right)}^{m} a^{2} c d m^{6} x^{2} e^{6} + 393 \, {\left(x e + d\right)}^{m} a c^{2} d m^{4} x^{4} e^{6} + 274 \, {\left(x e + d\right)}^{m} c^{3} d m^{2} x^{6} e^{6} - 192 \, {\left(x e + d\right)}^{m} a c^{2} d^{2} m^{4} x^{3} e^{5} - 300 \, {\left(x e + d\right)}^{m} c^{3} d^{2} m^{2} x^{5} e^{5} + 36 \, {\left(x e + d\right)}^{m} a c^{2} d^{3} m^{4} x^{2} e^{4} + 330 \, {\left(x e + d\right)}^{m} c^{3} d^{3} m^{2} x^{4} e^{4} - 360 \, {\left(x e + d\right)}^{m} c^{3} d^{4} m^{2} x^{3} e^{3} + 360 \, {\left(x e + d\right)}^{m} c^{3} d^{5} m^{2} x^{2} e^{2} + 75 \, {\left(x e + d\right)}^{m} a^{2} c m^{5} x^{3} e^{7} + 2775 \, {\left(x e + d\right)}^{m} a c^{2} m^{3} x^{5} e^{7} + 1764 \, {\left(x e + d\right)}^{m} c^{3} m x^{7} e^{7} + 69 \, {\left(x e + d\right)}^{m} a^{2} c d m^{5} x^{2} e^{6} + 1203 \, {\left(x e + d\right)}^{m} a c^{2} d m^{3} x^{4} e^{6} + 120 \, {\left(x e + d\right)}^{m} c^{3} d m x^{6} e^{6} - 6 \, {\left(x e + d\right)}^{m} a^{2} c d^{2} m^{5} x e^{5} - 996 \, {\left(x e + d\right)}^{m} a c^{2} d^{2} m^{3} x^{3} e^{5} - 144 \, {\left(x e + d\right)}^{m} c^{3} d^{2} m x^{5} e^{5} + 504 \, {\left(x e + d\right)}^{m} a c^{2} d^{3} m^{3} x^{2} e^{4} + 180 \, {\left(x e + d\right)}^{m} c^{3} d^{3} m x^{4} e^{4} - 72 \, {\left(x e + d\right)}^{m} a c^{2} d^{4} m^{3} x e^{3} - 240 \, {\left(x e + d\right)}^{m} c^{3} d^{4} m x^{3} e^{3} + 360 \, {\left(x e + d\right)}^{m} c^{3} d^{5} m x^{2} e^{2} - 720 \, {\left(x e + d\right)}^{m} c^{3} d^{6} m x e + {\left(x e + d\right)}^{m} a^{3} m^{6} x e^{7} + 741 \, {\left(x e + d\right)}^{m} a^{2} c m^{4} x^{3} e^{7} + 6432 \, {\left(x e + d\right)}^{m} a c^{2} m^{2} x^{5} e^{7} + 720 \, {\left(x e + d\right)}^{m} c^{3} x^{7} e^{7} + {\left(x e + d\right)}^{m} a^{3} d m^{6} e^{6} + 603 \, {\left(x e + d\right)}^{m} a^{2} c d m^{4} x^{2} e^{6} + 1620 \, {\left(x e + d\right)}^{m} a c^{2} d m^{2} x^{4} e^{6} - 132 \, {\left(x e + d\right)}^{m} a^{2} c d^{2} m^{4} x e^{5} - 1824 \, {\left(x e + d\right)}^{m} a c^{2} d^{2} m^{2} x^{3} e^{5} + 6 \, {\left(x e + d\right)}^{m} a^{2} c d^{3} m^{4} e^{4} + 1980 \, {\left(x e + d\right)}^{m} a c^{2} d^{3} m^{2} x^{2} e^{4} - 936 \, {\left(x e + d\right)}^{m} a c^{2} d^{4} m^{2} x e^{3} + 72 \, {\left(x e + d\right)}^{m} a c^{2} d^{5} m^{2} e^{2} + 720 \, {\left(x e + d\right)}^{m} c^{3} d^{7} + 27 \, {\left(x e + d\right)}^{m} a^{3} m^{5} x e^{7} + 3657 \, {\left(x e + d\right)}^{m} a^{2} c m^{3} x^{3} e^{7} + 7236 \, {\left(x e + d\right)}^{m} a c^{2} m x^{5} e^{7} + 27 \, {\left(x e + d\right)}^{m} a^{3} d m^{5} e^{6} + 2451 \, {\left(x e + d\right)}^{m} a^{2} c d m^{3} x^{2} e^{6} + 756 \, {\left(x e + d\right)}^{m} a c^{2} d m x^{4} e^{6} - 1074 \, {\left(x e + d\right)}^{m} a^{2} c d^{2} m^{3} x e^{5} - 1008 \, {\left(x e + d\right)}^{m} a c^{2} d^{2} m x^{3} e^{5} + 132 \, {\left(x e + d\right)}^{m} a^{2} c d^{3} m^{3} e^{4} + 1512 \, {\left(x e + d\right)}^{m} a c^{2} d^{3} m x^{2} e^{4} - 3024 \, {\left(x e + d\right)}^{m} a c^{2} d^{4} m x e^{3} + 936 \, {\left(x e + d\right)}^{m} a c^{2} d^{5} m e^{2} + 295 \, {\left(x e + d\right)}^{m} a^{3} m^{4} x e^{7} + 9336 \, {\left(x e + d\right)}^{m} a^{2} c m^{2} x^{3} e^{7} + 3024 \, {\left(x e + d\right)}^{m} a c^{2} x^{5} e^{7} + 295 \, {\left(x e + d\right)}^{m} a^{3} d m^{4} e^{6} + 4434 \, {\left(x e + d\right)}^{m} a^{2} c d m^{2} x^{2} e^{6} - 3828 \, {\left(x e + d\right)}^{m} a^{2} c d^{2} m^{2} x e^{5} + 1074 \, {\left(x e + d\right)}^{m} a^{2} c d^{3} m^{2} e^{4} + 3024 \, {\left(x e + d\right)}^{m} a c^{2} d^{5} e^{2} + 1665 \, {\left(x e + d\right)}^{m} a^{3} m^{3} x e^{7} + 11388 \, {\left(x e + d\right)}^{m} a^{2} c m x^{3} e^{7} + 1665 \, {\left(x e + d\right)}^{m} a^{3} d m^{3} e^{6} + 2520 \, {\left(x e + d\right)}^{m} a^{2} c d m x^{2} e^{6} - 5040 \, {\left(x e + d\right)}^{m} a^{2} c d^{2} m x e^{5} + 3828 \, {\left(x e + d\right)}^{m} a^{2} c d^{3} m e^{4} + 5104 \, {\left(x e + d\right)}^{m} a^{3} m^{2} x e^{7} + 5040 \, {\left(x e + d\right)}^{m} a^{2} c x^{3} e^{7} + 5104 \, {\left(x e + d\right)}^{m} a^{3} d m^{2} e^{6} + 5040 \, {\left(x e + d\right)}^{m} a^{2} c d^{3} e^{4} + 8028 \, {\left(x e + d\right)}^{m} a^{3} m x e^{7} + 8028 \, {\left(x e + d\right)}^{m} a^{3} d m e^{6} + 5040 \, {\left(x e + d\right)}^{m} a^{3} x e^{7} + 5040 \, {\left(x e + d\right)}^{m} a^{3} d e^{6}}{m^{7} e^{7} + 28 \, m^{6} e^{7} + 322 \, m^{5} e^{7} + 1960 \, m^{4} e^{7} + 6769 \, m^{3} e^{7} + 13132 \, m^{2} e^{7} + 13068 \, m e^{7} + 5040 \, e^{7}}"," ",0,"((x*e + d)^m*c^3*m^6*x^7*e^7 + (x*e + d)^m*c^3*d*m^6*x^6*e^6 + 21*(x*e + d)^m*c^3*m^5*x^7*e^7 + 15*(x*e + d)^m*c^3*d*m^5*x^6*e^6 - 6*(x*e + d)^m*c^3*d^2*m^5*x^5*e^5 + 3*(x*e + d)^m*a*c^2*m^6*x^5*e^7 + 175*(x*e + d)^m*c^3*m^4*x^7*e^7 + 3*(x*e + d)^m*a*c^2*d*m^6*x^4*e^6 + 85*(x*e + d)^m*c^3*d*m^4*x^6*e^6 - 60*(x*e + d)^m*c^3*d^2*m^4*x^5*e^5 + 30*(x*e + d)^m*c^3*d^3*m^4*x^4*e^4 + 69*(x*e + d)^m*a*c^2*m^5*x^5*e^7 + 735*(x*e + d)^m*c^3*m^3*x^7*e^7 + 57*(x*e + d)^m*a*c^2*d*m^5*x^4*e^6 + 225*(x*e + d)^m*c^3*d*m^3*x^6*e^6 - 12*(x*e + d)^m*a*c^2*d^2*m^5*x^3*e^5 - 210*(x*e + d)^m*c^3*d^2*m^3*x^5*e^5 + 180*(x*e + d)^m*c^3*d^3*m^3*x^4*e^4 - 120*(x*e + d)^m*c^3*d^4*m^3*x^3*e^3 + 3*(x*e + d)^m*a^2*c*m^6*x^3*e^7 + 621*(x*e + d)^m*a*c^2*m^4*x^5*e^7 + 1624*(x*e + d)^m*c^3*m^2*x^7*e^7 + 3*(x*e + d)^m*a^2*c*d*m^6*x^2*e^6 + 393*(x*e + d)^m*a*c^2*d*m^4*x^4*e^6 + 274*(x*e + d)^m*c^3*d*m^2*x^6*e^6 - 192*(x*e + d)^m*a*c^2*d^2*m^4*x^3*e^5 - 300*(x*e + d)^m*c^3*d^2*m^2*x^5*e^5 + 36*(x*e + d)^m*a*c^2*d^3*m^4*x^2*e^4 + 330*(x*e + d)^m*c^3*d^3*m^2*x^4*e^4 - 360*(x*e + d)^m*c^3*d^4*m^2*x^3*e^3 + 360*(x*e + d)^m*c^3*d^5*m^2*x^2*e^2 + 75*(x*e + d)^m*a^2*c*m^5*x^3*e^7 + 2775*(x*e + d)^m*a*c^2*m^3*x^5*e^7 + 1764*(x*e + d)^m*c^3*m*x^7*e^7 + 69*(x*e + d)^m*a^2*c*d*m^5*x^2*e^6 + 1203*(x*e + d)^m*a*c^2*d*m^3*x^4*e^6 + 120*(x*e + d)^m*c^3*d*m*x^6*e^6 - 6*(x*e + d)^m*a^2*c*d^2*m^5*x*e^5 - 996*(x*e + d)^m*a*c^2*d^2*m^3*x^3*e^5 - 144*(x*e + d)^m*c^3*d^2*m*x^5*e^5 + 504*(x*e + d)^m*a*c^2*d^3*m^3*x^2*e^4 + 180*(x*e + d)^m*c^3*d^3*m*x^4*e^4 - 72*(x*e + d)^m*a*c^2*d^4*m^3*x*e^3 - 240*(x*e + d)^m*c^3*d^4*m*x^3*e^3 + 360*(x*e + d)^m*c^3*d^5*m*x^2*e^2 - 720*(x*e + d)^m*c^3*d^6*m*x*e + (x*e + d)^m*a^3*m^6*x*e^7 + 741*(x*e + d)^m*a^2*c*m^4*x^3*e^7 + 6432*(x*e + d)^m*a*c^2*m^2*x^5*e^7 + 720*(x*e + d)^m*c^3*x^7*e^7 + (x*e + d)^m*a^3*d*m^6*e^6 + 603*(x*e + d)^m*a^2*c*d*m^4*x^2*e^6 + 1620*(x*e + d)^m*a*c^2*d*m^2*x^4*e^6 - 132*(x*e + d)^m*a^2*c*d^2*m^4*x*e^5 - 1824*(x*e + d)^m*a*c^2*d^2*m^2*x^3*e^5 + 6*(x*e + d)^m*a^2*c*d^3*m^4*e^4 + 1980*(x*e + d)^m*a*c^2*d^3*m^2*x^2*e^4 - 936*(x*e + d)^m*a*c^2*d^4*m^2*x*e^3 + 72*(x*e + d)^m*a*c^2*d^5*m^2*e^2 + 720*(x*e + d)^m*c^3*d^7 + 27*(x*e + d)^m*a^3*m^5*x*e^7 + 3657*(x*e + d)^m*a^2*c*m^3*x^3*e^7 + 7236*(x*e + d)^m*a*c^2*m*x^5*e^7 + 27*(x*e + d)^m*a^3*d*m^5*e^6 + 2451*(x*e + d)^m*a^2*c*d*m^3*x^2*e^6 + 756*(x*e + d)^m*a*c^2*d*m*x^4*e^6 - 1074*(x*e + d)^m*a^2*c*d^2*m^3*x*e^5 - 1008*(x*e + d)^m*a*c^2*d^2*m*x^3*e^5 + 132*(x*e + d)^m*a^2*c*d^3*m^3*e^4 + 1512*(x*e + d)^m*a*c^2*d^3*m*x^2*e^4 - 3024*(x*e + d)^m*a*c^2*d^4*m*x*e^3 + 936*(x*e + d)^m*a*c^2*d^5*m*e^2 + 295*(x*e + d)^m*a^3*m^4*x*e^7 + 9336*(x*e + d)^m*a^2*c*m^2*x^3*e^7 + 3024*(x*e + d)^m*a*c^2*x^5*e^7 + 295*(x*e + d)^m*a^3*d*m^4*e^6 + 4434*(x*e + d)^m*a^2*c*d*m^2*x^2*e^6 - 3828*(x*e + d)^m*a^2*c*d^2*m^2*x*e^5 + 1074*(x*e + d)^m*a^2*c*d^3*m^2*e^4 + 3024*(x*e + d)^m*a*c^2*d^5*e^2 + 1665*(x*e + d)^m*a^3*m^3*x*e^7 + 11388*(x*e + d)^m*a^2*c*m*x^3*e^7 + 1665*(x*e + d)^m*a^3*d*m^3*e^6 + 2520*(x*e + d)^m*a^2*c*d*m*x^2*e^6 - 5040*(x*e + d)^m*a^2*c*d^2*m*x*e^5 + 3828*(x*e + d)^m*a^2*c*d^3*m*e^4 + 5104*(x*e + d)^m*a^3*m^2*x*e^7 + 5040*(x*e + d)^m*a^2*c*x^3*e^7 + 5104*(x*e + d)^m*a^3*d*m^2*e^6 + 5040*(x*e + d)^m*a^2*c*d^3*e^4 + 8028*(x*e + d)^m*a^3*m*x*e^7 + 8028*(x*e + d)^m*a^3*d*m*e^6 + 5040*(x*e + d)^m*a^3*x*e^7 + 5040*(x*e + d)^m*a^3*d*e^6)/(m^7*e^7 + 28*m^6*e^7 + 322*m^5*e^7 + 1960*m^4*e^7 + 6769*m^3*e^7 + 13132*m^2*e^7 + 13068*m*e^7 + 5040*e^7)","B",0
722,1,848,0,0.186447," ","integrate((e*x+d)^m*(c*x^2+a)^2,x, algorithm=""giac"")","\frac{{\left(x e + d\right)}^{m} c^{2} m^{4} x^{5} e^{5} + {\left(x e + d\right)}^{m} c^{2} d m^{4} x^{4} e^{4} + 10 \, {\left(x e + d\right)}^{m} c^{2} m^{3} x^{5} e^{5} + 6 \, {\left(x e + d\right)}^{m} c^{2} d m^{3} x^{4} e^{4} - 4 \, {\left(x e + d\right)}^{m} c^{2} d^{2} m^{3} x^{3} e^{3} + 2 \, {\left(x e + d\right)}^{m} a c m^{4} x^{3} e^{5} + 35 \, {\left(x e + d\right)}^{m} c^{2} m^{2} x^{5} e^{5} + 2 \, {\left(x e + d\right)}^{m} a c d m^{4} x^{2} e^{4} + 11 \, {\left(x e + d\right)}^{m} c^{2} d m^{2} x^{4} e^{4} - 12 \, {\left(x e + d\right)}^{m} c^{2} d^{2} m^{2} x^{3} e^{3} + 12 \, {\left(x e + d\right)}^{m} c^{2} d^{3} m^{2} x^{2} e^{2} + 24 \, {\left(x e + d\right)}^{m} a c m^{3} x^{3} e^{5} + 50 \, {\left(x e + d\right)}^{m} c^{2} m x^{5} e^{5} + 20 \, {\left(x e + d\right)}^{m} a c d m^{3} x^{2} e^{4} + 6 \, {\left(x e + d\right)}^{m} c^{2} d m x^{4} e^{4} - 4 \, {\left(x e + d\right)}^{m} a c d^{2} m^{3} x e^{3} - 8 \, {\left(x e + d\right)}^{m} c^{2} d^{2} m x^{3} e^{3} + 12 \, {\left(x e + d\right)}^{m} c^{2} d^{3} m x^{2} e^{2} - 24 \, {\left(x e + d\right)}^{m} c^{2} d^{4} m x e + {\left(x e + d\right)}^{m} a^{2} m^{4} x e^{5} + 98 \, {\left(x e + d\right)}^{m} a c m^{2} x^{3} e^{5} + 24 \, {\left(x e + d\right)}^{m} c^{2} x^{5} e^{5} + {\left(x e + d\right)}^{m} a^{2} d m^{4} e^{4} + 58 \, {\left(x e + d\right)}^{m} a c d m^{2} x^{2} e^{4} - 36 \, {\left(x e + d\right)}^{m} a c d^{2} m^{2} x e^{3} + 4 \, {\left(x e + d\right)}^{m} a c d^{3} m^{2} e^{2} + 24 \, {\left(x e + d\right)}^{m} c^{2} d^{5} + 14 \, {\left(x e + d\right)}^{m} a^{2} m^{3} x e^{5} + 156 \, {\left(x e + d\right)}^{m} a c m x^{3} e^{5} + 14 \, {\left(x e + d\right)}^{m} a^{2} d m^{3} e^{4} + 40 \, {\left(x e + d\right)}^{m} a c d m x^{2} e^{4} - 80 \, {\left(x e + d\right)}^{m} a c d^{2} m x e^{3} + 36 \, {\left(x e + d\right)}^{m} a c d^{3} m e^{2} + 71 \, {\left(x e + d\right)}^{m} a^{2} m^{2} x e^{5} + 80 \, {\left(x e + d\right)}^{m} a c x^{3} e^{5} + 71 \, {\left(x e + d\right)}^{m} a^{2} d m^{2} e^{4} + 80 \, {\left(x e + d\right)}^{m} a c d^{3} e^{2} + 154 \, {\left(x e + d\right)}^{m} a^{2} m x e^{5} + 154 \, {\left(x e + d\right)}^{m} a^{2} d m e^{4} + 120 \, {\left(x e + d\right)}^{m} a^{2} x e^{5} + 120 \, {\left(x e + d\right)}^{m} a^{2} d e^{4}}{m^{5} e^{5} + 15 \, m^{4} e^{5} + 85 \, m^{3} e^{5} + 225 \, m^{2} e^{5} + 274 \, m e^{5} + 120 \, e^{5}}"," ",0,"((x*e + d)^m*c^2*m^4*x^5*e^5 + (x*e + d)^m*c^2*d*m^4*x^4*e^4 + 10*(x*e + d)^m*c^2*m^3*x^5*e^5 + 6*(x*e + d)^m*c^2*d*m^3*x^4*e^4 - 4*(x*e + d)^m*c^2*d^2*m^3*x^3*e^3 + 2*(x*e + d)^m*a*c*m^4*x^3*e^5 + 35*(x*e + d)^m*c^2*m^2*x^5*e^5 + 2*(x*e + d)^m*a*c*d*m^4*x^2*e^4 + 11*(x*e + d)^m*c^2*d*m^2*x^4*e^4 - 12*(x*e + d)^m*c^2*d^2*m^2*x^3*e^3 + 12*(x*e + d)^m*c^2*d^3*m^2*x^2*e^2 + 24*(x*e + d)^m*a*c*m^3*x^3*e^5 + 50*(x*e + d)^m*c^2*m*x^5*e^5 + 20*(x*e + d)^m*a*c*d*m^3*x^2*e^4 + 6*(x*e + d)^m*c^2*d*m*x^4*e^4 - 4*(x*e + d)^m*a*c*d^2*m^3*x*e^3 - 8*(x*e + d)^m*c^2*d^2*m*x^3*e^3 + 12*(x*e + d)^m*c^2*d^3*m*x^2*e^2 - 24*(x*e + d)^m*c^2*d^4*m*x*e + (x*e + d)^m*a^2*m^4*x*e^5 + 98*(x*e + d)^m*a*c*m^2*x^3*e^5 + 24*(x*e + d)^m*c^2*x^5*e^5 + (x*e + d)^m*a^2*d*m^4*e^4 + 58*(x*e + d)^m*a*c*d*m^2*x^2*e^4 - 36*(x*e + d)^m*a*c*d^2*m^2*x*e^3 + 4*(x*e + d)^m*a*c*d^3*m^2*e^2 + 24*(x*e + d)^m*c^2*d^5 + 14*(x*e + d)^m*a^2*m^3*x*e^5 + 156*(x*e + d)^m*a*c*m*x^3*e^5 + 14*(x*e + d)^m*a^2*d*m^3*e^4 + 40*(x*e + d)^m*a*c*d*m*x^2*e^4 - 80*(x*e + d)^m*a*c*d^2*m*x*e^3 + 36*(x*e + d)^m*a*c*d^3*m*e^2 + 71*(x*e + d)^m*a^2*m^2*x*e^5 + 80*(x*e + d)^m*a*c*x^3*e^5 + 71*(x*e + d)^m*a^2*d*m^2*e^4 + 80*(x*e + d)^m*a*c*d^3*e^2 + 154*(x*e + d)^m*a^2*m*x*e^5 + 154*(x*e + d)^m*a^2*d*m*e^4 + 120*(x*e + d)^m*a^2*x*e^5 + 120*(x*e + d)^m*a^2*d*e^4)/(m^5*e^5 + 15*m^4*e^5 + 85*m^3*e^5 + 225*m^2*e^5 + 274*m*e^5 + 120*e^5)","B",0
723,1,236,0,0.165123," ","integrate((e*x+d)^m*(c*x^2+a),x, algorithm=""giac"")","\frac{{\left(x e + d\right)}^{m} c m^{2} x^{3} e^{3} + {\left(x e + d\right)}^{m} c d m^{2} x^{2} e^{2} + 3 \, {\left(x e + d\right)}^{m} c m x^{3} e^{3} + {\left(x e + d\right)}^{m} c d m x^{2} e^{2} - 2 \, {\left(x e + d\right)}^{m} c d^{2} m x e + {\left(x e + d\right)}^{m} a m^{2} x e^{3} + 2 \, {\left(x e + d\right)}^{m} c x^{3} e^{3} + {\left(x e + d\right)}^{m} a d m^{2} e^{2} + 2 \, {\left(x e + d\right)}^{m} c d^{3} + 5 \, {\left(x e + d\right)}^{m} a m x e^{3} + 5 \, {\left(x e + d\right)}^{m} a d m e^{2} + 6 \, {\left(x e + d\right)}^{m} a x e^{3} + 6 \, {\left(x e + d\right)}^{m} a d e^{2}}{m^{3} e^{3} + 6 \, m^{2} e^{3} + 11 \, m e^{3} + 6 \, e^{3}}"," ",0,"((x*e + d)^m*c*m^2*x^3*e^3 + (x*e + d)^m*c*d*m^2*x^2*e^2 + 3*(x*e + d)^m*c*m*x^3*e^3 + (x*e + d)^m*c*d*m*x^2*e^2 - 2*(x*e + d)^m*c*d^2*m*x*e + (x*e + d)^m*a*m^2*x*e^3 + 2*(x*e + d)^m*c*x^3*e^3 + (x*e + d)^m*a*d*m^2*e^2 + 2*(x*e + d)^m*c*d^3 + 5*(x*e + d)^m*a*m*x*e^3 + 5*(x*e + d)^m*a*d*m*e^2 + 6*(x*e + d)^m*a*x*e^3 + 6*(x*e + d)^m*a*d*e^2)/(m^3*e^3 + 6*m^2*e^3 + 11*m*e^3 + 6*e^3)","B",0
724,0,0,0,0.000000," ","integrate((e*x+d)^m/(c*x^2+a),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{m}}{c x^{2} + a}\,{d x}"," ",0,"integrate((e*x + d)^m/(c*x^2 + a), x)","F",0
725,0,0,0,0.000000," ","integrate((e*x+d)^m/(c*x^2+a)^2,x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{m}}{{\left(c x^{2} + a\right)}^{2}}\,{d x}"," ",0,"integrate((e*x + d)^m/(c*x^2 + a)^2, x)","F",0
726,0,0,0,0.000000," ","integrate((e*x+d)^m/(c*x^2+a)^3,x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{m}}{{\left(c x^{2} + a\right)}^{3}}\,{d x}"," ",0,"integrate((e*x + d)^m/(c*x^2 + a)^3, x)","F",0
727,0,0,0,0.000000," ","integrate((e*x+d)^m*(c*x^2+a)^(3/2),x, algorithm=""giac"")","\int {\left(c x^{2} + a\right)}^{\frac{3}{2}} {\left(e x + d\right)}^{m}\,{d x}"," ",0,"integrate((c*x^2 + a)^(3/2)*(e*x + d)^m, x)","F",0
728,0,0,0,0.000000," ","integrate((e*x+d)^m*(c*x^2+a)^(1/2),x, algorithm=""giac"")","\int \sqrt{c x^{2} + a} {\left(e x + d\right)}^{m}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + a)*(e*x + d)^m, x)","F",0
729,0,0,0,0.000000," ","integrate((e*x+d)^m/(c*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{m}}{\sqrt{c x^{2} + a}}\,{d x}"," ",0,"integrate((e*x + d)^m/sqrt(c*x^2 + a), x)","F",0
730,0,0,0,0.000000," ","integrate((e*x+d)^m/(c*x^2+a)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{m}}{{\left(c x^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((e*x + d)^m/(c*x^2 + a)^(3/2), x)","F",0
731,0,0,0,0.000000," ","integrate((e*x+d)^m*(c*x^2+a)^p,x, algorithm=""giac"")","\int {\left(c x^{2} + a\right)}^{p} {\left(e x + d\right)}^{m}\,{d x}"," ",0,"integrate((c*x^2 + a)^p*(e*x + d)^m, x)","F",0
732,0,0,0,0.000000," ","integrate((e*x+d)^3*(c*x^2+a)^p,x, algorithm=""giac"")","\int {\left(e x + d\right)}^{3} {\left(c x^{2} + a\right)}^{p}\,{d x}"," ",0,"integrate((e*x + d)^3*(c*x^2 + a)^p, x)","F",0
733,0,0,0,0.000000," ","integrate((e*x+d)^2*(c*x^2+a)^p,x, algorithm=""giac"")","\int {\left(e x + d\right)}^{2} {\left(c x^{2} + a\right)}^{p}\,{d x}"," ",0,"integrate((e*x + d)^2*(c*x^2 + a)^p, x)","F",0
734,0,0,0,0.000000," ","integrate((e*x+d)*(c*x^2+a)^p,x, algorithm=""giac"")","\int {\left(e x + d\right)} {\left(c x^{2} + a\right)}^{p}\,{d x}"," ",0,"integrate((e*x + d)*(c*x^2 + a)^p, x)","F",0
735,0,0,0,0.000000," ","integrate((c*x^2+a)^p,x, algorithm=""giac"")","\int {\left(c x^{2} + a\right)}^{p}\,{d x}"," ",0,"integrate((c*x^2 + a)^p, x)","F",0
736,0,0,0,0.000000," ","integrate((c*x^2+a)^p/(e*x+d),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + a\right)}^{p}}{e x + d}\,{d x}"," ",0,"integrate((c*x^2 + a)^p/(e*x + d), x)","F",0
737,0,0,0,0.000000," ","integrate((c*x^2+a)^p/(e*x+d)^2,x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + a\right)}^{p}}{{\left(e x + d\right)}^{2}}\,{d x}"," ",0,"integrate((c*x^2 + a)^p/(e*x + d)^2, x)","F",0
738,0,0,0,0.000000," ","integrate((c*x^2+a)^p/(e*x+d)^3,x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + a\right)}^{p}}{{\left(e x + d\right)}^{3}}\,{d x}"," ",0,"integrate((c*x^2 + a)^p/(e*x + d)^3, x)","F",0
739,0,0,0,0.000000," ","integrate((c*x^2+a)^p/((e*x+d)^(2*p)),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + a\right)}^{p}}{{\left(e x + d\right)}^{2 \, p}}\,{d x}"," ",0,"integrate((c*x^2 + a)^p/(e*x + d)^(2*p), x)","F",0
740,0,0,0,0.000000," ","integrate((e*x+d)^(-1-2*p)*(c*x^2+a)^p,x, algorithm=""giac"")","\int {\left(c x^{2} + a\right)}^{p} {\left(e x + d\right)}^{-2 \, p - 1}\,{d x}"," ",0,"integrate((c*x^2 + a)^p*(e*x + d)^(-2*p - 1), x)","F",0
741,0,0,0,0.000000," ","integrate((e*x+d)^(-2-2*p)*(c*x^2+a)^p,x, algorithm=""giac"")","\int {\left(c x^{2} + a\right)}^{p} {\left(e x + d\right)}^{-2 \, p - 2}\,{d x}"," ",0,"integrate((c*x^2 + a)^p*(e*x + d)^(-2*p - 2), x)","F",0
742,0,0,0,0.000000," ","integrate((e*x+d)^(-3-2*p)*(c*x^2+a)^p,x, algorithm=""giac"")","\int {\left(c x^{2} + a\right)}^{p} {\left(e x + d\right)}^{-2 \, p - 3}\,{d x}"," ",0,"integrate((c*x^2 + a)^p*(e*x + d)^(-2*p - 3), x)","F",0
743,0,0,0,0.000000," ","integrate((e*x+d)^(-4-2*p)*(c*x^2+a)^p,x, algorithm=""giac"")","\int {\left(c x^{2} + a\right)}^{p} {\left(e x + d\right)}^{-2 \, p - 4}\,{d x}"," ",0,"integrate((c*x^2 + a)^p*(e*x + d)^(-2*p - 4), x)","F",0
744,0,0,0,0.000000," ","integrate((e*x+d)^(-5-2*p)*(c*x^2+a)^p,x, algorithm=""giac"")","\int {\left(c x^{2} + a\right)}^{p} {\left(e x + d\right)}^{-2 \, p - 5}\,{d x}"," ",0,"integrate((c*x^2 + a)^p*(e*x + d)^(-2*p - 5), x)","F",0
745,0,0,0,0.000000," ","integrate((e*x+d)^(-6-2*p)*(c*x^2+a)^p,x, algorithm=""giac"")","\int {\left(c x^{2} + a\right)}^{p} {\left(e x + d\right)}^{-2 \, p - 6}\,{d x}"," ",0,"integrate((c*x^2 + a)^p*(e*x + d)^(-2*p - 6), x)","F",0
746,0,0,0,0.000000," ","integrate((3-4*x)^n/(-x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(-4 \, x + 3\right)}^{n}}{\sqrt{-x^{2} + 1}}\,{d x}"," ",0,"integrate((-4*x + 3)^n/sqrt(-x^2 + 1), x)","F",0
747,1,72,0,0.167995," ","integrate((b*x+a)^6/(-b^2*x^2+a^2),x, algorithm=""giac"")","-\frac{32 \, a^{5} \log\left({\left| b x - a \right|}\right)}{b} - \frac{6 \, b^{9} x^{5} + 45 \, a b^{8} x^{4} + 160 \, a^{2} b^{7} x^{3} + 390 \, a^{3} b^{6} x^{2} + 930 \, a^{4} b^{5} x}{30 \, b^{5}}"," ",0,"-32*a^5*log(abs(b*x - a))/b - 1/30*(6*b^9*x^5 + 45*a*b^8*x^4 + 160*a^2*b^7*x^3 + 390*a^3*b^6*x^2 + 930*a^4*b^5*x)/b^5","A",0
748,1,61,0,0.159133," ","integrate((b*x+a)^5/(-b^2*x^2+a^2),x, algorithm=""giac"")","-\frac{16 \, a^{4} \log\left({\left| b x - a \right|}\right)}{b} - \frac{3 \, b^{7} x^{4} + 20 \, a b^{6} x^{3} + 66 \, a^{2} b^{5} x^{2} + 180 \, a^{3} b^{4} x}{12 \, b^{4}}"," ",0,"-16*a^4*log(abs(b*x - a))/b - 1/12*(3*b^7*x^4 + 20*a*b^6*x^3 + 66*a^2*b^5*x^2 + 180*a^3*b^4*x)/b^4","A",0
749,1,49,0,0.154106," ","integrate((b*x+a)^4/(-b^2*x^2+a^2),x, algorithm=""giac"")","-\frac{8 \, a^{3} \log\left({\left| b x - a \right|}\right)}{b} - \frac{b^{5} x^{3} + 6 \, a b^{4} x^{2} + 21 \, a^{2} b^{3} x}{3 \, b^{3}}"," ",0,"-8*a^3*log(abs(b*x - a))/b - 1/3*(b^5*x^3 + 6*a*b^4*x^2 + 21*a^2*b^3*x)/b^3","A",0
750,1,38,0,0.176637," ","integrate((b*x+a)^3/(-b^2*x^2+a^2),x, algorithm=""giac"")","-\frac{4 \, a^{2} \log\left({\left| b x - a \right|}\right)}{b} - \frac{b^{3} x^{2} + 6 \, a b^{2} x}{2 \, b^{2}}"," ",0,"-4*a^2*log(abs(b*x - a))/b - 1/2*(b^3*x^2 + 6*a*b^2*x)/b^2","A",0
751,1,19,0,0.157835," ","integrate((b*x+a)^2/(-b^2*x^2+a^2),x, algorithm=""giac"")","-x - \frac{2 \, a \log\left({\left| b x - a \right|}\right)}{b}"," ",0,"-x - 2*a*log(abs(b*x - a))/b","A",0
752,1,14,0,0.181464," ","integrate((b*x+a)/(-b^2*x^2+a^2),x, algorithm=""giac"")","-\frac{\log\left({\left| b x - a \right|}\right)}{b}"," ",0,"-log(abs(b*x - a))/b","A",0
753,1,48,0,0.157651," ","integrate(1/(b*x+a)/(-b^2*x^2+a^2),x, algorithm=""giac"")","\frac{\log\left({\left| b x + a \right|}\right)}{4 \, a^{2} b} - \frac{\log\left({\left| b x - a \right|}\right)}{4 \, a^{2} b} - \frac{1}{2 \, {\left(b x + a\right)} a b}"," ",0,"1/4*log(abs(b*x + a))/(a^2*b) - 1/4*log(abs(b*x - a))/(a^2*b) - 1/2/((b*x + a)*a*b)","A",0
754,1,51,0,0.155123," ","integrate(1/(b*x+a)^2/(-b^2*x^2+a^2),x, algorithm=""giac"")","-\frac{\frac{b}{b x + a} + \frac{a b}{{\left(b x + a\right)}^{2}}}{4 \, a^{2} b^{2}} - \frac{\log\left({\left| -\frac{2 \, a}{b x + a} + 1 \right|}\right)}{8 \, a^{3} b}"," ",0,"-1/4*(b/(b*x + a) + a*b/(b*x + a)^2)/(a^2*b^2) - 1/8*log(abs(-2*a/(b*x + a) + 1))/(a^3*b)","A",0
755,1,70,0,0.161793," ","integrate(1/(b*x+a)^3/(-b^2*x^2+a^2),x, algorithm=""giac"")","\frac{\log\left({\left| b x + a \right|}\right)}{16 \, a^{4} b} - \frac{\log\left({\left| b x - a \right|}\right)}{16 \, a^{4} b} - \frac{3 \, a b^{2} x^{2} + 9 \, a^{2} b x + 10 \, a^{3}}{24 \, {\left(b x + a\right)}^{3} a^{4} b}"," ",0,"1/16*log(abs(b*x + a))/(a^4*b) - 1/16*log(abs(b*x - a))/(a^4*b) - 1/24*(3*a*b^2*x^2 + 9*a^2*b*x + 10*a^3)/((b*x + a)^3*a^4*b)","A",0
756,1,81,0,0.164677," ","integrate(1/(b*x+a)^4/(-b^2*x^2+a^2),x, algorithm=""giac"")","\frac{\log\left({\left| b x + a \right|}\right)}{32 \, a^{5} b} - \frac{\log\left({\left| b x - a \right|}\right)}{32 \, a^{5} b} - \frac{3 \, a b^{3} x^{3} + 12 \, a^{2} b^{2} x^{2} + 19 \, a^{3} b x + 16 \, a^{4}}{48 \, {\left(b x + a\right)}^{4} a^{5} b}"," ",0,"1/32*log(abs(b*x + a))/(a^5*b) - 1/32*log(abs(b*x - a))/(a^5*b) - 1/48*(3*a*b^3*x^3 + 12*a^2*b^2*x^2 + 19*a^3*b*x + 16*a^4)/((b*x + a)^4*a^5*b)","A",0
757,1,78,0,0.166639," ","integrate((b*x+a)^7/(-b^2*x^2+a^2)^2,x, algorithm=""giac"")","\frac{80 \, a^{4} \log\left({\left| b x - a \right|}\right)}{b} - \frac{32 \, a^{5}}{{\left(b x - a\right)} b} + \frac{3 \, b^{11} x^{4} + 28 \, a b^{10} x^{3} + 138 \, a^{2} b^{9} x^{2} + 588 \, a^{3} b^{8} x}{12 \, b^{8}}"," ",0,"80*a^4*log(abs(b*x - a))/b - 32*a^5/((b*x - a)*b) + 1/12*(3*b^11*x^4 + 28*a*b^10*x^3 + 138*a^2*b^9*x^2 + 588*a^3*b^8*x)/b^8","A",0
758,1,66,0,0.190941," ","integrate((b*x+a)^6/(-b^2*x^2+a^2)^2,x, algorithm=""giac"")","\frac{32 \, a^{3} \log\left({\left| b x - a \right|}\right)}{b} - \frac{16 \, a^{4}}{{\left(b x - a\right)} b} + \frac{b^{8} x^{3} + 9 \, a b^{7} x^{2} + 51 \, a^{2} b^{6} x}{3 \, b^{6}}"," ",0,"32*a^3*log(abs(b*x - a))/b - 16*a^4/((b*x - a)*b) + 1/3*(b^8*x^3 + 9*a*b^7*x^2 + 51*a^2*b^6*x)/b^6","A",0
759,1,55,0,0.169612," ","integrate((b*x+a)^5/(-b^2*x^2+a^2)^2,x, algorithm=""giac"")","\frac{12 \, a^{2} \log\left({\left| b x - a \right|}\right)}{b} - \frac{8 \, a^{3}}{{\left(b x - a\right)} b} + \frac{b^{5} x^{2} + 10 \, a b^{4} x}{2 \, b^{4}}"," ",0,"12*a^2*log(abs(b*x - a))/b - 8*a^3/((b*x - a)*b) + 1/2*(b^5*x^2 + 10*a*b^4*x)/b^4","A",0
760,1,34,0,0.152381," ","integrate((b*x+a)^4/(-b^2*x^2+a^2)^2,x, algorithm=""giac"")","x + \frac{4 \, a \log\left({\left| b x - a \right|}\right)}{b} - \frac{4 \, a^{2}}{{\left(b x - a\right)} b}"," ",0,"x + 4*a*log(abs(b*x - a))/b - 4*a^2/((b*x - a)*b)","A",0
761,1,29,0,0.192935," ","integrate((b*x+a)^3/(-b^2*x^2+a^2)^2,x, algorithm=""giac"")","\frac{\log\left({\left| b x - a \right|}\right)}{b} - \frac{2 \, a}{{\left(b x - a\right)} b}"," ",0,"log(abs(b*x - a))/b - 2*a/((b*x - a)*b)","A",0
762,1,14,0,0.154000," ","integrate((b*x+a)^2/(-b^2*x^2+a^2)^2,x, algorithm=""giac"")","-\frac{1}{{\left(b x - a\right)} b}"," ",0,"-1/((b*x - a)*b)","A",0
763,1,50,0,0.160863," ","integrate((b*x+a)/(-b^2*x^2+a^2)^2,x, algorithm=""giac"")","\frac{\log\left({\left| b x + a \right|}\right)}{4 \, a^{2} b} - \frac{\log\left({\left| b x - a \right|}\right)}{4 \, a^{2} b} - \frac{1}{2 \, {\left(b x - a\right)} a b}"," ",0,"1/4*log(abs(b*x + a))/(a^2*b) - 1/4*log(abs(b*x - a))/(a^2*b) - 1/2/((b*x - a)*a*b)","A",0
764,1,79,0,0.157307," ","integrate(1/(b*x+a)/(-b^2*x^2+a^2)^2,x, algorithm=""giac"")","\frac{3 \, \log\left({\left| b x + a \right|}\right)}{16 \, a^{4} b} - \frac{3 \, \log\left({\left| b x - a \right|}\right)}{16 \, a^{4} b} - \frac{3 \, a b^{2} x^{2} + 3 \, a^{2} b x - 2 \, a^{3}}{8 \, {\left(b x + a\right)}^{2} {\left(b x - a\right)} a^{4} b}"," ",0,"3/16*log(abs(b*x + a))/(a^4*b) - 3/16*log(abs(b*x - a))/(a^4*b) - 1/8*(3*a*b^2*x^2 + 3*a^2*b*x - 2*a^3)/((b*x + a)^2*(b*x - a)*a^4*b)","A",0
765,1,99,0,0.193624," ","integrate(1/(b*x+a)^2/(-b^2*x^2+a^2)^2,x, algorithm=""giac"")","-\frac{\log\left({\left| -\frac{2 \, a}{b x + a} + 1 \right|}\right)}{8 \, a^{5} b} + \frac{1}{32 \, a^{5} b {\left(\frac{2 \, a}{b x + a} - 1\right)}} - \frac{\frac{9 \, a^{2} b^{5}}{b x + a} + \frac{6 \, a^{3} b^{5}}{{\left(b x + a\right)}^{2}} + \frac{4 \, a^{4} b^{5}}{{\left(b x + a\right)}^{3}}}{48 \, a^{6} b^{6}}"," ",0,"-1/8*log(abs(-2*a/(b*x + a) + 1))/(a^5*b) + 1/32/(a^5*b*(2*a/(b*x + a) - 1)) - 1/48*(9*a^2*b^5/(b*x + a) + 6*a^3*b^5/(b*x + a)^2 + 4*a^4*b^5/(b*x + a)^3)/(a^6*b^6)","A",0
766,1,101,0,0.165456," ","integrate(1/(b*x+a)^3/(-b^2*x^2+a^2)^2,x, algorithm=""giac"")","\frac{5 \, \log\left({\left| b x + a \right|}\right)}{64 \, a^{6} b} - \frac{5 \, \log\left({\left| b x - a \right|}\right)}{64 \, a^{6} b} - \frac{15 \, a b^{4} x^{4} + 45 \, a^{2} b^{3} x^{3} + 35 \, a^{3} b^{2} x^{2} - 15 \, a^{4} b x - 32 \, a^{5}}{96 \, {\left(b x + a\right)}^{4} {\left(b x - a\right)} a^{6} b}"," ",0,"5/64*log(abs(b*x + a))/(a^6*b) - 5/64*log(abs(b*x - a))/(a^6*b) - 1/96*(15*a*b^4*x^4 + 45*a^2*b^3*x^3 + 35*a^3*b^2*x^2 - 15*a^4*b*x - 32*a^5)/((b*x + a)^4*(b*x - a)*a^6*b)","A",0
767,1,76,0,0.163657," ","integrate((b*x+a)^8/(-b^2*x^2+a^2)^3,x, algorithm=""giac"")","-\frac{80 \, a^{3} \log\left({\left| b x - a \right|}\right)}{b} + \frac{16 \, {\left(5 \, a^{4} b x - 4 \, a^{5}\right)}}{{\left(b x - a\right)}^{2} b} - \frac{b^{11} x^{3} + 12 \, a b^{10} x^{2} + 93 \, a^{2} b^{9} x}{3 \, b^{9}}"," ",0,"-80*a^3*log(abs(b*x - a))/b + 16*(5*a^4*b*x - 4*a^5)/((b*x - a)^2*b) - 1/3*(b^11*x^3 + 12*a*b^10*x^2 + 93*a^2*b^9*x)/b^9","A",0
768,1,65,0,0.172663," ","integrate((b*x+a)^7/(-b^2*x^2+a^2)^3,x, algorithm=""giac"")","-\frac{24 \, a^{2} \log\left({\left| b x - a \right|}\right)}{b} + \frac{8 \, {\left(4 \, a^{3} b x - 3 \, a^{4}\right)}}{{\left(b x - a\right)}^{2} b} - \frac{b^{7} x^{2} + 14 \, a b^{6} x}{2 \, b^{6}}"," ",0,"-24*a^2*log(abs(b*x - a))/b + 8*(4*a^3*b*x - 3*a^4)/((b*x - a)^2*b) - 1/2*(b^7*x^2 + 14*a*b^6*x)/b^6","A",0
769,1,46,0,0.171361," ","integrate((b*x+a)^6/(-b^2*x^2+a^2)^3,x, algorithm=""giac"")","-x - \frac{6 \, a \log\left({\left| b x - a \right|}\right)}{b} + \frac{4 \, {\left(3 \, a^{2} b x - 2 \, a^{3}\right)}}{{\left(b x - a\right)}^{2} b}"," ",0,"-x - 6*a*log(abs(b*x - a))/b + 4*(3*a^2*b*x - 2*a^3)/((b*x - a)^2*b)","A",0
770,1,40,0,0.209837," ","integrate((b*x+a)^5/(-b^2*x^2+a^2)^3,x, algorithm=""giac"")","-\frac{\log\left({\left| b x - a \right|}\right)}{b} + \frac{2 \, {\left(2 \, a b x - a^{2}\right)}}{{\left(b x - a\right)}^{2} b}"," ",0,"-log(abs(b*x - a))/b + 2*(2*a*b*x - a^2)/((b*x - a)^2*b)","A",0
771,1,11,0,0.197729," ","integrate((b*x+a)^4/(-b^2*x^2+a^2)^3,x, algorithm=""giac"")","\frac{x}{{\left(b x - a\right)}^{2}}"," ",0,"x/(b*x - a)^2","A",0
772,1,14,0,0.159359," ","integrate((b*x+a)^3/(-b^2*x^2+a^2)^3,x, algorithm=""giac"")","\frac{1}{2 \, {\left(b x - a\right)}^{2} b}"," ",0,"1/2/((b*x - a)^2*b)","A",0
773,1,60,0,0.157783," ","integrate((b*x+a)^2/(-b^2*x^2+a^2)^3,x, algorithm=""giac"")","\frac{\log\left({\left| b x + a \right|}\right)}{8 \, a^{3} b} - \frac{\log\left({\left| b x - a \right|}\right)}{8 \, a^{3} b} - \frac{a b x - 2 \, a^{2}}{4 \, {\left(b x - a\right)}^{2} a^{3} b}"," ",0,"1/8*log(abs(b*x + a))/(a^3*b) - 1/8*log(abs(b*x - a))/(a^3*b) - 1/4*(a*b*x - 2*a^2)/((b*x - a)^2*a^3*b)","A",0
774,1,79,0,0.174361," ","integrate((b*x+a)/(-b^2*x^2+a^2)^3,x, algorithm=""giac"")","\frac{3 \, \log\left({\left| b x + a \right|}\right)}{16 \, a^{4} b} - \frac{3 \, \log\left({\left| b x - a \right|}\right)}{16 \, a^{4} b} - \frac{3 \, a b^{2} x^{2} - 3 \, a^{2} b x - 2 \, a^{3}}{8 \, {\left(b x + a\right)} {\left(b x - a\right)}^{2} a^{4} b}"," ",0,"3/16*log(abs(b*x + a))/(a^4*b) - 3/16*log(abs(b*x - a))/(a^4*b) - 1/8*(3*a*b^2*x^2 - 3*a^2*b*x - 2*a^3)/((b*x + a)*(b*x - a)^2*a^4*b)","A",0
775,1,101,0,0.158255," ","integrate(1/(b*x+a)/(-b^2*x^2+a^2)^3,x, algorithm=""giac"")","\frac{5 \, \log\left({\left| b x + a \right|}\right)}{32 \, a^{6} b} - \frac{5 \, \log\left({\left| b x - a \right|}\right)}{32 \, a^{6} b} - \frac{15 \, a b^{4} x^{4} + 15 \, a^{2} b^{3} x^{3} - 25 \, a^{3} b^{2} x^{2} - 25 \, a^{4} b x + 8 \, a^{5}}{48 \, {\left(b x + a\right)}^{3} {\left(b x - a\right)}^{2} a^{6} b}"," ",0,"5/32*log(abs(b*x + a))/(a^6*b) - 5/32*log(abs(b*x - a))/(a^6*b) - 1/48*(15*a*b^4*x^4 + 15*a^2*b^3*x^3 - 25*a^3*b^2*x^2 - 25*a^4*b*x + 8*a^5)/((b*x + a)^3*(b*x - a)^2*a^6*b)","A",0
776,1,125,0,0.166530," ","integrate(1/(b*x+a)^2/(-b^2*x^2+a^2)^3,x, algorithm=""giac"")","-\frac{15 \, \log\left({\left| -\frac{2 \, a}{b x + a} + 1 \right|}\right)}{128 \, a^{7} b} + \frac{\frac{24 \, a}{b x + a} - 11}{256 \, a^{7} b {\left(\frac{2 \, a}{b x + a} - 1\right)}^{2}} - \frac{\frac{5 \, a^{6} b^{11}}{b x + a} + \frac{3 \, a^{7} b^{11}}{{\left(b x + a\right)}^{2}} + \frac{2 \, a^{8} b^{11}}{{\left(b x + a\right)}^{3}} + \frac{a^{9} b^{11}}{{\left(b x + a\right)}^{4}}}{32 \, a^{12} b^{12}}"," ",0,"-15/128*log(abs(-2*a/(b*x + a) + 1))/(a^7*b) + 1/256*(24*a/(b*x + a) - 11)/(a^7*b*(2*a/(b*x + a) - 1)^2) - 1/32*(5*a^6*b^11/(b*x + a) + 3*a^7*b^11/(b*x + a)^2 + 2*a^8*b^11/(b*x + a)^3 + a^9*b^11/(b*x + a)^4)/(a^12*b^12)","A",0
777,1,91,0,0.204642," ","integrate((b*x+a)^4*(-b^2*x^2+a^2)^(1/2),x, algorithm=""giac"")","\frac{21 \, a^{6} \arcsin\left(\frac{b x}{a}\right) \mathrm{sgn}\left(a\right) \mathrm{sgn}\left(b\right)}{16 \, {\left| b \right|}} - \frac{1}{240} \, {\left(\frac{448 \, a^{5}}{b} + {\left(75 \, a^{4} - 2 \, {\left(128 \, a^{3} b + {\left(175 \, a^{2} b^{2} + 4 \, {\left(5 \, b^{4} x + 24 \, a b^{3}\right)} x\right)} x\right)} x\right)} x\right)} \sqrt{-b^{2} x^{2} + a^{2}}"," ",0,"21/16*a^6*arcsin(b*x/a)*sgn(a)*sgn(b)/abs(b) - 1/240*(448*a^5/b + (75*a^4 - 2*(128*a^3*b + (175*a^2*b^2 + 4*(5*b^4*x + 24*a*b^3)*x)*x)*x)*x)*sqrt(-b^2*x^2 + a^2)","A",0
778,1,81,0,0.213658," ","integrate((b*x+a)^3*(-b^2*x^2+a^2)^(1/2),x, algorithm=""giac"")","\frac{7 \, a^{5} \arcsin\left(\frac{b x}{a}\right) \mathrm{sgn}\left(a\right) \mathrm{sgn}\left(b\right)}{8 \, {\left| b \right|}} - \frac{1}{120} \, \sqrt{-b^{2} x^{2} + a^{2}} {\left(\frac{136 \, a^{4}}{b} - {\left(15 \, a^{3} + 2 \, {\left(56 \, a^{2} b + 3 \, {\left(4 \, b^{3} x + 15 \, a b^{2}\right)} x\right)} x\right)} x\right)}"," ",0,"7/8*a^5*arcsin(b*x/a)*sgn(a)*sgn(b)/abs(b) - 1/120*sqrt(-b^2*x^2 + a^2)*(136*a^4/b - (15*a^3 + 2*(56*a^2*b + 3*(4*b^3*x + 15*a*b^2)*x)*x)*x)","A",0
779,1,69,0,0.203341," ","integrate((b*x+a)^2*(-b^2*x^2+a^2)^(1/2),x, algorithm=""giac"")","\frac{5 \, a^{4} \arcsin\left(\frac{b x}{a}\right) \mathrm{sgn}\left(a\right) \mathrm{sgn}\left(b\right)}{8 \, {\left| b \right|}} - \frac{1}{24} \, \sqrt{-b^{2} x^{2} + a^{2}} {\left(\frac{16 \, a^{3}}{b} - {\left(9 \, a^{2} + 2 \, {\left(3 \, b^{2} x + 8 \, a b\right)} x\right)} x\right)}"," ",0,"5/8*a^4*arcsin(b*x/a)*sgn(a)*sgn(b)/abs(b) - 1/24*sqrt(-b^2*x^2 + a^2)*(16*a^3/b - (9*a^2 + 2*(3*b^2*x + 8*a*b)*x)*x)","A",0
780,1,56,0,0.198214," ","integrate((b*x+a)*(-b^2*x^2+a^2)^(1/2),x, algorithm=""giac"")","\frac{a^{3} \arcsin\left(\frac{b x}{a}\right) \mathrm{sgn}\left(a\right) \mathrm{sgn}\left(b\right)}{2 \, {\left| b \right|}} + \frac{1}{6} \, \sqrt{-b^{2} x^{2} + a^{2}} {\left({\left(2 \, b x + 3 \, a\right)} x - \frac{2 \, a^{2}}{b}\right)}"," ",0,"1/2*a^3*arcsin(b*x/a)*sgn(a)*sgn(b)/abs(b) + 1/6*sqrt(-b^2*x^2 + a^2)*((2*b*x + 3*a)*x - 2*a^2/b)","A",0
781,1,36,0,0.192236," ","integrate((-b^2*x^2+a^2)^(1/2)/(b*x+a),x, algorithm=""giac"")","\frac{a \arcsin\left(\frac{b x}{a}\right) \mathrm{sgn}\left(a\right) \mathrm{sgn}\left(b\right)}{{\left| b \right|}} + \frac{\sqrt{-b^{2} x^{2} + a^{2}}}{b}"," ",0,"a*arcsin(b*x/a)*sgn(a)*sgn(b)/abs(b) + sqrt(-b^2*x^2 + a^2)/b","A",0
782,-2,0,0,0.000000," ","integrate((-b^2*x^2+a^2)^(1/2)/(b*x+a)^2,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: abs(b)*(-(2*atan(i)-2*i)/b^2*sign((b*x+a)^-1)*sign(b)-2*a*(sqrt(2*a*b*(b*x+a)^-1/b-1)*sign((b*x+a)^-1)*sign(b)-sign((b*x+a)^-1)*sign(b)*atan(sqrt(2*a*b*(b*x+a)^-1/b-1)))/b^2/a)","F(-2)",0
783,1,74,0,0.225815," ","integrate((-b^2*x^2+a^2)^(1/2)/(b*x+a)^3,x, algorithm=""giac"")","\frac{2 \, {\left(\frac{3 \, {\left(a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}\right)}^{2}}{b^{4} x^{2}} + 1\right)}}{3 \, a {\left(\frac{a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}}{b^{2} x} + 1\right)}^{3} {\left| b \right|}}"," ",0,"2/3*(3*(a*b + sqrt(-b^2*x^2 + a^2)*abs(b))^2/(b^4*x^2) + 1)/(a*((a*b + sqrt(-b^2*x^2 + a^2)*abs(b))/(b^2*x) + 1)^3*abs(b))","B",0
784,1,165,0,0.225955," ","integrate((-b^2*x^2+a^2)^(1/2)/(b*x+a)^4,x, algorithm=""giac"")","\frac{2 \, {\left(\frac{5 \, {\left(a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}\right)}}{b^{2} x} + \frac{25 \, {\left(a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}\right)}^{2}}{b^{4} x^{2}} + \frac{15 \, {\left(a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}\right)}^{3}}{b^{6} x^{3}} + \frac{15 \, {\left(a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}\right)}^{4}}{b^{8} x^{4}} + 4\right)}}{15 \, a^{2} {\left(\frac{a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}}{b^{2} x} + 1\right)}^{5} {\left| b \right|}}"," ",0,"2/15*(5*(a*b + sqrt(-b^2*x^2 + a^2)*abs(b))/(b^2*x) + 25*(a*b + sqrt(-b^2*x^2 + a^2)*abs(b))^2/(b^4*x^2) + 15*(a*b + sqrt(-b^2*x^2 + a^2)*abs(b))^3/(b^6*x^3) + 15*(a*b + sqrt(-b^2*x^2 + a^2)*abs(b))^4/(b^8*x^4) + 4)/(a^2*((a*b + sqrt(-b^2*x^2 + a^2)*abs(b))/(b^2*x) + 1)^5*abs(b))","B",0
785,1,178,0,0.227681," ","integrate((-b^2*x^2+a^2)^(1/2)/(b*x+a)^5,x, algorithm=""giac"")","-\frac{1}{420} \, {\left(\frac{\frac{3 \, {\left(5 \, {\left(\frac{2 \, a}{b x + a} - 1\right)}^{\frac{7}{2}} + 21 \, {\left(\frac{2 \, a}{b x + a} - 1\right)}^{\frac{5}{2}} + 35 \, {\left(\frac{2 \, a}{b x + a} - 1\right)}^{\frac{3}{2}} + 35 \, \sqrt{\frac{2 \, a}{b x + a} - 1}\right)} \mathrm{sgn}\left(\frac{1}{b x + a}\right) \mathrm{sgn}\left(b\right)}{a^{2} b^{2}} - \frac{7 \, {\left(3 \, {\left(\frac{2 \, a}{b x + a} - 1\right)}^{\frac{5}{2}} + 10 \, {\left(\frac{2 \, a}{b x + a} - 1\right)}^{\frac{3}{2}} + 15 \, \sqrt{\frac{2 \, a}{b x + a} - 1}\right)} \mathrm{sgn}\left(\frac{1}{b x + a}\right) \mathrm{sgn}\left(b\right)}{a^{2} b^{2}}}{a} + \frac{8 i \, \mathrm{sgn}\left(\frac{1}{b x + a}\right) \mathrm{sgn}\left(b\right)}{a^{3} b^{2}}\right)} {\left| b \right|}"," ",0,"-1/420*((3*(5*(2*a/(b*x + a) - 1)^(7/2) + 21*(2*a/(b*x + a) - 1)^(5/2) + 35*(2*a/(b*x + a) - 1)^(3/2) + 35*sqrt(2*a/(b*x + a) - 1))*sgn(1/(b*x + a))*sgn(b)/(a^2*b^2) - 7*(3*(2*a/(b*x + a) - 1)^(5/2) + 10*(2*a/(b*x + a) - 1)^(3/2) + 15*sqrt(2*a/(b*x + a) - 1))*sgn(1/(b*x + a))*sgn(b)/(a^2*b^2))/a + 8*I*sgn(1/(b*x + a))*sgn(b)/(a^3*b^2))*abs(b)","C",0
786,1,289,0,0.236219," ","integrate((-b^2*x^2+a^2)^(1/2)/(b*x+a)^6,x, algorithm=""giac"")","\frac{2 \, {\left(\frac{207 \, {\left(a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}\right)}}{b^{2} x} + \frac{1143 \, {\left(a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}\right)}^{2}}{b^{4} x^{2}} + \frac{2247 \, {\left(a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}\right)}^{3}}{b^{6} x^{3}} + \frac{3843 \, {\left(a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}\right)}^{4}}{b^{8} x^{4}} + \frac{3465 \, {\left(a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}\right)}^{5}}{b^{10} x^{5}} + \frac{2625 \, {\left(a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}\right)}^{6}}{b^{12} x^{6}} + \frac{945 \, {\left(a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}\right)}^{7}}{b^{14} x^{7}} + \frac{315 \, {\left(a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}\right)}^{8}}{b^{16} x^{8}} + 58\right)}}{315 \, a^{4} {\left(\frac{a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}}{b^{2} x} + 1\right)}^{9} {\left| b \right|}}"," ",0,"2/315*(207*(a*b + sqrt(-b^2*x^2 + a^2)*abs(b))/(b^2*x) + 1143*(a*b + sqrt(-b^2*x^2 + a^2)*abs(b))^2/(b^4*x^2) + 2247*(a*b + sqrt(-b^2*x^2 + a^2)*abs(b))^3/(b^6*x^3) + 3843*(a*b + sqrt(-b^2*x^2 + a^2)*abs(b))^4/(b^8*x^4) + 3465*(a*b + sqrt(-b^2*x^2 + a^2)*abs(b))^5/(b^10*x^5) + 2625*(a*b + sqrt(-b^2*x^2 + a^2)*abs(b))^6/(b^12*x^6) + 945*(a*b + sqrt(-b^2*x^2 + a^2)*abs(b))^7/(b^14*x^7) + 315*(a*b + sqrt(-b^2*x^2 + a^2)*abs(b))^8/(b^16*x^8) + 58)/(a^4*((a*b + sqrt(-b^2*x^2 + a^2)*abs(b))/(b^2*x) + 1)^9*abs(b))","B",0
787,1,351,0,0.208310," ","integrate((-b^2*x^2+a^2)^(1/2)/(b*x+a)^7,x, algorithm=""giac"")","\frac{2 \, {\left(\frac{2552 \, {\left(a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}\right)}}{b^{2} x} + \frac{16225 \, {\left(a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}\right)}^{2}}{b^{4} x^{2}} + \frac{42900 \, {\left(a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}\right)}^{3}}{b^{6} x^{3}} + \frac{92730 \, {\left(a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}\right)}^{4}}{b^{8} x^{4}} + \frac{122892 \, {\left(a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}\right)}^{5}}{b^{10} x^{5}} + \frac{129822 \, {\left(a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}\right)}^{6}}{b^{12} x^{6}} + \frac{87780 \, {\left(a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}\right)}^{7}}{b^{14} x^{7}} + \frac{47355 \, {\left(a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}\right)}^{8}}{b^{16} x^{8}} + \frac{13860 \, {\left(a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}\right)}^{9}}{b^{18} x^{9}} + \frac{3465 \, {\left(a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}\right)}^{10}}{b^{20} x^{10}} + 547\right)}}{3465 \, a^{5} {\left(\frac{a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}}{b^{2} x} + 1\right)}^{11} {\left| b \right|}}"," ",0,"2/3465*(2552*(a*b + sqrt(-b^2*x^2 + a^2)*abs(b))/(b^2*x) + 16225*(a*b + sqrt(-b^2*x^2 + a^2)*abs(b))^2/(b^4*x^2) + 42900*(a*b + sqrt(-b^2*x^2 + a^2)*abs(b))^3/(b^6*x^3) + 92730*(a*b + sqrt(-b^2*x^2 + a^2)*abs(b))^4/(b^8*x^4) + 122892*(a*b + sqrt(-b^2*x^2 + a^2)*abs(b))^5/(b^10*x^5) + 129822*(a*b + sqrt(-b^2*x^2 + a^2)*abs(b))^6/(b^12*x^6) + 87780*(a*b + sqrt(-b^2*x^2 + a^2)*abs(b))^7/(b^14*x^7) + 47355*(a*b + sqrt(-b^2*x^2 + a^2)*abs(b))^8/(b^16*x^8) + 13860*(a*b + sqrt(-b^2*x^2 + a^2)*abs(b))^9/(b^18*x^9) + 3465*(a*b + sqrt(-b^2*x^2 + a^2)*abs(b))^10/(b^20*x^10) + 547)/(a^5*((a*b + sqrt(-b^2*x^2 + a^2)*abs(b))/(b^2*x) + 1)^11*abs(b))","B",0
788,1,104,0,0.320771," ","integrate((b*x+a)^3*(-b^2*x^2+a^2)^(3/2),x, algorithm=""giac"")","\frac{9 \, a^{7} \arcsin\left(\frac{b x}{a}\right) \mathrm{sgn}\left(a\right) \mathrm{sgn}\left(b\right)}{16 \, {\left| b \right|}} - \frac{1}{560} \, {\left(\frac{368 \, a^{6}}{b} - {\left(245 \, a^{5} + 2 \, {\left(328 \, a^{4} b + {\left(175 \, a^{3} b^{2} - 4 \, {\left(26 \, a^{2} b^{3} + 5 \, {\left(2 \, b^{5} x + 7 \, a b^{4}\right)} x\right)} x\right)} x\right)} x\right)} x\right)} \sqrt{-b^{2} x^{2} + a^{2}}"," ",0,"9/16*a^7*arcsin(b*x/a)*sgn(a)*sgn(b)/abs(b) - 1/560*(368*a^6/b - (245*a^5 + 2*(328*a^4*b + (175*a^3*b^2 - 4*(26*a^2*b^3 + 5*(2*b^5*x + 7*a*b^4)*x)*x)*x)*x)*x)*sqrt(-b^2*x^2 + a^2)","A",0
789,1,92,0,0.217672," ","integrate((b*x+a)^2*(-b^2*x^2+a^2)^(3/2),x, algorithm=""giac"")","\frac{7 \, a^{6} \arcsin\left(\frac{b x}{a}\right) \mathrm{sgn}\left(a\right) \mathrm{sgn}\left(b\right)}{16 \, {\left| b \right|}} - \frac{1}{240} \, {\left(\frac{96 \, a^{5}}{b} - {\left(135 \, a^{4} + 2 \, {\left(96 \, a^{3} b + {\left(5 \, a^{2} b^{2} - 4 \, {\left(5 \, b^{4} x + 12 \, a b^{3}\right)} x\right)} x\right)} x\right)} x\right)} \sqrt{-b^{2} x^{2} + a^{2}}"," ",0,"7/16*a^6*arcsin(b*x/a)*sgn(a)*sgn(b)/abs(b) - 1/240*(96*a^5/b - (135*a^4 + 2*(96*a^3*b + (5*a^2*b^2 - 4*(5*b^4*x + 12*a*b^3)*x)*x)*x)*x)*sqrt(-b^2*x^2 + a^2)","A",0
790,1,81,0,0.214593," ","integrate((b*x+a)*(-b^2*x^2+a^2)^(3/2),x, algorithm=""giac"")","\frac{3 \, a^{5} \arcsin\left(\frac{b x}{a}\right) \mathrm{sgn}\left(a\right) \mathrm{sgn}\left(b\right)}{8 \, {\left| b \right|}} - \frac{1}{40} \, \sqrt{-b^{2} x^{2} + a^{2}} {\left(\frac{8 \, a^{4}}{b} - {\left(25 \, a^{3} + 2 \, {\left(8 \, a^{2} b - {\left(4 \, b^{3} x + 5 \, a b^{2}\right)} x\right)} x\right)} x\right)}"," ",0,"3/8*a^5*arcsin(b*x/a)*sgn(a)*sgn(b)/abs(b) - 1/40*sqrt(-b^2*x^2 + a^2)*(8*a^4/b - (25*a^3 + 2*(8*a^2*b - (4*b^3*x + 5*a*b^2)*x)*x)*x)","A",0
791,1,56,0,0.210402," ","integrate((-b^2*x^2+a^2)^(3/2)/(b*x+a),x, algorithm=""giac"")","\frac{a^{3} \arcsin\left(\frac{b x}{a}\right) \mathrm{sgn}\left(a\right) \mathrm{sgn}\left(b\right)}{2 \, {\left| b \right|}} - \frac{1}{6} \, \sqrt{-b^{2} x^{2} + a^{2}} {\left({\left(2 \, b x - 3 \, a\right)} x - \frac{2 \, a^{2}}{b}\right)}"," ",0,"1/2*a^3*arcsin(b*x/a)*sgn(a)*sgn(b)/abs(b) - 1/6*sqrt(-b^2*x^2 + a^2)*((2*b*x - 3*a)*x - 2*a^2/b)","A",0
792,1,121,0,0.261838," ","integrate((-b^2*x^2+a^2)^(3/2)/(b*x+a)^2,x, algorithm=""giac"")","-\frac{{\left(12 \, a^{3} b^{3} \arctan\left(\sqrt{\frac{2 \, a}{b x + a} - 1}\right) \mathrm{sgn}\left(\frac{1}{b x + a}\right) \mathrm{sgn}\left(b\right) - \frac{{\left(5 \, a^{3} b^{3} {\left(\frac{2 \, a}{b x + a} - 1\right)}^{\frac{3}{2}} \mathrm{sgn}\left(\frac{1}{b x + a}\right) \mathrm{sgn}\left(b\right) + 3 \, a^{3} b^{3} \sqrt{\frac{2 \, a}{b x + a} - 1} \mathrm{sgn}\left(\frac{1}{b x + a}\right) \mathrm{sgn}\left(b\right)\right)} {\left(b x + a\right)}^{2}}{a^{2}}\right)} {\left| b \right|}}{4 \, a b^{5}}"," ",0,"-1/4*(12*a^3*b^3*arctan(sqrt(2*a/(b*x + a) - 1))*sgn(1/(b*x + a))*sgn(b) - (5*a^3*b^3*(2*a/(b*x + a) - 1)^(3/2)*sgn(1/(b*x + a))*sgn(b) + 3*a^3*b^3*sqrt(2*a/(b*x + a) - 1)*sgn(1/(b*x + a))*sgn(b))*(b*x + a)^2/a^2)*abs(b)/(a*b^5)","A",0
793,1,77,0,0.264732," ","integrate((-b^2*x^2+a^2)^(3/2)/(b*x+a)^3,x, algorithm=""giac"")","-\frac{3 \, a \arcsin\left(\frac{b x}{a}\right) \mathrm{sgn}\left(a\right) \mathrm{sgn}\left(b\right)}{{\left| b \right|}} - \frac{\sqrt{-b^{2} x^{2} + a^{2}}}{b} + \frac{8 \, a}{{\left(\frac{a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}}{b^{2} x} + 1\right)} {\left| b \right|}}"," ",0,"-3*a*arcsin(b*x/a)*sgn(a)*sgn(b)/abs(b) - sqrt(-b^2*x^2 + a^2)/b + 8*a/(((a*b + sqrt(-b^2*x^2 + a^2)*abs(b))/(b^2*x) + 1)*abs(b))","A",0
794,1,86,0,0.218024," ","integrate((-b^2*x^2+a^2)^(3/2)/(b*x+a)^4,x, algorithm=""giac"")","\frac{\arcsin\left(\frac{b x}{a}\right) \mathrm{sgn}\left(a\right) \mathrm{sgn}\left(b\right)}{{\left| b \right|}} - \frac{8 \, {\left(\frac{3 \, {\left(a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}\right)}}{b^{2} x} + 1\right)}}{3 \, {\left(\frac{a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}}{b^{2} x} + 1\right)}^{3} {\left| b \right|}}"," ",0,"arcsin(b*x/a)*sgn(a)*sgn(b)/abs(b) - 8/3*(3*(a*b + sqrt(-b^2*x^2 + a^2)*abs(b))/(b^2*x) + 1)/(((a*b + sqrt(-b^2*x^2 + a^2)*abs(b))/(b^2*x) + 1)^3*abs(b))","A",0
795,1,160,0,0.234514," ","integrate((-b^2*x^2+a^2)^(3/2)/(b*x+a)^5,x, algorithm=""giac"")","-\frac{1}{15} \, {\left(-\frac{3 i \, \mathrm{sgn}\left(\frac{1}{b x + a}\right) \mathrm{sgn}\left(b\right)}{a b^{2}} + \frac{{\left(3 \, {\left(\frac{2 \, a}{b x + a} - 1\right)}^{\frac{5}{2}} + 10 \, {\left(\frac{2 \, a}{b x + a} - 1\right)}^{\frac{3}{2}} + 15 \, \sqrt{\frac{2 \, a}{b x + a} - 1}\right)} \mathrm{sgn}\left(\frac{1}{b x + a}\right) \mathrm{sgn}\left(b\right) - 10 \, {\left({\left(\frac{2 \, a}{b x + a} - 1\right)}^{\frac{3}{2}} + 3 \, \sqrt{\frac{2 \, a}{b x + a} - 1}\right)} \mathrm{sgn}\left(\frac{1}{b x + a}\right) \mathrm{sgn}\left(b\right) + 15 \, \sqrt{\frac{2 \, a}{b x + a} - 1} \mathrm{sgn}\left(\frac{1}{b x + a}\right) \mathrm{sgn}\left(b\right)}{a b^{2}}\right)} {\left| b \right|}"," ",0,"-1/15*(-3*I*sgn(1/(b*x + a))*sgn(b)/(a*b^2) + ((3*(2*a/(b*x + a) - 1)^(5/2) + 10*(2*a/(b*x + a) - 1)^(3/2) + 15*sqrt(2*a/(b*x + a) - 1))*sgn(1/(b*x + a))*sgn(b) - 10*((2*a/(b*x + a) - 1)^(3/2) + 3*sqrt(2*a/(b*x + a) - 1))*sgn(1/(b*x + a))*sgn(b) + 15*sqrt(2*a/(b*x + a) - 1)*sgn(1/(b*x + a))*sgn(b))/(a*b^2))*abs(b)","C",0
796,1,227,0,0.220751," ","integrate((-b^2*x^2+a^2)^(3/2)/(b*x+a)^6,x, algorithm=""giac"")","\frac{2 \, {\left(\frac{7 \, {\left(a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}\right)}}{b^{2} x} + \frac{91 \, {\left(a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}\right)}^{2}}{b^{4} x^{2}} + \frac{70 \, {\left(a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}\right)}^{3}}{b^{6} x^{3}} + \frac{140 \, {\left(a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}\right)}^{4}}{b^{8} x^{4}} + \frac{35 \, {\left(a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}\right)}^{5}}{b^{10} x^{5}} + \frac{35 \, {\left(a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}\right)}^{6}}{b^{12} x^{6}} + 6\right)}}{35 \, a^{2} {\left(\frac{a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}}{b^{2} x} + 1\right)}^{7} {\left| b \right|}}"," ",0,"2/35*(7*(a*b + sqrt(-b^2*x^2 + a^2)*abs(b))/(b^2*x) + 91*(a*b + sqrt(-b^2*x^2 + a^2)*abs(b))^2/(b^4*x^2) + 70*(a*b + sqrt(-b^2*x^2 + a^2)*abs(b))^3/(b^6*x^3) + 140*(a*b + sqrt(-b^2*x^2 + a^2)*abs(b))^4/(b^8*x^4) + 35*(a*b + sqrt(-b^2*x^2 + a^2)*abs(b))^5/(b^10*x^5) + 35*(a*b + sqrt(-b^2*x^2 + a^2)*abs(b))^6/(b^12*x^6) + 6)/(a^2*((a*b + sqrt(-b^2*x^2 + a^2)*abs(b))/(b^2*x) + 1)^7*abs(b))","B",0
797,1,289,0,0.223571," ","integrate((-b^2*x^2+a^2)^(3/2)/(b*x+a)^7,x, algorithm=""giac"")","\frac{2 \, {\left(\frac{108 \, {\left(a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}\right)}}{b^{2} x} + \frac{1062 \, {\left(a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}\right)}^{2}}{b^{4} x^{2}} + \frac{1638 \, {\left(a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}\right)}^{3}}{b^{6} x^{3}} + \frac{3402 \, {\left(a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}\right)}^{4}}{b^{8} x^{4}} + \frac{2520 \, {\left(a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}\right)}^{5}}{b^{10} x^{5}} + \frac{2310 \, {\left(a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}\right)}^{6}}{b^{12} x^{6}} + \frac{630 \, {\left(a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}\right)}^{7}}{b^{14} x^{7}} + \frac{315 \, {\left(a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}\right)}^{8}}{b^{16} x^{8}} + 47\right)}}{315 \, a^{3} {\left(\frac{a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}}{b^{2} x} + 1\right)}^{9} {\left| b \right|}}"," ",0,"2/315*(108*(a*b + sqrt(-b^2*x^2 + a^2)*abs(b))/(b^2*x) + 1062*(a*b + sqrt(-b^2*x^2 + a^2)*abs(b))^2/(b^4*x^2) + 1638*(a*b + sqrt(-b^2*x^2 + a^2)*abs(b))^3/(b^6*x^3) + 3402*(a*b + sqrt(-b^2*x^2 + a^2)*abs(b))^4/(b^8*x^4) + 2520*(a*b + sqrt(-b^2*x^2 + a^2)*abs(b))^5/(b^10*x^5) + 2310*(a*b + sqrt(-b^2*x^2 + a^2)*abs(b))^6/(b^12*x^6) + 630*(a*b + sqrt(-b^2*x^2 + a^2)*abs(b))^7/(b^14*x^7) + 315*(a*b + sqrt(-b^2*x^2 + a^2)*abs(b))^8/(b^16*x^8) + 47)/(a^3*((a*b + sqrt(-b^2*x^2 + a^2)*abs(b))/(b^2*x) + 1)^9*abs(b))","B",0
798,1,351,0,0.230060," ","integrate((-b^2*x^2+a^2)^(3/2)/(b*x+a)^8,x, algorithm=""giac"")","\frac{2 \, {\left(\frac{517 \, {\left(a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}\right)}}{b^{2} x} + \frac{4895 \, {\left(a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}\right)}^{2}}{b^{4} x^{2}} + \frac{11220 \, {\left(a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}\right)}^{3}}{b^{6} x^{3}} + \frac{27060 \, {\left(a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}\right)}^{4}}{b^{8} x^{4}} + \frac{32802 \, {\left(a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}\right)}^{5}}{b^{10} x^{5}} + \frac{37422 \, {\left(a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}\right)}^{6}}{b^{12} x^{6}} + \frac{23100 \, {\left(a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}\right)}^{7}}{b^{14} x^{7}} + \frac{13860 \, {\left(a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}\right)}^{8}}{b^{16} x^{8}} + \frac{3465 \, {\left(a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}\right)}^{9}}{b^{18} x^{9}} + \frac{1155 \, {\left(a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}\right)}^{10}}{b^{20} x^{10}} + 152\right)}}{1155 \, a^{4} {\left(\frac{a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}}{b^{2} x} + 1\right)}^{11} {\left| b \right|}}"," ",0,"2/1155*(517*(a*b + sqrt(-b^2*x^2 + a^2)*abs(b))/(b^2*x) + 4895*(a*b + sqrt(-b^2*x^2 + a^2)*abs(b))^2/(b^4*x^2) + 11220*(a*b + sqrt(-b^2*x^2 + a^2)*abs(b))^3/(b^6*x^3) + 27060*(a*b + sqrt(-b^2*x^2 + a^2)*abs(b))^4/(b^8*x^4) + 32802*(a*b + sqrt(-b^2*x^2 + a^2)*abs(b))^5/(b^10*x^5) + 37422*(a*b + sqrt(-b^2*x^2 + a^2)*abs(b))^6/(b^12*x^6) + 23100*(a*b + sqrt(-b^2*x^2 + a^2)*abs(b))^7/(b^14*x^7) + 13860*(a*b + sqrt(-b^2*x^2 + a^2)*abs(b))^8/(b^16*x^8) + 3465*(a*b + sqrt(-b^2*x^2 + a^2)*abs(b))^9/(b^18*x^9) + 1155*(a*b + sqrt(-b^2*x^2 + a^2)*abs(b))^10/(b^20*x^10) + 152)/(a^4*((a*b + sqrt(-b^2*x^2 + a^2)*abs(b))/(b^2*x) + 1)^11*abs(b))","B",0
799,1,413,0,0.234007," ","integrate((-b^2*x^2+a^2)^(3/2)/(b*x+a)^9,x, algorithm=""giac"")","\frac{2 \, {\left(\frac{7904 \, {\left(a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}\right)}}{b^{2} x} + \frac{77454 \, {\left(a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}\right)}^{2}}{b^{4} x^{2}} + \frac{233948 \, {\left(a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}\right)}^{3}}{b^{6} x^{3}} + \frac{659945 \, {\left(a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}\right)}^{4}}{b^{8} x^{4}} + \frac{1094808 \, {\left(a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}\right)}^{5}}{b^{10} x^{5}} + \frac{1559844 \, {\left(a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}\right)}^{6}}{b^{12} x^{6}} + \frac{1465464 \, {\left(a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}\right)}^{7}}{b^{14} x^{7}} + \frac{1174173 \, {\left(a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}\right)}^{8}}{b^{16} x^{8}} + \frac{600600 \, {\left(a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}\right)}^{9}}{b^{18} x^{9}} + \frac{270270 \, {\left(a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}\right)}^{10}}{b^{20} x^{10}} + \frac{60060 \, {\left(a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}\right)}^{11}}{b^{22} x^{11}} + \frac{15015 \, {\left(a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}\right)}^{12}}{b^{24} x^{12}} + 1763\right)}}{15015 \, a^{5} {\left(\frac{a b + \sqrt{-b^{2} x^{2} + a^{2}} {\left| b \right|}}{b^{2} x} + 1\right)}^{13} {\left| b \right|}}"," ",0,"2/15015*(7904*(a*b + sqrt(-b^2*x^2 + a^2)*abs(b))/(b^2*x) + 77454*(a*b + sqrt(-b^2*x^2 + a^2)*abs(b))^2/(b^4*x^2) + 233948*(a*b + sqrt(-b^2*x^2 + a^2)*abs(b))^3/(b^6*x^3) + 659945*(a*b + sqrt(-b^2*x^2 + a^2)*abs(b))^4/(b^8*x^4) + 1094808*(a*b + sqrt(-b^2*x^2 + a^2)*abs(b))^5/(b^10*x^5) + 1559844*(a*b + sqrt(-b^2*x^2 + a^2)*abs(b))^6/(b^12*x^6) + 1465464*(a*b + sqrt(-b^2*x^2 + a^2)*abs(b))^7/(b^14*x^7) + 1174173*(a*b + sqrt(-b^2*x^2 + a^2)*abs(b))^8/(b^16*x^8) + 600600*(a*b + sqrt(-b^2*x^2 + a^2)*abs(b))^9/(b^18*x^9) + 270270*(a*b + sqrt(-b^2*x^2 + a^2)*abs(b))^10/(b^20*x^10) + 60060*(a*b + sqrt(-b^2*x^2 + a^2)*abs(b))^11/(b^22*x^11) + 15015*(a*b + sqrt(-b^2*x^2 + a^2)*abs(b))^12/(b^24*x^12) + 1763)/(a^5*((a*b + sqrt(-b^2*x^2 + a^2)*abs(b))/(b^2*x) + 1)^13*abs(b))","B",0
800,1,138,0,0.282430," ","integrate((e*x+d)^3*(-e^2*x^2+d^2)^(7/2),x, algorithm=""giac"")","\frac{91}{256} \, d^{11} \arcsin\left(\frac{x e}{d}\right) e^{\left(-1\right)} \mathrm{sgn}\left(d\right) - \frac{1}{126720} \, {\left(44800 \, d^{10} e^{\left(-1\right)} - {\left(81675 \, d^{9} + 2 \, {\left(83840 \, d^{8} e + {\left(6105 \, d^{7} e^{2} - 4 \, {\left(27840 \, d^{6} e^{3} + {\left(17787 \, d^{5} e^{4} - 2 \, {\left(6880 \, d^{4} e^{5} + {\left(8217 \, d^{3} e^{6} + 8 \, {\left(10 \, d^{2} e^{7} - 9 \, {\left(10 \, x e^{9} + 33 \, d e^{8}\right)} x\right)} x\right)} x\right)} x\right)} x\right)} x\right)} x\right)} x\right)} x\right)} \sqrt{-x^{2} e^{2} + d^{2}}"," ",0,"91/256*d^11*arcsin(x*e/d)*e^(-1)*sgn(d) - 1/126720*(44800*d^10*e^(-1) - (81675*d^9 + 2*(83840*d^8*e + (6105*d^7*e^2 - 4*(27840*d^6*e^3 + (17787*d^5*e^4 - 2*(6880*d^4*e^5 + (8217*d^3*e^6 + 8*(10*d^2*e^7 - 9*(10*x*e^9 + 33*d*e^8)*x)*x)*x)*x)*x)*x)*x)*x)*x)*sqrt(-x^2*e^2 + d^2)","A",0
801,1,128,0,0.247501," ","integrate((e*x+d)^2*(-e^2*x^2+d^2)^(7/2),x, algorithm=""giac"")","\frac{77}{256} \, d^{10} \arcsin\left(\frac{x e}{d}\right) e^{\left(-1\right)} \mathrm{sgn}\left(d\right) - \frac{1}{11520} \, {\left(2560 \, d^{9} e^{\left(-1\right)} - {\left(8055 \, d^{8} + 2 \, {\left(5120 \, d^{7} e - {\left(3075 \, d^{6} e^{2} + 4 \, {\left(1920 \, d^{5} e^{3} + {\left(39 \, d^{4} e^{4} - 2 \, {\left(640 \, d^{3} e^{5} + {\left(189 \, d^{2} e^{6} - 8 \, {\left(9 \, x e^{8} + 20 \, d e^{7}\right)} x\right)} x\right)} x\right)} x\right)} x\right)} x\right)} x\right)} x\right)} \sqrt{-x^{2} e^{2} + d^{2}}"," ",0,"77/256*d^10*arcsin(x*e/d)*e^(-1)*sgn(d) - 1/11520*(2560*d^9*e^(-1) - (8055*d^8 + 2*(5120*d^7*e - (3075*d^6*e^2 + 4*(1920*d^5*e^3 + (39*d^4*e^4 - 2*(640*d^3*e^5 + (189*d^2*e^6 - 8*(9*x*e^8 + 20*d*e^7)*x)*x)*x)*x)*x)*x)*x)*x)*sqrt(-x^2*e^2 + d^2)","A",0
802,1,119,0,0.278365," ","integrate((e*x+d)*(-e^2*x^2+d^2)^(7/2),x, algorithm=""giac"")","\frac{35}{128} \, d^{9} \arcsin\left(\frac{x e}{d}\right) e^{\left(-1\right)} \mathrm{sgn}\left(d\right) - \frac{1}{1152} \, {\left(128 \, d^{8} e^{\left(-1\right)} - {\left(837 \, d^{7} + 2 \, {\left(256 \, d^{6} e - {\left(489 \, d^{5} e^{2} + 4 \, {\left(96 \, d^{4} e^{3} - {\left(75 \, d^{3} e^{4} + 2 \, {\left(32 \, d^{2} e^{5} - {\left(8 \, x e^{7} + 9 \, d e^{6}\right)} x\right)} x\right)} x\right)} x\right)} x\right)} x\right)} x\right)} \sqrt{-x^{2} e^{2} + d^{2}}"," ",0,"35/128*d^9*arcsin(x*e/d)*e^(-1)*sgn(d) - 1/1152*(128*d^8*e^(-1) - (837*d^7 + 2*(256*d^6*e - (489*d^5*e^2 + 4*(96*d^4*e^3 - (75*d^3*e^4 + 2*(32*d^2*e^5 - (8*x*e^7 + 9*d*e^6)*x)*x)*x)*x)*x)*x)*x)*sqrt(-x^2*e^2 + d^2)","A",0
803,-2,0,0,0.000000," ","integrate((-e^2*x^2+d^2)^(7/2)/(e*x+d),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: 1/2*(16*d^7*exp(1)^6*exp(2)^2-24*d^7*exp(1)^4*exp(2)^3+12*d^7*exp(2)^5-4*d^7*exp(1)^8*exp(2))*atan((-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x+exp(2))/sqrt(-exp(1)^4+exp(2)^2))/sqrt(-exp(1)^4+exp(2)^2)/exp(1)^8/exp(1)+5/16*d^7*sign(d)*asin(x*exp(2)/d/exp(1))/exp(1)+2*((((((-92160*exp(1)^15*1/1290240/exp(1)^10*x+107520*exp(1)^14*d*1/1290240/exp(1)^10)*x+276480*exp(1)^13*d^2*1/1290240/exp(1)^10)*x-349440*exp(1)^12*d^3*1/1290240/exp(1)^10)*x-276480*exp(1)^11*d^4*1/1290240/exp(1)^10)*x+443520*exp(1)^10*d^5*1/1290240/exp(1)^10)*x+92160*exp(1)^9*d^6*1/1290240/exp(1)^10)*sqrt(d^2-x^2*exp(2))","F(-2)",0
804,0,0,0,0.000000," ","integrate((-e^2*x^2+d^2)^(7/2)/(e*x+d)^2,x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
805,-2,0,0,0.000000," ","integrate((-e^2*x^2+d^2)^(7/2)/(e*x+d)^3,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: (-2*d^5*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^10*exp(2)^2-28*d^5*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^10*exp(2)^2-12*d^5*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^8*exp(2)^3+37*d^5*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^8*exp(2)^3+19*d^5*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^6*exp(2)^4+2*d^5*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^6*exp(2)^4+6*d^5*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^4*exp(2)^5-d^5*exp(1)^8*exp(2)^3-5*d^5*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^4*exp(2)^5-14*d^5*exp(1)^6*exp(2)^4-11*d^5*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(2)^7+19*d^5*exp(1)^4*exp(2)^5-4*d^5*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(2)^7-4*d^5*exp(2)^7-2*d^5*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^12*exp(2)+37/2*d^5*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(2)^7/x/exp(2)-13*d^5*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^4*exp(2)^5/x/exp(2)-57/2*d^5*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^6*exp(2)^4/x/exp(2)+22*d^5*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^8*exp(2)^3/x/exp(2)+d^5*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^10*exp(2)^2/x/exp(2))/((-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(2)-(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x+exp(2))^2/(-exp(1)^11-exp(1)^7*exp(2)^2-2*exp(1)^9*exp(2))+1/2*(16*d^5*exp(1)^10*exp(2)^2-114*d^5*exp(1)^8*exp(2)^3+4*d^5*exp(1)^6*exp(2)^4+186*d^5*exp(1)^4*exp(2)^5-92*d^5*exp(2)^7)*atan((-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x+exp(2))/sqrt(-exp(1)^4+exp(2)^2))/sqrt(-exp(1)^4+exp(2)^2)/(exp(1)^13+exp(1)^9*exp(2)^2+2*exp(1)^11*exp(2))+7/8*d^5*sign(d)*asin(x*exp(2)/d/exp(1))/exp(1)+2*((((-192*exp(1)^9*1/1920/exp(1)^6*x+720*exp(1)^8*d*1/1920/exp(1)^6)*x-896*exp(1)^7*d^2*1/1920/exp(1)^6)*x+120*exp(1)^6*d^3*1/1920/exp(1)^6)*x+1088*exp(1)^5*d^4*1/1920/exp(1)^6)*sqrt(d^2-x^2*exp(2))","F(-2)",0
806,-2,0,0,0.000000," ","integrate((-e^2*x^2+d^2)^(7/2)/(e*x+d)^4,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: (12*d^4*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^14*exp(2)^2+6*d^4*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^12*exp(2)^3-8*d^4*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^14*exp(2)^2+36*d^4*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^12*exp(2)^3+18*d^4*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^10*exp(2)^4+12*d^4*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^14*exp(2)^2+568*d^4*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^12*exp(2)^3+540*d^4*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^10*exp(2)^4+126*d^4*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^8*exp(2)^5-60*d^4*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^12*exp(2)^3+296*d^4*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^10*exp(2)^4+228*d^4*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^8*exp(2)^5+42*d^4*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^6*exp(2)^6+1134*d^4*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^10*exp(2)^4+330*d^4*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^8*exp(2)^5-351*d^4*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^6*exp(2)^6-117*d^4*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^4*exp(2)^7+690*d^4*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^8*exp(2)^5+102*d^4*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^6*exp(2)^6-249*d^4*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^4*exp(2)^7+2*d^4*exp(1)^10*exp(2)^4-75*d^4*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(2)^9-744*d^4*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^6*exp(2)^6-756*d^4*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^4*exp(2)^7-2*d^4*exp(1)^8*exp(2)^5-216*d^4*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(2)^9-600*d^4*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^4*exp(2)^7+139*d^4*exp(1)^6*exp(2)^6-540*d^4*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(2)^9+77*d^4*exp(1)^4*exp(2)^7-432*d^4*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(2)^9-216*d^4*exp(2)^9+8*d^4*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^16*exp(2)+465/2*d^4*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(2)^9/x/exp(2)+639/2*d^4*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^4*exp(2)^7/x/exp(2)-210*d^4*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^6*exp(2)^6/x/exp(2)-354*d^4*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^8*exp(2)^5/x/exp(2)+15*d^4*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^10*exp(2)^4/x/exp(2)-3*d^4*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^12*exp(2)^3/x/exp(2))/((-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(2)-(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x+exp(2))^3/(3*exp(1)^13+9*exp(1)^9*exp(2)^2+3*exp(1)^7*exp(2)^3+9*exp(1)^11*exp(2))+1/2*(96*d^4*exp(1)^10*exp(2)^3-64*d^4*exp(1)^8*exp(2)^4-346*d^4*exp(1)^6*exp(2)^5-86*d^4*exp(1)^4*exp(2)^6+400*d^4*exp(2)^8)*atan((-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x+exp(2))/sqrt(-exp(1)^4+exp(2)^2))/sqrt(-exp(1)^4+exp(2)^2)/(exp(1)^15+3*exp(1)^11*exp(2)^2+exp(1)^9*exp(2)^3+3*exp(1)^13*exp(2))+35/8*d^4*sign(d)*asin(x*exp(2)/d/exp(1))/exp(1)+2*(((-12*exp(1)^6*1/96/exp(1)^4*x+64*exp(1)^5*d*1/96/exp(1)^4)*x-162*exp(1)^4*d^2*1/96/exp(1)^4)*x+320*exp(1)^3*d^3*1/96/exp(1)^4)*sqrt(d^2-x^2*exp(2))","F(-2)",0
807,0,0,0,0.000000," ","integrate((-e^2*x^2+d^2)^(7/2)/(e*x+d)^5,x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
808,-2,0,0,0.000000," ","integrate((-e^2*x^2+d^2)^(7/2)/(e*x+d)^6,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: (960*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^24*exp(2)^2+960*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^22*exp(2)^3+480*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^20*exp(2)^4+120*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^18*exp(2)^5+1280*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^24*exp(2)^2+3200*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^22*exp(2)^3+3200*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^20*exp(2)^4+1920*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^18*exp(2)^5+480*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^16*exp(2)^6+960*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^24*exp(2)^2+5152*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^22*exp(2)^3+3760*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^20*exp(2)^4+2800*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^18*exp(2)^5+2400*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^16*exp(2)^6+600*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^14*exp(2)^7+3200*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^22*exp(2)^3-53120*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^20*exp(2)^4-106560*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^18*exp(2)^5-72000*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^16*exp(2)^6-21120*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^14*exp(2)^7-2400*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^12*exp(2)^8+960*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^22*exp(2)^3+15280*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^20*exp(2)^4-81056*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^18*exp(2)^5-153520*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^16*exp(2)^6-101680*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^14*exp(2)^7-31440*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^12*exp(2)^8-3840*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^10*exp(2)^9+3200*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^20*exp(2)^4-181440*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^18*exp(2)^5-304160*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^16*exp(2)^6-170000*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^14*exp(2)^7-38960*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^12*exp(2)^8-3480*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^10*exp(2)^9-120*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^8*exp(2)^10+480*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^20*exp(2)^4+14320*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^18*exp(2)^5-311680*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^16*exp(2)^6-362660*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^14*exp(2)^7-53970*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^12*exp(2)^8+82170*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^10*exp(2)^9+40065*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^8*exp(2)^10+5385*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^6*exp(2)^11+1280*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^18*exp(2)^5-222400*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^16*exp(2)^6-320400*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^14*exp(2)^7-48880*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^12*exp(2)^8+152400*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^10*exp(2)^9+122160*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^8*exp(2)^10+38640*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^6*exp(2)^11+4560*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^4*exp(2)^12+5800*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^16*exp(2)^6-379920*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^14*exp(2)^7-73730*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^12*exp(2)^8+449970*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^10*exp(2)^9+374070*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^8*exp(2)^10+120090*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^6*exp(2)^11+17880*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^4*exp(2)^12+1200*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(2)^14-127280*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^14*exp(2)^7-154640*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^12*exp(2)^8+280800*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^10*exp(2)^9+520800*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^8*exp(2)^10+305760*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^6*exp(2)^11+76320*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^4*exp(2)^12+24*d^2*exp(1)^16*exp(2)^6+8520*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(2)^14-212390*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^12*exp(2)^8+277790*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^10*exp(2)^9+615920*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^8*exp(2)^10+370800*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^6*exp(2)^11+112560*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^4*exp(2)^12+80*d^2*exp(1)^14*exp(2)^7+20400*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(2)^14-37520*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^10*exp(2)^9+393040*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^8*exp(2)^10+495040*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^6*exp(2)^11+201600*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^4*exp(2)^12+202*d^2*exp(1)^12*exp(2)^8+34080*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(2)^14+231730*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^8*exp(2)^10+326310*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^6*exp(2)^11+179040*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^4*exp(2)^12-3720*d^2*exp(1)^10*exp(2)^9+54000*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(2)^14+227360*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^6*exp(2)^11+192480*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^4*exp(2)^12-6121*d^2*exp(1)^8*exp(2)^10+51120*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(2)^14+91920*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^4*exp(2)^12-560*d^2*exp(1)^6*exp(2)^11+51600*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(2)^14+7560*d^2*exp(1)^4*exp(2)^12+34080*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(2)^14+8520*d^2*exp(2)^14+384*d^2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^26*exp(2)-8400*d^2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(2)^14/x/exp(2)-31320*d^2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^4*exp(2)^12/x/exp(2)-70215/2*d^2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^6*exp(2)^11/x/exp(2)+2740*d^2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^8*exp(2)^10/x/exp(2)+28685*d^2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^10*exp(2)^9/x/exp(2)+17400*d^2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^12*exp(2)^8/x/exp(2)-710*d^2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^14*exp(2)^7/x/exp(2)-160*d^2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^16*exp(2)^6/x/exp(2)-60*d^2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^18*exp(2)^5/x/exp(2))/((-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(2)-(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x+exp(2))^5/(60*exp(1)^19+300*exp(1)^15*exp(2)^2-300*exp(1)^11*exp(2)^4-240*exp(1)^9*exp(2)^5-60*exp(1)^7*exp(2)^6+240*exp(1)^17*exp(2))+1/2*(-192*d^2*exp(1)^14*exp(2)^4-176*d^2*exp(1)^12*exp(2)^5+536*d^2*exp(1)^10*exp(2)^6+1207*d^2*exp(1)^8*exp(2)^7+464*d^2*exp(1)^6*exp(2)^8-632*d^2*exp(1)^4*exp(2)^9-808*d^2*exp(2)^11)*atan((-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x+exp(2))/sqrt(-exp(1)^4+exp(2)^2))/sqrt(-exp(1)^4+exp(2)^2)/(2*exp(1)^21+10*exp(1)^17*exp(2)^2-10*exp(1)^13*exp(2)^4-8*exp(1)^11*exp(2)^5-2*exp(1)^9*exp(2)^6+8*exp(1)^19*exp(2))+35/2*d^2*sign(d)*asin(x*exp(2)/d/exp(1))/exp(1)+2*(-2*exp(1)*1/8/exp(1)*x+24*d*1/8/exp(1))*sqrt(d^2-x^2*exp(2))","F(-2)",0
809,-2,0,0,0.000000," ","integrate((-e^2*x^2+d^2)^(7/2)/(e*x+d)^7,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: 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exp(2)^11+33960*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^10*exp(2)^12+2040*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^8*exp(2)^13-1200*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^24*exp(2)^5-16720*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^22*exp(2)^6+51480*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^20*exp(2)^7+2034984*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^18*exp(2)^8+3505280*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^16*exp(2)^9+2412120*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^14*exp(2)^10+727125*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^12*exp(2)^11+40825*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^10*exp(2)^12-23430*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^8*exp(2)^13-3570*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^6*exp(2)^14-3840*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^22*exp(2)^6-343680*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^20*exp(2)^7+1005600*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^18*exp(2)^8+2777280*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^16*exp(2)^9+2370640*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^14*exp(2)^10+883440*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^12*exp(2)^11+32040*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^10*exp(2)^12-92760*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^8*exp(2)^13-31200*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^6*exp(2)^14-3360*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^4*exp(2)^15-4200*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^20*exp(2)^7+65640*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^18*exp(2)^8+2729580*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^16*exp(2)^9+3564960*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^14*exp(2)^10+1142210*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^12*exp(2)^11-504930*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^10*exp(2)^12-450150*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^8*exp(2)^13-121830*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^6*exp(2)^14-15000*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^4*exp(2)^15-840*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(2)^17-133824*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^18*exp(2)^8+933120*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^16*exp(2)^9+2158320*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^14*exp(2)^10+1214160*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^12*exp(2)^11-465840*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^10*exp(2)^12-849360*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^8*exp(2)^13-394080*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^6*exp(2)^14-79200*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^4*exp(2)^15-40*d*exp(1)^20*exp(2)^7-7200*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(2)^17+33264*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^16*exp(2)^9+1947560*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^14*exp(2)^10+1342290*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^12*exp(2)^11-919470*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^10*exp(2)^12-1286860*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^8*exp(2)^13-566100*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^6*exp(2)^14-134520*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^4*exp(2)^15-144*d*exp(1)^18*exp(2)^8-19800*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(2)^17+410568*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^14*exp(2)^10+991320*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^12*exp(2)^11-178800*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^10*exp(2)^12-1358640*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^8*exp(2)^13-990400*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^6*exp(2)^14-283200*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^4*exp(2)^15-146*d*exp(1)^16*exp(2)^9-36000*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(2)^17+779757*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^12*exp(2)^11-131585*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^10*exp(2)^12-1126140*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^8*exp(2)^13-849900*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^6*exp(2)^14-319600*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^4*exp(2)^15-2312*d*exp(1)^14*exp(2)^10-70800*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(2)^17+293256*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^10*exp(2)^12-550440*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^8*exp(2)^13-918720*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^6*exp(2)^14-408000*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^4*exp(2)^15+1097*d*exp(1)^12*exp(2)^11-72000*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(2)^17-251406*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^8*exp(2)^13-470970*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^6*exp(2)^14-301680*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^4*exp(2)^15+8136*d*exp(1)^10*exp(2)^12-102000*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(2)^17-286560*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^6*exp(2)^14-266400*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^4*exp(2)^15+14594*d*exp(1)^8*exp(2)^13-72000*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(2)^17-107640*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^4*exp(2)^15+4640*d*exp(1)^6*exp(2)^14-66600*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(2)^17-6040*d*exp(1)^4*exp(2)^15-36000*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(2)^17-7200*d*exp(2)^17-1280*d*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^32*exp(2)+8220*d*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(2)^17/x/exp(2)+32880*d*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^4*exp(2)^15/x/exp(2)+34455*d*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^6*exp(2)^14/x/exp(2)-26820*d*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^8*exp(2)^13/x/exp(2)-165813/2*d*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^10*exp(2)^12/x/exp(2)-45396*d*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^12*exp(2)^11/x/exp(2)-4422*d*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^14*exp(2)^10/x/exp(2)+13872*d*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^16*exp(2)^9/x/exp(2)+396*d*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^18*exp(2)^8/x/exp(2)+384*d*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^20*exp(2)^7/x/exp(2)+120*d*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^22*exp(2)^6/x/exp(2))/((-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(2)-(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x+exp(2))^6/(-120*exp(1)^23-480*exp(1)^19*exp(2)^2+480*exp(1)^17*exp(2)^3+1200*exp(1)^15*exp(2)^4+480*exp(1)^13*exp(2)^5-480*exp(1)^11*exp(2)^6-480*exp(1)^9*exp(2)^7-120*exp(1)^7*exp(2)^8-480*exp(1)^21*exp(2))+1/2*(64*d*exp(1)^18*exp(2)^4-240*d*exp(1)^16*exp(2)^5-840*d*exp(1)^14*exp(2)^6-1133*d*exp(1)^12*exp(2)^7+248*d*exp(1)^10*exp(2)^8+1342*d*exp(1)^8*exp(2)^9+672*d*exp(1)^6*exp(2)^10-392*d*exp(1)^4*exp(2)^11-560*d*exp(2)^13)*atan((-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x+exp(2))/sqrt(-exp(1)^4+exp(2)^2))/sqrt(-exp(1)^4+exp(2)^2)/(4*exp(1)^25+16*exp(1)^21*exp(2)^2-16*exp(1)^19*exp(2)^3-40*exp(1)^17*exp(2)^4-16*exp(1)^15*exp(2)^5+16*exp(1)^13*exp(2)^6+16*exp(1)^11*exp(2)^7+4*exp(1)^9*exp(2)^8+16*exp(1)^23*exp(2))-7*d*sign(d)*asin(x*exp(2)/d/exp(1))/exp(1)-4*1/4/exp(1)*sqrt(d^2-x^2*exp(2))","F(-2)",0
810,-2,0,0,0.000000," ","integrate((-e^2*x^2+d^2)^(7/2)/(e*x+d)^8,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: (53760*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^36*exp(2)^2+80640*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^34*exp(2)^3+67200*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^32*exp(2)^4+33600*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^30*exp(2)^5+10080*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^28*exp(2)^6+1680*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^26*exp(2)^7+57344*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^36*exp(2)^2+200704*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^34*exp(2)^3+301056*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^32*exp(2)^4+250880*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^30*exp(2)^5+125440*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^28*exp(2)^6+40320*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^26*exp(2)^7+6720*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^24*exp(2)^8+53760*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^36*exp(2)^2+197632*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^34*exp(2)^3+328832*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^32*exp(2)^4+325248*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^30*exp(2)^5+182560*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^28*exp(2)^6+76160*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^26*exp(2)^7+30240*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^24*exp(2)^8+5040*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^22*exp(2)^9+200704*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^34*exp(2)^3+430080*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^32*exp(2)^4+365568*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^30*exp(2)^5-78848*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^28*exp(2)^6-380800*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^26*exp(2)^7-250880*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^24*exp(2)^8-80640*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^22*exp(2)^9-13440*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^20*exp(2)^10+80640*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^34*exp(2)^3+328832*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^32*exp(2)^4+1691136*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^30*exp(2)^5+3568320*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^28*exp(2)^6+3390800*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^26*exp(2)^7+1748320*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^24*exp(2)^8+452480*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^22*exp(2)^9+10080*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^20*exp(2)^10-11760*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^18*exp(2)^11+301056*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^32*exp(2)^4-64512*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^30*exp(2)^5+1017856*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^28*exp(2)^6+3729152*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^26*exp(2)^7+5040448*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^24*exp(2)^8+3664640*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^22*exp(2)^9+1388800*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^20*exp(2)^10+255360*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^18*exp(2)^11+20160*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^16*exp(2)^12+67200*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^32*exp(2)^4+325248*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^30*exp(2)^5+5342400*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^28*exp(2)^6+16528384*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^26*exp(2)^7+23906624*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^24*exp(2)^8+21140336*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^22*exp(2)^9+11792480*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^20*exp(2)^10+4043200*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^18*exp(2)^11+813120*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^16*exp(2)^12+75600*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^14*exp(2)^13+250880*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^30*exp(2)^5-723968*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^28*exp(2)^6+7008512*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^26*exp(2)^7+20439552*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^24*exp(2)^8+23982336*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^22*exp(2)^9+15710464*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^20*exp(2)^10+6202560*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^18*exp(2)^11+1646400*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^16*exp(2)^12+312480*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^14*exp(2)^13+30240*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^12*exp(2)^14+33600*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^30*exp(2)^5+236320*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^28*exp(2)^6+8928080*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^26*exp(2)^7+36357104*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^24*exp(2)^8+59975216*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^22*exp(2)^9+53901064*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^20*exp(2)^10+28133476*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^18*exp(2)^11+8689870*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^16*exp(2)^12+1610630*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^14*exp(2)^13+172095*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^12*exp(2)^14+8715*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^10*exp(2)^15+125440*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^28*exp(2)^6-748160*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^26*exp(2)^7+13888448*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^24*exp(2)^8+33914496*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^22*exp(2)^9+34642048*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^20*exp(2)^10+19550720*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^18*exp(2)^11+6273120*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^16*exp(2)^12+982800*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^14*exp(2)^13-85680*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^12*exp(2)^14-73080*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^10*exp(2)^15-9240*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^8*exp(2)^16+10080*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^28*exp(2)^6+103040*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^26*exp(2)^7+8188880*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^24*exp(2)^8+44412256*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^22*exp(2)^9+70938784*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^20*exp(2)^10+53067952*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^18*exp(2)^11+20015030*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^16*exp(2)^12+3643430*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^14*exp(2)^13+350560*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^12*exp(2)^14+77000*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^10*exp(2)^15+23730*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^8*exp(2)^16+2730*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^6*exp(2)^17+34944*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^26*exp(2)^7-426496*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^24*exp(2)^8+13351296*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^22*exp(2)^9+28594944*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^20*exp(2)^10+23569280*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^18*exp(2)^11+7454720*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^16*exp(2)^12-1730960*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^14*exp(2)^13-2131920*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^12*exp(2)^14-567840*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^10*exp(2)^15+16800*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^8*exp(2)^16+30240*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^6*exp(2)^17+3360*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^4*exp(2)^18+19152*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^24*exp(2)^8+4442032*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^22*exp(2)^9+33861408*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^20*exp(2)^10+44991576*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^18*exp(2)^11+22397900*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^16*exp(2)^12+4208540*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^14*exp(2)^13+1359715*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^12*exp(2)^14+1428875*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^10*exp(2)^15+647640*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^8*exp(2)^16+141960*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^6*exp(2)^17+15960*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^4*exp(2)^18+840*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(2)^20-138880*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^22*exp(2)^9+7448448*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^20*exp(2)^10+14516992*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^18*exp(2)^11+6608000*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^16*exp(2)^12-4051040*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^14*exp(2)^13-4037600*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^12*exp(2)^14+292040*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^10*exp(2)^15+1425480*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^8*exp(2)^16+618240*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^6*exp(2)^17+107520*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^4*exp(2)^18+240*exp(1)^24*exp(2)^8+8400*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(2)^20+1447936*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^20*exp(2)^10+16596720*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^18*exp(2)^11+14407820*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^16*exp(2)^12+2231740*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^14*exp(2)^13+1661800*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^12*exp(2)^14+4086600*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^10*exp(2)^15+2797410*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^8*exp(2)^16+969570*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^6*exp(2)^17+204960*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^4*exp(2)^18+896*exp(1)^22*exp(2)^9+26880*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(2)^20+2444736*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^18*exp(2)^11+4663232*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^16*exp(2)^12-1816192*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^14*exp(2)^13-4457600*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^12*exp(2)^14+1097600*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^10*exp(2)^15+3920000*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^8*exp(2)^16+2158240*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^6*exp(2)^17+487200*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^4*exp(2)^18+568*exp(1)^20*exp(2)^10+50400*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(2)^20+5063814*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^16*exp(2)^12+1122814*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^14*exp(2)^13-465899*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^12*exp(2)^14+3391745*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^10*exp(2)^15+4116000*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^8*exp(2)^16+2156000*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^6*exp(2)^17+665560*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^4*exp(2)^18-2688*exp(1)^18*exp(2)^11+121800*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(2)^20+991312*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^14*exp(2)^13-2286704*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^12*exp(2)^14-574056*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^10*exp(2)^15+3513720*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^8*exp(2)^16+3055360*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^6*exp(2)^17+940800*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^4*exp(2)^18+17310*exp(1)^16*exp(2)^12+126000*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(2)^20-599144*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^12*exp(2)^14+505904*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^10*exp(2)^15+2300886*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^8*exp(2)^16+2029230*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^6*exp(2)^17+931840*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^4*exp(2)^18+32368*exp(1)^14*exp(2)^13+235200*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(2)^20-872032*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^10*exp(2)^15+829920*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^8*exp(2)^16+1945440*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^6*exp(2)^17+924000*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^4*exp(2)^18+68521*exp(1)^12*exp(2)^14+168000*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(2)^20+347592*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^8*exp(2)^16+775320*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^6*exp(2)^17+612360*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^4*exp(2)^18+12824*exp(1)^10*exp(2)^15+231000*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(2)^20+448000*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^6*exp(2)^17+456960*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^4*exp(2)^18-10794*exp(1)^8*exp(2)^16+126000*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(2)^20+162400*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^4*exp(2)^18-12320*exp(1)^6*exp(2)^17+114240*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(2)^20+5320*exp(1)^4*exp(2)^18+50400*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(2)^20+8400*exp(2)^20+15360*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^38*exp(2)-11340*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(2)^20/x/exp(2)-45360*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^4*exp(2)^18/x/exp(2)-35875*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^6*exp(2)^17/x/exp(2)+81620*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^8*exp(2)^16/x/exp(2)+159831/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^10*exp(2)^15/x/exp(2)-74648*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^12*exp(2)^14/x/exp(2)-441847*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^14*exp(2)^13/x/exp(2)-216496*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^16*exp(2)^12/x/exp(2)-127050*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^18*exp(2)^11/x/exp(2)+12096*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^20*exp(2)^10/x/exp(2)-1456*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^22*exp(2)^9/x/exp(2)-2912*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^24*exp(2)^8/x/exp(2)-840*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^26*exp(2)^7/x/exp(2))/((-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(2)-(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x+exp(2))^7/(840*exp(1)^27+2520*exp(1)^23*exp(2)^2-6720*exp(1)^21*exp(2)^3-11760*exp(1)^19*exp(2)^4+11760*exp(1)^15*exp(2)^6+6720*exp(1)^13*exp(2)^7-2520*exp(1)^11*exp(2)^8-3360*exp(1)^9*exp(2)^9-840*exp(1)^7*exp(2)^10+3360*exp(1)^25*exp(2))+1/2*(-128*exp(1)^20*exp(2)^5-256*exp(1)^18*exp(2)^6-544*exp(1)^16*exp(2)^7-32*exp(1)^14*exp(2)^8+93*exp(1)^12*exp(2)^9+24*exp(1)^10*exp(2)^10-266*exp(1)^8*exp(2)^11-160*exp(1)^6*exp(2)^12+40*exp(1)^4*exp(2)^13+80*exp(2)^15)*atan((-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x+exp(2))/sqrt(-exp(1)^4+exp(2)^2))/sqrt(-exp(1)^4+exp(2)^2)/(-4*exp(1)^29-12*exp(1)^25*exp(2)^2+32*exp(1)^23*exp(2)^3+56*exp(1)^21*exp(2)^4-56*exp(1)^17*exp(2)^6-32*exp(1)^15*exp(2)^7+12*exp(1)^13*exp(2)^8+16*exp(1)^11*exp(2)^9+4*exp(1)^9*exp(2)^10-16*exp(1)^27*exp(2))+sign(d)*asin(x*exp(2)/d/exp(1))/exp(1)","F(-2)",0
811,-2,0,0,0.000000," ","integrate((-e^2*x^2+d^2)^(7/2)/(e*x+d)^9,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: (860160*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^36*exp(2)^2+1505280*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^34*exp(2)^3+1505280*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^32*exp(2)^4+940800*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^30*exp(2)^5+376320*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^28*exp(2)^6+94080*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^14*exp(1)^26*exp(2)^7+13440*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^15*exp(1)^24*exp(2)^8+819200*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^36*exp(2)^2+3276800*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^34*exp(2)^3+5734400*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^32*exp(2)^4+5734400*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^30*exp(2)^5+3584000*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^28*exp(2)^6+1433600*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^26*exp(2)^7+376320*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^14*exp(1)^24*exp(2)^8+53760*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^15*exp(1)^22*exp(2)^9+860160*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^36*exp(2)^2+3318784*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^34*exp(2)^3+5748736*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^32*exp(2)^4+5920768*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^30*exp(2)^5+4039168*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^28*exp(2)^6+1751680*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^26*exp(2)^7+568960*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^24*exp(2)^8+188160*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^14*exp(1)^22*exp(2)^9+26880*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^15*exp(1)^20*exp(2)^10+3276800*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^34*exp(2)^3+8839168*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^32*exp(2)^4+6684672*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^30*exp(2)^5-3211264*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^28*exp(2)^6-10379264*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^26*exp(2)^7-9300480*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^24*exp(2)^8-4247040*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^22*exp(2)^9-1128960*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^14*exp(1)^20*exp(2)^10-161280*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^15*exp(1)^18*exp(2)^11+1505280*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^34*exp(2)^3+5748736*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^32*exp(2)^4+1757952*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^30*exp(2)^5-15690752*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^28*exp(2)^6-30395008*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^26*exp(2)^7-29884288*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^24*exp(2)^8-17445120*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^22*exp(2)^9-6639360*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^20*exp(2)^10-1800960*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^14*exp(1)^18*exp(2)^11-241920*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^15*exp(1)^16*exp(2)^12+5734400*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^32*exp(2)^4+6684672*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^30*exp(2)^5-20967424*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^28*exp(2)^6-54050816*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^26*exp(2)^7-56637952*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^24*exp(2)^8-30008832*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^22*exp(2)^9-6021120*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^20*exp(2)^10+376320*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^18*exp(2)^11+349440*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^14*exp(1)^16*exp(2)^12+80640*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^15*exp(1)^14*exp(2)^13+1505280*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^32*exp(2)^4+5920768*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^30*exp(2)^5-29453312*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^28*exp(2)^6-150317440*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^26*exp(2)^7-287584640*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^24*exp(2)^8-306018048*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^22*exp(2)^9-192853248*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^20*exp(2)^10-73563840*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^18*exp(2)^11-15765120*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^16*exp(2)^12-1044960*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^14*exp(1)^14*exp(2)^13+131040*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^15*exp(1)^12*exp(2)^14+5734400*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^30*exp(2)^5-4931584*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^28*exp(2)^6-72974336*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^26*exp(2)^7-168851456*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^24*exp(2)^8-228785664*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^22*exp(2)^9-206244864*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^20*exp(2)^10-130980864*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^18*exp(2)^11-58752960*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^16*exp(2)^12-15711360*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^14*exp(2)^13-1918560*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^14*exp(1)^12*exp(2)^14-70560*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^15*exp(1)^10*exp(2)^15+940800*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^30*exp(2)^5+4039168*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^28*exp(2)^6-70822528*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^26*exp(2)^7-408867200*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^24*exp(2)^8-921069072*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^22*exp(2)^9-1173872448*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^20*exp(2)^10-970276272*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^18*exp(2)^11-561135792*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^16*exp(2)^12-227325210*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^14*exp(2)^13-61266660*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^12*exp(2)^14-10121685*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^14*exp(1)^10*exp(2)^15-796635*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^15*exp(1)^8*exp(2)^16+3584000*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^28*exp(2)^6-12099584*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^26*exp(2)^7-103839232*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^24*exp(2)^8-319640064*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^22*exp(2)^9-577667328*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^20*exp(2)^10-649377792*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^18*exp(2)^11-483383040*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^16*exp(2)^12-244702080*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^14*exp(2)^13-84574560*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^12*exp(2)^14-21171360*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^10*exp(2)^15-3800160*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^14*exp(1)^8*exp(2)^16-339360*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^15*exp(1)^6*exp(2)^17+376320*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^28*exp(2)^6+2074240*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^26*exp(2)^7-78985088*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^24*exp(2)^8-613381888*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^22*exp(2)^9-1597680448*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^20*exp(2)^10-2287565224*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^18*exp(2)^11-2092905136*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^16*exp(2)^12-1289631280*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^14*exp(2)^13-535877020*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^12*exp(2)^14-149727235*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^10*exp(2)^15-28368655*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^8*exp(2)^16-3491040*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^14*exp(1)^6*exp(2)^17-218400*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^15*exp(1)^4*exp(2)^18+1433600*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^26*exp(2)^7-9408000*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^24*exp(2)^8-93051392*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^22*exp(2)^9-415084544*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^20*exp(2)^10-865313792*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^18*exp(2)^11-1020797120*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^16*exp(2)^12-767406080*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^14*exp(2)^13-387238880*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^12*exp(2)^14-133605920*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^10*exp(2)^15-30937760*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^8*exp(2)^16-3856160*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^6*exp(2)^17-26880*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^14*exp(1)^4*exp(2)^18+26880*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^15*exp(2)^20+94080*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^26*exp(2)^7+697984*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^24*exp(2)^8-52657024*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^22*exp(2)^9-586342400*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^20*exp(2)^10-1737153264*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^18*exp(2)^11-2670468976*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^16*exp(2)^12-2484096650*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^14*exp(2)^13-1480690680*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^12*exp(2)^14-581958265*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^10*exp(2)^15-155101835*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^8*exp(2)^16-27824160*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^6*exp(2)^17-2892960*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^4*exp(2)^18-107520*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^14*exp(2)^20+340480*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^24*exp(2)^8-4239872*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^22*exp(2)^9-57100288*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^20*exp(2)^10-364105728*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^18*exp(2)^11-805839104*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^16*exp(2)^12-952860160*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^14*exp(2)^13-696376800*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^12*exp(2)^14-328297760*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^10*exp(2)^15-97723360*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^8*exp(2)^16-15840160*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^6*exp(2)^17-510720*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^4*exp(2)^18+134400*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(2)^20+94976*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^22*exp(2)^9-21797888*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^20*exp(2)^10-367222912*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^18*exp(2)^11-1264720240*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^16*exp(2)^12-2025169328*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^14*exp(2)^13-1818079480*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^12*exp(2)^14-1004159695*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^10*exp(2)^15-362210135*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^8*exp(2)^16-86931040*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^6*exp(2)^17-12529440*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^4*exp(2)^18-752640*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(2)^20-1120768*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^20*exp(2)^10-22475264*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^18*exp(2)^11-214765376*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^16*exp(2)^12-497483392*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^14*exp(2)^13-582216992*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^12*exp(2)^14-395437280*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^10*exp(2)^15-158129440*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^8*exp(2)^16-33827360*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^6*exp(2)^17-2284800*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^4*exp(2)^18+1680*exp(1)^22*exp(2)^9+241920*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(2)^20-5356512*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^18*exp(2)^11-150529120*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^16*exp(2)^12-643606670*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^14*exp(2)^13-1037059828*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^12*exp(2)^14-865313183*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^10*exp(2)^15-434710185*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^8*exp(2)^16-140124320*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^6*exp(2)^17-27058080*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^4*exp(2)^18+6400*exp(1)^20*exp(2)^10-2257920*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(2)^20-5463296*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^16*exp(2)^12-86536576*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^14*exp(2)^13-213138464*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^12*exp(2)^14-240423904*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^10*exp(2)^15-140230944*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^8*exp(2)^16-41436640*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^6*exp(2)^17-4704000*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^4*exp(2)^18+2408*exp(1)^18*exp(2)^11+134400*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(2)^20-39247040*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^14*exp(2)^13-230697292*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^12*exp(2)^14-358916873*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^10*exp(2)^15-274881397*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^8*exp(2)^16-125225632*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^6*exp(2)^17-33153120*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^4*exp(2)^18-20544*exp(1)^16*exp(2)^12-3763200*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(2)^20-22759584*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^12*exp(2)^14-63364448*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^10*exp(2)^15-65460192*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^8*exp(2)^16-29318240*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^6*exp(2)^17-5241600*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^4*exp(2)^18-64078*exp(1)^14*exp(2)^13-134400*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(2)^20-55765843*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^10*exp(2)^15-82846449*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^8*exp(2)^16-60190816*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^6*exp(2)^17-23597280*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^4*exp(2)^18-44192*exp(1)^12*exp(2)^14-3763200*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(2)^20-12990112*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^8*exp(2)^16-11196640*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^6*exp(2)^17-3252480*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^4*exp(2)^18-355173*exp(1)^10*exp(2)^15-241920*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(2)^20-13054496*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^6*exp(2)^17-9149280*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^4*exp(2)^18-217184*exp(1)^8*exp(2)^16-2257920*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(2)^20-1048320*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^4*exp(2)^18-562912*exp(1)^6*exp(2)^17-134400*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(2)^20-134400*exp(1)^4*exp(2)^18-752640*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(2)^20-107520*exp(2)^20+215040*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^38*exp(2)+13440*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(2)^20/x/exp(2)+750960*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^4*exp(2)^18/x/exp(2)+905520*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^6*exp(2)^17/x/exp(2)+8209957/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^8*exp(2)^16/x/exp(2)+1702192*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^10*exp(2)^15/x/exp(2)+2906904*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^12*exp(2)^14/x/exp(2)+393856*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^14*exp(2)^13/x/exp(2)+391664*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^16*exp(2)^12/x/exp(2)+83712*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^18*exp(2)^11/x/exp(2)-5824*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^20*exp(2)^10/x/exp(2)-24320*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^22*exp(2)^9/x/exp(2)-6720*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^24*exp(2)^8/x/exp(2))/((-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(2)-(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x+exp(2))^8/(6720*d*exp(1)^25+13440*d*exp(1)^21*exp(2)^2-80640*d*exp(1)^19*exp(2)^3-114240*d*exp(1)^17*exp(2)^4+53760*d*exp(1)^15*exp(2)^5+188160*d*exp(1)^13*exp(2)^6+53760*d*exp(1)^11*exp(2)^7-114240*d*exp(1)^9*exp(2)^8-80640*d*exp(1)^7*exp(2)^9+13440*d*exp(1)^5*exp(2)^10+26880*d*exp(1)^23*exp(2)+33600*d*exp(1)*exp(2)^12)+1/2*(-128*exp(1)^16*exp(2)^5-256*exp(1)^14*exp(2)^6-2336*exp(1)^12*exp(2)^7-1696*exp(1)^10*exp(2)^8-5411*exp(1)^8*exp(2)^9-1696*exp(1)^6*exp(2)^10-2336*exp(1)^4*exp(2)^11-384*exp(2)^13)*atan((-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x+exp(2))/sqrt(-exp(1)^4+exp(2)^2))/sqrt(-exp(1)^4+exp(2)^2)/(32*d*exp(1)^25+64*d*exp(1)^21*exp(2)^2-384*d*exp(1)^19*exp(2)^3-544*d*exp(1)^17*exp(2)^4+256*d*exp(1)^15*exp(2)^5+896*d*exp(1)^13*exp(2)^6+256*d*exp(1)^11*exp(2)^7-544*d*exp(1)^9*exp(2)^8-384*d*exp(1)^7*exp(2)^9+64*d*exp(1)^5*exp(2)^10+128*d*exp(1)^23*exp(2)+160*d*exp(1)*exp(2)^12)","F(-2)",0
812,-2,0,0,0.000000," ","integrate((-e^2*x^2+d^2)^(7/2)/(e*x+d)^10,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: 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2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^10*exp(2)^18-447288450*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^8*exp(2)^19-317016000*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^6*exp(2)^20-124205760*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^4*exp(2)^21-380328*exp(1)^12*exp(2)^17-20321280*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(2)^23-57775680*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^8*exp(2)^19-50070720*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^6*exp(2)^20-14676480*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^4*exp(2)^21-2295919*exp(1)^10*exp(2)^18-1128960*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(2)^23-58766400*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^6*exp(2)^20-40340160*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^4*exp(2)^21-919200*exp(1)^8*exp(2)^19-10160640*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(2)^23-4032000*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^4*exp(2)^21-2382240*exp(1)^6*exp(2)^20-483840*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(2)^23-456960*exp(1)^4*exp(2)^21-2903040*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(2)^23-362880*exp(2)^23-1146880*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^44*exp(2)+40320*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(2)^23/x/exp(2)+2837520*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^4*exp(2)^21/x/exp(2)+3462480*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^6*exp(2)^20/x/exp(2)+39381615/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^8*exp(2)^19/x/exp(2)+8241300*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^10*exp(2)^18/x/exp(2)+20688471*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^12*exp(2)^17/x/exp(2)+3322152*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^14*exp(2)^16/x/exp(2)+4934394*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^16*exp(2)^15/x/exp(2)+535536*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^18*exp(2)^14/x/exp(2)-269496*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^20*exp(2)^13/x/exp(2)-318528*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^22*exp(2)^12/x/exp(2)+1296*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^24*exp(2)^11/x/exp(2)+74880*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^26*exp(2)^10/x/exp(2)+20160*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^28*exp(2)^9/x/exp(2))/((-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(2)-(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x+exp(2))^9/(-20160*d^2*exp(1)^29-20160*d^2*exp(1)^25*exp(2)^2+322560*d^2*exp(1)^23*exp(2)^3+383040*d^2*exp(1)^21*exp(2)^4-403200*d^2*exp(1)^19*exp(2)^5-907200*d^2*exp(1)^17*exp(2)^6+907200*d^2*exp(1)^13*exp(2)^8+403200*d^2*exp(1)^11*exp(2)^9-383040*d^2*exp(1)^9*exp(2)^10-322560*d^2*exp(1)^7*exp(2)^11+20160*d^2*exp(1)^5*exp(2)^12-80640*d^2*exp(1)^27*exp(2)+100800*d^2*exp(1)*exp(2)^14)+1/2*(-640*exp(1)^16*exp(2)^7-640*exp(1)^14*exp(2)^8-5600*exp(1)^12*exp(2)^9-2760*exp(1)^10*exp(2)^10-8675*exp(1)^8*exp(2)^11-2080*exp(1)^6*exp(2)^12-2848*exp(1)^4*exp(2)^13-384*exp(2)^15)*atan((-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x+exp(2))/sqrt(-exp(1)^4+exp(2)^2))/sqrt(-exp(1)^4+exp(2)^2)/(-32*d^2*exp(1)^29-32*d^2*exp(1)^25*exp(2)^2+512*d^2*exp(1)^23*exp(2)^3+608*d^2*exp(1)^21*exp(2)^4-640*d^2*exp(1)^19*exp(2)^5-1440*d^2*exp(1)^17*exp(2)^6+1440*d^2*exp(1)^13*exp(2)^8+640*d^2*exp(1)^11*exp(2)^9-608*d^2*exp(1)^9*exp(2)^10-512*d^2*exp(1)^7*exp(2)^11+32*d^2*exp(1)^5*exp(2)^12-128*d^2*exp(1)^27*exp(2)+160*d^2*exp(1)*exp(2)^14)","F(-2)",0
813,-2,0,0,0.000000," ","integrate((-e^2*x^2+d^2)^(7/2)/(e*x+d)^11,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: 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))^11*exp(1)^38*exp(2)^7+1770455040*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^36*exp(2)^8+598425600*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^34*exp(2)^9-465346560*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^14*exp(1)^32*exp(2)^10-674365440*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^15*exp(1)^30*exp(2)^11-397931520*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^16*exp(1)^28*exp(2)^12-132357120*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^17*exp(1)^26*exp(2)^13-26127360*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^18*exp(1)^24*exp(2)^14-2903040*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^19*exp(1)^22*exp(2)^15-61931520*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^44*exp(2)^4-198973440*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^42*exp(2)^5+115159040*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^40*exp(2)^6+1340556288*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^38*exp(2)^7+2306288640*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^36*exp(2)^8+1459737600*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^34*exp(2)^9-446684160*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^32*exp(2)^10-1527751680*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^14*exp(1)^30*exp(2)^11-1334516736*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^15*exp(1)^28*exp(2)^12-660522240*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^16*exp(1)^26*exp(2)^13-210147840*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^17*exp(1)^24*exp(2)^14-45682560*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^18*exp(1)^22*exp(2)^15-5120640*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^19*exp(1)^20*exp(2)^16-240844800*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^42*exp(2)^5+77537280*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^40*exp(2)^6+1646469120*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^38*exp(2)^7+2091868160*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^36*exp(2)^8-266608640*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^34*exp(2)^9-2666035200*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^32*exp(2)^10-2572124160*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^30*exp(2)^11-1113584640*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^14*exp(1)^28*exp(2)^12-63974400*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^15*exp(1)^26*exp(2)^13+183939840*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^16*exp(1)^24*exp(2)^14+83381760*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^17*exp(1)^22*exp(2)^15+15281280*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^18*exp(1)^20*exp(2)^16+1653120*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^19*exp(1)^18*exp(2)^17-54190080*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^42*exp(2)^5-138854400*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^40*exp(2)^6+705223680*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^38*exp(2)^7+2574658560*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^36*exp(2)^8+3931833856*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^34*exp(2)^9+5765588480*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^32*exp(2)^10+9392079360*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^30*exp(2)^11+11610393600*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^28*exp(2)^12+9680697600*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^14*exp(1)^26*exp(2)^13+5513211648*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^15*exp(1)^24*exp(2)^14+2134265280*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^16*exp(1)^22*exp(2)^15+555340800*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^17*exp(1)^20*exp(2)^16+96536160*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^18*exp(1)^18*exp(2)^17+8900640*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^19*exp(1)^16*exp(2)^18-210739200*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^40*exp(2)^6+595107840*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^38*exp(2)^7+1770455040*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^36*exp(2)^8-60170240*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^34*exp(2)^9-2170340864*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^32*exp(2)^10+1602798080*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(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18970817040*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^10*exp(2)^21+4651879680*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^8*exp(2)^22+647082240*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^6*exp(2)^23+24729600*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^14*exp(1)^4*exp(2)^24-8064*exp(1)^30*exp(2)^11-3225600*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^15*exp(2)^26+11471680*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^26*exp(2)^13-90493920*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^24*exp(2)^14+10401732360*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^22*exp(2)^15+76918626504*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^20*exp(2)^16+203376842880*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^18*exp(2)^17+295411003440*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^16*exp(2)^18+271007541210*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^14*exp(2)^19+165831454530*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^12*exp(2)^20+69454965636*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^10*exp(2)^21+20254057740*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^8*exp(2)^22+4085679360*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^6*exp(2)^23+516337920*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^4*exp(2)^24-31360*exp(1)^28*exp(2)^12+29030400*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^14*exp(2)^26-26490560*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^24*exp(2)^14+184770240*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^22*exp(2)^15+5513823360*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^20*exp(2)^16+25493550912*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^18*exp(2)^17+51721682400*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^16*exp(2)^18+60273363360*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^14*exp(2)^19+44878066800*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^12*exp(2)^20+21879955440*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^10*exp(2)^21+6761591424*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^8*exp(2)^22+1180448640*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^6*exp(2)^23+73758720*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^4*exp(2)^24+3088*exp(1)^26*exp(2)^13-4515840*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(2)^26-14112520*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^22*exp(2)^15+3103252200*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^20*exp(2)^16+30052895160*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^18*exp(2)^17+86099072352*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^16*exp(2)^18+126610305060*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^14*exp(2)^19+111157085340*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^12*exp(2)^20+62345645460*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^10*exp(2)^21+23324927220*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^8*exp(2)^22+5904517248*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^6*exp(2)^23+935786880*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^4*exp(2)^24+159808*exp(1)^24*exp(2)^14+67737600*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(2)^26+42150720*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^20*exp(2)^16+1591686720*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^18*exp(2)^17+9211270560*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^16*exp(2)^18+19524015840*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^14*exp(2)^19+22238250720*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^12*exp(2)^20+15162930720*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^10*exp(2)^21+6188434560*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^8*exp(2)^22+1393580160*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^6*exp(2)^23+128701440*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^4*exp(2)^24+144200*exp(1)^22*exp(2)^15-2257920*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(2)^26+597529920*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^18*exp(2)^17+8373516720*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^16*exp(2)^18+27284576580*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^14*exp(2)^19+40282077636*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^12*exp(2)^20+32887950120*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^10*exp(2)^21+16541679000*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^8*exp(2)^22+5416494720*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^6*exp(2)^23+1096341120*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^4*exp(2)^24-301200*exp(1)^20*exp(2)^16+101606400*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(2)^26+297686440*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^16*exp(2)^18+2453117880*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^14*exp(2)^19+5481548640*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^12*exp(2)^20+5973274080*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^10*exp(2)^21+3501492480*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^8*exp(2)^22+1068936960*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^6*exp(2)^23+140743680*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^4*exp(2)^24-340206*exp(1)^18*exp(2)^17+2257920*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(2)^26+1580153255*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^14*exp(2)^19+6442776045*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^12*exp(2)^20+9327311880*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^10*exp(2)^21+6931281000*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^8*exp(2)^22+3110795520*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^6*exp(2)^23+838414080*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^4*exp(2)^24+335800*exp(1)^16*exp(2)^18+101606400*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(2)^26+457911560*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^12*exp(2)^20+1122424920*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^10*exp(2)^21+1130292480*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^8*exp(2)^22+515477760*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^6*exp(2)^23+97843200*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(1)^4*exp(2)^24+3874823*exp(1)^14*exp(2)^19+4515840*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(2)^26+1093846150*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^10*exp(2)^21+1514988930*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^8*exp(2)^22+1043723520*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^6*exp(2)^23+406022400*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^4*exp(2)^24+1823528*exp(1)^12*exp(2)^20+67737600*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^6*exp(2)^26+164998080*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^8*exp(2)^22+142336320*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^6*exp(2)^23+41932800*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^4*exp(2)^24+9127486*exp(1)^10*exp(2)^21+3225600*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(2)^26+169579200*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^6*exp(2)^23+113440320*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^4*exp(2)^24+2591424*exp(1)^8*exp(2)^22+29030400*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(2)^26+10053120*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^4*exp(2)^24+6541248*exp(1)^6*exp(2)^23+1128960*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(2)^26+1021440*exp(1)^4*exp(2)^24+7257600*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(2)^26+806400*exp(2)^26-4128768*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^50*exp(2)-80640*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(2)^26/x/exp(2)-6985440*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^4*exp(2)^24/x/exp(2)-8611680*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^6*exp(2)^23/x/exp(2)-60386655*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^8*exp(2)^22/x/exp(2)-25973460*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^10*exp(2)^21/x/exp(2)-179921675/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^12*exp(2)^20/x/exp(2)-16918580*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^14*exp(2)^19/x/exp(2)-34297910*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^16*exp(2)^18/x/exp(2)-2531440*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^18*exp(2)^17/x/exp(2)+841740*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^20*exp(2)^16/x/exp(2)+1560480*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^22*exp(2)^15/x/exp(2)-635600*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^24*exp(2)^14/x/exp(2)-791680*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^26*exp(2)^13/x/exp(2)-30880*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^28*exp(2)^12/x/exp(2)+152320*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^30*exp(2)^11/x/exp(2)+40320*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^32*exp(2)^10/x/exp(2))/((-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(2)-(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x+exp(2))^10/(-40320*d^3*exp(1)^33+806400*d^3*exp(1)^27*exp(2)^3+806400*d^3*exp(1)^25*exp(2)^4-1451520*d^3*exp(1)^23*exp(2)^5-2580480*d^3*exp(1)^21*exp(2)^6+806400*d^3*exp(1)^19*exp(2)^7+3628800*d^3*exp(1)^17*exp(2)^8+806400*d^3*exp(1)^15*exp(2)^9-2580480*d^3*exp(1)^13*exp(2)^10-1451520*d^3*exp(1)^11*exp(2)^11+806400*d^3*exp(1)^9*exp(2)^12+806400*d^3*exp(1)^7*exp(2)^13-161280*d^3*exp(1)^31*exp(2)-201600*d^3*exp(1)*exp(2)^16)+1/2*(-128*exp(1)^20*exp(2)^7-128*exp(1)^18*exp(2)^8-5216*exp(1)^16*exp(2)^9-3240*exp(1)^14*exp(2)^10-24727*exp(1)^12*exp(2)^11-8840*exp(1)^10*exp(2)^12-26790*exp(1)^8*exp(2)^13-5056*exp(1)^6*exp(2)^14-6848*exp(1)^4*exp(2)^15-768*exp(2)^17)*atan((-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x+exp(2))/sqrt(-exp(1)^4+exp(2)^2))/sqrt(-exp(1)^4+exp(2)^2)/(64*d^3*exp(1)^33-1280*d^3*exp(1)^27*exp(2)^3-1280*d^3*exp(1)^25*exp(2)^4+2304*d^3*exp(1)^23*exp(2)^5+4096*d^3*exp(1)^21*exp(2)^6-1280*d^3*exp(1)^19*exp(2)^7-5760*d^3*exp(1)^17*exp(2)^8-1280*d^3*exp(1)^15*exp(2)^9+4096*d^3*exp(1)^13*exp(2)^10+2304*d^3*exp(1)^11*exp(2)^11-1280*d^3*exp(1)^9*exp(2)^12-1280*d^3*exp(1)^7*exp(2)^13+256*d^3*exp(1)^31*exp(2)+320*d^3*exp(1)*exp(2)^16)","F(-2)",0
814,-2,0,0,0.000000," ","integrate((-e^2*x^2+d^2)^(7/2)/(e*x+d)^12,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: (454164480*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^54*exp(2)^2+1135411200*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^52*exp(2)^3+1703116800*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^14*exp(1)^50*exp(2)^4+1703116800*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^15*exp(1)^48*exp(2)^5+1192181760*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^16*exp(1)^46*exp(2)^6+596090880*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^17*exp(1)^44*exp(2)^7+212889600*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^18*exp(1)^42*exp(2)^8+53222400*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^19*exp(1)^40*exp(2)^9+8870400*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^20*exp(1)^38*exp(2)^10+887040*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^21*exp(1)^36*exp(2)^11+322961408*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^54*exp(2)^2+1776287744*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^52*exp(2)^3+4440719360*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^50*exp(2)^4+6661079040*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^14*exp(1)^48*exp(2)^5+6661079040*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^15*exp(1)^46*exp(2)^6+4662755328*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^16*exp(1)^44*exp(2)^7+2331377664*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^17*exp(1)^42*exp(2)^8+832634880*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^18*exp(1)^40*exp(2)^9+208158720*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^19*exp(1)^38*exp(2)^10+35481600*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^20*exp(1)^36*exp(2)^11+3548160*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^21*exp(1)^34*exp(2)^12+454164480*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^54*exp(2)^2+2162163712*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^52*exp(2)^3+4511727616*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^50*exp(2)^4+5318410240*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^48*exp(2)^5+3719823360*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^14*exp(1)^46*exp(2)^6+1335459840*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^15*exp(1)^44*exp(2)^7-78532608*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^16*exp(1)^42*exp(2)^8-358600704*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^17*exp(1)^40*exp(2)^9-206384640*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^18*exp(1)^38*exp(2)^10-62684160*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^19*exp(1)^36*exp(2)^11-8870400*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^20*exp(1)^34*exp(2)^12-887040*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^21*exp(1)^32*exp(2)^13+1776287744*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^52*exp(2)^3+6917718016*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^50*exp(2)^4+9182773248*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^48*exp(2)^5-356843520*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^46*exp(2)^6-17187962880*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^14*exp(1)^44*exp(2)^7-26513473536*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^15*exp(1)^42*exp(2)^8-22500065280*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^16*exp(1)^40*exp(2)^9-12498984960*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^17*exp(1)^38*exp(2)^10-4761630720*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^18*exp(1)^36*exp(2)^11-1234759680*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^19*exp(1)^34*exp(2)^12-212889600*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^20*exp(1)^32*exp(2)^13-21288960*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^21*exp(1)^30*exp(2)^14+1135411200*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^52*exp(2)^3+4511727616*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^50*exp(2)^4+5745688576*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^48*exp(2)^5-2968379392*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^46*exp(2)^6-20440330240*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^44*exp(2)^7-34036992000*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^14*exp(1)^42*exp(2)^8-33879926784*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^15*exp(1)^40*exp(2)^9-23075103744*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^16*exp(1)^38*exp(2)^10-11227974912*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^17*exp(1)^36*exp(2)^11-3885826560*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^18*exp(1)^34*exp(2)^12-960368640*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^19*exp(1)^32*exp(2)^13-177408000*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^20*exp(1)^30*exp(2)^14-17740800*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^21*exp(1)^28*exp(2)^15+4440719360*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^50*exp(2)^4+9182773248*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^48*exp(2)^5-9332719616*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^46*exp(2)^6-49010475008*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^44*exp(2)^7-62368317440*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^42*exp(2)^8-27230945280*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^14*exp(1)^40*exp(2)^9+17769185280*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^15*exp(1)^38*exp(2)^10+33476653056*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^16*exp(1)^36*exp(2)^11+23880772608*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^17*exp(1)^34*exp(2)^12+10327511040*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^18*exp(1)^32*exp(2)^13+2847989760*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^19*exp(1)^30*exp(2)^14+496742400*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^20*exp(1)^28*exp(2)^15+49674240*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^21*exp(1)^26*exp(2)^16+1703116800*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^50*exp(2)^4+5318410240*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^48*exp(2)^5-2968379392*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^46*exp(2)^6-35817684992*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^44*exp(2)^7-64475744256*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^42*exp(2)^8-42059888640*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^40*exp(2)^9+22106726400*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^14*exp(1)^38*exp(2)^10+68256933888*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^15*exp(1)^36*exp(2)^11+66571760640*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^16*exp(1)^34*exp(2)^12+39114620160*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^17*exp(1)^32*exp(2)^13+15179028480*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^18*exp(1)^30*exp(2)^14+4016517120*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^19*exp(1)^28*exp(2)^15+745113600*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^20*exp(1)^26*exp(2)^16+74511360*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^21*exp(1)^24*exp(2)^17+6661079040*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^48*exp(2)^5-356843520*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^46*exp(2)^6-49010475008*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^44*exp(2)^7-72072658944*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^42*exp(2)^8+8767356928*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^40*exp(2)^9+117226700800*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^38*exp(2)^10+131142696960*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^14*exp(1)^36*exp(2)^11+64189390848*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^15*exp(1)^34*exp(2)^12+5202075648*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^16*exp(1)^32*exp(2)^13-12890228736*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^17*exp(1)^30*exp(2)^14-8908247040*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^18*exp(1)^28*exp(2)^15-2847989760*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^19*exp(1)^26*exp(2)^16-496742400*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^20*exp(1)^24*exp(2)^17-49674240*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^21*exp(1)^22*exp(2)^18+1703116800*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^7*exp(1)^48*exp(2)^5+3719823360*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^8*exp(1)^46*exp(2)^6-20440330240*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^9*exp(1)^44*exp(2)^7-63794497536*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^10*exp(1)^42*exp(2)^8-17358155776*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^11*exp(1)^40*exp(2)^9+158830318592*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^12*exp(1)^38*exp(2)^10+291600826880*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^13*exp(1)^36*exp(2)^11+235916820480*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^14*exp(1)^34*exp(2)^12+81697228800*(-1/2*(-2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^36*exp(2)^11/x/exp(2))/((-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(2)-(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x+exp(2))^11/(443520*d^4*exp(1)^37-443520*d^4*exp(1)^33*exp(2)^2-10644480*d^4*exp(1)^31*exp(2)^3-8870400*d^4*exp(1)^29*exp(2)^4+24837120*d^4*exp(1)^27*exp(2)^5+37255680*d^4*exp(1)^25*exp(2)^6-24837120*d^4*exp(1)^23*exp(2)^7-68302080*d^4*exp(1)^21*exp(2)^8+68302080*d^4*exp(1)^17*exp(2)^10+24837120*d^4*exp(1)^15*exp(2)^11-37255680*d^4*exp(1)^13*exp(2)^12-24837120*d^4*exp(1)^11*exp(2)^13+8870400*d^4*exp(1)^9*exp(2)^14+10644480*d^4*exp(1)^7*exp(2)^15+443520*d^4*exp(1)^5*exp(2)^16+1774080*d^4*exp(1)^35*exp(2)-2217600*d^4*exp(1)*exp(2)^18)+1/2*(-1152*exp(1)^20*exp(2)^9-768*exp(1)^18*exp(2)^10-17072*exp(1)^16*exp(2)^11-7504*exp(1)^14*exp(2)^12-50261*exp(1)^12*exp(2)^13-13736*exp(1)^10*exp(2)^14-39910*exp(1)^8*exp(2)^15-6080*exp(1)^6*exp(2)^16-8128*exp(1)^4*exp(2)^17-768*exp(2)^19)*atan((-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x+exp(2))/sqrt(-exp(1)^4+exp(2)^2))/sqrt(-exp(1)^4+exp(2)^2)/(-64*d^4*exp(1)^37+64*d^4*exp(1)^33*exp(2)^2+1536*d^4*exp(1)^31*exp(2)^3+1280*d^4*exp(1)^29*exp(2)^4-3584*d^4*exp(1)^27*exp(2)^5-5376*d^4*exp(1)^25*exp(2)^6+3584*d^4*exp(1)^23*exp(2)^7+9856*d^4*exp(1)^21*exp(2)^8-9856*d^4*exp(1)^17*exp(2)^10-3584*d^4*exp(1)^15*exp(2)^11+5376*d^4*exp(1)^13*exp(2)^12+3584*d^4*exp(1)^11*exp(2)^13-1280*d^4*exp(1)^9*exp(2)^14-1536*d^4*exp(1)^7*exp(2)^15-64*d^4*exp(1)^5*exp(2)^16-256*d^4*exp(1)^35*exp(2)+320*d^4*exp(1)*exp(2)^18)","F(-2)",0
815,-2,0,0,0.000000," ","integrate((-e^2*x^2+d^2)^(7/2)/(e*x+d)^13,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: 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816,1,37,0,0.227448," ","integrate((-b^2*x^2+a^2)^(1/2)/(-b*x+a),x, algorithm=""giac"")","\frac{a \arcsin\left(\frac{b x}{a}\right) \mathrm{sgn}\left(a\right) \mathrm{sgn}\left(b\right)}{{\left| b \right|}} - \frac{\sqrt{-b^{2} x^{2} + a^{2}}}{b}"," ",0,"a*arcsin(b*x/a)*sgn(a)*sgn(b)/abs(b) - sqrt(-b^2*x^2 + a^2)/b","A",0
817,1,101,0,0.240211," ","integrate((b*x+a)^2*(-a^2*c/b^2+c*x^2)^(1/2),x, algorithm=""giac"")","\frac{{\left(\frac{15 \, a^{4} \sqrt{c} \log\left({\left| -\sqrt{b^{2} c} x + \sqrt{b^{2} c x^{2} - a^{2} c} \right|}\right)}{{\left| b \right|}} - \sqrt{b^{2} c x^{2} - a^{2} c} {\left(\frac{16 \, a^{3}}{b} - {\left(9 \, a^{2} + 2 \, {\left(3 \, b^{2} x + 8 \, a b\right)} x\right)} x\right)}\right)} {\left| b \right|}}{24 \, b^{2}}"," ",0,"1/24*(15*a^4*sqrt(c)*log(abs(-sqrt(b^2*c)*x + sqrt(b^2*c*x^2 - a^2*c)))/abs(b) - sqrt(b^2*c*x^2 - a^2*c)*(16*a^3/b - (9*a^2 + 2*(3*b^2*x + 8*a*b)*x)*x))*abs(b)/b^2","A",0
818,1,113,0,0.232620," ","integrate((b*x+a)^3*(-a^2*c/b^2+c*x^2)^(1/2),x, algorithm=""giac"")","\frac{{\left(\frac{105 \, a^{5} \sqrt{c} \log\left({\left| -\sqrt{b^{2} c} x + \sqrt{b^{2} c x^{2} - a^{2} c} \right|}\right)}{{\left| b \right|}} - \sqrt{b^{2} c x^{2} - a^{2} c} {\left(\frac{136 \, a^{4}}{b} - {\left(15 \, a^{3} + 2 \, {\left(56 \, a^{2} b + 3 \, {\left(4 \, b^{3} x + 15 \, a b^{2}\right)} x\right)} x\right)} x\right)}\right)} {\left| b \right|}}{120 \, b^{2}}"," ",0,"1/120*(105*a^5*sqrt(c)*log(abs(-sqrt(b^2*c)*x + sqrt(b^2*c*x^2 - a^2*c)))/abs(b) - sqrt(b^2*c*x^2 - a^2*c)*(136*a^4/b - (15*a^3 + 2*(56*a^2*b + 3*(4*b^3*x + 15*a*b^2)*x)*x)*x))*abs(b)/b^2","A",0
819,1,34,0,0.173515," ","integrate((1+x)*(x^2-1)^(1/2),x, algorithm=""giac"")","\frac{1}{6} \, {\left({\left(2 \, x + 3\right)} x - 2\right)} \sqrt{x^{2} - 1} + \frac{1}{2} \, \log\left({\left| -x + \sqrt{x^{2} - 1} \right|}\right)"," ",0,"1/6*((2*x + 3)*x - 2)*sqrt(x^2 - 1) + 1/2*log(abs(-x + sqrt(x^2 - 1)))","A",0
820,1,25,0,0.164406," ","integrate((1+x)*(-x^2+1)^(1/2),x, algorithm=""giac"")","\frac{1}{6} \, {\left({\left(2 \, x + 3\right)} x - 2\right)} \sqrt{-x^{2} + 1} + \frac{1}{2} \, \arcsin\left(x\right)"," ",0,"1/6*((2*x + 3)*x - 2)*sqrt(-x^2 + 1) + 1/2*arcsin(x)","A",0
821,1,12,0,0.176731," ","integrate((-x^2+1)^(1/2)/(1+x),x, algorithm=""giac"")","\sqrt{-x^{2} + 1} + \arcsin\left(x\right)"," ",0,"sqrt(-x^2 + 1) + arcsin(x)","A",0
822,1,25,0,0.165186," ","integrate((1-x)*(-x^2+1)^(1/2),x, algorithm=""giac"")","-\frac{1}{6} \, {\left({\left(2 \, x - 3\right)} x - 2\right)} \sqrt{-x^{2} + 1} + \frac{1}{2} \, \arcsin\left(x\right)"," ",0,"-1/6*((2*x - 3)*x - 2)*sqrt(-x^2 + 1) + 1/2*arcsin(x)","A",0
823,1,14,0,0.159505," ","integrate((-x^2+1)^(1/2)/(1-x),x, algorithm=""giac"")","-\sqrt{-x^{2} + 1} + \arcsin\left(x\right)"," ",0,"-sqrt(-x^2 + 1) + arcsin(x)","A",0
824,-2,0,0,0.000000," ","integrate((-x^2+1)^(1/2)/(1-x)^2,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: -(2*atan(i)-2*i)*sign((x-1)^-1)+2*(-sqrt(-2*(x-1)^-1-1)*sign((x-1)^-1)+sign((x-1)^-1)*atan(sqrt(-2*(x-1)^-1-1)))","F(-2)",0
825,1,41,0,0.167564," ","integrate((-x^2+1)^(1/2)/(1-x)^3,x, algorithm=""giac"")","\frac{2 \, {\left(\frac{3 \, {\left(\sqrt{-x^{2} + 1} - 1\right)}^{2}}{x^{2}} + 1\right)}}{3 \, {\left(\frac{\sqrt{-x^{2} + 1} - 1}{x} + 1\right)}^{3}}"," ",0,"2/3*(3*(sqrt(-x^2 + 1) - 1)^2/x^2 + 1)/((sqrt(-x^2 + 1) - 1)/x + 1)^3","B",0
826,1,73,0,0.269783," ","integrate((e*x+d)^5/(-e^2*x^2+d^2)^(1/2),x, algorithm=""giac"")","\frac{63}{8} \, d^{5} \arcsin\left(\frac{x e}{d}\right) e^{\left(-1\right)} \mathrm{sgn}\left(d\right) - \frac{1}{40} \, {\left(488 \, d^{4} e^{\left(-1\right)} + {\left(275 \, d^{3} + 2 \, {\left(72 \, d^{2} e + {\left(4 \, x e^{3} + 25 \, d e^{2}\right)} x\right)} x\right)} x\right)} \sqrt{-x^{2} e^{2} + d^{2}}"," ",0,"63/8*d^5*arcsin(x*e/d)*e^(-1)*sgn(d) - 1/40*(488*d^4*e^(-1) + (275*d^3 + 2*(72*d^2*e + (4*x*e^3 + 25*d*e^2)*x)*x)*x)*sqrt(-x^2*e^2 + d^2)","A",0
827,1,63,0,0.291265," ","integrate((e*x+d)^4/(-e^2*x^2+d^2)^(1/2),x, algorithm=""giac"")","\frac{35}{8} \, d^{4} \arcsin\left(\frac{x e}{d}\right) e^{\left(-1\right)} \mathrm{sgn}\left(d\right) - \frac{1}{24} \, {\left(160 \, d^{3} e^{\left(-1\right)} + {\left(81 \, d^{2} + 2 \, {\left(3 \, x e^{2} + 16 \, d e\right)} x\right)} x\right)} \sqrt{-x^{2} e^{2} + d^{2}}"," ",0,"35/8*d^4*arcsin(x*e/d)*e^(-1)*sgn(d) - 1/24*(160*d^3*e^(-1) + (81*d^2 + 2*(3*x*e^2 + 16*d*e)*x)*x)*sqrt(-x^2*e^2 + d^2)","A",0
828,1,52,0,0.308489," ","integrate((e*x+d)^3/(-e^2*x^2+d^2)^(1/2),x, algorithm=""giac"")","\frac{5}{2} \, d^{3} \arcsin\left(\frac{x e}{d}\right) e^{\left(-1\right)} \mathrm{sgn}\left(d\right) - \frac{1}{6} \, \sqrt{-x^{2} e^{2} + d^{2}} {\left(22 \, d^{2} e^{\left(-1\right)} + {\left(2 \, x e + 9 \, d\right)} x\right)}"," ",0,"5/2*d^3*arcsin(x*e/d)*e^(-1)*sgn(d) - 1/6*sqrt(-x^2*e^2 + d^2)*(22*d^2*e^(-1) + (2*x*e + 9*d)*x)","A",0
829,1,40,0,0.245388," ","integrate((e*x+d)^2/(-e^2*x^2+d^2)^(1/2),x, algorithm=""giac"")","\frac{3}{2} \, d^{2} \arcsin\left(\frac{x e}{d}\right) e^{\left(-1\right)} \mathrm{sgn}\left(d\right) - \frac{1}{2} \, \sqrt{-x^{2} e^{2} + d^{2}} {\left(4 \, d e^{\left(-1\right)} + x\right)}"," ",0,"3/2*d^2*arcsin(x*e/d)*e^(-1)*sgn(d) - 1/2*sqrt(-x^2*e^2 + d^2)*(4*d*e^(-1) + x)","A",0
830,1,32,0,0.236228," ","integrate((e*x+d)/(-e^2*x^2+d^2)^(1/2),x, algorithm=""giac"")","d \arcsin\left(\frac{x e}{d}\right) e^{\left(-1\right)} \mathrm{sgn}\left(d\right) - \sqrt{-x^{2} e^{2} + d^{2}} e^{\left(-1\right)}"," ",0,"d*arcsin(x*e/d)*e^(-1)*sgn(d) - sqrt(-x^2*e^2 + d^2)*e^(-1)","A",0
831,-2,0,0,0.000000," ","integrate(1/(e*x+d)/(-e^2*x^2+d^2)^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: -2*exp(2)*atan((-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x+exp(2))/sqrt(-exp(1)^4+exp(2)^2))/sqrt(-exp(1)^4+exp(2)^2)/d/exp(1)","F(-2)",0
832,-2,0,0,0.000000," ","integrate(1/(e*x+d)^2/(-e^2*x^2+d^2)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]index.cc index_m i_lex_is_greater Error: Bad Argument Value","F(-2)",0
833,-2,0,0,0.000000," ","integrate(1/(e*x+d)^3/(-e^2*x^2+d^2)^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: (7*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^6*exp(2)^3-2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^10*exp(2)-2*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^8*exp(2)^2+5*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^4*exp(2)^4-exp(1)^6*exp(2)^3+4*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(2)^6+4*exp(2)^6-11/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^4*exp(2)^4/x/exp(2)+(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^8*exp(2)^2/x/exp(2))/((-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(2)-(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x+exp(2))^2/(-d^3*exp(1)^9+2*d^3*exp(1)^5*exp(2)^2-d^3*exp(1)*exp(2)^4)+1/2*(-2*exp(1)^4*exp(2)^3-4*exp(2)^5)*atan((-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x+exp(2))/sqrt(-exp(1)^4+exp(2)^2))/sqrt(-exp(1)^4+exp(2)^2)/(d^3*exp(1)^9-2*d^3*exp(1)^5*exp(2)^2+d^3*exp(1)*exp(2)^4)","F(-2)",0
834,-2,0,0,0.000000," ","integrate(1/(e*x+d)^4/(-e^2*x^2+d^2)^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: (36*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(2)^9+8*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^16*exp(2)+12*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^14*exp(2)^2+6*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^12*exp(2)^3+12*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^14*exp(2)^2-8*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^12*exp(2)^3-36*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^10*exp(2)^4-18*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^8*exp(2)^5-18*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^10*exp(2)^4+42*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^8*exp(2)^5+81*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(1)^6*exp(2)^6+27*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^5*exp(1)^4*exp(2)^7+2*exp(1)^10*exp(2)^4+120*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(1)^6*exp(2)^6+108*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^3*exp(1)^4*exp(2)^7+18*(-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^4*exp(2)^9-5*exp(1)^6*exp(2)^6+18*exp(2)^9-81/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^4*exp(2)^7/x/exp(2)+6*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^8*exp(2)^5/x/exp(2)-3*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))*exp(1)^12*exp(2)^3/x/exp(2))/((-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x/exp(2))^2*exp(2)-(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x+exp(2))^3/(3*d^4*exp(1)^13-9*d^4*exp(1)^9*exp(2)^2+9*d^4*exp(1)^5*exp(2)^4-3*d^4*exp(1)*exp(2)^6)+1/2*(6*exp(1)^4*exp(2)^5+4*exp(2)^7)*atan((-1/2*(-2*d*exp(1)-2*sqrt(d^2-x^2*exp(2))*exp(1))/x+exp(2))/sqrt(-exp(1)^4+exp(2)^2))/sqrt(-exp(1)^4+exp(2)^2)/(d^4*exp(1)^13-3*d^4*exp(1)^9*exp(2)^2+3*d^4*exp(1)^5*exp(2)^4-d^4*exp(1)*exp(2)^6)","F(-2)",0
835,0,0,0,0.000000," ","integrate(1/(e*x+d)^5/(-e^2*x^2+d^2)^(1/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
836,1,97,0,0.311057," ","integrate((e*x+d)^6/(-e^2*x^2+d^2)^(5/2),x, algorithm=""giac"")","\frac{35}{2} \, d^{2} \arcsin\left(\frac{x e}{d}\right) e^{\left(-1\right)} \mathrm{sgn}\left(d\right) - \frac{{\left(164 \, d^{5} e^{\left(-1\right)} + {\left(99 \, d^{4} - {\left(264 \, d^{3} e + {\left(166 \, d^{2} e^{2} - 3 \, {\left(x e^{4} + 12 \, d e^{3}\right)} x\right)} x\right)} x\right)} x\right)} \sqrt{-x^{2} e^{2} + d^{2}}}{6 \, {\left(x^{2} e^{2} - d^{2}\right)}^{2}}"," ",0,"35/2*d^2*arcsin(x*e/d)*e^(-1)*sgn(d) - 1/6*(164*d^5*e^(-1) + (99*d^4 - (264*d^3*e + (166*d^2*e^2 - 3*(x*e^4 + 12*d*e^3)*x)*x)*x)*x)*sqrt(-x^2*e^2 + d^2)/(x^2*e^2 - d^2)^2","A",0
837,1,86,0,0.325048," ","integrate((e*x+d)^5/(-e^2*x^2+d^2)^(5/2),x, algorithm=""giac"")","5 \, d \arcsin\left(\frac{x e}{d}\right) e^{\left(-1\right)} \mathrm{sgn}\left(d\right) - \frac{{\left(23 \, d^{4} e^{\left(-1\right)} + {\left(12 \, d^{3} - {\left(42 \, d^{2} e - {\left(3 \, x e^{3} - 28 \, d e^{2}\right)} x\right)} x\right)} x\right)} \sqrt{-x^{2} e^{2} + d^{2}}}{3 \, {\left(x^{2} e^{2} - d^{2}\right)}^{2}}"," ",0,"5*d*arcsin(x*e/d)*e^(-1)*sgn(d) - 1/3*(23*d^4*e^(-1) + (12*d^3 - (42*d^2*e - (3*x*e^3 - 28*d*e^2)*x)*x)*x)*sqrt(-x^2*e^2 + d^2)/(x^2*e^2 - d^2)^2","A",0
838,1,66,0,0.340981," ","integrate((e*x+d)^4/(-e^2*x^2+d^2)^(5/2),x, algorithm=""giac"")","\arcsin\left(\frac{x e}{d}\right) e^{\left(-1\right)} \mathrm{sgn}\left(d\right) - \frac{4 \, {\left(d^{3} e^{\left(-1\right)} - {\left(2 \, x e^{2} + 3 \, d e\right)} x^{2}\right)} \sqrt{-x^{2} e^{2} + d^{2}}}{3 \, {\left(x^{2} e^{2} - d^{2}\right)}^{2}}"," ",0,"arcsin(x*e/d)*e^(-1)*sgn(d) - 4/3*(d^3*e^(-1) - (2*x*e^2 + 3*d*e)*x^2)*sqrt(-x^2*e^2 + d^2)/(x^2*e^2 - d^2)^2","A",0
839,1,56,0,0.283450," ","integrate((e*x+d)^3/(-e^2*x^2+d^2)^(5/2),x, algorithm=""giac"")","\frac{\sqrt{-x^{2} e^{2} + d^{2}} {\left(d^{2} e^{\left(-1\right)} + {\left(x {\left(\frac{x e^{2}}{d} + 3 \, e\right)} + 3 \, d\right)} x\right)}}{3 \, {\left(x^{2} e^{2} - d^{2}\right)}^{2}}"," ",0,"1/3*sqrt(-x^2*e^2 + d^2)*(d^2*e^(-1) + (x*(x*e^2/d + 3*e) + 3*d)*x)/(x^2*e^2 - d^2)^2","A",0
840,1,48,0,0.269825," ","integrate((e*x+d)^2/(-e^2*x^2+d^2)^(5/2),x, algorithm=""giac"")","-\frac{\sqrt{-x^{2} e^{2} + d^{2}} {\left(x {\left(\frac{x^{2} e^{2}}{d^{2}} - 3\right)} - 2 \, d e^{\left(-1\right)}\right)}}{3 \, {\left(x^{2} e^{2} - d^{2}\right)}^{2}}"," ",0,"-1/3*sqrt(-x^2*e^2 + d^2)*(x*(x^2*e^2/d^2 - 3) - 2*d*e^(-1))/(x^2*e^2 - d^2)^2","A",0
841,1,52,0,0.258833," ","integrate((e*x+d)/(-e^2*x^2+d^2)^(5/2),x, algorithm=""giac"")","-\frac{\sqrt{-x^{2} e^{2} + d^{2}} {\left(x {\left(\frac{2 \, x^{2} e^{2}}{d^{3}} - \frac{3}{d}\right)} - e^{\left(-1\right)}\right)}}{3 \, {\left(x^{2} e^{2} - d^{2}\right)}^{2}}"," ",0,"-1/3*sqrt(-x^2*e^2 + d^2)*(x*(2*x^2*e^2/d^3 - 3/d) - e^(-1))/(x^2*e^2 - d^2)^2","A",0
842,-2,0,0,0.000000," ","integrate(1/(e*x+d)/(-e^2*x^2+d^2)^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to transpose Error: Bad Argument Value","F(-2)",0
843,0,0,0,0.000000," ","integrate(1/(e*x+d)^2/(-e^2*x^2+d^2)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
844,-2,0,0,0.000000," ","integrate(1/(e*x+d)^3/(-e^2*x^2+d^2)^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to transpose Error: Bad Argument Value","F(-2)",0
845,-2,0,0,0.000000," ","integrate(1/(e*x+d)^4/(-e^2*x^2+d^2)^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to transpose Error: Bad Argument Value","F(-2)",0
846,1,129,0,0.372544," ","integrate((e*x+d)^9/(-e^2*x^2+d^2)^(7/2),x, algorithm=""giac"")","-\frac{231}{2} \, d^{3} \arcsin\left(\frac{x e}{d}\right) e^{\left(-1\right)} \mathrm{sgn}\left(d\right) - \frac{{\left(5446 \, d^{8} e^{\left(-1\right)} + {\left(3495 \, d^{7} - {\left(13480 \, d^{6} e + {\left(7765 \, d^{5} e^{2} - {\left(10740 \, d^{4} e^{3} + {\left(5941 \, d^{3} e^{4} - 5 \, {\left(232 \, d^{2} e^{5} + {\left(2 \, x e^{7} + 27 \, d e^{6}\right)} x\right)} x\right)} x\right)} x\right)} x\right)} x\right)} x\right)} \sqrt{-x^{2} e^{2} + d^{2}}}{30 \, {\left(x^{2} e^{2} - d^{2}\right)}^{3}}"," ",0,"-231/2*d^3*arcsin(x*e/d)*e^(-1)*sgn(d) - 1/30*(5446*d^8*e^(-1) + (3495*d^7 - (13480*d^6*e + (7765*d^5*e^2 - (10740*d^4*e^3 + (5941*d^3*e^4 - 5*(232*d^2*e^5 + (2*x*e^7 + 27*d*e^6)*x)*x)*x)*x)*x)*x)*x)*sqrt(-x^2*e^2 + d^2)/(x^2*e^2 - d^2)^3","A",0
847,1,118,0,0.332559," ","integrate((e*x+d)^8/(-e^2*x^2+d^2)^(7/2),x, algorithm=""giac"")","-\frac{63}{2} \, d^{2} \arcsin\left(\frac{x e}{d}\right) e^{\left(-1\right)} \mathrm{sgn}\left(d\right) - \frac{{\left(496 \, d^{7} e^{\left(-1\right)} + {\left(325 \, d^{6} - {\left(1200 \, d^{5} e + {\left(655 \, d^{4} e^{2} - {\left(1040 \, d^{3} e^{3} + {\left(591 \, d^{2} e^{4} - 5 \, {\left(x e^{6} + 16 \, d e^{5}\right)} x\right)} x\right)} x\right)} x\right)} x\right)} x\right)} \sqrt{-x^{2} e^{2} + d^{2}}}{10 \, {\left(x^{2} e^{2} - d^{2}\right)}^{3}}"," ",0,"-63/2*d^2*arcsin(x*e/d)*e^(-1)*sgn(d) - 1/10*(496*d^7*e^(-1) + (325*d^6 - (1200*d^5*e + (655*d^4*e^2 - (1040*d^3*e^3 + (591*d^2*e^4 - 5*(x*e^6 + 16*d*e^5)*x)*x)*x)*x)*x)*x)*sqrt(-x^2*e^2 + d^2)/(x^2*e^2 - d^2)^3","A",0
848,1,107,0,0.326707," ","integrate((e*x+d)^7/(-e^2*x^2+d^2)^(7/2),x, algorithm=""giac"")","-7 \, d \arcsin\left(\frac{x e}{d}\right) e^{\left(-1\right)} \mathrm{sgn}\left(d\right) - \frac{{\left(167 \, d^{6} e^{\left(-1\right)} + {\left(120 \, d^{5} - {\left(365 \, d^{4} e + {\left(160 \, d^{3} e^{2} - {\left(405 \, d^{2} e^{3} - {\left(15 \, x e^{5} - 232 \, d e^{4}\right)} x\right)} x\right)} x\right)} x\right)} x\right)} \sqrt{-x^{2} e^{2} + d^{2}}}{15 \, {\left(x^{2} e^{2} - d^{2}\right)}^{3}}"," ",0,"-7*d*arcsin(x*e/d)*e^(-1)*sgn(d) - 1/15*(167*d^6*e^(-1) + (120*d^5 - (365*d^4*e + (160*d^3*e^2 - (405*d^2*e^3 - (15*x*e^5 - 232*d*e^4)*x)*x)*x)*x)*x)*sqrt(-x^2*e^2 + d^2)/(x^2*e^2 - d^2)^3","A",0
849,1,95,0,0.360940," ","integrate((e*x+d)^6/(-e^2*x^2+d^2)^(7/2),x, algorithm=""giac"")","-\arcsin\left(\frac{x e}{d}\right) e^{\left(-1\right)} \mathrm{sgn}\left(d\right) - \frac{2 \, {\left(13 \, d^{5} e^{\left(-1\right)} + {\left(15 \, d^{4} - {\left(10 \, d^{3} e - {\left(10 \, d^{2} e^{2} + {\left(23 \, x e^{4} + 45 \, d e^{3}\right)} x\right)} x\right)} x\right)} x\right)} \sqrt{-x^{2} e^{2} + d^{2}}}{15 \, {\left(x^{2} e^{2} - d^{2}\right)}^{3}}"," ",0,"-arcsin(x*e/d)*e^(-1)*sgn(d) - 2/15*(13*d^5*e^(-1) + (15*d^4 - (10*d^3*e - (10*d^2*e^2 + (23*x*e^4 + 45*d*e^3)*x)*x)*x)*x)*sqrt(-x^2*e^2 + d^2)/(x^2*e^2 - d^2)^3","A",0
850,1,76,0,0.304842," ","integrate((e*x+d)^5/(-e^2*x^2+d^2)^(7/2),x, algorithm=""giac"")","-\frac{{\left(d^{4} e^{\left(-1\right)} + {\left(5 \, d^{3} + {\left(10 \, d^{2} e + {\left(x {\left(\frac{x e^{4}}{d} + 5 \, e^{3}\right)} + 10 \, d e^{2}\right)} x\right)} x\right)} x\right)} \sqrt{-x^{2} e^{2} + d^{2}}}{5 \, {\left(x^{2} e^{2} - d^{2}\right)}^{3}}"," ",0,"-1/5*(d^4*e^(-1) + (5*d^3 + (10*d^2*e + (x*(x*e^4/d + 5*e^3) + 10*d*e^2)*x)*x)*x)*sqrt(-x^2*e^2 + d^2)/(x^2*e^2 - d^2)^3","B",0
851,1,70,0,0.303036," ","integrate((e*x+d)^4/(-e^2*x^2+d^2)^(7/2),x, algorithm=""giac"")","-\frac{{\left(4 \, d^{3} e^{\left(-1\right)} + {\left(15 \, d^{2} - {\left(x {\left(\frac{x^{2} e^{4}}{d^{2}} - 10 \, e^{2}\right)} - 20 \, d e\right)} x\right)} x\right)} \sqrt{-x^{2} e^{2} + d^{2}}}{15 \, {\left(x^{2} e^{2} - d^{2}\right)}^{3}}"," ",0,"-1/15*(4*d^3*e^(-1) + (15*d^2 - (x*(x^2*e^4/d^2 - 10*e^2) - 20*d*e)*x)*x)*sqrt(-x^2*e^2 + d^2)/(x^2*e^2 - d^2)^3","A",0
852,1,70,0,0.306742," ","integrate((e*x+d)^3/(-e^2*x^2+d^2)^(7/2),x, algorithm=""giac"")","-\frac{\sqrt{-x^{2} e^{2} + d^{2}} {\left(7 \, d^{2} e^{\left(-1\right)} + {\left({\left(x {\left(\frac{2 \, x^{2} e^{4}}{d^{3}} - \frac{5 \, e^{2}}{d}\right)} + 5 \, e\right)} x + 15 \, d\right)} x\right)}}{15 \, {\left(x^{2} e^{2} - d^{2}\right)}^{3}}"," ",0,"-1/15*sqrt(-x^2*e^2 + d^2)*(7*d^2*e^(-1) + ((x*(2*x^2*e^4/d^3 - 5*e^2/d) + 5*e)*x + 15*d)*x)/(x^2*e^2 - d^2)^3","A",0
853,1,61,0,0.291077," ","integrate((e*x+d)^2/(-e^2*x^2+d^2)^(7/2),x, algorithm=""giac"")","-\frac{\sqrt{-x^{2} e^{2} + d^{2}} {\left({\left(x^{2} {\left(\frac{2 \, x^{2} e^{4}}{d^{4}} - \frac{5 \, e^{2}}{d^{2}}\right)} + 5\right)} x + 2 \, d e^{\left(-1\right)}\right)}}{5 \, {\left(x^{2} e^{2} - d^{2}\right)}^{3}}"," ",0,"-1/5*sqrt(-x^2*e^2 + d^2)*((x^2*(2*x^2*e^4/d^4 - 5*e^2/d^2) + 5)*x + 2*d*e^(-1))/(x^2*e^2 - d^2)^3","A",0
854,1,65,0,0.267164," ","integrate((e*x+d)/(-e^2*x^2+d^2)^(7/2),x, algorithm=""giac"")","-\frac{\sqrt{-x^{2} e^{2} + d^{2}} {\left({\left(4 \, x^{2} {\left(\frac{2 \, x^{2} e^{4}}{d^{5}} - \frac{5 \, e^{2}}{d^{3}}\right)} + \frac{15}{d}\right)} x + 3 \, e^{\left(-1\right)}\right)}}{15 \, {\left(x^{2} e^{2} - d^{2}\right)}^{3}}"," ",0,"-1/15*sqrt(-x^2*e^2 + d^2)*((4*x^2*(2*x^2*e^4/d^5 - 5*e^2/d^3) + 15/d)*x + 3*e^(-1))/(x^2*e^2 - d^2)^3","A",0
855,-2,0,0,0.000000," ","integrate(1/(e*x+d)/(-e^2*x^2+d^2)^(7/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to transpose Error: Bad Argument Value","F(-2)",0
856,0,0,0,0.000000," ","integrate(1/(e*x+d)^2/(-e^2*x^2+d^2)^(7/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
857,-2,0,0,0.000000," ","integrate(1/(e*x+d)^3/(-e^2*x^2+d^2)^(7/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to transpose Error: Bad Argument Value","F(-2)",0
858,-2,0,0,0.000000," ","integrate(1/(e*x+d)^4/(-e^2*x^2+d^2)^(7/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to transpose Error: Bad Argument Value","F(-2)",0
859,0,0,0,0.000000," ","integrate(1/(e*x+d)^5/(-e^2*x^2+d^2)^(7/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
860,1,14,0,0.177648," ","integrate((1+x)/(-x^2+1)^(1/2),x, algorithm=""giac"")","-\sqrt{-x^{2} + 1} + \arcsin\left(x\right)"," ",0,"-sqrt(-x^2 + 1) + arcsin(x)","A",0
861,1,12,0,0.191438," ","integrate((1-x)/(-x^2+1)^(1/2),x, algorithm=""giac"")","\sqrt{-x^{2} + 1} + \arcsin\left(x\right)"," ",0,"sqrt(-x^2 + 1) + arcsin(x)","A",0
862,0,0,0,0.000000," ","integrate((e*x+d)^(5/2)*(-c*e^2*x^2+c*d^2)^(1/2),x, algorithm=""giac"")","\int \sqrt{-c e^{2} x^{2} + c d^{2}} {\left(e x + d\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate(sqrt(-c*e^2*x^2 + c*d^2)*(e*x + d)^(5/2), x)","F",0
863,0,0,0,0.000000," ","integrate((e*x+d)^(3/2)*(-c*e^2*x^2+c*d^2)^(1/2),x, algorithm=""giac"")","\int \sqrt{-c e^{2} x^{2} + c d^{2}} {\left(e x + d\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(-c*e^2*x^2 + c*d^2)*(e*x + d)^(3/2), x)","F",0
864,0,0,0,0.000000," ","integrate((e*x+d)^(1/2)*(-c*e^2*x^2+c*d^2)^(1/2),x, algorithm=""giac"")","\int \sqrt{-c e^{2} x^{2} + c d^{2}} \sqrt{e x + d}\,{d x}"," ",0,"integrate(sqrt(-c*e^2*x^2 + c*d^2)*sqrt(e*x + d), x)","F",0
865,0,0,0,0.000000," ","integrate((-c*e^2*x^2+c*d^2)^(1/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-c e^{2} x^{2} + c d^{2}}}{\sqrt{e x + d}}\,{d x}"," ",0,"integrate(sqrt(-c*e^2*x^2 + c*d^2)/sqrt(e*x + d), x)","F",0
866,0,0,0,0.000000," ","integrate((-c*e^2*x^2+c*d^2)^(1/2)/(e*x+d)^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{-c e^{2} x^{2} + c d^{2}}}{{\left(e x + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(-c*e^2*x^2 + c*d^2)/(e*x + d)^(3/2), x)","F",0
867,0,0,0,0.000000," ","integrate((-c*e^2*x^2+c*d^2)^(1/2)/(e*x+d)^(5/2),x, algorithm=""giac"")","\int \frac{\sqrt{-c e^{2} x^{2} + c d^{2}}}{{\left(e x + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(-c*e^2*x^2 + c*d^2)/(e*x + d)^(5/2), x)","F",0
868,0,0,0,0.000000," ","integrate((-c*e^2*x^2+c*d^2)^(1/2)/(e*x+d)^(7/2),x, algorithm=""giac"")","\int \frac{\sqrt{-c e^{2} x^{2} + c d^{2}}}{{\left(e x + d\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(sqrt(-c*e^2*x^2 + c*d^2)/(e*x + d)^(7/2), x)","F",0
869,0,0,0,0.000000," ","integrate((e*x+d)^(5/2)*(-c*e^2*x^2+c*d^2)^(3/2),x, algorithm=""giac"")","\int {\left(-c e^{2} x^{2} + c d^{2}\right)}^{\frac{3}{2}} {\left(e x + d\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((-c*e^2*x^2 + c*d^2)^(3/2)*(e*x + d)^(5/2), x)","F",0
870,0,0,0,0.000000," ","integrate((e*x+d)^(3/2)*(-c*e^2*x^2+c*d^2)^(3/2),x, algorithm=""giac"")","\int {\left(-c e^{2} x^{2} + c d^{2}\right)}^{\frac{3}{2}} {\left(e x + d\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((-c*e^2*x^2 + c*d^2)^(3/2)*(e*x + d)^(3/2), x)","F",0
871,0,0,0,0.000000," ","integrate((e*x+d)^(1/2)*(-c*e^2*x^2+c*d^2)^(3/2),x, algorithm=""giac"")","\int {\left(-c e^{2} x^{2} + c d^{2}\right)}^{\frac{3}{2}} \sqrt{e x + d}\,{d x}"," ",0,"integrate((-c*e^2*x^2 + c*d^2)^(3/2)*sqrt(e*x + d), x)","F",0
872,0,0,0,0.000000," ","integrate((-c*e^2*x^2+c*d^2)^(3/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(-c e^{2} x^{2} + c d^{2}\right)}^{\frac{3}{2}}}{\sqrt{e x + d}}\,{d x}"," ",0,"integrate((-c*e^2*x^2 + c*d^2)^(3/2)/sqrt(e*x + d), x)","F",0
873,0,0,0,0.000000," ","integrate((-c*e^2*x^2+c*d^2)^(3/2)/(e*x+d)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(-c e^{2} x^{2} + c d^{2}\right)}^{\frac{3}{2}}}{{\left(e x + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((-c*e^2*x^2 + c*d^2)^(3/2)/(e*x + d)^(3/2), x)","F",0
874,-2,0,0,0.000000," ","integrate((-c*e^2*x^2+c*d^2)^(3/2)/(e*x+d)^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:index.cc index_m operator + Error: Bad Argument Valueindex.cc index_m operator + Error: Bad Argument Valueindex.cc index_m operator + Error: Bad Argument ValueEvaluation time: 1.39Done","F(-2)",0
875,-1,0,0,0.000000," ","integrate((-c*e^2*x^2+c*d^2)^(3/2)/(e*x+d)^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
876,-1,0,0,0.000000," ","integrate((-c*e^2*x^2+c*d^2)^(3/2)/(e*x+d)^(9/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
877,-1,0,0,0.000000," ","integrate((-c*e^2*x^2+c*d^2)^(3/2)/(e*x+d)^(11/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
878,-1,0,0,0.000000," ","integrate((-c*e^2*x^2+c*d^2)^(3/2)/(e*x+d)^(13/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
879,0,0,0,0.000000," ","integrate((e*x+d)^(7/2)/(-c*e^2*x^2+c*d^2)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{\frac{7}{2}}}{\sqrt{-c e^{2} x^{2} + c d^{2}}}\,{d x}"," ",0,"integrate((e*x + d)^(7/2)/sqrt(-c*e^2*x^2 + c*d^2), x)","F",0
880,0,0,0,0.000000," ","integrate((e*x+d)^(5/2)/(-c*e^2*x^2+c*d^2)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{\frac{5}{2}}}{\sqrt{-c e^{2} x^{2} + c d^{2}}}\,{d x}"," ",0,"integrate((e*x + d)^(5/2)/sqrt(-c*e^2*x^2 + c*d^2), x)","F",0
881,0,0,0,0.000000," ","integrate((e*x+d)^(3/2)/(-c*e^2*x^2+c*d^2)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{\frac{3}{2}}}{\sqrt{-c e^{2} x^{2} + c d^{2}}}\,{d x}"," ",0,"integrate((e*x + d)^(3/2)/sqrt(-c*e^2*x^2 + c*d^2), x)","F",0
882,0,0,0,0.000000," ","integrate((e*x+d)^(1/2)/(-c*e^2*x^2+c*d^2)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{e x + d}}{\sqrt{-c e^{2} x^{2} + c d^{2}}}\,{d x}"," ",0,"integrate(sqrt(e*x + d)/sqrt(-c*e^2*x^2 + c*d^2), x)","F",0
883,0,0,0,0.000000," ","integrate(1/(e*x+d)^(1/2)/(-c*e^2*x^2+c*d^2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-c e^{2} x^{2} + c d^{2}} \sqrt{e x + d}}\,{d x}"," ",0,"integrate(1/(sqrt(-c*e^2*x^2 + c*d^2)*sqrt(e*x + d)), x)","F",0
884,0,0,0,0.000000," ","integrate(1/(e*x+d)^(3/2)/(-c*e^2*x^2+c*d^2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-c e^{2} x^{2} + c d^{2}} {\left(e x + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(-c*e^2*x^2 + c*d^2)*(e*x + d)^(3/2)), x)","F",0
885,0,0,0,0.000000," ","integrate(1/(e*x+d)^(5/2)/(-c*e^2*x^2+c*d^2)^(1/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
886,0,0,0,0.000000," ","integrate((e*x+d)^(9/2)/(-c*e^2*x^2+c*d^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
887,0,0,0,0.000000," ","integrate((e*x+d)^(7/2)/(-c*e^2*x^2+c*d^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
888,0,0,0,0.000000," ","integrate((e*x+d)^(5/2)/(-c*e^2*x^2+c*d^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
889,0,0,0,0.000000," ","integrate((e*x+d)^(3/2)/(-c*e^2*x^2+c*d^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
890,0,0,0,0.000000," ","integrate((e*x+d)^(1/2)/(-c*e^2*x^2+c*d^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
891,0,0,0,0.000000," ","integrate(1/(e*x+d)^(1/2)/(-c*e^2*x^2+c*d^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
892,0,0,0,0.000000," ","integrate(1/(e*x+d)^(3/2)/(-c*e^2*x^2+c*d^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
893,1,36,0,0.183929," ","integrate(1/(-1+x)^(1/2)/(-x^2+1)^(1/2),x, algorithm=""giac"")","\frac{1}{2} i \, {\left(\sqrt{2} \log\left(\sqrt{2} + \sqrt{x + 1}\right) - \sqrt{2} \log\left(-\sqrt{2} + \sqrt{x + 1}\right)\right)} \mathrm{sgn}\left(x\right)"," ",0,"1/2*I*(sqrt(2)*log(sqrt(2) + sqrt(x + 1)) - sqrt(2)*log(-sqrt(2) + sqrt(x + 1)))*sgn(x)","C",0
894,-2,0,0,0.000000," ","integrate((e*x+2)^(5/2)*(-3*e^2*x^2+12)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error index.cc index_gcd Error: Bad Argument ValueError index.cc index_gcd Error: Bad Argument Value","F(-2)",0
895,0,0,0,0.000000," ","integrate((e*x+2)^(3/2)*(-3*e^2*x^2+12)^(1/2),x, algorithm=""giac"")","\int \sqrt{-3 \, e^{2} x^{2} + 12} {\left(e x + 2\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(-3*e^2*x^2 + 12)*(e*x + 2)^(3/2), x)","F",0
896,-2,0,0,0.000000," ","integrate((e*x+2)^(1/2)*(-3*e^2*x^2+12)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error index.cc index_gcd Error: Bad Argument ValueError index.cc index_gcd Error: Bad Argument Value","F(-2)",0
897,0,0,0,0.000000," ","integrate((-3*e^2*x^2+12)^(1/2)/(e*x+2)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-3 \, e^{2} x^{2} + 12}}{\sqrt{e x + 2}}\,{d x}"," ",0,"integrate(sqrt(-3*e^2*x^2 + 12)/sqrt(e*x + 2), x)","F",0
898,-2,0,0,0.000000," ","integrate((-3*e^2*x^2+12)^(1/2)/(e*x+2)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error index.cc index_gcd Error: Bad Argument ValueError index.cc index_gcd Error: Bad Argument Value","F(-2)",0
899,0,0,0,0.000000," ","integrate((-3*e^2*x^2+12)^(1/2)/(e*x+2)^(5/2),x, algorithm=""giac"")","\int \frac{\sqrt{-3 \, e^{2} x^{2} + 12}}{{\left(e x + 2\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(-3*e^2*x^2 + 12)/(e*x + 2)^(5/2), x)","F",0
900,-2,0,0,0.000000," ","integrate((-3*e^2*x^2+12)^(1/2)/(e*x+2)^(7/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error index.cc index_gcd Error: Bad Argument ValueError index.cc index_gcd Error: Bad Argument Value","F(-2)",0
901,-2,0,0,0.000000," ","integrate((e*x+2)^(5/2)*(-3*e^2*x^2+12)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error index.cc index_gcd Error: Bad Argument ValueError index.cc index_gcd Error: Bad Argument Value","F(-2)",0
902,0,0,0,0.000000," ","integrate((e*x+2)^(3/2)*(-3*e^2*x^2+12)^(3/2),x, algorithm=""giac"")","\int {\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{3}{2}} {\left(e x + 2\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((-3*e^2*x^2 + 12)^(3/2)*(e*x + 2)^(3/2), x)","F",0
903,-2,0,0,0.000000," ","integrate((e*x+2)^(1/2)*(-3*e^2*x^2+12)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error index.cc index_gcd Error: Bad Argument ValueError index.cc index_gcd Error: Bad Argument Value","F(-2)",0
904,0,0,0,0.000000," ","integrate((-3*e^2*x^2+12)^(3/2)/(e*x+2)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{3}{2}}}{\sqrt{e x + 2}}\,{d x}"," ",0,"integrate((-3*e^2*x^2 + 12)^(3/2)/sqrt(e*x + 2), x)","F",0
905,-2,0,0,0.000000," ","integrate((-3*e^2*x^2+12)^(3/2)/(e*x+2)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error index.cc index_gcd Error: Bad Argument ValueError index.cc index_gcd Error: Bad Argument Value","F(-2)",0
906,-2,0,0,0.000000," ","integrate((-3*e^2*x^2+12)^(3/2)/(e*x+2)^(5/2),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [exp(1),exp(2)]=[-55,-49]Precision problem choosing root in common_EXT, current precision 14Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [exp(1),exp(2)]=[-96,-85]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [exp(1),exp(2)]=[-7,4]Error: Bad Argument ValueError: Bad Argument ValueError: Bad Argument ValueLimit probably undefined, algorithm unable to handle rootof([[1,2*t^2-2*exp(2),-3*t^4+8*t^2*exp(2)-5*exp(2)^2,-18*t^6+34*t^4*exp(2)-14*t^2*exp(2)^2-2*exp(2)^3],[1,0,-6*t^4+16*t^2*exp(2)-10*exp(2)^2,-16*t^6+16*t^4*exp(2)+16*t^2*exp(2)^2-16*exp(2)^3,41*t^8-112*t^6*exp(2)+94*t^4*exp(2)^2-16*t^2*exp(2)^3-7*exp(2)^4]])Error: Bad Argument ValueError: Bad Argument ValueError: Bad Argument ValueLimit probably undefined, algorithm unable to handle rootof([[-1,-2*t^2+2*exp(2),3*t^4-8*t^2*exp(2)+5*exp(2)^2,18*t^6-34*t^4*exp(2)+14*t^2*exp(2)^2+2*exp(2)^3],[1,0,-6*t^4+16*t^2*exp(2)-10*exp(2)^2,-16*t^6+16*t^4*exp(2)+16*t^2*exp(2)^2-16*exp(2)^3,41*t^8-112*t^6*exp(2)+94*t^4*exp(2)^2-16*t^2*exp(2)^3-7*exp(2)^4]])Error: Bad Argument ValueError: Bad Argument ValueError: Bad Argument ValueLimit probably undefined, algorithm unable to handle rootof([[1,2*t^2-2*exp(2),-3*t^4+8*t^2*exp(2)-5*exp(2)^2,-18*t^6+34*t^4*exp(2)-14*t^2*exp(2)^2-2*exp(2)^3],[1,0,-6*t^4+16*t^2*exp(2)-10*exp(2)^2,-16*t^6+16*t^4*exp(2)+16*t^2*exp(2)^2-16*exp(2)^3,41*t^8-112*t^6*exp(2)+94*t^4*exp(2)^2-16*t^2*exp(2)^3-7*exp(2)^4]])Error: Bad Argument ValueError: Bad Argument ValueError: Bad Argument ValueLimit probably undefined, algorithm unable to handle rootof([[-1,-2*t^2+2*exp(2),3*t^4-8*t^2*exp(2)+5*exp(2)^2,18*t^6-34*t^4*exp(2)+14*t^2*exp(2)^2+2*exp(2)^3],[1,0,-6*t^4+16*t^2*exp(2)-10*exp(2)^2,-16*t^6+16*t^4*exp(2)+16*t^2*exp(2)^2-16*exp(2)^3,41*t^8-112*t^6*exp(2)+94*t^4*exp(2)^2-16*t^2*exp(2)^3-7*exp(2)^4]])Error: Bad Argument ValueError: Bad Argument ValueError: Bad Argument ValueLimit probably undefined, algorithm unable to handle rootof([[1,2*t^2-2*exp(2),-3*t^4+8*t^2*exp(2)-5*exp(2)^2,-18*t^6+34*t^4*exp(2)-14*t^2*exp(2)^2-2*exp(2)^3],[1,0,-6*t^4+16*t^2*exp(2)-10*exp(2)^2,-16*t^6+16*t^4*exp(2)+16*t^2*exp(2)^2-16*exp(2)^3,41*t^8-112*t^6*exp(2)+94*t^4*exp(2)^2-16*t^2*exp(2)^3-7*exp(2)^4]])Error: Bad Argument ValueError: Bad Argument ValueError: Bad Argument ValueLimit probably undefined, algorithm unable to handle rootof([[-1,-2*t^2+2*exp(2),3*t^4-8*t^2*exp(2)+5*exp(2)^2,18*t^6-34*t^4*exp(2)+14*t^2*exp(2)^2+2*exp(2)^3],[1,0,-6*t^4+16*t^2*exp(2)-10*exp(2)^2,-16*t^6+16*t^4*exp(2)+16*t^2*exp(2)^2-16*exp(2)^3,41*t^8-112*t^6*exp(2)+94*t^4*exp(2)^2-16*t^2*exp(2)^3-7*exp(2)^4]])Error: Bad Argument ValueError: Bad Argument ValueError: Bad Argument ValueLimit probably undefined, algorithm unable to handle rootof([[1,2*t^2-2*exp(2),-3*t^4+8*t^2*exp(2)-5*exp(2)^2,-18*t^6+34*t^4*exp(2)-14*t^2*exp(2)^2-2*exp(2)^3],[1,0,-6*t^4+16*t^2*exp(2)-10*exp(2)^2,-16*t^6+16*t^4*exp(2)+16*t^2*exp(2)^2-16*exp(2)^3,41*t^8-112*t^6*exp(2)+94*t^4*exp(2)^2-16*t^2*exp(2)^3-7*exp(2)^4]])Error: Bad Argument ValueError: Bad Argument ValueError: Bad Argument ValueLimit probably undefined, algorithm unable to handle rootof([[-1,-2*t^2+2*exp(2),3*t^4-8*t^2*exp(2)+5*exp(2)^2,18*t^6-34*t^4*exp(2)+14*t^2*exp(2)^2+2*exp(2)^3],[1,0,-6*t^4+16*t^2*exp(2)-10*exp(2)^2,-16*t^6+16*t^4*exp(2)+16*t^2*exp(2)^2-16*exp(2)^3,41*t^8-112*t^6*exp(2)+94*t^4*exp(2)^2-16*t^2*exp(2)^3-7*exp(2)^4]])Error: Bad Argument ValueError: Bad Argument ValueError: Bad Argument ValueLimit probably undefined, algorithm unable to handle rootof([[1,2*t^2-2*exp(2),-3*t^4+8*t^2*exp(2)-5*exp(2)^2,-18*t^6+34*t^4*exp(2)-14*t^2*exp(2)^2-2*exp(2)^3],[1,0,-6*t^4+16*t^2*exp(2)-10*exp(2)^2,-16*t^6+16*t^4*exp(2)+16*t^2*exp(2)^2-16*exp(2)^3,41*t^8-112*t^6*exp(2)+94*t^4*exp(2)^2-16*t^2*exp(2)^3-7*exp(2)^4]])Error: Bad Argument ValueError: Bad Argument ValueError: Bad Argument ValueLimit probably undefined, algorithm unable to handle rootof([[-1,-2*t^2+2*exp(2),3*t^4-8*t^2*exp(2)+5*exp(2)^2,18*t^6-34*t^4*exp(2)+14*t^2*exp(2)^2+2*exp(2)^3],[1,0,-6*t^4+16*t^2*exp(2)-10*exp(2)^2,-16*t^6+16*t^4*exp(2)+16*t^2*exp(2)^2-16*exp(2)^3,41*t^8-112*t^6*exp(2)+94*t^4*exp(2)^2-16*t^2*exp(2)^3-7*exp(2)^4]])Evaluation time: 1.68-sqrt(3)/exp(1)/2*exp(1)/2/exp(1)^2*C_0*sqrt(4/(x*exp(1)+2)^2*exp(1)^2-4/(x*exp(1)+2)^2*exp(2)+4/(x*exp(1)+2)*exp(2)-exp(2))+integrate(-sqrt(3)/exp(1)/2*exp(1)*(2*C_0/sqrt(x*exp(1)+2)+((416*exp(1)^10-704*exp(1)^8*exp(2)-96*exp(1)^6*exp(2)^2+384*exp(1)^2*exp(2)^4)/(x*exp(1)+2)^2+(-232*exp(1)^10+328*exp(1)^8*exp(2)-96*exp(1)^4*exp(2)^3-192*exp(1)^2*exp(2)^4)/(x*exp(1)+2)+64*exp(1)^10)/((8*exp(1)^10-8*exp(1)^8*exp(2))/(x*exp(1)+2)^3+(-4*exp(1)^10+4*exp(1)^8*exp(2))/(x*exp(1)+2)^2+exp(1)^10/(x*exp(1)+2)))/sqrt(4/(x*exp(1)+2)^2*exp(1)^2-4/(x*exp(1)+2)^2*exp(2)+4/(x*exp(1)+2)*exp(2)-exp(2))/sqrt(x*exp(1)+2)/sqrt(x*exp(1)+2)/2*exp(1)*(sqrt(x*exp(1)+2))^-1,x)-2*sqrt(3)/exp(1)^2*sqrt(x*exp(1)+2)*sqrt(-(x*exp(1)+2)^2*exp(2)+4*(x*exp(1)+2)*exp(2)+4*exp(1)^2-4*exp(2))","F(-2)",0
907,-2,0,0,0.000000," ","integrate((-3*e^2*x^2+12)^(3/2)/(e*x+2)^(7/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error index.cc index_gcd Error: Bad Argument ValueError index.cc index_gcd Error: Bad Argument Value","F(-2)",0
908,-2,0,0,0.000000," ","integrate((-3*e^2*x^2+12)^(3/2)/(e*x+2)^(9/2),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(-x*exp(1)^2-2*exp(1))]Evaluation time: 59.24Unable to transpose Error: Bad Argument Value","F(-2)",0
909,-2,0,0,0.000000," ","integrate((-3*e^2*x^2+12)^(3/2)/(e*x+2)^(11/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error index.cc index_gcd Error: Bad Argument ValueError index.cc index_gcd Error: Bad Argument Value","F(-2)",0
910,-1,0,0,0.000000," ","integrate((-3*e^2*x^2+12)^(3/2)/(e*x+2)^(13/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
911,0,0,0,0.000000," ","integrate((e*x+2)^(7/2)/(-3*e^2*x^2+12)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(e x + 2\right)}^{\frac{7}{2}}}{\sqrt{-3 \, e^{2} x^{2} + 12}}\,{d x}"," ",0,"integrate((e*x + 2)^(7/2)/sqrt(-3*e^2*x^2 + 12), x)","F",0
912,-2,0,0,0.000000," ","integrate((e*x+2)^(5/2)/(-3*e^2*x^2+12)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error index.cc index_gcd Error: Bad Argument ValueError index.cc index_gcd Error: Bad Argument Value","F(-2)",0
913,0,0,0,0.000000," ","integrate((e*x+2)^(3/2)/(-3*e^2*x^2+12)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(e x + 2\right)}^{\frac{3}{2}}}{\sqrt{-3 \, e^{2} x^{2} + 12}}\,{d x}"," ",0,"integrate((e*x + 2)^(3/2)/sqrt(-3*e^2*x^2 + 12), x)","F",0
914,0,0,0,0.000000," ","integrate((e*x+2)^(1/2)/(-3*e^2*x^2+12)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{e x + 2}}{\sqrt{-3 \, e^{2} x^{2} + 12}}\,{d x}"," ",0,"integrate(sqrt(e*x + 2)/sqrt(-3*e^2*x^2 + 12), x)","F",0
915,0,0,0,0.000000," ","integrate(1/(e*x+2)^(1/2)/(-3*e^2*x^2+12)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-3 \, e^{2} x^{2} + 12} \sqrt{e x + 2}}\,{d x}"," ",0,"integrate(1/(sqrt(-3*e^2*x^2 + 12)*sqrt(e*x + 2)), x)","F",0
916,-2,0,0,0.000000," ","integrate(1/(e*x+2)^(3/2)/(-3*e^2*x^2+12)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error index.cc index_gcd Error: Bad Argument ValueError index.cc index_gcd Error: Bad Argument Value","F(-2)",0
917,0,0,0,0.000000," ","integrate(1/(e*x+2)^(5/2)/(-3*e^2*x^2+12)^(1/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
918,0,0,0,0.000000," ","integrate((e*x+2)^(11/2)/(-3*e^2*x^2+12)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
919,-2,0,0,0.000000," ","integrate((e*x+2)^(9/2)/(-3*e^2*x^2+12)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error index.cc index_gcd Error: Bad Argument ValueError index.cc index_gcd Error: Bad Argument Value","F(-2)",0
920,0,0,0,0.000000," ","integrate((e*x+2)^(7/2)/(-3*e^2*x^2+12)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
921,-2,0,0,0.000000," ","integrate((e*x+2)^(5/2)/(-3*e^2*x^2+12)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error index.cc index_gcd Error: Bad Argument ValueError index.cc index_gcd Error: Bad Argument Value","F(-2)",0
922,0,0,0,0.000000," ","integrate((e*x+2)^(3/2)/(-3*e^2*x^2+12)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
923,0,0,0,0.000000," ","integrate((e*x+2)^(1/2)/(-3*e^2*x^2+12)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
924,0,0,0,0.000000," ","integrate(1/(e*x+2)^(1/2)/(-3*e^2*x^2+12)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
925,-2,0,0,0.000000," ","integrate(1/(e*x+2)^(3/2)/(-3*e^2*x^2+12)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error index.cc index_gcd Error: Bad Argument ValueError index.cc index_gcd Error: Bad Argument Value","F(-2)",0
926,1,38,0,0.159973," ","integrate(1/(1+x)/(1-x)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{2} \log\left(\sqrt{2} + \sqrt{-x + 1}\right) + \frac{1}{2} \, \sqrt{2} \log\left({\left| -\sqrt{2} + \sqrt{-x + 1} \right|}\right)"," ",0,"-1/2*sqrt(2)*log(sqrt(2) + sqrt(-x + 1)) + 1/2*sqrt(2)*log(abs(-sqrt(2) + sqrt(-x + 1)))","B",0
927,1,37,0,0.203321," ","integrate(1/(1+x)^(1/2)/(-x^2+1)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{2} \log\left(\sqrt{2} + \sqrt{-x + 1}\right) + \frac{1}{2} \, \sqrt{2} \log\left(\sqrt{2} - \sqrt{-x + 1}\right)"," ",0,"-1/2*sqrt(2)*log(sqrt(2) + sqrt(-x + 1)) + 1/2*sqrt(2)*log(sqrt(2) - sqrt(-x + 1))","B",0
928,1,42,0,0.179291," ","integrate(1/(a*x+1)/(-a*x+1)^(1/2),x, algorithm=""giac"")","\frac{\sqrt{2} \log\left(\frac{{\left| -2 \, \sqrt{2} + 2 \, \sqrt{-a x + 1} \right|}}{2 \, {\left(\sqrt{2} + \sqrt{-a x + 1}\right)}}\right)}{2 \, a}"," ",0,"1/2*sqrt(2)*log(1/2*abs(-2*sqrt(2) + 2*sqrt(-a*x + 1))/(sqrt(2) + sqrt(-a*x + 1)))/a","A",0
929,1,43,0,0.164205," ","integrate(1/(a*x+1)^(1/2)/(-a^2*x^2+1)^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{2} \log\left(\sqrt{2} + \sqrt{-a x + 1}\right) - \sqrt{2} \log\left(\sqrt{2} - \sqrt{-a x + 1}\right)}{2 \, a}"," ",0,"-1/2*(sqrt(2)*log(sqrt(2) + sqrt(-a*x + 1)) - sqrt(2)*log(sqrt(2) - sqrt(-a*x + 1)))/a","A",0
930,-2,0,0,0.000000," ","integrate((e*x+2)^(1/2)*(-3*e^2*x^2+12)^(1/4),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error index.cc index_gcd Error: Bad Argument ValueError index.cc index_gcd Error: Bad Argument Value","F(-2)",0
931,1,172,0,0.385928," ","integrate((-3*e^2*x^2+12)^(1/4)/(e*x+2)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \cdot 3^{\frac{1}{4}} {\left(2 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, {\left(\frac{4}{x e + 2} - 1\right)}^{\frac{1}{4}}\right)}\right) + 2 \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, {\left(\frac{4}{x e + 2} - 1\right)}^{\frac{1}{4}}\right)}\right) + \sqrt{2} \log\left(\sqrt{2} {\left(\frac{4}{x e + 2} - 1\right)}^{\frac{1}{4}} + \sqrt{\frac{4}{x e + 2} - 1} + 1\right) - \sqrt{2} \log\left(-\sqrt{2} {\left(\frac{4}{x e + 2} - 1\right)}^{\frac{1}{4}} + \sqrt{\frac{4}{x e + 2} - 1} + 1\right) - 2 \, {\left(x e + 2\right)} {\left(\frac{4}{x e + 2} - 1\right)}^{\frac{1}{4}}\right)} e^{\left(-1\right)}"," ",0,"-1/2*3^(1/4)*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*(4/(x*e + 2) - 1)^(1/4))) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*(4/(x*e + 2) - 1)^(1/4))) + sqrt(2)*log(sqrt(2)*(4/(x*e + 2) - 1)^(1/4) + sqrt(4/(x*e + 2) - 1) + 1) - sqrt(2)*log(-sqrt(2)*(4/(x*e + 2) - 1)^(1/4) + sqrt(4/(x*e + 2) - 1) + 1) - 2*(x*e + 2)*(4/(x*e + 2) - 1)^(1/4))*e^(-1)","A",0
932,-2,0,0,0.000000," ","integrate((-3*e^2*x^2+12)^(1/4)/(e*x+2)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error index.cc index_gcd Error: Bad Argument ValueError index.cc index_gcd Error: Bad Argument Value","F(-2)",0
933,1,46,0,0.271849," ","integrate((-3*e^2*x^2+12)^(1/4)/(e*x+2)^(5/2),x, algorithm=""giac"")","-\frac{3^{\frac{1}{4}} {\left(-{\left(x e + 2\right)}^{2} + 4 \, x e + 8\right)}^{\frac{1}{4}} {\left(\frac{4}{x e + 2} - 1\right)} e^{\left(-1\right)}}{5 \, \sqrt{x e + 2}}"," ",0,"-1/5*3^(1/4)*(-(x*e + 2)^2 + 4*x*e + 8)^(1/4)*(4/(x*e + 2) - 1)*e^(-1)/sqrt(x*e + 2)","A",0
934,-2,0,0,0.000000," ","integrate((-3*e^2*x^2+12)^(1/4)/(e*x+2)^(7/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error index.cc index_gcd Error: Bad Argument ValueError index.cc index_gcd Error: Bad Argument Value","F(-2)",0
935,1,146,0,0.385551," ","integrate((-3*e^2*x^2+12)^(1/4)/(e*x+2)^(9/2),x, algorithm=""giac"")","-\frac{1}{9360} \cdot 3^{\frac{1}{4}} {\left(\frac{117 \, {\left(-{\left(x e + 2\right)}^{2} + 4 \, x e + 8\right)}^{\frac{1}{4}} {\left(\frac{4}{x e + 2} - 1\right)}}{\sqrt{x e + 2}} + \frac{130 \, {\left({\left(x e + 2\right)}^{2} - 8 \, x e\right)} {\left(-{\left(x e + 2\right)}^{2} + 4 \, x e + 8\right)}^{\frac{1}{4}}}{{\left(x e + 2\right)}^{\frac{5}{2}}} - \frac{45 \, {\left({\left(x e + 2\right)}^{3} - 12 \, {\left(x e + 2\right)}^{2} + 48 \, x e + 32\right)} {\left(-{\left(x e + 2\right)}^{2} + 4 \, x e + 8\right)}^{\frac{1}{4}}}{{\left(x e + 2\right)}^{\frac{7}{2}}}\right)} e^{\left(-1\right)}"," ",0,"-1/9360*3^(1/4)*(117*(-(x*e + 2)^2 + 4*x*e + 8)^(1/4)*(4/(x*e + 2) - 1)/sqrt(x*e + 2) + 130*((x*e + 2)^2 - 8*x*e)*(-(x*e + 2)^2 + 4*x*e + 8)^(1/4)/(x*e + 2)^(5/2) - 45*((x*e + 2)^3 - 12*(x*e + 2)^2 + 48*x*e + 32)*(-(x*e + 2)^2 + 4*x*e + 8)^(1/4)/(x*e + 2)^(7/2))*e^(-1)","A",0
936,-2,0,0,0.000000," ","integrate((-3*e^2*x^2+12)^(1/4)/(e*x+2)^(11/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error index.cc index_gcd Error: Bad Argument ValueError index.cc index_gcd Error: Bad Argument Value","F(-2)",0
937,-2,0,0,0.000000," ","integrate((e*x+2)^(5/2)/(-3*e^2*x^2+12)^(1/4),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error index.cc index_gcd Error: Bad Argument ValueError index.cc index_gcd Error: Bad Argument Value","F(-2)",0
938,0,0,0,0.000000," ","integrate((e*x+2)^(3/2)/(-3*e^2*x^2+12)^(1/4),x, algorithm=""giac"")","\int \frac{{\left(e x + 2\right)}^{\frac{3}{2}}}{{\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((e*x + 2)^(3/2)/(-3*e^2*x^2 + 12)^(1/4), x)","F",0
939,0,0,0,0.000000," ","integrate((e*x+2)^(1/2)/(-3*e^2*x^2+12)^(1/4),x, algorithm=""giac"")","\int \frac{\sqrt{e x + 2}}{{\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(sqrt(e*x + 2)/(-3*e^2*x^2 + 12)^(1/4), x)","F",0
940,0,0,0,0.000000," ","integrate(1/(e*x+2)^(1/2)/(-3*e^2*x^2+12)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{1}{4}} \sqrt{e x + 2}}\,{d x}"," ",0,"integrate(1/((-3*e^2*x^2 + 12)^(1/4)*sqrt(e*x + 2)), x)","F",0
941,-2,0,0,0.000000," ","integrate(1/(e*x+2)^(3/2)/(-3*e^2*x^2+12)^(1/4),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error index.cc index_gcd Error: Bad Argument ValueError index.cc index_gcd Error: Bad Argument Value","F(-2)",0
942,0,0,0,0.000000," ","integrate(1/(e*x+2)^(5/2)/(-3*e^2*x^2+12)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{1}{4}} {\left(e x + 2\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((-3*e^2*x^2 + 12)^(1/4)*(e*x + 2)^(5/2)), x)","F",0
943,-2,0,0,0.000000," ","integrate(1/(e*x+2)^(7/2)/(-3*e^2*x^2+12)^(1/4),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error index.cc index_gcd Error: Bad Argument ValueError index.cc index_gcd Error: Bad Argument Value","F(-2)",0
944,0,0,0,0.000000," ","integrate(1/(e*x+2)^(9/2)/(-3*e^2*x^2+12)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{1}{4}} {\left(e x + 2\right)}^{\frac{9}{2}}}\,{d x}"," ",0,"integrate(1/((-3*e^2*x^2 + 12)^(1/4)*(e*x + 2)^(9/2)), x)","F",0
945,1,548,0,0.180550," ","integrate((b*x+a)^m*(-b^2*x^2+a^2)^3,x, algorithm=""giac"")","-\frac{{\left(b x + a\right)}^{m} b^{7} m^{3} x^{7} + {\left(b x + a\right)}^{m} a b^{6} m^{3} x^{6} + 15 \, {\left(b x + a\right)}^{m} b^{7} m^{2} x^{7} - 3 \, {\left(b x + a\right)}^{m} a^{2} b^{5} m^{3} x^{5} + 9 \, {\left(b x + a\right)}^{m} a b^{6} m^{2} x^{6} + 74 \, {\left(b x + a\right)}^{m} b^{7} m x^{7} - 3 \, {\left(b x + a\right)}^{m} a^{3} b^{4} m^{3} x^{4} - 57 \, {\left(b x + a\right)}^{m} a^{2} b^{5} m^{2} x^{5} + 20 \, {\left(b x + a\right)}^{m} a b^{6} m x^{6} + 120 \, {\left(b x + a\right)}^{m} b^{7} x^{7} + 3 \, {\left(b x + a\right)}^{m} a^{4} b^{3} m^{3} x^{3} - 39 \, {\left(b x + a\right)}^{m} a^{3} b^{4} m^{2} x^{4} - 306 \, {\left(b x + a\right)}^{m} a^{2} b^{5} m x^{5} + 3 \, {\left(b x + a\right)}^{m} a^{5} b^{2} m^{3} x^{2} + 69 \, {\left(b x + a\right)}^{m} a^{4} b^{3} m^{2} x^{3} - 96 \, {\left(b x + a\right)}^{m} a^{3} b^{4} m x^{4} - 504 \, {\left(b x + a\right)}^{m} a^{2} b^{5} x^{5} - {\left(b x + a\right)}^{m} a^{6} b m^{3} x + 51 \, {\left(b x + a\right)}^{m} a^{5} b^{2} m^{2} x^{2} + 486 \, {\left(b x + a\right)}^{m} a^{4} b^{3} m x^{3} - {\left(b x + a\right)}^{m} a^{7} m^{3} - 27 \, {\left(b x + a\right)}^{m} a^{6} b m^{2} x + 228 \, {\left(b x + a\right)}^{m} a^{5} b^{2} m x^{2} + 840 \, {\left(b x + a\right)}^{m} a^{4} b^{3} x^{3} - 21 \, {\left(b x + a\right)}^{m} a^{7} m^{2} - 254 \, {\left(b x + a\right)}^{m} a^{6} b m x - 152 \, {\left(b x + a\right)}^{m} a^{7} m - 840 \, {\left(b x + a\right)}^{m} a^{6} b x - 384 \, {\left(b x + a\right)}^{m} a^{7}}{b m^{4} + 22 \, b m^{3} + 179 \, b m^{2} + 638 \, b m + 840 \, b}"," ",0,"-((b*x + a)^m*b^7*m^3*x^7 + (b*x + a)^m*a*b^6*m^3*x^6 + 15*(b*x + a)^m*b^7*m^2*x^7 - 3*(b*x + a)^m*a^2*b^5*m^3*x^5 + 9*(b*x + a)^m*a*b^6*m^2*x^6 + 74*(b*x + a)^m*b^7*m*x^7 - 3*(b*x + a)^m*a^3*b^4*m^3*x^4 - 57*(b*x + a)^m*a^2*b^5*m^2*x^5 + 20*(b*x + a)^m*a*b^6*m*x^6 + 120*(b*x + a)^m*b^7*x^7 + 3*(b*x + a)^m*a^4*b^3*m^3*x^3 - 39*(b*x + a)^m*a^3*b^4*m^2*x^4 - 306*(b*x + a)^m*a^2*b^5*m*x^5 + 3*(b*x + a)^m*a^5*b^2*m^3*x^2 + 69*(b*x + a)^m*a^4*b^3*m^2*x^3 - 96*(b*x + a)^m*a^3*b^4*m*x^4 - 504*(b*x + a)^m*a^2*b^5*x^5 - (b*x + a)^m*a^6*b*m^3*x + 51*(b*x + a)^m*a^5*b^2*m^2*x^2 + 486*(b*x + a)^m*a^4*b^3*m*x^3 - (b*x + a)^m*a^7*m^3 - 27*(b*x + a)^m*a^6*b*m^2*x + 228*(b*x + a)^m*a^5*b^2*m*x^2 + 840*(b*x + a)^m*a^4*b^3*x^3 - 21*(b*x + a)^m*a^7*m^2 - 254*(b*x + a)^m*a^6*b*m*x - 152*(b*x + a)^m*a^7*m - 840*(b*x + a)^m*a^6*b*x - 384*(b*x + a)^m*a^7)/(b*m^4 + 22*b*m^3 + 179*b*m^2 + 638*b*m + 840*b)","B",0
946,1,288,0,0.238802," ","integrate((b*x+a)^m*(-b^2*x^2+a^2)^2,x, algorithm=""giac"")","\frac{{\left(b x + a\right)}^{m} b^{5} m^{2} x^{5} + {\left(b x + a\right)}^{m} a b^{4} m^{2} x^{4} + 7 \, {\left(b x + a\right)}^{m} b^{5} m x^{5} - 2 \, {\left(b x + a\right)}^{m} a^{2} b^{3} m^{2} x^{3} + 3 \, {\left(b x + a\right)}^{m} a b^{4} m x^{4} + 12 \, {\left(b x + a\right)}^{m} b^{5} x^{5} - 2 \, {\left(b x + a\right)}^{m} a^{3} b^{2} m^{2} x^{2} - 22 \, {\left(b x + a\right)}^{m} a^{2} b^{3} m x^{3} + {\left(b x + a\right)}^{m} a^{4} b m^{2} x - 14 \, {\left(b x + a\right)}^{m} a^{3} b^{2} m x^{2} - 40 \, {\left(b x + a\right)}^{m} a^{2} b^{3} x^{3} + {\left(b x + a\right)}^{m} a^{5} m^{2} + 15 \, {\left(b x + a\right)}^{m} a^{4} b m x + 11 \, {\left(b x + a\right)}^{m} a^{5} m + 60 \, {\left(b x + a\right)}^{m} a^{4} b x + 32 \, {\left(b x + a\right)}^{m} a^{5}}{b m^{3} + 12 \, b m^{2} + 47 \, b m + 60 \, b}"," ",0,"((b*x + a)^m*b^5*m^2*x^5 + (b*x + a)^m*a*b^4*m^2*x^4 + 7*(b*x + a)^m*b^5*m*x^5 - 2*(b*x + a)^m*a^2*b^3*m^2*x^3 + 3*(b*x + a)^m*a*b^4*m*x^4 + 12*(b*x + a)^m*b^5*x^5 - 2*(b*x + a)^m*a^3*b^2*m^2*x^2 - 22*(b*x + a)^m*a^2*b^3*m*x^3 + (b*x + a)^m*a^4*b*m^2*x - 14*(b*x + a)^m*a^3*b^2*m*x^2 - 40*(b*x + a)^m*a^2*b^3*x^3 + (b*x + a)^m*a^5*m^2 + 15*(b*x + a)^m*a^4*b*m*x + 11*(b*x + a)^m*a^5*m + 60*(b*x + a)^m*a^4*b*x + 32*(b*x + a)^m*a^5)/(b*m^3 + 12*b*m^2 + 47*b*m + 60*b)","B",0
947,1,118,0,0.194545," ","integrate((b*x+a)^m*(-b^2*x^2+a^2),x, algorithm=""giac"")","-\frac{{\left(b x + a\right)}^{m} b^{3} m x^{3} + {\left(b x + a\right)}^{m} a b^{2} m x^{2} + 2 \, {\left(b x + a\right)}^{m} b^{3} x^{3} - {\left(b x + a\right)}^{m} a^{2} b m x - {\left(b x + a\right)}^{m} a^{3} m - 6 \, {\left(b x + a\right)}^{m} a^{2} b x - 4 \, {\left(b x + a\right)}^{m} a^{3}}{b m^{2} + 5 \, b m + 6 \, b}"," ",0,"-((b*x + a)^m*b^3*m*x^3 + (b*x + a)^m*a*b^2*m*x^2 + 2*(b*x + a)^m*b^3*x^3 - (b*x + a)^m*a^2*b*m*x - (b*x + a)^m*a^3*m - 6*(b*x + a)^m*a^2*b*x - 4*(b*x + a)^m*a^3)/(b*m^2 + 5*b*m + 6*b)","B",0
948,0,0,0,0.000000," ","integrate((b*x+a)^m/(-b^2*x^2+a^2),x, algorithm=""giac"")","\int -\frac{{\left(b x + a\right)}^{m}}{b^{2} x^{2} - a^{2}}\,{d x}"," ",0,"integrate(-(b*x + a)^m/(b^2*x^2 - a^2), x)","F",0
949,0,0,0,0.000000," ","integrate((b*x+a)^m/(-b^2*x^2+a^2)^2,x, algorithm=""giac"")","\int \frac{{\left(b x + a\right)}^{m}}{{\left(b^{2} x^{2} - a^{2}\right)}^{2}}\,{d x}"," ",0,"integrate((b*x + a)^m/(b^2*x^2 - a^2)^2, x)","F",0
950,0,0,0,0.000000," ","integrate((b*x+a)^m/(-b^2*x^2+a^2)^3,x, algorithm=""giac"")","\int -\frac{{\left(b x + a\right)}^{m}}{{\left(b^{2} x^{2} - a^{2}\right)}^{3}}\,{d x}"," ",0,"integrate(-(b*x + a)^m/(b^2*x^2 - a^2)^3, x)","F",0
951,0,0,0,0.000000," ","integrate((e*x+d)^m*(-e^2*x^2+d^2)^(7/2),x, algorithm=""giac"")","\int {\left(-e^{2} x^{2} + d^{2}\right)}^{\frac{7}{2}} {\left(e x + d\right)}^{m}\,{d x}"," ",0,"integrate((-e^2*x^2 + d^2)^(7/2)*(e*x + d)^m, x)","F",0
952,0,0,0,0.000000," ","integrate((e*x+d)^m*(-e^2*x^2+d^2)^(5/2),x, algorithm=""giac"")","\int {\left(-e^{2} x^{2} + d^{2}\right)}^{\frac{5}{2}} {\left(e x + d\right)}^{m}\,{d x}"," ",0,"integrate((-e^2*x^2 + d^2)^(5/2)*(e*x + d)^m, x)","F",0
953,0,0,0,0.000000," ","integrate((e*x+d)^m*(-e^2*x^2+d^2)^(3/2),x, algorithm=""giac"")","\int {\left(-e^{2} x^{2} + d^{2}\right)}^{\frac{3}{2}} {\left(e x + d\right)}^{m}\,{d x}"," ",0,"integrate((-e^2*x^2 + d^2)^(3/2)*(e*x + d)^m, x)","F",0
954,0,0,0,0.000000," ","integrate((e*x+d)^m*(-e^2*x^2+d^2)^(1/2),x, algorithm=""giac"")","\int \sqrt{-e^{2} x^{2} + d^{2}} {\left(e x + d\right)}^{m}\,{d x}"," ",0,"integrate(sqrt(-e^2*x^2 + d^2)*(e*x + d)^m, x)","F",0
955,0,0,0,0.000000," ","integrate((e*x+d)^m/(-e^2*x^2+d^2)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{m}}{\sqrt{-e^{2} x^{2} + d^{2}}}\,{d x}"," ",0,"integrate((e*x + d)^m/sqrt(-e^2*x^2 + d^2), x)","F",0
956,0,0,0,0.000000," ","integrate((e*x+d)^m/(-e^2*x^2+d^2)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{m}}{{\left(-e^{2} x^{2} + d^{2}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((e*x + d)^m/(-e^2*x^2 + d^2)^(3/2), x)","F",0
957,0,0,0,0.000000," ","integrate((e*x+d)^m/(-e^2*x^2+d^2)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{m}}{{\left(-e^{2} x^{2} + d^{2}\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((e*x + d)^m/(-e^2*x^2 + d^2)^(5/2), x)","F",0
958,0,0,0,0.000000," ","integrate((e*x+d)^m/(-e^2*x^2+d^2)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{m}}{{\left(-e^{2} x^{2} + d^{2}\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((e*x + d)^m/(-e^2*x^2 + d^2)^(7/2), x)","F",0
959,0,0,0,0.000000," ","integrate((b*x+a)^m*(-b^2*x^2+a^2)^p,x, algorithm=""giac"")","\int {\left(-b^{2} x^{2} + a^{2}\right)}^{p} {\left(b x + a\right)}^{m}\,{d x}"," ",0,"integrate((-b^2*x^2 + a^2)^p*(b*x + a)^m, x)","F",0
960,0,0,0,0.000000," ","integrate((e*x+d)^3*(1-e^2*x^2/d^2)^p,x, algorithm=""giac"")","\int {\left(e x + d\right)}^{3} {\left(-\frac{e^{2} x^{2}}{d^{2}} + 1\right)}^{p}\,{d x}"," ",0,"integrate((e*x + d)^3*(-e^2*x^2/d^2 + 1)^p, x)","F",0
961,0,0,0,0.000000," ","integrate((e*x+d)^2*(1-e^2*x^2/d^2)^p,x, algorithm=""giac"")","\int {\left(e x + d\right)}^{2} {\left(-\frac{e^{2} x^{2}}{d^{2}} + 1\right)}^{p}\,{d x}"," ",0,"integrate((e*x + d)^2*(-e^2*x^2/d^2 + 1)^p, x)","F",0
962,0,0,0,0.000000," ","integrate((e*x+d)*(1-e^2*x^2/d^2)^p,x, algorithm=""giac"")","\int {\left(e x + d\right)} {\left(-\frac{e^{2} x^{2}}{d^{2}} + 1\right)}^{p}\,{d x}"," ",0,"integrate((e*x + d)*(-e^2*x^2/d^2 + 1)^p, x)","F",0
963,0,0,0,0.000000," ","integrate((1-e^2*x^2/d^2)^p,x, algorithm=""giac"")","\int {\left(-\frac{e^{2} x^{2}}{d^{2}} + 1\right)}^{p}\,{d x}"," ",0,"integrate((-e^2*x^2/d^2 + 1)^p, x)","F",0
964,0,0,0,0.000000," ","integrate((1-e^2*x^2/d^2)^p/(e*x+d),x, algorithm=""giac"")","\int \frac{{\left(-\frac{e^{2} x^{2}}{d^{2}} + 1\right)}^{p}}{e x + d}\,{d x}"," ",0,"integrate((-e^2*x^2/d^2 + 1)^p/(e*x + d), x)","F",0
965,0,0,0,0.000000," ","integrate((1-e^2*x^2/d^2)^p/(e*x+d)^2,x, algorithm=""giac"")","\int \frac{{\left(-\frac{e^{2} x^{2}}{d^{2}} + 1\right)}^{p}}{{\left(e x + d\right)}^{2}}\,{d x}"," ",0,"integrate((-e^2*x^2/d^2 + 1)^p/(e*x + d)^2, x)","F",0
966,0,0,0,0.000000," ","integrate((1-e^2*x^2/d^2)^p/(e*x+d)^3,x, algorithm=""giac"")","\int \frac{{\left(-\frac{e^{2} x^{2}}{d^{2}} + 1\right)}^{p}}{{\left(e x + d\right)}^{3}}\,{d x}"," ",0,"integrate((-e^2*x^2/d^2 + 1)^p/(e*x + d)^3, x)","F",0
967,0,0,0,0.000000," ","integrate((b*x+a)^3*(-b^2*x^2+a^2)^p,x, algorithm=""giac"")","\int {\left(b x + a\right)}^{3} {\left(-b^{2} x^{2} + a^{2}\right)}^{p}\,{d x}"," ",0,"integrate((b*x + a)^3*(-b^2*x^2 + a^2)^p, x)","F",0
968,0,0,0,0.000000," ","integrate((b*x+a)^2*(-b^2*x^2+a^2)^p,x, algorithm=""giac"")","\int {\left(b x + a\right)}^{2} {\left(-b^{2} x^{2} + a^{2}\right)}^{p}\,{d x}"," ",0,"integrate((b*x + a)^2*(-b^2*x^2 + a^2)^p, x)","F",0
969,0,0,0,0.000000," ","integrate((b*x+a)*(-b^2*x^2+a^2)^p,x, algorithm=""giac"")","\int {\left(b x + a\right)} {\left(-b^{2} x^{2} + a^{2}\right)}^{p}\,{d x}"," ",0,"integrate((b*x + a)*(-b^2*x^2 + a^2)^p, x)","F",0
970,0,0,0,0.000000," ","integrate((-b^2*x^2+a^2)^p/(b*x+a),x, algorithm=""giac"")","\int \frac{{\left(-b^{2} x^{2} + a^{2}\right)}^{p}}{b x + a}\,{d x}"," ",0,"integrate((-b^2*x^2 + a^2)^p/(b*x + a), x)","F",0
971,0,0,0,0.000000," ","integrate((-b^2*x^2+a^2)^p/(b*x+a)^2,x, algorithm=""giac"")","\int \frac{{\left(-b^{2} x^{2} + a^{2}\right)}^{p}}{{\left(b x + a\right)}^{2}}\,{d x}"," ",0,"integrate((-b^2*x^2 + a^2)^p/(b*x + a)^2, x)","F",0
972,0,0,0,0.000000," ","integrate((-b^2*x^2+a^2)^p/(b*x+a)^3,x, algorithm=""giac"")","\int \frac{{\left(-b^{2} x^{2} + a^{2}\right)}^{p}}{{\left(b x + a\right)}^{3}}\,{d x}"," ",0,"integrate((-b^2*x^2 + a^2)^p/(b*x + a)^3, x)","F",0
973,0,0,0,0.000000," ","integrate((b*x+a)^(3/2)*(-b^2*x^2+a^2)^p,x, algorithm=""giac"")","\int {\left(b x + a\right)}^{\frac{3}{2}} {\left(-b^{2} x^{2} + a^{2}\right)}^{p}\,{d x}"," ",0,"integrate((b*x + a)^(3/2)*(-b^2*x^2 + a^2)^p, x)","F",0
974,0,0,0,0.000000," ","integrate((b*x+a)^(1/2)*(-b^2*x^2+a^2)^p,x, algorithm=""giac"")","\int \sqrt{b x + a} {\left(-b^{2} x^{2} + a^{2}\right)}^{p}\,{d x}"," ",0,"integrate(sqrt(b*x + a)*(-b^2*x^2 + a^2)^p, x)","F",0
975,0,0,0,0.000000," ","integrate((-b^2*x^2+a^2)^p/(b*x+a)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(-b^{2} x^{2} + a^{2}\right)}^{p}}{\sqrt{b x + a}}\,{d x}"," ",0,"integrate((-b^2*x^2 + a^2)^p/sqrt(b*x + a), x)","F",0
976,0,0,0,0.000000," ","integrate((-b^2*x^2+a^2)^p/(b*x+a)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(-b^{2} x^{2} + a^{2}\right)}^{p}}{{\left(b x + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((-b^2*x^2 + a^2)^p/(b*x + a)^(3/2), x)","F",0
977,1,26,0,0.226528," ","integrate(-a*(-b^2*x^2+a^2)^p+(b*x+a)*(-b^2*x^2+a^2)^p,x, algorithm=""giac"")","-\frac{{\left(-b^{2} x^{2} + a^{2}\right)}^{p + 1}}{2 \, b {\left(p + 1\right)}}"," ",0,"-1/2*(-b^2*x^2 + a^2)^(p + 1)/(b*(p + 1))","A",0
978,1,45,0,0.162745," ","integrate((e*x+d)^2*(c*e^2*x^2+2*c*d*e*x+c*d^2),x, algorithm=""giac"")","\frac{1}{5} \, c x^{5} e^{4} + c d x^{4} e^{3} + 2 \, c d^{2} x^{3} e^{2} + 2 \, c d^{3} x^{2} e + c d^{4} x"," ",0,"1/5*c*x^5*e^4 + c*d*x^4*e^3 + 2*c*d^2*x^3*e^2 + 2*c*d^3*x^2*e + c*d^4*x","B",0
979,1,34,0,0.149793," ","integrate((e*x+d)*(c*e^2*x^2+2*c*d*e*x+c*d^2),x, algorithm=""giac"")","\frac{1}{4} \, c x^{4} e^{3} + c d x^{3} e^{2} + \frac{3}{2} \, c d^{2} x^{2} e + c d^{3} x"," ",0,"1/4*c*x^4*e^3 + c*d*x^3*e^2 + 3/2*c*d^2*x^2*e + c*d^3*x","B",0
980,1,23,0,0.152045," ","integrate(c*e^2*x^2+2*c*d*e*x+c*d^2,x, algorithm=""giac"")","\frac{1}{3} \, c x^{3} e^{2} + c d x^{2} e + c d^{2} x"," ",0,"1/3*c*x^3*e^2 + c*d*x^2*e + c*d^2*x","A",0
981,1,19,0,0.184489," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)/(e*x+d),x, algorithm=""giac"")","\frac{1}{2} \, {\left(c x^{2} e^{3} + 2 \, c d x e^{2}\right)} e^{\left(-2\right)}"," ",0,"1/2*(c*x^2*e^3 + 2*c*d*x*e^2)*e^(-2)","A",0
982,1,110,0,0.165563," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)/(e*x+d)^2,x, algorithm=""giac"")","-2 \, {\left(e^{\left(-1\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) - \frac{d e^{\left(-1\right)}}{x e + d}\right)} c d + {\left(2 \, d e^{\left(-3\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) + {\left(x e + d\right)} e^{\left(-3\right)} - \frac{d^{2} e^{\left(-3\right)}}{x e + d}\right)} c e^{2} - \frac{c d^{2} e^{\left(-1\right)}}{x e + d}"," ",0,"-2*(e^(-1)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) - d*e^(-1)/(x*e + d))*c*d + (2*d*e^(-3)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) + (x*e + d)*e^(-3) - d^2*e^(-3)/(x*e + d))*c*e^2 - c*d^2*e^(-1)/(x*e + d)","C",0
983,1,12,0,0.183922," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)/(e*x+d)^3,x, algorithm=""giac"")","c e^{\left(-1\right)} \log\left({\left| x e + d \right|}\right)"," ",0,"c*e^(-1)*log(abs(x*e + d))","A",0
984,1,34,0,0.154634," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)/(e*x+d)^4,x, algorithm=""giac"")","-\frac{{\left(c x^{2} e^{4} + 2 \, c d x e^{3} + c d^{2} e^{2}\right)} e^{\left(-3\right)}}{{\left(x e + d\right)}^{3}}"," ",0,"-(c*x^2*e^4 + 2*c*d*x*e^3 + c*d^2*e^2)*e^(-3)/(x*e + d)^3","B",0
985,1,13,0,0.156791," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)/(e*x+d)^5,x, algorithm=""giac"")","-\frac{c e^{\left(-1\right)}}{2 \, {\left(x e + d\right)}^{2}}"," ",0,"-1/2*c*e^(-1)/(x*e + d)^2","A",0
986,1,34,0,0.168504," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)/(e*x+d)^6,x, algorithm=""giac"")","-\frac{{\left(c x^{2} e^{4} + 2 \, c d x e^{3} + c d^{2} e^{2}\right)} e^{\left(-3\right)}}{3 \, {\left(x e + d\right)}^{5}}"," ",0,"-1/3*(c*x^2*e^4 + 2*c*d*x*e^3 + c*d^2*e^2)*e^(-3)/(x*e + d)^5","B",0
987,1,81,0,0.155790," ","integrate((e*x+d)^2*(c*e^2*x^2+2*c*d*e*x+c*d^2)^2,x, algorithm=""giac"")","\frac{1}{7} \, c^{2} x^{7} e^{6} + c^{2} d x^{6} e^{5} + 3 \, c^{2} d^{2} x^{5} e^{4} + 5 \, c^{2} d^{3} x^{4} e^{3} + 5 \, c^{2} d^{4} x^{3} e^{2} + 3 \, c^{2} d^{5} x^{2} e + c^{2} d^{6} x"," ",0,"1/7*c^2*x^7*e^6 + c^2*d*x^6*e^5 + 3*c^2*d^2*x^5*e^4 + 5*c^2*d^3*x^4*e^3 + 5*c^2*d^4*x^3*e^2 + 3*c^2*d^5*x^2*e + c^2*d^6*x","B",0
988,1,68,0,0.217652," ","integrate((e*x+d)*(c*e^2*x^2+2*c*d*e*x+c*d^2)^2,x, algorithm=""giac"")","\frac{1}{6} \, c^{2} x^{6} e^{5} + c^{2} d x^{5} e^{4} + \frac{5}{2} \, c^{2} d^{2} x^{4} e^{3} + \frac{10}{3} \, c^{2} d^{3} x^{3} e^{2} + \frac{5}{2} \, c^{2} d^{4} x^{2} e + c^{2} d^{5} x"," ",0,"1/6*c^2*x^6*e^5 + c^2*d*x^5*e^4 + 5/2*c^2*d^2*x^4*e^3 + 10/3*c^2*d^3*x^3*e^2 + 5/2*c^2*d^4*x^2*e + c^2*d^5*x","B",0
989,1,55,0,0.150842," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^2,x, algorithm=""giac"")","\frac{1}{5} \, c^{2} x^{5} e^{4} + c^{2} d x^{4} e^{3} + 2 \, c^{2} d^{2} x^{3} e^{2} + 2 \, c^{2} d^{3} x^{2} e + c^{2} d^{4} x"," ",0,"1/5*c^2*x^5*e^4 + c^2*d*x^4*e^3 + 2*c^2*d^2*x^3*e^2 + 2*c^2*d^3*x^2*e + c^2*d^4*x","B",0
990,1,49,0,0.172172," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^2/(e*x+d),x, algorithm=""giac"")","\frac{1}{4} \, {\left(c^{2} x^{4} e^{7} + 4 \, c^{2} d x^{3} e^{6} + 6 \, c^{2} d^{2} x^{2} e^{5} + 4 \, c^{2} d^{3} x e^{4}\right)} e^{\left(-4\right)}"," ",0,"1/4*(c^2*x^4*e^7 + 4*c^2*d*x^3*e^6 + 6*c^2*d^2*x^2*e^5 + 4*c^2*d^3*x*e^4)*e^(-4)","B",0
991,1,15,0,0.163764," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^2/(e*x+d)^2,x, algorithm=""giac"")","\frac{1}{3} \, {\left(x e + d\right)}^{3} c^{2} e^{\left(-1\right)}"," ",0,"1/3*(x*e + d)^3*c^2*e^(-1)","A",0
992,1,23,0,0.158072," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^2/(e*x+d)^3,x, algorithm=""giac"")","\frac{1}{2} \, {\left(c^{2} x^{2} e^{7} + 2 \, c^{2} d x e^{6}\right)} e^{\left(-6\right)}"," ",0,"1/2*(c^2*x^2*e^7 + 2*c^2*d*x*e^6)*e^(-6)","A",0
993,1,5,0,0.159009," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^2/(e*x+d)^4,x, algorithm=""giac"")","c^{2} x"," ",0,"c^2*x","A",0
994,1,26,0,0.166012," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^2/(e*x+d)^5,x, algorithm=""giac"")","-c^{2} e^{\left(-1\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right)"," ",0,"-c^2*e^(-1)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2)","A",0
995,1,66,0,0.176576," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^2/(e*x+d)^6,x, algorithm=""giac"")","-\frac{{\left(c^{2} x^{4} e^{8} + 4 \, c^{2} d x^{3} e^{7} + 6 \, c^{2} d^{2} x^{2} e^{6} + 4 \, c^{2} d^{3} x e^{5} + c^{2} d^{4} e^{4}\right)} e^{\left(-5\right)}}{{\left(x e + d\right)}^{5}}"," ",0,"-(c^2*x^4*e^8 + 4*c^2*d*x^3*e^7 + 6*c^2*d^2*x^2*e^6 + 4*c^2*d^3*x*e^5 + c^2*d^4*e^4)*e^(-5)/(x*e + d)^5","B",0
996,1,66,0,0.158435," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^2/(e*x+d)^7,x, algorithm=""giac"")","-\frac{{\left(c^{2} x^{4} e^{8} + 4 \, c^{2} d x^{3} e^{7} + 6 \, c^{2} d^{2} x^{2} e^{6} + 4 \, c^{2} d^{3} x e^{5} + c^{2} d^{4} e^{4}\right)} e^{\left(-5\right)}}{2 \, {\left(x e + d\right)}^{6}}"," ",0,"-1/2*(c^2*x^4*e^8 + 4*c^2*d*x^3*e^7 + 6*c^2*d^2*x^2*e^6 + 4*c^2*d^3*x*e^5 + c^2*d^4*e^4)*e^(-5)/(x*e + d)^6","B",0
997,1,66,0,0.154915," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^2/(e*x+d)^8,x, algorithm=""giac"")","-\frac{{\left(c^{2} x^{4} e^{8} + 4 \, c^{2} d x^{3} e^{7} + 6 \, c^{2} d^{2} x^{2} e^{6} + 4 \, c^{2} d^{3} x e^{5} + c^{2} d^{4} e^{4}\right)} e^{\left(-5\right)}}{3 \, {\left(x e + d\right)}^{7}}"," ",0,"-1/3*(c^2*x^4*e^8 + 4*c^2*d*x^3*e^7 + 6*c^2*d^2*x^2*e^6 + 4*c^2*d^3*x*e^5 + c^2*d^4*e^4)*e^(-5)/(x*e + d)^7","B",0
998,-2,0,0,0.000000," ","integrate((e*x+d)^5/(c*e^2*x^2+2*c*d*e*x+c*d^2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: (5*exp(2)^4*d^4*exp(1)-30*exp(2)^3*d^4*exp(1)^3+61*exp(2)^2*d^4*exp(1)^5-52*exp(2)*d^4*exp(1)^7+16*d^4*exp(1)^9)*1/2/c/exp(2)^5*ln(x^2*exp(2)+2*x*d*exp(1)+d^2)+(2*exp(2)^5*d^5-30*exp(2)^4*d^5*exp(1)^2+110*exp(2)^3*d^5*exp(1)^4-170*exp(2)^2*d^5*exp(1)^6+120*exp(2)*d^5*exp(1)^8-32*d^5*exp(1)^10)/c/exp(2)^5*1/2/d/sqrt(-exp(1)^2+exp(2))*atan((d*exp(1)+x*exp(2))/d/sqrt(-exp(1)^2+exp(2)))+(1/4*x^4*c^3*exp(2)^3*exp(1)^5+5/3*x^3*c^3*exp(2)^3*d*exp(1)^4-2/3*x^3*c^3*exp(2)^2*d*exp(1)^6+5*x^2*c^3*exp(2)^3*d^2*exp(1)^3-11/2*x^2*c^3*exp(2)^2*d^2*exp(1)^5+2*x^2*c^3*exp(2)*d^2*exp(1)^7+10*x*c^3*exp(2)^3*d^3*exp(1)^2-25*x*c^3*exp(2)^2*d^3*exp(1)^4+24*x*c^3*exp(2)*d^3*exp(1)^6-8*x*c^3*d^3*exp(1)^8)/c^4/exp(2)^4","F(-2)",0
999,-2,0,0,0.000000," ","integrate((e*x+d)^4/(c*e^2*x^2+2*c*d*e*x+c*d^2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: (2*exp(2)^3*d^3*exp(1)-8*exp(2)^2*d^3*exp(1)^3+10*exp(2)*d^3*exp(1)^5-4*d^3*exp(1)^7)/c/exp(2)^4*ln(x^2*exp(2)+2*x*d*exp(1)+d^2)+(2*exp(2)^4*d^4-20*exp(2)^3*d^4*exp(1)^2+50*exp(2)^2*d^4*exp(1)^4-48*exp(2)*d^4*exp(1)^6+16*d^4*exp(1)^8)/c/exp(2)^4*1/2/d/sqrt(-exp(1)^2+exp(2))*atan((d*exp(1)+x*exp(2))/d/sqrt(-exp(1)^2+exp(2)))+(1/3*x^3*c^2*exp(2)^2*exp(1)^4+2*x^2*c^2*exp(2)^2*d*exp(1)^3-x^2*c^2*exp(2)*d*exp(1)^5+6*x*c^2*exp(2)^2*d^2*exp(1)^2-9*x*c^2*exp(2)*d^2*exp(1)^4+4*x*c^2*d^2*exp(1)^6)/c^3/exp(2)^3","F(-2)",0
1000,-2,0,0,0.000000," ","integrate((e*x+d)^3/(c*e^2*x^2+2*c*d*e*x+c*d^2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: (3*exp(2)^2*d^2*exp(1)-7*exp(2)*d^2*exp(1)^3+4*d^2*exp(1)^5)*1/2/c/exp(2)^3*ln(x^2*exp(2)+2*x*d*exp(1)+d^2)+(2*exp(2)^3*d^3-12*exp(2)^2*d^3*exp(1)^2+18*exp(2)*d^3*exp(1)^4-8*d^3*exp(1)^6)/c/exp(2)^3*1/2/d/sqrt(-exp(1)^2+exp(2))*atan((d*exp(1)+x*exp(2))/d/sqrt(-exp(1)^2+exp(2)))+(1/2*x^2*c*exp(2)*exp(1)^3+3*x*c*exp(2)*d*exp(1)^2-2*x*c*d*exp(1)^4)/c^2/exp(2)^2","F(-2)",0
1001,-2,0,0,0.000000," ","integrate((e*x+d)^2/(c*e^2*x^2+2*c*d*e*x+c*d^2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: (exp(2)*d*exp(1)-d*exp(1)^3)/c/exp(2)^2*ln(x^2*exp(2)+2*x*d*exp(1)+d^2)+(2*exp(2)^2*d^2-6*exp(2)*d^2*exp(1)^2+4*d^2*exp(1)^4)/c/exp(2)^2*1/2/d/sqrt(-exp(1)^2+exp(2))*atan((d*exp(1)+x*exp(2))/d/sqrt(-exp(1)^2+exp(2)))+x*exp(1)^2/c/exp(2)","F(-2)",0
1002,-2,0,0,0.000000," ","integrate((e*x+d)/(c*e^2*x^2+2*c*d*e*x+c*d^2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: exp(1)*1/2/c/exp(2)*ln(x^2*exp(2)+2*x*d*exp(1)+d^2)+(2*exp(2)*d-2*d*exp(1)^2)/c/exp(2)*1/2/d/sqrt(-exp(1)^2+exp(2))*atan((d*exp(1)+x*exp(2))/d/sqrt(-exp(1)^2+exp(2)))","F(-2)",0
1003,-2,0,0,0.000000," ","integrate(1/(c*e^2*x^2+2*c*d*e*x+c*d^2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: 2/c*1/2/d/sqrt(-exp(1)^2+exp(2))*atan((d*exp(1)+x*exp(2))/d/sqrt(-exp(1)^2+exp(2)))","F(-2)",0
1004,-2,0,0,0.000000," ","integrate(1/(e*x+d)/(c*e^2*x^2+2*c*d*e*x+c*d^2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: exp(1)^2/(c*exp(2)*d^2*exp(1)-c*d^2*exp(1)^3)*ln(abs(x*exp(1)+d))-exp(1)/(2*c*exp(2)*d^2-2*c*d^2*exp(1)^2)*ln(x^2*exp(2)+2*x*d*exp(1)+d^2)+2/c/d*1/2/d/sqrt(-exp(1)^2+exp(2))*atan((d*exp(1)+x*exp(2))/d/sqrt(-exp(1)^2+exp(2)))","F(-2)",0
1005,-2,0,0,0.000000," ","integrate(1/(e*x+d)^2/(c*e^2*x^2+2*c*d*e*x+c*d^2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: exp(1)/(c*d^3*exp(1)^2-c*d^3*exp(2))*ln((-(exp(1)*x+d)^-1/exp(1))^2*d^2*exp(1)^4-(-(exp(1)*x+d)^-1/exp(1))^2*d^2*exp(1)^2*exp(2)-2*(exp(1)*x+d)^-1/exp(1)*d*exp(1)^3+2*(exp(1)*x+d)^-1/exp(1)*d*exp(1)*exp(2)-exp(2))+(-4*exp(1)^4+2*exp(1)^2*exp(2))/2/(c*d^2*exp(1)^2-c*d^2*exp(2))/d/sqrt(-exp(1)^2+exp(2))/exp(1)^2*atan((-d*(exp(1)*x+d)^-1/exp(1)*exp(1)^3+d*(exp(1)*x+d)^-1/exp(1)*exp(1)*exp(2)+exp(1)^2-exp(2))/sqrt(-exp(1)^2+exp(2))/exp(1))+(exp(1)*x+d)^-1/exp(1)*exp(1)^4/(c*d^2*exp(1)^4-c*d^2*exp(1)^2*exp(2))","F(-2)",0
1006,-2,0,0,0.000000," ","integrate(1/(e*x+d)^3/(c*e^2*x^2+2*c*d*e*x+c*d^2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: (-3*exp(2)*exp(1)+4*exp(1)^3)/(2*c*exp(2)^2*d^4-4*c*exp(2)*d^4*exp(1)^2+2*c*d^4*exp(1)^4)*ln(x^2*exp(2)+2*x*d*exp(1)+d^2)+(2*exp(2)-8*exp(1)^2)*1/2/(c*exp(2)*d^3-c*d^3*exp(1)^2)/d/sqrt(-exp(1)^2+exp(2))*atan((d*exp(1)+x*exp(2))/d/sqrt(-exp(1)^2+exp(2)))+(3*exp(2)*exp(1)^2-4*exp(1)^4)/(c*exp(2)^2*d^4*exp(1)-2*c*exp(2)*d^4*exp(1)^3+c*d^4*exp(1)^5)*ln(abs(x*exp(1)+d))+(-5*exp(2)*exp(1)*d^2+5*exp(1)^3*d^2+(-4*exp(2)*exp(1)^2*d+4*exp(1)^4*d)*x)/2/d^4/(exp(1)*x+d)^2/(exp(2)-exp(1)^2)^2/c","F(-2)",0
1007,-2,0,0,0.000000," ","integrate((e*x+d)^7/(c*e^2*x^2+2*c*d*e*x+c*d^2)^2,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: (1/4*x^4*c^6*exp(2)^6*exp(1)^7+7/3*x^3*c^6*exp(2)^6*d*exp(1)^6-4/3*x^3*c^6*exp(2)^5*d*exp(1)^8+21/2*x^2*c^6*exp(2)^6*d^2*exp(1)^5-15*x^2*c^6*exp(2)^5*d^2*exp(1)^7+6*x^2*c^6*exp(2)^4*d^2*exp(1)^9+35*x*c^6*exp(2)^6*d^3*exp(1)^4-98*x*c^6*exp(2)^5*d^3*exp(1)^6+96*x*c^6*exp(2)^4*d^3*exp(1)^8-32*x*c^6*exp(2)^3*d^3*exp(1)^10)/c^8/exp(2)^8+(-6*exp(2)^5*d^6*exp(1)+50*exp(2)^4*d^6*exp(1)^3-146*exp(2)^3*d^6*exp(1)^5+198*exp(2)^2*d^6*exp(1)^7-128*exp(2)*d^6*exp(1)^9+32*d^6*exp(1)^11+(exp(2)^6*d^5-27*exp(2)^5*d^5*exp(1)^2+155*exp(2)^4*d^5*exp(1)^4-377*exp(2)^3*d^5*exp(1)^6+456*exp(2)^2*d^5*exp(1)^8-272*exp(2)*d^5*exp(1)^10+64*d^5*exp(1)^12)*x)/2/exp(2)^6/c^2/(2*exp(1)*d*x+exp(2)*x^2+d^2)+(35*exp(2)^4*d^4*exp(1)^3-182*exp(2)^3*d^4*exp(1)^5+339*exp(2)^2*d^4*exp(1)^7-272*exp(2)*d^4*exp(1)^9+80*d^4*exp(1)^11)*1/2/c^2/exp(2)^6*ln(x^2*exp(2)+2*x*d*exp(1)+d^2)+(exp(2)^6*d^5+15*exp(2)^5*d^5*exp(1)^2-195*exp(2)^4*d^5*exp(1)^4+645*exp(2)^3*d^5*exp(1)^6-930*exp(2)^2*d^5*exp(1)^8+624*exp(2)*d^5*exp(1)^10-160*d^5*exp(1)^12)/c^2/exp(2)^6*1/2/d/sqrt(-exp(1)^2+exp(2))*atan((d*exp(1)+x*exp(2))/d/sqrt(-exp(1)^2+exp(2)))","F(-2)",0
1008,-2,0,0,0.000000," ","integrate((e*x+d)^6/(c*e^2*x^2+2*c*d*e*x+c*d^2)^2,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: (1/3*x^3*c^4*exp(2)^4*exp(1)^6+3*x^2*c^4*exp(2)^4*d*exp(1)^5-2*x^2*c^4*exp(2)^3*d*exp(1)^7+15*x*c^4*exp(2)^4*d^2*exp(1)^4-26*x*c^4*exp(2)^3*d^2*exp(1)^6+12*x*c^4*exp(2)^2*d^2*exp(1)^8)/c^6/exp(2)^6+(-5*exp(2)^4*d^5*exp(1)+30*exp(2)^3*d^5*exp(1)^3-61*exp(2)^2*d^5*exp(1)^5+52*exp(2)*d^5*exp(1)^7-16*d^5*exp(1)^9+(exp(2)^5*d^4-20*exp(2)^4*d^4*exp(1)^2+85*exp(2)^3*d^4*exp(1)^4-146*exp(2)^2*d^4*exp(1)^6+112*exp(2)*d^4*exp(1)^8-32*d^4*exp(1)^10)*x)/2/exp(2)^5/c^2/(2*exp(1)*d*x+exp(2)*x^2+d^2)+(10*exp(2)^3*d^3*exp(1)^3-36*exp(2)^2*d^3*exp(1)^5+42*exp(2)*d^3*exp(1)^7-16*d^3*exp(1)^9)/c^2/exp(2)^5*ln(x^2*exp(2)+2*x*d*exp(1)+d^2)+(exp(2)^5*d^4+10*exp(2)^4*d^4*exp(1)^2-95*exp(2)^3*d^4*exp(1)^4+220*exp(2)^2*d^4*exp(1)^6-200*exp(2)*d^4*exp(1)^8+64*d^4*exp(1)^10)/c^2/exp(2)^5*1/2/d/sqrt(-exp(1)^2+exp(2))*atan((d*exp(1)+x*exp(2))/d/sqrt(-exp(1)^2+exp(2)))","F(-2)",0
1009,-2,0,0,0.000000," ","integrate((e*x+d)^5/(c*e^2*x^2+2*c*d*e*x+c*d^2)^2,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: (1/2*x^2*c^2*exp(2)^2*exp(1)^5+5*x*c^2*exp(2)^2*d*exp(1)^4-4*x*c^2*exp(2)*d*exp(1)^6)/c^4/exp(2)^4+(-4*exp(2)^3*d^4*exp(1)+16*exp(2)^2*d^4*exp(1)^3-20*exp(2)*d^4*exp(1)^5+8*d^4*exp(1)^7+(exp(2)^4*d^3-14*exp(2)^3*d^3*exp(1)^2+41*exp(2)^2*d^3*exp(1)^4-44*exp(2)*d^3*exp(1)^6+16*d^3*exp(1)^8)*x)/2/exp(2)^4/c^2/(2*exp(1)*d*x+exp(2)*x^2+d^2)+(5*exp(2)^2*d^2*exp(1)^3-11*exp(2)*d^2*exp(1)^5+6*d^2*exp(1)^7)/c^2/exp(2)^4*ln(x^2*exp(2)+2*x*d*exp(1)+d^2)+(exp(2)^4*d^3+6*exp(2)^3*d^3*exp(1)^2-39*exp(2)^2*d^3*exp(1)^4+56*exp(2)*d^3*exp(1)^6-24*d^3*exp(1)^8)/c^2/exp(2)^4*1/2/d/sqrt(-exp(1)^2+exp(2))*atan((d*exp(1)+x*exp(2))/d/sqrt(-exp(1)^2+exp(2)))","F(-2)",0
1010,-2,0,0,0.000000," ","integrate((e*x+d)^4/(c*e^2*x^2+2*c*d*e*x+c*d^2)^2,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: x*exp(1)^4/c^2/exp(2)^2+((exp(2)^3*d^2-9*exp(2)^2*d^2*exp(1)^2+16*exp(2)*d^2*exp(1)^4-8*d^2*exp(1)^6)/exp(2)*x+(-3*exp(2)^2*d^3*exp(1)+7*exp(2)*d^3*exp(1)^3-4*d^3*exp(1)^5)/exp(2))/2/c^2/exp(2)^2/(2*exp(1)*d*x+exp(2)*x^2+d^2)+(2*exp(2)*d*exp(1)^3-2*d*exp(1)^5)/c^2/exp(2)^3*ln(x^2*exp(2)+2*x*d*exp(1)+d^2)+(exp(2)^3*d^2+3*exp(2)^2*d^2*exp(1)^2-12*exp(2)*d^2*exp(1)^4+8*d^2*exp(1)^6)/c^2/exp(2)^3*1/2/d/sqrt(-exp(1)^2+exp(2))*atan((d*exp(1)+x*exp(2))/d/sqrt(-exp(1)^2+exp(2)))","F(-2)",0
1011,-2,0,0,0.000000," ","integrate((e*x+d)^3/(c*e^2*x^2+2*c*d*e*x+c*d^2)^2,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: exp(1)^3*1/2/c^2/exp(2)^2*ln(x^2*exp(2)+2*x*d*exp(1)+d^2)-(-exp(2)^2*d-exp(2)*d*exp(1)^2+2*d*exp(1)^4)/c^2/exp(2)^2*1/2/d/sqrt(-exp(1)^2+exp(2))*atan((d*exp(1)+x*exp(2))/d/sqrt(-exp(1)^2+exp(2)))+(-2*exp(2)*exp(1)*d^2+2*exp(1)^3*d^2+(exp(2)^2*d-5*exp(2)*exp(1)^2*d+4*exp(1)^4*d)*x)/2/c^2/exp(2)^2/(2*exp(1)*x*d+exp(2)*x^2+d^2)","F(-2)",0
1012,-2,0,0,0.000000," ","integrate((e*x+d)^2/(c*e^2*x^2+2*c*d*e*x+c*d^2)^2,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: -(x*exp(2)-2*x*exp(1)^2-d*exp(1))*1/2/c^2/exp(2)/(-x^2*exp(2)-2*x*d*exp(1)-d^2)+1/2/c^2/d/sqrt(-exp(1)^2+exp(2))*atan((d*exp(1)+x*exp(2))/d/sqrt(-exp(1)^2+exp(2)))","F(-2)",0
1013,-2,0,0,0.000000," ","integrate((e*x+d)/(c*e^2*x^2+2*c*d*e*x+c*d^2)^2,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: -x*1/2/c^2/d/(-x^2*exp(2)-2*x*d*exp(1)-d^2)+1/c^2/d*1/2/d/sqrt(-exp(1)^2+exp(2))*atan((d*exp(1)+x*exp(2))/d/sqrt(-exp(1)^2+exp(2)))","F(-2)",0
1014,-2,0,0,0.000000," ","integrate(1/(c*e^2*x^2+2*c*d*e*x+c*d^2)^2,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: (x*exp(2)+d*exp(1))/(-2*c^2*exp(2)*d^2+2*c^2*d^2*exp(1)^2)/(-x^2*exp(2)-2*x*d*exp(1)-d^2)+exp(2)*1/2/(c^2*exp(2)*d^2-c^2*d^2*exp(1)^2)/d/sqrt(-exp(1)^2+exp(2))*atan((d*exp(1)+x*exp(2))/d/sqrt(-exp(1)^2+exp(2)))","F(-2)",0
1015,-2,0,0,0.000000," ","integrate(1/(e*x+d)/(c*e^2*x^2+2*c*d*e*x+c*d^2)^2,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: exp(1)^4/(c^2*exp(2)^2*d^4*exp(1)-2*c^2*exp(2)*d^4*exp(1)^3+c^2*d^4*exp(1)^5)*ln(abs(x*exp(1)+d))-exp(1)^3/(2*c^2*exp(2)^2*d^4-4*c^2*exp(2)*d^4*exp(1)^2+2*c^2*d^4*exp(1)^4)*ln(x^2*exp(2)+2*x*d*exp(1)+d^2)+(exp(2)+2*exp(1)^2)*1/2/(c^2*exp(2)*d^3-c^2*d^3*exp(1)^2)/d/sqrt(-exp(1)^2+exp(2))*atan((d*exp(1)+x*exp(2))/d/sqrt(-exp(1)^2+exp(2)))+(2*exp(2)*exp(1)*d^2-2*exp(1)^3*d^2+(exp(2)^2*d-exp(2)*exp(1)^2*d)*x)/2/d^4/c^2/(exp(2)-exp(1)^2)^2/(x^2*exp(2)+2*x*d*exp(1)+d^2)","F(-2)",0
1016,-2,0,0,0.000000," ","integrate(1/(e*x+d)^2/(c*e^2*x^2+2*c*d*e*x+c*d^2)^2,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: -(exp(1)*x+d)^-1/exp(1)*exp(1)^8/(c^2*d^4*exp(1)^8-2*c^2*d^4*exp(1)^6*exp(2)+c^2*d^4*exp(1)^4*exp(2)^2)+(4*exp(1)^3*exp(2)-exp(1)*exp(2)^2-(-8*d*exp(1)^6+8*d*exp(1)^4*exp(2)-d*exp(1)^2*exp(2)^2)*(exp(1)*x+d)^-1/exp(1))/2/d^5/(exp(2)-exp(1)^2)^2/c^2/((-(exp(1)*x+d)^-1/exp(1))^2*d^2*exp(1)^4-(-(exp(1)*x+d)^-1/exp(1))^2*d^2*exp(1)^2*exp(2)-2*(exp(1)*x+d)^-1/exp(1)*d*exp(1)^3+2*(exp(1)*x+d)^-1/exp(1)*d*exp(1)*exp(2)-exp(2))-2*exp(1)^3/(c^2*d^5*exp(1)^4-2*c^2*d^5*exp(1)^2*exp(2)+c^2*d^5*exp(2)^2)*ln((-(exp(1)*x+d)^-1/exp(1))^2*d^2*exp(1)^4-(-(exp(1)*x+d)^-1/exp(1))^2*d^2*exp(1)^2*exp(2)-2*(exp(1)*x+d)^-1/exp(1)*d*exp(1)^3+2*(exp(1)*x+d)^-1/exp(1)*d*exp(1)*exp(2)-exp(2))+(8*exp(1)^6-4*exp(1)^4*exp(2)-exp(1)^2*exp(2)^2)/2/(c^2*d^4*exp(1)^4-2*c^2*d^4*exp(1)^2*exp(2)+c^2*d^4*exp(2)^2)/d/sqrt(-exp(1)^2+exp(2))/exp(1)^2*atan((-d*(exp(1)*x+d)^-1/exp(1)*exp(1)^3+d*(exp(1)*x+d)^-1/exp(1)*exp(1)*exp(2)+exp(1)^2-exp(2))/sqrt(-exp(1)^2+exp(2))/exp(1))","F(-2)",0
1017,-2,0,0,0.000000," ","integrate((e*x+d)^9/(c*e^2*x^2+2*c*d*e*x+c*d^2)^3,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: (1/4*x^4*c^9*exp(2)^9*exp(1)^9+3*x^3*c^9*exp(2)^9*d*exp(1)^8-2*x^3*c^9*exp(2)^8*d*exp(1)^10+18*x^2*c^9*exp(2)^9*d^2*exp(1)^7-57/2*x^2*c^9*exp(2)^8*d^2*exp(1)^9+12*x^2*c^9*exp(2)^7*d^2*exp(1)^11+84*x*c^9*exp(2)^9*d^3*exp(1)^6-243*x*c^9*exp(2)^8*d^3*exp(1)^8+240*x*c^9*exp(2)^7*d^3*exp(1)^10-80*x*c^9*exp(2)^6*d^3*exp(1)^12)/c^12/exp(2)^12+((3*exp(2)^8*d^5+15*exp(2)^7*d^5*exp(1)^2-783*exp(2)^6*d^5*exp(1)^4+4341*exp(2)^5*d^5*exp(1)^6-10056*exp(2)^4*d^5*exp(1)^8+11664*exp(2)^3*d^5*exp(1)^10-6720*exp(2)^2*d^5*exp(1)^12+1536*exp(2)*d^5*exp(1)^14)*x^3+(9*exp(2)^7*d^6*exp(1)-291*exp(2)^6*d^6*exp(1)^3+675*exp(2)^5*d^6*exp(1)^5+2511*exp(2)^4*d^6*exp(1)^7-11624*exp(2)^3*d^6*exp(1)^9+17232*exp(2)^2*d^6*exp(1)^11-11328*exp(2)*d^6*exp(1)^13+2816*d^6*exp(1)^15)*x^2+(5*exp(2)^7*d^7-67*exp(2)^6*d^7*exp(1)^2-613*exp(2)^5*d^7*exp(1)^4+5519*exp(2)^4*d^7*exp(1)^6-15100*exp(2)^3*d^7*exp(1)^8+19216*exp(2)^2*d^7*exp(1)^10-11776*exp(2)*d^7*exp(1)^12+2816*d^7*exp(1)^14)*x-13*exp(2)^6*d^8*exp(1)-97*exp(2)^5*d^8*exp(1)^3+1121*exp(2)^4*d^8*exp(1)^5-3355*exp(2)^3*d^8*exp(1)^7+4504*exp(2)^2*d^8*exp(1)^9-2864*exp(2)*d^8*exp(1)^11+704*d^8*exp(1)^13)/8/exp(2)^7/c^3/(2*exp(1)*d*x+exp(2)*x^2+d^2)^2-(-63*exp(2)^4*d^4*exp(1)^5+306*exp(2)^3*d^4*exp(1)^7-543*exp(2)^2*d^4*exp(1)^9+420*exp(2)*d^4*exp(1)^11-120*d^4*exp(1)^13)/c^3/exp(2)^7*ln(x^2*exp(2)+2*x*d*exp(1)+d^2)-(-3*exp(2)^7*d^5-15*exp(2)^6*d^5*exp(1)^2-225*exp(2)^5*d^5*exp(1)^4+2715*exp(2)^4*d^5*exp(1)^6-8520*exp(2)^3*d^5*exp(1)^8+11808*exp(2)^2*d^5*exp(1)^10-7680*exp(2)*d^5*exp(1)^12+1920*d^5*exp(1)^14)*1/4/c^3/exp(2)^7*1/2/d/sqrt(-exp(1)^2+exp(2))*atan((d*exp(1)+x*exp(2))/d/sqrt(-exp(1)^2+exp(2)))","F(-2)",0
1018,-2,0,0,0.000000," ","integrate((e*x+d)^8/(c*e^2*x^2+2*c*d*e*x+c*d^2)^3,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: (1/3*x^3*c^6*exp(2)^6*exp(1)^8+4*x^2*c^6*exp(2)^6*d*exp(1)^7-3*x^2*c^6*exp(2)^5*d*exp(1)^9+28*x*c^6*exp(2)^6*d^2*exp(1)^6-51*x*c^6*exp(2)^5*d^2*exp(1)^8+24*x*c^6*exp(2)^4*d^2*exp(1)^10)/c^9/exp(2)^9+((3*exp(2)^7*d^4+10*exp(2)^6*d^4*exp(1)^2-445*exp(2)^5*d^4*exp(1)^4+1872*exp(2)^4*d^4*exp(1)^6-3104*exp(2)^3*d^4*exp(1)^8+2304*exp(2)^2*d^4*exp(1)^10-640*exp(2)*d^4*exp(1)^12)*x^3+(9*exp(2)^6*d^5*exp(1)-194*exp(2)^5*d^5*exp(1)^3+233*exp(2)^4*d^5*exp(1)^5+1488*exp(2)^3*d^5*exp(1)^7-4096*exp(2)^2*d^5*exp(1)^9+3712*exp(2)*d^5*exp(1)^11-1152*d^5*exp(1)^13)*x^2+(5*exp(2)^6*d^6-54*exp(2)^5*d^6*exp(1)^2-355*exp(2)^4*d^6*exp(1)^4+2452*exp(2)^3*d^6*exp(1)^6-4800*exp(2)^2*d^6*exp(1)^8+3904*exp(2)*d^6*exp(1)^10-1152*d^6*exp(1)^12)*x-11*exp(2)^5*d^7*exp(1)-60*exp(2)^4*d^7*exp(1)^3+521*exp(2)^3*d^7*exp(1)^5-1106*exp(2)^2*d^7*exp(1)^7+944*exp(2)*d^7*exp(1)^9-288*d^7*exp(1)^11)/8/exp(2)^6/c^3/(2*exp(1)*d*x+exp(2)*x^2+d^2)^2-(-28*exp(2)^3*d^3*exp(1)^5+96*exp(2)^2*d^3*exp(1)^7-108*exp(2)*d^3*exp(1)^9+40*d^3*exp(1)^11)/c^3/exp(2)^6*ln(x^2*exp(2)+2*x*d*exp(1)+d^2)-(-3*exp(2)^6*d^4-10*exp(2)^5*d^4*exp(1)^2-115*exp(2)^4*d^4*exp(1)^4+1040*exp(2)^3*d^4*exp(1)^6-2320*exp(2)^2*d^4*exp(1)^8+2048*exp(2)*d^4*exp(1)^10-640*d^4*exp(1)^12)*1/4/c^3/exp(2)^6*1/2/d/sqrt(-exp(1)^2+exp(2))*atan((d*exp(1)+x*exp(2))/d/sqrt(-exp(1)^2+exp(2)))","F(-2)",0
1019,-2,0,0,0.000000," ","integrate((e*x+d)^7/(c*e^2*x^2+2*c*d*e*x+c*d^2)^3,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: (1/2*x^2*c^3*exp(2)^3*exp(1)^7+7*x*c^3*exp(2)^3*d*exp(1)^6-6*x*c^3*exp(2)^2*d*exp(1)^8)/c^6/exp(2)^6+((3*exp(2)^6*d^3+6*exp(2)^5*d^3*exp(1)^2-229*exp(2)^4*d^3*exp(1)^4+684*exp(2)^3*d^3*exp(1)^6-720*exp(2)^2*d^3*exp(1)^8+256*exp(2)*d^3*exp(1)^10)*x^3+(9*exp(2)^5*d^4*exp(1)-122*exp(2)^4*d^4*exp(1)^3+41*exp(2)^3*d^4*exp(1)^5+696*exp(2)^2*d^4*exp(1)^7-1072*exp(2)*d^4*exp(1)^9+448*d^4*exp(1)^11)*x^2+(5*exp(2)^5*d^5-42*exp(2)^4*d^5*exp(1)^2-187*exp(2)^3*d^5*exp(1)^4+928*exp(2)^2*d^5*exp(1)^6-1152*exp(2)*d^5*exp(1)^8+448*d^5*exp(1)^10)*x-9*exp(2)^4*d^6*exp(1)-34*exp(2)^3*d^6*exp(1)^3+207*exp(2)^2*d^6*exp(1)^5-276*exp(2)*d^6*exp(1)^7+112*d^6*exp(1)^9)/8/exp(2)^5/c^3/(2*exp(1)*d*x+exp(2)*x^2+d^2)^2-(-21*exp(2)^2*d^2*exp(1)^5+45*exp(2)*d^2*exp(1)^7-24*d^2*exp(1)^9)*1/2/c^3/exp(2)^5*ln(x^2*exp(2)+2*x*d*exp(1)+d^2)-(-3*exp(2)^5*d^3-6*exp(2)^4*d^3*exp(1)^2-51*exp(2)^3*d^3*exp(1)^4+324*exp(2)^2*d^3*exp(1)^6-456*exp(2)*d^3*exp(1)^8+192*d^3*exp(1)^10)*1/4/c^3/exp(2)^5*1/2/d/sqrt(-exp(1)^2+exp(2))*atan((d*exp(1)+x*exp(2))/d/sqrt(-exp(1)^2+exp(2)))","F(-2)",0
1020,-2,0,0,0.000000," ","integrate((e*x+d)^6/(c*e^2*x^2+2*c*d*e*x+c*d^2)^3,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: x*exp(1)^6/c^3/exp(2)^3+((3*exp(2)^5*d^2+3*exp(2)^4*d^2*exp(1)^2-102*exp(2)^3*d^2*exp(1)^4+192*exp(2)^2*d^2*exp(1)^6-96*exp(2)*d^2*exp(1)^8)*x^3+(9*exp(2)^4*d^3*exp(1)-71*exp(2)^3*d^3*exp(1)^3-18*exp(2)^2*d^3*exp(1)^5+240*exp(2)*d^3*exp(1)^7-160*d^3*exp(1)^9)*x^2+(5*exp(2)^4*d^4-31*exp(2)^3*d^4*exp(1)^2-86*exp(2)^2*d^4*exp(1)^4+272*exp(2)*d^4*exp(1)^6-160*d^4*exp(1)^8)*x-7*exp(2)^3*d^5*exp(1)-17*exp(2)^2*d^5*exp(1)^3+64*exp(2)*d^5*exp(1)^5-40*d^5*exp(1)^7)/8/exp(2)^4/c^3/(2*exp(1)*d*x+exp(2)*x^2+d^2)^2-(-3*exp(2)*d*exp(1)^5+3*d*exp(1)^7)/c^3/exp(2)^4*ln(x^2*exp(2)+2*x*d*exp(1)+d^2)-(-3*exp(2)^4*d^2-3*exp(2)^3*d^2*exp(1)^2-18*exp(2)^2*d^2*exp(1)^4+72*exp(2)*d^2*exp(1)^6-48*d^2*exp(1)^8)*1/4/c^3/exp(2)^4*1/2/d/sqrt(-exp(1)^2+exp(2))*atan((d*exp(1)+x*exp(2))/d/sqrt(-exp(1)^2+exp(2)))","F(-2)",0
1021,-2,0,0,0.000000," ","integrate((e*x+d)^5/(c*e^2*x^2+2*c*d*e*x+c*d^2)^3,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: exp(1)^5*1/2/c^3/exp(2)^3*ln(x^2*exp(2)+2*x*d*exp(1)+d^2)-(-3*exp(2)^3*d-exp(2)^2*d*exp(1)^2-4*exp(2)*d*exp(1)^4+8*d*exp(1)^6)*1/4/c^3/exp(2)^3*1/2/d/sqrt(-exp(1)^2+exp(2))*atan((d*exp(1)+x*exp(2))/d/sqrt(-exp(1)^2+exp(2)))+((3*exp(2)^4*d+exp(2)^3*exp(1)^2*d-36*exp(2)^2*exp(1)^4*d+32*exp(2)*exp(1)^6*d)*x^3+(9*exp(2)^3*exp(1)*d^2-37*exp(2)^2*exp(1)^3*d^2-20*exp(2)*exp(1)^5*d^2+48*exp(1)^7*d^2)*x^2+(5*exp(2)^3*d^3-21*exp(2)^2*exp(1)^2*d^3-32*exp(2)*exp(1)^4*d^3+48*exp(1)^6*d^3)*x-5*exp(2)^2*exp(1)*d^4-7*exp(2)*exp(1)^3*d^4+12*exp(1)^5*d^4)/8/c^3/exp(2)^3/(2*exp(1)*x*d+exp(2)*x^2+d^2)^2","F(-2)",0
1022,-2,0,0,0.000000," ","integrate((e*x+d)^4/(c*e^2*x^2+2*c*d*e*x+c*d^2)^3,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: (3*x^3*exp(2)^3-8*x^3*exp(2)*exp(1)^4+9*x^2*exp(2)^2*d*exp(1)-16*x^2*exp(2)*d*exp(1)^3-8*x^2*d*exp(1)^5+5*x*exp(2)^2*d^2-12*x*exp(2)*d^2*exp(1)^2-8*x*d^2*exp(1)^4-3*exp(2)*d^3*exp(1)-2*d^3*exp(1)^3)*1/8/c^3/exp(2)^2/(-x^2*exp(2)-2*x*d*exp(1)-d^2)^2+3*1/4/c^3*1/2/d/sqrt(-exp(1)^2+exp(2))*atan((d*exp(1)+x*exp(2))/d/sqrt(-exp(1)^2+exp(2)))","F(-2)",0
1023,-2,0,0,0.000000," ","integrate((e*x+d)^3/(c*e^2*x^2+2*c*d*e*x+c*d^2)^3,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: (3*x^3*exp(2)^2+9*x^2*exp(2)*d*exp(1)-4*x^2*d*exp(1)^3+5*x*exp(2)*d^2-4*x*d^2*exp(1)^2-d^3*exp(1))*1/8/c^3/exp(2)/d/(-x^2*exp(2)-2*x*d*exp(1)-d^2)^2+3*1/4/c^3/d*1/2/d/sqrt(-exp(1)^2+exp(2))*atan((d*exp(1)+x*exp(2))/d/sqrt(-exp(1)^2+exp(2)))","F(-2)",0
1024,-2,0,0,0.000000," ","integrate((e*x+d)^2/(c*e^2*x^2+2*c*d*e*x+c*d^2)^3,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: (-3*x^3*exp(2)^2+2*x^3*exp(2)*exp(1)^2-9*x^2*exp(2)*d*exp(1)+6*x^2*d*exp(1)^3-5*x*exp(2)*d^2+2*x*d^2*exp(1)^2-d^3*exp(1))/(-8*c^3*exp(2)*d^2+8*c^3*d^2*exp(1)^2)/(-x^2*exp(2)-2*x*d*exp(1)-d^2)^2+(3*exp(2)-2*exp(1)^2)*1/2/(4*c^3*exp(2)*d^2-4*c^3*d^2*exp(1)^2)/d/sqrt(-exp(1)^2+exp(2))*atan((d*exp(1)+x*exp(2))/d/sqrt(-exp(1)^2+exp(2)))","F(-2)",0
1025,-2,0,0,0.000000," ","integrate((e*x+d)/(c*e^2*x^2+2*c*d*e*x+c*d^2)^3,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: (-3*x^3*exp(2)^2-9*x^2*exp(2)*d*exp(1)-5*x*exp(2)*d^2-4*x*d^2*exp(1)^2-3*d^3*exp(1))/(-8*c^3*exp(2)*d^3+8*c^3*d^3*exp(1)^2)/(-x^2*exp(2)-2*x*d*exp(1)-d^2)^2-3*exp(2)*1/2/(-4*c^3*exp(2)*d^3+4*c^3*d^3*exp(1)^2)/d/sqrt(-exp(1)^2+exp(2))*atan((d*exp(1)+x*exp(2))/d/sqrt(-exp(1)^2+exp(2)))","F(-2)",0
1026,-2,0,0,0.000000," ","integrate(1/(c*e^2*x^2+2*c*d*e*x+c*d^2)^3,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: (-3*x^3*exp(2)^3-9*x^2*exp(2)^2*d*exp(1)-5*x*exp(2)^2*d^2-4*x*exp(2)*d^2*exp(1)^2-5*exp(2)*d^3*exp(1)+2*d^3*exp(1)^3)/(-8*c^3*exp(2)^2*d^4+16*c^3*exp(2)*d^4*exp(1)^2-8*c^3*d^4*exp(1)^4)/(-x^2*exp(2)-2*x*d*exp(1)-d^2)^2+3*exp(2)^2*1/2/(4*c^3*exp(2)^2*d^4-8*c^3*exp(2)*d^4*exp(1)^2+4*c^3*d^4*exp(1)^4)/d/sqrt(-exp(1)^2+exp(2))*atan((d*exp(1)+x*exp(2))/d/sqrt(-exp(1)^2+exp(2)))","F(-2)",0
1027,-2,0,0,0.000000," ","integrate(1/(e*x+d)/(c*e^2*x^2+2*c*d*e*x+c*d^2)^3,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: exp(1)^6/(c^3*exp(2)^3*d^6*exp(1)-3*c^3*exp(2)^2*d^6*exp(1)^3+3*c^3*exp(2)*d^6*exp(1)^5-c^3*d^6*exp(1)^7)*ln(abs(x*exp(1)+d))-exp(1)^5/(2*c^3*exp(2)^3*d^6-6*c^3*exp(2)^2*d^6*exp(1)^2+6*c^3*exp(2)*d^6*exp(1)^4-2*c^3*d^6*exp(1)^6)*ln(x^2*exp(2)+2*x*d*exp(1)+d^2)+(3*exp(2)^2+4*exp(2)*exp(1)^2+8*exp(1)^4)*1/2/(4*c^3*exp(2)^2*d^5-8*c^3*exp(2)*d^5*exp(1)^2+4*c^3*d^5*exp(1)^4)/d/sqrt(-exp(1)^2+exp(2))*atan((d*exp(1)+x*exp(2))/d/sqrt(-exp(1)^2+exp(2)))+((3*exp(2)^4*d+exp(2)^3*exp(1)^2*d-4*exp(2)^2*exp(1)^4*d)*x^3+(9*exp(2)^3*exp(1)*d^2+7*exp(2)^2*exp(1)^3*d^2-16*exp(2)*exp(1)^5*d^2)*x^2+(5*exp(2)^3*d^3+3*exp(2)^2*exp(1)^2*d^3+8*exp(2)*exp(1)^4*d^3-16*exp(1)^6*d^3)*x+7*exp(2)^2*exp(1)*d^4-3*exp(2)*exp(1)^3*d^4-4*exp(1)^5*d^4)/8/d^6/(exp(2)-exp(1)^2)^3/(x^2*exp(2)+2*x*d*exp(1)+d^2)^2/c^3","F(-2)",0
1028,-2,0,0,0.000000," ","integrate(1/(e*x+d)^2/(c*e^2*x^2+2*c*d*e*x+c*d^2)^3,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: (exp(1)*x+d)^-1/exp(1)*exp(1)^12/(c^3*d^6*exp(1)^12-3*c^3*d^6*exp(1)^10*exp(2)+3*c^3*d^6*exp(1)^8*exp(2)^2-c^3*d^6*exp(1)^6*exp(2)^3)-((96*d^3*exp(1)^12-192*d^3*exp(1)^10*exp(2)+102*d^3*exp(1)^8*exp(2)^2-3*d^3*exp(1)^6*exp(2)^3-3*d^3*exp(1)^4*exp(2)^4)*(-(exp(1)*x+d)^-1/exp(1))^3+(160*d^2*exp(1)^11-368*d^2*exp(1)^9*exp(2)+226*d^2*exp(1)^7*exp(2)^2-9*d^2*exp(1)^5*exp(2)^3-9*d^2*exp(1)^3*exp(2)^4)*(-(exp(1)*x+d)^-1/exp(1))^2-(-160*d*exp(1)^8*exp(2)+176*d*exp(1)^6*exp(2)^2-14*d*exp(1)^4*exp(2)^3-9*d*exp(1)^2*exp(2)^4)*(exp(1)*x+d)^-1/exp(1)+40*exp(1)^5*exp(2)^2-8*exp(1)^3*exp(2)^3-3*exp(1)*exp(2)^4)/8/d^7/(exp(2)-exp(1)^2)^3/((-(exp(1)*x+d)^-1/exp(1))^2*exp(1)^4*d^2-(-(exp(1)*x+d)^-1/exp(1))^2*exp(1)^2*d^2*exp(2)-2*(exp(1)*x+d)^-1/exp(1)*exp(1)^3*d+2*(exp(1)*x+d)^-1/exp(1)*exp(1)*d*exp(2)-exp(2))^2/c^3-3*exp(1)^5/(-c^3*d^7*exp(1)^6+3*c^3*d^7*exp(1)^4*exp(2)-3*c^3*d^7*exp(1)^2*exp(2)^2+c^3*d^7*exp(2)^3)*ln((-(exp(1)*x+d)^-1/exp(1))^2*d^2*exp(1)^4-(-(exp(1)*x+d)^-1/exp(1))^2*d^2*exp(1)^2*exp(2)-2*(exp(1)*x+d)^-1/exp(1)*d*exp(1)^3+2*(exp(1)*x+d)^-1/exp(1)*d*exp(1)*exp(2)-exp(2))+(48*exp(1)^8-24*exp(1)^6*exp(2)-6*exp(1)^4*exp(2)^2-3*exp(1)^2*exp(2)^3)/2/(-4*c^3*d^6*exp(1)^6+12*c^3*d^6*exp(1)^4*exp(2)-12*c^3*d^6*exp(1)^2*exp(2)^2+4*c^3*d^6*exp(2)^3)/d/sqrt(-exp(1)^2+exp(2))/exp(1)^2*atan((-d*(exp(1)*x+d)^-1/exp(1)*exp(1)^3+d*(exp(1)*x+d)^-1/exp(1)*exp(1)*exp(2)+exp(1)^2-exp(2))/sqrt(-exp(1)^2+exp(2))/exp(1))","F(-2)",0
1029,1,61,0,0.239689," ","integrate((e*x+d)^3*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2),x, algorithm=""giac"")","\frac{1}{5} \, {\left(d^{4} e^{\left(-1\right)} + {\left(4 \, d^{3} + {\left(6 \, d^{2} e + {\left(x e^{3} + 4 \, d e^{2}\right)} x\right)} x\right)} x\right)} \sqrt{c x^{2} e^{2} + 2 \, c d x e + c d^{2}}"," ",0,"1/5*(d^4*e^(-1) + (4*d^3 + (6*d^2*e + (x*e^3 + 4*d*e^2)*x)*x)*x)*sqrt(c*x^2*e^2 + 2*c*d*x*e + c*d^2)","B",0
1030,1,51,0,0.300166," ","integrate((e*x+d)^2*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{c x^{2} e^{2} + 2 \, c d x e + c d^{2}} {\left(d^{3} e^{\left(-1\right)} + {\left(3 \, d^{2} + {\left(x e^{2} + 3 \, d e\right)} x\right)} x\right)}"," ",0,"1/4*sqrt(c*x^2*e^2 + 2*c*d*x*e + c*d^2)*(d^3*e^(-1) + (3*d^2 + (x*e^2 + 3*d*e)*x)*x)","A",0
1031,1,41,0,0.227750," ","integrate((e*x+d)*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2),x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{c x^{2} e^{2} + 2 \, c d x e + c d^{2}} {\left(d^{2} e^{\left(-1\right)} + {\left(x e + 2 \, d\right)} x\right)}"," ",0,"1/3*sqrt(c*x^2*e^2 + 2*c*d*x*e + c*d^2)*(d^2*e^(-1) + (x*e + 2*d)*x)","A",0
1032,1,30,0,0.167928," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{c x^{2} e^{2} + 2 \, c d x e + c d^{2}} {\left(d e^{\left(-1\right)} + x\right)}"," ",0,"1/2*sqrt(c*x^2*e^2 + 2*c*d*x*e + c*d^2)*(d*e^(-1) + x)","A",0
1033,-2,0,0,0.000000," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2)/(e*x+d),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: 4*1/4/exp(1)*sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))+2*(-c*d^2*exp(1)^2+c*d^2*exp(2))*2/2/exp(1)^2/d/sqrt(c*exp(1)^2-c*exp(2))*atan((-d*sqrt(c*exp(2))+(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*exp(1))/d/sqrt(c*exp(1)^2-c*exp(2)))","F(-2)",0
1034,1,8,0,0.570446," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2)/(e*x+d)^2,x, algorithm=""giac"")","2 \, C_{0} \sqrt{c} e^{3}"," ",0,"2*C_0*sqrt(c)*e^3","A",0
1035,-2,0,0,0.000000," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2)/(e*x+d)^3,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: 2*(-(-c*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^3*exp(1)^3+2*c*exp(2)*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^3*exp(1)-c*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^2*d*exp(1)^2-2*c*exp(2)*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^2*d+c^2*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*d^2*exp(1)^3+2*c^2*exp(2)*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*d^2*exp(1)-c^2*sqrt(c*exp(2))*d^3*exp(1)^2)/2/exp(1)^2/(-(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^2*exp(1)+2*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*d-c*d^2*exp(1))^2+c/2/d/sqrt(c*exp(1)^2-c*exp(2))*atan((-d*sqrt(c*exp(2))+(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*exp(1))/d/sqrt(c*exp(1)^2-c*exp(2))))","F(-2)",0
1036,-2,0,0,0.000000," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2)/(e*x+d)^4,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: 2*((-3*c*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^5*exp(1)^4+15*c*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^4*d*exp(1)^3-6*c*exp(2)*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^4*d*exp(1)-8*c^2*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^3*d^2*exp(1)^4-2*c^2*exp(2)*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^3*d^2*exp(1)^2+4*c^2*exp(2)^2*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^3*d^2-6*c^2*exp(2)*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^2*d^3*exp(1)+3*c^3*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*d^4*exp(1)^4+6*c^3*exp(2)*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*d^4*exp(1)^2-3*c^3*sqrt(c*exp(2))*d^5*exp(1)^3)/6/d/exp(1)^2/(-(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^2*exp(1)+2*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*d-c*d^2*exp(1))^3+c/d/2/d/sqrt(c*exp(1)^2-c*exp(2))*atan((-d*sqrt(c*exp(2))+(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*exp(1))/d/sqrt(c*exp(1)^2-c*exp(2))))","F(-2)",0
1037,-2,0,0,0.000000," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2)/(e*x+d)^5,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: exp(1)^2*(2*(-(exp(1)*x+d)^-1/exp(1)*(-C_1/exp(1)^2/c+1/6*c*(-(exp(1)*x+d)^-1/exp(1))^2*sign((exp(1)*x+d)^-1)*exp(2)/exp(1)^3/c)+C_0)*sqrt(c*exp(2)-c*d^2*(-(exp(1)*x+d)^-1/exp(1))^2*exp(1)^4+2*c*d*(exp(1)*x+d)^-1/exp(1)*exp(1)^3-2*c*d*(exp(1)*x+d)^-1/exp(1)*exp(1)*exp(2)+c*d^2*(-(exp(1)*x+d)^-1/exp(1))^2*exp(1)^2*exp(2))+2*C_1*sqrt(-c*exp(1)^2+c*exp(2))*ln(abs(-d*sqrt(-c*exp(1)^2+c*exp(2))+((exp(1)*x+d)^-1/exp(1)*sqrt(-c*d^2*exp(1)^4+c*d^2*exp(1)^2*exp(2))+sqrt(c*exp(2)-c*d^2*(-(exp(1)*x+d)^-1/exp(1))^2*exp(1)^4+2*c*d*(exp(1)*x+d)^-1/exp(1)*exp(1)^3-2*c*d*(exp(1)*x+d)^-1/exp(1)*exp(1)*exp(2)+c*d^2*(-(exp(1)*x+d)^-1/exp(1))^2*exp(1)^2*exp(2)))*abs(d)))/(c*exp(1)^3-c*exp(1)*exp(2))/abs(d))","F(-2)",0
1038,-2,0,0,0.000000," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2)/(e*x+d)^6,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: 2*((105*c*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^9*exp(1)^8-60*c*exp(2)*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^9*exp(1)^6-945*c*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^8*d*exp(1)^7+540*c*exp(2)*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^8*d*exp(1)^5+490*c^2*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^7*d^2*exp(1)^8+3010*c^2*exp(2)*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^7*d^2*exp(1)^6-1880*c^2*exp(2)^2*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^7*d^2*exp(1)^4-3430*c^2*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^6*d^3*exp(1)^7-3430*c^2*exp(2)*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^6*d^3*exp(1)^5+3320*c^2*exp(2)^2*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^6*d^3*exp(1)^3-240*c^2*exp(2)^3*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^6*d^3*exp(1)+896*c^3*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^5*d^4*exp(1)^8+7986*c^3*exp(2)*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^5*d^4*exp(1)^6-2364*c^3*exp(2)^2*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^5*d^4*exp(1)^4-944*c^3*exp(2)^3*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^5*d^4*exp(1)^2+96*c^3*exp(2)^4*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^5*d^4-4480*c^3*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^4*d^5*exp(1)^7-2590*c^3*exp(2)*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^4*d^5*exp(1)^5+1640*c^3*exp(2)^2*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^4*d^5*exp(1)^3-240*c^3*exp(2)^3*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^4*d^5*exp(1)+790*c^4*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^3*d^6*exp(1)^8+2710*c^4*exp(2)*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^3*d^6*exp(1)^6-200*c^4*exp(2)^2*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^3*d^6*exp(1)^4+480*c^4*exp(2)^3*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^3*d^6*exp(1)^2-450*c^4*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^2*d^7*exp(1)^7-450*c^4*exp(2)*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^2*d^7*exp(1)^5-720*c^4*exp(2)^2*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^2*d^7*exp(1)^3-105*c^5*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*d^8*exp(1)^8-30*c^5*exp(2)*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*d^8*exp(1)^6+540*c^5*exp(2)^2*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*d^8*exp(1)^4+105*c^5*sqrt(c*exp(2))*d^9*exp(1)^7-150*c^5*exp(2)*sqrt(c*exp(2))*d^9*exp(1)^5)/(-120*d^3*exp(1)^4+120*exp(2)*d^3*exp(1)^2)/(-(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^2*exp(1)+2*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*d-c*d^2*exp(1))^5+(7*c*exp(1)^2-4*c*exp(2))/2/(4*d^3*exp(1)^2-4*exp(2)*d^3)/d/sqrt(c*exp(1)^2-c*exp(2))*atan((-d*sqrt(c*exp(2))+(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*exp(1))/d/sqrt(c*exp(1)^2-c*exp(2))))","F(-2)",0
1039,1,88,0,0.270678," ","integrate((e*x+d)^3*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2),x, algorithm=""giac"")","\frac{1}{7} \, {\left(c d^{6} e^{\left(-1\right)} + {\left(6 \, c d^{5} + {\left(15 \, c d^{4} e + {\left(20 \, c d^{3} e^{2} + {\left(15 \, c d^{2} e^{3} + {\left(c x e^{5} + 6 \, c d e^{4}\right)} x\right)} x\right)} x\right)} x\right)} x\right)} \sqrt{c x^{2} e^{2} + 2 \, c d x e + c d^{2}}"," ",0,"1/7*(c*d^6*e^(-1) + (6*c*d^5 + (15*c*d^4*e + (20*c*d^3*e^2 + (15*c*d^2*e^3 + (c*x*e^5 + 6*c*d*e^4)*x)*x)*x)*x)*x)*sqrt(c*x^2*e^2 + 2*c*d*x*e + c*d^2)","B",0
1040,1,77,0,0.262970," ","integrate((e*x+d)^2*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2),x, algorithm=""giac"")","\frac{1}{6} \, {\left(c d^{5} e^{\left(-1\right)} + {\left(5 \, c d^{4} + {\left(10 \, c d^{3} e + {\left(10 \, c d^{2} e^{2} + {\left(c x e^{4} + 5 \, c d e^{3}\right)} x\right)} x\right)} x\right)} x\right)} \sqrt{c x^{2} e^{2} + 2 \, c d x e + c d^{2}}"," ",0,"1/6*(c*d^5*e^(-1) + (5*c*d^4 + (10*c*d^3*e + (10*c*d^2*e^2 + (c*x*e^4 + 5*c*d*e^3)*x)*x)*x)*x)*sqrt(c*x^2*e^2 + 2*c*d*x*e + c*d^2)","B",0
1041,1,66,0,0.252840," ","integrate((e*x+d)*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2),x, algorithm=""giac"")","\frac{1}{5} \, {\left(c d^{4} e^{\left(-1\right)} + {\left(4 \, c d^{3} + {\left(6 \, c d^{2} e + {\left(c x e^{3} + 4 \, c d e^{2}\right)} x\right)} x\right)} x\right)} \sqrt{c x^{2} e^{2} + 2 \, c d x e + c d^{2}}"," ",0,"1/5*(c*d^4*e^(-1) + (4*c*d^3 + (6*c*d^2*e + (c*x*e^3 + 4*c*d*e^2)*x)*x)*x)*sqrt(c*x^2*e^2 + 2*c*d*x*e + c*d^2)","B",0
1042,1,55,0,0.243325," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2),x, algorithm=""giac"")","\frac{1}{4} \, {\left(c d^{3} e^{\left(-1\right)} + {\left(3 \, c d^{2} + {\left(c x e^{2} + 3 \, c d e\right)} x\right)} x\right)} \sqrt{c x^{2} e^{2} + 2 \, c d x e + c d^{2}}"," ",0,"1/4*(c*d^3*e^(-1) + (3*c*d^2 + (c*x*e^2 + 3*c*d*e)*x)*x)*sqrt(c*x^2*e^2 + 2*c*d*x*e + c*d^2)","A",0
1043,-2,0,0,0.000000," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2)/(e*x+d),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: 2*((16*c*exp(1)^4*1/96/exp(1)^3*x+32*c*exp(1)^3*d*1/96/exp(1)^3)*x+16*c*exp(1)^2*d^2*1/96/exp(1)^3)*sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))+2*(c^2*d^4*exp(1)^4-2*c^2*d^4*exp(1)^2*exp(2)+c^2*d^4*exp(2)^2)*2/2/exp(1)^4/d/sqrt(c*exp(1)^2-c*exp(2))*atan((-d*sqrt(c*exp(2))+(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*exp(1))/d/sqrt(c*exp(1)^2-c*exp(2)))","F(-2)",0
1044,-2,0,0,0.000000," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2)/(e*x+d)^2,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]Evaluation time: 73.76Polynomial exponent overflow. Error: Bad Argument Value","F(-2)",0
1045,-2,0,0,0.000000," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2)/(e*x+d)^3,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: 4*c*1/4/exp(1)*sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))+2*(-(5*c^2*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^3*d^2*exp(1)^5-11*c^2*exp(2)*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^3*d^2*exp(1)^3+6*c^2*exp(2)^2*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^3*d^2*exp(1)-7*c^2*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^2*d^3*exp(1)^4+17*c^2*exp(2)*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^2*d^3*exp(1)^2-10*c^2*exp(2)^2*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^2*d^3+3*c^3*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*d^4*exp(1)^5-9*c^3*exp(2)*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*d^4*exp(1)^3+6*c^3*exp(2)^2*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*d^4*exp(1)+c^3*sqrt(c*exp(2))*d^5*exp(1)^4-c^3*exp(2)*sqrt(c*exp(2))*d^5*exp(1)^2)/2/exp(1)^4/(-(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^2*exp(1)+2*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*d-c*d^2*exp(1))^2+(3*c^2*d^2*exp(1)^4-9*c^2*exp(2)*d^2*exp(1)^2+6*c^2*exp(2)^2*d^2)/2/exp(1)^4/d/sqrt(c*exp(1)^2-c*exp(2))*atan((-d*sqrt(c*exp(2))+(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*exp(1))/d/sqrt(c*exp(1)^2-c*exp(2))))","F(-2)",0
1046,-2,0,0,0.000000," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2)/(e*x+d)^4,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: 2*(-c*sqrt(c*exp(2))/2/exp(2)*ln(abs(exp(2)*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)-sqrt(c*exp(2))*exp(1)*d))+(c^2*exp(1)^4*d+c^2*exp(2)*exp(1)^2*d-2*c^2*exp(2)^2*d)/2/exp(1)^4/d/sqrt(c*exp(1)^2-c*exp(2))*atan((-d*sqrt(c*exp(2))+(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*exp(1))/d/sqrt(c*exp(1)^2-c*exp(2)))+(3*c^2*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^5*exp(1)^6*d-21*c^2*exp(2)*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^5*exp(1)^4*d+18*c^2*exp(2)^2*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^5*exp(1)^2*d+9*c^2*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^4*exp(1)^5*d^2+45*c^2*exp(2)*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^4*exp(1)^3*d^2-54*c^2*exp(2)^2*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^4*exp(1)*d^2-8*c^3*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^3*exp(1)^6*d^3-42*c^3*exp(2)*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^3*exp(1)^4*d^3+6*c^3*exp(2)^2*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^3*exp(1)^2*d^3+44*c^3*exp(2)^3*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^3*d^3+24*c^3*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^2*exp(1)^5*d^4+30*c^3*exp(2)*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^2*exp(1)^3*d^4-54*c^3*exp(2)^2*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^2*exp(1)*d^4-3*c^4*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*exp(1)^6*d^5-21*c^4*exp(2)*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*exp(1)^4*d^5+24*c^4*exp(2)^2*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*exp(1)^2*d^5+3*c^4*sqrt(c*exp(2))*exp(1)^5*d^6-3*c^4*exp(2)*sqrt(c*exp(2))*exp(1)^3*d^6)/6/exp(1)^4/((sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^2*exp(1)-2*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*d+c*exp(1)*d^2)^3)","F(-2)",0
1047,-2,0,0,0.000000," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2)/(e*x+d)^5,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: exp(1)^2*(2*(-(exp(1)*x+d)^-1/exp(1)*(-C_1/exp(1)^2/c+1/2*c^2*sign((exp(1)*x+d)^-1)/exp(1)^3/c)+C_0)*sqrt(c*exp(2)-c*d^2*(-(exp(1)*x+d)^-1/exp(1))^2*exp(1)^4+2*c*d*(exp(1)*x+d)^-1/exp(1)*exp(1)^3-2*c*d*(exp(1)*x+d)^-1/exp(1)*exp(1)*exp(2)+c*d^2*(-(exp(1)*x+d)^-1/exp(1))^2*exp(1)^2*exp(2))+2*C_1*sqrt(-c*exp(1)^2+c*exp(2))*ln(abs(-d*sqrt(-c*exp(1)^2+c*exp(2))+((exp(1)*x+d)^-1/exp(1)*sqrt(-c*d^2*exp(1)^4+c*d^2*exp(1)^2*exp(2))+sqrt(c*exp(2)-c*d^2*(-(exp(1)*x+d)^-1/exp(1))^2*exp(1)^4+2*c*d*(exp(1)*x+d)^-1/exp(1)*exp(1)^3-2*c*d*(exp(1)*x+d)^-1/exp(1)*exp(1)*exp(2)+c*d^2*(-(exp(1)*x+d)^-1/exp(1))^2*exp(1)^2*exp(2)))*abs(d)))/(c*exp(1)^3-c*exp(1)*exp(2))/abs(d))","F(-2)",0
1048,-2,0,0,0.000000," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2)/(e*x+d)^6,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: 2*(-(15*c^2*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^9*exp(1)^8-135*c^2*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^8*d*exp(1)^7+40*c^2*exp(2)^2*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^8*d*exp(1)^3+70*c^3*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^7*d^2*exp(1)^8+470*c^3*exp(2)*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^7*d^2*exp(1)^6-240*c^3*exp(2)^2*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^7*d^2*exp(1)^4-80*c^3*exp(2)^3*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^7*d^2*exp(1)^2-490*c^3*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^6*d^3*exp(1)^7-130*c^3*exp(2)*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^6*d^3*exp(1)^5+400*c^3*exp(2)^2*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^6*d^3*exp(1)^3+80*c^3*exp(2)^3*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^6*d^3*exp(1)+128*c^4*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^5*d^4*exp(1)^8+318*c^4*exp(2)*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^5*d^4*exp(1)^6-492*c^4*exp(2)^2*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^5*d^4*exp(1)^4-272*c^4*exp(2)^3*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^5*d^4*exp(1)^2-32*c^4*exp(2)^4*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^5*d^4+430*c^4*exp(2)*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^4*d^5*exp(1)^5+400*c^4*exp(2)^2*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^4*d^5*exp(1)^3+80*c^4*exp(2)^3*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^4*d^5*exp(1)-70*c^5*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^3*d^6*exp(1)^8-430*c^5*exp(2)*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^3*d^6*exp(1)^6-400*c^5*exp(2)^2*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^3*d^6*exp(1)^4-80*c^5*exp(2)^3*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^3*d^6*exp(1)^2+210*c^5*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^2*d^7*exp(1)^7+330*c^5*exp(2)*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^2*d^7*exp(1)^5+40*c^5*exp(2)^2*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^2*d^7*exp(1)^3-15*c^6*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*d^8*exp(1)^8-150*c^6*exp(2)*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*d^8*exp(1)^6-20*c^6*exp(2)^2*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*d^8*exp(1)^4+15*c^6*sqrt(c*exp(2))*d^9*exp(1)^7+10*c^6*exp(2)*sqrt(c*exp(2))*d^9*exp(1)^5)/40/d/exp(1)^4/(-(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^2*exp(1)+2*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*d-c*d^2*exp(1))^5+3*c^2/4/d/2/d/sqrt(c*exp(1)^2-c*exp(2))*atan((-d*sqrt(c*exp(2))+(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*exp(1))/d/sqrt(c*exp(1)^2-c*exp(2))))","F(-2)",0
1049,-2,0,0,0.000000," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2)/(e*x+d)^7,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: 2*((-105*c^2*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^11*exp(1)^11+90*c^2*exp(2)*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^11*exp(1)^9+1155*c^2*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^10*d*exp(1)^10-990*c^2*exp(2)*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^10*d*exp(1)^8-595*c^3*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^9*d^2*exp(1)^11-4670*c^3*exp(2)*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^9*d^2*exp(1)^9+4440*c^3*exp(2)^2*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^9*d^2*exp(1)^7+320*c^3*exp(2)^3*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^9*d^2*exp(1)^5-320*c^3*exp(2)^4*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^9*d^2*exp(1)^3+5355*c^3*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^8*d^3*exp(1)^10+7380*c^3*exp(2)*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^8*d^3*exp(1)^8-12660*c^3*exp(2)^2*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^8*d^3*exp(1)^6+1920*c^3*exp(2)^3*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^8*d^3*exp(1)^4+480*c^3*exp(2)^4*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^8*d^3*exp(1)^2-1386*c^4*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^7*d^4*exp(1)^11-17460*c^4*exp(2)*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^7*d^4*exp(1)^9+9240*c^4*exp(2)^2*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^7*d^4*exp(1)^7+7920*c^4*exp(2)^3*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^7*d^4*exp(1)^5-2880*c^4*exp(2)^4*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^7*d^4*exp(1)^3-384*c^4*exp(2)^5*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^7*d^4*exp(1)+9702*c^4*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^6*d^5*exp(1)^10+8180*c^4*exp(2)*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^6*d^5*exp(1)^8-14840*c^4*exp(2)^2*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^6*d^5*exp(1)^6+2160*c^4*exp(2)^3*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^6*d^5*exp(1)^4+1600*c^4*exp(2)^4*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^6*d^5*exp(1)^2+128*c^4*exp(2)^5*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^6*d^5-1686*c^5*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^5*d^6*exp(1)^11-8340*c^5*exp(2)*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^5*d^6*exp(1)^9+6120*c^5*exp(2)^2*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^5*d^6*exp(1)^7+240*c^5*exp(2)^3*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^5*d^6*exp(1)^5-2880*c^5*exp(2)^4*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^5*d^6*exp(1)^3-384*c^5*exp(2)^5*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^5*d^6*exp(1)+750*c^5*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^4*d^7*exp(1)^10-1560*c^5*exp(2)*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^4*d^7*exp(1)^8+1440*c^5*exp(2)^2*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^4*d^7*exp(1)^6+3840*c^5*exp(2)^3*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^4*d^7*exp(1)^4+480*c^5*exp(2)^4*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^4*d^7*exp(1)^2+595*c^6*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^3*d^8*exp(1)^11+3290*c^6*exp(2)*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^3*d^8*exp(1)^9-1320*c^6*exp(2)^2*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^3*d^8*exp(1)^7-4720*c^6*exp(2)^3*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^3*d^8*exp(1)^5-320*c^6*exp(2)^4*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^3*d^8*exp(1)^3-1785*c^6*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^2*d^9*exp(1)^10-1350*c^6*exp(2)*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^2*d^9*exp(1)^8+3720*c^6*exp(2)^2*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^2*d^9*exp(1)^6+240*c^6*exp(2)^3*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^2*d^9*exp(1)^4+105*c^7*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*d^10*exp(1)^11+1170*c^7*exp(2)*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*d^10*exp(1)^9-1200*c^7*exp(2)^2*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*d^10*exp(1)^7-240*c^7*exp(2)^3*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*d^10*exp(1)^5-105*c^7*sqrt(c*exp(2))*d^11*exp(1)^10+20*c^7*exp(2)*sqrt(c*exp(2))*d^11*exp(1)^8+100*c^7*exp(2)^2*sqrt(c*exp(2))*d^11*exp(1)^6)/(-240*d^2*exp(1)^6+240*exp(2)*d^2*exp(1)^4)/(-(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^2*exp(1)+2*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*d-c*d^2*exp(1))^6+(7*c^2*exp(1)^2-6*c^2*exp(2))/2/(8*d^2*exp(1)^2-8*exp(2)*d^2)/d/sqrt(c*exp(1)^2-c*exp(2))*atan((-d*sqrt(c*exp(2))+(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*exp(1))/d/sqrt(c*exp(1)^2-c*exp(2))))","F(-2)",0
1050,1,128,0,0.302273," ","integrate((e*x+d)^3*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2),x, algorithm=""giac"")","\frac{1}{9} \, {\left(c^{2} d^{8} e^{\left(-1\right)} + {\left(8 \, c^{2} d^{7} + {\left(28 \, c^{2} d^{6} e + {\left(56 \, c^{2} d^{5} e^{2} + {\left(70 \, c^{2} d^{4} e^{3} + {\left(56 \, c^{2} d^{3} e^{4} + {\left(28 \, c^{2} d^{2} e^{5} + {\left(c^{2} x e^{7} + 8 \, c^{2} d e^{6}\right)} x\right)} x\right)} x\right)} x\right)} x\right)} x\right)} x\right)} \sqrt{c x^{2} e^{2} + 2 \, c d x e + c d^{2}}"," ",0,"1/9*(c^2*d^8*e^(-1) + (8*c^2*d^7 + (28*c^2*d^6*e + (56*c^2*d^5*e^2 + (70*c^2*d^4*e^3 + (56*c^2*d^3*e^4 + (28*c^2*d^2*e^5 + (c^2*x*e^7 + 8*c^2*d*e^6)*x)*x)*x)*x)*x)*x)*x)*sqrt(c*x^2*e^2 + 2*c*d*x*e + c*d^2)","B",0
1051,1,115,0,0.305489," ","integrate((e*x+d)^2*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2),x, algorithm=""giac"")","\frac{1}{8} \, {\left(c^{2} d^{7} e^{\left(-1\right)} + {\left(7 \, c^{2} d^{6} + {\left(21 \, c^{2} d^{5} e + {\left(35 \, c^{2} d^{4} e^{2} + {\left(35 \, c^{2} d^{3} e^{3} + {\left(21 \, c^{2} d^{2} e^{4} + {\left(c^{2} x e^{6} + 7 \, c^{2} d e^{5}\right)} x\right)} x\right)} x\right)} x\right)} x\right)} x\right)} \sqrt{c x^{2} e^{2} + 2 \, c d x e + c d^{2}}"," ",0,"1/8*(c^2*d^7*e^(-1) + (7*c^2*d^6 + (21*c^2*d^5*e + (35*c^2*d^4*e^2 + (35*c^2*d^3*e^3 + (21*c^2*d^2*e^4 + (c^2*x*e^6 + 7*c^2*d*e^5)*x)*x)*x)*x)*x)*x)*sqrt(c*x^2*e^2 + 2*c*d*x*e + c*d^2)","B",0
1052,1,102,0,0.281401," ","integrate((e*x+d)*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2),x, algorithm=""giac"")","\frac{1}{7} \, {\left(c^{2} d^{6} e^{\left(-1\right)} + {\left(6 \, c^{2} d^{5} + {\left(15 \, c^{2} d^{4} e + {\left(20 \, c^{2} d^{3} e^{2} + {\left(15 \, c^{2} d^{2} e^{3} + {\left(c^{2} x e^{5} + 6 \, c^{2} d e^{4}\right)} x\right)} x\right)} x\right)} x\right)} x\right)} \sqrt{c x^{2} e^{2} + 2 \, c d x e + c d^{2}}"," ",0,"1/7*(c^2*d^6*e^(-1) + (6*c^2*d^5 + (15*c^2*d^4*e + (20*c^2*d^3*e^2 + (15*c^2*d^2*e^3 + (c^2*x*e^5 + 6*c^2*d*e^4)*x)*x)*x)*x)*x)*sqrt(c*x^2*e^2 + 2*c*d*x*e + c*d^2)","B",0
1053,1,89,0,0.253594," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2),x, algorithm=""giac"")","\frac{1}{6} \, {\left(c^{2} d^{5} e^{\left(-1\right)} + {\left(5 \, c^{2} d^{4} + {\left(10 \, c^{2} d^{3} e + {\left(10 \, c^{2} d^{2} e^{2} + {\left(c^{2} x e^{4} + 5 \, c^{2} d e^{3}\right)} x\right)} x\right)} x\right)} x\right)} \sqrt{c x^{2} e^{2} + 2 \, c d x e + c d^{2}}"," ",0,"1/6*(c^2*d^5*e^(-1) + (5*c^2*d^4 + (10*c^2*d^3*e + (10*c^2*d^2*e^2 + (c^2*x*e^4 + 5*c^2*d*e^3)*x)*x)*x)*x)*sqrt(c*x^2*e^2 + 2*c*d*x*e + c*d^2)","B",0
1054,-2,0,0,0.000000," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2)/(e*x+d),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: 2*((((192*c^2*exp(1)^10*1/1920/exp(1)^7*x+768*c^2*exp(1)^9*d*1/1920/exp(1)^7)*x+1152*c^2*exp(1)^8*d^2*1/1920/exp(1)^7)*x+768*c^2*exp(1)^7*d^3*1/1920/exp(1)^7)*x+192*c^2*exp(1)^6*d^4*1/1920/exp(1)^7)*sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))+2*(-c^3*d^6*exp(1)^6+3*c^3*d^6*exp(1)^4*exp(2)-3*c^3*d^6*exp(1)^2*exp(2)^2+c^3*d^6*exp(2)^3)*2/2/exp(1)^6/d/sqrt(c*exp(1)^2-c*exp(2))*atan((-d*sqrt(c*exp(2))+(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*exp(1))/d/sqrt(c*exp(1)^2-c*exp(2)))","F(-2)",0
1055,-1,0,0,0.000000," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2)/(e*x+d)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1056,-2,0,0,0.000000," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2)/(e*x+d)^3,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: 2*((16*c^2*exp(1)^4*1/96/exp(1)^3*x+32*c^2*exp(1)^3*d*1/96/exp(1)^3)*x+16*c^2*exp(1)^2*d^2*1/96/exp(1)^3)*sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))+2*(-(-9*c^3*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^3*d^4*exp(1)^7+28*c^3*exp(2)*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^3*d^4*exp(1)^5-29*c^3*exp(2)^2*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^3*d^4*exp(1)^3+10*c^3*exp(2)^3*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^3*d^4*exp(1)+15*c^3*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^2*d^5*exp(1)^6-48*c^3*exp(2)*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^2*d^5*exp(1)^4+51*c^3*exp(2)^2*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^2*d^5*exp(1)^2-18*c^3*exp(2)^3*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^2*d^5-7*c^4*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*d^6*exp(1)^7+24*c^4*exp(2)*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*d^6*exp(1)^5-27*c^4*exp(2)^2*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*d^6*exp(1)^3+10*c^4*exp(2)^3*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*d^6*exp(1)-c^4*sqrt(c*exp(2))*d^7*exp(1)^6+2*c^4*exp(2)*sqrt(c*exp(2))*d^7*exp(1)^4-c^4*exp(2)^2*sqrt(c*exp(2))*d^7*exp(1)^2)/2/exp(1)^6/(-(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^2*exp(1)+2*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*d-c*d^2*exp(1))^2+(-15*c^3*d^4*exp(1)^6+50*c^3*exp(2)*d^4*exp(1)^4-55*c^3*exp(2)^2*d^4*exp(1)^2+20*c^3*exp(2)^3*d^4)/2/exp(1)^6/d/sqrt(c*exp(1)^2-c*exp(2))*atan((-d*sqrt(c*exp(2))+(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*exp(1))/d/sqrt(c*exp(1)^2-c*exp(2))))","F(-2)",0
1057,-2,0,0,0.000000," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2)/(e*x+d)^4,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: 2*(2*c^2*exp(1)*1/8/exp(1)*x+2*c^2*d*1/8/exp(1))*sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))+2*((33*c^3*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^5*d^3*exp(1)^8-126*c^3*exp(2)*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^5*d^3*exp(1)^6+153*c^3*exp(2)^2*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^5*d^3*exp(1)^4-60*c^3*exp(2)^3*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^5*d^3*exp(1)^2-93*c^3*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^4*d^4*exp(1)^7+396*c^3*exp(2)*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^4*d^4*exp(1)^5-513*c^3*exp(2)^2*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^4*d^4*exp(1)^3+210*c^3*exp(2)^3*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^4*d^4*exp(1)+40*c^4*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^3*d^5*exp(1)^8-130*c^4*exp(2)*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^3*d^5*exp(1)^6-48*c^4*exp(2)^2*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^3*d^5*exp(1)^4+326*c^4*exp(2)^3*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^3*d^5*exp(1)^2-188*c^4*exp(2)^4*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^3*d^5-48*c^4*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^2*d^6*exp(1)^7+306*c^4*exp(2)*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^2*d^6*exp(1)^5-468*c^4*exp(2)^2*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^2*d^6*exp(1)^3+210*c^4*exp(2)^3*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^2*d^6*exp(1)+15*c^5*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*d^7*exp(1)^8-108*c^5*exp(2)*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*d^7*exp(1)^6+171*c^5*exp(2)^2*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*d^7*exp(1)^4-78*c^5*exp(2)^3*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*d^7*exp(1)^2+9*c^5*sqrt(c*exp(2))*d^8*exp(1)^7-18*c^5*exp(2)*sqrt(c*exp(2))*d^8*exp(1)^5+9*c^5*exp(2)^2*sqrt(c*exp(2))*d^8*exp(1)^3)/6/exp(1)^6/(-(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^2*exp(1)+2*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*d-c*d^2*exp(1))^3+(5*c^3*d^3*exp(1)^6-30*c^3*exp(2)*d^3*exp(1)^4+45*c^3*exp(2)^2*d^3*exp(1)^2-20*c^3*exp(2)^3*d^3)/2/exp(1)^6/d/sqrt(c*exp(1)^2-c*exp(2))*atan((-d*sqrt(c*exp(2))+(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*exp(1))/d/sqrt(c*exp(1)^2-c*exp(2))))","F(-2)",0
1058,-2,0,0,0.000000," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2)/(e*x+d)^5,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]Evaluation time: 0.87Unable to divide, perhaps due to rounding error%%%{%%%{1,[0,12,0]%%%}+%%%{-2,[0,10,1]%%%}+%%%{1,[0,8,2]%%%},[4,0,0,4,0]%%%}+%%%{%%%{2,[0,10,1]%%%}+%%%{-2,[0,8,2]%%%},[4,0,0,2,2]%%%}+%%%{%%%{1,[0,8,2]%%%},[4,0,0,0,4]%%%}+%%%{%%%{-2,[1,12,1]%%%}+%%%{4,[1,10,2]%%%}+%%%{-2,[1,8,3]%%%},[2,0,0,4,0]%%%}+%%%{%%%{-4,[1,10,2]%%%}+%%%{4,[1,8,3]%%%},[2,0,0,2,2]%%%}+%%%{%%%{-2,[1,8,3]%%%},[2,0,0,0,4]%%%}+%%%{%%%{1,[2,12,2]%%%}+%%%{-2,[2,10,3]%%%}+%%%{1,[2,8,4]%%%},[0,0,0,4,0]%%%}+%%%{%%%{2,[2,10,3]%%%}+%%%{-2,[2,8,4]%%%},[0,0,0,2,2]%%%}+%%%{%%%{1,[2,8,4]%%%},[0,0,0,0,4]%%%} / %%%{%%%{-1,[1,2,0]%%%}+%%%{1,[1,0,1]%%%},[4,0,0,0,0]%%%}+%%%{%%%{2,[2,2,1]%%%}+%%%{-2,[2,0,2]%%%},[2,0,0,0,0]%%%}+%%%{%%%{-1,[3,2,2]%%%}+%%%{1,[3,0,3]%%%},[0,0,0,0,0]%%%} Error: Bad Argument Value","F(-2)",0
1059,-2,0,0,0.000000," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2)/(e*x+d)^6,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: 2*(-c^2*sqrt(c*exp(2))/2/exp(2)*ln(abs(exp(2)*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)-sqrt(c*exp(2))*exp(1)*d))+(3*c^3*exp(1)^6*d+c^3*exp(2)*exp(1)^4*d+4*c^3*exp(2)^2*exp(1)^2*d-8*c^3*exp(2)^3*d)/4/exp(1)^6/2/d/sqrt(c*exp(1)^2-c*exp(2))*atan((-d*sqrt(c*exp(2))+(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*exp(1))/d/sqrt(c*exp(1)^2-c*exp(2)))+(45*c^3*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^9*exp(1)^10*d+15*c^3*exp(2)*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^9*exp(1)^8*d-660*c^3*exp(2)^2*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^9*exp(1)^6*d+600*c^3*exp(2)^3*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^9*exp(1)^4*d-405*c^3*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^8*exp(1)^9*d^2+1305*c^3*exp(2)*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^8*exp(1)^7*d^2+2700*c^3*exp(2)^2*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^8*exp(1)^5*d^2-3600*c^3*exp(2)^3*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^8*exp(1)^3*d^2+210*c^4*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^7*exp(1)^10*d^3-760*c^4*exp(2)*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^7*exp(1)^8*d^3-5250*c^4*exp(2)^2*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^7*exp(1)^6*d^3-3000*c^4*exp(2)^3*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^7*exp(1)^4*d^3+8800*c^4*exp(2)^4*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^7*exp(1)^2*d^3+450*c^4*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^6*exp(1)^9*d^4+5200*c^4*exp(2)*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^6*exp(1)^7*d^4+9750*c^4*exp(2)^2*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^6*exp(1)^5*d^4-5400*c^4*exp(2)^3*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^6*exp(1)^3*d^4-10000*c^4*exp(2)^4*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^6*exp(1)*d^4-384*c^5*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^5*exp(1)^10*d^5-3590*c^5*exp(2)*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^5*exp(1)^8*d^5-9670*c^5*exp(2)^2*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^5*exp(1)^6*d^5-6180*c^5*exp(2)^3*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^5*exp(1)^4*d^5+15440*c^5*exp(2)^4*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^5*exp(1)^2*d^5+4384*c^5*exp(2)^5*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^5*d^5+1920*c^5*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^4*exp(1)^9*d^6+6250*c^5*exp(2)*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^4*exp(1)^7*d^6+8910*c^5*exp(2)^2*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^4*exp(1)^5*d^6-7080*c^5*exp(2)^3*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^4*exp(1)^3*d^6-10000*c^5*exp(2)^4*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^4*exp(1)*d^6-210*c^6*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^3*exp(1)^10*d^7-3280*c^6*exp(2)*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^3*exp(1)^8*d^7-4950*c^6*exp(2)^2*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^3*exp(1)^6*d^7-840*c^6*exp(2)^3*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^3*exp(1)^4*d^7+9280*c^6*exp(2)^4*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^3*exp(1)^2*d^7+630*c^6*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^2*exp(1)^9*d^8+2160*c^6*exp(2)*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^2*exp(1)^7*d^8+1530*c^6*exp(2)^2*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^2*exp(1)^5*d^8-4320*c^6*exp(2)^3*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^2*exp(1)^3*d^8-45*c^7*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*exp(1)^10*d^9-465*c^7*exp(2)*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*exp(1)^8*d^9-510*c^7*exp(2)^2*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*exp(1)^6*d^9+1020*c^7*exp(2)^3*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*exp(1)^4*d^9+45*c^7*sqrt(c*exp(2))*exp(1)^9*d^10+45*c^7*exp(2)*sqrt(c*exp(2))*exp(1)^7*d^10-90*c^7*exp(2)^2*sqrt(c*exp(2))*exp(1)^5*d^10)/120/exp(1)^6/((sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^2*exp(1)-2*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*d+c*exp(1)*d^2)^5)","F(-2)",0
1060,-2,0,0,0.000000," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2)/(e*x+d)^7,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: 2*(-(-15*c^3*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^11*exp(1)^11+48*c^3*exp(2)^3*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^11*exp(1)^5+165*c^3*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^10*d*exp(1)^10-288*c^3*exp(2)^2*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^10*d*exp(1)^6-240*c^3*exp(2)^3*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^10*d*exp(1)^4-85*c^4*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^9*d^2*exp(1)^11-740*c^4*exp(2)*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^9*d^2*exp(1)^9+960*c^4*exp(2)^2*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^9*d^2*exp(1)^7+1040*c^4*exp(2)^3*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^9*d^2*exp(1)^5+640*c^4*exp(2)^4*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^9*d^2*exp(1)^3+765*c^4*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^8*d^3*exp(1)^10-210*c^4*exp(2)*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^8*d^3*exp(1)^8-2880*c^4*exp(2)^2*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^8*d^3*exp(1)^6-2160*c^4*exp(2)^3*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^8*d^3*exp(1)^4-960*c^4*exp(2)^4*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^8*d^3*exp(1)^2-198*c^5*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^7*d^4*exp(1)^11-360*c^5*exp(2)*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^7*d^4*exp(1)^9+3480*c^5*exp(2)^2*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^7*d^4*exp(1)^7+4320*c^5*exp(2)^3*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^7*d^4*exp(1)^5+2880*c^5*exp(2)^4*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^7*d^4*exp(1)^3+768*c^5*exp(2)^5*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^7*d^4*exp(1)-150*c^5*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^6*d^5*exp(1)^10-2800*c^5*exp(2)*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^6*d^5*exp(1)^8-5480*c^5*exp(2)^2*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^6*d^5*exp(1)^6-4320*c^5*exp(2)^3*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^6*d^5*exp(1)^4-2240*c^5*exp(2)^4*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^6*d^5*exp(1)^2-256*c^5*exp(2)^5*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^6*d^5+198*c^6*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^5*d^6*exp(1)^11+2160*c^6*exp(2)*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^5*d^6*exp(1)^9+4920*c^6*exp(2)^2*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^5*d^6*exp(1)^7+4320*c^6*exp(2)^3*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^5*d^6*exp(1)^5+2880*c^6*exp(2)^4*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^5*d^6*exp(1)^3+768*c^6*exp(2)^5*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^5*d^6*exp(1)-990*c^6*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^4*d^7*exp(1)^10-3540*c^6*exp(2)*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^4*d^7*exp(1)^8-3240*c^6*exp(2)^2*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^4*d^7*exp(1)^6-2160*c^6*exp(2)^3*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^4*d^7*exp(1)^4-960*c^6*exp(2)^4*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^4*d^7*exp(1)^2+85*c^7*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^3*d^8*exp(1)^11+1640*c^7*exp(2)*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^3*d^8*exp(1)^9+2040*c^7*exp(2)^2*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^3*d^8*exp(1)^7+1040*c^7*exp(2)^3*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^3*d^8*exp(1)^5+640*c^7*exp(2)^4*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^3*d^8*exp(1)^3-255*c^7*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^2*d^9*exp(1)^10-960*c^7*exp(2)*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^2*d^9*exp(1)^8-360*c^7*exp(2)^2*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^2*d^9*exp(1)^6-240*c^7*exp(2)^3*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^2*d^9*exp(1)^4+15*c^8*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*d^10*exp(1)^11+180*c^8*exp(2)*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*d^10*exp(1)^9+120*c^8*exp(2)^2*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*d^10*exp(1)^7+48*c^8*exp(2)^3*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*d^10*exp(1)^5-15*c^8*sqrt(c*exp(2))*d^11*exp(1)^10-10*c^8*exp(2)*sqrt(c*exp(2))*d^11*exp(1)^8-8*c^8*exp(2)^2*sqrt(c*exp(2))*d^11*exp(1)^6)/48/exp(1)^6/(-(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^2*exp(1)+2*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*d-c*d^2*exp(1))^6+5*c^3/16/d/sqrt(c*exp(1)^2-c*exp(2))*atan((-d*sqrt(c*exp(2))+(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*exp(1))/d/sqrt(c*exp(1)^2-c*exp(2))))","F(-2)",0
1061,-2,0,0,0.000000," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2)/(e*x+d)^8,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: 2*((-105*c^3*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^13*exp(1)^12+1365*c^3*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^12*d*exp(1)^11-336*c^3*exp(2)^3*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^12*d*exp(1)^5-700*c^4*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^11*d^2*exp(1)^12-7490*c^4*exp(2)*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^11*d^2*exp(1)^10+2912*c^4*exp(2)^3*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^11*d^2*exp(1)^6+1120*c^4*exp(2)^4*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^11*d^2*exp(1)^4+7700*c^4*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^10*d^3*exp(1)^11+22330*c^4*exp(2)*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^10*d^3*exp(1)^9-12096*c^4*exp(2)^2*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^10*d^3*exp(1)^7-7840*c^4*exp(2)^3*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^10*d^3*exp(1)^5-2240*c^4*exp(2)^4*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^10*d^3*exp(1)^3-1981*c^5*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^9*d^4*exp(1)^12-34538*c^5*exp(2)*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^9*d^4*exp(1)^10-8988*c^5*exp(2)^2*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^9*d^4*exp(1)^8+29792*c^5*exp(2)^3*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^9*d^4*exp(1)^6+11872*c^5*exp(2)^4*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^9*d^4*exp(1)^4+2688*c^5*exp(2)^5*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^9*d^4*exp(1)^2+17829*c^5*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^8*d^5*exp(1)^11+35042*c^5*exp(2)*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^8*d^5*exp(1)^9-36008*c^5*exp(2)^2*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^8*d^5*exp(1)^7-34608*c^5*exp(2)^3*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^8*d^5*exp(1)^5-11648*c^5*exp(2)^4*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^8*d^5*exp(1)^3-1792*c^5*exp(2)^5*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^8*d^5*exp(1)-3072*c^6*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^7*d^6*exp(1)^12-20628*c^6*exp(2)*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^7*d^6*exp(1)^10+22352*c^6*exp(2)^2*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^7*d^6*exp(1)^8+54832*c^6*exp(2)^3*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^7*d^6*exp(1)^6+25152*c^6*exp(2)^4*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^7*d^6*exp(1)^4+6784*c^6*exp(2)^5*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^7*d^6*exp(1)^2+512*c^6*exp(2)^6*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^7*d^6-23548*c^6*exp(2)*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^6*d^7*exp(1)^9-58688*c^6*exp(2)^2*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^6*d^7*exp(1)^7-34608*c^6*exp(2)^3*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^6*d^7*exp(1)^5-11648*c^6*exp(2)^4*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^6*d^7*exp(1)^3-1792*c^6*exp(2)^5*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^6*d^7*exp(1)+1981*c^7*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^5*d^8*exp(1)^12+24332*c^7*exp(2)*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^5*d^8*exp(1)^10+55272*c^7*exp(2)^2*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^5*d^8*exp(1)^8+34832*c^7*exp(2)^3*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^5*d^8*exp(1)^6+11872*c^7*exp(2)^4*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^5*d^8*exp(1)^4+2688*c^7*exp(2)^5*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^5*d^8*exp(1)^2-9905*c^7*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^4*d^9*exp(1)^11-41020*c^7*exp(2)*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^4*d^9*exp(1)^9-30240*c^7*exp(2)^2*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^4*d^9*exp(1)^7-7840*c^7*exp(2)^3*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^4*d^9*exp(1)^5-2240*c^7*exp(2)^4*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^4*d^9*exp(1)^3+700*c^8*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^3*d^10*exp(1)^12+16310*c^8*exp(2)*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^3*d^10*exp(1)^10+21840*c^8*exp(2)^2*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^3*d^10*exp(1)^8+3920*c^8*exp(2)^3*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^3*d^10*exp(1)^6+1120*c^8*exp(2)^4*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^3*d^10*exp(1)^4-2100*c^8*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^2*d^11*exp(1)^11-9310*c^8*exp(2)*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^2*d^11*exp(1)^9-2240*c^8*exp(2)^2*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^2*d^11*exp(1)^7-336*c^8*exp(2)^3*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^2*d^11*exp(1)^5+105*c^9*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*d^12*exp(1)^12+1470*c^9*exp(2)*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*d^12*exp(1)^10+980*c^9*exp(2)^2*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*d^12*exp(1)^8+112*c^9*exp(2)^3*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*d^12*exp(1)^6-105*c^9*sqrt(c*exp(2))*d^13*exp(1)^11-70*c^9*exp(2)*sqrt(c*exp(2))*d^13*exp(1)^9-56*c^9*exp(2)^2*sqrt(c*exp(2))*d^13*exp(1)^7)/336/d/exp(1)^6/(-(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)^2*exp(1)+2*sqrt(c*exp(2))*(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*d-c*d^2*exp(1))^7+5*c^3/8/d/2/d/sqrt(c*exp(1)^2-c*exp(2))*atan((-d*sqrt(c*exp(2))+(sqrt(c*d^2+2*c*d*x*exp(1)+c*x^2*exp(2))-sqrt(c*exp(2))*x)*exp(1))/d/sqrt(c*exp(1)^2-c*exp(2))))","F(-2)",0
1062,1,63,0,0.719453," ","integrate((e*x+d)^4/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{c x^{2} e^{2} + 2 \, c d x e + c d^{2}} {\left(\frac{d^{3} e^{\left(-1\right)}}{c} + {\left(x {\left(\frac{x e^{2}}{c} + \frac{3 \, d e}{c}\right)} + \frac{3 \, d^{2}}{c}\right)} x\right)}"," ",0,"1/4*sqrt(c*x^2*e^2 + 2*c*d*x*e + c*d^2)*(d^3*e^(-1)/c + (x*(x*e^2/c + 3*d*e/c) + 3*d^2/c)*x)","A",0
1063,1,50,0,0.465035," ","integrate((e*x+d)^3/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2),x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{c x^{2} e^{2} + 2 \, c d x e + c d^{2}} {\left(x {\left(\frac{x e}{c} + \frac{2 \, d}{c}\right)} + \frac{d^{2} e^{\left(-1\right)}}{c}\right)}"," ",0,"1/3*sqrt(c*x^2*e^2 + 2*c*d*x*e + c*d^2)*(x*(x*e/c + 2*d/c) + d^2*e^(-1)/c)","A",0
1064,1,37,0,0.415457," ","integrate((e*x+d)^2/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{c x^{2} e^{2} + 2 \, c d x e + c d^{2}} {\left(\frac{d e^{\left(-1\right)}}{c} + \frac{x}{c}\right)}"," ",0,"1/2*sqrt(c*x^2*e^2 + 2*c*d*x*e + c*d^2)*(d*e^(-1)/c + x/c)","A",0
1065,1,28,0,0.379703," ","integrate((e*x+d)/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2),x, algorithm=""giac"")","\frac{\sqrt{c x^{2} e^{2} + 2 \, c d x e + c d^{2}} e^{\left(-1\right)}}{c}"," ",0,"sqrt(c*x^2*e^2 + 2*c*d*x*e + c*d^2)*e^(-1)/c","A",0
1066,1,54,0,0.329274," ","integrate(1/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2),x, algorithm=""giac"")","-\frac{e^{\left(-1\right)} \log\left({\left| -\sqrt{c} d e^{2} - {\left(\sqrt{c} x e - \sqrt{c x^{2} e^{2} + 2 \, c d x e + c d^{2}}\right)} e^{2} \right|}\right)}{\sqrt{c}}"," ",0,"-e^(-1)*log(abs(-sqrt(c)*d*e^2 - (sqrt(c)*x*e - sqrt(c*x^2*e^2 + 2*c*d*x*e + c*d^2))*e^2))/sqrt(c)","A",0
1067,-2,0,0,0.000000," ","integrate(1/(e*x+d)/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: 2/d/sqrt(c*exp(1)^2-c*exp(2))*atan((-d*sqrt(c*exp(2))+(sqrt(c*exp(2)*x^2+c*d*exp(1)*x*2+c*d^2)-sqrt(c*exp(2))*x)*exp(1))/d/sqrt(c*exp(1)^2-c*exp(2)))","F(-2)",0
1068,0,0,0,0.000000," ","integrate(1/(e*x+d)^2/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
1069,-2,0,0,0.000000," ","integrate(1/(e*x+d)^3/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: 2*((-3*(sqrt(c*exp(2)*x^2+c*d*exp(1)*x*2+c*d^2)-sqrt(c*exp(2))*x)^3*exp(1)^3+2*exp(2)*(sqrt(c*exp(2)*x^2+c*d*exp(1)*x*2+c*d^2)-sqrt(c*exp(2))*x)^3*exp(1)+9*sqrt(c*exp(2))*(sqrt(c*exp(2)*x^2+c*d*exp(1)*x*2+c*d^2)-sqrt(c*exp(2))*x)^2*d*exp(1)^2-6*exp(2)*sqrt(c*exp(2))*(sqrt(c*exp(2)*x^2+c*d*exp(1)*x*2+c*d^2)-sqrt(c*exp(2))*x)^2*d-5*c*(sqrt(c*exp(2)*x^2+c*d*exp(1)*x*2+c*d^2)-sqrt(c*exp(2))*x)*d^2*exp(1)^3+2*c*exp(2)*(sqrt(c*exp(2)*x^2+c*d*exp(1)*x*2+c*d^2)-sqrt(c*exp(2))*x)*d^2*exp(1)+c*sqrt(c*exp(2))*d^3*exp(1)^2)/(-2*d^2*exp(1)^2+2*exp(2)*d^2)/(-(sqrt(c*exp(2)*x^2+c*d*exp(1)*x*2+c*d^2)-sqrt(c*exp(2))*x)^2*exp(1)+2*sqrt(c*exp(2))*(sqrt(c*exp(2)*x^2+c*d*exp(1)*x*2+c*d^2)-sqrt(c*exp(2))*x)*d-c*d^2*exp(1))^2+(3*exp(1)^2-2*exp(2))/2/(d^2*exp(1)^2-exp(2)*d^2)/d/sqrt(c*exp(1)^2-c*exp(2))*atan((-d*sqrt(c*exp(2))+(sqrt(c*exp(2)*x^2+c*d*exp(1)*x*2+c*d^2)-sqrt(c*exp(2))*x)*exp(1))/d/sqrt(c*exp(1)^2-c*exp(2))))","F(-2)",0
1070,-2,0,0,0.000000," ","integrate(1/(e*x+d)^4/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: 2*((-15*(sqrt(c*exp(2)*x^2+c*d*exp(1)*x*2+c*d^2)-sqrt(c*exp(2))*x)^5*exp(1)^4+6*exp(2)*(sqrt(c*exp(2)*x^2+c*d*exp(1)*x*2+c*d^2)-sqrt(c*exp(2))*x)^5*exp(1)^2+75*sqrt(c*exp(2))*(sqrt(c*exp(2)*x^2+c*d*exp(1)*x*2+c*d^2)-sqrt(c*exp(2))*x)^4*d*exp(1)^3-30*exp(2)*sqrt(c*exp(2))*(sqrt(c*exp(2)*x^2+c*d*exp(1)*x*2+c*d^2)-sqrt(c*exp(2))*x)^4*d*exp(1)-40*c*(sqrt(c*exp(2)*x^2+c*d*exp(1)*x*2+c*d^2)-sqrt(c*exp(2))*x)^3*d^2*exp(1)^4-94*c*exp(2)*(sqrt(c*exp(2)*x^2+c*d*exp(1)*x*2+c*d^2)-sqrt(c*exp(2))*x)^3*d^2*exp(1)^2+44*c*exp(2)^2*(sqrt(c*exp(2)*x^2+c*d*exp(1)*x*2+c*d^2)-sqrt(c*exp(2))*x)^3*d^2+120*c*sqrt(c*exp(2))*(sqrt(c*exp(2)*x^2+c*d*exp(1)*x*2+c*d^2)-sqrt(c*exp(2))*x)^2*d^3*exp(1)^3-30*c*exp(2)*sqrt(c*exp(2))*(sqrt(c*exp(2)*x^2+c*d*exp(1)*x*2+c*d^2)-sqrt(c*exp(2))*x)^2*d^3*exp(1)-33*c^2*(sqrt(c*exp(2)*x^2+c*d*exp(1)*x*2+c*d^2)-sqrt(c*exp(2))*x)*d^4*exp(1)^4-12*c^2*exp(2)*(sqrt(c*exp(2)*x^2+c*d*exp(1)*x*2+c*d^2)-sqrt(c*exp(2))*x)*d^4*exp(1)^2+9*c^2*sqrt(c*exp(2))*d^5*exp(1)^3)/(6*d^3*exp(1)^2-6*exp(2)*d^3)/(-(sqrt(c*exp(2)*x^2+c*d*exp(1)*x*2+c*d^2)-sqrt(c*exp(2))*x)^2*exp(1)+2*sqrt(c*exp(2))*(sqrt(c*exp(2)*x^2+c*d*exp(1)*x*2+c*d^2)-sqrt(c*exp(2))*x)*d-c*d^2*exp(1))^3+(5*exp(1)^2-2*exp(2))/2/(d^3*exp(1)^2-exp(2)*d^3)/d/sqrt(c*exp(1)^2-c*exp(2))*atan((-d*sqrt(c*exp(2))+(sqrt(c*exp(2)*x^2+c*d*exp(1)*x*2+c*d^2)-sqrt(c*exp(2))*x)*exp(1))/d/sqrt(c*exp(1)^2-c*exp(2))))","F(-2)",0
1071,1,65,0,0.526676," ","integrate((e*x+d)^4/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2),x, algorithm=""giac"")","\frac{4 \, C_{0} d e^{\left(-1\right)} - \frac{2 \, d^{3} e^{\left(-1\right)}}{c} + {\left(x {\left(\frac{x e^{2}}{c} + \frac{3 \, d e}{c}\right)} + 4 \, C_{0}\right)} x}{2 \, \sqrt{c x^{2} e^{2} + 2 \, c d x e + c d^{2}}}"," ",0,"1/2*(4*C_0*d*e^(-1) - 2*d^3*e^(-1)/c + (x*(x*e^2/c + 3*d*e/c) + 4*C_0)*x)/sqrt(c*x^2*e^2 + 2*c*d*x*e + c*d^2)","A",0
1072,1,53,0,0.629487," ","integrate((e*x+d)^3/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2),x, algorithm=""giac"")","\frac{2 \, C_{0} d e^{\left(-1\right)} + {\left(2 \, C_{0} + \frac{x e}{c}\right)} x - \frac{d^{2} e^{\left(-1\right)}}{c}}{\sqrt{c x^{2} e^{2} + 2 \, c d x e + c d^{2}}}"," ",0,"(2*C_0*d*e^(-1) + (2*C_0 + x*e/c)*x - d^2*e^(-1)/c)/sqrt(c*x^2*e^2 + 2*c*d*x*e + c*d^2)","A",0
1073,1,88,0,0.676811," ","integrate((e*x+d)^2/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2),x, algorithm=""giac"")","\frac{2 \, {\left(C_{0} d e^{\left(-1\right)} + C_{0} x\right)}}{\sqrt{c x^{2} e^{2} + 2 \, c d x e + c d^{2}}} - \frac{e^{\left(-1\right)} \log\left({\left| -\sqrt{c} d e^{2} - {\left(\sqrt{c} x e - \sqrt{c x^{2} e^{2} + 2 \, c d x e + c d^{2}}\right)} e^{2} \right|}\right)}{c^{\frac{3}{2}}}"," ",0,"2*(C_0*d*e^(-1) + C_0*x)/sqrt(c*x^2*e^2 + 2*c*d*x*e + c*d^2) - e^(-1)*log(abs(-sqrt(c)*d*e^2 - (sqrt(c)*x*e - sqrt(c*x^2*e^2 + 2*c*d*x*e + c*d^2))*e^2))/c^(3/2)","B",0
1074,1,41,0,0.395808," ","integrate((e*x+d)/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2),x, algorithm=""giac"")","\frac{2 \, C_{0} d e^{\left(-1\right)} + 2 \, C_{0} x - \frac{e^{\left(-1\right)}}{c}}{\sqrt{c x^{2} e^{2} + 2 \, c d x e + c d^{2}}}"," ",0,"(2*C_0*d*e^(-1) + 2*C_0*x - e^(-1)/c)/sqrt(c*x^2*e^2 + 2*c*d*x*e + c*d^2)","A",0
1075,0,0,0,0.000000," ","integrate(1/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
1076,0,0,0,0.000000," ","integrate(1/(e*x+d)/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
1077,0,0,0,0.000000," ","integrate(1/(e*x+d)^2/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
1078,-2,0,0,0.000000," ","integrate(1/(e*x+d)^3/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to transpose Error: Bad Argument Value","F(-2)",0
1079,1,108,0,0.656472," ","integrate((e*x+d)^6/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2),x, algorithm=""giac"")","-\frac{\frac{9 \, d^{5} e^{\left(-1\right)}}{c} - 4 \, C_{0} d^{3} e^{\left(-3\right)} - {\left(12 \, C_{0} d^{2} e^{\left(-2\right)} - \frac{25 \, d^{4}}{c} - {\left(\frac{20 \, d^{3} e}{c} - 12 \, C_{0} d e^{\left(-1\right)} - {\left(x {\left(\frac{x e^{4}}{c} + \frac{5 \, d e^{3}}{c}\right)} + 4 \, C_{0}\right)} x\right)} x\right)} x}{2 \, {\left(c x^{2} e^{2} + 2 \, c d x e + c d^{2}\right)}^{\frac{3}{2}}}"," ",0,"-1/2*(9*d^5*e^(-1)/c - 4*C_0*d^3*e^(-3) - (12*C_0*d^2*e^(-2) - 25*d^4/c - (20*d^3*e/c - 12*C_0*d*e^(-1) - (x*(x*e^4/c + 5*d*e^3/c) + 4*C_0)*x)*x)*x)/(c*x^2*e^2 + 2*c*d*x*e + c*d^2)^(3/2)","B",0
1080,1,93,0,0.570749," ","integrate((e*x+d)^5/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2),x, algorithm=""giac"")","\frac{2 \, C_{0} d^{3} e^{\left(-3\right)} - \frac{3 \, d^{4} e^{\left(-1\right)}}{c} + {\left(6 \, C_{0} d^{2} e^{\left(-2\right)} - \frac{8 \, d^{3}}{c} + {\left(6 \, C_{0} d e^{\left(-1\right)} + {\left(2 \, C_{0} + \frac{x e^{3}}{c}\right)} x - \frac{6 \, d^{2} e}{c}\right)} x\right)} x}{{\left(c x^{2} e^{2} + 2 \, c d x e + c d^{2}\right)}^{\frac{3}{2}}}"," ",0,"(2*C_0*d^3*e^(-3) - 3*d^4*e^(-1)/c + (6*C_0*d^2*e^(-2) - 8*d^3/c + (6*C_0*d*e^(-1) + (2*C_0 + x*e^3/c)*x - 6*d^2*e/c)*x)*x)/(c*x^2*e^2 + 2*c*d*x*e + c*d^2)^(3/2)","B",0
1081,1,110,0,0.620309," ","integrate((e*x+d)^4/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2),x, algorithm=""giac"")","\frac{2 \, {\left(C_{0} d^{3} e^{\left(-3\right)} + {\left(3 \, C_{0} d^{2} e^{\left(-2\right)} + {\left(3 \, C_{0} d e^{\left(-1\right)} + C_{0} x\right)} x\right)} x\right)}}{{\left(c x^{2} e^{2} + 2 \, c d x e + c d^{2}\right)}^{\frac{3}{2}}} - \frac{e^{\left(-1\right)} \log\left({\left| -\sqrt{c} d e^{2} - {\left(\sqrt{c} x e - \sqrt{c x^{2} e^{2} + 2 \, c d x e + c d^{2}}\right)} e^{2} \right|}\right)}{c^{\frac{5}{2}}}"," ",0,"2*(C_0*d^3*e^(-3) + (3*C_0*d^2*e^(-2) + (3*C_0*d*e^(-1) + C_0*x)*x)*x)/(c*x^2*e^2 + 2*c*d*x*e + c*d^2)^(3/2) - e^(-1)*log(abs(-sqrt(c)*d*e^2 - (sqrt(c)*x*e - sqrt(c*x^2*e^2 + 2*c*d*x*e + c*d^2))*e^2))/c^(5/2)","B",0
1082,1,79,0,0.498649," ","integrate((e*x+d)^3/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2),x, algorithm=""giac"")","\frac{2 \, C_{0} d^{3} e^{\left(-3\right)} + {\left(6 \, C_{0} d^{2} e^{\left(-2\right)} + {\left(6 \, C_{0} d e^{\left(-1\right)} + 2 \, C_{0} x - \frac{e}{c}\right)} x - \frac{2 \, d}{c}\right)} x - \frac{d^{2} e^{\left(-1\right)}}{c}}{{\left(c x^{2} e^{2} + 2 \, c d x e + c d^{2}\right)}^{\frac{3}{2}}}"," ",0,"(2*C_0*d^3*e^(-3) + (6*C_0*d^2*e^(-2) + (6*C_0*d*e^(-1) + 2*C_0*x - e/c)*x - 2*d/c)*x - d^2*e^(-1)/c)/(c*x^2*e^2 + 2*c*d*x*e + c*d^2)^(3/2)","B",0
1083,1,70,0,0.465614," ","integrate((e*x+d)^2/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2),x, algorithm=""giac"")","\frac{4 \, C_{0} d^{3} e^{\left(-3\right)} + {\left(12 \, C_{0} d^{2} e^{\left(-2\right)} + 4 \, {\left(3 \, C_{0} d e^{\left(-1\right)} + C_{0} x\right)} x - \frac{1}{c}\right)} x - \frac{d e^{\left(-1\right)}}{c}}{2 \, {\left(c x^{2} e^{2} + 2 \, c d x e + c d^{2}\right)}^{\frac{3}{2}}}"," ",0,"1/2*(4*C_0*d^3*e^(-3) + (12*C_0*d^2*e^(-2) + 4*(3*C_0*d*e^(-1) + C_0*x)*x - 1/c)*x - d*e^(-1)/c)/(c*x^2*e^2 + 2*c*d*x*e + c*d^2)^(3/2)","A",0
1084,1,64,0,0.437491," ","integrate((e*x+d)/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2),x, algorithm=""giac"")","\frac{6 \, C_{0} d^{3} e^{\left(-3\right)} + 6 \, {\left(3 \, C_{0} d^{2} e^{\left(-2\right)} + {\left(3 \, C_{0} d e^{\left(-1\right)} + C_{0} x\right)} x\right)} x - \frac{e^{\left(-1\right)}}{c}}{3 \, {\left(c x^{2} e^{2} + 2 \, c d x e + c d^{2}\right)}^{\frac{3}{2}}}"," ",0,"1/3*(6*C_0*d^3*e^(-3) + 6*(3*C_0*d^2*e^(-2) + (3*C_0*d*e^(-1) + C_0*x)*x)*x - e^(-1)/c)/(c*x^2*e^2 + 2*c*d*x*e + c*d^2)^(3/2)","B",0
1085,0,0,0,0.000000," ","integrate(1/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
1086,-2,0,0,0.000000," ","integrate(1/(e*x+d)/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to transpose Error: Bad Argument Value","F(-2)",0
1087,0,0,0,0.000000," ","integrate(1/(e*x+d)^2/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
1088,-2,0,0,0.000000," ","integrate(1/(e*x+d)^3/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to transpose Error: Bad Argument Value","F(-2)",0
1089,1,125,0,0.249336," ","integrate((e*x+d)^m*(c*e^2*x^2+2*c*d*e*x+c*d^2)^2,x, algorithm=""giac"")","\frac{{\left(x e + d\right)}^{m} c^{2} x^{5} e^{5} + 5 \, {\left(x e + d\right)}^{m} c^{2} d x^{4} e^{4} + 10 \, {\left(x e + d\right)}^{m} c^{2} d^{2} x^{3} e^{3} + 10 \, {\left(x e + d\right)}^{m} c^{2} d^{3} x^{2} e^{2} + 5 \, {\left(x e + d\right)}^{m} c^{2} d^{4} x e + {\left(x e + d\right)}^{m} c^{2} d^{5}}{m e + 5 \, e}"," ",0,"((x*e + d)^m*c^2*x^5*e^5 + 5*(x*e + d)^m*c^2*d*x^4*e^4 + 10*(x*e + d)^m*c^2*d^2*x^3*e^3 + 10*(x*e + d)^m*c^2*d^3*x^2*e^2 + 5*(x*e + d)^m*c^2*d^4*x*e + (x*e + d)^m*c^2*d^5)/(m*e + 5*e)","B",0
1090,1,75,0,0.184618," ","integrate((e*x+d)^m*(c*e^2*x^2+2*c*d*e*x+c*d^2),x, algorithm=""giac"")","\frac{{\left(x e + d\right)}^{m} c x^{3} e^{3} + 3 \, {\left(x e + d\right)}^{m} c d x^{2} e^{2} + 3 \, {\left(x e + d\right)}^{m} c d^{2} x e + {\left(x e + d\right)}^{m} c d^{3}}{m e + 3 \, e}"," ",0,"((x*e + d)^m*c*x^3*e^3 + 3*(x*e + d)^m*c*d*x^2*e^2 + 3*(x*e + d)^m*c*d^2*x*e + (x*e + d)^m*c*d^3)/(m*e + 3*e)","B",0
1091,0,0,0,0.000000," ","integrate((e*x+d)^m/(c*e^2*x^2+2*c*d*e*x+c*d^2),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{m}}{c e^{2} x^{2} + 2 \, c d e x + c d^{2}}\,{d x}"," ",0,"integrate((e*x + d)^m/(c*e^2*x^2 + 2*c*d*e*x + c*d^2), x)","F",0
1092,0,0,0,0.000000," ","integrate((e*x+d)^m/(c*e^2*x^2+2*c*d*e*x+c*d^2)^2,x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{m}}{{\left(c e^{2} x^{2} + 2 \, c d e x + c d^{2}\right)}^{2}}\,{d x}"," ",0,"integrate((e*x + d)^m/(c*e^2*x^2 + 2*c*d*e*x + c*d^2)^2, x)","F",0
1093,0,0,0,0.000000," ","integrate((e*x+d)^m/(c*e^2*x^2+2*c*d*e*x+c*d^2)^3,x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{m}}{{\left(c e^{2} x^{2} + 2 \, c d e x + c d^{2}\right)}^{3}}\,{d x}"," ",0,"integrate((e*x + d)^m/(c*e^2*x^2 + 2*c*d*e*x + c*d^2)^3, x)","F",0
1094,0,0,0,0.000000," ","integrate((e*x+d)^m*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2),x, algorithm=""giac"")","\int {\left(c e^{2} x^{2} + 2 \, c d e x + c d^{2}\right)}^{\frac{3}{2}} {\left(e x + d\right)}^{m}\,{d x}"," ",0,"integrate((c*e^2*x^2 + 2*c*d*e*x + c*d^2)^(3/2)*(e*x + d)^m, x)","F",0
1095,0,0,0,0.000000," ","integrate((e*x+d)^m*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2),x, algorithm=""giac"")","\int \sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}} {\left(e x + d\right)}^{m}\,{d x}"," ",0,"integrate(sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)*(e*x + d)^m, x)","F",0
1096,0,0,0,0.000000," ","integrate((e*x+d)^m/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{m}}{\sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}}}\,{d x}"," ",0,"integrate((e*x + d)^m/sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2), x)","F",0
1097,0,0,0,0.000000," ","integrate((e*x+d)^m/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{m}}{{\left(c e^{2} x^{2} + 2 \, c d e x + c d^{2}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((e*x + d)^m/(c*e^2*x^2 + 2*c*d*e*x + c*d^2)^(3/2), x)","F",0
1098,1,69,0,0.209893," ","integrate((e*x+d)^m*(c*e^2*x^2+2*c*d*e*x+c*d^2)^p,x, algorithm=""giac"")","\frac{{\left(x e + d\right)}^{m} x e^{\left(2 \, p \log\left(x e + d\right) + p \log\left(c\right) + 1\right)} + {\left(x e + d\right)}^{m} d e^{\left(2 \, p \log\left(x e + d\right) + p \log\left(c\right)\right)}}{m e + 2 \, p e + e}"," ",0,"((x*e + d)^m*x*e^(2*p*log(x*e + d) + p*log(c) + 1) + (x*e + d)^m*d*e^(2*p*log(x*e + d) + p*log(c)))/(m*e + 2*p*e + e)","A",0
1099,1,69,0,0.212098," ","integrate((e*x+d)^p/((c*e^2*x^2+2*c*d*e*x+c*d^2)^p),x, algorithm=""giac"")","-\frac{{\left(x e + d\right)}^{p} x e^{\left(-2 \, p \log\left(x e + d\right) - p \log\left(c\right) + 1\right)} + {\left(x e + d\right)}^{p} d e^{\left(-2 \, p \log\left(x e + d\right) - p \log\left(c\right)\right)}}{p e - e}"," ",0,"-((x*e + d)^p*x*e^(-2*p*log(x*e + d) - p*log(c) + 1) + (x*e + d)^p*d*e^(-2*p*log(x*e + d) - p*log(c)))/(p*e - e)","A",0
1100,1,160,0,0.239098," ","integrate((e*x+d)^3*(c*e^2*x^2+2*c*d*e*x+c*d^2)^p,x, algorithm=""giac"")","\frac{{\left(c x^{2} e^{2} + 2 \, c d x e + c d^{2}\right)}^{p} x^{4} e^{4} + 4 \, {\left(c x^{2} e^{2} + 2 \, c d x e + c d^{2}\right)}^{p} d x^{3} e^{3} + 6 \, {\left(c x^{2} e^{2} + 2 \, c d x e + c d^{2}\right)}^{p} d^{2} x^{2} e^{2} + 4 \, {\left(c x^{2} e^{2} + 2 \, c d x e + c d^{2}\right)}^{p} d^{3} x e + {\left(c x^{2} e^{2} + 2 \, c d x e + c d^{2}\right)}^{p} d^{4}}{2 \, {\left(p e + 2 \, e\right)}}"," ",0,"1/2*((c*x^2*e^2 + 2*c*d*x*e + c*d^2)^p*x^4*e^4 + 4*(c*x^2*e^2 + 2*c*d*x*e + c*d^2)^p*d*x^3*e^3 + 6*(c*x^2*e^2 + 2*c*d*x*e + c*d^2)^p*d^2*x^2*e^2 + 4*(c*x^2*e^2 + 2*c*d*x*e + c*d^2)^p*d^3*x*e + (c*x^2*e^2 + 2*c*d*x*e + c*d^2)^p*d^4)/(p*e + 2*e)","B",0
1101,1,128,0,0.259875," ","integrate((e*x+d)^2*(c*e^2*x^2+2*c*d*e*x+c*d^2)^p,x, algorithm=""giac"")","\frac{{\left(c x^{2} e^{2} + 2 \, c d x e + c d^{2}\right)}^{p} x^{3} e^{3} + 3 \, {\left(c x^{2} e^{2} + 2 \, c d x e + c d^{2}\right)}^{p} d x^{2} e^{2} + 3 \, {\left(c x^{2} e^{2} + 2 \, c d x e + c d^{2}\right)}^{p} d^{2} x e + {\left(c x^{2} e^{2} + 2 \, c d x e + c d^{2}\right)}^{p} d^{3}}{2 \, p e + 3 \, e}"," ",0,"((c*x^2*e^2 + 2*c*d*x*e + c*d^2)^p*x^3*e^3 + 3*(c*x^2*e^2 + 2*c*d*x*e + c*d^2)^p*d*x^2*e^2 + 3*(c*x^2*e^2 + 2*c*d*x*e + c*d^2)^p*d^2*x*e + (c*x^2*e^2 + 2*c*d*x*e + c*d^2)^p*d^3)/(2*p*e + 3*e)","B",0
1102,1,94,0,0.211303," ","integrate((e*x+d)*(c*e^2*x^2+2*c*d*e*x+c*d^2)^p,x, algorithm=""giac"")","\frac{{\left(c x^{2} e^{2} + 2 \, c d x e + c d^{2}\right)}^{p} x^{2} e^{2} + 2 \, {\left(c x^{2} e^{2} + 2 \, c d x e + c d^{2}\right)}^{p} d x e + {\left(c x^{2} e^{2} + 2 \, c d x e + c d^{2}\right)}^{p} d^{2}}{2 \, {\left(p e + e\right)}}"," ",0,"1/2*((c*x^2*e^2 + 2*c*d*x*e + c*d^2)^p*x^2*e^2 + 2*(c*x^2*e^2 + 2*c*d*x*e + c*d^2)^p*d*x*e + (c*x^2*e^2 + 2*c*d*x*e + c*d^2)^p*d^2)/(p*e + e)","B",0
1103,1,62,0,0.185310," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^p,x, algorithm=""giac"")","\frac{{\left(c x^{2} e^{2} + 2 \, c d x e + c d^{2}\right)}^{p} x e + {\left(c x^{2} e^{2} + 2 \, c d x e + c d^{2}\right)}^{p} d}{2 \, p e + e}"," ",0,"((c*x^2*e^2 + 2*c*d*x*e + c*d^2)^p*x*e + (c*x^2*e^2 + 2*c*d*x*e + c*d^2)^p*d)/(2*p*e + e)","A",0
1104,0,0,0,0.000000," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^p/(e*x+d),x, algorithm=""giac"")","\int \frac{{\left(c e^{2} x^{2} + 2 \, c d e x + c d^{2}\right)}^{p}}{e x + d}\,{d x}"," ",0,"integrate((c*e^2*x^2 + 2*c*d*e*x + c*d^2)^p/(e*x + d), x)","F",0
1105,0,0,0,0.000000," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^p/(e*x+d)^2,x, algorithm=""giac"")","\int \frac{{\left(c e^{2} x^{2} + 2 \, c d e x + c d^{2}\right)}^{p}}{{\left(e x + d\right)}^{2}}\,{d x}"," ",0,"integrate((c*e^2*x^2 + 2*c*d*e*x + c*d^2)^p/(e*x + d)^2, x)","F",0
1106,0,0,0,0.000000," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^p/(e*x+d)^3,x, algorithm=""giac"")","\int \frac{{\left(c e^{2} x^{2} + 2 \, c d e x + c d^{2}\right)}^{p}}{{\left(e x + d\right)}^{3}}\,{d x}"," ",0,"integrate((c*e^2*x^2 + 2*c*d*e*x + c*d^2)^p/(e*x + d)^3, x)","F",0
1107,0,0,0,0.000000," ","integrate((e*x+d)^(-1-2*p)*(c*e^2*x^2+2*c*d*e*x+c*d^2)^p,x, algorithm=""giac"")","\int {\left(c e^{2} x^{2} + 2 \, c d e x + c d^{2}\right)}^{p} {\left(e x + d\right)}^{-2 \, p - 1}\,{d x}"," ",0,"integrate((c*e^2*x^2 + 2*c*d*e*x + c*d^2)^p*(e*x + d)^(-2*p - 1), x)","F",0
1108,0,0,0,0.000000," ","integrate((e*x+d)^(-1+2*p)/((c*e^2*x^2+2*c*d*e*x+c*d^2)^p),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{2 \, p - 1}}{{\left(c e^{2} x^{2} + 2 \, c d e x + c d^{2}\right)}^{p}}\,{d x}"," ",0,"integrate((e*x + d)^(2*p - 1)/(c*e^2*x^2 + 2*c*d*e*x + c*d^2)^p, x)","F",0
1109,1,137,0,0.168822," ","integrate((2*c*d*x+b*d)^4*(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{16}{7} \, c^{5} d^{4} x^{7} + 8 \, b c^{4} d^{4} x^{6} + \frac{56}{5} \, b^{2} c^{3} d^{4} x^{5} + \frac{16}{5} \, a c^{4} d^{4} x^{5} + 8 \, b^{3} c^{2} d^{4} x^{4} + 8 \, a b c^{3} d^{4} x^{4} + 3 \, b^{4} c d^{4} x^{3} + 8 \, a b^{2} c^{2} d^{4} x^{3} + \frac{1}{2} \, b^{5} d^{4} x^{2} + 4 \, a b^{3} c d^{4} x^{2} + a b^{4} d^{4} x"," ",0,"16/7*c^5*d^4*x^7 + 8*b*c^4*d^4*x^6 + 56/5*b^2*c^3*d^4*x^5 + 16/5*a*c^4*d^4*x^5 + 8*b^3*c^2*d^4*x^4 + 8*a*b*c^3*d^4*x^4 + 3*b^4*c*d^4*x^3 + 8*a*b^2*c^2*d^4*x^3 + 1/2*b^5*d^4*x^2 + 4*a*b^3*c*d^4*x^2 + a*b^4*d^4*x","B",0
1110,1,73,0,0.210495," ","integrate((2*c*d*x+b*d)^3*(c*x^2+b*x+a),x, algorithm=""giac"")","{\left(c d x^{2} + b d x\right)} a b^{2} d^{2} + \frac{1}{2} \, {\left(c d x^{2} + b d x\right)}^{2} b^{2} d + 2 \, {\left(c d x^{2} + b d x\right)}^{2} a c d + \frac{4}{3} \, {\left(c d x^{2} + b d x\right)}^{3} c"," ",0,"(c*d*x^2 + b*d*x)*a*b^2*d^2 + 1/2*(c*d*x^2 + b*d*x)^2*b^2*d + 2*(c*d*x^2 + b*d*x)^2*a*c*d + 4/3*(c*d*x^2 + b*d*x)^3*c","A",0
1111,1,79,0,0.182301," ","integrate((2*c*d*x+b*d)^2*(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{4}{5} \, c^{3} d^{2} x^{5} + 2 \, b c^{2} d^{2} x^{4} + \frac{5}{3} \, b^{2} c d^{2} x^{3} + \frac{4}{3} \, a c^{2} d^{2} x^{3} + \frac{1}{2} \, b^{3} d^{2} x^{2} + 2 \, a b c d^{2} x^{2} + a b^{2} d^{2} x"," ",0,"4/5*c^3*d^2*x^5 + 2*b*c^2*d^2*x^4 + 5/3*b^2*c*d^2*x^3 + 4/3*a*c^2*d^2*x^3 + 1/2*b^3*d^2*x^2 + 2*a*b*c*d^2*x^2 + a*b^2*d^2*x","A",0
1112,1,32,0,0.148641," ","integrate((2*c*d*x+b*d)*(c*x^2+b*x+a),x, algorithm=""giac"")","{\left(c d x^{2} + b d x\right)} a + \frac{{\left(c d x^{2} + b d x\right)}^{2}}{2 \, d}"," ",0,"(c*d*x^2 + b*d*x)*a + 1/2*(c*d*x^2 + b*d*x)^2/d","B",0
1113,1,47,0,0.155817," ","integrate((c*x^2+b*x+a)/(2*c*d*x+b*d),x, algorithm=""giac"")","-\frac{{\left(b^{2} - 4 \, a c\right)} \log\left({\left| 2 \, c x + b \right|}\right)}{8 \, c^{2} d} + \frac{c^{2} d x^{2} + b c d x}{4 \, c^{2} d^{2}}"," ",0,"-1/8*(b^2 - 4*a*c)*log(abs(2*c*x + b))/(c^2*d) + 1/4*(c^2*d*x^2 + b*c*d*x)/(c^2*d^2)","A",0
1114,1,170,0,0.155477," ","integrate((c*x^2+b*x+a)/(2*c*d*x+b*d)^2,x, algorithm=""giac"")","-\frac{1}{8} \, c {\left(\frac{b^{2}}{{\left(2 \, c d x + b d\right)} c^{3} d} - \frac{2 \, b \log\left(\frac{{\left| 2 \, c d x + b d \right|}}{2 \, {\left(2 \, c d x + b d\right)}^{2} {\left| c \right|} {\left| d \right|}}\right)}{c^{3} d^{2}} - \frac{2 \, c d x + b d}{c^{3} d^{3}}\right)} + \frac{b {\left(\frac{b}{{\left(2 \, c d x + b d\right)} c} - \frac{\log\left(\frac{{\left| 2 \, c d x + b d \right|}}{2 \, {\left(2 \, c d x + b d\right)}^{2} {\left| c \right|} {\left| d \right|}}\right)}{c d}\right)}}{4 \, c d} - \frac{a}{2 \, {\left(2 \, c d x + b d\right)} c d}"," ",0,"-1/8*c*(b^2/((2*c*d*x + b*d)*c^3*d) - 2*b*log(1/2*abs(2*c*d*x + b*d)/((2*c*d*x + b*d)^2*abs(c)*abs(d)))/(c^3*d^2) - (2*c*d*x + b*d)/(c^3*d^3)) + 1/4*b*(b/((2*c*d*x + b*d)*c) - log(1/2*abs(2*c*d*x + b*d)/((2*c*d*x + b*d)^2*abs(c)*abs(d)))/(c*d))/(c*d) - 1/2*a/((2*c*d*x + b*d)*c*d)","B",0
1115,1,41,0,0.153873," ","integrate((c*x^2+b*x+a)/(2*c*d*x+b*d)^3,x, algorithm=""giac"")","\frac{\log\left({\left| 2 \, c x + b \right|}\right)}{8 \, c^{2} d^{3}} + \frac{b^{2} - 4 \, a c}{16 \, {\left(2 \, c x + b\right)}^{2} c^{2} d^{3}}"," ",0,"1/8*log(abs(2*c*x + b))/(c^2*d^3) + 1/16*(b^2 - 4*a*c)/((2*c*x + b)^2*c^2*d^3)","A",0
1116,1,37,0,0.153167," ","integrate((c*x^2+b*x+a)/(2*c*d*x+b*d)^4,x, algorithm=""giac"")","-\frac{6 \, c^{2} x^{2} + 6 \, b c x + b^{2} + 2 \, a c}{12 \, {\left(2 \, c x + b\right)}^{3} c^{2} d^{4}}"," ",0,"-1/12*(6*c^2*x^2 + 6*b*c*x + b^2 + 2*a*c)/((2*c*x + b)^3*c^2*d^4)","A",0
1117,1,60,0,0.157232," ","integrate((c*x^2+b*x+a)/(2*c*d*x+b*d)^5,x, algorithm=""giac"")","\frac{\frac{b^{2}}{{\left(2 \, c d x + b d\right)}^{4} c^{2}} - \frac{4 \, a}{{\left(2 \, c d x + b d\right)}^{4} c} - \frac{2}{{\left(2 \, c d x + b d\right)}^{2} c^{2} d^{2}}}{32 \, d}"," ",0,"1/32*(b^2/((2*c*d*x + b*d)^4*c^2) - 4*a/((2*c*d*x + b*d)^4*c) - 2/((2*c*d*x + b*d)^2*c^2*d^2))/d","A",0
1118,1,37,0,0.186385," ","integrate((c*x^2+b*x+a)/(2*c*d*x+b*d)^6,x, algorithm=""giac"")","-\frac{10 \, c^{2} x^{2} + 10 \, b c x + b^{2} + 6 \, a c}{60 \, {\left(2 \, c x + b\right)}^{5} c^{2} d^{6}}"," ",0,"-1/60*(10*c^2*x^2 + 10*b*c*x + b^2 + 6*a*c)/((2*c*x + b)^5*c^2*d^6)","A",0
1119,1,37,0,0.168221," ","integrate((c*x^2+b*x+a)/(2*c*d*x+b*d)^7,x, algorithm=""giac"")","-\frac{12 \, c^{2} x^{2} + 12 \, b c x + b^{2} + 8 \, a c}{96 \, {\left(2 \, c x + b\right)}^{6} c^{2} d^{7}}"," ",0,"-1/96*(12*c^2*x^2 + 12*b*c*x + b^2 + 8*a*c)/((2*c*x + b)^6*c^2*d^7)","A",0
1120,1,37,0,0.153715," ","integrate((c*x^2+b*x+a)/(2*c*d*x+b*d)^8,x, algorithm=""giac"")","-\frac{14 \, c^{2} x^{2} + 14 \, b c x + b^{2} + 10 \, a c}{140 \, {\left(2 \, c x + b\right)}^{7} c^{2} d^{8}}"," ",0,"-1/140*(14*c^2*x^2 + 14*b*c*x + b^2 + 10*a*c)/((2*c*x + b)^7*c^2*d^8)","A",0
1121,1,286,0,0.173249," ","integrate((2*c*d*x+b*d)^5*(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{16}{5} \, c^{7} d^{5} x^{10} + 16 \, b c^{6} d^{5} x^{9} + 34 \, b^{2} c^{5} d^{5} x^{8} + 8 \, a c^{6} d^{5} x^{8} + 40 \, b^{3} c^{4} d^{5} x^{7} + 32 \, a b c^{5} d^{5} x^{7} + \frac{85}{3} \, b^{4} c^{3} d^{5} x^{6} + \frac{160}{3} \, a b^{2} c^{4} d^{5} x^{6} + \frac{16}{3} \, a^{2} c^{5} d^{5} x^{6} + \frac{61}{5} \, b^{5} c^{2} d^{5} x^{5} + 48 \, a b^{3} c^{3} d^{5} x^{5} + 16 \, a^{2} b c^{4} d^{5} x^{5} + 3 \, b^{6} c d^{5} x^{4} + 25 \, a b^{4} c^{2} d^{5} x^{4} + 20 \, a^{2} b^{2} c^{3} d^{5} x^{4} + \frac{1}{3} \, b^{7} d^{5} x^{3} + \frac{22}{3} \, a b^{5} c d^{5} x^{3} + \frac{40}{3} \, a^{2} b^{3} c^{2} d^{5} x^{3} + a b^{6} d^{5} x^{2} + 5 \, a^{2} b^{4} c d^{5} x^{2} + a^{2} b^{5} d^{5} x"," ",0,"16/5*c^7*d^5*x^10 + 16*b*c^6*d^5*x^9 + 34*b^2*c^5*d^5*x^8 + 8*a*c^6*d^5*x^8 + 40*b^3*c^4*d^5*x^7 + 32*a*b*c^5*d^5*x^7 + 85/3*b^4*c^3*d^5*x^6 + 160/3*a*b^2*c^4*d^5*x^6 + 16/3*a^2*c^5*d^5*x^6 + 61/5*b^5*c^2*d^5*x^5 + 48*a*b^3*c^3*d^5*x^5 + 16*a^2*b*c^4*d^5*x^5 + 3*b^6*c*d^5*x^4 + 25*a*b^4*c^2*d^5*x^4 + 20*a^2*b^2*c^3*d^5*x^4 + 1/3*b^7*d^5*x^3 + 22/3*a*b^5*c*d^5*x^3 + 40/3*a^2*b^3*c^2*d^5*x^3 + a*b^6*d^5*x^2 + 5*a^2*b^4*c*d^5*x^2 + a^2*b^5*d^5*x","B",0
1122,1,240,0,0.162207," ","integrate((2*c*d*x+b*d)^4*(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{16}{9} \, c^{6} d^{4} x^{9} + 8 \, b c^{5} d^{4} x^{8} + \frac{104}{7} \, b^{2} c^{4} d^{4} x^{7} + \frac{32}{7} \, a c^{5} d^{4} x^{7} + \frac{44}{3} \, b^{3} c^{3} d^{4} x^{6} + 16 \, a b c^{4} d^{4} x^{6} + \frac{41}{5} \, b^{4} c^{2} d^{4} x^{5} + \frac{112}{5} \, a b^{2} c^{3} d^{4} x^{5} + \frac{16}{5} \, a^{2} c^{4} d^{4} x^{5} + \frac{5}{2} \, b^{5} c d^{4} x^{4} + 16 \, a b^{3} c^{2} d^{4} x^{4} + 8 \, a^{2} b c^{3} d^{4} x^{4} + \frac{1}{3} \, b^{6} d^{4} x^{3} + 6 \, a b^{4} c d^{4} x^{3} + 8 \, a^{2} b^{2} c^{2} d^{4} x^{3} + a b^{5} d^{4} x^{2} + 4 \, a^{2} b^{3} c d^{4} x^{2} + a^{2} b^{4} d^{4} x"," ",0,"16/9*c^6*d^4*x^9 + 8*b*c^5*d^4*x^8 + 104/7*b^2*c^4*d^4*x^7 + 32/7*a*c^5*d^4*x^7 + 44/3*b^3*c^3*d^4*x^6 + 16*a*b*c^4*d^4*x^6 + 41/5*b^4*c^2*d^4*x^5 + 112/5*a*b^2*c^3*d^4*x^5 + 16/5*a^2*c^4*d^4*x^5 + 5/2*b^5*c*d^4*x^4 + 16*a*b^3*c^2*d^4*x^4 + 8*a^2*b*c^3*d^4*x^4 + 1/3*b^6*d^4*x^3 + 6*a*b^4*c*d^4*x^3 + 8*a^2*b^2*c^2*d^4*x^3 + a*b^5*d^4*x^2 + 4*a^2*b^3*c*d^4*x^2 + a^2*b^4*d^4*x","B",0
1123,1,124,0,0.187094," ","integrate((2*c*d*x+b*d)^3*(c*x^2+b*x+a)^2,x, algorithm=""giac"")","{\left(c d x^{2} + b d x\right)} a^{2} b^{2} d^{2} + \frac{3 \, {\left(c d x^{2} + b d x\right)}^{2} a b^{2} d^{2} + 6 \, {\left(c d x^{2} + b d x\right)}^{2} a^{2} c d^{2} + {\left(c d x^{2} + b d x\right)}^{3} b^{2} d + 8 \, {\left(c d x^{2} + b d x\right)}^{3} a c d + 3 \, {\left(c d x^{2} + b d x\right)}^{4} c}{3 \, d}"," ",0,"(c*d*x^2 + b*d*x)*a^2*b^2*d^2 + 1/3*(3*(c*d*x^2 + b*d*x)^2*a*b^2*d^2 + 6*(c*d*x^2 + b*d*x)^2*a^2*c*d^2 + (c*d*x^2 + b*d*x)^3*b^2*d + 8*(c*d*x^2 + b*d*x)^3*a*c*d + 3*(c*d*x^2 + b*d*x)^4*c)/d","B",0
1124,1,148,0,0.152317," ","integrate((2*c*d*x+b*d)^2*(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{4}{7} \, c^{4} d^{2} x^{7} + 2 \, b c^{3} d^{2} x^{6} + \frac{13}{5} \, b^{2} c^{2} d^{2} x^{5} + \frac{8}{5} \, a c^{3} d^{2} x^{5} + \frac{3}{2} \, b^{3} c d^{2} x^{4} + 4 \, a b c^{2} d^{2} x^{4} + \frac{1}{3} \, b^{4} d^{2} x^{3} + \frac{10}{3} \, a b^{2} c d^{2} x^{3} + \frac{4}{3} \, a^{2} c^{2} d^{2} x^{3} + a b^{3} d^{2} x^{2} + 2 \, a^{2} b c d^{2} x^{2} + a^{2} b^{2} d^{2} x"," ",0,"4/7*c^4*d^2*x^7 + 2*b*c^3*d^2*x^6 + 13/5*b^2*c^2*d^2*x^5 + 8/5*a*c^3*d^2*x^5 + 3/2*b^3*c*d^2*x^4 + 4*a*b*c^2*d^2*x^4 + 1/3*b^4*d^2*x^3 + 10/3*a*b^2*c*d^2*x^3 + 4/3*a^2*c^2*d^2*x^3 + a*b^3*d^2*x^2 + 2*a^2*b*c*d^2*x^2 + a^2*b^2*d^2*x","B",0
1125,1,52,0,0.175663," ","integrate((2*c*d*x+b*d)*(c*x^2+b*x+a)^2,x, algorithm=""giac"")","{\left(c d x^{2} + b d x\right)} a^{2} + \frac{3 \, {\left(c d x^{2} + b d x\right)}^{2} a d + {\left(c d x^{2} + b d x\right)}^{3}}{3 \, d^{2}}"," ",0,"(c*d*x^2 + b*d*x)*a^2 + 1/3*(3*(c*d*x^2 + b*d*x)^2*a*d + (c*d*x^2 + b*d*x)^3)/d^2","B",0
1126,1,116,0,0.151375," ","integrate((c*x^2+b*x+a)^2/(2*c*d*x+b*d),x, algorithm=""giac"")","\frac{{\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \log\left({\left| 2 \, c x + b \right|}\right)}{32 \, c^{3} d} + \frac{2 \, c^{5} d^{3} x^{4} + 4 \, b c^{4} d^{3} x^{3} + b^{2} c^{3} d^{3} x^{2} + 8 \, a c^{4} d^{3} x^{2} - b^{3} c^{2} d^{3} x + 8 \, a b c^{3} d^{3} x}{16 \, c^{4} d^{4}}"," ",0,"1/32*(b^4 - 8*a*b^2*c + 16*a^2*c^2)*log(abs(2*c*x + b))/(c^3*d) + 1/16*(2*c^5*d^3*x^4 + 4*b*c^4*d^3*x^3 + b^2*c^3*d^3*x^2 + 8*a*c^4*d^3*x^2 - b^3*c^2*d^3*x + 8*a*b*c^3*d^3*x)/(c^4*d^4)","A",0
1127,1,134,0,0.162752," ","integrate((c*x^2+b*x+a)^2/(2*c*d*x+b*d)^2,x, algorithm=""giac"")","-\frac{{\left(2 \, c d x + b d\right)}^{3} {\left(\frac{6 \, b^{2} d^{2}}{{\left(2 \, c d x + b d\right)}^{2}} - \frac{24 \, a c d^{2}}{{\left(2 \, c d x + b d\right)}^{2}} - 1\right)}}{96 \, c^{3} d^{5}} - \frac{\frac{b^{4} c^{3} d^{7}}{2 \, c d x + b d} - \frac{8 \, a b^{2} c^{4} d^{7}}{2 \, c d x + b d} + \frac{16 \, a^{2} c^{5} d^{7}}{2 \, c d x + b d}}{32 \, c^{6} d^{8}}"," ",0,"-1/96*(2*c*d*x + b*d)^3*(6*b^2*d^2/(2*c*d*x + b*d)^2 - 24*a*c*d^2/(2*c*d*x + b*d)^2 - 1)/(c^3*d^5) - 1/32*(b^4*c^3*d^7/(2*c*d*x + b*d) - 8*a*b^2*c^4*d^7/(2*c*d*x + b*d) + 16*a^2*c^5*d^7/(2*c*d*x + b*d))/(c^6*d^8)","B",0
1128,1,88,0,0.190988," ","integrate((c*x^2+b*x+a)^2/(2*c*d*x+b*d)^3,x, algorithm=""giac"")","-\frac{{\left(b^{2} - 4 \, a c\right)} \log\left({\left| 2 \, c x + b \right|}\right)}{16 \, c^{3} d^{3}} - \frac{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}}{64 \, {\left(2 \, c x + b\right)}^{2} c^{3} d^{3}} + \frac{c^{5} d^{3} x^{2} + b c^{4} d^{3} x}{16 \, c^{6} d^{6}}"," ",0,"-1/16*(b^2 - 4*a*c)*log(abs(2*c*x + b))/(c^3*d^3) - 1/64*(b^4 - 8*a*b^2*c + 16*a^2*c^2)/((2*c*x + b)^2*c^3*d^3) + 1/16*(c^5*d^3*x^2 + b*c^4*d^3*x)/(c^6*d^6)","A",0
1129,1,82,0,0.160514," ","integrate((c*x^2+b*x+a)^2/(2*c*d*x+b*d)^4,x, algorithm=""giac"")","\frac{x}{16 \, c^{2} d^{4}} + \frac{24 \, b^{2} c^{2} x^{2} - 96 \, a c^{3} x^{2} + 24 \, b^{3} c x - 96 \, a b c^{2} x + 5 \, b^{4} - 16 \, a b^{2} c - 16 \, a^{2} c^{2}}{96 \, {\left(2 \, c x + b\right)}^{3} c^{3} d^{4}}"," ",0,"1/16*x/(c^2*d^4) + 1/96*(24*b^2*c^2*x^2 - 96*a*c^3*x^2 + 24*b^3*c*x - 96*a*b*c^2*x + 5*b^4 - 16*a*b^2*c - 16*a^2*c^2)/((2*c*x + b)^3*c^3*d^4)","A",0
1130,1,146,0,0.247494," ","integrate((c*x^2+b*x+a)^2/(2*c*d*x+b*d)^5,x, algorithm=""giac"")","-\frac{\log\left(\frac{1}{4 \, {\left(2 \, c d x + b d\right)}^{2} c^{2} d^{2}}\right)}{64 \, c^{3} d^{5}} - \frac{\frac{b^{4} c^{3} d^{9}}{{\left(2 \, c d x + b d\right)}^{4}} - \frac{8 \, a b^{2} c^{4} d^{9}}{{\left(2 \, c d x + b d\right)}^{4}} + \frac{16 \, a^{2} c^{5} d^{9}}{{\left(2 \, c d x + b d\right)}^{4}} - \frac{4 \, b^{2} c^{3} d^{7}}{{\left(2 \, c d x + b d\right)}^{2}} + \frac{16 \, a c^{4} d^{7}}{{\left(2 \, c d x + b d\right)}^{2}}}{128 \, c^{6} d^{10}}"," ",0,"-1/64*log(1/4/((2*c*d*x + b*d)^2*c^2*d^2))/(c^3*d^5) - 1/128*(b^4*c^3*d^9/(2*c*d*x + b*d)^4 - 8*a*b^2*c^4*d^9/(2*c*d*x + b*d)^4 + 16*a^2*c^5*d^9/(2*c*d*x + b*d)^4 - 4*b^2*c^3*d^7/(2*c*d*x + b*d)^2 + 16*a*c^4*d^7/(2*c*d*x + b*d)^2)/(c^6*d^10)","B",0
1131,1,87,0,0.178285," ","integrate((c*x^2+b*x+a)^2/(2*c*d*x+b*d)^6,x, algorithm=""giac"")","-\frac{30 \, c^{4} x^{4} + 60 \, b c^{3} x^{3} + 40 \, b^{2} c^{2} x^{2} + 20 \, a c^{3} x^{2} + 10 \, b^{3} c x + 20 \, a b c^{2} x + b^{4} + 2 \, a b^{2} c + 6 \, a^{2} c^{2}}{60 \, {\left(2 \, c x + b\right)}^{5} c^{3} d^{6}}"," ",0,"-1/60*(30*c^4*x^4 + 60*b*c^3*x^3 + 40*b^2*c^2*x^2 + 20*a*c^3*x^2 + 10*b^3*c*x + 20*a*b*c^2*x + b^4 + 2*a*b^2*c + 6*a^2*c^2)/((2*c*x + b)^5*c^3*d^6)","A",0
1132,1,87,0,0.181086," ","integrate((c*x^2+b*x+a)^2/(2*c*d*x+b*d)^7,x, algorithm=""giac"")","-\frac{48 \, c^{4} x^{4} + 96 \, b c^{3} x^{3} + 60 \, b^{2} c^{2} x^{2} + 48 \, a c^{3} x^{2} + 12 \, b^{3} c x + 48 \, a b c^{2} x + b^{4} + 4 \, a b^{2} c + 16 \, a^{2} c^{2}}{192 \, {\left(2 \, c x + b\right)}^{6} c^{3} d^{7}}"," ",0,"-1/192*(48*c^4*x^4 + 96*b*c^3*x^3 + 60*b^2*c^2*x^2 + 48*a*c^3*x^2 + 12*b^3*c*x + 48*a*b*c^2*x + b^4 + 4*a*b^2*c + 16*a^2*c^2)/((2*c*x + b)^6*c^3*d^7)","B",0
1133,1,87,0,0.154575," ","integrate((c*x^2+b*x+a)^2/(2*c*d*x+b*d)^8,x, algorithm=""giac"")","-\frac{70 \, c^{4} x^{4} + 140 \, b c^{3} x^{3} + 84 \, b^{2} c^{2} x^{2} + 84 \, a c^{3} x^{2} + 14 \, b^{3} c x + 84 \, a b c^{2} x + b^{4} + 6 \, a b^{2} c + 30 \, a^{2} c^{2}}{420 \, {\left(2 \, c x + b\right)}^{7} c^{3} d^{8}}"," ",0,"-1/420*(70*c^4*x^4 + 140*b*c^3*x^3 + 84*b^2*c^2*x^2 + 84*a*c^3*x^2 + 14*b^3*c*x + 84*a*b*c^2*x + b^4 + 6*a*b^2*c + 30*a^2*c^2)/((2*c*x + b)^7*c^3*d^8)","A",0
1134,1,87,0,0.156612," ","integrate((c*x^2+b*x+a)^2/(2*c*d*x+b*d)^9,x, algorithm=""giac"")","-\frac{96 \, c^{4} x^{4} + 192 \, b c^{3} x^{3} + 112 \, b^{2} c^{2} x^{2} + 128 \, a c^{3} x^{2} + 16 \, b^{3} c x + 128 \, a b c^{2} x + b^{4} + 8 \, a b^{2} c + 48 \, a^{2} c^{2}}{768 \, {\left(2 \, c x + b\right)}^{8} c^{3} d^{9}}"," ",0,"-1/768*(96*c^4*x^4 + 192*b*c^3*x^3 + 112*b^2*c^2*x^2 + 128*a*c^3*x^2 + 16*b^3*c*x + 128*a*b*c^2*x + b^4 + 8*a*b^2*c + 48*a^2*c^2)/((2*c*x + b)^8*c^3*d^9)","A",0
1135,1,87,0,0.155779," ","integrate((c*x^2+b*x+a)^2/(2*c*d*x+b*d)^10,x, algorithm=""giac"")","-\frac{126 \, c^{4} x^{4} + 252 \, b c^{3} x^{3} + 144 \, b^{2} c^{2} x^{2} + 180 \, a c^{3} x^{2} + 18 \, b^{3} c x + 180 \, a b c^{2} x + b^{4} + 10 \, a b^{2} c + 70 \, a^{2} c^{2}}{1260 \, {\left(2 \, c x + b\right)}^{9} c^{3} d^{10}}"," ",0,"-1/1260*(126*c^4*x^4 + 252*b*c^3*x^3 + 144*b^2*c^2*x^2 + 180*a*c^3*x^2 + 18*b^3*c*x + 180*a*b*c^2*x + b^4 + 10*a*b^2*c + 70*a^2*c^2)/((2*c*x + b)^9*c^3*d^10)","A",0
1136,1,87,0,0.164795," ","integrate((c*x^2+b*x+a)^2/(2*c*d*x+b*d)^11,x, algorithm=""giac"")","-\frac{160 \, c^{4} x^{4} + 320 \, b c^{3} x^{3} + 180 \, b^{2} c^{2} x^{2} + 240 \, a c^{3} x^{2} + 20 \, b^{3} c x + 240 \, a b c^{2} x + b^{4} + 12 \, a b^{2} c + 96 \, a^{2} c^{2}}{1920 \, {\left(2 \, c x + b\right)}^{10} c^{3} d^{11}}"," ",0,"-1/1920*(160*c^4*x^4 + 320*b*c^3*x^3 + 180*b^2*c^2*x^2 + 240*a*c^3*x^2 + 20*b^3*c*x + 240*a*b*c^2*x + b^4 + 12*a*b^2*c + 96*a^2*c^2)/((2*c*x + b)^10*c^3*d^11)","A",0
1137,1,424,0,0.187579," ","integrate((2*c*d*x+b*d)^5*(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{8}{3} \, c^{8} d^{5} x^{12} + 16 \, b c^{7} d^{5} x^{11} + \frac{208}{5} \, b^{2} c^{6} d^{5} x^{10} + \frac{48}{5} \, a c^{7} d^{5} x^{10} + \frac{184}{3} \, b^{3} c^{5} d^{5} x^{9} + 48 \, a b c^{6} d^{5} x^{9} + \frac{225}{4} \, b^{4} c^{4} d^{5} x^{8} + 102 \, a b^{2} c^{5} d^{5} x^{8} + 12 \, a^{2} c^{6} d^{5} x^{8} + 33 \, b^{5} c^{3} d^{5} x^{7} + 120 \, a b^{3} c^{4} d^{5} x^{7} + 48 \, a^{2} b c^{5} d^{5} x^{7} + \frac{73}{6} \, b^{6} c^{2} d^{5} x^{6} + 85 \, a b^{4} c^{3} d^{5} x^{6} + 80 \, a^{2} b^{2} c^{4} d^{5} x^{6} + \frac{16}{3} \, a^{3} c^{5} d^{5} x^{6} + \frac{13}{5} \, b^{7} c d^{5} x^{5} + \frac{183}{5} \, a b^{5} c^{2} d^{5} x^{5} + 72 \, a^{2} b^{3} c^{3} d^{5} x^{5} + 16 \, a^{3} b c^{4} d^{5} x^{5} + \frac{1}{4} \, b^{8} d^{5} x^{4} + 9 \, a b^{6} c d^{5} x^{4} + \frac{75}{2} \, a^{2} b^{4} c^{2} d^{5} x^{4} + 20 \, a^{3} b^{2} c^{3} d^{5} x^{4} + a b^{7} d^{5} x^{3} + 11 \, a^{2} b^{5} c d^{5} x^{3} + \frac{40}{3} \, a^{3} b^{3} c^{2} d^{5} x^{3} + \frac{3}{2} \, a^{2} b^{6} d^{5} x^{2} + 5 \, a^{3} b^{4} c d^{5} x^{2} + a^{3} b^{5} d^{5} x"," ",0,"8/3*c^8*d^5*x^12 + 16*b*c^7*d^5*x^11 + 208/5*b^2*c^6*d^5*x^10 + 48/5*a*c^7*d^5*x^10 + 184/3*b^3*c^5*d^5*x^9 + 48*a*b*c^6*d^5*x^9 + 225/4*b^4*c^4*d^5*x^8 + 102*a*b^2*c^5*d^5*x^8 + 12*a^2*c^6*d^5*x^8 + 33*b^5*c^3*d^5*x^7 + 120*a*b^3*c^4*d^5*x^7 + 48*a^2*b*c^5*d^5*x^7 + 73/6*b^6*c^2*d^5*x^6 + 85*a*b^4*c^3*d^5*x^6 + 80*a^2*b^2*c^4*d^5*x^6 + 16/3*a^3*c^5*d^5*x^6 + 13/5*b^7*c*d^5*x^5 + 183/5*a*b^5*c^2*d^5*x^5 + 72*a^2*b^3*c^3*d^5*x^5 + 16*a^3*b*c^4*d^5*x^5 + 1/4*b^8*d^5*x^4 + 9*a*b^6*c*d^5*x^4 + 75/2*a^2*b^4*c^2*d^5*x^4 + 20*a^3*b^2*c^3*d^5*x^4 + a*b^7*d^5*x^3 + 11*a^2*b^5*c*d^5*x^3 + 40/3*a^3*b^3*c^2*d^5*x^3 + 3/2*a^2*b^6*d^5*x^2 + 5*a^3*b^4*c*d^5*x^2 + a^3*b^5*d^5*x","B",0
1138,1,361,0,0.160720," ","integrate((2*c*d*x+b*d)^4*(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{16}{11} \, c^{7} d^{4} x^{11} + 8 \, b c^{6} d^{4} x^{10} + \frac{56}{3} \, b^{2} c^{5} d^{4} x^{9} + \frac{16}{3} \, a c^{6} d^{4} x^{9} + 24 \, b^{3} c^{4} d^{4} x^{8} + 24 \, a b c^{5} d^{4} x^{8} + \frac{129}{7} \, b^{4} c^{3} d^{4} x^{7} + \frac{312}{7} \, a b^{2} c^{4} d^{4} x^{7} + \frac{48}{7} \, a^{2} c^{5} d^{4} x^{7} + \frac{17}{2} \, b^{5} c^{2} d^{4} x^{6} + 44 \, a b^{3} c^{3} d^{4} x^{6} + 24 \, a^{2} b c^{4} d^{4} x^{6} + \frac{11}{5} \, b^{6} c d^{4} x^{5} + \frac{123}{5} \, a b^{4} c^{2} d^{4} x^{5} + \frac{168}{5} \, a^{2} b^{2} c^{3} d^{4} x^{5} + \frac{16}{5} \, a^{3} c^{4} d^{4} x^{5} + \frac{1}{4} \, b^{7} d^{4} x^{4} + \frac{15}{2} \, a b^{5} c d^{4} x^{4} + 24 \, a^{2} b^{3} c^{2} d^{4} x^{4} + 8 \, a^{3} b c^{3} d^{4} x^{4} + a b^{6} d^{4} x^{3} + 9 \, a^{2} b^{4} c d^{4} x^{3} + 8 \, a^{3} b^{2} c^{2} d^{4} x^{3} + \frac{3}{2} \, a^{2} b^{5} d^{4} x^{2} + 4 \, a^{3} b^{3} c d^{4} x^{2} + a^{3} b^{4} d^{4} x"," ",0,"16/11*c^7*d^4*x^11 + 8*b*c^6*d^4*x^10 + 56/3*b^2*c^5*d^4*x^9 + 16/3*a*c^6*d^4*x^9 + 24*b^3*c^4*d^4*x^8 + 24*a*b*c^5*d^4*x^8 + 129/7*b^4*c^3*d^4*x^7 + 312/7*a*b^2*c^4*d^4*x^7 + 48/7*a^2*c^5*d^4*x^7 + 17/2*b^5*c^2*d^4*x^6 + 44*a*b^3*c^3*d^4*x^6 + 24*a^2*b*c^4*d^4*x^6 + 11/5*b^6*c*d^4*x^5 + 123/5*a*b^4*c^2*d^4*x^5 + 168/5*a^2*b^2*c^3*d^4*x^5 + 16/5*a^3*c^4*d^4*x^5 + 1/4*b^7*d^4*x^4 + 15/2*a*b^5*c*d^4*x^4 + 24*a^2*b^3*c^2*d^4*x^4 + 8*a^3*b*c^3*d^4*x^4 + a*b^6*d^4*x^3 + 9*a^2*b^4*c*d^4*x^3 + 8*a^3*b^2*c^2*d^4*x^3 + 3/2*a^2*b^5*d^4*x^2 + 4*a^3*b^3*c*d^4*x^2 + a^3*b^4*d^4*x","B",0
1139,1,171,0,0.178490," ","integrate((2*c*d*x+b*d)^3*(c*x^2+b*x+a)^3,x, algorithm=""giac"")","{\left(c d x^{2} + b d x\right)} a^{3} b^{2} d^{2} + \frac{30 \, {\left(c d x^{2} + b d x\right)}^{2} a^{2} b^{2} d^{3} + 40 \, {\left(c d x^{2} + b d x\right)}^{2} a^{3} c d^{3} + 20 \, {\left(c d x^{2} + b d x\right)}^{3} a b^{2} d^{2} + 80 \, {\left(c d x^{2} + b d x\right)}^{3} a^{2} c d^{2} + 5 \, {\left(c d x^{2} + b d x\right)}^{4} b^{2} d + 60 \, {\left(c d x^{2} + b d x\right)}^{4} a c d + 16 \, {\left(c d x^{2} + b d x\right)}^{5} c}{20 \, d^{2}}"," ",0,"(c*d*x^2 + b*d*x)*a^3*b^2*d^2 + 1/20*(30*(c*d*x^2 + b*d*x)^2*a^2*b^2*d^3 + 40*(c*d*x^2 + b*d*x)^2*a^3*c*d^3 + 20*(c*d*x^2 + b*d*x)^3*a*b^2*d^2 + 80*(c*d*x^2 + b*d*x)^3*a^2*c*d^2 + 5*(c*d*x^2 + b*d*x)^4*b^2*d + 60*(c*d*x^2 + b*d*x)^4*a*c*d + 16*(c*d*x^2 + b*d*x)^5*c)/d^2","B",0
1140,1,235,0,0.172745," ","integrate((2*c*d*x+b*d)^2*(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{4}{9} \, c^{5} d^{2} x^{9} + 2 \, b c^{4} d^{2} x^{8} + \frac{25}{7} \, b^{2} c^{3} d^{2} x^{7} + \frac{12}{7} \, a c^{4} d^{2} x^{7} + \frac{19}{6} \, b^{3} c^{2} d^{2} x^{6} + 6 \, a b c^{3} d^{2} x^{6} + \frac{7}{5} \, b^{4} c d^{2} x^{5} + \frac{39}{5} \, a b^{2} c^{2} d^{2} x^{5} + \frac{12}{5} \, a^{2} c^{3} d^{2} x^{5} + \frac{1}{4} \, b^{5} d^{2} x^{4} + \frac{9}{2} \, a b^{3} c d^{2} x^{4} + 6 \, a^{2} b c^{2} d^{2} x^{4} + a b^{4} d^{2} x^{3} + 5 \, a^{2} b^{2} c d^{2} x^{3} + \frac{4}{3} \, a^{3} c^{2} d^{2} x^{3} + \frac{3}{2} \, a^{2} b^{3} d^{2} x^{2} + 2 \, a^{3} b c d^{2} x^{2} + a^{3} b^{2} d^{2} x"," ",0,"4/9*c^5*d^2*x^9 + 2*b*c^4*d^2*x^8 + 25/7*b^2*c^3*d^2*x^7 + 12/7*a*c^4*d^2*x^7 + 19/6*b^3*c^2*d^2*x^6 + 6*a*b*c^3*d^2*x^6 + 7/5*b^4*c*d^2*x^5 + 39/5*a*b^2*c^2*d^2*x^5 + 12/5*a^2*c^3*d^2*x^5 + 1/4*b^5*d^2*x^4 + 9/2*a*b^3*c*d^2*x^4 + 6*a^2*b*c^2*d^2*x^4 + a*b^4*d^2*x^3 + 5*a^2*b^2*c*d^2*x^3 + 4/3*a^3*c^2*d^2*x^3 + 3/2*a^2*b^3*d^2*x^2 + 2*a^3*b*c*d^2*x^2 + a^3*b^2*d^2*x","B",0
1141,1,73,0,0.158614," ","integrate((2*c*d*x+b*d)*(c*x^2+b*x+a)^3,x, algorithm=""giac"")","{\left(c d x^{2} + b d x\right)} a^{3} + \frac{6 \, {\left(c d x^{2} + b d x\right)}^{2} a^{2} d^{2} + 4 \, {\left(c d x^{2} + b d x\right)}^{3} a d + {\left(c d x^{2} + b d x\right)}^{4}}{4 \, d^{3}}"," ",0,"(c*d*x^2 + b*d*x)*a^3 + 1/4*(6*(c*d*x^2 + b*d*x)^2*a^2*d^2 + 4*(c*d*x^2 + b*d*x)^3*a*d + (c*d*x^2 + b*d*x)^4)/d^3","B",0
1142,1,213,0,0.178786," ","integrate((c*x^2+b*x+a)^3/(2*c*d*x+b*d),x, algorithm=""giac"")","-\frac{{\left(b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} \log\left({\left| 2 \, c x + b \right|}\right)}{128 \, c^{4} d} + \frac{16 \, c^{8} d^{5} x^{6} + 48 \, b c^{7} d^{5} x^{5} + 42 \, b^{2} c^{6} d^{5} x^{4} + 72 \, a c^{7} d^{5} x^{4} + 4 \, b^{3} c^{5} d^{5} x^{3} + 144 \, a b c^{6} d^{5} x^{3} - 3 \, b^{4} c^{4} d^{5} x^{2} + 36 \, a b^{2} c^{5} d^{5} x^{2} + 144 \, a^{2} c^{6} d^{5} x^{2} + 3 \, b^{5} c^{3} d^{5} x - 36 \, a b^{3} c^{4} d^{5} x + 144 \, a^{2} b c^{5} d^{5} x}{192 \, c^{6} d^{6}}"," ",0,"-1/128*(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)*log(abs(2*c*x + b))/(c^4*d) + 1/192*(16*c^8*d^5*x^6 + 48*b*c^7*d^5*x^5 + 42*b^2*c^6*d^5*x^4 + 72*a*c^7*d^5*x^4 + 4*b^3*c^5*d^5*x^3 + 144*a*b*c^6*d^5*x^3 - 3*b^4*c^4*d^5*x^2 + 36*a*b^2*c^5*d^5*x^2 + 144*a^2*c^6*d^5*x^2 + 3*b^5*c^3*d^5*x - 36*a*b^3*c^4*d^5*x + 144*a^2*b*c^5*d^5*x)/(c^6*d^6)","B",0
1143,1,221,0,0.161597," ","integrate((c*x^2+b*x+a)^3/(2*c*d*x+b*d)^2,x, algorithm=""giac"")","\frac{{\left(\frac{15 \, b^{4} d^{4}}{{\left(2 \, c d x + b d\right)}^{4}} - \frac{120 \, a b^{2} c d^{4}}{{\left(2 \, c d x + b d\right)}^{4}} + \frac{240 \, a^{2} c^{2} d^{4}}{{\left(2 \, c d x + b d\right)}^{4}} - \frac{5 \, b^{2} d^{2}}{{\left(2 \, c d x + b d\right)}^{2}} + \frac{20 \, a c d^{2}}{{\left(2 \, c d x + b d\right)}^{2}} + 1\right)} {\left(2 \, c d x + b d\right)}^{5}}{640 \, c^{4} d^{7}} + \frac{\frac{b^{6} c^{5} d^{11}}{2 \, c d x + b d} - \frac{12 \, a b^{4} c^{6} d^{11}}{2 \, c d x + b d} + \frac{48 \, a^{2} b^{2} c^{7} d^{11}}{2 \, c d x + b d} - \frac{64 \, a^{3} c^{8} d^{11}}{2 \, c d x + b d}}{128 \, c^{9} d^{12}}"," ",0,"1/640*(15*b^4*d^4/(2*c*d*x + b*d)^4 - 120*a*b^2*c*d^4/(2*c*d*x + b*d)^4 + 240*a^2*c^2*d^4/(2*c*d*x + b*d)^4 - 5*b^2*d^2/(2*c*d*x + b*d)^2 + 20*a*c*d^2/(2*c*d*x + b*d)^2 + 1)*(2*c*d*x + b*d)^5/(c^4*d^7) + 1/128*(b^6*c^5*d^11/(2*c*d*x + b*d) - 12*a*b^4*c^6*d^11/(2*c*d*x + b*d) + 48*a^2*b^2*c^7*d^11/(2*c*d*x + b*d) - 64*a^3*c^8*d^11/(2*c*d*x + b*d))/(c^9*d^12)","B",0
1144,1,148,0,0.165008," ","integrate((c*x^2+b*x+a)^3/(2*c*d*x+b*d)^3,x, algorithm=""giac"")","\frac{3 \, {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \log\left({\left| 2 \, c x + b \right|}\right)}{128 \, c^{4} d^{3}} + \frac{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}}{256 \, {\left(2 \, c x + b\right)}^{2} c^{4} d^{3}} + \frac{c^{12} d^{9} x^{4} + 2 \, b c^{11} d^{9} x^{3} + 6 \, a c^{11} d^{9} x^{2} - b^{3} c^{9} d^{9} x + 6 \, a b c^{10} d^{9} x}{32 \, c^{12} d^{12}}"," ",0,"3/128*(b^4 - 8*a*b^2*c + 16*a^2*c^2)*log(abs(2*c*x + b))/(c^4*d^3) + 1/256*(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)/((2*c*x + b)^2*c^4*d^3) + 1/32*(c^12*d^9*x^4 + 2*b*c^11*d^9*x^3 + 6*a*c^11*d^9*x^2 - b^3*c^9*d^9*x + 6*a*b*c^10*d^9*x)/(c^12*d^12)","A",0
1145,1,164,0,0.166445," ","integrate((c*x^2+b*x+a)^3/(2*c*d*x+b*d)^4,x, algorithm=""giac"")","-\frac{9 \, b^{4} c^{2} x^{2} - 72 \, a b^{2} c^{3} x^{2} + 144 \, a^{2} c^{4} x^{2} + 9 \, b^{5} c x - 72 \, a b^{3} c^{2} x + 144 \, a^{2} b c^{3} x + 2 \, b^{6} - 15 \, a b^{4} c + 24 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3}}{96 \, {\left(2 \, c x + b\right)}^{3} c^{4} d^{4}} + \frac{2 \, c^{11} d^{8} x^{3} + 3 \, b c^{10} d^{8} x^{2} - 3 \, b^{2} c^{9} d^{8} x + 18 \, a c^{10} d^{8} x}{96 \, c^{12} d^{12}}"," ",0,"-1/96*(9*b^4*c^2*x^2 - 72*a*b^2*c^3*x^2 + 144*a^2*c^4*x^2 + 9*b^5*c*x - 72*a*b^3*c^2*x + 144*a^2*b*c^3*x + 2*b^6 - 15*a*b^4*c + 24*a^2*b^2*c^2 + 16*a^3*c^3)/((2*c*x + b)^3*c^4*d^4) + 1/96*(2*c^11*d^8*x^3 + 3*b*c^10*d^8*x^2 - 3*b^2*c^9*d^8*x + 18*a*c^10*d^8*x)/(c^12*d^12)","A",0
1146,1,262,0,0.216133," ","integrate((c*x^2+b*x+a)^3/(2*c*d*x+b*d)^5,x, algorithm=""giac"")","\frac{3 \, {\left(b^{2} - 4 \, a c\right)} \log\left(\frac{1}{4 \, {\left(2 \, c d x + b d\right)}^{2} c^{2} d^{2}}\right)}{256 \, c^{4} d^{5}} - \frac{{\left(2 \, c d x + b d\right)}^{2} {\left(\frac{3 \, b^{2} d^{2}}{{\left(2 \, c d x + b d\right)}^{2}} - \frac{12 \, a c d^{2}}{{\left(2 \, c d x + b d\right)}^{2}} - 1\right)}}{256 \, c^{4} d^{7}} + \frac{\frac{b^{6} c^{8} d^{17}}{{\left(2 \, c d x + b d\right)}^{4}} - \frac{12 \, a b^{4} c^{9} d^{17}}{{\left(2 \, c d x + b d\right)}^{4}} + \frac{48 \, a^{2} b^{2} c^{10} d^{17}}{{\left(2 \, c d x + b d\right)}^{4}} - \frac{64 \, a^{3} c^{11} d^{17}}{{\left(2 \, c d x + b d\right)}^{4}} - \frac{6 \, b^{4} c^{8} d^{15}}{{\left(2 \, c d x + b d\right)}^{2}} + \frac{48 \, a b^{2} c^{9} d^{15}}{{\left(2 \, c d x + b d\right)}^{2}} - \frac{96 \, a^{2} c^{10} d^{15}}{{\left(2 \, c d x + b d\right)}^{2}}}{512 \, c^{12} d^{18}}"," ",0,"3/256*(b^2 - 4*a*c)*log(1/4/((2*c*d*x + b*d)^2*c^2*d^2))/(c^4*d^5) - 1/256*(2*c*d*x + b*d)^2*(3*b^2*d^2/(2*c*d*x + b*d)^2 - 12*a*c*d^2/(2*c*d*x + b*d)^2 - 1)/(c^4*d^7) + 1/512*(b^6*c^8*d^17/(2*c*d*x + b*d)^4 - 12*a*b^4*c^9*d^17/(2*c*d*x + b*d)^4 + 48*a^2*b^2*c^10*d^17/(2*c*d*x + b*d)^4 - 64*a^3*c^11*d^17/(2*c*d*x + b*d)^4 - 6*b^4*c^8*d^15/(2*c*d*x + b*d)^2 + 48*a*b^2*c^9*d^15/(2*c*d*x + b*d)^2 - 96*a^2*c^10*d^15/(2*c*d*x + b*d)^2)/(c^12*d^18)","B",0
1147,1,160,0,0.184293," ","integrate((c*x^2+b*x+a)^3/(2*c*d*x+b*d)^6,x, algorithm=""giac"")","\frac{x}{64 \, c^{3} d^{6}} + \frac{240 \, b^{2} c^{4} x^{4} - 960 \, a c^{5} x^{4} + 480 \, b^{3} c^{3} x^{3} - 1920 \, a b c^{4} x^{3} + 340 \, b^{4} c^{2} x^{2} - 1280 \, a b^{2} c^{3} x^{2} - 320 \, a^{2} c^{4} x^{2} + 100 \, b^{5} c x - 320 \, a b^{3} c^{2} x - 320 \, a^{2} b c^{3} x + 11 \, b^{6} - 32 \, a b^{4} c - 32 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}}{640 \, {\left(2 \, c x + b\right)}^{5} c^{4} d^{6}}"," ",0,"1/64*x/(c^3*d^6) + 1/640*(240*b^2*c^4*x^4 - 960*a*c^5*x^4 + 480*b^3*c^3*x^3 - 1920*a*b*c^4*x^3 + 340*b^4*c^2*x^2 - 1280*a*b^2*c^3*x^2 - 320*a^2*c^4*x^2 + 100*b^5*c*x - 320*a*b^3*c^2*x - 320*a^2*b*c^3*x + 11*b^6 - 32*a*b^4*c - 32*a^2*b^2*c^2 - 64*a^3*c^3)/((2*c*x + b)^5*c^4*d^6)","A",0
1148,1,163,0,0.172528," ","integrate((c*x^2+b*x+a)^3/(2*c*d*x+b*d)^7,x, algorithm=""giac"")","\frac{\log\left({\left| 2 \, c x + b \right|}\right)}{128 \, c^{4} d^{7}} + \frac{11 \, b^{6} - 24 \, a b^{4} c - 48 \, a^{2} b^{2} c^{2} - 128 \, a^{3} c^{3} + 288 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} x^{4} + 576 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} x^{3} + 36 \, {\left(11 \, b^{4} c^{2} - 40 \, a b^{2} c^{3} - 16 \, a^{2} c^{4}\right)} x^{2} + 36 \, {\left(3 \, b^{5} c - 8 \, a b^{3} c^{2} - 16 \, a^{2} b c^{3}\right)} x}{1536 \, {\left(2 \, c x + b\right)}^{6} c^{4} d^{7}}"," ",0,"1/128*log(abs(2*c*x + b))/(c^4*d^7) + 1/1536*(11*b^6 - 24*a*b^4*c - 48*a^2*b^2*c^2 - 128*a^3*c^3 + 288*(b^2*c^4 - 4*a*c^5)*x^4 + 576*(b^3*c^3 - 4*a*b*c^4)*x^3 + 36*(11*b^4*c^2 - 40*a*b^2*c^3 - 16*a^2*c^4)*x^2 + 36*(3*b^5*c - 8*a*b^3*c^2 - 16*a^2*b*c^3)*x)/((2*c*x + b)^6*c^4*d^7)","A",0
1149,1,165,0,0.180360," ","integrate((c*x^2+b*x+a)^3/(2*c*d*x+b*d)^8,x, algorithm=""giac"")","-\frac{140 \, c^{6} x^{6} + 420 \, b c^{5} x^{5} + 490 \, b^{2} c^{4} x^{4} + 140 \, a c^{5} x^{4} + 280 \, b^{3} c^{3} x^{3} + 280 \, a b c^{4} x^{3} + 84 \, b^{4} c^{2} x^{2} + 168 \, a b^{2} c^{3} x^{2} + 84 \, a^{2} c^{4} x^{2} + 14 \, b^{5} c x + 28 \, a b^{3} c^{2} x + 84 \, a^{2} b c^{3} x + b^{6} + 2 \, a b^{4} c + 6 \, a^{2} b^{2} c^{2} + 20 \, a^{3} c^{3}}{280 \, {\left(2 \, c x + b\right)}^{7} c^{4} d^{8}}"," ",0,"-1/280*(140*c^6*x^6 + 420*b*c^5*x^5 + 490*b^2*c^4*x^4 + 140*a*c^5*x^4 + 280*b^3*c^3*x^3 + 280*a*b*c^4*x^3 + 84*b^4*c^2*x^2 + 168*a*b^2*c^3*x^2 + 84*a^2*c^4*x^2 + 14*b^5*c*x + 28*a*b^3*c^2*x + 84*a^2*b*c^3*x + b^6 + 2*a*b^4*c + 6*a^2*b^2*c^2 + 20*a^3*c^3)/((2*c*x + b)^7*c^4*d^8)","A",0
1150,1,165,0,0.160075," ","integrate((c*x^2+b*x+a)^3/(2*c*d*x+b*d)^9,x, algorithm=""giac"")","-\frac{256 \, c^{6} x^{6} + 768 \, b c^{5} x^{5} + 864 \, b^{2} c^{4} x^{4} + 384 \, a c^{5} x^{4} + 448 \, b^{3} c^{3} x^{3} + 768 \, a b c^{4} x^{3} + 112 \, b^{4} c^{2} x^{2} + 448 \, a b^{2} c^{3} x^{2} + 256 \, a^{2} c^{4} x^{2} + 16 \, b^{5} c x + 64 \, a b^{3} c^{2} x + 256 \, a^{2} b c^{3} x + b^{6} + 4 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2} + 64 \, a^{3} c^{3}}{1024 \, {\left(2 \, c x + b\right)}^{8} c^{4} d^{9}}"," ",0,"-1/1024*(256*c^6*x^6 + 768*b*c^5*x^5 + 864*b^2*c^4*x^4 + 384*a*c^5*x^4 + 448*b^3*c^3*x^3 + 768*a*b*c^4*x^3 + 112*b^4*c^2*x^2 + 448*a*b^2*c^3*x^2 + 256*a^2*c^4*x^2 + 16*b^5*c*x + 64*a*b^3*c^2*x + 256*a^2*b*c^3*x + b^6 + 4*a*b^4*c + 16*a^2*b^2*c^2 + 64*a^3*c^3)/((2*c*x + b)^8*c^4*d^9)","B",0
1151,1,165,0,0.158499," ","integrate((c*x^2+b*x+a)^3/(2*c*d*x+b*d)^10,x, algorithm=""giac"")","-\frac{420 \, c^{6} x^{6} + 1260 \, b c^{5} x^{5} + 1386 \, b^{2} c^{4} x^{4} + 756 \, a c^{5} x^{4} + 672 \, b^{3} c^{3} x^{3} + 1512 \, a b c^{4} x^{3} + 144 \, b^{4} c^{2} x^{2} + 864 \, a b^{2} c^{3} x^{2} + 540 \, a^{2} c^{4} x^{2} + 18 \, b^{5} c x + 108 \, a b^{3} c^{2} x + 540 \, a^{2} b c^{3} x + b^{6} + 6 \, a b^{4} c + 30 \, a^{2} b^{2} c^{2} + 140 \, a^{3} c^{3}}{2520 \, {\left(2 \, c x + b\right)}^{9} c^{4} d^{10}}"," ",0,"-1/2520*(420*c^6*x^6 + 1260*b*c^5*x^5 + 1386*b^2*c^4*x^4 + 756*a*c^5*x^4 + 672*b^3*c^3*x^3 + 1512*a*b*c^4*x^3 + 144*b^4*c^2*x^2 + 864*a*b^2*c^3*x^2 + 540*a^2*c^4*x^2 + 18*b^5*c*x + 108*a*b^3*c^2*x + 540*a^2*b*c^3*x + b^6 + 6*a*b^4*c + 30*a^2*b^2*c^2 + 140*a^3*c^3)/((2*c*x + b)^9*c^4*d^10)","A",0
1152,1,165,0,0.157311," ","integrate((c*x^2+b*x+a)^3/(2*c*d*x+b*d)^11,x, algorithm=""giac"")","-\frac{640 \, c^{6} x^{6} + 1920 \, b c^{5} x^{5} + 2080 \, b^{2} c^{4} x^{4} + 1280 \, a c^{5} x^{4} + 960 \, b^{3} c^{3} x^{3} + 2560 \, a b c^{4} x^{3} + 180 \, b^{4} c^{2} x^{2} + 1440 \, a b^{2} c^{3} x^{2} + 960 \, a^{2} c^{4} x^{2} + 20 \, b^{5} c x + 160 \, a b^{3} c^{2} x + 960 \, a^{2} b c^{3} x + b^{6} + 8 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} + 256 \, a^{3} c^{3}}{5120 \, {\left(2 \, c x + b\right)}^{10} c^{4} d^{11}}"," ",0,"-1/5120*(640*c^6*x^6 + 1920*b*c^5*x^5 + 2080*b^2*c^4*x^4 + 1280*a*c^5*x^4 + 960*b^3*c^3*x^3 + 2560*a*b*c^4*x^3 + 180*b^4*c^2*x^2 + 1440*a*b^2*c^3*x^2 + 960*a^2*c^4*x^2 + 20*b^5*c*x + 160*a*b^3*c^2*x + 960*a^2*b*c^3*x + b^6 + 8*a*b^4*c + 48*a^2*b^2*c^2 + 256*a^3*c^3)/((2*c*x + b)^10*c^4*d^11)","A",0
1153,1,165,0,0.157878," ","integrate((c*x^2+b*x+a)^3/(2*c*d*x+b*d)^12,x, algorithm=""giac"")","-\frac{924 \, c^{6} x^{6} + 2772 \, b c^{5} x^{5} + 2970 \, b^{2} c^{4} x^{4} + 1980 \, a c^{5} x^{4} + 1320 \, b^{3} c^{3} x^{3} + 3960 \, a b c^{4} x^{3} + 220 \, b^{4} c^{2} x^{2} + 2200 \, a b^{2} c^{3} x^{2} + 1540 \, a^{2} c^{4} x^{2} + 22 \, b^{5} c x + 220 \, a b^{3} c^{2} x + 1540 \, a^{2} b c^{3} x + b^{6} + 10 \, a b^{4} c + 70 \, a^{2} b^{2} c^{2} + 420 \, a^{3} c^{3}}{9240 \, {\left(2 \, c x + b\right)}^{11} c^{4} d^{12}}"," ",0,"-1/9240*(924*c^6*x^6 + 2772*b*c^5*x^5 + 2970*b^2*c^4*x^4 + 1980*a*c^5*x^4 + 1320*b^3*c^3*x^3 + 3960*a*b*c^4*x^3 + 220*b^4*c^2*x^2 + 2200*a*b^2*c^3*x^2 + 1540*a^2*c^4*x^2 + 22*b^5*c*x + 220*a*b^3*c^2*x + 1540*a^2*b*c^3*x + b^6 + 10*a*b^4*c + 70*a^2*b^2*c^2 + 420*a^3*c^3)/((2*c*x + b)^11*c^4*d^12)","A",0
1154,1,313,0,0.180967," ","integrate((2*c*d*x+b*d)^8/(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{2 \, {\left(b^{8} d^{8} - 16 \, a b^{6} c d^{8} + 96 \, a^{2} b^{4} c^{2} d^{8} - 256 \, a^{3} b^{2} c^{3} d^{8} + 256 \, a^{4} c^{4} d^{8}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{\sqrt{-b^{2} + 4 \, a c}} + \frac{16 \, {\left(240 \, c^{14} d^{8} x^{7} + 840 \, b c^{13} d^{8} x^{6} + 1344 \, b^{2} c^{12} d^{8} x^{5} - 336 \, a c^{13} d^{8} x^{5} + 1260 \, b^{3} c^{11} d^{8} x^{4} - 840 \, a b c^{12} d^{8} x^{4} + 770 \, b^{4} c^{10} d^{8} x^{3} - 1120 \, a b^{2} c^{11} d^{8} x^{3} + 560 \, a^{2} c^{12} d^{8} x^{3} + 315 \, b^{5} c^{9} d^{8} x^{2} - 840 \, a b^{3} c^{10} d^{8} x^{2} + 840 \, a^{2} b c^{11} d^{8} x^{2} + 105 \, b^{6} c^{8} d^{8} x - 630 \, a b^{4} c^{9} d^{8} x + 1680 \, a^{2} b^{2} c^{10} d^{8} x - 1680 \, a^{3} c^{11} d^{8} x\right)}}{105 \, c^{7}}"," ",0,"2*(b^8*d^8 - 16*a*b^6*c*d^8 + 96*a^2*b^4*c^2*d^8 - 256*a^3*b^2*c^3*d^8 + 256*a^4*c^4*d^8)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/sqrt(-b^2 + 4*a*c) + 16/105*(240*c^14*d^8*x^7 + 840*b*c^13*d^8*x^6 + 1344*b^2*c^12*d^8*x^5 - 336*a*c^13*d^8*x^5 + 1260*b^3*c^11*d^8*x^4 - 840*a*b*c^12*d^8*x^4 + 770*b^4*c^10*d^8*x^3 - 1120*a*b^2*c^11*d^8*x^3 + 560*a^2*c^12*d^8*x^3 + 315*b^5*c^9*d^8*x^2 - 840*a*b^3*c^10*d^8*x^2 + 840*a^2*b*c^11*d^8*x^2 + 105*b^6*c^8*d^8*x - 630*a*b^4*c^9*d^8*x + 1680*a^2*b^2*c^10*d^8*x - 1680*a^3*c^11*d^8*x)/c^7","B",0
1155,1,219,0,0.157147," ","integrate((2*c*d*x+b*d)^7/(c*x^2+b*x+a),x, algorithm=""giac"")","{\left(b^{6} d^{7} - 12 \, a b^{4} c d^{7} + 48 \, a^{2} b^{2} c^{2} d^{7} - 64 \, a^{3} c^{3} d^{7}\right)} \log\left(c x^{2} + b x + a\right) + \frac{4 \, {\left(16 \, c^{12} d^{7} x^{6} + 48 \, b c^{11} d^{7} x^{5} + 66 \, b^{2} c^{10} d^{7} x^{4} - 24 \, a c^{11} d^{7} x^{4} + 52 \, b^{3} c^{9} d^{7} x^{3} - 48 \, a b c^{10} d^{7} x^{3} + 27 \, b^{4} c^{8} d^{7} x^{2} - 60 \, a b^{2} c^{9} d^{7} x^{2} + 48 \, a^{2} c^{10} d^{7} x^{2} + 9 \, b^{5} c^{7} d^{7} x - 36 \, a b^{3} c^{8} d^{7} x + 48 \, a^{2} b c^{9} d^{7} x\right)}}{3 \, c^{6}}"," ",0,"(b^6*d^7 - 12*a*b^4*c*d^7 + 48*a^2*b^2*c^2*d^7 - 64*a^3*c^3*d^7)*log(c*x^2 + b*x + a) + 4/3*(16*c^12*d^7*x^6 + 48*b*c^11*d^7*x^5 + 66*b^2*c^10*d^7*x^4 - 24*a*c^11*d^7*x^4 + 52*b^3*c^9*d^7*x^3 - 48*a*b*c^10*d^7*x^3 + 27*b^4*c^8*d^7*x^2 - 60*a*b^2*c^9*d^7*x^2 + 48*a^2*c^10*d^7*x^2 + 9*b^5*c^7*d^7*x - 36*a*b^3*c^8*d^7*x + 48*a^2*b*c^9*d^7*x)/c^6","B",0
1156,1,197,0,0.193331," ","integrate((2*c*d*x+b*d)^6/(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{2 \, {\left(b^{6} d^{6} - 12 \, a b^{4} c d^{6} + 48 \, a^{2} b^{2} c^{2} d^{6} - 64 \, a^{3} c^{3} d^{6}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{\sqrt{-b^{2} + 4 \, a c}} + \frac{4 \, {\left(48 \, c^{10} d^{6} x^{5} + 120 \, b c^{9} d^{6} x^{4} + 140 \, b^{2} c^{8} d^{6} x^{3} - 80 \, a c^{9} d^{6} x^{3} + 90 \, b^{3} c^{7} d^{6} x^{2} - 120 \, a b c^{8} d^{6} x^{2} + 45 \, b^{4} c^{6} d^{6} x - 180 \, a b^{2} c^{7} d^{6} x + 240 \, a^{2} c^{8} d^{6} x\right)}}{15 \, c^{5}}"," ",0,"2*(b^6*d^6 - 12*a*b^4*c*d^6 + 48*a^2*b^2*c^2*d^6 - 64*a^3*c^3*d^6)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/sqrt(-b^2 + 4*a*c) + 4/15*(48*c^10*d^6*x^5 + 120*b*c^9*d^6*x^4 + 140*b^2*c^8*d^6*x^3 - 80*a*c^9*d^6*x^3 + 90*b^3*c^7*d^6*x^2 - 120*a*b*c^8*d^6*x^2 + 45*b^4*c^6*d^6*x - 180*a*b^2*c^7*d^6*x + 240*a^2*c^8*d^6*x)/c^5","B",0
1157,1,118,0,0.165256," ","integrate((2*c*d*x+b*d)^5/(c*x^2+b*x+a),x, algorithm=""giac"")","{\left(b^{4} d^{5} - 8 \, a b^{2} c d^{5} + 16 \, a^{2} c^{2} d^{5}\right)} \log\left(c x^{2} + b x + a\right) + \frac{8 \, {\left(c^{8} d^{5} x^{4} + 2 \, b c^{7} d^{5} x^{3} + 2 \, b^{2} c^{6} d^{5} x^{2} - 2 \, a c^{7} d^{5} x^{2} + b^{3} c^{5} d^{5} x - 2 \, a b c^{6} d^{5} x\right)}}{c^{4}}"," ",0,"(b^4*d^5 - 8*a*b^2*c*d^5 + 16*a^2*c^2*d^5)*log(c*x^2 + b*x + a) + 8*(c^8*d^5*x^4 + 2*b*c^7*d^5*x^3 + 2*b^2*c^6*d^5*x^2 - 2*a*c^7*d^5*x^2 + b^3*c^5*d^5*x - 2*a*b*c^6*d^5*x)/c^4","A",0
1158,1,115,0,0.173386," ","integrate((2*c*d*x+b*d)^4/(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{2 \, {\left(b^{4} d^{4} - 8 \, a b^{2} c d^{4} + 16 \, a^{2} c^{2} d^{4}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{\sqrt{-b^{2} + 4 \, a c}} + \frac{8 \, {\left(2 \, c^{6} d^{4} x^{3} + 3 \, b c^{5} d^{4} x^{2} + 3 \, b^{2} c^{4} d^{4} x - 6 \, a c^{5} d^{4} x\right)}}{3 \, c^{3}}"," ",0,"2*(b^4*d^4 - 8*a*b^2*c*d^4 + 16*a^2*c^2*d^4)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/sqrt(-b^2 + 4*a*c) + 8/3*(2*c^6*d^4*x^3 + 3*b*c^5*d^4*x^2 + 3*b^2*c^4*d^4*x - 6*a*c^5*d^4*x)/c^3","A",0
1159,1,50,0,0.150474," ","integrate((2*c*d*x+b*d)^3/(c*x^2+b*x+a),x, algorithm=""giac"")","4 \, {\left(c d x^{2} + b d x\right)} c d^{2} + {\left(b^{2} d^{3} - 4 \, a c d^{3}\right)} \log\left({\left| c d x^{2} + b d x + a d \right|}\right)"," ",0,"4*(c*d*x^2 + b*d*x)*c*d^2 + (b^2*d^3 - 4*a*c*d^3)*log(abs(c*d*x^2 + b*d*x + a*d))","A",0
1160,1,57,0,0.153184," ","integrate((2*c*d*x+b*d)^2/(c*x^2+b*x+a),x, algorithm=""giac"")","4 \, c d^{2} x + \frac{2 \, {\left(b^{2} d^{2} - 4 \, a c d^{2}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{\sqrt{-b^{2} + 4 \, a c}}"," ",0,"4*c*d^2*x + 2*(b^2*d^2 - 4*a*c*d^2)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/sqrt(-b^2 + 4*a*c)","A",0
1161,1,21,0,0.155008," ","integrate((2*c*d*x+b*d)/(c*x^2+b*x+a),x, algorithm=""giac"")","d \log\left({\left| a + \frac{c d x^{2} + b d x}{d} \right|}\right)"," ",0,"d*log(abs(a + (c*d*x^2 + b*d*x)/d))","A",0
1162,1,57,0,0.175819," ","integrate(1/(2*c*d*x+b*d)/(c*x^2+b*x+a),x, algorithm=""giac"")","-\frac{2 \, c^{2} \log\left({\left| 2 \, c x + b \right|}\right)}{b^{2} c^{2} d - 4 \, a c^{3} d} + \frac{\log\left(c x^{2} + b x + a\right)}{b^{2} d - 4 \, a c d}"," ",0,"-2*c^2*log(abs(2*c*x + b))/(b^2*c^2*d - 4*a*c^3*d) + log(c*x^2 + b*x + a)/(b^2*d - 4*a*c*d)","A",0
1163,1,117,0,0.163823," ","integrate(1/(2*c*d*x+b*d)^2/(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{2 \, c^{2} d^{3}}{{\left(b^{2} c^{2} d^{4} - 4 \, a c^{3} d^{4}\right)} {\left(2 \, c d x + b d\right)}} - \frac{2 \, \arctan\left(-\frac{\frac{b^{2} d}{2 \, c d x + b d} - \frac{4 \, a c d}{2 \, c d x + b d}}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{2} - 4 \, a c\right)} \sqrt{-b^{2} + 4 \, a c} d^{2}}"," ",0,"2*c^2*d^3/((b^2*c^2*d^4 - 4*a*c^3*d^4)*(2*c*d*x + b*d)) - 2*arctan(-(b^2*d/(2*c*d*x + b*d) - 4*a*c*d/(2*c*d*x + b*d))/sqrt(-b^2 + 4*a*c))/((b^2 - 4*a*c)*sqrt(-b^2 + 4*a*c)*d^2)","B",0
1164,1,111,0,0.160880," ","integrate(1/(2*c*d*x+b*d)^3/(c*x^2+b*x+a),x, algorithm=""giac"")","-\frac{2 \, c \log\left({\left| 2 \, c x + b \right|}\right)}{b^{4} c d^{3} - 8 \, a b^{2} c^{2} d^{3} + 16 \, a^{2} c^{3} d^{3}} + \frac{\log\left(c x^{2} + b x + a\right)}{b^{4} d^{3} - 8 \, a b^{2} c d^{3} + 16 \, a^{2} c^{2} d^{3}} + \frac{1}{{\left(b^{2} - 4 \, a c\right)} {\left(2 \, c x + b\right)}^{2} d^{3}}"," ",0,"-2*c*log(abs(2*c*x + b))/(b^4*c*d^3 - 8*a*b^2*c^2*d^3 + 16*a^2*c^3*d^3) + log(c*x^2 + b*x + a)/(b^4*d^3 - 8*a*b^2*c*d^3 + 16*a^2*c^2*d^3) + 1/((b^2 - 4*a*c)*(2*c*x + b)^2*d^3)","A",0
1165,1,128,0,0.164910," ","integrate(1/(2*c*d*x+b*d)^4/(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{2 \, \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{4} d^{4} - 8 \, a b^{2} c d^{4} + 16 \, a^{2} c^{2} d^{4}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{8 \, {\left(3 \, c^{2} x^{2} + 3 \, b c x + b^{2} - a c\right)}}{3 \, {\left(b^{4} d^{4} - 8 \, a b^{2} c d^{4} + 16 \, a^{2} c^{2} d^{4}\right)} {\left(2 \, c x + b\right)}^{3}}"," ",0,"2*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^4*d^4 - 8*a*b^2*c*d^4 + 16*a^2*c^2*d^4)*sqrt(-b^2 + 4*a*c)) + 8/3*(3*c^2*x^2 + 3*b*c*x + b^2 - a*c)/((b^4*d^4 - 8*a*b^2*c*d^4 + 16*a^2*c^2*d^4)*(2*c*x + b)^3)","A",0
1166,1,308,0,0.179096," ","integrate((2*c*d*x+b*d)^8/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{28 \, {\left(b^{6} c d^{8} - 12 \, a b^{4} c^{2} d^{8} + 48 \, a^{2} b^{2} c^{3} d^{8} - 64 \, a^{3} c^{4} d^{8}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{\sqrt{-b^{2} + 4 \, a c}} - \frac{2 \, b^{6} c d^{8} x - 24 \, a b^{4} c^{2} d^{8} x + 96 \, a^{2} b^{2} c^{3} d^{8} x - 128 \, a^{3} c^{4} d^{8} x + b^{7} d^{8} - 12 \, a b^{5} c d^{8} + 48 \, a^{2} b^{3} c^{2} d^{8} - 64 \, a^{3} b c^{3} d^{8}}{c x^{2} + b x + a} + \frac{32 \, {\left(24 \, c^{16} d^{8} x^{5} + 60 \, b c^{15} d^{8} x^{4} + 80 \, b^{2} c^{14} d^{8} x^{3} - 80 \, a c^{15} d^{8} x^{3} + 60 \, b^{3} c^{13} d^{8} x^{2} - 120 \, a b c^{14} d^{8} x^{2} + 45 \, b^{4} c^{12} d^{8} x - 240 \, a b^{2} c^{13} d^{8} x + 360 \, a^{2} c^{14} d^{8} x\right)}}{15 \, c^{10}}"," ",0,"28*(b^6*c*d^8 - 12*a*b^4*c^2*d^8 + 48*a^2*b^2*c^3*d^8 - 64*a^3*c^4*d^8)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/sqrt(-b^2 + 4*a*c) - (2*b^6*c*d^8*x - 24*a*b^4*c^2*d^8*x + 96*a^2*b^2*c^3*d^8*x - 128*a^3*c^4*d^8*x + b^7*d^8 - 12*a*b^5*c*d^8 + 48*a^2*b^3*c^2*d^8 - 64*a^3*b*c^3*d^8)/(c*x^2 + b*x + a) + 32/15*(24*c^16*d^8*x^5 + 60*b*c^15*d^8*x^4 + 80*b^2*c^14*d^8*x^3 - 80*a*c^15*d^8*x^3 + 60*b^3*c^13*d^8*x^2 - 120*a*b*c^14*d^8*x^2 + 45*b^4*c^12*d^8*x - 240*a*b^2*c^13*d^8*x + 360*a^2*c^14*d^8*x)/c^10","B",0
1167,1,181,0,0.166626," ","integrate((2*c*d*x+b*d)^7/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","12 \, {\left(b^{4} c d^{7} - 8 \, a b^{2} c^{2} d^{7} + 16 \, a^{2} c^{3} d^{7}\right)} \log\left(c x^{2} + b x + a\right) - \frac{b^{6} d^{7} - 12 \, a b^{4} c d^{7} + 48 \, a^{2} b^{2} c^{2} d^{7} - 64 \, a^{3} c^{3} d^{7}}{c x^{2} + b x + a} + \frac{16 \, {\left(2 \, c^{13} d^{7} x^{4} + 4 \, b c^{12} d^{7} x^{3} + 5 \, b^{2} c^{11} d^{7} x^{2} - 8 \, a c^{12} d^{7} x^{2} + 3 \, b^{3} c^{10} d^{7} x - 8 \, a b c^{11} d^{7} x\right)}}{c^{8}}"," ",0,"12*(b^4*c*d^7 - 8*a*b^2*c^2*d^7 + 16*a^2*c^3*d^7)*log(c*x^2 + b*x + a) - (b^6*d^7 - 12*a*b^4*c*d^7 + 48*a^2*b^2*c^2*d^7 - 64*a^3*c^3*d^7)/(c*x^2 + b*x + a) + 16*(2*c^13*d^7*x^4 + 4*b*c^12*d^7*x^3 + 5*b^2*c^11*d^7*x^2 - 8*a*c^12*d^7*x^2 + 3*b^3*c^10*d^7*x - 8*a*b*c^11*d^7*x)/c^8","B",0
1168,1,197,0,0.165947," ","integrate((2*c*d*x+b*d)^6/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{20 \, {\left(b^{4} c d^{6} - 8 \, a b^{2} c^{2} d^{6} + 16 \, a^{2} c^{3} d^{6}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{\sqrt{-b^{2} + 4 \, a c}} - \frac{2 \, b^{4} c d^{6} x - 16 \, a b^{2} c^{2} d^{6} x + 32 \, a^{2} c^{3} d^{6} x + b^{5} d^{6} - 8 \, a b^{3} c d^{6} + 16 \, a^{2} b c^{2} d^{6}}{c x^{2} + b x + a} + \frac{16 \, {\left(4 \, c^{10} d^{6} x^{3} + 6 \, b c^{9} d^{6} x^{2} + 9 \, b^{2} c^{8} d^{6} x - 24 \, a c^{9} d^{6} x\right)}}{3 \, c^{6}}"," ",0,"20*(b^4*c*d^6 - 8*a*b^2*c^2*d^6 + 16*a^2*c^3*d^6)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/sqrt(-b^2 + 4*a*c) - (2*b^4*c*d^6*x - 16*a*b^2*c^2*d^6*x + 32*a^2*c^3*d^6*x + b^5*d^6 - 8*a*b^3*c*d^6 + 16*a^2*b*c^2*d^6)/(c*x^2 + b*x + a) + 16/3*(4*c^10*d^6*x^3 + 6*b*c^9*d^6*x^2 + 9*b^2*c^8*d^6*x - 24*a*c^9*d^6*x)/c^6","B",0
1169,1,100,0,0.161653," ","integrate((2*c*d*x+b*d)^5/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","8 \, {\left(b^{2} c d^{5} - 4 \, a c^{2} d^{5}\right)} \log\left(c x^{2} + b x + a\right) - \frac{b^{4} d^{5} - 8 \, a b^{2} c d^{5} + 16 \, a^{2} c^{2} d^{5}}{c x^{2} + b x + a} + \frac{16 \, {\left(c^{7} d^{5} x^{2} + b c^{6} d^{5} x\right)}}{c^{4}}"," ",0,"8*(b^2*c*d^5 - 4*a*c^2*d^5)*log(c*x^2 + b*x + a) - (b^4*d^5 - 8*a*b^2*c*d^5 + 16*a^2*c^2*d^5)/(c*x^2 + b*x + a) + 16*(c^7*d^5*x^2 + b*c^6*d^5*x)/c^4","A",0
1170,1,112,0,0.157460," ","integrate((2*c*d*x+b*d)^4/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","16 \, c^{2} d^{4} x + \frac{12 \, {\left(b^{2} c d^{4} - 4 \, a c^{2} d^{4}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{\sqrt{-b^{2} + 4 \, a c}} - \frac{2 \, b^{2} c d^{4} x - 8 \, a c^{2} d^{4} x + b^{3} d^{4} - 4 \, a b c d^{4}}{c x^{2} + b x + a}"," ",0,"16*c^2*d^4*x + 12*(b^2*c*d^4 - 4*a*c^2*d^4)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/sqrt(-b^2 + 4*a*c) - (2*b^2*c*d^4*x - 8*a*c^2*d^4*x + b^3*d^4 - 4*a*b*c*d^4)/(c*x^2 + b*x + a)","A",0
1171,1,101,0,0.180743," ","integrate((2*c*d*x+b*d)^3/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","-4 \, {\left(d \log\left(\frac{{\left| a + \frac{c d x^{2} + b d x}{d} \right|} {\left| d \right|}}{{\left(a + \frac{c d x^{2} + b d x}{d}\right)}^{2}}\right) - \frac{a d}{a + \frac{c d x^{2} + b d x}{d}}\right)} c d^{2} - \frac{b^{2} d^{3}}{a + \frac{c d x^{2} + b d x}{d}}"," ",0,"-4*(d*log(abs(a + (c*d*x^2 + b*d*x)/d)*abs(d)/(a + (c*d*x^2 + b*d*x)/d)^2) - a*d/(a + (c*d*x^2 + b*d*x)/d))*c*d^2 - b^2*d^3/(a + (c*d*x^2 + b*d*x)/d)","B",0
1172,1,66,0,0.157999," ","integrate((2*c*d*x+b*d)^2/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{4 \, c d^{2} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{\sqrt{-b^{2} + 4 \, a c}} - \frac{2 \, c d^{2} x + b d^{2}}{c x^{2} + b x + a}"," ",0,"4*c*d^2*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/sqrt(-b^2 + 4*a*c) - (2*c*d^2*x + b*d^2)/(c*x^2 + b*x + a)","A",0
1173,1,22,0,0.149872," ","integrate((2*c*d*x+b*d)/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","-\frac{d}{a + \frac{c d x^{2} + b d x}{d}}"," ",0,"-d/(a + (c*d*x^2 + b*d*x)/d)","A",0
1174,1,108,0,0.193707," ","integrate(1/(2*c*d*x+b*d)/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{8 \, c^{2} \log\left({\left| 2 \, c x + b \right|}\right)}{b^{4} c d - 8 \, a b^{2} c^{2} d + 16 \, a^{2} c^{3} d} - \frac{4 \, c \log\left(c x^{2} + b x + a\right)}{b^{4} d - 8 \, a b^{2} c d + 16 \, a^{2} c^{2} d} - \frac{1}{{\left(c x^{2} + b x + a\right)} {\left(b^{2} - 4 \, a c\right)} d}"," ",0,"8*c^2*log(abs(2*c*x + b))/(b^4*c*d - 8*a*b^2*c^2*d + 16*a^2*c^3*d) - 4*c*log(c*x^2 + b*x + a)/(b^4*d - 8*a*b^2*c*d + 16*a^2*c^2*d) - 1/((c*x^2 + b*x + a)*(b^2 - 4*a*c)*d)","A",0
1175,1,220,0,0.166555," ","integrate(1/(2*c*d*x+b*d)^2/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","-\frac{8 \, c^{5} d^{7}}{{\left(b^{4} c^{4} d^{8} - 8 \, a b^{2} c^{5} d^{8} + 16 \, a^{2} c^{6} d^{8}\right)} {\left(2 \, c d x + b d\right)}} - \frac{12 \, c \arctan\left(\frac{\frac{b^{2} d}{2 \, c d x + b d} - \frac{4 \, a c d}{2 \, c d x + b d}}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{-b^{2} + 4 \, a c} d^{2}} + \frac{4 \, c}{{\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} {\left(2 \, c d x + b d\right)} {\left(\frac{b^{2} d^{2}}{{\left(2 \, c d x + b d\right)}^{2}} - \frac{4 \, a c d^{2}}{{\left(2 \, c d x + b d\right)}^{2}} - 1\right)} d}"," ",0,"-8*c^5*d^7/((b^4*c^4*d^8 - 8*a*b^2*c^5*d^8 + 16*a^2*c^6*d^8)*(2*c*d*x + b*d)) - 12*c*arctan((b^2*d/(2*c*d*x + b*d) - 4*a*c*d/(2*c*d*x + b*d))/sqrt(-b^2 + 4*a*c))/((b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(-b^2 + 4*a*c)*d^2) + 4*c/((b^4 - 8*a*b^2*c + 16*a^2*c^2)*(2*c*d*x + b*d)*(b^2*d^2/(2*c*d*x + b*d)^2 - 4*a*c*d^2/(2*c*d*x + b*d)^2 - 1)*d)","B",0
1176,1,203,0,0.179526," ","integrate(1/(2*c*d*x+b*d)^3/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{16 \, c^{2} \log\left({\left| 2 \, c x + b \right|}\right)}{b^{6} c d^{3} - 12 \, a b^{4} c^{2} d^{3} + 48 \, a^{2} b^{2} c^{3} d^{3} - 64 \, a^{3} c^{4} d^{3}} - \frac{8 \, c \log\left(c x^{2} + b x + a\right)}{b^{6} d^{3} - 12 \, a b^{4} c d^{3} + 48 \, a^{2} b^{2} c^{2} d^{3} - 64 \, a^{3} c^{3} d^{3}} - \frac{b^{4} - 16 \, a^{2} c^{2} + 8 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{2} + 8 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} x}{{\left(c x^{2} + b x + a\right)} {\left(b^{2} - 4 \, a c\right)}^{3} {\left(2 \, c x + b\right)}^{2} d^{3}}"," ",0,"16*c^2*log(abs(2*c*x + b))/(b^6*c*d^3 - 12*a*b^4*c^2*d^3 + 48*a^2*b^2*c^3*d^3 - 64*a^3*c^4*d^3) - 8*c*log(c*x^2 + b*x + a)/(b^6*d^3 - 12*a*b^4*c*d^3 + 48*a^2*b^2*c^2*d^3 - 64*a^3*c^3*d^3) - (b^4 - 16*a^2*c^2 + 8*(b^2*c^2 - 4*a*c^3)*x^2 + 8*(b^3*c - 4*a*b*c^2)*x)/((c*x^2 + b*x + a)*(b^2 - 4*a*c)^3*(2*c*x + b)^2*d^3)","A",0
1177,1,460,0,0.216007," ","integrate((2*c*d*x+b*d)^10/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{252 \, {\left(b^{6} c^{2} d^{10} - 12 \, a b^{4} c^{3} d^{10} + 48 \, a^{2} b^{2} c^{4} d^{10} - 64 \, a^{3} c^{5} d^{10}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{\sqrt{-b^{2} + 4 \, a c}} - \frac{68 \, b^{6} c^{3} d^{10} x^{3} - 816 \, a b^{4} c^{4} d^{10} x^{3} + 3264 \, a^{2} b^{2} c^{5} d^{10} x^{3} - 4352 \, a^{3} c^{6} d^{10} x^{3} + 102 \, b^{7} c^{2} d^{10} x^{2} - 1224 \, a b^{5} c^{3} d^{10} x^{2} + 4896 \, a^{2} b^{3} c^{4} d^{10} x^{2} - 6528 \, a^{3} b c^{5} d^{10} x^{2} + 36 \, b^{8} c d^{10} x - 372 \, a b^{6} c^{2} d^{10} x + 1008 \, a^{2} b^{4} c^{3} d^{10} x + 576 \, a^{3} b^{2} c^{4} d^{10} x - 3840 \, a^{4} c^{5} d^{10} x + b^{9} d^{10} + 18 \, a b^{7} c d^{10} - 312 \, a^{2} b^{5} c^{2} d^{10} + 1376 \, a^{3} b^{3} c^{3} d^{10} - 1920 \, a^{4} b c^{4} d^{10}}{2 \, {\left(c x^{2} + b x + a\right)}^{2}} + \frac{128 \, {\left(8 \, c^{22} d^{10} x^{5} + 20 \, b c^{21} d^{10} x^{4} + 30 \, b^{2} c^{20} d^{10} x^{3} - 40 \, a c^{21} d^{10} x^{3} + 25 \, b^{3} c^{19} d^{10} x^{2} - 60 \, a b c^{20} d^{10} x^{2} + 25 \, b^{4} c^{18} d^{10} x - 150 \, a b^{2} c^{19} d^{10} x + 240 \, a^{2} c^{20} d^{10} x\right)}}{5 \, c^{15}}"," ",0,"252*(b^6*c^2*d^10 - 12*a*b^4*c^3*d^10 + 48*a^2*b^2*c^4*d^10 - 64*a^3*c^5*d^10)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/sqrt(-b^2 + 4*a*c) - 1/2*(68*b^6*c^3*d^10*x^3 - 816*a*b^4*c^4*d^10*x^3 + 3264*a^2*b^2*c^5*d^10*x^3 - 4352*a^3*c^6*d^10*x^3 + 102*b^7*c^2*d^10*x^2 - 1224*a*b^5*c^3*d^10*x^2 + 4896*a^2*b^3*c^4*d^10*x^2 - 6528*a^3*b*c^5*d^10*x^2 + 36*b^8*c*d^10*x - 372*a*b^6*c^2*d^10*x + 1008*a^2*b^4*c^3*d^10*x + 576*a^3*b^2*c^4*d^10*x - 3840*a^4*c^5*d^10*x + b^9*d^10 + 18*a*b^7*c*d^10 - 312*a^2*b^5*c^2*d^10 + 1376*a^3*b^3*c^3*d^10 - 1920*a^4*b*c^4*d^10)/(c*x^2 + b*x + a)^2 + 128/5*(8*c^22*d^10*x^5 + 20*b*c^21*d^10*x^4 + 30*b^2*c^20*d^10*x^3 - 40*a*c^21*d^10*x^3 + 25*b^3*c^19*d^10*x^2 - 60*a*b*c^20*d^10*x^2 + 25*b^4*c^18*d^10*x - 150*a*b^2*c^19*d^10*x + 240*a^2*c^20*d^10*x)/c^15","B",0
1178,1,299,0,0.192216," ","integrate((2*c*d*x+b*d)^9/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","96 \, {\left(b^{4} c^{2} d^{9} - 8 \, a b^{2} c^{3} d^{9} + 16 \, a^{2} c^{4} d^{9}\right)} \log\left(c x^{2} + b x + a\right) - \frac{b^{8} d^{9} + 16 \, a b^{6} c d^{9} - 288 \, a^{2} b^{4} c^{2} d^{9} + 1280 \, a^{3} b^{2} c^{3} d^{9} - 1792 \, a^{4} c^{4} d^{9} + 32 \, {\left(b^{6} c^{2} d^{9} - 12 \, a b^{4} c^{3} d^{9} + 48 \, a^{2} b^{2} c^{4} d^{9} - 64 \, a^{3} c^{5} d^{9}\right)} x^{2} + 32 \, {\left(b^{7} c d^{9} - 12 \, a b^{5} c^{2} d^{9} + 48 \, a^{2} b^{3} c^{3} d^{9} - 64 \, a^{3} b c^{4} d^{9}\right)} x}{2 \, {\left(c x^{2} + b x + a\right)}^{2}} + \frac{128 \, {\left(c^{18} d^{9} x^{4} + 2 \, b c^{17} d^{9} x^{3} + 3 \, b^{2} c^{16} d^{9} x^{2} - 6 \, a c^{17} d^{9} x^{2} + 2 \, b^{3} c^{15} d^{9} x - 6 \, a b c^{16} d^{9} x\right)}}{c^{12}}"," ",0,"96*(b^4*c^2*d^9 - 8*a*b^2*c^3*d^9 + 16*a^2*c^4*d^9)*log(c*x^2 + b*x + a) - 1/2*(b^8*d^9 + 16*a*b^6*c*d^9 - 288*a^2*b^4*c^2*d^9 + 1280*a^3*b^2*c^3*d^9 - 1792*a^4*c^4*d^9 + 32*(b^6*c^2*d^9 - 12*a*b^4*c^3*d^9 + 48*a^2*b^2*c^4*d^9 - 64*a^3*c^5*d^9)*x^2 + 32*(b^7*c*d^9 - 12*a*b^5*c^2*d^9 + 48*a^2*b^3*c^3*d^9 - 64*a^3*b*c^4*d^9)*x)/(c*x^2 + b*x + a)^2 + 128*(c^18*d^9*x^4 + 2*b*c^17*d^9*x^3 + 3*b^2*c^16*d^9*x^2 - 6*a*c^17*d^9*x^2 + 2*b^3*c^15*d^9*x - 6*a*b*c^16*d^9*x)/c^12","B",0
1179,1,315,0,0.171626," ","integrate((2*c*d*x+b*d)^8/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{140 \, {\left(b^{4} c^{2} d^{8} - 8 \, a b^{2} c^{3} d^{8} + 16 \, a^{2} c^{4} d^{8}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{\sqrt{-b^{2} + 4 \, a c}} - \frac{52 \, b^{4} c^{3} d^{8} x^{3} - 416 \, a b^{2} c^{4} d^{8} x^{3} + 832 \, a^{2} c^{5} d^{8} x^{3} + 78 \, b^{5} c^{2} d^{8} x^{2} - 624 \, a b^{3} c^{3} d^{8} x^{2} + 1248 \, a^{2} b c^{4} d^{8} x^{2} + 28 \, b^{6} c d^{8} x - 180 \, a b^{4} c^{2} d^{8} x + 96 \, a^{2} b^{2} c^{3} d^{8} x + 704 \, a^{3} c^{4} d^{8} x + b^{7} d^{8} + 14 \, a b^{5} c d^{8} - 160 \, a^{2} b^{3} c^{2} d^{8} + 352 \, a^{3} b c^{3} d^{8}}{2 \, {\left(c x^{2} + b x + a\right)}^{2}} + \frac{128 \, {\left(2 \, c^{14} d^{8} x^{3} + 3 \, b c^{13} d^{8} x^{2} + 6 \, b^{2} c^{12} d^{8} x - 18 \, a c^{13} d^{8} x\right)}}{3 \, c^{9}}"," ",0,"140*(b^4*c^2*d^8 - 8*a*b^2*c^3*d^8 + 16*a^2*c^4*d^8)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/sqrt(-b^2 + 4*a*c) - 1/2*(52*b^4*c^3*d^8*x^3 - 416*a*b^2*c^4*d^8*x^3 + 832*a^2*c^5*d^8*x^3 + 78*b^5*c^2*d^8*x^2 - 624*a*b^3*c^3*d^8*x^2 + 1248*a^2*b*c^4*d^8*x^2 + 28*b^6*c*d^8*x - 180*a*b^4*c^2*d^8*x + 96*a^2*b^2*c^3*d^8*x + 704*a^3*c^4*d^8*x + b^7*d^8 + 14*a*b^5*c*d^8 - 160*a^2*b^3*c^2*d^8 + 352*a^3*b*c^3*d^8)/(c*x^2 + b*x + a)^2 + 128/3*(2*c^14*d^8*x^3 + 3*b*c^13*d^8*x^2 + 6*b^2*c^12*d^8*x - 18*a*c^13*d^8*x)/c^9","B",0
1180,1,191,0,0.171438," ","integrate((2*c*d*x+b*d)^7/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","48 \, {\left(b^{2} c^{2} d^{7} - 4 \, a c^{3} d^{7}\right)} \log\left(c x^{2} + b x + a\right) - \frac{b^{6} d^{7} + 12 \, a b^{4} c d^{7} - 144 \, a^{2} b^{2} c^{2} d^{7} + 320 \, a^{3} c^{3} d^{7} + 24 \, {\left(b^{4} c^{2} d^{7} - 8 \, a b^{2} c^{3} d^{7} + 16 \, a^{2} c^{4} d^{7}\right)} x^{2} + 24 \, {\left(b^{5} c d^{7} - 8 \, a b^{3} c^{2} d^{7} + 16 \, a^{2} b c^{3} d^{7}\right)} x}{2 \, {\left(c x^{2} + b x + a\right)}^{2}} + \frac{64 \, {\left(c^{10} d^{7} x^{2} + b c^{9} d^{7} x\right)}}{c^{6}}"," ",0,"48*(b^2*c^2*d^7 - 4*a*c^3*d^7)*log(c*x^2 + b*x + a) - 1/2*(b^6*d^7 + 12*a*b^4*c*d^7 - 144*a^2*b^2*c^2*d^7 + 320*a^3*c^3*d^7 + 24*(b^4*c^2*d^7 - 8*a*b^2*c^3*d^7 + 16*a^2*c^4*d^7)*x^2 + 24*(b^5*c*d^7 - 8*a*b^3*c^2*d^7 + 16*a^2*b*c^3*d^7)*x)/(c*x^2 + b*x + a)^2 + 64*(c^10*d^7*x^2 + b*c^9*d^7*x)/c^6","B",0
1181,1,196,0,0.170247," ","integrate((2*c*d*x+b*d)^6/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","64 \, c^{3} d^{6} x + \frac{60 \, {\left(b^{2} c^{2} d^{6} - 4 \, a c^{3} d^{6}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{\sqrt{-b^{2} + 4 \, a c}} - \frac{36 \, b^{2} c^{3} d^{6} x^{3} - 144 \, a c^{4} d^{6} x^{3} + 54 \, b^{3} c^{2} d^{6} x^{2} - 216 \, a b c^{3} d^{6} x^{2} + 20 \, b^{4} c d^{6} x - 52 \, a b^{2} c^{2} d^{6} x - 112 \, a^{2} c^{3} d^{6} x + b^{5} d^{6} + 10 \, a b^{3} c d^{6} - 56 \, a^{2} b c^{2} d^{6}}{2 \, {\left(c x^{2} + b x + a\right)}^{2}}"," ",0,"64*c^3*d^6*x + 60*(b^2*c^2*d^6 - 4*a*c^3*d^6)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/sqrt(-b^2 + 4*a*c) - 1/2*(36*b^2*c^3*d^6*x^3 - 144*a*c^4*d^6*x^3 + 54*b^3*c^2*d^6*x^2 - 216*a*b*c^3*d^6*x^2 + 20*b^4*c*d^6*x - 52*a*b^2*c^2*d^6*x - 112*a^2*c^3*d^6*x + b^5*d^6 + 10*a*b^3*c*d^6 - 56*a^2*b*c^2*d^6)/(c*x^2 + b*x + a)^2","A",0
1182,1,110,0,0.176527," ","integrate((2*c*d*x+b*d)^5/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","16 \, c^{2} d^{5} \log\left(c x^{2} + b x + a\right) - \frac{b^{4} d^{5} + 8 \, a b^{2} c d^{5} - 48 \, a^{2} c^{2} d^{5} + 16 \, {\left(b^{2} c^{2} d^{5} - 4 \, a c^{3} d^{5}\right)} x^{2} + 16 \, {\left(b^{3} c d^{5} - 4 \, a b c^{2} d^{5}\right)} x}{2 \, {\left(c x^{2} + b x + a\right)}^{2}}"," ",0,"16*c^2*d^5*log(c*x^2 + b*x + a) - 1/2*(b^4*d^5 + 8*a*b^2*c*d^5 - 48*a^2*c^2*d^5 + 16*(b^2*c^2*d^5 - 4*a*c^3*d^5)*x^2 + 16*(b^3*c*d^5 - 4*a*b*c^2*d^5)*x)/(c*x^2 + b*x + a)^2","A",0
1183,1,114,0,0.171734," ","integrate((2*c*d*x+b*d)^4/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{12 \, c^{2} d^{4} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{\sqrt{-b^{2} + 4 \, a c}} - \frac{20 \, c^{3} d^{4} x^{3} + 30 \, b c^{2} d^{4} x^{2} + 12 \, b^{2} c d^{4} x + 12 \, a c^{2} d^{4} x + b^{3} d^{4} + 6 \, a b c d^{4}}{2 \, {\left(c x^{2} + b x + a\right)}^{2}}"," ",0,"12*c^2*d^4*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/sqrt(-b^2 + 4*a*c) - 1/2*(20*c^3*d^4*x^3 + 30*b*c^2*d^4*x^2 + 12*b^2*c*d^4*x + 12*a*c^2*d^4*x + b^3*d^4 + 6*a*b*c*d^4)/(c*x^2 + b*x + a)^2","A",0
1184,1,50,0,0.189382," ","integrate((2*c*d*x+b*d)^3/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","-\frac{b^{2} d^{5} + 4 \, a c d^{5} + 8 \, {\left(c d x^{2} + b d x\right)} c d^{4}}{2 \, {\left(c d x^{2} + b d x + a d\right)}^{2}}"," ",0,"-1/2*(b^2*d^5 + 4*a*c*d^5 + 8*(c*d*x^2 + b*d*x)*c*d^4)/(c*d*x^2 + b*d*x + a*d)^2","A",0
1185,1,134,0,0.186625," ","integrate((2*c*d*x+b*d)^2/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","-\frac{4 \, c^{2} d^{2} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{2} - 4 \, a c\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{4 \, c^{3} d^{2} x^{3} + 6 \, b c^{2} d^{2} x^{2} + 4 \, b^{2} c d^{2} x - 4 \, a c^{2} d^{2} x + b^{3} d^{2} - 2 \, a b c d^{2}}{2 \, {\left(c x^{2} + b x + a\right)}^{2} {\left(b^{2} - 4 \, a c\right)}}"," ",0,"-4*c^2*d^2*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^2 - 4*a*c)*sqrt(-b^2 + 4*a*c)) - 1/2*(4*c^3*d^2*x^3 + 6*b*c^2*d^2*x^2 + 4*b^2*c*d^2*x - 4*a*c^2*d^2*x + b^3*d^2 - 2*a*b*c*d^2)/((c*x^2 + b*x + a)^2*(b^2 - 4*a*c))","A",0
1186,1,22,0,0.179902," ","integrate((2*c*d*x+b*d)/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","-\frac{d}{2 \, {\left(a + \frac{c d x^{2} + b d x}{d}\right)}^{2}}"," ",0,"-1/2*d/(a + (c*d*x^2 + b*d*x)/d)^2","A",0
1187,1,188,0,0.182245," ","integrate(1/(2*c*d*x+b*d)/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","-\frac{32 \, c^{3} \log\left({\left| 2 \, c x + b \right|}\right)}{b^{6} c d - 12 \, a b^{4} c^{2} d + 48 \, a^{2} b^{2} c^{3} d - 64 \, a^{3} c^{4} d} + \frac{16 \, c^{2} \log\left(c x^{2} + b x + a\right)}{b^{6} d - 12 \, a b^{4} c d + 48 \, a^{2} b^{2} c^{2} d - 64 \, a^{3} c^{3} d} - \frac{b^{4} - 16 \, a b^{2} c + 48 \, a^{2} c^{2} - 8 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{2} - 8 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} x}{2 \, {\left(c x^{2} + b x + a\right)}^{2} {\left(b^{2} - 4 \, a c\right)}^{3} d}"," ",0,"-32*c^3*log(abs(2*c*x + b))/(b^6*c*d - 12*a*b^4*c^2*d + 48*a^2*b^2*c^3*d - 64*a^3*c^4*d) + 16*c^2*log(c*x^2 + b*x + a)/(b^6*d - 12*a*b^4*c*d + 48*a^2*b^2*c^2*d - 64*a^3*c^3*d) - 1/2*(b^4 - 16*a*b^2*c + 48*a^2*c^2 - 8*(b^2*c^2 - 4*a*c^3)*x^2 - 8*(b^3*c - 4*a*b*c^2)*x)/((c*x^2 + b*x + a)^2*(b^2 - 4*a*c)^3*d)","A",0
1188,1,302,0,0.168971," ","integrate(1/(2*c*d*x+b*d)^2/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{32 \, c^{8} d^{11}}{{\left(b^{6} c^{6} d^{12} - 12 \, a b^{4} c^{7} d^{12} + 48 \, a^{2} b^{2} c^{8} d^{12} - 64 \, a^{3} c^{9} d^{12}\right)} {\left(2 \, c d x + b d\right)}} - \frac{60 \, c^{2} \arctan\left(-\frac{\frac{b^{2} d}{2 \, c d x + b d} - \frac{4 \, a c d}{2 \, c d x + b d}}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} \sqrt{-b^{2} + 4 \, a c} d^{2}} - \frac{4 \, {\left(\frac{9 \, b^{2} c^{2} d}{{\left(2 \, c d x + b d\right)}^{3}} - \frac{36 \, a c^{3} d}{{\left(2 \, c d x + b d\right)}^{3}} - \frac{7 \, c^{2}}{{\left(2 \, c d x + b d\right)} d}\right)}}{{\left(b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} {\left(\frac{b^{2} d^{2}}{{\left(2 \, c d x + b d\right)}^{2}} - \frac{4 \, a c d^{2}}{{\left(2 \, c d x + b d\right)}^{2}} - 1\right)}^{2}}"," ",0,"32*c^8*d^11/((b^6*c^6*d^12 - 12*a*b^4*c^7*d^12 + 48*a^2*b^2*c^8*d^12 - 64*a^3*c^9*d^12)*(2*c*d*x + b*d)) - 60*c^2*arctan(-(b^2*d/(2*c*d*x + b*d) - 4*a*c*d/(2*c*d*x + b*d))/sqrt(-b^2 + 4*a*c))/((b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)*sqrt(-b^2 + 4*a*c)*d^2) - 4*(9*b^2*c^2*d/(2*c*d*x + b*d)^3 - 36*a*c^3*d/(2*c*d*x + b*d)^3 - 7*c^2/((2*c*d*x + b*d)*d))/((b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)*(b^2*d^2/(2*c*d*x + b*d)^2 - 4*a*c*d^2/(2*c*d*x + b*d)^2 - 1)^2)","B",0
1189,1,302,0,0.436238," ","integrate(1/(2*c*d*x+b*d)^3/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","-\frac{96 \, c^{3} \log\left({\left| 2 \, c x + b \right|}\right)}{b^{8} c d^{3} - 16 \, a b^{6} c^{2} d^{3} + 96 \, a^{2} b^{4} c^{3} d^{3} - 256 \, a^{3} b^{2} c^{4} d^{3} + 256 \, a^{4} c^{5} d^{3}} + \frac{48 \, c^{2} \log\left(c x^{2} + b x + a\right)}{b^{8} d^{3} - 16 \, a b^{6} c d^{3} + 96 \, a^{2} b^{4} c^{2} d^{3} - 256 \, a^{3} b^{2} c^{3} d^{3} + 256 \, a^{4} c^{4} d^{3}} + \frac{96 \, c^{4} x^{4} + 192 \, b c^{3} x^{3} + 108 \, b^{2} c^{2} x^{2} + 144 \, a c^{3} x^{2} + 12 \, b^{3} c x + 144 \, a b c^{2} x - b^{4} + 20 \, a b^{2} c + 32 \, a^{2} c^{2}}{2 \, {\left(b^{6} d^{3} - 12 \, a b^{4} c d^{3} + 48 \, a^{2} b^{2} c^{2} d^{3} - 64 \, a^{3} c^{3} d^{3}\right)} {\left(2 \, c^{2} x^{3} + 3 \, b c x^{2} + b^{2} x + 2 \, a c x + a b\right)}^{2}}"," ",0,"-96*c^3*log(abs(2*c*x + b))/(b^8*c*d^3 - 16*a*b^6*c^2*d^3 + 96*a^2*b^4*c^3*d^3 - 256*a^3*b^2*c^4*d^3 + 256*a^4*c^5*d^3) + 48*c^2*log(c*x^2 + b*x + a)/(b^8*d^3 - 16*a*b^6*c*d^3 + 96*a^2*b^4*c^2*d^3 - 256*a^3*b^2*c^3*d^3 + 256*a^4*c^4*d^3) + 1/2*(96*c^4*x^4 + 192*b*c^3*x^3 + 108*b^2*c^2*x^2 + 144*a*c^3*x^2 + 12*b^3*c*x + 144*a*b*c^2*x - b^4 + 20*a*b^2*c + 32*a^2*c^2)/((b^6*d^3 - 12*a*b^4*c*d^3 + 48*a^2*b^2*c^2*d^3 - 64*a^3*c^3*d^3)*(2*c^2*x^3 + 3*b*c*x^2 + b^2*x + 2*a*c*x + a*b)^2)","A",0
1190,1,311,0,0.183312," ","integrate(1/(2*c*d*x+b*d)^4/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{140 \, c^{2} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{8} d^{4} - 16 \, a b^{6} c d^{4} + 96 \, a^{2} b^{4} c^{2} d^{4} - 256 \, a^{3} b^{2} c^{3} d^{4} + 256 \, a^{4} c^{4} d^{4}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{44 \, c^{3} x^{3} + 66 \, b c^{2} x^{2} + 20 \, b^{2} c x + 52 \, a c^{2} x - b^{3} + 26 \, a b c}{2 \, {\left(b^{8} d^{4} - 16 \, a b^{6} c d^{4} + 96 \, a^{2} b^{4} c^{2} d^{4} - 256 \, a^{3} b^{2} c^{3} d^{4} + 256 \, a^{4} c^{4} d^{4}\right)} {\left(c x^{2} + b x + a\right)}^{2}} + \frac{64 \, {\left(18 \, c^{4} x^{2} + 18 \, b c^{3} x + 5 \, b^{2} c^{2} - 2 \, a c^{3}\right)}}{3 \, {\left(b^{8} d^{4} - 16 \, a b^{6} c d^{4} + 96 \, a^{2} b^{4} c^{2} d^{4} - 256 \, a^{3} b^{2} c^{3} d^{4} + 256 \, a^{4} c^{4} d^{4}\right)} {\left(2 \, c x + b\right)}^{3}}"," ",0,"140*c^2*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^8*d^4 - 16*a*b^6*c*d^4 + 96*a^2*b^4*c^2*d^4 - 256*a^3*b^2*c^3*d^4 + 256*a^4*c^4*d^4)*sqrt(-b^2 + 4*a*c)) + 1/2*(44*c^3*x^3 + 66*b*c^2*x^2 + 20*b^2*c*x + 52*a*c^2*x - b^3 + 26*a*b*c)/((b^8*d^4 - 16*a*b^6*c*d^4 + 96*a^2*b^4*c^2*d^4 - 256*a^3*b^2*c^3*d^4 + 256*a^4*c^4*d^4)*(c*x^2 + b*x + a)^2) + 64/3*(18*c^4*x^2 + 18*b*c^3*x + 5*b^2*c^2 - 2*a*c^3)/((b^8*d^4 - 16*a*b^6*c*d^4 + 96*a^2*b^4*c^2*d^4 - 256*a^3*b^2*c^3*d^4 + 256*a^4*c^4*d^4)*(2*c*x + b)^3)","A",0
1191,1,259,0,0.241172," ","integrate((2*c*d*x+b*d)^4*(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\frac{1}{96} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(2 \, c^{4} d^{4} x + 5 \, b c^{3} d^{4}\right)} x + \frac{39 \, b^{2} c^{7} d^{4} + 4 \, a c^{8} d^{4}}{c^{5}}\right)} x + \frac{37 \, b^{3} c^{6} d^{4} + 12 \, a b c^{7} d^{4}}{c^{5}}\right)} x + \frac{31 \, b^{4} c^{5} d^{4} + 48 \, a b^{2} c^{6} d^{4} - 48 \, a^{2} c^{7} d^{4}}{c^{5}}\right)} x + \frac{3 \, b^{5} c^{4} d^{4} + 32 \, a b^{3} c^{5} d^{4} - 48 \, a^{2} b c^{6} d^{4}}{c^{5}}\right)} + \frac{{\left(b^{6} d^{4} - 12 \, a b^{4} c d^{4} + 48 \, a^{2} b^{2} c^{2} d^{4} - 64 \, a^{3} c^{3} d^{4}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{64 \, c^{\frac{3}{2}}}"," ",0,"1/96*sqrt(c*x^2 + b*x + a)*(2*(4*(2*(8*(2*c^4*d^4*x + 5*b*c^3*d^4)*x + (39*b^2*c^7*d^4 + 4*a*c^8*d^4)/c^5)*x + (37*b^3*c^6*d^4 + 12*a*b*c^7*d^4)/c^5)*x + (31*b^4*c^5*d^4 + 48*a*b^2*c^6*d^4 - 48*a^2*c^7*d^4)/c^5)*x + (3*b^5*c^4*d^4 + 32*a*b^3*c^5*d^4 - 48*a^2*b*c^6*d^4)/c^5) + 1/64*(b^6*d^4 - 12*a*b^4*c*d^4 + 48*a^2*b^2*c^2*d^4 - 64*a^3*c^3*d^4)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(3/2)","A",0
1192,1,58,0,0.155536," ","integrate((2*c*d*x+b*d)^3*(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\frac{2}{3} \, {\left(c x^{2} + b x + a\right)}^{\frac{3}{2}} b^{2} d^{3} + \frac{8}{5} \, {\left(c x^{2} + b x + a\right)}^{\frac{5}{2}} c d^{3} - \frac{8}{3} \, {\left(c x^{2} + b x + a\right)}^{\frac{3}{2}} a c d^{3}"," ",0,"2/3*(c*x^2 + b*x + a)^(3/2)*b^2*d^3 + 8/5*(c*x^2 + b*x + a)^(5/2)*c*d^3 - 8/3*(c*x^2 + b*x + a)^(3/2)*a*c*d^3","A",0
1193,1,155,0,0.241090," ","integrate((2*c*d*x+b*d)^2*(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\frac{1}{16} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(2 \, c^{2} d^{2} x + 3 \, b c d^{2}\right)} x + \frac{5 \, b^{2} c^{3} d^{2} + 4 \, a c^{4} d^{2}}{c^{3}}\right)} x + \frac{b^{3} c^{2} d^{2} + 4 \, a b c^{3} d^{2}}{c^{3}}\right)} + \frac{{\left(b^{4} d^{2} - 8 \, a b^{2} c d^{2} + 16 \, a^{2} c^{2} d^{2}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{32 \, c^{\frac{3}{2}}}"," ",0,"1/16*sqrt(c*x^2 + b*x + a)*(2*(4*(2*c^2*d^2*x + 3*b*c*d^2)*x + (5*b^2*c^3*d^2 + 4*a*c^4*d^2)/c^3)*x + (b^3*c^2*d^2 + 4*a*b*c^3*d^2)/c^3) + 1/32*(b^4*d^2 - 8*a*b^2*c*d^2 + 16*a^2*c^2*d^2)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(3/2)","A",0
1194,1,15,0,0.150710," ","integrate((2*c*d*x+b*d)*(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\frac{2}{3} \, {\left(c x^{2} + b x + a\right)}^{\frac{3}{2}} d"," ",0,"2/3*(c*x^2 + b*x + a)^(3/2)*d","A",0
1195,1,97,0,0.212100," ","integrate((c*x^2+b*x+a)^(1/2)/(2*c*d*x+b*d),x, algorithm=""giac"")","-\frac{{\left(b^{2} - 4 \, a c\right)} \arctan\left(-\frac{2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} c + b \sqrt{c}}{\sqrt{b^{2} c - 4 \, a c^{2}}}\right)}{2 \, \sqrt{b^{2} c - 4 \, a c^{2}} c d} + \frac{\sqrt{c x^{2} + b x + a}}{2 \, c d}"," ",0,"-1/2*(b^2 - 4*a*c)*arctan(-(2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*c + b*sqrt(c))/sqrt(b^2*c - 4*a*c^2))/(sqrt(b^2*c - 4*a*c^2)*c*d) + 1/2*sqrt(c*x^2 + b*x + a)/(c*d)","A",0
1196,1,215,0,0.601341," ","integrate((c*x^2+b*x+a)^(1/2)/(2*c*d*x+b*d)^2,x, algorithm=""giac"")","-\frac{1}{4} \, d^{2} {\left(\frac{\arctan\left(\frac{\sqrt{-\frac{b^{2} c d^{2}}{{\left(2 \, c d x + b d\right)}^{2}} + \frac{4 \, a c^{2} d^{2}}{{\left(2 \, c d x + b d\right)}^{2}} + c}}{\sqrt{-c}}\right) \mathrm{sgn}\left(\frac{1}{2 \, c d x + b d}\right) \mathrm{sgn}\left(c\right) \mathrm{sgn}\left(d\right)}{\sqrt{-c} c d^{4} {\left| c \right|}} - \frac{{\left(\sqrt{c} \arctan\left(\frac{\sqrt{c}}{\sqrt{-c}}\right) + \sqrt{-c}\right)} \mathrm{sgn}\left(\frac{1}{2 \, c d x + b d}\right) \mathrm{sgn}\left(c\right) \mathrm{sgn}\left(d\right)}{\sqrt{-c} c^{\frac{3}{2}} d^{4} {\left| c \right|}} + \frac{\sqrt{-\frac{b^{2} c d^{2}}{{\left(2 \, c d x + b d\right)}^{2}} + \frac{4 \, a c^{2} d^{2}}{{\left(2 \, c d x + b d\right)}^{2}} + c} \mathrm{sgn}\left(\frac{1}{2 \, c d x + b d}\right) \mathrm{sgn}\left(c\right) \mathrm{sgn}\left(d\right)}{c^{2} d^{4} {\left| c \right|}}\right)} {\left| c \right|}"," ",0,"-1/4*d^2*(arctan(sqrt(-b^2*c*d^2/(2*c*d*x + b*d)^2 + 4*a*c^2*d^2/(2*c*d*x + b*d)^2 + c)/sqrt(-c))*sgn(1/(2*c*d*x + b*d))*sgn(c)*sgn(d)/(sqrt(-c)*c*d^4*abs(c)) - (sqrt(c)*arctan(sqrt(c)/sqrt(-c)) + sqrt(-c))*sgn(1/(2*c*d*x + b*d))*sgn(c)*sgn(d)/(sqrt(-c)*c^(3/2)*d^4*abs(c)) + sqrt(-b^2*c*d^2/(2*c*d*x + b*d)^2 + 4*a*c^2*d^2/(2*c*d*x + b*d)^2 + c)*sgn(1/(2*c*d*x + b*d))*sgn(c)*sgn(d)/(c^2*d^4*abs(c)))*abs(c)","B",0
1197,-2,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(1/2)/(2*c*d*x+b*d)^3,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{%%%{8,[3]%%%},[6,3,0,0]%%%}+%%%{%%{[%%%{-24,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,3,1,0]%%%}+%%%{%%%{36,[2]%%%},[4,3,2,0]%%%}+%%%{%%%{-24,[3]%%%},[4,3,0,1]%%%}+%%%{%%{[%%%{-32,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,3,3,0]%%%}+%%%{%%{[%%%{48,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,3,1,1]%%%}+%%%{%%%{18,[1]%%%},[2,3,4,0]%%%}+%%%{%%%{-48,[2]%%%},[2,3,2,1]%%%}+%%%{%%%{24,[3]%%%},[2,3,0,2]%%%}+%%%{%%{[-6,0]:[1,0,%%%{-1,[1]%%%}]%%},[1,3,5,0]%%%}+%%%{%%{[%%%{24,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,3,3,1]%%%}+%%%{%%{[%%%{-24,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,3,1,2]%%%}+%%%{1,[0,3,6,0]%%%}+%%%{%%%{-6,[1]%%%},[0,3,4,1]%%%}+%%%{%%%{12,[2]%%%},[0,3,2,2]%%%}+%%%{%%%{-8,[3]%%%},[0,3,0,3]%%%} / %%%{%%{poly1[%%%{-8,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[6,0,0,0]%%%}+%%%{%%%{24,[4]%%%},[5,0,1,0]%%%}+%%%{%%{poly1[%%%{-36,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,2,0]%%%}+%%%{%%{[%%%{24,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,0,1]%%%}+%%%{%%%{32,[3]%%%},[3,0,3,0]%%%}+%%%{%%%{-48,[4]%%%},[3,0,1,1]%%%}+%%%{%%{poly1[%%%{-18,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,4,0]%%%}+%%%{%%{[%%%{48,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,2,1]%%%}+%%%{%%{[%%%{-24,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,0,2]%%%}+%%%{%%%{6,[2]%%%},[1,0,5,0]%%%}+%%%{%%%{-24,[3]%%%},[1,0,3,1]%%%}+%%%{%%%{24,[4]%%%},[1,0,1,2]%%%}+%%%{%%{poly1[%%%{-1,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,6,0]%%%}+%%%{%%{[%%%{6,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,4,1]%%%}+%%%{%%{[%%%{-12,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,2,2]%%%}+%%%{%%{[%%%{8,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,0,3]%%%} Error: Bad Argument Value","F(-2)",0
1198,1,205,0,0.325240," ","integrate((c*x^2+b*x+a)^(1/2)/(2*c*d*x+b*d)^4,x, algorithm=""giac"")","\frac{12 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} c^{\frac{5}{2}} + 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b c^{2} + 18 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{2} c^{\frac{3}{2}} + 6 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{3} c + b^{4} \sqrt{c} - 2 \, a b^{2} c^{\frac{3}{2}} + 4 \, a^{2} c^{\frac{5}{2}}}{12 \, {\left(2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} c + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b \sqrt{c} + b^{2} - 2 \, a c\right)}^{3} c^{2} d^{4}}"," ",0,"1/12*(12*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*c^(5/2) + 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b*c^2 + 18*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^2*c^(3/2) + 6*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^3*c + b^4*sqrt(c) - 2*a*b^2*c^(3/2) + 4*a^2*c^(5/2))/((2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*c + 2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b*sqrt(c) + b^2 - 2*a*c)^3*c^2*d^4)","B",0
1199,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(1/2)/(2*c*d*x+b*d)^5,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1200,1,423,0,0.449567," ","integrate((c*x^2+b*x+a)^(1/2)/(2*c*d*x+b*d)^6,x, algorithm=""giac"")","\frac{60 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} c^{\frac{7}{2}} + 180 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} b c^{3} + 220 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} b^{2} c^{\frac{5}{2}} + 20 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a c^{\frac{7}{2}} + 140 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{3} c^{2} + 40 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b c^{3} + 50 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{4} c^{\frac{3}{2}} + 20 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a b^{2} c^{\frac{5}{2}} + 20 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{2} c^{\frac{7}{2}} + 10 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{5} c + 20 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} b c^{3} + b^{6} \sqrt{c} - 2 \, a b^{4} c^{\frac{3}{2}} + 8 \, a^{2} b^{2} c^{\frac{5}{2}} - 4 \, a^{3} c^{\frac{7}{2}}}{30 \, {\left(2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} c + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b \sqrt{c} + b^{2} - 2 \, a c\right)}^{5} c^{2} d^{6}}"," ",0,"1/30*(60*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*c^(7/2) + 180*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b*c^3 + 220*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^2*c^(5/2) + 20*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*c^(7/2) + 140*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^3*c^2 + 40*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b*c^3 + 50*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^4*c^(3/2) + 20*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^2*c^(5/2) + 20*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*c^(7/2) + 10*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^5*c + 20*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b*c^3 + b^6*sqrt(c) - 2*a*b^4*c^(3/2) + 8*a^2*b^2*c^(5/2) - 4*a^3*c^(7/2))/((2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*c + 2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b*sqrt(c) + b^2 - 2*a*c)^5*c^2*d^6)","B",0
1201,-2,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(1/2)/(2*c*d*x+b*d)^7,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{%%%{128,[7]%%%},[14,7,0,0]%%%}+%%%{%%{[%%%{-896,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[13,7,1,0]%%%}+%%%{%%%{3136,[6]%%%},[12,7,2,0]%%%}+%%%{%%%{-896,[7]%%%},[12,7,0,1]%%%}+%%%{%%{[%%%{-7168,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[11,7,3,0]%%%}+%%%{%%{[%%%{5376,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[11,7,1,1]%%%}+%%%{%%%{11872,[5]%%%},[10,7,4,0]%%%}+%%%{%%%{-16128,[6]%%%},[10,7,2,1]%%%}+%%%{%%%{2688,[7]%%%},[10,7,0,2]%%%}+%%%{%%{[%%%{-15008,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[9,7,5,0]%%%}+%%%{%%{[%%%{31360,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[9,7,3,1]%%%}+%%%{%%{[%%%{-13440,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[9,7,1,2]%%%}+%%%{%%%{14896,[4]%%%},[8,7,6,0]%%%}+%%%{%%%{-43680,[5]%%%},[8,7,4,1]%%%}+%%%{%%%{33600,[6]%%%},[8,7,2,2]%%%}+%%%{%%%{-4480,[7]%%%},[8,7,0,3]%%%}+%%%{%%{[%%%{-11776,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,7,7,0]%%%}+%%%{%%{[%%%{45696,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,7,5,1]%%%}+%%%{%%{[%%%{-53760,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,7,3,2]%%%}+%%%{%%{[%%%{17920,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,7,1,3]%%%}+%%%{%%%{7448,[3]%%%},[6,7,8,0]%%%}+%%%{%%%{-36736,[4]%%%},[6,7,6,1]%%%}+%%%{%%%{60480,[5]%%%},[6,7,4,2]%%%}+%%%{%%%{-35840,[6]%%%},[6,7,2,3]%%%}+%%%{%%%{4480,[7]%%%},[6,7,0,4]%%%}+%%%{%%{[%%%{-3752,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,7,9,0]%%%}+%%%{%%{[%%%{22848,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,7,7,1]%%%}+%%%{%%{[%%%{-49728,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,7,5,2]%%%}+%%%{%%{[%%%{44800,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,7,3,3]%%%}+%%%{%%{[%%%{-13440,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,7,1,4]%%%}+%%%{%%%{1484,[2]%%%},[4,7,10,0]%%%}+%%%{%%%{-10920,[3]%%%},[4,7,8,1]%%%}+%%%{%%%{30240,[4]%%%},[4,7,6,2]%%%}+%%%{%%%{-38080,[5]%%%},[4,7,4,3]%%%}+%%%{%%%{20160,[6]%%%},[4,7,2,4]%%%}+%%%{%%%{-2688,[7]%%%},[4,7,0,5]%%%}+%%%{%%{[%%%{-448,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,7,11,0]%%%}+%%%{%%{[%%%{3920,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,7,9,1]%%%}+%%%{%%{[%%%{-13440,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,7,7,2]%%%}+%%%{%%{[%%%{22400,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,7,5,3]%%%}+%%%{%%{[%%%{-17920,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,7,3,4]%%%}+%%%{%%{[%%%{5376,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,7,1,5]%%%}+%%%{%%%{98,[1]%%%},[2,7,12,0]%%%}+%%%{%%%{-1008,[2]%%%},[2,7,10,1]%%%}+%%%{%%%{4200,[3]%%%},[2,7,8,2]%%%}+%%%{%%%{-8960,[4]%%%},[2,7,6,3]%%%}+%%%{%%%{10080,[5]%%%},[2,7,4,4]%%%}+%%%{%%%{-5376,[6]%%%},[2,7,2,5]%%%}+%%%{%%%{896,[7]%%%},[2,7,0,6]%%%}+%%%{%%{[-14,0]:[1,0,%%%{-1,[1]%%%}]%%},[1,7,13,0]%%%}+%%%{%%{[%%%{168,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,7,11,1]%%%}+%%%{%%{[%%%{-840,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,7,9,2]%%%}+%%%{%%{[%%%{2240,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,7,7,3]%%%}+%%%{%%{[%%%{-3360,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,7,5,4]%%%}+%%%{%%{[%%%{2688,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,7,3,5]%%%}+%%%{%%{[%%%{-896,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,7,1,6]%%%}+%%%{1,[0,7,14,0]%%%}+%%%{%%%{-14,[1]%%%},[0,7,12,1]%%%}+%%%{%%%{84,[2]%%%},[0,7,10,2]%%%}+%%%{%%%{-280,[3]%%%},[0,7,8,3]%%%}+%%%{%%%{560,[4]%%%},[0,7,6,4]%%%}+%%%{%%%{-672,[5]%%%},[0,7,4,5]%%%}+%%%{%%%{448,[6]%%%},[0,7,2,6]%%%}+%%%{%%%{-128,[7]%%%},[0,7,0,7]%%%} / %%%{%%{poly1[%%%{-128,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[14,0,0,0]%%%}+%%%{%%%{896,[10]%%%},[13,0,1,0]%%%}+%%%{%%{poly1[%%%{-3136,[9]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[12,0,2,0]%%%}+%%%{%%{[%%%{896,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[12,0,0,1]%%%}+%%%{%%%{7168,[9]%%%},[11,0,3,0]%%%}+%%%{%%%{-5376,[10]%%%},[11,0,1,1]%%%}+%%%{%%{poly1[%%%{-11872,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[10,0,4,0]%%%}+%%%{%%{[%%%{16128,[9]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[10,0,2,1]%%%}+%%%{%%{poly1[%%%{-2688,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[10,0,0,2]%%%}+%%%{%%%{15008,[8]%%%},[9,0,5,0]%%%}+%%%{%%%{-31360,[9]%%%},[9,0,3,1]%%%}+%%%{%%%{13440,[10]%%%},[9,0,1,2]%%%}+%%%{%%{poly1[%%%{-14896,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[8,0,6,0]%%%}+%%%{%%{[%%%{43680,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[8,0,4,1]%%%}+%%%{%%{poly1[%%%{-33600,[9]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[8,0,2,2]%%%}+%%%{%%{[%%%{4480,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[8,0,0,3]%%%}+%%%{%%%{11776,[7]%%%},[7,0,7,0]%%%}+%%%{%%%{-45696,[8]%%%},[7,0,5,1]%%%}+%%%{%%%{53760,[9]%%%},[7,0,3,2]%%%}+%%%{%%%{-17920,[10]%%%},[7,0,1,3]%%%}+%%%{%%{poly1[%%%{-7448,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[6,0,8,0]%%%}+%%%{%%{[%%%{36736,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[6,0,6,1]%%%}+%%%{%%{poly1[%%%{-60480,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[6,0,4,2]%%%}+%%%{%%{[%%%{35840,[9]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[6,0,2,3]%%%}+%%%{%%{poly1[%%%{-4480,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[6,0,0,4]%%%}+%%%{%%%{3752,[6]%%%},[5,0,9,0]%%%}+%%%{%%%{-22848,[7]%%%},[5,0,7,1]%%%}+%%%{%%%{49728,[8]%%%},[5,0,5,2]%%%}+%%%{%%%{-44800,[9]%%%},[5,0,3,3]%%%}+%%%{%%%{13440,[10]%%%},[5,0,1,4]%%%}+%%%{%%{poly1[%%%{-1484,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,10,0]%%%}+%%%{%%{[%%%{10920,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,8,1]%%%}+%%%{%%{poly1[%%%{-30240,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,6,2]%%%}+%%%{%%{[%%%{38080,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,4,3]%%%}+%%%{%%{poly1[%%%{-20160,[9]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,2,4]%%%}+%%%{%%{[%%%{2688,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,0,5]%%%}+%%%{%%%{448,[5]%%%},[3,0,11,0]%%%}+%%%{%%%{-3920,[6]%%%},[3,0,9,1]%%%}+%%%{%%%{13440,[7]%%%},[3,0,7,2]%%%}+%%%{%%%{-22400,[8]%%%},[3,0,5,3]%%%}+%%%{%%%{17920,[9]%%%},[3,0,3,4]%%%}+%%%{%%%{-5376,[10]%%%},[3,0,1,5]%%%}+%%%{%%{poly1[%%%{-98,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,12,0]%%%}+%%%{%%{[%%%{1008,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,10,1]%%%}+%%%{%%{poly1[%%%{-4200,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,8,2]%%%}+%%%{%%{[%%%{8960,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,6,3]%%%}+%%%{%%{poly1[%%%{-10080,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,4,4]%%%}+%%%{%%{[%%%{5376,[9]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,2,5]%%%}+%%%{%%{[%%%{-896,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,0,6]%%%}+%%%{%%%{14,[4]%%%},[1,0,13,0]%%%}+%%%{%%%{-168,[5]%%%},[1,0,11,1]%%%}+%%%{%%%{840,[6]%%%},[1,0,9,2]%%%}+%%%{%%%{-2240,[7]%%%},[1,0,7,3]%%%}+%%%{%%%{3360,[8]%%%},[1,0,5,4]%%%}+%%%{%%%{-2688,[9]%%%},[1,0,3,5]%%%}+%%%{%%%{896,[10]%%%},[1,0,1,6]%%%}+%%%{%%{poly1[%%%{-1,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,14,0]%%%}+%%%{%%{[%%%{14,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,12,1]%%%}+%%%{%%{poly1[%%%{-84,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,10,2]%%%}+%%%{%%{[%%%{280,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,8,3]%%%}+%%%{%%{poly1[%%%{-560,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,6,4]%%%}+%%%{%%{[%%%{672,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,4,5]%%%}+%%%{%%{[%%%{-448,[9]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,2,6]%%%}+%%%{%%{[%%%{128,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,0,7]%%%} Error: Bad Argument Value","F(-2)",0
1202,1,128,0,0.243889," ","integrate((2*c*d*x+b*d)^5*(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\frac{2}{5} \, {\left(c x^{2} + b x + a\right)}^{\frac{5}{2}} b^{4} d^{5} + \frac{16}{7} \, {\left(c x^{2} + b x + a\right)}^{\frac{7}{2}} b^{2} c d^{5} - \frac{16}{5} \, {\left(c x^{2} + b x + a\right)}^{\frac{5}{2}} a b^{2} c d^{5} + \frac{32}{9} \, {\left(c x^{2} + b x + a\right)}^{\frac{9}{2}} c^{2} d^{5} - \frac{64}{7} \, {\left(c x^{2} + b x + a\right)}^{\frac{7}{2}} a c^{2} d^{5} + \frac{32}{5} \, {\left(c x^{2} + b x + a\right)}^{\frac{5}{2}} a^{2} c^{2} d^{5}"," ",0,"2/5*(c*x^2 + b*x + a)^(5/2)*b^4*d^5 + 16/7*(c*x^2 + b*x + a)^(7/2)*b^2*c*d^5 - 16/5*(c*x^2 + b*x + a)^(5/2)*a*b^2*c*d^5 + 32/9*(c*x^2 + b*x + a)^(9/2)*c^2*d^5 - 64/7*(c*x^2 + b*x + a)^(7/2)*a*c^2*d^5 + 32/5*(c*x^2 + b*x + a)^(5/2)*a^2*c^2*d^5","A",0
1203,1,391,0,0.305669," ","integrate((2*c*d*x+b*d)^4*(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\frac{1}{1024} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(2 \, {\left(4 \, {\left(2 \, c^{5} d^{4} x + 7 \, b c^{4} d^{4}\right)} x + \frac{3 \, {\left(13 \, b^{2} c^{10} d^{4} + 4 \, a c^{11} d^{4}\right)}}{c^{7}}\right)} x + \frac{5 \, {\left(11 \, b^{3} c^{9} d^{4} + 12 \, a b c^{10} d^{4}\right)}}{c^{7}}\right)} x + \frac{161 \, b^{4} c^{8} d^{4} + 472 \, a b^{2} c^{9} d^{4} + 16 \, a^{2} c^{10} d^{4}}{c^{7}}\right)} x + \frac{3 \, {\left(17 \, b^{5} c^{7} d^{4} + 152 \, a b^{3} c^{8} d^{4} + 16 \, a^{2} b c^{9} d^{4}\right)}}{c^{7}}\right)} x + \frac{b^{6} c^{6} d^{4} + 396 \, a b^{4} c^{7} d^{4} + 240 \, a^{2} b^{2} c^{8} d^{4} - 192 \, a^{3} c^{9} d^{4}}{c^{7}}\right)} x - \frac{3 \, b^{7} c^{5} d^{4} - 44 \, a b^{5} c^{6} d^{4} - 176 \, a^{2} b^{3} c^{7} d^{4} + 192 \, a^{3} b c^{8} d^{4}}{c^{7}}\right)} - \frac{3 \, {\left(b^{8} d^{4} - 16 \, a b^{6} c d^{4} + 96 \, a^{2} b^{4} c^{2} d^{4} - 256 \, a^{3} b^{2} c^{3} d^{4} + 256 \, a^{4} c^{4} d^{4}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{2048 \, c^{\frac{5}{2}}}"," ",0,"1/1024*sqrt(c*x^2 + b*x + a)*(2*(4*(2*(8*(2*(4*(2*c^5*d^4*x + 7*b*c^4*d^4)*x + 3*(13*b^2*c^10*d^4 + 4*a*c^11*d^4)/c^7)*x + 5*(11*b^3*c^9*d^4 + 12*a*b*c^10*d^4)/c^7)*x + (161*b^4*c^8*d^4 + 472*a*b^2*c^9*d^4 + 16*a^2*c^10*d^4)/c^7)*x + 3*(17*b^5*c^7*d^4 + 152*a*b^3*c^8*d^4 + 16*a^2*b*c^9*d^4)/c^7)*x + (b^6*c^6*d^4 + 396*a*b^4*c^7*d^4 + 240*a^2*b^2*c^8*d^4 - 192*a^3*c^9*d^4)/c^7)*x - (3*b^7*c^5*d^4 - 44*a*b^5*c^6*d^4 - 176*a^2*b^3*c^7*d^4 + 192*a^3*b*c^8*d^4)/c^7) - 3/2048*(b^8*d^4 - 16*a*b^6*c*d^4 + 96*a^2*b^4*c^2*d^4 - 256*a^3*b^2*c^3*d^4 + 256*a^4*c^4*d^4)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(5/2)","B",0
1204,1,58,0,0.185313," ","integrate((2*c*d*x+b*d)^3*(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\frac{2}{5} \, {\left(c x^{2} + b x + a\right)}^{\frac{5}{2}} b^{2} d^{3} + \frac{8}{7} \, {\left(c x^{2} + b x + a\right)}^{\frac{7}{2}} c d^{3} - \frac{8}{5} \, {\left(c x^{2} + b x + a\right)}^{\frac{5}{2}} a c d^{3}"," ",0,"2/5*(c*x^2 + b*x + a)^(5/2)*b^2*d^3 + 8/7*(c*x^2 + b*x + a)^(7/2)*c*d^3 - 8/5*(c*x^2 + b*x + a)^(5/2)*a*c*d^3","A",0
1205,1,259,0,0.288877," ","integrate((2*c*d*x+b*d)^2*(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\frac{1}{384} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(2 \, c^{3} d^{2} x + 5 \, b c^{2} d^{2}\right)} x + \frac{33 \, b^{2} c^{6} d^{2} + 28 \, a c^{7} d^{2}}{c^{5}}\right)} x + \frac{19 \, b^{3} c^{5} d^{2} + 84 \, a b c^{6} d^{2}}{c^{5}}\right)} x + \frac{b^{4} c^{4} d^{2} + 144 \, a b^{2} c^{5} d^{2} + 48 \, a^{2} c^{6} d^{2}}{c^{5}}\right)} x - \frac{3 \, b^{5} c^{3} d^{2} - 32 \, a b^{3} c^{4} d^{2} - 48 \, a^{2} b c^{5} d^{2}}{c^{5}}\right)} - \frac{{\left(b^{6} d^{2} - 12 \, a b^{4} c d^{2} + 48 \, a^{2} b^{2} c^{2} d^{2} - 64 \, a^{3} c^{3} d^{2}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{256 \, c^{\frac{5}{2}}}"," ",0,"1/384*sqrt(c*x^2 + b*x + a)*(2*(4*(2*(8*(2*c^3*d^2*x + 5*b*c^2*d^2)*x + (33*b^2*c^6*d^2 + 28*a*c^7*d^2)/c^5)*x + (19*b^3*c^5*d^2 + 84*a*b*c^6*d^2)/c^5)*x + (b^4*c^4*d^2 + 144*a*b^2*c^5*d^2 + 48*a^2*c^6*d^2)/c^5)*x - (3*b^5*c^3*d^2 - 32*a*b^3*c^4*d^2 - 48*a^2*b*c^5*d^2)/c^5) - 1/256*(b^6*d^2 - 12*a*b^4*c*d^2 + 48*a^2*b^2*c^2*d^2 - 64*a^3*c^3*d^2)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(5/2)","A",0
1206,1,15,0,0.213588," ","integrate((2*c*d*x+b*d)*(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\frac{2}{5} \, {\left(c x^{2} + b x + a\right)}^{\frac{5}{2}} d"," ",0,"2/5*(c*x^2 + b*x + a)^(5/2)*d","A",0
1207,1,149,0,0.279389," ","integrate((c*x^2+b*x+a)^(3/2)/(2*c*d*x+b*d),x, algorithm=""giac"")","\frac{1}{24} \, \sqrt{c x^{2} + b x + a} {\left(4 \, x {\left(\frac{x}{d} + \frac{b}{c d}\right)} - \frac{3 \, b^{2} c^{3} d^{3} - 16 \, a c^{4} d^{3}}{c^{5} d^{4}}\right)} + \frac{{\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \arctan\left(-\frac{2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} c + b \sqrt{c}}{\sqrt{b^{2} c - 4 \, a c^{2}}}\right)}{8 \, \sqrt{b^{2} c - 4 \, a c^{2}} c^{2} d}"," ",0,"1/24*sqrt(c*x^2 + b*x + a)*(4*x*(x/d + b/(c*d)) - (3*b^2*c^3*d^3 - 16*a*c^4*d^3)/(c^5*d^4)) + 1/8*(b^4 - 8*a*b^2*c + 16*a^2*c^2)*arctan(-(2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*c + b*sqrt(c))/sqrt(b^2*c - 4*a*c^2))/(sqrt(b^2*c - 4*a*c^2)*c^2*d)","A",0
1208,1,440,0,0.513570," ","integrate((c*x^2+b*x+a)^(3/2)/(2*c*d*x+b*d)^2,x, algorithm=""giac"")","\frac{1}{32} \, d^{2} {\left(\frac{3 \, {\left(b^{2} \mathrm{sgn}\left(\frac{1}{2 \, c d x + b d}\right) \mathrm{sgn}\left(c\right) \mathrm{sgn}\left(d\right) - 4 \, a c \mathrm{sgn}\left(\frac{1}{2 \, c d x + b d}\right) \mathrm{sgn}\left(c\right) \mathrm{sgn}\left(d\right)\right)} \arctan\left(\frac{\sqrt{-\frac{b^{2} c d^{2}}{{\left(2 \, c d x + b d\right)}^{2}} + \frac{4 \, a c^{2} d^{2}}{{\left(2 \, c d x + b d\right)}^{2}} + c}}{\sqrt{-c}}\right)}{\sqrt{-c} c^{2} d^{4} {\left| c \right|}} + \frac{2 \, {\left(\sqrt{-\frac{b^{2} c d^{2}}{{\left(2 \, c d x + b d\right)}^{2}} + \frac{4 \, a c^{2} d^{2}}{{\left(2 \, c d x + b d\right)}^{2}} + c} b^{2} \mathrm{sgn}\left(\frac{1}{2 \, c d x + b d}\right) \mathrm{sgn}\left(c\right) \mathrm{sgn}\left(d\right) - 4 \, \sqrt{-\frac{b^{2} c d^{2}}{{\left(2 \, c d x + b d\right)}^{2}} + \frac{4 \, a c^{2} d^{2}}{{\left(2 \, c d x + b d\right)}^{2}} + c} a c \mathrm{sgn}\left(\frac{1}{2 \, c d x + b d}\right) \mathrm{sgn}\left(c\right) \mathrm{sgn}\left(d\right)\right)}}{c^{3} d^{4} {\left| c \right|}} + \frac{\sqrt{-\frac{b^{2} c d^{2}}{{\left(2 \, c d x + b d\right)}^{2}} + \frac{4 \, a c^{2} d^{2}}{{\left(2 \, c d x + b d\right)}^{2}} + c} b^{2} \mathrm{sgn}\left(\frac{1}{2 \, c d x + b d}\right) \mathrm{sgn}\left(c\right) \mathrm{sgn}\left(d\right) - 4 \, \sqrt{-\frac{b^{2} c d^{2}}{{\left(2 \, c d x + b d\right)}^{2}} + \frac{4 \, a c^{2} d^{2}}{{\left(2 \, c d x + b d\right)}^{2}} + c} a c \mathrm{sgn}\left(\frac{1}{2 \, c d x + b d}\right) \mathrm{sgn}\left(c\right) \mathrm{sgn}\left(d\right)}{{\left(\frac{b^{2} c d^{2}}{{\left(2 \, c d x + b d\right)}^{2}} - \frac{4 \, a c^{2} d^{2}}{{\left(2 \, c d x + b d\right)}^{2}}\right)} c^{2} d^{4} {\left| c \right|}}\right)} {\left| c \right|}"," ",0,"1/32*d^2*(3*(b^2*sgn(1/(2*c*d*x + b*d))*sgn(c)*sgn(d) - 4*a*c*sgn(1/(2*c*d*x + b*d))*sgn(c)*sgn(d))*arctan(sqrt(-b^2*c*d^2/(2*c*d*x + b*d)^2 + 4*a*c^2*d^2/(2*c*d*x + b*d)^2 + c)/sqrt(-c))/(sqrt(-c)*c^2*d^4*abs(c)) + 2*(sqrt(-b^2*c*d^2/(2*c*d*x + b*d)^2 + 4*a*c^2*d^2/(2*c*d*x + b*d)^2 + c)*b^2*sgn(1/(2*c*d*x + b*d))*sgn(c)*sgn(d) - 4*sqrt(-b^2*c*d^2/(2*c*d*x + b*d)^2 + 4*a*c^2*d^2/(2*c*d*x + b*d)^2 + c)*a*c*sgn(1/(2*c*d*x + b*d))*sgn(c)*sgn(d))/(c^3*d^4*abs(c)) + (sqrt(-b^2*c*d^2/(2*c*d*x + b*d)^2 + 4*a*c^2*d^2/(2*c*d*x + b*d)^2 + c)*b^2*sgn(1/(2*c*d*x + b*d))*sgn(c)*sgn(d) - 4*sqrt(-b^2*c*d^2/(2*c*d*x + b*d)^2 + 4*a*c^2*d^2/(2*c*d*x + b*d)^2 + c)*a*c*sgn(1/(2*c*d*x + b*d))*sgn(c)*sgn(d))/((b^2*c*d^2/(2*c*d*x + b*d)^2 - 4*a*c^2*d^2/(2*c*d*x + b*d)^2)*c^2*d^4*abs(c)))*abs(c)","B",0
1209,1,387,0,0.360087," ","integrate((c*x^2+b*x+a)^(3/2)/(2*c*d*x+b*d)^3,x, algorithm=""giac"")","-\frac{3 \, {\left(b^{2} - 4 \, a c\right)} \arctan\left(-\frac{2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} c + b \sqrt{c}}{\sqrt{b^{2} c - 4 \, a c^{2}}}\right)}{16 \, \sqrt{b^{2} c - 4 \, a c^{2}} c^{2} d^{3}} + \frac{\sqrt{c x^{2} + b x + a}}{8 \, c^{2} d^{3}} - \frac{2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{2} c^{\frac{3}{2}} - 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a c^{\frac{5}{2}} + 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{3} c - 12 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a b c^{2} + {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{4} \sqrt{c} - 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{2} c^{\frac{3}{2}} - 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} c^{\frac{5}{2}} + a b^{3} c - 4 \, a^{2} b c^{2}}{16 \, {\left(2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} c^{\frac{3}{2}} + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b c + b^{2} \sqrt{c} - 2 \, a c^{\frac{3}{2}}\right)}^{2} c^{\frac{3}{2}} d^{3}}"," ",0,"-3/16*(b^2 - 4*a*c)*arctan(-(2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*c + b*sqrt(c))/sqrt(b^2*c - 4*a*c^2))/(sqrt(b^2*c - 4*a*c^2)*c^2*d^3) + 1/8*sqrt(c*x^2 + b*x + a)/(c^2*d^3) - 1/16*(2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^2*c^(3/2) - 8*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*c^(5/2) + 3*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^3*c - 12*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b*c^2 + (sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^4*sqrt(c) - 2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^2*c^(3/2) - 8*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*c^(5/2) + a*b^3*c - 4*a^2*b*c^2)/((2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*c^(3/2) + 2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b*c + b^2*sqrt(c) - 2*a*c^(3/2))^2*c^(3/2)*d^3)","B",0
1210,-2,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)/(2*c*d*x+b*d)^4,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{%%%{16,[4]%%%},[8,4,8,0]%%%}+%%%{%%%{-256,[5]%%%},[8,4,6,1]%%%}+%%%{%%%{1536,[6]%%%},[8,4,4,2]%%%}+%%%{%%%{-4096,[7]%%%},[8,4,2,3]%%%}+%%%{%%%{4096,[8]%%%},[8,4,0,4]%%%}+%%%{%%{[%%%{-64,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,4,9,0]%%%}+%%%{%%{[%%%{1024,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,4,7,1]%%%}+%%%{%%{[%%%{-6144,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,4,5,2]%%%}+%%%{%%{[%%%{16384,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,4,3,3]%%%}+%%%{%%{[%%%{-16384,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,4,1,4]%%%}+%%%{%%%{128,[3]%%%},[6,4,10,0]%%%}+%%%{%%%{-2112,[4]%%%},[6,4,8,1]%%%}+%%%{%%%{13312,[5]%%%},[6,4,6,2]%%%}+%%%{%%%{-38912,[6]%%%},[6,4,4,3]%%%}+%%%{%%%{49152,[7]%%%},[6,4,2,4]%%%}+%%%{%%%{-16384,[8]%%%},[6,4,0,5]%%%}+%%%{%%{[%%%{-160,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,4,11,0]%%%}+%%%{%%{[%%%{2752,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,4,9,1]%%%}+%%%{%%{[%%%{-18432,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,4,7,2]%%%}+%%%{%%{[%%%{59392,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,4,5,3]%%%}+%%%{%%{[%%%{-90112,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,4,3,4]%%%}+%%%{%%{[%%%{49152,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,4,1,5]%%%}+%%%{%%%{136,[2]%%%},[4,4,12,0]%%%}+%%%{%%%{-2464,[3]%%%},[4,4,10,1]%%%}+%%%{%%%{17760,[4]%%%},[4,4,8,2]%%%}+%%%{%%%{-64000,[5]%%%},[4,4,6,3]%%%}+%%%{%%%{117760,[6]%%%},[4,4,4,4]%%%}+%%%{%%%{-98304,[7]%%%},[4,4,2,5]%%%}+%%%{%%%{24576,[8]%%%},[4,4,0,6]%%%}+%%%{%%{[%%%{-80,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,4,13,0]%%%}+%%%{%%{[%%%{1536,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,4,11,1]%%%}+%%%{%%{[%%%{-11968,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,4,9,2]%%%}+%%%{%%{[%%%{48128,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,4,7,3]%%%}+%%%{%%{[%%%{-104448,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,4,5,4]%%%}+%%%{%%{[%%%{114688,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,4,3,5]%%%}+%%%{%%{[%%%{-49152,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,4,1,6]%%%}+%%%{%%%{32,[1]%%%},[2,4,14,0]%%%}+%%%{%%%{-656,[2]%%%},[2,4,12,1]%%%}+%%%{%%%{5568,[3]%%%},[2,4,10,2]%%%}+%%%{%%%{-25152,[4]%%%},[2,4,8,3]%%%}+%%%{%%%{64512,[5]%%%},[2,4,6,4]%%%}+%%%{%%%{-92160,[6]%%%},[2,4,4,5]%%%}+%%%{%%%{65536,[7]%%%},[2,4,2,6]%%%}+%%%{%%%{-16384,[8]%%%},[2,4,0,7]%%%}+%%%{%%{[-8,0]:[1,0,%%%{-1,[1]%%%}]%%},[1,4,15,0]%%%}+%%%{%%{[%%%{176,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,4,13,1]%%%}+%%%{%%{[%%%{-1632,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,4,11,2]%%%}+%%%{%%{[%%%{8256,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,4,9,3]%%%}+%%%{%%{[%%%{-24576,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,4,7,4]%%%}+%%%{%%{[%%%{43008,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,4,5,5]%%%}+%%%{%%{[%%%{-40960,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,4,3,6]%%%}+%%%{%%{[%%%{16384,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,4,1,7]%%%}+%%%{1,[0,4,16,0]%%%}+%%%{%%%{-24,[1]%%%},[0,4,14,1]%%%}+%%%{%%%{248,[2]%%%},[0,4,12,2]%%%}+%%%{%%%{-1440,[3]%%%},[0,4,10,3]%%%}+%%%{%%%{5136,[4]%%%},[0,4,8,4]%%%}+%%%{%%%{-11520,[5]%%%},[0,4,6,5]%%%}+%%%{%%%{15872,[6]%%%},[0,4,4,6]%%%}+%%%{%%%{-12288,[7]%%%},[0,4,2,7]%%%}+%%%{%%%{4096,[8]%%%},[0,4,0,8]%%%} / %%%{%%%{16,[6]%%%},[8,0,0,0]%%%}+%%%{%%{poly1[%%%{-64,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,0,1,0]%%%}+%%%{%%%{128,[5]%%%},[6,0,2,0]%%%}+%%%{%%%{-64,[6]%%%},[6,0,0,1]%%%}+%%%{%%{poly1[%%%{-160,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,0,3,0]%%%}+%%%{%%{[%%%{192,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,0,1,1]%%%}+%%%{%%%{136,[4]%%%},[4,0,4,0]%%%}+%%%{%%%{-288,[5]%%%},[4,0,2,1]%%%}+%%%{%%%{96,[6]%%%},[4,0,0,2]%%%}+%%%{%%{poly1[%%%{-80,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,0,5,0]%%%}+%%%{%%{[%%%{256,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,0,3,1]%%%}+%%%{%%{poly1[%%%{-192,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,0,1,2]%%%}+%%%{%%%{32,[3]%%%},[2,0,6,0]%%%}+%%%{%%%{-144,[4]%%%},[2,0,4,1]%%%}+%%%{%%%{192,[5]%%%},[2,0,2,2]%%%}+%%%{%%%{-64,[6]%%%},[2,0,0,3]%%%}+%%%{%%{poly1[%%%{-8,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,0,7,0]%%%}+%%%{%%{[%%%{48,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,0,5,1]%%%}+%%%{%%{poly1[%%%{-96,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,0,3,2]%%%}+%%%{%%{[%%%{64,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,0,1,3]%%%}+%%%{%%%{1,[2]%%%},[0,0,8,0]%%%}+%%%{%%%{-8,[3]%%%},[0,0,6,1]%%%}+%%%{%%%{24,[4]%%%},[0,0,4,2]%%%}+%%%{%%%{-32,[5]%%%},[0,0,2,3]%%%}+%%%{%%%{16,[6]%%%},[0,0,0,4]%%%} Error: Bad Argument Value","F(-2)",0
1211,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)/(2*c*d*x+b*d)^5,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1212,1,594,0,0.614789," ","integrate((c*x^2+b*x+a)^(3/2)/(2*c*d*x+b*d)^6,x, algorithm=""giac"")","\frac{80 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} c^{\frac{9}{2}} + 320 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} b c^{4} + 560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} b^{2} c^{\frac{7}{2}} + 560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} b^{3} c^{3} + 360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} b^{4} c^{\frac{5}{2}} - 80 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a b^{2} c^{\frac{7}{2}} + 160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{2} c^{\frac{9}{2}} + 160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{5} c^{2} - 160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b^{3} c^{3} + 320 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{2} b c^{4} + 50 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{6} c^{\frac{3}{2}} - 120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a b^{4} c^{\frac{5}{2}} + 240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{2} b^{2} c^{\frac{7}{2}} + 10 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{7} c - 40 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{5} c^{2} + 80 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} b^{3} c^{3} + b^{8} \sqrt{c} - 6 \, a b^{6} c^{\frac{3}{2}} + 16 \, a^{2} b^{4} c^{\frac{5}{2}} - 16 \, a^{3} b^{2} c^{\frac{7}{2}} + 16 \, a^{4} c^{\frac{9}{2}}}{80 \, {\left(2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} c + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b \sqrt{c} + b^{2} - 2 \, a c\right)}^{5} c^{3} d^{6}}"," ",0,"1/80*(80*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*c^(9/2) + 320*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*b*c^4 + 560*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*b^2*c^(7/2) + 560*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b^3*c^3 + 360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^4*c^(5/2) - 80*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*b^2*c^(7/2) + 160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^2*c^(9/2) + 160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^5*c^2 - 160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^3*c^3 + 320*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*b*c^4 + 50*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^6*c^(3/2) - 120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^4*c^(5/2) + 240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*b^2*c^(7/2) + 10*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^7*c - 40*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^5*c^2 + 80*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b^3*c^3 + b^8*sqrt(c) - 6*a*b^6*c^(3/2) + 16*a^2*b^4*c^(5/2) - 16*a^3*b^2*c^(7/2) + 16*a^4*c^(9/2))/((2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*c + 2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b*sqrt(c) + b^2 - 2*a*c)^5*c^3*d^6)","B",0
1213,-2,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)/(2*c*d*x+b*d)^7,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{%%%{128,[7]%%%},[14,7,0,0]%%%}+%%%{%%{[%%%{-896,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[13,7,1,0]%%%}+%%%{%%%{3136,[6]%%%},[12,7,2,0]%%%}+%%%{%%%{-896,[7]%%%},[12,7,0,1]%%%}+%%%{%%{[%%%{-7168,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[11,7,3,0]%%%}+%%%{%%{[%%%{5376,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[11,7,1,1]%%%}+%%%{%%%{11872,[5]%%%},[10,7,4,0]%%%}+%%%{%%%{-16128,[6]%%%},[10,7,2,1]%%%}+%%%{%%%{2688,[7]%%%},[10,7,0,2]%%%}+%%%{%%{[%%%{-15008,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[9,7,5,0]%%%}+%%%{%%{[%%%{31360,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[9,7,3,1]%%%}+%%%{%%{[%%%{-13440,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[9,7,1,2]%%%}+%%%{%%%{14896,[4]%%%},[8,7,6,0]%%%}+%%%{%%%{-43680,[5]%%%},[8,7,4,1]%%%}+%%%{%%%{33600,[6]%%%},[8,7,2,2]%%%}+%%%{%%%{-4480,[7]%%%},[8,7,0,3]%%%}+%%%{%%{[%%%{-11776,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,7,7,0]%%%}+%%%{%%{[%%%{45696,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,7,5,1]%%%}+%%%{%%{[%%%{-53760,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,7,3,2]%%%}+%%%{%%{[%%%{17920,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,7,1,3]%%%}+%%%{%%%{7448,[3]%%%},[6,7,8,0]%%%}+%%%{%%%{-36736,[4]%%%},[6,7,6,1]%%%}+%%%{%%%{60480,[5]%%%},[6,7,4,2]%%%}+%%%{%%%{-35840,[6]%%%},[6,7,2,3]%%%}+%%%{%%%{4480,[7]%%%},[6,7,0,4]%%%}+%%%{%%{[%%%{-3752,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,7,9,0]%%%}+%%%{%%{[%%%{22848,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,7,7,1]%%%}+%%%{%%{[%%%{-49728,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,7,5,2]%%%}+%%%{%%{[%%%{44800,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,7,3,3]%%%}+%%%{%%{[%%%{-13440,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,7,1,4]%%%}+%%%{%%%{1484,[2]%%%},[4,7,10,0]%%%}+%%%{%%%{-10920,[3]%%%},[4,7,8,1]%%%}+%%%{%%%{30240,[4]%%%},[4,7,6,2]%%%}+%%%{%%%{-38080,[5]%%%},[4,7,4,3]%%%}+%%%{%%%{20160,[6]%%%},[4,7,2,4]%%%}+%%%{%%%{-2688,[7]%%%},[4,7,0,5]%%%}+%%%{%%{[%%%{-448,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,7,11,0]%%%}+%%%{%%{[%%%{3920,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,7,9,1]%%%}+%%%{%%{[%%%{-13440,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,7,7,2]%%%}+%%%{%%{[%%%{22400,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,7,5,3]%%%}+%%%{%%{[%%%{-17920,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,7,3,4]%%%}+%%%{%%{[%%%{5376,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,7,1,5]%%%}+%%%{%%%{98,[1]%%%},[2,7,12,0]%%%}+%%%{%%%{-1008,[2]%%%},[2,7,10,1]%%%}+%%%{%%%{4200,[3]%%%},[2,7,8,2]%%%}+%%%{%%%{-8960,[4]%%%},[2,7,6,3]%%%}+%%%{%%%{10080,[5]%%%},[2,7,4,4]%%%}+%%%{%%%{-5376,[6]%%%},[2,7,2,5]%%%}+%%%{%%%{896,[7]%%%},[2,7,0,6]%%%}+%%%{%%{[-14,0]:[1,0,%%%{-1,[1]%%%}]%%},[1,7,13,0]%%%}+%%%{%%{[%%%{168,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,7,11,1]%%%}+%%%{%%{[%%%{-840,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,7,9,2]%%%}+%%%{%%{[%%%{2240,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,7,7,3]%%%}+%%%{%%{[%%%{-3360,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,7,5,4]%%%}+%%%{%%{[%%%{2688,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,7,3,5]%%%}+%%%{%%{[%%%{-896,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,7,1,6]%%%}+%%%{1,[0,7,14,0]%%%}+%%%{%%%{-14,[1]%%%},[0,7,12,1]%%%}+%%%{%%%{84,[2]%%%},[0,7,10,2]%%%}+%%%{%%%{-280,[3]%%%},[0,7,8,3]%%%}+%%%{%%%{560,[4]%%%},[0,7,6,4]%%%}+%%%{%%%{-672,[5]%%%},[0,7,4,5]%%%}+%%%{%%%{448,[6]%%%},[0,7,2,6]%%%}+%%%{%%%{-128,[7]%%%},[0,7,0,7]%%%} / %%%{%%{poly1[%%%{-128,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[14,0,0,0]%%%}+%%%{%%%{896,[10]%%%},[13,0,1,0]%%%}+%%%{%%{poly1[%%%{-3136,[9]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[12,0,2,0]%%%}+%%%{%%{[%%%{896,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[12,0,0,1]%%%}+%%%{%%%{7168,[9]%%%},[11,0,3,0]%%%}+%%%{%%%{-5376,[10]%%%},[11,0,1,1]%%%}+%%%{%%{poly1[%%%{-11872,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[10,0,4,0]%%%}+%%%{%%{[%%%{16128,[9]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[10,0,2,1]%%%}+%%%{%%{poly1[%%%{-2688,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[10,0,0,2]%%%}+%%%{%%%{15008,[8]%%%},[9,0,5,0]%%%}+%%%{%%%{-31360,[9]%%%},[9,0,3,1]%%%}+%%%{%%%{13440,[10]%%%},[9,0,1,2]%%%}+%%%{%%{poly1[%%%{-14896,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[8,0,6,0]%%%}+%%%{%%{[%%%{43680,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[8,0,4,1]%%%}+%%%{%%{poly1[%%%{-33600,[9]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[8,0,2,2]%%%}+%%%{%%{[%%%{4480,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[8,0,0,3]%%%}+%%%{%%%{11776,[7]%%%},[7,0,7,0]%%%}+%%%{%%%{-45696,[8]%%%},[7,0,5,1]%%%}+%%%{%%%{53760,[9]%%%},[7,0,3,2]%%%}+%%%{%%%{-17920,[10]%%%},[7,0,1,3]%%%}+%%%{%%{poly1[%%%{-7448,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[6,0,8,0]%%%}+%%%{%%{[%%%{36736,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[6,0,6,1]%%%}+%%%{%%{poly1[%%%{-60480,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[6,0,4,2]%%%}+%%%{%%{[%%%{35840,[9]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[6,0,2,3]%%%}+%%%{%%{poly1[%%%{-4480,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[6,0,0,4]%%%}+%%%{%%%{3752,[6]%%%},[5,0,9,0]%%%}+%%%{%%%{-22848,[7]%%%},[5,0,7,1]%%%}+%%%{%%%{49728,[8]%%%},[5,0,5,2]%%%}+%%%{%%%{-44800,[9]%%%},[5,0,3,3]%%%}+%%%{%%%{13440,[10]%%%},[5,0,1,4]%%%}+%%%{%%{poly1[%%%{-1484,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,10,0]%%%}+%%%{%%{[%%%{10920,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,8,1]%%%}+%%%{%%{poly1[%%%{-30240,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,6,2]%%%}+%%%{%%{[%%%{38080,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,4,3]%%%}+%%%{%%{poly1[%%%{-20160,[9]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,2,4]%%%}+%%%{%%{[%%%{2688,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,0,5]%%%}+%%%{%%%{448,[5]%%%},[3,0,11,0]%%%}+%%%{%%%{-3920,[6]%%%},[3,0,9,1]%%%}+%%%{%%%{13440,[7]%%%},[3,0,7,2]%%%}+%%%{%%%{-22400,[8]%%%},[3,0,5,3]%%%}+%%%{%%%{17920,[9]%%%},[3,0,3,4]%%%}+%%%{%%%{-5376,[10]%%%},[3,0,1,5]%%%}+%%%{%%{poly1[%%%{-98,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,12,0]%%%}+%%%{%%{[%%%{1008,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,10,1]%%%}+%%%{%%{poly1[%%%{-4200,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,8,2]%%%}+%%%{%%{[%%%{8960,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,6,3]%%%}+%%%{%%{poly1[%%%{-10080,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,4,4]%%%}+%%%{%%{[%%%{5376,[9]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,2,5]%%%}+%%%{%%{[%%%{-896,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,0,6]%%%}+%%%{%%%{14,[4]%%%},[1,0,13,0]%%%}+%%%{%%%{-168,[5]%%%},[1,0,11,1]%%%}+%%%{%%%{840,[6]%%%},[1,0,9,2]%%%}+%%%{%%%{-2240,[7]%%%},[1,0,7,3]%%%}+%%%{%%%{3360,[8]%%%},[1,0,5,4]%%%}+%%%{%%%{-2688,[9]%%%},[1,0,3,5]%%%}+%%%{%%%{896,[10]%%%},[1,0,1,6]%%%}+%%%{%%{poly1[%%%{-1,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,14,0]%%%}+%%%{%%{[%%%{14,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,12,1]%%%}+%%%{%%{poly1[%%%{-84,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,10,2]%%%}+%%%{%%{[%%%{280,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,8,3]%%%}+%%%{%%{poly1[%%%{-560,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,6,4]%%%}+%%%{%%{[%%%{672,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,4,5]%%%}+%%%{%%{[%%%{-448,[9]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,2,6]%%%}+%%%{%%{[%%%{128,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,0,7]%%%} Error: Bad Argument Value","F(-2)",0
1214,1,1003,0,0.902116," ","integrate((c*x^2+b*x+a)^(3/2)/(2*c*d*x+b*d)^8,x, algorithm=""giac"")","\frac{560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{10} c^{\frac{11}{2}} + 2800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} b c^{5} + 6160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} b^{2} c^{\frac{9}{2}} + 560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} a c^{\frac{11}{2}} + 7840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} b^{3} c^{4} + 2240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} a b c^{5} + 6440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} b^{4} c^{\frac{7}{2}} + 3360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} a b^{2} c^{\frac{9}{2}} + 1120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} a^{2} c^{\frac{11}{2}} + 3640 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} b^{5} c^{3} + 2240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a b^{3} c^{4} + 3360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{2} b c^{5} + 1484 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} b^{6} c^{\frac{5}{2}} + 392 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a b^{4} c^{\frac{7}{2}} + 4032 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{2} b^{2} c^{\frac{9}{2}} + 224 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{3} c^{\frac{11}{2}} + 448 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{7} c^{2} - 336 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b^{5} c^{3} + 2464 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{2} b^{3} c^{4} + 448 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{3} b c^{5} + 98 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{8} c^{\frac{3}{2}} - 224 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a b^{6} c^{\frac{5}{2}} + 840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{2} b^{4} c^{\frac{7}{2}} + 224 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{3} b^{2} c^{\frac{9}{2}} + 112 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{4} c^{\frac{11}{2}} + 14 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{9} c - 56 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{7} c^{2} + 168 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} b^{5} c^{3} + 112 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{4} b c^{5} + b^{10} \sqrt{c} - 6 \, a b^{8} c^{\frac{3}{2}} + 20 \, a^{2} b^{6} c^{\frac{5}{2}} - 24 \, a^{3} b^{4} c^{\frac{7}{2}} + 48 \, a^{4} b^{2} c^{\frac{9}{2}} - 16 \, a^{5} c^{\frac{11}{2}}}{280 \, {\left(2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} c + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b \sqrt{c} + b^{2} - 2 \, a c\right)}^{7} c^{3} d^{8}}"," ",0,"1/280*(560*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^10*c^(11/2) + 2800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*b*c^5 + 6160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*b^2*c^(9/2) + 560*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a*c^(11/2) + 7840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*b^3*c^4 + 2240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a*b*c^5 + 6440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*b^4*c^(7/2) + 3360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a*b^2*c^(9/2) + 1120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^2*c^(11/2) + 3640*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b^5*c^3 + 2240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*b^3*c^4 + 3360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^2*b*c^5 + 1484*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^6*c^(5/2) + 392*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*b^4*c^(7/2) + 4032*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^2*b^2*c^(9/2) + 224*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^3*c^(11/2) + 448*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^7*c^2 - 336*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^5*c^3 + 2464*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*b^3*c^4 + 448*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^3*b*c^5 + 98*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^8*c^(3/2) - 224*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^6*c^(5/2) + 840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*b^4*c^(7/2) + 224*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^3*b^2*c^(9/2) + 112*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^4*c^(11/2) + 14*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^9*c - 56*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^7*c^2 + 168*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b^5*c^3 + 112*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^4*b*c^5 + b^10*sqrt(c) - 6*a*b^8*c^(3/2) + 20*a^2*b^6*c^(5/2) - 24*a^3*b^4*c^(7/2) + 48*a^4*b^2*c^(9/2) - 16*a^5*c^(11/2))/((2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*c + 2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b*sqrt(c) + b^2 - 2*a*c)^7*c^3*d^8)","B",0
1215,-2,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)/(2*c*d*x+b*d)^9,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{%%%{512,[9]%%%},[18,9,0,0]%%%}+%%%{%%{[%%%{-4608,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[17,9,1,0]%%%}+%%%{%%%{20736,[8]%%%},[16,9,2,0]%%%}+%%%{%%%{-4608,[9]%%%},[16,9,0,1]%%%}+%%%{%%{[%%%{-61440,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[15,9,3,0]%%%}+%%%{%%{[%%%{36864,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[15,9,1,1]%%%}+%%%{%%%{133632,[7]%%%},[14,9,4,0]%%%}+%%%{%%%{-147456,[8]%%%},[14,9,2,1]%%%}+%%%{%%%{18432,[9]%%%},[14,9,0,2]%%%}+%%%{%%{[%%%{-225792,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[13,9,5,0]%%%}+%%%{%%{[%%%{387072,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[13,9,3,1]%%%}+%%%{%%{[%%%{-129024,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[13,9,1,2]%%%}+%%%{%%%{306432,[6]%%%},[12,9,6,0]%%%}+%%%{%%%{-741888,[7]%%%},[12,9,4,1]%%%}+%%%{%%%{451584,[8]%%%},[12,9,2,2]%%%}+%%%{%%%{-43008,[9]%%%},[12,9,0,3]%%%}+%%%{%%{[%%%{-340992,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[11,9,7,0]%%%}+%%%{%%{[%%%{1096704,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[11,9,5,1]%%%}+%%%{%%{[%%%{-1032192,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[11,9,3,2]%%%}+%%%{%%{[%%%{258048,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[11,9,1,3]%%%}+%%%{%%%{315072,[5]%%%},[10,9,8,0]%%%}+%%%{%%%{-1290240,[6]%%%},[10,9,6,1]%%%}+%%%{%%%{1709568,[7]%%%},[10,9,4,2]%%%}+%%%{%%%{-774144,[8]%%%},[10,9,2,3]%%%}+%%%{%%%{64512,[9]%%%},[10,9,0,4]%%%}+%%%{%%{[%%%{-243392,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[9,9,9,0]%%%}+%%%{%%{[%%%{1230336,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[9,9,7,1]%%%}+%%%{%%{[%%%{-2161152,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[9,9,5,2]%%%}+%%%{%%{[%%%{1505280,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[9,9,3,3]%%%}+%%%{%%{[%%%{-322560,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[9,9,1,4]%%%}+%%%{%%%{157536,[4]%%%},[8,9,10,0]%%%}+%%%{%%%{-960192,[5]%%%},[8,9,8,1]%%%}+%%%{%%%{2145024,[6]%%%},[8,9,6,2]%%%}+%%%{%%%{-2096640,[7]%%%},[8,9,4,3]%%%}+%%%{%%%{806400,[8]%%%},[8,9,2,4]%%%}+%%%{%%%{-64512,[9]%%%},[8,9,0,5]%%%}+%%%{%%{[%%%{-85248,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,9,11,0]%%%}+%%%{%%{[%%%{615168,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,9,9,1]%%%}+%%%{%%{[%%%{-1695744,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,9,7,2]%%%}+%%%{%%{[%%%{2193408,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,9,5,3]%%%}+%%%{%%{[%%%{-1290240,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,9,3,4]%%%}+%%%{%%{[%%%{258048,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,9,1,5]%%%}+%%%{%%%{38304,[3]%%%},[6,9,12,0]%%%}+%%%{%%%{-322560,[4]%%%},[6,9,10,1]%%%}+%%%{%%%{1072512,[5]%%%},[6,9,8,2]%%%}+%%%{%%%{-1763328,[6]%%%},[6,9,6,3]%%%}+%%%{%%%{1451520,[7]%%%},[6,9,4,4]%%%}+%%%{%%%{-516096,[8]%%%},[6,9,2,5]%%%}+%%%{%%%{43008,[9]%%%},[6,9,0,6]%%%}+%%%{%%{[%%%{-14112,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,9,13,0]%%%}+%%%{%%{[%%%{137088,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,9,11,1]%%%}+%%%{%%{[%%%{-540288,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,9,9,2]%%%}+%%%{%%{[%%%{1096704,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,9,7,3]%%%}+%%%{%%{[%%%{-1193472,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,9,5,4]%%%}+%%%{%%{[%%%{645120,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,9,3,5]%%%}+%%%{%%{[%%%{-129024,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,9,1,6]%%%}+%%%{%%%{4176,[2]%%%},[4,9,14,0]%%%}+%%%{%%%{-46368,[3]%%%},[4,9,12,1]%%%}+%%%{%%%{213696,[4]%%%},[4,9,10,2]%%%}+%%%{%%%{-524160,[5]%%%},[4,9,8,3]%%%}+%%%{%%%{725760,[6]%%%},[4,9,6,4]%%%}+%%%{%%%{-548352,[7]%%%},[4,9,4,5]%%%}+%%%{%%%{193536,[8]%%%},[4,9,2,6]%%%}+%%%{%%%{-18432,[9]%%%},[4,9,0,7]%%%}+%%%{%%{[%%%{-960,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,9,15,0]%%%}+%%%{%%{[%%%{12096,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,9,13,1]%%%}+%%%{%%{[%%%{-64512,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,9,11,2]%%%}+%%%{%%{[%%%{188160,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,9,9,3]%%%}+%%%{%%{[%%%{-322560,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,9,7,4]%%%}+%%%{%%{[%%%{322560,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,9,5,5]%%%}+%%%{%%{[%%%{-172032,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,9,3,6]%%%}+%%%{%%{[%%%{36864,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,9,1,7]%%%}+%%%{%%%{162,[1]%%%},[2,9,16,0]%%%}+%%%{%%%{-2304,[2]%%%},[2,9,14,1]%%%}+%%%{%%%{14112,[3]%%%},[2,9,12,2]%%%}+%%%{%%%{-48384,[4]%%%},[2,9,10,3]%%%}+%%%{%%%{100800,[5]%%%},[2,9,8,4]%%%}+%%%{%%%{-129024,[6]%%%},[2,9,6,5]%%%}+%%%{%%%{96768,[7]%%%},[2,9,4,6]%%%}+%%%{%%%{-36864,[8]%%%},[2,9,2,7]%%%}+%%%{%%%{4608,[9]%%%},[2,9,0,8]%%%}+%%%{%%{[-18,0]:[1,0,%%%{-1,[1]%%%}]%%},[1,9,17,0]%%%}+%%%{%%{[%%%{288,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,9,15,1]%%%}+%%%{%%{[%%%{-2016,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,9,13,2]%%%}+%%%{%%{[%%%{8064,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,9,11,3]%%%}+%%%{%%{[%%%{-20160,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,9,9,4]%%%}+%%%{%%{[%%%{32256,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,9,7,5]%%%}+%%%{%%{[%%%{-32256,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,9,5,6]%%%}+%%%{%%{[%%%{18432,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,9,3,7]%%%}+%%%{%%{[%%%{-4608,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,9,1,8]%%%}+%%%{1,[0,9,18,0]%%%}+%%%{%%%{-18,[1]%%%},[0,9,16,1]%%%}+%%%{%%%{144,[2]%%%},[0,9,14,2]%%%}+%%%{%%%{-672,[3]%%%},[0,9,12,3]%%%}+%%%{%%%{2016,[4]%%%},[0,9,10,4]%%%}+%%%{%%%{-4032,[5]%%%},[0,9,8,5]%%%}+%%%{%%%{5376,[6]%%%},[0,9,6,6]%%%}+%%%{%%%{-4608,[7]%%%},[0,9,4,7]%%%}+%%%{%%%{2304,[8]%%%},[0,9,2,8]%%%}+%%%{%%%{-512,[9]%%%},[0,9,0,9]%%%} / %%%{%%{poly1[%%%{-512,[13]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[18,0,0,0]%%%}+%%%{%%%{4608,[13]%%%},[17,0,1,0]%%%}+%%%{%%{poly1[%%%{-20736,[12]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[16,0,2,0]%%%}+%%%{%%{[%%%{4608,[13]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[16,0,0,1]%%%}+%%%{%%%{61440,[12]%%%},[15,0,3,0]%%%}+%%%{%%%{-36864,[13]%%%},[15,0,1,1]%%%}+%%%{%%{poly1[%%%{-133632,[11]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[14,0,4,0]%%%}+%%%{%%{[%%%{147456,[12]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[14,0,2,1]%%%}+%%%{%%{poly1[%%%{-18432,[13]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[14,0,0,2]%%%}+%%%{%%%{225792,[11]%%%},[13,0,5,0]%%%}+%%%{%%%{-387072,[12]%%%},[13,0,3,1]%%%}+%%%{%%%{129024,[13]%%%},[13,0,1,2]%%%}+%%%{%%{poly1[%%%{-306432,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[12,0,6,0]%%%}+%%%{%%{[%%%{741888,[11]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[12,0,4,1]%%%}+%%%{%%{poly1[%%%{-451584,[12]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[12,0,2,2]%%%}+%%%{%%{[%%%{43008,[13]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[12,0,0,3]%%%}+%%%{%%%{340992,[10]%%%},[11,0,7,0]%%%}+%%%{%%%{-1096704,[11]%%%},[11,0,5,1]%%%}+%%%{%%%{1032192,[12]%%%},[11,0,3,2]%%%}+%%%{%%%{-258048,[13]%%%},[11,0,1,3]%%%}+%%%{%%{poly1[%%%{-315072,[9]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[10,0,8,0]%%%}+%%%{%%{[%%%{1290240,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[10,0,6,1]%%%}+%%%{%%{poly1[%%%{-1709568,[11]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[10,0,4,2]%%%}+%%%{%%{[%%%{774144,[12]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[10,0,2,3]%%%}+%%%{%%{poly1[%%%{-64512,[13]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[10,0,0,4]%%%}+%%%{%%%{243392,[9]%%%},[9,0,9,0]%%%}+%%%{%%%{-1230336,[10]%%%},[9,0,7,1]%%%}+%%%{%%%{2161152,[11]%%%},[9,0,5,2]%%%}+%%%{%%%{-1505280,[12]%%%},[9,0,3,3]%%%}+%%%{%%%{322560,[13]%%%},[9,0,1,4]%%%}+%%%{%%{poly1[%%%{-157536,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[8,0,10,0]%%%}+%%%{%%{[%%%{960192,[9]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[8,0,8,1]%%%}+%%%{%%{poly1[%%%{-2145024,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[8,0,6,2]%%%}+%%%{%%{[%%%{2096640,[11]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[8,0,4,3]%%%}+%%%{%%{poly1[%%%{-806400,[12]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[8,0,2,4]%%%}+%%%{%%{[%%%{64512,[13]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[8,0,0,5]%%%}+%%%{%%%{85248,[8]%%%},[7,0,11,0]%%%}+%%%{%%%{-615168,[9]%%%},[7,0,9,1]%%%}+%%%{%%%{1695744,[10]%%%},[7,0,7,2]%%%}+%%%{%%%{-2193408,[11]%%%},[7,0,5,3]%%%}+%%%{%%%{1290240,[12]%%%},[7,0,3,4]%%%}+%%%{%%%{-258048,[13]%%%},[7,0,1,5]%%%}+%%%{%%{poly1[%%%{-38304,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[6,0,12,0]%%%}+%%%{%%{[%%%{322560,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[6,0,10,1]%%%}+%%%{%%{poly1[%%%{-1072512,[9]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[6,0,8,2]%%%}+%%%{%%{[%%%{1763328,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[6,0,6,3]%%%}+%%%{%%{poly1[%%%{-1451520,[11]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[6,0,4,4]%%%}+%%%{%%{[%%%{516096,[12]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[6,0,2,5]%%%}+%%%{%%{poly1[%%%{-43008,[13]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[6,0,0,6]%%%}+%%%{%%%{14112,[7]%%%},[5,0,13,0]%%%}+%%%{%%%{-137088,[8]%%%},[5,0,11,1]%%%}+%%%{%%%{540288,[9]%%%},[5,0,9,2]%%%}+%%%{%%%{-1096704,[10]%%%},[5,0,7,3]%%%}+%%%{%%%{1193472,[11]%%%},[5,0,5,4]%%%}+%%%{%%%{-645120,[12]%%%},[5,0,3,5]%%%}+%%%{%%%{129024,[13]%%%},[5,0,1,6]%%%}+%%%{%%{poly1[%%%{-4176,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,14,0]%%%}+%%%{%%{[%%%{46368,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,12,1]%%%}+%%%{%%{poly1[%%%{-213696,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,10,2]%%%}+%%%{%%{[%%%{524160,[9]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,8,3]%%%}+%%%{%%{poly1[%%%{-725760,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,6,4]%%%}+%%%{%%{[%%%{548352,[11]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,4,5]%%%}+%%%{%%{poly1[%%%{-193536,[12]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,2,6]%%%}+%%%{%%{[%%%{18432,[13]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,0,7]%%%}+%%%{%%%{960,[6]%%%},[3,0,15,0]%%%}+%%%{%%%{-12096,[7]%%%},[3,0,13,1]%%%}+%%%{%%%{64512,[8]%%%},[3,0,11,2]%%%}+%%%{%%%{-188160,[9]%%%},[3,0,9,3]%%%}+%%%{%%%{322560,[10]%%%},[3,0,7,4]%%%}+%%%{%%%{-322560,[11]%%%},[3,0,5,5]%%%}+%%%{%%%{172032,[12]%%%},[3,0,3,6]%%%}+%%%{%%%{-36864,[13]%%%},[3,0,1,7]%%%}+%%%{%%{poly1[%%%{-162,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,16,0]%%%}+%%%{%%{[%%%{2304,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,14,1]%%%}+%%%{%%{poly1[%%%{-14112,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,12,2]%%%}+%%%{%%{[%%%{48384,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,10,3]%%%}+%%%{%%{poly1[%%%{-100800,[9]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,8,4]%%%}+%%%{%%{[%%%{129024,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,6,5]%%%}+%%%{%%{poly1[%%%{-96768,[11]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,4,6]%%%}+%%%{%%{[%%%{36864,[12]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,2,7]%%%}+%%%{%%{[%%%{-4608,[13]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,0,8]%%%}+%%%{%%%{18,[5]%%%},[1,0,17,0]%%%}+%%%{%%%{-288,[6]%%%},[1,0,15,1]%%%}+%%%{%%%{2016,[7]%%%},[1,0,13,2]%%%}+%%%{%%%{-8064,[8]%%%},[1,0,11,3]%%%}+%%%{%%%{20160,[9]%%%},[1,0,9,4]%%%}+%%%{%%%{-32256,[10]%%%},[1,0,7,5]%%%}+%%%{%%%{32256,[11]%%%},[1,0,5,6]%%%}+%%%{%%%{-18432,[12]%%%},[1,0,3,7]%%%}+%%%{%%%{4608,[13]%%%},[1,0,1,8]%%%}+%%%{%%{poly1[%%%{-1,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,18,0]%%%}+%%%{%%{[%%%{18,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,16,1]%%%}+%%%{%%{poly1[%%%{-144,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,14,2]%%%}+%%%{%%{[%%%{672,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,12,3]%%%}+%%%{%%{poly1[%%%{-2016,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,10,4]%%%}+%%%{%%{[%%%{4032,[9]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,8,5]%%%}+%%%{%%{poly1[%%%{-5376,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,6,6]%%%}+%%%{%%{[%%%{4608,[11]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,4,7]%%%}+%%%{%%{[%%%{-2304,[12]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,2,8]%%%}+%%%{%%{[%%%{512,[13]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,0,9]%%%} Error: Bad Argument Value","F(-2)",0
1216,1,1393,0,1.822076," ","integrate((c*x^2+b*x+a)^(3/2)/(2*c*d*x+b*d)^10,x, algorithm=""giac"")","\frac{3360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{12} c^{\frac{13}{2}} + 20160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} b c^{6} + 54180 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{10} b^{2} c^{\frac{11}{2}} + 5040 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{10} a c^{\frac{13}{2}} + 86100 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} b^{3} c^{5} + 25200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} a b c^{6} + 90216 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} b^{4} c^{\frac{9}{2}} + 53172 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} a b^{2} c^{\frac{11}{2}} + 7056 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} a^{2} c^{\frac{13}{2}} + 66024 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} b^{5} c^{4} + 61488 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} a b^{3} c^{5} + 28224 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} a^{2} b c^{6} + 35028 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} b^{6} c^{\frac{7}{2}} + 41832 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} a b^{4} c^{\frac{9}{2}} + 47880 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} a^{2} b^{2} c^{\frac{11}{2}} + 2016 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} a^{3} c^{\frac{13}{2}} + 13860 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} b^{7} c^{3} + 16128 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a b^{5} c^{4} + 44856 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{2} b^{3} c^{5} + 6048 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{3} b c^{6} + 4176 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} b^{8} c^{\frac{5}{2}} + 2484 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a b^{6} c^{\frac{7}{2}} + 25416 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{2} b^{4} c^{\frac{9}{2}} + 6984 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{3} b^{2} c^{\frac{11}{2}} + 576 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{4} c^{\frac{13}{2}} + 960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{9} c^{2} - 576 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b^{7} c^{3} + 9000 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{2} b^{5} c^{4} + 3888 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{3} b^{3} c^{5} + 1152 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{4} b c^{6} + 162 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{10} c^{\frac{3}{2}} - 360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a b^{8} c^{\frac{5}{2}} + 2016 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{2} b^{6} c^{\frac{7}{2}} + 936 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{3} b^{4} c^{\frac{9}{2}} + 1044 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{4} b^{2} c^{\frac{11}{2}} - 144 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{5} c^{\frac{13}{2}} + 18 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{11} c - 72 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{9} c^{2} + 288 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} b^{7} c^{3} + 468 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{4} b^{3} c^{5} - 144 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{5} b c^{6} + b^{12} \sqrt{c} - 6 \, a b^{10} c^{\frac{3}{2}} + 24 \, a^{2} b^{8} c^{\frac{5}{2}} - 32 \, a^{3} b^{6} c^{\frac{7}{2}} + 96 \, a^{4} b^{4} c^{\frac{9}{2}} - 60 \, a^{5} b^{2} c^{\frac{11}{2}} + 16 \, a^{6} c^{\frac{13}{2}}}{630 \, {\left(2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} c + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b \sqrt{c} + b^{2} - 2 \, a c\right)}^{9} c^{3} d^{10}}"," ",0,"1/630*(3360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^12*c^(13/2) + 20160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*b*c^6 + 54180*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^10*b^2*c^(11/2) + 5040*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^10*a*c^(13/2) + 86100*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*b^3*c^5 + 25200*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*a*b*c^6 + 90216*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*b^4*c^(9/2) + 53172*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a*b^2*c^(11/2) + 7056*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a^2*c^(13/2) + 66024*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*b^5*c^4 + 61488*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a*b^3*c^5 + 28224*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^2*b*c^6 + 35028*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*b^6*c^(7/2) + 41832*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a*b^4*c^(9/2) + 47880*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^2*b^2*c^(11/2) + 2016*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^3*c^(13/2) + 13860*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b^7*c^3 + 16128*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*b^5*c^4 + 44856*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^2*b^3*c^5 + 6048*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^3*b*c^6 + 4176*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^8*c^(5/2) + 2484*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*b^6*c^(7/2) + 25416*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^2*b^4*c^(9/2) + 6984*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^3*b^2*c^(11/2) + 576*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^4*c^(13/2) + 960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^9*c^2 - 576*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^7*c^3 + 9000*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*b^5*c^4 + 3888*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^3*b^3*c^5 + 1152*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^4*b*c^6 + 162*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^10*c^(3/2) - 360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^8*c^(5/2) + 2016*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*b^6*c^(7/2) + 936*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^3*b^4*c^(9/2) + 1044*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^4*b^2*c^(11/2) - 144*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^5*c^(13/2) + 18*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^11*c - 72*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^9*c^2 + 288*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b^7*c^3 + 468*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^4*b^3*c^5 - 144*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^5*b*c^6 + b^12*sqrt(c) - 6*a*b^10*c^(3/2) + 24*a^2*b^8*c^(5/2) - 32*a^3*b^6*c^(7/2) + 96*a^4*b^4*c^(9/2) - 60*a^5*b^2*c^(11/2) + 16*a^6*c^(13/2))/((2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*c + 2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b*sqrt(c) + b^2 - 2*a*c)^9*c^3*d^10)","B",0
1217,1,128,0,0.186942," ","integrate((2*c*d*x+b*d)^5*(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\frac{2}{7} \, {\left(c x^{2} + b x + a\right)}^{\frac{7}{2}} b^{4} d^{5} + \frac{16}{9} \, {\left(c x^{2} + b x + a\right)}^{\frac{9}{2}} b^{2} c d^{5} - \frac{16}{7} \, {\left(c x^{2} + b x + a\right)}^{\frac{7}{2}} a b^{2} c d^{5} + \frac{32}{11} \, {\left(c x^{2} + b x + a\right)}^{\frac{11}{2}} c^{2} d^{5} - \frac{64}{9} \, {\left(c x^{2} + b x + a\right)}^{\frac{9}{2}} a c^{2} d^{5} + \frac{32}{7} \, {\left(c x^{2} + b x + a\right)}^{\frac{7}{2}} a^{2} c^{2} d^{5}"," ",0,"2/7*(c*x^2 + b*x + a)^(7/2)*b^4*d^5 + 16/9*(c*x^2 + b*x + a)^(9/2)*b^2*c*d^5 - 16/7*(c*x^2 + b*x + a)^(7/2)*a*b^2*c*d^5 + 32/11*(c*x^2 + b*x + a)^(11/2)*c^2*d^5 - 64/9*(c*x^2 + b*x + a)^(9/2)*a*c^2*d^5 + 32/7*(c*x^2 + b*x + a)^(7/2)*a^2*c^2*d^5","A",0
1218,1,547,0,0.329060," ","integrate((2*c*d*x+b*d)^4*(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\frac{1}{40960} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(2 \, {\left(4 \, {\left(2 \, {\left(16 \, {\left(2 \, c^{6} d^{4} x + 9 \, b c^{5} d^{4}\right)} x + \frac{3 \, {\left(89 \, b^{2} c^{13} d^{4} + 28 \, a c^{14} d^{4}\right)}}{c^{9}}\right)} x + \frac{21 \, {\left(25 \, b^{3} c^{12} d^{4} + 28 \, a b c^{13} d^{4}\right)}}{c^{9}}\right)} x + \frac{1165 \, b^{4} c^{11} d^{4} + 3280 \, a b^{2} c^{12} d^{4} + 496 \, a^{2} c^{13} d^{4}}{c^{9}}\right)} x + \frac{701 \, b^{5} c^{10} d^{4} + 4640 \, a b^{3} c^{11} d^{4} + 2480 \, a^{2} b c^{12} d^{4}}{c^{9}}\right)} x + \frac{731 \, b^{6} c^{9} d^{4} + 13660 \, a b^{4} c^{10} d^{4} + 19600 \, a^{2} b^{2} c^{11} d^{4} + 320 \, a^{3} c^{12} d^{4}}{c^{9}}\right)} x + \frac{b^{7} c^{8} d^{4} + 4372 \, a b^{5} c^{9} d^{4} + 19120 \, a^{2} b^{3} c^{10} d^{4} + 960 \, a^{3} b c^{11} d^{4}}{c^{9}}\right)} x - \frac{5 \, b^{8} c^{7} d^{4} - 88 \, a b^{6} c^{8} d^{4} - 16960 \, a^{2} b^{4} c^{9} d^{4} - 5760 \, a^{3} b^{2} c^{10} d^{4} + 3840 \, a^{4} c^{11} d^{4}}{c^{9}}\right)} x + \frac{15 \, b^{9} c^{6} d^{4} - 280 \, a b^{7} c^{7} d^{4} + 2048 \, a^{2} b^{5} c^{8} d^{4} + 4480 \, a^{3} b^{3} c^{9} d^{4} - 3840 \, a^{4} b c^{10} d^{4}}{c^{9}}\right)} + \frac{3 \, {\left(b^{10} d^{4} - 20 \, a b^{8} c d^{4} + 160 \, a^{2} b^{6} c^{2} d^{4} - 640 \, a^{3} b^{4} c^{3} d^{4} + 1280 \, a^{4} b^{2} c^{4} d^{4} - 1024 \, a^{5} c^{5} d^{4}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{16384 \, c^{\frac{7}{2}}}"," ",0,"1/40960*sqrt(c*x^2 + b*x + a)*(2*(4*(2*(8*(2*(4*(2*(16*(2*c^6*d^4*x + 9*b*c^5*d^4)*x + 3*(89*b^2*c^13*d^4 + 28*a*c^14*d^4)/c^9)*x + 21*(25*b^3*c^12*d^4 + 28*a*b*c^13*d^4)/c^9)*x + (1165*b^4*c^11*d^4 + 3280*a*b^2*c^12*d^4 + 496*a^2*c^13*d^4)/c^9)*x + (701*b^5*c^10*d^4 + 4640*a*b^3*c^11*d^4 + 2480*a^2*b*c^12*d^4)/c^9)*x + (731*b^6*c^9*d^4 + 13660*a*b^4*c^10*d^4 + 19600*a^2*b^2*c^11*d^4 + 320*a^3*c^12*d^4)/c^9)*x + (b^7*c^8*d^4 + 4372*a*b^5*c^9*d^4 + 19120*a^2*b^3*c^10*d^4 + 960*a^3*b*c^11*d^4)/c^9)*x - (5*b^8*c^7*d^4 - 88*a*b^6*c^8*d^4 - 16960*a^2*b^4*c^9*d^4 - 5760*a^3*b^2*c^10*d^4 + 3840*a^4*c^11*d^4)/c^9)*x + (15*b^9*c^6*d^4 - 280*a*b^7*c^7*d^4 + 2048*a^2*b^5*c^8*d^4 + 4480*a^3*b^3*c^9*d^4 - 3840*a^4*b*c^10*d^4)/c^9) + 3/16384*(b^10*d^4 - 20*a*b^8*c*d^4 + 160*a^2*b^6*c^2*d^4 - 640*a^3*b^4*c^3*d^4 + 1280*a^4*b^2*c^4*d^4 - 1024*a^5*c^5*d^4)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(7/2)","B",0
1219,1,58,0,0.196959," ","integrate((2*c*d*x+b*d)^3*(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\frac{2}{7} \, {\left(c x^{2} + b x + a\right)}^{\frac{7}{2}} b^{2} d^{3} + \frac{8}{9} \, {\left(c x^{2} + b x + a\right)}^{\frac{9}{2}} c d^{3} - \frac{8}{7} \, {\left(c x^{2} + b x + a\right)}^{\frac{7}{2}} a c d^{3}"," ",0,"2/7*(c*x^2 + b*x + a)^(7/2)*b^2*d^3 + 8/9*(c*x^2 + b*x + a)^(9/2)*c*d^3 - 8/7*(c*x^2 + b*x + a)^(7/2)*a*c*d^3","A",0
1220,1,389,0,0.259095," ","integrate((2*c*d*x+b*d)^2*(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\frac{1}{12288} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(2 \, {\left(12 \, {\left(2 \, c^{4} d^{2} x + 7 \, b c^{3} d^{2}\right)} x + \frac{109 \, b^{2} c^{9} d^{2} + 68 \, a c^{10} d^{2}}{c^{7}}\right)} x + \frac{5 \, {\left(25 \, b^{3} c^{8} d^{2} + 68 \, a b c^{9} d^{2}\right)}}{c^{7}}\right)} x + \frac{219 \, b^{4} c^{7} d^{2} + 2248 \, a b^{2} c^{8} d^{2} + 944 \, a^{2} c^{9} d^{2}}{c^{7}}\right)} x + \frac{b^{5} c^{6} d^{2} + 1304 \, a b^{3} c^{7} d^{2} + 2832 \, a^{2} b c^{8} d^{2}}{c^{7}}\right)} x - \frac{5 \, b^{6} c^{5} d^{2} - 68 \, a b^{4} c^{6} d^{2} - 4944 \, a^{2} b^{2} c^{7} d^{2} - 960 \, a^{3} c^{8} d^{2}}{c^{7}}\right)} x + \frac{15 \, b^{7} c^{4} d^{2} - 220 \, a b^{5} c^{5} d^{2} + 1168 \, a^{2} b^{3} c^{6} d^{2} + 960 \, a^{3} b c^{7} d^{2}}{c^{7}}\right)} + \frac{5 \, {\left(b^{8} d^{2} - 16 \, a b^{6} c d^{2} + 96 \, a^{2} b^{4} c^{2} d^{2} - 256 \, a^{3} b^{2} c^{3} d^{2} + 256 \, a^{4} c^{4} d^{2}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{8192 \, c^{\frac{7}{2}}}"," ",0,"1/12288*sqrt(c*x^2 + b*x + a)*(2*(4*(2*(8*(2*(12*(2*c^4*d^2*x + 7*b*c^3*d^2)*x + (109*b^2*c^9*d^2 + 68*a*c^10*d^2)/c^7)*x + 5*(25*b^3*c^8*d^2 + 68*a*b*c^9*d^2)/c^7)*x + (219*b^4*c^7*d^2 + 2248*a*b^2*c^8*d^2 + 944*a^2*c^9*d^2)/c^7)*x + (b^5*c^6*d^2 + 1304*a*b^3*c^7*d^2 + 2832*a^2*b*c^8*d^2)/c^7)*x - (5*b^6*c^5*d^2 - 68*a*b^4*c^6*d^2 - 4944*a^2*b^2*c^7*d^2 - 960*a^3*c^8*d^2)/c^7)*x + (15*b^7*c^4*d^2 - 220*a*b^5*c^5*d^2 + 1168*a^2*b^3*c^6*d^2 + 960*a^3*b*c^7*d^2)/c^7) + 5/8192*(b^8*d^2 - 16*a*b^6*c*d^2 + 96*a^2*b^4*c^2*d^2 - 256*a^3*b^2*c^3*d^2 + 256*a^4*c^4*d^2)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(7/2)","B",0
1221,1,15,0,0.153742," ","integrate((2*c*d*x+b*d)*(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\frac{2}{7} \, {\left(c x^{2} + b x + a\right)}^{\frac{7}{2}} d"," ",0,"2/7*(c*x^2 + b*x + a)^(7/2)*d","A",0
1222,1,237,0,0.241735," ","integrate((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d),x, algorithm=""giac"")","\frac{1}{480} \, \sqrt{c x^{2} + b x + a} {\left(4 \, {\left({\left(12 \, {\left(\frac{c x}{d} + \frac{2 \, b}{d}\right)} x + \frac{7 \, b^{2} c^{9} d^{5} + 44 \, a c^{10} d^{5}}{c^{10} d^{6}}\right)} x - \frac{5 \, b^{3} c^{8} d^{5} - 44 \, a b c^{9} d^{5}}{c^{10} d^{6}}\right)} x + \frac{15 \, b^{4} c^{7} d^{5} - 140 \, a b^{2} c^{8} d^{5} + 368 \, a^{2} c^{9} d^{5}}{c^{10} d^{6}}\right)} - \frac{{\left(b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} \arctan\left(-\frac{2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} c + b \sqrt{c}}{\sqrt{b^{2} c - 4 \, a c^{2}}}\right)}{32 \, \sqrt{b^{2} c - 4 \, a c^{2}} c^{3} d}"," ",0,"1/480*sqrt(c*x^2 + b*x + a)*(4*((12*(c*x/d + 2*b/d)*x + (7*b^2*c^9*d^5 + 44*a*c^10*d^5)/(c^10*d^6))*x - (5*b^3*c^8*d^5 - 44*a*b*c^9*d^5)/(c^10*d^6))*x + (15*b^4*c^7*d^5 - 140*a*b^2*c^8*d^5 + 368*a^2*c^9*d^5)/(c^10*d^6)) - 1/32*(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)*arctan(-(2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*c + b*sqrt(c))/sqrt(b^2*c - 4*a*c^2))/(sqrt(b^2*c - 4*a*c^2)*c^3*d)","A",0
1223,1,814,0,1.252568," ","integrate((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^2,x, algorithm=""giac"")","-\frac{1}{512} \, d^{2} {\left(\frac{15 \, {\left(b^{4} \mathrm{sgn}\left(\frac{1}{2 \, c d x + b d}\right) \mathrm{sgn}\left(c\right) \mathrm{sgn}\left(d\right) - 8 \, a b^{2} c \mathrm{sgn}\left(\frac{1}{2 \, c d x + b d}\right) \mathrm{sgn}\left(c\right) \mathrm{sgn}\left(d\right) + 16 \, a^{2} c^{2} \mathrm{sgn}\left(\frac{1}{2 \, c d x + b d}\right) \mathrm{sgn}\left(c\right) \mathrm{sgn}\left(d\right)\right)} \arctan\left(\frac{\sqrt{-\frac{b^{2} c d^{2}}{{\left(2 \, c d x + b d\right)}^{2}} + \frac{4 \, a c^{2} d^{2}}{{\left(2 \, c d x + b d\right)}^{2}} + c}}{\sqrt{-c}}\right)}{\sqrt{-c} c^{3} d^{4} {\left| c \right|}} + \frac{8 \, {\left(\sqrt{-\frac{b^{2} c d^{2}}{{\left(2 \, c d x + b d\right)}^{2}} + \frac{4 \, a c^{2} d^{2}}{{\left(2 \, c d x + b d\right)}^{2}} + c} b^{4} \mathrm{sgn}\left(\frac{1}{2 \, c d x + b d}\right) \mathrm{sgn}\left(c\right) \mathrm{sgn}\left(d\right) - 8 \, \sqrt{-\frac{b^{2} c d^{2}}{{\left(2 \, c d x + b d\right)}^{2}} + \frac{4 \, a c^{2} d^{2}}{{\left(2 \, c d x + b d\right)}^{2}} + c} a b^{2} c \mathrm{sgn}\left(\frac{1}{2 \, c d x + b d}\right) \mathrm{sgn}\left(c\right) \mathrm{sgn}\left(d\right) + 16 \, \sqrt{-\frac{b^{2} c d^{2}}{{\left(2 \, c d x + b d\right)}^{2}} + \frac{4 \, a c^{2} d^{2}}{{\left(2 \, c d x + b d\right)}^{2}} + c} a^{2} c^{2} \mathrm{sgn}\left(\frac{1}{2 \, c d x + b d}\right) \mathrm{sgn}\left(c\right) \mathrm{sgn}\left(d\right)\right)}}{c^{4} d^{4} {\left| c \right|}} - \frac{9 \, {\left(-\frac{b^{2} c d^{2}}{{\left(2 \, c d x + b d\right)}^{2}} + \frac{4 \, a c^{2} d^{2}}{{\left(2 \, c d x + b d\right)}^{2}} + c\right)}^{\frac{3}{2}} b^{4} \mathrm{sgn}\left(\frac{1}{2 \, c d x + b d}\right) \mathrm{sgn}\left(c\right) \mathrm{sgn}\left(d\right) - 72 \, {\left(-\frac{b^{2} c d^{2}}{{\left(2 \, c d x + b d\right)}^{2}} + \frac{4 \, a c^{2} d^{2}}{{\left(2 \, c d x + b d\right)}^{2}} + c\right)}^{\frac{3}{2}} a b^{2} c \mathrm{sgn}\left(\frac{1}{2 \, c d x + b d}\right) \mathrm{sgn}\left(c\right) \mathrm{sgn}\left(d\right) - 7 \, \sqrt{-\frac{b^{2} c d^{2}}{{\left(2 \, c d x + b d\right)}^{2}} + \frac{4 \, a c^{2} d^{2}}{{\left(2 \, c d x + b d\right)}^{2}} + c} b^{4} c \mathrm{sgn}\left(\frac{1}{2 \, c d x + b d}\right) \mathrm{sgn}\left(c\right) \mathrm{sgn}\left(d\right) + 144 \, {\left(-\frac{b^{2} c d^{2}}{{\left(2 \, c d x + b d\right)}^{2}} + \frac{4 \, a c^{2} d^{2}}{{\left(2 \, c d x + b d\right)}^{2}} + c\right)}^{\frac{3}{2}} a^{2} c^{2} \mathrm{sgn}\left(\frac{1}{2 \, c d x + b d}\right) \mathrm{sgn}\left(c\right) \mathrm{sgn}\left(d\right) + 56 \, \sqrt{-\frac{b^{2} c d^{2}}{{\left(2 \, c d x + b d\right)}^{2}} + \frac{4 \, a c^{2} d^{2}}{{\left(2 \, c d x + b d\right)}^{2}} + c} a b^{2} c^{2} \mathrm{sgn}\left(\frac{1}{2 \, c d x + b d}\right) \mathrm{sgn}\left(c\right) \mathrm{sgn}\left(d\right) - 112 \, \sqrt{-\frac{b^{2} c d^{2}}{{\left(2 \, c d x + b d\right)}^{2}} + \frac{4 \, a c^{2} d^{2}}{{\left(2 \, c d x + b d\right)}^{2}} + c} a^{2} c^{3} \mathrm{sgn}\left(\frac{1}{2 \, c d x + b d}\right) \mathrm{sgn}\left(c\right) \mathrm{sgn}\left(d\right)}{{\left(\frac{b^{2} c d^{2}}{{\left(2 \, c d x + b d\right)}^{2}} - \frac{4 \, a c^{2} d^{2}}{{\left(2 \, c d x + b d\right)}^{2}}\right)}^{2} c^{3} d^{4} {\left| c \right|}}\right)} {\left| c \right|}"," ",0,"-1/512*d^2*(15*(b^4*sgn(1/(2*c*d*x + b*d))*sgn(c)*sgn(d) - 8*a*b^2*c*sgn(1/(2*c*d*x + b*d))*sgn(c)*sgn(d) + 16*a^2*c^2*sgn(1/(2*c*d*x + b*d))*sgn(c)*sgn(d))*arctan(sqrt(-b^2*c*d^2/(2*c*d*x + b*d)^2 + 4*a*c^2*d^2/(2*c*d*x + b*d)^2 + c)/sqrt(-c))/(sqrt(-c)*c^3*d^4*abs(c)) + 8*(sqrt(-b^2*c*d^2/(2*c*d*x + b*d)^2 + 4*a*c^2*d^2/(2*c*d*x + b*d)^2 + c)*b^4*sgn(1/(2*c*d*x + b*d))*sgn(c)*sgn(d) - 8*sqrt(-b^2*c*d^2/(2*c*d*x + b*d)^2 + 4*a*c^2*d^2/(2*c*d*x + b*d)^2 + c)*a*b^2*c*sgn(1/(2*c*d*x + b*d))*sgn(c)*sgn(d) + 16*sqrt(-b^2*c*d^2/(2*c*d*x + b*d)^2 + 4*a*c^2*d^2/(2*c*d*x + b*d)^2 + c)*a^2*c^2*sgn(1/(2*c*d*x + b*d))*sgn(c)*sgn(d))/(c^4*d^4*abs(c)) - (9*(-b^2*c*d^2/(2*c*d*x + b*d)^2 + 4*a*c^2*d^2/(2*c*d*x + b*d)^2 + c)^(3/2)*b^4*sgn(1/(2*c*d*x + b*d))*sgn(c)*sgn(d) - 72*(-b^2*c*d^2/(2*c*d*x + b*d)^2 + 4*a*c^2*d^2/(2*c*d*x + b*d)^2 + c)^(3/2)*a*b^2*c*sgn(1/(2*c*d*x + b*d))*sgn(c)*sgn(d) - 7*sqrt(-b^2*c*d^2/(2*c*d*x + b*d)^2 + 4*a*c^2*d^2/(2*c*d*x + b*d)^2 + c)*b^4*c*sgn(1/(2*c*d*x + b*d))*sgn(c)*sgn(d) + 144*(-b^2*c*d^2/(2*c*d*x + b*d)^2 + 4*a*c^2*d^2/(2*c*d*x + b*d)^2 + c)^(3/2)*a^2*c^2*sgn(1/(2*c*d*x + b*d))*sgn(c)*sgn(d) + 56*sqrt(-b^2*c*d^2/(2*c*d*x + b*d)^2 + 4*a*c^2*d^2/(2*c*d*x + b*d)^2 + c)*a*b^2*c^2*sgn(1/(2*c*d*x + b*d))*sgn(c)*sgn(d) - 112*sqrt(-b^2*c*d^2/(2*c*d*x + b*d)^2 + 4*a*c^2*d^2/(2*c*d*x + b*d)^2 + c)*a^2*c^3*sgn(1/(2*c*d*x + b*d))*sgn(c)*sgn(d))/((b^2*c*d^2/(2*c*d*x + b*d)^2 - 4*a*c^2*d^2/(2*c*d*x + b*d)^2)^2*c^3*d^4*abs(c)))*abs(c)","B",0
1224,1,519,0,0.357709," ","integrate((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^3,x, algorithm=""giac"")","\frac{1}{48} \, \sqrt{c x^{2} + b x + a} {\left(2 \, x {\left(\frac{x}{c d^{3}} + \frac{b}{c^{2} d^{3}}\right)} - \frac{3 \, b^{2} c^{5} d^{9} - 14 \, a c^{6} d^{9}}{c^{8} d^{12}}\right)} + \frac{5 \, {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \arctan\left(-\frac{2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} c + b \sqrt{c}}{\sqrt{b^{2} c - 4 \, a c^{2}}}\right)}{64 \, \sqrt{b^{2} c - 4 \, a c^{2}} c^{3} d^{3}} + \frac{2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{4} c^{\frac{3}{2}} - 16 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b^{2} c^{\frac{5}{2}} + 32 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{2} c^{\frac{7}{2}} + 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{5} c - 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a b^{3} c^{2} + 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{2} b c^{3} + {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{6} \sqrt{c} - 6 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{4} c^{\frac{3}{2}} + 32 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{3} c^{\frac{7}{2}} + a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}}{64 \, {\left(2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} c^{\frac{3}{2}} + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b c + b^{2} \sqrt{c} - 2 \, a c^{\frac{3}{2}}\right)}^{2} c^{\frac{5}{2}} d^{3}}"," ",0,"1/48*sqrt(c*x^2 + b*x + a)*(2*x*(x/(c*d^3) + b/(c^2*d^3)) - (3*b^2*c^5*d^9 - 14*a*c^6*d^9)/(c^8*d^12)) + 5/64*(b^4 - 8*a*b^2*c + 16*a^2*c^2)*arctan(-(2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*c + b*sqrt(c))/sqrt(b^2*c - 4*a*c^2))/(sqrt(b^2*c - 4*a*c^2)*c^3*d^3) + 1/64*(2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^4*c^(3/2) - 16*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^2*c^(5/2) + 32*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*c^(7/2) + 3*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^5*c - 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^3*c^2 + 48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*b*c^3 + (sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^6*sqrt(c) - 6*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^4*c^(3/2) + 32*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*c^(7/2) + a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)/((2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*c^(3/2) + 2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b*c + b^2*sqrt(c) - 2*a*c^(3/2))^2*c^(5/2)*d^3)","B",0
1225,1,623,0,0.739814," ","integrate((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^4,x, algorithm=""giac"")","\frac{1}{64} \, \sqrt{c x^{2} + b x + a} {\left(\frac{2 \, x}{c^{2} d^{4}} + \frac{b}{c^{3} d^{4}}\right)} + \frac{5 \, {\left(b^{2} - 4 \, a c\right)} \log\left({\left| 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} + b \right|}\right)}{128 \, c^{\frac{7}{2}} d^{4}} + \frac{36 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} b^{4} c^{\frac{5}{2}} - 288 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a b^{2} c^{\frac{7}{2}} + 576 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{2} c^{\frac{9}{2}} + 72 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{5} c^{2} - 576 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b^{3} c^{3} + 1152 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{2} b c^{4} + 66 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{6} c^{\frac{3}{2}} - 576 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a b^{4} c^{\frac{5}{2}} + 1440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{2} b^{2} c^{\frac{7}{2}} - 768 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{3} c^{\frac{9}{2}} + 30 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{7} c - 288 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{5} c^{2} + 864 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} b^{3} c^{3} - 768 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{3} b c^{4} + 7 \, b^{8} \sqrt{c} - 82 \, a b^{6} c^{\frac{3}{2}} + 348 \, a^{2} b^{4} c^{\frac{5}{2}} - 640 \, a^{3} b^{2} c^{\frac{7}{2}} + 448 \, a^{4} c^{\frac{9}{2}}}{192 \, {\left(2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} c^{\frac{3}{2}} + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b c + b^{2} \sqrt{c} - 2 \, a c^{\frac{3}{2}}\right)}^{3} c^{\frac{5}{2}} d^{4}}"," ",0,"1/64*sqrt(c*x^2 + b*x + a)*(2*x/(c^2*d^4) + b/(c^3*d^4)) + 5/128*(b^2 - 4*a*c)*log(abs(2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) + b))/(c^(7/2)*d^4) + 1/192*(36*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^4*c^(5/2) - 288*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*b^2*c^(7/2) + 576*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^2*c^(9/2) + 72*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^5*c^2 - 576*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^3*c^3 + 1152*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*b*c^4 + 66*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^6*c^(3/2) - 576*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^4*c^(5/2) + 1440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*b^2*c^(7/2) - 768*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^3*c^(9/2) + 30*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^7*c - 288*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^5*c^2 + 864*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b^3*c^3 - 768*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*b*c^4 + 7*b^8*sqrt(c) - 82*a*b^6*c^(3/2) + 348*a^2*b^4*c^(5/2) - 640*a^3*b^2*c^(7/2) + 448*a^4*c^(9/2))/((2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*c^(3/2) + 2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b*c + b^2*sqrt(c) - 2*a*c^(3/2))^3*c^(5/2)*d^4)","B",0
1226,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^5,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1227,-2,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^6,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{%%%{64,[6]%%%},[12,6,12,0]%%%}+%%%{%%%{-1536,[7]%%%},[12,6,10,1]%%%}+%%%{%%%{15360,[8]%%%},[12,6,8,2]%%%}+%%%{%%%{-81920,[9]%%%},[12,6,6,3]%%%}+%%%{%%%{245760,[10]%%%},[12,6,4,4]%%%}+%%%{%%%{-393216,[11]%%%},[12,6,2,5]%%%}+%%%{%%%{262144,[12]%%%},[12,6,0,6]%%%}+%%%{%%{[%%%{-384,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[11,6,13,0]%%%}+%%%{%%{[%%%{9216,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[11,6,11,1]%%%}+%%%{%%{[%%%{-92160,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[11,6,9,2]%%%}+%%%{%%{[%%%{491520,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[11,6,7,3]%%%}+%%%{%%{[%%%{-1474560,[9]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[11,6,5,4]%%%}+%%%{%%{[%%%{2359296,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[11,6,3,5]%%%}+%%%{%%{[%%%{-1572864,[11]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[11,6,1,6]%%%}+%%%{%%%{1152,[5]%%%},[10,6,14,0]%%%}+%%%{%%%{-28032,[6]%%%},[10,6,12,1]%%%}+%%%{%%%{285696,[7]%%%},[10,6,10,2]%%%}+%%%{%%%{-1566720,[8]%%%},[10,6,8,3]%%%}+%%%{%%%{4915200,[9]%%%},[10,6,6,4]%%%}+%%%{%%%{-8552448,[10]%%%},[10,6,4,5]%%%}+%%%{%%%{7077888,[11]%%%},[10,6,2,6]%%%}+%%%{%%%{-1572864,[12]%%%},[10,6,0,7]%%%}+%%%{%%{[%%%{-2240,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[9,6,15,0]%%%}+%%%{%%{[%%%{55680,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[9,6,13,1]%%%}+%%%{%%{[%%%{-583680,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[9,6,11,2]%%%}+%%%{%%{[%%%{3328000,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[9,6,9,3]%%%}+%%%{%%{[%%%{-11059200,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[9,6,7,4]%%%}+%%%{%%{[%%%{21135360,[9]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[9,6,5,5]%%%}+%%%{%%{[%%%{-20971520,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[9,6,3,6]%%%}+%%%{%%{[%%%{7864320,[11]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[9,6,1,7]%%%}+%%%{%%%{3120,[4]%%%},[8,6,16,0]%%%}+%%%{%%%{-79680,[5]%%%},[8,6,14,1]%%%}+%%%{%%%{864960,[6]%%%},[8,6,12,2]%%%}+%%%{%%%{-5168640,[7]%%%},[8,6,10,3]%%%}+%%%{%%%{18355200,[8]%%%},[8,6,8,4]%%%}+%%%{%%%{-38830080,[9]%%%},[8,6,6,5]%%%}+%%%{%%%{45957120,[10]%%%},[8,6,4,6]%%%}+%%%{%%%{-25559040,[11]%%%},[8,6,2,7]%%%}+%%%{%%%{3932160,[12]%%%},[8,6,0,8]%%%}+%%%{%%{[%%%{-3264,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,6,17,0]%%%}+%%%{%%{[%%%{86016,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,6,15,1]%%%}+%%%{%%{[%%%{-971520,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,6,13,2]%%%}+%%%{%%{[%%%{6113280,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,6,11,3]%%%}+%%%{%%{[%%%{-23285760,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,6,9,4]%%%}+%%%{%%{[%%%{54460416,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,6,7,5]%%%}+%%%{%%{[%%%{-75300864,[9]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,6,5,6]%%%}+%%%{%%{[%%%{55050240,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,6,3,7]%%%}+%%%{%%{[%%%{-15728640,[11]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,6,1,8]%%%}+%%%{%%%{2624,[3]%%%},[6,6,18,0]%%%}+%%%{%%%{-71616,[4]%%%},[6,6,16,1]%%%}+%%%{%%%{844800,[5]%%%},[6,6,14,2]%%%}+%%%{%%%{-5617920,[6]%%%},[6,6,12,3]%%%}+%%%{%%%{23009280,[7]%%%},[6,6,10,4]%%%}+%%%{%%%{-59437056,[8]%%%},[6,6,8,5]%%%}+%%%{%%%{94961664,[9]%%%},[6,6,6,6]%%%}+%%%{%%%{-87490560,[10]%%%},[6,6,4,7]%%%}+%%%{%%%{39321600,[11]%%%},[6,6,2,8]%%%}+%%%{%%%{-5242880,[12]%%%},[6,6,0,9]%%%}+%%%{%%{[%%%{-1632,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,6,19,0]%%%}+%%%{%%{[%%%{46272,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,6,17,1]%%%}+%%%{%%{[%%%{-571776,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,6,15,2]%%%}+%%%{%%{[%%%{4028160,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,6,13,3]%%%}+%%%{%%{[%%%{-17756160,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,6,11,4]%%%}+%%%{%%{[%%%{50515968,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,6,9,5]%%%}+%%%{%%{[%%%{-92110848,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,6,7,6]%%%}+%%%{%%{[%%%{102825984,[9]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,6,5,7]%%%}+%%%{%%{[%%%{-62914560,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,6,3,8]%%%}+%%%{%%{[%%%{15728640,[11]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,6,1,9]%%%}+%%%{%%%{780,[2]%%%},[4,6,20,0]%%%}+%%%{%%%{-23040,[3]%%%},[4,6,18,1]%%%}+%%%{%%%{299040,[4]%%%},[4,6,16,2]%%%}+%%%{%%%{-2236800,[5]%%%},[4,6,14,3]%%%}+%%%{%%%{10622400,[6]%%%},[4,6,12,4]%%%}+%%%{%%%{-33231360,[7]%%%},[4,6,10,5]%%%}+%%%{%%%{68674560,[8]%%%},[4,6,8,6]%%%}+%%%{%%%{-91176960,[9]%%%},[4,6,6,7]%%%}+%%%{%%%{72499200,[10]%%%},[4,6,4,8]%%%}+%%%{%%%{-29491200,[11]%%%},[4,6,2,9]%%%}+%%%{%%%{3932160,[12]%%%},[4,6,0,10]%%%}+%%%{%%{[%%%{-280,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,6,21,0]%%%}+%%%{%%{[%%%{8640,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,6,19,1]%%%}+%%%{%%{[%%%{-118080,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,6,17,2]%%%}+%%%{%%{[%%%{939520,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,6,15,3]%%%}+%%%{%%{[%%%{-4809600,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,6,13,4]%%%}+%%%{%%{[%%%{16512000,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,6,11,5]%%%}+%%%{%%{[%%%{-38389760,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,6,9,6]%%%}+%%%{%%{[%%%{59473920,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,6,7,7]%%%}+%%%{%%{[%%%{-58490880,[9]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,6,5,8]%%%}+%%%{%%{[%%%{32768000,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,6,3,9]%%%}+%%%{%%{[%%%{-7864320,[11]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,6,1,10]%%%}+%%%{%%%{72,[1]%%%},[2,6,22,0]%%%}+%%%{%%%{-2328,[2]%%%},[2,6,20,1]%%%}+%%%{%%%{33600,[3]%%%},[2,6,18,2]%%%}+%%%{%%%{-285120,[4]%%%},[2,6,16,3]%%%}+%%%{%%%{1576320,[5]%%%},[2,6,14,4]%%%}+%%%{%%%{-5941632,[6]%%%},[2,6,12,5]%%%}+%%%{%%%{15510528,[7]%%%},[2,6,10,6]%%%}+%%%{%%%{-27863040,[8]%%%},[2,6,8,7]%%%}+%%%{%%%{33423360,[9]%%%},[2,6,6,8]%%%}+%%%{%%%{-25067520,[10]%%%},[2,6,4,9]%%%}+%%%{%%%{10223616,[11]%%%},[2,6,2,10]%%%}+%%%{%%%{-1572864,[12]%%%},[2,6,0,11]%%%}+%%%{%%{[-12,0]:[1,0,%%%{-1,[1]%%%}]%%},[1,6,23,0]%%%}+%%%{%%{[%%%{408,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,6,21,1]%%%}+%%%{%%{[%%%{-6240,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,6,19,2]%%%}+%%%{%%{[%%%{56640,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,6,17,3]%%%}+%%%{%%{[%%%{-338880,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,6,15,4]%%%}+%%%{%%{[%%%{1402752,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,6,13,5]%%%}+%%%{%%{[%%%{-4098048,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,6,11,6]%%%}+%%%{%%{[%%%{8448000,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,6,9,7]%%%}+%%%{%%{[%%%{-12042240,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,6,7,8]%%%}+%%%{%%{[%%%{11304960,[9]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,6,5,9]%%%}+%%%{%%{[%%%{-6291456,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,6,3,10]%%%}+%%%{%%{[%%%{1572864,[11]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,6,1,11]%%%}+%%%{1,[0,6,24,0]%%%}+%%%{%%%{-36,[1]%%%},[0,6,22,1]%%%}+%%%{%%%{588,[2]%%%},[0,6,20,2]%%%}+%%%{%%%{-5760,[3]%%%},[0,6,18,3]%%%}+%%%{%%%{37680,[4]%%%},[0,6,16,4]%%%}+%%%{%%%{-173376,[5]%%%},[0,6,14,5]%%%}+%%%{%%%{575296,[6]%%%},[0,6,12,6]%%%}+%%%{%%%{-1387008,[7]%%%},[0,6,10,7]%%%}+%%%{%%%{2411520,[8]%%%},[0,6,8,8]%%%}+%%%{%%%{-2949120,[9]%%%},[0,6,6,9]%%%}+%%%{%%%{2408448,[10]%%%},[0,6,4,10]%%%}+%%%{%%%{-1179648,[11]%%%},[0,6,2,11]%%%}+%%%{%%%{262144,[12]%%%},[0,6,0,12]%%%} / %%%{%%%{64,[9]%%%},[12,0,0,0]%%%}+%%%{%%{poly1[%%%{-384,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[11,0,1,0]%%%}+%%%{%%%{1152,[8]%%%},[10,0,2,0]%%%}+%%%{%%%{-384,[9]%%%},[10,0,0,1]%%%}+%%%{%%{poly1[%%%{-2240,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[9,0,3,0]%%%}+%%%{%%{[%%%{1920,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[9,0,1,1]%%%}+%%%{%%%{3120,[7]%%%},[8,0,4,0]%%%}+%%%{%%%{-4800,[8]%%%},[8,0,2,1]%%%}+%%%{%%%{960,[9]%%%},[8,0,0,2]%%%}+%%%{%%{poly1[%%%{-3264,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,0,5,0]%%%}+%%%{%%{[%%%{7680,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,0,3,1]%%%}+%%%{%%{poly1[%%%{-3840,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,0,1,2]%%%}+%%%{%%%{2624,[6]%%%},[6,0,6,0]%%%}+%%%{%%%{-8640,[7]%%%},[6,0,4,1]%%%}+%%%{%%%{7680,[8]%%%},[6,0,2,2]%%%}+%%%{%%%{-1280,[9]%%%},[6,0,0,3]%%%}+%%%{%%{poly1[%%%{-1632,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,0,7,0]%%%}+%%%{%%{[%%%{7104,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,0,5,1]%%%}+%%%{%%{poly1[%%%{-9600,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,0,3,2]%%%}+%%%{%%{[%%%{3840,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,0,1,3]%%%}+%%%{%%%{780,[5]%%%},[4,0,8,0]%%%}+%%%{%%%{-4320,[6]%%%},[4,0,6,1]%%%}+%%%{%%%{8160,[7]%%%},[4,0,4,2]%%%}+%%%{%%%{-5760,[8]%%%},[4,0,2,3]%%%}+%%%{%%%{960,[9]%%%},[4,0,0,4]%%%}+%%%{%%{poly1[%%%{-280,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,0,9,0]%%%}+%%%{%%{[%%%{1920,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,0,7,1]%%%}+%%%{%%{poly1[%%%{-4800,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,0,5,2]%%%}+%%%{%%{[%%%{5120,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,0,3,3]%%%}+%%%{%%{poly1[%%%{-1920,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,0,1,4]%%%}+%%%{%%%{72,[4]%%%},[2,0,10,0]%%%}+%%%{%%%{-600,[5]%%%},[2,0,8,1]%%%}+%%%{%%%{1920,[6]%%%},[2,0,6,2]%%%}+%%%{%%%{-2880,[7]%%%},[2,0,4,3]%%%}+%%%{%%%{1920,[8]%%%},[2,0,2,4]%%%}+%%%{%%%{-384,[9]%%%},[2,0,0,5]%%%}+%%%{%%{poly1[%%%{-12,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,0,11,0]%%%}+%%%{%%{[%%%{120,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,0,9,1]%%%}+%%%{%%{poly1[%%%{-480,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,0,7,2]%%%}+%%%{%%{[%%%{960,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,0,5,3]%%%}+%%%{%%{poly1[%%%{-960,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,0,3,4]%%%}+%%%{%%{[%%%{384,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,0,1,5]%%%}+%%%{%%%{1,[3]%%%},[0,0,12,0]%%%}+%%%{%%%{-12,[4]%%%},[0,0,10,1]%%%}+%%%{%%%{60,[5]%%%},[0,0,8,2]%%%}+%%%{%%%{-160,[6]%%%},[0,0,6,3]%%%}+%%%{%%%{240,[7]%%%},[0,0,4,4]%%%}+%%%{%%%{-192,[8]%%%},[0,0,2,5]%%%}+%%%{%%%{64,[9]%%%},[0,0,0,6]%%%} Error: Bad Argument Value","F(-2)",0
1228,-2,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^7,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{%%%{128,[7]%%%},[14,7,0,0]%%%}+%%%{%%{[%%%{-896,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[13,7,1,0]%%%}+%%%{%%%{3136,[6]%%%},[12,7,2,0]%%%}+%%%{%%%{-896,[7]%%%},[12,7,0,1]%%%}+%%%{%%{[%%%{-7168,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[11,7,3,0]%%%}+%%%{%%{[%%%{5376,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[11,7,1,1]%%%}+%%%{%%%{11872,[5]%%%},[10,7,4,0]%%%}+%%%{%%%{-16128,[6]%%%},[10,7,2,1]%%%}+%%%{%%%{2688,[7]%%%},[10,7,0,2]%%%}+%%%{%%{[%%%{-15008,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[9,7,5,0]%%%}+%%%{%%{[%%%{31360,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[9,7,3,1]%%%}+%%%{%%{[%%%{-13440,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[9,7,1,2]%%%}+%%%{%%%{14896,[4]%%%},[8,7,6,0]%%%}+%%%{%%%{-43680,[5]%%%},[8,7,4,1]%%%}+%%%{%%%{33600,[6]%%%},[8,7,2,2]%%%}+%%%{%%%{-4480,[7]%%%},[8,7,0,3]%%%}+%%%{%%{[%%%{-11776,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,7,7,0]%%%}+%%%{%%{[%%%{45696,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,7,5,1]%%%}+%%%{%%{[%%%{-53760,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,7,3,2]%%%}+%%%{%%{[%%%{17920,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,7,1,3]%%%}+%%%{%%%{7448,[3]%%%},[6,7,8,0]%%%}+%%%{%%%{-36736,[4]%%%},[6,7,6,1]%%%}+%%%{%%%{60480,[5]%%%},[6,7,4,2]%%%}+%%%{%%%{-35840,[6]%%%},[6,7,2,3]%%%}+%%%{%%%{4480,[7]%%%},[6,7,0,4]%%%}+%%%{%%{[%%%{-3752,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,7,9,0]%%%}+%%%{%%{[%%%{22848,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,7,7,1]%%%}+%%%{%%{[%%%{-49728,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,7,5,2]%%%}+%%%{%%{[%%%{44800,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,7,3,3]%%%}+%%%{%%{[%%%{-13440,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,7,1,4]%%%}+%%%{%%%{1484,[2]%%%},[4,7,10,0]%%%}+%%%{%%%{-10920,[3]%%%},[4,7,8,1]%%%}+%%%{%%%{30240,[4]%%%},[4,7,6,2]%%%}+%%%{%%%{-38080,[5]%%%},[4,7,4,3]%%%}+%%%{%%%{20160,[6]%%%},[4,7,2,4]%%%}+%%%{%%%{-2688,[7]%%%},[4,7,0,5]%%%}+%%%{%%{[%%%{-448,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,7,11,0]%%%}+%%%{%%{[%%%{3920,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,7,9,1]%%%}+%%%{%%{[%%%{-13440,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,7,7,2]%%%}+%%%{%%{[%%%{22400,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,7,5,3]%%%}+%%%{%%{[%%%{-17920,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,7,3,4]%%%}+%%%{%%{[%%%{5376,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,7,1,5]%%%}+%%%{%%%{98,[1]%%%},[2,7,12,0]%%%}+%%%{%%%{-1008,[2]%%%},[2,7,10,1]%%%}+%%%{%%%{4200,[3]%%%},[2,7,8,2]%%%}+%%%{%%%{-8960,[4]%%%},[2,7,6,3]%%%}+%%%{%%%{10080,[5]%%%},[2,7,4,4]%%%}+%%%{%%%{-5376,[6]%%%},[2,7,2,5]%%%}+%%%{%%%{896,[7]%%%},[2,7,0,6]%%%}+%%%{%%{[-14,0]:[1,0,%%%{-1,[1]%%%}]%%},[1,7,13,0]%%%}+%%%{%%{[%%%{168,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,7,11,1]%%%}+%%%{%%{[%%%{-840,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,7,9,2]%%%}+%%%{%%{[%%%{2240,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,7,7,3]%%%}+%%%{%%{[%%%{-3360,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,7,5,4]%%%}+%%%{%%{[%%%{2688,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,7,3,5]%%%}+%%%{%%{[%%%{-896,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,7,1,6]%%%}+%%%{1,[0,7,14,0]%%%}+%%%{%%%{-14,[1]%%%},[0,7,12,1]%%%}+%%%{%%%{84,[2]%%%},[0,7,10,2]%%%}+%%%{%%%{-280,[3]%%%},[0,7,8,3]%%%}+%%%{%%%{560,[4]%%%},[0,7,6,4]%%%}+%%%{%%%{-672,[5]%%%},[0,7,4,5]%%%}+%%%{%%%{448,[6]%%%},[0,7,2,6]%%%}+%%%{%%%{-128,[7]%%%},[0,7,0,7]%%%} / %%%{%%{poly1[%%%{-128,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[14,0,0,0]%%%}+%%%{%%%{896,[10]%%%},[13,0,1,0]%%%}+%%%{%%{poly1[%%%{-3136,[9]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[12,0,2,0]%%%}+%%%{%%{[%%%{896,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[12,0,0,1]%%%}+%%%{%%%{7168,[9]%%%},[11,0,3,0]%%%}+%%%{%%%{-5376,[10]%%%},[11,0,1,1]%%%}+%%%{%%{poly1[%%%{-11872,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[10,0,4,0]%%%}+%%%{%%{[%%%{16128,[9]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[10,0,2,1]%%%}+%%%{%%{poly1[%%%{-2688,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[10,0,0,2]%%%}+%%%{%%%{15008,[8]%%%},[9,0,5,0]%%%}+%%%{%%%{-31360,[9]%%%},[9,0,3,1]%%%}+%%%{%%%{13440,[10]%%%},[9,0,1,2]%%%}+%%%{%%{poly1[%%%{-14896,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[8,0,6,0]%%%}+%%%{%%{[%%%{43680,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[8,0,4,1]%%%}+%%%{%%{poly1[%%%{-33600,[9]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[8,0,2,2]%%%}+%%%{%%{[%%%{4480,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[8,0,0,3]%%%}+%%%{%%%{11776,[7]%%%},[7,0,7,0]%%%}+%%%{%%%{-45696,[8]%%%},[7,0,5,1]%%%}+%%%{%%%{53760,[9]%%%},[7,0,3,2]%%%}+%%%{%%%{-17920,[10]%%%},[7,0,1,3]%%%}+%%%{%%{poly1[%%%{-7448,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[6,0,8,0]%%%}+%%%{%%{[%%%{36736,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[6,0,6,1]%%%}+%%%{%%{poly1[%%%{-60480,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[6,0,4,2]%%%}+%%%{%%{[%%%{35840,[9]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[6,0,2,3]%%%}+%%%{%%{poly1[%%%{-4480,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[6,0,0,4]%%%}+%%%{%%%{3752,[6]%%%},[5,0,9,0]%%%}+%%%{%%%{-22848,[7]%%%},[5,0,7,1]%%%}+%%%{%%%{49728,[8]%%%},[5,0,5,2]%%%}+%%%{%%%{-44800,[9]%%%},[5,0,3,3]%%%}+%%%{%%%{13440,[10]%%%},[5,0,1,4]%%%}+%%%{%%{poly1[%%%{-1484,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,10,0]%%%}+%%%{%%{[%%%{10920,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,8,1]%%%}+%%%{%%{poly1[%%%{-30240,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,6,2]%%%}+%%%{%%{[%%%{38080,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,4,3]%%%}+%%%{%%{poly1[%%%{-20160,[9]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,2,4]%%%}+%%%{%%{[%%%{2688,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,0,5]%%%}+%%%{%%%{448,[5]%%%},[3,0,11,0]%%%}+%%%{%%%{-3920,[6]%%%},[3,0,9,1]%%%}+%%%{%%%{13440,[7]%%%},[3,0,7,2]%%%}+%%%{%%%{-22400,[8]%%%},[3,0,5,3]%%%}+%%%{%%%{17920,[9]%%%},[3,0,3,4]%%%}+%%%{%%%{-5376,[10]%%%},[3,0,1,5]%%%}+%%%{%%{poly1[%%%{-98,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,12,0]%%%}+%%%{%%{[%%%{1008,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,10,1]%%%}+%%%{%%{poly1[%%%{-4200,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,8,2]%%%}+%%%{%%{[%%%{8960,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,6,3]%%%}+%%%{%%{poly1[%%%{-10080,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,4,4]%%%}+%%%{%%{[%%%{5376,[9]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,2,5]%%%}+%%%{%%{[%%%{-896,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,0,6]%%%}+%%%{%%%{14,[4]%%%},[1,0,13,0]%%%}+%%%{%%%{-168,[5]%%%},[1,0,11,1]%%%}+%%%{%%%{840,[6]%%%},[1,0,9,2]%%%}+%%%{%%%{-2240,[7]%%%},[1,0,7,3]%%%}+%%%{%%%{3360,[8]%%%},[1,0,5,4]%%%}+%%%{%%%{-2688,[9]%%%},[1,0,3,5]%%%}+%%%{%%%{896,[10]%%%},[1,0,1,6]%%%}+%%%{%%{poly1[%%%{-1,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,14,0]%%%}+%%%{%%{[%%%{14,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,12,1]%%%}+%%%{%%{poly1[%%%{-84,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,10,2]%%%}+%%%{%%{[%%%{280,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,8,3]%%%}+%%%{%%{poly1[%%%{-560,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,6,4]%%%}+%%%{%%{[%%%{672,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,4,5]%%%}+%%%{%%{[%%%{-448,[9]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,2,6]%%%}+%%%{%%{[%%%{128,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,0,7]%%%} Error: Bad Argument Value","F(-2)",0
1229,1,1247,0,1.068052," ","integrate((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^8,x, algorithm=""giac"")","\frac{448 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{12} c^{\frac{13}{2}} + 2688 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} b c^{6} + 7392 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{10} b^{2} c^{\frac{11}{2}} + 12320 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} b^{3} c^{5} + 14000 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} b^{4} c^{\frac{9}{2}} - 1120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} a b^{2} c^{\frac{11}{2}} + 2240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} a^{2} c^{\frac{13}{2}} + 11648 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} b^{5} c^{4} - 4480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} a b^{3} c^{5} + 8960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} a^{2} b c^{6} + 7448 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} b^{6} c^{\frac{7}{2}} - 7840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} a b^{4} c^{\frac{9}{2}} + 15680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} a^{2} b^{2} c^{\frac{11}{2}} + 3752 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} b^{7} c^{3} - 7840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a b^{5} c^{4} + 15680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{2} b^{3} c^{5} + 1484 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} b^{8} c^{\frac{5}{2}} - 4984 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a b^{6} c^{\frac{7}{2}} + 10304 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{2} b^{4} c^{\frac{9}{2}} - 1344 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{3} b^{2} c^{\frac{11}{2}} + 1344 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{4} c^{\frac{13}{2}} + 448 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{9} c^{2} - 2128 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b^{7} c^{3} + 4928 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{2} b^{5} c^{4} - 2688 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{3} b^{3} c^{5} + 2688 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{4} b c^{6} + 98 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{10} c^{\frac{3}{2}} - 616 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a b^{8} c^{\frac{5}{2}} + 1736 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{2} b^{6} c^{\frac{7}{2}} - 2016 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{3} b^{4} c^{\frac{9}{2}} + 2016 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{4} b^{2} c^{\frac{11}{2}} + 14 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{11} c - 112 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{9} c^{2} + 392 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} b^{7} c^{3} - 672 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{3} b^{5} c^{4} + 672 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{4} b^{3} c^{5} + b^{12} \sqrt{c} - 10 \, a b^{10} c^{\frac{3}{2}} + 44 \, a^{2} b^{8} c^{\frac{5}{2}} - 104 \, a^{3} b^{6} c^{\frac{7}{2}} + 144 \, a^{4} b^{4} c^{\frac{9}{2}} - 96 \, a^{5} b^{2} c^{\frac{11}{2}} + 64 \, a^{6} c^{\frac{13}{2}}}{448 \, {\left(2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} c + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b \sqrt{c} + b^{2} - 2 \, a c\right)}^{7} c^{4} d^{8}}"," ",0,"1/448*(448*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^12*c^(13/2) + 2688*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*b*c^6 + 7392*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^10*b^2*c^(11/2) + 12320*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*b^3*c^5 + 14000*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*b^4*c^(9/2) - 1120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a*b^2*c^(11/2) + 2240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a^2*c^(13/2) + 11648*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*b^5*c^4 - 4480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a*b^3*c^5 + 8960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^2*b*c^6 + 7448*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*b^6*c^(7/2) - 7840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a*b^4*c^(9/2) + 15680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^2*b^2*c^(11/2) + 3752*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b^7*c^3 - 7840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*b^5*c^4 + 15680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^2*b^3*c^5 + 1484*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^8*c^(5/2) - 4984*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*b^6*c^(7/2) + 10304*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^2*b^4*c^(9/2) - 1344*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^3*b^2*c^(11/2) + 1344*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^4*c^(13/2) + 448*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^9*c^2 - 2128*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^7*c^3 + 4928*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*b^5*c^4 - 2688*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^3*b^3*c^5 + 2688*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^4*b*c^6 + 98*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^10*c^(3/2) - 616*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^8*c^(5/2) + 1736*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*b^6*c^(7/2) - 2016*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^3*b^4*c^(9/2) + 2016*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^4*b^2*c^(11/2) + 14*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^11*c - 112*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^9*c^2 + 392*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b^7*c^3 - 672*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*b^5*c^4 + 672*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^4*b^3*c^5 + b^12*sqrt(c) - 10*a*b^10*c^(3/2) + 44*a^2*b^8*c^(5/2) - 104*a^3*b^6*c^(7/2) + 144*a^4*b^4*c^(9/2) - 96*a^5*b^2*c^(11/2) + 64*a^6*c^(13/2))/((2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*c + 2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b*sqrt(c) + b^2 - 2*a*c)^7*c^4*d^8)","B",0
1230,-2,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^9,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{%%%{512,[9]%%%},[18,9,0,0]%%%}+%%%{%%{[%%%{-4608,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[17,9,1,0]%%%}+%%%{%%%{20736,[8]%%%},[16,9,2,0]%%%}+%%%{%%%{-4608,[9]%%%},[16,9,0,1]%%%}+%%%{%%{[%%%{-61440,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[15,9,3,0]%%%}+%%%{%%{[%%%{36864,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[15,9,1,1]%%%}+%%%{%%%{133632,[7]%%%},[14,9,4,0]%%%}+%%%{%%%{-147456,[8]%%%},[14,9,2,1]%%%}+%%%{%%%{18432,[9]%%%},[14,9,0,2]%%%}+%%%{%%{[%%%{-225792,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[13,9,5,0]%%%}+%%%{%%{[%%%{387072,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[13,9,3,1]%%%}+%%%{%%{[%%%{-129024,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[13,9,1,2]%%%}+%%%{%%%{306432,[6]%%%},[12,9,6,0]%%%}+%%%{%%%{-741888,[7]%%%},[12,9,4,1]%%%}+%%%{%%%{451584,[8]%%%},[12,9,2,2]%%%}+%%%{%%%{-43008,[9]%%%},[12,9,0,3]%%%}+%%%{%%{[%%%{-340992,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[11,9,7,0]%%%}+%%%{%%{[%%%{1096704,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[11,9,5,1]%%%}+%%%{%%{[%%%{-1032192,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[11,9,3,2]%%%}+%%%{%%{[%%%{258048,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[11,9,1,3]%%%}+%%%{%%%{315072,[5]%%%},[10,9,8,0]%%%}+%%%{%%%{-1290240,[6]%%%},[10,9,6,1]%%%}+%%%{%%%{1709568,[7]%%%},[10,9,4,2]%%%}+%%%{%%%{-774144,[8]%%%},[10,9,2,3]%%%}+%%%{%%%{64512,[9]%%%},[10,9,0,4]%%%}+%%%{%%{[%%%{-243392,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[9,9,9,0]%%%}+%%%{%%{[%%%{1230336,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[9,9,7,1]%%%}+%%%{%%{[%%%{-2161152,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[9,9,5,2]%%%}+%%%{%%{[%%%{1505280,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[9,9,3,3]%%%}+%%%{%%{[%%%{-322560,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[9,9,1,4]%%%}+%%%{%%%{157536,[4]%%%},[8,9,10,0]%%%}+%%%{%%%{-960192,[5]%%%},[8,9,8,1]%%%}+%%%{%%%{2145024,[6]%%%},[8,9,6,2]%%%}+%%%{%%%{-2096640,[7]%%%},[8,9,4,3]%%%}+%%%{%%%{806400,[8]%%%},[8,9,2,4]%%%}+%%%{%%%{-64512,[9]%%%},[8,9,0,5]%%%}+%%%{%%{[%%%{-85248,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,9,11,0]%%%}+%%%{%%{[%%%{615168,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,9,9,1]%%%}+%%%{%%{[%%%{-1695744,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,9,7,2]%%%}+%%%{%%{[%%%{2193408,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,9,5,3]%%%}+%%%{%%{[%%%{-1290240,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,9,3,4]%%%}+%%%{%%{[%%%{258048,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,9,1,5]%%%}+%%%{%%%{38304,[3]%%%},[6,9,12,0]%%%}+%%%{%%%{-322560,[4]%%%},[6,9,10,1]%%%}+%%%{%%%{1072512,[5]%%%},[6,9,8,2]%%%}+%%%{%%%{-1763328,[6]%%%},[6,9,6,3]%%%}+%%%{%%%{1451520,[7]%%%},[6,9,4,4]%%%}+%%%{%%%{-516096,[8]%%%},[6,9,2,5]%%%}+%%%{%%%{43008,[9]%%%},[6,9,0,6]%%%}+%%%{%%{[%%%{-14112,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,9,13,0]%%%}+%%%{%%{[%%%{137088,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,9,11,1]%%%}+%%%{%%{[%%%{-540288,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,9,9,2]%%%}+%%%{%%{[%%%{1096704,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,9,7,3]%%%}+%%%{%%{[%%%{-1193472,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,9,5,4]%%%}+%%%{%%{[%%%{645120,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,9,3,5]%%%}+%%%{%%{[%%%{-129024,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,9,1,6]%%%}+%%%{%%%{4176,[2]%%%},[4,9,14,0]%%%}+%%%{%%%{-46368,[3]%%%},[4,9,12,1]%%%}+%%%{%%%{213696,[4]%%%},[4,9,10,2]%%%}+%%%{%%%{-524160,[5]%%%},[4,9,8,3]%%%}+%%%{%%%{725760,[6]%%%},[4,9,6,4]%%%}+%%%{%%%{-548352,[7]%%%},[4,9,4,5]%%%}+%%%{%%%{193536,[8]%%%},[4,9,2,6]%%%}+%%%{%%%{-18432,[9]%%%},[4,9,0,7]%%%}+%%%{%%{[%%%{-960,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,9,15,0]%%%}+%%%{%%{[%%%{12096,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,9,13,1]%%%}+%%%{%%{[%%%{-64512,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,9,11,2]%%%}+%%%{%%{[%%%{188160,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,9,9,3]%%%}+%%%{%%{[%%%{-322560,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,9,7,4]%%%}+%%%{%%{[%%%{322560,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,9,5,5]%%%}+%%%{%%{[%%%{-172032,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,9,3,6]%%%}+%%%{%%{[%%%{36864,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,9,1,7]%%%}+%%%{%%%{162,[1]%%%},[2,9,16,0]%%%}+%%%{%%%{-2304,[2]%%%},[2,9,14,1]%%%}+%%%{%%%{14112,[3]%%%},[2,9,12,2]%%%}+%%%{%%%{-48384,[4]%%%},[2,9,10,3]%%%}+%%%{%%%{100800,[5]%%%},[2,9,8,4]%%%}+%%%{%%%{-129024,[6]%%%},[2,9,6,5]%%%}+%%%{%%%{96768,[7]%%%},[2,9,4,6]%%%}+%%%{%%%{-36864,[8]%%%},[2,9,2,7]%%%}+%%%{%%%{4608,[9]%%%},[2,9,0,8]%%%}+%%%{%%{[-18,0]:[1,0,%%%{-1,[1]%%%}]%%},[1,9,17,0]%%%}+%%%{%%{[%%%{288,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,9,15,1]%%%}+%%%{%%{[%%%{-2016,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,9,13,2]%%%}+%%%{%%{[%%%{8064,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,9,11,3]%%%}+%%%{%%{[%%%{-20160,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,9,9,4]%%%}+%%%{%%{[%%%{32256,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,9,7,5]%%%}+%%%{%%{[%%%{-32256,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,9,5,6]%%%}+%%%{%%{[%%%{18432,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,9,3,7]%%%}+%%%{%%{[%%%{-4608,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,9,1,8]%%%}+%%%{1,[0,9,18,0]%%%}+%%%{%%%{-18,[1]%%%},[0,9,16,1]%%%}+%%%{%%%{144,[2]%%%},[0,9,14,2]%%%}+%%%{%%%{-672,[3]%%%},[0,9,12,3]%%%}+%%%{%%%{2016,[4]%%%},[0,9,10,4]%%%}+%%%{%%%{-4032,[5]%%%},[0,9,8,5]%%%}+%%%{%%%{5376,[6]%%%},[0,9,6,6]%%%}+%%%{%%%{-4608,[7]%%%},[0,9,4,7]%%%}+%%%{%%%{2304,[8]%%%},[0,9,2,8]%%%}+%%%{%%%{-512,[9]%%%},[0,9,0,9]%%%} / %%%{%%{poly1[%%%{-512,[13]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[18,0,0,0]%%%}+%%%{%%%{4608,[13]%%%},[17,0,1,0]%%%}+%%%{%%{poly1[%%%{-20736,[12]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[16,0,2,0]%%%}+%%%{%%{[%%%{4608,[13]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[16,0,0,1]%%%}+%%%{%%%{61440,[12]%%%},[15,0,3,0]%%%}+%%%{%%%{-36864,[13]%%%},[15,0,1,1]%%%}+%%%{%%{poly1[%%%{-133632,[11]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[14,0,4,0]%%%}+%%%{%%{[%%%{147456,[12]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[14,0,2,1]%%%}+%%%{%%{poly1[%%%{-18432,[13]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[14,0,0,2]%%%}+%%%{%%%{225792,[11]%%%},[13,0,5,0]%%%}+%%%{%%%{-387072,[12]%%%},[13,0,3,1]%%%}+%%%{%%%{129024,[13]%%%},[13,0,1,2]%%%}+%%%{%%{poly1[%%%{-306432,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[12,0,6,0]%%%}+%%%{%%{[%%%{741888,[11]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[12,0,4,1]%%%}+%%%{%%{poly1[%%%{-451584,[12]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[12,0,2,2]%%%}+%%%{%%{[%%%{43008,[13]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[12,0,0,3]%%%}+%%%{%%%{340992,[10]%%%},[11,0,7,0]%%%}+%%%{%%%{-1096704,[11]%%%},[11,0,5,1]%%%}+%%%{%%%{1032192,[12]%%%},[11,0,3,2]%%%}+%%%{%%%{-258048,[13]%%%},[11,0,1,3]%%%}+%%%{%%{poly1[%%%{-315072,[9]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[10,0,8,0]%%%}+%%%{%%{[%%%{1290240,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[10,0,6,1]%%%}+%%%{%%{poly1[%%%{-1709568,[11]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[10,0,4,2]%%%}+%%%{%%{[%%%{774144,[12]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[10,0,2,3]%%%}+%%%{%%{poly1[%%%{-64512,[13]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[10,0,0,4]%%%}+%%%{%%%{243392,[9]%%%},[9,0,9,0]%%%}+%%%{%%%{-1230336,[10]%%%},[9,0,7,1]%%%}+%%%{%%%{2161152,[11]%%%},[9,0,5,2]%%%}+%%%{%%%{-1505280,[12]%%%},[9,0,3,3]%%%}+%%%{%%%{322560,[13]%%%},[9,0,1,4]%%%}+%%%{%%{poly1[%%%{-157536,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[8,0,10,0]%%%}+%%%{%%{[%%%{960192,[9]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[8,0,8,1]%%%}+%%%{%%{poly1[%%%{-2145024,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[8,0,6,2]%%%}+%%%{%%{[%%%{2096640,[11]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[8,0,4,3]%%%}+%%%{%%{poly1[%%%{-806400,[12]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[8,0,2,4]%%%}+%%%{%%{[%%%{64512,[13]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[8,0,0,5]%%%}+%%%{%%%{85248,[8]%%%},[7,0,11,0]%%%}+%%%{%%%{-615168,[9]%%%},[7,0,9,1]%%%}+%%%{%%%{1695744,[10]%%%},[7,0,7,2]%%%}+%%%{%%%{-2193408,[11]%%%},[7,0,5,3]%%%}+%%%{%%%{1290240,[12]%%%},[7,0,3,4]%%%}+%%%{%%%{-258048,[13]%%%},[7,0,1,5]%%%}+%%%{%%{poly1[%%%{-38304,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[6,0,12,0]%%%}+%%%{%%{[%%%{322560,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[6,0,10,1]%%%}+%%%{%%{poly1[%%%{-1072512,[9]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[6,0,8,2]%%%}+%%%{%%{[%%%{1763328,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[6,0,6,3]%%%}+%%%{%%{poly1[%%%{-1451520,[11]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[6,0,4,4]%%%}+%%%{%%{[%%%{516096,[12]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[6,0,2,5]%%%}+%%%{%%{poly1[%%%{-43008,[13]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[6,0,0,6]%%%}+%%%{%%%{14112,[7]%%%},[5,0,13,0]%%%}+%%%{%%%{-137088,[8]%%%},[5,0,11,1]%%%}+%%%{%%%{540288,[9]%%%},[5,0,9,2]%%%}+%%%{%%%{-1096704,[10]%%%},[5,0,7,3]%%%}+%%%{%%%{1193472,[11]%%%},[5,0,5,4]%%%}+%%%{%%%{-645120,[12]%%%},[5,0,3,5]%%%}+%%%{%%%{129024,[13]%%%},[5,0,1,6]%%%}+%%%{%%{poly1[%%%{-4176,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,14,0]%%%}+%%%{%%{[%%%{46368,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,12,1]%%%}+%%%{%%{poly1[%%%{-213696,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,10,2]%%%}+%%%{%%{[%%%{524160,[9]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,8,3]%%%}+%%%{%%{poly1[%%%{-725760,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,6,4]%%%}+%%%{%%{[%%%{548352,[11]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,4,5]%%%}+%%%{%%{poly1[%%%{-193536,[12]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,2,6]%%%}+%%%{%%{[%%%{18432,[13]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,0,7]%%%}+%%%{%%%{960,[6]%%%},[3,0,15,0]%%%}+%%%{%%%{-12096,[7]%%%},[3,0,13,1]%%%}+%%%{%%%{64512,[8]%%%},[3,0,11,2]%%%}+%%%{%%%{-188160,[9]%%%},[3,0,9,3]%%%}+%%%{%%%{322560,[10]%%%},[3,0,7,4]%%%}+%%%{%%%{-322560,[11]%%%},[3,0,5,5]%%%}+%%%{%%%{172032,[12]%%%},[3,0,3,6]%%%}+%%%{%%%{-36864,[13]%%%},[3,0,1,7]%%%}+%%%{%%{poly1[%%%{-162,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,16,0]%%%}+%%%{%%{[%%%{2304,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,14,1]%%%}+%%%{%%{poly1[%%%{-14112,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,12,2]%%%}+%%%{%%{[%%%{48384,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,10,3]%%%}+%%%{%%{poly1[%%%{-100800,[9]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,8,4]%%%}+%%%{%%{[%%%{129024,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,6,5]%%%}+%%%{%%{poly1[%%%{-96768,[11]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,4,6]%%%}+%%%{%%{[%%%{36864,[12]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,2,7]%%%}+%%%{%%{[%%%{-4608,[13]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,0,8]%%%}+%%%{%%%{18,[5]%%%},[1,0,17,0]%%%}+%%%{%%%{-288,[6]%%%},[1,0,15,1]%%%}+%%%{%%%{2016,[7]%%%},[1,0,13,2]%%%}+%%%{%%%{-8064,[8]%%%},[1,0,11,3]%%%}+%%%{%%%{20160,[9]%%%},[1,0,9,4]%%%}+%%%{%%%{-32256,[10]%%%},[1,0,7,5]%%%}+%%%{%%%{32256,[11]%%%},[1,0,5,6]%%%}+%%%{%%%{-18432,[12]%%%},[1,0,3,7]%%%}+%%%{%%%{4608,[13]%%%},[1,0,1,8]%%%}+%%%{%%{poly1[%%%{-1,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,18,0]%%%}+%%%{%%{[%%%{18,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,16,1]%%%}+%%%{%%{poly1[%%%{-144,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,14,2]%%%}+%%%{%%{[%%%{672,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,12,3]%%%}+%%%{%%{poly1[%%%{-2016,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,10,4]%%%}+%%%{%%{[%%%{4032,[9]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,8,5]%%%}+%%%{%%{poly1[%%%{-5376,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,6,6]%%%}+%%%{%%{[%%%{4608,[11]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,4,7]%%%}+%%%{%%{[%%%{-2304,[12]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,2,8]%%%}+%%%{%%{[%%%{512,[13]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,0,9]%%%} Error: Bad Argument Value","F(-2)",0
1231,1,1849,0,2.792474," ","integrate((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^10,x, algorithm=""giac"")","\frac{4032 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{14} c^{\frac{15}{2}} + 28224 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{13} b c^{7} + 90048 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{12} b^{2} c^{\frac{13}{2}} + 6720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{12} a c^{\frac{15}{2}} + 173376 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} b^{3} c^{6} + 40320 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} a b c^{7} + 225792 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{10} b^{4} c^{\frac{11}{2}} + 100800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{10} a b^{2} c^{\frac{13}{2}} + 20160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{10} a^{2} c^{\frac{15}{2}} + 212352 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} b^{5} c^{5} + 134400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} a b^{3} c^{6} + 100800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} a^{2} b c^{7} + 151200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} b^{6} c^{\frac{9}{2}} + 96768 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} a b^{4} c^{\frac{11}{2}} + 217728 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} a^{2} b^{2} c^{\frac{13}{2}} + 12096 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} a^{3} c^{\frac{15}{2}} + 84672 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} b^{7} c^{4} + 24192 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} a b^{5} c^{5} + 266112 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} a^{2} b^{3} c^{6} + 48384 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} a^{3} b c^{7} + 38304 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} b^{8} c^{\frac{7}{2}} - 20160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} a b^{6} c^{\frac{9}{2}} + 205632 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} a^{2} b^{4} c^{\frac{11}{2}} + 72576 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} a^{3} b^{2} c^{\frac{13}{2}} + 12096 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} a^{4} c^{\frac{15}{2}} + 14112 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} b^{9} c^{3} - 24192 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a b^{7} c^{4} + 108864 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{2} b^{5} c^{5} + 48384 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{3} b^{3} c^{6} + 36288 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{4} b c^{7} + 4176 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} b^{10} c^{\frac{5}{2}} - 12960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a b^{8} c^{\frac{7}{2}} + 43200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{2} b^{6} c^{\frac{9}{2}} + 8640 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{3} b^{4} c^{\frac{11}{2}} + 43200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{4} b^{2} c^{\frac{13}{2}} + 1728 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{5} c^{\frac{15}{2}} + 960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{11} c^{2} - 4416 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b^{9} c^{3} + 13824 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{2} b^{7} c^{4} - 6912 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{3} b^{5} c^{5} + 25920 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{4} b^{3} c^{6} + 3456 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{5} b c^{7} + 162 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{12} c^{\frac{3}{2}} - 1008 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a b^{10} c^{\frac{5}{2}} + 3456 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{2} b^{8} c^{\frac{7}{2}} - 4608 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{3} b^{6} c^{\frac{9}{2}} + 8640 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{4} b^{4} c^{\frac{11}{2}} + 1728 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{5} b^{2} c^{\frac{13}{2}} + 576 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{6} c^{\frac{15}{2}} + 18 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{13} c - 144 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{11} c^{2} + 576 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} b^{9} c^{3} - 1152 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{3} b^{7} c^{4} + 1728 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{4} b^{5} c^{5} + 576 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{6} b c^{7} + b^{14} \sqrt{c} - 10 \, a b^{12} c^{\frac{3}{2}} + 48 \, a^{2} b^{10} c^{\frac{5}{2}} - 128 \, a^{3} b^{8} c^{\frac{7}{2}} + 224 \, a^{4} b^{6} c^{\frac{9}{2}} - 192 \, a^{5} b^{4} c^{\frac{11}{2}} + 256 \, a^{6} b^{2} c^{\frac{13}{2}} - 64 \, a^{7} c^{\frac{15}{2}}}{2016 \, {\left(2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} c + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b \sqrt{c} + b^{2} - 2 \, a c\right)}^{9} c^{4} d^{10}}"," ",0,"1/2016*(4032*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^14*c^(15/2) + 28224*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^13*b*c^7 + 90048*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^12*b^2*c^(13/2) + 6720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^12*a*c^(15/2) + 173376*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*b^3*c^6 + 40320*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*a*b*c^7 + 225792*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^10*b^4*c^(11/2) + 100800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^10*a*b^2*c^(13/2) + 20160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^10*a^2*c^(15/2) + 212352*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*b^5*c^5 + 134400*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*a*b^3*c^6 + 100800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*a^2*b*c^7 + 151200*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*b^6*c^(9/2) + 96768*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a*b^4*c^(11/2) + 217728*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a^2*b^2*c^(13/2) + 12096*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a^3*c^(15/2) + 84672*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*b^7*c^4 + 24192*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a*b^5*c^5 + 266112*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^2*b^3*c^6 + 48384*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^3*b*c^7 + 38304*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*b^8*c^(7/2) - 20160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a*b^6*c^(9/2) + 205632*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^2*b^4*c^(11/2) + 72576*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^3*b^2*c^(13/2) + 12096*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^4*c^(15/2) + 14112*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b^9*c^3 - 24192*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*b^7*c^4 + 108864*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^2*b^5*c^5 + 48384*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^3*b^3*c^6 + 36288*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^4*b*c^7 + 4176*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^10*c^(5/2) - 12960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*b^8*c^(7/2) + 43200*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^2*b^6*c^(9/2) + 8640*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^3*b^4*c^(11/2) + 43200*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^4*b^2*c^(13/2) + 1728*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^5*c^(15/2) + 960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^11*c^2 - 4416*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^9*c^3 + 13824*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*b^7*c^4 - 6912*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^3*b^5*c^5 + 25920*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^4*b^3*c^6 + 3456*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^5*b*c^7 + 162*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^12*c^(3/2) - 1008*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^10*c^(5/2) + 3456*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*b^8*c^(7/2) - 4608*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^3*b^6*c^(9/2) + 8640*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^4*b^4*c^(11/2) + 1728*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^5*b^2*c^(13/2) + 576*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^6*c^(15/2) + 18*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^13*c - 144*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^11*c^2 + 576*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b^9*c^3 - 1152*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*b^7*c^4 + 1728*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^4*b^5*c^5 + 576*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^6*b*c^7 + b^14*sqrt(c) - 10*a*b^12*c^(3/2) + 48*a^2*b^10*c^(5/2) - 128*a^3*b^8*c^(7/2) + 224*a^4*b^6*c^(9/2) - 192*a^5*b^4*c^(11/2) + 256*a^6*b^2*c^(13/2) - 64*a^7*c^(15/2))/((2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*c + 2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b*sqrt(c) + b^2 - 2*a*c)^9*c^4*d^10)","B",0
1232,-2,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^11,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{%%%{2048,[11]%%%},[22,11,0,0]%%%}+%%%{%%{[%%%{-22528,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[21,11,1,0]%%%}+%%%{%%%{123904,[10]%%%},[20,11,2,0]%%%}+%%%{%%%{-22528,[11]%%%},[20,11,0,1]%%%}+%%%{%%{[%%%{-450560,[9]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[19,11,3,0]%%%}+%%%{%%{[%%%{225280,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[19,11,1,1]%%%}+%%%{%%%{1210880,[9]%%%},[18,11,4,0]%%%}+%%%{%%%{-1126400,[10]%%%},[18,11,2,1]%%%}+%%%{%%%{112640,[11]%%%},[18,11,0,2]%%%}+%%%{%%{[%%%{-2551296,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[17,11,5,0]%%%}+%%%{%%{[%%%{3717120,[9]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[17,11,3,1]%%%}+%%%{%%{[%%%{-1013760,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[17,11,1,2]%%%}+%%%{%%%{4367616,[8]%%%},[16,11,6,0]%%%}+%%%{%%%{-9039360,[9]%%%},[16,11,4,1]%%%}+%%%{%%%{4561920,[10]%%%},[16,11,2,2]%%%}+%%%{%%%{-337920,[11]%%%},[16,11,0,3]%%%}+%%%{%%{[%%%{-6217728,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[15,11,7,0]%%%}+%%%{%%{[%%%{17166336,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[15,11,5,1]%%%}+%%%{%%{[%%%{-13516800,[9]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[15,11,3,2]%%%}+%%%{%%{[%%%{2703360,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[15,11,1,3]%%%}+%%%{%%%{7476480,[7]%%%},[14,11,8,0]%%%}+%%%{%%%{-26357760,[8]%%%},[14,11,6,1]%%%}+%%%{%%%{29399040,[9]%%%},[14,11,4,2]%%%}+%%%{%%%{-10813440,[10]%%%},[14,11,2,3]%%%}+%%%{%%%{675840,[11]%%%},[14,11,0,4]%%%}+%%%{%%{[%%%{-7673600,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[13,11,9,0]%%%}+%%%{%%{[%%%{33454080,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[13,11,7,1]%%%}+%%%{%%{[%%%{-49674240,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[13,11,5,2]%%%}+%%%{%%{[%%%{28385280,[9]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[13,11,3,3]%%%}+%%%{%%{[%%%{-4730880,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[13,11,1,4]%%%}+%%%{%%%{6768256,[6]%%%},[12,11,10,0]%%%}+%%%{%%%{-35608320,[7]%%%},[12,11,8,1]%%%}+%%%{%%%{67415040,[8]%%%},[12,11,6,2]%%%}+%%%{%%%{-54405120,[9]%%%},[12,11,4,3]%%%}+%%%{%%%{16558080,[10]%%%},[12,11,2,4]%%%}+%%%{%%%{-946176,[11]%%%},[12,11,0,5]%%%}+%%%{%%{[%%%{-5149696,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[11,11,11,0]%%%}+%%%{%%{[%%%{32074240,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[11,11,9,1]%%%}+%%%{%%{[%%%{-75018240,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[11,11,7,2]%%%}+%%%{%%{[%%%{80424960,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[11,11,5,3]%%%}+%%%{%%{[%%%{-37847040,[9]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[11,11,3,4]%%%}+%%%{%%{[%%%{5677056,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[11,11,1,5]%%%}+%%%{%%%{3384128,[5]%%%},[10,11,12,0]%%%}+%%%{%%%{-24572416,[6]%%%},[10,11,10,1]%%%}+%%%{%%%{69315840,[7]%%%},[10,11,8,2]%%%}+%%%{%%%{-94617600,[8]%%%},[10,11,6,3]%%%}+%%%{%%%{62684160,[9]%%%},[10,11,4,4]%%%}+%%%{%%%{-17031168,[10]%%%},[10,11,2,5]%%%}+%%%{%%%{946176,[11]%%%},[10,11,0,6]%%%}+%%%{%%{[%%%{-1918400,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[9,11,13,0]%%%}+%%%{%%{[%%%{16037120,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[9,11,11,1]%%%}+%%%{%%{[%%%{-53546240,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[9,11,9,2]%%%}+%%%{%%{[%%%{90224640,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[9,11,7,3]%%%}+%%%{%%{[%%%{-79242240,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[9,11,5,4]%%%}+%%%{%%{[%%%{33116160,[9]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[9,11,3,5]%%%}+%%%{%%{[%%%{-4730880,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[9,11,1,6]%%%}+%%%{%%%{934560,[4]%%%},[8,11,14,0]%%%}+%%%{%%%{-8902080,[5]%%%},[8,11,12,1]%%%}+%%%{%%%{34657920,[6]%%%},[8,11,10,2]%%%}+%%%{%%%{-70414080,[7]%%%},[8,11,8,3]%%%}+%%%{%%%{78650880,[8]%%%},[8,11,6,4]%%%}+%%%{%%%{-46126080,[9]%%%},[8,11,4,5]%%%}+%%%{%%%{11827200,[10]%%%},[8,11,2,6]%%%}+%%%{%%%{-675840,[11]%%%},[8,11,0,7]%%%}+%%%{%%{[%%%{-388608,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,11,15,0]%%%}+%%%{%%{[%%%{4181760,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,11,13,1]%%%}+%%%{%%{[%%%{-18754560,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,11,11,2]%%%}+%%%{%%{[%%%{45112320,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,11,9,3]%%%}+%%%{%%{[%%%{-62177280,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,11,7,4]%%%}+%%%{%%{[%%%{48254976,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,11,5,5]%%%}+%%%{%%{[%%%{-18923520,[9]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,11,3,6]%%%}+%%%{%%{[%%%{2703360,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,11,1,7]%%%}+%%%{%%%{136488,[3]%%%},[6,11,16,0]%%%}+%%%{%%%{-1647360,[4]%%%},[6,11,14,1]%%%}+%%%{%%%{8426880,[5]%%%},[6,11,12,2]%%%}+%%%{%%%{-23654400,[6]%%%},[6,11,10,3]%%%}+%%%{%%%{39325440,[7]%%%},[6,11,8,4]%%%}+%%%{%%%{-38793216,[8]%%%},[6,11,6,5]%%%}+%%%{%%%{21288960,[9]%%%},[6,11,4,6]%%%}+%%%{%%%{-5406720,[10]%%%},[6,11,2,7]%%%}+%%%{%%%{337920,[11]%%%},[6,11,0,8]%%%}+%%%{%%{[%%%{-39864,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,11,17,0]%%%}+%%%{%%{[%%%{536448,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,11,15,1]%%%}+%%%{%%{[%%%{-3104640,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,11,13,2]%%%}+%%%{%%{[%%%{10053120,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,11,11,3]%%%}+%%%{%%{[%%%{-19810560,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,11,9,4]%%%}+%%%{%%{[%%%{24127488,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,11,7,5]%%%}+%%%{%%{[%%%{-17504256,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,11,5,6]%%%}+%%%{%%{[%%%{6758400,[9]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,11,3,7]%%%}+%%%{%%{[%%%{-1013760,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,11,1,8]%%%}+%%%{%%%{9460,[2]%%%},[4,11,18,0]%%%}+%%%{%%%{-141240,[3]%%%},[4,11,16,1]%%%}+%%%{%%%{918720,[4]%%%},[4,11,14,2]%%%}+%%%{%%%{-3400320,[5]%%%},[4,11,12,3]%%%}+%%%{%%%{7835520,[6]%%%},[4,11,10,4]%%%}+%%%{%%%{-11531520,[7]%%%},[4,11,8,5]%%%}+%%%{%%%{10644480,[8]%%%},[4,11,6,6]%%%}+%%%{%%%{-5744640,[9]%%%},[4,11,4,7]%%%}+%%%{%%%{1520640,[10]%%%},[4,11,2,8]%%%}+%%%{%%%{-112640,[11]%%%},[4,11,0,9]%%%}+%%%{%%{[%%%{-1760,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,11,19,0]%%%}+%%%{%%{[%%%{29040,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,11,17,1]%%%}+%%%{%%{[%%%{-211200,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,11,15,2]%%%}+%%%{%%{[%%%{887040,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,11,13,3]%%%}+%%%{%%{[%%%{-2365440,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,11,11,4]%%%}+%%%{%%{[%%%{4139520,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,11,9,5]%%%}+%%%{%%{[%%%{-4730880,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,11,7,6]%%%}+%%%{%%{[%%%{3379200,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,11,5,7]%%%}+%%%{%%{[%%%{-1351680,[9]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,11,3,8]%%%}+%%%{%%{[%%%{225280,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,11,1,9]%%%}+%%%{%%%{242,[1]%%%},[2,11,20,0]%%%}+%%%{%%%{-4400,[2]%%%},[2,11,18,1]%%%}+%%%{%%%{35640,[3]%%%},[2,11,16,2]%%%}+%%%{%%%{-168960,[4]%%%},[2,11,14,3]%%%}+%%%{%%%{517440,[5]%%%},[2,11,12,4]%%%}+%%%{%%%{-1064448,[6]%%%},[2,11,10,5]%%%}+%%%{%%%{1478400,[7]%%%},[2,11,8,6]%%%}+%%%{%%%{-1351680,[8]%%%},[2,11,6,7]%%%}+%%%{%%%{760320,[9]%%%},[2,11,4,8]%%%}+%%%{%%%{-225280,[10]%%%},[2,11,2,9]%%%}+%%%{%%%{22528,[11]%%%},[2,11,0,10]%%%}+%%%{%%{[-22,0]:[1,0,%%%{-1,[1]%%%}]%%},[1,11,21,0]%%%}+%%%{%%{[%%%{440,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,11,19,1]%%%}+%%%{%%{[%%%{-3960,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,11,17,2]%%%}+%%%{%%{[%%%{21120,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,11,15,3]%%%}+%%%{%%{[%%%{-73920,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,11,13,4]%%%}+%%%{%%{[%%%{177408,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,11,11,5]%%%}+%%%{%%{[%%%{-295680,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,11,9,6]%%%}+%%%{%%{[%%%{337920,[7]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,11,7,7]%%%}+%%%{%%{[%%%{-253440,[8]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,11,5,8]%%%}+%%%{%%{[%%%{112640,[9]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,11,3,9]%%%}+%%%{%%{[%%%{-22528,[10]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,11,1,10]%%%}+%%%{1,[0,11,22,0]%%%}+%%%{%%%{-22,[1]%%%},[0,11,20,1]%%%}+%%%{%%%{220,[2]%%%},[0,11,18,2]%%%}+%%%{%%%{-1320,[3]%%%},[0,11,16,3]%%%}+%%%{%%%{5280,[4]%%%},[0,11,14,4]%%%}+%%%{%%%{-14784,[5]%%%},[0,11,12,5]%%%}+%%%{%%%{29568,[6]%%%},[0,11,10,6]%%%}+%%%{%%%{-42240,[7]%%%},[0,11,8,7]%%%}+%%%{%%%{42240,[8]%%%},[0,11,6,8]%%%}+%%%{%%%{-28160,[9]%%%},[0,11,4,9]%%%}+%%%{%%%{11264,[10]%%%},[0,11,2,10]%%%}+%%%{%%%{-2048,[11]%%%},[0,11,0,11]%%%} / 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Error: Bad Argument Value","F(-2)",0
1233,1,2371,0,4.900838," ","integrate((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^12,x, algorithm=""giac"")","\frac{29568 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{16} c^{\frac{17}{2}} + 236544 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{15} b c^{8} + 868560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{14} b^{2} c^{\frac{15}{2}} + 73920 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{14} a c^{\frac{17}{2}} + 1940400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{13} b^{3} c^{7} + 517440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{13} a b c^{8} + 2953104 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{12} b^{4} c^{\frac{13}{2}} + 1600368 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{12} a b^{2} c^{\frac{15}{2}} + 162624 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{12} a^{2} c^{\frac{17}{2}} + 3256176 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} b^{5} c^{6} + 2875488 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} a b^{3} c^{7} + 975744 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{11} a^{2} b c^{8} + 2709168 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{10} b^{6} c^{\frac{11}{2}} + 3307920 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{10} a b^{4} c^{\frac{13}{2}} + 2583504 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{10} a^{2} b^{2} c^{\frac{15}{2}} + 133056 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{10} a^{3} c^{\frac{17}{2}} + 1755600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} b^{7} c^{5} + 2513280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} a b^{5} c^{6} + 3973200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} a^{2} b^{3} c^{7} + 665280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} a^{3} b c^{8} + 910800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} b^{8} c^{\frac{9}{2}} + 1227600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} a b^{6} c^{\frac{11}{2}} + 3944160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} a^{2} b^{4} c^{\frac{13}{2}} + 1401840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} a^{3} b^{2} c^{\frac{15}{2}} + 95040 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} a^{4} c^{\frac{17}{2}} + 387024 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} b^{9} c^{4} + 319968 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} a b^{7} c^{5} + 2670624 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} a^{2} b^{5} c^{6} + 1615680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} a^{3} b^{3} c^{7} + 380160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} a^{4} b c^{8} + 136488 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} b^{10} c^{\frac{7}{2}} - 20592 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} a b^{8} c^{\frac{9}{2}} + 1284624 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} a^{2} b^{6} c^{\frac{11}{2}} + 1092960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} a^{3} b^{4} c^{\frac{13}{2}} + 641520 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} a^{4} b^{2} c^{\frac{15}{2}} + 19008 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} a^{5} c^{\frac{17}{2}} + 39864 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} b^{11} c^{3} - 58080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a b^{9} c^{4} + 460944 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{2} b^{7} c^{5} + 418176 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{3} b^{5} c^{6} + 594000 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{4} b^{3} c^{7} + 57024 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{5} b c^{8} + 9460 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} b^{12} c^{\frac{5}{2}} - 27720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a b^{10} c^{\frac{7}{2}} + 132000 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{2} b^{8} c^{\frac{9}{2}} + 64240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{3} b^{6} c^{\frac{11}{2}} + 330000 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{4} b^{4} c^{\frac{13}{2}} + 66000 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{5} b^{2} c^{\frac{15}{2}} + 3520 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{6} c^{\frac{17}{2}} + 1760 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{13} c^{2} - 7920 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b^{11} c^{3} + 31680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{2} b^{9} c^{4} - 14080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{3} b^{7} c^{5} + 113520 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{4} b^{5} c^{6} + 36960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{5} b^{3} c^{7} + 7040 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{6} b c^{8} + 242 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{14} c^{\frac{3}{2}} - 1496 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a b^{12} c^{\frac{5}{2}} + 6072 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{2} b^{10} c^{\frac{7}{2}} - 8800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{3} b^{8} c^{\frac{9}{2}} + 24640 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{4} b^{6} c^{\frac{11}{2}} + 8976 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{5} b^{4} c^{\frac{13}{2}} + 6512 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{6} b^{2} c^{\frac{15}{2}} - 704 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{7} c^{\frac{17}{2}} + 22 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{15} c - 176 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{13} c^{2} + 792 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} b^{11} c^{3} - 1760 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{3} b^{9} c^{4} + 3520 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{4} b^{7} c^{5} + 2992 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{6} b^{3} c^{7} - 704 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{7} b c^{8} + b^{16} \sqrt{c} - 10 \, a b^{14} c^{\frac{3}{2}} + 52 \, a^{2} b^{12} c^{\frac{5}{2}} - 152 \, a^{3} b^{10} c^{\frac{7}{2}} + 320 \, a^{4} b^{8} c^{\frac{9}{2}} - 320 \, a^{5} b^{6} c^{\frac{11}{2}} + 640 \, a^{6} b^{4} c^{\frac{13}{2}} - 304 \, a^{7} b^{2} c^{\frac{15}{2}} + 64 \, a^{8} c^{\frac{17}{2}}}{5544 \, {\left(2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} c + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b \sqrt{c} + b^{2} - 2 \, a c\right)}^{11} c^{4} d^{12}}"," ",0,"1/5544*(29568*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^16*c^(17/2) + 236544*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^15*b*c^8 + 868560*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^14*b^2*c^(15/2) + 73920*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^14*a*c^(17/2) + 1940400*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^13*b^3*c^7 + 517440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^13*a*b*c^8 + 2953104*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^12*b^4*c^(13/2) + 1600368*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^12*a*b^2*c^(15/2) + 162624*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^12*a^2*c^(17/2) + 3256176*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*b^5*c^6 + 2875488*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*a*b^3*c^7 + 975744*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*a^2*b*c^8 + 2709168*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^10*b^6*c^(11/2) + 3307920*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^10*a*b^4*c^(13/2) + 2583504*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^10*a^2*b^2*c^(15/2) + 133056*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^10*a^3*c^(17/2) + 1755600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*b^7*c^5 + 2513280*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*a*b^5*c^6 + 3973200*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*a^2*b^3*c^7 + 665280*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*a^3*b*c^8 + 910800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*b^8*c^(9/2) + 1227600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a*b^6*c^(11/2) + 3944160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a^2*b^4*c^(13/2) + 1401840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a^3*b^2*c^(15/2) + 95040*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a^4*c^(17/2) + 387024*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*b^9*c^4 + 319968*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a*b^7*c^5 + 2670624*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^2*b^5*c^6 + 1615680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^3*b^3*c^7 + 380160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^4*b*c^8 + 136488*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*b^10*c^(7/2) - 20592*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a*b^8*c^(9/2) + 1284624*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^2*b^6*c^(11/2) + 1092960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^3*b^4*c^(13/2) + 641520*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^4*b^2*c^(15/2) + 19008*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^5*c^(17/2) + 39864*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b^11*c^3 - 58080*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*b^9*c^4 + 460944*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^2*b^7*c^5 + 418176*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^3*b^5*c^6 + 594000*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^4*b^3*c^7 + 57024*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^5*b*c^8 + 9460*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^12*c^(5/2) - 27720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*b^10*c^(7/2) + 132000*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^2*b^8*c^(9/2) + 64240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^3*b^6*c^(11/2) + 330000*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^4*b^4*c^(13/2) + 66000*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^5*b^2*c^(15/2) + 3520*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^6*c^(17/2) + 1760*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^13*c^2 - 7920*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^11*c^3 + 31680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*b^9*c^4 - 14080*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^3*b^7*c^5 + 113520*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^4*b^5*c^6 + 36960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^5*b^3*c^7 + 7040*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^6*b*c^8 + 242*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^14*c^(3/2) - 1496*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^12*c^(5/2) + 6072*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*b^10*c^(7/2) - 8800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^3*b^8*c^(9/2) + 24640*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^4*b^6*c^(11/2) + 8976*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^5*b^4*c^(13/2) + 6512*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^6*b^2*c^(15/2) - 704*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^7*c^(17/2) + 22*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^15*c - 176*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^13*c^2 + 792*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b^11*c^3 - 1760*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*b^9*c^4 + 3520*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^4*b^7*c^5 + 2992*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^6*b^3*c^7 - 704*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^7*b*c^8 + b^16*sqrt(c) - 10*a*b^14*c^(3/2) + 52*a^2*b^12*c^(5/2) - 152*a^3*b^10*c^(7/2) + 320*a^4*b^8*c^(9/2) - 320*a^5*b^6*c^(11/2) + 640*a^6*b^4*c^(13/2) - 304*a^7*b^2*c^(15/2) + 64*a^8*c^(17/2))/((2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*c + 2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b*sqrt(c) + b^2 - 2*a*c)^11*c^4*d^12)","B",0
1234,1,159,0,0.276850," ","integrate((2*c*d*x+b*d)^4/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(2 \, c^{3} d^{4} x + 3 \, b c^{2} d^{4}\right)} x + \frac{3 \, {\left(3 \, b^{2} c^{4} d^{4} - 4 \, a c^{5} d^{4}\right)}}{c^{3}}\right)} x + \frac{5 \, b^{3} c^{3} d^{4} - 12 \, a b c^{4} d^{4}}{c^{3}}\right)} - \frac{3 \, {\left(b^{4} d^{4} - 8 \, a b^{2} c d^{4} + 16 \, a^{2} c^{2} d^{4}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{8 \, \sqrt{c}}"," ",0,"1/4*sqrt(c*x^2 + b*x + a)*(2*(4*(2*c^3*d^4*x + 3*b*c^2*d^4)*x + 3*(3*b^2*c^4*d^4 - 4*a*c^5*d^4)/c^3)*x + (5*b^3*c^3*d^4 - 12*a*b*c^4*d^4)/c^3) - 3/8*(b^4*d^4 - 8*a*b^2*c*d^4 + 16*a^2*c^2*d^4)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/sqrt(c)","A",0
1235,1,58,0,0.162737," ","integrate((2*c*d*x+b*d)^3/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","2 \, \sqrt{c x^{2} + b x + a} b^{2} d^{3} + \frac{8}{3} \, {\left(c x^{2} + b x + a\right)}^{\frac{3}{2}} c d^{3} - 8 \, \sqrt{c x^{2} + b x + a} a c d^{3}"," ",0,"2*sqrt(c*x^2 + b*x + a)*b^2*d^3 + 8/3*(c*x^2 + b*x + a)^(3/2)*c*d^3 - 8*sqrt(c*x^2 + b*x + a)*a*c*d^3","A",0
1236,1,78,0,0.249500," ","integrate((2*c*d*x+b*d)^2/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","{\left(2 \, c d^{2} x + b d^{2}\right)} \sqrt{c x^{2} + b x + a} - \frac{{\left(b^{2} d^{2} - 4 \, a c d^{2}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{2 \, \sqrt{c}}"," ",0,"(2*c*d^2*x + b*d^2)*sqrt(c*x^2 + b*x + a) - 1/2*(b^2*d^2 - 4*a*c*d^2)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/sqrt(c)","A",0
1237,1,15,0,0.155258," ","integrate((2*c*d*x+b*d)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","2 \, \sqrt{c x^{2} + b x + a} d"," ",0,"2*sqrt(c*x^2 + b*x + a)*d","A",0
1238,1,65,0,0.241313," ","integrate(1/(2*c*d*x+b*d)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\frac{2 \, \arctan\left(-\frac{2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} c + b \sqrt{c}}{\sqrt{b^{2} c - 4 \, a c^{2}}}\right)}{\sqrt{b^{2} c - 4 \, a c^{2}} d}"," ",0,"2*arctan(-(2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*c + b*sqrt(c))/sqrt(b^2*c - 4*a*c^2))/(sqrt(b^2*c - 4*a*c^2)*d)","A",0
1239,1,139,0,0.248940," ","integrate(1/(2*c*d*x+b*d)^2/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{c} \mathrm{sgn}\left(\frac{1}{2 \, c d x + b d}\right) \mathrm{sgn}\left(c\right) \mathrm{sgn}\left(d\right)}{b^{2} c d^{2} - 4 \, a c^{2} d^{2}} + \frac{\sqrt{-\frac{b^{2} c d^{2}}{{\left(2 \, c d x + b d\right)}^{2}} + \frac{4 \, a c^{2} d^{2}}{{\left(2 \, c d x + b d\right)}^{2}} + c}}{b^{2} c d^{2} \mathrm{sgn}\left(\frac{1}{2 \, c d x + b d}\right) \mathrm{sgn}\left(c\right) \mathrm{sgn}\left(d\right) - 4 \, a c^{2} d^{2} \mathrm{sgn}\left(\frac{1}{2 \, c d x + b d}\right) \mathrm{sgn}\left(c\right) \mathrm{sgn}\left(d\right)}"," ",0,"-sqrt(c)*sgn(1/(2*c*d*x + b*d))*sgn(c)*sgn(d)/(b^2*c*d^2 - 4*a*c^2*d^2) + sqrt(-b^2*c*d^2/(2*c*d*x + b*d)^2 + 4*a*c^2*d^2/(2*c*d*x + b*d)^2 + c)/(b^2*c*d^2*sgn(1/(2*c*d*x + b*d))*sgn(c)*sgn(d) - 4*a*c^2*d^2*sgn(1/(2*c*d*x + b*d))*sgn(c)*sgn(d))","B",0
1240,-2,0,0,0.000000," ","integrate(1/(2*c*d*x+b*d)^3/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{%%%{8,[3]%%%},[6,3,0,0]%%%}+%%%{%%{[%%%{-24,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,3,1,0]%%%}+%%%{%%%{36,[2]%%%},[4,3,2,0]%%%}+%%%{%%%{-24,[3]%%%},[4,3,0,1]%%%}+%%%{%%{[%%%{-32,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,3,3,0]%%%}+%%%{%%{[%%%{48,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,3,1,1]%%%}+%%%{%%%{18,[1]%%%},[2,3,4,0]%%%}+%%%{%%%{-48,[2]%%%},[2,3,2,1]%%%}+%%%{%%%{24,[3]%%%},[2,3,0,2]%%%}+%%%{%%{[-6,0]:[1,0,%%%{-1,[1]%%%}]%%},[1,3,5,0]%%%}+%%%{%%{[%%%{24,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,3,3,1]%%%}+%%%{%%{[%%%{-24,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,3,1,2]%%%}+%%%{1,[0,3,6,0]%%%}+%%%{%%%{-6,[1]%%%},[0,3,4,1]%%%}+%%%{%%%{12,[2]%%%},[0,3,2,2]%%%}+%%%{%%%{-8,[3]%%%},[0,3,0,3]%%%} / %%%{%%{poly1[%%%{-8,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[6,0,0,0]%%%}+%%%{%%%{24,[4]%%%},[5,0,1,0]%%%}+%%%{%%{poly1[%%%{-36,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,2,0]%%%}+%%%{%%{[%%%{24,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,0,1]%%%}+%%%{%%%{32,[3]%%%},[3,0,3,0]%%%}+%%%{%%%{-48,[4]%%%},[3,0,1,1]%%%}+%%%{%%{poly1[%%%{-18,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,4,0]%%%}+%%%{%%{[%%%{48,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,2,1]%%%}+%%%{%%{[%%%{-24,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,0,2]%%%}+%%%{%%%{6,[2]%%%},[1,0,5,0]%%%}+%%%{%%%{-24,[3]%%%},[1,0,3,1]%%%}+%%%{%%%{24,[4]%%%},[1,0,1,2]%%%}+%%%{%%{poly1[%%%{-1,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,6,0]%%%}+%%%{%%{[%%%{6,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,4,1]%%%}+%%%{%%{[%%%{-12,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,2,2]%%%}+%%%{%%{[%%%{8,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,0,3]%%%} Error: Bad Argument Value","F(-2)",0
1241,1,134,0,0.344411," ","integrate(1/(2*c*d*x+b*d)^4/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} c^{\frac{3}{2}} + 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b c + b^{2} \sqrt{c} - a c^{\frac{3}{2}}\right)}}{3 \, {\left(2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} c + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b \sqrt{c} + b^{2} - 2 \, a c\right)}^{3} c d^{4}}"," ",0,"2/3*(3*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*c^(3/2) + 3*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b*c + b^2*sqrt(c) - a*c^(3/2))/((2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*c + 2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b*sqrt(c) + b^2 - 2*a*c)^3*c*d^4)","A",0
1242,1,249,0,0.271274," ","integrate((2*c*d*x+b*d)^4/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","-\frac{6 \, {\left(b^{2} c d^{4} - 4 \, a c^{2} d^{4}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{\sqrt{c}} + \frac{2 \, {\left(2 \, {\left({\left(\frac{2 \, {\left(b^{2} c^{5} d^{4} - 4 \, a c^{6} d^{4}\right)} x}{b^{2} c^{2} - 4 \, a c^{3}} + \frac{3 \, {\left(b^{3} c^{4} d^{4} - 4 \, a b c^{5} d^{4}\right)}}{b^{2} c^{2} - 4 \, a c^{3}}\right)} x + \frac{6 \, {\left(a b^{2} c^{4} d^{4} - 4 \, a^{2} c^{5} d^{4}\right)}}{b^{2} c^{2} - 4 \, a c^{3}}\right)} x - \frac{b^{5} c^{2} d^{4} - 10 \, a b^{3} c^{3} d^{4} + 24 \, a^{2} b c^{4} d^{4}}{b^{2} c^{2} - 4 \, a c^{3}}\right)}}{\sqrt{c x^{2} + b x + a}}"," ",0,"-6*(b^2*c*d^4 - 4*a*c^2*d^4)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/sqrt(c) + 2*(2*((2*(b^2*c^5*d^4 - 4*a*c^6*d^4)*x/(b^2*c^2 - 4*a*c^3) + 3*(b^3*c^4*d^4 - 4*a*b*c^5*d^4)/(b^2*c^2 - 4*a*c^3))*x + 6*(a*b^2*c^4*d^4 - 4*a^2*c^5*d^4)/(b^2*c^2 - 4*a*c^3))*x - (b^5*c^2*d^4 - 10*a*b^3*c^3*d^4 + 24*a^2*b*c^4*d^4)/(b^2*c^2 - 4*a*c^3))/sqrt(c*x^2 + b*x + a)","B",0
1243,1,48,0,0.176885," ","integrate((2*c*d*x+b*d)^3/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","8 \, \sqrt{c x^{2} + b x + a} c d^{3} - \frac{2 \, {\left(b^{2} d^{3} - 4 \, a c d^{3}\right)}}{\sqrt{c x^{2} + b x + a}}"," ",0,"8*sqrt(c*x^2 + b*x + a)*c*d^3 - 2*(b^2*d^3 - 4*a*c*d^3)/sqrt(c*x^2 + b*x + a)","A",0
1244,1,113,0,0.290853," ","integrate((2*c*d*x+b*d)^2/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","-4 \, \sqrt{c} d^{2} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right) - \frac{2 \, {\left(\frac{2 \, {\left(b^{2} c d^{2} - 4 \, a c^{2} d^{2}\right)} x}{b^{2} - 4 \, a c} + \frac{b^{3} d^{2} - 4 \, a b c d^{2}}{b^{2} - 4 \, a c}\right)}}{\sqrt{c x^{2} + b x + a}}"," ",0,"-4*sqrt(c)*d^2*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b)) - 2*(2*(b^2*c*d^2 - 4*a*c^2*d^2)*x/(b^2 - 4*a*c) + (b^3*d^2 - 4*a*b*c*d^2)/(b^2 - 4*a*c))/sqrt(c*x^2 + b*x + a)","B",0
1245,1,15,0,0.158036," ","integrate((2*c*d*x+b*d)/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","-\frac{2 \, d}{\sqrt{c x^{2} + b x + a}}"," ",0,"-2*d/sqrt(c*x^2 + b*x + a)","A",0
1246,1,158,0,0.261052," ","integrate(1/(2*c*d*x+b*d)/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\frac{8 \, c \arctan\left(\frac{2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} c + b \sqrt{c}}{\sqrt{b^{2} c - 4 \, a c^{2}}}\right)}{\sqrt{b^{2} c - 4 \, a c^{2}} {\left(b^{2} d - 4 \, a c d\right)}} - \frac{2 \, {\left(b^{4} d - 8 \, a b^{2} c d + 16 \, a^{2} c^{2} d\right)}}{{\left(b^{6} d^{2} - 12 \, a b^{4} c d^{2} + 48 \, a^{2} b^{2} c^{2} d^{2} - 64 \, a^{3} c^{3} d^{2}\right)} \sqrt{c x^{2} + b x + a}}"," ",0,"8*c*arctan((2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*c + b*sqrt(c))/sqrt(b^2*c - 4*a*c^2))/(sqrt(b^2*c - 4*a*c^2)*(b^2*d - 4*a*c*d)) - 2*(b^4*d - 8*a*b^2*c*d + 16*a^2*c^2*d)/((b^6*d^2 - 12*a*b^4*c*d^2 + 48*a^2*b^2*c^2*d^2 - 64*a^3*c^3*d^2)*sqrt(c*x^2 + b*x + a))","B",0
1247,1,266,0,0.318483," ","integrate(1/(2*c*d*x+b*d)^2/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","-\frac{4 \, {\left(\frac{c^{2} d^{4} {\left(\frac{\sqrt{-\frac{b^{2} c d^{2}}{{\left(2 \, c d x + b d\right)}^{2}} + \frac{4 \, a c^{2} d^{2}}{{\left(2 \, c d x + b d\right)}^{2}} + c} c}{b^{2} \mathrm{sgn}\left(\frac{1}{2 \, c d x + b d}\right) \mathrm{sgn}\left(c\right) \mathrm{sgn}\left(d\right) - 4 \, a c \mathrm{sgn}\left(\frac{1}{2 \, c d x + b d}\right) \mathrm{sgn}\left(c\right) \mathrm{sgn}\left(d\right)} + \frac{c^{2}}{{\left(b^{2} \mathrm{sgn}\left(\frac{1}{2 \, c d x + b d}\right) \mathrm{sgn}\left(c\right) \mathrm{sgn}\left(d\right) - 4 \, a c \mathrm{sgn}\left(\frac{1}{2 \, c d x + b d}\right) \mathrm{sgn}\left(c\right) \mathrm{sgn}\left(d\right)\right)} \sqrt{-\frac{b^{2} c d^{2}}{{\left(2 \, c d x + b d\right)}^{2}} + \frac{4 \, a c^{2} d^{2}}{{\left(2 \, c d x + b d\right)}^{2}} + c}}\right)} {\left| c \right|}}{b^{2} c^{3} d^{4} - 4 \, a c^{4} d^{4}} - \frac{2 \, \sqrt{c} {\left| c \right|} \mathrm{sgn}\left(\frac{1}{2 \, c d x + b d}\right) \mathrm{sgn}\left(c\right) \mathrm{sgn}\left(d\right)}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}}\right)}}{d^{2} {\left| c \right|}}"," ",0,"-4*(c^2*d^4*(sqrt(-b^2*c*d^2/(2*c*d*x + b*d)^2 + 4*a*c^2*d^2/(2*c*d*x + b*d)^2 + c)*c/(b^2*sgn(1/(2*c*d*x + b*d))*sgn(c)*sgn(d) - 4*a*c*sgn(1/(2*c*d*x + b*d))*sgn(c)*sgn(d)) + c^2/((b^2*sgn(1/(2*c*d*x + b*d))*sgn(c)*sgn(d) - 4*a*c*sgn(1/(2*c*d*x + b*d))*sgn(c)*sgn(d))*sqrt(-b^2*c*d^2/(2*c*d*x + b*d)^2 + 4*a*c^2*d^2/(2*c*d*x + b*d)^2 + c)))*abs(c)/(b^2*c^3*d^4 - 4*a*c^4*d^4) - 2*sqrt(c)*abs(c)*sgn(1/(2*c*d*x + b*d))*sgn(c)*sgn(d)/(b^4 - 8*a*b^2*c + 16*a^2*c^2))/(d^2*abs(c))","B",0
1248,-2,0,0,0.000000," ","integrate(1/(2*c*d*x+b*d)^3/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{%%%{128,[5]%%%},[6,2,3,0]%%%}+%%%{%%%{-64,[4]%%%},[6,1,3,2]%%%}+%%%{%%%{8,[3]%%%},[6,0,3,4]%%%}+%%%{%%{[%%%{-384,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,2,3,1]%%%}+%%%{%%{[%%%{192,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,1,3,3]%%%}+%%%{%%{[%%%{-24,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,0,3,5]%%%}+%%%{%%%{-384,[5]%%%},[4,3,3,0]%%%}+%%%{%%%{768,[4]%%%},[4,2,3,2]%%%}+%%%{%%%{-312,[3]%%%},[4,1,3,4]%%%}+%%%{%%%{36,[2]%%%},[4,0,3,6]%%%}+%%%{%%{[%%%{768,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,3,3,1]%%%}+%%%{%%{[%%%{-896,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,2,3,3]%%%}+%%%{%%{[%%%{304,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,1,3,5]%%%}+%%%{%%{[%%%{-32,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,0,3,7]%%%}+%%%{%%%{384,[5]%%%},[2,4,3,0]%%%}+%%%{%%%{-960,[4]%%%},[2,3,3,2]%%%}+%%%{%%%{696,[3]%%%},[2,2,3,4]%%%}+%%%{%%%{-192,[2]%%%},[2,1,3,6]%%%}+%%%{%%%{18,[1]%%%},[2,0,3,8]%%%}+%%%{%%{[%%%{-384,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,4,3,1]%%%}+%%%{%%{[%%%{576,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,3,3,3]%%%}+%%%{%%{[%%%{-312,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,2,3,5]%%%}+%%%{%%{[%%%{72,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,1,3,7]%%%}+%%%{%%{[-6,0]:[1,0,%%%{-1,[1]%%%}]%%},[1,0,3,9]%%%}+%%%{%%%{-128,[5]%%%},[0,5,3,0]%%%}+%%%{%%%{256,[4]%%%},[0,4,3,2]%%%}+%%%{%%%{-200,[3]%%%},[0,3,3,4]%%%}+%%%{%%%{76,[2]%%%},[0,2,3,6]%%%}+%%%{%%%{-14,[1]%%%},[0,1,3,8]%%%}+%%%{1,[0,0,3,10]%%%} / %%%{%%{poly1[%%%{-8,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[6,0,0,0]%%%}+%%%{%%%{24,[4]%%%},[5,0,0,1]%%%}+%%%{%%{[%%%{24,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,1,0,0]%%%}+%%%{%%{poly1[%%%{-36,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,0,2]%%%}+%%%{%%%{-48,[4]%%%},[3,1,0,1]%%%}+%%%{%%%{32,[3]%%%},[3,0,0,3]%%%}+%%%{%%{[%%%{-24,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,2,0,0]%%%}+%%%{%%{[%%%{48,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,1,0,2]%%%}+%%%{%%{poly1[%%%{-18,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,0,4]%%%}+%%%{%%%{24,[4]%%%},[1,2,0,1]%%%}+%%%{%%%{-24,[3]%%%},[1,1,0,3]%%%}+%%%{%%%{6,[2]%%%},[1,0,0,5]%%%}+%%%{%%{[%%%{8,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,3,0,0]%%%}+%%%{%%{[%%%{-12,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,2,0,2]%%%}+%%%{%%{[%%%{6,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,1,0,4]%%%}+%%%{%%{poly1[%%%{-1,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,0,6]%%%} Error: Bad Argument Value","F(-2)",0
1249,-2,0,0,0.000000," ","integrate(1/(2*c*d*x+b*d)^4/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{%%%{256,[6]%%%},[8,2,4,0]%%%}+%%%{%%%{-128,[5]%%%},[8,1,4,2]%%%}+%%%{%%%{16,[4]%%%},[8,0,4,4]%%%}+%%%{%%{[%%%{-1024,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,2,4,1]%%%}+%%%{%%{[%%%{512,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,1,4,3]%%%}+%%%{%%{[%%%{-64,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,0,4,5]%%%}+%%%{%%%{-1024,[6]%%%},[6,3,4,0]%%%}+%%%{%%%{2560,[5]%%%},[6,2,4,2]%%%}+%%%{%%%{-1088,[4]%%%},[6,1,4,4]%%%}+%%%{%%%{128,[3]%%%},[6,0,4,6]%%%}+%%%{%%{[%%%{3072,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,3,4,1]%%%}+%%%{%%{[%%%{-4096,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,2,4,3]%%%}+%%%{%%{[%%%{1472,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,1,4,5]%%%}+%%%{%%{[%%%{-160,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,0,4,7]%%%}+%%%{%%%{1536,[6]%%%},[4,4,4,0]%%%}+%%%{%%%{-5376,[5]%%%},[4,3,4,2]%%%}+%%%{%%%{4576,[4]%%%},[4,2,4,4]%%%}+%%%{%%%{-1376,[3]%%%},[4,1,4,6]%%%}+%%%{%%%{136,[2]%%%},[4,0,4,8]%%%}+%%%{%%{[%%%{-3072,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,4,4,1]%%%}+%%%{%%{[%%%{5632,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,3,4,3]%%%}+%%%{%%{[%%%{-3520,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,2,4,5]%%%}+%%%{%%{[%%%{896,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,1,4,7]%%%}+%%%{%%{[%%%{-80,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,0,4,9]%%%}+%%%{%%%{-1024,[6]%%%},[2,5,4,0]%%%}+%%%{%%%{3584,[5]%%%},[2,4,4,2]%%%}+%%%{%%%{-3904,[4]%%%},[2,3,4,4]%%%}+%%%{%%%{1856,[3]%%%},[2,2,4,6]%%%}+%%%{%%%{-400,[2]%%%},[2,1,4,8]%%%}+%%%{%%%{32,[1]%%%},[2,0,4,10]%%%}+%%%{%%{[%%%{1024,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,5,4,1]%%%}+%%%{%%{[%%%{-2048,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,4,4,3]%%%}+%%%{%%{[%%%{1600,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,3,4,5]%%%}+%%%{%%{[%%%{-608,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,2,4,7]%%%}+%%%{%%{[%%%{112,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,1,4,9]%%%}+%%%{%%{[-8,0]:[1,0,%%%{-1,[1]%%%}]%%},[1,0,4,11]%%%}+%%%{%%%{256,[6]%%%},[0,6,4,0]%%%}+%%%{%%%{-640,[5]%%%},[0,5,4,2]%%%}+%%%{%%%{656,[4]%%%},[0,4,4,4]%%%}+%%%{%%%{-352,[3]%%%},[0,3,4,6]%%%}+%%%{%%%{104,[2]%%%},[0,2,4,8]%%%}+%%%{%%%{-16,[1]%%%},[0,1,4,10]%%%}+%%%{1,[0,0,4,12]%%%} / %%%{%%%{16,[6]%%%},[8,0,0,0]%%%}+%%%{%%{poly1[%%%{-64,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,0,0,1]%%%}+%%%{%%%{-64,[6]%%%},[6,1,0,0]%%%}+%%%{%%%{128,[5]%%%},[6,0,0,2]%%%}+%%%{%%{[%%%{192,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,1,0,1]%%%}+%%%{%%{poly1[%%%{-160,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,0,0,3]%%%}+%%%{%%%{96,[6]%%%},[4,2,0,0]%%%}+%%%{%%%{-288,[5]%%%},[4,1,0,2]%%%}+%%%{%%%{136,[4]%%%},[4,0,0,4]%%%}+%%%{%%{poly1[%%%{-192,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,2,0,1]%%%}+%%%{%%{[%%%{256,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,1,0,3]%%%}+%%%{%%{poly1[%%%{-80,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,0,0,5]%%%}+%%%{%%%{-64,[6]%%%},[2,3,0,0]%%%}+%%%{%%%{192,[5]%%%},[2,2,0,2]%%%}+%%%{%%%{-144,[4]%%%},[2,1,0,4]%%%}+%%%{%%%{32,[3]%%%},[2,0,0,6]%%%}+%%%{%%{[%%%{64,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,3,0,1]%%%}+%%%{%%{poly1[%%%{-96,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,2,0,3]%%%}+%%%{%%{[%%%{48,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,1,0,5]%%%}+%%%{%%{poly1[%%%{-8,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,0,0,7]%%%}+%%%{%%%{16,[6]%%%},[0,4,0,0]%%%}+%%%{%%%{-32,[5]%%%},[0,3,0,2]%%%}+%%%{%%%{24,[4]%%%},[0,2,0,4]%%%}+%%%{%%%{-8,[3]%%%},[0,1,0,6]%%%}+%%%{%%%{1,[2]%%%},[0,0,0,8]%%%} Error: Bad Argument Value","F(-2)",0
1250,1,528,0,0.313983," ","integrate((2*c*d*x+b*d)^6/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","-\frac{40 \, {\left(b^{2} c^{2} d^{6} - 4 \, a c^{3} d^{6}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{\sqrt{c}} + \frac{2 \, {\left(2 \, {\left(2 \, {\left(2 \, {\left(3 \, {\left(\frac{2 \, {\left(b^{4} c^{8} d^{6} - 8 \, a b^{2} c^{9} d^{6} + 16 \, a^{2} c^{10} d^{6}\right)} x}{b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}} + \frac{5 \, {\left(b^{5} c^{7} d^{6} - 8 \, a b^{3} c^{8} d^{6} + 16 \, a^{2} b c^{9} d^{6}\right)}}{b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}\right)} x + \frac{5 \, {\left(b^{6} c^{6} d^{6} - 48 \, a^{2} b^{2} c^{8} d^{6} + 128 \, a^{3} c^{9} d^{6}\right)}}{b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}\right)} x - \frac{15 \, {\left(b^{7} c^{5} d^{6} - 16 \, a b^{5} c^{6} d^{6} + 80 \, a^{2} b^{3} c^{7} d^{6} - 128 \, a^{3} b c^{8} d^{6}\right)}}{b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}\right)} x - \frac{15 \, {\left(b^{8} c^{4} d^{6} - 12 \, a b^{6} c^{5} d^{6} + 40 \, a^{2} b^{4} c^{6} d^{6} - 128 \, a^{4} c^{8} d^{6}\right)}}{b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}\right)} x - \frac{b^{9} c^{3} d^{6} + 12 \, a b^{7} c^{4} d^{6} - 264 \, a^{2} b^{5} c^{5} d^{6} + 1280 \, a^{3} b^{3} c^{6} d^{6} - 1920 \, a^{4} b c^{7} d^{6}}{b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}\right)}}{3 \, {\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}"," ",0,"-40*(b^2*c^2*d^6 - 4*a*c^3*d^6)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/sqrt(c) + 2/3*(2*(2*(2*(3*(2*(b^4*c^8*d^6 - 8*a*b^2*c^9*d^6 + 16*a^2*c^10*d^6)*x/(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5) + 5*(b^5*c^7*d^6 - 8*a*b^3*c^8*d^6 + 16*a^2*b*c^9*d^6)/(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5))*x + 5*(b^6*c^6*d^6 - 48*a^2*b^2*c^8*d^6 + 128*a^3*c^9*d^6)/(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5))*x - 15*(b^7*c^5*d^6 - 16*a*b^5*c^6*d^6 + 80*a^2*b^3*c^7*d^6 - 128*a^3*b*c^8*d^6)/(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5))*x - 15*(b^8*c^4*d^6 - 12*a*b^6*c^5*d^6 + 40*a^2*b^4*c^6*d^6 - 128*a^4*c^8*d^6)/(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5))*x - (b^9*c^3*d^6 + 12*a*b^7*c^4*d^6 - 264*a^2*b^5*c^5*d^6 + 1280*a^3*b^3*c^6*d^6 - 1920*a^4*b*c^7*d^6)/(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5))/(c*x^2 + b*x + a)^(3/2)","B",0
1251,1,386,0,0.391291," ","integrate((2*c*d*x+b*d)^5/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\frac{2 \, {\left(24 \, {\left({\left(2 \, {\left(\frac{{\left(b^{4} c^{6} d^{5} - 8 \, a b^{2} c^{7} d^{5} + 16 \, a^{2} c^{8} d^{5}\right)} x}{b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}} + \frac{2 \, {\left(b^{5} c^{5} d^{5} - 8 \, a b^{3} c^{6} d^{5} + 16 \, a^{2} b c^{7} d^{5}\right)}}{b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}}\right)} x + \frac{b^{6} c^{4} d^{5} - 48 \, a^{2} b^{2} c^{6} d^{5} + 128 \, a^{3} c^{7} d^{5}}{b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}}\right)} x - \frac{b^{7} c^{3} d^{5} - 16 \, a b^{5} c^{4} d^{5} + 80 \, a^{2} b^{3} c^{5} d^{5} - 128 \, a^{3} b c^{6} d^{5}}{b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}}\right)} x - \frac{b^{8} c^{2} d^{5} + 8 \, a b^{6} c^{3} d^{5} - 240 \, a^{2} b^{4} c^{4} d^{5} + 1280 \, a^{3} b^{2} c^{5} d^{5} - 2048 \, a^{4} c^{6} d^{5}}{b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}}\right)}}{3 \, {\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}"," ",0,"2/3*(24*((2*((b^4*c^6*d^5 - 8*a*b^2*c^7*d^5 + 16*a^2*c^8*d^5)*x/(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4) + 2*(b^5*c^5*d^5 - 8*a*b^3*c^6*d^5 + 16*a^2*b*c^7*d^5)/(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4))*x + (b^6*c^4*d^5 - 48*a^2*b^2*c^6*d^5 + 128*a^3*c^7*d^5)/(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4))*x - (b^7*c^3*d^5 - 16*a*b^5*c^4*d^5 + 80*a^2*b^3*c^5*d^5 - 128*a^3*b*c^6*d^5)/(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4))*x - (b^8*c^2*d^5 + 8*a*b^6*c^3*d^5 - 240*a^2*b^4*c^4*d^5 + 1280*a^3*b^2*c^5*d^5 - 2048*a^4*c^6*d^5)/(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4))/(c*x^2 + b*x + a)^(3/2)","B",0
1252,1,315,0,0.305780," ","integrate((2*c*d*x+b*d)^4/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","-16 \, c^{\frac{3}{2}} d^{4} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right) - \frac{2 \, {\left(2 \, {\left(8 \, {\left(\frac{2 \, {\left(b^{4} c^{3} d^{4} - 8 \, a b^{2} c^{4} d^{4} + 16 \, a^{2} c^{5} d^{4}\right)} x}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}} + \frac{3 \, {\left(b^{5} c^{2} d^{4} - 8 \, a b^{3} c^{3} d^{4} + 16 \, a^{2} b c^{4} d^{4}\right)}}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}}\right)} x + \frac{3 \, {\left(3 \, b^{6} c d^{4} - 20 \, a b^{4} c^{2} d^{4} + 16 \, a^{2} b^{2} c^{3} d^{4} + 64 \, a^{3} c^{4} d^{4}\right)}}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}}\right)} x + \frac{b^{7} d^{4} + 4 \, a b^{5} c d^{4} - 80 \, a^{2} b^{3} c^{2} d^{4} + 192 \, a^{3} b c^{3} d^{4}}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}}\right)}}{3 \, {\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}"," ",0,"-16*c^(3/2)*d^4*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b)) - 2/3*(2*(8*(2*(b^4*c^3*d^4 - 8*a*b^2*c^4*d^4 + 16*a^2*c^5*d^4)*x/(b^4 - 8*a*b^2*c + 16*a^2*c^2) + 3*(b^5*c^2*d^4 - 8*a*b^3*c^3*d^4 + 16*a^2*b*c^4*d^4)/(b^4 - 8*a*b^2*c + 16*a^2*c^2))*x + 3*(3*b^6*c*d^4 - 20*a*b^4*c^2*d^4 + 16*a^2*b^2*c^3*d^4 + 64*a^3*c^4*d^4)/(b^4 - 8*a*b^2*c + 16*a^2*c^2))*x + (b^7*d^4 + 4*a*b^5*c*d^4 - 80*a^2*b^3*c^2*d^4 + 192*a^3*b*c^3*d^4)/(b^4 - 8*a*b^2*c + 16*a^2*c^2))/(c*x^2 + b*x + a)^(3/2)","B",0
1253,1,74,0,0.222827," ","integrate((2*c*d*x+b*d)^3/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","-\frac{2 \, {\left(b^{2} d^{3} - 4 \, a c d^{3} + 12 \, {\left(c d x^{2} + b d x + a d\right)} c d^{2}\right)} d}{3 \, {\left(c d x^{2} + b d x + a d\right)} \sqrt{\frac{c d x^{2} + b d x + a d}{d}}}"," ",0,"-2/3*(b^2*d^3 - 4*a*c*d^3 + 12*(c*d*x^2 + b*d*x + a*d)*c*d^2)*d/((c*d*x^2 + b*d*x + a*d)*sqrt((c*d*x^2 + b*d*x + a*d)/d))","A",0
1254,1,195,0,0.268600," ","integrate((2*c*d*x+b*d)^2/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","-\frac{2 \, {\left(2 \, {\left(2 \, {\left(\frac{2 \, {\left(b^{2} c^{3} d^{2} - 4 \, a c^{4} d^{2}\right)} x}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}} + \frac{3 \, {\left(b^{3} c^{2} d^{2} - 4 \, a b c^{3} d^{2}\right)}}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}}\right)} x + \frac{3 \, {\left(b^{4} c d^{2} - 4 \, a b^{2} c^{2} d^{2}\right)}}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}}\right)} x + \frac{b^{5} d^{2} - 4 \, a b^{3} c d^{2}}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}}\right)}}{3 \, {\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}"," ",0,"-2/3*(2*(2*(2*(b^2*c^3*d^2 - 4*a*c^4*d^2)*x/(b^4 - 8*a*b^2*c + 16*a^2*c^2) + 3*(b^3*c^2*d^2 - 4*a*b*c^3*d^2)/(b^4 - 8*a*b^2*c + 16*a^2*c^2))*x + 3*(b^4*c*d^2 - 4*a*b^2*c^2*d^2)/(b^4 - 8*a*b^2*c + 16*a^2*c^2))*x + (b^5*d^2 - 4*a*b^3*c*d^2)/(b^4 - 8*a*b^2*c + 16*a^2*c^2))/(c*x^2 + b*x + a)^(3/2)","B",0
1255,1,41,0,0.198057," ","integrate((2*c*d*x+b*d)/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","-\frac{2 \, d^{2}}{3 \, {\left(c d x^{2} + b d x + a d\right)} \sqrt{\frac{c d x^{2} + b d x + a d}{d}}}"," ",0,"-2/3*d^2/((c*d*x^2 + b*d*x + a*d)*sqrt((c*d*x^2 + b*d*x + a*d)/d))","B",0
1256,1,906,0,0.304906," ","integrate(1/(2*c*d*x+b*d)/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\frac{32 \, c^{2} \arctan\left(-\frac{2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} c + b \sqrt{c}}{\sqrt{b^{2} c - 4 \, a c^{2}}}\right)}{{\left(b^{4} d - 8 \, a b^{2} c d + 16 \, a^{2} c^{2} d\right)} \sqrt{b^{2} c - 4 \, a c^{2}}} + \frac{2 \, {\left(12 \, {\left(\frac{{\left(b^{16} c^{2} d^{3} - 32 \, a b^{14} c^{3} d^{3} + 448 \, a^{2} b^{12} c^{4} d^{3} - 3584 \, a^{3} b^{10} c^{5} d^{3} + 17920 \, a^{4} b^{8} c^{6} d^{3} - 57344 \, a^{5} b^{6} c^{7} d^{3} + 114688 \, a^{6} b^{4} c^{8} d^{3} - 131072 \, a^{7} b^{2} c^{9} d^{3} + 65536 \, a^{8} c^{10} d^{3}\right)} x}{b^{20} d^{4} - 40 \, a b^{18} c d^{4} + 720 \, a^{2} b^{16} c^{2} d^{4} - 7680 \, a^{3} b^{14} c^{3} d^{4} + 53760 \, a^{4} b^{12} c^{4} d^{4} - 258048 \, a^{5} b^{10} c^{5} d^{4} + 860160 \, a^{6} b^{8} c^{6} d^{4} - 1966080 \, a^{7} b^{6} c^{7} d^{4} + 2949120 \, a^{8} b^{4} c^{8} d^{4} - 2621440 \, a^{9} b^{2} c^{9} d^{4} + 1048576 \, a^{10} c^{10} d^{4}} + \frac{b^{17} c d^{3} - 32 \, a b^{15} c^{2} d^{3} + 448 \, a^{2} b^{13} c^{3} d^{3} - 3584 \, a^{3} b^{11} c^{4} d^{3} + 17920 \, a^{4} b^{9} c^{5} d^{3} - 57344 \, a^{5} b^{7} c^{6} d^{3} + 114688 \, a^{6} b^{5} c^{7} d^{3} - 131072 \, a^{7} b^{3} c^{8} d^{3} + 65536 \, a^{8} b c^{9} d^{3}}{b^{20} d^{4} - 40 \, a b^{18} c d^{4} + 720 \, a^{2} b^{16} c^{2} d^{4} - 7680 \, a^{3} b^{14} c^{3} d^{4} + 53760 \, a^{4} b^{12} c^{4} d^{4} - 258048 \, a^{5} b^{10} c^{5} d^{4} + 860160 \, a^{6} b^{8} c^{6} d^{4} - 1966080 \, a^{7} b^{6} c^{7} d^{4} + 2949120 \, a^{8} b^{4} c^{8} d^{4} - 2621440 \, a^{9} b^{2} c^{9} d^{4} + 1048576 \, a^{10} c^{10} d^{4}}\right)} x - \frac{b^{18} d^{3} - 48 \, a b^{16} c d^{3} + 960 \, a^{2} b^{14} c^{2} d^{3} - 10752 \, a^{3} b^{12} c^{3} d^{3} + 75264 \, a^{4} b^{10} c^{4} d^{3} - 344064 \, a^{5} b^{8} c^{5} d^{3} + 1032192 \, a^{6} b^{6} c^{6} d^{3} - 1966080 \, a^{7} b^{4} c^{7} d^{3} + 2162688 \, a^{8} b^{2} c^{8} d^{3} - 1048576 \, a^{9} c^{9} d^{3}}{b^{20} d^{4} - 40 \, a b^{18} c d^{4} + 720 \, a^{2} b^{16} c^{2} d^{4} - 7680 \, a^{3} b^{14} c^{3} d^{4} + 53760 \, a^{4} b^{12} c^{4} d^{4} - 258048 \, a^{5} b^{10} c^{5} d^{4} + 860160 \, a^{6} b^{8} c^{6} d^{4} - 1966080 \, a^{7} b^{6} c^{7} d^{4} + 2949120 \, a^{8} b^{4} c^{8} d^{4} - 2621440 \, a^{9} b^{2} c^{9} d^{4} + 1048576 \, a^{10} c^{10} d^{4}}\right)}}{3 \, {\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}"," ",0,"32*c^2*arctan(-(2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*c + b*sqrt(c))/sqrt(b^2*c - 4*a*c^2))/((b^4*d - 8*a*b^2*c*d + 16*a^2*c^2*d)*sqrt(b^2*c - 4*a*c^2)) + 2/3*(12*((b^16*c^2*d^3 - 32*a*b^14*c^3*d^3 + 448*a^2*b^12*c^4*d^3 - 3584*a^3*b^10*c^5*d^3 + 17920*a^4*b^8*c^6*d^3 - 57344*a^5*b^6*c^7*d^3 + 114688*a^6*b^4*c^8*d^3 - 131072*a^7*b^2*c^9*d^3 + 65536*a^8*c^10*d^3)*x/(b^20*d^4 - 40*a*b^18*c*d^4 + 720*a^2*b^16*c^2*d^4 - 7680*a^3*b^14*c^3*d^4 + 53760*a^4*b^12*c^4*d^4 - 258048*a^5*b^10*c^5*d^4 + 860160*a^6*b^8*c^6*d^4 - 1966080*a^7*b^6*c^7*d^4 + 2949120*a^8*b^4*c^8*d^4 - 2621440*a^9*b^2*c^9*d^4 + 1048576*a^10*c^10*d^4) + (b^17*c*d^3 - 32*a*b^15*c^2*d^3 + 448*a^2*b^13*c^3*d^3 - 3584*a^3*b^11*c^4*d^3 + 17920*a^4*b^9*c^5*d^3 - 57344*a^5*b^7*c^6*d^3 + 114688*a^6*b^5*c^7*d^3 - 131072*a^7*b^3*c^8*d^3 + 65536*a^8*b*c^9*d^3)/(b^20*d^4 - 40*a*b^18*c*d^4 + 720*a^2*b^16*c^2*d^4 - 7680*a^3*b^14*c^3*d^4 + 53760*a^4*b^12*c^4*d^4 - 258048*a^5*b^10*c^5*d^4 + 860160*a^6*b^8*c^6*d^4 - 1966080*a^7*b^6*c^7*d^4 + 2949120*a^8*b^4*c^8*d^4 - 2621440*a^9*b^2*c^9*d^4 + 1048576*a^10*c^10*d^4))*x - (b^18*d^3 - 48*a*b^16*c*d^3 + 960*a^2*b^14*c^2*d^3 - 10752*a^3*b^12*c^3*d^3 + 75264*a^4*b^10*c^4*d^3 - 344064*a^5*b^8*c^5*d^3 + 1032192*a^6*b^6*c^6*d^3 - 1966080*a^7*b^4*c^7*d^3 + 2162688*a^8*b^2*c^8*d^3 - 1048576*a^9*c^9*d^3)/(b^20*d^4 - 40*a*b^18*c*d^4 + 720*a^2*b^16*c^2*d^4 - 7680*a^3*b^14*c^3*d^4 + 53760*a^4*b^12*c^4*d^4 - 258048*a^5*b^10*c^5*d^4 + 860160*a^6*b^8*c^6*d^4 - 1966080*a^7*b^6*c^7*d^4 + 2949120*a^8*b^4*c^8*d^4 - 2621440*a^9*b^2*c^9*d^4 + 1048576*a^10*c^10*d^4))/(c*x^2 + b*x + a)^(3/2)","B",0
1257,1,374,0,0.604030," ","integrate(1/(2*c*d*x+b*d)^2/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\frac{16 \, {\left(\frac{{\left(\frac{3 \, \sqrt{-\frac{b^{2} c d^{2}}{{\left(2 \, c d x + b d\right)}^{2}} + \frac{4 \, a c^{2} d^{2}}{{\left(2 \, c d x + b d\right)}^{2}} + c} c^{2}}{b^{2} \mathrm{sgn}\left(\frac{1}{2 \, c d x + b d}\right) \mathrm{sgn}\left(c\right) \mathrm{sgn}\left(d\right) - 4 \, a c \mathrm{sgn}\left(\frac{1}{2 \, c d x + b d}\right) \mathrm{sgn}\left(c\right) \mathrm{sgn}\left(d\right)} + \frac{6 \, {\left(\frac{b^{2} c d^{2}}{{\left(2 \, c d x + b d\right)}^{2}} - \frac{4 \, a c^{2} d^{2}}{{\left(2 \, c d x + b d\right)}^{2}} - c\right)} c^{3} + c^{4}}{{\left(b^{2} \mathrm{sgn}\left(\frac{1}{2 \, c d x + b d}\right) \mathrm{sgn}\left(c\right) \mathrm{sgn}\left(d\right) - 4 \, a c \mathrm{sgn}\left(\frac{1}{2 \, c d x + b d}\right) \mathrm{sgn}\left(c\right) \mathrm{sgn}\left(d\right)\right)} {\left(\frac{b^{2} c d^{2}}{{\left(2 \, c d x + b d\right)}^{2}} - \frac{4 \, a c^{2} d^{2}}{{\left(2 \, c d x + b d\right)}^{2}} - c\right)} \sqrt{-\frac{b^{2} c d^{2}}{{\left(2 \, c d x + b d\right)}^{2}} + \frac{4 \, a c^{2} d^{2}}{{\left(2 \, c d x + b d\right)}^{2}} + c}}\right)} c^{5} d^{8} {\left| c \right|}}{{\left(b^{2} c^{3} d^{4} - 4 \, a c^{4} d^{4}\right)}^{2}} - \frac{8 \, c^{\frac{3}{2}} {\left| c \right|} \mathrm{sgn}\left(\frac{1}{2 \, c d x + b d}\right) \mathrm{sgn}\left(c\right) \mathrm{sgn}\left(d\right)}{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}}\right)}}{3 \, d^{2} {\left| c \right|}}"," ",0,"16/3*((3*sqrt(-b^2*c*d^2/(2*c*d*x + b*d)^2 + 4*a*c^2*d^2/(2*c*d*x + b*d)^2 + c)*c^2/(b^2*sgn(1/(2*c*d*x + b*d))*sgn(c)*sgn(d) - 4*a*c*sgn(1/(2*c*d*x + b*d))*sgn(c)*sgn(d)) + (6*(b^2*c*d^2/(2*c*d*x + b*d)^2 - 4*a*c^2*d^2/(2*c*d*x + b*d)^2 - c)*c^3 + c^4)/((b^2*sgn(1/(2*c*d*x + b*d))*sgn(c)*sgn(d) - 4*a*c*sgn(1/(2*c*d*x + b*d))*sgn(c)*sgn(d))*(b^2*c*d^2/(2*c*d*x + b*d)^2 - 4*a*c^2*d^2/(2*c*d*x + b*d)^2 - c)*sqrt(-b^2*c*d^2/(2*c*d*x + b*d)^2 + 4*a*c^2*d^2/(2*c*d*x + b*d)^2 + c)))*c^5*d^8*abs(c)/(b^2*c^3*d^4 - 4*a*c^4*d^4)^2 - 8*c^(3/2)*abs(c)*sgn(1/(2*c*d*x + b*d))*sgn(c)*sgn(d)/(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3))/(d^2*abs(c))","B",0
1258,-2,0,0,0.000000," ","integrate(1/(2*c*d*x+b*d)^3/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 0.41Unable to divide, perhaps due to rounding error%%%{%%%{512,[6]%%%},[6,3,3,0]%%%}+%%%{%%%{-384,[5]%%%},[6,2,3,2]%%%}+%%%{%%%{96,[4]%%%},[6,1,3,4]%%%}+%%%{%%%{-8,[3]%%%},[6,0,3,6]%%%}+%%%{%%{[%%%{-1536,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,3,3,1]%%%}+%%%{%%{[%%%{1152,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,2,3,3]%%%}+%%%{%%{[%%%{-288,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,1,3,5]%%%}+%%%{%%{[%%%{24,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,0,3,7]%%%}+%%%{%%%{-1536,[6]%%%},[4,4,3,0]%%%}+%%%{%%%{3456,[5]%%%},[4,3,3,2]%%%}+%%%{%%%{-2016,[4]%%%},[4,2,3,4]%%%}+%%%{%%%{456,[3]%%%},[4,1,3,6]%%%}+%%%{%%%{-36,[2]%%%},[4,0,3,8]%%%}+%%%{%%{[%%%{3072,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,4,3,1]%%%}+%%%{%%{[%%%{-4352,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,3,3,3]%%%}+%%%{%%{[%%%{2112,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,2,3,5]%%%}+%%%{%%{[%%%{-432,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,1,3,7]%%%}+%%%{%%{[%%%{32,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,0,3,9]%%%}+%%%{%%%{1536,[6]%%%},[2,5,3,0]%%%}+%%%{%%%{-4224,[5]%%%},[2,4,3,2]%%%}+%%%{%%%{3744,[4]%%%},[2,3,3,4]%%%}+%%%{%%%{-1464,[3]%%%},[2,2,3,6]%%%}+%%%{%%%{264,[2]%%%},[2,1,3,8]%%%}+%%%{%%%{-18,[1]%%%},[2,0,3,10]%%%}+%%%{%%{[%%%{-1536,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,5,3,1]%%%}+%%%{%%{[%%%{2688,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,4,3,3]%%%}+%%%{%%{[%%%{-1824,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,3,3,5]%%%}+%%%{%%{[%%%{600,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,2,3,7]%%%}+%%%{%%{[%%%{-96,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,1,3,9]%%%}+%%%{%%{[6,0]:[1,0,%%%{-1,[1]%%%}]%%},[1,0,3,11]%%%}+%%%{%%%{-512,[6]%%%},[0,6,3,0]%%%}+%%%{%%%{1152,[5]%%%},[0,5,3,2]%%%}+%%%{%%%{-1056,[4]%%%},[0,4,3,4]%%%}+%%%{%%%{504,[3]%%%},[0,3,3,6]%%%}+%%%{%%%{-132,[2]%%%},[0,2,3,8]%%%}+%%%{%%%{18,[1]%%%},[0,1,3,10]%%%}+%%%{-1,[0,0,3,12]%%%} / %%%{%%{poly1[%%%{-8,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[6,0,0,0]%%%}+%%%{%%%{24,[4]%%%},[5,0,0,1]%%%}+%%%{%%{[%%%{24,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,1,0,0]%%%}+%%%{%%{poly1[%%%{-36,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,0,2]%%%}+%%%{%%%{-48,[4]%%%},[3,1,0,1]%%%}+%%%{%%%{32,[3]%%%},[3,0,0,3]%%%}+%%%{%%{[%%%{-24,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,2,0,0]%%%}+%%%{%%{[%%%{48,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,1,0,2]%%%}+%%%{%%{poly1[%%%{-18,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,0,4]%%%}+%%%{%%%{24,[4]%%%},[1,2,0,1]%%%}+%%%{%%%{-24,[3]%%%},[1,1,0,3]%%%}+%%%{%%%{6,[2]%%%},[1,0,0,5]%%%}+%%%{%%{[%%%{8,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,3,0,0]%%%}+%%%{%%{[%%%{-12,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,2,0,2]%%%}+%%%{%%{[%%%{6,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,1,0,4]%%%}+%%%{%%{poly1[%%%{-1,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,0,6]%%%} Error: Bad Argument Value","F(-2)",0
1259,-2,0,0,0.000000," ","integrate(1/(2*c*d*x+b*d)^4/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{%%%{1024,[7]%%%},[8,3,4,0]%%%}+%%%{%%%{-768,[6]%%%},[8,2,4,2]%%%}+%%%{%%%{192,[5]%%%},[8,1,4,4]%%%}+%%%{%%%{-16,[4]%%%},[8,0,4,6]%%%}+%%%{%%{[%%%{-4096,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,3,4,1]%%%}+%%%{%%{[%%%{3072,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,2,4,3]%%%}+%%%{%%{[%%%{-768,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,1,4,5]%%%}+%%%{%%{[%%%{64,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,0,4,7]%%%}+%%%{%%%{-4096,[7]%%%},[6,4,4,0]%%%}+%%%{%%%{11264,[6]%%%},[6,3,4,2]%%%}+%%%{%%%{-6912,[5]%%%},[6,2,4,4]%%%}+%%%{%%%{1600,[4]%%%},[6,1,4,6]%%%}+%%%{%%%{-128,[3]%%%},[6,0,4,8]%%%}+%%%{%%{[%%%{12288,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,4,4,1]%%%}+%%%{%%{[%%%{-19456,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,3,4,3]%%%}+%%%{%%{[%%%{9984,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,2,4,5]%%%}+%%%{%%{[%%%{-2112,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,1,4,7]%%%}+%%%{%%{[%%%{160,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,0,4,9]%%%}+%%%{%%%{6144,[7]%%%},[4,5,4,0]%%%}+%%%{%%%{-23040,[6]%%%},[4,4,4,2]%%%}+%%%{%%%{23680,[5]%%%},[4,3,4,4]%%%}+%%%{%%%{-10080,[4]%%%},[4,2,4,6]%%%}+%%%{%%%{1920,[3]%%%},[4,1,4,8]%%%}+%%%{%%%{-136,[2]%%%},[4,0,4,10]%%%}+%%%{%%{[%%%{-12288,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,5,4,1]%%%}+%%%{%%{[%%%{25600,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,4,4,3]%%%}+%%%{%%{[%%%{-19712,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,3,4,5]%%%}+%%%{%%{[%%%{7104,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,2,4,7]%%%}+%%%{%%{[%%%{-1216,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,1,4,9]%%%}+%%%{%%{[%%%{80,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,0,4,11]%%%}+%%%{%%%{-4096,[7]%%%},[2,6,4,0]%%%}+%%%{%%%{15360,[6]%%%},[2,5,4,2]%%%}+%%%{%%%{-19200,[5]%%%},[2,4,4,4]%%%}+%%%{%%%{11328,[4]%%%},[2,3,4,6]%%%}+%%%{%%%{-3456,[3]%%%},[2,2,4,8]%%%}+%%%{%%%{528,[2]%%%},[2,1,4,10]%%%}+%%%{%%%{-32,[1]%%%},[2,0,4,12]%%%}+%%%{%%{[%%%{4096,[6]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,6,4,1]%%%}+%%%{%%{[%%%{-9216,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,5,4,3]%%%}+%%%{%%{[%%%{8448,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,4,4,5]%%%}+%%%{%%{[%%%{-4032,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,3,4,7]%%%}+%%%{%%{[%%%{1056,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,2,4,9]%%%}+%%%{%%{[%%%{-144,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,1,4,11]%%%}+%%%{%%{[8,0]:[1,0,%%%{-1,[1]%%%}]%%},[1,0,4,13]%%%}+%%%{%%%{1024,[7]%%%},[0,7,4,0]%%%}+%%%{%%%{-2816,[6]%%%},[0,6,4,2]%%%}+%%%{%%%{3264,[5]%%%},[0,5,4,4]%%%}+%%%{%%%{-2064,[4]%%%},[0,4,4,6]%%%}+%%%{%%%{768,[3]%%%},[0,3,4,8]%%%}+%%%{%%%{-168,[2]%%%},[0,2,4,10]%%%}+%%%{%%%{20,[1]%%%},[0,1,4,12]%%%}+%%%{-1,[0,0,4,14]%%%} / %%%{%%%{16,[6]%%%},[8,0,0,0]%%%}+%%%{%%{poly1[%%%{-64,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,0,0,1]%%%}+%%%{%%%{-64,[6]%%%},[6,1,0,0]%%%}+%%%{%%%{128,[5]%%%},[6,0,0,2]%%%}+%%%{%%{[%%%{192,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,1,0,1]%%%}+%%%{%%{poly1[%%%{-160,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,0,0,3]%%%}+%%%{%%%{96,[6]%%%},[4,2,0,0]%%%}+%%%{%%%{-288,[5]%%%},[4,1,0,2]%%%}+%%%{%%%{136,[4]%%%},[4,0,0,4]%%%}+%%%{%%{poly1[%%%{-192,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,2,0,1]%%%}+%%%{%%{[%%%{256,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,1,0,3]%%%}+%%%{%%{poly1[%%%{-80,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,0,0,5]%%%}+%%%{%%%{-64,[6]%%%},[2,3,0,0]%%%}+%%%{%%%{192,[5]%%%},[2,2,0,2]%%%}+%%%{%%%{-144,[4]%%%},[2,1,0,4]%%%}+%%%{%%%{32,[3]%%%},[2,0,0,6]%%%}+%%%{%%{[%%%{64,[5]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,3,0,1]%%%}+%%%{%%{poly1[%%%{-96,[4]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,2,0,3]%%%}+%%%{%%{[%%%{48,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,1,0,5]%%%}+%%%{%%{poly1[%%%{-8,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,0,0,7]%%%}+%%%{%%%{16,[6]%%%},[0,4,0,0]%%%}+%%%{%%%{-32,[5]%%%},[0,3,0,2]%%%}+%%%{%%%{24,[4]%%%},[0,2,0,4]%%%}+%%%{%%%{-8,[3]%%%},[0,1,0,6]%%%}+%%%{%%%{1,[2]%%%},[0,0,0,8]%%%} Error: Bad Argument Value","F(-2)",0
1260,1,89,0,0.331657," ","integrate(1/(b*x+a)/(b^2*x^2+2*a*b*x+a^2+1)^(1/2),x, algorithm=""giac"")","\frac{\log\left(\frac{{\left| -2 \, {\left(x {\left| b \right|} - \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)} b - 2 \, a {\left| b \right|} - 2 \, {\left| b \right|} \right|}}{{\left| -2 \, {\left(x {\left| b \right|} - \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)} b - 2 \, a {\left| b \right|} + 2 \, {\left| b \right|} \right|}}\right)}{{\left| b \right|}}"," ",0,"log(abs(-2*(x*abs(b) - sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))*b - 2*a*abs(b) - 2*abs(b))/abs(-2*(x*abs(b) - sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1))*b - 2*a*abs(b) + 2*abs(b)))/abs(b)","B",0
1261,1,567,0,0.188345," ","integrate((2*c*d*x+b*d)^(5/2)*(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{13860 \, \sqrt{2 \, c d x + b d} a b^{3} d^{2} - 13860 \, {\left(3 \, \sqrt{2 \, c d x + b d} b d - {\left(2 \, c d x + b d\right)}^{\frac{3}{2}}\right)} a b^{2} d - \frac{2310 \, {\left(3 \, \sqrt{2 \, c d x + b d} b d - {\left(2 \, c d x + b d\right)}^{\frac{3}{2}}\right)} b^{4} d}{c} + 2772 \, {\left(15 \, \sqrt{2 \, c d x + b d} b^{2} d^{2} - 10 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b d + 3 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}}\right)} a b + \frac{1617 \, {\left(15 \, \sqrt{2 \, c d x + b d} b^{2} d^{2} - 10 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b d + 3 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}}\right)} b^{3}}{c} - \frac{396 \, {\left(35 \, \sqrt{2 \, c d x + b d} b^{3} d^{3} - 35 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b^{2} d^{2} + 21 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}} b d - 5 \, {\left(2 \, c d x + b d\right)}^{\frac{7}{2}}\right)} a}{d} - \frac{891 \, {\left(35 \, \sqrt{2 \, c d x + b d} b^{3} d^{3} - 35 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b^{2} d^{2} + 21 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}} b d - 5 \, {\left(2 \, c d x + b d\right)}^{\frac{7}{2}}\right)} b^{2}}{c d} + \frac{55 \, {\left(315 \, \sqrt{2 \, c d x + b d} b^{4} d^{4} - 420 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b^{3} d^{3} + 378 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}} b^{2} d^{2} - 180 \, {\left(2 \, c d x + b d\right)}^{\frac{7}{2}} b d + 35 \, {\left(2 \, c d x + b d\right)}^{\frac{9}{2}}\right)} b}{c d^{2}} - \frac{5 \, {\left(693 \, \sqrt{2 \, c d x + b d} b^{5} d^{5} - 1155 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b^{4} d^{4} + 1386 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}} b^{3} d^{3} - 990 \, {\left(2 \, c d x + b d\right)}^{\frac{7}{2}} b^{2} d^{2} + 385 \, {\left(2 \, c d x + b d\right)}^{\frac{9}{2}} b d - 63 \, {\left(2 \, c d x + b d\right)}^{\frac{11}{2}}\right)}}{c d^{3}}}{13860 \, c}"," ",0,"1/13860*(13860*sqrt(2*c*d*x + b*d)*a*b^3*d^2 - 13860*(3*sqrt(2*c*d*x + b*d)*b*d - (2*c*d*x + b*d)^(3/2))*a*b^2*d - 2310*(3*sqrt(2*c*d*x + b*d)*b*d - (2*c*d*x + b*d)^(3/2))*b^4*d/c + 2772*(15*sqrt(2*c*d*x + b*d)*b^2*d^2 - 10*(2*c*d*x + b*d)^(3/2)*b*d + 3*(2*c*d*x + b*d)^(5/2))*a*b + 1617*(15*sqrt(2*c*d*x + b*d)*b^2*d^2 - 10*(2*c*d*x + b*d)^(3/2)*b*d + 3*(2*c*d*x + b*d)^(5/2))*b^3/c - 396*(35*sqrt(2*c*d*x + b*d)*b^3*d^3 - 35*(2*c*d*x + b*d)^(3/2)*b^2*d^2 + 21*(2*c*d*x + b*d)^(5/2)*b*d - 5*(2*c*d*x + b*d)^(7/2))*a/d - 891*(35*sqrt(2*c*d*x + b*d)*b^3*d^3 - 35*(2*c*d*x + b*d)^(3/2)*b^2*d^2 + 21*(2*c*d*x + b*d)^(5/2)*b*d - 5*(2*c*d*x + b*d)^(7/2))*b^2/(c*d) + 55*(315*sqrt(2*c*d*x + b*d)*b^4*d^4 - 420*(2*c*d*x + b*d)^(3/2)*b^3*d^3 + 378*(2*c*d*x + b*d)^(5/2)*b^2*d^2 - 180*(2*c*d*x + b*d)^(7/2)*b*d + 35*(2*c*d*x + b*d)^(9/2))*b/(c*d^2) - 5*(693*sqrt(2*c*d*x + b*d)*b^5*d^5 - 1155*(2*c*d*x + b*d)^(3/2)*b^4*d^4 + 1386*(2*c*d*x + b*d)^(5/2)*b^3*d^3 - 990*(2*c*d*x + b*d)^(7/2)*b^2*d^2 + 385*(2*c*d*x + b*d)^(9/2)*b*d - 63*(2*c*d*x + b*d)^(11/2))/(c*d^3))/c","B",0
1262,1,376,0,0.177873," ","integrate((2*c*d*x+b*d)^(3/2)*(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{1260 \, \sqrt{2 \, c d x + b d} a b^{2} d - 840 \, {\left(3 \, \sqrt{2 \, c d x + b d} b d - {\left(2 \, c d x + b d\right)}^{\frac{3}{2}}\right)} a b - \frac{210 \, {\left(3 \, \sqrt{2 \, c d x + b d} b d - {\left(2 \, c d x + b d\right)}^{\frac{3}{2}}\right)} b^{3}}{c} + \frac{84 \, {\left(15 \, \sqrt{2 \, c d x + b d} b^{2} d^{2} - 10 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b d + 3 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}}\right)} a}{d} + \frac{105 \, {\left(15 \, \sqrt{2 \, c d x + b d} b^{2} d^{2} - 10 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b d + 3 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}}\right)} b^{2}}{c d} - \frac{36 \, {\left(35 \, \sqrt{2 \, c d x + b d} b^{3} d^{3} - 35 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b^{2} d^{2} + 21 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}} b d - 5 \, {\left(2 \, c d x + b d\right)}^{\frac{7}{2}}\right)} b}{c d^{2}} + \frac{315 \, \sqrt{2 \, c d x + b d} b^{4} d^{4} - 420 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b^{3} d^{3} + 378 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}} b^{2} d^{2} - 180 \, {\left(2 \, c d x + b d\right)}^{\frac{7}{2}} b d + 35 \, {\left(2 \, c d x + b d\right)}^{\frac{9}{2}}}{c d^{3}}}{1260 \, c}"," ",0,"1/1260*(1260*sqrt(2*c*d*x + b*d)*a*b^2*d - 840*(3*sqrt(2*c*d*x + b*d)*b*d - (2*c*d*x + b*d)^(3/2))*a*b - 210*(3*sqrt(2*c*d*x + b*d)*b*d - (2*c*d*x + b*d)^(3/2))*b^3/c + 84*(15*sqrt(2*c*d*x + b*d)*b^2*d^2 - 10*(2*c*d*x + b*d)^(3/2)*b*d + 3*(2*c*d*x + b*d)^(5/2))*a/d + 105*(15*sqrt(2*c*d*x + b*d)*b^2*d^2 - 10*(2*c*d*x + b*d)^(3/2)*b*d + 3*(2*c*d*x + b*d)^(5/2))*b^2/(c*d) - 36*(35*sqrt(2*c*d*x + b*d)*b^3*d^3 - 35*(2*c*d*x + b*d)^(3/2)*b^2*d^2 + 21*(2*c*d*x + b*d)^(5/2)*b*d - 5*(2*c*d*x + b*d)^(7/2))*b/(c*d^2) + (315*sqrt(2*c*d*x + b*d)*b^4*d^4 - 420*(2*c*d*x + b*d)^(3/2)*b^3*d^3 + 378*(2*c*d*x + b*d)^(5/2)*b^2*d^2 - 180*(2*c*d*x + b*d)^(7/2)*b*d + 35*(2*c*d*x + b*d)^(9/2))/(c*d^3))/c","B",0
1263,1,228,0,0.164498," ","integrate((2*c*d*x+b*d)^(1/2)*(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{420 \, \sqrt{2 \, c d x + b d} a b - \frac{140 \, {\left(3 \, \sqrt{2 \, c d x + b d} b d - {\left(2 \, c d x + b d\right)}^{\frac{3}{2}}\right)} a}{d} - \frac{70 \, {\left(3 \, \sqrt{2 \, c d x + b d} b d - {\left(2 \, c d x + b d\right)}^{\frac{3}{2}}\right)} b^{2}}{c d} + \frac{21 \, {\left(15 \, \sqrt{2 \, c d x + b d} b^{2} d^{2} - 10 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b d + 3 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}}\right)} b}{c d^{2}} - \frac{3 \, {\left(35 \, \sqrt{2 \, c d x + b d} b^{3} d^{3} - 35 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b^{2} d^{2} + 21 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}} b d - 5 \, {\left(2 \, c d x + b d\right)}^{\frac{7}{2}}\right)}}{c d^{3}}}{420 \, c}"," ",0,"1/420*(420*sqrt(2*c*d*x + b*d)*a*b - 140*(3*sqrt(2*c*d*x + b*d)*b*d - (2*c*d*x + b*d)^(3/2))*a/d - 70*(3*sqrt(2*c*d*x + b*d)*b*d - (2*c*d*x + b*d)^(3/2))*b^2/(c*d) + 21*(15*sqrt(2*c*d*x + b*d)*b^2*d^2 - 10*(2*c*d*x + b*d)^(3/2)*b*d + 3*(2*c*d*x + b*d)^(5/2))*b/(c*d^2) - 3*(35*sqrt(2*c*d*x + b*d)*b^3*d^3 - 35*(2*c*d*x + b*d)^(3/2)*b^2*d^2 + 21*(2*c*d*x + b*d)^(5/2)*b*d - 5*(2*c*d*x + b*d)^(7/2))/(c*d^3))/c","B",0
1264,1,116,0,0.204499," ","integrate((c*x^2+b*x+a)/(2*c*d*x+b*d)^(1/2),x, algorithm=""giac"")","\frac{60 \, \sqrt{2 \, c d x + b d} a - \frac{10 \, {\left(3 \, \sqrt{2 \, c d x + b d} b d - {\left(2 \, c d x + b d\right)}^{\frac{3}{2}}\right)} b}{c d} + \frac{15 \, \sqrt{2 \, c d x + b d} b^{2} d^{2} - 10 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b d + 3 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}}}{c d^{2}}}{60 \, c d}"," ",0,"1/60*(60*sqrt(2*c*d*x + b*d)*a - 10*(3*sqrt(2*c*d*x + b*d)*b*d - (2*c*d*x + b*d)^(3/2))*b/(c*d) + (15*sqrt(2*c*d*x + b*d)*b^2*d^2 - 10*(2*c*d*x + b*d)^(3/2)*b*d + 3*(2*c*d*x + b*d)^(5/2))/(c*d^2))/(c*d)","B",0
1265,1,47,0,0.223248," ","integrate((c*x^2+b*x+a)/(2*c*d*x+b*d)^(3/2),x, algorithm=""giac"")","\frac{b^{2} - 4 \, a c}{4 \, \sqrt{2 \, c d x + b d} c^{2} d} + \frac{{\left(2 \, c d x + b d\right)}^{\frac{3}{2}}}{12 \, c^{2} d^{3}}"," ",0,"1/4*(b^2 - 4*a*c)/(sqrt(2*c*d*x + b*d)*c^2*d) + 1/12*(2*c*d*x + b*d)^(3/2)/(c^2*d^3)","A",0
1266,1,47,0,0.176562," ","integrate((c*x^2+b*x+a)/(2*c*d*x+b*d)^(5/2),x, algorithm=""giac"")","\frac{b^{2} - 4 \, a c}{12 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} c^{2} d} + \frac{\sqrt{2 \, c d x + b d}}{4 \, c^{2} d^{3}}"," ",0,"1/12*(b^2 - 4*a*c)/((2*c*d*x + b*d)^(3/2)*c^2*d) + 1/4*sqrt(2*c*d*x + b*d)/(c^2*d^3)","A",0
1267,1,47,0,0.178162," ","integrate((c*x^2+b*x+a)/(2*c*d*x+b*d)^(7/2),x, algorithm=""giac"")","\frac{b^{2} d^{2} - 4 \, a c d^{2} - 5 \, {\left(2 \, c d x + b d\right)}^{2}}{20 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}} c^{2} d^{3}}"," ",0,"1/20*(b^2*d^2 - 4*a*c*d^2 - 5*(2*c*d*x + b*d)^2)/((2*c*d*x + b*d)^(5/2)*c^2*d^3)","A",0
1268,1,48,0,0.201532," ","integrate((c*x^2+b*x+a)/(2*c*d*x+b*d)^(9/2),x, algorithm=""giac"")","\frac{3 \, b^{2} d^{2} - 12 \, a c d^{2} - 7 \, {\left(2 \, c d x + b d\right)}^{2}}{84 \, {\left(2 \, c d x + b d\right)}^{\frac{7}{2}} c^{2} d^{3}}"," ",0,"1/84*(3*b^2*d^2 - 12*a*c*d^2 - 7*(2*c*d*x + b*d)^2)/((2*c*d*x + b*d)^(7/2)*c^2*d^3)","A",0
1269,1,867,0,0.201617," ","integrate((2*c*d*x+b*d)^(3/2)*(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{720720 \, \sqrt{2 \, c d x + b d} a^{2} b^{2} d - 480480 \, {\left(3 \, \sqrt{2 \, c d x + b d} b d - {\left(2 \, c d x + b d\right)}^{\frac{3}{2}}\right)} a^{2} b - \frac{240240 \, {\left(3 \, \sqrt{2 \, c d x + b d} b d - {\left(2 \, c d x + b d\right)}^{\frac{3}{2}}\right)} a b^{3}}{c} + \frac{48048 \, {\left(15 \, \sqrt{2 \, c d x + b d} b^{2} d^{2} - 10 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b d + 3 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}}\right)} a^{2}}{d} + \frac{12012 \, {\left(15 \, \sqrt{2 \, c d x + b d} b^{2} d^{2} - 10 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b d + 3 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}}\right)} b^{4}}{c^{2} d} + \frac{120120 \, {\left(15 \, \sqrt{2 \, c d x + b d} b^{2} d^{2} - 10 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b d + 3 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}}\right)} a b^{2}}{c d} - \frac{15444 \, {\left(35 \, \sqrt{2 \, c d x + b d} b^{3} d^{3} - 35 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b^{2} d^{2} + 21 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}} b d - 5 \, {\left(2 \, c d x + b d\right)}^{\frac{7}{2}}\right)} b^{3}}{c^{2} d^{2}} - \frac{41184 \, {\left(35 \, \sqrt{2 \, c d x + b d} b^{3} d^{3} - 35 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b^{2} d^{2} + 21 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}} b d - 5 \, {\left(2 \, c d x + b d\right)}^{\frac{7}{2}}\right)} a b}{c d^{2}} + \frac{1859 \, {\left(315 \, \sqrt{2 \, c d x + b d} b^{4} d^{4} - 420 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b^{3} d^{3} + 378 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}} b^{2} d^{2} - 180 \, {\left(2 \, c d x + b d\right)}^{\frac{7}{2}} b d + 35 \, {\left(2 \, c d x + b d\right)}^{\frac{9}{2}}\right)} b^{2}}{c^{2} d^{3}} + \frac{1144 \, {\left(315 \, \sqrt{2 \, c d x + b d} b^{4} d^{4} - 420 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b^{3} d^{3} + 378 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}} b^{2} d^{2} - 180 \, {\left(2 \, c d x + b d\right)}^{\frac{7}{2}} b d + 35 \, {\left(2 \, c d x + b d\right)}^{\frac{9}{2}}\right)} a}{c d^{3}} - \frac{390 \, {\left(693 \, \sqrt{2 \, c d x + b d} b^{5} d^{5} - 1155 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b^{4} d^{4} + 1386 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}} b^{3} d^{3} - 990 \, {\left(2 \, c d x + b d\right)}^{\frac{7}{2}} b^{2} d^{2} + 385 \, {\left(2 \, c d x + b d\right)}^{\frac{9}{2}} b d - 63 \, {\left(2 \, c d x + b d\right)}^{\frac{11}{2}}\right)} b}{c^{2} d^{4}} + \frac{15 \, {\left(3003 \, \sqrt{2 \, c d x + b d} b^{6} d^{6} - 6006 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b^{5} d^{5} + 9009 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}} b^{4} d^{4} - 8580 \, {\left(2 \, c d x + b d\right)}^{\frac{7}{2}} b^{3} d^{3} + 5005 \, {\left(2 \, c d x + b d\right)}^{\frac{9}{2}} b^{2} d^{2} - 1638 \, {\left(2 \, c d x + b d\right)}^{\frac{11}{2}} b d + 231 \, {\left(2 \, c d x + b d\right)}^{\frac{13}{2}}\right)}}{c^{2} d^{5}}}{720720 \, c}"," ",0,"1/720720*(720720*sqrt(2*c*d*x + b*d)*a^2*b^2*d - 480480*(3*sqrt(2*c*d*x + b*d)*b*d - (2*c*d*x + b*d)^(3/2))*a^2*b - 240240*(3*sqrt(2*c*d*x + b*d)*b*d - (2*c*d*x + b*d)^(3/2))*a*b^3/c + 48048*(15*sqrt(2*c*d*x + b*d)*b^2*d^2 - 10*(2*c*d*x + b*d)^(3/2)*b*d + 3*(2*c*d*x + b*d)^(5/2))*a^2/d + 12012*(15*sqrt(2*c*d*x + b*d)*b^2*d^2 - 10*(2*c*d*x + b*d)^(3/2)*b*d + 3*(2*c*d*x + b*d)^(5/2))*b^4/(c^2*d) + 120120*(15*sqrt(2*c*d*x + b*d)*b^2*d^2 - 10*(2*c*d*x + b*d)^(3/2)*b*d + 3*(2*c*d*x + b*d)^(5/2))*a*b^2/(c*d) - 15444*(35*sqrt(2*c*d*x + b*d)*b^3*d^3 - 35*(2*c*d*x + b*d)^(3/2)*b^2*d^2 + 21*(2*c*d*x + b*d)^(5/2)*b*d - 5*(2*c*d*x + b*d)^(7/2))*b^3/(c^2*d^2) - 41184*(35*sqrt(2*c*d*x + b*d)*b^3*d^3 - 35*(2*c*d*x + b*d)^(3/2)*b^2*d^2 + 21*(2*c*d*x + b*d)^(5/2)*b*d - 5*(2*c*d*x + b*d)^(7/2))*a*b/(c*d^2) + 1859*(315*sqrt(2*c*d*x + b*d)*b^4*d^4 - 420*(2*c*d*x + b*d)^(3/2)*b^3*d^3 + 378*(2*c*d*x + b*d)^(5/2)*b^2*d^2 - 180*(2*c*d*x + b*d)^(7/2)*b*d + 35*(2*c*d*x + b*d)^(9/2))*b^2/(c^2*d^3) + 1144*(315*sqrt(2*c*d*x + b*d)*b^4*d^4 - 420*(2*c*d*x + b*d)^(3/2)*b^3*d^3 + 378*(2*c*d*x + b*d)^(5/2)*b^2*d^2 - 180*(2*c*d*x + b*d)^(7/2)*b*d + 35*(2*c*d*x + b*d)^(9/2))*a/(c*d^3) - 390*(693*sqrt(2*c*d*x + b*d)*b^5*d^5 - 1155*(2*c*d*x + b*d)^(3/2)*b^4*d^4 + 1386*(2*c*d*x + b*d)^(5/2)*b^3*d^3 - 990*(2*c*d*x + b*d)^(7/2)*b^2*d^2 + 385*(2*c*d*x + b*d)^(9/2)*b*d - 63*(2*c*d*x + b*d)^(11/2))*b/(c^2*d^4) + 15*(3003*sqrt(2*c*d*x + b*d)*b^6*d^6 - 6006*(2*c*d*x + b*d)^(3/2)*b^5*d^5 + 9009*(2*c*d*x + b*d)^(5/2)*b^4*d^4 - 8580*(2*c*d*x + b*d)^(7/2)*b^3*d^3 + 5005*(2*c*d*x + b*d)^(9/2)*b^2*d^2 - 1638*(2*c*d*x + b*d)^(11/2)*b*d + 231*(2*c*d*x + b*d)^(13/2))/(c^2*d^5))/c","B",0
1270,1,580,0,0.192610," ","integrate((2*c*d*x+b*d)^(1/2)*(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{55440 \, \sqrt{2 \, c d x + b d} a^{2} b - \frac{18480 \, {\left(3 \, \sqrt{2 \, c d x + b d} b d - {\left(2 \, c d x + b d\right)}^{\frac{3}{2}}\right)} a^{2}}{d} - \frac{18480 \, {\left(3 \, \sqrt{2 \, c d x + b d} b d - {\left(2 \, c d x + b d\right)}^{\frac{3}{2}}\right)} a b^{2}}{c d} + \frac{924 \, {\left(15 \, \sqrt{2 \, c d x + b d} b^{2} d^{2} - 10 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b d + 3 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}}\right)} b^{3}}{c^{2} d^{2}} + \frac{5544 \, {\left(15 \, \sqrt{2 \, c d x + b d} b^{2} d^{2} - 10 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b d + 3 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}}\right)} a b}{c d^{2}} - \frac{792 \, {\left(35 \, \sqrt{2 \, c d x + b d} b^{3} d^{3} - 35 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b^{2} d^{2} + 21 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}} b d - 5 \, {\left(2 \, c d x + b d\right)}^{\frac{7}{2}}\right)} b^{2}}{c^{2} d^{3}} - \frac{792 \, {\left(35 \, \sqrt{2 \, c d x + b d} b^{3} d^{3} - 35 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b^{2} d^{2} + 21 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}} b d - 5 \, {\left(2 \, c d x + b d\right)}^{\frac{7}{2}}\right)} a}{c d^{3}} + \frac{55 \, {\left(315 \, \sqrt{2 \, c d x + b d} b^{4} d^{4} - 420 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b^{3} d^{3} + 378 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}} b^{2} d^{2} - 180 \, {\left(2 \, c d x + b d\right)}^{\frac{7}{2}} b d + 35 \, {\left(2 \, c d x + b d\right)}^{\frac{9}{2}}\right)} b}{c^{2} d^{4}} - \frac{5 \, {\left(693 \, \sqrt{2 \, c d x + b d} b^{5} d^{5} - 1155 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b^{4} d^{4} + 1386 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}} b^{3} d^{3} - 990 \, {\left(2 \, c d x + b d\right)}^{\frac{7}{2}} b^{2} d^{2} + 385 \, {\left(2 \, c d x + b d\right)}^{\frac{9}{2}} b d - 63 \, {\left(2 \, c d x + b d\right)}^{\frac{11}{2}}\right)}}{c^{2} d^{5}}}{55440 \, c}"," ",0,"1/55440*(55440*sqrt(2*c*d*x + b*d)*a^2*b - 18480*(3*sqrt(2*c*d*x + b*d)*b*d - (2*c*d*x + b*d)^(3/2))*a^2/d - 18480*(3*sqrt(2*c*d*x + b*d)*b*d - (2*c*d*x + b*d)^(3/2))*a*b^2/(c*d) + 924*(15*sqrt(2*c*d*x + b*d)*b^2*d^2 - 10*(2*c*d*x + b*d)^(3/2)*b*d + 3*(2*c*d*x + b*d)^(5/2))*b^3/(c^2*d^2) + 5544*(15*sqrt(2*c*d*x + b*d)*b^2*d^2 - 10*(2*c*d*x + b*d)^(3/2)*b*d + 3*(2*c*d*x + b*d)^(5/2))*a*b/(c*d^2) - 792*(35*sqrt(2*c*d*x + b*d)*b^3*d^3 - 35*(2*c*d*x + b*d)^(3/2)*b^2*d^2 + 21*(2*c*d*x + b*d)^(5/2)*b*d - 5*(2*c*d*x + b*d)^(7/2))*b^2/(c^2*d^3) - 792*(35*sqrt(2*c*d*x + b*d)*b^3*d^3 - 35*(2*c*d*x + b*d)^(3/2)*b^2*d^2 + 21*(2*c*d*x + b*d)^(5/2)*b*d - 5*(2*c*d*x + b*d)^(7/2))*a/(c*d^3) + 55*(315*sqrt(2*c*d*x + b*d)*b^4*d^4 - 420*(2*c*d*x + b*d)^(3/2)*b^3*d^3 + 378*(2*c*d*x + b*d)^(5/2)*b^2*d^2 - 180*(2*c*d*x + b*d)^(7/2)*b*d + 35*(2*c*d*x + b*d)^(9/2))*b/(c^2*d^4) - 5*(693*sqrt(2*c*d*x + b*d)*b^5*d^5 - 1155*(2*c*d*x + b*d)^(3/2)*b^4*d^4 + 1386*(2*c*d*x + b*d)^(5/2)*b^3*d^3 - 990*(2*c*d*x + b*d)^(7/2)*b^2*d^2 + 385*(2*c*d*x + b*d)^(9/2)*b*d - 63*(2*c*d*x + b*d)^(11/2))/(c^2*d^5))/c","B",0
1271,1,349,0,0.183091," ","integrate((c*x^2+b*x+a)^2/(2*c*d*x+b*d)^(1/2),x, algorithm=""giac"")","\frac{5040 \, \sqrt{2 \, c d x + b d} a^{2} - \frac{1680 \, {\left(3 \, \sqrt{2 \, c d x + b d} b d - {\left(2 \, c d x + b d\right)}^{\frac{3}{2}}\right)} a b}{c d} + \frac{84 \, {\left(15 \, \sqrt{2 \, c d x + b d} b^{2} d^{2} - 10 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b d + 3 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}}\right)} b^{2}}{c^{2} d^{2}} + \frac{168 \, {\left(15 \, \sqrt{2 \, c d x + b d} b^{2} d^{2} - 10 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b d + 3 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}}\right)} a}{c d^{2}} - \frac{36 \, {\left(35 \, \sqrt{2 \, c d x + b d} b^{3} d^{3} - 35 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b^{2} d^{2} + 21 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}} b d - 5 \, {\left(2 \, c d x + b d\right)}^{\frac{7}{2}}\right)} b}{c^{2} d^{3}} + \frac{315 \, \sqrt{2 \, c d x + b d} b^{4} d^{4} - 420 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b^{3} d^{3} + 378 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}} b^{2} d^{2} - 180 \, {\left(2 \, c d x + b d\right)}^{\frac{7}{2}} b d + 35 \, {\left(2 \, c d x + b d\right)}^{\frac{9}{2}}}{c^{2} d^{4}}}{5040 \, c d}"," ",0,"1/5040*(5040*sqrt(2*c*d*x + b*d)*a^2 - 1680*(3*sqrt(2*c*d*x + b*d)*b*d - (2*c*d*x + b*d)^(3/2))*a*b/(c*d) + 84*(15*sqrt(2*c*d*x + b*d)*b^2*d^2 - 10*(2*c*d*x + b*d)^(3/2)*b*d + 3*(2*c*d*x + b*d)^(5/2))*b^2/(c^2*d^2) + 168*(15*sqrt(2*c*d*x + b*d)*b^2*d^2 - 10*(2*c*d*x + b*d)^(3/2)*b*d + 3*(2*c*d*x + b*d)^(5/2))*a/(c*d^2) - 36*(35*sqrt(2*c*d*x + b*d)*b^3*d^3 - 35*(2*c*d*x + b*d)^(3/2)*b^2*d^2 + 21*(2*c*d*x + b*d)^(5/2)*b*d - 5*(2*c*d*x + b*d)^(7/2))*b/(c^2*d^3) + (315*sqrt(2*c*d*x + b*d)*b^4*d^4 - 420*(2*c*d*x + b*d)^(3/2)*b^3*d^3 + 378*(2*c*d*x + b*d)^(5/2)*b^2*d^2 - 180*(2*c*d*x + b*d)^(7/2)*b*d + 35*(2*c*d*x + b*d)^(9/2))/(c^2*d^4))/(c*d)","B",0
1272,1,109,0,0.195971," ","integrate((c*x^2+b*x+a)^2/(2*c*d*x+b*d)^(3/2),x, algorithm=""giac"")","-\frac{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}}{16 \, \sqrt{2 \, c d x + b d} c^{3} d} - \frac{14 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b^{2} c^{18} d^{32} - 56 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} a c^{19} d^{32} - 3 \, {\left(2 \, c d x + b d\right)}^{\frac{7}{2}} c^{18} d^{30}}{336 \, c^{21} d^{35}}"," ",0,"-1/16*(b^4 - 8*a*b^2*c + 16*a^2*c^2)/(sqrt(2*c*d*x + b*d)*c^3*d) - 1/336*(14*(2*c*d*x + b*d)^(3/2)*b^2*c^18*d^32 - 56*(2*c*d*x + b*d)^(3/2)*a*c^19*d^32 - 3*(2*c*d*x + b*d)^(7/2)*c^18*d^30)/(c^21*d^35)","A",0
1273,1,109,0,0.201164," ","integrate((c*x^2+b*x+a)^2/(2*c*d*x+b*d)^(5/2),x, algorithm=""giac"")","-\frac{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}}{48 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} c^{3} d} - \frac{10 \, \sqrt{2 \, c d x + b d} b^{2} c^{12} d^{22} - 40 \, \sqrt{2 \, c d x + b d} a c^{13} d^{22} - {\left(2 \, c d x + b d\right)}^{\frac{5}{2}} c^{12} d^{20}}{80 \, c^{15} d^{25}}"," ",0,"-1/48*(b^4 - 8*a*b^2*c + 16*a^2*c^2)/((2*c*d*x + b*d)^(3/2)*c^3*d) - 1/80*(10*sqrt(2*c*d*x + b*d)*b^2*c^12*d^22 - 40*sqrt(2*c*d*x + b*d)*a*c^13*d^22 - (2*c*d*x + b*d)^(5/2)*c^12*d^20)/(c^15*d^25)","A",0
1274,1,99,0,0.208303," ","integrate((c*x^2+b*x+a)^2/(2*c*d*x+b*d)^(7/2),x, algorithm=""giac"")","\frac{{\left(2 \, c d x + b d\right)}^{\frac{3}{2}}}{48 \, c^{3} d^{5}} - \frac{b^{4} d^{2} - 8 \, a b^{2} c d^{2} + 16 \, a^{2} c^{2} d^{2} - 10 \, {\left(2 \, c d x + b d\right)}^{2} b^{2} + 40 \, {\left(2 \, c d x + b d\right)}^{2} a c}{80 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}} c^{3} d^{3}}"," ",0,"1/48*(2*c*d*x + b*d)^(3/2)/(c^3*d^5) - 1/80*(b^4*d^2 - 8*a*b^2*c*d^2 + 16*a^2*c^2*d^2 - 10*(2*c*d*x + b*d)^2*b^2 + 40*(2*c*d*x + b*d)^2*a*c)/((2*c*d*x + b*d)^(5/2)*c^3*d^3)","A",0
1275,1,100,0,0.228166," ","integrate((c*x^2+b*x+a)^2/(2*c*d*x+b*d)^(9/2),x, algorithm=""giac"")","\frac{\sqrt{2 \, c d x + b d}}{16 \, c^{3} d^{5}} - \frac{3 \, b^{4} d^{2} - 24 \, a b^{2} c d^{2} + 48 \, a^{2} c^{2} d^{2} - 14 \, {\left(2 \, c d x + b d\right)}^{2} b^{2} + 56 \, {\left(2 \, c d x + b d\right)}^{2} a c}{336 \, {\left(2 \, c d x + b d\right)}^{\frac{7}{2}} c^{3} d^{3}}"," ",0,"1/16*sqrt(2*c*d*x + b*d)/(c^3*d^5) - 1/336*(3*b^4*d^2 - 24*a*b^2*c*d^2 + 48*a^2*c^2*d^2 - 14*(2*c*d*x + b*d)^2*b^2 + 56*(2*c*d*x + b*d)^2*a*c)/((2*c*d*x + b*d)^(7/2)*c^3*d^3)","A",0
1276,1,99,0,0.211797," ","integrate((c*x^2+b*x+a)^2/(2*c*d*x+b*d)^(11/2),x, algorithm=""giac"")","-\frac{5 \, b^{4} d^{4} - 40 \, a b^{2} c d^{4} + 80 \, a^{2} c^{2} d^{4} - 18 \, {\left(2 \, c d x + b d\right)}^{2} b^{2} d^{2} + 72 \, {\left(2 \, c d x + b d\right)}^{2} a c d^{2} + 45 \, {\left(2 \, c d x + b d\right)}^{4}}{720 \, {\left(2 \, c d x + b d\right)}^{\frac{9}{2}} c^{3} d^{5}}"," ",0,"-1/720*(5*b^4*d^4 - 40*a*b^2*c*d^4 + 80*a^2*c^2*d^4 - 18*(2*c*d*x + b*d)^2*b^2*d^2 + 72*(2*c*d*x + b*d)^2*a*c*d^2 + 45*(2*c*d*x + b*d)^4)/((2*c*d*x + b*d)^(9/2)*c^3*d^5)","A",0
1277,1,1165,0,0.226750," ","integrate((2*c*d*x+b*d)^(1/2)*(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{2882880 \, \sqrt{2 \, c d x + b d} a^{3} b - \frac{960960 \, {\left(3 \, \sqrt{2 \, c d x + b d} b d - {\left(2 \, c d x + b d\right)}^{\frac{3}{2}}\right)} a^{3}}{d} - \frac{1441440 \, {\left(3 \, \sqrt{2 \, c d x + b d} b d - {\left(2 \, c d x + b d\right)}^{\frac{3}{2}}\right)} a^{2} b^{2}}{c d} + \frac{144144 \, {\left(15 \, \sqrt{2 \, c d x + b d} b^{2} d^{2} - 10 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b d + 3 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}}\right)} a b^{3}}{c^{2} d^{2}} + \frac{432432 \, {\left(15 \, \sqrt{2 \, c d x + b d} b^{2} d^{2} - 10 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b d + 3 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}}\right)} a^{2} b}{c d^{2}} - \frac{10296 \, {\left(35 \, \sqrt{2 \, c d x + b d} b^{3} d^{3} - 35 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b^{2} d^{2} + 21 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}} b d - 5 \, {\left(2 \, c d x + b d\right)}^{\frac{7}{2}}\right)} b^{4}}{c^{3} d^{3}} - \frac{123552 \, {\left(35 \, \sqrt{2 \, c d x + b d} b^{3} d^{3} - 35 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b^{2} d^{2} + 21 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}} b d - 5 \, {\left(2 \, c d x + b d\right)}^{\frac{7}{2}}\right)} a b^{2}}{c^{2} d^{3}} - \frac{61776 \, {\left(35 \, \sqrt{2 \, c d x + b d} b^{3} d^{3} - 35 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b^{2} d^{2} + 21 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}} b d - 5 \, {\left(2 \, c d x + b d\right)}^{\frac{7}{2}}\right)} a^{2}}{c d^{3}} + \frac{2860 \, {\left(315 \, \sqrt{2 \, c d x + b d} b^{4} d^{4} - 420 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b^{3} d^{3} + 378 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}} b^{2} d^{2} - 180 \, {\left(2 \, c d x + b d\right)}^{\frac{7}{2}} b d + 35 \, {\left(2 \, c d x + b d\right)}^{\frac{9}{2}}\right)} b^{3}}{c^{3} d^{4}} + \frac{8580 \, {\left(315 \, \sqrt{2 \, c d x + b d} b^{4} d^{4} - 420 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b^{3} d^{3} + 378 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}} b^{2} d^{2} - 180 \, {\left(2 \, c d x + b d\right)}^{\frac{7}{2}} b d + 35 \, {\left(2 \, c d x + b d\right)}^{\frac{9}{2}}\right)} a b}{c^{2} d^{4}} - \frac{1170 \, {\left(693 \, \sqrt{2 \, c d x + b d} b^{5} d^{5} - 1155 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b^{4} d^{4} + 1386 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}} b^{3} d^{3} - 990 \, {\left(2 \, c d x + b d\right)}^{\frac{7}{2}} b^{2} d^{2} + 385 \, {\left(2 \, c d x + b d\right)}^{\frac{9}{2}} b d - 63 \, {\left(2 \, c d x + b d\right)}^{\frac{11}{2}}\right)} b^{2}}{c^{3} d^{5}} - \frac{780 \, {\left(693 \, \sqrt{2 \, c d x + b d} b^{5} d^{5} - 1155 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b^{4} d^{4} + 1386 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}} b^{3} d^{3} - 990 \, {\left(2 \, c d x + b d\right)}^{\frac{7}{2}} b^{2} d^{2} + 385 \, {\left(2 \, c d x + b d\right)}^{\frac{9}{2}} b d - 63 \, {\left(2 \, c d x + b d\right)}^{\frac{11}{2}}\right)} a}{c^{2} d^{5}} + \frac{105 \, {\left(3003 \, \sqrt{2 \, c d x + b d} b^{6} d^{6} - 6006 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b^{5} d^{5} + 9009 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}} b^{4} d^{4} - 8580 \, {\left(2 \, c d x + b d\right)}^{\frac{7}{2}} b^{3} d^{3} + 5005 \, {\left(2 \, c d x + b d\right)}^{\frac{9}{2}} b^{2} d^{2} - 1638 \, {\left(2 \, c d x + b d\right)}^{\frac{11}{2}} b d + 231 \, {\left(2 \, c d x + b d\right)}^{\frac{13}{2}}\right)} b}{c^{3} d^{6}} - \frac{7 \, {\left(6435 \, \sqrt{2 \, c d x + b d} b^{7} d^{7} - 15015 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b^{6} d^{6} + 27027 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}} b^{5} d^{5} - 32175 \, {\left(2 \, c d x + b d\right)}^{\frac{7}{2}} b^{4} d^{4} + 25025 \, {\left(2 \, c d x + b d\right)}^{\frac{9}{2}} b^{3} d^{3} - 12285 \, {\left(2 \, c d x + b d\right)}^{\frac{11}{2}} b^{2} d^{2} + 3465 \, {\left(2 \, c d x + b d\right)}^{\frac{13}{2}} b d - 429 \, {\left(2 \, c d x + b d\right)}^{\frac{15}{2}}\right)}}{c^{3} d^{7}}}{2882880 \, c}"," ",0,"1/2882880*(2882880*sqrt(2*c*d*x + b*d)*a^3*b - 960960*(3*sqrt(2*c*d*x + b*d)*b*d - (2*c*d*x + b*d)^(3/2))*a^3/d - 1441440*(3*sqrt(2*c*d*x + b*d)*b*d - (2*c*d*x + b*d)^(3/2))*a^2*b^2/(c*d) + 144144*(15*sqrt(2*c*d*x + b*d)*b^2*d^2 - 10*(2*c*d*x + b*d)^(3/2)*b*d + 3*(2*c*d*x + b*d)^(5/2))*a*b^3/(c^2*d^2) + 432432*(15*sqrt(2*c*d*x + b*d)*b^2*d^2 - 10*(2*c*d*x + b*d)^(3/2)*b*d + 3*(2*c*d*x + b*d)^(5/2))*a^2*b/(c*d^2) - 10296*(35*sqrt(2*c*d*x + b*d)*b^3*d^3 - 35*(2*c*d*x + b*d)^(3/2)*b^2*d^2 + 21*(2*c*d*x + b*d)^(5/2)*b*d - 5*(2*c*d*x + b*d)^(7/2))*b^4/(c^3*d^3) - 123552*(35*sqrt(2*c*d*x + b*d)*b^3*d^3 - 35*(2*c*d*x + b*d)^(3/2)*b^2*d^2 + 21*(2*c*d*x + b*d)^(5/2)*b*d - 5*(2*c*d*x + b*d)^(7/2))*a*b^2/(c^2*d^3) - 61776*(35*sqrt(2*c*d*x + b*d)*b^3*d^3 - 35*(2*c*d*x + b*d)^(3/2)*b^2*d^2 + 21*(2*c*d*x + b*d)^(5/2)*b*d - 5*(2*c*d*x + b*d)^(7/2))*a^2/(c*d^3) + 2860*(315*sqrt(2*c*d*x + b*d)*b^4*d^4 - 420*(2*c*d*x + b*d)^(3/2)*b^3*d^3 + 378*(2*c*d*x + b*d)^(5/2)*b^2*d^2 - 180*(2*c*d*x + b*d)^(7/2)*b*d + 35*(2*c*d*x + b*d)^(9/2))*b^3/(c^3*d^4) + 8580*(315*sqrt(2*c*d*x + b*d)*b^4*d^4 - 420*(2*c*d*x + b*d)^(3/2)*b^3*d^3 + 378*(2*c*d*x + b*d)^(5/2)*b^2*d^2 - 180*(2*c*d*x + b*d)^(7/2)*b*d + 35*(2*c*d*x + b*d)^(9/2))*a*b/(c^2*d^4) - 1170*(693*sqrt(2*c*d*x + b*d)*b^5*d^5 - 1155*(2*c*d*x + b*d)^(3/2)*b^4*d^4 + 1386*(2*c*d*x + b*d)^(5/2)*b^3*d^3 - 990*(2*c*d*x + b*d)^(7/2)*b^2*d^2 + 385*(2*c*d*x + b*d)^(9/2)*b*d - 63*(2*c*d*x + b*d)^(11/2))*b^2/(c^3*d^5) - 780*(693*sqrt(2*c*d*x + b*d)*b^5*d^5 - 1155*(2*c*d*x + b*d)^(3/2)*b^4*d^4 + 1386*(2*c*d*x + b*d)^(5/2)*b^3*d^3 - 990*(2*c*d*x + b*d)^(7/2)*b^2*d^2 + 385*(2*c*d*x + b*d)^(9/2)*b*d - 63*(2*c*d*x + b*d)^(11/2))*a/(c^2*d^5) + 105*(3003*sqrt(2*c*d*x + b*d)*b^6*d^6 - 6006*(2*c*d*x + b*d)^(3/2)*b^5*d^5 + 9009*(2*c*d*x + b*d)^(5/2)*b^4*d^4 - 8580*(2*c*d*x + b*d)^(7/2)*b^3*d^3 + 5005*(2*c*d*x + b*d)^(9/2)*b^2*d^2 - 1638*(2*c*d*x + b*d)^(11/2)*b*d + 231*(2*c*d*x + b*d)^(13/2))*b/(c^3*d^6) - 7*(6435*sqrt(2*c*d*x + b*d)*b^7*d^7 - 15015*(2*c*d*x + b*d)^(3/2)*b^6*d^6 + 27027*(2*c*d*x + b*d)^(5/2)*b^5*d^5 - 32175*(2*c*d*x + b*d)^(7/2)*b^4*d^4 + 25025*(2*c*d*x + b*d)^(9/2)*b^3*d^3 - 12285*(2*c*d*x + b*d)^(11/2)*b^2*d^2 + 3465*(2*c*d*x + b*d)^(13/2)*b*d - 429*(2*c*d*x + b*d)^(15/2))/(c^3*d^7))/c","B",0
1278,1,778,0,0.220230," ","integrate((c*x^2+b*x+a)^3/(2*c*d*x+b*d)^(1/2),x, algorithm=""giac"")","\frac{960960 \, \sqrt{2 \, c d x + b d} a^{3} - \frac{480480 \, {\left(3 \, \sqrt{2 \, c d x + b d} b d - {\left(2 \, c d x + b d\right)}^{\frac{3}{2}}\right)} a^{2} b}{c d} + \frac{48048 \, {\left(15 \, \sqrt{2 \, c d x + b d} b^{2} d^{2} - 10 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b d + 3 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}}\right)} a b^{2}}{c^{2} d^{2}} + \frac{48048 \, {\left(15 \, \sqrt{2 \, c d x + b d} b^{2} d^{2} - 10 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b d + 3 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}}\right)} a^{2}}{c d^{2}} - \frac{3432 \, {\left(35 \, \sqrt{2 \, c d x + b d} b^{3} d^{3} - 35 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b^{2} d^{2} + 21 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}} b d - 5 \, {\left(2 \, c d x + b d\right)}^{\frac{7}{2}}\right)} b^{3}}{c^{3} d^{3}} - \frac{20592 \, {\left(35 \, \sqrt{2 \, c d x + b d} b^{3} d^{3} - 35 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b^{2} d^{2} + 21 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}} b d - 5 \, {\left(2 \, c d x + b d\right)}^{\frac{7}{2}}\right)} a b}{c^{2} d^{3}} + \frac{572 \, {\left(315 \, \sqrt{2 \, c d x + b d} b^{4} d^{4} - 420 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b^{3} d^{3} + 378 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}} b^{2} d^{2} - 180 \, {\left(2 \, c d x + b d\right)}^{\frac{7}{2}} b d + 35 \, {\left(2 \, c d x + b d\right)}^{\frac{9}{2}}\right)} b^{2}}{c^{3} d^{4}} + \frac{572 \, {\left(315 \, \sqrt{2 \, c d x + b d} b^{4} d^{4} - 420 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b^{3} d^{3} + 378 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}} b^{2} d^{2} - 180 \, {\left(2 \, c d x + b d\right)}^{\frac{7}{2}} b d + 35 \, {\left(2 \, c d x + b d\right)}^{\frac{9}{2}}\right)} a}{c^{2} d^{4}} - \frac{130 \, {\left(693 \, \sqrt{2 \, c d x + b d} b^{5} d^{5} - 1155 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b^{4} d^{4} + 1386 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}} b^{3} d^{3} - 990 \, {\left(2 \, c d x + b d\right)}^{\frac{7}{2}} b^{2} d^{2} + 385 \, {\left(2 \, c d x + b d\right)}^{\frac{9}{2}} b d - 63 \, {\left(2 \, c d x + b d\right)}^{\frac{11}{2}}\right)} b}{c^{3} d^{5}} + \frac{5 \, {\left(3003 \, \sqrt{2 \, c d x + b d} b^{6} d^{6} - 6006 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b^{5} d^{5} + 9009 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}} b^{4} d^{4} - 8580 \, {\left(2 \, c d x + b d\right)}^{\frac{7}{2}} b^{3} d^{3} + 5005 \, {\left(2 \, c d x + b d\right)}^{\frac{9}{2}} b^{2} d^{2} - 1638 \, {\left(2 \, c d x + b d\right)}^{\frac{11}{2}} b d + 231 \, {\left(2 \, c d x + b d\right)}^{\frac{13}{2}}\right)}}{c^{3} d^{6}}}{960960 \, c d}"," ",0,"1/960960*(960960*sqrt(2*c*d*x + b*d)*a^3 - 480480*(3*sqrt(2*c*d*x + b*d)*b*d - (2*c*d*x + b*d)^(3/2))*a^2*b/(c*d) + 48048*(15*sqrt(2*c*d*x + b*d)*b^2*d^2 - 10*(2*c*d*x + b*d)^(3/2)*b*d + 3*(2*c*d*x + b*d)^(5/2))*a*b^2/(c^2*d^2) + 48048*(15*sqrt(2*c*d*x + b*d)*b^2*d^2 - 10*(2*c*d*x + b*d)^(3/2)*b*d + 3*(2*c*d*x + b*d)^(5/2))*a^2/(c*d^2) - 3432*(35*sqrt(2*c*d*x + b*d)*b^3*d^3 - 35*(2*c*d*x + b*d)^(3/2)*b^2*d^2 + 21*(2*c*d*x + b*d)^(5/2)*b*d - 5*(2*c*d*x + b*d)^(7/2))*b^3/(c^3*d^3) - 20592*(35*sqrt(2*c*d*x + b*d)*b^3*d^3 - 35*(2*c*d*x + b*d)^(3/2)*b^2*d^2 + 21*(2*c*d*x + b*d)^(5/2)*b*d - 5*(2*c*d*x + b*d)^(7/2))*a*b/(c^2*d^3) + 572*(315*sqrt(2*c*d*x + b*d)*b^4*d^4 - 420*(2*c*d*x + b*d)^(3/2)*b^3*d^3 + 378*(2*c*d*x + b*d)^(5/2)*b^2*d^2 - 180*(2*c*d*x + b*d)^(7/2)*b*d + 35*(2*c*d*x + b*d)^(9/2))*b^2/(c^3*d^4) + 572*(315*sqrt(2*c*d*x + b*d)*b^4*d^4 - 420*(2*c*d*x + b*d)^(3/2)*b^3*d^3 + 378*(2*c*d*x + b*d)^(5/2)*b^2*d^2 - 180*(2*c*d*x + b*d)^(7/2)*b*d + 35*(2*c*d*x + b*d)^(9/2))*a/(c^2*d^4) - 130*(693*sqrt(2*c*d*x + b*d)*b^5*d^5 - 1155*(2*c*d*x + b*d)^(3/2)*b^4*d^4 + 1386*(2*c*d*x + b*d)^(5/2)*b^3*d^3 - 990*(2*c*d*x + b*d)^(7/2)*b^2*d^2 + 385*(2*c*d*x + b*d)^(9/2)*b*d - 63*(2*c*d*x + b*d)^(11/2))*b/(c^3*d^5) + 5*(3003*sqrt(2*c*d*x + b*d)*b^6*d^6 - 6006*(2*c*d*x + b*d)^(3/2)*b^5*d^5 + 9009*(2*c*d*x + b*d)^(5/2)*b^4*d^4 - 8580*(2*c*d*x + b*d)^(7/2)*b^3*d^3 + 5005*(2*c*d*x + b*d)^(9/2)*b^2*d^2 - 1638*(2*c*d*x + b*d)^(11/2)*b*d + 231*(2*c*d*x + b*d)^(13/2))/(c^3*d^6))/(c*d)","B",0
1279,1,187,0,0.230653," ","integrate((c*x^2+b*x+a)^3/(2*c*d*x+b*d)^(3/2),x, algorithm=""giac"")","\frac{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}}{64 \, \sqrt{2 \, c d x + b d} c^{4} d} + \frac{77 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b^{4} c^{40} d^{74} - 616 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} a b^{2} c^{41} d^{74} + 1232 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} a^{2} c^{42} d^{74} - 33 \, {\left(2 \, c d x + b d\right)}^{\frac{7}{2}} b^{2} c^{40} d^{72} + 132 \, {\left(2 \, c d x + b d\right)}^{\frac{7}{2}} a c^{41} d^{72} + 7 \, {\left(2 \, c d x + b d\right)}^{\frac{11}{2}} c^{40} d^{70}}{4928 \, c^{44} d^{77}}"," ",0,"1/64*(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)/(sqrt(2*c*d*x + b*d)*c^4*d) + 1/4928*(77*(2*c*d*x + b*d)^(3/2)*b^4*c^40*d^74 - 616*(2*c*d*x + b*d)^(3/2)*a*b^2*c^41*d^74 + 1232*(2*c*d*x + b*d)^(3/2)*a^2*c^42*d^74 - 33*(2*c*d*x + b*d)^(7/2)*b^2*c^40*d^72 + 132*(2*c*d*x + b*d)^(7/2)*a*c^41*d^72 + 7*(2*c*d*x + b*d)^(11/2)*c^40*d^70)/(c^44*d^77)","A",0
1280,1,187,0,0.636620," ","integrate((c*x^2+b*x+a)^3/(2*c*d*x+b*d)^(5/2),x, algorithm=""giac"")","\frac{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}}{192 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} c^{4} d} + \frac{135 \, \sqrt{2 \, c d x + b d} b^{4} c^{32} d^{60} - 1080 \, \sqrt{2 \, c d x + b d} a b^{2} c^{33} d^{60} + 2160 \, \sqrt{2 \, c d x + b d} a^{2} c^{34} d^{60} - 27 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}} b^{2} c^{32} d^{58} + 108 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}} a c^{33} d^{58} + 5 \, {\left(2 \, c d x + b d\right)}^{\frac{9}{2}} c^{32} d^{56}}{2880 \, c^{36} d^{63}}"," ",0,"1/192*(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)/((2*c*d*x + b*d)^(3/2)*c^4*d) + 1/2880*(135*sqrt(2*c*d*x + b*d)*b^4*c^32*d^60 - 1080*sqrt(2*c*d*x + b*d)*a*b^2*c^33*d^60 + 2160*sqrt(2*c*d*x + b*d)*a^2*c^34*d^60 - 27*(2*c*d*x + b*d)^(5/2)*b^2*c^32*d^58 + 108*(2*c*d*x + b*d)^(5/2)*a*c^33*d^58 + 5*(2*c*d*x + b*d)^(9/2)*c^32*d^56)/(c^36*d^63)","A",0
1281,1,186,0,0.274084," ","integrate((c*x^2+b*x+a)^3/(2*c*d*x+b*d)^(7/2),x, algorithm=""giac"")","\frac{b^{6} d^{2} - 12 \, a b^{4} c d^{2} + 48 \, a^{2} b^{2} c^{2} d^{2} - 64 \, a^{3} c^{3} d^{2} - 15 \, {\left(2 \, c d x + b d\right)}^{2} b^{4} + 120 \, {\left(2 \, c d x + b d\right)}^{2} a b^{2} c - 240 \, {\left(2 \, c d x + b d\right)}^{2} a^{2} c^{2}}{320 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}} c^{4} d^{3}} - \frac{7 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b^{2} c^{24} d^{44} - 28 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} a c^{25} d^{44} - {\left(2 \, c d x + b d\right)}^{\frac{7}{2}} c^{24} d^{42}}{448 \, c^{28} d^{49}}"," ",0,"1/320*(b^6*d^2 - 12*a*b^4*c*d^2 + 48*a^2*b^2*c^2*d^2 - 64*a^3*c^3*d^2 - 15*(2*c*d*x + b*d)^2*b^4 + 120*(2*c*d*x + b*d)^2*a*b^2*c - 240*(2*c*d*x + b*d)^2*a^2*c^2)/((2*c*d*x + b*d)^(5/2)*c^4*d^3) - 1/448*(7*(2*c*d*x + b*d)^(3/2)*b^2*c^24*d^44 - 28*(2*c*d*x + b*d)^(3/2)*a*c^25*d^44 - (2*c*d*x + b*d)^(7/2)*c^24*d^42)/(c^28*d^49)","A",0
1282,1,186,0,0.693438," ","integrate((c*x^2+b*x+a)^3/(2*c*d*x+b*d)^(9/2),x, algorithm=""giac"")","\frac{b^{6} d^{2} - 12 \, a b^{4} c d^{2} + 48 \, a^{2} b^{2} c^{2} d^{2} - 64 \, a^{3} c^{3} d^{2} - 7 \, {\left(2 \, c d x + b d\right)}^{2} b^{4} + 56 \, {\left(2 \, c d x + b d\right)}^{2} a b^{2} c - 112 \, {\left(2 \, c d x + b d\right)}^{2} a^{2} c^{2}}{448 \, {\left(2 \, c d x + b d\right)}^{\frac{7}{2}} c^{4} d^{3}} - \frac{15 \, \sqrt{2 \, c d x + b d} b^{2} c^{16} d^{30} - 60 \, \sqrt{2 \, c d x + b d} a c^{17} d^{30} - {\left(2 \, c d x + b d\right)}^{\frac{5}{2}} c^{16} d^{28}}{320 \, c^{20} d^{35}}"," ",0,"1/448*(b^6*d^2 - 12*a*b^4*c*d^2 + 48*a^2*b^2*c^2*d^2 - 64*a^3*c^3*d^2 - 7*(2*c*d*x + b*d)^2*b^4 + 56*(2*c*d*x + b*d)^2*a*b^2*c - 112*(2*c*d*x + b*d)^2*a^2*c^2)/((2*c*d*x + b*d)^(7/2)*c^4*d^3) - 1/320*(15*sqrt(2*c*d*x + b*d)*b^2*c^16*d^30 - 60*sqrt(2*c*d*x + b*d)*a*c^17*d^30 - (2*c*d*x + b*d)^(5/2)*c^16*d^28)/(c^20*d^35)","A",0
1283,1,176,0,0.254008," ","integrate((c*x^2+b*x+a)^3/(2*c*d*x+b*d)^(11/2),x, algorithm=""giac"")","\frac{{\left(2 \, c d x + b d\right)}^{\frac{3}{2}}}{192 \, c^{4} d^{7}} + \frac{5 \, b^{6} d^{4} - 60 \, a b^{4} c d^{4} + 240 \, a^{2} b^{2} c^{2} d^{4} - 320 \, a^{3} c^{3} d^{4} - 27 \, {\left(2 \, c d x + b d\right)}^{2} b^{4} d^{2} + 216 \, {\left(2 \, c d x + b d\right)}^{2} a b^{2} c d^{2} - 432 \, {\left(2 \, c d x + b d\right)}^{2} a^{2} c^{2} d^{2} + 135 \, {\left(2 \, c d x + b d\right)}^{4} b^{2} - 540 \, {\left(2 \, c d x + b d\right)}^{4} a c}{2880 \, {\left(2 \, c d x + b d\right)}^{\frac{9}{2}} c^{4} d^{5}}"," ",0,"1/192*(2*c*d*x + b*d)^(3/2)/(c^4*d^7) + 1/2880*(5*b^6*d^4 - 60*a*b^4*c*d^4 + 240*a^2*b^2*c^2*d^4 - 320*a^3*c^3*d^4 - 27*(2*c*d*x + b*d)^2*b^4*d^2 + 216*(2*c*d*x + b*d)^2*a*b^2*c*d^2 - 432*(2*c*d*x + b*d)^2*a^2*c^2*d^2 + 135*(2*c*d*x + b*d)^4*b^2 - 540*(2*c*d*x + b*d)^4*a*c)/((2*c*d*x + b*d)^(9/2)*c^4*d^5)","A",0
1284,1,176,0,0.281988," ","integrate((c*x^2+b*x+a)^3/(2*c*d*x+b*d)^(13/2),x, algorithm=""giac"")","\frac{\sqrt{2 \, c d x + b d}}{64 \, c^{4} d^{7}} + \frac{7 \, b^{6} d^{4} - 84 \, a b^{4} c d^{4} + 336 \, a^{2} b^{2} c^{2} d^{4} - 448 \, a^{3} c^{3} d^{4} - 33 \, {\left(2 \, c d x + b d\right)}^{2} b^{4} d^{2} + 264 \, {\left(2 \, c d x + b d\right)}^{2} a b^{2} c d^{2} - 528 \, {\left(2 \, c d x + b d\right)}^{2} a^{2} c^{2} d^{2} + 77 \, {\left(2 \, c d x + b d\right)}^{4} b^{2} - 308 \, {\left(2 \, c d x + b d\right)}^{4} a c}{4928 \, {\left(2 \, c d x + b d\right)}^{\frac{11}{2}} c^{4} d^{5}}"," ",0,"1/64*sqrt(2*c*d*x + b*d)/(c^4*d^7) + 1/4928*(7*b^6*d^4 - 84*a*b^4*c*d^4 + 336*a^2*b^2*c^2*d^4 - 448*a^3*c^3*d^4 - 33*(2*c*d*x + b*d)^2*b^4*d^2 + 264*(2*c*d*x + b*d)^2*a*b^2*c*d^2 - 528*(2*c*d*x + b*d)^2*a^2*c^2*d^2 + 77*(2*c*d*x + b*d)^4*b^2 - 308*(2*c*d*x + b*d)^4*a*c)/((2*c*d*x + b*d)^(11/2)*c^4*d^5)","A",0
1285,1,733,0,0.387686," ","integrate((2*c*d*x+b*d)^(11/2)/(c*x^2+b*x+a),x, algorithm=""giac"")","4 \, \sqrt{2 \, c d x + b d} b^{4} d^{5} - 32 \, \sqrt{2 \, c d x + b d} a b^{2} c d^{5} + 64 \, \sqrt{2 \, c d x + b d} a^{2} c^{2} d^{5} + \frac{4}{5} \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}} b^{2} d^{3} - \frac{16}{5} \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}} a c d^{3} + \frac{4}{9} \, {\left(2 \, c d x + b d\right)}^{\frac{9}{2}} d - {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} b^{4} d^{5} - 8 \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} a b^{2} c d^{5} + 16 \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} a^{2} c^{2} d^{5}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} + 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right) - {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} b^{4} d^{5} - 8 \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} a b^{2} c d^{5} + 16 \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} a^{2} c^{2} d^{5}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} - 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right) - \frac{1}{2} \, {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} b^{4} d^{5} - 8 \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} a b^{2} c d^{5} + 16 \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} a^{2} c^{2} d^{5}\right)} \log\left(2 \, c d x + b d + \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right) + \frac{1}{2} \, {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} b^{4} d^{5} - 8 \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} a b^{2} c d^{5} + 16 \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} a^{2} c^{2} d^{5}\right)} \log\left(2 \, c d x + b d - \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right)"," ",0,"4*sqrt(2*c*d*x + b*d)*b^4*d^5 - 32*sqrt(2*c*d*x + b*d)*a*b^2*c*d^5 + 64*sqrt(2*c*d*x + b*d)*a^2*c^2*d^5 + 4/5*(2*c*d*x + b*d)^(5/2)*b^2*d^3 - 16/5*(2*c*d*x + b*d)^(5/2)*a*c*d^3 + 4/9*(2*c*d*x + b*d)^(9/2)*d - (sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*b^4*d^5 - 8*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*a*b^2*c*d^5 + 16*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*a^2*c^2*d^5)*arctan(1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) + 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4)) - (sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*b^4*d^5 - 8*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*a*b^2*c*d^5 + 16*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*a^2*c^2*d^5)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) - 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4)) - 1/2*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*b^4*d^5 - 8*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*a*b^2*c*d^5 + 16*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*a^2*c^2*d^5)*log(2*c*d*x + b*d + sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2)) + 1/2*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*b^4*d^5 - 8*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*a*b^2*c*d^5 + 16*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*a^2*c^2*d^5)*log(2*c*d*x + b*d - sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2))","B",0
1286,1,531,0,0.311412," ","integrate((2*c*d*x+b*d)^(9/2)/(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{4}{3} \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b^{2} d^{3} - \frac{16}{3} \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} a c d^{3} + \frac{4}{7} \, {\left(2 \, c d x + b d\right)}^{\frac{7}{2}} d - {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} b^{2} d^{3} - 4 \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} a c d^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} + 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right) - {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} b^{2} d^{3} - 4 \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} a c d^{3}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} - 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right) + \frac{1}{2} \, {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} b^{2} d^{3} - 4 \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} a c d^{3}\right)} \log\left(2 \, c d x + b d + \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right) - \frac{1}{2} \, {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} b^{2} d^{3} - 4 \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} a c d^{3}\right)} \log\left(2 \, c d x + b d - \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right)"," ",0,"4/3*(2*c*d*x + b*d)^(3/2)*b^2*d^3 - 16/3*(2*c*d*x + b*d)^(3/2)*a*c*d^3 + 4/7*(2*c*d*x + b*d)^(7/2)*d - (sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*b^2*d^3 - 4*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*a*c*d^3)*arctan(1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) + 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4)) - (sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*b^2*d^3 - 4*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*a*c*d^3)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) - 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4)) + 1/2*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*b^2*d^3 - 4*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*a*c*d^3)*log(2*c*d*x + b*d + sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2)) - 1/2*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*b^2*d^3 - 4*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*a*c*d^3)*log(2*c*d*x + b*d - sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2))","B",0
1287,1,531,0,0.237791," ","integrate((2*c*d*x+b*d)^(7/2)/(c*x^2+b*x+a),x, algorithm=""giac"")","4 \, \sqrt{2 \, c d x + b d} b^{2} d^{3} - 16 \, \sqrt{2 \, c d x + b d} a c d^{3} + \frac{4}{5} \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}} d - {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} b^{2} d^{3} - 4 \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} a c d^{3}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} + 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right) - {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} b^{2} d^{3} - 4 \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} a c d^{3}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} - 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right) - \frac{1}{2} \, {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} b^{2} d^{3} - 4 \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} a c d^{3}\right)} \log\left(2 \, c d x + b d + \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right) + \frac{1}{2} \, {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} b^{2} d^{3} - 4 \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} a c d^{3}\right)} \log\left(2 \, c d x + b d - \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right)"," ",0,"4*sqrt(2*c*d*x + b*d)*b^2*d^3 - 16*sqrt(2*c*d*x + b*d)*a*c*d^3 + 4/5*(2*c*d*x + b*d)^(5/2)*d - (sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*b^2*d^3 - 4*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*a*c*d^3)*arctan(1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) + 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4)) - (sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*b^2*d^3 - 4*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*a*c*d^3)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) - 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4)) - 1/2*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*b^2*d^3 - 4*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*a*c*d^3)*log(2*c*d*x + b*d + sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2)) + 1/2*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*b^2*d^3 - 4*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*a*c*d^3)*log(2*c*d*x + b*d - sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2))","B",0
1288,1,354,0,0.263193," ","integrate((2*c*d*x+b*d)^(5/2)/(c*x^2+b*x+a),x, algorithm=""giac"")","-\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} d \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} + 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right) - \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} d \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} - 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right) + \frac{1}{2} \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} d \log\left(2 \, c d x + b d + \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right) - \frac{1}{2} \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} d \log\left(2 \, c d x + b d - \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right) + \frac{4}{3} \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} d"," ",0,"-sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*d*arctan(1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) + 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4)) - sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*d*arctan(-1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) - 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4)) + 1/2*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*d*log(2*c*d*x + b*d + sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2)) - 1/2*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*d*log(2*c*d*x + b*d - sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2)) + 4/3*(2*c*d*x + b*d)^(3/2)*d","B",0
1289,1,354,0,0.207700," ","integrate((2*c*d*x+b*d)^(3/2)/(c*x^2+b*x+a),x, algorithm=""giac"")","-\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} d \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} + 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right) - \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} d \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} - 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right) - \frac{1}{2} \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} d \log\left(2 \, c d x + b d + \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right) + \frac{1}{2} \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} d \log\left(2 \, c d x + b d - \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right) + 4 \, \sqrt{2 \, c d x + b d} d"," ",0,"-sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*d*arctan(1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) + 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4)) - sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*d*arctan(-1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) - 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4)) - 1/2*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*d*log(2*c*d*x + b*d + sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2)) + 1/2*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*d*log(2*c*d*x + b*d - sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2)) + 4*sqrt(2*c*d*x + b*d)*d","B",0
1290,1,393,0,0.200239," ","integrate((2*c*d*x+b*d)^(1/2)/(c*x^2+b*x+a),x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} + 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right)}{b^{2} d - 4 \, a c d} - \frac{\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} - 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right)}{b^{2} d - 4 \, a c d} + \frac{{\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} \log\left(2 \, c d x + b d + \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right)}{\sqrt{2} b^{2} d - 4 \, \sqrt{2} a c d} - \frac{{\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} \log\left(2 \, c d x + b d - \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right)}{\sqrt{2} b^{2} d - 4 \, \sqrt{2} a c d}"," ",0,"-sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) + 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4))/(b^2*d - 4*a*c*d) - sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) - 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4))/(b^2*d - 4*a*c*d) + (-b^2*d^2 + 4*a*c*d^2)^(3/4)*log(2*c*d*x + b*d + sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2))/(sqrt(2)*b^2*d - 4*sqrt(2)*a*c*d) - (-b^2*d^2 + 4*a*c*d^2)^(3/4)*log(2*c*d*x + b*d - sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2))/(sqrt(2)*b^2*d - 4*sqrt(2)*a*c*d)","B",0
1291,1,393,0,0.200934," ","integrate(1/(2*c*d*x+b*d)^(1/2)/(c*x^2+b*x+a),x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} + 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right)}{b^{2} d - 4 \, a c d} - \frac{\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} - 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right)}{b^{2} d - 4 \, a c d} - \frac{{\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \log\left(2 \, c d x + b d + \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right)}{\sqrt{2} b^{2} d - 4 \, \sqrt{2} a c d} + \frac{{\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \log\left(2 \, c d x + b d - \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right)}{\sqrt{2} b^{2} d - 4 \, \sqrt{2} a c d}"," ",0,"-sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) + 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4))/(b^2*d - 4*a*c*d) - sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) - 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4))/(b^2*d - 4*a*c*d) - (-b^2*d^2 + 4*a*c*d^2)^(1/4)*log(2*c*d*x + b*d + sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2))/(sqrt(2)*b^2*d - 4*sqrt(2)*a*c*d) + (-b^2*d^2 + 4*a*c*d^2)^(1/4)*log(2*c*d*x + b*d - sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2))/(sqrt(2)*b^2*d - 4*sqrt(2)*a*c*d)","B",0
1292,1,497,0,0.233433," ","integrate(1/(2*c*d*x+b*d)^(3/2)/(c*x^2+b*x+a),x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} + 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right)}{b^{4} d^{3} - 8 \, a b^{2} c d^{3} + 16 \, a^{2} c^{2} d^{3}} - \frac{\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} - 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right)}{b^{4} d^{3} - 8 \, a b^{2} c d^{3} + 16 \, a^{2} c^{2} d^{3}} + \frac{{\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} \log\left(2 \, c d x + b d + \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right)}{\sqrt{2} b^{4} d^{3} - 8 \, \sqrt{2} a b^{2} c d^{3} + 16 \, \sqrt{2} a^{2} c^{2} d^{3}} - \frac{{\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} \log\left(2 \, c d x + b d - \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right)}{\sqrt{2} b^{4} d^{3} - 8 \, \sqrt{2} a b^{2} c d^{3} + 16 \, \sqrt{2} a^{2} c^{2} d^{3}} + \frac{4}{{\left(b^{2} d - 4 \, a c d\right)} \sqrt{2 \, c d x + b d}}"," ",0,"-sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) + 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4))/(b^4*d^3 - 8*a*b^2*c*d^3 + 16*a^2*c^2*d^3) - sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) - 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4))/(b^4*d^3 - 8*a*b^2*c*d^3 + 16*a^2*c^2*d^3) + (-b^2*d^2 + 4*a*c*d^2)^(3/4)*log(2*c*d*x + b*d + sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2))/(sqrt(2)*b^4*d^3 - 8*sqrt(2)*a*b^2*c*d^3 + 16*sqrt(2)*a^2*c^2*d^3) - (-b^2*d^2 + 4*a*c*d^2)^(3/4)*log(2*c*d*x + b*d - sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2))/(sqrt(2)*b^4*d^3 - 8*sqrt(2)*a*b^2*c*d^3 + 16*sqrt(2)*a^2*c^2*d^3) + 4/((b^2*d - 4*a*c*d)*sqrt(2*c*d*x + b*d))","B",0
1293,1,497,0,0.214974," ","integrate(1/(2*c*d*x+b*d)^(5/2)/(c*x^2+b*x+a),x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} + 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right)}{b^{4} d^{3} - 8 \, a b^{2} c d^{3} + 16 \, a^{2} c^{2} d^{3}} - \frac{\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} - 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right)}{b^{4} d^{3} - 8 \, a b^{2} c d^{3} + 16 \, a^{2} c^{2} d^{3}} - \frac{{\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \log\left(2 \, c d x + b d + \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right)}{\sqrt{2} b^{4} d^{3} - 8 \, \sqrt{2} a b^{2} c d^{3} + 16 \, \sqrt{2} a^{2} c^{2} d^{3}} + \frac{{\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \log\left(2 \, c d x + b d - \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right)}{\sqrt{2} b^{4} d^{3} - 8 \, \sqrt{2} a b^{2} c d^{3} + 16 \, \sqrt{2} a^{2} c^{2} d^{3}} + \frac{4}{3 \, {\left(b^{2} d - 4 \, a c d\right)} {\left(2 \, c d x + b d\right)}^{\frac{3}{2}}}"," ",0,"-sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) + 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4))/(b^4*d^3 - 8*a*b^2*c*d^3 + 16*a^2*c^2*d^3) - sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) - 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4))/(b^4*d^3 - 8*a*b^2*c*d^3 + 16*a^2*c^2*d^3) - (-b^2*d^2 + 4*a*c*d^2)^(1/4)*log(2*c*d*x + b*d + sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2))/(sqrt(2)*b^4*d^3 - 8*sqrt(2)*a*b^2*c*d^3 + 16*sqrt(2)*a^2*c^2*d^3) + (-b^2*d^2 + 4*a*c*d^2)^(1/4)*log(2*c*d*x + b*d - sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2))/(sqrt(2)*b^4*d^3 - 8*sqrt(2)*a*b^2*c*d^3 + 16*sqrt(2)*a^2*c^2*d^3) + 4/3/((b^2*d - 4*a*c*d)*(2*c*d*x + b*d)^(3/2))","B",0
1294,1,605,0,0.268844," ","integrate(1/(2*c*d*x+b*d)^(7/2)/(c*x^2+b*x+a),x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} + 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right)}{b^{6} d^{5} - 12 \, a b^{4} c d^{5} + 48 \, a^{2} b^{2} c^{2} d^{5} - 64 \, a^{3} c^{3} d^{5}} - \frac{\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} - 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right)}{b^{6} d^{5} - 12 \, a b^{4} c d^{5} + 48 \, a^{2} b^{2} c^{2} d^{5} - 64 \, a^{3} c^{3} d^{5}} + \frac{{\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} \log\left(2 \, c d x + b d + \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right)}{\sqrt{2} b^{6} d^{5} - 12 \, \sqrt{2} a b^{4} c d^{5} + 48 \, \sqrt{2} a^{2} b^{2} c^{2} d^{5} - 64 \, \sqrt{2} a^{3} c^{3} d^{5}} - \frac{{\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} \log\left(2 \, c d x + b d - \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right)}{\sqrt{2} b^{6} d^{5} - 12 \, \sqrt{2} a b^{4} c d^{5} + 48 \, \sqrt{2} a^{2} b^{2} c^{2} d^{5} - 64 \, \sqrt{2} a^{3} c^{3} d^{5}} + \frac{4 \, {\left(b^{2} d^{2} - 4 \, a c d^{2} + 5 \, {\left(2 \, c d x + b d\right)}^{2}\right)}}{5 \, {\left(b^{4} d^{3} - 8 \, a b^{2} c d^{3} + 16 \, a^{2} c^{2} d^{3}\right)} {\left(2 \, c d x + b d\right)}^{\frac{5}{2}}}"," ",0,"-sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) + 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4))/(b^6*d^5 - 12*a*b^4*c*d^5 + 48*a^2*b^2*c^2*d^5 - 64*a^3*c^3*d^5) - sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) - 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4))/(b^6*d^5 - 12*a*b^4*c*d^5 + 48*a^2*b^2*c^2*d^5 - 64*a^3*c^3*d^5) + (-b^2*d^2 + 4*a*c*d^2)^(3/4)*log(2*c*d*x + b*d + sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2))/(sqrt(2)*b^6*d^5 - 12*sqrt(2)*a*b^4*c*d^5 + 48*sqrt(2)*a^2*b^2*c^2*d^5 - 64*sqrt(2)*a^3*c^3*d^5) - (-b^2*d^2 + 4*a*c*d^2)^(3/4)*log(2*c*d*x + b*d - sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2))/(sqrt(2)*b^6*d^5 - 12*sqrt(2)*a*b^4*c*d^5 + 48*sqrt(2)*a^2*b^2*c^2*d^5 - 64*sqrt(2)*a^3*c^3*d^5) + 4/5*(b^2*d^2 - 4*a*c*d^2 + 5*(2*c*d*x + b*d)^2)/((b^4*d^3 - 8*a*b^2*c*d^3 + 16*a^2*c^2*d^3)*(2*c*d*x + b*d)^(5/2))","B",0
1295,1,876,0,0.336531," ","integrate((2*c*d*x+b*d)^(15/2)/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","48 \, \sqrt{2 \, c d x + b d} b^{4} c d^{7} - 384 \, \sqrt{2 \, c d x + b d} a b^{2} c^{2} d^{7} + 768 \, \sqrt{2 \, c d x + b d} a^{2} c^{3} d^{7} + \frac{32}{5} \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}} b^{2} c d^{5} - \frac{128}{5} \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}} a c^{2} d^{5} + \frac{16}{9} \, {\left(2 \, c d x + b d\right)}^{\frac{9}{2}} c d^{3} - 13 \, {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} b^{4} c d^{7} - 8 \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} a b^{2} c^{2} d^{7} + 16 \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} a^{2} c^{3} d^{7}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} + 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right) - 13 \, {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} b^{4} c d^{7} - 8 \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} a b^{2} c^{2} d^{7} + 16 \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} a^{2} c^{3} d^{7}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} - 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right) - \frac{13}{2} \, {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} b^{4} c d^{7} - 8 \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} a b^{2} c^{2} d^{7} + 16 \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} a^{2} c^{3} d^{7}\right)} \log\left(2 \, c d x + b d + \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right) + \frac{13}{2} \, {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} b^{4} c d^{7} - 8 \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} a b^{2} c^{2} d^{7} + 16 \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} a^{2} c^{3} d^{7}\right)} \log\left(2 \, c d x + b d - \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right) + \frac{4 \, {\left(\sqrt{2 \, c d x + b d} b^{6} c d^{9} - 12 \, \sqrt{2 \, c d x + b d} a b^{4} c^{2} d^{9} + 48 \, \sqrt{2 \, c d x + b d} a^{2} b^{2} c^{3} d^{9} - 64 \, \sqrt{2 \, c d x + b d} a^{3} c^{4} d^{9}\right)}}{b^{2} d^{2} - 4 \, a c d^{2} - {\left(2 \, c d x + b d\right)}^{2}}"," ",0,"48*sqrt(2*c*d*x + b*d)*b^4*c*d^7 - 384*sqrt(2*c*d*x + b*d)*a*b^2*c^2*d^7 + 768*sqrt(2*c*d*x + b*d)*a^2*c^3*d^7 + 32/5*(2*c*d*x + b*d)^(5/2)*b^2*c*d^5 - 128/5*(2*c*d*x + b*d)^(5/2)*a*c^2*d^5 + 16/9*(2*c*d*x + b*d)^(9/2)*c*d^3 - 13*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*b^4*c*d^7 - 8*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*a*b^2*c^2*d^7 + 16*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*a^2*c^3*d^7)*arctan(1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) + 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4)) - 13*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*b^4*c*d^7 - 8*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*a*b^2*c^2*d^7 + 16*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*a^2*c^3*d^7)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) - 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4)) - 13/2*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*b^4*c*d^7 - 8*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*a*b^2*c^2*d^7 + 16*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*a^2*c^3*d^7)*log(2*c*d*x + b*d + sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2)) + 13/2*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*b^4*c*d^7 - 8*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*a*b^2*c^2*d^7 + 16*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*a^2*c^3*d^7)*log(2*c*d*x + b*d - sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2)) + 4*(sqrt(2*c*d*x + b*d)*b^6*c*d^9 - 12*sqrt(2*c*d*x + b*d)*a*b^4*c^2*d^9 + 48*sqrt(2*c*d*x + b*d)*a^2*b^2*c^3*d^9 - 64*sqrt(2*c*d*x + b*d)*a^3*c^4*d^9)/(b^2*d^2 - 4*a*c*d^2 - (2*c*d*x + b*d)^2)","B",0
1296,1,646,0,0.319633," ","integrate((2*c*d*x+b*d)^(13/2)/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{32}{3} \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b^{2} c d^{5} - \frac{128}{3} \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} a c^{2} d^{5} + \frac{16}{7} \, {\left(2 \, c d x + b d\right)}^{\frac{7}{2}} c d^{3} - 11 \, {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} b^{2} c d^{5} - 4 \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} a c^{2} d^{5}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} + 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right) - 11 \, {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} b^{2} c d^{5} - 4 \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} a c^{2} d^{5}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} - 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right) + \frac{11}{2} \, {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} b^{2} c d^{5} - 4 \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} a c^{2} d^{5}\right)} \log\left(2 \, c d x + b d + \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right) - \frac{11}{2} \, {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} b^{2} c d^{5} - 4 \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} a c^{2} d^{5}\right)} \log\left(2 \, c d x + b d - \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right) + \frac{4 \, {\left({\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b^{4} c d^{7} - 8 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} a b^{2} c^{2} d^{7} + 16 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} a^{2} c^{3} d^{7}\right)}}{b^{2} d^{2} - 4 \, a c d^{2} - {\left(2 \, c d x + b d\right)}^{2}}"," ",0,"32/3*(2*c*d*x + b*d)^(3/2)*b^2*c*d^5 - 128/3*(2*c*d*x + b*d)^(3/2)*a*c^2*d^5 + 16/7*(2*c*d*x + b*d)^(7/2)*c*d^3 - 11*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*b^2*c*d^5 - 4*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*a*c^2*d^5)*arctan(1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) + 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4)) - 11*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*b^2*c*d^5 - 4*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*a*c^2*d^5)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) - 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4)) + 11/2*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*b^2*c*d^5 - 4*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*a*c^2*d^5)*log(2*c*d*x + b*d + sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2)) - 11/2*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*b^2*c*d^5 - 4*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*a*c^2*d^5)*log(2*c*d*x + b*d - sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2)) + 4*((2*c*d*x + b*d)^(3/2)*b^4*c*d^7 - 8*(2*c*d*x + b*d)^(3/2)*a*b^2*c^2*d^7 + 16*(2*c*d*x + b*d)^(3/2)*a^2*c^3*d^7)/(b^2*d^2 - 4*a*c*d^2 - (2*c*d*x + b*d)^2)","B",0
1297,1,646,0,0.288672," ","integrate((2*c*d*x+b*d)^(11/2)/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","32 \, \sqrt{2 \, c d x + b d} b^{2} c d^{5} - 128 \, \sqrt{2 \, c d x + b d} a c^{2} d^{5} + \frac{16}{5} \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}} c d^{3} - 9 \, {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} b^{2} c d^{5} - 4 \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} a c^{2} d^{5}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} + 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right) - 9 \, {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} b^{2} c d^{5} - 4 \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} a c^{2} d^{5}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} - 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right) - \frac{9}{2} \, {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} b^{2} c d^{5} - 4 \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} a c^{2} d^{5}\right)} \log\left(2 \, c d x + b d + \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right) + \frac{9}{2} \, {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} b^{2} c d^{5} - 4 \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} a c^{2} d^{5}\right)} \log\left(2 \, c d x + b d - \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right) + \frac{4 \, {\left(\sqrt{2 \, c d x + b d} b^{4} c d^{7} - 8 \, \sqrt{2 \, c d x + b d} a b^{2} c^{2} d^{7} + 16 \, \sqrt{2 \, c d x + b d} a^{2} c^{3} d^{7}\right)}}{b^{2} d^{2} - 4 \, a c d^{2} - {\left(2 \, c d x + b d\right)}^{2}}"," ",0,"32*sqrt(2*c*d*x + b*d)*b^2*c*d^5 - 128*sqrt(2*c*d*x + b*d)*a*c^2*d^5 + 16/5*(2*c*d*x + b*d)^(5/2)*c*d^3 - 9*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*b^2*c*d^5 - 4*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*a*c^2*d^5)*arctan(1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) + 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4)) - 9*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*b^2*c*d^5 - 4*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*a*c^2*d^5)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) - 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4)) - 9/2*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*b^2*c*d^5 - 4*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*a*c^2*d^5)*log(2*c*d*x + b*d + sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2)) + 9/2*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*b^2*c*d^5 - 4*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*a*c^2*d^5)*log(2*c*d*x + b*d - sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2)) + 4*(sqrt(2*c*d*x + b*d)*b^4*c*d^7 - 8*sqrt(2*c*d*x + b*d)*a*b^2*c^2*d^7 + 16*sqrt(2*c*d*x + b*d)*a^2*c^3*d^7)/(b^2*d^2 - 4*a*c*d^2 - (2*c*d*x + b*d)^2)","B",0
1298,1,441,0,0.281451," ","integrate((2*c*d*x+b*d)^(9/2)/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","-7 \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} c d^{3} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} + 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right) - 7 \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} c d^{3} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} - 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right) + \frac{7}{2} \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} c d^{3} \log\left(2 \, c d x + b d + \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right) - \frac{7}{2} \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} c d^{3} \log\left(2 \, c d x + b d - \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right) + \frac{16}{3} \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} c d^{3} + \frac{4 \, {\left({\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b^{2} c d^{5} - 4 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} a c^{2} d^{5}\right)}}{b^{2} d^{2} - 4 \, a c d^{2} - {\left(2 \, c d x + b d\right)}^{2}}"," ",0,"-7*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*c*d^3*arctan(1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) + 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4)) - 7*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*c*d^3*arctan(-1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) - 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4)) + 7/2*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*c*d^3*log(2*c*d*x + b*d + sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2)) - 7/2*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*c*d^3*log(2*c*d*x + b*d - sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2)) + 16/3*(2*c*d*x + b*d)^(3/2)*c*d^3 + 4*((2*c*d*x + b*d)^(3/2)*b^2*c*d^5 - 4*(2*c*d*x + b*d)^(3/2)*a*c^2*d^5)/(b^2*d^2 - 4*a*c*d^2 - (2*c*d*x + b*d)^2)","B",0
1299,1,441,0,0.252657," ","integrate((2*c*d*x+b*d)^(7/2)/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","-5 \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} c d^{3} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} + 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right) - 5 \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} c d^{3} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} - 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right) - \frac{5}{2} \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} c d^{3} \log\left(2 \, c d x + b d + \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right) + \frac{5}{2} \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} c d^{3} \log\left(2 \, c d x + b d - \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right) + 16 \, \sqrt{2 \, c d x + b d} c d^{3} + \frac{4 \, {\left(\sqrt{2 \, c d x + b d} b^{2} c d^{5} - 4 \, \sqrt{2 \, c d x + b d} a c^{2} d^{5}\right)}}{b^{2} d^{2} - 4 \, a c d^{2} - {\left(2 \, c d x + b d\right)}^{2}}"," ",0,"-5*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*c*d^3*arctan(1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) + 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4)) - 5*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*c*d^3*arctan(-1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) - 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4)) - 5/2*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*c*d^3*log(2*c*d*x + b*d + sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2)) + 5/2*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*c*d^3*log(2*c*d*x + b*d - sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2)) + 16*sqrt(2*c*d*x + b*d)*c*d^3 + 4*(sqrt(2*c*d*x + b*d)*b^2*c*d^5 - 4*sqrt(2*c*d*x + b*d)*a*c^2*d^5)/(b^2*d^2 - 4*a*c*d^2 - (2*c*d*x + b*d)^2)","B",0
1300,1,439,0,0.263469," ","integrate((2*c*d*x+b*d)^(5/2)/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{4 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} c d^{3}}{b^{2} d^{2} - 4 \, a c d^{2} - {\left(2 \, c d x + b d\right)}^{2}} - \frac{3 \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} c d \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} + 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right)}{b^{2} - 4 \, a c} - \frac{3 \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} c d \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} - 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right)}{b^{2} - 4 \, a c} + \frac{3 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} c d \log\left(2 \, c d x + b d + \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right)}{\sqrt{2} b^{2} - 4 \, \sqrt{2} a c} - \frac{3 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} c d \log\left(2 \, c d x + b d - \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right)}{\sqrt{2} b^{2} - 4 \, \sqrt{2} a c}"," ",0,"4*(2*c*d*x + b*d)^(3/2)*c*d^3/(b^2*d^2 - 4*a*c*d^2 - (2*c*d*x + b*d)^2) - 3*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*c*d*arctan(1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) + 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4))/(b^2 - 4*a*c) - 3*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*c*d*arctan(-1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) - 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4))/(b^2 - 4*a*c) + 3*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*c*d*log(2*c*d*x + b*d + sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2))/(sqrt(2)*b^2 - 4*sqrt(2)*a*c) - 3*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*c*d*log(2*c*d*x + b*d - sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2))/(sqrt(2)*b^2 - 4*sqrt(2)*a*c)","B",0
1301,1,438,0,0.251319," ","integrate((2*c*d*x+b*d)^(3/2)/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{4 \, \sqrt{2 \, c d x + b d} c d^{3}}{b^{2} d^{2} - 4 \, a c d^{2} - {\left(2 \, c d x + b d\right)}^{2}} - \frac{\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} c d \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} + 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right)}{b^{2} - 4 \, a c} - \frac{\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} c d \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} - 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right)}{b^{2} - 4 \, a c} - \frac{{\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} c d \log\left(2 \, c d x + b d + \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right)}{\sqrt{2} b^{2} - 4 \, \sqrt{2} a c} + \frac{{\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} c d \log\left(2 \, c d x + b d - \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right)}{\sqrt{2} b^{2} - 4 \, \sqrt{2} a c}"," ",0,"4*sqrt(2*c*d*x + b*d)*c*d^3/(b^2*d^2 - 4*a*c*d^2 - (2*c*d*x + b*d)^2) - sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*c*d*arctan(1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) + 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4))/(b^2 - 4*a*c) - sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*c*d*arctan(-1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) - 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4))/(b^2 - 4*a*c) - (-b^2*d^2 + 4*a*c*d^2)^(1/4)*c*d*log(2*c*d*x + b*d + sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2))/(sqrt(2)*b^2 - 4*sqrt(2)*a*c) + (-b^2*d^2 + 4*a*c*d^2)^(1/4)*c*d*log(2*c*d*x + b*d - sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2))/(sqrt(2)*b^2 - 4*sqrt(2)*a*c)","B",0
1302,1,504,0,0.233803," ","integrate((2*c*d*x+b*d)^(1/2)/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} c \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} + 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right)}{b^{4} d - 8 \, a b^{2} c d + 16 \, a^{2} c^{2} d} + \frac{\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} c \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} - 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right)}{b^{4} d - 8 \, a b^{2} c d + 16 \, a^{2} c^{2} d} - \frac{{\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} c \log\left(2 \, c d x + b d + \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right)}{\sqrt{2} b^{4} d - 8 \, \sqrt{2} a b^{2} c d + 16 \, \sqrt{2} a^{2} c^{2} d} + \frac{{\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} c \log\left(2 \, c d x + b d - \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right)}{\sqrt{2} b^{4} d - 8 \, \sqrt{2} a b^{2} c d + 16 \, \sqrt{2} a^{2} c^{2} d} + \frac{4 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} c d}{{\left(b^{2} d^{2} - 4 \, a c d^{2} - {\left(2 \, c d x + b d\right)}^{2}\right)} {\left(b^{2} - 4 \, a c\right)}}"," ",0,"sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*c*arctan(1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) + 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4))/(b^4*d - 8*a*b^2*c*d + 16*a^2*c^2*d) + sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*c*arctan(-1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) - 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4))/(b^4*d - 8*a*b^2*c*d + 16*a^2*c^2*d) - (-b^2*d^2 + 4*a*c*d^2)^(3/4)*c*log(2*c*d*x + b*d + sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2))/(sqrt(2)*b^4*d - 8*sqrt(2)*a*b^2*c*d + 16*sqrt(2)*a^2*c^2*d) + (-b^2*d^2 + 4*a*c*d^2)^(3/4)*c*log(2*c*d*x + b*d - sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2))/(sqrt(2)*b^4*d - 8*sqrt(2)*a*b^2*c*d + 16*sqrt(2)*a^2*c^2*d) + 4*(2*c*d*x + b*d)^(3/2)*c*d/((b^2*d^2 - 4*a*c*d^2 - (2*c*d*x + b*d)^2)*(b^2 - 4*a*c))","B",0
1303,1,507,0,0.218881," ","integrate(1/(2*c*d*x+b*d)^(1/2)/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{3 \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} c \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} + 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right)}{b^{4} d - 8 \, a b^{2} c d + 16 \, a^{2} c^{2} d} + \frac{3 \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} c \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} - 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right)}{b^{4} d - 8 \, a b^{2} c d + 16 \, a^{2} c^{2} d} + \frac{3 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} c \log\left(2 \, c d x + b d + \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right)}{\sqrt{2} b^{4} d - 8 \, \sqrt{2} a b^{2} c d + 16 \, \sqrt{2} a^{2} c^{2} d} - \frac{3 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} c \log\left(2 \, c d x + b d - \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right)}{\sqrt{2} b^{4} d - 8 \, \sqrt{2} a b^{2} c d + 16 \, \sqrt{2} a^{2} c^{2} d} + \frac{4 \, \sqrt{2 \, c d x + b d} c d}{{\left(b^{2} d^{2} - 4 \, a c d^{2} - {\left(2 \, c d x + b d\right)}^{2}\right)} {\left(b^{2} - 4 \, a c\right)}}"," ",0,"3*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*c*arctan(1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) + 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4))/(b^4*d - 8*a*b^2*c*d + 16*a^2*c^2*d) + 3*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*c*arctan(-1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) - 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4))/(b^4*d - 8*a*b^2*c*d + 16*a^2*c^2*d) + 3*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*c*log(2*c*d*x + b*d + sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2))/(sqrt(2)*b^4*d - 8*sqrt(2)*a*b^2*c*d + 16*sqrt(2)*a^2*c^2*d) - 3*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*c*log(2*c*d*x + b*d - sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2))/(sqrt(2)*b^4*d - 8*sqrt(2)*a*b^2*c*d + 16*sqrt(2)*a^2*c^2*d) + 4*sqrt(2*c*d*x + b*d)*c*d/((b^2*d^2 - 4*a*c*d^2 - (2*c*d*x + b*d)^2)*(b^2 - 4*a*c))","B",0
1304,1,650,0,0.288245," ","integrate(1/(2*c*d*x+b*d)^(3/2)/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{5 \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} c \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} + 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right)}{b^{6} d^{3} - 12 \, a b^{4} c d^{3} + 48 \, a^{2} b^{2} c^{2} d^{3} - 64 \, a^{3} c^{3} d^{3}} + \frac{5 \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} c \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} - 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right)}{b^{6} d^{3} - 12 \, a b^{4} c d^{3} + 48 \, a^{2} b^{2} c^{2} d^{3} - 64 \, a^{3} c^{3} d^{3}} - \frac{5 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} c \log\left(2 \, c d x + b d + \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right)}{\sqrt{2} b^{6} d^{3} - 12 \, \sqrt{2} a b^{4} c d^{3} + 48 \, \sqrt{2} a^{2} b^{2} c^{2} d^{3} - 64 \, \sqrt{2} a^{3} c^{3} d^{3}} + \frac{5 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} c \log\left(2 \, c d x + b d - \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right)}{\sqrt{2} b^{6} d^{3} - 12 \, \sqrt{2} a b^{4} c d^{3} + 48 \, \sqrt{2} a^{2} b^{2} c^{2} d^{3} - 64 \, \sqrt{2} a^{3} c^{3} d^{3}} - \frac{4 \, {\left(4 \, b^{2} c d^{2} - 16 \, a c^{2} d^{2} - 5 \, {\left(2 \, c d x + b d\right)}^{2} c\right)}}{{\left(b^{4} d - 8 \, a b^{2} c d + 16 \, a^{2} c^{2} d\right)} {\left(\sqrt{2 \, c d x + b d} b^{2} d^{2} - 4 \, \sqrt{2 \, c d x + b d} a c d^{2} - {\left(2 \, c d x + b d\right)}^{\frac{5}{2}}\right)}}"," ",0,"5*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*c*arctan(1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) + 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4))/(b^6*d^3 - 12*a*b^4*c*d^3 + 48*a^2*b^2*c^2*d^3 - 64*a^3*c^3*d^3) + 5*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*c*arctan(-1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) - 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4))/(b^6*d^3 - 12*a*b^4*c*d^3 + 48*a^2*b^2*c^2*d^3 - 64*a^3*c^3*d^3) - 5*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*c*log(2*c*d*x + b*d + sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2))/(sqrt(2)*b^6*d^3 - 12*sqrt(2)*a*b^4*c*d^3 + 48*sqrt(2)*a^2*b^2*c^2*d^3 - 64*sqrt(2)*a^3*c^3*d^3) + 5*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*c*log(2*c*d*x + b*d - sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2))/(sqrt(2)*b^6*d^3 - 12*sqrt(2)*a*b^4*c*d^3 + 48*sqrt(2)*a^2*b^2*c^2*d^3 - 64*sqrt(2)*a^3*c^3*d^3) - 4*(4*b^2*c*d^2 - 16*a*c^2*d^2 - 5*(2*c*d*x + b*d)^2*c)/((b^4*d - 8*a*b^2*c*d + 16*a^2*c^2*d)*(sqrt(2*c*d*x + b*d)*b^2*d^2 - 4*sqrt(2*c*d*x + b*d)*a*c*d^2 - (2*c*d*x + b*d)^(5/2)))","B",0
1305,1,646,0,0.286194," ","integrate(1/(2*c*d*x+b*d)^(5/2)/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{7 \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} c \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} + 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right)}{b^{6} d^{3} - 12 \, a b^{4} c d^{3} + 48 \, a^{2} b^{2} c^{2} d^{3} - 64 \, a^{3} c^{3} d^{3}} + \frac{7 \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} c \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} - 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right)}{b^{6} d^{3} - 12 \, a b^{4} c d^{3} + 48 \, a^{2} b^{2} c^{2} d^{3} - 64 \, a^{3} c^{3} d^{3}} + \frac{7 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} c \log\left(2 \, c d x + b d + \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right)}{\sqrt{2} b^{6} d^{3} - 12 \, \sqrt{2} a b^{4} c d^{3} + 48 \, \sqrt{2} a^{2} b^{2} c^{2} d^{3} - 64 \, \sqrt{2} a^{3} c^{3} d^{3}} - \frac{7 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} c \log\left(2 \, c d x + b d - \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right)}{\sqrt{2} b^{6} d^{3} - 12 \, \sqrt{2} a b^{4} c d^{3} + 48 \, \sqrt{2} a^{2} b^{2} c^{2} d^{3} - 64 \, \sqrt{2} a^{3} c^{3} d^{3}} + \frac{4 \, \sqrt{2 \, c d x + b d} c}{{\left(b^{4} d - 8 \, a b^{2} c d + 16 \, a^{2} c^{2} d\right)} {\left(b^{2} d^{2} - 4 \, a c d^{2} - {\left(2 \, c d x + b d\right)}^{2}\right)}} - \frac{16 \, c}{3 \, {\left(b^{4} d - 8 \, a b^{2} c d + 16 \, a^{2} c^{2} d\right)} {\left(2 \, c d x + b d\right)}^{\frac{3}{2}}}"," ",0,"7*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*c*arctan(1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) + 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4))/(b^6*d^3 - 12*a*b^4*c*d^3 + 48*a^2*b^2*c^2*d^3 - 64*a^3*c^3*d^3) + 7*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*c*arctan(-1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) - 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4))/(b^6*d^3 - 12*a*b^4*c*d^3 + 48*a^2*b^2*c^2*d^3 - 64*a^3*c^3*d^3) + 7*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*c*log(2*c*d*x + b*d + sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2))/(sqrt(2)*b^6*d^3 - 12*sqrt(2)*a*b^4*c*d^3 + 48*sqrt(2)*a^2*b^2*c^2*d^3 - 64*sqrt(2)*a^3*c^3*d^3) - 7*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*c*log(2*c*d*x + b*d - sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2))/(sqrt(2)*b^6*d^3 - 12*sqrt(2)*a*b^4*c*d^3 + 48*sqrt(2)*a^2*b^2*c^2*d^3 - 64*sqrt(2)*a^3*c^3*d^3) + 4*sqrt(2*c*d*x + b*d)*c/((b^4*d - 8*a*b^2*c*d + 16*a^2*c^2*d)*(b^2*d^2 - 4*a*c*d^2 - (2*c*d*x + b*d)^2)) - 16/3*c/((b^4*d - 8*a*b^2*c*d + 16*a^2*c^2*d)*(2*c*d*x + b*d)^(3/2))","B",0
1306,1,779,0,0.332908," ","integrate(1/(2*c*d*x+b*d)^(7/2)/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{9 \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} c \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} + 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right)}{b^{8} d^{5} - 16 \, a b^{6} c d^{5} + 96 \, a^{2} b^{4} c^{2} d^{5} - 256 \, a^{3} b^{2} c^{3} d^{5} + 256 \, a^{4} c^{4} d^{5}} + \frac{9 \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} c \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} - 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right)}{b^{8} d^{5} - 16 \, a b^{6} c d^{5} + 96 \, a^{2} b^{4} c^{2} d^{5} - 256 \, a^{3} b^{2} c^{3} d^{5} + 256 \, a^{4} c^{4} d^{5}} - \frac{9 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} c \log\left(2 \, c d x + b d + \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right)}{\sqrt{2} b^{8} d^{5} - 16 \, \sqrt{2} a b^{6} c d^{5} + 96 \, \sqrt{2} a^{2} b^{4} c^{2} d^{5} - 256 \, \sqrt{2} a^{3} b^{2} c^{3} d^{5} + 256 \, \sqrt{2} a^{4} c^{4} d^{5}} + \frac{9 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} c \log\left(2 \, c d x + b d - \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right)}{\sqrt{2} b^{8} d^{5} - 16 \, \sqrt{2} a b^{6} c d^{5} + 96 \, \sqrt{2} a^{2} b^{4} c^{2} d^{5} - 256 \, \sqrt{2} a^{3} b^{2} c^{3} d^{5} + 256 \, \sqrt{2} a^{4} c^{4} d^{5}} + \frac{4 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} c}{{\left(b^{6} d^{3} - 12 \, a b^{4} c d^{3} + 48 \, a^{2} b^{2} c^{2} d^{3} - 64 \, a^{3} c^{3} d^{3}\right)} {\left(b^{2} d^{2} - 4 \, a c d^{2} - {\left(2 \, c d x + b d\right)}^{2}\right)}} - \frac{16 \, {\left(b^{2} c d^{2} - 4 \, a c^{2} d^{2} + 10 \, {\left(2 \, c d x + b d\right)}^{2} c\right)}}{5 \, {\left(b^{6} d^{3} - 12 \, a b^{4} c d^{3} + 48 \, a^{2} b^{2} c^{2} d^{3} - 64 \, a^{3} c^{3} d^{3}\right)} {\left(2 \, c d x + b d\right)}^{\frac{5}{2}}}"," ",0,"9*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*c*arctan(1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) + 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4))/(b^8*d^5 - 16*a*b^6*c*d^5 + 96*a^2*b^4*c^2*d^5 - 256*a^3*b^2*c^3*d^5 + 256*a^4*c^4*d^5) + 9*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*c*arctan(-1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) - 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4))/(b^8*d^5 - 16*a*b^6*c*d^5 + 96*a^2*b^4*c^2*d^5 - 256*a^3*b^2*c^3*d^5 + 256*a^4*c^4*d^5) - 9*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*c*log(2*c*d*x + b*d + sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2))/(sqrt(2)*b^8*d^5 - 16*sqrt(2)*a*b^6*c*d^5 + 96*sqrt(2)*a^2*b^4*c^2*d^5 - 256*sqrt(2)*a^3*b^2*c^3*d^5 + 256*sqrt(2)*a^4*c^4*d^5) + 9*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*c*log(2*c*d*x + b*d - sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2))/(sqrt(2)*b^8*d^5 - 16*sqrt(2)*a*b^6*c*d^5 + 96*sqrt(2)*a^2*b^4*c^2*d^5 - 256*sqrt(2)*a^3*b^2*c^3*d^5 + 256*sqrt(2)*a^4*c^4*d^5) + 4*(2*c*d*x + b*d)^(3/2)*c/((b^6*d^3 - 12*a*b^4*c*d^3 + 48*a^2*b^2*c^2*d^3 - 64*a^3*c^3*d^3)*(b^2*d^2 - 4*a*c*d^2 - (2*c*d*x + b*d)^2)) - 16/5*(b^2*c*d^2 - 4*a*c^2*d^2 + 10*(2*c*d*x + b*d)^2*c)/((b^6*d^3 - 12*a*b^4*c*d^3 + 48*a^2*b^2*c^2*d^3 - 64*a^3*c^3*d^3)*(2*c*d*x + b*d)^(5/2))","B",0
1307,1,753,0,0.407042," ","integrate((2*c*d*x+b*d)^(17/2)/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","64 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b^{2} c^{2} d^{7} - 256 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} a c^{3} d^{7} + \frac{64}{7} \, {\left(2 \, c d x + b d\right)}^{\frac{7}{2}} c^{2} d^{5} - \frac{165}{2} \, {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} b^{2} c^{2} d^{7} - 4 \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} a c^{3} d^{7}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} + 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right) - \frac{165}{2} \, {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} b^{2} c^{2} d^{7} - 4 \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} a c^{3} d^{7}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} - 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right) + \frac{165}{4} \, {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} b^{2} c^{2} d^{7} - 4 \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} a c^{3} d^{7}\right)} \log\left(2 \, c d x + b d + \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right) - \frac{165}{4} \, {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} b^{2} c^{2} d^{7} - 4 \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} a c^{3} d^{7}\right)} \log\left(2 \, c d x + b d - \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right) + \frac{2 \, {\left(23 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b^{6} c^{2} d^{11} - 276 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} a b^{4} c^{3} d^{11} + 1104 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} a^{2} b^{2} c^{4} d^{11} - 1472 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} a^{3} c^{5} d^{11} - 27 \, {\left(2 \, c d x + b d\right)}^{\frac{7}{2}} b^{4} c^{2} d^{9} + 216 \, {\left(2 \, c d x + b d\right)}^{\frac{7}{2}} a b^{2} c^{3} d^{9} - 432 \, {\left(2 \, c d x + b d\right)}^{\frac{7}{2}} a^{2} c^{4} d^{9}\right)}}{{\left(b^{2} d^{2} - 4 \, a c d^{2} - {\left(2 \, c d x + b d\right)}^{2}\right)}^{2}}"," ",0,"64*(2*c*d*x + b*d)^(3/2)*b^2*c^2*d^7 - 256*(2*c*d*x + b*d)^(3/2)*a*c^3*d^7 + 64/7*(2*c*d*x + b*d)^(7/2)*c^2*d^5 - 165/2*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*b^2*c^2*d^7 - 4*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*a*c^3*d^7)*arctan(1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) + 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4)) - 165/2*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*b^2*c^2*d^7 - 4*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*a*c^3*d^7)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) - 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4)) + 165/4*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*b^2*c^2*d^7 - 4*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*a*c^3*d^7)*log(2*c*d*x + b*d + sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2)) - 165/4*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*b^2*c^2*d^7 - 4*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*a*c^3*d^7)*log(2*c*d*x + b*d - sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2)) + 2*(23*(2*c*d*x + b*d)^(3/2)*b^6*c^2*d^11 - 276*(2*c*d*x + b*d)^(3/2)*a*b^4*c^3*d^11 + 1104*(2*c*d*x + b*d)^(3/2)*a^2*b^2*c^4*d^11 - 1472*(2*c*d*x + b*d)^(3/2)*a^3*c^5*d^11 - 27*(2*c*d*x + b*d)^(7/2)*b^4*c^2*d^9 + 216*(2*c*d*x + b*d)^(7/2)*a*b^2*c^3*d^9 - 432*(2*c*d*x + b*d)^(7/2)*a^2*c^4*d^9)/(b^2*d^2 - 4*a*c*d^2 - (2*c*d*x + b*d)^2)^2","B",0
1308,1,753,0,0.391361," ","integrate((2*c*d*x+b*d)^(15/2)/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","192 \, \sqrt{2 \, c d x + b d} b^{2} c^{2} d^{7} - 768 \, \sqrt{2 \, c d x + b d} a c^{3} d^{7} + \frac{64}{5} \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}} c^{2} d^{5} - \frac{117}{2} \, {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} b^{2} c^{2} d^{7} - 4 \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} a c^{3} d^{7}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} + 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right) - \frac{117}{2} \, {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} b^{2} c^{2} d^{7} - 4 \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} a c^{3} d^{7}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} - 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right) - \frac{117}{4} \, {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} b^{2} c^{2} d^{7} - 4 \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} a c^{3} d^{7}\right)} \log\left(2 \, c d x + b d + \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right) + \frac{117}{4} \, {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} b^{2} c^{2} d^{7} - 4 \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} a c^{3} d^{7}\right)} \log\left(2 \, c d x + b d - \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right) + \frac{2 \, {\left(21 \, \sqrt{2 \, c d x + b d} b^{6} c^{2} d^{11} - 252 \, \sqrt{2 \, c d x + b d} a b^{4} c^{3} d^{11} + 1008 \, \sqrt{2 \, c d x + b d} a^{2} b^{2} c^{4} d^{11} - 1344 \, \sqrt{2 \, c d x + b d} a^{3} c^{5} d^{11} - 25 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}} b^{4} c^{2} d^{9} + 200 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}} a b^{2} c^{3} d^{9} - 400 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}} a^{2} c^{4} d^{9}\right)}}{{\left(b^{2} d^{2} - 4 \, a c d^{2} - {\left(2 \, c d x + b d\right)}^{2}\right)}^{2}}"," ",0,"192*sqrt(2*c*d*x + b*d)*b^2*c^2*d^7 - 768*sqrt(2*c*d*x + b*d)*a*c^3*d^7 + 64/5*(2*c*d*x + b*d)^(5/2)*c^2*d^5 - 117/2*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*b^2*c^2*d^7 - 4*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*a*c^3*d^7)*arctan(1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) + 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4)) - 117/2*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*b^2*c^2*d^7 - 4*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*a*c^3*d^7)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) - 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4)) - 117/4*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*b^2*c^2*d^7 - 4*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*a*c^3*d^7)*log(2*c*d*x + b*d + sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2)) + 117/4*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*b^2*c^2*d^7 - 4*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*a*c^3*d^7)*log(2*c*d*x + b*d - sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2)) + 2*(21*sqrt(2*c*d*x + b*d)*b^6*c^2*d^11 - 252*sqrt(2*c*d*x + b*d)*a*b^4*c^3*d^11 + 1008*sqrt(2*c*d*x + b*d)*a^2*b^2*c^4*d^11 - 1344*sqrt(2*c*d*x + b*d)*a^3*c^5*d^11 - 25*(2*c*d*x + b*d)^(5/2)*b^4*c^2*d^9 + 200*(2*c*d*x + b*d)^(5/2)*a*b^2*c^3*d^9 - 400*(2*c*d*x + b*d)^(5/2)*a^2*c^4*d^9)/(b^2*d^2 - 4*a*c*d^2 - (2*c*d*x + b*d)^2)^2","B",0
1309,1,521,0,0.341789," ","integrate((2*c*d*x+b*d)^(13/2)/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","-\frac{77}{2} \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} c^{2} d^{5} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} + 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right) - \frac{77}{2} \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} c^{2} d^{5} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} - 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right) + \frac{77}{4} \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} c^{2} d^{5} \log\left(2 \, c d x + b d + \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right) - \frac{77}{4} \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} c^{2} d^{5} \log\left(2 \, c d x + b d - \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right) + \frac{64}{3} \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} c^{2} d^{5} + \frac{2 \, {\left(15 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b^{4} c^{2} d^{9} - 120 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} a b^{2} c^{3} d^{9} + 240 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} a^{2} c^{4} d^{9} - 19 \, {\left(2 \, c d x + b d\right)}^{\frac{7}{2}} b^{2} c^{2} d^{7} + 76 \, {\left(2 \, c d x + b d\right)}^{\frac{7}{2}} a c^{3} d^{7}\right)}}{{\left(b^{2} d^{2} - 4 \, a c d^{2} - {\left(2 \, c d x + b d\right)}^{2}\right)}^{2}}"," ",0,"-77/2*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*c^2*d^5*arctan(1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) + 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4)) - 77/2*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*c^2*d^5*arctan(-1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) - 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4)) + 77/4*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*c^2*d^5*log(2*c*d*x + b*d + sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2)) - 77/4*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*c^2*d^5*log(2*c*d*x + b*d - sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2)) + 64/3*(2*c*d*x + b*d)^(3/2)*c^2*d^5 + 2*(15*(2*c*d*x + b*d)^(3/2)*b^4*c^2*d^9 - 120*(2*c*d*x + b*d)^(3/2)*a*b^2*c^3*d^9 + 240*(2*c*d*x + b*d)^(3/2)*a^2*c^4*d^9 - 19*(2*c*d*x + b*d)^(7/2)*b^2*c^2*d^7 + 76*(2*c*d*x + b*d)^(7/2)*a*c^3*d^7)/(b^2*d^2 - 4*a*c*d^2 - (2*c*d*x + b*d)^2)^2","B",0
1310,1,521,0,0.351319," ","integrate((2*c*d*x+b*d)^(11/2)/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","-\frac{45}{2} \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} c^{2} d^{5} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} + 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right) - \frac{45}{2} \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} c^{2} d^{5} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} - 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right) - \frac{45}{4} \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} c^{2} d^{5} \log\left(2 \, c d x + b d + \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right) + \frac{45}{4} \, \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} c^{2} d^{5} \log\left(2 \, c d x + b d - \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right) + 64 \, \sqrt{2 \, c d x + b d} c^{2} d^{5} + \frac{2 \, {\left(13 \, \sqrt{2 \, c d x + b d} b^{4} c^{2} d^{9} - 104 \, \sqrt{2 \, c d x + b d} a b^{2} c^{3} d^{9} + 208 \, \sqrt{2 \, c d x + b d} a^{2} c^{4} d^{9} - 17 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}} b^{2} c^{2} d^{7} + 68 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}} a c^{3} d^{7}\right)}}{{\left(b^{2} d^{2} - 4 \, a c d^{2} - {\left(2 \, c d x + b d\right)}^{2}\right)}^{2}}"," ",0,"-45/2*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*c^2*d^5*arctan(1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) + 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4)) - 45/2*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*c^2*d^5*arctan(-1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) - 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4)) - 45/4*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*c^2*d^5*log(2*c*d*x + b*d + sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2)) + 45/4*sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*c^2*d^5*log(2*c*d*x + b*d - sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2)) + 64*sqrt(2*c*d*x + b*d)*c^2*d^5 + 2*(13*sqrt(2*c*d*x + b*d)*b^4*c^2*d^9 - 104*sqrt(2*c*d*x + b*d)*a*b^2*c^3*d^9 + 208*sqrt(2*c*d*x + b*d)*a^2*c^4*d^9 - 17*(2*c*d*x + b*d)^(5/2)*b^2*c^2*d^7 + 68*(2*c*d*x + b*d)^(5/2)*a*c^3*d^7)/(b^2*d^2 - 4*a*c*d^2 - (2*c*d*x + b*d)^2)^2","B",0
1311,1,510,0,0.315618," ","integrate((2*c*d*x+b*d)^(9/2)/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","-\frac{21 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} c^{2} d^{3} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} + 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right)}{\sqrt{2} b^{2} - 4 \, \sqrt{2} a c} - \frac{21 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} c^{2} d^{3} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} - 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right)}{\sqrt{2} b^{2} - 4 \, \sqrt{2} a c} + \frac{21 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} c^{2} d^{3} \log\left(2 \, c d x + b d + \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right)}{2 \, {\left(\sqrt{2} b^{2} - 4 \, \sqrt{2} a c\right)}} - \frac{21 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} c^{2} d^{3} \log\left(2 \, c d x + b d - \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right)}{2 \, {\left(\sqrt{2} b^{2} - 4 \, \sqrt{2} a c\right)}} + \frac{2 \, {\left(7 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b^{2} c^{2} d^{7} - 28 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} a c^{3} d^{7} - 11 \, {\left(2 \, c d x + b d\right)}^{\frac{7}{2}} c^{2} d^{5}\right)}}{{\left(b^{2} d^{2} - 4 \, a c d^{2} - {\left(2 \, c d x + b d\right)}^{2}\right)}^{2}}"," ",0,"-21*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*c^2*d^3*arctan(1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) + 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4))/(sqrt(2)*b^2 - 4*sqrt(2)*a*c) - 21*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*c^2*d^3*arctan(-1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) - 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4))/(sqrt(2)*b^2 - 4*sqrt(2)*a*c) + 21/2*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*c^2*d^3*log(2*c*d*x + b*d + sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2))/(sqrt(2)*b^2 - 4*sqrt(2)*a*c) - 21/2*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*c^2*d^3*log(2*c*d*x + b*d - sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2))/(sqrt(2)*b^2 - 4*sqrt(2)*a*c) + 2*(7*(2*c*d*x + b*d)^(3/2)*b^2*c^2*d^7 - 28*(2*c*d*x + b*d)^(3/2)*a*c^3*d^7 - 11*(2*c*d*x + b*d)^(7/2)*c^2*d^5)/(b^2*d^2 - 4*a*c*d^2 - (2*c*d*x + b*d)^2)^2","B",0
1312,1,510,0,0.286700," ","integrate((2*c*d*x+b*d)^(7/2)/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","-\frac{5 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} c^{2} d^{3} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} + 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right)}{\sqrt{2} b^{2} - 4 \, \sqrt{2} a c} - \frac{5 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} c^{2} d^{3} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} - 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right)}{\sqrt{2} b^{2} - 4 \, \sqrt{2} a c} - \frac{5 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} c^{2} d^{3} \log\left(2 \, c d x + b d + \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right)}{2 \, {\left(\sqrt{2} b^{2} - 4 \, \sqrt{2} a c\right)}} + \frac{5 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} c^{2} d^{3} \log\left(2 \, c d x + b d - \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right)}{2 \, {\left(\sqrt{2} b^{2} - 4 \, \sqrt{2} a c\right)}} + \frac{2 \, {\left(5 \, \sqrt{2 \, c d x + b d} b^{2} c^{2} d^{7} - 20 \, \sqrt{2 \, c d x + b d} a c^{3} d^{7} - 9 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}} c^{2} d^{5}\right)}}{{\left(b^{2} d^{2} - 4 \, a c d^{2} - {\left(2 \, c d x + b d\right)}^{2}\right)}^{2}}"," ",0,"-5*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*c^2*d^3*arctan(1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) + 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4))/(sqrt(2)*b^2 - 4*sqrt(2)*a*c) - 5*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*c^2*d^3*arctan(-1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) - 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4))/(sqrt(2)*b^2 - 4*sqrt(2)*a*c) - 5/2*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*c^2*d^3*log(2*c*d*x + b*d + sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2))/(sqrt(2)*b^2 - 4*sqrt(2)*a*c) + 5/2*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*c^2*d^3*log(2*c*d*x + b*d - sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2))/(sqrt(2)*b^2 - 4*sqrt(2)*a*c) + 2*(5*sqrt(2*c*d*x + b*d)*b^2*c^2*d^7 - 20*sqrt(2*c*d*x + b*d)*a*c^3*d^7 - 9*(2*c*d*x + b*d)^(5/2)*c^2*d^5)/(b^2*d^2 - 4*a*c*d^2 - (2*c*d*x + b*d)^2)^2","B",0
1313,1,567,0,0.316087," ","integrate((2*c*d*x+b*d)^(5/2)/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{3 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} c^{2} d \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} + 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right)}{\sqrt{2} b^{4} - 8 \, \sqrt{2} a b^{2} c + 16 \, \sqrt{2} a^{2} c^{2}} + \frac{3 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} c^{2} d \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} - 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right)}{\sqrt{2} b^{4} - 8 \, \sqrt{2} a b^{2} c + 16 \, \sqrt{2} a^{2} c^{2}} - \frac{3 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} c^{2} d \log\left(2 \, c d x + b d + \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right)}{2 \, {\left(\sqrt{2} b^{4} - 8 \, \sqrt{2} a b^{2} c + 16 \, \sqrt{2} a^{2} c^{2}\right)}} + \frac{3 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} c^{2} d \log\left(2 \, c d x + b d - \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right)}{2 \, {\left(\sqrt{2} b^{4} - 8 \, \sqrt{2} a b^{2} c + 16 \, \sqrt{2} a^{2} c^{2}\right)}} - \frac{2 \, {\left({\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b^{2} c^{2} d^{5} - 4 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} a c^{3} d^{5} + 3 \, {\left(2 \, c d x + b d\right)}^{\frac{7}{2}} c^{2} d^{3}\right)}}{{\left(b^{2} d^{2} - 4 \, a c d^{2} - {\left(2 \, c d x + b d\right)}^{2}\right)}^{2} {\left(b^{2} - 4 \, a c\right)}}"," ",0,"3*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*c^2*d*arctan(1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) + 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4))/(sqrt(2)*b^4 - 8*sqrt(2)*a*b^2*c + 16*sqrt(2)*a^2*c^2) + 3*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*c^2*d*arctan(-1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) - 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4))/(sqrt(2)*b^4 - 8*sqrt(2)*a*b^2*c + 16*sqrt(2)*a^2*c^2) - 3/2*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*c^2*d*log(2*c*d*x + b*d + sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2))/(sqrt(2)*b^4 - 8*sqrt(2)*a*b^2*c + 16*sqrt(2)*a^2*c^2) + 3/2*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*c^2*d*log(2*c*d*x + b*d - sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2))/(sqrt(2)*b^4 - 8*sqrt(2)*a*b^2*c + 16*sqrt(2)*a^2*c^2) - 2*((2*c*d*x + b*d)^(3/2)*b^2*c^2*d^5 - 4*(2*c*d*x + b*d)^(3/2)*a*c^3*d^5 + 3*(2*c*d*x + b*d)^(7/2)*c^2*d^3)/((b^2*d^2 - 4*a*c*d^2 - (2*c*d*x + b*d)^2)^2*(b^2 - 4*a*c))","B",0
1314,1,567,0,0.285576," ","integrate((2*c*d*x+b*d)^(3/2)/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{3 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} c^{2} d \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} + 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right)}{\sqrt{2} b^{4} - 8 \, \sqrt{2} a b^{2} c + 16 \, \sqrt{2} a^{2} c^{2}} + \frac{3 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} c^{2} d \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} - 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right)}{\sqrt{2} b^{4} - 8 \, \sqrt{2} a b^{2} c + 16 \, \sqrt{2} a^{2} c^{2}} + \frac{3 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} c^{2} d \log\left(2 \, c d x + b d + \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right)}{2 \, {\left(\sqrt{2} b^{4} - 8 \, \sqrt{2} a b^{2} c + 16 \, \sqrt{2} a^{2} c^{2}\right)}} - \frac{3 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} c^{2} d \log\left(2 \, c d x + b d - \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right)}{2 \, {\left(\sqrt{2} b^{4} - 8 \, \sqrt{2} a b^{2} c + 16 \, \sqrt{2} a^{2} c^{2}\right)}} - \frac{2 \, {\left(3 \, \sqrt{2 \, c d x + b d} b^{2} c^{2} d^{5} - 12 \, \sqrt{2 \, c d x + b d} a c^{3} d^{5} + {\left(2 \, c d x + b d\right)}^{\frac{5}{2}} c^{2} d^{3}\right)}}{{\left(b^{2} d^{2} - 4 \, a c d^{2} - {\left(2 \, c d x + b d\right)}^{2}\right)}^{2} {\left(b^{2} - 4 \, a c\right)}}"," ",0,"3*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*c^2*d*arctan(1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) + 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4))/(sqrt(2)*b^4 - 8*sqrt(2)*a*b^2*c + 16*sqrt(2)*a^2*c^2) + 3*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*c^2*d*arctan(-1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) - 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4))/(sqrt(2)*b^4 - 8*sqrt(2)*a*b^2*c + 16*sqrt(2)*a^2*c^2) + 3/2*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*c^2*d*log(2*c*d*x + b*d + sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2))/(sqrt(2)*b^4 - 8*sqrt(2)*a*b^2*c + 16*sqrt(2)*a^2*c^2) - 3/2*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*c^2*d*log(2*c*d*x + b*d - sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2))/(sqrt(2)*b^4 - 8*sqrt(2)*a*b^2*c + 16*sqrt(2)*a^2*c^2) - 2*(3*sqrt(2*c*d*x + b*d)*b^2*c^2*d^5 - 12*sqrt(2*c*d*x + b*d)*a*c^3*d^5 + (2*c*d*x + b*d)^(5/2)*c^2*d^3)/((b^2*d^2 - 4*a*c*d^2 - (2*c*d*x + b*d)^2)^2*(b^2 - 4*a*c))","B",0
1315,1,645,0,0.281509," ","integrate((2*c*d*x+b*d)^(1/2)/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","-\frac{5 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} c^{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} + 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right)}{\sqrt{2} b^{6} d - 12 \, \sqrt{2} a b^{4} c d + 48 \, \sqrt{2} a^{2} b^{2} c^{2} d - 64 \, \sqrt{2} a^{3} c^{3} d} - \frac{5 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} c^{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} - 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right)}{\sqrt{2} b^{6} d - 12 \, \sqrt{2} a b^{4} c d + 48 \, \sqrt{2} a^{2} b^{2} c^{2} d - 64 \, \sqrt{2} a^{3} c^{3} d} + \frac{5 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} c^{2} \log\left(2 \, c d x + b d + \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right)}{2 \, {\left(\sqrt{2} b^{6} d - 12 \, \sqrt{2} a b^{4} c d + 48 \, \sqrt{2} a^{2} b^{2} c^{2} d - 64 \, \sqrt{2} a^{3} c^{3} d\right)}} - \frac{5 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} c^{2} \log\left(2 \, c d x + b d - \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right)}{2 \, {\left(\sqrt{2} b^{6} d - 12 \, \sqrt{2} a b^{4} c d + 48 \, \sqrt{2} a^{2} b^{2} c^{2} d - 64 \, \sqrt{2} a^{3} c^{3} d\right)}} - \frac{2 \, {\left(9 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b^{2} c^{2} d^{3} - 36 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} a c^{3} d^{3} - 5 \, {\left(2 \, c d x + b d\right)}^{\frac{7}{2}} c^{2} d\right)}}{{\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} {\left(b^{2} d^{2} - 4 \, a c d^{2} - {\left(2 \, c d x + b d\right)}^{2}\right)}^{2}}"," ",0,"-5*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*c^2*arctan(1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) + 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4))/(sqrt(2)*b^6*d - 12*sqrt(2)*a*b^4*c*d + 48*sqrt(2)*a^2*b^2*c^2*d - 64*sqrt(2)*a^3*c^3*d) - 5*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*c^2*arctan(-1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) - 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4))/(sqrt(2)*b^6*d - 12*sqrt(2)*a*b^4*c*d + 48*sqrt(2)*a^2*b^2*c^2*d - 64*sqrt(2)*a^3*c^3*d) + 5/2*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*c^2*log(2*c*d*x + b*d + sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2))/(sqrt(2)*b^6*d - 12*sqrt(2)*a*b^4*c*d + 48*sqrt(2)*a^2*b^2*c^2*d - 64*sqrt(2)*a^3*c^3*d) - 5/2*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*c^2*log(2*c*d*x + b*d - sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2))/(sqrt(2)*b^6*d - 12*sqrt(2)*a*b^4*c*d + 48*sqrt(2)*a^2*b^2*c^2*d - 64*sqrt(2)*a^3*c^3*d) - 2*(9*(2*c*d*x + b*d)^(3/2)*b^2*c^2*d^3 - 36*(2*c*d*x + b*d)^(3/2)*a*c^3*d^3 - 5*(2*c*d*x + b*d)^(7/2)*c^2*d)/((b^4 - 8*a*b^2*c + 16*a^2*c^2)*(b^2*d^2 - 4*a*c*d^2 - (2*c*d*x + b*d)^2)^2)","B",0
1316,1,645,0,0.267939," ","integrate(1/(2*c*d*x+b*d)^(1/2)/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","-\frac{21 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} c^{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} + 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right)}{\sqrt{2} b^{6} d - 12 \, \sqrt{2} a b^{4} c d + 48 \, \sqrt{2} a^{2} b^{2} c^{2} d - 64 \, \sqrt{2} a^{3} c^{3} d} - \frac{21 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} c^{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} - 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right)}{\sqrt{2} b^{6} d - 12 \, \sqrt{2} a b^{4} c d + 48 \, \sqrt{2} a^{2} b^{2} c^{2} d - 64 \, \sqrt{2} a^{3} c^{3} d} - \frac{21 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} c^{2} \log\left(2 \, c d x + b d + \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right)}{2 \, {\left(\sqrt{2} b^{6} d - 12 \, \sqrt{2} a b^{4} c d + 48 \, \sqrt{2} a^{2} b^{2} c^{2} d - 64 \, \sqrt{2} a^{3} c^{3} d\right)}} + \frac{21 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} c^{2} \log\left(2 \, c d x + b d - \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right)}{2 \, {\left(\sqrt{2} b^{6} d - 12 \, \sqrt{2} a b^{4} c d + 48 \, \sqrt{2} a^{2} b^{2} c^{2} d - 64 \, \sqrt{2} a^{3} c^{3} d\right)}} - \frac{2 \, {\left(11 \, \sqrt{2 \, c d x + b d} b^{2} c^{2} d^{3} - 44 \, \sqrt{2 \, c d x + b d} a c^{3} d^{3} - 7 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}} c^{2} d\right)}}{{\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} {\left(b^{2} d^{2} - 4 \, a c d^{2} - {\left(2 \, c d x + b d\right)}^{2}\right)}^{2}}"," ",0,"-21*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*c^2*arctan(1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) + 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4))/(sqrt(2)*b^6*d - 12*sqrt(2)*a*b^4*c*d + 48*sqrt(2)*a^2*b^2*c^2*d - 64*sqrt(2)*a^3*c^3*d) - 21*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*c^2*arctan(-1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) - 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4))/(sqrt(2)*b^6*d - 12*sqrt(2)*a*b^4*c*d + 48*sqrt(2)*a^2*b^2*c^2*d - 64*sqrt(2)*a^3*c^3*d) - 21/2*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*c^2*log(2*c*d*x + b*d + sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2))/(sqrt(2)*b^6*d - 12*sqrt(2)*a*b^4*c*d + 48*sqrt(2)*a^2*b^2*c^2*d - 64*sqrt(2)*a^3*c^3*d) + 21/2*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*c^2*log(2*c*d*x + b*d - sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2))/(sqrt(2)*b^6*d - 12*sqrt(2)*a*b^4*c*d + 48*sqrt(2)*a^2*b^2*c^2*d - 64*sqrt(2)*a^3*c^3*d) - 2*(11*sqrt(2*c*d*x + b*d)*b^2*c^2*d^3 - 44*sqrt(2*c*d*x + b*d)*a*c^3*d^3 - 7*(2*c*d*x + b*d)^(5/2)*c^2*d)/((b^4 - 8*a*b^2*c + 16*a^2*c^2)*(b^2*d^2 - 4*a*c*d^2 - (2*c*d*x + b*d)^2)^2)","B",0
1317,1,813,0,0.354899," ","integrate(1/(2*c*d*x+b*d)^(3/2)/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","-\frac{45 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} c^{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} + 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right)}{\sqrt{2} b^{8} d^{3} - 16 \, \sqrt{2} a b^{6} c d^{3} + 96 \, \sqrt{2} a^{2} b^{4} c^{2} d^{3} - 256 \, \sqrt{2} a^{3} b^{2} c^{3} d^{3} + 256 \, \sqrt{2} a^{4} c^{4} d^{3}} - \frac{45 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} c^{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} - 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right)}{\sqrt{2} b^{8} d^{3} - 16 \, \sqrt{2} a b^{6} c d^{3} + 96 \, \sqrt{2} a^{2} b^{4} c^{2} d^{3} - 256 \, \sqrt{2} a^{3} b^{2} c^{3} d^{3} + 256 \, \sqrt{2} a^{4} c^{4} d^{3}} + \frac{45 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} c^{2} \log\left(2 \, c d x + b d + \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right)}{2 \, {\left(\sqrt{2} b^{8} d^{3} - 16 \, \sqrt{2} a b^{6} c d^{3} + 96 \, \sqrt{2} a^{2} b^{4} c^{2} d^{3} - 256 \, \sqrt{2} a^{3} b^{2} c^{3} d^{3} + 256 \, \sqrt{2} a^{4} c^{4} d^{3}\right)}} - \frac{45 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} c^{2} \log\left(2 \, c d x + b d - \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right)}{2 \, {\left(\sqrt{2} b^{8} d^{3} - 16 \, \sqrt{2} a b^{6} c d^{3} + 96 \, \sqrt{2} a^{2} b^{4} c^{2} d^{3} - 256 \, \sqrt{2} a^{3} b^{2} c^{3} d^{3} + 256 \, \sqrt{2} a^{4} c^{4} d^{3}\right)}} + \frac{64 \, c^{2}}{{\left(b^{6} d - 12 \, a b^{4} c d + 48 \, a^{2} b^{2} c^{2} d - 64 \, a^{3} c^{3} d\right)} \sqrt{2 \, c d x + b d}} - \frac{2 \, {\left(17 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b^{2} c^{2} d^{2} - 68 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} a c^{3} d^{2} - 13 \, {\left(2 \, c d x + b d\right)}^{\frac{7}{2}} c^{2}\right)}}{{\left(b^{6} d - 12 \, a b^{4} c d + 48 \, a^{2} b^{2} c^{2} d - 64 \, a^{3} c^{3} d\right)} {\left(b^{2} d^{2} - 4 \, a c d^{2} - {\left(2 \, c d x + b d\right)}^{2}\right)}^{2}}"," ",0,"-45*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*c^2*arctan(1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) + 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4))/(sqrt(2)*b^8*d^3 - 16*sqrt(2)*a*b^6*c*d^3 + 96*sqrt(2)*a^2*b^4*c^2*d^3 - 256*sqrt(2)*a^3*b^2*c^3*d^3 + 256*sqrt(2)*a^4*c^4*d^3) - 45*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*c^2*arctan(-1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) - 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4))/(sqrt(2)*b^8*d^3 - 16*sqrt(2)*a*b^6*c*d^3 + 96*sqrt(2)*a^2*b^4*c^2*d^3 - 256*sqrt(2)*a^3*b^2*c^3*d^3 + 256*sqrt(2)*a^4*c^4*d^3) + 45/2*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*c^2*log(2*c*d*x + b*d + sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2))/(sqrt(2)*b^8*d^3 - 16*sqrt(2)*a*b^6*c*d^3 + 96*sqrt(2)*a^2*b^4*c^2*d^3 - 256*sqrt(2)*a^3*b^2*c^3*d^3 + 256*sqrt(2)*a^4*c^4*d^3) - 45/2*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*c^2*log(2*c*d*x + b*d - sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2))/(sqrt(2)*b^8*d^3 - 16*sqrt(2)*a*b^6*c*d^3 + 96*sqrt(2)*a^2*b^4*c^2*d^3 - 256*sqrt(2)*a^3*b^2*c^3*d^3 + 256*sqrt(2)*a^4*c^4*d^3) + 64*c^2/((b^6*d - 12*a*b^4*c*d + 48*a^2*b^2*c^2*d - 64*a^3*c^3*d)*sqrt(2*c*d*x + b*d)) - 2*(17*(2*c*d*x + b*d)^(3/2)*b^2*c^2*d^2 - 68*(2*c*d*x + b*d)^(3/2)*a*c^3*d^2 - 13*(2*c*d*x + b*d)^(7/2)*c^2)/((b^6*d - 12*a*b^4*c*d + 48*a^2*b^2*c^2*d - 64*a^3*c^3*d)*(b^2*d^2 - 4*a*c*d^2 - (2*c*d*x + b*d)^2)^2)","B",0
1318,1,813,0,0.349745," ","integrate(1/(2*c*d*x+b*d)^(5/2)/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","-\frac{77 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} c^{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} + 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right)}{\sqrt{2} b^{8} d^{3} - 16 \, \sqrt{2} a b^{6} c d^{3} + 96 \, \sqrt{2} a^{2} b^{4} c^{2} d^{3} - 256 \, \sqrt{2} a^{3} b^{2} c^{3} d^{3} + 256 \, \sqrt{2} a^{4} c^{4} d^{3}} - \frac{77 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} c^{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} - 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right)}{\sqrt{2} b^{8} d^{3} - 16 \, \sqrt{2} a b^{6} c d^{3} + 96 \, \sqrt{2} a^{2} b^{4} c^{2} d^{3} - 256 \, \sqrt{2} a^{3} b^{2} c^{3} d^{3} + 256 \, \sqrt{2} a^{4} c^{4} d^{3}} - \frac{77 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} c^{2} \log\left(2 \, c d x + b d + \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right)}{2 \, {\left(\sqrt{2} b^{8} d^{3} - 16 \, \sqrt{2} a b^{6} c d^{3} + 96 \, \sqrt{2} a^{2} b^{4} c^{2} d^{3} - 256 \, \sqrt{2} a^{3} b^{2} c^{3} d^{3} + 256 \, \sqrt{2} a^{4} c^{4} d^{3}\right)}} + \frac{77 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} c^{2} \log\left(2 \, c d x + b d - \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right)}{2 \, {\left(\sqrt{2} b^{8} d^{3} - 16 \, \sqrt{2} a b^{6} c d^{3} + 96 \, \sqrt{2} a^{2} b^{4} c^{2} d^{3} - 256 \, \sqrt{2} a^{3} b^{2} c^{3} d^{3} + 256 \, \sqrt{2} a^{4} c^{4} d^{3}\right)}} + \frac{64 \, c^{2}}{3 \, {\left(b^{6} d - 12 \, a b^{4} c d + 48 \, a^{2} b^{2} c^{2} d - 64 \, a^{3} c^{3} d\right)} {\left(2 \, c d x + b d\right)}^{\frac{3}{2}}} - \frac{2 \, {\left(19 \, \sqrt{2 \, c d x + b d} b^{2} c^{2} d^{2} - 76 \, \sqrt{2 \, c d x + b d} a c^{3} d^{2} - 15 \, {\left(2 \, c d x + b d\right)}^{\frac{5}{2}} c^{2}\right)}}{{\left(b^{6} d - 12 \, a b^{4} c d + 48 \, a^{2} b^{2} c^{2} d - 64 \, a^{3} c^{3} d\right)} {\left(b^{2} d^{2} - 4 \, a c d^{2} - {\left(2 \, c d x + b d\right)}^{2}\right)}^{2}}"," ",0,"-77*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*c^2*arctan(1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) + 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4))/(sqrt(2)*b^8*d^3 - 16*sqrt(2)*a*b^6*c*d^3 + 96*sqrt(2)*a^2*b^4*c^2*d^3 - 256*sqrt(2)*a^3*b^2*c^3*d^3 + 256*sqrt(2)*a^4*c^4*d^3) - 77*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*c^2*arctan(-1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) - 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4))/(sqrt(2)*b^8*d^3 - 16*sqrt(2)*a*b^6*c*d^3 + 96*sqrt(2)*a^2*b^4*c^2*d^3 - 256*sqrt(2)*a^3*b^2*c^3*d^3 + 256*sqrt(2)*a^4*c^4*d^3) - 77/2*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*c^2*log(2*c*d*x + b*d + sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2))/(sqrt(2)*b^8*d^3 - 16*sqrt(2)*a*b^6*c*d^3 + 96*sqrt(2)*a^2*b^4*c^2*d^3 - 256*sqrt(2)*a^3*b^2*c^3*d^3 + 256*sqrt(2)*a^4*c^4*d^3) + 77/2*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*c^2*log(2*c*d*x + b*d - sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2))/(sqrt(2)*b^8*d^3 - 16*sqrt(2)*a*b^6*c*d^3 + 96*sqrt(2)*a^2*b^4*c^2*d^3 - 256*sqrt(2)*a^3*b^2*c^3*d^3 + 256*sqrt(2)*a^4*c^4*d^3) + 64/3*c^2/((b^6*d - 12*a*b^4*c*d + 48*a^2*b^2*c^2*d - 64*a^3*c^3*d)*(2*c*d*x + b*d)^(3/2)) - 2*(19*sqrt(2*c*d*x + b*d)*b^2*c^2*d^2 - 76*sqrt(2*c*d*x + b*d)*a*c^3*d^2 - 15*(2*c*d*x + b*d)^(5/2)*c^2)/((b^6*d - 12*a*b^4*c*d + 48*a^2*b^2*c^2*d - 64*a^3*c^3*d)*(b^2*d^2 - 4*a*c*d^2 - (2*c*d*x + b*d)^2)^2)","B",0
1319,1,958,0,0.447265," ","integrate(1/(2*c*d*x+b*d)^(7/2)/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","-\frac{117 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} c^{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} + 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right)}{\sqrt{2} b^{10} d^{5} - 20 \, \sqrt{2} a b^{8} c d^{5} + 160 \, \sqrt{2} a^{2} b^{6} c^{2} d^{5} - 640 \, \sqrt{2} a^{3} b^{4} c^{3} d^{5} + 1280 \, \sqrt{2} a^{4} b^{2} c^{4} d^{5} - 1024 \, \sqrt{2} a^{5} c^{5} d^{5}} - \frac{117 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} c^{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} - 2 \, \sqrt{2 \, c d x + b d}\right)}}{2 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}}}\right)}{\sqrt{2} b^{10} d^{5} - 20 \, \sqrt{2} a b^{8} c d^{5} + 160 \, \sqrt{2} a^{2} b^{6} c^{2} d^{5} - 640 \, \sqrt{2} a^{3} b^{4} c^{3} d^{5} + 1280 \, \sqrt{2} a^{4} b^{2} c^{4} d^{5} - 1024 \, \sqrt{2} a^{5} c^{5} d^{5}} + \frac{117 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} c^{2} \log\left(2 \, c d x + b d + \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right)}{2 \, {\left(\sqrt{2} b^{10} d^{5} - 20 \, \sqrt{2} a b^{8} c d^{5} + 160 \, \sqrt{2} a^{2} b^{6} c^{2} d^{5} - 640 \, \sqrt{2} a^{3} b^{4} c^{3} d^{5} + 1280 \, \sqrt{2} a^{4} b^{2} c^{4} d^{5} - 1024 \, \sqrt{2} a^{5} c^{5} d^{5}\right)}} - \frac{117 \, {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{3}{4}} c^{2} \log\left(2 \, c d x + b d - \sqrt{2} {\left(-b^{2} d^{2} + 4 \, a c d^{2}\right)}^{\frac{1}{4}} \sqrt{2 \, c d x + b d} + \sqrt{-b^{2} d^{2} + 4 \, a c d^{2}}\right)}{2 \, {\left(\sqrt{2} b^{10} d^{5} - 20 \, \sqrt{2} a b^{8} c d^{5} + 160 \, \sqrt{2} a^{2} b^{6} c^{2} d^{5} - 640 \, \sqrt{2} a^{3} b^{4} c^{3} d^{5} + 1280 \, \sqrt{2} a^{4} b^{2} c^{4} d^{5} - 1024 \, \sqrt{2} a^{5} c^{5} d^{5}\right)}} - \frac{2 \, {\left(25 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} b^{2} c^{2} d^{2} - 100 \, {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} a c^{3} d^{2} - 21 \, {\left(2 \, c d x + b d\right)}^{\frac{7}{2}} c^{2}\right)}}{{\left(b^{8} d^{3} - 16 \, a b^{6} c d^{3} + 96 \, a^{2} b^{4} c^{2} d^{3} - 256 \, a^{3} b^{2} c^{3} d^{3} + 256 \, a^{4} c^{4} d^{3}\right)} {\left(b^{2} d^{2} - 4 \, a c d^{2} - {\left(2 \, c d x + b d\right)}^{2}\right)}^{2}} + \frac{64 \, {\left(b^{2} c^{2} d^{2} - 4 \, a c^{3} d^{2} + 15 \, {\left(2 \, c d x + b d\right)}^{2} c^{2}\right)}}{5 \, {\left(b^{8} d^{3} - 16 \, a b^{6} c d^{3} + 96 \, a^{2} b^{4} c^{2} d^{3} - 256 \, a^{3} b^{2} c^{3} d^{3} + 256 \, a^{4} c^{4} d^{3}\right)} {\left(2 \, c d x + b d\right)}^{\frac{5}{2}}}"," ",0,"-117*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*c^2*arctan(1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) + 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4))/(sqrt(2)*b^10*d^5 - 20*sqrt(2)*a*b^8*c*d^5 + 160*sqrt(2)*a^2*b^6*c^2*d^5 - 640*sqrt(2)*a^3*b^4*c^3*d^5 + 1280*sqrt(2)*a^4*b^2*c^4*d^5 - 1024*sqrt(2)*a^5*c^5*d^5) - 117*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*c^2*arctan(-1/2*sqrt(2)*(sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4) - 2*sqrt(2*c*d*x + b*d))/(-b^2*d^2 + 4*a*c*d^2)^(1/4))/(sqrt(2)*b^10*d^5 - 20*sqrt(2)*a*b^8*c*d^5 + 160*sqrt(2)*a^2*b^6*c^2*d^5 - 640*sqrt(2)*a^3*b^4*c^3*d^5 + 1280*sqrt(2)*a^4*b^2*c^4*d^5 - 1024*sqrt(2)*a^5*c^5*d^5) + 117/2*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*c^2*log(2*c*d*x + b*d + sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2))/(sqrt(2)*b^10*d^5 - 20*sqrt(2)*a*b^8*c*d^5 + 160*sqrt(2)*a^2*b^6*c^2*d^5 - 640*sqrt(2)*a^3*b^4*c^3*d^5 + 1280*sqrt(2)*a^4*b^2*c^4*d^5 - 1024*sqrt(2)*a^5*c^5*d^5) - 117/2*(-b^2*d^2 + 4*a*c*d^2)^(3/4)*c^2*log(2*c*d*x + b*d - sqrt(2)*(-b^2*d^2 + 4*a*c*d^2)^(1/4)*sqrt(2*c*d*x + b*d) + sqrt(-b^2*d^2 + 4*a*c*d^2))/(sqrt(2)*b^10*d^5 - 20*sqrt(2)*a*b^8*c*d^5 + 160*sqrt(2)*a^2*b^6*c^2*d^5 - 640*sqrt(2)*a^3*b^4*c^3*d^5 + 1280*sqrt(2)*a^4*b^2*c^4*d^5 - 1024*sqrt(2)*a^5*c^5*d^5) - 2*(25*(2*c*d*x + b*d)^(3/2)*b^2*c^2*d^2 - 100*(2*c*d*x + b*d)^(3/2)*a*c^3*d^2 - 21*(2*c*d*x + b*d)^(7/2)*c^2)/((b^8*d^3 - 16*a*b^6*c*d^3 + 96*a^2*b^4*c^2*d^3 - 256*a^3*b^2*c^3*d^3 + 256*a^4*c^4*d^3)*(b^2*d^2 - 4*a*c*d^2 - (2*c*d*x + b*d)^2)^2) + 64/5*(b^2*c^2*d^2 - 4*a*c^3*d^2 + 15*(2*c*d*x + b*d)^2*c^2)/((b^8*d^3 - 16*a*b^6*c*d^3 + 96*a^2*b^4*c^2*d^3 - 256*a^3*b^2*c^3*d^3 + 256*a^4*c^4*d^3)*(2*c*d*x + b*d)^(5/2))","B",0
1320,1,138,0,0.205950," ","integrate((1+2*x)^(7/2)/(x^2+x+1),x, algorithm=""giac"")","\frac{4}{5} \, {\left(2 \, x + 1\right)}^{\frac{5}{2}} + 3 \cdot 12^{\frac{1}{4}} \arctan\left(\frac{1}{6} \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(3^{\frac{1}{4}} \sqrt{2} + 2 \, \sqrt{2 \, x + 1}\right)}\right) + 3 \cdot 12^{\frac{1}{4}} \arctan\left(-\frac{1}{6} \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(3^{\frac{1}{4}} \sqrt{2} - 2 \, \sqrt{2 \, x + 1}\right)}\right) + \frac{3}{2} \cdot 12^{\frac{1}{4}} \log\left(3^{\frac{1}{4}} \sqrt{2} \sqrt{2 \, x + 1} + 2 \, x + \sqrt{3} + 1\right) - \frac{3}{2} \cdot 12^{\frac{1}{4}} \log\left(-3^{\frac{1}{4}} \sqrt{2} \sqrt{2 \, x + 1} + 2 \, x + \sqrt{3} + 1\right) - 12 \, \sqrt{2 \, x + 1}"," ",0,"4/5*(2*x + 1)^(5/2) + 3*12^(1/4)*arctan(1/6*3^(3/4)*sqrt(2)*(3^(1/4)*sqrt(2) + 2*sqrt(2*x + 1))) + 3*12^(1/4)*arctan(-1/6*3^(3/4)*sqrt(2)*(3^(1/4)*sqrt(2) - 2*sqrt(2*x + 1))) + 3/2*12^(1/4)*log(3^(1/4)*sqrt(2)*sqrt(2*x + 1) + 2*x + sqrt(3) + 1) - 3/2*12^(1/4)*log(-3^(1/4)*sqrt(2)*sqrt(2*x + 1) + 2*x + sqrt(3) + 1) - 12*sqrt(2*x + 1)","A",0
1321,1,129,0,0.215315," ","integrate((1+2*x)^(5/2)/(x^2+x+1),x, algorithm=""giac"")","\frac{4}{3} \, {\left(2 \, x + 1\right)}^{\frac{3}{2}} - 108^{\frac{1}{4}} \arctan\left(\frac{1}{6} \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(3^{\frac{1}{4}} \sqrt{2} + 2 \, \sqrt{2 \, x + 1}\right)}\right) - 108^{\frac{1}{4}} \arctan\left(-\frac{1}{6} \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(3^{\frac{1}{4}} \sqrt{2} - 2 \, \sqrt{2 \, x + 1}\right)}\right) + \frac{1}{2} \cdot 108^{\frac{1}{4}} \log\left(3^{\frac{1}{4}} \sqrt{2} \sqrt{2 \, x + 1} + 2 \, x + \sqrt{3} + 1\right) - \frac{1}{2} \cdot 108^{\frac{1}{4}} \log\left(-3^{\frac{1}{4}} \sqrt{2} \sqrt{2 \, x + 1} + 2 \, x + \sqrt{3} + 1\right)"," ",0,"4/3*(2*x + 1)^(3/2) - 108^(1/4)*arctan(1/6*3^(3/4)*sqrt(2)*(3^(1/4)*sqrt(2) + 2*sqrt(2*x + 1))) - 108^(1/4)*arctan(-1/6*3^(3/4)*sqrt(2)*(3^(1/4)*sqrt(2) - 2*sqrt(2*x + 1))) + 1/2*108^(1/4)*log(3^(1/4)*sqrt(2)*sqrt(2*x + 1) + 2*x + sqrt(3) + 1) - 1/2*108^(1/4)*log(-3^(1/4)*sqrt(2)*sqrt(2*x + 1) + 2*x + sqrt(3) + 1)","A",0
1322,1,129,0,0.210998," ","integrate((1+2*x)^(3/2)/(x^2+x+1),x, algorithm=""giac"")","-12^{\frac{1}{4}} \arctan\left(\frac{1}{6} \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(3^{\frac{1}{4}} \sqrt{2} + 2 \, \sqrt{2 \, x + 1}\right)}\right) - 12^{\frac{1}{4}} \arctan\left(-\frac{1}{6} \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(3^{\frac{1}{4}} \sqrt{2} - 2 \, \sqrt{2 \, x + 1}\right)}\right) - \frac{1}{2} \cdot 12^{\frac{1}{4}} \log\left(3^{\frac{1}{4}} \sqrt{2} \sqrt{2 \, x + 1} + 2 \, x + \sqrt{3} + 1\right) + \frac{1}{2} \cdot 12^{\frac{1}{4}} \log\left(-3^{\frac{1}{4}} \sqrt{2} \sqrt{2 \, x + 1} + 2 \, x + \sqrt{3} + 1\right) + 4 \, \sqrt{2 \, x + 1}"," ",0,"-12^(1/4)*arctan(1/6*3^(3/4)*sqrt(2)*(3^(1/4)*sqrt(2) + 2*sqrt(2*x + 1))) - 12^(1/4)*arctan(-1/6*3^(3/4)*sqrt(2)*(3^(1/4)*sqrt(2) - 2*sqrt(2*x + 1))) - 1/2*12^(1/4)*log(3^(1/4)*sqrt(2)*sqrt(2*x + 1) + 2*x + sqrt(3) + 1) + 1/2*12^(1/4)*log(-3^(1/4)*sqrt(2)*sqrt(2*x + 1) + 2*x + sqrt(3) + 1) + 4*sqrt(2*x + 1)","A",0
1323,1,120,0,0.193112," ","integrate((1+2*x)^(1/2)/(x^2+x+1),x, algorithm=""giac"")","\frac{1}{3} \cdot 108^{\frac{1}{4}} \arctan\left(\frac{1}{6} \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(3^{\frac{1}{4}} \sqrt{2} + 2 \, \sqrt{2 \, x + 1}\right)}\right) + \frac{1}{3} \cdot 108^{\frac{1}{4}} \arctan\left(-\frac{1}{6} \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(3^{\frac{1}{4}} \sqrt{2} - 2 \, \sqrt{2 \, x + 1}\right)}\right) - \frac{1}{6} \cdot 108^{\frac{1}{4}} \log\left(3^{\frac{1}{4}} \sqrt{2} \sqrt{2 \, x + 1} + 2 \, x + \sqrt{3} + 1\right) + \frac{1}{6} \cdot 108^{\frac{1}{4}} \log\left(-3^{\frac{1}{4}} \sqrt{2} \sqrt{2 \, x + 1} + 2 \, x + \sqrt{3} + 1\right)"," ",0,"1/3*108^(1/4)*arctan(1/6*3^(3/4)*sqrt(2)*(3^(1/4)*sqrt(2) + 2*sqrt(2*x + 1))) + 1/3*108^(1/4)*arctan(-1/6*3^(3/4)*sqrt(2)*(3^(1/4)*sqrt(2) - 2*sqrt(2*x + 1))) - 1/6*108^(1/4)*log(3^(1/4)*sqrt(2)*sqrt(2*x + 1) + 2*x + sqrt(3) + 1) + 1/6*108^(1/4)*log(-3^(1/4)*sqrt(2)*sqrt(2*x + 1) + 2*x + sqrt(3) + 1)","A",0
1324,1,120,0,0.174886," ","integrate(1/(1+2*x)^(1/2)/(x^2+x+1),x, algorithm=""giac"")","\frac{1}{3} \cdot 12^{\frac{1}{4}} \arctan\left(\frac{1}{6} \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(3^{\frac{1}{4}} \sqrt{2} + 2 \, \sqrt{2 \, x + 1}\right)}\right) + \frac{1}{3} \cdot 12^{\frac{1}{4}} \arctan\left(-\frac{1}{6} \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(3^{\frac{1}{4}} \sqrt{2} - 2 \, \sqrt{2 \, x + 1}\right)}\right) + \frac{1}{6} \cdot 12^{\frac{1}{4}} \log\left(3^{\frac{1}{4}} \sqrt{2} \sqrt{2 \, x + 1} + 2 \, x + \sqrt{3} + 1\right) - \frac{1}{6} \cdot 12^{\frac{1}{4}} \log\left(-3^{\frac{1}{4}} \sqrt{2} \sqrt{2 \, x + 1} + 2 \, x + \sqrt{3} + 1\right)"," ",0,"1/3*12^(1/4)*arctan(1/6*3^(3/4)*sqrt(2)*(3^(1/4)*sqrt(2) + 2*sqrt(2*x + 1))) + 1/3*12^(1/4)*arctan(-1/6*3^(3/4)*sqrt(2)*(3^(1/4)*sqrt(2) - 2*sqrt(2*x + 1))) + 1/6*12^(1/4)*log(3^(1/4)*sqrt(2)*sqrt(2*x + 1) + 2*x + sqrt(3) + 1) - 1/6*12^(1/4)*log(-3^(1/4)*sqrt(2)*sqrt(2*x + 1) + 2*x + sqrt(3) + 1)","A",0
1325,1,129,0,0.203735," ","integrate(1/(1+2*x)^(3/2)/(x^2+x+1),x, algorithm=""giac"")","-\frac{1}{9} \cdot 108^{\frac{1}{4}} \arctan\left(\frac{1}{6} \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(3^{\frac{1}{4}} \sqrt{2} + 2 \, \sqrt{2 \, x + 1}\right)}\right) - \frac{1}{9} \cdot 108^{\frac{1}{4}} \arctan\left(-\frac{1}{6} \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(3^{\frac{1}{4}} \sqrt{2} - 2 \, \sqrt{2 \, x + 1}\right)}\right) + \frac{1}{18} \cdot 108^{\frac{1}{4}} \log\left(3^{\frac{1}{4}} \sqrt{2} \sqrt{2 \, x + 1} + 2 \, x + \sqrt{3} + 1\right) - \frac{1}{18} \cdot 108^{\frac{1}{4}} \log\left(-3^{\frac{1}{4}} \sqrt{2} \sqrt{2 \, x + 1} + 2 \, x + \sqrt{3} + 1\right) - \frac{4}{3 \, \sqrt{2 \, x + 1}}"," ",0,"-1/9*108^(1/4)*arctan(1/6*3^(3/4)*sqrt(2)*(3^(1/4)*sqrt(2) + 2*sqrt(2*x + 1))) - 1/9*108^(1/4)*arctan(-1/6*3^(3/4)*sqrt(2)*(3^(1/4)*sqrt(2) - 2*sqrt(2*x + 1))) + 1/18*108^(1/4)*log(3^(1/4)*sqrt(2)*sqrt(2*x + 1) + 2*x + sqrt(3) + 1) - 1/18*108^(1/4)*log(-3^(1/4)*sqrt(2)*sqrt(2*x + 1) + 2*x + sqrt(3) + 1) - 4/3/sqrt(2*x + 1)","A",0
1326,1,129,0,0.198051," ","integrate(1/(1+2*x)^(5/2)/(x^2+x+1),x, algorithm=""giac"")","-\frac{1}{9} \cdot 12^{\frac{1}{4}} \arctan\left(\frac{1}{6} \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(3^{\frac{1}{4}} \sqrt{2} + 2 \, \sqrt{2 \, x + 1}\right)}\right) - \frac{1}{9} \cdot 12^{\frac{1}{4}} \arctan\left(-\frac{1}{6} \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(3^{\frac{1}{4}} \sqrt{2} - 2 \, \sqrt{2 \, x + 1}\right)}\right) - \frac{1}{18} \cdot 12^{\frac{1}{4}} \log\left(3^{\frac{1}{4}} \sqrt{2} \sqrt{2 \, x + 1} + 2 \, x + \sqrt{3} + 1\right) + \frac{1}{18} \cdot 12^{\frac{1}{4}} \log\left(-3^{\frac{1}{4}} \sqrt{2} \sqrt{2 \, x + 1} + 2 \, x + \sqrt{3} + 1\right) - \frac{4}{9 \, {\left(2 \, x + 1\right)}^{\frac{3}{2}}}"," ",0,"-1/9*12^(1/4)*arctan(1/6*3^(3/4)*sqrt(2)*(3^(1/4)*sqrt(2) + 2*sqrt(2*x + 1))) - 1/9*12^(1/4)*arctan(-1/6*3^(3/4)*sqrt(2)*(3^(1/4)*sqrt(2) - 2*sqrt(2*x + 1))) - 1/18*12^(1/4)*log(3^(1/4)*sqrt(2)*sqrt(2*x + 1) + 2*x + sqrt(3) + 1) + 1/18*12^(1/4)*log(-3^(1/4)*sqrt(2)*sqrt(2*x + 1) + 2*x + sqrt(3) + 1) - 4/9/(2*x + 1)^(3/2)","A",0
1327,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)^(7/2)*(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int {\left(2 \, c d x + b d\right)}^{\frac{7}{2}} \sqrt{c x^{2} + b x + a}\,{d x}"," ",0,"integrate((2*c*d*x + b*d)^(7/2)*sqrt(c*x^2 + b*x + a), x)","F",0
1328,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)^(3/2)*(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} \sqrt{c x^{2} + b x + a}\,{d x}"," ",0,"integrate((2*c*d*x + b*d)^(3/2)*sqrt(c*x^2 + b*x + a), x)","F",0
1329,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(1/2)/(2*c*d*x+b*d)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{c x^{2} + b x + a}}{\sqrt{2 \, c d x + b d}}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + b*x + a)/sqrt(2*c*d*x + b*d), x)","F",0
1330,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(1/2)/(2*c*d*x+b*d)^(5/2),x, algorithm=""giac"")","\int \frac{\sqrt{c x^{2} + b x + a}}{{\left(2 \, c d x + b d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + b*x + a)/(2*c*d*x + b*d)^(5/2), x)","F",0
1331,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(1/2)/(2*c*d*x+b*d)^(9/2),x, algorithm=""giac"")","\int \frac{\sqrt{c x^{2} + b x + a}}{{\left(2 \, c d x + b d\right)}^{\frac{9}{2}}}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + b*x + a)/(2*c*d*x + b*d)^(9/2), x)","F",0
1332,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(1/2)/(2*c*d*x+b*d)^(13/2),x, algorithm=""giac"")","\int \frac{\sqrt{c x^{2} + b x + a}}{{\left(2 \, c d x + b d\right)}^{\frac{13}{2}}}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + b*x + a)/(2*c*d*x + b*d)^(13/2), x)","F",0
1333,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)^(5/2)*(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int {\left(2 \, c d x + b d\right)}^{\frac{5}{2}} \sqrt{c x^{2} + b x + a}\,{d x}"," ",0,"integrate((2*c*d*x + b*d)^(5/2)*sqrt(c*x^2 + b*x + a), x)","F",0
1334,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)^(1/2)*(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int \sqrt{2 \, c d x + b d} \sqrt{c x^{2} + b x + a}\,{d x}"," ",0,"integrate(sqrt(2*c*d*x + b*d)*sqrt(c*x^2 + b*x + a), x)","F",0
1335,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(1/2)/(2*c*d*x+b*d)^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{c x^{2} + b x + a}}{{\left(2 \, c d x + b d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + b*x + a)/(2*c*d*x + b*d)^(3/2), x)","F",0
1336,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(1/2)/(2*c*d*x+b*d)^(7/2),x, algorithm=""giac"")","\int \frac{\sqrt{c x^{2} + b x + a}}{{\left(2 \, c d x + b d\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + b*x + a)/(2*c*d*x + b*d)^(7/2), x)","F",0
1337,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)^(7/2)*(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\int {\left(2 \, c d x + b d\right)}^{\frac{7}{2}} {\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((2*c*d*x + b*d)^(7/2)*(c*x^2 + b*x + a)^(3/2), x)","F",0
1338,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)^(3/2)*(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\int {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} {\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((2*c*d*x + b*d)^(3/2)*(c*x^2 + b*x + a)^(3/2), x)","F",0
1339,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)/(2*c*d*x+b*d)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}{\sqrt{2 \, c d x + b d}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(3/2)/sqrt(2*c*d*x + b*d), x)","F",0
1340,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)/(2*c*d*x+b*d)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}{{\left(2 \, c d x + b d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(3/2)/(2*c*d*x + b*d)^(5/2), x)","F",0
1341,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)/(2*c*d*x+b*d)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}{{\left(2 \, c d x + b d\right)}^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(3/2)/(2*c*d*x + b*d)^(9/2), x)","F",0
1342,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)/(2*c*d*x+b*d)^(13/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}{{\left(2 \, c d x + b d\right)}^{\frac{13}{2}}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(3/2)/(2*c*d*x + b*d)^(13/2), x)","F",0
1343,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)/(2*c*d*x+b*d)^(17/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}{{\left(2 \, c d x + b d\right)}^{\frac{17}{2}}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(3/2)/(2*c*d*x + b*d)^(17/2), x)","F",0
1344,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)^(5/2)*(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\int {\left(2 \, c d x + b d\right)}^{\frac{5}{2}} {\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((2*c*d*x + b*d)^(5/2)*(c*x^2 + b*x + a)^(3/2), x)","F",0
1345,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)^(1/2)*(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\int \sqrt{2 \, c d x + b d} {\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(2*c*d*x + b*d)*(c*x^2 + b*x + a)^(3/2), x)","F",0
1346,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)/(2*c*d*x+b*d)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}{{\left(2 \, c d x + b d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(3/2)/(2*c*d*x + b*d)^(3/2), x)","F",0
1347,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)/(2*c*d*x+b*d)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}{{\left(2 \, c d x + b d\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(3/2)/(2*c*d*x + b*d)^(7/2), x)","F",0
1348,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)/(2*c*d*x+b*d)^(11/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}{{\left(2 \, c d x + b d\right)}^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(3/2)/(2*c*d*x + b*d)^(11/2), x)","F",0
1349,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)^(7/2)*(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\int {\left(2 \, c d x + b d\right)}^{\frac{7}{2}} {\left(c x^{2} + b x + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((2*c*d*x + b*d)^(7/2)*(c*x^2 + b*x + a)^(5/2), x)","F",0
1350,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)^(3/2)*(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\int {\left(2 \, c d x + b d\right)}^{\frac{3}{2}} {\left(c x^{2} + b x + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((2*c*d*x + b*d)^(3/2)*(c*x^2 + b*x + a)^(5/2), x)","F",0
1351,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{\frac{5}{2}}}{\sqrt{2 \, c d x + b d}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(5/2)/sqrt(2*c*d*x + b*d), x)","F",0
1352,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{\frac{5}{2}}}{{\left(2 \, c d x + b d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(5/2)/(2*c*d*x + b*d)^(5/2), x)","F",0
1353,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{\frac{5}{2}}}{{\left(2 \, c d x + b d\right)}^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(5/2)/(2*c*d*x + b*d)^(9/2), x)","F",0
1354,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^(13/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{\frac{5}{2}}}{{\left(2 \, c d x + b d\right)}^{\frac{13}{2}}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(5/2)/(2*c*d*x + b*d)^(13/2), x)","F",0
1355,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^(17/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{\frac{5}{2}}}{{\left(2 \, c d x + b d\right)}^{\frac{17}{2}}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(5/2)/(2*c*d*x + b*d)^(17/2), x)","F",0
1356,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^(21/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{\frac{5}{2}}}{{\left(2 \, c d x + b d\right)}^{\frac{21}{2}}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(5/2)/(2*c*d*x + b*d)^(21/2), x)","F",0
1357,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)^(5/2)*(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\int {\left(2 \, c d x + b d\right)}^{\frac{5}{2}} {\left(c x^{2} + b x + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((2*c*d*x + b*d)^(5/2)*(c*x^2 + b*x + a)^(5/2), x)","F",0
1358,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)^(1/2)*(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\int \sqrt{2 \, c d x + b d} {\left(c x^{2} + b x + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate(sqrt(2*c*d*x + b*d)*(c*x^2 + b*x + a)^(5/2), x)","F",0
1359,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{\frac{5}{2}}}{{\left(2 \, c d x + b d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(5/2)/(2*c*d*x + b*d)^(3/2), x)","F",0
1360,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{\frac{5}{2}}}{{\left(2 \, c d x + b d\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(5/2)/(2*c*d*x + b*d)^(7/2), x)","F",0
1361,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^(11/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{\frac{5}{2}}}{{\left(2 \, c d x + b d\right)}^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(5/2)/(2*c*d*x + b*d)^(11/2), x)","F",0
1362,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^(15/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{\frac{5}{2}}}{{\left(2 \, c d x + b d\right)}^{\frac{15}{2}}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(5/2)/(2*c*d*x + b*d)^(15/2), x)","F",0
1363,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)^(7/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(2 \, c d x + b d\right)}^{\frac{7}{2}}}{\sqrt{c x^{2} + b x + a}}\,{d x}"," ",0,"integrate((2*c*d*x + b*d)^(7/2)/sqrt(c*x^2 + b*x + a), x)","F",0
1364,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)^(3/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(2 \, c d x + b d\right)}^{\frac{3}{2}}}{\sqrt{c x^{2} + b x + a}}\,{d x}"," ",0,"integrate((2*c*d*x + b*d)^(3/2)/sqrt(c*x^2 + b*x + a), x)","F",0
1365,0,0,0,0.000000," ","integrate(1/(2*c*d*x+b*d)^(1/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{2 \, c d x + b d} \sqrt{c x^{2} + b x + a}}\,{d x}"," ",0,"integrate(1/(sqrt(2*c*d*x + b*d)*sqrt(c*x^2 + b*x + a)), x)","F",0
1366,0,0,0,0.000000," ","integrate(1/(2*c*d*x+b*d)^(5/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{{\left(2 \, c d x + b d\right)}^{\frac{5}{2}} \sqrt{c x^{2} + b x + a}}\,{d x}"," ",0,"integrate(1/((2*c*d*x + b*d)^(5/2)*sqrt(c*x^2 + b*x + a)), x)","F",0
1367,0,0,0,0.000000," ","integrate(1/(2*c*d*x+b*d)^(9/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{{\left(2 \, c d x + b d\right)}^{\frac{9}{2}} \sqrt{c x^{2} + b x + a}}\,{d x}"," ",0,"integrate(1/((2*c*d*x + b*d)^(9/2)*sqrt(c*x^2 + b*x + a)), x)","F",0
1368,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)^(9/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(2 \, c d x + b d\right)}^{\frac{9}{2}}}{\sqrt{c x^{2} + b x + a}}\,{d x}"," ",0,"integrate((2*c*d*x + b*d)^(9/2)/sqrt(c*x^2 + b*x + a), x)","F",0
1369,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)^(5/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(2 \, c d x + b d\right)}^{\frac{5}{2}}}{\sqrt{c x^{2} + b x + a}}\,{d x}"," ",0,"integrate((2*c*d*x + b*d)^(5/2)/sqrt(c*x^2 + b*x + a), x)","F",0
1370,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)^(1/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{2 \, c d x + b d}}{\sqrt{c x^{2} + b x + a}}\,{d x}"," ",0,"integrate(sqrt(2*c*d*x + b*d)/sqrt(c*x^2 + b*x + a), x)","F",0
1371,0,0,0,0.000000," ","integrate(1/(2*c*d*x+b*d)^(3/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{{\left(2 \, c d x + b d\right)}^{\frac{3}{2}} \sqrt{c x^{2} + b x + a}}\,{d x}"," ",0,"integrate(1/((2*c*d*x + b*d)^(3/2)*sqrt(c*x^2 + b*x + a)), x)","F",0
1372,0,0,0,0.000000," ","integrate(1/(2*c*d*x+b*d)^(7/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{{\left(2 \, c d x + b d\right)}^{\frac{7}{2}} \sqrt{c x^{2} + b x + a}}\,{d x}"," ",0,"integrate(1/((2*c*d*x + b*d)^(7/2)*sqrt(c*x^2 + b*x + a)), x)","F",0
1373,0,0,0,0.000000," ","integrate((3-2*x)^(3/2)/(x^2-3*x+1)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(-2 \, x + 3\right)}^{\frac{3}{2}}}{\sqrt{x^{2} - 3 \, x + 1}}\,{d x}"," ",0,"integrate((-2*x + 3)^(3/2)/sqrt(x^2 - 3*x + 1), x)","F",0
1374,0,0,0,0.000000," ","integrate(1/(3-2*x)^(1/2)/(x^2-3*x+1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{2} - 3 \, x + 1} \sqrt{-2 \, x + 3}}\,{d x}"," ",0,"integrate(1/(sqrt(x^2 - 3*x + 1)*sqrt(-2*x + 3)), x)","F",0
1375,0,0,0,0.000000," ","integrate(1/(3-2*x)^(5/2)/(x^2-3*x+1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{2} - 3 \, x + 1} {\left(-2 \, x + 3\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(x^2 - 3*x + 1)*(-2*x + 3)^(5/2)), x)","F",0
1376,0,0,0,0.000000," ","integrate((3-2*x)^(5/2)/(x^2-3*x+1)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(-2 \, x + 3\right)}^{\frac{5}{2}}}{\sqrt{x^{2} - 3 \, x + 1}}\,{d x}"," ",0,"integrate((-2*x + 3)^(5/2)/sqrt(x^2 - 3*x + 1), x)","F",0
1377,0,0,0,0.000000," ","integrate((3-2*x)^(1/2)/(x^2-3*x+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-2 \, x + 3}}{\sqrt{x^{2} - 3 \, x + 1}}\,{d x}"," ",0,"integrate(sqrt(-2*x + 3)/sqrt(x^2 - 3*x + 1), x)","F",0
1378,0,0,0,0.000000," ","integrate(1/(3-2*x)^(3/2)/(x^2-3*x+1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{2} - 3 \, x + 1} {\left(-2 \, x + 3\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(x^2 - 3*x + 1)*(-2*x + 3)^(3/2)), x)","F",0
1379,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)^(11/2)/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(2 \, c d x + b d\right)}^{\frac{11}{2}}}{{\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((2*c*d*x + b*d)^(11/2)/(c*x^2 + b*x + a)^(3/2), x)","F",0
1380,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)^(7/2)/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(2 \, c d x + b d\right)}^{\frac{7}{2}}}{{\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((2*c*d*x + b*d)^(7/2)/(c*x^2 + b*x + a)^(3/2), x)","F",0
1381,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)^(3/2)/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(2 \, c d x + b d\right)}^{\frac{3}{2}}}{{\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((2*c*d*x + b*d)^(3/2)/(c*x^2 + b*x + a)^(3/2), x)","F",0
1382,0,0,0,0.000000," ","integrate(1/(2*c*d*x+b*d)^(1/2)/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{2 \, c d x + b d} {\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(2*c*d*x + b*d)*(c*x^2 + b*x + a)^(3/2)), x)","F",0
1383,0,0,0,0.000000," ","integrate(1/(2*c*d*x+b*d)^(5/2)/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(2 \, c d x + b d\right)}^{\frac{5}{2}} {\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((2*c*d*x + b*d)^(5/2)*(c*x^2 + b*x + a)^(3/2)), x)","F",0
1384,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)^(9/2)/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(2 \, c d x + b d\right)}^{\frac{9}{2}}}{{\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((2*c*d*x + b*d)^(9/2)/(c*x^2 + b*x + a)^(3/2), x)","F",0
1385,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)^(5/2)/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(2 \, c d x + b d\right)}^{\frac{5}{2}}}{{\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((2*c*d*x + b*d)^(5/2)/(c*x^2 + b*x + a)^(3/2), x)","F",0
1386,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)^(1/2)/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{2 \, c d x + b d}}{{\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(2*c*d*x + b*d)/(c*x^2 + b*x + a)^(3/2), x)","F",0
1387,0,0,0,0.000000," ","integrate(1/(2*c*d*x+b*d)^(3/2)/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(2 \, c d x + b d\right)}^{\frac{3}{2}} {\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((2*c*d*x + b*d)^(3/2)*(c*x^2 + b*x + a)^(3/2)), x)","F",0
1388,0,0,0,0.000000," ","integrate(1/(2*c*d*x+b*d)^(7/2)/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(2 \, c d x + b d\right)}^{\frac{7}{2}} {\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((2*c*d*x + b*d)^(7/2)*(c*x^2 + b*x + a)^(3/2)), x)","F",0
1389,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)^(15/2)/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(2 \, c d x + b d\right)}^{\frac{15}{2}}}{{\left(c x^{2} + b x + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((2*c*d*x + b*d)^(15/2)/(c*x^2 + b*x + a)^(5/2), x)","F",0
1390,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)^(11/2)/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(2 \, c d x + b d\right)}^{\frac{11}{2}}}{{\left(c x^{2} + b x + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((2*c*d*x + b*d)^(11/2)/(c*x^2 + b*x + a)^(5/2), x)","F",0
1391,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)^(7/2)/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(2 \, c d x + b d\right)}^{\frac{7}{2}}}{{\left(c x^{2} + b x + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((2*c*d*x + b*d)^(7/2)/(c*x^2 + b*x + a)^(5/2), x)","F",0
1392,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)^(3/2)/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(2 \, c d x + b d\right)}^{\frac{3}{2}}}{{\left(c x^{2} + b x + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((2*c*d*x + b*d)^(3/2)/(c*x^2 + b*x + a)^(5/2), x)","F",0
1393,0,0,0,0.000000," ","integrate(1/(2*c*d*x+b*d)^(1/2)/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{2 \, c d x + b d} {\left(c x^{2} + b x + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(2*c*d*x + b*d)*(c*x^2 + b*x + a)^(5/2)), x)","F",0
1394,0,0,0,0.000000," ","integrate(1/(2*c*d*x+b*d)^(5/2)/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(2 \, c d x + b d\right)}^{\frac{5}{2}} {\left(c x^{2} + b x + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((2*c*d*x + b*d)^(5/2)*(c*x^2 + b*x + a)^(5/2)), x)","F",0
1395,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)^(13/2)/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(2 \, c d x + b d\right)}^{\frac{13}{2}}}{{\left(c x^{2} + b x + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((2*c*d*x + b*d)^(13/2)/(c*x^2 + b*x + a)^(5/2), x)","F",0
1396,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)^(9/2)/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(2 \, c d x + b d\right)}^{\frac{9}{2}}}{{\left(c x^{2} + b x + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((2*c*d*x + b*d)^(9/2)/(c*x^2 + b*x + a)^(5/2), x)","F",0
1397,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)^(5/2)/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(2 \, c d x + b d\right)}^{\frac{5}{2}}}{{\left(c x^{2} + b x + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((2*c*d*x + b*d)^(5/2)/(c*x^2 + b*x + a)^(5/2), x)","F",0
1398,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)^(1/2)/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\int \frac{\sqrt{2 \, c d x + b d}}{{\left(c x^{2} + b x + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(2*c*d*x + b*d)/(c*x^2 + b*x + a)^(5/2), x)","F",0
1399,0,0,0,0.000000," ","integrate(1/(2*c*d*x+b*d)^(3/2)/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(2 \, c d x + b d\right)}^{\frac{3}{2}} {\left(c x^{2} + b x + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((2*c*d*x + b*d)^(3/2)*(c*x^2 + b*x + a)^(5/2)), x)","F",0
1400,0,0,0,0.000000," ","integrate((d*e*x+c*e)^(11/2)/(-d^2*x^2-2*c*d*x-c^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(d e x + c e\right)}^{\frac{11}{2}}}{\sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1}}\,{d x}"," ",0,"integrate((d*e*x + c*e)^(11/2)/sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1), x)","F",0
1401,0,0,0,0.000000," ","integrate((d*e*x+c*e)^(7/2)/(-d^2*x^2-2*c*d*x-c^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(d e x + c e\right)}^{\frac{7}{2}}}{\sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1}}\,{d x}"," ",0,"integrate((d*e*x + c*e)^(7/2)/sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1), x)","F",0
1402,0,0,0,0.000000," ","integrate((d*e*x+c*e)^(3/2)/(-d^2*x^2-2*c*d*x-c^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(d e x + c e\right)}^{\frac{3}{2}}}{\sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1}}\,{d x}"," ",0,"integrate((d*e*x + c*e)^(3/2)/sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1), x)","F",0
1403,0,0,0,0.000000," ","integrate(1/(d*e*x+c*e)^(1/2)/(-d^2*x^2-2*c*d*x-c^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} \sqrt{d e x + c e}}\,{d x}"," ",0,"integrate(1/(sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*sqrt(d*e*x + c*e)), x)","F",0
1404,0,0,0,0.000000," ","integrate(1/(d*e*x+c*e)^(5/2)/(-d^2*x^2-2*c*d*x-c^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} {\left(d e x + c e\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*(d*e*x + c*e)^(5/2)), x)","F",0
1405,0,0,0,0.000000," ","integrate(1/(d*e*x+c*e)^(9/2)/(-d^2*x^2-2*c*d*x-c^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} {\left(d e x + c e\right)}^{\frac{9}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*(d*e*x + c*e)^(9/2)), x)","F",0
1406,0,0,0,0.000000," ","integrate(1/(d*e*x+c*e)^(13/2)/(-d^2*x^2-2*c*d*x-c^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} {\left(d e x + c e\right)}^{\frac{13}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*(d*e*x + c*e)^(13/2)), x)","F",0
1407,0,0,0,0.000000," ","integrate((d*e*x+c*e)^(9/2)/(-d^2*x^2-2*c*d*x-c^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(d e x + c e\right)}^{\frac{9}{2}}}{\sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1}}\,{d x}"," ",0,"integrate((d*e*x + c*e)^(9/2)/sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1), x)","F",0
1408,0,0,0,0.000000," ","integrate((d*e*x+c*e)^(5/2)/(-d^2*x^2-2*c*d*x-c^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(d e x + c e\right)}^{\frac{5}{2}}}{\sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1}}\,{d x}"," ",0,"integrate((d*e*x + c*e)^(5/2)/sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1), x)","F",0
1409,0,0,0,0.000000," ","integrate((d*e*x+c*e)^(1/2)/(-d^2*x^2-2*c*d*x-c^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{d e x + c e}}{\sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1}}\,{d x}"," ",0,"integrate(sqrt(d*e*x + c*e)/sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1), x)","F",0
1410,0,0,0,0.000000," ","integrate(1/(d*e*x+c*e)^(3/2)/(-d^2*x^2-2*c*d*x-c^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} {\left(d e x + c e\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*(d*e*x + c*e)^(3/2)), x)","F",0
1411,0,0,0,0.000000," ","integrate(1/(d*e*x+c*e)^(7/2)/(-d^2*x^2-2*c*d*x-c^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} {\left(d e x + c e\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*(d*e*x + c*e)^(7/2)), x)","F",0
1412,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(4/3)/(2*c*d*x+b*d)^(11/3),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{\frac{4}{3}}}{{\left(2 \, c d x + b d\right)}^{\frac{11}{3}}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(4/3)/(2*c*d*x + b*d)^(11/3), x)","F",0
1413,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(4/3)/(2*c*d*x+b*d)^(17/3),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{\frac{4}{3}}}{{\left(2 \, c d x + b d\right)}^{\frac{17}{3}}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(4/3)/(2*c*d*x + b*d)^(17/3), x)","F",0
1414,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(4/3)/(2*c*d*x+b*d)^(23/3),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{\frac{4}{3}}}{{\left(2 \, c d x + b d\right)}^{\frac{23}{3}}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(4/3)/(2*c*d*x + b*d)^(23/3), x)","F",0
1415,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(4/3)/(2*c*d*x+b*d)^(29/3),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{\frac{4}{3}}}{{\left(2 \, c d x + b d\right)}^{\frac{29}{3}}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(4/3)/(2*c*d*x + b*d)^(29/3), x)","F",0
1416,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(4/3)/(2*c*d*x+b*d)^(2/3),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{\frac{4}{3}}}{{\left(2 \, c d x + b d\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(4/3)/(2*c*d*x + b*d)^(2/3), x)","F",0
1417,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(4/3)/(2*c*d*x+b*d)^(8/3),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{\frac{4}{3}}}{{\left(2 \, c d x + b d\right)}^{\frac{8}{3}}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(4/3)/(2*c*d*x + b*d)^(8/3), x)","F",0
1418,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(4/3)/(2*c*d*x+b*d)^(14/3),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{\frac{4}{3}}}{{\left(2 \, c d x + b d\right)}^{\frac{14}{3}}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(4/3)/(2*c*d*x + b*d)^(14/3), x)","F",0
1419,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(4/3)/(2*c*d*x+b*d)^(20/3),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{\frac{4}{3}}}{{\left(2 \, c d x + b d\right)}^{\frac{20}{3}}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(4/3)/(2*c*d*x + b*d)^(20/3), x)","F",0
1420,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(4/3)/(2*c*d*x+b*d)^(4/3),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{\frac{4}{3}}}{{\left(2 \, c d x + b d\right)}^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(4/3)/(2*c*d*x + b*d)^(4/3), x)","F",0
1421,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(4/3)/(2*c*d*x+b*d)^(10/3),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{\frac{4}{3}}}{{\left(2 \, c d x + b d\right)}^{\frac{10}{3}}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(4/3)/(2*c*d*x + b*d)^(10/3), x)","F",0
1422,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(4/3)/(2*c*d*x+b*d)^(16/3),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{\frac{4}{3}}}{{\left(2 \, c d x + b d\right)}^{\frac{16}{3}}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(4/3)/(2*c*d*x + b*d)^(16/3), x)","F",0
1423,1,1506,0,0.247941," ","integrate((2*c*d*x+b*d)^m*(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{8 \, {\left(2 \, c d x + b d\right)}^{m} c^{7} m^{3} x^{7} + 28 \, {\left(2 \, c d x + b d\right)}^{m} b c^{6} m^{3} x^{6} + 72 \, {\left(2 \, c d x + b d\right)}^{m} c^{7} m^{2} x^{7} + 36 \, {\left(2 \, c d x + b d\right)}^{m} b^{2} c^{5} m^{3} x^{5} + 24 \, {\left(2 \, c d x + b d\right)}^{m} a c^{6} m^{3} x^{5} + 252 \, {\left(2 \, c d x + b d\right)}^{m} b c^{6} m^{2} x^{6} + 184 \, {\left(2 \, c d x + b d\right)}^{m} c^{7} m x^{7} + 20 \, {\left(2 \, c d x + b d\right)}^{m} b^{3} c^{4} m^{3} x^{4} + 60 \, {\left(2 \, c d x + b d\right)}^{m} a b c^{5} m^{3} x^{4} + 312 \, {\left(2 \, c d x + b d\right)}^{m} b^{2} c^{5} m^{2} x^{5} + 264 \, {\left(2 \, c d x + b d\right)}^{m} a c^{6} m^{2} x^{5} + 644 \, {\left(2 \, c d x + b d\right)}^{m} b c^{6} m x^{6} + 120 \, {\left(2 \, c d x + b d\right)}^{m} c^{7} x^{7} + 4 \, {\left(2 \, c d x + b d\right)}^{m} b^{4} c^{3} m^{3} x^{3} + 48 \, {\left(2 \, c d x + b d\right)}^{m} a b^{2} c^{4} m^{3} x^{3} + 24 \, {\left(2 \, c d x + b d\right)}^{m} a^{2} c^{5} m^{3} x^{3} + 150 \, {\left(2 \, c d x + b d\right)}^{m} b^{3} c^{4} m^{2} x^{4} + 660 \, {\left(2 \, c d x + b d\right)}^{m} a b c^{5} m^{2} x^{4} + 780 \, {\left(2 \, c d x + b d\right)}^{m} b^{2} c^{5} m x^{5} + 744 \, {\left(2 \, c d x + b d\right)}^{m} a c^{6} m x^{5} + 420 \, {\left(2 \, c d x + b d\right)}^{m} b c^{6} x^{6} + 12 \, {\left(2 \, c d x + b d\right)}^{m} a b^{3} c^{3} m^{3} x^{2} + 36 \, {\left(2 \, c d x + b d\right)}^{m} a^{2} b c^{4} m^{3} x^{2} + 12 \, {\left(2 \, c d x + b d\right)}^{m} b^{4} c^{3} m^{2} x^{3} + 504 \, {\left(2 \, c d x + b d\right)}^{m} a b^{2} c^{4} m^{2} x^{3} + 312 \, {\left(2 \, c d x + b d\right)}^{m} a^{2} c^{5} m^{2} x^{3} + 340 \, {\left(2 \, c d x + b d\right)}^{m} b^{3} c^{4} m x^{4} + 1860 \, {\left(2 \, c d x + b d\right)}^{m} a b c^{5} m x^{4} + 504 \, {\left(2 \, c d x + b d\right)}^{m} b^{2} c^{5} x^{5} + 504 \, {\left(2 \, c d x + b d\right)}^{m} a c^{6} x^{5} + 12 \, {\left(2 \, c d x + b d\right)}^{m} a^{2} b^{2} c^{3} m^{3} x + 8 \, {\left(2 \, c d x + b d\right)}^{m} a^{3} c^{4} m^{3} x - 6 \, {\left(2 \, c d x + b d\right)}^{m} b^{5} c^{2} m^{2} x^{2} + 96 \, {\left(2 \, c d x + b d\right)}^{m} a b^{3} c^{3} m^{2} x^{2} + 468 \, {\left(2 \, c d x + b d\right)}^{m} a^{2} b c^{4} m^{2} x^{2} + 8 \, {\left(2 \, c d x + b d\right)}^{m} b^{4} c^{3} m x^{3} + 1296 \, {\left(2 \, c d x + b d\right)}^{m} a b^{2} c^{4} m x^{3} + 1128 \, {\left(2 \, c d x + b d\right)}^{m} a^{2} c^{5} m x^{3} + 210 \, {\left(2 \, c d x + b d\right)}^{m} b^{3} c^{4} x^{4} + 1260 \, {\left(2 \, c d x + b d\right)}^{m} a b c^{5} x^{4} + 4 \, {\left(2 \, c d x + b d\right)}^{m} a^{3} b c^{3} m^{3} - 12 \, {\left(2 \, c d x + b d\right)}^{m} a b^{4} c^{2} m^{2} x + 144 \, {\left(2 \, c d x + b d\right)}^{m} a^{2} b^{2} c^{3} m^{2} x + 120 \, {\left(2 \, c d x + b d\right)}^{m} a^{3} c^{4} m^{2} x - 6 \, {\left(2 \, c d x + b d\right)}^{m} b^{5} c^{2} m x^{2} + 84 \, {\left(2 \, c d x + b d\right)}^{m} a b^{3} c^{3} m x^{2} + 1692 \, {\left(2 \, c d x + b d\right)}^{m} a^{2} b c^{4} m x^{2} + 840 \, {\left(2 \, c d x + b d\right)}^{m} a b^{2} c^{4} x^{3} + 840 \, {\left(2 \, c d x + b d\right)}^{m} a^{2} c^{5} x^{3} - 6 \, {\left(2 \, c d x + b d\right)}^{m} a^{2} b^{3} c^{2} m^{2} + 60 \, {\left(2 \, c d x + b d\right)}^{m} a^{3} b c^{3} m^{2} + 6 \, {\left(2 \, c d x + b d\right)}^{m} b^{6} c m x - 84 \, {\left(2 \, c d x + b d\right)}^{m} a b^{4} c^{2} m x + 420 \, {\left(2 \, c d x + b d\right)}^{m} a^{2} b^{2} c^{3} m x + 568 \, {\left(2 \, c d x + b d\right)}^{m} a^{3} c^{4} m x + 1260 \, {\left(2 \, c d x + b d\right)}^{m} a^{2} b c^{4} x^{2} + 6 \, {\left(2 \, c d x + b d\right)}^{m} a b^{5} c m - 72 \, {\left(2 \, c d x + b d\right)}^{m} a^{2} b^{3} c^{2} m + 284 \, {\left(2 \, c d x + b d\right)}^{m} a^{3} b c^{3} m + 840 \, {\left(2 \, c d x + b d\right)}^{m} a^{3} c^{4} x - 3 \, {\left(2 \, c d x + b d\right)}^{m} b^{7} + 42 \, {\left(2 \, c d x + b d\right)}^{m} a b^{5} c - 210 \, {\left(2 \, c d x + b d\right)}^{m} a^{2} b^{3} c^{2} + 420 \, {\left(2 \, c d x + b d\right)}^{m} a^{3} b c^{3}}{8 \, {\left(c^{4} m^{4} + 16 \, c^{4} m^{3} + 86 \, c^{4} m^{2} + 176 \, c^{4} m + 105 \, c^{4}\right)}}"," ",0,"1/8*(8*(2*c*d*x + b*d)^m*c^7*m^3*x^7 + 28*(2*c*d*x + b*d)^m*b*c^6*m^3*x^6 + 72*(2*c*d*x + b*d)^m*c^7*m^2*x^7 + 36*(2*c*d*x + b*d)^m*b^2*c^5*m^3*x^5 + 24*(2*c*d*x + b*d)^m*a*c^6*m^3*x^5 + 252*(2*c*d*x + b*d)^m*b*c^6*m^2*x^6 + 184*(2*c*d*x + b*d)^m*c^7*m*x^7 + 20*(2*c*d*x + b*d)^m*b^3*c^4*m^3*x^4 + 60*(2*c*d*x + b*d)^m*a*b*c^5*m^3*x^4 + 312*(2*c*d*x + b*d)^m*b^2*c^5*m^2*x^5 + 264*(2*c*d*x + b*d)^m*a*c^6*m^2*x^5 + 644*(2*c*d*x + b*d)^m*b*c^6*m*x^6 + 120*(2*c*d*x + b*d)^m*c^7*x^7 + 4*(2*c*d*x + b*d)^m*b^4*c^3*m^3*x^3 + 48*(2*c*d*x + b*d)^m*a*b^2*c^4*m^3*x^3 + 24*(2*c*d*x + b*d)^m*a^2*c^5*m^3*x^3 + 150*(2*c*d*x + b*d)^m*b^3*c^4*m^2*x^4 + 660*(2*c*d*x + b*d)^m*a*b*c^5*m^2*x^4 + 780*(2*c*d*x + b*d)^m*b^2*c^5*m*x^5 + 744*(2*c*d*x + b*d)^m*a*c^6*m*x^5 + 420*(2*c*d*x + b*d)^m*b*c^6*x^6 + 12*(2*c*d*x + b*d)^m*a*b^3*c^3*m^3*x^2 + 36*(2*c*d*x + b*d)^m*a^2*b*c^4*m^3*x^2 + 12*(2*c*d*x + b*d)^m*b^4*c^3*m^2*x^3 + 504*(2*c*d*x + b*d)^m*a*b^2*c^4*m^2*x^3 + 312*(2*c*d*x + b*d)^m*a^2*c^5*m^2*x^3 + 340*(2*c*d*x + b*d)^m*b^3*c^4*m*x^4 + 1860*(2*c*d*x + b*d)^m*a*b*c^5*m*x^4 + 504*(2*c*d*x + b*d)^m*b^2*c^5*x^5 + 504*(2*c*d*x + b*d)^m*a*c^6*x^5 + 12*(2*c*d*x + b*d)^m*a^2*b^2*c^3*m^3*x + 8*(2*c*d*x + b*d)^m*a^3*c^4*m^3*x - 6*(2*c*d*x + b*d)^m*b^5*c^2*m^2*x^2 + 96*(2*c*d*x + b*d)^m*a*b^3*c^3*m^2*x^2 + 468*(2*c*d*x + b*d)^m*a^2*b*c^4*m^2*x^2 + 8*(2*c*d*x + b*d)^m*b^4*c^3*m*x^3 + 1296*(2*c*d*x + b*d)^m*a*b^2*c^4*m*x^3 + 1128*(2*c*d*x + b*d)^m*a^2*c^5*m*x^3 + 210*(2*c*d*x + b*d)^m*b^3*c^4*x^4 + 1260*(2*c*d*x + b*d)^m*a*b*c^5*x^4 + 4*(2*c*d*x + b*d)^m*a^3*b*c^3*m^3 - 12*(2*c*d*x + b*d)^m*a*b^4*c^2*m^2*x + 144*(2*c*d*x + b*d)^m*a^2*b^2*c^3*m^2*x + 120*(2*c*d*x + b*d)^m*a^3*c^4*m^2*x - 6*(2*c*d*x + b*d)^m*b^5*c^2*m*x^2 + 84*(2*c*d*x + b*d)^m*a*b^3*c^3*m*x^2 + 1692*(2*c*d*x + b*d)^m*a^2*b*c^4*m*x^2 + 840*(2*c*d*x + b*d)^m*a*b^2*c^4*x^3 + 840*(2*c*d*x + b*d)^m*a^2*c^5*x^3 - 6*(2*c*d*x + b*d)^m*a^2*b^3*c^2*m^2 + 60*(2*c*d*x + b*d)^m*a^3*b*c^3*m^2 + 6*(2*c*d*x + b*d)^m*b^6*c*m*x - 84*(2*c*d*x + b*d)^m*a*b^4*c^2*m*x + 420*(2*c*d*x + b*d)^m*a^2*b^2*c^3*m*x + 568*(2*c*d*x + b*d)^m*a^3*c^4*m*x + 1260*(2*c*d*x + b*d)^m*a^2*b*c^4*x^2 + 6*(2*c*d*x + b*d)^m*a*b^5*c*m - 72*(2*c*d*x + b*d)^m*a^2*b^3*c^2*m + 284*(2*c*d*x + b*d)^m*a^3*b*c^3*m + 840*(2*c*d*x + b*d)^m*a^3*c^4*x - 3*(2*c*d*x + b*d)^m*b^7 + 42*(2*c*d*x + b*d)^m*a*b^5*c - 210*(2*c*d*x + b*d)^m*a^2*b^3*c^2 + 420*(2*c*d*x + b*d)^m*a^3*b*c^3)/(c^4*m^4 + 16*c^4*m^3 + 86*c^4*m^2 + 176*c^4*m + 105*c^4)","B",0
1424,1,651,0,0.268861," ","integrate((2*c*d*x+b*d)^m*(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{4 \, {\left(2 \, c d x + b d\right)}^{m} c^{5} m^{2} x^{5} + 10 \, {\left(2 \, c d x + b d\right)}^{m} b c^{4} m^{2} x^{4} + 16 \, {\left(2 \, c d x + b d\right)}^{m} c^{5} m x^{5} + 8 \, {\left(2 \, c d x + b d\right)}^{m} b^{2} c^{3} m^{2} x^{3} + 8 \, {\left(2 \, c d x + b d\right)}^{m} a c^{4} m^{2} x^{3} + 40 \, {\left(2 \, c d x + b d\right)}^{m} b c^{4} m x^{4} + 12 \, {\left(2 \, c d x + b d\right)}^{m} c^{5} x^{5} + 2 \, {\left(2 \, c d x + b d\right)}^{m} b^{3} c^{2} m^{2} x^{2} + 12 \, {\left(2 \, c d x + b d\right)}^{m} a b c^{3} m^{2} x^{2} + 28 \, {\left(2 \, c d x + b d\right)}^{m} b^{2} c^{3} m x^{3} + 48 \, {\left(2 \, c d x + b d\right)}^{m} a c^{4} m x^{3} + 30 \, {\left(2 \, c d x + b d\right)}^{m} b c^{4} x^{4} + 4 \, {\left(2 \, c d x + b d\right)}^{m} a b^{2} c^{2} m^{2} x + 4 \, {\left(2 \, c d x + b d\right)}^{m} a^{2} c^{3} m^{2} x + 2 \, {\left(2 \, c d x + b d\right)}^{m} b^{3} c^{2} m x^{2} + 72 \, {\left(2 \, c d x + b d\right)}^{m} a b c^{3} m x^{2} + 20 \, {\left(2 \, c d x + b d\right)}^{m} b^{2} c^{3} x^{3} + 40 \, {\left(2 \, c d x + b d\right)}^{m} a c^{4} x^{3} + 2 \, {\left(2 \, c d x + b d\right)}^{m} a^{2} b c^{2} m^{2} - 2 \, {\left(2 \, c d x + b d\right)}^{m} b^{4} c m x + 20 \, {\left(2 \, c d x + b d\right)}^{m} a b^{2} c^{2} m x + 32 \, {\left(2 \, c d x + b d\right)}^{m} a^{2} c^{3} m x + 60 \, {\left(2 \, c d x + b d\right)}^{m} a b c^{3} x^{2} - 2 \, {\left(2 \, c d x + b d\right)}^{m} a b^{3} c m + 16 \, {\left(2 \, c d x + b d\right)}^{m} a^{2} b c^{2} m + 60 \, {\left(2 \, c d x + b d\right)}^{m} a^{2} c^{3} x + {\left(2 \, c d x + b d\right)}^{m} b^{5} - 10 \, {\left(2 \, c d x + b d\right)}^{m} a b^{3} c + 30 \, {\left(2 \, c d x + b d\right)}^{m} a^{2} b c^{2}}{4 \, {\left(c^{3} m^{3} + 9 \, c^{3} m^{2} + 23 \, c^{3} m + 15 \, c^{3}\right)}}"," ",0,"1/4*(4*(2*c*d*x + b*d)^m*c^5*m^2*x^5 + 10*(2*c*d*x + b*d)^m*b*c^4*m^2*x^4 + 16*(2*c*d*x + b*d)^m*c^5*m*x^5 + 8*(2*c*d*x + b*d)^m*b^2*c^3*m^2*x^3 + 8*(2*c*d*x + b*d)^m*a*c^4*m^2*x^3 + 40*(2*c*d*x + b*d)^m*b*c^4*m*x^4 + 12*(2*c*d*x + b*d)^m*c^5*x^5 + 2*(2*c*d*x + b*d)^m*b^3*c^2*m^2*x^2 + 12*(2*c*d*x + b*d)^m*a*b*c^3*m^2*x^2 + 28*(2*c*d*x + b*d)^m*b^2*c^3*m*x^3 + 48*(2*c*d*x + b*d)^m*a*c^4*m*x^3 + 30*(2*c*d*x + b*d)^m*b*c^4*x^4 + 4*(2*c*d*x + b*d)^m*a*b^2*c^2*m^2*x + 4*(2*c*d*x + b*d)^m*a^2*c^3*m^2*x + 2*(2*c*d*x + b*d)^m*b^3*c^2*m*x^2 + 72*(2*c*d*x + b*d)^m*a*b*c^3*m*x^2 + 20*(2*c*d*x + b*d)^m*b^2*c^3*x^3 + 40*(2*c*d*x + b*d)^m*a*c^4*x^3 + 2*(2*c*d*x + b*d)^m*a^2*b*c^2*m^2 - 2*(2*c*d*x + b*d)^m*b^4*c*m*x + 20*(2*c*d*x + b*d)^m*a*b^2*c^2*m*x + 32*(2*c*d*x + b*d)^m*a^2*c^3*m*x + 60*(2*c*d*x + b*d)^m*a*b*c^3*x^2 - 2*(2*c*d*x + b*d)^m*a*b^3*c*m + 16*(2*c*d*x + b*d)^m*a^2*b*c^2*m + 60*(2*c*d*x + b*d)^m*a^2*c^3*x + (2*c*d*x + b*d)^m*b^5 - 10*(2*c*d*x + b*d)^m*a*b^3*c + 30*(2*c*d*x + b*d)^m*a^2*b*c^2)/(c^3*m^3 + 9*c^3*m^2 + 23*c^3*m + 15*c^3)","B",0
1425,1,209,0,0.197652," ","integrate((2*c*d*x+b*d)^m*(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{4 \, {\left(2 \, c d x + b d\right)}^{m} c^{3} m x^{3} + 6 \, {\left(2 \, c d x + b d\right)}^{m} b c^{2} m x^{2} + 4 \, {\left(2 \, c d x + b d\right)}^{m} c^{3} x^{3} + 2 \, {\left(2 \, c d x + b d\right)}^{m} b^{2} c m x + 4 \, {\left(2 \, c d x + b d\right)}^{m} a c^{2} m x + 6 \, {\left(2 \, c d x + b d\right)}^{m} b c^{2} x^{2} + 2 \, {\left(2 \, c d x + b d\right)}^{m} a b c m + 12 \, {\left(2 \, c d x + b d\right)}^{m} a c^{2} x - {\left(2 \, c d x + b d\right)}^{m} b^{3} + 6 \, {\left(2 \, c d x + b d\right)}^{m} a b c}{4 \, {\left(c^{2} m^{2} + 4 \, c^{2} m + 3 \, c^{2}\right)}}"," ",0,"1/4*(4*(2*c*d*x + b*d)^m*c^3*m*x^3 + 6*(2*c*d*x + b*d)^m*b*c^2*m*x^2 + 4*(2*c*d*x + b*d)^m*c^3*x^3 + 2*(2*c*d*x + b*d)^m*b^2*c*m*x + 4*(2*c*d*x + b*d)^m*a*c^2*m*x + 6*(2*c*d*x + b*d)^m*b*c^2*x^2 + 2*(2*c*d*x + b*d)^m*a*b*c*m + 12*(2*c*d*x + b*d)^m*a*c^2*x - (2*c*d*x + b*d)^m*b^3 + 6*(2*c*d*x + b*d)^m*a*b*c)/(c^2*m^2 + 4*c^2*m + 3*c^2)","B",0
1426,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)^m/(c*x^2+b*x+a),x, algorithm=""giac"")","\int \frac{{\left(2 \, c d x + b d\right)}^{m}}{c x^{2} + b x + a}\,{d x}"," ",0,"integrate((2*c*d*x + b*d)^m/(c*x^2 + b*x + a), x)","F",0
1427,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)^m/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\int \frac{{\left(2 \, c d x + b d\right)}^{m}}{{\left(c x^{2} + b x + a\right)}^{2}}\,{d x}"," ",0,"integrate((2*c*d*x + b*d)^m/(c*x^2 + b*x + a)^2, x)","F",0
1428,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)^m/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\int \frac{{\left(2 \, c d x + b d\right)}^{m}}{{\left(c x^{2} + b x + a\right)}^{3}}\,{d x}"," ",0,"integrate((2*c*d*x + b*d)^m/(c*x^2 + b*x + a)^3, x)","F",0
1429,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)^m*(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\int {\left(c x^{2} + b x + a\right)}^{\frac{5}{2}} {\left(2 \, c d x + b d\right)}^{m}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(5/2)*(2*c*d*x + b*d)^m, x)","F",0
1430,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)^m*(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\int {\left(c x^{2} + b x + a\right)}^{\frac{3}{2}} {\left(2 \, c d x + b d\right)}^{m}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(3/2)*(2*c*d*x + b*d)^m, x)","F",0
1431,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)^m*(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int \sqrt{c x^{2} + b x + a} {\left(2 \, c d x + b d\right)}^{m}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + b*x + a)*(2*c*d*x + b*d)^m, x)","F",0
1432,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)^m/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(2 \, c d x + b d\right)}^{m}}{\sqrt{c x^{2} + b x + a}}\,{d x}"," ",0,"integrate((2*c*d*x + b*d)^m/sqrt(c*x^2 + b*x + a), x)","F",0
1433,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)^m/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(2 \, c d x + b d\right)}^{m}}{{\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((2*c*d*x + b*d)^m/(c*x^2 + b*x + a)^(3/2), x)","F",0
1434,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)^m/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(2 \, c d x + b d\right)}^{m}}{{\left(c x^{2} + b x + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((2*c*d*x + b*d)^m/(c*x^2 + b*x + a)^(5/2), x)","F",0
1435,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)^m*(c*x^2+b*x+a)^p,x, algorithm=""giac"")","\int {\left(2 \, c d x + b d\right)}^{m} {\left(c x^{2} + b x + a\right)}^{p}\,{d x}"," ",0,"integrate((2*c*d*x + b*d)^m*(c*x^2 + b*x + a)^p, x)","F",0
1436,1,877,0,0.264173," ","integrate((2*c*d*x+b*d)^5*(c*x^2+b*x+a)^p,x, algorithm=""giac"")","\frac{16 \, {\left(c x^{2} + b x + a\right)}^{p} c^{5} d^{5} p^{2} x^{6} + 48 \, {\left(c x^{2} + b x + a\right)}^{p} b c^{4} d^{5} p^{2} x^{5} + 48 \, {\left(c x^{2} + b x + a\right)}^{p} c^{5} d^{5} p x^{6} + 56 \, {\left(c x^{2} + b x + a\right)}^{p} b^{2} c^{3} d^{5} p^{2} x^{4} + 16 \, {\left(c x^{2} + b x + a\right)}^{p} a c^{4} d^{5} p^{2} x^{4} + 144 \, {\left(c x^{2} + b x + a\right)}^{p} b c^{4} d^{5} p x^{5} + 32 \, {\left(c x^{2} + b x + a\right)}^{p} c^{5} d^{5} x^{6} + 32 \, {\left(c x^{2} + b x + a\right)}^{p} b^{3} c^{2} d^{5} p^{2} x^{3} + 32 \, {\left(c x^{2} + b x + a\right)}^{p} a b c^{3} d^{5} p^{2} x^{3} + 176 \, {\left(c x^{2} + b x + a\right)}^{p} b^{2} c^{3} d^{5} p x^{4} + 16 \, {\left(c x^{2} + b x + a\right)}^{p} a c^{4} d^{5} p x^{4} + 96 \, {\left(c x^{2} + b x + a\right)}^{p} b c^{4} d^{5} x^{5} + 9 \, {\left(c x^{2} + b x + a\right)}^{p} b^{4} c d^{5} p^{2} x^{2} + 24 \, {\left(c x^{2} + b x + a\right)}^{p} a b^{2} c^{2} d^{5} p^{2} x^{2} + 112 \, {\left(c x^{2} + b x + a\right)}^{p} b^{3} c^{2} d^{5} p x^{3} + 32 \, {\left(c x^{2} + b x + a\right)}^{p} a b c^{3} d^{5} p x^{3} + 120 \, {\left(c x^{2} + b x + a\right)}^{p} b^{2} c^{3} d^{5} x^{4} + {\left(c x^{2} + b x + a\right)}^{p} b^{5} d^{5} p^{2} x + 8 \, {\left(c x^{2} + b x + a\right)}^{p} a b^{3} c d^{5} p^{2} x + 37 \, {\left(c x^{2} + b x + a\right)}^{p} b^{4} c d^{5} p x^{2} + 40 \, {\left(c x^{2} + b x + a\right)}^{p} a b^{2} c^{2} d^{5} p x^{2} - 32 \, {\left(c x^{2} + b x + a\right)}^{p} a^{2} c^{3} d^{5} p x^{2} + 80 \, {\left(c x^{2} + b x + a\right)}^{p} b^{3} c^{2} d^{5} x^{3} + {\left(c x^{2} + b x + a\right)}^{p} a b^{4} d^{5} p^{2} + 5 \, {\left(c x^{2} + b x + a\right)}^{p} b^{5} d^{5} p x + 24 \, {\left(c x^{2} + b x + a\right)}^{p} a b^{3} c d^{5} p x - 32 \, {\left(c x^{2} + b x + a\right)}^{p} a^{2} b c^{2} d^{5} p x + 30 \, {\left(c x^{2} + b x + a\right)}^{p} b^{4} c d^{5} x^{2} + 5 \, {\left(c x^{2} + b x + a\right)}^{p} a b^{4} d^{5} p - 8 \, {\left(c x^{2} + b x + a\right)}^{p} a^{2} b^{2} c d^{5} p + 6 \, {\left(c x^{2} + b x + a\right)}^{p} b^{5} d^{5} x + 6 \, {\left(c x^{2} + b x + a\right)}^{p} a b^{4} d^{5} - 24 \, {\left(c x^{2} + b x + a\right)}^{p} a^{2} b^{2} c d^{5} + 32 \, {\left(c x^{2} + b x + a\right)}^{p} a^{3} c^{2} d^{5}}{p^{3} + 6 \, p^{2} + 11 \, p + 6}"," ",0,"(16*(c*x^2 + b*x + a)^p*c^5*d^5*p^2*x^6 + 48*(c*x^2 + b*x + a)^p*b*c^4*d^5*p^2*x^5 + 48*(c*x^2 + b*x + a)^p*c^5*d^5*p*x^6 + 56*(c*x^2 + b*x + a)^p*b^2*c^3*d^5*p^2*x^4 + 16*(c*x^2 + b*x + a)^p*a*c^4*d^5*p^2*x^4 + 144*(c*x^2 + b*x + a)^p*b*c^4*d^5*p*x^5 + 32*(c*x^2 + b*x + a)^p*c^5*d^5*x^6 + 32*(c*x^2 + b*x + a)^p*b^3*c^2*d^5*p^2*x^3 + 32*(c*x^2 + b*x + a)^p*a*b*c^3*d^5*p^2*x^3 + 176*(c*x^2 + b*x + a)^p*b^2*c^3*d^5*p*x^4 + 16*(c*x^2 + b*x + a)^p*a*c^4*d^5*p*x^4 + 96*(c*x^2 + b*x + a)^p*b*c^4*d^5*x^5 + 9*(c*x^2 + b*x + a)^p*b^4*c*d^5*p^2*x^2 + 24*(c*x^2 + b*x + a)^p*a*b^2*c^2*d^5*p^2*x^2 + 112*(c*x^2 + b*x + a)^p*b^3*c^2*d^5*p*x^3 + 32*(c*x^2 + b*x + a)^p*a*b*c^3*d^5*p*x^3 + 120*(c*x^2 + b*x + a)^p*b^2*c^3*d^5*x^4 + (c*x^2 + b*x + a)^p*b^5*d^5*p^2*x + 8*(c*x^2 + b*x + a)^p*a*b^3*c*d^5*p^2*x + 37*(c*x^2 + b*x + a)^p*b^4*c*d^5*p*x^2 + 40*(c*x^2 + b*x + a)^p*a*b^2*c^2*d^5*p*x^2 - 32*(c*x^2 + b*x + a)^p*a^2*c^3*d^5*p*x^2 + 80*(c*x^2 + b*x + a)^p*b^3*c^2*d^5*x^3 + (c*x^2 + b*x + a)^p*a*b^4*d^5*p^2 + 5*(c*x^2 + b*x + a)^p*b^5*d^5*p*x + 24*(c*x^2 + b*x + a)^p*a*b^3*c*d^5*p*x - 32*(c*x^2 + b*x + a)^p*a^2*b*c^2*d^5*p*x + 30*(c*x^2 + b*x + a)^p*b^4*c*d^5*x^2 + 5*(c*x^2 + b*x + a)^p*a*b^4*d^5*p - 8*(c*x^2 + b*x + a)^p*a^2*b^2*c*d^5*p + 6*(c*x^2 + b*x + a)^p*b^5*d^5*x + 6*(c*x^2 + b*x + a)^p*a*b^4*d^5 - 24*(c*x^2 + b*x + a)^p*a^2*b^2*c*d^5 + 32*(c*x^2 + b*x + a)^p*a^3*c^2*d^5)/(p^3 + 6*p^2 + 11*p + 6)","B",0
1437,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)^4*(c*x^2+b*x+a)^p,x, algorithm=""giac"")","\int {\left(2 \, c d x + b d\right)}^{4} {\left(c x^{2} + b x + a\right)}^{p}\,{d x}"," ",0,"integrate((2*c*d*x + b*d)^4*(c*x^2 + b*x + a)^p, x)","F",0
1438,1,291,0,0.185007," ","integrate((2*c*d*x+b*d)^3*(c*x^2+b*x+a)^p,x, algorithm=""giac"")","\frac{a b^{2} d^{3} p \left(\frac{c d x^{2} + b d x + a d}{d}\right)^{p} + 2 \, a b^{2} d^{3} \left(\frac{c d x^{2} + b d x + a d}{d}\right)^{p} - 4 \, a^{2} c d^{3} \left(\frac{c d x^{2} + b d x + a d}{d}\right)^{p} + {\left(c d x^{2} + b d x\right)} b^{2} d^{2} p \left(\frac{c d x^{2} + b d x + a d}{d}\right)^{p} + 4 \, {\left(c d x^{2} + b d x\right)} a c d^{2} p \left(\frac{c d x^{2} + b d x + a d}{d}\right)^{p} + 2 \, {\left(c d x^{2} + b d x\right)} b^{2} d^{2} \left(\frac{c d x^{2} + b d x + a d}{d}\right)^{p} + 4 \, {\left(c d x^{2} + b d x\right)}^{2} c d p \left(\frac{c d x^{2} + b d x + a d}{d}\right)^{p} + 4 \, {\left(c d x^{2} + b d x\right)}^{2} c d \left(\frac{c d x^{2} + b d x + a d}{d}\right)^{p}}{p^{2} + 3 \, p + 2}"," ",0,"(a*b^2*d^3*p*((c*d*x^2 + b*d*x + a*d)/d)^p + 2*a*b^2*d^3*((c*d*x^2 + b*d*x + a*d)/d)^p - 4*a^2*c*d^3*((c*d*x^2 + b*d*x + a*d)/d)^p + (c*d*x^2 + b*d*x)*b^2*d^2*p*((c*d*x^2 + b*d*x + a*d)/d)^p + 4*(c*d*x^2 + b*d*x)*a*c*d^2*p*((c*d*x^2 + b*d*x + a*d)/d)^p + 2*(c*d*x^2 + b*d*x)*b^2*d^2*((c*d*x^2 + b*d*x + a*d)/d)^p + 4*(c*d*x^2 + b*d*x)^2*c*d*p*((c*d*x^2 + b*d*x + a*d)/d)^p + 4*(c*d*x^2 + b*d*x)^2*c*d*((c*d*x^2 + b*d*x + a*d)/d)^p)/(p^2 + 3*p + 2)","B",0
1439,0,0,0,0.000000," ","integrate((2*c*d*x+b*d)^2*(c*x^2+b*x+a)^p,x, algorithm=""giac"")","\int {\left(2 \, c d x + b d\right)}^{2} {\left(c x^{2} + b x + a\right)}^{p}\,{d x}"," ",0,"integrate((2*c*d*x + b*d)^2*(c*x^2 + b*x + a)^p, x)","F",0
1440,1,21,0,0.162717," ","integrate((2*c*d*x+b*d)*(c*x^2+b*x+a)^p,x, algorithm=""giac"")","\frac{{\left(c x^{2} + b x + a\right)}^{p + 1} d}{p + 1}"," ",0,"(c*x^2 + b*x + a)^(p + 1)*d/(p + 1)","A",0
1441,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^p/(2*c*d*x+b*d),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{p}}{2 \, c d x + b d}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^p/(2*c*d*x + b*d), x)","F",0
1442,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^p/(2*c*d*x+b*d)^2,x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{p}}{{\left(2 \, c d x + b d\right)}^{2}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^p/(2*c*d*x + b*d)^2, x)","F",0
1443,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^p/(2*c*d*x+b*d)^3,x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{p}}{{\left(2 \, c d x + b d\right)}^{3}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^p/(2*c*d*x + b*d)^3, x)","F",0
1444,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^p/(2*c*d*x+b*d)^4,x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{p}}{{\left(2 \, c d x + b d\right)}^{4}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^p/(2*c*d*x + b*d)^4, x)","F",0
1445,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^p/(2*c*d*x+b*d)^5,x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{p}}{{\left(2 \, c d x + b d\right)}^{5}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^p/(2*c*d*x + b*d)^5, x)","F",0
1446,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^p/(2*c*d*x+b*d)^6,x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{p}}{{\left(2 \, c d x + b d\right)}^{6}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^p/(2*c*d*x + b*d)^6, x)","F",0
1447,1,12,0,0.156492," ","integrate((1+x)/(x^2+2*x-3)^(2/3),x, algorithm=""giac"")","\frac{3}{2} \, {\left(x^{2} + 2 \, x - 3\right)}^{\frac{1}{3}}"," ",0,"3/2*(x^2 + 2*x - 3)^(1/3)","A",0
1448,1,15,0,0.159942," ","integrate((c*x+b)/(c*x^2+2*b*x+a)^(3/7),x, algorithm=""giac"")","\frac{7}{8} \, {\left(c x^{2} + 2 \, b x + a\right)}^{\frac{4}{7}}"," ",0,"7/8*(c*x^2 + 2*b*x + a)^(4/7)","A",0
1449,1,37,0,0.165797," ","integrate((1+x)^m*(x^2+2*x+1)^n,x, algorithm=""giac"")","\frac{{\left(x + 1\right)}^{m} {\left(x + 1\right)}^{2 \, n} x + {\left(x + 1\right)}^{m} {\left(x + 1\right)}^{2 \, n}}{m + 2 \, n + 1}"," ",0,"((x + 1)^m*(x + 1)^(2*n)*x + (x + 1)^m*(x + 1)^(2*n))/(m + 2*n + 1)","A",0
1450,1,104,0,0.237420," ","integrate((1/2*b*e/c+e*x)^m*(1/4/c*b^2+b*x+c*x^2)^n,x, algorithm=""giac"")","\frac{2 \, c x e^{\left(-m \log\left(2\right) - 2 \, n \log\left(2\right) + m \log\left(2 \, c x + b\right) + 2 \, n \log\left(2 \, c x + b\right) - m \log\left(c\right) - n \log\left(c\right) + m\right)} + b e^{\left(-m \log\left(2\right) - 2 \, n \log\left(2\right) + m \log\left(2 \, c x + b\right) + 2 \, n \log\left(2 \, c x + b\right) - m \log\left(c\right) - n \log\left(c\right) + m\right)}}{2 \, {\left(c m + 2 \, c n + c\right)}}"," ",0,"1/2*(2*c*x*e^(-m*log(2) - 2*n*log(2) + m*log(2*c*x + b) + 2*n*log(2*c*x + b) - m*log(c) - n*log(c) + m) + b*e^(-m*log(2) - 2*n*log(2) + m*log(2*c*x + b) + 2*n*log(2*c*x + b) - m*log(c) - n*log(c) + m))/(c*m + 2*c*n + c)","B",0
1451,1,164,0,0.162831," ","integrate((e*x+d)^4*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{1}{7} \, b^{2} x^{7} e^{4} + \frac{2}{3} \, b^{2} d x^{6} e^{3} + \frac{6}{5} \, b^{2} d^{2} x^{5} e^{2} + b^{2} d^{3} x^{4} e + \frac{1}{3} \, b^{2} d^{4} x^{3} + \frac{1}{3} \, a b x^{6} e^{4} + \frac{8}{5} \, a b d x^{5} e^{3} + 3 \, a b d^{2} x^{4} e^{2} + \frac{8}{3} \, a b d^{3} x^{3} e + a b d^{4} x^{2} + \frac{1}{5} \, a^{2} x^{5} e^{4} + a^{2} d x^{4} e^{3} + 2 \, a^{2} d^{2} x^{3} e^{2} + 2 \, a^{2} d^{3} x^{2} e + a^{2} d^{4} x"," ",0,"1/7*b^2*x^7*e^4 + 2/3*b^2*d*x^6*e^3 + 6/5*b^2*d^2*x^5*e^2 + b^2*d^3*x^4*e + 1/3*b^2*d^4*x^3 + 1/3*a*b*x^6*e^4 + 8/5*a*b*d*x^5*e^3 + 3*a*b*d^2*x^4*e^2 + 8/3*a*b*d^3*x^3*e + a*b*d^4*x^2 + 1/5*a^2*x^5*e^4 + a^2*d*x^4*e^3 + 2*a^2*d^2*x^3*e^2 + 2*a^2*d^3*x^2*e + a^2*d^4*x","B",0
1452,1,127,0,0.157323," ","integrate((e*x+d)^3*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{1}{6} \, b^{2} x^{6} e^{3} + \frac{3}{5} \, b^{2} d x^{5} e^{2} + \frac{3}{4} \, b^{2} d^{2} x^{4} e + \frac{1}{3} \, b^{2} d^{3} x^{3} + \frac{2}{5} \, a b x^{5} e^{3} + \frac{3}{2} \, a b d x^{4} e^{2} + 2 \, a b d^{2} x^{3} e + a b d^{3} x^{2} + \frac{1}{4} \, a^{2} x^{4} e^{3} + a^{2} d x^{3} e^{2} + \frac{3}{2} \, a^{2} d^{2} x^{2} e + a^{2} d^{3} x"," ",0,"1/6*b^2*x^6*e^3 + 3/5*b^2*d*x^5*e^2 + 3/4*b^2*d^2*x^4*e + 1/3*b^2*d^3*x^3 + 2/5*a*b*x^5*e^3 + 3/2*a*b*d*x^4*e^2 + 2*a*b*d^2*x^3*e + a*b*d^3*x^2 + 1/4*a^2*x^4*e^3 + a^2*d*x^3*e^2 + 3/2*a^2*d^2*x^2*e + a^2*d^3*x","B",0
1453,1,89,0,0.160188," ","integrate((e*x+d)^2*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{1}{5} \, b^{2} x^{5} e^{2} + \frac{1}{2} \, b^{2} d x^{4} e + \frac{1}{3} \, b^{2} d^{2} x^{3} + \frac{1}{2} \, a b x^{4} e^{2} + \frac{4}{3} \, a b d x^{3} e + a b d^{2} x^{2} + \frac{1}{3} \, a^{2} x^{3} e^{2} + a^{2} d x^{2} e + a^{2} d^{2} x"," ",0,"1/5*b^2*x^5*e^2 + 1/2*b^2*d*x^4*e + 1/3*b^2*d^2*x^3 + 1/2*a*b*x^4*e^2 + 4/3*a*b*d*x^3*e + a*b*d^2*x^2 + 1/3*a^2*x^3*e^2 + a^2*d*x^2*e + a^2*d^2*x","A",0
1454,1,52,0,0.154217," ","integrate((e*x+d)*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{1}{4} \, b^{2} x^{4} e + \frac{1}{3} \, b^{2} d x^{3} + \frac{2}{3} \, a b x^{3} e + a b d x^{2} + \frac{1}{2} \, a^{2} x^{2} e + a^{2} d x"," ",0,"1/4*b^2*x^4*e + 1/3*b^2*d*x^3 + 2/3*a*b*x^3*e + a*b*d*x^2 + 1/2*a^2*x^2*e + a^2*d*x","A",0
1455,1,20,0,0.181296," ","integrate(b^2*x^2+2*a*b*x+a^2,x, algorithm=""giac"")","\frac{1}{3} \, b^{2} x^{3} + a b x^{2} + a^{2} x"," ",0,"1/3*b^2*x^3 + a*b*x^2 + a^2*x","A",0
1456,1,61,0,0.152610," ","integrate((b^2*x^2+2*a*b*x+a^2)/(e*x+d),x, algorithm=""giac"")","{\left(b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}\right)} e^{\left(-3\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{2} \, {\left(b^{2} x^{2} e - 2 \, b^{2} d x + 4 \, a b x e\right)} e^{\left(-2\right)}"," ",0,"(b^2*d^2 - 2*a*b*d*e + a^2*e^2)*e^(-3)*log(abs(x*e + d)) + 1/2*(b^2*x^2*e - 2*b^2*d*x + 4*a*b*x*e)*e^(-2)","A",0
1457,1,111,0,0.155454," ","integrate((b^2*x^2+2*a*b*x+a^2)/(e*x+d)^2,x, algorithm=""giac"")","-2 \, {\left(e^{\left(-1\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) - \frac{d e^{\left(-1\right)}}{x e + d}\right)} a b e^{\left(-1\right)} + {\left(2 \, d e^{\left(-3\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) + {\left(x e + d\right)} e^{\left(-3\right)} - \frac{d^{2} e^{\left(-3\right)}}{x e + d}\right)} b^{2} - \frac{a^{2} e^{\left(-1\right)}}{x e + d}"," ",0,"-2*(e^(-1)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) - d*e^(-1)/(x*e + d))*a*b*e^(-1) + (2*d*e^(-3)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) + (x*e + d)*e^(-3) - d^2*e^(-3)/(x*e + d))*b^2 - a^2*e^(-1)/(x*e + d)","B",0
1458,1,69,0,0.156910," ","integrate((b^2*x^2+2*a*b*x+a^2)/(e*x+d)^3,x, algorithm=""giac"")","b^{2} e^{\left(-3\right)} \log\left({\left| x e + d \right|}\right) + \frac{{\left(4 \, {\left(b^{2} d - a b e\right)} x + {\left(3 \, b^{2} d^{2} - 2 \, a b d e - a^{2} e^{2}\right)} e^{\left(-1\right)}\right)} e^{\left(-2\right)}}{2 \, {\left(x e + d\right)}^{2}}"," ",0,"b^2*e^(-3)*log(abs(x*e + d)) + 1/2*(4*(b^2*d - a*b*e)*x + (3*b^2*d^2 - 2*a*b*d*e - a^2*e^2)*e^(-1))*e^(-2)/(x*e + d)^2","A",0
1459,1,58,0,0.152499," ","integrate((b^2*x^2+2*a*b*x+a^2)/(e*x+d)^4,x, algorithm=""giac"")","-\frac{{\left(3 \, b^{2} x^{2} e^{2} + 3 \, b^{2} d x e + b^{2} d^{2} + 3 \, a b x e^{2} + a b d e + a^{2} e^{2}\right)} e^{\left(-3\right)}}{3 \, {\left(x e + d\right)}^{3}}"," ",0,"-1/3*(3*b^2*x^2*e^2 + 3*b^2*d*x*e + b^2*d^2 + 3*a*b*x*e^2 + a*b*d*e + a^2*e^2)*e^(-3)/(x*e + d)^3","B",0
1460,1,96,0,0.178543," ","integrate((b^2*x^2+2*a*b*x+a^2)/(e*x+d)^5,x, algorithm=""giac"")","-\frac{1}{12} \, {\left(\frac{6 \, b^{2} e^{\left(-2\right)}}{{\left(x e + d\right)}^{2}} - \frac{8 \, b^{2} d e^{\left(-2\right)}}{{\left(x e + d\right)}^{3}} + \frac{3 \, b^{2} d^{2} e^{\left(-2\right)}}{{\left(x e + d\right)}^{4}} + \frac{8 \, a b e^{\left(-1\right)}}{{\left(x e + d\right)}^{3}} - \frac{6 \, a b d e^{\left(-1\right)}}{{\left(x e + d\right)}^{4}} + \frac{3 \, a^{2}}{{\left(x e + d\right)}^{4}}\right)} e^{\left(-1\right)}"," ",0,"-1/12*(6*b^2*e^(-2)/(x*e + d)^2 - 8*b^2*d*e^(-2)/(x*e + d)^3 + 3*b^2*d^2*e^(-2)/(x*e + d)^4 + 8*a*b*e^(-1)/(x*e + d)^3 - 6*a*b*d*e^(-1)/(x*e + d)^4 + 3*a^2/(x*e + d)^4)*e^(-1)","A",0
1461,1,60,0,0.151400," ","integrate((b^2*x^2+2*a*b*x+a^2)/(e*x+d)^6,x, algorithm=""giac"")","-\frac{{\left(10 \, b^{2} x^{2} e^{2} + 5 \, b^{2} d x e + b^{2} d^{2} + 15 \, a b x e^{2} + 3 \, a b d e + 6 \, a^{2} e^{2}\right)} e^{\left(-3\right)}}{30 \, {\left(x e + d\right)}^{5}}"," ",0,"-1/30*(10*b^2*x^2*e^2 + 5*b^2*d*x*e + b^2*d^2 + 15*a*b*x*e^2 + 3*a*b*d*e + 6*a^2*e^2)*e^(-3)/(x*e + d)^5","A",0
1462,1,60,0,0.178167," ","integrate((b^2*x^2+2*a*b*x+a^2)/(e*x+d)^7,x, algorithm=""giac"")","-\frac{{\left(15 \, b^{2} x^{2} e^{2} + 6 \, b^{2} d x e + b^{2} d^{2} + 24 \, a b x e^{2} + 4 \, a b d e + 10 \, a^{2} e^{2}\right)} e^{\left(-3\right)}}{60 \, {\left(x e + d\right)}^{6}}"," ",0,"-1/60*(15*b^2*x^2*e^2 + 6*b^2*d*x*e + b^2*d^2 + 24*a*b*x*e^2 + 4*a*b*d*e + 10*a^2*e^2)*e^(-3)/(x*e + d)^6","A",0
1463,1,450,0,0.169563," ","integrate((e*x+d)^6*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{1}{11} \, b^{4} x^{11} e^{6} + \frac{3}{5} \, b^{4} d x^{10} e^{5} + \frac{5}{3} \, b^{4} d^{2} x^{9} e^{4} + \frac{5}{2} \, b^{4} d^{3} x^{8} e^{3} + \frac{15}{7} \, b^{4} d^{4} x^{7} e^{2} + b^{4} d^{5} x^{6} e + \frac{1}{5} \, b^{4} d^{6} x^{5} + \frac{2}{5} \, a b^{3} x^{10} e^{6} + \frac{8}{3} \, a b^{3} d x^{9} e^{5} + \frac{15}{2} \, a b^{3} d^{2} x^{8} e^{4} + \frac{80}{7} \, a b^{3} d^{3} x^{7} e^{3} + 10 \, a b^{3} d^{4} x^{6} e^{2} + \frac{24}{5} \, a b^{3} d^{5} x^{5} e + a b^{3} d^{6} x^{4} + \frac{2}{3} \, a^{2} b^{2} x^{9} e^{6} + \frac{9}{2} \, a^{2} b^{2} d x^{8} e^{5} + \frac{90}{7} \, a^{2} b^{2} d^{2} x^{7} e^{4} + 20 \, a^{2} b^{2} d^{3} x^{6} e^{3} + 18 \, a^{2} b^{2} d^{4} x^{5} e^{2} + 9 \, a^{2} b^{2} d^{5} x^{4} e + 2 \, a^{2} b^{2} d^{6} x^{3} + \frac{1}{2} \, a^{3} b x^{8} e^{6} + \frac{24}{7} \, a^{3} b d x^{7} e^{5} + 10 \, a^{3} b d^{2} x^{6} e^{4} + 16 \, a^{3} b d^{3} x^{5} e^{3} + 15 \, a^{3} b d^{4} x^{4} e^{2} + 8 \, a^{3} b d^{5} x^{3} e + 2 \, a^{3} b d^{6} x^{2} + \frac{1}{7} \, a^{4} x^{7} e^{6} + a^{4} d x^{6} e^{5} + 3 \, a^{4} d^{2} x^{5} e^{4} + 5 \, a^{4} d^{3} x^{4} e^{3} + 5 \, a^{4} d^{4} x^{3} e^{2} + 3 \, a^{4} d^{5} x^{2} e + a^{4} d^{6} x"," ",0,"1/11*b^4*x^11*e^6 + 3/5*b^4*d*x^10*e^5 + 5/3*b^4*d^2*x^9*e^4 + 5/2*b^4*d^3*x^8*e^3 + 15/7*b^4*d^4*x^7*e^2 + b^4*d^5*x^6*e + 1/5*b^4*d^6*x^5 + 2/5*a*b^3*x^10*e^6 + 8/3*a*b^3*d*x^9*e^5 + 15/2*a*b^3*d^2*x^8*e^4 + 80/7*a*b^3*d^3*x^7*e^3 + 10*a*b^3*d^4*x^6*e^2 + 24/5*a*b^3*d^5*x^5*e + a*b^3*d^6*x^4 + 2/3*a^2*b^2*x^9*e^6 + 9/2*a^2*b^2*d*x^8*e^5 + 90/7*a^2*b^2*d^2*x^7*e^4 + 20*a^2*b^2*d^3*x^6*e^3 + 18*a^2*b^2*d^4*x^5*e^2 + 9*a^2*b^2*d^5*x^4*e + 2*a^2*b^2*d^6*x^3 + 1/2*a^3*b*x^8*e^6 + 24/7*a^3*b*d*x^7*e^5 + 10*a^3*b*d^2*x^6*e^4 + 16*a^3*b*d^3*x^5*e^3 + 15*a^3*b*d^4*x^4*e^2 + 8*a^3*b*d^5*x^3*e + 2*a^3*b*d^6*x^2 + 1/7*a^4*x^7*e^6 + a^4*d*x^6*e^5 + 3*a^4*d^2*x^5*e^4 + 5*a^4*d^3*x^4*e^3 + 5*a^4*d^4*x^3*e^2 + 3*a^4*d^5*x^2*e + a^4*d^6*x","B",0
1464,1,381,0,0.194993," ","integrate((e*x+d)^5*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{1}{10} \, b^{4} x^{10} e^{5} + \frac{5}{9} \, b^{4} d x^{9} e^{4} + \frac{5}{4} \, b^{4} d^{2} x^{8} e^{3} + \frac{10}{7} \, b^{4} d^{3} x^{7} e^{2} + \frac{5}{6} \, b^{4} d^{4} x^{6} e + \frac{1}{5} \, b^{4} d^{5} x^{5} + \frac{4}{9} \, a b^{3} x^{9} e^{5} + \frac{5}{2} \, a b^{3} d x^{8} e^{4} + \frac{40}{7} \, a b^{3} d^{2} x^{7} e^{3} + \frac{20}{3} \, a b^{3} d^{3} x^{6} e^{2} + 4 \, a b^{3} d^{4} x^{5} e + a b^{3} d^{5} x^{4} + \frac{3}{4} \, a^{2} b^{2} x^{8} e^{5} + \frac{30}{7} \, a^{2} b^{2} d x^{7} e^{4} + 10 \, a^{2} b^{2} d^{2} x^{6} e^{3} + 12 \, a^{2} b^{2} d^{3} x^{5} e^{2} + \frac{15}{2} \, a^{2} b^{2} d^{4} x^{4} e + 2 \, a^{2} b^{2} d^{5} x^{3} + \frac{4}{7} \, a^{3} b x^{7} e^{5} + \frac{10}{3} \, a^{3} b d x^{6} e^{4} + 8 \, a^{3} b d^{2} x^{5} e^{3} + 10 \, a^{3} b d^{3} x^{4} e^{2} + \frac{20}{3} \, a^{3} b d^{4} x^{3} e + 2 \, a^{3} b d^{5} x^{2} + \frac{1}{6} \, a^{4} x^{6} e^{5} + a^{4} d x^{5} e^{4} + \frac{5}{2} \, a^{4} d^{2} x^{4} e^{3} + \frac{10}{3} \, a^{4} d^{3} x^{3} e^{2} + \frac{5}{2} \, a^{4} d^{4} x^{2} e + a^{4} d^{5} x"," ",0,"1/10*b^4*x^10*e^5 + 5/9*b^4*d*x^9*e^4 + 5/4*b^4*d^2*x^8*e^3 + 10/7*b^4*d^3*x^7*e^2 + 5/6*b^4*d^4*x^6*e + 1/5*b^4*d^5*x^5 + 4/9*a*b^3*x^9*e^5 + 5/2*a*b^3*d*x^8*e^4 + 40/7*a*b^3*d^2*x^7*e^3 + 20/3*a*b^3*d^3*x^6*e^2 + 4*a*b^3*d^4*x^5*e + a*b^3*d^5*x^4 + 3/4*a^2*b^2*x^8*e^5 + 30/7*a^2*b^2*d*x^7*e^4 + 10*a^2*b^2*d^2*x^6*e^3 + 12*a^2*b^2*d^3*x^5*e^2 + 15/2*a^2*b^2*d^4*x^4*e + 2*a^2*b^2*d^5*x^3 + 4/7*a^3*b*x^7*e^5 + 10/3*a^3*b*d*x^6*e^4 + 8*a^3*b*d^2*x^5*e^3 + 10*a^3*b*d^3*x^4*e^2 + 20/3*a^3*b*d^4*x^3*e + 2*a^3*b*d^5*x^2 + 1/6*a^4*x^6*e^5 + a^4*d*x^5*e^4 + 5/2*a^4*d^2*x^4*e^3 + 10/3*a^4*d^3*x^3*e^2 + 5/2*a^4*d^4*x^2*e + a^4*d^5*x","B",0
1465,1,311,0,0.155084," ","integrate((e*x+d)^4*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{1}{9} \, b^{4} x^{9} e^{4} + \frac{1}{2} \, b^{4} d x^{8} e^{3} + \frac{6}{7} \, b^{4} d^{2} x^{7} e^{2} + \frac{2}{3} \, b^{4} d^{3} x^{6} e + \frac{1}{5} \, b^{4} d^{4} x^{5} + \frac{1}{2} \, a b^{3} x^{8} e^{4} + \frac{16}{7} \, a b^{3} d x^{7} e^{3} + 4 \, a b^{3} d^{2} x^{6} e^{2} + \frac{16}{5} \, a b^{3} d^{3} x^{5} e + a b^{3} d^{4} x^{4} + \frac{6}{7} \, a^{2} b^{2} x^{7} e^{4} + 4 \, a^{2} b^{2} d x^{6} e^{3} + \frac{36}{5} \, a^{2} b^{2} d^{2} x^{5} e^{2} + 6 \, a^{2} b^{2} d^{3} x^{4} e + 2 \, a^{2} b^{2} d^{4} x^{3} + \frac{2}{3} \, a^{3} b x^{6} e^{4} + \frac{16}{5} \, a^{3} b d x^{5} e^{3} + 6 \, a^{3} b d^{2} x^{4} e^{2} + \frac{16}{3} \, a^{3} b d^{3} x^{3} e + 2 \, a^{3} b d^{4} x^{2} + \frac{1}{5} \, a^{4} x^{5} e^{4} + a^{4} d x^{4} e^{3} + 2 \, a^{4} d^{2} x^{3} e^{2} + 2 \, a^{4} d^{3} x^{2} e + a^{4} d^{4} x"," ",0,"1/9*b^4*x^9*e^4 + 1/2*b^4*d*x^8*e^3 + 6/7*b^4*d^2*x^7*e^2 + 2/3*b^4*d^3*x^6*e + 1/5*b^4*d^4*x^5 + 1/2*a*b^3*x^8*e^4 + 16/7*a*b^3*d*x^7*e^3 + 4*a*b^3*d^2*x^6*e^2 + 16/5*a*b^3*d^3*x^5*e + a*b^3*d^4*x^4 + 6/7*a^2*b^2*x^7*e^4 + 4*a^2*b^2*d*x^6*e^3 + 36/5*a^2*b^2*d^2*x^5*e^2 + 6*a^2*b^2*d^3*x^4*e + 2*a^2*b^2*d^4*x^3 + 2/3*a^3*b*x^6*e^4 + 16/5*a^3*b*d*x^5*e^3 + 6*a^3*b*d^2*x^4*e^2 + 16/3*a^3*b*d^3*x^3*e + 2*a^3*b*d^4*x^2 + 1/5*a^4*x^5*e^4 + a^4*d*x^4*e^3 + 2*a^4*d^2*x^3*e^2 + 2*a^4*d^3*x^2*e + a^4*d^4*x","B",0
1466,1,240,0,0.168292," ","integrate((e*x+d)^3*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{1}{8} \, b^{4} x^{8} e^{3} + \frac{3}{7} \, b^{4} d x^{7} e^{2} + \frac{1}{2} \, b^{4} d^{2} x^{6} e + \frac{1}{5} \, b^{4} d^{3} x^{5} + \frac{4}{7} \, a b^{3} x^{7} e^{3} + 2 \, a b^{3} d x^{6} e^{2} + \frac{12}{5} \, a b^{3} d^{2} x^{5} e + a b^{3} d^{3} x^{4} + a^{2} b^{2} x^{6} e^{3} + \frac{18}{5} \, a^{2} b^{2} d x^{5} e^{2} + \frac{9}{2} \, a^{2} b^{2} d^{2} x^{4} e + 2 \, a^{2} b^{2} d^{3} x^{3} + \frac{4}{5} \, a^{3} b x^{5} e^{3} + 3 \, a^{3} b d x^{4} e^{2} + 4 \, a^{3} b d^{2} x^{3} e + 2 \, a^{3} b d^{3} x^{2} + \frac{1}{4} \, a^{4} x^{4} e^{3} + a^{4} d x^{3} e^{2} + \frac{3}{2} \, a^{4} d^{2} x^{2} e + a^{4} d^{3} x"," ",0,"1/8*b^4*x^8*e^3 + 3/7*b^4*d*x^7*e^2 + 1/2*b^4*d^2*x^6*e + 1/5*b^4*d^3*x^5 + 4/7*a*b^3*x^7*e^3 + 2*a*b^3*d*x^6*e^2 + 12/5*a*b^3*d^2*x^5*e + a*b^3*d^3*x^4 + a^2*b^2*x^6*e^3 + 18/5*a^2*b^2*d*x^5*e^2 + 9/2*a^2*b^2*d^2*x^4*e + 2*a^2*b^2*d^3*x^3 + 4/5*a^3*b*x^5*e^3 + 3*a^3*b*d*x^4*e^2 + 4*a^3*b*d^2*x^3*e + 2*a^3*b*d^3*x^2 + 1/4*a^4*x^4*e^3 + a^4*d*x^3*e^2 + 3/2*a^4*d^2*x^2*e + a^4*d^3*x","B",0
1467,1,170,0,0.153426," ","integrate((e*x+d)^2*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{1}{7} \, b^{4} x^{7} e^{2} + \frac{1}{3} \, b^{4} d x^{6} e + \frac{1}{5} \, b^{4} d^{2} x^{5} + \frac{2}{3} \, a b^{3} x^{6} e^{2} + \frac{8}{5} \, a b^{3} d x^{5} e + a b^{3} d^{2} x^{4} + \frac{6}{5} \, a^{2} b^{2} x^{5} e^{2} + 3 \, a^{2} b^{2} d x^{4} e + 2 \, a^{2} b^{2} d^{2} x^{3} + a^{3} b x^{4} e^{2} + \frac{8}{3} \, a^{3} b d x^{3} e + 2 \, a^{3} b d^{2} x^{2} + \frac{1}{3} \, a^{4} x^{3} e^{2} + a^{4} d x^{2} e + a^{4} d^{2} x"," ",0,"1/7*b^4*x^7*e^2 + 1/3*b^4*d*x^6*e + 1/5*b^4*d^2*x^5 + 2/3*a*b^3*x^6*e^2 + 8/5*a*b^3*d*x^5*e + a*b^3*d^2*x^4 + 6/5*a^2*b^2*x^5*e^2 + 3*a^2*b^2*d*x^4*e + 2*a^2*b^2*d^2*x^3 + a^3*b*x^4*e^2 + 8/3*a^3*b*d*x^3*e + 2*a^3*b*d^2*x^2 + 1/3*a^4*x^3*e^2 + a^4*d*x^2*e + a^4*d^2*x","B",0
1468,1,102,0,0.156671," ","integrate((e*x+d)*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{1}{6} \, b^{4} x^{6} e + \frac{1}{5} \, b^{4} d x^{5} + \frac{4}{5} \, a b^{3} x^{5} e + a b^{3} d x^{4} + \frac{3}{2} \, a^{2} b^{2} x^{4} e + 2 \, a^{2} b^{2} d x^{3} + \frac{4}{3} \, a^{3} b x^{3} e + 2 \, a^{3} b d x^{2} + \frac{1}{2} \, a^{4} x^{2} e + a^{4} d x"," ",0,"1/6*b^4*x^6*e + 1/5*b^4*d*x^5 + 4/5*a*b^3*x^5*e + a*b^3*d*x^4 + 3/2*a^2*b^2*x^4*e + 2*a^2*b^2*d*x^3 + 4/3*a^3*b*x^3*e + 2*a^3*b*d*x^2 + 1/2*a^4*x^2*e + a^4*d*x","B",0
1469,1,42,0,0.164725," ","integrate((b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\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*a^2*b^2*x^3 + 2*a^3*b*x^2 + a^4*x","B",0
1470,1,176,0,0.161578," ","integrate((b^2*x^2+2*a*b*x+a^2)^2/(e*x+d),x, algorithm=""giac"")","{\left(b^{4} d^{4} - 4 \, a b^{3} d^{3} e + 6 \, a^{2} b^{2} d^{2} e^{2} - 4 \, a^{3} b d e^{3} + a^{4} e^{4}\right)} e^{\left(-5\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{12} \, {\left(3 \, b^{4} x^{4} e^{3} - 4 \, b^{4} d x^{3} e^{2} + 6 \, b^{4} d^{2} x^{2} e - 12 \, b^{4} d^{3} x + 16 \, a b^{3} x^{3} e^{3} - 24 \, a b^{3} d x^{2} e^{2} + 48 \, a b^{3} d^{2} x e + 36 \, a^{2} b^{2} x^{2} e^{3} - 72 \, a^{2} b^{2} d x e^{2} + 48 \, a^{3} b x e^{3}\right)} e^{\left(-4\right)}"," ",0,"(b^4*d^4 - 4*a*b^3*d^3*e + 6*a^2*b^2*d^2*e^2 - 4*a^3*b*d*e^3 + a^4*e^4)*e^(-5)*log(abs(x*e + d)) + 1/12*(3*b^4*x^4*e^3 - 4*b^4*d*x^3*e^2 + 6*b^4*d^2*x^2*e - 12*b^4*d^3*x + 16*a*b^3*x^3*e^3 - 24*a*b^3*d*x^2*e^2 + 48*a*b^3*d^2*x*e + 36*a^2*b^2*x^2*e^3 - 72*a^2*b^2*d*x*e^2 + 48*a^3*b*x*e^3)*e^(-4)","A",0
1471,1,239,0,0.208353," ","integrate((b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^2,x, algorithm=""giac"")","\frac{1}{3} \, {\left(b^{4} - \frac{6 \, {\left(b^{4} d e - a b^{3} e^{2}\right)} e^{\left(-1\right)}}{x e + d} + \frac{18 \, {\left(b^{4} d^{2} e^{2} - 2 \, a b^{3} d e^{3} + a^{2} b^{2} e^{4}\right)} e^{\left(-2\right)}}{{\left(x e + d\right)}^{2}}\right)} {\left(x e + d\right)}^{3} e^{\left(-5\right)} + 4 \, {\left(b^{4} d^{3} - 3 \, a b^{3} d^{2} e + 3 \, a^{2} b^{2} d e^{2} - a^{3} b e^{3}\right)} e^{\left(-5\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) - {\left(\frac{b^{4} d^{4} e^{3}}{x e + d} - \frac{4 \, a b^{3} d^{3} e^{4}}{x e + d} + \frac{6 \, a^{2} b^{2} d^{2} e^{5}}{x e + d} - \frac{4 \, a^{3} b d e^{6}}{x e + d} + \frac{a^{4} e^{7}}{x e + d}\right)} e^{\left(-8\right)}"," ",0,"1/3*(b^4 - 6*(b^4*d*e - a*b^3*e^2)*e^(-1)/(x*e + d) + 18*(b^4*d^2*e^2 - 2*a*b^3*d*e^3 + a^2*b^2*e^4)*e^(-2)/(x*e + d)^2)*(x*e + d)^3*e^(-5) + 4*(b^4*d^3 - 3*a*b^3*d^2*e + 3*a^2*b^2*d*e^2 - a^3*b*e^3)*e^(-5)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) - (b^4*d^4*e^3/(x*e + d) - 4*a*b^3*d^3*e^4/(x*e + d) + 6*a^2*b^2*d^2*e^5/(x*e + d) - 4*a^3*b*d*e^6/(x*e + d) + a^4*e^7/(x*e + d))*e^(-8)","B",0
1472,1,175,0,0.159049," ","integrate((b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^3,x, algorithm=""giac"")","6 \, {\left(b^{4} d^{2} - 2 \, a b^{3} d e + a^{2} b^{2} e^{2}\right)} e^{\left(-5\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{2} \, {\left(b^{4} x^{2} e^{3} - 6 \, b^{4} d x e^{2} + 8 \, a b^{3} x e^{3}\right)} e^{\left(-6\right)} + \frac{{\left(7 \, b^{4} d^{4} - 20 \, a b^{3} d^{3} e + 18 \, a^{2} b^{2} d^{2} e^{2} - 4 \, a^{3} b d e^{3} - a^{4} e^{4} + 8 \, {\left(b^{4} d^{3} e - 3 \, a b^{3} d^{2} e^{2} + 3 \, a^{2} b^{2} d e^{3} - a^{3} b e^{4}\right)} x\right)} e^{\left(-5\right)}}{2 \, {\left(x e + d\right)}^{2}}"," ",0,"6*(b^4*d^2 - 2*a*b^3*d*e + a^2*b^2*e^2)*e^(-5)*log(abs(x*e + d)) + 1/2*(b^4*x^2*e^3 - 6*b^4*d*x*e^2 + 8*a*b^3*x*e^3)*e^(-6) + 1/2*(7*b^4*d^4 - 20*a*b^3*d^3*e + 18*a^2*b^2*d^2*e^2 - 4*a^3*b*d*e^3 - a^4*e^4 + 8*(b^4*d^3*e - 3*a*b^3*d^2*e^2 + 3*a^2*b^2*d*e^3 - a^3*b*e^4)*x)*e^(-5)/(x*e + d)^2","A",0
1473,1,170,0,0.175445," ","integrate((b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^4,x, algorithm=""giac"")","b^{4} x e^{\left(-4\right)} - 4 \, {\left(b^{4} d - a b^{3} e\right)} e^{\left(-5\right)} \log\left({\left| x e + d \right|}\right) - \frac{{\left(13 \, b^{4} d^{4} - 22 \, a b^{3} d^{3} e + 6 \, a^{2} b^{2} d^{2} e^{2} + 2 \, a^{3} b d e^{3} + a^{4} e^{4} + 18 \, {\left(b^{4} d^{2} e^{2} - 2 \, a b^{3} d e^{3} + a^{2} b^{2} e^{4}\right)} x^{2} + 6 \, {\left(5 \, b^{4} d^{3} e - 9 \, a b^{3} d^{2} e^{2} + 3 \, a^{2} b^{2} d e^{3} + a^{3} b e^{4}\right)} x\right)} e^{\left(-5\right)}}{3 \, {\left(x e + d\right)}^{3}}"," ",0,"b^4*x*e^(-4) - 4*(b^4*d - a*b^3*e)*e^(-5)*log(abs(x*e + d)) - 1/3*(13*b^4*d^4 - 22*a*b^3*d^3*e + 6*a^2*b^2*d^2*e^2 + 2*a^3*b*d*e^3 + a^4*e^4 + 18*(b^4*d^2*e^2 - 2*a*b^3*d*e^3 + a^2*b^2*e^4)*x^2 + 6*(5*b^4*d^3*e - 9*a*b^3*d^2*e^2 + 3*a^2*b^2*d*e^3 + a^3*b*e^4)*x)*e^(-5)/(x*e + d)^3","A",0
1474,1,279,0,0.181054," ","integrate((b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^5,x, algorithm=""giac"")","-b^{4} e^{\left(-5\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) + \frac{1}{12} \, {\left(\frac{48 \, b^{4} d e^{15}}{x e + d} - \frac{36 \, b^{4} d^{2} e^{15}}{{\left(x e + d\right)}^{2}} + \frac{16 \, b^{4} d^{3} e^{15}}{{\left(x e + d\right)}^{3}} - \frac{3 \, b^{4} d^{4} e^{15}}{{\left(x e + d\right)}^{4}} - \frac{48 \, a b^{3} e^{16}}{x e + d} + \frac{72 \, a b^{3} d e^{16}}{{\left(x e + d\right)}^{2}} - \frac{48 \, a b^{3} d^{2} e^{16}}{{\left(x e + d\right)}^{3}} + \frac{12 \, a b^{3} d^{3} e^{16}}{{\left(x e + d\right)}^{4}} - \frac{36 \, a^{2} b^{2} e^{17}}{{\left(x e + d\right)}^{2}} + \frac{48 \, a^{2} b^{2} d e^{17}}{{\left(x e + d\right)}^{3}} - \frac{18 \, a^{2} b^{2} d^{2} e^{17}}{{\left(x e + d\right)}^{4}} - \frac{16 \, a^{3} b e^{18}}{{\left(x e + d\right)}^{3}} + \frac{12 \, a^{3} b d e^{18}}{{\left(x e + d\right)}^{4}} - \frac{3 \, a^{4} e^{19}}{{\left(x e + d\right)}^{4}}\right)} e^{\left(-20\right)}"," ",0,"-b^4*e^(-5)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) + 1/12*(48*b^4*d*e^15/(x*e + d) - 36*b^4*d^2*e^15/(x*e + d)^2 + 16*b^4*d^3*e^15/(x*e + d)^3 - 3*b^4*d^4*e^15/(x*e + d)^4 - 48*a*b^3*e^16/(x*e + d) + 72*a*b^3*d*e^16/(x*e + d)^2 - 48*a*b^3*d^2*e^16/(x*e + d)^3 + 12*a*b^3*d^3*e^16/(x*e + d)^4 - 36*a^2*b^2*e^17/(x*e + d)^2 + 48*a^2*b^2*d*e^17/(x*e + d)^3 - 18*a^2*b^2*d^2*e^17/(x*e + d)^4 - 16*a^3*b*e^18/(x*e + d)^3 + 12*a^3*b*d*e^18/(x*e + d)^4 - 3*a^4*e^19/(x*e + d)^4)*e^(-20)","B",0
1475,1,170,0,0.154915," ","integrate((b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^6,x, algorithm=""giac"")","-\frac{{\left(5 \, b^{4} x^{4} e^{4} + 10 \, b^{4} d x^{3} e^{3} + 10 \, b^{4} d^{2} x^{2} e^{2} + 5 \, b^{4} d^{3} x e + b^{4} d^{4} + 10 \, a b^{3} x^{3} e^{4} + 10 \, a b^{3} d x^{2} e^{3} + 5 \, a b^{3} d^{2} x e^{2} + a b^{3} d^{3} e + 10 \, a^{2} b^{2} x^{2} e^{4} + 5 \, a^{2} b^{2} d x e^{3} + a^{2} b^{2} d^{2} e^{2} + 5 \, a^{3} b x e^{4} + a^{3} b d e^{3} + a^{4} e^{4}\right)} e^{\left(-5\right)}}{5 \, {\left(x e + d\right)}^{5}}"," ",0,"-1/5*(5*b^4*x^4*e^4 + 10*b^4*d*x^3*e^3 + 10*b^4*d^2*x^2*e^2 + 5*b^4*d^3*x*e + b^4*d^4 + 10*a*b^3*x^3*e^4 + 10*a*b^3*d*x^2*e^3 + 5*a*b^3*d^2*x*e^2 + a*b^3*d^3*e + 10*a^2*b^2*x^2*e^4 + 5*a^2*b^2*d*x*e^3 + a^2*b^2*d^2*e^2 + 5*a^3*b*x*e^4 + a^3*b*d*e^3 + a^4*e^4)*e^(-5)/(x*e + d)^5","B",0
1476,1,174,0,0.177793," ","integrate((b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^7,x, algorithm=""giac"")","-\frac{{\left(15 \, b^{4} x^{4} e^{4} + 20 \, b^{4} d x^{3} e^{3} + 15 \, b^{4} d^{2} x^{2} e^{2} + 6 \, b^{4} d^{3} x e + b^{4} d^{4} + 40 \, a b^{3} x^{3} e^{4} + 30 \, a b^{3} d x^{2} e^{3} + 12 \, a b^{3} d^{2} x e^{2} + 2 \, a b^{3} d^{3} e + 45 \, a^{2} b^{2} x^{2} e^{4} + 18 \, a^{2} b^{2} d x e^{3} + 3 \, a^{2} b^{2} d^{2} e^{2} + 24 \, a^{3} b x e^{4} + 4 \, a^{3} b d e^{3} + 5 \, a^{4} e^{4}\right)} e^{\left(-5\right)}}{30 \, {\left(x e + d\right)}^{6}}"," ",0,"-1/30*(15*b^4*x^4*e^4 + 20*b^4*d*x^3*e^3 + 15*b^4*d^2*x^2*e^2 + 6*b^4*d^3*x*e + b^4*d^4 + 40*a*b^3*x^3*e^4 + 30*a*b^3*d*x^2*e^3 + 12*a*b^3*d^2*x*e^2 + 2*a*b^3*d^3*e + 45*a^2*b^2*x^2*e^4 + 18*a^2*b^2*d*x*e^3 + 3*a^2*b^2*d^2*e^2 + 24*a^3*b*x*e^4 + 4*a^3*b*d*e^3 + 5*a^4*e^4)*e^(-5)/(x*e + d)^6","B",0
1477,1,174,0,0.157307," ","integrate((b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^8,x, algorithm=""giac"")","-\frac{{\left(35 \, b^{4} x^{4} e^{4} + 35 \, b^{4} d x^{3} e^{3} + 21 \, b^{4} d^{2} x^{2} e^{2} + 7 \, b^{4} d^{3} x e + b^{4} d^{4} + 105 \, a b^{3} x^{3} e^{4} + 63 \, a b^{3} d x^{2} e^{3} + 21 \, a b^{3} d^{2} x e^{2} + 3 \, a b^{3} d^{3} e + 126 \, a^{2} b^{2} x^{2} e^{4} + 42 \, a^{2} b^{2} d x e^{3} + 6 \, a^{2} b^{2} d^{2} e^{2} + 70 \, a^{3} b x e^{4} + 10 \, a^{3} b d e^{3} + 15 \, a^{4} e^{4}\right)} e^{\left(-5\right)}}{105 \, {\left(x e + d\right)}^{7}}"," ",0,"-1/105*(35*b^4*x^4*e^4 + 35*b^4*d*x^3*e^3 + 21*b^4*d^2*x^2*e^2 + 7*b^4*d^3*x*e + b^4*d^4 + 105*a*b^3*x^3*e^4 + 63*a*b^3*d*x^2*e^3 + 21*a*b^3*d^2*x*e^2 + 3*a*b^3*d^3*e + 126*a^2*b^2*x^2*e^4 + 42*a^2*b^2*d*x*e^3 + 6*a^2*b^2*d^2*e^2 + 70*a^3*b*x*e^4 + 10*a^3*b*d*e^3 + 15*a^4*e^4)*e^(-5)/(x*e + d)^7","B",0
1478,1,174,0,0.162807," ","integrate((b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^9,x, algorithm=""giac"")","-\frac{{\left(70 \, b^{4} x^{4} e^{4} + 56 \, b^{4} d x^{3} e^{3} + 28 \, b^{4} d^{2} x^{2} e^{2} + 8 \, b^{4} d^{3} x e + b^{4} d^{4} + 224 \, a b^{3} x^{3} e^{4} + 112 \, a b^{3} d x^{2} e^{3} + 32 \, a b^{3} d^{2} x e^{2} + 4 \, a b^{3} d^{3} e + 280 \, a^{2} b^{2} x^{2} e^{4} + 80 \, a^{2} b^{2} d x e^{3} + 10 \, a^{2} b^{2} d^{2} e^{2} + 160 \, a^{3} b x e^{4} + 20 \, a^{3} b d e^{3} + 35 \, a^{4} e^{4}\right)} e^{\left(-5\right)}}{280 \, {\left(x e + d\right)}^{8}}"," ",0,"-1/280*(70*b^4*x^4*e^4 + 56*b^4*d*x^3*e^3 + 28*b^4*d^2*x^2*e^2 + 8*b^4*d^3*x*e + b^4*d^4 + 224*a*b^3*x^3*e^4 + 112*a*b^3*d*x^2*e^3 + 32*a*b^3*d^2*x*e^2 + 4*a*b^3*d^3*e + 280*a^2*b^2*x^2*e^4 + 80*a^2*b^2*d*x*e^3 + 10*a^2*b^2*d^2*e^2 + 160*a^3*b*x*e^4 + 20*a^3*b*d*e^3 + 35*a^4*e^4)*e^(-5)/(x*e + d)^8","A",0
1479,1,174,0,0.158235," ","integrate((b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^10,x, algorithm=""giac"")","-\frac{{\left(126 \, b^{4} x^{4} e^{4} + 84 \, b^{4} d x^{3} e^{3} + 36 \, b^{4} d^{2} x^{2} e^{2} + 9 \, b^{4} d^{3} x e + b^{4} d^{4} + 420 \, a b^{3} x^{3} e^{4} + 180 \, a b^{3} d x^{2} e^{3} + 45 \, a b^{3} d^{2} x e^{2} + 5 \, a b^{3} d^{3} e + 540 \, a^{2} b^{2} x^{2} e^{4} + 135 \, a^{2} b^{2} d x e^{3} + 15 \, a^{2} b^{2} d^{2} e^{2} + 315 \, a^{3} b x e^{4} + 35 \, a^{3} b d e^{3} + 70 \, a^{4} e^{4}\right)} e^{\left(-5\right)}}{630 \, {\left(x e + d\right)}^{9}}"," ",0,"-1/630*(126*b^4*x^4*e^4 + 84*b^4*d*x^3*e^3 + 36*b^4*d^2*x^2*e^2 + 9*b^4*d^3*x*e + b^4*d^4 + 420*a*b^3*x^3*e^4 + 180*a*b^3*d*x^2*e^3 + 45*a*b^3*d^2*x*e^2 + 5*a*b^3*d^3*e + 540*a^2*b^2*x^2*e^4 + 135*a^2*b^2*d*x*e^3 + 15*a^2*b^2*d^2*e^2 + 315*a^3*b*x*e^4 + 35*a^3*b*d*e^3 + 70*a^4*e^4)*e^(-5)/(x*e + d)^9","A",0
1480,1,174,0,0.160989," ","integrate((b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^11,x, algorithm=""giac"")","-\frac{{\left(210 \, b^{4} x^{4} e^{4} + 120 \, b^{4} d x^{3} e^{3} + 45 \, b^{4} d^{2} x^{2} e^{2} + 10 \, b^{4} d^{3} x e + b^{4} d^{4} + 720 \, a b^{3} x^{3} e^{4} + 270 \, a b^{3} d x^{2} e^{3} + 60 \, a b^{3} d^{2} x e^{2} + 6 \, a b^{3} d^{3} e + 945 \, a^{2} b^{2} x^{2} e^{4} + 210 \, a^{2} b^{2} d x e^{3} + 21 \, a^{2} b^{2} d^{2} e^{2} + 560 \, a^{3} b x e^{4} + 56 \, a^{3} b d e^{3} + 126 \, a^{4} e^{4}\right)} e^{\left(-5\right)}}{1260 \, {\left(x e + d\right)}^{10}}"," ",0,"-1/1260*(210*b^4*x^4*e^4 + 120*b^4*d*x^3*e^3 + 45*b^4*d^2*x^2*e^2 + 10*b^4*d^3*x*e + b^4*d^4 + 720*a*b^3*x^3*e^4 + 270*a*b^3*d*x^2*e^3 + 60*a*b^3*d^2*x*e^2 + 6*a*b^3*d^3*e + 945*a^2*b^2*x^2*e^4 + 210*a^2*b^2*d*x*e^3 + 21*a^2*b^2*d^2*e^2 + 560*a^3*b*x*e^4 + 56*a^3*b*d*e^3 + 126*a^4*e^4)*e^(-5)/(x*e + d)^10","A",0
1481,1,864,0,0.200718," ","integrate((e*x+d)^8*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{1}{15} \, b^{6} x^{15} e^{8} + \frac{4}{7} \, b^{6} d x^{14} e^{7} + \frac{28}{13} \, b^{6} d^{2} x^{13} e^{6} + \frac{14}{3} \, b^{6} d^{3} x^{12} e^{5} + \frac{70}{11} \, b^{6} d^{4} x^{11} e^{4} + \frac{28}{5} \, b^{6} d^{5} x^{10} e^{3} + \frac{28}{9} \, b^{6} d^{6} x^{9} e^{2} + b^{6} d^{7} x^{8} e + \frac{1}{7} \, b^{6} d^{8} x^{7} + \frac{3}{7} \, a b^{5} x^{14} e^{8} + \frac{48}{13} \, a b^{5} d x^{13} e^{7} + 14 \, a b^{5} d^{2} x^{12} e^{6} + \frac{336}{11} \, a b^{5} d^{3} x^{11} e^{5} + 42 \, a b^{5} d^{4} x^{10} e^{4} + \frac{112}{3} \, a b^{5} d^{5} x^{9} e^{3} + 21 \, a b^{5} d^{6} x^{8} e^{2} + \frac{48}{7} \, a b^{5} d^{7} x^{7} e + a b^{5} d^{8} x^{6} + \frac{15}{13} \, a^{2} b^{4} x^{13} e^{8} + 10 \, a^{2} b^{4} d x^{12} e^{7} + \frac{420}{11} \, a^{2} b^{4} d^{2} x^{11} e^{6} + 84 \, a^{2} b^{4} d^{3} x^{10} e^{5} + \frac{350}{3} \, a^{2} b^{4} d^{4} x^{9} e^{4} + 105 \, a^{2} b^{4} d^{5} x^{8} e^{3} + 60 \, a^{2} b^{4} d^{6} x^{7} e^{2} + 20 \, a^{2} b^{4} d^{7} x^{6} e + 3 \, a^{2} b^{4} d^{8} x^{5} + \frac{5}{3} \, a^{3} b^{3} x^{12} e^{8} + \frac{160}{11} \, a^{3} b^{3} d x^{11} e^{7} + 56 \, a^{3} b^{3} d^{2} x^{10} e^{6} + \frac{1120}{9} \, a^{3} b^{3} d^{3} x^{9} e^{5} + 175 \, a^{3} b^{3} d^{4} x^{8} e^{4} + 160 \, a^{3} b^{3} d^{5} x^{7} e^{3} + \frac{280}{3} \, a^{3} b^{3} d^{6} x^{6} e^{2} + 32 \, a^{3} b^{3} d^{7} x^{5} e + 5 \, a^{3} b^{3} d^{8} x^{4} + \frac{15}{11} \, a^{4} b^{2} x^{11} e^{8} + 12 \, a^{4} b^{2} d x^{10} e^{7} + \frac{140}{3} \, a^{4} b^{2} d^{2} x^{9} e^{6} + 105 \, a^{4} b^{2} d^{3} x^{8} e^{5} + 150 \, a^{4} b^{2} d^{4} x^{7} e^{4} + 140 \, a^{4} b^{2} d^{5} x^{6} e^{3} + 84 \, a^{4} b^{2} d^{6} x^{5} e^{2} + 30 \, a^{4} b^{2} d^{7} x^{4} e + 5 \, a^{4} b^{2} d^{8} x^{3} + \frac{3}{5} \, a^{5} b x^{10} e^{8} + \frac{16}{3} \, a^{5} b d x^{9} e^{7} + 21 \, a^{5} b d^{2} x^{8} e^{6} + 48 \, a^{5} b d^{3} x^{7} e^{5} + 70 \, a^{5} b d^{4} x^{6} e^{4} + \frac{336}{5} \, a^{5} b d^{5} x^{5} e^{3} + 42 \, a^{5} b d^{6} x^{4} e^{2} + 16 \, a^{5} b d^{7} x^{3} e + 3 \, a^{5} b d^{8} x^{2} + \frac{1}{9} \, a^{6} x^{9} e^{8} + a^{6} d x^{8} e^{7} + 4 \, a^{6} d^{2} x^{7} e^{6} + \frac{28}{3} \, a^{6} d^{3} x^{6} e^{5} + 14 \, a^{6} d^{4} x^{5} e^{4} + 14 \, a^{6} d^{5} x^{4} e^{3} + \frac{28}{3} \, a^{6} d^{6} x^{3} e^{2} + 4 \, a^{6} d^{7} x^{2} e + a^{6} d^{8} x"," ",0,"1/15*b^6*x^15*e^8 + 4/7*b^6*d*x^14*e^7 + 28/13*b^6*d^2*x^13*e^6 + 14/3*b^6*d^3*x^12*e^5 + 70/11*b^6*d^4*x^11*e^4 + 28/5*b^6*d^5*x^10*e^3 + 28/9*b^6*d^6*x^9*e^2 + b^6*d^7*x^8*e + 1/7*b^6*d^8*x^7 + 3/7*a*b^5*x^14*e^8 + 48/13*a*b^5*d*x^13*e^7 + 14*a*b^5*d^2*x^12*e^6 + 336/11*a*b^5*d^3*x^11*e^5 + 42*a*b^5*d^4*x^10*e^4 + 112/3*a*b^5*d^5*x^9*e^3 + 21*a*b^5*d^6*x^8*e^2 + 48/7*a*b^5*d^7*x^7*e + a*b^5*d^8*x^6 + 15/13*a^2*b^4*x^13*e^8 + 10*a^2*b^4*d*x^12*e^7 + 420/11*a^2*b^4*d^2*x^11*e^6 + 84*a^2*b^4*d^3*x^10*e^5 + 350/3*a^2*b^4*d^4*x^9*e^4 + 105*a^2*b^4*d^5*x^8*e^3 + 60*a^2*b^4*d^6*x^7*e^2 + 20*a^2*b^4*d^7*x^6*e + 3*a^2*b^4*d^8*x^5 + 5/3*a^3*b^3*x^12*e^8 + 160/11*a^3*b^3*d*x^11*e^7 + 56*a^3*b^3*d^2*x^10*e^6 + 1120/9*a^3*b^3*d^3*x^9*e^5 + 175*a^3*b^3*d^4*x^8*e^4 + 160*a^3*b^3*d^5*x^7*e^3 + 280/3*a^3*b^3*d^6*x^6*e^2 + 32*a^3*b^3*d^7*x^5*e + 5*a^3*b^3*d^8*x^4 + 15/11*a^4*b^2*x^11*e^8 + 12*a^4*b^2*d*x^10*e^7 + 140/3*a^4*b^2*d^2*x^9*e^6 + 105*a^4*b^2*d^3*x^8*e^5 + 150*a^4*b^2*d^4*x^7*e^4 + 140*a^4*b^2*d^5*x^6*e^3 + 84*a^4*b^2*d^6*x^5*e^2 + 30*a^4*b^2*d^7*x^4*e + 5*a^4*b^2*d^8*x^3 + 3/5*a^5*b*x^10*e^8 + 16/3*a^5*b*d*x^9*e^7 + 21*a^5*b*d^2*x^8*e^6 + 48*a^5*b*d^3*x^7*e^5 + 70*a^5*b*d^4*x^6*e^4 + 336/5*a^5*b*d^5*x^5*e^3 + 42*a^5*b*d^6*x^4*e^2 + 16*a^5*b*d^7*x^3*e + 3*a^5*b*d^8*x^2 + 1/9*a^6*x^9*e^8 + a^6*d*x^8*e^7 + 4*a^6*d^2*x^7*e^6 + 28/3*a^6*d^3*x^6*e^5 + 14*a^6*d^4*x^5*e^4 + 14*a^6*d^5*x^4*e^3 + 28/3*a^6*d^6*x^3*e^2 + 4*a^6*d^7*x^2*e + a^6*d^8*x","B",0
1482,1,763,0,0.164996," ","integrate((e*x+d)^7*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{1}{14} \, b^{6} x^{14} e^{7} + \frac{7}{13} \, b^{6} d x^{13} e^{6} + \frac{7}{4} \, b^{6} d^{2} x^{12} e^{5} + \frac{35}{11} \, b^{6} d^{3} x^{11} e^{4} + \frac{7}{2} \, b^{6} d^{4} x^{10} e^{3} + \frac{7}{3} \, b^{6} d^{5} x^{9} e^{2} + \frac{7}{8} \, b^{6} d^{6} x^{8} e + \frac{1}{7} \, b^{6} d^{7} x^{7} + \frac{6}{13} \, a b^{5} x^{13} e^{7} + \frac{7}{2} \, a b^{5} d x^{12} e^{6} + \frac{126}{11} \, a b^{5} d^{2} x^{11} e^{5} + 21 \, a b^{5} d^{3} x^{10} e^{4} + \frac{70}{3} \, a b^{5} d^{4} x^{9} e^{3} + \frac{63}{4} \, a b^{5} d^{5} x^{8} e^{2} + 6 \, a b^{5} d^{6} x^{7} e + a b^{5} d^{7} x^{6} + \frac{5}{4} \, a^{2} b^{4} x^{12} e^{7} + \frac{105}{11} \, a^{2} b^{4} d x^{11} e^{6} + \frac{63}{2} \, a^{2} b^{4} d^{2} x^{10} e^{5} + \frac{175}{3} \, a^{2} b^{4} d^{3} x^{9} e^{4} + \frac{525}{8} \, a^{2} b^{4} d^{4} x^{8} e^{3} + 45 \, a^{2} b^{4} d^{5} x^{7} e^{2} + \frac{35}{2} \, a^{2} b^{4} d^{6} x^{6} e + 3 \, a^{2} b^{4} d^{7} x^{5} + \frac{20}{11} \, a^{3} b^{3} x^{11} e^{7} + 14 \, a^{3} b^{3} d x^{10} e^{6} + \frac{140}{3} \, a^{3} b^{3} d^{2} x^{9} e^{5} + \frac{175}{2} \, a^{3} b^{3} d^{3} x^{8} e^{4} + 100 \, a^{3} b^{3} d^{4} x^{7} e^{3} + 70 \, a^{3} b^{3} d^{5} x^{6} e^{2} + 28 \, a^{3} b^{3} d^{6} x^{5} e + 5 \, a^{3} b^{3} d^{7} x^{4} + \frac{3}{2} \, a^{4} b^{2} x^{10} e^{7} + \frac{35}{3} \, a^{4} b^{2} d x^{9} e^{6} + \frac{315}{8} \, a^{4} b^{2} d^{2} x^{8} e^{5} + 75 \, a^{4} b^{2} d^{3} x^{7} e^{4} + \frac{175}{2} \, a^{4} b^{2} d^{4} x^{6} e^{3} + 63 \, a^{4} b^{2} d^{5} x^{5} e^{2} + \frac{105}{4} \, a^{4} b^{2} d^{6} x^{4} e + 5 \, a^{4} b^{2} d^{7} x^{3} + \frac{2}{3} \, a^{5} b x^{9} e^{7} + \frac{21}{4} \, a^{5} b d x^{8} e^{6} + 18 \, a^{5} b d^{2} x^{7} e^{5} + 35 \, a^{5} b d^{3} x^{6} e^{4} + 42 \, a^{5} b d^{4} x^{5} e^{3} + \frac{63}{2} \, a^{5} b d^{5} x^{4} e^{2} + 14 \, a^{5} b d^{6} x^{3} e + 3 \, a^{5} b d^{7} x^{2} + \frac{1}{8} \, a^{6} x^{8} e^{7} + a^{6} d x^{7} e^{6} + \frac{7}{2} \, a^{6} d^{2} x^{6} e^{5} + 7 \, a^{6} d^{3} x^{5} e^{4} + \frac{35}{4} \, a^{6} d^{4} x^{4} e^{3} + 7 \, a^{6} d^{5} x^{3} e^{2} + \frac{7}{2} \, a^{6} d^{6} x^{2} e + a^{6} d^{7} x"," ",0,"1/14*b^6*x^14*e^7 + 7/13*b^6*d*x^13*e^6 + 7/4*b^6*d^2*x^12*e^5 + 35/11*b^6*d^3*x^11*e^4 + 7/2*b^6*d^4*x^10*e^3 + 7/3*b^6*d^5*x^9*e^2 + 7/8*b^6*d^6*x^8*e + 1/7*b^6*d^7*x^7 + 6/13*a*b^5*x^13*e^7 + 7/2*a*b^5*d*x^12*e^6 + 126/11*a*b^5*d^2*x^11*e^5 + 21*a*b^5*d^3*x^10*e^4 + 70/3*a*b^5*d^4*x^9*e^3 + 63/4*a*b^5*d^5*x^8*e^2 + 6*a*b^5*d^6*x^7*e + a*b^5*d^7*x^6 + 5/4*a^2*b^4*x^12*e^7 + 105/11*a^2*b^4*d*x^11*e^6 + 63/2*a^2*b^4*d^2*x^10*e^5 + 175/3*a^2*b^4*d^3*x^9*e^4 + 525/8*a^2*b^4*d^4*x^8*e^3 + 45*a^2*b^4*d^5*x^7*e^2 + 35/2*a^2*b^4*d^6*x^6*e + 3*a^2*b^4*d^7*x^5 + 20/11*a^3*b^3*x^11*e^7 + 14*a^3*b^3*d*x^10*e^6 + 140/3*a^3*b^3*d^2*x^9*e^5 + 175/2*a^3*b^3*d^3*x^8*e^4 + 100*a^3*b^3*d^4*x^7*e^3 + 70*a^3*b^3*d^5*x^6*e^2 + 28*a^3*b^3*d^6*x^5*e + 5*a^3*b^3*d^7*x^4 + 3/2*a^4*b^2*x^10*e^7 + 35/3*a^4*b^2*d*x^9*e^6 + 315/8*a^4*b^2*d^2*x^8*e^5 + 75*a^4*b^2*d^3*x^7*e^4 + 175/2*a^4*b^2*d^4*x^6*e^3 + 63*a^4*b^2*d^5*x^5*e^2 + 105/4*a^4*b^2*d^6*x^4*e + 5*a^4*b^2*d^7*x^3 + 2/3*a^5*b*x^9*e^7 + 21/4*a^5*b*d*x^8*e^6 + 18*a^5*b*d^2*x^7*e^5 + 35*a^5*b*d^3*x^6*e^4 + 42*a^5*b*d^4*x^5*e^3 + 63/2*a^5*b*d^5*x^4*e^2 + 14*a^5*b*d^6*x^3*e + 3*a^5*b*d^7*x^2 + 1/8*a^6*x^8*e^7 + a^6*d*x^7*e^6 + 7/2*a^6*d^2*x^6*e^5 + 7*a^6*d^3*x^5*e^4 + 35/4*a^6*d^4*x^4*e^3 + 7*a^6*d^5*x^3*e^2 + 7/2*a^6*d^6*x^2*e + a^6*d^7*x","B",0
1483,1,661,0,0.174728," ","integrate((e*x+d)^6*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{1}{13} \, b^{6} x^{13} e^{6} + \frac{1}{2} \, b^{6} d x^{12} e^{5} + \frac{15}{11} \, b^{6} d^{2} x^{11} e^{4} + 2 \, b^{6} d^{3} x^{10} e^{3} + \frac{5}{3} \, b^{6} d^{4} x^{9} e^{2} + \frac{3}{4} \, b^{6} d^{5} x^{8} e + \frac{1}{7} \, b^{6} d^{6} x^{7} + \frac{1}{2} \, a b^{5} x^{12} e^{6} + \frac{36}{11} \, a b^{5} d x^{11} e^{5} + 9 \, a b^{5} d^{2} x^{10} e^{4} + \frac{40}{3} \, a b^{5} d^{3} x^{9} e^{3} + \frac{45}{4} \, a b^{5} d^{4} x^{8} e^{2} + \frac{36}{7} \, a b^{5} d^{5} x^{7} e + a b^{5} d^{6} x^{6} + \frac{15}{11} \, a^{2} b^{4} x^{11} e^{6} + 9 \, a^{2} b^{4} d x^{10} e^{5} + 25 \, a^{2} b^{4} d^{2} x^{9} e^{4} + \frac{75}{2} \, a^{2} b^{4} d^{3} x^{8} e^{3} + \frac{225}{7} \, a^{2} b^{4} d^{4} x^{7} e^{2} + 15 \, a^{2} b^{4} d^{5} x^{6} e + 3 \, a^{2} b^{4} d^{6} x^{5} + 2 \, a^{3} b^{3} x^{10} e^{6} + \frac{40}{3} \, a^{3} b^{3} d x^{9} e^{5} + \frac{75}{2} \, a^{3} b^{3} d^{2} x^{8} e^{4} + \frac{400}{7} \, a^{3} b^{3} d^{3} x^{7} e^{3} + 50 \, a^{3} b^{3} d^{4} x^{6} e^{2} + 24 \, a^{3} b^{3} d^{5} x^{5} e + 5 \, a^{3} b^{3} d^{6} x^{4} + \frac{5}{3} \, a^{4} b^{2} x^{9} e^{6} + \frac{45}{4} \, a^{4} b^{2} d x^{8} e^{5} + \frac{225}{7} \, a^{4} b^{2} d^{2} x^{7} e^{4} + 50 \, a^{4} b^{2} d^{3} x^{6} e^{3} + 45 \, a^{4} b^{2} d^{4} x^{5} e^{2} + \frac{45}{2} \, a^{4} b^{2} d^{5} x^{4} e + 5 \, a^{4} b^{2} d^{6} x^{3} + \frac{3}{4} \, a^{5} b x^{8} e^{6} + \frac{36}{7} \, a^{5} b d x^{7} e^{5} + 15 \, a^{5} b d^{2} x^{6} e^{4} + 24 \, a^{5} b d^{3} x^{5} e^{3} + \frac{45}{2} \, a^{5} b d^{4} x^{4} e^{2} + 12 \, a^{5} b d^{5} x^{3} e + 3 \, a^{5} b d^{6} x^{2} + \frac{1}{7} \, a^{6} x^{7} e^{6} + a^{6} d x^{6} e^{5} + 3 \, a^{6} d^{2} x^{5} e^{4} + 5 \, a^{6} d^{3} x^{4} e^{3} + 5 \, a^{6} d^{4} x^{3} e^{2} + 3 \, a^{6} d^{5} x^{2} e + a^{6} d^{6} x"," ",0,"1/13*b^6*x^13*e^6 + 1/2*b^6*d*x^12*e^5 + 15/11*b^6*d^2*x^11*e^4 + 2*b^6*d^3*x^10*e^3 + 5/3*b^6*d^4*x^9*e^2 + 3/4*b^6*d^5*x^8*e + 1/7*b^6*d^6*x^7 + 1/2*a*b^5*x^12*e^6 + 36/11*a*b^5*d*x^11*e^5 + 9*a*b^5*d^2*x^10*e^4 + 40/3*a*b^5*d^3*x^9*e^3 + 45/4*a*b^5*d^4*x^8*e^2 + 36/7*a*b^5*d^5*x^7*e + a*b^5*d^6*x^6 + 15/11*a^2*b^4*x^11*e^6 + 9*a^2*b^4*d*x^10*e^5 + 25*a^2*b^4*d^2*x^9*e^4 + 75/2*a^2*b^4*d^3*x^8*e^3 + 225/7*a^2*b^4*d^4*x^7*e^2 + 15*a^2*b^4*d^5*x^6*e + 3*a^2*b^4*d^6*x^5 + 2*a^3*b^3*x^10*e^6 + 40/3*a^3*b^3*d*x^9*e^5 + 75/2*a^3*b^3*d^2*x^8*e^4 + 400/7*a^3*b^3*d^3*x^7*e^3 + 50*a^3*b^3*d^4*x^6*e^2 + 24*a^3*b^3*d^5*x^5*e + 5*a^3*b^3*d^6*x^4 + 5/3*a^4*b^2*x^9*e^6 + 45/4*a^4*b^2*d*x^8*e^5 + 225/7*a^4*b^2*d^2*x^7*e^4 + 50*a^4*b^2*d^3*x^6*e^3 + 45*a^4*b^2*d^4*x^5*e^2 + 45/2*a^4*b^2*d^5*x^4*e + 5*a^4*b^2*d^6*x^3 + 3/4*a^5*b*x^8*e^6 + 36/7*a^5*b*d*x^7*e^5 + 15*a^5*b*d^2*x^6*e^4 + 24*a^5*b*d^3*x^5*e^3 + 45/2*a^5*b*d^4*x^4*e^2 + 12*a^5*b*d^5*x^3*e + 3*a^5*b*d^6*x^2 + 1/7*a^6*x^7*e^6 + a^6*d*x^6*e^5 + 3*a^6*d^2*x^5*e^4 + 5*a^6*d^3*x^4*e^3 + 5*a^6*d^4*x^3*e^2 + 3*a^6*d^5*x^2*e + a^6*d^6*x","B",0
1484,1,558,0,0.198977," ","integrate((e*x+d)^5*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{1}{12} \, b^{6} x^{12} e^{5} + \frac{5}{11} \, b^{6} d x^{11} e^{4} + b^{6} d^{2} x^{10} e^{3} + \frac{10}{9} \, b^{6} d^{3} x^{9} e^{2} + \frac{5}{8} \, b^{6} d^{4} x^{8} e + \frac{1}{7} \, b^{6} d^{5} x^{7} + \frac{6}{11} \, a b^{5} x^{11} e^{5} + 3 \, a b^{5} d x^{10} e^{4} + \frac{20}{3} \, a b^{5} d^{2} x^{9} e^{3} + \frac{15}{2} \, a b^{5} d^{3} x^{8} e^{2} + \frac{30}{7} \, a b^{5} d^{4} x^{7} e + a b^{5} d^{5} x^{6} + \frac{3}{2} \, a^{2} b^{4} x^{10} e^{5} + \frac{25}{3} \, a^{2} b^{4} d x^{9} e^{4} + \frac{75}{4} \, a^{2} b^{4} d^{2} x^{8} e^{3} + \frac{150}{7} \, a^{2} b^{4} d^{3} x^{7} e^{2} + \frac{25}{2} \, a^{2} b^{4} d^{4} x^{6} e + 3 \, a^{2} b^{4} d^{5} x^{5} + \frac{20}{9} \, a^{3} b^{3} x^{9} e^{5} + \frac{25}{2} \, a^{3} b^{3} d x^{8} e^{4} + \frac{200}{7} \, a^{3} b^{3} d^{2} x^{7} e^{3} + \frac{100}{3} \, a^{3} b^{3} d^{3} x^{6} e^{2} + 20 \, a^{3} b^{3} d^{4} x^{5} e + 5 \, a^{3} b^{3} d^{5} x^{4} + \frac{15}{8} \, a^{4} b^{2} x^{8} e^{5} + \frac{75}{7} \, a^{4} b^{2} d x^{7} e^{4} + 25 \, a^{4} b^{2} d^{2} x^{6} e^{3} + 30 \, a^{4} b^{2} d^{3} x^{5} e^{2} + \frac{75}{4} \, a^{4} b^{2} d^{4} x^{4} e + 5 \, a^{4} b^{2} d^{5} x^{3} + \frac{6}{7} \, a^{5} b x^{7} e^{5} + 5 \, a^{5} b d x^{6} e^{4} + 12 \, a^{5} b d^{2} x^{5} e^{3} + 15 \, a^{5} b d^{3} x^{4} e^{2} + 10 \, a^{5} b d^{4} x^{3} e + 3 \, a^{5} b d^{5} x^{2} + \frac{1}{6} \, a^{6} x^{6} e^{5} + a^{6} d x^{5} e^{4} + \frac{5}{2} \, a^{6} d^{2} x^{4} e^{3} + \frac{10}{3} \, a^{6} d^{3} x^{3} e^{2} + \frac{5}{2} \, a^{6} d^{4} x^{2} e + a^{6} d^{5} x"," ",0,"1/12*b^6*x^12*e^5 + 5/11*b^6*d*x^11*e^4 + b^6*d^2*x^10*e^3 + 10/9*b^6*d^3*x^9*e^2 + 5/8*b^6*d^4*x^8*e + 1/7*b^6*d^5*x^7 + 6/11*a*b^5*x^11*e^5 + 3*a*b^5*d*x^10*e^4 + 20/3*a*b^5*d^2*x^9*e^3 + 15/2*a*b^5*d^3*x^8*e^2 + 30/7*a*b^5*d^4*x^7*e + a*b^5*d^5*x^6 + 3/2*a^2*b^4*x^10*e^5 + 25/3*a^2*b^4*d*x^9*e^4 + 75/4*a^2*b^4*d^2*x^8*e^3 + 150/7*a^2*b^4*d^3*x^7*e^2 + 25/2*a^2*b^4*d^4*x^6*e + 3*a^2*b^4*d^5*x^5 + 20/9*a^3*b^3*x^9*e^5 + 25/2*a^3*b^3*d*x^8*e^4 + 200/7*a^3*b^3*d^2*x^7*e^3 + 100/3*a^3*b^3*d^3*x^6*e^2 + 20*a^3*b^3*d^4*x^5*e + 5*a^3*b^3*d^5*x^4 + 15/8*a^4*b^2*x^8*e^5 + 75/7*a^4*b^2*d*x^7*e^4 + 25*a^4*b^2*d^2*x^6*e^3 + 30*a^4*b^2*d^3*x^5*e^2 + 75/4*a^4*b^2*d^4*x^4*e + 5*a^4*b^2*d^5*x^3 + 6/7*a^5*b*x^7*e^5 + 5*a^5*b*d*x^6*e^4 + 12*a^5*b*d^2*x^5*e^3 + 15*a^5*b*d^3*x^4*e^2 + 10*a^5*b*d^4*x^3*e + 3*a^5*b*d^5*x^2 + 1/6*a^6*x^6*e^5 + a^6*d*x^5*e^4 + 5/2*a^6*d^2*x^4*e^3 + 10/3*a^6*d^3*x^3*e^2 + 5/2*a^6*d^4*x^2*e + a^6*d^5*x","B",0
1485,1,456,0,0.178277," ","integrate((e*x+d)^4*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{1}{11} \, b^{6} x^{11} e^{4} + \frac{2}{5} \, b^{6} d x^{10} e^{3} + \frac{2}{3} \, b^{6} d^{2} x^{9} e^{2} + \frac{1}{2} \, b^{6} d^{3} x^{8} e + \frac{1}{7} \, b^{6} d^{4} x^{7} + \frac{3}{5} \, a b^{5} x^{10} e^{4} + \frac{8}{3} \, a b^{5} d x^{9} e^{3} + \frac{9}{2} \, a b^{5} d^{2} x^{8} e^{2} + \frac{24}{7} \, a b^{5} d^{3} x^{7} e + a b^{5} d^{4} x^{6} + \frac{5}{3} \, a^{2} b^{4} x^{9} e^{4} + \frac{15}{2} \, a^{2} b^{4} d x^{8} e^{3} + \frac{90}{7} \, a^{2} b^{4} d^{2} x^{7} e^{2} + 10 \, a^{2} b^{4} d^{3} x^{6} e + 3 \, a^{2} b^{4} d^{4} x^{5} + \frac{5}{2} \, a^{3} b^{3} x^{8} e^{4} + \frac{80}{7} \, a^{3} b^{3} d x^{7} e^{3} + 20 \, a^{3} b^{3} d^{2} x^{6} e^{2} + 16 \, a^{3} b^{3} d^{3} x^{5} e + 5 \, a^{3} b^{3} d^{4} x^{4} + \frac{15}{7} \, a^{4} b^{2} x^{7} e^{4} + 10 \, a^{4} b^{2} d x^{6} e^{3} + 18 \, a^{4} b^{2} d^{2} x^{5} e^{2} + 15 \, a^{4} b^{2} d^{3} x^{4} e + 5 \, a^{4} b^{2} d^{4} x^{3} + a^{5} b x^{6} e^{4} + \frac{24}{5} \, a^{5} b d x^{5} e^{3} + 9 \, a^{5} b d^{2} x^{4} e^{2} + 8 \, a^{5} b d^{3} x^{3} e + 3 \, a^{5} b d^{4} x^{2} + \frac{1}{5} \, a^{6} x^{5} e^{4} + a^{6} d x^{4} e^{3} + 2 \, a^{6} d^{2} x^{3} e^{2} + 2 \, a^{6} d^{3} x^{2} e + a^{6} d^{4} x"," ",0,"1/11*b^6*x^11*e^4 + 2/5*b^6*d*x^10*e^3 + 2/3*b^6*d^2*x^9*e^2 + 1/2*b^6*d^3*x^8*e + 1/7*b^6*d^4*x^7 + 3/5*a*b^5*x^10*e^4 + 8/3*a*b^5*d*x^9*e^3 + 9/2*a*b^5*d^2*x^8*e^2 + 24/7*a*b^5*d^3*x^7*e + a*b^5*d^4*x^6 + 5/3*a^2*b^4*x^9*e^4 + 15/2*a^2*b^4*d*x^8*e^3 + 90/7*a^2*b^4*d^2*x^7*e^2 + 10*a^2*b^4*d^3*x^6*e + 3*a^2*b^4*d^4*x^5 + 5/2*a^3*b^3*x^8*e^4 + 80/7*a^3*b^3*d*x^7*e^3 + 20*a^3*b^3*d^2*x^6*e^2 + 16*a^3*b^3*d^3*x^5*e + 5*a^3*b^3*d^4*x^4 + 15/7*a^4*b^2*x^7*e^4 + 10*a^4*b^2*d*x^6*e^3 + 18*a^4*b^2*d^2*x^5*e^2 + 15*a^4*b^2*d^3*x^4*e + 5*a^4*b^2*d^4*x^3 + a^5*b*x^6*e^4 + 24/5*a^5*b*d*x^5*e^3 + 9*a^5*b*d^2*x^4*e^2 + 8*a^5*b*d^3*x^3*e + 3*a^5*b*d^4*x^2 + 1/5*a^6*x^5*e^4 + a^6*d*x^4*e^3 + 2*a^6*d^2*x^3*e^2 + 2*a^6*d^3*x^2*e + a^6*d^4*x","B",0
1486,1,355,0,0.186357," ","integrate((e*x+d)^3*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{1}{10} \, b^{6} x^{10} e^{3} + \frac{1}{3} \, b^{6} d x^{9} e^{2} + \frac{3}{8} \, b^{6} d^{2} x^{8} e + \frac{1}{7} \, b^{6} d^{3} x^{7} + \frac{2}{3} \, a b^{5} x^{9} e^{3} + \frac{9}{4} \, a b^{5} d x^{8} e^{2} + \frac{18}{7} \, a b^{5} d^{2} x^{7} e + a b^{5} d^{3} x^{6} + \frac{15}{8} \, a^{2} b^{4} x^{8} e^{3} + \frac{45}{7} \, a^{2} b^{4} d x^{7} e^{2} + \frac{15}{2} \, a^{2} b^{4} d^{2} x^{6} e + 3 \, a^{2} b^{4} d^{3} x^{5} + \frac{20}{7} \, a^{3} b^{3} x^{7} e^{3} + 10 \, a^{3} b^{3} d x^{6} e^{2} + 12 \, a^{3} b^{3} d^{2} x^{5} e + 5 \, a^{3} b^{3} d^{3} x^{4} + \frac{5}{2} \, a^{4} b^{2} x^{6} e^{3} + 9 \, a^{4} b^{2} d x^{5} e^{2} + \frac{45}{4} \, a^{4} b^{2} d^{2} x^{4} e + 5 \, a^{4} b^{2} d^{3} x^{3} + \frac{6}{5} \, a^{5} b x^{5} e^{3} + \frac{9}{2} \, a^{5} b d x^{4} e^{2} + 6 \, a^{5} b d^{2} x^{3} e + 3 \, a^{5} b d^{3} x^{2} + \frac{1}{4} \, a^{6} x^{4} e^{3} + a^{6} d x^{3} e^{2} + \frac{3}{2} \, a^{6} d^{2} x^{2} e + a^{6} d^{3} x"," ",0,"1/10*b^6*x^10*e^3 + 1/3*b^6*d*x^9*e^2 + 3/8*b^6*d^2*x^8*e + 1/7*b^6*d^3*x^7 + 2/3*a*b^5*x^9*e^3 + 9/4*a*b^5*d*x^8*e^2 + 18/7*a*b^5*d^2*x^7*e + a*b^5*d^3*x^6 + 15/8*a^2*b^4*x^8*e^3 + 45/7*a^2*b^4*d*x^7*e^2 + 15/2*a^2*b^4*d^2*x^6*e + 3*a^2*b^4*d^3*x^5 + 20/7*a^3*b^3*x^7*e^3 + 10*a^3*b^3*d*x^6*e^2 + 12*a^3*b^3*d^2*x^5*e + 5*a^3*b^3*d^3*x^4 + 5/2*a^4*b^2*x^6*e^3 + 9*a^4*b^2*d*x^5*e^2 + 45/4*a^4*b^2*d^2*x^4*e + 5*a^4*b^2*d^3*x^3 + 6/5*a^5*b*x^5*e^3 + 9/2*a^5*b*d*x^4*e^2 + 6*a^5*b*d^2*x^3*e + 3*a^5*b*d^3*x^2 + 1/4*a^6*x^4*e^3 + a^6*d*x^3*e^2 + 3/2*a^6*d^2*x^2*e + a^6*d^3*x","B",0
1487,1,253,0,0.179854," ","integrate((e*x+d)^2*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{1}{9} \, b^{6} x^{9} e^{2} + \frac{1}{4} \, b^{6} d x^{8} e + \frac{1}{7} \, b^{6} d^{2} x^{7} + \frac{3}{4} \, a b^{5} x^{8} e^{2} + \frac{12}{7} \, a b^{5} d x^{7} e + a b^{5} d^{2} x^{6} + \frac{15}{7} \, a^{2} b^{4} x^{7} e^{2} + 5 \, a^{2} b^{4} d x^{6} e + 3 \, a^{2} b^{4} d^{2} x^{5} + \frac{10}{3} \, a^{3} b^{3} x^{6} e^{2} + 8 \, a^{3} b^{3} d x^{5} e + 5 \, a^{3} b^{3} d^{2} x^{4} + 3 \, a^{4} b^{2} x^{5} e^{2} + \frac{15}{2} \, a^{4} b^{2} d x^{4} e + 5 \, a^{4} b^{2} d^{2} x^{3} + \frac{3}{2} \, a^{5} b x^{4} e^{2} + 4 \, a^{5} b d x^{3} e + 3 \, a^{5} b d^{2} x^{2} + \frac{1}{3} \, a^{6} x^{3} e^{2} + a^{6} d x^{2} e + a^{6} d^{2} x"," ",0,"1/9*b^6*x^9*e^2 + 1/4*b^6*d*x^8*e + 1/7*b^6*d^2*x^7 + 3/4*a*b^5*x^8*e^2 + 12/7*a*b^5*d*x^7*e + a*b^5*d^2*x^6 + 15/7*a^2*b^4*x^7*e^2 + 5*a^2*b^4*d*x^6*e + 3*a^2*b^4*d^2*x^5 + 10/3*a^3*b^3*x^6*e^2 + 8*a^3*b^3*d*x^5*e + 5*a^3*b^3*d^2*x^4 + 3*a^4*b^2*x^5*e^2 + 15/2*a^4*b^2*d*x^4*e + 5*a^4*b^2*d^2*x^3 + 3/2*a^5*b*x^4*e^2 + 4*a^5*b*d*x^3*e + 3*a^5*b*d^2*x^2 + 1/3*a^6*x^3*e^2 + a^6*d*x^2*e + a^6*d^2*x","B",0
1488,1,152,0,0.157173," ","integrate((e*x+d)*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{1}{8} \, b^{6} x^{8} e + \frac{1}{7} \, b^{6} d x^{7} + \frac{6}{7} \, a b^{5} x^{7} e + a b^{5} d x^{6} + \frac{5}{2} \, a^{2} b^{4} x^{6} e + 3 \, a^{2} b^{4} d x^{5} + 4 \, a^{3} b^{3} x^{5} e + 5 \, a^{3} b^{3} d x^{4} + \frac{15}{4} \, a^{4} b^{2} x^{4} e + 5 \, a^{4} b^{2} d x^{3} + 2 \, a^{5} b x^{3} e + 3 \, a^{5} b d x^{2} + \frac{1}{2} \, a^{6} x^{2} e + a^{6} d x"," ",0,"1/8*b^6*x^8*e + 1/7*b^6*d*x^7 + 6/7*a*b^5*x^7*e + a*b^5*d*x^6 + 5/2*a^2*b^4*x^6*e + 3*a^2*b^4*d*x^5 + 4*a^3*b^3*x^5*e + 5*a^3*b^3*d*x^4 + 15/4*a^4*b^2*x^4*e + 5*a^4*b^2*d*x^3 + 2*a^5*b*x^3*e + 3*a^5*b*d*x^2 + 1/2*a^6*x^2*e + a^6*d*x","B",0
1489,1,64,0,0.151380," ","integrate((b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\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",0
1490,1,354,0,0.158403," ","integrate((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d),x, algorithm=""giac"")","{\left(b^{6} d^{6} - 6 \, a b^{5} d^{5} e + 15 \, a^{2} b^{4} d^{4} e^{2} - 20 \, a^{3} b^{3} d^{3} e^{3} + 15 \, a^{4} b^{2} d^{2} e^{4} - 6 \, a^{5} b d e^{5} + a^{6} e^{6}\right)} e^{\left(-7\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{60} \, {\left(10 \, b^{6} x^{6} e^{5} - 12 \, b^{6} d x^{5} e^{4} + 15 \, b^{6} d^{2} x^{4} e^{3} - 20 \, b^{6} d^{3} x^{3} e^{2} + 30 \, b^{6} d^{4} x^{2} e - 60 \, b^{6} d^{5} x + 72 \, a b^{5} x^{5} e^{5} - 90 \, a b^{5} d x^{4} e^{4} + 120 \, a b^{5} d^{2} x^{3} e^{3} - 180 \, a b^{5} d^{3} x^{2} e^{2} + 360 \, a b^{5} d^{4} x e + 225 \, a^{2} b^{4} x^{4} e^{5} - 300 \, a^{2} b^{4} d x^{3} e^{4} + 450 \, a^{2} b^{4} d^{2} x^{2} e^{3} - 900 \, a^{2} b^{4} d^{3} x e^{2} + 400 \, a^{3} b^{3} x^{3} e^{5} - 600 \, a^{3} b^{3} d x^{2} e^{4} + 1200 \, a^{3} b^{3} d^{2} x e^{3} + 450 \, a^{4} b^{2} x^{2} e^{5} - 900 \, a^{4} b^{2} d x e^{4} + 360 \, a^{5} b x e^{5}\right)} e^{\left(-6\right)}"," ",0,"(b^6*d^6 - 6*a*b^5*d^5*e + 15*a^2*b^4*d^4*e^2 - 20*a^3*b^3*d^3*e^3 + 15*a^4*b^2*d^2*e^4 - 6*a^5*b*d*e^5 + a^6*e^6)*e^(-7)*log(abs(x*e + d)) + 1/60*(10*b^6*x^6*e^5 - 12*b^6*d*x^5*e^4 + 15*b^6*d^2*x^4*e^3 - 20*b^6*d^3*x^3*e^2 + 30*b^6*d^4*x^2*e - 60*b^6*d^5*x + 72*a*b^5*x^5*e^5 - 90*a*b^5*d*x^4*e^4 + 120*a*b^5*d^2*x^3*e^3 - 180*a*b^5*d^3*x^2*e^2 + 360*a*b^5*d^4*x*e + 225*a^2*b^4*x^4*e^5 - 300*a^2*b^4*d*x^3*e^4 + 450*a^2*b^4*d^2*x^2*e^3 - 900*a^2*b^4*d^3*x*e^2 + 400*a^3*b^3*x^3*e^5 - 600*a^3*b^3*d*x^2*e^4 + 1200*a^3*b^3*d^2*x*e^3 + 450*a^4*b^2*x^2*e^5 - 900*a^4*b^2*d*x*e^4 + 360*a^5*b*x*e^5)*e^(-6)","B",0
1491,1,429,0,0.174001," ","integrate((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^2,x, algorithm=""giac"")","\frac{1}{10} \, {\left(2 \, b^{6} - \frac{15 \, {\left(b^{6} d e - a b^{5} e^{2}\right)} e^{\left(-1\right)}}{x e + d} + \frac{50 \, {\left(b^{6} d^{2} e^{2} - 2 \, a b^{5} d e^{3} + a^{2} b^{4} e^{4}\right)} e^{\left(-2\right)}}{{\left(x e + d\right)}^{2}} - \frac{100 \, {\left(b^{6} d^{3} e^{3} - 3 \, a b^{5} d^{2} e^{4} + 3 \, a^{2} b^{4} d e^{5} - a^{3} b^{3} e^{6}\right)} e^{\left(-3\right)}}{{\left(x e + d\right)}^{3}} + \frac{150 \, {\left(b^{6} d^{4} e^{4} - 4 \, a b^{5} d^{3} e^{5} + 6 \, a^{2} b^{4} d^{2} e^{6} - 4 \, a^{3} b^{3} d e^{7} + a^{4} b^{2} e^{8}\right)} e^{\left(-4\right)}}{{\left(x e + d\right)}^{4}}\right)} {\left(x e + d\right)}^{5} e^{\left(-7\right)} + 6 \, {\left(b^{6} d^{5} - 5 \, a b^{5} d^{4} e + 10 \, a^{2} b^{4} d^{3} e^{2} - 10 \, a^{3} b^{3} d^{2} e^{3} + 5 \, a^{4} b^{2} d e^{4} - a^{5} b e^{5}\right)} e^{\left(-7\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) - {\left(\frac{b^{6} d^{6} e^{5}}{x e + d} - \frac{6 \, a b^{5} d^{5} e^{6}}{x e + d} + \frac{15 \, a^{2} b^{4} d^{4} e^{7}}{x e + d} - \frac{20 \, a^{3} b^{3} d^{3} e^{8}}{x e + d} + \frac{15 \, a^{4} b^{2} d^{2} e^{9}}{x e + d} - \frac{6 \, a^{5} b d e^{10}}{x e + d} + \frac{a^{6} e^{11}}{x e + d}\right)} e^{\left(-12\right)}"," ",0,"1/10*(2*b^6 - 15*(b^6*d*e - a*b^5*e^2)*e^(-1)/(x*e + d) + 50*(b^6*d^2*e^2 - 2*a*b^5*d*e^3 + a^2*b^4*e^4)*e^(-2)/(x*e + d)^2 - 100*(b^6*d^3*e^3 - 3*a*b^5*d^2*e^4 + 3*a^2*b^4*d*e^5 - a^3*b^3*e^6)*e^(-3)/(x*e + d)^3 + 150*(b^6*d^4*e^4 - 4*a*b^5*d^3*e^5 + 6*a^2*b^4*d^2*e^6 - 4*a^3*b^3*d*e^7 + a^4*b^2*e^8)*e^(-4)/(x*e + d)^4)*(x*e + d)^5*e^(-7) + 6*(b^6*d^5 - 5*a*b^5*d^4*e + 10*a^2*b^4*d^3*e^2 - 10*a^3*b^3*d^2*e^3 + 5*a^4*b^2*d*e^4 - a^5*b*e^5)*e^(-7)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) - (b^6*d^6*e^5/(x*e + d) - 6*a*b^5*d^5*e^6/(x*e + d) + 15*a^2*b^4*d^4*e^7/(x*e + d) - 20*a^3*b^3*d^3*e^8/(x*e + d) + 15*a^4*b^2*d^2*e^9/(x*e + d) - 6*a^5*b*d*e^10/(x*e + d) + a^6*e^11/(x*e + d))*e^(-12)","B",0
1492,1,341,0,0.192260," ","integrate((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^3,x, algorithm=""giac"")","15 \, {\left(b^{6} d^{4} - 4 \, a b^{5} d^{3} e + 6 \, a^{2} b^{4} d^{2} e^{2} - 4 \, a^{3} b^{3} d e^{3} + a^{4} b^{2} e^{4}\right)} e^{\left(-7\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{4} \, {\left(b^{6} x^{4} e^{9} - 4 \, b^{6} d x^{3} e^{8} + 12 \, b^{6} d^{2} x^{2} e^{7} - 40 \, b^{6} d^{3} x e^{6} + 8 \, a b^{5} x^{3} e^{9} - 36 \, a b^{5} d x^{2} e^{8} + 144 \, a b^{5} d^{2} x e^{7} + 30 \, a^{2} b^{4} x^{2} e^{9} - 180 \, a^{2} b^{4} d x e^{8} + 80 \, a^{3} b^{3} x e^{9}\right)} e^{\left(-12\right)} + \frac{{\left(11 \, b^{6} d^{6} - 54 \, a b^{5} d^{5} e + 105 \, a^{2} b^{4} d^{4} e^{2} - 100 \, a^{3} b^{3} d^{3} e^{3} + 45 \, a^{4} b^{2} d^{2} e^{4} - 6 \, a^{5} b d e^{5} - a^{6} e^{6} + 12 \, {\left(b^{6} d^{5} e - 5 \, a b^{5} d^{4} e^{2} + 10 \, a^{2} b^{4} d^{3} e^{3} - 10 \, a^{3} b^{3} d^{2} e^{4} + 5 \, a^{4} b^{2} d e^{5} - a^{5} b e^{6}\right)} x\right)} e^{\left(-7\right)}}{2 \, {\left(x e + d\right)}^{2}}"," ",0,"15*(b^6*d^4 - 4*a*b^5*d^3*e + 6*a^2*b^4*d^2*e^2 - 4*a^3*b^3*d*e^3 + a^4*b^2*e^4)*e^(-7)*log(abs(x*e + d)) + 1/4*(b^6*x^4*e^9 - 4*b^6*d*x^3*e^8 + 12*b^6*d^2*x^2*e^7 - 40*b^6*d^3*x*e^6 + 8*a*b^5*x^3*e^9 - 36*a*b^5*d*x^2*e^8 + 144*a*b^5*d^2*x*e^7 + 30*a^2*b^4*x^2*e^9 - 180*a^2*b^4*d*x*e^8 + 80*a^3*b^3*x*e^9)*e^(-12) + 1/2*(11*b^6*d^6 - 54*a*b^5*d^5*e + 105*a^2*b^4*d^4*e^2 - 100*a^3*b^3*d^3*e^3 + 45*a^4*b^2*d^2*e^4 - 6*a^5*b*d*e^5 - a^6*e^6 + 12*(b^6*d^5*e - 5*a*b^5*d^4*e^2 + 10*a^2*b^4*d^3*e^3 - 10*a^3*b^3*d^2*e^4 + 5*a^4*b^2*d*e^5 - a^5*b*e^6)*x)*e^(-7)/(x*e + d)^2","B",0
1493,1,335,0,0.213019," ","integrate((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^4,x, algorithm=""giac"")","-20 \, {\left(b^{6} d^{3} - 3 \, a b^{5} d^{2} e + 3 \, a^{2} b^{4} d e^{2} - a^{3} b^{3} e^{3}\right)} e^{\left(-7\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{3} \, {\left(b^{6} x^{3} e^{8} - 6 \, b^{6} d x^{2} e^{7} + 30 \, b^{6} d^{2} x e^{6} + 9 \, a b^{5} x^{2} e^{8} - 72 \, a b^{5} d x e^{7} + 45 \, a^{2} b^{4} x e^{8}\right)} e^{\left(-12\right)} - \frac{{\left(37 \, b^{6} d^{6} - 141 \, a b^{5} d^{5} e + 195 \, a^{2} b^{4} d^{4} e^{2} - 110 \, a^{3} b^{3} d^{3} e^{3} + 15 \, a^{4} b^{2} d^{2} e^{4} + 3 \, a^{5} b d e^{5} + a^{6} e^{6} + 45 \, {\left(b^{6} d^{4} e^{2} - 4 \, a b^{5} d^{3} e^{3} + 6 \, a^{2} b^{4} d^{2} e^{4} - 4 \, a^{3} b^{3} d e^{5} + a^{4} b^{2} e^{6}\right)} x^{2} + 9 \, {\left(9 \, b^{6} d^{5} e - 35 \, a b^{5} d^{4} e^{2} + 50 \, a^{2} b^{4} d^{3} e^{3} - 30 \, a^{3} b^{3} d^{2} e^{4} + 5 \, a^{4} b^{2} d e^{5} + a^{5} b e^{6}\right)} x\right)} e^{\left(-7\right)}}{3 \, {\left(x e + d\right)}^{3}}"," ",0,"-20*(b^6*d^3 - 3*a*b^5*d^2*e + 3*a^2*b^4*d*e^2 - a^3*b^3*e^3)*e^(-7)*log(abs(x*e + d)) + 1/3*(b^6*x^3*e^8 - 6*b^6*d*x^2*e^7 + 30*b^6*d^2*x*e^6 + 9*a*b^5*x^2*e^8 - 72*a*b^5*d*x*e^7 + 45*a^2*b^4*x*e^8)*e^(-12) - 1/3*(37*b^6*d^6 - 141*a*b^5*d^5*e + 195*a^2*b^4*d^4*e^2 - 110*a^3*b^3*d^3*e^3 + 15*a^4*b^2*d^2*e^4 + 3*a^5*b*d*e^5 + a^6*e^6 + 45*(b^6*d^4*e^2 - 4*a*b^5*d^3*e^3 + 6*a^2*b^4*d^2*e^4 - 4*a^3*b^3*d*e^5 + a^4*b^2*e^6)*x^2 + 9*(9*b^6*d^5*e - 35*a*b^5*d^4*e^2 + 50*a^2*b^4*d^3*e^3 - 30*a^3*b^3*d^2*e^4 + 5*a^4*b^2*d*e^5 + a^5*b*e^6)*x)*e^(-7)/(x*e + d)^3","B",0
1494,1,514,0,0.182025," ","integrate((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^5,x, algorithm=""giac"")","\frac{1}{2} \, {\left(b^{6} - \frac{12 \, {\left(b^{6} d e - a b^{5} e^{2}\right)} e^{\left(-1\right)}}{x e + d}\right)} {\left(x e + d\right)}^{2} e^{\left(-7\right)} - 15 \, {\left(b^{6} d^{2} - 2 \, a b^{5} d e + a^{2} b^{4} e^{2}\right)} e^{\left(-7\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) + \frac{1}{4} \, {\left(\frac{80 \, b^{6} d^{3} e^{29}}{x e + d} - \frac{30 \, b^{6} d^{4} e^{29}}{{\left(x e + d\right)}^{2}} + \frac{8 \, b^{6} d^{5} e^{29}}{{\left(x e + d\right)}^{3}} - \frac{b^{6} d^{6} e^{29}}{{\left(x e + d\right)}^{4}} - \frac{240 \, a b^{5} d^{2} e^{30}}{x e + d} + \frac{120 \, a b^{5} d^{3} e^{30}}{{\left(x e + d\right)}^{2}} - \frac{40 \, a b^{5} d^{4} e^{30}}{{\left(x e + d\right)}^{3}} + \frac{6 \, a b^{5} d^{5} e^{30}}{{\left(x e + d\right)}^{4}} + \frac{240 \, a^{2} b^{4} d e^{31}}{x e + d} - \frac{180 \, a^{2} b^{4} d^{2} e^{31}}{{\left(x e + d\right)}^{2}} + \frac{80 \, a^{2} b^{4} d^{3} e^{31}}{{\left(x e + d\right)}^{3}} - \frac{15 \, a^{2} b^{4} d^{4} e^{31}}{{\left(x e + d\right)}^{4}} - \frac{80 \, a^{3} b^{3} e^{32}}{x e + d} + \frac{120 \, a^{3} b^{3} d e^{32}}{{\left(x e + d\right)}^{2}} - \frac{80 \, a^{3} b^{3} d^{2} e^{32}}{{\left(x e + d\right)}^{3}} + \frac{20 \, a^{3} b^{3} d^{3} e^{32}}{{\left(x e + d\right)}^{4}} - \frac{30 \, a^{4} b^{2} e^{33}}{{\left(x e + d\right)}^{2}} + \frac{40 \, a^{4} b^{2} d e^{33}}{{\left(x e + d\right)}^{3}} - \frac{15 \, a^{4} b^{2} d^{2} e^{33}}{{\left(x e + d\right)}^{4}} - \frac{8 \, a^{5} b e^{34}}{{\left(x e + d\right)}^{3}} + \frac{6 \, a^{5} b d e^{34}}{{\left(x e + d\right)}^{4}} - \frac{a^{6} e^{35}}{{\left(x e + d\right)}^{4}}\right)} e^{\left(-36\right)}"," ",0,"1/2*(b^6 - 12*(b^6*d*e - a*b^5*e^2)*e^(-1)/(x*e + d))*(x*e + d)^2*e^(-7) - 15*(b^6*d^2 - 2*a*b^5*d*e + a^2*b^4*e^2)*e^(-7)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) + 1/4*(80*b^6*d^3*e^29/(x*e + d) - 30*b^6*d^4*e^29/(x*e + d)^2 + 8*b^6*d^5*e^29/(x*e + d)^3 - b^6*d^6*e^29/(x*e + d)^4 - 240*a*b^5*d^2*e^30/(x*e + d) + 120*a*b^5*d^3*e^30/(x*e + d)^2 - 40*a*b^5*d^4*e^30/(x*e + d)^3 + 6*a*b^5*d^5*e^30/(x*e + d)^4 + 240*a^2*b^4*d*e^31/(x*e + d) - 180*a^2*b^4*d^2*e^31/(x*e + d)^2 + 80*a^2*b^4*d^3*e^31/(x*e + d)^3 - 15*a^2*b^4*d^4*e^31/(x*e + d)^4 - 80*a^3*b^3*e^32/(x*e + d) + 120*a^3*b^3*d*e^32/(x*e + d)^2 - 80*a^3*b^3*d^2*e^32/(x*e + d)^3 + 20*a^3*b^3*d^3*e^32/(x*e + d)^4 - 30*a^4*b^2*e^33/(x*e + d)^2 + 40*a^4*b^2*d*e^33/(x*e + d)^3 - 15*a^4*b^2*d^2*e^33/(x*e + d)^4 - 8*a^5*b*e^34/(x*e + d)^3 + 6*a^5*b*d*e^34/(x*e + d)^4 - a^6*e^35/(x*e + d)^4)*e^(-36)","B",0
1495,1,331,0,0.161322," ","integrate((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^6,x, algorithm=""giac"")","b^{6} x e^{\left(-6\right)} - 6 \, {\left(b^{6} d - a b^{5} e\right)} e^{\left(-7\right)} \log\left({\left| x e + d \right|}\right) - \frac{{\left(87 \, b^{6} d^{6} - 137 \, a b^{5} d^{5} e + 30 \, a^{2} b^{4} d^{4} e^{2} + 10 \, a^{3} b^{3} d^{3} e^{3} + 5 \, a^{4} b^{2} d^{2} e^{4} + 3 \, a^{5} b d e^{5} + 2 \, a^{6} e^{6} + 150 \, {\left(b^{6} d^{2} e^{4} - 2 \, a b^{5} d e^{5} + a^{2} b^{4} e^{6}\right)} x^{4} + 100 \, {\left(5 \, b^{6} d^{3} e^{3} - 9 \, a b^{5} d^{2} e^{4} + 3 \, a^{2} b^{4} d e^{5} + a^{3} b^{3} e^{6}\right)} x^{3} + 50 \, {\left(13 \, b^{6} d^{4} e^{2} - 22 \, a b^{5} d^{3} e^{3} + 6 \, a^{2} b^{4} d^{2} e^{4} + 2 \, a^{3} b^{3} d e^{5} + a^{4} b^{2} e^{6}\right)} x^{2} + 5 \, {\left(77 \, b^{6} d^{5} e - 125 \, a b^{5} d^{4} e^{2} + 30 \, a^{2} b^{4} d^{3} e^{3} + 10 \, a^{3} b^{3} d^{2} e^{4} + 5 \, a^{4} b^{2} d e^{5} + 3 \, a^{5} b e^{6}\right)} x\right)} e^{\left(-7\right)}}{10 \, {\left(x e + d\right)}^{5}}"," ",0,"b^6*x*e^(-6) - 6*(b^6*d - a*b^5*e)*e^(-7)*log(abs(x*e + d)) - 1/10*(87*b^6*d^6 - 137*a*b^5*d^5*e + 30*a^2*b^4*d^4*e^2 + 10*a^3*b^3*d^3*e^3 + 5*a^4*b^2*d^2*e^4 + 3*a^5*b*d*e^5 + 2*a^6*e^6 + 150*(b^6*d^2*e^4 - 2*a*b^5*d*e^5 + a^2*b^4*e^6)*x^4 + 100*(5*b^6*d^3*e^3 - 9*a*b^5*d^2*e^4 + 3*a^2*b^4*d*e^5 + a^3*b^3*e^6)*x^3 + 50*(13*b^6*d^4*e^2 - 22*a*b^5*d^3*e^3 + 6*a^2*b^4*d^2*e^4 + 2*a^3*b^3*d*e^5 + a^4*b^2*e^6)*x^2 + 5*(77*b^6*d^5*e - 125*a*b^5*d^4*e^2 + 30*a^2*b^4*d^3*e^3 + 10*a^3*b^3*d^2*e^4 + 5*a^4*b^2*d*e^5 + 3*a^5*b*e^6)*x)*e^(-7)/(x*e + d)^5","B",0
1496,1,339,0,0.165607," ","integrate((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^7,x, algorithm=""giac"")","b^{6} e^{\left(-7\right)} \log\left({\left| x e + d \right|}\right) + \frac{{\left(360 \, {\left(b^{6} d e^{4} - a b^{5} e^{5}\right)} x^{5} + 450 \, {\left(3 \, b^{6} d^{2} e^{3} - 2 \, a b^{5} d e^{4} - a^{2} b^{4} e^{5}\right)} x^{4} + 200 \, {\left(11 \, b^{6} d^{3} e^{2} - 6 \, a b^{5} d^{2} e^{3} - 3 \, a^{2} b^{4} d e^{4} - 2 \, a^{3} b^{3} e^{5}\right)} x^{3} + 75 \, {\left(25 \, b^{6} d^{4} e - 12 \, a b^{5} d^{3} e^{2} - 6 \, a^{2} b^{4} d^{2} e^{3} - 4 \, a^{3} b^{3} d e^{4} - 3 \, a^{4} b^{2} e^{5}\right)} x^{2} + 6 \, {\left(137 \, b^{6} d^{5} - 60 \, a b^{5} d^{4} e - 30 \, a^{2} b^{4} d^{3} e^{2} - 20 \, a^{3} b^{3} d^{2} e^{3} - 15 \, a^{4} b^{2} d e^{4} - 12 \, a^{5} b e^{5}\right)} x + {\left(147 \, b^{6} d^{6} - 60 \, a b^{5} d^{5} e - 30 \, a^{2} b^{4} d^{4} e^{2} - 20 \, a^{3} b^{3} d^{3} e^{3} - 15 \, a^{4} b^{2} d^{2} e^{4} - 12 \, a^{5} b d e^{5} - 10 \, a^{6} e^{6}\right)} e^{\left(-1\right)}\right)} e^{\left(-6\right)}}{60 \, {\left(x e + d\right)}^{6}}"," ",0,"b^6*e^(-7)*log(abs(x*e + d)) + 1/60*(360*(b^6*d*e^4 - a*b^5*e^5)*x^5 + 450*(3*b^6*d^2*e^3 - 2*a*b^5*d*e^4 - a^2*b^4*e^5)*x^4 + 200*(11*b^6*d^3*e^2 - 6*a*b^5*d^2*e^3 - 3*a^2*b^4*d*e^4 - 2*a^3*b^3*e^5)*x^3 + 75*(25*b^6*d^4*e - 12*a*b^5*d^3*e^2 - 6*a^2*b^4*d^2*e^3 - 4*a^3*b^3*d*e^4 - 3*a^4*b^2*e^5)*x^2 + 6*(137*b^6*d^5 - 60*a*b^5*d^4*e - 30*a^2*b^4*d^3*e^2 - 20*a^3*b^3*d^2*e^3 - 15*a^4*b^2*d*e^4 - 12*a^5*b*e^5)*x + (147*b^6*d^6 - 60*a*b^5*d^5*e - 30*a^2*b^4*d^4*e^2 - 20*a^3*b^3*d^3*e^3 - 15*a^4*b^2*d^2*e^4 - 12*a^5*b*d*e^5 - 10*a^6*e^6)*e^(-1))*e^(-6)/(x*e + d)^6","B",0
1497,1,346,0,0.183016," ","integrate((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^8,x, algorithm=""giac"")","-\frac{{\left(7 \, b^{6} x^{6} e^{6} + 21 \, b^{6} d x^{5} e^{5} + 35 \, b^{6} d^{2} x^{4} e^{4} + 35 \, b^{6} d^{3} x^{3} e^{3} + 21 \, b^{6} d^{4} x^{2} e^{2} + 7 \, b^{6} d^{5} x e + b^{6} d^{6} + 21 \, a b^{5} x^{5} e^{6} + 35 \, a b^{5} d x^{4} e^{5} + 35 \, a b^{5} d^{2} x^{3} e^{4} + 21 \, a b^{5} d^{3} x^{2} e^{3} + 7 \, a b^{5} d^{4} x e^{2} + a b^{5} d^{5} e + 35 \, a^{2} b^{4} x^{4} e^{6} + 35 \, a^{2} b^{4} d x^{3} e^{5} + 21 \, a^{2} b^{4} d^{2} x^{2} e^{4} + 7 \, a^{2} b^{4} d^{3} x e^{3} + a^{2} b^{4} d^{4} e^{2} + 35 \, a^{3} b^{3} x^{3} e^{6} + 21 \, a^{3} b^{3} d x^{2} e^{5} + 7 \, a^{3} b^{3} d^{2} x e^{4} + a^{3} b^{3} d^{3} e^{3} + 21 \, a^{4} b^{2} x^{2} e^{6} + 7 \, a^{4} b^{2} d x e^{5} + a^{4} b^{2} d^{2} e^{4} + 7 \, a^{5} b x e^{6} + a^{5} b d e^{5} + a^{6} e^{6}\right)} e^{\left(-7\right)}}{7 \, {\left(x e + d\right)}^{7}}"," ",0,"-1/7*(7*b^6*x^6*e^6 + 21*b^6*d*x^5*e^5 + 35*b^6*d^2*x^4*e^4 + 35*b^6*d^3*x^3*e^3 + 21*b^6*d^4*x^2*e^2 + 7*b^6*d^5*x*e + b^6*d^6 + 21*a*b^5*x^5*e^6 + 35*a*b^5*d*x^4*e^5 + 35*a*b^5*d^2*x^3*e^4 + 21*a*b^5*d^3*x^2*e^3 + 7*a*b^5*d^4*x*e^2 + a*b^5*d^5*e + 35*a^2*b^4*x^4*e^6 + 35*a^2*b^4*d*x^3*e^5 + 21*a^2*b^4*d^2*x^2*e^4 + 7*a^2*b^4*d^3*x*e^3 + a^2*b^4*d^4*e^2 + 35*a^3*b^3*x^3*e^6 + 21*a^3*b^3*d*x^2*e^5 + 7*a^3*b^3*d^2*x*e^4 + a^3*b^3*d^3*e^3 + 21*a^4*b^2*x^2*e^6 + 7*a^4*b^2*d*x*e^5 + a^4*b^2*d^2*e^4 + 7*a^5*b*x*e^6 + a^5*b*d*e^5 + a^6*e^6)*e^(-7)/(x*e + d)^7","B",0
1498,1,352,0,0.165545," ","integrate((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^9,x, algorithm=""giac"")","-\frac{{\left(28 \, b^{6} x^{6} e^{6} + 56 \, b^{6} d x^{5} e^{5} + 70 \, b^{6} d^{2} x^{4} e^{4} + 56 \, b^{6} d^{3} x^{3} e^{3} + 28 \, b^{6} d^{4} x^{2} e^{2} + 8 \, b^{6} d^{5} x e + b^{6} d^{6} + 112 \, a b^{5} x^{5} e^{6} + 140 \, a b^{5} d x^{4} e^{5} + 112 \, a b^{5} d^{2} x^{3} e^{4} + 56 \, a b^{5} d^{3} x^{2} e^{3} + 16 \, a b^{5} d^{4} x e^{2} + 2 \, a b^{5} d^{5} e + 210 \, a^{2} b^{4} x^{4} e^{6} + 168 \, a^{2} b^{4} d x^{3} e^{5} + 84 \, a^{2} b^{4} d^{2} x^{2} e^{4} + 24 \, a^{2} b^{4} d^{3} x e^{3} + 3 \, a^{2} b^{4} d^{4} e^{2} + 224 \, a^{3} b^{3} x^{3} e^{6} + 112 \, a^{3} b^{3} d x^{2} e^{5} + 32 \, a^{3} b^{3} d^{2} x e^{4} + 4 \, a^{3} b^{3} d^{3} e^{3} + 140 \, a^{4} b^{2} x^{2} e^{6} + 40 \, a^{4} b^{2} d x e^{5} + 5 \, a^{4} b^{2} d^{2} e^{4} + 48 \, a^{5} b x e^{6} + 6 \, a^{5} b d e^{5} + 7 \, a^{6} e^{6}\right)} e^{\left(-7\right)}}{56 \, {\left(x e + d\right)}^{8}}"," ",0,"-1/56*(28*b^6*x^6*e^6 + 56*b^6*d*x^5*e^5 + 70*b^6*d^2*x^4*e^4 + 56*b^6*d^3*x^3*e^3 + 28*b^6*d^4*x^2*e^2 + 8*b^6*d^5*x*e + b^6*d^6 + 112*a*b^5*x^5*e^6 + 140*a*b^5*d*x^4*e^5 + 112*a*b^5*d^2*x^3*e^4 + 56*a*b^5*d^3*x^2*e^3 + 16*a*b^5*d^4*x*e^2 + 2*a*b^5*d^5*e + 210*a^2*b^4*x^4*e^6 + 168*a^2*b^4*d*x^3*e^5 + 84*a^2*b^4*d^2*x^2*e^4 + 24*a^2*b^4*d^3*x*e^3 + 3*a^2*b^4*d^4*e^2 + 224*a^3*b^3*x^3*e^6 + 112*a^3*b^3*d*x^2*e^5 + 32*a^3*b^3*d^2*x*e^4 + 4*a^3*b^3*d^3*e^3 + 140*a^4*b^2*x^2*e^6 + 40*a^4*b^2*d*x*e^5 + 5*a^4*b^2*d^2*e^4 + 48*a^5*b*x*e^6 + 6*a^5*b*d*e^5 + 7*a^6*e^6)*e^(-7)/(x*e + d)^8","B",0
1499,1,352,0,0.162107," ","integrate((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^10,x, algorithm=""giac"")","-\frac{{\left(84 \, b^{6} x^{6} e^{6} + 126 \, b^{6} d x^{5} e^{5} + 126 \, b^{6} d^{2} x^{4} e^{4} + 84 \, b^{6} d^{3} x^{3} e^{3} + 36 \, b^{6} d^{4} x^{2} e^{2} + 9 \, b^{6} d^{5} x e + b^{6} d^{6} + 378 \, a b^{5} x^{5} e^{6} + 378 \, a b^{5} d x^{4} e^{5} + 252 \, a b^{5} d^{2} x^{3} e^{4} + 108 \, a b^{5} d^{3} x^{2} e^{3} + 27 \, a b^{5} d^{4} x e^{2} + 3 \, a b^{5} d^{5} e + 756 \, a^{2} b^{4} x^{4} e^{6} + 504 \, a^{2} b^{4} d x^{3} e^{5} + 216 \, a^{2} b^{4} d^{2} x^{2} e^{4} + 54 \, a^{2} b^{4} d^{3} x e^{3} + 6 \, a^{2} b^{4} d^{4} e^{2} + 840 \, a^{3} b^{3} x^{3} e^{6} + 360 \, a^{3} b^{3} d x^{2} e^{5} + 90 \, a^{3} b^{3} d^{2} x e^{4} + 10 \, a^{3} b^{3} d^{3} e^{3} + 540 \, a^{4} b^{2} x^{2} e^{6} + 135 \, a^{4} b^{2} d x e^{5} + 15 \, a^{4} b^{2} d^{2} e^{4} + 189 \, a^{5} b x e^{6} + 21 \, a^{5} b d e^{5} + 28 \, a^{6} e^{6}\right)} e^{\left(-7\right)}}{252 \, {\left(x e + d\right)}^{9}}"," ",0,"-1/252*(84*b^6*x^6*e^6 + 126*b^6*d*x^5*e^5 + 126*b^6*d^2*x^4*e^4 + 84*b^6*d^3*x^3*e^3 + 36*b^6*d^4*x^2*e^2 + 9*b^6*d^5*x*e + b^6*d^6 + 378*a*b^5*x^5*e^6 + 378*a*b^5*d*x^4*e^5 + 252*a*b^5*d^2*x^3*e^4 + 108*a*b^5*d^3*x^2*e^3 + 27*a*b^5*d^4*x*e^2 + 3*a*b^5*d^5*e + 756*a^2*b^4*x^4*e^6 + 504*a^2*b^4*d*x^3*e^5 + 216*a^2*b^4*d^2*x^2*e^4 + 54*a^2*b^4*d^3*x*e^3 + 6*a^2*b^4*d^4*e^2 + 840*a^3*b^3*x^3*e^6 + 360*a^3*b^3*d*x^2*e^5 + 90*a^3*b^3*d^2*x*e^4 + 10*a^3*b^3*d^3*e^3 + 540*a^4*b^2*x^2*e^6 + 135*a^4*b^2*d*x*e^5 + 15*a^4*b^2*d^2*e^4 + 189*a^5*b*x*e^6 + 21*a^5*b*d*e^5 + 28*a^6*e^6)*e^(-7)/(x*e + d)^9","B",0
1500,1,352,0,0.165019," ","integrate((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^11,x, algorithm=""giac"")","-\frac{{\left(210 \, b^{6} x^{6} e^{6} + 252 \, b^{6} d x^{5} e^{5} + 210 \, b^{6} d^{2} x^{4} e^{4} + 120 \, b^{6} d^{3} x^{3} e^{3} + 45 \, b^{6} d^{4} x^{2} e^{2} + 10 \, b^{6} d^{5} x e + b^{6} d^{6} + 1008 \, a b^{5} x^{5} e^{6} + 840 \, a b^{5} d x^{4} e^{5} + 480 \, a b^{5} d^{2} x^{3} e^{4} + 180 \, a b^{5} d^{3} x^{2} e^{3} + 40 \, a b^{5} d^{4} x e^{2} + 4 \, a b^{5} d^{5} e + 2100 \, a^{2} b^{4} x^{4} e^{6} + 1200 \, a^{2} b^{4} d x^{3} e^{5} + 450 \, a^{2} b^{4} d^{2} x^{2} e^{4} + 100 \, a^{2} b^{4} d^{3} x e^{3} + 10 \, a^{2} b^{4} d^{4} e^{2} + 2400 \, a^{3} b^{3} x^{3} e^{6} + 900 \, a^{3} b^{3} d x^{2} e^{5} + 200 \, a^{3} b^{3} d^{2} x e^{4} + 20 \, a^{3} b^{3} d^{3} e^{3} + 1575 \, a^{4} b^{2} x^{2} e^{6} + 350 \, a^{4} b^{2} d x e^{5} + 35 \, a^{4} b^{2} d^{2} e^{4} + 560 \, a^{5} b x e^{6} + 56 \, a^{5} b d e^{5} + 84 \, a^{6} e^{6}\right)} e^{\left(-7\right)}}{840 \, {\left(x e + d\right)}^{10}}"," ",0,"-1/840*(210*b^6*x^6*e^6 + 252*b^6*d*x^5*e^5 + 210*b^6*d^2*x^4*e^4 + 120*b^6*d^3*x^3*e^3 + 45*b^6*d^4*x^2*e^2 + 10*b^6*d^5*x*e + b^6*d^6 + 1008*a*b^5*x^5*e^6 + 840*a*b^5*d*x^4*e^5 + 480*a*b^5*d^2*x^3*e^4 + 180*a*b^5*d^3*x^2*e^3 + 40*a*b^5*d^4*x*e^2 + 4*a*b^5*d^5*e + 2100*a^2*b^4*x^4*e^6 + 1200*a^2*b^4*d*x^3*e^5 + 450*a^2*b^4*d^2*x^2*e^4 + 100*a^2*b^4*d^3*x*e^3 + 10*a^2*b^4*d^4*e^2 + 2400*a^3*b^3*x^3*e^6 + 900*a^3*b^3*d*x^2*e^5 + 200*a^3*b^3*d^2*x*e^4 + 20*a^3*b^3*d^3*e^3 + 1575*a^4*b^2*x^2*e^6 + 350*a^4*b^2*d*x*e^5 + 35*a^4*b^2*d^2*e^4 + 560*a^5*b*x*e^6 + 56*a^5*b*d*e^5 + 84*a^6*e^6)*e^(-7)/(x*e + d)^10","B",0
1501,1,352,0,0.162487," ","integrate((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^12,x, algorithm=""giac"")","-\frac{{\left(462 \, b^{6} x^{6} e^{6} + 462 \, b^{6} d x^{5} e^{5} + 330 \, b^{6} d^{2} x^{4} e^{4} + 165 \, b^{6} d^{3} x^{3} e^{3} + 55 \, b^{6} d^{4} x^{2} e^{2} + 11 \, b^{6} d^{5} x e + b^{6} d^{6} + 2310 \, a b^{5} x^{5} e^{6} + 1650 \, a b^{5} d x^{4} e^{5} + 825 \, a b^{5} d^{2} x^{3} e^{4} + 275 \, a b^{5} d^{3} x^{2} e^{3} + 55 \, a b^{5} d^{4} x e^{2} + 5 \, a b^{5} d^{5} e + 4950 \, a^{2} b^{4} x^{4} e^{6} + 2475 \, a^{2} b^{4} d x^{3} e^{5} + 825 \, a^{2} b^{4} d^{2} x^{2} e^{4} + 165 \, a^{2} b^{4} d^{3} x e^{3} + 15 \, a^{2} b^{4} d^{4} e^{2} + 5775 \, a^{3} b^{3} x^{3} e^{6} + 1925 \, a^{3} b^{3} d x^{2} e^{5} + 385 \, a^{3} b^{3} d^{2} x e^{4} + 35 \, a^{3} b^{3} d^{3} e^{3} + 3850 \, a^{4} b^{2} x^{2} e^{6} + 770 \, a^{4} b^{2} d x e^{5} + 70 \, a^{4} b^{2} d^{2} e^{4} + 1386 \, a^{5} b x e^{6} + 126 \, a^{5} b d e^{5} + 210 \, a^{6} e^{6}\right)} e^{\left(-7\right)}}{2310 \, {\left(x e + d\right)}^{11}}"," ",0,"-1/2310*(462*b^6*x^6*e^6 + 462*b^6*d*x^5*e^5 + 330*b^6*d^2*x^4*e^4 + 165*b^6*d^3*x^3*e^3 + 55*b^6*d^4*x^2*e^2 + 11*b^6*d^5*x*e + b^6*d^6 + 2310*a*b^5*x^5*e^6 + 1650*a*b^5*d*x^4*e^5 + 825*a*b^5*d^2*x^3*e^4 + 275*a*b^5*d^3*x^2*e^3 + 55*a*b^5*d^4*x*e^2 + 5*a*b^5*d^5*e + 4950*a^2*b^4*x^4*e^6 + 2475*a^2*b^4*d*x^3*e^5 + 825*a^2*b^4*d^2*x^2*e^4 + 165*a^2*b^4*d^3*x*e^3 + 15*a^2*b^4*d^4*e^2 + 5775*a^3*b^3*x^3*e^6 + 1925*a^3*b^3*d*x^2*e^5 + 385*a^3*b^3*d^2*x*e^4 + 35*a^3*b^3*d^3*e^3 + 3850*a^4*b^2*x^2*e^6 + 770*a^4*b^2*d*x*e^5 + 70*a^4*b^2*d^2*e^4 + 1386*a^5*b*x*e^6 + 126*a^5*b*d*e^5 + 210*a^6*e^6)*e^(-7)/(x*e + d)^11","B",0
1502,1,352,0,0.170163," ","integrate((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^13,x, algorithm=""giac"")","-\frac{{\left(924 \, b^{6} x^{6} e^{6} + 792 \, b^{6} d x^{5} e^{5} + 495 \, b^{6} d^{2} x^{4} e^{4} + 220 \, b^{6} d^{3} x^{3} e^{3} + 66 \, b^{6} d^{4} x^{2} e^{2} + 12 \, b^{6} d^{5} x e + b^{6} d^{6} + 4752 \, a b^{5} x^{5} e^{6} + 2970 \, a b^{5} d x^{4} e^{5} + 1320 \, a b^{5} d^{2} x^{3} e^{4} + 396 \, a b^{5} d^{3} x^{2} e^{3} + 72 \, a b^{5} d^{4} x e^{2} + 6 \, a b^{5} d^{5} e + 10395 \, a^{2} b^{4} x^{4} e^{6} + 4620 \, a^{2} b^{4} d x^{3} e^{5} + 1386 \, a^{2} b^{4} d^{2} x^{2} e^{4} + 252 \, a^{2} b^{4} d^{3} x e^{3} + 21 \, a^{2} b^{4} d^{4} e^{2} + 12320 \, a^{3} b^{3} x^{3} e^{6} + 3696 \, a^{3} b^{3} d x^{2} e^{5} + 672 \, a^{3} b^{3} d^{2} x e^{4} + 56 \, a^{3} b^{3} d^{3} e^{3} + 8316 \, a^{4} b^{2} x^{2} e^{6} + 1512 \, a^{4} b^{2} d x e^{5} + 126 \, a^{4} b^{2} d^{2} e^{4} + 3024 \, a^{5} b x e^{6} + 252 \, a^{5} b d e^{5} + 462 \, a^{6} e^{6}\right)} e^{\left(-7\right)}}{5544 \, {\left(x e + d\right)}^{12}}"," ",0,"-1/5544*(924*b^6*x^6*e^6 + 792*b^6*d*x^5*e^5 + 495*b^6*d^2*x^4*e^4 + 220*b^6*d^3*x^3*e^3 + 66*b^6*d^4*x^2*e^2 + 12*b^6*d^5*x*e + b^6*d^6 + 4752*a*b^5*x^5*e^6 + 2970*a*b^5*d*x^4*e^5 + 1320*a*b^5*d^2*x^3*e^4 + 396*a*b^5*d^3*x^2*e^3 + 72*a*b^5*d^4*x*e^2 + 6*a*b^5*d^5*e + 10395*a^2*b^4*x^4*e^6 + 4620*a^2*b^4*d*x^3*e^5 + 1386*a^2*b^4*d^2*x^2*e^4 + 252*a^2*b^4*d^3*x*e^3 + 21*a^2*b^4*d^4*e^2 + 12320*a^3*b^3*x^3*e^6 + 3696*a^3*b^3*d*x^2*e^5 + 672*a^3*b^3*d^2*x*e^4 + 56*a^3*b^3*d^3*e^3 + 8316*a^4*b^2*x^2*e^6 + 1512*a^4*b^2*d*x*e^5 + 126*a^4*b^2*d^2*e^4 + 3024*a^5*b*x*e^6 + 252*a^5*b*d*e^5 + 462*a^6*e^6)*e^(-7)/(x*e + d)^12","B",0
1503,1,352,0,0.165053," ","integrate((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^14,x, algorithm=""giac"")","-\frac{{\left(1716 \, b^{6} x^{6} e^{6} + 1287 \, b^{6} d x^{5} e^{5} + 715 \, b^{6} d^{2} x^{4} e^{4} + 286 \, b^{6} d^{3} x^{3} e^{3} + 78 \, b^{6} d^{4} x^{2} e^{2} + 13 \, b^{6} d^{5} x e + b^{6} d^{6} + 9009 \, a b^{5} x^{5} e^{6} + 5005 \, a b^{5} d x^{4} e^{5} + 2002 \, a b^{5} d^{2} x^{3} e^{4} + 546 \, a b^{5} d^{3} x^{2} e^{3} + 91 \, a b^{5} d^{4} x e^{2} + 7 \, a b^{5} d^{5} e + 20020 \, a^{2} b^{4} x^{4} e^{6} + 8008 \, a^{2} b^{4} d x^{3} e^{5} + 2184 \, a^{2} b^{4} d^{2} x^{2} e^{4} + 364 \, a^{2} b^{4} d^{3} x e^{3} + 28 \, a^{2} b^{4} d^{4} e^{2} + 24024 \, a^{3} b^{3} x^{3} e^{6} + 6552 \, a^{3} b^{3} d x^{2} e^{5} + 1092 \, a^{3} b^{3} d^{2} x e^{4} + 84 \, a^{3} b^{3} d^{3} e^{3} + 16380 \, a^{4} b^{2} x^{2} e^{6} + 2730 \, a^{4} b^{2} d x e^{5} + 210 \, a^{4} b^{2} d^{2} e^{4} + 6006 \, a^{5} b x e^{6} + 462 \, a^{5} b d e^{5} + 924 \, a^{6} e^{6}\right)} e^{\left(-7\right)}}{12012 \, {\left(x e + d\right)}^{13}}"," ",0,"-1/12012*(1716*b^6*x^6*e^6 + 1287*b^6*d*x^5*e^5 + 715*b^6*d^2*x^4*e^4 + 286*b^6*d^3*x^3*e^3 + 78*b^6*d^4*x^2*e^2 + 13*b^6*d^5*x*e + b^6*d^6 + 9009*a*b^5*x^5*e^6 + 5005*a*b^5*d*x^4*e^5 + 2002*a*b^5*d^2*x^3*e^4 + 546*a*b^5*d^3*x^2*e^3 + 91*a*b^5*d^4*x*e^2 + 7*a*b^5*d^5*e + 20020*a^2*b^4*x^4*e^6 + 8008*a^2*b^4*d*x^3*e^5 + 2184*a^2*b^4*d^2*x^2*e^4 + 364*a^2*b^4*d^3*x*e^3 + 28*a^2*b^4*d^4*e^2 + 24024*a^3*b^3*x^3*e^6 + 6552*a^3*b^3*d*x^2*e^5 + 1092*a^3*b^3*d^2*x*e^4 + 84*a^3*b^3*d^3*e^3 + 16380*a^4*b^2*x^2*e^6 + 2730*a^4*b^2*d*x*e^5 + 210*a^4*b^2*d^2*e^4 + 6006*a^5*b*x*e^6 + 462*a^5*b*d*e^5 + 924*a^6*e^6)*e^(-7)/(x*e + d)^13","B",0
1504,1,352,0,0.193980," ","integrate((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^15,x, algorithm=""giac"")","-\frac{{\left(3003 \, b^{6} x^{6} e^{6} + 2002 \, b^{6} d x^{5} e^{5} + 1001 \, b^{6} d^{2} x^{4} e^{4} + 364 \, b^{6} d^{3} x^{3} e^{3} + 91 \, b^{6} d^{4} x^{2} e^{2} + 14 \, b^{6} d^{5} x e + b^{6} d^{6} + 16016 \, a b^{5} x^{5} e^{6} + 8008 \, a b^{5} d x^{4} e^{5} + 2912 \, a b^{5} d^{2} x^{3} e^{4} + 728 \, a b^{5} d^{3} x^{2} e^{3} + 112 \, a b^{5} d^{4} x e^{2} + 8 \, a b^{5} d^{5} e + 36036 \, a^{2} b^{4} x^{4} e^{6} + 13104 \, a^{2} b^{4} d x^{3} e^{5} + 3276 \, a^{2} b^{4} d^{2} x^{2} e^{4} + 504 \, a^{2} b^{4} d^{3} x e^{3} + 36 \, a^{2} b^{4} d^{4} e^{2} + 43680 \, a^{3} b^{3} x^{3} e^{6} + 10920 \, a^{3} b^{3} d x^{2} e^{5} + 1680 \, a^{3} b^{3} d^{2} x e^{4} + 120 \, a^{3} b^{3} d^{3} e^{3} + 30030 \, a^{4} b^{2} x^{2} e^{6} + 4620 \, a^{4} b^{2} d x e^{5} + 330 \, a^{4} b^{2} d^{2} e^{4} + 11088 \, a^{5} b x e^{6} + 792 \, a^{5} b d e^{5} + 1716 \, a^{6} e^{6}\right)} e^{\left(-7\right)}}{24024 \, {\left(x e + d\right)}^{14}}"," ",0,"-1/24024*(3003*b^6*x^6*e^6 + 2002*b^6*d*x^5*e^5 + 1001*b^6*d^2*x^4*e^4 + 364*b^6*d^3*x^3*e^3 + 91*b^6*d^4*x^2*e^2 + 14*b^6*d^5*x*e + b^6*d^6 + 16016*a*b^5*x^5*e^6 + 8008*a*b^5*d*x^4*e^5 + 2912*a*b^5*d^2*x^3*e^4 + 728*a*b^5*d^3*x^2*e^3 + 112*a*b^5*d^4*x*e^2 + 8*a*b^5*d^5*e + 36036*a^2*b^4*x^4*e^6 + 13104*a^2*b^4*d*x^3*e^5 + 3276*a^2*b^4*d^2*x^2*e^4 + 504*a^2*b^4*d^3*x*e^3 + 36*a^2*b^4*d^4*e^2 + 43680*a^3*b^3*x^3*e^6 + 10920*a^3*b^3*d*x^2*e^5 + 1680*a^3*b^3*d^2*x*e^4 + 120*a^3*b^3*d^3*e^3 + 30030*a^4*b^2*x^2*e^6 + 4620*a^4*b^2*d*x*e^5 + 330*a^4*b^2*d^2*e^4 + 11088*a^5*b*x*e^6 + 792*a^5*b*d*e^5 + 1716*a^6*e^6)*e^(-7)/(x*e + d)^14","B",0
1505,1,257,0,0.189075," ","integrate((e*x+d)^5/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{5 \, {\left(b^{4} d^{4} e - 4 \, a b^{3} d^{3} e^{2} + 6 \, a^{2} b^{2} d^{2} e^{3} - 4 \, a^{3} b d e^{4} + a^{4} e^{5}\right)} \log\left({\left| b x + a \right|}\right)}{b^{6}} - \frac{b^{5} d^{5} - 5 \, a b^{4} d^{4} e + 10 \, a^{2} b^{3} d^{3} e^{2} - 10 \, a^{3} b^{2} d^{2} e^{3} + 5 \, a^{4} b d e^{4} - a^{5} e^{5}}{{\left(b x + a\right)} b^{6}} + \frac{3 \, b^{6} x^{4} e^{5} + 20 \, b^{6} d x^{3} e^{4} + 60 \, b^{6} d^{2} x^{2} e^{3} + 120 \, b^{6} d^{3} x e^{2} - 8 \, a b^{5} x^{3} e^{5} - 60 \, a b^{5} d x^{2} e^{4} - 240 \, a b^{5} d^{2} x e^{3} + 18 \, a^{2} b^{4} x^{2} e^{5} + 180 \, a^{2} b^{4} d x e^{4} - 48 \, a^{3} b^{3} x e^{5}}{12 \, b^{8}}"," ",0,"5*(b^4*d^4*e - 4*a*b^3*d^3*e^2 + 6*a^2*b^2*d^2*e^3 - 4*a^3*b*d*e^4 + a^4*e^5)*log(abs(b*x + a))/b^6 - (b^5*d^5 - 5*a*b^4*d^4*e + 10*a^2*b^3*d^3*e^2 - 10*a^3*b^2*d^2*e^3 + 5*a^4*b*d*e^4 - a^5*e^5)/((b*x + a)*b^6) + 1/12*(3*b^6*x^4*e^5 + 20*b^6*d*x^3*e^4 + 60*b^6*d^2*x^2*e^3 + 120*b^6*d^3*x*e^2 - 8*a*b^5*x^3*e^5 - 60*a*b^5*d*x^2*e^4 - 240*a*b^5*d^2*x*e^3 + 18*a^2*b^4*x^2*e^5 + 180*a^2*b^4*d*x*e^4 - 48*a^3*b^3*x*e^5)/b^8","B",0
1506,1,178,0,0.156768," ","integrate((e*x+d)^4/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{4 \, {\left(b^{3} d^{3} e - 3 \, a b^{2} d^{2} e^{2} + 3 \, a^{2} b d e^{3} - a^{3} e^{4}\right)} \log\left({\left| b x + a \right|}\right)}{b^{5}} + \frac{b^{4} x^{3} e^{4} + 6 \, b^{4} d x^{2} e^{3} + 18 \, b^{4} d^{2} x e^{2} - 3 \, a b^{3} x^{2} e^{4} - 24 \, a b^{3} d x e^{3} + 9 \, a^{2} b^{2} x e^{4}}{3 \, b^{6}} - \frac{b^{4} d^{4} - 4 \, a b^{3} d^{3} e + 6 \, a^{2} b^{2} d^{2} e^{2} - 4 \, a^{3} b d e^{3} + a^{4} e^{4}}{{\left(b x + a\right)} b^{5}}"," ",0,"4*(b^3*d^3*e - 3*a*b^2*d^2*e^2 + 3*a^2*b*d*e^3 - a^3*e^4)*log(abs(b*x + a))/b^5 + 1/3*(b^4*x^3*e^4 + 6*b^4*d*x^2*e^3 + 18*b^4*d^2*x*e^2 - 3*a*b^3*x^2*e^4 - 24*a*b^3*d*x*e^3 + 9*a^2*b^2*x*e^4)/b^6 - (b^4*d^4 - 4*a*b^3*d^3*e + 6*a^2*b^2*d^2*e^2 - 4*a^3*b*d*e^3 + a^4*e^4)/((b*x + a)*b^5)","A",0
1507,1,114,0,0.151452," ","integrate((e*x+d)^3/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{3 \, {\left(b^{2} d^{2} e - 2 \, a b d e^{2} + a^{2} e^{3}\right)} \log\left({\left| b x + a \right|}\right)}{b^{4}} + \frac{b^{2} x^{2} e^{3} + 6 \, b^{2} d x e^{2} - 4 \, a b x e^{3}}{2 \, b^{4}} - \frac{b^{3} d^{3} - 3 \, a b^{2} d^{2} e + 3 \, a^{2} b d e^{2} - a^{3} e^{3}}{{\left(b x + a\right)} b^{4}}"," ",0,"3*(b^2*d^2*e - 2*a*b*d*e^2 + a^2*e^3)*log(abs(b*x + a))/b^4 + 1/2*(b^2*x^2*e^3 + 6*b^2*d*x*e^2 - 4*a*b*x*e^3)/b^4 - (b^3*d^3 - 3*a*b^2*d^2*e + 3*a^2*b*d*e^2 - a^3*e^3)/((b*x + a)*b^4)","A",0
1508,1,64,0,0.187546," ","integrate((e*x+d)^2/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{x e^{2}}{b^{2}} + \frac{2 \, {\left(b d e - a e^{2}\right)} \log\left({\left| b x + a \right|}\right)}{b^{3}} - \frac{b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}}{{\left(b x + a\right)} b^{3}}"," ",0,"x*e^2/b^2 + 2*(b*d*e - a*e^2)*log(abs(b*x + a))/b^3 - (b^2*d^2 - 2*a*b*d*e + a^2*e^2)/((b*x + a)*b^3)","A",0
1509,1,35,0,0.153014," ","integrate((e*x+d)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{e \log\left({\left| b x + a \right|}\right)}{b^{2}} - \frac{b d - a e}{{\left(b x + a\right)} b^{2}}"," ",0,"e*log(abs(b*x + a))/b^2 - (b*d - a*e)/((b*x + a)*b^2)","A",0
1510,1,12,0,0.149251," ","integrate(1/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","-\frac{1}{{\left(b x + a\right)} b}"," ",0,"-1/((b*x + a)*b)","A",0
1511,1,95,0,0.156114," ","integrate(1/(e*x+d)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","-\frac{b e \log\left({\left| b x + a \right|}\right)}{b^{3} d^{2} - 2 \, a b^{2} d e + a^{2} b e^{2}} + \frac{e^{2} \log\left({\left| x e + d \right|}\right)}{b^{2} d^{2} e - 2 \, a b d e^{2} + a^{2} e^{3}} - \frac{1}{{\left(b d - a e\right)} {\left(b x + a\right)}}"," ",0,"-b*e*log(abs(b*x + a))/(b^3*d^2 - 2*a*b^2*d*e + a^2*b*e^2) + e^2*log(abs(x*e + d))/(b^2*d^2*e - 2*a*b*d*e^2 + a^2*e^3) - 1/((b*d - a*e)*(b*x + a))","A",0
1512,1,156,0,0.211184," ","integrate(1/(e*x+d)^2/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","-\frac{2 \, b e^{2} \log\left({\left| b - \frac{b d}{x e + d} + \frac{a e}{x e + d} \right|}\right)}{b^{3} d^{3} e - 3 \, a b^{2} d^{2} e^{2} + 3 \, a^{2} b d e^{3} - a^{3} e^{4}} - \frac{e^{3}}{{\left(b^{2} d^{2} e^{2} - 2 \, a b d e^{3} + a^{2} e^{4}\right)} {\left(x e + d\right)}} - \frac{b^{2} e}{{\left(b d - a e\right)}^{3} {\left(b - \frac{b d}{x e + d} + \frac{a e}{x e + d}\right)}}"," ",0,"-2*b*e^2*log(abs(b - b*d/(x*e + d) + a*e/(x*e + d)))/(b^3*d^3*e - 3*a*b^2*d^2*e^2 + 3*a^2*b*d*e^3 - a^3*e^4) - e^3/((b^2*d^2*e^2 - 2*a*b*d*e^3 + a^2*e^4)*(x*e + d)) - b^2*e/((b*d - a*e)^3*(b - b*d/(x*e + d) + a*e/(x*e + d)))","A",0
1513,1,248,0,0.161458," ","integrate(1/(e*x+d)^3/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","-\frac{3 \, b^{3} e \log\left({\left| b x + a \right|}\right)}{b^{5} d^{4} - 4 \, a b^{4} d^{3} e + 6 \, a^{2} b^{3} d^{2} e^{2} - 4 \, a^{3} b^{2} d e^{3} + a^{4} b e^{4}} + \frac{3 \, b^{2} e^{2} \log\left({\left| x e + d \right|}\right)}{b^{4} d^{4} e - 4 \, a b^{3} d^{3} e^{2} + 6 \, a^{2} b^{2} d^{2} e^{3} - 4 \, a^{3} b d e^{4} + a^{4} e^{5}} - \frac{2 \, b^{3} d^{3} + 3 \, a b^{2} d^{2} e - 6 \, a^{2} b d e^{2} + a^{3} e^{3} + 6 \, {\left(b^{3} d e^{2} - a b^{2} e^{3}\right)} x^{2} + 3 \, {\left(3 \, b^{3} d^{2} e - 2 \, a b^{2} d e^{2} - a^{2} b e^{3}\right)} x}{2 \, {\left(b d - a e\right)}^{4} {\left(b x + a\right)} {\left(x e + d\right)}^{2}}"," ",0,"-3*b^3*e*log(abs(b*x + a))/(b^5*d^4 - 4*a*b^4*d^3*e + 6*a^2*b^3*d^2*e^2 - 4*a^3*b^2*d*e^3 + a^4*b*e^4) + 3*b^2*e^2*log(abs(x*e + d))/(b^4*d^4*e - 4*a*b^3*d^3*e^2 + 6*a^2*b^2*d^2*e^3 - 4*a^3*b*d*e^4 + a^4*e^5) - 1/2*(2*b^3*d^3 + 3*a*b^2*d^2*e - 6*a^2*b*d*e^2 + a^3*e^3 + 6*(b^3*d*e^2 - a*b^2*e^3)*x^2 + 3*(3*b^3*d^2*e - 2*a*b^2*d*e^2 - a^2*b*e^3)*x)/((b*d - a*e)^4*(b*x + a)*(x*e + d)^2)","B",0
1514,1,337,0,0.167060," ","integrate(1/(e*x+d)^4/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","-\frac{4 \, b^{4} e \log\left({\left| b x + a \right|}\right)}{b^{6} d^{5} - 5 \, a b^{5} d^{4} e + 10 \, a^{2} b^{4} d^{3} e^{2} - 10 \, a^{3} b^{3} d^{2} e^{3} + 5 \, a^{4} b^{2} d e^{4} - a^{5} b e^{5}} + \frac{4 \, b^{3} e^{2} \log\left({\left| x e + d \right|}\right)}{b^{5} d^{5} e - 5 \, a b^{4} d^{4} e^{2} + 10 \, a^{2} b^{3} d^{3} e^{3} - 10 \, a^{3} b^{2} d^{2} e^{4} + 5 \, a^{4} b d e^{5} - a^{5} e^{6}} - \frac{3 \, b^{4} d^{4} + 10 \, a b^{3} d^{3} e - 18 \, a^{2} b^{2} d^{2} e^{2} + 6 \, a^{3} b d e^{3} - a^{4} e^{4} + 12 \, {\left(b^{4} d e^{3} - a b^{3} e^{4}\right)} x^{3} + 6 \, {\left(5 \, b^{4} d^{2} e^{2} - 4 \, a b^{3} d e^{3} - a^{2} b^{2} e^{4}\right)} x^{2} + 2 \, {\left(11 \, b^{4} d^{3} e - 3 \, a b^{3} d^{2} e^{2} - 9 \, a^{2} b^{2} d e^{3} + a^{3} b e^{4}\right)} x}{3 \, {\left(b d - a e\right)}^{5} {\left(b x + a\right)} {\left(x e + d\right)}^{3}}"," ",0,"-4*b^4*e*log(abs(b*x + a))/(b^6*d^5 - 5*a*b^5*d^4*e + 10*a^2*b^4*d^3*e^2 - 10*a^3*b^3*d^2*e^3 + 5*a^4*b^2*d*e^4 - a^5*b*e^5) + 4*b^3*e^2*log(abs(x*e + d))/(b^5*d^5*e - 5*a*b^4*d^4*e^2 + 10*a^2*b^3*d^3*e^3 - 10*a^3*b^2*d^2*e^4 + 5*a^4*b*d*e^5 - a^5*e^6) - 1/3*(3*b^4*d^4 + 10*a*b^3*d^3*e - 18*a^2*b^2*d^2*e^2 + 6*a^3*b*d*e^3 - a^4*e^4 + 12*(b^4*d*e^3 - a*b^3*e^4)*x^3 + 6*(5*b^4*d^2*e^2 - 4*a*b^3*d*e^3 - a^2*b^2*e^4)*x^2 + 2*(11*b^4*d^3*e - 3*a*b^3*d^2*e^2 - 9*a^2*b^2*d*e^3 + a^3*b*e^4)*x)/((b*d - a*e)^5*(b*x + a)*(x*e + d)^3)","B",0
1515,1,333,0,0.181292," ","integrate((e*x+d)^6/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{20 \, {\left(b^{3} d^{3} e^{3} - 3 \, a b^{2} d^{2} e^{4} + 3 \, a^{2} b d e^{5} - a^{3} e^{6}\right)} \log\left({\left| b x + a \right|}\right)}{b^{7}} - \frac{b^{6} d^{6} + 3 \, a b^{5} d^{5} e + 15 \, a^{2} b^{4} d^{4} e^{2} - 110 \, a^{3} b^{3} d^{3} e^{3} + 195 \, a^{4} b^{2} d^{2} e^{4} - 141 \, a^{5} b d e^{5} + 37 \, a^{6} e^{6} + 45 \, {\left(b^{6} d^{4} e^{2} - 4 \, a b^{5} d^{3} e^{3} + 6 \, a^{2} b^{4} d^{2} e^{4} - 4 \, a^{3} b^{3} d e^{5} + a^{4} b^{2} e^{6}\right)} x^{2} + 9 \, {\left(b^{6} d^{5} e + 5 \, a b^{5} d^{4} e^{2} - 30 \, a^{2} b^{4} d^{3} e^{3} + 50 \, a^{3} b^{3} d^{2} e^{4} - 35 \, a^{4} b^{2} d e^{5} + 9 \, a^{5} b e^{6}\right)} x}{3 \, {\left(b x + a\right)}^{3} b^{7}} + \frac{b^{8} x^{3} e^{6} + 9 \, b^{8} d x^{2} e^{5} + 45 \, b^{8} d^{2} x e^{4} - 6 \, a b^{7} x^{2} e^{6} - 72 \, a b^{7} d x e^{5} + 30 \, a^{2} b^{6} x e^{6}}{3 \, b^{12}}"," ",0,"20*(b^3*d^3*e^3 - 3*a*b^2*d^2*e^4 + 3*a^2*b*d*e^5 - a^3*e^6)*log(abs(b*x + a))/b^7 - 1/3*(b^6*d^6 + 3*a*b^5*d^5*e + 15*a^2*b^4*d^4*e^2 - 110*a^3*b^3*d^3*e^3 + 195*a^4*b^2*d^2*e^4 - 141*a^5*b*d*e^5 + 37*a^6*e^6 + 45*(b^6*d^4*e^2 - 4*a*b^5*d^3*e^3 + 6*a^2*b^4*d^2*e^4 - 4*a^3*b^3*d*e^5 + a^4*b^2*e^6)*x^2 + 9*(b^6*d^5*e + 5*a*b^5*d^4*e^2 - 30*a^2*b^4*d^3*e^3 + 50*a^3*b^3*d^2*e^4 - 35*a^4*b^2*d*e^5 + 9*a^5*b*e^6)*x)/((b*x + a)^3*b^7) + 1/3*(b^8*x^3*e^6 + 9*b^8*d*x^2*e^5 + 45*b^8*d^2*x*e^4 - 6*a*b^7*x^2*e^6 - 72*a*b^7*d*x*e^5 + 30*a^2*b^6*x*e^6)/b^12","B",0
1516,1,246,0,0.160181," ","integrate((e*x+d)^5/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{10 \, {\left(b^{2} d^{2} e^{3} - 2 \, a b d e^{4} + a^{2} e^{5}\right)} \log\left({\left| b x + a \right|}\right)}{b^{6}} + \frac{b^{4} x^{2} e^{5} + 10 \, b^{4} d x e^{4} - 8 \, a b^{3} x e^{5}}{2 \, b^{8}} - \frac{2 \, b^{5} d^{5} + 5 \, a b^{4} d^{4} e + 20 \, a^{2} b^{3} d^{3} e^{2} - 110 \, a^{3} b^{2} d^{2} e^{3} + 130 \, a^{4} b d e^{4} - 47 \, a^{5} e^{5} + 60 \, {\left(b^{5} d^{3} e^{2} - 3 \, a b^{4} d^{2} e^{3} + 3 \, a^{2} b^{3} d e^{4} - a^{3} b^{2} e^{5}\right)} x^{2} + 15 \, {\left(b^{5} d^{4} e + 4 \, a b^{4} d^{3} e^{2} - 18 \, a^{2} b^{3} d^{2} e^{3} + 20 \, a^{3} b^{2} d e^{4} - 7 \, a^{4} b e^{5}\right)} x}{6 \, {\left(b x + a\right)}^{3} b^{6}}"," ",0,"10*(b^2*d^2*e^3 - 2*a*b*d*e^4 + a^2*e^5)*log(abs(b*x + a))/b^6 + 1/2*(b^4*x^2*e^5 + 10*b^4*d*x*e^4 - 8*a*b^3*x*e^5)/b^8 - 1/6*(2*b^5*d^5 + 5*a*b^4*d^4*e + 20*a^2*b^3*d^3*e^2 - 110*a^3*b^2*d^2*e^3 + 130*a^4*b*d*e^4 - 47*a^5*e^5 + 60*(b^5*d^3*e^2 - 3*a*b^4*d^2*e^3 + 3*a^2*b^3*d*e^4 - a^3*b^2*e^5)*x^2 + 15*(b^5*d^4*e + 4*a*b^4*d^3*e^2 - 18*a^2*b^3*d^2*e^3 + 20*a^3*b^2*d*e^4 - 7*a^4*b*e^5)*x)/((b*x + a)^3*b^6)","A",0
1517,1,167,0,0.168450," ","integrate((e*x+d)^4/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{x e^{4}}{b^{4}} + \frac{4 \, {\left(b d e^{3} - a e^{4}\right)} \log\left({\left| b x + a \right|}\right)}{b^{5}} - \frac{b^{4} d^{4} + 2 \, a b^{3} d^{3} e + 6 \, a^{2} b^{2} d^{2} e^{2} - 22 \, a^{3} b d e^{3} + 13 \, a^{4} e^{4} + 18 \, {\left(b^{4} d^{2} e^{2} - 2 \, a b^{3} d e^{3} + a^{2} b^{2} e^{4}\right)} x^{2} + 6 \, {\left(b^{4} d^{3} e + 3 \, a b^{3} d^{2} e^{2} - 9 \, a^{2} b^{2} d e^{3} + 5 \, a^{3} b e^{4}\right)} x}{3 \, {\left(b x + a\right)}^{3} b^{5}}"," ",0,"x*e^4/b^4 + 4*(b*d*e^3 - a*e^4)*log(abs(b*x + a))/b^5 - 1/3*(b^4*d^4 + 2*a*b^3*d^3*e + 6*a^2*b^2*d^2*e^2 - 22*a^3*b*d*e^3 + 13*a^4*e^4 + 18*(b^4*d^2*e^2 - 2*a*b^3*d*e^3 + a^2*b^2*e^4)*x^2 + 6*(b^4*d^3*e + 3*a*b^3*d^2*e^2 - 9*a^2*b^2*d*e^3 + 5*a^3*b*e^4)*x)/((b*x + a)^3*b^5)","A",0
1518,1,113,0,0.152525," ","integrate((e*x+d)^3/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{e^{3} \log\left({\left| b x + a \right|}\right)}{b^{4}} - \frac{18 \, {\left(b^{2} d e^{2} - a b e^{3}\right)} x^{2} + 9 \, {\left(b^{2} d^{2} e + 2 \, a b d e^{2} - 3 \, a^{2} e^{3}\right)} x + \frac{2 \, b^{3} d^{3} + 3 \, a b^{2} d^{2} e + 6 \, a^{2} b d e^{2} - 11 \, a^{3} e^{3}}{b}}{6 \, {\left(b x + a\right)}^{3} b^{3}}"," ",0,"e^3*log(abs(b*x + a))/b^4 - 1/6*(18*(b^2*d*e^2 - a*b*e^3)*x^2 + 9*(b^2*d^2*e + 2*a*b*d*e^2 - 3*a^2*e^3)*x + (2*b^3*d^3 + 3*a*b^2*d^2*e + 6*a^2*b*d*e^2 - 11*a^3*e^3)/b)/((b*x + a)^3*b^3)","A",0
1519,1,58,0,0.158584," ","integrate((e*x+d)^2/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","-\frac{3 \, b^{2} x^{2} e^{2} + 3 \, b^{2} d x e + b^{2} d^{2} + 3 \, a b x e^{2} + a b d e + a^{2} e^{2}}{3 \, {\left(b x + a\right)}^{3} b^{3}}"," ",0,"-1/3*(3*b^2*x^2*e^2 + 3*b^2*d*x*e + b^2*d^2 + 3*a*b*x*e^2 + a*b*d*e + a^2*e^2)/((b*x + a)^3*b^3)","B",0
1520,1,27,0,0.169619," ","integrate((e*x+d)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","-\frac{3 \, b x e + 2 \, b d + a e}{6 \, {\left(b x + a\right)}^{3} b^{2}}"," ",0,"-1/6*(3*b*x*e + 2*b*d + a*e)/((b*x + a)^3*b^2)","A",0
1521,1,12,0,0.166983," ","integrate(1/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","-\frac{1}{3 \, {\left(b x + a\right)}^{3} b}"," ",0,"-1/3/((b*x + a)^3*b)","A",0
1522,1,234,0,0.158887," ","integrate(1/(e*x+d)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","-\frac{b e^{3} \log\left({\left| b x + a \right|}\right)}{b^{5} d^{4} - 4 \, a b^{4} d^{3} e + 6 \, a^{2} b^{3} d^{2} e^{2} - 4 \, a^{3} b^{2} d e^{3} + a^{4} b e^{4}} + \frac{e^{4} \log\left({\left| x e + d \right|}\right)}{b^{4} d^{4} e - 4 \, a b^{3} d^{3} e^{2} + 6 \, a^{2} b^{2} d^{2} e^{3} - 4 \, a^{3} b d e^{4} + a^{4} e^{5}} - \frac{2 \, b^{3} d^{3} - 9 \, a b^{2} d^{2} e + 18 \, a^{2} b d e^{2} - 11 \, a^{3} e^{3} + 6 \, {\left(b^{3} d e^{2} - a b^{2} e^{3}\right)} x^{2} - 3 \, {\left(b^{3} d^{2} e - 6 \, a b^{2} d e^{2} + 5 \, a^{2} b e^{3}\right)} x}{6 \, {\left(b d - a e\right)}^{4} {\left(b x + a\right)}^{3}}"," ",0,"-b*e^3*log(abs(b*x + a))/(b^5*d^4 - 4*a*b^4*d^3*e + 6*a^2*b^3*d^2*e^2 - 4*a^3*b^2*d*e^3 + a^4*b*e^4) + e^4*log(abs(x*e + d))/(b^4*d^4*e - 4*a*b^3*d^3*e^2 + 6*a^2*b^2*d^2*e^3 - 4*a^3*b*d*e^4 + a^4*e^5) - 1/6*(2*b^3*d^3 - 9*a*b^2*d^2*e + 18*a^2*b*d*e^2 - 11*a^3*e^3 + 6*(b^3*d*e^2 - a*b^2*e^3)*x^2 - 3*(b^3*d^2*e - 6*a*b^2*d*e^2 + 5*a^2*b*e^3)*x)/((b*d - a*e)^4*(b*x + a)^3)","B",0
1523,1,279,0,0.173256," ","integrate(1/(e*x+d)^2/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","-\frac{4 \, b e^{4} \log\left({\left| b - \frac{b d}{x e + d} + \frac{a e}{x e + d} \right|}\right)}{b^{5} d^{5} e - 5 \, a b^{4} d^{4} e^{2} + 10 \, a^{2} b^{3} d^{3} e^{3} - 10 \, a^{3} b^{2} d^{2} e^{4} + 5 \, a^{4} b d e^{5} - a^{5} e^{6}} - \frac{e^{7}}{{\left(b^{4} d^{4} e^{4} - 4 \, a b^{3} d^{3} e^{5} + 6 \, a^{2} b^{2} d^{2} e^{6} - 4 \, a^{3} b d e^{7} + a^{4} e^{8}\right)} {\left(x e + d\right)}} - \frac{13 \, b^{4} e^{3} - \frac{30 \, {\left(b^{4} d e^{4} - a b^{3} e^{5}\right)} e^{\left(-1\right)}}{x e + d} + \frac{18 \, {\left(b^{4} d^{2} e^{5} - 2 \, a b^{3} d e^{6} + a^{2} b^{2} e^{7}\right)} e^{\left(-2\right)}}{{\left(x e + d\right)}^{2}}}{3 \, {\left(b d - a e\right)}^{5} {\left(b - \frac{b d}{x e + d} + \frac{a e}{x e + d}\right)}^{3}}"," ",0,"-4*b*e^4*log(abs(b - b*d/(x*e + d) + a*e/(x*e + d)))/(b^5*d^5*e - 5*a*b^4*d^4*e^2 + 10*a^2*b^3*d^3*e^3 - 10*a^3*b^2*d^2*e^4 + 5*a^4*b*d*e^5 - a^5*e^6) - e^7/((b^4*d^4*e^4 - 4*a*b^3*d^3*e^5 + 6*a^2*b^2*d^2*e^6 - 4*a^3*b*d*e^7 + a^4*e^8)*(x*e + d)) - 1/3*(13*b^4*e^3 - 30*(b^4*d*e^4 - a*b^3*e^5)*e^(-1)/(x*e + d) + 18*(b^4*d^2*e^5 - 2*a*b^3*d*e^6 + a^2*b^2*e^7)*e^(-2)/(x*e + d)^2)/((b*d - a*e)^5*(b - b*d/(x*e + d) + a*e/(x*e + d))^3)","B",0
1524,1,435,0,0.175524," ","integrate(1/(e*x+d)^3/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","-\frac{10 \, b^{3} e^{3} \log\left({\left| b x + a \right|}\right)}{b^{7} d^{6} - 6 \, a b^{6} d^{5} e + 15 \, a^{2} b^{5} d^{4} e^{2} - 20 \, a^{3} b^{4} d^{3} e^{3} + 15 \, a^{4} b^{3} d^{2} e^{4} - 6 \, a^{5} b^{2} d e^{5} + a^{6} b e^{6}} + \frac{10 \, b^{2} e^{4} \log\left({\left| x e + d \right|}\right)}{b^{6} d^{6} e - 6 \, a b^{5} d^{5} e^{2} + 15 \, a^{2} b^{4} d^{4} e^{3} - 20 \, a^{3} b^{3} d^{3} e^{4} + 15 \, a^{4} b^{2} d^{2} e^{5} - 6 \, a^{5} b d e^{6} + a^{6} e^{7}} - \frac{2 \, b^{5} d^{5} - 15 \, a b^{4} d^{4} e + 60 \, a^{2} b^{3} d^{3} e^{2} - 20 \, a^{3} b^{2} d^{2} e^{3} - 30 \, a^{4} b d e^{4} + 3 \, a^{5} e^{5} + 60 \, {\left(b^{5} d e^{4} - a b^{4} e^{5}\right)} x^{4} + 30 \, {\left(3 \, b^{5} d^{2} e^{3} + 2 \, a b^{4} d e^{4} - 5 \, a^{2} b^{3} e^{5}\right)} x^{3} + 10 \, {\left(2 \, b^{5} d^{3} e^{2} + 21 \, a b^{4} d^{2} e^{3} - 12 \, a^{2} b^{3} d e^{4} - 11 \, a^{3} b^{2} e^{5}\right)} x^{2} - 5 \, {\left(b^{5} d^{4} e - 12 \, a b^{4} d^{3} e^{2} - 24 \, a^{2} b^{3} d^{2} e^{3} + 32 \, a^{3} b^{2} d e^{4} + 3 \, a^{4} b e^{5}\right)} x}{6 \, {\left(b d - a e\right)}^{6} {\left(b x + a\right)}^{3} {\left(x e + d\right)}^{2}}"," ",0,"-10*b^3*e^3*log(abs(b*x + a))/(b^7*d^6 - 6*a*b^6*d^5*e + 15*a^2*b^5*d^4*e^2 - 20*a^3*b^4*d^3*e^3 + 15*a^4*b^3*d^2*e^4 - 6*a^5*b^2*d*e^5 + a^6*b*e^6) + 10*b^2*e^4*log(abs(x*e + d))/(b^6*d^6*e - 6*a*b^5*d^5*e^2 + 15*a^2*b^4*d^4*e^3 - 20*a^3*b^3*d^3*e^4 + 15*a^4*b^2*d^2*e^5 - 6*a^5*b*d*e^6 + a^6*e^7) - 1/6*(2*b^5*d^5 - 15*a*b^4*d^4*e + 60*a^2*b^3*d^3*e^2 - 20*a^3*b^2*d^2*e^3 - 30*a^4*b*d*e^4 + 3*a^5*e^5 + 60*(b^5*d*e^4 - a*b^4*e^5)*x^4 + 30*(3*b^5*d^2*e^3 + 2*a*b^4*d*e^4 - 5*a^2*b^3*e^5)*x^3 + 10*(2*b^5*d^3*e^2 + 21*a*b^4*d^2*e^3 - 12*a^2*b^3*d*e^4 - 11*a^3*b^2*e^5)*x^2 - 5*(b^5*d^4*e - 12*a*b^4*d^3*e^2 - 24*a^2*b^3*d^2*e^3 + 32*a^3*b^2*d*e^4 + 3*a^4*b*e^5)*x)/((b*d - a*e)^6*(b*x + a)^3*(x*e + d)^2)","B",0
1525,1,546,0,0.162842," ","integrate((e*x+d)^8/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{56 \, {\left(b^{3} d^{3} e^{5} - 3 \, a b^{2} d^{2} e^{6} + 3 \, a^{2} b d e^{7} - a^{3} e^{8}\right)} \log\left({\left| b x + a \right|}\right)}{b^{9}} - \frac{3 \, b^{8} d^{8} + 6 \, a b^{7} d^{7} e + 14 \, a^{2} b^{6} d^{6} e^{2} + 42 \, a^{3} b^{5} d^{5} e^{3} + 210 \, a^{4} b^{4} d^{4} e^{4} - 1918 \, a^{5} b^{3} d^{3} e^{5} + 3654 \, a^{6} b^{2} d^{2} e^{6} - 2754 \, a^{7} b d e^{7} + 743 \, a^{8} e^{8} + 1050 \, {\left(b^{8} d^{4} e^{4} - 4 \, a b^{7} d^{3} e^{5} + 6 \, a^{2} b^{6} d^{2} e^{6} - 4 \, a^{3} b^{5} d e^{7} + a^{4} b^{4} e^{8}\right)} x^{4} + 420 \, {\left(b^{8} d^{5} e^{3} + 5 \, a b^{7} d^{4} e^{4} - 30 \, a^{2} b^{6} d^{3} e^{5} + 50 \, a^{3} b^{5} d^{2} e^{6} - 35 \, a^{4} b^{4} d e^{7} + 9 \, a^{5} b^{3} e^{8}\right)} x^{3} + 140 \, {\left(b^{8} d^{6} e^{2} + 3 \, a b^{7} d^{5} e^{3} + 15 \, a^{2} b^{6} d^{4} e^{4} - 110 \, a^{3} b^{5} d^{3} e^{5} + 195 \, a^{4} b^{4} d^{2} e^{6} - 141 \, a^{5} b^{3} d e^{7} + 37 \, a^{6} b^{2} e^{8}\right)} x^{2} + 10 \, {\left(3 \, b^{8} d^{7} e + 7 \, a b^{7} d^{6} e^{2} + 21 \, a^{2} b^{6} d^{5} e^{3} + 105 \, a^{3} b^{5} d^{4} e^{4} - 875 \, a^{4} b^{4} d^{3} e^{5} + 1617 \, a^{5} b^{3} d^{2} e^{6} - 1197 \, a^{6} b^{2} d e^{7} + 319 \, a^{7} b e^{8}\right)} x}{15 \, {\left(b x + a\right)}^{5} b^{9}} + \frac{b^{12} x^{3} e^{8} + 12 \, b^{12} d x^{2} e^{7} + 84 \, b^{12} d^{2} x e^{6} - 9 \, a b^{11} x^{2} e^{8} - 144 \, a b^{11} d x e^{7} + 63 \, a^{2} b^{10} x e^{8}}{3 \, b^{18}}"," ",0,"56*(b^3*d^3*e^5 - 3*a*b^2*d^2*e^6 + 3*a^2*b*d*e^7 - a^3*e^8)*log(abs(b*x + a))/b^9 - 1/15*(3*b^8*d^8 + 6*a*b^7*d^7*e + 14*a^2*b^6*d^6*e^2 + 42*a^3*b^5*d^5*e^3 + 210*a^4*b^4*d^4*e^4 - 1918*a^5*b^3*d^3*e^5 + 3654*a^6*b^2*d^2*e^6 - 2754*a^7*b*d*e^7 + 743*a^8*e^8 + 1050*(b^8*d^4*e^4 - 4*a*b^7*d^3*e^5 + 6*a^2*b^6*d^2*e^6 - 4*a^3*b^5*d*e^7 + a^4*b^4*e^8)*x^4 + 420*(b^8*d^5*e^3 + 5*a*b^7*d^4*e^4 - 30*a^2*b^6*d^3*e^5 + 50*a^3*b^5*d^2*e^6 - 35*a^4*b^4*d*e^7 + 9*a^5*b^3*e^8)*x^3 + 140*(b^8*d^6*e^2 + 3*a*b^7*d^5*e^3 + 15*a^2*b^6*d^4*e^4 - 110*a^3*b^5*d^3*e^5 + 195*a^4*b^4*d^2*e^6 - 141*a^5*b^3*d*e^7 + 37*a^6*b^2*e^8)*x^2 + 10*(3*b^8*d^7*e + 7*a*b^7*d^6*e^2 + 21*a^2*b^6*d^5*e^3 + 105*a^3*b^5*d^4*e^4 - 875*a^4*b^4*d^3*e^5 + 1617*a^5*b^3*d^2*e^6 - 1197*a^6*b^2*d*e^7 + 319*a^7*b*e^8)*x)/((b*x + a)^5*b^9) + 1/3*(b^12*x^3*e^8 + 12*b^12*d*x^2*e^7 + 84*b^12*d^2*x*e^6 - 9*a*b^11*x^2*e^8 - 144*a*b^11*d*x*e^7 + 63*a^2*b^10*x*e^8)/b^18","B",0
1526,1,432,0,0.171625," ","integrate((e*x+d)^7/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{21 \, {\left(b^{2} d^{2} e^{5} - 2 \, a b d e^{6} + a^{2} e^{7}\right)} \log\left({\left| b x + a \right|}\right)}{b^{8}} + \frac{b^{6} x^{2} e^{7} + 14 \, b^{6} d x e^{6} - 12 \, a b^{5} x e^{7}}{2 \, b^{12}} - \frac{4 \, b^{7} d^{7} + 7 \, a b^{6} d^{6} e + 14 \, a^{2} b^{5} d^{5} e^{2} + 35 \, a^{3} b^{4} d^{4} e^{3} + 140 \, a^{4} b^{3} d^{3} e^{4} - 959 \, a^{5} b^{2} d^{2} e^{5} + 1218 \, a^{6} b d e^{6} - 459 \, a^{7} e^{7} + 700 \, {\left(b^{7} d^{3} e^{4} - 3 \, a b^{6} d^{2} e^{5} + 3 \, a^{2} b^{5} d e^{6} - a^{3} b^{4} e^{7}\right)} x^{4} + 350 \, {\left(b^{7} d^{4} e^{3} + 4 \, a b^{6} d^{3} e^{4} - 18 \, a^{2} b^{5} d^{2} e^{5} + 20 \, a^{3} b^{4} d e^{6} - 7 \, a^{4} b^{3} e^{7}\right)} x^{3} + 70 \, {\left(2 \, b^{7} d^{5} e^{2} + 5 \, a b^{6} d^{4} e^{3} + 20 \, a^{2} b^{5} d^{3} e^{4} - 110 \, a^{3} b^{4} d^{2} e^{5} + 130 \, a^{4} b^{3} d e^{6} - 47 \, a^{5} b^{2} e^{7}\right)} x^{2} + 35 \, {\left(b^{7} d^{6} e + 2 \, a b^{6} d^{5} e^{2} + 5 \, a^{2} b^{5} d^{4} e^{3} + 20 \, a^{3} b^{4} d^{3} e^{4} - 125 \, a^{4} b^{3} d^{2} e^{5} + 154 \, a^{5} b^{2} d e^{6} - 57 \, a^{6} b e^{7}\right)} x}{20 \, {\left(b x + a\right)}^{5} b^{8}}"," ",0,"21*(b^2*d^2*e^5 - 2*a*b*d*e^6 + a^2*e^7)*log(abs(b*x + a))/b^8 + 1/2*(b^6*x^2*e^7 + 14*b^6*d*x*e^6 - 12*a*b^5*x*e^7)/b^12 - 1/20*(4*b^7*d^7 + 7*a*b^6*d^6*e + 14*a^2*b^5*d^5*e^2 + 35*a^3*b^4*d^4*e^3 + 140*a^4*b^3*d^3*e^4 - 959*a^5*b^2*d^2*e^5 + 1218*a^6*b*d*e^6 - 459*a^7*e^7 + 700*(b^7*d^3*e^4 - 3*a*b^6*d^2*e^5 + 3*a^2*b^5*d*e^6 - a^3*b^4*e^7)*x^4 + 350*(b^7*d^4*e^3 + 4*a*b^6*d^3*e^4 - 18*a^2*b^5*d^2*e^5 + 20*a^3*b^4*d*e^6 - 7*a^4*b^3*e^7)*x^3 + 70*(2*b^7*d^5*e^2 + 5*a*b^6*d^4*e^3 + 20*a^2*b^5*d^3*e^4 - 110*a^3*b^4*d^2*e^5 + 130*a^4*b^3*d*e^6 - 47*a^5*b^2*e^7)*x^2 + 35*(b^7*d^6*e + 2*a*b^6*d^5*e^2 + 5*a^2*b^5*d^4*e^3 + 20*a^3*b^4*d^3*e^4 - 125*a^4*b^3*d^2*e^5 + 154*a^5*b^2*d*e^6 - 57*a^6*b*e^7)*x)/((b*x + a)^5*b^8)","B",0
1527,1,328,0,0.179403," ","integrate((e*x+d)^6/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{x e^{6}}{b^{6}} + \frac{6 \, {\left(b d e^{5} - a e^{6}\right)} \log\left({\left| b x + a \right|}\right)}{b^{7}} - \frac{2 \, b^{6} d^{6} + 3 \, a b^{5} d^{5} e + 5 \, a^{2} b^{4} d^{4} e^{2} + 10 \, a^{3} b^{3} d^{3} e^{3} + 30 \, a^{4} b^{2} d^{2} e^{4} - 137 \, a^{5} b d e^{5} + 87 \, a^{6} e^{6} + 150 \, {\left(b^{6} d^{2} e^{4} - 2 \, a b^{5} d e^{5} + a^{2} b^{4} e^{6}\right)} x^{4} + 100 \, {\left(b^{6} d^{3} e^{3} + 3 \, a b^{5} d^{2} e^{4} - 9 \, a^{2} b^{4} d e^{5} + 5 \, a^{3} b^{3} e^{6}\right)} x^{3} + 50 \, {\left(b^{6} d^{4} e^{2} + 2 \, a b^{5} d^{3} e^{3} + 6 \, a^{2} b^{4} d^{2} e^{4} - 22 \, a^{3} b^{3} d e^{5} + 13 \, a^{4} b^{2} e^{6}\right)} x^{2} + 5 \, {\left(3 \, b^{6} d^{5} e + 5 \, a b^{5} d^{4} e^{2} + 10 \, a^{2} b^{4} d^{3} e^{3} + 30 \, a^{3} b^{3} d^{2} e^{4} - 125 \, a^{4} b^{2} d e^{5} + 77 \, a^{5} b e^{6}\right)} x}{10 \, {\left(b x + a\right)}^{5} b^{7}}"," ",0,"x*e^6/b^6 + 6*(b*d*e^5 - a*e^6)*log(abs(b*x + a))/b^7 - 1/10*(2*b^6*d^6 + 3*a*b^5*d^5*e + 5*a^2*b^4*d^4*e^2 + 10*a^3*b^3*d^3*e^3 + 30*a^4*b^2*d^2*e^4 - 137*a^5*b*d*e^5 + 87*a^6*e^6 + 150*(b^6*d^2*e^4 - 2*a*b^5*d*e^5 + a^2*b^4*e^6)*x^4 + 100*(b^6*d^3*e^3 + 3*a*b^5*d^2*e^4 - 9*a^2*b^4*d*e^5 + 5*a^3*b^3*e^6)*x^3 + 50*(b^6*d^4*e^2 + 2*a*b^5*d^3*e^3 + 6*a^2*b^4*d^2*e^4 - 22*a^3*b^3*d*e^5 + 13*a^4*b^2*e^6)*x^2 + 5*(3*b^6*d^5*e + 5*a*b^5*d^4*e^2 + 10*a^2*b^4*d^3*e^3 + 30*a^3*b^3*d^2*e^4 - 125*a^4*b^2*d*e^5 + 77*a^5*b*e^6)*x)/((b*x + a)^5*b^7)","B",0
1528,1,248,0,0.180486," ","integrate((e*x+d)^5/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{e^{5} \log\left({\left| b x + a \right|}\right)}{b^{6}} - \frac{300 \, {\left(b^{4} d e^{4} - a b^{3} e^{5}\right)} x^{4} + 300 \, {\left(b^{4} d^{2} e^{3} + 2 \, a b^{3} d e^{4} - 3 \, a^{2} b^{2} e^{5}\right)} x^{3} + 100 \, {\left(2 \, b^{4} d^{3} e^{2} + 3 \, a b^{3} d^{2} e^{3} + 6 \, a^{2} b^{2} d e^{4} - 11 \, a^{3} b e^{5}\right)} x^{2} + 25 \, {\left(3 \, b^{4} d^{4} e + 4 \, a b^{3} d^{3} e^{2} + 6 \, a^{2} b^{2} d^{2} e^{3} + 12 \, a^{3} b d e^{4} - 25 \, a^{4} e^{5}\right)} x + \frac{12 \, b^{5} d^{5} + 15 \, a b^{4} d^{4} e + 20 \, a^{2} b^{3} d^{3} e^{2} + 30 \, a^{3} b^{2} d^{2} e^{3} + 60 \, a^{4} b d e^{4} - 137 \, a^{5} e^{5}}{b}}{60 \, {\left(b x + a\right)}^{5} b^{5}}"," ",0,"e^5*log(abs(b*x + a))/b^6 - 1/60*(300*(b^4*d*e^4 - a*b^3*e^5)*x^4 + 300*(b^4*d^2*e^3 + 2*a*b^3*d*e^4 - 3*a^2*b^2*e^5)*x^3 + 100*(2*b^4*d^3*e^2 + 3*a*b^3*d^2*e^3 + 6*a^2*b^2*d*e^4 - 11*a^3*b*e^5)*x^2 + 25*(3*b^4*d^4*e + 4*a*b^3*d^3*e^2 + 6*a^2*b^2*d^2*e^3 + 12*a^3*b*d*e^4 - 25*a^4*e^5)*x + (12*b^5*d^5 + 15*a*b^4*d^4*e + 20*a^2*b^3*d^3*e^2 + 30*a^3*b^2*d^2*e^3 + 60*a^4*b*d*e^4 - 137*a^5*e^5)/b)/((b*x + a)^5*b^5)","A",0
1529,1,170,0,0.175204," ","integrate((e*x+d)^4/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","-\frac{5 \, b^{4} x^{4} e^{4} + 10 \, b^{4} d x^{3} e^{3} + 10 \, b^{4} d^{2} x^{2} e^{2} + 5 \, b^{4} d^{3} x e + b^{4} d^{4} + 10 \, a b^{3} x^{3} e^{4} + 10 \, a b^{3} d x^{2} e^{3} + 5 \, a b^{3} d^{2} x e^{2} + a b^{3} d^{3} e + 10 \, a^{2} b^{2} x^{2} e^{4} + 5 \, a^{2} b^{2} d x e^{3} + a^{2} b^{2} d^{2} e^{2} + 5 \, a^{3} b x e^{4} + a^{3} b d e^{3} + a^{4} e^{4}}{5 \, {\left(b x + a\right)}^{5} b^{5}}"," ",0,"-1/5*(5*b^4*x^4*e^4 + 10*b^4*d*x^3*e^3 + 10*b^4*d^2*x^2*e^2 + 5*b^4*d^3*x*e + b^4*d^4 + 10*a*b^3*x^3*e^4 + 10*a*b^3*d*x^2*e^3 + 5*a*b^3*d^2*x*e^2 + a*b^3*d^3*e + 10*a^2*b^2*x^2*e^4 + 5*a^2*b^2*d*x*e^3 + a^2*b^2*d^2*e^2 + 5*a^3*b*x*e^4 + a^3*b*d*e^3 + a^4*e^4)/((b*x + a)^5*b^5)","B",0
1530,1,109,0,0.161288," ","integrate((e*x+d)^3/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","-\frac{10 \, b^{3} x^{3} e^{3} + 20 \, b^{3} d x^{2} e^{2} + 15 \, b^{3} d^{2} x e + 4 \, b^{3} d^{3} + 10 \, a b^{2} x^{2} e^{3} + 10 \, a b^{2} d x e^{2} + 3 \, a b^{2} d^{2} e + 5 \, a^{2} b x e^{3} + 2 \, a^{2} b d e^{2} + a^{3} e^{3}}{20 \, {\left(b x + a\right)}^{5} b^{4}}"," ",0,"-1/20*(10*b^3*x^3*e^3 + 20*b^3*d*x^2*e^2 + 15*b^3*d^2*x*e + 4*b^3*d^3 + 10*a*b^2*x^2*e^3 + 10*a*b^2*d*x*e^2 + 3*a*b^2*d^2*e + 5*a^2*b*x*e^3 + 2*a^2*b*d*e^2 + a^3*e^3)/((b*x + a)^5*b^4)","B",0
1531,1,60,0,0.156038," ","integrate((e*x+d)^2/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","-\frac{10 \, b^{2} x^{2} e^{2} + 15 \, b^{2} d x e + 6 \, b^{2} d^{2} + 5 \, a b x e^{2} + 3 \, a b d e + a^{2} e^{2}}{30 \, {\left(b x + a\right)}^{5} b^{3}}"," ",0,"-1/30*(10*b^2*x^2*e^2 + 15*b^2*d*x*e + 6*b^2*d^2 + 5*a*b*x*e^2 + 3*a*b*d*e + a^2*e^2)/((b*x + a)^5*b^3)","A",0
1532,1,27,0,0.153346," ","integrate((e*x+d)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","-\frac{5 \, b x e + 4 \, b d + a e}{20 \, {\left(b x + a\right)}^{5} b^{2}}"," ",0,"-1/20*(5*b*x*e + 4*b*d + a*e)/((b*x + a)^5*b^2)","A",0
1533,1,12,0,0.154412," ","integrate(1/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","-\frac{1}{5 \, {\left(b x + a\right)}^{5} b}"," ",0,"-1/5/((b*x + a)^5*b)","A",0
1534,1,421,0,0.169129," ","integrate(1/(e*x+d)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","-\frac{b e^{5} \log\left({\left| b x + a \right|}\right)}{b^{7} d^{6} - 6 \, a b^{6} d^{5} e + 15 \, a^{2} b^{5} d^{4} e^{2} - 20 \, a^{3} b^{4} d^{3} e^{3} + 15 \, a^{4} b^{3} d^{2} e^{4} - 6 \, a^{5} b^{2} d e^{5} + a^{6} b e^{6}} + \frac{e^{6} \log\left({\left| x e + d \right|}\right)}{b^{6} d^{6} e - 6 \, a b^{5} d^{5} e^{2} + 15 \, a^{2} b^{4} d^{4} e^{3} - 20 \, a^{3} b^{3} d^{3} e^{4} + 15 \, a^{4} b^{2} d^{2} e^{5} - 6 \, a^{5} b d e^{6} + a^{6} e^{7}} - \frac{12 \, b^{5} d^{5} - 75 \, a b^{4} d^{4} e + 200 \, a^{2} b^{3} d^{3} e^{2} - 300 \, a^{3} b^{2} d^{2} e^{3} + 300 \, a^{4} b d e^{4} - 137 \, a^{5} e^{5} + 60 \, {\left(b^{5} d e^{4} - a b^{4} e^{5}\right)} x^{4} - 30 \, {\left(b^{5} d^{2} e^{3} - 10 \, a b^{4} d e^{4} + 9 \, a^{2} b^{3} e^{5}\right)} x^{3} + 10 \, {\left(2 \, b^{5} d^{3} e^{2} - 15 \, a b^{4} d^{2} e^{3} + 60 \, a^{2} b^{3} d e^{4} - 47 \, a^{3} b^{2} e^{5}\right)} x^{2} - 5 \, {\left(3 \, b^{5} d^{4} e - 20 \, a b^{4} d^{3} e^{2} + 60 \, a^{2} b^{3} d^{2} e^{3} - 120 \, a^{3} b^{2} d e^{4} + 77 \, a^{4} b e^{5}\right)} x}{60 \, {\left(b d - a e\right)}^{6} {\left(b x + a\right)}^{5}}"," ",0,"-b*e^5*log(abs(b*x + a))/(b^7*d^6 - 6*a*b^6*d^5*e + 15*a^2*b^5*d^4*e^2 - 20*a^3*b^4*d^3*e^3 + 15*a^4*b^3*d^2*e^4 - 6*a^5*b^2*d*e^5 + a^6*b*e^6) + e^6*log(abs(x*e + d))/(b^6*d^6*e - 6*a*b^5*d^5*e^2 + 15*a^2*b^4*d^4*e^3 - 20*a^3*b^3*d^3*e^4 + 15*a^4*b^2*d^2*e^5 - 6*a^5*b*d*e^6 + a^6*e^7) - 1/60*(12*b^5*d^5 - 75*a*b^4*d^4*e + 200*a^2*b^3*d^3*e^2 - 300*a^3*b^2*d^2*e^3 + 300*a^4*b*d*e^4 - 137*a^5*e^5 + 60*(b^5*d*e^4 - a*b^4*e^5)*x^4 - 30*(b^5*d^2*e^3 - 10*a*b^4*d*e^4 + 9*a^2*b^3*e^5)*x^3 + 10*(2*b^5*d^3*e^2 - 15*a*b^4*d^2*e^3 + 60*a^2*b^3*d*e^4 - 47*a^3*b^2*e^5)*x^2 - 5*(3*b^5*d^4*e - 20*a*b^4*d^3*e^2 + 60*a^2*b^3*d^2*e^3 - 120*a^3*b^2*d*e^4 + 77*a^4*b*e^5)*x)/((b*d - a*e)^6*(b*x + a)^5)","B",0
1535,1,451,0,0.205465," ","integrate(1/(e*x+d)^2/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","-\frac{6 \, b e^{6} \log\left({\left| b - \frac{b d}{x e + d} + \frac{a e}{x e + d} \right|}\right)}{b^{7} d^{7} e - 7 \, a b^{6} d^{6} e^{2} + 21 \, a^{2} b^{5} d^{5} e^{3} - 35 \, a^{3} b^{4} d^{4} e^{4} + 35 \, a^{4} b^{3} d^{3} e^{5} - 21 \, a^{5} b^{2} d^{2} e^{6} + 7 \, a^{6} b d e^{7} - a^{7} e^{8}} - \frac{e^{11}}{{\left(b^{6} d^{6} e^{6} - 6 \, a b^{5} d^{5} e^{7} + 15 \, a^{2} b^{4} d^{4} e^{8} - 20 \, a^{3} b^{3} d^{3} e^{9} + 15 \, a^{4} b^{2} d^{2} e^{10} - 6 \, a^{5} b d e^{11} + a^{6} e^{12}\right)} {\left(x e + d\right)}} - \frac{87 \, b^{6} e^{5} - \frac{385 \, {\left(b^{6} d e^{6} - a b^{5} e^{7}\right)} e^{\left(-1\right)}}{x e + d} + \frac{650 \, {\left(b^{6} d^{2} e^{7} - 2 \, a b^{5} d e^{8} + a^{2} b^{4} e^{9}\right)} e^{\left(-2\right)}}{{\left(x e + d\right)}^{2}} - \frac{500 \, {\left(b^{6} d^{3} e^{8} - 3 \, a b^{5} d^{2} e^{9} + 3 \, a^{2} b^{4} d e^{10} - a^{3} b^{3} e^{11}\right)} e^{\left(-3\right)}}{{\left(x e + d\right)}^{3}} + \frac{150 \, {\left(b^{6} d^{4} e^{9} - 4 \, a b^{5} d^{3} e^{10} + 6 \, a^{2} b^{4} d^{2} e^{11} - 4 \, a^{3} b^{3} d e^{12} + a^{4} b^{2} e^{13}\right)} e^{\left(-4\right)}}{{\left(x e + d\right)}^{4}}}{10 \, {\left(b d - a e\right)}^{7} {\left(b - \frac{b d}{x e + d} + \frac{a e}{x e + d}\right)}^{5}}"," ",0,"-6*b*e^6*log(abs(b - b*d/(x*e + d) + a*e/(x*e + d)))/(b^7*d^7*e - 7*a*b^6*d^6*e^2 + 21*a^2*b^5*d^5*e^3 - 35*a^3*b^4*d^4*e^4 + 35*a^4*b^3*d^3*e^5 - 21*a^5*b^2*d^2*e^6 + 7*a^6*b*d*e^7 - a^7*e^8) - e^11/((b^6*d^6*e^6 - 6*a*b^5*d^5*e^7 + 15*a^2*b^4*d^4*e^8 - 20*a^3*b^3*d^3*e^9 + 15*a^4*b^2*d^2*e^10 - 6*a^5*b*d*e^11 + a^6*e^12)*(x*e + d)) - 1/10*(87*b^6*e^5 - 385*(b^6*d*e^6 - a*b^5*e^7)*e^(-1)/(x*e + d) + 650*(b^6*d^2*e^7 - 2*a*b^5*d*e^8 + a^2*b^4*e^9)*e^(-2)/(x*e + d)^2 - 500*(b^6*d^3*e^8 - 3*a*b^5*d^2*e^9 + 3*a^2*b^4*d*e^10 - a^3*b^3*e^11)*e^(-3)/(x*e + d)^3 + 150*(b^6*d^4*e^9 - 4*a*b^5*d^3*e^10 + 6*a^2*b^4*d^2*e^11 - 4*a^3*b^3*d*e^12 + a^4*b^2*e^13)*e^(-4)/(x*e + d)^4)/((b*d - a*e)^7*(b - b*d/(x*e + d) + a*e/(x*e + d))^5)","B",0
1536,1,672,0,0.187314," ","integrate(1/(e*x+d)^3/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","-\frac{21 \, b^{3} e^{5} \log\left({\left| b x + a \right|}\right)}{b^{9} d^{8} - 8 \, a b^{8} d^{7} e + 28 \, a^{2} b^{7} d^{6} e^{2} - 56 \, a^{3} b^{6} d^{5} e^{3} + 70 \, a^{4} b^{5} d^{4} e^{4} - 56 \, a^{5} b^{4} d^{3} e^{5} + 28 \, a^{6} b^{3} d^{2} e^{6} - 8 \, a^{7} b^{2} d e^{7} + a^{8} b e^{8}} + \frac{21 \, b^{2} e^{6} \log\left({\left| x e + d \right|}\right)}{b^{8} d^{8} e - 8 \, a b^{7} d^{7} e^{2} + 28 \, a^{2} b^{6} d^{6} e^{3} - 56 \, a^{3} b^{5} d^{5} e^{4} + 70 \, a^{4} b^{4} d^{4} e^{5} - 56 \, a^{5} b^{3} d^{3} e^{6} + 28 \, a^{6} b^{2} d^{2} e^{7} - 8 \, a^{7} b d e^{8} + a^{8} e^{9}} - \frac{4 \, b^{7} d^{7} - 35 \, a b^{6} d^{6} e + 140 \, a^{2} b^{5} d^{5} e^{2} - 350 \, a^{3} b^{4} d^{4} e^{3} + 700 \, a^{4} b^{3} d^{3} e^{4} - 329 \, a^{5} b^{2} d^{2} e^{5} - 140 \, a^{6} b d e^{6} + 10 \, a^{7} e^{7} + 420 \, {\left(b^{7} d e^{6} - a b^{6} e^{7}\right)} x^{6} + 630 \, {\left(b^{7} d^{2} e^{5} + 2 \, a b^{6} d e^{6} - 3 \, a^{2} b^{5} e^{7}\right)} x^{5} + 70 \, {\left(2 \, b^{7} d^{3} e^{4} + 39 \, a b^{6} d^{2} e^{5} + 6 \, a^{2} b^{5} d e^{6} - 47 \, a^{3} b^{4} e^{7}\right)} x^{4} - 35 \, {\left(b^{7} d^{4} e^{3} - 20 \, a b^{6} d^{3} e^{4} - 126 \, a^{2} b^{5} d^{2} e^{5} + 68 \, a^{3} b^{4} d e^{6} + 77 \, a^{4} b^{3} e^{7}\right)} x^{3} + 7 \, {\left(2 \, b^{7} d^{5} e^{2} - 25 \, a b^{6} d^{4} e^{3} + 200 \, a^{2} b^{5} d^{3} e^{4} + 430 \, a^{3} b^{4} d^{2} e^{5} - 470 \, a^{4} b^{3} d e^{6} - 137 \, a^{5} b^{2} e^{7}\right)} x^{2} - 7 \, {\left(b^{7} d^{6} e - 10 \, a b^{6} d^{5} e^{2} + 50 \, a^{2} b^{5} d^{4} e^{3} - 200 \, a^{3} b^{4} d^{3} e^{4} - 65 \, a^{4} b^{3} d^{2} e^{5} + 214 \, a^{5} b^{2} d e^{6} + 10 \, a^{6} b e^{7}\right)} x}{20 \, {\left(b d - a e\right)}^{8} {\left(b x + a\right)}^{5} {\left(x e + d\right)}^{2}}"," ",0,"-21*b^3*e^5*log(abs(b*x + a))/(b^9*d^8 - 8*a*b^8*d^7*e + 28*a^2*b^7*d^6*e^2 - 56*a^3*b^6*d^5*e^3 + 70*a^4*b^5*d^4*e^4 - 56*a^5*b^4*d^3*e^5 + 28*a^6*b^3*d^2*e^6 - 8*a^7*b^2*d*e^7 + a^8*b*e^8) + 21*b^2*e^6*log(abs(x*e + d))/(b^8*d^8*e - 8*a*b^7*d^7*e^2 + 28*a^2*b^6*d^6*e^3 - 56*a^3*b^5*d^5*e^4 + 70*a^4*b^4*d^4*e^5 - 56*a^5*b^3*d^3*e^6 + 28*a^6*b^2*d^2*e^7 - 8*a^7*b*d*e^8 + a^8*e^9) - 1/20*(4*b^7*d^7 - 35*a*b^6*d^6*e + 140*a^2*b^5*d^5*e^2 - 350*a^3*b^4*d^4*e^3 + 700*a^4*b^3*d^3*e^4 - 329*a^5*b^2*d^2*e^5 - 140*a^6*b*d*e^6 + 10*a^7*e^7 + 420*(b^7*d*e^6 - a*b^6*e^7)*x^6 + 630*(b^7*d^2*e^5 + 2*a*b^6*d*e^6 - 3*a^2*b^5*e^7)*x^5 + 70*(2*b^7*d^3*e^4 + 39*a*b^6*d^2*e^5 + 6*a^2*b^5*d*e^6 - 47*a^3*b^4*e^7)*x^4 - 35*(b^7*d^4*e^3 - 20*a*b^6*d^3*e^4 - 126*a^2*b^5*d^2*e^5 + 68*a^3*b^4*d*e^6 + 77*a^4*b^3*e^7)*x^3 + 7*(2*b^7*d^5*e^2 - 25*a*b^6*d^4*e^3 + 200*a^2*b^5*d^3*e^4 + 430*a^3*b^4*d^2*e^5 - 470*a^4*b^3*d*e^6 - 137*a^5*b^2*e^7)*x^2 - 7*(b^7*d^6*e - 10*a*b^6*d^5*e^2 + 50*a^2*b^5*d^4*e^3 - 200*a^3*b^4*d^3*e^4 - 65*a^4*b^3*d^2*e^5 + 214*a^5*b^2*d*e^6 + 10*a^6*b*e^7)*x)/((b*d - a*e)^8*(b*x + a)^5*(x*e + d)^2)","B",0
1537,1,90,0,0.154296," ","integrate((e*x+d)*(4*x^2+12*x+9)^3,x, algorithm=""giac"")","8 \, x^{8} e + \frac{64}{7} \, d x^{7} + \frac{576}{7} \, x^{7} e + 96 \, d x^{6} + 360 \, x^{6} e + 432 \, d x^{5} + 864 \, x^{5} e + 1080 \, d x^{4} + 1215 \, x^{4} e + 1620 \, d x^{3} + 972 \, x^{3} e + 1458 \, d x^{2} + \frac{729}{2} \, x^{2} e + 729 \, d x"," ",0,"8*x^8*e + 64/7*d*x^7 + 576/7*x^7*e + 96*d*x^6 + 360*x^6*e + 432*d*x^5 + 864*x^5*e + 1080*d*x^4 + 1215*x^4*e + 1620*d*x^3 + 972*x^3*e + 1458*d*x^2 + 729/2*x^2*e + 729*d*x","B",0
1538,1,64,0,0.151463," ","integrate((e*x+d)*(4*x^2+12*x+9)^2,x, algorithm=""giac"")","\frac{8}{3} \, x^{6} e + \frac{16}{5} \, d x^{5} + \frac{96}{5} \, x^{5} e + 24 \, d x^{4} + 54 \, x^{4} e + 72 \, d x^{3} + 72 \, x^{3} e + 108 \, d x^{2} + \frac{81}{2} \, x^{2} e + 81 \, d x"," ",0,"8/3*x^6*e + 16/5*d*x^5 + 96/5*x^5*e + 24*d*x^4 + 54*x^4*e + 72*d*x^3 + 72*x^3*e + 108*d*x^2 + 81/2*x^2*e + 81*d*x","B",0
1539,1,37,0,0.150861," ","integrate((e*x+d)*(4*x^2+12*x+9),x, algorithm=""giac"")","x^{4} e + \frac{4}{3} \, d x^{3} + 4 \, x^{3} e + 6 \, d x^{2} + \frac{9}{2} \, x^{2} e + 9 \, d x"," ",0,"x^4*e + 4/3*d*x^3 + 4*x^3*e + 6*d*x^2 + 9/2*x^2*e + 9*d*x","A",0
1540,1,29,0,0.185691," ","integrate((e*x+d)/(4*x^2+12*x+9),x, algorithm=""giac"")","\frac{1}{4} \, e \log\left({\left| 2 \, x + 3 \right|}\right) - \frac{2 \, d - 3 \, e}{4 \, {\left(2 \, x + 3\right)}}"," ",0,"1/4*e*log(abs(2*x + 3)) - 1/4*(2*d - 3*e)/(2*x + 3)","A",0
1541,1,22,0,0.187140," ","integrate((e*x+d)/(4*x^2+12*x+9)^2,x, algorithm=""giac"")","-\frac{6 \, x e + 4 \, d + 3 \, e}{24 \, {\left(2 \, x + 3\right)}^{3}}"," ",0,"-1/24*(6*x*e + 4*d + 3*e)/(2*x + 3)^3","A",0
1542,1,22,0,0.155480," ","integrate((e*x+d)/(4*x^2+12*x+9)^3,x, algorithm=""giac"")","-\frac{10 \, x e + 8 \, d + 3 \, e}{80 \, {\left(2 \, x + 3\right)}^{5}}"," ",0,"-1/80*(10*x*e + 8*d + 3*e)/(2*x + 3)^5","A",0
1543,1,153,0,0.161918," ","integrate((e*x+d)^4*((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{6} \, b x^{6} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{4}{5} \, b d x^{5} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{3}{2} \, b d^{2} x^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{4}{3} \, b d^{3} x^{3} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, b d^{4} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{5} \, a x^{5} e^{4} \mathrm{sgn}\left(b x + a\right) + a d x^{4} e^{3} \mathrm{sgn}\left(b x + a\right) + 2 \, a d^{2} x^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + 2 \, a d^{3} x^{2} e \mathrm{sgn}\left(b x + a\right) + a d^{4} x \mathrm{sgn}\left(b x + a\right)"," ",0,"1/6*b*x^6*e^4*sgn(b*x + a) + 4/5*b*d*x^5*e^3*sgn(b*x + a) + 3/2*b*d^2*x^4*e^2*sgn(b*x + a) + 4/3*b*d^3*x^3*e*sgn(b*x + a) + 1/2*b*d^4*x^2*sgn(b*x + a) + 1/5*a*x^5*e^4*sgn(b*x + a) + a*d*x^4*e^3*sgn(b*x + a) + 2*a*d^2*x^3*e^2*sgn(b*x + a) + 2*a*d^3*x^2*e*sgn(b*x + a) + a*d^4*x*sgn(b*x + a)","B",0
1544,1,118,0,0.173866," ","integrate((e*x+d)^3*((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{5} \, b x^{5} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{3}{4} \, b d x^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + b d^{2} x^{3} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, b d^{3} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{4} \, a x^{4} e^{3} \mathrm{sgn}\left(b x + a\right) + a d x^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{3}{2} \, a d^{2} x^{2} e \mathrm{sgn}\left(b x + a\right) + a d^{3} x \mathrm{sgn}\left(b x + a\right)"," ",0,"1/5*b*x^5*e^3*sgn(b*x + a) + 3/4*b*d*x^4*e^2*sgn(b*x + a) + b*d^2*x^3*e*sgn(b*x + a) + 1/2*b*d^3*x^2*sgn(b*x + a) + 1/4*a*x^4*e^3*sgn(b*x + a) + a*d*x^3*e^2*sgn(b*x + a) + 3/2*a*d^2*x^2*e*sgn(b*x + a) + a*d^3*x*sgn(b*x + a)","A",0
1545,1,85,0,0.180164," ","integrate((e*x+d)^2*((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{4} \, b x^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{2}{3} \, b d x^{3} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, b d^{2} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{3} \, a x^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + a d x^{2} e \mathrm{sgn}\left(b x + a\right) + a d^{2} x \mathrm{sgn}\left(b x + a\right)"," ",0,"1/4*b*x^4*e^2*sgn(b*x + a) + 2/3*b*d*x^3*e*sgn(b*x + a) + 1/2*b*d^2*x^2*sgn(b*x + a) + 1/3*a*x^3*e^2*sgn(b*x + a) + a*d*x^2*e*sgn(b*x + a) + a*d^2*x*sgn(b*x + a)","A",0
1546,1,52,0,0.156724," ","integrate((e*x+d)*((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{3} \, b x^{3} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, b d x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, a x^{2} e \mathrm{sgn}\left(b x + a\right) + a d x \mathrm{sgn}\left(b x + a\right)"," ",0,"1/3*b*x^3*e*sgn(b*x + a) + 1/2*b*d*x^2*sgn(b*x + a) + 1/2*a*x^2*e*sgn(b*x + a) + a*d*x*sgn(b*x + a)","A",0
1547,1,33,0,0.156137," ","integrate(((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, {\left(b x^{2} + 2 \, a x\right)} \mathrm{sgn}\left(b x + a\right) + \frac{a^{2} \mathrm{sgn}\left(b x + a\right)}{2 \, b}"," ",0,"1/2*(b*x^2 + 2*a*x)*sgn(b*x + a) + 1/2*a^2*sgn(b*x + a)/b","A",0
1548,1,45,0,0.153036," ","integrate(((b*x+a)^2)^(1/2)/(e*x+d),x, algorithm=""giac"")","b x e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) - {\left(b d \mathrm{sgn}\left(b x + a\right) - a e \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-2\right)} \log\left({\left| x e + d \right|}\right)"," ",0,"b*x*e^(-1)*sgn(b*x + a) - (b*d*sgn(b*x + a) - a*e*sgn(b*x + a))*e^(-2)*log(abs(x*e + d))","A",0
1549,1,51,0,0.183898," ","integrate(((b*x+a)^2)^(1/2)/(e*x+d)^2,x, algorithm=""giac"")","b e^{\left(-2\right)} \log\left({\left| x e + d \right|}\right) \mathrm{sgn}\left(b x + a\right) + \frac{{\left(b d \mathrm{sgn}\left(b x + a\right) - a e \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-2\right)}}{x e + d}"," ",0,"b*e^(-2)*log(abs(x*e + d))*sgn(b*x + a) + (b*d*sgn(b*x + a) - a*e*sgn(b*x + a))*e^(-2)/(x*e + d)","A",0
1550,1,44,0,0.157710," ","integrate(((b*x+a)^2)^(1/2)/(e*x+d)^3,x, algorithm=""giac"")","-\frac{{\left(2 \, b x e \mathrm{sgn}\left(b x + a\right) + b d \mathrm{sgn}\left(b x + a\right) + a e \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-2\right)}}{2 \, {\left(x e + d\right)}^{2}}"," ",0,"-1/2*(2*b*x*e*sgn(b*x + a) + b*d*sgn(b*x + a) + a*e*sgn(b*x + a))*e^(-2)/(x*e + d)^2","A",0
1551,1,45,0,0.157429," ","integrate(((b*x+a)^2)^(1/2)/(e*x+d)^4,x, algorithm=""giac"")","-\frac{{\left(3 \, b x e \mathrm{sgn}\left(b x + a\right) + b d \mathrm{sgn}\left(b x + a\right) + 2 \, a e \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-2\right)}}{6 \, {\left(x e + d\right)}^{3}}"," ",0,"-1/6*(3*b*x*e*sgn(b*x + a) + b*d*sgn(b*x + a) + 2*a*e*sgn(b*x + a))*e^(-2)/(x*e + d)^3","A",0
1552,1,45,0,0.160757," ","integrate(((b*x+a)^2)^(1/2)/(e*x+d)^5,x, algorithm=""giac"")","-\frac{{\left(4 \, b x e \mathrm{sgn}\left(b x + a\right) + b d \mathrm{sgn}\left(b x + a\right) + 3 \, a e \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-2\right)}}{12 \, {\left(x e + d\right)}^{4}}"," ",0,"-1/12*(4*b*x*e*sgn(b*x + a) + b*d*sgn(b*x + a) + 3*a*e*sgn(b*x + a))*e^(-2)/(x*e + d)^4","A",0
1553,1,45,0,0.186993," ","integrate(((b*x+a)^2)^(1/2)/(e*x+d)^6,x, algorithm=""giac"")","-\frac{{\left(5 \, b x e \mathrm{sgn}\left(b x + a\right) + b d \mathrm{sgn}\left(b x + a\right) + 4 \, a e \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-2\right)}}{20 \, {\left(x e + d\right)}^{5}}"," ",0,"-1/20*(5*b*x*e*sgn(b*x + a) + b*d*sgn(b*x + a) + 4*a*e*sgn(b*x + a))*e^(-2)/(x*e + d)^5","A",0
1554,1,435,0,0.180105," ","integrate((e*x+d)^5*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{1}{9} \, b^{3} x^{9} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{5}{8} \, b^{3} d x^{8} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{10}{7} \, b^{3} d^{2} x^{7} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{5}{3} \, b^{3} d^{3} x^{6} e^{2} \mathrm{sgn}\left(b x + a\right) + b^{3} d^{4} x^{5} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{4} \, b^{3} d^{5} x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{3}{8} \, a b^{2} x^{8} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{15}{7} \, a b^{2} d x^{7} e^{4} \mathrm{sgn}\left(b x + a\right) + 5 \, a b^{2} d^{2} x^{6} e^{3} \mathrm{sgn}\left(b x + a\right) + 6 \, a b^{2} d^{3} x^{5} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{15}{4} \, a b^{2} d^{4} x^{4} e \mathrm{sgn}\left(b x + a\right) + a b^{2} d^{5} x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{3}{7} \, a^{2} b x^{7} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, a^{2} b d x^{6} e^{4} \mathrm{sgn}\left(b x + a\right) + 6 \, a^{2} b d^{2} x^{5} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{15}{2} \, a^{2} b d^{3} x^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 5 \, a^{2} b d^{4} x^{3} e \mathrm{sgn}\left(b x + a\right) + \frac{3}{2} \, a^{2} b d^{5} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{6} \, a^{3} x^{6} e^{5} \mathrm{sgn}\left(b x + a\right) + a^{3} d x^{5} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, a^{3} d^{2} x^{4} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{10}{3} \, a^{3} d^{3} x^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, a^{3} d^{4} x^{2} e \mathrm{sgn}\left(b x + a\right) + a^{3} d^{5} x \mathrm{sgn}\left(b x + a\right)"," ",0,"1/9*b^3*x^9*e^5*sgn(b*x + a) + 5/8*b^3*d*x^8*e^4*sgn(b*x + a) + 10/7*b^3*d^2*x^7*e^3*sgn(b*x + a) + 5/3*b^3*d^3*x^6*e^2*sgn(b*x + a) + b^3*d^4*x^5*e*sgn(b*x + a) + 1/4*b^3*d^5*x^4*sgn(b*x + a) + 3/8*a*b^2*x^8*e^5*sgn(b*x + a) + 15/7*a*b^2*d*x^7*e^4*sgn(b*x + a) + 5*a*b^2*d^2*x^6*e^3*sgn(b*x + a) + 6*a*b^2*d^3*x^5*e^2*sgn(b*x + a) + 15/4*a*b^2*d^4*x^4*e*sgn(b*x + a) + a*b^2*d^5*x^3*sgn(b*x + a) + 3/7*a^2*b*x^7*e^5*sgn(b*x + a) + 5/2*a^2*b*d*x^6*e^4*sgn(b*x + a) + 6*a^2*b*d^2*x^5*e^3*sgn(b*x + a) + 15/2*a^2*b*d^3*x^4*e^2*sgn(b*x + a) + 5*a^2*b*d^4*x^3*e*sgn(b*x + a) + 3/2*a^2*b*d^5*x^2*sgn(b*x + a) + 1/6*a^3*x^6*e^5*sgn(b*x + a) + a^3*d*x^5*e^4*sgn(b*x + a) + 5/2*a^3*d^2*x^4*e^3*sgn(b*x + a) + 10/3*a^3*d^3*x^3*e^2*sgn(b*x + a) + 5/2*a^3*d^4*x^2*e*sgn(b*x + a) + a^3*d^5*x*sgn(b*x + a)","B",0
1555,1,357,0,0.171448," ","integrate((e*x+d)^4*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{1}{8} \, b^{3} x^{8} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{4}{7} \, b^{3} d x^{7} e^{3} \mathrm{sgn}\left(b x + a\right) + b^{3} d^{2} x^{6} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{4}{5} \, b^{3} d^{3} x^{5} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{4} \, b^{3} d^{4} x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{3}{7} \, a b^{2} x^{7} e^{4} \mathrm{sgn}\left(b x + a\right) + 2 \, a b^{2} d x^{6} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{18}{5} \, a b^{2} d^{2} x^{5} e^{2} \mathrm{sgn}\left(b x + a\right) + 3 \, a b^{2} d^{3} x^{4} e \mathrm{sgn}\left(b x + a\right) + a b^{2} d^{4} x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, a^{2} b x^{6} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{12}{5} \, a^{2} b d x^{5} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{9}{2} \, a^{2} b d^{2} x^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 4 \, a^{2} b d^{3} x^{3} e \mathrm{sgn}\left(b x + a\right) + \frac{3}{2} \, a^{2} b d^{4} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{5} \, a^{3} x^{5} e^{4} \mathrm{sgn}\left(b x + a\right) + a^{3} d x^{4} e^{3} \mathrm{sgn}\left(b x + a\right) + 2 \, a^{3} d^{2} x^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + 2 \, a^{3} d^{3} x^{2} e \mathrm{sgn}\left(b x + a\right) + a^{3} d^{4} x \mathrm{sgn}\left(b x + a\right)"," ",0,"1/8*b^3*x^8*e^4*sgn(b*x + a) + 4/7*b^3*d*x^7*e^3*sgn(b*x + a) + b^3*d^2*x^6*e^2*sgn(b*x + a) + 4/5*b^3*d^3*x^5*e*sgn(b*x + a) + 1/4*b^3*d^4*x^4*sgn(b*x + a) + 3/7*a*b^2*x^7*e^4*sgn(b*x + a) + 2*a*b^2*d*x^6*e^3*sgn(b*x + a) + 18/5*a*b^2*d^2*x^5*e^2*sgn(b*x + a) + 3*a*b^2*d^3*x^4*e*sgn(b*x + a) + a*b^2*d^4*x^3*sgn(b*x + a) + 1/2*a^2*b*x^6*e^4*sgn(b*x + a) + 12/5*a^2*b*d*x^5*e^3*sgn(b*x + a) + 9/2*a^2*b*d^2*x^4*e^2*sgn(b*x + a) + 4*a^2*b*d^3*x^3*e*sgn(b*x + a) + 3/2*a^2*b*d^4*x^2*sgn(b*x + a) + 1/5*a^3*x^5*e^4*sgn(b*x + a) + a^3*d*x^4*e^3*sgn(b*x + a) + 2*a^3*d^2*x^3*e^2*sgn(b*x + a) + 2*a^3*d^3*x^2*e*sgn(b*x + a) + a^3*d^4*x*sgn(b*x + a)","B",0
1556,1,280,0,0.170242," ","integrate((e*x+d)^3*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{1}{7} \, b^{3} x^{7} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, b^{3} d x^{6} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{3}{5} \, b^{3} d^{2} x^{5} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{4} \, b^{3} d^{3} x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, a b^{2} x^{6} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{9}{5} \, a b^{2} d x^{5} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{9}{4} \, a b^{2} d^{2} x^{4} e \mathrm{sgn}\left(b x + a\right) + a b^{2} d^{3} x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{3}{5} \, a^{2} b x^{5} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{9}{4} \, a^{2} b d x^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 3 \, a^{2} b d^{2} x^{3} e \mathrm{sgn}\left(b x + a\right) + \frac{3}{2} \, a^{2} b d^{3} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{4} \, a^{3} x^{4} e^{3} \mathrm{sgn}\left(b x + a\right) + a^{3} d x^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{3}{2} \, a^{3} d^{2} x^{2} e \mathrm{sgn}\left(b x + a\right) + a^{3} d^{3} x \mathrm{sgn}\left(b x + a\right)"," ",0,"1/7*b^3*x^7*e^3*sgn(b*x + a) + 1/2*b^3*d*x^6*e^2*sgn(b*x + a) + 3/5*b^3*d^2*x^5*e*sgn(b*x + a) + 1/4*b^3*d^3*x^4*sgn(b*x + a) + 1/2*a*b^2*x^6*e^3*sgn(b*x + a) + 9/5*a*b^2*d*x^5*e^2*sgn(b*x + a) + 9/4*a*b^2*d^2*x^4*e*sgn(b*x + a) + a*b^2*d^3*x^3*sgn(b*x + a) + 3/5*a^2*b*x^5*e^3*sgn(b*x + a) + 9/4*a^2*b*d*x^4*e^2*sgn(b*x + a) + 3*a^2*b*d^2*x^3*e*sgn(b*x + a) + 3/2*a^2*b*d^3*x^2*sgn(b*x + a) + 1/4*a^3*x^4*e^3*sgn(b*x + a) + a^3*d*x^3*e^2*sgn(b*x + a) + 3/2*a^3*d^2*x^2*e*sgn(b*x + a) + a^3*d^3*x*sgn(b*x + a)","B",0
1557,1,202,0,0.163221," ","integrate((e*x+d)^2*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{1}{6} \, b^{3} x^{6} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{2}{5} \, b^{3} d x^{5} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{4} \, b^{3} d^{2} x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{3}{5} \, a b^{2} x^{5} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{3}{2} \, a b^{2} d x^{4} e \mathrm{sgn}\left(b x + a\right) + a b^{2} d^{2} x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{3}{4} \, a^{2} b x^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 2 \, a^{2} b d x^{3} e \mathrm{sgn}\left(b x + a\right) + \frac{3}{2} \, a^{2} b d^{2} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{3} \, a^{3} x^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + a^{3} d x^{2} e \mathrm{sgn}\left(b x + a\right) + a^{3} d^{2} x \mathrm{sgn}\left(b x + a\right)"," ",0,"1/6*b^3*x^6*e^2*sgn(b*x + a) + 2/5*b^3*d*x^5*e*sgn(b*x + a) + 1/4*b^3*d^2*x^4*sgn(b*x + a) + 3/5*a*b^2*x^5*e^2*sgn(b*x + a) + 3/2*a*b^2*d*x^4*e*sgn(b*x + a) + a*b^2*d^2*x^3*sgn(b*x + a) + 3/4*a^2*b*x^4*e^2*sgn(b*x + a) + 2*a^2*b*d*x^3*e*sgn(b*x + a) + 3/2*a^2*b*d^2*x^2*sgn(b*x + a) + 1/3*a^3*x^3*e^2*sgn(b*x + a) + a^3*d*x^2*e*sgn(b*x + a) + a^3*d^2*x*sgn(b*x + a)","A",0
1558,1,124,0,0.162327," ","integrate((e*x+d)*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{1}{5} \, b^{3} x^{5} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{4} \, b^{3} d x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{3}{4} \, a b^{2} x^{4} e \mathrm{sgn}\left(b x + a\right) + a b^{2} d x^{3} \mathrm{sgn}\left(b x + a\right) + a^{2} b x^{3} e \mathrm{sgn}\left(b x + a\right) + \frac{3}{2} \, a^{2} b d x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, a^{3} x^{2} e \mathrm{sgn}\left(b x + a\right) + a^{3} d x \mathrm{sgn}\left(b x + a\right)"," ",0,"1/5*b^3*x^5*e*sgn(b*x + a) + 1/4*b^3*d*x^4*sgn(b*x + a) + 3/4*a*b^2*x^4*e*sgn(b*x + a) + a*b^2*d*x^3*sgn(b*x + a) + a^2*b*x^3*e*sgn(b*x + a) + 3/2*a^2*b*d*x^2*sgn(b*x + a) + 1/2*a^3*x^2*e*sgn(b*x + a) + a^3*d*x*sgn(b*x + a)","B",0
1559,1,57,0,0.160492," ","integrate((b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{1}{2} \, {\left(b x^{2} + 2 \, a x\right)} a^{2} \mathrm{sgn}\left(b x + a\right) + \frac{a^{4} \mathrm{sgn}\left(b x + a\right)}{4 \, b} + \frac{1}{4} \, {\left(b x^{2} + 2 \, a x\right)}^{2} b \mathrm{sgn}\left(b x + a\right)"," ",0,"1/2*(b*x^2 + 2*a*x)*a^2*sgn(b*x + a) + 1/4*a^4*sgn(b*x + a)/b + 1/4*(b*x^2 + 2*a*x)^2*b*sgn(b*x + a)","B",0
1560,1,173,0,0.183629," ","integrate((b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d),x, algorithm=""giac"")","-{\left(b^{3} d^{3} \mathrm{sgn}\left(b x + a\right) - 3 \, a b^{2} d^{2} e \mathrm{sgn}\left(b x + a\right) + 3 \, a^{2} b d e^{2} \mathrm{sgn}\left(b x + a\right) - a^{3} e^{3} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-4\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{6} \, {\left(2 \, b^{3} x^{3} e^{2} \mathrm{sgn}\left(b x + a\right) - 3 \, b^{3} d x^{2} e \mathrm{sgn}\left(b x + a\right) + 6 \, b^{3} d^{2} x \mathrm{sgn}\left(b x + a\right) + 9 \, a b^{2} x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) - 18 \, a b^{2} d x e \mathrm{sgn}\left(b x + a\right) + 18 \, a^{2} b x e^{2} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-3\right)}"," ",0,"-(b^3*d^3*sgn(b*x + a) - 3*a*b^2*d^2*e*sgn(b*x + a) + 3*a^2*b*d*e^2*sgn(b*x + a) - a^3*e^3*sgn(b*x + a))*e^(-4)*log(abs(x*e + d)) + 1/6*(2*b^3*x^3*e^2*sgn(b*x + a) - 3*b^3*d*x^2*e*sgn(b*x + a) + 6*b^3*d^2*x*sgn(b*x + a) + 9*a*b^2*x^2*e^2*sgn(b*x + a) - 18*a*b^2*d*x*e*sgn(b*x + a) + 18*a^2*b*x*e^2*sgn(b*x + a))*e^(-3)","A",0
1561,1,175,0,0.167680," ","integrate((b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^2,x, algorithm=""giac"")","3 \, {\left(b^{3} d^{2} \mathrm{sgn}\left(b x + a\right) - 2 \, a b^{2} d e \mathrm{sgn}\left(b x + a\right) + a^{2} b e^{2} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-4\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{2} \, {\left(b^{3} x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) - 4 \, b^{3} d x e \mathrm{sgn}\left(b x + a\right) + 6 \, a b^{2} x e^{2} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-4\right)} + \frac{{\left(b^{3} d^{3} \mathrm{sgn}\left(b x + a\right) - 3 \, a b^{2} d^{2} e \mathrm{sgn}\left(b x + a\right) + 3 \, a^{2} b d e^{2} \mathrm{sgn}\left(b x + a\right) - a^{3} e^{3} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-4\right)}}{x e + d}"," ",0,"3*(b^3*d^2*sgn(b*x + a) - 2*a*b^2*d*e*sgn(b*x + a) + a^2*b*e^2*sgn(b*x + a))*e^(-4)*log(abs(x*e + d)) + 1/2*(b^3*x^2*e^2*sgn(b*x + a) - 4*b^3*d*x*e*sgn(b*x + a) + 6*a*b^2*x*e^2*sgn(b*x + a))*e^(-4) + (b^3*d^3*sgn(b*x + a) - 3*a*b^2*d^2*e*sgn(b*x + a) + 3*a^2*b*d*e^2*sgn(b*x + a) - a^3*e^3*sgn(b*x + a))*e^(-4)/(x*e + d)","A",0
1562,1,170,0,0.216938," ","integrate((b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^3,x, algorithm=""giac"")","b^{3} x e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) - 3 \, {\left(b^{3} d \mathrm{sgn}\left(b x + a\right) - a b^{2} e \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-4\right)} \log\left({\left| x e + d \right|}\right) - \frac{{\left(5 \, b^{3} d^{3} \mathrm{sgn}\left(b x + a\right) - 9 \, a b^{2} d^{2} e \mathrm{sgn}\left(b x + a\right) + 3 \, a^{2} b d e^{2} \mathrm{sgn}\left(b x + a\right) + a^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 6 \, {\left(b^{3} d^{2} e \mathrm{sgn}\left(b x + a\right) - 2 \, a b^{2} d e^{2} \mathrm{sgn}\left(b x + a\right) + a^{2} b e^{3} \mathrm{sgn}\left(b x + a\right)\right)} x\right)} e^{\left(-4\right)}}{2 \, {\left(x e + d\right)}^{2}}"," ",0,"b^3*x*e^(-3)*sgn(b*x + a) - 3*(b^3*d*sgn(b*x + a) - a*b^2*e*sgn(b*x + a))*e^(-4)*log(abs(x*e + d)) - 1/2*(5*b^3*d^3*sgn(b*x + a) - 9*a*b^2*d^2*e*sgn(b*x + a) + 3*a^2*b*d*e^2*sgn(b*x + a) + a^3*e^3*sgn(b*x + a) + 6*(b^3*d^2*e*sgn(b*x + a) - 2*a*b^2*d*e^2*sgn(b*x + a) + a^2*b*e^3*sgn(b*x + a))*x)*e^(-4)/(x*e + d)^2","A",0
1563,1,177,0,0.171323," ","integrate((b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^4,x, algorithm=""giac"")","b^{3} e^{\left(-4\right)} \log\left({\left| x e + d \right|}\right) \mathrm{sgn}\left(b x + a\right) + \frac{{\left(18 \, {\left(b^{3} d e \mathrm{sgn}\left(b x + a\right) - a b^{2} e^{2} \mathrm{sgn}\left(b x + a\right)\right)} x^{2} + 9 \, {\left(3 \, b^{3} d^{2} \mathrm{sgn}\left(b x + a\right) - 2 \, a b^{2} d e \mathrm{sgn}\left(b x + a\right) - a^{2} b e^{2} \mathrm{sgn}\left(b x + a\right)\right)} x + {\left(11 \, b^{3} d^{3} \mathrm{sgn}\left(b x + a\right) - 6 \, a b^{2} d^{2} e \mathrm{sgn}\left(b x + a\right) - 3 \, a^{2} b d e^{2} \mathrm{sgn}\left(b x + a\right) - 2 \, a^{3} e^{3} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-1\right)}\right)} e^{\left(-3\right)}}{6 \, {\left(x e + d\right)}^{3}}"," ",0,"b^3*e^(-4)*log(abs(x*e + d))*sgn(b*x + a) + 1/6*(18*(b^3*d*e*sgn(b*x + a) - a*b^2*e^2*sgn(b*x + a))*x^2 + 9*(3*b^3*d^2*sgn(b*x + a) - 2*a*b^2*d*e*sgn(b*x + a) - a^2*b*e^2*sgn(b*x + a))*x + (11*b^3*d^3*sgn(b*x + a) - 6*a*b^2*d^2*e*sgn(b*x + a) - 3*a^2*b*d*e^2*sgn(b*x + a) - 2*a^3*e^3*sgn(b*x + a))*e^(-1))*e^(-3)/(x*e + d)^3","A",0
1564,1,166,0,0.189040," ","integrate((b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^5,x, algorithm=""giac"")","-\frac{{\left(4 \, b^{3} x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 6 \, b^{3} d x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 4 \, b^{3} d^{2} x e \mathrm{sgn}\left(b x + a\right) + b^{3} d^{3} \mathrm{sgn}\left(b x + a\right) + 6 \, a b^{2} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 4 \, a b^{2} d x e^{2} \mathrm{sgn}\left(b x + a\right) + a b^{2} d^{2} e \mathrm{sgn}\left(b x + a\right) + 4 \, a^{2} b x e^{3} \mathrm{sgn}\left(b x + a\right) + a^{2} b d e^{2} \mathrm{sgn}\left(b x + a\right) + a^{3} e^{3} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-4\right)}}{4 \, {\left(x e + d\right)}^{4}}"," ",0,"-1/4*(4*b^3*x^3*e^3*sgn(b*x + a) + 6*b^3*d*x^2*e^2*sgn(b*x + a) + 4*b^3*d^2*x*e*sgn(b*x + a) + b^3*d^3*sgn(b*x + a) + 6*a*b^2*x^2*e^3*sgn(b*x + a) + 4*a*b^2*d*x*e^2*sgn(b*x + a) + a*b^2*d^2*e*sgn(b*x + a) + 4*a^2*b*x*e^3*sgn(b*x + a) + a^2*b*d*e^2*sgn(b*x + a) + a^3*e^3*sgn(b*x + a))*e^(-4)/(x*e + d)^4","B",0
1565,1,169,0,0.183166," ","integrate((b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^6,x, algorithm=""giac"")","-\frac{{\left(10 \, b^{3} x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 10 \, b^{3} d x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 5 \, b^{3} d^{2} x e \mathrm{sgn}\left(b x + a\right) + b^{3} d^{3} \mathrm{sgn}\left(b x + a\right) + 20 \, a b^{2} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 10 \, a b^{2} d x e^{2} \mathrm{sgn}\left(b x + a\right) + 2 \, a b^{2} d^{2} e \mathrm{sgn}\left(b x + a\right) + 15 \, a^{2} b x e^{3} \mathrm{sgn}\left(b x + a\right) + 3 \, a^{2} b d e^{2} \mathrm{sgn}\left(b x + a\right) + 4 \, a^{3} e^{3} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-4\right)}}{20 \, {\left(x e + d\right)}^{5}}"," ",0,"-1/20*(10*b^3*x^3*e^3*sgn(b*x + a) + 10*b^3*d*x^2*e^2*sgn(b*x + a) + 5*b^3*d^2*x*e*sgn(b*x + a) + b^3*d^3*sgn(b*x + a) + 20*a*b^2*x^2*e^3*sgn(b*x + a) + 10*a*b^2*d*x*e^2*sgn(b*x + a) + 2*a*b^2*d^2*e*sgn(b*x + a) + 15*a^2*b*x*e^3*sgn(b*x + a) + 3*a^2*b*d*e^2*sgn(b*x + a) + 4*a^3*e^3*sgn(b*x + a))*e^(-4)/(x*e + d)^5","B",0
1566,1,169,0,0.171455," ","integrate((b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^7,x, algorithm=""giac"")","-\frac{{\left(20 \, b^{3} x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 15 \, b^{3} d x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 6 \, b^{3} d^{2} x e \mathrm{sgn}\left(b x + a\right) + b^{3} d^{3} \mathrm{sgn}\left(b x + a\right) + 45 \, a b^{2} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 18 \, a b^{2} d x e^{2} \mathrm{sgn}\left(b x + a\right) + 3 \, a b^{2} d^{2} e \mathrm{sgn}\left(b x + a\right) + 36 \, a^{2} b x e^{3} \mathrm{sgn}\left(b x + a\right) + 6 \, a^{2} b d e^{2} \mathrm{sgn}\left(b x + a\right) + 10 \, a^{3} e^{3} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-4\right)}}{60 \, {\left(x e + d\right)}^{6}}"," ",0,"-1/60*(20*b^3*x^3*e^3*sgn(b*x + a) + 15*b^3*d*x^2*e^2*sgn(b*x + a) + 6*b^3*d^2*x*e*sgn(b*x + a) + b^3*d^3*sgn(b*x + a) + 45*a*b^2*x^2*e^3*sgn(b*x + a) + 18*a*b^2*d*x*e^2*sgn(b*x + a) + 3*a*b^2*d^2*e*sgn(b*x + a) + 36*a^2*b*x*e^3*sgn(b*x + a) + 6*a^2*b*d*e^2*sgn(b*x + a) + 10*a^3*e^3*sgn(b*x + a))*e^(-4)/(x*e + d)^6","A",0
1567,1,169,0,0.192160," ","integrate((b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^8,x, algorithm=""giac"")","-\frac{{\left(35 \, b^{3} x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 21 \, b^{3} d x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 7 \, b^{3} d^{2} x e \mathrm{sgn}\left(b x + a\right) + b^{3} d^{3} \mathrm{sgn}\left(b x + a\right) + 84 \, a b^{2} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 28 \, a b^{2} d x e^{2} \mathrm{sgn}\left(b x + a\right) + 4 \, a b^{2} d^{2} e \mathrm{sgn}\left(b x + a\right) + 70 \, a^{2} b x e^{3} \mathrm{sgn}\left(b x + a\right) + 10 \, a^{2} b d e^{2} \mathrm{sgn}\left(b x + a\right) + 20 \, a^{3} e^{3} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-4\right)}}{140 \, {\left(x e + d\right)}^{7}}"," ",0,"-1/140*(35*b^3*x^3*e^3*sgn(b*x + a) + 21*b^3*d*x^2*e^2*sgn(b*x + a) + 7*b^3*d^2*x*e*sgn(b*x + a) + b^3*d^3*sgn(b*x + a) + 84*a*b^2*x^2*e^3*sgn(b*x + a) + 28*a*b^2*d*x*e^2*sgn(b*x + a) + 4*a*b^2*d^2*e*sgn(b*x + a) + 70*a^2*b*x*e^3*sgn(b*x + a) + 10*a^2*b*d*e^2*sgn(b*x + a) + 20*a^3*e^3*sgn(b*x + a))*e^(-4)/(x*e + d)^7","A",0
1568,1,169,0,0.189518," ","integrate((b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^9,x, algorithm=""giac"")","-\frac{{\left(56 \, b^{3} x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 28 \, b^{3} d x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 8 \, b^{3} d^{2} x e \mathrm{sgn}\left(b x + a\right) + b^{3} d^{3} \mathrm{sgn}\left(b x + a\right) + 140 \, a b^{2} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 40 \, a b^{2} d x e^{2} \mathrm{sgn}\left(b x + a\right) + 5 \, a b^{2} d^{2} e \mathrm{sgn}\left(b x + a\right) + 120 \, a^{2} b x e^{3} \mathrm{sgn}\left(b x + a\right) + 15 \, a^{2} b d e^{2} \mathrm{sgn}\left(b x + a\right) + 35 \, a^{3} e^{3} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-4\right)}}{280 \, {\left(x e + d\right)}^{8}}"," ",0,"-1/280*(56*b^3*x^3*e^3*sgn(b*x + a) + 28*b^3*d*x^2*e^2*sgn(b*x + a) + 8*b^3*d^2*x*e*sgn(b*x + a) + b^3*d^3*sgn(b*x + a) + 140*a*b^2*x^2*e^3*sgn(b*x + a) + 40*a*b^2*d*x*e^2*sgn(b*x + a) + 5*a*b^2*d^2*e*sgn(b*x + a) + 120*a^2*b*x*e^3*sgn(b*x + a) + 15*a^2*b*d*e^2*sgn(b*x + a) + 35*a^3*e^3*sgn(b*x + a))*e^(-4)/(x*e + d)^8","A",0
1569,1,686,0,0.211792," ","integrate((e*x+d)^5*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{11} \, b^{5} x^{11} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, b^{5} d x^{10} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{10}{9} \, b^{5} d^{2} x^{9} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{5}{4} \, b^{5} d^{3} x^{8} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{5}{7} \, b^{5} d^{4} x^{7} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{6} \, b^{5} d^{5} x^{6} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, a b^{4} x^{10} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{25}{9} \, a b^{4} d x^{9} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{25}{4} \, a b^{4} d^{2} x^{8} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{50}{7} \, a b^{4} d^{3} x^{7} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{25}{6} \, a b^{4} d^{4} x^{6} e \mathrm{sgn}\left(b x + a\right) + a b^{4} d^{5} x^{5} \mathrm{sgn}\left(b x + a\right) + \frac{10}{9} \, a^{2} b^{3} x^{9} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{25}{4} \, a^{2} b^{3} d x^{8} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{100}{7} \, a^{2} b^{3} d^{2} x^{7} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{50}{3} \, a^{2} b^{3} d^{3} x^{6} e^{2} \mathrm{sgn}\left(b x + a\right) + 10 \, a^{2} b^{3} d^{4} x^{5} e \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, a^{2} b^{3} d^{5} x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{5}{4} \, a^{3} b^{2} x^{8} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{50}{7} \, a^{3} b^{2} d x^{7} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{50}{3} \, a^{3} b^{2} d^{2} x^{6} e^{3} \mathrm{sgn}\left(b x + a\right) + 20 \, a^{3} b^{2} d^{3} x^{5} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{25}{2} \, a^{3} b^{2} d^{4} x^{4} e \mathrm{sgn}\left(b x + a\right) + \frac{10}{3} \, a^{3} b^{2} d^{5} x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{5}{7} \, a^{4} b x^{7} e^{5} \mathrm{sgn}\left(b x + a\right) + \frac{25}{6} \, a^{4} b d x^{6} e^{4} \mathrm{sgn}\left(b x + a\right) + 10 \, a^{4} b d^{2} x^{5} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{25}{2} \, a^{4} b d^{3} x^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{25}{3} \, a^{4} b d^{4} x^{3} e \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, a^{4} b d^{5} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{6} \, a^{5} x^{6} e^{5} \mathrm{sgn}\left(b x + a\right) + a^{5} d x^{5} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, a^{5} d^{2} x^{4} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{10}{3} \, a^{5} d^{3} x^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, a^{5} d^{4} x^{2} e \mathrm{sgn}\left(b x + a\right) + a^{5} d^{5} x \mathrm{sgn}\left(b x + a\right)"," ",0,"1/11*b^5*x^11*e^5*sgn(b*x + a) + 1/2*b^5*d*x^10*e^4*sgn(b*x + a) + 10/9*b^5*d^2*x^9*e^3*sgn(b*x + a) + 5/4*b^5*d^3*x^8*e^2*sgn(b*x + a) + 5/7*b^5*d^4*x^7*e*sgn(b*x + a) + 1/6*b^5*d^5*x^6*sgn(b*x + a) + 1/2*a*b^4*x^10*e^5*sgn(b*x + a) + 25/9*a*b^4*d*x^9*e^4*sgn(b*x + a) + 25/4*a*b^4*d^2*x^8*e^3*sgn(b*x + a) + 50/7*a*b^4*d^3*x^7*e^2*sgn(b*x + a) + 25/6*a*b^4*d^4*x^6*e*sgn(b*x + a) + a*b^4*d^5*x^5*sgn(b*x + a) + 10/9*a^2*b^3*x^9*e^5*sgn(b*x + a) + 25/4*a^2*b^3*d*x^8*e^4*sgn(b*x + a) + 100/7*a^2*b^3*d^2*x^7*e^3*sgn(b*x + a) + 50/3*a^2*b^3*d^3*x^6*e^2*sgn(b*x + a) + 10*a^2*b^3*d^4*x^5*e*sgn(b*x + a) + 5/2*a^2*b^3*d^5*x^4*sgn(b*x + a) + 5/4*a^3*b^2*x^8*e^5*sgn(b*x + a) + 50/7*a^3*b^2*d*x^7*e^4*sgn(b*x + a) + 50/3*a^3*b^2*d^2*x^6*e^3*sgn(b*x + a) + 20*a^3*b^2*d^3*x^5*e^2*sgn(b*x + a) + 25/2*a^3*b^2*d^4*x^4*e*sgn(b*x + a) + 10/3*a^3*b^2*d^5*x^3*sgn(b*x + a) + 5/7*a^4*b*x^7*e^5*sgn(b*x + a) + 25/6*a^4*b*d*x^6*e^4*sgn(b*x + a) + 10*a^4*b*d^2*x^5*e^3*sgn(b*x + a) + 25/2*a^4*b*d^3*x^4*e^2*sgn(b*x + a) + 25/3*a^4*b*d^4*x^3*e*sgn(b*x + a) + 5/2*a^4*b*d^5*x^2*sgn(b*x + a) + 1/6*a^5*x^6*e^5*sgn(b*x + a) + a^5*d*x^5*e^4*sgn(b*x + a) + 5/2*a^5*d^2*x^4*e^3*sgn(b*x + a) + 10/3*a^5*d^3*x^3*e^2*sgn(b*x + a) + 5/2*a^5*d^4*x^2*e*sgn(b*x + a) + a^5*d^5*x*sgn(b*x + a)","B",0
1570,1,564,0,0.192277," ","integrate((e*x+d)^4*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{10} \, b^{5} x^{10} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{4}{9} \, b^{5} d x^{9} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{3}{4} \, b^{5} d^{2} x^{8} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{4}{7} \, b^{5} d^{3} x^{7} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{6} \, b^{5} d^{4} x^{6} \mathrm{sgn}\left(b x + a\right) + \frac{5}{9} \, a b^{4} x^{9} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, a b^{4} d x^{8} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{30}{7} \, a b^{4} d^{2} x^{7} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{10}{3} \, a b^{4} d^{3} x^{6} e \mathrm{sgn}\left(b x + a\right) + a b^{4} d^{4} x^{5} \mathrm{sgn}\left(b x + a\right) + \frac{5}{4} \, a^{2} b^{3} x^{8} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{40}{7} \, a^{2} b^{3} d x^{7} e^{3} \mathrm{sgn}\left(b x + a\right) + 10 \, a^{2} b^{3} d^{2} x^{6} e^{2} \mathrm{sgn}\left(b x + a\right) + 8 \, a^{2} b^{3} d^{3} x^{5} e \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, a^{2} b^{3} d^{4} x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{10}{7} \, a^{3} b^{2} x^{7} e^{4} \mathrm{sgn}\left(b x + a\right) + \frac{20}{3} \, a^{3} b^{2} d x^{6} e^{3} \mathrm{sgn}\left(b x + a\right) + 12 \, a^{3} b^{2} d^{2} x^{5} e^{2} \mathrm{sgn}\left(b x + a\right) + 10 \, a^{3} b^{2} d^{3} x^{4} e \mathrm{sgn}\left(b x + a\right) + \frac{10}{3} \, a^{3} b^{2} d^{4} x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{5}{6} \, a^{4} b x^{6} e^{4} \mathrm{sgn}\left(b x + a\right) + 4 \, a^{4} b d x^{5} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{15}{2} \, a^{4} b d^{2} x^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{20}{3} \, a^{4} b d^{3} x^{3} e \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, a^{4} b d^{4} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{5} \, a^{5} x^{5} e^{4} \mathrm{sgn}\left(b x + a\right) + a^{5} d x^{4} e^{3} \mathrm{sgn}\left(b x + a\right) + 2 \, a^{5} d^{2} x^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + 2 \, a^{5} d^{3} x^{2} e \mathrm{sgn}\left(b x + a\right) + a^{5} d^{4} x \mathrm{sgn}\left(b x + a\right)"," ",0,"1/10*b^5*x^10*e^4*sgn(b*x + a) + 4/9*b^5*d*x^9*e^3*sgn(b*x + a) + 3/4*b^5*d^2*x^8*e^2*sgn(b*x + a) + 4/7*b^5*d^3*x^7*e*sgn(b*x + a) + 1/6*b^5*d^4*x^6*sgn(b*x + a) + 5/9*a*b^4*x^9*e^4*sgn(b*x + a) + 5/2*a*b^4*d*x^8*e^3*sgn(b*x + a) + 30/7*a*b^4*d^2*x^7*e^2*sgn(b*x + a) + 10/3*a*b^4*d^3*x^6*e*sgn(b*x + a) + a*b^4*d^4*x^5*sgn(b*x + a) + 5/4*a^2*b^3*x^8*e^4*sgn(b*x + a) + 40/7*a^2*b^3*d*x^7*e^3*sgn(b*x + a) + 10*a^2*b^3*d^2*x^6*e^2*sgn(b*x + a) + 8*a^2*b^3*d^3*x^5*e*sgn(b*x + a) + 5/2*a^2*b^3*d^4*x^4*sgn(b*x + a) + 10/7*a^3*b^2*x^7*e^4*sgn(b*x + a) + 20/3*a^3*b^2*d*x^6*e^3*sgn(b*x + a) + 12*a^3*b^2*d^2*x^5*e^2*sgn(b*x + a) + 10*a^3*b^2*d^3*x^4*e*sgn(b*x + a) + 10/3*a^3*b^2*d^4*x^3*sgn(b*x + a) + 5/6*a^4*b*x^6*e^4*sgn(b*x + a) + 4*a^4*b*d*x^5*e^3*sgn(b*x + a) + 15/2*a^4*b*d^2*x^4*e^2*sgn(b*x + a) + 20/3*a^4*b*d^3*x^3*e*sgn(b*x + a) + 5/2*a^4*b*d^4*x^2*sgn(b*x + a) + 1/5*a^5*x^5*e^4*sgn(b*x + a) + a^5*d*x^4*e^3*sgn(b*x + a) + 2*a^5*d^2*x^3*e^2*sgn(b*x + a) + 2*a^5*d^3*x^2*e*sgn(b*x + a) + a^5*d^4*x*sgn(b*x + a)","B",0
1571,1,441,0,0.181611," ","integrate((e*x+d)^3*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{9} \, b^{5} x^{9} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{3}{8} \, b^{5} d x^{8} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{3}{7} \, b^{5} d^{2} x^{7} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{6} \, b^{5} d^{3} x^{6} \mathrm{sgn}\left(b x + a\right) + \frac{5}{8} \, a b^{4} x^{8} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{15}{7} \, a b^{4} d x^{7} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, a b^{4} d^{2} x^{6} e \mathrm{sgn}\left(b x + a\right) + a b^{4} d^{3} x^{5} \mathrm{sgn}\left(b x + a\right) + \frac{10}{7} \, a^{2} b^{3} x^{7} e^{3} \mathrm{sgn}\left(b x + a\right) + 5 \, a^{2} b^{3} d x^{6} e^{2} \mathrm{sgn}\left(b x + a\right) + 6 \, a^{2} b^{3} d^{2} x^{5} e \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, a^{2} b^{3} d^{3} x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{5}{3} \, a^{3} b^{2} x^{6} e^{3} \mathrm{sgn}\left(b x + a\right) + 6 \, a^{3} b^{2} d x^{5} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{15}{2} \, a^{3} b^{2} d^{2} x^{4} e \mathrm{sgn}\left(b x + a\right) + \frac{10}{3} \, a^{3} b^{2} d^{3} x^{3} \mathrm{sgn}\left(b x + a\right) + a^{4} b x^{5} e^{3} \mathrm{sgn}\left(b x + a\right) + \frac{15}{4} \, a^{4} b d x^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 5 \, a^{4} b d^{2} x^{3} e \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, a^{4} b d^{3} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{4} \, a^{5} x^{4} e^{3} \mathrm{sgn}\left(b x + a\right) + a^{5} d x^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{3}{2} \, a^{5} d^{2} x^{2} e \mathrm{sgn}\left(b x + a\right) + a^{5} d^{3} x \mathrm{sgn}\left(b x + a\right)"," ",0,"1/9*b^5*x^9*e^3*sgn(b*x + a) + 3/8*b^5*d*x^8*e^2*sgn(b*x + a) + 3/7*b^5*d^2*x^7*e*sgn(b*x + a) + 1/6*b^5*d^3*x^6*sgn(b*x + a) + 5/8*a*b^4*x^8*e^3*sgn(b*x + a) + 15/7*a*b^4*d*x^7*e^2*sgn(b*x + a) + 5/2*a*b^4*d^2*x^6*e*sgn(b*x + a) + a*b^4*d^3*x^5*sgn(b*x + a) + 10/7*a^2*b^3*x^7*e^3*sgn(b*x + a) + 5*a^2*b^3*d*x^6*e^2*sgn(b*x + a) + 6*a^2*b^3*d^2*x^5*e*sgn(b*x + a) + 5/2*a^2*b^3*d^3*x^4*sgn(b*x + a) + 5/3*a^3*b^2*x^6*e^3*sgn(b*x + a) + 6*a^3*b^2*d*x^5*e^2*sgn(b*x + a) + 15/2*a^3*b^2*d^2*x^4*e*sgn(b*x + a) + 10/3*a^3*b^2*d^3*x^3*sgn(b*x + a) + a^4*b*x^5*e^3*sgn(b*x + a) + 15/4*a^4*b*d*x^4*e^2*sgn(b*x + a) + 5*a^4*b*d^2*x^3*e*sgn(b*x + a) + 5/2*a^4*b*d^3*x^2*sgn(b*x + a) + 1/4*a^5*x^4*e^3*sgn(b*x + a) + a^5*d*x^3*e^2*sgn(b*x + a) + 3/2*a^5*d^2*x^2*e*sgn(b*x + a) + a^5*d^3*x*sgn(b*x + a)","B",0
1572,1,320,0,0.172680," ","integrate((e*x+d)^2*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{8} \, b^{5} x^{8} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{2}{7} \, b^{5} d x^{7} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{6} \, b^{5} d^{2} x^{6} \mathrm{sgn}\left(b x + a\right) + \frac{5}{7} \, a b^{4} x^{7} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{5}{3} \, a b^{4} d x^{6} e \mathrm{sgn}\left(b x + a\right) + a b^{4} d^{2} x^{5} \mathrm{sgn}\left(b x + a\right) + \frac{5}{3} \, a^{2} b^{3} x^{6} e^{2} \mathrm{sgn}\left(b x + a\right) + 4 \, a^{2} b^{3} d x^{5} e \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, a^{2} b^{3} d^{2} x^{4} \mathrm{sgn}\left(b x + a\right) + 2 \, a^{3} b^{2} x^{5} e^{2} \mathrm{sgn}\left(b x + a\right) + 5 \, a^{3} b^{2} d x^{4} e \mathrm{sgn}\left(b x + a\right) + \frac{10}{3} \, a^{3} b^{2} d^{2} x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{5}{4} \, a^{4} b x^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + \frac{10}{3} \, a^{4} b d x^{3} e \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, a^{4} b d^{2} x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{3} \, a^{5} x^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + a^{5} d x^{2} e \mathrm{sgn}\left(b x + a\right) + a^{5} d^{2} x \mathrm{sgn}\left(b x + a\right)"," ",0,"1/8*b^5*x^8*e^2*sgn(b*x + a) + 2/7*b^5*d*x^7*e*sgn(b*x + a) + 1/6*b^5*d^2*x^6*sgn(b*x + a) + 5/7*a*b^4*x^7*e^2*sgn(b*x + a) + 5/3*a*b^4*d*x^6*e*sgn(b*x + a) + a*b^4*d^2*x^5*sgn(b*x + a) + 5/3*a^2*b^3*x^6*e^2*sgn(b*x + a) + 4*a^2*b^3*d*x^5*e*sgn(b*x + a) + 5/2*a^2*b^3*d^2*x^4*sgn(b*x + a) + 2*a^3*b^2*x^5*e^2*sgn(b*x + a) + 5*a^3*b^2*d*x^4*e*sgn(b*x + a) + 10/3*a^3*b^2*d^2*x^3*sgn(b*x + a) + 5/4*a^4*b*x^4*e^2*sgn(b*x + a) + 10/3*a^4*b*d*x^3*e*sgn(b*x + a) + 5/2*a^4*b*d^2*x^2*sgn(b*x + a) + 1/3*a^5*x^3*e^2*sgn(b*x + a) + a^5*d*x^2*e*sgn(b*x + a) + a^5*d^2*x*sgn(b*x + a)","B",0
1573,1,199,0,0.172091," ","integrate((e*x+d)*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{7} \, b^{5} x^{7} e \mathrm{sgn}\left(b x + a\right) + \frac{1}{6} \, b^{5} d x^{6} \mathrm{sgn}\left(b x + a\right) + \frac{5}{6} \, a b^{4} x^{6} e \mathrm{sgn}\left(b x + a\right) + a b^{4} d x^{5} \mathrm{sgn}\left(b x + a\right) + 2 \, a^{2} b^{3} x^{5} e \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, a^{2} b^{3} d x^{4} \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, a^{3} b^{2} x^{4} e \mathrm{sgn}\left(b x + a\right) + \frac{10}{3} \, a^{3} b^{2} d x^{3} \mathrm{sgn}\left(b x + a\right) + \frac{5}{3} \, a^{4} b x^{3} e \mathrm{sgn}\left(b x + a\right) + \frac{5}{2} \, a^{4} b d x^{2} \mathrm{sgn}\left(b x + a\right) + \frac{1}{2} \, a^{5} x^{2} e \mathrm{sgn}\left(b x + a\right) + a^{5} d x \mathrm{sgn}\left(b x + a\right)"," ",0,"1/7*b^5*x^7*e*sgn(b*x + a) + 1/6*b^5*d*x^6*sgn(b*x + a) + 5/6*a*b^4*x^6*e*sgn(b*x + a) + a*b^4*d*x^5*sgn(b*x + a) + 2*a^2*b^3*x^5*e*sgn(b*x + a) + 5/2*a^2*b^3*d*x^4*sgn(b*x + a) + 5/2*a^3*b^2*x^4*e*sgn(b*x + a) + 10/3*a^3*b^2*d*x^3*sgn(b*x + a) + 5/3*a^4*b*x^3*e*sgn(b*x + a) + 5/2*a^4*b*d*x^2*sgn(b*x + a) + 1/2*a^5*x^2*e*sgn(b*x + a) + a^5*d*x*sgn(b*x + a)","B",0
1574,1,83,0,0.224409," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{1}{2} \, {\left(b x^{2} + 2 \, a x\right)} a^{4} \mathrm{sgn}\left(b x + a\right) + \frac{a^{6} \mathrm{sgn}\left(b x + a\right)}{6 \, b} + \frac{1}{2} \, {\left(b x^{2} + 2 \, a x\right)}^{2} a^{2} b \mathrm{sgn}\left(b x + a\right) + \frac{1}{6} \, {\left(b x^{2} + 2 \, a x\right)}^{3} b^{2} \mathrm{sgn}\left(b x + a\right)"," ",0,"1/2*(b*x^2 + 2*a*x)*a^4*sgn(b*x + a) + 1/6*a^6*sgn(b*x + a)/b + 1/2*(b*x^2 + 2*a*x)^2*a^2*b*sgn(b*x + a) + 1/6*(b*x^2 + 2*a*x)^3*b^2*sgn(b*x + a)","B",0
1575,1,385,0,0.194804," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d),x, algorithm=""giac"")","-{\left(b^{5} d^{5} \mathrm{sgn}\left(b x + a\right) - 5 \, a b^{4} d^{4} e \mathrm{sgn}\left(b x + a\right) + 10 \, a^{2} b^{3} d^{3} e^{2} \mathrm{sgn}\left(b x + a\right) - 10 \, a^{3} b^{2} d^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 5 \, a^{4} b d e^{4} \mathrm{sgn}\left(b x + a\right) - a^{5} e^{5} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-6\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{60} \, {\left(12 \, b^{5} x^{5} e^{4} \mathrm{sgn}\left(b x + a\right) - 15 \, b^{5} d x^{4} e^{3} \mathrm{sgn}\left(b x + a\right) + 20 \, b^{5} d^{2} x^{3} e^{2} \mathrm{sgn}\left(b x + a\right) - 30 \, b^{5} d^{3} x^{2} e \mathrm{sgn}\left(b x + a\right) + 60 \, b^{5} d^{4} x \mathrm{sgn}\left(b x + a\right) + 75 \, a b^{4} x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) - 100 \, a b^{4} d x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 150 \, a b^{4} d^{2} x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) - 300 \, a b^{4} d^{3} x e \mathrm{sgn}\left(b x + a\right) + 200 \, a^{2} b^{3} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) - 300 \, a^{2} b^{3} d x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 600 \, a^{2} b^{3} d^{2} x e^{2} \mathrm{sgn}\left(b x + a\right) + 300 \, a^{3} b^{2} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) - 600 \, a^{3} b^{2} d x e^{3} \mathrm{sgn}\left(b x + a\right) + 300 \, a^{4} b x e^{4} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-5\right)}"," ",0,"-(b^5*d^5*sgn(b*x + a) - 5*a*b^4*d^4*e*sgn(b*x + a) + 10*a^2*b^3*d^3*e^2*sgn(b*x + a) - 10*a^3*b^2*d^2*e^3*sgn(b*x + a) + 5*a^4*b*d*e^4*sgn(b*x + a) - a^5*e^5*sgn(b*x + a))*e^(-6)*log(abs(x*e + d)) + 1/60*(12*b^5*x^5*e^4*sgn(b*x + a) - 15*b^5*d*x^4*e^3*sgn(b*x + a) + 20*b^5*d^2*x^3*e^2*sgn(b*x + a) - 30*b^5*d^3*x^2*e*sgn(b*x + a) + 60*b^5*d^4*x*sgn(b*x + a) + 75*a*b^4*x^4*e^4*sgn(b*x + a) - 100*a*b^4*d*x^3*e^3*sgn(b*x + a) + 150*a*b^4*d^2*x^2*e^2*sgn(b*x + a) - 300*a*b^4*d^3*x*e*sgn(b*x + a) + 200*a^2*b^3*x^3*e^4*sgn(b*x + a) - 300*a^2*b^3*d*x^2*e^3*sgn(b*x + a) + 600*a^2*b^3*d^2*x*e^2*sgn(b*x + a) + 300*a^3*b^2*x^2*e^4*sgn(b*x + a) - 600*a^3*b^2*d*x*e^3*sgn(b*x + a) + 300*a^4*b*x*e^4*sgn(b*x + a))*e^(-5)","B",0
1576,1,382,0,0.195940," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^2,x, algorithm=""giac"")","5 \, {\left(b^{5} d^{4} \mathrm{sgn}\left(b x + a\right) - 4 \, a b^{4} d^{3} e \mathrm{sgn}\left(b x + a\right) + 6 \, a^{2} b^{3} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) - 4 \, a^{3} b^{2} d e^{3} \mathrm{sgn}\left(b x + a\right) + a^{4} b e^{4} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-6\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{12} \, {\left(3 \, b^{5} x^{4} e^{6} \mathrm{sgn}\left(b x + a\right) - 8 \, b^{5} d x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) + 18 \, b^{5} d^{2} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) - 48 \, b^{5} d^{3} x e^{3} \mathrm{sgn}\left(b x + a\right) + 20 \, a b^{4} x^{3} e^{6} \mathrm{sgn}\left(b x + a\right) - 60 \, a b^{4} d x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) + 180 \, a b^{4} d^{2} x e^{4} \mathrm{sgn}\left(b x + a\right) + 60 \, a^{2} b^{3} x^{2} e^{6} \mathrm{sgn}\left(b x + a\right) - 240 \, a^{2} b^{3} d x e^{5} \mathrm{sgn}\left(b x + a\right) + 120 \, a^{3} b^{2} x e^{6} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-8\right)} + \frac{{\left(b^{5} d^{5} \mathrm{sgn}\left(b x + a\right) - 5 \, a b^{4} d^{4} e \mathrm{sgn}\left(b x + a\right) + 10 \, a^{2} b^{3} d^{3} e^{2} \mathrm{sgn}\left(b x + a\right) - 10 \, a^{3} b^{2} d^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 5 \, a^{4} b d e^{4} \mathrm{sgn}\left(b x + a\right) - a^{5} e^{5} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-6\right)}}{x e + d}"," ",0,"5*(b^5*d^4*sgn(b*x + a) - 4*a*b^4*d^3*e*sgn(b*x + a) + 6*a^2*b^3*d^2*e^2*sgn(b*x + a) - 4*a^3*b^2*d*e^3*sgn(b*x + a) + a^4*b*e^4*sgn(b*x + a))*e^(-6)*log(abs(x*e + d)) + 1/12*(3*b^5*x^4*e^6*sgn(b*x + a) - 8*b^5*d*x^3*e^5*sgn(b*x + a) + 18*b^5*d^2*x^2*e^4*sgn(b*x + a) - 48*b^5*d^3*x*e^3*sgn(b*x + a) + 20*a*b^4*x^3*e^6*sgn(b*x + a) - 60*a*b^4*d*x^2*e^5*sgn(b*x + a) + 180*a*b^4*d^2*x*e^4*sgn(b*x + a) + 60*a^2*b^3*x^2*e^6*sgn(b*x + a) - 240*a^2*b^3*d*x*e^5*sgn(b*x + a) + 120*a^3*b^2*x*e^6*sgn(b*x + a))*e^(-8) + (b^5*d^5*sgn(b*x + a) - 5*a*b^4*d^4*e*sgn(b*x + a) + 10*a^2*b^3*d^3*e^2*sgn(b*x + a) - 10*a^3*b^2*d^2*e^3*sgn(b*x + a) + 5*a^4*b*d*e^4*sgn(b*x + a) - a^5*e^5*sgn(b*x + a))*e^(-6)/(x*e + d)","A",0
1577,1,376,0,0.184598," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^3,x, algorithm=""giac"")","-10 \, {\left(b^{5} d^{3} \mathrm{sgn}\left(b x + a\right) - 3 \, a b^{4} d^{2} e \mathrm{sgn}\left(b x + a\right) + 3 \, a^{2} b^{3} d e^{2} \mathrm{sgn}\left(b x + a\right) - a^{3} b^{2} e^{3} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-6\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{6} \, {\left(2 \, b^{5} x^{3} e^{6} \mathrm{sgn}\left(b x + a\right) - 9 \, b^{5} d x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) + 36 \, b^{5} d^{2} x e^{4} \mathrm{sgn}\left(b x + a\right) + 15 \, a b^{4} x^{2} e^{6} \mathrm{sgn}\left(b x + a\right) - 90 \, a b^{4} d x e^{5} \mathrm{sgn}\left(b x + a\right) + 60 \, a^{2} b^{3} x e^{6} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-9\right)} - \frac{{\left(9 \, b^{5} d^{5} \mathrm{sgn}\left(b x + a\right) - 35 \, a b^{4} d^{4} e \mathrm{sgn}\left(b x + a\right) + 50 \, a^{2} b^{3} d^{3} e^{2} \mathrm{sgn}\left(b x + a\right) - 30 \, a^{3} b^{2} d^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 5 \, a^{4} b d e^{4} \mathrm{sgn}\left(b x + a\right) + a^{5} e^{5} \mathrm{sgn}\left(b x + a\right) + 10 \, {\left(b^{5} d^{4} e \mathrm{sgn}\left(b x + a\right) - 4 \, a b^{4} d^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + 6 \, a^{2} b^{3} d^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - 4 \, a^{3} b^{2} d e^{4} \mathrm{sgn}\left(b x + a\right) + a^{4} b e^{5} \mathrm{sgn}\left(b x + a\right)\right)} x\right)} e^{\left(-6\right)}}{2 \, {\left(x e + d\right)}^{2}}"," ",0,"-10*(b^5*d^3*sgn(b*x + a) - 3*a*b^4*d^2*e*sgn(b*x + a) + 3*a^2*b^3*d*e^2*sgn(b*x + a) - a^3*b^2*e^3*sgn(b*x + a))*e^(-6)*log(abs(x*e + d)) + 1/6*(2*b^5*x^3*e^6*sgn(b*x + a) - 9*b^5*d*x^2*e^5*sgn(b*x + a) + 36*b^5*d^2*x*e^4*sgn(b*x + a) + 15*a*b^4*x^2*e^6*sgn(b*x + a) - 90*a*b^4*d*x*e^5*sgn(b*x + a) + 60*a^2*b^3*x*e^6*sgn(b*x + a))*e^(-9) - 1/2*(9*b^5*d^5*sgn(b*x + a) - 35*a*b^4*d^4*e*sgn(b*x + a) + 50*a^2*b^3*d^3*e^2*sgn(b*x + a) - 30*a^3*b^2*d^2*e^3*sgn(b*x + a) + 5*a^4*b*d*e^4*sgn(b*x + a) + a^5*e^5*sgn(b*x + a) + 10*(b^5*d^4*e*sgn(b*x + a) - 4*a*b^4*d^3*e^2*sgn(b*x + a) + 6*a^2*b^3*d^2*e^3*sgn(b*x + a) - 4*a^3*b^2*d*e^4*sgn(b*x + a) + a^4*b*e^5*sgn(b*x + a))*x)*e^(-6)/(x*e + d)^2","A",0
1578,1,375,0,0.185047," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^4,x, algorithm=""giac"")","10 \, {\left(b^{5} d^{2} \mathrm{sgn}\left(b x + a\right) - 2 \, a b^{4} d e \mathrm{sgn}\left(b x + a\right) + a^{2} b^{3} e^{2} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-6\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{2} \, {\left(b^{5} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) - 8 \, b^{5} d x e^{3} \mathrm{sgn}\left(b x + a\right) + 10 \, a b^{4} x e^{4} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-8\right)} + \frac{{\left(47 \, b^{5} d^{5} \mathrm{sgn}\left(b x + a\right) - 130 \, a b^{4} d^{4} e \mathrm{sgn}\left(b x + a\right) + 110 \, a^{2} b^{3} d^{3} e^{2} \mathrm{sgn}\left(b x + a\right) - 20 \, a^{3} b^{2} d^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - 5 \, a^{4} b d e^{4} \mathrm{sgn}\left(b x + a\right) - 2 \, a^{5} e^{5} \mathrm{sgn}\left(b x + a\right) + 60 \, {\left(b^{5} d^{3} e^{2} \mathrm{sgn}\left(b x + a\right) - 3 \, a b^{4} d^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 3 \, a^{2} b^{3} d e^{4} \mathrm{sgn}\left(b x + a\right) - a^{3} b^{2} e^{5} \mathrm{sgn}\left(b x + a\right)\right)} x^{2} + 15 \, {\left(7 \, b^{5} d^{4} e \mathrm{sgn}\left(b x + a\right) - 20 \, a b^{4} d^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + 18 \, a^{2} b^{3} d^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - 4 \, a^{3} b^{2} d e^{4} \mathrm{sgn}\left(b x + a\right) - a^{4} b e^{5} \mathrm{sgn}\left(b x + a\right)\right)} x\right)} e^{\left(-6\right)}}{6 \, {\left(x e + d\right)}^{3}}"," ",0,"10*(b^5*d^2*sgn(b*x + a) - 2*a*b^4*d*e*sgn(b*x + a) + a^2*b^3*e^2*sgn(b*x + a))*e^(-6)*log(abs(x*e + d)) + 1/2*(b^5*x^2*e^4*sgn(b*x + a) - 8*b^5*d*x*e^3*sgn(b*x + a) + 10*a*b^4*x*e^4*sgn(b*x + a))*e^(-8) + 1/6*(47*b^5*d^5*sgn(b*x + a) - 130*a*b^4*d^4*e*sgn(b*x + a) + 110*a^2*b^3*d^3*e^2*sgn(b*x + a) - 20*a^3*b^2*d^2*e^3*sgn(b*x + a) - 5*a^4*b*d*e^4*sgn(b*x + a) - 2*a^5*e^5*sgn(b*x + a) + 60*(b^5*d^3*e^2*sgn(b*x + a) - 3*a*b^4*d^2*e^3*sgn(b*x + a) + 3*a^2*b^3*d*e^4*sgn(b*x + a) - a^3*b^2*e^5*sgn(b*x + a))*x^2 + 15*(7*b^5*d^4*e*sgn(b*x + a) - 20*a*b^4*d^3*e^2*sgn(b*x + a) + 18*a^2*b^3*d^2*e^3*sgn(b*x + a) - 4*a^3*b^2*d*e^4*sgn(b*x + a) - a^4*b*e^5*sgn(b*x + a))*x)*e^(-6)/(x*e + d)^3","A",0
1579,1,370,0,0.189135," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^5,x, algorithm=""giac"")","b^{5} x e^{\left(-5\right)} \mathrm{sgn}\left(b x + a\right) - 5 \, {\left(b^{5} d \mathrm{sgn}\left(b x + a\right) - a b^{4} e \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-6\right)} \log\left({\left| x e + d \right|}\right) - \frac{{\left(77 \, b^{5} d^{5} \mathrm{sgn}\left(b x + a\right) - 125 \, a b^{4} d^{4} e \mathrm{sgn}\left(b x + a\right) + 30 \, a^{2} b^{3} d^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + 10 \, a^{3} b^{2} d^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 5 \, a^{4} b d e^{4} \mathrm{sgn}\left(b x + a\right) + 3 \, a^{5} e^{5} \mathrm{sgn}\left(b x + a\right) + 120 \, {\left(b^{5} d^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - 2 \, a b^{4} d e^{4} \mathrm{sgn}\left(b x + a\right) + a^{2} b^{3} e^{5} \mathrm{sgn}\left(b x + a\right)\right)} x^{3} + 60 \, {\left(5 \, b^{5} d^{3} e^{2} \mathrm{sgn}\left(b x + a\right) - 9 \, a b^{4} d^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 3 \, a^{2} b^{3} d e^{4} \mathrm{sgn}\left(b x + a\right) + a^{3} b^{2} e^{5} \mathrm{sgn}\left(b x + a\right)\right)} x^{2} + 20 \, {\left(13 \, b^{5} d^{4} e \mathrm{sgn}\left(b x + a\right) - 22 \, a b^{4} d^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + 6 \, a^{2} b^{3} d^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 2 \, a^{3} b^{2} d e^{4} \mathrm{sgn}\left(b x + a\right) + a^{4} b e^{5} \mathrm{sgn}\left(b x + a\right)\right)} x\right)} e^{\left(-6\right)}}{12 \, {\left(x e + d\right)}^{4}}"," ",0,"b^5*x*e^(-5)*sgn(b*x + a) - 5*(b^5*d*sgn(b*x + a) - a*b^4*e*sgn(b*x + a))*e^(-6)*log(abs(x*e + d)) - 1/12*(77*b^5*d^5*sgn(b*x + a) - 125*a*b^4*d^4*e*sgn(b*x + a) + 30*a^2*b^3*d^3*e^2*sgn(b*x + a) + 10*a^3*b^2*d^2*e^3*sgn(b*x + a) + 5*a^4*b*d*e^4*sgn(b*x + a) + 3*a^5*e^5*sgn(b*x + a) + 120*(b^5*d^2*e^3*sgn(b*x + a) - 2*a*b^4*d*e^4*sgn(b*x + a) + a^2*b^3*e^5*sgn(b*x + a))*x^3 + 60*(5*b^5*d^3*e^2*sgn(b*x + a) - 9*a*b^4*d^2*e^3*sgn(b*x + a) + 3*a^2*b^3*d*e^4*sgn(b*x + a) + a^3*b^2*e^5*sgn(b*x + a))*x^2 + 20*(13*b^5*d^4*e*sgn(b*x + a) - 22*a*b^4*d^3*e^2*sgn(b*x + a) + 6*a^2*b^3*d^2*e^3*sgn(b*x + a) + 2*a^3*b^2*d*e^4*sgn(b*x + a) + a^4*b*e^5*sgn(b*x + a))*x)*e^(-6)/(x*e + d)^4","A",0
1580,1,378,0,0.218094," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^6,x, algorithm=""giac"")","b^{5} e^{\left(-6\right)} \log\left({\left| x e + d \right|}\right) \mathrm{sgn}\left(b x + a\right) + \frac{{\left(300 \, {\left(b^{5} d e^{3} \mathrm{sgn}\left(b x + a\right) - a b^{4} e^{4} \mathrm{sgn}\left(b x + a\right)\right)} x^{4} + 300 \, {\left(3 \, b^{5} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) - 2 \, a b^{4} d e^{3} \mathrm{sgn}\left(b x + a\right) - a^{2} b^{3} e^{4} \mathrm{sgn}\left(b x + a\right)\right)} x^{3} + 100 \, {\left(11 \, b^{5} d^{3} e \mathrm{sgn}\left(b x + a\right) - 6 \, a b^{4} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) - 3 \, a^{2} b^{3} d e^{3} \mathrm{sgn}\left(b x + a\right) - 2 \, a^{3} b^{2} e^{4} \mathrm{sgn}\left(b x + a\right)\right)} x^{2} + 25 \, {\left(25 \, b^{5} d^{4} \mathrm{sgn}\left(b x + a\right) - 12 \, a b^{4} d^{3} e \mathrm{sgn}\left(b x + a\right) - 6 \, a^{2} b^{3} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) - 4 \, a^{3} b^{2} d e^{3} \mathrm{sgn}\left(b x + a\right) - 3 \, a^{4} b e^{4} \mathrm{sgn}\left(b x + a\right)\right)} x + {\left(137 \, b^{5} d^{5} \mathrm{sgn}\left(b x + a\right) - 60 \, a b^{4} d^{4} e \mathrm{sgn}\left(b x + a\right) - 30 \, a^{2} b^{3} d^{3} e^{2} \mathrm{sgn}\left(b x + a\right) - 20 \, a^{3} b^{2} d^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - 15 \, a^{4} b d e^{4} \mathrm{sgn}\left(b x + a\right) - 12 \, a^{5} e^{5} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-1\right)}\right)} e^{\left(-5\right)}}{60 \, {\left(x e + d\right)}^{5}}"," ",0,"b^5*e^(-6)*log(abs(x*e + d))*sgn(b*x + a) + 1/60*(300*(b^5*d*e^3*sgn(b*x + a) - a*b^4*e^4*sgn(b*x + a))*x^4 + 300*(3*b^5*d^2*e^2*sgn(b*x + a) - 2*a*b^4*d*e^3*sgn(b*x + a) - a^2*b^3*e^4*sgn(b*x + a))*x^3 + 100*(11*b^5*d^3*e*sgn(b*x + a) - 6*a*b^4*d^2*e^2*sgn(b*x + a) - 3*a^2*b^3*d*e^3*sgn(b*x + a) - 2*a^3*b^2*e^4*sgn(b*x + a))*x^2 + 25*(25*b^5*d^4*sgn(b*x + a) - 12*a*b^4*d^3*e*sgn(b*x + a) - 6*a^2*b^3*d^2*e^2*sgn(b*x + a) - 4*a^3*b^2*d*e^3*sgn(b*x + a) - 3*a^4*b*e^4*sgn(b*x + a))*x + (137*b^5*d^5*sgn(b*x + a) - 60*a*b^4*d^4*e*sgn(b*x + a) - 30*a^2*b^3*d^3*e^2*sgn(b*x + a) - 20*a^3*b^2*d^2*e^3*sgn(b*x + a) - 15*a^4*b*d*e^4*sgn(b*x + a) - 12*a^5*e^5*sgn(b*x + a))*e^(-1))*e^(-5)/(x*e + d)^5","A",0
1581,1,376,0,0.210101," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^7,x, algorithm=""giac"")","-\frac{{\left(6 \, b^{5} x^{5} e^{5} \mathrm{sgn}\left(b x + a\right) + 15 \, b^{5} d x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) + 20 \, b^{5} d^{2} x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 15 \, b^{5} d^{3} x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 6 \, b^{5} d^{4} x e \mathrm{sgn}\left(b x + a\right) + b^{5} d^{5} \mathrm{sgn}\left(b x + a\right) + 15 \, a b^{4} x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) + 20 \, a b^{4} d x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 15 \, a b^{4} d^{2} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 6 \, a b^{4} d^{3} x e^{2} \mathrm{sgn}\left(b x + a\right) + a b^{4} d^{4} e \mathrm{sgn}\left(b x + a\right) + 20 \, a^{2} b^{3} x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) + 15 \, a^{2} b^{3} d x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 6 \, a^{2} b^{3} d^{2} x e^{3} \mathrm{sgn}\left(b x + a\right) + a^{2} b^{3} d^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + 15 \, a^{3} b^{2} x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) + 6 \, a^{3} b^{2} d x e^{4} \mathrm{sgn}\left(b x + a\right) + a^{3} b^{2} d^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 6 \, a^{4} b x e^{5} \mathrm{sgn}\left(b x + a\right) + a^{4} b d e^{4} \mathrm{sgn}\left(b x + a\right) + a^{5} e^{5} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-6\right)}}{6 \, {\left(x e + d\right)}^{6}}"," ",0,"-1/6*(6*b^5*x^5*e^5*sgn(b*x + a) + 15*b^5*d*x^4*e^4*sgn(b*x + a) + 20*b^5*d^2*x^3*e^3*sgn(b*x + a) + 15*b^5*d^3*x^2*e^2*sgn(b*x + a) + 6*b^5*d^4*x*e*sgn(b*x + a) + b^5*d^5*sgn(b*x + a) + 15*a*b^4*x^4*e^5*sgn(b*x + a) + 20*a*b^4*d*x^3*e^4*sgn(b*x + a) + 15*a*b^4*d^2*x^2*e^3*sgn(b*x + a) + 6*a*b^4*d^3*x*e^2*sgn(b*x + a) + a*b^4*d^4*e*sgn(b*x + a) + 20*a^2*b^3*x^3*e^5*sgn(b*x + a) + 15*a^2*b^3*d*x^2*e^4*sgn(b*x + a) + 6*a^2*b^3*d^2*x*e^3*sgn(b*x + a) + a^2*b^3*d^3*e^2*sgn(b*x + a) + 15*a^3*b^2*x^2*e^5*sgn(b*x + a) + 6*a^3*b^2*d*x*e^4*sgn(b*x + a) + a^3*b^2*d^2*e^3*sgn(b*x + a) + 6*a^4*b*x*e^5*sgn(b*x + a) + a^4*b*d*e^4*sgn(b*x + a) + a^5*e^5*sgn(b*x + a))*e^(-6)/(x*e + d)^6","B",0
1582,1,381,0,0.181239," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^8,x, algorithm=""giac"")","-\frac{{\left(21 \, b^{5} x^{5} e^{5} \mathrm{sgn}\left(b x + a\right) + 35 \, b^{5} d x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) + 35 \, b^{5} d^{2} x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 21 \, b^{5} d^{3} x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 7 \, b^{5} d^{4} x e \mathrm{sgn}\left(b x + a\right) + b^{5} d^{5} \mathrm{sgn}\left(b x + a\right) + 70 \, a b^{4} x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) + 70 \, a b^{4} d x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 42 \, a b^{4} d^{2} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 14 \, a b^{4} d^{3} x e^{2} \mathrm{sgn}\left(b x + a\right) + 2 \, a b^{4} d^{4} e \mathrm{sgn}\left(b x + a\right) + 105 \, a^{2} b^{3} x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) + 63 \, a^{2} b^{3} d x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 21 \, a^{2} b^{3} d^{2} x e^{3} \mathrm{sgn}\left(b x + a\right) + 3 \, a^{2} b^{3} d^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + 84 \, a^{3} b^{2} x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) + 28 \, a^{3} b^{2} d x e^{4} \mathrm{sgn}\left(b x + a\right) + 4 \, a^{3} b^{2} d^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 35 \, a^{4} b x e^{5} \mathrm{sgn}\left(b x + a\right) + 5 \, a^{4} b d e^{4} \mathrm{sgn}\left(b x + a\right) + 6 \, a^{5} e^{5} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-6\right)}}{42 \, {\left(x e + d\right)}^{7}}"," ",0,"-1/42*(21*b^5*x^5*e^5*sgn(b*x + a) + 35*b^5*d*x^4*e^4*sgn(b*x + a) + 35*b^5*d^2*x^3*e^3*sgn(b*x + a) + 21*b^5*d^3*x^2*e^2*sgn(b*x + a) + 7*b^5*d^4*x*e*sgn(b*x + a) + b^5*d^5*sgn(b*x + a) + 70*a*b^4*x^4*e^5*sgn(b*x + a) + 70*a*b^4*d*x^3*e^4*sgn(b*x + a) + 42*a*b^4*d^2*x^2*e^3*sgn(b*x + a) + 14*a*b^4*d^3*x*e^2*sgn(b*x + a) + 2*a*b^4*d^4*e*sgn(b*x + a) + 105*a^2*b^3*x^3*e^5*sgn(b*x + a) + 63*a^2*b^3*d*x^2*e^4*sgn(b*x + a) + 21*a^2*b^3*d^2*x*e^3*sgn(b*x + a) + 3*a^2*b^3*d^3*e^2*sgn(b*x + a) + 84*a^3*b^2*x^2*e^5*sgn(b*x + a) + 28*a^3*b^2*d*x*e^4*sgn(b*x + a) + 4*a^3*b^2*d^2*e^3*sgn(b*x + a) + 35*a^4*b*x*e^5*sgn(b*x + a) + 5*a^4*b*d*e^4*sgn(b*x + a) + 6*a^5*e^5*sgn(b*x + a))*e^(-6)/(x*e + d)^7","B",0
1583,1,381,0,0.187281," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^9,x, algorithm=""giac"")","-\frac{{\left(56 \, b^{5} x^{5} e^{5} \mathrm{sgn}\left(b x + a\right) + 70 \, b^{5} d x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) + 56 \, b^{5} d^{2} x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 28 \, b^{5} d^{3} x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 8 \, b^{5} d^{4} x e \mathrm{sgn}\left(b x + a\right) + b^{5} d^{5} \mathrm{sgn}\left(b x + a\right) + 210 \, a b^{4} x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) + 168 \, a b^{4} d x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 84 \, a b^{4} d^{2} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 24 \, a b^{4} d^{3} x e^{2} \mathrm{sgn}\left(b x + a\right) + 3 \, a b^{4} d^{4} e \mathrm{sgn}\left(b x + a\right) + 336 \, a^{2} b^{3} x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) + 168 \, a^{2} b^{3} d x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 48 \, a^{2} b^{3} d^{2} x e^{3} \mathrm{sgn}\left(b x + a\right) + 6 \, a^{2} b^{3} d^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + 280 \, a^{3} b^{2} x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) + 80 \, a^{3} b^{2} d x e^{4} \mathrm{sgn}\left(b x + a\right) + 10 \, a^{3} b^{2} d^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 120 \, a^{4} b x e^{5} \mathrm{sgn}\left(b x + a\right) + 15 \, a^{4} b d e^{4} \mathrm{sgn}\left(b x + a\right) + 21 \, a^{5} e^{5} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-6\right)}}{168 \, {\left(x e + d\right)}^{8}}"," ",0,"-1/168*(56*b^5*x^5*e^5*sgn(b*x + a) + 70*b^5*d*x^4*e^4*sgn(b*x + a) + 56*b^5*d^2*x^3*e^3*sgn(b*x + a) + 28*b^5*d^3*x^2*e^2*sgn(b*x + a) + 8*b^5*d^4*x*e*sgn(b*x + a) + b^5*d^5*sgn(b*x + a) + 210*a*b^4*x^4*e^5*sgn(b*x + a) + 168*a*b^4*d*x^3*e^4*sgn(b*x + a) + 84*a*b^4*d^2*x^2*e^3*sgn(b*x + a) + 24*a*b^4*d^3*x*e^2*sgn(b*x + a) + 3*a*b^4*d^4*e*sgn(b*x + a) + 336*a^2*b^3*x^3*e^5*sgn(b*x + a) + 168*a^2*b^3*d*x^2*e^4*sgn(b*x + a) + 48*a^2*b^3*d^2*x*e^3*sgn(b*x + a) + 6*a^2*b^3*d^3*e^2*sgn(b*x + a) + 280*a^3*b^2*x^2*e^5*sgn(b*x + a) + 80*a^3*b^2*d*x*e^4*sgn(b*x + a) + 10*a^3*b^2*d^2*e^3*sgn(b*x + a) + 120*a^4*b*x*e^5*sgn(b*x + a) + 15*a^4*b*d*e^4*sgn(b*x + a) + 21*a^5*e^5*sgn(b*x + a))*e^(-6)/(x*e + d)^8","B",0
1584,1,381,0,0.183293," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^10,x, algorithm=""giac"")","-\frac{{\left(126 \, b^{5} x^{5} e^{5} \mathrm{sgn}\left(b x + a\right) + 126 \, b^{5} d x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) + 84 \, b^{5} d^{2} x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 36 \, b^{5} d^{3} x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 9 \, b^{5} d^{4} x e \mathrm{sgn}\left(b x + a\right) + b^{5} d^{5} \mathrm{sgn}\left(b x + a\right) + 504 \, a b^{4} x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) + 336 \, a b^{4} d x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 144 \, a b^{4} d^{2} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 36 \, a b^{4} d^{3} x e^{2} \mathrm{sgn}\left(b x + a\right) + 4 \, a b^{4} d^{4} e \mathrm{sgn}\left(b x + a\right) + 840 \, a^{2} b^{3} x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) + 360 \, a^{2} b^{3} d x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 90 \, a^{2} b^{3} d^{2} x e^{3} \mathrm{sgn}\left(b x + a\right) + 10 \, a^{2} b^{3} d^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + 720 \, a^{3} b^{2} x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) + 180 \, a^{3} b^{2} d x e^{4} \mathrm{sgn}\left(b x + a\right) + 20 \, a^{3} b^{2} d^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 315 \, a^{4} b x e^{5} \mathrm{sgn}\left(b x + a\right) + 35 \, a^{4} b d e^{4} \mathrm{sgn}\left(b x + a\right) + 56 \, a^{5} e^{5} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-6\right)}}{504 \, {\left(x e + d\right)}^{9}}"," ",0,"-1/504*(126*b^5*x^5*e^5*sgn(b*x + a) + 126*b^5*d*x^4*e^4*sgn(b*x + a) + 84*b^5*d^2*x^3*e^3*sgn(b*x + a) + 36*b^5*d^3*x^2*e^2*sgn(b*x + a) + 9*b^5*d^4*x*e*sgn(b*x + a) + b^5*d^5*sgn(b*x + a) + 504*a*b^4*x^4*e^5*sgn(b*x + a) + 336*a*b^4*d*x^3*e^4*sgn(b*x + a) + 144*a*b^4*d^2*x^2*e^3*sgn(b*x + a) + 36*a*b^4*d^3*x*e^2*sgn(b*x + a) + 4*a*b^4*d^4*e*sgn(b*x + a) + 840*a^2*b^3*x^3*e^5*sgn(b*x + a) + 360*a^2*b^3*d*x^2*e^4*sgn(b*x + a) + 90*a^2*b^3*d^2*x*e^3*sgn(b*x + a) + 10*a^2*b^3*d^3*e^2*sgn(b*x + a) + 720*a^3*b^2*x^2*e^5*sgn(b*x + a) + 180*a^3*b^2*d*x*e^4*sgn(b*x + a) + 20*a^3*b^2*d^2*e^3*sgn(b*x + a) + 315*a^4*b*x*e^5*sgn(b*x + a) + 35*a^4*b*d*e^4*sgn(b*x + a) + 56*a^5*e^5*sgn(b*x + a))*e^(-6)/(x*e + d)^9","B",0
1585,1,381,0,0.182131," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^11,x, algorithm=""giac"")","-\frac{{\left(252 \, b^{5} x^{5} e^{5} \mathrm{sgn}\left(b x + a\right) + 210 \, b^{5} d x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) + 120 \, b^{5} d^{2} x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 45 \, b^{5} d^{3} x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 10 \, b^{5} d^{4} x e \mathrm{sgn}\left(b x + a\right) + b^{5} d^{5} \mathrm{sgn}\left(b x + a\right) + 1050 \, a b^{4} x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) + 600 \, a b^{4} d x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 225 \, a b^{4} d^{2} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 50 \, a b^{4} d^{3} x e^{2} \mathrm{sgn}\left(b x + a\right) + 5 \, a b^{4} d^{4} e \mathrm{sgn}\left(b x + a\right) + 1800 \, a^{2} b^{3} x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) + 675 \, a^{2} b^{3} d x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 150 \, a^{2} b^{3} d^{2} x e^{3} \mathrm{sgn}\left(b x + a\right) + 15 \, a^{2} b^{3} d^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + 1575 \, a^{3} b^{2} x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) + 350 \, a^{3} b^{2} d x e^{4} \mathrm{sgn}\left(b x + a\right) + 35 \, a^{3} b^{2} d^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 700 \, a^{4} b x e^{5} \mathrm{sgn}\left(b x + a\right) + 70 \, a^{4} b d e^{4} \mathrm{sgn}\left(b x + a\right) + 126 \, a^{5} e^{5} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-6\right)}}{1260 \, {\left(x e + d\right)}^{10}}"," ",0,"-1/1260*(252*b^5*x^5*e^5*sgn(b*x + a) + 210*b^5*d*x^4*e^4*sgn(b*x + a) + 120*b^5*d^2*x^3*e^3*sgn(b*x + a) + 45*b^5*d^3*x^2*e^2*sgn(b*x + a) + 10*b^5*d^4*x*e*sgn(b*x + a) + b^5*d^5*sgn(b*x + a) + 1050*a*b^4*x^4*e^5*sgn(b*x + a) + 600*a*b^4*d*x^3*e^4*sgn(b*x + a) + 225*a*b^4*d^2*x^2*e^3*sgn(b*x + a) + 50*a*b^4*d^3*x*e^2*sgn(b*x + a) + 5*a*b^4*d^4*e*sgn(b*x + a) + 1800*a^2*b^3*x^3*e^5*sgn(b*x + a) + 675*a^2*b^3*d*x^2*e^4*sgn(b*x + a) + 150*a^2*b^3*d^2*x*e^3*sgn(b*x + a) + 15*a^2*b^3*d^3*e^2*sgn(b*x + a) + 1575*a^3*b^2*x^2*e^5*sgn(b*x + a) + 350*a^3*b^2*d*x*e^4*sgn(b*x + a) + 35*a^3*b^2*d^2*e^3*sgn(b*x + a) + 700*a^4*b*x*e^5*sgn(b*x + a) + 70*a^4*b*d*e^4*sgn(b*x + a) + 126*a^5*e^5*sgn(b*x + a))*e^(-6)/(x*e + d)^10","A",0
1586,1,381,0,0.190402," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^12,x, algorithm=""giac"")","-\frac{{\left(462 \, b^{5} x^{5} e^{5} \mathrm{sgn}\left(b x + a\right) + 330 \, b^{5} d x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) + 165 \, b^{5} d^{2} x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 55 \, b^{5} d^{3} x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 11 \, b^{5} d^{4} x e \mathrm{sgn}\left(b x + a\right) + b^{5} d^{5} \mathrm{sgn}\left(b x + a\right) + 1980 \, a b^{4} x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) + 990 \, a b^{4} d x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 330 \, a b^{4} d^{2} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 66 \, a b^{4} d^{3} x e^{2} \mathrm{sgn}\left(b x + a\right) + 6 \, a b^{4} d^{4} e \mathrm{sgn}\left(b x + a\right) + 3465 \, a^{2} b^{3} x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) + 1155 \, a^{2} b^{3} d x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 231 \, a^{2} b^{3} d^{2} x e^{3} \mathrm{sgn}\left(b x + a\right) + 21 \, a^{2} b^{3} d^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + 3080 \, a^{3} b^{2} x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) + 616 \, a^{3} b^{2} d x e^{4} \mathrm{sgn}\left(b x + a\right) + 56 \, a^{3} b^{2} d^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 1386 \, a^{4} b x e^{5} \mathrm{sgn}\left(b x + a\right) + 126 \, a^{4} b d e^{4} \mathrm{sgn}\left(b x + a\right) + 252 \, a^{5} e^{5} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-6\right)}}{2772 \, {\left(x e + d\right)}^{11}}"," ",0,"-1/2772*(462*b^5*x^5*e^5*sgn(b*x + a) + 330*b^5*d*x^4*e^4*sgn(b*x + a) + 165*b^5*d^2*x^3*e^3*sgn(b*x + a) + 55*b^5*d^3*x^2*e^2*sgn(b*x + a) + 11*b^5*d^4*x*e*sgn(b*x + a) + b^5*d^5*sgn(b*x + a) + 1980*a*b^4*x^4*e^5*sgn(b*x + a) + 990*a*b^4*d*x^3*e^4*sgn(b*x + a) + 330*a*b^4*d^2*x^2*e^3*sgn(b*x + a) + 66*a*b^4*d^3*x*e^2*sgn(b*x + a) + 6*a*b^4*d^4*e*sgn(b*x + a) + 3465*a^2*b^3*x^3*e^5*sgn(b*x + a) + 1155*a^2*b^3*d*x^2*e^4*sgn(b*x + a) + 231*a^2*b^3*d^2*x*e^3*sgn(b*x + a) + 21*a^2*b^3*d^3*e^2*sgn(b*x + a) + 3080*a^3*b^2*x^2*e^5*sgn(b*x + a) + 616*a^3*b^2*d*x*e^4*sgn(b*x + a) + 56*a^3*b^2*d^2*e^3*sgn(b*x + a) + 1386*a^4*b*x*e^5*sgn(b*x + a) + 126*a^4*b*d*e^4*sgn(b*x + a) + 252*a^5*e^5*sgn(b*x + a))*e^(-6)/(x*e + d)^11","A",0
1587,1,264,0,0.181184," ","integrate((e*x+d)^4/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{3 \, b^{3} x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) + 16 \, b^{3} d x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 36 \, b^{3} d^{2} x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 48 \, b^{3} d^{3} x e \mathrm{sgn}\left(b x + a\right) - 4 \, a b^{2} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) - 24 \, a b^{2} d x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - 72 \, a b^{2} d^{2} x e^{2} \mathrm{sgn}\left(b x + a\right) + 6 \, a^{2} b x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 48 \, a^{2} b d x e^{3} \mathrm{sgn}\left(b x + a\right) - 12 \, a^{3} x e^{4} \mathrm{sgn}\left(b x + a\right)}{12 \, b^{4}} + \frac{{\left(b^{4} d^{4} \mathrm{sgn}\left(b x + a\right) - 4 \, a b^{3} d^{3} e \mathrm{sgn}\left(b x + a\right) + 6 \, a^{2} b^{2} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) - 4 \, a^{3} b d e^{3} \mathrm{sgn}\left(b x + a\right) + a^{4} e^{4} \mathrm{sgn}\left(b x + a\right)\right)} \log\left({\left| b x + a \right|}\right)}{b^{5}}"," ",0,"1/12*(3*b^3*x^4*e^4*sgn(b*x + a) + 16*b^3*d*x^3*e^3*sgn(b*x + a) + 36*b^3*d^2*x^2*e^2*sgn(b*x + a) + 48*b^3*d^3*x*e*sgn(b*x + a) - 4*a*b^2*x^3*e^4*sgn(b*x + a) - 24*a*b^2*d*x^2*e^3*sgn(b*x + a) - 72*a*b^2*d^2*x*e^2*sgn(b*x + a) + 6*a^2*b*x^2*e^4*sgn(b*x + a) + 48*a^2*b*d*x*e^3*sgn(b*x + a) - 12*a^3*x*e^4*sgn(b*x + a))/b^4 + (b^4*d^4*sgn(b*x + a) - 4*a*b^3*d^3*e*sgn(b*x + a) + 6*a^2*b^2*d^2*e^2*sgn(b*x + a) - 4*a^3*b*d*e^3*sgn(b*x + a) + a^4*e^4*sgn(b*x + a))*log(abs(b*x + a))/b^5","A",0
1588,1,170,0,0.164640," ","integrate((e*x+d)^3/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{2 \, b^{2} x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 9 \, b^{2} d x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 18 \, b^{2} d^{2} x e \mathrm{sgn}\left(b x + a\right) - 3 \, a b x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - 18 \, a b d x e^{2} \mathrm{sgn}\left(b x + a\right) + 6 \, a^{2} x e^{3} \mathrm{sgn}\left(b x + a\right)}{6 \, b^{3}} + \frac{{\left(b^{3} d^{3} \mathrm{sgn}\left(b x + a\right) - 3 \, a b^{2} d^{2} e \mathrm{sgn}\left(b x + a\right) + 3 \, a^{2} b d e^{2} \mathrm{sgn}\left(b x + a\right) - a^{3} e^{3} \mathrm{sgn}\left(b x + a\right)\right)} \log\left({\left| b x + a \right|}\right)}{b^{4}}"," ",0,"1/6*(2*b^2*x^3*e^3*sgn(b*x + a) + 9*b^2*d*x^2*e^2*sgn(b*x + a) + 18*b^2*d^2*x*e*sgn(b*x + a) - 3*a*b*x^2*e^3*sgn(b*x + a) - 18*a*b*d*x*e^2*sgn(b*x + a) + 6*a^2*x*e^3*sgn(b*x + a))/b^3 + (b^3*d^3*sgn(b*x + a) - 3*a*b^2*d^2*e*sgn(b*x + a) + 3*a^2*b*d*e^2*sgn(b*x + a) - a^3*e^3*sgn(b*x + a))*log(abs(b*x + a))/b^4","A",0
1589,1,95,0,0.166138," ","integrate((e*x+d)^2/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{b x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 4 \, b d x e \mathrm{sgn}\left(b x + a\right) - 2 \, a x e^{2} \mathrm{sgn}\left(b x + a\right)}{2 \, b^{2}} + \frac{{\left(b^{2} d^{2} \mathrm{sgn}\left(b x + a\right) - 2 \, a b d e \mathrm{sgn}\left(b x + a\right) + a^{2} e^{2} \mathrm{sgn}\left(b x + a\right)\right)} \log\left({\left| b x + a \right|}\right)}{b^{3}}"," ",0,"1/2*(b*x^2*e^2*sgn(b*x + a) + 4*b*d*x*e*sgn(b*x + a) - 2*a*x*e^2*sgn(b*x + a))/b^2 + (b^2*d^2*sgn(b*x + a) - 2*a*b*d*e*sgn(b*x + a) + a^2*e^2*sgn(b*x + a))*log(abs(b*x + a))/b^3","A",0
1590,1,46,0,0.159221," ","integrate((e*x+d)/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{x e \mathrm{sgn}\left(b x + a\right)}{b} + \frac{{\left(b d \mathrm{sgn}\left(b x + a\right) - a e \mathrm{sgn}\left(b x + a\right)\right)} \log\left({\left| b x + a \right|}\right)}{b^{2}}"," ",0,"x*e*sgn(b*x + a)/b + (b*d*sgn(b*x + a) - a*e*sgn(b*x + a))*log(abs(b*x + a))/b^2","A",0
1591,1,17,0,0.156202," ","integrate(1/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{\log\left({\left| b x + a \right|}\right) \mathrm{sgn}\left(b x + a\right)}{b}"," ",0,"log(abs(b*x + a))*sgn(b*x + a)/b","A",0
1592,1,56,0,0.157866," ","integrate(1/(e*x+d)/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","{\left(\frac{b \log\left({\left| b x + a \right|}\right)}{b^{2} d - a b e} - \frac{e \log\left({\left| x e + d \right|}\right)}{b d e - a e^{2}}\right)} \mathrm{sgn}\left(b x + a\right)"," ",0,"(b*log(abs(b*x + a))/(b^2*d - a*b*e) - e*log(abs(x*e + d))/(b*d*e - a*e^2))*sgn(b*x + a)","A",0
1593,1,103,0,0.170680," ","integrate(1/(e*x+d)^2/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","{\left(\frac{b^{2} \log\left({\left| b x + a \right|}\right)}{b^{3} d^{2} - 2 \, a b^{2} d e + a^{2} b e^{2}} - \frac{b e \log\left({\left| x e + d \right|}\right)}{b^{2} d^{2} e - 2 \, a b d e^{2} + a^{2} e^{3}} + \frac{1}{{\left(b d - a e\right)} {\left(x e + d\right)}}\right)} \mathrm{sgn}\left(b x + a\right)"," ",0,"(b^2*log(abs(b*x + a))/(b^3*d^2 - 2*a*b^2*d*e + a^2*b*e^2) - b*e*log(abs(x*e + d))/(b^2*d^2*e - 2*a*b*d*e^2 + a^2*e^3) + 1/((b*d - a*e)*(x*e + d)))*sgn(b*x + a)","A",0
1594,1,174,0,0.191598," ","integrate(1/(e*x+d)^3/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, {\left(\frac{2 \, b^{3} \log\left({\left| b x + a \right|}\right)}{b^{4} d^{3} - 3 \, a b^{3} d^{2} e + 3 \, a^{2} b^{2} d e^{2} - a^{3} b e^{3}} - \frac{2 \, b^{2} e \log\left({\left| x e + d \right|}\right)}{b^{3} d^{3} e - 3 \, a b^{2} d^{2} e^{2} + 3 \, a^{2} b d e^{3} - a^{3} e^{4}} + \frac{3 \, b^{2} d^{2} - 4 \, a b d e + a^{2} e^{2} + 2 \, {\left(b^{2} d e - a b e^{2}\right)} x}{{\left(b d - a e\right)}^{3} {\left(x e + d\right)}^{2}}\right)} \mathrm{sgn}\left(b x + a\right)"," ",0,"1/2*(2*b^3*log(abs(b*x + a))/(b^4*d^3 - 3*a*b^3*d^2*e + 3*a^2*b^2*d*e^2 - a^3*b*e^3) - 2*b^2*e*log(abs(x*e + d))/(b^3*d^3*e - 3*a*b^2*d^2*e^2 + 3*a^2*b*d*e^3 - a^3*e^4) + (3*b^2*d^2 - 4*a*b*d*e + a^2*e^2 + 2*(b^2*d*e - a*b*e^2)*x)/((b*d - a*e)^3*(x*e + d)^2))*sgn(b*x + a)","A",0
1595,1,246,0,0.194534," ","integrate(1/(e*x+d)^4/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{6} \, {\left(\frac{6 \, b^{4} \log\left({\left| b x + a \right|}\right)}{b^{5} d^{4} - 4 \, a b^{4} d^{3} e + 6 \, a^{2} b^{3} d^{2} e^{2} - 4 \, a^{3} b^{2} d e^{3} + a^{4} b e^{4}} - \frac{6 \, b^{3} e \log\left({\left| x e + d \right|}\right)}{b^{4} d^{4} e - 4 \, a b^{3} d^{3} e^{2} + 6 \, a^{2} b^{2} d^{2} e^{3} - 4 \, a^{3} b d e^{4} + a^{4} e^{5}} + \frac{11 \, b^{3} d^{3} - 18 \, a b^{2} d^{2} e + 9 \, a^{2} b d e^{2} - 2 \, a^{3} e^{3} + 6 \, {\left(b^{3} d e^{2} - a b^{2} e^{3}\right)} x^{2} + 3 \, {\left(5 \, b^{3} d^{2} e - 6 \, a b^{2} d e^{2} + a^{2} b e^{3}\right)} x}{{\left(b d - a e\right)}^{4} {\left(x e + d\right)}^{3}}\right)} \mathrm{sgn}\left(b x + a\right)"," ",0,"1/6*(6*b^4*log(abs(b*x + a))/(b^5*d^4 - 4*a*b^4*d^3*e + 6*a^2*b^3*d^2*e^2 - 4*a^3*b^2*d*e^3 + a^4*b*e^4) - 6*b^3*e*log(abs(x*e + d))/(b^4*d^4*e - 4*a*b^3*d^3*e^2 + 6*a^2*b^2*d^2*e^3 - 4*a^3*b*d*e^4 + a^4*e^5) + (11*b^3*d^3 - 18*a*b^2*d^2*e + 9*a^2*b*d*e^2 - 2*a^3*e^3 + 6*(b^3*d*e^2 - a*b^2*e^3)*x^2 + 3*(5*b^3*d^2*e - 6*a*b^2*d*e^2 + a^2*b*e^3)*x)/((b*d - a*e)^4*(x*e + d)^3))*sgn(b*x + a)","A",0
1596,0,0,0,0.000000," ","integrate((e*x+d)^4/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
1597,0,0,0,0.000000," ","integrate((e*x+d)^3/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
1598,0,0,0,0.000000," ","integrate((e*x+d)^2/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
1599,0,0,0,0.000000," ","integrate((e*x+d)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
1600,0,0,0,0.000000," ","integrate(1/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
1601,0,0,0,0.000000," ","integrate(1/(e*x+d)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
1602,1,627,0,0.426608," ","integrate(1/(e*x+d)^2/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","-\frac{3 \, b e^{3} \log\left({\left| -b + \frac{b d}{x e + d} - \frac{a e}{x e + d} \right|}\right)}{b^{4} d^{4} e \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right) - 4 \, a b^{3} d^{3} e^{2} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right) + 6 \, a^{2} b^{2} d^{2} e^{3} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right) - 4 \, a^{3} b d e^{4} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right) + a^{4} e^{5} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right)} - \frac{e^{5}}{{\left(b^{3} d^{3} e^{3} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right) - 3 \, a b^{2} d^{2} e^{4} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right) + 3 \, a^{2} b d e^{5} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right) - a^{3} e^{6} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right)\right)} {\left(x e + d\right)}} - \frac{5 \, b^{3} e^{2} - \frac{6 \, {\left(b^{3} d e^{3} - a b^{2} e^{4}\right)} e^{\left(-1\right)}}{x e + d}}{2 \, {\left(b d - a e\right)}^{4} {\left(b - \frac{b d}{x e + d} + \frac{a e}{x e + d}\right)}^{2} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right)}"," ",0,"-3*b*e^3*log(abs(-b + b*d/(x*e + d) - a*e/(x*e + d)))/(b^4*d^4*e*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2) - 4*a*b^3*d^3*e^2*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2) + 6*a^2*b^2*d^2*e^3*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2) - 4*a^3*b*d*e^4*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2) + a^4*e^5*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2)) - e^5/((b^3*d^3*e^3*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2) - 3*a*b^2*d^2*e^4*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2) + 3*a^2*b*d*e^5*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2) - a^3*e^6*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2))*(x*e + d)) - 1/2*(5*b^3*e^2 - 6*(b^3*d*e^3 - a*b^2*e^4)*e^(-1)/(x*e + d))/((b*d - a*e)^4*(b - b*d/(x*e + d) + a*e/(x*e + d))^2*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2))","B",0
1603,0,0,0,0.000000," ","integrate(1/(e*x+d)^3/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
1604,0,0,0,0.000000," ","integrate((e*x+d)^6/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
1605,0,0,0,0.000000," ","integrate((e*x+d)^5/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
1606,0,0,0,0.000000," ","integrate((e*x+d)^4/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
1607,0,0,0,0.000000," ","integrate((e*x+d)^3/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
1608,0,0,0,0.000000," ","integrate((e*x+d)^2/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
1609,0,0,0,0.000000," ","integrate((e*x+d)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
1610,0,0,0,0.000000," ","integrate(1/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
1611,0,0,0,0.000000," ","integrate(1/(e*x+d)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
1612,1,937,0,0.706632," ","integrate(1/(e*x+d)^2/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","-\frac{5 \, b e^{5} \log\left({\left| -b + \frac{b d}{x e + d} - \frac{a e}{x e + d} \right|}\right)}{b^{6} d^{6} e \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right) - 6 \, a b^{5} d^{5} e^{2} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right) + 15 \, a^{2} b^{4} d^{4} e^{3} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right) - 20 \, a^{3} b^{3} d^{3} e^{4} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right) + 15 \, a^{4} b^{2} d^{2} e^{5} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right) - 6 \, a^{5} b d e^{6} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right) + a^{6} e^{7} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right)} - \frac{e^{9}}{{\left(b^{5} d^{5} e^{5} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right) - 5 \, a b^{4} d^{4} e^{6} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right) + 10 \, a^{2} b^{3} d^{3} e^{7} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right) - 10 \, a^{3} b^{2} d^{2} e^{8} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right) + 5 \, a^{4} b d e^{9} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right) - a^{5} e^{10} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right)\right)} {\left(x e + d\right)}} - \frac{77 \, b^{5} e^{4} - \frac{260 \, {\left(b^{5} d e^{5} - a b^{4} e^{6}\right)} e^{\left(-1\right)}}{x e + d} + \frac{300 \, {\left(b^{5} d^{2} e^{6} - 2 \, a b^{4} d e^{7} + a^{2} b^{3} e^{8}\right)} e^{\left(-2\right)}}{{\left(x e + d\right)}^{2}} - \frac{120 \, {\left(b^{5} d^{3} e^{7} - 3 \, a b^{4} d^{2} e^{8} + 3 \, a^{2} b^{3} d e^{9} - a^{3} b^{2} e^{10}\right)} e^{\left(-3\right)}}{{\left(x e + d\right)}^{3}}}{12 \, {\left(b d - a e\right)}^{6} {\left(b - \frac{b d}{x e + d} + \frac{a e}{x e + d}\right)}^{4} \mathrm{sgn}\left(-\frac{b e}{x e + d} + \frac{b d e}{{\left(x e + d\right)}^{2}} - \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right)}"," ",0,"-5*b*e^5*log(abs(-b + b*d/(x*e + d) - a*e/(x*e + d)))/(b^6*d^6*e*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2) - 6*a*b^5*d^5*e^2*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2) + 15*a^2*b^4*d^4*e^3*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2) - 20*a^3*b^3*d^3*e^4*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2) + 15*a^4*b^2*d^2*e^5*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2) - 6*a^5*b*d*e^6*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2) + a^6*e^7*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2)) - e^9/((b^5*d^5*e^5*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2) - 5*a*b^4*d^4*e^6*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2) + 10*a^2*b^3*d^3*e^7*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2) - 10*a^3*b^2*d^2*e^8*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2) + 5*a^4*b*d*e^9*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2) - a^5*e^10*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2))*(x*e + d)) - 1/12*(77*b^5*e^4 - 260*(b^5*d*e^5 - a*b^4*e^6)*e^(-1)/(x*e + d) + 300*(b^5*d^2*e^6 - 2*a*b^4*d*e^7 + a^2*b^3*e^8)*e^(-2)/(x*e + d)^2 - 120*(b^5*d^3*e^7 - 3*a*b^4*d^2*e^8 + 3*a^2*b^3*d*e^9 - a^3*b^2*e^10)*e^(-3)/(x*e + d)^3)/((b*d - a*e)^6*(b - b*d/(x*e + d) + a*e/(x*e + d))^4*sgn(-b*e/(x*e + d) + b*d*e/(x*e + d)^2 - a*e^2/(x*e + d)^2))","B",0
1613,0,0,0,0.000000," ","integrate(1/(e*x+d)^3/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
1614,1,165,0,0.163437," ","integrate((e*x+d)*(4*x^2+12*x+9)^(5/2),x, algorithm=""giac"")","\frac{32}{7} \, x^{7} e \mathrm{sgn}\left(2 \, x + 3\right) + \frac{16}{3} \, d x^{6} \mathrm{sgn}\left(2 \, x + 3\right) + 40 \, x^{6} e \mathrm{sgn}\left(2 \, x + 3\right) + 48 \, d x^{5} \mathrm{sgn}\left(2 \, x + 3\right) + 144 \, x^{5} e \mathrm{sgn}\left(2 \, x + 3\right) + 180 \, d x^{4} \mathrm{sgn}\left(2 \, x + 3\right) + 270 \, x^{4} e \mathrm{sgn}\left(2 \, x + 3\right) + 360 \, d x^{3} \mathrm{sgn}\left(2 \, x + 3\right) + 270 \, x^{3} e \mathrm{sgn}\left(2 \, x + 3\right) + 405 \, d x^{2} \mathrm{sgn}\left(2 \, x + 3\right) + \frac{243}{2} \, x^{2} e \mathrm{sgn}\left(2 \, x + 3\right) + 243 \, d x \mathrm{sgn}\left(2 \, x + 3\right) + \frac{243}{56} \, {\left(14 \, d - 3 \, e\right)} \mathrm{sgn}\left(2 \, x + 3\right)"," ",0,"32/7*x^7*e*sgn(2*x + 3) + 16/3*d*x^6*sgn(2*x + 3) + 40*x^6*e*sgn(2*x + 3) + 48*d*x^5*sgn(2*x + 3) + 144*x^5*e*sgn(2*x + 3) + 180*d*x^4*sgn(2*x + 3) + 270*x^4*e*sgn(2*x + 3) + 360*d*x^3*sgn(2*x + 3) + 270*x^3*e*sgn(2*x + 3) + 405*d*x^2*sgn(2*x + 3) + 243/2*x^2*e*sgn(2*x + 3) + 243*d*x*sgn(2*x + 3) + 243/56*(14*d - 3*e)*sgn(2*x + 3)","B",0
1615,1,115,0,0.163064," ","integrate((e*x+d)*(4*x^2+12*x+9)^(3/2),x, algorithm=""giac"")","\frac{8}{5} \, x^{5} e \mathrm{sgn}\left(2 \, x + 3\right) + 2 \, d x^{4} \mathrm{sgn}\left(2 \, x + 3\right) + 9 \, x^{4} e \mathrm{sgn}\left(2 \, x + 3\right) + 12 \, d x^{3} \mathrm{sgn}\left(2 \, x + 3\right) + 18 \, x^{3} e \mathrm{sgn}\left(2 \, x + 3\right) + 27 \, d x^{2} \mathrm{sgn}\left(2 \, x + 3\right) + \frac{27}{2} \, x^{2} e \mathrm{sgn}\left(2 \, x + 3\right) + 27 \, d x \mathrm{sgn}\left(2 \, x + 3\right) + \frac{81}{80} \, {\left(10 \, d - 3 \, e\right)} \mathrm{sgn}\left(2 \, x + 3\right)"," ",0,"8/5*x^5*e*sgn(2*x + 3) + 2*d*x^4*sgn(2*x + 3) + 9*x^4*e*sgn(2*x + 3) + 12*d*x^3*sgn(2*x + 3) + 18*x^3*e*sgn(2*x + 3) + 27*d*x^2*sgn(2*x + 3) + 27/2*x^2*e*sgn(2*x + 3) + 27*d*x*sgn(2*x + 3) + 81/80*(10*d - 3*e)*sgn(2*x + 3)","B",0
1616,1,64,0,0.159264," ","integrate((e*x+d)*(4*x^2+12*x+9)^(1/2),x, algorithm=""giac"")","\frac{2}{3} \, x^{3} e \mathrm{sgn}\left(2 \, x + 3\right) + d x^{2} \mathrm{sgn}\left(2 \, x + 3\right) + \frac{3}{2} \, x^{2} e \mathrm{sgn}\left(2 \, x + 3\right) + 3 \, d x \mathrm{sgn}\left(2 \, x + 3\right) + \frac{9}{8} \, {\left(2 \, d - e\right)} \mathrm{sgn}\left(2 \, x + 3\right)"," ",0,"2/3*x^3*e*sgn(2*x + 3) + d*x^2*sgn(2*x + 3) + 3/2*x^2*e*sgn(2*x + 3) + 3*d*x*sgn(2*x + 3) + 9/8*(2*d - e)*sgn(2*x + 3)","A",0
1617,1,46,0,0.199081," ","integrate((e*x+d)/(4*x^2+12*x+9)^(1/2),x, algorithm=""giac"")","-\frac{1}{4} \, {\left(2 \, d - 3 \, e\right)} \log\left({\left| -2 \, x + \sqrt{4 \, x^{2} + 12 \, x + 9} - 3 \right|}\right) + \frac{1}{4} \, \sqrt{4 \, x^{2} + 12 \, x + 9} e"," ",0,"-1/4*(2*d - 3*e)*log(abs(-2*x + sqrt(4*x^2 + 12*x + 9) - 3)) + 1/4*sqrt(4*x^2 + 12*x + 9)*e","A",0
1618,0,0,0,0.000000," ","integrate((e*x+d)/(4*x^2+12*x+9)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
1619,0,0,0,0.000000," ","integrate((e*x+d)/(4*x^2+12*x+9)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
1620,0,0,0,0.000000," ","integrate((e*x+d)/(4*x^2+12*x+9)^(7/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
1621,1,840,0,0.222020," ","integrate((e*x+d)^(7/2)*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{2}{45045} \, {\left(30030 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a b d^{4} e^{\left(-1\right)} + 3003 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} b^{2} d^{4} e^{\left(-2\right)} + 24024 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a b d^{3} e^{\left(-1\right)} + 5148 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b^{2} d^{3} e^{\left(-2\right)} + 45045 \, \sqrt{x e + d} a^{2} d^{4} + 60060 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{2} d^{3} + 15444 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a b d^{2} e^{\left(-1\right)} + 858 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b^{2} d^{2} e^{\left(-2\right)} + 18018 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{2} d^{2} + 1144 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a b d e^{\left(-1\right)} + 260 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b^{2} d e^{\left(-2\right)} + 5148 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{2} d + 130 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a b e^{\left(-1\right)} + 15 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} b^{2} e^{\left(-2\right)} + 143 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{2}\right)} e^{\left(-1\right)}"," ",0,"2/45045*(30030*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a*b*d^4*e^(-1) + 3003*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*b^2*d^4*e^(-2) + 24024*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a*b*d^3*e^(-1) + 5148*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b^2*d^3*e^(-2) + 45045*sqrt(x*e + d)*a^2*d^4 + 60060*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^2*d^3 + 15444*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*b*d^2*e^(-1) + 858*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b^2*d^2*e^(-2) + 18018*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^2*d^2 + 1144*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*b*d*e^(-1) + 260*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b^2*d*e^(-2) + 5148*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^2*d + 130*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a*b*e^(-1) + 15*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*b^2*e^(-2) + 143*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^2)*e^(-1)","B",0
1622,1,591,0,0.193873," ","integrate((e*x+d)^(5/2)*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{2}{3465} \, {\left(2310 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a b d^{3} e^{\left(-1\right)} + 231 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} b^{2} d^{3} e^{\left(-2\right)} + 1386 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a b d^{2} e^{\left(-1\right)} + 297 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b^{2} d^{2} e^{\left(-2\right)} + 3465 \, \sqrt{x e + d} a^{2} d^{3} + 3465 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{2} d^{2} + 594 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a b d e^{\left(-1\right)} + 33 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b^{2} d e^{\left(-2\right)} + 693 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{2} d + 22 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a b e^{\left(-1\right)} + 5 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b^{2} e^{\left(-2\right)} + 99 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{2}\right)} e^{\left(-1\right)}"," ",0,"2/3465*(2310*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a*b*d^3*e^(-1) + 231*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*b^2*d^3*e^(-2) + 1386*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a*b*d^2*e^(-1) + 297*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b^2*d^2*e^(-2) + 3465*sqrt(x*e + d)*a^2*d^3 + 3465*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^2*d^2 + 594*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*b*d*e^(-1) + 33*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b^2*d*e^(-2) + 693*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^2*d + 22*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*b*e^(-1) + 5*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b^2*e^(-2) + 99*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^2)*e^(-1)","B",0
1623,1,380,0,0.195702," ","integrate((e*x+d)^(3/2)*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{2}{315} \, {\left(210 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a b d^{2} e^{\left(-1\right)} + 21 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} b^{2} d^{2} e^{\left(-2\right)} + 84 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a b d e^{\left(-1\right)} + 18 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b^{2} d e^{\left(-2\right)} + 315 \, \sqrt{x e + d} a^{2} d^{2} + 210 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{2} d + 18 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a b e^{\left(-1\right)} + {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b^{2} e^{\left(-2\right)} + 21 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{2}\right)} e^{\left(-1\right)}"," ",0,"2/315*(210*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a*b*d^2*e^(-1) + 21*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*b^2*d^2*e^(-2) + 84*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a*b*d*e^(-1) + 18*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b^2*d*e^(-2) + 315*sqrt(x*e + d)*a^2*d^2 + 210*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^2*d + 18*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*b*e^(-1) + (35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b^2*e^(-2) + 21*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^2)*e^(-1)","B",0
1624,1,210,0,0.183767," ","integrate((b^2*x^2+2*a*b*x+a^2)*(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{105} \, {\left(70 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a b d e^{\left(-1\right)} + 7 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} b^{2} d e^{\left(-2\right)} + 14 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a b e^{\left(-1\right)} + 3 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b^{2} e^{\left(-2\right)} + 105 \, \sqrt{x e + d} a^{2} d + 35 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{2}\right)} e^{\left(-1\right)}"," ",0,"2/105*(70*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a*b*d*e^(-1) + 7*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*b^2*d*e^(-2) + 14*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a*b*e^(-1) + 3*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b^2*e^(-2) + 105*sqrt(x*e + d)*a^2*d + 35*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^2)*e^(-1)","B",0
1625,1,85,0,0.192445," ","integrate((b^2*x^2+2*a*b*x+a^2)/(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{15} \, {\left(10 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a b e^{\left(-1\right)} + {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} b^{2} e^{\left(-2\right)} + 15 \, \sqrt{x e + d} a^{2}\right)} e^{\left(-1\right)}"," ",0,"2/15*(10*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a*b*e^(-1) + (3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*b^2*e^(-2) + 15*sqrt(x*e + d)*a^2)*e^(-1)","A",0
1626,1,83,0,0.185688," ","integrate((b^2*x^2+2*a*b*x+a^2)/(e*x+d)^(3/2),x, algorithm=""giac"")","\frac{2}{3} \, {\left({\left(x e + d\right)}^{\frac{3}{2}} b^{2} e^{6} - 6 \, \sqrt{x e + d} b^{2} d e^{6} + 6 \, \sqrt{x e + d} a b e^{7}\right)} e^{\left(-9\right)} - \frac{2 \, {\left(b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}\right)} e^{\left(-3\right)}}{\sqrt{x e + d}}"," ",0,"2/3*((x*e + d)^(3/2)*b^2*e^6 - 6*sqrt(x*e + d)*b^2*d*e^6 + 6*sqrt(x*e + d)*a*b*e^7)*e^(-9) - 2*(b^2*d^2 - 2*a*b*d*e + a^2*e^2)*e^(-3)/sqrt(x*e + d)","A",0
1627,1,75,0,0.176382," ","integrate((b^2*x^2+2*a*b*x+a^2)/(e*x+d)^(5/2),x, algorithm=""giac"")","2 \, \sqrt{x e + d} b^{2} e^{\left(-3\right)} + \frac{2 \, {\left(6 \, {\left(x e + d\right)} b^{2} d - b^{2} d^{2} - 6 \, {\left(x e + d\right)} a b e + 2 \, a b d e - a^{2} e^{2}\right)} e^{\left(-3\right)}}{3 \, {\left(x e + d\right)}^{\frac{3}{2}}}"," ",0,"2*sqrt(x*e + d)*b^2*e^(-3) + 2/3*(6*(x*e + d)*b^2*d - b^2*d^2 - 6*(x*e + d)*a*b*e + 2*a*b*d*e - a^2*e^2)*e^(-3)/(x*e + d)^(3/2)","A",0
1628,1,72,0,0.188314," ","integrate((b^2*x^2+2*a*b*x+a^2)/(e*x+d)^(7/2),x, algorithm=""giac"")","-\frac{2 \, {\left(15 \, {\left(x e + d\right)}^{2} b^{2} - 10 \, {\left(x e + d\right)} b^{2} d + 3 \, b^{2} d^{2} + 10 \, {\left(x e + d\right)} a b e - 6 \, a b d e + 3 \, a^{2} e^{2}\right)} e^{\left(-3\right)}}{15 \, {\left(x e + d\right)}^{\frac{5}{2}}}"," ",0,"-2/15*(15*(x*e + d)^2*b^2 - 10*(x*e + d)*b^2*d + 3*b^2*d^2 + 10*(x*e + d)*a*b*e - 6*a*b*d*e + 3*a^2*e^2)*e^(-3)/(x*e + d)^(5/2)","A",0
1629,1,1765,0,0.301255," ","integrate((e*x+d)^(7/2)*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{2}{765765} \, {\left(1021020 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{3} b d^{4} e^{\left(-1\right)} + 306306 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{2} b^{2} d^{4} e^{\left(-2\right)} + 87516 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a b^{3} d^{4} e^{\left(-3\right)} + 2431 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b^{4} d^{4} e^{\left(-4\right)} + 816816 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{3} b d^{3} e^{\left(-1\right)} + 525096 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{2} b^{2} d^{3} e^{\left(-2\right)} + 38896 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a b^{3} d^{3} e^{\left(-3\right)} + 4420 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b^{4} d^{3} e^{\left(-4\right)} + 765765 \, \sqrt{x e + d} a^{4} d^{4} + 1021020 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{4} d^{3} + 525096 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{3} b d^{2} e^{\left(-1\right)} + 87516 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{2} b^{2} d^{2} e^{\left(-2\right)} + 26520 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a b^{3} d^{2} e^{\left(-3\right)} + 1530 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} b^{4} d^{2} e^{\left(-4\right)} + 306306 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{4} d^{2} + 38896 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{3} b d e^{\left(-1\right)} + 26520 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a^{2} b^{2} d e^{\left(-2\right)} + 4080 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} a b^{3} d e^{\left(-3\right)} + 476 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} b^{4} d e^{\left(-4\right)} + 87516 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{4} d + 4420 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a^{3} b e^{\left(-1\right)} + 1530 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} a^{2} b^{2} e^{\left(-2\right)} + 476 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} a b^{3} e^{\left(-3\right)} + 7 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} b^{4} e^{\left(-4\right)} + 2431 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{4}\right)} e^{\left(-1\right)}"," ",0,"2/765765*(1021020*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^3*b*d^4*e^(-1) + 306306*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^2*b^2*d^4*e^(-2) + 87516*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*b^3*d^4*e^(-3) + 2431*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b^4*d^4*e^(-4) + 816816*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^3*b*d^3*e^(-1) + 525096*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^2*b^2*d^3*e^(-2) + 38896*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*b^3*d^3*e^(-3) + 4420*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b^4*d^3*e^(-4) + 765765*sqrt(x*e + d)*a^4*d^4 + 1021020*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^4*d^3 + 525096*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^3*b*d^2*e^(-1) + 87516*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^2*b^2*d^2*e^(-2) + 26520*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a*b^3*d^2*e^(-3) + 1530*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*b^4*d^2*e^(-4) + 306306*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^4*d^2 + 38896*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^3*b*d*e^(-1) + 26520*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a^2*b^2*d*e^(-2) + 4080*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*a*b^3*d*e^(-3) + 476*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*b^4*d*e^(-4) + 87516*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^4*d + 4420*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a^3*b*e^(-1) + 1530*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*a^2*b^2*e^(-2) + 476*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*a*b^3*e^(-3) + 7*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*b^4*e^(-4) + 2431*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^4)*e^(-1)","B",0
1630,1,1277,0,0.244839," ","integrate((e*x+d)^(5/2)*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{2}{45045} \, {\left(60060 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{3} b d^{3} e^{\left(-1\right)} + 18018 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{2} b^{2} d^{3} e^{\left(-2\right)} + 5148 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a b^{3} d^{3} e^{\left(-3\right)} + 143 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b^{4} d^{3} e^{\left(-4\right)} + 36036 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{3} b d^{2} e^{\left(-1\right)} + 23166 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{2} b^{2} d^{2} e^{\left(-2\right)} + 1716 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a b^{3} d^{2} e^{\left(-3\right)} + 195 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b^{4} d^{2} e^{\left(-4\right)} + 45045 \, \sqrt{x e + d} a^{4} d^{3} + 45045 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{4} d^{2} + 15444 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{3} b d e^{\left(-1\right)} + 2574 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{2} b^{2} d e^{\left(-2\right)} + 780 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a b^{3} d e^{\left(-3\right)} + 45 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} b^{4} d e^{\left(-4\right)} + 9009 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{4} d + 572 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{3} b e^{\left(-1\right)} + 390 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a^{2} b^{2} e^{\left(-2\right)} + 60 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} a b^{3} e^{\left(-3\right)} + 7 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} b^{4} e^{\left(-4\right)} + 1287 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{4}\right)} e^{\left(-1\right)}"," ",0,"2/45045*(60060*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^3*b*d^3*e^(-1) + 18018*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^2*b^2*d^3*e^(-2) + 5148*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*b^3*d^3*e^(-3) + 143*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b^4*d^3*e^(-4) + 36036*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^3*b*d^2*e^(-1) + 23166*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^2*b^2*d^2*e^(-2) + 1716*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*b^3*d^2*e^(-3) + 195*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b^4*d^2*e^(-4) + 45045*sqrt(x*e + d)*a^4*d^3 + 45045*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^4*d^2 + 15444*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^3*b*d*e^(-1) + 2574*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^2*b^2*d*e^(-2) + 780*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a*b^3*d*e^(-3) + 45*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*b^4*d*e^(-4) + 9009*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^4*d + 572*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^3*b*e^(-1) + 390*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a^2*b^2*e^(-2) + 60*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*a*b^3*e^(-3) + 7*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*b^4*e^(-4) + 1287*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^4)*e^(-1)","B",0
1631,1,854,0,0.241216," ","integrate((e*x+d)^(3/2)*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{2}{45045} \, {\left(60060 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{3} b d^{2} e^{\left(-1\right)} + 18018 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{2} b^{2} d^{2} e^{\left(-2\right)} + 5148 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a b^{3} d^{2} e^{\left(-3\right)} + 143 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b^{4} d^{2} e^{\left(-4\right)} + 24024 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{3} b d e^{\left(-1\right)} + 15444 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{2} b^{2} d e^{\left(-2\right)} + 1144 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a b^{3} d e^{\left(-3\right)} + 130 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b^{4} d e^{\left(-4\right)} + 45045 \, \sqrt{x e + d} a^{4} d^{2} + 30030 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{4} d + 5148 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{3} b e^{\left(-1\right)} + 858 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{2} b^{2} e^{\left(-2\right)} + 260 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a b^{3} e^{\left(-3\right)} + 15 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} b^{4} e^{\left(-4\right)} + 3003 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{4}\right)} e^{\left(-1\right)}"," ",0,"2/45045*(60060*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^3*b*d^2*e^(-1) + 18018*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^2*b^2*d^2*e^(-2) + 5148*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*b^3*d^2*e^(-3) + 143*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b^4*d^2*e^(-4) + 24024*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^3*b*d*e^(-1) + 15444*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^2*b^2*d*e^(-2) + 1144*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*b^3*d*e^(-3) + 130*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b^4*d*e^(-4) + 45045*sqrt(x*e + d)*a^4*d^2 + 30030*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^4*d + 5148*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^3*b*e^(-1) + 858*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^2*b^2*e^(-2) + 260*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a*b^3*e^(-3) + 15*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*b^4*e^(-4) + 3003*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^4)*e^(-1)","B",0
1632,1,496,0,0.203497," ","integrate((b^2*x^2+2*a*b*x+a^2)^2*(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{3465} \, {\left(4620 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{3} b d e^{\left(-1\right)} + 1386 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{2} b^{2} d e^{\left(-2\right)} + 396 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a b^{3} d e^{\left(-3\right)} + 11 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b^{4} d e^{\left(-4\right)} + 924 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{3} b e^{\left(-1\right)} + 594 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{2} b^{2} e^{\left(-2\right)} + 44 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a b^{3} e^{\left(-3\right)} + 5 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b^{4} e^{\left(-4\right)} + 3465 \, \sqrt{x e + d} a^{4} d + 1155 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{4}\right)} e^{\left(-1\right)}"," ",0,"2/3465*(4620*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^3*b*d*e^(-1) + 1386*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^2*b^2*d*e^(-2) + 396*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*b^3*d*e^(-3) + 11*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b^4*d*e^(-4) + 924*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^3*b*e^(-1) + 594*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^2*b^2*e^(-2) + 44*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*b^3*e^(-3) + 5*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b^4*e^(-4) + 3465*sqrt(x*e + d)*a^4*d + 1155*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^4)*e^(-1)","B",0
1633,1,214,0,0.216284," ","integrate((b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{315} \, {\left(420 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{3} b e^{\left(-1\right)} + 126 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{2} b^{2} e^{\left(-2\right)} + 36 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a b^{3} e^{\left(-3\right)} + {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b^{4} e^{\left(-4\right)} + 315 \, \sqrt{x e + d} a^{4}\right)} e^{\left(-1\right)}"," ",0,"2/315*(420*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^3*b*e^(-1) + 126*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^2*b^2*e^(-2) + 36*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*b^3*e^(-3) + (35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b^4*e^(-4) + 315*sqrt(x*e + d)*a^4)*e^(-1)","A",0
1634,1,237,0,0.189349," ","integrate((b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^(3/2),x, algorithm=""giac"")","\frac{2}{35} \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{4} e^{30} - 28 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{4} d e^{30} + 70 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{4} d^{2} e^{30} - 140 \, \sqrt{x e + d} b^{4} d^{3} e^{30} + 28 \, {\left(x e + d\right)}^{\frac{5}{2}} a b^{3} e^{31} - 140 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{3} d e^{31} + 420 \, \sqrt{x e + d} a b^{3} d^{2} e^{31} + 70 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} b^{2} e^{32} - 420 \, \sqrt{x e + d} a^{2} b^{2} d e^{32} + 140 \, \sqrt{x e + d} a^{3} b e^{33}\right)} e^{\left(-35\right)} - \frac{2 \, {\left(b^{4} d^{4} - 4 \, a b^{3} d^{3} e + 6 \, a^{2} b^{2} d^{2} e^{2} - 4 \, a^{3} b d e^{3} + a^{4} e^{4}\right)} e^{\left(-5\right)}}{\sqrt{x e + d}}"," ",0,"2/35*(5*(x*e + d)^(7/2)*b^4*e^30 - 28*(x*e + d)^(5/2)*b^4*d*e^30 + 70*(x*e + d)^(3/2)*b^4*d^2*e^30 - 140*sqrt(x*e + d)*b^4*d^3*e^30 + 28*(x*e + d)^(5/2)*a*b^3*e^31 - 140*(x*e + d)^(3/2)*a*b^3*d*e^31 + 420*sqrt(x*e + d)*a*b^3*d^2*e^31 + 70*(x*e + d)^(3/2)*a^2*b^2*e^32 - 420*sqrt(x*e + d)*a^2*b^2*d*e^32 + 140*sqrt(x*e + d)*a^3*b*e^33)*e^(-35) - 2*(b^4*d^4 - 4*a*b^3*d^3*e + 6*a^2*b^2*d^2*e^2 - 4*a^3*b*d*e^3 + a^4*e^4)*e^(-5)/sqrt(x*e + d)","B",0
1635,1,229,0,0.197721," ","integrate((b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^(5/2),x, algorithm=""giac"")","\frac{2}{15} \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{4} e^{20} - 20 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{4} d e^{20} + 90 \, \sqrt{x e + d} b^{4} d^{2} e^{20} + 20 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{3} e^{21} - 180 \, \sqrt{x e + d} a b^{3} d e^{21} + 90 \, \sqrt{x e + d} a^{2} b^{2} e^{22}\right)} e^{\left(-25\right)} + \frac{2 \, {\left(12 \, {\left(x e + d\right)} b^{4} d^{3} - b^{4} d^{4} - 36 \, {\left(x e + d\right)} a b^{3} d^{2} e + 4 \, a b^{3} d^{3} e + 36 \, {\left(x e + d\right)} a^{2} b^{2} d e^{2} - 6 \, a^{2} b^{2} d^{2} e^{2} - 12 \, {\left(x e + d\right)} a^{3} b e^{3} + 4 \, a^{3} b d e^{3} - a^{4} e^{4}\right)} e^{\left(-5\right)}}{3 \, {\left(x e + d\right)}^{\frac{3}{2}}}"," ",0,"2/15*(3*(x*e + d)^(5/2)*b^4*e^20 - 20*(x*e + d)^(3/2)*b^4*d*e^20 + 90*sqrt(x*e + d)*b^4*d^2*e^20 + 20*(x*e + d)^(3/2)*a*b^3*e^21 - 180*sqrt(x*e + d)*a*b^3*d*e^21 + 90*sqrt(x*e + d)*a^2*b^2*e^22)*e^(-25) + 2/3*(12*(x*e + d)*b^4*d^3 - b^4*d^4 - 36*(x*e + d)*a*b^3*d^2*e + 4*a*b^3*d^3*e + 36*(x*e + d)*a^2*b^2*d*e^2 - 6*a^2*b^2*d^2*e^2 - 12*(x*e + d)*a^3*b*e^3 + 4*a^3*b*d*e^3 - a^4*e^4)*e^(-5)/(x*e + d)^(3/2)","B",0
1636,1,226,0,0.190139," ","integrate((b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^(7/2),x, algorithm=""giac"")","\frac{2}{3} \, {\left({\left(x e + d\right)}^{\frac{3}{2}} b^{4} e^{10} - 12 \, \sqrt{x e + d} b^{4} d e^{10} + 12 \, \sqrt{x e + d} a b^{3} e^{11}\right)} e^{\left(-15\right)} - \frac{2 \, {\left(90 \, {\left(x e + d\right)}^{2} b^{4} d^{2} - 20 \, {\left(x e + d\right)} b^{4} d^{3} + 3 \, b^{4} d^{4} - 180 \, {\left(x e + d\right)}^{2} a b^{3} d e + 60 \, {\left(x e + d\right)} a b^{3} d^{2} e - 12 \, a b^{3} d^{3} e + 90 \, {\left(x e + d\right)}^{2} a^{2} b^{2} e^{2} - 60 \, {\left(x e + d\right)} a^{2} b^{2} d e^{2} + 18 \, a^{2} b^{2} d^{2} e^{2} + 20 \, {\left(x e + d\right)} a^{3} b e^{3} - 12 \, a^{3} b d e^{3} + 3 \, a^{4} e^{4}\right)} e^{\left(-5\right)}}{15 \, {\left(x e + d\right)}^{\frac{5}{2}}}"," ",0,"2/3*((x*e + d)^(3/2)*b^4*e^10 - 12*sqrt(x*e + d)*b^4*d*e^10 + 12*sqrt(x*e + d)*a*b^3*e^11)*e^(-15) - 2/15*(90*(x*e + d)^2*b^4*d^2 - 20*(x*e + d)*b^4*d^3 + 3*b^4*d^4 - 180*(x*e + d)^2*a*b^3*d*e + 60*(x*e + d)*a*b^3*d^2*e - 12*a*b^3*d^3*e + 90*(x*e + d)^2*a^2*b^2*e^2 - 60*(x*e + d)*a^2*b^2*d*e^2 + 18*a^2*b^2*d^2*e^2 + 20*(x*e + d)*a^3*b*e^3 - 12*a^3*b*d*e^3 + 3*a^4*e^4)*e^(-5)/(x*e + d)^(5/2)","B",0
1637,1,2950,0,0.381559," ","integrate((e*x+d)^(7/2)*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{2}{14549535} \, {\left(29099070 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{5} b d^{4} e^{\left(-1\right)} + 14549535 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{4} b^{2} d^{4} e^{\left(-2\right)} + 8314020 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{3} b^{3} d^{4} e^{\left(-3\right)} + 692835 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{2} b^{4} d^{4} e^{\left(-4\right)} + 125970 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a b^{5} d^{4} e^{\left(-5\right)} + 4845 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} b^{6} d^{4} e^{\left(-6\right)} + 23279256 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{5} b d^{3} e^{\left(-1\right)} + 24942060 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{4} b^{2} d^{3} e^{\left(-2\right)} + 3695120 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{3} b^{3} d^{3} e^{\left(-3\right)} + 1259700 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a^{2} b^{4} d^{3} e^{\left(-4\right)} + 116280 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} a b^{5} d^{3} e^{\left(-5\right)} + 9044 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} b^{6} d^{3} e^{\left(-6\right)} + 14549535 \, \sqrt{x e + d} a^{6} d^{4} + 19399380 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{6} d^{3} + 14965236 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{5} b d^{2} e^{\left(-1\right)} + 4157010 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{4} b^{2} d^{2} e^{\left(-2\right)} + 2519400 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a^{3} b^{3} d^{2} e^{\left(-3\right)} + 436050 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} a^{2} b^{4} d^{2} e^{\left(-4\right)} + 81396 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} a b^{5} d^{2} e^{\left(-5\right)} + 798 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} b^{6} d^{2} e^{\left(-6\right)} + 5819814 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{6} d^{2} + 1108536 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{5} b d e^{\left(-1\right)} + 1259700 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a^{4} b^{2} d e^{\left(-2\right)} + 387600 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} a^{3} b^{3} d e^{\left(-3\right)} + 135660 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} a^{2} b^{4} d e^{\left(-4\right)} + 3192 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} a b^{5} d e^{\left(-5\right)} + 252 \, {\left(12155 \, {\left(x e + d\right)}^{\frac{19}{2}} - 122265 \, {\left(x e + d\right)}^{\frac{17}{2}} d + 554268 \, {\left(x e + d\right)}^{\frac{15}{2}} d^{2} - 1492260 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{3} + 2645370 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{4} - 3233230 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{5} + 2771340 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{6} - 1662804 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{7} + 692835 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{8} - 230945 \, \sqrt{x e + d} d^{9}\right)} b^{6} d e^{\left(-6\right)} + 1662804 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{6} d + 125970 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a^{5} b e^{\left(-1\right)} + 72675 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} a^{4} b^{2} e^{\left(-2\right)} + 45220 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} a^{3} b^{3} e^{\left(-3\right)} + 1995 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} a^{2} b^{4} e^{\left(-4\right)} + 378 \, {\left(12155 \, {\left(x e + d\right)}^{\frac{19}{2}} - 122265 \, {\left(x e + d\right)}^{\frac{17}{2}} d + 554268 \, {\left(x e + d\right)}^{\frac{15}{2}} d^{2} - 1492260 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{3} + 2645370 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{4} - 3233230 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{5} + 2771340 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{6} - 1662804 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{7} + 692835 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{8} - 230945 \, \sqrt{x e + d} d^{9}\right)} a b^{5} e^{\left(-5\right)} + 15 \, {\left(46189 \, {\left(x e + d\right)}^{\frac{21}{2}} - 510510 \, {\left(x e + d\right)}^{\frac{19}{2}} d + 2567565 \, {\left(x e + d\right)}^{\frac{17}{2}} d^{2} - 7759752 \, {\left(x e + d\right)}^{\frac{15}{2}} d^{3} + 15668730 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{4} - 22221108 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{5} + 22632610 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{6} - 16628040 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{7} + 8729721 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{8} - 3233230 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{9} + 969969 \, \sqrt{x e + d} d^{10}\right)} b^{6} e^{\left(-6\right)} + 46189 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{6}\right)} e^{\left(-1\right)}"," ",0,"2/14549535*(29099070*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^5*b*d^4*e^(-1) + 14549535*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^4*b^2*d^4*e^(-2) + 8314020*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^3*b^3*d^4*e^(-3) + 692835*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^2*b^4*d^4*e^(-4) + 125970*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a*b^5*d^4*e^(-5) + 4845*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*b^6*d^4*e^(-6) + 23279256*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^5*b*d^3*e^(-1) + 24942060*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^4*b^2*d^3*e^(-2) + 3695120*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^3*b^3*d^3*e^(-3) + 1259700*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a^2*b^4*d^3*e^(-4) + 116280*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*a*b^5*d^3*e^(-5) + 9044*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*b^6*d^3*e^(-6) + 14549535*sqrt(x*e + d)*a^6*d^4 + 19399380*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^6*d^3 + 14965236*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^5*b*d^2*e^(-1) + 4157010*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^4*b^2*d^2*e^(-2) + 2519400*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a^3*b^3*d^2*e^(-3) + 436050*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*a^2*b^4*d^2*e^(-4) + 81396*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*a*b^5*d^2*e^(-5) + 798*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*b^6*d^2*e^(-6) + 5819814*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^6*d^2 + 1108536*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^5*b*d*e^(-1) + 1259700*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a^4*b^2*d*e^(-2) + 387600*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*a^3*b^3*d*e^(-3) + 135660*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*a^2*b^4*d*e^(-4) + 3192*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*a*b^5*d*e^(-5) + 252*(12155*(x*e + d)^(19/2) - 122265*(x*e + d)^(17/2)*d + 554268*(x*e + d)^(15/2)*d^2 - 1492260*(x*e + d)^(13/2)*d^3 + 2645370*(x*e + d)^(11/2)*d^4 - 3233230*(x*e + d)^(9/2)*d^5 + 2771340*(x*e + d)^(7/2)*d^6 - 1662804*(x*e + d)^(5/2)*d^7 + 692835*(x*e + d)^(3/2)*d^8 - 230945*sqrt(x*e + d)*d^9)*b^6*d*e^(-6) + 1662804*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^6*d + 125970*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a^5*b*e^(-1) + 72675*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*a^4*b^2*e^(-2) + 45220*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*a^3*b^3*e^(-3) + 1995*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*a^2*b^4*e^(-4) + 378*(12155*(x*e + d)^(19/2) - 122265*(x*e + d)^(17/2)*d + 554268*(x*e + d)^(15/2)*d^2 - 1492260*(x*e + d)^(13/2)*d^3 + 2645370*(x*e + d)^(11/2)*d^4 - 3233230*(x*e + d)^(9/2)*d^5 + 2771340*(x*e + d)^(7/2)*d^6 - 1662804*(x*e + d)^(5/2)*d^7 + 692835*(x*e + d)^(3/2)*d^8 - 230945*sqrt(x*e + d)*d^9)*a*b^5*e^(-5) + 15*(46189*(x*e + d)^(21/2) - 510510*(x*e + d)^(19/2)*d + 2567565*(x*e + d)^(17/2)*d^2 - 7759752*(x*e + d)^(15/2)*d^3 + 15668730*(x*e + d)^(13/2)*d^4 - 22221108*(x*e + d)^(11/2)*d^5 + 22632610*(x*e + d)^(9/2)*d^6 - 16628040*(x*e + d)^(7/2)*d^7 + 8729721*(x*e + d)^(5/2)*d^8 - 3233230*(x*e + d)^(3/2)*d^9 + 969969*sqrt(x*e + d)*d^10)*b^6*e^(-6) + 46189*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^6)*e^(-1)","B",0
1638,1,2171,0,0.305964," ","integrate((e*x+d)^(5/2)*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{2}{4849845} \, {\left(9699690 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{5} b d^{3} e^{\left(-1\right)} + 4849845 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{4} b^{2} d^{3} e^{\left(-2\right)} + 2771340 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{3} b^{3} d^{3} e^{\left(-3\right)} + 230945 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{2} b^{4} d^{3} e^{\left(-4\right)} + 41990 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a b^{5} d^{3} e^{\left(-5\right)} + 1615 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} b^{6} d^{3} e^{\left(-6\right)} + 5819814 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{5} b d^{2} e^{\left(-1\right)} + 6235515 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{4} b^{2} d^{2} e^{\left(-2\right)} + 923780 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{3} b^{3} d^{2} e^{\left(-3\right)} + 314925 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a^{2} b^{4} d^{2} e^{\left(-4\right)} + 29070 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} a b^{5} d^{2} e^{\left(-5\right)} + 2261 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} b^{6} d^{2} e^{\left(-6\right)} + 4849845 \, \sqrt{x e + d} a^{6} d^{3} + 4849845 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{6} d^{2} + 2494206 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{5} b d e^{\left(-1\right)} + 692835 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{4} b^{2} d e^{\left(-2\right)} + 419900 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a^{3} b^{3} d e^{\left(-3\right)} + 72675 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} a^{2} b^{4} d e^{\left(-4\right)} + 13566 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} a b^{5} d e^{\left(-5\right)} + 133 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} b^{6} d e^{\left(-6\right)} + 969969 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{6} d + 92378 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{5} b e^{\left(-1\right)} + 104975 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a^{4} b^{2} e^{\left(-2\right)} + 32300 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} a^{3} b^{3} e^{\left(-3\right)} + 11305 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} a^{2} b^{4} e^{\left(-4\right)} + 266 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} a b^{5} e^{\left(-5\right)} + 21 \, {\left(12155 \, {\left(x e + d\right)}^{\frac{19}{2}} - 122265 \, {\left(x e + d\right)}^{\frac{17}{2}} d + 554268 \, {\left(x e + d\right)}^{\frac{15}{2}} d^{2} - 1492260 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{3} + 2645370 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{4} - 3233230 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{5} + 2771340 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{6} - 1662804 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{7} + 692835 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{8} - 230945 \, \sqrt{x e + d} d^{9}\right)} b^{6} e^{\left(-6\right)} + 138567 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{6}\right)} e^{\left(-1\right)}"," ",0,"2/4849845*(9699690*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^5*b*d^3*e^(-1) + 4849845*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^4*b^2*d^3*e^(-2) + 2771340*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^3*b^3*d^3*e^(-3) + 230945*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^2*b^4*d^3*e^(-4) + 41990*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a*b^5*d^3*e^(-5) + 1615*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*b^6*d^3*e^(-6) + 5819814*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^5*b*d^2*e^(-1) + 6235515*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^4*b^2*d^2*e^(-2) + 923780*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^3*b^3*d^2*e^(-3) + 314925*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a^2*b^4*d^2*e^(-4) + 29070*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*a*b^5*d^2*e^(-5) + 2261*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*b^6*d^2*e^(-6) + 4849845*sqrt(x*e + d)*a^6*d^3 + 4849845*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^6*d^2 + 2494206*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^5*b*d*e^(-1) + 692835*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^4*b^2*d*e^(-2) + 419900*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a^3*b^3*d*e^(-3) + 72675*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*a^2*b^4*d*e^(-4) + 13566*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*a*b^5*d*e^(-5) + 133*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*b^6*d*e^(-6) + 969969*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^6*d + 92378*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^5*b*e^(-1) + 104975*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a^4*b^2*e^(-2) + 32300*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*a^3*b^3*e^(-3) + 11305*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*a^2*b^4*e^(-4) + 266*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*a*b^5*e^(-5) + 21*(12155*(x*e + d)^(19/2) - 122265*(x*e + d)^(17/2)*d + 554268*(x*e + d)^(15/2)*d^2 - 1492260*(x*e + d)^(13/2)*d^3 + 2645370*(x*e + d)^(11/2)*d^4 - 3233230*(x*e + d)^(9/2)*d^5 + 2771340*(x*e + d)^(7/2)*d^6 - 1662804*(x*e + d)^(5/2)*d^7 + 692835*(x*e + d)^(3/2)*d^8 - 230945*sqrt(x*e + d)*d^9)*b^6*e^(-6) + 138567*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^6)*e^(-1)","B",0
1639,1,1483,0,0.259192," ","integrate((e*x+d)^(3/2)*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{2}{765765} \, {\left(1531530 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{5} b d^{2} e^{\left(-1\right)} + 765765 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{4} b^{2} d^{2} e^{\left(-2\right)} + 437580 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{3} b^{3} d^{2} e^{\left(-3\right)} + 36465 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{2} b^{4} d^{2} e^{\left(-4\right)} + 6630 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a b^{5} d^{2} e^{\left(-5\right)} + 255 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} b^{6} d^{2} e^{\left(-6\right)} + 612612 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{5} b d e^{\left(-1\right)} + 656370 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{4} b^{2} d e^{\left(-2\right)} + 97240 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{3} b^{3} d e^{\left(-3\right)} + 33150 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a^{2} b^{4} d e^{\left(-4\right)} + 3060 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} a b^{5} d e^{\left(-5\right)} + 238 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} b^{6} d e^{\left(-6\right)} + 765765 \, \sqrt{x e + d} a^{6} d^{2} + 510510 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{6} d + 131274 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{5} b e^{\left(-1\right)} + 36465 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{4} b^{2} e^{\left(-2\right)} + 22100 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a^{3} b^{3} e^{\left(-3\right)} + 3825 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} a^{2} b^{4} e^{\left(-4\right)} + 714 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} a b^{5} e^{\left(-5\right)} + 7 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} b^{6} e^{\left(-6\right)} + 51051 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{6}\right)} e^{\left(-1\right)}"," ",0,"2/765765*(1531530*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^5*b*d^2*e^(-1) + 765765*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^4*b^2*d^2*e^(-2) + 437580*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^3*b^3*d^2*e^(-3) + 36465*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^2*b^4*d^2*e^(-4) + 6630*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a*b^5*d^2*e^(-5) + 255*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*b^6*d^2*e^(-6) + 612612*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^5*b*d*e^(-1) + 656370*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^4*b^2*d*e^(-2) + 97240*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^3*b^3*d*e^(-3) + 33150*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a^2*b^4*d*e^(-4) + 3060*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*a*b^5*d*e^(-5) + 238*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*b^6*d*e^(-6) + 765765*sqrt(x*e + d)*a^6*d^2 + 510510*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^6*d + 131274*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^5*b*e^(-1) + 36465*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^4*b^2*e^(-2) + 22100*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a^3*b^3*e^(-3) + 3825*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*a^2*b^4*e^(-4) + 714*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*a*b^5*e^(-5) + 7*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*b^6*e^(-6) + 51051*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^6)*e^(-1)","B",0
1640,1,886,0,0.212753," ","integrate((b^2*x^2+2*a*b*x+a^2)^3*(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{45045} \, {\left(90090 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{5} b d e^{\left(-1\right)} + 45045 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{4} b^{2} d e^{\left(-2\right)} + 25740 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{3} b^{3} d e^{\left(-3\right)} + 2145 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{2} b^{4} d e^{\left(-4\right)} + 390 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a b^{5} d e^{\left(-5\right)} + 15 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} b^{6} d e^{\left(-6\right)} + 18018 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{5} b e^{\left(-1\right)} + 19305 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{4} b^{2} e^{\left(-2\right)} + 2860 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{3} b^{3} e^{\left(-3\right)} + 975 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a^{2} b^{4} e^{\left(-4\right)} + 90 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} a b^{5} e^{\left(-5\right)} + 7 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} b^{6} e^{\left(-6\right)} + 45045 \, \sqrt{x e + d} a^{6} d + 15015 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{6}\right)} e^{\left(-1\right)}"," ",0,"2/45045*(90090*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^5*b*d*e^(-1) + 45045*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^4*b^2*d*e^(-2) + 25740*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^3*b^3*d*e^(-3) + 2145*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^2*b^4*d*e^(-4) + 390*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a*b^5*d*e^(-5) + 15*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*b^6*d*e^(-6) + 18018*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^5*b*e^(-1) + 19305*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^4*b^2*e^(-2) + 2860*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^3*b^3*e^(-3) + 975*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a^2*b^4*e^(-4) + 90*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*a*b^5*e^(-5) + 7*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*b^6*e^(-6) + 45045*sqrt(x*e + d)*a^6*d + 15015*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^6)*e^(-1)","B",0
1641,1,395,0,0.218300," ","integrate((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{3003} \, {\left(6006 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{5} b e^{\left(-1\right)} + 3003 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{4} b^{2} e^{\left(-2\right)} + 1716 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{3} b^{3} e^{\left(-3\right)} + 143 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{2} b^{4} e^{\left(-4\right)} + 26 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a b^{5} e^{\left(-5\right)} + {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} b^{6} e^{\left(-6\right)} + 3003 \, \sqrt{x e + d} a^{6}\right)} e^{\left(-1\right)}"," ",0,"2/3003*(6006*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^5*b*e^(-1) + 3003*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^4*b^2*e^(-2) + 1716*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^3*b^3*e^(-3) + 143*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^2*b^4*e^(-4) + 26*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a*b^5*e^(-5) + (231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*b^6*e^(-6) + 3003*sqrt(x*e + d)*a^6)*e^(-1)","B",0
1642,1,474,0,0.263784," ","integrate((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^(3/2),x, algorithm=""giac"")","\frac{2}{231} \, {\left(21 \, {\left(x e + d\right)}^{\frac{11}{2}} b^{6} e^{70} - 154 \, {\left(x e + d\right)}^{\frac{9}{2}} b^{6} d e^{70} + 495 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{6} d^{2} e^{70} - 924 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{6} d^{3} e^{70} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{6} d^{4} e^{70} - 1386 \, \sqrt{x e + d} b^{6} d^{5} e^{70} + 154 \, {\left(x e + d\right)}^{\frac{9}{2}} a b^{5} e^{71} - 990 \, {\left(x e + d\right)}^{\frac{7}{2}} a b^{5} d e^{71} + 2772 \, {\left(x e + d\right)}^{\frac{5}{2}} a b^{5} d^{2} e^{71} - 4620 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{5} d^{3} e^{71} + 6930 \, \sqrt{x e + d} a b^{5} d^{4} e^{71} + 495 \, {\left(x e + d\right)}^{\frac{7}{2}} a^{2} b^{4} e^{72} - 2772 \, {\left(x e + d\right)}^{\frac{5}{2}} a^{2} b^{4} d e^{72} + 6930 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} b^{4} d^{2} e^{72} - 13860 \, \sqrt{x e + d} a^{2} b^{4} d^{3} e^{72} + 924 \, {\left(x e + d\right)}^{\frac{5}{2}} a^{3} b^{3} e^{73} - 4620 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{3} b^{3} d e^{73} + 13860 \, \sqrt{x e + d} a^{3} b^{3} d^{2} e^{73} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{4} b^{2} e^{74} - 6930 \, \sqrt{x e + d} a^{4} b^{2} d e^{74} + 1386 \, \sqrt{x e + d} a^{5} b e^{75}\right)} e^{\left(-77\right)} - \frac{2 \, {\left(b^{6} d^{6} - 6 \, a b^{5} d^{5} e + 15 \, a^{2} b^{4} d^{4} e^{2} - 20 \, a^{3} b^{3} d^{3} e^{3} + 15 \, a^{4} b^{2} d^{2} e^{4} - 6 \, a^{5} b d e^{5} + a^{6} e^{6}\right)} e^{\left(-7\right)}}{\sqrt{x e + d}}"," ",0,"2/231*(21*(x*e + d)^(11/2)*b^6*e^70 - 154*(x*e + d)^(9/2)*b^6*d*e^70 + 495*(x*e + d)^(7/2)*b^6*d^2*e^70 - 924*(x*e + d)^(5/2)*b^6*d^3*e^70 + 1155*(x*e + d)^(3/2)*b^6*d^4*e^70 - 1386*sqrt(x*e + d)*b^6*d^5*e^70 + 154*(x*e + d)^(9/2)*a*b^5*e^71 - 990*(x*e + d)^(7/2)*a*b^5*d*e^71 + 2772*(x*e + d)^(5/2)*a*b^5*d^2*e^71 - 4620*(x*e + d)^(3/2)*a*b^5*d^3*e^71 + 6930*sqrt(x*e + d)*a*b^5*d^4*e^71 + 495*(x*e + d)^(7/2)*a^2*b^4*e^72 - 2772*(x*e + d)^(5/2)*a^2*b^4*d*e^72 + 6930*(x*e + d)^(3/2)*a^2*b^4*d^2*e^72 - 13860*sqrt(x*e + d)*a^2*b^4*d^3*e^72 + 924*(x*e + d)^(5/2)*a^3*b^3*e^73 - 4620*(x*e + d)^(3/2)*a^3*b^3*d*e^73 + 13860*sqrt(x*e + d)*a^3*b^3*d^2*e^73 + 1155*(x*e + d)^(3/2)*a^4*b^2*e^74 - 6930*sqrt(x*e + d)*a^4*b^2*d*e^74 + 1386*sqrt(x*e + d)*a^5*b*e^75)*e^(-77) - 2*(b^6*d^6 - 6*a*b^5*d^5*e + 15*a^2*b^4*d^4*e^2 - 20*a^3*b^3*d^3*e^3 + 15*a^4*b^2*d^2*e^4 - 6*a^5*b*d*e^5 + a^6*e^6)*e^(-7)/sqrt(x*e + d)","B",0
1643,1,462,0,0.238412," ","integrate((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^(5/2),x, algorithm=""giac"")","\frac{2}{63} \, {\left(7 \, {\left(x e + d\right)}^{\frac{9}{2}} b^{6} e^{56} - 54 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{6} d e^{56} + 189 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{6} d^{2} e^{56} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{6} d^{3} e^{56} + 945 \, \sqrt{x e + d} b^{6} d^{4} e^{56} + 54 \, {\left(x e + d\right)}^{\frac{7}{2}} a b^{5} e^{57} - 378 \, {\left(x e + d\right)}^{\frac{5}{2}} a b^{5} d e^{57} + 1260 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{5} d^{2} e^{57} - 3780 \, \sqrt{x e + d} a b^{5} d^{3} e^{57} + 189 \, {\left(x e + d\right)}^{\frac{5}{2}} a^{2} b^{4} e^{58} - 1260 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} b^{4} d e^{58} + 5670 \, \sqrt{x e + d} a^{2} b^{4} d^{2} e^{58} + 420 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{3} b^{3} e^{59} - 3780 \, \sqrt{x e + d} a^{3} b^{3} d e^{59} + 945 \, \sqrt{x e + d} a^{4} b^{2} e^{60}\right)} e^{\left(-63\right)} + \frac{2 \, {\left(18 \, {\left(x e + d\right)} b^{6} d^{5} - b^{6} d^{6} - 90 \, {\left(x e + d\right)} a b^{5} d^{4} e + 6 \, a b^{5} d^{5} e + 180 \, {\left(x e + d\right)} a^{2} b^{4} d^{3} e^{2} - 15 \, a^{2} b^{4} d^{4} e^{2} - 180 \, {\left(x e + d\right)} a^{3} b^{3} d^{2} e^{3} + 20 \, a^{3} b^{3} d^{3} e^{3} + 90 \, {\left(x e + d\right)} a^{4} b^{2} d e^{4} - 15 \, a^{4} b^{2} d^{2} e^{4} - 18 \, {\left(x e + d\right)} a^{5} b e^{5} + 6 \, a^{5} b d e^{5} - a^{6} e^{6}\right)} e^{\left(-7\right)}}{3 \, {\left(x e + d\right)}^{\frac{3}{2}}}"," ",0,"2/63*(7*(x*e + d)^(9/2)*b^6*e^56 - 54*(x*e + d)^(7/2)*b^6*d*e^56 + 189*(x*e + d)^(5/2)*b^6*d^2*e^56 - 420*(x*e + d)^(3/2)*b^6*d^3*e^56 + 945*sqrt(x*e + d)*b^6*d^4*e^56 + 54*(x*e + d)^(7/2)*a*b^5*e^57 - 378*(x*e + d)^(5/2)*a*b^5*d*e^57 + 1260*(x*e + d)^(3/2)*a*b^5*d^2*e^57 - 3780*sqrt(x*e + d)*a*b^5*d^3*e^57 + 189*(x*e + d)^(5/2)*a^2*b^4*e^58 - 1260*(x*e + d)^(3/2)*a^2*b^4*d*e^58 + 5670*sqrt(x*e + d)*a^2*b^4*d^2*e^58 + 420*(x*e + d)^(3/2)*a^3*b^3*e^59 - 3780*sqrt(x*e + d)*a^3*b^3*d*e^59 + 945*sqrt(x*e + d)*a^4*b^2*e^60)*e^(-63) + 2/3*(18*(x*e + d)*b^6*d^5 - b^6*d^6 - 90*(x*e + d)*a*b^5*d^4*e + 6*a*b^5*d^5*e + 180*(x*e + d)*a^2*b^4*d^3*e^2 - 15*a^2*b^4*d^4*e^2 - 180*(x*e + d)*a^3*b^3*d^2*e^3 + 20*a^3*b^3*d^3*e^3 + 90*(x*e + d)*a^4*b^2*d*e^4 - 15*a^4*b^2*d^2*e^4 - 18*(x*e + d)*a^5*b*e^5 + 6*a^5*b*d*e^5 - a^6*e^6)*e^(-7)/(x*e + d)^(3/2)","B",0
1644,1,458,0,0.221794," ","integrate((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^(7/2),x, algorithm=""giac"")","\frac{2}{35} \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{6} e^{42} - 42 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{6} d e^{42} + 175 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{6} d^{2} e^{42} - 700 \, \sqrt{x e + d} b^{6} d^{3} e^{42} + 42 \, {\left(x e + d\right)}^{\frac{5}{2}} a b^{5} e^{43} - 350 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{5} d e^{43} + 2100 \, \sqrt{x e + d} a b^{5} d^{2} e^{43} + 175 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} b^{4} e^{44} - 2100 \, \sqrt{x e + d} a^{2} b^{4} d e^{44} + 700 \, \sqrt{x e + d} a^{3} b^{3} e^{45}\right)} e^{\left(-49\right)} - \frac{2 \, {\left(75 \, {\left(x e + d\right)}^{2} b^{6} d^{4} - 10 \, {\left(x e + d\right)} b^{6} d^{5} + b^{6} d^{6} - 300 \, {\left(x e + d\right)}^{2} a b^{5} d^{3} e + 50 \, {\left(x e + d\right)} a b^{5} d^{4} e - 6 \, a b^{5} d^{5} e + 450 \, {\left(x e + d\right)}^{2} a^{2} b^{4} d^{2} e^{2} - 100 \, {\left(x e + d\right)} a^{2} b^{4} d^{3} e^{2} + 15 \, a^{2} b^{4} d^{4} e^{2} - 300 \, {\left(x e + d\right)}^{2} a^{3} b^{3} d e^{3} + 100 \, {\left(x e + d\right)} a^{3} b^{3} d^{2} e^{3} - 20 \, a^{3} b^{3} d^{3} e^{3} + 75 \, {\left(x e + d\right)}^{2} a^{4} b^{2} e^{4} - 50 \, {\left(x e + d\right)} a^{4} b^{2} d e^{4} + 15 \, a^{4} b^{2} d^{2} e^{4} + 10 \, {\left(x e + d\right)} a^{5} b e^{5} - 6 \, a^{5} b d e^{5} + a^{6} e^{6}\right)} e^{\left(-7\right)}}{5 \, {\left(x e + d\right)}^{\frac{5}{2}}}"," ",0,"2/35*(5*(x*e + d)^(7/2)*b^6*e^42 - 42*(x*e + d)^(5/2)*b^6*d*e^42 + 175*(x*e + d)^(3/2)*b^6*d^2*e^42 - 700*sqrt(x*e + d)*b^6*d^3*e^42 + 42*(x*e + d)^(5/2)*a*b^5*e^43 - 350*(x*e + d)^(3/2)*a*b^5*d*e^43 + 2100*sqrt(x*e + d)*a*b^5*d^2*e^43 + 175*(x*e + d)^(3/2)*a^2*b^4*e^44 - 2100*sqrt(x*e + d)*a^2*b^4*d*e^44 + 700*sqrt(x*e + d)*a^3*b^3*e^45)*e^(-49) - 2/5*(75*(x*e + d)^2*b^6*d^4 - 10*(x*e + d)*b^6*d^5 + b^6*d^6 - 300*(x*e + d)^2*a*b^5*d^3*e + 50*(x*e + d)*a*b^5*d^4*e - 6*a*b^5*d^5*e + 450*(x*e + d)^2*a^2*b^4*d^2*e^2 - 100*(x*e + d)*a^2*b^4*d^3*e^2 + 15*a^2*b^4*d^4*e^2 - 300*(x*e + d)^2*a^3*b^3*d*e^3 + 100*(x*e + d)*a^3*b^3*d^2*e^3 - 20*a^3*b^3*d^3*e^3 + 75*(x*e + d)^2*a^4*b^2*e^4 - 50*(x*e + d)*a^4*b^2*d*e^4 + 15*a^4*b^2*d^2*e^4 + 10*(x*e + d)*a^5*b*e^5 - 6*a^5*b*d*e^5 + a^6*e^6)*e^(-7)/(x*e + d)^(5/2)","B",0
1645,1,387,0,0.196226," ","integrate((e*x+d)^(9/2)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{9 \, {\left(b^{4} d^{4} e - 4 \, a b^{3} d^{3} e^{2} + 6 \, a^{2} b^{2} d^{2} e^{3} - 4 \, a^{3} b d e^{4} + a^{4} e^{5}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{\sqrt{-b^{2} d + a b e} b^{5}} - \frac{\sqrt{x e + d} b^{4} d^{4} e - 4 \, \sqrt{x e + d} a b^{3} d^{3} e^{2} + 6 \, \sqrt{x e + d} a^{2} b^{2} d^{2} e^{3} - 4 \, \sqrt{x e + d} a^{3} b d e^{4} + \sqrt{x e + d} a^{4} e^{5}}{{\left({\left(x e + d\right)} b - b d + a e\right)} b^{5}} + \frac{2 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{12} e + 14 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{12} d e + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{12} d^{2} e + 140 \, \sqrt{x e + d} b^{12} d^{3} e - 14 \, {\left(x e + d\right)}^{\frac{5}{2}} a b^{11} e^{2} - 70 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{11} d e^{2} - 420 \, \sqrt{x e + d} a b^{11} d^{2} e^{2} + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} b^{10} e^{3} + 420 \, \sqrt{x e + d} a^{2} b^{10} d e^{3} - 140 \, \sqrt{x e + d} a^{3} b^{9} e^{4}\right)}}{35 \, b^{14}}"," ",0,"9*(b^4*d^4*e - 4*a*b^3*d^3*e^2 + 6*a^2*b^2*d^2*e^3 - 4*a^3*b*d*e^4 + a^4*e^5)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/(sqrt(-b^2*d + a*b*e)*b^5) - (sqrt(x*e + d)*b^4*d^4*e - 4*sqrt(x*e + d)*a*b^3*d^3*e^2 + 6*sqrt(x*e + d)*a^2*b^2*d^2*e^3 - 4*sqrt(x*e + d)*a^3*b*d*e^4 + sqrt(x*e + d)*a^4*e^5)/(((x*e + d)*b - b*d + a*e)*b^5) + 2/35*(5*(x*e + d)^(7/2)*b^12*e + 14*(x*e + d)^(5/2)*b^12*d*e + 35*(x*e + d)^(3/2)*b^12*d^2*e + 140*sqrt(x*e + d)*b^12*d^3*e - 14*(x*e + d)^(5/2)*a*b^11*e^2 - 70*(x*e + d)^(3/2)*a*b^11*d*e^2 - 420*sqrt(x*e + d)*a*b^11*d^2*e^2 + 35*(x*e + d)^(3/2)*a^2*b^10*e^3 + 420*sqrt(x*e + d)*a^2*b^10*d*e^3 - 140*sqrt(x*e + d)*a^3*b^9*e^4)/b^14","B",0
1646,1,281,0,0.190499," ","integrate((e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{7 \, {\left(b^{3} d^{3} e - 3 \, a b^{2} d^{2} e^{2} + 3 \, a^{2} b d e^{3} - a^{3} e^{4}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{\sqrt{-b^{2} d + a b e} b^{4}} - \frac{\sqrt{x e + d} b^{3} d^{3} e - 3 \, \sqrt{x e + d} a b^{2} d^{2} e^{2} + 3 \, \sqrt{x e + d} a^{2} b d e^{3} - \sqrt{x e + d} a^{3} e^{4}}{{\left({\left(x e + d\right)} b - b d + a e\right)} b^{4}} + \frac{2 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{8} e + 10 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{8} d e + 45 \, \sqrt{x e + d} b^{8} d^{2} e - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{7} e^{2} - 90 \, \sqrt{x e + d} a b^{7} d e^{2} + 45 \, \sqrt{x e + d} a^{2} b^{6} e^{3}\right)}}{15 \, b^{10}}"," ",0,"7*(b^3*d^3*e - 3*a*b^2*d^2*e^2 + 3*a^2*b*d*e^3 - a^3*e^4)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/(sqrt(-b^2*d + a*b*e)*b^4) - (sqrt(x*e + d)*b^3*d^3*e - 3*sqrt(x*e + d)*a*b^2*d^2*e^2 + 3*sqrt(x*e + d)*a^2*b*d*e^3 - sqrt(x*e + d)*a^3*e^4)/(((x*e + d)*b - b*d + a*e)*b^4) + 2/15*(3*(x*e + d)^(5/2)*b^8*e + 10*(x*e + d)^(3/2)*b^8*d*e + 45*sqrt(x*e + d)*b^8*d^2*e - 10*(x*e + d)^(3/2)*a*b^7*e^2 - 90*sqrt(x*e + d)*a*b^7*d*e^2 + 45*sqrt(x*e + d)*a^2*b^6*e^3)/b^10","B",0
1647,1,191,0,0.182238," ","integrate((e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{5 \, {\left(b^{2} d^{2} e - 2 \, a b d e^{2} + a^{2} e^{3}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{\sqrt{-b^{2} d + a b e} b^{3}} - \frac{\sqrt{x e + d} b^{2} d^{2} e - 2 \, \sqrt{x e + d} a b d e^{2} + \sqrt{x e + d} a^{2} e^{3}}{{\left({\left(x e + d\right)} b - b d + a e\right)} b^{3}} + \frac{2 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} b^{4} e + 6 \, \sqrt{x e + d} b^{4} d e - 6 \, \sqrt{x e + d} a b^{3} e^{2}\right)}}{3 \, b^{6}}"," ",0,"5*(b^2*d^2*e - 2*a*b*d*e^2 + a^2*e^3)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/(sqrt(-b^2*d + a*b*e)*b^3) - (sqrt(x*e + d)*b^2*d^2*e - 2*sqrt(x*e + d)*a*b*d*e^2 + sqrt(x*e + d)*a^2*e^3)/(((x*e + d)*b - b*d + a*e)*b^3) + 2/3*((x*e + d)^(3/2)*b^4*e + 6*sqrt(x*e + d)*b^4*d*e - 6*sqrt(x*e + d)*a*b^3*e^2)/b^6","B",0
1648,1,122,0,0.205543," ","integrate((e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{3 \, {\left(b d e - a e^{2}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{\sqrt{-b^{2} d + a b e} b^{2}} + \frac{2 \, \sqrt{x e + d} e}{b^{2}} - \frac{\sqrt{x e + d} b d e - \sqrt{x e + d} a e^{2}}{{\left({\left(x e + d\right)} b - b d + a e\right)} b^{2}}"," ",0,"3*(b*d*e - a*e^2)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/(sqrt(-b^2*d + a*b*e)*b^2) + 2*sqrt(x*e + d)*e/b^2 - (sqrt(x*e + d)*b*d*e - sqrt(x*e + d)*a*e^2)/(((x*e + d)*b - b*d + a*e)*b^2)","A",0
1649,1,80,0,0.182631," ","integrate((e*x+d)^(1/2)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{\arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e}{\sqrt{-b^{2} d + a b e} b} - \frac{\sqrt{x e + d} e}{{\left({\left(x e + d\right)} b - b d + a e\right)} b}"," ",0,"arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e/(sqrt(-b^2*d + a*b*e)*b) - sqrt(x*e + d)*e/(((x*e + d)*b - b*d + a*e)*b)","A",0
1650,1,97,0,0.171723," ","integrate(1/(e*x+d)^(1/2)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","-\frac{\arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e}{\sqrt{-b^{2} d + a b e} {\left(b d - a e\right)}} - \frac{\sqrt{x e + d} e}{{\left({\left(x e + d\right)} b - b d + a e\right)} {\left(b d - a e\right)}}"," ",0,"-arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e/(sqrt(-b^2*d + a*b*e)*(b*d - a*e)) - sqrt(x*e + d)*e/(((x*e + d)*b - b*d + a*e)*(b*d - a*e))","A",0
1651,1,153,0,0.179575," ","integrate(1/(e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","-\frac{3 \, b \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e}{{\left(b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}\right)} \sqrt{-b^{2} d + a b e}} - \frac{3 \, {\left(x e + d\right)} b e - 2 \, b d e + 2 \, a e^{2}}{{\left(b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}\right)} {\left({\left(x e + d\right)}^{\frac{3}{2}} b - \sqrt{x e + d} b d + \sqrt{x e + d} a e\right)}}"," ",0,"-3*b*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e/((b^2*d^2 - 2*a*b*d*e + a^2*e^2)*sqrt(-b^2*d + a*b*e)) - (3*(x*e + d)*b*e - 2*b*d*e + 2*a*e^2)/((b^2*d^2 - 2*a*b*d*e + a^2*e^2)*((x*e + d)^(3/2)*b - sqrt(x*e + d)*b*d + sqrt(x*e + d)*a*e))","A",0
1652,1,224,0,0.191977," ","integrate(1/(e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","-\frac{5 \, b^{2} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e}{{\left(b^{3} d^{3} - 3 \, a b^{2} d^{2} e + 3 \, a^{2} b d e^{2} - a^{3} e^{3}\right)} \sqrt{-b^{2} d + a b e}} - \frac{\sqrt{x e + d} b^{2} e}{{\left(b^{3} d^{3} - 3 \, a b^{2} d^{2} e + 3 \, a^{2} b d e^{2} - a^{3} e^{3}\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}} - \frac{2 \, {\left(6 \, {\left(x e + d\right)} b e + b d e - a e^{2}\right)}}{3 \, {\left(b^{3} d^{3} - 3 \, a b^{2} d^{2} e + 3 \, a^{2} b d e^{2} - a^{3} e^{3}\right)} {\left(x e + d\right)}^{\frac{3}{2}}}"," ",0,"-5*b^2*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e/((b^3*d^3 - 3*a*b^2*d^2*e + 3*a^2*b*d*e^2 - a^3*e^3)*sqrt(-b^2*d + a*b*e)) - sqrt(x*e + d)*b^2*e/((b^3*d^3 - 3*a*b^2*d^2*e + 3*a^2*b*d*e^2 - a^3*e^3)*((x*e + d)*b - b*d + a*e)) - 2/3*(6*(x*e + d)*b*e + b*d*e - a*e^2)/((b^3*d^3 - 3*a*b^2*d^2*e + 3*a^2*b*d*e^2 - a^3*e^3)*(x*e + d)^(3/2))","B",0
1653,1,304,0,0.202855," ","integrate(1/(e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","-\frac{7 \, b^{3} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e}{{\left(b^{4} d^{4} - 4 \, a b^{3} d^{3} e + 6 \, a^{2} b^{2} d^{2} e^{2} - 4 \, a^{3} b d e^{3} + a^{4} e^{4}\right)} \sqrt{-b^{2} d + a b e}} - \frac{\sqrt{x e + d} b^{3} e}{{\left(b^{4} d^{4} - 4 \, a b^{3} d^{3} e + 6 \, a^{2} b^{2} d^{2} e^{2} - 4 \, a^{3} b d e^{3} + a^{4} e^{4}\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}} - \frac{2 \, {\left(45 \, {\left(x e + d\right)}^{2} b^{2} e + 10 \, {\left(x e + d\right)} b^{2} d e + 3 \, b^{2} d^{2} e - 10 \, {\left(x e + d\right)} a b e^{2} - 6 \, a b d e^{2} + 3 \, a^{2} e^{3}\right)}}{15 \, {\left(b^{4} d^{4} - 4 \, a b^{3} d^{3} e + 6 \, a^{2} b^{2} d^{2} e^{2} - 4 \, a^{3} b d e^{3} + a^{4} e^{4}\right)} {\left(x e + d\right)}^{\frac{5}{2}}}"," ",0,"-7*b^3*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e/((b^4*d^4 - 4*a*b^3*d^3*e + 6*a^2*b^2*d^2*e^2 - 4*a^3*b*d*e^3 + a^4*e^4)*sqrt(-b^2*d + a*b*e)) - sqrt(x*e + d)*b^3*e/((b^4*d^4 - 4*a*b^3*d^3*e + 6*a^2*b^2*d^2*e^2 - 4*a^3*b*d*e^3 + a^4*e^4)*((x*e + d)*b - b*d + a*e)) - 2/15*(45*(x*e + d)^2*b^2*e + 10*(x*e + d)*b^2*d*e + 3*b^2*d^2*e - 10*(x*e + d)*a*b*e^2 - 6*a*b*d*e^2 + 3*a^2*e^3)/((b^4*d^4 - 4*a*b^3*d^3*e + 6*a^2*b^2*d^2*e^2 - 4*a^3*b*d*e^3 + a^4*e^4)*(x*e + d)^(5/2))","B",0
1654,1,491,0,0.238539," ","integrate((e*x+d)^(11/2)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{231 \, {\left(b^{3} d^{3} e^{3} - 3 \, a b^{2} d^{2} e^{4} + 3 \, a^{2} b d e^{5} - a^{3} e^{6}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{8 \, \sqrt{-b^{2} d + a b e} b^{6}} - \frac{267 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{5} d^{3} e^{3} - 472 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{5} d^{4} e^{3} + 213 \, \sqrt{x e + d} b^{5} d^{5} e^{3} - 801 \, {\left(x e + d\right)}^{\frac{5}{2}} a b^{4} d^{2} e^{4} + 1888 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{4} d^{3} e^{4} - 1065 \, \sqrt{x e + d} a b^{4} d^{4} e^{4} + 801 \, {\left(x e + d\right)}^{\frac{5}{2}} a^{2} b^{3} d e^{5} - 2832 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} b^{3} d^{2} e^{5} + 2130 \, \sqrt{x e + d} a^{2} b^{3} d^{3} e^{5} - 267 \, {\left(x e + d\right)}^{\frac{5}{2}} a^{3} b^{2} e^{6} + 1888 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{3} b^{2} d e^{6} - 2130 \, \sqrt{x e + d} a^{3} b^{2} d^{2} e^{6} - 472 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{4} b e^{7} + 1065 \, \sqrt{x e + d} a^{4} b d e^{7} - 213 \, \sqrt{x e + d} a^{5} e^{8}}{24 \, {\left({\left(x e + d\right)} b - b d + a e\right)}^{3} b^{6}} + \frac{2 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{16} e^{3} + 20 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{16} d e^{3} + 150 \, \sqrt{x e + d} b^{16} d^{2} e^{3} - 20 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{15} e^{4} - 300 \, \sqrt{x e + d} a b^{15} d e^{4} + 150 \, \sqrt{x e + d} a^{2} b^{14} e^{5}\right)}}{15 \, b^{20}}"," ",0,"231/8*(b^3*d^3*e^3 - 3*a*b^2*d^2*e^4 + 3*a^2*b*d*e^5 - a^3*e^6)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/(sqrt(-b^2*d + a*b*e)*b^6) - 1/24*(267*(x*e + d)^(5/2)*b^5*d^3*e^3 - 472*(x*e + d)^(3/2)*b^5*d^4*e^3 + 213*sqrt(x*e + d)*b^5*d^5*e^3 - 801*(x*e + d)^(5/2)*a*b^4*d^2*e^4 + 1888*(x*e + d)^(3/2)*a*b^4*d^3*e^4 - 1065*sqrt(x*e + d)*a*b^4*d^4*e^4 + 801*(x*e + d)^(5/2)*a^2*b^3*d*e^5 - 2832*(x*e + d)^(3/2)*a^2*b^3*d^2*e^5 + 2130*sqrt(x*e + d)*a^2*b^3*d^3*e^5 - 267*(x*e + d)^(5/2)*a^3*b^2*e^6 + 1888*(x*e + d)^(3/2)*a^3*b^2*d*e^6 - 2130*sqrt(x*e + d)*a^3*b^2*d^2*e^6 - 472*(x*e + d)^(3/2)*a^4*b*e^7 + 1065*sqrt(x*e + d)*a^4*b*d*e^7 - 213*sqrt(x*e + d)*a^5*e^8)/(((x*e + d)*b - b*d + a*e)^3*b^6) + 2/15*(3*(x*e + d)^(5/2)*b^16*e^3 + 20*(x*e + d)^(3/2)*b^16*d*e^3 + 150*sqrt(x*e + d)*b^16*d^2*e^3 - 20*(x*e + d)^(3/2)*a*b^15*e^4 - 300*sqrt(x*e + d)*a*b^15*d*e^4 + 150*sqrt(x*e + d)*a^2*b^14*e^5)/b^20","B",0
1655,1,360,0,0.223059," ","integrate((e*x+d)^(9/2)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{105 \, {\left(b^{2} d^{2} e^{3} - 2 \, a b d e^{4} + a^{2} e^{5}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{8 \, \sqrt{-b^{2} d + a b e} b^{5}} - \frac{165 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{4} d^{2} e^{3} - 280 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{4} d^{3} e^{3} + 123 \, \sqrt{x e + d} b^{4} d^{4} e^{3} - 330 \, {\left(x e + d\right)}^{\frac{5}{2}} a b^{3} d e^{4} + 840 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{3} d^{2} e^{4} - 492 \, \sqrt{x e + d} a b^{3} d^{3} e^{4} + 165 \, {\left(x e + d\right)}^{\frac{5}{2}} a^{2} b^{2} e^{5} - 840 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} b^{2} d e^{5} + 738 \, \sqrt{x e + d} a^{2} b^{2} d^{2} e^{5} + 280 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{3} b e^{6} - 492 \, \sqrt{x e + d} a^{3} b d e^{6} + 123 \, \sqrt{x e + d} a^{4} e^{7}}{24 \, {\left({\left(x e + d\right)} b - b d + a e\right)}^{3} b^{5}} + \frac{2 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} b^{8} e^{3} + 12 \, \sqrt{x e + d} b^{8} d e^{3} - 12 \, \sqrt{x e + d} a b^{7} e^{4}\right)}}{3 \, b^{12}}"," ",0,"105/8*(b^2*d^2*e^3 - 2*a*b*d*e^4 + a^2*e^5)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/(sqrt(-b^2*d + a*b*e)*b^5) - 1/24*(165*(x*e + d)^(5/2)*b^4*d^2*e^3 - 280*(x*e + d)^(3/2)*b^4*d^3*e^3 + 123*sqrt(x*e + d)*b^4*d^4*e^3 - 330*(x*e + d)^(5/2)*a*b^3*d*e^4 + 840*(x*e + d)^(3/2)*a*b^3*d^2*e^4 - 492*sqrt(x*e + d)*a*b^3*d^3*e^4 + 165*(x*e + d)^(5/2)*a^2*b^2*e^5 - 840*(x*e + d)^(3/2)*a^2*b^2*d*e^5 + 738*sqrt(x*e + d)*a^2*b^2*d^2*e^5 + 280*(x*e + d)^(3/2)*a^3*b*e^6 - 492*sqrt(x*e + d)*a^3*b*d*e^6 + 123*sqrt(x*e + d)*a^4*e^7)/(((x*e + d)*b - b*d + a*e)^3*b^5) + 2/3*((x*e + d)^(3/2)*b^8*e^3 + 12*sqrt(x*e + d)*b^8*d*e^3 - 12*sqrt(x*e + d)*a*b^7*e^4)/b^12","B",0
1656,1,248,0,0.217096," ","integrate((e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{35 \, {\left(b d e^{3} - a e^{4}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{8 \, \sqrt{-b^{2} d + a b e} b^{4}} + \frac{2 \, \sqrt{x e + d} e^{3}}{b^{4}} - \frac{87 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{3} d e^{3} - 136 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{3} d^{2} e^{3} + 57 \, \sqrt{x e + d} b^{3} d^{3} e^{3} - 87 \, {\left(x e + d\right)}^{\frac{5}{2}} a b^{2} e^{4} + 272 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{2} d e^{4} - 171 \, \sqrt{x e + d} a b^{2} d^{2} e^{4} - 136 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} b e^{5} + 171 \, \sqrt{x e + d} a^{2} b d e^{5} - 57 \, \sqrt{x e + d} a^{3} e^{6}}{24 \, {\left({\left(x e + d\right)} b - b d + a e\right)}^{3} b^{4}}"," ",0,"35/8*(b*d*e^3 - a*e^4)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/(sqrt(-b^2*d + a*b*e)*b^4) + 2*sqrt(x*e + d)*e^3/b^4 - 1/24*(87*(x*e + d)^(5/2)*b^3*d*e^3 - 136*(x*e + d)^(3/2)*b^3*d^2*e^3 + 57*sqrt(x*e + d)*b^3*d^3*e^3 - 87*(x*e + d)^(5/2)*a*b^2*e^4 + 272*(x*e + d)^(3/2)*a*b^2*d*e^4 - 171*sqrt(x*e + d)*a*b^2*d^2*e^4 - 136*(x*e + d)^(3/2)*a^2*b*e^5 + 171*sqrt(x*e + d)*a^2*b*d*e^5 - 57*sqrt(x*e + d)*a^3*e^6)/(((x*e + d)*b - b*d + a*e)^3*b^4)","B",0
1657,1,165,0,0.205391," ","integrate((e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{5 \, \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e^{3}}{8 \, \sqrt{-b^{2} d + a b e} b^{3}} - \frac{33 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{2} e^{3} - 40 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{2} d e^{3} + 15 \, \sqrt{x e + d} b^{2} d^{2} e^{3} + 40 \, {\left(x e + d\right)}^{\frac{3}{2}} a b e^{4} - 30 \, \sqrt{x e + d} a b d e^{4} + 15 \, \sqrt{x e + d} a^{2} e^{5}}{24 \, {\left({\left(x e + d\right)} b - b d + a e\right)}^{3} b^{3}}"," ",0,"5/8*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e^3/(sqrt(-b^2*d + a*b*e)*b^3) - 1/24*(33*(x*e + d)^(5/2)*b^2*e^3 - 40*(x*e + d)^(3/2)*b^2*d*e^3 + 15*sqrt(x*e + d)*b^2*d^2*e^3 + 40*(x*e + d)^(3/2)*a*b*e^4 - 30*sqrt(x*e + d)*a*b*d*e^4 + 15*sqrt(x*e + d)*a^2*e^5)/(((x*e + d)*b - b*d + a*e)^3*b^3)","A",0
1658,1,191,0,0.192859," ","integrate((e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","-\frac{\arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e^{3}}{8 \, {\left(b^{3} d - a b^{2} e\right)} \sqrt{-b^{2} d + a b e}} - \frac{3 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{2} e^{3} + 8 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{2} d e^{3} - 3 \, \sqrt{x e + d} b^{2} d^{2} e^{3} - 8 \, {\left(x e + d\right)}^{\frac{3}{2}} a b e^{4} + 6 \, \sqrt{x e + d} a b d e^{4} - 3 \, \sqrt{x e + d} a^{2} e^{5}}{24 \, {\left(b^{3} d - a b^{2} e\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{3}}"," ",0,"-1/8*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e^3/((b^3*d - a*b^2*e)*sqrt(-b^2*d + a*b*e)) - 1/24*(3*(x*e + d)^(5/2)*b^2*e^3 + 8*(x*e + d)^(3/2)*b^2*d*e^3 - 3*sqrt(x*e + d)*b^2*d^2*e^3 - 8*(x*e + d)^(3/2)*a*b*e^4 + 6*sqrt(x*e + d)*a*b*d*e^4 - 3*sqrt(x*e + d)*a^2*e^5)/((b^3*d - a*b^2*e)*((x*e + d)*b - b*d + a*e)^3)","A",0
1659,1,211,0,0.184918," ","integrate((e*x+d)^(1/2)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{\arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e^{3}}{8 \, {\left(b^{3} d^{2} - 2 \, a b^{2} d e + a^{2} b e^{2}\right)} \sqrt{-b^{2} d + a b e}} + \frac{3 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{2} e^{3} - 8 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{2} d e^{3} - 3 \, \sqrt{x e + d} b^{2} d^{2} e^{3} + 8 \, {\left(x e + d\right)}^{\frac{3}{2}} a b e^{4} + 6 \, \sqrt{x e + d} a b d e^{4} - 3 \, \sqrt{x e + d} a^{2} e^{5}}{24 \, {\left(b^{3} d^{2} - 2 \, a b^{2} d e + a^{2} b e^{2}\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{3}}"," ",0,"1/8*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e^3/((b^3*d^2 - 2*a*b^2*d*e + a^2*b*e^2)*sqrt(-b^2*d + a*b*e)) + 1/24*(3*(x*e + d)^(5/2)*b^2*e^3 - 8*(x*e + d)^(3/2)*b^2*d*e^3 - 3*sqrt(x*e + d)*b^2*d^2*e^3 + 8*(x*e + d)^(3/2)*a*b*e^4 + 6*sqrt(x*e + d)*a*b*d*e^4 - 3*sqrt(x*e + d)*a^2*e^5)/((b^3*d^2 - 2*a*b^2*d*e + a^2*b*e^2)*((x*e + d)*b - b*d + a*e)^3)","A",0
1660,1,233,0,0.174947," ","integrate(1/(e*x+d)^(1/2)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","-\frac{5 \, \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e^{3}}{8 \, {\left(b^{3} d^{3} - 3 \, a b^{2} d^{2} e + 3 \, a^{2} b d e^{2} - a^{3} e^{3}\right)} \sqrt{-b^{2} d + a b e}} - \frac{15 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{2} e^{3} - 40 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{2} d e^{3} + 33 \, \sqrt{x e + d} b^{2} d^{2} e^{3} + 40 \, {\left(x e + d\right)}^{\frac{3}{2}} a b e^{4} - 66 \, \sqrt{x e + d} a b d e^{4} + 33 \, \sqrt{x e + d} a^{2} e^{5}}{24 \, {\left(b^{3} d^{3} - 3 \, a b^{2} d^{2} e + 3 \, a^{2} b d e^{2} - a^{3} e^{3}\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{3}}"," ",0,"-5/8*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e^3/((b^3*d^3 - 3*a*b^2*d^2*e + 3*a^2*b*d*e^2 - a^3*e^3)*sqrt(-b^2*d + a*b*e)) - 1/24*(15*(x*e + d)^(5/2)*b^2*e^3 - 40*(x*e + d)^(3/2)*b^2*d*e^3 + 33*sqrt(x*e + d)*b^2*d^2*e^3 + 40*(x*e + d)^(3/2)*a*b*e^4 - 66*sqrt(x*e + d)*a*b*d*e^4 + 33*sqrt(x*e + d)*a^2*e^5)/((b^3*d^3 - 3*a*b^2*d^2*e + 3*a^2*b*d*e^2 - a^3*e^3)*((x*e + d)*b - b*d + a*e)^3)","A",0
1661,1,324,0,0.222646," ","integrate(1/(e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","-\frac{35 \, b \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e^{3}}{8 \, {\left(b^{4} d^{4} - 4 \, a b^{3} d^{3} e + 6 \, a^{2} b^{2} d^{2} e^{2} - 4 \, a^{3} b d e^{3} + a^{4} e^{4}\right)} \sqrt{-b^{2} d + a b e}} - \frac{2 \, e^{3}}{{\left(b^{4} d^{4} - 4 \, a b^{3} d^{3} e + 6 \, a^{2} b^{2} d^{2} e^{2} - 4 \, a^{3} b d e^{3} + a^{4} e^{4}\right)} \sqrt{x e + d}} - \frac{57 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{3} e^{3} - 136 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{3} d e^{3} + 87 \, \sqrt{x e + d} b^{3} d^{2} e^{3} + 136 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{2} e^{4} - 174 \, \sqrt{x e + d} a b^{2} d e^{4} + 87 \, \sqrt{x e + d} a^{2} b e^{5}}{24 \, {\left(b^{4} d^{4} - 4 \, a b^{3} d^{3} e + 6 \, a^{2} b^{2} d^{2} e^{2} - 4 \, a^{3} b d e^{3} + a^{4} e^{4}\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{3}}"," ",0,"-35/8*b*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e^3/((b^4*d^4 - 4*a*b^3*d^3*e + 6*a^2*b^2*d^2*e^2 - 4*a^3*b*d*e^3 + a^4*e^4)*sqrt(-b^2*d + a*b*e)) - 2*e^3/((b^4*d^4 - 4*a*b^3*d^3*e + 6*a^2*b^2*d^2*e^2 - 4*a^3*b*d*e^3 + a^4*e^4)*sqrt(x*e + d)) - 1/24*(57*(x*e + d)^(5/2)*b^3*e^3 - 136*(x*e + d)^(3/2)*b^3*d*e^3 + 87*sqrt(x*e + d)*b^3*d^2*e^3 + 136*(x*e + d)^(3/2)*a*b^2*e^4 - 174*sqrt(x*e + d)*a*b^2*d*e^4 + 87*sqrt(x*e + d)*a^2*b*e^5)/((b^4*d^4 - 4*a*b^3*d^3*e + 6*a^2*b^2*d^2*e^2 - 4*a^3*b*d*e^3 + a^4*e^4)*((x*e + d)*b - b*d + a*e)^3)","B",0
1662,1,427,0,0.234275," ","integrate(1/(e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","-\frac{105 \, b^{2} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e^{3}}{8 \, {\left(b^{5} d^{5} - 5 \, a b^{4} d^{4} e + 10 \, a^{2} b^{3} d^{3} e^{2} - 10 \, a^{3} b^{2} d^{2} e^{3} + 5 \, a^{4} b d e^{4} - a^{5} e^{5}\right)} \sqrt{-b^{2} d + a b e}} - \frac{315 \, {\left(x e + d\right)}^{4} b^{4} e^{3} - 840 \, {\left(x e + d\right)}^{3} b^{4} d e^{3} + 693 \, {\left(x e + d\right)}^{2} b^{4} d^{2} e^{3} - 144 \, {\left(x e + d\right)} b^{4} d^{3} e^{3} - 16 \, b^{4} d^{4} e^{3} + 840 \, {\left(x e + d\right)}^{3} a b^{3} e^{4} - 1386 \, {\left(x e + d\right)}^{2} a b^{3} d e^{4} + 432 \, {\left(x e + d\right)} a b^{3} d^{2} e^{4} + 64 \, a b^{3} d^{3} e^{4} + 693 \, {\left(x e + d\right)}^{2} a^{2} b^{2} e^{5} - 432 \, {\left(x e + d\right)} a^{2} b^{2} d e^{5} - 96 \, a^{2} b^{2} d^{2} e^{5} + 144 \, {\left(x e + d\right)} a^{3} b e^{6} + 64 \, a^{3} b d e^{6} - 16 \, a^{4} e^{7}}{24 \, {\left(b^{5} d^{5} - 5 \, a b^{4} d^{4} e + 10 \, a^{2} b^{3} d^{3} e^{2} - 10 \, a^{3} b^{2} d^{2} e^{3} + 5 \, a^{4} b d e^{4} - a^{5} e^{5}\right)} {\left({\left(x e + d\right)}^{\frac{3}{2}} b - \sqrt{x e + d} b d + \sqrt{x e + d} a e\right)}^{3}}"," ",0,"-105/8*b^2*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e^3/((b^5*d^5 - 5*a*b^4*d^4*e + 10*a^2*b^3*d^3*e^2 - 10*a^3*b^2*d^2*e^3 + 5*a^4*b*d*e^4 - a^5*e^5)*sqrt(-b^2*d + a*b*e)) - 1/24*(315*(x*e + d)^4*b^4*e^3 - 840*(x*e + d)^3*b^4*d*e^3 + 693*(x*e + d)^2*b^4*d^2*e^3 - 144*(x*e + d)*b^4*d^3*e^3 - 16*b^4*d^4*e^3 + 840*(x*e + d)^3*a*b^3*e^4 - 1386*(x*e + d)^2*a*b^3*d*e^4 + 432*(x*e + d)*a*b^3*d^2*e^4 + 64*a*b^3*d^3*e^4 + 693*(x*e + d)^2*a^2*b^2*e^5 - 432*(x*e + d)*a^2*b^2*d*e^5 - 96*a^2*b^2*d^2*e^5 + 144*(x*e + d)*a^3*b*e^6 + 64*a^3*b*d*e^6 - 16*a^4*e^7)/((b^5*d^5 - 5*a*b^4*d^4*e + 10*a^2*b^3*d^3*e^2 - 10*a^3*b^2*d^2*e^3 + 5*a^4*b*d*e^4 - a^5*e^5)*((x*e + d)^(3/2)*b - sqrt(x*e + d)*b*d + sqrt(x*e + d)*a*e)^3)","B",0
1663,1,470,0,0.245036," ","integrate(1/(e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","-\frac{231 \, b^{3} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e^{3}}{8 \, {\left(b^{6} d^{6} - 6 \, a b^{5} d^{5} e + 15 \, a^{2} b^{4} d^{4} e^{2} - 20 \, a^{3} b^{3} d^{3} e^{3} + 15 \, a^{4} b^{2} d^{2} e^{4} - 6 \, a^{5} b d e^{5} + a^{6} e^{6}\right)} \sqrt{-b^{2} d + a b e}} - \frac{2 \, {\left(150 \, {\left(x e + d\right)}^{2} b^{2} e^{3} + 20 \, {\left(x e + d\right)} b^{2} d e^{3} + 3 \, b^{2} d^{2} e^{3} - 20 \, {\left(x e + d\right)} a b e^{4} - 6 \, a b d e^{4} + 3 \, a^{2} e^{5}\right)}}{15 \, {\left(b^{6} d^{6} - 6 \, a b^{5} d^{5} e + 15 \, a^{2} b^{4} d^{4} e^{2} - 20 \, a^{3} b^{3} d^{3} e^{3} + 15 \, a^{4} b^{2} d^{2} e^{4} - 6 \, a^{5} b d e^{5} + a^{6} e^{6}\right)} {\left(x e + d\right)}^{\frac{5}{2}}} - \frac{213 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{5} e^{3} - 472 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{5} d e^{3} + 267 \, \sqrt{x e + d} b^{5} d^{2} e^{3} + 472 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{4} e^{4} - 534 \, \sqrt{x e + d} a b^{4} d e^{4} + 267 \, \sqrt{x e + d} a^{2} b^{3} e^{5}}{24 \, {\left(b^{6} d^{6} - 6 \, a b^{5} d^{5} e + 15 \, a^{2} b^{4} d^{4} e^{2} - 20 \, a^{3} b^{3} d^{3} e^{3} + 15 \, a^{4} b^{2} d^{2} e^{4} - 6 \, a^{5} b d e^{5} + a^{6} e^{6}\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{3}}"," ",0,"-231/8*b^3*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e^3/((b^6*d^6 - 6*a*b^5*d^5*e + 15*a^2*b^4*d^4*e^2 - 20*a^3*b^3*d^3*e^3 + 15*a^4*b^2*d^2*e^4 - 6*a^5*b*d*e^5 + a^6*e^6)*sqrt(-b^2*d + a*b*e)) - 2/15*(150*(x*e + d)^2*b^2*e^3 + 20*(x*e + d)*b^2*d*e^3 + 3*b^2*d^2*e^3 - 20*(x*e + d)*a*b*e^4 - 6*a*b*d*e^4 + 3*a^2*e^5)/((b^6*d^6 - 6*a*b^5*d^5*e + 15*a^2*b^4*d^4*e^2 - 20*a^3*b^3*d^3*e^3 + 15*a^4*b^2*d^2*e^4 - 6*a^5*b*d*e^5 + a^6*e^6)*(x*e + d)^(5/2)) - 1/24*(213*(x*e + d)^(5/2)*b^5*e^3 - 472*(x*e + d)^(3/2)*b^5*d*e^3 + 267*sqrt(x*e + d)*b^5*d^2*e^3 + 472*(x*e + d)^(3/2)*a*b^4*e^4 - 534*sqrt(x*e + d)*a*b^4*d*e^4 + 267*sqrt(x*e + d)*a^2*b^3*e^5)/((b^6*d^6 - 6*a*b^5*d^5*e + 15*a^2*b^4*d^4*e^2 - 20*a^3*b^3*d^3*e^3 + 15*a^4*b^2*d^2*e^4 - 6*a^5*b*d*e^5 + a^6*e^6)*((x*e + d)*b - b*d + a*e)^3)","B",0
1664,1,785,0,0.299736," ","integrate((e*x+d)^(15/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{9009 \, {\left(b^{3} d^{3} e^{5} - 3 \, a b^{2} d^{2} e^{6} + 3 \, a^{2} b d e^{7} - a^{3} e^{8}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{128 \, \sqrt{-b^{2} d + a b e} b^{8}} - \frac{26635 \, {\left(x e + d\right)}^{\frac{9}{2}} b^{7} d^{3} e^{5} - 94430 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{7} d^{4} e^{5} + 128128 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{7} d^{5} e^{5} - 78370 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{7} d^{6} e^{5} + 18165 \, \sqrt{x e + d} b^{7} d^{7} e^{5} - 79905 \, {\left(x e + d\right)}^{\frac{9}{2}} a b^{6} d^{2} e^{6} + 377720 \, {\left(x e + d\right)}^{\frac{7}{2}} a b^{6} d^{3} e^{6} - 640640 \, {\left(x e + d\right)}^{\frac{5}{2}} a b^{6} d^{4} e^{6} + 470220 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{6} d^{5} e^{6} - 127155 \, \sqrt{x e + d} a b^{6} d^{6} e^{6} + 79905 \, {\left(x e + d\right)}^{\frac{9}{2}} a^{2} b^{5} d e^{7} - 566580 \, {\left(x e + d\right)}^{\frac{7}{2}} a^{2} b^{5} d^{2} e^{7} + 1281280 \, {\left(x e + d\right)}^{\frac{5}{2}} a^{2} b^{5} d^{3} e^{7} - 1175550 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} b^{5} d^{4} e^{7} + 381465 \, \sqrt{x e + d} a^{2} b^{5} d^{5} e^{7} - 26635 \, {\left(x e + d\right)}^{\frac{9}{2}} a^{3} b^{4} e^{8} + 377720 \, {\left(x e + d\right)}^{\frac{7}{2}} a^{3} b^{4} d e^{8} - 1281280 \, {\left(x e + d\right)}^{\frac{5}{2}} a^{3} b^{4} d^{2} e^{8} + 1567400 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{3} b^{4} d^{3} e^{8} - 635775 \, \sqrt{x e + d} a^{3} b^{4} d^{4} e^{8} - 94430 \, {\left(x e + d\right)}^{\frac{7}{2}} a^{4} b^{3} e^{9} + 640640 \, {\left(x e + d\right)}^{\frac{5}{2}} a^{4} b^{3} d e^{9} - 1175550 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{4} b^{3} d^{2} e^{9} + 635775 \, \sqrt{x e + d} a^{4} b^{3} d^{3} e^{9} - 128128 \, {\left(x e + d\right)}^{\frac{5}{2}} a^{5} b^{2} e^{10} + 470220 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{5} b^{2} d e^{10} - 381465 \, \sqrt{x e + d} a^{5} b^{2} d^{2} e^{10} - 78370 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{6} b e^{11} + 127155 \, \sqrt{x e + d} a^{6} b d e^{11} - 18165 \, \sqrt{x e + d} a^{7} e^{12}}{640 \, {\left({\left(x e + d\right)} b - b d + a e\right)}^{5} b^{8}} + \frac{2 \, {\left({\left(x e + d\right)}^{\frac{5}{2}} b^{24} e^{5} + 10 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{24} d e^{5} + 105 \, \sqrt{x e + d} b^{24} d^{2} e^{5} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{23} e^{6} - 210 \, \sqrt{x e + d} a b^{23} d e^{6} + 105 \, \sqrt{x e + d} a^{2} b^{22} e^{7}\right)}}{5 \, b^{30}}"," ",0,"9009/128*(b^3*d^3*e^5 - 3*a*b^2*d^2*e^6 + 3*a^2*b*d*e^7 - a^3*e^8)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/(sqrt(-b^2*d + a*b*e)*b^8) - 1/640*(26635*(x*e + d)^(9/2)*b^7*d^3*e^5 - 94430*(x*e + d)^(7/2)*b^7*d^4*e^5 + 128128*(x*e + d)^(5/2)*b^7*d^5*e^5 - 78370*(x*e + d)^(3/2)*b^7*d^6*e^5 + 18165*sqrt(x*e + d)*b^7*d^7*e^5 - 79905*(x*e + d)^(9/2)*a*b^6*d^2*e^6 + 377720*(x*e + d)^(7/2)*a*b^6*d^3*e^6 - 640640*(x*e + d)^(5/2)*a*b^6*d^4*e^6 + 470220*(x*e + d)^(3/2)*a*b^6*d^5*e^6 - 127155*sqrt(x*e + d)*a*b^6*d^6*e^6 + 79905*(x*e + d)^(9/2)*a^2*b^5*d*e^7 - 566580*(x*e + d)^(7/2)*a^2*b^5*d^2*e^7 + 1281280*(x*e + d)^(5/2)*a^2*b^5*d^3*e^7 - 1175550*(x*e + d)^(3/2)*a^2*b^5*d^4*e^7 + 381465*sqrt(x*e + d)*a^2*b^5*d^5*e^7 - 26635*(x*e + d)^(9/2)*a^3*b^4*e^8 + 377720*(x*e + d)^(7/2)*a^3*b^4*d*e^8 - 1281280*(x*e + d)^(5/2)*a^3*b^4*d^2*e^8 + 1567400*(x*e + d)^(3/2)*a^3*b^4*d^3*e^8 - 635775*sqrt(x*e + d)*a^3*b^4*d^4*e^8 - 94430*(x*e + d)^(7/2)*a^4*b^3*e^9 + 640640*(x*e + d)^(5/2)*a^4*b^3*d*e^9 - 1175550*(x*e + d)^(3/2)*a^4*b^3*d^2*e^9 + 635775*sqrt(x*e + d)*a^4*b^3*d^3*e^9 - 128128*(x*e + d)^(5/2)*a^5*b^2*e^10 + 470220*(x*e + d)^(3/2)*a^5*b^2*d*e^10 - 381465*sqrt(x*e + d)*a^5*b^2*d^2*e^10 - 78370*(x*e + d)^(3/2)*a^6*b*e^11 + 127155*sqrt(x*e + d)*a^6*b*d*e^11 - 18165*sqrt(x*e + d)*a^7*e^12)/(((x*e + d)*b - b*d + a*e)^5*b^8) + 2/5*((x*e + d)^(5/2)*b^24*e^5 + 10*(x*e + d)^(3/2)*b^24*d*e^5 + 105*sqrt(x*e + d)*b^24*d^2*e^5 - 10*(x*e + d)^(3/2)*a*b^23*e^6 - 210*sqrt(x*e + d)*a*b^23*d*e^6 + 105*sqrt(x*e + d)*a^2*b^22*e^7)/b^30","B",0
1665,1,613,0,0.269813," ","integrate((e*x+d)^(13/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{3003 \, {\left(b^{2} d^{2} e^{5} - 2 \, a b d e^{6} + a^{2} e^{7}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{128 \, \sqrt{-b^{2} d + a b e} b^{7}} - \frac{35595 \, {\left(x e + d\right)}^{\frac{9}{2}} b^{6} d^{2} e^{5} - 121310 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{6} d^{3} e^{5} + 160384 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{6} d^{4} e^{5} - 96290 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{6} d^{5} e^{5} + 22005 \, \sqrt{x e + d} b^{6} d^{6} e^{5} - 71190 \, {\left(x e + d\right)}^{\frac{9}{2}} a b^{5} d e^{6} + 363930 \, {\left(x e + d\right)}^{\frac{7}{2}} a b^{5} d^{2} e^{6} - 641536 \, {\left(x e + d\right)}^{\frac{5}{2}} a b^{5} d^{3} e^{6} + 481450 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{5} d^{4} e^{6} - 132030 \, \sqrt{x e + d} a b^{5} d^{5} e^{6} + 35595 \, {\left(x e + d\right)}^{\frac{9}{2}} a^{2} b^{4} e^{7} - 363930 \, {\left(x e + d\right)}^{\frac{7}{2}} a^{2} b^{4} d e^{7} + 962304 \, {\left(x e + d\right)}^{\frac{5}{2}} a^{2} b^{4} d^{2} e^{7} - 962900 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} b^{4} d^{3} e^{7} + 330075 \, \sqrt{x e + d} a^{2} b^{4} d^{4} e^{7} + 121310 \, {\left(x e + d\right)}^{\frac{7}{2}} a^{3} b^{3} e^{8} - 641536 \, {\left(x e + d\right)}^{\frac{5}{2}} a^{3} b^{3} d e^{8} + 962900 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{3} b^{3} d^{2} e^{8} - 440100 \, \sqrt{x e + d} a^{3} b^{3} d^{3} e^{8} + 160384 \, {\left(x e + d\right)}^{\frac{5}{2}} a^{4} b^{2} e^{9} - 481450 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{4} b^{2} d e^{9} + 330075 \, \sqrt{x e + d} a^{4} b^{2} d^{2} e^{9} + 96290 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{5} b e^{10} - 132030 \, \sqrt{x e + d} a^{5} b d e^{10} + 22005 \, \sqrt{x e + d} a^{6} e^{11}}{1920 \, {\left({\left(x e + d\right)} b - b d + a e\right)}^{5} b^{7}} + \frac{2 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} b^{12} e^{5} + 18 \, \sqrt{x e + d} b^{12} d e^{5} - 18 \, \sqrt{x e + d} a b^{11} e^{6}\right)}}{3 \, b^{18}}"," ",0,"3003/128*(b^2*d^2*e^5 - 2*a*b*d*e^6 + a^2*e^7)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/(sqrt(-b^2*d + a*b*e)*b^7) - 1/1920*(35595*(x*e + d)^(9/2)*b^6*d^2*e^5 - 121310*(x*e + d)^(7/2)*b^6*d^3*e^5 + 160384*(x*e + d)^(5/2)*b^6*d^4*e^5 - 96290*(x*e + d)^(3/2)*b^6*d^5*e^5 + 22005*sqrt(x*e + d)*b^6*d^6*e^5 - 71190*(x*e + d)^(9/2)*a*b^5*d*e^6 + 363930*(x*e + d)^(7/2)*a*b^5*d^2*e^6 - 641536*(x*e + d)^(5/2)*a*b^5*d^3*e^6 + 481450*(x*e + d)^(3/2)*a*b^5*d^4*e^6 - 132030*sqrt(x*e + d)*a*b^5*d^5*e^6 + 35595*(x*e + d)^(9/2)*a^2*b^4*e^7 - 363930*(x*e + d)^(7/2)*a^2*b^4*d*e^7 + 962304*(x*e + d)^(5/2)*a^2*b^4*d^2*e^7 - 962900*(x*e + d)^(3/2)*a^2*b^4*d^3*e^7 + 330075*sqrt(x*e + d)*a^2*b^4*d^4*e^7 + 121310*(x*e + d)^(7/2)*a^3*b^3*e^8 - 641536*(x*e + d)^(5/2)*a^3*b^3*d*e^8 + 962900*(x*e + d)^(3/2)*a^3*b^3*d^2*e^8 - 440100*sqrt(x*e + d)*a^3*b^3*d^3*e^8 + 160384*(x*e + d)^(5/2)*a^4*b^2*e^9 - 481450*(x*e + d)^(3/2)*a^4*b^2*d*e^9 + 330075*sqrt(x*e + d)*a^4*b^2*d^2*e^9 + 96290*(x*e + d)^(3/2)*a^5*b*e^10 - 132030*sqrt(x*e + d)*a^5*b*d*e^10 + 22005*sqrt(x*e + d)*a^6*e^11)/(((x*e + d)*b - b*d + a*e)^5*b^7) + 2/3*((x*e + d)^(3/2)*b^12*e^5 + 18*sqrt(x*e + d)*b^12*d*e^5 - 18*sqrt(x*e + d)*a*b^11*e^6)/b^18","B",0
1666,1,459,0,0.286559," ","integrate((e*x+d)^(11/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{693 \, {\left(b d e^{5} - a e^{6}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{128 \, \sqrt{-b^{2} d + a b e} b^{6}} + \frac{2 \, \sqrt{x e + d} e^{5}}{b^{6}} - \frac{4215 \, {\left(x e + d\right)}^{\frac{9}{2}} b^{5} d e^{5} - 13270 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{5} d^{2} e^{5} + 16768 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{5} d^{3} e^{5} - 9770 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{5} d^{4} e^{5} + 2185 \, \sqrt{x e + d} b^{5} d^{5} e^{5} - 4215 \, {\left(x e + d\right)}^{\frac{9}{2}} a b^{4} e^{6} + 26540 \, {\left(x e + d\right)}^{\frac{7}{2}} a b^{4} d e^{6} - 50304 \, {\left(x e + d\right)}^{\frac{5}{2}} a b^{4} d^{2} e^{6} + 39080 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{4} d^{3} e^{6} - 10925 \, \sqrt{x e + d} a b^{4} d^{4} e^{6} - 13270 \, {\left(x e + d\right)}^{\frac{7}{2}} a^{2} b^{3} e^{7} + 50304 \, {\left(x e + d\right)}^{\frac{5}{2}} a^{2} b^{3} d e^{7} - 58620 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} b^{3} d^{2} e^{7} + 21850 \, \sqrt{x e + d} a^{2} b^{3} d^{3} e^{7} - 16768 \, {\left(x e + d\right)}^{\frac{5}{2}} a^{3} b^{2} e^{8} + 39080 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{3} b^{2} d e^{8} - 21850 \, \sqrt{x e + d} a^{3} b^{2} d^{2} e^{8} - 9770 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{4} b e^{9} + 10925 \, \sqrt{x e + d} a^{4} b d e^{9} - 2185 \, \sqrt{x e + d} a^{5} e^{10}}{640 \, {\left({\left(x e + d\right)} b - b d + a e\right)}^{5} b^{6}}"," ",0,"693/128*(b*d*e^5 - a*e^6)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/(sqrt(-b^2*d + a*b*e)*b^6) + 2*sqrt(x*e + d)*e^5/b^6 - 1/640*(4215*(x*e + d)^(9/2)*b^5*d*e^5 - 13270*(x*e + d)^(7/2)*b^5*d^2*e^5 + 16768*(x*e + d)^(5/2)*b^5*d^3*e^5 - 9770*(x*e + d)^(3/2)*b^5*d^4*e^5 + 2185*sqrt(x*e + d)*b^5*d^5*e^5 - 4215*(x*e + d)^(9/2)*a*b^4*e^6 + 26540*(x*e + d)^(7/2)*a*b^4*d*e^6 - 50304*(x*e + d)^(5/2)*a*b^4*d^2*e^6 + 39080*(x*e + d)^(3/2)*a*b^4*d^3*e^6 - 10925*sqrt(x*e + d)*a*b^4*d^4*e^6 - 13270*(x*e + d)^(7/2)*a^2*b^3*e^7 + 50304*(x*e + d)^(5/2)*a^2*b^3*d*e^7 - 58620*(x*e + d)^(3/2)*a^2*b^3*d^2*e^7 + 21850*sqrt(x*e + d)*a^2*b^3*d^3*e^7 - 16768*(x*e + d)^(5/2)*a^3*b^2*e^8 + 39080*(x*e + d)^(3/2)*a^3*b^2*d*e^8 - 21850*sqrt(x*e + d)*a^3*b^2*d^2*e^8 - 9770*(x*e + d)^(3/2)*a^4*b*e^9 + 10925*sqrt(x*e + d)*a^4*b*d*e^9 - 2185*sqrt(x*e + d)*a^5*e^10)/(((x*e + d)*b - b*d + a*e)^5*b^6)","B",0
1667,1,334,0,0.238525," ","integrate((e*x+d)^(9/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{63 \, \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e^{5}}{128 \, \sqrt{-b^{2} d + a b e} b^{5}} - \frac{965 \, {\left(x e + d\right)}^{\frac{9}{2}} b^{4} e^{5} - 2370 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{4} d e^{5} + 2688 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{4} d^{2} e^{5} - 1470 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{4} d^{3} e^{5} + 315 \, \sqrt{x e + d} b^{4} d^{4} e^{5} + 2370 \, {\left(x e + d\right)}^{\frac{7}{2}} a b^{3} e^{6} - 5376 \, {\left(x e + d\right)}^{\frac{5}{2}} a b^{3} d e^{6} + 4410 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{3} d^{2} e^{6} - 1260 \, \sqrt{x e + d} a b^{3} d^{3} e^{6} + 2688 \, {\left(x e + d\right)}^{\frac{5}{2}} a^{2} b^{2} e^{7} - 4410 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} b^{2} d e^{7} + 1890 \, \sqrt{x e + d} a^{2} b^{2} d^{2} e^{7} + 1470 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{3} b e^{8} - 1260 \, \sqrt{x e + d} a^{3} b d e^{8} + 315 \, \sqrt{x e + d} a^{4} e^{9}}{640 \, {\left({\left(x e + d\right)} b - b d + a e\right)}^{5} b^{5}}"," ",0,"63/128*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e^5/(sqrt(-b^2*d + a*b*e)*b^5) - 1/640*(965*(x*e + d)^(9/2)*b^4*e^5 - 2370*(x*e + d)^(7/2)*b^4*d*e^5 + 2688*(x*e + d)^(5/2)*b^4*d^2*e^5 - 1470*(x*e + d)^(3/2)*b^4*d^3*e^5 + 315*sqrt(x*e + d)*b^4*d^4*e^5 + 2370*(x*e + d)^(7/2)*a*b^3*e^6 - 5376*(x*e + d)^(5/2)*a*b^3*d*e^6 + 4410*(x*e + d)^(3/2)*a*b^3*d^2*e^6 - 1260*sqrt(x*e + d)*a*b^3*d^3*e^6 + 2688*(x*e + d)^(5/2)*a^2*b^2*e^7 - 4410*(x*e + d)^(3/2)*a^2*b^2*d*e^7 + 1890*sqrt(x*e + d)*a^2*b^2*d^2*e^7 + 1470*(x*e + d)^(3/2)*a^3*b*e^8 - 1260*sqrt(x*e + d)*a^3*b*d*e^8 + 315*sqrt(x*e + d)*a^4*e^9)/(((x*e + d)*b - b*d + a*e)^5*b^5)","B",0
1668,1,360,0,0.236093," ","integrate((e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","-\frac{7 \, \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e^{5}}{128 \, {\left(b^{5} d - a b^{4} e\right)} \sqrt{-b^{2} d + a b e}} - \frac{105 \, {\left(x e + d\right)}^{\frac{9}{2}} b^{4} e^{5} + 790 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{4} d e^{5} - 896 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{4} d^{2} e^{5} + 490 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{4} d^{3} e^{5} - 105 \, \sqrt{x e + d} b^{4} d^{4} e^{5} - 790 \, {\left(x e + d\right)}^{\frac{7}{2}} a b^{3} e^{6} + 1792 \, {\left(x e + d\right)}^{\frac{5}{2}} a b^{3} d e^{6} - 1470 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{3} d^{2} e^{6} + 420 \, \sqrt{x e + d} a b^{3} d^{3} e^{6} - 896 \, {\left(x e + d\right)}^{\frac{5}{2}} a^{2} b^{2} e^{7} + 1470 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} b^{2} d e^{7} - 630 \, \sqrt{x e + d} a^{2} b^{2} d^{2} e^{7} - 490 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{3} b e^{8} + 420 \, \sqrt{x e + d} a^{3} b d e^{8} - 105 \, \sqrt{x e + d} a^{4} e^{9}}{1920 \, {\left(b^{5} d - a b^{4} e\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{5}}"," ",0,"-7/128*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e^5/((b^5*d - a*b^4*e)*sqrt(-b^2*d + a*b*e)) - 1/1920*(105*(x*e + d)^(9/2)*b^4*e^5 + 790*(x*e + d)^(7/2)*b^4*d*e^5 - 896*(x*e + d)^(5/2)*b^4*d^2*e^5 + 490*(x*e + d)^(3/2)*b^4*d^3*e^5 - 105*sqrt(x*e + d)*b^4*d^4*e^5 - 790*(x*e + d)^(7/2)*a*b^3*e^6 + 1792*(x*e + d)^(5/2)*a*b^3*d*e^6 - 1470*(x*e + d)^(3/2)*a*b^3*d^2*e^6 + 420*sqrt(x*e + d)*a*b^3*d^3*e^6 - 896*(x*e + d)^(5/2)*a^2*b^2*e^7 + 1470*(x*e + d)^(3/2)*a^2*b^2*d*e^7 - 630*sqrt(x*e + d)*a^2*b^2*d^2*e^7 - 490*(x*e + d)^(3/2)*a^3*b*e^8 + 420*sqrt(x*e + d)*a^3*b*d*e^8 - 105*sqrt(x*e + d)*a^4*e^9)/((b^5*d - a*b^4*e)*((x*e + d)*b - b*d + a*e)^5)","B",0
1669,1,384,0,0.229406," ","integrate((e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{3 \, \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e^{5}}{128 \, {\left(b^{5} d^{2} - 2 \, a b^{4} d e + a^{2} b^{3} e^{2}\right)} \sqrt{-b^{2} d + a b e}} + \frac{15 \, {\left(x e + d\right)}^{\frac{9}{2}} b^{4} e^{5} - 70 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{4} d e^{5} - 128 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{4} d^{2} e^{5} + 70 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{4} d^{3} e^{5} - 15 \, \sqrt{x e + d} b^{4} d^{4} e^{5} + 70 \, {\left(x e + d\right)}^{\frac{7}{2}} a b^{3} e^{6} + 256 \, {\left(x e + d\right)}^{\frac{5}{2}} a b^{3} d e^{6} - 210 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{3} d^{2} e^{6} + 60 \, \sqrt{x e + d} a b^{3} d^{3} e^{6} - 128 \, {\left(x e + d\right)}^{\frac{5}{2}} a^{2} b^{2} e^{7} + 210 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} b^{2} d e^{7} - 90 \, \sqrt{x e + d} a^{2} b^{2} d^{2} e^{7} - 70 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{3} b e^{8} + 60 \, \sqrt{x e + d} a^{3} b d e^{8} - 15 \, \sqrt{x e + d} a^{4} e^{9}}{640 \, {\left(b^{5} d^{2} - 2 \, a b^{4} d e + a^{2} b^{3} e^{2}\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{5}}"," ",0,"3/128*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e^5/((b^5*d^2 - 2*a*b^4*d*e + a^2*b^3*e^2)*sqrt(-b^2*d + a*b*e)) + 1/640*(15*(x*e + d)^(9/2)*b^4*e^5 - 70*(x*e + d)^(7/2)*b^4*d*e^5 - 128*(x*e + d)^(5/2)*b^4*d^2*e^5 + 70*(x*e + d)^(3/2)*b^4*d^3*e^5 - 15*sqrt(x*e + d)*b^4*d^4*e^5 + 70*(x*e + d)^(7/2)*a*b^3*e^6 + 256*(x*e + d)^(5/2)*a*b^3*d*e^6 - 210*(x*e + d)^(3/2)*a*b^3*d^2*e^6 + 60*sqrt(x*e + d)*a*b^3*d^3*e^6 - 128*(x*e + d)^(5/2)*a^2*b^2*e^7 + 210*(x*e + d)^(3/2)*a^2*b^2*d*e^7 - 90*sqrt(x*e + d)*a^2*b^2*d^2*e^7 - 70*(x*e + d)^(3/2)*a^3*b*e^8 + 60*sqrt(x*e + d)*a^3*b*d*e^8 - 15*sqrt(x*e + d)*a^4*e^9)/((b^5*d^2 - 2*a*b^4*d*e + a^2*b^3*e^2)*((x*e + d)*b - b*d + a*e)^5)","B",0
1670,1,412,0,0.221750," ","integrate((e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","-\frac{3 \, \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e^{5}}{128 \, {\left(b^{5} d^{3} - 3 \, a b^{4} d^{2} e + 3 \, a^{2} b^{3} d e^{2} - a^{3} b^{2} e^{3}\right)} \sqrt{-b^{2} d + a b e}} - \frac{15 \, {\left(x e + d\right)}^{\frac{9}{2}} b^{4} e^{5} - 70 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{4} d e^{5} + 128 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{4} d^{2} e^{5} + 70 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{4} d^{3} e^{5} - 15 \, \sqrt{x e + d} b^{4} d^{4} e^{5} + 70 \, {\left(x e + d\right)}^{\frac{7}{2}} a b^{3} e^{6} - 256 \, {\left(x e + d\right)}^{\frac{5}{2}} a b^{3} d e^{6} - 210 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{3} d^{2} e^{6} + 60 \, \sqrt{x e + d} a b^{3} d^{3} e^{6} + 128 \, {\left(x e + d\right)}^{\frac{5}{2}} a^{2} b^{2} e^{7} + 210 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} b^{2} d e^{7} - 90 \, \sqrt{x e + d} a^{2} b^{2} d^{2} e^{7} - 70 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{3} b e^{8} + 60 \, \sqrt{x e + d} a^{3} b d e^{8} - 15 \, \sqrt{x e + d} a^{4} e^{9}}{640 \, {\left(b^{5} d^{3} - 3 \, a b^{4} d^{2} e + 3 \, a^{2} b^{3} d e^{2} - a^{3} b^{2} e^{3}\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{5}}"," ",0,"-3/128*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e^5/((b^5*d^3 - 3*a*b^4*d^2*e + 3*a^2*b^3*d*e^2 - a^3*b^2*e^3)*sqrt(-b^2*d + a*b*e)) - 1/640*(15*(x*e + d)^(9/2)*b^4*e^5 - 70*(x*e + d)^(7/2)*b^4*d*e^5 + 128*(x*e + d)^(5/2)*b^4*d^2*e^5 + 70*(x*e + d)^(3/2)*b^4*d^3*e^5 - 15*sqrt(x*e + d)*b^4*d^4*e^5 + 70*(x*e + d)^(7/2)*a*b^3*e^6 - 256*(x*e + d)^(5/2)*a*b^3*d*e^6 - 210*(x*e + d)^(3/2)*a*b^3*d^2*e^6 + 60*sqrt(x*e + d)*a*b^3*d^3*e^6 + 128*(x*e + d)^(5/2)*a^2*b^2*e^7 + 210*(x*e + d)^(3/2)*a^2*b^2*d*e^7 - 90*sqrt(x*e + d)*a^2*b^2*d^2*e^7 - 70*(x*e + d)^(3/2)*a^3*b*e^8 + 60*sqrt(x*e + d)*a^3*b*d*e^8 - 15*sqrt(x*e + d)*a^4*e^9)/((b^5*d^3 - 3*a*b^4*d^2*e + 3*a^2*b^3*d*e^2 - a^3*b^2*e^3)*((x*e + d)*b - b*d + a*e)^5)","B",0
1671,1,432,0,0.218945," ","integrate((e*x+d)^(1/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{7 \, \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e^{5}}{128 \, {\left(b^{5} d^{4} - 4 \, a b^{4} d^{3} e + 6 \, a^{2} b^{3} d^{2} e^{2} - 4 \, a^{3} b^{2} d e^{3} + a^{4} b e^{4}\right)} \sqrt{-b^{2} d + a b e}} + \frac{105 \, {\left(x e + d\right)}^{\frac{9}{2}} b^{4} e^{5} - 490 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{4} d e^{5} + 896 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{4} d^{2} e^{5} - 790 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{4} d^{3} e^{5} - 105 \, \sqrt{x e + d} b^{4} d^{4} e^{5} + 490 \, {\left(x e + d\right)}^{\frac{7}{2}} a b^{3} e^{6} - 1792 \, {\left(x e + d\right)}^{\frac{5}{2}} a b^{3} d e^{6} + 2370 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{3} d^{2} e^{6} + 420 \, \sqrt{x e + d} a b^{3} d^{3} e^{6} + 896 \, {\left(x e + d\right)}^{\frac{5}{2}} a^{2} b^{2} e^{7} - 2370 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} b^{2} d e^{7} - 630 \, \sqrt{x e + d} a^{2} b^{2} d^{2} e^{7} + 790 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{3} b e^{8} + 420 \, \sqrt{x e + d} a^{3} b d e^{8} - 105 \, \sqrt{x e + d} a^{4} e^{9}}{1920 \, {\left(b^{5} d^{4} - 4 \, a b^{4} d^{3} e + 6 \, a^{2} b^{3} d^{2} e^{2} - 4 \, a^{3} b^{2} d e^{3} + a^{4} b e^{4}\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{5}}"," ",0,"7/128*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e^5/((b^5*d^4 - 4*a*b^4*d^3*e + 6*a^2*b^3*d^2*e^2 - 4*a^3*b^2*d*e^3 + a^4*b*e^4)*sqrt(-b^2*d + a*b*e)) + 1/1920*(105*(x*e + d)^(9/2)*b^4*e^5 - 490*(x*e + d)^(7/2)*b^4*d*e^5 + 896*(x*e + d)^(5/2)*b^4*d^2*e^5 - 790*(x*e + d)^(3/2)*b^4*d^3*e^5 - 105*sqrt(x*e + d)*b^4*d^4*e^5 + 490*(x*e + d)^(7/2)*a*b^3*e^6 - 1792*(x*e + d)^(5/2)*a*b^3*d*e^6 + 2370*(x*e + d)^(3/2)*a*b^3*d^2*e^6 + 420*sqrt(x*e + d)*a*b^3*d^3*e^6 + 896*(x*e + d)^(5/2)*a^2*b^2*e^7 - 2370*(x*e + d)^(3/2)*a^2*b^2*d*e^7 - 630*sqrt(x*e + d)*a^2*b^2*d^2*e^7 + 790*(x*e + d)^(3/2)*a^3*b*e^8 + 420*sqrt(x*e + d)*a^3*b*d*e^8 - 105*sqrt(x*e + d)*a^4*e^9)/((b^5*d^4 - 4*a*b^4*d^3*e + 6*a^2*b^3*d^2*e^2 - 4*a^3*b^2*d*e^3 + a^4*b*e^4)*((x*e + d)*b - b*d + a*e)^5)","B",0
1672,1,454,0,0.200531," ","integrate(1/(e*x+d)^(1/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","-\frac{63 \, \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e^{5}}{128 \, {\left(b^{5} d^{5} - 5 \, a b^{4} d^{4} e + 10 \, a^{2} b^{3} d^{3} e^{2} - 10 \, a^{3} b^{2} d^{2} e^{3} + 5 \, a^{4} b d e^{4} - a^{5} e^{5}\right)} \sqrt{-b^{2} d + a b e}} - \frac{315 \, {\left(x e + d\right)}^{\frac{9}{2}} b^{4} e^{5} - 1470 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{4} d e^{5} + 2688 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{4} d^{2} e^{5} - 2370 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{4} d^{3} e^{5} + 965 \, \sqrt{x e + d} b^{4} d^{4} e^{5} + 1470 \, {\left(x e + d\right)}^{\frac{7}{2}} a b^{3} e^{6} - 5376 \, {\left(x e + d\right)}^{\frac{5}{2}} a b^{3} d e^{6} + 7110 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{3} d^{2} e^{6} - 3860 \, \sqrt{x e + d} a b^{3} d^{3} e^{6} + 2688 \, {\left(x e + d\right)}^{\frac{5}{2}} a^{2} b^{2} e^{7} - 7110 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} b^{2} d e^{7} + 5790 \, \sqrt{x e + d} a^{2} b^{2} d^{2} e^{7} + 2370 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{3} b e^{8} - 3860 \, \sqrt{x e + d} a^{3} b d e^{8} + 965 \, \sqrt{x e + d} a^{4} e^{9}}{640 \, {\left(b^{5} d^{5} - 5 \, a b^{4} d^{4} e + 10 \, a^{2} b^{3} d^{3} e^{2} - 10 \, a^{3} b^{2} d^{2} e^{3} + 5 \, a^{4} b d e^{4} - a^{5} e^{5}\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{5}}"," ",0,"-63/128*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e^5/((b^5*d^5 - 5*a*b^4*d^4*e + 10*a^2*b^3*d^3*e^2 - 10*a^3*b^2*d^2*e^3 + 5*a^4*b*d*e^4 - a^5*e^5)*sqrt(-b^2*d + a*b*e)) - 1/640*(315*(x*e + d)^(9/2)*b^4*e^5 - 1470*(x*e + d)^(7/2)*b^4*d*e^5 + 2688*(x*e + d)^(5/2)*b^4*d^2*e^5 - 2370*(x*e + d)^(3/2)*b^4*d^3*e^5 + 965*sqrt(x*e + d)*b^4*d^4*e^5 + 1470*(x*e + d)^(7/2)*a*b^3*e^6 - 5376*(x*e + d)^(5/2)*a*b^3*d*e^6 + 7110*(x*e + d)^(3/2)*a*b^3*d^2*e^6 - 3860*sqrt(x*e + d)*a*b^3*d^3*e^6 + 2688*(x*e + d)^(5/2)*a^2*b^2*e^7 - 7110*(x*e + d)^(3/2)*a^2*b^2*d*e^7 + 5790*sqrt(x*e + d)*a^2*b^2*d^2*e^7 + 2370*(x*e + d)^(3/2)*a^3*b*e^8 - 3860*sqrt(x*e + d)*a^3*b*d*e^8 + 965*sqrt(x*e + d)*a^4*e^9)/((b^5*d^5 - 5*a*b^4*d^4*e + 10*a^2*b^3*d^3*e^2 - 10*a^3*b^2*d^2*e^3 + 5*a^4*b*d*e^4 - a^5*e^5)*((x*e + d)*b - b*d + a*e)^5)","B",0
1673,1,571,0,0.247198," ","integrate(1/(e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","-\frac{693 \, b \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e^{5}}{128 \, {\left(b^{6} d^{6} - 6 \, a b^{5} d^{5} e + 15 \, a^{2} b^{4} d^{4} e^{2} - 20 \, a^{3} b^{3} d^{3} e^{3} + 15 \, a^{4} b^{2} d^{2} e^{4} - 6 \, a^{5} b d e^{5} + a^{6} e^{6}\right)} \sqrt{-b^{2} d + a b e}} - \frac{2 \, e^{5}}{{\left(b^{6} d^{6} - 6 \, a b^{5} d^{5} e + 15 \, a^{2} b^{4} d^{4} e^{2} - 20 \, a^{3} b^{3} d^{3} e^{3} + 15 \, a^{4} b^{2} d^{2} e^{4} - 6 \, a^{5} b d e^{5} + a^{6} e^{6}\right)} \sqrt{x e + d}} - \frac{2185 \, {\left(x e + d\right)}^{\frac{9}{2}} b^{5} e^{5} - 9770 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{5} d e^{5} + 16768 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{5} d^{2} e^{5} - 13270 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{5} d^{3} e^{5} + 4215 \, \sqrt{x e + d} b^{5} d^{4} e^{5} + 9770 \, {\left(x e + d\right)}^{\frac{7}{2}} a b^{4} e^{6} - 33536 \, {\left(x e + d\right)}^{\frac{5}{2}} a b^{4} d e^{6} + 39810 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{4} d^{2} e^{6} - 16860 \, \sqrt{x e + d} a b^{4} d^{3} e^{6} + 16768 \, {\left(x e + d\right)}^{\frac{5}{2}} a^{2} b^{3} e^{7} - 39810 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} b^{3} d e^{7} + 25290 \, \sqrt{x e + d} a^{2} b^{3} d^{2} e^{7} + 13270 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{3} b^{2} e^{8} - 16860 \, \sqrt{x e + d} a^{3} b^{2} d e^{8} + 4215 \, \sqrt{x e + d} a^{4} b e^{9}}{640 \, {\left(b^{6} d^{6} - 6 \, a b^{5} d^{5} e + 15 \, a^{2} b^{4} d^{4} e^{2} - 20 \, a^{3} b^{3} d^{3} e^{3} + 15 \, a^{4} b^{2} d^{2} e^{4} - 6 \, a^{5} b d e^{5} + a^{6} e^{6}\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{5}}"," ",0,"-693/128*b*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e^5/((b^6*d^6 - 6*a*b^5*d^5*e + 15*a^2*b^4*d^4*e^2 - 20*a^3*b^3*d^3*e^3 + 15*a^4*b^2*d^2*e^4 - 6*a^5*b*d*e^5 + a^6*e^6)*sqrt(-b^2*d + a*b*e)) - 2*e^5/((b^6*d^6 - 6*a*b^5*d^5*e + 15*a^2*b^4*d^4*e^2 - 20*a^3*b^3*d^3*e^3 + 15*a^4*b^2*d^2*e^4 - 6*a^5*b*d*e^5 + a^6*e^6)*sqrt(x*e + d)) - 1/640*(2185*(x*e + d)^(9/2)*b^5*e^5 - 9770*(x*e + d)^(7/2)*b^5*d*e^5 + 16768*(x*e + d)^(5/2)*b^5*d^2*e^5 - 13270*(x*e + d)^(3/2)*b^5*d^3*e^5 + 4215*sqrt(x*e + d)*b^5*d^4*e^5 + 9770*(x*e + d)^(7/2)*a*b^4*e^6 - 33536*(x*e + d)^(5/2)*a*b^4*d*e^6 + 39810*(x*e + d)^(3/2)*a*b^4*d^2*e^6 - 16860*sqrt(x*e + d)*a*b^4*d^3*e^6 + 16768*(x*e + d)^(5/2)*a^2*b^3*e^7 - 39810*(x*e + d)^(3/2)*a^2*b^3*d*e^7 + 25290*sqrt(x*e + d)*a^2*b^3*d^2*e^7 + 13270*(x*e + d)^(3/2)*a^3*b^2*e^8 - 16860*sqrt(x*e + d)*a^3*b^2*d*e^8 + 4215*sqrt(x*e + d)*a^4*b*e^9)/((b^6*d^6 - 6*a*b^5*d^5*e + 15*a^2*b^4*d^4*e^2 - 20*a^3*b^3*d^3*e^3 + 15*a^4*b^2*d^2*e^4 - 6*a^5*b*d*e^5 + a^6*e^6)*((x*e + d)*b - b*d + a*e)^5)","B",0
1674,1,637,0,0.284752," ","integrate(1/(e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","-\frac{3003 \, b^{2} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e^{5}}{128 \, {\left(b^{7} d^{7} - 7 \, a b^{6} d^{6} e + 21 \, a^{2} b^{5} d^{5} e^{2} - 35 \, a^{3} b^{4} d^{4} e^{3} + 35 \, a^{4} b^{3} d^{3} e^{4} - 21 \, a^{5} b^{2} d^{2} e^{5} + 7 \, a^{6} b d e^{6} - a^{7} e^{7}\right)} \sqrt{-b^{2} d + a b e}} - \frac{2 \, {\left(18 \, {\left(x e + d\right)} b e^{5} + b d e^{5} - a e^{6}\right)}}{3 \, {\left(b^{7} d^{7} - 7 \, a b^{6} d^{6} e + 21 \, a^{2} b^{5} d^{5} e^{2} - 35 \, a^{3} b^{4} d^{4} e^{3} + 35 \, a^{4} b^{3} d^{3} e^{4} - 21 \, a^{5} b^{2} d^{2} e^{5} + 7 \, a^{6} b d e^{6} - a^{7} e^{7}\right)} {\left(x e + d\right)}^{\frac{3}{2}}} - \frac{22005 \, {\left(x e + d\right)}^{\frac{9}{2}} b^{6} e^{5} - 96290 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{6} d e^{5} + 160384 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{6} d^{2} e^{5} - 121310 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{6} d^{3} e^{5} + 35595 \, \sqrt{x e + d} b^{6} d^{4} e^{5} + 96290 \, {\left(x e + d\right)}^{\frac{7}{2}} a b^{5} e^{6} - 320768 \, {\left(x e + d\right)}^{\frac{5}{2}} a b^{5} d e^{6} + 363930 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{5} d^{2} e^{6} - 142380 \, \sqrt{x e + d} a b^{5} d^{3} e^{6} + 160384 \, {\left(x e + d\right)}^{\frac{5}{2}} a^{2} b^{4} e^{7} - 363930 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} b^{4} d e^{7} + 213570 \, \sqrt{x e + d} a^{2} b^{4} d^{2} e^{7} + 121310 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{3} b^{3} e^{8} - 142380 \, \sqrt{x e + d} a^{3} b^{3} d e^{8} + 35595 \, \sqrt{x e + d} a^{4} b^{2} e^{9}}{1920 \, {\left(b^{7} d^{7} - 7 \, a b^{6} d^{6} e + 21 \, a^{2} b^{5} d^{5} e^{2} - 35 \, a^{3} b^{4} d^{4} e^{3} + 35 \, a^{4} b^{3} d^{3} e^{4} - 21 \, a^{5} b^{2} d^{2} e^{5} + 7 \, a^{6} b d e^{6} - a^{7} e^{7}\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{5}}"," ",0,"-3003/128*b^2*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e^5/((b^7*d^7 - 7*a*b^6*d^6*e + 21*a^2*b^5*d^5*e^2 - 35*a^3*b^4*d^4*e^3 + 35*a^4*b^3*d^3*e^4 - 21*a^5*b^2*d^2*e^5 + 7*a^6*b*d*e^6 - a^7*e^7)*sqrt(-b^2*d + a*b*e)) - 2/3*(18*(x*e + d)*b*e^5 + b*d*e^5 - a*e^6)/((b^7*d^7 - 7*a*b^6*d^6*e + 21*a^2*b^5*d^5*e^2 - 35*a^3*b^4*d^4*e^3 + 35*a^4*b^3*d^3*e^4 - 21*a^5*b^2*d^2*e^5 + 7*a^6*b*d*e^6 - a^7*e^7)*(x*e + d)^(3/2)) - 1/1920*(22005*(x*e + d)^(9/2)*b^6*e^5 - 96290*(x*e + d)^(7/2)*b^6*d*e^5 + 160384*(x*e + d)^(5/2)*b^6*d^2*e^5 - 121310*(x*e + d)^(3/2)*b^6*d^3*e^5 + 35595*sqrt(x*e + d)*b^6*d^4*e^5 + 96290*(x*e + d)^(7/2)*a*b^5*e^6 - 320768*(x*e + d)^(5/2)*a*b^5*d*e^6 + 363930*(x*e + d)^(3/2)*a*b^5*d^2*e^6 - 142380*sqrt(x*e + d)*a*b^5*d^3*e^6 + 160384*(x*e + d)^(5/2)*a^2*b^4*e^7 - 363930*(x*e + d)^(3/2)*a^2*b^4*d*e^7 + 213570*sqrt(x*e + d)*a^2*b^4*d^2*e^7 + 121310*(x*e + d)^(3/2)*a^3*b^3*e^8 - 142380*sqrt(x*e + d)*a^3*b^3*d*e^8 + 35595*sqrt(x*e + d)*a^4*b^2*e^9)/((b^7*d^7 - 7*a*b^6*d^6*e + 21*a^2*b^5*d^5*e^2 - 35*a^3*b^4*d^4*e^3 + 35*a^4*b^3*d^3*e^4 - 21*a^5*b^2*d^2*e^5 + 7*a^6*b*d*e^6 - a^7*e^7)*((x*e + d)*b - b*d + a*e)^5)","B",0
1675,1,884,0,0.293173," ","integrate(1/(e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","-\frac{9009 \, b^{3} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e^{5}}{128 \, {\left(b^{8} d^{8} - 8 \, a b^{7} d^{7} e + 28 \, a^{2} b^{6} d^{6} e^{2} - 56 \, a^{3} b^{5} d^{5} e^{3} + 70 \, a^{4} b^{4} d^{4} e^{4} - 56 \, a^{5} b^{3} d^{3} e^{5} + 28 \, a^{6} b^{2} d^{2} e^{6} - 8 \, a^{7} b d e^{7} + a^{8} e^{8}\right)} \sqrt{-b^{2} d + a b e}} - \frac{45045 \, {\left(x e + d\right)}^{7} b^{7} e^{5} - 210210 \, {\left(x e + d\right)}^{6} b^{7} d e^{5} + 384384 \, {\left(x e + d\right)}^{5} b^{7} d^{2} e^{5} - 338910 \, {\left(x e + d\right)}^{4} b^{7} d^{3} e^{5} + 137995 \, {\left(x e + d\right)}^{3} b^{7} d^{4} e^{5} - 16640 \, {\left(x e + d\right)}^{2} b^{7} d^{5} e^{5} - 1280 \, {\left(x e + d\right)} b^{7} d^{6} e^{5} - 256 \, b^{7} d^{7} e^{5} + 210210 \, {\left(x e + d\right)}^{6} a b^{6} e^{6} - 768768 \, {\left(x e + d\right)}^{5} a b^{6} d e^{6} + 1016730 \, {\left(x e + d\right)}^{4} a b^{6} d^{2} e^{6} - 551980 \, {\left(x e + d\right)}^{3} a b^{6} d^{3} e^{6} + 83200 \, {\left(x e + d\right)}^{2} a b^{6} d^{4} e^{6} + 7680 \, {\left(x e + d\right)} a b^{6} d^{5} e^{6} + 1792 \, a b^{6} d^{6} e^{6} + 384384 \, {\left(x e + d\right)}^{5} a^{2} b^{5} e^{7} - 1016730 \, {\left(x e + d\right)}^{4} a^{2} b^{5} d e^{7} + 827970 \, {\left(x e + d\right)}^{3} a^{2} b^{5} d^{2} e^{7} - 166400 \, {\left(x e + d\right)}^{2} a^{2} b^{5} d^{3} e^{7} - 19200 \, {\left(x e + d\right)} a^{2} b^{5} d^{4} e^{7} - 5376 \, a^{2} b^{5} d^{5} e^{7} + 338910 \, {\left(x e + d\right)}^{4} a^{3} b^{4} e^{8} - 551980 \, {\left(x e + d\right)}^{3} a^{3} b^{4} d e^{8} + 166400 \, {\left(x e + d\right)}^{2} a^{3} b^{4} d^{2} e^{8} + 25600 \, {\left(x e + d\right)} a^{3} b^{4} d^{3} e^{8} + 8960 \, a^{3} b^{4} d^{4} e^{8} + 137995 \, {\left(x e + d\right)}^{3} a^{4} b^{3} e^{9} - 83200 \, {\left(x e + d\right)}^{2} a^{4} b^{3} d e^{9} - 19200 \, {\left(x e + d\right)} a^{4} b^{3} d^{2} e^{9} - 8960 \, a^{4} b^{3} d^{3} e^{9} + 16640 \, {\left(x e + d\right)}^{2} a^{5} b^{2} e^{10} + 7680 \, {\left(x e + d\right)} a^{5} b^{2} d e^{10} + 5376 \, a^{5} b^{2} d^{2} e^{10} - 1280 \, {\left(x e + d\right)} a^{6} b e^{11} - 1792 \, a^{6} b d e^{11} + 256 \, a^{7} e^{12}}{640 \, {\left(b^{8} d^{8} - 8 \, a b^{7} d^{7} e + 28 \, a^{2} b^{6} d^{6} e^{2} - 56 \, a^{3} b^{5} d^{5} e^{3} + 70 \, a^{4} b^{4} d^{4} e^{4} - 56 \, a^{5} b^{3} d^{3} e^{5} + 28 \, a^{6} b^{2} d^{2} e^{6} - 8 \, a^{7} b d e^{7} + a^{8} e^{8}\right)} {\left({\left(x e + d\right)}^{\frac{3}{2}} b - \sqrt{x e + d} b d + \sqrt{x e + d} a e\right)}^{5}}"," ",0,"-9009/128*b^3*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e^5/((b^8*d^8 - 8*a*b^7*d^7*e + 28*a^2*b^6*d^6*e^2 - 56*a^3*b^5*d^5*e^3 + 70*a^4*b^4*d^4*e^4 - 56*a^5*b^3*d^3*e^5 + 28*a^6*b^2*d^2*e^6 - 8*a^7*b*d*e^7 + a^8*e^8)*sqrt(-b^2*d + a*b*e)) - 1/640*(45045*(x*e + d)^7*b^7*e^5 - 210210*(x*e + d)^6*b^7*d*e^5 + 384384*(x*e + d)^5*b^7*d^2*e^5 - 338910*(x*e + d)^4*b^7*d^3*e^5 + 137995*(x*e + d)^3*b^7*d^4*e^5 - 16640*(x*e + d)^2*b^7*d^5*e^5 - 1280*(x*e + d)*b^7*d^6*e^5 - 256*b^7*d^7*e^5 + 210210*(x*e + d)^6*a*b^6*e^6 - 768768*(x*e + d)^5*a*b^6*d*e^6 + 1016730*(x*e + d)^4*a*b^6*d^2*e^6 - 551980*(x*e + d)^3*a*b^6*d^3*e^6 + 83200*(x*e + d)^2*a*b^6*d^4*e^6 + 7680*(x*e + d)*a*b^6*d^5*e^6 + 1792*a*b^6*d^6*e^6 + 384384*(x*e + d)^5*a^2*b^5*e^7 - 1016730*(x*e + d)^4*a^2*b^5*d*e^7 + 827970*(x*e + d)^3*a^2*b^5*d^2*e^7 - 166400*(x*e + d)^2*a^2*b^5*d^3*e^7 - 19200*(x*e + d)*a^2*b^5*d^4*e^7 - 5376*a^2*b^5*d^5*e^7 + 338910*(x*e + d)^4*a^3*b^4*e^8 - 551980*(x*e + d)^3*a^3*b^4*d*e^8 + 166400*(x*e + d)^2*a^3*b^4*d^2*e^8 + 25600*(x*e + d)*a^3*b^4*d^3*e^8 + 8960*a^3*b^4*d^4*e^8 + 137995*(x*e + d)^3*a^4*b^3*e^9 - 83200*(x*e + d)^2*a^4*b^3*d*e^9 - 19200*(x*e + d)*a^4*b^3*d^2*e^9 - 8960*a^4*b^3*d^3*e^9 + 16640*(x*e + d)^2*a^5*b^2*e^10 + 7680*(x*e + d)*a^5*b^2*d*e^10 + 5376*a^5*b^2*d^2*e^10 - 1280*(x*e + d)*a^6*b*e^11 - 1792*a^6*b*d*e^11 + 256*a^7*e^12)/((b^8*d^8 - 8*a*b^7*d^7*e + 28*a^2*b^6*d^6*e^2 - 56*a^3*b^5*d^5*e^3 + 70*a^4*b^4*d^4*e^4 - 56*a^5*b^3*d^3*e^5 + 28*a^6*b^2*d^2*e^6 - 8*a^7*b*d*e^7 + a^8*e^8)*((x*e + d)^(3/2)*b - sqrt(x*e + d)*b*d + sqrt(x*e + d)*a*e)^5)","B",0
1676,1,373,0,0.212800," ","integrate((e*x+d)^(5/2)*((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{2}{315} \, {\left(105 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} b d^{3} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 63 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} b d^{2} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 315 \, \sqrt{x e + d} a d^{3} \mathrm{sgn}\left(b x + a\right) + 315 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a d^{2} \mathrm{sgn}\left(b x + a\right) + 27 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b d e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 63 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a d \mathrm{sgn}\left(b x + a\right) + {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 9 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-1\right)}"," ",0,"2/315*(105*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*b*d^3*e^(-1)*sgn(b*x + a) + 63*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*b*d^2*e^(-1)*sgn(b*x + a) + 315*sqrt(x*e + d)*a*d^3*sgn(b*x + a) + 315*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a*d^2*sgn(b*x + a) + 27*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b*d*e^(-1)*sgn(b*x + a) + 63*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a*d*sgn(b*x + a) + (35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b*e^(-1)*sgn(b*x + a) + 9*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*sgn(b*x + a))*e^(-1)","B",0
1677,1,239,0,0.179240," ","integrate((e*x+d)^(3/2)*((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{2}{105} \, {\left(35 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} b d^{2} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 14 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} b d e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 105 \, \sqrt{x e + d} a d^{2} \mathrm{sgn}\left(b x + a\right) + 70 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a d \mathrm{sgn}\left(b x + a\right) + 3 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 7 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-1\right)}"," ",0,"2/105*(35*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*b*d^2*e^(-1)*sgn(b*x + a) + 14*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*b*d*e^(-1)*sgn(b*x + a) + 105*sqrt(x*e + d)*a*d^2*sgn(b*x + a) + 70*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a*d*sgn(b*x + a) + 3*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b*e^(-1)*sgn(b*x + a) + 7*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a*sgn(b*x + a))*e^(-1)","B",0
1678,1,129,0,0.163560," ","integrate((e*x+d)^(1/2)*((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{2}{15} \, {\left(5 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} b d e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} b e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 15 \, \sqrt{x e + d} a d \mathrm{sgn}\left(b x + a\right) + 5 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-1\right)}"," ",0,"2/15*(5*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*b*d*e^(-1)*sgn(b*x + a) + (3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*b*e^(-1)*sgn(b*x + a) + 15*sqrt(x*e + d)*a*d*sgn(b*x + a) + 5*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a*sgn(b*x + a))*e^(-1)","A",0
1679,1,52,0,0.157113," ","integrate(((b*x+a)^2)^(1/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{3} \, {\left({\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} b e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 3 \, \sqrt{x e + d} a \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-1\right)}"," ",0,"2/3*(((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*b*e^(-1)*sgn(b*x + a) + 3*sqrt(x*e + d)*a*sgn(b*x + a))*e^(-1)","A",0
1680,1,53,0,0.172048," ","integrate(((b*x+a)^2)^(1/2)/(e*x+d)^(3/2),x, algorithm=""giac"")","2 \, \sqrt{x e + d} b e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + \frac{2 \, {\left(b d \mathrm{sgn}\left(b x + a\right) - a e \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-2\right)}}{\sqrt{x e + d}}"," ",0,"2*sqrt(x*e + d)*b*e^(-2)*sgn(b*x + a) + 2*(b*d*sgn(b*x + a) - a*e*sgn(b*x + a))*e^(-2)/sqrt(x*e + d)","A",0
1681,1,48,0,0.184947," ","integrate(((b*x+a)^2)^(1/2)/(e*x+d)^(5/2),x, algorithm=""giac"")","-\frac{2 \, {\left(3 \, {\left(x e + d\right)} b \mathrm{sgn}\left(b x + a\right) - b d \mathrm{sgn}\left(b x + a\right) + a e \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-2\right)}}{3 \, {\left(x e + d\right)}^{\frac{3}{2}}}"," ",0,"-2/3*(3*(x*e + d)*b*sgn(b*x + a) - b*d*sgn(b*x + a) + a*e*sgn(b*x + a))*e^(-2)/(x*e + d)^(3/2)","A",0
1682,1,49,0,0.196944," ","integrate(((b*x+a)^2)^(1/2)/(e*x+d)^(7/2),x, algorithm=""giac"")","-\frac{2 \, {\left(5 \, {\left(x e + d\right)} b \mathrm{sgn}\left(b x + a\right) - 3 \, b d \mathrm{sgn}\left(b x + a\right) + 3 \, a e \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-2\right)}}{15 \, {\left(x e + d\right)}^{\frac{5}{2}}}"," ",0,"-2/15*(5*(x*e + d)*b*sgn(b*x + a) - 3*b*d*sgn(b*x + a) + 3*a*e*sgn(b*x + a))*e^(-2)/(x*e + d)^(5/2)","A",0
1683,1,1004,0,0.271460," ","integrate((e*x+d)^(5/2)*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{2}{15015} \, {\left(15015 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{2} b d^{3} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 3003 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a b^{2} d^{3} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 429 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b^{3} d^{3} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 9009 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{2} b d^{2} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 3861 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a b^{2} d^{2} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 143 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b^{3} d^{2} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 15015 \, \sqrt{x e + d} a^{3} d^{3} \mathrm{sgn}\left(b x + a\right) + 15015 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{3} d^{2} \mathrm{sgn}\left(b x + a\right) + 3861 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{2} b d e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 429 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a b^{2} d e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 65 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b^{3} d e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 3003 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{3} d \mathrm{sgn}\left(b x + a\right) + 143 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{2} b e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 65 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a b^{2} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 5 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} b^{3} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 429 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{3} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-1\right)}"," ",0,"2/15015*(15015*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^2*b*d^3*e^(-1)*sgn(b*x + a) + 3003*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a*b^2*d^3*e^(-2)*sgn(b*x + a) + 429*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b^3*d^3*e^(-3)*sgn(b*x + a) + 9009*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^2*b*d^2*e^(-1)*sgn(b*x + a) + 3861*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*b^2*d^2*e^(-2)*sgn(b*x + a) + 143*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b^3*d^2*e^(-3)*sgn(b*x + a) + 15015*sqrt(x*e + d)*a^3*d^3*sgn(b*x + a) + 15015*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^3*d^2*sgn(b*x + a) + 3861*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^2*b*d*e^(-1)*sgn(b*x + a) + 429*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*b^2*d*e^(-2)*sgn(b*x + a) + 65*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b^3*d*e^(-3)*sgn(b*x + a) + 3003*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^3*d*sgn(b*x + a) + 143*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^2*b*e^(-1)*sgn(b*x + a) + 65*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a*b^2*e^(-2)*sgn(b*x + a) + 5*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*b^3*e^(-3)*sgn(b*x + a) + 429*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^3*sgn(b*x + a))*e^(-1)","B",0
1684,1,670,0,0.230510," ","integrate((e*x+d)^(3/2)*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{2}{3465} \, {\left(3465 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{2} b d^{2} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 693 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a b^{2} d^{2} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 99 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b^{3} d^{2} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 1386 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{2} b d e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 594 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a b^{2} d e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 22 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b^{3} d e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 3465 \, \sqrt{x e + d} a^{3} d^{2} \mathrm{sgn}\left(b x + a\right) + 2310 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{3} d \mathrm{sgn}\left(b x + a\right) + 297 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{2} b e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 33 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a b^{2} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 5 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b^{3} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 231 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{3} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-1\right)}"," ",0,"2/3465*(3465*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^2*b*d^2*e^(-1)*sgn(b*x + a) + 693*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a*b^2*d^2*e^(-2)*sgn(b*x + a) + 99*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b^3*d^2*e^(-3)*sgn(b*x + a) + 1386*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^2*b*d*e^(-1)*sgn(b*x + a) + 594*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*b^2*d*e^(-2)*sgn(b*x + a) + 22*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b^3*d*e^(-3)*sgn(b*x + a) + 3465*sqrt(x*e + d)*a^3*d^2*sgn(b*x + a) + 2310*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^3*d*sgn(b*x + a) + 297*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^2*b*e^(-1)*sgn(b*x + a) + 33*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*b^2*e^(-2)*sgn(b*x + a) + 5*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b^3*e^(-3)*sgn(b*x + a) + 231*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^3*sgn(b*x + a))*e^(-1)","B",0
1685,1,387,0,0.211732," ","integrate((b^2*x^2+2*a*b*x+a^2)^(3/2)*(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{315} \, {\left(315 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{2} b d e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 63 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a b^{2} d e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 9 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b^{3} d e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 63 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{2} b e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 27 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a b^{2} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b^{3} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 315 \, \sqrt{x e + d} a^{3} d \mathrm{sgn}\left(b x + a\right) + 105 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{3} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-1\right)}"," ",0,"2/315*(315*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^2*b*d*e^(-1)*sgn(b*x + a) + 63*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a*b^2*d*e^(-2)*sgn(b*x + a) + 9*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b^3*d*e^(-3)*sgn(b*x + a) + 63*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^2*b*e^(-1)*sgn(b*x + a) + 27*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*b^2*e^(-2)*sgn(b*x + a) + (35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b^3*e^(-3)*sgn(b*x + a) + 315*sqrt(x*e + d)*a^3*d*sgn(b*x + a) + 105*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^3*sgn(b*x + a))*e^(-1)","B",0
1686,1,167,0,0.186367," ","integrate((b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{35} \, {\left(35 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{2} b e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 7 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a b^{2} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b^{3} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 35 \, \sqrt{x e + d} a^{3} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-1\right)}"," ",0,"2/35*(35*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^2*b*e^(-1)*sgn(b*x + a) + 7*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a*b^2*e^(-2)*sgn(b*x + a) + (5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b^3*e^(-3)*sgn(b*x + a) + 35*sqrt(x*e + d)*a^3*sgn(b*x + a))*e^(-1)","A",0
1687,1,210,0,0.227401," ","integrate((b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^(3/2),x, algorithm=""giac"")","\frac{2}{5} \, {\left({\left(x e + d\right)}^{\frac{5}{2}} b^{3} e^{16} \mathrm{sgn}\left(b x + a\right) - 5 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{3} d e^{16} \mathrm{sgn}\left(b x + a\right) + 15 \, \sqrt{x e + d} b^{3} d^{2} e^{16} \mathrm{sgn}\left(b x + a\right) + 5 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{2} e^{17} \mathrm{sgn}\left(b x + a\right) - 30 \, \sqrt{x e + d} a b^{2} d e^{17} \mathrm{sgn}\left(b x + a\right) + 15 \, \sqrt{x e + d} a^{2} b e^{18} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-20\right)} + \frac{2 \, {\left(b^{3} d^{3} \mathrm{sgn}\left(b x + a\right) - 3 \, a b^{2} d^{2} e \mathrm{sgn}\left(b x + a\right) + 3 \, a^{2} b d e^{2} \mathrm{sgn}\left(b x + a\right) - a^{3} e^{3} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-4\right)}}{\sqrt{x e + d}}"," ",0,"2/5*((x*e + d)^(5/2)*b^3*e^16*sgn(b*x + a) - 5*(x*e + d)^(3/2)*b^3*d*e^16*sgn(b*x + a) + 15*sqrt(x*e + d)*b^3*d^2*e^16*sgn(b*x + a) + 5*(x*e + d)^(3/2)*a*b^2*e^17*sgn(b*x + a) - 30*sqrt(x*e + d)*a*b^2*d*e^17*sgn(b*x + a) + 15*sqrt(x*e + d)*a^2*b*e^18*sgn(b*x + a))*e^(-20) + 2*(b^3*d^3*sgn(b*x + a) - 3*a*b^2*d^2*e*sgn(b*x + a) + 3*a^2*b*d*e^2*sgn(b*x + a) - a^3*e^3*sgn(b*x + a))*e^(-4)/sqrt(x*e + d)","A",0
1688,1,202,0,0.216024," ","integrate((b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^(5/2),x, algorithm=""giac"")","\frac{2}{3} \, {\left({\left(x e + d\right)}^{\frac{3}{2}} b^{3} e^{8} \mathrm{sgn}\left(b x + a\right) - 9 \, \sqrt{x e + d} b^{3} d e^{8} \mathrm{sgn}\left(b x + a\right) + 9 \, \sqrt{x e + d} a b^{2} e^{9} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-12\right)} - \frac{2 \, {\left(9 \, {\left(x e + d\right)} b^{3} d^{2} \mathrm{sgn}\left(b x + a\right) - b^{3} d^{3} \mathrm{sgn}\left(b x + a\right) - 18 \, {\left(x e + d\right)} a b^{2} d e \mathrm{sgn}\left(b x + a\right) + 3 \, a b^{2} d^{2} e \mathrm{sgn}\left(b x + a\right) + 9 \, {\left(x e + d\right)} a^{2} b e^{2} \mathrm{sgn}\left(b x + a\right) - 3 \, a^{2} b d e^{2} \mathrm{sgn}\left(b x + a\right) + a^{3} e^{3} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-4\right)}}{3 \, {\left(x e + d\right)}^{\frac{3}{2}}}"," ",0,"2/3*((x*e + d)^(3/2)*b^3*e^8*sgn(b*x + a) - 9*sqrt(x*e + d)*b^3*d*e^8*sgn(b*x + a) + 9*sqrt(x*e + d)*a*b^2*e^9*sgn(b*x + a))*e^(-12) - 2/3*(9*(x*e + d)*b^3*d^2*sgn(b*x + a) - b^3*d^3*sgn(b*x + a) - 18*(x*e + d)*a*b^2*d*e*sgn(b*x + a) + 3*a*b^2*d^2*e*sgn(b*x + a) + 9*(x*e + d)*a^2*b*e^2*sgn(b*x + a) - 3*a^2*b*d*e^2*sgn(b*x + a) + a^3*e^3*sgn(b*x + a))*e^(-4)/(x*e + d)^(3/2)","A",0
1689,1,196,0,0.300329," ","integrate((b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^(7/2),x, algorithm=""giac"")","2 \, \sqrt{x e + d} b^{3} e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + \frac{2 \, {\left(15 \, {\left(x e + d\right)}^{2} b^{3} d \mathrm{sgn}\left(b x + a\right) - 5 \, {\left(x e + d\right)} b^{3} d^{2} \mathrm{sgn}\left(b x + a\right) + b^{3} d^{3} \mathrm{sgn}\left(b x + a\right) - 15 \, {\left(x e + d\right)}^{2} a b^{2} e \mathrm{sgn}\left(b x + a\right) + 10 \, {\left(x e + d\right)} a b^{2} d e \mathrm{sgn}\left(b x + a\right) - 3 \, a b^{2} d^{2} e \mathrm{sgn}\left(b x + a\right) - 5 \, {\left(x e + d\right)} a^{2} b e^{2} \mathrm{sgn}\left(b x + a\right) + 3 \, a^{2} b d e^{2} \mathrm{sgn}\left(b x + a\right) - a^{3} e^{3} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-4\right)}}{5 \, {\left(x e + d\right)}^{\frac{5}{2}}}"," ",0,"2*sqrt(x*e + d)*b^3*e^(-4)*sgn(b*x + a) + 2/5*(15*(x*e + d)^2*b^3*d*sgn(b*x + a) - 5*(x*e + d)*b^3*d^2*sgn(b*x + a) + b^3*d^3*sgn(b*x + a) - 15*(x*e + d)^2*a*b^2*e*sgn(b*x + a) + 10*(x*e + d)*a*b^2*d*e*sgn(b*x + a) - 3*a*b^2*d^2*e*sgn(b*x + a) - 5*(x*e + d)*a^2*b*e^2*sgn(b*x + a) + 3*a^2*b*d*e^2*sgn(b*x + a) - a^3*e^3*sgn(b*x + a))*e^(-4)/(x*e + d)^(5/2)","A",0
1690,1,194,0,0.205937," ","integrate((b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^(9/2),x, algorithm=""giac"")","-\frac{2 \, {\left(35 \, {\left(x e + d\right)}^{3} b^{3} \mathrm{sgn}\left(b x + a\right) - 35 \, {\left(x e + d\right)}^{2} b^{3} d \mathrm{sgn}\left(b x + a\right) + 21 \, {\left(x e + d\right)} b^{3} d^{2} \mathrm{sgn}\left(b x + a\right) - 5 \, b^{3} d^{3} \mathrm{sgn}\left(b x + a\right) + 35 \, {\left(x e + d\right)}^{2} a b^{2} e \mathrm{sgn}\left(b x + a\right) - 42 \, {\left(x e + d\right)} a b^{2} d e \mathrm{sgn}\left(b x + a\right) + 15 \, a b^{2} d^{2} e \mathrm{sgn}\left(b x + a\right) + 21 \, {\left(x e + d\right)} a^{2} b e^{2} \mathrm{sgn}\left(b x + a\right) - 15 \, a^{2} b d e^{2} \mathrm{sgn}\left(b x + a\right) + 5 \, a^{3} e^{3} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-4\right)}}{35 \, {\left(x e + d\right)}^{\frac{7}{2}}}"," ",0,"-2/35*(35*(x*e + d)^3*b^3*sgn(b*x + a) - 35*(x*e + d)^2*b^3*d*sgn(b*x + a) + 21*(x*e + d)*b^3*d^2*sgn(b*x + a) - 5*b^3*d^3*sgn(b*x + a) + 35*(x*e + d)^2*a*b^2*e*sgn(b*x + a) - 42*(x*e + d)*a*b^2*d*e*sgn(b*x + a) + 15*a*b^2*d^2*e*sgn(b*x + a) + 21*(x*e + d)*a^2*b*e^2*sgn(b*x + a) - 15*a^2*b*d*e^2*sgn(b*x + a) + 5*a^3*e^3*sgn(b*x + a))*e^(-4)/(x*e + d)^(7/2)","A",0
1691,1,194,0,0.250299," ","integrate((b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^(11/2),x, algorithm=""giac"")","-\frac{2 \, {\left(105 \, {\left(x e + d\right)}^{3} b^{3} \mathrm{sgn}\left(b x + a\right) - 189 \, {\left(x e + d\right)}^{2} b^{3} d \mathrm{sgn}\left(b x + a\right) + 135 \, {\left(x e + d\right)} b^{3} d^{2} \mathrm{sgn}\left(b x + a\right) - 35 \, b^{3} d^{3} \mathrm{sgn}\left(b x + a\right) + 189 \, {\left(x e + d\right)}^{2} a b^{2} e \mathrm{sgn}\left(b x + a\right) - 270 \, {\left(x e + d\right)} a b^{2} d e \mathrm{sgn}\left(b x + a\right) + 105 \, a b^{2} d^{2} e \mathrm{sgn}\left(b x + a\right) + 135 \, {\left(x e + d\right)} a^{2} b e^{2} \mathrm{sgn}\left(b x + a\right) - 105 \, a^{2} b d e^{2} \mathrm{sgn}\left(b x + a\right) + 35 \, a^{3} e^{3} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-4\right)}}{315 \, {\left(x e + d\right)}^{\frac{9}{2}}}"," ",0,"-2/315*(105*(x*e + d)^3*b^3*sgn(b*x + a) - 189*(x*e + d)^2*b^3*d*sgn(b*x + a) + 135*(x*e + d)*b^3*d^2*sgn(b*x + a) - 35*b^3*d^3*sgn(b*x + a) + 189*(x*e + d)^2*a*b^2*e*sgn(b*x + a) - 270*(x*e + d)*a*b^2*d*e*sgn(b*x + a) + 105*a*b^2*d^2*e*sgn(b*x + a) + 135*(x*e + d)*a^2*b*e^2*sgn(b*x + a) - 105*a^2*b*d*e^2*sgn(b*x + a) + 35*a^3*e^3*sgn(b*x + a))*e^(-4)/(x*e + d)^(9/2)","A",0
1692,1,1842,0,0.384689," ","integrate((e*x+d)^(5/2)*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{2}{765765} \, {\left(1276275 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{4} b d^{3} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 510510 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{3} b^{2} d^{3} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 218790 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{2} b^{3} d^{3} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 12155 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a b^{4} d^{3} e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 1105 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b^{5} d^{3} e^{\left(-5\right)} \mathrm{sgn}\left(b x + a\right) + 765765 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{4} b d^{2} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 656370 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{3} b^{2} d^{2} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 72930 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{2} b^{3} d^{2} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 16575 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a b^{4} d^{2} e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 765 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} b^{5} d^{2} e^{\left(-5\right)} \mathrm{sgn}\left(b x + a\right) + 765765 \, \sqrt{x e + d} a^{5} d^{3} \mathrm{sgn}\left(b x + a\right) + 765765 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{5} d^{2} \mathrm{sgn}\left(b x + a\right) + 328185 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{4} b d e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 72930 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{3} b^{2} d e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 33150 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a^{2} b^{3} d e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 3825 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} a b^{4} d e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 357 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} b^{5} d e^{\left(-5\right)} \mathrm{sgn}\left(b x + a\right) + 153153 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{5} d \mathrm{sgn}\left(b x + a\right) + 12155 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{4} b e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 11050 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a^{3} b^{2} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 2550 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} a^{2} b^{3} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 595 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} a b^{4} e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 7 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} b^{5} e^{\left(-5\right)} \mathrm{sgn}\left(b x + a\right) + 21879 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{5} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-1\right)}"," ",0,"2/765765*(1276275*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^4*b*d^3*e^(-1)*sgn(b*x + a) + 510510*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^3*b^2*d^3*e^(-2)*sgn(b*x + a) + 218790*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^2*b^3*d^3*e^(-3)*sgn(b*x + a) + 12155*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*b^4*d^3*e^(-4)*sgn(b*x + a) + 1105*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b^5*d^3*e^(-5)*sgn(b*x + a) + 765765*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^4*b*d^2*e^(-1)*sgn(b*x + a) + 656370*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^3*b^2*d^2*e^(-2)*sgn(b*x + a) + 72930*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^2*b^3*d^2*e^(-3)*sgn(b*x + a) + 16575*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a*b^4*d^2*e^(-4)*sgn(b*x + a) + 765*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*b^5*d^2*e^(-5)*sgn(b*x + a) + 765765*sqrt(x*e + d)*a^5*d^3*sgn(b*x + a) + 765765*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^5*d^2*sgn(b*x + a) + 328185*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^4*b*d*e^(-1)*sgn(b*x + a) + 72930*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^3*b^2*d*e^(-2)*sgn(b*x + a) + 33150*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a^2*b^3*d*e^(-3)*sgn(b*x + a) + 3825*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*a*b^4*d*e^(-4)*sgn(b*x + a) + 357*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*b^5*d*e^(-5)*sgn(b*x + a) + 153153*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^5*d*sgn(b*x + a) + 12155*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^4*b*e^(-1)*sgn(b*x + a) + 11050*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a^3*b^2*e^(-2)*sgn(b*x + a) + 2550*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*a^2*b^3*e^(-3)*sgn(b*x + a) + 595*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*a*b^4*e^(-4)*sgn(b*x + a) + 7*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*b^5*e^(-5)*sgn(b*x + a) + 21879*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^5*sgn(b*x + a))*e^(-1)","B",0
1693,1,1257,0,0.316113," ","integrate((e*x+d)^(3/2)*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{2}{45045} \, {\left(75075 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{4} b d^{2} e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 30030 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{3} b^{2} d^{2} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 12870 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{2} b^{3} d^{2} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 715 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a b^{4} d^{2} e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 65 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b^{5} d^{2} e^{\left(-5\right)} \mathrm{sgn}\left(b x + a\right) + 30030 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{4} b d e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 25740 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{3} b^{2} d e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 2860 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{2} b^{3} d e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 650 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a b^{4} d e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 30 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} b^{5} d e^{\left(-5\right)} \mathrm{sgn}\left(b x + a\right) + 45045 \, \sqrt{x e + d} a^{5} d^{2} \mathrm{sgn}\left(b x + a\right) + 30030 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{5} d \mathrm{sgn}\left(b x + a\right) + 6435 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{4} b e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 1430 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{3} b^{2} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 650 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a^{2} b^{3} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 75 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} a b^{4} e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 7 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} b^{5} e^{\left(-5\right)} \mathrm{sgn}\left(b x + a\right) + 3003 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{5} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-1\right)}"," ",0,"2/45045*(75075*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^4*b*d^2*e^(-1)*sgn(b*x + a) + 30030*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^3*b^2*d^2*e^(-2)*sgn(b*x + a) + 12870*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^2*b^3*d^2*e^(-3)*sgn(b*x + a) + 715*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*b^4*d^2*e^(-4)*sgn(b*x + a) + 65*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b^5*d^2*e^(-5)*sgn(b*x + a) + 30030*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^4*b*d*e^(-1)*sgn(b*x + a) + 25740*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^3*b^2*d*e^(-2)*sgn(b*x + a) + 2860*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^2*b^3*d*e^(-3)*sgn(b*x + a) + 650*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a*b^4*d*e^(-4)*sgn(b*x + a) + 30*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*b^5*d*e^(-5)*sgn(b*x + a) + 45045*sqrt(x*e + d)*a^5*d^2*sgn(b*x + a) + 30030*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^5*d*sgn(b*x + a) + 6435*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^4*b*e^(-1)*sgn(b*x + a) + 1430*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^3*b^2*e^(-2)*sgn(b*x + a) + 650*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a^2*b^3*e^(-3)*sgn(b*x + a) + 75*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*a*b^4*e^(-4)*sgn(b*x + a) + 7*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*b^5*e^(-5)*sgn(b*x + a) + 3003*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^5*sgn(b*x + a))*e^(-1)","B",0
1694,1,750,0,0.368261," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)*(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{9009} \, {\left(15015 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{4} b d e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 6006 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{3} b^{2} d e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 2574 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{2} b^{3} d e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 143 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a b^{4} d e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 13 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b^{5} d e^{\left(-5\right)} \mathrm{sgn}\left(b x + a\right) + 3003 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{4} b e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 2574 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{3} b^{2} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 286 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{2} b^{3} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 65 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a b^{4} e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + 3 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} b^{5} e^{\left(-5\right)} \mathrm{sgn}\left(b x + a\right) + 9009 \, \sqrt{x e + d} a^{5} d \mathrm{sgn}\left(b x + a\right) + 3003 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{5} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-1\right)}"," ",0,"2/9009*(15015*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^4*b*d*e^(-1)*sgn(b*x + a) + 6006*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^3*b^2*d*e^(-2)*sgn(b*x + a) + 2574*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^2*b^3*d*e^(-3)*sgn(b*x + a) + 143*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*b^4*d*e^(-4)*sgn(b*x + a) + 13*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b^5*d*e^(-5)*sgn(b*x + a) + 3003*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^4*b*e^(-1)*sgn(b*x + a) + 2574*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^3*b^2*e^(-2)*sgn(b*x + a) + 286*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^2*b^3*e^(-3)*sgn(b*x + a) + 65*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a*b^4*e^(-4)*sgn(b*x + a) + 3*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*b^5*e^(-5)*sgn(b*x + a) + 9009*sqrt(x*e + d)*a^5*d*sgn(b*x + a) + 3003*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^5*sgn(b*x + a))*e^(-1)","B",0
1695,1,334,0,0.196503," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{693} \, {\left(1155 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{4} b e^{\left(-1\right)} \mathrm{sgn}\left(b x + a\right) + 462 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{3} b^{2} e^{\left(-2\right)} \mathrm{sgn}\left(b x + a\right) + 198 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{2} b^{3} e^{\left(-3\right)} \mathrm{sgn}\left(b x + a\right) + 11 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a b^{4} e^{\left(-4\right)} \mathrm{sgn}\left(b x + a\right) + {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b^{5} e^{\left(-5\right)} \mathrm{sgn}\left(b x + a\right) + 693 \, \sqrt{x e + d} a^{5} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-1\right)}"," ",0,"2/693*(1155*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^4*b*e^(-1)*sgn(b*x + a) + 462*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^3*b^2*e^(-2)*sgn(b*x + a) + 198*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^2*b^3*e^(-3)*sgn(b*x + a) + 11*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*b^4*e^(-4)*sgn(b*x + a) + (63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b^5*e^(-5)*sgn(b*x + a) + 693*sqrt(x*e + d)*a^5*sgn(b*x + a))*e^(-1)","A",0
1696,1,472,0,0.234622," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^(3/2),x, algorithm=""giac"")","\frac{2}{63} \, {\left(7 \, {\left(x e + d\right)}^{\frac{9}{2}} b^{5} e^{48} \mathrm{sgn}\left(b x + a\right) - 45 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{5} d e^{48} \mathrm{sgn}\left(b x + a\right) + 126 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{5} d^{2} e^{48} \mathrm{sgn}\left(b x + a\right) - 210 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{5} d^{3} e^{48} \mathrm{sgn}\left(b x + a\right) + 315 \, \sqrt{x e + d} b^{5} d^{4} e^{48} \mathrm{sgn}\left(b x + a\right) + 45 \, {\left(x e + d\right)}^{\frac{7}{2}} a b^{4} e^{49} \mathrm{sgn}\left(b x + a\right) - 252 \, {\left(x e + d\right)}^{\frac{5}{2}} a b^{4} d e^{49} \mathrm{sgn}\left(b x + a\right) + 630 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{4} d^{2} e^{49} \mathrm{sgn}\left(b x + a\right) - 1260 \, \sqrt{x e + d} a b^{4} d^{3} e^{49} \mathrm{sgn}\left(b x + a\right) + 126 \, {\left(x e + d\right)}^{\frac{5}{2}} a^{2} b^{3} e^{50} \mathrm{sgn}\left(b x + a\right) - 630 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} b^{3} d e^{50} \mathrm{sgn}\left(b x + a\right) + 1890 \, \sqrt{x e + d} a^{2} b^{3} d^{2} e^{50} \mathrm{sgn}\left(b x + a\right) + 210 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{3} b^{2} e^{51} \mathrm{sgn}\left(b x + a\right) - 1260 \, \sqrt{x e + d} a^{3} b^{2} d e^{51} \mathrm{sgn}\left(b x + a\right) + 315 \, \sqrt{x e + d} a^{4} b e^{52} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-54\right)} + \frac{2 \, {\left(b^{5} d^{5} \mathrm{sgn}\left(b x + a\right) - 5 \, a b^{4} d^{4} e \mathrm{sgn}\left(b x + a\right) + 10 \, a^{2} b^{3} d^{3} e^{2} \mathrm{sgn}\left(b x + a\right) - 10 \, a^{3} b^{2} d^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 5 \, a^{4} b d e^{4} \mathrm{sgn}\left(b x + a\right) - a^{5} e^{5} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-6\right)}}{\sqrt{x e + d}}"," ",0,"2/63*(7*(x*e + d)^(9/2)*b^5*e^48*sgn(b*x + a) - 45*(x*e + d)^(7/2)*b^5*d*e^48*sgn(b*x + a) + 126*(x*e + d)^(5/2)*b^5*d^2*e^48*sgn(b*x + a) - 210*(x*e + d)^(3/2)*b^5*d^3*e^48*sgn(b*x + a) + 315*sqrt(x*e + d)*b^5*d^4*e^48*sgn(b*x + a) + 45*(x*e + d)^(7/2)*a*b^4*e^49*sgn(b*x + a) - 252*(x*e + d)^(5/2)*a*b^4*d*e^49*sgn(b*x + a) + 630*(x*e + d)^(3/2)*a*b^4*d^2*e^49*sgn(b*x + a) - 1260*sqrt(x*e + d)*a*b^4*d^3*e^49*sgn(b*x + a) + 126*(x*e + d)^(5/2)*a^2*b^3*e^50*sgn(b*x + a) - 630*(x*e + d)^(3/2)*a^2*b^3*d*e^50*sgn(b*x + a) + 1890*sqrt(x*e + d)*a^2*b^3*d^2*e^50*sgn(b*x + a) + 210*(x*e + d)^(3/2)*a^3*b^2*e^51*sgn(b*x + a) - 1260*sqrt(x*e + d)*a^3*b^2*d*e^51*sgn(b*x + a) + 315*sqrt(x*e + d)*a^4*b*e^52*sgn(b*x + a))*e^(-54) + 2*(b^5*d^5*sgn(b*x + a) - 5*a*b^4*d^4*e*sgn(b*x + a) + 10*a^2*b^3*d^3*e^2*sgn(b*x + a) - 10*a^3*b^2*d^2*e^3*sgn(b*x + a) + 5*a^4*b*d*e^4*sgn(b*x + a) - a^5*e^5*sgn(b*x + a))*e^(-6)/sqrt(x*e + d)","B",0
1697,1,460,0,0.248871," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^(5/2),x, algorithm=""giac"")","\frac{2}{21} \, {\left(3 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{5} e^{36} \mathrm{sgn}\left(b x + a\right) - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{5} d e^{36} \mathrm{sgn}\left(b x + a\right) + 70 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{5} d^{2} e^{36} \mathrm{sgn}\left(b x + a\right) - 210 \, \sqrt{x e + d} b^{5} d^{3} e^{36} \mathrm{sgn}\left(b x + a\right) + 21 \, {\left(x e + d\right)}^{\frac{5}{2}} a b^{4} e^{37} \mathrm{sgn}\left(b x + a\right) - 140 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{4} d e^{37} \mathrm{sgn}\left(b x + a\right) + 630 \, \sqrt{x e + d} a b^{4} d^{2} e^{37} \mathrm{sgn}\left(b x + a\right) + 70 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} b^{3} e^{38} \mathrm{sgn}\left(b x + a\right) - 630 \, \sqrt{x e + d} a^{2} b^{3} d e^{38} \mathrm{sgn}\left(b x + a\right) + 210 \, \sqrt{x e + d} a^{3} b^{2} e^{39} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-42\right)} - \frac{2 \, {\left(15 \, {\left(x e + d\right)} b^{5} d^{4} \mathrm{sgn}\left(b x + a\right) - b^{5} d^{5} \mathrm{sgn}\left(b x + a\right) - 60 \, {\left(x e + d\right)} a b^{4} d^{3} e \mathrm{sgn}\left(b x + a\right) + 5 \, a b^{4} d^{4} e \mathrm{sgn}\left(b x + a\right) + 90 \, {\left(x e + d\right)} a^{2} b^{3} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) - 10 \, a^{2} b^{3} d^{3} e^{2} \mathrm{sgn}\left(b x + a\right) - 60 \, {\left(x e + d\right)} a^{3} b^{2} d e^{3} \mathrm{sgn}\left(b x + a\right) + 10 \, a^{3} b^{2} d^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 15 \, {\left(x e + d\right)} a^{4} b e^{4} \mathrm{sgn}\left(b x + a\right) - 5 \, a^{4} b d e^{4} \mathrm{sgn}\left(b x + a\right) + a^{5} e^{5} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-6\right)}}{3 \, {\left(x e + d\right)}^{\frac{3}{2}}}"," ",0,"2/21*(3*(x*e + d)^(7/2)*b^5*e^36*sgn(b*x + a) - 21*(x*e + d)^(5/2)*b^5*d*e^36*sgn(b*x + a) + 70*(x*e + d)^(3/2)*b^5*d^2*e^36*sgn(b*x + a) - 210*sqrt(x*e + d)*b^5*d^3*e^36*sgn(b*x + a) + 21*(x*e + d)^(5/2)*a*b^4*e^37*sgn(b*x + a) - 140*(x*e + d)^(3/2)*a*b^4*d*e^37*sgn(b*x + a) + 630*sqrt(x*e + d)*a*b^4*d^2*e^37*sgn(b*x + a) + 70*(x*e + d)^(3/2)*a^2*b^3*e^38*sgn(b*x + a) - 630*sqrt(x*e + d)*a^2*b^3*d*e^38*sgn(b*x + a) + 210*sqrt(x*e + d)*a^3*b^2*e^39*sgn(b*x + a))*e^(-42) - 2/3*(15*(x*e + d)*b^5*d^4*sgn(b*x + a) - b^5*d^5*sgn(b*x + a) - 60*(x*e + d)*a*b^4*d^3*e*sgn(b*x + a) + 5*a*b^4*d^4*e*sgn(b*x + a) + 90*(x*e + d)*a^2*b^3*d^2*e^2*sgn(b*x + a) - 10*a^2*b^3*d^3*e^2*sgn(b*x + a) - 60*(x*e + d)*a^3*b^2*d*e^3*sgn(b*x + a) + 10*a^3*b^2*d^2*e^3*sgn(b*x + a) + 15*(x*e + d)*a^4*b*e^4*sgn(b*x + a) - 5*a^4*b*d*e^4*sgn(b*x + a) + a^5*e^5*sgn(b*x + a))*e^(-6)/(x*e + d)^(3/2)","A",0
1698,1,459,0,0.272676," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^(7/2),x, algorithm=""giac"")","\frac{2}{15} \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{5} e^{24} \mathrm{sgn}\left(b x + a\right) - 25 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{5} d e^{24} \mathrm{sgn}\left(b x + a\right) + 150 \, \sqrt{x e + d} b^{5} d^{2} e^{24} \mathrm{sgn}\left(b x + a\right) + 25 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{4} e^{25} \mathrm{sgn}\left(b x + a\right) - 300 \, \sqrt{x e + d} a b^{4} d e^{25} \mathrm{sgn}\left(b x + a\right) + 150 \, \sqrt{x e + d} a^{2} b^{3} e^{26} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-30\right)} + \frac{2 \, {\left(150 \, {\left(x e + d\right)}^{2} b^{5} d^{3} \mathrm{sgn}\left(b x + a\right) - 25 \, {\left(x e + d\right)} b^{5} d^{4} \mathrm{sgn}\left(b x + a\right) + 3 \, b^{5} d^{5} \mathrm{sgn}\left(b x + a\right) - 450 \, {\left(x e + d\right)}^{2} a b^{4} d^{2} e \mathrm{sgn}\left(b x + a\right) + 100 \, {\left(x e + d\right)} a b^{4} d^{3} e \mathrm{sgn}\left(b x + a\right) - 15 \, a b^{4} d^{4} e \mathrm{sgn}\left(b x + a\right) + 450 \, {\left(x e + d\right)}^{2} a^{2} b^{3} d e^{2} \mathrm{sgn}\left(b x + a\right) - 150 \, {\left(x e + d\right)} a^{2} b^{3} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 30 \, a^{2} b^{3} d^{3} e^{2} \mathrm{sgn}\left(b x + a\right) - 150 \, {\left(x e + d\right)}^{2} a^{3} b^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 100 \, {\left(x e + d\right)} a^{3} b^{2} d e^{3} \mathrm{sgn}\left(b x + a\right) - 30 \, a^{3} b^{2} d^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - 25 \, {\left(x e + d\right)} a^{4} b e^{4} \mathrm{sgn}\left(b x + a\right) + 15 \, a^{4} b d e^{4} \mathrm{sgn}\left(b x + a\right) - 3 \, a^{5} e^{5} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-6\right)}}{15 \, {\left(x e + d\right)}^{\frac{5}{2}}}"," ",0,"2/15*(3*(x*e + d)^(5/2)*b^5*e^24*sgn(b*x + a) - 25*(x*e + d)^(3/2)*b^5*d*e^24*sgn(b*x + a) + 150*sqrt(x*e + d)*b^5*d^2*e^24*sgn(b*x + a) + 25*(x*e + d)^(3/2)*a*b^4*e^25*sgn(b*x + a) - 300*sqrt(x*e + d)*a*b^4*d*e^25*sgn(b*x + a) + 150*sqrt(x*e + d)*a^2*b^3*e^26*sgn(b*x + a))*e^(-30) + 2/15*(150*(x*e + d)^2*b^5*d^3*sgn(b*x + a) - 25*(x*e + d)*b^5*d^4*sgn(b*x + a) + 3*b^5*d^5*sgn(b*x + a) - 450*(x*e + d)^2*a*b^4*d^2*e*sgn(b*x + a) + 100*(x*e + d)*a*b^4*d^3*e*sgn(b*x + a) - 15*a*b^4*d^4*e*sgn(b*x + a) + 450*(x*e + d)^2*a^2*b^3*d*e^2*sgn(b*x + a) - 150*(x*e + d)*a^2*b^3*d^2*e^2*sgn(b*x + a) + 30*a^2*b^3*d^3*e^2*sgn(b*x + a) - 150*(x*e + d)^2*a^3*b^2*e^3*sgn(b*x + a) + 100*(x*e + d)*a^3*b^2*d*e^3*sgn(b*x + a) - 30*a^3*b^2*d^2*e^3*sgn(b*x + a) - 25*(x*e + d)*a^4*b*e^4*sgn(b*x + a) + 15*a^4*b*d*e^4*sgn(b*x + a) - 3*a^5*e^5*sgn(b*x + a))*e^(-6)/(x*e + d)^(5/2)","A",0
1699,1,456,0,0.256374," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^(9/2),x, algorithm=""giac"")","\frac{2}{3} \, {\left({\left(x e + d\right)}^{\frac{3}{2}} b^{5} e^{12} \mathrm{sgn}\left(b x + a\right) - 15 \, \sqrt{x e + d} b^{5} d e^{12} \mathrm{sgn}\left(b x + a\right) + 15 \, \sqrt{x e + d} a b^{4} e^{13} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-18\right)} - \frac{2 \, {\left(210 \, {\left(x e + d\right)}^{3} b^{5} d^{2} \mathrm{sgn}\left(b x + a\right) - 70 \, {\left(x e + d\right)}^{2} b^{5} d^{3} \mathrm{sgn}\left(b x + a\right) + 21 \, {\left(x e + d\right)} b^{5} d^{4} \mathrm{sgn}\left(b x + a\right) - 3 \, b^{5} d^{5} \mathrm{sgn}\left(b x + a\right) - 420 \, {\left(x e + d\right)}^{3} a b^{4} d e \mathrm{sgn}\left(b x + a\right) + 210 \, {\left(x e + d\right)}^{2} a b^{4} d^{2} e \mathrm{sgn}\left(b x + a\right) - 84 \, {\left(x e + d\right)} a b^{4} d^{3} e \mathrm{sgn}\left(b x + a\right) + 15 \, a b^{4} d^{4} e \mathrm{sgn}\left(b x + a\right) + 210 \, {\left(x e + d\right)}^{3} a^{2} b^{3} e^{2} \mathrm{sgn}\left(b x + a\right) - 210 \, {\left(x e + d\right)}^{2} a^{2} b^{3} d e^{2} \mathrm{sgn}\left(b x + a\right) + 126 \, {\left(x e + d\right)} a^{2} b^{3} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) - 30 \, a^{2} b^{3} d^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + 70 \, {\left(x e + d\right)}^{2} a^{3} b^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - 84 \, {\left(x e + d\right)} a^{3} b^{2} d e^{3} \mathrm{sgn}\left(b x + a\right) + 30 \, a^{3} b^{2} d^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 21 \, {\left(x e + d\right)} a^{4} b e^{4} \mathrm{sgn}\left(b x + a\right) - 15 \, a^{4} b d e^{4} \mathrm{sgn}\left(b x + a\right) + 3 \, a^{5} e^{5} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-6\right)}}{21 \, {\left(x e + d\right)}^{\frac{7}{2}}}"," ",0,"2/3*((x*e + d)^(3/2)*b^5*e^12*sgn(b*x + a) - 15*sqrt(x*e + d)*b^5*d*e^12*sgn(b*x + a) + 15*sqrt(x*e + d)*a*b^4*e^13*sgn(b*x + a))*e^(-18) - 2/21*(210*(x*e + d)^3*b^5*d^2*sgn(b*x + a) - 70*(x*e + d)^2*b^5*d^3*sgn(b*x + a) + 21*(x*e + d)*b^5*d^4*sgn(b*x + a) - 3*b^5*d^5*sgn(b*x + a) - 420*(x*e + d)^3*a*b^4*d*e*sgn(b*x + a) + 210*(x*e + d)^2*a*b^4*d^2*e*sgn(b*x + a) - 84*(x*e + d)*a*b^4*d^3*e*sgn(b*x + a) + 15*a*b^4*d^4*e*sgn(b*x + a) + 210*(x*e + d)^3*a^2*b^3*e^2*sgn(b*x + a) - 210*(x*e + d)^2*a^2*b^3*d*e^2*sgn(b*x + a) + 126*(x*e + d)*a^2*b^3*d^2*e^2*sgn(b*x + a) - 30*a^2*b^3*d^3*e^2*sgn(b*x + a) + 70*(x*e + d)^2*a^3*b^2*e^3*sgn(b*x + a) - 84*(x*e + d)*a^3*b^2*d*e^3*sgn(b*x + a) + 30*a^3*b^2*d^2*e^3*sgn(b*x + a) + 21*(x*e + d)*a^4*b*e^4*sgn(b*x + a) - 15*a^4*b*d*e^4*sgn(b*x + a) + 3*a^5*e^5*sgn(b*x + a))*e^(-6)/(x*e + d)^(7/2)","A",0
1700,1,450,0,0.256546," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^(11/2),x, algorithm=""giac"")","2 \, \sqrt{x e + d} b^{5} e^{\left(-6\right)} \mathrm{sgn}\left(b x + a\right) + \frac{2 \, {\left(315 \, {\left(x e + d\right)}^{4} b^{5} d \mathrm{sgn}\left(b x + a\right) - 210 \, {\left(x e + d\right)}^{3} b^{5} d^{2} \mathrm{sgn}\left(b x + a\right) + 126 \, {\left(x e + d\right)}^{2} b^{5} d^{3} \mathrm{sgn}\left(b x + a\right) - 45 \, {\left(x e + d\right)} b^{5} d^{4} \mathrm{sgn}\left(b x + a\right) + 7 \, b^{5} d^{5} \mathrm{sgn}\left(b x + a\right) - 315 \, {\left(x e + d\right)}^{4} a b^{4} e \mathrm{sgn}\left(b x + a\right) + 420 \, {\left(x e + d\right)}^{3} a b^{4} d e \mathrm{sgn}\left(b x + a\right) - 378 \, {\left(x e + d\right)}^{2} a b^{4} d^{2} e \mathrm{sgn}\left(b x + a\right) + 180 \, {\left(x e + d\right)} a b^{4} d^{3} e \mathrm{sgn}\left(b x + a\right) - 35 \, a b^{4} d^{4} e \mathrm{sgn}\left(b x + a\right) - 210 \, {\left(x e + d\right)}^{3} a^{2} b^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + 378 \, {\left(x e + d\right)}^{2} a^{2} b^{3} d e^{2} \mathrm{sgn}\left(b x + a\right) - 270 \, {\left(x e + d\right)} a^{2} b^{3} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 70 \, a^{2} b^{3} d^{3} e^{2} \mathrm{sgn}\left(b x + a\right) - 126 \, {\left(x e + d\right)}^{2} a^{3} b^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 180 \, {\left(x e + d\right)} a^{3} b^{2} d e^{3} \mathrm{sgn}\left(b x + a\right) - 70 \, a^{3} b^{2} d^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - 45 \, {\left(x e + d\right)} a^{4} b e^{4} \mathrm{sgn}\left(b x + a\right) + 35 \, a^{4} b d e^{4} \mathrm{sgn}\left(b x + a\right) - 7 \, a^{5} e^{5} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-6\right)}}{63 \, {\left(x e + d\right)}^{\frac{9}{2}}}"," ",0,"2*sqrt(x*e + d)*b^5*e^(-6)*sgn(b*x + a) + 2/63*(315*(x*e + d)^4*b^5*d*sgn(b*x + a) - 210*(x*e + d)^3*b^5*d^2*sgn(b*x + a) + 126*(x*e + d)^2*b^5*d^3*sgn(b*x + a) - 45*(x*e + d)*b^5*d^4*sgn(b*x + a) + 7*b^5*d^5*sgn(b*x + a) - 315*(x*e + d)^4*a*b^4*e*sgn(b*x + a) + 420*(x*e + d)^3*a*b^4*d*e*sgn(b*x + a) - 378*(x*e + d)^2*a*b^4*d^2*e*sgn(b*x + a) + 180*(x*e + d)*a*b^4*d^3*e*sgn(b*x + a) - 35*a*b^4*d^4*e*sgn(b*x + a) - 210*(x*e + d)^3*a^2*b^3*e^2*sgn(b*x + a) + 378*(x*e + d)^2*a^2*b^3*d*e^2*sgn(b*x + a) - 270*(x*e + d)*a^2*b^3*d^2*e^2*sgn(b*x + a) + 70*a^2*b^3*d^3*e^2*sgn(b*x + a) - 126*(x*e + d)^2*a^3*b^2*e^3*sgn(b*x + a) + 180*(x*e + d)*a^3*b^2*d*e^3*sgn(b*x + a) - 70*a^3*b^2*d^2*e^3*sgn(b*x + a) - 45*(x*e + d)*a^4*b*e^4*sgn(b*x + a) + 35*a^4*b*d*e^4*sgn(b*x + a) - 7*a^5*e^5*sgn(b*x + a))*e^(-6)/(x*e + d)^(9/2)","A",0
1701,1,447,0,0.291118," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^(13/2),x, algorithm=""giac"")","-\frac{2 \, {\left(693 \, {\left(x e + d\right)}^{5} b^{5} \mathrm{sgn}\left(b x + a\right) - 1155 \, {\left(x e + d\right)}^{4} b^{5} d \mathrm{sgn}\left(b x + a\right) + 1386 \, {\left(x e + d\right)}^{3} b^{5} d^{2} \mathrm{sgn}\left(b x + a\right) - 990 \, {\left(x e + d\right)}^{2} b^{5} d^{3} \mathrm{sgn}\left(b x + a\right) + 385 \, {\left(x e + d\right)} b^{5} d^{4} \mathrm{sgn}\left(b x + a\right) - 63 \, b^{5} d^{5} \mathrm{sgn}\left(b x + a\right) + 1155 \, {\left(x e + d\right)}^{4} a b^{4} e \mathrm{sgn}\left(b x + a\right) - 2772 \, {\left(x e + d\right)}^{3} a b^{4} d e \mathrm{sgn}\left(b x + a\right) + 2970 \, {\left(x e + d\right)}^{2} a b^{4} d^{2} e \mathrm{sgn}\left(b x + a\right) - 1540 \, {\left(x e + d\right)} a b^{4} d^{3} e \mathrm{sgn}\left(b x + a\right) + 315 \, a b^{4} d^{4} e \mathrm{sgn}\left(b x + a\right) + 1386 \, {\left(x e + d\right)}^{3} a^{2} b^{3} e^{2} \mathrm{sgn}\left(b x + a\right) - 2970 \, {\left(x e + d\right)}^{2} a^{2} b^{3} d e^{2} \mathrm{sgn}\left(b x + a\right) + 2310 \, {\left(x e + d\right)} a^{2} b^{3} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) - 630 \, a^{2} b^{3} d^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + 990 \, {\left(x e + d\right)}^{2} a^{3} b^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - 1540 \, {\left(x e + d\right)} a^{3} b^{2} d e^{3} \mathrm{sgn}\left(b x + a\right) + 630 \, a^{3} b^{2} d^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 385 \, {\left(x e + d\right)} a^{4} b e^{4} \mathrm{sgn}\left(b x + a\right) - 315 \, a^{4} b d e^{4} \mathrm{sgn}\left(b x + a\right) + 63 \, a^{5} e^{5} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-6\right)}}{693 \, {\left(x e + d\right)}^{\frac{11}{2}}}"," ",0,"-2/693*(693*(x*e + d)^5*b^5*sgn(b*x + a) - 1155*(x*e + d)^4*b^5*d*sgn(b*x + a) + 1386*(x*e + d)^3*b^5*d^2*sgn(b*x + a) - 990*(x*e + d)^2*b^5*d^3*sgn(b*x + a) + 385*(x*e + d)*b^5*d^4*sgn(b*x + a) - 63*b^5*d^5*sgn(b*x + a) + 1155*(x*e + d)^4*a*b^4*e*sgn(b*x + a) - 2772*(x*e + d)^3*a*b^4*d*e*sgn(b*x + a) + 2970*(x*e + d)^2*a*b^4*d^2*e*sgn(b*x + a) - 1540*(x*e + d)*a*b^4*d^3*e*sgn(b*x + a) + 315*a*b^4*d^4*e*sgn(b*x + a) + 1386*(x*e + d)^3*a^2*b^3*e^2*sgn(b*x + a) - 2970*(x*e + d)^2*a^2*b^3*d*e^2*sgn(b*x + a) + 2310*(x*e + d)*a^2*b^3*d^2*e^2*sgn(b*x + a) - 630*a^2*b^3*d^3*e^2*sgn(b*x + a) + 990*(x*e + d)^2*a^3*b^2*e^3*sgn(b*x + a) - 1540*(x*e + d)*a^3*b^2*d*e^3*sgn(b*x + a) + 630*a^3*b^2*d^2*e^3*sgn(b*x + a) + 385*(x*e + d)*a^4*b*e^4*sgn(b*x + a) - 315*a^4*b*d*e^4*sgn(b*x + a) + 63*a^5*e^5*sgn(b*x + a))*e^(-6)/(x*e + d)^(11/2)","A",0
1702,1,447,0,0.351621," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^(15/2),x, algorithm=""giac"")","-\frac{2 \, {\left(3003 \, {\left(x e + d\right)}^{5} b^{5} \mathrm{sgn}\left(b x + a\right) - 9009 \, {\left(x e + d\right)}^{4} b^{5} d \mathrm{sgn}\left(b x + a\right) + 12870 \, {\left(x e + d\right)}^{3} b^{5} d^{2} \mathrm{sgn}\left(b x + a\right) - 10010 \, {\left(x e + d\right)}^{2} b^{5} d^{3} \mathrm{sgn}\left(b x + a\right) + 4095 \, {\left(x e + d\right)} b^{5} d^{4} \mathrm{sgn}\left(b x + a\right) - 693 \, b^{5} d^{5} \mathrm{sgn}\left(b x + a\right) + 9009 \, {\left(x e + d\right)}^{4} a b^{4} e \mathrm{sgn}\left(b x + a\right) - 25740 \, {\left(x e + d\right)}^{3} a b^{4} d e \mathrm{sgn}\left(b x + a\right) + 30030 \, {\left(x e + d\right)}^{2} a b^{4} d^{2} e \mathrm{sgn}\left(b x + a\right) - 16380 \, {\left(x e + d\right)} a b^{4} d^{3} e \mathrm{sgn}\left(b x + a\right) + 3465 \, a b^{4} d^{4} e \mathrm{sgn}\left(b x + a\right) + 12870 \, {\left(x e + d\right)}^{3} a^{2} b^{3} e^{2} \mathrm{sgn}\left(b x + a\right) - 30030 \, {\left(x e + d\right)}^{2} a^{2} b^{3} d e^{2} \mathrm{sgn}\left(b x + a\right) + 24570 \, {\left(x e + d\right)} a^{2} b^{3} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) - 6930 \, a^{2} b^{3} d^{3} e^{2} \mathrm{sgn}\left(b x + a\right) + 10010 \, {\left(x e + d\right)}^{2} a^{3} b^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - 16380 \, {\left(x e + d\right)} a^{3} b^{2} d e^{3} \mathrm{sgn}\left(b x + a\right) + 6930 \, a^{3} b^{2} d^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 4095 \, {\left(x e + d\right)} a^{4} b e^{4} \mathrm{sgn}\left(b x + a\right) - 3465 \, a^{4} b d e^{4} \mathrm{sgn}\left(b x + a\right) + 693 \, a^{5} e^{5} \mathrm{sgn}\left(b x + a\right)\right)} e^{\left(-6\right)}}{9009 \, {\left(x e + d\right)}^{\frac{13}{2}}}"," ",0,"-2/9009*(3003*(x*e + d)^5*b^5*sgn(b*x + a) - 9009*(x*e + d)^4*b^5*d*sgn(b*x + a) + 12870*(x*e + d)^3*b^5*d^2*sgn(b*x + a) - 10010*(x*e + d)^2*b^5*d^3*sgn(b*x + a) + 4095*(x*e + d)*b^5*d^4*sgn(b*x + a) - 693*b^5*d^5*sgn(b*x + a) + 9009*(x*e + d)^4*a*b^4*e*sgn(b*x + a) - 25740*(x*e + d)^3*a*b^4*d*e*sgn(b*x + a) + 30030*(x*e + d)^2*a*b^4*d^2*e*sgn(b*x + a) - 16380*(x*e + d)*a*b^4*d^3*e*sgn(b*x + a) + 3465*a*b^4*d^4*e*sgn(b*x + a) + 12870*(x*e + d)^3*a^2*b^3*e^2*sgn(b*x + a) - 30030*(x*e + d)^2*a^2*b^3*d*e^2*sgn(b*x + a) + 24570*(x*e + d)*a^2*b^3*d^2*e^2*sgn(b*x + a) - 6930*a^2*b^3*d^3*e^2*sgn(b*x + a) + 10010*(x*e + d)^2*a^3*b^2*e^3*sgn(b*x + a) - 16380*(x*e + d)*a^3*b^2*d*e^3*sgn(b*x + a) + 6930*a^3*b^2*d^2*e^3*sgn(b*x + a) + 4095*(x*e + d)*a^4*b*e^4*sgn(b*x + a) - 3465*a^4*b*d*e^4*sgn(b*x + a) + 693*a^5*e^5*sgn(b*x + a))*e^(-6)/(x*e + d)^(13/2)","A",0
1703,1,354,0,0.273834," ","integrate((e*x+d)^(7/2)/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(b^{4} d^{4} \mathrm{sgn}\left(b x + a\right) - 4 \, a b^{3} d^{3} e \mathrm{sgn}\left(b x + a\right) + 6 \, a^{2} b^{2} d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) - 4 \, a^{3} b d e^{3} \mathrm{sgn}\left(b x + a\right) + a^{4} e^{4} \mathrm{sgn}\left(b x + a\right)\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{\sqrt{-b^{2} d + a b e} b^{4}} + \frac{2 \, {\left(15 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{6} \mathrm{sgn}\left(b x + a\right) + 21 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{6} d \mathrm{sgn}\left(b x + a\right) + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{6} d^{2} \mathrm{sgn}\left(b x + a\right) + 105 \, \sqrt{x e + d} b^{6} d^{3} \mathrm{sgn}\left(b x + a\right) - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} a b^{5} e \mathrm{sgn}\left(b x + a\right) - 70 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{5} d e \mathrm{sgn}\left(b x + a\right) - 315 \, \sqrt{x e + d} a b^{5} d^{2} e \mathrm{sgn}\left(b x + a\right) + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} b^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 315 \, \sqrt{x e + d} a^{2} b^{4} d e^{2} \mathrm{sgn}\left(b x + a\right) - 105 \, \sqrt{x e + d} a^{3} b^{3} e^{3} \mathrm{sgn}\left(b x + a\right)\right)}}{105 \, b^{7}}"," ",0,"2*(b^4*d^4*sgn(b*x + a) - 4*a*b^3*d^3*e*sgn(b*x + a) + 6*a^2*b^2*d^2*e^2*sgn(b*x + a) - 4*a^3*b*d*e^3*sgn(b*x + a) + a^4*e^4*sgn(b*x + a))*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/(sqrt(-b^2*d + a*b*e)*b^4) + 2/105*(15*(x*e + d)^(7/2)*b^6*sgn(b*x + a) + 21*(x*e + d)^(5/2)*b^6*d*sgn(b*x + a) + 35*(x*e + d)^(3/2)*b^6*d^2*sgn(b*x + a) + 105*sqrt(x*e + d)*b^6*d^3*sgn(b*x + a) - 21*(x*e + d)^(5/2)*a*b^5*e*sgn(b*x + a) - 70*(x*e + d)^(3/2)*a*b^5*d*e*sgn(b*x + a) - 315*sqrt(x*e + d)*a*b^5*d^2*e*sgn(b*x + a) + 35*(x*e + d)^(3/2)*a^2*b^4*e^2*sgn(b*x + a) + 315*sqrt(x*e + d)*a^2*b^4*d*e^2*sgn(b*x + a) - 105*sqrt(x*e + d)*a^3*b^3*e^3*sgn(b*x + a))/b^7","A",0
1704,1,240,0,0.191748," ","integrate((e*x+d)^(5/2)/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(b^{3} d^{3} \mathrm{sgn}\left(b x + a\right) - 3 \, a b^{2} d^{2} e \mathrm{sgn}\left(b x + a\right) + 3 \, a^{2} b d e^{2} \mathrm{sgn}\left(b x + a\right) - a^{3} e^{3} \mathrm{sgn}\left(b x + a\right)\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{\sqrt{-b^{2} d + a b e} b^{3}} + \frac{2 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{4} \mathrm{sgn}\left(b x + a\right) + 5 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{4} d \mathrm{sgn}\left(b x + a\right) + 15 \, \sqrt{x e + d} b^{4} d^{2} \mathrm{sgn}\left(b x + a\right) - 5 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{3} e \mathrm{sgn}\left(b x + a\right) - 30 \, \sqrt{x e + d} a b^{3} d e \mathrm{sgn}\left(b x + a\right) + 15 \, \sqrt{x e + d} a^{2} b^{2} e^{2} \mathrm{sgn}\left(b x + a\right)\right)}}{15 \, b^{5}}"," ",0,"2*(b^3*d^3*sgn(b*x + a) - 3*a*b^2*d^2*e*sgn(b*x + a) + 3*a^2*b*d*e^2*sgn(b*x + a) - a^3*e^3*sgn(b*x + a))*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/(sqrt(-b^2*d + a*b*e)*b^3) + 2/15*(3*(x*e + d)^(5/2)*b^4*sgn(b*x + a) + 5*(x*e + d)^(3/2)*b^4*d*sgn(b*x + a) + 15*sqrt(x*e + d)*b^4*d^2*sgn(b*x + a) - 5*(x*e + d)^(3/2)*a*b^3*e*sgn(b*x + a) - 30*sqrt(x*e + d)*a*b^3*d*e*sgn(b*x + a) + 15*sqrt(x*e + d)*a^2*b^2*e^2*sgn(b*x + a))/b^5","A",0
1705,1,148,0,0.185418," ","integrate((e*x+d)^(3/2)/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(b^{2} d^{2} \mathrm{sgn}\left(b x + a\right) - 2 \, a b d e \mathrm{sgn}\left(b x + a\right) + a^{2} e^{2} \mathrm{sgn}\left(b x + a\right)\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{\sqrt{-b^{2} d + a b e} b^{2}} + \frac{2 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} b^{2} \mathrm{sgn}\left(b x + a\right) + 3 \, \sqrt{x e + d} b^{2} d \mathrm{sgn}\left(b x + a\right) - 3 \, \sqrt{x e + d} a b e \mathrm{sgn}\left(b x + a\right)\right)}}{3 \, b^{3}}"," ",0,"2*(b^2*d^2*sgn(b*x + a) - 2*a*b*d*e*sgn(b*x + a) + a^2*e^2*sgn(b*x + a))*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/(sqrt(-b^2*d + a*b*e)*b^2) + 2/3*((x*e + d)^(3/2)*b^2*sgn(b*x + a) + 3*sqrt(x*e + d)*b^2*d*sgn(b*x + a) - 3*sqrt(x*e + d)*a*b*e*sgn(b*x + a))/b^3","A",0
1706,1,85,0,0.233212," ","integrate((e*x+d)^(1/2)/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(b d \mathrm{sgn}\left(b x + a\right) - a e \mathrm{sgn}\left(b x + a\right)\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{\sqrt{-b^{2} d + a b e} b} + \frac{2 \, \sqrt{x e + d} \mathrm{sgn}\left(b x + a\right)}{b}"," ",0,"2*(b*d*sgn(b*x + a) - a*e*sgn(b*x + a))*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/(sqrt(-b^2*d + a*b*e)*b) + 2*sqrt(x*e + d)*sgn(b*x + a)/b","A",0
1707,1,47,0,0.195424," ","integrate(1/(e*x+d)^(1/2)/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{2 \, \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) \mathrm{sgn}\left(b x + a\right)}{\sqrt{-b^{2} d + a b e}}"," ",0,"2*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*sgn(b*x + a)/sqrt(-b^2*d + a*b*e)","A",0
1708,1,81,0,0.235112," ","integrate(1/(e*x+d)^(3/2)/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","2 \, {\left(\frac{b \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{\sqrt{-b^{2} d + a b e} {\left(b d - a e\right)}} + \frac{1}{{\left(b d - a e\right)} \sqrt{x e + d}}\right)} \mathrm{sgn}\left(b x + a\right)"," ",0,"2*(b*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/(sqrt(-b^2*d + a*b*e)*(b*d - a*e)) + 1/((b*d - a*e)*sqrt(x*e + d)))*sgn(b*x + a)","A",0
1709,1,126,0,0.181885," ","integrate(1/(e*x+d)^(5/2)/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{2}{3} \, {\left(\frac{3 \, b^{2} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{{\left(b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}\right)} \sqrt{-b^{2} d + a b e}} + \frac{3 \, {\left(x e + d\right)} b + b d - a e}{{\left(b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}\right)} {\left(x e + d\right)}^{\frac{3}{2}}}\right)} \mathrm{sgn}\left(b x + a\right)"," ",0,"2/3*(3*b^2*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/((b^2*d^2 - 2*a*b*d*e + a^2*e^2)*sqrt(-b^2*d + a*b*e)) + (3*(x*e + d)*b + b*d - a*e)/((b^2*d^2 - 2*a*b*d*e + a^2*e^2)*(x*e + d)^(3/2)))*sgn(b*x + a)","A",0
1710,1,196,0,0.189747," ","integrate(1/(e*x+d)^(7/2)/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","\frac{2}{15} \, {\left(\frac{15 \, b^{3} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{{\left(b^{3} d^{3} - 3 \, a b^{2} d^{2} e + 3 \, a^{2} b d e^{2} - a^{3} e^{3}\right)} \sqrt{-b^{2} d + a b e}} + \frac{15 \, {\left(x e + d\right)}^{2} b^{2} + 5 \, {\left(x e + d\right)} b^{2} d + 3 \, b^{2} d^{2} - 5 \, {\left(x e + d\right)} a b e - 6 \, a b d e + 3 \, a^{2} e^{2}}{{\left(b^{3} d^{3} - 3 \, a b^{2} d^{2} e + 3 \, a^{2} b d e^{2} - a^{3} e^{3}\right)} {\left(x e + d\right)}^{\frac{5}{2}}}\right)} \mathrm{sgn}\left(b x + a\right)"," ",0,"2/15*(15*b^3*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/((b^3*d^3 - 3*a*b^2*d^2*e + 3*a^2*b*d*e^2 - a^3*e^3)*sqrt(-b^2*d + a*b*e)) + (15*(x*e + d)^2*b^2 + 5*(x*e + d)*b^2*d + 3*b^2*d^2 - 5*(x*e + d)*a*b*e - 6*a*b*d*e + 3*a^2*e^2)/((b^3*d^3 - 3*a*b^2*d^2*e + 3*a^2*b*d*e^2 - a^3*e^3)*(x*e + d)^(5/2)))*sgn(b*x + a)","A",0
1711,1,446,0,0.331011," ","integrate((e*x+d)^(9/2)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{63 \, {\left(b^{3} d^{3} e^{2} - 3 \, a b^{2} d^{2} e^{3} + 3 \, a^{2} b d e^{4} - a^{3} e^{5}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{4 \, \sqrt{-b^{2} d + a b e} b^{5} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)} - \frac{17 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{4} d^{3} e^{2} - 15 \, \sqrt{x e + d} b^{4} d^{4} e^{2} - 51 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{3} d^{2} e^{3} + 60 \, \sqrt{x e + d} a b^{3} d^{3} e^{3} + 51 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} b^{2} d e^{4} - 90 \, \sqrt{x e + d} a^{2} b^{2} d^{2} e^{4} - 17 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{3} b e^{5} + 60 \, \sqrt{x e + d} a^{3} b d e^{5} - 15 \, \sqrt{x e + d} a^{4} e^{6}}{4 \, {\left({\left(x e + d\right)} b - b d + a e\right)}^{2} b^{5} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)} + \frac{2 \, {\left({\left(x e + d\right)}^{\frac{5}{2}} b^{12} e^{2} + 5 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{12} d e^{2} + 30 \, \sqrt{x e + d} b^{12} d^{2} e^{2} - 5 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{11} e^{3} - 60 \, \sqrt{x e + d} a b^{11} d e^{3} + 30 \, \sqrt{x e + d} a^{2} b^{10} e^{4}\right)}}{5 \, b^{15} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)}"," ",0,"63/4*(b^3*d^3*e^2 - 3*a*b^2*d^2*e^3 + 3*a^2*b*d*e^4 - a^3*e^5)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/(sqrt(-b^2*d + a*b*e)*b^5*sgn((x*e + d)*b*e - b*d*e + a*e^2)) - 1/4*(17*(x*e + d)^(3/2)*b^4*d^3*e^2 - 15*sqrt(x*e + d)*b^4*d^4*e^2 - 51*(x*e + d)^(3/2)*a*b^3*d^2*e^3 + 60*sqrt(x*e + d)*a*b^3*d^3*e^3 + 51*(x*e + d)^(3/2)*a^2*b^2*d*e^4 - 90*sqrt(x*e + d)*a^2*b^2*d^2*e^4 - 17*(x*e + d)^(3/2)*a^3*b*e^5 + 60*sqrt(x*e + d)*a^3*b*d*e^5 - 15*sqrt(x*e + d)*a^4*e^6)/(((x*e + d)*b - b*d + a*e)^2*b^5*sgn((x*e + d)*b*e - b*d*e + a*e^2)) + 2/5*((x*e + d)^(5/2)*b^12*e^2 + 5*(x*e + d)^(3/2)*b^12*d*e^2 + 30*sqrt(x*e + d)*b^12*d^2*e^2 - 5*(x*e + d)^(3/2)*a*b^11*e^3 - 60*sqrt(x*e + d)*a*b^11*d*e^3 + 30*sqrt(x*e + d)*a^2*b^10*e^4)/(b^15*sgn((x*e + d)*b*e - b*d*e + a*e^2))","B",0
1712,1,337,0,0.302649," ","integrate((e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{35 \, {\left(b^{2} d^{2} e^{2} - 2 \, a b d e^{3} + a^{2} e^{4}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{4 \, \sqrt{-b^{2} d + a b e} b^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)} - \frac{13 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{3} d^{2} e^{2} - 11 \, \sqrt{x e + d} b^{3} d^{3} e^{2} - 26 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{2} d e^{3} + 33 \, \sqrt{x e + d} a b^{2} d^{2} e^{3} + 13 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} b e^{4} - 33 \, \sqrt{x e + d} a^{2} b d e^{4} + 11 \, \sqrt{x e + d} a^{3} e^{5}}{4 \, {\left({\left(x e + d\right)} b - b d + a e\right)}^{2} b^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)} + \frac{2 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} b^{6} e^{2} + 9 \, \sqrt{x e + d} b^{6} d e^{2} - 9 \, \sqrt{x e + d} a b^{5} e^{3}\right)}}{3 \, b^{9} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)}"," ",0,"35/4*(b^2*d^2*e^2 - 2*a*b*d*e^3 + a^2*e^4)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/(sqrt(-b^2*d + a*b*e)*b^4*sgn((x*e + d)*b*e - b*d*e + a*e^2)) - 1/4*(13*(x*e + d)^(3/2)*b^3*d^2*e^2 - 11*sqrt(x*e + d)*b^3*d^3*e^2 - 26*(x*e + d)^(3/2)*a*b^2*d*e^3 + 33*sqrt(x*e + d)*a*b^2*d^2*e^3 + 13*(x*e + d)^(3/2)*a^2*b*e^4 - 33*sqrt(x*e + d)*a^2*b*d*e^4 + 11*sqrt(x*e + d)*a^3*e^5)/(((x*e + d)*b - b*d + a*e)^2*b^4*sgn((x*e + d)*b*e - b*d*e + a*e^2)) + 2/3*((x*e + d)^(3/2)*b^6*e^2 + 9*sqrt(x*e + d)*b^6*d*e^2 - 9*sqrt(x*e + d)*a*b^5*e^3)/(b^9*sgn((x*e + d)*b*e - b*d*e + a*e^2))","A",0
1713,1,246,0,0.275326," ","integrate((e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{15 \, {\left(b d e^{2} - a e^{3}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{4 \, \sqrt{-b^{2} d + a b e} b^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)} + \frac{2 \, \sqrt{x e + d} e^{2}}{b^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)} - \frac{9 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{2} d e^{2} - 7 \, \sqrt{x e + d} b^{2} d^{2} e^{2} - 9 \, {\left(x e + d\right)}^{\frac{3}{2}} a b e^{3} + 14 \, \sqrt{x e + d} a b d e^{3} - 7 \, \sqrt{x e + d} a^{2} e^{4}}{4 \, {\left({\left(x e + d\right)} b - b d + a e\right)}^{2} b^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)}"," ",0,"15/4*(b*d*e^2 - a*e^3)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/(sqrt(-b^2*d + a*b*e)*b^3*sgn((x*e + d)*b*e - b*d*e + a*e^2)) + 2*sqrt(x*e + d)*e^2/(b^3*sgn((x*e + d)*b*e - b*d*e + a*e^2)) - 1/4*(9*(x*e + d)^(3/2)*b^2*d*e^2 - 7*sqrt(x*e + d)*b^2*d^2*e^2 - 9*(x*e + d)^(3/2)*a*b*e^3 + 14*sqrt(x*e + d)*a*b*d*e^3 - 7*sqrt(x*e + d)*a^2*e^4)/(((x*e + d)*b - b*d + a*e)^2*b^3*sgn((x*e + d)*b*e - b*d*e + a*e^2))","A",0
1714,1,160,0,0.284867," ","integrate((e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{3 \, \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e^{2}}{4 \, \sqrt{-b^{2} d + a b e} b^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)} - \frac{5 \, {\left(x e + d\right)}^{\frac{3}{2}} b e^{2} - 3 \, \sqrt{x e + d} b d e^{2} + 3 \, \sqrt{x e + d} a e^{3}}{4 \, {\left({\left(x e + d\right)} b - b d + a e\right)}^{2} b^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)}"," ",0,"3/4*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e^2/(sqrt(-b^2*d + a*b*e)*b^2*sgn((x*e + d)*b*e - b*d*e + a*e^2)) - 1/4*(5*(x*e + d)^(3/2)*b*e^2 - 3*sqrt(x*e + d)*b*d*e^2 + 3*sqrt(x*e + d)*a*e^3)/(((x*e + d)*b - b*d + a*e)^2*b^2*sgn((x*e + d)*b*e - b*d*e + a*e^2))","A",0
1715,1,220,0,0.244333," ","integrate((e*x+d)^(1/2)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","-\frac{\arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e^{2}}{4 \, {\left(b^{2} d \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - a b e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} \sqrt{-b^{2} d + a b e}} - \frac{{\left(x e + d\right)}^{\frac{3}{2}} b e^{2} + \sqrt{x e + d} b d e^{2} - \sqrt{x e + d} a e^{3}}{4 \, {\left(b^{2} d \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - a b e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{2}}"," ",0,"-1/4*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e^2/((b^2*d*sgn((x*e + d)*b*e - b*d*e + a*e^2) - a*b*e*sgn((x*e + d)*b*e - b*d*e + a*e^2))*sqrt(-b^2*d + a*b*e)) - 1/4*((x*e + d)^(3/2)*b*e^2 + sqrt(x*e + d)*b*d*e^2 - sqrt(x*e + d)*a*e^3)/((b^2*d*sgn((x*e + d)*b*e - b*d*e + a*e^2) - a*b*e*sgn((x*e + d)*b*e - b*d*e + a*e^2))*((x*e + d)*b - b*d + a*e)^2)","A",0
1716,1,284,0,0.258472," ","integrate(1/(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{3 \, \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e^{2}}{4 \, {\left(b^{2} d^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 2 \, a b d e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + a^{2} e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} \sqrt{-b^{2} d + a b e}} + \frac{3 \, {\left(x e + d\right)}^{\frac{3}{2}} b e^{2} - 5 \, \sqrt{x e + d} b d e^{2} + 5 \, \sqrt{x e + d} a e^{3}}{4 \, {\left(b^{2} d^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 2 \, a b d e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + a^{2} e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{2}}"," ",0,"3/4*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e^2/((b^2*d^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 2*a*b*d*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) + a^2*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2))*sqrt(-b^2*d + a*b*e)) + 1/4*(3*(x*e + d)^(3/2)*b*e^2 - 5*sqrt(x*e + d)*b*d*e^2 + 5*sqrt(x*e + d)*a*e^3)/((b^2*d^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 2*a*b*d*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) + a^2*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2))*((x*e + d)*b - b*d + a*e)^2)","B",0
1717,1,499,0,0.339537," ","integrate(1/(e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{15 \, b \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e^{2}}{4 \, {\left(b^{3} d^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 3 \, a b^{2} d^{2} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 3 \, a^{2} b d e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - a^{3} e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} \sqrt{-b^{2} d + a b e}} + \frac{2 \, e^{2}}{{\left(b^{3} d^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 3 \, a b^{2} d^{2} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 3 \, a^{2} b d e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - a^{3} e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} \sqrt{x e + d}} + \frac{7 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{2} e^{2} - 9 \, \sqrt{x e + d} b^{2} d e^{2} + 9 \, \sqrt{x e + d} a b e^{3}}{4 \, {\left(b^{3} d^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 3 \, a b^{2} d^{2} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 3 \, a^{2} b d e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - a^{3} e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{2}}"," ",0,"15/4*b*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e^2/((b^3*d^3*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 3*a*b^2*d^2*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 3*a^2*b*d*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) - a^3*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2))*sqrt(-b^2*d + a*b*e)) + 2*e^2/((b^3*d^3*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 3*a*b^2*d^2*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 3*a^2*b*d*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) - a^3*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2))*sqrt(x*e + d)) + 1/4*(7*(x*e + d)^(3/2)*b^2*e^2 - 9*sqrt(x*e + d)*b^2*d*e^2 + 9*sqrt(x*e + d)*a*b*e^3)/((b^3*d^3*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 3*a*b^2*d^2*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 3*a^2*b*d*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) - a^3*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2))*((x*e + d)*b - b*d + a*e)^2)","B",0
1718,1,625,0,0.403348," ","integrate(1/(e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{35 \, b^{2} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e^{2}}{4 \, {\left(b^{4} d^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 4 \, a b^{3} d^{3} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 6 \, a^{2} b^{2} d^{2} e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 4 \, a^{3} b d e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + a^{4} e^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} \sqrt{-b^{2} d + a b e}} + \frac{2 \, {\left(9 \, {\left(x e + d\right)} b e^{2} + b d e^{2} - a e^{3}\right)}}{3 \, {\left(b^{4} d^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 4 \, a b^{3} d^{3} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 6 \, a^{2} b^{2} d^{2} e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 4 \, a^{3} b d e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + a^{4} e^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} {\left(x e + d\right)}^{\frac{3}{2}}} + \frac{11 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{3} e^{2} - 13 \, \sqrt{x e + d} b^{3} d e^{2} + 13 \, \sqrt{x e + d} a b^{2} e^{3}}{4 \, {\left(b^{4} d^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 4 \, a b^{3} d^{3} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 6 \, a^{2} b^{2} d^{2} e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 4 \, a^{3} b d e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + a^{4} e^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{2}}"," ",0,"35/4*b^2*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e^2/((b^4*d^4*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 4*a*b^3*d^3*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 6*a^2*b^2*d^2*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 4*a^3*b*d*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2) + a^4*e^4*sgn((x*e + d)*b*e - b*d*e + a*e^2))*sqrt(-b^2*d + a*b*e)) + 2/3*(9*(x*e + d)*b*e^2 + b*d*e^2 - a*e^3)/((b^4*d^4*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 4*a*b^3*d^3*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 6*a^2*b^2*d^2*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 4*a^3*b*d*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2) + a^4*e^4*sgn((x*e + d)*b*e - b*d*e + a*e^2))*(x*e + d)^(3/2)) + 1/4*(11*(x*e + d)^(3/2)*b^3*e^2 - 13*sqrt(x*e + d)*b^3*d*e^2 + 13*sqrt(x*e + d)*a*b^2*e^3)/((b^4*d^4*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 4*a*b^3*d^3*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 6*a^2*b^2*d^2*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 4*a^3*b*d*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2) + a^4*e^4*sgn((x*e + d)*b*e - b*d*e + a*e^2))*((x*e + d)*b - b*d + a*e)^2)","B",0
1719,1,775,0,0.461876," ","integrate(1/(e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{63 \, b^{3} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e^{2}}{4 \, {\left(b^{5} d^{5} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 5 \, a b^{4} d^{4} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 10 \, a^{2} b^{3} d^{3} e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 10 \, a^{3} b^{2} d^{2} e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 5 \, a^{4} b d e^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - a^{5} e^{5} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} \sqrt{-b^{2} d + a b e}} + \frac{15 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{4} e^{2} - 17 \, \sqrt{x e + d} b^{4} d e^{2} + 17 \, \sqrt{x e + d} a b^{3} e^{3}}{4 \, {\left(b^{5} d^{5} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 5 \, a b^{4} d^{4} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 10 \, a^{2} b^{3} d^{3} e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 10 \, a^{3} b^{2} d^{2} e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 5 \, a^{4} b d e^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - a^{5} e^{5} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{2}} + \frac{2 \, {\left(30 \, {\left(x e + d\right)}^{2} b^{2} e^{2} + 5 \, {\left(x e + d\right)} b^{2} d e^{2} + b^{2} d^{2} e^{2} - 5 \, {\left(x e + d\right)} a b e^{3} - 2 \, a b d e^{3} + a^{2} e^{4}\right)}}{5 \, {\left(b^{5} d^{5} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 5 \, a b^{4} d^{4} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 10 \, a^{2} b^{3} d^{3} e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 10 \, a^{3} b^{2} d^{2} e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 5 \, a^{4} b d e^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - a^{5} e^{5} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} {\left(x e + d\right)}^{\frac{5}{2}}}"," ",0,"63/4*b^3*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e^2/((b^5*d^5*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 5*a*b^4*d^4*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 10*a^2*b^3*d^3*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 10*a^3*b^2*d^2*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 5*a^4*b*d*e^4*sgn((x*e + d)*b*e - b*d*e + a*e^2) - a^5*e^5*sgn((x*e + d)*b*e - b*d*e + a*e^2))*sqrt(-b^2*d + a*b*e)) + 1/4*(15*(x*e + d)^(3/2)*b^4*e^2 - 17*sqrt(x*e + d)*b^4*d*e^2 + 17*sqrt(x*e + d)*a*b^3*e^3)/((b^5*d^5*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 5*a*b^4*d^4*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 10*a^2*b^3*d^3*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 10*a^3*b^2*d^2*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 5*a^4*b*d*e^4*sgn((x*e + d)*b*e - b*d*e + a*e^2) - a^5*e^5*sgn((x*e + d)*b*e - b*d*e + a*e^2))*((x*e + d)*b - b*d + a*e)^2) + 2/5*(30*(x*e + d)^2*b^2*e^2 + 5*(x*e + d)*b^2*d*e^2 + b^2*d^2*e^2 - 5*(x*e + d)*a*b*e^3 - 2*a*b*d*e^3 + a^2*e^4)/((b^5*d^5*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 5*a*b^4*d^4*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 10*a^2*b^3*d^3*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 10*a^3*b^2*d^2*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 5*a^4*b*d*e^4*sgn((x*e + d)*b*e - b*d*e + a*e^2) - a^5*e^5*sgn((x*e + d)*b*e - b*d*e + a*e^2))*(x*e + d)^(5/2))","B",0
1720,1,700,0,0.448806," ","integrate((e*x+d)^(13/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{3003 \, {\left(b^{3} d^{3} e^{4} - 3 \, a b^{2} d^{2} e^{5} + 3 \, a^{2} b d e^{6} - a^{3} e^{7}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{64 \, \sqrt{-b^{2} d + a b e} b^{7} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)} - \frac{4431 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{6} d^{3} e^{4} - 11767 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{6} d^{4} e^{4} + 10633 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{6} d^{5} e^{4} - 3249 \, \sqrt{x e + d} b^{6} d^{6} e^{4} - 13293 \, {\left(x e + d\right)}^{\frac{7}{2}} a b^{5} d^{2} e^{5} + 47068 \, {\left(x e + d\right)}^{\frac{5}{2}} a b^{5} d^{3} e^{5} - 53165 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{5} d^{4} e^{5} + 19494 \, \sqrt{x e + d} a b^{5} d^{5} e^{5} + 13293 \, {\left(x e + d\right)}^{\frac{7}{2}} a^{2} b^{4} d e^{6} - 70602 \, {\left(x e + d\right)}^{\frac{5}{2}} a^{2} b^{4} d^{2} e^{6} + 106330 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} b^{4} d^{3} e^{6} - 48735 \, \sqrt{x e + d} a^{2} b^{4} d^{4} e^{6} - 4431 \, {\left(x e + d\right)}^{\frac{7}{2}} a^{3} b^{3} e^{7} + 47068 \, {\left(x e + d\right)}^{\frac{5}{2}} a^{3} b^{3} d e^{7} - 106330 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{3} b^{3} d^{2} e^{7} + 64980 \, \sqrt{x e + d} a^{3} b^{3} d^{3} e^{7} - 11767 \, {\left(x e + d\right)}^{\frac{5}{2}} a^{4} b^{2} e^{8} + 53165 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{4} b^{2} d e^{8} - 48735 \, \sqrt{x e + d} a^{4} b^{2} d^{2} e^{8} - 10633 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{5} b e^{9} + 19494 \, \sqrt{x e + d} a^{5} b d e^{9} - 3249 \, \sqrt{x e + d} a^{6} e^{10}}{192 \, {\left({\left(x e + d\right)} b - b d + a e\right)}^{4} b^{7} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)} + \frac{2 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{20} e^{4} + 25 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{20} d e^{4} + 225 \, \sqrt{x e + d} b^{20} d^{2} e^{4} - 25 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{19} e^{5} - 450 \, \sqrt{x e + d} a b^{19} d e^{5} + 225 \, \sqrt{x e + d} a^{2} b^{18} e^{6}\right)}}{15 \, b^{25} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)}"," ",0,"3003/64*(b^3*d^3*e^4 - 3*a*b^2*d^2*e^5 + 3*a^2*b*d*e^6 - a^3*e^7)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/(sqrt(-b^2*d + a*b*e)*b^7*sgn((x*e + d)*b*e - b*d*e + a*e^2)) - 1/192*(4431*(x*e + d)^(7/2)*b^6*d^3*e^4 - 11767*(x*e + d)^(5/2)*b^6*d^4*e^4 + 10633*(x*e + d)^(3/2)*b^6*d^5*e^4 - 3249*sqrt(x*e + d)*b^6*d^6*e^4 - 13293*(x*e + d)^(7/2)*a*b^5*d^2*e^5 + 47068*(x*e + d)^(5/2)*a*b^5*d^3*e^5 - 53165*(x*e + d)^(3/2)*a*b^5*d^4*e^5 + 19494*sqrt(x*e + d)*a*b^5*d^5*e^5 + 13293*(x*e + d)^(7/2)*a^2*b^4*d*e^6 - 70602*(x*e + d)^(5/2)*a^2*b^4*d^2*e^6 + 106330*(x*e + d)^(3/2)*a^2*b^4*d^3*e^6 - 48735*sqrt(x*e + d)*a^2*b^4*d^4*e^6 - 4431*(x*e + d)^(7/2)*a^3*b^3*e^7 + 47068*(x*e + d)^(5/2)*a^3*b^3*d*e^7 - 106330*(x*e + d)^(3/2)*a^3*b^3*d^2*e^7 + 64980*sqrt(x*e + d)*a^3*b^3*d^3*e^7 - 11767*(x*e + d)^(5/2)*a^4*b^2*e^8 + 53165*(x*e + d)^(3/2)*a^4*b^2*d*e^8 - 48735*sqrt(x*e + d)*a^4*b^2*d^2*e^8 - 10633*(x*e + d)^(3/2)*a^5*b*e^9 + 19494*sqrt(x*e + d)*a^5*b*d*e^9 - 3249*sqrt(x*e + d)*a^6*e^10)/(((x*e + d)*b - b*d + a*e)^4*b^7*sgn((x*e + d)*b*e - b*d*e + a*e^2)) + 2/15*(3*(x*e + d)^(5/2)*b^20*e^4 + 25*(x*e + d)^(3/2)*b^20*d*e^4 + 225*sqrt(x*e + d)*b^20*d^2*e^4 - 25*(x*e + d)^(3/2)*a*b^19*e^5 - 450*sqrt(x*e + d)*a*b^19*d*e^5 + 225*sqrt(x*e + d)*a^2*b^18*e^6)/(b^25*sgn((x*e + d)*b*e - b*d*e + a*e^2))","B",0
1721,1,548,0,0.431138," ","integrate((e*x+d)^(11/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{1155 \, {\left(b^{2} d^{2} e^{4} - 2 \, a b d e^{5} + a^{2} e^{6}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{64 \, \sqrt{-b^{2} d + a b e} b^{6} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)} - \frac{2295 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{5} d^{2} e^{4} - 5855 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{5} d^{3} e^{4} + 5153 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{5} d^{4} e^{4} - 1545 \, \sqrt{x e + d} b^{5} d^{5} e^{4} - 4590 \, {\left(x e + d\right)}^{\frac{7}{2}} a b^{4} d e^{5} + 17565 \, {\left(x e + d\right)}^{\frac{5}{2}} a b^{4} d^{2} e^{5} - 20612 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{4} d^{3} e^{5} + 7725 \, \sqrt{x e + d} a b^{4} d^{4} e^{5} + 2295 \, {\left(x e + d\right)}^{\frac{7}{2}} a^{2} b^{3} e^{6} - 17565 \, {\left(x e + d\right)}^{\frac{5}{2}} a^{2} b^{3} d e^{6} + 30918 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} b^{3} d^{2} e^{6} - 15450 \, \sqrt{x e + d} a^{2} b^{3} d^{3} e^{6} + 5855 \, {\left(x e + d\right)}^{\frac{5}{2}} a^{3} b^{2} e^{7} - 20612 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{3} b^{2} d e^{7} + 15450 \, \sqrt{x e + d} a^{3} b^{2} d^{2} e^{7} + 5153 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{4} b e^{8} - 7725 \, \sqrt{x e + d} a^{4} b d e^{8} + 1545 \, \sqrt{x e + d} a^{5} e^{9}}{192 \, {\left({\left(x e + d\right)} b - b d + a e\right)}^{4} b^{6} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)} + \frac{2 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} b^{10} e^{4} + 15 \, \sqrt{x e + d} b^{10} d e^{4} - 15 \, \sqrt{x e + d} a b^{9} e^{5}\right)}}{3 \, b^{15} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)}"," ",0,"1155/64*(b^2*d^2*e^4 - 2*a*b*d*e^5 + a^2*e^6)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/(sqrt(-b^2*d + a*b*e)*b^6*sgn((x*e + d)*b*e - b*d*e + a*e^2)) - 1/192*(2295*(x*e + d)^(7/2)*b^5*d^2*e^4 - 5855*(x*e + d)^(5/2)*b^5*d^3*e^4 + 5153*(x*e + d)^(3/2)*b^5*d^4*e^4 - 1545*sqrt(x*e + d)*b^5*d^5*e^4 - 4590*(x*e + d)^(7/2)*a*b^4*d*e^5 + 17565*(x*e + d)^(5/2)*a*b^4*d^2*e^5 - 20612*(x*e + d)^(3/2)*a*b^4*d^3*e^5 + 7725*sqrt(x*e + d)*a*b^4*d^4*e^5 + 2295*(x*e + d)^(7/2)*a^2*b^3*e^6 - 17565*(x*e + d)^(5/2)*a^2*b^3*d*e^6 + 30918*(x*e + d)^(3/2)*a^2*b^3*d^2*e^6 - 15450*sqrt(x*e + d)*a^2*b^3*d^3*e^6 + 5855*(x*e + d)^(5/2)*a^3*b^2*e^7 - 20612*(x*e + d)^(3/2)*a^3*b^2*d*e^7 + 15450*sqrt(x*e + d)*a^3*b^2*d^2*e^7 + 5153*(x*e + d)^(3/2)*a^4*b*e^8 - 7725*sqrt(x*e + d)*a^4*b*d*e^8 + 1545*sqrt(x*e + d)*a^5*e^9)/(((x*e + d)*b - b*d + a*e)^4*b^6*sgn((x*e + d)*b*e - b*d*e + a*e^2)) + 2/3*((x*e + d)^(3/2)*b^10*e^4 + 15*sqrt(x*e + d)*b^10*d*e^4 - 15*sqrt(x*e + d)*a*b^9*e^5)/(b^15*sgn((x*e + d)*b*e - b*d*e + a*e^2))","B",0
1722,1,415,0,0.369485," ","integrate((e*x+d)^(9/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{315 \, {\left(b d e^{4} - a e^{5}\right)} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right)}{64 \, \sqrt{-b^{2} d + a b e} b^{5} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)} + \frac{2 \, \sqrt{x e + d} e^{4}}{b^{5} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)} - \frac{325 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{4} d e^{4} - 765 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{4} d^{2} e^{4} + 643 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{4} d^{3} e^{4} - 187 \, \sqrt{x e + d} b^{4} d^{4} e^{4} - 325 \, {\left(x e + d\right)}^{\frac{7}{2}} a b^{3} e^{5} + 1530 \, {\left(x e + d\right)}^{\frac{5}{2}} a b^{3} d e^{5} - 1929 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{3} d^{2} e^{5} + 748 \, \sqrt{x e + d} a b^{3} d^{3} e^{5} - 765 \, {\left(x e + d\right)}^{\frac{5}{2}} a^{2} b^{2} e^{6} + 1929 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} b^{2} d e^{6} - 1122 \, \sqrt{x e + d} a^{2} b^{2} d^{2} e^{6} - 643 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{3} b e^{7} + 748 \, \sqrt{x e + d} a^{3} b d e^{7} - 187 \, \sqrt{x e + d} a^{4} e^{8}}{64 \, {\left({\left(x e + d\right)} b - b d + a e\right)}^{4} b^{5} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)}"," ",0,"315/64*(b*d*e^4 - a*e^5)*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))/(sqrt(-b^2*d + a*b*e)*b^5*sgn((x*e + d)*b*e - b*d*e + a*e^2)) + 2*sqrt(x*e + d)*e^4/(b^5*sgn((x*e + d)*b*e - b*d*e + a*e^2)) - 1/64*(325*(x*e + d)^(7/2)*b^4*d*e^4 - 765*(x*e + d)^(5/2)*b^4*d^2*e^4 + 643*(x*e + d)^(3/2)*b^4*d^3*e^4 - 187*sqrt(x*e + d)*b^4*d^4*e^4 - 325*(x*e + d)^(7/2)*a*b^3*e^5 + 1530*(x*e + d)^(5/2)*a*b^3*d*e^5 - 1929*(x*e + d)^(3/2)*a*b^3*d^2*e^5 + 748*sqrt(x*e + d)*a*b^3*d^3*e^5 - 765*(x*e + d)^(5/2)*a^2*b^2*e^6 + 1929*(x*e + d)^(3/2)*a^2*b^2*d*e^6 - 1122*sqrt(x*e + d)*a^2*b^2*d^2*e^6 - 643*(x*e + d)^(3/2)*a^3*b*e^7 + 748*sqrt(x*e + d)*a^3*b*d*e^7 - 187*sqrt(x*e + d)*a^4*e^8)/(((x*e + d)*b - b*d + a*e)^4*b^5*sgn((x*e + d)*b*e - b*d*e + a*e^2))","B",0
1723,1,287,0,0.384615," ","integrate((e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{35 \, \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e^{4}}{64 \, \sqrt{-b^{2} d + a b e} b^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)} - \frac{279 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{3} e^{4} - 511 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{3} d e^{4} + 385 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{3} d^{2} e^{4} - 105 \, \sqrt{x e + d} b^{3} d^{3} e^{4} + 511 \, {\left(x e + d\right)}^{\frac{5}{2}} a b^{2} e^{5} - 770 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{2} d e^{5} + 315 \, \sqrt{x e + d} a b^{2} d^{2} e^{5} + 385 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} b e^{6} - 315 \, \sqrt{x e + d} a^{2} b d e^{6} + 105 \, \sqrt{x e + d} a^{3} e^{7}}{192 \, {\left({\left(x e + d\right)} b - b d + a e\right)}^{4} b^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)}"," ",0,"35/64*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e^4/(sqrt(-b^2*d + a*b*e)*b^4*sgn((x*e + d)*b*e - b*d*e + a*e^2)) - 1/192*(279*(x*e + d)^(7/2)*b^3*e^4 - 511*(x*e + d)^(5/2)*b^3*d*e^4 + 385*(x*e + d)^(3/2)*b^3*d^2*e^4 - 105*sqrt(x*e + d)*b^3*d^3*e^4 + 511*(x*e + d)^(5/2)*a*b^2*e^5 - 770*(x*e + d)^(3/2)*a*b^2*d*e^5 + 315*sqrt(x*e + d)*a*b^2*d^2*e^5 + 385*(x*e + d)^(3/2)*a^2*b*e^6 - 315*sqrt(x*e + d)*a^2*b*d*e^6 + 105*sqrt(x*e + d)*a^3*e^7)/(((x*e + d)*b - b*d + a*e)^4*b^4*sgn((x*e + d)*b*e - b*d*e + a*e^2))","A",0
1724,1,353,0,0.387067," ","integrate((e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","-\frac{5 \, \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e^{4}}{64 \, {\left(b^{4} d \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - a b^{3} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} \sqrt{-b^{2} d + a b e}} - \frac{15 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{3} e^{4} + 73 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{3} d e^{4} - 55 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{3} d^{2} e^{4} + 15 \, \sqrt{x e + d} b^{3} d^{3} e^{4} - 73 \, {\left(x e + d\right)}^{\frac{5}{2}} a b^{2} e^{5} + 110 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{2} d e^{5} - 45 \, \sqrt{x e + d} a b^{2} d^{2} e^{5} - 55 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} b e^{6} + 45 \, \sqrt{x e + d} a^{2} b d e^{6} - 15 \, \sqrt{x e + d} a^{3} e^{7}}{192 \, {\left(b^{4} d \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - a b^{3} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{4}}"," ",0,"-5/64*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e^4/((b^4*d*sgn((x*e + d)*b*e - b*d*e + a*e^2) - a*b^3*e*sgn((x*e + d)*b*e - b*d*e + a*e^2))*sqrt(-b^2*d + a*b*e)) - 1/192*(15*(x*e + d)^(7/2)*b^3*e^4 + 73*(x*e + d)^(5/2)*b^3*d*e^4 - 55*(x*e + d)^(3/2)*b^3*d^2*e^4 + 15*sqrt(x*e + d)*b^3*d^3*e^4 - 73*(x*e + d)^(5/2)*a*b^2*e^5 + 110*(x*e + d)^(3/2)*a*b^2*d*e^5 - 45*sqrt(x*e + d)*a*b^2*d^2*e^5 - 55*(x*e + d)^(3/2)*a^2*b*e^6 + 45*sqrt(x*e + d)*a^2*b*d*e^6 - 15*sqrt(x*e + d)*a^3*e^7)/((b^4*d*sgn((x*e + d)*b*e - b*d*e + a*e^2) - a*b^3*e*sgn((x*e + d)*b*e - b*d*e + a*e^2))*((x*e + d)*b - b*d + a*e)^4)","A",0
1725,1,421,0,0.349130," ","integrate((e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{3 \, \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e^{4}}{64 \, {\left(b^{4} d^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 2 \, a b^{3} d e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + a^{2} b^{2} e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} \sqrt{-b^{2} d + a b e}} + \frac{3 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{3} e^{4} - 11 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{3} d e^{4} - 11 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{3} d^{2} e^{4} + 3 \, \sqrt{x e + d} b^{3} d^{3} e^{4} + 11 \, {\left(x e + d\right)}^{\frac{5}{2}} a b^{2} e^{5} + 22 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{2} d e^{5} - 9 \, \sqrt{x e + d} a b^{2} d^{2} e^{5} - 11 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} b e^{6} + 9 \, \sqrt{x e + d} a^{2} b d e^{6} - 3 \, \sqrt{x e + d} a^{3} e^{7}}{64 \, {\left(b^{4} d^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 2 \, a b^{3} d e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + a^{2} b^{2} e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{4}}"," ",0,"3/64*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e^4/((b^4*d^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 2*a*b^3*d*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) + a^2*b^2*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2))*sqrt(-b^2*d + a*b*e)) + 1/64*(3*(x*e + d)^(7/2)*b^3*e^4 - 11*(x*e + d)^(5/2)*b^3*d*e^4 - 11*(x*e + d)^(3/2)*b^3*d^2*e^4 + 3*sqrt(x*e + d)*b^3*d^3*e^4 + 11*(x*e + d)^(5/2)*a*b^2*e^5 + 22*(x*e + d)^(3/2)*a*b^2*d*e^5 - 9*sqrt(x*e + d)*a*b^2*d^2*e^5 - 11*(x*e + d)^(3/2)*a^2*b*e^6 + 9*sqrt(x*e + d)*a^2*b*d*e^6 - 3*sqrt(x*e + d)*a^3*e^7)/((b^4*d^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 2*a*b^3*d*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) + a^2*b^2*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2))*((x*e + d)*b - b*d + a*e)^4)","B",0
1726,1,489,0,0.317673," ","integrate((e*x+d)^(1/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","-\frac{5 \, \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e^{4}}{64 \, {\left(b^{4} d^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 3 \, a b^{3} d^{2} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 3 \, a^{2} b^{2} d e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - a^{3} b e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} \sqrt{-b^{2} d + a b e}} - \frac{15 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{3} e^{4} - 55 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{3} d e^{4} + 73 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{3} d^{2} e^{4} + 15 \, \sqrt{x e + d} b^{3} d^{3} e^{4} + 55 \, {\left(x e + d\right)}^{\frac{5}{2}} a b^{2} e^{5} - 146 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{2} d e^{5} - 45 \, \sqrt{x e + d} a b^{2} d^{2} e^{5} + 73 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} b e^{6} + 45 \, \sqrt{x e + d} a^{2} b d e^{6} - 15 \, \sqrt{x e + d} a^{3} e^{7}}{192 \, {\left(b^{4} d^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 3 \, a b^{3} d^{2} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 3 \, a^{2} b^{2} d e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - a^{3} b e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{4}}"," ",0,"-5/64*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e^4/((b^4*d^3*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 3*a*b^3*d^2*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 3*a^2*b^2*d*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) - a^3*b*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2))*sqrt(-b^2*d + a*b*e)) - 1/192*(15*(x*e + d)^(7/2)*b^3*e^4 - 55*(x*e + d)^(5/2)*b^3*d*e^4 + 73*(x*e + d)^(3/2)*b^3*d^2*e^4 + 15*sqrt(x*e + d)*b^3*d^3*e^4 + 55*(x*e + d)^(5/2)*a*b^2*e^5 - 146*(x*e + d)^(3/2)*a*b^2*d*e^5 - 45*sqrt(x*e + d)*a*b^2*d^2*e^5 + 73*(x*e + d)^(3/2)*a^2*b*e^6 + 45*sqrt(x*e + d)*a^2*b*d*e^6 - 15*sqrt(x*e + d)*a^3*e^7)/((b^4*d^3*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 3*a*b^3*d^2*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 3*a^2*b^2*d*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) - a^3*b*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2))*((x*e + d)*b - b*d + a*e)^4)","B",0
1727,1,551,0,0.327847," ","integrate(1/(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{35 \, \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e^{4}}{64 \, {\left(b^{4} d^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 4 \, a b^{3} d^{3} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 6 \, a^{2} b^{2} d^{2} e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 4 \, a^{3} b d e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + a^{4} e^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} \sqrt{-b^{2} d + a b e}} + \frac{105 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{3} e^{4} - 385 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{3} d e^{4} + 511 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{3} d^{2} e^{4} - 279 \, \sqrt{x e + d} b^{3} d^{3} e^{4} + 385 \, {\left(x e + d\right)}^{\frac{5}{2}} a b^{2} e^{5} - 1022 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{2} d e^{5} + 837 \, \sqrt{x e + d} a b^{2} d^{2} e^{5} + 511 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} b e^{6} - 837 \, \sqrt{x e + d} a^{2} b d e^{6} + 279 \, \sqrt{x e + d} a^{3} e^{7}}{192 \, {\left(b^{4} d^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 4 \, a b^{3} d^{3} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 6 \, a^{2} b^{2} d^{2} e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 4 \, a^{3} b d e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + a^{4} e^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{4}}"," ",0,"35/64*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e^4/((b^4*d^4*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 4*a*b^3*d^3*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 6*a^2*b^2*d^2*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 4*a^3*b*d*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2) + a^4*e^4*sgn((x*e + d)*b*e - b*d*e + a*e^2))*sqrt(-b^2*d + a*b*e)) + 1/192*(105*(x*e + d)^(7/2)*b^3*e^4 - 385*(x*e + d)^(5/2)*b^3*d*e^4 + 511*(x*e + d)^(3/2)*b^3*d^2*e^4 - 279*sqrt(x*e + d)*b^3*d^3*e^4 + 385*(x*e + d)^(5/2)*a*b^2*e^5 - 1022*(x*e + d)^(3/2)*a*b^2*d*e^5 + 837*sqrt(x*e + d)*a*b^2*d^2*e^5 + 511*(x*e + d)^(3/2)*a^2*b*e^6 - 837*sqrt(x*e + d)*a^2*b*d*e^6 + 279*sqrt(x*e + d)*a^3*e^7)/((b^4*d^4*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 4*a*b^3*d^3*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 6*a^2*b^2*d^2*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 4*a^3*b*d*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2) + a^4*e^4*sgn((x*e + d)*b*e - b*d*e + a*e^2))*((x*e + d)*b - b*d + a*e)^4)","B",0
1728,1,836,0,0.583560," ","integrate(1/(e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{315 \, b \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e^{4}}{64 \, {\left(b^{5} d^{5} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 5 \, a b^{4} d^{4} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 10 \, a^{2} b^{3} d^{3} e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 10 \, a^{3} b^{2} d^{2} e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 5 \, a^{4} b d e^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - a^{5} e^{5} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} \sqrt{-b^{2} d + a b e}} + \frac{2 \, e^{4}}{{\left(b^{5} d^{5} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 5 \, a b^{4} d^{4} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 10 \, a^{2} b^{3} d^{3} e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 10 \, a^{3} b^{2} d^{2} e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 5 \, a^{4} b d e^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - a^{5} e^{5} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} \sqrt{x e + d}} + \frac{187 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{4} e^{4} - 643 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{4} d e^{4} + 765 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{4} d^{2} e^{4} - 325 \, \sqrt{x e + d} b^{4} d^{3} e^{4} + 643 \, {\left(x e + d\right)}^{\frac{5}{2}} a b^{3} e^{5} - 1530 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{3} d e^{5} + 975 \, \sqrt{x e + d} a b^{3} d^{2} e^{5} + 765 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} b^{2} e^{6} - 975 \, \sqrt{x e + d} a^{2} b^{2} d e^{6} + 325 \, \sqrt{x e + d} a^{3} b e^{7}}{64 \, {\left(b^{5} d^{5} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 5 \, a b^{4} d^{4} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 10 \, a^{2} b^{3} d^{3} e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 10 \, a^{3} b^{2} d^{2} e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 5 \, a^{4} b d e^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - a^{5} e^{5} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{4}}"," ",0,"315/64*b*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e^4/((b^5*d^5*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 5*a*b^4*d^4*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 10*a^2*b^3*d^3*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 10*a^3*b^2*d^2*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 5*a^4*b*d*e^4*sgn((x*e + d)*b*e - b*d*e + a*e^2) - a^5*e^5*sgn((x*e + d)*b*e - b*d*e + a*e^2))*sqrt(-b^2*d + a*b*e)) + 2*e^4/((b^5*d^5*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 5*a*b^4*d^4*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 10*a^2*b^3*d^3*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 10*a^3*b^2*d^2*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 5*a^4*b*d*e^4*sgn((x*e + d)*b*e - b*d*e + a*e^2) - a^5*e^5*sgn((x*e + d)*b*e - b*d*e + a*e^2))*sqrt(x*e + d)) + 1/64*(187*(x*e + d)^(7/2)*b^4*e^4 - 643*(x*e + d)^(5/2)*b^4*d*e^4 + 765*(x*e + d)^(3/2)*b^4*d^2*e^4 - 325*sqrt(x*e + d)*b^4*d^3*e^4 + 643*(x*e + d)^(5/2)*a*b^3*e^5 - 1530*(x*e + d)^(3/2)*a*b^3*d*e^5 + 975*sqrt(x*e + d)*a*b^3*d^2*e^5 + 765*(x*e + d)^(3/2)*a^2*b^2*e^6 - 975*sqrt(x*e + d)*a^2*b^2*d*e^6 + 325*sqrt(x*e + d)*a^3*b*e^7)/((b^5*d^5*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 5*a*b^4*d^4*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 10*a^2*b^3*d^3*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 10*a^3*b^2*d^2*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 5*a^4*b*d*e^4*sgn((x*e + d)*b*e - b*d*e + a*e^2) - a^5*e^5*sgn((x*e + d)*b*e - b*d*e + a*e^2))*((x*e + d)*b - b*d + a*e)^4)","B",0
1729,1,962,0,0.559348," ","integrate(1/(e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{1155 \, b^{2} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e^{4}}{64 \, {\left(b^{6} d^{6} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 6 \, a b^{5} d^{5} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 15 \, a^{2} b^{4} d^{4} e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 20 \, a^{3} b^{3} d^{3} e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 15 \, a^{4} b^{2} d^{2} e^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 6 \, a^{5} b d e^{5} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + a^{6} e^{6} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} \sqrt{-b^{2} d + a b e}} + \frac{2 \, {\left(15 \, {\left(x e + d\right)} b e^{4} + b d e^{4} - a e^{5}\right)}}{3 \, {\left(b^{6} d^{6} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 6 \, a b^{5} d^{5} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 15 \, a^{2} b^{4} d^{4} e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 20 \, a^{3} b^{3} d^{3} e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 15 \, a^{4} b^{2} d^{2} e^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 6 \, a^{5} b d e^{5} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + a^{6} e^{6} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} {\left(x e + d\right)}^{\frac{3}{2}}} + \frac{1545 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{5} e^{4} - 5153 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{5} d e^{4} + 5855 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{5} d^{2} e^{4} - 2295 \, \sqrt{x e + d} b^{5} d^{3} e^{4} + 5153 \, {\left(x e + d\right)}^{\frac{5}{2}} a b^{4} e^{5} - 11710 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{4} d e^{5} + 6885 \, \sqrt{x e + d} a b^{4} d^{2} e^{5} + 5855 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} b^{3} e^{6} - 6885 \, \sqrt{x e + d} a^{2} b^{3} d e^{6} + 2295 \, \sqrt{x e + d} a^{3} b^{2} e^{7}}{192 \, {\left(b^{6} d^{6} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 6 \, a b^{5} d^{5} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 15 \, a^{2} b^{4} d^{4} e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 20 \, a^{3} b^{3} d^{3} e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 15 \, a^{4} b^{2} d^{2} e^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 6 \, a^{5} b d e^{5} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + a^{6} e^{6} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{4}}"," ",0,"1155/64*b^2*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e^4/((b^6*d^6*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 6*a*b^5*d^5*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 15*a^2*b^4*d^4*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 20*a^3*b^3*d^3*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 15*a^4*b^2*d^2*e^4*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 6*a^5*b*d*e^5*sgn((x*e + d)*b*e - b*d*e + a*e^2) + a^6*e^6*sgn((x*e + d)*b*e - b*d*e + a*e^2))*sqrt(-b^2*d + a*b*e)) + 2/3*(15*(x*e + d)*b*e^4 + b*d*e^4 - a*e^5)/((b^6*d^6*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 6*a*b^5*d^5*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 15*a^2*b^4*d^4*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 20*a^3*b^3*d^3*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 15*a^4*b^2*d^2*e^4*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 6*a^5*b*d*e^5*sgn((x*e + d)*b*e - b*d*e + a*e^2) + a^6*e^6*sgn((x*e + d)*b*e - b*d*e + a*e^2))*(x*e + d)^(3/2)) + 1/192*(1545*(x*e + d)^(7/2)*b^5*e^4 - 5153*(x*e + d)^(5/2)*b^5*d*e^4 + 5855*(x*e + d)^(3/2)*b^5*d^2*e^4 - 2295*sqrt(x*e + d)*b^5*d^3*e^4 + 5153*(x*e + d)^(5/2)*a*b^4*e^5 - 11710*(x*e + d)^(3/2)*a*b^4*d*e^5 + 6885*sqrt(x*e + d)*a*b^4*d^2*e^5 + 5855*(x*e + d)^(3/2)*a^2*b^3*e^6 - 6885*sqrt(x*e + d)*a^2*b^3*d*e^6 + 2295*sqrt(x*e + d)*a^3*b^2*e^7)/((b^6*d^6*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 6*a*b^5*d^5*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 15*a^2*b^4*d^4*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 20*a^3*b^3*d^3*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 15*a^4*b^2*d^2*e^4*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 6*a^5*b*d*e^5*sgn((x*e + d)*b*e - b*d*e + a*e^2) + a^6*e^6*sgn((x*e + d)*b*e - b*d*e + a*e^2))*((x*e + d)*b - b*d + a*e)^4)","B",0
1730,1,1114,0,0.664297," ","integrate(1/(e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{3003 \, b^{3} \arctan\left(\frac{\sqrt{x e + d} b}{\sqrt{-b^{2} d + a b e}}\right) e^{4}}{64 \, {\left(b^{7} d^{7} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 7 \, a b^{6} d^{6} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 21 \, a^{2} b^{5} d^{5} e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 35 \, a^{3} b^{4} d^{4} e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 35 \, a^{4} b^{3} d^{3} e^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 21 \, a^{5} b^{2} d^{2} e^{5} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 7 \, a^{6} b d e^{6} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - a^{7} e^{7} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} \sqrt{-b^{2} d + a b e}} + \frac{2 \, {\left(225 \, {\left(x e + d\right)}^{2} b^{2} e^{4} + 25 \, {\left(x e + d\right)} b^{2} d e^{4} + 3 \, b^{2} d^{2} e^{4} - 25 \, {\left(x e + d\right)} a b e^{5} - 6 \, a b d e^{5} + 3 \, a^{2} e^{6}\right)}}{15 \, {\left(b^{7} d^{7} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 7 \, a b^{6} d^{6} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 21 \, a^{2} b^{5} d^{5} e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 35 \, a^{3} b^{4} d^{4} e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 35 \, a^{4} b^{3} d^{3} e^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 21 \, a^{5} b^{2} d^{2} e^{5} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 7 \, a^{6} b d e^{6} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - a^{7} e^{7} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} {\left(x e + d\right)}^{\frac{5}{2}}} + \frac{3249 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{6} e^{4} - 10633 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{6} d e^{4} + 11767 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{6} d^{2} e^{4} - 4431 \, \sqrt{x e + d} b^{6} d^{3} e^{4} + 10633 \, {\left(x e + d\right)}^{\frac{5}{2}} a b^{5} e^{5} - 23534 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{5} d e^{5} + 13293 \, \sqrt{x e + d} a b^{5} d^{2} e^{5} + 11767 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} b^{4} e^{6} - 13293 \, \sqrt{x e + d} a^{2} b^{4} d e^{6} + 4431 \, \sqrt{x e + d} a^{3} b^{3} e^{7}}{192 \, {\left(b^{7} d^{7} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 7 \, a b^{6} d^{6} e \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 21 \, a^{2} b^{5} d^{5} e^{2} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 35 \, a^{3} b^{4} d^{4} e^{3} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 35 \, a^{4} b^{3} d^{3} e^{4} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - 21 \, a^{5} b^{2} d^{2} e^{5} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) + 7 \, a^{6} b d e^{6} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right) - a^{7} e^{7} \mathrm{sgn}\left({\left(x e + d\right)} b e - b d e + a e^{2}\right)\right)} {\left({\left(x e + d\right)} b - b d + a e\right)}^{4}}"," ",0,"3003/64*b^3*arctan(sqrt(x*e + d)*b/sqrt(-b^2*d + a*b*e))*e^4/((b^7*d^7*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 7*a*b^6*d^6*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 21*a^2*b^5*d^5*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 35*a^3*b^4*d^4*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 35*a^4*b^3*d^3*e^4*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 21*a^5*b^2*d^2*e^5*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 7*a^6*b*d*e^6*sgn((x*e + d)*b*e - b*d*e + a*e^2) - a^7*e^7*sgn((x*e + d)*b*e - b*d*e + a*e^2))*sqrt(-b^2*d + a*b*e)) + 2/15*(225*(x*e + d)^2*b^2*e^4 + 25*(x*e + d)*b^2*d*e^4 + 3*b^2*d^2*e^4 - 25*(x*e + d)*a*b*e^5 - 6*a*b*d*e^5 + 3*a^2*e^6)/((b^7*d^7*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 7*a*b^6*d^6*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 21*a^2*b^5*d^5*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 35*a^3*b^4*d^4*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 35*a^4*b^3*d^3*e^4*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 21*a^5*b^2*d^2*e^5*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 7*a^6*b*d*e^6*sgn((x*e + d)*b*e - b*d*e + a*e^2) - a^7*e^7*sgn((x*e + d)*b*e - b*d*e + a*e^2))*(x*e + d)^(5/2)) + 1/192*(3249*(x*e + d)^(7/2)*b^6*e^4 - 10633*(x*e + d)^(5/2)*b^6*d*e^4 + 11767*(x*e + d)^(3/2)*b^6*d^2*e^4 - 4431*sqrt(x*e + d)*b^6*d^3*e^4 + 10633*(x*e + d)^(5/2)*a*b^5*e^5 - 23534*(x*e + d)^(3/2)*a*b^5*d*e^5 + 13293*sqrt(x*e + d)*a*b^5*d^2*e^5 + 11767*(x*e + d)^(3/2)*a^2*b^4*e^6 - 13293*sqrt(x*e + d)*a^2*b^4*d*e^6 + 4431*sqrt(x*e + d)*a^3*b^3*e^7)/((b^7*d^7*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 7*a*b^6*d^6*e*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 21*a^2*b^5*d^5*e^2*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 35*a^3*b^4*d^4*e^3*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 35*a^4*b^3*d^3*e^4*sgn((x*e + d)*b*e - b*d*e + a*e^2) - 21*a^5*b^2*d^2*e^5*sgn((x*e + d)*b*e - b*d*e + a*e^2) + 7*a^6*b*d*e^6*sgn((x*e + d)*b*e - b*d*e + a*e^2) - a^7*e^7*sgn((x*e + d)*b*e - b*d*e + a*e^2))*((x*e + d)*b - b*d + a*e)^4)","B",0
1731,1,3877,0,0.303344," ","integrate((e*x+d)^m*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\frac{{\left(x e + d\right)}^{m} b^{6} m^{6} x^{7} e^{7} + {\left(x e + d\right)}^{m} b^{6} d m^{6} x^{6} e^{6} + 6 \, {\left(x e + d\right)}^{m} a b^{5} m^{6} x^{6} e^{7} + 21 \, {\left(x e + d\right)}^{m} b^{6} m^{5} x^{7} e^{7} + 6 \, {\left(x e + d\right)}^{m} a b^{5} d m^{6} x^{5} e^{6} + 15 \, {\left(x e + d\right)}^{m} b^{6} d m^{5} x^{6} e^{6} - 6 \, {\left(x e + d\right)}^{m} b^{6} d^{2} m^{5} x^{5} e^{5} + 15 \, {\left(x e + d\right)}^{m} a^{2} b^{4} m^{6} x^{5} e^{7} + 132 \, {\left(x e + d\right)}^{m} a b^{5} m^{5} x^{6} e^{7} + 175 \, {\left(x e + d\right)}^{m} b^{6} m^{4} x^{7} e^{7} + 15 \, {\left(x e + d\right)}^{m} a^{2} b^{4} d m^{6} x^{4} e^{6} + 102 \, {\left(x e + d\right)}^{m} a b^{5} d m^{5} x^{5} e^{6} + 85 \, {\left(x e + d\right)}^{m} b^{6} d m^{4} x^{6} e^{6} - 30 \, {\left(x e + d\right)}^{m} a b^{5} d^{2} m^{5} x^{4} e^{5} - 60 \, {\left(x e + d\right)}^{m} b^{6} d^{2} m^{4} x^{5} e^{5} + 30 \, {\left(x e + d\right)}^{m} b^{6} d^{3} m^{4} x^{4} e^{4} + 20 \, {\left(x e + d\right)}^{m} a^{3} b^{3} m^{6} x^{4} e^{7} + 345 \, {\left(x e + d\right)}^{m} a^{2} b^{4} m^{5} x^{5} e^{7} + 1140 \, {\left(x e + d\right)}^{m} a b^{5} m^{4} x^{6} e^{7} + 735 \, {\left(x e + d\right)}^{m} b^{6} m^{3} x^{7} e^{7} + 20 \, {\left(x e + d\right)}^{m} a^{3} b^{3} d m^{6} x^{3} e^{6} + 285 \, {\left(x e + d\right)}^{m} a^{2} b^{4} d m^{5} x^{4} e^{6} + 630 \, {\left(x e + d\right)}^{m} a b^{5} d m^{4} x^{5} e^{6} + 225 \, {\left(x e + d\right)}^{m} b^{6} d m^{3} x^{6} e^{6} - 60 \, {\left(x e + d\right)}^{m} a^{2} b^{4} d^{2} m^{5} x^{3} e^{5} - 390 \, {\left(x e + d\right)}^{m} a b^{5} d^{2} m^{4} x^{4} e^{5} - 210 \, {\left(x e + d\right)}^{m} b^{6} d^{2} m^{3} x^{5} e^{5} + 120 \, {\left(x e + d\right)}^{m} a b^{5} d^{3} m^{4} x^{3} e^{4} + 180 \, {\left(x e + d\right)}^{m} b^{6} d^{3} m^{3} x^{4} e^{4} - 120 \, {\left(x e + d\right)}^{m} b^{6} d^{4} m^{3} x^{3} e^{3} + 15 \, {\left(x e + d\right)}^{m} a^{4} b^{2} m^{6} x^{3} e^{7} + 480 \, {\left(x e + d\right)}^{m} a^{3} b^{3} m^{5} x^{4} e^{7} + 3105 \, {\left(x e + d\right)}^{m} a^{2} b^{4} m^{4} x^{5} e^{7} + 4920 \, {\left(x e + d\right)}^{m} a b^{5} m^{3} x^{6} e^{7} + 1624 \, {\left(x e + d\right)}^{m} b^{6} m^{2} x^{7} e^{7} + 15 \, {\left(x e + d\right)}^{m} a^{4} b^{2} d m^{6} x^{2} e^{6} + 420 \, {\left(x e + d\right)}^{m} a^{3} b^{3} d m^{5} x^{3} e^{6} + 1965 \, {\left(x e + d\right)}^{m} a^{2} b^{4} d m^{4} x^{4} e^{6} + 1770 \, {\left(x e + d\right)}^{m} a b^{5} d m^{3} x^{5} e^{6} + 274 \, {\left(x e + d\right)}^{m} b^{6} d m^{2} x^{6} e^{6} - 60 \, {\left(x e + d\right)}^{m} a^{3} b^{3} d^{2} m^{5} x^{2} e^{5} - 960 \, {\left(x e + d\right)}^{m} a^{2} b^{4} d^{2} m^{4} x^{3} e^{5} - 1590 \, {\left(x e + d\right)}^{m} a b^{5} d^{2} m^{3} x^{4} e^{5} - 300 \, {\left(x e + d\right)}^{m} b^{6} d^{2} m^{2} x^{5} e^{5} + 180 \, {\left(x e + d\right)}^{m} a^{2} b^{4} d^{3} m^{4} x^{2} e^{4} + 1200 \, {\left(x e + d\right)}^{m} a b^{5} d^{3} m^{3} x^{3} e^{4} + 330 \, {\left(x e + d\right)}^{m} b^{6} d^{3} m^{2} x^{4} e^{4} - 360 \, {\left(x e + d\right)}^{m} a b^{5} d^{4} m^{3} x^{2} e^{3} - 360 \, {\left(x e + d\right)}^{m} b^{6} d^{4} m^{2} x^{3} e^{3} + 360 \, {\left(x e + d\right)}^{m} b^{6} d^{5} m^{2} x^{2} e^{2} + 6 \, {\left(x e + d\right)}^{m} a^{5} b m^{6} x^{2} e^{7} + 375 \, {\left(x e + d\right)}^{m} a^{4} b^{2} m^{5} x^{3} e^{7} + 4520 \, {\left(x e + d\right)}^{m} a^{3} b^{3} m^{4} x^{4} e^{7} + 13875 \, {\left(x e + d\right)}^{m} a^{2} b^{4} m^{3} x^{5} e^{7} + 11094 \, {\left(x e + d\right)}^{m} a b^{5} m^{2} x^{6} e^{7} + 1764 \, {\left(x e + d\right)}^{m} b^{6} m x^{7} e^{7} + 6 \, {\left(x e + d\right)}^{m} a^{5} b d m^{6} x e^{6} + 345 \, {\left(x e + d\right)}^{m} a^{4} b^{2} d m^{5} x^{2} e^{6} + 3260 \, {\left(x e + d\right)}^{m} a^{3} b^{3} d m^{4} x^{3} e^{6} + 6015 \, {\left(x e + d\right)}^{m} a^{2} b^{4} d m^{3} x^{4} e^{6} + 2244 \, {\left(x e + d\right)}^{m} a b^{5} d m^{2} x^{5} e^{6} + 120 \, {\left(x e + d\right)}^{m} b^{6} d m x^{6} e^{6} - 30 \, {\left(x e + d\right)}^{m} a^{4} b^{2} d^{2} m^{5} x e^{5} - 1140 \, {\left(x e + d\right)}^{m} a^{3} b^{3} d^{2} m^{4} x^{2} e^{5} - 4980 \, {\left(x e + d\right)}^{m} a^{2} b^{4} d^{2} m^{3} x^{3} e^{5} - 2490 \, {\left(x e + d\right)}^{m} a b^{5} d^{2} m^{2} x^{4} e^{5} - 144 \, {\left(x e + d\right)}^{m} b^{6} d^{2} m x^{5} e^{5} + 120 \, {\left(x e + d\right)}^{m} a^{3} b^{3} d^{3} m^{4} x e^{4} + 2520 \, {\left(x e + d\right)}^{m} a^{2} b^{4} d^{3} m^{3} x^{2} e^{4} + 2760 \, {\left(x e + d\right)}^{m} a b^{5} d^{3} m^{2} x^{3} e^{4} + 180 \, {\left(x e + d\right)}^{m} b^{6} d^{3} m x^{4} e^{4} - 360 \, {\left(x e + d\right)}^{m} a^{2} b^{4} d^{4} m^{3} x e^{3} - 2880 \, {\left(x e + d\right)}^{m} a b^{5} d^{4} m^{2} x^{2} e^{3} - 240 \, {\left(x e + d\right)}^{m} b^{6} d^{4} m x^{3} e^{3} + 720 \, {\left(x e + d\right)}^{m} a b^{5} d^{5} m^{2} x e^{2} + 360 \, {\left(x e + d\right)}^{m} b^{6} d^{5} m x^{2} e^{2} - 720 \, {\left(x e + d\right)}^{m} b^{6} d^{6} m x e + {\left(x e + d\right)}^{m} a^{6} m^{6} x e^{7} + 156 \, {\left(x e + d\right)}^{m} a^{5} b m^{5} x^{2} e^{7} + 3705 \, {\left(x e + d\right)}^{m} a^{4} b^{2} m^{4} x^{3} e^{7} + 21120 \, {\left(x e + d\right)}^{m} a^{3} b^{3} m^{3} x^{4} e^{7} + 32160 \, {\left(x e + d\right)}^{m} a^{2} b^{4} m^{2} x^{5} e^{7} + 12228 \, {\left(x e + d\right)}^{m} a b^{5} m x^{6} e^{7} + 720 \, {\left(x e + d\right)}^{m} b^{6} x^{7} e^{7} + {\left(x e + d\right)}^{m} a^{6} d m^{6} e^{6} + 150 \, {\left(x e + d\right)}^{m} a^{5} b d m^{5} x e^{6} + 3015 \, {\left(x e + d\right)}^{m} a^{4} b^{2} d m^{4} x^{2} e^{6} + 11340 \, {\left(x e + d\right)}^{m} a^{3} b^{3} d m^{3} x^{3} e^{6} + 8100 \, {\left(x e + d\right)}^{m} a^{2} b^{4} d m^{2} x^{4} e^{6} + 1008 \, {\left(x e + d\right)}^{m} a b^{5} d m x^{5} e^{6} - 6 \, {\left(x e + d\right)}^{m} a^{5} b d^{2} m^{5} e^{5} - 660 \, {\left(x e + d\right)}^{m} a^{4} b^{2} d^{2} m^{4} x e^{5} - 7500 \, {\left(x e + d\right)}^{m} a^{3} b^{3} d^{2} m^{3} x^{2} e^{5} - 9120 \, {\left(x e + d\right)}^{m} a^{2} b^{4} d^{2} m^{2} x^{3} e^{5} - 1260 \, {\left(x e + d\right)}^{m} a b^{5} d^{2} m x^{4} e^{5} + 30 \, {\left(x e + d\right)}^{m} a^{4} b^{2} d^{3} m^{4} e^{4} + 2160 \, {\left(x e + d\right)}^{m} a^{3} b^{3} d^{3} m^{3} x e^{4} + 9900 \, {\left(x e + d\right)}^{m} a^{2} b^{4} d^{3} m^{2} x^{2} e^{4} + 1680 \, {\left(x e + d\right)}^{m} a b^{5} d^{3} m x^{3} e^{4} - 120 \, {\left(x e + d\right)}^{m} a^{3} b^{3} d^{4} m^{3} e^{3} - 4680 \, {\left(x e + d\right)}^{m} a^{2} b^{4} d^{4} m^{2} x e^{3} - 2520 \, {\left(x e + d\right)}^{m} a b^{5} d^{4} m x^{2} e^{3} + 360 \, {\left(x e + d\right)}^{m} a^{2} b^{4} d^{5} m^{2} e^{2} + 5040 \, {\left(x e + d\right)}^{m} a b^{5} d^{5} m x e^{2} - 720 \, {\left(x e + d\right)}^{m} a b^{5} d^{6} m e + 720 \, {\left(x e + d\right)}^{m} b^{6} d^{7} + 27 \, {\left(x e + d\right)}^{m} a^{6} m^{5} x e^{7} + 1620 \, {\left(x e + d\right)}^{m} a^{5} b m^{4} x^{2} e^{7} + 18285 \, {\left(x e + d\right)}^{m} a^{4} b^{2} m^{3} x^{3} e^{7} + 50900 \, {\left(x e + d\right)}^{m} a^{3} b^{3} m^{2} x^{4} e^{7} + 36180 \, {\left(x e + d\right)}^{m} a^{2} b^{4} m x^{5} e^{7} + 5040 \, {\left(x e + d\right)}^{m} a b^{5} x^{6} e^{7} + 27 \, {\left(x e + d\right)}^{m} a^{6} d m^{5} e^{6} + 1470 \, {\left(x e + d\right)}^{m} a^{5} b d m^{4} x e^{6} + 12255 \, {\left(x e + d\right)}^{m} a^{4} b^{2} d m^{3} x^{2} e^{6} + 16880 \, {\left(x e + d\right)}^{m} a^{3} b^{3} d m^{2} x^{3} e^{6} + 3780 \, {\left(x e + d\right)}^{m} a^{2} b^{4} d m x^{4} e^{6} - 150 \, {\left(x e + d\right)}^{m} a^{5} b d^{2} m^{4} e^{5} - 5370 \, {\left(x e + d\right)}^{m} a^{4} b^{2} d^{2} m^{3} x e^{5} - 19020 \, {\left(x e + d\right)}^{m} a^{3} b^{3} d^{2} m^{2} x^{2} e^{5} - 5040 \, {\left(x e + d\right)}^{m} a^{2} b^{4} d^{2} m x^{3} e^{5} + 660 \, {\left(x e + d\right)}^{m} a^{4} b^{2} d^{3} m^{3} e^{4} + 12840 \, {\left(x e + d\right)}^{m} a^{3} b^{3} d^{3} m^{2} x e^{4} + 7560 \, {\left(x e + d\right)}^{m} a^{2} b^{4} d^{3} m x^{2} e^{4} - 2160 \, {\left(x e + d\right)}^{m} a^{3} b^{3} d^{4} m^{2} e^{3} - 15120 \, {\left(x e + d\right)}^{m} a^{2} b^{4} d^{4} m x e^{3} + 4680 \, {\left(x e + d\right)}^{m} a^{2} b^{4} d^{5} m e^{2} - 5040 \, {\left(x e + d\right)}^{m} a b^{5} d^{6} e + 295 \, {\left(x e + d\right)}^{m} a^{6} m^{4} x e^{7} + 8520 \, {\left(x e + d\right)}^{m} a^{5} b m^{3} x^{2} e^{7} + 46680 \, {\left(x e + d\right)}^{m} a^{4} b^{2} m^{2} x^{3} e^{7} + 59040 \, {\left(x e + d\right)}^{m} a^{3} b^{3} m x^{4} e^{7} + 15120 \, {\left(x e + d\right)}^{m} a^{2} b^{4} x^{5} e^{7} + 295 \, {\left(x e + d\right)}^{m} a^{6} d m^{4} e^{6} + 7050 \, {\left(x e + d\right)}^{m} a^{5} b d m^{3} x e^{6} + 22170 \, {\left(x e + d\right)}^{m} a^{4} b^{2} d m^{2} x^{2} e^{6} + 8400 \, {\left(x e + d\right)}^{m} a^{3} b^{3} d m x^{3} e^{6} - 1470 \, {\left(x e + d\right)}^{m} a^{5} b d^{2} m^{3} e^{5} - 19140 \, {\left(x e + d\right)}^{m} a^{4} b^{2} d^{2} m^{2} x e^{5} - 12600 \, {\left(x e + d\right)}^{m} a^{3} b^{3} d^{2} m x^{2} e^{5} + 5370 \, {\left(x e + d\right)}^{m} a^{4} b^{2} d^{3} m^{2} e^{4} + 25200 \, {\left(x e + d\right)}^{m} a^{3} b^{3} d^{3} m x e^{4} - 12840 \, {\left(x e + d\right)}^{m} a^{3} b^{3} d^{4} m e^{3} + 15120 \, {\left(x e + d\right)}^{m} a^{2} b^{4} d^{5} e^{2} + 1665 \, {\left(x e + d\right)}^{m} a^{6} m^{3} x e^{7} + 23574 \, {\left(x e + d\right)}^{m} a^{5} b m^{2} x^{2} e^{7} + 56940 \, {\left(x e + d\right)}^{m} a^{4} b^{2} m x^{3} e^{7} + 25200 \, {\left(x e + d\right)}^{m} a^{3} b^{3} x^{4} e^{7} + 1665 \, {\left(x e + d\right)}^{m} a^{6} d m^{3} e^{6} + 16524 \, {\left(x e + d\right)}^{m} a^{5} b d m^{2} x e^{6} + 12600 \, {\left(x e + d\right)}^{m} a^{4} b^{2} d m x^{2} e^{6} - 7050 \, {\left(x e + d\right)}^{m} a^{5} b d^{2} m^{2} e^{5} - 25200 \, {\left(x e + d\right)}^{m} a^{4} b^{2} d^{2} m x e^{5} + 19140 \, {\left(x e + d\right)}^{m} a^{4} b^{2} d^{3} m e^{4} - 25200 \, {\left(x e + d\right)}^{m} a^{3} b^{3} d^{4} e^{3} + 5104 \, {\left(x e + d\right)}^{m} a^{6} m^{2} x e^{7} + 31644 \, {\left(x e + d\right)}^{m} a^{5} b m x^{2} e^{7} + 25200 \, {\left(x e + d\right)}^{m} a^{4} b^{2} x^{3} e^{7} + 5104 \, {\left(x e + d\right)}^{m} a^{6} d m^{2} e^{6} + 15120 \, {\left(x e + d\right)}^{m} a^{5} b d m x e^{6} - 16524 \, {\left(x e + d\right)}^{m} a^{5} b d^{2} m e^{5} + 25200 \, {\left(x e + d\right)}^{m} a^{4} b^{2} d^{3} e^{4} + 8028 \, {\left(x e + d\right)}^{m} a^{6} m x e^{7} + 15120 \, {\left(x e + d\right)}^{m} a^{5} b x^{2} e^{7} + 8028 \, {\left(x e + d\right)}^{m} a^{6} d m e^{6} - 15120 \, {\left(x e + d\right)}^{m} a^{5} b d^{2} e^{5} + 5040 \, {\left(x e + d\right)}^{m} a^{6} x e^{7} + 5040 \, {\left(x e + d\right)}^{m} a^{6} d e^{6}}{m^{7} e^{7} + 28 \, m^{6} e^{7} + 322 \, m^{5} e^{7} + 1960 \, m^{4} e^{7} + 6769 \, m^{3} e^{7} + 13132 \, m^{2} e^{7} + 13068 \, m e^{7} + 5040 \, e^{7}}"," ",0,"((x*e + d)^m*b^6*m^6*x^7*e^7 + (x*e + d)^m*b^6*d*m^6*x^6*e^6 + 6*(x*e + d)^m*a*b^5*m^6*x^6*e^7 + 21*(x*e + d)^m*b^6*m^5*x^7*e^7 + 6*(x*e + d)^m*a*b^5*d*m^6*x^5*e^6 + 15*(x*e + d)^m*b^6*d*m^5*x^6*e^6 - 6*(x*e + d)^m*b^6*d^2*m^5*x^5*e^5 + 15*(x*e + d)^m*a^2*b^4*m^6*x^5*e^7 + 132*(x*e + d)^m*a*b^5*m^5*x^6*e^7 + 175*(x*e + d)^m*b^6*m^4*x^7*e^7 + 15*(x*e + d)^m*a^2*b^4*d*m^6*x^4*e^6 + 102*(x*e + d)^m*a*b^5*d*m^5*x^5*e^6 + 85*(x*e + d)^m*b^6*d*m^4*x^6*e^6 - 30*(x*e + d)^m*a*b^5*d^2*m^5*x^4*e^5 - 60*(x*e + d)^m*b^6*d^2*m^4*x^5*e^5 + 30*(x*e + d)^m*b^6*d^3*m^4*x^4*e^4 + 20*(x*e + d)^m*a^3*b^3*m^6*x^4*e^7 + 345*(x*e + d)^m*a^2*b^4*m^5*x^5*e^7 + 1140*(x*e + d)^m*a*b^5*m^4*x^6*e^7 + 735*(x*e + d)^m*b^6*m^3*x^7*e^7 + 20*(x*e + d)^m*a^3*b^3*d*m^6*x^3*e^6 + 285*(x*e + d)^m*a^2*b^4*d*m^5*x^4*e^6 + 630*(x*e + d)^m*a*b^5*d*m^4*x^5*e^6 + 225*(x*e + d)^m*b^6*d*m^3*x^6*e^6 - 60*(x*e + d)^m*a^2*b^4*d^2*m^5*x^3*e^5 - 390*(x*e + d)^m*a*b^5*d^2*m^4*x^4*e^5 - 210*(x*e + d)^m*b^6*d^2*m^3*x^5*e^5 + 120*(x*e + d)^m*a*b^5*d^3*m^4*x^3*e^4 + 180*(x*e + d)^m*b^6*d^3*m^3*x^4*e^4 - 120*(x*e + d)^m*b^6*d^4*m^3*x^3*e^3 + 15*(x*e + d)^m*a^4*b^2*m^6*x^3*e^7 + 480*(x*e + d)^m*a^3*b^3*m^5*x^4*e^7 + 3105*(x*e + d)^m*a^2*b^4*m^4*x^5*e^7 + 4920*(x*e + d)^m*a*b^5*m^3*x^6*e^7 + 1624*(x*e + d)^m*b^6*m^2*x^7*e^7 + 15*(x*e + d)^m*a^4*b^2*d*m^6*x^2*e^6 + 420*(x*e + d)^m*a^3*b^3*d*m^5*x^3*e^6 + 1965*(x*e + d)^m*a^2*b^4*d*m^4*x^4*e^6 + 1770*(x*e + d)^m*a*b^5*d*m^3*x^5*e^6 + 274*(x*e + d)^m*b^6*d*m^2*x^6*e^6 - 60*(x*e + d)^m*a^3*b^3*d^2*m^5*x^2*e^5 - 960*(x*e + d)^m*a^2*b^4*d^2*m^4*x^3*e^5 - 1590*(x*e + d)^m*a*b^5*d^2*m^3*x^4*e^5 - 300*(x*e + d)^m*b^6*d^2*m^2*x^5*e^5 + 180*(x*e + d)^m*a^2*b^4*d^3*m^4*x^2*e^4 + 1200*(x*e + d)^m*a*b^5*d^3*m^3*x^3*e^4 + 330*(x*e + d)^m*b^6*d^3*m^2*x^4*e^4 - 360*(x*e + d)^m*a*b^5*d^4*m^3*x^2*e^3 - 360*(x*e + d)^m*b^6*d^4*m^2*x^3*e^3 + 360*(x*e + d)^m*b^6*d^5*m^2*x^2*e^2 + 6*(x*e + d)^m*a^5*b*m^6*x^2*e^7 + 375*(x*e + d)^m*a^4*b^2*m^5*x^3*e^7 + 4520*(x*e + d)^m*a^3*b^3*m^4*x^4*e^7 + 13875*(x*e + d)^m*a^2*b^4*m^3*x^5*e^7 + 11094*(x*e + d)^m*a*b^5*m^2*x^6*e^7 + 1764*(x*e + d)^m*b^6*m*x^7*e^7 + 6*(x*e + d)^m*a^5*b*d*m^6*x*e^6 + 345*(x*e + d)^m*a^4*b^2*d*m^5*x^2*e^6 + 3260*(x*e + d)^m*a^3*b^3*d*m^4*x^3*e^6 + 6015*(x*e + d)^m*a^2*b^4*d*m^3*x^4*e^6 + 2244*(x*e + d)^m*a*b^5*d*m^2*x^5*e^6 + 120*(x*e + d)^m*b^6*d*m*x^6*e^6 - 30*(x*e + d)^m*a^4*b^2*d^2*m^5*x*e^5 - 1140*(x*e + d)^m*a^3*b^3*d^2*m^4*x^2*e^5 - 4980*(x*e + d)^m*a^2*b^4*d^2*m^3*x^3*e^5 - 2490*(x*e + d)^m*a*b^5*d^2*m^2*x^4*e^5 - 144*(x*e + d)^m*b^6*d^2*m*x^5*e^5 + 120*(x*e + d)^m*a^3*b^3*d^3*m^4*x*e^4 + 2520*(x*e + d)^m*a^2*b^4*d^3*m^3*x^2*e^4 + 2760*(x*e + d)^m*a*b^5*d^3*m^2*x^3*e^4 + 180*(x*e + d)^m*b^6*d^3*m*x^4*e^4 - 360*(x*e + d)^m*a^2*b^4*d^4*m^3*x*e^3 - 2880*(x*e + d)^m*a*b^5*d^4*m^2*x^2*e^3 - 240*(x*e + d)^m*b^6*d^4*m*x^3*e^3 + 720*(x*e + d)^m*a*b^5*d^5*m^2*x*e^2 + 360*(x*e + d)^m*b^6*d^5*m*x^2*e^2 - 720*(x*e + d)^m*b^6*d^6*m*x*e + (x*e + d)^m*a^6*m^6*x*e^7 + 156*(x*e + d)^m*a^5*b*m^5*x^2*e^7 + 3705*(x*e + d)^m*a^4*b^2*m^4*x^3*e^7 + 21120*(x*e + d)^m*a^3*b^3*m^3*x^4*e^7 + 32160*(x*e + d)^m*a^2*b^4*m^2*x^5*e^7 + 12228*(x*e + d)^m*a*b^5*m*x^6*e^7 + 720*(x*e + d)^m*b^6*x^7*e^7 + (x*e + d)^m*a^6*d*m^6*e^6 + 150*(x*e + d)^m*a^5*b*d*m^5*x*e^6 + 3015*(x*e + d)^m*a^4*b^2*d*m^4*x^2*e^6 + 11340*(x*e + d)^m*a^3*b^3*d*m^3*x^3*e^6 + 8100*(x*e + d)^m*a^2*b^4*d*m^2*x^4*e^6 + 1008*(x*e + d)^m*a*b^5*d*m*x^5*e^6 - 6*(x*e + d)^m*a^5*b*d^2*m^5*e^5 - 660*(x*e + d)^m*a^4*b^2*d^2*m^4*x*e^5 - 7500*(x*e + d)^m*a^3*b^3*d^2*m^3*x^2*e^5 - 9120*(x*e + d)^m*a^2*b^4*d^2*m^2*x^3*e^5 - 1260*(x*e + d)^m*a*b^5*d^2*m*x^4*e^5 + 30*(x*e + d)^m*a^4*b^2*d^3*m^4*e^4 + 2160*(x*e + d)^m*a^3*b^3*d^3*m^3*x*e^4 + 9900*(x*e + d)^m*a^2*b^4*d^3*m^2*x^2*e^4 + 1680*(x*e + d)^m*a*b^5*d^3*m*x^3*e^4 - 120*(x*e + d)^m*a^3*b^3*d^4*m^3*e^3 - 4680*(x*e + d)^m*a^2*b^4*d^4*m^2*x*e^3 - 2520*(x*e + d)^m*a*b^5*d^4*m*x^2*e^3 + 360*(x*e + d)^m*a^2*b^4*d^5*m^2*e^2 + 5040*(x*e + d)^m*a*b^5*d^5*m*x*e^2 - 720*(x*e + d)^m*a*b^5*d^6*m*e + 720*(x*e + d)^m*b^6*d^7 + 27*(x*e + d)^m*a^6*m^5*x*e^7 + 1620*(x*e + d)^m*a^5*b*m^4*x^2*e^7 + 18285*(x*e + d)^m*a^4*b^2*m^3*x^3*e^7 + 50900*(x*e + d)^m*a^3*b^3*m^2*x^4*e^7 + 36180*(x*e + d)^m*a^2*b^4*m*x^5*e^7 + 5040*(x*e + d)^m*a*b^5*x^6*e^7 + 27*(x*e + d)^m*a^6*d*m^5*e^6 + 1470*(x*e + d)^m*a^5*b*d*m^4*x*e^6 + 12255*(x*e + d)^m*a^4*b^2*d*m^3*x^2*e^6 + 16880*(x*e + d)^m*a^3*b^3*d*m^2*x^3*e^6 + 3780*(x*e + d)^m*a^2*b^4*d*m*x^4*e^6 - 150*(x*e + d)^m*a^5*b*d^2*m^4*e^5 - 5370*(x*e + d)^m*a^4*b^2*d^2*m^3*x*e^5 - 19020*(x*e + d)^m*a^3*b^3*d^2*m^2*x^2*e^5 - 5040*(x*e + d)^m*a^2*b^4*d^2*m*x^3*e^5 + 660*(x*e + d)^m*a^4*b^2*d^3*m^3*e^4 + 12840*(x*e + d)^m*a^3*b^3*d^3*m^2*x*e^4 + 7560*(x*e + d)^m*a^2*b^4*d^3*m*x^2*e^4 - 2160*(x*e + d)^m*a^3*b^3*d^4*m^2*e^3 - 15120*(x*e + d)^m*a^2*b^4*d^4*m*x*e^3 + 4680*(x*e + d)^m*a^2*b^4*d^5*m*e^2 - 5040*(x*e + d)^m*a*b^5*d^6*e + 295*(x*e + d)^m*a^6*m^4*x*e^7 + 8520*(x*e + d)^m*a^5*b*m^3*x^2*e^7 + 46680*(x*e + d)^m*a^4*b^2*m^2*x^3*e^7 + 59040*(x*e + d)^m*a^3*b^3*m*x^4*e^7 + 15120*(x*e + d)^m*a^2*b^4*x^5*e^7 + 295*(x*e + d)^m*a^6*d*m^4*e^6 + 7050*(x*e + d)^m*a^5*b*d*m^3*x*e^6 + 22170*(x*e + d)^m*a^4*b^2*d*m^2*x^2*e^6 + 8400*(x*e + d)^m*a^3*b^3*d*m*x^3*e^6 - 1470*(x*e + d)^m*a^5*b*d^2*m^3*e^5 - 19140*(x*e + d)^m*a^4*b^2*d^2*m^2*x*e^5 - 12600*(x*e + d)^m*a^3*b^3*d^2*m*x^2*e^5 + 5370*(x*e + d)^m*a^4*b^2*d^3*m^2*e^4 + 25200*(x*e + d)^m*a^3*b^3*d^3*m*x*e^4 - 12840*(x*e + d)^m*a^3*b^3*d^4*m*e^3 + 15120*(x*e + d)^m*a^2*b^4*d^5*e^2 + 1665*(x*e + d)^m*a^6*m^3*x*e^7 + 23574*(x*e + d)^m*a^5*b*m^2*x^2*e^7 + 56940*(x*e + d)^m*a^4*b^2*m*x^3*e^7 + 25200*(x*e + d)^m*a^3*b^3*x^4*e^7 + 1665*(x*e + d)^m*a^6*d*m^3*e^6 + 16524*(x*e + d)^m*a^5*b*d*m^2*x*e^6 + 12600*(x*e + d)^m*a^4*b^2*d*m*x^2*e^6 - 7050*(x*e + d)^m*a^5*b*d^2*m^2*e^5 - 25200*(x*e + d)^m*a^4*b^2*d^2*m*x*e^5 + 19140*(x*e + d)^m*a^4*b^2*d^3*m*e^4 - 25200*(x*e + d)^m*a^3*b^3*d^4*e^3 + 5104*(x*e + d)^m*a^6*m^2*x*e^7 + 31644*(x*e + d)^m*a^5*b*m*x^2*e^7 + 25200*(x*e + d)^m*a^4*b^2*x^3*e^7 + 5104*(x*e + d)^m*a^6*d*m^2*e^6 + 15120*(x*e + d)^m*a^5*b*d*m*x*e^6 - 16524*(x*e + d)^m*a^5*b*d^2*m*e^5 + 25200*(x*e + d)^m*a^4*b^2*d^3*e^4 + 8028*(x*e + d)^m*a^6*m*x*e^7 + 15120*(x*e + d)^m*a^5*b*x^2*e^7 + 8028*(x*e + d)^m*a^6*d*m*e^6 - 15120*(x*e + d)^m*a^5*b*d^2*e^5 + 5040*(x*e + d)^m*a^6*x*e^7 + 5040*(x*e + d)^m*a^6*d*e^6)/(m^7*e^7 + 28*m^6*e^7 + 322*m^5*e^7 + 1960*m^4*e^7 + 6769*m^3*e^7 + 13132*m^2*e^7 + 13068*m*e^7 + 5040*e^7)","B",0
1732,1,1529,0,0.216975," ","integrate((e*x+d)^m*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\frac{{\left(x e + d\right)}^{m} b^{4} m^{4} x^{5} e^{5} + {\left(x e + d\right)}^{m} b^{4} d m^{4} x^{4} e^{4} + 4 \, {\left(x e + d\right)}^{m} a b^{3} m^{4} x^{4} e^{5} + 10 \, {\left(x e + d\right)}^{m} b^{4} m^{3} x^{5} e^{5} + 4 \, {\left(x e + d\right)}^{m} a b^{3} d m^{4} x^{3} e^{4} + 6 \, {\left(x e + d\right)}^{m} b^{4} d m^{3} x^{4} e^{4} - 4 \, {\left(x e + d\right)}^{m} b^{4} d^{2} m^{3} x^{3} e^{3} + 6 \, {\left(x e + d\right)}^{m} a^{2} b^{2} m^{4} x^{3} e^{5} + 44 \, {\left(x e + d\right)}^{m} a b^{3} m^{3} x^{4} e^{5} + 35 \, {\left(x e + d\right)}^{m} b^{4} m^{2} x^{5} e^{5} + 6 \, {\left(x e + d\right)}^{m} a^{2} b^{2} d m^{4} x^{2} e^{4} + 32 \, {\left(x e + d\right)}^{m} a b^{3} d m^{3} x^{3} e^{4} + 11 \, {\left(x e + d\right)}^{m} b^{4} d m^{2} x^{4} e^{4} - 12 \, {\left(x e + d\right)}^{m} a b^{3} d^{2} m^{3} x^{2} e^{3} - 12 \, {\left(x e + d\right)}^{m} b^{4} d^{2} m^{2} x^{3} e^{3} + 12 \, {\left(x e + d\right)}^{m} b^{4} d^{3} m^{2} x^{2} e^{2} + 4 \, {\left(x e + d\right)}^{m} a^{3} b m^{4} x^{2} e^{5} + 72 \, {\left(x e + d\right)}^{m} a^{2} b^{2} m^{3} x^{3} e^{5} + 164 \, {\left(x e + d\right)}^{m} a b^{3} m^{2} x^{4} e^{5} + 50 \, {\left(x e + d\right)}^{m} b^{4} m x^{5} e^{5} + 4 \, {\left(x e + d\right)}^{m} a^{3} b d m^{4} x e^{4} + 60 \, {\left(x e + d\right)}^{m} a^{2} b^{2} d m^{3} x^{2} e^{4} + 68 \, {\left(x e + d\right)}^{m} a b^{3} d m^{2} x^{3} e^{4} + 6 \, {\left(x e + d\right)}^{m} b^{4} d m x^{4} e^{4} - 12 \, {\left(x e + d\right)}^{m} a^{2} b^{2} d^{2} m^{3} x e^{3} - 72 \, {\left(x e + d\right)}^{m} a b^{3} d^{2} m^{2} x^{2} e^{3} - 8 \, {\left(x e + d\right)}^{m} b^{4} d^{2} m x^{3} e^{3} + 24 \, {\left(x e + d\right)}^{m} a b^{3} d^{3} m^{2} x e^{2} + 12 \, {\left(x e + d\right)}^{m} b^{4} d^{3} m x^{2} e^{2} - 24 \, {\left(x e + d\right)}^{m} b^{4} d^{4} m x e + {\left(x e + d\right)}^{m} a^{4} m^{4} x e^{5} + 52 \, {\left(x e + d\right)}^{m} a^{3} b m^{3} x^{2} e^{5} + 294 \, {\left(x e + d\right)}^{m} a^{2} b^{2} m^{2} x^{3} e^{5} + 244 \, {\left(x e + d\right)}^{m} a b^{3} m x^{4} e^{5} + 24 \, {\left(x e + d\right)}^{m} b^{4} x^{5} e^{5} + {\left(x e + d\right)}^{m} a^{4} d m^{4} e^{4} + 48 \, {\left(x e + d\right)}^{m} a^{3} b d m^{3} x e^{4} + 174 \, {\left(x e + d\right)}^{m} a^{2} b^{2} d m^{2} x^{2} e^{4} + 40 \, {\left(x e + d\right)}^{m} a b^{3} d m x^{3} e^{4} - 4 \, {\left(x e + d\right)}^{m} a^{3} b d^{2} m^{3} e^{3} - 108 \, {\left(x e + d\right)}^{m} a^{2} b^{2} d^{2} m^{2} x e^{3} - 60 \, {\left(x e + d\right)}^{m} a b^{3} d^{2} m x^{2} e^{3} + 12 \, {\left(x e + d\right)}^{m} a^{2} b^{2} d^{3} m^{2} e^{2} + 120 \, {\left(x e + d\right)}^{m} a b^{3} d^{3} m x e^{2} - 24 \, {\left(x e + d\right)}^{m} a b^{3} d^{4} m e + 24 \, {\left(x e + d\right)}^{m} b^{4} d^{5} + 14 \, {\left(x e + d\right)}^{m} a^{4} m^{3} x e^{5} + 236 \, {\left(x e + d\right)}^{m} a^{3} b m^{2} x^{2} e^{5} + 468 \, {\left(x e + d\right)}^{m} a^{2} b^{2} m x^{3} e^{5} + 120 \, {\left(x e + d\right)}^{m} a b^{3} x^{4} e^{5} + 14 \, {\left(x e + d\right)}^{m} a^{4} d m^{3} e^{4} + 188 \, {\left(x e + d\right)}^{m} a^{3} b d m^{2} x e^{4} + 120 \, {\left(x e + d\right)}^{m} a^{2} b^{2} d m x^{2} e^{4} - 48 \, {\left(x e + d\right)}^{m} a^{3} b d^{2} m^{2} e^{3} - 240 \, {\left(x e + d\right)}^{m} a^{2} b^{2} d^{2} m x e^{3} + 108 \, {\left(x e + d\right)}^{m} a^{2} b^{2} d^{3} m e^{2} - 120 \, {\left(x e + d\right)}^{m} a b^{3} d^{4} e + 71 \, {\left(x e + d\right)}^{m} a^{4} m^{2} x e^{5} + 428 \, {\left(x e + d\right)}^{m} a^{3} b m x^{2} e^{5} + 240 \, {\left(x e + d\right)}^{m} a^{2} b^{2} x^{3} e^{5} + 71 \, {\left(x e + d\right)}^{m} a^{4} d m^{2} e^{4} + 240 \, {\left(x e + d\right)}^{m} a^{3} b d m x e^{4} - 188 \, {\left(x e + d\right)}^{m} a^{3} b d^{2} m e^{3} + 240 \, {\left(x e + d\right)}^{m} a^{2} b^{2} d^{3} e^{2} + 154 \, {\left(x e + d\right)}^{m} a^{4} m x e^{5} + 240 \, {\left(x e + d\right)}^{m} a^{3} b x^{2} e^{5} + 154 \, {\left(x e + d\right)}^{m} a^{4} d m e^{4} - 240 \, {\left(x e + d\right)}^{m} a^{3} b d^{2} e^{3} + 120 \, {\left(x e + d\right)}^{m} a^{4} x e^{5} + 120 \, {\left(x e + d\right)}^{m} a^{4} d e^{4}}{m^{5} e^{5} + 15 \, m^{4} e^{5} + 85 \, m^{3} e^{5} + 225 \, m^{2} e^{5} + 274 \, m e^{5} + 120 \, e^{5}}"," ",0,"((x*e + d)^m*b^4*m^4*x^5*e^5 + (x*e + d)^m*b^4*d*m^4*x^4*e^4 + 4*(x*e + d)^m*a*b^3*m^4*x^4*e^5 + 10*(x*e + d)^m*b^4*m^3*x^5*e^5 + 4*(x*e + d)^m*a*b^3*d*m^4*x^3*e^4 + 6*(x*e + d)^m*b^4*d*m^3*x^4*e^4 - 4*(x*e + d)^m*b^4*d^2*m^3*x^3*e^3 + 6*(x*e + d)^m*a^2*b^2*m^4*x^3*e^5 + 44*(x*e + d)^m*a*b^3*m^3*x^4*e^5 + 35*(x*e + d)^m*b^4*m^2*x^5*e^5 + 6*(x*e + d)^m*a^2*b^2*d*m^4*x^2*e^4 + 32*(x*e + d)^m*a*b^3*d*m^3*x^3*e^4 + 11*(x*e + d)^m*b^4*d*m^2*x^4*e^4 - 12*(x*e + d)^m*a*b^3*d^2*m^3*x^2*e^3 - 12*(x*e + d)^m*b^4*d^2*m^2*x^3*e^3 + 12*(x*e + d)^m*b^4*d^3*m^2*x^2*e^2 + 4*(x*e + d)^m*a^3*b*m^4*x^2*e^5 + 72*(x*e + d)^m*a^2*b^2*m^3*x^3*e^5 + 164*(x*e + d)^m*a*b^3*m^2*x^4*e^5 + 50*(x*e + d)^m*b^4*m*x^5*e^5 + 4*(x*e + d)^m*a^3*b*d*m^4*x*e^4 + 60*(x*e + d)^m*a^2*b^2*d*m^3*x^2*e^4 + 68*(x*e + d)^m*a*b^3*d*m^2*x^3*e^4 + 6*(x*e + d)^m*b^4*d*m*x^4*e^4 - 12*(x*e + d)^m*a^2*b^2*d^2*m^3*x*e^3 - 72*(x*e + d)^m*a*b^3*d^2*m^2*x^2*e^3 - 8*(x*e + d)^m*b^4*d^2*m*x^3*e^3 + 24*(x*e + d)^m*a*b^3*d^3*m^2*x*e^2 + 12*(x*e + d)^m*b^4*d^3*m*x^2*e^2 - 24*(x*e + d)^m*b^4*d^4*m*x*e + (x*e + d)^m*a^4*m^4*x*e^5 + 52*(x*e + d)^m*a^3*b*m^3*x^2*e^5 + 294*(x*e + d)^m*a^2*b^2*m^2*x^3*e^5 + 244*(x*e + d)^m*a*b^3*m*x^4*e^5 + 24*(x*e + d)^m*b^4*x^5*e^5 + (x*e + d)^m*a^4*d*m^4*e^4 + 48*(x*e + d)^m*a^3*b*d*m^3*x*e^4 + 174*(x*e + d)^m*a^2*b^2*d*m^2*x^2*e^4 + 40*(x*e + d)^m*a*b^3*d*m*x^3*e^4 - 4*(x*e + d)^m*a^3*b*d^2*m^3*e^3 - 108*(x*e + d)^m*a^2*b^2*d^2*m^2*x*e^3 - 60*(x*e + d)^m*a*b^3*d^2*m*x^2*e^3 + 12*(x*e + d)^m*a^2*b^2*d^3*m^2*e^2 + 120*(x*e + d)^m*a*b^3*d^3*m*x*e^2 - 24*(x*e + d)^m*a*b^3*d^4*m*e + 24*(x*e + d)^m*b^4*d^5 + 14*(x*e + d)^m*a^4*m^3*x*e^5 + 236*(x*e + d)^m*a^3*b*m^2*x^2*e^5 + 468*(x*e + d)^m*a^2*b^2*m*x^3*e^5 + 120*(x*e + d)^m*a*b^3*x^4*e^5 + 14*(x*e + d)^m*a^4*d*m^3*e^4 + 188*(x*e + d)^m*a^3*b*d*m^2*x*e^4 + 120*(x*e + d)^m*a^2*b^2*d*m*x^2*e^4 - 48*(x*e + d)^m*a^3*b*d^2*m^2*e^3 - 240*(x*e + d)^m*a^2*b^2*d^2*m*x*e^3 + 108*(x*e + d)^m*a^2*b^2*d^3*m*e^2 - 120*(x*e + d)^m*a*b^3*d^4*e + 71*(x*e + d)^m*a^4*m^2*x*e^5 + 428*(x*e + d)^m*a^3*b*m*x^2*e^5 + 240*(x*e + d)^m*a^2*b^2*x^3*e^5 + 71*(x*e + d)^m*a^4*d*m^2*e^4 + 240*(x*e + d)^m*a^3*b*d*m*x*e^4 - 188*(x*e + d)^m*a^3*b*d^2*m*e^3 + 240*(x*e + d)^m*a^2*b^2*d^3*e^2 + 154*(x*e + d)^m*a^4*m*x*e^5 + 240*(x*e + d)^m*a^3*b*x^2*e^5 + 154*(x*e + d)^m*a^4*d*m*e^4 - 240*(x*e + d)^m*a^3*b*d^2*e^3 + 120*(x*e + d)^m*a^4*x*e^5 + 120*(x*e + d)^m*a^4*d*e^4)/(m^5*e^5 + 15*m^4*e^5 + 85*m^3*e^5 + 225*m^2*e^5 + 274*m*e^5 + 120*e^5)","B",0
1733,1,388,0,0.175163," ","integrate((e*x+d)^m*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\frac{{\left(x e + d\right)}^{m} b^{2} m^{2} x^{3} e^{3} + {\left(x e + d\right)}^{m} b^{2} d m^{2} x^{2} e^{2} + 2 \, {\left(x e + d\right)}^{m} a b m^{2} x^{2} e^{3} + 3 \, {\left(x e + d\right)}^{m} b^{2} m x^{3} e^{3} + 2 \, {\left(x e + d\right)}^{m} a b d m^{2} x e^{2} + {\left(x e + d\right)}^{m} b^{2} d m x^{2} e^{2} - 2 \, {\left(x e + d\right)}^{m} b^{2} d^{2} m x e + {\left(x e + d\right)}^{m} a^{2} m^{2} x e^{3} + 8 \, {\left(x e + d\right)}^{m} a b m x^{2} e^{3} + 2 \, {\left(x e + d\right)}^{m} b^{2} x^{3} e^{3} + {\left(x e + d\right)}^{m} a^{2} d m^{2} e^{2} + 6 \, {\left(x e + d\right)}^{m} a b d m x e^{2} - 2 \, {\left(x e + d\right)}^{m} a b d^{2} m e + 2 \, {\left(x e + d\right)}^{m} b^{2} d^{3} + 5 \, {\left(x e + d\right)}^{m} a^{2} m x e^{3} + 6 \, {\left(x e + d\right)}^{m} a b x^{2} e^{3} + 5 \, {\left(x e + d\right)}^{m} a^{2} d m e^{2} - 6 \, {\left(x e + d\right)}^{m} a b d^{2} e + 6 \, {\left(x e + d\right)}^{m} a^{2} x e^{3} + 6 \, {\left(x e + d\right)}^{m} a^{2} d e^{2}}{m^{3} e^{3} + 6 \, m^{2} e^{3} + 11 \, m e^{3} + 6 \, e^{3}}"," ",0,"((x*e + d)^m*b^2*m^2*x^3*e^3 + (x*e + d)^m*b^2*d*m^2*x^2*e^2 + 2*(x*e + d)^m*a*b*m^2*x^2*e^3 + 3*(x*e + d)^m*b^2*m*x^3*e^3 + 2*(x*e + d)^m*a*b*d*m^2*x*e^2 + (x*e + d)^m*b^2*d*m*x^2*e^2 - 2*(x*e + d)^m*b^2*d^2*m*x*e + (x*e + d)^m*a^2*m^2*x*e^3 + 8*(x*e + d)^m*a*b*m*x^2*e^3 + 2*(x*e + d)^m*b^2*x^3*e^3 + (x*e + d)^m*a^2*d*m^2*e^2 + 6*(x*e + d)^m*a*b*d*m*x*e^2 - 2*(x*e + d)^m*a*b*d^2*m*e + 2*(x*e + d)^m*b^2*d^3 + 5*(x*e + d)^m*a^2*m*x*e^3 + 6*(x*e + d)^m*a*b*x^2*e^3 + 5*(x*e + d)^m*a^2*d*m*e^2 - 6*(x*e + d)^m*a*b*d^2*e + 6*(x*e + d)^m*a^2*x*e^3 + 6*(x*e + d)^m*a^2*d*e^2)/(m^3*e^3 + 6*m^2*e^3 + 11*m*e^3 + 6*e^3)","B",0
1734,0,0,0,0.000000," ","integrate((e*x+d)^m/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{m}}{b^{2} x^{2} + 2 \, a b x + a^{2}}\,{d x}"," ",0,"integrate((e*x + d)^m/(b^2*x^2 + 2*a*b*x + a^2), x)","F",0
1735,0,0,0,0.000000," ","integrate((e*x+d)^m/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{m}}{{\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{2}}\,{d x}"," ",0,"integrate((e*x + d)^m/(b^2*x^2 + 2*a*b*x + a^2)^2, x)","F",0
1736,0,0,0,0.000000," ","integrate((e*x+d)^m/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{m}}{{\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{3}}\,{d x}"," ",0,"integrate((e*x + d)^m/(b^2*x^2 + 2*a*b*x + a^2)^3, x)","F",0
1737,1,3197,0,0.481607," ","integrate((e*x+d)^m*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\frac{{\left(x e + d\right)}^{m} b^{5} m^{5} x^{6} e^{6} \mathrm{sgn}\left(b x + a\right) + {\left(x e + d\right)}^{m} b^{5} d m^{5} x^{5} e^{5} \mathrm{sgn}\left(b x + a\right) + 5 \, {\left(x e + d\right)}^{m} a b^{4} m^{5} x^{5} e^{6} \mathrm{sgn}\left(b x + a\right) + 15 \, {\left(x e + d\right)}^{m} b^{5} m^{4} x^{6} e^{6} \mathrm{sgn}\left(b x + a\right) + 5 \, {\left(x e + d\right)}^{m} a b^{4} d m^{5} x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) + 10 \, {\left(x e + d\right)}^{m} b^{5} d m^{4} x^{5} e^{5} \mathrm{sgn}\left(b x + a\right) - 5 \, {\left(x e + d\right)}^{m} b^{5} d^{2} m^{4} x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) + 10 \, {\left(x e + d\right)}^{m} a^{2} b^{3} m^{5} x^{4} e^{6} \mathrm{sgn}\left(b x + a\right) + 80 \, {\left(x e + d\right)}^{m} a b^{4} m^{4} x^{5} e^{6} \mathrm{sgn}\left(b x + a\right) + 85 \, {\left(x e + d\right)}^{m} b^{5} m^{3} x^{6} e^{6} \mathrm{sgn}\left(b x + a\right) + 10 \, {\left(x e + d\right)}^{m} a^{2} b^{3} d m^{5} x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) + 60 \, {\left(x e + d\right)}^{m} a b^{4} d m^{4} x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) + 35 \, {\left(x e + d\right)}^{m} b^{5} d m^{3} x^{5} e^{5} \mathrm{sgn}\left(b x + a\right) - 20 \, {\left(x e + d\right)}^{m} a b^{4} d^{2} m^{4} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) - 30 \, {\left(x e + d\right)}^{m} b^{5} d^{2} m^{3} x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) + 20 \, {\left(x e + d\right)}^{m} b^{5} d^{3} m^{3} x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 10 \, {\left(x e + d\right)}^{m} a^{3} b^{2} m^{5} x^{3} e^{6} \mathrm{sgn}\left(b x + a\right) + 170 \, {\left(x e + d\right)}^{m} a^{2} b^{3} m^{4} x^{4} e^{6} \mathrm{sgn}\left(b x + a\right) + 475 \, {\left(x e + d\right)}^{m} a b^{4} m^{3} x^{5} e^{6} \mathrm{sgn}\left(b x + a\right) + 225 \, {\left(x e + d\right)}^{m} b^{5} m^{2} x^{6} e^{6} \mathrm{sgn}\left(b x + a\right) + 10 \, {\left(x e + d\right)}^{m} a^{3} b^{2} d m^{5} x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) + 140 \, {\left(x e + d\right)}^{m} a^{2} b^{3} d m^{4} x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) + 235 \, {\left(x e + d\right)}^{m} a b^{4} d m^{3} x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) + 50 \, {\left(x e + d\right)}^{m} b^{5} d m^{2} x^{5} e^{5} \mathrm{sgn}\left(b x + a\right) - 30 \, {\left(x e + d\right)}^{m} a^{2} b^{3} d^{2} m^{4} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) - 180 \, {\left(x e + d\right)}^{m} a b^{4} d^{2} m^{3} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) - 55 \, {\left(x e + d\right)}^{m} b^{5} d^{2} m^{2} x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) + 60 \, {\left(x e + d\right)}^{m} a b^{4} d^{3} m^{3} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 60 \, {\left(x e + d\right)}^{m} b^{5} d^{3} m^{2} x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) - 60 \, {\left(x e + d\right)}^{m} b^{5} d^{4} m^{2} x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 5 \, {\left(x e + d\right)}^{m} a^{4} b m^{5} x^{2} e^{6} \mathrm{sgn}\left(b x + a\right) + 180 \, {\left(x e + d\right)}^{m} a^{3} b^{2} m^{4} x^{3} e^{6} \mathrm{sgn}\left(b x + a\right) + 1070 \, {\left(x e + d\right)}^{m} a^{2} b^{3} m^{3} x^{4} e^{6} \mathrm{sgn}\left(b x + a\right) + 1300 \, {\left(x e + d\right)}^{m} a b^{4} m^{2} x^{5} e^{6} \mathrm{sgn}\left(b x + a\right) + 274 \, {\left(x e + d\right)}^{m} b^{5} m x^{6} e^{6} \mathrm{sgn}\left(b x + a\right) + 5 \, {\left(x e + d\right)}^{m} a^{4} b d m^{5} x e^{5} \mathrm{sgn}\left(b x + a\right) + 160 \, {\left(x e + d\right)}^{m} a^{3} b^{2} d m^{4} x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) + 650 \, {\left(x e + d\right)}^{m} a^{2} b^{3} d m^{3} x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) + 360 \, {\left(x e + d\right)}^{m} a b^{4} d m^{2} x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) + 24 \, {\left(x e + d\right)}^{m} b^{5} d m x^{5} e^{5} \mathrm{sgn}\left(b x + a\right) - 20 \, {\left(x e + d\right)}^{m} a^{3} b^{2} d^{2} m^{4} x e^{4} \mathrm{sgn}\left(b x + a\right) - 360 \, {\left(x e + d\right)}^{m} a^{2} b^{3} d^{2} m^{3} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) - 400 \, {\left(x e + d\right)}^{m} a b^{4} d^{2} m^{2} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) - 30 \, {\left(x e + d\right)}^{m} b^{5} d^{2} m x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) + 60 \, {\left(x e + d\right)}^{m} a^{2} b^{3} d^{3} m^{3} x e^{3} \mathrm{sgn}\left(b x + a\right) + 420 \, {\left(x e + d\right)}^{m} a b^{4} d^{3} m^{2} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 40 \, {\left(x e + d\right)}^{m} b^{5} d^{3} m x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) - 120 \, {\left(x e + d\right)}^{m} a b^{4} d^{4} m^{2} x e^{2} \mathrm{sgn}\left(b x + a\right) - 60 \, {\left(x e + d\right)}^{m} b^{5} d^{4} m x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 120 \, {\left(x e + d\right)}^{m} b^{5} d^{5} m x e \mathrm{sgn}\left(b x + a\right) + {\left(x e + d\right)}^{m} a^{5} m^{5} x e^{6} \mathrm{sgn}\left(b x + a\right) + 95 \, {\left(x e + d\right)}^{m} a^{4} b m^{4} x^{2} e^{6} \mathrm{sgn}\left(b x + a\right) + 1210 \, {\left(x e + d\right)}^{m} a^{3} b^{2} m^{3} x^{3} e^{6} \mathrm{sgn}\left(b x + a\right) + 3070 \, {\left(x e + d\right)}^{m} a^{2} b^{3} m^{2} x^{4} e^{6} \mathrm{sgn}\left(b x + a\right) + 1620 \, {\left(x e + d\right)}^{m} a b^{4} m x^{5} e^{6} \mathrm{sgn}\left(b x + a\right) + 120 \, {\left(x e + d\right)}^{m} b^{5} x^{6} e^{6} \mathrm{sgn}\left(b x + a\right) + {\left(x e + d\right)}^{m} a^{5} d m^{5} e^{5} \mathrm{sgn}\left(b x + a\right) + 90 \, {\left(x e + d\right)}^{m} a^{4} b d m^{4} x e^{5} \mathrm{sgn}\left(b x + a\right) + 890 \, {\left(x e + d\right)}^{m} a^{3} b^{2} d m^{3} x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) + 1120 \, {\left(x e + d\right)}^{m} a^{2} b^{3} d m^{2} x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) + 180 \, {\left(x e + d\right)}^{m} a b^{4} d m x^{4} e^{5} \mathrm{sgn}\left(b x + a\right) - 5 \, {\left(x e + d\right)}^{m} a^{4} b d^{2} m^{4} e^{4} \mathrm{sgn}\left(b x + a\right) - 300 \, {\left(x e + d\right)}^{m} a^{3} b^{2} d^{2} m^{3} x e^{4} \mathrm{sgn}\left(b x + a\right) - 1230 \, {\left(x e + d\right)}^{m} a^{2} b^{3} d^{2} m^{2} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) - 240 \, {\left(x e + d\right)}^{m} a b^{4} d^{2} m x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 20 \, {\left(x e + d\right)}^{m} a^{3} b^{2} d^{3} m^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 660 \, {\left(x e + d\right)}^{m} a^{2} b^{3} d^{3} m^{2} x e^{3} \mathrm{sgn}\left(b x + a\right) + 360 \, {\left(x e + d\right)}^{m} a b^{4} d^{3} m x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - 60 \, {\left(x e + d\right)}^{m} a^{2} b^{3} d^{4} m^{2} e^{2} \mathrm{sgn}\left(b x + a\right) - 720 \, {\left(x e + d\right)}^{m} a b^{4} d^{4} m x e^{2} \mathrm{sgn}\left(b x + a\right) + 120 \, {\left(x e + d\right)}^{m} a b^{4} d^{5} m e \mathrm{sgn}\left(b x + a\right) - 120 \, {\left(x e + d\right)}^{m} b^{5} d^{6} \mathrm{sgn}\left(b x + a\right) + 20 \, {\left(x e + d\right)}^{m} a^{5} m^{4} x e^{6} \mathrm{sgn}\left(b x + a\right) + 685 \, {\left(x e + d\right)}^{m} a^{4} b m^{3} x^{2} e^{6} \mathrm{sgn}\left(b x + a\right) + 3720 \, {\left(x e + d\right)}^{m} a^{3} b^{2} m^{2} x^{3} e^{6} \mathrm{sgn}\left(b x + a\right) + 3960 \, {\left(x e + d\right)}^{m} a^{2} b^{3} m x^{4} e^{6} \mathrm{sgn}\left(b x + a\right) + 720 \, {\left(x e + d\right)}^{m} a b^{4} x^{5} e^{6} \mathrm{sgn}\left(b x + a\right) + 20 \, {\left(x e + d\right)}^{m} a^{5} d m^{4} e^{5} \mathrm{sgn}\left(b x + a\right) + 595 \, {\left(x e + d\right)}^{m} a^{4} b d m^{3} x e^{5} \mathrm{sgn}\left(b x + a\right) + 1940 \, {\left(x e + d\right)}^{m} a^{3} b^{2} d m^{2} x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) + 600 \, {\left(x e + d\right)}^{m} a^{2} b^{3} d m x^{3} e^{5} \mathrm{sgn}\left(b x + a\right) - 90 \, {\left(x e + d\right)}^{m} a^{4} b d^{2} m^{3} e^{4} \mathrm{sgn}\left(b x + a\right) - 1480 \, {\left(x e + d\right)}^{m} a^{3} b^{2} d^{2} m^{2} x e^{4} \mathrm{sgn}\left(b x + a\right) - 900 \, {\left(x e + d\right)}^{m} a^{2} b^{3} d^{2} m x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 300 \, {\left(x e + d\right)}^{m} a^{3} b^{2} d^{3} m^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 1800 \, {\left(x e + d\right)}^{m} a^{2} b^{3} d^{3} m x e^{3} \mathrm{sgn}\left(b x + a\right) - 660 \, {\left(x e + d\right)}^{m} a^{2} b^{3} d^{4} m e^{2} \mathrm{sgn}\left(b x + a\right) + 720 \, {\left(x e + d\right)}^{m} a b^{4} d^{5} e \mathrm{sgn}\left(b x + a\right) + 155 \, {\left(x e + d\right)}^{m} a^{5} m^{3} x e^{6} \mathrm{sgn}\left(b x + a\right) + 2305 \, {\left(x e + d\right)}^{m} a^{4} b m^{2} x^{2} e^{6} \mathrm{sgn}\left(b x + a\right) + 5080 \, {\left(x e + d\right)}^{m} a^{3} b^{2} m x^{3} e^{6} \mathrm{sgn}\left(b x + a\right) + 1800 \, {\left(x e + d\right)}^{m} a^{2} b^{3} x^{4} e^{6} \mathrm{sgn}\left(b x + a\right) + 155 \, {\left(x e + d\right)}^{m} a^{5} d m^{3} e^{5} \mathrm{sgn}\left(b x + a\right) + 1710 \, {\left(x e + d\right)}^{m} a^{4} b d m^{2} x e^{5} \mathrm{sgn}\left(b x + a\right) + 1200 \, {\left(x e + d\right)}^{m} a^{3} b^{2} d m x^{2} e^{5} \mathrm{sgn}\left(b x + a\right) - 595 \, {\left(x e + d\right)}^{m} a^{4} b d^{2} m^{2} e^{4} \mathrm{sgn}\left(b x + a\right) - 2400 \, {\left(x e + d\right)}^{m} a^{3} b^{2} d^{2} m x e^{4} \mathrm{sgn}\left(b x + a\right) + 1480 \, {\left(x e + d\right)}^{m} a^{3} b^{2} d^{3} m e^{3} \mathrm{sgn}\left(b x + a\right) - 1800 \, {\left(x e + d\right)}^{m} a^{2} b^{3} d^{4} e^{2} \mathrm{sgn}\left(b x + a\right) + 580 \, {\left(x e + d\right)}^{m} a^{5} m^{2} x e^{6} \mathrm{sgn}\left(b x + a\right) + 3510 \, {\left(x e + d\right)}^{m} a^{4} b m x^{2} e^{6} \mathrm{sgn}\left(b x + a\right) + 2400 \, {\left(x e + d\right)}^{m} a^{3} b^{2} x^{3} e^{6} \mathrm{sgn}\left(b x + a\right) + 580 \, {\left(x e + d\right)}^{m} a^{5} d m^{2} e^{5} \mathrm{sgn}\left(b x + a\right) + 1800 \, {\left(x e + d\right)}^{m} a^{4} b d m x e^{5} \mathrm{sgn}\left(b x + a\right) - 1710 \, {\left(x e + d\right)}^{m} a^{4} b d^{2} m e^{4} \mathrm{sgn}\left(b x + a\right) + 2400 \, {\left(x e + d\right)}^{m} a^{3} b^{2} d^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 1044 \, {\left(x e + d\right)}^{m} a^{5} m x e^{6} \mathrm{sgn}\left(b x + a\right) + 1800 \, {\left(x e + d\right)}^{m} a^{4} b x^{2} e^{6} \mathrm{sgn}\left(b x + a\right) + 1044 \, {\left(x e + d\right)}^{m} a^{5} d m e^{5} \mathrm{sgn}\left(b x + a\right) - 1800 \, {\left(x e + d\right)}^{m} a^{4} b d^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 720 \, {\left(x e + d\right)}^{m} a^{5} x e^{6} \mathrm{sgn}\left(b x + a\right) + 720 \, {\left(x e + d\right)}^{m} a^{5} d e^{5} \mathrm{sgn}\left(b x + a\right)}{m^{6} e^{6} + 21 \, m^{5} e^{6} + 175 \, m^{4} e^{6} + 735 \, m^{3} e^{6} + 1624 \, m^{2} e^{6} + 1764 \, m e^{6} + 720 \, e^{6}}"," ",0,"((x*e + d)^m*b^5*m^5*x^6*e^6*sgn(b*x + a) + (x*e + d)^m*b^5*d*m^5*x^5*e^5*sgn(b*x + a) + 5*(x*e + d)^m*a*b^4*m^5*x^5*e^6*sgn(b*x + a) + 15*(x*e + d)^m*b^5*m^4*x^6*e^6*sgn(b*x + a) + 5*(x*e + d)^m*a*b^4*d*m^5*x^4*e^5*sgn(b*x + a) + 10*(x*e + d)^m*b^5*d*m^4*x^5*e^5*sgn(b*x + a) - 5*(x*e + d)^m*b^5*d^2*m^4*x^4*e^4*sgn(b*x + a) + 10*(x*e + d)^m*a^2*b^3*m^5*x^4*e^6*sgn(b*x + a) + 80*(x*e + d)^m*a*b^4*m^4*x^5*e^6*sgn(b*x + a) + 85*(x*e + d)^m*b^5*m^3*x^6*e^6*sgn(b*x + a) + 10*(x*e + d)^m*a^2*b^3*d*m^5*x^3*e^5*sgn(b*x + a) + 60*(x*e + d)^m*a*b^4*d*m^4*x^4*e^5*sgn(b*x + a) + 35*(x*e + d)^m*b^5*d*m^3*x^5*e^5*sgn(b*x + a) - 20*(x*e + d)^m*a*b^4*d^2*m^4*x^3*e^4*sgn(b*x + a) - 30*(x*e + d)^m*b^5*d^2*m^3*x^4*e^4*sgn(b*x + a) + 20*(x*e + d)^m*b^5*d^3*m^3*x^3*e^3*sgn(b*x + a) + 10*(x*e + d)^m*a^3*b^2*m^5*x^3*e^6*sgn(b*x + a) + 170*(x*e + d)^m*a^2*b^3*m^4*x^4*e^6*sgn(b*x + a) + 475*(x*e + d)^m*a*b^4*m^3*x^5*e^6*sgn(b*x + a) + 225*(x*e + d)^m*b^5*m^2*x^6*e^6*sgn(b*x + a) + 10*(x*e + d)^m*a^3*b^2*d*m^5*x^2*e^5*sgn(b*x + a) + 140*(x*e + d)^m*a^2*b^3*d*m^4*x^3*e^5*sgn(b*x + a) + 235*(x*e + d)^m*a*b^4*d*m^3*x^4*e^5*sgn(b*x + a) + 50*(x*e + d)^m*b^5*d*m^2*x^5*e^5*sgn(b*x + a) - 30*(x*e + d)^m*a^2*b^3*d^2*m^4*x^2*e^4*sgn(b*x + a) - 180*(x*e + d)^m*a*b^4*d^2*m^3*x^3*e^4*sgn(b*x + a) - 55*(x*e + d)^m*b^5*d^2*m^2*x^4*e^4*sgn(b*x + a) + 60*(x*e + d)^m*a*b^4*d^3*m^3*x^2*e^3*sgn(b*x + a) + 60*(x*e + d)^m*b^5*d^3*m^2*x^3*e^3*sgn(b*x + a) - 60*(x*e + d)^m*b^5*d^4*m^2*x^2*e^2*sgn(b*x + a) + 5*(x*e + d)^m*a^4*b*m^5*x^2*e^6*sgn(b*x + a) + 180*(x*e + d)^m*a^3*b^2*m^4*x^3*e^6*sgn(b*x + a) + 1070*(x*e + d)^m*a^2*b^3*m^3*x^4*e^6*sgn(b*x + a) + 1300*(x*e + d)^m*a*b^4*m^2*x^5*e^6*sgn(b*x + a) + 274*(x*e + d)^m*b^5*m*x^6*e^6*sgn(b*x + a) + 5*(x*e + d)^m*a^4*b*d*m^5*x*e^5*sgn(b*x + a) + 160*(x*e + d)^m*a^3*b^2*d*m^4*x^2*e^5*sgn(b*x + a) + 650*(x*e + d)^m*a^2*b^3*d*m^3*x^3*e^5*sgn(b*x + a) + 360*(x*e + d)^m*a*b^4*d*m^2*x^4*e^5*sgn(b*x + a) + 24*(x*e + d)^m*b^5*d*m*x^5*e^5*sgn(b*x + a) - 20*(x*e + d)^m*a^3*b^2*d^2*m^4*x*e^4*sgn(b*x + a) - 360*(x*e + d)^m*a^2*b^3*d^2*m^3*x^2*e^4*sgn(b*x + a) - 400*(x*e + d)^m*a*b^4*d^2*m^2*x^3*e^4*sgn(b*x + a) - 30*(x*e + d)^m*b^5*d^2*m*x^4*e^4*sgn(b*x + a) + 60*(x*e + d)^m*a^2*b^3*d^3*m^3*x*e^3*sgn(b*x + a) + 420*(x*e + d)^m*a*b^4*d^3*m^2*x^2*e^3*sgn(b*x + a) + 40*(x*e + d)^m*b^5*d^3*m*x^3*e^3*sgn(b*x + a) - 120*(x*e + d)^m*a*b^4*d^4*m^2*x*e^2*sgn(b*x + a) - 60*(x*e + d)^m*b^5*d^4*m*x^2*e^2*sgn(b*x + a) + 120*(x*e + d)^m*b^5*d^5*m*x*e*sgn(b*x + a) + (x*e + d)^m*a^5*m^5*x*e^6*sgn(b*x + a) + 95*(x*e + d)^m*a^4*b*m^4*x^2*e^6*sgn(b*x + a) + 1210*(x*e + d)^m*a^3*b^2*m^3*x^3*e^6*sgn(b*x + a) + 3070*(x*e + d)^m*a^2*b^3*m^2*x^4*e^6*sgn(b*x + a) + 1620*(x*e + d)^m*a*b^4*m*x^5*e^6*sgn(b*x + a) + 120*(x*e + d)^m*b^5*x^6*e^6*sgn(b*x + a) + (x*e + d)^m*a^5*d*m^5*e^5*sgn(b*x + a) + 90*(x*e + d)^m*a^4*b*d*m^4*x*e^5*sgn(b*x + a) + 890*(x*e + d)^m*a^3*b^2*d*m^3*x^2*e^5*sgn(b*x + a) + 1120*(x*e + d)^m*a^2*b^3*d*m^2*x^3*e^5*sgn(b*x + a) + 180*(x*e + d)^m*a*b^4*d*m*x^4*e^5*sgn(b*x + a) - 5*(x*e + d)^m*a^4*b*d^2*m^4*e^4*sgn(b*x + a) - 300*(x*e + d)^m*a^3*b^2*d^2*m^3*x*e^4*sgn(b*x + a) - 1230*(x*e + d)^m*a^2*b^3*d^2*m^2*x^2*e^4*sgn(b*x + a) - 240*(x*e + d)^m*a*b^4*d^2*m*x^3*e^4*sgn(b*x + a) + 20*(x*e + d)^m*a^3*b^2*d^3*m^3*e^3*sgn(b*x + a) + 660*(x*e + d)^m*a^2*b^3*d^3*m^2*x*e^3*sgn(b*x + a) + 360*(x*e + d)^m*a*b^4*d^3*m*x^2*e^3*sgn(b*x + a) - 60*(x*e + d)^m*a^2*b^3*d^4*m^2*e^2*sgn(b*x + a) - 720*(x*e + d)^m*a*b^4*d^4*m*x*e^2*sgn(b*x + a) + 120*(x*e + d)^m*a*b^4*d^5*m*e*sgn(b*x + a) - 120*(x*e + d)^m*b^5*d^6*sgn(b*x + a) + 20*(x*e + d)^m*a^5*m^4*x*e^6*sgn(b*x + a) + 685*(x*e + d)^m*a^4*b*m^3*x^2*e^6*sgn(b*x + a) + 3720*(x*e + d)^m*a^3*b^2*m^2*x^3*e^6*sgn(b*x + a) + 3960*(x*e + d)^m*a^2*b^3*m*x^4*e^6*sgn(b*x + a) + 720*(x*e + d)^m*a*b^4*x^5*e^6*sgn(b*x + a) + 20*(x*e + d)^m*a^5*d*m^4*e^5*sgn(b*x + a) + 595*(x*e + d)^m*a^4*b*d*m^3*x*e^5*sgn(b*x + a) + 1940*(x*e + d)^m*a^3*b^2*d*m^2*x^2*e^5*sgn(b*x + a) + 600*(x*e + d)^m*a^2*b^3*d*m*x^3*e^5*sgn(b*x + a) - 90*(x*e + d)^m*a^4*b*d^2*m^3*e^4*sgn(b*x + a) - 1480*(x*e + d)^m*a^3*b^2*d^2*m^2*x*e^4*sgn(b*x + a) - 900*(x*e + d)^m*a^2*b^3*d^2*m*x^2*e^4*sgn(b*x + a) + 300*(x*e + d)^m*a^3*b^2*d^3*m^2*e^3*sgn(b*x + a) + 1800*(x*e + d)^m*a^2*b^3*d^3*m*x*e^3*sgn(b*x + a) - 660*(x*e + d)^m*a^2*b^3*d^4*m*e^2*sgn(b*x + a) + 720*(x*e + d)^m*a*b^4*d^5*e*sgn(b*x + a) + 155*(x*e + d)^m*a^5*m^3*x*e^6*sgn(b*x + a) + 2305*(x*e + d)^m*a^4*b*m^2*x^2*e^6*sgn(b*x + a) + 5080*(x*e + d)^m*a^3*b^2*m*x^3*e^6*sgn(b*x + a) + 1800*(x*e + d)^m*a^2*b^3*x^4*e^6*sgn(b*x + a) + 155*(x*e + d)^m*a^5*d*m^3*e^5*sgn(b*x + a) + 1710*(x*e + d)^m*a^4*b*d*m^2*x*e^5*sgn(b*x + a) + 1200*(x*e + d)^m*a^3*b^2*d*m*x^2*e^5*sgn(b*x + a) - 595*(x*e + d)^m*a^4*b*d^2*m^2*e^4*sgn(b*x + a) - 2400*(x*e + d)^m*a^3*b^2*d^2*m*x*e^4*sgn(b*x + a) + 1480*(x*e + d)^m*a^3*b^2*d^3*m*e^3*sgn(b*x + a) - 1800*(x*e + d)^m*a^2*b^3*d^4*e^2*sgn(b*x + a) + 580*(x*e + d)^m*a^5*m^2*x*e^6*sgn(b*x + a) + 3510*(x*e + d)^m*a^4*b*m*x^2*e^6*sgn(b*x + a) + 2400*(x*e + d)^m*a^3*b^2*x^3*e^6*sgn(b*x + a) + 580*(x*e + d)^m*a^5*d*m^2*e^5*sgn(b*x + a) + 1800*(x*e + d)^m*a^4*b*d*m*x*e^5*sgn(b*x + a) - 1710*(x*e + d)^m*a^4*b*d^2*m*e^4*sgn(b*x + a) + 2400*(x*e + d)^m*a^3*b^2*d^3*e^3*sgn(b*x + a) + 1044*(x*e + d)^m*a^5*m*x*e^6*sgn(b*x + a) + 1800*(x*e + d)^m*a^4*b*x^2*e^6*sgn(b*x + a) + 1044*(x*e + d)^m*a^5*d*m*e^5*sgn(b*x + a) - 1800*(x*e + d)^m*a^4*b*d^2*e^4*sgn(b*x + a) + 720*(x*e + d)^m*a^5*x*e^6*sgn(b*x + a) + 720*(x*e + d)^m*a^5*d*e^5*sgn(b*x + a))/(m^6*e^6 + 21*m^5*e^6 + 175*m^4*e^6 + 735*m^3*e^6 + 1624*m^2*e^6 + 1764*m*e^6 + 720*e^6)","B",0
1738,1,1075,0,0.254133," ","integrate((e*x+d)^m*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\frac{{\left(x e + d\right)}^{m} b^{3} m^{3} x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) + {\left(x e + d\right)}^{m} b^{3} d m^{3} x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 3 \, {\left(x e + d\right)}^{m} a b^{2} m^{3} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 6 \, {\left(x e + d\right)}^{m} b^{3} m^{2} x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) + 3 \, {\left(x e + d\right)}^{m} a b^{2} d m^{3} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 3 \, {\left(x e + d\right)}^{m} b^{3} d m^{2} x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) - 3 \, {\left(x e + d\right)}^{m} b^{3} d^{2} m^{2} x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 3 \, {\left(x e + d\right)}^{m} a^{2} b m^{3} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 21 \, {\left(x e + d\right)}^{m} a b^{2} m^{2} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 11 \, {\left(x e + d\right)}^{m} b^{3} m x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) + 3 \, {\left(x e + d\right)}^{m} a^{2} b d m^{3} x e^{3} \mathrm{sgn}\left(b x + a\right) + 15 \, {\left(x e + d\right)}^{m} a b^{2} d m^{2} x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 2 \, {\left(x e + d\right)}^{m} b^{3} d m x^{3} e^{3} \mathrm{sgn}\left(b x + a\right) - 6 \, {\left(x e + d\right)}^{m} a b^{2} d^{2} m^{2} x e^{2} \mathrm{sgn}\left(b x + a\right) - 3 \, {\left(x e + d\right)}^{m} b^{3} d^{2} m x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 6 \, {\left(x e + d\right)}^{m} b^{3} d^{3} m x e \mathrm{sgn}\left(b x + a\right) + {\left(x e + d\right)}^{m} a^{3} m^{3} x e^{4} \mathrm{sgn}\left(b x + a\right) + 24 \, {\left(x e + d\right)}^{m} a^{2} b m^{2} x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 42 \, {\left(x e + d\right)}^{m} a b^{2} m x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 6 \, {\left(x e + d\right)}^{m} b^{3} x^{4} e^{4} \mathrm{sgn}\left(b x + a\right) + {\left(x e + d\right)}^{m} a^{3} d m^{3} e^{3} \mathrm{sgn}\left(b x + a\right) + 21 \, {\left(x e + d\right)}^{m} a^{2} b d m^{2} x e^{3} \mathrm{sgn}\left(b x + a\right) + 12 \, {\left(x e + d\right)}^{m} a b^{2} d m x^{2} e^{3} \mathrm{sgn}\left(b x + a\right) - 3 \, {\left(x e + d\right)}^{m} a^{2} b d^{2} m^{2} e^{2} \mathrm{sgn}\left(b x + a\right) - 24 \, {\left(x e + d\right)}^{m} a b^{2} d^{2} m x e^{2} \mathrm{sgn}\left(b x + a\right) + 6 \, {\left(x e + d\right)}^{m} a b^{2} d^{3} m e \mathrm{sgn}\left(b x + a\right) - 6 \, {\left(x e + d\right)}^{m} b^{3} d^{4} \mathrm{sgn}\left(b x + a\right) + 9 \, {\left(x e + d\right)}^{m} a^{3} m^{2} x e^{4} \mathrm{sgn}\left(b x + a\right) + 57 \, {\left(x e + d\right)}^{m} a^{2} b m x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 24 \, {\left(x e + d\right)}^{m} a b^{2} x^{3} e^{4} \mathrm{sgn}\left(b x + a\right) + 9 \, {\left(x e + d\right)}^{m} a^{3} d m^{2} e^{3} \mathrm{sgn}\left(b x + a\right) + 36 \, {\left(x e + d\right)}^{m} a^{2} b d m x e^{3} \mathrm{sgn}\left(b x + a\right) - 21 \, {\left(x e + d\right)}^{m} a^{2} b d^{2} m e^{2} \mathrm{sgn}\left(b x + a\right) + 24 \, {\left(x e + d\right)}^{m} a b^{2} d^{3} e \mathrm{sgn}\left(b x + a\right) + 26 \, {\left(x e + d\right)}^{m} a^{3} m x e^{4} \mathrm{sgn}\left(b x + a\right) + 36 \, {\left(x e + d\right)}^{m} a^{2} b x^{2} e^{4} \mathrm{sgn}\left(b x + a\right) + 26 \, {\left(x e + d\right)}^{m} a^{3} d m e^{3} \mathrm{sgn}\left(b x + a\right) - 36 \, {\left(x e + d\right)}^{m} a^{2} b d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 24 \, {\left(x e + d\right)}^{m} a^{3} x e^{4} \mathrm{sgn}\left(b x + a\right) + 24 \, {\left(x e + d\right)}^{m} a^{3} d e^{3} \mathrm{sgn}\left(b x + a\right)}{m^{4} e^{4} + 10 \, m^{3} e^{4} + 35 \, m^{2} e^{4} + 50 \, m e^{4} + 24 \, e^{4}}"," ",0,"((x*e + d)^m*b^3*m^3*x^4*e^4*sgn(b*x + a) + (x*e + d)^m*b^3*d*m^3*x^3*e^3*sgn(b*x + a) + 3*(x*e + d)^m*a*b^2*m^3*x^3*e^4*sgn(b*x + a) + 6*(x*e + d)^m*b^3*m^2*x^4*e^4*sgn(b*x + a) + 3*(x*e + d)^m*a*b^2*d*m^3*x^2*e^3*sgn(b*x + a) + 3*(x*e + d)^m*b^3*d*m^2*x^3*e^3*sgn(b*x + a) - 3*(x*e + d)^m*b^3*d^2*m^2*x^2*e^2*sgn(b*x + a) + 3*(x*e + d)^m*a^2*b*m^3*x^2*e^4*sgn(b*x + a) + 21*(x*e + d)^m*a*b^2*m^2*x^3*e^4*sgn(b*x + a) + 11*(x*e + d)^m*b^3*m*x^4*e^4*sgn(b*x + a) + 3*(x*e + d)^m*a^2*b*d*m^3*x*e^3*sgn(b*x + a) + 15*(x*e + d)^m*a*b^2*d*m^2*x^2*e^3*sgn(b*x + a) + 2*(x*e + d)^m*b^3*d*m*x^3*e^3*sgn(b*x + a) - 6*(x*e + d)^m*a*b^2*d^2*m^2*x*e^2*sgn(b*x + a) - 3*(x*e + d)^m*b^3*d^2*m*x^2*e^2*sgn(b*x + a) + 6*(x*e + d)^m*b^3*d^3*m*x*e*sgn(b*x + a) + (x*e + d)^m*a^3*m^3*x*e^4*sgn(b*x + a) + 24*(x*e + d)^m*a^2*b*m^2*x^2*e^4*sgn(b*x + a) + 42*(x*e + d)^m*a*b^2*m*x^3*e^4*sgn(b*x + a) + 6*(x*e + d)^m*b^3*x^4*e^4*sgn(b*x + a) + (x*e + d)^m*a^3*d*m^3*e^3*sgn(b*x + a) + 21*(x*e + d)^m*a^2*b*d*m^2*x*e^3*sgn(b*x + a) + 12*(x*e + d)^m*a*b^2*d*m*x^2*e^3*sgn(b*x + a) - 3*(x*e + d)^m*a^2*b*d^2*m^2*e^2*sgn(b*x + a) - 24*(x*e + d)^m*a*b^2*d^2*m*x*e^2*sgn(b*x + a) + 6*(x*e + d)^m*a*b^2*d^3*m*e*sgn(b*x + a) - 6*(x*e + d)^m*b^3*d^4*sgn(b*x + a) + 9*(x*e + d)^m*a^3*m^2*x*e^4*sgn(b*x + a) + 57*(x*e + d)^m*a^2*b*m*x^2*e^4*sgn(b*x + a) + 24*(x*e + d)^m*a*b^2*x^3*e^4*sgn(b*x + a) + 9*(x*e + d)^m*a^3*d*m^2*e^3*sgn(b*x + a) + 36*(x*e + d)^m*a^2*b*d*m*x*e^3*sgn(b*x + a) - 21*(x*e + d)^m*a^2*b*d^2*m*e^2*sgn(b*x + a) + 24*(x*e + d)^m*a*b^2*d^3*e*sgn(b*x + a) + 26*(x*e + d)^m*a^3*m*x*e^4*sgn(b*x + a) + 36*(x*e + d)^m*a^2*b*x^2*e^4*sgn(b*x + a) + 26*(x*e + d)^m*a^3*d*m*e^3*sgn(b*x + a) - 36*(x*e + d)^m*a^2*b*d^2*e^2*sgn(b*x + a) + 24*(x*e + d)^m*a^3*x*e^4*sgn(b*x + a) + 24*(x*e + d)^m*a^3*d*e^3*sgn(b*x + a))/(m^4*e^4 + 10*m^3*e^4 + 35*m^2*e^4 + 50*m*e^4 + 24*e^4)","B",0
1739,1,184,0,0.196751," ","integrate((e*x+d)^m*(b^2*x^2+2*a*b*x+a^2)^(1/2),x, algorithm=""giac"")","\frac{{\left(x e + d\right)}^{m} b m x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + {\left(x e + d\right)}^{m} b d m x e \mathrm{sgn}\left(b x + a\right) + {\left(x e + d\right)}^{m} a m x e^{2} \mathrm{sgn}\left(b x + a\right) + {\left(x e + d\right)}^{m} b x^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + {\left(x e + d\right)}^{m} a d m e \mathrm{sgn}\left(b x + a\right) - {\left(x e + d\right)}^{m} b d^{2} \mathrm{sgn}\left(b x + a\right) + 2 \, {\left(x e + d\right)}^{m} a x e^{2} \mathrm{sgn}\left(b x + a\right) + 2 \, {\left(x e + d\right)}^{m} a d e \mathrm{sgn}\left(b x + a\right)}{m^{2} e^{2} + 3 \, m e^{2} + 2 \, e^{2}}"," ",0,"((x*e + d)^m*b*m*x^2*e^2*sgn(b*x + a) + (x*e + d)^m*b*d*m*x*e*sgn(b*x + a) + (x*e + d)^m*a*m*x*e^2*sgn(b*x + a) + (x*e + d)^m*b*x^2*e^2*sgn(b*x + a) + (x*e + d)^m*a*d*m*e*sgn(b*x + a) - (x*e + d)^m*b*d^2*sgn(b*x + a) + 2*(x*e + d)^m*a*x*e^2*sgn(b*x + a) + 2*(x*e + d)^m*a*d*e*sgn(b*x + a))/(m^2*e^2 + 3*m*e^2 + 2*e^2)","B",0
1740,0,0,0,0.000000," ","integrate((e*x+d)^m/(b^2*x^2+2*a*b*x+a^2)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{m}}{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2}}}\,{d x}"," ",0,"integrate((e*x + d)^m/sqrt(b^2*x^2 + 2*a*b*x + a^2), x)","F",0
1741,0,0,0,0.000000," ","integrate((e*x+d)^m/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{m}}{{\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((e*x + d)^m/(b^2*x^2 + 2*a*b*x + a^2)^(3/2), x)","F",0
1742,0,0,0,0.000000," ","integrate((e*x+d)^m/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{m}}{{\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((e*x + d)^m/(b^2*x^2 + 2*a*b*x + a^2)^(5/2), x)","F",0
1743,0,0,0,0.000000," ","integrate((e*x+d)^m*(b^2*x^2+2*a*b*x+a^2)^p,x, algorithm=""giac"")","\int {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} {\left(e x + d\right)}^{m}\,{d x}"," ",0,"integrate((b^2*x^2 + 2*a*b*x + a^2)^p*(e*x + d)^m, x)","F",0
1744,1,1267,0,0.229936," ","integrate((e*x+d)^3*(b^2*x^2+2*a*b*x+a^2)^p,x, algorithm=""giac"")","\frac{4 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{4} p^{3} x^{4} e^{3} + 12 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{4} d p^{3} x^{3} e^{2} + 12 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{4} d^{2} p^{3} x^{2} e + 4 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{4} d^{3} p^{3} x + 4 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b^{3} p^{3} x^{3} e^{3} + 12 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{4} p^{2} x^{4} e^{3} + 12 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b^{3} d p^{3} x^{2} e^{2} + 42 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{4} d p^{2} x^{3} e^{2} + 12 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b^{3} d^{2} p^{3} x e + 48 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{4} d^{2} p^{2} x^{2} e + 4 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b^{3} d^{3} p^{3} + 18 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{4} d^{3} p^{2} x + 6 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b^{3} p^{2} x^{3} e^{3} + 11 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{4} p x^{4} e^{3} + 30 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b^{3} d p^{2} x^{2} e^{2} + 42 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{4} d p x^{3} e^{2} + 42 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b^{3} d^{2} p^{2} x e + 57 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{4} d^{2} p x^{2} e + 18 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b^{3} d^{3} p^{2} + 26 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{4} d^{3} p x - 6 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{2} b^{2} p^{2} x^{2} e^{3} + 2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b^{3} p x^{3} e^{3} + 3 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{4} x^{4} e^{3} - 12 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{2} b^{2} d p^{2} x e^{2} + 12 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b^{3} d p x^{2} e^{2} + 12 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{4} d x^{3} e^{2} - 6 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{2} b^{2} d^{2} p^{2} e + 36 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b^{3} d^{2} p x e + 18 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{4} d^{2} x^{2} e + 26 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b^{3} d^{3} p + 12 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{4} d^{3} x - 3 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{2} b^{2} p x^{2} e^{3} - 24 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{2} b^{2} d p x e^{2} - 21 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{2} b^{2} d^{2} p e + 12 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b^{3} d^{3} + 6 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{3} b p x e^{3} + 6 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{3} b d p e^{2} - 18 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{2} b^{2} d^{2} e + 12 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{3} b d e^{2} - 3 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{4} e^{3}}{2 \, {\left(4 \, b^{4} p^{4} + 20 \, b^{4} p^{3} + 35 \, b^{4} p^{2} + 25 \, b^{4} p + 6 \, b^{4}\right)}}"," ",0,"1/2*(4*(b^2*x^2 + 2*a*b*x + a^2)^p*b^4*p^3*x^4*e^3 + 12*(b^2*x^2 + 2*a*b*x + a^2)^p*b^4*d*p^3*x^3*e^2 + 12*(b^2*x^2 + 2*a*b*x + a^2)^p*b^4*d^2*p^3*x^2*e + 4*(b^2*x^2 + 2*a*b*x + a^2)^p*b^4*d^3*p^3*x + 4*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b^3*p^3*x^3*e^3 + 12*(b^2*x^2 + 2*a*b*x + a^2)^p*b^4*p^2*x^4*e^3 + 12*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b^3*d*p^3*x^2*e^2 + 42*(b^2*x^2 + 2*a*b*x + a^2)^p*b^4*d*p^2*x^3*e^2 + 12*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b^3*d^2*p^3*x*e + 48*(b^2*x^2 + 2*a*b*x + a^2)^p*b^4*d^2*p^2*x^2*e + 4*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b^3*d^3*p^3 + 18*(b^2*x^2 + 2*a*b*x + a^2)^p*b^4*d^3*p^2*x + 6*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b^3*p^2*x^3*e^3 + 11*(b^2*x^2 + 2*a*b*x + a^2)^p*b^4*p*x^4*e^3 + 30*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b^3*d*p^2*x^2*e^2 + 42*(b^2*x^2 + 2*a*b*x + a^2)^p*b^4*d*p*x^3*e^2 + 42*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b^3*d^2*p^2*x*e + 57*(b^2*x^2 + 2*a*b*x + a^2)^p*b^4*d^2*p*x^2*e + 18*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b^3*d^3*p^2 + 26*(b^2*x^2 + 2*a*b*x + a^2)^p*b^4*d^3*p*x - 6*(b^2*x^2 + 2*a*b*x + a^2)^p*a^2*b^2*p^2*x^2*e^3 + 2*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b^3*p*x^3*e^3 + 3*(b^2*x^2 + 2*a*b*x + a^2)^p*b^4*x^4*e^3 - 12*(b^2*x^2 + 2*a*b*x + a^2)^p*a^2*b^2*d*p^2*x*e^2 + 12*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b^3*d*p*x^2*e^2 + 12*(b^2*x^2 + 2*a*b*x + a^2)^p*b^4*d*x^3*e^2 - 6*(b^2*x^2 + 2*a*b*x + a^2)^p*a^2*b^2*d^2*p^2*e + 36*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b^3*d^2*p*x*e + 18*(b^2*x^2 + 2*a*b*x + a^2)^p*b^4*d^2*x^2*e + 26*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b^3*d^3*p + 12*(b^2*x^2 + 2*a*b*x + a^2)^p*b^4*d^3*x - 3*(b^2*x^2 + 2*a*b*x + a^2)^p*a^2*b^2*p*x^2*e^3 - 24*(b^2*x^2 + 2*a*b*x + a^2)^p*a^2*b^2*d*p*x*e^2 - 21*(b^2*x^2 + 2*a*b*x + a^2)^p*a^2*b^2*d^2*p*e + 12*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b^3*d^3 + 6*(b^2*x^2 + 2*a*b*x + a^2)^p*a^3*b*p*x*e^3 + 6*(b^2*x^2 + 2*a*b*x + a^2)^p*a^3*b*d*p*e^2 - 18*(b^2*x^2 + 2*a*b*x + a^2)^p*a^2*b^2*d^2*e + 12*(b^2*x^2 + 2*a*b*x + a^2)^p*a^3*b*d*e^2 - 3*(b^2*x^2 + 2*a*b*x + a^2)^p*a^4*e^3)/(4*b^4*p^4 + 20*b^4*p^3 + 35*b^4*p^2 + 25*b^4*p + 6*b^4)","B",0
1745,1,608,0,0.205386," ","integrate((e*x+d)^2*(b^2*x^2+2*a*b*x+a^2)^p,x, algorithm=""giac"")","\frac{2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{3} p^{2} x^{3} e^{2} + 4 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{3} d p^{2} x^{2} e + 2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{3} d^{2} p^{2} x + 2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b^{2} p^{2} x^{2} e^{2} + 3 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{3} p x^{3} e^{2} + 4 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b^{2} d p^{2} x e + 8 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{3} d p x^{2} e + 2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b^{2} d^{2} p^{2} + 5 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{3} d^{2} p x + {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b^{2} p x^{2} e^{2} + {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{3} x^{3} e^{2} + 6 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b^{2} d p x e + 3 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{3} d x^{2} e + 5 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b^{2} d^{2} p + 3 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{3} d^{2} x - 2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{2} b p x e^{2} - 2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{2} b d p e + 3 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b^{2} d^{2} - 3 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{2} b d e + {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{3} e^{2}}{4 \, b^{3} p^{3} + 12 \, b^{3} p^{2} + 11 \, b^{3} p + 3 \, b^{3}}"," ",0,"(2*(b^2*x^2 + 2*a*b*x + a^2)^p*b^3*p^2*x^3*e^2 + 4*(b^2*x^2 + 2*a*b*x + a^2)^p*b^3*d*p^2*x^2*e + 2*(b^2*x^2 + 2*a*b*x + a^2)^p*b^3*d^2*p^2*x + 2*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b^2*p^2*x^2*e^2 + 3*(b^2*x^2 + 2*a*b*x + a^2)^p*b^3*p*x^3*e^2 + 4*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b^2*d*p^2*x*e + 8*(b^2*x^2 + 2*a*b*x + a^2)^p*b^3*d*p*x^2*e + 2*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b^2*d^2*p^2 + 5*(b^2*x^2 + 2*a*b*x + a^2)^p*b^3*d^2*p*x + (b^2*x^2 + 2*a*b*x + a^2)^p*a*b^2*p*x^2*e^2 + (b^2*x^2 + 2*a*b*x + a^2)^p*b^3*x^3*e^2 + 6*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b^2*d*p*x*e + 3*(b^2*x^2 + 2*a*b*x + a^2)^p*b^3*d*x^2*e + 5*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b^2*d^2*p + 3*(b^2*x^2 + 2*a*b*x + a^2)^p*b^3*d^2*x - 2*(b^2*x^2 + 2*a*b*x + a^2)^p*a^2*b*p*x*e^2 - 2*(b^2*x^2 + 2*a*b*x + a^2)^p*a^2*b*d*p*e + 3*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b^2*d^2 - 3*(b^2*x^2 + 2*a*b*x + a^2)^p*a^2*b*d*e + (b^2*x^2 + 2*a*b*x + a^2)^p*a^3*e^2)/(4*b^3*p^3 + 12*b^3*p^2 + 11*b^3*p + 3*b^3)","B",0
1746,1,228,0,0.202102," ","integrate((e*x+d)*(b^2*x^2+2*a*b*x+a^2)^p,x, algorithm=""giac"")","\frac{2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{2} p x^{2} e + 2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{2} d p x + 2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b p x e + {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{2} x^{2} e + 2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b d p + 2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b^{2} d x + 2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a b d - {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a^{2} e}{2 \, {\left(2 \, b^{2} p^{2} + 3 \, b^{2} p + b^{2}\right)}}"," ",0,"1/2*(2*(b^2*x^2 + 2*a*b*x + a^2)^p*b^2*p*x^2*e + 2*(b^2*x^2 + 2*a*b*x + a^2)^p*b^2*d*p*x + 2*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b*p*x*e + (b^2*x^2 + 2*a*b*x + a^2)^p*b^2*x^2*e + 2*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b*d*p + 2*(b^2*x^2 + 2*a*b*x + a^2)^p*b^2*d*x + 2*(b^2*x^2 + 2*a*b*x + a^2)^p*a*b*d - (b^2*x^2 + 2*a*b*x + a^2)^p*a^2*e)/(2*b^2*p^2 + 3*b^2*p + b^2)","B",0
1747,1,51,0,0.197330," ","integrate((b^2*x^2+2*a*b*x+a^2)^p,x, algorithm=""giac"")","\frac{{\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} b x + {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} a}{2 \, b p + b}"," ",0,"((b^2*x^2 + 2*a*b*x + a^2)^p*b*x + (b^2*x^2 + 2*a*b*x + a^2)^p*a)/(2*b*p + b)","A",0
1748,0,0,0,0.000000," ","integrate((b^2*x^2+2*a*b*x+a^2)^p/(e*x+d),x, algorithm=""giac"")","\int \frac{{\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p}}{e x + d}\,{d x}"," ",0,"integrate((b^2*x^2 + 2*a*b*x + a^2)^p/(e*x + d), x)","F",0
1749,0,0,0,0.000000," ","integrate((b^2*x^2+2*a*b*x+a^2)^p/(e*x+d)^2,x, algorithm=""giac"")","\int \frac{{\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p}}{{\left(e x + d\right)}^{2}}\,{d x}"," ",0,"integrate((b^2*x^2 + 2*a*b*x + a^2)^p/(e*x + d)^2, x)","F",0
1750,0,0,0,0.000000," ","integrate((b^2*x^2+2*a*b*x+a^2)^p/(e*x+d)^3,x, algorithm=""giac"")","\int \frac{{\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p}}{{\left(e x + d\right)}^{3}}\,{d x}"," ",0,"integrate((b^2*x^2 + 2*a*b*x + a^2)^p/(e*x + d)^3, x)","F",0
1751,0,0,0,0.000000," ","integrate((e*x+d)^(3/2)*(b^2*x^2+2*a*b*x+a^2)^p,x, algorithm=""giac"")","\int {\left(e x + d\right)}^{\frac{3}{2}} {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p}\,{d x}"," ",0,"integrate((e*x + d)^(3/2)*(b^2*x^2 + 2*a*b*x + a^2)^p, x)","F",0
1752,0,0,0,0.000000," ","integrate((e*x+d)^(1/2)*(b^2*x^2+2*a*b*x+a^2)^p,x, algorithm=""giac"")","\int \sqrt{e x + d} {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p}\,{d x}"," ",0,"integrate(sqrt(e*x + d)*(b^2*x^2 + 2*a*b*x + a^2)^p, x)","F",0
1753,0,0,0,0.000000," ","integrate((b^2*x^2+2*a*b*x+a^2)^p/(e*x+d)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p}}{\sqrt{e x + d}}\,{d x}"," ",0,"integrate((b^2*x^2 + 2*a*b*x + a^2)^p/sqrt(e*x + d), x)","F",0
1754,0,0,0,0.000000," ","integrate((b^2*x^2+2*a*b*x+a^2)^p/(e*x+d)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p}}{{\left(e x + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b^2*x^2 + 2*a*b*x + a^2)^p/(e*x + d)^(3/2), x)","F",0
1755,0,0,0,0.000000," ","integrate((b^2*x^2+2*a*b*x+a^2)^p/(e*x+d)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p}}{{\left(e x + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b^2*x^2 + 2*a*b*x + a^2)^p/(e*x + d)^(5/2), x)","F",0
1756,0,0,0,0.000000," ","integrate((e*x+d)^m*(b^2*x^2+2*a*b*x+a^2)^(5+p),x, algorithm=""giac"")","\int {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p + 5} {\left(e x + d\right)}^{m}\,{d x}"," ",0,"integrate((b^2*x^2 + 2*a*b*x + a^2)^(p + 5)*(e*x + d)^m, x)","F",0
1757,0,0,0,0.000000," ","integrate((e*x+d)^(-3-2*p)*(b^2*x^2+2*a*b*x+a^2)^p,x, algorithm=""giac"")","\int {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} {\left(e x + d\right)}^{-2 \, p - 3}\,{d x}"," ",0,"integrate((b^2*x^2 + 2*a*b*x + a^2)^p*(e*x + d)^(-2*p - 3), x)","F",0
1758,1,152,0,0.178804," ","integrate((e*x+d)*(4*x^2+12*x+9)^p,x, algorithm=""giac"")","\frac{8 \, {\left(4 \, x^{2} + 12 \, x + 9\right)}^{p} p x^{2} e + 8 \, {\left(4 \, x^{2} + 12 \, x + 9\right)}^{p} d p x + 12 \, {\left(4 \, x^{2} + 12 \, x + 9\right)}^{p} p x e + 4 \, {\left(4 \, x^{2} + 12 \, x + 9\right)}^{p} x^{2} e + 12 \, {\left(4 \, x^{2} + 12 \, x + 9\right)}^{p} d p + 8 \, {\left(4 \, x^{2} + 12 \, x + 9\right)}^{p} d x + 12 \, {\left(4 \, x^{2} + 12 \, x + 9\right)}^{p} d - 9 \, {\left(4 \, x^{2} + 12 \, x + 9\right)}^{p} e}{8 \, {\left(2 \, p^{2} + 3 \, p + 1\right)}}"," ",0,"1/8*(8*(4*x^2 + 12*x + 9)^p*p*x^2*e + 8*(4*x^2 + 12*x + 9)^p*d*p*x + 12*(4*x^2 + 12*x + 9)^p*p*x*e + 4*(4*x^2 + 12*x + 9)^p*x^2*e + 12*(4*x^2 + 12*x + 9)^p*d*p + 8*(4*x^2 + 12*x + 9)^p*d*x + 12*(4*x^2 + 12*x + 9)^p*d - 9*(4*x^2 + 12*x + 9)^p*e)/(2*p^2 + 3*p + 1)","B",0
1759,1,97,0,0.173472," ","integrate((b*x+a)^3*(a*c+(a*d+b*c)*x+b*d*x^2),x, algorithm=""giac"")","\frac{1}{6} \, b^{4} d x^{6} + \frac{1}{5} \, b^{4} c x^{5} + \frac{4}{5} \, a b^{3} d x^{5} + a b^{3} c x^{4} + \frac{3}{2} \, a^{2} b^{2} d x^{4} + 2 \, a^{2} b^{2} c x^{3} + \frac{4}{3} \, a^{3} b d x^{3} + 2 \, a^{3} b c x^{2} + \frac{1}{2} \, a^{4} d x^{2} + a^{4} c x"," ",0,"1/6*b^4*d*x^6 + 1/5*b^4*c*x^5 + 4/5*a*b^3*d*x^5 + a*b^3*c*x^4 + 3/2*a^2*b^2*d*x^4 + 2*a^2*b^2*c*x^3 + 4/3*a^3*b*d*x^3 + 2*a^3*b*c*x^2 + 1/2*a^4*d*x^2 + a^4*c*x","B",0
1760,1,72,0,0.149523," ","integrate((b*x+a)^2*(a*c+(a*d+b*c)*x+b*d*x^2),x, algorithm=""giac"")","\frac{1}{5} \, b^{3} d x^{5} + \frac{1}{4} \, b^{3} c x^{4} + \frac{3}{4} \, a b^{2} d x^{4} + a b^{2} c x^{3} + a^{2} b d x^{3} + \frac{3}{2} \, a^{2} b c x^{2} + \frac{1}{2} \, a^{3} d x^{2} + a^{3} c x"," ",0,"1/5*b^3*d*x^5 + 1/4*b^3*c*x^4 + 3/4*a*b^2*d*x^4 + a*b^2*c*x^3 + a^2*b*d*x^3 + 3/2*a^2*b*c*x^2 + 1/2*a^3*d*x^2 + a^3*c*x","B",0
1761,1,49,0,0.152424," ","integrate((b*x+a)*(a*c+(a*d+b*c)*x+b*d*x^2),x, algorithm=""giac"")","\frac{1}{4} \, b^{2} d x^{4} + \frac{1}{3} \, b^{2} c x^{3} + \frac{2}{3} \, a b d x^{3} + a b c x^{2} + \frac{1}{2} \, a^{2} d x^{2} + a^{2} c x"," ",0,"1/4*b^2*d*x^4 + 1/3*b^2*c*x^3 + 2/3*a*b*d*x^3 + a*b*c*x^2 + 1/2*a^2*d*x^2 + a^2*c*x","A",0
1762,1,24,0,0.162364," ","integrate(a*c+(a*d+b*c)*x+b*d*x^2,x, algorithm=""giac"")","\frac{1}{3} \, b d x^{3} + a c x + \frac{1}{2} \, {\left(b c + a d\right)} x^{2}"," ",0,"1/3*b*d*x^3 + a*c*x + 1/2*(b*c + a*d)*x^2","A",0
1763,1,10,0,0.154241," ","integrate((a*c+(a*d+b*c)*x+b*d*x^2)/(b*x+a),x, algorithm=""giac"")","\frac{1}{2} \, d x^{2} + c x"," ",0,"1/2*d*x^2 + c*x","A",0
1764,1,117,0,0.162314," ","integrate((a*c+(a*d+b*c)*x+b*d*x^2)/(b*x+a)^2,x, algorithm=""giac"")","b d {\left(\frac{2 \, a \log\left(\frac{{\left| b x + a \right|}}{{\left(b x + a\right)}^{2} {\left| b \right|}}\right)}{b^{3}} + \frac{b x + a}{b^{3}} - \frac{a^{2}}{{\left(b x + a\right)} b^{3}}\right)} - \frac{{\left(b c + a d\right)} {\left(\frac{\log\left(\frac{{\left| b x + a \right|}}{{\left(b x + a\right)}^{2} {\left| b \right|}}\right)}{b} - \frac{a}{{\left(b x + a\right)} b}\right)}}{b} - \frac{a c}{{\left(b x + a\right)} b}"," ",0,"b*d*(2*a*log(abs(b*x + a)/((b*x + a)^2*abs(b)))/b^3 + (b*x + a)/b^3 - a^2/((b*x + a)*b^3)) - (b*c + a*d)*(log(abs(b*x + a)/((b*x + a)^2*abs(b)))/b - a/((b*x + a)*b))/b - a*c/((b*x + a)*b)","B",0
1765,1,33,0,0.178584," ","integrate((a*c+(a*d+b*c)*x+b*d*x^2)/(b*x+a)^3,x, algorithm=""giac"")","\frac{d \log\left({\left| b x + a \right|}\right)}{b^{2}} - \frac{b c - a d}{{\left(b x + a\right)} b^{2}}"," ",0,"d*log(abs(b*x + a))/b^2 - (b*c - a*d)/((b*x + a)*b^2)","A",0
1766,1,24,0,0.157299," ","integrate((a*c+(a*d+b*c)*x+b*d*x^2)/(b*x+a)^4,x, algorithm=""giac"")","-\frac{2 \, b d x + b c + a d}{2 \, {\left(b x + a\right)}^{2} b^{2}}"," ",0,"-1/2*(2*b*d*x + b*c + a*d)/((b*x + a)^2*b^2)","A",0
1767,1,41,0,0.154840," ","integrate((a*c+(a*d+b*c)*x+b*d*x^2)/(b*x+a)^5,x, algorithm=""giac"")","-\frac{c}{3 \, {\left(b x + a\right)}^{3} b} - \frac{d}{2 \, {\left(b x + a\right)}^{2} b^{2}} + \frac{a d}{3 \, {\left(b x + a\right)}^{3} b^{2}}"," ",0,"-1/3*c/((b*x + a)^3*b) - 1/2*d/((b*x + a)^2*b^2) + 1/3*a*d/((b*x + a)^3*b^2)","A",0
1768,1,25,0,0.154331," ","integrate((a*c+(a*d+b*c)*x+b*d*x^2)/(b*x+a)^6,x, algorithm=""giac"")","-\frac{4 \, b d x + 3 \, b c + a d}{12 \, {\left(b x + a\right)}^{4} b^{2}}"," ",0,"-1/12*(4*b*d*x + 3*b*c + a*d)/((b*x + a)^4*b^2)","A",0
1769,1,212,0,0.181183," ","integrate((b*x+a)^3*(a*c+(a*d+b*c)*x+b*d*x^2)^2,x, algorithm=""giac"")","\frac{1}{8} \, b^{5} d^{2} x^{8} + \frac{2}{7} \, b^{5} c d x^{7} + \frac{5}{7} \, a b^{4} d^{2} x^{7} + \frac{1}{6} \, b^{5} c^{2} x^{6} + \frac{5}{3} \, a b^{4} c d x^{6} + \frac{5}{3} \, a^{2} b^{3} d^{2} x^{6} + a b^{4} c^{2} x^{5} + 4 \, a^{2} b^{3} c d x^{5} + 2 \, a^{3} b^{2} d^{2} x^{5} + \frac{5}{2} \, a^{2} b^{3} c^{2} x^{4} + 5 \, a^{3} b^{2} c d x^{4} + \frac{5}{4} \, a^{4} b d^{2} x^{4} + \frac{10}{3} \, a^{3} b^{2} c^{2} x^{3} + \frac{10}{3} \, a^{4} b c d x^{3} + \frac{1}{3} \, a^{5} d^{2} x^{3} + \frac{5}{2} \, a^{4} b c^{2} x^{2} + a^{5} c d x^{2} + a^{5} c^{2} x"," ",0,"1/8*b^5*d^2*x^8 + 2/7*b^5*c*d*x^7 + 5/7*a*b^4*d^2*x^7 + 1/6*b^5*c^2*x^6 + 5/3*a*b^4*c*d*x^6 + 5/3*a^2*b^3*d^2*x^6 + a*b^4*c^2*x^5 + 4*a^2*b^3*c*d*x^5 + 2*a^3*b^2*d^2*x^5 + 5/2*a^2*b^3*c^2*x^4 + 5*a^3*b^2*c*d*x^4 + 5/4*a^4*b*d^2*x^4 + 10/3*a^3*b^2*c^2*x^3 + 10/3*a^4*b*c*d*x^3 + 1/3*a^5*d^2*x^3 + 5/2*a^4*b*c^2*x^2 + a^5*c*d*x^2 + a^5*c^2*x","B",0
1770,1,170,0,0.156326," ","integrate((b*x+a)^2*(a*c+(a*d+b*c)*x+b*d*x^2)^2,x, algorithm=""giac"")","\frac{1}{7} \, b^{4} d^{2} x^{7} + \frac{1}{3} \, b^{4} c d x^{6} + \frac{2}{3} \, a b^{3} d^{2} x^{6} + \frac{1}{5} \, b^{4} c^{2} x^{5} + \frac{8}{5} \, a b^{3} c d x^{5} + \frac{6}{5} \, a^{2} b^{2} d^{2} x^{5} + a b^{3} c^{2} x^{4} + 3 \, a^{2} b^{2} c d x^{4} + a^{3} b d^{2} x^{4} + 2 \, a^{2} b^{2} c^{2} x^{3} + \frac{8}{3} \, a^{3} b c d x^{3} + \frac{1}{3} \, a^{4} d^{2} x^{3} + 2 \, a^{3} b c^{2} x^{2} + a^{4} c d x^{2} + a^{4} c^{2} x"," ",0,"1/7*b^4*d^2*x^7 + 1/3*b^4*c*d*x^6 + 2/3*a*b^3*d^2*x^6 + 1/5*b^4*c^2*x^5 + 8/5*a*b^3*c*d*x^5 + 6/5*a^2*b^2*d^2*x^5 + a*b^3*c^2*x^4 + 3*a^2*b^2*c*d*x^4 + a^3*b*d^2*x^4 + 2*a^2*b^2*c^2*x^3 + 8/3*a^3*b*c*d*x^3 + 1/3*a^4*d^2*x^3 + 2*a^3*b*c^2*x^2 + a^4*c*d*x^2 + a^4*c^2*x","B",0
1771,1,130,0,0.153052," ","integrate((b*x+a)*(a*c+(a*d+b*c)*x+b*d*x^2)^2,x, algorithm=""giac"")","\frac{1}{6} \, b^{3} d^{2} x^{6} + \frac{2}{5} \, b^{3} c d x^{5} + \frac{3}{5} \, a b^{2} d^{2} x^{5} + \frac{1}{4} \, b^{3} c^{2} x^{4} + \frac{3}{2} \, a b^{2} c d x^{4} + \frac{3}{4} \, a^{2} b d^{2} x^{4} + a b^{2} c^{2} x^{3} + 2 \, a^{2} b c d x^{3} + \frac{1}{3} \, a^{3} d^{2} x^{3} + \frac{3}{2} \, a^{2} b c^{2} x^{2} + a^{3} c d x^{2} + a^{3} c^{2} x"," ",0,"1/6*b^3*d^2*x^6 + 2/5*b^3*c*d*x^5 + 3/5*a*b^2*d^2*x^5 + 1/4*b^3*c^2*x^4 + 3/2*a*b^2*c*d*x^4 + 3/4*a^2*b*d^2*x^4 + a*b^2*c^2*x^3 + 2*a^2*b*c*d*x^3 + 1/3*a^3*d^2*x^3 + 3/2*a^2*b*c^2*x^2 + a^3*c*d*x^2 + a^3*c^2*x","B",0
1772,1,89,0,0.153671," ","integrate((a*c+(a*d+b*c)*x+b*d*x^2)^2,x, algorithm=""giac"")","\frac{1}{5} \, b^{2} d^{2} x^{5} + \frac{1}{2} \, b^{2} c d x^{4} + \frac{1}{2} \, a b d^{2} x^{4} + \frac{1}{3} \, b^{2} c^{2} x^{3} + \frac{4}{3} \, a b c d x^{3} + \frac{1}{3} \, a^{2} d^{2} x^{3} + a b c^{2} x^{2} + a^{2} c d x^{2} + a^{2} c^{2} x"," ",0,"1/5*b^2*d^2*x^5 + 1/2*b^2*c*d*x^4 + 1/2*a*b*d^2*x^4 + 1/3*b^2*c^2*x^3 + 4/3*a*b*c*d*x^3 + 1/3*a^2*d^2*x^3 + a*b*c^2*x^2 + a^2*c*d*x^2 + a^2*c^2*x","A",0
1773,1,49,0,0.199769," ","integrate((a*c+(a*d+b*c)*x+b*d*x^2)^2/(b*x+a),x, algorithm=""giac"")","\frac{1}{4} \, b d^{2} x^{4} + \frac{2}{3} \, b c d x^{3} + \frac{1}{3} \, a d^{2} x^{3} + \frac{1}{2} \, b c^{2} x^{2} + a c d x^{2} + a c^{2} x"," ",0,"1/4*b*d^2*x^4 + 2/3*b*c*d*x^3 + 1/3*a*d^2*x^3 + 1/2*b*c^2*x^2 + a*c*d*x^2 + a*c^2*x","A",0
1774,1,84,0,0.170053," ","integrate((a*c+(a*d+b*c)*x+b*d*x^2)^2/(b*x+a)^2,x, algorithm=""giac"")","\frac{{\left(\frac{3 \, b^{2} c^{2}}{{\left(b x + a\right)}^{2}} + \frac{3 \, b c d}{b x + a} - \frac{6 \, a b c d}{{\left(b x + a\right)}^{2}} - \frac{3 \, a d^{2}}{b x + a} + \frac{3 \, a^{2} d^{2}}{{\left(b x + a\right)}^{2}} + d^{2}\right)} {\left(b x + a\right)}^{3}}{3 \, b^{3}}"," ",0,"1/3*(3*b^2*c^2/(b*x + a)^2 + 3*b*c*d/(b*x + a) - 6*a*b*c*d/(b*x + a)^2 - 3*a*d^2/(b*x + a) + 3*a^2*d^2/(b*x + a)^2 + d^2)*(b*x + a)^3/b^3","B",0
1775,1,60,0,0.150782," ","integrate((a*c+(a*d+b*c)*x+b*d*x^2)^2/(b*x+a)^3,x, algorithm=""giac"")","\frac{b d^{2} x^{2} + 4 \, b c d x - 2 \, a d^{2} x}{2 \, b^{2}} + \frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left({\left| b x + a \right|}\right)}{b^{3}}"," ",0,"1/2*(b*d^2*x^2 + 4*b*c*d*x - 2*a*d^2*x)/b^2 + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(abs(b*x + a))/b^3","A",0
1776,1,65,0,0.157765," ","integrate((a*c+(a*d+b*c)*x+b*d*x^2)^2/(b*x+a)^4,x, algorithm=""giac"")","\frac{d^{2} x}{b^{2}} + \frac{2 \, {\left(b c d - a d^{2}\right)} \log\left({\left| b x + a \right|}\right)}{b^{3}} - \frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{{\left(b x + a\right)} b^{3}}"," ",0,"d^2*x/b^2 + 2*(b*c*d - a*d^2)*log(abs(b*x + a))/b^3 - (b^2*c^2 - 2*a*b*c*d + a^2*d^2)/((b*x + a)*b^3)","A",0
1777,1,110,0,0.168004," ","integrate((a*c+(a*d+b*c)*x+b*d*x^2)^2/(b*x+a)^5,x, algorithm=""giac"")","-\frac{d^{2} \log\left(\frac{{\left| b x + a \right|}}{{\left(b x + a\right)}^{2} {\left| b \right|}}\right)}{b^{3}} - \frac{\frac{b^{5} c^{2}}{{\left(b x + a\right)}^{2}} + \frac{4 \, b^{4} c d}{b x + a} - \frac{2 \, a b^{4} c d}{{\left(b x + a\right)}^{2}} - \frac{4 \, a b^{3} d^{2}}{b x + a} + \frac{a^{2} b^{3} d^{2}}{{\left(b x + a\right)}^{2}}}{2 \, b^{6}}"," ",0,"-d^2*log(abs(b*x + a)/((b*x + a)^2*abs(b)))/b^3 - 1/2*(b^5*c^2/(b*x + a)^2 + 4*b^4*c*d/(b*x + a) - 2*a*b^4*c*d/(b*x + a)^2 - 4*a*b^3*d^2/(b*x + a) + a^2*b^3*d^2/(b*x + a)^2)/b^6","A",0
1778,1,59,0,0.158921," ","integrate((a*c+(a*d+b*c)*x+b*d*x^2)^2/(b*x+a)^6,x, algorithm=""giac"")","-\frac{3 \, b^{2} d^{2} x^{2} + 3 \, b^{2} c d x + 3 \, a b d^{2} x + b^{2} c^{2} + a b c d + a^{2} d^{2}}{3 \, {\left(b x + a\right)}^{3} b^{3}}"," ",0,"-1/3*(3*b^2*d^2*x^2 + 3*b^2*c*d*x + 3*a*b*d^2*x + b^2*c^2 + a*b*c*d + a^2*d^2)/((b*x + a)^3*b^3)","B",0
1779,1,61,0,0.156043," ","integrate((a*c+(a*d+b*c)*x+b*d*x^2)^2/(b*x+a)^7,x, algorithm=""giac"")","-\frac{6 \, b^{2} d^{2} x^{2} + 8 \, b^{2} c d x + 4 \, a b d^{2} x + 3 \, b^{2} c^{2} + 2 \, a b c d + a^{2} d^{2}}{12 \, {\left(b x + a\right)}^{4} b^{3}}"," ",0,"-1/12*(6*b^2*d^2*x^2 + 8*b^2*c*d*x + 4*a*b*d^2*x + 3*b^2*c^2 + 2*a*b*c*d + a^2*d^2)/((b*x + a)^4*b^3)","A",0
1780,1,61,0,0.202132," ","integrate((a*c+(a*d+b*c)*x+b*d*x^2)^2/(b*x+a)^8,x, algorithm=""giac"")","-\frac{10 \, b^{2} d^{2} x^{2} + 15 \, b^{2} c d x + 5 \, a b d^{2} x + 6 \, b^{2} c^{2} + 3 \, a b c d + a^{2} d^{2}}{30 \, {\left(b x + a\right)}^{5} b^{3}}"," ",0,"-1/30*(10*b^2*d^2*x^2 + 15*b^2*c*d*x + 5*a*b*d^2*x + 6*b^2*c^2 + 3*a*b*c*d + a^2*d^2)/((b*x + a)^5*b^3)","A",0
1781,1,61,0,0.158399," ","integrate((a*c+(a*d+b*c)*x+b*d*x^2)^2/(b*x+a)^9,x, algorithm=""giac"")","-\frac{15 \, b^{2} d^{2} x^{2} + 24 \, b^{2} c d x + 6 \, a b d^{2} x + 10 \, b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}}{60 \, {\left(b x + a\right)}^{6} b^{3}}"," ",0,"-1/60*(15*b^2*d^2*x^2 + 24*b^2*c*d*x + 6*a*b*d^2*x + 10*b^2*c^2 + 4*a*b*c*d + a^2*d^2)/((b*x + a)^6*b^3)","A",0
1782,1,61,0,0.169142," ","integrate((a*c+(a*d+b*c)*x+b*d*x^2)^2/(b*x+a)^10,x, algorithm=""giac"")","-\frac{21 \, b^{2} d^{2} x^{2} + 35 \, b^{2} c d x + 7 \, a b d^{2} x + 15 \, b^{2} c^{2} + 5 \, a b c d + a^{2} d^{2}}{105 \, {\left(b x + a\right)}^{7} b^{3}}"," ",0,"-1/105*(21*b^2*d^2*x^2 + 35*b^2*c*d*x + 7*a*b*d^2*x + 15*b^2*c^2 + 5*a*b*c*d + a^2*d^2)/((b*x + a)^7*b^3)","A",0
1783,1,362,0,0.165326," ","integrate((b*x+a)^3*(a*c+(a*d+b*c)*x+b*d*x^2)^3,x, algorithm=""giac"")","\frac{1}{10} \, b^{6} d^{3} x^{10} + \frac{1}{3} \, b^{6} c d^{2} x^{9} + \frac{2}{3} \, a b^{5} d^{3} x^{9} + \frac{3}{8} \, b^{6} c^{2} d x^{8} + \frac{9}{4} \, a b^{5} c d^{2} x^{8} + \frac{15}{8} \, a^{2} b^{4} d^{3} x^{8} + \frac{1}{7} \, b^{6} c^{3} x^{7} + \frac{18}{7} \, a b^{5} c^{2} d x^{7} + \frac{45}{7} \, a^{2} b^{4} c d^{2} x^{7} + \frac{20}{7} \, a^{3} b^{3} d^{3} x^{7} + a b^{5} c^{3} x^{6} + \frac{15}{2} \, a^{2} b^{4} c^{2} d x^{6} + 10 \, a^{3} b^{3} c d^{2} x^{6} + \frac{5}{2} \, a^{4} b^{2} d^{3} x^{6} + 3 \, a^{2} b^{4} c^{3} x^{5} + 12 \, a^{3} b^{3} c^{2} d x^{5} + 9 \, a^{4} b^{2} c d^{2} x^{5} + \frac{6}{5} \, a^{5} b d^{3} x^{5} + 5 \, a^{3} b^{3} c^{3} x^{4} + \frac{45}{4} \, a^{4} b^{2} c^{2} d x^{4} + \frac{9}{2} \, a^{5} b c d^{2} x^{4} + \frac{1}{4} \, a^{6} d^{3} x^{4} + 5 \, a^{4} b^{2} c^{3} x^{3} + 6 \, a^{5} b c^{2} d x^{3} + a^{6} c d^{2} x^{3} + 3 \, a^{5} b c^{3} x^{2} + \frac{3}{2} \, a^{6} c^{2} d x^{2} + a^{6} c^{3} x"," ",0,"1/10*b^6*d^3*x^10 + 1/3*b^6*c*d^2*x^9 + 2/3*a*b^5*d^3*x^9 + 3/8*b^6*c^2*d*x^8 + 9/4*a*b^5*c*d^2*x^8 + 15/8*a^2*b^4*d^3*x^8 + 1/7*b^6*c^3*x^7 + 18/7*a*b^5*c^2*d*x^7 + 45/7*a^2*b^4*c*d^2*x^7 + 20/7*a^3*b^3*d^3*x^7 + a*b^5*c^3*x^6 + 15/2*a^2*b^4*c^2*d*x^6 + 10*a^3*b^3*c*d^2*x^6 + 5/2*a^4*b^2*d^3*x^6 + 3*a^2*b^4*c^3*x^5 + 12*a^3*b^3*c^2*d*x^5 + 9*a^4*b^2*c*d^2*x^5 + 6/5*a^5*b*d^3*x^5 + 5*a^3*b^3*c^3*x^4 + 45/4*a^4*b^2*c^2*d*x^4 + 9/2*a^5*b*c*d^2*x^4 + 1/4*a^6*d^3*x^4 + 5*a^4*b^2*c^3*x^3 + 6*a^5*b*c^2*d*x^3 + a^6*c*d^2*x^3 + 3*a^5*b*c^3*x^2 + 3/2*a^6*c^2*d*x^2 + a^6*c^3*x","B",0
1784,1,303,0,0.189261," ","integrate((b*x+a)^2*(a*c+(a*d+b*c)*x+b*d*x^2)^3,x, algorithm=""giac"")","\frac{1}{9} \, b^{5} d^{3} x^{9} + \frac{3}{8} \, b^{5} c d^{2} x^{8} + \frac{5}{8} \, a b^{4} d^{3} x^{8} + \frac{3}{7} \, b^{5} c^{2} d x^{7} + \frac{15}{7} \, a b^{4} c d^{2} x^{7} + \frac{10}{7} \, a^{2} b^{3} d^{3} x^{7} + \frac{1}{6} \, b^{5} c^{3} x^{6} + \frac{5}{2} \, a b^{4} c^{2} d x^{6} + 5 \, a^{2} b^{3} c d^{2} x^{6} + \frac{5}{3} \, a^{3} b^{2} d^{3} x^{6} + a b^{4} c^{3} x^{5} + 6 \, a^{2} b^{3} c^{2} d x^{5} + 6 \, a^{3} b^{2} c d^{2} x^{5} + a^{4} b d^{3} x^{5} + \frac{5}{2} \, a^{2} b^{3} c^{3} x^{4} + \frac{15}{2} \, a^{3} b^{2} c^{2} d x^{4} + \frac{15}{4} \, a^{4} b c d^{2} x^{4} + \frac{1}{4} \, a^{5} d^{3} x^{4} + \frac{10}{3} \, a^{3} b^{2} c^{3} x^{3} + 5 \, a^{4} b c^{2} d x^{3} + a^{5} c d^{2} x^{3} + \frac{5}{2} \, a^{4} b c^{3} x^{2} + \frac{3}{2} \, a^{5} c^{2} d x^{2} + a^{5} c^{3} x"," ",0,"1/9*b^5*d^3*x^9 + 3/8*b^5*c*d^2*x^8 + 5/8*a*b^4*d^3*x^8 + 3/7*b^5*c^2*d*x^7 + 15/7*a*b^4*c*d^2*x^7 + 10/7*a^2*b^3*d^3*x^7 + 1/6*b^5*c^3*x^6 + 5/2*a*b^4*c^2*d*x^6 + 5*a^2*b^3*c*d^2*x^6 + 5/3*a^3*b^2*d^3*x^6 + a*b^4*c^3*x^5 + 6*a^2*b^3*c^2*d*x^5 + 6*a^3*b^2*c*d^2*x^5 + a^4*b*d^3*x^5 + 5/2*a^2*b^3*c^3*x^4 + 15/2*a^3*b^2*c^2*d*x^4 + 15/4*a^4*b*c*d^2*x^4 + 1/4*a^5*d^3*x^4 + 10/3*a^3*b^2*c^3*x^3 + 5*a^4*b*c^2*d*x^3 + a^5*c*d^2*x^3 + 5/2*a^4*b*c^3*x^2 + 3/2*a^5*c^2*d*x^2 + a^5*c^3*x","B",0
1785,1,245,0,0.200379," ","integrate((b*x+a)*(a*c+(a*d+b*c)*x+b*d*x^2)^3,x, algorithm=""giac"")","\frac{1}{8} \, b^{4} d^{3} x^{8} + \frac{3}{7} \, b^{4} c d^{2} x^{7} + \frac{4}{7} \, a b^{3} d^{3} x^{7} + \frac{1}{2} \, b^{4} c^{2} d x^{6} + 2 \, a b^{3} c d^{2} x^{6} + a^{2} b^{2} d^{3} x^{6} + \frac{1}{5} \, b^{4} c^{3} x^{5} + \frac{12}{5} \, a b^{3} c^{2} d x^{5} + \frac{18}{5} \, a^{2} b^{2} c d^{2} x^{5} + \frac{4}{5} \, a^{3} b d^{3} x^{5} + a b^{3} c^{3} x^{4} + \frac{9}{2} \, a^{2} b^{2} c^{2} d x^{4} + 3 \, a^{3} b c d^{2} x^{4} + \frac{1}{4} \, a^{4} d^{3} x^{4} + 2 \, a^{2} b^{2} c^{3} x^{3} + 4 \, a^{3} b c^{2} d x^{3} + a^{4} c d^{2} x^{3} + 2 \, a^{3} b c^{3} x^{2} + \frac{3}{2} \, a^{4} c^{2} d x^{2} + a^{4} c^{3} x"," ",0,"1/8*b^4*d^3*x^8 + 3/7*b^4*c*d^2*x^7 + 4/7*a*b^3*d^3*x^7 + 1/2*b^4*c^2*d*x^6 + 2*a*b^3*c*d^2*x^6 + a^2*b^2*d^3*x^6 + 1/5*b^4*c^3*x^5 + 12/5*a*b^3*c^2*d*x^5 + 18/5*a^2*b^2*c*d^2*x^5 + 4/5*a^3*b*d^3*x^5 + a*b^3*c^3*x^4 + 9/2*a^2*b^2*c^2*d*x^4 + 3*a^3*b*c*d^2*x^4 + 1/4*a^4*d^3*x^4 + 2*a^2*b^2*c^3*x^3 + 4*a^3*b*c^2*d*x^3 + a^4*c*d^2*x^3 + 2*a^3*b*c^3*x^2 + 3/2*a^4*c^2*d*x^2 + a^4*c^3*x","B",0
1786,1,188,0,0.159985," ","integrate((a*c+(a*d+b*c)*x+b*d*x^2)^3,x, algorithm=""giac"")","\frac{1}{7} \, b^{3} d^{3} x^{7} + \frac{1}{2} \, b^{3} c d^{2} x^{6} + \frac{1}{2} \, a b^{2} d^{3} x^{6} + \frac{3}{5} \, b^{3} c^{2} d x^{5} + \frac{9}{5} \, a b^{2} c d^{2} x^{5} + \frac{3}{5} \, a^{2} b d^{3} x^{5} + \frac{1}{4} \, b^{3} c^{3} x^{4} + \frac{9}{4} \, a b^{2} c^{2} d x^{4} + \frac{9}{4} \, a^{2} b c d^{2} x^{4} + \frac{1}{4} \, a^{3} d^{3} x^{4} + a b^{2} c^{3} x^{3} + 3 \, a^{2} b c^{2} d x^{3} + a^{3} c d^{2} x^{3} + \frac{3}{2} \, a^{2} b c^{3} x^{2} + \frac{3}{2} \, a^{3} c^{2} d x^{2} + a^{3} c^{3} x"," ",0,"1/7*b^3*d^3*x^7 + 1/2*b^3*c*d^2*x^6 + 1/2*a*b^2*d^3*x^6 + 3/5*b^3*c^2*d*x^5 + 9/5*a*b^2*c*d^2*x^5 + 3/5*a^2*b*d^3*x^5 + 1/4*b^3*c^3*x^4 + 9/4*a*b^2*c^2*d*x^4 + 9/4*a^2*b*c*d^2*x^4 + 1/4*a^3*d^3*x^4 + a*b^2*c^3*x^3 + 3*a^2*b*c^2*d*x^3 + a^3*c*d^2*x^3 + 3/2*a^2*b*c^3*x^2 + 3/2*a^3*c^2*d*x^2 + a^3*c^3*x","B",0
1787,1,130,0,0.160159," ","integrate((a*c+(a*d+b*c)*x+b*d*x^2)^3/(b*x+a),x, algorithm=""giac"")","\frac{1}{6} \, b^{2} d^{3} x^{6} + \frac{3}{5} \, b^{2} c d^{2} x^{5} + \frac{2}{5} \, a b d^{3} x^{5} + \frac{3}{4} \, b^{2} c^{2} d x^{4} + \frac{3}{2} \, a b c d^{2} x^{4} + \frac{1}{4} \, a^{2} d^{3} x^{4} + \frac{1}{3} \, b^{2} c^{3} x^{3} + 2 \, a b c^{2} d x^{3} + a^{2} c d^{2} x^{3} + a b c^{3} x^{2} + \frac{3}{2} \, a^{2} c^{2} d x^{2} + a^{2} c^{3} x"," ",0,"1/6*b^2*d^3*x^6 + 3/5*b^2*c*d^2*x^5 + 2/5*a*b*d^3*x^5 + 3/4*b^2*c^2*d*x^4 + 3/2*a*b*c*d^2*x^4 + 1/4*a^2*d^3*x^4 + 1/3*b^2*c^3*x^3 + 2*a*b*c^2*d*x^3 + a^2*c*d^2*x^3 + a*b*c^3*x^2 + 3/2*a^2*c^2*d*x^2 + a^2*c^3*x","B",0
1788,1,155,0,0.173595," ","integrate((a*c+(a*d+b*c)*x+b*d*x^2)^3/(b*x+a)^2,x, algorithm=""giac"")","\frac{{\left(\frac{10 \, b^{3} c^{3}}{{\left(b x + a\right)}^{3}} + \frac{20 \, b^{2} c^{2} d}{{\left(b x + a\right)}^{2}} - \frac{30 \, a b^{2} c^{2} d}{{\left(b x + a\right)}^{3}} + \frac{15 \, b c d^{2}}{b x + a} - \frac{40 \, a b c d^{2}}{{\left(b x + a\right)}^{2}} + \frac{30 \, a^{2} b c d^{2}}{{\left(b x + a\right)}^{3}} - \frac{15 \, a d^{3}}{b x + a} + \frac{20 \, a^{2} d^{3}}{{\left(b x + a\right)}^{2}} - \frac{10 \, a^{3} d^{3}}{{\left(b x + a\right)}^{3}} + 4 \, d^{3}\right)} {\left(b x + a\right)}^{5}}{20 \, b^{4}}"," ",0,"1/20*(10*b^3*c^3/(b*x + a)^3 + 20*b^2*c^2*d/(b*x + a)^2 - 30*a*b^2*c^2*d/(b*x + a)^3 + 15*b*c*d^2/(b*x + a) - 40*a*b*c*d^2/(b*x + a)^2 + 30*a^2*b*c*d^2/(b*x + a)^3 - 15*a*d^3/(b*x + a) + 20*a^2*d^3/(b*x + a)^2 - 10*a^3*d^3/(b*x + a)^3 + 4*d^3)*(b*x + a)^5/b^4","B",0
1789,1,31,0,0.166801," ","integrate((a*c+(a*d+b*c)*x+b*d*x^2)^3/(b*x+a)^3,x, algorithm=""giac"")","\frac{1}{4} \, d^{3} x^{4} + c d^{2} x^{3} + \frac{3}{2} \, c^{2} d x^{2} + c^{3} x"," ",0,"1/4*d^3*x^4 + c*d^2*x^3 + 3/2*c^2*d*x^2 + c^3*x","B",0
1790,1,115,0,0.172513," ","integrate((a*c+(a*d+b*c)*x+b*d*x^2)^3/(b*x+a)^4,x, algorithm=""giac"")","\frac{2 \, b^{2} d^{3} x^{3} + 9 \, b^{2} c d^{2} x^{2} - 3 \, a b d^{3} x^{2} + 18 \, b^{2} c^{2} d x - 18 \, a b c d^{2} x + 6 \, a^{2} d^{3} x}{6 \, b^{3}} + \frac{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left({\left| b x + a \right|}\right)}{b^{4}}"," ",0,"1/6*(2*b^2*d^3*x^3 + 9*b^2*c*d^2*x^2 - 3*a*b*d^3*x^2 + 18*b^2*c^2*d*x - 18*a*b*c*d^2*x + 6*a^2*d^3*x)/b^3 + (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(abs(b*x + a))/b^4","A",0
1791,1,167,0,0.184344," ","integrate((a*c+(a*d+b*c)*x+b*d*x^2)^3/(b*x+a)^5,x, algorithm=""giac"")","\frac{{\left(d^{3} + \frac{6 \, {\left(b^{2} c d^{2} - a b d^{3}\right)}}{{\left(b x + a\right)} b}\right)} {\left(b x + a\right)}^{2}}{2 \, b^{4}} - \frac{3 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \log\left(\frac{{\left| b x + a \right|}}{{\left(b x + a\right)}^{2} {\left| b \right|}}\right)}{b^{4}} - \frac{\frac{b^{5} c^{3}}{b x + a} - \frac{3 \, a b^{4} c^{2} d}{b x + a} + \frac{3 \, a^{2} b^{3} c d^{2}}{b x + a} - \frac{a^{3} b^{2} d^{3}}{b x + a}}{b^{6}}"," ",0,"1/2*(d^3 + 6*(b^2*c*d^2 - a*b*d^3)/((b*x + a)*b))*(b*x + a)^2/b^4 - 3*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*log(abs(b*x + a)/((b*x + a)^2*abs(b)))/b^4 - (b^5*c^3/(b*x + a) - 3*a*b^4*c^2*d/(b*x + a) + 3*a^2*b^3*c*d^2/(b*x + a) - a^3*b^2*d^3/(b*x + a))/b^6","B",0
1792,1,112,0,0.379697," ","integrate((a*c+(a*d+b*c)*x+b*d*x^2)^3/(b*x+a)^6,x, algorithm=""giac"")","\frac{d^{3} x}{b^{3}} + \frac{3 \, {\left(b c d^{2} - a d^{3}\right)} \log\left({\left| b x + a \right|}\right)}{b^{4}} - \frac{b^{3} c^{3} + 3 \, a b^{2} c^{2} d - 9 \, a^{2} b c d^{2} + 5 \, a^{3} d^{3} + 6 \, {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x}{2 \, {\left(b x + a\right)}^{2} b^{4}}"," ",0,"d^3*x/b^3 + 3*(b*c*d^2 - a*d^3)*log(abs(b*x + a))/b^4 - 1/2*(b^3*c^3 + 3*a*b^2*c^2*d - 9*a^2*b*c*d^2 + 5*a^3*d^3 + 6*(b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*x)/((b*x + a)^2*b^4)","A",0
1793,1,118,0,0.174234," ","integrate((a*c+(a*d+b*c)*x+b*d*x^2)^3/(b*x+a)^7,x, algorithm=""giac"")","\frac{d^{3} \log\left({\left| b x + a \right|}\right)}{b^{4}} - \frac{18 \, {\left(b^{2} c d^{2} - a b d^{3}\right)} x^{2} + 9 \, {\left(b^{2} c^{2} d + 2 \, a b c d^{2} - 3 \, a^{2} d^{3}\right)} x + \frac{2 \, b^{3} c^{3} + 3 \, a b^{2} c^{2} d + 6 \, a^{2} b c d^{2} - 11 \, a^{3} d^{3}}{b}}{6 \, {\left(b x + a\right)}^{3} b^{3}}"," ",0,"d^3*log(abs(b*x + a))/b^4 - 1/6*(18*(b^2*c*d^2 - a*b*d^3)*x^2 + 9*(b^2*c^2*d + 2*a*b*c*d^2 - 3*a^2*d^3)*x + (2*b^3*c^3 + 3*a*b^2*c^2*d + 6*a^2*b*c*d^2 - 11*a^3*d^3)/b)/((b*x + a)^3*b^3)","A",0
1794,1,111,0,0.161518," ","integrate((a*c+(a*d+b*c)*x+b*d*x^2)^3/(b*x+a)^8,x, algorithm=""giac"")","-\frac{4 \, b^{3} d^{3} x^{3} + 6 \, b^{3} c d^{2} x^{2} + 6 \, a b^{2} d^{3} x^{2} + 4 \, b^{3} c^{2} d x + 4 \, a b^{2} c d^{2} x + 4 \, a^{2} b d^{3} x + b^{3} c^{3} + a b^{2} c^{2} d + a^{2} b c d^{2} + a^{3} d^{3}}{4 \, {\left(b x + a\right)}^{4} b^{4}}"," ",0,"-1/4*(4*b^3*d^3*x^3 + 6*b^3*c*d^2*x^2 + 6*a*b^2*d^3*x^2 + 4*b^3*c^2*d*x + 4*a*b^2*c*d^2*x + 4*a^2*b*d^3*x + b^3*c^3 + a*b^2*c^2*d + a^2*b*c*d^2 + a^3*d^3)/((b*x + a)^4*b^4)","B",0
1795,1,114,0,0.186937," ","integrate((a*c+(a*d+b*c)*x+b*d*x^2)^3/(b*x+a)^9,x, algorithm=""giac"")","-\frac{10 \, b^{3} d^{3} x^{3} + 20 \, b^{3} c d^{2} x^{2} + 10 \, a b^{2} d^{3} x^{2} + 15 \, b^{3} c^{2} d x + 10 \, a b^{2} c d^{2} x + 5 \, a^{2} b d^{3} x + 4 \, b^{3} c^{3} + 3 \, a b^{2} c^{2} d + 2 \, a^{2} b c d^{2} + a^{3} d^{3}}{20 \, {\left(b x + a\right)}^{5} b^{4}}"," ",0,"-1/20*(10*b^3*d^3*x^3 + 20*b^3*c*d^2*x^2 + 10*a*b^2*d^3*x^2 + 15*b^3*c^2*d*x + 10*a*b^2*c*d^2*x + 5*a^2*b*d^3*x + 4*b^3*c^3 + 3*a*b^2*c^2*d + 2*a^2*b*c*d^2 + a^3*d^3)/((b*x + a)^5*b^4)","B",0
1796,1,114,0,0.186810," ","integrate((a*c+(a*d+b*c)*x+b*d*x^2)^3/(b*x+a)^10,x, algorithm=""giac"")","-\frac{20 \, b^{3} d^{3} x^{3} + 45 \, b^{3} c d^{2} x^{2} + 15 \, a b^{2} d^{3} x^{2} + 36 \, b^{3} c^{2} d x + 18 \, a b^{2} c d^{2} x + 6 \, a^{2} b d^{3} x + 10 \, b^{3} c^{3} + 6 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} + a^{3} d^{3}}{60 \, {\left(b x + a\right)}^{6} b^{4}}"," ",0,"-1/60*(20*b^3*d^3*x^3 + 45*b^3*c*d^2*x^2 + 15*a*b^2*d^3*x^2 + 36*b^3*c^2*d*x + 18*a*b^2*c*d^2*x + 6*a^2*b*d^3*x + 10*b^3*c^3 + 6*a*b^2*c^2*d + 3*a^2*b*c*d^2 + a^3*d^3)/((b*x + a)^6*b^4)","A",0
1797,1,114,0,0.162410," ","integrate((a*c+(a*d+b*c)*x+b*d*x^2)^3/(b*x+a)^11,x, algorithm=""giac"")","-\frac{35 \, b^{3} d^{3} x^{3} + 84 \, b^{3} c d^{2} x^{2} + 21 \, a b^{2} d^{3} x^{2} + 70 \, b^{3} c^{2} d x + 28 \, a b^{2} c d^{2} x + 7 \, a^{2} b d^{3} x + 20 \, b^{3} c^{3} + 10 \, a b^{2} c^{2} d + 4 \, a^{2} b c d^{2} + a^{3} d^{3}}{140 \, {\left(b x + a\right)}^{7} b^{4}}"," ",0,"-1/140*(35*b^3*d^3*x^3 + 84*b^3*c*d^2*x^2 + 21*a*b^2*d^3*x^2 + 70*b^3*c^2*d*x + 28*a*b^2*c*d^2*x + 7*a^2*b*d^3*x + 20*b^3*c^3 + 10*a*b^2*c^2*d + 4*a^2*b*c*d^2 + a^3*d^3)/((b*x + a)^7*b^4)","A",0
1798,1,114,0,0.160842," ","integrate((a*c+(a*d+b*c)*x+b*d*x^2)^3/(b*x+a)^12,x, algorithm=""giac"")","-\frac{56 \, b^{3} d^{3} x^{3} + 140 \, b^{3} c d^{2} x^{2} + 28 \, a b^{2} d^{3} x^{2} + 120 \, b^{3} c^{2} d x + 40 \, a b^{2} c d^{2} x + 8 \, a^{2} b d^{3} x + 35 \, b^{3} c^{3} + 15 \, a b^{2} c^{2} d + 5 \, a^{2} b c d^{2} + a^{3} d^{3}}{280 \, {\left(b x + a\right)}^{8} b^{4}}"," ",0,"-1/280*(56*b^3*d^3*x^3 + 140*b^3*c*d^2*x^2 + 28*a*b^2*d^3*x^2 + 120*b^3*c^2*d*x + 40*a*b^2*c*d^2*x + 8*a^2*b*d^3*x + 35*b^3*c^3 + 15*a*b^2*c^2*d + 5*a^2*b*c*d^2 + a^3*d^3)/((b*x + a)^8*b^4)","A",0
1799,1,273,0,0.158278," ","integrate((b*x+a)^6/(a*c+(a*d+b*c)*x+b*d*x^2),x, algorithm=""giac"")","\frac{12 \, b^{5} d^{4} x^{5} - 15 \, b^{5} c d^{3} x^{4} + 75 \, a b^{4} d^{4} x^{4} + 20 \, b^{5} c^{2} d^{2} x^{3} - 100 \, a b^{4} c d^{3} x^{3} + 200 \, a^{2} b^{3} d^{4} x^{3} - 30 \, b^{5} c^{3} d x^{2} + 150 \, a b^{4} c^{2} d^{2} x^{2} - 300 \, a^{2} b^{3} c d^{3} x^{2} + 300 \, a^{3} b^{2} d^{4} x^{2} + 60 \, b^{5} c^{4} x - 300 \, a b^{4} c^{3} d x + 600 \, a^{2} b^{3} c^{2} d^{2} x - 600 \, a^{3} b^{2} c d^{3} x + 300 \, a^{4} b d^{4} x}{60 \, d^{5}} - \frac{{\left(b^{5} c^{5} - 5 \, a b^{4} c^{4} d + 10 \, a^{2} b^{3} c^{3} d^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} + 5 \, a^{4} b c d^{4} - a^{5} d^{5}\right)} \log\left({\left| d x + c \right|}\right)}{d^{6}}"," ",0,"1/60*(12*b^5*d^4*x^5 - 15*b^5*c*d^3*x^4 + 75*a*b^4*d^4*x^4 + 20*b^5*c^2*d^2*x^3 - 100*a*b^4*c*d^3*x^3 + 200*a^2*b^3*d^4*x^3 - 30*b^5*c^3*d*x^2 + 150*a*b^4*c^2*d^2*x^2 - 300*a^2*b^3*c*d^3*x^2 + 300*a^3*b^2*d^4*x^2 + 60*b^5*c^4*x - 300*a*b^4*c^3*d*x + 600*a^2*b^3*c^2*d^2*x - 600*a^3*b^2*c*d^3*x + 300*a^4*b*d^4*x)/d^5 - (b^5*c^5 - 5*a*b^4*c^4*d + 10*a^2*b^3*c^3*d^2 - 10*a^3*b^2*c^2*d^3 + 5*a^4*b*c*d^4 - a^5*d^5)*log(abs(d*x + c))/d^6","B",0
1800,1,184,0,0.160025," ","integrate((b*x+a)^5/(a*c+(a*d+b*c)*x+b*d*x^2),x, algorithm=""giac"")","\frac{3 \, b^{4} d^{3} x^{4} - 4 \, b^{4} c d^{2} x^{3} + 16 \, a b^{3} d^{3} x^{3} + 6 \, b^{4} c^{2} d x^{2} - 24 \, a b^{3} c d^{2} x^{2} + 36 \, a^{2} b^{2} d^{3} x^{2} - 12 \, b^{4} c^{3} x + 48 \, a b^{3} c^{2} d x - 72 \, a^{2} b^{2} c d^{2} x + 48 \, a^{3} b d^{3} x}{12 \, d^{4}} + \frac{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \log\left({\left| d x + c \right|}\right)}{d^{5}}"," ",0,"1/12*(3*b^4*d^3*x^4 - 4*b^4*c*d^2*x^3 + 16*a*b^3*d^3*x^3 + 6*b^4*c^2*d*x^2 - 24*a*b^3*c*d^2*x^2 + 36*a^2*b^2*d^3*x^2 - 12*b^4*c^3*x + 48*a*b^3*c^2*d*x - 72*a^2*b^2*c*d^2*x + 48*a^3*b*d^3*x)/d^4 + (b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*log(abs(d*x + c))/d^5","A",0
1801,1,116,0,0.179010," ","integrate((b*x+a)^4/(a*c+(a*d+b*c)*x+b*d*x^2),x, algorithm=""giac"")","\frac{2 \, b^{3} d^{2} x^{3} - 3 \, b^{3} c d x^{2} + 9 \, a b^{2} d^{2} x^{2} + 6 \, b^{3} c^{2} x - 18 \, a b^{2} c d x + 18 \, a^{2} b d^{2} x}{6 \, d^{3}} - \frac{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left({\left| d x + c \right|}\right)}{d^{4}}"," ",0,"1/6*(2*b^3*d^2*x^3 - 3*b^3*c*d*x^2 + 9*a*b^2*d^2*x^2 + 6*b^3*c^2*x - 18*a*b^2*c*d*x + 18*a^2*b*d^2*x)/d^3 - (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(abs(d*x + c))/d^4","A",0
1802,1,60,0,0.163886," ","integrate((b*x+a)^3/(a*c+(a*d+b*c)*x+b*d*x^2),x, algorithm=""giac"")","\frac{b^{2} d x^{2} - 2 \, b^{2} c x + 4 \, a b d x}{2 \, d^{2}} + \frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left({\left| d x + c \right|}\right)}{d^{3}}"," ",0,"1/2*(b^2*d*x^2 - 2*b^2*c*x + 4*a*b*d*x)/d^2 + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(abs(d*x + c))/d^3","A",0
1803,1,27,0,0.156337," ","integrate((b*x+a)^2/(a*c+(a*d+b*c)*x+b*d*x^2),x, algorithm=""giac"")","\frac{b x}{d} - \frac{{\left(b c - a d\right)} \log\left({\left| d x + c \right|}\right)}{d^{2}}"," ",0,"b*x/d - (b*c - a*d)*log(abs(d*x + c))/d^2","A",0
1804,1,11,0,0.150736," ","integrate((b*x+a)/(a*c+(a*d+b*c)*x+b*d*x^2),x, algorithm=""giac"")","\frac{\log\left({\left| d x + c \right|}\right)}{d}"," ",0,"log(abs(d*x + c))/d","A",0
1805,1,46,0,0.166430," ","integrate(1/(a*c+(a*d+b*c)*x+b*d*x^2),x, algorithm=""giac"")","\frac{b \log\left({\left| b x + a \right|}\right)}{b^{2} c - a b d} - \frac{d \log\left({\left| d x + c \right|}\right)}{b c d - a d^{2}}"," ",0,"b*log(abs(b*x + a))/(b^2*c - a*b*d) - d*log(abs(d*x + c))/(b*c*d - a*d^2)","A",0
1806,1,94,0,0.189099," ","integrate(1/(b*x+a)/(a*c+(a*d+b*c)*x+b*d*x^2),x, algorithm=""giac"")","-\frac{b d \log\left({\left| b x + a \right|}\right)}{b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}} + \frac{d^{2} \log\left({\left| d x + c \right|}\right)}{b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}} - \frac{1}{{\left(b c - a d\right)} {\left(b x + a\right)}}"," ",0,"-b*d*log(abs(b*x + a))/(b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2) + d^2*log(abs(d*x + c))/(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3) - 1/((b*c - a*d)*(b*x + a))","A",0
1807,1,145,0,0.199619," ","integrate(1/(b*x+a)^2/(a*c+(a*d+b*c)*x+b*d*x^2),x, algorithm=""giac"")","-\frac{b d^{2} \log\left({\left| -\frac{b c}{b x + a} + \frac{a d}{b x + a} - d \right|}\right)}{b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}} - \frac{\frac{b^{3} c}{{\left(b x + a\right)}^{2}} - \frac{2 \, b^{2} d}{b x + a} - \frac{a b^{2} d}{{\left(b x + a\right)}^{2}}}{2 \, {\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)}}"," ",0,"-b*d^2*log(abs(-b*c/(b*x + a) + a*d/(b*x + a) - d))/(b^4*c^3 - 3*a*b^3*c^2*d + 3*a^2*b^2*c*d^2 - a^3*b*d^3) - 1/2*(b^3*c/(b*x + a)^2 - 2*b^2*d/(b*x + a) - a*b^2*d/(b*x + a)^2)/(b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)","A",0
1808,1,243,0,0.180318," ","integrate(1/(b*x+a)^3/(a*c+(a*d+b*c)*x+b*d*x^2),x, algorithm=""giac"")","-\frac{b d^{3} \log\left({\left| b x + a \right|}\right)}{b^{5} c^{4} - 4 \, a b^{4} c^{3} d + 6 \, a^{2} b^{3} c^{2} d^{2} - 4 \, a^{3} b^{2} c d^{3} + a^{4} b d^{4}} + \frac{d^{4} \log\left({\left| d x + c \right|}\right)}{b^{4} c^{4} d - 4 \, a b^{3} c^{3} d^{2} + 6 \, a^{2} b^{2} c^{2} d^{3} - 4 \, a^{3} b c d^{4} + a^{4} d^{5}} - \frac{2 \, b^{3} c^{3} - 9 \, a b^{2} c^{2} d + 18 \, a^{2} b c d^{2} - 11 \, a^{3} d^{3} + 6 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{2} - 3 \, {\left(b^{3} c^{2} d - 6 \, a b^{2} c d^{2} + 5 \, a^{2} b d^{3}\right)} x}{6 \, {\left(b c - a d\right)}^{4} {\left(b x + a\right)}^{3}}"," ",0,"-b*d^3*log(abs(b*x + a))/(b^5*c^4 - 4*a*b^4*c^3*d + 6*a^2*b^3*c^2*d^2 - 4*a^3*b^2*c*d^3 + a^4*b*d^4) + d^4*log(abs(d*x + c))/(b^4*c^4*d - 4*a*b^3*c^3*d^2 + 6*a^2*b^2*c^2*d^3 - 4*a^3*b*c*d^4 + a^4*d^5) - 1/6*(2*b^3*c^3 - 9*a*b^2*c^2*d + 18*a^2*b*c*d^2 - 11*a^3*d^3 + 6*(b^3*c*d^2 - a*b^2*d^3)*x^2 - 3*(b^3*c^2*d - 6*a*b^2*c*d^2 + 5*a^2*b*d^3)*x)/((b*c - a*d)^4*(b*x + a)^3)","B",0
1809,1,338,0,0.171128," ","integrate(1/(b*x+a)^4/(a*c+(a*d+b*c)*x+b*d*x^2),x, algorithm=""giac"")","\frac{b d^{4} \log\left({\left| b x + a \right|}\right)}{b^{6} c^{5} - 5 \, a b^{5} c^{4} d + 10 \, a^{2} b^{4} c^{3} d^{2} - 10 \, a^{3} b^{3} c^{2} d^{3} + 5 \, a^{4} b^{2} c d^{4} - a^{5} b d^{5}} - \frac{d^{5} \log\left({\left| d x + c \right|}\right)}{b^{5} c^{5} d - 5 \, a b^{4} c^{4} d^{2} + 10 \, a^{2} b^{3} c^{3} d^{3} - 10 \, a^{3} b^{2} c^{2} d^{4} + 5 \, a^{4} b c d^{5} - a^{5} d^{6}} - \frac{3 \, b^{4} c^{4} - 16 \, a b^{3} c^{3} d + 36 \, a^{2} b^{2} c^{2} d^{2} - 48 \, a^{3} b c d^{3} + 25 \, a^{4} d^{4} - 12 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{3} + 6 \, {\left(b^{4} c^{2} d^{2} - 8 \, a b^{3} c d^{3} + 7 \, a^{2} b^{2} d^{4}\right)} x^{2} - 4 \, {\left(b^{4} c^{3} d - 6 \, a b^{3} c^{2} d^{2} + 18 \, a^{2} b^{2} c d^{3} - 13 \, a^{3} b d^{4}\right)} x}{12 \, {\left(b c - a d\right)}^{5} {\left(b x + a\right)}^{4}}"," ",0,"b*d^4*log(abs(b*x + a))/(b^6*c^5 - 5*a*b^5*c^4*d + 10*a^2*b^4*c^3*d^2 - 10*a^3*b^3*c^2*d^3 + 5*a^4*b^2*c*d^4 - a^5*b*d^5) - d^5*log(abs(d*x + c))/(b^5*c^5*d - 5*a*b^4*c^4*d^2 + 10*a^2*b^3*c^3*d^3 - 10*a^3*b^2*c^2*d^4 + 5*a^4*b*c*d^5 - a^5*d^6) - 1/12*(3*b^4*c^4 - 16*a*b^3*c^3*d + 36*a^2*b^2*c^2*d^2 - 48*a^3*b*c*d^3 + 25*a^4*d^4 - 12*(b^4*c*d^3 - a*b^3*d^4)*x^3 + 6*(b^4*c^2*d^2 - 8*a*b^3*c*d^3 + 7*a^2*b^2*d^4)*x^2 - 4*(b^4*c^3*d - 6*a*b^3*c^2*d^2 + 18*a^2*b^2*c*d^3 - 13*a^3*b*d^4)*x)/((b*c - a*d)^5*(b*x + a)^4)","B",0
1810,1,188,0,0.165787," ","integrate((b*x+a)^6/(a*c+(a*d+b*c)*x+b*d*x^2)^2,x, algorithm=""giac"")","-\frac{4 \, {\left(b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} \log\left({\left| d x + c \right|}\right)}{d^{5}} + \frac{b^{4} d^{4} x^{3} - 3 \, b^{4} c d^{3} x^{2} + 6 \, a b^{3} d^{4} x^{2} + 9 \, b^{4} c^{2} d^{2} x - 24 \, a b^{3} c d^{3} x + 18 \, a^{2} b^{2} d^{4} x}{3 \, d^{6}} - \frac{b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}}{{\left(d x + c\right)} d^{5}}"," ",0,"-4*(b^4*c^3 - 3*a*b^3*c^2*d + 3*a^2*b^2*c*d^2 - a^3*b*d^3)*log(abs(d*x + c))/d^5 + 1/3*(b^4*d^4*x^3 - 3*b^4*c*d^3*x^2 + 6*a*b^3*d^4*x^2 + 9*b^4*c^2*d^2*x - 24*a*b^3*c*d^3*x + 18*a^2*b^2*d^4*x)/d^6 - (b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)/((d*x + c)*d^5)","A",0
1811,1,118,0,0.192716," ","integrate((b*x+a)^5/(a*c+(a*d+b*c)*x+b*d*x^2)^2,x, algorithm=""giac"")","\frac{3 \, {\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} \log\left({\left| d x + c \right|}\right)}{d^{4}} + \frac{b^{3} d^{2} x^{2} - 4 \, b^{3} c d x + 6 \, a b^{2} d^{2} x}{2 \, d^{4}} + \frac{b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}}{{\left(d x + c\right)} d^{4}}"," ",0,"3*(b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*log(abs(d*x + c))/d^4 + 1/2*(b^3*d^2*x^2 - 4*b^3*c*d*x + 6*a*b^2*d^2*x)/d^4 + (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)/((d*x + c)*d^4)","A",0
1812,1,65,0,0.170543," ","integrate((b*x+a)^4/(a*c+(a*d+b*c)*x+b*d*x^2)^2,x, algorithm=""giac"")","\frac{b^{2} x}{d^{2}} - \frac{2 \, {\left(b^{2} c - a b d\right)} \log\left({\left| d x + c \right|}\right)}{d^{3}} - \frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{{\left(d x + c\right)} d^{3}}"," ",0,"b^2*x/d^2 - 2*(b^2*c - a*b*d)*log(abs(d*x + c))/d^3 - (b^2*c^2 - 2*a*b*c*d + a^2*d^2)/((d*x + c)*d^3)","A",0
1813,1,32,0,0.215951," ","integrate((b*x+a)^3/(a*c+(a*d+b*c)*x+b*d*x^2)^2,x, algorithm=""giac"")","\frac{b \log\left({\left| d x + c \right|}\right)}{d^{2}} + \frac{b c - a d}{{\left(d x + c\right)} d^{2}}"," ",0,"b*log(abs(d*x + c))/d^2 + (b*c - a*d)/((d*x + c)*d^2)","A",0
1814,1,12,0,0.174841," ","integrate((b*x+a)^2/(a*c+(a*d+b*c)*x+b*d*x^2)^2,x, algorithm=""giac"")","-\frac{1}{{\left(d x + c\right)} d}"," ",0,"-1/((d*x + c)*d)","A",0
1815,1,93,0,0.202959," ","integrate((b*x+a)/(a*c+(a*d+b*c)*x+b*d*x^2)^2,x, algorithm=""giac"")","\frac{b^{2} \log\left({\left| b x + a \right|}\right)}{b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}} - \frac{b d \log\left({\left| d x + c \right|}\right)}{b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}} + \frac{1}{{\left(b c - a d\right)} {\left(d x + c\right)}}"," ",0,"b^2*log(abs(b*x + a))/(b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2) - b*d*log(abs(d*x + c))/(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3) + 1/((b*c - a*d)*(d*x + c))","A",0
1816,1,166,0,0.191609," ","integrate(1/(a*c+(a*d+b*c)*x+b*d*x^2)^2,x, algorithm=""giac"")","-\frac{2 \, b^{2} d \log\left({\left| b x + a \right|}\right)}{b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}} + \frac{2 \, b d^{2} \log\left({\left| d x + c \right|}\right)}{b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - a^{3} d^{4}} - \frac{2 \, b d x + b c + a d}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} {\left(b d x^{2} + b c x + a d x + a c\right)}}"," ",0,"-2*b^2*d*log(abs(b*x + a))/(b^4*c^3 - 3*a*b^3*c^2*d + 3*a^2*b^2*c*d^2 - a^3*b*d^3) + 2*b*d^2*log(abs(d*x + c))/(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4) - (2*b*d*x + b*c + a*d)/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*(b*d*x^2 + b*c*x + a*d*x + a*c))","A",0
1817,1,253,0,0.172173," ","integrate(1/(b*x+a)/(a*c+(a*d+b*c)*x+b*d*x^2)^2,x, algorithm=""giac"")","\frac{3 \, b^{2} d^{2} \log\left({\left| b x + a \right|}\right)}{b^{5} c^{4} - 4 \, a b^{4} c^{3} d + 6 \, a^{2} b^{3} c^{2} d^{2} - 4 \, a^{3} b^{2} c d^{3} + a^{4} b d^{4}} - \frac{3 \, b d^{3} \log\left({\left| d x + c \right|}\right)}{b^{4} c^{4} d - 4 \, a b^{3} c^{3} d^{2} + 6 \, a^{2} b^{2} c^{2} d^{3} - 4 \, a^{3} b c d^{4} + a^{4} d^{5}} - \frac{b^{3} c^{3} - 6 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} + 2 \, a^{3} d^{3} - 6 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{2} - 3 \, {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2} - 3 \, a^{2} b d^{3}\right)} x}{2 \, {\left(b c - a d\right)}^{4} {\left(b x + a\right)}^{2} {\left(d x + c\right)}}"," ",0,"3*b^2*d^2*log(abs(b*x + a))/(b^5*c^4 - 4*a*b^4*c^3*d + 6*a^2*b^3*c^2*d^2 - 4*a^3*b^2*c*d^3 + a^4*b*d^4) - 3*b*d^3*log(abs(d*x + c))/(b^4*c^4*d - 4*a*b^3*c^3*d^2 + 6*a^2*b^2*c^2*d^3 - 4*a^3*b*c*d^4 + a^4*d^5) - 1/2*(b^3*c^3 - 6*a*b^2*c^2*d + 3*a^2*b*c*d^2 + 2*a^3*d^3 - 6*(b^3*c*d^2 - a*b^2*d^3)*x^2 - 3*(b^3*c^2*d + 2*a*b^2*c*d^2 - 3*a^2*b*d^3)*x)/((b*c - a*d)^4*(b*x + a)^2*(d*x + c))","B",0
1818,1,264,0,0.181214," ","integrate((b*x+a)^8/(a*c+(a*d+b*c)*x+b*d*x^2)^3,x, algorithm=""giac"")","-\frac{10 \, {\left(b^{5} c^{3} - 3 \, a b^{4} c^{2} d + 3 \, a^{2} b^{3} c d^{2} - a^{3} b^{2} d^{3}\right)} \log\left({\left| d x + c \right|}\right)}{d^{6}} - \frac{9 \, b^{5} c^{5} - 35 \, a b^{4} c^{4} d + 50 \, a^{2} b^{3} c^{3} d^{2} - 30 \, a^{3} b^{2} c^{2} d^{3} + 5 \, a^{4} b c d^{4} + a^{5} d^{5} + 10 \, {\left(b^{5} c^{4} d - 4 \, a b^{4} c^{3} d^{2} + 6 \, a^{2} b^{3} c^{2} d^{3} - 4 \, a^{3} b^{2} c d^{4} + a^{4} b d^{5}\right)} x}{2 \, {\left(d x + c\right)}^{2} d^{6}} + \frac{2 \, b^{5} d^{6} x^{3} - 9 \, b^{5} c d^{5} x^{2} + 15 \, a b^{4} d^{6} x^{2} + 36 \, b^{5} c^{2} d^{4} x - 90 \, a b^{4} c d^{5} x + 60 \, a^{2} b^{3} d^{6} x}{6 \, d^{9}}"," ",0,"-10*(b^5*c^3 - 3*a*b^4*c^2*d + 3*a^2*b^3*c*d^2 - a^3*b^2*d^3)*log(abs(d*x + c))/d^6 - 1/2*(9*b^5*c^5 - 35*a*b^4*c^4*d + 50*a^2*b^3*c^3*d^2 - 30*a^3*b^2*c^2*d^3 + 5*a^4*b*c*d^4 + a^5*d^5 + 10*(b^5*c^4*d - 4*a*b^4*c^3*d^2 + 6*a^2*b^3*c^2*d^3 - 4*a^3*b^2*c*d^4 + a^4*b*d^5)*x)/((d*x + c)^2*d^6) + 1/6*(2*b^5*d^6*x^3 - 9*b^5*c*d^5*x^2 + 15*a*b^4*d^6*x^2 + 36*b^5*c^2*d^4*x - 90*a*b^4*c*d^5*x + 60*a^2*b^3*d^6*x)/d^9","B",0
1819,1,183,0,0.173517," ","integrate((b*x+a)^7/(a*c+(a*d+b*c)*x+b*d*x^2)^3,x, algorithm=""giac"")","\frac{6 \, {\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} \log\left({\left| d x + c \right|}\right)}{d^{5}} + \frac{b^{4} d^{3} x^{2} - 6 \, b^{4} c d^{2} x + 8 \, a b^{3} d^{3} x}{2 \, d^{6}} + \frac{7 \, b^{4} c^{4} - 20 \, a b^{3} c^{3} d + 18 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} - a^{4} d^{4} + 8 \, {\left(b^{4} c^{3} d - 3 \, a b^{3} c^{2} d^{2} + 3 \, a^{2} b^{2} c d^{3} - a^{3} b d^{4}\right)} x}{2 \, {\left(d x + c\right)}^{2} d^{5}}"," ",0,"6*(b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*log(abs(d*x + c))/d^5 + 1/2*(b^4*d^3*x^2 - 6*b^4*c*d^2*x + 8*a*b^3*d^3*x)/d^6 + 1/2*(7*b^4*c^4 - 20*a*b^3*c^3*d + 18*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 - a^4*d^4 + 8*(b^4*c^3*d - 3*a*b^3*c^2*d^2 + 3*a^2*b^2*c*d^3 - a^3*b*d^4)*x)/((d*x + c)^2*d^5)","A",0
1820,1,112,0,0.174714," ","integrate((b*x+a)^6/(a*c+(a*d+b*c)*x+b*d*x^2)^3,x, algorithm=""giac"")","\frac{b^{3} x}{d^{3}} - \frac{3 \, {\left(b^{3} c - a b^{2} d\right)} \log\left({\left| d x + c \right|}\right)}{d^{4}} - \frac{5 \, b^{3} c^{3} - 9 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} + a^{3} d^{3} + 6 \, {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x}{2 \, {\left(d x + c\right)}^{2} d^{4}}"," ",0,"b^3*x/d^3 - 3*(b^3*c - a*b^2*d)*log(abs(d*x + c))/d^4 - 1/2*(5*b^3*c^3 - 9*a*b^2*c^2*d + 3*a^2*b*c*d^2 + a^3*d^3 + 6*(b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*x)/((d*x + c)^2*d^4)","A",0
1821,1,69,0,0.175622," ","integrate((b*x+a)^5/(a*c+(a*d+b*c)*x+b*d*x^2)^3,x, algorithm=""giac"")","\frac{b^{2} \log\left({\left| d x + c \right|}\right)}{d^{3}} + \frac{4 \, {\left(b^{2} c - a b d\right)} x + \frac{3 \, b^{2} c^{2} - 2 \, a b c d - a^{2} d^{2}}{d}}{2 \, {\left(d x + c\right)}^{2} d^{2}}"," ",0,"b^2*log(abs(d*x + c))/d^3 + 1/2*(4*(b^2*c - a*b*d)*x + (3*b^2*c^2 - 2*a*b*c*d - a^2*d^2)/d)/((d*x + c)^2*d^2)","A",0
1822,1,24,0,0.205154," ","integrate((b*x+a)^4/(a*c+(a*d+b*c)*x+b*d*x^2)^3,x, algorithm=""giac"")","-\frac{2 \, b d x + b c + a d}{2 \, {\left(d x + c\right)}^{2} d^{2}}"," ",0,"-1/2*(2*b*d*x + b*c + a*d)/((d*x + c)^2*d^2)","A",0
1823,1,12,0,0.174114," ","integrate((b*x+a)^3/(a*c+(a*d+b*c)*x+b*d*x^2)^3,x, algorithm=""giac"")","-\frac{1}{2 \, {\left(d x + c\right)}^{2} d}"," ",0,"-1/2/((d*x + c)^2*d)","A",0
1824,1,165,0,0.185331," ","integrate((b*x+a)^2/(a*c+(a*d+b*c)*x+b*d*x^2)^3,x, algorithm=""giac"")","\frac{b^{3} \log\left({\left| b x + a \right|}\right)}{b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}} - \frac{b^{2} d \log\left({\left| d x + c \right|}\right)}{b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - a^{3} d^{4}} + \frac{3 \, b^{2} c^{2} - 4 \, a b c d + a^{2} d^{2} + 2 \, {\left(b^{2} c d - a b d^{2}\right)} x}{2 \, {\left(b c - a d\right)}^{3} {\left(d x + c\right)}^{2}}"," ",0,"b^3*log(abs(b*x + a))/(b^4*c^3 - 3*a*b^3*c^2*d + 3*a^2*b^2*c*d^2 - a^3*b*d^3) - b^2*d*log(abs(d*x + c))/(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4) + 1/2*(3*b^2*c^2 - 4*a*b*c*d + a^2*d^2 + 2*(b^2*c*d - a*b*d^2)*x)/((b*c - a*d)^3*(d*x + c)^2)","B",0
1825,1,254,0,0.177747," ","integrate((b*x+a)/(a*c+(a*d+b*c)*x+b*d*x^2)^3,x, algorithm=""giac"")","-\frac{3 \, b^{3} d \log\left({\left| b x + a \right|}\right)}{b^{5} c^{4} - 4 \, a b^{4} c^{3} d + 6 \, a^{2} b^{3} c^{2} d^{2} - 4 \, a^{3} b^{2} c d^{3} + a^{4} b d^{4}} + \frac{3 \, b^{2} d^{2} \log\left({\left| d x + c \right|}\right)}{b^{4} c^{4} d - 4 \, a b^{3} c^{3} d^{2} + 6 \, a^{2} b^{2} c^{2} d^{3} - 4 \, a^{3} b c d^{4} + a^{4} d^{5}} - \frac{2 \, b^{3} c^{3} + 3 \, a b^{2} c^{2} d - 6 \, a^{2} b c d^{2} + a^{3} d^{3} + 6 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{2} + 3 \, {\left(3 \, b^{3} c^{2} d - 2 \, a b^{2} c d^{2} - a^{2} b d^{3}\right)} x}{2 \, {\left(b c - a d\right)}^{4} {\left(b x + a\right)} {\left(d x + c\right)}^{2}}"," ",0,"-3*b^3*d*log(abs(b*x + a))/(b^5*c^4 - 4*a*b^4*c^3*d + 6*a^2*b^3*c^2*d^2 - 4*a^3*b^2*c*d^3 + a^4*b*d^4) + 3*b^2*d^2*log(abs(d*x + c))/(b^4*c^4*d - 4*a*b^3*c^3*d^2 + 6*a^2*b^2*c^2*d^3 - 4*a^3*b*c*d^4 + a^4*d^5) - 1/2*(2*b^3*c^3 + 3*a*b^2*c^2*d - 6*a^2*b*c*d^2 + a^3*d^3 + 6*(b^3*c*d^2 - a*b^2*d^3)*x^2 + 3*(3*b^3*c^2*d - 2*a*b^2*c*d^2 - a^2*b*d^3)*x)/((b*c - a*d)^4*(b*x + a)*(d*x + c)^2)","B",0
1826,1,345,0,0.156549," ","integrate(1/(a*c+(a*d+b*c)*x+b*d*x^2)^3,x, algorithm=""giac"")","\frac{6 \, b^{3} d^{2} \log\left({\left| b x + a \right|}\right)}{b^{6} c^{5} - 5 \, a b^{5} c^{4} d + 10 \, a^{2} b^{4} c^{3} d^{2} - 10 \, a^{3} b^{3} c^{2} d^{3} + 5 \, a^{4} b^{2} c d^{4} - a^{5} b d^{5}} - \frac{6 \, b^{2} d^{3} \log\left({\left| d x + c \right|}\right)}{b^{5} c^{5} d - 5 \, a b^{4} c^{4} d^{2} + 10 \, a^{2} b^{3} c^{3} d^{3} - 10 \, a^{3} b^{2} c^{2} d^{4} + 5 \, a^{4} b c d^{5} - a^{5} d^{6}} + \frac{12 \, b^{3} d^{3} x^{3} + 18 \, b^{3} c d^{2} x^{2} + 18 \, a b^{2} d^{3} x^{2} + 4 \, b^{3} c^{2} d x + 28 \, a b^{2} c d^{2} x + 4 \, a^{2} b d^{3} x - b^{3} c^{3} + 7 \, a b^{2} c^{2} d + 7 \, a^{2} b c d^{2} - a^{3} d^{3}}{2 \, {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} {\left(b d x^{2} + b c x + a d x + a c\right)}^{2}}"," ",0,"6*b^3*d^2*log(abs(b*x + a))/(b^6*c^5 - 5*a*b^5*c^4*d + 10*a^2*b^4*c^3*d^2 - 10*a^3*b^3*c^2*d^3 + 5*a^4*b^2*c*d^4 - a^5*b*d^5) - 6*b^2*d^3*log(abs(d*x + c))/(b^5*c^5*d - 5*a*b^4*c^4*d^2 + 10*a^2*b^3*c^3*d^3 - 10*a^3*b^2*c^2*d^4 + 5*a^4*b*c*d^5 - a^5*d^6) + 1/2*(12*b^3*d^3*x^3 + 18*b^3*c*d^2*x^2 + 18*a*b^2*d^3*x^2 + 4*b^3*c^2*d*x + 28*a*b^2*c*d^2*x + 4*a^2*b*d^3*x - b^3*c^3 + 7*a*b^2*c^2*d + 7*a^2*b*c*d^2 - a^3*d^3)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*(b*d*x^2 + b*c*x + a*d*x + a*c)^2)","B",0
1827,1,458,0,0.258377," ","integrate(1/(b*x+a)/(a*c+(a*d+b*c)*x+b*d*x^2)^3,x, algorithm=""giac"")","-\frac{10 \, b^{3} d^{3} \log\left({\left| b x + a \right|}\right)}{b^{7} c^{6} - 6 \, a b^{6} c^{5} d + 15 \, a^{2} b^{5} c^{4} d^{2} - 20 \, a^{3} b^{4} c^{3} d^{3} + 15 \, a^{4} b^{3} c^{2} d^{4} - 6 \, a^{5} b^{2} c d^{5} + a^{6} b d^{6}} + \frac{10 \, b^{2} d^{4} \log\left({\left| d x + c \right|}\right)}{b^{6} c^{6} d - 6 \, a b^{5} c^{5} d^{2} + 15 \, a^{2} b^{4} c^{4} d^{3} - 20 \, a^{3} b^{3} c^{3} d^{4} + 15 \, a^{4} b^{2} c^{2} d^{5} - 6 \, a^{5} b c d^{6} + a^{6} d^{7}} - \frac{2 \, b^{5} c^{5} - 15 \, a b^{4} c^{4} d + 60 \, a^{2} b^{3} c^{3} d^{2} - 20 \, a^{3} b^{2} c^{2} d^{3} - 30 \, a^{4} b c d^{4} + 3 \, a^{5} d^{5} + 60 \, {\left(b^{5} c d^{4} - a b^{4} d^{5}\right)} x^{4} + 30 \, {\left(3 \, b^{5} c^{2} d^{3} + 2 \, a b^{4} c d^{4} - 5 \, a^{2} b^{3} d^{5}\right)} x^{3} + 10 \, {\left(2 \, b^{5} c^{3} d^{2} + 21 \, a b^{4} c^{2} d^{3} - 12 \, a^{2} b^{3} c d^{4} - 11 \, a^{3} b^{2} d^{5}\right)} x^{2} - 5 \, {\left(b^{5} c^{4} d - 12 \, a b^{4} c^{3} d^{2} - 24 \, a^{2} b^{3} c^{2} d^{3} + 32 \, a^{3} b^{2} c d^{4} + 3 \, a^{4} b d^{5}\right)} x}{6 \, {\left(b c - a d\right)}^{6} {\left(b x + a\right)}^{3} {\left(d x + c\right)}^{2}}"," ",0,"-10*b^3*d^3*log(abs(b*x + a))/(b^7*c^6 - 6*a*b^6*c^5*d + 15*a^2*b^5*c^4*d^2 - 20*a^3*b^4*c^3*d^3 + 15*a^4*b^3*c^2*d^4 - 6*a^5*b^2*c*d^5 + a^6*b*d^6) + 10*b^2*d^4*log(abs(d*x + c))/(b^6*c^6*d - 6*a*b^5*c^5*d^2 + 15*a^2*b^4*c^4*d^3 - 20*a^3*b^3*c^3*d^4 + 15*a^4*b^2*c^2*d^5 - 6*a^5*b*c*d^6 + a^6*d^7) - 1/6*(2*b^5*c^5 - 15*a*b^4*c^4*d + 60*a^2*b^3*c^3*d^2 - 20*a^3*b^2*c^2*d^3 - 30*a^4*b*c*d^4 + 3*a^5*d^5 + 60*(b^5*c*d^4 - a*b^4*d^5)*x^4 + 30*(3*b^5*c^2*d^3 + 2*a*b^4*c*d^4 - 5*a^2*b^3*d^5)*x^3 + 10*(2*b^5*c^3*d^2 + 21*a*b^4*c^2*d^3 - 12*a^2*b^3*c*d^4 - 11*a^3*b^2*d^5)*x^2 - 5*(b^5*c^4*d - 12*a*b^4*c^3*d^2 - 24*a^2*b^3*c^2*d^3 + 32*a^3*b^2*c*d^4 + 3*a^4*b*d^5)*x)/((b*c - a*d)^6*(b*x + a)^3*(d*x + c)^2)","B",0
1828,1,120,0,0.153067," ","integrate((e*x+d)^4*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x, algorithm=""giac"")","\frac{1}{7} \, c d x^{7} e^{5} + \frac{5}{6} \, c d^{2} x^{6} e^{4} + 2 \, c d^{3} x^{5} e^{3} + \frac{5}{2} \, c d^{4} x^{4} e^{2} + \frac{5}{3} \, c d^{5} x^{3} e + \frac{1}{2} \, c d^{6} x^{2} + \frac{1}{6} \, a x^{6} e^{6} + a d x^{5} e^{5} + \frac{5}{2} \, a d^{2} x^{4} e^{4} + \frac{10}{3} \, a d^{3} x^{3} e^{3} + \frac{5}{2} \, a d^{4} x^{2} e^{2} + a d^{5} x e"," ",0,"1/7*c*d*x^7*e^5 + 5/6*c*d^2*x^6*e^4 + 2*c*d^3*x^5*e^3 + 5/2*c*d^4*x^4*e^2 + 5/3*c*d^5*x^3*e + 1/2*c*d^6*x^2 + 1/6*a*x^6*e^6 + a*d*x^5*e^5 + 5/2*a*d^2*x^4*e^4 + 10/3*a*d^3*x^3*e^3 + 5/2*a*d^4*x^2*e^2 + a*d^5*x*e","B",0
1829,1,98,0,0.153759," ","integrate((e*x+d)^3*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x, algorithm=""giac"")","\frac{1}{6} \, c d x^{6} e^{4} + \frac{4}{5} \, c d^{2} x^{5} e^{3} + \frac{3}{2} \, c d^{3} x^{4} e^{2} + \frac{4}{3} \, c d^{4} x^{3} e + \frac{1}{2} \, c d^{5} x^{2} + \frac{1}{5} \, a x^{5} e^{5} + a d x^{4} e^{4} + 2 \, a d^{2} x^{3} e^{3} + 2 \, a d^{3} x^{2} e^{2} + a d^{4} x e"," ",0,"1/6*c*d*x^6*e^4 + 4/5*c*d^2*x^5*e^3 + 3/2*c*d^3*x^4*e^2 + 4/3*c*d^4*x^3*e + 1/2*c*d^5*x^2 + 1/5*a*x^5*e^5 + a*d*x^4*e^4 + 2*a*d^2*x^3*e^3 + 2*a*d^3*x^2*e^2 + a*d^4*x*e","B",0
1830,1,75,0,0.160753," ","integrate((e*x+d)^2*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x, algorithm=""giac"")","\frac{1}{5} \, c d x^{5} e^{3} + \frac{3}{4} \, c d^{2} x^{4} e^{2} + c d^{3} x^{3} e + \frac{1}{2} \, c d^{4} x^{2} + \frac{1}{4} \, a x^{4} e^{4} + a d x^{3} e^{3} + \frac{3}{2} \, a d^{2} x^{2} e^{2} + a d^{3} x e"," ",0,"1/5*c*d*x^5*e^3 + 3/4*c*d^2*x^4*e^2 + c*d^3*x^3*e + 1/2*c*d^4*x^2 + 1/4*a*x^4*e^4 + a*d*x^3*e^3 + 3/2*a*d^2*x^2*e^2 + a*d^3*x*e","B",0
1831,1,54,0,0.191621," ","integrate((e*x+d)*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x, algorithm=""giac"")","\frac{1}{4} \, c d x^{4} e^{2} + \frac{2}{3} \, c d^{2} x^{3} e + \frac{1}{2} \, c d^{3} x^{2} + \frac{1}{3} \, a x^{3} e^{3} + a d x^{2} e^{2} + a d^{2} x e"," ",0,"1/4*c*d*x^4*e^2 + 2/3*c*d^2*x^3*e + 1/2*c*d^3*x^2 + 1/3*a*x^3*e^3 + a*d*x^2*e^2 + a*d^2*x*e","A",0
1832,1,31,0,0.171408," ","integrate(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2,x, algorithm=""giac"")","\frac{1}{3} \, c d x^{3} e + a d x e + \frac{1}{2} \, {\left(c d^{2} + a e^{2}\right)} x^{2}"," ",0,"1/3*c*d*x^3*e + a*d*x*e + 1/2*(c*d^2 + a*e^2)*x^2","A",0
1833,1,19,0,0.261641," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)/(e*x+d),x, algorithm=""giac"")","\frac{1}{2} \, {\left(c d x^{2} e^{2} + 2 \, a x e^{3}\right)} e^{\left(-2\right)}"," ",0,"1/2*(c*d*x^2*e^2 + 2*a*x*e^3)*e^(-2)","A",0
1834,1,117,0,0.157913," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)/(e*x+d)^2,x, algorithm=""giac"")","{\left(2 \, d e^{\left(-3\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) + {\left(x e + d\right)} e^{\left(-3\right)} - \frac{d^{2} e^{\left(-3\right)}}{x e + d}\right)} c d e - {\left(c d^{2} + a e^{2}\right)} {\left(e^{\left(-1\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) - \frac{d e^{\left(-1\right)}}{x e + d}\right)} e^{\left(-1\right)} - \frac{a d}{x e + d}"," ",0,"(2*d*e^(-3)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) + (x*e + d)*e^(-3) - d^2*e^(-3)/(x*e + d))*c*d*e - (c*d^2 + a*e^2)*(e^(-1)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) - d*e^(-1)/(x*e + d))*e^(-1) - a*d/(x*e + d)","B",0
1835,1,52,0,0.169088," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)/(e*x+d)^3,x, algorithm=""giac"")","c d e^{\left(-2\right)} \log\left({\left| x e + d \right|}\right) + \frac{{\left(c d^{3} - a d e^{2} + {\left(c d^{2} e - a e^{3}\right)} x\right)} e^{\left(-2\right)}}{{\left(x e + d\right)}^{2}}"," ",0,"c*d*e^(-2)*log(abs(x*e + d)) + (c*d^3 - a*d*e^2 + (c*d^2*e - a*e^3)*x)*e^(-2)/(x*e + d)^2","A",0
1836,1,46,0,0.161088," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)/(e*x+d)^4,x, algorithm=""giac"")","-\frac{{\left(2 \, c d x^{2} e^{2} + 3 \, c d^{2} x e + c d^{3} + a x e^{3} + a d e^{2}\right)} e^{\left(-2\right)}}{2 \, {\left(x e + d\right)}^{3}}"," ",0,"-1/2*(2*c*d*x^2*e^2 + 3*c*d^2*x*e + c*d^3 + a*x*e^3 + a*d*e^2)*e^(-2)/(x*e + d)^3","A",0
1837,1,42,0,0.178265," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)/(e*x+d)^5,x, algorithm=""giac"")","-\frac{c d e^{\left(-2\right)}}{2 \, {\left(x e + d\right)}^{2}} + \frac{c d^{2} e^{\left(-2\right)}}{3 \, {\left(x e + d\right)}^{3}} - \frac{a}{3 \, {\left(x e + d\right)}^{3}}"," ",0,"-1/2*c*d*e^(-2)/(x*e + d)^2 + 1/3*c*d^2*e^(-2)/(x*e + d)^3 - 1/3*a/(x*e + d)^3","A",0
1838,1,48,0,0.159594," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)/(e*x+d)^6,x, algorithm=""giac"")","-\frac{{\left(4 \, c d x^{2} e^{2} + 5 \, c d^{2} x e + c d^{3} + 3 \, a x e^{3} + 3 \, a d e^{2}\right)} e^{\left(-2\right)}}{12 \, {\left(x e + d\right)}^{5}}"," ",0,"-1/12*(4*c*d*x^2*e^2 + 5*c*d^2*x*e + c*d^3 + 3*a*x*e^3 + 3*a*d*e^2)*e^(-2)/(x*e + d)^5","A",0
1839,1,176,0,0.177258," ","integrate((e*x+d)^2*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x, algorithm=""giac"")","\frac{1}{7} \, c^{2} d^{2} x^{7} e^{4} + \frac{2}{3} \, c^{2} d^{3} x^{6} e^{3} + \frac{6}{5} \, c^{2} d^{4} x^{5} e^{2} + c^{2} d^{5} x^{4} e + \frac{1}{3} \, c^{2} d^{6} x^{3} + \frac{1}{3} \, a c d x^{6} e^{5} + \frac{8}{5} \, a c d^{2} x^{5} e^{4} + 3 \, a c d^{3} x^{4} e^{3} + \frac{8}{3} \, a c d^{4} x^{3} e^{2} + a c d^{5} x^{2} e + \frac{1}{5} \, a^{2} x^{5} e^{6} + a^{2} d x^{4} e^{5} + 2 \, a^{2} d^{2} x^{3} e^{4} + 2 \, a^{2} d^{3} x^{2} e^{3} + a^{2} d^{4} x e^{2}"," ",0,"1/7*c^2*d^2*x^7*e^4 + 2/3*c^2*d^3*x^6*e^3 + 6/5*c^2*d^4*x^5*e^2 + c^2*d^5*x^4*e + 1/3*c^2*d^6*x^3 + 1/3*a*c*d*x^6*e^5 + 8/5*a*c*d^2*x^5*e^4 + 3*a*c*d^3*x^4*e^3 + 8/3*a*c*d^4*x^3*e^2 + a*c*d^5*x^2*e + 1/5*a^2*x^5*e^6 + a^2*d*x^4*e^5 + 2*a^2*d^2*x^3*e^4 + 2*a^2*d^3*x^2*e^3 + a^2*d^4*x*e^2","B",0
1840,1,139,0,0.157485," ","integrate((e*x+d)*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x, algorithm=""giac"")","\frac{1}{6} \, c^{2} d^{2} x^{6} e^{3} + \frac{3}{5} \, c^{2} d^{3} x^{5} e^{2} + \frac{3}{4} \, c^{2} d^{4} x^{4} e + \frac{1}{3} \, c^{2} d^{5} x^{3} + \frac{2}{5} \, a c d x^{5} e^{4} + \frac{3}{2} \, a c d^{2} x^{4} e^{3} + 2 \, a c d^{3} x^{3} e^{2} + a c d^{4} x^{2} e + \frac{1}{4} \, a^{2} x^{4} e^{5} + a^{2} d x^{3} e^{4} + \frac{3}{2} \, a^{2} d^{2} x^{2} e^{3} + a^{2} d^{3} x e^{2}"," ",0,"1/6*c^2*d^2*x^6*e^3 + 3/5*c^2*d^3*x^5*e^2 + 3/4*c^2*d^4*x^4*e + 1/3*c^2*d^5*x^3 + 2/5*a*c*d*x^5*e^4 + 3/2*a*c*d^2*x^4*e^3 + 2*a*c*d^3*x^3*e^2 + a*c*d^4*x^2*e + 1/4*a^2*x^4*e^5 + a^2*d*x^3*e^4 + 3/2*a^2*d^2*x^2*e^3 + a^2*d^3*x*e^2","A",0
1841,1,101,0,0.157491," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x, algorithm=""giac"")","\frac{1}{5} \, c^{2} d^{2} x^{5} e^{2} + \frac{1}{2} \, c^{2} d^{3} x^{4} e + \frac{1}{3} \, c^{2} d^{4} x^{3} + \frac{1}{2} \, a c d x^{4} e^{3} + \frac{4}{3} \, a c d^{2} x^{3} e^{2} + a c d^{3} x^{2} e + \frac{1}{3} \, a^{2} x^{3} e^{4} + a^{2} d x^{2} e^{3} + a^{2} d^{2} x e^{2}"," ",0,"1/5*c^2*d^2*x^5*e^2 + 1/2*c^2*d^3*x^4*e + 1/3*c^2*d^4*x^3 + 1/2*a*c*d*x^4*e^3 + 4/3*a*c*d^2*x^3*e^2 + a*c*d^3*x^2*e + 1/3*a^2*x^3*e^4 + a^2*d*x^2*e^3 + a^2*d^2*x*e^2","A",0
1842,1,72,0,0.164347," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2/(e*x+d),x, algorithm=""giac"")","\frac{1}{12} \, {\left(3 \, c^{2} d^{2} x^{4} e^{5} + 4 \, c^{2} d^{3} x^{3} e^{4} + 8 \, a c d x^{3} e^{6} + 12 \, a c d^{2} x^{2} e^{5} + 6 \, a^{2} x^{2} e^{7} + 12 \, a^{2} d x e^{6}\right)} e^{\left(-4\right)}"," ",0,"1/12*(3*c^2*d^2*x^4*e^5 + 4*c^2*d^3*x^3*e^4 + 8*a*c*d*x^3*e^6 + 12*a*c*d^2*x^2*e^5 + 6*a^2*x^2*e^7 + 12*a^2*d*x*e^6)*e^(-4)","A",0
1843,1,86,0,0.165014," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2/(e*x+d)^2,x, algorithm=""giac"")","\frac{1}{3} \, {\left(c^{2} d^{2} - \frac{3 \, {\left(c^{2} d^{3} e - a c d e^{3}\right)} e^{\left(-1\right)}}{x e + d} + \frac{3 \, {\left(c^{2} d^{4} e^{2} - 2 \, a c d^{2} e^{4} + a^{2} e^{6}\right)} e^{\left(-2\right)}}{{\left(x e + d\right)}^{2}}\right)} {\left(x e + d\right)}^{3} e^{\left(-3\right)}"," ",0,"1/3*(c^2*d^2 - 3*(c^2*d^3*e - a*c*d*e^3)*e^(-1)/(x*e + d) + 3*(c^2*d^4*e^2 - 2*a*c*d^2*e^4 + a^2*e^6)*e^(-2)/(x*e + d)^2)*(x*e + d)^3*e^(-3)","B",0
1844,1,71,0,0.173625," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2/(e*x+d)^3,x, algorithm=""giac"")","{\left(c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} e^{\left(-3\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{2} \, {\left(c^{2} d^{2} x^{2} e^{5} - 2 \, c^{2} d^{3} x e^{4} + 4 \, a c d x e^{6}\right)} e^{\left(-6\right)}"," ",0,"(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*e^(-3)*log(abs(x*e + d)) + 1/2*(c^2*d^2*x^2*e^5 - 2*c^2*d^3*x*e^4 + 4*a*c*d*x*e^6)*e^(-6)","A",0
1845,1,134,0,0.176691," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2/(e*x+d)^4,x, algorithm=""giac"")","c^{2} d^{2} x e^{\left(-2\right)} - 2 \, {\left(c^{2} d^{3} - a c d e^{2}\right)} e^{\left(-3\right)} \log\left({\left| x e + d \right|}\right) - \frac{{\left(c^{2} d^{6} - 2 \, a c d^{4} e^{2} + a^{2} d^{2} e^{4} + {\left(c^{2} d^{4} e^{2} - 2 \, a c d^{2} e^{4} + a^{2} e^{6}\right)} x^{2} + 2 \, {\left(c^{2} d^{5} e - 2 \, a c d^{3} e^{3} + a^{2} d e^{5}\right)} x\right)} e^{\left(-3\right)}}{{\left(x e + d\right)}^{3}}"," ",0,"c^2*d^2*x*e^(-2) - 2*(c^2*d^3 - a*c*d*e^2)*e^(-3)*log(abs(x*e + d)) - (c^2*d^6 - 2*a*c*d^4*e^2 + a^2*d^2*e^4 + (c^2*d^4*e^2 - 2*a*c*d^2*e^4 + a^2*e^6)*x^2 + 2*(c^2*d^5*e - 2*a*c*d^3*e^3 + a^2*d*e^5)*x)*e^(-3)/(x*e + d)^3","B",0
1846,1,118,0,0.250719," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2/(e*x+d)^5,x, algorithm=""giac"")","-c^{2} d^{2} e^{\left(-3\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) + \frac{1}{2} \, {\left(\frac{4 \, c^{2} d^{3} e^{9}}{x e + d} - \frac{c^{2} d^{4} e^{9}}{{\left(x e + d\right)}^{2}} - \frac{4 \, a c d e^{11}}{x e + d} + \frac{2 \, a c d^{2} e^{11}}{{\left(x e + d\right)}^{2}} - \frac{a^{2} e^{13}}{{\left(x e + d\right)}^{2}}\right)} e^{\left(-12\right)}"," ",0,"-c^2*d^2*e^(-3)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) + 1/2*(4*c^2*d^3*e^9/(x*e + d) - c^2*d^4*e^9/(x*e + d)^2 - 4*a*c*d*e^11/(x*e + d) + 2*a*c*d^2*e^11/(x*e + d)^2 - a^2*e^13/(x*e + d)^2)*e^(-12)","A",0
1847,1,137,0,0.175150," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2/(e*x+d)^6,x, algorithm=""giac"")","-\frac{{\left(3 \, c^{2} d^{2} x^{4} e^{4} + 9 \, c^{2} d^{3} x^{3} e^{3} + 10 \, c^{2} d^{4} x^{2} e^{2} + 5 \, c^{2} d^{5} x e + c^{2} d^{6} + 3 \, a c d x^{3} e^{5} + 7 \, a c d^{2} x^{2} e^{4} + 5 \, a c d^{3} x e^{3} + a c d^{4} e^{2} + a^{2} x^{2} e^{6} + 2 \, a^{2} d x e^{5} + a^{2} d^{2} e^{4}\right)} e^{\left(-3\right)}}{3 \, {\left(x e + d\right)}^{5}}"," ",0,"-1/3*(3*c^2*d^2*x^4*e^4 + 9*c^2*d^3*x^3*e^3 + 10*c^2*d^4*x^2*e^2 + 5*c^2*d^5*x*e + c^2*d^6 + 3*a*c*d*x^3*e^5 + 7*a*c*d^2*x^2*e^4 + 5*a*c*d^3*x*e^3 + a*c*d^4*e^2 + a^2*x^2*e^6 + 2*a^2*d*x*e^5 + a^2*d^2*e^4)*e^(-3)/(x*e + d)^5","B",0
1848,1,140,0,0.166686," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2/(e*x+d)^7,x, algorithm=""giac"")","-\frac{{\left(6 \, c^{2} d^{2} x^{4} e^{4} + 16 \, c^{2} d^{3} x^{3} e^{3} + 15 \, c^{2} d^{4} x^{2} e^{2} + 6 \, c^{2} d^{5} x e + c^{2} d^{6} + 8 \, a c d x^{3} e^{5} + 18 \, a c d^{2} x^{2} e^{4} + 12 \, a c d^{3} x e^{3} + 2 \, a c d^{4} e^{2} + 3 \, a^{2} x^{2} e^{6} + 6 \, a^{2} d x e^{5} + 3 \, a^{2} d^{2} e^{4}\right)} e^{\left(-3\right)}}{12 \, {\left(x e + d\right)}^{6}}"," ",0,"-1/12*(6*c^2*d^2*x^4*e^4 + 16*c^2*d^3*x^3*e^3 + 15*c^2*d^4*x^2*e^2 + 6*c^2*d^5*x*e + c^2*d^6 + 8*a*c*d*x^3*e^5 + 18*a*c*d^2*x^2*e^4 + 12*a*c*d^3*x*e^3 + 2*a*c*d^4*e^2 + 3*a^2*x^2*e^6 + 6*a^2*d*x*e^5 + 3*a^2*d^2*e^4)*e^(-3)/(x*e + d)^6","A",0
1849,1,140,0,0.176860," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2/(e*x+d)^8,x, algorithm=""giac"")","-\frac{{\left(10 \, c^{2} d^{2} x^{4} e^{4} + 25 \, c^{2} d^{3} x^{3} e^{3} + 21 \, c^{2} d^{4} x^{2} e^{2} + 7 \, c^{2} d^{5} x e + c^{2} d^{6} + 15 \, a c d x^{3} e^{5} + 33 \, a c d^{2} x^{2} e^{4} + 21 \, a c d^{3} x e^{3} + 3 \, a c d^{4} e^{2} + 6 \, a^{2} x^{2} e^{6} + 12 \, a^{2} d x e^{5} + 6 \, a^{2} d^{2} e^{4}\right)} e^{\left(-3\right)}}{30 \, {\left(x e + d\right)}^{7}}"," ",0,"-1/30*(10*c^2*d^2*x^4*e^4 + 25*c^2*d^3*x^3*e^3 + 21*c^2*d^4*x^2*e^2 + 7*c^2*d^5*x*e + c^2*d^6 + 15*a*c*d*x^3*e^5 + 33*a*c*d^2*x^2*e^4 + 21*a*c*d^3*x*e^3 + 3*a*c*d^4*e^2 + 6*a^2*x^2*e^6 + 12*a^2*d*x*e^5 + 6*a^2*d^2*e^4)*e^(-3)/(x*e + d)^7","A",0
1850,1,140,0,0.183884," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2/(e*x+d)^9,x, algorithm=""giac"")","-\frac{{\left(15 \, c^{2} d^{2} x^{4} e^{4} + 36 \, c^{2} d^{3} x^{3} e^{3} + 28 \, c^{2} d^{4} x^{2} e^{2} + 8 \, c^{2} d^{5} x e + c^{2} d^{6} + 24 \, a c d x^{3} e^{5} + 52 \, a c d^{2} x^{2} e^{4} + 32 \, a c d^{3} x e^{3} + 4 \, a c d^{4} e^{2} + 10 \, a^{2} x^{2} e^{6} + 20 \, a^{2} d x e^{5} + 10 \, a^{2} d^{2} e^{4}\right)} e^{\left(-3\right)}}{60 \, {\left(x e + d\right)}^{8}}"," ",0,"-1/60*(15*c^2*d^2*x^4*e^4 + 36*c^2*d^3*x^3*e^3 + 28*c^2*d^4*x^2*e^2 + 8*c^2*d^5*x*e + c^2*d^6 + 24*a*c*d*x^3*e^5 + 52*a*c*d^2*x^2*e^4 + 32*a*c*d^3*x*e^3 + 4*a*c*d^4*e^2 + 10*a^2*x^2*e^6 + 20*a^2*d*x*e^5 + 10*a^2*d^2*e^4)*e^(-3)/(x*e + d)^8","A",0
1851,1,310,0,0.164471," ","integrate((e*x+d)^2*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x, algorithm=""giac"")","\frac{1}{9} \, c^{3} d^{3} x^{9} e^{5} + \frac{5}{8} \, c^{3} d^{4} x^{8} e^{4} + \frac{10}{7} \, c^{3} d^{5} x^{7} e^{3} + \frac{5}{3} \, c^{3} d^{6} x^{6} e^{2} + c^{3} d^{7} x^{5} e + \frac{1}{4} \, c^{3} d^{8} x^{4} + \frac{3}{8} \, a c^{2} d^{2} x^{8} e^{6} + \frac{15}{7} \, a c^{2} d^{3} x^{7} e^{5} + 5 \, a c^{2} d^{4} x^{6} e^{4} + 6 \, a c^{2} d^{5} x^{5} e^{3} + \frac{15}{4} \, a c^{2} d^{6} x^{4} e^{2} + a c^{2} d^{7} x^{3} e + \frac{3}{7} \, a^{2} c d x^{7} e^{7} + \frac{5}{2} \, a^{2} c d^{2} x^{6} e^{6} + 6 \, a^{2} c d^{3} x^{5} e^{5} + \frac{15}{2} \, a^{2} c d^{4} x^{4} e^{4} + 5 \, a^{2} c d^{5} x^{3} e^{3} + \frac{3}{2} \, a^{2} c d^{6} x^{2} e^{2} + \frac{1}{6} \, a^{3} x^{6} e^{8} + a^{3} d x^{5} e^{7} + \frac{5}{2} \, a^{3} d^{2} x^{4} e^{6} + \frac{10}{3} \, a^{3} d^{3} x^{3} e^{5} + \frac{5}{2} \, a^{3} d^{4} x^{2} e^{4} + a^{3} d^{5} x e^{3}"," ",0,"1/9*c^3*d^3*x^9*e^5 + 5/8*c^3*d^4*x^8*e^4 + 10/7*c^3*d^5*x^7*e^3 + 5/3*c^3*d^6*x^6*e^2 + c^3*d^7*x^5*e + 1/4*c^3*d^8*x^4 + 3/8*a*c^2*d^2*x^8*e^6 + 15/7*a*c^2*d^3*x^7*e^5 + 5*a*c^2*d^4*x^6*e^4 + 6*a*c^2*d^5*x^5*e^3 + 15/4*a*c^2*d^6*x^4*e^2 + a*c^2*d^7*x^3*e + 3/7*a^2*c*d*x^7*e^7 + 5/2*a^2*c*d^2*x^6*e^6 + 6*a^2*c*d^3*x^5*e^5 + 15/2*a^2*c*d^4*x^4*e^4 + 5*a^2*c*d^5*x^3*e^3 + 3/2*a^2*c*d^6*x^2*e^2 + 1/6*a^3*x^6*e^8 + a^3*d*x^5*e^7 + 5/2*a^3*d^2*x^4*e^6 + 10/3*a^3*d^3*x^3*e^5 + 5/2*a^3*d^4*x^2*e^4 + a^3*d^5*x*e^3","B",0
1852,1,256,0,0.188213," ","integrate((e*x+d)*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x, algorithm=""giac"")","\frac{1}{8} \, c^{3} d^{3} x^{8} e^{4} + \frac{4}{7} \, c^{3} d^{4} x^{7} e^{3} + c^{3} d^{5} x^{6} e^{2} + \frac{4}{5} \, c^{3} d^{6} x^{5} e + \frac{1}{4} \, c^{3} d^{7} x^{4} + \frac{3}{7} \, a c^{2} d^{2} x^{7} e^{5} + 2 \, a c^{2} d^{3} x^{6} e^{4} + \frac{18}{5} \, a c^{2} d^{4} x^{5} e^{3} + 3 \, a c^{2} d^{5} x^{4} e^{2} + a c^{2} d^{6} x^{3} e + \frac{1}{2} \, a^{2} c d x^{6} e^{6} + \frac{12}{5} \, a^{2} c d^{2} x^{5} e^{5} + \frac{9}{2} \, a^{2} c d^{3} x^{4} e^{4} + 4 \, a^{2} c d^{4} x^{3} e^{3} + \frac{3}{2} \, a^{2} c d^{5} x^{2} e^{2} + \frac{1}{5} \, a^{3} x^{5} e^{7} + a^{3} d x^{4} e^{6} + 2 \, a^{3} d^{2} x^{3} e^{5} + 2 \, a^{3} d^{3} x^{2} e^{4} + a^{3} d^{4} x e^{3}"," ",0,"1/8*c^3*d^3*x^8*e^4 + 4/7*c^3*d^4*x^7*e^3 + c^3*d^5*x^6*e^2 + 4/5*c^3*d^6*x^5*e + 1/4*c^3*d^7*x^4 + 3/7*a*c^2*d^2*x^7*e^5 + 2*a*c^2*d^3*x^6*e^4 + 18/5*a*c^2*d^4*x^5*e^3 + 3*a*c^2*d^5*x^4*e^2 + a*c^2*d^6*x^3*e + 1/2*a^2*c*d*x^6*e^6 + 12/5*a^2*c*d^2*x^5*e^5 + 9/2*a^2*c*d^3*x^4*e^4 + 4*a^2*c*d^4*x^3*e^3 + 3/2*a^2*c*d^5*x^2*e^2 + 1/5*a^3*x^5*e^7 + a^3*d*x^4*e^6 + 2*a^3*d^2*x^3*e^5 + 2*a^3*d^3*x^2*e^4 + a^3*d^4*x*e^3","B",0
1853,1,203,0,0.155088," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x, algorithm=""giac"")","\frac{1}{7} \, c^{3} d^{3} x^{7} e^{3} + \frac{1}{2} \, c^{3} d^{4} x^{6} e^{2} + \frac{3}{5} \, c^{3} d^{5} x^{5} e + \frac{1}{4} \, c^{3} d^{6} x^{4} + \frac{1}{2} \, a c^{2} d^{2} x^{6} e^{4} + \frac{9}{5} \, a c^{2} d^{3} x^{5} e^{3} + \frac{9}{4} \, a c^{2} d^{4} x^{4} e^{2} + a c^{2} d^{5} x^{3} e + \frac{3}{5} \, a^{2} c d x^{5} e^{5} + \frac{9}{4} \, a^{2} c d^{2} x^{4} e^{4} + 3 \, a^{2} c d^{3} x^{3} e^{3} + \frac{3}{2} \, a^{2} c d^{4} x^{2} e^{2} + \frac{1}{4} \, a^{3} x^{4} e^{6} + a^{3} d x^{3} e^{5} + \frac{3}{2} \, a^{3} d^{2} x^{2} e^{4} + a^{3} d^{3} x e^{3}"," ",0,"1/7*c^3*d^3*x^7*e^3 + 1/2*c^3*d^4*x^6*e^2 + 3/5*c^3*d^5*x^5*e + 1/4*c^3*d^6*x^4 + 1/2*a*c^2*d^2*x^6*e^4 + 9/5*a*c^2*d^3*x^5*e^3 + 9/4*a*c^2*d^4*x^4*e^2 + a*c^2*d^5*x^3*e + 3/5*a^2*c*d*x^5*e^5 + 9/4*a^2*c*d^2*x^4*e^4 + 3*a^2*c*d^3*x^3*e^3 + 3/2*a^2*c*d^4*x^2*e^2 + 1/4*a^3*x^4*e^6 + a^3*d*x^3*e^5 + 3/2*a^3*d^2*x^2*e^4 + a^3*d^3*x*e^3","A",0
1854,1,158,0,0.162589," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3/(e*x+d),x, algorithm=""giac"")","\frac{1}{60} \, {\left(10 \, c^{3} d^{3} x^{6} e^{8} + 24 \, c^{3} d^{4} x^{5} e^{7} + 15 \, c^{3} d^{5} x^{4} e^{6} + 36 \, a c^{2} d^{2} x^{5} e^{9} + 90 \, a c^{2} d^{3} x^{4} e^{8} + 60 \, a c^{2} d^{4} x^{3} e^{7} + 45 \, a^{2} c d x^{4} e^{10} + 120 \, a^{2} c d^{2} x^{3} e^{9} + 90 \, a^{2} c d^{3} x^{2} e^{8} + 20 \, a^{3} x^{3} e^{11} + 60 \, a^{3} d x^{2} e^{10} + 60 \, a^{3} d^{2} x e^{9}\right)} e^{\left(-6\right)}"," ",0,"1/60*(10*c^3*d^3*x^6*e^8 + 24*c^3*d^4*x^5*e^7 + 15*c^3*d^5*x^4*e^6 + 36*a*c^2*d^2*x^5*e^9 + 90*a*c^2*d^3*x^4*e^8 + 60*a*c^2*d^4*x^3*e^7 + 45*a^2*c*d*x^4*e^10 + 120*a^2*c*d^2*x^3*e^9 + 90*a^2*c*d^3*x^2*e^8 + 20*a^3*x^3*e^11 + 60*a^3*d*x^2*e^10 + 60*a^3*d^2*x*e^9)*e^(-6)","A",0
1855,1,146,0,0.190800," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3/(e*x+d)^2,x, algorithm=""giac"")","\frac{1}{20} \, {\left(4 \, c^{3} d^{3} - \frac{15 \, {\left(c^{3} d^{4} e - a c^{2} d^{2} e^{3}\right)} e^{\left(-1\right)}}{x e + d} + \frac{20 \, {\left(c^{3} d^{5} e^{2} - 2 \, a c^{2} d^{3} e^{4} + a^{2} c d e^{6}\right)} e^{\left(-2\right)}}{{\left(x e + d\right)}^{2}} - \frac{10 \, {\left(c^{3} d^{6} e^{3} - 3 \, a c^{2} d^{4} e^{5} + 3 \, a^{2} c d^{2} e^{7} - a^{3} e^{9}\right)} e^{\left(-3\right)}}{{\left(x e + d\right)}^{3}}\right)} {\left(x e + d\right)}^{5} e^{\left(-4\right)}"," ",0,"1/20*(4*c^3*d^3 - 15*(c^3*d^4*e - a*c^2*d^2*e^3)*e^(-1)/(x*e + d) + 20*(c^3*d^5*e^2 - 2*a*c^2*d^3*e^4 + a^2*c*d*e^6)*e^(-2)/(x*e + d)^2 - 10*(c^3*d^6*e^3 - 3*a*c^2*d^4*e^5 + 3*a^2*c*d^2*e^7 - a^3*e^9)*e^(-3)/(x*e + d)^3)*(x*e + d)^5*e^(-4)","B",0
1856,1,51,0,0.164550," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3/(e*x+d)^3,x, algorithm=""giac"")","\frac{1}{4} \, {\left(c^{3} d^{3} x^{4} e^{12} + 4 \, a c^{2} d^{2} x^{3} e^{13} + 6 \, a^{2} c d x^{2} e^{14} + 4 \, a^{3} x e^{15}\right)} e^{\left(-12\right)}"," ",0,"1/4*(c^3*d^3*x^4*e^12 + 4*a*c^2*d^2*x^3*e^13 + 6*a^2*c*d*x^2*e^14 + 4*a^3*x*e^15)*e^(-12)","B",0
1857,1,128,0,0.169935," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3/(e*x+d)^4,x, algorithm=""giac"")","-{\left(c^{3} d^{6} - 3 \, a c^{2} d^{4} e^{2} + 3 \, a^{2} c d^{2} e^{4} - a^{3} e^{6}\right)} e^{\left(-4\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{6} \, {\left(2 \, c^{3} d^{3} x^{3} e^{11} - 3 \, c^{3} d^{4} x^{2} e^{10} + 6 \, c^{3} d^{5} x e^{9} + 9 \, a c^{2} d^{2} x^{2} e^{12} - 18 \, a c^{2} d^{3} x e^{11} + 18 \, a^{2} c d x e^{13}\right)} e^{\left(-12\right)}"," ",0,"-(c^3*d^6 - 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4 - a^3*e^6)*e^(-4)*log(abs(x*e + d)) + 1/6*(2*c^3*d^3*x^3*e^11 - 3*c^3*d^4*x^2*e^10 + 6*c^3*d^5*x*e^9 + 9*a*c^2*d^2*x^2*e^12 - 18*a*c^2*d^3*x*e^11 + 18*a^2*c*d*x*e^13)*e^(-12)","A",0
1858,1,178,0,0.192398," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3/(e*x+d)^5,x, algorithm=""giac"")","\frac{1}{2} \, {\left(c^{3} d^{3} - \frac{6 \, {\left(c^{3} d^{4} e - a c^{2} d^{2} e^{3}\right)} e^{\left(-1\right)}}{x e + d}\right)} {\left(x e + d\right)}^{2} e^{\left(-4\right)} - 3 \, {\left(c^{3} d^{5} - 2 \, a c^{2} d^{3} e^{2} + a^{2} c d e^{4}\right)} e^{\left(-4\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) + {\left(\frac{c^{3} d^{6} e^{20}}{x e + d} - \frac{3 \, a c^{2} d^{4} e^{22}}{x e + d} + \frac{3 \, a^{2} c d^{2} e^{24}}{x e + d} - \frac{a^{3} e^{26}}{x e + d}\right)} e^{\left(-24\right)}"," ",0,"1/2*(c^3*d^3 - 6*(c^3*d^4*e - a*c^2*d^2*e^3)*e^(-1)/(x*e + d))*(x*e + d)^2*e^(-4) - 3*(c^3*d^5 - 2*a*c^2*d^3*e^2 + a^2*c*d*e^4)*e^(-4)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) + (c^3*d^6*e^20/(x*e + d) - 3*a*c^2*d^4*e^22/(x*e + d) + 3*a^2*c*d^2*e^24/(x*e + d) - a^3*e^26/(x*e + d))*e^(-24)","A",0
1859,1,261,0,0.175685," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3/(e*x+d)^6,x, algorithm=""giac"")","c^{3} d^{3} x e^{\left(-3\right)} - 3 \, {\left(c^{3} d^{4} - a c^{2} d^{2} e^{2}\right)} e^{\left(-4\right)} \log\left({\left| x e + d \right|}\right) - \frac{{\left(5 \, c^{3} d^{9} - 9 \, a c^{2} d^{7} e^{2} + 3 \, a^{2} c d^{5} e^{4} + a^{3} d^{3} e^{6} + 6 \, {\left(c^{3} d^{5} e^{4} - 2 \, a c^{2} d^{3} e^{6} + a^{2} c d e^{8}\right)} x^{4} + {\left(23 \, c^{3} d^{6} e^{3} - 45 \, a c^{2} d^{4} e^{5} + 21 \, a^{2} c d^{2} e^{7} + a^{3} e^{9}\right)} x^{3} + 3 \, {\left(11 \, c^{3} d^{7} e^{2} - 21 \, a c^{2} d^{5} e^{4} + 9 \, a^{2} c d^{3} e^{6} + a^{3} d e^{8}\right)} x^{2} + 3 \, {\left(7 \, c^{3} d^{8} e - 13 \, a c^{2} d^{6} e^{3} + 5 \, a^{2} c d^{4} e^{5} + a^{3} d^{2} e^{7}\right)} x\right)} e^{\left(-4\right)}}{2 \, {\left(x e + d\right)}^{5}}"," ",0,"c^3*d^3*x*e^(-3) - 3*(c^3*d^4 - a*c^2*d^2*e^2)*e^(-4)*log(abs(x*e + d)) - 1/2*(5*c^3*d^9 - 9*a*c^2*d^7*e^2 + 3*a^2*c*d^5*e^4 + a^3*d^3*e^6 + 6*(c^3*d^5*e^4 - 2*a*c^2*d^3*e^6 + a^2*c*d*e^8)*x^4 + (23*c^3*d^6*e^3 - 45*a*c^2*d^4*e^5 + 21*a^2*c*d^2*e^7 + a^3*e^9)*x^3 + 3*(11*c^3*d^7*e^2 - 21*a*c^2*d^5*e^4 + 9*a^2*c*d^3*e^6 + a^3*d*e^8)*x^2 + 3*(7*c^3*d^8*e - 13*a*c^2*d^6*e^3 + 5*a^2*c*d^4*e^5 + a^3*d^2*e^7)*x)*e^(-4)/(x*e + d)^5","B",0
1860,1,270,0,0.166526," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3/(e*x+d)^7,x, algorithm=""giac"")","c^{3} d^{3} e^{\left(-4\right)} \log\left({\left| x e + d \right|}\right) + \frac{{\left(11 \, c^{3} d^{9} - 6 \, a c^{2} d^{7} e^{2} - 3 \, a^{2} c d^{5} e^{4} - 2 \, a^{3} d^{3} e^{6} + 18 \, {\left(c^{3} d^{4} e^{5} - a c^{2} d^{2} e^{7}\right)} x^{5} + 9 \, {\left(9 \, c^{3} d^{5} e^{4} - 8 \, a c^{2} d^{3} e^{6} - a^{2} c d e^{8}\right)} x^{4} + 2 \, {\left(73 \, c^{3} d^{6} e^{3} - 57 \, a c^{2} d^{4} e^{5} - 15 \, a^{2} c d^{2} e^{7} - a^{3} e^{9}\right)} x^{3} + 6 \, {\left(22 \, c^{3} d^{7} e^{2} - 15 \, a c^{2} d^{5} e^{4} - 6 \, a^{2} c d^{3} e^{6} - a^{3} d e^{8}\right)} x^{2} + 6 \, {\left(10 \, c^{3} d^{8} e - 6 \, a c^{2} d^{6} e^{3} - 3 \, a^{2} c d^{4} e^{5} - a^{3} d^{2} e^{7}\right)} x\right)} e^{\left(-4\right)}}{6 \, {\left(x e + d\right)}^{6}}"," ",0,"c^3*d^3*e^(-4)*log(abs(x*e + d)) + 1/6*(11*c^3*d^9 - 6*a*c^2*d^7*e^2 - 3*a^2*c*d^5*e^4 - 2*a^3*d^3*e^6 + 18*(c^3*d^4*e^5 - a*c^2*d^2*e^7)*x^5 + 9*(9*c^3*d^5*e^4 - 8*a*c^2*d^3*e^6 - a^2*c*d*e^8)*x^4 + 2*(73*c^3*d^6*e^3 - 57*a*c^2*d^4*e^5 - 15*a^2*c*d^2*e^7 - a^3*e^9)*x^3 + 6*(22*c^3*d^7*e^2 - 15*a*c^2*d^5*e^4 - 6*a^2*c*d^3*e^6 - a^3*d*e^8)*x^2 + 6*(10*c^3*d^8*e - 6*a*c^2*d^6*e^3 - 3*a^2*c*d^4*e^5 - a^3*d^2*e^7)*x)*e^(-4)/(x*e + d)^6","B",0
1861,1,276,0,0.174234," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3/(e*x+d)^8,x, algorithm=""giac"")","-\frac{{\left(4 \, c^{3} d^{3} x^{6} e^{6} + 18 \, c^{3} d^{4} x^{5} e^{5} + 34 \, c^{3} d^{5} x^{4} e^{4} + 35 \, c^{3} d^{6} x^{3} e^{3} + 21 \, c^{3} d^{7} x^{2} e^{2} + 7 \, c^{3} d^{8} x e + c^{3} d^{9} + 6 \, a c^{2} d^{2} x^{5} e^{7} + 22 \, a c^{2} d^{3} x^{4} e^{6} + 31 \, a c^{2} d^{4} x^{3} e^{5} + 21 \, a c^{2} d^{5} x^{2} e^{4} + 7 \, a c^{2} d^{6} x e^{3} + a c^{2} d^{7} e^{2} + 4 \, a^{2} c d x^{4} e^{8} + 13 \, a^{2} c d^{2} x^{3} e^{7} + 15 \, a^{2} c d^{3} x^{2} e^{6} + 7 \, a^{2} c d^{4} x e^{5} + a^{2} c d^{5} e^{4} + a^{3} x^{3} e^{9} + 3 \, a^{3} d x^{2} e^{8} + 3 \, a^{3} d^{2} x e^{7} + a^{3} d^{3} e^{6}\right)} e^{\left(-4\right)}}{4 \, {\left(x e + d\right)}^{7}}"," ",0,"-1/4*(4*c^3*d^3*x^6*e^6 + 18*c^3*d^4*x^5*e^5 + 34*c^3*d^5*x^4*e^4 + 35*c^3*d^6*x^3*e^3 + 21*c^3*d^7*x^2*e^2 + 7*c^3*d^8*x*e + c^3*d^9 + 6*a*c^2*d^2*x^5*e^7 + 22*a*c^2*d^3*x^4*e^6 + 31*a*c^2*d^4*x^3*e^5 + 21*a*c^2*d^5*x^2*e^4 + 7*a*c^2*d^6*x*e^3 + a*c^2*d^7*e^2 + 4*a^2*c*d*x^4*e^8 + 13*a^2*c*d^2*x^3*e^7 + 15*a^2*c*d^3*x^2*e^6 + 7*a^2*c*d^4*x*e^5 + a^2*c*d^5*e^4 + a^3*x^3*e^9 + 3*a^3*d*x^2*e^8 + 3*a^3*d^2*x*e^7 + a^3*d^3*e^6)*e^(-4)/(x*e + d)^7","B",0
1862,1,280,0,0.173929," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3/(e*x+d)^9,x, algorithm=""giac"")","-\frac{{\left(10 \, c^{3} d^{3} x^{6} e^{6} + 40 \, c^{3} d^{4} x^{5} e^{5} + 65 \, c^{3} d^{5} x^{4} e^{4} + 56 \, c^{3} d^{6} x^{3} e^{3} + 28 \, c^{3} d^{7} x^{2} e^{2} + 8 \, c^{3} d^{8} x e + c^{3} d^{9} + 20 \, a c^{2} d^{2} x^{5} e^{7} + 70 \, a c^{2} d^{3} x^{4} e^{6} + 92 \, a c^{2} d^{4} x^{3} e^{5} + 56 \, a c^{2} d^{5} x^{2} e^{4} + 16 \, a c^{2} d^{6} x e^{3} + 2 \, a c^{2} d^{7} e^{2} + 15 \, a^{2} c d x^{4} e^{8} + 48 \, a^{2} c d^{2} x^{3} e^{7} + 54 \, a^{2} c d^{3} x^{2} e^{6} + 24 \, a^{2} c d^{4} x e^{5} + 3 \, a^{2} c d^{5} e^{4} + 4 \, a^{3} x^{3} e^{9} + 12 \, a^{3} d x^{2} e^{8} + 12 \, a^{3} d^{2} x e^{7} + 4 \, a^{3} d^{3} e^{6}\right)} e^{\left(-4\right)}}{20 \, {\left(x e + d\right)}^{8}}"," ",0,"-1/20*(10*c^3*d^3*x^6*e^6 + 40*c^3*d^4*x^5*e^5 + 65*c^3*d^5*x^4*e^4 + 56*c^3*d^6*x^3*e^3 + 28*c^3*d^7*x^2*e^2 + 8*c^3*d^8*x*e + c^3*d^9 + 20*a*c^2*d^2*x^5*e^7 + 70*a*c^2*d^3*x^4*e^6 + 92*a*c^2*d^4*x^3*e^5 + 56*a*c^2*d^5*x^2*e^4 + 16*a*c^2*d^6*x*e^3 + 2*a*c^2*d^7*e^2 + 15*a^2*c*d*x^4*e^8 + 48*a^2*c*d^2*x^3*e^7 + 54*a^2*c*d^3*x^2*e^6 + 24*a^2*c*d^4*x*e^5 + 3*a^2*c*d^5*e^4 + 4*a^3*x^3*e^9 + 12*a^3*d*x^2*e^8 + 12*a^3*d^2*x*e^7 + 4*a^3*d^3*e^6)*e^(-4)/(x*e + d)^8","B",0
1863,1,280,0,0.202778," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3/(e*x+d)^10,x, algorithm=""giac"")","-\frac{{\left(20 \, c^{3} d^{3} x^{6} e^{6} + 75 \, c^{3} d^{4} x^{5} e^{5} + 111 \, c^{3} d^{5} x^{4} e^{4} + 84 \, c^{3} d^{6} x^{3} e^{3} + 36 \, c^{3} d^{7} x^{2} e^{2} + 9 \, c^{3} d^{8} x e + c^{3} d^{9} + 45 \, a c^{2} d^{2} x^{5} e^{7} + 153 \, a c^{2} d^{3} x^{4} e^{6} + 192 \, a c^{2} d^{4} x^{3} e^{5} + 108 \, a c^{2} d^{5} x^{2} e^{4} + 27 \, a c^{2} d^{6} x e^{3} + 3 \, a c^{2} d^{7} e^{2} + 36 \, a^{2} c d x^{4} e^{8} + 114 \, a^{2} c d^{2} x^{3} e^{7} + 126 \, a^{2} c d^{3} x^{2} e^{6} + 54 \, a^{2} c d^{4} x e^{5} + 6 \, a^{2} c d^{5} e^{4} + 10 \, a^{3} x^{3} e^{9} + 30 \, a^{3} d x^{2} e^{8} + 30 \, a^{3} d^{2} x e^{7} + 10 \, a^{3} d^{3} e^{6}\right)} e^{\left(-4\right)}}{60 \, {\left(x e + d\right)}^{9}}"," ",0,"-1/60*(20*c^3*d^3*x^6*e^6 + 75*c^3*d^4*x^5*e^5 + 111*c^3*d^5*x^4*e^4 + 84*c^3*d^6*x^3*e^3 + 36*c^3*d^7*x^2*e^2 + 9*c^3*d^8*x*e + c^3*d^9 + 45*a*c^2*d^2*x^5*e^7 + 153*a*c^2*d^3*x^4*e^6 + 192*a*c^2*d^4*x^3*e^5 + 108*a*c^2*d^5*x^2*e^4 + 27*a*c^2*d^6*x*e^3 + 3*a*c^2*d^7*e^2 + 36*a^2*c*d*x^4*e^8 + 114*a^2*c*d^2*x^3*e^7 + 126*a^2*c*d^3*x^2*e^6 + 54*a^2*c*d^4*x*e^5 + 6*a^2*c*d^5*e^4 + 10*a^3*x^3*e^9 + 30*a^3*d*x^2*e^8 + 30*a^3*d^2*x*e^7 + 10*a^3*d^3*e^6)*e^(-4)/(x*e + d)^9","B",0
1864,1,280,0,0.179439," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3/(e*x+d)^11,x, algorithm=""giac"")","-\frac{{\left(35 \, c^{3} d^{3} x^{6} e^{6} + 126 \, c^{3} d^{4} x^{5} e^{5} + 175 \, c^{3} d^{5} x^{4} e^{4} + 120 \, c^{3} d^{6} x^{3} e^{3} + 45 \, c^{3} d^{7} x^{2} e^{2} + 10 \, c^{3} d^{8} x e + c^{3} d^{9} + 84 \, a c^{2} d^{2} x^{5} e^{7} + 280 \, a c^{2} d^{3} x^{4} e^{6} + 340 \, a c^{2} d^{4} x^{3} e^{5} + 180 \, a c^{2} d^{5} x^{2} e^{4} + 40 \, a c^{2} d^{6} x e^{3} + 4 \, a c^{2} d^{7} e^{2} + 70 \, a^{2} c d x^{4} e^{8} + 220 \, a^{2} c d^{2} x^{3} e^{7} + 240 \, a^{2} c d^{3} x^{2} e^{6} + 100 \, a^{2} c d^{4} x e^{5} + 10 \, a^{2} c d^{5} e^{4} + 20 \, a^{3} x^{3} e^{9} + 60 \, a^{3} d x^{2} e^{8} + 60 \, a^{3} d^{2} x e^{7} + 20 \, a^{3} d^{3} e^{6}\right)} e^{\left(-4\right)}}{140 \, {\left(x e + d\right)}^{10}}"," ",0,"-1/140*(35*c^3*d^3*x^6*e^6 + 126*c^3*d^4*x^5*e^5 + 175*c^3*d^5*x^4*e^4 + 120*c^3*d^6*x^3*e^3 + 45*c^3*d^7*x^2*e^2 + 10*c^3*d^8*x*e + c^3*d^9 + 84*a*c^2*d^2*x^5*e^7 + 280*a*c^2*d^3*x^4*e^6 + 340*a*c^2*d^4*x^3*e^5 + 180*a*c^2*d^5*x^2*e^4 + 40*a*c^2*d^6*x*e^3 + 4*a*c^2*d^7*e^2 + 70*a^2*c*d*x^4*e^8 + 220*a^2*c*d^2*x^3*e^7 + 240*a^2*c*d^3*x^2*e^6 + 100*a^2*c*d^4*x*e^5 + 10*a^2*c*d^5*e^4 + 20*a^3*x^3*e^9 + 60*a^3*d*x^2*e^8 + 60*a^3*d^2*x*e^7 + 20*a^3*d^3*e^6)*e^(-4)/(x*e + d)^10","B",0
1865,1,360,0,0.182339," ","integrate((e*x+d)^5/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x, algorithm=""giac"")","\frac{{\left(3 \, c^{3} d^{3} x^{4} e^{8} + 16 \, c^{3} d^{4} x^{3} e^{7} + 36 \, c^{3} d^{5} x^{2} e^{6} + 48 \, c^{3} d^{6} x e^{5} - 4 \, a c^{2} d^{2} x^{3} e^{9} - 24 \, a c^{2} d^{3} x^{2} e^{8} - 72 \, a c^{2} d^{4} x e^{7} + 6 \, a^{2} c d x^{2} e^{10} + 48 \, a^{2} c d^{2} x e^{9} - 12 \, a^{3} x e^{11}\right)} e^{\left(-4\right)}}{12 \, c^{4} d^{4}} + \frac{{\left(c^{4} d^{8} - 4 \, a c^{3} d^{6} e^{2} + 6 \, a^{2} c^{2} d^{4} e^{4} - 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}\right)} \log\left(c d x^{2} e + c d^{2} x + a x e^{2} + a d e\right)}{2 \, c^{5} d^{5}} + \frac{{\left(c^{5} d^{10} - 5 \, a c^{4} d^{8} e^{2} + 10 \, a^{2} c^{3} d^{6} e^{4} - 10 \, a^{3} c^{2} d^{4} e^{6} + 5 \, a^{4} c d^{2} e^{8} - a^{5} e^{10}\right)} \arctan\left(\frac{2 \, c d x e + c d^{2} + a e^{2}}{\sqrt{-c^{2} d^{4} + 2 \, a c d^{2} e^{2} - a^{2} e^{4}}}\right)}{\sqrt{-c^{2} d^{4} + 2 \, a c d^{2} e^{2} - a^{2} e^{4}} c^{5} d^{5}}"," ",0,"1/12*(3*c^3*d^3*x^4*e^8 + 16*c^3*d^4*x^3*e^7 + 36*c^3*d^5*x^2*e^6 + 48*c^3*d^6*x*e^5 - 4*a*c^2*d^2*x^3*e^9 - 24*a*c^2*d^3*x^2*e^8 - 72*a*c^2*d^4*x*e^7 + 6*a^2*c*d*x^2*e^10 + 48*a^2*c*d^2*x*e^9 - 12*a^3*x*e^11)*e^(-4)/(c^4*d^4) + 1/2*(c^4*d^8 - 4*a*c^3*d^6*e^2 + 6*a^2*c^2*d^4*e^4 - 4*a^3*c*d^2*e^6 + a^4*e^8)*log(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e)/(c^5*d^5) + (c^5*d^10 - 5*a*c^4*d^8*e^2 + 10*a^2*c^3*d^6*e^4 - 10*a^3*c^2*d^4*e^6 + 5*a^4*c*d^2*e^8 - a^5*e^10)*arctan((2*c*d*x*e + c*d^2 + a*e^2)/sqrt(-c^2*d^4 + 2*a*c*d^2*e^2 - a^2*e^4))/(sqrt(-c^2*d^4 + 2*a*c*d^2*e^2 - a^2*e^4)*c^5*d^5)","B",0
1866,1,277,0,0.194311," ","integrate((e*x+d)^4/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x, algorithm=""giac"")","\frac{{\left(2 \, c^{2} d^{2} x^{3} e^{6} + 9 \, c^{2} d^{3} x^{2} e^{5} + 18 \, c^{2} d^{4} x e^{4} - 3 \, a c d x^{2} e^{7} - 18 \, a c d^{2} x e^{6} + 6 \, a^{2} x e^{8}\right)} e^{\left(-3\right)}}{6 \, c^{3} d^{3}} + \frac{{\left(c^{3} d^{6} - 3 \, a c^{2} d^{4} e^{2} + 3 \, a^{2} c d^{2} e^{4} - a^{3} e^{6}\right)} \log\left(c d x^{2} e + c d^{2} x + a x e^{2} + a d e\right)}{2 \, c^{4} d^{4}} + \frac{{\left(c^{4} d^{8} - 4 \, a c^{3} d^{6} e^{2} + 6 \, a^{2} c^{2} d^{4} e^{4} - 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}\right)} \arctan\left(\frac{2 \, c d x e + c d^{2} + a e^{2}}{\sqrt{-c^{2} d^{4} + 2 \, a c d^{2} e^{2} - a^{2} e^{4}}}\right)}{\sqrt{-c^{2} d^{4} + 2 \, a c d^{2} e^{2} - a^{2} e^{4}} c^{4} d^{4}}"," ",0,"1/6*(2*c^2*d^2*x^3*e^6 + 9*c^2*d^3*x^2*e^5 + 18*c^2*d^4*x*e^4 - 3*a*c*d*x^2*e^7 - 18*a*c*d^2*x*e^6 + 6*a^2*x*e^8)*e^(-3)/(c^3*d^3) + 1/2*(c^3*d^6 - 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4 - a^3*e^6)*log(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e)/(c^4*d^4) + (c^4*d^8 - 4*a*c^3*d^6*e^2 + 6*a^2*c^2*d^4*e^4 - 4*a^3*c*d^2*e^6 + a^4*e^8)*arctan((2*c*d*x*e + c*d^2 + a*e^2)/sqrt(-c^2*d^4 + 2*a*c*d^2*e^2 - a^2*e^4))/(sqrt(-c^2*d^4 + 2*a*c*d^2*e^2 - a^2*e^4)*c^4*d^4)","B",0
1867,1,209,0,0.185735," ","integrate((e*x+d)^3/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x, algorithm=""giac"")","\frac{{\left(c d x^{2} e^{4} + 4 \, c d^{2} x e^{3} - 2 \, a x e^{5}\right)} e^{\left(-2\right)}}{2 \, c^{2} d^{2}} + \frac{{\left(c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} \log\left(c d x^{2} e + c d^{2} x + a x e^{2} + a d e\right)}{2 \, c^{3} d^{3}} + \frac{{\left(c^{3} d^{6} - 3 \, a c^{2} d^{4} e^{2} + 3 \, a^{2} c d^{2} e^{4} - a^{3} e^{6}\right)} \arctan\left(\frac{2 \, c d x e + c d^{2} + a e^{2}}{\sqrt{-c^{2} d^{4} + 2 \, a c d^{2} e^{2} - a^{2} e^{4}}}\right)}{\sqrt{-c^{2} d^{4} + 2 \, a c d^{2} e^{2} - a^{2} e^{4}} c^{3} d^{3}}"," ",0,"1/2*(c*d*x^2*e^4 + 4*c*d^2*x*e^3 - 2*a*x*e^5)*e^(-2)/(c^2*d^2) + 1/2*(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*log(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e)/(c^3*d^3) + (c^3*d^6 - 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4 - a^3*e^6)*arctan((2*c*d*x*e + c*d^2 + a*e^2)/sqrt(-c^2*d^4 + 2*a*c*d^2*e^2 - a^2*e^4))/(sqrt(-c^2*d^4 + 2*a*c*d^2*e^2 - a^2*e^4)*c^3*d^3)","B",0
1868,1,159,0,0.197877," ","integrate((e*x+d)^2/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x, algorithm=""giac"")","\frac{x e}{c d} + \frac{{\left(c d^{2} - a e^{2}\right)} \log\left(c d x^{2} e + c d^{2} x + a x e^{2} + a d e\right)}{2 \, c^{2} d^{2}} + \frac{{\left(c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} \arctan\left(\frac{2 \, c d x e + c d^{2} + a e^{2}}{\sqrt{-c^{2} d^{4} + 2 \, a c d^{2} e^{2} - a^{2} e^{4}}}\right)}{\sqrt{-c^{2} d^{4} + 2 \, a c d^{2} e^{2} - a^{2} e^{4}} c^{2} d^{2}}"," ",0,"x*e/(c*d) + 1/2*(c*d^2 - a*e^2)*log(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e)/(c^2*d^2) + (c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*arctan((2*c*d*x*e + c*d^2 + a*e^2)/sqrt(-c^2*d^4 + 2*a*c*d^2*e^2 - a^2*e^4))/(sqrt(-c^2*d^4 + 2*a*c*d^2*e^2 - a^2*e^4)*c^2*d^2)","B",0
1869,1,126,0,0.175362," ","integrate((e*x+d)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x, algorithm=""giac"")","\frac{{\left(c d^{2} - a e^{2}\right)} \arctan\left(\frac{2 \, c d x e + c d^{2} + a e^{2}}{\sqrt{-c^{2} d^{4} + 2 \, a c d^{2} e^{2} - a^{2} e^{4}}}\right)}{\sqrt{-c^{2} d^{4} + 2 \, a c d^{2} e^{2} - a^{2} e^{4}} c d} + \frac{\log\left(c d x^{2} e + c d^{2} x + a x e^{2} + a d e\right)}{2 \, c d}"," ",0,"(c*d^2 - a*e^2)*arctan((2*c*d*x*e + c*d^2 + a*e^2)/sqrt(-c^2*d^4 + 2*a*c*d^2*e^2 - a^2*e^4))/(sqrt(-c^2*d^4 + 2*a*c*d^2*e^2 - a^2*e^4)*c*d) + 1/2*log(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e)/(c*d)","B",0
1870,1,75,0,0.167114," ","integrate(1/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x, algorithm=""giac"")","\frac{2 \, \arctan\left(\frac{2 \, c d x e + c d^{2} + a e^{2}}{\sqrt{-c^{2} d^{4} + 2 \, a c d^{2} e^{2} - a^{2} e^{4}}}\right)}{\sqrt{-c^{2} d^{4} + 2 \, a c d^{2} e^{2} - a^{2} e^{4}}}"," ",0,"2*arctan((2*c*d*x*e + c*d^2 + a*e^2)/sqrt(-c^2*d^4 + 2*a*c*d^2*e^2 - a^2*e^4))/sqrt(-c^2*d^4 + 2*a*c*d^2*e^2 - a^2*e^4)","A",0
1871,-2,0,0,0.000000," ","integrate(1/(e*x+d)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: exp(1)^2/(d*exp(1)^4*a-d*exp(1)^2*a*exp(2))*ln(abs(x*exp(1)+d))-1/(2*d*exp(1)^2*a-2*d*a*exp(2))*ln(x^2*c*d*exp(1)+x*c*d^2+x*a*exp(2)+d*exp(1)*a)+(c*d^2-a*exp(2))/(d*exp(1)^2*a-d*a*exp(2))/sqrt(-c^2*d^4+4*a*c*d^2*exp(1)^2-a^2*exp(2)^2-2*a*c*d^2*exp(2))*atan((a*exp(2)+c*d^2+2*c*d*x*exp(1))/sqrt(-c^2*d^4+4*a*c*d^2*exp(1)^2-a^2*exp(2)^2-2*a*c*d^2*exp(2)))","F(-2)",0
1872,-2,0,0,0.000000," ","integrate(1/(e*x+d)^2/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: (a*exp(2)-d^2*c)/(2*a^2*d^2*exp(1)^4-4*a^2*d^2*exp(1)^2*exp(2)+2*a^2*d^2*exp(2)^2)*ln((-(exp(1)*x+d)^-1/exp(1))^2*a*d*exp(1)^4-(-(exp(1)*x+d)^-1/exp(1))^2*a*d*exp(1)^2*exp(2)+(exp(1)*x+d)^-1/exp(1)*a*exp(1)*exp(2)-(exp(1)*x+d)^-1/exp(1)*d^2*exp(1)*c+d*c)+(a^2*exp(1)*exp(2)^2-2*a*d^2*exp(1)^3*c+d^4*exp(1)*c^2)/(a^2*d^2*exp(1)^4-2*a^2*d^2*exp(1)^2*exp(2)+a^2*d^2*exp(2)^2)/sqrt(-c^2*d^4+4*a*c*d^2*exp(1)^2-a^2*exp(2)^2-2*a*c*d^2*exp(2))/exp(1)*atan((-2*a*d*(exp(1)*x+d)^-1/exp(1)*exp(1)^3+2*a*d*(exp(1)*x+d)^-1/exp(1)*exp(1)*exp(2)-a*exp(2)+c*d^2)/sqrt(-c^2*d^4+4*a*c*d^2*exp(1)^2-a^2*exp(2)^2-2*a*c*d^2*exp(2)))-(exp(1)*x+d)^-1/exp(1)*exp(1)^3/(a*d*exp(1)^4-a*d*exp(1)^2*exp(2))","F(-2)",0
1873,-2,0,0,0.000000," ","integrate(1/(e*x+d)^3/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: (-c^2*d^4+c*d^2*exp(1)^2*a+c*d^2*a*exp(2)-a^2*exp(2)^2)/(2*d^3*exp(1)^6*a^3-6*d^3*exp(1)^4*a^3*exp(2)+6*d^3*exp(1)^2*a^3*exp(2)^2-2*d^3*a^3*exp(2)^3)*ln(x^2*c*d*exp(1)+x*c*d^2+x*a*exp(2)+d*exp(1)*a)+(c^3*d^6-3*c^2*d^4*exp(1)^2*a+3*c*d^2*exp(1)^2*a^2*exp(2)-a^3*exp(2)^3)/(d^3*exp(1)^6*a^3-3*d^3*exp(1)^4*a^3*exp(2)+3*d^3*exp(1)^2*a^3*exp(2)^2-d^3*a^3*exp(2)^3)/sqrt(-c^2*d^4+4*a*c*d^2*exp(1)^2-a^2*exp(2)^2-2*a*c*d^2*exp(2))*atan((a*exp(2)+c*d^2+2*c*d*x*exp(1))/sqrt(-c^2*d^4+4*a*c*d^2*exp(1)^2-a^2*exp(2)^2-2*a*c*d^2*exp(2)))+(c^2*d^4*exp(1)-c*d^2*exp(1)^3*a-c*d^2*exp(1)*a*exp(2)+exp(1)*a^2*exp(2)^2)/(d^3*exp(1)^7*a^3-3*d^3*exp(1)^5*a^3*exp(2)+3*d^3*exp(1)^3*a^3*exp(2)^2-d^3*exp(1)*a^3*exp(2)^3)*ln(abs(x*exp(1)+d))-(-2*c*d^4*exp(1)^2*a+2*c*d^4*a*exp(2)-d^2*exp(1)^4*a^2+4*d^2*exp(1)^2*a^2*exp(2)-3*d^2*a^2*exp(2)^2+(-2*c*d^3*exp(1)^3*a+2*c*d^3*exp(1)*a*exp(2)+2*d*exp(1)^3*a^2*exp(2)-2*d*exp(1)*a^2*exp(2)^2)*x)/2/(exp(2)-exp(1)^2)^3/a^3/d^3/(x*exp(1)+d)^2","F(-2)",0
1874,1,796,0,0.448712," ","integrate((e*x+d)^8/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x, algorithm=""giac"")","\frac{6 \, {\left(c^{8} d^{16} e - 8 \, a c^{7} d^{14} e^{3} + 28 \, a^{2} c^{6} d^{12} e^{5} - 56 \, a^{3} c^{5} d^{10} e^{7} + 70 \, a^{4} c^{4} d^{8} e^{9} - 56 \, a^{5} c^{3} d^{6} e^{11} + 28 \, a^{6} c^{2} d^{4} e^{13} - 8 \, a^{7} c d^{2} e^{15} + a^{8} e^{17}\right)} \arctan\left(\frac{2 \, c d x e + c d^{2} + a e^{2}}{\sqrt{-c^{2} d^{4} + 2 \, a c d^{2} e^{2} - a^{2} e^{4}}}\right)}{{\left(c^{9} d^{11} - 2 \, a c^{8} d^{9} e^{2} + a^{2} c^{7} d^{7} e^{4}\right)} \sqrt{-c^{2} d^{4} + 2 \, a c d^{2} e^{2} - a^{2} e^{4}}} + \frac{3 \, {\left(c^{5} d^{10} e - 5 \, a c^{4} d^{8} e^{3} + 10 \, a^{2} c^{3} d^{6} e^{5} - 10 \, a^{3} c^{2} d^{4} e^{7} + 5 \, a^{4} c d^{2} e^{9} - a^{5} e^{11}\right)} \log\left(c d x^{2} e + c d^{2} x + a x e^{2} + a d e\right)}{c^{7} d^{7}} - \frac{c^{8} d^{17} - 8 \, a c^{7} d^{15} e^{2} + 28 \, a^{2} c^{6} d^{13} e^{4} - 56 \, a^{3} c^{5} d^{11} e^{6} + 70 \, a^{4} c^{4} d^{9} e^{8} - 56 \, a^{5} c^{3} d^{7} e^{10} + 28 \, a^{6} c^{2} d^{5} e^{12} - 8 \, a^{7} c d^{3} e^{14} + a^{8} d e^{16} + {\left(c^{8} d^{16} e - 8 \, a c^{7} d^{14} e^{3} + 28 \, a^{2} c^{6} d^{12} e^{5} - 56 \, a^{3} c^{5} d^{10} e^{7} + 70 \, a^{4} c^{4} d^{8} e^{9} - 56 \, a^{5} c^{3} d^{6} e^{11} + 28 \, a^{6} c^{2} d^{4} e^{13} - 8 \, a^{7} c d^{2} e^{15} + a^{8} e^{17}\right)} x}{{\left(c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} {\left(c d x^{2} e + c d^{2} x + a x e^{2} + a d e\right)} c^{7} d^{7}} + \frac{{\left(2 \, c^{8} d^{8} x^{5} e^{16} + 15 \, c^{8} d^{9} x^{4} e^{15} + 50 \, c^{8} d^{10} x^{3} e^{14} + 100 \, c^{8} d^{11} x^{2} e^{13} + 150 \, c^{8} d^{12} x e^{12} - 5 \, a c^{7} d^{7} x^{4} e^{17} - 40 \, a c^{7} d^{8} x^{3} e^{16} - 150 \, a c^{7} d^{9} x^{2} e^{15} - 400 \, a c^{7} d^{10} x e^{14} + 10 \, a^{2} c^{6} d^{6} x^{3} e^{18} + 90 \, a^{2} c^{6} d^{7} x^{2} e^{17} + 450 \, a^{2} c^{6} d^{8} x e^{16} - 20 \, a^{3} c^{5} d^{5} x^{2} e^{19} - 240 \, a^{3} c^{5} d^{6} x e^{18} + 50 \, a^{4} c^{4} d^{4} x e^{20}\right)} e^{\left(-10\right)}}{10 \, c^{10} d^{10}}"," ",0,"6*(c^8*d^16*e - 8*a*c^7*d^14*e^3 + 28*a^2*c^6*d^12*e^5 - 56*a^3*c^5*d^10*e^7 + 70*a^4*c^4*d^8*e^9 - 56*a^5*c^3*d^6*e^11 + 28*a^6*c^2*d^4*e^13 - 8*a^7*c*d^2*e^15 + a^8*e^17)*arctan((2*c*d*x*e + c*d^2 + a*e^2)/sqrt(-c^2*d^4 + 2*a*c*d^2*e^2 - a^2*e^4))/((c^9*d^11 - 2*a*c^8*d^9*e^2 + a^2*c^7*d^7*e^4)*sqrt(-c^2*d^4 + 2*a*c*d^2*e^2 - a^2*e^4)) + 3*(c^5*d^10*e - 5*a*c^4*d^8*e^3 + 10*a^2*c^3*d^6*e^5 - 10*a^3*c^2*d^4*e^7 + 5*a^4*c*d^2*e^9 - a^5*e^11)*log(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e)/(c^7*d^7) - (c^8*d^17 - 8*a*c^7*d^15*e^2 + 28*a^2*c^6*d^13*e^4 - 56*a^3*c^5*d^11*e^6 + 70*a^4*c^4*d^9*e^8 - 56*a^5*c^3*d^7*e^10 + 28*a^6*c^2*d^5*e^12 - 8*a^7*c*d^3*e^14 + a^8*d*e^16 + (c^8*d^16*e - 8*a*c^7*d^14*e^3 + 28*a^2*c^6*d^12*e^5 - 56*a^3*c^5*d^10*e^7 + 70*a^4*c^4*d^8*e^9 - 56*a^5*c^3*d^6*e^11 + 28*a^6*c^2*d^4*e^13 - 8*a^7*c*d^2*e^15 + a^8*e^17)*x)/((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e)*c^7*d^7) + 1/10*(2*c^8*d^8*x^5*e^16 + 15*c^8*d^9*x^4*e^15 + 50*c^8*d^10*x^3*e^14 + 100*c^8*d^11*x^2*e^13 + 150*c^8*d^12*x*e^12 - 5*a*c^7*d^7*x^4*e^17 - 40*a*c^7*d^8*x^3*e^16 - 150*a*c^7*d^9*x^2*e^15 - 400*a*c^7*d^10*x*e^14 + 10*a^2*c^6*d^6*x^3*e^18 + 90*a^2*c^6*d^7*x^2*e^17 + 450*a^2*c^6*d^8*x*e^16 - 20*a^3*c^5*d^5*x^2*e^19 - 240*a^3*c^5*d^6*x*e^18 + 50*a^4*c^4*d^4*x*e^20)*e^(-10)/(c^10*d^10)","B",0
1875,1,673,0,0.419697," ","integrate((e*x+d)^7/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x, algorithm=""giac"")","\frac{5 \, {\left(c^{7} d^{14} e - 7 \, a c^{6} d^{12} e^{3} + 21 \, a^{2} c^{5} d^{10} e^{5} - 35 \, a^{3} c^{4} d^{8} e^{7} + 35 \, a^{4} c^{3} d^{6} e^{9} - 21 \, a^{5} c^{2} d^{4} e^{11} + 7 \, a^{6} c d^{2} e^{13} - a^{7} e^{15}\right)} \arctan\left(\frac{2 \, c d x e + c d^{2} + a e^{2}}{\sqrt{-c^{2} d^{4} + 2 \, a c d^{2} e^{2} - a^{2} e^{4}}}\right)}{{\left(c^{8} d^{10} - 2 \, a c^{7} d^{8} e^{2} + a^{2} c^{6} d^{6} e^{4}\right)} \sqrt{-c^{2} d^{4} + 2 \, a c d^{2} e^{2} - a^{2} e^{4}}} + \frac{5 \, {\left(c^{4} d^{8} e - 4 \, a c^{3} d^{6} e^{3} + 6 \, a^{2} c^{2} d^{4} e^{5} - 4 \, a^{3} c d^{2} e^{7} + a^{4} e^{9}\right)} \log\left(c d x^{2} e + c d^{2} x + a x e^{2} + a d e\right)}{2 \, c^{6} d^{6}} - \frac{c^{7} d^{15} - 7 \, a c^{6} d^{13} e^{2} + 21 \, a^{2} c^{5} d^{11} e^{4} - 35 \, a^{3} c^{4} d^{9} e^{6} + 35 \, a^{4} c^{3} d^{7} e^{8} - 21 \, a^{5} c^{2} d^{5} e^{10} + 7 \, a^{6} c d^{3} e^{12} - a^{7} d e^{14} + {\left(c^{7} d^{14} e - 7 \, a c^{6} d^{12} e^{3} + 21 \, a^{2} c^{5} d^{10} e^{5} - 35 \, a^{3} c^{4} d^{8} e^{7} + 35 \, a^{4} c^{3} d^{6} e^{9} - 21 \, a^{5} c^{2} d^{4} e^{11} + 7 \, a^{6} c d^{2} e^{13} - a^{7} e^{15}\right)} x}{{\left(c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} {\left(c d x^{2} e + c d^{2} x + a x e^{2} + a d e\right)} c^{6} d^{6}} + \frac{{\left(3 \, c^{6} d^{6} x^{4} e^{13} + 20 \, c^{6} d^{7} x^{3} e^{12} + 60 \, c^{6} d^{8} x^{2} e^{11} + 120 \, c^{6} d^{9} x e^{10} - 8 \, a c^{5} d^{5} x^{3} e^{14} - 60 \, a c^{5} d^{6} x^{2} e^{13} - 240 \, a c^{5} d^{7} x e^{12} + 18 \, a^{2} c^{4} d^{4} x^{2} e^{15} + 180 \, a^{2} c^{4} d^{5} x e^{14} - 48 \, a^{3} c^{3} d^{3} x e^{16}\right)} e^{\left(-8\right)}}{12 \, c^{8} d^{8}}"," ",0,"5*(c^7*d^14*e - 7*a*c^6*d^12*e^3 + 21*a^2*c^5*d^10*e^5 - 35*a^3*c^4*d^8*e^7 + 35*a^4*c^3*d^6*e^9 - 21*a^5*c^2*d^4*e^11 + 7*a^6*c*d^2*e^13 - a^7*e^15)*arctan((2*c*d*x*e + c*d^2 + a*e^2)/sqrt(-c^2*d^4 + 2*a*c*d^2*e^2 - a^2*e^4))/((c^8*d^10 - 2*a*c^7*d^8*e^2 + a^2*c^6*d^6*e^4)*sqrt(-c^2*d^4 + 2*a*c*d^2*e^2 - a^2*e^4)) + 5/2*(c^4*d^8*e - 4*a*c^3*d^6*e^3 + 6*a^2*c^2*d^4*e^5 - 4*a^3*c*d^2*e^7 + a^4*e^9)*log(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e)/(c^6*d^6) - (c^7*d^15 - 7*a*c^6*d^13*e^2 + 21*a^2*c^5*d^11*e^4 - 35*a^3*c^4*d^9*e^6 + 35*a^4*c^3*d^7*e^8 - 21*a^5*c^2*d^5*e^10 + 7*a^6*c*d^3*e^12 - a^7*d*e^14 + (c^7*d^14*e - 7*a*c^6*d^12*e^3 + 21*a^2*c^5*d^10*e^5 - 35*a^3*c^4*d^8*e^7 + 35*a^4*c^3*d^6*e^9 - 21*a^5*c^2*d^4*e^11 + 7*a^6*c*d^2*e^13 - a^7*e^15)*x)/((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e)*c^6*d^6) + 1/12*(3*c^6*d^6*x^4*e^13 + 20*c^6*d^7*x^3*e^12 + 60*c^6*d^8*x^2*e^11 + 120*c^6*d^9*x*e^10 - 8*a*c^5*d^5*x^3*e^14 - 60*a*c^5*d^6*x^2*e^13 - 240*a*c^5*d^7*x*e^12 + 18*a^2*c^4*d^4*x^2*e^15 + 180*a^2*c^4*d^5*x*e^14 - 48*a^3*c^3*d^3*x*e^16)*e^(-8)/(c^8*d^8)","B",0
1876,1,561,0,0.354879," ","integrate((e*x+d)^6/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x, algorithm=""giac"")","\frac{4 \, {\left(c^{6} d^{12} e - 6 \, a c^{5} d^{10} e^{3} + 15 \, a^{2} c^{4} d^{8} e^{5} - 20 \, a^{3} c^{3} d^{6} e^{7} + 15 \, a^{4} c^{2} d^{4} e^{9} - 6 \, a^{5} c d^{2} e^{11} + a^{6} e^{13}\right)} \arctan\left(\frac{2 \, c d x e + c d^{2} + a e^{2}}{\sqrt{-c^{2} d^{4} + 2 \, a c d^{2} e^{2} - a^{2} e^{4}}}\right)}{{\left(c^{7} d^{9} - 2 \, a c^{6} d^{7} e^{2} + a^{2} c^{5} d^{5} e^{4}\right)} \sqrt{-c^{2} d^{4} + 2 \, a c d^{2} e^{2} - a^{2} e^{4}}} + \frac{2 \, {\left(c^{3} d^{6} e - 3 \, a c^{2} d^{4} e^{3} + 3 \, a^{2} c d^{2} e^{5} - a^{3} e^{7}\right)} \log\left(c d x^{2} e + c d^{2} x + a x e^{2} + a d e\right)}{c^{5} d^{5}} + \frac{{\left(c^{4} d^{4} x^{3} e^{10} + 6 \, c^{4} d^{5} x^{2} e^{9} + 18 \, c^{4} d^{6} x e^{8} - 3 \, a c^{3} d^{3} x^{2} e^{11} - 24 \, a c^{3} d^{4} x e^{10} + 9 \, a^{2} c^{2} d^{2} x e^{12}\right)} e^{\left(-6\right)}}{3 \, c^{6} d^{6}} - \frac{c^{6} d^{13} - 6 \, a c^{5} d^{11} e^{2} + 15 \, a^{2} c^{4} d^{9} e^{4} - 20 \, a^{3} c^{3} d^{7} e^{6} + 15 \, a^{4} c^{2} d^{5} e^{8} - 6 \, a^{5} c d^{3} e^{10} + a^{6} d e^{12} + {\left(c^{6} d^{12} e - 6 \, a c^{5} d^{10} e^{3} + 15 \, a^{2} c^{4} d^{8} e^{5} - 20 \, a^{3} c^{3} d^{6} e^{7} + 15 \, a^{4} c^{2} d^{4} e^{9} - 6 \, a^{5} c d^{2} e^{11} + a^{6} e^{13}\right)} x}{{\left(c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} {\left(c d x^{2} e + c d^{2} x + a x e^{2} + a d e\right)} c^{5} d^{5}}"," ",0,"4*(c^6*d^12*e - 6*a*c^5*d^10*e^3 + 15*a^2*c^4*d^8*e^5 - 20*a^3*c^3*d^6*e^7 + 15*a^4*c^2*d^4*e^9 - 6*a^5*c*d^2*e^11 + a^6*e^13)*arctan((2*c*d*x*e + c*d^2 + a*e^2)/sqrt(-c^2*d^4 + 2*a*c*d^2*e^2 - a^2*e^4))/((c^7*d^9 - 2*a*c^6*d^7*e^2 + a^2*c^5*d^5*e^4)*sqrt(-c^2*d^4 + 2*a*c*d^2*e^2 - a^2*e^4)) + 2*(c^3*d^6*e - 3*a*c^2*d^4*e^3 + 3*a^2*c*d^2*e^5 - a^3*e^7)*log(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e)/(c^5*d^5) + 1/3*(c^4*d^4*x^3*e^10 + 6*c^4*d^5*x^2*e^9 + 18*c^4*d^6*x*e^8 - 3*a*c^3*d^3*x^2*e^11 - 24*a*c^3*d^4*x*e^10 + 9*a^2*c^2*d^2*x*e^12)*e^(-6)/(c^6*d^6) - (c^6*d^13 - 6*a*c^5*d^11*e^2 + 15*a^2*c^4*d^9*e^4 - 20*a^3*c^3*d^7*e^6 + 15*a^4*c^2*d^5*e^8 - 6*a^5*c*d^3*e^10 + a^6*d*e^12 + (c^6*d^12*e - 6*a*c^5*d^10*e^3 + 15*a^2*c^4*d^8*e^5 - 20*a^3*c^3*d^6*e^7 + 15*a^4*c^2*d^4*e^9 - 6*a^5*c*d^2*e^11 + a^6*e^13)*x)/((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e)*c^5*d^5)","B",0
1877,1,466,0,0.343333," ","integrate((e*x+d)^5/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x, algorithm=""giac"")","\frac{3 \, {\left(c^{5} d^{10} e - 5 \, a c^{4} d^{8} e^{3} + 10 \, a^{2} c^{3} d^{6} e^{5} - 10 \, a^{3} c^{2} d^{4} e^{7} + 5 \, a^{4} c d^{2} e^{9} - a^{5} e^{11}\right)} \arctan\left(\frac{2 \, c d x e + c d^{2} + a e^{2}}{\sqrt{-c^{2} d^{4} + 2 \, a c d^{2} e^{2} - a^{2} e^{4}}}\right)}{{\left(c^{6} d^{8} - 2 \, a c^{5} d^{6} e^{2} + a^{2} c^{4} d^{4} e^{4}\right)} \sqrt{-c^{2} d^{4} + 2 \, a c d^{2} e^{2} - a^{2} e^{4}}} + \frac{{\left(c^{2} d^{2} x^{2} e^{7} + 6 \, c^{2} d^{3} x e^{6} - 4 \, a c d x e^{8}\right)} e^{\left(-4\right)}}{2 \, c^{4} d^{4}} + \frac{3 \, {\left(c^{2} d^{4} e - 2 \, a c d^{2} e^{3} + a^{2} e^{5}\right)} \log\left(c d x^{2} e + c d^{2} x + a x e^{2} + a d e\right)}{2 \, c^{4} d^{4}} - \frac{c^{5} d^{11} - 5 \, a c^{4} d^{9} e^{2} + 10 \, a^{2} c^{3} d^{7} e^{4} - 10 \, a^{3} c^{2} d^{5} e^{6} + 5 \, a^{4} c d^{3} e^{8} - a^{5} d e^{10} + {\left(c^{5} d^{10} e - 5 \, a c^{4} d^{8} e^{3} + 10 \, a^{2} c^{3} d^{6} e^{5} - 10 \, a^{3} c^{2} d^{4} e^{7} + 5 \, a^{4} c d^{2} e^{9} - a^{5} e^{11}\right)} x}{{\left(c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} {\left(c d x^{2} e + c d^{2} x + a x e^{2} + a d e\right)} c^{4} d^{4}}"," ",0,"3*(c^5*d^10*e - 5*a*c^4*d^8*e^3 + 10*a^2*c^3*d^6*e^5 - 10*a^3*c^2*d^4*e^7 + 5*a^4*c*d^2*e^9 - a^5*e^11)*arctan((2*c*d*x*e + c*d^2 + a*e^2)/sqrt(-c^2*d^4 + 2*a*c*d^2*e^2 - a^2*e^4))/((c^6*d^8 - 2*a*c^5*d^6*e^2 + a^2*c^4*d^4*e^4)*sqrt(-c^2*d^4 + 2*a*c*d^2*e^2 - a^2*e^4)) + 1/2*(c^2*d^2*x^2*e^7 + 6*c^2*d^3*x*e^6 - 4*a*c*d*x*e^8)*e^(-4)/(c^4*d^4) + 3/2*(c^2*d^4*e - 2*a*c*d^2*e^3 + a^2*e^5)*log(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e)/(c^4*d^4) - (c^5*d^11 - 5*a*c^4*d^9*e^2 + 10*a^2*c^3*d^7*e^4 - 10*a^3*c^2*d^5*e^6 + 5*a^4*c*d^3*e^8 - a^5*d*e^10 + (c^5*d^10*e - 5*a*c^4*d^8*e^3 + 10*a^2*c^3*d^6*e^5 - 10*a^3*c^2*d^4*e^7 + 5*a^4*c*d^2*e^9 - a^5*e^11)*x)/((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e)*c^4*d^4)","B",0
1878,1,389,0,0.199034," ","integrate((e*x+d)^4/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x, algorithm=""giac"")","\frac{2 \, {\left(c^{4} d^{8} e - 4 \, a c^{3} d^{6} e^{3} + 6 \, a^{2} c^{2} d^{4} e^{5} - 4 \, a^{3} c d^{2} e^{7} + a^{4} e^{9}\right)} \arctan\left(\frac{2 \, c d x e + c d^{2} + a e^{2}}{\sqrt{-c^{2} d^{4} + 2 \, a c d^{2} e^{2} - a^{2} e^{4}}}\right)}{{\left(c^{5} d^{7} - 2 \, a c^{4} d^{5} e^{2} + a^{2} c^{3} d^{3} e^{4}\right)} \sqrt{-c^{2} d^{4} + 2 \, a c d^{2} e^{2} - a^{2} e^{4}}} + \frac{x e^{2}}{c^{2} d^{2}} + \frac{{\left(c d^{2} e - a e^{3}\right)} \log\left(c d x^{2} e + c d^{2} x + a x e^{2} + a d e\right)}{c^{3} d^{3}} - \frac{\frac{c^{4} d^{8} - 4 \, a c^{3} d^{6} e^{2} + 6 \, a^{2} c^{2} d^{4} e^{4} - 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{c} + \frac{{\left(c^{4} d^{8} e - 4 \, a c^{3} d^{6} e^{3} + 6 \, a^{2} c^{2} d^{4} e^{5} - 4 \, a^{3} c d^{2} e^{7} + a^{4} e^{9}\right)} x}{c d}}{{\left(c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} {\left(c d x^{2} e + c d^{2} x + a x e^{2} + a d e\right)} c^{2} d^{2}}"," ",0,"2*(c^4*d^8*e - 4*a*c^3*d^6*e^3 + 6*a^2*c^2*d^4*e^5 - 4*a^3*c*d^2*e^7 + a^4*e^9)*arctan((2*c*d*x*e + c*d^2 + a*e^2)/sqrt(-c^2*d^4 + 2*a*c*d^2*e^2 - a^2*e^4))/((c^5*d^7 - 2*a*c^4*d^5*e^2 + a^2*c^3*d^3*e^4)*sqrt(-c^2*d^4 + 2*a*c*d^2*e^2 - a^2*e^4)) + x*e^2/(c^2*d^2) + (c*d^2*e - a*e^3)*log(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e)/(c^3*d^3) - ((c^4*d^8 - 4*a*c^3*d^6*e^2 + 6*a^2*c^2*d^4*e^4 - 4*a^3*c*d^2*e^6 + a^4*e^8)/c + (c^4*d^8*e - 4*a*c^3*d^6*e^3 + 6*a^2*c^2*d^4*e^5 - 4*a^3*c*d^2*e^7 + a^4*e^9)*x/(c*d))/((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e)*c^2*d^2)","B",0
1879,1,322,0,0.259953," ","integrate((e*x+d)^3/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x, algorithm=""giac"")","\frac{{\left(c^{3} d^{6} e - 3 \, a c^{2} d^{4} e^{3} + 3 \, a^{2} c d^{2} e^{5} - a^{3} e^{7}\right)} \arctan\left(\frac{2 \, c d x e + c d^{2} + a e^{2}}{\sqrt{-c^{2} d^{4} + 2 \, a c d^{2} e^{2} - a^{2} e^{4}}}\right)}{{\left(c^{4} d^{6} - 2 \, a c^{3} d^{4} e^{2} + a^{2} c^{2} d^{2} e^{4}\right)} \sqrt{-c^{2} d^{4} + 2 \, a c d^{2} e^{2} - a^{2} e^{4}}} + \frac{e \log\left(c d x^{2} e + c d^{2} x + a x e^{2} + a d e\right)}{2 \, c^{2} d^{2}} - \frac{c^{3} d^{7} - 3 \, a c^{2} d^{5} e^{2} + 3 \, a^{2} c d^{3} e^{4} - a^{3} d e^{6} + {\left(c^{3} d^{6} e - 3 \, a c^{2} d^{4} e^{3} + 3 \, a^{2} c d^{2} e^{5} - a^{3} e^{7}\right)} x}{{\left(c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} {\left(c d x^{2} e + c d^{2} x + a x e^{2} + a d e\right)} c^{2} d^{2}}"," ",0,"(c^3*d^6*e - 3*a*c^2*d^4*e^3 + 3*a^2*c*d^2*e^5 - a^3*e^7)*arctan((2*c*d*x*e + c*d^2 + a*e^2)/sqrt(-c^2*d^4 + 2*a*c*d^2*e^2 - a^2*e^4))/((c^4*d^6 - 2*a*c^3*d^4*e^2 + a^2*c^2*d^2*e^4)*sqrt(-c^2*d^4 + 2*a*c*d^2*e^2 - a^2*e^4)) + 1/2*e*log(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e)/(c^2*d^2) - (c^3*d^7 - 3*a*c^2*d^5*e^2 + 3*a^2*c*d^3*e^4 - a^3*d*e^6 + (c^3*d^6*e - 3*a*c^2*d^4*e^3 + 3*a^2*c*d^2*e^5 - a^3*e^7)*x)/((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e)*c^2*d^2)","B",0
1880,1,109,0,0.190919," ","integrate((e*x+d)^2/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x, algorithm=""giac"")","-\frac{c^{2} d^{4} x e + c^{2} d^{5} - 2 \, a c d^{2} x e^{3} - 2 \, a c d^{3} e^{2} + a^{2} x e^{5} + a^{2} d e^{4}}{{\left(c^{3} d^{5} - 2 \, a c^{2} d^{3} e^{2} + a^{2} c d e^{4}\right)} {\left(c d x^{2} e + c d^{2} x + a x e^{2} + a d e\right)}}"," ",0,"-(c^2*d^4*x*e + c^2*d^5 - 2*a*c*d^2*x*e^3 - 2*a*c*d^3*e^2 + a^2*x*e^5 + a^2*d*e^4)/((c^3*d^5 - 2*a*c^2*d^3*e^2 + a^2*c*d*e^4)*(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e))","B",0
1881,1,194,0,0.187103," ","integrate((e*x+d)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x, algorithm=""giac"")","-\frac{2 \, {\left(c d^{2} e - a e^{3}\right)} \arctan\left(\frac{2 \, c d x e + c d^{2} + a e^{2}}{\sqrt{-c^{2} d^{4} + 2 \, a c d^{2} e^{2} - a^{2} e^{4}}}\right)}{{\left(c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} \sqrt{-c^{2} d^{4} + 2 \, a c d^{2} e^{2} - a^{2} e^{4}}} - \frac{c d^{2} x e + c d^{3} - a x e^{3} - a d e^{2}}{{\left(c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} {\left(c d x^{2} e + c d^{2} x + a x e^{2} + a d e\right)}}"," ",0,"-2*(c*d^2*e - a*e^3)*arctan((2*c*d*x*e + c*d^2 + a*e^2)/sqrt(-c^2*d^4 + 2*a*c*d^2*e^2 - a^2*e^4))/((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-c^2*d^4 + 2*a*c*d^2*e^2 - a^2*e^4)) - (c*d^2*x*e + c*d^3 - a*x*e^3 - a*d*e^2)/((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e))","B",0
1882,1,176,0,0.183521," ","integrate(1/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x, algorithm=""giac"")","-\frac{4 \, c d \arctan\left(\frac{2 \, c d x e + c d^{2} + a e^{2}}{\sqrt{-c^{2} d^{4} + 2 \, a c d^{2} e^{2} - a^{2} e^{4}}}\right) e}{{\left(c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} \sqrt{-c^{2} d^{4} + 2 \, a c d^{2} e^{2} - a^{2} e^{4}}} - \frac{2 \, c d x e + c d^{2} + a e^{2}}{{\left(c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} {\left(c d x^{2} e + c d^{2} x + a x e^{2} + a d e\right)}}"," ",0,"-4*c*d*arctan((2*c*d*x*e + c*d^2 + a*e^2)/sqrt(-c^2*d^4 + 2*a*c*d^2*e^2 - a^2*e^4))*e/((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-c^2*d^4 + 2*a*c*d^2*e^2 - a^2*e^4)) - (2*c*d*x*e + c*d^2 + a*e^2)/((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e))","A",0
1883,-2,0,0,0.000000," ","integrate(1/(e*x+d)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: exp(1)^2/(d^2*exp(1)^5*a^2-2*d^2*exp(1)^3*a^2*exp(2)+d^2*exp(1)*a^2*exp(2)^2)*ln(abs(x*exp(1)+d))+exp(1)/(-2*d^2*exp(1)^4*a^2+4*d^2*exp(1)^2*a^2*exp(2)-2*d^2*a^2*exp(2)^2)*ln(x^2*c*d*exp(1)+x*c*d^2+x*a*exp(2)+d*exp(1)*a)+(-c^3*d^6*exp(1)+6*c^2*d^4*exp(1)^3*a-3*c^2*d^4*exp(1)*a*exp(2)-6*c*d^2*exp(1)^3*a^2*exp(2)+3*c*d^2*exp(1)*a^2*exp(2)^2+exp(1)*a^3*exp(2)^3)/(-c^2*d^6*exp(1)^4*a^2+2*c^2*d^6*exp(1)^2*a^2*exp(2)-c^2*d^6*a^2*exp(2)^2+4*c*d^4*exp(1)^6*a^3-10*c*d^4*exp(1)^4*a^3*exp(2)+8*c*d^4*exp(1)^2*a^3*exp(2)^2-2*c*d^4*a^3*exp(2)^3-d^2*exp(1)^4*a^4*exp(2)^2+2*d^2*exp(1)^2*a^4*exp(2)^3-d^2*a^4*exp(2)^4)/sqrt(-c^2*d^4+4*a*c*d^2*exp(1)^2-a^2*exp(2)^2-2*a*c*d^2*exp(2))*atan((a*exp(2)+c*d^2+2*c*d*x*exp(1))/sqrt(-c^2*d^4+4*a*c*d^2*exp(1)^2-a^2*exp(2)^2-2*a*c*d^2*exp(2)))+(-4*c*d^3*exp(1)^4*a^2+6*c*d^3*exp(1)^2*a^2*exp(2)-2*c*d^3*a^2*exp(2)^2+2*d*exp(1)^2*a^3*exp(2)^2-2*d*a^3*exp(2)^3+(-2*c^2*d^4*exp(1)^3*a+2*c^2*d^4*exp(1)*a*exp(2)+2*c*d^2*exp(1)^3*a^2*exp(2)-2*c*d^2*exp(1)*a^2*exp(2)^2)*x)/2/(exp(2)-exp(1)^2)^2/a^2/d^2/(c^2*d^4-4*c*d^2*exp(1)^2*a+2*c*d^2*a*exp(2)+a^2*exp(2)^2)/(x^2*c*d*exp(1)+x*c*d^2+x*a*exp(2)+d*exp(1)*a)","F(-2)",0
1884,-2,0,0,0.000000," ","integrate(1/(e*x+d)^2/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: -(exp(1)*x+d)^-1/exp(1)*exp(1)^6/(a^2*d^2*exp(1)^8-2*a^2*d^2*exp(1)^6*exp(2)+a^2*d^2*exp(1)^4*exp(2)^2)+(-(-a^4*exp(1)^2*exp(2)^4+4*a^3*exp(1)^4*exp(2)^2*d^2*c-2*a^2*exp(1)^6*d^4*c^2-4*a^2*exp(1)^4*exp(2)*d^4*c^2+4*a*exp(1)^4*d^6*c^3-exp(1)^2*d^8*c^4)/(a*exp(1)^2*d-a*exp(2)*d)*(exp(1)*x+d)^-1/exp(1)+(a^3*exp(1)*exp(2)^3*c-3*a^2*exp(1)^3*exp(2)*d^2*c^2+3*a*exp(1)^3*d^4*c^3-exp(1)*d^6*c^4)/(a*exp(1)^2-a*exp(2)))/a^2/d^2/(exp(2)-exp(1)^2)^2/(c^2*d^4-4*c*exp(1)^2*d^2*a+2*c*exp(2)*d^2*a+exp(2)^2*a^2)/((-(exp(1)*x+d)^-1/exp(1))^2*a*exp(1)^4*d-(-(exp(1)*x+d)^-1/exp(1))^2*a*exp(1)^2*exp(2)*d+(exp(1)*x+d)^-1/exp(1)*a*exp(1)*exp(2)-(exp(1)*x+d)^-1/exp(1)*exp(1)*d^2*c+d*c)+(a*exp(1)*exp(2)-d^2*exp(1)*c)/(a^3*d^3*exp(1)^6-3*a^3*d^3*exp(1)^4*exp(2)+3*a^3*d^3*exp(1)^2*exp(2)^2-a^3*d^3*exp(2)^3)*ln((-(exp(1)*x+d)^-1/exp(1))^2*a*d*exp(1)^4-(-(exp(1)*x+d)^-1/exp(1))^2*a*d*exp(1)^2*exp(2)+(exp(1)*x+d)^-1/exp(1)*a*exp(1)*exp(2)-(exp(1)*x+d)^-1/exp(1)*d^2*exp(1)*c+d*c)+(2*a^4*exp(1)^2*exp(2)^4-12*a^3*d^2*exp(1)^4*exp(2)^2*c+4*a^3*d^2*exp(1)^2*exp(2)^3*c+12*a^2*d^4*exp(1)^6*c^2-12*a*d^6*exp(1)^4*c^3+4*a*d^6*exp(1)^2*exp(2)*c^3+2*d^8*exp(1)^2*c^4)/(a^5*d^3*exp(1)^6*exp(2)^2-3*a^5*d^3*exp(1)^4*exp(2)^3+3*a^5*d^3*exp(1)^2*exp(2)^4-a^5*d^3*exp(2)^5-4*a^4*d^5*exp(1)^8*c+14*a^4*d^5*exp(1)^6*exp(2)*c-18*a^4*d^5*exp(1)^4*exp(2)^2*c+10*a^4*d^5*exp(1)^2*exp(2)^3*c-2*a^4*d^5*exp(2)^4*c+a^3*d^7*exp(1)^6*c^2-3*a^3*d^7*exp(1)^4*exp(2)*c^2+3*a^3*d^7*exp(1)^2*exp(2)^2*c^2-a^3*d^7*exp(2)^3*c^2)/sqrt(-c^2*d^4+4*a*c*d^2*exp(1)^2-a^2*exp(2)^2-2*a*c*d^2*exp(2))/exp(1)*atan((-2*a*d*(exp(1)*x+d)^-1/exp(1)*exp(1)^3+2*a*d*(exp(1)*x+d)^-1/exp(1)*exp(1)*exp(2)-a*exp(2)+c*d^2)/sqrt(-c^2*d^4+4*a*c*d^2*exp(1)^2-a^2*exp(2)^2-2*a*c*d^2*exp(2)))","F(-2)",0
1885,1,1068,0,15.081243," ","integrate((e*x+d)^9/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x, algorithm=""giac"")","\frac{15 \, {\left(c^{9} d^{18} e^{2} - 9 \, a c^{8} d^{16} e^{4} + 36 \, a^{2} c^{7} d^{14} e^{6} - 84 \, a^{3} c^{6} d^{12} e^{8} + 126 \, a^{4} c^{5} d^{10} e^{10} - 126 \, a^{5} c^{4} d^{8} e^{12} + 84 \, a^{6} c^{3} d^{6} e^{14} - 36 \, a^{7} c^{2} d^{4} e^{16} + 9 \, a^{8} c d^{2} e^{18} - a^{9} e^{20}\right)} \arctan\left(\frac{2 \, c d x e + c d^{2} + a e^{2}}{\sqrt{-c^{2} d^{4} + 2 \, a c d^{2} e^{2} - a^{2} e^{4}}}\right)}{{\left(c^{11} d^{15} - 4 \, a c^{10} d^{13} e^{2} + 6 \, a^{2} c^{9} d^{11} e^{4} - 4 \, a^{3} c^{8} d^{9} e^{6} + a^{4} c^{7} d^{7} e^{8}\right)} \sqrt{-c^{2} d^{4} + 2 \, a c d^{2} e^{2} - a^{2} e^{4}}} + \frac{15 \, {\left(c^{4} d^{8} e^{2} - 4 \, a c^{3} d^{6} e^{4} + 6 \, a^{2} c^{2} d^{4} e^{6} - 4 \, a^{3} c d^{2} e^{8} + a^{4} e^{10}\right)} \log\left(c d x^{2} e + c d^{2} x + a x e^{2} + a d e\right)}{2 \, c^{7} d^{7}} - \frac{c^{10} d^{22} + 2 \, a c^{9} d^{20} e^{2} - 63 \, a^{2} c^{8} d^{18} e^{4} + 312 \, a^{3} c^{7} d^{16} e^{6} - 798 \, a^{4} c^{6} d^{14} e^{8} + 1260 \, a^{5} c^{5} d^{12} e^{10} - 1302 \, a^{6} c^{4} d^{10} e^{12} + 888 \, a^{7} c^{3} d^{8} e^{14} - 387 \, a^{8} c^{2} d^{6} e^{16} + 98 \, a^{9} c d^{4} e^{18} - 11 \, a^{10} d^{2} e^{20} + 12 \, {\left(c^{10} d^{19} e^{3} - 9 \, a c^{9} d^{17} e^{5} + 36 \, a^{2} c^{8} d^{15} e^{7} - 84 \, a^{3} c^{7} d^{13} e^{9} + 126 \, a^{4} c^{6} d^{11} e^{11} - 126 \, a^{5} c^{5} d^{9} e^{13} + 84 \, a^{6} c^{4} d^{7} e^{15} - 36 \, a^{7} c^{3} d^{5} e^{17} + 9 \, a^{8} c^{2} d^{3} e^{19} - a^{9} c d e^{21}\right)} x^{3} + {\left(25 \, c^{10} d^{20} e^{2} - 214 \, a c^{9} d^{18} e^{4} + 801 \, a^{2} c^{8} d^{16} e^{6} - 1704 \, a^{3} c^{7} d^{14} e^{8} + 2226 \, a^{4} c^{6} d^{12} e^{10} - 1764 \, a^{5} c^{5} d^{10} e^{12} + 714 \, a^{6} c^{4} d^{8} e^{14} + 24 \, a^{7} c^{3} d^{6} e^{16} - 171 \, a^{8} c^{2} d^{4} e^{18} + 74 \, a^{9} c d^{2} e^{20} - 11 \, a^{10} e^{22}\right)} x^{2} + 2 \, {\left(7 \, c^{10} d^{21} e - 52 \, a c^{9} d^{19} e^{3} + 153 \, a^{2} c^{8} d^{17} e^{5} - 192 \, a^{3} c^{7} d^{15} e^{7} - 42 \, a^{4} c^{6} d^{13} e^{9} + 504 \, a^{5} c^{5} d^{11} e^{11} - 798 \, a^{6} c^{4} d^{9} e^{13} + 672 \, a^{7} c^{3} d^{7} e^{15} - 333 \, a^{8} c^{2} d^{5} e^{17} + 92 \, a^{9} c d^{3} e^{19} - 11 \, a^{10} d e^{21}\right)} x}{2 \, {\left(c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)}^{2} {\left(c d x^{2} e + c d^{2} x + a x e^{2} + a d e\right)}^{2} c^{7} d^{7}} + \frac{{\left(c^{9} d^{9} x^{4} e^{18} + 8 \, c^{9} d^{10} x^{3} e^{17} + 30 \, c^{9} d^{11} x^{2} e^{16} + 80 \, c^{9} d^{12} x e^{15} - 4 \, a c^{8} d^{8} x^{3} e^{19} - 36 \, a c^{8} d^{9} x^{2} e^{18} - 180 \, a c^{8} d^{10} x e^{17} + 12 \, a^{2} c^{7} d^{7} x^{2} e^{20} + 144 \, a^{2} c^{7} d^{8} x e^{19} - 40 \, a^{3} c^{6} d^{6} x e^{21}\right)} e^{\left(-12\right)}}{4 \, c^{12} d^{12}}"," ",0,"15*(c^9*d^18*e^2 - 9*a*c^8*d^16*e^4 + 36*a^2*c^7*d^14*e^6 - 84*a^3*c^6*d^12*e^8 + 126*a^4*c^5*d^10*e^10 - 126*a^5*c^4*d^8*e^12 + 84*a^6*c^3*d^6*e^14 - 36*a^7*c^2*d^4*e^16 + 9*a^8*c*d^2*e^18 - a^9*e^20)*arctan((2*c*d*x*e + c*d^2 + a*e^2)/sqrt(-c^2*d^4 + 2*a*c*d^2*e^2 - a^2*e^4))/((c^11*d^15 - 4*a*c^10*d^13*e^2 + 6*a^2*c^9*d^11*e^4 - 4*a^3*c^8*d^9*e^6 + a^4*c^7*d^7*e^8)*sqrt(-c^2*d^4 + 2*a*c*d^2*e^2 - a^2*e^4)) + 15/2*(c^4*d^8*e^2 - 4*a*c^3*d^6*e^4 + 6*a^2*c^2*d^4*e^6 - 4*a^3*c*d^2*e^8 + a^4*e^10)*log(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e)/(c^7*d^7) - 1/2*(c^10*d^22 + 2*a*c^9*d^20*e^2 - 63*a^2*c^8*d^18*e^4 + 312*a^3*c^7*d^16*e^6 - 798*a^4*c^6*d^14*e^8 + 1260*a^5*c^5*d^12*e^10 - 1302*a^6*c^4*d^10*e^12 + 888*a^7*c^3*d^8*e^14 - 387*a^8*c^2*d^6*e^16 + 98*a^9*c*d^4*e^18 - 11*a^10*d^2*e^20 + 12*(c^10*d^19*e^3 - 9*a*c^9*d^17*e^5 + 36*a^2*c^8*d^15*e^7 - 84*a^3*c^7*d^13*e^9 + 126*a^4*c^6*d^11*e^11 - 126*a^5*c^5*d^9*e^13 + 84*a^6*c^4*d^7*e^15 - 36*a^7*c^3*d^5*e^17 + 9*a^8*c^2*d^3*e^19 - a^9*c*d*e^21)*x^3 + (25*c^10*d^20*e^2 - 214*a*c^9*d^18*e^4 + 801*a^2*c^8*d^16*e^6 - 1704*a^3*c^7*d^14*e^8 + 2226*a^4*c^6*d^12*e^10 - 1764*a^5*c^5*d^10*e^12 + 714*a^6*c^4*d^8*e^14 + 24*a^7*c^3*d^6*e^16 - 171*a^8*c^2*d^4*e^18 + 74*a^9*c*d^2*e^20 - 11*a^10*e^22)*x^2 + 2*(7*c^10*d^21*e - 52*a*c^9*d^19*e^3 + 153*a^2*c^8*d^17*e^5 - 192*a^3*c^7*d^15*e^7 - 42*a^4*c^6*d^13*e^9 + 504*a^5*c^5*d^11*e^11 - 798*a^6*c^4*d^9*e^13 + 672*a^7*c^3*d^7*e^15 - 333*a^8*c^2*d^5*e^17 + 92*a^9*c*d^3*e^19 - 11*a^10*d*e^21)*x)/((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)^2*(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e)^2*c^7*d^7) + 1/4*(c^9*d^9*x^4*e^18 + 8*c^9*d^10*x^3*e^17 + 30*c^9*d^11*x^2*e^16 + 80*c^9*d^12*x*e^15 - 4*a*c^8*d^8*x^3*e^19 - 36*a*c^8*d^9*x^2*e^18 - 180*a*c^8*d^10*x*e^17 + 12*a^2*c^7*d^7*x^2*e^20 + 144*a^2*c^7*d^8*x*e^19 - 40*a^3*c^6*d^6*x*e^21)*e^(-12)/(c^12*d^12)","B",0
1886,1,933,0,12.110071," ","integrate((e*x+d)^8/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x, algorithm=""giac"")","\frac{10 \, {\left(c^{8} d^{16} e^{2} - 8 \, a c^{7} d^{14} e^{4} + 28 \, a^{2} c^{6} d^{12} e^{6} - 56 \, a^{3} c^{5} d^{10} e^{8} + 70 \, a^{4} c^{4} d^{8} e^{10} - 56 \, a^{5} c^{3} d^{6} e^{12} + 28 \, a^{6} c^{2} d^{4} e^{14} - 8 \, a^{7} c d^{2} e^{16} + a^{8} e^{18}\right)} \arctan\left(\frac{2 \, c d x e + c d^{2} + a e^{2}}{\sqrt{-c^{2} d^{4} + 2 \, a c d^{2} e^{2} - a^{2} e^{4}}}\right)}{{\left(c^{10} d^{14} - 4 \, a c^{9} d^{12} e^{2} + 6 \, a^{2} c^{8} d^{10} e^{4} - 4 \, a^{3} c^{7} d^{8} e^{6} + a^{4} c^{6} d^{6} e^{8}\right)} \sqrt{-c^{2} d^{4} + 2 \, a c d^{2} e^{2} - a^{2} e^{4}}} + \frac{5 \, {\left(c^{3} d^{6} e^{2} - 3 \, a c^{2} d^{4} e^{4} + 3 \, a^{2} c d^{2} e^{6} - a^{3} e^{8}\right)} \log\left(c d x^{2} e + c d^{2} x + a x e^{2} + a d e\right)}{c^{6} d^{6}} - \frac{c^{9} d^{20} + a c^{8} d^{18} e^{2} - 44 \, a^{2} c^{7} d^{16} e^{4} + 196 \, a^{3} c^{6} d^{14} e^{6} - 434 \, a^{4} c^{5} d^{12} e^{8} + 574 \, a^{5} c^{4} d^{10} e^{10} - 476 \, a^{6} c^{3} d^{8} e^{12} + 244 \, a^{7} c^{2} d^{6} e^{14} - 71 \, a^{8} c d^{4} e^{16} + 9 \, a^{9} d^{2} e^{18} + 10 \, {\left(c^{9} d^{17} e^{3} - 8 \, a c^{8} d^{15} e^{5} + 28 \, a^{2} c^{7} d^{13} e^{7} - 56 \, a^{3} c^{6} d^{11} e^{9} + 70 \, a^{4} c^{5} d^{9} e^{11} - 56 \, a^{5} c^{4} d^{7} e^{13} + 28 \, a^{6} c^{3} d^{5} e^{15} - 8 \, a^{7} c^{2} d^{3} e^{17} + a^{8} c d e^{19}\right)} x^{3} + 3 \, {\left(7 \, c^{9} d^{18} e^{2} - 53 \, a c^{8} d^{16} e^{4} + 172 \, a^{2} c^{7} d^{14} e^{6} - 308 \, a^{3} c^{6} d^{12} e^{8} + 322 \, a^{4} c^{5} d^{10} e^{10} - 182 \, a^{5} c^{4} d^{8} e^{12} + 28 \, a^{6} c^{3} d^{6} e^{14} + 28 \, a^{7} c^{2} d^{4} e^{16} - 17 \, a^{8} c d^{2} e^{18} + 3 \, a^{9} e^{20}\right)} x^{2} + 6 \, {\left(2 \, c^{9} d^{19} e - 13 \, a c^{8} d^{17} e^{3} + 32 \, a^{2} c^{7} d^{15} e^{5} - 28 \, a^{3} c^{6} d^{13} e^{7} - 28 \, a^{4} c^{5} d^{11} e^{9} + 98 \, a^{5} c^{4} d^{9} e^{11} - 112 \, a^{6} c^{3} d^{7} e^{13} + 68 \, a^{7} c^{2} d^{5} e^{15} - 22 \, a^{8} c d^{3} e^{17} + 3 \, a^{9} d e^{19}\right)} x}{2 \, {\left(c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)}^{2} {\left(c d x^{2} e + c d^{2} x + a x e^{2} + a d e\right)}^{2} c^{6} d^{6}} + \frac{{\left(2 \, c^{6} d^{6} x^{3} e^{14} + 15 \, c^{6} d^{7} x^{2} e^{13} + 60 \, c^{6} d^{8} x e^{12} - 9 \, a c^{5} d^{5} x^{2} e^{15} - 90 \, a c^{5} d^{6} x e^{14} + 36 \, a^{2} c^{4} d^{4} x e^{16}\right)} e^{\left(-9\right)}}{6 \, c^{9} d^{9}}"," ",0,"10*(c^8*d^16*e^2 - 8*a*c^7*d^14*e^4 + 28*a^2*c^6*d^12*e^6 - 56*a^3*c^5*d^10*e^8 + 70*a^4*c^4*d^8*e^10 - 56*a^5*c^3*d^6*e^12 + 28*a^6*c^2*d^4*e^14 - 8*a^7*c*d^2*e^16 + a^8*e^18)*arctan((2*c*d*x*e + c*d^2 + a*e^2)/sqrt(-c^2*d^4 + 2*a*c*d^2*e^2 - a^2*e^4))/((c^10*d^14 - 4*a*c^9*d^12*e^2 + 6*a^2*c^8*d^10*e^4 - 4*a^3*c^7*d^8*e^6 + a^4*c^6*d^6*e^8)*sqrt(-c^2*d^4 + 2*a*c*d^2*e^2 - a^2*e^4)) + 5*(c^3*d^6*e^2 - 3*a*c^2*d^4*e^4 + 3*a^2*c*d^2*e^6 - a^3*e^8)*log(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e)/(c^6*d^6) - 1/2*(c^9*d^20 + a*c^8*d^18*e^2 - 44*a^2*c^7*d^16*e^4 + 196*a^3*c^6*d^14*e^6 - 434*a^4*c^5*d^12*e^8 + 574*a^5*c^4*d^10*e^10 - 476*a^6*c^3*d^8*e^12 + 244*a^7*c^2*d^6*e^14 - 71*a^8*c*d^4*e^16 + 9*a^9*d^2*e^18 + 10*(c^9*d^17*e^3 - 8*a*c^8*d^15*e^5 + 28*a^2*c^7*d^13*e^7 - 56*a^3*c^6*d^11*e^9 + 70*a^4*c^5*d^9*e^11 - 56*a^5*c^4*d^7*e^13 + 28*a^6*c^3*d^5*e^15 - 8*a^7*c^2*d^3*e^17 + a^8*c*d*e^19)*x^3 + 3*(7*c^9*d^18*e^2 - 53*a*c^8*d^16*e^4 + 172*a^2*c^7*d^14*e^6 - 308*a^3*c^6*d^12*e^8 + 322*a^4*c^5*d^10*e^10 - 182*a^5*c^4*d^8*e^12 + 28*a^6*c^3*d^6*e^14 + 28*a^7*c^2*d^4*e^16 - 17*a^8*c*d^2*e^18 + 3*a^9*e^20)*x^2 + 6*(2*c^9*d^19*e - 13*a*c^8*d^17*e^3 + 32*a^2*c^7*d^15*e^5 - 28*a^3*c^6*d^13*e^7 - 28*a^4*c^5*d^11*e^9 + 98*a^5*c^4*d^9*e^11 - 112*a^6*c^3*d^7*e^13 + 68*a^7*c^2*d^5*e^15 - 22*a^8*c*d^3*e^17 + 3*a^9*d*e^19)*x)/((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)^2*(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e)^2*c^6*d^6) + 1/6*(2*c^6*d^6*x^3*e^14 + 15*c^6*d^7*x^2*e^13 + 60*c^6*d^8*x*e^12 - 9*a*c^5*d^5*x^2*e^15 - 90*a*c^5*d^6*x*e^14 + 36*a^2*c^4*d^4*x*e^16)*e^(-9)/(c^9*d^9)","B",0
1887,1,803,0,11.630687," ","integrate((e*x+d)^7/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x, algorithm=""giac"")","\frac{6 \, {\left(c^{7} d^{14} e^{2} - 7 \, a c^{6} d^{12} e^{4} + 21 \, a^{2} c^{5} d^{10} e^{6} - 35 \, a^{3} c^{4} d^{8} e^{8} + 35 \, a^{4} c^{3} d^{6} e^{10} - 21 \, a^{5} c^{2} d^{4} e^{12} + 7 \, a^{6} c d^{2} e^{14} - a^{7} e^{16}\right)} \arctan\left(\frac{2 \, c d x e + c d^{2} + a e^{2}}{\sqrt{-c^{2} d^{4} + 2 \, a c d^{2} e^{2} - a^{2} e^{4}}}\right)}{{\left(c^{9} d^{13} - 4 \, a c^{8} d^{11} e^{2} + 6 \, a^{2} c^{7} d^{9} e^{4} - 4 \, a^{3} c^{6} d^{7} e^{6} + a^{4} c^{5} d^{5} e^{8}\right)} \sqrt{-c^{2} d^{4} + 2 \, a c d^{2} e^{2} - a^{2} e^{4}}} + \frac{3 \, {\left(c^{2} d^{4} e^{2} - 2 \, a c d^{2} e^{4} + a^{2} e^{6}\right)} \log\left(c d x^{2} e + c d^{2} x + a x e^{2} + a d e\right)}{c^{5} d^{5}} + \frac{{\left(c^{3} d^{3} x^{2} e^{10} + 8 \, c^{3} d^{4} x e^{9} - 6 \, a c^{2} d^{2} x e^{11}\right)} e^{\left(-6\right)}}{2 \, c^{6} d^{6}} - \frac{c^{8} d^{18} - 28 \, a^{2} c^{6} d^{14} e^{4} + 112 \, a^{3} c^{5} d^{12} e^{6} - 210 \, a^{4} c^{4} d^{10} e^{8} + 224 \, a^{5} c^{3} d^{8} e^{10} - 140 \, a^{6} c^{2} d^{6} e^{12} + 48 \, a^{7} c d^{4} e^{14} - 7 \, a^{8} d^{2} e^{16} + 8 \, {\left(c^{8} d^{15} e^{3} - 7 \, a c^{7} d^{13} e^{5} + 21 \, a^{2} c^{6} d^{11} e^{7} - 35 \, a^{3} c^{5} d^{9} e^{9} + 35 \, a^{4} c^{4} d^{7} e^{11} - 21 \, a^{5} c^{3} d^{5} e^{13} + 7 \, a^{6} c^{2} d^{3} e^{15} - a^{7} c d e^{17}\right)} x^{3} + {\left(17 \, c^{8} d^{16} e^{2} - 112 \, a c^{7} d^{14} e^{4} + 308 \, a^{2} c^{6} d^{12} e^{6} - 448 \, a^{3} c^{5} d^{10} e^{8} + 350 \, a^{4} c^{4} d^{8} e^{10} - 112 \, a^{5} c^{3} d^{6} e^{12} - 28 \, a^{6} c^{2} d^{4} e^{14} + 32 \, a^{7} c d^{2} e^{16} - 7 \, a^{8} e^{18}\right)} x^{2} + 2 \, {\left(5 \, c^{8} d^{17} e - 28 \, a c^{7} d^{15} e^{3} + 56 \, a^{2} c^{6} d^{13} e^{5} - 28 \, a^{3} c^{5} d^{11} e^{7} - 70 \, a^{4} c^{4} d^{9} e^{9} + 140 \, a^{5} c^{3} d^{7} e^{11} - 112 \, a^{6} c^{2} d^{5} e^{13} + 44 \, a^{7} c d^{3} e^{15} - 7 \, a^{8} d e^{17}\right)} x}{2 \, {\left(c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)}^{2} {\left(c d x^{2} e + c d^{2} x + a x e^{2} + a d e\right)}^{2} c^{5} d^{5}}"," ",0,"6*(c^7*d^14*e^2 - 7*a*c^6*d^12*e^4 + 21*a^2*c^5*d^10*e^6 - 35*a^3*c^4*d^8*e^8 + 35*a^4*c^3*d^6*e^10 - 21*a^5*c^2*d^4*e^12 + 7*a^6*c*d^2*e^14 - a^7*e^16)*arctan((2*c*d*x*e + c*d^2 + a*e^2)/sqrt(-c^2*d^4 + 2*a*c*d^2*e^2 - a^2*e^4))/((c^9*d^13 - 4*a*c^8*d^11*e^2 + 6*a^2*c^7*d^9*e^4 - 4*a^3*c^6*d^7*e^6 + a^4*c^5*d^5*e^8)*sqrt(-c^2*d^4 + 2*a*c*d^2*e^2 - a^2*e^4)) + 3*(c^2*d^4*e^2 - 2*a*c*d^2*e^4 + a^2*e^6)*log(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e)/(c^5*d^5) + 1/2*(c^3*d^3*x^2*e^10 + 8*c^3*d^4*x*e^9 - 6*a*c^2*d^2*x*e^11)*e^(-6)/(c^6*d^6) - 1/2*(c^8*d^18 - 28*a^2*c^6*d^14*e^4 + 112*a^3*c^5*d^12*e^6 - 210*a^4*c^4*d^10*e^8 + 224*a^5*c^3*d^8*e^10 - 140*a^6*c^2*d^6*e^12 + 48*a^7*c*d^4*e^14 - 7*a^8*d^2*e^16 + 8*(c^8*d^15*e^3 - 7*a*c^7*d^13*e^5 + 21*a^2*c^6*d^11*e^7 - 35*a^3*c^5*d^9*e^9 + 35*a^4*c^4*d^7*e^11 - 21*a^5*c^3*d^5*e^13 + 7*a^6*c^2*d^3*e^15 - a^7*c*d*e^17)*x^3 + (17*c^8*d^16*e^2 - 112*a*c^7*d^14*e^4 + 308*a^2*c^6*d^12*e^6 - 448*a^3*c^5*d^10*e^8 + 350*a^4*c^4*d^8*e^10 - 112*a^5*c^3*d^6*e^12 - 28*a^6*c^2*d^4*e^14 + 32*a^7*c*d^2*e^16 - 7*a^8*e^18)*x^2 + 2*(5*c^8*d^17*e - 28*a*c^7*d^15*e^3 + 56*a^2*c^6*d^13*e^5 - 28*a^3*c^5*d^11*e^7 - 70*a^4*c^4*d^9*e^9 + 140*a^5*c^3*d^7*e^11 - 112*a^6*c^2*d^5*e^13 + 44*a^7*c*d^3*e^15 - 7*a^8*d*e^17)*x)/((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)^2*(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e)^2*c^5*d^5)","B",0
1888,1,699,0,0.345580," ","integrate((e*x+d)^6/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x, algorithm=""giac"")","\frac{3 \, {\left(c^{6} d^{12} e^{2} - 6 \, a c^{5} d^{10} e^{4} + 15 \, a^{2} c^{4} d^{8} e^{6} - 20 \, a^{3} c^{3} d^{6} e^{8} + 15 \, a^{4} c^{2} d^{4} e^{10} - 6 \, a^{5} c d^{2} e^{12} + a^{6} e^{14}\right)} \arctan\left(\frac{2 \, c d x e + c d^{2} + a e^{2}}{\sqrt{-c^{2} d^{4} + 2 \, a c d^{2} e^{2} - a^{2} e^{4}}}\right)}{{\left(c^{8} d^{12} - 4 \, a c^{7} d^{10} e^{2} + 6 \, a^{2} c^{6} d^{8} e^{4} - 4 \, a^{3} c^{5} d^{6} e^{6} + a^{4} c^{4} d^{4} e^{8}\right)} \sqrt{-c^{2} d^{4} + 2 \, a c d^{2} e^{2} - a^{2} e^{4}}} + \frac{x e^{3}}{c^{3} d^{3}} + \frac{3 \, {\left(c d^{2} e^{2} - a e^{4}\right)} \log\left(c d x^{2} e + c d^{2} x + a x e^{2} + a d e\right)}{2 \, c^{4} d^{4}} - \frac{c^{7} d^{16} - a c^{6} d^{14} e^{2} - 15 \, a^{2} c^{5} d^{12} e^{4} + 55 \, a^{3} c^{4} d^{10} e^{6} - 85 \, a^{4} c^{3} d^{8} e^{8} + 69 \, a^{5} c^{2} d^{6} e^{10} - 29 \, a^{6} c d^{4} e^{12} + 5 \, a^{7} d^{2} e^{14} + 6 \, {\left(c^{7} d^{13} e^{3} - 6 \, a c^{6} d^{11} e^{5} + 15 \, a^{2} c^{5} d^{9} e^{7} - 20 \, a^{3} c^{4} d^{7} e^{9} + 15 \, a^{4} c^{3} d^{5} e^{11} - 6 \, a^{5} c^{2} d^{3} e^{13} + a^{6} c d e^{15}\right)} x^{3} + {\left(13 \, c^{7} d^{14} e^{2} - 73 \, a c^{6} d^{12} e^{4} + 165 \, a^{2} c^{5} d^{10} e^{6} - 185 \, a^{3} c^{4} d^{8} e^{8} + 95 \, a^{4} c^{3} d^{6} e^{10} - 3 \, a^{5} c^{2} d^{4} e^{12} - 17 \, a^{6} c d^{2} e^{14} + 5 \, a^{7} e^{16}\right)} x^{2} + 2 \, {\left(4 \, c^{7} d^{15} e - 19 \, a c^{6} d^{13} e^{3} + 30 \, a^{2} c^{5} d^{11} e^{5} - 5 \, a^{3} c^{4} d^{9} e^{7} - 40 \, a^{4} c^{3} d^{7} e^{9} + 51 \, a^{5} c^{2} d^{5} e^{11} - 26 \, a^{6} c d^{3} e^{13} + 5 \, a^{7} d e^{15}\right)} x}{2 \, {\left(c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)}^{2} {\left(c d x^{2} e + c d^{2} x + a x e^{2} + a d e\right)}^{2} c^{4} d^{4}}"," ",0,"3*(c^6*d^12*e^2 - 6*a*c^5*d^10*e^4 + 15*a^2*c^4*d^8*e^6 - 20*a^3*c^3*d^6*e^8 + 15*a^4*c^2*d^4*e^10 - 6*a^5*c*d^2*e^12 + a^6*e^14)*arctan((2*c*d*x*e + c*d^2 + a*e^2)/sqrt(-c^2*d^4 + 2*a*c*d^2*e^2 - a^2*e^4))/((c^8*d^12 - 4*a*c^7*d^10*e^2 + 6*a^2*c^6*d^8*e^4 - 4*a^3*c^5*d^6*e^6 + a^4*c^4*d^4*e^8)*sqrt(-c^2*d^4 + 2*a*c*d^2*e^2 - a^2*e^4)) + x*e^3/(c^3*d^3) + 3/2*(c*d^2*e^2 - a*e^4)*log(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e)/(c^4*d^4) - 1/2*(c^7*d^16 - a*c^6*d^14*e^2 - 15*a^2*c^5*d^12*e^4 + 55*a^3*c^4*d^10*e^6 - 85*a^4*c^3*d^8*e^8 + 69*a^5*c^2*d^6*e^10 - 29*a^6*c*d^4*e^12 + 5*a^7*d^2*e^14 + 6*(c^7*d^13*e^3 - 6*a*c^6*d^11*e^5 + 15*a^2*c^5*d^9*e^7 - 20*a^3*c^4*d^7*e^9 + 15*a^4*c^3*d^5*e^11 - 6*a^5*c^2*d^3*e^13 + a^6*c*d*e^15)*x^3 + (13*c^7*d^14*e^2 - 73*a*c^6*d^12*e^4 + 165*a^2*c^5*d^10*e^6 - 185*a^3*c^4*d^8*e^8 + 95*a^4*c^3*d^6*e^10 - 3*a^5*c^2*d^4*e^12 - 17*a^6*c*d^2*e^14 + 5*a^7*e^16)*x^2 + 2*(4*c^7*d^15*e - 19*a*c^6*d^13*e^3 + 30*a^2*c^5*d^11*e^5 - 5*a^3*c^4*d^9*e^7 - 40*a^4*c^3*d^7*e^9 + 51*a^5*c^2*d^5*e^11 - 26*a^6*c*d^3*e^13 + 5*a^7*d*e^15)*x)/((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)^2*(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e)^2*c^4*d^4)","B",0
1889,1,601,0,0.329181," ","integrate((e*x+d)^5/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x, algorithm=""giac"")","\frac{{\left(c^{5} d^{10} e^{2} - 5 \, a c^{4} d^{8} e^{4} + 10 \, a^{2} c^{3} d^{6} e^{6} - 10 \, a^{3} c^{2} d^{4} e^{8} + 5 \, a^{4} c d^{2} e^{10} - a^{5} e^{12}\right)} \arctan\left(\frac{2 \, c d x e + c d^{2} + a e^{2}}{\sqrt{-c^{2} d^{4} + 2 \, a c d^{2} e^{2} - a^{2} e^{4}}}\right)}{{\left(c^{7} d^{11} - 4 \, a c^{6} d^{9} e^{2} + 6 \, a^{2} c^{5} d^{7} e^{4} - 4 \, a^{3} c^{4} d^{5} e^{6} + a^{4} c^{3} d^{3} e^{8}\right)} \sqrt{-c^{2} d^{4} + 2 \, a c d^{2} e^{2} - a^{2} e^{4}}} + \frac{e^{2} \log\left(c d x^{2} e + c d^{2} x + a x e^{2} + a d e\right)}{2 \, c^{3} d^{3}} - \frac{c^{6} d^{14} - 2 \, a c^{5} d^{12} e^{2} - 5 \, a^{2} c^{4} d^{10} e^{4} + 20 \, a^{3} c^{3} d^{8} e^{6} - 25 \, a^{4} c^{2} d^{6} e^{8} + 14 \, a^{5} c d^{4} e^{10} - 3 \, a^{6} d^{2} e^{12} + 4 \, {\left(c^{6} d^{11} e^{3} - 5 \, a c^{5} d^{9} e^{5} + 10 \, a^{2} c^{4} d^{7} e^{7} - 10 \, a^{3} c^{3} d^{5} e^{9} + 5 \, a^{4} c^{2} d^{3} e^{11} - a^{5} c d e^{13}\right)} x^{3} + 3 \, {\left(3 \, c^{6} d^{12} e^{2} - 14 \, a c^{5} d^{10} e^{4} + 25 \, a^{2} c^{4} d^{8} e^{6} - 20 \, a^{3} c^{3} d^{6} e^{8} + 5 \, a^{4} c^{2} d^{4} e^{10} + 2 \, a^{5} c d^{2} e^{12} - a^{6} e^{14}\right)} x^{2} + 6 \, {\left(c^{6} d^{13} e - 4 \, a c^{5} d^{11} e^{3} + 5 \, a^{2} c^{4} d^{9} e^{5} - 5 \, a^{4} c^{2} d^{5} e^{9} + 4 \, a^{5} c d^{3} e^{11} - a^{6} d e^{13}\right)} x}{2 \, {\left(c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)}^{2} {\left(c d x^{2} e + c d^{2} x + a x e^{2} + a d e\right)}^{2} c^{3} d^{3}}"," ",0,"(c^5*d^10*e^2 - 5*a*c^4*d^8*e^4 + 10*a^2*c^3*d^6*e^6 - 10*a^3*c^2*d^4*e^8 + 5*a^4*c*d^2*e^10 - a^5*e^12)*arctan((2*c*d*x*e + c*d^2 + a*e^2)/sqrt(-c^2*d^4 + 2*a*c*d^2*e^2 - a^2*e^4))/((c^7*d^11 - 4*a*c^6*d^9*e^2 + 6*a^2*c^5*d^7*e^4 - 4*a^3*c^4*d^5*e^6 + a^4*c^3*d^3*e^8)*sqrt(-c^2*d^4 + 2*a*c*d^2*e^2 - a^2*e^4)) + 1/2*e^2*log(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e)/(c^3*d^3) - 1/2*(c^6*d^14 - 2*a*c^5*d^12*e^2 - 5*a^2*c^4*d^10*e^4 + 20*a^3*c^3*d^8*e^6 - 25*a^4*c^2*d^6*e^8 + 14*a^5*c*d^4*e^10 - 3*a^6*d^2*e^12 + 4*(c^6*d^11*e^3 - 5*a*c^5*d^9*e^5 + 10*a^2*c^4*d^7*e^7 - 10*a^3*c^3*d^5*e^9 + 5*a^4*c^2*d^3*e^11 - a^5*c*d*e^13)*x^3 + 3*(3*c^6*d^12*e^2 - 14*a*c^5*d^10*e^4 + 25*a^2*c^4*d^8*e^6 - 20*a^3*c^3*d^6*e^8 + 5*a^4*c^2*d^4*e^10 + 2*a^5*c*d^2*e^12 - a^6*e^14)*x^2 + 6*(c^6*d^13*e - 4*a*c^5*d^11*e^3 + 5*a^2*c^4*d^9*e^5 - 5*a^4*c^2*d^5*e^9 + 4*a^5*c*d^3*e^11 - a^6*d*e^13)*x)/((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)^2*(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e)^2*c^3*d^3)","B",0
1890,1,377,0,1.697700," ","integrate((e*x+d)^4/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x, algorithm=""giac"")","-\frac{2 \, c^{5} d^{9} x^{3} e^{3} + 5 \, c^{5} d^{10} x^{2} e^{2} + 4 \, c^{5} d^{11} x e + c^{5} d^{12} - 8 \, a c^{4} d^{7} x^{3} e^{5} - 19 \, a c^{4} d^{8} x^{2} e^{4} - 14 \, a c^{4} d^{9} x e^{3} - 3 \, a c^{4} d^{10} e^{2} + 12 \, a^{2} c^{3} d^{5} x^{3} e^{7} + 26 \, a^{2} c^{3} d^{6} x^{2} e^{6} + 16 \, a^{2} c^{3} d^{7} x e^{5} + 2 \, a^{2} c^{3} d^{8} e^{4} - 8 \, a^{3} c^{2} d^{3} x^{3} e^{9} - 14 \, a^{3} c^{2} d^{4} x^{2} e^{8} - 4 \, a^{3} c^{2} d^{5} x e^{7} + 2 \, a^{3} c^{2} d^{6} e^{6} + 2 \, a^{4} c d x^{3} e^{11} + a^{4} c d^{2} x^{2} e^{10} - 4 \, a^{4} c d^{3} x e^{9} - 3 \, a^{4} c d^{4} e^{8} + a^{5} x^{2} e^{12} + 2 \, a^{5} d x e^{11} + a^{5} d^{2} e^{10}}{2 \, {\left(c^{6} d^{10} - 4 \, a c^{5} d^{8} e^{2} + 6 \, a^{2} c^{4} d^{6} e^{4} - 4 \, a^{3} c^{3} d^{4} e^{6} + a^{4} c^{2} d^{2} e^{8}\right)} {\left(c d x^{2} e + c d^{2} x + a x e^{2} + a d e\right)}^{2}}"," ",0,"-1/2*(2*c^5*d^9*x^3*e^3 + 5*c^5*d^10*x^2*e^2 + 4*c^5*d^11*x*e + c^5*d^12 - 8*a*c^4*d^7*x^3*e^5 - 19*a*c^4*d^8*x^2*e^4 - 14*a*c^4*d^9*x*e^3 - 3*a*c^4*d^10*e^2 + 12*a^2*c^3*d^5*x^3*e^7 + 26*a^2*c^3*d^6*x^2*e^6 + 16*a^2*c^3*d^7*x*e^5 + 2*a^2*c^3*d^8*e^4 - 8*a^3*c^2*d^3*x^3*e^9 - 14*a^3*c^2*d^4*x^2*e^8 - 4*a^3*c^2*d^5*x*e^7 + 2*a^3*c^2*d^6*e^6 + 2*a^4*c*d*x^3*e^11 + a^4*c*d^2*x^2*e^10 - 4*a^4*c*d^3*x*e^9 - 3*a^4*c*d^4*e^8 + a^5*x^2*e^12 + 2*a^5*d*x*e^11 + a^5*d^2*e^10)/((c^6*d^10 - 4*a*c^5*d^8*e^2 + 6*a^2*c^4*d^6*e^4 - 4*a^3*c^3*d^4*e^6 + a^4*c^2*d^2*e^8)*(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e)^2)","B",0
1891,1,259,0,0.232033," ","integrate((e*x+d)^3/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x, algorithm=""giac"")","-\frac{c^{4} d^{8} x^{2} e^{2} + 2 \, c^{4} d^{9} x e + c^{4} d^{10} - 4 \, a c^{3} d^{6} x^{2} e^{4} - 8 \, a c^{3} d^{7} x e^{3} - 4 \, a c^{3} d^{8} e^{2} + 6 \, a^{2} c^{2} d^{4} x^{2} e^{6} + 12 \, a^{2} c^{2} d^{5} x e^{5} + 6 \, a^{2} c^{2} d^{6} e^{4} - 4 \, a^{3} c d^{2} x^{2} e^{8} - 8 \, a^{3} c d^{3} x e^{7} - 4 \, a^{3} c d^{4} e^{6} + a^{4} x^{2} e^{10} + 2 \, a^{4} d x e^{9} + a^{4} d^{2} e^{8}}{2 \, {\left(c^{5} d^{9} - 4 \, a c^{4} d^{7} e^{2} + 6 \, a^{2} c^{3} d^{5} e^{4} - 4 \, a^{3} c^{2} d^{3} e^{6} + a^{4} c d e^{8}\right)} {\left(c d x^{2} e + c d^{2} x + a x e^{2} + a d e\right)}^{2}}"," ",0,"-1/2*(c^4*d^8*x^2*e^2 + 2*c^4*d^9*x*e + c^4*d^10 - 4*a*c^3*d^6*x^2*e^4 - 8*a*c^3*d^7*x*e^3 - 4*a*c^3*d^8*e^2 + 6*a^2*c^2*d^4*x^2*e^6 + 12*a^2*c^2*d^5*x*e^5 + 6*a^2*c^2*d^6*e^4 - 4*a^3*c*d^2*x^2*e^8 - 8*a^3*c*d^3*x*e^7 - 4*a^3*c*d^4*e^6 + a^4*x^2*e^10 + 2*a^4*d*x*e^9 + a^4*d^2*e^8)/((c^5*d^9 - 4*a*c^4*d^7*e^2 + 6*a^2*c^3*d^5*e^4 - 4*a^3*c^2*d^3*e^6 + a^4*c*d*e^8)*(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e)^2)","B",0
1892,1,396,0,0.235482," ","integrate((e*x+d)^2/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x, algorithm=""giac"")","\frac{2 \, {\left(c^{2} d^{4} e^{2} - 2 \, a c d^{2} e^{4} + a^{2} e^{6}\right)} \arctan\left(\frac{2 \, c d x e + c d^{2} + a e^{2}}{\sqrt{-c^{2} d^{4} + 2 \, a c d^{2} e^{2} - a^{2} e^{4}}}\right)}{{\left(c^{4} d^{8} - 4 \, a c^{3} d^{6} e^{2} + 6 \, a^{2} c^{2} d^{4} e^{4} - 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}\right)} \sqrt{-c^{2} d^{4} + 2 \, a c d^{2} e^{2} - a^{2} e^{4}}} + \frac{2 \, c^{3} d^{5} x^{3} e^{3} + 3 \, c^{3} d^{6} x^{2} e^{2} - c^{3} d^{8} - 4 \, a c^{2} d^{3} x^{3} e^{5} - 3 \, a c^{2} d^{4} x^{2} e^{4} + 6 \, a c^{2} d^{5} x e^{3} + 5 \, a c^{2} d^{6} e^{2} + 2 \, a^{2} c d x^{3} e^{7} - 3 \, a^{2} c d^{2} x^{2} e^{6} - 12 \, a^{2} c d^{3} x e^{5} - 7 \, a^{2} c d^{4} e^{4} + 3 \, a^{3} x^{2} e^{8} + 6 \, a^{3} d x e^{7} + 3 \, a^{3} d^{2} e^{6}}{2 \, {\left(c^{4} d^{8} - 4 \, a c^{3} d^{6} e^{2} + 6 \, a^{2} c^{2} d^{4} e^{4} - 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}\right)} {\left(c d x^{2} e + c d^{2} x + a x e^{2} + a d e\right)}^{2}}"," ",0,"2*(c^2*d^4*e^2 - 2*a*c*d^2*e^4 + a^2*e^6)*arctan((2*c*d*x*e + c*d^2 + a*e^2)/sqrt(-c^2*d^4 + 2*a*c*d^2*e^2 - a^2*e^4))/((c^4*d^8 - 4*a*c^3*d^6*e^2 + 6*a^2*c^2*d^4*e^4 - 4*a^3*c*d^2*e^6 + a^4*e^8)*sqrt(-c^2*d^4 + 2*a*c*d^2*e^2 - a^2*e^4)) + 1/2*(2*c^3*d^5*x^3*e^3 + 3*c^3*d^6*x^2*e^2 - c^3*d^8 - 4*a*c^2*d^3*x^3*e^5 - 3*a*c^2*d^4*x^2*e^4 + 6*a*c^2*d^5*x*e^3 + 5*a*c^2*d^6*e^2 + 2*a^2*c*d*x^3*e^7 - 3*a^2*c*d^2*x^2*e^6 - 12*a^2*c*d^3*x*e^5 - 7*a^2*c*d^4*e^4 + 3*a^3*x^2*e^8 + 6*a^3*d*x*e^7 + 3*a^3*d^2*e^6)/((c^4*d^8 - 4*a*c^3*d^6*e^2 + 6*a^2*c^2*d^4*e^4 - 4*a^3*c*d^2*e^6 + a^4*e^8)*(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e)^2)","B",0
1893,1,358,0,0.216974," ","integrate((e*x+d)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x, algorithm=""giac"")","\frac{6 \, {\left(c^{2} d^{3} e^{2} - a c d e^{4}\right)} \arctan\left(\frac{2 \, c d x e + c d^{2} + a e^{2}}{\sqrt{-c^{2} d^{4} + 2 \, a c d^{2} e^{2} - a^{2} e^{4}}}\right)}{{\left(c^{4} d^{8} - 4 \, a c^{3} d^{6} e^{2} + 6 \, a^{2} c^{2} d^{4} e^{4} - 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}\right)} \sqrt{-c^{2} d^{4} + 2 \, a c d^{2} e^{2} - a^{2} e^{4}}} + \frac{6 \, c^{3} d^{4} x^{3} e^{3} + 9 \, c^{3} d^{5} x^{2} e^{2} + 2 \, c^{3} d^{6} x e - c^{3} d^{7} - 6 \, a c^{2} d^{2} x^{3} e^{5} + 12 \, a c^{2} d^{4} x e^{3} + 6 \, a c^{2} d^{5} e^{2} - 9 \, a^{2} c d x^{2} e^{6} - 12 \, a^{2} c d^{2} x e^{5} - 3 \, a^{2} c d^{3} e^{4} - 2 \, a^{3} x e^{7} - 2 \, a^{3} d e^{6}}{2 \, {\left(c^{4} d^{8} - 4 \, a c^{3} d^{6} e^{2} + 6 \, a^{2} c^{2} d^{4} e^{4} - 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}\right)} {\left(c d x^{2} e + c d^{2} x + a x e^{2} + a d e\right)}^{2}}"," ",0,"6*(c^2*d^3*e^2 - a*c*d*e^4)*arctan((2*c*d*x*e + c*d^2 + a*e^2)/sqrt(-c^2*d^4 + 2*a*c*d^2*e^2 - a^2*e^4))/((c^4*d^8 - 4*a*c^3*d^6*e^2 + 6*a^2*c^2*d^4*e^4 - 4*a^3*c*d^2*e^6 + a^4*e^8)*sqrt(-c^2*d^4 + 2*a*c*d^2*e^2 - a^2*e^4)) + 1/2*(6*c^3*d^4*x^3*e^3 + 9*c^3*d^5*x^2*e^2 + 2*c^3*d^6*x*e - c^3*d^7 - 6*a*c^2*d^2*x^3*e^5 + 12*a*c^2*d^4*x*e^3 + 6*a*c^2*d^5*e^2 - 9*a^2*c*d*x^2*e^6 - 12*a^2*c*d^2*x*e^5 - 3*a^2*c*d^3*e^4 - 2*a^3*x*e^7 - 2*a^3*d*e^6)/((c^4*d^8 - 4*a*c^3*d^6*e^2 + 6*a^2*c^2*d^4*e^4 - 4*a^3*c*d^2*e^6 + a^4*e^8)*(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e)^2)","B",0
1894,1,326,0,0.174468," ","integrate(1/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x, algorithm=""giac"")","\frac{12 \, c^{2} d^{2} \arctan\left(\frac{2 \, c d x e + c d^{2} + a e^{2}}{\sqrt{-c^{2} d^{4} + 2 \, a c d^{2} e^{2} - a^{2} e^{4}}}\right) e^{2}}{{\left(c^{4} d^{8} - 4 \, a c^{3} d^{6} e^{2} + 6 \, a^{2} c^{2} d^{4} e^{4} - 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}\right)} \sqrt{-c^{2} d^{4} + 2 \, a c d^{2} e^{2} - a^{2} e^{4}}} + \frac{12 \, c^{3} d^{3} x^{3} e^{3} + 18 \, c^{3} d^{4} x^{2} e^{2} + 4 \, c^{3} d^{5} x e - c^{3} d^{6} + 18 \, a c^{2} d^{2} x^{2} e^{4} + 28 \, a c^{2} d^{3} x e^{3} + 7 \, a c^{2} d^{4} e^{2} + 4 \, a^{2} c d x e^{5} + 7 \, a^{2} c d^{2} e^{4} - a^{3} e^{6}}{2 \, {\left(c^{4} d^{8} - 4 \, a c^{3} d^{6} e^{2} + 6 \, a^{2} c^{2} d^{4} e^{4} - 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}\right)} {\left(c d x^{2} e + c d^{2} x + a x e^{2} + a d e\right)}^{2}}"," ",0,"12*c^2*d^2*arctan((2*c*d*x*e + c*d^2 + a*e^2)/sqrt(-c^2*d^4 + 2*a*c*d^2*e^2 - a^2*e^4))*e^2/((c^4*d^8 - 4*a*c^3*d^6*e^2 + 6*a^2*c^2*d^4*e^4 - 4*a^3*c*d^2*e^6 + a^4*e^8)*sqrt(-c^2*d^4 + 2*a*c*d^2*e^2 - a^2*e^4)) + 1/2*(12*c^3*d^3*x^3*e^3 + 18*c^3*d^4*x^2*e^2 + 4*c^3*d^5*x*e - c^3*d^6 + 18*a*c^2*d^2*x^2*e^4 + 28*a*c^2*d^3*x*e^3 + 7*a*c^2*d^4*e^2 + 4*a^2*c*d*x*e^5 + 7*a^2*c*d^2*e^4 - a^3*e^6)/((c^4*d^8 - 4*a*c^3*d^6*e^2 + 6*a^2*c^2*d^4*e^4 - 4*a^3*c*d^2*e^6 + a^4*e^8)*(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e)^2)","A",0
1895,-2,0,0,0.000000," ","integrate(1/(e*x+d)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: exp(1)^3/(d^3*exp(1)^7*a^3-3*d^3*exp(1)^5*a^3*exp(2)+3*d^3*exp(1)^3*a^3*exp(2)^2-d^3*exp(1)*a^3*exp(2)^3)*ln(abs(x*exp(1)+d))-exp(1)^2/(2*d^3*exp(1)^6*a^3-6*d^3*exp(1)^4*a^3*exp(2)+6*d^3*exp(1)^2*a^3*exp(2)^2-2*d^3*a^3*exp(2)^3)*ln(x^2*c*d*exp(1)+x*c*d^2+x*a*exp(2)+d*exp(1)*a)+(c^5*d^10*exp(1)^2-10*c^4*d^8*exp(1)^4*a+5*c^4*d^8*exp(1)^2*a*exp(2)+30*c^3*d^6*exp(1)^6*a^2-30*c^3*d^6*exp(1)^4*a^2*exp(2)+10*c^3*d^6*exp(1)^2*a^2*exp(2)^2-30*c^2*d^4*exp(1)^6*a^3*exp(2)+30*c^2*d^4*exp(1)^4*a^3*exp(2)^2-10*c^2*d^4*exp(1)^2*a^3*exp(2)^3+10*c*d^2*exp(1)^4*a^4*exp(2)^3-5*c*d^2*exp(1)^2*a^4*exp(2)^4-exp(1)^2*a^5*exp(2)^5)/(c^4*d^11*exp(1)^6*a^3-3*c^4*d^11*exp(1)^4*a^3*exp(2)+3*c^4*d^11*exp(1)^2*a^3*exp(2)^2-c^4*d^11*a^3*exp(2)^3-8*c^3*d^9*exp(1)^8*a^4+28*c^3*d^9*exp(1)^6*a^4*exp(2)-36*c^3*d^9*exp(1)^4*a^4*exp(2)^2+20*c^3*d^9*exp(1)^2*a^4*exp(2)^3-4*c^3*d^9*a^4*exp(2)^4+16*c^2*d^7*exp(1)^10*a^5-64*c^2*d^7*exp(1)^8*a^5*exp(2)+102*c^2*d^7*exp(1)^6*a^5*exp(2)^2-82*c^2*d^7*exp(1)^4*a^5*exp(2)^3+34*c^2*d^7*exp(1)^2*a^5*exp(2)^4-6*c^2*d^7*a^5*exp(2)^5-8*c*d^5*exp(1)^8*a^6*exp(2)^2+28*c*d^5*exp(1)^6*a^6*exp(2)^3-36*c*d^5*exp(1)^4*a^6*exp(2)^4+20*c*d^5*exp(1)^2*a^6*exp(2)^5-4*c*d^5*a^6*exp(2)^6+d^3*exp(1)^6*a^7*exp(2)^4-3*d^3*exp(1)^4*a^7*exp(2)^5+3*d^3*exp(1)^2*a^7*exp(2)^6-d^3*a^7*exp(2)^7)/sqrt(-c^2*d^4+4*a*c*d^2*exp(1)^2-a^2*exp(2)^2-2*a*c*d^2*exp(2))*atan((a*exp(2)+c*d^2+2*c*d*x*exp(1))/sqrt(-c^2*d^4+4*a*c*d^2*exp(1)^2-a^2*exp(2)^2-2*a*c*d^2*exp(2)))-((-4*c^5*d^9*exp(1)^5*a+4*c^5*d^9*exp(1)^3*a*exp(2)+28*c^4*d^7*exp(1)^7*a^2-44*c^4*d^7*exp(1)^5*a^2*exp(2)+16*c^4*d^7*exp(1)^3*a^2*exp(2)^2-28*c^3*d^5*exp(1)^7*a^3*exp(2)+44*c^3*d^5*exp(1)^5*a^3*exp(2)^2-16*c^3*d^5*exp(1)^3*a^3*exp(2)^3+4*c^2*d^3*exp(1)^5*a^4*exp(2)^3-4*c^2*d^3*exp(1)^3*a^4*exp(2)^4)*x^3+(-4*c^5*d^10*exp(1)^4*a+4*c^5*d^10*exp(1)^2*a*exp(2)+26*c^4*d^8*exp(1)^6*a^2-48*c^4*d^8*exp(1)^4*a^2*exp(2)+22*c^4*d^8*exp(1)^2*a^2*exp(2)^2+32*c^3*d^6*exp(1)^8*a^3-64*c^3*d^6*exp(1)^6*a^3*exp(2)+44*c^3*d^6*exp(1)^4*a^3*exp(2)^2-12*c^3*d^6*exp(1)^2*a^3*exp(2)^3-58*c^2*d^4*exp(1)^6*a^4*exp(2)^2+96*c^2*d^4*exp(1)^4*a^4*exp(2)^3-38*c^2*d^4*exp(1)^2*a^4*exp(2)^4+8*c*d^2*exp(1)^4*a^5*exp(2)^4-8*c*d^2*exp(1)^2*a^5*exp(2)^5)*x^2+(-8*c^4*d^9*exp(1)^5*a^2+8*c^4*d^9*exp(1)^3*a^2*exp(2)+68*c^3*d^7*exp(1)^7*a^3-128*c^3*d^7*exp(1)^5*a^3*exp(2)+72*c^3*d^7*exp(1)^3*a^3*exp(2)^2-12*c^3*d^7*exp(1)*a^3*exp(2)^3-4*c^2*d^5*exp(1)^7*a^4*exp(2)-32*c^2*d^5*exp(1)^5*a^4*exp(2)^2+64*c^2*d^5*exp(1)^3*a^4*exp(2)^3-28*c^2*d^5*exp(1)*a^4*exp(2)^4-24*c*d^3*exp(1)^5*a^5*exp(2)^3+44*c*d^3*exp(1)^3*a^5*exp(2)^4-20*c*d^3*exp(1)*a^5*exp(2)^5+4*d*exp(1)^3*a^6*exp(2)^5-4*d*exp(1)*a^6*exp(2)^6)*x-6*c^3*d^8*exp(1)^6*a^3+10*c^3*d^8*exp(1)^4*a^3*exp(2)-6*c^3*d^8*exp(1)^2*a^3*exp(2)^2+2*c^3*d^8*a^3*exp(2)^3+48*c^2*d^6*exp(1)^8*a^4-112*c^2*d^6*exp(1)^6*a^4*exp(2)+98*c^2*d^6*exp(1)^4*a^4*exp(2)^2-40*c^2*d^6*exp(1)^2*a^4*exp(2)^3+6*c^2*d^6*a^4*exp(2)^4-42*c*d^4*exp(1)^6*a^5*exp(2)^2+78*c*d^4*exp(1)^4*a^5*exp(2)^3-42*c*d^4*exp(1)^2*a^5*exp(2)^4+6*c*d^4*a^5*exp(2)^5+6*d^2*exp(1)^4*a^6*exp(2)^4-8*d^2*exp(1)^2*a^6*exp(2)^5+2*d^2*a^6*exp(2)^6)/4/(exp(2)-exp(1)^2)^3/a^3/d^3/(c^2*d^4-4*c*d^2*exp(1)^2*a+2*c*d^2*a*exp(2)+a^2*exp(2)^2)^2/(x^2*c*d*exp(1)+x*c*d^2+x*a*exp(2)+d*exp(1)*a)^2","F(-2)",0
1896,0,0,0,0.000000," ","integrate((e*x+d)^10/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^4,x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
1897,-1,0,0,0.000000," ","integrate((e*x+d)^9/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^4,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1898,0,0,0,0.000000," ","integrate((e*x+d)^8/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^4,x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
1899,-1,0,0,0.000000," ","integrate((e*x+d)^7/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^4,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1900,1,822,0,112.400335," ","integrate((e*x+d)^6/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^4,x, algorithm=""giac"")","-\frac{3 \, c^{8} d^{14} x^{5} e^{5} + 12 \, c^{8} d^{15} x^{4} e^{4} + 19 \, c^{8} d^{16} x^{3} e^{3} + 15 \, c^{8} d^{17} x^{2} e^{2} + 6 \, c^{8} d^{18} x e + c^{8} d^{19} - 18 \, a c^{7} d^{12} x^{5} e^{7} - 69 \, a c^{7} d^{13} x^{4} e^{6} - 104 \, a c^{7} d^{14} x^{3} e^{5} - 78 \, a c^{7} d^{15} x^{2} e^{4} - 30 \, a c^{7} d^{16} x e^{3} - 5 \, a c^{7} d^{17} e^{2} + 45 \, a^{2} c^{6} d^{10} x^{5} e^{9} + 162 \, a^{2} c^{6} d^{11} x^{4} e^{8} + 226 \, a^{2} c^{6} d^{12} x^{3} e^{7} + 156 \, a^{2} c^{6} d^{13} x^{2} e^{6} + 57 \, a^{2} c^{6} d^{14} x e^{5} + 10 \, a^{2} c^{6} d^{15} e^{4} - 60 \, a^{3} c^{5} d^{8} x^{5} e^{11} - 195 \, a^{3} c^{5} d^{9} x^{4} e^{10} - 236 \, a^{3} c^{5} d^{10} x^{3} e^{9} - 138 \, a^{3} c^{5} d^{11} x^{2} e^{8} - 48 \, a^{3} c^{5} d^{12} x e^{7} - 11 \, a^{3} c^{5} d^{13} e^{6} + 45 \, a^{4} c^{4} d^{6} x^{5} e^{13} + 120 \, a^{4} c^{4} d^{7} x^{4} e^{12} + 100 \, a^{4} c^{4} d^{8} x^{3} e^{11} + 30 \, a^{4} c^{4} d^{9} x^{2} e^{10} + 15 \, a^{4} c^{4} d^{10} x e^{9} + 10 \, a^{4} c^{4} d^{11} e^{8} - 18 \, a^{5} c^{3} d^{4} x^{5} e^{15} - 27 \, a^{5} c^{3} d^{5} x^{4} e^{14} + 16 \, a^{5} c^{3} d^{6} x^{3} e^{13} + 30 \, a^{5} c^{3} d^{7} x^{2} e^{12} - 6 \, a^{5} c^{3} d^{8} x e^{11} - 11 \, a^{5} c^{3} d^{9} e^{10} + 3 \, a^{6} c^{2} d^{2} x^{5} e^{17} - 6 \, a^{6} c^{2} d^{3} x^{4} e^{16} - 26 \, a^{6} c^{2} d^{4} x^{3} e^{15} - 12 \, a^{6} c^{2} d^{5} x^{2} e^{14} + 15 \, a^{6} c^{2} d^{6} x e^{13} + 10 \, a^{6} c^{2} d^{7} e^{12} + 3 \, a^{7} c d x^{4} e^{18} + 4 \, a^{7} c d^{2} x^{3} e^{17} - 6 \, a^{7} c d^{3} x^{2} e^{16} - 12 \, a^{7} c d^{4} x e^{15} - 5 \, a^{7} c d^{5} e^{14} + a^{8} x^{3} e^{19} + 3 \, a^{8} d x^{2} e^{18} + 3 \, a^{8} d^{2} x e^{17} + a^{8} d^{3} e^{16}}{3 \, {\left(c^{9} d^{15} - 6 \, a c^{8} d^{13} e^{2} + 15 \, a^{2} c^{7} d^{11} e^{4} - 20 \, a^{3} c^{6} d^{9} e^{6} + 15 \, a^{4} c^{5} d^{7} e^{8} - 6 \, a^{5} c^{4} d^{5} e^{10} + a^{6} c^{3} d^{3} e^{12}\right)} {\left(c d x^{2} e + c d^{2} x + a x e^{2} + a d e\right)}^{3}}"," ",0,"-1/3*(3*c^8*d^14*x^5*e^5 + 12*c^8*d^15*x^4*e^4 + 19*c^8*d^16*x^3*e^3 + 15*c^8*d^17*x^2*e^2 + 6*c^8*d^18*x*e + c^8*d^19 - 18*a*c^7*d^12*x^5*e^7 - 69*a*c^7*d^13*x^4*e^6 - 104*a*c^7*d^14*x^3*e^5 - 78*a*c^7*d^15*x^2*e^4 - 30*a*c^7*d^16*x*e^3 - 5*a*c^7*d^17*e^2 + 45*a^2*c^6*d^10*x^5*e^9 + 162*a^2*c^6*d^11*x^4*e^8 + 226*a^2*c^6*d^12*x^3*e^7 + 156*a^2*c^6*d^13*x^2*e^6 + 57*a^2*c^6*d^14*x*e^5 + 10*a^2*c^6*d^15*e^4 - 60*a^3*c^5*d^8*x^5*e^11 - 195*a^3*c^5*d^9*x^4*e^10 - 236*a^3*c^5*d^10*x^3*e^9 - 138*a^3*c^5*d^11*x^2*e^8 - 48*a^3*c^5*d^12*x*e^7 - 11*a^3*c^5*d^13*e^6 + 45*a^4*c^4*d^6*x^5*e^13 + 120*a^4*c^4*d^7*x^4*e^12 + 100*a^4*c^4*d^8*x^3*e^11 + 30*a^4*c^4*d^9*x^2*e^10 + 15*a^4*c^4*d^10*x*e^9 + 10*a^4*c^4*d^11*e^8 - 18*a^5*c^3*d^4*x^5*e^15 - 27*a^5*c^3*d^5*x^4*e^14 + 16*a^5*c^3*d^6*x^3*e^13 + 30*a^5*c^3*d^7*x^2*e^12 - 6*a^5*c^3*d^8*x*e^11 - 11*a^5*c^3*d^9*e^10 + 3*a^6*c^2*d^2*x^5*e^17 - 6*a^6*c^2*d^3*x^4*e^16 - 26*a^6*c^2*d^4*x^3*e^15 - 12*a^6*c^2*d^5*x^2*e^14 + 15*a^6*c^2*d^6*x*e^13 + 10*a^6*c^2*d^7*e^12 + 3*a^7*c*d*x^4*e^18 + 4*a^7*c*d^2*x^3*e^17 - 6*a^7*c*d^3*x^2*e^16 - 12*a^7*c*d^4*x*e^15 - 5*a^7*c*d^5*e^14 + a^8*x^3*e^19 + 3*a^8*d*x^2*e^18 + 3*a^8*d^2*x*e^17 + a^8*d^3*e^16)/((c^9*d^15 - 6*a*c^8*d^13*e^2 + 15*a^2*c^7*d^11*e^4 - 20*a^3*c^6*d^9*e^6 + 15*a^4*c^5*d^7*e^8 - 6*a^5*c^4*d^5*e^10 + a^6*c^3*d^3*e^12)*(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e)^3)","B",0
1901,1,641,0,0.446324," ","integrate((e*x+d)^5/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^4,x, algorithm=""giac"")","-\frac{3 \, c^{7} d^{13} x^{4} e^{4} + 11 \, c^{7} d^{14} x^{3} e^{3} + 15 \, c^{7} d^{15} x^{2} e^{2} + 9 \, c^{7} d^{16} x e + 2 \, c^{7} d^{17} - 18 \, a c^{6} d^{11} x^{4} e^{6} - 65 \, a c^{6} d^{12} x^{3} e^{5} - 87 \, a c^{6} d^{13} x^{2} e^{4} - 51 \, a c^{6} d^{14} x e^{3} - 11 \, a c^{6} d^{15} e^{2} + 45 \, a^{2} c^{5} d^{9} x^{4} e^{8} + 159 \, a^{2} c^{5} d^{10} x^{3} e^{7} + 207 \, a^{2} c^{5} d^{11} x^{2} e^{6} + 117 \, a^{2} c^{5} d^{12} x e^{5} + 24 \, a^{2} c^{5} d^{13} e^{4} - 60 \, a^{3} c^{4} d^{7} x^{4} e^{10} - 205 \, a^{3} c^{4} d^{8} x^{3} e^{9} - 255 \, a^{3} c^{4} d^{9} x^{2} e^{8} - 135 \, a^{3} c^{4} d^{10} x e^{7} - 25 \, a^{3} c^{4} d^{11} e^{6} + 45 \, a^{4} c^{3} d^{5} x^{4} e^{12} + 145 \, a^{4} c^{3} d^{6} x^{3} e^{11} + 165 \, a^{4} c^{3} d^{7} x^{2} e^{10} + 75 \, a^{4} c^{3} d^{8} x e^{9} + 10 \, a^{4} c^{3} d^{9} e^{8} - 18 \, a^{5} c^{2} d^{3} x^{4} e^{14} - 51 \, a^{5} c^{2} d^{4} x^{3} e^{13} - 45 \, a^{5} c^{2} d^{5} x^{2} e^{12} - 9 \, a^{5} c^{2} d^{6} x e^{11} + 3 \, a^{5} c^{2} d^{7} e^{10} + 3 \, a^{6} c d x^{4} e^{16} + 5 \, a^{6} c d^{2} x^{3} e^{15} - 3 \, a^{6} c d^{3} x^{2} e^{14} - 9 \, a^{6} c d^{4} x e^{13} - 4 \, a^{6} c d^{5} e^{12} + a^{7} x^{3} e^{17} + 3 \, a^{7} d x^{2} e^{16} + 3 \, a^{7} d^{2} x e^{15} + a^{7} d^{3} e^{14}}{6 \, {\left(c^{8} d^{14} - 6 \, a c^{7} d^{12} e^{2} + 15 \, a^{2} c^{6} d^{10} e^{4} - 20 \, a^{3} c^{5} d^{8} e^{6} + 15 \, a^{4} c^{4} d^{6} e^{8} - 6 \, a^{5} c^{3} d^{4} e^{10} + a^{6} c^{2} d^{2} e^{12}\right)} {\left(c d x^{2} e + c d^{2} x + a x e^{2} + a d e\right)}^{3}}"," ",0,"-1/6*(3*c^7*d^13*x^4*e^4 + 11*c^7*d^14*x^3*e^3 + 15*c^7*d^15*x^2*e^2 + 9*c^7*d^16*x*e + 2*c^7*d^17 - 18*a*c^6*d^11*x^4*e^6 - 65*a*c^6*d^12*x^3*e^5 - 87*a*c^6*d^13*x^2*e^4 - 51*a*c^6*d^14*x*e^3 - 11*a*c^6*d^15*e^2 + 45*a^2*c^5*d^9*x^4*e^8 + 159*a^2*c^5*d^10*x^3*e^7 + 207*a^2*c^5*d^11*x^2*e^6 + 117*a^2*c^5*d^12*x*e^5 + 24*a^2*c^5*d^13*e^4 - 60*a^3*c^4*d^7*x^4*e^10 - 205*a^3*c^4*d^8*x^3*e^9 - 255*a^3*c^4*d^9*x^2*e^8 - 135*a^3*c^4*d^10*x*e^7 - 25*a^3*c^4*d^11*e^6 + 45*a^4*c^3*d^5*x^4*e^12 + 145*a^4*c^3*d^6*x^3*e^11 + 165*a^4*c^3*d^7*x^2*e^10 + 75*a^4*c^3*d^8*x*e^9 + 10*a^4*c^3*d^9*e^8 - 18*a^5*c^2*d^3*x^4*e^14 - 51*a^5*c^2*d^4*x^3*e^13 - 45*a^5*c^2*d^5*x^2*e^12 - 9*a^5*c^2*d^6*x*e^11 + 3*a^5*c^2*d^7*e^10 + 3*a^6*c*d*x^4*e^16 + 5*a^6*c*d^2*x^3*e^15 - 3*a^6*c*d^3*x^2*e^14 - 9*a^6*c*d^4*x*e^13 - 4*a^6*c*d^5*e^12 + a^7*x^3*e^17 + 3*a^7*d*x^2*e^16 + 3*a^7*d^2*x*e^15 + a^7*d^3*e^14)/((c^8*d^14 - 6*a*c^7*d^12*e^2 + 15*a^2*c^6*d^10*e^4 - 20*a^3*c^5*d^8*e^6 + 15*a^4*c^4*d^6*e^8 - 6*a^5*c^3*d^4*e^10 + a^6*c^2*d^2*e^12)*(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e)^3)","B",0
1902,1,473,0,3.290197," ","integrate((e*x+d)^4/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^4,x, algorithm=""giac"")","-\frac{c^{6} d^{12} x^{3} e^{3} + 3 \, c^{6} d^{13} x^{2} e^{2} + 3 \, c^{6} d^{14} x e + c^{6} d^{15} - 6 \, a c^{5} d^{10} x^{3} e^{5} - 18 \, a c^{5} d^{11} x^{2} e^{4} - 18 \, a c^{5} d^{12} x e^{3} - 6 \, a c^{5} d^{13} e^{2} + 15 \, a^{2} c^{4} d^{8} x^{3} e^{7} + 45 \, a^{2} c^{4} d^{9} x^{2} e^{6} + 45 \, a^{2} c^{4} d^{10} x e^{5} + 15 \, a^{2} c^{4} d^{11} e^{4} - 20 \, a^{3} c^{3} d^{6} x^{3} e^{9} - 60 \, a^{3} c^{3} d^{7} x^{2} e^{8} - 60 \, a^{3} c^{3} d^{8} x e^{7} - 20 \, a^{3} c^{3} d^{9} e^{6} + 15 \, a^{4} c^{2} d^{4} x^{3} e^{11} + 45 \, a^{4} c^{2} d^{5} x^{2} e^{10} + 45 \, a^{4} c^{2} d^{6} x e^{9} + 15 \, a^{4} c^{2} d^{7} e^{8} - 6 \, a^{5} c d^{2} x^{3} e^{13} - 18 \, a^{5} c d^{3} x^{2} e^{12} - 18 \, a^{5} c d^{4} x e^{11} - 6 \, a^{5} c d^{5} e^{10} + a^{6} x^{3} e^{15} + 3 \, a^{6} d x^{2} e^{14} + 3 \, a^{6} d^{2} x e^{13} + a^{6} d^{3} e^{12}}{3 \, {\left(c^{7} d^{13} - 6 \, a c^{6} d^{11} e^{2} + 15 \, a^{2} c^{5} d^{9} e^{4} - 20 \, a^{3} c^{4} d^{7} e^{6} + 15 \, a^{4} c^{3} d^{5} e^{8} - 6 \, a^{5} c^{2} d^{3} e^{10} + a^{6} c d e^{12}\right)} {\left(c d x^{2} e + c d^{2} x + a x e^{2} + a d e\right)}^{3}}"," ",0,"-1/3*(c^6*d^12*x^3*e^3 + 3*c^6*d^13*x^2*e^2 + 3*c^6*d^14*x*e + c^6*d^15 - 6*a*c^5*d^10*x^3*e^5 - 18*a*c^5*d^11*x^2*e^4 - 18*a*c^5*d^12*x*e^3 - 6*a*c^5*d^13*e^2 + 15*a^2*c^4*d^8*x^3*e^7 + 45*a^2*c^4*d^9*x^2*e^6 + 45*a^2*c^4*d^10*x*e^5 + 15*a^2*c^4*d^11*e^4 - 20*a^3*c^3*d^6*x^3*e^9 - 60*a^3*c^3*d^7*x^2*e^8 - 60*a^3*c^3*d^8*x*e^7 - 20*a^3*c^3*d^9*e^6 + 15*a^4*c^2*d^4*x^3*e^11 + 45*a^4*c^2*d^5*x^2*e^10 + 45*a^4*c^2*d^6*x*e^9 + 15*a^4*c^2*d^7*e^8 - 6*a^5*c*d^2*x^3*e^13 - 18*a^5*c*d^3*x^2*e^12 - 18*a^5*c*d^4*x*e^11 - 6*a^5*c*d^5*e^10 + a^6*x^3*e^15 + 3*a^6*d*x^2*e^14 + 3*a^6*d^2*x*e^13 + a^6*d^3*e^12)/((c^7*d^13 - 6*a*c^6*d^11*e^2 + 15*a^2*c^5*d^9*e^4 - 20*a^3*c^4*d^7*e^6 + 15*a^4*c^3*d^5*e^8 - 6*a^5*c^2*d^3*e^10 + a^6*c*d*e^12)*(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e)^3)","B",0
1903,1,721,0,0.374452," ","integrate((e*x+d)^3/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^4,x, algorithm=""giac"")","\frac{2 \, {\left(c^{3} d^{6} e^{3} - 3 \, a c^{2} d^{4} e^{5} + 3 \, a^{2} c d^{2} e^{7} - a^{3} e^{9}\right)} \arctan\left(-\frac{2 \, c d x e + c d^{2} + a e^{2}}{\sqrt{-c^{2} d^{4} + 2 \, a c d^{2} e^{2} - a^{2} e^{4}}}\right)}{{\left(c^{6} d^{12} - 6 \, a c^{5} d^{10} e^{2} + 15 \, a^{2} c^{4} d^{8} e^{4} - 20 \, a^{3} c^{3} d^{6} e^{6} + 15 \, a^{4} c^{2} d^{4} e^{8} - 6 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}\right)} \sqrt{-c^{2} d^{4} + 2 \, a c d^{2} e^{2} - a^{2} e^{4}}} - \frac{6 \, c^{5} d^{8} x^{5} e^{5} + 15 \, c^{5} d^{9} x^{4} e^{4} + 11 \, c^{5} d^{10} x^{3} e^{3} + 3 \, c^{5} d^{11} x^{2} e^{2} + 3 \, c^{5} d^{12} x e + 2 \, c^{5} d^{13} - 18 \, a c^{4} d^{6} x^{5} e^{7} - 30 \, a c^{4} d^{7} x^{4} e^{6} + 5 \, a c^{4} d^{8} x^{3} e^{5} + 15 \, a c^{4} d^{9} x^{2} e^{4} - 15 \, a c^{4} d^{10} x e^{3} - 13 \, a c^{4} d^{11} e^{2} + 18 \, a^{2} c^{3} d^{4} x^{5} e^{9} - 70 \, a^{2} c^{3} d^{6} x^{3} e^{7} - 30 \, a^{2} c^{3} d^{7} x^{2} e^{6} + 60 \, a^{2} c^{3} d^{8} x e^{5} + 38 \, a^{2} c^{3} d^{9} e^{4} - 6 \, a^{3} c^{2} d^{2} x^{5} e^{11} + 30 \, a^{3} c^{2} d^{3} x^{4} e^{10} + 70 \, a^{3} c^{2} d^{4} x^{3} e^{9} - 30 \, a^{3} c^{2} d^{5} x^{2} e^{8} - 120 \, a^{3} c^{2} d^{6} x e^{7} - 56 \, a^{3} c^{2} d^{7} e^{6} - 15 \, a^{4} c d x^{4} e^{12} - 5 \, a^{4} c d^{2} x^{3} e^{11} + 75 \, a^{4} c d^{3} x^{2} e^{10} + 105 \, a^{4} c d^{4} x e^{9} + 40 \, a^{4} c d^{5} e^{8} - 11 \, a^{5} x^{3} e^{13} - 33 \, a^{5} d x^{2} e^{12} - 33 \, a^{5} d^{2} x e^{11} - 11 \, a^{5} d^{3} e^{10}}{6 \, {\left(c^{6} d^{12} - 6 \, a c^{5} d^{10} e^{2} + 15 \, a^{2} c^{4} d^{8} e^{4} - 20 \, a^{3} c^{3} d^{6} e^{6} + 15 \, a^{4} c^{2} d^{4} e^{8} - 6 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}\right)} {\left(c d x^{2} e + c d^{2} x + a x e^{2} + a d e\right)}^{3}}"," ",0,"2*(c^3*d^6*e^3 - 3*a*c^2*d^4*e^5 + 3*a^2*c*d^2*e^7 - a^3*e^9)*arctan(-(2*c*d*x*e + c*d^2 + a*e^2)/sqrt(-c^2*d^4 + 2*a*c*d^2*e^2 - a^2*e^4))/((c^6*d^12 - 6*a*c^5*d^10*e^2 + 15*a^2*c^4*d^8*e^4 - 20*a^3*c^3*d^6*e^6 + 15*a^4*c^2*d^4*e^8 - 6*a^5*c*d^2*e^10 + a^6*e^12)*sqrt(-c^2*d^4 + 2*a*c*d^2*e^2 - a^2*e^4)) - 1/6*(6*c^5*d^8*x^5*e^5 + 15*c^5*d^9*x^4*e^4 + 11*c^5*d^10*x^3*e^3 + 3*c^5*d^11*x^2*e^2 + 3*c^5*d^12*x*e + 2*c^5*d^13 - 18*a*c^4*d^6*x^5*e^7 - 30*a*c^4*d^7*x^4*e^6 + 5*a*c^4*d^8*x^3*e^5 + 15*a*c^4*d^9*x^2*e^4 - 15*a*c^4*d^10*x*e^3 - 13*a*c^4*d^11*e^2 + 18*a^2*c^3*d^4*x^5*e^9 - 70*a^2*c^3*d^6*x^3*e^7 - 30*a^2*c^3*d^7*x^2*e^6 + 60*a^2*c^3*d^8*x*e^5 + 38*a^2*c^3*d^9*e^4 - 6*a^3*c^2*d^2*x^5*e^11 + 30*a^3*c^2*d^3*x^4*e^10 + 70*a^3*c^2*d^4*x^3*e^9 - 30*a^3*c^2*d^5*x^2*e^8 - 120*a^3*c^2*d^6*x*e^7 - 56*a^3*c^2*d^7*e^6 - 15*a^4*c*d*x^4*e^12 - 5*a^4*c*d^2*x^3*e^11 + 75*a^4*c*d^3*x^2*e^10 + 105*a^4*c*d^4*x*e^9 + 40*a^4*c*d^5*e^8 - 11*a^5*x^3*e^13 - 33*a^5*d*x^2*e^12 - 33*a^5*d^2*x*e^11 - 11*a^5*d^3*e^10)/((c^6*d^12 - 6*a*c^5*d^10*e^2 + 15*a^2*c^4*d^8*e^4 - 20*a^3*c^3*d^6*e^6 + 15*a^4*c^2*d^4*e^8 - 6*a^5*c*d^2*e^10 + a^6*e^12)*(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e)^3)","B",0
1904,1,672,0,0.320280," ","integrate((e*x+d)^2/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^4,x, algorithm=""giac"")","\frac{8 \, {\left(c^{3} d^{5} e^{3} - 2 \, a c^{2} d^{3} e^{5} + a^{2} c d e^{7}\right)} \arctan\left(-\frac{2 \, c d x e + c d^{2} + a e^{2}}{\sqrt{-c^{2} d^{4} + 2 \, a c d^{2} e^{2} - a^{2} e^{4}}}\right)}{{\left(c^{6} d^{12} - 6 \, a c^{5} d^{10} e^{2} + 15 \, a^{2} c^{4} d^{8} e^{4} - 20 \, a^{3} c^{3} d^{6} e^{6} + 15 \, a^{4} c^{2} d^{4} e^{8} - 6 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}\right)} \sqrt{-c^{2} d^{4} + 2 \, a c d^{2} e^{2} - a^{2} e^{4}}} - \frac{12 \, c^{5} d^{7} x^{5} e^{5} + 30 \, c^{5} d^{8} x^{4} e^{4} + 22 \, c^{5} d^{9} x^{3} e^{3} + 3 \, c^{5} d^{10} x^{2} e^{2} + c^{5} d^{12} - 24 \, a c^{4} d^{5} x^{5} e^{7} - 30 \, a c^{4} d^{6} x^{4} e^{6} + 32 \, a c^{4} d^{7} x^{3} e^{5} + 51 \, a c^{4} d^{8} x^{2} e^{4} + 6 \, a c^{4} d^{9} x e^{3} - 7 \, a c^{4} d^{10} e^{2} + 12 \, a^{2} c^{3} d^{3} x^{5} e^{9} - 30 \, a^{2} c^{3} d^{4} x^{4} e^{8} - 108 \, a^{2} c^{3} d^{5} x^{3} e^{7} - 54 \, a^{2} c^{3} d^{6} x^{2} e^{6} + 36 \, a^{2} c^{3} d^{7} x e^{5} + 24 \, a^{2} c^{3} d^{8} e^{4} + 30 \, a^{3} c^{2} d^{2} x^{4} e^{10} + 32 \, a^{3} c^{2} d^{3} x^{3} e^{9} - 54 \, a^{3} c^{2} d^{4} x^{2} e^{8} - 84 \, a^{3} c^{2} d^{5} x e^{7} - 28 \, a^{3} c^{2} d^{6} e^{6} + 22 \, a^{4} c d x^{3} e^{11} + 51 \, a^{4} c d^{2} x^{2} e^{10} + 36 \, a^{4} c d^{3} x e^{9} + 7 \, a^{4} c d^{4} e^{8} + 3 \, a^{5} x^{2} e^{12} + 6 \, a^{5} d x e^{11} + 3 \, a^{5} d^{2} e^{10}}{3 \, {\left(c^{6} d^{12} - 6 \, a c^{5} d^{10} e^{2} + 15 \, a^{2} c^{4} d^{8} e^{4} - 20 \, a^{3} c^{3} d^{6} e^{6} + 15 \, a^{4} c^{2} d^{4} e^{8} - 6 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}\right)} {\left(c d x^{2} e + c d^{2} x + a x e^{2} + a d e\right)}^{3}}"," ",0,"8*(c^3*d^5*e^3 - 2*a*c^2*d^3*e^5 + a^2*c*d*e^7)*arctan(-(2*c*d*x*e + c*d^2 + a*e^2)/sqrt(-c^2*d^4 + 2*a*c*d^2*e^2 - a^2*e^4))/((c^6*d^12 - 6*a*c^5*d^10*e^2 + 15*a^2*c^4*d^8*e^4 - 20*a^3*c^3*d^6*e^6 + 15*a^4*c^2*d^4*e^8 - 6*a^5*c*d^2*e^10 + a^6*e^12)*sqrt(-c^2*d^4 + 2*a*c*d^2*e^2 - a^2*e^4)) - 1/3*(12*c^5*d^7*x^5*e^5 + 30*c^5*d^8*x^4*e^4 + 22*c^5*d^9*x^3*e^3 + 3*c^5*d^10*x^2*e^2 + c^5*d^12 - 24*a*c^4*d^5*x^5*e^7 - 30*a*c^4*d^6*x^4*e^6 + 32*a*c^4*d^7*x^3*e^5 + 51*a*c^4*d^8*x^2*e^4 + 6*a*c^4*d^9*x*e^3 - 7*a*c^4*d^10*e^2 + 12*a^2*c^3*d^3*x^5*e^9 - 30*a^2*c^3*d^4*x^4*e^8 - 108*a^2*c^3*d^5*x^3*e^7 - 54*a^2*c^3*d^6*x^2*e^6 + 36*a^2*c^3*d^7*x*e^5 + 24*a^2*c^3*d^8*e^4 + 30*a^3*c^2*d^2*x^4*e^10 + 32*a^3*c^2*d^3*x^3*e^9 - 54*a^3*c^2*d^4*x^2*e^8 - 84*a^3*c^2*d^5*x*e^7 - 28*a^3*c^2*d^6*e^6 + 22*a^4*c*d*x^3*e^11 + 51*a^4*c*d^2*x^2*e^10 + 36*a^4*c*d^3*x*e^9 + 7*a^4*c*d^4*e^8 + 3*a^5*x^2*e^12 + 6*a^5*d*x*e^11 + 3*a^5*d^2*e^10)/((c^6*d^12 - 6*a*c^5*d^10*e^2 + 15*a^2*c^4*d^8*e^4 - 20*a^3*c^3*d^6*e^6 + 15*a^4*c^2*d^4*e^8 - 6*a^5*c*d^2*e^10 + a^6*e^12)*(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e)^3)","B",0
1905,1,586,0,0.314327," ","integrate((e*x+d)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^4,x, algorithm=""giac"")","-\frac{20 \, {\left(c^{3} d^{4} e^{3} - a c^{2} d^{2} e^{5}\right)} \arctan\left(\frac{2 \, c d x e + c d^{2} + a e^{2}}{\sqrt{-c^{2} d^{4} + 2 \, a c d^{2} e^{2} - a^{2} e^{4}}}\right)}{{\left(c^{6} d^{12} - 6 \, a c^{5} d^{10} e^{2} + 15 \, a^{2} c^{4} d^{8} e^{4} - 20 \, a^{3} c^{3} d^{6} e^{6} + 15 \, a^{4} c^{2} d^{4} e^{8} - 6 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}\right)} \sqrt{-c^{2} d^{4} + 2 \, a c d^{2} e^{2} - a^{2} e^{4}}} - \frac{60 \, c^{5} d^{6} x^{5} e^{5} + 150 \, c^{5} d^{7} x^{4} e^{4} + 110 \, c^{5} d^{8} x^{3} e^{3} + 15 \, c^{5} d^{9} x^{2} e^{2} - 3 \, c^{5} d^{10} x e + 2 \, c^{5} d^{11} - 60 \, a c^{4} d^{4} x^{5} e^{7} + 270 \, a c^{4} d^{6} x^{3} e^{5} + 270 \, a c^{4} d^{7} x^{2} e^{4} + 45 \, a c^{4} d^{8} x e^{3} - 15 \, a c^{4} d^{9} e^{2} - 150 \, a^{2} c^{3} d^{3} x^{4} e^{8} - 270 \, a^{2} c^{3} d^{4} x^{3} e^{7} + 180 \, a^{2} c^{3} d^{6} x e^{5} + 60 \, a^{2} c^{3} d^{7} e^{4} - 110 \, a^{3} c^{2} d^{2} x^{3} e^{9} - 270 \, a^{3} c^{2} d^{3} x^{2} e^{8} - 180 \, a^{3} c^{2} d^{4} x e^{7} - 20 \, a^{3} c^{2} d^{5} e^{6} - 15 \, a^{4} c d x^{2} e^{10} - 45 \, a^{4} c d^{2} x e^{9} - 30 \, a^{4} c d^{3} e^{8} + 3 \, a^{5} x e^{11} + 3 \, a^{5} d e^{10}}{6 \, {\left(c^{6} d^{12} - 6 \, a c^{5} d^{10} e^{2} + 15 \, a^{2} c^{4} d^{8} e^{4} - 20 \, a^{3} c^{3} d^{6} e^{6} + 15 \, a^{4} c^{2} d^{4} e^{8} - 6 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}\right)} {\left(c d x^{2} e + c d^{2} x + a x e^{2} + a d e\right)}^{3}}"," ",0,"-20*(c^3*d^4*e^3 - a*c^2*d^2*e^5)*arctan((2*c*d*x*e + c*d^2 + a*e^2)/sqrt(-c^2*d^4 + 2*a*c*d^2*e^2 - a^2*e^4))/((c^6*d^12 - 6*a*c^5*d^10*e^2 + 15*a^2*c^4*d^8*e^4 - 20*a^3*c^3*d^6*e^6 + 15*a^4*c^2*d^4*e^8 - 6*a^5*c*d^2*e^10 + a^6*e^12)*sqrt(-c^2*d^4 + 2*a*c*d^2*e^2 - a^2*e^4)) - 1/6*(60*c^5*d^6*x^5*e^5 + 150*c^5*d^7*x^4*e^4 + 110*c^5*d^8*x^3*e^3 + 15*c^5*d^9*x^2*e^2 - 3*c^5*d^10*x*e + 2*c^5*d^11 - 60*a*c^4*d^4*x^5*e^7 + 270*a*c^4*d^6*x^3*e^5 + 270*a*c^4*d^7*x^2*e^4 + 45*a*c^4*d^8*x*e^3 - 15*a*c^4*d^9*e^2 - 150*a^2*c^3*d^3*x^4*e^8 - 270*a^2*c^3*d^4*x^3*e^7 + 180*a^2*c^3*d^6*x*e^5 + 60*a^2*c^3*d^7*e^4 - 110*a^3*c^2*d^2*x^3*e^9 - 270*a^3*c^2*d^3*x^2*e^8 - 180*a^3*c^2*d^4*x*e^7 - 20*a^3*c^2*d^5*e^6 - 15*a^4*c*d*x^2*e^10 - 45*a^4*c*d^2*x*e^9 - 30*a^4*c*d^3*e^8 + 3*a^5*x*e^11 + 3*a^5*d*e^10)/((c^6*d^12 - 6*a*c^5*d^10*e^2 + 15*a^2*c^4*d^8*e^4 - 20*a^3*c^3*d^6*e^6 + 15*a^4*c^2*d^4*e^8 - 6*a^5*c*d^2*e^10 + a^6*e^12)*(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e)^3)","B",0
1906,1,532,0,0.217671," ","integrate(1/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^4,x, algorithm=""giac"")","-\frac{40 \, c^{3} d^{3} \arctan\left(\frac{2 \, c d x e + c d^{2} + a e^{2}}{\sqrt{-c^{2} d^{4} + 2 \, a c d^{2} e^{2} - a^{2} e^{4}}}\right) e^{3}}{{\left(c^{6} d^{12} - 6 \, a c^{5} d^{10} e^{2} + 15 \, a^{2} c^{4} d^{8} e^{4} - 20 \, a^{3} c^{3} d^{6} e^{6} + 15 \, a^{4} c^{2} d^{4} e^{8} - 6 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}\right)} \sqrt{-c^{2} d^{4} + 2 \, a c d^{2} e^{2} - a^{2} e^{4}}} - \frac{60 \, c^{5} d^{5} x^{5} e^{5} + 150 \, c^{5} d^{6} x^{4} e^{4} + 110 \, c^{5} d^{7} x^{3} e^{3} + 15 \, c^{5} d^{8} x^{2} e^{2} - 3 \, c^{5} d^{9} x e + c^{5} d^{10} + 150 \, a c^{4} d^{4} x^{4} e^{6} + 380 \, a c^{4} d^{5} x^{3} e^{5} + 285 \, a c^{4} d^{6} x^{2} e^{4} + 42 \, a c^{4} d^{7} x e^{3} - 8 \, a c^{4} d^{8} e^{2} + 110 \, a^{2} c^{3} d^{3} x^{3} e^{7} + 285 \, a^{2} c^{3} d^{4} x^{2} e^{6} + 222 \, a^{2} c^{3} d^{5} x e^{5} + 37 \, a^{2} c^{3} d^{6} e^{4} + 15 \, a^{3} c^{2} d^{2} x^{2} e^{8} + 42 \, a^{3} c^{2} d^{3} x e^{7} + 37 \, a^{3} c^{2} d^{4} e^{6} - 3 \, a^{4} c d x e^{9} - 8 \, a^{4} c d^{2} e^{8} + a^{5} e^{10}}{3 \, {\left(c^{6} d^{12} - 6 \, a c^{5} d^{10} e^{2} + 15 \, a^{2} c^{4} d^{8} e^{4} - 20 \, a^{3} c^{3} d^{6} e^{6} + 15 \, a^{4} c^{2} d^{4} e^{8} - 6 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}\right)} {\left(c d x^{2} e + c d^{2} x + a x e^{2} + a d e\right)}^{3}}"," ",0,"-40*c^3*d^3*arctan((2*c*d*x*e + c*d^2 + a*e^2)/sqrt(-c^2*d^4 + 2*a*c*d^2*e^2 - a^2*e^4))*e^3/((c^6*d^12 - 6*a*c^5*d^10*e^2 + 15*a^2*c^4*d^8*e^4 - 20*a^3*c^3*d^6*e^6 + 15*a^4*c^2*d^4*e^8 - 6*a^5*c*d^2*e^10 + a^6*e^12)*sqrt(-c^2*d^4 + 2*a*c*d^2*e^2 - a^2*e^4)) - 1/3*(60*c^5*d^5*x^5*e^5 + 150*c^5*d^6*x^4*e^4 + 110*c^5*d^7*x^3*e^3 + 15*c^5*d^8*x^2*e^2 - 3*c^5*d^9*x*e + c^5*d^10 + 150*a*c^4*d^4*x^4*e^6 + 380*a*c^4*d^5*x^3*e^5 + 285*a*c^4*d^6*x^2*e^4 + 42*a*c^4*d^7*x*e^3 - 8*a*c^4*d^8*e^2 + 110*a^2*c^3*d^3*x^3*e^7 + 285*a^2*c^3*d^4*x^2*e^6 + 222*a^2*c^3*d^5*x*e^5 + 37*a^2*c^3*d^6*e^4 + 15*a^3*c^2*d^2*x^2*e^8 + 42*a^3*c^2*d^3*x*e^7 + 37*a^3*c^2*d^4*e^6 - 3*a^4*c*d*x*e^9 - 8*a^4*c*d^2*e^8 + a^5*e^10)/((c^6*d^12 - 6*a*c^5*d^10*e^2 + 15*a^2*c^4*d^8*e^4 - 20*a^3*c^3*d^6*e^6 + 15*a^4*c^2*d^4*e^8 - 6*a^5*c*d^2*e^10 + a^6*e^12)*(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e)^3)","B",0
1907,1,476,0,0.492648," ","integrate((e*x+d)^4*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""giac"")","\frac{1}{7680} \, \sqrt{c d x^{2} e + c d^{2} x + a x e^{2} + a d e} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(10 \, x e^{4} + \frac{{\left(49 \, c^{5} d^{6} e^{8} + a c^{4} d^{4} e^{10}\right)} e^{\left(-5\right)}}{c^{5} d^{5}}\right)} x + \frac{{\left(759 \, c^{5} d^{7} e^{7} + 50 \, a c^{4} d^{5} e^{9} - 9 \, a^{2} c^{3} d^{3} e^{11}\right)} e^{\left(-5\right)}}{c^{5} d^{5}}\right)} x + \frac{{\left(1429 \, c^{5} d^{8} e^{6} + 267 \, a c^{4} d^{6} e^{8} - 117 \, a^{2} c^{3} d^{4} e^{10} + 21 \, a^{3} c^{2} d^{2} e^{12}\right)} e^{\left(-5\right)}}{c^{5} d^{5}}\right)} x + \frac{{\left(2455 \, c^{5} d^{9} e^{5} + 1612 \, a c^{4} d^{7} e^{7} - 1350 \, a^{2} c^{3} d^{5} e^{9} + 588 \, a^{3} c^{2} d^{3} e^{11} - 105 \, a^{4} c d e^{13}\right)} e^{\left(-5\right)}}{c^{5} d^{5}}\right)} x + \frac{{\left(315 \, c^{5} d^{10} e^{4} + 3335 \, a c^{4} d^{8} e^{6} - 5058 \, a^{2} c^{3} d^{6} e^{8} + 4158 \, a^{3} c^{2} d^{4} e^{10} - 1785 \, a^{4} c d^{2} e^{12} + 315 \, a^{5} e^{14}\right)} e^{\left(-5\right)}}{c^{5} d^{5}}\right)} + \frac{21 \, {\left(c^{6} d^{12} - 6 \, a c^{5} d^{10} e^{2} + 15 \, a^{2} c^{4} d^{8} e^{4} - 20 \, a^{3} c^{3} d^{6} e^{6} + 15 \, a^{4} c^{2} d^{4} e^{8} - 6 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}\right)} e^{\left(-\frac{3}{2}\right)} \log\left({\left| -c d^{2} - 2 \, {\left(\sqrt{c d} x e^{\frac{1}{2}} - \sqrt{c d x^{2} e + c d^{2} x + a x e^{2} + a d e}\right)} \sqrt{c d} e^{\frac{1}{2}} - a e^{2} \right|}\right)}{1024 \, \sqrt{c d} c^{5} d^{5}}"," ",0,"1/7680*sqrt(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e)*(2*(4*(2*(8*(10*x*e^4 + (49*c^5*d^6*e^8 + a*c^4*d^4*e^10)*e^(-5)/(c^5*d^5))*x + (759*c^5*d^7*e^7 + 50*a*c^4*d^5*e^9 - 9*a^2*c^3*d^3*e^11)*e^(-5)/(c^5*d^5))*x + (1429*c^5*d^8*e^6 + 267*a*c^4*d^6*e^8 - 117*a^2*c^3*d^4*e^10 + 21*a^3*c^2*d^2*e^12)*e^(-5)/(c^5*d^5))*x + (2455*c^5*d^9*e^5 + 1612*a*c^4*d^7*e^7 - 1350*a^2*c^3*d^5*e^9 + 588*a^3*c^2*d^3*e^11 - 105*a^4*c*d*e^13)*e^(-5)/(c^5*d^5))*x + (315*c^5*d^10*e^4 + 3335*a*c^4*d^8*e^6 - 5058*a^2*c^3*d^6*e^8 + 4158*a^3*c^2*d^4*e^10 - 1785*a^4*c*d^2*e^12 + 315*a^5*e^14)*e^(-5)/(c^5*d^5)) + 21/1024*(c^6*d^12 - 6*a*c^5*d^10*e^2 + 15*a^2*c^4*d^8*e^4 - 20*a^3*c^3*d^6*e^6 + 15*a^4*c^2*d^4*e^8 - 6*a^5*c*d^2*e^10 + a^6*e^12)*e^(-3/2)*log(abs(-c*d^2 - 2*(sqrt(c*d)*x*e^(1/2) - sqrt(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e))*sqrt(c*d)*e^(1/2) - a*e^2))/(sqrt(c*d)*c^5*d^5)","A",0
1908,1,377,0,0.424923," ","integrate((e*x+d)^3*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""giac"")","\frac{1}{1920} \, \sqrt{c d x^{2} e + c d^{2} x + a x e^{2} + a d e} {\left(2 \, {\left(4 \, {\left(6 \, {\left(8 \, x e^{3} + \frac{{\left(31 \, c^{4} d^{5} e^{6} + a c^{3} d^{3} e^{8}\right)} e^{\left(-4\right)}}{c^{4} d^{4}}\right)} x + \frac{{\left(263 \, c^{4} d^{6} e^{5} + 32 \, a c^{3} d^{4} e^{7} - 7 \, a^{2} c^{2} d^{2} e^{9}\right)} e^{\left(-4\right)}}{c^{4} d^{4}}\right)} x + \frac{{\left(605 \, c^{4} d^{7} e^{4} + 289 \, a c^{3} d^{5} e^{6} - 161 \, a^{2} c^{2} d^{3} e^{8} + 35 \, a^{3} c d e^{10}\right)} e^{\left(-4\right)}}{c^{4} d^{4}}\right)} x + \frac{{\left(105 \, c^{4} d^{8} e^{3} + 790 \, a c^{3} d^{6} e^{5} - 896 \, a^{2} c^{2} d^{4} e^{7} + 490 \, a^{3} c d^{2} e^{9} - 105 \, a^{4} e^{11}\right)} e^{\left(-4\right)}}{c^{4} d^{4}}\right)} + \frac{7 \, {\left(c^{5} d^{10} - 5 \, a c^{4} d^{8} e^{2} + 10 \, a^{2} c^{3} d^{6} e^{4} - 10 \, a^{3} c^{2} d^{4} e^{6} + 5 \, a^{4} c d^{2} e^{8} - a^{5} e^{10}\right)} e^{\left(-\frac{3}{2}\right)} \log\left({\left| -c d^{2} - 2 \, {\left(\sqrt{c d} x e^{\frac{1}{2}} - \sqrt{c d x^{2} e + c d^{2} x + a x e^{2} + a d e}\right)} \sqrt{c d} e^{\frac{1}{2}} - a e^{2} \right|}\right)}{256 \, \sqrt{c d} c^{4} d^{4}}"," ",0,"1/1920*sqrt(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e)*(2*(4*(6*(8*x*e^3 + (31*c^4*d^5*e^6 + a*c^3*d^3*e^8)*e^(-4)/(c^4*d^4))*x + (263*c^4*d^6*e^5 + 32*a*c^3*d^4*e^7 - 7*a^2*c^2*d^2*e^9)*e^(-4)/(c^4*d^4))*x + (605*c^4*d^7*e^4 + 289*a*c^3*d^5*e^6 - 161*a^2*c^2*d^3*e^8 + 35*a^3*c*d*e^10)*e^(-4)/(c^4*d^4))*x + (105*c^4*d^8*e^3 + 790*a*c^3*d^6*e^5 - 896*a^2*c^2*d^4*e^7 + 490*a^3*c*d^2*e^9 - 105*a^4*e^11)*e^(-4)/(c^4*d^4)) + 7/256*(c^5*d^10 - 5*a*c^4*d^8*e^2 + 10*a^2*c^3*d^6*e^4 - 10*a^3*c^2*d^4*e^6 + 5*a^4*c*d^2*e^8 - a^5*e^10)*e^(-3/2)*log(abs(-c*d^2 - 2*(sqrt(c*d)*x*e^(1/2) - sqrt(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e))*sqrt(c*d)*e^(1/2) - a*e^2))/(sqrt(c*d)*c^4*d^4)","A",0
1909,1,289,0,0.552873," ","integrate((e*x+d)^2*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""giac"")","\frac{1}{192} \, \sqrt{c d x^{2} e + c d^{2} x + a x e^{2} + a d e} {\left(2 \, {\left(4 \, {\left(6 \, x e^{2} + \frac{{\left(17 \, c^{3} d^{4} e^{4} + a c^{2} d^{2} e^{6}\right)} e^{\left(-3\right)}}{c^{3} d^{3}}\right)} x + \frac{{\left(59 \, c^{3} d^{5} e^{3} + 18 \, a c^{2} d^{3} e^{5} - 5 \, a^{2} c d e^{7}\right)} e^{\left(-3\right)}}{c^{3} d^{3}}\right)} x + \frac{{\left(15 \, c^{3} d^{6} e^{2} + 73 \, a c^{2} d^{4} e^{4} - 55 \, a^{2} c d^{2} e^{6} + 15 \, a^{3} e^{8}\right)} e^{\left(-3\right)}}{c^{3} d^{3}}\right)} + \frac{5 \, {\left(c^{4} d^{8} - 4 \, a c^{3} d^{6} e^{2} + 6 \, a^{2} c^{2} d^{4} e^{4} - 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}\right)} e^{\left(-\frac{3}{2}\right)} \log\left({\left| -c d^{2} - 2 \, {\left(\sqrt{c d} x e^{\frac{1}{2}} - \sqrt{c d x^{2} e + c d^{2} x + a x e^{2} + a d e}\right)} \sqrt{c d} e^{\frac{1}{2}} - a e^{2} \right|}\right)}{128 \, \sqrt{c d} c^{3} d^{3}}"," ",0,"1/192*sqrt(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e)*(2*(4*(6*x*e^2 + (17*c^3*d^4*e^4 + a*c^2*d^2*e^6)*e^(-3)/(c^3*d^3))*x + (59*c^3*d^5*e^3 + 18*a*c^2*d^3*e^5 - 5*a^2*c*d*e^7)*e^(-3)/(c^3*d^3))*x + (15*c^3*d^6*e^2 + 73*a*c^2*d^4*e^4 - 55*a^2*c*d^2*e^6 + 15*a^3*e^8)*e^(-3)/(c^3*d^3)) + 5/128*(c^4*d^8 - 4*a*c^3*d^6*e^2 + 6*a^2*c^2*d^4*e^4 - 4*a^3*c*d^2*e^6 + a^4*e^8)*e^(-3/2)*log(abs(-c*d^2 - 2*(sqrt(c*d)*x*e^(1/2) - sqrt(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e))*sqrt(c*d)*e^(1/2) - a*e^2))/(sqrt(c*d)*c^3*d^3)","A",0
1910,1,216,0,0.418008," ","integrate((e*x+d)*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""giac"")","\frac{1}{24} \, \sqrt{c d x^{2} e + c d^{2} x + a x e^{2} + a d e} {\left(2 \, {\left(4 \, x e + \frac{{\left(7 \, c^{2} d^{3} e^{2} + a c d e^{4}\right)} e^{\left(-2\right)}}{c^{2} d^{2}}\right)} x + \frac{{\left(3 \, c^{2} d^{4} e + 8 \, a c d^{2} e^{3} - 3 \, a^{2} e^{5}\right)} e^{\left(-2\right)}}{c^{2} d^{2}}\right)} + \frac{{\left(c^{3} d^{6} - 3 \, a c^{2} d^{4} e^{2} + 3 \, a^{2} c d^{2} e^{4} - a^{3} e^{6}\right)} e^{\left(-\frac{3}{2}\right)} \log\left({\left| -c d^{2} - 2 \, {\left(\sqrt{c d} x e^{\frac{1}{2}} - \sqrt{c d x^{2} e + c d^{2} x + a x e^{2} + a d e}\right)} \sqrt{c d} e^{\frac{1}{2}} - a e^{2} \right|}\right)}{16 \, \sqrt{c d} c^{2} d^{2}}"," ",0,"1/24*sqrt(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e)*(2*(4*x*e + (7*c^2*d^3*e^2 + a*c*d*e^4)*e^(-2)/(c^2*d^2))*x + (3*c^2*d^4*e + 8*a*c*d^2*e^3 - 3*a^2*e^5)*e^(-2)/(c^2*d^2)) + 1/16*(c^3*d^6 - 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4 - a^3*e^6)*e^(-3/2)*log(abs(-c*d^2 - 2*(sqrt(c*d)*x*e^(1/2) - sqrt(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e))*sqrt(c*d)*e^(1/2) - a*e^2))/(sqrt(c*d)*c^2*d^2)","A",0
1911,1,153,0,0.263789," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{c d x^{2} e + c d^{2} x + a x e^{2} + a d e} {\left(2 \, x + \frac{{\left(c d^{2} + a e^{2}\right)} e^{\left(-1\right)}}{c d}\right)} + \frac{{\left(c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} e^{\left(-\frac{3}{2}\right)} \log\left({\left| -c d^{2} - 2 \, {\left(\sqrt{c d} x e^{\frac{1}{2}} - \sqrt{c d x^{2} e + c d^{2} x + a x e^{2} + a d e}\right)} \sqrt{c d} e^{\frac{1}{2}} - a e^{2} \right|}\right)}{8 \, \sqrt{c d} c d}"," ",0,"1/4*sqrt(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e)*(2*x + (c*d^2 + a*e^2)*e^(-1)/(c*d)) + 1/8*(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*e^(-3/2)*log(abs(-c*d^2 - 2*(sqrt(c*d)*x*e^(1/2) - sqrt(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e))*sqrt(c*d)*e^(1/2) - a*e^2))/(sqrt(c*d)*c*d)","A",0
1912,-2,0,0,0.000000," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)/(e*x+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error: Bad Argument Type","F(-2)",0
1913,-2,0,0,0.000000," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)/(e*x+d)^2,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]Evaluation time: 0.48Error: Bad Argument Type","F(-2)",0
1914,-2,0,0,0.000000," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)/(e*x+d)^3,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: 2*((-exp(1)^2*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a^2*exp(2)^2+6*c*d^2*exp(1)^2*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a*exp(2)-4*c*d^2*exp(1)^4*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3*a-c^2*d^4*exp(1)^2*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^3-5*d*exp(1)*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^2*a^2*exp(2)^2+8*d*exp(1)^3*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^2*a^2*exp(2)-10*c*d^3*exp(1)*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^2*a*exp(2)+4*c*d^3*exp(1)^3*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^2*a+3*c^2*d^5*exp(1)*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^2+d*exp(1)*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^3*exp(2)^3-d*exp(1)^3*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^3*exp(2)^2+7*c*d^3*exp(1)*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^2*exp(2)^2-6*c*d^3*exp(1)^3*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^2*exp(2)-4*c*d^3*exp(1)^5*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^2+3*c^2*d^5*exp(1)*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a*exp(2)+3*c^2*d^5*exp(1)^3*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a-3*c^3*d^7*exp(1)*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)-d^2*sqrt(c*d*exp(1))*a^3*exp(2)^3+d^2*exp(1)^2*sqrt(c*d*exp(1))*a^3*exp(2)^2-c*d^4*sqrt(c*d*exp(1))*a^2*exp(2)^2-2*c*d^4*exp(1)^2*sqrt(c*d*exp(1))*a^2*exp(2)+4*c*d^4*exp(1)^4*sqrt(c*d*exp(1))*a^2+c^2*d^6*sqrt(c*d*exp(1))*a*exp(2)-3*c^2*d^6*exp(1)^2*sqrt(c*d*exp(1))*a+c^3*d^8*sqrt(c*d*exp(1)))/(-8*d*exp(1)^2*a*exp(2)+8*d*exp(1)^4*a)/(-exp(1)*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^2+2*d*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)-d*a*exp(2)+d*exp(1)^2*a-c*d^3)^2+(a^2*exp(2)^2+2*c*d^2*a*exp(2)-4*c*d^2*exp(1)^2*a+c^2*d^4)/2/(4*d*exp(1)*a*exp(2)-4*d*exp(1)^3*a)/sqrt(-a*d*exp(1)^3+a*d*exp(1)*exp(2))*atan((-d*sqrt(c*d*exp(1))+(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*exp(1))/sqrt(-a*d*exp(1)^3+a*d*exp(1)*exp(2))))","F(-2)",0
1915,-2,0,0,0.000000," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)/(e*x+d)^4,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
1916,-2,0,0,0.000000," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)/(e*x+d)^5,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: exp(1)*(2*(-(exp(1)*x+d)^-1/exp(1)*(-(exp(1)*x+d)^-1/exp(1)*(-(-3*c^3*d^5*sign((exp(1)*x+d)^-1)*exp(1)^3+6*a*c^2*d^3*sign((exp(1)*x+d)^-1)*exp(1)^5-3*a^2*c*d*sign((exp(1)*x+d)^-1)*exp(1)^7)/(-105*a^3*exp(1)^10+105*c^3*d^6*exp(1)^4-315*a*c^2*d^4*exp(1)^6+315*a^2*c*d^2*exp(1)^8)+(exp(1)*x+d)^-1/exp(1)*(15*a^3*sign((exp(1)*x+d)^-1)*exp(1)^10-15*c^3*d^6*sign((exp(1)*x+d)^-1)*exp(1)^4+45*a*c^2*d^4*sign((exp(1)*x+d)^-1)*exp(1)^6-45*a^2*c*d^2*sign((exp(1)*x+d)^-1)*exp(1)^8)/(-105*a^3*exp(1)^10+105*c^3*d^6*exp(1)^4-315*a*c^2*d^4*exp(1)^6+315*a^2*c*d^2*exp(1)^8))-(4*c^3*d^4*sign((exp(1)*x+d)^-1)*exp(2)-4*a*c^2*d^2*sign((exp(1)*x+d)^-1)*exp(1)^4)/(-105*a^3*exp(1)^10+105*c^3*d^6*exp(1)^4-315*a*c^2*d^4*exp(1)^6+315*a^2*c*d^2*exp(1)^8))-C_0*(210*a^2*exp(1)^6+210*c^2*d^4*exp(2)-420*a*c*d^2*exp(1)^4)/(-105*a^3*exp(1)^10+105*c^3*d^6*exp(1)^4-315*a*c^2*d^4*exp(1)^6+315*a^2*c*d^2*exp(1)^8)+8*c^3*d^3*sign((exp(1)*x+d)^-1)*exp(1)/(-105*a^3*exp(1)^10+105*c^3*d^6*exp(1)^4-315*a*c^2*d^4*exp(1)^6+315*a^2*c*d^2*exp(1)^8))*sqrt(c*d*exp(1)+a*d*(-(exp(1)*x+d)^-1/exp(1))^2*exp(1)^5+a*(exp(1)*x+d)^-1/exp(1)*exp(1)^2*exp(2)-c*d^2*(exp(1)*x+d)^-1/exp(1)*exp(1)^2-a*d*(-(exp(1)*x+d)^-1/exp(1))^2*exp(1)^3*exp(2))-4*C_0*sqrt(a*d*exp(1)^3-a*d*exp(1)*exp(2))*ln(abs(a*sqrt(a*d*exp(1)^3-a*d*exp(1)*exp(2))*exp(2)-c*d^2*sqrt(a*d*exp(1)^3-a*d*exp(1)*exp(2))))/(2*a*d*exp(1)^4-2*a*d*exp(2)^2)+16*c^3*d^3*sqrt(c*d*exp(1))/(105*a^3*exp(1)^9-315*a^2*c*d^2*exp(1)^7+315*a*c^2*d^4*exp(1)^5-105*c^3*d^6*exp(1)^3)*sign((exp(1)*x+d)^-1))","F(-2)",0
1917,-2,0,0,0.000000," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)/(e*x+d)^6,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: 2*((105*exp(1)^5*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^9*a^5*exp(2)^5+75*c*d^2*exp(1)^5*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^9*a^4*exp(2)^4-600*c*d^2*exp(1)^7*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^9*a^4*exp(2)^3-30*c^2*d^4*exp(1)^5*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^9*a^3*exp(2)^3+360*c^2*d^4*exp(1)^7*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^9*a^3*exp(2)^2+720*c^2*d^4*exp(1)^9*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^9*a^3*exp(2)+30*c^3*d^6*exp(1)^5*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^9*a^2*exp(2)^2-360*c^3*d^6*exp(1)^7*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^9*a^2*exp(2)-720*c^3*d^6*exp(1)^9*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^9*a^2-75*c^4*d^8*exp(1)^5*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^9*a*exp(2)+600*c^4*d^8*exp(1)^7*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^9*a-105*c^5*d^10*exp(1)^5*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^9-945*d*exp(1)^4*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^8*a^5*exp(2)^5-675*c*d^3*exp(1)^4*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^8*a^4*exp(2)^4+5400*c*d^3*exp(1)^6*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^8*a^4*exp(2)^3+270*c^2*d^5*exp(1)^4*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^8*a^3*exp(2)^3-3240*c^2*d^5*exp(1)^6*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^8*a^3*exp(2)^2-6480*c^2*d^5*exp(1)^8*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^8*a^3*exp(2)-270*c^3*d^7*exp(1)^4*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^8*a^2*exp(2)^2+3240*c^3*d^7*exp(1)^6*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^8*a^2*exp(2)+6480*c^3*d^7*exp(1)^8*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^8*a^2+675*c^4*d^9*exp(1)^4*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^8*a*exp(2)-5400*c^4*d^9*exp(1)^6*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^8*a+945*c^5*d^11*exp(1)^4*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^8+490*d*exp(1)^4*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^7*a^6*exp(2)^6-490*d*exp(1)^6*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^7*a^6*exp(2)^5+4130*c*d^3*exp(1)^4*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^7*a^5*exp(2)^5-3150*c*d^3*exp(1)^6*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^7*a^5*exp(2)^4+2800*c*d^3*exp(1)^8*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^7*a^5*exp(2)^3+2560*c^2*d^5*exp(1)^4*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^7*a^4*exp(2)^4-19780*c^2*d^5*exp(1)^6*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^7*a^4*exp(2)^3+1680*c^2*d^5*exp(1)^8*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^7*a^4*exp(2)^2-3360*c^2*d^5*exp(1)^10*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^7*a^4*exp(2)-940*c^3*d^7*exp(1)^4*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^7*a^3*exp(2)^3+11140*c^3*d^7*exp(1)^6*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^7*a^3*exp(2)^2+24240*c^3*d^7*exp(1)^8*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^7*a^3*exp(2)+3360*c^3*d^7*exp(1)^10*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^7*a^3+730*c^4*d^9*exp(1)^4*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^7*a^2*exp(2)^2-9810*c^4*d^9*exp(1)^6*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^7*a^2*exp(2)-28720*c^4*d^9*exp(1)^8*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^7*a^2-3190*c^5*d^11*exp(1)^4*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^7*a*exp(2)+22090*c^5*d^11*exp(1)^6*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^7*a-3780*c^6*d^13*exp(1)^4*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^7-3430*d^2*exp(1)^3*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^6*a^6*exp(2)^6+3430*d^2*exp(1)^5*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^6*a^6*exp(2)^5-11270*c*d^4*exp(1)^3*sqrt(c*d*exp(1))*(sqrt(a*d*e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*x)*a^6-5910*c^4*d^12*exp(1)*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^5*exp(2)^5+23030*c^4*d^12*exp(1)^3*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^5*exp(2)^4-33770*c^4*d^12*exp(1)^5*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^5*exp(2)^3+27480*c^4*d^12*exp(1)^7*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^5*exp(2)^2-28645*c^4*d^12*exp(1)^9*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^5*exp(2)+18760*c^4*d^12*exp(1)^11*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^5-2990*c^5*d^14*exp(1)*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^4*exp(2)^4+17130*c^5*d^14*exp(1)^3*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^4*exp(2)^3-46300*c^5*d^14*exp(1)^5*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^4*exp(2)^2+73970*c^5*d^14*exp(1)^7*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^4*exp(2)-46535*c^5*d^14*exp(1)^9*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^4-4860*c^6*d^16*exp(1)*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^3*exp(2)^3+29610*c^6*d^16*exp(1)^3*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^3*exp(2)^2-66790*c^6*d^16*exp(1)^5*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^3*exp(2)+51490*c^6*d^16*exp(1)^7*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^3-6660*c^7*d^18*exp(1)*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^2*exp(2)^2+27770*c^7*d^18*exp(1)^3*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^2*exp(2)-30560*c^7*d^18*exp(1)^5*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^2-4105*c^8*d^20*exp(1)*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a*exp(2)+8830*c^8*d^20*exp(1)^3*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a-945*c^9*d^22*exp(1)*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)+105*d^5*sqrt(c*d*exp(1))*a^9*exp(2)^9-420*d^5*exp(1)^2*sqrt(c*d*exp(1))*a^9*exp(2)^8+630*d^5*exp(1)^4*sqrt(c*d*exp(1))*a^9*exp(2)^7-420*d^5*exp(1)^6*sqrt(c*d*exp(1))*a^9*exp(2)^6+105*d^5*exp(1)^8*sqrt(c*d*exp(1))*a^9*exp(2)^5+565*c*d^7*sqrt(c*d*exp(1))*a^8*exp(2)^8-2370*c*d^7*exp(1)^2*sqrt(c*d*exp(1))*a^8*exp(2)^7+4320*c*d^7*exp(1)^4*sqrt(c*d*exp(1))*a^8*exp(2)^6-5670*c*d^7*exp(1)^6*sqrt(c*d*exp(1))*a^8*exp(2)^5+6315*c*d^7*exp(1)^8*sqrt(c*d*exp(1))*a^8*exp(2)^4-4440*c*d^7*exp(1)^10*sqrt(c*d*exp(1))*a^8*exp(2)^3+1280*c*d^7*exp(1)^12*sqrt(c*d*exp(1))*a^8*exp(2)^2+1216*c^2*d^9*sqrt(c*d*exp(1))*a^7*exp(2)^7-5162*c^2*d^9*exp(1)^2*sqrt(c*d*exp(1))*a^7*exp(2)^6+9446*c^2*d^9*exp(1)^4*sqrt(c*d*exp(1))*a^7*exp(2)^5-10630*c^2*d^9*exp(1)^6*sqrt(c*d*exp(1))*a^7*exp(2)^4+8210*c^2*d^9*exp(1)^8*sqrt(c*d*exp(1))*a^7*exp(2)^3-4312*c^2*d^9*exp(1)^10*sqrt(c*d*exp(1))*a^7*exp(2)^2+1744*c^2*d^9*exp(1)^12*sqrt(c*d*exp(1))*a^7*exp(2)-512*c^2*d^9*exp(1)^14*sqrt(c*d*exp(1))*a^7+1320*c^3*d^11*sqrt(c*d*exp(1))*a^6*exp(2)^6-5570*c^3*d^11*exp(1)^2*sqrt(c*d*exp(1))*a^6*exp(2)^5+9680*c^3*d^11*exp(1)^4*sqrt(c*d*exp(1))*a^6*exp(2)^4-9420*c^3*d^11*exp(1)^6*sqrt(c*d*exp(1))*a^6*exp(2)^3+8110*c^3*d^11*exp(1)^8*sqrt(c*d*exp(1))*a^6*exp(2)^2-7240*c^3*d^11*exp(1)^10*sqrt(c*d*exp(1))*a^6*exp(2)+3120*c^3*d^11*exp(1)^12*sqrt(c*d*exp(1))*a^6+890*c^4*d^13*sqrt(c*d*exp(1))*a^5*exp(2)^5-4450*c^4*d^13*exp(1)^2*sqrt(c*d*exp(1))*a^5*exp(2)^4+10530*c^4*d^13*exp(1)^4*sqrt(c*d*exp(1))*a^5*exp(2)^3-16800*c^4*d^13*exp(1)^6*sqrt(c*d*exp(1))*a^5*exp(2)^2+17285*c^4*d^13*exp(1)^8*sqrt(c*d*exp(1))*a^5*exp(2)-7560*c^4*d^13*exp(1)^10*sqrt(c*d*exp(1))*a^5+890*c^5*d^15*sqrt(c*d*exp(1))*a^4*exp(2)^4-5910*c^5*d^15*exp(1)^2*sqrt(c*d*exp(1))*a^4*exp(2)^3+16400*c^5*d^15*exp(1)^4*sqrt(c*d*exp(1))*a^4*exp(2)^2-22030*c^5*d^15*exp(1)^6*sqrt(c*d*exp(1))*a^4*exp(2)+11175*c^5*d^15*exp(1)^8*sqrt(c*d*exp(1))*a^4+1320*c^6*d^17*sqrt(c*d*exp(1))*a^3*exp(2)^3-7310*c^6*d^17*exp(1)^2*sqrt(c*d*exp(1))*a^3*exp(2)^2+14210*c^6*d^17*exp(1)^4*sqrt(c*d*exp(1))*a^3*exp(2)-9270*c^6*d^17*exp(1)^6*sqrt(c*d*exp(1))*a^3+1216*c^7*d^19*sqrt(c*d*exp(1))*a^2*exp(2)^2-4582*c^7*d^19*exp(1)^2*sqrt(c*d*exp(1))*a^2*exp(2)+4416*c^7*d^19*exp(1)^4*sqrt(c*d*exp(1))*a^2+565*c^8*d^21*sqrt(c*d*exp(1))*a*exp(2)-1090*c^8*d^21*exp(1)^2*sqrt(c*d*exp(1))*a+105*c^9*d^23*sqrt(c*d*exp(1)))/(-3840*d^4*exp(1)^2*a^4*exp(2)^4+15360*d^4*exp(1)^4*a^4*exp(2)^3-23040*d^4*exp(1)^6*a^4*exp(2)^2+15360*d^4*exp(1)^8*a^4*exp(2)-3840*d^4*exp(1)^10*a^4)/(-exp(1)*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^2+2*d*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)-d*a*exp(2)+d*exp(1)^2*a-c*d^3)^5+(7*a^5*exp(2)^5+5*c*d^2*a^4*exp(2)^4-40*c*d^2*exp(1)^2*a^4*exp(2)^3-2*c^2*d^4*a^3*exp(2)^3+24*c^2*d^4*exp(1)^2*a^3*exp(2)^2+48*c^2*d^4*exp(1)^4*a^3*exp(2)+2*c^3*d^6*a^2*exp(2)^2-24*c^3*d^6*exp(1)^2*a^2*exp(2)-48*c^3*d^6*exp(1)^4*a^2-5*c^4*d^8*a*exp(2)+40*c^4*d^8*exp(1)^2*a-7*c^5*d^10)/2/(128*d^4*exp(1)*a^4*exp(2)^4-512*d^4*exp(1)^3*a^4*exp(2)^3+768*d^4*exp(1)^5*a^4*exp(2)^2-512*d^4*exp(1)^7*a^4*exp(2)+128*d^4*exp(1)^9*a^4)/sqrt(-a*d*exp(1)^3+a*d*exp(1)*exp(2))*atan((-d*sqrt(c*d*exp(1))+(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*exp(1))/sqrt(-a*d*exp(1)^3+a*d*exp(1)*exp(2))))","F(-2)",0
1918,1,726,0,0.628546," ","integrate((e*x+d)^4*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""giac"")","\frac{1}{573440} \, \sqrt{c d x^{2} e + c d^{2} x + a x e^{2} + a d e} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(10 \, {\left(4 \, {\left(14 \, c d x e^{5} + \frac{{\left(81 \, c^{8} d^{9} e^{11} + 17 \, a c^{7} d^{7} e^{13}\right)} e^{\left(-7\right)}}{c^{7} d^{7}}\right)} x + \frac{{\left(769 \, c^{8} d^{10} e^{10} + 406 \, a c^{7} d^{8} e^{12} + a^{2} c^{6} d^{6} e^{14}\right)} e^{\left(-7\right)}}{c^{7} d^{7}}\right)} x + \frac{{\left(9461 \, c^{8} d^{11} e^{9} + 10067 \, a c^{7} d^{9} e^{11} + 83 \, a^{2} c^{6} d^{7} e^{13} - 11 \, a^{3} c^{5} d^{5} e^{15}\right)} e^{\left(-7\right)}}{c^{7} d^{7}}\right)} x + \frac{{\left(49251 \, c^{8} d^{12} e^{8} + 105748 \, a c^{7} d^{10} e^{10} + 2450 \, a^{2} c^{6} d^{8} e^{12} - 748 \, a^{3} c^{5} d^{6} e^{14} + 99 \, a^{4} c^{4} d^{4} e^{16}\right)} e^{\left(-7\right)}}{c^{7} d^{7}}\right)} x + \frac{{\left(28441 \, c^{8} d^{13} e^{7} + 153301 \, a c^{7} d^{11} e^{9} + 10642 \, a^{2} c^{6} d^{9} e^{11} - 5742 \, a^{3} c^{5} d^{7} e^{13} + 1749 \, a^{4} c^{4} d^{5} e^{15} - 231 \, a^{5} c^{3} d^{3} e^{17}\right)} e^{\left(-7\right)}}{c^{7} d^{7}}\right)} x + \frac{{\left(1155 \, c^{8} d^{14} e^{6} + 220598 \, a c^{7} d^{12} e^{8} + 61709 \, a^{2} c^{6} d^{10} e^{10} - 53900 \, a^{3} c^{5} d^{8} e^{12} + 28941 \, a^{4} c^{4} d^{6} e^{14} - 8778 \, a^{5} c^{3} d^{4} e^{16} + 1155 \, a^{6} c^{2} d^{2} e^{18}\right)} e^{\left(-7\right)}}{c^{7} d^{7}}\right)} x - \frac{{\left(3465 \, c^{8} d^{15} e^{5} - 26565 \, a c^{7} d^{13} e^{7} - 140903 \, a^{2} c^{6} d^{11} e^{9} + 193699 \, a^{3} c^{5} d^{9} e^{11} - 166749 \, a^{4} c^{4} d^{7} e^{13} + 88473 \, a^{5} c^{3} d^{5} e^{15} - 26565 \, a^{6} c^{2} d^{3} e^{17} + 3465 \, a^{7} c d e^{19}\right)} e^{\left(-7\right)}}{c^{7} d^{7}}\right)} - \frac{99 \, {\left(c^{8} d^{16} - 8 \, a c^{7} d^{14} e^{2} + 28 \, a^{2} c^{6} d^{12} e^{4} - 56 \, a^{3} c^{5} d^{10} e^{6} + 70 \, a^{4} c^{4} d^{8} e^{8} - 56 \, a^{5} c^{3} d^{6} e^{10} + 28 \, a^{6} c^{2} d^{4} e^{12} - 8 \, a^{7} c d^{2} e^{14} + a^{8} e^{16}\right)} e^{\left(-\frac{5}{2}\right)} \log\left({\left| -c d^{2} - 2 \, {\left(\sqrt{c d} x e^{\frac{1}{2}} - \sqrt{c d x^{2} e + c d^{2} x + a x e^{2} + a d e}\right)} \sqrt{c d} e^{\frac{1}{2}} - a e^{2} \right|}\right)}{32768 \, \sqrt{c d} c^{6} d^{6}}"," ",0,"1/573440*sqrt(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e)*(2*(4*(2*(8*(10*(4*(14*c*d*x*e^5 + (81*c^8*d^9*e^11 + 17*a*c^7*d^7*e^13)*e^(-7)/(c^7*d^7))*x + (769*c^8*d^10*e^10 + 406*a*c^7*d^8*e^12 + a^2*c^6*d^6*e^14)*e^(-7)/(c^7*d^7))*x + (9461*c^8*d^11*e^9 + 10067*a*c^7*d^9*e^11 + 83*a^2*c^6*d^7*e^13 - 11*a^3*c^5*d^5*e^15)*e^(-7)/(c^7*d^7))*x + (49251*c^8*d^12*e^8 + 105748*a*c^7*d^10*e^10 + 2450*a^2*c^6*d^8*e^12 - 748*a^3*c^5*d^6*e^14 + 99*a^4*c^4*d^4*e^16)*e^(-7)/(c^7*d^7))*x + (28441*c^8*d^13*e^7 + 153301*a*c^7*d^11*e^9 + 10642*a^2*c^6*d^9*e^11 - 5742*a^3*c^5*d^7*e^13 + 1749*a^4*c^4*d^5*e^15 - 231*a^5*c^3*d^3*e^17)*e^(-7)/(c^7*d^7))*x + (1155*c^8*d^14*e^6 + 220598*a*c^7*d^12*e^8 + 61709*a^2*c^6*d^10*e^10 - 53900*a^3*c^5*d^8*e^12 + 28941*a^4*c^4*d^6*e^14 - 8778*a^5*c^3*d^4*e^16 + 1155*a^6*c^2*d^2*e^18)*e^(-7)/(c^7*d^7))*x - (3465*c^8*d^15*e^5 - 26565*a*c^7*d^13*e^7 - 140903*a^2*c^6*d^11*e^9 + 193699*a^3*c^5*d^9*e^11 - 166749*a^4*c^4*d^7*e^13 + 88473*a^5*c^3*d^5*e^15 - 26565*a^6*c^2*d^3*e^17 + 3465*a^7*c*d*e^19)*e^(-7)/(c^7*d^7)) - 99/32768*(c^8*d^16 - 8*a*c^7*d^14*e^2 + 28*a^2*c^6*d^12*e^4 - 56*a^3*c^5*d^10*e^6 + 70*a^4*c^4*d^8*e^8 - 56*a^5*c^3*d^6*e^10 + 28*a^6*c^2*d^4*e^12 - 8*a^7*c*d^2*e^14 + a^8*e^16)*e^(-5/2)*log(abs(-c*d^2 - 2*(sqrt(c*d)*x*e^(1/2) - sqrt(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e))*sqrt(c*d)*e^(1/2) - a*e^2))/(sqrt(c*d)*c^6*d^6)","A",0
1919,1,601,0,0.530514," ","integrate((e*x+d)^3*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""giac"")","\frac{1}{35840} \, \sqrt{c d x^{2} e + c d^{2} x + a x e^{2} + a d e} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(10 \, {\left(4 \, c d x e^{4} + \frac{{\left(19 \, c^{7} d^{8} e^{9} + 5 \, a c^{6} d^{6} e^{11}\right)} e^{\left(-6\right)}}{c^{6} d^{6}}\right)} x + \frac{{\left(351 \, c^{7} d^{9} e^{8} + 248 \, a c^{6} d^{7} e^{10} + a^{2} c^{5} d^{5} e^{12}\right)} e^{\left(-6\right)}}{c^{6} d^{6}}\right)} x + \frac{{\left(2441 \, c^{7} d^{10} e^{7} + 3909 \, a c^{6} d^{8} e^{9} + 59 \, a^{2} c^{5} d^{6} e^{11} - 9 \, a^{3} c^{4} d^{4} e^{13}\right)} e^{\left(-6\right)}}{c^{6} d^{6}}\right)} x + \frac{{\left(1771 \, c^{7} d^{11} e^{6} + 7562 \, a c^{6} d^{9} e^{8} + 384 \, a^{2} c^{5} d^{7} e^{10} - 138 \, a^{3} c^{4} d^{5} e^{12} + 21 \, a^{4} c^{3} d^{3} e^{14}\right)} e^{\left(-6\right)}}{c^{6} d^{6}}\right)} x + \frac{{\left(105 \, c^{7} d^{12} e^{5} + 13643 \, a c^{6} d^{10} e^{7} + 2962 \, a^{2} c^{5} d^{8} e^{9} - 1938 \, a^{3} c^{4} d^{6} e^{11} + 693 \, a^{4} c^{3} d^{4} e^{13} - 105 \, a^{5} c^{2} d^{2} e^{15}\right)} e^{\left(-6\right)}}{c^{6} d^{6}}\right)} x - \frac{{\left(315 \, c^{7} d^{13} e^{4} - 2100 \, a c^{6} d^{11} e^{6} - 8393 \, a^{2} c^{5} d^{9} e^{8} + 9216 \, a^{3} c^{4} d^{7} e^{10} - 5943 \, a^{4} c^{3} d^{5} e^{12} + 2100 \, a^{5} c^{2} d^{3} e^{14} - 315 \, a^{6} c d e^{16}\right)} e^{\left(-6\right)}}{c^{6} d^{6}}\right)} - \frac{9 \, {\left(c^{7} d^{14} - 7 \, a c^{6} d^{12} e^{2} + 21 \, a^{2} c^{5} d^{10} e^{4} - 35 \, a^{3} c^{4} d^{8} e^{6} + 35 \, a^{4} c^{3} d^{6} e^{8} - 21 \, a^{5} c^{2} d^{4} e^{10} + 7 \, a^{6} c d^{2} e^{12} - a^{7} e^{14}\right)} e^{\left(-\frac{5}{2}\right)} \log\left({\left| -c d^{2} - 2 \, {\left(\sqrt{c d} x e^{\frac{1}{2}} - \sqrt{c d x^{2} e + c d^{2} x + a x e^{2} + a d e}\right)} \sqrt{c d} e^{\frac{1}{2}} - a e^{2} \right|}\right)}{2048 \, \sqrt{c d} c^{5} d^{5}}"," ",0,"1/35840*sqrt(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e)*(2*(4*(2*(8*(10*(4*c*d*x*e^4 + (19*c^7*d^8*e^9 + 5*a*c^6*d^6*e^11)*e^(-6)/(c^6*d^6))*x + (351*c^7*d^9*e^8 + 248*a*c^6*d^7*e^10 + a^2*c^5*d^5*e^12)*e^(-6)/(c^6*d^6))*x + (2441*c^7*d^10*e^7 + 3909*a*c^6*d^8*e^9 + 59*a^2*c^5*d^6*e^11 - 9*a^3*c^4*d^4*e^13)*e^(-6)/(c^6*d^6))*x + (1771*c^7*d^11*e^6 + 7562*a*c^6*d^9*e^8 + 384*a^2*c^5*d^7*e^10 - 138*a^3*c^4*d^5*e^12 + 21*a^4*c^3*d^3*e^14)*e^(-6)/(c^6*d^6))*x + (105*c^7*d^12*e^5 + 13643*a*c^6*d^10*e^7 + 2962*a^2*c^5*d^8*e^9 - 1938*a^3*c^4*d^6*e^11 + 693*a^4*c^3*d^4*e^13 - 105*a^5*c^2*d^2*e^15)*e^(-6)/(c^6*d^6))*x - (315*c^7*d^13*e^4 - 2100*a*c^6*d^11*e^6 - 8393*a^2*c^5*d^9*e^8 + 9216*a^3*c^4*d^7*e^10 - 5943*a^4*c^3*d^5*e^12 + 2100*a^5*c^2*d^3*e^14 - 315*a^6*c*d*e^16)*e^(-6)/(c^6*d^6)) - 9/2048*(c^7*d^14 - 7*a*c^6*d^12*e^2 + 21*a^2*c^5*d^10*e^4 - 35*a^3*c^4*d^8*e^6 + 35*a^4*c^3*d^6*e^8 - 21*a^5*c^2*d^4*e^10 + 7*a^6*c*d^2*e^12 - a^7*e^14)*e^(-5/2)*log(abs(-c*d^2 - 2*(sqrt(c*d)*x*e^(1/2) - sqrt(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e))*sqrt(c*d)*e^(1/2) - a*e^2))/(sqrt(c*d)*c^5*d^5)","A",0
1920,1,488,0,0.567480," ","integrate((e*x+d)^2*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""giac"")","\frac{1}{7680} \, \sqrt{c d x^{2} e + c d^{2} x + a x e^{2} + a d e} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(10 \, c d x e^{3} + \frac{{\left(37 \, c^{6} d^{7} e^{7} + 13 \, a c^{5} d^{5} e^{9}\right)} e^{\left(-5\right)}}{c^{5} d^{5}}\right)} x + \frac{{\left(387 \, c^{6} d^{8} e^{6} + 410 \, a c^{5} d^{6} e^{8} + 3 \, a^{2} c^{4} d^{4} e^{10}\right)} e^{\left(-5\right)}}{c^{5} d^{5}}\right)} x + \frac{{\left(377 \, c^{6} d^{9} e^{5} + 1191 \, a c^{5} d^{7} e^{7} + 39 \, a^{2} c^{4} d^{5} e^{9} - 7 \, a^{3} c^{3} d^{3} e^{11}\right)} e^{\left(-5\right)}}{c^{5} d^{5}}\right)} x + \frac{{\left(35 \, c^{6} d^{10} e^{4} + 2876 \, a c^{5} d^{8} e^{6} + 450 \, a^{2} c^{4} d^{6} e^{8} - 196 \, a^{3} c^{3} d^{4} e^{10} + 35 \, a^{4} c^{2} d^{2} e^{12}\right)} e^{\left(-5\right)}}{c^{5} d^{5}}\right)} x - \frac{{\left(105 \, c^{6} d^{11} e^{3} - 595 \, a c^{5} d^{9} e^{5} - 1686 \, a^{2} c^{4} d^{7} e^{7} + 1386 \, a^{3} c^{3} d^{5} e^{9} - 595 \, a^{4} c^{2} d^{3} e^{11} + 105 \, a^{5} c d e^{13}\right)} e^{\left(-5\right)}}{c^{5} d^{5}}\right)} - \frac{7 \, {\left(c^{6} d^{12} - 6 \, a c^{5} d^{10} e^{2} + 15 \, a^{2} c^{4} d^{8} e^{4} - 20 \, a^{3} c^{3} d^{6} e^{6} + 15 \, a^{4} c^{2} d^{4} e^{8} - 6 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}\right)} e^{\left(-\frac{5}{2}\right)} \log\left({\left| -c d^{2} - 2 \, {\left(\sqrt{c d} x e^{\frac{1}{2}} - \sqrt{c d x^{2} e + c d^{2} x + a x e^{2} + a d e}\right)} \sqrt{c d} e^{\frac{1}{2}} - a e^{2} \right|}\right)}{1024 \, \sqrt{c d} c^{4} d^{4}}"," ",0,"1/7680*sqrt(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e)*(2*(4*(2*(8*(10*c*d*x*e^3 + (37*c^6*d^7*e^7 + 13*a*c^5*d^5*e^9)*e^(-5)/(c^5*d^5))*x + (387*c^6*d^8*e^6 + 410*a*c^5*d^6*e^8 + 3*a^2*c^4*d^4*e^10)*e^(-5)/(c^5*d^5))*x + (377*c^6*d^9*e^5 + 1191*a*c^5*d^7*e^7 + 39*a^2*c^4*d^5*e^9 - 7*a^3*c^3*d^3*e^11)*e^(-5)/(c^5*d^5))*x + (35*c^6*d^10*e^4 + 2876*a*c^5*d^8*e^6 + 450*a^2*c^4*d^6*e^8 - 196*a^3*c^3*d^4*e^10 + 35*a^4*c^2*d^2*e^12)*e^(-5)/(c^5*d^5))*x - (105*c^6*d^11*e^3 - 595*a*c^5*d^9*e^5 - 1686*a^2*c^4*d^7*e^7 + 1386*a^3*c^3*d^5*e^9 - 595*a^4*c^2*d^3*e^11 + 105*a^5*c*d*e^13)*e^(-5)/(c^5*d^5)) - 7/1024*(c^6*d^12 - 6*a*c^5*d^10*e^2 + 15*a^2*c^4*d^8*e^4 - 20*a^3*c^3*d^6*e^6 + 15*a^4*c^2*d^4*e^8 - 6*a^5*c*d^2*e^10 + a^6*e^12)*e^(-5/2)*log(abs(-c*d^2 - 2*(sqrt(c*d)*x*e^(1/2) - sqrt(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e))*sqrt(c*d)*e^(1/2) - a*e^2))/(sqrt(c*d)*c^4*d^4)","A",0
1921,1,388,0,0.543620," ","integrate((e*x+d)*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""giac"")","\frac{1}{640} \, \sqrt{c d x^{2} e + c d^{2} x + a x e^{2} + a d e} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, c d x e^{2} + \frac{{\left(21 \, c^{5} d^{6} e^{5} + 11 \, a c^{4} d^{4} e^{7}\right)} e^{\left(-4\right)}}{c^{4} d^{4}}\right)} x + \frac{{\left(31 \, c^{5} d^{7} e^{4} + 64 \, a c^{4} d^{5} e^{6} + a^{2} c^{3} d^{3} e^{8}\right)} e^{\left(-4\right)}}{c^{4} d^{4}}\right)} x + \frac{{\left(5 \, c^{5} d^{8} e^{3} + 233 \, a c^{4} d^{6} e^{5} + 23 \, a^{2} c^{3} d^{4} e^{7} - 5 \, a^{3} c^{2} d^{2} e^{9}\right)} e^{\left(-4\right)}}{c^{4} d^{4}}\right)} x - \frac{{\left(15 \, c^{5} d^{9} e^{2} - 70 \, a c^{4} d^{7} e^{4} - 128 \, a^{2} c^{3} d^{5} e^{6} + 70 \, a^{3} c^{2} d^{3} e^{8} - 15 \, a^{4} c d e^{10}\right)} e^{\left(-4\right)}}{c^{4} d^{4}}\right)} - \frac{3 \, {\left(c^{5} d^{10} - 5 \, a c^{4} d^{8} e^{2} + 10 \, a^{2} c^{3} d^{6} e^{4} - 10 \, a^{3} c^{2} d^{4} e^{6} + 5 \, a^{4} c d^{2} e^{8} - a^{5} e^{10}\right)} e^{\left(-\frac{5}{2}\right)} \log\left({\left| -c d^{2} - 2 \, {\left(\sqrt{c d} x e^{\frac{1}{2}} - \sqrt{c d x^{2} e + c d^{2} x + a x e^{2} + a d e}\right)} \sqrt{c d} e^{\frac{1}{2}} - a e^{2} \right|}\right)}{256 \, \sqrt{c d} c^{3} d^{3}}"," ",0,"1/640*sqrt(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e)*(2*(4*(2*(8*c*d*x*e^2 + (21*c^5*d^6*e^5 + 11*a*c^4*d^4*e^7)*e^(-4)/(c^4*d^4))*x + (31*c^5*d^7*e^4 + 64*a*c^4*d^5*e^6 + a^2*c^3*d^3*e^8)*e^(-4)/(c^4*d^4))*x + (5*c^5*d^8*e^3 + 233*a*c^4*d^6*e^5 + 23*a^2*c^3*d^4*e^7 - 5*a^3*c^2*d^2*e^9)*e^(-4)/(c^4*d^4))*x - (15*c^5*d^9*e^2 - 70*a*c^4*d^7*e^4 - 128*a^2*c^3*d^5*e^6 + 70*a^3*c^2*d^3*e^8 - 15*a^4*c*d*e^10)*e^(-4)/(c^4*d^4)) - 3/256*(c^5*d^10 - 5*a*c^4*d^8*e^2 + 10*a^2*c^3*d^6*e^4 - 10*a^3*c^2*d^4*e^6 + 5*a^4*c*d^2*e^8 - a^5*e^10)*e^(-5/2)*log(abs(-c*d^2 - 2*(sqrt(c*d)*x*e^(1/2) - sqrt(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e))*sqrt(c*d)*e^(1/2) - a*e^2))/(sqrt(c*d)*c^3*d^3)","A",0
1922,1,298,0,0.527518," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""giac"")","\frac{1}{64} \, \sqrt{c d x^{2} e + c d^{2} x + a x e^{2} + a d e} {\left(2 \, {\left(4 \, {\left(2 \, c d x e + \frac{3 \, {\left(c^{4} d^{5} e^{3} + a c^{3} d^{3} e^{5}\right)} e^{\left(-3\right)}}{c^{3} d^{3}}\right)} x + \frac{{\left(c^{4} d^{6} e^{2} + 22 \, a c^{3} d^{4} e^{4} + a^{2} c^{2} d^{2} e^{6}\right)} e^{\left(-3\right)}}{c^{3} d^{3}}\right)} x - \frac{{\left(3 \, c^{4} d^{7} e - 11 \, a c^{3} d^{5} e^{3} - 11 \, a^{2} c^{2} d^{3} e^{5} + 3 \, a^{3} c d e^{7}\right)} e^{\left(-3\right)}}{c^{3} d^{3}}\right)} - \frac{3 \, {\left(c^{4} d^{8} - 4 \, a c^{3} d^{6} e^{2} + 6 \, a^{2} c^{2} d^{4} e^{4} - 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}\right)} e^{\left(-\frac{5}{2}\right)} \log\left({\left| -c d^{2} - 2 \, {\left(\sqrt{c d} x e^{\frac{1}{2}} - \sqrt{c d x^{2} e + c d^{2} x + a x e^{2} + a d e}\right)} \sqrt{c d} e^{\frac{1}{2}} - a e^{2} \right|}\right)}{128 \, \sqrt{c d} c^{2} d^{2}}"," ",0,"1/64*sqrt(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e)*(2*(4*(2*c*d*x*e + 3*(c^4*d^5*e^3 + a*c^3*d^3*e^5)*e^(-3)/(c^3*d^3))*x + (c^4*d^6*e^2 + 22*a*c^3*d^4*e^4 + a^2*c^2*d^2*e^6)*e^(-3)/(c^3*d^3))*x - (3*c^4*d^7*e - 11*a*c^3*d^5*e^3 - 11*a^2*c^2*d^3*e^5 + 3*a^3*c*d*e^7)*e^(-3)/(c^3*d^3)) - 3/128*(c^4*d^8 - 4*a*c^3*d^6*e^2 + 6*a^2*c^2*d^4*e^4 - 4*a^3*c*d^2*e^6 + a^4*e^8)*e^(-5/2)*log(abs(-c*d^2 - 2*(sqrt(c*d)*x*e^(1/2) - sqrt(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e))*sqrt(c*d)*e^(1/2) - a*e^2))/(sqrt(c*d)*c^2*d^2)","A",0
1923,-2,0,0,0.000000," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)/(e*x+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Error: Bad Argument Type","F(-2)",0
1924,-1,0,0,0.000000," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)/(e*x+d)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1925,-2,0,0,0.000000," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)/(e*x+d)^3,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 0.46Unable to divide, perhaps due to rounding error%%%{%%%{2,[0,0,5]%%%},[6,6,6]%%%}+%%%{%%%{12,[1,2,5]%%%},[6,5,5]%%%}+%%%{%%%{-24,[1,2,7]%%%},[6,5,4]%%%}+%%%{%%%{30,[2,4,5]%%%},[6,4,4]%%%}+%%%{%%%{-96,[2,4,7]%%%},[6,4,3]%%%}+%%%{%%%{96,[2,4,9]%%%},[6,4,2]%%%}+%%%{%%%{40,[3,6,5]%%%},[6,3,3]%%%}+%%%{%%%{-144,[3,6,7]%%%},[6,3,2]%%%}+%%%{%%%{192,[3,6,9]%%%},[6,3,1]%%%}+%%%{%%%{-128,[3,6,11]%%%},[6,3,0]%%%}+%%%{%%%{30,[4,8,5]%%%},[6,2,2]%%%}+%%%{%%%{-96,[4,8,7]%%%},[6,2,1]%%%}+%%%{%%%{96,[4,8,9]%%%},[6,2,0]%%%}+%%%{%%%{12,[5,10,5]%%%},[6,1,1]%%%}+%%%{%%%{-24,[5,10,7]%%%},[6,1,0]%%%}+%%%{%%%{2,[6,12,5]%%%},[6,0,0]%%%}+%%%{%%{[%%%{-12,[0,1,4]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,6,6]%%%}+%%%{%%{[%%%{-72,[1,3,4]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,5,5]%%%}+%%%{%%{[%%%{144,[1,3,6]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,5,4]%%%}+%%%{%%{[%%%{-180,[2,5,4]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,4,4]%%%}+%%%{%%{[%%%{576,[2,5,6]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,4,3]%%%}+%%%{%%{[%%%{-576,[2,5,8]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,4,2]%%%}+%%%{%%{[%%%{-240,[3,7,4]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,3,3]%%%}+%%%{%%{[%%%{864,[3,7,6]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,3,2]%%%}+%%%{%%{[%%%{-1152,[3,7,8]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,3,1]%%%}+%%%{%%{[%%%{768,[3,7,10]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,3,0]%%%}+%%%{%%{[%%%{-180,[4,9,4]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,2,2]%%%}+%%%{%%{[%%%{576,[4,9,6]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,2,1]%%%}+%%%{%%{[%%%{-576,[4,9,8]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,2,0]%%%}+%%%{%%{[%%%{-72,[5,11,4]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,1,1]%%%}+%%%{%%{[%%%{144,[5,11,6]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,1,0]%%%}+%%%{%%{[%%%{-12,[6,13,4]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,0,0]%%%}+%%%{%%%{6,[0,1,4]%%%},[4,7,7]%%%}+%%%{%%%{-6,[0,1,6]%%%},[4,7,6]%%%}+%%%{%%%{66,[1,3,4]%%%},[4,6,6]%%%}+%%%{%%%{-108,[1,3,6]%%%},[4,6,5]%%%}+%%%{%%%{72,[1,3,8]%%%},[4,6,4]%%%}+%%%{%%%{270,[2,5,4]%%%},[4,5,5]%%%}+%%%{%%%{-738,[2,5,6]%%%},[4,5,4]%%%}+%%%{%%%{576,[2,5,8]%%%},[4,5,3]%%%}+%%%{%%%{-288,[2,5,10]%%%},[4,5,2]%%%}+%%%{%%%{570,[3,7,4]%%%},[4,4,4]%%%}+%%%{%%%{-1992,[3,7,6]%%%},[4,4,3]%%%}+%%%{%%%{2448,[3,7,8]%%%},[4,4,2]%%%}+%%%{%%%{-960,[3,7,10]%%%},[4,4,1]%%%}+%%%{%%%{384,[3,7,12]%%%},[4,4,0]%%%}+%%%{%%%{690,[4,9,4]%%%},[4,3,3]%%%}+%%%{%%%{-2538,[4,9,6]%%%},[4,3,2]%%%}+%%%{%%%{3456,[4,9,8]%%%},[4,3,1]%%%}+%%%{%%%{-2208,[4,9,10]%%%},[4,3,0]%%%}+%%%{%%%{486,[5,11,4]%%%},[4,2,2]%%%}+%%%{%%%{-1548,[5,11,6]%%%},[4,2,1]%%%}+%%%{%%%{1512,[5,11,8]%%%},[4,2,0]%%%}+%%%{%%%{186,[6,13,4]%%%},[4,1,1]%%%}+%%%{%%%{-366,[6,13,6]%%%},[4,1,0]%%%}+%%%{%%%{30,[7,15,4]%%%},[4,0,0]%%%}+%%%{%%{[%%%{-24,[0,2,3]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,7,7]%%%}+%%%{%%{[%%%{24,[0,2,5]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,7,6]%%%}+%%%{%%{[%%%{-184,[1,4,3]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,6,6]%%%}+%%%{%%{[%%%{432,[1,4,5]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,6,5]%%%}+%%%{%%{[%%%{-288,[1,4,7]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,6,4]%%%}+%%%{%%{[%%%{-600,[2,6,3]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,5,5]%%%}+%%%{%%{[%%%{1992,[2,6,5]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,5,4]%%%}+%%%{%%{[%%%{-2304,[2,6,7]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,5,3]%%%}+%%%{%%{[%%%{1152,[2,6,9]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,5,2]%%%}+%%%{%%{[%%%{-1080,[3,8,3]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,4,4]%%%}+%%%{%%{[%%%{4128,[3,8,5]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,4,3]%%%}+%%%{%%{[%%%{-5952,[3,8,7]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,4,2]%%%}+%%%{%%{[%%%{3840,[3,8,9]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,4,1]%%%}+%%%{%%{[%%%{-1536,[3,8,11]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,4,0]%%%}+%%%{%%{[%%%{-1160,[4,10,3]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,3,3]%%%}+%%%{%%{[%%%{4392,[4,10,5]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,3,2]%%%}+%%%{%%{[%%%{-6144,[4,10,7]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,3,1]%%%}+%%%{%%{[%%%{3712,[4,10,9]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,3,0]%%%}+%%%{%%{[%%%{-744,[5,12,3]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,2,2]%%%}+%%%{%%{[%%%{2352,[5,12,5]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,2,1]%%%}+%%%{%%{[%%%{-2208,[5,12,7]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,2,0]%%%}+%%%{%%{[%%%{-264,[6,14,3]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,1,1]%%%}+%%%{%%{[%%%{504,[6,14,5]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,1,0]%%%}+%%%{%%{[%%%{-40,[7,16,3]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,0,0]%%%}+%%%{%%%{6,[0,2,3]%%%},[2,8,8]%%%}+%%%{%%%{-12,[0,2,5]%%%},[2,8,7]%%%}+%%%{%%%{6,[0,2,7]%%%},[2,8,6]%%%}+%%%{%%%{72,[1,4,3]%%%},[2,7,7]%%%}+%%%{%%%{-180,[1,4,5]%%%},[2,7,6]%%%}+%%%{%%%{180,[1,4,7]%%%},[2,7,5]%%%}+%%%{%%%{-72,[1,4,9]%%%},[2,7,4]%%%}+%%%{%%%{336,[2,6,3]%%%},[2,6,6]%%%}+%%%{%%%{-1116,[2,6,5]%%%},[2,6,5]%%%}+%%%{%%%{1386,[2,6,7]%%%},[2,6,4]%%%}+%%%{%%%{-864,[2,6,9]%%%},[2,6,3]%%%}+%%%{%%%{288,[2,6,11]%%%},[2,6,2]%%%}+%%%{%%%{840,[3,8,3]%%%},[2,5,5]%%%}+%%%{%%%{-3300,[3,8,5]%%%},[2,5,4]%%%}+%%%{%%%{5016,[3,8,7]%%%},[2,5,3]%%%}+%%%{%%%{-3696,[3,8,9]%%%},[2,5,2]%%%}+%%%{%%%{1344,[3,8,11]%%%},[2,5,1]%%%}+%%%{%%%{-384,[3,8,13]%%%},[2,5,0]%%%}+%%%{%%%{1260,[4,10,3]%%%},[2,4,4]%%%}+%%%{%%%{-5220,[4,10,5]%%%},[2,4,3]%%%}+%%%{%%%{8442,[4,10,7]%%%},[2,4,2]%%%}+%%%{%%%{-6624,[4,10,9]%%%},[2,4,1]%%%}+%%%{%%%{2592,[4,10,11]%%%},[2,4,0]%%%}+%%%{%%%{1176,[5,12,3]%%%},[2,3,3]%%%}+%%%{%%%{-4572,[5,12,5]%%%},[2,3,2]%%%}+%%%{%%%{6516,[5,12,7]%%%},[2,3,1]%%%}+%%%{%%%{-3720,[5,12,9]%%%},[2,3,0]%%%}+%%%{%%%{672,[6,14,3]%%%},[2,2,2]%%%}+%%%{%%%{-2100,[6,14,5]%%%},[2,2,1]%%%}+%%%{%%%{1878,[6,14,7]%%%},[2,2,0]%%%}+%%%{%%%{216,[7,16,3]%%%},[2,1,1]%%%}+%%%{%%%{-396,[7,16,5]%%%},[2,1,0]%%%}+%%%{%%%{30,[8,18,3]%%%},[2,0,0]%%%}+%%%{%%{[%%%{-12,[0,3,2]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,8,8]%%%}+%%%{%%{[%%%{24,[0,3,4]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,8,7]%%%}+%%%{%%{[%%%{-12,[0,3,6]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,8,6]%%%}+%%%{%%{[%%%{-96,[1,5,2]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,7,7]%%%}+%%%{%%{[%%%{312,[1,5,4]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,7,6]%%%}+%%%{%%{[%%%{-360,[1,5,6]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,7,5]%%%}+%%%{%%{[%%%{144,[1,5,8]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,7,4]%%%}+%%%{%%{[%%%{-336,[2,7,2]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,6,6]%%%}+%%%{%%{[%%%{1368,[2,7,4]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,6,5]%%%}+%%%{%%{[%%%{-2196,[2,7,6]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,6,4]%%%}+%%%{%%{[%%%{1728,[2,7,8]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,6,3]%%%}+%%%{%%{[%%%{-576,[2,7,10]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,6,2]%%%}+%%%{%%{[%%%{-672,[3,9,2]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,5,5]%%%}+%%%{%%{[%%%{3000,[3,9,4]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,5,4]%%%}+%%%{%%{[%%%{-5424,[3,9,6]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,5,3]%%%}+%%%{%%{[%%%{5088,[3,9,8]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,5,2]%%%}+%%%{%%{[%%%{-2688,[3,9,10]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,5,1]%%%}+%%%{%%{[%%%{768,[3,9,12]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,5,0]%%%}+%%%{%%{[%%%{-840,[4,11,2]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,4,4]%%%}+%%%{%%{[%%%{3720,[4,11,4]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,4,3]%%%}+%%%{%%{[%%%{-6516,[4,11,6]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,4,2]%%%}+%%%{%%{[%%%{5568,[4,11,8]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,4,1]%%%}+%%%{%%{[%%%{-2112,[4,11,10]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,4,0]%%%}+%%%{%%{[%%%{-672,[5,13,2]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,3,3]%%%}+%%%{%%{[%%%{2664,[5,13,4]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,3,2]%%%}+%%%{%%{[%%%{-3816,[5,13,6]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,3,1]%%%}+%%%{%%{[%%%{2064,[5,13,8]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,3,0]%%%}+%%%{%%{[%%%{-336,[6,15,2]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,2,2]%%%}+%%%{%%{[%%%{1032,[6,15,4]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,2,1]%%%}+%%%{%%{[%%%{-876,[6,15,6]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,2,0]%%%}+%%%{%%{[%%%{-96,[7,17,2]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,1,1]%%%}+%%%{%%{[%%%{168,[7,17,4]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,1,0]%%%}+%%%{%%{[%%%{-12,[8,19,2]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,0,0]%%%}+%%%{%%%{2,[0,3,2]%%%},[0,9,9]%%%}+%%%{%%%{-6,[0,3,4]%%%},[0,9,8]%%%}+%%%{%%%{6,[0,3,6]%%%},[0,9,7]%%%}+%%%{%%%{-2,[0,3,8]%%%},[0,9,6]%%%}+%%%{%%%{18,[1,5,2]%%%},[0,8,8]%%%}+%%%{%%%{-72,[1,5,4]%%%},[0,8,7]%%%}+%%%{%%%{114,[1,5,6]%%%},[0,8,6]%%%}+%%%{%%%{-84,[1,5,8]%%%},[0,8,5]%%%}+%%%{%%%{24,[1,5,10]%%%},[0,8,4]%%%}+%%%{%%%{72,[2,7,2]%%%},[0,7,7]%%%}+%%%{%%%{-336,[2,7,4]%%%},[0,7,6]%%%}+%%%{%%%{654,[2,7,6]%%%},[0,7,5]%%%}+%%%{%%%{-678,[2,7,8]%%%},[0,7,4]%%%}+%%%{%%%{384,[2,7,10]%%%},[0,7,3]%%%}+%%%{%%%{-96,[2,7,12]%%%},[0,7,2]%%%}+%%%{%%%{168,[3,9,2]%%%},[0,6,6]%%%}+%%%{%%%{-840,[3,9,4]%%%},[0,6,5]%%%}+%%%{%%%{1770,[3,9,6]%%%},[0,6,4]%%%}+%%%{%%%{-2040,[3,9,8]%%%},[0,6,3]%%%}+%%%{%%%{1392,[3,9,10]%%%},[0,6,2]%%%}+%%%{%%%{-576,[3,9,12]%%%},[0,6,1]%%%}+%%%{%%%{128,[3,9,14]%%%},[0,6,0]%%%}+%%%{%%%{252,[4,11,2]%%%},[0,5,5]%%%}+%%%{%%%{-1260,[4,11,4]%%%},[0,5,4]%%%}+%%%{%%%{2610,[4,11,6]%%%},[0,5,3]%%%}+%%%{%%%{-2862,[4,11,8]%%%},[0,5,2]%%%}+%%%{%%%{1728,[4,11,10]%%%},[0,5,1]%%%}+%%%{%%%{-480,[4,11,12]%%%},[0,5,0]%%%}+%%%{%%%{252,[5,13,2]%%%},[0,4,4]%%%}+%%%{%%%{-1176,[5,13,4]%%%},[0,4,3]%%%}+%%%{%%%{2166,[5,13,6]%%%},[0,4,2]%%%}+%%%{%%%{-1908,[5,13,8]%%%},[0,4,1]%%%}+%%%{%%%{696,[5,13,10]%%%},[0,4,0]%%%}+%%%{%%%{168,[6,15,2]%%%},[0,3,3]%%%}+%%%{%%%{-672,[6,15,4]%%%},[0,3,2]%%%}+%%%{%%%{954,[6,15,6]%%%},[0,3,1]%%%}+%%%{%%%{-490,[6,15,8]%%%},[0,3,0]%%%}+%%%{%%%{72,[7,17,2]%%%},[0,2,2]%%%}+%%%{%%%{-216,[7,17,4]%%%},[0,2,1]%%%}+%%%{%%%{174,[7,17,6]%%%},[0,2,0]%%%}+%%%{%%%{18,[8,19,2]%%%},[0,1,1]%%%}+%%%{%%%{-30,[8,19,4]%%%},[0,1,0]%%%}+%%%{%%%{2,[9,21,2]%%%},[0,0,0]%%%} / %%%{%%{poly1[%%%{-1,[1,1,4]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[6,0,0]%%%}+%%%{%%%{6,[2,3,4]%%%},[5,0,0]%%%}+%%%{%%{poly1[%%%{-3,[1,2,3]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[4,1,1]%%%}+%%%{%%{poly1[%%%{3,[1,2,5]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[4,1,0]%%%}+%%%{%%{poly1[%%%{-15,[2,4,3]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[4,0,0]%%%}+%%%{%%%{12,[2,4,3]%%%},[3,1,1]%%%}+%%%{%%%{-12,[2,4,5]%%%},[3,1,0]%%%}+%%%{%%%{20,[3,6,3]%%%},[3,0,0]%%%}+%%%{%%{poly1[%%%{-3,[1,3,2]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[2,2,2]%%%}+%%%{%%{poly1[%%%{6,[1,3,4]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[2,2,1]%%%}+%%%{%%{poly1[%%%{-3,[1,3,6]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[2,2,0]%%%}+%%%{%%{poly1[%%%{-18,[2,5,2]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[2,1,1]%%%}+%%%{%%{poly1[%%%{18,[2,5,4]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[2,1,0]%%%}+%%%{%%{poly1[%%%{-15,[3,7,2]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[2,0,0]%%%}+%%%{%%%{6,[2,5,2]%%%},[1,2,2]%%%}+%%%{%%%{-12,[2,5,4]%%%},[1,2,1]%%%}+%%%{%%%{6,[2,5,6]%%%},[1,2,0]%%%}+%%%{%%%{12,[3,7,2]%%%},[1,1,1]%%%}+%%%{%%%{-12,[3,7,4]%%%},[1,1,0]%%%}+%%%{%%%{6,[4,9,2]%%%},[1,0,0]%%%}+%%%{%%{poly1[%%%{-1,[1,4,1]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[0,3,3]%%%}+%%%{%%{poly1[%%%{3,[1,4,3]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[0,3,2]%%%}+%%%{%%{poly1[%%%{-3,[1,4,5]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[0,3,1]%%%}+%%%{%%{poly1[%%%{1,[1,4,7]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[0,3,0]%%%}+%%%{%%{poly1[%%%{-3,[2,6,1]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[0,2,2]%%%}+%%%{%%{poly1[%%%{6,[2,6,3]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[0,2,1]%%%}+%%%{%%{poly1[%%%{-3,[2,6,5]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[0,2,0]%%%}+%%%{%%{poly1[%%%{-3,[3,8,1]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[0,1,1]%%%}+%%%{%%{poly1[%%%{3,[3,8,3]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[0,1,0]%%%}+%%%{%%{poly1[%%%{-1,[4,10,1]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[0,0,0]%%%} Error: Bad Argument Value","F(-2)",0
1926,-2,0,0,0.000000," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)/(e*x+d)^4,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 0.58Unable to divide, perhaps due to rounding error%%%{%%%{1,[0,0,4]%%%},[8,8,8]%%%}+%%%{%%%{8,[1,2,4]%%%},[8,7,7]%%%}+%%%{%%%{-16,[1,2,6]%%%},[8,7,6]%%%}+%%%{%%%{28,[2,4,4]%%%},[8,6,6]%%%}+%%%{%%%{-96,[2,4,6]%%%},[8,6,5]%%%}+%%%{%%%{96,[2,4,8]%%%},[8,6,4]%%%}+%%%{%%%{56,[3,6,4]%%%},[8,5,5]%%%}+%%%{%%%{-240,[3,6,6]%%%},[8,5,4]%%%}+%%%{%%%{384,[3,6,8]%%%},[8,5,3]%%%}+%%%{%%%{-256,[3,6,10]%%%},[8,5,2]%%%}+%%%{%%%{70,[4,8,4]%%%},[8,4,4]%%%}+%%%{%%%{-320,[4,8,6]%%%},[8,4,3]%%%}+%%%{%%%{576,[4,8,8]%%%},[8,4,2]%%%}+%%%{%%%{-512,[4,8,10]%%%},[8,4,1]%%%}+%%%{%%%{256,[4,8,12]%%%},[8,4,0]%%%}+%%%{%%%{56,[5,10,4]%%%},[8,3,3]%%%}+%%%{%%%{-240,[5,10,6]%%%},[8,3,2]%%%}+%%%{%%%{384,[5,10,8]%%%},[8,3,1]%%%}+%%%{%%%{-256,[5,10,10]%%%},[8,3,0]%%%}+%%%{%%%{28,[6,12,4]%%%},[8,2,2]%%%}+%%%{%%%{-96,[6,12,6]%%%},[8,2,1]%%%}+%%%{%%%{96,[6,12,8]%%%},[8,2,0]%%%}+%%%{%%%{8,[7,14,4]%%%},[8,1,1]%%%}+%%%{%%%{-16,[7,14,6]%%%},[8,1,0]%%%}+%%%{%%%{1,[8,16,4]%%%},[8,0,0]%%%}+%%%{%%{[%%%{-8,[0,1,3]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[7,8,8]%%%}+%%%{%%{[%%%{-64,[1,3,3]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[7,7,7]%%%}+%%%{%%{[%%%{128,[1,3,5]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[7,7,6]%%%}+%%%{%%{[%%%{-224,[2,5,3]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[7,6,6]%%%}+%%%{%%{[%%%{768,[2,5,5]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[7,6,5]%%%}+%%%{%%{[%%%{-768,[2,5,7]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[7,6,4]%%%}+%%%{%%{[%%%{-448,[3,7,3]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[7,5,5]%%%}+%%%{%%{[%%%{1920,[3,7,5]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[7,5,4]%%%}+%%%{%%{[%%%{-3072,[3,7,7]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[7,5,3]%%%}+%%%{%%{[%%%{2048,[3,7,9]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[7,5,2]%%%}+%%%{%%{[%%%{-560,[4,9,3]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[7,4,4]%%%}+%%%{%%{[%%%{2560,[4,9,5]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[7,4,3]%%%}+%%%{%%{[%%%{-4608,[4,9,7]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[7,4,2]%%%}+%%%{%%{[%%%{4096,[4,9,9]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[7,4,1]%%%}+%%%{%%{[%%%{-2048,[4,9,11]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[7,4,0]%%%}+%%%{%%{[%%%{-448,[5,11,3]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[7,3,3]%%%}+%%%{%%{[%%%{1920,[5,11,5]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[7,3,2]%%%}+%%%{%%{[%%%{-3072,[5,11,7]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[7,3,1]%%%}+%%%{%%{[%%%{2048,[5,11,9]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[7,3,0]%%%}+%%%{%%{[%%%{-224,[6,13,3]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[7,2,2]%%%}+%%%{%%{[%%%{768,[6,13,5]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[7,2,1]%%%}+%%%{%%{[%%%{-768,[6,13,7]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[7,2,0]%%%}+%%%{%%{[%%%{-64,[7,15,3]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[7,1,1]%%%}+%%%{%%{[%%%{128,[7,15,5]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[7,1,0]%%%}+%%%{%%{[%%%{-8,[8,17,3]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[7,0,0]%%%}+%%%{%%%{4,[0,1,3]%%%},[6,9,9]%%%}+%%%{%%%{-4,[0,1,5]%%%},[6,9,8]%%%}+%%%{%%%{60,[1,3,3]%%%},[6,8,8]%%%}+%%%{%%%{-96,[1,3,5]%%%},[6,8,7]%%%}+%%%{%%%{64,[1,3,7]%%%},[6,8,6]%%%}+%%%{%%%{336,[2,5,3]%%%},[6,7,7]%%%}+%%%{%%%{-944,[2,5,5]%%%},[6,7,6]%%%}+%%%{%%%{768,[2,5,7]%%%},[6,7,5]%%%}+%%%{%%%{-384,[2,5,9]%%%},[6,7,4]%%%}+%%%{%%%{1008,[3,7,3]%%%},[6,6,6]%%%}+%%%{%%%{-3872,[3,7,5]%%%},[6,6,5]%%%}+%%%{%%%{5184,[3,7,7]%%%},[6,6,4]%%%}+%%%{%%%{-2560,[3,7,9]%%%},[6,6,3]%%%}+%%%{%%%{1024,[3,7,11]%%%},[6,6,2]%%%}+%%%{%%%{1848,[4,9,3]%%%},[6,5,5]%%%}+%%%{%%%{-8280,[4,9,5]%%%},[6,5,4]%%%}+%%%{%%%{14336,[4,9,7]%%%},[6,5,3]%%%}+%%%{%%%{-11520,[4,9,9]%%%},[6,5,2]%%%}+%%%{%%%{3072,[4,9,11]%%%},[6,5,1]%%%}+%%%{%%%{-1024,[4,9,13]%%%},[6,5,0]%%%}+%%%{%%%{2184,[5,11,3]%%%},[6,4,4]%%%}+%%%{%%%{-10144,[5,11,5]%%%},[6,4,3]%%%}+%%%{%%%{18624,[5,11,7]%%%},[6,4,2]%%%}+%%%{%%%{-16896,[5,11,9]%%%},[6,4,1]%%%}+%%%{%%%{8192,[5,11,11]%%%},[6,4,0]%%%}+%%%{%%%{1680,[6,13,3]%%%},[6,3,3]%%%}+%%%{%%%{-7216,[6,13,5]%%%},[6,3,2]%%%}+%%%{%%%{11520,[6,13,7]%%%},[6,3,1]%%%}+%%%{%%%{-7552,[6,13,9]%%%},[6,3,0]%%%}+%%%{%%%{816,[7,15,3]%%%},[6,2,2]%%%}+%%%{%%%{-2784,[7,15,5]%%%},[6,2,1]%%%}+%%%{%%%{2752,[7,15,7]%%%},[6,2,0]%%%}+%%%{%%%{228,[8,17,3]%%%},[6,1,1]%%%}+%%%{%%%{-452,[8,17,5]%%%},[6,1,0]%%%}+%%%{%%%{28,[9,19,3]%%%},[6,0,0]%%%}+%%%{%%{[%%%{-24,[0,2,2]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,9,9]%%%}+%%%{%%{[%%%{24,[0,2,4]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,9,8]%%%}+%%%{%%{[%%%{-248,[1,4,2]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,8,8]%%%}+%%%{%%{[%%%{576,[1,4,4]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,8,7]%%%}+%%%{%%{[%%%{-384,[1,4,6]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,8,6]%%%}+%%%{%%{[%%%{-1120,[2,6,2]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,7,7]%%%}+%%%{%%{[%%%{3872,[2,6,4]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,7,6]%%%}+%%%{%%{[%%%{-4608,[2,6,6]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,7,5]%%%}+%%%{%%{[%%%{2304,[2,6,8]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,7,4]%%%}+%%%{%%{[%%%{-2912,[3,8,2]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,6,6]%%%}+%%%{%%{[%%%{12480,[3,8,4]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,6,5]%%%}+%%%{%%{[%%%{-20352,[3,8,6]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,6,4]%%%}+%%%{%%{[%%%{15360,[3,8,8]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,6,3]%%%}+%%%{%%{[%%%{-6144,[3,8,10]%%%},0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/ %%%{%%%{1,[2,2,6]%%%},[8,0,0]%%%}+%%%{%%{poly1[%%%{-8,[2,3,5]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[7,0,0]%%%}+%%%{%%%{4,[2,3,5]%%%},[6,1,1]%%%}+%%%{%%%{-4,[2,3,7]%%%},[6,1,0]%%%}+%%%{%%%{28,[3,5,5]%%%},[6,0,0]%%%}+%%%{%%{poly1[%%%{-24,[2,4,4]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,1,1]%%%}+%%%{%%{poly1[%%%{24,[2,4,6]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,1,0]%%%}+%%%{%%{poly1[%%%{-56,[3,6,4]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,0,0]%%%}+%%%{%%%{6,[2,4,4]%%%},[4,2,2]%%%}+%%%{%%%{-12,[2,4,6]%%%},[4,2,1]%%%}+%%%{%%%{6,[2,4,8]%%%},[4,2,0]%%%}+%%%{%%%{60,[3,6,4]%%%},[4,1,1]%%%}+%%%{%%%{-60,[3,6,6]%%%},[4,1,0]%%%}+%%%{%%%{70,[4,8,4]%%%},[4,0,0]%%%}+%%%{%%{poly1[%%%{-24,[2,5,3]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,2,2]%%%}+%%%{%%{poly1[%%%{48,[2,5,5]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,2,1]%%%}+%%%{%%{poly1[%%%{-24,[2,5,7]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,2,0]%%%}+%%%{%%{poly1[%%%{-80,[3,7,3]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,1,1]%%%}+%%%{%%{poly1[%%%{80,[3,7,5]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,1,0]%%%}+%%%{%%{poly1[%%%{-56,[4,9,3]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,0,0]%%%}+%%%{%%%{4,[2,5,3]%%%},[2,3,3]%%%}+%%%{%%%{-12,[2,5,5]%%%},[2,3,2]%%%}+%%%{%%%{12,[2,5,7]%%%},[2,3,1]%%%}+%%%{%%%{-4,[2,5,9]%%%},[2,3,0]%%%}+%%%{%%%{36,[3,7,3]%%%},[2,2,2]%%%}+%%%{%%%{-72,[3,7,5]%%%},[2,2,1]%%%}+%%%{%%%{36,[3,7,7]%%%},[2,2,0]%%%}+%%%{%%%{60,[4,9,3]%%%},[2,1,1]%%%}+%%%{%%%{-60,[4,9,5]%%%},[2,1,0]%%%}+%%%{%%%{28,[5,11,3]%%%},[2,0,0]%%%}+%%%{%%{poly1[%%%{-8,[2,6,2]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,3,3]%%%}+%%%{%%{poly1[%%%{24,[2,6,4]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,3,2]%%%}+%%%{%%{poly1[%%%{-24,[2,6,6]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,3,1]%%%}+%%%{%%{poly1[%%%{8,[2,6,8]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,3,0]%%%}+%%%{%%{poly1[%%%{-24,[3,8,2]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,2,2]%%%}+%%%{%%{poly1[%%%{48,[3,8,4]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,2,1]%%%}+%%%{%%{poly1[%%%{-24,[3,8,6]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,2,0]%%%}+%%%{%%{poly1[%%%{-24,[4,10,2]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,1,1]%%%}+%%%{%%{poly1[%%%{24,[4,10,4]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,1,0]%%%}+%%%{%%{poly1[%%%{-8,[5,12,2]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,0,0]%%%}+%%%{%%%{1,[2,6,2]%%%},[0,4,4]%%%}+%%%{%%%{-4,[2,6,4]%%%},[0,4,3]%%%}+%%%{%%%{6,[2,6,6]%%%},[0,4,2]%%%}+%%%{%%%{-4,[2,6,8]%%%},[0,4,1]%%%}+%%%{%%%{1,[2,6,10]%%%},[0,4,0]%%%}+%%%{%%%{4,[3,8,2]%%%},[0,3,3]%%%}+%%%{%%%{-12,[3,8,4]%%%},[0,3,2]%%%}+%%%{%%%{12,[3,8,6]%%%},[0,3,1]%%%}+%%%{%%%{-4,[3,8,8]%%%},[0,3,0]%%%}+%%%{%%%{6,[4,10,2]%%%},[0,2,2]%%%}+%%%{%%%{-12,[4,10,4]%%%},[0,2,1]%%%}+%%%{%%%{6,[4,10,6]%%%},[0,2,0]%%%}+%%%{%%%{4,[5,12,2]%%%},[0,1,1]%%%}+%%%{%%%{-4,[5,12,4]%%%},[0,1,0]%%%}+%%%{%%%{1,[6,14,2]%%%},[0,0,0]%%%} Error: Bad Argument Value","F(-2)",0
1927,-2,0,0,0.000000," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)/(e*x+d)^5,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: exp(1)*(2*(-(exp(1)*x+d)^-1/exp(1)*(-(-6*c^4*d^7*sign((exp(1)*x+d)^-1)*exp(1)^6+18*a*c^3*d^5*sign((exp(1)*x+d)^-1)*exp(1)^8-18*a^2*c^2*d^3*sign((exp(1)*x+d)^-1)*exp(1)^10+6*a^3*c*d*sign((exp(1)*x+d)^-1)*exp(1)^12)/(-15*a^3*exp(1)^15+15*c^3*d^6*exp(1)^9-45*a*c^2*d^4*exp(1)^11+45*a^2*c*d^2*exp(1)^13)+(exp(1)*x+d)^-1/exp(1)*(-3*a^4*sign((exp(1)*x+d)^-1)*exp(1)^15-3*c^4*d^8*sign((exp(1)*x+d)^-1)*exp(1)^7+12*a*c^3*d^6*sign((exp(1)*x+d)^-1)*exp(1)^9-18*a^2*c^2*d^4*sign((exp(1)*x+d)^-1)*exp(1)^11+12*a^3*c*d^2*sign((exp(1)*x+d)^-1)*exp(1)^13)/(-15*a^3*exp(1)^15+15*c^3*d^6*exp(1)^9-45*a*c^2*d^4*exp(1)^11+45*a^2*c*d^2*exp(1)^13))-(-3*c^4*d^6*sign((exp(1)*x+d)^-1)*exp(1)^5+6*a*c^3*d^4*sign((exp(1)*x+d)^-1)*exp(1)^7-3*a^2*c^2*d^2*sign((exp(1)*x+d)^-1)*exp(1)^9)/(-15*a^3*exp(1)^15+15*c^3*d^6*exp(1)^9-45*a*c^2*d^4*exp(1)^11+45*a^2*c*d^2*exp(1)^13)-C_0*(30*a^2*exp(1)^11+30*c^2*d^4*exp(1)^7-60*a*c*d^2*exp(1)^9)/(-15*a^3*exp(1)^15+15*c^3*d^6*exp(1)^9-45*a*c^2*d^4*exp(1)^11+45*a^2*c*d^2*exp(1)^13))*sqrt(c*d*exp(1)+a*d*(-(exp(1)*x+d)^-1/exp(1))^2*exp(1)^5+a*(exp(1)*x+d)^-1/exp(1)*exp(1)^2*exp(2)-c*d^2*(exp(1)*x+d)^-1/exp(1)*exp(1)^2-a*d*(-(exp(1)*x+d)^-1/exp(1))^2*exp(1)^3*exp(2))-4*C_0*sqrt(a*d*exp(1)^3-a*d*exp(1)*exp(2))*ln(abs(a*sqrt(a*d*exp(1)^3-a*d*exp(1)*exp(2))*exp(2)-c*d^2*sqrt(a*d*exp(1)^3-a*d*exp(1)*exp(2))))/(2*a*d*exp(1)^4-2*a*d*exp(2)^2)+2*c^2*d^2*sqrt(c*d*exp(1))/(5*a*exp(1)^6-5*c*d^2*exp(1)^4)*sign((exp(1)*x+d)^-1))","F(-2)",0
1928,-2,0,0,0.000000," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)/(e*x+d)^6,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: 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x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^5*exp(2)^5+18250*c^4*d^12*exp(1)^3*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^5*exp(2)^4-33030*c^4*d^12*exp(1)^5*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^5*exp(2)^3+34760*c^4*d^12*exp(1)^7*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^5*exp(2)^2-23555*c^4*d^12*exp(1)^9*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^5*exp(2)+8040*c^4*d^12*exp(1)^11*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^5-4370*c^5*d^14*exp(1)*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^4*exp(2)^4+19830*c^5*d^14*exp(1)^3*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^4*exp(2)^3-37540*c^5*d^14*exp(1)^5*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^4*exp(2)^2+36350*c^5*d^14*exp(1)^7*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^4*exp(2)-14945*c^5*d^14*exp(1)^9*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^4-3700*c^6*d^16*exp(1)*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^3*exp(2)^3+15990*c^6*d^16*exp(1)^3*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^3*exp(2)^2-24970*c^6*d^16*exp(1)^5*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^3*exp(2)+14030*c^6*d^16*exp(1)^7*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^3-2380*c^7*d^18*exp(1)*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^2*exp(2)^2+7750*c^7*d^18*exp(1)^3*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^2*exp(2)-6720*c^7*d^18*exp(1)^5*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a^2-895*c^8*d^20*exp(1)*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a*exp(2)+1570*c^8*d^20*exp(1)^3*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*a-135*c^9*d^22*exp(1)*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)+15*d^5*sqrt(c*d*exp(1))*a^9*exp(2)^9-60*d^5*exp(1)^2*sqrt(c*d*exp(1))*a^9*exp(2)^8+90*d^5*exp(1)^4*sqrt(c*d*exp(1))*a^9*exp(2)^7-60*d^5*exp(1)^6*sqrt(c*d*exp(1))*a^9*exp(2)^6+15*d^5*exp(1)^8*sqrt(c*d*exp(1))*a^9*exp(2)^5+115*c*d^7*sqrt(c*d*exp(1))*a^8*exp(2)^8-510*c*d^7*exp(1)^2*sqrt(c*d*exp(1))*a^8*exp(2)^7+960*c*d^7*exp(1)^4*sqrt(c*d*exp(1))*a^8*exp(2)^6-970*c*d^7*exp(1)^6*sqrt(c*d*exp(1))*a^8*exp(2)^5+525*c*d^7*exp(1)^8*sqrt(c*d*exp(1))*a^8*exp(2)^4-120*c*d^7*exp(1)^10*sqrt(c*d*exp(1))*a^8*exp(2)^3+368*c^2*d^9*sqrt(c*d*exp(1))*a^7*exp(2)^7-1686*c^2*d^9*exp(1)^2*sqrt(c*d*exp(1))*a^7*exp(2)^6+3338*c^2*d^9*exp(1)^4*sqrt(c*d*exp(1))*a^7*exp(2)^5-3690*c^2*d^9*exp(1)^6*sqrt(c*d*exp(1))*a^7*exp(2)^4+2510*c^2*d^9*exp(1)^8*sqrt(c*d*exp(1))*a^7*exp(2)^3-1336*c^2*d^9*exp(1)^10*sqrt(c*d*exp(1))*a^7*exp(2)^2+752*c^2*d^9*exp(1)^12*sqrt(c*d*exp(1))*a^7*exp(2)-256*c^2*d^9*exp(1)^14*sqrt(c*d*exp(1))*a^7+680*c^3*d^11*sqrt(c*d*exp(1))*a^6*exp(2)^6-3230*c^3*d^11*exp(1)^2*sqrt(c*d*exp(1))*a^6*exp(2)^5+6800*c^3*d^11*exp(1)^4*sqrt(c*d*exp(1))*a^6*exp(2)^4-8500*c^3*d^11*exp(1)^6*sqrt(c*d*exp(1))*a^6*exp(2)^3+7090*c^3*d^11*exp(1)^8*sqrt(c*d*exp(1))*a^6*exp(2)^2-3880*c^3*d^11*exp(1)^10*sqrt(c*d*exp(1))*a^6*exp(2)+1040*c^3*d^11*exp(1)^12*sqrt(c*d*exp(1))*a^6+870*c^4*d^13*sqrt(c*d*exp(1))*a^5*exp(2)^5-4350*c^4*d^13*exp(1)^2*sqrt(c*d*exp(1))*a^5*exp(2)^4+9550*c^4*d^13*exp(1)^4*sqrt(c*d*exp(1))*a^5*exp(2)^3-11840*c^4*d^13*exp(1)^6*sqrt(c*d*exp(1))*a^5*exp(2)^2+8355*c^4*d^13*exp(1)^8*sqrt(c*d*exp(1))*a^5*exp(2)-2600*c^4*d^13*exp(1)^10*sqrt(c*d*exp(1))*a^5+870*c^5*d^15*sqrt(c*d*exp(1))*a^4*exp(2)^4-4330*c^5*d^15*exp(1)^2*sqrt(c*d*exp(1))*a^4*exp(2)^3+8720*c^5*d^15*exp(1)^4*sqrt(c*d*exp(1))*a^4*exp(2)^2-8450*c^5*d^15*exp(1)^6*sqrt(c*d*exp(1))*a^4*exp(2)+3265*c^5*d^15*exp(1)^8*sqrt(c*d*exp(1))*a^4+680*c^6*d^17*sqrt(c*d*exp(1))*a^3*exp(2)^3-2930*c^6*d^17*exp(1)^2*sqrt(c*d*exp(1))*a^3*exp(2)^2+4430*c^6*d^17*exp(1)^4*sqrt(c*d*exp(1))*a^3*exp(2)-2330*c^6*d^17*exp(1)^6*sqrt(c*d*exp(1))*a^3+368*c^7*d^19*sqrt(c*d*exp(1))*a^2*exp(2)^2-1146*c^7*d^19*exp(1)^2*sqrt(c*d*exp(1))*a^2*exp(2)+928*c^7*d^19*exp(1)^4*sqrt(c*d*exp(1))*a^2+115*c^8*d^21*sqrt(c*d*exp(1))*a*exp(2)-190*c^8*d^21*exp(1)^2*sqrt(c*d*exp(1))*a+15*c^9*d^23*sqrt(c*d*exp(1)))/(-1280*d^3*exp(1)^3*a^3*exp(2)^3+3840*d^3*exp(1)^5*a^3*exp(2)^2-3840*d^3*exp(1)^7*a^3*exp(2)+1280*d^3*exp(1)^9*a^3)/(-exp(1)*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^2+2*d*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)-d*a*exp(2)+d*exp(1)^2*a-c*d^3)^5+(3*a^5*exp(2)^5+9*c*d^2*a^4*exp(2)^4-24*c*d^2*exp(1)^2*a^4*exp(2)^3+6*c^2*d^4*a^3*exp(2)^3-24*c^2*d^4*exp(1)^2*a^3*exp(2)^2+48*c^2*d^4*exp(1)^4*a^3*exp(2)-6*c^3*d^6*a^2*exp(2)^2+24*c^3*d^6*exp(1)^2*a^2*exp(2)-48*c^3*d^6*exp(1)^4*a^2-9*c^4*d^8*a*exp(2)+24*c^4*d^8*exp(1)^2*a-3*c^5*d^10)/2/(128*d^3*exp(1)^2*a^3*exp(2)^3-384*d^3*exp(1)^4*a^3*exp(2)^2+384*d^3*exp(1)^6*a^3*exp(2)-128*d^3*exp(1)^8*a^3)/sqrt(-a*d*exp(1)^3+a*d*exp(1)*exp(2))*atan((-d*sqrt(c*d*exp(1))+(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*exp(1))/sqrt(-a*d*exp(1)^3+a*d*exp(1)*exp(2))))","F(-2)",0
1929,-2,0,0,0.000000," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)/(e*x+d)^7,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: 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exp(2)^4-86880*c^5*d^16*exp(1)^6*sqrt(c*d*exp(1))*a^6*exp(2)^3+148005*c^5*d^16*exp(1)^8*sqrt(c*d*exp(1))*a^6*exp(2)^2-119790*c^5*d^16*exp(1)^10*sqrt(c*d*exp(1))*a^6*exp(2)+38700*c^5*d^16*exp(1)^12*sqrt(c*d*exp(1))*a^6+2970*c^6*d^18*sqrt(c*d*exp(1))*a^5*exp(2)^5-28110*c^6*d^18*exp(1)^2*sqrt(c*d*exp(1))*a^5*exp(2)^4+99840*c^6*d^18*exp(1)^4*sqrt(c*d*exp(1))*a^5*exp(2)^3-175680*c^6*d^18*exp(1)^6*sqrt(c*d*exp(1))*a^5*exp(2)^2+156105*c^6*d^18*exp(1)^8*sqrt(c*d*exp(1))*a^5*exp(2)-55755*c^6*d^18*exp(1)^10*sqrt(c*d*exp(1))*a^5+6634*c^7*d^20*sqrt(c*d*exp(1))*a^4*exp(2)^4-41752*c^7*d^20*exp(1)^2*sqrt(c*d*exp(1))*a^4*exp(2)^3+101952*c^7*d^20*exp(1)^4*sqrt(c*d*exp(1))*a^4*exp(2)^2-114384*c^7*d^20*exp(1)^6*sqrt(c*d*exp(1))*a^4*exp(2)+49125*c^7*d^20*exp(1)^8*sqrt(c*d*exp(1))*a^4+5955*c^8*d^22*sqrt(c*d*exp(1))*a^3*exp(2)^3-28551*c^8*d^22*exp(1)^2*sqrt(c*d*exp(1))*a^3*exp(2)^2+47262*c^8*d^22*exp(1)^4*sqrt(c*d*exp(1))*a^3*exp(2)-26766*c^8*d^22*exp(1)^6*sqrt(c*d*exp(1))*a^3+3051*c^9*d^24*sqrt(c*d*exp(1))*a^2*exp(2)^2-10122*c^9*d^24*exp(1)^2*sqrt(c*d*exp(1))*a^2*exp(2)+8646*c^9*d^24*exp(1)^4*sqrt(c*d*exp(1))*a^2+865*c^10*d^26*sqrt(c*d*exp(1))*a*exp(2)-1495*c^10*d^26*exp(1)^2*sqrt(c*d*exp(1))*a+105*c^11*d^28*sqrt(c*d*exp(1)))/(-15360*d^4*exp(1)^3*a^4*exp(2)^4+61440*d^4*exp(1)^5*a^4*exp(2)^3-92160*d^4*exp(1)^7*a^4*exp(2)^2+61440*d^4*exp(1)^9*a^4*exp(2)-15360*d^4*exp(1)^11*a^4)/(-exp(1)*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^2+2*d*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)-d*a*exp(2)+d*exp(1)^2*a-c*d^3)^6+(7*a^6*exp(2)^6+18*c*d^2*a^5*exp(2)^5-60*c*d^2*exp(1)^2*a^5*exp(2)^4+9*c^2*d^4*a^4*exp(2)^4-48*c^2*d^4*exp(1)^2*a^4*exp(2)^3+144*c^2*d^4*exp(1)^4*a^4*exp(2)^2-4*c^3*d^6*a^3*exp(2)^3+24*c^3*d^6*exp(1)^2*a^3*exp(2)^2-96*c^3*d^6*exp(1)^4*a^3*exp(2)-64*c^3*d^6*exp(1)^6*a^3+9*c^4*d^8*a^2*exp(2)^2-48*c^4*d^8*exp(1)^2*a^2*exp(2)+144*c^4*d^8*exp(1)^4*a^2+18*c^5*d^10*a*exp(2)-60*c^5*d^10*exp(1)^2*a+7*c^6*d^12)/2/(512*d^4*exp(1)^2*a^4*exp(2)^4-2048*d^4*exp(1)^4*a^4*exp(2)^3+3072*d^4*exp(1)^6*a^4*exp(2)^2-2048*d^4*exp(1)^8*a^4*exp(2)+512*d^4*exp(1)^10*a^4)/sqrt(-a*d*exp(1)^3+a*d*exp(1)*exp(2))*atan((-d*sqrt(c*d*exp(1))+(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*exp(1))/sqrt(-a*d*exp(1)^3+a*d*exp(1)*exp(2))))","F(-2)",0
1930,-1,0,0,0.000000," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)/(e*x+d)^8,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1931,1,1026,0,0.802608," ","integrate((e*x+d)^4*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2),x, algorithm=""giac"")","\frac{1}{41287680} \, \sqrt{c d x^{2} e + c d^{2} x + a x e^{2} + a d e} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(2 \, {\left(4 \, {\left(14 \, {\left(16 \, {\left(18 \, c^{2} d^{2} x e^{6} + \frac{{\left(121 \, c^{11} d^{12} e^{14} + 41 \, a c^{10} d^{10} e^{16}\right)} e^{\left(-9\right)}}{c^{9} d^{9}}\right)} x + \frac{{\left(5503 \, c^{11} d^{13} e^{13} + 4482 \, a c^{10} d^{11} e^{15} + 383 \, a^{2} c^{9} d^{9} e^{17}\right)} e^{\left(-9\right)}}{c^{9} d^{9}}\right)} x + \frac{{\left(119055 \, c^{11} d^{14} e^{12} + 182129 \, a c^{10} d^{12} e^{14} + 37489 \, a^{2} c^{9} d^{10} e^{16} + 15 \, a^{3} c^{8} d^{8} e^{18}\right)} e^{\left(-9\right)}}{c^{9} d^{9}}\right)} x + \frac{{\left(424895 \, c^{11} d^{15} e^{11} + 1157740 \, a c^{10} d^{13} e^{13} + 448938 \, a^{2} c^{9} d^{11} e^{15} + 620 \, a^{3} c^{8} d^{9} e^{17} - 65 \, a^{4} c^{7} d^{7} e^{19}\right)} e^{\left(-9\right)}}{c^{9} d^{9}}\right)} x + \frac{{\left(419983 \, c^{11} d^{16} e^{10} + 2149035 \, a c^{10} d^{14} e^{12} + 1490630 \, a^{2} c^{9} d^{12} e^{14} + 5830 \, a^{3} c^{8} d^{10} e^{16} - 1365 \, a^{4} c^{7} d^{8} e^{18} + 143 \, a^{5} c^{6} d^{6} e^{20}\right)} e^{\left(-9\right)}}{c^{9} d^{9}}\right)} x + \frac{{\left(735993 \, c^{11} d^{17} e^{9} + 9023498 \, a c^{10} d^{15} e^{11} + 11825815 \, a^{2} c^{9} d^{13} e^{13} + 132300 \, a^{3} c^{8} d^{11} e^{15} - 52585 \, a^{4} c^{7} d^{9} e^{17} + 12298 \, a^{5} c^{6} d^{7} e^{19} - 1287 \, a^{6} c^{5} d^{5} e^{21}\right)} e^{\left(-9\right)}}{c^{9} d^{9}}\right)} x + \frac{{\left(3003 \, c^{11} d^{18} e^{8} + 4394937 \, a c^{10} d^{16} e^{10} + 13885683 \, a^{2} c^{9} d^{14} e^{12} + 508825 \, a^{3} c^{8} d^{12} e^{14} - 310375 \, a^{4} c^{7} d^{10} e^{16} + 123123 \, a^{5} c^{6} d^{8} e^{18} - 28743 \, a^{6} c^{5} d^{6} e^{20} + 3003 \, a^{7} c^{4} d^{4} e^{22}\right)} e^{\left(-9\right)}}{c^{9} d^{9}}\right)} x - \frac{{\left(15015 \, c^{11} d^{19} e^{7} - 144144 \, a c^{10} d^{17} e^{9} - 17075244 \, a^{2} c^{9} d^{15} e^{11} - 2878000 \, a^{3} c^{8} d^{13} e^{13} + 2579850 \, a^{4} c^{7} d^{11} e^{15} - 1567280 \, a^{5} c^{6} d^{9} e^{17} + 619476 \, a^{6} c^{5} d^{7} e^{19} - 144144 \, a^{7} c^{4} d^{5} e^{21} + 15015 \, a^{8} c^{3} d^{3} e^{23}\right)} e^{\left(-9\right)}}{c^{9} d^{9}}\right)} x + \frac{{\left(45045 \, c^{11} d^{20} e^{6} - 435435 \, a c^{10} d^{18} e^{8} + 1885884 \, a^{2} c^{9} d^{16} e^{10} + 6983100 \, a^{3} c^{8} d^{14} e^{12} - 9035650 \, a^{4} c^{7} d^{12} e^{14} + 8003710 \, a^{5} c^{6} d^{10} e^{16} - 4813380 \, a^{6} c^{5} d^{8} e^{18} + 1885884 \, a^{7} c^{4} d^{6} e^{20} - 435435 \, a^{8} c^{3} d^{4} e^{22} + 45045 \, a^{9} c^{2} d^{2} e^{24}\right)} e^{\left(-9\right)}}{c^{9} d^{9}}\right)} + \frac{143 \, {\left(c^{10} d^{20} - 10 \, a c^{9} d^{18} e^{2} + 45 \, a^{2} c^{8} d^{16} e^{4} - 120 \, a^{3} c^{7} d^{14} e^{6} + 210 \, a^{4} c^{6} d^{12} e^{8} - 252 \, a^{5} c^{5} d^{10} e^{10} + 210 \, a^{6} c^{4} d^{8} e^{12} - 120 \, a^{7} c^{3} d^{6} e^{14} + 45 \, a^{8} c^{2} d^{4} e^{16} - 10 \, a^{9} c d^{2} e^{18} + a^{10} e^{20}\right)} e^{\left(-\frac{7}{2}\right)} \log\left({\left| -c d^{2} - 2 \, {\left(\sqrt{c d} x e^{\frac{1}{2}} - \sqrt{c d x^{2} e + c d^{2} x + a x e^{2} + a d e}\right)} \sqrt{c d} e^{\frac{1}{2}} - a e^{2} \right|}\right)}{262144 \, \sqrt{c d} c^{7} d^{7}}"," ",0,"1/41287680*sqrt(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e)*(2*(4*(2*(8*(2*(4*(14*(16*(18*c^2*d^2*x*e^6 + (121*c^11*d^12*e^14 + 41*a*c^10*d^10*e^16)*e^(-9)/(c^9*d^9))*x + (5503*c^11*d^13*e^13 + 4482*a*c^10*d^11*e^15 + 383*a^2*c^9*d^9*e^17)*e^(-9)/(c^9*d^9))*x + (119055*c^11*d^14*e^12 + 182129*a*c^10*d^12*e^14 + 37489*a^2*c^9*d^10*e^16 + 15*a^3*c^8*d^8*e^18)*e^(-9)/(c^9*d^9))*x + (424895*c^11*d^15*e^11 + 1157740*a*c^10*d^13*e^13 + 448938*a^2*c^9*d^11*e^15 + 620*a^3*c^8*d^9*e^17 - 65*a^4*c^7*d^7*e^19)*e^(-9)/(c^9*d^9))*x + (419983*c^11*d^16*e^10 + 2149035*a*c^10*d^14*e^12 + 1490630*a^2*c^9*d^12*e^14 + 5830*a^3*c^8*d^10*e^16 - 1365*a^4*c^7*d^8*e^18 + 143*a^5*c^6*d^6*e^20)*e^(-9)/(c^9*d^9))*x + (735993*c^11*d^17*e^9 + 9023498*a*c^10*d^15*e^11 + 11825815*a^2*c^9*d^13*e^13 + 132300*a^3*c^8*d^11*e^15 - 52585*a^4*c^7*d^9*e^17 + 12298*a^5*c^6*d^7*e^19 - 1287*a^6*c^5*d^5*e^21)*e^(-9)/(c^9*d^9))*x + (3003*c^11*d^18*e^8 + 4394937*a*c^10*d^16*e^10 + 13885683*a^2*c^9*d^14*e^12 + 508825*a^3*c^8*d^12*e^14 - 310375*a^4*c^7*d^10*e^16 + 123123*a^5*c^6*d^8*e^18 - 28743*a^6*c^5*d^6*e^20 + 3003*a^7*c^4*d^4*e^22)*e^(-9)/(c^9*d^9))*x - (15015*c^11*d^19*e^7 - 144144*a*c^10*d^17*e^9 - 17075244*a^2*c^9*d^15*e^11 - 2878000*a^3*c^8*d^13*e^13 + 2579850*a^4*c^7*d^11*e^15 - 1567280*a^5*c^6*d^9*e^17 + 619476*a^6*c^5*d^7*e^19 - 144144*a^7*c^4*d^5*e^21 + 15015*a^8*c^3*d^3*e^23)*e^(-9)/(c^9*d^9))*x + (45045*c^11*d^20*e^6 - 435435*a*c^10*d^18*e^8 + 1885884*a^2*c^9*d^16*e^10 + 6983100*a^3*c^8*d^14*e^12 - 9035650*a^4*c^7*d^12*e^14 + 8003710*a^5*c^6*d^10*e^16 - 4813380*a^6*c^5*d^8*e^18 + 1885884*a^7*c^4*d^6*e^20 - 435435*a^8*c^3*d^4*e^22 + 45045*a^9*c^2*d^2*e^24)*e^(-9)/(c^9*d^9)) + 143/262144*(c^10*d^20 - 10*a*c^9*d^18*e^2 + 45*a^2*c^8*d^16*e^4 - 120*a^3*c^7*d^14*e^6 + 210*a^4*c^6*d^12*e^8 - 252*a^5*c^5*d^10*e^10 + 210*a^6*c^4*d^8*e^12 - 120*a^7*c^3*d^6*e^14 + 45*a^8*c^2*d^4*e^16 - 10*a^9*c*d^2*e^18 + a^10*e^20)*e^(-7/2)*log(abs(-c*d^2 - 2*(sqrt(c*d)*x*e^(1/2) - sqrt(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e))*sqrt(c*d)*e^(1/2) - a*e^2))/(sqrt(c*d)*c^7*d^7)","B",0
1932,1,875,0,0.685887," ","integrate((e*x+d)^3*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2),x, algorithm=""giac"")","\frac{1}{2064384} \, \sqrt{c d x^{2} e + c d^{2} x + a x e^{2} + a d e} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(2 \, {\left(4 \, {\left(14 \, {\left(16 \, c^{2} d^{2} x e^{5} + \frac{{\left(91 \, c^{10} d^{11} e^{12} + 37 \, a c^{9} d^{9} e^{14}\right)} e^{\left(-8\right)}}{c^{8} d^{8}}\right)} x + \frac{{\left(2955 \, c^{10} d^{12} e^{11} + 3008 \, a c^{9} d^{10} e^{13} + 309 \, a^{2} c^{8} d^{8} e^{15}\right)} e^{\left(-8\right)}}{c^{8} d^{8}}\right)} x + \frac{{\left(14075 \, c^{10} d^{13} e^{10} + 28695 \, a c^{9} d^{11} e^{12} + 7401 \, a^{2} c^{8} d^{9} e^{14} + 5 \, a^{3} c^{7} d^{7} e^{16}\right)} e^{\left(-8\right)}}{c^{8} d^{8}}\right)} x + \frac{{\left(17419 \, c^{10} d^{14} e^{9} + 71074 \, a c^{9} d^{12} e^{11} + 36864 \, a^{2} c^{8} d^{10} e^{13} + 94 \, a^{3} c^{7} d^{8} e^{15} - 11 \, a^{4} c^{6} d^{6} e^{17}\right)} e^{\left(-8\right)}}{c^{8} d^{8}}\right)} x + \frac{{\left(36765 \, c^{10} d^{15} e^{8} + 373583 \, a c^{9} d^{13} e^{10} + 390018 \, a^{2} c^{8} d^{11} e^{12} + 3198 \, a^{3} c^{7} d^{9} e^{14} - 847 \, a^{4} c^{6} d^{7} e^{16} + 99 \, a^{5} c^{5} d^{5} e^{18}\right)} e^{\left(-8\right)}}{c^{8} d^{8}}\right)} x + \frac{{\left(231 \, c^{10} d^{16} e^{7} + 219204 \, a c^{9} d^{14} e^{9} + 572739 \, a^{2} c^{8} d^{12} e^{11} + 16384 \, a^{3} c^{7} d^{10} e^{13} - 7491 \, a^{4} c^{6} d^{8} e^{15} + 1980 \, a^{5} c^{5} d^{6} e^{17} - 231 \, a^{6} c^{4} d^{4} e^{19}\right)} e^{\left(-8\right)}}{c^{8} d^{8}}\right)} x - \frac{{\left(1155 \, c^{10} d^{17} e^{6} - 9933 \, a c^{9} d^{15} e^{8} - 847017 \, a^{2} c^{8} d^{13} e^{10} - 115609 \, a^{3} c^{7} d^{11} e^{12} + 82841 \, a^{4} c^{6} d^{9} e^{14} - 37719 \, a^{5} c^{5} d^{7} e^{16} + 9933 \, a^{6} c^{4} d^{5} e^{18} - 1155 \, a^{7} c^{3} d^{3} e^{20}\right)} e^{\left(-8\right)}}{c^{8} d^{8}}\right)} x + \frac{{\left(3465 \, c^{10} d^{18} e^{5} - 30030 \, a c^{9} d^{16} e^{7} + 115038 \, a^{2} c^{8} d^{14} e^{9} + 334602 \, a^{3} c^{7} d^{12} e^{11} - 360448 \, a^{4} c^{6} d^{10} e^{13} + 255222 \, a^{5} c^{5} d^{8} e^{15} - 115038 \, a^{6} c^{4} d^{6} e^{17} + 30030 \, a^{7} c^{3} d^{4} e^{19} - 3465 \, a^{8} c^{2} d^{2} e^{21}\right)} e^{\left(-8\right)}}{c^{8} d^{8}}\right)} + \frac{55 \, {\left(c^{9} d^{18} - 9 \, a c^{8} d^{16} e^{2} + 36 \, a^{2} c^{7} d^{14} e^{4} - 84 \, a^{3} c^{6} d^{12} e^{6} + 126 \, a^{4} c^{5} d^{10} e^{8} - 126 \, a^{5} c^{4} d^{8} e^{10} + 84 \, a^{6} c^{3} d^{6} e^{12} - 36 \, a^{7} c^{2} d^{4} e^{14} + 9 \, a^{8} c d^{2} e^{16} - a^{9} e^{18}\right)} e^{\left(-\frac{7}{2}\right)} \log\left({\left| -c d^{2} - 2 \, {\left(\sqrt{c d} x e^{\frac{1}{2}} - \sqrt{c d x^{2} e + c d^{2} x + a x e^{2} + a d e}\right)} \sqrt{c d} e^{\frac{1}{2}} - a e^{2} \right|}\right)}{65536 \, \sqrt{c d} c^{6} d^{6}}"," ",0,"1/2064384*sqrt(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e)*(2*(4*(2*(8*(2*(4*(14*(16*c^2*d^2*x*e^5 + (91*c^10*d^11*e^12 + 37*a*c^9*d^9*e^14)*e^(-8)/(c^8*d^8))*x + (2955*c^10*d^12*e^11 + 3008*a*c^9*d^10*e^13 + 309*a^2*c^8*d^8*e^15)*e^(-8)/(c^8*d^8))*x + (14075*c^10*d^13*e^10 + 28695*a*c^9*d^11*e^12 + 7401*a^2*c^8*d^9*e^14 + 5*a^3*c^7*d^7*e^16)*e^(-8)/(c^8*d^8))*x + (17419*c^10*d^14*e^9 + 71074*a*c^9*d^12*e^11 + 36864*a^2*c^8*d^10*e^13 + 94*a^3*c^7*d^8*e^15 - 11*a^4*c^6*d^6*e^17)*e^(-8)/(c^8*d^8))*x + (36765*c^10*d^15*e^8 + 373583*a*c^9*d^13*e^10 + 390018*a^2*c^8*d^11*e^12 + 3198*a^3*c^7*d^9*e^14 - 847*a^4*c^6*d^7*e^16 + 99*a^5*c^5*d^5*e^18)*e^(-8)/(c^8*d^8))*x + (231*c^10*d^16*e^7 + 219204*a*c^9*d^14*e^9 + 572739*a^2*c^8*d^12*e^11 + 16384*a^3*c^7*d^10*e^13 - 7491*a^4*c^6*d^8*e^15 + 1980*a^5*c^5*d^6*e^17 - 231*a^6*c^4*d^4*e^19)*e^(-8)/(c^8*d^8))*x - (1155*c^10*d^17*e^6 - 9933*a*c^9*d^15*e^8 - 847017*a^2*c^8*d^13*e^10 - 115609*a^3*c^7*d^11*e^12 + 82841*a^4*c^6*d^9*e^14 - 37719*a^5*c^5*d^7*e^16 + 9933*a^6*c^4*d^5*e^18 - 1155*a^7*c^3*d^3*e^20)*e^(-8)/(c^8*d^8))*x + (3465*c^10*d^18*e^5 - 30030*a*c^9*d^16*e^7 + 115038*a^2*c^8*d^14*e^9 + 334602*a^3*c^7*d^12*e^11 - 360448*a^4*c^6*d^10*e^13 + 255222*a^5*c^5*d^8*e^15 - 115038*a^6*c^4*d^6*e^17 + 30030*a^7*c^3*d^4*e^19 - 3465*a^8*c^2*d^2*e^21)*e^(-8)/(c^8*d^8)) + 55/65536*(c^9*d^18 - 9*a*c^8*d^16*e^2 + 36*a^2*c^7*d^14*e^4 - 84*a^3*c^6*d^12*e^6 + 126*a^4*c^5*d^10*e^8 - 126*a^5*c^4*d^8*e^10 + 84*a^6*c^3*d^6*e^12 - 36*a^7*c^2*d^4*e^14 + 9*a^8*c*d^2*e^16 - a^9*e^18)*e^(-7/2)*log(abs(-c*d^2 - 2*(sqrt(c*d)*x*e^(1/2) - sqrt(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e))*sqrt(c*d)*e^(1/2) - a*e^2))/(sqrt(c*d)*c^6*d^6)","B",0
1933,1,736,0,0.679236," ","integrate((e*x+d)^2*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2),x, algorithm=""giac"")","\frac{1}{114688} \, \sqrt{c d x^{2} e + c d^{2} x + a x e^{2} + a d e} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(2 \, {\left(4 \, {\left(14 \, c^{2} d^{2} x e^{4} + \frac{{\left(65 \, c^{9} d^{10} e^{10} + 33 \, a c^{8} d^{8} e^{12}\right)} e^{\left(-7\right)}}{c^{7} d^{7}}\right)} x + \frac{3 \, {\left(155 \, c^{9} d^{11} e^{9} + 210 \, a c^{8} d^{9} e^{11} + 27 \, a^{2} c^{7} d^{7} e^{13}\right)} e^{\left(-7\right)}}{c^{7} d^{7}}\right)} x + \frac{{\left(769 \, c^{9} d^{12} e^{8} + 2343 \, a c^{8} d^{10} e^{10} + 807 \, a^{2} c^{7} d^{8} e^{12} + a^{3} c^{6} d^{6} e^{14}\right)} e^{\left(-7\right)}}{c^{7} d^{7}}\right)} x + \frac{{\left(2039 \, c^{9} d^{13} e^{7} + 16452 \, a c^{8} d^{11} e^{9} + 12810 \, a^{2} c^{7} d^{9} e^{11} + 68 \, a^{3} c^{6} d^{7} e^{13} - 9 \, a^{4} c^{5} d^{5} e^{15}\right)} e^{\left(-7\right)}}{c^{7} d^{7}}\right)} x + \frac{3 \, {\left(7 \, c^{9} d^{14} e^{6} + 4043 \, a c^{8} d^{12} e^{8} + 8366 \, a^{2} c^{7} d^{10} e^{10} + 174 \, a^{3} c^{6} d^{8} e^{12} - 53 \, a^{4} c^{5} d^{6} e^{14} + 7 \, a^{5} c^{4} d^{4} e^{16}\right)} e^{\left(-7\right)}}{c^{7} d^{7}}\right)} x - \frac{{\left(105 \, c^{9} d^{15} e^{5} - 798 \, a c^{8} d^{13} e^{7} - 46521 \, a^{2} c^{7} d^{11} e^{9} - 4900 \, a^{3} c^{6} d^{9} e^{11} + 2631 \, a^{4} c^{5} d^{7} e^{13} - 798 \, a^{5} c^{4} d^{5} e^{15} + 105 \, a^{6} c^{3} d^{3} e^{17}\right)} e^{\left(-7\right)}}{c^{7} d^{7}}\right)} x + \frac{{\left(315 \, c^{9} d^{16} e^{4} - 2415 \, a c^{8} d^{14} e^{6} + 8043 \, a^{2} c^{7} d^{12} e^{8} + 17609 \, a^{3} c^{6} d^{10} e^{10} - 15159 \, a^{4} c^{5} d^{8} e^{12} + 8043 \, a^{5} c^{4} d^{6} e^{14} - 2415 \, a^{6} c^{3} d^{4} e^{16} + 315 \, a^{7} c^{2} d^{2} e^{18}\right)} e^{\left(-7\right)}}{c^{7} d^{7}}\right)} + \frac{45 \, {\left(c^{8} d^{16} - 8 \, a c^{7} d^{14} e^{2} + 28 \, a^{2} c^{6} d^{12} e^{4} - 56 \, a^{3} c^{5} d^{10} e^{6} + 70 \, a^{4} c^{4} d^{8} e^{8} - 56 \, a^{5} c^{3} d^{6} e^{10} + 28 \, a^{6} c^{2} d^{4} e^{12} - 8 \, a^{7} c d^{2} e^{14} + a^{8} e^{16}\right)} e^{\left(-\frac{7}{2}\right)} \log\left({\left| -c d^{2} - 2 \, {\left(\sqrt{c d} x e^{\frac{1}{2}} - \sqrt{c d x^{2} e + c d^{2} x + a x e^{2} + a d e}\right)} \sqrt{c d} e^{\frac{1}{2}} - a e^{2} \right|}\right)}{32768 \, \sqrt{c d} c^{5} d^{5}}"," ",0,"1/114688*sqrt(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e)*(2*(4*(2*(8*(2*(4*(14*c^2*d^2*x*e^4 + (65*c^9*d^10*e^10 + 33*a*c^8*d^8*e^12)*e^(-7)/(c^7*d^7))*x + 3*(155*c^9*d^11*e^9 + 210*a*c^8*d^9*e^11 + 27*a^2*c^7*d^7*e^13)*e^(-7)/(c^7*d^7))*x + (769*c^9*d^12*e^8 + 2343*a*c^8*d^10*e^10 + 807*a^2*c^7*d^8*e^12 + a^3*c^6*d^6*e^14)*e^(-7)/(c^7*d^7))*x + (2039*c^9*d^13*e^7 + 16452*a*c^8*d^11*e^9 + 12810*a^2*c^7*d^9*e^11 + 68*a^3*c^6*d^7*e^13 - 9*a^4*c^5*d^5*e^15)*e^(-7)/(c^7*d^7))*x + 3*(7*c^9*d^14*e^6 + 4043*a*c^8*d^12*e^8 + 8366*a^2*c^7*d^10*e^10 + 174*a^3*c^6*d^8*e^12 - 53*a^4*c^5*d^6*e^14 + 7*a^5*c^4*d^4*e^16)*e^(-7)/(c^7*d^7))*x - (105*c^9*d^15*e^5 - 798*a*c^8*d^13*e^7 - 46521*a^2*c^7*d^11*e^9 - 4900*a^3*c^6*d^9*e^11 + 2631*a^4*c^5*d^7*e^13 - 798*a^5*c^4*d^5*e^15 + 105*a^6*c^3*d^3*e^17)*e^(-7)/(c^7*d^7))*x + (315*c^9*d^16*e^4 - 2415*a*c^8*d^14*e^6 + 8043*a^2*c^7*d^12*e^8 + 17609*a^3*c^6*d^10*e^10 - 15159*a^4*c^5*d^8*e^12 + 8043*a^5*c^4*d^6*e^14 - 2415*a^6*c^3*d^4*e^16 + 315*a^7*c^2*d^2*e^18)*e^(-7)/(c^7*d^7)) + 45/32768*(c^8*d^16 - 8*a*c^7*d^14*e^2 + 28*a^2*c^6*d^12*e^4 - 56*a^3*c^5*d^10*e^6 + 70*a^4*c^4*d^8*e^8 - 56*a^5*c^3*d^6*e^10 + 28*a^6*c^2*d^4*e^12 - 8*a^7*c*d^2*e^14 + a^8*e^16)*e^(-7/2)*log(abs(-c*d^2 - 2*(sqrt(c*d)*x*e^(1/2) - sqrt(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e))*sqrt(c*d)*e^(1/2) - a*e^2))/(sqrt(c*d)*c^5*d^5)","A",0
1934,1,610,0,0.598013," ","integrate((e*x+d)*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2),x, algorithm=""giac"")","\frac{1}{21504} \, \sqrt{c d x^{2} e + c d^{2} x + a x e^{2} + a d e} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(2 \, {\left(12 \, c^{2} d^{2} x e^{3} + \frac{{\left(43 \, c^{8} d^{9} e^{8} + 29 \, a c^{7} d^{7} e^{10}\right)} e^{\left(-6\right)}}{c^{6} d^{6}}\right)} x + \frac{{\left(107 \, c^{8} d^{10} e^{7} + 216 \, a c^{7} d^{8} e^{9} + 37 \, a^{2} c^{6} d^{6} e^{11}\right)} e^{\left(-6\right)}}{c^{6} d^{6}}\right)} x + \frac{{\left(381 \, c^{8} d^{11} e^{6} + 2281 \, a c^{7} d^{9} e^{8} + 1175 \, a^{2} c^{6} d^{7} e^{10} + 3 \, a^{3} c^{5} d^{5} e^{12}\right)} e^{\left(-6\right)}}{c^{6} d^{6}}\right)} x + \frac{{\left(7 \, c^{8} d^{12} e^{5} + 2258 \, a c^{7} d^{10} e^{7} + 3456 \, a^{2} c^{6} d^{8} e^{9} + 46 \, a^{3} c^{5} d^{6} e^{11} - 7 \, a^{4} c^{4} d^{4} e^{13}\right)} e^{\left(-6\right)}}{c^{6} d^{6}}\right)} x - \frac{{\left(35 \, c^{8} d^{13} e^{4} - 231 \, a c^{7} d^{11} e^{6} - 8570 \, a^{2} c^{6} d^{9} e^{8} - 646 \, a^{3} c^{5} d^{7} e^{10} + 231 \, a^{4} c^{4} d^{5} e^{12} - 35 \, a^{5} c^{3} d^{3} e^{14}\right)} e^{\left(-6\right)}}{c^{6} d^{6}}\right)} x + \frac{{\left(105 \, c^{8} d^{14} e^{3} - 700 \, a c^{7} d^{12} e^{5} + 1981 \, a^{2} c^{6} d^{10} e^{7} + 3072 \, a^{3} c^{5} d^{8} e^{9} - 1981 \, a^{4} c^{4} d^{6} e^{11} + 700 \, a^{5} c^{3} d^{4} e^{13} - 105 \, a^{6} c^{2} d^{2} e^{15}\right)} e^{\left(-6\right)}}{c^{6} d^{6}}\right)} + \frac{5 \, {\left(c^{7} d^{14} - 7 \, a c^{6} d^{12} e^{2} + 21 \, a^{2} c^{5} d^{10} e^{4} - 35 \, a^{3} c^{4} d^{8} e^{6} + 35 \, a^{4} c^{3} d^{6} e^{8} - 21 \, a^{5} c^{2} d^{4} e^{10} + 7 \, a^{6} c d^{2} e^{12} - a^{7} e^{14}\right)} e^{\left(-\frac{7}{2}\right)} \log\left({\left| -c d^{2} - 2 \, {\left(\sqrt{c d} x e^{\frac{1}{2}} - \sqrt{c d x^{2} e + c d^{2} x + a x e^{2} + a d e}\right)} \sqrt{c d} e^{\frac{1}{2}} - a e^{2} \right|}\right)}{2048 \, \sqrt{c d} c^{4} d^{4}}"," ",0,"1/21504*sqrt(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e)*(2*(4*(2*(8*(2*(12*c^2*d^2*x*e^3 + (43*c^8*d^9*e^8 + 29*a*c^7*d^7*e^10)*e^(-6)/(c^6*d^6))*x + (107*c^8*d^10*e^7 + 216*a*c^7*d^8*e^9 + 37*a^2*c^6*d^6*e^11)*e^(-6)/(c^6*d^6))*x + (381*c^8*d^11*e^6 + 2281*a*c^7*d^9*e^8 + 1175*a^2*c^6*d^7*e^10 + 3*a^3*c^5*d^5*e^12)*e^(-6)/(c^6*d^6))*x + (7*c^8*d^12*e^5 + 2258*a*c^7*d^10*e^7 + 3456*a^2*c^6*d^8*e^9 + 46*a^3*c^5*d^6*e^11 - 7*a^4*c^4*d^4*e^13)*e^(-6)/(c^6*d^6))*x - (35*c^8*d^13*e^4 - 231*a*c^7*d^11*e^6 - 8570*a^2*c^6*d^9*e^8 - 646*a^3*c^5*d^7*e^10 + 231*a^4*c^4*d^5*e^12 - 35*a^5*c^3*d^3*e^14)*e^(-6)/(c^6*d^6))*x + (105*c^8*d^14*e^3 - 700*a*c^7*d^12*e^5 + 1981*a^2*c^6*d^10*e^7 + 3072*a^3*c^5*d^8*e^9 - 1981*a^4*c^4*d^6*e^11 + 700*a^5*c^3*d^4*e^13 - 105*a^6*c^2*d^2*e^15)*e^(-6)/(c^6*d^6)) + 5/2048*(c^7*d^14 - 7*a*c^6*d^12*e^2 + 21*a^2*c^5*d^10*e^4 - 35*a^3*c^4*d^8*e^6 + 35*a^4*c^3*d^6*e^8 - 21*a^5*c^2*d^4*e^10 + 7*a^6*c*d^2*e^12 - a^7*e^14)*e^(-7/2)*log(abs(-c*d^2 - 2*(sqrt(c*d)*x*e^(1/2) - sqrt(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e))*sqrt(c*d)*e^(1/2) - a*e^2))/(sqrt(c*d)*c^4*d^4)","A",0
1935,1,493,0,0.553927," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2),x, algorithm=""giac"")","\frac{1}{1536} \, \sqrt{c d x^{2} e + c d^{2} x + a x e^{2} + a d e} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(2 \, c^{2} d^{2} x e^{2} + \frac{5 \, {\left(c^{7} d^{8} e^{6} + a c^{6} d^{6} e^{8}\right)} e^{\left(-5\right)}}{c^{5} d^{5}}\right)} x + \frac{{\left(27 \, c^{7} d^{9} e^{5} + 106 \, a c^{6} d^{7} e^{7} + 27 \, a^{2} c^{5} d^{5} e^{9}\right)} e^{\left(-5\right)}}{c^{5} d^{5}}\right)} x + \frac{{\left(c^{7} d^{10} e^{4} + 159 \, a c^{6} d^{8} e^{6} + 159 \, a^{2} c^{5} d^{6} e^{8} + a^{3} c^{4} d^{4} e^{10}\right)} e^{\left(-5\right)}}{c^{5} d^{5}}\right)} x - \frac{{\left(5 \, c^{7} d^{11} e^{3} - 28 \, a c^{6} d^{9} e^{5} - 594 \, a^{2} c^{5} d^{7} e^{7} - 28 \, a^{3} c^{4} d^{5} e^{9} + 5 \, a^{4} c^{3} d^{3} e^{11}\right)} e^{\left(-5\right)}}{c^{5} d^{5}}\right)} x + \frac{{\left(15 \, c^{7} d^{12} e^{2} - 85 \, a c^{6} d^{10} e^{4} + 198 \, a^{2} c^{5} d^{8} e^{6} + 198 \, a^{3} c^{4} d^{6} e^{8} - 85 \, a^{4} c^{3} d^{4} e^{10} + 15 \, a^{5} c^{2} d^{2} e^{12}\right)} e^{\left(-5\right)}}{c^{5} d^{5}}\right)} + \frac{5 \, {\left(c^{6} d^{12} - 6 \, a c^{5} d^{10} e^{2} + 15 \, a^{2} c^{4} d^{8} e^{4} - 20 \, a^{3} c^{3} d^{6} e^{6} + 15 \, a^{4} c^{2} d^{4} e^{8} - 6 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}\right)} e^{\left(-\frac{7}{2}\right)} \log\left({\left| -c d^{2} - 2 \, {\left(\sqrt{c d} x e^{\frac{1}{2}} - \sqrt{c d x^{2} e + c d^{2} x + a x e^{2} + a d e}\right)} \sqrt{c d} e^{\frac{1}{2}} - a e^{2} \right|}\right)}{1024 \, \sqrt{c d} c^{3} d^{3}}"," ",0,"1/1536*sqrt(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e)*(2*(4*(2*(8*(2*c^2*d^2*x*e^2 + 5*(c^7*d^8*e^6 + a*c^6*d^6*e^8)*e^(-5)/(c^5*d^5))*x + (27*c^7*d^9*e^5 + 106*a*c^6*d^7*e^7 + 27*a^2*c^5*d^5*e^9)*e^(-5)/(c^5*d^5))*x + (c^7*d^10*e^4 + 159*a*c^6*d^8*e^6 + 159*a^2*c^5*d^6*e^8 + a^3*c^4*d^4*e^10)*e^(-5)/(c^5*d^5))*x - (5*c^7*d^11*e^3 - 28*a*c^6*d^9*e^5 - 594*a^2*c^5*d^7*e^7 - 28*a^3*c^4*d^5*e^9 + 5*a^4*c^3*d^3*e^11)*e^(-5)/(c^5*d^5))*x + (15*c^7*d^12*e^2 - 85*a*c^6*d^10*e^4 + 198*a^2*c^5*d^8*e^6 + 198*a^3*c^4*d^6*e^8 - 85*a^4*c^3*d^4*e^10 + 15*a^5*c^2*d^2*e^12)*e^(-5)/(c^5*d^5)) + 5/1024*(c^6*d^12 - 6*a*c^5*d^10*e^2 + 15*a^2*c^4*d^8*e^4 - 20*a^3*c^3*d^6*e^6 + 15*a^4*c^2*d^4*e^8 - 6*a^5*c*d^2*e^10 + a^6*e^12)*e^(-7/2)*log(abs(-c*d^2 - 2*(sqrt(c*d)*x*e^(1/2) - sqrt(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e))*sqrt(c*d)*e^(1/2) - a*e^2))/(sqrt(c*d)*c^3*d^3)","A",0
1936,-2,0,0,0.000000," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/(e*x+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Evaluation time: 0.44Error: Bad Argument Type","F(-2)",0
1937,-1,0,0,0.000000," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/(e*x+d)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1938,-2,0,0,0.000000," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/(e*x+d)^3,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 0.61Unable to divide, perhaps due to rounding error%%%{%%%{16,[0,0,6]%%%},[6,6,6]%%%}+%%%{%%%{96,[1,2,6]%%%},[6,5,5]%%%}+%%%{%%%{-192,[1,2,8]%%%},[6,5,4]%%%}+%%%{%%%{240,[2,4,6]%%%},[6,4,4]%%%}+%%%{%%%{-768,[2,4,8]%%%},[6,4,3]%%%}+%%%{%%%{768,[2,4,10]%%%},[6,4,2]%%%}+%%%{%%%{320,[3,6,6]%%%},[6,3,3]%%%}+%%%{%%%{-1152,[3,6,8]%%%},[6,3,2]%%%}+%%%{%%%{1536,[3,6,10]%%%},[6,3,1]%%%}+%%%{%%%{-1024,[3,6,12]%%%},[6,3,0]%%%}+%%%{%%%{240,[4,8,6]%%%},[6,2,2]%%%}+%%%{%%%{-768,[4,8,8]%%%},[6,2,1]%%%}+%%%{%%%{768,[4,8,10]%%%},[6,2,0]%%%}+%%%{%%%{96,[5,10,6]%%%},[6,1,1]%%%}+%%%{%%%{-192,[5,10,8]%%%},[6,1,0]%%%}+%%%{%%%{16,[6,12,6]%%%},[6,0,0]%%%}+%%%{%%{[%%%{-96,[0,1,5]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,6,6]%%%}+%%%{%%{[%%%{-576,[1,3,5]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,5,5]%%%}+%%%{%%{[%%%{1152,[1,3,7]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,5,4]%%%}+%%%{%%{[%%%{-1440,[2,5,5]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,4,4]%%%}+%%%{%%{[%%%{4608,[2,5,7]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,4,3]%%%}+%%%{%%{[%%%{-4608,[2,5,9]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,4,2]%%%}+%%%{%%{[%%%{-1920,[3,7,5]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,3,3]%%%}+%%%{%%{[%%%{6912,[3,7,7]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,3,2]%%%}+%%%{%%{[%%%{-9216,[3,7,9]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,3,1]%%%}+%%%{%%{[%%%{6144,[3,7,11]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,3,0]%%%}+%%%{%%{[%%%{-1440,[4,9,5]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,2,2]%%%}+%%%{%%{[%%%{4608,[4,9,7]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,2,1]%%%}+%%%{%%{[%%%{-4608,[4,9,9]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,2,0]%%%}+%%%{%%{[%%%{-576,[5,11,5]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,1,1]%%%}+%%%{%%{[%%%{1152,[5,11,7]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,1,0]%%%}+%%%{%%{[%%%{-96,[6,13,5]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,0,0]%%%}+%%%{%%%{48,[0,1,5]%%%},[4,7,7]%%%}+%%%{%%%{-48,[0,1,7]%%%},[4,7,6]%%%}+%%%{%%%{528,[1,3,5]%%%},[4,6,6]%%%}+%%%{%%%{-864,[1,3,7]%%%},[4,6,5]%%%}+%%%{%%%{576,[1,3,9]%%%},[4,6,4]%%%}+%%%{%%%{2160,[2,5,5]%%%},[4,5,5]%%%}+%%%{%%%{-5904,[2,5,7]%%%},[4,5,4]%%%}+%%%{%%%{4608,[2,5,9]%%%},[4,5,3]%%%}+%%%{%%%{-2304,[2,5,11]%%%},[4,5,2]%%%}+%%%{%%%{4560,[3,7,5]%%%},[4,4,4]%%%}+%%%{%%%{-15936,[3,7,7]%%%},[4,4,3]%%%}+%%%{%%%{19584,[3,7,9]%%%},[4,4,2]%%%}+%%%{%%%{-7680,[3,7,11]%%%},[4,4,1]%%%}+%%%{%%%{3072,[3,7,13]%%%},[4,4,0]%%%}+%%%{%%%{5520,[4,9,5]%%%},[4,3,3]%%%}+%%%{%%%{-20304,[4,9,7]%%%},[4,3,2]%%%}+%%%{%%%{27648,[4,9,9]%%%},[4,3,1]%%%}+%%%{%%%{-17664,[4,9,11]%%%},[4,3,0]%%%}+%%%{%%%{3888,[5,11,5]%%%},[4,2,2]%%%}+%%%{%%%{-12384,[5,11,7]%%%},[4,2,1]%%%}+%%%{%%%{12096,[5,11,9]%%%},[4,2,0]%%%}+%%%{%%%{1488,[6,13,5]%%%},[4,1,1]%%%}+%%%{%%%{-2928,[6,13,7]%%%},[4,1,0]%%%}+%%%{%%%{240,[7,15,5]%%%},[4,0,0]%%%}+%%%{%%{[%%%{-192,[0,2,4]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,7,7]%%%}+%%%{%%{[%%%{192,[0,2,6]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,7,6]%%%}+%%%{%%{[%%%{-1472,[1,4,4]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,6,6]%%%}+%%%{%%{[%%%{3456,[1,4,6]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,6,5]%%%}+%%%{%%{[%%%{-2304,[1,4,8]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,6,4]%%%}+%%%{%%{[%%%{-4800,[2,6,4]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,5,5]%%%}+%%%{%%{[%%%{15936,[2,6,6]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,5,4]%%%}+%%%{%%{[%%%{-18432,[2,6,8]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,5,3]%%%}+%%%{%%{[%%%{9216,[2,6,10]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,5,2]%%%}+%%%{%%{[%%%{-8640,[3,8,4]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,4,4]%%%}+%%%{%%{[%%%{33024,[3,8,6]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,4,3]%%%}+%%%{%%{[%%%{-47616,[3,8,8]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,4,2]%%%}+%%%{%%{[%%%{30720,[3,8,10]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,4,1]%%%}+%%%{%%{[%%%{-12288,[3,8,12]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,4,0]%%%}+%%%{%%{[%%%{-9280,[4,10,4]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,3,3]%%%}+%%%{%%{[%%%{35136,[4,10,6]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,3,2]%%%}+%%%{%%{[%%%{-49152,[4,10,8]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,3,1]%%%}+%%%{%%{[%%%{29696,[4,10,10]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,3,0]%%%}+%%%{%%{[%%%{-5952,[5,12,4]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,2,2]%%%}+%%%{%%{[%%%{18816,[5,12,6]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,2,1]%%%}+%%%{%%{[%%%{-17664,[5,12,8]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,2,0]%%%}+%%%{%%{[%%%{-2112,[6,14,4]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,1,1]%%%}+%%%{%%{[%%%{4032,[6,14,6]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,1,0]%%%}+%%%{%%{[%%%{-320,[7,16,4]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,0,0]%%%}+%%%{%%%{48,[0,2,4]%%%},[2,8,8]%%%}+%%%{%%%{-96,[0,2,6]%%%},[2,8,7]%%%}+%%%{%%%{48,[0,2,8]%%%},[2,8,6]%%%}+%%%{%%%{576,[1,4,4]%%%},[2,7,7]%%%}+%%%{%%%{-1440,[1,4,6]%%%},[2,7,6]%%%}+%%%{%%%{1440,[1,4,8]%%%},[2,7,5]%%%}+%%%{%%%{-576,[1,4,10]%%%},[2,7,4]%%%}+%%%{%%%{2688,[2,6,4]%%%},[2,6,6]%%%}+%%%{%%%{-8928,[2,6,6]%%%},[2,6,5]%%%}+%%%{%%%{11088,[2,6,8]%%%},[2,6,4]%%%}+%%%{%%%{-6912,[2,6,10]%%%},[2,6,3]%%%}+%%%{%%%{2304,[2,6,12]%%%},[2,6,2]%%%}+%%%{%%%{6720,[3,8,4]%%%},[2,5,5]%%%}+%%%{%%%{-26400,[3,8,6]%%%},[2,5,4]%%%}+%%%{%%%{40128,[3,8,8]%%%},[2,5,3]%%%}+%%%{%%%{-29568,[3,8,10]%%%},[2,5,2]%%%}+%%%{%%%{10752,[3,8,12]%%%},[2,5,1]%%%}+%%%{%%%{-3072,[3,8,14]%%%},[2,5,0]%%%}+%%%{%%%{10080,[4,10,4]%%%},[2,4,4]%%%}+%%%{%%%{-41760,[4,10,6]%%%},[2,4,3]%%%}+%%%{%%%{67536,[4,10,8]%%%},[2,4,2]%%%}+%%%{%%%{-52992,[4,10,10]%%%},[2,4,1]%%%}+%%%{%%%{20736,[4,10,12]%%%},[2,4,0]%%%}+%%%{%%%{9408,[5,12,4]%%%},[2,3,3]%%%}+%%%{%%%{-36576,[5,12,6]%%%},[2,3,2]%%%}+%%%{%%%{52128,[5,12,8]%%%},[2,3,1]%%%}+%%%{%%%{-29760,[5,12,10]%%%},[2,3,0]%%%}+%%%{%%%{5376,[6,14,4]%%%},[2,2,2]%%%}+%%%{%%%{-16800,[6,14,6]%%%},[2,2,1]%%%}+%%%{%%%{15024,[6,14,8]%%%},[2,2,0]%%%}+%%%{%%%{1728,[7,16,4]%%%},[2,1,1]%%%}+%%%{%%%{-3168,[7,16,6]%%%},[2,1,0]%%%}+%%%{%%%{240,[8,18,4]%%%},[2,0,0]%%%}+%%%{%%{[%%%{-96,[0,3,3]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,8,8]%%%}+%%%{%%{[%%%{192,[0,3,5]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,8,7]%%%}+%%%{%%{[%%%{-96,[0,3,7]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,8,6]%%%}+%%%{%%{[%%%{-768,[1,5,3]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,7,7]%%%}+%%%{%%{[%%%{2496,[1,5,5]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,7,6]%%%}+%%%{%%{[%%%{-2880,[1,5,7]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,7,5]%%%}+%%%{%%{[%%%{1152,[1,5,9]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,7,4]%%%}+%%%{%%{[%%%{-2688,[2,7,3]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,6,6]%%%}+%%%{%%{[%%%{10944,[2,7,5]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,6,5]%%%}+%%%{%%{[%%%{-17568,[2,7,7]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,6,4]%%%}+%%%{%%{[%%%{13824,[2,7,9]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,6,3]%%%}+%%%{%%{[%%%{-4608,[2,7,11]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,6,2]%%%}+%%%{%%{[%%%{-5376,[3,9,3]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,5,5]%%%}+%%%{%%{[%%%{24000,[3,9,5]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,5,4]%%%}+%%%{%%{[%%%{-43392,[3,9,7]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,5,3]%%%}+%%%{%%{[%%%{40704,[3,9,9]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,5,2]%%%}+%%%{%%{[%%%{-21504,[3,9,11]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,5,1]%%%}+%%%{%%{[%%%{6144,[3,9,13]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,5,0]%%%}+%%%{%%{[%%%{-6720,[4,11,3]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,4,4]%%%}+%%%{%%{[%%%{29760,[4,11,5]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,4,3]%%%}+%%%{%%{[%%%{-52128,[4,11,7]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,4,2]%%%}+%%%{%%{[%%%{44544,[4,11,9]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,4,1]%%%}+%%%{%%{[%%%{-16896,[4,11,11]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,4,0]%%%}+%%%{%%{[%%%{-5376,[5,13,3]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,3,3]%%%}+%%%{%%{[%%%{21312,[5,13,5]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,3,2]%%%}+%%%{%%{[%%%{-30528,[5,13,7]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,3,1]%%%}+%%%{%%{[%%%{16512,[5,13,9]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,3,0]%%%}+%%%{%%{[%%%{-2688,[6,15,3]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,2,2]%%%}+%%%{%%{[%%%{8256,[6,15,5]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,2,1]%%%}+%%%{%%{[%%%{-7008,[6,15,7]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,2,0]%%%}+%%%{%%{[%%%{-768,[7,17,3]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,1,1]%%%}+%%%{%%{[%%%{1344,[7,17,5]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,1,0]%%%}+%%%{%%{[%%%{-96,[8,19,3]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,0,0]%%%}+%%%{%%%{16,[0,3,3]%%%},[0,9,9]%%%}+%%%{%%%{-48,[0,3,5]%%%},[0,9,8]%%%}+%%%{%%%{48,[0,3,7]%%%},[0,9,7]%%%}+%%%{%%%{-16,[0,3,9]%%%},[0,9,6]%%%}+%%%{%%%{144,[1,5,3]%%%},[0,8,8]%%%}+%%%{%%%{-576,[1,5,5]%%%},[0,8,7]%%%}+%%%{%%%{912,[1,5,7]%%%},[0,8,6]%%%}+%%%{%%%{-672,[1,5,9]%%%},[0,8,5]%%%}+%%%{%%%{192,[1,5,11]%%%},[0,8,4]%%%}+%%%{%%%{576,[2,7,3]%%%},[0,7,7]%%%}+%%%{%%%{-2688,[2,7,5]%%%},[0,7,6]%%%}+%%%{%%%{5232,[2,7,7]%%%},[0,7,5]%%%}+%%%{%%%{-5424,[2,7,9]%%%},[0,7,4]%%%}+%%%{%%%{3072,[2,7,11]%%%},[0,7,3]%%%}+%%%{%%%{-768,[2,7,13]%%%},[0,7,2]%%%}+%%%{%%%{1344,[3,9,3]%%%},[0,6,6]%%%}+%%%{%%%{-6720,[3,9,5]%%%},[0,6,5]%%%}+%%%{%%%{14160,[3,9,7]%%%},[0,6,4]%%%}+%%%{%%%{-16320,[3,9,9]%%%},[0,6,3]%%%}+%%%{%%%{11136,[3,9,11]%%%},[0,6,2]%%%}+%%%{%%%{-4608,[3,9,13]%%%},[0,6,1]%%%}+%%%{%%%{1024,[3,9,15]%%%},[0,6,0]%%%}+%%%{%%%{2016,[4,11,3]%%%},[0,5,5]%%%}+%%%{%%%{-10080,[4,11,5]%%%},[0,5,4]%%%}+%%%{%%%{20880,[4,11,7]%%%},[0,5,3]%%%}+%%%{%%%{-22896,[4,11,9]%%%},[0,5,2]%%%}+%%%{%%%{13824,[4,11,11]%%%},[0,5,1]%%%}+%%%{%%%{-3840,[4,11,13]%%%},[0,5,0]%%%}+%%%{%%%{2016,[5,13,3]%%%},[0,4,4]%%%}+%%%{%%%{-9408,[5,13,5]%%%},[0,4,3]%%%}+%%%{%%%{17328,[5,13,7]%%%},[0,4,2]%%%}+%%%{%%%{-15264,[5,13,9]%%%},[0,4,1]%%%}+%%%{%%%{5568,[5,13,11]%%%},[0,4,0]%%%}+%%%{%%%{1344,[6,15,3]%%%},[0,3,3]%%%}+%%%{%%%{-5376,[6,15,5]%%%},[0,3,2]%%%}+%%%{%%%{7632,[6,15,7]%%%},[0,3,1]%%%}+%%%{%%%{-3920,[6,15,9]%%%},[0,3,0]%%%}+%%%{%%%{576,[7,17,3]%%%},[0,2,2]%%%}+%%%{%%%{-1728,[7,17,5]%%%},[0,2,1]%%%}+%%%{%%%{1392,[7,17,7]%%%},[0,2,0]%%%}+%%%{%%%{144,[8,19,3]%%%},[0,1,1]%%%}+%%%{%%%{-240,[8,19,5]%%%},[0,1,0]%%%}+%%%{%%%{16,[9,21,3]%%%},[0,0,0]%%%} / %%%{%%{poly1[%%%{-1,[1,1,4]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[6,0,0]%%%}+%%%{%%%{6,[2,3,4]%%%},[5,0,0]%%%}+%%%{%%{poly1[%%%{-3,[1,2,3]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[4,1,1]%%%}+%%%{%%{poly1[%%%{3,[1,2,5]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[4,1,0]%%%}+%%%{%%{poly1[%%%{-15,[2,4,3]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[4,0,0]%%%}+%%%{%%%{12,[2,4,3]%%%},[3,1,1]%%%}+%%%{%%%{-12,[2,4,5]%%%},[3,1,0]%%%}+%%%{%%%{20,[3,6,3]%%%},[3,0,0]%%%}+%%%{%%{poly1[%%%{-3,[1,3,2]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[2,2,2]%%%}+%%%{%%{poly1[%%%{6,[1,3,4]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[2,2,1]%%%}+%%%{%%{poly1[%%%{-3,[1,3,6]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[2,2,0]%%%}+%%%{%%{poly1[%%%{-18,[2,5,2]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[2,1,1]%%%}+%%%{%%{poly1[%%%{18,[2,5,4]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[2,1,0]%%%}+%%%{%%{poly1[%%%{-15,[3,7,2]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[2,0,0]%%%}+%%%{%%%{6,[2,5,2]%%%},[1,2,2]%%%}+%%%{%%%{-12,[2,5,4]%%%},[1,2,1]%%%}+%%%{%%%{6,[2,5,6]%%%},[1,2,0]%%%}+%%%{%%%{12,[3,7,2]%%%},[1,1,1]%%%}+%%%{%%%{-12,[3,7,4]%%%},[1,1,0]%%%}+%%%{%%%{6,[4,9,2]%%%},[1,0,0]%%%}+%%%{%%{poly1[%%%{-1,[1,4,1]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[0,3,3]%%%}+%%%{%%{poly1[%%%{3,[1,4,3]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[0,3,2]%%%}+%%%{%%{poly1[%%%{-3,[1,4,5]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[0,3,1]%%%}+%%%{%%{poly1[%%%{1,[1,4,7]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[0,3,0]%%%}+%%%{%%{poly1[%%%{-3,[2,6,1]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[0,2,2]%%%}+%%%{%%{poly1[%%%{6,[2,6,3]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[0,2,1]%%%}+%%%{%%{poly1[%%%{-3,[2,6,5]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[0,2,0]%%%}+%%%{%%{poly1[%%%{-3,[3,8,1]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[0,1,1]%%%}+%%%{%%{poly1[%%%{3,[3,8,3]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[0,1,0]%%%}+%%%{%%{poly1[%%%{-1,[4,10,1]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[0,0,0]%%%} Error: Bad Argument Value","F(-2)",0
1939,-2,0,0,0.000000," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/(e*x+d)^4,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 0.81Unable to divide, perhaps due to rounding error%%%{%%%{8,[0,0,7]%%%},[8,8,8]%%%}+%%%{%%%{64,[1,2,7]%%%},[8,7,7]%%%}+%%%{%%%{-128,[1,2,9]%%%},[8,7,6]%%%}+%%%{%%%{224,[2,4,7]%%%},[8,6,6]%%%}+%%%{%%%{-768,[2,4,9]%%%},[8,6,5]%%%}+%%%{%%%{768,[2,4,11]%%%},[8,6,4]%%%}+%%%{%%%{448,[3,6,7]%%%},[8,5,5]%%%}+%%%{%%%{-1920,[3,6,9]%%%},[8,5,4]%%%}+%%%{%%%{3072,[3,6,11]%%%},[8,5,3]%%%}+%%%{%%%{-2048,[3,6,13]%%%},[8,5,2]%%%}+%%%{%%%{560,[4,8,7]%%%},[8,4,4]%%%}+%%%{%%%{-2560,[4,8,9]%%%},[8,4,3]%%%}+%%%{%%%{4608,[4,8,11]%%%},[8,4,2]%%%}+%%%{%%%{-4096,[4,8,13]%%%},[8,4,1]%%%}+%%%{%%%{2048,[4,8,15]%%%},[8,4,0]%%%}+%%%{%%%{448,[5,10,7]%%%},[8,3,3]%%%}+%%%{%%%{-1920,[5,10,9]%%%},[8,3,2]%%%}+%%%{%%%{3072,[5,10,11]%%%},[8,3,1]%%%}+%%%{%%%{-2048,[5,10,13]%%%},[8,3,0]%%%}+%%%{%%%{224,[6,12,7]%%%},[8,2,2]%%%}+%%%{%%%{-768,[6,12,9]%%%},[8,2,1]%%%}+%%%{%%%{768,[6,12,11]%%%},[8,2,0]%%%}+%%%{%%%{64,[7,14,7]%%%},[8,1,1]%%%}+%%%{%%%{-128,[7,14,9]%%%},[8,1,0]%%%}+%%%{%%%{8,[8,16,7]%%%},[8,0,0]%%%}+%%%{%%{[%%%{-64,[0,1,6]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[7,8,8]%%%}+%%%{%%{[%%%{-512,[1,3,6]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[7,7,7]%%%}+%%%{%%{[%%%{1024,[1,3,8]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[7,7,6]%%%}+%%%{%%{[%%%{-1792,[2,5,6]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[7,6,6]%%%}+%%%{%%{[%%%{6144,[2,5,8]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[7,6,5]%%%}+%%%{%%{[%%%{-6144,[2,5,10]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[7,6,4]%%%}+%%%{%%{[%%%{-3584,[3,7,6]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[7,5,5]%%%}+%%%{%%{[%%%{15360,[3,7,8]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[7,5,4]%%%}+%%%{%%{[%%%{-24576,[3,7,10]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[7,5,3]%%%}+%%%{%%{[%%%{16384,[3,7,12]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[7,5,2]%%%}+%%%{%%{[%%%{-4480,[4,9,6]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[7,4,4]%%%}+%%%{%%{[%%%{20480,[4,9,8]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[7,4,3]%%%}+%%%{%%{[%%%{-36864,[4,9,10]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[7,4,2]%%%}+%%%{%%{[%%%{32768,[4,9,12]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[7,4,1]%%%}+%%%{%%{[%%%{-16384,[4,9,14]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[7,4,0]%%%}+%%%{%%{[%%%{-3584,[5,11,6]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[7,3,3]%%%}+%%%{%%{[%%%{15360,[5,11,8]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[7,3,2]%%%}+%%%{%%{[%%%{-24576,[5,11,10]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[7,3,1]%%%}+%%%{%%{[%%%{16384,[5,11,12]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[7,3,0]%%%}+%%%{%%{[%%%{-1792,[6,13,6]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[7,2,2]%%%}+%%%{%%{[%%%{6144,[6,13,8]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[7,2,1]%%%}+%%%{%%{[%%%{-6144,[6,13,10]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[7,2,0]%%%}+%%%{%%{[%%%{-512,[7,15,6]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[7,1,1]%%%}+%%%{%%{[%%%{1024,[7,15,8]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[7,1,0]%%%}+%%%{%%{[%%%{-64,[8,17,6]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[7,0,0]%%%}+%%%{%%%{32,[0,1,6]%%%},[6,9,9]%%%}+%%%{%%%{-32,[0,1,8]%%%},[6,9,8]%%%}+%%%{%%%{480,[1,3,6]%%%},[6,8,8]%%%}+%%%{%%%{-768,[1,3,8]%%%},[6,8,7]%%%}+%%%{%%%{512,[1,3,10]%%%},[6,8,6]%%%}+%%%{%%%{2688,[2,5,6]%%%},[6,7,7]%%%}+%%%{%%%{-7552,[2,5,8]%%%},[6,7,6]%%%}+%%%{%%%{6144,[2,5,10]%%%},[6,7,5]%%%}+%%%{%%%{-3072,[2,5,12]%%%},[6,7,4]%%%}+%%%{%%%{8064,[3,7,6]%%%},[6,6,6]%%%}+%%%{%%%{-30976,[3,7,8]%%%},[6,6,5]%%%}+%%%{%%%{41472,[3,7,10]%%%},[6,6,4]%%%}+%%%{%%%{-20480,[3,7,12]%%%},[6,6,3]%%%}+%%%{%%%{8192,[3,7,14]%%%},[6,6,2]%%%}+%%%{%%%{14784,[4,9,6]%%%},[6,5,5]%%%}+%%%{%%%{-66240,[4,9,8]%%%},[6,5,4]%%%}+%%%{%%%{114688,[4,9,10]%%%},[6,5,3]%%%}+%%%{%%%{-92160,[4,9,12]%%%},[6,5,2]%%%}+%%%{%%%{24576,[4,9,14]%%%},[6,5,1]%%%}+%%%{%%%{-8192,[4,9,16]%%%},[6,5,0]%%%}+%%%{%%%{17472,[5,11,6]%%%},[6,4,4]%%%}+%%%{%%%{-81152,[5,11,8]%%%},[6,4,3]%%%}+%%%{%%%{148992,[5,11,10]%%%},[6,4,2]%%%}+%%%{%%%{-135168,[5,11,12]%%%},[6,4,1]%%%}+%%%{%%%{65536,[5,11,14]%%%},[6,4,0]%%%}+%%%{%%%{13440,[6,13,6]%%%},[6,3,3]%%%}+%%%{%%%{-57728,[6,13,8]%%%},[6,3,2]%%%}+%%%{%%%{92160,[6,13,10]%%%},[6,3,1]%%%}+%%%{%%%{-60416,[6,13,12]%%%},[6,3,0]%%%}+%%%{%%%{6528,[7,15,6]%%%},[6,2,2]%%%}+%%%{%%%{-22272,[7,15,8]%%%},[6,2,1]%%%}+%%%{%%%{22016,[7,15,10]%%%},[6,2,0]%%%}+%%%{%%%{1824,[8,17,6]%%%},[6,1,1]%%%}+%%%{%%%{-3616,[8,17,8]%%%},[6,1,0]%%%}+%%%{%%%{224,[9,19,6]%%%},[6,0,0]%%%}+%%%{%%{[%%%{-192,[0,2,5]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,9,9]%%%}+%%%{%%{[%%%{192,[0,2,7]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,9,8]%%%}+%%%{%%{[%%%{-1984,[1,4,5]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,8,8]%%%}+%%%{%%{[%%%{4608,[1,4,7]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,8,7]%%%}+%%%{%%{[%%%{-3072,[1,4,9]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,8,6]%%%}+%%%{%%{[%%%{-8960,[2,6,5]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,7,7]%%%}+%%%{%%{[%%%{30976,[2,6,7]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,7,6]%%%}+%%%{%%{[%%%{-36864,[2,6,9]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,7,5]%%%}+%%%{%%{[%%%{18432,[2,6,11]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,7,4]%%%}+%%%{%%{[%%%{-23296,[3,8,5]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,6,6]%%%}+%%%{%%{[%%%{99840,[3,8,7]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,6,5]%%%}+%%%{%%{[%%%{-162816,[3,8,9]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,6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/ %%%{%%%{1,[2,2,6]%%%},[8,0,0]%%%}+%%%{%%{poly1[%%%{-8,[2,3,5]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[7,0,0]%%%}+%%%{%%%{4,[2,3,5]%%%},[6,1,1]%%%}+%%%{%%%{-4,[2,3,7]%%%},[6,1,0]%%%}+%%%{%%%{28,[3,5,5]%%%},[6,0,0]%%%}+%%%{%%{poly1[%%%{-24,[2,4,4]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,1,1]%%%}+%%%{%%{poly1[%%%{24,[2,4,6]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,1,0]%%%}+%%%{%%{poly1[%%%{-56,[3,6,4]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[5,0,0]%%%}+%%%{%%%{6,[2,4,4]%%%},[4,2,2]%%%}+%%%{%%%{-12,[2,4,6]%%%},[4,2,1]%%%}+%%%{%%%{6,[2,4,8]%%%},[4,2,0]%%%}+%%%{%%%{60,[3,6,4]%%%},[4,1,1]%%%}+%%%{%%%{-60,[3,6,6]%%%},[4,1,0]%%%}+%%%{%%%{70,[4,8,4]%%%},[4,0,0]%%%}+%%%{%%{poly1[%%%{-24,[2,5,3]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,2,2]%%%}+%%%{%%{poly1[%%%{48,[2,5,5]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,2,1]%%%}+%%%{%%{poly1[%%%{-24,[2,5,7]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,2,0]%%%}+%%%{%%{poly1[%%%{-80,[3,7,3]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,1,1]%%%}+%%%{%%{poly1[%%%{80,[3,7,5]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,1,0]%%%}+%%%{%%{poly1[%%%{-56,[4,9,3]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[3,0,0]%%%}+%%%{%%%{4,[2,5,3]%%%},[2,3,3]%%%}+%%%{%%%{-12,[2,5,5]%%%},[2,3,2]%%%}+%%%{%%%{12,[2,5,7]%%%},[2,3,1]%%%}+%%%{%%%{-4,[2,5,9]%%%},[2,3,0]%%%}+%%%{%%%{36,[3,7,3]%%%},[2,2,2]%%%}+%%%{%%%{-72,[3,7,5]%%%},[2,2,1]%%%}+%%%{%%%{36,[3,7,7]%%%},[2,2,0]%%%}+%%%{%%%{60,[4,9,3]%%%},[2,1,1]%%%}+%%%{%%%{-60,[4,9,5]%%%},[2,1,0]%%%}+%%%{%%%{28,[5,11,3]%%%},[2,0,0]%%%}+%%%{%%{poly1[%%%{-8,[2,6,2]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,3,3]%%%}+%%%{%%{poly1[%%%{24,[2,6,4]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,3,2]%%%}+%%%{%%{poly1[%%%{-24,[2,6,6]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,3,1]%%%}+%%%{%%{poly1[%%%{8,[2,6,8]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,3,0]%%%}+%%%{%%{poly1[%%%{-24,[3,8,2]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,2,2]%%%}+%%%{%%{poly1[%%%{48,[3,8,4]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,2,1]%%%}+%%%{%%{poly1[%%%{-24,[3,8,6]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,2,0]%%%}+%%%{%%{poly1[%%%{-24,[4,10,2]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,1,1]%%%}+%%%{%%{poly1[%%%{24,[4,10,4]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,1,0]%%%}+%%%{%%{poly1[%%%{-8,[5,12,2]%%%},0]:[1,0,%%%{-1,[1,1,1]%%%}]%%},[1,0,0]%%%}+%%%{%%%{1,[2,6,2]%%%},[0,4,4]%%%}+%%%{%%%{-4,[2,6,4]%%%},[0,4,3]%%%}+%%%{%%%{6,[2,6,6]%%%},[0,4,2]%%%}+%%%{%%%{-4,[2,6,8]%%%},[0,4,1]%%%}+%%%{%%%{1,[2,6,10]%%%},[0,4,0]%%%}+%%%{%%%{4,[3,8,2]%%%},[0,3,3]%%%}+%%%{%%%{-12,[3,8,4]%%%},[0,3,2]%%%}+%%%{%%%{12,[3,8,6]%%%},[0,3,1]%%%}+%%%{%%%{-4,[3,8,8]%%%},[0,3,0]%%%}+%%%{%%%{6,[4,10,2]%%%},[0,2,2]%%%}+%%%{%%%{-12,[4,10,4]%%%},[0,2,1]%%%}+%%%{%%%{6,[4,10,6]%%%},[0,2,0]%%%}+%%%{%%%{4,[5,12,2]%%%},[0,1,1]%%%}+%%%{%%%{-4,[5,12,4]%%%},[0,1,0]%%%}+%%%{%%%{1,[6,14,2]%%%},[0,0,0]%%%} Error: Bad Argument Value","F(-2)",0
1940,-1,0,0,0.000000," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/(e*x+d)^5,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1941,-1,0,0,0.000000," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/(e*x+d)^6,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1942,-2,0,0,0.000000," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/(e*x+d)^7,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: 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2880*c^6*d^18*exp(1)^6*sqrt(c*d*exp(1))*a^5*exp(2)^2+69255*c^6*d^18*exp(1)^8*sqrt(c*d*exp(1))*a^5*exp(2)-20565*c^6*d^18*exp(1)^10*sqrt(c*d*exp(1))*a^5+3622*c^7*d^20*sqrt(c*d*exp(1))*a^4*exp(2)^4-20776*c^7*d^20*exp(1)^2*sqrt(c*d*exp(1))*a^4*exp(2)^3+44496*c^7*d^20*exp(1)^4*sqrt(c*d*exp(1))*a^4*exp(2)^2-42672*c^7*d^20*exp(1)^6*sqrt(c*d*exp(1))*a^4*exp(2)+15555*c^7*d^20*exp(1)^8*sqrt(c*d*exp(1))*a^4+2565*c^8*d^22*sqrt(c*d*exp(1))*a^3*exp(2)^3-10593*c^8*d^22*exp(1)^2*sqrt(c*d*exp(1))*a^3*exp(2)^2+14946*c^8*d^22*exp(1)^4*sqrt(c*d*exp(1))*a^3*exp(2)-7218*c^8*d^22*exp(1)^6*sqrt(c*d*exp(1))*a^3+933*c^9*d^24*sqrt(c*d*exp(1))*a^2*exp(2)^2-2646*c^9*d^24*exp(1)^2*sqrt(c*d*exp(1))*a^2*exp(2)+1938*c^9*d^24*exp(1)^4*sqrt(c*d*exp(1))*a^2+175*c^10*d^26*sqrt(c*d*exp(1))*a*exp(2)-265*c^10*d^26*exp(1)^2*sqrt(c*d*exp(1))*a+15*c^11*d^28*sqrt(c*d*exp(1)))/(-3072*d^3*exp(1)^4*a^3*exp(2)^3+9216*d^3*exp(1)^6*a^3*exp(2)^2-9216*d^3*exp(1)^8*a^3*exp(2)+3072*d^3*exp(1)^10*a^3)/(-exp(1)*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)^2+2*d*sqrt(c*d*exp(1))*(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)-d*a*exp(2)+d*exp(1)^2*a-c*d^3)^6+(5*a^6*exp(2)^6+30*c*d^2*a^5*exp(2)^5-60*c*d^2*exp(1)^2*a^5*exp(2)^4+75*c^2*d^4*a^4*exp(2)^4-240*c^2*d^4*exp(1)^2*a^4*exp(2)^3+240*c^2*d^4*exp(1)^4*a^4*exp(2)^2+100*c^3*d^6*a^3*exp(2)^3-360*c^3*d^6*exp(1)^2*a^3*exp(2)^2+480*c^3*d^6*exp(1)^4*a^3*exp(2)-320*c^3*d^6*exp(1)^6*a^3+75*c^4*d^8*a^2*exp(2)^2-240*c^4*d^8*exp(1)^2*a^2*exp(2)+240*c^4*d^8*exp(1)^4*a^2+30*c^5*d^10*a*exp(2)-60*c^5*d^10*exp(1)^2*a+5*c^6*d^12)/2/(512*d^3*exp(1)^3*a^3*exp(2)^3-1536*d^3*exp(1)^5*a^3*exp(2)^2+1536*d^3*exp(1)^7*a^3*exp(2)-512*d^3*exp(1)^9*a^3)/sqrt(-a*d*exp(1)^3+a*d*exp(1)*exp(2))*atan((-d*sqrt(c*d*exp(1))+(sqrt(a*d*exp(1)+a*x*exp(2)+c*d^2*x+c*d*x^2*exp(1))-sqrt(c*d*exp(1))*x)*exp(1))/sqrt(-a*d*exp(1)^3+a*d*exp(1)*exp(2))))","F(-2)",0
1943,-1,0,0,0.000000," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/(e*x+d)^8,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1944,-1,0,0,0.000000," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/(e*x+d)^9,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1945,-1,0,0,0.000000," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/(e*x+d)^10,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1946,1,234,0,0.983159," ","integrate((e*x+d)^3/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""giac"")","\frac{1}{24} \, \sqrt{c d x^{2} e + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, x {\left(\frac{4 \, x e^{2}}{c d} + \frac{{\left(13 \, c^{2} d^{3} e^{3} - 5 \, a c d e^{5}\right)} e^{\left(-2\right)}}{c^{3} d^{3}}\right)} + \frac{{\left(33 \, c^{2} d^{4} e^{2} - 40 \, a c d^{2} e^{4} + 15 \, a^{2} e^{6}\right)} e^{\left(-2\right)}}{c^{3} d^{3}}\right)} - \frac{5 \, {\left(c^{3} d^{6} - 3 \, a c^{2} d^{4} e^{2} + 3 \, a^{2} c d^{2} e^{4} - a^{3} e^{6}\right)} \sqrt{c d} e^{\left(-\frac{1}{2}\right)} \log\left({\left| -\sqrt{c d} c d^{2} e^{\frac{1}{2}} - 2 \, {\left(\sqrt{c d} x e^{\frac{1}{2}} - \sqrt{c d x^{2} e + a d e + {\left(c d^{2} + a e^{2}\right)} x}\right)} c d e - \sqrt{c d} a e^{\frac{5}{2}} \right|}\right)}{16 \, c^{4} d^{4}}"," ",0,"1/24*sqrt(c*d*x^2*e + a*d*e + (c*d^2 + a*e^2)*x)*(2*x*(4*x*e^2/(c*d) + (13*c^2*d^3*e^3 - 5*a*c*d*e^5)*e^(-2)/(c^3*d^3)) + (33*c^2*d^4*e^2 - 40*a*c*d^2*e^4 + 15*a^2*e^6)*e^(-2)/(c^3*d^3)) - 5/16*(c^3*d^6 - 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4 - a^3*e^6)*sqrt(c*d)*e^(-1/2)*log(abs(-sqrt(c*d)*c*d^2*e^(1/2) - 2*(sqrt(c*d)*x*e^(1/2) - sqrt(c*d*x^2*e + a*d*e + (c*d^2 + a*e^2)*x))*c*d*e - sqrt(c*d)*a*e^(5/2)))/(c^4*d^4)","A",0
1947,1,176,0,0.799267," ","integrate((e*x+d)^2/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{c d x^{2} e + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(\frac{2 \, x e}{c d} + \frac{{\left(5 \, c d^{2} e - 3 \, a e^{3}\right)} e^{\left(-1\right)}}{c^{2} d^{2}}\right)} - \frac{3 \, {\left(c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} \sqrt{c d} e^{\left(-\frac{1}{2}\right)} \log\left({\left| -\sqrt{c d} c d^{2} e^{\frac{1}{2}} - 2 \, {\left(\sqrt{c d} x e^{\frac{1}{2}} - \sqrt{c d x^{2} e + a d e + {\left(c d^{2} + a e^{2}\right)} x}\right)} c d e - \sqrt{c d} a e^{\frac{5}{2}} \right|}\right)}{8 \, c^{3} d^{3}}"," ",0,"1/4*sqrt(c*d*x^2*e + a*d*e + (c*d^2 + a*e^2)*x)*(2*x*e/(c*d) + (5*c*d^2*e - 3*a*e^3)*e^(-1)/(c^2*d^2)) - 3/8*(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(c*d)*e^(-1/2)*log(abs(-sqrt(c*d)*c*d^2*e^(1/2) - 2*(sqrt(c*d)*x*e^(1/2) - sqrt(c*d*x^2*e + a*d*e + (c*d^2 + a*e^2)*x))*c*d*e - sqrt(c*d)*a*e^(5/2)))/(c^3*d^3)","A",0
1948,1,134,0,0.828604," ","integrate((e*x+d)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""giac"")","-\frac{{\left(c d^{2} - a e^{2}\right)} \sqrt{c d} e^{\left(-\frac{1}{2}\right)} \log\left({\left| -\sqrt{c d} c d^{2} e^{\frac{1}{2}} - 2 \, {\left(\sqrt{c d} x e^{\frac{1}{2}} - \sqrt{c d x^{2} e + a d e + {\left(c d^{2} + a e^{2}\right)} x}\right)} c d e - \sqrt{c d} a e^{\frac{5}{2}} \right|}\right)}{2 \, c^{2} d^{2}} + \frac{\sqrt{c d x^{2} e + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{c d}"," ",0,"-1/2*(c*d^2 - a*e^2)*sqrt(c*d)*e^(-1/2)*log(abs(-sqrt(c*d)*c*d^2*e^(1/2) - 2*(sqrt(c*d)*x*e^(1/2) - sqrt(c*d*x^2*e + a*d*e + (c*d^2 + a*e^2)*x))*c*d*e - sqrt(c*d)*a*e^(5/2)))/(c^2*d^2) + sqrt(c*d*x^2*e + a*d*e + (c*d^2 + a*e^2)*x)/(c*d)","A",0
1949,1,86,0,0.726071," ","integrate(1/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{c d} e^{\left(-\frac{1}{2}\right)} \log\left({\left| -\sqrt{c d} c d^{2} e^{\frac{1}{2}} - 2 \, {\left(\sqrt{c d} x e^{\frac{1}{2}} - \sqrt{c d x^{2} e + c d^{2} x + a x e^{2} + a d e}\right)} c d e - \sqrt{c d} a e^{\frac{5}{2}} \right|}\right)}{c d}"," ",0,"-sqrt(c*d)*e^(-1/2)*log(abs(-sqrt(c*d)*c*d^2*e^(1/2) - 2*(sqrt(c*d)*x*e^(1/2) - sqrt(c*d*x^2*e + c*d^2*x + a*x*e^2 + a*d*e))*c*d*e - sqrt(c*d)*a*e^(5/2)))/(c*d)","A",0
1950,-2,0,0,0.000000," ","integrate(1/(e*x+d)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: 2/sqrt(-a*d*exp(1)^3+a*d*exp(1)*exp(2))*atan((-d*sqrt(c*d*exp(1))+(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)*exp(1))/sqrt(-a*d*exp(1)^3+a*d*exp(1)*exp(2)))","F(-2)",0
1951,-2,0,0,0.000000," ","integrate(1/(e*x+d)^2/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]Evaluation time: 0.7Error: Bad Argument Type","F(-2)",0
1952,-2,0,0,0.000000," ","integrate(1/(e*x+d)^3/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: 2*((-3*exp(1)^2*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)^3*a^2*exp(2)^2+2*c*d^2*exp(1)^2*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)^3*a*exp(2)+4*c*d^2*exp(1)^4*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)^3*a-3*c^2*d^4*exp(1)^2*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)^3+9*d*exp(1)*sqrt(c*d*exp(1))*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)^2*a^2*exp(2)^2-6*c*d^3*exp(1)*sqrt(c*d*exp(1))*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)^2*a*exp(2)-12*c*d^3*exp(1)^3*sqrt(c*d*exp(1))*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)^2*a+9*c^2*d^5*exp(1)*sqrt(c*d*exp(1))*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)^2-5*d*exp(1)*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)*a^3*exp(2)^3+5*d*exp(1)^3*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)*a^3*exp(2)^2+5*c*d^3*exp(1)*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)*a^2*exp(2)^2-18*c*d^3*exp(1)^3*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)*a^2*exp(2)+4*c*d^3*exp(1)^5*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)*a^2+c^2*d^5*exp(1)*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)*a*exp(2)+17*c^2*d^5*exp(1)^3*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)*a-9*c^3*d^7*exp(1)*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)-3*d^2*sqrt(c*d*exp(1))*a^3*exp(2)^3+11*d^2*exp(1)^2*sqrt(c*d*exp(1))*a^3*exp(2)^2-8*d^2*exp(1)^4*sqrt(c*d*exp(1))*a^3*exp(2)-3*c*d^4*sqrt(c*d*exp(1))*a^2*exp(2)^2+2*c*d^4*exp(1)^2*sqrt(c*d*exp(1))*a^2*exp(2)+4*c*d^4*exp(1)^4*sqrt(c*d*exp(1))*a^2+3*c^2*d^6*sqrt(c*d*exp(1))*a*exp(2)-9*c^2*d^6*exp(1)^2*sqrt(c*d*exp(1))*a+3*c^3*d^8*sqrt(c*d*exp(1)))/(-8*d^2*exp(1)*a^2*exp(2)^2+16*d^2*exp(1)^3*a^2*exp(2)-8*d^2*exp(1)^5*a^2)/(-exp(1)*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)^2+2*d*sqrt(c*d*exp(1))*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)-d*a*exp(2)+d*exp(1)^2*a-c*d^3)^2+(3*a^2*exp(2)^2-2*c*d^2*a*exp(2)-4*c*d^2*exp(1)^2*a+3*c^2*d^4)/2/(4*d^2*a^2*exp(2)^2-8*d^2*exp(1)^2*a^2*exp(2)+4*d^2*exp(1)^4*a^2)/sqrt(-a*d*exp(1)^3+a*d*exp(1)*exp(2))*atan((-d*sqrt(c*d*exp(1))+(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)*exp(1))/sqrt(-a*d*exp(1)^3+a*d*exp(1)*exp(2))))","F(-2)",0
1953,-2,0,0,0.000000," ","integrate(1/(e*x+d)^4/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: 2*((-15*exp(1)^3*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)^5*a^3*exp(2)^3+9*c*d^2*exp(1)^3*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)^5*a^2*exp(2)^2+36*c*d^2*exp(1)^5*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)^5*a^2*exp(2)-9*c^2*d^4*exp(1)^3*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)^5*a*exp(2)-36*c^2*d^4*exp(1)^5*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)^5*a+15*c^3*d^6*exp(1)^3*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)^5+75*d*exp(1)^2*sqrt(c*d*exp(1))*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)^4*a^3*exp(2)^3-45*c*d^3*exp(1)^2*sqrt(c*d*exp(1))*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)^4*a^2*exp(2)^2-180*c*d^3*exp(1)^4*sqrt(c*d*exp(1))*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)^4*a^2*exp(2)+45*c^2*d^5*exp(1)^2*sqrt(c*d*exp(1))*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)^4*a*exp(2)+180*c^2*d^5*exp(1)^4*sqrt(c*d*exp(1))*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)^4*a-75*c^3*d^7*exp(1)^2*sqrt(c*d*exp(1))*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)^4-40*d*exp(1)^2*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)^3*a^4*exp(2)^4+40*d*exp(1)^4*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)^3*a^4*exp(2)^3-126*c*d^3*exp(1)^2*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)^3*a^3*exp(2)^3+72*c*d^3*exp(1)^4*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)^3*a^3*exp(2)^2-96*c*d^3*exp(1)^6*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)^3*a^3*exp(2)+66*c^2*d^5*exp(1)^2*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)^3*a^2*exp(2)^2+288*c^2*d^5*exp(1)^4*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)^3*a^2*exp(2)+96*c^2*d^5*exp(1)^6*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)^3*a^2-50*c^3*d^7*exp(1)^2*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)^3*a*exp(2)-400*c^3*d^7*exp(1)^4*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)^3*a+150*c^4*d^9*exp(1)^2*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)^3+120*d^2*exp(1)*sqrt(c*d*exp(1))*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)^2*a^4*exp(2)^4-120*d^2*exp(1)^3*sqrt(c*d*exp(1))*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)^2*a^4*exp(2)^3-18*c*d^4*exp(1)*sqrt(c*d*exp(1))*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)^2*a^3*exp(2)^3+72*c*d^4*exp(1)^3*sqrt(c*d*exp(1))*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)^2*a^3*exp(2)^2+96*c*d^4*exp(1)^7*sqrt(c*d*exp(1))*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)^2*a^3-18*c^2*d^6*exp(1)*sqrt(c*d*exp(1))*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)^2*a^2*exp(2)^2-144*c^2*d^6*exp(1)^3*sqrt(c*d*exp(1))*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)^2*a^2*exp(2)-288*c^2*d^6*exp(1)^5*sqrt(c*d*exp(1))*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)^2*a^2-30*c^3*d^8*exp(1)*sqrt(c*d*exp(1))*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)^2*a*exp(2)+480*c^3*d^8*exp(1)^3*sqrt(c*d*exp(1))*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)^2*a-150*c^4*d^10*exp(1)*sqrt(c*d*exp(1))*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)^2-33*d^2*exp(1)*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)*a^5*exp(2)^5+66*d^2*exp(1)^3*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)*a^5*exp(2)^4-33*d^2*exp(1)^5*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)*a^5*exp(2)^3+15*c*d^4*exp(1)*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)*a^4*exp(2)^4-186*c*d^4*exp(1)^3*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)*a^4*exp(2)^3+207*c*d^4*exp(1)^5*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)*a^4*exp(2)^2-36*c*d^4*exp(1)^7*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)*a^4*exp(2)+54*c^2*d^6*exp(1)*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)*a^3*exp(2)^3-54*c^2*d^6*exp(1)^3*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)*a^3*exp(2)^2+81*c^2*d^6*exp(1)^5*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)*a^3*exp(2)-156*c^2*d^6*exp(1)^7*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)*a^3+6*c^3*d^8*exp(1)*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)*a^2*exp(2)^2-102*c^3*d^8*exp(1)^3*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)*a^2*exp(2)+321*c^3*d^8*exp(1)^5*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)*a^2+75*c^4*d^10*exp(1)*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)*a*exp(2)-300*c^4*d^10*exp(1)^3*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)*a+75*c^5*d^12*exp(1)*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)-15*d^3*sqrt(c*d*exp(1))*a^5*exp(2)^5+78*d^3*exp(1)^2*sqrt(c*d*exp(1))*a^5*exp(2)^4-111*d^3*exp(1)^4*sqrt(c*d*exp(1))*a^5*exp(2)^3+48*d^3*exp(1)^6*sqrt(c*d*exp(1))*a^5*exp(2)^2-31*c*d^5*sqrt(c*d*exp(1))*a^4*exp(2)^4+106*c*d^5*exp(1)^2*sqrt(c*d*exp(1))*a^4*exp(2)^3-111*c*d^5*exp(1)^4*sqrt(c*d*exp(1))*a^4*exp(2)^2+68*c*d^5*exp(1)^6*sqrt(c*d*exp(1))*a^4*exp(2)-32*c*d^5*exp(1)^8*sqrt(c*d*exp(1))*a^4-18*c^2*d^7*sqrt(c*d*exp(1))*a^3*exp(2)^3+54*c^2*d^7*exp(1)^2*sqrt(c*d*exp(1))*a^3*exp(2)^2-129*c^2*d^7*exp(1)^4*sqrt(c*d*exp(1))*a^3*exp(2)+108*c^2*d^7*exp(1)^6*sqrt(c*d*exp(1))*a^3-18*c^3*d^9*sqrt(c*d*exp(1))*a^2*exp(2)^2+102*c^3*d^9*exp(1)^2*sqrt(c*d*exp(1))*a^2*exp(2)-129*c^3*d^9*exp(1)^4*sqrt(c*d*exp(1))*a^2-31*c^4*d^11*sqrt(c*d*exp(1))*a*exp(2)+76*c^4*d^11*exp(1)^2*sqrt(c*d*exp(1))*a-15*c^5*d^13*sqrt(c*d*exp(1)))/(48*d^3*exp(1)*a^3*exp(2)^3-144*d^3*exp(1)^3*a^3*exp(2)^2+144*d^3*exp(1)^5*a^3*exp(2)-48*d^3*exp(1)^7*a^3)/(-exp(1)*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)^2+2*d*sqrt(c*d*exp(1))*(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)-d*a*exp(2)+d*exp(1)^2*a-c*d^3)^3+(5*a^3*exp(2)^3-3*c*d^2*a^2*exp(2)^2-12*c*d^2*exp(1)^2*a^2*exp(2)+3*c^2*d^4*a*exp(2)+12*c^2*d^4*exp(1)^2*a-5*c^3*d^6)/2/(8*d^3*a^3*exp(2)^3-24*d^3*exp(1)^2*a^3*exp(2)^2+24*d^3*exp(1)^4*a^3*exp(2)-8*d^3*exp(1)^6*a^3)/sqrt(-a*d*exp(1)^3+a*d*exp(1)*exp(2))*atan((-d*sqrt(c*d*exp(1))+(sqrt(c*d*exp(1)*x^2+a*d*exp(1)+(c*d^2+a*exp(2))*x)-sqrt(c*d*exp(1))*x)*exp(1))/sqrt(-a*d*exp(1)^3+a*d*exp(1)*exp(2))))","F(-2)",0
1954,1,622,0,0.674951," ","integrate((e*x+d)^5/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""giac"")","\frac{{\left({\left(2 \, {\left(\frac{4 \, {\left(c^{5} d^{7} e^{7} - 2 \, a c^{4} d^{5} e^{9} + a^{2} c^{3} d^{3} e^{11}\right)} x}{c^{6} d^{8} e^{3} - 2 \, a c^{5} d^{6} e^{5} + a^{2} c^{4} d^{4} e^{7}} + \frac{23 \, c^{5} d^{8} e^{6} - 53 \, a c^{4} d^{6} e^{8} + 37 \, a^{2} c^{3} d^{4} e^{10} - 7 \, a^{3} c^{2} d^{2} e^{12}}{c^{6} d^{8} e^{3} - 2 \, a c^{5} d^{6} e^{5} + a^{2} c^{4} d^{4} e^{7}}\right)} x + \frac{125 \, c^{5} d^{9} e^{5} - 362 \, a c^{4} d^{7} e^{7} + 384 \, a^{2} c^{3} d^{5} e^{9} - 182 \, a^{3} c^{2} d^{3} e^{11} + 35 \, a^{4} c d e^{13}}{c^{6} d^{8} e^{3} - 2 \, a c^{5} d^{6} e^{5} + a^{2} c^{4} d^{4} e^{7}}\right)} x + \frac{39 \, c^{5} d^{10} e^{4} + 55 \, a c^{4} d^{8} e^{6} - 472 \, a^{2} c^{3} d^{6} e^{8} + 728 \, a^{3} c^{2} d^{4} e^{10} - 455 \, a^{4} c d^{2} e^{12} + 105 \, a^{5} e^{14}}{c^{6} d^{8} e^{3} - 2 \, a c^{5} d^{6} e^{5} + a^{2} c^{4} d^{4} e^{7}}\right)} x - \frac{48 \, c^{5} d^{11} e^{3} - 327 \, a c^{4} d^{9} e^{5} + 790 \, a^{2} c^{3} d^{7} e^{7} - 896 \, a^{3} c^{2} d^{5} e^{9} + 490 \, a^{4} c d^{3} e^{11} - 105 \, a^{5} d e^{13}}{c^{6} d^{8} e^{3} - 2 \, a c^{5} d^{6} e^{5} + a^{2} c^{4} d^{4} e^{7}}}{24 \, \sqrt{c d x^{2} e + a d e + {\left(c d^{2} + a e^{2}\right)} x}} - \frac{35 \, {\left(c^{3} d^{6} e - 3 \, a c^{2} d^{4} e^{3} + 3 \, a^{2} c d^{2} e^{5} - a^{3} e^{7}\right)} \sqrt{c d} e^{\left(-\frac{1}{2}\right)} \log\left({\left| -\sqrt{c d} c d^{2} e^{\frac{1}{2}} - 2 \, {\left(\sqrt{c d} x e^{\frac{1}{2}} - \sqrt{c d x^{2} e + a d e + {\left(c d^{2} + a e^{2}\right)} x}\right)} c d e - \sqrt{c d} a e^{\frac{5}{2}} \right|}\right)}{16 \, c^{5} d^{5}}"," ",0,"1/24*(((2*(4*(c^5*d^7*e^7 - 2*a*c^4*d^5*e^9 + a^2*c^3*d^3*e^11)*x/(c^6*d^8*e^3 - 2*a*c^5*d^6*e^5 + a^2*c^4*d^4*e^7) + (23*c^5*d^8*e^6 - 53*a*c^4*d^6*e^8 + 37*a^2*c^3*d^4*e^10 - 7*a^3*c^2*d^2*e^12)/(c^6*d^8*e^3 - 2*a*c^5*d^6*e^5 + a^2*c^4*d^4*e^7))*x + (125*c^5*d^9*e^5 - 362*a*c^4*d^7*e^7 + 384*a^2*c^3*d^5*e^9 - 182*a^3*c^2*d^3*e^11 + 35*a^4*c*d*e^13)/(c^6*d^8*e^3 - 2*a*c^5*d^6*e^5 + a^2*c^4*d^4*e^7))*x + (39*c^5*d^10*e^4 + 55*a*c^4*d^8*e^6 - 472*a^2*c^3*d^6*e^8 + 728*a^3*c^2*d^4*e^10 - 455*a^4*c*d^2*e^12 + 105*a^5*e^14)/(c^6*d^8*e^3 - 2*a*c^5*d^6*e^5 + a^2*c^4*d^4*e^7))*x - (48*c^5*d^11*e^3 - 327*a*c^4*d^9*e^5 + 790*a^2*c^3*d^7*e^7 - 896*a^3*c^2*d^5*e^9 + 490*a^4*c*d^3*e^11 - 105*a^5*d*e^13)/(c^6*d^8*e^3 - 2*a*c^5*d^6*e^5 + a^2*c^4*d^4*e^7))/sqrt(c*d*x^2*e + a*d*e + (c*d^2 + a*e^2)*x) - 35/16*(c^3*d^6*e - 3*a*c^2*d^4*e^3 + 3*a^2*c*d^2*e^5 - a^3*e^7)*sqrt(c*d)*e^(-1/2)*log(abs(-sqrt(c*d)*c*d^2*e^(1/2) - 2*(sqrt(c*d)*x*e^(1/2) - sqrt(c*d*x^2*e + a*d*e + (c*d^2 + a*e^2)*x))*c*d*e - sqrt(c*d)*a*e^(5/2)))/(c^5*d^5)","B",0
1955,1,480,0,0.743832," ","integrate((e*x+d)^4/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""giac"")","\frac{{\left({\left(\frac{2 \, {\left(c^{4} d^{6} e^{5} - 2 \, a c^{3} d^{4} e^{7} + a^{2} c^{2} d^{2} e^{9}\right)} x}{c^{5} d^{7} e^{2} - 2 \, a c^{4} d^{5} e^{4} + a^{2} c^{3} d^{3} e^{6}} + \frac{11 \, c^{4} d^{7} e^{4} - 27 \, a c^{3} d^{5} e^{6} + 21 \, a^{2} c^{2} d^{3} e^{8} - 5 \, a^{3} c d e^{10}}{c^{5} d^{7} e^{2} - 2 \, a c^{4} d^{5} e^{4} + a^{2} c^{3} d^{3} e^{6}}\right)} x + \frac{c^{4} d^{8} e^{3} + 18 \, a c^{3} d^{6} e^{5} - 54 \, a^{2} c^{2} d^{4} e^{7} + 50 \, a^{3} c d^{2} e^{9} - 15 \, a^{4} e^{11}}{c^{5} d^{7} e^{2} - 2 \, a c^{4} d^{5} e^{4} + a^{2} c^{3} d^{3} e^{6}}\right)} x - \frac{8 \, c^{4} d^{9} e^{2} - 41 \, a c^{3} d^{7} e^{4} + 73 \, a^{2} c^{2} d^{5} e^{6} - 55 \, a^{3} c d^{3} e^{8} + 15 \, a^{4} d e^{10}}{c^{5} d^{7} e^{2} - 2 \, a c^{4} d^{5} e^{4} + a^{2} c^{3} d^{3} e^{6}}}{4 \, \sqrt{c d x^{2} e + a d e + {\left(c d^{2} + a e^{2}\right)} x}} - \frac{15 \, {\left(c^{2} d^{4} e - 2 \, a c d^{2} e^{3} + a^{2} e^{5}\right)} \sqrt{c d} e^{\left(-\frac{1}{2}\right)} \log\left({\left| -\sqrt{c d} c d^{2} e^{\frac{1}{2}} - 2 \, {\left(\sqrt{c d} x e^{\frac{1}{2}} - \sqrt{c d x^{2} e + a d e + {\left(c d^{2} + a e^{2}\right)} x}\right)} c d e - \sqrt{c d} a e^{\frac{5}{2}} \right|}\right)}{8 \, c^{4} d^{4}}"," ",0,"1/4*(((2*(c^4*d^6*e^5 - 2*a*c^3*d^4*e^7 + a^2*c^2*d^2*e^9)*x/(c^5*d^7*e^2 - 2*a*c^4*d^5*e^4 + a^2*c^3*d^3*e^6) + (11*c^4*d^7*e^4 - 27*a*c^3*d^5*e^6 + 21*a^2*c^2*d^3*e^8 - 5*a^3*c*d*e^10)/(c^5*d^7*e^2 - 2*a*c^4*d^5*e^4 + a^2*c^3*d^3*e^6))*x + (c^4*d^8*e^3 + 18*a*c^3*d^6*e^5 - 54*a^2*c^2*d^4*e^7 + 50*a^3*c*d^2*e^9 - 15*a^4*e^11)/(c^5*d^7*e^2 - 2*a*c^4*d^5*e^4 + a^2*c^3*d^3*e^6))*x - (8*c^4*d^9*e^2 - 41*a*c^3*d^7*e^4 + 73*a^2*c^2*d^5*e^6 - 55*a^3*c*d^3*e^8 + 15*a^4*d*e^10)/(c^5*d^7*e^2 - 2*a*c^4*d^5*e^4 + a^2*c^3*d^3*e^6))/sqrt(c*d*x^2*e + a*d*e + (c*d^2 + a*e^2)*x) - 15/8*(c^2*d^4*e - 2*a*c*d^2*e^3 + a^2*e^5)*sqrt(c*d)*e^(-1/2)*log(abs(-sqrt(c*d)*c*d^2*e^(1/2) - 2*(sqrt(c*d)*x*e^(1/2) - sqrt(c*d*x^2*e + a*d*e + (c*d^2 + a*e^2)*x))*c*d*e - sqrt(c*d)*a*e^(5/2)))/(c^4*d^4)","B",0
1956,1,354,0,0.631280," ","integrate((e*x+d)^3/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""giac"")","\frac{{\left(\frac{{\left(c^{3} d^{5} e^{3} - 2 \, a c^{2} d^{3} e^{5} + a^{2} c d e^{7}\right)} x}{c^{4} d^{6} e - 2 \, a c^{3} d^{4} e^{3} + a^{2} c^{2} d^{2} e^{5}} - \frac{c^{3} d^{6} e^{2} - 5 \, a c^{2} d^{4} e^{4} + 7 \, a^{2} c d^{2} e^{6} - 3 \, a^{3} e^{8}}{c^{4} d^{6} e - 2 \, a c^{3} d^{4} e^{3} + a^{2} c^{2} d^{2} e^{5}}\right)} x - \frac{2 \, c^{3} d^{7} e - 7 \, a c^{2} d^{5} e^{3} + 8 \, a^{2} c d^{3} e^{5} - 3 \, a^{3} d e^{7}}{c^{4} d^{6} e - 2 \, a c^{3} d^{4} e^{3} + a^{2} c^{2} d^{2} e^{5}}}{\sqrt{c d x^{2} e + a d e + {\left(c d^{2} + a e^{2}\right)} x}} - \frac{3 \, {\left(c d^{2} e - a e^{3}\right)} \sqrt{c d} e^{\left(-\frac{1}{2}\right)} \log\left({\left| -\sqrt{c d} c d^{2} e^{\frac{1}{2}} - 2 \, {\left(\sqrt{c d} x e^{\frac{1}{2}} - \sqrt{c d x^{2} e + a d e + {\left(c d^{2} + a e^{2}\right)} x}\right)} c d e - \sqrt{c d} a e^{\frac{5}{2}} \right|}\right)}{2 \, c^{3} d^{3}}"," ",0,"(((c^3*d^5*e^3 - 2*a*c^2*d^3*e^5 + a^2*c*d*e^7)*x/(c^4*d^6*e - 2*a*c^3*d^4*e^3 + a^2*c^2*d^2*e^5) - (c^3*d^6*e^2 - 5*a*c^2*d^4*e^4 + 7*a^2*c*d^2*e^6 - 3*a^3*e^8)/(c^4*d^6*e - 2*a*c^3*d^4*e^3 + a^2*c^2*d^2*e^5))*x - (2*c^3*d^7*e - 7*a*c^2*d^5*e^3 + 8*a^2*c*d^3*e^5 - 3*a^3*d*e^7)/(c^4*d^6*e - 2*a*c^3*d^4*e^3 + a^2*c^2*d^2*e^5))/sqrt(c*d*x^2*e + a*d*e + (c*d^2 + a*e^2)*x) - 3/2*(c*d^2*e - a*e^3)*sqrt(c*d)*e^(-1/2)*log(abs(-sqrt(c*d)*c*d^2*e^(1/2) - 2*(sqrt(c*d)*x*e^(1/2) - sqrt(c*d*x^2*e + a*d*e + (c*d^2 + a*e^2)*x))*c*d*e - sqrt(c*d)*a*e^(5/2)))/(c^3*d^3)","B",0
1957,1,229,0,1.152641," ","integrate((e*x+d)^2/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{{\left(c^{2} d^{4} e - 2 \, a c d^{2} e^{3} + a^{2} e^{5}\right)} x}{c^{3} d^{5} - 2 \, a c^{2} d^{3} e^{2} + a^{2} c d e^{4}} + \frac{c^{2} d^{5} - 2 \, a c d^{3} e^{2} + a^{2} d e^{4}}{c^{3} d^{5} - 2 \, a c^{2} d^{3} e^{2} + a^{2} c d e^{4}}\right)}}{\sqrt{c d x^{2} e + a d e + {\left(c d^{2} + a e^{2}\right)} x}} - \frac{\sqrt{c d} e^{\frac{1}{2}} \log\left({\left| -\sqrt{c d} c d^{2} e^{\frac{1}{2}} - 2 \, {\left(\sqrt{c d} x e^{\frac{1}{2}} - \sqrt{c d x^{2} e + a d e + {\left(c d^{2} + a e^{2}\right)} x}\right)} c d e - \sqrt{c d} a e^{\frac{5}{2}} \right|}\right)}{c^{2} d^{2}}"," ",0,"-2*((c^2*d^4*e - 2*a*c*d^2*e^3 + a^2*e^5)*x/(c^3*d^5 - 2*a*c^2*d^3*e^2 + a^2*c*d*e^4) + (c^2*d^5 - 2*a*c*d^3*e^2 + a^2*d*e^4)/(c^3*d^5 - 2*a*c^2*d^3*e^2 + a^2*c*d*e^4))/sqrt(c*d*x^2*e + a*d*e + (c*d^2 + a*e^2)*x) - sqrt(c*d)*e^(1/2)*log(abs(-sqrt(c*d)*c*d^2*e^(1/2) - 2*(sqrt(c*d)*x*e^(1/2) - sqrt(c*d*x^2*e + a*d*e + (c*d^2 + a*e^2)*x))*c*d*e - sqrt(c*d)*a*e^(5/2)))/(c^2*d^2)","B",0
1958,1,109,0,0.522007," ","integrate((e*x+d)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{{\left(c d^{2} e - a e^{3}\right)} x}{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} + \frac{c d^{3} - a d e^{2}}{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}\right)}}{\sqrt{c d x^{2} e + a d e + {\left(c d^{2} + a e^{2}\right)} x}}"," ",0,"-2*((c*d^2*e - a*e^3)*x/(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4) + (c*d^3 - a*d*e^2)/(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4))/sqrt(c*d*x^2*e + a*d*e + (c*d^2 + a*e^2)*x)","B",0
1959,1,99,0,0.497955," ","integrate(1/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{2 \, c d x e}{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} + \frac{c d^{2} + a e^{2}}{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}\right)}}{\sqrt{c d x^{2} e + a d e + {\left(c d^{2} + a e^{2}\right)} x}}"," ",0,"-2*(2*c*d*x*e/(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4) + (c*d^2 + a*e^2)/(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4))/sqrt(c*d*x^2*e + a*d*e + (c*d^2 + a*e^2)*x)","A",0
1960,-2,0,0,0.000000," ","integrate(1/(e*x+d)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to transpose Error: Bad Argument Value","F(-2)",0
1961,0,0,0,0.000000," ","integrate(1/(e*x+d)^2/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
1962,-2,0,0,0.000000," ","integrate(1/(e*x+d)^3/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 0.43Unable to transpose Error: Bad Argument Value","F(-2)",0
1963,-2,0,0,0.000000," ","integrate(1/(e*x+d)^4/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 0.46Unable to transpose Error: Bad Argument Value","F(-2)",0
1964,1,1030,0,0.795321," ","integrate((e*x+d)^6/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2),x, algorithm=""giac"")","\frac{{\left({\left({\left(3 \, {\left(\frac{2 \, {\left(c^{7} d^{11} e^{8} - 4 \, a c^{6} d^{9} e^{10} + 6 \, a^{2} c^{5} d^{7} e^{12} - 4 \, a^{3} c^{4} d^{5} e^{14} + a^{4} c^{3} d^{3} e^{16}\right)} x}{c^{8} d^{12} e^{3} - 4 \, a c^{7} d^{10} e^{5} + 6 \, a^{2} c^{6} d^{8} e^{7} - 4 \, a^{3} c^{5} d^{6} e^{9} + a^{4} c^{4} d^{4} e^{11}} + \frac{17 \, c^{7} d^{12} e^{7} - 75 \, a c^{6} d^{10} e^{9} + 130 \, a^{2} c^{5} d^{8} e^{11} - 110 \, a^{3} c^{4} d^{6} e^{13} + 45 \, a^{4} c^{3} d^{4} e^{15} - 7 \, a^{5} c^{2} d^{2} e^{17}}{c^{8} d^{12} e^{3} - 4 \, a c^{7} d^{10} e^{5} + 6 \, a^{2} c^{6} d^{8} e^{7} - 4 \, a^{3} c^{5} d^{6} e^{9} + a^{4} c^{4} d^{4} e^{11}}\right)} x + \frac{4 \, {\left(c^{7} d^{13} e^{6} + 45 \, a c^{6} d^{11} e^{8} - 225 \, a^{2} c^{5} d^{9} e^{10} + 430 \, a^{3} c^{4} d^{7} e^{12} - 405 \, a^{4} c^{3} d^{5} e^{14} + 189 \, a^{5} c^{2} d^{3} e^{16} - 35 \, a^{6} c d e^{18}\right)}}{c^{8} d^{12} e^{3} - 4 \, a c^{7} d^{10} e^{5} + 6 \, a^{2} c^{6} d^{8} e^{7} - 4 \, a^{3} c^{5} d^{6} e^{9} + a^{4} c^{4} d^{4} e^{11}}\right)} x - \frac{3 \, {\left(43 \, c^{7} d^{14} e^{5} - 305 \, a c^{6} d^{12} e^{7} + 825 \, a^{2} c^{5} d^{10} e^{9} - 1075 \, a^{3} c^{4} d^{8} e^{11} + 645 \, a^{4} c^{3} d^{6} e^{13} - 63 \, a^{5} c^{2} d^{4} e^{15} - 105 \, a^{6} c d^{2} e^{17} + 35 \, a^{7} e^{19}\right)}}{c^{8} d^{12} e^{3} - 4 \, a c^{7} d^{10} e^{5} + 6 \, a^{2} c^{6} d^{8} e^{7} - 4 \, a^{3} c^{5} d^{6} e^{9} + a^{4} c^{4} d^{4} e^{11}}\right)} x - \frac{6 \, {\left(16 \, c^{7} d^{15} e^{4} - 85 \, a c^{6} d^{13} e^{6} + 145 \, a^{2} c^{5} d^{11} e^{8} - 15 \, a^{3} c^{4} d^{9} e^{10} - 250 \, a^{4} c^{3} d^{7} e^{12} + 329 \, a^{5} c^{2} d^{5} e^{14} - 175 \, a^{6} c d^{3} e^{16} + 35 \, a^{7} d e^{18}\right)}}{c^{8} d^{12} e^{3} - 4 \, a c^{7} d^{10} e^{5} + 6 \, a^{2} c^{6} d^{8} e^{7} - 4 \, a^{3} c^{5} d^{6} e^{9} + a^{4} c^{4} d^{4} e^{11}}\right)} x - \frac{8 \, c^{7} d^{16} e^{3} + 24 \, a c^{6} d^{14} e^{5} - 351 \, a^{2} c^{5} d^{12} e^{7} + 1109 \, a^{3} c^{4} d^{10} e^{9} - 1686 \, a^{4} c^{3} d^{8} e^{11} + 1386 \, a^{5} c^{2} d^{6} e^{13} - 595 \, a^{6} c d^{4} e^{15} + 105 \, a^{7} d^{2} e^{17}}{c^{8} d^{12} e^{3} - 4 \, a c^{7} d^{10} e^{5} + 6 \, a^{2} c^{6} d^{8} e^{7} - 4 \, a^{3} c^{5} d^{6} e^{9} + a^{4} c^{4} d^{4} e^{11}}}{12 \, {\left(c d x^{2} e + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)}^{\frac{3}{2}}} - \frac{35 \, {\left(c^{2} d^{4} e^{2} - 2 \, a c d^{2} e^{4} + a^{2} e^{6}\right)} \sqrt{c d} e^{\left(-\frac{1}{2}\right)} \log\left({\left| -\sqrt{c d} c d^{2} e^{\frac{1}{2}} - 2 \, {\left(\sqrt{c d} x e^{\frac{1}{2}} - \sqrt{c d x^{2} e + a d e + {\left(c d^{2} + a e^{2}\right)} x}\right)} c d e - \sqrt{c d} a e^{\frac{5}{2}} \right|}\right)}{8 \, c^{5} d^{5}}"," ",0,"1/12*((((3*(2*(c^7*d^11*e^8 - 4*a*c^6*d^9*e^10 + 6*a^2*c^5*d^7*e^12 - 4*a^3*c^4*d^5*e^14 + a^4*c^3*d^3*e^16)*x/(c^8*d^12*e^3 - 4*a*c^7*d^10*e^5 + 6*a^2*c^6*d^8*e^7 - 4*a^3*c^5*d^6*e^9 + a^4*c^4*d^4*e^11) + (17*c^7*d^12*e^7 - 75*a*c^6*d^10*e^9 + 130*a^2*c^5*d^8*e^11 - 110*a^3*c^4*d^6*e^13 + 45*a^4*c^3*d^4*e^15 - 7*a^5*c^2*d^2*e^17)/(c^8*d^12*e^3 - 4*a*c^7*d^10*e^5 + 6*a^2*c^6*d^8*e^7 - 4*a^3*c^5*d^6*e^9 + a^4*c^4*d^4*e^11))*x + 4*(c^7*d^13*e^6 + 45*a*c^6*d^11*e^8 - 225*a^2*c^5*d^9*e^10 + 430*a^3*c^4*d^7*e^12 - 405*a^4*c^3*d^5*e^14 + 189*a^5*c^2*d^3*e^16 - 35*a^6*c*d*e^18)/(c^8*d^12*e^3 - 4*a*c^7*d^10*e^5 + 6*a^2*c^6*d^8*e^7 - 4*a^3*c^5*d^6*e^9 + a^4*c^4*d^4*e^11))*x - 3*(43*c^7*d^14*e^5 - 305*a*c^6*d^12*e^7 + 825*a^2*c^5*d^10*e^9 - 1075*a^3*c^4*d^8*e^11 + 645*a^4*c^3*d^6*e^13 - 63*a^5*c^2*d^4*e^15 - 105*a^6*c*d^2*e^17 + 35*a^7*e^19)/(c^8*d^12*e^3 - 4*a*c^7*d^10*e^5 + 6*a^2*c^6*d^8*e^7 - 4*a^3*c^5*d^6*e^9 + a^4*c^4*d^4*e^11))*x - 6*(16*c^7*d^15*e^4 - 85*a*c^6*d^13*e^6 + 145*a^2*c^5*d^11*e^8 - 15*a^3*c^4*d^9*e^10 - 250*a^4*c^3*d^7*e^12 + 329*a^5*c^2*d^5*e^14 - 175*a^6*c*d^3*e^16 + 35*a^7*d*e^18)/(c^8*d^12*e^3 - 4*a*c^7*d^10*e^5 + 6*a^2*c^6*d^8*e^7 - 4*a^3*c^5*d^6*e^9 + a^4*c^4*d^4*e^11))*x - (8*c^7*d^16*e^3 + 24*a*c^6*d^14*e^5 - 351*a^2*c^5*d^12*e^7 + 1109*a^3*c^4*d^10*e^9 - 1686*a^4*c^3*d^8*e^11 + 1386*a^5*c^2*d^6*e^13 - 595*a^6*c*d^4*e^15 + 105*a^7*d^2*e^17)/(c^8*d^12*e^3 - 4*a*c^7*d^10*e^5 + 6*a^2*c^6*d^8*e^7 - 4*a^3*c^5*d^6*e^9 + a^4*c^4*d^4*e^11))/(c*d*x^2*e + a*d*e + (c*d^2 + a*e^2)*x)^(3/2) - 35/8*(c^2*d^4*e^2 - 2*a*c*d^2*e^4 + a^2*e^6)*sqrt(c*d)*e^(-1/2)*log(abs(-sqrt(c*d)*c*d^2*e^(1/2) - 2*(sqrt(c*d)*x*e^(1/2) - sqrt(c*d*x^2*e + a*d*e + (c*d^2 + a*e^2)*x))*c*d*e - sqrt(c*d)*a*e^(5/2)))/(c^5*d^5)","B",0
1965,1,827,0,0.770937," ","integrate((e*x+d)^5/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2),x, algorithm=""giac"")","\frac{{\left({\left({\left(\frac{3 \, {\left(c^{6} d^{10} e^{6} - 4 \, a c^{5} d^{8} e^{8} + 6 \, a^{2} c^{4} d^{6} e^{10} - 4 \, a^{3} c^{3} d^{4} e^{12} + a^{4} c^{2} d^{2} e^{14}\right)} x}{c^{7} d^{11} e^{2} - 4 \, a c^{6} d^{9} e^{4} + 6 \, a^{2} c^{5} d^{7} e^{6} - 4 \, a^{3} c^{4} d^{5} e^{8} + a^{4} c^{3} d^{3} e^{10}} - \frac{4 \, {\left(2 \, c^{6} d^{11} e^{5} - 13 \, a c^{5} d^{9} e^{7} + 32 \, a^{2} c^{4} d^{7} e^{9} - 38 \, a^{3} c^{3} d^{5} e^{11} + 22 \, a^{4} c^{2} d^{3} e^{13} - 5 \, a^{5} c d e^{15}\right)}}{c^{7} d^{11} e^{2} - 4 \, a c^{6} d^{9} e^{4} + 6 \, a^{2} c^{5} d^{7} e^{6} - 4 \, a^{3} c^{4} d^{5} e^{8} + a^{4} c^{3} d^{3} e^{10}}\right)} x - \frac{3 \, {\left(9 \, c^{6} d^{12} e^{4} - 46 \, a c^{5} d^{10} e^{6} + 89 \, a^{2} c^{4} d^{8} e^{8} - 76 \, a^{3} c^{3} d^{6} e^{10} + 19 \, a^{4} c^{2} d^{4} e^{12} + 10 \, a^{5} c d^{2} e^{14} - 5 \, a^{6} e^{16}\right)}}{c^{7} d^{11} e^{2} - 4 \, a c^{6} d^{9} e^{4} + 6 \, a^{2} c^{5} d^{7} e^{6} - 4 \, a^{3} c^{4} d^{5} e^{8} + a^{4} c^{3} d^{3} e^{10}}\right)} x - \frac{6 \, {\left(3 \, c^{6} d^{13} e^{3} - 12 \, a c^{5} d^{11} e^{5} + 13 \, a^{2} c^{4} d^{9} e^{7} + 8 \, a^{3} c^{3} d^{7} e^{9} - 27 \, a^{4} c^{2} d^{5} e^{11} + 20 \, a^{5} c d^{3} e^{13} - 5 \, a^{6} d e^{15}\right)}}{c^{7} d^{11} e^{2} - 4 \, a c^{6} d^{9} e^{4} + 6 \, a^{2} c^{5} d^{7} e^{6} - 4 \, a^{3} c^{4} d^{5} e^{8} + a^{4} c^{3} d^{3} e^{10}}\right)} x - \frac{2 \, c^{6} d^{14} e^{2} + 2 \, a c^{5} d^{12} e^{4} - 43 \, a^{2} c^{4} d^{10} e^{6} + 112 \, a^{3} c^{3} d^{8} e^{8} - 128 \, a^{4} c^{2} d^{6} e^{10} + 70 \, a^{5} c d^{4} e^{12} - 15 \, a^{6} d^{2} e^{14}}{c^{7} d^{11} e^{2} - 4 \, a c^{6} d^{9} e^{4} + 6 \, a^{2} c^{5} d^{7} e^{6} - 4 \, a^{3} c^{4} d^{5} e^{8} + a^{4} c^{3} d^{3} e^{10}}}{3 \, {\left(c d x^{2} e + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)}^{\frac{3}{2}}} - \frac{5 \, {\left(c d^{2} e^{2} - a e^{4}\right)} \sqrt{c d} e^{\left(-\frac{1}{2}\right)} \log\left({\left| -\sqrt{c d} c d^{2} e^{\frac{1}{2}} - 2 \, {\left(\sqrt{c d} x e^{\frac{1}{2}} - \sqrt{c d x^{2} e + a d e + {\left(c d^{2} + a e^{2}\right)} x}\right)} c d e - \sqrt{c d} a e^{\frac{5}{2}} \right|}\right)}{2 \, c^{4} d^{4}}"," ",0,"1/3*((((3*(c^6*d^10*e^6 - 4*a*c^5*d^8*e^8 + 6*a^2*c^4*d^6*e^10 - 4*a^3*c^3*d^4*e^12 + a^4*c^2*d^2*e^14)*x/(c^7*d^11*e^2 - 4*a*c^6*d^9*e^4 + 6*a^2*c^5*d^7*e^6 - 4*a^3*c^4*d^5*e^8 + a^4*c^3*d^3*e^10) - 4*(2*c^6*d^11*e^5 - 13*a*c^5*d^9*e^7 + 32*a^2*c^4*d^7*e^9 - 38*a^3*c^3*d^5*e^11 + 22*a^4*c^2*d^3*e^13 - 5*a^5*c*d*e^15)/(c^7*d^11*e^2 - 4*a*c^6*d^9*e^4 + 6*a^2*c^5*d^7*e^6 - 4*a^3*c^4*d^5*e^8 + a^4*c^3*d^3*e^10))*x - 3*(9*c^6*d^12*e^4 - 46*a*c^5*d^10*e^6 + 89*a^2*c^4*d^8*e^8 - 76*a^3*c^3*d^6*e^10 + 19*a^4*c^2*d^4*e^12 + 10*a^5*c*d^2*e^14 - 5*a^6*e^16)/(c^7*d^11*e^2 - 4*a*c^6*d^9*e^4 + 6*a^2*c^5*d^7*e^6 - 4*a^3*c^4*d^5*e^8 + a^4*c^3*d^3*e^10))*x - 6*(3*c^6*d^13*e^3 - 12*a*c^5*d^11*e^5 + 13*a^2*c^4*d^9*e^7 + 8*a^3*c^3*d^7*e^9 - 27*a^4*c^2*d^5*e^11 + 20*a^5*c*d^3*e^13 - 5*a^6*d*e^15)/(c^7*d^11*e^2 - 4*a*c^6*d^9*e^4 + 6*a^2*c^5*d^7*e^6 - 4*a^3*c^4*d^5*e^8 + a^4*c^3*d^3*e^10))*x - (2*c^6*d^14*e^2 + 2*a*c^5*d^12*e^4 - 43*a^2*c^4*d^10*e^6 + 112*a^3*c^3*d^8*e^8 - 128*a^4*c^2*d^6*e^10 + 70*a^5*c*d^4*e^12 - 15*a^6*d^2*e^14)/(c^7*d^11*e^2 - 4*a*c^6*d^9*e^4 + 6*a^2*c^5*d^7*e^6 - 4*a^3*c^4*d^5*e^8 + a^4*c^3*d^3*e^10))/(c*d*x^2*e + a*d*e + (c*d^2 + a*e^2)*x)^(3/2) - 5/2*(c*d^2*e^2 - a*e^4)*sqrt(c*d)*e^(-1/2)*log(abs(-sqrt(c*d)*c*d^2*e^(1/2) - 2*(sqrt(c*d)*x*e^(1/2) - sqrt(c*d*x^2*e + a*d*e + (c*d^2 + a*e^2)*x))*c*d*e - sqrt(c*d)*a*e^(5/2)))/(c^4*d^4)","B",0
1966,1,620,0,0.767157," ","integrate((e*x+d)^4/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2),x, algorithm=""giac"")","-\frac{2 \, {\left({\left({\left(\frac{4 \, {\left(c^{5} d^{9} e^{3} - 4 \, a c^{4} d^{7} e^{5} + 6 \, a^{2} c^{3} d^{5} e^{7} - 4 \, a^{3} c^{2} d^{3} e^{9} + a^{4} c d e^{11}\right)} x}{c^{6} d^{10} - 4 \, a c^{5} d^{8} e^{2} + 6 \, a^{2} c^{4} d^{6} e^{4} - 4 \, a^{3} c^{3} d^{4} e^{6} + a^{4} c^{2} d^{2} e^{8}} + \frac{3 \, {\left(3 \, c^{5} d^{10} e^{2} - 11 \, a c^{4} d^{8} e^{4} + 14 \, a^{2} c^{3} d^{6} e^{6} - 6 \, a^{3} c^{2} d^{4} e^{8} - a^{4} c d^{2} e^{10} + a^{5} e^{12}\right)}}{c^{6} d^{10} - 4 \, a c^{5} d^{8} e^{2} + 6 \, a^{2} c^{4} d^{6} e^{4} - 4 \, a^{3} c^{3} d^{4} e^{6} + a^{4} c^{2} d^{2} e^{8}}\right)} x + \frac{6 \, {\left(c^{5} d^{11} e - 3 \, a c^{4} d^{9} e^{3} + 2 \, a^{2} c^{3} d^{7} e^{5} + 2 \, a^{3} c^{2} d^{5} e^{7} - 3 \, a^{4} c d^{3} e^{9} + a^{5} d e^{11}\right)}}{c^{6} d^{10} - 4 \, a c^{5} d^{8} e^{2} + 6 \, a^{2} c^{4} d^{6} e^{4} - 4 \, a^{3} c^{3} d^{4} e^{6} + a^{4} c^{2} d^{2} e^{8}}\right)} x + \frac{c^{5} d^{12} - a c^{4} d^{10} e^{2} - 6 \, a^{2} c^{3} d^{8} e^{4} + 14 \, a^{3} c^{2} d^{6} e^{6} - 11 \, a^{4} c d^{4} e^{8} + 3 \, a^{5} d^{2} e^{10}}{c^{6} d^{10} - 4 \, a c^{5} d^{8} e^{2} + 6 \, a^{2} c^{4} d^{6} e^{4} - 4 \, a^{3} c^{3} d^{4} e^{6} + a^{4} c^{2} d^{2} e^{8}}\right)}}{3 \, {\left(c d x^{2} e + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)}^{\frac{3}{2}}} - \frac{\sqrt{c d} e^{\frac{3}{2}} \log\left({\left| -\sqrt{c d} c d^{2} e^{\frac{1}{2}} - 2 \, {\left(\sqrt{c d} x e^{\frac{1}{2}} - \sqrt{c d x^{2} e + a d e + {\left(c d^{2} + a e^{2}\right)} x}\right)} c d e - \sqrt{c d} a e^{\frac{5}{2}} \right|}\right)}{c^{3} d^{3}}"," ",0,"-2/3*(((4*(c^5*d^9*e^3 - 4*a*c^4*d^7*e^5 + 6*a^2*c^3*d^5*e^7 - 4*a^3*c^2*d^3*e^9 + a^4*c*d*e^11)*x/(c^6*d^10 - 4*a*c^5*d^8*e^2 + 6*a^2*c^4*d^6*e^4 - 4*a^3*c^3*d^4*e^6 + a^4*c^2*d^2*e^8) + 3*(3*c^5*d^10*e^2 - 11*a*c^4*d^8*e^4 + 14*a^2*c^3*d^6*e^6 - 6*a^3*c^2*d^4*e^8 - a^4*c*d^2*e^10 + a^5*e^12)/(c^6*d^10 - 4*a*c^5*d^8*e^2 + 6*a^2*c^4*d^6*e^4 - 4*a^3*c^3*d^4*e^6 + a^4*c^2*d^2*e^8))*x + 6*(c^5*d^11*e - 3*a*c^4*d^9*e^3 + 2*a^2*c^3*d^7*e^5 + 2*a^3*c^2*d^5*e^7 - 3*a^4*c*d^3*e^9 + a^5*d*e^11)/(c^6*d^10 - 4*a*c^5*d^8*e^2 + 6*a^2*c^4*d^6*e^4 - 4*a^3*c^3*d^4*e^6 + a^4*c^2*d^2*e^8))*x + (c^5*d^12 - a*c^4*d^10*e^2 - 6*a^2*c^3*d^8*e^4 + 14*a^3*c^2*d^6*e^6 - 11*a^4*c*d^4*e^8 + 3*a^5*d^2*e^10)/(c^6*d^10 - 4*a*c^5*d^8*e^2 + 6*a^2*c^4*d^6*e^4 - 4*a^3*c^3*d^4*e^6 + a^4*c^2*d^2*e^8))/(c*d*x^2*e + a*d*e + (c*d^2 + a*e^2)*x)^(3/2) - sqrt(c*d)*e^(3/2)*log(abs(-sqrt(c*d)*c*d^2*e^(1/2) - 2*(sqrt(c*d)*x*e^(1/2) - sqrt(c*d*x^2*e + a*d*e + (c*d^2 + a*e^2)*x))*c*d*e - sqrt(c*d)*a*e^(5/2)))/(c^3*d^3)","B",0
1967,1,409,0,0.636960," ","integrate((e*x+d)^3/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2),x, algorithm=""giac"")","-\frac{2 \, {\left({\left({\left(\frac{{\left(c^{3} d^{6} e^{3} - 3 \, a c^{2} d^{4} e^{5} + 3 \, a^{2} c d^{2} e^{7} - a^{3} e^{9}\right)} x}{c^{4} d^{8} - 4 \, a c^{3} d^{6} e^{2} + 6 \, a^{2} c^{2} d^{4} e^{4} - 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}} + \frac{3 \, {\left(c^{3} d^{7} e^{2} - 3 \, a c^{2} d^{5} e^{4} + 3 \, a^{2} c d^{3} e^{6} - a^{3} d e^{8}\right)}}{c^{4} d^{8} - 4 \, a c^{3} d^{6} e^{2} + 6 \, a^{2} c^{2} d^{4} e^{4} - 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}\right)} x + \frac{3 \, {\left(c^{3} d^{8} e - 3 \, a c^{2} d^{6} e^{3} + 3 \, a^{2} c d^{4} e^{5} - a^{3} d^{2} e^{7}\right)}}{c^{4} d^{8} - 4 \, a c^{3} d^{6} e^{2} + 6 \, a^{2} c^{2} d^{4} e^{4} - 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}\right)} x + \frac{c^{3} d^{9} - 3 \, a c^{2} d^{7} e^{2} + 3 \, a^{2} c d^{5} e^{4} - a^{3} d^{3} e^{6}}{c^{4} d^{8} - 4 \, a c^{3} d^{6} e^{2} + 6 \, a^{2} c^{2} d^{4} e^{4} - 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}\right)}}{3 \, {\left(c d x^{2} e + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)}^{\frac{3}{2}}}"," ",0,"-2/3*((((c^3*d^6*e^3 - 3*a*c^2*d^4*e^5 + 3*a^2*c*d^2*e^7 - a^3*e^9)*x/(c^4*d^8 - 4*a*c^3*d^6*e^2 + 6*a^2*c^2*d^4*e^4 - 4*a^3*c*d^2*e^6 + a^4*e^8) + 3*(c^3*d^7*e^2 - 3*a*c^2*d^5*e^4 + 3*a^2*c*d^3*e^6 - a^3*d*e^8)/(c^4*d^8 - 4*a*c^3*d^6*e^2 + 6*a^2*c^2*d^4*e^4 - 4*a^3*c*d^2*e^6 + a^4*e^8))*x + 3*(c^3*d^8*e - 3*a*c^2*d^6*e^3 + 3*a^2*c*d^4*e^5 - a^3*d^2*e^7)/(c^4*d^8 - 4*a*c^3*d^6*e^2 + 6*a^2*c^2*d^4*e^4 - 4*a^3*c*d^2*e^6 + a^4*e^8))*x + (c^3*d^9 - 3*a*c^2*d^7*e^2 + 3*a^2*c*d^5*e^4 - a^3*d^3*e^6)/(c^4*d^8 - 4*a*c^3*d^6*e^2 + 6*a^2*c^2*d^4*e^4 - 4*a^3*c*d^2*e^6 + a^4*e^8))/(c*d*x^2*e + a*d*e + (c*d^2 + a*e^2)*x)^(3/2)","B",0
1968,1,386,0,0.648621," ","integrate((e*x+d)^2/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2),x, algorithm=""giac"")","\frac{2 \, {\left({\left({\left(\frac{2 \, {\left(c^{3} d^{5} e^{3} - 2 \, a c^{2} d^{3} e^{5} + a^{2} c d e^{7}\right)} x}{c^{4} d^{8} - 4 \, a c^{3} d^{6} e^{2} + 6 \, a^{2} c^{2} d^{4} e^{4} - 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}} + \frac{3 \, {\left(c^{3} d^{6} e^{2} - a c^{2} d^{4} e^{4} - a^{2} c d^{2} e^{6} + a^{3} e^{8}\right)}}{c^{4} d^{8} - 4 \, a c^{3} d^{6} e^{2} + 6 \, a^{2} c^{2} d^{4} e^{4} - 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}\right)} x + \frac{6 \, {\left(a c^{2} d^{5} e^{3} - 2 \, a^{2} c d^{3} e^{5} + a^{3} d e^{7}\right)}}{c^{4} d^{8} - 4 \, a c^{3} d^{6} e^{2} + 6 \, a^{2} c^{2} d^{4} e^{4} - 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}\right)} x - \frac{c^{3} d^{8} - 5 \, a c^{2} d^{6} e^{2} + 7 \, a^{2} c d^{4} e^{4} - 3 \, a^{3} d^{2} e^{6}}{c^{4} d^{8} - 4 \, a c^{3} d^{6} e^{2} + 6 \, a^{2} c^{2} d^{4} e^{4} - 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}\right)}}{3 \, {\left(c d x^{2} e + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)}^{\frac{3}{2}}}"," ",0,"2/3*(((2*(c^3*d^5*e^3 - 2*a*c^2*d^3*e^5 + a^2*c*d*e^7)*x/(c^4*d^8 - 4*a*c^3*d^6*e^2 + 6*a^2*c^2*d^4*e^4 - 4*a^3*c*d^2*e^6 + a^4*e^8) + 3*(c^3*d^6*e^2 - a*c^2*d^4*e^4 - a^2*c*d^2*e^6 + a^3*e^8)/(c^4*d^8 - 4*a*c^3*d^6*e^2 + 6*a^2*c^2*d^4*e^4 - 4*a^3*c*d^2*e^6 + a^4*e^8))*x + 6*(a*c^2*d^5*e^3 - 2*a^2*c*d^3*e^5 + a^3*d*e^7)/(c^4*d^8 - 4*a*c^3*d^6*e^2 + 6*a^2*c^2*d^4*e^4 - 4*a^3*c*d^2*e^6 + a^4*e^8))*x - (c^3*d^8 - 5*a*c^2*d^6*e^2 + 7*a^2*c*d^4*e^4 - 3*a^3*d^2*e^6)/(c^4*d^8 - 4*a*c^3*d^6*e^2 + 6*a^2*c^2*d^4*e^4 - 4*a^3*c*d^2*e^6 + a^4*e^8))/(c*d*x^2*e + a*d*e + (c*d^2 + a*e^2)*x)^(3/2)","B",0
1969,1,368,0,0.590016," ","integrate((e*x+d)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2),x, algorithm=""giac"")","\frac{2 \, {\left({\left(4 \, {\left(\frac{2 \, {\left(c^{3} d^{4} e^{3} - a c^{2} d^{2} e^{5}\right)} x}{c^{4} d^{8} - 4 \, a c^{3} d^{6} e^{2} + 6 \, a^{2} c^{2} d^{4} e^{4} - 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}} + \frac{3 \, {\left(c^{3} d^{5} e^{2} - a^{2} c d e^{6}\right)}}{c^{4} d^{8} - 4 \, a c^{3} d^{6} e^{2} + 6 \, a^{2} c^{2} d^{4} e^{4} - 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}\right)} x + \frac{3 \, {\left(c^{3} d^{6} e + 5 \, a c^{2} d^{4} e^{3} - 5 \, a^{2} c d^{2} e^{5} - a^{3} e^{7}\right)}}{c^{4} d^{8} - 4 \, a c^{3} d^{6} e^{2} + 6 \, a^{2} c^{2} d^{4} e^{4} - 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}\right)} x - \frac{c^{3} d^{7} - 7 \, a c^{2} d^{5} e^{2} + 3 \, a^{2} c d^{3} e^{4} + 3 \, a^{3} d e^{6}}{c^{4} d^{8} - 4 \, a c^{3} d^{6} e^{2} + 6 \, a^{2} c^{2} d^{4} e^{4} - 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}\right)}}{3 \, {\left(c d x^{2} e + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)}^{\frac{3}{2}}}"," ",0,"2/3*((4*(2*(c^3*d^4*e^3 - a*c^2*d^2*e^5)*x/(c^4*d^8 - 4*a*c^3*d^6*e^2 + 6*a^2*c^2*d^4*e^4 - 4*a^3*c*d^2*e^6 + a^4*e^8) + 3*(c^3*d^5*e^2 - a^2*c*d*e^6)/(c^4*d^8 - 4*a*c^3*d^6*e^2 + 6*a^2*c^2*d^4*e^4 - 4*a^3*c*d^2*e^6 + a^4*e^8))*x + 3*(c^3*d^6*e + 5*a*c^2*d^4*e^3 - 5*a^2*c*d^2*e^5 - a^3*e^7)/(c^4*d^8 - 4*a*c^3*d^6*e^2 + 6*a^2*c^2*d^4*e^4 - 4*a^3*c*d^2*e^6 + a^4*e^8))*x - (c^3*d^7 - 7*a*c^2*d^5*e^2 + 3*a^2*c*d^3*e^4 + 3*a^3*d*e^6)/(c^4*d^8 - 4*a*c^3*d^6*e^2 + 6*a^2*c^2*d^4*e^4 - 4*a^3*c*d^2*e^6 + a^4*e^8))/(c*d*x^2*e + a*d*e + (c*d^2 + a*e^2)*x)^(3/2)","B",0
1970,1,345,0,0.573011," ","integrate(1/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2),x, algorithm=""giac"")","\frac{2 \, {\left(2 \, {\left(4 \, {\left(\frac{2 \, c^{3} d^{3} x e^{3}}{c^{4} d^{8} - 4 \, a c^{3} d^{6} e^{2} + 6 \, a^{2} c^{2} d^{4} e^{4} - 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}} + \frac{3 \, {\left(c^{3} d^{4} e^{2} + a c^{2} d^{2} e^{4}\right)}}{c^{4} d^{8} - 4 \, a c^{3} d^{6} e^{2} + 6 \, a^{2} c^{2} d^{4} e^{4} - 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}\right)} x + \frac{3 \, {\left(c^{3} d^{5} e + 6 \, a c^{2} d^{3} e^{3} + a^{2} c d e^{5}\right)}}{c^{4} d^{8} - 4 \, a c^{3} d^{6} e^{2} + 6 \, a^{2} c^{2} d^{4} e^{4} - 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}\right)} x - \frac{c^{3} d^{6} - 9 \, a c^{2} d^{4} e^{2} - 9 \, a^{2} c d^{2} e^{4} + a^{3} e^{6}}{c^{4} d^{8} - 4 \, a c^{3} d^{6} e^{2} + 6 \, a^{2} c^{2} d^{4} e^{4} - 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}\right)}}{3 \, {\left(c d x^{2} e + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)}^{\frac{3}{2}}}"," ",0,"2/3*(2*(4*(2*c^3*d^3*x*e^3/(c^4*d^8 - 4*a*c^3*d^6*e^2 + 6*a^2*c^2*d^4*e^4 - 4*a^3*c*d^2*e^6 + a^4*e^8) + 3*(c^3*d^4*e^2 + a*c^2*d^2*e^4)/(c^4*d^8 - 4*a*c^3*d^6*e^2 + 6*a^2*c^2*d^4*e^4 - 4*a^3*c*d^2*e^6 + a^4*e^8))*x + 3*(c^3*d^5*e + 6*a*c^2*d^3*e^3 + a^2*c*d*e^5)/(c^4*d^8 - 4*a*c^3*d^6*e^2 + 6*a^2*c^2*d^4*e^4 - 4*a^3*c*d^2*e^6 + a^4*e^8))*x - (c^3*d^6 - 9*a*c^2*d^4*e^2 - 9*a^2*c*d^2*e^4 + a^3*e^6)/(c^4*d^8 - 4*a*c^3*d^6*e^2 + 6*a^2*c^2*d^4*e^4 - 4*a^3*c*d^2*e^6 + a^4*e^8))/(c*d*x^2*e + a*d*e + (c*d^2 + a*e^2)*x)^(3/2)","B",0
1971,-2,0,0,0.000000," ","integrate(1/(e*x+d)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 0.47Unable to transpose Error: Bad Argument Value","F(-2)",0
1972,0,0,0,0.000000," ","integrate(1/(e*x+d)^2/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
1973,-2,0,0,0.000000," ","integrate(1/(e*x+d)^3/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 0.57Unable to transpose Error: Bad Argument Value","F(-2)",0
1974,0,0,0,0.000000," ","integrate((e*x+d)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/3),x, algorithm=""giac"")","\int \frac{e x + d}{{\left(c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((e*x + d)/(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)^(1/3), x)","F",0
1975,0,0,0,0.000000," ","integrate(1/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)^(-1/3), x)","F",0
1976,1,336,0,0.177684," ","integrate((e*x+d)^(3/2)*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x, algorithm=""giac"")","\frac{2}{315} \, {\left(105 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} c d^{4} e^{\left(-1\right)} + 63 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} c d^{3} e^{\left(-1\right)} + 315 \, \sqrt{x e + d} a d^{3} e + 315 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a d^{2} e + 27 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} c d^{2} e^{\left(-1\right)} + 63 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a d e + {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} c d e^{\left(-1\right)} + 9 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a e\right)} e^{\left(-1\right)}"," ",0,"2/315*(105*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*c*d^4*e^(-1) + 63*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*c*d^3*e^(-1) + 315*sqrt(x*e + d)*a*d^3*e + 315*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a*d^2*e + 27*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*c*d^2*e^(-1) + 63*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a*d*e + (35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*c*d*e^(-1) + 9*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*e)*e^(-1)","B",0
1977,1,212,0,0.165962," ","integrate((e*x+d)^(1/2)*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x, algorithm=""giac"")","\frac{2}{105} \, {\left(35 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} c d^{3} e^{\left(-1\right)} + 14 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} c d^{2} e^{\left(-1\right)} + 105 \, \sqrt{x e + d} a d^{2} e + 70 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a d e + 3 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} c d e^{\left(-1\right)} + 7 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a e\right)} e^{\left(-1\right)}"," ",0,"2/105*(35*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*c*d^3*e^(-1) + 14*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*c*d^2*e^(-1) + 105*sqrt(x*e + d)*a*d^2*e + 70*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a*d*e + 3*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*c*d*e^(-1) + 7*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a*e)*e^(-1)","B",0
1978,1,112,0,0.159291," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)/(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{15} \, {\left(5 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} c d^{2} e^{\left(-1\right)} + {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} c d e^{\left(-1\right)} + 15 \, \sqrt{x e + d} a d e + 5 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a e\right)} e^{\left(-1\right)}"," ",0,"2/15*(5*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*c*d^2*e^(-1) + (3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*c*d*e^(-1) + 15*sqrt(x*e + d)*a*d*e + 5*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a*e)*e^(-1)","B",0
1979,1,47,0,0.216129," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)/(e*x+d)^(3/2),x, algorithm=""giac"")","\frac{2}{3} \, {\left({\left(x e + d\right)}^{\frac{3}{2}} c d e^{4} - 3 \, \sqrt{x e + d} c d^{2} e^{4} + 3 \, \sqrt{x e + d} a e^{6}\right)} e^{\left(-6\right)}"," ",0,"2/3*((x*e + d)^(3/2)*c*d*e^4 - 3*sqrt(x*e + d)*c*d^2*e^4 + 3*sqrt(x*e + d)*a*e^6)*e^(-6)","A",0
1980,1,50,0,0.211335," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)/(e*x+d)^(5/2),x, algorithm=""giac"")","2 \, \sqrt{x e + d} c d e^{\left(-2\right)} + \frac{2 \, {\left({\left(x e + d\right)} c d^{2} - {\left(x e + d\right)} a e^{2}\right)} e^{\left(-2\right)}}{{\left(x e + d\right)}^{\frac{3}{2}}}"," ",0,"2*sqrt(x*e + d)*c*d*e^(-2) + 2*((x*e + d)*c*d^2 - (x*e + d)*a*e^2)*e^(-2)/(x*e + d)^(3/2)","A",0
1981,1,47,0,0.210548," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)/(e*x+d)^(7/2),x, algorithm=""giac"")","-\frac{2 \, {\left(3 \, {\left(x e + d\right)}^{2} c d - {\left(x e + d\right)} c d^{2} + {\left(x e + d\right)} a e^{2}\right)} e^{\left(-2\right)}}{3 \, {\left(x e + d\right)}^{\frac{5}{2}}}"," ",0,"-2/3*(3*(x*e + d)^2*c*d - (x*e + d)*c*d^2 + (x*e + d)*a*e^2)*e^(-2)/(x*e + d)^(5/2)","A",0
1982,1,48,0,0.172676," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)/(e*x+d)^(9/2),x, algorithm=""giac"")","-\frac{2 \, {\left(5 \, {\left(x e + d\right)}^{2} c d - 3 \, {\left(x e + d\right)} c d^{2} + 3 \, {\left(x e + d\right)} a e^{2}\right)} e^{\left(-2\right)}}{15 \, {\left(x e + d\right)}^{\frac{7}{2}}}"," ",0,"-2/15*(5*(x*e + d)^2*c*d - 3*(x*e + d)*c*d^2 + 3*(x*e + d)*a*e^2)*e^(-2)/(x*e + d)^(7/2)","A",0
1983,1,48,0,0.242303," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)/(e*x+d)^(11/2),x, algorithm=""giac"")","-\frac{2 \, {\left(7 \, {\left(x e + d\right)}^{2} c d - 5 \, {\left(x e + d\right)} c d^{2} + 5 \, {\left(x e + d\right)} a e^{2}\right)} e^{\left(-2\right)}}{35 \, {\left(x e + d\right)}^{\frac{9}{2}}}"," ",0,"-2/35*(7*(x*e + d)^2*c*d - 5*(x*e + d)*c*d^2 + 5*(x*e + d)*a*e^2)*e^(-2)/(x*e + d)^(9/2)","A",0
1984,1,599,0,0.200356," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2*(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{3465} \, {\left(231 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} c^{2} d^{5} e^{\left(-2\right)} + 297 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} c^{2} d^{4} e^{\left(-2\right)} + 2310 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a c d^{4} + 33 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} c^{2} d^{3} e^{\left(-2\right)} + 3465 \, \sqrt{x e + d} a^{2} d^{3} e^{2} + 1386 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a c d^{3} + 3465 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{2} d^{2} e^{2} + 5 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} c^{2} d^{2} e^{\left(-2\right)} + 594 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a c d^{2} + 693 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{2} d e^{2} + 22 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a c d + 99 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{2} e^{2}\right)} e^{\left(-1\right)}"," ",0,"2/3465*(231*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*c^2*d^5*e^(-2) + 297*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*c^2*d^4*e^(-2) + 2310*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a*c*d^4 + 33*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*c^2*d^3*e^(-2) + 3465*sqrt(x*e + d)*a^2*d^3*e^2 + 1386*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a*c*d^3 + 3465*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^2*d^2*e^2 + 5*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*c^2*d^2*e^(-2) + 594*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*c*d^2 + 693*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^2*d*e^2 + 22*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*c*d + 99*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^2*e^2)*e^(-1)","B",0
1985,1,388,0,0.213266," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2/(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{315} \, {\left(21 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} c^{2} d^{4} e^{\left(-2\right)} + 18 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} c^{2} d^{3} e^{\left(-2\right)} + 210 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a c d^{3} + {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} c^{2} d^{2} e^{\left(-2\right)} + 315 \, \sqrt{x e + d} a^{2} d^{2} e^{2} + 84 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a c d^{2} + 210 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{2} d e^{2} + 18 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a c d + 21 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{2} e^{2}\right)} e^{\left(-1\right)}"," ",0,"2/315*(21*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*c^2*d^4*e^(-2) + 18*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*c^2*d^3*e^(-2) + 210*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a*c*d^3 + (35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*c^2*d^2*e^(-2) + 315*sqrt(x*e + d)*a^2*d^2*e^2 + 84*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a*c*d^2 + 210*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^2*d*e^2 + 18*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*c*d + 21*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^2*e^2)*e^(-1)","B",0
1986,1,106,0,0.204011," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2/(e*x+d)^(3/2),x, algorithm=""giac"")","\frac{2}{105} \, {\left(15 \, {\left(x e + d\right)}^{\frac{7}{2}} c^{2} d^{2} e^{18} - 42 \, {\left(x e + d\right)}^{\frac{5}{2}} c^{2} d^{3} e^{18} + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{2} d^{4} e^{18} + 42 \, {\left(x e + d\right)}^{\frac{5}{2}} a c d e^{20} - 70 \, {\left(x e + d\right)}^{\frac{3}{2}} a c d^{2} e^{20} + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} e^{22}\right)} e^{\left(-21\right)}"," ",0,"2/105*(15*(x*e + d)^(7/2)*c^2*d^2*e^18 - 42*(x*e + d)^(5/2)*c^2*d^3*e^18 + 35*(x*e + d)^(3/2)*c^2*d^4*e^18 + 42*(x*e + d)^(5/2)*a*c*d*e^20 - 70*(x*e + d)^(3/2)*a*c*d^2*e^20 + 35*(x*e + d)^(3/2)*a^2*e^22)*e^(-21)","A",0
1987,1,106,0,0.676833," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2/(e*x+d)^(5/2),x, algorithm=""giac"")","\frac{2}{15} \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} c^{2} d^{2} e^{12} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{2} d^{3} e^{12} + 15 \, \sqrt{x e + d} c^{2} d^{4} e^{12} + 10 \, {\left(x e + d\right)}^{\frac{3}{2}} a c d e^{14} - 30 \, \sqrt{x e + d} a c d^{2} e^{14} + 15 \, \sqrt{x e + d} a^{2} e^{16}\right)} e^{\left(-15\right)}"," ",0,"2/15*(3*(x*e + d)^(5/2)*c^2*d^2*e^12 - 10*(x*e + d)^(3/2)*c^2*d^3*e^12 + 15*sqrt(x*e + d)*c^2*d^4*e^12 + 10*(x*e + d)^(3/2)*a*c*d*e^14 - 30*sqrt(x*e + d)*a*c*d^2*e^14 + 15*sqrt(x*e + d)*a^2*e^16)*e^(-15)","A",0
1988,1,115,0,0.267317," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2/(e*x+d)^(7/2),x, algorithm=""giac"")","\frac{2}{3} \, {\left({\left(x e + d\right)}^{\frac{3}{2}} c^{2} d^{2} e^{6} - 6 \, \sqrt{x e + d} c^{2} d^{3} e^{6} + 6 \, \sqrt{x e + d} a c d e^{8}\right)} e^{\left(-9\right)} - \frac{2 \, {\left({\left(x e + d\right)}^{2} c^{2} d^{4} - 2 \, {\left(x e + d\right)}^{2} a c d^{2} e^{2} + {\left(x e + d\right)}^{2} a^{2} e^{4}\right)} e^{\left(-3\right)}}{{\left(x e + d\right)}^{\frac{5}{2}}}"," ",0,"2/3*((x*e + d)^(3/2)*c^2*d^2*e^6 - 6*sqrt(x*e + d)*c^2*d^3*e^6 + 6*sqrt(x*e + d)*a*c*d*e^8)*e^(-9) - 2*((x*e + d)^2*c^2*d^4 - 2*(x*e + d)^2*a*c*d^2*e^2 + (x*e + d)^2*a^2*e^4)*e^(-3)/(x*e + d)^(5/2)","A",0
1989,1,111,0,0.218245," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2/(e*x+d)^(9/2),x, algorithm=""giac"")","2 \, \sqrt{x e + d} c^{2} d^{2} e^{\left(-3\right)} + \frac{2 \, {\left(6 \, {\left(x e + d\right)}^{3} c^{2} d^{3} - {\left(x e + d\right)}^{2} c^{2} d^{4} - 6 \, {\left(x e + d\right)}^{3} a c d e^{2} + 2 \, {\left(x e + d\right)}^{2} a c d^{2} e^{2} - {\left(x e + d\right)}^{2} a^{2} e^{4}\right)} e^{\left(-3\right)}}{3 \, {\left(x e + d\right)}^{\frac{7}{2}}}"," ",0,"2*sqrt(x*e + d)*c^2*d^2*e^(-3) + 2/3*(6*(x*e + d)^3*c^2*d^3 - (x*e + d)^2*c^2*d^4 - 6*(x*e + d)^3*a*c*d*e^2 + 2*(x*e + d)^2*a*c*d^2*e^2 - (x*e + d)^2*a^2*e^4)*e^(-3)/(x*e + d)^(7/2)","A",0
1990,1,108,0,0.220977," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2/(e*x+d)^(11/2),x, algorithm=""giac"")","-\frac{2 \, {\left(15 \, {\left(x e + d\right)}^{4} c^{2} d^{2} - 10 \, {\left(x e + d\right)}^{3} c^{2} d^{3} + 3 \, {\left(x e + d\right)}^{2} c^{2} d^{4} + 10 \, {\left(x e + d\right)}^{3} a c d e^{2} - 6 \, {\left(x e + d\right)}^{2} a c d^{2} e^{2} + 3 \, {\left(x e + d\right)}^{2} a^{2} e^{4}\right)} e^{\left(-3\right)}}{15 \, {\left(x e + d\right)}^{\frac{9}{2}}}"," ",0,"-2/15*(15*(x*e + d)^4*c^2*d^2 - 10*(x*e + d)^3*c^2*d^3 + 3*(x*e + d)^2*c^2*d^4 + 10*(x*e + d)^3*a*c*d*e^2 - 6*(x*e + d)^2*a*c*d^2*e^2 + 3*(x*e + d)^2*a^2*e^4)*e^(-3)/(x*e + d)^(9/2)","A",0
1991,1,108,0,0.246906," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2/(e*x+d)^(13/2),x, algorithm=""giac"")","-\frac{2 \, {\left(35 \, {\left(x e + d\right)}^{4} c^{2} d^{2} - 42 \, {\left(x e + d\right)}^{3} c^{2} d^{3} + 15 \, {\left(x e + d\right)}^{2} c^{2} d^{4} + 42 \, {\left(x e + d\right)}^{3} a c d e^{2} - 30 \, {\left(x e + d\right)}^{2} a c d^{2} e^{2} + 15 \, {\left(x e + d\right)}^{2} a^{2} e^{4}\right)} e^{\left(-3\right)}}{105 \, {\left(x e + d\right)}^{\frac{11}{2}}}"," ",0,"-2/105*(35*(x*e + d)^4*c^2*d^2 - 42*(x*e + d)^3*c^2*d^3 + 15*(x*e + d)^2*c^2*d^4 + 42*(x*e + d)^3*a*c*d*e^2 - 30*(x*e + d)^2*a*c*d^2*e^2 + 15*(x*e + d)^2*a^2*e^4)*e^(-3)/(x*e + d)^(11/2)","A",0
1992,1,1293,0,0.286870," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3*(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{45045} \, {\left(1287 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} c^{3} d^{7} e^{\left(-3\right)} + 9009 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a c^{2} d^{6} e^{\left(-1\right)} + 572 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} c^{3} d^{6} e^{\left(-3\right)} + 45045 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{2} c d^{5} e + 15444 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a c^{2} d^{5} e^{\left(-1\right)} + 390 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} c^{3} d^{5} e^{\left(-3\right)} + 36036 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{2} c d^{4} e + 2574 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a c^{2} d^{4} e^{\left(-1\right)} + 60 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} c^{3} d^{4} e^{\left(-3\right)} + 45045 \, \sqrt{x e + d} a^{3} d^{4} e^{3} + 60060 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{3} d^{3} e^{3} + 23166 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{2} c d^{3} e + 780 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a c^{2} d^{3} e^{\left(-1\right)} + 7 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} c^{3} d^{3} e^{\left(-3\right)} + 18018 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{3} d^{2} e^{3} + 1716 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{2} c d^{2} e + 45 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} a c^{2} d^{2} e^{\left(-1\right)} + 5148 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{3} d e^{3} + 195 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a^{2} c d e + 143 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{3} e^{3}\right)} e^{\left(-1\right)}"," ",0,"2/45045*(1287*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*c^3*d^7*e^(-3) + 9009*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a*c^2*d^6*e^(-1) + 572*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*c^3*d^6*e^(-3) + 45045*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^2*c*d^5*e + 15444*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*c^2*d^5*e^(-1) + 390*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*c^3*d^5*e^(-3) + 36036*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^2*c*d^4*e + 2574*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*c^2*d^4*e^(-1) + 60*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*c^3*d^4*e^(-3) + 45045*sqrt(x*e + d)*a^3*d^4*e^3 + 60060*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^3*d^3*e^3 + 23166*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^2*c*d^3*e + 780*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a*c^2*d^3*e^(-1) + 7*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*c^3*d^3*e^(-3) + 18018*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^3*d^2*e^3 + 1716*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^2*c*d^2*e + 45*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*a*c^2*d^2*e^(-1) + 5148*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^3*d*e^3 + 195*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a^2*c*d*e + 143*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^3*e^3)*e^(-1)","B",0
1993,1,929,0,0.302747," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3/(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{15015} \, {\left(429 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} c^{3} d^{6} e^{\left(-3\right)} + 3003 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a c^{2} d^{5} e^{\left(-1\right)} + 143 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} c^{3} d^{5} e^{\left(-3\right)} + 15015 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{2} c d^{4} e + 3861 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a c^{2} d^{4} e^{\left(-1\right)} + 65 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} c^{3} d^{4} e^{\left(-3\right)} + 9009 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{2} c d^{3} e + 429 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a c^{2} d^{3} e^{\left(-1\right)} + 5 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} c^{3} d^{3} e^{\left(-3\right)} + 15015 \, \sqrt{x e + d} a^{3} d^{3} e^{3} + 15015 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{3} d^{2} e^{3} + 3861 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{2} c d^{2} e + 65 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a c^{2} d^{2} e^{\left(-1\right)} + 3003 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{3} d e^{3} + 143 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{2} c d e + 429 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{3} e^{3}\right)} e^{\left(-1\right)}"," ",0,"2/15015*(429*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*c^3*d^6*e^(-3) + 3003*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a*c^2*d^5*e^(-1) + 143*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*c^3*d^5*e^(-3) + 15015*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^2*c*d^4*e + 3861*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*c^2*d^4*e^(-1) + 65*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*c^3*d^4*e^(-3) + 9009*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^2*c*d^3*e + 429*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*c^2*d^3*e^(-1) + 5*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*c^3*d^3*e^(-3) + 15015*sqrt(x*e + d)*a^3*d^3*e^3 + 15015*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^3*d^2*e^3 + 3861*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^2*c*d^2*e + 65*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a*c^2*d^2*e^(-1) + 3003*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^3*d*e^3 + 143*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^2*c*d*e + 429*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^3*e^3)*e^(-1)","B",0
1994,1,185,0,0.286161," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3/(e*x+d)^(3/2),x, algorithm=""giac"")","\frac{2}{1155} \, {\left(105 \, {\left(x e + d\right)}^{\frac{11}{2}} c^{3} d^{3} e^{40} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} c^{3} d^{4} e^{40} + 495 \, {\left(x e + d\right)}^{\frac{7}{2}} c^{3} d^{5} e^{40} - 231 \, {\left(x e + d\right)}^{\frac{5}{2}} c^{3} d^{6} e^{40} + 385 \, {\left(x e + d\right)}^{\frac{9}{2}} a c^{2} d^{2} e^{42} - 990 \, {\left(x e + d\right)}^{\frac{7}{2}} a c^{2} d^{3} e^{42} + 693 \, {\left(x e + d\right)}^{\frac{5}{2}} a c^{2} d^{4} e^{42} + 495 \, {\left(x e + d\right)}^{\frac{7}{2}} a^{2} c d e^{44} - 693 \, {\left(x e + d\right)}^{\frac{5}{2}} a^{2} c d^{2} e^{44} + 231 \, {\left(x e + d\right)}^{\frac{5}{2}} a^{3} e^{46}\right)} e^{\left(-44\right)}"," ",0,"2/1155*(105*(x*e + d)^(11/2)*c^3*d^3*e^40 - 385*(x*e + d)^(9/2)*c^3*d^4*e^40 + 495*(x*e + d)^(7/2)*c^3*d^5*e^40 - 231*(x*e + d)^(5/2)*c^3*d^6*e^40 + 385*(x*e + d)^(9/2)*a*c^2*d^2*e^42 - 990*(x*e + d)^(7/2)*a*c^2*d^3*e^42 + 693*(x*e + d)^(5/2)*a*c^2*d^4*e^42 + 495*(x*e + d)^(7/2)*a^2*c*d*e^44 - 693*(x*e + d)^(5/2)*a^2*c*d^2*e^44 + 231*(x*e + d)^(5/2)*a^3*e^46)*e^(-44)","A",0
1995,1,185,0,0.345248," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3/(e*x+d)^(5/2),x, algorithm=""giac"")","\frac{2}{315} \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} c^{3} d^{3} e^{32} - 135 \, {\left(x e + d\right)}^{\frac{7}{2}} c^{3} d^{4} e^{32} + 189 \, {\left(x e + d\right)}^{\frac{5}{2}} c^{3} d^{5} e^{32} - 105 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{3} d^{6} e^{32} + 135 \, {\left(x e + d\right)}^{\frac{7}{2}} a c^{2} d^{2} e^{34} - 378 \, {\left(x e + d\right)}^{\frac{5}{2}} a c^{2} d^{3} e^{34} + 315 \, {\left(x e + d\right)}^{\frac{3}{2}} a c^{2} d^{4} e^{34} + 189 \, {\left(x e + d\right)}^{\frac{5}{2}} a^{2} c d e^{36} - 315 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} c d^{2} e^{36} + 105 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{3} e^{38}\right)} e^{\left(-36\right)}"," ",0,"2/315*(35*(x*e + d)^(9/2)*c^3*d^3*e^32 - 135*(x*e + d)^(7/2)*c^3*d^4*e^32 + 189*(x*e + d)^(5/2)*c^3*d^5*e^32 - 105*(x*e + d)^(3/2)*c^3*d^6*e^32 + 135*(x*e + d)^(7/2)*a*c^2*d^2*e^34 - 378*(x*e + d)^(5/2)*a*c^2*d^3*e^34 + 315*(x*e + d)^(3/2)*a*c^2*d^4*e^34 + 189*(x*e + d)^(5/2)*a^2*c*d*e^36 - 315*(x*e + d)^(3/2)*a^2*c*d^2*e^36 + 105*(x*e + d)^(3/2)*a^3*e^38)*e^(-36)","A",0
1996,1,185,0,0.313780," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3/(e*x+d)^(7/2),x, algorithm=""giac"")","\frac{2}{35} \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} c^{3} d^{3} e^{24} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} c^{3} d^{4} e^{24} + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{3} d^{5} e^{24} - 35 \, \sqrt{x e + d} c^{3} d^{6} e^{24} + 21 \, {\left(x e + d\right)}^{\frac{5}{2}} a c^{2} d^{2} e^{26} - 70 \, {\left(x e + d\right)}^{\frac{3}{2}} a c^{2} d^{3} e^{26} + 105 \, \sqrt{x e + d} a c^{2} d^{4} e^{26} + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} c d e^{28} - 105 \, \sqrt{x e + d} a^{2} c d^{2} e^{28} + 35 \, \sqrt{x e + d} a^{3} e^{30}\right)} e^{\left(-28\right)}"," ",0,"2/35*(5*(x*e + d)^(7/2)*c^3*d^3*e^24 - 21*(x*e + d)^(5/2)*c^3*d^4*e^24 + 35*(x*e + d)^(3/2)*c^3*d^5*e^24 - 35*sqrt(x*e + d)*c^3*d^6*e^24 + 21*(x*e + d)^(5/2)*a*c^2*d^2*e^26 - 70*(x*e + d)^(3/2)*a*c^2*d^3*e^26 + 105*sqrt(x*e + d)*a*c^2*d^4*e^26 + 35*(x*e + d)^(3/2)*a^2*c*d*e^28 - 105*sqrt(x*e + d)*a^2*c*d^2*e^28 + 35*sqrt(x*e + d)*a^3*e^30)*e^(-28)","A",0
1997,1,195,0,0.309992," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3/(e*x+d)^(9/2),x, algorithm=""giac"")","\frac{2}{5} \, {\left({\left(x e + d\right)}^{\frac{5}{2}} c^{3} d^{3} e^{16} - 5 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{3} d^{4} e^{16} + 15 \, \sqrt{x e + d} c^{3} d^{5} e^{16} + 5 \, {\left(x e + d\right)}^{\frac{3}{2}} a c^{2} d^{2} e^{18} - 30 \, \sqrt{x e + d} a c^{2} d^{3} e^{18} + 15 \, \sqrt{x e + d} a^{2} c d e^{20}\right)} e^{\left(-20\right)} + \frac{2 \, {\left({\left(x e + d\right)}^{3} c^{3} d^{6} - 3 \, {\left(x e + d\right)}^{3} a c^{2} d^{4} e^{2} + 3 \, {\left(x e + d\right)}^{3} a^{2} c d^{2} e^{4} - {\left(x e + d\right)}^{3} a^{3} e^{6}\right)} e^{\left(-4\right)}}{{\left(x e + d\right)}^{\frac{7}{2}}}"," ",0,"2/5*((x*e + d)^(5/2)*c^3*d^3*e^16 - 5*(x*e + d)^(3/2)*c^3*d^4*e^16 + 15*sqrt(x*e + d)*c^3*d^5*e^16 + 5*(x*e + d)^(3/2)*a*c^2*d^2*e^18 - 30*sqrt(x*e + d)*a*c^2*d^3*e^18 + 15*sqrt(x*e + d)*a^2*c*d*e^20)*e^(-20) + 2*((x*e + d)^3*c^3*d^6 - 3*(x*e + d)^3*a*c^2*d^4*e^2 + 3*(x*e + d)^3*a^2*c*d^2*e^4 - (x*e + d)^3*a^3*e^6)*e^(-4)/(x*e + d)^(7/2)","A",0
1998,1,193,0,0.328267," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3/(e*x+d)^(11/2),x, algorithm=""giac"")","\frac{2}{3} \, {\left({\left(x e + d\right)}^{\frac{3}{2}} c^{3} d^{3} e^{8} - 9 \, \sqrt{x e + d} c^{3} d^{4} e^{8} + 9 \, \sqrt{x e + d} a c^{2} d^{2} e^{10}\right)} e^{\left(-12\right)} - \frac{2 \, {\left(9 \, {\left(x e + d\right)}^{4} c^{3} d^{5} - {\left(x e + d\right)}^{3} c^{3} d^{6} - 18 \, {\left(x e + d\right)}^{4} a c^{2} d^{3} e^{2} + 3 \, {\left(x e + d\right)}^{3} a c^{2} d^{4} e^{2} + 9 \, {\left(x e + d\right)}^{4} a^{2} c d e^{4} - 3 \, {\left(x e + d\right)}^{3} a^{2} c d^{2} e^{4} + {\left(x e + d\right)}^{3} a^{3} e^{6}\right)} e^{\left(-4\right)}}{3 \, {\left(x e + d\right)}^{\frac{9}{2}}}"," ",0,"2/3*((x*e + d)^(3/2)*c^3*d^3*e^8 - 9*sqrt(x*e + d)*c^3*d^4*e^8 + 9*sqrt(x*e + d)*a*c^2*d^2*e^10)*e^(-12) - 2/3*(9*(x*e + d)^4*c^3*d^5 - (x*e + d)^3*c^3*d^6 - 18*(x*e + d)^4*a*c^2*d^3*e^2 + 3*(x*e + d)^3*a*c^2*d^4*e^2 + 9*(x*e + d)^4*a^2*c*d*e^4 - 3*(x*e + d)^3*a^2*c*d^2*e^4 + (x*e + d)^3*a^3*e^6)*e^(-4)/(x*e + d)^(9/2)","A",0
1999,1,187,0,0.365127," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3/(e*x+d)^(13/2),x, algorithm=""giac"")","2 \, \sqrt{x e + d} c^{3} d^{3} e^{\left(-4\right)} + \frac{2 \, {\left(15 \, {\left(x e + d\right)}^{5} c^{3} d^{4} - 5 \, {\left(x e + d\right)}^{4} c^{3} d^{5} + {\left(x e + d\right)}^{3} c^{3} d^{6} - 15 \, {\left(x e + d\right)}^{5} a c^{2} d^{2} e^{2} + 10 \, {\left(x e + d\right)}^{4} a c^{2} d^{3} e^{2} - 3 \, {\left(x e + d\right)}^{3} a c^{2} d^{4} e^{2} - 5 \, {\left(x e + d\right)}^{4} a^{2} c d e^{4} + 3 \, {\left(x e + d\right)}^{3} a^{2} c d^{2} e^{4} - {\left(x e + d\right)}^{3} a^{3} e^{6}\right)} e^{\left(-4\right)}}{5 \, {\left(x e + d\right)}^{\frac{11}{2}}}"," ",0,"2*sqrt(x*e + d)*c^3*d^3*e^(-4) + 2/5*(15*(x*e + d)^5*c^3*d^4 - 5*(x*e + d)^4*c^3*d^5 + (x*e + d)^3*c^3*d^6 - 15*(x*e + d)^5*a*c^2*d^2*e^2 + 10*(x*e + d)^4*a*c^2*d^3*e^2 - 3*(x*e + d)^3*a*c^2*d^4*e^2 - 5*(x*e + d)^4*a^2*c*d*e^4 + 3*(x*e + d)^3*a^2*c*d^2*e^4 - (x*e + d)^3*a^3*e^6)*e^(-4)/(x*e + d)^(11/2)","A",0
2000,-1,0,0,0.000000," ","integrate((e*x+d)^(9/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2001,-2,0,0,0.000000," ","integrate((e*x+d)^(7/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: ((4*a^7*c^2*d^2*exp(2)^7-2*a^7*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^7-40*a^6*c^3*d^4*exp(1)^2*exp(2)^5+12*a^6*c^3*d^4*exp(2)^6+20*a^6*c*d^2*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^5-6*a^6*c*d^2*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^6+4*a^6*c*d*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^6+128*a^5*c^4*d^6*exp(1)^4*exp(2)^3-56*a^5*c^4*d^6*exp(1)^2*exp(2)^4+12*a^5*c^4*d^6*exp(2)^5-64*a^5*c^2*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)^3+28*a^5*c^2*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^4-6*a^5*c^2*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^5-24*a^5*c^2*d^3*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^4-2*a^5*c^2*d^2*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^5-4*a^5*c^2*d^2*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^5-128*a^4*c^5*d^8*exp(1)^6*exp(2)-16*a^4*c^5*d^8*exp(1)^2*exp(2)^3+4*a^4*c^5*d^8*exp(2)^4+64*a^4*c^3*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^6*exp(2)+8*a^4*c^3*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^3-2*a^4*c^3*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^4+32*a^4*c^3*d^5*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)^2+32*a^4*c^3*d^5*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^3-4*a^4*c^3*d^5*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^4+12*a^4*c^3*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^3-2*a^4*c^3*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^4+24*a^4*c^3*d^4*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^3-4*a^4*c^3*d^4*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^4+128*a^3*c^6*d^10*exp(1)^6+16*a^3*c^6*d^10*exp(1)^2*exp(2)^2-4*a^3*c^6*d^10*exp(2)^3-64*a^3*c^4*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^6-8*a^3*c^4*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2+2*a^3*c^4*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^3-64*a^3*c^4*d^7*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)-16*a^3*c^4*d^7*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2-16*a^3*c^4*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)-4*a^3*c^4*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2-32*a^3*c^4*d^6*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)-8*a^3*c^4*d^6*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2-128*a^2*c^7*d^12*exp(1)^4+56*a^2*c^7*d^12*exp(1)^2*exp(2)-12*a^2*c^7*d^12*exp(2)^2+64*a^2*c^5*d^10*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4-28*a^2*c^5*d^10*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)+6*a^2*c^5*d^10*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^2+32*a^2*c^5*d^9*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4+32*a^2*c^5*d^9*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)-4*a^2*c^5*d^9*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^2+16*a^2*c^5*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4+4*a^2*c^5*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)+32*a^2*c^5*d^8*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4+8*a^2*c^5*d^8*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)+40*a*c^8*d^14*exp(1)^2-12*a*c^8*d^14*exp(2)-20*a*c^6*d^12*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2+6*a*c^6*d^12*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)-24*a*c^6*d^11*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2-12*a*c^6*d^10*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2+2*a*c^6*d^10*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)-24*a*c^6*d^10*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2+4*a*c^6*d^10*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)-4*c^9*d^16+2*c^7*d^14*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+4*c^7*d^13*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+2*c^7*d^12*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+4*c^7*d^12*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2)))*c^2*d^2+(-8*a^7*c^3*d^4*exp(1)^2*exp(2)^6+8*a^7*c^3*d^4*exp(2)^7-4*a^7*c^2*d^3*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^6+4*a^7*c^2*d^3*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^7+72*a^6*c^4*d^6*exp(1)^4*exp(2)^4-96*a^6*c^4*d^6*exp(1)^2*exp(2)^5+24*a^6*c^4*d^6*exp(2)^6+36*a^6*c^3*d^5*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)^4-48*a^6*c^3*d^5*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^5+12*a^6*c^3*d^5*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^6+8*a^6*c^3*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^5-8*a^6*c^3*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2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xp(2)^2+32*a^3*c^5*d^8*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^6-16*a^3*c^5*d^8*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)-16*a^3*c^5*d^8*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2+72*a^2*c^8*d^14*exp(1)^4-96*a^2*c^8*d^14*exp(1)^2*exp(2)+24*a^2*c^8*d^14*exp(2)^2+36*a^2*c^7*d^13*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4-48*a^2*c^7*d^13*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)+12*a^2*c^7*d^13*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^2+40*a^2*c^7*d^12*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4-40*a^2*c^7*d^12*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)+20*a^2*c^7*d^11*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4-24*a^2*c^7*d^11*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)+4*a^2*c^7*d^11*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^2-40*a^2*c^6*d^10*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4+48*a^2*c^6*d^10*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)-8*a^2*c^6*d^10*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^2-8*a*c^9*d^16*exp(1)^2+8*a*c^9*d^16*exp(2)-4*a*c^8*d^15*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2+4*a*c^8*d^15*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)-8*a*c^8*d^14*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2+8*a*c^8*d^14*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)-4*a*c^8*d^13*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2+4*a*c^8*d^13*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)+8*a*c^7*d^12*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2-8*a*c^7*d^12*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2))*abs(c)*abs(d)-4*a^7*c^4*d^4*exp(2)^7+2*a^7*c^2*d^2*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^7+32*a^6*c^5*d^6*exp(1)^2*exp(2)^5-4*a^6*c^5*d^6*exp(2)^6-16*a^6*c^3*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^5+2*a^6*c^3*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^6-4*a^6*c^3*d^3*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^6-72*a^5*c^6*d^8*exp(1)^4*exp(2)^3-16*a^5*c^6*d^8*exp(1)^2*exp(2)^4+4*a^5*c^6*d^8*exp(2)^5+36*a^5*c^4*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)^3+8*a^5*c^4*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^4-2*a^5*c^4*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^5+16*a^5*c^4*d^5*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^4+8*a^5*c^4*d^5*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^5+2*a^5*c^4*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^5+4*a^5*c^4*d^4*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^5+32*a^4*c^7*d^10*exp(1)^6*exp(2)+120*a^4*c^7*d^10*exp(1)^4*exp(2)^2-16*a^4*c^7*d^10*exp(1)^2*exp(2)^3+4*a^4*c^7*d^10*exp(2)^4-16*a^4*c^5*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^6*exp(2)-60*a^4*c^5*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)^2+8*a^4*c^5*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^3-2*a^4*c^5*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^4-8*a^4*c^5*d^7*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)^2-48*a^4*c^5*d^7*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^3-4*a^4*c^5*d^7*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^4-8*a^4*c^5*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^3-2*a^4*c^5*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^4-16*a^4*c^5*d^6*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^3-4*a^4*c^5*d^6*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^4-32*a^3*c^8*d^12*exp(1)^6-120*a^3*c^8*d^12*exp(1)^4*exp(2)+16*a^3*c^8*d^12*exp(1)^2*exp(2)^2-4*a^3*c^8*d^12*exp(2)^3+16*a^3*c^6*d^10*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^6+60*a^3*c^6*d^10*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)-8*a^3*c^6*d^10*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2+2*a^3*c^6*d^10*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^3+16*a^3*c^6*d^9*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)+64*a^3*c^6*d^9*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2+4*a^3*c^6*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)+16*a^3*c^6*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2+8*a^3*c^6*d^8*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)+32*a^3*c^6*d^8*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2+72*a^2*c^9*d^14*exp(1)^4+16*a^2*c^9*d^14*exp(1)^2*exp(2)-4*a^2*c^9*d^14*exp(2)^2-36*a^2*c^7*d^12*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4-8*a^2*c^7*d^12*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)+2*a^2*c^7*d^12*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^2-8*a^2*c^7*d^11*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4-48*a^2*c^7*d^11*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)-4*a^2*c^7*d^11*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^2-4*a^2*c^7*d^10*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4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^5*c^2*d^3*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^4-2*a^5*c^2*d^2*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^5-4*a^5*c^2*d^2*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^5-128*a^4*c^5*d^8*exp(1)^6*exp(2)-16*a^4*c^5*d^8*exp(1)^2*exp(2)^3+4*a^4*c^5*d^8*exp(2)^4+64*a^4*c^3*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^6*exp(2)+8*a^4*c^3*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^3-2*a^4*c^3*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^4+32*a^4*c^3*d^5*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)^2+32*a^4*c^3*d^5*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^3-4*a^4*c^3*d^5*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^4+12*a^4*c^3*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^3-2*a^4*c^3*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^4+24*a^4*c^3*d^4*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^3-4*a^4*c^3*d^4*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^4+128*a^3*c^6*d^10*exp(1)^6+16*a^3*c^6*d^10*exp(1)^2*exp(2)^2-4*a^3*c^6*d^10*exp(2)^3-64*a^3*c^4*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^6-8*a^3*c^4*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2+2*a^3*c^4*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^3-64*a^3*c^4*d^7*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)-16*a^3*c^4*d^7*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2-16*a^3*c^4*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)-4*a^3*c^4*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2-32*a^3*c^4*d^6*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)-8*a^3*c^4*d^6*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2-128*a^2*c^7*d^12*exp(1)^4+56*a^2*c^7*d^12*exp(1)^2*exp(2)-12*a^2*c^7*d^12*exp(2)^2+64*a^2*c^5*d^10*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4-28*a^2*c^5*d^10*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)+6*a^2*c^5*d^10*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^2+32*a^2*c^5*d^9*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4+32*a^2*c^5*d^9*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)-4*a^2*c^5*d^9*sqrt(-c^2*d^3+c*d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^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^4-16*a^4*c^5*d^6*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^3-4*a^4*c^5*d^6*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^4-32*a^3*c^8*d^12*exp(1)^6-120*a^3*c^8*d^12*exp(1)^4*exp(2)+16*a^3*c^8*d^12*exp(1)^2*exp(2)^2-4*a^3*c^8*d^12*exp(2)^3+16*a^3*c^6*d^10*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^6+60*a^3*c^6*d^10*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)-8*a^3*c^6*d^10*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2+2*a^3*c^6*d^10*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^3+16*a^3*c^6*d^9*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)+64*a^3*c^6*d^9*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2+4*a^3*c^6*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)+16*a^3*c^6*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2+8*a^3*c^6*d^8*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)+32*a^3*c^6*d^8*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2+72*a^2*c^9*d^14*exp(1)^4+16*a^2*c^9*d^14*exp(1)^2*exp(2)-4*a^2*c^9*d^14*exp(2)^2-36*a^2*c^7*d^12*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4-8*a^2*c^7*d^12*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)+2*a^2*c^7*d^12*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^2-8*a^2*c^7*d^11*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4-48*a^2*c^7*d^11*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)-4*a^2*c^7*d^11*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^2-4*a^2*c^7*d^10*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4-16*a^2*c^7*d^10*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)-8*a^2*c^7*d^10*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4-32*a^2*c^7*d^10*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)-32*a*c^10*d^16*exp(1)^2+4*a*c^10*d^16*exp(2)+16*a*c^8*d^14*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2-2*a*c^8*d^14*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)+16*a*c^8*d^13*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2+8*a*c^8*d^13*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)+8*a*c^8*d^12*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2+2*a*c^8*d^12*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)+16*a*c^8*d^12*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2+4*a*c^8*d^12*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)+4*c^11*d^18-2*c^9*d^16*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))-4*c^9*d^15*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))-2*c^9*d^14*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))-4*c^9*d^14*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2)))/(8*a^5*c^5*d^6*exp(1)^2*exp(2)^4-8*a^5*c^5*d^6*exp(2)^5-64*a^4*c^6*d^8*exp(1)^4*exp(2)^2+96*a^4*c^6*d^8*exp(1)^2*exp(2)^3-32*a^4*c^6*d^8*exp(2)^4-16*a^4*c^6*d^7*exp(1)^2*exp(2)^3+16*a^4*c^6*d^7*exp(2)^4+128*a^3*c^7*d^10*exp(1)^6-256*a^3*c^7*d^10*exp(1)^4*exp(2)+176*a^3*c^7*d^10*exp(1)^2*exp(2)^2-48*a^3*c^7*d^10*exp(2)^3+64*a^3*c^7*d^9*exp(1)^4*exp(2)-80*a^3*c^7*d^9*exp(1)^2*exp(2)^2+16*a^3*c^7*d^9*exp(2)^3+8*a^3*c^7*d^8*exp(1)^2*exp(2)^2-8*a^3*c^7*d^8*exp(2)^3-64*a^2*c^8*d^12*exp(1)^4+96*a^2*c^8*d^12*exp(1)^2*exp(2)-32*a^2*c^8*d^12*exp(2)^2-64*a^2*c^8*d^11*exp(1)^4+80*a^2*c^8*d^11*exp(1)^2*exp(2)-16*a^2*c^8*d^11*exp(2)^2-32*a^2*c^8*d^10*exp(1)^4+48*a^2*c^8*d^10*exp(1)^2*exp(2)-16*a^2*c^8*d^10*exp(2)^2+8*a*c^9*d^14*exp(1)^2-8*a*c^9*d^14*exp(2)+16*a*c^9*d^13*exp(1)^2-16*a*c^9*d^13*exp(2)+8*a*c^9*d^12*exp(1)^2-8*a*c^9*d^12*exp(2))/c^2/d^2*atan(sqrt(d+x*exp(1))/sqrt(-(d^7*c^6-d^5*c^5*a*exp(2)-sqrt((-d^7*c^6+d^5*c^5*a*exp(2))*(-d^7*c^6+d^5*c^5*a*exp(2))-4*d^6*c^6*(d^6*exp(1)^2*c^5*a-d^6*c^5*a*exp(2))))/2/d^6/c^6))+(2/5*sqrt(d+x*exp(1))*(d+x*exp(1))^2*d^4*c^4+2/3*sqrt(d+x*exp(1))*(d+x*exp(1))*d^5*c^4-2/3*sqrt(d+x*exp(1))*(d+x*exp(1))*d^3*c^3*a*exp(2)+2*sqrt(d+x*exp(1))*d^6*c^4-2*sqrt(d+x*exp(1))*d^4*exp(1)^2*c^3*a-2*sqrt(d+x*exp(1))*d^4*c^3*a*exp(2)+2*sqrt(d+x*exp(1))*d^2*c^2*a^2*exp(2)^2)/d^5/c^5","F(-2)",0
2002,-2,0,0,0.000000," ","integrate((e*x+d)^(5/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: ((-4*a^6*c^2*d^2*exp(2)^6+2*a^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^6+36*a^5*c^3*d^4*exp(1)^2*exp(2)^4-12*a^5*c^3*d^4*exp(2)^5-18*a^5*c*d^2*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^4+6*a^5*c*d^2*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^5-4*a^5*c*d*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^5-96*a^4*c^4*d^6*exp(1)^4*exp(2)^2+48*a^4*c^4*d^6*exp(1)^2*exp(2)^3-12*a^4*c^4*d^6*exp(2)^4+48*a^4*c^2*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)^2-24*a^4*c^2*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^3+6*a^4*c^2*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^4+20*a^4*c^2*d^3*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^3+2*a^4*c^2*d^2*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^4+4*a^4*c^2*d^2*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^4+64*a^3*c^5*d^8*exp(1)^6+24*a^3*c^5*d^8*exp(1)^2*exp(2)^2-8*a^3*c^5*d^8*exp(2)^3-32*a^3*c^3*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^6-12*a^3*c^3*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2+4*a^3*c^3*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^3-16*a^3*c^3*d^5*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)-28*a^3*c^3*d^5*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2+4*a^3*c^3*d^5*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^3-10*a^3*c^3*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2+2*a^3*c^3*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^3-20*a^3*c^3*d^4*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2+4*a^3*c^3*d^4*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^3-96*a^2*c^6*d^10*exp(1)^4+48*a^2*c^6*d^10*exp(1)^2*exp(2)-12*a^2*c^6*d^10*exp(2)^2+48*a^2*c^4*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4-24*a^2*c^4*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)+6*a^2*c^4*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^2+16*a^2*c^4*d^7*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4+28*a^2*c^4*d^7*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)-4*a^2*c^4*d^7*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^2+8*a^2*c^4*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4+4*a^2*c^4*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)+16*a^2*c^4*d^6*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4+8*a^2*c^4*d^6*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)+36*a*c^7*d^12*exp(1)^2-12*a*c^7*d^12*exp(2)-18*a*c^5*d^10*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2+6*a*c^5*d^10*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)-20*a*c^5*d^9*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2-10*a*c^5*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2+2*a*c^5*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)-20*a*c^5*d^8*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2+4*a*c^5*d^8*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)-4*c^8*d^14+2*c^6*d^12*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+4*c^6*d^11*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+2*c^6*d^10*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+4*c^6*d^10*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2)))*c^2*d^2+(8*a^6*c^3*d^4*exp(1)^2*exp(2)^5-8*a^6*c^3*d^4*exp(2)^6+4*a^6*c^2*d^3*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^5-4*a^6*c^2*d^3*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^6-64*a^5*c^4*d^6*exp(1)^4*exp(2)^3+88*a^5*c^4*d^6*exp(1)^2*exp(2)^4-24*a^5*c^4*d^6*exp(2)^5-32*a^5*c^3*d^5*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)^3+44*a^5*c^3*d^5*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^4-12*a^5*c^3*d^5*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^5-8*a^5*c^3*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^4+8*a^5*c^3*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^5+128*a^4*c^5*d^8*exp(1)^6*exp(2)-192*a^4*c^5*d^8*exp(1)^4*exp(2)^2+80*a^4*c^5*d^8*exp(1)^2*exp(2)^3-16*a^4*c^5*d^8*exp(2)^4+64*a^4*c^4*d^7*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^6*exp(2)-96*a^4*c^4*d^7*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)^2+40*a^4*c^4*d^7*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^3-8*a^4*c^4*d^7*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^4+32*a^4*c^4*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)^2-32*a^4*c^4*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^3+4*a^4*c^4*d^5*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^3-4*a^4*c^4*d^5*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^4-8*a^4*c^3*d^4*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^3+8*a^4*c^3*d^4*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^4-128*a^3*c^6*d^10*exp(1)^6+192*a^3*c^6*d^10*exp(1)^4*exp(2)-80*a^3*c^6*d^10*exp(1)^2*exp(2)^2+16*a^3*c^6*d^10*exp(2)^3-64*a^3*c^5*d^9*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^6+96*a^3*c^5*d^9*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)-40*a^3*c^5*d^9*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^2+8*a^3*c^5*d^9*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^3-64*a^3*c^5*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)+80*a^3*c^5*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^2-16*a^3*c^5*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^3-16*a^3*c^5*d^7*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)+20*a^3*c^5*d^7*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^2-4*a^3*c^5*d^7*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^3+32*a^3*c^4*d^6*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)-40*a^3*c^4*d^6*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2+8*a^3*c^4*d^6*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^3+64*a^2*c^7*d^12*exp(1)^4-88*a^2*c^7*d^12*exp(1)^2*exp(2)+24*a^2*c^7*d^12*exp(2)^2+32*a^2*c^6*d^11*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4-44*a^2*c^6*d^11*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)+12*a^2*c^6*d^11*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^2+32*a^2*c^6*d^10*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4-32*a^2*c^6*d^10*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)+16*a^2*c^6*d^9*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4-20*a^2*c^6*d^9*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)+4*a^2*c^6*d^9*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^2-32*a^2*c^5*d^8*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4+40*a^2*c^5*d^8*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)-8*a^2*c^5*d^8*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^2-8*a*c^8*d^14*exp(1)^2+8*a*c^8*d^14*exp(2)-4*a*c^7*d^13*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2+4*a*c^7*d^13*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)-8*a*c^7*d^12*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2+8*a*c^7*d^12*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)-4*a*c^7*d^11*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2+4*a*c^7*d^11*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)+8*a*c^6*d^10*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2-8*a*c^6*d^10*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2))*abs(c)*abs(d)+4*a^6*c^4*d^4*exp(2)^6-2*a^6*c^2*d^2*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^6-28*a^5*c^5*d^6*exp(1)^2*exp(2)^4+4*a^5*c^5*d^6*exp(2)^5+14*a^5*c^3*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^4-2*a^5*c^3*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^5+4*a^5*c^3*d^3*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^5+48*a^4*c^6*d^8*exp(1)^4*exp(2)^2+16*a^4*c^6*d^8*exp(1)^2*exp(2)^3-4*a^4*c^6*d^8*exp(2)^4-24*a^4*c^4*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)^2-8*a^4*c^4*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^3+2*a^4*c^4*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^4-12*a^4*c^4*d^5*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^3-8*a^4*c^4*d^5*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^4-2*a^4*c^4*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^4-4*a^4*c^4*d^4*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^4-96*a^3*c^7*d^10*exp(1)^4*exp(2)+24*a^3*c^7*d^10*exp(1)^2*exp(2)^2-8*a^3*c^7*d^10*exp(2)^3+48*a^3*c^5*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)-12*a^3*c^5*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2+4*a^3*c^5*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^3+36*a^3*c^5*d^7*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2+4*a^3*c^5*d^7*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^3+6*a^3*c^5*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2+2*a^3*c^5*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^3+12*a^3*c^5*d^6*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2+4*a^3*c^5*d^6*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^3+48*a^2*c^8*d^12*exp(1)^4+16*a^2*c^8*d^12*exp(1)^2*exp(2)-4*a^2*c^8*d^12*exp(2)^2-24*a^2*c^6*d^10*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4-8*a^2*c^6*d^10*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)+2*a^2*c^6*d^10*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^2-36*a^2*c^6*d^9*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)-4*a^2*c^6*d^9*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^2-12*a^2*c^6*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)-24*a^2*c^6*d^8*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)-28*a*c^9*d^14*exp(1)^2+4*a*c^9*d^14*exp(2)+14*a*c^7*d^12*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2-2*a*c^7*d^12*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)+12*a*c^7*d^11*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2+8*a*c^7*d^11*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)+6*a*c^7*d^10*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2+2*a*c^7*d^10*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)+12*a*c^7*d^10*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2+4*a*c^7*d^10*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)+4*c^10*d^16-2*c^8*d^14*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))-4*c^8*d^13*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))-2*c^8*d^12*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))-4*c^8*d^12*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2)))/(8*a^5*c^4*d^5*exp(1)^2*exp(2)^4-8*a^5*c^4*d^5*exp(2)^5-64*a^4*c^5*d^7*exp(1)^4*exp(2)^2+96*a^4*c^5*d^7*exp(1)^2*exp(2)^3-32*a^4*c^5*d^7*exp(2)^4-16*a^4*c^5*d^6*exp(1)^2*exp(2)^3+16*a^4*c^5*d^6*exp(2)^4+128*a^3*c^6*d^9*exp(1)^6-256*a^3*c^6*d^9*exp(1)^4*exp(2)+176*a^3*c^6*d^9*exp(1)^2*exp(2)^2-48*a^3*c^6*d^9*exp(2)^3+64*a^3*c^6*d^8*exp(1)^4*exp(2)-80*a^3*c^6*d^8*exp(1)^2*exp(2)^2+16*a^3*c^6*d^8*exp(2)^3+8*a^3*c^6*d^7*exp(1)^2*exp(2)^2-8*a^3*c^6*d^7*exp(2)^3-64*a^2*c^7*d^11*exp(1)^4+96*a^2*c^7*d^11*exp(1)^2*exp(2)-32*a^2*c^7*d^11*exp(2)^2-64*a^2*c^7*d^10*exp(1)^4+80*a^2*c^7*d^10*exp(1)^2*exp(2)-16*a^2*c^7*d^10*exp(2)^2-32*a^2*c^7*d^9*exp(1)^4+48*a^2*c^7*d^9*exp(1)^2*exp(2)-16*a^2*c^7*d^9*exp(2)^2+8*a*c^8*d^13*exp(1)^2-8*a*c^8*d^13*exp(2)+16*a*c^8*d^12*exp(1)^2-16*a*c^8*d^12*exp(2)+8*a*c^8*d^11*exp(1)^2-8*a*c^8*d^11*exp(2))/c^2/d^2*atan(sqrt(d+x*exp(1))/sqrt(-(d^5*c^4-d^3*c^3*a*exp(2)+sqrt((-d^5*c^4+d^3*c^3*a*exp(2))*(-d^5*c^4+d^3*c^3*a*exp(2))-4*d^4*c^4*(d^4*exp(1)^2*c^3*a-d^4*c^3*a*exp(2))))/2/d^4/c^4))-((-4*a^6*c^2*d^2*exp(2)^6+2*a^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^6+36*a^5*c^3*d^4*exp(1)^2*exp(2)^4-12*a^5*c^3*d^4*exp(2)^5-18*a^5*c*d^2*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^4+6*a^5*c*d^2*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^5-4*a^5*c*d*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^5-96*a^4*c^4*d^6*exp(1)^4*exp(2)^2+48*a^4*c^4*d^6*exp(1)^2*exp(2)^3-12*a^4*c^4*d^6*exp(2)^4+48*a^4*c^2*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)^2-24*a^4*c^2*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^3+6*a^4*c^2*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^4+20*a^4*c^2*d^3*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^3+2*a^4*c^2*d^2*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^4+4*a^4*c^2*d^2*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^4+64*a^3*c^5*d^8*exp(1)^6+24*a^3*c^5*d^8*exp(1)^2*exp(2)^2-8*a^3*c^5*d^8*exp(2)^3-32*a^3*c^3*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^6-12*a^3*c^3*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2+4*a^3*c^3*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^3-16*a^3*c^3*d^5*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)-28*a^3*c^3*d^5*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2+4*a^3*c^3*d^5*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^3-10*a^3*c^3*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2+2*a^3*c^3*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^3-20*a^3*c^3*d^4*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2+4*a^3*c^3*d^4*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^3-96*a^2*c^6*d^10*exp(1)^4+48*a^2*c^6*d^10*exp(1)^2*exp(2)-12*a^2*c^6*d^10*exp(2)^2+48*a^2*c^4*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4-24*a^2*c^4*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)+6*a^2*c^4*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^2+16*a^2*c^4*d^7*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4+28*a^2*c^4*d^7*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)-4*a^2*c^4*d^7*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^2+8*a^2*c^4*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4+4*a^2*c^4*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)+16*a^2*c^4*d^6*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4+8*a^2*c^4*d^6*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)+36*a*c^7*d^12*exp(1)^2-12*a*c^7*d^12*exp(2)-18*a*c^5*d^10*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2+6*a*c^5*d^10*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)-20*a*c^5*d^9*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2-10*a*c^5*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2+2*a*c^5*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)-20*a*c^5*d^8*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2+4*a*c^5*d^8*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)-4*c^8*d^14+2*c^6*d^12*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+4*c^6*d^11*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+2*c^6*d^10*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+4*c^6*d^10*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2)))*c^2*d^2+(8*a^6*c^3*d^4*exp(1)^2*exp(2)^5-8*a^6*c^3*d^4*exp(2)^6-4*a^6*c^2*d^3*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^5+4*a^6*c^2*d^3*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^6-64*a^5*c^4*d^6*exp(1)^4*exp(2)^3+88*a^5*c^4*d^6*exp(1)^2*exp(2)^4-24*a^5*c^4*d^6*exp(2)^5+32*a^5*c^3*d^5*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)^3-44*a^5*c^3*d^5*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^4+12*a^5*c^3*d^5*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*e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*d*exp(2))*sqrt(2)*exp(2)+8*a*c^7*d^12*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2-8*a*c^7*d^12*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)+4*a*c^7*d^11*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2-4*a*c^7*d^11*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)+8*a*c^6*d^10*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2-8*a*c^6*d^10*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2))*abs(c)*abs(d)+4*a^6*c^4*d^4*exp(2)^6-2*a^6*c^2*d^2*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^6-28*a^5*c^5*d^6*exp(1)^2*exp(2)^4+4*a^5*c^5*d^6*exp(2)^5+14*a^5*c^3*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^4-2*a^5*c^3*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^5+4*a^5*c^3*d^3*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^5+48*a^4*c^6*d^8*exp(1)^4*exp(2)^2+16*a^4*c^6*d^8*exp(1)^2*exp(2)^3-4*a^4*c^6*d^8*exp(2)^4-24*a^4*c^4*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)^2-8*a^4*c^4*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^3+2*a^4*c^4*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^4-12*a^4*c^4*d^5*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^3-8*a^4*c^4*d^5*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^4-2*a^4*c^4*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^4-4*a^4*c^4*d^4*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^4-96*a^3*c^7*d^10*exp(1)^4*exp(2)+24*a^3*c^7*d^10*exp(1)^2*exp(2)^2-8*a^3*c^7*d^10*exp(2)^3+48*a^3*c^5*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)-12*a^3*c^5*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2+4*a^3*c^5*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^3+36*a^3*c^5*d^7*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2+4*a^3*c^5*d^7*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^3+6*a^3*c^5*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2+2*a^3*c^5*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^3+12*a^3*c^5*d^6*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2+4*a^3*c^5*d^6*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^3+48*a^2*c^8*d^12*exp(1)^4+16*a^2*c^8*d^12*exp(1)^2*exp(2)-4*a^2*c^8*d^12*exp(2)^2-24*a^2*c^6*d^10*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4-8*a^2*c^6*d^10*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)+2*a^2*c^6*d^10*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^2-36*a^2*c^6*d^9*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)-4*a^2*c^6*d^9*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^2-12*a^2*c^6*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)-24*a^2*c^6*d^8*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)-28*a*c^9*d^14*exp(1)^2+4*a*c^9*d^14*exp(2)+14*a*c^7*d^12*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2-2*a*c^7*d^12*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)+12*a*c^7*d^11*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2+8*a*c^7*d^11*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)+6*a*c^7*d^10*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2+2*a*c^7*d^10*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)+12*a*c^7*d^10*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2+4*a*c^7*d^10*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)+4*c^10*d^16-2*c^8*d^14*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))-4*c^8*d^13*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))-2*c^8*d^12*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))-4*c^8*d^12*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2)))/(8*a^5*c^4*d^5*exp(1)^2*exp(2)^4-8*a^5*c^4*d^5*exp(2)^5-64*a^4*c^5*d^7*exp(1)^4*exp(2)^2+96*a^4*c^5*d^7*exp(1)^2*exp(2)^3-32*a^4*c^5*d^7*exp(2)^4-16*a^4*c^5*d^6*exp(1)^2*exp(2)^3+16*a^4*c^5*d^6*exp(2)^4+128*a^3*c^6*d^9*exp(1)^6-256*a^3*c^6*d^9*exp(1)^4*exp(2)+176*a^3*c^6*d^9*exp(1)^2*exp(2)^2-48*a^3*c^6*d^9*exp(2)^3+64*a^3*c^6*d^8*exp(1)^4*exp(2)-80*a^3*c^6*d^8*exp(1)^2*exp(2)^2+16*a^3*c^6*d^8*exp(2)^3+8*a^3*c^6*d^7*exp(1)^2*exp(2)^2-8*a^3*c^6*d^7*exp(2)^3-64*a^2*c^7*d^11*exp(1)^4+96*a^2*c^7*d^11*exp(1)^2*exp(2)-32*a^2*c^7*d^11*exp(2)^2-64*a^2*c^7*d^10*exp(1)^4+80*a^2*c^7*d^10*exp(1)^2*exp(2)-16*a^2*c^7*d^10*exp(2)^2-32*a^2*c^7*d^9*exp(1)^4+48*a^2*c^7*d^9*exp(1)^2*exp(2)-16*a^2*c^7*d^9*exp(2)^2+8*a*c^8*d^13*exp(1)^2-8*a*c^8*d^13*exp(2)+16*a*c^8*d^12*exp(1)^2-16*a*c^8*d^12*exp(2)+8*a*c^8*d^11*exp(1)^2-8*a*c^8*d^11*exp(2))/c^2/d^2*atan(sqrt(d+x*exp(1))/sqrt(-(d^5*c^4-d^3*c^3*a*exp(2)-sqrt((-d^5*c^4+d^3*c^3*a*exp(2))*(-d^5*c^4+d^3*c^3*a*exp(2))-4*d^4*c^4*(d^4*exp(1)^2*c^3*a-d^4*c^3*a*exp(2))))/2/d^4/c^4))+(2/3*sqrt(d+x*exp(1))*(d+x*exp(1))*d^2*c^2+2*sqrt(d+x*exp(1))*d^3*c^2-2*sqrt(d+x*exp(1))*d*c*a*exp(2))/d^3/c^3","F(-2)",0
2003,-2,0,0,0.000000," ","integrate((e*x+d)^(3/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: ((4*a^5*c^2*d^2*exp(2)^5-2*a^5*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^5-32*a^4*c^3*d^4*exp(1)^2*exp(2)^3+12*a^4*c^3*d^4*exp(2)^4+16*a^4*c*d^2*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^3-6*a^4*c*d^2*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^4+4*a^4*c*d*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^4+64*a^3*c^4*d^6*exp(1)^4*exp(2)-32*a^3*c^4*d^6*exp(1)^2*exp(2)^2+8*a^3*c^4*d^6*exp(2)^3-32*a^3*c^2*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)+16*a^3*c^2*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2-4*a^3*c^2*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^3-16*a^3*c^2*d^3*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2-2*a^3*c^2*d^2*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^3-4*a^3*c^2*d^2*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^3-64*a^2*c^5*d^8*exp(1)^4+32*a^2*c^5*d^8*exp(1)^2*exp(2)-8*a^2*c^5*d^8*exp(2)^2+32*a^2*c^3*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4-16*a^2*c^3*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)+4*a^2*c^3*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^2+32*a^2*c^3*d^5*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)-8*a^2*c^3*d^5*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^2+8*a^2*c^3*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)-2*a^2*c^3*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^2+16*a^2*c^3*d^4*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)-4*a^2*c^3*d^4*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^2+32*a*c^6*d^10*exp(1)^2-12*a*c^6*d^10*exp(2)-16*a*c^4*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2+6*a*c^4*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)-16*a*c^4*d^7*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2-8*a*c^4*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2+2*a*c^4*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)-16*a*c^4*d^6*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2+4*a*c^4*d^6*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)-4*c^7*d^12+2*c^5*d^10*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+4*c^5*d^9*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+2*c^5*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+4*c^5*d^8*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2)))*c^2*d^2+(-8*a^5*c^3*d^4*exp(1)^2*exp(2)^4+8*a^5*c^3*d^4*exp(2)^5-4*a^5*c^2*d^3*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^4+4*a^5*c^2*d^3*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^5+64*a^4*c^4*d^6*exp(1)^4*exp(2)^2-96*a^4*c^4*d^6*exp(1)^2*exp(2)^3+32*a^4*c^4*d^6*exp(2)^4+32*a^4*c^3*d^5*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)^2-48*a^4*c^3*d^5*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^3+16*a^4*c^3*d^5*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^4+8*a^4*c^3*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^3-8*a^4*c^3*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^4-128*a^3*c^5*d^8*exp(1)^6+256*a^3*c^5*d^8*exp(1)^4*exp(2)-176*a^3*c^5*d^8*exp(1)^2*exp(2)^2+48*a^3*c^5*d^8*exp(2)^3-64*a^3*c^4*d^7*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^6+128*a^3*c^4*d^7*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)-88*a^3*c^4*d^7*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^2+24*a^3*c^4*d^7*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^3-32*a^3*c^4*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)+40*a^3*c^4*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^2-8*a^3*c^4*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^3-4*a^3*c^4*d^5*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^2+4*a^3*c^4*d^5*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^3+8*a^3*c^3*d^4*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2-8*a^3*c^3*d^4*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^3+64*a^2*c^6*d^10*exp(1)^4-96*a^2*c^6*d^10*exp(1)^2*exp(2)+32*a^2*c^6*d^10*exp(2)^2+32*a^2*c^5*d^9*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4-48*a^2*c^5*d^9*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)+16*a^2*c^5*d^9*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^2+32*a^2*c^5*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4-40*a^2*c^5*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)+8*a^2*c^5*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^2+16*a^2*c^5*d^7*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4-24*a^2*c^5*d^7*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)+8*a^2*c^5*d^7*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^2-32*a^2*c^4*d^6*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4+48*a^2*c^4*d^6*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)-16*a^2*c^4*d^6*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^2-8*a*c^7*d^12*exp(1)^2+8*a*c^7*d^12*exp(2)-4*a*c^6*d^11*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2+4*a*c^6*d^11*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)-8*a*c^6*d^10*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2+8*a*c^6*d^10*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)-4*a*c^6*d^9*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2+4*a*c^6*d^9*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)+8*a*c^5*d^8*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2-8*a*c^5*d^8*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2))*abs(c)*abs(d)-4*a^5*c^4*d^4*exp(2)^5+2*a^5*c^2*d^2*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^5+24*a^4*c^5*d^6*exp(1)^2*exp(2)^3-4*a^4*c^5*d^6*exp(2)^4-12*a^4*c^3*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^3+2*a^4*c^3*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^4-4*a^4*c^3*d^3*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^4-32*a^3*c^6*d^8*exp(1)^4*exp(2)-8*a^3*c^6*d^8*exp(1)^2*exp(2)^2+16*a^3*c^4*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)+4*a^3*c^4*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2+8*a^3*c^4*d^5*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2+8*a^3*c^4*d^5*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^3+2*a^3*c^4*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^3+4*a^3*c^4*d^4*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^3+32*a^2*c^7*d^10*exp(1)^4+8*a^2*c^7*d^10*exp(1)^2*exp(2)-16*a^2*c^5*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4-4*a^2*c^5*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)-16*a^2*c^5*d^7*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)-8*a^2*c^5*d^7*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^2-4*a^2*c^5*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)-2*a^2*c^5*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^2-8*a^2*c^5*d^6*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)-4*a^2*c^5*d^6*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^2-24*a*c^8*d^12*exp(1)^2+4*a*c^8*d^12*exp(2)+12*a*c^6*d^10*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2-2*a*c^6*d^10*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)+8*a*c^6*d^9*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2+8*a*c^6*d^9*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)+4*a*c^6*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2+2*a*c^6*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)+8*a*c^6*d^8*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2+4*a*c^6*d^8*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)+4*c^9*d^14-2*c^7*d^12*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))-4*c^7*d^11*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))-2*c^7*d^10*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))-4*c^7*d^10*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2)))/(8*a^5*c^3*d^4*exp(1)^2*exp(2)^4-8*a^5*c^3*d^4*exp(2)^5-64*a^4*c^4*d^6*exp(1)^4*exp(2)^2+96*a^4*c^4*d^6*exp(1)^2*exp(2)^3-32*a^4*c^4*d^6*exp(2)^4-16*a^4*c^4*d^5*exp(1)^2*exp(2)^3+16*a^4*c^4*d^5*exp(2)^4+128*a^3*c^5*d^8*exp(1)^6-256*a^3*c^5*d^8*exp(1)^4*exp(2)+176*a^3*c^5*d^8*exp(1)^2*exp(2)^2-48*a^3*c^5*d^8*exp(2)^3+64*a^3*c^5*d^7*exp(1)^4*exp(2)-80*a^3*c^5*d^7*exp(1)^2*exp(2)^2+16*a^3*c^5*d^7*exp(2)^3+8*a^3*c^5*d^6*exp(1)^2*exp(2)^2-8*a^3*c^5*d^6*exp(2)^3-64*a^2*c^6*d^10*exp(1)^4+96*a^2*c^6*d^10*exp(1)^2*exp(2)-32*a^2*c^6*d^10*exp(2)^2-64*a^2*c^6*d^9*exp(1)^4+80*a^2*c^6*d^9*exp(1)^2*exp(2)-16*a^2*c^6*d^9*exp(2)^2-32*a^2*c^6*d^8*exp(1)^4+48*a^2*c^6*d^8*exp(1)^2*exp(2)-16*a^2*c^6*d^8*exp(2)^2+8*a*c^7*d^12*exp(1)^2-8*a*c^7*d^12*exp(2)+16*a*c^7*d^11*exp(1)^2-16*a*c^7*d^11*exp(2)+8*a*c^7*d^10*exp(1)^2-8*a*c^7*d^10*exp(2))/c^2/d^2*atan(sqrt(d+x*exp(1))/sqrt(-(d^3*c^2-d*c*a*exp(2)+sqrt((-d^3*c^2+d*c*a*exp(2))*(-d^3*c^2+d*c*a*exp(2))-4*d^2*c^2*(d^2*exp(1)^2*c*a-d^2*c*a*exp(2))))/2/d^2/c^2))-((4*a^5*c^2*d^2*exp(2)^5-2*a^5*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^5-32*a^4*c^3*d^4*exp(1)^2*exp(2)^3+12*a^4*c^3*d^4*exp(2)^4+16*a^4*c*d^2*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^3-6*a^4*c*d^2*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^4+4*a^4*c*d*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^4+64*a^3*c^4*d^6*exp(1)^4*exp(2)-32*a^3*c^4*d^6*exp(1)^2*exp(2)^2+8*a^3*c^4*d^6*exp(2)^3-32*a^3*c^2*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)+16*a^3*c^2*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2-4*a^3*c^2*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^3-16*a^3*c^2*d^3*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2-2*a^3*c^2*d^2*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^3-4*a^3*c^2*d^2*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^3-64*a^2*c^5*d^8*exp(1)^4+32*a^2*c^5*d^8*exp(1)^2*exp(2)-8*a^2*c^5*d^8*exp(2)^2+32*a^2*c^3*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4-16*a^2*c^3*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)+4*a^2*c^3*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^2+32*a^2*c^3*d^5*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)-8*a^2*c^3*d^5*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^2+8*a^2*c^3*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)-2*a^2*c^3*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^2+16*a^2*c^3*d^4*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)-4*a^2*c^3*d^4*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^2+32*a*c^6*d^10*exp(1)^2-12*a*c^6*d^10*exp(2)-16*a*c^4*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2+6*a*c^4*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)-16*a*c^4*d^7*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2-8*a*c^4*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2+2*a*c^4*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)-16*a*c^4*d^6*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2+4*a*c^4*d^6*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)-4*c^7*d^12+2*c^5*d^10*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+4*c^5*d^9*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+2*c^5*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+4*c^5*d^8*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2)))*c^2*d^2+(-8*a^5*c^3*d^4*exp(1)^2*exp(2)^4+8*a^5*c^3*d^4*exp(2)^5+4*a^5*c^2*d^3*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^4-4*a^5*c^2*d^3*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^5+64*a^4*c^4*d^6*exp(1)^4*exp(2)^2-96*a^4*c^4*d^6*exp(1)^2*exp(2)^3+32*a^4*c^4*d^6*exp(2)^4-32*a^4*c^3*d^5*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)^2+48*a^4*c^3*d^5*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^3-16*a^4*c^3*d^5*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^4-8*a^4*c^3*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^3+8*a^4*c^3*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^4-128*a^3*c^5*d^8*exp(1)^6+256*a^3*c^5*d^8*exp(1)^4*exp(2)-176*a^3*c^5*d^8*exp(1)^2*exp(2)^2+48*a^3*c^5*d^8*exp(2)^3+64*a^3*c^4*d^7*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^6-128*a^3*c^4*d^7*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)+88*a^3*c^4*d^7*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^2-24*a^3*c^4*d^7*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^3+32*a^3*c^4*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)-40*a^3*c^4*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^2+8*a^3*c^4*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^3+4*a^3*c^4*d^5*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^2-4*a^3*c^4*d^5*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^3+8*a^3*c^3*d^4*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2-8*a^3*c^3*d^4*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^3+64*a^2*c^6*d^10*exp(1)^4-96*a^2*c^6*d^10*exp(1)^2*exp(2)+32*a^2*c^6*d^10*exp(2)^2-32*a^2*c^5*d^9*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4+48*a^2*c^5*d^9*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)-16*a^2*c^5*d^9*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^2-32*a^2*c^5*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4+40*a^2*c^5*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)-8*a^2*c^5*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^2-16*a^2*c^5*d^7*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4+24*a^2*c^5*d^7*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)-8*a^2*c^5*d^7*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^2-32*a^2*c^4*d^6*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4+48*a^2*c^4*d^6*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)-16*a^2*c^4*d^6*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^2-8*a*c^7*d^12*exp(1)^2+8*a*c^7*d^12*exp(2)+4*a*c^6*d^11*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2-4*a*c^6*d^11*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)+8*a*c^6*d^10*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2-8*a*c^6*d^10*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)+4*a*c^6*d^9*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2-4*a*c^6*d^9*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)+8*a*c^5*d^8*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2-8*a*c^5*d^8*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2))*abs(c)*abs(d)-4*a^5*c^4*d^4*exp(2)^5+2*a^5*c^2*d^2*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^5+24*a^4*c^5*d^6*exp(1)^2*exp(2)^3-4*a^4*c^5*d^6*exp(2)^4-12*a^4*c^3*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^3+2*a^4*c^3*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^4-4*a^4*c^3*d^3*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^4-32*a^3*c^6*d^8*exp(1)^4*exp(2)-8*a^3*c^6*d^8*exp(1)^2*exp(2)^2+16*a^3*c^4*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)+4*a^3*c^4*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2+8*a^3*c^4*d^5*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2+8*a^3*c^4*d^5*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^3+2*a^3*c^4*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^3+4*a^3*c^4*d^4*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^3+32*a^2*c^7*d^10*exp(1)^4+8*a^2*c^7*d^10*exp(1)^2*exp(2)-16*a^2*c^5*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4-4*a^2*c^5*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)-16*a^2*c^5*d^7*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)-8*a^2*c^5*d^7*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^2-4*a^2*c^5*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)-2*a^2*c^5*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^2-8*a^2*c^5*d^6*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)-4*a^2*c^5*d^6*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^2-24*a*c^8*d^12*exp(1)^2+4*a*c^8*d^12*exp(2)+12*a*c^6*d^10*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2-2*a*c^6*d^10*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)+8*a*c^6*d^9*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2+8*a*c^6*d^9*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)+4*a*c^6*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2+2*a*c^6*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)+8*a*c^6*d^8*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2+4*a*c^6*d^8*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)+4*c^9*d^14-2*c^7*d^12*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))-4*c^7*d^11*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))-2*c^7*d^10*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))-4*c^7*d^10*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2)))/(8*a^5*c^3*d^4*exp(1)^2*exp(2)^4-8*a^5*c^3*d^4*exp(2)^5-64*a^4*c^4*d^6*exp(1)^4*exp(2)^2+96*a^4*c^4*d^6*exp(1)^2*exp(2)^3-32*a^4*c^4*d^6*exp(2)^4-16*a^4*c^4*d^5*exp(1)^2*exp(2)^3+16*a^4*c^4*d^5*exp(2)^4+128*a^3*c^5*d^8*exp(1)^6-256*a^3*c^5*d^8*exp(1)^4*exp(2)+176*a^3*c^5*d^8*exp(1)^2*exp(2)^2-48*a^3*c^5*d^8*exp(2)^3+64*a^3*c^5*d^7*exp(1)^4*exp(2)-80*a^3*c^5*d^7*exp(1)^2*exp(2)^2+16*a^3*c^5*d^7*exp(2)^3+8*a^3*c^5*d^6*exp(1)^2*exp(2)^2-8*a^3*c^5*d^6*exp(2)^3-64*a^2*c^6*d^10*exp(1)^4+96*a^2*c^6*d^10*exp(1)^2*exp(2)-32*a^2*c^6*d^10*exp(2)^2-64*a^2*c^6*d^9*exp(1)^4+80*a^2*c^6*d^9*exp(1)^2*exp(2)-16*a^2*c^6*d^9*exp(2)^2-32*a^2*c^6*d^8*exp(1)^4+48*a^2*c^6*d^8*exp(1)^2*exp(2)-16*a^2*c^6*d^8*exp(2)^2+8*a*c^7*d^12*exp(1)^2-8*a*c^7*d^12*exp(2)+16*a*c^7*d^11*exp(1)^2-16*a*c^7*d^11*exp(2)+8*a*c^7*d^10*exp(1)^2-8*a*c^7*d^10*exp(2))/c^2/d^2*atan(sqrt(d+x*exp(1))/sqrt(-(d^3*c^2-d*c*a*exp(2)-sqrt((-d^3*c^2+d*c*a*exp(2))*(-d^3*c^2+d*c*a*exp(2))-4*d^2*c^2*(d^2*exp(1)^2*c*a-d^2*c*a*exp(2))))/2/d^2/c^2))+2*sqrt(d+x*exp(1))/d/c","F(-2)",0
2004,1,1470,0,7.796039," ","integrate((e*x+d)^(1/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x, algorithm=""giac"")","\frac{{\left(2 \, c^{4} d^{6} - 4 \, a c^{3} d^{4} e^{2} - \sqrt{2} \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} \sqrt{-c^{2} d^{3} + a c d e^{2} - \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} c^{2} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{4} - 2 \, \sqrt{2} \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} \sqrt{-c^{2} d^{3} + a c d e^{2} - \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} c^{2} d^{3} + 2 \, \sqrt{2} \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} \sqrt{-c^{2} d^{3} + a c d e^{2} - \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} a c d^{2} e^{2} - \sqrt{2} \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} \sqrt{-c^{2} d^{3} + a c d e^{2} - \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} c^{2} d^{2} + 2 \, \sqrt{2} \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} \sqrt{-c^{2} d^{3} + a c d e^{2} - \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} a c d e^{2} - 2 \, {\left(c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} c^{2} d^{2} - \sqrt{2} \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} \sqrt{-c^{2} d^{3} + a c d e^{2} - \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} a^{2} e^{4}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{c d^{2} - a e^{2} + \sqrt{{\left(c d^{2} - a e^{2}\right)}^{2}}}{c d}}}\right)}{{\left(c^{4} d^{8} + 2 \, c^{4} d^{7} - 4 \, a c^{3} d^{6} e^{2} + c^{4} d^{6} - 6 \, a c^{3} d^{5} e^{2} + 6 \, a^{2} c^{2} d^{4} e^{4} - 2 \, a c^{3} d^{4} e^{2} + 6 \, a^{2} c^{2} d^{3} e^{4} - 4 \, a^{3} c d^{2} e^{6} + a^{2} c^{2} d^{2} e^{4} - 2 \, a^{3} c d e^{6} + a^{4} e^{8}\right)} {\left| c \right|} {\left| d \right|}} - \frac{{\left(2 \, c^{4} d^{6} - 4 \, a c^{3} d^{4} e^{2} - \sqrt{2} \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} \sqrt{-c^{2} d^{3} + a c d e^{2} + \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} c^{2} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{4} - 2 \, \sqrt{2} \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} \sqrt{-c^{2} d^{3} + a c d e^{2} + \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} c^{2} d^{3} + 2 \, \sqrt{2} \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} \sqrt{-c^{2} d^{3} + a c d e^{2} + \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} a c d^{2} e^{2} - \sqrt{2} \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} \sqrt{-c^{2} d^{3} + a c d e^{2} + \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} c^{2} d^{2} + 2 \, \sqrt{2} \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} \sqrt{-c^{2} d^{3} + a c d e^{2} + \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} a c d e^{2} - 2 \, {\left(c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} c^{2} d^{2} - \sqrt{2} \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} \sqrt{-c^{2} d^{3} + a c d e^{2} + \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} a^{2} e^{4}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{c d^{2} - a e^{2} - \sqrt{{\left(c d^{2} - a e^{2}\right)}^{2}}}{c d}}}\right)}{{\left(c^{4} d^{8} + 2 \, c^{4} d^{7} - 4 \, a c^{3} d^{6} e^{2} + c^{4} d^{6} - 6 \, a c^{3} d^{5} e^{2} + 6 \, a^{2} c^{2} d^{4} e^{4} - 2 \, a c^{3} d^{4} e^{2} + 6 \, a^{2} c^{2} d^{3} e^{4} - 4 \, a^{3} c d^{2} e^{6} + a^{2} c^{2} d^{2} e^{4} - 2 \, a^{3} c d e^{6} + a^{4} e^{8}\right)} {\left| c \right|} {\left| d \right|}}"," ",0,"(2*c^4*d^6 - 4*a*c^3*d^4*e^2 - sqrt(2)*sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-c^2*d^3 + a*c*d*e^2 - sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*c^2*d^4 + 2*a^2*c^2*d^2*e^4 - 2*sqrt(2)*sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-c^2*d^3 + a*c*d*e^2 - sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*c^2*d^3 + 2*sqrt(2)*sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-c^2*d^3 + a*c*d*e^2 - sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*a*c*d^2*e^2 - sqrt(2)*sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-c^2*d^3 + a*c*d*e^2 - sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*c^2*d^2 + 2*sqrt(2)*sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-c^2*d^3 + a*c*d*e^2 - sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*a*c*d*e^2 - 2*(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c^2*d^2 - sqrt(2)*sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-c^2*d^3 + a*c*d*e^2 - sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*a^2*e^4)*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(c*d^2 - a*e^2 + sqrt((c*d^2 - a*e^2)^2))/(c*d)))/((c^4*d^8 + 2*c^4*d^7 - 4*a*c^3*d^6*e^2 + c^4*d^6 - 6*a*c^3*d^5*e^2 + 6*a^2*c^2*d^4*e^4 - 2*a*c^3*d^4*e^2 + 6*a^2*c^2*d^3*e^4 - 4*a^3*c*d^2*e^6 + a^2*c^2*d^2*e^4 - 2*a^3*c*d*e^6 + a^4*e^8)*abs(c)*abs(d)) - (2*c^4*d^6 - 4*a*c^3*d^4*e^2 - sqrt(2)*sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-c^2*d^3 + a*c*d*e^2 + sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*c^2*d^4 + 2*a^2*c^2*d^2*e^4 - 2*sqrt(2)*sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-c^2*d^3 + a*c*d*e^2 + sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*c^2*d^3 + 2*sqrt(2)*sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-c^2*d^3 + a*c*d*e^2 + sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*a*c*d^2*e^2 - sqrt(2)*sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-c^2*d^3 + a*c*d*e^2 + sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*c^2*d^2 + 2*sqrt(2)*sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-c^2*d^3 + a*c*d*e^2 + sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*a*c*d*e^2 - 2*(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c^2*d^2 - sqrt(2)*sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-c^2*d^3 + a*c*d*e^2 + sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*a^2*e^4)*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(c*d^2 - a*e^2 - sqrt((c*d^2 - a*e^2)^2))/(c*d)))/((c^4*d^8 + 2*c^4*d^7 - 4*a*c^3*d^6*e^2 + c^4*d^6 - 6*a*c^3*d^5*e^2 + 6*a^2*c^2*d^4*e^4 - 2*a*c^3*d^4*e^2 + 6*a^2*c^2*d^3*e^4 - 4*a^3*c*d^2*e^6 + a^2*c^2*d^2*e^4 - 2*a^3*c*d*e^6 + a^4*e^8)*abs(c)*abs(d))","B",0
2005,-2,0,0,0.000000," ","integrate(1/(e*x+d)^(1/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: 2*((4*a^4*c*d*exp(2)^4+2*a^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^4-32*a^3*c^2*d^3*exp(1)^2*exp(2)^2+16*a^3*c^2*d^3*exp(2)^3-4*a^3*c^2*d^2*exp(2)^3-16*a^3*c*d^2*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^2+8*a^3*c*d^2*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^3-4*a^3*c*d*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^3+2*a^3*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^3+64*a^2*c^3*d^5*exp(1)^4-64*a^2*c^3*d^5*exp(1)^2*exp(2)+24*a^2*c^3*d^5*exp(2)^2+16*a^2*c^3*d^4*exp(1)^2*exp(2)-4*a^2*c^3*d^4*exp(2)^2+32*a^2*c^2*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4-32*a^2*c^2*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)+12*a^2*c^2*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^2+16*a^2*c^2*d^3*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)-4*a^2*c^2*d^3*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^2+2*a^2*c^2*d^2*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^2-8*a^2*c*d^2*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)+2*a^2*c*d^2*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^2-4*a^2*c*d*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^2-4*a^2*c*d*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^2-32*a*c^4*d^7*exp(1)^2+16*a*c^4*d^7*exp(2)-16*a*c^4*d^6*exp(1)^2+4*a*c^4*d^6*exp(2)-16*a*c^3*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2+8*a*c^3*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)-16*a*c^3*d^5*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2+4*a*c^3*d^5*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)-8*a*c^3*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2+4*a*c^3*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)+8*a*c^2*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2-2*a*c^2*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)+8*a*c^2*d^3*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)+16*a*c^2*d^3*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2-8*a*c^2*d^3*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)+2*a*c^2*d^2*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)+4*a*c^2*d^2*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)+4*c^5*d^9+4*c^5*d^8+2*c^4*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)+4*c^4*d^7*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)+2*c^4*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)-2*c^3*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))-4*c^3*d^5*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))-4*c^3*d^5*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))-2*c^3*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))-4*c^3*d^4*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2)))/(8*a^5*d*exp(1)^2*exp(2)^4-8*a^5*d*exp(2)^5-64*a^4*c*d^3*exp(1)^4*exp(2)^2+96*a^4*c*d^3*exp(1)^2*exp(2)^3-32*a^4*c*d^3*exp(2)^4-16*a^4*c*d^2*exp(1)^2*exp(2)^3+16*a^4*c*d^2*exp(2)^4+128*a^3*c^2*d^5*exp(1)^6-256*a^3*c^2*d^5*exp(1)^4*exp(2)+176*a^3*c^2*d^5*exp(1)^2*exp(2)^2-48*a^3*c^2*d^5*exp(2)^3+64*a^3*c^2*d^4*exp(1)^4*exp(2)-80*a^3*c^2*d^4*exp(1)^2*exp(2)^2+16*a^3*c^2*d^4*exp(2)^3+8*a^3*c^2*d^3*exp(1)^2*exp(2)^2-8*a^3*c^2*d^3*exp(2)^3-64*a^2*c^3*d^7*exp(1)^4+96*a^2*c^3*d^7*exp(1)^2*exp(2)-32*a^2*c^3*d^7*exp(2)^2-64*a^2*c^3*d^6*exp(1)^4+80*a^2*c^3*d^6*exp(1)^2*exp(2)-16*a^2*c^3*d^6*exp(2)^2-32*a^2*c^3*d^5*exp(1)^4+48*a^2*c^3*d^5*exp(1)^2*exp(2)-16*a^2*c^3*d^5*exp(2)^2+8*a*c^4*d^9*exp(1)^2-8*a*c^4*d^9*exp(2)+16*a*c^4*d^8*exp(1)^2-16*a*c^4*d^8*exp(2)+8*a*c^4*d^7*exp(1)^2-8*a*c^4*d^7*exp(2))/abs(c)/abs(d)*atan(sqrt(d+x*exp(1))/sqrt(-(c*d^2-a*exp(2)+sqrt((-c*d^2+a*exp(2))*(-c*d^2+a*exp(2))-4*c*d*(d*exp(1)^2*a-d*a*exp(2))))/2/c/d))-(4*a^4*c*d*exp(2)^4-2*a^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^4-32*a^3*c^2*d^3*exp(1)^2*exp(2)^2+16*a^3*c^2*d^3*exp(2)^3-4*a^3*c^2*d^2*exp(2)^3+16*a^3*c*d^2*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^2-8*a^3*c*d^2*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^3+4*a^3*c*d*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^3+2*a^3*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^3+64*a^2*c^3*d^5*exp(1)^4-64*a^2*c^3*d^5*exp(1)^2*exp(2)+24*a^2*c^3*d^5*exp(2)^2+16*a^2*c^3*d^4*exp(1)^2*exp(2)-4*a^2*c^3*d^4*exp(2)^2-32*a^2*c^2*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4+32*a^2*c^2*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)-12*a^2*c^2*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^2-16*a^2*c^2*d^3*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)+4*a^2*c^2*d^3*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^2-2*a^2*c^2*d^2*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^2-8*a^2*c*d^2*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)+2*a^2*c*d^2*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^2-4*a^2*c*d*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^2-4*a^2*c*d*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^2-32*a*c^4*d^7*exp(1)^2+16*a*c^4*d^7*exp(2)-16*a*c^4*d^6*exp(1)^2+4*a*c^4*d^6*exp(2)+16*a*c^3*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2-8*a*c^3*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)+16*a*c^3*d^5*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2-4*a*c^3*d^5*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)+8*a*c^3*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2-4*a*c^3*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)+8*a*c^2*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2-2*a*c^2*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)+8*a*c^2*d^3*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)+16*a*c^2*d^3*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2-8*a*c^2*d^3*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)+2*a*c^2*d^2*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)+4*a*c^2*d^2*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)+4*c^5*d^9+4*c^5*d^8-2*c^4*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)-4*c^4*d^7*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)-2*c^4*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)-2*c^3*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))-4*c^3*d^5*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))-4*c^3*d^5*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))-2*c^3*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))-4*c^3*d^4*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2)))/(8*a^5*d*exp(1)^2*exp(2)^4-8*a^5*d*exp(2)^5-64*a^4*c*d^3*exp(1)^4*exp(2)^2+96*a^4*c*d^3*exp(1)^2*exp(2)^3-32*a^4*c*d^3*exp(2)^4-16*a^4*c*d^2*exp(1)^2*exp(2)^3+16*a^4*c*d^2*exp(2)^4+128*a^3*c^2*d^5*exp(1)^6-256*a^3*c^2*d^5*exp(1)^4*exp(2)+176*a^3*c^2*d^5*exp(1)^2*exp(2)^2-48*a^3*c^2*d^5*exp(2)^3+64*a^3*c^2*d^4*exp(1)^4*exp(2)-80*a^3*c^2*d^4*exp(1)^2*exp(2)^2+16*a^3*c^2*d^4*exp(2)^3+8*a^3*c^2*d^3*exp(1)^2*exp(2)^2-8*a^3*c^2*d^3*exp(2)^3-64*a^2*c^3*d^7*exp(1)^4+96*a^2*c^3*d^7*exp(1)^2*exp(2)-32*a^2*c^3*d^7*exp(2)^2-64*a^2*c^3*d^6*exp(1)^4+80*a^2*c^3*d^6*exp(1)^2*exp(2)-16*a^2*c^3*d^6*exp(2)^2-32*a^2*c^3*d^5*exp(1)^4+48*a^2*c^3*d^5*exp(1)^2*exp(2)-16*a^2*c^3*d^5*exp(2)^2+8*a*c^4*d^9*exp(1)^2-8*a*c^4*d^9*exp(2)+16*a*c^4*d^8*exp(1)^2-16*a*c^4*d^8*exp(2)+8*a*c^4*d^7*exp(1)^2-8*a*c^4*d^7*exp(2))/abs(c)/abs(d)*atan(sqrt(d+x*exp(1))/sqrt(-(c*d^2-a*exp(2)-sqrt((-c*d^2+a*exp(2))*(-c*d^2+a*exp(2))-4*c*d*(d*exp(1)^2*a-d*a*exp(2))))/2/c/d)))","F(-2)",0
2006,-1,0,0,0.000000," ","integrate(1/(e*x+d)^(3/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2007,-2,0,0,0.000000," ","integrate(1/(e*x+d)^(5/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: 2*((4*a^6*c*d*exp(2)^6+2*a^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^6-36*a^5*c^2*d^3*exp(1)^2*exp(2)^4+12*a^5*c^2*d^3*exp(2)^5-4*a^5*c^2*d^2*exp(2)^5-18*a^5*c*d^2*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^4+6*a^5*c*d^2*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^5-4*a^5*c*d*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^5+2*a^5*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^5+96*a^4*c^3*d^5*exp(1)^4*exp(2)^2-48*a^4*c^3*d^5*exp(1)^2*exp(2)^3+12*a^4*c^3*d^5*exp(2)^4+28*a^4*c^3*d^4*exp(1)^2*exp(2)^3-8*a^4*c^3*d^4*exp(2)^4+48*a^4*c^2*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)^2-24*a^4*c^2*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^3+6*a^4*c^2*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^4+20*a^4*c^2*d^3*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^3+2*a^4*c^2*d^2*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^4-14*a^4*c*d^2*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^3+4*a^4*c*d^2*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^4-4*a^4*c*d*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^4-4*a^4*c*d*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^4-64*a^3*c^4*d^7*exp(1)^6-24*a^3*c^4*d^7*exp(1)^2*exp(2)^2+8*a^3*c^4*d^7*exp(2)^3-48*a^3*c^4*d^6*exp(1)^4*exp(2)+12*a^3*c^4*d^6*exp(1)^2*exp(2)^2-4*a^3*c^4*d^6*exp(2)^3-32*a^3*c^3*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^6-12*a^3*c^3*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^2+4*a^3*c^3*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^3-16*a^3*c^3*d^5*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)-28*a^3*c^3*d^5*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^2+4*a^3*c^3*d^5*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^3-10*a^3*c^3*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^2+2*a^3*c^3*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^3+24*a^3*c^2*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)-6*a^3*c^2*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2+2*a^3*c^2*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^3+12*a^3*c^2*d^3*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2+4*a^3*c^2*d^3*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^3+20*a^3*c^2*d^3*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2-4*a^3*c^2*d^3*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^3+2*a^3*c^2*d^2*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^3+4*a^3*c^2*d^2*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^3+96*a^2*c^5*d^9*exp(1)^4-48*a^2*c^5*d^9*exp(1)^2*exp(2)+12*a^2*c^5*d^9*exp(2)^2+48*a^2*c^5*d^8*exp(1)^4-12*a^2*c^5*d^8*exp(1)^2*exp(2)+4*a^2*c^5*d^8*exp(2)^2+48*a^2*c^4*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4-24*a^2*c^4*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)+6*a^2*c^4*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^2+16*a^2*c^4*d^7*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4+28*a^2*c^4*d^7*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)-4*a^2*c^4*d^7*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^2+8*a^2*c^4*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4+4*a^2*c^4*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)-24*a^2*c^3*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4+6*a^2*c^3*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)-2*a^2*c^3*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^2-24*a^2*c^3*d^5*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)-16*a^2*c^3*d^5*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4-8*a^2*c^3*d^5*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)-6*a^2*c^3*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)-12*a^2*c^3*d^4*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)-36*a*c^6*d^11*exp(1)^2+12*a*c^6*d^11*exp(2)-28*a*c^6*d^10*exp(1)^2+8*a*c^6*d^10*exp(2)-18*a*c^5*d^10*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2+6*a*c^5*d^10*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)-20*a*c^5*d^9*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2-10*a*c^5*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2+2*a*c^5*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)+14*a*c^4*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2-4*a*c^4*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)+12*a*c^4*d^7*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2+4*a*c^4*d^7*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)+20*a*c^4*d^7*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2-4*a*c^4*d^7*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)+6*a*c^4*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2+12*a*c^4*d^6*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2+4*c^7*d^13+4*c^7*d^12+2*c^6*d^12*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)+4*c^6*d^11*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)+2*c^6*d^10*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)-2*c^5*d^10*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))-4*c^5*d^9*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))-4*c^5*d^9*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))-2*c^5*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*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(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^6+12*a^3*c^3*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^2-4*a^3*c^3*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^3+16*a^3*c^3*d^5*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)+28*a^3*c^3*d^5*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^2-4*a^3*c^3*d^5*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^3+10*a^3*c^3*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^2-2*a^3*c^3*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^3+24*a^3*c^2*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)-6*a^3*c^2*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2+2*a^3*c^2*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^3+12*a^3*c^2*d^3*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2+4*a^3*c^2*d^3*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^3+20*a^3*c^2*d^3*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2-4*a^3*c^2*d^3*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^3+2*a^3*c^2*d^2*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^3+4*a^3*c^2*d^2*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^3+96*a^2*c^5*d^9*exp(1)^4-48*a^2*c^5*d^9*exp(1)^2*exp(2)+12*a^2*c^5*d^9*exp(2)^2+48*a^2*c^5*d^8*exp(1)^4-12*a^2*c^5*d^8*exp(1)^2*exp(2)+4*a^2*c^5*d^8*exp(2)^2-48*a^2*c^4*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4+24*a^2*c^4*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)-6*a^2*c^4*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^2-16*a^2*c^4*d^7*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4-28*a^2*c^4*d^7*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)+4*a^2*c^4*d^7*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)^2-8*a^2*c^4*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4-4*a^2*c^4*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)-24*a^2*c^3*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4+6*a^2*c^3*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)-2*a^2*c^3*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)^2-24*a^2*c^3*d^5*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)-16*a^2*c^3*d^5*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4-8*a^2*c^3*d^5*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)-6*a^2*c^3*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)-12*a^2*c^3*d^4*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)-36*a*c^6*d^11*exp(1)^2+12*a*c^6*d^11*exp(2)-28*a*c^6*d^10*exp(1)^2+8*a*c^6*d^10*exp(2)+18*a*c^5*d^10*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2-6*a*c^5*d^10*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)+20*a*c^5*d^9*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2+10*a*c^5*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2-2*a*c^5*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(2)+14*a*c^4*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2-4*a*c^4*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)+12*a*c^4*d^7*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2+4*a*c^4*d^7*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)+20*a*c^4*d^7*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2-4*a*c^4*d^7*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(2)+6*a*c^4*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2+12*a*c^4*d^6*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2+4*c^7*d^13+4*c^7*d^12-2*c^6*d^12*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)-4*c^6*d^11*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)-2*c^6*d^10*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)-2*c^5*d^10*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))-4*c^5*d^9*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))-4*c^5*d^9*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))-2*c^5*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))-4*c^5*d^8*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2)))/(8*a^7*d^3*exp(1)^6*exp(2)^4-24*a^7*d^3*exp(1)^4*exp(2)^5+24*a^7*d^3*exp(1)^2*exp(2)^6-8*a^7*d^3*exp(2)^7-64*a^6*c*d^5*exp(1)^8*exp(2)^2+224*a^6*c*d^5*exp(1)^6*exp(2)^3-288*a^6*c*d^5*exp(1)^4*exp(2)^4+160*a^6*c*d^5*exp(1)^2*exp(2)^5-32*a^6*c*d^5*exp(2)^6-16*a^6*c*d^4*exp(1)^6*exp(2)^3+48*a^6*c*d^4*exp(1)^4*exp(2)^4-48*a^6*c*d^4*exp(1)^2*exp(2)^5+16*a^6*c*d^4*exp(2)^6+128*a^5*c^2*d^7*exp(1)^10-512*a^5*c^2*d^7*exp(1)^8*exp(2)+816*a^5*c^2*d^7*exp(1)^6*exp(2)^2-656*a^5*c^2*d^7*exp(1)^4*exp(2)^3+272*a^5*c^2*d^7*exp(1)^2*exp(2)^4-48*a^5*c^2*d^7*exp(2)^5+64*a^5*c^2*d^6*exp(1)^8*exp(2)-208*a^5*c^2*d^6*exp(1)^6*exp(2)^2+240*a^5*c^2*d^6*exp(1)^4*exp(2)^3-112*a^5*c^2*d^6*exp(1)^2*exp(2)^4+16*a^5*c^2*d^6*exp(2)^5+8*a^5*c^2*d^5*exp(1)^6*exp(2)^2-24*a^5*c^2*d^5*exp(1)^4*exp(2)^3+24*a^5*c^2*d^5*exp(1)^2*exp(2)^4-8*a^5*c^2*d^5*exp(2)^5-64*a^4*c^3*d^9*exp(1)^8+224*a^4*c^3*d^9*exp(1)^6*exp(2)-288*a^4*c^3*d^9*exp(1)^4*exp(2)^2+160*a^4*c^3*d^9*exp(1)^2*exp(2)^3-32*a^4*c^3*d^9*exp(2)^4-64*a^4*c^3*d^8*exp(1)^8+208*a^4*c^3*d^8*exp(1)^6*exp(2)-240*a^4*c^3*d^8*exp(1)^4*exp(2)^2+112*a^4*c^3*d^8*exp(1)^2*exp(2)^3-16*a^4*c^3*d^8*exp(2)^4-32*a^4*c^3*d^7*exp(1)^8+112*a^4*c^3*d^7*exp(1)^6*exp(2)-144*a^4*c^3*d^7*exp(1)^4*exp(2)^2+80*a^4*c^3*d^7*exp(1)^2*exp(2)^3-16*a^4*c^3*d^7*exp(2)^4+8*a^3*c^4*d^11*exp(1)^6-24*a^3*c^4*d^11*exp(1)^4*exp(2)+24*a^3*c^4*d^11*exp(1)^2*exp(2)^2-8*a^3*c^4*d^11*exp(2)^3+16*a^3*c^4*d^10*exp(1)^6-48*a^3*c^4*d^10*exp(1)^4*exp(2)+48*a^3*c^4*d^10*exp(1)^2*exp(2)^2-16*a^3*c^4*d^10*exp(2)^3+8*a^3*c^4*d^9*exp(1)^6-24*a^3*c^4*d^9*exp(1)^4*exp(2)+24*a^3*c^4*d^9*exp(1)^2*exp(2)^2-8*a^3*c^4*d^9*exp(2)^3)/abs(c)/abs(d)*atan(sqrt(d+x*exp(1))/sqrt(-(-c*d^4*exp(1)^4*a^2+2*c*d^4*exp(1)^2*a^2*exp(2)-c*d^4*a^2*exp(2)^2+d^2*exp(1)^4*a^3*exp(2)-2*d^2*exp(1)^2*a^3*exp(2)^2+d^2*a^3*exp(2)^3-sqrt((c*d^4*exp(1)^4*a^2-2*c*d^4*exp(1)^2*a^2*exp(2)+c*d^4*a^2*exp(2)^2-d^2*exp(1)^4*a^3*exp(2)+2*d^2*exp(1)^2*a^3*exp(2)^2-d^2*a^3*exp(2)^3)*(c*d^4*exp(1)^4*a^2-2*c*d^4*exp(1)^2*a^2*exp(2)+c*d^4*a^2*exp(2)^2-d^2*exp(1)^4*a^3*exp(2)+2*d^2*exp(1)^2*a^3*exp(2)^2-d^2*a^3*exp(2)^3)-4*(-c*d^3*exp(1)^4*a^2+2*c*d^3*exp(1)^2*a^2*exp(2)-c*d^3*a^2*exp(2)^2)*(-d^3*exp(1)^6*a^3+3*d^3*exp(1)^4*a^3*exp(2)-3*d^3*exp(1)^2*a^3*exp(2)^2+d^3*a^3*exp(2)^3)))/2/(-c*d^3*exp(1)^4*a^2+2*c*d^3*exp(1)^2*a^2*exp(2)-c*d^3*a^2*exp(2)^2)))+(3*(d+x*exp(1))*c*d^2-3*(d+x*exp(1))*a*exp(2)+d*exp(1)^2*a-d*a*exp(2))/(-3*d^2*exp(1)^4*a^2+6*d^2*exp(1)^2*a^2*exp(2)-3*d^2*a^2*exp(2)^2)/sqrt(d+x*exp(1))/(d+x*exp(1)))","F(-2)",0
2008,-1,0,0,0.000000," ","integrate(1/(e*x+d)^(7/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2009,-1,0,0,0.000000," ","integrate((e*x+d)^(13/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2010,-1,0,0,0.000000," ","integrate((e*x+d)^(11/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2011,-1,0,0,0.000000," ","integrate((e*x+d)^(9/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2012,-1,0,0,0.000000," ","integrate((e*x+d)^(7/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2013,-1,0,0,0.000000," ","integrate((e*x+d)^(5/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2014,-1,0,0,0.000000," ","integrate((e*x+d)^(3/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2015,-1,0,0,0.000000," ","integrate((e*x+d)^(1/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2016,-1,0,0,0.000000," ","integrate(1/(e*x+d)^(1/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2017,-2,0,0,0.000000," ","integrate(1/(e*x+d)^(3/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: 2*((12*a^7*c*d*exp(1)*exp(2)^7-6*a^7*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)*exp(2)^7-148*a^6*c^2*d^3*exp(1)^3*exp(2)^5+64*a^6*c^2*d^3*exp(1)*exp(2)^6-12*a^6*c^2*d^2*exp(1)*exp(2)^6+74*a^6*c*d^2*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^3*exp(2)^5-32*a^6*c*d^2*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)*exp(2)^6+12*a^6*c*d*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)*exp(2)^6+6*a^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)*exp(2)^6+608*a^5*c^3*d^5*exp(1)^5*exp(2)^3-476*a^5*c^3*d^5*exp(1)^3*exp(2)^4+120*a^5*c^3*d^5*exp(1)*exp(2)^5+124*a^5*c^3*d^4*exp(1)^3*exp(2)^4-52*a^5*c^3*d^4*exp(1)*exp(2)^5-304*a^5*c^2*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^5*exp(2)^3+238*a^5*c^2*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^3*exp(2)^4-60*a^5*c^2*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)*exp(2)^5-100*a^5*c^2*d^3*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^3*exp(2)^4+28*a^5*c^2*d^3*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)*exp(2)^5-6*a^5*c^2*d^2*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)*exp(2)^5-62*a^5*c*d^2*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^3*exp(2)^4+26*a^5*c*d^2*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)*exp(2)^5-12*a^5*c*d*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)*exp(2)^5-12*a^5*c*d*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)*exp(2)^5-832*a^4*c^4*d^7*exp(1)^7*exp(2)+672*a^4*c^4*d^7*exp(1)^5*exp(2)^2-328*a^4*c^4*d^7*exp(1)^3*exp(2)^3+68*a^4*c^4*d^7*exp(1)*exp(2)^4-384*a^4*c^4*d^6*exp(1)^5*exp(2)^2+272*a^4*c^4*d^6*exp(1)^3*exp(2)^3-68*a^4*c^4*d^6*exp(1)*exp(2)^4+416*a^4*c^3*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^7*exp(2)-336*a^4*c^3*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^5*exp(2)^2+164*a^4*c^3*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^3*exp(2)^3-34*a^4*c^3*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)*exp(2)^4+208*a^4*c^3*d^5*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^5*exp(2)^2-16*a^4*c^3*d^5*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^3*exp(2)^3-12*a^4*c^3*d^5*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)*exp(2)^4+50*a^4*c^3*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^3*exp(2)^3-20*a^4*c^3*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)*exp(2)^4+192*a^4*c^2*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^5*exp(2)^2-136*a^4*c^2*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^3*exp(2)^3+34*a^4*c^2*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)*exp(2)^4+76*a^4*c^2*d^3*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^3*exp(2)^3-16*a^4*c^2*d^3*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)*exp(2)^4+100*a^4*c^2*d^3*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^3*exp(2)^3-40*a^4*c^2*d^3*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)*exp(2)^4+6*a^4*c^2*d^2*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)*exp(2)^4+12*a^4*c^2*d^2*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)*exp(2)^4+832*a^3*c^5*d^9*exp(1)^7-672*a^3*c^5*d^9*exp(1)^5*exp(2)+328*a^3*c^5*d^9*exp(1)^3*exp(2)^2-68*a^3*c^5*d^9*exp(1)*exp(2)^3+320*a^3*c^5*d^8*exp(1)^7-192*a^3*c^5*d^8*exp(1)^5*exp(2)+168*a^3*c^5*d^8*exp(1)^3*exp(2)^2-56*a^3*c^5*d^8*exp(1)*exp(2)^3-416*a^3*c^4*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^7+336*a^3*c^4*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^5*exp(2)-164*a^3*c^4*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^3*exp(2)^2+34*a^3*c^4*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)*exp(2)^3-416*a^3*c^4*d^7*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^5*exp(2)+232*a^3*c^4*d^7*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^3*exp(2)^2-56*a^3*c^4*d^7*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)*exp(2)^3-104*a^3*c^4*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^5*exp(2)+58*a^3*c^4*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^3*exp(2)^2-14*a^3*c^4*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)*exp(2)^3-160*a^3*c^3*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^7+96*a^3*c^3*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^5*exp(2)-84*a^3*c^3*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^3*exp(2)^2+28*a^3*c^3*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)*exp(2)^3-80*a^3*c^3*d^5*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^5*exp(2)-68*a^3*c^3*d^5*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^3*exp(2)^2+28*a^3*c^3*d^5*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)*exp(2)^3-208*a^3*c^3*d^5*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^5*exp(2)+116*a^3*c^3*d^5*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^3*exp(2)^2-28*a^3*c^3*d^5*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)*exp(2)^3-38*a^3*c^3*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^3*exp(2)^2+14*a^3*c^3*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)*exp(2)^3-76*a^3*c^3*d^4*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^3*exp(2)^2+28*a^3*c^3*d^4*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)*exp(2)^3-608*a^2*c^6*d^11*exp(1)^5+476*a^2*c^6*d^11*exp(1)^3*exp(2)-120*a^2*c^6*d^11*exp(1)*exp(2)^2-384*a^2*c^6*d^10*exp(1)^5+272*a^2*c^6*d^10*exp(1)^3*exp(2)-68*a^2*c^6*d^10*exp(1)*exp(2)^2+304*a^2*c^5*d^10*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^5-238*a^2*c^5*d^10*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^3*exp(2)+60*a^2*c^5*d^10*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)*exp(2)^2+208*a^2*c^5*d^9*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^5-16*a^2*c^5*d^9*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)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2018,-1,0,0,0.000000," ","integrate((e*x+d)^(15/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2019,-1,0,0,0.000000," ","integrate((e*x+d)^(13/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2020,-2,0,0,0.000000," ","integrate((e*x+d)^(11/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,c,d,exp(1),exp(2)]=[-83,-8,-38,29,40]Precision problem choosing root in common_EXT, current precision 14Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,c,d,exp(1),exp(2)]=[69,-62,15,83,-10]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,c,d,exp(1),exp(2)]=[61,93,-2,-73,84]Unable to divide, perhaps due to rounding error%%%{-7680,[6,6,12,6,0]%%%}+%%%{16384,[5,7,14,5,0]%%%}+%%%{3840,[5,7,13,5,0]%%%}+%%%{1920,[5,7,12,5,0]%%%}+%%%{13312,[5,6,12,6,1]%%%}+%%%{-3840,[5,6,11,6,1]%%%}+%%%{16384,[5,5,10,7,2]%%%}+%%%{-12736,[4,8,16,4,0]%%%}+%%%{-7232,[4,8,15,4,0]%%%}+%%%{-3616,[4,8,14,4,0]%%%}+%%%{-30976,[4,7,14,5,1]%%%}+%%%{2496,[4,7,13,5,1]%%%}+%%%{-2368,[4,7,12,5,1]%%%}+%%%{-27776,[4,6,12,6,2]%%%}+%%%{-2496,[4,6,11,6,2]%%%}+%%%{-3616,[4,6,10,6,2]%%%}+%%%{-30976,[4,5,10,7,3]%%%}+%%%{7232,[4,5,9,7,3]%%%}+%%%{-12736,[4,4,8,8,4]%%%}+%%%{4928,[3,9,18,3,0]%%%}+%%%{4560,[3,9,17,3,0]%%%}+%%%{2280,[3,9,16,3,0]%%%}+%%%{21376,[3,8,16,4,1]%%%}+%%%{6128,[3,8,15,4,1]%%%}+%%%{5344,[3,8,14,4,1]%%%}+%%%{33984,[3,7,14,5,2]%%%}+%%%{-2784,[3,7,13,5,2]%%%}+%%%{3952,[3,7,12,5,2]%%%}+%%%{33024,[3,6,12,6,3]%%%}+%%%{2784,[3,6,11,6,3]%%%}+%%%{5344,[3,6,10,6,3]%%%}+%%%{33984,[3,5,10,7,4]%%%}+%%%{-6128,[3,5,9,7,4]%%%}+%%%{2280,[3,5,8,7,4]%%%}+%%%{21376,[3,4,8,8,5]%%%}+%%%{-4560,[3,4,7,8,5]%%%}+%%%{4928,[3,3,6,9,6]%%%}+%%%{-1030,[2,10,20,2,0]%%%}+%%%{-1324,[2,10,19,2,0]%%%}+%%%{-662,[2,10,18,2,0]%%%}+%%%{-6544,[2,9,18,3,1]%%%}+%%%{-4412,[2,9,17,3,1]%%%}+%%%{-2868,[2,9,16,3,1]%%%}+%%%{-16552,[2,8,16,4,2]%%%}+%%%{-2796,[2,8,15,4,2]%%%}+%%%{-4266,[2,8,14,4,2]%%%}+%%%{-22256,[2,7,14,5,3]%%%}+%%%{1316,[2,7,13,5,3]%%%}+%%%{-3608,[2,7,12,5,3]%%%}+%%%{-22436,[2,6,12,6,4]%%%}+%%%{-1316,[2,6,11,6,4]%%%}+%%%{-4266,[2,6,10,6,4]%%%}+%%%{-22256,[2,5,10,7,5]%%%}+%%%{2796,[2,5,9,7,5]%%%}+%%%{-2868,[2,5,8,7,5]%%%}+%%%{-16552,[2,4,8,8,6]%%%}+%%%{4412,[2,4,7,8,6]%%%}+%%%{-662,[2,4,6,8,6]%%%}+%%%{-6544,[2,3,6,9,7]%%%}+%%%{1324,[2,3,5,9,7]%%%}+%%%{-1030,[2,2,4,10,8]%%%}+%%%{112,[1,11,22,1,0]%%%}+%%%{184,[1,11,21,1,0]%%%}+%%%{92,[1,11,20,1,0]%%%}+%%%{940,[1,10,20,2,1]%%%}+%%%{992,[1,10,19,2,1]%%%}+%%%{588,[1,10,18,2,1]%%%}+%%%{3344,[1,9,18,3,2]%%%}+%%%{1768,[1,9,17,3,2]%%%}+%%%{1472,[1,9,16,3,2]%%%}+%%%{6480,[1,8,16,4,3]%%%}+%%%{680,[1,8,15,4,3]%%%}+%%%{1812,[1,8,14,4,3]%%%}+%%%{8064,[1,7,14,5,4]%%%}+%%%{-280,[1,7,13,5,4]%%%}+%%%{1672,[1,7,12,5,4]%%%}+%%%{8200,[1,6,12,6,5]%%%}+%%%{280,[1,6,11,6,5]%%%}+%%%{1812,[1,6,10,6,5]%%%}+%%%{8064,[1,5,10,7,6]%%%}+%%%{-680,[1,5,9,7,6]%%%}+%%%{1472,[1,5,8,7,6]%%%}+%%%{6480,[1,4,8,8,7]%%%}+%%%{-1768,[1,4,7,8,7]%%%}+%%%{588,[1,4,6,8,7]%%%}+%%%{3344,[1,3,6,9,8]%%%}+%%%{-992,[1,3,5,9,8]%%%}+%%%{92,[1,3,4,9,8]%%%}+%%%{940,[1,2,4,10,9]%%%}+%%%{-184,[1,2,3,10,9]%%%}+%%%{112,[1,1,2,11,10]%%%}+%%%{-5,[0,12,24,0,0]%%%}+%%%{-10,[0,12,23,0,0]%%%}+%%%{-5,[0,12,22,0,0]%%%}+%%%{-52,[0,11,22,1,1]%%%}+%%%{-74,[0,11,21,1,1]%%%}+%%%{-42,[0,11,20,1,1]%%%}+%%%{-240,[0,10,20,2,2]%%%}+%%%{-218,[0,10,19,2,2]%%%}+%%%{-151,[0,10,18,2,2]%%%}+%%%{-628,[0,9,18,3,3]%%%}+%%%{-266,[0,9,17,3,3]%%%}+%%%{-284,[0,9,16,3,3]%%%}+%%%{-1043,[0,8,16,4,4]%%%}+%%%{-80,[0,8,15,4,4]%%%}+%%%{-324,[0,8,14,4,4]%%%}+%%%{-1240,[0,7,14,5,5]%%%}+%%%{32,[0,7,13,5,5]%%%}+%%%{-308,[0,7,12,5,5]%%%}+%%%{-1264,[0,6,12,6,6]%%%}+%%%{-32,[0,6,11,6,6]%%%}+%%%{-324,[0,6,10,6,6]%%%}+%%%{-1240,[0,5,10,7,7]%%%}+%%%{80,[0,5,9,7,7]%%%}+%%%{-284,[0,5,8,7,7]%%%}+%%%{-1043,[0,4,8,8,8]%%%}+%%%{266,[0,4,7,8,8]%%%}+%%%{-151,[0,4,6,8,8]%%%}+%%%{-628,[0,3,6,9,9]%%%}+%%%{218,[0,3,5,9,9]%%%}+%%%{-42,[0,3,4,9,9]%%%}+%%%{-240,[0,2,4,10,10]%%%}+%%%{74,[0,2,3,10,10]%%%}+%%%{-5,[0,2,2,10,10]%%%}+%%%{-52,[0,1,2,11,11]%%%}+%%%{10,[0,1,1,11,11]%%%}+%%%{-5,[0,0,0,12,12]%%%} / %%%{16,[2,2,4,2,0]%%%} Error: Bad Argument ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,c,d,exp(1),exp(2)]=[-92,88,73,-29,8]Unable to divide, perhaps due to rounding error%%%{-7680,[6,6,12,6,0]%%%}+%%%{16384,[5,7,14,5,0]%%%}+%%%{3840,[5,7,13,5,0]%%%}+%%%{1920,[5,7,12,5,0]%%%}+%%%{13312,[5,6,12,6,1]%%%}+%%%{-3840,[5,6,11,6,1]%%%}+%%%{16384,[5,5,10,7,2]%%%}+%%%{-12736,[4,8,16,4,0]%%%}+%%%{-7232,[4,8,15,4,0]%%%}+%%%{-3616,[4,8,14,4,0]%%%}+%%%{-30976,[4,7,14,5,1]%%%}+%%%{2496,[4,7,13,5,1]%%%}+%%%{-2368,[4,7,12,5,1]%%%}+%%%{-27776,[4,6,12,6,2]%%%}+%%%{-2496,[4,6,11,6,2]%%%}+%%%{-3616,[4,6,10,6,2]%%%}+%%%{-30976,[4,5,10,7,3]%%%}+%%%{7232,[4,5,9,7,3]%%%}+%%%{-12736,[4,4,8,8,4]%%%}+%%%{4928,[3,9,18,3,0]%%%}+%%%{4560,[3,9,17,3,0]%%%}+%%%{2280,[3,9,16,3,0]%%%}+%%%{21376,[3,8,16,4,1]%%%}+%%%{6128,[3,8,15,4,1]%%%}+%%%{5344,[3,8,14,4,1]%%%}+%%%{33984,[3,7,14,5,2]%%%}+%%%{-2784,[3,7,13,5,2]%%%}+%%%{3952,[3,7,12,5,2]%%%}+%%%{33024,[3,6,12,6,3]%%%}+%%%{2784,[3,6,11,6,3]%%%}+%%%{5344,[3,6,10,6,3]%%%}+%%%{33984,[3,5,10,7,4]%%%}+%%%{-6128,[3,5,9,7,4]%%%}+%%%{2280,[3,5,8,7,4]%%%}+%%%{21376,[3,4,8,8,5]%%%}+%%%{-4560,[3,4,7,8,5]%%%}+%%%{4928,[3,3,6,9,6]%%%}+%%%{-1030,[2,10,20,2,0]%%%}+%%%{-1324,[2,10,19,2,0]%%%}+%%%{-662,[2,10,18,2,0]%%%}+%%%{-6544,[2,9,18,3,1]%%%}+%%%{-4412,[2,9,17,3,1]%%%}+%%%{-2868,[2,9,16,3,1]%%%}+%%%{-16552,[2,8,16,4,2]%%%}+%%%{-2796,[2,8,15,4,2]%%%}+%%%{-4266,[2,8,14,4,2]%%%}+%%%{-22256,[2,7,14,5,3]%%%}+%%%{1316,[2,7,13,5,3]%%%}+%%%{-3608,[2,7,12,5,3]%%%}+%%%{-22436,[2,6,12,6,4]%%%}+%%%{-1316,[2,6,11,6,4]%%%}+%%%{-4266,[2,6,10,6,4]%%%}+%%%{-22256,[2,5,10,7,5]%%%}+%%%{2796,[2,5,9,7,5]%%%}+%%%{-2868,[2,5,8,7,5]%%%}+%%%{-16552,[2,4,8,8,6]%%%}+%%%{4412,[2,4,7,8,6]%%%}+%%%{-662,[2,4,6,8,6]%%%}+%%%{-6544,[2,3,6,9,7]%%%}+%%%{1324,[2,3,5,9,7]%%%}+%%%{-1030,[2,2,4,10,8]%%%}+%%%{112,[1,11,22,1,0]%%%}+%%%{184,[1,11,21,1,0]%%%}+%%%{92,[1,11,20,1,0]%%%}+%%%{940,[1,10,20,2,1]%%%}+%%%{992,[1,10,19,2,1]%%%}+%%%{588,[1,10,18,2,1]%%%}+%%%{3344,[1,9,18,3,2]%%%}+%%%{1768,[1,9,17,3,2]%%%}+%%%{1472,[1,9,16,3,2]%%%}+%%%{6480,[1,8,16,4,3]%%%}+%%%{680,[1,8,15,4,3]%%%}+%%%{1812,[1,8,14,4,3]%%%}+%%%{8064,[1,7,14,5,4]%%%}+%%%{-280,[1,7,13,5,4]%%%}+%%%{1672,[1,7,12,5,4]%%%}+%%%{8200,[1,6,12,6,5]%%%}+%%%{280,[1,6,11,6,5]%%%}+%%%{1812,[1,6,10,6,5]%%%}+%%%{8064,[1,5,10,7,6]%%%}+%%%{-680,[1,5,9,7,6]%%%}+%%%{1472,[1,5,8,7,6]%%%}+%%%{6480,[1,4,8,8,7]%%%}+%%%{-1768,[1,4,7,8,7]%%%}+%%%{588,[1,4,6,8,7]%%%}+%%%{3344,[1,3,6,9,8]%%%}+%%%{-992,[1,3,5,9,8]%%%}+%%%{92,[1,3,4,9,8]%%%}+%%%{940,[1,2,4,10,9]%%%}+%%%{-184,[1,2,3,10,9]%%%}+%%%{112,[1,1,2,11,10]%%%}+%%%{-5,[0,12,24,0,0]%%%}+%%%{-10,[0,12,23,0,0]%%%}+%%%{-5,[0,12,22,0,0]%%%}+%%%{-52,[0,11,22,1,1]%%%}+%%%{-74,[0,11,21,1,1]%%%}+%%%{-42,[0,11,20,1,1]%%%}+%%%{-240,[0,10,20,2,2]%%%}+%%%{-218,[0,10,19,2,2]%%%}+%%%{-151,[0,10,18,2,2]%%%}+%%%{-628,[0,9,18,3,3]%%%}+%%%{-266,[0,9,17,3,3]%%%}+%%%{-284,[0,9,16,3,3]%%%}+%%%{-1043,[0,8,16,4,4]%%%}+%%%{-80,[0,8,15,4,4]%%%}+%%%{-324,[0,8,14,4,4]%%%}+%%%{-1240,[0,7,14,5,5]%%%}+%%%{32,[0,7,13,5,5]%%%}+%%%{-308,[0,7,12,5,5]%%%}+%%%{-1264,[0,6,12,6,6]%%%}+%%%{-32,[0,6,11,6,6]%%%}+%%%{-324,[0,6,10,6,6]%%%}+%%%{-1240,[0,5,10,7,7]%%%}+%%%{80,[0,5,9,7,7]%%%}+%%%{-284,[0,5,8,7,7]%%%}+%%%{-1043,[0,4,8,8,8]%%%}+%%%{266,[0,4,7,8,8]%%%}+%%%{-151,[0,4,6,8,8]%%%}+%%%{-628,[0,3,6,9,9]%%%}+%%%{218,[0,3,5,9,9]%%%}+%%%{-42,[0,3,4,9,9]%%%}+%%%{-240,[0,2,4,10,10]%%%}+%%%{74,[0,2,3,10,10]%%%}+%%%{-5,[0,2,2,10,10]%%%}+%%%{-52,[0,1,2,11,11]%%%}+%%%{10,[0,1,1,11,11]%%%}+%%%{-5,[0,0,0,12,12]%%%} / %%%{16,[2,2,4,2,0]%%%} Error: Bad Argument ValueEvaluation time: 251.21Done","F(-2)",0
2021,-1,0,0,0.000000," ","integrate((e*x+d)^(9/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2022,-1,0,0,0.000000," ","integrate((e*x+d)^(7/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2023,1,5749,0,82.082410," ","integrate((e*x+d)^(5/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x, algorithm=""giac"")","\frac{3 \, {\left(4 \, c^{6} d^{11} e^{2} + 2 \, \sqrt{2} \sqrt{-c^{2} d^{3} + a c d e^{2} - \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} c^{5} d^{10} e^{2} + 6 \, c^{6} d^{10} e^{2} - 20 \, a c^{5} d^{9} e^{4} + 4 \, \sqrt{2} \sqrt{-c^{2} d^{3} + a c d e^{2} - \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} c^{5} d^{9} e^{2} - 10 \, \sqrt{2} \sqrt{-c^{2} d^{3} + a c d e^{2} - \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} a c^{4} d^{8} e^{4} - 24 \, a c^{5} d^{8} e^{4} + 2 \, \sqrt{2} \sqrt{-c^{2} d^{3} + a c d e^{2} - \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} c^{5} d^{8} e^{2} - 3 \, \sqrt{2} \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} \sqrt{-c^{2} d^{3} + a c d e^{2} - \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} c^{4} d^{8} e^{2} + 40 \, a^{2} c^{4} d^{7} e^{6} - 16 \, \sqrt{2} \sqrt{-c^{2} d^{3} + a c d e^{2} - \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} a c^{4} d^{7} e^{4} - 6 \, \sqrt{2} \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} \sqrt{-c^{2} d^{3} + a c d e^{2} - \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} c^{4} d^{7} e^{2} + 20 \, \sqrt{2} \sqrt{-c^{2} d^{3} + a c d e^{2} - \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} a^{2} c^{3} d^{6} e^{6} + 36 \, a^{2} c^{4} d^{6} e^{6} - 6 \, \sqrt{2} \sqrt{-c^{2} d^{3} + a c d e^{2} - \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} a c^{4} d^{6} e^{4} - 4 \, {\left(c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} c^{4} d^{7} e^{2} + 12 \, \sqrt{2} \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} \sqrt{-c^{2} d^{3} + a c d e^{2} - \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} a c^{3} d^{6} e^{4} - 3 \, \sqrt{2} \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} \sqrt{-c^{2} d^{3} + a c d e^{2} - \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} c^{4} d^{6} e^{2} - 40 \, a^{3} c^{3} d^{5} e^{8} + 24 \, \sqrt{2} \sqrt{-c^{2} d^{3} + a c d e^{2} - \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} a^{2} c^{3} d^{5} e^{6} - 6 \, {\left(c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} c^{4} d^{6} e^{2} + 18 \, \sqrt{2} \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} \sqrt{-c^{2} d^{3} + a c d e^{2} - \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} a c^{3} d^{5} e^{4} - 20 \, \sqrt{2} \sqrt{-c^{2} d^{3} + a c d e^{2} - \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} a^{3} c^{2} d^{4} e^{8} - 24 \, a^{3} c^{3} d^{4} e^{8} + 6 \, \sqrt{2} \sqrt{-c^{2} d^{3} + a c d e^{2} - \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} a^{2} c^{3} d^{4} e^{6} + 12 \, {\left(c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} a c^{3} d^{5} e^{4} - 18 \, \sqrt{2} \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} \sqrt{-c^{2} d^{3} + a c d e^{2} - \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} a^{2} c^{2} d^{4} e^{6} + 6 \, \sqrt{2} \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} \sqrt{-c^{2} d^{3} + a c d e^{2} - \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} a c^{3} d^{4} e^{4} + 20 \, a^{4} c^{2} d^{3} e^{10} - 16 \, \sqrt{2} \sqrt{-c^{2} d^{3} + a c d e^{2} - \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} a^{3} c^{2} d^{3} e^{8} + 12 \, {\left(c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} a c^{3} d^{4} e^{4} - 18 \, \sqrt{2} \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} \sqrt{-c^{2} d^{3} + a c d e^{2} - \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} a^{2} c^{2} d^{3} e^{6} + 10 \, \sqrt{2} \sqrt{-c^{2} d^{3} + a c d e^{2} - \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} a^{4} c d^{2} e^{10} + 6 \, a^{4} c^{2} d^{2} e^{10} - 2 \, \sqrt{2} \sqrt{-c^{2} d^{3} + a c d e^{2} - \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} a^{3} c^{2} d^{2} e^{8} - 12 \, {\left(c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} a^{2} c^{2} d^{3} e^{6} + 12 \, \sqrt{2} \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} \sqrt{-c^{2} d^{3} + a c d e^{2} - \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} a^{3} c d^{2} e^{8} - 3 \, \sqrt{2} \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} \sqrt{-c^{2} d^{3} + a c d e^{2} - \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} a^{2} c^{2} d^{2} e^{6} - 4 \, a^{5} c d e^{12} + 4 \, \sqrt{2} \sqrt{-c^{2} d^{3} + a c d e^{2} - \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} a^{4} c d e^{10} - 6 \, {\left(c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} a^{2} c^{2} d^{2} e^{6} + 6 \, \sqrt{2} \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} \sqrt{-c^{2} d^{3} + a c d e^{2} - \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} a^{3} c d e^{8} - 2 \, \sqrt{2} \sqrt{-c^{2} d^{3} + a c d e^{2} - \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} a^{5} e^{12} + 4 \, {\left(c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} a^{3} c d e^{8} - 3 \, \sqrt{2} \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} \sqrt{-c^{2} d^{3} + a c d e^{2} - \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} a^{4} e^{10}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{c^{5} d^{10} - 5 \, a c^{4} d^{8} e^{2} + 10 \, a^{2} c^{3} d^{6} e^{4} - 10 \, a^{3} c^{2} d^{4} e^{6} + 5 \, a^{4} c d^{2} e^{8} - a^{5} e^{10} + \sqrt{{\left(c^{5} d^{10} - 5 \, a c^{4} d^{8} e^{2} + 10 \, a^{2} c^{3} d^{6} e^{4} - 10 \, a^{3} c^{2} d^{4} e^{6} + 5 \, a^{4} c d^{2} e^{8} - a^{5} e^{10}\right)}^{2}}}{c^{5} d^{9} - 4 \, a c^{4} d^{7} e^{2} + 6 \, a^{2} c^{3} d^{5} e^{4} - 4 \, a^{3} c^{2} d^{3} e^{6} + a^{4} c d e^{8}}}}\right)}{8 \, {\left(c^{8} d^{16} + 2 \, c^{8} d^{15} - 8 \, a c^{7} d^{14} e^{2} + c^{8} d^{14} - 14 \, a c^{7} d^{13} e^{2} + 28 \, a^{2} c^{6} d^{12} e^{4} - 6 \, a c^{7} d^{12} e^{2} + 42 \, a^{2} c^{6} d^{11} e^{4} - 56 \, a^{3} c^{5} d^{10} e^{6} + 15 \, a^{2} c^{6} d^{10} e^{4} - 70 \, a^{3} c^{5} d^{9} e^{6} + 70 \, a^{4} c^{4} d^{8} e^{8} - 20 \, a^{3} c^{5} d^{8} e^{6} + 70 \, a^{4} c^{4} d^{7} e^{8} - 56 \, a^{5} c^{3} d^{6} e^{10} + 15 \, a^{4} c^{4} d^{6} e^{8} - 42 \, a^{5} c^{3} d^{5} e^{10} + 28 \, a^{6} c^{2} d^{4} e^{12} - 6 \, a^{5} c^{3} d^{4} e^{10} + 14 \, a^{6} c^{2} d^{3} e^{12} - 8 \, a^{7} c d^{2} e^{14} + a^{6} c^{2} d^{2} e^{12} - 2 \, a^{7} c d e^{14} + a^{8} e^{16}\right)} {\left| c \right|} {\left| d \right|}} - \frac{3 \, {\left(4 \, c^{6} d^{11} e^{2} - 2 \, \sqrt{2} \sqrt{-c^{2} d^{3} + a c d e^{2} + \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} c^{5} d^{10} e^{2} + 6 \, c^{6} d^{10} e^{2} - 20 \, a c^{5} d^{9} e^{4} - 4 \, \sqrt{2} \sqrt{-c^{2} d^{3} + a c d e^{2} + \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} c^{5} d^{9} e^{2} + 10 \, \sqrt{2} \sqrt{-c^{2} d^{3} + a c d e^{2} + \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} a c^{4} d^{8} e^{4} - 24 \, a c^{5} d^{8} e^{4} - 2 \, \sqrt{2} \sqrt{-c^{2} d^{3} + a c d e^{2} + \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} c^{5} d^{8} e^{2} - 3 \, \sqrt{2} \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} \sqrt{-c^{2} d^{3} + a c d e^{2} + \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} c^{4} d^{8} e^{2} + 40 \, a^{2} c^{4} d^{7} e^{6} + 16 \, \sqrt{2} \sqrt{-c^{2} d^{3} + a c d e^{2} + \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} a c^{4} d^{7} e^{4} - 6 \, \sqrt{2} \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} \sqrt{-c^{2} d^{3} + a c d e^{2} + \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} c^{4} d^{7} e^{2} - 20 \, \sqrt{2} \sqrt{-c^{2} d^{3} + a c d e^{2} + \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} a^{2} c^{3} d^{6} e^{6} + 36 \, a^{2} c^{4} d^{6} e^{6} + 6 \, \sqrt{2} \sqrt{-c^{2} d^{3} + a c d e^{2} + \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} a c^{4} d^{6} e^{4} - 4 \, {\left(c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} c^{4} d^{7} e^{2} + 12 \, \sqrt{2} \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} \sqrt{-c^{2} d^{3} + a c d e^{2} + \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} a c^{3} d^{6} e^{4} - 3 \, \sqrt{2} \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} \sqrt{-c^{2} d^{3} + a c d e^{2} + \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} c^{4} d^{6} e^{2} - 40 \, a^{3} c^{3} d^{5} e^{8} - 24 \, \sqrt{2} \sqrt{-c^{2} d^{3} + a c d e^{2} + \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} a^{2} c^{3} d^{5} e^{6} - 6 \, {\left(c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} c^{4} d^{6} e^{2} + 18 \, \sqrt{2} \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} \sqrt{-c^{2} d^{3} + a c d e^{2} + \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} a c^{3} d^{5} e^{4} + 20 \, \sqrt{2} \sqrt{-c^{2} d^{3} + a c d e^{2} + \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} a^{3} c^{2} d^{4} e^{8} - 24 \, a^{3} c^{3} d^{4} e^{8} - 6 \, \sqrt{2} \sqrt{-c^{2} d^{3} + a c d e^{2} + \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} a^{2} c^{3} d^{4} e^{6} + 12 \, {\left(c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} a c^{3} d^{5} e^{4} - 18 \, \sqrt{2} \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} \sqrt{-c^{2} d^{3} + a c d e^{2} + \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} a^{2} c^{2} d^{4} e^{6} + 6 \, \sqrt{2} \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} \sqrt{-c^{2} d^{3} + a c d e^{2} + \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} a c^{3} d^{4} e^{4} + 20 \, a^{4} c^{2} d^{3} e^{10} + 16 \, \sqrt{2} \sqrt{-c^{2} d^{3} + a c d e^{2} + \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} a^{3} c^{2} d^{3} e^{8} + 12 \, {\left(c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} a c^{3} d^{4} e^{4} - 18 \, \sqrt{2} \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} \sqrt{-c^{2} d^{3} + a c d e^{2} + \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} a^{2} c^{2} d^{3} e^{6} - 10 \, \sqrt{2} \sqrt{-c^{2} d^{3} + a c d e^{2} + \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} a^{4} c d^{2} e^{10} + 6 \, a^{4} c^{2} d^{2} e^{10} + 2 \, \sqrt{2} \sqrt{-c^{2} d^{3} + a c d e^{2} + \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} a^{3} c^{2} d^{2} e^{8} - 12 \, {\left(c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} a^{2} c^{2} d^{3} e^{6} + 12 \, \sqrt{2} \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} \sqrt{-c^{2} d^{3} + a c d e^{2} + \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} a^{3} c d^{2} e^{8} - 3 \, \sqrt{2} \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} \sqrt{-c^{2} d^{3} + a c d e^{2} + \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} a^{2} c^{2} d^{2} e^{6} - 4 \, a^{5} c d e^{12} - 4 \, \sqrt{2} \sqrt{-c^{2} d^{3} + a c d e^{2} + \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} a^{4} c d e^{10} - 6 \, {\left(c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} a^{2} c^{2} d^{2} e^{6} + 6 \, \sqrt{2} \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} \sqrt{-c^{2} d^{3} + a c d e^{2} + \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} a^{3} c d e^{8} + 2 \, \sqrt{2} \sqrt{-c^{2} d^{3} + a c d e^{2} + \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} a^{5} e^{12} + 4 \, {\left(c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} a^{3} c d e^{8} - 3 \, \sqrt{2} \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} \sqrt{-c^{2} d^{3} + a c d e^{2} + \sqrt{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}} c d} a^{4} e^{10}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{c^{5} d^{10} - 5 \, a c^{4} d^{8} e^{2} + 10 \, a^{2} c^{3} d^{6} e^{4} - 10 \, a^{3} c^{2} d^{4} e^{6} + 5 \, a^{4} c d^{2} e^{8} - a^{5} e^{10} - \sqrt{{\left(c^{5} d^{10} - 5 \, a c^{4} d^{8} e^{2} + 10 \, a^{2} c^{3} d^{6} e^{4} - 10 \, a^{3} c^{2} d^{4} e^{6} + 5 \, a^{4} c d^{2} e^{8} - a^{5} e^{10}\right)}^{2}}}{c^{5} d^{9} - 4 \, a c^{4} d^{7} e^{2} + 6 \, a^{2} c^{3} d^{5} e^{4} - 4 \, a^{3} c^{2} d^{3} e^{6} + a^{4} c d e^{8}}}}\right)}{8 \, {\left(c^{8} d^{16} + 2 \, c^{8} d^{15} - 8 \, a c^{7} d^{14} e^{2} + c^{8} d^{14} - 14 \, a c^{7} d^{13} e^{2} + 28 \, a^{2} c^{6} d^{12} e^{4} - 6 \, a c^{7} d^{12} e^{2} + 42 \, a^{2} c^{6} d^{11} e^{4} - 56 \, a^{3} c^{5} d^{10} e^{6} + 15 \, a^{2} c^{6} d^{10} e^{4} - 70 \, a^{3} c^{5} d^{9} e^{6} + 70 \, a^{4} c^{4} d^{8} e^{8} - 20 \, a^{3} c^{5} d^{8} e^{6} + 70 \, a^{4} c^{4} d^{7} e^{8} - 56 \, a^{5} c^{3} d^{6} e^{10} + 15 \, a^{4} c^{4} d^{6} e^{8} - 42 \, a^{5} c^{3} d^{5} e^{10} + 28 \, a^{6} c^{2} d^{4} e^{12} - 6 \, a^{5} c^{3} d^{4} e^{10} + 14 \, a^{6} c^{2} d^{3} e^{12} - 8 \, a^{7} c d^{2} e^{14} + a^{6} c^{2} d^{2} e^{12} - 2 \, a^{7} c d e^{14} + a^{8} e^{16}\right)} {\left| c \right|} {\left| d \right|}} + \frac{3 \, {\left(x e + d\right)}^{\frac{7}{2}} c^{3} d^{5} e^{2} - 5 \, {\left(x e + d\right)}^{\frac{5}{2}} c^{3} d^{6} e^{2} - 6 \, {\left(x e + d\right)}^{\frac{7}{2}} a c^{2} d^{3} e^{4} + 15 \, {\left(x e + d\right)}^{\frac{5}{2}} a c^{2} d^{4} e^{4} + 3 \, {\left(x e + d\right)}^{\frac{7}{2}} a^{2} c d e^{6} - 15 \, {\left(x e + d\right)}^{\frac{5}{2}} a^{2} c d^{2} e^{6} + 5 \, {\left(x e + d\right)}^{\frac{5}{2}} a^{3} e^{8}}{4 \, {\left(c^{4} d^{8} - 4 \, a c^{3} d^{6} e^{2} + 6 \, a^{2} c^{2} d^{4} e^{4} - 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}\right)} {\left({\left(x e + d\right)}^{2} c d - {\left(x e + d\right)} c d^{2} + {\left(x e + d\right)} a e^{2}\right)}^{2}}"," ",0,"3/8*(4*c^6*d^11*e^2 + 2*sqrt(2)*sqrt(-c^2*d^3 + a*c*d*e^2 - sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*c^5*d^10*e^2 + 6*c^6*d^10*e^2 - 20*a*c^5*d^9*e^4 + 4*sqrt(2)*sqrt(-c^2*d^3 + a*c*d*e^2 - sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*c^5*d^9*e^2 - 10*sqrt(2)*sqrt(-c^2*d^3 + a*c*d*e^2 - sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*a*c^4*d^8*e^4 - 24*a*c^5*d^8*e^4 + 2*sqrt(2)*sqrt(-c^2*d^3 + a*c*d*e^2 - sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*c^5*d^8*e^2 - 3*sqrt(2)*sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-c^2*d^3 + a*c*d*e^2 - sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*c^4*d^8*e^2 + 40*a^2*c^4*d^7*e^6 - 16*sqrt(2)*sqrt(-c^2*d^3 + a*c*d*e^2 - sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*a*c^4*d^7*e^4 - 6*sqrt(2)*sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-c^2*d^3 + a*c*d*e^2 - sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*c^4*d^7*e^2 + 20*sqrt(2)*sqrt(-c^2*d^3 + a*c*d*e^2 - sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*a^2*c^3*d^6*e^6 + 36*a^2*c^4*d^6*e^6 - 6*sqrt(2)*sqrt(-c^2*d^3 + a*c*d*e^2 - sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*a*c^4*d^6*e^4 - 4*(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c^4*d^7*e^2 + 12*sqrt(2)*sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-c^2*d^3 + a*c*d*e^2 - sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*a*c^3*d^6*e^4 - 3*sqrt(2)*sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-c^2*d^3 + a*c*d*e^2 - sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*c^4*d^6*e^2 - 40*a^3*c^3*d^5*e^8 + 24*sqrt(2)*sqrt(-c^2*d^3 + a*c*d*e^2 - sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*a^2*c^3*d^5*e^6 - 6*(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c^4*d^6*e^2 + 18*sqrt(2)*sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-c^2*d^3 + a*c*d*e^2 - sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*a*c^3*d^5*e^4 - 20*sqrt(2)*sqrt(-c^2*d^3 + a*c*d*e^2 - sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*a^3*c^2*d^4*e^8 - 24*a^3*c^3*d^4*e^8 + 6*sqrt(2)*sqrt(-c^2*d^3 + a*c*d*e^2 - sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*a^2*c^3*d^4*e^6 + 12*(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*a*c^3*d^5*e^4 - 18*sqrt(2)*sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-c^2*d^3 + a*c*d*e^2 - sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*a^2*c^2*d^4*e^6 + 6*sqrt(2)*sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-c^2*d^3 + a*c*d*e^2 - sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*a*c^3*d^4*e^4 + 20*a^4*c^2*d^3*e^10 - 16*sqrt(2)*sqrt(-c^2*d^3 + a*c*d*e^2 - sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*a^3*c^2*d^3*e^8 + 12*(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*a*c^3*d^4*e^4 - 18*sqrt(2)*sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-c^2*d^3 + a*c*d*e^2 - sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*a^2*c^2*d^3*e^6 + 10*sqrt(2)*sqrt(-c^2*d^3 + a*c*d*e^2 - sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*a^4*c*d^2*e^10 + 6*a^4*c^2*d^2*e^10 - 2*sqrt(2)*sqrt(-c^2*d^3 + a*c*d*e^2 - sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*a^3*c^2*d^2*e^8 - 12*(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*a^2*c^2*d^3*e^6 + 12*sqrt(2)*sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-c^2*d^3 + a*c*d*e^2 - sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*a^3*c*d^2*e^8 - 3*sqrt(2)*sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-c^2*d^3 + a*c*d*e^2 - sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*a^2*c^2*d^2*e^6 - 4*a^5*c*d*e^12 + 4*sqrt(2)*sqrt(-c^2*d^3 + a*c*d*e^2 - sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*a^4*c*d*e^10 - 6*(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*a^2*c^2*d^2*e^6 + 6*sqrt(2)*sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-c^2*d^3 + a*c*d*e^2 - sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*a^3*c*d*e^8 - 2*sqrt(2)*sqrt(-c^2*d^3 + a*c*d*e^2 - sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*a^5*e^12 + 4*(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*a^3*c*d*e^8 - 3*sqrt(2)*sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-c^2*d^3 + a*c*d*e^2 - sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*a^4*e^10)*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(c^5*d^10 - 5*a*c^4*d^8*e^2 + 10*a^2*c^3*d^6*e^4 - 10*a^3*c^2*d^4*e^6 + 5*a^4*c*d^2*e^8 - a^5*e^10 + sqrt((c^5*d^10 - 5*a*c^4*d^8*e^2 + 10*a^2*c^3*d^6*e^4 - 10*a^3*c^2*d^4*e^6 + 5*a^4*c*d^2*e^8 - a^5*e^10)^2))/(c^5*d^9 - 4*a*c^4*d^7*e^2 + 6*a^2*c^3*d^5*e^4 - 4*a^3*c^2*d^3*e^6 + a^4*c*d*e^8)))/((c^8*d^16 + 2*c^8*d^15 - 8*a*c^7*d^14*e^2 + c^8*d^14 - 14*a*c^7*d^13*e^2 + 28*a^2*c^6*d^12*e^4 - 6*a*c^7*d^12*e^2 + 42*a^2*c^6*d^11*e^4 - 56*a^3*c^5*d^10*e^6 + 15*a^2*c^6*d^10*e^4 - 70*a^3*c^5*d^9*e^6 + 70*a^4*c^4*d^8*e^8 - 20*a^3*c^5*d^8*e^6 + 70*a^4*c^4*d^7*e^8 - 56*a^5*c^3*d^6*e^10 + 15*a^4*c^4*d^6*e^8 - 42*a^5*c^3*d^5*e^10 + 28*a^6*c^2*d^4*e^12 - 6*a^5*c^3*d^4*e^10 + 14*a^6*c^2*d^3*e^12 - 8*a^7*c*d^2*e^14 + a^6*c^2*d^2*e^12 - 2*a^7*c*d*e^14 + a^8*e^16)*abs(c)*abs(d)) - 3/8*(4*c^6*d^11*e^2 - 2*sqrt(2)*sqrt(-c^2*d^3 + a*c*d*e^2 + sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*c^5*d^10*e^2 + 6*c^6*d^10*e^2 - 20*a*c^5*d^9*e^4 - 4*sqrt(2)*sqrt(-c^2*d^3 + a*c*d*e^2 + sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*c^5*d^9*e^2 + 10*sqrt(2)*sqrt(-c^2*d^3 + a*c*d*e^2 + sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*a*c^4*d^8*e^4 - 24*a*c^5*d^8*e^4 - 2*sqrt(2)*sqrt(-c^2*d^3 + a*c*d*e^2 + sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*c^5*d^8*e^2 - 3*sqrt(2)*sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-c^2*d^3 + a*c*d*e^2 + sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*c^4*d^8*e^2 + 40*a^2*c^4*d^7*e^6 + 16*sqrt(2)*sqrt(-c^2*d^3 + a*c*d*e^2 + sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*a*c^4*d^7*e^4 - 6*sqrt(2)*sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-c^2*d^3 + a*c*d*e^2 + sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*c^4*d^7*e^2 - 20*sqrt(2)*sqrt(-c^2*d^3 + a*c*d*e^2 + sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*a^2*c^3*d^6*e^6 + 36*a^2*c^4*d^6*e^6 + 6*sqrt(2)*sqrt(-c^2*d^3 + a*c*d*e^2 + sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*a*c^4*d^6*e^4 - 4*(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c^4*d^7*e^2 + 12*sqrt(2)*sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-c^2*d^3 + a*c*d*e^2 + sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*a*c^3*d^6*e^4 - 3*sqrt(2)*sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-c^2*d^3 + a*c*d*e^2 + sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*c^4*d^6*e^2 - 40*a^3*c^3*d^5*e^8 - 24*sqrt(2)*sqrt(-c^2*d^3 + a*c*d*e^2 + sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*a^2*c^3*d^5*e^6 - 6*(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c^4*d^6*e^2 + 18*sqrt(2)*sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-c^2*d^3 + a*c*d*e^2 + sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*a*c^3*d^5*e^4 + 20*sqrt(2)*sqrt(-c^2*d^3 + a*c*d*e^2 + sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*a^3*c^2*d^4*e^8 - 24*a^3*c^3*d^4*e^8 - 6*sqrt(2)*sqrt(-c^2*d^3 + a*c*d*e^2 + sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*a^2*c^3*d^4*e^6 + 12*(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*a*c^3*d^5*e^4 - 18*sqrt(2)*sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-c^2*d^3 + a*c*d*e^2 + sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*a^2*c^2*d^4*e^6 + 6*sqrt(2)*sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-c^2*d^3 + a*c*d*e^2 + sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*a*c^3*d^4*e^4 + 20*a^4*c^2*d^3*e^10 + 16*sqrt(2)*sqrt(-c^2*d^3 + a*c*d*e^2 + sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*a^3*c^2*d^3*e^8 + 12*(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*a*c^3*d^4*e^4 - 18*sqrt(2)*sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-c^2*d^3 + a*c*d*e^2 + sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*a^2*c^2*d^3*e^6 - 10*sqrt(2)*sqrt(-c^2*d^3 + a*c*d*e^2 + sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*a^4*c*d^2*e^10 + 6*a^4*c^2*d^2*e^10 + 2*sqrt(2)*sqrt(-c^2*d^3 + a*c*d*e^2 + sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*a^3*c^2*d^2*e^8 - 12*(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*a^2*c^2*d^3*e^6 + 12*sqrt(2)*sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-c^2*d^3 + a*c*d*e^2 + sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*a^3*c*d^2*e^8 - 3*sqrt(2)*sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-c^2*d^3 + a*c*d*e^2 + sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*a^2*c^2*d^2*e^6 - 4*a^5*c*d*e^12 - 4*sqrt(2)*sqrt(-c^2*d^3 + a*c*d*e^2 + sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*a^4*c*d*e^10 - 6*(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*a^2*c^2*d^2*e^6 + 6*sqrt(2)*sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-c^2*d^3 + a*c*d*e^2 + sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*a^3*c*d*e^8 + 2*sqrt(2)*sqrt(-c^2*d^3 + a*c*d*e^2 + sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*a^5*e^12 + 4*(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*a^3*c*d*e^8 - 3*sqrt(2)*sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-c^2*d^3 + a*c*d*e^2 + sqrt(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*c*d)*a^4*e^10)*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(c^5*d^10 - 5*a*c^4*d^8*e^2 + 10*a^2*c^3*d^6*e^4 - 10*a^3*c^2*d^4*e^6 + 5*a^4*c*d^2*e^8 - a^5*e^10 - sqrt((c^5*d^10 - 5*a*c^4*d^8*e^2 + 10*a^2*c^3*d^6*e^4 - 10*a^3*c^2*d^4*e^6 + 5*a^4*c*d^2*e^8 - a^5*e^10)^2))/(c^5*d^9 - 4*a*c^4*d^7*e^2 + 6*a^2*c^3*d^5*e^4 - 4*a^3*c^2*d^3*e^6 + a^4*c*d*e^8)))/((c^8*d^16 + 2*c^8*d^15 - 8*a*c^7*d^14*e^2 + c^8*d^14 - 14*a*c^7*d^13*e^2 + 28*a^2*c^6*d^12*e^4 - 6*a*c^7*d^12*e^2 + 42*a^2*c^6*d^11*e^4 - 56*a^3*c^5*d^10*e^6 + 15*a^2*c^6*d^10*e^4 - 70*a^3*c^5*d^9*e^6 + 70*a^4*c^4*d^8*e^8 - 20*a^3*c^5*d^8*e^6 + 70*a^4*c^4*d^7*e^8 - 56*a^5*c^3*d^6*e^10 + 15*a^4*c^4*d^6*e^8 - 42*a^5*c^3*d^5*e^10 + 28*a^6*c^2*d^4*e^12 - 6*a^5*c^3*d^4*e^10 + 14*a^6*c^2*d^3*e^12 - 8*a^7*c*d^2*e^14 + a^6*c^2*d^2*e^12 - 2*a^7*c*d*e^14 + a^8*e^16)*abs(c)*abs(d)) + 1/4*(3*(x*e + d)^(7/2)*c^3*d^5*e^2 - 5*(x*e + d)^(5/2)*c^3*d^6*e^2 - 6*(x*e + d)^(7/2)*a*c^2*d^3*e^4 + 15*(x*e + d)^(5/2)*a*c^2*d^4*e^4 + 3*(x*e + d)^(7/2)*a^2*c*d*e^6 - 15*(x*e + d)^(5/2)*a^2*c*d^2*e^6 + 5*(x*e + d)^(5/2)*a^3*e^8)/((c^4*d^8 - 4*a*c^3*d^6*e^2 + 6*a^2*c^2*d^4*e^4 - 4*a^3*c*d^2*e^6 + a^4*e^8)*((x*e + d)^2*c*d - (x*e + d)*c*d^2 + (x*e + d)*a*e^2)^2)","B",0
2024,-2,0,0,0.000000," ","integrate((e*x+d)^(3/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: (12*a^6*c*d*exp(1)^2*exp(2)^6+6*a^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^6-48*a^5*c^2*d^3*exp(1)^4*exp(2)^4-24*a^5*c^2*d^3*exp(1)^2*exp(2)^5-12*a^5*c^2*d^2*exp(1)^2*exp(2)^5-24*a^5*c*d^2*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)^4-12*a^5*c*d^2*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^5-12*a^5*c*d*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^5+6*a^5*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^5-192*a^4*c^3*d^5*exp(1)^6*exp(2)^2+576*a^4*c^3*d^5*exp(1)^4*exp(2)^3-204*a^4*c^3*d^5*exp(1)^2*exp(2)^4-96*a^4*c^3*d^4*exp(1)^4*exp(2)^3+156*a^4*c^3*d^4*exp(1)^2*exp(2)^4-96*a^4*c^2*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^6*exp(2)^2+288*a^4*c^2*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)^3-102*a^4*c^2*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^4+60*a^4*c^2*d^3*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^4+6*a^4*c^2*d^2*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^4+48*a^4*c*d^2*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)^3-78*a^4*c*d^2*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^4-12*a^4*c*d*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^4-12*a^4*c*d*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^4+768*a^3*c^4*d^7*exp(1)^8-1920*a^3*c^4*d^7*exp(1)^6*exp(2)+1248*a^3*c^4*d^7*exp(1)^4*exp(2)^2-336*a^3*c^4*d^7*exp(1)^2*exp(2)^3+576*a^3*c^4*d^6*exp(1)^6*exp(2)-864*a^3*c^4*d^6*exp(1)^4*exp(2)^2+168*a^3*c^4*d^6*exp(1)^2*exp(2)^3+384*a^3*c^3*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^8-960*a^3*c^3*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^6*exp(2)+624*a^3*c^3*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)^2-168*a^3*c^3*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^3+192*a^3*c^3*d^5*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^6*exp(2)-384*a^3*c^3*d^5*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)^2+72*a^3*c^3*d^5*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^3-24*a^3*c^3*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^3-288*a^3*c^2*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^6*exp(2)+432*a^3*c^2*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)^2-84*a^3*c^2*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^3-144*a^3*c^2*d^3*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)^2+192*a^3*c^2*d^3*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^3+48*a^3*c^2*d^3*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^3+6*a^3*c^2*d^2*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^3+12*a^3*c^2*d^2*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^3-192*a^2*c^5*d^9*exp(1)^6+576*a^2*c^5*d^9*exp(1)^4*exp(2)-204*a^2*c^5*d^9*exp(1)^2*exp(2)^2-576*a^2*c^5*d^8*exp(1)^6+864*a^2*c^5*d^8*exp(1)^4*exp(2)-168*a^2*c^5*d^8*exp(1)^2*exp(2)^2-96*a^2*c^4*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^6+288*a^2*c^4*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)-102*a^2*c^4*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^2-192*a^2*c^4*d^7*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^6+384*a^2*c^4*d^7*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)-72*a^2*c^4*d^7*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^2-96*a^2*c^4*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^6+192*a^2*c^4*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)-60*a^2*c^4*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^2+288*a^2*c^3*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^6-432*a^2*c^3*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)+84*a^2*c^3*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2+288*a^2*c^3*d^5*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)-360*a^2*c^3*d^5*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2+192*a^2*c^3*d^5*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^6-384*a^2*c^3*d^5*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)+120*a^2*c^3*d^5*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2+72*a^2*c^3*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)-90*a^2*c^3*d^4*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2+144*a^2*c^3*d^4*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)-180*a^2*c^3*d^4*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2-48*a*c^6*d^11*exp(1)^4-24*a*c^6*d^11*exp(1)^2*exp(2)+96*a*c^6*d^10*exp(1)^4-156*a*c^6*d^10*exp(1)^2*exp(2)-24*a*c^5*d^10*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4-12*a*c^5*d^10*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)-60*a*c^5*d^9*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)-24*a*c^5*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)-48*a*c^4*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4+78*a*c^4*d^8*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)-144*a*c^4*d^7*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4+192*a*c^4*d^7*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)+48*a*c^4*d^7*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)-72*a*c^4*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4+90*a*c^4*d^6*sqrt(-c^2*d^3-c*d*sqrt(c^2*d^4-4*a*c*d^2*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a^3*c^2*d^3*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)^2+192*a^3*c^2*d^3*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^3+48*a^3*c^2*d^3*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^3+6*a^3*c^2*d^2*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^3+12*a^3*c^2*d^2*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^3-192*a^2*c^5*d^9*exp(1)^6+576*a^2*c^5*d^9*exp(1)^4*exp(2)-204*a^2*c^5*d^9*exp(1)^2*exp(2)^2-576*a^2*c^5*d^8*exp(1)^6+864*a^2*c^5*d^8*exp(1)^4*exp(2)-168*a^2*c^5*d^8*exp(1)^2*exp(2)^2+96*a^2*c^4*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^6-288*a^2*c^4*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)+102*a^2*c^4*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^2+192*a^2*c^4*d^7*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^6-384*a^2*c^4*d^7*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)+72*a^2*c^4*d^7*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^2+96*a^2*c^4*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^6-192*a^2*c^4*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)+60*a^2*c^4*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^2+288*a^2*c^3*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^6-432*a^2*c^3*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)+84*a^2*c^3*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2+288*a^2*c^3*d^5*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)-360*a^2*c^3*d^5*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2+192*a^2*c^3*d^5*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^6-384*a^2*c^3*d^5*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)+120*a^2*c^3*d^5*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2+72*a^2*c^3*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)-90*a^2*c^3*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2+144*a^2*c^3*d^4*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)-180*a^2*c^3*d^4*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^2-48*a*c^6*d^11*exp(1)^4-24*a*c^6*d^11*exp(1)^2*exp(2)+96*a*c^6*d^10*exp(1)^4-156*a*c^6*d^10*exp(1)^2*exp(2)+24*a*c^5*d^10*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4+12*a*c^5*d^10*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)+60*a*c^5*d^9*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)+24*a*c^5*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)-48*a*c^4*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4+78*a*c^4*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(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*d^2*exp(1)^2*a^4*exp(2)^3*c-12*d^2*a^4*exp(2)^4*c-4*a^5*exp(2)^5-sqrt((-4*d^10*c^5+32*d^8*exp(1)^2*a*c^4-12*d^8*a*exp(2)*c^4-64*d^6*exp(1)^4*a^2*c^3+32*d^6*exp(1)^2*a^2*exp(2)*c^3-8*d^6*a^2*exp(2)^2*c^3+64*d^4*exp(1)^4*a^3*exp(2)*c^2-32*d^4*exp(1)^2*a^3*exp(2)^2*c^2+8*d^4*a^3*exp(2)^3*c^2-32*d^2*exp(1)^2*a^4*exp(2)^3*c+12*d^2*a^4*exp(2)^4*c+4*a^5*exp(2)^5)*(-4*d^10*c^5+32*d^8*exp(1)^2*a*c^4-12*d^8*a*exp(2)*c^4-64*d^6*exp(1)^4*a^2*c^3+32*d^6*exp(1)^2*a^2*exp(2)*c^3-8*d^6*a^2*exp(2)^2*c^3+64*d^4*exp(1)^4*a^3*exp(2)*c^2-32*d^4*exp(1)^2*a^3*exp(2)^2*c^2+8*d^4*a^3*exp(2)^3*c^2-32*d^2*exp(1)^2*a^4*exp(2)^3*c+12*d^2*a^4*exp(2)^4*c+4*a^5*exp(2)^5)-4*(4*d^9*c^5-32*d^7*exp(1)^2*a*c^4+16*d^7*a*exp(2)*c^4+64*d^5*exp(1)^4*a^2*c^3-64*d^5*exp(1)^2*a^2*exp(2)*c^3+24*d^5*a^2*exp(2)^2*c^3-32*d^3*exp(1)^2*a^3*exp(2)^2*c^2+16*d^3*a^3*exp(2)^3*c^2+4*d*a^4*exp(2)^4*c)*(4*d^9*exp(1)^2*a*c^4-4*d^9*a*exp(2)*c^4-32*d^7*exp(1)^4*a^2*c^3+48*d^7*exp(1)^2*a^2*exp(2)*c^3-16*d^7*a^2*exp(2)^2*c^3+64*d^5*exp(1)^6*a^3*c^2-128*d^5*exp(1)^4*a^3*exp(2)*c^2+88*d^5*exp(1)^2*a^3*exp(2)^2*c^2-24*d^5*a^3*exp(2)^3*c^2-32*d^3*exp(1)^4*a^4*exp(2)^2*c+48*d^3*exp(1)^2*a^4*exp(2)^3*c-16*d^3*a^4*exp(2)^4*c+4*d*exp(1)^2*a^5*exp(2)^4-4*d*a^5*exp(2)^5)))/2/(4*d^9*c^5-32*d^7*exp(1)^2*a*c^4+16*d^7*a*exp(2)*c^4+64*d^5*exp(1)^4*a^2*c^3-64*d^5*exp(1)^2*a^2*exp(2)*c^3+24*d^5*a^2*exp(2)^2*c^3-32*d^3*exp(1)^2*a^3*exp(2)^2*c^2+16*d^3*a^3*exp(2)^3*c^2+4*d*a^4*exp(2)^4*c)))+(-12*sqrt(d+x*exp(1))*(d+x*exp(1))^3*d^4*exp(1)^2*c^3+12*sqrt(d+x*exp(1))*(d+x*exp(1))^3*d^2*exp(1)^2*a*exp(2)*c^2+19*sqrt(d+x*exp(1))*(d+x*exp(1))^2*d^5*exp(1)^2*c^3-4*sqrt(d+x*exp(1))*(d+x*exp(1))^2*d^3*exp(1)^4*a*c^2-34*sqrt(d+x*exp(1))*(d+x*exp(1))^2*d^3*exp(1)^2*a*exp(2)*c^2+19*sqrt(d+x*exp(1))*(d+x*exp(1))^2*d*exp(1)^2*a^2*exp(2)^2*c-5*sqrt(d+x*exp(1))*(d+x*exp(1))*d^6*exp(1)^2*c^3-16*sqrt(d+x*exp(1))*(d+x*exp(1))*d^4*exp(1)^4*a*c^2+31*sqrt(d+x*exp(1))*(d+x*exp(1))*d^4*exp(1)^2*a*exp(2)*c^2+16*sqrt(d+x*exp(1))*(d+x*exp(1))*d^2*exp(1)^4*a^2*exp(2)*c-31*sqrt(d+x*exp(1))*(d+x*exp(1))*d^2*exp(1)^2*a^2*exp(2)^2*c+5*sqrt(d+x*exp(1))*(d+x*exp(1))*exp(1)^2*a^3*exp(2)^3+3*sqrt(d+x*exp(1))*d^5*exp(1)^4*a*c^2-3*sqrt(d+x*exp(1))*d^5*exp(1)^2*a*exp(2)*c^2+12*sqrt(d+x*exp(1))*d^3*exp(1)^6*a^2*c-30*sqrt(d+x*exp(1))*d^3*exp(1)^4*a^2*exp(2)*c+18*sqrt(d+x*exp(1))*d^3*exp(1)^2*a^2*exp(2)^2*c+3*sqrt(d+x*exp(1))*d*exp(1)^4*a^3*exp(2)^2-3*sqrt(d+x*exp(1))*d*exp(1)^2*a^3*exp(2)^3)/(-4*d^8*c^4+32*d^6*exp(1)^2*a*c^3-16*d^6*a*exp(2)*c^3-64*d^4*exp(1)^4*a^2*c^2+64*d^4*exp(1)^2*a^2*exp(2)*c^2-24*d^4*a^2*exp(2)^2*c^2+32*d^2*exp(1)^2*a^3*exp(2)^2*c-16*d^2*a^3*exp(2)^3*c-4*a^4*exp(2)^4)/((d+x*exp(1))^2*d*c-(d+x*exp(1))*d^2*c+(d+x*exp(1))*a*exp(2)+d*exp(1)^2*a-d*a*exp(2))^2","F(-2)",0
2025,-1,0,0,0.000000," ","integrate((e*x+d)^(1/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2026,-2,0,0,0.000000," ","integrate(1/(e*x+d)^(1/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: 2*((-12*a^8*c*d*exp(1)^2*exp(2)^8+6*a^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^8+204*a^7*c^2*d^3*exp(1)^4*exp(2)^6-108*a^7*c^2*d^3*exp(1)^2*exp(2)^7+12*a^7*c^2*d^2*exp(1)^2*exp(2)^7-102*a^7*c*d^2*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)^6+54*a^7*c*d^2*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^7-12*a^7*c*d*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^7-6*a^7*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^7-1392*a^6*c^3*d^5*exp(1)^6*exp(2)^4+1560*a^6*c^3*d^5*exp(1)^4*exp(2)^5-504*a^6*c^3*d^5*exp(1)^2*exp(2)^6-180*a^6*c^3*d^4*exp(1)^4*exp(2)^5+96*a^6*c^3*d^4*exp(1)^2*exp(2)^6+696*a^6*c^2*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^6*exp(2)^4-780*a^6*c^2*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)^5+252*a^6*c^2*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^6+156*a^6*c^2*d^3*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)^5-72*a^6*c^2*d^3*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^6+6*a^6*c^2*d^2*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^6+90*a^6*c*d^2*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)^5-48*a^6*c*d^2*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^6+12*a^6*c*d*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^6+12*a^6*c*d*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^6+4416*a^5*c^4*d^7*exp(1)^8*exp(2)^2-7680*a^5*c^4*d^7*exp(1)^6*exp(2)^3+5172*a^5*c^4*d^7*exp(1)^4*exp(2)^4-1236*a^5*c^4*d^7*exp(1)^2*exp(2)^5+1056*a^5*c^4*d^6*exp(1)^6*exp(2)^3-1212*a^5*c^4*d^6*exp(1)^4*exp(2)^4+408*a^5*c^4*d^6*exp(1)^2*exp(2)^5-2208*a^5*c^3*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^8*exp(2)^2+3840*a^5*c^3*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^6*exp(2)^3-2586*a^5*c^3*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)^4+618*a^5*c^3*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^5-768*a^5*c^3*d^5*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^6*exp(2)^3+756*a^5*c^3*d^5*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)^4-240*a^5*c^3*d^5*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^5-78*a^5*c^3*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)^4+42*a^5*c^3*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^5-528*a^5*c^2*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^6*exp(2)^3+606*a^5*c^2*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)^4-204*a^5*c^2*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^5-132*a^5*c^2*d^3*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)^4+60*a^5*c^2*d^3*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^5-156*a^5*c^2*d^3*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)^4+84*a^5*c^2*d^3*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^5-6*a^5*c^2*d^2*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^5-12*a^5*c^2*d^2*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^5-5376*a^4*c^5*d^9*exp(1)^10+12672*a^4*c^5*d^9*exp(1)^8*exp(2)-14112*a^4*c^5*d^9*exp(1)^6*exp(2)^2+7632*a^4*c^5*d^9*exp(1)^4*exp(2)^3-1656*a^4*c^5*d^9*exp(1)^2*exp(2)^4-2112*a^4*c^5*d^8*exp(1)^8*exp(2)+3168*a^4*c^5*d^8*exp(1)^6*exp(2)^2-1800*a^4*c^5*d^8*exp(1)^4*exp(2)^3+324*a^4*c^5*d^8*exp(1)^2*exp(2)^4+2688*a^4*c^4*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^10-6336*a^4*c^4*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^8*exp(2)+7056*a^4*c^4*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^6*exp(2)^2-3816*a^4*c^4*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)^3+828*a^4*c^4*d^8*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^4+1344*a^4*c^4*d^7*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^8*exp(2)-1728*a^4*c^4*d^7*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^6*exp(2)^2+984*a^4*c^4*d^7*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)^3-180*a^4*c^4*d^7*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^4+384*a^4*c^4*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^6*exp(2)^2-456*a^4*c^4*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^4*exp(2)^3+162*a^4*c^4*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*exp(1)^2*exp(2)^4+1056*a^4*c^3*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^8*exp(2)-1584*a^4*c^3*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^6*exp(2)^2+900*a^4*c^3*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)^3-162*a^4*c^3*d^6*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^4+528*a^4*c^3*d^5*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^6*exp(2)^2-528*a^4*c^3*d^5*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)^3+180*a^4*c^3*d^5*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^4+768*a^4*c^3*d^5*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^6*exp(2)^2-912*a^4*c^3*d^5*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)^3+324*a^4*c^3*d^5*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^4+66*a^4*c^3*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)^3-36*a^4*c^3*d^4*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))+a*c*d*exp(2))*sqrt(2)*sqrt(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^4+132*a^4*c^3*d^4*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^4*exp(2)^3-72*a^4*c^3*d^4*(c^2*d^4-4*a*c*d^2*exp(1)^2+a^2*exp(2)^2+2*a*c*d^2*exp(2))*exp(1)^2*exp(2)^4+4416*a^3*c^6*d^11*exp(1)^8-7680*a^3*c^6*d^11*exp(1)^6*exp(2)+5172*a^3*c^6*d^11*exp(1)^4*exp(2)^2-1236*a^3*c^6*d^11*exp(1)^2*exp(2)^3+2112*a^3*c^6*d^10*exp(1)^8-3168*a^3*c^6*d^10*exp(1)^6*exp(2)+1800*a^3*c^6*d^10*exp(1)^4*exp(2)^2-324*a^3*c^6*d^10*exp(1)^2*exp(2)^3-2208*a^3*c^5*d^10*sqrt(-c^2*d^3+c*d*sqrt(c^2*d^4-4*a*c*d^2*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2027,0,0,0,0.000000," ","integrate((e*x+d)^(7/2)*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""giac"")","\int \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(e x + d\right)}^{\frac{7}{2}}\,{d x}"," ",0,"integrate(sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(e*x + d)^(7/2), x)","F",0
2028,0,0,0,0.000000," ","integrate((e*x+d)^(5/2)*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""giac"")","\int \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(e x + d\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate(sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(e*x + d)^(5/2), x)","F",0
2029,0,0,0,0.000000," ","integrate((e*x+d)^(3/2)*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""giac"")","\int \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(e x + d\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(e*x + d)^(3/2), x)","F",0
2030,0,0,0,0.000000," ","integrate((e*x+d)^(1/2)*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""giac"")","\int \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}\,{d x}"," ",0,"integrate(sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d), x)","F",0
2031,0,0,0,0.000000," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{\sqrt{e x + d}}\,{d x}"," ",0,"integrate(sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)/sqrt(e*x + d), x)","F",0
2032,0,0,0,0.000000," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)/(e*x+d)^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{{\left(e x + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)/(e*x + d)^(3/2), x)","F",0
2033,0,0,0,0.000000," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)/(e*x+d)^(5/2),x, algorithm=""giac"")","\int \frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{{\left(e x + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)/(e*x + d)^(5/2), x)","F",0
2034,0,0,0,0.000000," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)/(e*x+d)^(7/2),x, algorithm=""giac"")","\int \frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{{\left(e x + d\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)/(e*x + d)^(7/2), x)","F",0
2035,0,0,0,0.000000," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)/(e*x+d)^(9/2),x, algorithm=""giac"")","\int \frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{{\left(e x + d\right)}^{\frac{9}{2}}}\,{d x}"," ",0,"integrate(sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)/(e*x + d)^(9/2), x)","F",0
2036,0,0,0,0.000000," ","integrate((e*x+d)^(5/2)*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""giac"")","\int {\left(c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)}^{\frac{3}{2}} {\left(e x + d\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)^(3/2)*(e*x + d)^(5/2), x)","F",0
2037,0,0,0,0.000000," ","integrate((e*x+d)^(3/2)*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""giac"")","\int {\left(c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)}^{\frac{3}{2}} {\left(e x + d\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)^(3/2)*(e*x + d)^(3/2), x)","F",0
2038,0,0,0,0.000000," ","integrate((e*x+d)^(1/2)*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""giac"")","\int {\left(c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)}^{\frac{3}{2}} \sqrt{e x + d}\,{d x}"," ",0,"integrate((c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)^(3/2)*sqrt(e*x + d), x)","F",0
2039,0,0,0,0.000000," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)}^{\frac{3}{2}}}{\sqrt{e x + d}}\,{d x}"," ",0,"integrate((c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)^(3/2)/sqrt(e*x + d), x)","F",0
2040,0,0,0,0.000000," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)/(e*x+d)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)}^{\frac{3}{2}}}{{\left(e x + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)^(3/2)/(e*x + d)^(3/2), x)","F",0
2041,-2,0,0,0.000000," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)/(e*x+d)^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:index.cc index_m operator + Error: Bad Argument Valueindex.cc index_m operator + Error: Bad Argument Valueindex.cc index_m operator + Error: Bad Argument ValueEvaluation time: 1.57Done","F(-2)",0
2042,-2,0,0,0.000000," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)/(e*x+d)^(7/2),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(d*exp(1)+x*exp(1)^2)]Evaluation time: 39.62Unable to transpose Error: Bad Argument Value","F(-2)",0
2043,-2,0,0,0.000000," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)/(e*x+d)^(9/2),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(d*exp(1)+x*exp(1)^2)]Evaluation time: 39.2Unable to transpose Error: Bad Argument Value","F(-2)",0
2044,-2,0,0,0.000000," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)/(e*x+d)^(11/2),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(d*exp(1)+x*exp(1)^2)]Evaluation time: 57.73Unable to transpose Error: Bad Argument Value","F(-2)",0
2045,-2,0,0,0.000000," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)/(e*x+d)^(13/2),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(d*exp(1)+x*exp(1)^2)]Evaluation time: 80.07Unable to transpose Error: Bad Argument Value","F(-2)",0
2046,-1,0,0,0.000000," ","integrate((e*x+d)^(3/2)*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2047,0,0,0,0.000000," ","integrate((e*x+d)^(1/2)*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2),x, algorithm=""giac"")","\int {\left(c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)}^{\frac{5}{2}} \sqrt{e x + d}\,{d x}"," ",0,"integrate((c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)^(5/2)*sqrt(e*x + d), x)","F",0
2048,0,0,0,0.000000," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)}^{\frac{5}{2}}}{\sqrt{e x + d}}\,{d x}"," ",0,"integrate((c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)^(5/2)/sqrt(e*x + d), x)","F",0
2049,0,0,0,0.000000," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/(e*x+d)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)}^{\frac{5}{2}}}{{\left(e x + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)^(5/2)/(e*x + d)^(3/2), x)","F",0
2050,-2,0,0,0.000000," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/(e*x+d)^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:index.cc index_m operator + Error: Bad Argument Valueindex.cc index_m operator + Error: Bad Argument Valueindex.cc index_m operator + Error: Bad Argument ValueEvaluation time: 3.16Done","F(-2)",0
2051,-1,0,0,0.000000," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/(e*x+d)^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2052,-1,0,0,0.000000," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/(e*x+d)^(9/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2053,-1,0,0,0.000000," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/(e*x+d)^(11/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2054,-1,0,0,0.000000," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/(e*x+d)^(13/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2055,-1,0,0,0.000000," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/(e*x+d)^(15/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2056,-1,0,0,0.000000," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/(e*x+d)^(17/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2057,0,0,0,0.000000," ","integrate((e*x+d)^(7/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{\frac{7}{2}}}{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}\,{d x}"," ",0,"integrate((e*x + d)^(7/2)/sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x), x)","F",0
2058,0,0,0,0.000000," ","integrate((e*x+d)^(5/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{\frac{5}{2}}}{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}\,{d x}"," ",0,"integrate((e*x + d)^(5/2)/sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x), x)","F",0
2059,0,0,0,0.000000," ","integrate((e*x+d)^(3/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{\frac{3}{2}}}{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}\,{d x}"," ",0,"integrate((e*x + d)^(3/2)/sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x), x)","F",0
2060,0,0,0,0.000000," ","integrate((e*x+d)^(1/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{e x + d}}{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}\,{d x}"," ",0,"integrate(sqrt(e*x + d)/sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x), x)","F",0
2061,0,0,0,0.000000," ","integrate(1/(e*x+d)^(1/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}\,{d x}"," ",0,"integrate(1/(sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)), x)","F",0
2062,0,0,0,0.000000," ","integrate(1/(e*x+d)^(3/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(e x + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(e*x + d)^(3/2)), x)","F",0
2063,0,0,0,0.000000," ","integrate(1/(e*x+d)^(5/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
2064,0,0,0,0.000000," ","integrate(1/(e*x+d)^(7/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
2065,-2,0,0,0.000000," ","integrate((e*x+d)^(7/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 0.81Unable to transpose Error: Bad Argument Value","F(-2)",0
2066,-2,0,0,0.000000," ","integrate((e*x+d)^(5/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 0.71Unable to transpose Error: Bad Argument Value","F(-2)",0
2067,-2,0,0,0.000000," ","integrate((e*x+d)^(3/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 0.65Unable to transpose Error: Bad Argument Value","F(-2)",0
2068,-2,0,0,0.000000," ","integrate((e*x+d)^(1/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 0.54Unable to transpose Error: Bad Argument Value","F(-2)",0
2069,-2,0,0,0.000000," ","integrate(1/(e*x+d)^(1/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to transpose Error: Bad Argument Value","F(-2)",0
2070,-2,0,0,0.000000," ","integrate(1/(e*x+d)^(3/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,c,d,exp(1),exp(2)]=[-23,67,97,57,86]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,c,d,exp(1),exp(2)]=[-4,-41,-80,-82,20]Evaluation time: 34.57Not invertible Error: Bad Argument Value","F(-2)",0
2071,-1,0,0,0.000000," ","integrate(1/(e*x+d)^(5/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2072,-1,0,0,0.000000," ","integrate(1/(e*x+d)^(7/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2073,-2,0,0,0.000000," ","integrate((e*x+d)^(7/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 2.24Unable to transpose Error: Bad Argument Value","F(-2)",0
2074,-2,0,0,0.000000," ","integrate((e*x+d)^(5/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 2.01Unable to transpose Error: Bad Argument Value","F(-2)",0
2075,-2,0,0,0.000000," ","integrate((e*x+d)^(3/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 1.78Unable to transpose Error: Bad Argument Value","F(-2)",0
2076,-2,0,0,0.000000," ","integrate((e*x+d)^(1/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 1.51Unable to transpose Error: Bad Argument Value","F(-2)",0
2077,-2,0,0,0.000000," ","integrate(1/(e*x+d)^(1/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 0.8Unable to transpose Error: Bad Argument Value","F(-2)",0
2078,-2,0,0,0.000000," ","integrate(1/(e*x+d)^(3/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 1.1Unable to transpose Error: Bad Argument Value","F(-2)",0
2079,-2,0,0,0.000000," ","integrate(1/(e*x+d)^(5/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 1.45Unable to transpose Error: Bad Argument Value","F(-2)",0
2080,-2,0,0,0.000000," ","integrate(1/(e*x+d)^(7/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 1.78Unable to transpose Error: Bad Argument Value","F(-2)",0
2081,0,0,0,0.000000," ","integrate(1/(e*x+d)^(1/2)/(-e^2*x^2+d^2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-e^{2} x^{2} + d^{2}} \sqrt{e x + d}}\,{d x}"," ",0,"integrate(1/(sqrt(-e^2*x^2 + d^2)*sqrt(e*x + d)), x)","F",0
2082,0,0,0,0.000000," ","integrate(1/(e*x-d)^(1/2)/(-e^2*x^2+d^2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-e^{2} x^{2} + d^{2}} \sqrt{e x - d}}\,{d x}"," ",0,"integrate(1/(sqrt(-e^2*x^2 + d^2)*sqrt(e*x - d)), x)","F",0
2083,0,0,0,0.000000," ","integrate((e*x+d)^(2/3)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{\frac{2}{3}}}{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}\,{d x}"," ",0,"integrate((e*x + d)^(2/3)/sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x), x)","F",0
2084,1,1997,0,0.355996," ","integrate((e*x+d)^m*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x, algorithm=""giac"")","\frac{{\left(x e + d\right)}^{m} c^{3} d^{3} m^{3} x^{7} e^{7} + 4 \, {\left(x e + d\right)}^{m} c^{3} d^{4} m^{3} x^{6} e^{6} + 6 \, {\left(x e + d\right)}^{m} c^{3} d^{5} m^{3} x^{5} e^{5} + 4 \, {\left(x e + d\right)}^{m} c^{3} d^{6} m^{3} x^{4} e^{4} + {\left(x e + d\right)}^{m} c^{3} d^{7} m^{3} x^{3} e^{3} + 15 \, {\left(x e + d\right)}^{m} c^{3} d^{3} m^{2} x^{7} e^{7} + 57 \, {\left(x e + d\right)}^{m} c^{3} d^{4} m^{2} x^{6} e^{6} + 78 \, {\left(x e + d\right)}^{m} c^{3} d^{5} m^{2} x^{5} e^{5} + 42 \, {\left(x e + d\right)}^{m} c^{3} d^{6} m^{2} x^{4} e^{4} + 3 \, {\left(x e + d\right)}^{m} c^{3} d^{7} m^{2} x^{3} e^{3} - 3 \, {\left(x e + d\right)}^{m} c^{3} d^{8} m^{2} x^{2} e^{2} + 3 \, {\left(x e + d\right)}^{m} a c^{2} d^{2} m^{3} x^{6} e^{8} + 12 \, {\left(x e + d\right)}^{m} a c^{2} d^{3} m^{3} x^{5} e^{7} + 74 \, {\left(x e + d\right)}^{m} c^{3} d^{3} m x^{7} e^{7} + 18 \, {\left(x e + d\right)}^{m} a c^{2} d^{4} m^{3} x^{4} e^{6} + 269 \, {\left(x e + d\right)}^{m} c^{3} d^{4} m x^{6} e^{6} + 12 \, {\left(x e + d\right)}^{m} a c^{2} d^{5} m^{3} x^{3} e^{5} + 342 \, {\left(x e + d\right)}^{m} c^{3} d^{5} m x^{5} e^{5} + 3 \, {\left(x e + d\right)}^{m} a c^{2} d^{6} m^{3} x^{2} e^{4} + 158 \, {\left(x e + d\right)}^{m} c^{3} d^{6} m x^{4} e^{4} + 2 \, {\left(x e + d\right)}^{m} c^{3} d^{7} m x^{3} e^{3} - 3 \, {\left(x e + d\right)}^{m} c^{3} d^{8} m x^{2} e^{2} + 6 \, {\left(x e + d\right)}^{m} c^{3} d^{9} m x e + 48 \, {\left(x e + d\right)}^{m} a c^{2} d^{2} m^{2} x^{6} e^{8} + 186 \, {\left(x e + d\right)}^{m} a c^{2} d^{3} m^{2} x^{5} e^{7} + 120 \, {\left(x e + d\right)}^{m} c^{3} d^{3} x^{7} e^{7} + 264 \, {\left(x e + d\right)}^{m} a c^{2} d^{4} m^{2} x^{4} e^{6} + 420 \, {\left(x e + d\right)}^{m} c^{3} d^{4} x^{6} e^{6} + 156 \, {\left(x e + d\right)}^{m} a c^{2} d^{5} m^{2} x^{3} e^{5} + 504 \, {\left(x e + d\right)}^{m} c^{3} d^{5} x^{5} e^{5} + 24 \, {\left(x e + d\right)}^{m} a c^{2} d^{6} m^{2} x^{2} e^{4} + 210 \, {\left(x e + d\right)}^{m} c^{3} d^{6} x^{4} e^{4} - 6 \, {\left(x e + d\right)}^{m} a c^{2} d^{7} m^{2} x e^{3} - 6 \, {\left(x e + d\right)}^{m} c^{3} d^{10} + 3 \, {\left(x e + d\right)}^{m} a^{2} c d m^{3} x^{5} e^{9} + 12 \, {\left(x e + d\right)}^{m} a^{2} c d^{2} m^{3} x^{4} e^{8} + 249 \, {\left(x e + d\right)}^{m} a c^{2} d^{2} m x^{6} e^{8} + 18 \, {\left(x e + d\right)}^{m} a^{2} c d^{3} m^{3} x^{3} e^{7} + 930 \, {\left(x e + d\right)}^{m} a c^{2} d^{3} m x^{5} e^{7} + 12 \, {\left(x e + d\right)}^{m} a^{2} c d^{4} m^{3} x^{2} e^{6} + 1236 \, {\left(x e + d\right)}^{m} a c^{2} d^{4} m x^{4} e^{6} + 3 \, {\left(x e + d\right)}^{m} a^{2} c d^{5} m^{3} x e^{5} + 624 \, {\left(x e + d\right)}^{m} a c^{2} d^{5} m x^{3} e^{5} + 21 \, {\left(x e + d\right)}^{m} a c^{2} d^{6} m x^{2} e^{4} - 42 \, {\left(x e + d\right)}^{m} a c^{2} d^{7} m x e^{3} + 6 \, {\left(x e + d\right)}^{m} a c^{2} d^{8} m e^{2} + 51 \, {\left(x e + d\right)}^{m} a^{2} c d m^{2} x^{5} e^{9} + 201 \, {\left(x e + d\right)}^{m} a^{2} c d^{2} m^{2} x^{4} e^{8} + 420 \, {\left(x e + d\right)}^{m} a c^{2} d^{2} x^{6} e^{8} + 294 \, {\left(x e + d\right)}^{m} a^{2} c d^{3} m^{2} x^{3} e^{7} + 1512 \, {\left(x e + d\right)}^{m} a c^{2} d^{3} x^{5} e^{7} + 186 \, {\left(x e + d\right)}^{m} a^{2} c d^{4} m^{2} x^{2} e^{6} + 1890 \, {\left(x e + d\right)}^{m} a c^{2} d^{4} x^{4} e^{6} + 39 \, {\left(x e + d\right)}^{m} a^{2} c d^{5} m^{2} x e^{5} + 840 \, {\left(x e + d\right)}^{m} a c^{2} d^{5} x^{3} e^{5} - 3 \, {\left(x e + d\right)}^{m} a^{2} c d^{6} m^{2} e^{4} + 42 \, {\left(x e + d\right)}^{m} a c^{2} d^{8} e^{2} + {\left(x e + d\right)}^{m} a^{3} m^{3} x^{4} e^{10} + 4 \, {\left(x e + d\right)}^{m} a^{3} d m^{3} x^{3} e^{9} + 282 \, {\left(x e + d\right)}^{m} a^{2} c d m x^{5} e^{9} + 6 \, {\left(x e + d\right)}^{m} a^{3} d^{2} m^{3} x^{2} e^{8} + 1089 \, {\left(x e + d\right)}^{m} a^{2} c d^{2} m x^{4} e^{8} + 4 \, {\left(x e + d\right)}^{m} a^{3} d^{3} m^{3} x e^{7} + 1536 \, {\left(x e + d\right)}^{m} a^{2} c d^{3} m x^{3} e^{7} + {\left(x e + d\right)}^{m} a^{3} d^{4} m^{3} e^{6} + 894 \, {\left(x e + d\right)}^{m} a^{2} c d^{4} m x^{2} e^{6} + 126 \, {\left(x e + d\right)}^{m} a^{2} c d^{5} m x e^{5} - 39 \, {\left(x e + d\right)}^{m} a^{2} c d^{6} m e^{4} + 18 \, {\left(x e + d\right)}^{m} a^{3} m^{2} x^{4} e^{10} + 72 \, {\left(x e + d\right)}^{m} a^{3} d m^{2} x^{3} e^{9} + 504 \, {\left(x e + d\right)}^{m} a^{2} c d x^{5} e^{9} + 108 \, {\left(x e + d\right)}^{m} a^{3} d^{2} m^{2} x^{2} e^{8} + 1890 \, {\left(x e + d\right)}^{m} a^{2} c d^{2} x^{4} e^{8} + 72 \, {\left(x e + d\right)}^{m} a^{3} d^{3} m^{2} x e^{7} + 2520 \, {\left(x e + d\right)}^{m} a^{2} c d^{3} x^{3} e^{7} + 18 \, {\left(x e + d\right)}^{m} a^{3} d^{4} m^{2} e^{6} + 1260 \, {\left(x e + d\right)}^{m} a^{2} c d^{4} x^{2} e^{6} - 126 \, {\left(x e + d\right)}^{m} a^{2} c d^{6} e^{4} + 107 \, {\left(x e + d\right)}^{m} a^{3} m x^{4} e^{10} + 428 \, {\left(x e + d\right)}^{m} a^{3} d m x^{3} e^{9} + 642 \, {\left(x e + d\right)}^{m} a^{3} d^{2} m x^{2} e^{8} + 428 \, {\left(x e + d\right)}^{m} a^{3} d^{3} m x e^{7} + 107 \, {\left(x e + d\right)}^{m} a^{3} d^{4} m e^{6} + 210 \, {\left(x e + d\right)}^{m} a^{3} x^{4} e^{10} + 840 \, {\left(x e + d\right)}^{m} a^{3} d x^{3} e^{9} + 1260 \, {\left(x e + d\right)}^{m} a^{3} d^{2} x^{2} e^{8} + 840 \, {\left(x e + d\right)}^{m} a^{3} d^{3} x e^{7} + 210 \, {\left(x e + d\right)}^{m} a^{3} d^{4} e^{6}}{m^{4} e^{4} + 22 \, m^{3} e^{4} + 179 \, m^{2} e^{4} + 638 \, m e^{4} + 840 \, e^{4}}"," ",0,"((x*e + d)^m*c^3*d^3*m^3*x^7*e^7 + 4*(x*e + d)^m*c^3*d^4*m^3*x^6*e^6 + 6*(x*e + d)^m*c^3*d^5*m^3*x^5*e^5 + 4*(x*e + d)^m*c^3*d^6*m^3*x^4*e^4 + (x*e + d)^m*c^3*d^7*m^3*x^3*e^3 + 15*(x*e + d)^m*c^3*d^3*m^2*x^7*e^7 + 57*(x*e + d)^m*c^3*d^4*m^2*x^6*e^6 + 78*(x*e + d)^m*c^3*d^5*m^2*x^5*e^5 + 42*(x*e + d)^m*c^3*d^6*m^2*x^4*e^4 + 3*(x*e + d)^m*c^3*d^7*m^2*x^3*e^3 - 3*(x*e + d)^m*c^3*d^8*m^2*x^2*e^2 + 3*(x*e + d)^m*a*c^2*d^2*m^3*x^6*e^8 + 12*(x*e + d)^m*a*c^2*d^3*m^3*x^5*e^7 + 74*(x*e + d)^m*c^3*d^3*m*x^7*e^7 + 18*(x*e + d)^m*a*c^2*d^4*m^3*x^4*e^6 + 269*(x*e + d)^m*c^3*d^4*m*x^6*e^6 + 12*(x*e + d)^m*a*c^2*d^5*m^3*x^3*e^5 + 342*(x*e + d)^m*c^3*d^5*m*x^5*e^5 + 3*(x*e + d)^m*a*c^2*d^6*m^3*x^2*e^4 + 158*(x*e + d)^m*c^3*d^6*m*x^4*e^4 + 2*(x*e + d)^m*c^3*d^7*m*x^3*e^3 - 3*(x*e + d)^m*c^3*d^8*m*x^2*e^2 + 6*(x*e + d)^m*c^3*d^9*m*x*e + 48*(x*e + d)^m*a*c^2*d^2*m^2*x^6*e^8 + 186*(x*e + d)^m*a*c^2*d^3*m^2*x^5*e^7 + 120*(x*e + d)^m*c^3*d^3*x^7*e^7 + 264*(x*e + d)^m*a*c^2*d^4*m^2*x^4*e^6 + 420*(x*e + d)^m*c^3*d^4*x^6*e^6 + 156*(x*e + d)^m*a*c^2*d^5*m^2*x^3*e^5 + 504*(x*e + d)^m*c^3*d^5*x^5*e^5 + 24*(x*e + d)^m*a*c^2*d^6*m^2*x^2*e^4 + 210*(x*e + d)^m*c^3*d^6*x^4*e^4 - 6*(x*e + d)^m*a*c^2*d^7*m^2*x*e^3 - 6*(x*e + d)^m*c^3*d^10 + 3*(x*e + d)^m*a^2*c*d*m^3*x^5*e^9 + 12*(x*e + d)^m*a^2*c*d^2*m^3*x^4*e^8 + 249*(x*e + d)^m*a*c^2*d^2*m*x^6*e^8 + 18*(x*e + d)^m*a^2*c*d^3*m^3*x^3*e^7 + 930*(x*e + d)^m*a*c^2*d^3*m*x^5*e^7 + 12*(x*e + d)^m*a^2*c*d^4*m^3*x^2*e^6 + 1236*(x*e + d)^m*a*c^2*d^4*m*x^4*e^6 + 3*(x*e + d)^m*a^2*c*d^5*m^3*x*e^5 + 624*(x*e + d)^m*a*c^2*d^5*m*x^3*e^5 + 21*(x*e + d)^m*a*c^2*d^6*m*x^2*e^4 - 42*(x*e + d)^m*a*c^2*d^7*m*x*e^3 + 6*(x*e + d)^m*a*c^2*d^8*m*e^2 + 51*(x*e + d)^m*a^2*c*d*m^2*x^5*e^9 + 201*(x*e + d)^m*a^2*c*d^2*m^2*x^4*e^8 + 420*(x*e + d)^m*a*c^2*d^2*x^6*e^8 + 294*(x*e + d)^m*a^2*c*d^3*m^2*x^3*e^7 + 1512*(x*e + d)^m*a*c^2*d^3*x^5*e^7 + 186*(x*e + d)^m*a^2*c*d^4*m^2*x^2*e^6 + 1890*(x*e + d)^m*a*c^2*d^4*x^4*e^6 + 39*(x*e + d)^m*a^2*c*d^5*m^2*x*e^5 + 840*(x*e + d)^m*a*c^2*d^5*x^3*e^5 - 3*(x*e + d)^m*a^2*c*d^6*m^2*e^4 + 42*(x*e + d)^m*a*c^2*d^8*e^2 + (x*e + d)^m*a^3*m^3*x^4*e^10 + 4*(x*e + d)^m*a^3*d*m^3*x^3*e^9 + 282*(x*e + d)^m*a^2*c*d*m*x^5*e^9 + 6*(x*e + d)^m*a^3*d^2*m^3*x^2*e^8 + 1089*(x*e + d)^m*a^2*c*d^2*m*x^4*e^8 + 4*(x*e + d)^m*a^3*d^3*m^3*x*e^7 + 1536*(x*e + d)^m*a^2*c*d^3*m*x^3*e^7 + (x*e + d)^m*a^3*d^4*m^3*e^6 + 894*(x*e + d)^m*a^2*c*d^4*m*x^2*e^6 + 126*(x*e + d)^m*a^2*c*d^5*m*x*e^5 - 39*(x*e + d)^m*a^2*c*d^6*m*e^4 + 18*(x*e + d)^m*a^3*m^2*x^4*e^10 + 72*(x*e + d)^m*a^3*d*m^2*x^3*e^9 + 504*(x*e + d)^m*a^2*c*d*x^5*e^9 + 108*(x*e + d)^m*a^3*d^2*m^2*x^2*e^8 + 1890*(x*e + d)^m*a^2*c*d^2*x^4*e^8 + 72*(x*e + d)^m*a^3*d^3*m^2*x*e^7 + 2520*(x*e + d)^m*a^2*c*d^3*x^3*e^7 + 18*(x*e + d)^m*a^3*d^4*m^2*e^6 + 1260*(x*e + d)^m*a^2*c*d^4*x^2*e^6 - 126*(x*e + d)^m*a^2*c*d^6*e^4 + 107*(x*e + d)^m*a^3*m*x^4*e^10 + 428*(x*e + d)^m*a^3*d*m*x^3*e^9 + 642*(x*e + d)^m*a^3*d^2*m*x^2*e^8 + 428*(x*e + d)^m*a^3*d^3*m*x*e^7 + 107*(x*e + d)^m*a^3*d^4*m*e^6 + 210*(x*e + d)^m*a^3*x^4*e^10 + 840*(x*e + d)^m*a^3*d*x^3*e^9 + 1260*(x*e + d)^m*a^3*d^2*x^2*e^8 + 840*(x*e + d)^m*a^3*d^3*x*e^7 + 210*(x*e + d)^m*a^3*d^4*e^6)/(m^4*e^4 + 22*m^3*e^4 + 179*m^2*e^4 + 638*m*e^4 + 840*e^4)","B",0
2085,1,804,0,0.237368," ","integrate((e*x+d)^m*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x, algorithm=""giac"")","\frac{{\left(x e + d\right)}^{m} c^{2} d^{2} m^{2} x^{5} e^{5} + 3 \, {\left(x e + d\right)}^{m} c^{2} d^{3} m^{2} x^{4} e^{4} + 3 \, {\left(x e + d\right)}^{m} c^{2} d^{4} m^{2} x^{3} e^{3} + {\left(x e + d\right)}^{m} c^{2} d^{5} m^{2} x^{2} e^{2} + 7 \, {\left(x e + d\right)}^{m} c^{2} d^{2} m x^{5} e^{5} + 19 \, {\left(x e + d\right)}^{m} c^{2} d^{3} m x^{4} e^{4} + 15 \, {\left(x e + d\right)}^{m} c^{2} d^{4} m x^{3} e^{3} + {\left(x e + d\right)}^{m} c^{2} d^{5} m x^{2} e^{2} - 2 \, {\left(x e + d\right)}^{m} c^{2} d^{6} m x e + 2 \, {\left(x e + d\right)}^{m} a c d m^{2} x^{4} e^{6} + 6 \, {\left(x e + d\right)}^{m} a c d^{2} m^{2} x^{3} e^{5} + 12 \, {\left(x e + d\right)}^{m} c^{2} d^{2} x^{5} e^{5} + 6 \, {\left(x e + d\right)}^{m} a c d^{3} m^{2} x^{2} e^{4} + 30 \, {\left(x e + d\right)}^{m} c^{2} d^{3} x^{4} e^{4} + 2 \, {\left(x e + d\right)}^{m} a c d^{4} m^{2} x e^{3} + 20 \, {\left(x e + d\right)}^{m} c^{2} d^{4} x^{3} e^{3} + 2 \, {\left(x e + d\right)}^{m} c^{2} d^{7} + 16 \, {\left(x e + d\right)}^{m} a c d m x^{4} e^{6} + 46 \, {\left(x e + d\right)}^{m} a c d^{2} m x^{3} e^{5} + 42 \, {\left(x e + d\right)}^{m} a c d^{3} m x^{2} e^{4} + 10 \, {\left(x e + d\right)}^{m} a c d^{4} m x e^{3} - 2 \, {\left(x e + d\right)}^{m} a c d^{5} m e^{2} + {\left(x e + d\right)}^{m} a^{2} m^{2} x^{3} e^{7} + 3 \, {\left(x e + d\right)}^{m} a^{2} d m^{2} x^{2} e^{6} + 30 \, {\left(x e + d\right)}^{m} a c d x^{4} e^{6} + 3 \, {\left(x e + d\right)}^{m} a^{2} d^{2} m^{2} x e^{5} + 80 \, {\left(x e + d\right)}^{m} a c d^{2} x^{3} e^{5} + {\left(x e + d\right)}^{m} a^{2} d^{3} m^{2} e^{4} + 60 \, {\left(x e + d\right)}^{m} a c d^{3} x^{2} e^{4} - 10 \, {\left(x e + d\right)}^{m} a c d^{5} e^{2} + 9 \, {\left(x e + d\right)}^{m} a^{2} m x^{3} e^{7} + 27 \, {\left(x e + d\right)}^{m} a^{2} d m x^{2} e^{6} + 27 \, {\left(x e + d\right)}^{m} a^{2} d^{2} m x e^{5} + 9 \, {\left(x e + d\right)}^{m} a^{2} d^{3} m e^{4} + 20 \, {\left(x e + d\right)}^{m} a^{2} x^{3} e^{7} + 60 \, {\left(x e + d\right)}^{m} a^{2} d x^{2} e^{6} + 60 \, {\left(x e + d\right)}^{m} a^{2} d^{2} x e^{5} + 20 \, {\left(x e + d\right)}^{m} a^{2} d^{3} e^{4}}{m^{3} e^{3} + 12 \, m^{2} e^{3} + 47 \, m e^{3} + 60 \, e^{3}}"," ",0,"((x*e + d)^m*c^2*d^2*m^2*x^5*e^5 + 3*(x*e + d)^m*c^2*d^3*m^2*x^4*e^4 + 3*(x*e + d)^m*c^2*d^4*m^2*x^3*e^3 + (x*e + d)^m*c^2*d^5*m^2*x^2*e^2 + 7*(x*e + d)^m*c^2*d^2*m*x^5*e^5 + 19*(x*e + d)^m*c^2*d^3*m*x^4*e^4 + 15*(x*e + d)^m*c^2*d^4*m*x^3*e^3 + (x*e + d)^m*c^2*d^5*m*x^2*e^2 - 2*(x*e + d)^m*c^2*d^6*m*x*e + 2*(x*e + d)^m*a*c*d*m^2*x^4*e^6 + 6*(x*e + d)^m*a*c*d^2*m^2*x^3*e^5 + 12*(x*e + d)^m*c^2*d^2*x^5*e^5 + 6*(x*e + d)^m*a*c*d^3*m^2*x^2*e^4 + 30*(x*e + d)^m*c^2*d^3*x^4*e^4 + 2*(x*e + d)^m*a*c*d^4*m^2*x*e^3 + 20*(x*e + d)^m*c^2*d^4*x^3*e^3 + 2*(x*e + d)^m*c^2*d^7 + 16*(x*e + d)^m*a*c*d*m*x^4*e^6 + 46*(x*e + d)^m*a*c*d^2*m*x^3*e^5 + 42*(x*e + d)^m*a*c*d^3*m*x^2*e^4 + 10*(x*e + d)^m*a*c*d^4*m*x*e^3 - 2*(x*e + d)^m*a*c*d^5*m*e^2 + (x*e + d)^m*a^2*m^2*x^3*e^7 + 3*(x*e + d)^m*a^2*d*m^2*x^2*e^6 + 30*(x*e + d)^m*a*c*d*x^4*e^6 + 3*(x*e + d)^m*a^2*d^2*m^2*x*e^5 + 80*(x*e + d)^m*a*c*d^2*x^3*e^5 + (x*e + d)^m*a^2*d^3*m^2*e^4 + 60*(x*e + d)^m*a*c*d^3*x^2*e^4 - 10*(x*e + d)^m*a*c*d^5*e^2 + 9*(x*e + d)^m*a^2*m*x^3*e^7 + 27*(x*e + d)^m*a^2*d*m*x^2*e^6 + 27*(x*e + d)^m*a^2*d^2*m*x*e^5 + 9*(x*e + d)^m*a^2*d^3*m*e^4 + 20*(x*e + d)^m*a^2*x^3*e^7 + 60*(x*e + d)^m*a^2*d*x^2*e^6 + 60*(x*e + d)^m*a^2*d^2*x*e^5 + 20*(x*e + d)^m*a^2*d^3*e^4)/(m^3*e^3 + 12*m^2*e^3 + 47*m*e^3 + 60*e^3)","B",0
2086,1,219,0,0.177421," ","integrate((e*x+d)^m*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x, algorithm=""giac"")","\frac{{\left(x e + d\right)}^{m} c d m x^{3} e^{3} + 2 \, {\left(x e + d\right)}^{m} c d^{2} m x^{2} e^{2} + {\left(x e + d\right)}^{m} c d^{3} m x e + 2 \, {\left(x e + d\right)}^{m} c d x^{3} e^{3} + 3 \, {\left(x e + d\right)}^{m} c d^{2} x^{2} e^{2} - {\left(x e + d\right)}^{m} c d^{4} + {\left(x e + d\right)}^{m} a m x^{2} e^{4} + 2 \, {\left(x e + d\right)}^{m} a d m x e^{3} + {\left(x e + d\right)}^{m} a d^{2} m e^{2} + 3 \, {\left(x e + d\right)}^{m} a x^{2} e^{4} + 6 \, {\left(x e + d\right)}^{m} a d x e^{3} + 3 \, {\left(x e + d\right)}^{m} a d^{2} e^{2}}{m^{2} e^{2} + 5 \, m e^{2} + 6 \, e^{2}}"," ",0,"((x*e + d)^m*c*d*m*x^3*e^3 + 2*(x*e + d)^m*c*d^2*m*x^2*e^2 + (x*e + d)^m*c*d^3*m*x*e + 2*(x*e + d)^m*c*d*x^3*e^3 + 3*(x*e + d)^m*c*d^2*x^2*e^2 - (x*e + d)^m*c*d^4 + (x*e + d)^m*a*m*x^2*e^4 + 2*(x*e + d)^m*a*d*m*x*e^3 + (x*e + d)^m*a*d^2*m*e^2 + 3*(x*e + d)^m*a*x^2*e^4 + 6*(x*e + d)^m*a*d*x*e^3 + 3*(x*e + d)^m*a*d^2*e^2)/(m^2*e^2 + 5*m*e^2 + 6*e^2)","B",0
2087,0,0,0,0.000000," ","integrate((e*x+d)^m/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{m}}{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}\,{d x}"," ",0,"integrate((e*x + d)^m/(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x), x)","F",0
2088,0,0,0,0.000000," ","integrate((e*x+d)^m/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{m}}{{\left(c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)}^{2}}\,{d x}"," ",0,"integrate((e*x + d)^m/(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)^2, x)","F",0
2089,0,0,0,0.000000," ","integrate((e*x+d)^m/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{m}}{{\left(c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)}^{3}}\,{d x}"," ",0,"integrate((e*x + d)^m/(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)^3, x)","F",0
2090,0,0,0,0.000000," ","integrate((e*x+d)^m/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^4,x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{m}}{{\left(c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)}^{4}}\,{d x}"," ",0,"integrate((e*x + d)^m/(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)^4, x)","F",0
2091,0,0,0,0.000000," ","integrate((e*x+d)^m*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^p,x, algorithm=""giac"")","\int {\left(c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)}^{p} {\left(e x + d\right)}^{m}\,{d x}"," ",0,"integrate((c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)^p*(e*x + d)^m, x)","F",0
2092,0,0,0,0.000000," ","integrate((e*x+d)^3*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^p,x, algorithm=""giac"")","\int {\left(e x + d\right)}^{3} {\left(c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)}^{p}\,{d x}"," ",0,"integrate((e*x + d)^3*(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)^p, x)","F",0
2093,0,0,0,0.000000," ","integrate((e*x+d)^2*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^p,x, algorithm=""giac"")","\int {\left(e x + d\right)}^{2} {\left(c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)}^{p}\,{d x}"," ",0,"integrate((e*x + d)^2*(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)^p, x)","F",0
2094,0,0,0,0.000000," ","integrate((e*x+d)*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^p,x, algorithm=""giac"")","\int {\left(e x + d\right)} {\left(c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)}^{p}\,{d x}"," ",0,"integrate((e*x + d)*(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)^p, x)","F",0
2095,0,0,0,0.000000," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^p,x, algorithm=""giac"")","\int {\left(c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)}^{p}\,{d x}"," ",0,"integrate((c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)^p, x)","F",0
2096,0,0,0,0.000000," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^p/(e*x+d),x, algorithm=""giac"")","\int \frac{{\left(c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)}^{p}}{e x + d}\,{d x}"," ",0,"integrate((c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)^p/(e*x + d), x)","F",0
2097,0,0,0,0.000000," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^p/(e*x+d)^2,x, algorithm=""giac"")","\int \frac{{\left(c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)}^{p}}{{\left(e x + d\right)}^{2}}\,{d x}"," ",0,"integrate((c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)^p/(e*x + d)^2, x)","F",0
2098,0,0,0,0.000000," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^p/(e*x+d)^3,x, algorithm=""giac"")","\int \frac{{\left(c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)}^{p}}{{\left(e x + d\right)}^{3}}\,{d x}"," ",0,"integrate((c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)^p/(e*x + d)^3, x)","F",0
2099,0,0,0,0.000000," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^p/((e*x+d)^(2*p)),x, algorithm=""giac"")","\int \frac{{\left(c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)}^{p}}{{\left(e x + d\right)}^{2 \, p}}\,{d x}"," ",0,"integrate((c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)^p/(e*x + d)^(2*p), x)","F",0
2100,0,0,0,0.000000," ","integrate((e*x+d)^(-1-2*p)*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^p,x, algorithm=""giac"")","\int {\left(c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)}^{p} {\left(e x + d\right)}^{-2 \, p - 1}\,{d x}"," ",0,"integrate((c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)^p*(e*x + d)^(-2*p - 1), x)","F",0
2101,0,0,0,0.000000," ","integrate((e*x+d)^(-2-2*p)*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^p,x, algorithm=""giac"")","\int {\left(c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)}^{p} {\left(e x + d\right)}^{-2 \, p - 2}\,{d x}"," ",0,"integrate((c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)^p*(e*x + d)^(-2*p - 2), x)","F",0
2102,0,0,0,0.000000," ","integrate((e*x+d)^(-3-2*p)*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^p,x, algorithm=""giac"")","\int {\left(c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)}^{p} {\left(e x + d\right)}^{-2 \, p - 3}\,{d x}"," ",0,"integrate((c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)^p*(e*x + d)^(-2*p - 3), x)","F",0
2103,0,0,0,0.000000," ","integrate((e*x+d)^(-4-2*p)*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^p,x, algorithm=""giac"")","\int {\left(c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)}^{p} {\left(e x + d\right)}^{-2 \, p - 4}\,{d x}"," ",0,"integrate((c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)^p*(e*x + d)^(-2*p - 4), x)","F",0
2104,0,0,0,0.000000," ","integrate((e*x+d)^(-5-2*p)*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^p,x, algorithm=""giac"")","\int {\left(c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)}^{p} {\left(e x + d\right)}^{-2 \, p - 5}\,{d x}"," ",0,"integrate((c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)^p*(e*x + d)^(-2*p - 5), x)","F",0
2105,1,87,0,0.256517," ","integrate((e*x+d)^m/((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^m),x, algorithm=""giac"")","-\frac{{\left(x e + d\right)}^{m} c d x e^{\left(-m \log\left(c d x + a e\right) - m \log\left(x e + d\right)\right)} + {\left(x e + d\right)}^{m} a e^{\left(-m \log\left(c d x + a e\right) - m \log\left(x e + d\right) + 1\right)}}{c d m - c d}"," ",0,"-((x*e + d)^m*c*d*x*e^(-m*log(c*d*x + a*e) - m*log(x*e + d)) + (x*e + d)^m*a*e^(-m*log(c*d*x + a*e) - m*log(x*e + d) + 1))/(c*d*m - c*d)","A",0
2106,1,85,0,0.229523," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^p/((e*x+d)^p),x, algorithm=""giac"")","\frac{\frac{c d x e^{\left(p \log\left(c d x + a e\right) + p \log\left(x e + d\right)\right)}}{{\left(x e + d\right)}^{p}} + \frac{a e^{\left(p \log\left(c d x + a e\right) + p \log\left(x e + d\right) + 1\right)}}{{\left(x e + d\right)}^{p}}}{c d p + c d}"," ",0,"(c*d*x*e^(p*log(c*d*x + a*e) + p*log(x*e + d))/(x*e + d)^p + a*e^(p*log(c*d*x + a*e) + p*log(x*e + d) + 1)/(x*e + d)^p)/(c*d*p + c*d)","A",0
2107,1,140,0,0.149395," ","integrate((e*x+d)^4*(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{1}{7} \, c x^{7} e^{4} + \frac{2}{3} \, c d x^{6} e^{3} + \frac{6}{5} \, c d^{2} x^{5} e^{2} + c d^{3} x^{4} e + \frac{1}{3} \, c d^{4} x^{3} + \frac{1}{6} \, b x^{6} e^{4} + \frac{4}{5} \, b d x^{5} e^{3} + \frac{3}{2} \, b d^{2} x^{4} e^{2} + \frac{4}{3} \, b d^{3} x^{3} e + \frac{1}{2} \, b d^{4} x^{2} + \frac{1}{5} \, a x^{5} e^{4} + a d x^{4} e^{3} + 2 \, a d^{2} x^{3} e^{2} + 2 \, a d^{3} x^{2} e + a d^{4} x"," ",0,"1/7*c*x^7*e^4 + 2/3*c*d*x^6*e^3 + 6/5*c*d^2*x^5*e^2 + c*d^3*x^4*e + 1/3*c*d^4*x^3 + 1/6*b*x^6*e^4 + 4/5*b*d*x^5*e^3 + 3/2*b*d^2*x^4*e^2 + 4/3*b*d^3*x^3*e + 1/2*b*d^4*x^2 + 1/5*a*x^5*e^4 + a*d*x^4*e^3 + 2*a*d^2*x^3*e^2 + 2*a*d^3*x^2*e + a*d^4*x","B",0
2108,1,107,0,0.152879," ","integrate((e*x+d)^3*(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{1}{6} \, c x^{6} e^{3} + \frac{3}{5} \, c d x^{5} e^{2} + \frac{3}{4} \, c d^{2} x^{4} e + \frac{1}{3} \, c d^{3} x^{3} + \frac{1}{5} \, b x^{5} e^{3} + \frac{3}{4} \, b d x^{4} e^{2} + b d^{2} x^{3} e + \frac{1}{2} \, b d^{3} x^{2} + \frac{1}{4} \, a x^{4} e^{3} + a d x^{3} e^{2} + \frac{3}{2} \, a d^{2} x^{2} e + a d^{3} x"," ",0,"1/6*c*x^6*e^3 + 3/5*c*d*x^5*e^2 + 3/4*c*d^2*x^4*e + 1/3*c*d^3*x^3 + 1/5*b*x^5*e^3 + 3/4*b*d*x^4*e^2 + b*d^2*x^3*e + 1/2*b*d^3*x^2 + 1/4*a*x^4*e^3 + a*d*x^3*e^2 + 3/2*a*d^2*x^2*e + a*d^3*x","A",0
2109,1,75,0,0.148689," ","integrate((e*x+d)^2*(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{1}{5} \, c x^{5} e^{2} + \frac{1}{2} \, c d x^{4} e + \frac{1}{3} \, c d^{2} x^{3} + \frac{1}{4} \, b x^{4} e^{2} + \frac{2}{3} \, b d x^{3} e + \frac{1}{2} \, b d^{2} x^{2} + \frac{1}{3} \, a x^{3} e^{2} + a d x^{2} e + a d^{2} x"," ",0,"1/5*c*x^5*e^2 + 1/2*c*d*x^4*e + 1/3*c*d^2*x^3 + 1/4*b*x^4*e^2 + 2/3*b*d*x^3*e + 1/2*b*d^2*x^2 + 1/3*a*x^3*e^2 + a*d*x^2*e + a*d^2*x","A",0
2110,1,43,0,0.148705," ","integrate((e*x+d)*(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{1}{4} \, c x^{4} e + \frac{1}{3} \, c d x^{3} + \frac{1}{3} \, b x^{3} e + \frac{1}{2} \, b d x^{2} + \frac{1}{2} \, a x^{2} e + a d x"," ",0,"1/4*c*x^4*e + 1/3*c*d*x^3 + 1/3*b*x^3*e + 1/2*b*d*x^2 + 1/2*a*x^2*e + a*d*x","A",0
2111,1,16,0,0.148798," ","integrate(c*x^2+b*x+a,x, algorithm=""giac"")","\frac{1}{3} \, c x^{3} + \frac{1}{2} \, b x^{2} + a x"," ",0,"1/3*c*x^3 + 1/2*b*x^2 + a*x","A",0
2112,1,51,0,0.163432," ","integrate((c*x^2+b*x+a)/(e*x+d),x, algorithm=""giac"")","{\left(c d^{2} - b d e + a e^{2}\right)} e^{\left(-3\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{2} \, {\left(c x^{2} e - 2 \, c d x + 2 \, b x e\right)} e^{\left(-2\right)}"," ",0,"(c*d^2 - b*d*e + a*e^2)*e^(-3)*log(abs(x*e + d)) + 1/2*(c*x^2*e - 2*c*d*x + 2*b*x*e)*e^(-2)","A",0
2113,1,106,0,0.157650," ","integrate((c*x^2+b*x+a)/(e*x+d)^2,x, algorithm=""giac"")","-{\left(e^{\left(-1\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) - \frac{d e^{\left(-1\right)}}{x e + d}\right)} b e^{\left(-1\right)} + {\left(2 \, d e^{\left(-3\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) + {\left(x e + d\right)} e^{\left(-3\right)} - \frac{d^{2} e^{\left(-3\right)}}{x e + d}\right)} c - \frac{a e^{\left(-1\right)}}{x e + d}"," ",0,"-(e^(-1)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) - d*e^(-1)/(x*e + d))*b*e^(-1) + (2*d*e^(-3)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) + (x*e + d)*e^(-3) - d^2*e^(-3)/(x*e + d))*c - a*e^(-1)/(x*e + d)","A",0
2114,1,60,0,0.151146," ","integrate((c*x^2+b*x+a)/(e*x+d)^3,x, algorithm=""giac"")","c e^{\left(-3\right)} \log\left({\left| x e + d \right|}\right) + \frac{{\left(2 \, {\left(2 \, c d - b e\right)} x + {\left(3 \, c d^{2} - b d e - a e^{2}\right)} e^{\left(-1\right)}\right)} e^{\left(-2\right)}}{2 \, {\left(x e + d\right)}^{2}}"," ",0,"c*e^(-3)*log(abs(x*e + d)) + 1/2*(2*(2*c*d - b*e)*x + (3*c*d^2 - b*d*e - a*e^2)*e^(-1))*e^(-2)/(x*e + d)^2","A",0
2115,1,50,0,0.154745," ","integrate((c*x^2+b*x+a)/(e*x+d)^4,x, algorithm=""giac"")","-\frac{{\left(6 \, c x^{2} e^{2} + 6 \, c d x e + 2 \, c d^{2} + 3 \, b x e^{2} + b d e + 2 \, a e^{2}\right)} e^{\left(-3\right)}}{6 \, {\left(x e + d\right)}^{3}}"," ",0,"-1/6*(6*c*x^2*e^2 + 6*c*d*x*e + 2*c*d^2 + 3*b*x*e^2 + b*d*e + 2*a*e^2)*e^(-3)/(x*e + d)^3","A",0
2116,1,86,0,0.160903," ","integrate((c*x^2+b*x+a)/(e*x+d)^5,x, algorithm=""giac"")","-\frac{1}{12} \, {\left(\frac{6 \, c e^{\left(-2\right)}}{{\left(x e + d\right)}^{2}} - \frac{8 \, c d e^{\left(-2\right)}}{{\left(x e + d\right)}^{3}} + \frac{3 \, c d^{2} e^{\left(-2\right)}}{{\left(x e + d\right)}^{4}} + \frac{4 \, b e^{\left(-1\right)}}{{\left(x e + d\right)}^{3}} - \frac{3 \, b d e^{\left(-1\right)}}{{\left(x e + d\right)}^{4}} + \frac{3 \, a}{{\left(x e + d\right)}^{4}}\right)} e^{\left(-1\right)}"," ",0,"-1/12*(6*c*e^(-2)/(x*e + d)^2 - 8*c*d*e^(-2)/(x*e + d)^3 + 3*c*d^2*e^(-2)/(x*e + d)^4 + 4*b*e^(-1)/(x*e + d)^3 - 3*b*d*e^(-1)/(x*e + d)^4 + 3*a/(x*e + d)^4)*e^(-1)","A",0
2117,1,51,0,0.150259," ","integrate((c*x^2+b*x+a)/(e*x+d)^6,x, algorithm=""giac"")","-\frac{{\left(20 \, c x^{2} e^{2} + 10 \, c d x e + 2 \, c d^{2} + 15 \, b x e^{2} + 3 \, b d e + 12 \, a e^{2}\right)} e^{\left(-3\right)}}{60 \, {\left(x e + d\right)}^{5}}"," ",0,"-1/60*(20*c*x^2*e^2 + 10*c*d*x*e + 2*c*d^2 + 15*b*x*e^2 + 3*b*d*e + 12*a*e^2)*e^(-3)/(x*e + d)^5","A",0
2118,1,328,0,0.158910," ","integrate((e*x+d)^4*(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{1}{9} \, c^{2} x^{9} e^{4} + \frac{1}{2} \, c^{2} d x^{8} e^{3} + \frac{6}{7} \, c^{2} d^{2} x^{7} e^{2} + \frac{2}{3} \, c^{2} d^{3} x^{6} e + \frac{1}{5} \, c^{2} d^{4} x^{5} + \frac{1}{4} \, b c x^{8} e^{4} + \frac{8}{7} \, b c d x^{7} e^{3} + 2 \, b c d^{2} x^{6} e^{2} + \frac{8}{5} \, b c d^{3} x^{5} e + \frac{1}{2} \, b c d^{4} x^{4} + \frac{1}{7} \, b^{2} x^{7} e^{4} + \frac{2}{7} \, a c x^{7} e^{4} + \frac{2}{3} \, b^{2} d x^{6} e^{3} + \frac{4}{3} \, a c d x^{6} e^{3} + \frac{6}{5} \, b^{2} d^{2} x^{5} e^{2} + \frac{12}{5} \, a c d^{2} x^{5} e^{2} + b^{2} d^{3} x^{4} e + 2 \, a c d^{3} x^{4} e + \frac{1}{3} \, b^{2} d^{4} x^{3} + \frac{2}{3} \, a c d^{4} x^{3} + \frac{1}{3} \, a b x^{6} e^{4} + \frac{8}{5} \, a b d x^{5} e^{3} + 3 \, a b d^{2} x^{4} e^{2} + \frac{8}{3} \, a b d^{3} x^{3} e + a b d^{4} x^{2} + \frac{1}{5} \, a^{2} x^{5} e^{4} + a^{2} d x^{4} e^{3} + 2 \, a^{2} d^{2} x^{3} e^{2} + 2 \, a^{2} d^{3} x^{2} e + a^{2} d^{4} x"," ",0,"1/9*c^2*x^9*e^4 + 1/2*c^2*d*x^8*e^3 + 6/7*c^2*d^2*x^7*e^2 + 2/3*c^2*d^3*x^6*e + 1/5*c^2*d^4*x^5 + 1/4*b*c*x^8*e^4 + 8/7*b*c*d*x^7*e^3 + 2*b*c*d^2*x^6*e^2 + 8/5*b*c*d^3*x^5*e + 1/2*b*c*d^4*x^4 + 1/7*b^2*x^7*e^4 + 2/7*a*c*x^7*e^4 + 2/3*b^2*d*x^6*e^3 + 4/3*a*c*d*x^6*e^3 + 6/5*b^2*d^2*x^5*e^2 + 12/5*a*c*d^2*x^5*e^2 + b^2*d^3*x^4*e + 2*a*c*d^3*x^4*e + 1/3*b^2*d^4*x^3 + 2/3*a*c*d^4*x^3 + 1/3*a*b*x^6*e^4 + 8/5*a*b*d*x^5*e^3 + 3*a*b*d^2*x^4*e^2 + 8/3*a*b*d^3*x^3*e + a*b*d^4*x^2 + 1/5*a^2*x^5*e^4 + a^2*d*x^4*e^3 + 2*a^2*d^2*x^3*e^2 + 2*a^2*d^3*x^2*e + a^2*d^4*x","B",0
2119,1,253,0,0.170971," ","integrate((e*x+d)^3*(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{1}{8} \, c^{2} x^{8} e^{3} + \frac{3}{7} \, c^{2} d x^{7} e^{2} + \frac{1}{2} \, c^{2} d^{2} x^{6} e + \frac{1}{5} \, c^{2} d^{3} x^{5} + \frac{2}{7} \, b c x^{7} e^{3} + b c d x^{6} e^{2} + \frac{6}{5} \, b c d^{2} x^{5} e + \frac{1}{2} \, b c d^{3} x^{4} + \frac{1}{6} \, b^{2} x^{6} e^{3} + \frac{1}{3} \, a c x^{6} e^{3} + \frac{3}{5} \, b^{2} d x^{5} e^{2} + \frac{6}{5} \, a c d x^{5} e^{2} + \frac{3}{4} \, b^{2} d^{2} x^{4} e + \frac{3}{2} \, a c d^{2} x^{4} e + \frac{1}{3} \, b^{2} d^{3} x^{3} + \frac{2}{3} \, a c d^{3} x^{3} + \frac{2}{5} \, a b x^{5} e^{3} + \frac{3}{2} \, a b d x^{4} e^{2} + 2 \, a b d^{2} x^{3} e + a b d^{3} x^{2} + \frac{1}{4} \, a^{2} x^{4} e^{3} + a^{2} d x^{3} e^{2} + \frac{3}{2} \, a^{2} d^{2} x^{2} e + a^{2} d^{3} x"," ",0,"1/8*c^2*x^8*e^3 + 3/7*c^2*d*x^7*e^2 + 1/2*c^2*d^2*x^6*e + 1/5*c^2*d^3*x^5 + 2/7*b*c*x^7*e^3 + b*c*d*x^6*e^2 + 6/5*b*c*d^2*x^5*e + 1/2*b*c*d^3*x^4 + 1/6*b^2*x^6*e^3 + 1/3*a*c*x^6*e^3 + 3/5*b^2*d*x^5*e^2 + 6/5*a*c*d*x^5*e^2 + 3/4*b^2*d^2*x^4*e + 3/2*a*c*d^2*x^4*e + 1/3*b^2*d^3*x^3 + 2/3*a*c*d^3*x^3 + 2/5*a*b*x^5*e^3 + 3/2*a*b*d*x^4*e^2 + 2*a*b*d^2*x^3*e + a*b*d^3*x^2 + 1/4*a^2*x^4*e^3 + a^2*d*x^3*e^2 + 3/2*a^2*d^2*x^2*e + a^2*d^3*x","A",0
2120,1,178,0,0.153953," ","integrate((e*x+d)^2*(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{1}{7} \, c^{2} x^{7} e^{2} + \frac{1}{3} \, c^{2} d x^{6} e + \frac{1}{5} \, c^{2} d^{2} x^{5} + \frac{1}{3} \, b c x^{6} e^{2} + \frac{4}{5} \, b c d x^{5} e + \frac{1}{2} \, b c d^{2} x^{4} + \frac{1}{5} \, b^{2} x^{5} e^{2} + \frac{2}{5} \, a c x^{5} e^{2} + \frac{1}{2} \, b^{2} d x^{4} e + a c d x^{4} e + \frac{1}{3} \, b^{2} d^{2} x^{3} + \frac{2}{3} \, a c d^{2} x^{3} + \frac{1}{2} \, a b x^{4} e^{2} + \frac{4}{3} \, a b d x^{3} e + a b d^{2} x^{2} + \frac{1}{3} \, a^{2} x^{3} e^{2} + a^{2} d x^{2} e + a^{2} d^{2} x"," ",0,"1/7*c^2*x^7*e^2 + 1/3*c^2*d*x^6*e + 1/5*c^2*d^2*x^5 + 1/3*b*c*x^6*e^2 + 4/5*b*c*d*x^5*e + 1/2*b*c*d^2*x^4 + 1/5*b^2*x^5*e^2 + 2/5*a*c*x^5*e^2 + 1/2*b^2*d*x^4*e + a*c*d*x^4*e + 1/3*b^2*d^2*x^3 + 2/3*a*c*d^2*x^3 + 1/2*a*b*x^4*e^2 + 4/3*a*b*d*x^3*e + a*b*d^2*x^2 + 1/3*a^2*x^3*e^2 + a^2*d*x^2*e + a^2*d^2*x","A",0
2121,1,105,0,0.151610," ","integrate((e*x+d)*(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{1}{6} \, c^{2} x^{6} e + \frac{1}{5} \, c^{2} d x^{5} + \frac{2}{5} \, b c x^{5} e + \frac{1}{2} \, b c d x^{4} + \frac{1}{4} \, b^{2} x^{4} e + \frac{1}{2} \, a c x^{4} e + \frac{1}{3} \, b^{2} d x^{3} + \frac{2}{3} \, a c d x^{3} + \frac{2}{3} \, a b x^{3} e + a b d x^{2} + \frac{1}{2} \, a^{2} x^{2} e + a^{2} d x"," ",0,"1/6*c^2*x^6*e + 1/5*c^2*d*x^5 + 2/5*b*c*x^5*e + 1/2*b*c*d*x^4 + 1/4*b^2*x^4*e + 1/2*a*c*x^4*e + 1/3*b^2*d*x^3 + 2/3*a*c*d*x^3 + 2/3*a*b*x^3*e + a*b*d*x^2 + 1/2*a^2*x^2*e + a^2*d*x","A",0
2122,1,42,0,0.155059," ","integrate((c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{1}{5} \, c^{2} x^{5} + \frac{1}{2} \, b c x^{4} + \frac{1}{3} \, b^{2} x^{3} + \frac{2}{3} \, a c x^{3} + a b x^{2} + a^{2} x"," ",0,"1/5*c^2*x^5 + 1/2*b*c*x^4 + 1/3*b^2*x^3 + 2/3*a*c*x^3 + a*b*x^2 + a^2*x","A",0
2123,1,180,0,0.151706," ","integrate((c*x^2+b*x+a)^2/(e*x+d),x, algorithm=""giac"")","{\left(c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2} + 2 \, a c d^{2} e^{2} - 2 \, a b d e^{3} + a^{2} e^{4}\right)} e^{\left(-5\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{12} \, {\left(3 \, c^{2} x^{4} e^{3} - 4 \, c^{2} d x^{3} e^{2} + 6 \, c^{2} d^{2} x^{2} e - 12 \, c^{2} d^{3} x + 8 \, b c x^{3} e^{3} - 12 \, b c d x^{2} e^{2} + 24 \, b c d^{2} x e + 6 \, b^{2} x^{2} e^{3} + 12 \, a c x^{2} e^{3} - 12 \, b^{2} d x e^{2} - 24 \, a c d x e^{2} + 24 \, a b x e^{3}\right)} e^{\left(-4\right)}"," ",0,"(c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2 + 2*a*c*d^2*e^2 - 2*a*b*d*e^3 + a^2*e^4)*e^(-5)*log(abs(x*e + d)) + 1/12*(3*c^2*x^4*e^3 - 4*c^2*d*x^3*e^2 + 6*c^2*d^2*x^2*e - 12*c^2*d^3*x + 8*b*c*x^3*e^3 - 12*b*c*d*x^2*e^2 + 24*b*c*d^2*x*e + 6*b^2*x^2*e^3 + 12*a*c*x^2*e^3 - 12*b^2*d*x*e^2 - 24*a*c*d*x*e^2 + 24*a*b*x*e^3)*e^(-4)","A",0
2124,1,249,0,0.244166," ","integrate((c*x^2+b*x+a)^2/(e*x+d)^2,x, algorithm=""giac"")","\frac{1}{3} \, {\left(c^{2} - \frac{3 \, {\left(2 \, c^{2} d e - b c e^{2}\right)} e^{\left(-1\right)}}{x e + d} + \frac{3 \, {\left(6 \, c^{2} d^{2} e^{2} - 6 \, b c d e^{3} + b^{2} e^{4} + 2 \, a c e^{4}\right)} e^{\left(-2\right)}}{{\left(x e + d\right)}^{2}}\right)} {\left(x e + d\right)}^{3} e^{\left(-5\right)} + 2 \, {\left(2 \, c^{2} d^{3} - 3 \, b c d^{2} e + b^{2} d e^{2} + 2 \, a c d e^{2} - a b e^{3}\right)} e^{\left(-5\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) - {\left(\frac{c^{2} d^{4} e^{3}}{x e + d} - \frac{2 \, b c d^{3} e^{4}}{x e + d} + \frac{b^{2} d^{2} e^{5}}{x e + d} + \frac{2 \, a c d^{2} e^{5}}{x e + d} - \frac{2 \, a b d e^{6}}{x e + d} + \frac{a^{2} e^{7}}{x e + d}\right)} e^{\left(-8\right)}"," ",0,"1/3*(c^2 - 3*(2*c^2*d*e - b*c*e^2)*e^(-1)/(x*e + d) + 3*(6*c^2*d^2*e^2 - 6*b*c*d*e^3 + b^2*e^4 + 2*a*c*e^4)*e^(-2)/(x*e + d)^2)*(x*e + d)^3*e^(-5) + 2*(2*c^2*d^3 - 3*b*c*d^2*e + b^2*d*e^2 + 2*a*c*d*e^2 - a*b*e^3)*e^(-5)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) - (c^2*d^4*e^3/(x*e + d) - 2*b*c*d^3*e^4/(x*e + d) + b^2*d^2*e^5/(x*e + d) + 2*a*c*d^2*e^5/(x*e + d) - 2*a*b*d*e^6/(x*e + d) + a^2*e^7/(x*e + d))*e^(-8)","A",0
2125,1,176,0,0.165092," ","integrate((c*x^2+b*x+a)^2/(e*x+d)^3,x, algorithm=""giac"")","{\left(6 \, c^{2} d^{2} - 6 \, b c d e + b^{2} e^{2} + 2 \, a c e^{2}\right)} e^{\left(-5\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{2} \, {\left(c^{2} x^{2} e^{3} - 6 \, c^{2} d x e^{2} + 4 \, b c x e^{3}\right)} e^{\left(-6\right)} + \frac{{\left(7 \, c^{2} d^{4} - 10 \, b c d^{3} e + 3 \, b^{2} d^{2} e^{2} + 6 \, a c d^{2} e^{2} - 2 \, a b d e^{3} - a^{2} e^{4} + 4 \, {\left(2 \, c^{2} d^{3} e - 3 \, b c d^{2} e^{2} + b^{2} d e^{3} + 2 \, a c d e^{3} - a b e^{4}\right)} x\right)} e^{\left(-5\right)}}{2 \, {\left(x e + d\right)}^{2}}"," ",0,"(6*c^2*d^2 - 6*b*c*d*e + b^2*e^2 + 2*a*c*e^2)*e^(-5)*log(abs(x*e + d)) + 1/2*(c^2*x^2*e^3 - 6*c^2*d*x*e^2 + 4*b*c*x*e^3)*e^(-6) + 1/2*(7*c^2*d^4 - 10*b*c*d^3*e + 3*b^2*d^2*e^2 + 6*a*c*d^2*e^2 - 2*a*b*d*e^3 - a^2*e^4 + 4*(2*c^2*d^3*e - 3*b*c*d^2*e^2 + b^2*d*e^3 + 2*a*c*d*e^3 - a*b*e^4)*x)*e^(-5)/(x*e + d)^2","A",0
2126,1,170,0,0.152254," ","integrate((c*x^2+b*x+a)^2/(e*x+d)^4,x, algorithm=""giac"")","c^{2} x e^{\left(-4\right)} - 2 \, {\left(2 \, c^{2} d - b c e\right)} e^{\left(-5\right)} \log\left({\left| x e + d \right|}\right) - \frac{{\left(13 \, c^{2} d^{4} - 11 \, b c d^{3} e + b^{2} d^{2} e^{2} + 2 \, a c d^{2} e^{2} + a b d e^{3} + 3 \, {\left(6 \, c^{2} d^{2} e^{2} - 6 \, b c d e^{3} + b^{2} e^{4} + 2 \, a c e^{4}\right)} x^{2} + a^{2} e^{4} + 3 \, {\left(10 \, c^{2} d^{3} e - 9 \, b c d^{2} e^{2} + b^{2} d e^{3} + 2 \, a c d e^{3} + a b e^{4}\right)} x\right)} e^{\left(-5\right)}}{3 \, {\left(x e + d\right)}^{3}}"," ",0,"c^2*x*e^(-4) - 2*(2*c^2*d - b*c*e)*e^(-5)*log(abs(x*e + d)) - 1/3*(13*c^2*d^4 - 11*b*c*d^3*e + b^2*d^2*e^2 + 2*a*c*d^2*e^2 + a*b*d*e^3 + 3*(6*c^2*d^2*e^2 - 6*b*c*d*e^3 + b^2*e^4 + 2*a*c*e^4)*x^2 + a^2*e^4 + 3*(10*c^2*d^3*e - 9*b*c*d^2*e^2 + b^2*d*e^3 + 2*a*c*d*e^3 + a*b*e^4)*x)*e^(-5)/(x*e + d)^3","A",0
2127,1,304,0,0.182051," ","integrate((c*x^2+b*x+a)^2/(e*x+d)^5,x, algorithm=""giac"")","-c^{2} e^{\left(-5\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) + \frac{1}{12} \, {\left(\frac{48 \, c^{2} d e^{15}}{x e + d} - \frac{36 \, c^{2} d^{2} e^{15}}{{\left(x e + d\right)}^{2}} + \frac{16 \, c^{2} d^{3} e^{15}}{{\left(x e + d\right)}^{3}} - \frac{3 \, c^{2} d^{4} e^{15}}{{\left(x e + d\right)}^{4}} - \frac{24 \, b c e^{16}}{x e + d} + \frac{36 \, b c d e^{16}}{{\left(x e + d\right)}^{2}} - \frac{24 \, b c d^{2} e^{16}}{{\left(x e + d\right)}^{3}} + \frac{6 \, b c d^{3} e^{16}}{{\left(x e + d\right)}^{4}} - \frac{6 \, b^{2} e^{17}}{{\left(x e + d\right)}^{2}} - \frac{12 \, a c e^{17}}{{\left(x e + d\right)}^{2}} + \frac{8 \, b^{2} d e^{17}}{{\left(x e + d\right)}^{3}} + \frac{16 \, a c d e^{17}}{{\left(x e + d\right)}^{3}} - \frac{3 \, b^{2} d^{2} e^{17}}{{\left(x e + d\right)}^{4}} - \frac{6 \, a c d^{2} e^{17}}{{\left(x e + d\right)}^{4}} - \frac{8 \, a b e^{18}}{{\left(x e + d\right)}^{3}} + \frac{6 \, a b d e^{18}}{{\left(x e + d\right)}^{4}} - \frac{3 \, a^{2} e^{19}}{{\left(x e + d\right)}^{4}}\right)} e^{\left(-20\right)}"," ",0,"-c^2*e^(-5)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) + 1/12*(48*c^2*d*e^15/(x*e + d) - 36*c^2*d^2*e^15/(x*e + d)^2 + 16*c^2*d^3*e^15/(x*e + d)^3 - 3*c^2*d^4*e^15/(x*e + d)^4 - 24*b*c*e^16/(x*e + d) + 36*b*c*d*e^16/(x*e + d)^2 - 24*b*c*d^2*e^16/(x*e + d)^3 + 6*b*c*d^3*e^16/(x*e + d)^4 - 6*b^2*e^17/(x*e + d)^2 - 12*a*c*e^17/(x*e + d)^2 + 8*b^2*d*e^17/(x*e + d)^3 + 16*a*c*d*e^17/(x*e + d)^3 - 3*b^2*d^2*e^17/(x*e + d)^4 - 6*a*c*d^2*e^17/(x*e + d)^4 - 8*a*b*e^18/(x*e + d)^3 + 6*a*b*d*e^18/(x*e + d)^4 - 3*a^2*e^19/(x*e + d)^4)*e^(-20)","B",0
2128,1,179,0,0.157553," ","integrate((c*x^2+b*x+a)^2/(e*x+d)^6,x, algorithm=""giac"")","-\frac{{\left(30 \, c^{2} x^{4} e^{4} + 60 \, c^{2} d x^{3} e^{3} + 60 \, c^{2} d^{2} x^{2} e^{2} + 30 \, c^{2} d^{3} x e + 6 \, c^{2} d^{4} + 30 \, b c x^{3} e^{4} + 30 \, b c d x^{2} e^{3} + 15 \, b c d^{2} x e^{2} + 3 \, b c d^{3} e + 10 \, b^{2} x^{2} e^{4} + 20 \, a c x^{2} e^{4} + 5 \, b^{2} d x e^{3} + 10 \, a c d x e^{3} + b^{2} d^{2} e^{2} + 2 \, a c d^{2} e^{2} + 15 \, a b x e^{4} + 3 \, a b d e^{3} + 6 \, a^{2} e^{4}\right)} e^{\left(-5\right)}}{30 \, {\left(x e + d\right)}^{5}}"," ",0,"-1/30*(30*c^2*x^4*e^4 + 60*c^2*d*x^3*e^3 + 60*c^2*d^2*x^2*e^2 + 30*c^2*d^3*x*e + 6*c^2*d^4 + 30*b*c*x^3*e^4 + 30*b*c*d*x^2*e^3 + 15*b*c*d^2*x*e^2 + 3*b*c*d^3*e + 10*b^2*x^2*e^4 + 20*a*c*x^2*e^4 + 5*b^2*d*x*e^3 + 10*a*c*d*x*e^3 + b^2*d^2*e^2 + 2*a*c*d^2*e^2 + 15*a*b*x*e^4 + 3*a*b*d*e^3 + 6*a^2*e^4)*e^(-5)/(x*e + d)^5","A",0
2129,1,179,0,0.156354," ","integrate((c*x^2+b*x+a)^2/(e*x+d)^7,x, algorithm=""giac"")","-\frac{{\left(30 \, c^{2} x^{4} e^{4} + 40 \, c^{2} d x^{3} e^{3} + 30 \, c^{2} d^{2} x^{2} e^{2} + 12 \, c^{2} d^{3} x e + 2 \, c^{2} d^{4} + 40 \, b c x^{3} e^{4} + 30 \, b c d x^{2} e^{3} + 12 \, b c d^{2} x e^{2} + 2 \, b c d^{3} e + 15 \, b^{2} x^{2} e^{4} + 30 \, a c x^{2} e^{4} + 6 \, b^{2} d x e^{3} + 12 \, a c d x e^{3} + b^{2} d^{2} e^{2} + 2 \, a c d^{2} e^{2} + 24 \, a b x e^{4} + 4 \, a b d e^{3} + 10 \, a^{2} e^{4}\right)} e^{\left(-5\right)}}{60 \, {\left(x e + d\right)}^{6}}"," ",0,"-1/60*(30*c^2*x^4*e^4 + 40*c^2*d*x^3*e^3 + 30*c^2*d^2*x^2*e^2 + 12*c^2*d^3*x*e + 2*c^2*d^4 + 40*b*c*x^3*e^4 + 30*b*c*d*x^2*e^3 + 12*b*c*d^2*x*e^2 + 2*b*c*d^3*e + 15*b^2*x^2*e^4 + 30*a*c*x^2*e^4 + 6*b^2*d*x*e^3 + 12*a*c*d*x*e^3 + b^2*d^2*e^2 + 2*a*c*d^2*e^2 + 24*a*b*x*e^4 + 4*a*b*d*e^3 + 10*a^2*e^4)*e^(-5)/(x*e + d)^6","A",0
2130,1,180,0,0.179821," ","integrate((c*x^2+b*x+a)^2/(e*x+d)^8,x, algorithm=""giac"")","-\frac{{\left(70 \, c^{2} x^{4} e^{4} + 70 \, c^{2} d x^{3} e^{3} + 42 \, c^{2} d^{2} x^{2} e^{2} + 14 \, c^{2} d^{3} x e + 2 \, c^{2} d^{4} + 105 \, b c x^{3} e^{4} + 63 \, b c d x^{2} e^{3} + 21 \, b c d^{2} x e^{2} + 3 \, b c d^{3} e + 42 \, b^{2} x^{2} e^{4} + 84 \, a c x^{2} e^{4} + 14 \, b^{2} d x e^{3} + 28 \, a c d x e^{3} + 2 \, b^{2} d^{2} e^{2} + 4 \, a c d^{2} e^{2} + 70 \, a b x e^{4} + 10 \, a b d e^{3} + 30 \, a^{2} e^{4}\right)} e^{\left(-5\right)}}{210 \, {\left(x e + d\right)}^{7}}"," ",0,"-1/210*(70*c^2*x^4*e^4 + 70*c^2*d*x^3*e^3 + 42*c^2*d^2*x^2*e^2 + 14*c^2*d^3*x*e + 2*c^2*d^4 + 105*b*c*x^3*e^4 + 63*b*c*d*x^2*e^3 + 21*b*c*d^2*x*e^2 + 3*b*c*d^3*e + 42*b^2*x^2*e^4 + 84*a*c*x^2*e^4 + 14*b^2*d*x*e^3 + 28*a*c*d*x*e^3 + 2*b^2*d^2*e^2 + 4*a*c*d^2*e^2 + 70*a*b*x*e^4 + 10*a*b*d*e^3 + 30*a^2*e^4)*e^(-5)/(x*e + d)^7","A",0
2131,1,604,0,0.197353," ","integrate((e*x+d)^4*(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{1}{11} \, c^{3} x^{11} e^{4} + \frac{2}{5} \, c^{3} d x^{10} e^{3} + \frac{2}{3} \, c^{3} d^{2} x^{9} e^{2} + \frac{1}{2} \, c^{3} d^{3} x^{8} e + \frac{1}{7} \, c^{3} d^{4} x^{7} + \frac{3}{10} \, b c^{2} x^{10} e^{4} + \frac{4}{3} \, b c^{2} d x^{9} e^{3} + \frac{9}{4} \, b c^{2} d^{2} x^{8} e^{2} + \frac{12}{7} \, b c^{2} d^{3} x^{7} e + \frac{1}{2} \, b c^{2} d^{4} x^{6} + \frac{1}{3} \, b^{2} c x^{9} e^{4} + \frac{1}{3} \, a c^{2} x^{9} e^{4} + \frac{3}{2} \, b^{2} c d x^{8} e^{3} + \frac{3}{2} \, a c^{2} d x^{8} e^{3} + \frac{18}{7} \, b^{2} c d^{2} x^{7} e^{2} + \frac{18}{7} \, a c^{2} d^{2} x^{7} e^{2} + 2 \, b^{2} c d^{3} x^{6} e + 2 \, a c^{2} d^{3} x^{6} e + \frac{3}{5} \, b^{2} c d^{4} x^{5} + \frac{3}{5} \, a c^{2} d^{4} x^{5} + \frac{1}{8} \, b^{3} x^{8} e^{4} + \frac{3}{4} \, a b c x^{8} e^{4} + \frac{4}{7} \, b^{3} d x^{7} e^{3} + \frac{24}{7} \, a b c d x^{7} e^{3} + b^{3} d^{2} x^{6} e^{2} + 6 \, a b c d^{2} x^{6} e^{2} + \frac{4}{5} \, b^{3} d^{3} x^{5} e + \frac{24}{5} \, a b c d^{3} x^{5} e + \frac{1}{4} \, b^{3} d^{4} x^{4} + \frac{3}{2} \, a b c d^{4} x^{4} + \frac{3}{7} \, a b^{2} x^{7} e^{4} + \frac{3}{7} \, a^{2} c x^{7} e^{4} + 2 \, a b^{2} d x^{6} e^{3} + 2 \, a^{2} c d x^{6} e^{3} + \frac{18}{5} \, a b^{2} d^{2} x^{5} e^{2} + \frac{18}{5} \, a^{2} c d^{2} x^{5} e^{2} + 3 \, a b^{2} d^{3} x^{4} e + 3 \, a^{2} c d^{3} x^{4} e + a b^{2} d^{4} x^{3} + a^{2} c d^{4} x^{3} + \frac{1}{2} \, a^{2} b x^{6} e^{4} + \frac{12}{5} \, a^{2} b d x^{5} e^{3} + \frac{9}{2} \, a^{2} b d^{2} x^{4} e^{2} + 4 \, a^{2} b d^{3} x^{3} e + \frac{3}{2} \, a^{2} b d^{4} x^{2} + \frac{1}{5} \, a^{3} x^{5} e^{4} + a^{3} d x^{4} e^{3} + 2 \, a^{3} d^{2} x^{3} e^{2} + 2 \, a^{3} d^{3} x^{2} e + a^{3} d^{4} x"," ",0,"1/11*c^3*x^11*e^4 + 2/5*c^3*d*x^10*e^3 + 2/3*c^3*d^2*x^9*e^2 + 1/2*c^3*d^3*x^8*e + 1/7*c^3*d^4*x^7 + 3/10*b*c^2*x^10*e^4 + 4/3*b*c^2*d*x^9*e^3 + 9/4*b*c^2*d^2*x^8*e^2 + 12/7*b*c^2*d^3*x^7*e + 1/2*b*c^2*d^4*x^6 + 1/3*b^2*c*x^9*e^4 + 1/3*a*c^2*x^9*e^4 + 3/2*b^2*c*d*x^8*e^3 + 3/2*a*c^2*d*x^8*e^3 + 18/7*b^2*c*d^2*x^7*e^2 + 18/7*a*c^2*d^2*x^7*e^2 + 2*b^2*c*d^3*x^6*e + 2*a*c^2*d^3*x^6*e + 3/5*b^2*c*d^4*x^5 + 3/5*a*c^2*d^4*x^5 + 1/8*b^3*x^8*e^4 + 3/4*a*b*c*x^8*e^4 + 4/7*b^3*d*x^7*e^3 + 24/7*a*b*c*d*x^7*e^3 + b^3*d^2*x^6*e^2 + 6*a*b*c*d^2*x^6*e^2 + 4/5*b^3*d^3*x^5*e + 24/5*a*b*c*d^3*x^5*e + 1/4*b^3*d^4*x^4 + 3/2*a*b*c*d^4*x^4 + 3/7*a*b^2*x^7*e^4 + 3/7*a^2*c*x^7*e^4 + 2*a*b^2*d*x^6*e^3 + 2*a^2*c*d*x^6*e^3 + 18/5*a*b^2*d^2*x^5*e^2 + 18/5*a^2*c*d^2*x^5*e^2 + 3*a*b^2*d^3*x^4*e + 3*a^2*c*d^3*x^4*e + a*b^2*d^4*x^3 + a^2*c*d^4*x^3 + 1/2*a^2*b*x^6*e^4 + 12/5*a^2*b*d*x^5*e^3 + 9/2*a^2*b*d^2*x^4*e^2 + 4*a^2*b*d^3*x^3*e + 3/2*a^2*b*d^4*x^2 + 1/5*a^3*x^5*e^4 + a^3*d*x^4*e^3 + 2*a^3*d^2*x^3*e^2 + 2*a^3*d^3*x^2*e + a^3*d^4*x","B",0
2132,1,469,0,0.162990," ","integrate((e*x+d)^3*(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{1}{10} \, c^{3} x^{10} e^{3} + \frac{1}{3} \, c^{3} d x^{9} e^{2} + \frac{3}{8} \, c^{3} d^{2} x^{8} e + \frac{1}{7} \, c^{3} d^{3} x^{7} + \frac{1}{3} \, b c^{2} x^{9} e^{3} + \frac{9}{8} \, b c^{2} d x^{8} e^{2} + \frac{9}{7} \, b c^{2} d^{2} x^{7} e + \frac{1}{2} \, b c^{2} d^{3} x^{6} + \frac{3}{8} \, b^{2} c x^{8} e^{3} + \frac{3}{8} \, a c^{2} x^{8} e^{3} + \frac{9}{7} \, b^{2} c d x^{7} e^{2} + \frac{9}{7} \, a c^{2} d x^{7} e^{2} + \frac{3}{2} \, b^{2} c d^{2} x^{6} e + \frac{3}{2} \, a c^{2} d^{2} x^{6} e + \frac{3}{5} \, b^{2} c d^{3} x^{5} + \frac{3}{5} \, a c^{2} d^{3} x^{5} + \frac{1}{7} \, b^{3} x^{7} e^{3} + \frac{6}{7} \, a b c x^{7} e^{3} + \frac{1}{2} \, b^{3} d x^{6} e^{2} + 3 \, a b c d x^{6} e^{2} + \frac{3}{5} \, b^{3} d^{2} x^{5} e + \frac{18}{5} \, a b c d^{2} x^{5} e + \frac{1}{4} \, b^{3} d^{3} x^{4} + \frac{3}{2} \, a b c d^{3} x^{4} + \frac{1}{2} \, a b^{2} x^{6} e^{3} + \frac{1}{2} \, a^{2} c x^{6} e^{3} + \frac{9}{5} \, a b^{2} d x^{5} e^{2} + \frac{9}{5} \, a^{2} c d x^{5} e^{2} + \frac{9}{4} \, a b^{2} d^{2} x^{4} e + \frac{9}{4} \, a^{2} c d^{2} x^{4} e + a b^{2} d^{3} x^{3} + a^{2} c d^{3} x^{3} + \frac{3}{5} \, a^{2} b x^{5} e^{3} + \frac{9}{4} \, a^{2} b d x^{4} e^{2} + 3 \, a^{2} b d^{2} x^{3} e + \frac{3}{2} \, a^{2} b d^{3} x^{2} + \frac{1}{4} \, a^{3} x^{4} e^{3} + a^{3} d x^{3} e^{2} + \frac{3}{2} \, a^{3} d^{2} x^{2} e + a^{3} d^{3} x"," ",0,"1/10*c^3*x^10*e^3 + 1/3*c^3*d*x^9*e^2 + 3/8*c^3*d^2*x^8*e + 1/7*c^3*d^3*x^7 + 1/3*b*c^2*x^9*e^3 + 9/8*b*c^2*d*x^8*e^2 + 9/7*b*c^2*d^2*x^7*e + 1/2*b*c^2*d^3*x^6 + 3/8*b^2*c*x^8*e^3 + 3/8*a*c^2*x^8*e^3 + 9/7*b^2*c*d*x^7*e^2 + 9/7*a*c^2*d*x^7*e^2 + 3/2*b^2*c*d^2*x^6*e + 3/2*a*c^2*d^2*x^6*e + 3/5*b^2*c*d^3*x^5 + 3/5*a*c^2*d^3*x^5 + 1/7*b^3*x^7*e^3 + 6/7*a*b*c*x^7*e^3 + 1/2*b^3*d*x^6*e^2 + 3*a*b*c*d*x^6*e^2 + 3/5*b^3*d^2*x^5*e + 18/5*a*b*c*d^2*x^5*e + 1/4*b^3*d^3*x^4 + 3/2*a*b*c*d^3*x^4 + 1/2*a*b^2*x^6*e^3 + 1/2*a^2*c*x^6*e^3 + 9/5*a*b^2*d*x^5*e^2 + 9/5*a^2*c*d*x^5*e^2 + 9/4*a*b^2*d^2*x^4*e + 9/4*a^2*c*d^2*x^4*e + a*b^2*d^3*x^3 + a^2*c*d^3*x^3 + 3/5*a^2*b*x^5*e^3 + 9/4*a^2*b*d*x^4*e^2 + 3*a^2*b*d^2*x^3*e + 3/2*a^2*b*d^3*x^2 + 1/4*a^3*x^4*e^3 + a^3*d*x^3*e^2 + 3/2*a^3*d^2*x^2*e + a^3*d^3*x","A",0
2133,1,330,0,0.156865," ","integrate((e*x+d)^2*(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{1}{9} \, c^{3} x^{9} e^{2} + \frac{1}{4} \, c^{3} d x^{8} e + \frac{1}{7} \, c^{3} d^{2} x^{7} + \frac{3}{8} \, b c^{2} x^{8} e^{2} + \frac{6}{7} \, b c^{2} d x^{7} e + \frac{1}{2} \, b c^{2} d^{2} x^{6} + \frac{3}{7} \, b^{2} c x^{7} e^{2} + \frac{3}{7} \, a c^{2} x^{7} e^{2} + b^{2} c d x^{6} e + a c^{2} d x^{6} e + \frac{3}{5} \, b^{2} c d^{2} x^{5} + \frac{3}{5} \, a c^{2} d^{2} x^{5} + \frac{1}{6} \, b^{3} x^{6} e^{2} + a b c x^{6} e^{2} + \frac{2}{5} \, b^{3} d x^{5} e + \frac{12}{5} \, a b c d x^{5} e + \frac{1}{4} \, b^{3} d^{2} x^{4} + \frac{3}{2} \, a b c d^{2} x^{4} + \frac{3}{5} \, a b^{2} x^{5} e^{2} + \frac{3}{5} \, a^{2} c x^{5} e^{2} + \frac{3}{2} \, a b^{2} d x^{4} e + \frac{3}{2} \, a^{2} c d x^{4} e + a b^{2} d^{2} x^{3} + a^{2} c d^{2} x^{3} + \frac{3}{4} \, a^{2} b x^{4} e^{2} + 2 \, a^{2} b d x^{3} e + \frac{3}{2} \, a^{2} b d^{2} x^{2} + \frac{1}{3} \, a^{3} x^{3} e^{2} + a^{3} d x^{2} e + a^{3} d^{2} x"," ",0,"1/9*c^3*x^9*e^2 + 1/4*c^3*d*x^8*e + 1/7*c^3*d^2*x^7 + 3/8*b*c^2*x^8*e^2 + 6/7*b*c^2*d*x^7*e + 1/2*b*c^2*d^2*x^6 + 3/7*b^2*c*x^7*e^2 + 3/7*a*c^2*x^7*e^2 + b^2*c*d*x^6*e + a*c^2*d*x^6*e + 3/5*b^2*c*d^2*x^5 + 3/5*a*c^2*d^2*x^5 + 1/6*b^3*x^6*e^2 + a*b*c*x^6*e^2 + 2/5*b^3*d*x^5*e + 12/5*a*b*c*d*x^5*e + 1/4*b^3*d^2*x^4 + 3/2*a*b*c*d^2*x^4 + 3/5*a*b^2*x^5*e^2 + 3/5*a^2*c*x^5*e^2 + 3/2*a*b^2*d*x^4*e + 3/2*a^2*c*d*x^4*e + a*b^2*d^2*x^3 + a^2*c*d^2*x^3 + 3/4*a^2*b*x^4*e^2 + 2*a^2*b*d*x^3*e + 3/2*a^2*b*d^2*x^2 + 1/3*a^3*x^3*e^2 + a^3*d*x^2*e + a^3*d^2*x","A",0
2134,1,197,0,0.161162," ","integrate((e*x+d)*(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{1}{8} \, c^{3} x^{8} e + \frac{1}{7} \, c^{3} d x^{7} + \frac{3}{7} \, b c^{2} x^{7} e + \frac{1}{2} \, b c^{2} d x^{6} + \frac{1}{2} \, b^{2} c x^{6} e + \frac{1}{2} \, a c^{2} x^{6} e + \frac{3}{5} \, b^{2} c d x^{5} + \frac{3}{5} \, a c^{2} d x^{5} + \frac{1}{5} \, b^{3} x^{5} e + \frac{6}{5} \, a b c x^{5} e + \frac{1}{4} \, b^{3} d x^{4} + \frac{3}{2} \, a b c d x^{4} + \frac{3}{4} \, a b^{2} x^{4} e + \frac{3}{4} \, a^{2} c x^{4} e + a b^{2} d x^{3} + a^{2} c d x^{3} + a^{2} b x^{3} e + \frac{3}{2} \, a^{2} b d x^{2} + \frac{1}{2} \, a^{3} x^{2} e + a^{3} d x"," ",0,"1/8*c^3*x^8*e + 1/7*c^3*d*x^7 + 3/7*b*c^2*x^7*e + 1/2*b*c^2*d*x^6 + 1/2*b^2*c*x^6*e + 1/2*a*c^2*x^6*e + 3/5*b^2*c*d*x^5 + 3/5*a*c^2*d*x^5 + 1/5*b^3*x^5*e + 6/5*a*b*c*x^5*e + 1/4*b^3*d*x^4 + 3/2*a*b*c*d*x^4 + 3/4*a*b^2*x^4*e + 3/4*a^2*c*x^4*e + a*b^2*d*x^3 + a^2*c*d*x^3 + a^2*b*x^3*e + 3/2*a^2*b*d*x^2 + 1/2*a^3*x^2*e + a^3*d*x","A",0
2135,1,82,0,0.149186," ","integrate((c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{1}{7} \, c^{3} x^{7} + \frac{1}{2} \, b c^{2} x^{6} + \frac{3}{5} \, b^{2} c x^{5} + \frac{3}{5} \, a c^{2} x^{5} + \frac{1}{4} \, b^{3} x^{4} + \frac{3}{2} \, a b c x^{4} + a b^{2} x^{3} + a^{2} c x^{3} + \frac{3}{2} \, a^{2} b x^{2} + a^{3} x"," ",0,"1/7*c^3*x^7 + 1/2*b*c^2*x^6 + 3/5*b^2*c*x^5 + 3/5*a*c^2*x^5 + 1/4*b^3*x^4 + 3/2*a*b*c*x^4 + a*b^2*x^3 + a^2*c*x^3 + 3/2*a^2*b*x^2 + a^3*x","A",0
2136,1,460,0,0.159070," ","integrate((c*x^2+b*x+a)^3/(e*x+d),x, algorithm=""giac"")","{\left(c^{3} d^{6} - 3 \, b c^{2} d^{5} e + 3 \, b^{2} c d^{4} e^{2} + 3 \, a c^{2} d^{4} e^{2} - b^{3} d^{3} e^{3} - 6 \, a b c d^{3} e^{3} + 3 \, a b^{2} d^{2} e^{4} + 3 \, a^{2} c d^{2} e^{4} - 3 \, a^{2} b d e^{5} + a^{3} e^{6}\right)} e^{\left(-7\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{60} \, {\left(10 \, c^{3} x^{6} e^{5} - 12 \, c^{3} d x^{5} e^{4} + 15 \, c^{3} d^{2} x^{4} e^{3} - 20 \, c^{3} d^{3} x^{3} e^{2} + 30 \, c^{3} d^{4} x^{2} e - 60 \, c^{3} d^{5} x + 36 \, b c^{2} x^{5} e^{5} - 45 \, b c^{2} d x^{4} e^{4} + 60 \, b c^{2} d^{2} x^{3} e^{3} - 90 \, b c^{2} d^{3} x^{2} e^{2} + 180 \, b c^{2} d^{4} x e + 45 \, b^{2} c x^{4} e^{5} + 45 \, a c^{2} x^{4} e^{5} - 60 \, b^{2} c d x^{3} e^{4} - 60 \, a c^{2} d x^{3} e^{4} + 90 \, b^{2} c d^{2} x^{2} e^{3} + 90 \, a c^{2} d^{2} x^{2} e^{3} - 180 \, b^{2} c d^{3} x e^{2} - 180 \, a c^{2} d^{3} x e^{2} + 20 \, b^{3} x^{3} e^{5} + 120 \, a b c x^{3} e^{5} - 30 \, b^{3} d x^{2} e^{4} - 180 \, a b c d x^{2} e^{4} + 60 \, b^{3} d^{2} x e^{3} + 360 \, a b c d^{2} x e^{3} + 90 \, a b^{2} x^{2} e^{5} + 90 \, a^{2} c x^{2} e^{5} - 180 \, a b^{2} d x e^{4} - 180 \, a^{2} c d x e^{4} + 180 \, a^{2} b x e^{5}\right)} e^{\left(-6\right)}"," ",0,"(c^3*d^6 - 3*b*c^2*d^5*e + 3*b^2*c*d^4*e^2 + 3*a*c^2*d^4*e^2 - b^3*d^3*e^3 - 6*a*b*c*d^3*e^3 + 3*a*b^2*d^2*e^4 + 3*a^2*c*d^2*e^4 - 3*a^2*b*d*e^5 + a^3*e^6)*e^(-7)*log(abs(x*e + d)) + 1/60*(10*c^3*x^6*e^5 - 12*c^3*d*x^5*e^4 + 15*c^3*d^2*x^4*e^3 - 20*c^3*d^3*x^3*e^2 + 30*c^3*d^4*x^2*e - 60*c^3*d^5*x + 36*b*c^2*x^5*e^5 - 45*b*c^2*d*x^4*e^4 + 60*b*c^2*d^2*x^3*e^3 - 90*b*c^2*d^3*x^2*e^2 + 180*b*c^2*d^4*x*e + 45*b^2*c*x^4*e^5 + 45*a*c^2*x^4*e^5 - 60*b^2*c*d*x^3*e^4 - 60*a*c^2*d*x^3*e^4 + 90*b^2*c*d^2*x^2*e^3 + 90*a*c^2*d^2*x^2*e^3 - 180*b^2*c*d^3*x*e^2 - 180*a*c^2*d^3*x*e^2 + 20*b^3*x^3*e^5 + 120*a*b*c*x^3*e^5 - 30*b^3*d*x^2*e^4 - 180*a*b*c*d*x^2*e^4 + 60*b^3*d^2*x*e^3 + 360*a*b*c*d^2*x*e^3 + 90*a*b^2*x^2*e^5 + 90*a^2*c*x^2*e^5 - 180*a*b^2*d*x*e^4 - 180*a^2*c*d*x*e^4 + 180*a^2*b*x*e^5)*e^(-6)","A",0
2137,1,541,0,0.220794," ","integrate((c*x^2+b*x+a)^3/(e*x+d)^2,x, algorithm=""giac"")","\frac{1}{20} \, {\left(4 \, c^{3} - \frac{15 \, {\left(2 \, c^{3} d e - b c^{2} e^{2}\right)} e^{\left(-1\right)}}{x e + d} + \frac{20 \, {\left(5 \, c^{3} d^{2} e^{2} - 5 \, b c^{2} d e^{3} + b^{2} c e^{4} + a c^{2} e^{4}\right)} e^{\left(-2\right)}}{{\left(x e + d\right)}^{2}} - \frac{10 \, {\left(20 \, c^{3} d^{3} e^{3} - 30 \, b c^{2} d^{2} e^{4} + 12 \, b^{2} c d e^{5} + 12 \, a c^{2} d e^{5} - b^{3} e^{6} - 6 \, a b c e^{6}\right)} e^{\left(-3\right)}}{{\left(x e + d\right)}^{3}} + \frac{60 \, {\left(5 \, c^{3} d^{4} e^{4} - 10 \, b c^{2} d^{3} e^{5} + 6 \, b^{2} c d^{2} e^{6} + 6 \, a c^{2} d^{2} e^{6} - b^{3} d e^{7} - 6 \, a b c d e^{7} + a b^{2} e^{8} + a^{2} c e^{8}\right)} e^{\left(-4\right)}}{{\left(x e + d\right)}^{4}}\right)} {\left(x e + d\right)}^{5} e^{\left(-7\right)} + 3 \, {\left(2 \, c^{3} d^{5} - 5 \, b c^{2} d^{4} e + 4 \, b^{2} c d^{3} e^{2} + 4 \, a c^{2} d^{3} e^{2} - b^{3} d^{2} e^{3} - 6 \, a b c d^{2} e^{3} + 2 \, a b^{2} d e^{4} + 2 \, a^{2} c d e^{4} - a^{2} b e^{5}\right)} e^{\left(-7\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) - {\left(\frac{c^{3} d^{6} e^{5}}{x e + d} - \frac{3 \, b c^{2} d^{5} e^{6}}{x e + d} + \frac{3 \, b^{2} c d^{4} e^{7}}{x e + d} + \frac{3 \, a c^{2} d^{4} e^{7}}{x e + d} - \frac{b^{3} d^{3} e^{8}}{x e + d} - \frac{6 \, a b c d^{3} e^{8}}{x e + d} + \frac{3 \, a b^{2} d^{2} e^{9}}{x e + d} + \frac{3 \, a^{2} c d^{2} e^{9}}{x e + d} - \frac{3 \, a^{2} b d e^{10}}{x e + d} + \frac{a^{3} e^{11}}{x e + d}\right)} e^{\left(-12\right)}"," ",0,"1/20*(4*c^3 - 15*(2*c^3*d*e - b*c^2*e^2)*e^(-1)/(x*e + d) + 20*(5*c^3*d^2*e^2 - 5*b*c^2*d*e^3 + b^2*c*e^4 + a*c^2*e^4)*e^(-2)/(x*e + d)^2 - 10*(20*c^3*d^3*e^3 - 30*b*c^2*d^2*e^4 + 12*b^2*c*d*e^5 + 12*a*c^2*d*e^5 - b^3*e^6 - 6*a*b*c*e^6)*e^(-3)/(x*e + d)^3 + 60*(5*c^3*d^4*e^4 - 10*b*c^2*d^3*e^5 + 6*b^2*c*d^2*e^6 + 6*a*c^2*d^2*e^6 - b^3*d*e^7 - 6*a*b*c*d*e^7 + a*b^2*e^8 + a^2*c*e^8)*e^(-4)/(x*e + d)^4)*(x*e + d)^5*e^(-7) + 3*(2*c^3*d^5 - 5*b*c^2*d^4*e + 4*b^2*c*d^3*e^2 + 4*a*c^2*d^3*e^2 - b^3*d^2*e^3 - 6*a*b*c*d^2*e^3 + 2*a*b^2*d*e^4 + 2*a^2*c*d*e^4 - a^2*b*e^5)*e^(-7)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) - (c^3*d^6*e^5/(x*e + d) - 3*b*c^2*d^5*e^6/(x*e + d) + 3*b^2*c*d^4*e^7/(x*e + d) + 3*a*c^2*d^4*e^7/(x*e + d) - b^3*d^3*e^8/(x*e + d) - 6*a*b*c*d^3*e^8/(x*e + d) + 3*a*b^2*d^2*e^9/(x*e + d) + 3*a^2*c*d^2*e^9/(x*e + d) - 3*a^2*b*d*e^10/(x*e + d) + a^3*e^11/(x*e + d))*e^(-12)","B",0
2138,1,432,0,0.164029," ","integrate((c*x^2+b*x+a)^3/(e*x+d)^3,x, algorithm=""giac"")","3 \, {\left(5 \, c^{3} d^{4} - 10 \, b c^{2} d^{3} e + 6 \, b^{2} c d^{2} e^{2} + 6 \, a c^{2} d^{2} e^{2} - b^{3} d e^{3} - 6 \, a b c d e^{3} + a b^{2} e^{4} + a^{2} c e^{4}\right)} e^{\left(-7\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{4} \, {\left(c^{3} x^{4} e^{9} - 4 \, c^{3} d x^{3} e^{8} + 12 \, c^{3} d^{2} x^{2} e^{7} - 40 \, c^{3} d^{3} x e^{6} + 4 \, b c^{2} x^{3} e^{9} - 18 \, b c^{2} d x^{2} e^{8} + 72 \, b c^{2} d^{2} x e^{7} + 6 \, b^{2} c x^{2} e^{9} + 6 \, a c^{2} x^{2} e^{9} - 36 \, b^{2} c d x e^{8} - 36 \, a c^{2} d x e^{8} + 4 \, b^{3} x e^{9} + 24 \, a b c x e^{9}\right)} e^{\left(-12\right)} + \frac{{\left(11 \, c^{3} d^{6} - 27 \, b c^{2} d^{5} e + 21 \, b^{2} c d^{4} e^{2} + 21 \, a c^{2} d^{4} e^{2} - 5 \, b^{3} d^{3} e^{3} - 30 \, a b c d^{3} e^{3} + 9 \, a b^{2} d^{2} e^{4} + 9 \, a^{2} c d^{2} e^{4} - 3 \, a^{2} b d e^{5} - a^{3} e^{6} + 6 \, {\left(2 \, c^{3} d^{5} e - 5 \, b c^{2} d^{4} e^{2} + 4 \, b^{2} c d^{3} e^{3} + 4 \, a c^{2} d^{3} e^{3} - b^{3} d^{2} e^{4} - 6 \, a b c d^{2} e^{4} + 2 \, a b^{2} d e^{5} + 2 \, a^{2} c d e^{5} - a^{2} b e^{6}\right)} x\right)} e^{\left(-7\right)}}{2 \, {\left(x e + d\right)}^{2}}"," ",0,"3*(5*c^3*d^4 - 10*b*c^2*d^3*e + 6*b^2*c*d^2*e^2 + 6*a*c^2*d^2*e^2 - b^3*d*e^3 - 6*a*b*c*d*e^3 + a*b^2*e^4 + a^2*c*e^4)*e^(-7)*log(abs(x*e + d)) + 1/4*(c^3*x^4*e^9 - 4*c^3*d*x^3*e^8 + 12*c^3*d^2*x^2*e^7 - 40*c^3*d^3*x*e^6 + 4*b*c^2*x^3*e^9 - 18*b*c^2*d*x^2*e^8 + 72*b*c^2*d^2*x*e^7 + 6*b^2*c*x^2*e^9 + 6*a*c^2*x^2*e^9 - 36*b^2*c*d*x*e^8 - 36*a*c^2*d*x*e^8 + 4*b^3*x*e^9 + 24*a*b*c*x*e^9)*e^(-12) + 1/2*(11*c^3*d^6 - 27*b*c^2*d^5*e + 21*b^2*c*d^4*e^2 + 21*a*c^2*d^4*e^2 - 5*b^3*d^3*e^3 - 30*a*b*c*d^3*e^3 + 9*a*b^2*d^2*e^4 + 9*a^2*c*d^2*e^4 - 3*a^2*b*d*e^5 - a^3*e^6 + 6*(2*c^3*d^5*e - 5*b*c^2*d^4*e^2 + 4*b^2*c*d^3*e^3 + 4*a*c^2*d^3*e^3 - b^3*d^2*e^4 - 6*a*b*c*d^2*e^4 + 2*a*b^2*d*e^5 + 2*a^2*c*d*e^5 - a^2*b*e^6)*x)*e^(-7)/(x*e + d)^2","A",0
2139,1,424,0,0.163779," ","integrate((c*x^2+b*x+a)^3/(e*x+d)^4,x, algorithm=""giac"")","-{\left(20 \, c^{3} d^{3} - 30 \, b c^{2} d^{2} e + 12 \, b^{2} c d e^{2} + 12 \, a c^{2} d e^{2} - b^{3} e^{3} - 6 \, a b c e^{3}\right)} e^{\left(-7\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{6} \, {\left(2 \, c^{3} x^{3} e^{8} - 12 \, c^{3} d x^{2} e^{7} + 60 \, c^{3} d^{2} x e^{6} + 9 \, b c^{2} x^{2} e^{8} - 72 \, b c^{2} d x e^{7} + 18 \, b^{2} c x e^{8} + 18 \, a c^{2} x e^{8}\right)} e^{\left(-12\right)} - \frac{{\left(74 \, c^{3} d^{6} - 141 \, b c^{2} d^{5} e + 78 \, b^{2} c d^{4} e^{2} + 78 \, a c^{2} d^{4} e^{2} - 11 \, b^{3} d^{3} e^{3} - 66 \, a b c d^{3} e^{3} + 6 \, a b^{2} d^{2} e^{4} + 6 \, a^{2} c d^{2} e^{4} + 3 \, a^{2} b d e^{5} + 2 \, a^{3} e^{6} + 18 \, {\left(5 \, c^{3} d^{4} e^{2} - 10 \, b c^{2} d^{3} e^{3} + 6 \, b^{2} c d^{2} e^{4} + 6 \, a c^{2} d^{2} e^{4} - b^{3} d e^{5} - 6 \, a b c d e^{5} + a b^{2} e^{6} + a^{2} c e^{6}\right)} x^{2} + 9 \, {\left(18 \, c^{3} d^{5} e - 35 \, b c^{2} d^{4} e^{2} + 20 \, b^{2} c d^{3} e^{3} + 20 \, a c^{2} d^{3} e^{3} - 3 \, b^{3} d^{2} e^{4} - 18 \, a b c d^{2} e^{4} + 2 \, a b^{2} d e^{5} + 2 \, a^{2} c d e^{5} + a^{2} b e^{6}\right)} x\right)} e^{\left(-7\right)}}{6 \, {\left(x e + d\right)}^{3}}"," ",0,"-(20*c^3*d^3 - 30*b*c^2*d^2*e + 12*b^2*c*d*e^2 + 12*a*c^2*d*e^2 - b^3*e^3 - 6*a*b*c*e^3)*e^(-7)*log(abs(x*e + d)) + 1/6*(2*c^3*x^3*e^8 - 12*c^3*d*x^2*e^7 + 60*c^3*d^2*x*e^6 + 9*b*c^2*x^2*e^8 - 72*b*c^2*d*x*e^7 + 18*b^2*c*x*e^8 + 18*a*c^2*x*e^8)*e^(-12) - 1/6*(74*c^3*d^6 - 141*b*c^2*d^5*e + 78*b^2*c*d^4*e^2 + 78*a*c^2*d^4*e^2 - 11*b^3*d^3*e^3 - 66*a*b*c*d^3*e^3 + 6*a*b^2*d^2*e^4 + 6*a^2*c*d^2*e^4 + 3*a^2*b*d*e^5 + 2*a^3*e^6 + 18*(5*c^3*d^4*e^2 - 10*b*c^2*d^3*e^3 + 6*b^2*c*d^2*e^4 + 6*a*c^2*d^2*e^4 - b^3*d*e^5 - 6*a*b*c*d*e^5 + a*b^2*e^6 + a^2*c*e^6)*x^2 + 9*(18*c^3*d^5*e - 35*b*c^2*d^4*e^2 + 20*b^2*c*d^3*e^3 + 20*a*c^2*d^3*e^3 - 3*b^3*d^2*e^4 - 18*a*b*c*d^2*e^4 + 2*a*b^2*d*e^5 + 2*a^2*c*d*e^5 + a^2*b*e^6)*x)*e^(-7)/(x*e + d)^3","A",0
2140,1,687,0,0.190563," ","integrate((c*x^2+b*x+a)^3/(e*x+d)^5,x, algorithm=""giac"")","\frac{1}{2} \, {\left(c^{3} - \frac{6 \, {\left(2 \, c^{3} d e - b c^{2} e^{2}\right)} e^{\left(-1\right)}}{x e + d}\right)} {\left(x e + d\right)}^{2} e^{\left(-7\right)} - 3 \, {\left(5 \, c^{3} d^{2} - 5 \, b c^{2} d e + b^{2} c e^{2} + a c^{2} e^{2}\right)} e^{\left(-7\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) + \frac{1}{4} \, {\left(\frac{80 \, c^{3} d^{3} e^{29}}{x e + d} - \frac{30 \, c^{3} d^{4} e^{29}}{{\left(x e + d\right)}^{2}} + \frac{8 \, c^{3} d^{5} e^{29}}{{\left(x e + d\right)}^{3}} - \frac{c^{3} d^{6} e^{29}}{{\left(x e + d\right)}^{4}} - \frac{120 \, b c^{2} d^{2} e^{30}}{x e + d} + \frac{60 \, b c^{2} d^{3} e^{30}}{{\left(x e + d\right)}^{2}} - \frac{20 \, b c^{2} d^{4} e^{30}}{{\left(x e + d\right)}^{3}} + \frac{3 \, b c^{2} d^{5} e^{30}}{{\left(x e + d\right)}^{4}} + \frac{48 \, b^{2} c d e^{31}}{x e + d} + \frac{48 \, a c^{2} d e^{31}}{x e + d} - \frac{36 \, b^{2} c d^{2} e^{31}}{{\left(x e + d\right)}^{2}} - \frac{36 \, a c^{2} d^{2} e^{31}}{{\left(x e + d\right)}^{2}} + \frac{16 \, b^{2} c d^{3} e^{31}}{{\left(x e + d\right)}^{3}} + \frac{16 \, a c^{2} d^{3} e^{31}}{{\left(x e + d\right)}^{3}} - \frac{3 \, b^{2} c d^{4} e^{31}}{{\left(x e + d\right)}^{4}} - \frac{3 \, a c^{2} d^{4} e^{31}}{{\left(x e + d\right)}^{4}} - \frac{4 \, b^{3} e^{32}}{x e + d} - \frac{24 \, a b c e^{32}}{x e + d} + \frac{6 \, b^{3} d e^{32}}{{\left(x e + d\right)}^{2}} + \frac{36 \, a b c d e^{32}}{{\left(x e + d\right)}^{2}} - \frac{4 \, b^{3} d^{2} e^{32}}{{\left(x e + d\right)}^{3}} - \frac{24 \, a b c d^{2} e^{32}}{{\left(x e + d\right)}^{3}} + \frac{b^{3} d^{3} e^{32}}{{\left(x e + d\right)}^{4}} + \frac{6 \, a b c d^{3} e^{32}}{{\left(x e + d\right)}^{4}} - \frac{6 \, a b^{2} e^{33}}{{\left(x e + d\right)}^{2}} - \frac{6 \, a^{2} c e^{33}}{{\left(x e + d\right)}^{2}} + \frac{8 \, a b^{2} d e^{33}}{{\left(x e + d\right)}^{3}} + \frac{8 \, a^{2} c d e^{33}}{{\left(x e + d\right)}^{3}} - \frac{3 \, a b^{2} d^{2} e^{33}}{{\left(x e + d\right)}^{4}} - \frac{3 \, a^{2} c d^{2} e^{33}}{{\left(x e + d\right)}^{4}} - \frac{4 \, a^{2} b e^{34}}{{\left(x e + d\right)}^{3}} + \frac{3 \, a^{2} b d e^{34}}{{\left(x e + d\right)}^{4}} - \frac{a^{3} e^{35}}{{\left(x e + d\right)}^{4}}\right)} e^{\left(-36\right)}"," ",0,"1/2*(c^3 - 6*(2*c^3*d*e - b*c^2*e^2)*e^(-1)/(x*e + d))*(x*e + d)^2*e^(-7) - 3*(5*c^3*d^2 - 5*b*c^2*d*e + b^2*c*e^2 + a*c^2*e^2)*e^(-7)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) + 1/4*(80*c^3*d^3*e^29/(x*e + d) - 30*c^3*d^4*e^29/(x*e + d)^2 + 8*c^3*d^5*e^29/(x*e + d)^3 - c^3*d^6*e^29/(x*e + d)^4 - 120*b*c^2*d^2*e^30/(x*e + d) + 60*b*c^2*d^3*e^30/(x*e + d)^2 - 20*b*c^2*d^4*e^30/(x*e + d)^3 + 3*b*c^2*d^5*e^30/(x*e + d)^4 + 48*b^2*c*d*e^31/(x*e + d) + 48*a*c^2*d*e^31/(x*e + d) - 36*b^2*c*d^2*e^31/(x*e + d)^2 - 36*a*c^2*d^2*e^31/(x*e + d)^2 + 16*b^2*c*d^3*e^31/(x*e + d)^3 + 16*a*c^2*d^3*e^31/(x*e + d)^3 - 3*b^2*c*d^4*e^31/(x*e + d)^4 - 3*a*c^2*d^4*e^31/(x*e + d)^4 - 4*b^3*e^32/(x*e + d) - 24*a*b*c*e^32/(x*e + d) + 6*b^3*d*e^32/(x*e + d)^2 + 36*a*b*c*d*e^32/(x*e + d)^2 - 4*b^3*d^2*e^32/(x*e + d)^3 - 24*a*b*c*d^2*e^32/(x*e + d)^3 + b^3*d^3*e^32/(x*e + d)^4 + 6*a*b*c*d^3*e^32/(x*e + d)^4 - 6*a*b^2*e^33/(x*e + d)^2 - 6*a^2*c*e^33/(x*e + d)^2 + 8*a*b^2*d*e^33/(x*e + d)^3 + 8*a^2*c*d*e^33/(x*e + d)^3 - 3*a*b^2*d^2*e^33/(x*e + d)^4 - 3*a^2*c*d^2*e^33/(x*e + d)^4 - 4*a^2*b*e^34/(x*e + d)^3 + 3*a^2*b*d*e^34/(x*e + d)^4 - a^3*e^35/(x*e + d)^4)*e^(-36)","B",0
2141,1,415,0,0.162456," ","integrate((c*x^2+b*x+a)^3/(e*x+d)^6,x, algorithm=""giac"")","c^{3} x e^{\left(-6\right)} - 3 \, {\left(2 \, c^{3} d - b c^{2} e\right)} e^{\left(-7\right)} \log\left({\left| x e + d \right|}\right) - \frac{{\left(174 \, c^{3} d^{6} - 137 \, b c^{2} d^{5} e + 12 \, b^{2} c d^{4} e^{2} + 12 \, a c^{2} d^{4} e^{2} + b^{3} d^{3} e^{3} + 6 \, a b c d^{3} e^{3} + 2 \, a b^{2} d^{2} e^{4} + 2 \, a^{2} c d^{2} e^{4} + 60 \, {\left(5 \, c^{3} d^{2} e^{4} - 5 \, b c^{2} d e^{5} + b^{2} c e^{6} + a c^{2} e^{6}\right)} x^{4} + 3 \, a^{2} b d e^{5} + 10 \, {\left(100 \, c^{3} d^{3} e^{3} - 90 \, b c^{2} d^{2} e^{4} + 12 \, b^{2} c d e^{5} + 12 \, a c^{2} d e^{5} + b^{3} e^{6} + 6 \, a b c e^{6}\right)} x^{3} + 4 \, a^{3} e^{6} + 10 \, {\left(130 \, c^{3} d^{4} e^{2} - 110 \, b c^{2} d^{3} e^{3} + 12 \, b^{2} c d^{2} e^{4} + 12 \, a c^{2} d^{2} e^{4} + b^{3} d e^{5} + 6 \, a b c d e^{5} + 2 \, a b^{2} e^{6} + 2 \, a^{2} c e^{6}\right)} x^{2} + 5 \, {\left(154 \, c^{3} d^{5} e - 125 \, b c^{2} d^{4} e^{2} + 12 \, b^{2} c d^{3} e^{3} + 12 \, a c^{2} d^{3} e^{3} + b^{3} d^{2} e^{4} + 6 \, a b c d^{2} e^{4} + 2 \, a b^{2} d e^{5} + 2 \, a^{2} c d e^{5} + 3 \, a^{2} b e^{6}\right)} x\right)} e^{\left(-7\right)}}{20 \, {\left(x e + d\right)}^{5}}"," ",0,"c^3*x*e^(-6) - 3*(2*c^3*d - b*c^2*e)*e^(-7)*log(abs(x*e + d)) - 1/20*(174*c^3*d^6 - 137*b*c^2*d^5*e + 12*b^2*c*d^4*e^2 + 12*a*c^2*d^4*e^2 + b^3*d^3*e^3 + 6*a*b*c*d^3*e^3 + 2*a*b^2*d^2*e^4 + 2*a^2*c*d^2*e^4 + 60*(5*c^3*d^2*e^4 - 5*b*c^2*d*e^5 + b^2*c*e^6 + a*c^2*e^6)*x^4 + 3*a^2*b*d*e^5 + 10*(100*c^3*d^3*e^3 - 90*b*c^2*d^2*e^4 + 12*b^2*c*d*e^5 + 12*a*c^2*d*e^5 + b^3*e^6 + 6*a*b*c*e^6)*x^3 + 4*a^3*e^6 + 10*(130*c^3*d^4*e^2 - 110*b*c^2*d^3*e^3 + 12*b^2*c*d^2*e^4 + 12*a*c^2*d^2*e^4 + b^3*d*e^5 + 6*a*b*c*d*e^5 + 2*a*b^2*e^6 + 2*a^2*c*e^6)*x^2 + 5*(154*c^3*d^5*e - 125*b*c^2*d^4*e^2 + 12*b^2*c*d^3*e^3 + 12*a*c^2*d^3*e^3 + b^3*d^2*e^4 + 6*a*b*c*d^2*e^4 + 2*a*b^2*d*e^5 + 2*a^2*c*d*e^5 + 3*a^2*b*e^6)*x)*e^(-7)/(x*e + d)^5","A",0
2142,1,425,0,0.184878," ","integrate((c*x^2+b*x+a)^3/(e*x+d)^7,x, algorithm=""giac"")","c^{3} e^{\left(-7\right)} \log\left({\left| x e + d \right|}\right) + \frac{{\left(180 \, {\left(2 \, c^{3} d e^{4} - b c^{2} e^{5}\right)} x^{5} + 90 \, {\left(15 \, c^{3} d^{2} e^{3} - 5 \, b c^{2} d e^{4} - b^{2} c e^{5} - a c^{2} e^{5}\right)} x^{4} + 20 \, {\left(110 \, c^{3} d^{3} e^{2} - 30 \, b c^{2} d^{2} e^{3} - 6 \, b^{2} c d e^{4} - 6 \, a c^{2} d e^{4} - b^{3} e^{5} - 6 \, a b c e^{5}\right)} x^{3} + 15 \, {\left(125 \, c^{3} d^{4} e - 30 \, b c^{2} d^{3} e^{2} - 6 \, b^{2} c d^{2} e^{3} - 6 \, a c^{2} d^{2} e^{3} - b^{3} d e^{4} - 6 \, a b c d e^{4} - 3 \, a b^{2} e^{5} - 3 \, a^{2} c e^{5}\right)} x^{2} + 6 \, {\left(137 \, c^{3} d^{5} - 30 \, b c^{2} d^{4} e - 6 \, b^{2} c d^{3} e^{2} - 6 \, a c^{2} d^{3} e^{2} - b^{3} d^{2} e^{3} - 6 \, a b c d^{2} e^{3} - 3 \, a b^{2} d e^{4} - 3 \, a^{2} c d e^{4} - 6 \, a^{2} b e^{5}\right)} x + {\left(147 \, c^{3} d^{6} - 30 \, b c^{2} d^{5} e - 6 \, b^{2} c d^{4} e^{2} - 6 \, a c^{2} d^{4} e^{2} - b^{3} d^{3} e^{3} - 6 \, a b c d^{3} e^{3} - 3 \, a b^{2} d^{2} e^{4} - 3 \, a^{2} c d^{2} e^{4} - 6 \, a^{2} b d e^{5} - 10 \, a^{3} e^{6}\right)} e^{\left(-1\right)}\right)} e^{\left(-6\right)}}{60 \, {\left(x e + d\right)}^{6}}"," ",0,"c^3*e^(-7)*log(abs(x*e + d)) + 1/60*(180*(2*c^3*d*e^4 - b*c^2*e^5)*x^5 + 90*(15*c^3*d^2*e^3 - 5*b*c^2*d*e^4 - b^2*c*e^5 - a*c^2*e^5)*x^4 + 20*(110*c^3*d^3*e^2 - 30*b*c^2*d^2*e^3 - 6*b^2*c*d*e^4 - 6*a*c^2*d*e^4 - b^3*e^5 - 6*a*b*c*e^5)*x^3 + 15*(125*c^3*d^4*e - 30*b*c^2*d^3*e^2 - 6*b^2*c*d^2*e^3 - 6*a*c^2*d^2*e^3 - b^3*d*e^4 - 6*a*b*c*d*e^4 - 3*a*b^2*e^5 - 3*a^2*c*e^5)*x^2 + 6*(137*c^3*d^5 - 30*b*c^2*d^4*e - 6*b^2*c*d^3*e^2 - 6*a*c^2*d^3*e^2 - b^3*d^2*e^3 - 6*a*b*c*d^2*e^3 - 3*a*b^2*d*e^4 - 3*a^2*c*d*e^4 - 6*a^2*b*e^5)*x + (147*c^3*d^6 - 30*b*c^2*d^5*e - 6*b^2*c*d^4*e^2 - 6*a*c^2*d^4*e^2 - b^3*d^3*e^3 - 6*a*b*c*d^3*e^3 - 3*a*b^2*d^2*e^4 - 3*a^2*c*d^2*e^4 - 6*a^2*b*d*e^5 - 10*a^3*e^6)*e^(-1))*e^(-6)/(x*e + d)^6","A",0
2143,1,458,0,0.163700," ","integrate((c*x^2+b*x+a)^3/(e*x+d)^8,x, algorithm=""giac"")","-\frac{{\left(140 \, c^{3} x^{6} e^{6} + 420 \, c^{3} d x^{5} e^{5} + 700 \, c^{3} d^{2} x^{4} e^{4} + 700 \, c^{3} d^{3} x^{3} e^{3} + 420 \, c^{3} d^{4} x^{2} e^{2} + 140 \, c^{3} d^{5} x e + 20 \, c^{3} d^{6} + 210 \, b c^{2} x^{5} e^{6} + 350 \, b c^{2} d x^{4} e^{5} + 350 \, b c^{2} d^{2} x^{3} e^{4} + 210 \, b c^{2} d^{3} x^{2} e^{3} + 70 \, b c^{2} d^{4} x e^{2} + 10 \, b c^{2} d^{5} e + 140 \, b^{2} c x^{4} e^{6} + 140 \, a c^{2} x^{4} e^{6} + 140 \, b^{2} c d x^{3} e^{5} + 140 \, a c^{2} d x^{3} e^{5} + 84 \, b^{2} c d^{2} x^{2} e^{4} + 84 \, a c^{2} d^{2} x^{2} e^{4} + 28 \, b^{2} c d^{3} x e^{3} + 28 \, a c^{2} d^{3} x e^{3} + 4 \, b^{2} c d^{4} e^{2} + 4 \, a c^{2} d^{4} e^{2} + 35 \, b^{3} x^{3} e^{6} + 210 \, a b c x^{3} e^{6} + 21 \, b^{3} d x^{2} e^{5} + 126 \, a b c d x^{2} e^{5} + 7 \, b^{3} d^{2} x e^{4} + 42 \, a b c d^{2} x e^{4} + b^{3} d^{3} e^{3} + 6 \, a b c d^{3} e^{3} + 84 \, a b^{2} x^{2} e^{6} + 84 \, a^{2} c x^{2} e^{6} + 28 \, a b^{2} d x e^{5} + 28 \, a^{2} c d x e^{5} + 4 \, a b^{2} d^{2} e^{4} + 4 \, a^{2} c d^{2} e^{4} + 70 \, a^{2} b x e^{6} + 10 \, a^{2} b d e^{5} + 20 \, a^{3} e^{6}\right)} e^{\left(-7\right)}}{140 \, {\left(x e + d\right)}^{7}}"," ",0,"-1/140*(140*c^3*x^6*e^6 + 420*c^3*d*x^5*e^5 + 700*c^3*d^2*x^4*e^4 + 700*c^3*d^3*x^3*e^3 + 420*c^3*d^4*x^2*e^2 + 140*c^3*d^5*x*e + 20*c^3*d^6 + 210*b*c^2*x^5*e^6 + 350*b*c^2*d*x^4*e^5 + 350*b*c^2*d^2*x^3*e^4 + 210*b*c^2*d^3*x^2*e^3 + 70*b*c^2*d^4*x*e^2 + 10*b*c^2*d^5*e + 140*b^2*c*x^4*e^6 + 140*a*c^2*x^4*e^6 + 140*b^2*c*d*x^3*e^5 + 140*a*c^2*d*x^3*e^5 + 84*b^2*c*d^2*x^2*e^4 + 84*a*c^2*d^2*x^2*e^4 + 28*b^2*c*d^3*x*e^3 + 28*a*c^2*d^3*x*e^3 + 4*b^2*c*d^4*e^2 + 4*a*c^2*d^4*e^2 + 35*b^3*x^3*e^6 + 210*a*b*c*x^3*e^6 + 21*b^3*d*x^2*e^5 + 126*a*b*c*d*x^2*e^5 + 7*b^3*d^2*x*e^4 + 42*a*b*c*d^2*x*e^4 + b^3*d^3*e^3 + 6*a*b*c*d^3*e^3 + 84*a*b^2*x^2*e^6 + 84*a^2*c*x^2*e^6 + 28*a*b^2*d*x*e^5 + 28*a^2*c*d*x*e^5 + 4*a*b^2*d^2*e^4 + 4*a^2*c*d^2*e^4 + 70*a^2*b*x*e^6 + 10*a^2*b*d*e^5 + 20*a^3*e^6)*e^(-7)/(x*e + d)^7","A",0
2144,1,458,0,0.182099," ","integrate((c*x^2+b*x+a)^3/(e*x+d)^9,x, algorithm=""giac"")","-\frac{{\left(140 \, c^{3} x^{6} e^{6} + 280 \, c^{3} d x^{5} e^{5} + 350 \, c^{3} d^{2} x^{4} e^{4} + 280 \, c^{3} d^{3} x^{3} e^{3} + 140 \, c^{3} d^{4} x^{2} e^{2} + 40 \, c^{3} d^{5} x e + 5 \, c^{3} d^{6} + 280 \, b c^{2} x^{5} e^{6} + 350 \, b c^{2} d x^{4} e^{5} + 280 \, b c^{2} d^{2} x^{3} e^{4} + 140 \, b c^{2} d^{3} x^{2} e^{3} + 40 \, b c^{2} d^{4} x e^{2} + 5 \, b c^{2} d^{5} e + 210 \, b^{2} c x^{4} e^{6} + 210 \, a c^{2} x^{4} e^{6} + 168 \, b^{2} c d x^{3} e^{5} + 168 \, a c^{2} d x^{3} e^{5} + 84 \, b^{2} c d^{2} x^{2} e^{4} + 84 \, a c^{2} d^{2} x^{2} e^{4} + 24 \, b^{2} c d^{3} x e^{3} + 24 \, a c^{2} d^{3} x e^{3} + 3 \, b^{2} c d^{4} e^{2} + 3 \, a c^{2} d^{4} e^{2} + 56 \, b^{3} x^{3} e^{6} + 336 \, a b c x^{3} e^{6} + 28 \, b^{3} d x^{2} e^{5} + 168 \, a b c d x^{2} e^{5} + 8 \, b^{3} d^{2} x e^{4} + 48 \, a b c d^{2} x e^{4} + b^{3} d^{3} e^{3} + 6 \, a b c d^{3} e^{3} + 140 \, a b^{2} x^{2} e^{6} + 140 \, a^{2} c x^{2} e^{6} + 40 \, a b^{2} d x e^{5} + 40 \, a^{2} c d x e^{5} + 5 \, a b^{2} d^{2} e^{4} + 5 \, a^{2} c d^{2} e^{4} + 120 \, a^{2} b x e^{6} + 15 \, a^{2} b d e^{5} + 35 \, a^{3} e^{6}\right)} e^{\left(-7\right)}}{280 \, {\left(x e + d\right)}^{8}}"," ",0,"-1/280*(140*c^3*x^6*e^6 + 280*c^3*d*x^5*e^5 + 350*c^3*d^2*x^4*e^4 + 280*c^3*d^3*x^3*e^3 + 140*c^3*d^4*x^2*e^2 + 40*c^3*d^5*x*e + 5*c^3*d^6 + 280*b*c^2*x^5*e^6 + 350*b*c^2*d*x^4*e^5 + 280*b*c^2*d^2*x^3*e^4 + 140*b*c^2*d^3*x^2*e^3 + 40*b*c^2*d^4*x*e^2 + 5*b*c^2*d^5*e + 210*b^2*c*x^4*e^6 + 210*a*c^2*x^4*e^6 + 168*b^2*c*d*x^3*e^5 + 168*a*c^2*d*x^3*e^5 + 84*b^2*c*d^2*x^2*e^4 + 84*a*c^2*d^2*x^2*e^4 + 24*b^2*c*d^3*x*e^3 + 24*a*c^2*d^3*x*e^3 + 3*b^2*c*d^4*e^2 + 3*a*c^2*d^4*e^2 + 56*b^3*x^3*e^6 + 336*a*b*c*x^3*e^6 + 28*b^3*d*x^2*e^5 + 168*a*b*c*d*x^2*e^5 + 8*b^3*d^2*x*e^4 + 48*a*b*c*d^2*x*e^4 + b^3*d^3*e^3 + 6*a*b*c*d^3*e^3 + 140*a*b^2*x^2*e^6 + 140*a^2*c*x^2*e^6 + 40*a*b^2*d*x*e^5 + 40*a^2*c*d*x*e^5 + 5*a*b^2*d^2*e^4 + 5*a^2*c*d^2*e^4 + 120*a^2*b*x*e^6 + 15*a^2*b*d*e^5 + 35*a^3*e^6)*e^(-7)/(x*e + d)^8","A",0
2145,1,459,0,0.165167," ","integrate((c*x^2+b*x+a)^3/(e*x+d)^10,x, algorithm=""giac"")","-\frac{{\left(840 \, c^{3} x^{6} e^{6} + 1260 \, c^{3} d x^{5} e^{5} + 1260 \, c^{3} d^{2} x^{4} e^{4} + 840 \, c^{3} d^{3} x^{3} e^{3} + 360 \, c^{3} d^{4} x^{2} e^{2} + 90 \, c^{3} d^{5} x e + 10 \, c^{3} d^{6} + 1890 \, b c^{2} x^{5} e^{6} + 1890 \, b c^{2} d x^{4} e^{5} + 1260 \, b c^{2} d^{2} x^{3} e^{4} + 540 \, b c^{2} d^{3} x^{2} e^{3} + 135 \, b c^{2} d^{4} x e^{2} + 15 \, b c^{2} d^{5} e + 1512 \, b^{2} c x^{4} e^{6} + 1512 \, a c^{2} x^{4} e^{6} + 1008 \, b^{2} c d x^{3} e^{5} + 1008 \, a c^{2} d x^{3} e^{5} + 432 \, b^{2} c d^{2} x^{2} e^{4} + 432 \, a c^{2} d^{2} x^{2} e^{4} + 108 \, b^{2} c d^{3} x e^{3} + 108 \, a c^{2} d^{3} x e^{3} + 12 \, b^{2} c d^{4} e^{2} + 12 \, a c^{2} d^{4} e^{2} + 420 \, b^{3} x^{3} e^{6} + 2520 \, a b c x^{3} e^{6} + 180 \, b^{3} d x^{2} e^{5} + 1080 \, a b c d x^{2} e^{5} + 45 \, b^{3} d^{2} x e^{4} + 270 \, a b c d^{2} x e^{4} + 5 \, b^{3} d^{3} e^{3} + 30 \, a b c d^{3} e^{3} + 1080 \, a b^{2} x^{2} e^{6} + 1080 \, a^{2} c x^{2} e^{6} + 270 \, a b^{2} d x e^{5} + 270 \, a^{2} c d x e^{5} + 30 \, a b^{2} d^{2} e^{4} + 30 \, a^{2} c d^{2} e^{4} + 945 \, a^{2} b x e^{6} + 105 \, a^{2} b d e^{5} + 280 \, a^{3} e^{6}\right)} e^{\left(-7\right)}}{2520 \, {\left(x e + d\right)}^{9}}"," ",0,"-1/2520*(840*c^3*x^6*e^6 + 1260*c^3*d*x^5*e^5 + 1260*c^3*d^2*x^4*e^4 + 840*c^3*d^3*x^3*e^3 + 360*c^3*d^4*x^2*e^2 + 90*c^3*d^5*x*e + 10*c^3*d^6 + 1890*b*c^2*x^5*e^6 + 1890*b*c^2*d*x^4*e^5 + 1260*b*c^2*d^2*x^3*e^4 + 540*b*c^2*d^3*x^2*e^3 + 135*b*c^2*d^4*x*e^2 + 15*b*c^2*d^5*e + 1512*b^2*c*x^4*e^6 + 1512*a*c^2*x^4*e^6 + 1008*b^2*c*d*x^3*e^5 + 1008*a*c^2*d*x^3*e^5 + 432*b^2*c*d^2*x^2*e^4 + 432*a*c^2*d^2*x^2*e^4 + 108*b^2*c*d^3*x*e^3 + 108*a*c^2*d^3*x*e^3 + 12*b^2*c*d^4*e^2 + 12*a*c^2*d^4*e^2 + 420*b^3*x^3*e^6 + 2520*a*b*c*x^3*e^6 + 180*b^3*d*x^2*e^5 + 1080*a*b*c*d*x^2*e^5 + 45*b^3*d^2*x*e^4 + 270*a*b*c*d^2*x*e^4 + 5*b^3*d^3*e^3 + 30*a*b*c*d^3*e^3 + 1080*a*b^2*x^2*e^6 + 1080*a^2*c*x^2*e^6 + 270*a*b^2*d*x*e^5 + 270*a^2*c*d*x*e^5 + 30*a*b^2*d^2*e^4 + 30*a^2*c*d^2*e^4 + 945*a^2*b*x*e^6 + 105*a^2*b*d*e^5 + 280*a^3*e^6)*e^(-7)/(x*e + d)^9","A",0
2146,1,971,0,0.173893," ","integrate((e*x+d)^4*(c*x^2+b*x+a)^4,x, algorithm=""giac"")","\frac{1}{13} \, c^{4} x^{13} e^{4} + \frac{1}{3} \, c^{4} d x^{12} e^{3} + \frac{6}{11} \, c^{4} d^{2} x^{11} e^{2} + \frac{2}{5} \, c^{4} d^{3} x^{10} e + \frac{1}{9} \, c^{4} d^{4} x^{9} + \frac{1}{3} \, b c^{3} x^{12} e^{4} + \frac{16}{11} \, b c^{3} d x^{11} e^{3} + \frac{12}{5} \, b c^{3} d^{2} x^{10} e^{2} + \frac{16}{9} \, b c^{3} d^{3} x^{9} e + \frac{1}{2} \, b c^{3} d^{4} x^{8} + \frac{6}{11} \, b^{2} c^{2} x^{11} e^{4} + \frac{4}{11} \, a c^{3} x^{11} e^{4} + \frac{12}{5} \, b^{2} c^{2} d x^{10} e^{3} + \frac{8}{5} \, a c^{3} d x^{10} e^{3} + 4 \, b^{2} c^{2} d^{2} x^{9} e^{2} + \frac{8}{3} \, a c^{3} d^{2} x^{9} e^{2} + 3 \, b^{2} c^{2} d^{3} x^{8} e + 2 \, a c^{3} d^{3} x^{8} e + \frac{6}{7} \, b^{2} c^{2} d^{4} x^{7} + \frac{4}{7} \, a c^{3} d^{4} x^{7} + \frac{2}{5} \, b^{3} c x^{10} e^{4} + \frac{6}{5} \, a b c^{2} x^{10} e^{4} + \frac{16}{9} \, b^{3} c d x^{9} e^{3} + \frac{16}{3} \, a b c^{2} d x^{9} e^{3} + 3 \, b^{3} c d^{2} x^{8} e^{2} + 9 \, a b c^{2} d^{2} x^{8} e^{2} + \frac{16}{7} \, b^{3} c d^{3} x^{7} e + \frac{48}{7} \, a b c^{2} d^{3} x^{7} e + \frac{2}{3} \, b^{3} c d^{4} x^{6} + 2 \, a b c^{2} d^{4} x^{6} + \frac{1}{9} \, b^{4} x^{9} e^{4} + \frac{4}{3} \, a b^{2} c x^{9} e^{4} + \frac{2}{3} \, a^{2} c^{2} x^{9} e^{4} + \frac{1}{2} \, b^{4} d x^{8} e^{3} + 6 \, a b^{2} c d x^{8} e^{3} + 3 \, a^{2} c^{2} d x^{8} e^{3} + \frac{6}{7} \, b^{4} d^{2} x^{7} e^{2} + \frac{72}{7} \, a b^{2} c d^{2} x^{7} e^{2} + \frac{36}{7} \, a^{2} c^{2} d^{2} x^{7} e^{2} + \frac{2}{3} \, b^{4} d^{3} x^{6} e + 8 \, a b^{2} c d^{3} x^{6} e + 4 \, a^{2} c^{2} d^{3} x^{6} e + \frac{1}{5} \, b^{4} d^{4} x^{5} + \frac{12}{5} \, a b^{2} c d^{4} x^{5} + \frac{6}{5} \, a^{2} c^{2} d^{4} x^{5} + \frac{1}{2} \, a b^{3} x^{8} e^{4} + \frac{3}{2} \, a^{2} b c x^{8} e^{4} + \frac{16}{7} \, a b^{3} d x^{7} e^{3} + \frac{48}{7} \, a^{2} b c d x^{7} e^{3} + 4 \, a b^{3} d^{2} x^{6} e^{2} + 12 \, a^{2} b c d^{2} x^{6} e^{2} + \frac{16}{5} \, a b^{3} d^{3} x^{5} e + \frac{48}{5} \, a^{2} b c d^{3} x^{5} e + a b^{3} d^{4} x^{4} + 3 \, a^{2} b c d^{4} x^{4} + \frac{6}{7} \, a^{2} b^{2} x^{7} e^{4} + \frac{4}{7} \, a^{3} c x^{7} e^{4} + 4 \, a^{2} b^{2} d x^{6} e^{3} + \frac{8}{3} \, a^{3} c d x^{6} e^{3} + \frac{36}{5} \, a^{2} b^{2} d^{2} x^{5} e^{2} + \frac{24}{5} \, a^{3} c d^{2} x^{5} e^{2} + 6 \, a^{2} b^{2} d^{3} x^{4} e + 4 \, a^{3} c d^{3} x^{4} e + 2 \, a^{2} b^{2} d^{4} x^{3} + \frac{4}{3} \, a^{3} c d^{4} x^{3} + \frac{2}{3} \, a^{3} b x^{6} e^{4} + \frac{16}{5} \, a^{3} b d x^{5} e^{3} + 6 \, a^{3} b d^{2} x^{4} e^{2} + \frac{16}{3} \, a^{3} b d^{3} x^{3} e + 2 \, a^{3} b d^{4} x^{2} + \frac{1}{5} \, a^{4} x^{5} e^{4} + a^{4} d x^{4} e^{3} + 2 \, a^{4} d^{2} x^{3} e^{2} + 2 \, a^{4} d^{3} x^{2} e + a^{4} d^{4} x"," ",0,"1/13*c^4*x^13*e^4 + 1/3*c^4*d*x^12*e^3 + 6/11*c^4*d^2*x^11*e^2 + 2/5*c^4*d^3*x^10*e + 1/9*c^4*d^4*x^9 + 1/3*b*c^3*x^12*e^4 + 16/11*b*c^3*d*x^11*e^3 + 12/5*b*c^3*d^2*x^10*e^2 + 16/9*b*c^3*d^3*x^9*e + 1/2*b*c^3*d^4*x^8 + 6/11*b^2*c^2*x^11*e^4 + 4/11*a*c^3*x^11*e^4 + 12/5*b^2*c^2*d*x^10*e^3 + 8/5*a*c^3*d*x^10*e^3 + 4*b^2*c^2*d^2*x^9*e^2 + 8/3*a*c^3*d^2*x^9*e^2 + 3*b^2*c^2*d^3*x^8*e + 2*a*c^3*d^3*x^8*e + 6/7*b^2*c^2*d^4*x^7 + 4/7*a*c^3*d^4*x^7 + 2/5*b^3*c*x^10*e^4 + 6/5*a*b*c^2*x^10*e^4 + 16/9*b^3*c*d*x^9*e^3 + 16/3*a*b*c^2*d*x^9*e^3 + 3*b^3*c*d^2*x^8*e^2 + 9*a*b*c^2*d^2*x^8*e^2 + 16/7*b^3*c*d^3*x^7*e + 48/7*a*b*c^2*d^3*x^7*e + 2/3*b^3*c*d^4*x^6 + 2*a*b*c^2*d^4*x^6 + 1/9*b^4*x^9*e^4 + 4/3*a*b^2*c*x^9*e^4 + 2/3*a^2*c^2*x^9*e^4 + 1/2*b^4*d*x^8*e^3 + 6*a*b^2*c*d*x^8*e^3 + 3*a^2*c^2*d*x^8*e^3 + 6/7*b^4*d^2*x^7*e^2 + 72/7*a*b^2*c*d^2*x^7*e^2 + 36/7*a^2*c^2*d^2*x^7*e^2 + 2/3*b^4*d^3*x^6*e + 8*a*b^2*c*d^3*x^6*e + 4*a^2*c^2*d^3*x^6*e + 1/5*b^4*d^4*x^5 + 12/5*a*b^2*c*d^4*x^5 + 6/5*a^2*c^2*d^4*x^5 + 1/2*a*b^3*x^8*e^4 + 3/2*a^2*b*c*x^8*e^4 + 16/7*a*b^3*d*x^7*e^3 + 48/7*a^2*b*c*d*x^7*e^3 + 4*a*b^3*d^2*x^6*e^2 + 12*a^2*b*c*d^2*x^6*e^2 + 16/5*a*b^3*d^3*x^5*e + 48/5*a^2*b*c*d^3*x^5*e + a*b^3*d^4*x^4 + 3*a^2*b*c*d^4*x^4 + 6/7*a^2*b^2*x^7*e^4 + 4/7*a^3*c*x^7*e^4 + 4*a^2*b^2*d*x^6*e^3 + 8/3*a^3*c*d*x^6*e^3 + 36/5*a^2*b^2*d^2*x^5*e^2 + 24/5*a^3*c*d^2*x^5*e^2 + 6*a^2*b^2*d^3*x^4*e + 4*a^3*c*d^3*x^4*e + 2*a^2*b^2*d^4*x^3 + 4/3*a^3*c*d^4*x^3 + 2/3*a^3*b*x^6*e^4 + 16/5*a^3*b*d*x^5*e^3 + 6*a^3*b*d^2*x^4*e^2 + 16/3*a^3*b*d^3*x^3*e + 2*a^3*b*d^4*x^2 + 1/5*a^4*x^5*e^4 + a^4*d*x^4*e^3 + 2*a^4*d^2*x^3*e^2 + 2*a^4*d^3*x^2*e + a^4*d^4*x","B",0
2147,1,754,0,0.171037," ","integrate((e*x+d)^3*(c*x^2+b*x+a)^4,x, algorithm=""giac"")","\frac{1}{12} \, c^{4} x^{12} e^{3} + \frac{3}{11} \, c^{4} d x^{11} e^{2} + \frac{3}{10} \, c^{4} d^{2} x^{10} e + \frac{1}{9} \, c^{4} d^{3} x^{9} + \frac{4}{11} \, b c^{3} x^{11} e^{3} + \frac{6}{5} \, b c^{3} d x^{10} e^{2} + \frac{4}{3} \, b c^{3} d^{2} x^{9} e + \frac{1}{2} \, b c^{3} d^{3} x^{8} + \frac{3}{5} \, b^{2} c^{2} x^{10} e^{3} + \frac{2}{5} \, a c^{3} x^{10} e^{3} + 2 \, b^{2} c^{2} d x^{9} e^{2} + \frac{4}{3} \, a c^{3} d x^{9} e^{2} + \frac{9}{4} \, b^{2} c^{2} d^{2} x^{8} e + \frac{3}{2} \, a c^{3} d^{2} x^{8} e + \frac{6}{7} \, b^{2} c^{2} d^{3} x^{7} + \frac{4}{7} \, a c^{3} d^{3} x^{7} + \frac{4}{9} \, b^{3} c x^{9} e^{3} + \frac{4}{3} \, a b c^{2} x^{9} e^{3} + \frac{3}{2} \, b^{3} c d x^{8} e^{2} + \frac{9}{2} \, a b c^{2} d x^{8} e^{2} + \frac{12}{7} \, b^{3} c d^{2} x^{7} e + \frac{36}{7} \, a b c^{2} d^{2} x^{7} e + \frac{2}{3} \, b^{3} c d^{3} x^{6} + 2 \, a b c^{2} d^{3} x^{6} + \frac{1}{8} \, b^{4} x^{8} e^{3} + \frac{3}{2} \, a b^{2} c x^{8} e^{3} + \frac{3}{4} \, a^{2} c^{2} x^{8} e^{3} + \frac{3}{7} \, b^{4} d x^{7} e^{2} + \frac{36}{7} \, a b^{2} c d x^{7} e^{2} + \frac{18}{7} \, a^{2} c^{2} d x^{7} e^{2} + \frac{1}{2} \, b^{4} d^{2} x^{6} e + 6 \, a b^{2} c d^{2} x^{6} e + 3 \, a^{2} c^{2} d^{2} x^{6} e + \frac{1}{5} \, b^{4} d^{3} x^{5} + \frac{12}{5} \, a b^{2} c d^{3} x^{5} + \frac{6}{5} \, a^{2} c^{2} d^{3} x^{5} + \frac{4}{7} \, a b^{3} x^{7} e^{3} + \frac{12}{7} \, a^{2} b c x^{7} e^{3} + 2 \, a b^{3} d x^{6} e^{2} + 6 \, a^{2} b c d x^{6} e^{2} + \frac{12}{5} \, a b^{3} d^{2} x^{5} e + \frac{36}{5} \, a^{2} b c d^{2} x^{5} e + a b^{3} d^{3} x^{4} + 3 \, a^{2} b c d^{3} x^{4} + a^{2} b^{2} x^{6} e^{3} + \frac{2}{3} \, a^{3} c x^{6} e^{3} + \frac{18}{5} \, a^{2} b^{2} d x^{5} e^{2} + \frac{12}{5} \, a^{3} c d x^{5} e^{2} + \frac{9}{2} \, a^{2} b^{2} d^{2} x^{4} e + 3 \, a^{3} c d^{2} x^{4} e + 2 \, a^{2} b^{2} d^{3} x^{3} + \frac{4}{3} \, a^{3} c d^{3} x^{3} + \frac{4}{5} \, a^{3} b x^{5} e^{3} + 3 \, a^{3} b d x^{4} e^{2} + 4 \, a^{3} b d^{2} x^{3} e + 2 \, a^{3} b d^{3} x^{2} + \frac{1}{4} \, a^{4} x^{4} e^{3} + a^{4} d x^{3} e^{2} + \frac{3}{2} \, a^{4} d^{2} x^{2} e + a^{4} d^{3} x"," ",0,"1/12*c^4*x^12*e^3 + 3/11*c^4*d*x^11*e^2 + 3/10*c^4*d^2*x^10*e + 1/9*c^4*d^3*x^9 + 4/11*b*c^3*x^11*e^3 + 6/5*b*c^3*d*x^10*e^2 + 4/3*b*c^3*d^2*x^9*e + 1/2*b*c^3*d^3*x^8 + 3/5*b^2*c^2*x^10*e^3 + 2/5*a*c^3*x^10*e^3 + 2*b^2*c^2*d*x^9*e^2 + 4/3*a*c^3*d*x^9*e^2 + 9/4*b^2*c^2*d^2*x^8*e + 3/2*a*c^3*d^2*x^8*e + 6/7*b^2*c^2*d^3*x^7 + 4/7*a*c^3*d^3*x^7 + 4/9*b^3*c*x^9*e^3 + 4/3*a*b*c^2*x^9*e^3 + 3/2*b^3*c*d*x^8*e^2 + 9/2*a*b*c^2*d*x^8*e^2 + 12/7*b^3*c*d^2*x^7*e + 36/7*a*b*c^2*d^2*x^7*e + 2/3*b^3*c*d^3*x^6 + 2*a*b*c^2*d^3*x^6 + 1/8*b^4*x^8*e^3 + 3/2*a*b^2*c*x^8*e^3 + 3/4*a^2*c^2*x^8*e^3 + 3/7*b^4*d*x^7*e^2 + 36/7*a*b^2*c*d*x^7*e^2 + 18/7*a^2*c^2*d*x^7*e^2 + 1/2*b^4*d^2*x^6*e + 6*a*b^2*c*d^2*x^6*e + 3*a^2*c^2*d^2*x^6*e + 1/5*b^4*d^3*x^5 + 12/5*a*b^2*c*d^3*x^5 + 6/5*a^2*c^2*d^3*x^5 + 4/7*a*b^3*x^7*e^3 + 12/7*a^2*b*c*x^7*e^3 + 2*a*b^3*d*x^6*e^2 + 6*a^2*b*c*d*x^6*e^2 + 12/5*a*b^3*d^2*x^5*e + 36/5*a^2*b*c*d^2*x^5*e + a*b^3*d^3*x^4 + 3*a^2*b*c*d^3*x^4 + a^2*b^2*x^6*e^3 + 2/3*a^3*c*x^6*e^3 + 18/5*a^2*b^2*d*x^5*e^2 + 12/5*a^3*c*d*x^5*e^2 + 9/2*a^2*b^2*d^2*x^4*e + 3*a^3*c*d^2*x^4*e + 2*a^2*b^2*d^3*x^3 + 4/3*a^3*c*d^3*x^3 + 4/5*a^3*b*x^5*e^3 + 3*a^3*b*d*x^4*e^2 + 4*a^3*b*d^2*x^3*e + 2*a^3*b*d^3*x^2 + 1/4*a^4*x^4*e^3 + a^4*d*x^3*e^2 + 3/2*a^4*d^2*x^2*e + a^4*d^3*x","A",0
2148,1,537,0,0.159636," ","integrate((e*x+d)^2*(c*x^2+b*x+a)^4,x, algorithm=""giac"")","\frac{1}{11} \, c^{4} x^{11} e^{2} + \frac{1}{5} \, c^{4} d x^{10} e + \frac{1}{9} \, c^{4} d^{2} x^{9} + \frac{2}{5} \, b c^{3} x^{10} e^{2} + \frac{8}{9} \, b c^{3} d x^{9} e + \frac{1}{2} \, b c^{3} d^{2} x^{8} + \frac{2}{3} \, b^{2} c^{2} x^{9} e^{2} + \frac{4}{9} \, a c^{3} x^{9} e^{2} + \frac{3}{2} \, b^{2} c^{2} d x^{8} e + a c^{3} d x^{8} e + \frac{6}{7} \, b^{2} c^{2} d^{2} x^{7} + \frac{4}{7} \, a c^{3} d^{2} x^{7} + \frac{1}{2} \, b^{3} c x^{8} e^{2} + \frac{3}{2} \, a b c^{2} x^{8} e^{2} + \frac{8}{7} \, b^{3} c d x^{7} e + \frac{24}{7} \, a b c^{2} d x^{7} e + \frac{2}{3} \, b^{3} c d^{2} x^{6} + 2 \, a b c^{2} d^{2} x^{6} + \frac{1}{7} \, b^{4} x^{7} e^{2} + \frac{12}{7} \, a b^{2} c x^{7} e^{2} + \frac{6}{7} \, a^{2} c^{2} x^{7} e^{2} + \frac{1}{3} \, b^{4} d x^{6} e + 4 \, a b^{2} c d x^{6} e + 2 \, a^{2} c^{2} d x^{6} e + \frac{1}{5} \, b^{4} d^{2} x^{5} + \frac{12}{5} \, a b^{2} c d^{2} x^{5} + \frac{6}{5} \, a^{2} c^{2} d^{2} x^{5} + \frac{2}{3} \, a b^{3} x^{6} e^{2} + 2 \, a^{2} b c x^{6} e^{2} + \frac{8}{5} \, a b^{3} d x^{5} e + \frac{24}{5} \, a^{2} b c d x^{5} e + a b^{3} d^{2} x^{4} + 3 \, a^{2} b c d^{2} x^{4} + \frac{6}{5} \, a^{2} b^{2} x^{5} e^{2} + \frac{4}{5} \, a^{3} c x^{5} e^{2} + 3 \, a^{2} b^{2} d x^{4} e + 2 \, a^{3} c d x^{4} e + 2 \, a^{2} b^{2} d^{2} x^{3} + \frac{4}{3} \, a^{3} c d^{2} x^{3} + a^{3} b x^{4} e^{2} + \frac{8}{3} \, a^{3} b d x^{3} e + 2 \, a^{3} b d^{2} x^{2} + \frac{1}{3} \, a^{4} x^{3} e^{2} + a^{4} d x^{2} e + a^{4} d^{2} x"," ",0,"1/11*c^4*x^11*e^2 + 1/5*c^4*d*x^10*e + 1/9*c^4*d^2*x^9 + 2/5*b*c^3*x^10*e^2 + 8/9*b*c^3*d*x^9*e + 1/2*b*c^3*d^2*x^8 + 2/3*b^2*c^2*x^9*e^2 + 4/9*a*c^3*x^9*e^2 + 3/2*b^2*c^2*d*x^8*e + a*c^3*d*x^8*e + 6/7*b^2*c^2*d^2*x^7 + 4/7*a*c^3*d^2*x^7 + 1/2*b^3*c*x^8*e^2 + 3/2*a*b*c^2*x^8*e^2 + 8/7*b^3*c*d*x^7*e + 24/7*a*b*c^2*d*x^7*e + 2/3*b^3*c*d^2*x^6 + 2*a*b*c^2*d^2*x^6 + 1/7*b^4*x^7*e^2 + 12/7*a*b^2*c*x^7*e^2 + 6/7*a^2*c^2*x^7*e^2 + 1/3*b^4*d*x^6*e + 4*a*b^2*c*d*x^6*e + 2*a^2*c^2*d*x^6*e + 1/5*b^4*d^2*x^5 + 12/5*a*b^2*c*d^2*x^5 + 6/5*a^2*c^2*d^2*x^5 + 2/3*a*b^3*x^6*e^2 + 2*a^2*b*c*x^6*e^2 + 8/5*a*b^3*d*x^5*e + 24/5*a^2*b*c*d*x^5*e + a*b^3*d^2*x^4 + 3*a^2*b*c*d^2*x^4 + 6/5*a^2*b^2*x^5*e^2 + 4/5*a^3*c*x^5*e^2 + 3*a^2*b^2*d*x^4*e + 2*a^3*c*d*x^4*e + 2*a^2*b^2*d^2*x^3 + 4/3*a^3*c*d^2*x^3 + a^3*b*x^4*e^2 + 8/3*a^3*b*d*x^3*e + 2*a^3*b*d^2*x^2 + 1/3*a^4*x^3*e^2 + a^4*d*x^2*e + a^4*d^2*x","A",0
2149,1,322,0,0.169422," ","integrate((e*x+d)*(c*x^2+b*x+a)^4,x, algorithm=""giac"")","\frac{1}{10} \, c^{4} x^{10} e + \frac{1}{9} \, c^{4} d x^{9} + \frac{4}{9} \, b c^{3} x^{9} e + \frac{1}{2} \, b c^{3} d x^{8} + \frac{3}{4} \, b^{2} c^{2} x^{8} e + \frac{1}{2} \, a c^{3} x^{8} e + \frac{6}{7} \, b^{2} c^{2} d x^{7} + \frac{4}{7} \, a c^{3} d x^{7} + \frac{4}{7} \, b^{3} c x^{7} e + \frac{12}{7} \, a b c^{2} x^{7} e + \frac{2}{3} \, b^{3} c d x^{6} + 2 \, a b c^{2} d x^{6} + \frac{1}{6} \, b^{4} x^{6} e + 2 \, a b^{2} c x^{6} e + a^{2} c^{2} x^{6} e + \frac{1}{5} \, b^{4} d x^{5} + \frac{12}{5} \, a b^{2} c d x^{5} + \frac{6}{5} \, a^{2} c^{2} d x^{5} + \frac{4}{5} \, a b^{3} x^{5} e + \frac{12}{5} \, a^{2} b c x^{5} e + a b^{3} d x^{4} + 3 \, a^{2} b c d x^{4} + \frac{3}{2} \, a^{2} b^{2} x^{4} e + a^{3} c x^{4} e + 2 \, a^{2} b^{2} d x^{3} + \frac{4}{3} \, a^{3} c d x^{3} + \frac{4}{3} \, a^{3} b x^{3} e + 2 \, a^{3} b d x^{2} + \frac{1}{2} \, a^{4} x^{2} e + a^{4} d x"," ",0,"1/10*c^4*x^10*e + 1/9*c^4*d*x^9 + 4/9*b*c^3*x^9*e + 1/2*b*c^3*d*x^8 + 3/4*b^2*c^2*x^8*e + 1/2*a*c^3*x^8*e + 6/7*b^2*c^2*d*x^7 + 4/7*a*c^3*d*x^7 + 4/7*b^3*c*x^7*e + 12/7*a*b*c^2*x^7*e + 2/3*b^3*c*d*x^6 + 2*a*b*c^2*d*x^6 + 1/6*b^4*x^6*e + 2*a*b^2*c*x^6*e + a^2*c^2*x^6*e + 1/5*b^4*d*x^5 + 12/5*a*b^2*c*d*x^5 + 6/5*a^2*c^2*d*x^5 + 4/5*a*b^3*x^5*e + 12/5*a^2*b*c*x^5*e + a*b^3*d*x^4 + 3*a^2*b*c*d*x^4 + 3/2*a^2*b^2*x^4*e + a^3*c*x^4*e + 2*a^2*b^2*d*x^3 + 4/3*a^3*c*d*x^3 + 4/3*a^3*b*x^3*e + 2*a^3*b*d*x^2 + 1/2*a^4*x^2*e + a^4*d*x","A",0
2150,1,138,0,0.151655," ","integrate((c*x^2+b*x+a)^4,x, algorithm=""giac"")","\frac{1}{9} \, c^{4} x^{9} + \frac{1}{2} \, b c^{3} x^{8} + \frac{6}{7} \, b^{2} c^{2} x^{7} + \frac{4}{7} \, a c^{3} x^{7} + \frac{2}{3} \, b^{3} c x^{6} + 2 \, a b c^{2} x^{6} + \frac{1}{5} \, b^{4} x^{5} + \frac{12}{5} \, a b^{2} c x^{5} + \frac{6}{5} \, a^{2} c^{2} x^{5} + a b^{3} x^{4} + 3 \, a^{2} b c x^{4} + 2 \, a^{2} b^{2} x^{3} + \frac{4}{3} \, a^{3} c x^{3} + 2 \, a^{3} b x^{2} + a^{4} x"," ",0,"1/9*c^4*x^9 + 1/2*b*c^3*x^8 + 6/7*b^2*c^2*x^7 + 4/7*a*c^3*x^7 + 2/3*b^3*c*x^6 + 2*a*b*c^2*x^6 + 1/5*b^4*x^5 + 12/5*a*b^2*c*x^5 + 6/5*a^2*c^2*x^5 + a*b^3*x^4 + 3*a^2*b*c*x^4 + 2*a^2*b^2*x^3 + 4/3*a^3*c*x^3 + 2*a^3*b*x^2 + a^4*x","A",0
2151,1,945,0,0.170033," ","integrate((c*x^2+b*x+a)^4/(e*x+d),x, algorithm=""giac"")","{\left(c^{4} d^{8} - 4 \, b c^{3} d^{7} e + 6 \, b^{2} c^{2} d^{6} e^{2} + 4 \, a c^{3} d^{6} e^{2} - 4 \, b^{3} c d^{5} e^{3} - 12 \, a b c^{2} d^{5} e^{3} + b^{4} d^{4} e^{4} + 12 \, a b^{2} c d^{4} e^{4} + 6 \, a^{2} c^{2} d^{4} e^{4} - 4 \, a b^{3} d^{3} e^{5} - 12 \, a^{2} b c d^{3} e^{5} + 6 \, a^{2} b^{2} d^{2} e^{6} + 4 \, a^{3} c d^{2} e^{6} - 4 \, a^{3} b d e^{7} + a^{4} e^{8}\right)} e^{\left(-9\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{840} \, {\left(105 \, c^{4} x^{8} e^{7} - 120 \, c^{4} d x^{7} e^{6} + 140 \, c^{4} d^{2} x^{6} e^{5} - 168 \, c^{4} d^{3} x^{5} e^{4} + 210 \, c^{4} d^{4} x^{4} e^{3} - 280 \, c^{4} d^{5} x^{3} e^{2} + 420 \, c^{4} d^{6} x^{2} e - 840 \, c^{4} d^{7} x + 480 \, b c^{3} x^{7} e^{7} - 560 \, b c^{3} d x^{6} e^{6} + 672 \, b c^{3} d^{2} x^{5} e^{5} - 840 \, b c^{3} d^{3} x^{4} e^{4} + 1120 \, b c^{3} d^{4} x^{3} e^{3} - 1680 \, b c^{3} d^{5} x^{2} e^{2} + 3360 \, b c^{3} d^{6} x e + 840 \, b^{2} c^{2} x^{6} e^{7} + 560 \, a c^{3} x^{6} e^{7} - 1008 \, b^{2} c^{2} d x^{5} e^{6} - 672 \, a c^{3} d x^{5} e^{6} + 1260 \, b^{2} c^{2} d^{2} x^{4} e^{5} + 840 \, a c^{3} d^{2} x^{4} e^{5} - 1680 \, b^{2} c^{2} d^{3} x^{3} e^{4} - 1120 \, a c^{3} d^{3} x^{3} e^{4} + 2520 \, b^{2} c^{2} d^{4} x^{2} e^{3} + 1680 \, a c^{3} d^{4} x^{2} e^{3} - 5040 \, b^{2} c^{2} d^{5} x e^{2} - 3360 \, a c^{3} d^{5} x e^{2} + 672 \, b^{3} c x^{5} e^{7} + 2016 \, a b c^{2} x^{5} e^{7} - 840 \, b^{3} c d x^{4} e^{6} - 2520 \, a b c^{2} d x^{4} e^{6} + 1120 \, b^{3} c d^{2} x^{3} e^{5} + 3360 \, a b c^{2} d^{2} x^{3} e^{5} - 1680 \, b^{3} c d^{3} x^{2} e^{4} - 5040 \, a b c^{2} d^{3} x^{2} e^{4} + 3360 \, b^{3} c d^{4} x e^{3} + 10080 \, a b c^{2} d^{4} x e^{3} + 210 \, b^{4} x^{4} e^{7} + 2520 \, a b^{2} c x^{4} e^{7} + 1260 \, a^{2} c^{2} x^{4} e^{7} - 280 \, b^{4} d x^{3} e^{6} - 3360 \, a b^{2} c d x^{3} e^{6} - 1680 \, a^{2} c^{2} d x^{3} e^{6} + 420 \, b^{4} d^{2} x^{2} e^{5} + 5040 \, a b^{2} c d^{2} x^{2} e^{5} + 2520 \, a^{2} c^{2} d^{2} x^{2} e^{5} - 840 \, b^{4} d^{3} x e^{4} - 10080 \, a b^{2} c d^{3} x e^{4} - 5040 \, a^{2} c^{2} d^{3} x e^{4} + 1120 \, a b^{3} x^{3} e^{7} + 3360 \, a^{2} b c x^{3} e^{7} - 1680 \, a b^{3} d x^{2} e^{6} - 5040 \, a^{2} b c d x^{2} e^{6} + 3360 \, a b^{3} d^{2} x e^{5} + 10080 \, a^{2} b c d^{2} x e^{5} + 2520 \, a^{2} b^{2} x^{2} e^{7} + 1680 \, a^{3} c x^{2} e^{7} - 5040 \, a^{2} b^{2} d x e^{6} - 3360 \, a^{3} c d x e^{6} + 3360 \, a^{3} b x e^{7}\right)} e^{\left(-8\right)}"," ",0,"(c^4*d^8 - 4*b*c^3*d^7*e + 6*b^2*c^2*d^6*e^2 + 4*a*c^3*d^6*e^2 - 4*b^3*c*d^5*e^3 - 12*a*b*c^2*d^5*e^3 + b^4*d^4*e^4 + 12*a*b^2*c*d^4*e^4 + 6*a^2*c^2*d^4*e^4 - 4*a*b^3*d^3*e^5 - 12*a^2*b*c*d^3*e^5 + 6*a^2*b^2*d^2*e^6 + 4*a^3*c*d^2*e^6 - 4*a^3*b*d*e^7 + a^4*e^8)*e^(-9)*log(abs(x*e + d)) + 1/840*(105*c^4*x^8*e^7 - 120*c^4*d*x^7*e^6 + 140*c^4*d^2*x^6*e^5 - 168*c^4*d^3*x^5*e^4 + 210*c^4*d^4*x^4*e^3 - 280*c^4*d^5*x^3*e^2 + 420*c^4*d^6*x^2*e - 840*c^4*d^7*x + 480*b*c^3*x^7*e^7 - 560*b*c^3*d*x^6*e^6 + 672*b*c^3*d^2*x^5*e^5 - 840*b*c^3*d^3*x^4*e^4 + 1120*b*c^3*d^4*x^3*e^3 - 1680*b*c^3*d^5*x^2*e^2 + 3360*b*c^3*d^6*x*e + 840*b^2*c^2*x^6*e^7 + 560*a*c^3*x^6*e^7 - 1008*b^2*c^2*d*x^5*e^6 - 672*a*c^3*d*x^5*e^6 + 1260*b^2*c^2*d^2*x^4*e^5 + 840*a*c^3*d^2*x^4*e^5 - 1680*b^2*c^2*d^3*x^3*e^4 - 1120*a*c^3*d^3*x^3*e^4 + 2520*b^2*c^2*d^4*x^2*e^3 + 1680*a*c^3*d^4*x^2*e^3 - 5040*b^2*c^2*d^5*x*e^2 - 3360*a*c^3*d^5*x*e^2 + 672*b^3*c*x^5*e^7 + 2016*a*b*c^2*x^5*e^7 - 840*b^3*c*d*x^4*e^6 - 2520*a*b*c^2*d*x^4*e^6 + 1120*b^3*c*d^2*x^3*e^5 + 3360*a*b*c^2*d^2*x^3*e^5 - 1680*b^3*c*d^3*x^2*e^4 - 5040*a*b*c^2*d^3*x^2*e^4 + 3360*b^3*c*d^4*x*e^3 + 10080*a*b*c^2*d^4*x*e^3 + 210*b^4*x^4*e^7 + 2520*a*b^2*c*x^4*e^7 + 1260*a^2*c^2*x^4*e^7 - 280*b^4*d*x^3*e^6 - 3360*a*b^2*c*d*x^3*e^6 - 1680*a^2*c^2*d*x^3*e^6 + 420*b^4*d^2*x^2*e^5 + 5040*a*b^2*c*d^2*x^2*e^5 + 2520*a^2*c^2*d^2*x^2*e^5 - 840*b^4*d^3*x*e^4 - 10080*a*b^2*c*d^3*x*e^4 - 5040*a^2*c^2*d^3*x*e^4 + 1120*a*b^3*x^3*e^7 + 3360*a^2*b*c*x^3*e^7 - 1680*a*b^3*d*x^2*e^6 - 5040*a^2*b*c*d*x^2*e^6 + 3360*a*b^3*d^2*x*e^5 + 10080*a^2*b*c*d^2*x*e^5 + 2520*a^2*b^2*x^2*e^7 + 1680*a^3*c*x^2*e^7 - 5040*a^2*b^2*d*x*e^6 - 3360*a^3*c*d*x*e^6 + 3360*a^3*b*x*e^7)*e^(-8)","B",0
2152,1,1013,0,0.195346," ","integrate((c*x^2+b*x+a)^4/(e*x+d)^2,x, algorithm=""giac"")","\frac{1}{105} \, {\left(15 \, c^{4} - \frac{70 \, {\left(2 \, c^{4} d e - b c^{3} e^{2}\right)} e^{\left(-1\right)}}{x e + d} + \frac{42 \, {\left(14 \, c^{4} d^{2} e^{2} - 14 \, b c^{3} d e^{3} + 3 \, b^{2} c^{2} e^{4} + 2 \, a c^{3} e^{4}\right)} e^{\left(-2\right)}}{{\left(x e + d\right)}^{2}} - \frac{105 \, {\left(14 \, c^{4} d^{3} e^{3} - 21 \, b c^{3} d^{2} e^{4} + 9 \, b^{2} c^{2} d e^{5} + 6 \, a c^{3} d e^{5} - b^{3} c e^{6} - 3 \, a b c^{2} e^{6}\right)} e^{\left(-3\right)}}{{\left(x e + d\right)}^{3}} + \frac{35 \, {\left(70 \, c^{4} d^{4} e^{4} - 140 \, b c^{3} d^{3} e^{5} + 90 \, b^{2} c^{2} d^{2} e^{6} + 60 \, a c^{3} d^{2} e^{6} - 20 \, b^{3} c d e^{7} - 60 \, a b c^{2} d e^{7} + b^{4} e^{8} + 12 \, a b^{2} c e^{8} + 6 \, a^{2} c^{2} e^{8}\right)} e^{\left(-4\right)}}{{\left(x e + d\right)}^{4}} - \frac{210 \, {\left(14 \, c^{4} d^{5} e^{5} - 35 \, b c^{3} d^{4} e^{6} + 30 \, b^{2} c^{2} d^{3} e^{7} + 20 \, a c^{3} d^{3} e^{7} - 10 \, b^{3} c d^{2} e^{8} - 30 \, a b c^{2} d^{2} e^{8} + b^{4} d e^{9} + 12 \, a b^{2} c d e^{9} + 6 \, a^{2} c^{2} d e^{9} - a b^{3} e^{10} - 3 \, a^{2} b c e^{10}\right)} e^{\left(-5\right)}}{{\left(x e + d\right)}^{5}} + \frac{210 \, {\left(14 \, c^{4} d^{6} e^{6} - 42 \, b c^{3} d^{5} e^{7} + 45 \, b^{2} c^{2} d^{4} e^{8} + 30 \, a c^{3} d^{4} e^{8} - 20 \, b^{3} c d^{3} e^{9} - 60 \, a b c^{2} d^{3} e^{9} + 3 \, b^{4} d^{2} e^{10} + 36 \, a b^{2} c d^{2} e^{10} + 18 \, a^{2} c^{2} d^{2} e^{10} - 6 \, a b^{3} d e^{11} - 18 \, a^{2} b c d e^{11} + 3 \, a^{2} b^{2} e^{12} + 2 \, a^{3} c e^{12}\right)} e^{\left(-6\right)}}{{\left(x e + d\right)}^{6}}\right)} {\left(x e + d\right)}^{7} e^{\left(-9\right)} + 4 \, {\left(2 \, c^{4} d^{7} - 7 \, b c^{3} d^{6} e + 9 \, b^{2} c^{2} d^{5} e^{2} + 6 \, a c^{3} d^{5} e^{2} - 5 \, b^{3} c d^{4} e^{3} - 15 \, a b c^{2} d^{4} e^{3} + b^{4} d^{3} e^{4} + 12 \, a b^{2} c d^{3} e^{4} + 6 \, a^{2} c^{2} d^{3} e^{4} - 3 \, a b^{3} d^{2} e^{5} - 9 \, a^{2} b c d^{2} e^{5} + 3 \, a^{2} b^{2} d e^{6} + 2 \, a^{3} c d e^{6} - a^{3} b e^{7}\right)} e^{\left(-9\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) - {\left(\frac{c^{4} d^{8} e^{7}}{x e + d} - \frac{4 \, b c^{3} d^{7} e^{8}}{x e + d} + \frac{6 \, b^{2} c^{2} d^{6} e^{9}}{x e + d} + \frac{4 \, a c^{3} d^{6} e^{9}}{x e + d} - \frac{4 \, b^{3} c d^{5} e^{10}}{x e + d} - \frac{12 \, a b c^{2} d^{5} e^{10}}{x e + d} + \frac{b^{4} d^{4} e^{11}}{x e + d} + \frac{12 \, a b^{2} c d^{4} e^{11}}{x e + d} + \frac{6 \, a^{2} c^{2} d^{4} e^{11}}{x e + d} - \frac{4 \, a b^{3} d^{3} e^{12}}{x e + d} - \frac{12 \, a^{2} b c d^{3} e^{12}}{x e + d} + \frac{6 \, a^{2} b^{2} d^{2} e^{13}}{x e + d} + \frac{4 \, a^{3} c d^{2} e^{13}}{x e + d} - \frac{4 \, a^{3} b d e^{14}}{x e + d} + \frac{a^{4} e^{15}}{x e + d}\right)} e^{\left(-16\right)}"," ",0,"1/105*(15*c^4 - 70*(2*c^4*d*e - b*c^3*e^2)*e^(-1)/(x*e + d) + 42*(14*c^4*d^2*e^2 - 14*b*c^3*d*e^3 + 3*b^2*c^2*e^4 + 2*a*c^3*e^4)*e^(-2)/(x*e + d)^2 - 105*(14*c^4*d^3*e^3 - 21*b*c^3*d^2*e^4 + 9*b^2*c^2*d*e^5 + 6*a*c^3*d*e^5 - b^3*c*e^6 - 3*a*b*c^2*e^6)*e^(-3)/(x*e + d)^3 + 35*(70*c^4*d^4*e^4 - 140*b*c^3*d^3*e^5 + 90*b^2*c^2*d^2*e^6 + 60*a*c^3*d^2*e^6 - 20*b^3*c*d*e^7 - 60*a*b*c^2*d*e^7 + b^4*e^8 + 12*a*b^2*c*e^8 + 6*a^2*c^2*e^8)*e^(-4)/(x*e + d)^4 - 210*(14*c^4*d^5*e^5 - 35*b*c^3*d^4*e^6 + 30*b^2*c^2*d^3*e^7 + 20*a*c^3*d^3*e^7 - 10*b^3*c*d^2*e^8 - 30*a*b*c^2*d^2*e^8 + b^4*d*e^9 + 12*a*b^2*c*d*e^9 + 6*a^2*c^2*d*e^9 - a*b^3*e^10 - 3*a^2*b*c*e^10)*e^(-5)/(x*e + d)^5 + 210*(14*c^4*d^6*e^6 - 42*b*c^3*d^5*e^7 + 45*b^2*c^2*d^4*e^8 + 30*a*c^3*d^4*e^8 - 20*b^3*c*d^3*e^9 - 60*a*b*c^2*d^3*e^9 + 3*b^4*d^2*e^10 + 36*a*b^2*c*d^2*e^10 + 18*a^2*c^2*d^2*e^10 - 6*a*b^3*d*e^11 - 18*a^2*b*c*d*e^11 + 3*a^2*b^2*e^12 + 2*a^3*c*e^12)*e^(-6)/(x*e + d)^6)*(x*e + d)^7*e^(-9) + 4*(2*c^4*d^7 - 7*b*c^3*d^6*e + 9*b^2*c^2*d^5*e^2 + 6*a*c^3*d^5*e^2 - 5*b^3*c*d^4*e^3 - 15*a*b*c^2*d^4*e^3 + b^4*d^3*e^4 + 12*a*b^2*c*d^3*e^4 + 6*a^2*c^2*d^3*e^4 - 3*a*b^3*d^2*e^5 - 9*a^2*b*c*d^2*e^5 + 3*a^2*b^2*d*e^6 + 2*a^3*c*d*e^6 - a^3*b*e^7)*e^(-9)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) - (c^4*d^8*e^7/(x*e + d) - 4*b*c^3*d^7*e^8/(x*e + d) + 6*b^2*c^2*d^6*e^9/(x*e + d) + 4*a*c^3*d^6*e^9/(x*e + d) - 4*b^3*c*d^5*e^10/(x*e + d) - 12*a*b*c^2*d^5*e^10/(x*e + d) + b^4*d^4*e^11/(x*e + d) + 12*a*b^2*c*d^4*e^11/(x*e + d) + 6*a^2*c^2*d^4*e^11/(x*e + d) - 4*a*b^3*d^3*e^12/(x*e + d) - 12*a^2*b*c*d^3*e^12/(x*e + d) + 6*a^2*b^2*d^2*e^13/(x*e + d) + 4*a^3*c*d^2*e^13/(x*e + d) - 4*a^3*b*d*e^14/(x*e + d) + a^4*e^15/(x*e + d))*e^(-16)","B",0
2153,1,890,0,0.168322," ","integrate((c*x^2+b*x+a)^4/(e*x+d)^3,x, algorithm=""giac"")","2 \, {\left(14 \, c^{4} d^{6} - 42 \, b c^{3} d^{5} e + 45 \, b^{2} c^{2} d^{4} e^{2} + 30 \, a c^{3} d^{4} e^{2} - 20 \, b^{3} c d^{3} e^{3} - 60 \, a b c^{2} d^{3} e^{3} + 3 \, b^{4} d^{2} e^{4} + 36 \, a b^{2} c d^{2} e^{4} + 18 \, a^{2} c^{2} d^{2} e^{4} - 6 \, a b^{3} d e^{5} - 18 \, a^{2} b c d e^{5} + 3 \, a^{2} b^{2} e^{6} + 2 \, a^{3} c e^{6}\right)} e^{\left(-9\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{30} \, {\left(5 \, c^{4} x^{6} e^{15} - 18 \, c^{4} d x^{5} e^{14} + 45 \, c^{4} d^{2} x^{4} e^{13} - 100 \, c^{4} d^{3} x^{3} e^{12} + 225 \, c^{4} d^{4} x^{2} e^{11} - 630 \, c^{4} d^{5} x e^{10} + 24 \, b c^{3} x^{5} e^{15} - 90 \, b c^{3} d x^{4} e^{14} + 240 \, b c^{3} d^{2} x^{3} e^{13} - 600 \, b c^{3} d^{3} x^{2} e^{12} + 1800 \, b c^{3} d^{4} x e^{11} + 45 \, b^{2} c^{2} x^{4} e^{15} + 30 \, a c^{3} x^{4} e^{15} - 180 \, b^{2} c^{2} d x^{3} e^{14} - 120 \, a c^{3} d x^{3} e^{14} + 540 \, b^{2} c^{2} d^{2} x^{2} e^{13} + 360 \, a c^{3} d^{2} x^{2} e^{13} - 1800 \, b^{2} c^{2} d^{3} x e^{12} - 1200 \, a c^{3} d^{3} x e^{12} + 40 \, b^{3} c x^{3} e^{15} + 120 \, a b c^{2} x^{3} e^{15} - 180 \, b^{3} c d x^{2} e^{14} - 540 \, a b c^{2} d x^{2} e^{14} + 720 \, b^{3} c d^{2} x e^{13} + 2160 \, a b c^{2} d^{2} x e^{13} + 15 \, b^{4} x^{2} e^{15} + 180 \, a b^{2} c x^{2} e^{15} + 90 \, a^{2} c^{2} x^{2} e^{15} - 90 \, b^{4} d x e^{14} - 1080 \, a b^{2} c d x e^{14} - 540 \, a^{2} c^{2} d x e^{14} + 120 \, a b^{3} x e^{15} + 360 \, a^{2} b c x e^{15}\right)} e^{\left(-18\right)} + \frac{{\left(15 \, c^{4} d^{8} - 52 \, b c^{3} d^{7} e + 66 \, b^{2} c^{2} d^{6} e^{2} + 44 \, a c^{3} d^{6} e^{2} - 36 \, b^{3} c d^{5} e^{3} - 108 \, a b c^{2} d^{5} e^{3} + 7 \, b^{4} d^{4} e^{4} + 84 \, a b^{2} c d^{4} e^{4} + 42 \, a^{2} c^{2} d^{4} e^{4} - 20 \, a b^{3} d^{3} e^{5} - 60 \, a^{2} b c d^{3} e^{5} + 18 \, a^{2} b^{2} d^{2} e^{6} + 12 \, a^{3} c d^{2} e^{6} - 4 \, a^{3} b d e^{7} - a^{4} e^{8} + 8 \, {\left(2 \, c^{4} d^{7} e - 7 \, b c^{3} d^{6} e^{2} + 9 \, b^{2} c^{2} d^{5} e^{3} + 6 \, a c^{3} d^{5} e^{3} - 5 \, b^{3} c d^{4} e^{4} - 15 \, a b c^{2} d^{4} e^{4} + b^{4} d^{3} e^{5} + 12 \, a b^{2} c d^{3} e^{5} + 6 \, a^{2} c^{2} d^{3} e^{5} - 3 \, a b^{3} d^{2} e^{6} - 9 \, a^{2} b c d^{2} e^{6} + 3 \, a^{2} b^{2} d e^{7} + 2 \, a^{3} c d e^{7} - a^{3} b e^{8}\right)} x\right)} e^{\left(-9\right)}}{2 \, {\left(x e + d\right)}^{2}}"," ",0,"2*(14*c^4*d^6 - 42*b*c^3*d^5*e + 45*b^2*c^2*d^4*e^2 + 30*a*c^3*d^4*e^2 - 20*b^3*c*d^3*e^3 - 60*a*b*c^2*d^3*e^3 + 3*b^4*d^2*e^4 + 36*a*b^2*c*d^2*e^4 + 18*a^2*c^2*d^2*e^4 - 6*a*b^3*d*e^5 - 18*a^2*b*c*d*e^5 + 3*a^2*b^2*e^6 + 2*a^3*c*e^6)*e^(-9)*log(abs(x*e + d)) + 1/30*(5*c^4*x^6*e^15 - 18*c^4*d*x^5*e^14 + 45*c^4*d^2*x^4*e^13 - 100*c^4*d^3*x^3*e^12 + 225*c^4*d^4*x^2*e^11 - 630*c^4*d^5*x*e^10 + 24*b*c^3*x^5*e^15 - 90*b*c^3*d*x^4*e^14 + 240*b*c^3*d^2*x^3*e^13 - 600*b*c^3*d^3*x^2*e^12 + 1800*b*c^3*d^4*x*e^11 + 45*b^2*c^2*x^4*e^15 + 30*a*c^3*x^4*e^15 - 180*b^2*c^2*d*x^3*e^14 - 120*a*c^3*d*x^3*e^14 + 540*b^2*c^2*d^2*x^2*e^13 + 360*a*c^3*d^2*x^2*e^13 - 1800*b^2*c^2*d^3*x*e^12 - 1200*a*c^3*d^3*x*e^12 + 40*b^3*c*x^3*e^15 + 120*a*b*c^2*x^3*e^15 - 180*b^3*c*d*x^2*e^14 - 540*a*b*c^2*d*x^2*e^14 + 720*b^3*c*d^2*x*e^13 + 2160*a*b*c^2*d^2*x*e^13 + 15*b^4*x^2*e^15 + 180*a*b^2*c*x^2*e^15 + 90*a^2*c^2*x^2*e^15 - 90*b^4*d*x*e^14 - 1080*a*b^2*c*d*x*e^14 - 540*a^2*c^2*d*x*e^14 + 120*a*b^3*x*e^15 + 360*a^2*b*c*x*e^15)*e^(-18) + 1/2*(15*c^4*d^8 - 52*b*c^3*d^7*e + 66*b^2*c^2*d^6*e^2 + 44*a*c^3*d^6*e^2 - 36*b^3*c*d^5*e^3 - 108*a*b*c^2*d^5*e^3 + 7*b^4*d^4*e^4 + 84*a*b^2*c*d^4*e^4 + 42*a^2*c^2*d^4*e^4 - 20*a*b^3*d^3*e^5 - 60*a^2*b*c*d^3*e^5 + 18*a^2*b^2*d^2*e^6 + 12*a^3*c*d^2*e^6 - 4*a^3*b*d*e^7 - a^4*e^8 + 8*(2*c^4*d^7*e - 7*b*c^3*d^6*e^2 + 9*b^2*c^2*d^5*e^3 + 6*a*c^3*d^5*e^3 - 5*b^3*c*d^4*e^4 - 15*a*b*c^2*d^4*e^4 + b^4*d^3*e^5 + 12*a*b^2*c*d^3*e^5 + 6*a^2*c^2*d^3*e^5 - 3*a*b^3*d^2*e^6 - 9*a^2*b*c*d^2*e^6 + 3*a^2*b^2*d*e^7 + 2*a^3*c*d*e^7 - a^3*b*e^8)*x)*e^(-9)/(x*e + d)^2","B",0
2154,1,865,0,0.174054," ","integrate((c*x^2+b*x+a)^4/(e*x+d)^4,x, algorithm=""giac"")","-4 \, {\left(14 \, c^{4} d^{5} - 35 \, b c^{3} d^{4} e + 30 \, b^{2} c^{2} d^{3} e^{2} + 20 \, a c^{3} d^{3} e^{2} - 10 \, b^{3} c d^{2} e^{3} - 30 \, a b c^{2} d^{2} e^{3} + b^{4} d e^{4} + 12 \, a b^{2} c d e^{4} + 6 \, a^{2} c^{2} d e^{4} - a b^{3} e^{5} - 3 \, a^{2} b c e^{5}\right)} e^{\left(-9\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{15} \, {\left(3 \, c^{4} x^{5} e^{16} - 15 \, c^{4} d x^{4} e^{15} + 50 \, c^{4} d^{2} x^{3} e^{14} - 150 \, c^{4} d^{3} x^{2} e^{13} + 525 \, c^{4} d^{4} x e^{12} + 15 \, b c^{3} x^{4} e^{16} - 80 \, b c^{3} d x^{3} e^{15} + 300 \, b c^{3} d^{2} x^{2} e^{14} - 1200 \, b c^{3} d^{3} x e^{13} + 30 \, b^{2} c^{2} x^{3} e^{16} + 20 \, a c^{3} x^{3} e^{16} - 180 \, b^{2} c^{2} d x^{2} e^{15} - 120 \, a c^{3} d x^{2} e^{15} + 900 \, b^{2} c^{2} d^{2} x e^{14} + 600 \, a c^{3} d^{2} x e^{14} + 30 \, b^{3} c x^{2} e^{16} + 90 \, a b c^{2} x^{2} e^{16} - 240 \, b^{3} c d x e^{15} - 720 \, a b c^{2} d x e^{15} + 15 \, b^{4} x e^{16} + 180 \, a b^{2} c x e^{16} + 90 \, a^{2} c^{2} x e^{16}\right)} e^{\left(-20\right)} - \frac{{\left(73 \, c^{4} d^{8} - 214 \, b c^{3} d^{7} e + 222 \, b^{2} c^{2} d^{6} e^{2} + 148 \, a c^{3} d^{6} e^{2} - 94 \, b^{3} c d^{5} e^{3} - 282 \, a b c^{2} d^{5} e^{3} + 13 \, b^{4} d^{4} e^{4} + 156 \, a b^{2} c d^{4} e^{4} + 78 \, a^{2} c^{2} d^{4} e^{4} - 22 \, a b^{3} d^{3} e^{5} - 66 \, a^{2} b c d^{3} e^{5} + 6 \, a^{2} b^{2} d^{2} e^{6} + 4 \, a^{3} c d^{2} e^{6} + 2 \, a^{3} b d e^{7} + a^{4} e^{8} + 6 \, {\left(14 \, c^{4} d^{6} e^{2} - 42 \, b c^{3} d^{5} e^{3} + 45 \, b^{2} c^{2} d^{4} e^{4} + 30 \, a c^{3} d^{4} e^{4} - 20 \, b^{3} c d^{3} e^{5} - 60 \, a b c^{2} d^{3} e^{5} + 3 \, b^{4} d^{2} e^{6} + 36 \, a b^{2} c d^{2} e^{6} + 18 \, a^{2} c^{2} d^{2} e^{6} - 6 \, a b^{3} d e^{7} - 18 \, a^{2} b c d e^{7} + 3 \, a^{2} b^{2} e^{8} + 2 \, a^{3} c e^{8}\right)} x^{2} + 6 \, {\left(26 \, c^{4} d^{7} e - 77 \, b c^{3} d^{6} e^{2} + 81 \, b^{2} c^{2} d^{5} e^{3} + 54 \, a c^{3} d^{5} e^{3} - 35 \, b^{3} c d^{4} e^{4} - 105 \, a b c^{2} d^{4} e^{4} + 5 \, b^{4} d^{3} e^{5} + 60 \, a b^{2} c d^{3} e^{5} + 30 \, a^{2} c^{2} d^{3} e^{5} - 9 \, a b^{3} d^{2} e^{6} - 27 \, a^{2} b c d^{2} e^{6} + 3 \, a^{2} b^{2} d e^{7} + 2 \, a^{3} c d e^{7} + a^{3} b e^{8}\right)} x\right)} e^{\left(-9\right)}}{3 \, {\left(x e + d\right)}^{3}}"," ",0,"-4*(14*c^4*d^5 - 35*b*c^3*d^4*e + 30*b^2*c^2*d^3*e^2 + 20*a*c^3*d^3*e^2 - 10*b^3*c*d^2*e^3 - 30*a*b*c^2*d^2*e^3 + b^4*d*e^4 + 12*a*b^2*c*d*e^4 + 6*a^2*c^2*d*e^4 - a*b^3*e^5 - 3*a^2*b*c*e^5)*e^(-9)*log(abs(x*e + d)) + 1/15*(3*c^4*x^5*e^16 - 15*c^4*d*x^4*e^15 + 50*c^4*d^2*x^3*e^14 - 150*c^4*d^3*x^2*e^13 + 525*c^4*d^4*x*e^12 + 15*b*c^3*x^4*e^16 - 80*b*c^3*d*x^3*e^15 + 300*b*c^3*d^2*x^2*e^14 - 1200*b*c^3*d^3*x*e^13 + 30*b^2*c^2*x^3*e^16 + 20*a*c^3*x^3*e^16 - 180*b^2*c^2*d*x^2*e^15 - 120*a*c^3*d*x^2*e^15 + 900*b^2*c^2*d^2*x*e^14 + 600*a*c^3*d^2*x*e^14 + 30*b^3*c*x^2*e^16 + 90*a*b*c^2*x^2*e^16 - 240*b^3*c*d*x*e^15 - 720*a*b*c^2*d*x*e^15 + 15*b^4*x*e^16 + 180*a*b^2*c*x*e^16 + 90*a^2*c^2*x*e^16)*e^(-20) - 1/3*(73*c^4*d^8 - 214*b*c^3*d^7*e + 222*b^2*c^2*d^6*e^2 + 148*a*c^3*d^6*e^2 - 94*b^3*c*d^5*e^3 - 282*a*b*c^2*d^5*e^3 + 13*b^4*d^4*e^4 + 156*a*b^2*c*d^4*e^4 + 78*a^2*c^2*d^4*e^4 - 22*a*b^3*d^3*e^5 - 66*a^2*b*c*d^3*e^5 + 6*a^2*b^2*d^2*e^6 + 4*a^3*c*d^2*e^6 + 2*a^3*b*d*e^7 + a^4*e^8 + 6*(14*c^4*d^6*e^2 - 42*b*c^3*d^5*e^3 + 45*b^2*c^2*d^4*e^4 + 30*a*c^3*d^4*e^4 - 20*b^3*c*d^3*e^5 - 60*a*b*c^2*d^3*e^5 + 3*b^4*d^2*e^6 + 36*a*b^2*c*d^2*e^6 + 18*a^2*c^2*d^2*e^6 - 6*a*b^3*d*e^7 - 18*a^2*b*c*d*e^7 + 3*a^2*b^2*e^8 + 2*a^3*c*e^8)*x^2 + 6*(26*c^4*d^7*e - 77*b*c^3*d^6*e^2 + 81*b^2*c^2*d^5*e^3 + 54*a*c^3*d^5*e^3 - 35*b^3*c*d^4*e^4 - 105*a*b*c^2*d^4*e^4 + 5*b^4*d^3*e^5 + 60*a*b^2*c*d^3*e^5 + 30*a^2*c^2*d^3*e^5 - 9*a*b^3*d^2*e^6 - 27*a^2*b*c*d^2*e^6 + 3*a^2*b^2*d*e^7 + 2*a^3*c*d*e^7 + a^3*b*e^8)*x)*e^(-9)/(x*e + d)^3","B",0
2155,1,1283,0,0.219332," ","integrate((c*x^2+b*x+a)^4/(e*x+d)^5,x, algorithm=""giac"")","\frac{1}{12} \, {\left(3 \, c^{4} - \frac{16 \, {\left(2 \, c^{4} d e - b c^{3} e^{2}\right)} e^{\left(-1\right)}}{x e + d} + \frac{12 \, {\left(14 \, c^{4} d^{2} e^{2} - 14 \, b c^{3} d e^{3} + 3 \, b^{2} c^{2} e^{4} + 2 \, a c^{3} e^{4}\right)} e^{\left(-2\right)}}{{\left(x e + d\right)}^{2}} - \frac{48 \, {\left(14 \, c^{4} d^{3} e^{3} - 21 \, b c^{3} d^{2} e^{4} + 9 \, b^{2} c^{2} d e^{5} + 6 \, a c^{3} d e^{5} - b^{3} c e^{6} - 3 \, a b c^{2} e^{6}\right)} e^{\left(-3\right)}}{{\left(x e + d\right)}^{3}}\right)} {\left(x e + d\right)}^{4} e^{\left(-9\right)} - {\left(70 \, c^{4} d^{4} - 140 \, b c^{3} d^{3} e + 90 \, b^{2} c^{2} d^{2} e^{2} + 60 \, a c^{3} d^{2} e^{2} - 20 \, b^{3} c d e^{3} - 60 \, a b c^{2} d e^{3} + b^{4} e^{4} + 12 \, a b^{2} c e^{4} + 6 \, a^{2} c^{2} e^{4}\right)} e^{\left(-9\right)} \log\left(\frac{{\left| x e + d \right|} e^{\left(-1\right)}}{{\left(x e + d\right)}^{2}}\right) + \frac{1}{12} \, {\left(\frac{672 \, c^{4} d^{5} e^{43}}{x e + d} - \frac{168 \, c^{4} d^{6} e^{43}}{{\left(x e + d\right)}^{2}} + \frac{32 \, c^{4} d^{7} e^{43}}{{\left(x e + d\right)}^{3}} - \frac{3 \, c^{4} d^{8} e^{43}}{{\left(x e + d\right)}^{4}} - \frac{1680 \, b c^{3} d^{4} e^{44}}{x e + d} + \frac{504 \, b c^{3} d^{5} e^{44}}{{\left(x e + d\right)}^{2}} - \frac{112 \, b c^{3} d^{6} e^{44}}{{\left(x e + d\right)}^{3}} + \frac{12 \, b c^{3} d^{7} e^{44}}{{\left(x e + d\right)}^{4}} + \frac{1440 \, b^{2} c^{2} d^{3} e^{45}}{x e + d} + \frac{960 \, a c^{3} d^{3} e^{45}}{x e + d} - \frac{540 \, b^{2} c^{2} d^{4} e^{45}}{{\left(x e + d\right)}^{2}} - \frac{360 \, a c^{3} d^{4} e^{45}}{{\left(x e + d\right)}^{2}} + \frac{144 \, b^{2} c^{2} d^{5} e^{45}}{{\left(x e + d\right)}^{3}} + \frac{96 \, a c^{3} d^{5} e^{45}}{{\left(x e + d\right)}^{3}} - \frac{18 \, b^{2} c^{2} d^{6} e^{45}}{{\left(x e + d\right)}^{4}} - \frac{12 \, a c^{3} d^{6} e^{45}}{{\left(x e + d\right)}^{4}} - \frac{480 \, b^{3} c d^{2} e^{46}}{x e + d} - \frac{1440 \, a b c^{2} d^{2} e^{46}}{x e + d} + \frac{240 \, b^{3} c d^{3} e^{46}}{{\left(x e + d\right)}^{2}} + \frac{720 \, a b c^{2} d^{3} e^{46}}{{\left(x e + d\right)}^{2}} - \frac{80 \, b^{3} c d^{4} e^{46}}{{\left(x e + d\right)}^{3}} - \frac{240 \, a b c^{2} d^{4} e^{46}}{{\left(x e + d\right)}^{3}} + \frac{12 \, b^{3} c d^{5} e^{46}}{{\left(x e + d\right)}^{4}} + \frac{36 \, a b c^{2} d^{5} e^{46}}{{\left(x e + d\right)}^{4}} + \frac{48 \, b^{4} d e^{47}}{x e + d} + \frac{576 \, a b^{2} c d e^{47}}{x e + d} + \frac{288 \, a^{2} c^{2} d e^{47}}{x e + d} - \frac{36 \, b^{4} d^{2} e^{47}}{{\left(x e + d\right)}^{2}} - \frac{432 \, a b^{2} c d^{2} e^{47}}{{\left(x e + d\right)}^{2}} - \frac{216 \, a^{2} c^{2} d^{2} e^{47}}{{\left(x e + d\right)}^{2}} + \frac{16 \, b^{4} d^{3} e^{47}}{{\left(x e + d\right)}^{3}} + \frac{192 \, a b^{2} c d^{3} e^{47}}{{\left(x e + d\right)}^{3}} + \frac{96 \, a^{2} c^{2} d^{3} e^{47}}{{\left(x e + d\right)}^{3}} - \frac{3 \, b^{4} d^{4} e^{47}}{{\left(x e + d\right)}^{4}} - \frac{36 \, a b^{2} c d^{4} e^{47}}{{\left(x e + d\right)}^{4}} - \frac{18 \, a^{2} c^{2} d^{4} e^{47}}{{\left(x e + d\right)}^{4}} - \frac{48 \, a b^{3} e^{48}}{x e + d} - \frac{144 \, a^{2} b c e^{48}}{x e + d} + \frac{72 \, a b^{3} d e^{48}}{{\left(x e + d\right)}^{2}} + \frac{216 \, a^{2} b c d e^{48}}{{\left(x e + d\right)}^{2}} - \frac{48 \, a b^{3} d^{2} e^{48}}{{\left(x e + d\right)}^{3}} - \frac{144 \, a^{2} b c d^{2} e^{48}}{{\left(x e + d\right)}^{3}} + \frac{12 \, a b^{3} d^{3} e^{48}}{{\left(x e + d\right)}^{4}} + \frac{36 \, a^{2} b c d^{3} e^{48}}{{\left(x e + d\right)}^{4}} - \frac{36 \, a^{2} b^{2} e^{49}}{{\left(x e + d\right)}^{2}} - \frac{24 \, a^{3} c e^{49}}{{\left(x e + d\right)}^{2}} + \frac{48 \, a^{2} b^{2} d e^{49}}{{\left(x e + d\right)}^{3}} + \frac{32 \, a^{3} c d e^{49}}{{\left(x e + d\right)}^{3}} - \frac{18 \, a^{2} b^{2} d^{2} e^{49}}{{\left(x e + d\right)}^{4}} - \frac{12 \, a^{3} c d^{2} e^{49}}{{\left(x e + d\right)}^{4}} - \frac{16 \, a^{3} b e^{50}}{{\left(x e + d\right)}^{3}} + \frac{12 \, a^{3} b d e^{50}}{{\left(x e + d\right)}^{4}} - \frac{3 \, a^{4} e^{51}}{{\left(x e + d\right)}^{4}}\right)} e^{\left(-52\right)}"," ",0,"1/12*(3*c^4 - 16*(2*c^4*d*e - b*c^3*e^2)*e^(-1)/(x*e + d) + 12*(14*c^4*d^2*e^2 - 14*b*c^3*d*e^3 + 3*b^2*c^2*e^4 + 2*a*c^3*e^4)*e^(-2)/(x*e + d)^2 - 48*(14*c^4*d^3*e^3 - 21*b*c^3*d^2*e^4 + 9*b^2*c^2*d*e^5 + 6*a*c^3*d*e^5 - b^3*c*e^6 - 3*a*b*c^2*e^6)*e^(-3)/(x*e + d)^3)*(x*e + d)^4*e^(-9) - (70*c^4*d^4 - 140*b*c^3*d^3*e + 90*b^2*c^2*d^2*e^2 + 60*a*c^3*d^2*e^2 - 20*b^3*c*d*e^3 - 60*a*b*c^2*d*e^3 + b^4*e^4 + 12*a*b^2*c*e^4 + 6*a^2*c^2*e^4)*e^(-9)*log(abs(x*e + d)*e^(-1)/(x*e + d)^2) + 1/12*(672*c^4*d^5*e^43/(x*e + d) - 168*c^4*d^6*e^43/(x*e + d)^2 + 32*c^4*d^7*e^43/(x*e + d)^3 - 3*c^4*d^8*e^43/(x*e + d)^4 - 1680*b*c^3*d^4*e^44/(x*e + d) + 504*b*c^3*d^5*e^44/(x*e + d)^2 - 112*b*c^3*d^6*e^44/(x*e + d)^3 + 12*b*c^3*d^7*e^44/(x*e + d)^4 + 1440*b^2*c^2*d^3*e^45/(x*e + d) + 960*a*c^3*d^3*e^45/(x*e + d) - 540*b^2*c^2*d^4*e^45/(x*e + d)^2 - 360*a*c^3*d^4*e^45/(x*e + d)^2 + 144*b^2*c^2*d^5*e^45/(x*e + d)^3 + 96*a*c^3*d^5*e^45/(x*e + d)^3 - 18*b^2*c^2*d^6*e^45/(x*e + d)^4 - 12*a*c^3*d^6*e^45/(x*e + d)^4 - 480*b^3*c*d^2*e^46/(x*e + d) - 1440*a*b*c^2*d^2*e^46/(x*e + d) + 240*b^3*c*d^3*e^46/(x*e + d)^2 + 720*a*b*c^2*d^3*e^46/(x*e + d)^2 - 80*b^3*c*d^4*e^46/(x*e + d)^3 - 240*a*b*c^2*d^4*e^46/(x*e + d)^3 + 12*b^3*c*d^5*e^46/(x*e + d)^4 + 36*a*b*c^2*d^5*e^46/(x*e + d)^4 + 48*b^4*d*e^47/(x*e + d) + 576*a*b^2*c*d*e^47/(x*e + d) + 288*a^2*c^2*d*e^47/(x*e + d) - 36*b^4*d^2*e^47/(x*e + d)^2 - 432*a*b^2*c*d^2*e^47/(x*e + d)^2 - 216*a^2*c^2*d^2*e^47/(x*e + d)^2 + 16*b^4*d^3*e^47/(x*e + d)^3 + 192*a*b^2*c*d^3*e^47/(x*e + d)^3 + 96*a^2*c^2*d^3*e^47/(x*e + d)^3 - 3*b^4*d^4*e^47/(x*e + d)^4 - 36*a*b^2*c*d^4*e^47/(x*e + d)^4 - 18*a^2*c^2*d^4*e^47/(x*e + d)^4 - 48*a*b^3*e^48/(x*e + d) - 144*a^2*b*c*e^48/(x*e + d) + 72*a*b^3*d*e^48/(x*e + d)^2 + 216*a^2*b*c*d*e^48/(x*e + d)^2 - 48*a*b^3*d^2*e^48/(x*e + d)^3 - 144*a^2*b*c*d^2*e^48/(x*e + d)^3 + 12*a*b^3*d^3*e^48/(x*e + d)^4 + 36*a^2*b*c*d^3*e^48/(x*e + d)^4 - 36*a^2*b^2*e^49/(x*e + d)^2 - 24*a^3*c*e^49/(x*e + d)^2 + 48*a^2*b^2*d*e^49/(x*e + d)^3 + 32*a^3*c*d*e^49/(x*e + d)^3 - 18*a^2*b^2*d^2*e^49/(x*e + d)^4 - 12*a^3*c*d^2*e^49/(x*e + d)^4 - 16*a^3*b*e^50/(x*e + d)^3 + 12*a^3*b*d*e^50/(x*e + d)^4 - 3*a^4*e^51/(x*e + d)^4)*e^(-52)","B",0
2156,1,841,0,0.187242," ","integrate((c*x^2+b*x+a)^4/(e*x+d)^6,x, algorithm=""giac"")","-4 \, {\left(14 \, c^{4} d^{3} - 21 \, b c^{3} d^{2} e + 9 \, b^{2} c^{2} d e^{2} + 6 \, a c^{3} d e^{2} - b^{3} c e^{3} - 3 \, a b c^{2} e^{3}\right)} e^{\left(-9\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{3} \, {\left(c^{4} x^{3} e^{12} - 9 \, c^{4} d x^{2} e^{11} + 63 \, c^{4} d^{2} x e^{10} + 6 \, b c^{3} x^{2} e^{12} - 72 \, b c^{3} d x e^{11} + 18 \, b^{2} c^{2} x e^{12} + 12 \, a c^{3} x e^{12}\right)} e^{\left(-18\right)} - \frac{{\left(743 \, c^{4} d^{8} - 1377 \, b c^{3} d^{7} e + 783 \, b^{2} c^{2} d^{6} e^{2} + 522 \, a c^{3} d^{6} e^{2} - 137 \, b^{3} c d^{5} e^{3} - 411 \, a b c^{2} d^{5} e^{3} + 3 \, b^{4} d^{4} e^{4} + 36 \, a b^{2} c d^{4} e^{4} + 18 \, a^{2} c^{2} d^{4} e^{4} + 3 \, a b^{3} d^{3} e^{5} + 9 \, a^{2} b c d^{3} e^{5} + 3 \, a^{2} b^{2} d^{2} e^{6} + 2 \, a^{3} c d^{2} e^{6} + 3 \, a^{3} b d e^{7} + 15 \, {\left(70 \, c^{4} d^{4} e^{4} - 140 \, b c^{3} d^{3} e^{5} + 90 \, b^{2} c^{2} d^{2} e^{6} + 60 \, a c^{3} d^{2} e^{6} - 20 \, b^{3} c d e^{7} - 60 \, a b c^{2} d e^{7} + b^{4} e^{8} + 12 \, a b^{2} c e^{8} + 6 \, a^{2} c^{2} e^{8}\right)} x^{4} + 3 \, a^{4} e^{8} + 30 \, {\left(126 \, c^{4} d^{5} e^{3} - 245 \, b c^{3} d^{4} e^{4} + 150 \, b^{2} c^{2} d^{3} e^{5} + 100 \, a c^{3} d^{3} e^{5} - 30 \, b^{3} c d^{2} e^{6} - 90 \, a b c^{2} d^{2} e^{6} + b^{4} d e^{7} + 12 \, a b^{2} c d e^{7} + 6 \, a^{2} c^{2} d e^{7} + a b^{3} e^{8} + 3 \, a^{2} b c e^{8}\right)} x^{3} + 10 \, {\left(518 \, c^{4} d^{6} e^{2} - 987 \, b c^{3} d^{5} e^{3} + 585 \, b^{2} c^{2} d^{4} e^{4} + 390 \, a c^{3} d^{4} e^{4} - 110 \, b^{3} c d^{3} e^{5} - 330 \, a b c^{2} d^{3} e^{5} + 3 \, b^{4} d^{2} e^{6} + 36 \, a b^{2} c d^{2} e^{6} + 18 \, a^{2} c^{2} d^{2} e^{6} + 3 \, a b^{3} d e^{7} + 9 \, a^{2} b c d e^{7} + 3 \, a^{2} b^{2} e^{8} + 2 \, a^{3} c e^{8}\right)} x^{2} + 5 \, {\left(638 \, c^{4} d^{7} e - 1197 \, b c^{3} d^{6} e^{2} + 693 \, b^{2} c^{2} d^{5} e^{3} + 462 \, a c^{3} d^{5} e^{3} - 125 \, b^{3} c d^{4} e^{4} - 375 \, a b c^{2} d^{4} e^{4} + 3 \, b^{4} d^{3} e^{5} + 36 \, a b^{2} c d^{3} e^{5} + 18 \, a^{2} c^{2} d^{3} e^{5} + 3 \, a b^{3} d^{2} e^{6} + 9 \, a^{2} b c d^{2} e^{6} + 3 \, a^{2} b^{2} d e^{7} + 2 \, a^{3} c d e^{7} + 3 \, a^{3} b e^{8}\right)} x\right)} e^{\left(-9\right)}}{15 \, {\left(x e + d\right)}^{5}}"," ",0,"-4*(14*c^4*d^3 - 21*b*c^3*d^2*e + 9*b^2*c^2*d*e^2 + 6*a*c^3*d*e^2 - b^3*c*e^3 - 3*a*b*c^2*e^3)*e^(-9)*log(abs(x*e + d)) + 1/3*(c^4*x^3*e^12 - 9*c^4*d*x^2*e^11 + 63*c^4*d^2*x*e^10 + 6*b*c^3*x^2*e^12 - 72*b*c^3*d*x*e^11 + 18*b^2*c^2*x*e^12 + 12*a*c^3*x*e^12)*e^(-18) - 1/15*(743*c^4*d^8 - 1377*b*c^3*d^7*e + 783*b^2*c^2*d^6*e^2 + 522*a*c^3*d^6*e^2 - 137*b^3*c*d^5*e^3 - 411*a*b*c^2*d^5*e^3 + 3*b^4*d^4*e^4 + 36*a*b^2*c*d^4*e^4 + 18*a^2*c^2*d^4*e^4 + 3*a*b^3*d^3*e^5 + 9*a^2*b*c*d^3*e^5 + 3*a^2*b^2*d^2*e^6 + 2*a^3*c*d^2*e^6 + 3*a^3*b*d*e^7 + 15*(70*c^4*d^4*e^4 - 140*b*c^3*d^3*e^5 + 90*b^2*c^2*d^2*e^6 + 60*a*c^3*d^2*e^6 - 20*b^3*c*d*e^7 - 60*a*b*c^2*d*e^7 + b^4*e^8 + 12*a*b^2*c*e^8 + 6*a^2*c^2*e^8)*x^4 + 3*a^4*e^8 + 30*(126*c^4*d^5*e^3 - 245*b*c^3*d^4*e^4 + 150*b^2*c^2*d^3*e^5 + 100*a*c^3*d^3*e^5 - 30*b^3*c*d^2*e^6 - 90*a*b*c^2*d^2*e^6 + b^4*d*e^7 + 12*a*b^2*c*d*e^7 + 6*a^2*c^2*d*e^7 + a*b^3*e^8 + 3*a^2*b*c*e^8)*x^3 + 10*(518*c^4*d^6*e^2 - 987*b*c^3*d^5*e^3 + 585*b^2*c^2*d^4*e^4 + 390*a*c^3*d^4*e^4 - 110*b^3*c*d^3*e^5 - 330*a*b*c^2*d^3*e^5 + 3*b^4*d^2*e^6 + 36*a*b^2*c*d^2*e^6 + 18*a^2*c^2*d^2*e^6 + 3*a*b^3*d*e^7 + 9*a^2*b*c*d*e^7 + 3*a^2*b^2*e^8 + 2*a^3*c*e^8)*x^2 + 5*(638*c^4*d^7*e - 1197*b*c^3*d^6*e^2 + 693*b^2*c^2*d^5*e^3 + 462*a*c^3*d^5*e^3 - 125*b^3*c*d^4*e^4 - 375*a*b*c^2*d^4*e^4 + 3*b^4*d^3*e^5 + 36*a*b^2*c*d^3*e^5 + 18*a^2*c^2*d^3*e^5 + 3*a*b^3*d^2*e^6 + 9*a^2*b*c*d^2*e^6 + 3*a^2*b^2*d*e^7 + 2*a^3*c*d*e^7 + 3*a^3*b*e^8)*x)*e^(-9)/(x*e + d)^5","B",0
2157,1,842,0,0.209985," ","integrate((c*x^2+b*x+a)^4/(e*x+d)^7,x, algorithm=""giac"")","2 \, {\left(14 \, c^{4} d^{2} - 14 \, b c^{3} d e + 3 \, b^{2} c^{2} e^{2} + 2 \, a c^{3} e^{2}\right)} e^{\left(-9\right)} \log\left({\left| x e + d \right|}\right) + \frac{1}{2} \, {\left(c^{4} x^{2} e^{7} - 14 \, c^{4} d x e^{6} + 8 \, b c^{3} x e^{7}\right)} e^{\left(-14\right)} + \frac{{\left(1023 \, c^{4} d^{8} - 1338 \, b c^{3} d^{7} e + 441 \, b^{2} c^{2} d^{6} e^{2} + 294 \, a c^{3} d^{6} e^{2} - 20 \, b^{3} c d^{5} e^{3} - 60 \, a b c^{2} d^{5} e^{3} - b^{4} d^{4} e^{4} - 12 \, a b^{2} c d^{4} e^{4} - 6 \, a^{2} c^{2} d^{4} e^{4} - 2 \, a b^{3} d^{3} e^{5} - 6 \, a^{2} b c d^{3} e^{5} - 3 \, a^{2} b^{2} d^{2} e^{6} - 2 \, a^{3} c d^{2} e^{6} + 120 \, {\left(14 \, c^{4} d^{3} e^{5} - 21 \, b c^{3} d^{2} e^{6} + 9 \, b^{2} c^{2} d e^{7} + 6 \, a c^{3} d e^{7} - b^{3} c e^{8} - 3 \, a b c^{2} e^{8}\right)} x^{5} - 4 \, a^{3} b d e^{7} + 15 \, {\left(490 \, c^{4} d^{4} e^{4} - 700 \, b c^{3} d^{3} e^{5} + 270 \, b^{2} c^{2} d^{2} e^{6} + 180 \, a c^{3} d^{2} e^{6} - 20 \, b^{3} c d e^{7} - 60 \, a b c^{2} d e^{7} - b^{4} e^{8} - 12 \, a b^{2} c e^{8} - 6 \, a^{2} c^{2} e^{8}\right)} x^{4} - 5 \, a^{4} e^{8} + 20 \, {\left(658 \, c^{4} d^{5} e^{3} - 910 \, b c^{3} d^{4} e^{4} + 330 \, b^{2} c^{2} d^{3} e^{5} + 220 \, a c^{3} d^{3} e^{5} - 20 \, b^{3} c d^{2} e^{6} - 60 \, a b c^{2} d^{2} e^{6} - b^{4} d e^{7} - 12 \, a b^{2} c d e^{7} - 6 \, a^{2} c^{2} d e^{7} - 2 \, a b^{3} e^{8} - 6 \, a^{2} b c e^{8}\right)} x^{3} + 15 \, {\left(798 \, c^{4} d^{6} e^{2} - 1078 \, b c^{3} d^{5} e^{3} + 375 \, b^{2} c^{2} d^{4} e^{4} + 250 \, a c^{3} d^{4} e^{4} - 20 \, b^{3} c d^{3} e^{5} - 60 \, a b c^{2} d^{3} e^{5} - b^{4} d^{2} e^{6} - 12 \, a b^{2} c d^{2} e^{6} - 6 \, a^{2} c^{2} d^{2} e^{6} - 2 \, a b^{3} d e^{7} - 6 \, a^{2} b c d e^{7} - 3 \, a^{2} b^{2} e^{8} - 2 \, a^{3} c e^{8}\right)} x^{2} + 6 \, {\left(918 \, c^{4} d^{7} e - 1218 \, b c^{3} d^{6} e^{2} + 411 \, b^{2} c^{2} d^{5} e^{3} + 274 \, a c^{3} d^{5} e^{3} - 20 \, b^{3} c d^{4} e^{4} - 60 \, a b c^{2} d^{4} e^{4} - b^{4} d^{3} e^{5} - 12 \, a b^{2} c d^{3} e^{5} - 6 \, a^{2} c^{2} d^{3} e^{5} - 2 \, a b^{3} d^{2} e^{6} - 6 \, a^{2} b c d^{2} e^{6} - 3 \, a^{2} b^{2} d e^{7} - 2 \, a^{3} c d e^{7} - 4 \, a^{3} b e^{8}\right)} x\right)} e^{\left(-9\right)}}{30 \, {\left(x e + d\right)}^{6}}"," ",0,"2*(14*c^4*d^2 - 14*b*c^3*d*e + 3*b^2*c^2*e^2 + 2*a*c^3*e^2)*e^(-9)*log(abs(x*e + d)) + 1/2*(c^4*x^2*e^7 - 14*c^4*d*x*e^6 + 8*b*c^3*x*e^7)*e^(-14) + 1/30*(1023*c^4*d^8 - 1338*b*c^3*d^7*e + 441*b^2*c^2*d^6*e^2 + 294*a*c^3*d^6*e^2 - 20*b^3*c*d^5*e^3 - 60*a*b*c^2*d^5*e^3 - b^4*d^4*e^4 - 12*a*b^2*c*d^4*e^4 - 6*a^2*c^2*d^4*e^4 - 2*a*b^3*d^3*e^5 - 6*a^2*b*c*d^3*e^5 - 3*a^2*b^2*d^2*e^6 - 2*a^3*c*d^2*e^6 + 120*(14*c^4*d^3*e^5 - 21*b*c^3*d^2*e^6 + 9*b^2*c^2*d*e^7 + 6*a*c^3*d*e^7 - b^3*c*e^8 - 3*a*b*c^2*e^8)*x^5 - 4*a^3*b*d*e^7 + 15*(490*c^4*d^4*e^4 - 700*b*c^3*d^3*e^5 + 270*b^2*c^2*d^2*e^6 + 180*a*c^3*d^2*e^6 - 20*b^3*c*d*e^7 - 60*a*b*c^2*d*e^7 - b^4*e^8 - 12*a*b^2*c*e^8 - 6*a^2*c^2*e^8)*x^4 - 5*a^4*e^8 + 20*(658*c^4*d^5*e^3 - 910*b*c^3*d^4*e^4 + 330*b^2*c^2*d^3*e^5 + 220*a*c^3*d^3*e^5 - 20*b^3*c*d^2*e^6 - 60*a*b*c^2*d^2*e^6 - b^4*d*e^7 - 12*a*b^2*c*d*e^7 - 6*a^2*c^2*d*e^7 - 2*a*b^3*e^8 - 6*a^2*b*c*e^8)*x^3 + 15*(798*c^4*d^6*e^2 - 1078*b*c^3*d^5*e^3 + 375*b^2*c^2*d^4*e^4 + 250*a*c^3*d^4*e^4 - 20*b^3*c*d^3*e^5 - 60*a*b*c^2*d^3*e^5 - b^4*d^2*e^6 - 12*a*b^2*c*d^2*e^6 - 6*a^2*c^2*d^2*e^6 - 2*a*b^3*d*e^7 - 6*a^2*b*c*d*e^7 - 3*a^2*b^2*e^8 - 2*a^3*c*e^8)*x^2 + 6*(918*c^4*d^7*e - 1218*b*c^3*d^6*e^2 + 411*b^2*c^2*d^5*e^3 + 274*a*c^3*d^5*e^3 - 20*b^3*c*d^4*e^4 - 60*a*b*c^2*d^4*e^4 - b^4*d^3*e^5 - 12*a*b^2*c*d^3*e^5 - 6*a^2*c^2*d^3*e^5 - 2*a*b^3*d^2*e^6 - 6*a^2*b*c*d^2*e^6 - 3*a^2*b^2*d*e^7 - 2*a^3*c*d*e^7 - 4*a^3*b*e^8)*x)*e^(-9)/(x*e + d)^6","B",0
2158,1,833,0,0.169317," ","integrate((c*x^2+b*x+a)^4/(e*x+d)^8,x, algorithm=""giac"")","c^{4} x e^{\left(-8\right)} - 4 \, {\left(2 \, c^{4} d - b c^{3} e\right)} e^{\left(-9\right)} \log\left({\left| x e + d \right|}\right) - \frac{{\left(1443 \, c^{4} d^{8} - 1089 \, b c^{3} d^{7} e + 90 \, b^{2} c^{2} d^{6} e^{2} + 60 \, a c^{3} d^{6} e^{2} + 10 \, b^{3} c d^{5} e^{3} + 30 \, a b c^{2} d^{5} e^{3} + b^{4} d^{4} e^{4} + 12 \, a b^{2} c d^{4} e^{4} + 6 \, a^{2} c^{2} d^{4} e^{4} + 3 \, a b^{3} d^{3} e^{5} + 9 \, a^{2} b c d^{3} e^{5} + 210 \, {\left(14 \, c^{4} d^{2} e^{6} - 14 \, b c^{3} d e^{7} + 3 \, b^{2} c^{2} e^{8} + 2 \, a c^{3} e^{8}\right)} x^{6} + 6 \, a^{2} b^{2} d^{2} e^{6} + 4 \, a^{3} c d^{2} e^{6} + 210 \, {\left(70 \, c^{4} d^{3} e^{5} - 63 \, b c^{3} d^{2} e^{6} + 9 \, b^{2} c^{2} d e^{7} + 6 \, a c^{3} d e^{7} + b^{3} c e^{8} + 3 \, a b c^{2} e^{8}\right)} x^{5} + 10 \, a^{3} b d e^{7} + 35 \, {\left(910 \, c^{4} d^{4} e^{4} - 770 \, b c^{3} d^{3} e^{5} + 90 \, b^{2} c^{2} d^{2} e^{6} + 60 \, a c^{3} d^{2} e^{6} + 10 \, b^{3} c d e^{7} + 30 \, a b c^{2} d e^{7} + b^{4} e^{8} + 12 \, a b^{2} c e^{8} + 6 \, a^{2} c^{2} e^{8}\right)} x^{4} + 15 \, a^{4} e^{8} + 35 \, {\left(1078 \, c^{4} d^{5} e^{3} - 875 \, b c^{3} d^{4} e^{4} + 90 \, b^{2} c^{2} d^{3} e^{5} + 60 \, a c^{3} d^{3} e^{5} + 10 \, b^{3} c d^{2} e^{6} + 30 \, a b c^{2} d^{2} e^{6} + b^{4} d e^{7} + 12 \, a b^{2} c d e^{7} + 6 \, a^{2} c^{2} d e^{7} + 3 \, a b^{3} e^{8} + 9 \, a^{2} b c e^{8}\right)} x^{3} + 21 \, {\left(1218 \, c^{4} d^{6} e^{2} - 959 \, b c^{3} d^{5} e^{3} + 90 \, b^{2} c^{2} d^{4} e^{4} + 60 \, a c^{3} d^{4} e^{4} + 10 \, b^{3} c d^{3} e^{5} + 30 \, a b c^{2} d^{3} e^{5} + b^{4} d^{2} e^{6} + 12 \, a b^{2} c d^{2} e^{6} + 6 \, a^{2} c^{2} d^{2} e^{6} + 3 \, a b^{3} d e^{7} + 9 \, a^{2} b c d e^{7} + 6 \, a^{2} b^{2} e^{8} + 4 \, a^{3} c e^{8}\right)} x^{2} + 7 \, {\left(1338 \, c^{4} d^{7} e - 1029 \, b c^{3} d^{6} e^{2} + 90 \, b^{2} c^{2} d^{5} e^{3} + 60 \, a c^{3} d^{5} e^{3} + 10 \, b^{3} c d^{4} e^{4} + 30 \, a b c^{2} d^{4} e^{4} + b^{4} d^{3} e^{5} + 12 \, a b^{2} c d^{3} e^{5} + 6 \, a^{2} c^{2} d^{3} e^{5} + 3 \, a b^{3} d^{2} e^{6} + 9 \, a^{2} b c d^{2} e^{6} + 6 \, a^{2} b^{2} d e^{7} + 4 \, a^{3} c d e^{7} + 10 \, a^{3} b e^{8}\right)} x\right)} e^{\left(-9\right)}}{105 \, {\left(x e + d\right)}^{7}}"," ",0,"c^4*x*e^(-8) - 4*(2*c^4*d - b*c^3*e)*e^(-9)*log(abs(x*e + d)) - 1/105*(1443*c^4*d^8 - 1089*b*c^3*d^7*e + 90*b^2*c^2*d^6*e^2 + 60*a*c^3*d^6*e^2 + 10*b^3*c*d^5*e^3 + 30*a*b*c^2*d^5*e^3 + b^4*d^4*e^4 + 12*a*b^2*c*d^4*e^4 + 6*a^2*c^2*d^4*e^4 + 3*a*b^3*d^3*e^5 + 9*a^2*b*c*d^3*e^5 + 210*(14*c^4*d^2*e^6 - 14*b*c^3*d*e^7 + 3*b^2*c^2*e^8 + 2*a*c^3*e^8)*x^6 + 6*a^2*b^2*d^2*e^6 + 4*a^3*c*d^2*e^6 + 210*(70*c^4*d^3*e^5 - 63*b*c^3*d^2*e^6 + 9*b^2*c^2*d*e^7 + 6*a*c^3*d*e^7 + b^3*c*e^8 + 3*a*b*c^2*e^8)*x^5 + 10*a^3*b*d*e^7 + 35*(910*c^4*d^4*e^4 - 770*b*c^3*d^3*e^5 + 90*b^2*c^2*d^2*e^6 + 60*a*c^3*d^2*e^6 + 10*b^3*c*d*e^7 + 30*a*b*c^2*d*e^7 + b^4*e^8 + 12*a*b^2*c*e^8 + 6*a^2*c^2*e^8)*x^4 + 15*a^4*e^8 + 35*(1078*c^4*d^5*e^3 - 875*b*c^3*d^4*e^4 + 90*b^2*c^2*d^3*e^5 + 60*a*c^3*d^3*e^5 + 10*b^3*c*d^2*e^6 + 30*a*b*c^2*d^2*e^6 + b^4*d*e^7 + 12*a*b^2*c*d*e^7 + 6*a^2*c^2*d*e^7 + 3*a*b^3*e^8 + 9*a^2*b*c*e^8)*x^3 + 21*(1218*c^4*d^6*e^2 - 959*b*c^3*d^5*e^3 + 90*b^2*c^2*d^4*e^4 + 60*a*c^3*d^4*e^4 + 10*b^3*c*d^3*e^5 + 30*a*b*c^2*d^3*e^5 + b^4*d^2*e^6 + 12*a*b^2*c*d^2*e^6 + 6*a^2*c^2*d^2*e^6 + 3*a*b^3*d*e^7 + 9*a^2*b*c*d*e^7 + 6*a^2*b^2*e^8 + 4*a^3*c*e^8)*x^2 + 7*(1338*c^4*d^7*e - 1029*b*c^3*d^6*e^2 + 90*b^2*c^2*d^5*e^3 + 60*a*c^3*d^5*e^3 + 10*b^3*c*d^4*e^4 + 30*a*b*c^2*d^4*e^4 + b^4*d^3*e^5 + 12*a*b^2*c*d^3*e^5 + 6*a^2*c^2*d^3*e^5 + 3*a*b^3*d^2*e^6 + 9*a^2*b*c*d^2*e^6 + 6*a^2*b^2*d*e^7 + 4*a^3*c*d*e^7 + 10*a^3*b*e^8)*x)*e^(-9)/(x*e + d)^7","B",0
2159,1,843,0,0.193871," ","integrate((c*x^2+b*x+a)^4/(e*x+d)^9,x, algorithm=""giac"")","c^{4} e^{\left(-9\right)} \log\left({\left| x e + d \right|}\right) + \frac{{\left(3360 \, {\left(2 \, c^{4} d e^{6} - b c^{3} e^{7}\right)} x^{7} + 840 \, {\left(42 \, c^{4} d^{2} e^{5} - 14 \, b c^{3} d e^{6} - 3 \, b^{2} c^{2} e^{7} - 2 \, a c^{3} e^{7}\right)} x^{6} + 560 \, {\left(154 \, c^{4} d^{3} e^{4} - 42 \, b c^{3} d^{2} e^{5} - 9 \, b^{2} c^{2} d e^{6} - 6 \, a c^{3} d e^{6} - 2 \, b^{3} c e^{7} - 6 \, a b c^{2} e^{7}\right)} x^{5} + 70 \, {\left(1750 \, c^{4} d^{4} e^{3} - 420 \, b c^{3} d^{3} e^{4} - 90 \, b^{2} c^{2} d^{2} e^{5} - 60 \, a c^{3} d^{2} e^{5} - 20 \, b^{3} c d e^{6} - 60 \, a b c^{2} d e^{6} - 3 \, b^{4} e^{7} - 36 \, a b^{2} c e^{7} - 18 \, a^{2} c^{2} e^{7}\right)} x^{4} + 56 \, {\left(1918 \, c^{4} d^{5} e^{2} - 420 \, b c^{3} d^{4} e^{3} - 90 \, b^{2} c^{2} d^{3} e^{4} - 60 \, a c^{3} d^{3} e^{4} - 20 \, b^{3} c d^{2} e^{5} - 60 \, a b c^{2} d^{2} e^{5} - 3 \, b^{4} d e^{6} - 36 \, a b^{2} c d e^{6} - 18 \, a^{2} c^{2} d e^{6} - 12 \, a b^{3} e^{7} - 36 \, a^{2} b c e^{7}\right)} x^{3} + 28 \, {\left(2058 \, c^{4} d^{6} e - 420 \, b c^{3} d^{5} e^{2} - 90 \, b^{2} c^{2} d^{4} e^{3} - 60 \, a c^{3} d^{4} e^{3} - 20 \, b^{3} c d^{3} e^{4} - 60 \, a b c^{2} d^{3} e^{4} - 3 \, b^{4} d^{2} e^{5} - 36 \, a b^{2} c d^{2} e^{5} - 18 \, a^{2} c^{2} d^{2} e^{5} - 12 \, a b^{3} d e^{6} - 36 \, a^{2} b c d e^{6} - 30 \, a^{2} b^{2} e^{7} - 20 \, a^{3} c e^{7}\right)} x^{2} + 8 \, {\left(2178 \, c^{4} d^{7} - 420 \, b c^{3} d^{6} e - 90 \, b^{2} c^{2} d^{5} e^{2} - 60 \, a c^{3} d^{5} e^{2} - 20 \, b^{3} c d^{4} e^{3} - 60 \, a b c^{2} d^{4} e^{3} - 3 \, b^{4} d^{3} e^{4} - 36 \, a b^{2} c d^{3} e^{4} - 18 \, a^{2} c^{2} d^{3} e^{4} - 12 \, a b^{3} d^{2} e^{5} - 36 \, a^{2} b c d^{2} e^{5} - 30 \, a^{2} b^{2} d e^{6} - 20 \, a^{3} c d e^{6} - 60 \, a^{3} b e^{7}\right)} x + {\left(2283 \, c^{4} d^{8} - 420 \, b c^{3} d^{7} e - 90 \, b^{2} c^{2} d^{6} e^{2} - 60 \, a c^{3} d^{6} e^{2} - 20 \, b^{3} c d^{5} e^{3} - 60 \, a b c^{2} d^{5} e^{3} - 3 \, b^{4} d^{4} e^{4} - 36 \, a b^{2} c d^{4} e^{4} - 18 \, a^{2} c^{2} d^{4} e^{4} - 12 \, a b^{3} d^{3} e^{5} - 36 \, a^{2} b c d^{3} e^{5} - 30 \, a^{2} b^{2} d^{2} e^{6} - 20 \, a^{3} c d^{2} e^{6} - 60 \, a^{3} b d e^{7} - 105 \, a^{4} e^{8}\right)} e^{\left(-1\right)}\right)} e^{\left(-8\right)}}{840 \, {\left(x e + d\right)}^{8}}"," ",0,"c^4*e^(-9)*log(abs(x*e + d)) + 1/840*(3360*(2*c^4*d*e^6 - b*c^3*e^7)*x^7 + 840*(42*c^4*d^2*e^5 - 14*b*c^3*d*e^6 - 3*b^2*c^2*e^7 - 2*a*c^3*e^7)*x^6 + 560*(154*c^4*d^3*e^4 - 42*b*c^3*d^2*e^5 - 9*b^2*c^2*d*e^6 - 6*a*c^3*d*e^6 - 2*b^3*c*e^7 - 6*a*b*c^2*e^7)*x^5 + 70*(1750*c^4*d^4*e^3 - 420*b*c^3*d^3*e^4 - 90*b^2*c^2*d^2*e^5 - 60*a*c^3*d^2*e^5 - 20*b^3*c*d*e^6 - 60*a*b*c^2*d*e^6 - 3*b^4*e^7 - 36*a*b^2*c*e^7 - 18*a^2*c^2*e^7)*x^4 + 56*(1918*c^4*d^5*e^2 - 420*b*c^3*d^4*e^3 - 90*b^2*c^2*d^3*e^4 - 60*a*c^3*d^3*e^4 - 20*b^3*c*d^2*e^5 - 60*a*b*c^2*d^2*e^5 - 3*b^4*d*e^6 - 36*a*b^2*c*d*e^6 - 18*a^2*c^2*d*e^6 - 12*a*b^3*e^7 - 36*a^2*b*c*e^7)*x^3 + 28*(2058*c^4*d^6*e - 420*b*c^3*d^5*e^2 - 90*b^2*c^2*d^4*e^3 - 60*a*c^3*d^4*e^3 - 20*b^3*c*d^3*e^4 - 60*a*b*c^2*d^3*e^4 - 3*b^4*d^2*e^5 - 36*a*b^2*c*d^2*e^5 - 18*a^2*c^2*d^2*e^5 - 12*a*b^3*d*e^6 - 36*a^2*b*c*d*e^6 - 30*a^2*b^2*e^7 - 20*a^3*c*e^7)*x^2 + 8*(2178*c^4*d^7 - 420*b*c^3*d^6*e - 90*b^2*c^2*d^5*e^2 - 60*a*c^3*d^5*e^2 - 20*b^3*c*d^4*e^3 - 60*a*b*c^2*d^4*e^3 - 3*b^4*d^3*e^4 - 36*a*b^2*c*d^3*e^4 - 18*a^2*c^2*d^3*e^4 - 12*a*b^3*d^2*e^5 - 36*a^2*b*c*d^2*e^5 - 30*a^2*b^2*d*e^6 - 20*a^3*c*d*e^6 - 60*a^3*b*e^7)*x + (2283*c^4*d^8 - 420*b*c^3*d^7*e - 90*b^2*c^2*d^6*e^2 - 60*a*c^3*d^6*e^2 - 20*b^3*c*d^5*e^3 - 60*a*b*c^2*d^5*e^3 - 3*b^4*d^4*e^4 - 36*a*b^2*c*d^4*e^4 - 18*a^2*c^2*d^4*e^4 - 12*a*b^3*d^3*e^5 - 36*a^2*b*c*d^3*e^5 - 30*a^2*b^2*d^2*e^6 - 20*a^3*c*d^2*e^6 - 60*a^3*b*d*e^7 - 105*a^4*e^8)*e^(-1))*e^(-8)/(x*e + d)^8","A",0
2160,1,944,0,0.187397," ","integrate((c*x^2+b*x+a)^4/(e*x+d)^10,x, algorithm=""giac"")","-\frac{{\left(630 \, c^{4} x^{8} e^{8} + 2520 \, c^{4} d x^{7} e^{7} + 5880 \, c^{4} d^{2} x^{6} e^{6} + 8820 \, c^{4} d^{3} x^{5} e^{5} + 8820 \, c^{4} d^{4} x^{4} e^{4} + 5880 \, c^{4} d^{5} x^{3} e^{3} + 2520 \, c^{4} d^{6} x^{2} e^{2} + 630 \, c^{4} d^{7} x e + 70 \, c^{4} d^{8} + 1260 \, b c^{3} x^{7} e^{8} + 2940 \, b c^{3} d x^{6} e^{7} + 4410 \, b c^{3} d^{2} x^{5} e^{6} + 4410 \, b c^{3} d^{3} x^{4} e^{5} + 2940 \, b c^{3} d^{4} x^{3} e^{4} + 1260 \, b c^{3} d^{5} x^{2} e^{3} + 315 \, b c^{3} d^{6} x e^{2} + 35 \, b c^{3} d^{7} e + 1260 \, b^{2} c^{2} x^{6} e^{8} + 840 \, a c^{3} x^{6} e^{8} + 1890 \, b^{2} c^{2} d x^{5} e^{7} + 1260 \, a c^{3} d x^{5} e^{7} + 1890 \, b^{2} c^{2} d^{2} x^{4} e^{6} + 1260 \, a c^{3} d^{2} x^{4} e^{6} + 1260 \, b^{2} c^{2} d^{3} x^{3} e^{5} + 840 \, a c^{3} d^{3} x^{3} e^{5} + 540 \, b^{2} c^{2} d^{4} x^{2} e^{4} + 360 \, a c^{3} d^{4} x^{2} e^{4} + 135 \, b^{2} c^{2} d^{5} x e^{3} + 90 \, a c^{3} d^{5} x e^{3} + 15 \, b^{2} c^{2} d^{6} e^{2} + 10 \, a c^{3} d^{6} e^{2} + 630 \, b^{3} c x^{5} e^{8} + 1890 \, a b c^{2} x^{5} e^{8} + 630 \, b^{3} c d x^{4} e^{7} + 1890 \, a b c^{2} d x^{4} e^{7} + 420 \, b^{3} c d^{2} x^{3} e^{6} + 1260 \, a b c^{2} d^{2} x^{3} e^{6} + 180 \, b^{3} c d^{3} x^{2} e^{5} + 540 \, a b c^{2} d^{3} x^{2} e^{5} + 45 \, b^{3} c d^{4} x e^{4} + 135 \, a b c^{2} d^{4} x e^{4} + 5 \, b^{3} c d^{5} e^{3} + 15 \, a b c^{2} d^{5} e^{3} + 126 \, b^{4} x^{4} e^{8} + 1512 \, a b^{2} c x^{4} e^{8} + 756 \, a^{2} c^{2} x^{4} e^{8} + 84 \, b^{4} d x^{3} e^{7} + 1008 \, a b^{2} c d x^{3} e^{7} + 504 \, a^{2} c^{2} d x^{3} e^{7} + 36 \, b^{4} d^{2} x^{2} e^{6} + 432 \, a b^{2} c d^{2} x^{2} e^{6} + 216 \, a^{2} c^{2} d^{2} x^{2} e^{6} + 9 \, b^{4} d^{3} x e^{5} + 108 \, a b^{2} c d^{3} x e^{5} + 54 \, a^{2} c^{2} d^{3} x e^{5} + b^{4} d^{4} e^{4} + 12 \, a b^{2} c d^{4} e^{4} + 6 \, a^{2} c^{2} d^{4} e^{4} + 420 \, a b^{3} x^{3} e^{8} + 1260 \, a^{2} b c x^{3} e^{8} + 180 \, a b^{3} d x^{2} e^{7} + 540 \, a^{2} b c d x^{2} e^{7} + 45 \, a b^{3} d^{2} x e^{6} + 135 \, a^{2} b c d^{2} x e^{6} + 5 \, a b^{3} d^{3} e^{5} + 15 \, a^{2} b c d^{3} e^{5} + 540 \, a^{2} b^{2} x^{2} e^{8} + 360 \, a^{3} c x^{2} e^{8} + 135 \, a^{2} b^{2} d x e^{7} + 90 \, a^{3} c d x e^{7} + 15 \, a^{2} b^{2} d^{2} e^{6} + 10 \, a^{3} c d^{2} e^{6} + 315 \, a^{3} b x e^{8} + 35 \, a^{3} b d e^{7} + 70 \, a^{4} e^{8}\right)} e^{\left(-9\right)}}{630 \, {\left(x e + d\right)}^{9}}"," ",0,"-1/630*(630*c^4*x^8*e^8 + 2520*c^4*d*x^7*e^7 + 5880*c^4*d^2*x^6*e^6 + 8820*c^4*d^3*x^5*e^5 + 8820*c^4*d^4*x^4*e^4 + 5880*c^4*d^5*x^3*e^3 + 2520*c^4*d^6*x^2*e^2 + 630*c^4*d^7*x*e + 70*c^4*d^8 + 1260*b*c^3*x^7*e^8 + 2940*b*c^3*d*x^6*e^7 + 4410*b*c^3*d^2*x^5*e^6 + 4410*b*c^3*d^3*x^4*e^5 + 2940*b*c^3*d^4*x^3*e^4 + 1260*b*c^3*d^5*x^2*e^3 + 315*b*c^3*d^6*x*e^2 + 35*b*c^3*d^7*e + 1260*b^2*c^2*x^6*e^8 + 840*a*c^3*x^6*e^8 + 1890*b^2*c^2*d*x^5*e^7 + 1260*a*c^3*d*x^5*e^7 + 1890*b^2*c^2*d^2*x^4*e^6 + 1260*a*c^3*d^2*x^4*e^6 + 1260*b^2*c^2*d^3*x^3*e^5 + 840*a*c^3*d^3*x^3*e^5 + 540*b^2*c^2*d^4*x^2*e^4 + 360*a*c^3*d^4*x^2*e^4 + 135*b^2*c^2*d^5*x*e^3 + 90*a*c^3*d^5*x*e^3 + 15*b^2*c^2*d^6*e^2 + 10*a*c^3*d^6*e^2 + 630*b^3*c*x^5*e^8 + 1890*a*b*c^2*x^5*e^8 + 630*b^3*c*d*x^4*e^7 + 1890*a*b*c^2*d*x^4*e^7 + 420*b^3*c*d^2*x^3*e^6 + 1260*a*b*c^2*d^2*x^3*e^6 + 180*b^3*c*d^3*x^2*e^5 + 540*a*b*c^2*d^3*x^2*e^5 + 45*b^3*c*d^4*x*e^4 + 135*a*b*c^2*d^4*x*e^4 + 5*b^3*c*d^5*e^3 + 15*a*b*c^2*d^5*e^3 + 126*b^4*x^4*e^8 + 1512*a*b^2*c*x^4*e^8 + 756*a^2*c^2*x^4*e^8 + 84*b^4*d*x^3*e^7 + 1008*a*b^2*c*d*x^3*e^7 + 504*a^2*c^2*d*x^3*e^7 + 36*b^4*d^2*x^2*e^6 + 432*a*b^2*c*d^2*x^2*e^6 + 216*a^2*c^2*d^2*x^2*e^6 + 9*b^4*d^3*x*e^5 + 108*a*b^2*c*d^3*x*e^5 + 54*a^2*c^2*d^3*x*e^5 + b^4*d^4*e^4 + 12*a*b^2*c*d^4*e^4 + 6*a^2*c^2*d^4*e^4 + 420*a*b^3*x^3*e^8 + 1260*a^2*b*c*x^3*e^8 + 180*a*b^3*d*x^2*e^7 + 540*a^2*b*c*d*x^2*e^7 + 45*a*b^3*d^2*x*e^6 + 135*a^2*b*c*d^2*x*e^6 + 5*a*b^3*d^3*e^5 + 15*a^2*b*c*d^3*e^5 + 540*a^2*b^2*x^2*e^8 + 360*a^3*c*x^2*e^8 + 135*a^2*b^2*d*x*e^7 + 90*a^3*c*d*x*e^7 + 15*a^2*b^2*d^2*e^6 + 10*a^3*c*d^2*e^6 + 315*a^3*b*x*e^8 + 35*a^3*b*d*e^7 + 70*a^4*e^8)*e^(-9)/(x*e + d)^9","B",0
2161,1,944,0,0.221277," ","integrate((c*x^2+b*x+a)^4/(e*x+d)^11,x, algorithm=""giac"")","-\frac{{\left(630 \, c^{4} x^{8} e^{8} + 1680 \, c^{4} d x^{7} e^{7} + 2940 \, c^{4} d^{2} x^{6} e^{6} + 3528 \, c^{4} d^{3} x^{5} e^{5} + 2940 \, c^{4} d^{4} x^{4} e^{4} + 1680 \, c^{4} d^{5} x^{3} e^{3} + 630 \, c^{4} d^{6} x^{2} e^{2} + 140 \, c^{4} d^{7} x e + 14 \, c^{4} d^{8} + 1680 \, b c^{3} x^{7} e^{8} + 2940 \, b c^{3} d x^{6} e^{7} + 3528 \, b c^{3} d^{2} x^{5} e^{6} + 2940 \, b c^{3} d^{3} x^{4} e^{5} + 1680 \, b c^{3} d^{4} x^{3} e^{4} + 630 \, b c^{3} d^{5} x^{2} e^{3} + 140 \, b c^{3} d^{6} x e^{2} + 14 \, b c^{3} d^{7} e + 1890 \, b^{2} c^{2} x^{6} e^{8} + 1260 \, a c^{3} x^{6} e^{8} + 2268 \, b^{2} c^{2} d x^{5} e^{7} + 1512 \, a c^{3} d x^{5} e^{7} + 1890 \, b^{2} c^{2} d^{2} x^{4} e^{6} + 1260 \, a c^{3} d^{2} x^{4} e^{6} + 1080 \, b^{2} c^{2} d^{3} x^{3} e^{5} + 720 \, a c^{3} d^{3} x^{3} e^{5} + 405 \, b^{2} c^{2} d^{4} x^{2} e^{4} + 270 \, a c^{3} d^{4} x^{2} e^{4} + 90 \, b^{2} c^{2} d^{5} x e^{3} + 60 \, a c^{3} d^{5} x e^{3} + 9 \, b^{2} c^{2} d^{6} e^{2} + 6 \, a c^{3} d^{6} e^{2} + 1008 \, b^{3} c x^{5} e^{8} + 3024 \, a b c^{2} x^{5} e^{8} + 840 \, b^{3} c d x^{4} e^{7} + 2520 \, a b c^{2} d x^{4} e^{7} + 480 \, b^{3} c d^{2} x^{3} e^{6} + 1440 \, a b c^{2} d^{2} x^{3} e^{6} + 180 \, b^{3} c d^{3} x^{2} e^{5} + 540 \, a b c^{2} d^{3} x^{2} e^{5} + 40 \, b^{3} c d^{4} x e^{4} + 120 \, a b c^{2} d^{4} x e^{4} + 4 \, b^{3} c d^{5} e^{3} + 12 \, a b c^{2} d^{5} e^{3} + 210 \, b^{4} x^{4} e^{8} + 2520 \, a b^{2} c x^{4} e^{8} + 1260 \, a^{2} c^{2} x^{4} e^{8} + 120 \, b^{4} d x^{3} e^{7} + 1440 \, a b^{2} c d x^{3} e^{7} + 720 \, a^{2} c^{2} d x^{3} e^{7} + 45 \, b^{4} d^{2} x^{2} e^{6} + 540 \, a b^{2} c d^{2} x^{2} e^{6} + 270 \, a^{2} c^{2} d^{2} x^{2} e^{6} + 10 \, b^{4} d^{3} x e^{5} + 120 \, a b^{2} c d^{3} x e^{5} + 60 \, a^{2} c^{2} d^{3} x e^{5} + b^{4} d^{4} e^{4} + 12 \, a b^{2} c d^{4} e^{4} + 6 \, a^{2} c^{2} d^{4} e^{4} + 720 \, a b^{3} x^{3} e^{8} + 2160 \, a^{2} b c x^{3} e^{8} + 270 \, a b^{3} d x^{2} e^{7} + 810 \, a^{2} b c d x^{2} e^{7} + 60 \, a b^{3} d^{2} x e^{6} + 180 \, a^{2} b c d^{2} x e^{6} + 6 \, a b^{3} d^{3} e^{5} + 18 \, a^{2} b c d^{3} e^{5} + 945 \, a^{2} b^{2} x^{2} e^{8} + 630 \, a^{3} c x^{2} e^{8} + 210 \, a^{2} b^{2} d x e^{7} + 140 \, a^{3} c d x e^{7} + 21 \, a^{2} b^{2} d^{2} e^{6} + 14 \, a^{3} c d^{2} e^{6} + 560 \, a^{3} b x e^{8} + 56 \, a^{3} b d e^{7} + 126 \, a^{4} e^{8}\right)} e^{\left(-9\right)}}{1260 \, {\left(x e + d\right)}^{10}}"," ",0,"-1/1260*(630*c^4*x^8*e^8 + 1680*c^4*d*x^7*e^7 + 2940*c^4*d^2*x^6*e^6 + 3528*c^4*d^3*x^5*e^5 + 2940*c^4*d^4*x^4*e^4 + 1680*c^4*d^5*x^3*e^3 + 630*c^4*d^6*x^2*e^2 + 140*c^4*d^7*x*e + 14*c^4*d^8 + 1680*b*c^3*x^7*e^8 + 2940*b*c^3*d*x^6*e^7 + 3528*b*c^3*d^2*x^5*e^6 + 2940*b*c^3*d^3*x^4*e^5 + 1680*b*c^3*d^4*x^3*e^4 + 630*b*c^3*d^5*x^2*e^3 + 140*b*c^3*d^6*x*e^2 + 14*b*c^3*d^7*e + 1890*b^2*c^2*x^6*e^8 + 1260*a*c^3*x^6*e^8 + 2268*b^2*c^2*d*x^5*e^7 + 1512*a*c^3*d*x^5*e^7 + 1890*b^2*c^2*d^2*x^4*e^6 + 1260*a*c^3*d^2*x^4*e^6 + 1080*b^2*c^2*d^3*x^3*e^5 + 720*a*c^3*d^3*x^3*e^5 + 405*b^2*c^2*d^4*x^2*e^4 + 270*a*c^3*d^4*x^2*e^4 + 90*b^2*c^2*d^5*x*e^3 + 60*a*c^3*d^5*x*e^3 + 9*b^2*c^2*d^6*e^2 + 6*a*c^3*d^6*e^2 + 1008*b^3*c*x^5*e^8 + 3024*a*b*c^2*x^5*e^8 + 840*b^3*c*d*x^4*e^7 + 2520*a*b*c^2*d*x^4*e^7 + 480*b^3*c*d^2*x^3*e^6 + 1440*a*b*c^2*d^2*x^3*e^6 + 180*b^3*c*d^3*x^2*e^5 + 540*a*b*c^2*d^3*x^2*e^5 + 40*b^3*c*d^4*x*e^4 + 120*a*b*c^2*d^4*x*e^4 + 4*b^3*c*d^5*e^3 + 12*a*b*c^2*d^5*e^3 + 210*b^4*x^4*e^8 + 2520*a*b^2*c*x^4*e^8 + 1260*a^2*c^2*x^4*e^8 + 120*b^4*d*x^3*e^7 + 1440*a*b^2*c*d*x^3*e^7 + 720*a^2*c^2*d*x^3*e^7 + 45*b^4*d^2*x^2*e^6 + 540*a*b^2*c*d^2*x^2*e^6 + 270*a^2*c^2*d^2*x^2*e^6 + 10*b^4*d^3*x*e^5 + 120*a*b^2*c*d^3*x*e^5 + 60*a^2*c^2*d^3*x*e^5 + b^4*d^4*e^4 + 12*a*b^2*c*d^4*e^4 + 6*a^2*c^2*d^4*e^4 + 720*a*b^3*x^3*e^8 + 2160*a^2*b*c*x^3*e^8 + 270*a*b^3*d*x^2*e^7 + 810*a^2*b*c*d*x^2*e^7 + 60*a*b^3*d^2*x*e^6 + 180*a^2*b*c*d^2*x*e^6 + 6*a*b^3*d^3*e^5 + 18*a^2*b*c*d^3*e^5 + 945*a^2*b^2*x^2*e^8 + 630*a^3*c*x^2*e^8 + 210*a^2*b^2*d*x*e^7 + 140*a^3*c*d*x*e^7 + 21*a^2*b^2*d^2*e^6 + 14*a^3*c*d^2*e^6 + 560*a^3*b*x*e^8 + 56*a^3*b*d*e^7 + 126*a^4*e^8)*e^(-9)/(x*e + d)^10","B",0
2162,1,945,0,0.203618," ","integrate((c*x^2+b*x+a)^4/(e*x+d)^12,x, algorithm=""giac"")","-\frac{{\left(2310 \, c^{4} x^{8} e^{8} + 4620 \, c^{4} d x^{7} e^{7} + 6468 \, c^{4} d^{2} x^{6} e^{6} + 6468 \, c^{4} d^{3} x^{5} e^{5} + 4620 \, c^{4} d^{4} x^{4} e^{4} + 2310 \, c^{4} d^{5} x^{3} e^{3} + 770 \, c^{4} d^{6} x^{2} e^{2} + 154 \, c^{4} d^{7} x e + 14 \, c^{4} d^{8} + 6930 \, b c^{3} x^{7} e^{8} + 9702 \, b c^{3} d x^{6} e^{7} + 9702 \, b c^{3} d^{2} x^{5} e^{6} + 6930 \, b c^{3} d^{3} x^{4} e^{5} + 3465 \, b c^{3} d^{4} x^{3} e^{4} + 1155 \, b c^{3} d^{5} x^{2} e^{3} + 231 \, b c^{3} d^{6} x e^{2} + 21 \, b c^{3} d^{7} e + 8316 \, b^{2} c^{2} x^{6} e^{8} + 5544 \, a c^{3} x^{6} e^{8} + 8316 \, b^{2} c^{2} d x^{5} e^{7} + 5544 \, a c^{3} d x^{5} e^{7} + 5940 \, b^{2} c^{2} d^{2} x^{4} e^{6} + 3960 \, a c^{3} d^{2} x^{4} e^{6} + 2970 \, b^{2} c^{2} d^{3} x^{3} e^{5} + 1980 \, a c^{3} d^{3} x^{3} e^{5} + 990 \, b^{2} c^{2} d^{4} x^{2} e^{4} + 660 \, a c^{3} d^{4} x^{2} e^{4} + 198 \, b^{2} c^{2} d^{5} x e^{3} + 132 \, a c^{3} d^{5} x e^{3} + 18 \, b^{2} c^{2} d^{6} e^{2} + 12 \, a c^{3} d^{6} e^{2} + 4620 \, b^{3} c x^{5} e^{8} + 13860 \, a b c^{2} x^{5} e^{8} + 3300 \, b^{3} c d x^{4} e^{7} + 9900 \, a b c^{2} d x^{4} e^{7} + 1650 \, b^{3} c d^{2} x^{3} e^{6} + 4950 \, a b c^{2} d^{2} x^{3} e^{6} + 550 \, b^{3} c d^{3} x^{2} e^{5} + 1650 \, a b c^{2} d^{3} x^{2} e^{5} + 110 \, b^{3} c d^{4} x e^{4} + 330 \, a b c^{2} d^{4} x e^{4} + 10 \, b^{3} c d^{5} e^{3} + 30 \, a b c^{2} d^{5} e^{3} + 990 \, b^{4} x^{4} e^{8} + 11880 \, a b^{2} c x^{4} e^{8} + 5940 \, a^{2} c^{2} x^{4} e^{8} + 495 \, b^{4} d x^{3} e^{7} + 5940 \, a b^{2} c d x^{3} e^{7} + 2970 \, a^{2} c^{2} d x^{3} e^{7} + 165 \, b^{4} d^{2} x^{2} e^{6} + 1980 \, a b^{2} c d^{2} x^{2} e^{6} + 990 \, a^{2} c^{2} d^{2} x^{2} e^{6} + 33 \, b^{4} d^{3} x e^{5} + 396 \, a b^{2} c d^{3} x e^{5} + 198 \, a^{2} c^{2} d^{3} x e^{5} + 3 \, b^{4} d^{4} e^{4} + 36 \, a b^{2} c d^{4} e^{4} + 18 \, a^{2} c^{2} d^{4} e^{4} + 3465 \, a b^{3} x^{3} e^{8} + 10395 \, a^{2} b c x^{3} e^{8} + 1155 \, a b^{3} d x^{2} e^{7} + 3465 \, a^{2} b c d x^{2} e^{7} + 231 \, a b^{3} d^{2} x e^{6} + 693 \, a^{2} b c d^{2} x e^{6} + 21 \, a b^{3} d^{3} e^{5} + 63 \, a^{2} b c d^{3} e^{5} + 4620 \, a^{2} b^{2} x^{2} e^{8} + 3080 \, a^{3} c x^{2} e^{8} + 924 \, a^{2} b^{2} d x e^{7} + 616 \, a^{3} c d x e^{7} + 84 \, a^{2} b^{2} d^{2} e^{6} + 56 \, a^{3} c d^{2} e^{6} + 2772 \, a^{3} b x e^{8} + 252 \, a^{3} b d e^{7} + 630 \, a^{4} e^{8}\right)} e^{\left(-9\right)}}{6930 \, {\left(x e + d\right)}^{11}}"," ",0,"-1/6930*(2310*c^4*x^8*e^8 + 4620*c^4*d*x^7*e^7 + 6468*c^4*d^2*x^6*e^6 + 6468*c^4*d^3*x^5*e^5 + 4620*c^4*d^4*x^4*e^4 + 2310*c^4*d^5*x^3*e^3 + 770*c^4*d^6*x^2*e^2 + 154*c^4*d^7*x*e + 14*c^4*d^8 + 6930*b*c^3*x^7*e^8 + 9702*b*c^3*d*x^6*e^7 + 9702*b*c^3*d^2*x^5*e^6 + 6930*b*c^3*d^3*x^4*e^5 + 3465*b*c^3*d^4*x^3*e^4 + 1155*b*c^3*d^5*x^2*e^3 + 231*b*c^3*d^6*x*e^2 + 21*b*c^3*d^7*e + 8316*b^2*c^2*x^6*e^8 + 5544*a*c^3*x^6*e^8 + 8316*b^2*c^2*d*x^5*e^7 + 5544*a*c^3*d*x^5*e^7 + 5940*b^2*c^2*d^2*x^4*e^6 + 3960*a*c^3*d^2*x^4*e^6 + 2970*b^2*c^2*d^3*x^3*e^5 + 1980*a*c^3*d^3*x^3*e^5 + 990*b^2*c^2*d^4*x^2*e^4 + 660*a*c^3*d^4*x^2*e^4 + 198*b^2*c^2*d^5*x*e^3 + 132*a*c^3*d^5*x*e^3 + 18*b^2*c^2*d^6*e^2 + 12*a*c^3*d^6*e^2 + 4620*b^3*c*x^5*e^8 + 13860*a*b*c^2*x^5*e^8 + 3300*b^3*c*d*x^4*e^7 + 9900*a*b*c^2*d*x^4*e^7 + 1650*b^3*c*d^2*x^3*e^6 + 4950*a*b*c^2*d^2*x^3*e^6 + 550*b^3*c*d^3*x^2*e^5 + 1650*a*b*c^2*d^3*x^2*e^5 + 110*b^3*c*d^4*x*e^4 + 330*a*b*c^2*d^4*x*e^4 + 10*b^3*c*d^5*e^3 + 30*a*b*c^2*d^5*e^3 + 990*b^4*x^4*e^8 + 11880*a*b^2*c*x^4*e^8 + 5940*a^2*c^2*x^4*e^8 + 495*b^4*d*x^3*e^7 + 5940*a*b^2*c*d*x^3*e^7 + 2970*a^2*c^2*d*x^3*e^7 + 165*b^4*d^2*x^2*e^6 + 1980*a*b^2*c*d^2*x^2*e^6 + 990*a^2*c^2*d^2*x^2*e^6 + 33*b^4*d^3*x*e^5 + 396*a*b^2*c*d^3*x*e^5 + 198*a^2*c^2*d^3*x*e^5 + 3*b^4*d^4*e^4 + 36*a*b^2*c*d^4*e^4 + 18*a^2*c^2*d^4*e^4 + 3465*a*b^3*x^3*e^8 + 10395*a^2*b*c*x^3*e^8 + 1155*a*b^3*d*x^2*e^7 + 3465*a^2*b*c*d*x^2*e^7 + 231*a*b^3*d^2*x*e^6 + 693*a^2*b*c*d^2*x*e^6 + 21*a*b^3*d^3*e^5 + 63*a^2*b*c*d^3*e^5 + 4620*a^2*b^2*x^2*e^8 + 3080*a^3*c*x^2*e^8 + 924*a^2*b^2*d*x*e^7 + 616*a^3*c*d*x*e^7 + 84*a^2*b^2*d^2*e^6 + 56*a^3*c*d^2*e^6 + 2772*a^3*b*x*e^8 + 252*a^3*b*d*e^7 + 630*a^4*e^8)*e^(-9)/(x*e + d)^11","B",0
2163,1,26,0,0.152420," ","integrate(x^4*(x^2-4*x+3)^2,x, algorithm=""giac"")","\frac{1}{9} \, x^{9} - x^{8} + \frac{22}{7} \, x^{7} - 4 \, x^{6} + \frac{9}{5} \, x^{5}"," ",0,"1/9*x^9 - x^8 + 22/7*x^7 - 4*x^6 + 9/5*x^5","A",0
2164,1,26,0,0.147827," ","integrate(x^3*(x^2-4*x+3)^2,x, algorithm=""giac"")","\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,"1/8*x^8 - 8/7*x^7 + 11/3*x^6 - 24/5*x^5 + 9/4*x^4","A",0
2165,1,26,0,0.184689," ","integrate(x^2*(x^2-4*x+3)^2,x, algorithm=""giac"")","\frac{1}{7} \, x^{7} - \frac{4}{3} \, x^{6} + \frac{22}{5} \, x^{5} - 6 \, x^{4} + 3 \, x^{3}"," ",0,"1/7*x^7 - 4/3*x^6 + 22/5*x^5 - 6*x^4 + 3*x^3","A",0
2166,1,26,0,0.152904," ","integrate(x*(x^2-4*x+3)^2,x, algorithm=""giac"")","\frac{1}{6} \, x^{6} - \frac{8}{5} \, x^{5} + \frac{11}{2} \, x^{4} - 8 \, x^{3} + \frac{9}{2} \, x^{2}"," ",0,"1/6*x^6 - 8/5*x^5 + 11/2*x^4 - 8*x^3 + 9/2*x^2","A",0
2167,1,24,0,0.165741," ","integrate((x^2-4*x+3)^2,x, algorithm=""giac"")","\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",0
2168,1,24,0,0.148688," ","integrate((x^2-4*x+3)^2/x,x, algorithm=""giac"")","\frac{1}{4} \, x^{4} - \frac{8}{3} \, x^{3} + 11 \, x^{2} - 24 \, x + 9 \, \log\left({\left| x \right|}\right)"," ",0,"1/4*x^4 - 8/3*x^3 + 11*x^2 - 24*x + 9*log(abs(x))","A",0
2169,1,24,0,0.147486," ","integrate((x^2-4*x+3)^2/x^2,x, algorithm=""giac"")","\frac{1}{3} \, x^{3} - 4 \, x^{2} + 22 \, x - \frac{9}{x} - 24 \, \log\left({\left| x \right|}\right)"," ",0,"1/3*x^3 - 4*x^2 + 22*x - 9/x - 24*log(abs(x))","A",0
2170,1,24,0,0.149988," ","integrate((x^2-4*x+3)^2/x^3,x, algorithm=""giac"")","\frac{1}{2} \, x^{2} - 8 \, x + \frac{3 \, {\left(16 \, x - 3\right)}}{2 \, x^{2}} + 22 \, \log\left({\left| x \right|}\right)"," ",0,"1/2*x^2 - 8*x + 3/2*(16*x - 3)/x^2 + 22*log(abs(x))","A",0
2171,1,22,0,0.157148," ","integrate((x^2-4*x+3)^2/x^4,x, algorithm=""giac"")","x - \frac{22 \, x^{2} - 12 \, x + 3}{x^{3}} - 8 \, \log\left({\left| x \right|}\right)"," ",0,"x - (22*x^2 - 12*x + 3)/x^3 - 8*log(abs(x))","A",0
2172,1,24,0,0.152387," ","integrate((x^2-4*x+3)^2/x^5,x, algorithm=""giac"")","\frac{32 \, x^{3} - 44 \, x^{2} + 32 \, x - 9}{4 \, x^{4}} + \log\left({\left| x \right|}\right)"," ",0,"1/4*(32*x^3 - 44*x^2 + 32*x - 9)/x^4 + log(abs(x))","A",0
2173,1,25,0,0.148839," ","integrate((x^2-4*x+3)^2/x^6,x, algorithm=""giac"")","-\frac{15 \, x^{4} - 60 \, x^{3} + 110 \, x^{2} - 90 \, x + 27}{15 \, x^{5}}"," ",0,"-1/15*(15*x^4 - 60*x^3 + 110*x^2 - 90*x + 27)/x^5","A",0
2174,1,25,0,0.163056," ","integrate((x^2-4*x+3)^2/x^7,x, algorithm=""giac"")","-\frac{15 \, x^{4} - 80 \, x^{3} + 165 \, x^{2} - 144 \, x + 45}{30 \, x^{6}}"," ",0,"-1/30*(15*x^4 - 80*x^3 + 165*x^2 - 144*x + 45)/x^6","A",0
2175,1,13,0,0.171201," ","integrate((x^2+2*x+2)/(2+x),x, algorithm=""giac"")","\frac{1}{2} \, x^{2} + 2 \, \log\left({\left| x + 2 \right|}\right)"," ",0,"1/2*x^2 + 2*log(abs(x + 2))","A",0
2176,1,16,0,0.201610," ","integrate((x^2+4*x+5)/(-2+x),x, algorithm=""giac"")","\frac{1}{2} \, x^{2} + 6 \, x + 17 \, \log\left({\left| x - 2 \right|}\right)"," ",0,"1/2*x^2 + 6*x + 17*log(abs(x - 2))","A",0
2177,1,13,0,0.153605," ","integrate((x^2+2*x+2)/(1+x)^3,x, algorithm=""giac"")","-\frac{1}{2 \, {\left(x + 1\right)}^{2}} + \log\left({\left| x + 1 \right|}\right)"," ",0,"-1/2/(x + 1)^2 + log(abs(x + 1))","A",0
2178,1,15,0,0.147388," ","integrate((2*x^2+3*x+3)/(1+x)^3,x, algorithm=""giac"")","\frac{x}{{\left(x + 1\right)}^{2}} + 2 \, \log\left({\left| x + 1 \right|}\right)"," ",0,"x/(x + 1)^2 + 2*log(abs(x + 1))","A",0
2179,1,10,0,0.149921," ","integrate((x^2+x+1)/x,x, algorithm=""giac"")","\frac{1}{2} \, x^{2} + x + \log\left({\left| x \right|}\right)"," ",0,"1/2*x^2 + x + log(abs(x))","A",0
2180,1,12,0,0.165370," ","integrate((x^2+6*x+9)/x^2,x, algorithm=""giac"")","x - \frac{9}{x} + 6 \, \log\left({\left| x \right|}\right)"," ",0,"x - 9/x + 6*log(abs(x))","A",0
2181,1,15,0,0.148093," ","integrate((x^2+2*x+1)/x^4,x, algorithm=""giac"")","-\frac{3 \, x^{2} + 3 \, x + 1}{3 \, x^{3}}"," ",0,"-1/3*(3*x^2 + 3*x + 1)/x^3","A",0
2182,1,265,0,0.158925," ","integrate((e*x+d)^4/(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{2 \, c^{2} x^{3} e^{4} + 12 \, c^{2} d x^{2} e^{3} + 36 \, c^{2} d^{2} x e^{2} - 3 \, b c x^{2} e^{4} - 24 \, b c d x e^{3} + 6 \, b^{2} x e^{4} - 6 \, a c x e^{4}}{6 \, c^{3}} + \frac{{\left(4 \, c^{3} d^{3} e - 6 \, b c^{2} d^{2} e^{2} + 4 \, b^{2} c d e^{3} - 4 \, a c^{2} d e^{3} - b^{3} e^{4} + 2 \, a b c e^{4}\right)} \log\left(c x^{2} + b x + a\right)}{2 \, c^{4}} + \frac{{\left(2 \, c^{4} d^{4} - 4 \, b c^{3} d^{3} e + 6 \, b^{2} c^{2} d^{2} e^{2} - 12 \, a c^{3} d^{2} e^{2} - 4 \, b^{3} c d e^{3} + 12 \, a b c^{2} d e^{3} + b^{4} e^{4} - 4 \, a b^{2} c e^{4} + 2 \, a^{2} c^{2} e^{4}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{\sqrt{-b^{2} + 4 \, a c} c^{4}}"," ",0,"1/6*(2*c^2*x^3*e^4 + 12*c^2*d*x^2*e^3 + 36*c^2*d^2*x*e^2 - 3*b*c*x^2*e^4 - 24*b*c*d*x*e^3 + 6*b^2*x*e^4 - 6*a*c*x*e^4)/c^3 + 1/2*(4*c^3*d^3*e - 6*b*c^2*d^2*e^2 + 4*b^2*c*d*e^3 - 4*a*c^2*d*e^3 - b^3*e^4 + 2*a*b*c*e^4)*log(c*x^2 + b*x + a)/c^4 + (2*c^4*d^4 - 4*b*c^3*d^3*e + 6*b^2*c^2*d^2*e^2 - 12*a*c^3*d^2*e^2 - 4*b^3*c*d*e^3 + 12*a*b*c^2*d*e^3 + b^4*e^4 - 4*a*b^2*c*e^4 + 2*a^2*c^2*e^4)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*c^4)","A",0
2183,1,161,0,0.176054," ","integrate((e*x+d)^3/(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{c x^{2} e^{3} + 6 \, c d x e^{2} - 2 \, b x e^{3}}{2 \, c^{2}} + \frac{{\left(3 \, c^{2} d^{2} e - 3 \, b c d e^{2} + b^{2} e^{3} - a c e^{3}\right)} \log\left(c x^{2} + b x + a\right)}{2 \, c^{3}} + \frac{{\left(2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e + 3 \, b^{2} c d e^{2} - 6 \, a c^{2} d e^{2} - b^{3} e^{3} + 3 \, a b c e^{3}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{\sqrt{-b^{2} + 4 \, a c} c^{3}}"," ",0,"1/2*(c*x^2*e^3 + 6*c*d*x*e^2 - 2*b*x*e^3)/c^2 + 1/2*(3*c^2*d^2*e - 3*b*c*d*e^2 + b^2*e^3 - a*c*e^3)*log(c*x^2 + b*x + a)/c^3 + (2*c^3*d^3 - 3*b*c^2*d^2*e + 3*b^2*c*d*e^2 - 6*a*c^2*d*e^2 - b^3*e^3 + 3*a*b*c*e^3)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*c^3)","A",0
2184,1,100,0,0.156458," ","integrate((e*x+d)^2/(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{x e^{2}}{c} + \frac{{\left(2 \, c d e - b e^{2}\right)} \log\left(c x^{2} + b x + a\right)}{2 \, c^{2}} + \frac{{\left(2 \, c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2} - 2 \, a c e^{2}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{\sqrt{-b^{2} + 4 \, a c} c^{2}}"," ",0,"x*e^2/c + 1/2*(2*c*d*e - b*e^2)*log(c*x^2 + b*x + a)/c^2 + (2*c^2*d^2 - 2*b*c*d*e + b^2*e^2 - 2*a*c*e^2)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*c^2)","A",0
2185,1,65,0,0.196686," ","integrate((e*x+d)/(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{e \log\left(c x^{2} + b x + a\right)}{2 \, c} + \frac{{\left(2 \, c d - b e\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{\sqrt{-b^{2} + 4 \, a c} c}"," ",0,"1/2*e*log(c*x^2 + b*x + a)/c + (2*c*d - b*e)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/(sqrt(-b^2 + 4*a*c)*c)","A",0
2186,1,34,0,0.152358," ","integrate(1/(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{2 \, \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{\sqrt{-b^{2} + 4 \, a c}}"," ",0,"2*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/sqrt(-b^2 + 4*a*c)","A",0
2187,1,126,0,0.158561," ","integrate(1/(e*x+d)/(c*x^2+b*x+a),x, algorithm=""giac"")","-\frac{e \log\left(c x^{2} + b x + a\right)}{2 \, {\left(c d^{2} - b d e + a e^{2}\right)}} + \frac{e^{2} \log\left({\left| x e + d \right|}\right)}{c d^{2} e - b d e^{2} + a e^{3}} + \frac{{\left(2 \, c d - b e\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{-b^{2} + 4 \, a c}}"," ",0,"-1/2*e*log(c*x^2 + b*x + a)/(c*d^2 - b*d*e + a*e^2) + e^2*log(abs(x*e + d))/(c*d^2*e - b*d*e^2 + a*e^3) + (2*c*d - b*e)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((c*d^2 - b*d*e + a*e^2)*sqrt(-b^2 + 4*a*c))","A",0
2188,1,325,0,0.165829," ","integrate(1/(e*x+d)^2/(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{{\left(2 \, c^{2} d^{2} e^{2} - 2 \, b c d e^{3} + b^{2} e^{4} - 2 \, a c e^{4}\right)} \arctan\left(\frac{{\left(2 \, c d - \frac{2 \, c d^{2}}{x e + d} - b e + \frac{2 \, b d e}{x e + d} - \frac{2 \, a e^{2}}{x e + d}\right)} e^{\left(-1\right)}}{\sqrt{-b^{2} + 4 \, a c}}\right) e^{\left(-2\right)}}{{\left(c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2} + 2 \, a c d^{2} e^{2} - 2 \, a b d e^{3} + a^{2} e^{4}\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{{\left(2 \, c d e - b e^{2}\right)} \log\left(c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{b e}{x e + d} - \frac{b d e}{{\left(x e + d\right)}^{2}} + \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right)}{2 \, {\left(c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2} + 2 \, a c d^{2} e^{2} - 2 \, a b d e^{3} + a^{2} e^{4}\right)}} - \frac{e^{3}}{{\left(c d^{2} e^{2} - b d e^{3} + a e^{4}\right)} {\left(x e + d\right)}}"," ",0,"(2*c^2*d^2*e^2 - 2*b*c*d*e^3 + b^2*e^4 - 2*a*c*e^4)*arctan((2*c*d - 2*c*d^2/(x*e + d) - b*e + 2*b*d*e/(x*e + d) - 2*a*e^2/(x*e + d))*e^(-1)/sqrt(-b^2 + 4*a*c))*e^(-2)/((c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2 + 2*a*c*d^2*e^2 - 2*a*b*d*e^3 + a^2*e^4)*sqrt(-b^2 + 4*a*c)) - 1/2*(2*c*d*e - b*e^2)*log(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + b*e/(x*e + d) - b*d*e/(x*e + d)^2 + a*e^2/(x*e + d)^2)/(c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2 + 2*a*c*d^2*e^2 - 2*a*b*d*e^3 + a^2*e^4) - e^3/((c*d^2*e^2 - b*d*e^3 + a*e^4)*(x*e + d))","A",0
2189,1,593,0,0.164505," ","integrate(1/(e*x+d)^3/(c*x^2+b*x+a),x, algorithm=""giac"")","-\frac{{\left(3 \, c^{2} d^{2} e - 3 \, b c d e^{2} + b^{2} e^{3} - a c e^{3}\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(c^{3} d^{6} - 3 \, b c^{2} d^{5} e + 3 \, b^{2} c d^{4} e^{2} + 3 \, a c^{2} d^{4} e^{2} - b^{3} d^{3} e^{3} - 6 \, a b c d^{3} e^{3} + 3 \, a b^{2} d^{2} e^{4} + 3 \, a^{2} c d^{2} e^{4} - 3 \, a^{2} b d e^{5} + a^{3} e^{6}\right)}} + \frac{{\left(3 \, c^{2} d^{2} e^{2} - 3 \, b c d e^{3} + b^{2} e^{4} - a c e^{4}\right)} \log\left({\left| x e + d \right|}\right)}{c^{3} d^{6} e - 3 \, b c^{2} d^{5} e^{2} + 3 \, b^{2} c d^{4} e^{3} + 3 \, a c^{2} d^{4} e^{3} - b^{3} d^{3} e^{4} - 6 \, a b c d^{3} e^{4} + 3 \, a b^{2} d^{2} e^{5} + 3 \, a^{2} c d^{2} e^{5} - 3 \, a^{2} b d e^{6} + a^{3} e^{7}} + \frac{{\left(2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e + 3 \, b^{2} c d e^{2} - 6 \, a c^{2} d e^{2} - b^{3} e^{3} + 3 \, a b c e^{3}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(c^{3} d^{6} - 3 \, b c^{2} d^{5} e + 3 \, b^{2} c d^{4} e^{2} + 3 \, a c^{2} d^{4} e^{2} - b^{3} d^{3} e^{3} - 6 \, a b c d^{3} e^{3} + 3 \, a b^{2} d^{2} e^{4} + 3 \, a^{2} c d^{2} e^{4} - 3 \, a^{2} b d e^{5} + a^{3} e^{6}\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{5 \, c^{2} d^{4} e - 8 \, b c d^{3} e^{2} + 3 \, b^{2} d^{2} e^{3} + 6 \, a c d^{2} e^{3} - 4 \, a b d e^{4} + a^{2} e^{5} + 2 \, {\left(2 \, c^{2} d^{3} e^{2} - 3 \, b c d^{2} e^{3} + b^{2} d e^{4} + 2 \, a c d e^{4} - a b e^{5}\right)} x}{2 \, {\left(c d^{2} - b d e + a e^{2}\right)}^{3} {\left(x e + d\right)}^{2}}"," ",0,"-1/2*(3*c^2*d^2*e - 3*b*c*d*e^2 + b^2*e^3 - a*c*e^3)*log(c*x^2 + b*x + a)/(c^3*d^6 - 3*b*c^2*d^5*e + 3*b^2*c*d^4*e^2 + 3*a*c^2*d^4*e^2 - b^3*d^3*e^3 - 6*a*b*c*d^3*e^3 + 3*a*b^2*d^2*e^4 + 3*a^2*c*d^2*e^4 - 3*a^2*b*d*e^5 + a^3*e^6) + (3*c^2*d^2*e^2 - 3*b*c*d*e^3 + b^2*e^4 - a*c*e^4)*log(abs(x*e + d))/(c^3*d^6*e - 3*b*c^2*d^5*e^2 + 3*b^2*c*d^4*e^3 + 3*a*c^2*d^4*e^3 - b^3*d^3*e^4 - 6*a*b*c*d^3*e^4 + 3*a*b^2*d^2*e^5 + 3*a^2*c*d^2*e^5 - 3*a^2*b*d*e^6 + a^3*e^7) + (2*c^3*d^3 - 3*b*c^2*d^2*e + 3*b^2*c*d*e^2 - 6*a*c^2*d*e^2 - b^3*e^3 + 3*a*b*c*e^3)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((c^3*d^6 - 3*b*c^2*d^5*e + 3*b^2*c*d^4*e^2 + 3*a*c^2*d^4*e^2 - b^3*d^3*e^3 - 6*a*b*c*d^3*e^3 + 3*a*b^2*d^2*e^4 + 3*a^2*c*d^2*e^4 - 3*a^2*b*d*e^5 + a^3*e^6)*sqrt(-b^2 + 4*a*c)) - 1/2*(5*c^2*d^4*e - 8*b*c*d^3*e^2 + 3*b^2*d^2*e^3 + 6*a*c*d^2*e^3 - 4*a*b*d*e^4 + a^2*e^5 + 2*(2*c^2*d^3*e^2 - 3*b*c*d^2*e^3 + b^2*d*e^4 + 2*a*c*d*e^4 - a*b*e^5)*x)/((c*d^2 - b*d*e + a*e^2)^3*(x*e + d)^2)","B",0
2190,1,511,0,0.236934," ","integrate((e*x+d)^5/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","-\frac{{\left(4 \, c^{5} d^{5} - 10 \, b c^{4} d^{4} e + 40 \, a c^{4} d^{3} e^{2} + 10 \, b^{3} c^{2} d^{2} e^{3} - 60 \, a b c^{3} d^{2} e^{3} - 10 \, b^{4} c d e^{4} + 60 \, a b^{2} c^{2} d e^{4} - 60 \, a^{2} c^{3} d e^{4} + 3 \, b^{5} e^{5} - 20 \, a b^{3} c e^{5} + 30 \, a^{2} b c^{2} e^{5}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{{\left(10 \, c^{2} d^{2} e^{3} - 10 \, b c d e^{4} + 3 \, b^{2} e^{5} - 2 \, a c e^{5}\right)} \log\left(c x^{2} + b x + a\right)}{2 \, c^{4}} + \frac{c^{2} x^{2} e^{5} + 10 \, c^{2} d x e^{4} - 4 \, b c x e^{5}}{2 \, c^{4}} - \frac{b c^{4} d^{5} - 10 \, a c^{4} d^{4} e + 10 \, a b c^{3} d^{3} e^{2} - 10 \, a b^{2} c^{2} d^{2} e^{3} + 20 \, a^{2} c^{3} d^{2} e^{3} + 5 \, a b^{3} c d e^{4} - 15 \, a^{2} b c^{2} d e^{4} - a b^{4} e^{5} + 4 \, a^{2} b^{2} c e^{5} - 2 \, a^{3} c^{2} e^{5} + {\left(2 \, c^{5} d^{5} - 5 \, b c^{4} d^{4} e + 10 \, b^{2} c^{3} d^{3} e^{2} - 20 \, a c^{4} d^{3} e^{2} - 10 \, b^{3} c^{2} d^{2} e^{3} + 30 \, a b c^{3} d^{2} e^{3} + 5 \, b^{4} c d e^{4} - 20 \, a b^{2} c^{2} d e^{4} + 10 \, a^{2} c^{3} d e^{4} - b^{5} e^{5} + 5 \, a b^{3} c e^{5} - 5 \, a^{2} b c^{2} e^{5}\right)} x}{{\left(c x^{2} + b x + a\right)} {\left(b^{2} - 4 \, a c\right)} c^{4}}"," ",0,"-(4*c^5*d^5 - 10*b*c^4*d^4*e + 40*a*c^4*d^3*e^2 + 10*b^3*c^2*d^2*e^3 - 60*a*b*c^3*d^2*e^3 - 10*b^4*c*d*e^4 + 60*a*b^2*c^2*d*e^4 - 60*a^2*c^3*d*e^4 + 3*b^5*e^5 - 20*a*b^3*c*e^5 + 30*a^2*b*c^2*e^5)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^2*c^4 - 4*a*c^5)*sqrt(-b^2 + 4*a*c)) + 1/2*(10*c^2*d^2*e^3 - 10*b*c*d*e^4 + 3*b^2*e^5 - 2*a*c*e^5)*log(c*x^2 + b*x + a)/c^4 + 1/2*(c^2*x^2*e^5 + 10*c^2*d*x*e^4 - 4*b*c*x*e^5)/c^4 - (b*c^4*d^5 - 10*a*c^4*d^4*e + 10*a*b*c^3*d^3*e^2 - 10*a*b^2*c^2*d^2*e^3 + 20*a^2*c^3*d^2*e^3 + 5*a*b^3*c*d*e^4 - 15*a^2*b*c^2*d*e^4 - a*b^4*e^5 + 4*a^2*b^2*c*e^5 - 2*a^3*c^2*e^5 + (2*c^5*d^5 - 5*b*c^4*d^4*e + 10*b^2*c^3*d^3*e^2 - 20*a*c^4*d^3*e^2 - 10*b^3*c^2*d^2*e^3 + 30*a*b*c^3*d^2*e^3 + 5*b^4*c*d*e^4 - 20*a*b^2*c^2*d*e^4 + 10*a^2*c^3*d*e^4 - b^5*e^5 + 5*a*b^3*c*e^5 - 5*a^2*b*c^2*e^5)*x)/((c*x^2 + b*x + a)*(b^2 - 4*a*c)*c^4)","A",0
2191,1,355,0,0.179121," ","integrate((e*x+d)^4/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","-\frac{2 \, {\left(2 \, c^{4} d^{4} - 4 \, b c^{3} d^{3} e + 12 \, a c^{3} d^{2} e^{2} + 2 \, b^{3} c d e^{3} - 12 \, a b c^{2} d e^{3} - b^{4} e^{4} + 6 \, a b^{2} c e^{4} - 6 \, a^{2} c^{2} e^{4}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{x e^{4}}{c^{2}} + \frac{{\left(2 \, c d e^{3} - b e^{4}\right)} \log\left(c x^{2} + b x + a\right)}{c^{3}} - \frac{\frac{{\left(2 \, c^{4} d^{4} - 4 \, b c^{3} d^{3} e + 6 \, b^{2} c^{2} d^{2} e^{2} - 12 \, a c^{3} d^{2} e^{2} - 4 \, b^{3} c d e^{3} + 12 \, a b c^{2} d e^{3} + b^{4} e^{4} - 4 \, a b^{2} c e^{4} + 2 \, a^{2} c^{2} e^{4}\right)} x}{c} + \frac{b c^{3} d^{4} - 8 \, a c^{3} d^{3} e + 6 \, a b c^{2} d^{2} e^{2} - 4 \, a b^{2} c d e^{3} + 8 \, a^{2} c^{2} d e^{3} + a b^{3} e^{4} - 3 \, a^{2} b c e^{4}}{c}}{{\left(c x^{2} + b x + a\right)} {\left(b^{2} - 4 \, a c\right)} c^{2}}"," ",0,"-2*(2*c^4*d^4 - 4*b*c^3*d^3*e + 12*a*c^3*d^2*e^2 + 2*b^3*c*d*e^3 - 12*a*b*c^2*d*e^3 - b^4*e^4 + 6*a*b^2*c*e^4 - 6*a^2*c^2*e^4)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^2*c^3 - 4*a*c^4)*sqrt(-b^2 + 4*a*c)) + x*e^4/c^2 + (2*c*d*e^3 - b*e^4)*log(c*x^2 + b*x + a)/c^3 - ((2*c^4*d^4 - 4*b*c^3*d^3*e + 6*b^2*c^2*d^2*e^2 - 12*a*c^3*d^2*e^2 - 4*b^3*c*d*e^3 + 12*a*b*c^2*d*e^3 + b^4*e^4 - 4*a*b^2*c*e^4 + 2*a^2*c^2*e^4)*x/c + (b*c^3*d^4 - 8*a*c^3*d^3*e + 6*a*b*c^2*d^2*e^2 - 4*a*b^2*c*d*e^3 + 8*a^2*c^2*d*e^3 + a*b^3*e^4 - 3*a^2*b*c*e^4)/c)/((c*x^2 + b*x + a)*(b^2 - 4*a*c)*c^2)","A",0
2192,1,236,0,0.161780," ","integrate((e*x+d)^3/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","-\frac{{\left(4 \, c^{3} d^{3} - 6 \, b c^{2} d^{2} e + 12 \, a c^{2} d e^{2} + b^{3} e^{3} - 6 \, a b c e^{3}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{e^{3} \log\left(c x^{2} + b x + a\right)}{2 \, c^{2}} - \frac{b c^{2} d^{3} - 6 \, a c^{2} d^{2} e + 3 \, a b c d e^{2} - a b^{2} e^{3} + 2 \, a^{2} c e^{3} + {\left(2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e + 3 \, b^{2} c d e^{2} - 6 \, a c^{2} d e^{2} - b^{3} e^{3} + 3 \, a b c e^{3}\right)} x}{{\left(c x^{2} + b x + a\right)} {\left(b^{2} - 4 \, a c\right)} c^{2}}"," ",0,"-(4*c^3*d^3 - 6*b*c^2*d^2*e + 12*a*c^2*d*e^2 + b^3*e^3 - 6*a*b*c*e^3)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^2*c^2 - 4*a*c^3)*sqrt(-b^2 + 4*a*c)) + 1/2*e^3*log(c*x^2 + b*x + a)/c^2 - (b*c^2*d^3 - 6*a*c^2*d^2*e + 3*a*b*c*d*e^2 - a*b^2*e^3 + 2*a^2*c*e^3 + (2*c^3*d^3 - 3*b*c^2*d^2*e + 3*b^2*c*d*e^2 - 6*a*c^2*d*e^2 - b^3*e^3 + 3*a*b*c*e^3)*x)/((c*x^2 + b*x + a)*(b^2 - 4*a*c)*c^2)","A",0
2193,1,139,0,0.159268," ","integrate((e*x+d)^2/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","-\frac{4 \, {\left(c d^{2} - b d e + a e^{2}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{2} - 4 \, a c\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{2 \, c^{2} d^{2} x - 2 \, b c d x e + b c d^{2} + b^{2} x e^{2} - 2 \, a c x e^{2} - 4 \, a c d e + a b e^{2}}{{\left(b^{2} c - 4 \, a c^{2}\right)} {\left(c x^{2} + b x + a\right)}}"," ",0,"-4*(c*d^2 - b*d*e + a*e^2)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^2 - 4*a*c)*sqrt(-b^2 + 4*a*c)) - (2*c^2*d^2*x - 2*b*c*d*x*e + b*c*d^2 + b^2*x*e^2 - 2*a*c*x*e^2 - 4*a*c*d*e + a*b*e^2)/((b^2*c - 4*a*c^2)*(c*x^2 + b*x + a))","A",0
2194,1,99,0,0.159720," ","integrate((e*x+d)/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","-\frac{2 \, {\left(2 \, c d - b e\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{2} - 4 \, a c\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{2 \, c d x - b x e + b d - 2 \, a e}{{\left(c x^{2} + b x + a\right)} {\left(b^{2} - 4 \, a c\right)}}"," ",0,"-2*(2*c*d - b*e)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^2 - 4*a*c)*sqrt(-b^2 + 4*a*c)) - (2*c*d*x - b*x*e + b*d - 2*a*e)/((c*x^2 + b*x + a)*(b^2 - 4*a*c))","A",0
2195,1,76,0,0.193238," ","integrate(1/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","-\frac{4 \, c \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{2} - 4 \, a c\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{2 \, c x + b}{{\left(c x^{2} + b x + a\right)} {\left(b^{2} - 4 \, a c\right)}}"," ",0,"-4*c*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^2 - 4*a*c)*sqrt(-b^2 + 4*a*c)) - (2*c*x + b)/((c*x^2 + b*x + a)*(b^2 - 4*a*c))","A",0
2196,1,470,0,0.253770," ","integrate(1/(e*x+d)/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","-\frac{e^{3} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2} + 2 \, a c d^{2} e^{2} - 2 \, a b d e^{3} + a^{2} e^{4}\right)}} + \frac{e^{4} \log\left({\left| x e + d \right|}\right)}{c^{2} d^{4} e - 2 \, b c d^{3} e^{2} + b^{2} d^{2} e^{3} + 2 \, a c d^{2} e^{3} - 2 \, a b d e^{4} + a^{2} e^{5}} - \frac{{\left(4 \, c^{3} d^{3} - 6 \, b c^{2} d^{2} e + 12 \, a c^{2} d e^{2} + b^{3} e^{3} - 6 \, a b c e^{3}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{2} c^{2} d^{4} - 4 \, a c^{3} d^{4} - 2 \, b^{3} c d^{3} e + 8 \, a b c^{2} d^{3} e + b^{4} d^{2} e^{2} - 2 \, a b^{2} c d^{2} e^{2} - 8 \, a^{2} c^{2} d^{2} e^{2} - 2 \, a b^{3} d e^{3} + 8 \, a^{2} b c d e^{3} + a^{2} b^{2} e^{4} - 4 \, a^{3} c e^{4}\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{b c^{2} d^{3} - 2 \, b^{2} c d^{2} e + 2 \, a c^{2} d^{2} e + b^{3} d e^{2} - a b c d e^{2} - a b^{2} e^{3} + 2 \, a^{2} c e^{3} + {\left(2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e + b^{2} c d e^{2} + 2 \, a c^{2} d e^{2} - a b c e^{3}\right)} x}{{\left(c d^{2} - b d e + a e^{2}\right)}^{2} {\left(c x^{2} + b x + a\right)} {\left(b^{2} - 4 \, a c\right)}}"," ",0,"-1/2*e^3*log(c*x^2 + b*x + a)/(c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2 + 2*a*c*d^2*e^2 - 2*a*b*d*e^3 + a^2*e^4) + e^4*log(abs(x*e + d))/(c^2*d^4*e - 2*b*c*d^3*e^2 + b^2*d^2*e^3 + 2*a*c*d^2*e^3 - 2*a*b*d*e^4 + a^2*e^5) - (4*c^3*d^3 - 6*b*c^2*d^2*e + 12*a*c^2*d*e^2 + b^3*e^3 - 6*a*b*c*e^3)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^2*c^2*d^4 - 4*a*c^3*d^4 - 2*b^3*c*d^3*e + 8*a*b*c^2*d^3*e + b^4*d^2*e^2 - 2*a*b^2*c*d^2*e^2 - 8*a^2*c^2*d^2*e^2 - 2*a*b^3*d*e^3 + 8*a^2*b*c*d*e^3 + a^2*b^2*e^4 - 4*a^3*c*e^4)*sqrt(-b^2 + 4*a*c)) - (b*c^2*d^3 - 2*b^2*c*d^2*e + 2*a*c^2*d^2*e + b^3*d*e^2 - a*b*c*d*e^2 - a*b^2*e^3 + 2*a^2*c*e^3 + (2*c^3*d^3 - 3*b*c^2*d^2*e + b^2*c*d*e^2 + 2*a*c^2*d*e^2 - a*b*c*e^3)*x)/((c*d^2 - b*d*e + a*e^2)^2*(c*x^2 + b*x + a)*(b^2 - 4*a*c))","B",0
2197,1,899,0,0.216268," ","integrate(1/(e*x+d)^2/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","-\frac{2 \, {\left(2 \, c^{4} d^{4} e^{2} - 4 \, b c^{3} d^{3} e^{3} + 12 \, a c^{3} d^{2} e^{4} + 2 \, b^{3} c d e^{5} - 12 \, a b c^{2} d e^{5} - b^{4} e^{6} + 6 \, a b^{2} c e^{6} - 6 \, a^{2} c^{2} e^{6}\right)} \arctan\left(\frac{{\left(2 \, c d - \frac{2 \, c d^{2}}{x e + d} - b e + \frac{2 \, b d e}{x e + d} - \frac{2 \, a e^{2}}{x e + d}\right)} e^{\left(-1\right)}}{\sqrt{-b^{2} + 4 \, a c}}\right) e^{\left(-2\right)}}{{\left(b^{2} c^{3} d^{6} - 4 \, a c^{4} d^{6} - 3 \, b^{3} c^{2} d^{5} e + 12 \, a b c^{3} d^{5} e + 3 \, b^{4} c d^{4} e^{2} - 9 \, a b^{2} c^{2} d^{4} e^{2} - 12 \, a^{2} c^{3} d^{4} e^{2} - b^{5} d^{3} e^{3} - 2 \, a b^{3} c d^{3} e^{3} + 24 \, a^{2} b c^{2} d^{3} e^{3} + 3 \, a b^{4} d^{2} e^{4} - 9 \, a^{2} b^{2} c d^{2} e^{4} - 12 \, a^{3} c^{2} d^{2} e^{4} - 3 \, a^{2} b^{3} d e^{5} + 12 \, a^{3} b c d e^{5} + a^{3} b^{2} e^{6} - 4 \, a^{4} c e^{6}\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{{\left(2 \, c d e^{3} - b e^{4}\right)} \log\left(c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{b e}{x e + d} - \frac{b d e}{{\left(x e + d\right)}^{2}} + \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right)}{c^{3} d^{6} - 3 \, b c^{2} d^{5} e + 3 \, b^{2} c d^{4} e^{2} + 3 \, a c^{2} d^{4} e^{2} - b^{3} d^{3} e^{3} - 6 \, a b c d^{3} e^{3} + 3 \, a b^{2} d^{2} e^{4} + 3 \, a^{2} c d^{2} e^{4} - 3 \, a^{2} b d e^{5} + a^{3} e^{6}} - \frac{e^{7}}{{\left(c^{2} d^{4} e^{4} - 2 \, b c d^{3} e^{5} + b^{2} d^{2} e^{6} + 2 \, a c d^{2} e^{6} - 2 \, a b d e^{7} + a^{2} e^{8}\right)} {\left(x e + d\right)}} - \frac{\frac{2 \, c^{4} d^{3} e - 3 \, b c^{3} d^{2} e^{2} + 3 \, b^{2} c^{2} d e^{3} - 6 \, a c^{3} d e^{3} - b^{3} c e^{4} + 3 \, a b c^{2} e^{4}}{c d^{2} - b d e + a e^{2}} - \frac{{\left(2 \, c^{4} d^{4} e^{2} - 4 \, b c^{3} d^{3} e^{3} + 6 \, b^{2} c^{2} d^{2} e^{4} - 12 \, a c^{3} d^{2} e^{4} - 4 \, b^{3} c d e^{5} + 12 \, a b c^{2} d e^{5} + b^{4} e^{6} - 4 \, a b^{2} c e^{6} + 2 \, a^{2} c^{2} e^{6}\right)} e^{\left(-1\right)}}{{\left(c d^{2} - b d e + a e^{2}\right)} {\left(x e + d\right)}}}{{\left(c d^{2} - b d e + a e^{2}\right)}^{2} {\left(b^{2} - 4 \, a c\right)} {\left(c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{b e}{x e + d} - \frac{b d e}{{\left(x e + d\right)}^{2}} + \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right)}}"," ",0,"-2*(2*c^4*d^4*e^2 - 4*b*c^3*d^3*e^3 + 12*a*c^3*d^2*e^4 + 2*b^3*c*d*e^5 - 12*a*b*c^2*d*e^5 - b^4*e^6 + 6*a*b^2*c*e^6 - 6*a^2*c^2*e^6)*arctan((2*c*d - 2*c*d^2/(x*e + d) - b*e + 2*b*d*e/(x*e + d) - 2*a*e^2/(x*e + d))*e^(-1)/sqrt(-b^2 + 4*a*c))*e^(-2)/((b^2*c^3*d^6 - 4*a*c^4*d^6 - 3*b^3*c^2*d^5*e + 12*a*b*c^3*d^5*e + 3*b^4*c*d^4*e^2 - 9*a*b^2*c^2*d^4*e^2 - 12*a^2*c^3*d^4*e^2 - b^5*d^3*e^3 - 2*a*b^3*c*d^3*e^3 + 24*a^2*b*c^2*d^3*e^3 + 3*a*b^4*d^2*e^4 - 9*a^2*b^2*c*d^2*e^4 - 12*a^3*c^2*d^2*e^4 - 3*a^2*b^3*d*e^5 + 12*a^3*b*c*d*e^5 + a^3*b^2*e^6 - 4*a^4*c*e^6)*sqrt(-b^2 + 4*a*c)) - (2*c*d*e^3 - b*e^4)*log(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + b*e/(x*e + d) - b*d*e/(x*e + d)^2 + a*e^2/(x*e + d)^2)/(c^3*d^6 - 3*b*c^2*d^5*e + 3*b^2*c*d^4*e^2 + 3*a*c^2*d^4*e^2 - b^3*d^3*e^3 - 6*a*b*c*d^3*e^3 + 3*a*b^2*d^2*e^4 + 3*a^2*c*d^2*e^4 - 3*a^2*b*d*e^5 + a^3*e^6) - e^7/((c^2*d^4*e^4 - 2*b*c*d^3*e^5 + b^2*d^2*e^6 + 2*a*c*d^2*e^6 - 2*a*b*d*e^7 + a^2*e^8)*(x*e + d)) - ((2*c^4*d^3*e - 3*b*c^3*d^2*e^2 + 3*b^2*c^2*d*e^3 - 6*a*c^3*d*e^3 - b^3*c*e^4 + 3*a*b*c^2*e^4)/(c*d^2 - b*d*e + a*e^2) - (2*c^4*d^4*e^2 - 4*b*c^3*d^3*e^3 + 6*b^2*c^2*d^2*e^4 - 12*a*c^3*d^2*e^4 - 4*b^3*c*d*e^5 + 12*a*b*c^2*d*e^5 + b^4*e^6 - 4*a*b^2*c*e^6 + 2*a^2*c^2*e^6)*e^(-1)/((c*d^2 - b*d*e + a*e^2)*(x*e + d)))/((c*d^2 - b*d*e + a*e^2)^2*(b^2 - 4*a*c)*(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + b*e/(x*e + d) - b*d*e/(x*e + d)^2 + a*e^2/(x*e + d)^2))","B",0
2198,1,1612,0,0.216750," ","integrate(1/(e*x+d)^3/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","-\frac{{\left(10 \, c^{2} d^{2} e^{3} - 10 \, b c d e^{4} + 3 \, b^{2} e^{5} - 2 \, a c e^{5}\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(c^{4} d^{8} - 4 \, b c^{3} d^{7} e + 6 \, b^{2} c^{2} d^{6} e^{2} + 4 \, a c^{3} d^{6} e^{2} - 4 \, b^{3} c d^{5} e^{3} - 12 \, a b c^{2} d^{5} e^{3} + b^{4} d^{4} e^{4} + 12 \, a b^{2} c d^{4} e^{4} + 6 \, a^{2} c^{2} d^{4} e^{4} - 4 \, a b^{3} d^{3} e^{5} - 12 \, a^{2} b c d^{3} e^{5} + 6 \, a^{2} b^{2} d^{2} e^{6} + 4 \, a^{3} c d^{2} e^{6} - 4 \, a^{3} b d e^{7} + a^{4} e^{8}\right)}} + \frac{{\left(10 \, c^{2} d^{2} e^{4} - 10 \, b c d e^{5} + 3 \, b^{2} e^{6} - 2 \, a c e^{6}\right)} \log\left({\left| x e + d \right|}\right)}{c^{4} d^{8} e - 4 \, b c^{3} d^{7} e^{2} + 6 \, b^{2} c^{2} d^{6} e^{3} + 4 \, a c^{3} d^{6} e^{3} - 4 \, b^{3} c d^{5} e^{4} - 12 \, a b c^{2} d^{5} e^{4} + b^{4} d^{4} e^{5} + 12 \, a b^{2} c d^{4} e^{5} + 6 \, a^{2} c^{2} d^{4} e^{5} - 4 \, a b^{3} d^{3} e^{6} - 12 \, a^{2} b c d^{3} e^{6} + 6 \, a^{2} b^{2} d^{2} e^{7} + 4 \, a^{3} c d^{2} e^{7} - 4 \, a^{3} b d e^{8} + a^{4} e^{9}} - \frac{{\left(4 \, c^{5} d^{5} - 10 \, b c^{4} d^{4} e + 40 \, a c^{4} d^{3} e^{2} + 10 \, b^{3} c^{2} d^{2} e^{3} - 60 \, a b c^{3} d^{2} e^{3} - 10 \, b^{4} c d e^{4} + 60 \, a b^{2} c^{2} d e^{4} - 60 \, a^{2} c^{3} d e^{4} + 3 \, b^{5} e^{5} - 20 \, a b^{3} c e^{5} + 30 \, a^{2} b c^{2} e^{5}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{2} c^{4} d^{8} - 4 \, a c^{5} d^{8} - 4 \, b^{3} c^{3} d^{7} e + 16 \, a b c^{4} d^{7} e + 6 \, b^{4} c^{2} d^{6} e^{2} - 20 \, a b^{2} c^{3} d^{6} e^{2} - 16 \, a^{2} c^{4} d^{6} e^{2} - 4 \, b^{5} c d^{5} e^{3} + 4 \, a b^{3} c^{2} d^{5} e^{3} + 48 \, a^{2} b c^{3} d^{5} e^{3} + b^{6} d^{4} e^{4} + 8 \, a b^{4} c d^{4} e^{4} - 42 \, a^{2} b^{2} c^{2} d^{4} e^{4} - 24 \, a^{3} c^{3} d^{4} e^{4} - 4 \, a b^{5} d^{3} e^{5} + 4 \, a^{2} b^{3} c d^{3} e^{5} + 48 \, a^{3} b c^{2} d^{3} e^{5} + 6 \, a^{2} b^{4} d^{2} e^{6} - 20 \, a^{3} b^{2} c d^{2} e^{6} - 16 \, a^{4} c^{2} d^{2} e^{6} - 4 \, a^{3} b^{3} d e^{7} + 16 \, a^{4} b c d e^{7} + a^{4} b^{2} e^{8} - 4 \, a^{5} c e^{8}\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{2 \, b c^{4} d^{7} - 8 \, b^{2} c^{3} d^{6} e + 12 \, a c^{4} d^{6} e + 12 \, b^{3} c^{2} d^{5} e^{2} - 28 \, a b c^{3} d^{5} e^{2} - 8 \, b^{4} c d^{4} e^{3} + 29 \, a b^{2} c^{2} d^{4} e^{3} - 28 \, a^{2} c^{3} d^{4} e^{3} + 2 \, b^{5} d^{3} e^{4} - 16 \, a b^{3} c d^{3} e^{4} + 42 \, a^{2} b c^{2} d^{3} e^{4} + 3 \, a b^{4} d^{2} e^{5} - 2 \, a^{2} b^{2} c d^{2} e^{5} - 44 \, a^{3} c^{2} d^{2} e^{5} - 6 \, a^{2} b^{3} d e^{6} + 24 \, a^{3} b c d e^{6} + a^{3} b^{2} e^{7} - 4 \, a^{4} c e^{7} + 2 \, {\left(2 \, c^{5} d^{5} e^{2} - 5 \, b c^{4} d^{4} e^{3} + 10 \, b^{2} c^{3} d^{3} e^{4} - 20 \, a c^{4} d^{3} e^{4} - 10 \, b^{3} c^{2} d^{2} e^{5} + 30 \, a b c^{3} d^{2} e^{5} + 3 \, b^{4} c d e^{6} - 4 \, a b^{2} c^{2} d e^{6} - 22 \, a^{2} c^{3} d e^{6} - 3 \, a b^{3} c e^{7} + 11 \, a^{2} b c^{2} e^{7}\right)} x^{3} + {\left(8 \, c^{5} d^{6} e - 18 \, b c^{4} d^{5} e^{2} + 25 \, b^{2} c^{3} d^{4} e^{3} - 40 \, a c^{4} d^{4} e^{3} - 10 \, b^{3} c^{2} d^{3} e^{4} + 20 \, a b c^{3} d^{3} e^{4} - 11 \, b^{4} c d^{2} e^{5} + 58 \, a b^{2} c^{2} d^{2} e^{5} - 56 \, a^{2} c^{3} d^{2} e^{5} + 6 \, b^{5} d e^{6} - 20 \, a b^{3} c d e^{6} - 10 \, a^{2} b c^{2} d e^{6} - 6 \, a b^{4} e^{7} + 25 \, a^{2} b^{2} c e^{7} - 8 \, a^{3} c^{2} e^{7}\right)} x^{2} + {\left(4 \, c^{5} d^{7} - 6 \, b c^{4} d^{6} e - 4 \, b^{2} c^{3} d^{5} e^{2} + 16 \, a c^{4} d^{5} e^{2} + 25 \, b^{3} c^{2} d^{4} e^{3} - 80 \, a b c^{3} d^{4} e^{3} - 28 \, b^{4} c d^{3} e^{4} + 104 \, a b^{2} c^{2} d^{3} e^{4} - 28 \, a^{2} c^{3} d^{3} e^{4} + 9 \, b^{5} d^{2} e^{5} - 28 \, a b^{3} c d^{2} e^{5} - 14 \, a^{2} b c^{2} d^{2} e^{5} - 6 \, a b^{4} d e^{6} + 32 \, a^{2} b^{2} c d e^{6} - 40 \, a^{3} c^{2} d e^{6} - 3 \, a^{2} b^{3} e^{7} + 12 \, a^{3} b c e^{7}\right)} x}{2 \, {\left(c d^{2} - b d e + a e^{2}\right)}^{4} {\left(c x^{2} + b x + a\right)} {\left(b^{2} - 4 \, a c\right)} {\left(x e + d\right)}^{2}}"," ",0,"-1/2*(10*c^2*d^2*e^3 - 10*b*c*d*e^4 + 3*b^2*e^5 - 2*a*c*e^5)*log(c*x^2 + b*x + a)/(c^4*d^8 - 4*b*c^3*d^7*e + 6*b^2*c^2*d^6*e^2 + 4*a*c^3*d^6*e^2 - 4*b^3*c*d^5*e^3 - 12*a*b*c^2*d^5*e^3 + b^4*d^4*e^4 + 12*a*b^2*c*d^4*e^4 + 6*a^2*c^2*d^4*e^4 - 4*a*b^3*d^3*e^5 - 12*a^2*b*c*d^3*e^5 + 6*a^2*b^2*d^2*e^6 + 4*a^3*c*d^2*e^6 - 4*a^3*b*d*e^7 + a^4*e^8) + (10*c^2*d^2*e^4 - 10*b*c*d*e^5 + 3*b^2*e^6 - 2*a*c*e^6)*log(abs(x*e + d))/(c^4*d^8*e - 4*b*c^3*d^7*e^2 + 6*b^2*c^2*d^6*e^3 + 4*a*c^3*d^6*e^3 - 4*b^3*c*d^5*e^4 - 12*a*b*c^2*d^5*e^4 + b^4*d^4*e^5 + 12*a*b^2*c*d^4*e^5 + 6*a^2*c^2*d^4*e^5 - 4*a*b^3*d^3*e^6 - 12*a^2*b*c*d^3*e^6 + 6*a^2*b^2*d^2*e^7 + 4*a^3*c*d^2*e^7 - 4*a^3*b*d*e^8 + a^4*e^9) - (4*c^5*d^5 - 10*b*c^4*d^4*e + 40*a*c^4*d^3*e^2 + 10*b^3*c^2*d^2*e^3 - 60*a*b*c^3*d^2*e^3 - 10*b^4*c*d*e^4 + 60*a*b^2*c^2*d*e^4 - 60*a^2*c^3*d*e^4 + 3*b^5*e^5 - 20*a*b^3*c*e^5 + 30*a^2*b*c^2*e^5)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^2*c^4*d^8 - 4*a*c^5*d^8 - 4*b^3*c^3*d^7*e + 16*a*b*c^4*d^7*e + 6*b^4*c^2*d^6*e^2 - 20*a*b^2*c^3*d^6*e^2 - 16*a^2*c^4*d^6*e^2 - 4*b^5*c*d^5*e^3 + 4*a*b^3*c^2*d^5*e^3 + 48*a^2*b*c^3*d^5*e^3 + b^6*d^4*e^4 + 8*a*b^4*c*d^4*e^4 - 42*a^2*b^2*c^2*d^4*e^4 - 24*a^3*c^3*d^4*e^4 - 4*a*b^5*d^3*e^5 + 4*a^2*b^3*c*d^3*e^5 + 48*a^3*b*c^2*d^3*e^5 + 6*a^2*b^4*d^2*e^6 - 20*a^3*b^2*c*d^2*e^6 - 16*a^4*c^2*d^2*e^6 - 4*a^3*b^3*d*e^7 + 16*a^4*b*c*d*e^7 + a^4*b^2*e^8 - 4*a^5*c*e^8)*sqrt(-b^2 + 4*a*c)) - 1/2*(2*b*c^4*d^7 - 8*b^2*c^3*d^6*e + 12*a*c^4*d^6*e + 12*b^3*c^2*d^5*e^2 - 28*a*b*c^3*d^5*e^2 - 8*b^4*c*d^4*e^3 + 29*a*b^2*c^2*d^4*e^3 - 28*a^2*c^3*d^4*e^3 + 2*b^5*d^3*e^4 - 16*a*b^3*c*d^3*e^4 + 42*a^2*b*c^2*d^3*e^4 + 3*a*b^4*d^2*e^5 - 2*a^2*b^2*c*d^2*e^5 - 44*a^3*c^2*d^2*e^5 - 6*a^2*b^3*d*e^6 + 24*a^3*b*c*d*e^6 + a^3*b^2*e^7 - 4*a^4*c*e^7 + 2*(2*c^5*d^5*e^2 - 5*b*c^4*d^4*e^3 + 10*b^2*c^3*d^3*e^4 - 20*a*c^4*d^3*e^4 - 10*b^3*c^2*d^2*e^5 + 30*a*b*c^3*d^2*e^5 + 3*b^4*c*d*e^6 - 4*a*b^2*c^2*d*e^6 - 22*a^2*c^3*d*e^6 - 3*a*b^3*c*e^7 + 11*a^2*b*c^2*e^7)*x^3 + (8*c^5*d^6*e - 18*b*c^4*d^5*e^2 + 25*b^2*c^3*d^4*e^3 - 40*a*c^4*d^4*e^3 - 10*b^3*c^2*d^3*e^4 + 20*a*b*c^3*d^3*e^4 - 11*b^4*c*d^2*e^5 + 58*a*b^2*c^2*d^2*e^5 - 56*a^2*c^3*d^2*e^5 + 6*b^5*d*e^6 - 20*a*b^3*c*d*e^6 - 10*a^2*b*c^2*d*e^6 - 6*a*b^4*e^7 + 25*a^2*b^2*c*e^7 - 8*a^3*c^2*e^7)*x^2 + (4*c^5*d^7 - 6*b*c^4*d^6*e - 4*b^2*c^3*d^5*e^2 + 16*a*c^4*d^5*e^2 + 25*b^3*c^2*d^4*e^3 - 80*a*b*c^3*d^4*e^3 - 28*b^4*c*d^3*e^4 + 104*a*b^2*c^2*d^3*e^4 - 28*a^2*c^3*d^3*e^4 + 9*b^5*d^2*e^5 - 28*a*b^3*c*d^2*e^5 - 14*a^2*b*c^2*d^2*e^5 - 6*a*b^4*d*e^6 + 32*a^2*b^2*c*d*e^6 - 40*a^3*c^2*d*e^6 - 3*a^2*b^3*e^7 + 12*a^3*b*c*e^7)*x)/((c*d^2 - b*d*e + a*e^2)^4*(c*x^2 + b*x + a)*(b^2 - 4*a*c)*(x*e + d)^2)","B",0
2199,1,332,0,0.221452," ","integrate(x^7/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","-\frac{3 \, {\left(2 \, b^{7} - 21 \, a b^{5} c + 70 \, a^{2} b^{3} c^{2} - 70 \, a^{3} b c^{3}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{3 \, {\left(2 \, b^{2} - a c\right)} \log\left(c x^{2} + b x + a\right)}{2 \, c^{5}} + \frac{c^{3} x^{2} - 6 \, b c^{2} x}{2 \, c^{6}} + \frac{7 \, a^{2} b^{6} - 55 \, a^{3} b^{4} c + 115 \, a^{4} b^{2} c^{2} - 40 \, a^{5} c^{3} + 2 \, {\left(4 \, b^{7} c - 35 \, a b^{5} c^{2} + 91 \, a^{2} b^{3} c^{3} - 63 \, a^{3} b c^{4}\right)} x^{3} + {\left(7 \, b^{8} - 53 \, a b^{6} c + 94 \, a^{2} b^{4} c^{2} + 27 \, a^{3} b^{2} c^{3} - 48 \, a^{4} c^{4}\right)} x^{2} + 2 \, {\left(7 \, a b^{7} - 58 \, a^{2} b^{5} c + 136 \, a^{3} b^{3} c^{2} - 73 \, a^{4} b c^{3}\right)} x}{2 \, {\left(c x^{2} + b x + a\right)}^{2} {\left(b^{2} - 4 \, a c\right)}^{2} c^{5}}"," ",0,"-3*(2*b^7 - 21*a*b^5*c + 70*a^2*b^3*c^2 - 70*a^3*b*c^3)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*sqrt(-b^2 + 4*a*c)) + 3/2*(2*b^2 - a*c)*log(c*x^2 + b*x + a)/c^5 + 1/2*(c^3*x^2 - 6*b*c^2*x)/c^6 + 1/2*(7*a^2*b^6 - 55*a^3*b^4*c + 115*a^4*b^2*c^2 - 40*a^5*c^3 + 2*(4*b^7*c - 35*a*b^5*c^2 + 91*a^2*b^3*c^3 - 63*a^3*b*c^4)*x^3 + (7*b^8 - 53*a*b^6*c + 94*a^2*b^4*c^2 + 27*a^3*b^2*c^3 - 48*a^4*c^4)*x^2 + 2*(7*a*b^7 - 58*a^2*b^5*c + 136*a^3*b^3*c^2 - 73*a^4*b*c^3)*x)/((c*x^2 + b*x + a)^2*(b^2 - 4*a*c)^2*c^5)","A",0
2200,1,282,0,0.179120," ","integrate(x^6/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{3 \, {\left(b^{6} - 10 \, a b^{4} c + 30 \, a^{2} b^{2} c^{2} - 20 \, a^{3} c^{3}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{x}{c^{3}} - \frac{3 \, b \log\left(c x^{2} + b x + a\right)}{2 \, c^{4}} - \frac{5 \, a^{2} b^{5} - 36 \, a^{3} b^{3} c + 58 \, a^{4} b c^{2} + 6 \, {\left(b^{6} c - 8 \, a b^{4} c^{2} + 17 \, a^{2} b^{2} c^{3} - 6 \, a^{3} c^{4}\right)} x^{3} + {\left(5 \, b^{7} - 34 \, a b^{5} c + 41 \, a^{2} b^{3} c^{2} + 42 \, a^{3} b c^{3}\right)} x^{2} + 2 \, {\left(5 \, a b^{6} - 38 \, a^{2} b^{4} c + 71 \, a^{3} b^{2} c^{2} - 14 \, a^{4} c^{3}\right)} x}{2 \, {\left(c x^{2} + b x + a\right)}^{2} {\left(b^{2} - 4 \, a c\right)}^{2} c^{4}}"," ",0,"3*(b^6 - 10*a*b^4*c + 30*a^2*b^2*c^2 - 20*a^3*c^3)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*sqrt(-b^2 + 4*a*c)) + x/c^3 - 3/2*b*log(c*x^2 + b*x + a)/c^4 - 1/2*(5*a^2*b^5 - 36*a^3*b^3*c + 58*a^4*b*c^2 + 6*(b^6*c - 8*a*b^4*c^2 + 17*a^2*b^2*c^3 - 6*a^3*c^4)*x^3 + (5*b^7 - 34*a*b^5*c + 41*a^2*b^3*c^2 + 42*a^3*b*c^3)*x^2 + 2*(5*a*b^6 - 38*a^2*b^4*c + 71*a^3*b^2*c^2 - 14*a^4*c^3)*x)/((c*x^2 + b*x + a)^2*(b^2 - 4*a*c)^2*c^4)","A",0
2201,1,805,0,0.185665," ","integrate((e*x+d)^5/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{{\left(12 \, c^{5} d^{5} - 30 \, b c^{4} d^{4} e + 20 \, b^{2} c^{3} d^{3} e^{2} + 40 \, a c^{4} d^{3} e^{2} - 60 \, a b c^{3} d^{2} e^{3} + 60 \, a^{2} c^{3} d e^{4} - b^{5} e^{5} + 10 \, a b^{3} c e^{5} - 30 \, a^{2} b c^{2} e^{5}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{e^{5} \log\left(c x^{2} + b x + a\right)}{2 \, c^{3}} - \frac{b^{3} c^{3} d^{5} - 10 \, a b c^{4} d^{5} + 5 \, a b^{2} c^{3} d^{4} e + 40 \, a^{2} c^{4} d^{4} e - 60 \, a^{2} b c^{3} d^{3} e^{2} + 10 \, a^{2} b^{2} c^{2} d^{2} e^{3} + 80 \, a^{3} c^{3} d^{2} e^{3} + 5 \, a^{2} b^{3} c d e^{4} - 50 \, a^{3} b c^{2} d e^{4} - 3 \, a^{2} b^{4} e^{5} + 21 \, a^{3} b^{2} c e^{5} - 24 \, a^{4} c^{2} e^{5} - 2 \, {\left(6 \, c^{6} d^{5} - 15 \, b c^{5} d^{4} e + 10 \, b^{2} c^{4} d^{3} e^{2} + 20 \, a c^{5} d^{3} e^{2} - 30 \, a b c^{4} d^{2} e^{3} - 5 \, b^{4} c^{2} d e^{4} + 40 \, a b^{2} c^{3} d e^{4} - 50 \, a^{2} c^{4} d e^{4} + 2 \, b^{5} c e^{5} - 15 \, a b^{3} c^{2} e^{5} + 25 \, a^{2} b c^{3} e^{5}\right)} x^{3} - {\left(18 \, b c^{5} d^{5} - 45 \, b^{2} c^{4} d^{4} e + 30 \, b^{3} c^{3} d^{3} e^{2} + 60 \, a b c^{4} d^{3} e^{2} - 10 \, b^{4} c^{2} d^{2} e^{3} - 10 \, a b^{2} c^{3} d^{2} e^{3} - 160 \, a^{2} c^{4} d^{2} e^{3} - 5 \, b^{5} c d e^{4} + 40 \, a b^{3} c^{2} d e^{4} + 10 \, a^{2} b c^{3} d e^{4} + 3 \, b^{6} e^{5} - 19 \, a b^{4} c e^{5} + 11 \, a^{2} b^{2} c^{2} e^{5} + 32 \, a^{3} c^{3} e^{5}\right)} x^{2} - 2 \, {\left(2 \, b^{2} c^{4} d^{5} + 10 \, a c^{5} d^{5} - 5 \, b^{3} c^{3} d^{4} e - 25 \, a b c^{4} d^{4} e + 50 \, a b^{2} c^{3} d^{3} e^{2} - 20 \, a^{2} c^{4} d^{3} e^{2} - 10 \, a b^{3} c^{2} d^{2} e^{3} - 50 \, a^{2} b c^{3} d^{2} e^{3} - 5 \, a b^{4} c d e^{4} + 50 \, a^{2} b^{2} c^{2} d e^{4} - 30 \, a^{3} c^{3} d e^{4} + 3 \, a b^{5} e^{5} - 22 \, a^{2} b^{3} c e^{5} + 31 \, a^{3} b c^{2} e^{5}\right)} x}{2 \, {\left(c x^{2} + b x + a\right)}^{2} {\left(b^{2} - 4 \, a c\right)}^{2} c^{3}}"," ",0,"(12*c^5*d^5 - 30*b*c^4*d^4*e + 20*b^2*c^3*d^3*e^2 + 40*a*c^4*d^3*e^2 - 60*a*b*c^3*d^2*e^3 + 60*a^2*c^3*d*e^4 - b^5*e^5 + 10*a*b^3*c*e^5 - 30*a^2*b*c^2*e^5)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*sqrt(-b^2 + 4*a*c)) + 1/2*e^5*log(c*x^2 + b*x + a)/c^3 - 1/2*(b^3*c^3*d^5 - 10*a*b*c^4*d^5 + 5*a*b^2*c^3*d^4*e + 40*a^2*c^4*d^4*e - 60*a^2*b*c^3*d^3*e^2 + 10*a^2*b^2*c^2*d^2*e^3 + 80*a^3*c^3*d^2*e^3 + 5*a^2*b^3*c*d*e^4 - 50*a^3*b*c^2*d*e^4 - 3*a^2*b^4*e^5 + 21*a^3*b^2*c*e^5 - 24*a^4*c^2*e^5 - 2*(6*c^6*d^5 - 15*b*c^5*d^4*e + 10*b^2*c^4*d^3*e^2 + 20*a*c^5*d^3*e^2 - 30*a*b*c^4*d^2*e^3 - 5*b^4*c^2*d*e^4 + 40*a*b^2*c^3*d*e^4 - 50*a^2*c^4*d*e^4 + 2*b^5*c*e^5 - 15*a*b^3*c^2*e^5 + 25*a^2*b*c^3*e^5)*x^3 - (18*b*c^5*d^5 - 45*b^2*c^4*d^4*e + 30*b^3*c^3*d^3*e^2 + 60*a*b*c^4*d^3*e^2 - 10*b^4*c^2*d^2*e^3 - 10*a*b^2*c^3*d^2*e^3 - 160*a^2*c^4*d^2*e^3 - 5*b^5*c*d*e^4 + 40*a*b^3*c^2*d*e^4 + 10*a^2*b*c^3*d*e^4 + 3*b^6*e^5 - 19*a*b^4*c*e^5 + 11*a^2*b^2*c^2*e^5 + 32*a^3*c^3*e^5)*x^2 - 2*(2*b^2*c^4*d^5 + 10*a*c^5*d^5 - 5*b^3*c^3*d^4*e - 25*a*b*c^4*d^4*e + 50*a*b^2*c^3*d^3*e^2 - 20*a^2*c^4*d^3*e^2 - 10*a*b^3*c^2*d^2*e^3 - 50*a^2*b*c^3*d^2*e^3 - 5*a*b^4*c*d*e^4 + 50*a^2*b^2*c^2*d*e^4 - 30*a^3*c^3*d*e^4 + 3*a*b^5*e^5 - 22*a^2*b^3*c*e^5 + 31*a^3*b*c^2*e^5)*x)/((c*x^2 + b*x + a)^2*(b^2 - 4*a*c)^2*c^3)","B",0
2202,1,626,0,0.197744," ","integrate((e*x+d)^4/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{12 \, {\left(c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2} + 2 \, a c d^{2} e^{2} - 2 \, a b d e^{3} + a^{2} e^{4}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{12 \, c^{5} d^{4} x^{3} - 24 \, b c^{4} d^{3} x^{3} e + 18 \, b c^{4} d^{4} x^{2} + 12 \, b^{2} c^{3} d^{2} x^{3} e^{2} + 24 \, a c^{4} d^{2} x^{3} e^{2} - 36 \, b^{2} c^{3} d^{3} x^{2} e + 4 \, b^{2} c^{3} d^{4} x + 20 \, a c^{4} d^{4} x - 24 \, a b c^{3} d x^{3} e^{3} + 18 \, b^{3} c^{2} d^{2} x^{2} e^{2} + 36 \, a b c^{3} d^{2} x^{2} e^{2} - 8 \, b^{3} c^{2} d^{3} x e - 40 \, a b c^{3} d^{3} x e - b^{3} c^{2} d^{4} + 10 \, a b c^{3} d^{4} - 2 \, b^{4} c x^{3} e^{4} + 16 \, a b^{2} c^{2} x^{3} e^{4} - 20 \, a^{2} c^{3} x^{3} e^{4} - 4 \, b^{4} c d x^{2} e^{3} - 4 \, a b^{2} c^{2} d x^{2} e^{3} - 64 \, a^{2} c^{3} d x^{2} e^{3} + 60 \, a b^{2} c^{2} d^{2} x e^{2} - 24 \, a^{2} c^{3} d^{2} x e^{2} - 4 \, a b^{2} c^{2} d^{3} e - 32 \, a^{2} c^{3} d^{3} e - b^{5} x^{2} e^{4} + 8 \, a b^{3} c x^{2} e^{4} + 2 \, a^{2} b c^{2} x^{2} e^{4} - 8 \, a b^{3} c d x e^{3} - 40 \, a^{2} b c^{2} d x e^{3} + 36 \, a^{2} b c^{2} d^{2} e^{2} - 2 \, a b^{4} x e^{4} + 20 \, a^{2} b^{2} c x e^{4} - 12 \, a^{3} c^{2} x e^{4} - 4 \, a^{2} b^{2} c d e^{3} - 32 \, a^{3} c^{2} d e^{3} - a^{2} b^{3} e^{4} + 10 \, a^{3} b c e^{4}}{2 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} {\left(c x^{2} + b x + a\right)}^{2}}"," ",0,"12*(c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2 + 2*a*c*d^2*e^2 - 2*a*b*d*e^3 + a^2*e^4)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(-b^2 + 4*a*c)) + 1/2*(12*c^5*d^4*x^3 - 24*b*c^4*d^3*x^3*e + 18*b*c^4*d^4*x^2 + 12*b^2*c^3*d^2*x^3*e^2 + 24*a*c^4*d^2*x^3*e^2 - 36*b^2*c^3*d^3*x^2*e + 4*b^2*c^3*d^4*x + 20*a*c^4*d^4*x - 24*a*b*c^3*d*x^3*e^3 + 18*b^3*c^2*d^2*x^2*e^2 + 36*a*b*c^3*d^2*x^2*e^2 - 8*b^3*c^2*d^3*x*e - 40*a*b*c^3*d^3*x*e - b^3*c^2*d^4 + 10*a*b*c^3*d^4 - 2*b^4*c*x^3*e^4 + 16*a*b^2*c^2*x^3*e^4 - 20*a^2*c^3*x^3*e^4 - 4*b^4*c*d*x^2*e^3 - 4*a*b^2*c^2*d*x^2*e^3 - 64*a^2*c^3*d*x^2*e^3 + 60*a*b^2*c^2*d^2*x*e^2 - 24*a^2*c^3*d^2*x*e^2 - 4*a*b^2*c^2*d^3*e - 32*a^2*c^3*d^3*e - b^5*x^2*e^4 + 8*a*b^3*c*x^2*e^4 + 2*a^2*b*c^2*x^2*e^4 - 8*a*b^3*c*d*x*e^3 - 40*a^2*b*c^2*d*x*e^3 + 36*a^2*b*c^2*d^2*e^2 - 2*a*b^4*x*e^4 + 20*a^2*b^2*c*x*e^4 - 12*a^3*c^2*x*e^4 - 4*a^2*b^2*c*d*e^3 - 32*a^3*c^2*d*e^3 - a^2*b^3*e^4 + 10*a^3*b*c*e^4)/((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*(c*x^2 + b*x + a)^2)","B",0
2203,1,446,0,0.172108," ","integrate((e*x+d)^3/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{6 \, {\left(2 \, c^{2} d^{3} - 3 \, b c d^{2} e + b^{2} d e^{2} + 2 \, a c d e^{2} - a b e^{3}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{12 \, c^{4} d^{3} x^{3} - 18 \, b c^{3} d^{2} x^{3} e + 18 \, b c^{3} d^{3} x^{2} + 6 \, b^{2} c^{2} d x^{3} e^{2} + 12 \, a c^{3} d x^{3} e^{2} - 27 \, b^{2} c^{2} d^{2} x^{2} e + 4 \, b^{2} c^{2} d^{3} x + 20 \, a c^{3} d^{3} x - 6 \, a b c^{2} x^{3} e^{3} + 9 \, b^{3} c d x^{2} e^{2} + 18 \, a b c^{2} d x^{2} e^{2} - 6 \, b^{3} c d^{2} x e - 30 \, a b c^{2} d^{2} x e - b^{3} c d^{3} + 10 \, a b c^{2} d^{3} - b^{4} x^{2} e^{3} - a b^{2} c x^{2} e^{3} - 16 \, a^{2} c^{2} x^{2} e^{3} + 30 \, a b^{2} c d x e^{2} - 12 \, a^{2} c^{2} d x e^{2} - 3 \, a b^{2} c d^{2} e - 24 \, a^{2} c^{2} d^{2} e - 2 \, a b^{3} x e^{3} - 10 \, a^{2} b c x e^{3} + 18 \, a^{2} b c d e^{2} - a^{2} b^{2} e^{3} - 8 \, a^{3} c e^{3}}{2 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} {\left(c x^{2} + b x + a\right)}^{2}}"," ",0,"6*(2*c^2*d^3 - 3*b*c*d^2*e + b^2*d*e^2 + 2*a*c*d*e^2 - a*b*e^3)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(-b^2 + 4*a*c)) + 1/2*(12*c^4*d^3*x^3 - 18*b*c^3*d^2*x^3*e + 18*b*c^3*d^3*x^2 + 6*b^2*c^2*d*x^3*e^2 + 12*a*c^3*d*x^3*e^2 - 27*b^2*c^2*d^2*x^2*e + 4*b^2*c^2*d^3*x + 20*a*c^3*d^3*x - 6*a*b*c^2*x^3*e^3 + 9*b^3*c*d*x^2*e^2 + 18*a*b*c^2*d*x^2*e^2 - 6*b^3*c*d^2*x*e - 30*a*b*c^2*d^2*x*e - b^3*c*d^3 + 10*a*b*c^2*d^3 - b^4*x^2*e^3 - a*b^2*c*x^2*e^3 - 16*a^2*c^2*x^2*e^3 + 30*a*b^2*c*d*x*e^2 - 12*a^2*c^2*d*x*e^2 - 3*a*b^2*c*d^2*e - 24*a^2*c^2*d^2*e - 2*a*b^3*x*e^3 - 10*a^2*b*c*x*e^3 + 18*a^2*b*c*d*e^2 - a^2*b^2*e^3 - 8*a^3*c*e^3)/((b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*(c*x^2 + b*x + a)^2)","B",0
2204,1,307,0,0.164641," ","integrate((e*x+d)^2/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{2 \, {\left(6 \, c^{2} d^{2} - 6 \, b c d e + b^{2} e^{2} + 2 \, a c e^{2}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{12 \, c^{3} d^{2} x^{3} - 12 \, b c^{2} d x^{3} e + 18 \, b c^{2} d^{2} x^{2} + 2 \, b^{2} c x^{3} e^{2} + 4 \, a c^{2} x^{3} e^{2} - 18 \, b^{2} c d x^{2} e + 4 \, b^{2} c d^{2} x + 20 \, a c^{2} d^{2} x + 3 \, b^{3} x^{2} e^{2} + 6 \, a b c x^{2} e^{2} - 4 \, b^{3} d x e - 20 \, a b c d x e - b^{3} d^{2} + 10 \, a b c d^{2} + 10 \, a b^{2} x e^{2} - 4 \, a^{2} c x e^{2} - 2 \, a b^{2} d e - 16 \, a^{2} c d e + 6 \, a^{2} b e^{2}}{2 \, {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} {\left(c x^{2} + b x + a\right)}^{2}}"," ",0,"2*(6*c^2*d^2 - 6*b*c*d*e + b^2*e^2 + 2*a*c*e^2)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(-b^2 + 4*a*c)) + 1/2*(12*c^3*d^2*x^3 - 12*b*c^2*d*x^3*e + 18*b*c^2*d^2*x^2 + 2*b^2*c*x^3*e^2 + 4*a*c^2*x^3*e^2 - 18*b^2*c*d*x^2*e + 4*b^2*c*d^2*x + 20*a*c^2*d^2*x + 3*b^3*x^2*e^2 + 6*a*b*c*x^2*e^2 - 4*b^3*d*x*e - 20*a*b*c*d*x*e - b^3*d^2 + 10*a*b*c*d^2 + 10*a*b^2*x*e^2 - 4*a^2*c*x*e^2 - 2*a*b^2*d*e - 16*a^2*c*d*e + 6*a^2*b*e^2)/((b^4 - 8*a*b^2*c + 16*a^2*c^2)*(c*x^2 + b*x + a)^2)","A",0
2205,1,206,0,0.169919," ","integrate((e*x+d)/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{6 \, {\left(2 \, c^{2} d - b c e\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{12 \, c^{3} d x^{3} - 6 \, b c^{2} x^{3} e + 18 \, b c^{2} d x^{2} - 9 \, b^{2} c x^{2} e + 4 \, b^{2} c d x + 20 \, a c^{2} d x - 2 \, b^{3} x e - 10 \, a b c x e - b^{3} d + 10 \, a b c d - a b^{2} e - 8 \, a^{2} c e}{2 \, {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} {\left(c x^{2} + b x + a\right)}^{2}}"," ",0,"6*(2*c^2*d - b*c*e)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(-b^2 + 4*a*c)) + 1/2*(12*c^3*d*x^3 - 6*b*c^2*x^3*e + 18*b*c^2*d*x^2 - 9*b^2*c*x^2*e + 4*b^2*c*d*x + 20*a*c^2*d*x - 2*b^3*x*e - 10*a*b*c*x*e - b^3*d + 10*a*b*c*d - a*b^2*e - 8*a^2*c*e)/((b^4 - 8*a*b^2*c + 16*a^2*c^2)*(c*x^2 + b*x + a)^2)","A",0
2206,1,136,0,0.157389," ","integrate(1/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{12 \, c^{2} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{12 \, c^{3} x^{3} + 18 \, b c^{2} x^{2} + 4 \, b^{2} c x + 20 \, a c^{2} x - b^{3} + 10 \, a b c}{2 \, {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} {\left(c x^{2} + b x + a\right)}^{2}}"," ",0,"12*c^2*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(-b^2 + 4*a*c)) + 1/2*(12*c^3*x^3 + 18*b*c^2*x^2 + 4*b^2*c*x + 20*a*c^2*x - b^3 + 10*a*b*c)/((b^4 - 8*a*b^2*c + 16*a^2*c^2)*(c*x^2 + b*x + a)^2)","A",0
2207,1,1386,0,0.231173," ","integrate(1/(e*x+d)/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","-\frac{e^{5} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(c^{3} d^{6} - 3 \, b c^{2} d^{5} e + 3 \, b^{2} c d^{4} e^{2} + 3 \, a c^{2} d^{4} e^{2} - b^{3} d^{3} e^{3} - 6 \, a b c d^{3} e^{3} + 3 \, a b^{2} d^{2} e^{4} + 3 \, a^{2} c d^{2} e^{4} - 3 \, a^{2} b d e^{5} + a^{3} e^{6}\right)}} + \frac{e^{6} \log\left({\left| x e + d \right|}\right)}{c^{3} d^{6} e - 3 \, b c^{2} d^{5} e^{2} + 3 \, b^{2} c d^{4} e^{3} + 3 \, a c^{2} d^{4} e^{3} - b^{3} d^{3} e^{4} - 6 \, a b c d^{3} e^{4} + 3 \, a b^{2} d^{2} e^{5} + 3 \, a^{2} c d^{2} e^{5} - 3 \, a^{2} b d e^{6} + a^{3} e^{7}} + \frac{{\left(12 \, c^{5} d^{5} - 30 \, b c^{4} d^{4} e + 20 \, b^{2} c^{3} d^{3} e^{2} + 40 \, a c^{4} d^{3} e^{2} - 60 \, a b c^{3} d^{2} e^{3} + 60 \, a^{2} c^{3} d e^{4} - b^{5} e^{5} + 10 \, a b^{3} c e^{5} - 30 \, a^{2} b c^{2} e^{5}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{4} c^{3} d^{6} - 8 \, a b^{2} c^{4} d^{6} + 16 \, a^{2} c^{5} d^{6} - 3 \, b^{5} c^{2} d^{5} e + 24 \, a b^{3} c^{3} d^{5} e - 48 \, a^{2} b c^{4} d^{5} e + 3 \, b^{6} c d^{4} e^{2} - 21 \, a b^{4} c^{2} d^{4} e^{2} + 24 \, a^{2} b^{2} c^{3} d^{4} e^{2} + 48 \, a^{3} c^{4} d^{4} e^{2} - b^{7} d^{3} e^{3} + 2 \, a b^{5} c d^{3} e^{3} + 32 \, a^{2} b^{3} c^{2} d^{3} e^{3} - 96 \, a^{3} b c^{3} d^{3} e^{3} + 3 \, a b^{6} d^{2} e^{4} - 21 \, a^{2} b^{4} c d^{2} e^{4} + 24 \, a^{3} b^{2} c^{2} d^{2} e^{4} + 48 \, a^{4} c^{3} d^{2} e^{4} - 3 \, a^{2} b^{5} d e^{5} + 24 \, a^{3} b^{3} c d e^{5} - 48 \, a^{4} b c^{2} d e^{5} + a^{3} b^{4} e^{6} - 8 \, a^{4} b^{2} c e^{6} + 16 \, a^{5} c^{2} e^{6}\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{b^{3} c^{3} d^{5} - 10 \, a b c^{4} d^{5} - 3 \, b^{4} c^{2} d^{4} e + 29 \, a b^{2} c^{3} d^{4} e - 8 \, a^{2} c^{4} d^{4} e + 3 \, b^{5} c d^{3} e^{2} - 24 \, a b^{3} c^{2} d^{3} e^{2} - 12 \, a^{2} b c^{3} d^{3} e^{2} - b^{6} d^{2} e^{3} + a b^{4} c d^{2} e^{3} + 50 \, a^{2} b^{2} c^{2} d^{2} e^{3} - 32 \, a^{3} c^{3} d^{2} e^{3} + 4 \, a b^{5} d e^{4} - 27 \, a^{2} b^{3} c d e^{4} + 14 \, a^{3} b c^{2} d e^{4} - 3 \, a^{2} b^{4} e^{5} + 21 \, a^{3} b^{2} c e^{5} - 24 \, a^{4} c^{2} e^{5} - 2 \, {\left(6 \, c^{6} d^{5} - 15 \, b c^{5} d^{4} e + 10 \, b^{2} c^{4} d^{3} e^{2} + 20 \, a c^{5} d^{3} e^{2} - 30 \, a b c^{4} d^{2} e^{3} - b^{4} c^{2} d e^{4} + 8 \, a b^{2} c^{3} d e^{4} + 14 \, a^{2} c^{4} d e^{4} + a b^{3} c^{2} e^{5} - 7 \, a^{2} b c^{3} e^{5}\right)} x^{3} - {\left(18 \, b c^{5} d^{5} - 45 \, b^{2} c^{4} d^{4} e + 30 \, b^{3} c^{3} d^{3} e^{2} + 60 \, a b c^{4} d^{3} e^{2} + b^{4} c^{2} d^{2} e^{3} - 98 \, a b^{2} c^{3} d^{2} e^{3} + 16 \, a^{2} c^{4} d^{2} e^{3} - 4 \, b^{5} c d e^{4} + 32 \, a b^{3} c^{2} d e^{4} + 26 \, a^{2} b c^{3} d e^{4} + 4 \, a b^{4} c e^{5} - 29 \, a^{2} b^{2} c^{2} e^{5} + 16 \, a^{3} c^{3} e^{5}\right)} x^{2} - 2 \, {\left(2 \, b^{2} c^{4} d^{5} + 10 \, a c^{5} d^{5} - 5 \, b^{3} c^{3} d^{4} e - 25 \, a b c^{4} d^{4} e + 3 \, b^{4} c^{2} d^{3} e^{2} + 26 \, a b^{2} c^{3} d^{3} e^{2} + 28 \, a^{2} c^{4} d^{3} e^{2} + b^{5} c d^{2} e^{3} - 18 \, a b^{3} c^{2} d^{2} e^{3} - 34 \, a^{2} b c^{3} d^{2} e^{3} - b^{6} d e^{4} + 6 \, a b^{4} c d e^{4} + 10 \, a^{2} b^{2} c^{2} d e^{4} + 18 \, a^{3} c^{3} d e^{4} + a b^{5} e^{5} - 6 \, a^{2} b^{3} c e^{5} - a^{3} b c^{2} e^{5}\right)} x}{2 \, {\left(c d^{2} - b d e + a e^{2}\right)}^{3} {\left(c x^{2} + b x + a\right)}^{2} {\left(b^{2} - 4 \, a c\right)}^{2}}"," ",0,"-1/2*e^5*log(c*x^2 + b*x + a)/(c^3*d^6 - 3*b*c^2*d^5*e + 3*b^2*c*d^4*e^2 + 3*a*c^2*d^4*e^2 - b^3*d^3*e^3 - 6*a*b*c*d^3*e^3 + 3*a*b^2*d^2*e^4 + 3*a^2*c*d^2*e^4 - 3*a^2*b*d*e^5 + a^3*e^6) + e^6*log(abs(x*e + d))/(c^3*d^6*e - 3*b*c^2*d^5*e^2 + 3*b^2*c*d^4*e^3 + 3*a*c^2*d^4*e^3 - b^3*d^3*e^4 - 6*a*b*c*d^3*e^4 + 3*a*b^2*d^2*e^5 + 3*a^2*c*d^2*e^5 - 3*a^2*b*d*e^6 + a^3*e^7) + (12*c^5*d^5 - 30*b*c^4*d^4*e + 20*b^2*c^3*d^3*e^2 + 40*a*c^4*d^3*e^2 - 60*a*b*c^3*d^2*e^3 + 60*a^2*c^3*d*e^4 - b^5*e^5 + 10*a*b^3*c*e^5 - 30*a^2*b*c^2*e^5)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^4*c^3*d^6 - 8*a*b^2*c^4*d^6 + 16*a^2*c^5*d^6 - 3*b^5*c^2*d^5*e + 24*a*b^3*c^3*d^5*e - 48*a^2*b*c^4*d^5*e + 3*b^6*c*d^4*e^2 - 21*a*b^4*c^2*d^4*e^2 + 24*a^2*b^2*c^3*d^4*e^2 + 48*a^3*c^4*d^4*e^2 - b^7*d^3*e^3 + 2*a*b^5*c*d^3*e^3 + 32*a^2*b^3*c^2*d^3*e^3 - 96*a^3*b*c^3*d^3*e^3 + 3*a*b^6*d^2*e^4 - 21*a^2*b^4*c*d^2*e^4 + 24*a^3*b^2*c^2*d^2*e^4 + 48*a^4*c^3*d^2*e^4 - 3*a^2*b^5*d*e^5 + 24*a^3*b^3*c*d*e^5 - 48*a^4*b*c^2*d*e^5 + a^3*b^4*e^6 - 8*a^4*b^2*c*e^6 + 16*a^5*c^2*e^6)*sqrt(-b^2 + 4*a*c)) - 1/2*(b^3*c^3*d^5 - 10*a*b*c^4*d^5 - 3*b^4*c^2*d^4*e + 29*a*b^2*c^3*d^4*e - 8*a^2*c^4*d^4*e + 3*b^5*c*d^3*e^2 - 24*a*b^3*c^2*d^3*e^2 - 12*a^2*b*c^3*d^3*e^2 - b^6*d^2*e^3 + a*b^4*c*d^2*e^3 + 50*a^2*b^2*c^2*d^2*e^3 - 32*a^3*c^3*d^2*e^3 + 4*a*b^5*d*e^4 - 27*a^2*b^3*c*d*e^4 + 14*a^3*b*c^2*d*e^4 - 3*a^2*b^4*e^5 + 21*a^3*b^2*c*e^5 - 24*a^4*c^2*e^5 - 2*(6*c^6*d^5 - 15*b*c^5*d^4*e + 10*b^2*c^4*d^3*e^2 + 20*a*c^5*d^3*e^2 - 30*a*b*c^4*d^2*e^3 - b^4*c^2*d*e^4 + 8*a*b^2*c^3*d*e^4 + 14*a^2*c^4*d*e^4 + a*b^3*c^2*e^5 - 7*a^2*b*c^3*e^5)*x^3 - (18*b*c^5*d^5 - 45*b^2*c^4*d^4*e + 30*b^3*c^3*d^3*e^2 + 60*a*b*c^4*d^3*e^2 + b^4*c^2*d^2*e^3 - 98*a*b^2*c^3*d^2*e^3 + 16*a^2*c^4*d^2*e^3 - 4*b^5*c*d*e^4 + 32*a*b^3*c^2*d*e^4 + 26*a^2*b*c^3*d*e^4 + 4*a*b^4*c*e^5 - 29*a^2*b^2*c^2*e^5 + 16*a^3*c^3*e^5)*x^2 - 2*(2*b^2*c^4*d^5 + 10*a*c^5*d^5 - 5*b^3*c^3*d^4*e - 25*a*b*c^4*d^4*e + 3*b^4*c^2*d^3*e^2 + 26*a*b^2*c^3*d^3*e^2 + 28*a^2*c^4*d^3*e^2 + b^5*c*d^2*e^3 - 18*a*b^3*c^2*d^2*e^3 - 34*a^2*b*c^3*d^2*e^3 - b^6*d*e^4 + 6*a*b^4*c*d*e^4 + 10*a^2*b^2*c^2*d*e^4 + 18*a^3*c^3*d*e^4 + a*b^5*e^5 - 6*a^2*b^3*c*e^5 - a^3*b*c^2*e^5)*x)/((c*d^2 - b*d*e + a*e^2)^3*(c*x^2 + b*x + a)^2*(b^2 - 4*a*c)^2)","B",0
2208,1,309,0,0.177204," ","integrate(1/x^2/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{3 \, {\left(b^{6} - 10 \, a b^{4} c + 30 \, a^{2} b^{2} c^{2} - 20 \, a^{3} c^{3}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{3 \, b \log\left(c x^{2} + b x + a\right)}{2 \, a^{4}} - \frac{3 \, b \log\left({\left| x \right|}\right)}{a^{4}} - \frac{2 \, a^{3} b^{4} - 16 \, a^{4} b^{2} c + 32 \, a^{5} c^{2} + 6 \, {\left(a b^{4} c^{2} - 7 \, a^{2} b^{2} c^{3} + 10 \, a^{3} c^{4}\right)} x^{4} + 3 \, {\left(4 \, a b^{5} c - 29 \, a^{2} b^{3} c^{2} + 46 \, a^{3} b c^{3}\right)} x^{3} + 2 \, {\left(3 \, a b^{6} - 18 \, a^{2} b^{4} c + 7 \, a^{3} b^{2} c^{2} + 50 \, a^{4} c^{3}\right)} x^{2} + {\left(9 \, a^{2} b^{5} - 68 \, a^{3} b^{3} c + 122 \, a^{4} b c^{2}\right)} x}{2 \, {\left(c x^{2} + b x + a\right)}^{2} {\left(b^{2} - 4 \, a c\right)}^{2} a^{4} x}"," ",0,"3*(b^6 - 10*a*b^4*c + 30*a^2*b^2*c^2 - 20*a^3*c^3)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2)*sqrt(-b^2 + 4*a*c)) + 3/2*b*log(c*x^2 + b*x + a)/a^4 - 3*b*log(abs(x))/a^4 - 1/2*(2*a^3*b^4 - 16*a^4*b^2*c + 32*a^5*c^2 + 6*(a*b^4*c^2 - 7*a^2*b^2*c^3 + 10*a^3*c^4)*x^4 + 3*(4*a*b^5*c - 29*a^2*b^3*c^2 + 46*a^3*b*c^3)*x^3 + 2*(3*a*b^6 - 18*a^2*b^4*c + 7*a^3*b^2*c^2 + 50*a^4*c^3)*x^2 + (9*a^2*b^5 - 68*a^3*b^3*c + 122*a^4*b*c^2)*x)/((c*x^2 + b*x + a)^2*(b^2 - 4*a*c)^2*a^4*x)","A",0
2209,1,410,0,0.169473," ","integrate(1/x^3/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","-\frac{3 \, {\left(2 \, b^{7} - 21 \, a b^{5} c + 70 \, a^{2} b^{3} c^{2} - 70 \, a^{3} b c^{3}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{12 \, b^{5} c^{2} x^{5} - 90 \, a b^{3} c^{3} x^{5} + 162 \, a^{2} b c^{4} x^{5} + 24 \, b^{6} c x^{4} - 186 \, a b^{4} c^{2} x^{4} + 363 \, a^{2} b^{2} c^{3} x^{4} - 48 \, a^{3} c^{4} x^{4} + 12 \, b^{7} x^{3} - 78 \, a b^{5} c x^{3} + 64 \, a^{2} b^{3} c^{2} x^{3} + 206 \, a^{3} b c^{3} x^{3} + 18 \, a b^{6} x^{2} - 145 \, a^{2} b^{4} c x^{2} + 307 \, a^{3} b^{2} c^{2} x^{2} - 72 \, a^{4} c^{3} x^{2} + 4 \, a^{2} b^{5} x - 32 \, a^{3} b^{3} c x + 64 \, a^{4} b c^{2} x - a^{3} b^{4} + 8 \, a^{4} b^{2} c - 16 \, a^{5} c^{2}}{2 \, {\left(a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2}\right)} {\left(c x^{3} + b x^{2} + a x\right)}^{2}} - \frac{3 \, {\left(2 \, b^{2} - a c\right)} \log\left(c x^{2} + b x + a\right)}{2 \, a^{5}} + \frac{3 \, {\left(2 \, b^{2} - a c\right)} \log\left({\left| x \right|}\right)}{a^{5}}"," ",0,"-3*(2*b^7 - 21*a*b^5*c + 70*a^2*b^3*c^2 - 70*a^3*b*c^3)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*sqrt(-b^2 + 4*a*c)) + 1/2*(12*b^5*c^2*x^5 - 90*a*b^3*c^3*x^5 + 162*a^2*b*c^4*x^5 + 24*b^6*c*x^4 - 186*a*b^4*c^2*x^4 + 363*a^2*b^2*c^3*x^4 - 48*a^3*c^4*x^4 + 12*b^7*x^3 - 78*a*b^5*c*x^3 + 64*a^2*b^3*c^2*x^3 + 206*a^3*b*c^3*x^3 + 18*a*b^6*x^2 - 145*a^2*b^4*c*x^2 + 307*a^3*b^2*c^2*x^2 - 72*a^4*c^3*x^2 + 4*a^2*b^5*x - 32*a^3*b^3*c*x + 64*a^4*b*c^2*x - a^3*b^4 + 8*a^4*b^2*c - 16*a^5*c^2)/((a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2)*(c*x^3 + b*x^2 + a*x)^2) - 3/2*(2*b^2 - a*c)*log(c*x^2 + b*x + a)/a^5 + 3*(2*b^2 - a*c)*log(abs(x))/a^5","A",0
2210,1,467,0,0.184757," ","integrate(x^8/(c*x^2+b*x+a)^4,x, algorithm=""giac"")","\frac{4 \, {\left(b^{8} - 14 \, a b^{6} c + 70 \, a^{2} b^{4} c^{2} - 140 \, a^{3} b^{2} c^{3} + 70 \, a^{4} c^{4}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{x}{c^{4}} - \frac{2 \, b \log\left(c x^{2} + b x + a\right)}{c^{5}} - \frac{13 \, a^{3} b^{7} - 147 \, a^{4} b^{5} c + 535 \, a^{5} b^{3} c^{2} - 590 \, a^{6} b c^{3} + 6 \, {\left(3 \, b^{8} c^{2} - 36 \, a b^{6} c^{3} + 146 \, a^{2} b^{4} c^{4} - 212 \, a^{3} b^{2} c^{5} + 58 \, a^{4} c^{6}\right)} x^{5} + 6 \, {\left(5 \, b^{9} c - 57 \, a b^{7} c^{2} + 209 \, a^{2} b^{5} c^{3} - 226 \, a^{3} b^{3} c^{4} - 47 \, a^{4} b c^{5}\right)} x^{4} + {\left(13 \, b^{10} - 96 \, a b^{8} c - 68 \, a^{2} b^{6} c^{2} + 1788 \, a^{3} b^{4} c^{3} - 3234 \, a^{4} b^{2} c^{4} + 544 \, a^{5} c^{5}\right)} x^{3} + 3 \, {\left(13 \, a b^{9} - 143 \, a^{2} b^{7} c + 486 \, a^{3} b^{5} c^{2} - 387 \, a^{4} b^{3} c^{3} - 304 \, a^{5} b c^{4}\right)} x^{2} + 3 \, {\left(13 \, a^{2} b^{8} - 150 \, a^{3} b^{6} c + 567 \, a^{4} b^{4} c^{2} - 694 \, a^{5} b^{2} c^{3} + 76 \, a^{6} c^{4}\right)} x}{3 \, {\left(c x^{2} + b x + a\right)}^{3} {\left(b^{2} - 4 \, a c\right)}^{3} c^{5}}"," ",0,"4*(b^8 - 14*a*b^6*c + 70*a^2*b^4*c^2 - 140*a^3*b^2*c^3 + 70*a^4*c^4)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8)*sqrt(-b^2 + 4*a*c)) + x/c^4 - 2*b*log(c*x^2 + b*x + a)/c^5 - 1/3*(13*a^3*b^7 - 147*a^4*b^5*c + 535*a^5*b^3*c^2 - 590*a^6*b*c^3 + 6*(3*b^8*c^2 - 36*a*b^6*c^3 + 146*a^2*b^4*c^4 - 212*a^3*b^2*c^5 + 58*a^4*c^6)*x^5 + 6*(5*b^9*c - 57*a*b^7*c^2 + 209*a^2*b^5*c^3 - 226*a^3*b^3*c^4 - 47*a^4*b*c^5)*x^4 + (13*b^10 - 96*a*b^8*c - 68*a^2*b^6*c^2 + 1788*a^3*b^4*c^3 - 3234*a^4*b^2*c^4 + 544*a^5*c^5)*x^3 + 3*(13*a*b^9 - 143*a^2*b^7*c + 486*a^3*b^5*c^2 - 387*a^4*b^3*c^3 - 304*a^5*b*c^4)*x^2 + 3*(13*a^2*b^8 - 150*a^3*b^6*c + 567*a^4*b^4*c^2 - 694*a^5*b^2*c^3 + 76*a^6*c^4)*x)/((c*x^2 + b*x + a)^3*(b^2 - 4*a*c)^3*c^5)","A",0
2211,1,418,0,0.177811," ","integrate(x^7/(c*x^2+b*x+a)^4,x, algorithm=""giac"")","-\frac{{\left(b^{7} - 14 \, a b^{5} c + 70 \, a^{2} b^{3} c^{2} - 140 \, a^{3} b c^{3}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{\log\left(c x^{2} + b x + a\right)}{2 \, c^{4}} + \frac{11 \, a^{3} b^{6} - 124 \, a^{4} b^{4} c + 438 \, a^{5} b^{2} c^{2} - 352 \, a^{6} c^{3} + 6 \, {\left(3 \, b^{7} c^{2} - 35 \, a b^{5} c^{3} + 133 \, a^{2} b^{3} c^{4} - 154 \, a^{3} b c^{5}\right)} x^{5} + 3 \, {\left(9 \, b^{8} c - 100 \, a b^{6} c^{2} + 341 \, a^{2} b^{4} c^{3} - 242 \, a^{3} b^{2} c^{4} - 192 \, a^{4} c^{5}\right)} x^{4} + {\left(11 \, b^{9} - 76 \, a b^{7} c - 117 \, a^{2} b^{5} c^{2} + 1698 \, a^{3} b^{3} c^{3} - 2272 \, a^{4} b c^{4}\right)} x^{3} + 3 \, {\left(11 \, a b^{8} - 119 \, a^{2} b^{6} c + 381 \, a^{3} b^{4} c^{2} - 152 \, a^{4} b^{2} c^{3} - 288 \, a^{5} c^{4}\right)} x^{2} + 3 \, {\left(11 \, a^{2} b^{7} - 126 \, a^{3} b^{5} c + 460 \, a^{4} b^{3} c^{2} - 428 \, a^{5} b c^{3}\right)} x}{6 \, {\left(c x^{2} + b x + a\right)}^{3} {\left(b^{2} - 4 \, a c\right)}^{3} c^{4}}"," ",0,"-(b^7 - 14*a*b^5*c + 70*a^2*b^3*c^2 - 140*a^3*b*c^3)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)*sqrt(-b^2 + 4*a*c)) + 1/2*log(c*x^2 + b*x + a)/c^4 + 1/6*(11*a^3*b^6 - 124*a^4*b^4*c + 438*a^5*b^2*c^2 - 352*a^6*c^3 + 6*(3*b^7*c^2 - 35*a*b^5*c^3 + 133*a^2*b^3*c^4 - 154*a^3*b*c^5)*x^5 + 3*(9*b^8*c - 100*a*b^6*c^2 + 341*a^2*b^4*c^3 - 242*a^3*b^2*c^4 - 192*a^4*c^5)*x^4 + (11*b^9 - 76*a*b^7*c - 117*a^2*b^5*c^2 + 1698*a^3*b^3*c^3 - 2272*a^4*b*c^4)*x^3 + 3*(11*a*b^8 - 119*a^2*b^6*c + 381*a^3*b^4*c^2 - 152*a^4*b^2*c^3 - 288*a^5*c^4)*x^2 + 3*(11*a^2*b^7 - 126*a^3*b^5*c + 460*a^4*b^3*c^2 - 428*a^5*b*c^3)*x)/((c*x^2 + b*x + a)^3*(b^2 - 4*a*c)^3*c^4)","A",0
2212,1,386,0,0.202773," ","integrate(x^6/(c*x^2+b*x+a)^4,x, algorithm=""giac"")","-\frac{40 \, a^{3} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{3 \, b^{6} c^{2} x^{5} - 36 \, a b^{4} c^{3} x^{5} + 144 \, a^{2} b^{2} c^{4} x^{5} - 132 \, a^{3} c^{5} x^{5} + 3 \, b^{7} c x^{4} - 36 \, a b^{5} c^{2} x^{4} + 144 \, a^{2} b^{3} c^{3} x^{4} - 42 \, a^{3} b c^{4} x^{4} + b^{8} x^{3} - 7 \, a b^{6} c x^{3} - 12 \, a^{2} b^{4} c^{2} x^{3} + 286 \, a^{3} b^{2} c^{3} x^{3} - 160 \, a^{4} c^{4} x^{3} + 3 \, a b^{7} x^{2} - 36 \, a^{2} b^{5} c x^{2} + 159 \, a^{3} b^{3} c^{2} x^{2} + 48 \, a^{4} b c^{3} x^{2} + 3 \, a^{2} b^{6} x - 39 \, a^{3} b^{4} c x + 198 \, a^{4} b^{2} c^{2} x - 60 \, a^{5} c^{3} x + a^{3} b^{5} - 13 \, a^{4} b^{3} c + 66 \, a^{5} b c^{2}}{3 \, {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} {\left(c x^{2} + b x + a\right)}^{3}}"," ",0,"-40*a^3*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)*sqrt(-b^2 + 4*a*c)) - 1/3*(3*b^6*c^2*x^5 - 36*a*b^4*c^3*x^5 + 144*a^2*b^2*c^4*x^5 - 132*a^3*c^5*x^5 + 3*b^7*c*x^4 - 36*a*b^5*c^2*x^4 + 144*a^2*b^3*c^3*x^4 - 42*a^3*b*c^4*x^4 + b^8*x^3 - 7*a*b^6*c*x^3 - 12*a^2*b^4*c^2*x^3 + 286*a^3*b^2*c^3*x^3 - 160*a^4*c^4*x^3 + 3*a*b^7*x^2 - 36*a^2*b^5*c*x^2 + 159*a^3*b^3*c^2*x^2 + 48*a^4*b*c^3*x^2 + 3*a^2*b^6*x - 39*a^3*b^4*c*x + 198*a^4*b^2*c^2*x - 60*a^5*c^3*x + a^3*b^5 - 13*a^4*b^3*c + 66*a^5*b*c^2)/((b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*(c*x^2 + b*x + a)^3)","B",0
2213,1,326,0,0.248692," ","integrate(x^5/(c*x^2+b*x+a)^4,x, algorithm=""giac"")","\frac{20 \, a^{2} b \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{60 \, a^{2} b c^{4} x^{5} - 3 \, b^{6} c x^{4} + 36 \, a b^{4} c^{2} x^{4} + 6 \, a^{2} b^{2} c^{3} x^{4} + 192 \, a^{3} c^{4} x^{4} - b^{7} x^{3} + 12 \, a b^{5} c x^{3} + 62 \, a^{2} b^{3} c^{2} x^{3} + 224 \, a^{3} b c^{3} x^{3} - 3 \, a b^{6} x^{2} + 51 \, a^{2} b^{4} c x^{2} + 96 \, a^{3} b^{2} c^{2} x^{2} + 192 \, a^{4} c^{3} x^{2} - 3 \, a^{2} b^{5} x + 54 \, a^{3} b^{3} c x + 132 \, a^{4} b c^{2} x - a^{3} b^{4} + 18 \, a^{4} b^{2} c + 64 \, a^{5} c^{2}}{6 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} {\left(c x^{2} + b x + a\right)}^{3}}"," ",0,"20*a^2*b*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)*sqrt(-b^2 + 4*a*c)) + 1/6*(60*a^2*b*c^4*x^5 - 3*b^6*c*x^4 + 36*a*b^4*c^2*x^4 + 6*a^2*b^2*c^3*x^4 + 192*a^3*c^4*x^4 - b^7*x^3 + 12*a*b^5*c*x^3 + 62*a^2*b^3*c^2*x^3 + 224*a^3*b*c^3*x^3 - 3*a*b^6*x^2 + 51*a^2*b^4*c*x^2 + 96*a^3*b^2*c^2*x^2 + 192*a^4*c^3*x^2 - 3*a^2*b^5*x + 54*a^3*b^3*c*x + 132*a^4*b*c^2*x - a^3*b^4 + 18*a^4*b^2*c + 64*a^5*c^2)/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*(c*x^2 + b*x + a)^3)","B",0
2214,1,1129,0,0.213209," ","integrate((e*x+d)^4/(c*x^2+b*x+a)^4,x, algorithm=""giac"")","-\frac{8 \, {\left(5 \, c^{3} d^{4} - 10 \, b c^{2} d^{3} e + 6 \, b^{2} c d^{2} e^{2} + 6 \, a c^{2} d^{2} e^{2} - b^{3} d e^{3} - 6 \, a b c d e^{3} + a b^{2} e^{4} + a^{2} c e^{4}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{60 \, c^{6} d^{4} x^{5} - 120 \, b c^{5} d^{3} x^{5} e + 150 \, b c^{5} d^{4} x^{4} + 72 \, b^{2} c^{4} d^{2} x^{5} e^{2} + 72 \, a c^{5} d^{2} x^{5} e^{2} - 300 \, b^{2} c^{4} d^{3} x^{4} e + 110 \, b^{2} c^{4} d^{4} x^{3} + 160 \, a c^{5} d^{4} x^{3} - 12 \, b^{3} c^{3} d x^{5} e^{3} - 72 \, a b c^{4} d x^{5} e^{3} + 180 \, b^{3} c^{3} d^{2} x^{4} e^{2} + 180 \, a b c^{4} d^{2} x^{4} e^{2} - 220 \, b^{3} c^{3} d^{3} x^{3} e - 320 \, a b c^{4} d^{3} x^{3} e + 15 \, b^{3} c^{3} d^{4} x^{2} + 240 \, a b c^{4} d^{4} x^{2} + 12 \, a b^{2} c^{3} x^{5} e^{4} + 12 \, a^{2} c^{4} x^{5} e^{4} - 30 \, b^{4} c^{2} d x^{4} e^{3} - 180 \, a b^{2} c^{3} d x^{4} e^{3} + 132 \, b^{4} c^{2} d^{2} x^{3} e^{2} + 324 \, a b^{2} c^{3} d^{2} x^{3} e^{2} + 192 \, a^{2} c^{4} d^{2} x^{3} e^{2} - 30 \, b^{4} c^{2} d^{3} x^{2} e - 480 \, a b^{2} c^{3} d^{3} x^{2} e - 3 \, b^{4} c^{2} d^{4} x + 54 \, a b^{2} c^{3} d^{4} x + 132 \, a^{2} c^{4} d^{4} x + 30 \, a b^{3} c^{2} x^{4} e^{4} + 30 \, a^{2} b c^{3} x^{4} e^{4} - 22 \, b^{5} c d x^{3} e^{3} - 164 \, a b^{3} c^{2} d x^{3} e^{3} - 192 \, a^{2} b c^{3} d x^{3} e^{3} + 18 \, b^{5} c d^{2} x^{2} e^{2} + 306 \, a b^{3} c^{2} d^{2} x^{2} e^{2} + 288 \, a^{2} b c^{3} d^{2} x^{2} e^{2} + 6 \, b^{5} c d^{3} x e - 108 \, a b^{3} c^{2} d^{3} x e - 264 \, a^{2} b c^{3} d^{3} x e + b^{5} c d^{4} - 13 \, a b^{3} c^{2} d^{4} + 66 \, a^{2} b c^{3} d^{4} + b^{6} x^{3} e^{4} + 10 \, a b^{4} c x^{3} e^{4} + 102 \, a^{2} b^{2} c^{2} x^{3} e^{4} - 32 \, a^{3} c^{3} x^{3} e^{4} - 102 \, a b^{4} c d x^{2} e^{3} - 144 \, a^{2} b^{2} c^{2} d x^{2} e^{3} - 192 \, a^{3} c^{3} d x^{2} e^{3} + 18 \, a b^{4} c d^{2} x e^{2} + 396 \, a^{2} b^{2} c^{2} d^{2} x e^{2} - 72 \, a^{3} c^{3} d^{2} x e^{2} + 2 \, a b^{4} c d^{3} e - 36 \, a^{2} b^{2} c^{2} d^{3} e - 128 \, a^{3} c^{3} d^{3} e + 3 \, a b^{5} x^{2} e^{4} + 51 \, a^{2} b^{3} c x^{2} e^{4} + 48 \, a^{3} b c^{2} x^{2} e^{4} - 120 \, a^{2} b^{3} c d x e^{3} - 120 \, a^{3} b c^{2} d x e^{3} + 6 \, a^{2} b^{3} c d^{2} e^{2} + 156 \, a^{3} b c^{2} d^{2} e^{2} + 3 \, a^{2} b^{4} x e^{4} + 66 \, a^{3} b^{2} c x e^{4} - 12 \, a^{4} c^{2} x e^{4} - 44 \, a^{3} b^{2} c d e^{3} - 64 \, a^{4} c^{2} d e^{3} + a^{3} b^{3} e^{4} + 26 \, a^{4} b c e^{4}}{3 \, {\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} {\left(c x^{2} + b x + a\right)}^{3}}"," ",0,"-8*(5*c^3*d^4 - 10*b*c^2*d^3*e + 6*b^2*c*d^2*e^2 + 6*a*c^2*d^2*e^2 - b^3*d*e^3 - 6*a*b*c*d*e^3 + a*b^2*e^4 + a^2*c*e^4)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)*sqrt(-b^2 + 4*a*c)) - 1/3*(60*c^6*d^4*x^5 - 120*b*c^5*d^3*x^5*e + 150*b*c^5*d^4*x^4 + 72*b^2*c^4*d^2*x^5*e^2 + 72*a*c^5*d^2*x^5*e^2 - 300*b^2*c^4*d^3*x^4*e + 110*b^2*c^4*d^4*x^3 + 160*a*c^5*d^4*x^3 - 12*b^3*c^3*d*x^5*e^3 - 72*a*b*c^4*d*x^5*e^3 + 180*b^3*c^3*d^2*x^4*e^2 + 180*a*b*c^4*d^2*x^4*e^2 - 220*b^3*c^3*d^3*x^3*e - 320*a*b*c^4*d^3*x^3*e + 15*b^3*c^3*d^4*x^2 + 240*a*b*c^4*d^4*x^2 + 12*a*b^2*c^3*x^5*e^4 + 12*a^2*c^4*x^5*e^4 - 30*b^4*c^2*d*x^4*e^3 - 180*a*b^2*c^3*d*x^4*e^3 + 132*b^4*c^2*d^2*x^3*e^2 + 324*a*b^2*c^3*d^2*x^3*e^2 + 192*a^2*c^4*d^2*x^3*e^2 - 30*b^4*c^2*d^3*x^2*e - 480*a*b^2*c^3*d^3*x^2*e - 3*b^4*c^2*d^4*x + 54*a*b^2*c^3*d^4*x + 132*a^2*c^4*d^4*x + 30*a*b^3*c^2*x^4*e^4 + 30*a^2*b*c^3*x^4*e^4 - 22*b^5*c*d*x^3*e^3 - 164*a*b^3*c^2*d*x^3*e^3 - 192*a^2*b*c^3*d*x^3*e^3 + 18*b^5*c*d^2*x^2*e^2 + 306*a*b^3*c^2*d^2*x^2*e^2 + 288*a^2*b*c^3*d^2*x^2*e^2 + 6*b^5*c*d^3*x*e - 108*a*b^3*c^2*d^3*x*e - 264*a^2*b*c^3*d^3*x*e + b^5*c*d^4 - 13*a*b^3*c^2*d^4 + 66*a^2*b*c^3*d^4 + b^6*x^3*e^4 + 10*a*b^4*c*x^3*e^4 + 102*a^2*b^2*c^2*x^3*e^4 - 32*a^3*c^3*x^3*e^4 - 102*a*b^4*c*d*x^2*e^3 - 144*a^2*b^2*c^2*d*x^2*e^3 - 192*a^3*c^3*d*x^2*e^3 + 18*a*b^4*c*d^2*x*e^2 + 396*a^2*b^2*c^2*d^2*x*e^2 - 72*a^3*c^3*d^2*x*e^2 + 2*a*b^4*c*d^3*e - 36*a^2*b^2*c^2*d^3*e - 128*a^3*c^3*d^3*e + 3*a*b^5*x^2*e^4 + 51*a^2*b^3*c*x^2*e^4 + 48*a^3*b*c^2*x^2*e^4 - 120*a^2*b^3*c*d*x*e^3 - 120*a^3*b*c^2*d*x*e^3 + 6*a^2*b^3*c*d^2*e^2 + 156*a^3*b*c^2*d^2*e^2 + 3*a^2*b^4*x*e^4 + 66*a^3*b^2*c*x*e^4 - 12*a^4*c^2*x*e^4 - 44*a^3*b^2*c*d*e^3 - 64*a^4*c^2*d*e^3 + a^3*b^3*e^4 + 26*a^4*b*c*e^4)/((b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*(c*x^2 + b*x + a)^3)","B",0
2215,1,828,0,0.185207," ","integrate((e*x+d)^3/(c*x^2+b*x+a)^4,x, algorithm=""giac"")","-\frac{2 \, {\left(20 \, c^{3} d^{3} - 30 \, b c^{2} d^{2} e + 12 \, b^{2} c d e^{2} + 12 \, a c^{2} d e^{2} - b^{3} e^{3} - 6 \, a b c e^{3}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{120 \, c^{5} d^{3} x^{5} - 180 \, b c^{4} d^{2} x^{5} e + 300 \, b c^{4} d^{3} x^{4} + 72 \, b^{2} c^{3} d x^{5} e^{2} + 72 \, a c^{4} d x^{5} e^{2} - 450 \, b^{2} c^{3} d^{2} x^{4} e + 220 \, b^{2} c^{3} d^{3} x^{3} + 320 \, a c^{4} d^{3} x^{3} - 6 \, b^{3} c^{2} x^{5} e^{3} - 36 \, a b c^{3} x^{5} e^{3} + 180 \, b^{3} c^{2} d x^{4} e^{2} + 180 \, a b c^{3} d x^{4} e^{2} - 330 \, b^{3} c^{2} d^{2} x^{3} e - 480 \, a b c^{3} d^{2} x^{3} e + 30 \, b^{3} c^{2} d^{3} x^{2} + 480 \, a b c^{3} d^{3} x^{2} - 15 \, b^{4} c x^{4} e^{3} - 90 \, a b^{2} c^{2} x^{4} e^{3} + 132 \, b^{4} c d x^{3} e^{2} + 324 \, a b^{2} c^{2} d x^{3} e^{2} + 192 \, a^{2} c^{3} d x^{3} e^{2} - 45 \, b^{4} c d^{2} x^{2} e - 720 \, a b^{2} c^{2} d^{2} x^{2} e - 6 \, b^{4} c d^{3} x + 108 \, a b^{2} c^{2} d^{3} x + 264 \, a^{2} c^{3} d^{3} x - 11 \, b^{5} x^{3} e^{3} - 82 \, a b^{3} c x^{3} e^{3} - 96 \, a^{2} b c^{2} x^{3} e^{3} + 18 \, b^{5} d x^{2} e^{2} + 306 \, a b^{3} c d x^{2} e^{2} + 288 \, a^{2} b c^{2} d x^{2} e^{2} + 9 \, b^{5} d^{2} x e - 162 \, a b^{3} c d^{2} x e - 396 \, a^{2} b c^{2} d^{2} x e + 2 \, b^{5} d^{3} - 26 \, a b^{3} c d^{3} + 132 \, a^{2} b c^{2} d^{3} - 51 \, a b^{4} x^{2} e^{3} - 72 \, a^{2} b^{2} c x^{2} e^{3} - 96 \, a^{3} c^{2} x^{2} e^{3} + 18 \, a b^{4} d x e^{2} + 396 \, a^{2} b^{2} c d x e^{2} - 72 \, a^{3} c^{2} d x e^{2} + 3 \, a b^{4} d^{2} e - 54 \, a^{2} b^{2} c d^{2} e - 192 \, a^{3} c^{2} d^{2} e - 60 \, a^{2} b^{3} x e^{3} - 60 \, a^{3} b c x e^{3} + 6 \, a^{2} b^{3} d e^{2} + 156 \, a^{3} b c d e^{2} - 22 \, a^{3} b^{2} e^{3} - 32 \, a^{4} c e^{3}}{6 \, {\left(b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} {\left(c x^{2} + b x + a\right)}^{3}}"," ",0,"-2*(20*c^3*d^3 - 30*b*c^2*d^2*e + 12*b^2*c*d*e^2 + 12*a*c^2*d*e^2 - b^3*e^3 - 6*a*b*c*e^3)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)*sqrt(-b^2 + 4*a*c)) - 1/6*(120*c^5*d^3*x^5 - 180*b*c^4*d^2*x^5*e + 300*b*c^4*d^3*x^4 + 72*b^2*c^3*d*x^5*e^2 + 72*a*c^4*d*x^5*e^2 - 450*b^2*c^3*d^2*x^4*e + 220*b^2*c^3*d^3*x^3 + 320*a*c^4*d^3*x^3 - 6*b^3*c^2*x^5*e^3 - 36*a*b*c^3*x^5*e^3 + 180*b^3*c^2*d*x^4*e^2 + 180*a*b*c^3*d*x^4*e^2 - 330*b^3*c^2*d^2*x^3*e - 480*a*b*c^3*d^2*x^3*e + 30*b^3*c^2*d^3*x^2 + 480*a*b*c^3*d^3*x^2 - 15*b^4*c*x^4*e^3 - 90*a*b^2*c^2*x^4*e^3 + 132*b^4*c*d*x^3*e^2 + 324*a*b^2*c^2*d*x^3*e^2 + 192*a^2*c^3*d*x^3*e^2 - 45*b^4*c*d^2*x^2*e - 720*a*b^2*c^2*d^2*x^2*e - 6*b^4*c*d^3*x + 108*a*b^2*c^2*d^3*x + 264*a^2*c^3*d^3*x - 11*b^5*x^3*e^3 - 82*a*b^3*c*x^3*e^3 - 96*a^2*b*c^2*x^3*e^3 + 18*b^5*d*x^2*e^2 + 306*a*b^3*c*d*x^2*e^2 + 288*a^2*b*c^2*d*x^2*e^2 + 9*b^5*d^2*x*e - 162*a*b^3*c*d^2*x*e - 396*a^2*b*c^2*d^2*x*e + 2*b^5*d^3 - 26*a*b^3*c*d^3 + 132*a^2*b*c^2*d^3 - 51*a*b^4*x^2*e^3 - 72*a^2*b^2*c*x^2*e^3 - 96*a^3*c^2*x^2*e^3 + 18*a*b^4*d*x*e^2 + 396*a^2*b^2*c*d*x*e^2 - 72*a^3*c^2*d*x*e^2 + 3*a*b^4*d^2*e - 54*a^2*b^2*c*d^2*e - 192*a^3*c^2*d^2*e - 60*a^2*b^3*x*e^3 - 60*a^3*b*c*x*e^3 + 6*a^2*b^3*d*e^2 + 156*a^3*b*c*d*e^2 - 22*a^3*b^2*e^3 - 32*a^4*c*e^3)/((b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)*(c*x^2 + b*x + a)^3)","B",0
2216,1,603,0,0.176440," ","integrate((e*x+d)^2/(c*x^2+b*x+a)^4,x, algorithm=""giac"")","-\frac{8 \, {\left(5 \, c^{3} d^{2} - 5 \, b c^{2} d e + b^{2} c e^{2} + a c^{2} e^{2}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{60 \, c^{5} d^{2} x^{5} - 60 \, b c^{4} d x^{5} e + 150 \, b c^{4} d^{2} x^{4} + 12 \, b^{2} c^{3} x^{5} e^{2} + 12 \, a c^{4} x^{5} e^{2} - 150 \, b^{2} c^{3} d x^{4} e + 110 \, b^{2} c^{3} d^{2} x^{3} + 160 \, a c^{4} d^{2} x^{3} + 30 \, b^{3} c^{2} x^{4} e^{2} + 30 \, a b c^{3} x^{4} e^{2} - 110 \, b^{3} c^{2} d x^{3} e - 160 \, a b c^{3} d x^{3} e + 15 \, b^{3} c^{2} d^{2} x^{2} + 240 \, a b c^{3} d^{2} x^{2} + 22 \, b^{4} c x^{3} e^{2} + 54 \, a b^{2} c^{2} x^{3} e^{2} + 32 \, a^{2} c^{3} x^{3} e^{2} - 15 \, b^{4} c d x^{2} e - 240 \, a b^{2} c^{2} d x^{2} e - 3 \, b^{4} c d^{2} x + 54 \, a b^{2} c^{2} d^{2} x + 132 \, a^{2} c^{3} d^{2} x + 3 \, b^{5} x^{2} e^{2} + 51 \, a b^{3} c x^{2} e^{2} + 48 \, a^{2} b c^{2} x^{2} e^{2} + 3 \, b^{5} d x e - 54 \, a b^{3} c d x e - 132 \, a^{2} b c^{2} d x e + b^{5} d^{2} - 13 \, a b^{3} c d^{2} + 66 \, a^{2} b c^{2} d^{2} + 3 \, a b^{4} x e^{2} + 66 \, a^{2} b^{2} c x e^{2} - 12 \, a^{3} c^{2} x e^{2} + a b^{4} d e - 18 \, a^{2} b^{2} c d e - 64 \, a^{3} c^{2} d e + a^{2} b^{3} e^{2} + 26 \, a^{3} b c e^{2}}{3 \, {\left(b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} {\left(c x^{2} + b x + a\right)}^{3}}"," ",0,"-8*(5*c^3*d^2 - 5*b*c^2*d*e + b^2*c*e^2 + a*c^2*e^2)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)*sqrt(-b^2 + 4*a*c)) - 1/3*(60*c^5*d^2*x^5 - 60*b*c^4*d*x^5*e + 150*b*c^4*d^2*x^4 + 12*b^2*c^3*x^5*e^2 + 12*a*c^4*x^5*e^2 - 150*b^2*c^3*d*x^4*e + 110*b^2*c^3*d^2*x^3 + 160*a*c^4*d^2*x^3 + 30*b^3*c^2*x^4*e^2 + 30*a*b*c^3*x^4*e^2 - 110*b^3*c^2*d*x^3*e - 160*a*b*c^3*d*x^3*e + 15*b^3*c^2*d^2*x^2 + 240*a*b*c^3*d^2*x^2 + 22*b^4*c*x^3*e^2 + 54*a*b^2*c^2*x^3*e^2 + 32*a^2*c^3*x^3*e^2 - 15*b^4*c*d*x^2*e - 240*a*b^2*c^2*d*x^2*e - 3*b^4*c*d^2*x + 54*a*b^2*c^2*d^2*x + 132*a^2*c^3*d^2*x + 3*b^5*x^2*e^2 + 51*a*b^3*c*x^2*e^2 + 48*a^2*b*c^2*x^2*e^2 + 3*b^5*d*x*e - 54*a*b^3*c*d*x*e - 132*a^2*b*c^2*d*x*e + b^5*d^2 - 13*a*b^3*c*d^2 + 66*a^2*b*c^2*d^2 + 3*a*b^4*x*e^2 + 66*a^2*b^2*c*x*e^2 - 12*a^3*c^2*x*e^2 + a*b^4*d*e - 18*a^2*b^2*c*d*e - 64*a^3*c^2*d*e + a^2*b^3*e^2 + 26*a^3*b*c*e^2)/((b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)*(c*x^2 + b*x + a)^3)","B",0
2217,1,378,0,0.184155," ","integrate((e*x+d)/(c*x^2+b*x+a)^4,x, algorithm=""giac"")","-\frac{20 \, {\left(2 \, c^{3} d - b c^{2} e\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{120 \, c^{5} d x^{5} - 60 \, b c^{4} x^{5} e + 300 \, b c^{4} d x^{4} - 150 \, b^{2} c^{3} x^{4} e + 220 \, b^{2} c^{3} d x^{3} + 320 \, a c^{4} d x^{3} - 110 \, b^{3} c^{2} x^{3} e - 160 \, a b c^{3} x^{3} e + 30 \, b^{3} c^{2} d x^{2} + 480 \, a b c^{3} d x^{2} - 15 \, b^{4} c x^{2} e - 240 \, a b^{2} c^{2} x^{2} e - 6 \, b^{4} c d x + 108 \, a b^{2} c^{2} d x + 264 \, a^{2} c^{3} d x + 3 \, b^{5} x e - 54 \, a b^{3} c x e - 132 \, a^{2} b c^{2} x e + 2 \, b^{5} d - 26 \, a b^{3} c d + 132 \, a^{2} b c^{2} d + a b^{4} e - 18 \, a^{2} b^{2} c e - 64 \, a^{3} c^{2} e}{6 \, {\left(b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} {\left(c x^{2} + b x + a\right)}^{3}}"," ",0,"-20*(2*c^3*d - b*c^2*e)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)*sqrt(-b^2 + 4*a*c)) - 1/6*(120*c^5*d*x^5 - 60*b*c^4*x^5*e + 300*b*c^4*d*x^4 - 150*b^2*c^3*x^4*e + 220*b^2*c^3*d*x^3 + 320*a*c^4*d*x^3 - 110*b^3*c^2*x^3*e - 160*a*b*c^3*x^3*e + 30*b^3*c^2*d*x^2 + 480*a*b*c^3*d*x^2 - 15*b^4*c*x^2*e - 240*a*b^2*c^2*x^2*e - 6*b^4*c*d*x + 108*a*b^2*c^2*d*x + 264*a^2*c^3*d*x + 3*b^5*x*e - 54*a*b^3*c*x*e - 132*a^2*b*c^2*x*e + 2*b^5*d - 26*a*b^3*c*d + 132*a^2*b*c^2*d + a*b^4*e - 18*a^2*b^2*c*e - 64*a^3*c^2*e)/((b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)*(c*x^2 + b*x + a)^3)","B",0
2218,1,220,0,0.218278," ","integrate(1/(c*x^2+b*x+a)^4,x, algorithm=""giac"")","-\frac{40 \, c^{3} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{60 \, c^{5} x^{5} + 150 \, b c^{4} x^{4} + 110 \, b^{2} c^{3} x^{3} + 160 \, a c^{4} x^{3} + 15 \, b^{3} c^{2} x^{2} + 240 \, a b c^{3} x^{2} - 3 \, b^{4} c x + 54 \, a b^{2} c^{2} x + 132 \, a^{2} c^{3} x + b^{5} - 13 \, a b^{3} c + 66 \, a^{2} b c^{2}}{3 \, {\left(b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} {\left(c x^{2} + b x + a\right)}^{3}}"," ",0,"-40*c^3*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)*sqrt(-b^2 + 4*a*c)) - 1/3*(60*c^5*x^5 + 150*b*c^4*x^4 + 110*b^2*c^3*x^3 + 160*a*c^4*x^3 + 15*b^3*c^2*x^2 + 240*a*b*c^3*x^2 - 3*b^4*c*x + 54*a*b^2*c^2*x + 132*a^2*c^3*x + b^5 - 13*a*b^3*c + 66*a^2*b*c^2)/((b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)*(c*x^2 + b*x + a)^3)","A",0
2219,1,3230,0,0.321152," ","integrate(1/(e*x+d)/(c*x^2+b*x+a)^4,x, algorithm=""giac"")","-\frac{e^{7} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(c^{4} d^{8} - 4 \, b c^{3} d^{7} e + 6 \, b^{2} c^{2} d^{6} e^{2} + 4 \, a c^{3} d^{6} e^{2} - 4 \, b^{3} c d^{5} e^{3} - 12 \, a b c^{2} d^{5} e^{3} + b^{4} d^{4} e^{4} + 12 \, a b^{2} c d^{4} e^{4} + 6 \, a^{2} c^{2} d^{4} e^{4} - 4 \, a b^{3} d^{3} e^{5} - 12 \, a^{2} b c d^{3} e^{5} + 6 \, a^{2} b^{2} d^{2} e^{6} + 4 \, a^{3} c d^{2} e^{6} - 4 \, a^{3} b d e^{7} + a^{4} e^{8}\right)}} + \frac{e^{8} \log\left({\left| x e + d \right|}\right)}{c^{4} d^{8} e - 4 \, b c^{3} d^{7} e^{2} + 6 \, b^{2} c^{2} d^{6} e^{3} + 4 \, a c^{3} d^{6} e^{3} - 4 \, b^{3} c d^{5} e^{4} - 12 \, a b c^{2} d^{5} e^{4} + b^{4} d^{4} e^{5} + 12 \, a b^{2} c d^{4} e^{5} + 6 \, a^{2} c^{2} d^{4} e^{5} - 4 \, a b^{3} d^{3} e^{6} - 12 \, a^{2} b c d^{3} e^{6} + 6 \, a^{2} b^{2} d^{2} e^{7} + 4 \, a^{3} c d^{2} e^{7} - 4 \, a^{3} b d e^{8} + a^{4} e^{9}} - \frac{{\left(40 \, c^{7} d^{7} - 140 \, b c^{6} d^{6} e + 168 \, b^{2} c^{5} d^{5} e^{2} + 168 \, a c^{6} d^{5} e^{2} - 70 \, b^{3} c^{4} d^{4} e^{3} - 420 \, a b c^{5} d^{4} e^{3} + 280 \, a b^{2} c^{4} d^{3} e^{4} + 280 \, a^{2} c^{5} d^{3} e^{4} - 420 \, a^{2} b c^{4} d^{2} e^{5} + 280 \, a^{3} c^{4} d e^{6} + b^{7} e^{7} - 14 \, a b^{5} c e^{7} + 70 \, a^{2} b^{3} c^{2} e^{7} - 140 \, a^{3} b c^{3} e^{7}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{6} c^{4} d^{8} - 12 \, a b^{4} c^{5} d^{8} + 48 \, a^{2} b^{2} c^{6} d^{8} - 64 \, a^{3} c^{7} d^{8} - 4 \, b^{7} c^{3} d^{7} e + 48 \, a b^{5} c^{4} d^{7} e - 192 \, a^{2} b^{3} c^{5} d^{7} e + 256 \, a^{3} b c^{6} d^{7} e + 6 \, b^{8} c^{2} d^{6} e^{2} - 68 \, a b^{6} c^{3} d^{6} e^{2} + 240 \, a^{2} b^{4} c^{4} d^{6} e^{2} - 192 \, a^{3} b^{2} c^{5} d^{6} e^{2} - 256 \, a^{4} c^{6} d^{6} e^{2} - 4 \, b^{9} c d^{5} e^{3} + 36 \, a b^{7} c^{2} d^{5} e^{3} - 48 \, a^{2} b^{5} c^{3} d^{5} e^{3} - 320 \, a^{3} b^{3} c^{4} d^{5} e^{3} + 768 \, a^{4} b c^{5} d^{5} e^{3} + b^{10} d^{4} e^{4} - 90 \, a^{2} b^{6} c^{2} d^{4} e^{4} + 440 \, a^{3} b^{4} c^{3} d^{4} e^{4} - 480 \, a^{4} b^{2} c^{4} d^{4} e^{4} - 384 \, a^{5} c^{5} d^{4} e^{4} - 4 \, a b^{9} d^{3} e^{5} + 36 \, a^{2} b^{7} c d^{3} e^{5} - 48 \, a^{3} b^{5} c^{2} d^{3} e^{5} - 320 \, a^{4} b^{3} c^{3} d^{3} e^{5} + 768 \, a^{5} b c^{4} d^{3} e^{5} + 6 \, a^{2} b^{8} d^{2} e^{6} - 68 \, a^{3} b^{6} c d^{2} e^{6} + 240 \, a^{4} b^{4} c^{2} d^{2} e^{6} - 192 \, a^{5} b^{2} c^{3} d^{2} e^{6} - 256 \, a^{6} c^{4} d^{2} e^{6} - 4 \, a^{3} b^{7} d e^{7} + 48 \, a^{4} b^{5} c d e^{7} - 192 \, a^{5} b^{3} c^{2} d e^{7} + 256 \, a^{6} b c^{3} d e^{7} + a^{4} b^{6} e^{8} - 12 \, a^{5} b^{4} c e^{8} + 48 \, a^{6} b^{2} c^{2} e^{8} - 64 \, a^{7} c^{3} e^{8}\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{2 \, b^{5} c^{4} d^{7} - 26 \, a b^{3} c^{5} d^{7} + 132 \, a^{2} b c^{6} d^{7} - 8 \, b^{6} c^{3} d^{6} e + 103 \, a b^{4} c^{4} d^{6} e - 510 \, a^{2} b^{2} c^{5} d^{6} e + 64 \, a^{3} c^{6} d^{6} e + 12 \, b^{7} c^{2} d^{5} e^{2} - 144 \, a b^{5} c^{3} d^{5} e^{2} + 618 \, a^{2} b^{3} c^{4} d^{5} e^{2} + 324 \, a^{3} b c^{5} d^{5} e^{2} - 8 \, b^{8} c d^{4} e^{3} + 74 \, a b^{6} c^{2} d^{4} e^{3} - 120 \, a^{2} b^{4} c^{3} d^{4} e^{3} - 1314 \, a^{3} b^{2} c^{4} d^{4} e^{3} + 288 \, a^{4} c^{5} d^{4} e^{3} + 2 \, b^{9} d^{3} e^{4} + 2 \, a b^{7} c d^{3} e^{4} - 216 \, a^{2} b^{5} c^{2} d^{3} e^{4} + 1190 \, a^{3} b^{3} c^{3} d^{3} e^{4} + 156 \, a^{4} b c^{4} d^{3} e^{4} - 9 \, a b^{8} d^{2} e^{5} + 78 \, a^{2} b^{6} c d^{2} e^{5} - 51 \, a^{3} b^{4} c^{2} d^{2} e^{5} - 1242 \, a^{4} b^{2} c^{3} d^{2} e^{5} + 576 \, a^{5} c^{4} d^{2} e^{5} + 18 \, a^{2} b^{7} d e^{6} - 202 \, a^{3} b^{5} c d e^{6} + 682 \, a^{4} b^{3} c^{2} d e^{6} - 228 \, a^{5} b c^{3} d e^{6} - 11 \, a^{3} b^{6} e^{7} + 124 \, a^{4} b^{4} c e^{7} - 438 \, a^{5} b^{2} c^{2} e^{7} + 352 \, a^{6} c^{3} e^{7} + 6 \, {\left(20 \, c^{9} d^{7} - 70 \, b c^{8} d^{6} e + 84 \, b^{2} c^{7} d^{5} e^{2} + 84 \, a c^{8} d^{5} e^{2} - 35 \, b^{3} c^{6} d^{4} e^{3} - 210 \, a b c^{7} d^{4} e^{3} + 140 \, a b^{2} c^{6} d^{3} e^{4} + 140 \, a^{2} c^{7} d^{3} e^{4} - 210 \, a^{2} b c^{6} d^{2} e^{5} + b^{6} c^{3} d e^{6} - 12 \, a b^{4} c^{4} d e^{6} + 48 \, a^{2} b^{2} c^{5} d e^{6} + 76 \, a^{3} c^{6} d e^{6} - a b^{5} c^{3} e^{7} + 11 \, a^{2} b^{3} c^{4} e^{7} - 38 \, a^{3} b c^{5} e^{7}\right)} x^{5} + 3 \, {\left(100 \, b c^{8} d^{7} - 350 \, b^{2} c^{7} d^{6} e + 420 \, b^{3} c^{6} d^{5} e^{2} + 420 \, a b c^{7} d^{5} e^{2} - 175 \, b^{4} c^{5} d^{4} e^{3} - 1050 \, a b^{2} c^{6} d^{4} e^{3} + 700 \, a b^{3} c^{5} d^{3} e^{4} + 700 \, a^{2} b c^{6} d^{3} e^{4} - b^{6} c^{3} d^{2} e^{5} + 12 \, a b^{4} c^{4} d^{2} e^{5} - 1098 \, a^{2} b^{2} c^{5} d^{2} e^{5} + 64 \, a^{3} c^{6} d^{2} e^{5} + 6 \, b^{7} c^{2} d e^{6} - 72 \, a b^{5} c^{3} d e^{6} + 288 \, a^{2} b^{3} c^{4} d e^{6} + 316 \, a^{3} b c^{5} d e^{6} - 6 \, a b^{6} c^{2} e^{7} + 67 \, a^{2} b^{4} c^{3} e^{7} - 238 \, a^{3} b^{2} c^{4} e^{7} + 64 \, a^{4} c^{5} e^{7}\right)} x^{4} + {\left(220 \, b^{2} c^{7} d^{7} + 320 \, a c^{8} d^{7} - 770 \, b^{3} c^{6} d^{6} e - 1120 \, a b c^{7} d^{6} e + 924 \, b^{4} c^{5} d^{5} e^{2} + 2268 \, a b^{2} c^{6} d^{5} e^{2} + 1344 \, a^{2} c^{7} d^{5} e^{2} - 385 \, b^{5} c^{4} d^{4} e^{3} - 2870 \, a b^{3} c^{5} d^{4} e^{3} - 3360 \, a^{2} b c^{6} d^{4} e^{3} + 2 \, b^{6} c^{3} d^{3} e^{4} + 1516 \, a b^{4} c^{4} d^{3} e^{4} + 3876 \, a^{2} b^{2} c^{5} d^{3} e^{4} + 2112 \, a^{3} c^{6} d^{3} e^{4} - 9 \, b^{7} c^{2} d^{2} e^{5} + 108 \, a b^{5} c^{3} d^{2} e^{5} - 2742 \, a^{2} b^{3} c^{4} d^{2} e^{5} - 2784 \, a^{3} b c^{5} d^{2} e^{5} + 18 \, b^{8} c d e^{6} - 198 \, a b^{6} c^{2} d e^{6} + 648 \, a^{2} b^{4} c^{3} d e^{6} + 1252 \, a^{3} b^{2} c^{4} d e^{6} + 1088 \, a^{4} c^{5} d e^{6} - 18 \, a b^{7} c e^{7} + 189 \, a^{2} b^{5} c^{2} e^{7} - 578 \, a^{3} b^{3} c^{3} e^{7} - 160 \, a^{4} b c^{4} e^{7}\right)} x^{3} + 3 \, {\left(10 \, b^{3} c^{6} d^{7} + 160 \, a b c^{7} d^{7} - 35 \, b^{4} c^{5} d^{6} e - 560 \, a b^{2} c^{6} d^{6} e + 42 \, b^{5} c^{4} d^{5} e^{2} + 714 \, a b^{3} c^{5} d^{5} e^{2} + 672 \, a^{2} b c^{6} d^{5} e^{2} - 18 \, b^{6} c^{3} d^{4} e^{3} - 379 \, a b^{4} c^{4} d^{4} e^{3} - 1704 \, a^{2} b^{2} c^{5} d^{4} e^{3} + 32 \, a^{3} c^{6} d^{4} e^{3} + 2 \, b^{7} c^{2} d^{3} e^{4} + 46 \, a b^{5} c^{3} d^{3} e^{4} + 1286 \, a^{2} b^{3} c^{4} d^{3} e^{4} + 992 \, a^{3} b c^{5} d^{3} e^{4} - 3 \, b^{8} c d^{2} e^{5} + 33 \, a b^{6} c^{2} d^{2} e^{5} - 213 \, a^{2} b^{4} c^{3} d^{2} e^{5} - 1632 \, a^{3} b^{2} c^{4} d^{2} e^{5} + 192 \, a^{4} c^{5} d^{2} e^{5} + 2 \, b^{9} d e^{6} - 12 \, a b^{7} c d e^{6} - 48 \, a^{2} b^{5} c^{2} d e^{6} + 518 \, a^{3} b^{3} c^{3} d e^{6} + 352 \, a^{4} b c^{4} d e^{6} - 2 \, a b^{8} e^{7} + 13 \, a^{2} b^{6} c e^{7} + 27 \, a^{3} b^{4} c^{2} e^{7} - 328 \, a^{4} b^{2} c^{3} e^{7} + 160 \, a^{5} c^{4} e^{7}\right)} x^{2} - 3 \, {\left(2 \, b^{4} c^{5} d^{7} - 36 \, a b^{2} c^{6} d^{7} - 88 \, a^{2} c^{7} d^{7} - 7 \, b^{5} c^{4} d^{6} e + 126 \, a b^{3} c^{5} d^{6} e + 308 \, a^{2} b c^{6} d^{6} e + 8 \, b^{6} c^{3} d^{5} e^{2} - 138 \, a b^{4} c^{4} d^{5} e^{2} - 540 \, a^{2} b^{2} c^{5} d^{5} e^{2} - 344 \, a^{3} c^{6} d^{5} e^{2} - 2 \, b^{7} c^{2} d^{4} e^{3} + 24 \, a b^{5} c^{3} d^{4} e^{3} + 604 \, a^{2} b^{3} c^{4} d^{4} e^{3} + 828 \, a^{3} b c^{5} d^{4} e^{3} - 2 \, b^{8} c d^{3} e^{4} + 36 \, a b^{6} c^{2} d^{3} e^{4} - 310 \, a^{2} b^{4} c^{3} d^{3} e^{4} - 836 \, a^{3} b^{2} c^{4} d^{3} e^{4} - 488 \, a^{4} c^{5} d^{3} e^{4} + b^{9} d^{2} e^{5} - 6 \, a b^{7} c d^{2} e^{5} - 45 \, a^{2} b^{5} c^{2} d^{2} e^{5} + 602 \, a^{3} b^{3} c^{3} d^{2} e^{5} + 540 \, a^{4} b c^{4} d^{2} e^{5} - 6 \, a b^{8} d e^{6} + 66 \, a^{2} b^{6} c d e^{6} - 202 \, a^{3} b^{4} c^{2} d e^{6} - 156 \, a^{4} b^{2} c^{3} d e^{6} - 232 \, a^{5} c^{4} d e^{6} + 5 \, a^{2} b^{7} e^{7} - 54 \, a^{3} b^{5} c e^{7} + 172 \, a^{4} b^{3} c^{2} e^{7} - 44 \, a^{5} b c^{3} e^{7}\right)} x}{6 \, {\left(c d^{2} - b d e + a e^{2}\right)}^{4} {\left(c x^{2} + b x + a\right)}^{3} {\left(b^{2} - 4 \, a c\right)}^{3}}"," ",0,"-1/2*e^7*log(c*x^2 + b*x + a)/(c^4*d^8 - 4*b*c^3*d^7*e + 6*b^2*c^2*d^6*e^2 + 4*a*c^3*d^6*e^2 - 4*b^3*c*d^5*e^3 - 12*a*b*c^2*d^5*e^3 + b^4*d^4*e^4 + 12*a*b^2*c*d^4*e^4 + 6*a^2*c^2*d^4*e^4 - 4*a*b^3*d^3*e^5 - 12*a^2*b*c*d^3*e^5 + 6*a^2*b^2*d^2*e^6 + 4*a^3*c*d^2*e^6 - 4*a^3*b*d*e^7 + a^4*e^8) + e^8*log(abs(x*e + d))/(c^4*d^8*e - 4*b*c^3*d^7*e^2 + 6*b^2*c^2*d^6*e^3 + 4*a*c^3*d^6*e^3 - 4*b^3*c*d^5*e^4 - 12*a*b*c^2*d^5*e^4 + b^4*d^4*e^5 + 12*a*b^2*c*d^4*e^5 + 6*a^2*c^2*d^4*e^5 - 4*a*b^3*d^3*e^6 - 12*a^2*b*c*d^3*e^6 + 6*a^2*b^2*d^2*e^7 + 4*a^3*c*d^2*e^7 - 4*a^3*b*d*e^8 + a^4*e^9) - (40*c^7*d^7 - 140*b*c^6*d^6*e + 168*b^2*c^5*d^5*e^2 + 168*a*c^6*d^5*e^2 - 70*b^3*c^4*d^4*e^3 - 420*a*b*c^5*d^4*e^3 + 280*a*b^2*c^4*d^3*e^4 + 280*a^2*c^5*d^3*e^4 - 420*a^2*b*c^4*d^2*e^5 + 280*a^3*c^4*d*e^6 + b^7*e^7 - 14*a*b^5*c*e^7 + 70*a^2*b^3*c^2*e^7 - 140*a^3*b*c^3*e^7)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^6*c^4*d^8 - 12*a*b^4*c^5*d^8 + 48*a^2*b^2*c^6*d^8 - 64*a^3*c^7*d^8 - 4*b^7*c^3*d^7*e + 48*a*b^5*c^4*d^7*e - 192*a^2*b^3*c^5*d^7*e + 256*a^3*b*c^6*d^7*e + 6*b^8*c^2*d^6*e^2 - 68*a*b^6*c^3*d^6*e^2 + 240*a^2*b^4*c^4*d^6*e^2 - 192*a^3*b^2*c^5*d^6*e^2 - 256*a^4*c^6*d^6*e^2 - 4*b^9*c*d^5*e^3 + 36*a*b^7*c^2*d^5*e^3 - 48*a^2*b^5*c^3*d^5*e^3 - 320*a^3*b^3*c^4*d^5*e^3 + 768*a^4*b*c^5*d^5*e^3 + b^10*d^4*e^4 - 90*a^2*b^6*c^2*d^4*e^4 + 440*a^3*b^4*c^3*d^4*e^4 - 480*a^4*b^2*c^4*d^4*e^4 - 384*a^5*c^5*d^4*e^4 - 4*a*b^9*d^3*e^5 + 36*a^2*b^7*c*d^3*e^5 - 48*a^3*b^5*c^2*d^3*e^5 - 320*a^4*b^3*c^3*d^3*e^5 + 768*a^5*b*c^4*d^3*e^5 + 6*a^2*b^8*d^2*e^6 - 68*a^3*b^6*c*d^2*e^6 + 240*a^4*b^4*c^2*d^2*e^6 - 192*a^5*b^2*c^3*d^2*e^6 - 256*a^6*c^4*d^2*e^6 - 4*a^3*b^7*d*e^7 + 48*a^4*b^5*c*d*e^7 - 192*a^5*b^3*c^2*d*e^7 + 256*a^6*b*c^3*d*e^7 + a^4*b^6*e^8 - 12*a^5*b^4*c*e^8 + 48*a^6*b^2*c^2*e^8 - 64*a^7*c^3*e^8)*sqrt(-b^2 + 4*a*c)) - 1/6*(2*b^5*c^4*d^7 - 26*a*b^3*c^5*d^7 + 132*a^2*b*c^6*d^7 - 8*b^6*c^3*d^6*e + 103*a*b^4*c^4*d^6*e - 510*a^2*b^2*c^5*d^6*e + 64*a^3*c^6*d^6*e + 12*b^7*c^2*d^5*e^2 - 144*a*b^5*c^3*d^5*e^2 + 618*a^2*b^3*c^4*d^5*e^2 + 324*a^3*b*c^5*d^5*e^2 - 8*b^8*c*d^4*e^3 + 74*a*b^6*c^2*d^4*e^3 - 120*a^2*b^4*c^3*d^4*e^3 - 1314*a^3*b^2*c^4*d^4*e^3 + 288*a^4*c^5*d^4*e^3 + 2*b^9*d^3*e^4 + 2*a*b^7*c*d^3*e^4 - 216*a^2*b^5*c^2*d^3*e^4 + 1190*a^3*b^3*c^3*d^3*e^4 + 156*a^4*b*c^4*d^3*e^4 - 9*a*b^8*d^2*e^5 + 78*a^2*b^6*c*d^2*e^5 - 51*a^3*b^4*c^2*d^2*e^5 - 1242*a^4*b^2*c^3*d^2*e^5 + 576*a^5*c^4*d^2*e^5 + 18*a^2*b^7*d*e^6 - 202*a^3*b^5*c*d*e^6 + 682*a^4*b^3*c^2*d*e^6 - 228*a^5*b*c^3*d*e^6 - 11*a^3*b^6*e^7 + 124*a^4*b^4*c*e^7 - 438*a^5*b^2*c^2*e^7 + 352*a^6*c^3*e^7 + 6*(20*c^9*d^7 - 70*b*c^8*d^6*e + 84*b^2*c^7*d^5*e^2 + 84*a*c^8*d^5*e^2 - 35*b^3*c^6*d^4*e^3 - 210*a*b*c^7*d^4*e^3 + 140*a*b^2*c^6*d^3*e^4 + 140*a^2*c^7*d^3*e^4 - 210*a^2*b*c^6*d^2*e^5 + b^6*c^3*d*e^6 - 12*a*b^4*c^4*d*e^6 + 48*a^2*b^2*c^5*d*e^6 + 76*a^3*c^6*d*e^6 - a*b^5*c^3*e^7 + 11*a^2*b^3*c^4*e^7 - 38*a^3*b*c^5*e^7)*x^5 + 3*(100*b*c^8*d^7 - 350*b^2*c^7*d^6*e + 420*b^3*c^6*d^5*e^2 + 420*a*b*c^7*d^5*e^2 - 175*b^4*c^5*d^4*e^3 - 1050*a*b^2*c^6*d^4*e^3 + 700*a*b^3*c^5*d^3*e^4 + 700*a^2*b*c^6*d^3*e^4 - b^6*c^3*d^2*e^5 + 12*a*b^4*c^4*d^2*e^5 - 1098*a^2*b^2*c^5*d^2*e^5 + 64*a^3*c^6*d^2*e^5 + 6*b^7*c^2*d*e^6 - 72*a*b^5*c^3*d*e^6 + 288*a^2*b^3*c^4*d*e^6 + 316*a^3*b*c^5*d*e^6 - 6*a*b^6*c^2*e^7 + 67*a^2*b^4*c^3*e^7 - 238*a^3*b^2*c^4*e^7 + 64*a^4*c^5*e^7)*x^4 + (220*b^2*c^7*d^7 + 320*a*c^8*d^7 - 770*b^3*c^6*d^6*e - 1120*a*b*c^7*d^6*e + 924*b^4*c^5*d^5*e^2 + 2268*a*b^2*c^6*d^5*e^2 + 1344*a^2*c^7*d^5*e^2 - 385*b^5*c^4*d^4*e^3 - 2870*a*b^3*c^5*d^4*e^3 - 3360*a^2*b*c^6*d^4*e^3 + 2*b^6*c^3*d^3*e^4 + 1516*a*b^4*c^4*d^3*e^4 + 3876*a^2*b^2*c^5*d^3*e^4 + 2112*a^3*c^6*d^3*e^4 - 9*b^7*c^2*d^2*e^5 + 108*a*b^5*c^3*d^2*e^5 - 2742*a^2*b^3*c^4*d^2*e^5 - 2784*a^3*b*c^5*d^2*e^5 + 18*b^8*c*d*e^6 - 198*a*b^6*c^2*d*e^6 + 648*a^2*b^4*c^3*d*e^6 + 1252*a^3*b^2*c^4*d*e^6 + 1088*a^4*c^5*d*e^6 - 18*a*b^7*c*e^7 + 189*a^2*b^5*c^2*e^7 - 578*a^3*b^3*c^3*e^7 - 160*a^4*b*c^4*e^7)*x^3 + 3*(10*b^3*c^6*d^7 + 160*a*b*c^7*d^7 - 35*b^4*c^5*d^6*e - 560*a*b^2*c^6*d^6*e + 42*b^5*c^4*d^5*e^2 + 714*a*b^3*c^5*d^5*e^2 + 672*a^2*b*c^6*d^5*e^2 - 18*b^6*c^3*d^4*e^3 - 379*a*b^4*c^4*d^4*e^3 - 1704*a^2*b^2*c^5*d^4*e^3 + 32*a^3*c^6*d^4*e^3 + 2*b^7*c^2*d^3*e^4 + 46*a*b^5*c^3*d^3*e^4 + 1286*a^2*b^3*c^4*d^3*e^4 + 992*a^3*b*c^5*d^3*e^4 - 3*b^8*c*d^2*e^5 + 33*a*b^6*c^2*d^2*e^5 - 213*a^2*b^4*c^3*d^2*e^5 - 1632*a^3*b^2*c^4*d^2*e^5 + 192*a^4*c^5*d^2*e^5 + 2*b^9*d*e^6 - 12*a*b^7*c*d*e^6 - 48*a^2*b^5*c^2*d*e^6 + 518*a^3*b^3*c^3*d*e^6 + 352*a^4*b*c^4*d*e^6 - 2*a*b^8*e^7 + 13*a^2*b^6*c*e^7 + 27*a^3*b^4*c^2*e^7 - 328*a^4*b^2*c^3*e^7 + 160*a^5*c^4*e^7)*x^2 - 3*(2*b^4*c^5*d^7 - 36*a*b^2*c^6*d^7 - 88*a^2*c^7*d^7 - 7*b^5*c^4*d^6*e + 126*a*b^3*c^5*d^6*e + 308*a^2*b*c^6*d^6*e + 8*b^6*c^3*d^5*e^2 - 138*a*b^4*c^4*d^5*e^2 - 540*a^2*b^2*c^5*d^5*e^2 - 344*a^3*c^6*d^5*e^2 - 2*b^7*c^2*d^4*e^3 + 24*a*b^5*c^3*d^4*e^3 + 604*a^2*b^3*c^4*d^4*e^3 + 828*a^3*b*c^5*d^4*e^3 - 2*b^8*c*d^3*e^4 + 36*a*b^6*c^2*d^3*e^4 - 310*a^2*b^4*c^3*d^3*e^4 - 836*a^3*b^2*c^4*d^3*e^4 - 488*a^4*c^5*d^3*e^4 + b^9*d^2*e^5 - 6*a*b^7*c*d^2*e^5 - 45*a^2*b^5*c^2*d^2*e^5 + 602*a^3*b^3*c^3*d^2*e^5 + 540*a^4*b*c^4*d^2*e^5 - 6*a*b^8*d*e^6 + 66*a^2*b^6*c*d*e^6 - 202*a^3*b^4*c^2*d*e^6 - 156*a^4*b^2*c^3*d*e^6 - 232*a^5*c^4*d*e^6 + 5*a^2*b^7*e^7 - 54*a^3*b^5*c*e^7 + 172*a^4*b^3*c^2*e^7 - 44*a^5*b*c^3*e^7)*x)/((c*d^2 - b*d*e + a*e^2)^4*(c*x^2 + b*x + a)^3*(b^2 - 4*a*c)^3)","B",0
2220,1,496,0,0.229648," ","integrate(1/x^2/(c*x^2+b*x+a)^4,x, algorithm=""giac"")","\frac{4 \, {\left(b^{8} - 14 \, a b^{6} c + 70 \, a^{2} b^{4} c^{2} - 140 \, a^{3} b^{2} c^{3} + 70 \, a^{4} c^{4}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(a^{5} b^{6} - 12 \, a^{6} b^{4} c + 48 \, a^{7} b^{2} c^{2} - 64 \, a^{8} c^{3}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{2 \, b \log\left(c x^{2} + b x + a\right)}{a^{5}} - \frac{4 \, b \log\left({\left| x \right|}\right)}{a^{5}} - \frac{3 \, a^{4} b^{6} - 36 \, a^{5} b^{4} c + 144 \, a^{6} b^{2} c^{2} - 192 \, a^{7} c^{3} + 12 \, {\left(a b^{6} c^{3} - 11 \, a^{2} b^{4} c^{4} + 38 \, a^{3} b^{2} c^{5} - 35 \, a^{4} c^{6}\right)} x^{6} + 6 \, {\left(6 \, a b^{7} c^{2} - 67 \, a^{2} b^{5} c^{3} + 238 \, a^{3} b^{3} c^{4} - 239 \, a^{4} b c^{5}\right)} x^{5} + 2 \, {\left(18 \, a b^{8} c - 189 \, a^{2} b^{6} c^{2} + 578 \, a^{3} b^{4} c^{3} - 225 \, a^{4} b^{2} c^{4} - 560 \, a^{5} c^{5}\right)} x^{4} + 3 \, {\left(4 \, a b^{9} - 26 \, a^{2} b^{7} c - 54 \, a^{3} b^{5} c^{2} + 621 \, a^{4} b^{3} c^{3} - 880 \, a^{5} b c^{4}\right)} x^{3} + 3 \, {\left(10 \, a^{2} b^{8} - 108 \, a^{3} b^{6} c + 351 \, a^{4} b^{4} c^{2} - 214 \, a^{5} b^{2} c^{3} - 308 \, a^{6} c^{4}\right)} x^{2} + {\left(22 \, a^{3} b^{7} - 255 \, a^{4} b^{5} c + 967 \, a^{5} b^{3} c^{2} - 1166 \, a^{6} b c^{3}\right)} x}{3 \, {\left(c x^{2} + b x + a\right)}^{3} {\left(b^{2} - 4 \, a c\right)}^{3} a^{5} x}"," ",0,"4*(b^8 - 14*a*b^6*c + 70*a^2*b^4*c^2 - 140*a^3*b^2*c^3 + 70*a^4*c^4)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((a^5*b^6 - 12*a^6*b^4*c + 48*a^7*b^2*c^2 - 64*a^8*c^3)*sqrt(-b^2 + 4*a*c)) + 2*b*log(c*x^2 + b*x + a)/a^5 - 4*b*log(abs(x))/a^5 - 1/3*(3*a^4*b^6 - 36*a^5*b^4*c + 144*a^6*b^2*c^2 - 192*a^7*c^3 + 12*(a*b^6*c^3 - 11*a^2*b^4*c^4 + 38*a^3*b^2*c^5 - 35*a^4*c^6)*x^6 + 6*(6*a*b^7*c^2 - 67*a^2*b^5*c^3 + 238*a^3*b^3*c^4 - 239*a^4*b*c^5)*x^5 + 2*(18*a*b^8*c - 189*a^2*b^6*c^2 + 578*a^3*b^4*c^3 - 225*a^4*b^2*c^4 - 560*a^5*c^5)*x^4 + 3*(4*a*b^9 - 26*a^2*b^7*c - 54*a^3*b^5*c^2 + 621*a^4*b^3*c^3 - 880*a^5*b*c^4)*x^3 + 3*(10*a^2*b^8 - 108*a^3*b^6*c + 351*a^4*b^4*c^2 - 214*a^5*b^2*c^3 - 308*a^6*c^4)*x^2 + (22*a^3*b^7 - 255*a^4*b^5*c + 967*a^5*b^3*c^2 - 1166*a^6*b*c^3)*x)/((c*x^2 + b*x + a)^3*(b^2 - 4*a*c)^3*a^5*x)","A",0
2221,1,2342,0,0.257181," ","integrate((e*x+d)^5/(c*x^2+b*x+a)^5,x, algorithm=""giac"")","\frac{10 \, {\left(14 \, c^{4} d^{5} - 35 \, b c^{3} d^{4} e + 30 \, b^{2} c^{2} d^{3} e^{2} + 20 \, a c^{3} d^{3} e^{2} - 10 \, b^{3} c d^{2} e^{3} - 30 \, a b c^{2} d^{2} e^{3} + b^{4} d e^{4} + 12 \, a b^{2} c d e^{4} + 6 \, a^{2} c^{2} d e^{4} - a b^{3} e^{5} - 3 \, a^{2} b c e^{5}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{8} - 16 \, a b^{6} c + 96 \, a^{2} b^{4} c^{2} - 256 \, a^{3} b^{2} c^{3} + 256 \, a^{4} c^{4}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{840 \, c^{8} d^{5} x^{7} - 2100 \, b c^{7} d^{4} x^{7} e + 2940 \, b c^{7} d^{5} x^{6} + 1800 \, b^{2} c^{6} d^{3} x^{7} e^{2} + 1200 \, a c^{7} d^{3} x^{7} e^{2} - 7350 \, b^{2} c^{6} d^{4} x^{6} e + 3640 \, b^{2} c^{6} d^{5} x^{5} + 3080 \, a c^{7} d^{5} x^{5} - 600 \, b^{3} c^{5} d^{2} x^{7} e^{3} - 1800 \, a b c^{6} d^{2} x^{7} e^{3} + 6300 \, b^{3} c^{5} d^{3} x^{6} e^{2} + 4200 \, a b c^{6} d^{3} x^{6} e^{2} - 9100 \, b^{3} c^{5} d^{4} x^{5} e - 7700 \, a b c^{6} d^{4} x^{5} e + 1750 \, b^{3} c^{5} d^{5} x^{4} + 7700 \, a b c^{6} d^{5} x^{4} + 60 \, b^{4} c^{4} d x^{7} e^{4} + 720 \, a b^{2} c^{5} d x^{7} e^{4} + 360 \, a^{2} c^{6} d x^{7} e^{4} - 2100 \, b^{4} c^{4} d^{2} x^{6} e^{3} - 6300 \, a b^{2} c^{5} d^{2} x^{6} e^{3} + 7800 \, b^{4} c^{4} d^{3} x^{5} e^{2} + 11800 \, a b^{2} c^{5} d^{3} x^{5} e^{2} + 4400 \, a^{2} c^{6} d^{3} x^{5} e^{2} - 4375 \, b^{4} c^{4} d^{4} x^{4} e - 19250 \, a b^{2} c^{5} d^{4} x^{4} e + 168 \, b^{4} c^{4} d^{5} x^{3} + 5656 \, a b^{2} c^{5} d^{5} x^{3} + 4088 \, a^{2} c^{6} d^{5} x^{3} - 60 \, a b^{3} c^{4} x^{7} e^{5} - 180 \, a^{2} b c^{5} x^{7} e^{5} + 210 \, b^{5} c^{3} d x^{6} e^{4} + 2520 \, a b^{3} c^{4} d x^{6} e^{4} + 1260 \, a^{2} b c^{5} d x^{6} e^{4} - 2600 \, b^{5} c^{3} d^{2} x^{5} e^{3} - 10000 \, a b^{3} c^{4} d^{2} x^{5} e^{3} - 6600 \, a^{2} b c^{5} d^{2} x^{5} e^{3} + 3750 \, b^{5} c^{3} d^{3} x^{4} e^{2} + 19000 \, a b^{3} c^{4} d^{3} x^{4} e^{2} + 11000 \, a^{2} b c^{5} d^{3} x^{4} e^{2} - 420 \, b^{5} c^{3} d^{4} x^{3} e - 14140 \, a b^{3} c^{4} d^{4} x^{3} e - 10220 \, a^{2} b c^{5} d^{4} x^{3} e - 28 \, b^{5} c^{3} d^{5} x^{2} + 784 \, a b^{3} c^{4} d^{5} x^{2} + 6132 \, a^{2} b c^{5} d^{5} x^{2} - 210 \, a b^{4} c^{3} x^{6} e^{5} - 630 \, a^{2} b^{2} c^{4} x^{6} e^{5} + 260 \, b^{6} c^{2} d x^{5} e^{4} + 3340 \, a b^{4} c^{3} d x^{5} e^{4} + 4200 \, a^{2} b^{2} c^{4} d x^{5} e^{4} + 1320 \, a^{3} c^{5} d x^{5} e^{4} - 1250 \, b^{6} c^{2} d^{2} x^{4} e^{3} - 9250 \, a b^{4} c^{3} d^{2} x^{4} e^{3} - 16500 \, a^{2} b^{2} c^{4} d^{2} x^{4} e^{3} + 360 \, b^{6} c^{2} d^{3} x^{3} e^{2} + 12360 \, a b^{4} c^{3} d^{3} x^{3} e^{2} + 16840 \, a^{2} b^{2} c^{4} d^{3} x^{3} e^{2} + 5840 \, a^{3} c^{5} d^{3} x^{3} e^{2} + 70 \, b^{6} c^{2} d^{4} x^{2} e - 1960 \, a b^{4} c^{3} d^{4} x^{2} e - 15330 \, a^{2} b^{2} c^{4} d^{4} x^{2} e + 8 \, b^{6} c^{2} d^{5} x - 152 \, a b^{4} c^{3} d^{5} x + 1392 \, a^{2} b^{2} c^{4} d^{5} x + 2232 \, a^{3} c^{5} d^{5} x - 260 \, a b^{5} c^{2} x^{5} e^{5} - 1000 \, a^{2} b^{3} c^{3} x^{5} e^{5} - 660 \, a^{3} b c^{4} x^{5} e^{5} + 125 \, b^{7} c d x^{4} e^{4} + 2050 \, a b^{5} c^{2} d x^{4} e^{4} + 7350 \, a^{2} b^{3} c^{3} d x^{4} e^{4} + 3300 \, a^{3} b c^{4} d x^{4} e^{4} - 120 \, b^{7} c d^{2} x^{3} e^{3} - 4400 \, a b^{5} c^{2} d^{2} x^{3} e^{3} - 15040 \, a^{2} b^{3} c^{3} d^{2} x^{3} e^{3} - 8760 \, a^{3} b c^{4} d^{2} x^{3} e^{3} - 60 \, b^{7} c d^{3} x^{2} e^{2} + 1640 \, a b^{5} c^{2} d^{3} x^{2} e^{2} + 14260 \, a^{2} b^{3} c^{3} d^{3} x^{2} e^{2} + 8760 \, a^{3} b c^{4} d^{3} x^{2} e^{2} - 20 \, b^{7} c d^{4} x e + 380 \, a b^{5} c^{2} d^{4} x e - 3480 \, a^{2} b^{3} c^{3} d^{4} x e - 5580 \, a^{3} b c^{4} d^{4} x e - 3 \, b^{7} c d^{5} + 50 \, a b^{5} c^{2} d^{5} - 326 \, a^{2} b^{3} c^{3} d^{5} + 1116 \, a^{3} b c^{4} d^{5} - 3 \, b^{8} x^{4} e^{5} - 77 \, a b^{6} c x^{4} e^{5} - 1213 \, a^{2} b^{4} c^{2} x^{4} e^{5} - 882 \, a^{3} b^{2} c^{3} x^{4} e^{5} - 768 \, a^{4} c^{4} x^{4} e^{5} + 740 \, a b^{6} c d x^{3} e^{4} + 4060 \, a^{2} b^{4} c^{2} d x^{3} e^{4} + 9000 \, a^{3} b^{2} c^{3} d x^{3} e^{4} - 1320 \, a^{4} c^{4} d x^{3} e^{4} - 180 \, a b^{6} c d^{2} x^{2} e^{3} - 7980 \, a^{2} b^{4} c^{2} d^{2} x^{2} e^{3} - 8020 \, a^{3} b^{2} c^{3} d^{2} x^{2} e^{3} - 5120 \, a^{4} c^{4} d^{2} x^{2} e^{3} - 40 \, a b^{6} c d^{3} x e^{2} + 1120 \, a^{2} b^{4} c^{2} d^{3} x e^{2} + 11160 \, a^{3} b^{2} c^{3} d^{3} x e^{2} - 1200 \, a^{4} c^{4} d^{3} x e^{2} - 5 \, a b^{6} c d^{4} e + 95 \, a^{2} b^{4} c^{2} d^{4} e - 870 \, a^{3} b^{2} c^{3} d^{4} e - 1920 \, a^{4} c^{4} d^{4} e - 12 \, a b^{7} x^{3} e^{5} - 440 \, a^{2} b^{5} c x^{3} e^{5} - 1504 \, a^{3} b^{3} c^{2} x^{3} e^{5} - 876 \, a^{4} b c^{3} x^{3} e^{5} + 1290 \, a^{2} b^{5} c d x^{2} e^{4} + 5080 \, a^{3} b^{3} c^{2} d x^{2} e^{4} + 3140 \, a^{4} b c^{3} d x^{2} e^{4} - 120 \, a^{2} b^{5} c d^{2} x e^{3} - 6040 \, a^{3} b^{3} c^{2} d^{2} x e^{3} - 3320 \, a^{4} b c^{3} d^{2} x e^{3} - 10 \, a^{2} b^{5} c d^{3} e^{2} + 280 \, a^{3} b^{3} c^{2} d^{3} e^{2} + 3240 \, a^{4} b c^{3} d^{3} e^{2} - 18 \, a^{2} b^{6} x^{2} e^{5} - 798 \, a^{3} b^{4} c x^{2} e^{5} - 802 \, a^{4} b^{2} c^{2} x^{2} e^{5} - 512 \, a^{5} c^{3} x^{2} e^{5} + 940 \, a^{3} b^{4} c d x e^{4} + 3680 \, a^{4} b^{2} c^{2} d x e^{4} - 360 \, a^{5} c^{3} d x e^{4} - 30 \, a^{3} b^{4} c d^{2} e^{3} - 1660 \, a^{4} b^{2} c^{2} d^{2} e^{3} - 1280 \, a^{5} c^{3} d^{2} e^{3} - 12 \, a^{3} b^{5} x e^{5} - 604 \, a^{4} b^{3} c x e^{5} - 332 \, a^{5} b c^{2} x e^{5} + 250 \, a^{4} b^{3} c d e^{4} + 1100 \, a^{5} b c^{2} d e^{4} - 3 \, a^{4} b^{4} e^{5} - 166 \, a^{5} b^{2} c e^{5} - 128 \, a^{6} c^{2} e^{5}}{12 \, {\left(b^{8} c - 16 \, a b^{6} c^{2} + 96 \, a^{2} b^{4} c^{3} - 256 \, a^{3} b^{2} c^{4} + 256 \, a^{4} c^{5}\right)} {\left(c x^{2} + b x + a\right)}^{4}}"," ",0,"10*(14*c^4*d^5 - 35*b*c^3*d^4*e + 30*b^2*c^2*d^3*e^2 + 20*a*c^3*d^3*e^2 - 10*b^3*c*d^2*e^3 - 30*a*b*c^2*d^2*e^3 + b^4*d*e^4 + 12*a*b^2*c*d*e^4 + 6*a^2*c^2*d*e^4 - a*b^3*e^5 - 3*a^2*b*c*e^5)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^8 - 16*a*b^6*c + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 + 256*a^4*c^4)*sqrt(-b^2 + 4*a*c)) + 1/12*(840*c^8*d^5*x^7 - 2100*b*c^7*d^4*x^7*e + 2940*b*c^7*d^5*x^6 + 1800*b^2*c^6*d^3*x^7*e^2 + 1200*a*c^7*d^3*x^7*e^2 - 7350*b^2*c^6*d^4*x^6*e + 3640*b^2*c^6*d^5*x^5 + 3080*a*c^7*d^5*x^5 - 600*b^3*c^5*d^2*x^7*e^3 - 1800*a*b*c^6*d^2*x^7*e^3 + 6300*b^3*c^5*d^3*x^6*e^2 + 4200*a*b*c^6*d^3*x^6*e^2 - 9100*b^3*c^5*d^4*x^5*e - 7700*a*b*c^6*d^4*x^5*e + 1750*b^3*c^5*d^5*x^4 + 7700*a*b*c^6*d^5*x^4 + 60*b^4*c^4*d*x^7*e^4 + 720*a*b^2*c^5*d*x^7*e^4 + 360*a^2*c^6*d*x^7*e^4 - 2100*b^4*c^4*d^2*x^6*e^3 - 6300*a*b^2*c^5*d^2*x^6*e^3 + 7800*b^4*c^4*d^3*x^5*e^2 + 11800*a*b^2*c^5*d^3*x^5*e^2 + 4400*a^2*c^6*d^3*x^5*e^2 - 4375*b^4*c^4*d^4*x^4*e - 19250*a*b^2*c^5*d^4*x^4*e + 168*b^4*c^4*d^5*x^3 + 5656*a*b^2*c^5*d^5*x^3 + 4088*a^2*c^6*d^5*x^3 - 60*a*b^3*c^4*x^7*e^5 - 180*a^2*b*c^5*x^7*e^5 + 210*b^5*c^3*d*x^6*e^4 + 2520*a*b^3*c^4*d*x^6*e^4 + 1260*a^2*b*c^5*d*x^6*e^4 - 2600*b^5*c^3*d^2*x^5*e^3 - 10000*a*b^3*c^4*d^2*x^5*e^3 - 6600*a^2*b*c^5*d^2*x^5*e^3 + 3750*b^5*c^3*d^3*x^4*e^2 + 19000*a*b^3*c^4*d^3*x^4*e^2 + 11000*a^2*b*c^5*d^3*x^4*e^2 - 420*b^5*c^3*d^4*x^3*e - 14140*a*b^3*c^4*d^4*x^3*e - 10220*a^2*b*c^5*d^4*x^3*e - 28*b^5*c^3*d^5*x^2 + 784*a*b^3*c^4*d^5*x^2 + 6132*a^2*b*c^5*d^5*x^2 - 210*a*b^4*c^3*x^6*e^5 - 630*a^2*b^2*c^4*x^6*e^5 + 260*b^6*c^2*d*x^5*e^4 + 3340*a*b^4*c^3*d*x^5*e^4 + 4200*a^2*b^2*c^4*d*x^5*e^4 + 1320*a^3*c^5*d*x^5*e^4 - 1250*b^6*c^2*d^2*x^4*e^3 - 9250*a*b^4*c^3*d^2*x^4*e^3 - 16500*a^2*b^2*c^4*d^2*x^4*e^3 + 360*b^6*c^2*d^3*x^3*e^2 + 12360*a*b^4*c^3*d^3*x^3*e^2 + 16840*a^2*b^2*c^4*d^3*x^3*e^2 + 5840*a^3*c^5*d^3*x^3*e^2 + 70*b^6*c^2*d^4*x^2*e - 1960*a*b^4*c^3*d^4*x^2*e - 15330*a^2*b^2*c^4*d^4*x^2*e + 8*b^6*c^2*d^5*x - 152*a*b^4*c^3*d^5*x + 1392*a^2*b^2*c^4*d^5*x + 2232*a^3*c^5*d^5*x - 260*a*b^5*c^2*x^5*e^5 - 1000*a^2*b^3*c^3*x^5*e^5 - 660*a^3*b*c^4*x^5*e^5 + 125*b^7*c*d*x^4*e^4 + 2050*a*b^5*c^2*d*x^4*e^4 + 7350*a^2*b^3*c^3*d*x^4*e^4 + 3300*a^3*b*c^4*d*x^4*e^4 - 120*b^7*c*d^2*x^3*e^3 - 4400*a*b^5*c^2*d^2*x^3*e^3 - 15040*a^2*b^3*c^3*d^2*x^3*e^3 - 8760*a^3*b*c^4*d^2*x^3*e^3 - 60*b^7*c*d^3*x^2*e^2 + 1640*a*b^5*c^2*d^3*x^2*e^2 + 14260*a^2*b^3*c^3*d^3*x^2*e^2 + 8760*a^3*b*c^4*d^3*x^2*e^2 - 20*b^7*c*d^4*x*e + 380*a*b^5*c^2*d^4*x*e - 3480*a^2*b^3*c^3*d^4*x*e - 5580*a^3*b*c^4*d^4*x*e - 3*b^7*c*d^5 + 50*a*b^5*c^2*d^5 - 326*a^2*b^3*c^3*d^5 + 1116*a^3*b*c^4*d^5 - 3*b^8*x^4*e^5 - 77*a*b^6*c*x^4*e^5 - 1213*a^2*b^4*c^2*x^4*e^5 - 882*a^3*b^2*c^3*x^4*e^5 - 768*a^4*c^4*x^4*e^5 + 740*a*b^6*c*d*x^3*e^4 + 4060*a^2*b^4*c^2*d*x^3*e^4 + 9000*a^3*b^2*c^3*d*x^3*e^4 - 1320*a^4*c^4*d*x^3*e^4 - 180*a*b^6*c*d^2*x^2*e^3 - 7980*a^2*b^4*c^2*d^2*x^2*e^3 - 8020*a^3*b^2*c^3*d^2*x^2*e^3 - 5120*a^4*c^4*d^2*x^2*e^3 - 40*a*b^6*c*d^3*x*e^2 + 1120*a^2*b^4*c^2*d^3*x*e^2 + 11160*a^3*b^2*c^3*d^3*x*e^2 - 1200*a^4*c^4*d^3*x*e^2 - 5*a*b^6*c*d^4*e + 95*a^2*b^4*c^2*d^4*e - 870*a^3*b^2*c^3*d^4*e - 1920*a^4*c^4*d^4*e - 12*a*b^7*x^3*e^5 - 440*a^2*b^5*c*x^3*e^5 - 1504*a^3*b^3*c^2*x^3*e^5 - 876*a^4*b*c^3*x^3*e^5 + 1290*a^2*b^5*c*d*x^2*e^4 + 5080*a^3*b^3*c^2*d*x^2*e^4 + 3140*a^4*b*c^3*d*x^2*e^4 - 120*a^2*b^5*c*d^2*x*e^3 - 6040*a^3*b^3*c^2*d^2*x*e^3 - 3320*a^4*b*c^3*d^2*x*e^3 - 10*a^2*b^5*c*d^3*e^2 + 280*a^3*b^3*c^2*d^3*e^2 + 3240*a^4*b*c^3*d^3*e^2 - 18*a^2*b^6*x^2*e^5 - 798*a^3*b^4*c*x^2*e^5 - 802*a^4*b^2*c^2*x^2*e^5 - 512*a^5*c^3*x^2*e^5 + 940*a^3*b^4*c*d*x*e^4 + 3680*a^4*b^2*c^2*d*x*e^4 - 360*a^5*c^3*d*x*e^4 - 30*a^3*b^4*c*d^2*e^3 - 1660*a^4*b^2*c^2*d^2*e^3 - 1280*a^5*c^3*d^2*e^3 - 12*a^3*b^5*x*e^5 - 604*a^4*b^3*c*x*e^5 - 332*a^5*b*c^2*x*e^5 + 250*a^4*b^3*c*d*e^4 + 1100*a^5*b*c^2*d*e^4 - 3*a^4*b^4*e^5 - 166*a^5*b^2*c*e^5 - 128*a^6*c^2*e^5)/((b^8*c - 16*a*b^6*c^2 + 96*a^2*b^4*c^3 - 256*a^3*b^2*c^4 + 256*a^4*c^5)*(c*x^2 + b*x + a)^4)","B",0
2222,1,1839,0,0.239115," ","integrate((e*x+d)^4/(c*x^2+b*x+a)^5,x, algorithm=""giac"")","\frac{2 \, {\left(70 \, c^{4} d^{4} - 140 \, b c^{3} d^{3} e + 90 \, b^{2} c^{2} d^{2} e^{2} + 60 \, a c^{3} d^{2} e^{2} - 20 \, b^{3} c d e^{3} - 60 \, a b c^{2} d e^{3} + b^{4} e^{4} + 12 \, a b^{2} c e^{4} + 6 \, a^{2} c^{2} e^{4}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{8} - 16 \, a b^{6} c + 96 \, a^{2} b^{4} c^{2} - 256 \, a^{3} b^{2} c^{3} + 256 \, a^{4} c^{4}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{840 \, c^{7} d^{4} x^{7} - 1680 \, b c^{6} d^{3} x^{7} e + 2940 \, b c^{6} d^{4} x^{6} + 1080 \, b^{2} c^{5} d^{2} x^{7} e^{2} + 720 \, a c^{6} d^{2} x^{7} e^{2} - 5880 \, b^{2} c^{5} d^{3} x^{6} e + 3640 \, b^{2} c^{5} d^{4} x^{5} + 3080 \, a c^{6} d^{4} x^{5} - 240 \, b^{3} c^{4} d x^{7} e^{3} - 720 \, a b c^{5} d x^{7} e^{3} + 3780 \, b^{3} c^{4} d^{2} x^{6} e^{2} + 2520 \, a b c^{5} d^{2} x^{6} e^{2} - 7280 \, b^{3} c^{4} d^{3} x^{5} e - 6160 \, a b c^{5} d^{3} x^{5} e + 1750 \, b^{3} c^{4} d^{4} x^{4} + 7700 \, a b c^{5} d^{4} x^{4} + 12 \, b^{4} c^{3} x^{7} e^{4} + 144 \, a b^{2} c^{4} x^{7} e^{4} + 72 \, a^{2} c^{5} x^{7} e^{4} - 840 \, b^{4} c^{3} d x^{6} e^{3} - 2520 \, a b^{2} c^{4} d x^{6} e^{3} + 4680 \, b^{4} c^{3} d^{2} x^{5} e^{2} + 7080 \, a b^{2} c^{4} d^{2} x^{5} e^{2} + 2640 \, a^{2} c^{5} d^{2} x^{5} e^{2} - 3500 \, b^{4} c^{3} d^{3} x^{4} e - 15400 \, a b^{2} c^{4} d^{3} x^{4} e + 168 \, b^{4} c^{3} d^{4} x^{3} + 5656 \, a b^{2} c^{4} d^{4} x^{3} + 4088 \, a^{2} c^{5} d^{4} x^{3} + 42 \, b^{5} c^{2} x^{6} e^{4} + 504 \, a b^{3} c^{3} x^{6} e^{4} + 252 \, a^{2} b c^{4} x^{6} e^{4} - 1040 \, b^{5} c^{2} d x^{5} e^{3} - 4000 \, a b^{3} c^{3} d x^{5} e^{3} - 2640 \, a^{2} b c^{4} d x^{5} e^{3} + 2250 \, b^{5} c^{2} d^{2} x^{4} e^{2} + 11400 \, a b^{3} c^{3} d^{2} x^{4} e^{2} + 6600 \, a^{2} b c^{4} d^{2} x^{4} e^{2} - 336 \, b^{5} c^{2} d^{3} x^{3} e - 11312 \, a b^{3} c^{3} d^{3} x^{3} e - 8176 \, a^{2} b c^{4} d^{3} x^{3} e - 28 \, b^{5} c^{2} d^{4} x^{2} + 784 \, a b^{3} c^{3} d^{4} x^{2} + 6132 \, a^{2} b c^{4} d^{4} x^{2} + 52 \, b^{6} c x^{5} e^{4} + 668 \, a b^{4} c^{2} x^{5} e^{4} + 840 \, a^{2} b^{2} c^{3} x^{5} e^{4} + 264 \, a^{3} c^{4} x^{5} e^{4} - 500 \, b^{6} c d x^{4} e^{3} - 3700 \, a b^{4} c^{2} d x^{4} e^{3} - 6600 \, a^{2} b^{2} c^{3} d x^{4} e^{3} + 216 \, b^{6} c d^{2} x^{3} e^{2} + 7416 \, a b^{4} c^{2} d^{2} x^{3} e^{2} + 10104 \, a^{2} b^{2} c^{3} d^{2} x^{3} e^{2} + 3504 \, a^{3} c^{4} d^{2} x^{3} e^{2} + 56 \, b^{6} c d^{3} x^{2} e - 1568 \, a b^{4} c^{2} d^{3} x^{2} e - 12264 \, a^{2} b^{2} c^{3} d^{3} x^{2} e + 8 \, b^{6} c d^{4} x - 152 \, a b^{4} c^{2} d^{4} x + 1392 \, a^{2} b^{2} c^{3} d^{4} x + 2232 \, a^{3} c^{4} d^{4} x + 25 \, b^{7} x^{4} e^{4} + 410 \, a b^{5} c x^{4} e^{4} + 1470 \, a^{2} b^{3} c^{2} x^{4} e^{4} + 660 \, a^{3} b c^{3} x^{4} e^{4} - 48 \, b^{7} d x^{3} e^{3} - 1760 \, a b^{5} c d x^{3} e^{3} - 6016 \, a^{2} b^{3} c^{2} d x^{3} e^{3} - 3504 \, a^{3} b c^{3} d x^{3} e^{3} - 36 \, b^{7} d^{2} x^{2} e^{2} + 984 \, a b^{5} c d^{2} x^{2} e^{2} + 8556 \, a^{2} b^{3} c^{2} d^{2} x^{2} e^{2} + 5256 \, a^{3} b c^{3} d^{2} x^{2} e^{2} - 16 \, b^{7} d^{3} x e + 304 \, a b^{5} c d^{3} x e - 2784 \, a^{2} b^{3} c^{2} d^{3} x e - 4464 \, a^{3} b c^{3} d^{3} x e - 3 \, b^{7} d^{4} + 50 \, a b^{5} c d^{4} - 326 \, a^{2} b^{3} c^{2} d^{4} + 1116 \, a^{3} b c^{3} d^{4} + 148 \, a b^{6} x^{3} e^{4} + 812 \, a^{2} b^{4} c x^{3} e^{4} + 1800 \, a^{3} b^{2} c^{2} x^{3} e^{4} - 264 \, a^{4} c^{3} x^{3} e^{4} - 72 \, a b^{6} d x^{2} e^{3} - 3192 \, a^{2} b^{4} c d x^{2} e^{3} - 3208 \, a^{3} b^{2} c^{2} d x^{2} e^{3} - 2048 \, a^{4} c^{3} d x^{2} e^{3} - 24 \, a b^{6} d^{2} x e^{2} + 672 \, a^{2} b^{4} c d^{2} x e^{2} + 6696 \, a^{3} b^{2} c^{2} d^{2} x e^{2} - 720 \, a^{4} c^{3} d^{2} x e^{2} - 4 \, a b^{6} d^{3} e + 76 \, a^{2} b^{4} c d^{3} e - 696 \, a^{3} b^{2} c^{2} d^{3} e - 1536 \, a^{4} c^{3} d^{3} e + 258 \, a^{2} b^{5} x^{2} e^{4} + 1016 \, a^{3} b^{3} c x^{2} e^{4} + 628 \, a^{4} b c^{2} x^{2} e^{4} - 48 \, a^{2} b^{5} d x e^{3} - 2416 \, a^{3} b^{3} c d x e^{3} - 1328 \, a^{4} b c^{2} d x e^{3} - 6 \, a^{2} b^{5} d^{2} e^{2} + 168 \, a^{3} b^{3} c d^{2} e^{2} + 1944 \, a^{4} b c^{2} d^{2} e^{2} + 188 \, a^{3} b^{4} x e^{4} + 736 \, a^{4} b^{2} c x e^{4} - 72 \, a^{5} c^{2} x e^{4} - 12 \, a^{3} b^{4} d e^{3} - 664 \, a^{4} b^{2} c d e^{3} - 512 \, a^{5} c^{2} d e^{3} + 50 \, a^{4} b^{3} e^{4} + 220 \, a^{5} b c e^{4}}{12 \, {\left(b^{8} - 16 \, a b^{6} c + 96 \, a^{2} b^{4} c^{2} - 256 \, a^{3} b^{2} c^{3} + 256 \, a^{4} c^{4}\right)} {\left(c x^{2} + b x + a\right)}^{4}}"," ",0,"2*(70*c^4*d^4 - 140*b*c^3*d^3*e + 90*b^2*c^2*d^2*e^2 + 60*a*c^3*d^2*e^2 - 20*b^3*c*d*e^3 - 60*a*b*c^2*d*e^3 + b^4*e^4 + 12*a*b^2*c*e^4 + 6*a^2*c^2*e^4)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^8 - 16*a*b^6*c + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 + 256*a^4*c^4)*sqrt(-b^2 + 4*a*c)) + 1/12*(840*c^7*d^4*x^7 - 1680*b*c^6*d^3*x^7*e + 2940*b*c^6*d^4*x^6 + 1080*b^2*c^5*d^2*x^7*e^2 + 720*a*c^6*d^2*x^7*e^2 - 5880*b^2*c^5*d^3*x^6*e + 3640*b^2*c^5*d^4*x^5 + 3080*a*c^6*d^4*x^5 - 240*b^3*c^4*d*x^7*e^3 - 720*a*b*c^5*d*x^7*e^3 + 3780*b^3*c^4*d^2*x^6*e^2 + 2520*a*b*c^5*d^2*x^6*e^2 - 7280*b^3*c^4*d^3*x^5*e - 6160*a*b*c^5*d^3*x^5*e + 1750*b^3*c^4*d^4*x^4 + 7700*a*b*c^5*d^4*x^4 + 12*b^4*c^3*x^7*e^4 + 144*a*b^2*c^4*x^7*e^4 + 72*a^2*c^5*x^7*e^4 - 840*b^4*c^3*d*x^6*e^3 - 2520*a*b^2*c^4*d*x^6*e^3 + 4680*b^4*c^3*d^2*x^5*e^2 + 7080*a*b^2*c^4*d^2*x^5*e^2 + 2640*a^2*c^5*d^2*x^5*e^2 - 3500*b^4*c^3*d^3*x^4*e - 15400*a*b^2*c^4*d^3*x^4*e + 168*b^4*c^3*d^4*x^3 + 5656*a*b^2*c^4*d^4*x^3 + 4088*a^2*c^5*d^4*x^3 + 42*b^5*c^2*x^6*e^4 + 504*a*b^3*c^3*x^6*e^4 + 252*a^2*b*c^4*x^6*e^4 - 1040*b^5*c^2*d*x^5*e^3 - 4000*a*b^3*c^3*d*x^5*e^3 - 2640*a^2*b*c^4*d*x^5*e^3 + 2250*b^5*c^2*d^2*x^4*e^2 + 11400*a*b^3*c^3*d^2*x^4*e^2 + 6600*a^2*b*c^4*d^2*x^4*e^2 - 336*b^5*c^2*d^3*x^3*e - 11312*a*b^3*c^3*d^3*x^3*e - 8176*a^2*b*c^4*d^3*x^3*e - 28*b^5*c^2*d^4*x^2 + 784*a*b^3*c^3*d^4*x^2 + 6132*a^2*b*c^4*d^4*x^2 + 52*b^6*c*x^5*e^4 + 668*a*b^4*c^2*x^5*e^4 + 840*a^2*b^2*c^3*x^5*e^4 + 264*a^3*c^4*x^5*e^4 - 500*b^6*c*d*x^4*e^3 - 3700*a*b^4*c^2*d*x^4*e^3 - 6600*a^2*b^2*c^3*d*x^4*e^3 + 216*b^6*c*d^2*x^3*e^2 + 7416*a*b^4*c^2*d^2*x^3*e^2 + 10104*a^2*b^2*c^3*d^2*x^3*e^2 + 3504*a^3*c^4*d^2*x^3*e^2 + 56*b^6*c*d^3*x^2*e - 1568*a*b^4*c^2*d^3*x^2*e - 12264*a^2*b^2*c^3*d^3*x^2*e + 8*b^6*c*d^4*x - 152*a*b^4*c^2*d^4*x + 1392*a^2*b^2*c^3*d^4*x + 2232*a^3*c^4*d^4*x + 25*b^7*x^4*e^4 + 410*a*b^5*c*x^4*e^4 + 1470*a^2*b^3*c^2*x^4*e^4 + 660*a^3*b*c^3*x^4*e^4 - 48*b^7*d*x^3*e^3 - 1760*a*b^5*c*d*x^3*e^3 - 6016*a^2*b^3*c^2*d*x^3*e^3 - 3504*a^3*b*c^3*d*x^3*e^3 - 36*b^7*d^2*x^2*e^2 + 984*a*b^5*c*d^2*x^2*e^2 + 8556*a^2*b^3*c^2*d^2*x^2*e^2 + 5256*a^3*b*c^3*d^2*x^2*e^2 - 16*b^7*d^3*x*e + 304*a*b^5*c*d^3*x*e - 2784*a^2*b^3*c^2*d^3*x*e - 4464*a^3*b*c^3*d^3*x*e - 3*b^7*d^4 + 50*a*b^5*c*d^4 - 326*a^2*b^3*c^2*d^4 + 1116*a^3*b*c^3*d^4 + 148*a*b^6*x^3*e^4 + 812*a^2*b^4*c*x^3*e^4 + 1800*a^3*b^2*c^2*x^3*e^4 - 264*a^4*c^3*x^3*e^4 - 72*a*b^6*d*x^2*e^3 - 3192*a^2*b^4*c*d*x^2*e^3 - 3208*a^3*b^2*c^2*d*x^2*e^3 - 2048*a^4*c^3*d*x^2*e^3 - 24*a*b^6*d^2*x*e^2 + 672*a^2*b^4*c*d^2*x*e^2 + 6696*a^3*b^2*c^2*d^2*x*e^2 - 720*a^4*c^3*d^2*x*e^2 - 4*a*b^6*d^3*e + 76*a^2*b^4*c*d^3*e - 696*a^3*b^2*c^2*d^3*e - 1536*a^4*c^3*d^3*e + 258*a^2*b^5*x^2*e^4 + 1016*a^3*b^3*c*x^2*e^4 + 628*a^4*b*c^2*x^2*e^4 - 48*a^2*b^5*d*x*e^3 - 2416*a^3*b^3*c*d*x*e^3 - 1328*a^4*b*c^2*d*x*e^3 - 6*a^2*b^5*d^2*e^2 + 168*a^3*b^3*c*d^2*e^2 + 1944*a^4*b*c^2*d^2*e^2 + 188*a^3*b^4*x*e^4 + 736*a^4*b^2*c*x*e^4 - 72*a^5*c^2*x*e^4 - 12*a^3*b^4*d*e^3 - 664*a^4*b^2*c*d*e^3 - 512*a^5*c^2*d*e^3 + 50*a^4*b^3*e^4 + 220*a^5*b*c*e^4)/((b^8 - 16*a*b^6*c + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 + 256*a^4*c^4)*(c*x^2 + b*x + a)^4)","B",0
2223,1,1399,0,0.230518," ","integrate((e*x+d)^3/(c*x^2+b*x+a)^5,x, algorithm=""giac"")","\frac{10 \, {\left(14 \, c^{4} d^{3} - 21 \, b c^{3} d^{2} e + 9 \, b^{2} c^{2} d e^{2} + 6 \, a c^{3} d e^{2} - b^{3} c e^{3} - 3 \, a b c^{2} e^{3}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{8} - 16 \, a b^{6} c + 96 \, a^{2} b^{4} c^{2} - 256 \, a^{3} b^{2} c^{3} + 256 \, a^{4} c^{4}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{840 \, c^{7} d^{3} x^{7} - 1260 \, b c^{6} d^{2} x^{7} e + 2940 \, b c^{6} d^{3} x^{6} + 540 \, b^{2} c^{5} d x^{7} e^{2} + 360 \, a c^{6} d x^{7} e^{2} - 4410 \, b^{2} c^{5} d^{2} x^{6} e + 3640 \, b^{2} c^{5} d^{3} x^{5} + 3080 \, a c^{6} d^{3} x^{5} - 60 \, b^{3} c^{4} x^{7} e^{3} - 180 \, a b c^{5} x^{7} e^{3} + 1890 \, b^{3} c^{4} d x^{6} e^{2} + 1260 \, a b c^{5} d x^{6} e^{2} - 5460 \, b^{3} c^{4} d^{2} x^{5} e - 4620 \, a b c^{5} d^{2} x^{5} e + 1750 \, b^{3} c^{4} d^{3} x^{4} + 7700 \, a b c^{5} d^{3} x^{4} - 210 \, b^{4} c^{3} x^{6} e^{3} - 630 \, a b^{2} c^{4} x^{6} e^{3} + 2340 \, b^{4} c^{3} d x^{5} e^{2} + 3540 \, a b^{2} c^{4} d x^{5} e^{2} + 1320 \, a^{2} c^{5} d x^{5} e^{2} - 2625 \, b^{4} c^{3} d^{2} x^{4} e - 11550 \, a b^{2} c^{4} d^{2} x^{4} e + 168 \, b^{4} c^{3} d^{3} x^{3} + 5656 \, a b^{2} c^{4} d^{3} x^{3} + 4088 \, a^{2} c^{5} d^{3} x^{3} - 260 \, b^{5} c^{2} x^{5} e^{3} - 1000 \, a b^{3} c^{3} x^{5} e^{3} - 660 \, a^{2} b c^{4} x^{5} e^{3} + 1125 \, b^{5} c^{2} d x^{4} e^{2} + 5700 \, a b^{3} c^{3} d x^{4} e^{2} + 3300 \, a^{2} b c^{4} d x^{4} e^{2} - 252 \, b^{5} c^{2} d^{2} x^{3} e - 8484 \, a b^{3} c^{3} d^{2} x^{3} e - 6132 \, a^{2} b c^{4} d^{2} x^{3} e - 28 \, b^{5} c^{2} d^{3} x^{2} + 784 \, a b^{3} c^{3} d^{3} x^{2} + 6132 \, a^{2} b c^{4} d^{3} x^{2} - 125 \, b^{6} c x^{4} e^{3} - 925 \, a b^{4} c^{2} x^{4} e^{3} - 1650 \, a^{2} b^{2} c^{3} x^{4} e^{3} + 108 \, b^{6} c d x^{3} e^{2} + 3708 \, a b^{4} c^{2} d x^{3} e^{2} + 5052 \, a^{2} b^{2} c^{3} d x^{3} e^{2} + 1752 \, a^{3} c^{4} d x^{3} e^{2} + 42 \, b^{6} c d^{2} x^{2} e - 1176 \, a b^{4} c^{2} d^{2} x^{2} e - 9198 \, a^{2} b^{2} c^{3} d^{2} x^{2} e + 8 \, b^{6} c d^{3} x - 152 \, a b^{4} c^{2} d^{3} x + 1392 \, a^{2} b^{2} c^{3} d^{3} x + 2232 \, a^{3} c^{4} d^{3} x - 12 \, b^{7} x^{3} e^{3} - 440 \, a b^{5} c x^{3} e^{3} - 1504 \, a^{2} b^{3} c^{2} x^{3} e^{3} - 876 \, a^{3} b c^{3} x^{3} e^{3} - 18 \, b^{7} d x^{2} e^{2} + 492 \, a b^{5} c d x^{2} e^{2} + 4278 \, a^{2} b^{3} c^{2} d x^{2} e^{2} + 2628 \, a^{3} b c^{3} d x^{2} e^{2} - 12 \, b^{7} d^{2} x e + 228 \, a b^{5} c d^{2} x e - 2088 \, a^{2} b^{3} c^{2} d^{2} x e - 3348 \, a^{3} b c^{3} d^{2} x e - 3 \, b^{7} d^{3} + 50 \, a b^{5} c d^{3} - 326 \, a^{2} b^{3} c^{2} d^{3} + 1116 \, a^{3} b c^{3} d^{3} - 18 \, a b^{6} x^{2} e^{3} - 798 \, a^{2} b^{4} c x^{2} e^{3} - 802 \, a^{3} b^{2} c^{2} x^{2} e^{3} - 512 \, a^{4} c^{3} x^{2} e^{3} - 12 \, a b^{6} d x e^{2} + 336 \, a^{2} b^{4} c d x e^{2} + 3348 \, a^{3} b^{2} c^{2} d x e^{2} - 360 \, a^{4} c^{3} d x e^{2} - 3 \, a b^{6} d^{2} e + 57 \, a^{2} b^{4} c d^{2} e - 522 \, a^{3} b^{2} c^{2} d^{2} e - 1152 \, a^{4} c^{3} d^{2} e - 12 \, a^{2} b^{5} x e^{3} - 604 \, a^{3} b^{3} c x e^{3} - 332 \, a^{4} b c^{2} x e^{3} - 3 \, a^{2} b^{5} d e^{2} + 84 \, a^{3} b^{3} c d e^{2} + 972 \, a^{4} b c^{2} d e^{2} - 3 \, a^{3} b^{4} e^{3} - 166 \, a^{4} b^{2} c e^{3} - 128 \, a^{5} c^{2} e^{3}}{12 \, {\left(b^{8} - 16 \, a b^{6} c + 96 \, a^{2} b^{4} c^{2} - 256 \, a^{3} b^{2} c^{3} + 256 \, a^{4} c^{4}\right)} {\left(c x^{2} + b x + a\right)}^{4}}"," ",0,"10*(14*c^4*d^3 - 21*b*c^3*d^2*e + 9*b^2*c^2*d*e^2 + 6*a*c^3*d*e^2 - b^3*c*e^3 - 3*a*b*c^2*e^3)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^8 - 16*a*b^6*c + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 + 256*a^4*c^4)*sqrt(-b^2 + 4*a*c)) + 1/12*(840*c^7*d^3*x^7 - 1260*b*c^6*d^2*x^7*e + 2940*b*c^6*d^3*x^6 + 540*b^2*c^5*d*x^7*e^2 + 360*a*c^6*d*x^7*e^2 - 4410*b^2*c^5*d^2*x^6*e + 3640*b^2*c^5*d^3*x^5 + 3080*a*c^6*d^3*x^5 - 60*b^3*c^4*x^7*e^3 - 180*a*b*c^5*x^7*e^3 + 1890*b^3*c^4*d*x^6*e^2 + 1260*a*b*c^5*d*x^6*e^2 - 5460*b^3*c^4*d^2*x^5*e - 4620*a*b*c^5*d^2*x^5*e + 1750*b^3*c^4*d^3*x^4 + 7700*a*b*c^5*d^3*x^4 - 210*b^4*c^3*x^6*e^3 - 630*a*b^2*c^4*x^6*e^3 + 2340*b^4*c^3*d*x^5*e^2 + 3540*a*b^2*c^4*d*x^5*e^2 + 1320*a^2*c^5*d*x^5*e^2 - 2625*b^4*c^3*d^2*x^4*e - 11550*a*b^2*c^4*d^2*x^4*e + 168*b^4*c^3*d^3*x^3 + 5656*a*b^2*c^4*d^3*x^3 + 4088*a^2*c^5*d^3*x^3 - 260*b^5*c^2*x^5*e^3 - 1000*a*b^3*c^3*x^5*e^3 - 660*a^2*b*c^4*x^5*e^3 + 1125*b^5*c^2*d*x^4*e^2 + 5700*a*b^3*c^3*d*x^4*e^2 + 3300*a^2*b*c^4*d*x^4*e^2 - 252*b^5*c^2*d^2*x^3*e - 8484*a*b^3*c^3*d^2*x^3*e - 6132*a^2*b*c^4*d^2*x^3*e - 28*b^5*c^2*d^3*x^2 + 784*a*b^3*c^3*d^3*x^2 + 6132*a^2*b*c^4*d^3*x^2 - 125*b^6*c*x^4*e^3 - 925*a*b^4*c^2*x^4*e^3 - 1650*a^2*b^2*c^3*x^4*e^3 + 108*b^6*c*d*x^3*e^2 + 3708*a*b^4*c^2*d*x^3*e^2 + 5052*a^2*b^2*c^3*d*x^3*e^2 + 1752*a^3*c^4*d*x^3*e^2 + 42*b^6*c*d^2*x^2*e - 1176*a*b^4*c^2*d^2*x^2*e - 9198*a^2*b^2*c^3*d^2*x^2*e + 8*b^6*c*d^3*x - 152*a*b^4*c^2*d^3*x + 1392*a^2*b^2*c^3*d^3*x + 2232*a^3*c^4*d^3*x - 12*b^7*x^3*e^3 - 440*a*b^5*c*x^3*e^3 - 1504*a^2*b^3*c^2*x^3*e^3 - 876*a^3*b*c^3*x^3*e^3 - 18*b^7*d*x^2*e^2 + 492*a*b^5*c*d*x^2*e^2 + 4278*a^2*b^3*c^2*d*x^2*e^2 + 2628*a^3*b*c^3*d*x^2*e^2 - 12*b^7*d^2*x*e + 228*a*b^5*c*d^2*x*e - 2088*a^2*b^3*c^2*d^2*x*e - 3348*a^3*b*c^3*d^2*x*e - 3*b^7*d^3 + 50*a*b^5*c*d^3 - 326*a^2*b^3*c^2*d^3 + 1116*a^3*b*c^3*d^3 - 18*a*b^6*x^2*e^3 - 798*a^2*b^4*c*x^2*e^3 - 802*a^3*b^2*c^2*x^2*e^3 - 512*a^4*c^3*x^2*e^3 - 12*a*b^6*d*x*e^2 + 336*a^2*b^4*c*d*x*e^2 + 3348*a^3*b^2*c^2*d*x*e^2 - 360*a^4*c^3*d*x*e^2 - 3*a*b^6*d^2*e + 57*a^2*b^4*c*d^2*e - 522*a^3*b^2*c^2*d^2*e - 1152*a^4*c^3*d^2*e - 12*a^2*b^5*x*e^3 - 604*a^3*b^3*c*x*e^3 - 332*a^4*b*c^2*x*e^3 - 3*a^2*b^5*d*e^2 + 84*a^3*b^3*c*d*e^2 + 972*a^4*b*c^2*d*e^2 - 3*a^3*b^4*e^3 - 166*a^4*b^2*c*e^3 - 128*a^5*c^2*e^3)/((b^8 - 16*a*b^6*c + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 + 256*a^4*c^4)*(c*x^2 + b*x + a)^4)","B",0
2224,1,1007,0,0.224961," ","integrate((e*x+d)^2/(c*x^2+b*x+a)^5,x, algorithm=""giac"")","\frac{10 \, {\left(14 \, c^{4} d^{2} - 14 \, b c^{3} d e + 3 \, b^{2} c^{2} e^{2} + 2 \, a c^{3} e^{2}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{8} - 16 \, a b^{6} c + 96 \, a^{2} b^{4} c^{2} - 256 \, a^{3} b^{2} c^{3} + 256 \, a^{4} c^{4}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{840 \, c^{7} d^{2} x^{7} - 840 \, b c^{6} d x^{7} e + 2940 \, b c^{6} d^{2} x^{6} + 180 \, b^{2} c^{5} x^{7} e^{2} + 120 \, a c^{6} x^{7} e^{2} - 2940 \, b^{2} c^{5} d x^{6} e + 3640 \, b^{2} c^{5} d^{2} x^{5} + 3080 \, a c^{6} d^{2} x^{5} + 630 \, b^{3} c^{4} x^{6} e^{2} + 420 \, a b c^{5} x^{6} e^{2} - 3640 \, b^{3} c^{4} d x^{5} e - 3080 \, a b c^{5} d x^{5} e + 1750 \, b^{3} c^{4} d^{2} x^{4} + 7700 \, a b c^{5} d^{2} x^{4} + 780 \, b^{4} c^{3} x^{5} e^{2} + 1180 \, a b^{2} c^{4} x^{5} e^{2} + 440 \, a^{2} c^{5} x^{5} e^{2} - 1750 \, b^{4} c^{3} d x^{4} e - 7700 \, a b^{2} c^{4} d x^{4} e + 168 \, b^{4} c^{3} d^{2} x^{3} + 5656 \, a b^{2} c^{4} d^{2} x^{3} + 4088 \, a^{2} c^{5} d^{2} x^{3} + 375 \, b^{5} c^{2} x^{4} e^{2} + 1900 \, a b^{3} c^{3} x^{4} e^{2} + 1100 \, a^{2} b c^{4} x^{4} e^{2} - 168 \, b^{5} c^{2} d x^{3} e - 5656 \, a b^{3} c^{3} d x^{3} e - 4088 \, a^{2} b c^{4} d x^{3} e - 28 \, b^{5} c^{2} d^{2} x^{2} + 784 \, a b^{3} c^{3} d^{2} x^{2} + 6132 \, a^{2} b c^{4} d^{2} x^{2} + 36 \, b^{6} c x^{3} e^{2} + 1236 \, a b^{4} c^{2} x^{3} e^{2} + 1684 \, a^{2} b^{2} c^{3} x^{3} e^{2} + 584 \, a^{3} c^{4} x^{3} e^{2} + 28 \, b^{6} c d x^{2} e - 784 \, a b^{4} c^{2} d x^{2} e - 6132 \, a^{2} b^{2} c^{3} d x^{2} e + 8 \, b^{6} c d^{2} x - 152 \, a b^{4} c^{2} d^{2} x + 1392 \, a^{2} b^{2} c^{3} d^{2} x + 2232 \, a^{3} c^{4} d^{2} x - 6 \, b^{7} x^{2} e^{2} + 164 \, a b^{5} c x^{2} e^{2} + 1426 \, a^{2} b^{3} c^{2} x^{2} e^{2} + 876 \, a^{3} b c^{3} x^{2} e^{2} - 8 \, b^{7} d x e + 152 \, a b^{5} c d x e - 1392 \, a^{2} b^{3} c^{2} d x e - 2232 \, a^{3} b c^{3} d x e - 3 \, b^{7} d^{2} + 50 \, a b^{5} c d^{2} - 326 \, a^{2} b^{3} c^{2} d^{2} + 1116 \, a^{3} b c^{3} d^{2} - 4 \, a b^{6} x e^{2} + 112 \, a^{2} b^{4} c x e^{2} + 1116 \, a^{3} b^{2} c^{2} x e^{2} - 120 \, a^{4} c^{3} x e^{2} - 2 \, a b^{6} d e + 38 \, a^{2} b^{4} c d e - 348 \, a^{3} b^{2} c^{2} d e - 768 \, a^{4} c^{3} d e - a^{2} b^{5} e^{2} + 28 \, a^{3} b^{3} c e^{2} + 324 \, a^{4} b c^{2} e^{2}}{12 \, {\left(b^{8} - 16 \, a b^{6} c + 96 \, a^{2} b^{4} c^{2} - 256 \, a^{3} b^{2} c^{3} + 256 \, a^{4} c^{4}\right)} {\left(c x^{2} + b x + a\right)}^{4}}"," ",0,"10*(14*c^4*d^2 - 14*b*c^3*d*e + 3*b^2*c^2*e^2 + 2*a*c^3*e^2)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^8 - 16*a*b^6*c + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 + 256*a^4*c^4)*sqrt(-b^2 + 4*a*c)) + 1/12*(840*c^7*d^2*x^7 - 840*b*c^6*d*x^7*e + 2940*b*c^6*d^2*x^6 + 180*b^2*c^5*x^7*e^2 + 120*a*c^6*x^7*e^2 - 2940*b^2*c^5*d*x^6*e + 3640*b^2*c^5*d^2*x^5 + 3080*a*c^6*d^2*x^5 + 630*b^3*c^4*x^6*e^2 + 420*a*b*c^5*x^6*e^2 - 3640*b^3*c^4*d*x^5*e - 3080*a*b*c^5*d*x^5*e + 1750*b^3*c^4*d^2*x^4 + 7700*a*b*c^5*d^2*x^4 + 780*b^4*c^3*x^5*e^2 + 1180*a*b^2*c^4*x^5*e^2 + 440*a^2*c^5*x^5*e^2 - 1750*b^4*c^3*d*x^4*e - 7700*a*b^2*c^4*d*x^4*e + 168*b^4*c^3*d^2*x^3 + 5656*a*b^2*c^4*d^2*x^3 + 4088*a^2*c^5*d^2*x^3 + 375*b^5*c^2*x^4*e^2 + 1900*a*b^3*c^3*x^4*e^2 + 1100*a^2*b*c^4*x^4*e^2 - 168*b^5*c^2*d*x^3*e - 5656*a*b^3*c^3*d*x^3*e - 4088*a^2*b*c^4*d*x^3*e - 28*b^5*c^2*d^2*x^2 + 784*a*b^3*c^3*d^2*x^2 + 6132*a^2*b*c^4*d^2*x^2 + 36*b^6*c*x^3*e^2 + 1236*a*b^4*c^2*x^3*e^2 + 1684*a^2*b^2*c^3*x^3*e^2 + 584*a^3*c^4*x^3*e^2 + 28*b^6*c*d*x^2*e - 784*a*b^4*c^2*d*x^2*e - 6132*a^2*b^2*c^3*d*x^2*e + 8*b^6*c*d^2*x - 152*a*b^4*c^2*d^2*x + 1392*a^2*b^2*c^3*d^2*x + 2232*a^3*c^4*d^2*x - 6*b^7*x^2*e^2 + 164*a*b^5*c*x^2*e^2 + 1426*a^2*b^3*c^2*x^2*e^2 + 876*a^3*b*c^3*x^2*e^2 - 8*b^7*d*x*e + 152*a*b^5*c*d*x*e - 1392*a^2*b^3*c^2*d*x*e - 2232*a^3*b*c^3*d*x*e - 3*b^7*d^2 + 50*a*b^5*c*d^2 - 326*a^2*b^3*c^2*d^2 + 1116*a^3*b*c^3*d^2 - 4*a*b^6*x*e^2 + 112*a^2*b^4*c*x*e^2 + 1116*a^3*b^2*c^2*x*e^2 - 120*a^4*c^3*x*e^2 - 2*a*b^6*d*e + 38*a^2*b^4*c*d*e - 348*a^3*b^2*c^2*d*e - 768*a^4*c^3*d*e - a^2*b^5*e^2 + 28*a^3*b^3*c*e^2 + 324*a^4*b*c^2*e^2)/((b^8 - 16*a*b^6*c + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 + 256*a^4*c^4)*(c*x^2 + b*x + a)^4)","B",0
2225,1,612,0,0.193560," ","integrate((e*x+d)/(c*x^2+b*x+a)^5,x, algorithm=""giac"")","\frac{70 \, {\left(2 \, c^{4} d - b c^{3} e\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{8} - 16 \, a b^{6} c + 96 \, a^{2} b^{4} c^{2} - 256 \, a^{3} b^{2} c^{3} + 256 \, a^{4} c^{4}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{840 \, c^{7} d x^{7} - 420 \, b c^{6} x^{7} e + 2940 \, b c^{6} d x^{6} - 1470 \, b^{2} c^{5} x^{6} e + 3640 \, b^{2} c^{5} d x^{5} + 3080 \, a c^{6} d x^{5} - 1820 \, b^{3} c^{4} x^{5} e - 1540 \, a b c^{5} x^{5} e + 1750 \, b^{3} c^{4} d x^{4} + 7700 \, a b c^{5} d x^{4} - 875 \, b^{4} c^{3} x^{4} e - 3850 \, a b^{2} c^{4} x^{4} e + 168 \, b^{4} c^{3} d x^{3} + 5656 \, a b^{2} c^{4} d x^{3} + 4088 \, a^{2} c^{5} d x^{3} - 84 \, b^{5} c^{2} x^{3} e - 2828 \, a b^{3} c^{3} x^{3} e - 2044 \, a^{2} b c^{4} x^{3} e - 28 \, b^{5} c^{2} d x^{2} + 784 \, a b^{3} c^{3} d x^{2} + 6132 \, a^{2} b c^{4} d x^{2} + 14 \, b^{6} c x^{2} e - 392 \, a b^{4} c^{2} x^{2} e - 3066 \, a^{2} b^{2} c^{3} x^{2} e + 8 \, b^{6} c d x - 152 \, a b^{4} c^{2} d x + 1392 \, a^{2} b^{2} c^{3} d x + 2232 \, a^{3} c^{4} d x - 4 \, b^{7} x e + 76 \, a b^{5} c x e - 696 \, a^{2} b^{3} c^{2} x e - 1116 \, a^{3} b c^{3} x e - 3 \, b^{7} d + 50 \, a b^{5} c d - 326 \, a^{2} b^{3} c^{2} d + 1116 \, a^{3} b c^{3} d - a b^{6} e + 19 \, a^{2} b^{4} c e - 174 \, a^{3} b^{2} c^{2} e - 384 \, a^{4} c^{3} e}{12 \, {\left(b^{8} - 16 \, a b^{6} c + 96 \, a^{2} b^{4} c^{2} - 256 \, a^{3} b^{2} c^{3} + 256 \, a^{4} c^{4}\right)} {\left(c x^{2} + b x + a\right)}^{4}}"," ",0,"70*(2*c^4*d - b*c^3*e)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^8 - 16*a*b^6*c + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 + 256*a^4*c^4)*sqrt(-b^2 + 4*a*c)) + 1/12*(840*c^7*d*x^7 - 420*b*c^6*x^7*e + 2940*b*c^6*d*x^6 - 1470*b^2*c^5*x^6*e + 3640*b^2*c^5*d*x^5 + 3080*a*c^6*d*x^5 - 1820*b^3*c^4*x^5*e - 1540*a*b*c^5*x^5*e + 1750*b^3*c^4*d*x^4 + 7700*a*b*c^5*d*x^4 - 875*b^4*c^3*x^4*e - 3850*a*b^2*c^4*x^4*e + 168*b^4*c^3*d*x^3 + 5656*a*b^2*c^4*d*x^3 + 4088*a^2*c^5*d*x^3 - 84*b^5*c^2*x^3*e - 2828*a*b^3*c^3*x^3*e - 2044*a^2*b*c^4*x^3*e - 28*b^5*c^2*d*x^2 + 784*a*b^3*c^3*d*x^2 + 6132*a^2*b*c^4*d*x^2 + 14*b^6*c*x^2*e - 392*a*b^4*c^2*x^2*e - 3066*a^2*b^2*c^3*x^2*e + 8*b^6*c*d*x - 152*a*b^4*c^2*d*x + 1392*a^2*b^2*c^3*d*x + 2232*a^3*c^4*d*x - 4*b^7*x*e + 76*a*b^5*c*x*e - 696*a^2*b^3*c^2*x*e - 1116*a^3*b*c^3*x*e - 3*b^7*d + 50*a*b^5*c*d - 326*a^2*b^3*c^2*d + 1116*a^3*b*c^3*d - a*b^6*e + 19*a^2*b^4*c*e - 174*a^3*b^2*c^2*e - 384*a^4*c^3*e)/((b^8 - 16*a*b^6*c + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 + 256*a^4*c^4)*(c*x^2 + b*x + a)^4)","B",0
2226,1,336,0,0.169909," ","integrate(1/(c*x^2+b*x+a)^5,x, algorithm=""giac"")","\frac{140 \, c^{4} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{8} - 16 \, a b^{6} c + 96 \, a^{2} b^{4} c^{2} - 256 \, a^{3} b^{2} c^{3} + 256 \, a^{4} c^{4}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{840 \, c^{7} x^{7} + 2940 \, b c^{6} x^{6} + 3640 \, b^{2} c^{5} x^{5} + 3080 \, a c^{6} x^{5} + 1750 \, b^{3} c^{4} x^{4} + 7700 \, a b c^{5} x^{4} + 168 \, b^{4} c^{3} x^{3} + 5656 \, a b^{2} c^{4} x^{3} + 4088 \, a^{2} c^{5} x^{3} - 28 \, b^{5} c^{2} x^{2} + 784 \, a b^{3} c^{3} x^{2} + 6132 \, a^{2} b c^{4} x^{2} + 8 \, b^{6} c x - 152 \, a b^{4} c^{2} x + 1392 \, a^{2} b^{2} c^{3} x + 2232 \, a^{3} c^{4} x - 3 \, b^{7} + 50 \, a b^{5} c - 326 \, a^{2} b^{3} c^{2} + 1116 \, a^{3} b c^{3}}{12 \, {\left(b^{8} - 16 \, a b^{6} c + 96 \, a^{2} b^{4} c^{2} - 256 \, a^{3} b^{2} c^{3} + 256 \, a^{4} c^{4}\right)} {\left(c x^{2} + b x + a\right)}^{4}}"," ",0,"140*c^4*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^8 - 16*a*b^6*c + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 + 256*a^4*c^4)*sqrt(-b^2 + 4*a*c)) + 1/12*(840*c^7*x^7 + 2940*b*c^6*x^6 + 3640*b^2*c^5*x^5 + 3080*a*c^6*x^5 + 1750*b^3*c^4*x^4 + 7700*a*b*c^5*x^4 + 168*b^4*c^3*x^3 + 5656*a*b^2*c^4*x^3 + 4088*a^2*c^5*x^3 - 28*b^5*c^2*x^2 + 784*a*b^3*c^3*x^2 + 6132*a^2*b*c^4*x^2 + 8*b^6*c*x - 152*a*b^4*c^2*x + 1392*a^2*b^2*c^3*x + 2232*a^3*c^4*x - 3*b^7 + 50*a*b^5*c - 326*a^2*b^3*c^2 + 1116*a^3*b*c^3)/((b^8 - 16*a*b^6*c + 96*a^2*b^4*c^2 - 256*a^3*b^2*c^3 + 256*a^4*c^4)*(c*x^2 + b*x + a)^4)","B",0
2227,1,6368,0,0.482991," ","integrate(1/(e*x+d)/(c*x^2+b*x+a)^5,x, algorithm=""giac"")","-\frac{e^{9} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(c^{5} d^{10} - 5 \, b c^{4} d^{9} e + 10 \, b^{2} c^{3} d^{8} e^{2} + 5 \, a c^{4} d^{8} e^{2} - 10 \, b^{3} c^{2} d^{7} e^{3} - 20 \, a b c^{3} d^{7} e^{3} + 5 \, b^{4} c d^{6} e^{4} + 30 \, a b^{2} c^{2} d^{6} e^{4} + 10 \, a^{2} c^{3} d^{6} e^{4} - b^{5} d^{5} e^{5} - 20 \, a b^{3} c d^{5} e^{5} - 30 \, a^{2} b c^{2} d^{5} e^{5} + 5 \, a b^{4} d^{4} e^{6} + 30 \, a^{2} b^{2} c d^{4} e^{6} + 10 \, a^{3} c^{2} d^{4} e^{6} - 10 \, a^{2} b^{3} d^{3} e^{7} - 20 \, a^{3} b c d^{3} e^{7} + 10 \, a^{3} b^{2} d^{2} e^{8} + 5 \, a^{4} c d^{2} e^{8} - 5 \, a^{4} b d e^{9} + a^{5} e^{10}\right)}} + \frac{e^{10} \log\left({\left| x e + d \right|}\right)}{c^{5} d^{10} e - 5 \, b c^{4} d^{9} e^{2} + 10 \, b^{2} c^{3} d^{8} e^{3} + 5 \, a c^{4} d^{8} e^{3} - 10 \, b^{3} c^{2} d^{7} e^{4} - 20 \, a b c^{3} d^{7} e^{4} + 5 \, b^{4} c d^{6} e^{5} + 30 \, a b^{2} c^{2} d^{6} e^{5} + 10 \, a^{2} c^{3} d^{6} e^{5} - b^{5} d^{5} e^{6} - 20 \, a b^{3} c d^{5} e^{6} - 30 \, a^{2} b c^{2} d^{5} e^{6} + 5 \, a b^{4} d^{4} e^{7} + 30 \, a^{2} b^{2} c d^{4} e^{7} + 10 \, a^{3} c^{2} d^{4} e^{7} - 10 \, a^{2} b^{3} d^{3} e^{8} - 20 \, a^{3} b c d^{3} e^{8} + 10 \, a^{3} b^{2} d^{2} e^{9} + 5 \, a^{4} c d^{2} e^{9} - 5 \, a^{4} b d e^{10} + a^{5} e^{11}} + \frac{{\left(140 \, c^{9} d^{9} - 630 \, b c^{8} d^{8} e + 1080 \, b^{2} c^{7} d^{7} e^{2} + 720 \, a c^{8} d^{7} e^{2} - 840 \, b^{3} c^{6} d^{6} e^{3} - 2520 \, a b c^{7} d^{6} e^{3} + 252 \, b^{4} c^{5} d^{5} e^{4} + 3024 \, a b^{2} c^{6} d^{5} e^{4} + 1512 \, a^{2} c^{7} d^{5} e^{4} - 1260 \, a b^{3} c^{5} d^{4} e^{5} - 3780 \, a^{2} b c^{6} d^{4} e^{5} + 2520 \, a^{2} b^{2} c^{5} d^{3} e^{6} + 1680 \, a^{3} c^{6} d^{3} e^{6} - 2520 \, a^{3} b c^{5} d^{2} e^{7} + 1260 \, a^{4} c^{5} d e^{8} - b^{9} e^{9} + 18 \, a b^{7} c e^{9} - 126 \, a^{2} b^{5} c^{2} e^{9} + 420 \, a^{3} b^{3} c^{3} e^{9} - 630 \, a^{4} b c^{4} e^{9}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{8} c^{5} d^{10} - 16 \, a b^{6} c^{6} d^{10} + 96 \, a^{2} b^{4} c^{7} d^{10} - 256 \, a^{3} b^{2} c^{8} d^{10} + 256 \, a^{4} c^{9} d^{10} - 5 \, b^{9} c^{4} d^{9} e + 80 \, a b^{7} c^{5} d^{9} e - 480 \, a^{2} b^{5} c^{6} d^{9} e + 1280 \, a^{3} b^{3} c^{7} d^{9} e - 1280 \, a^{4} b c^{8} d^{9} e + 10 \, b^{10} c^{3} d^{8} e^{2} - 155 \, a b^{8} c^{4} d^{8} e^{2} + 880 \, a^{2} b^{6} c^{5} d^{8} e^{2} - 2080 \, a^{3} b^{4} c^{6} d^{8} e^{2} + 1280 \, a^{4} b^{2} c^{7} d^{8} e^{2} + 1280 \, a^{5} c^{8} d^{8} e^{2} - 10 \, b^{11} c^{2} d^{7} e^{3} + 140 \, a b^{9} c^{3} d^{7} e^{3} - 640 \, a^{2} b^{7} c^{4} d^{7} e^{3} + 640 \, a^{3} b^{5} c^{5} d^{7} e^{3} + 2560 \, a^{4} b^{3} c^{6} d^{7} e^{3} - 5120 \, a^{5} b c^{7} d^{7} e^{3} + 5 \, b^{12} c d^{6} e^{4} - 50 \, a b^{10} c^{2} d^{6} e^{4} + 10 \, a^{2} b^{8} c^{3} d^{6} e^{4} + 1440 \, a^{3} b^{6} c^{4} d^{6} e^{4} - 5440 \, a^{4} b^{4} c^{5} d^{6} e^{4} + 5120 \, a^{5} b^{2} c^{6} d^{6} e^{4} + 2560 \, a^{6} c^{7} d^{6} e^{4} - b^{13} d^{5} e^{5} - 4 \, a b^{11} c d^{5} e^{5} + 194 \, a^{2} b^{9} c^{2} d^{5} e^{5} - 1184 \, a^{3} b^{7} c^{3} d^{5} e^{5} + 1984 \, a^{4} b^{5} c^{4} d^{5} e^{5} + 2560 \, a^{5} b^{3} c^{5} d^{5} e^{5} - 7680 \, a^{6} b c^{6} d^{5} e^{5} + 5 \, a b^{12} d^{4} e^{6} - 50 \, a^{2} b^{10} c d^{4} e^{6} + 10 \, a^{3} b^{8} c^{2} d^{4} e^{6} + 1440 \, a^{4} b^{6} c^{3} d^{4} e^{6} - 5440 \, a^{5} b^{4} c^{4} d^{4} e^{6} + 5120 \, a^{6} b^{2} c^{5} d^{4} e^{6} + 2560 \, a^{7} c^{6} d^{4} e^{6} - 10 \, a^{2} b^{11} d^{3} e^{7} + 140 \, a^{3} b^{9} c d^{3} e^{7} - 640 \, a^{4} b^{7} c^{2} d^{3} e^{7} + 640 \, a^{5} b^{5} c^{3} d^{3} e^{7} + 2560 \, a^{6} b^{3} c^{4} d^{3} e^{7} - 5120 \, a^{7} b c^{5} d^{3} e^{7} + 10 \, a^{3} b^{10} d^{2} e^{8} - 155 \, a^{4} b^{8} c d^{2} e^{8} + 880 \, a^{5} b^{6} c^{2} d^{2} e^{8} - 2080 \, a^{6} b^{4} c^{3} d^{2} e^{8} + 1280 \, a^{7} b^{2} c^{4} d^{2} e^{8} + 1280 \, a^{8} c^{5} d^{2} e^{8} - 5 \, a^{4} b^{9} d e^{9} + 80 \, a^{5} b^{7} c d e^{9} - 480 \, a^{6} b^{5} c^{2} d e^{9} + 1280 \, a^{7} b^{3} c^{3} d e^{9} - 1280 \, a^{8} b c^{4} d e^{9} + a^{5} b^{8} e^{10} - 16 \, a^{6} b^{6} c e^{10} + 96 \, a^{7} b^{4} c^{2} e^{10} - 256 \, a^{8} b^{2} c^{3} e^{10} + 256 \, a^{9} c^{4} e^{10}\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{3 \, b^{7} c^{5} d^{9} - 50 \, a b^{5} c^{6} d^{9} + 326 \, a^{2} b^{3} c^{7} d^{9} - 1116 \, a^{3} b c^{8} d^{9} - 15 \, b^{8} c^{4} d^{8} e + 249 \, a b^{6} c^{5} d^{8} e - 1611 \, a^{2} b^{4} c^{6} d^{8} e + 5406 \, a^{3} b^{2} c^{7} d^{8} e - 384 \, a^{4} c^{8} d^{8} e + 30 \, b^{9} c^{3} d^{7} e^{2} - 480 \, a b^{7} c^{4} d^{7} e^{2} + 2916 \, a^{2} b^{5} c^{5} d^{7} e^{2} - 8688 \, a^{3} b^{3} c^{6} d^{7} e^{2} - 3984 \, a^{4} b c^{7} d^{7} e^{2} - 30 \, b^{10} c^{2} d^{6} e^{3} + 430 \, a b^{8} c^{3} d^{6} e^{3} - 2080 \, a^{2} b^{6} c^{4} d^{6} e^{3} + 3132 \, a^{3} b^{4} c^{5} d^{6} e^{3} + 19064 \, a^{4} b^{2} c^{6} d^{6} e^{3} - 2048 \, a^{5} c^{7} d^{6} e^{3} + 15 \, b^{11} c d^{5} e^{4} - 150 \, a b^{9} c^{2} d^{5} e^{4} + 4800 \, a^{3} b^{5} c^{4} d^{5} e^{4} - 25500 \, a^{4} b^{3} c^{5} d^{5} e^{4} - 4680 \, a^{5} b c^{6} d^{5} e^{4} - 3 \, b^{12} d^{4} e^{5} - 15 \, a b^{10} c d^{4} e^{5} + 639 \, a^{2} b^{8} c^{2} d^{4} e^{5} - 3984 \, a^{3} b^{6} c^{3} d^{4} e^{5} + 7962 \, a^{4} b^{4} c^{4} d^{4} e^{5} + 25524 \, a^{5} b^{2} c^{5} d^{4} e^{5} - 4608 \, a^{6} c^{6} d^{4} e^{5} + 16 \, a b^{11} d^{3} e^{6} - 154 \, a^{2} b^{9} c d^{3} e^{6} - 96 \, a^{3} b^{7} c^{2} d^{3} e^{6} + 5780 \, a^{4} b^{5} c^{3} d^{3} e^{6} - 24368 \, a^{5} b^{3} c^{4} d^{3} e^{6} - 1104 \, a^{6} b c^{5} d^{3} e^{6} - 36 \, a^{2} b^{10} d^{2} e^{7} + 498 \, a^{3} b^{8} c d^{2} e^{7} - 2172 \, a^{4} b^{6} c^{2} d^{2} e^{7} + 1044 \, a^{5} b^{4} c^{3} d^{2} e^{7} + 17016 \, a^{6} b^{2} c^{4} d^{2} e^{7} - 6144 \, a^{7} c^{5} d^{2} e^{7} + 48 \, a^{3} b^{9} d e^{8} - 741 \, a^{4} b^{7} c d e^{8} + 4158 \, a^{5} b^{5} c^{2} d e^{8} - 9354 \, a^{6} b^{3} c^{3} d e^{8} + 2244 \, a^{7} b c^{4} d e^{8} - 25 \, a^{4} b^{8} e^{9} + 385 \, a^{5} b^{6} c e^{9} - 2175 \, a^{6} b^{4} c^{2} e^{9} + 5150 \, a^{7} b^{2} c^{3} e^{9} - 3200 \, a^{8} c^{4} e^{9} - 12 \, {\left(70 \, c^{12} d^{9} - 315 \, b c^{11} d^{8} e + 540 \, b^{2} c^{10} d^{7} e^{2} + 360 \, a c^{11} d^{7} e^{2} - 420 \, b^{3} c^{9} d^{6} e^{3} - 1260 \, a b c^{10} d^{6} e^{3} + 126 \, b^{4} c^{8} d^{5} e^{4} + 1512 \, a b^{2} c^{9} d^{5} e^{4} + 756 \, a^{2} c^{10} d^{5} e^{4} - 630 \, a b^{3} c^{8} d^{4} e^{5} - 1890 \, a^{2} b c^{9} d^{4} e^{5} + 1260 \, a^{2} b^{2} c^{8} d^{3} e^{6} + 840 \, a^{3} c^{9} d^{3} e^{6} - 1260 \, a^{3} b c^{8} d^{2} e^{7} - b^{8} c^{4} d e^{8} + 16 \, a b^{6} c^{5} d e^{8} - 96 \, a^{2} b^{4} c^{6} d e^{8} + 256 \, a^{3} b^{2} c^{7} d e^{8} + 374 \, a^{4} c^{8} d e^{8} + a b^{7} c^{4} e^{9} - 15 \, a^{2} b^{5} c^{5} e^{9} + 82 \, a^{3} b^{3} c^{6} e^{9} - 187 \, a^{4} b c^{7} e^{9}\right)} x^{7} - 6 \, {\left(490 \, b c^{11} d^{9} - 2205 \, b^{2} c^{10} d^{8} e + 3780 \, b^{3} c^{9} d^{7} e^{2} + 2520 \, a b c^{10} d^{7} e^{2} - 2940 \, b^{4} c^{8} d^{6} e^{3} - 8820 \, a b^{2} c^{9} d^{6} e^{3} + 882 \, b^{5} c^{7} d^{5} e^{4} + 10584 \, a b^{3} c^{8} d^{5} e^{4} + 5292 \, a^{2} b c^{9} d^{5} e^{4} - 4410 \, a b^{4} c^{7} d^{4} e^{5} - 13230 \, a^{2} b^{2} c^{8} d^{4} e^{5} + 8820 \, a^{2} b^{3} c^{7} d^{3} e^{6} + 5880 \, a^{3} b c^{8} d^{3} e^{6} + b^{8} c^{4} d^{2} e^{7} - 16 \, a b^{6} c^{5} d^{2} e^{7} + 96 \, a^{2} b^{4} c^{6} d^{2} e^{7} - 9076 \, a^{3} b^{2} c^{7} d^{2} e^{7} + 256 \, a^{4} c^{8} d^{2} e^{7} - 8 \, b^{9} c^{3} d e^{8} + 128 \, a b^{7} c^{4} d e^{8} - 768 \, a^{2} b^{5} c^{5} d e^{8} + 2048 \, a^{3} b^{3} c^{6} d e^{8} + 2362 \, a^{4} b c^{7} d e^{8} + 8 \, a b^{8} c^{3} e^{9} - 121 \, a^{2} b^{6} c^{4} e^{9} + 670 \, a^{3} b^{4} c^{5} e^{9} - 1565 \, a^{4} b^{2} c^{6} e^{9} + 256 \, a^{5} c^{7} e^{9}\right)} x^{6} - 4 \, {\left(910 \, b^{2} c^{10} d^{9} + 770 \, a c^{11} d^{9} - 4095 \, b^{3} c^{9} d^{8} e - 3465 \, a b c^{10} d^{8} e + 7020 \, b^{4} c^{8} d^{7} e^{2} + 10620 \, a b^{2} c^{9} d^{7} e^{2} + 3960 \, a^{2} c^{10} d^{7} e^{2} - 5460 \, b^{5} c^{7} d^{6} e^{3} - 21000 \, a b^{3} c^{8} d^{6} e^{3} - 13860 \, a^{2} b c^{9} d^{6} e^{3} + 1638 \, b^{6} c^{6} d^{5} e^{4} + 21042 \, a b^{4} c^{7} d^{5} e^{4} + 26460 \, a^{2} b^{2} c^{8} d^{5} e^{4} + 8316 \, a^{3} c^{9} d^{5} e^{4} - 8190 \, a b^{5} c^{6} d^{4} e^{5} - 31500 \, a^{2} b^{3} c^{7} d^{4} e^{5} - 20790 \, a^{3} b c^{8} d^{4} e^{5} - b^{8} c^{4} d^{3} e^{6} + 16 \, a b^{6} c^{5} d^{3} e^{6} + 16284 \, a^{2} b^{4} c^{6} d^{3} e^{6} + 25036 \, a^{3} b^{2} c^{7} d^{3} e^{6} + 8984 \, a^{4} c^{8} d^{3} e^{6} + 6 \, b^{9} c^{3} d^{2} e^{7} - 96 \, a b^{7} c^{4} d^{2} e^{7} + 576 \, a^{2} b^{5} c^{5} d^{2} e^{7} - 17916 \, a^{3} b^{3} c^{6} d^{2} e^{7} - 12324 \, a^{4} b c^{7} d^{2} e^{7} - 18 \, b^{10} c^{2} d e^{8} + 276 \, a b^{8} c^{3} d e^{8} - 1536 \, a^{2} b^{6} c^{4} d e^{8} + 3456 \, a^{3} b^{4} c^{5} d e^{8} + 6654 \, a^{4} b^{2} c^{6} d e^{8} + 3858 \, a^{5} c^{7} d e^{8} + 18 \, a b^{9} c^{2} e^{9} - 264 \, a^{2} b^{7} c^{3} e^{9} + 1381 \, a^{3} b^{5} c^{4} e^{9} - 2809 \, a^{4} b^{3} c^{5} e^{9} - 777 \, a^{5} b c^{6} e^{9}\right)} x^{5} - {\left(1750 \, b^{3} c^{9} d^{9} + 7700 \, a b c^{10} d^{9} - 7875 \, b^{4} c^{8} d^{8} e - 34650 \, a b^{2} c^{9} d^{8} e + 13500 \, b^{5} c^{7} d^{7} e^{2} + 68400 \, a b^{3} c^{8} d^{7} e^{2} + 39600 \, a^{2} b c^{9} d^{7} e^{2} - 10500 \, b^{6} c^{6} d^{6} e^{3} - 77700 \, a b^{4} c^{7} d^{6} e^{3} - 138600 \, a^{2} b^{2} c^{8} d^{6} e^{3} + 3150 \, b^{7} c^{5} d^{5} e^{4} + 51660 \, a b^{5} c^{6} d^{5} e^{4} + 185220 \, a^{2} b^{3} c^{7} d^{5} e^{4} + 83160 \, a^{3} b c^{8} d^{5} e^{4} + 3 \, b^{8} c^{4} d^{4} e^{5} - 15798 \, a b^{6} c^{5} d^{4} e^{5} - 116262 \, a^{2} b^{4} c^{6} d^{4} e^{5} - 208668 \, a^{3} b^{2} c^{7} d^{4} e^{5} + 768 \, a^{4} c^{8} d^{4} e^{5} - 16 \, b^{9} c^{3} d^{3} e^{6} + 256 \, a b^{7} c^{4} d^{3} e^{6} + 29964 \, a^{2} b^{5} c^{5} d^{3} e^{6} + 163696 \, a^{3} b^{3} c^{6} d^{3} e^{6} + 88304 \, a^{4} b c^{7} d^{3} e^{6} + 36 \, b^{10} c^{2} d^{2} e^{7} - 552 \, a b^{8} c^{3} d^{2} e^{7} + 3072 \, a^{2} b^{6} c^{4} d^{2} e^{7} - 38412 \, a^{3} b^{4} c^{5} d^{2} e^{7} - 135528 \, a^{4} b^{2} c^{6} d^{2} e^{7} + 6144 \, a^{5} c^{7} d^{2} e^{7} - 48 \, b^{11} c d e^{8} + 624 \, a b^{9} c^{2} d e^{8} - 2304 \, a^{2} b^{7} c^{3} d e^{8} - 1536 \, a^{3} b^{5} c^{4} d e^{8} + 40326 \, a^{4} b^{3} c^{5} d e^{8} + 32436 \, a^{5} b c^{6} d e^{8} + 48 \, a b^{10} c e^{9} - 612 \, a^{2} b^{8} c^{2} e^{9} + 2272 \, a^{3} b^{6} c^{3} e^{9} + 473 \, a^{4} b^{4} c^{4} e^{9} - 20058 \, a^{5} b^{2} c^{5} e^{9} + 5376 \, a^{6} c^{6} e^{9}\right)} x^{4} - 4 \, {\left(42 \, b^{4} c^{8} d^{9} + 1414 \, a b^{2} c^{9} d^{9} + 1022 \, a^{2} c^{10} d^{9} - 189 \, b^{5} c^{7} d^{8} e - 6363 \, a b^{3} c^{8} d^{8} e - 4599 \, a^{2} b c^{9} d^{8} e + 324 \, b^{6} c^{6} d^{7} e^{2} + 11124 \, a b^{4} c^{7} d^{7} e^{2} + 15156 \, a^{2} b^{2} c^{8} d^{7} e^{2} + 5256 \, a^{3} c^{9} d^{7} e^{2} - 252 \, b^{7} c^{5} d^{6} e^{3} - 9240 \, a b^{5} c^{6} d^{6} e^{3} - 31584 \, a^{2} b^{3} c^{7} d^{6} e^{3} - 18396 \, a^{3} b c^{8} d^{6} e^{3} + 75 \, b^{8} c^{4} d^{5} e^{4} + 3462 \, a b^{6} c^{5} d^{5} e^{4} + 32778 \, a^{2} b^{4} c^{6} d^{5} e^{4} + 37500 \, a^{3} b^{2} c^{7} d^{5} e^{4} + 10884 \, a^{4} c^{8} d^{5} e^{4} + 3 \, b^{9} c^{3} d^{4} e^{5} - 426 \, a b^{7} c^{4} d^{4} e^{5} - 13572 \, a^{2} b^{5} c^{5} d^{4} e^{5} - 48144 \, a^{3} b^{3} c^{6} d^{4} e^{5} - 26826 \, a^{4} b c^{7} d^{4} e^{5} - 6 \, b^{10} c^{2} d^{3} e^{6} + 92 \, a b^{8} c^{3} d^{3} e^{6} + 244 \, a^{2} b^{6} c^{4} d^{3} e^{6} + 27108 \, a^{3} b^{4} c^{5} d^{3} e^{6} + 34852 \, a^{4} b^{2} c^{6} d^{3} e^{6} + 11240 \, a^{5} c^{7} d^{3} e^{6} + 6 \, b^{11} c d^{2} e^{7} - 78 \, a b^{9} c^{2} d^{2} e^{7} + 288 \, a^{2} b^{7} c^{3} d^{2} e^{7} - 564 \, a^{3} b^{5} c^{4} d^{2} e^{7} - 28524 \, a^{4} b^{3} c^{5} d^{2} e^{7} - 13788 \, a^{5} b c^{6} d^{2} e^{7} - 3 \, b^{12} d e^{8} + 12 \, a b^{10} c d e^{8} + 270 \, a^{2} b^{8} c^{2} d e^{8} - 2400 \, a^{3} b^{6} c^{3} d e^{8} + 7098 \, a^{4} b^{4} c^{4} d e^{8} + 8118 \, a^{5} b^{2} c^{5} d e^{8} + 4590 \, a^{6} c^{6} d e^{8} + 3 \, a b^{11} e^{9} - 15 \, a^{2} b^{9} c e^{9} - 204 \, a^{3} b^{7} c^{2} e^{9} + 1882 \, a^{4} b^{5} c^{3} e^{9} - 5089 \, a^{5} b^{3} c^{4} e^{9} + 393 \, a^{6} b c^{5} e^{9}\right)} x^{3} + 2 \, {\left(14 \, b^{5} c^{7} d^{9} - 392 \, a b^{3} c^{8} d^{9} - 3066 \, a^{2} b c^{9} d^{9} - 63 \, b^{6} c^{6} d^{8} e + 1764 \, a b^{4} c^{7} d^{8} e + 13797 \, a^{2} b^{2} c^{8} d^{8} e + 108 \, b^{7} c^{5} d^{7} e^{2} - 2952 \, a b^{5} c^{6} d^{7} e^{2} - 25668 \, a^{2} b^{3} c^{7} d^{7} e^{2} - 15768 \, a^{3} b c^{8} d^{7} e^{2} - 85 \, b^{8} c^{4} d^{6} e^{3} + 2116 \, a b^{6} c^{5} d^{6} e^{3} + 25356 \, a^{2} b^{4} c^{6} d^{6} e^{3} + 55444 \, a^{3} b^{2} c^{7} d^{6} e^{3} - 256 \, a^{4} c^{8} d^{6} e^{3} + 30 \, b^{9} c^{3} d^{5} e^{4} - 480 \, a b^{7} c^{4} d^{5} e^{4} - 13374 \, a^{2} b^{5} c^{5} d^{5} e^{4} - 71688 \, a^{3} b^{3} c^{6} d^{5} e^{4} - 31884 \, a^{4} b c^{7} d^{5} e^{4} - 9 \, b^{10} c^{2} d^{4} e^{5} + 12 \, a b^{8} c^{3} d^{4} e^{5} + 2382 \, a^{2} b^{6} c^{4} d^{4} e^{5} + 39906 \, a^{3} b^{4} c^{5} d^{4} e^{5} + 82014 \, a^{4} b^{2} c^{6} d^{4} e^{5} - 1536 \, a^{5} c^{7} d^{4} e^{5} + 8 \, b^{11} c d^{3} e^{6} - 104 \, a b^{9} c^{2} d^{3} e^{6} + 636 \, a^{2} b^{7} c^{3} d^{3} e^{6} - 6632 \, a^{3} b^{5} c^{4} d^{3} e^{6} - 63988 \, a^{4} b^{3} c^{5} d^{3} e^{6} - 30648 \, a^{5} b c^{6} d^{3} e^{6} - 3 \, b^{12} d^{2} e^{7} + 12 \, a b^{10} c d^{2} e^{7} + 270 \, a^{2} b^{8} c^{2} d^{2} e^{7} - 2652 \, a^{3} b^{6} c^{3} d^{2} e^{7} + 13776 \, a^{4} b^{4} c^{4} d^{2} e^{7} + 50580 \, a^{5} b^{2} c^{5} d^{2} e^{7} - 4608 \, a^{6} c^{6} d^{2} e^{7} + 24 \, a b^{11} d e^{8} - 312 \, a^{2} b^{9} c d e^{8} + 1152 \, a^{3} b^{7} c^{2} d e^{8} + 894 \, a^{4} b^{5} c^{3} d e^{8} - 15816 \, a^{5} b^{3} c^{4} d e^{8} - 9162 \, a^{6} b c^{5} d e^{8} - 21 \, a^{2} b^{10} e^{9} + 274 \, a^{3} b^{8} c e^{9} - 1078 \, a^{4} b^{6} c^{2} e^{9} + 150 \, a^{5} b^{4} c^{3} e^{9} + 7525 \, a^{6} b^{2} c^{4} e^{9} - 3328 \, a^{7} c^{5} e^{9}\right)} x^{2} - 4 \, {\left(2 \, b^{6} c^{6} d^{9} - 38 \, a b^{4} c^{7} d^{9} + 348 \, a^{2} b^{2} c^{8} d^{9} + 558 \, a^{3} c^{9} d^{9} - 9 \, b^{7} c^{5} d^{8} e + 171 \, a b^{5} c^{6} d^{8} e - 1566 \, a^{2} b^{3} c^{7} d^{8} e - 2511 \, a^{3} b c^{8} d^{8} e + 15 \, b^{8} c^{4} d^{7} e^{2} - 276 \, a b^{6} c^{5} d^{7} e^{2} + 2448 \, a^{2} b^{4} c^{6} d^{7} e^{2} + 6204 \, a^{3} b^{2} c^{7} d^{7} e^{2} + 2760 \, a^{4} c^{8} d^{7} e^{2} - 10 \, b^{9} c^{3} d^{6} e^{3} + 160 \, a b^{7} c^{4} d^{6} e^{3} - 1212 \, a^{2} b^{5} c^{5} d^{6} e^{3} - 10124 \, a^{3} b^{3} c^{6} d^{6} e^{3} - 9532 \, a^{4} b c^{7} d^{6} e^{3} + 30 \, a b^{8} c^{3} d^{5} e^{4} - 480 \, a^{2} b^{6} c^{4} d^{5} e^{4} + 8802 \, a^{3} b^{4} c^{5} d^{5} e^{4} + 15504 \, a^{4} b^{2} c^{6} d^{5} e^{4} + 5412 \, a^{5} c^{7} d^{5} e^{4} + 3 \, b^{11} c d^{4} e^{5} - 57 \, a b^{9} c^{2} d^{4} e^{5} + 432 \, a^{2} b^{7} c^{3} d^{4} e^{5} - 2010 \, a^{3} b^{5} c^{4} d^{4} e^{5} - 15954 \, a^{4} b^{3} c^{5} d^{4} e^{5} - 12762 \, a^{5} b c^{6} d^{4} e^{5} - b^{12} d^{3} e^{6} + 4 \, a b^{10} c d^{3} e^{6} + 126 \, a^{2} b^{8} c^{2} d^{3} e^{6} - 1460 \, a^{3} b^{6} c^{3} d^{3} e^{6} + 8048 \, a^{4} b^{4} c^{4} d^{3} e^{6} + 12684 \, a^{5} b^{2} c^{5} d^{3} e^{6} + 5160 \, a^{6} c^{6} d^{3} e^{6} + 6 \, a b^{11} d^{2} e^{7} - 78 \, a^{2} b^{9} c d^{2} e^{7} + 252 \, a^{3} b^{7} c^{2} d^{2} e^{7} + 876 \, a^{4} b^{5} c^{3} d^{2} e^{7} - 9336 \, a^{5} b^{3} c^{4} d^{2} e^{7} - 5436 \, a^{6} b c^{5} d^{2} e^{7} - 18 \, a^{2} b^{10} d e^{8} + 276 \, a^{3} b^{8} c d e^{8} - 1518 \, a^{4} b^{6} c^{2} d e^{8} + 3114 \, a^{5} b^{4} c^{3} d e^{8} + 1596 \, a^{6} b^{2} c^{4} d e^{8} + 1950 \, a^{7} c^{5} d e^{8} + 13 \, a^{3} b^{9} e^{9} - 196 \, a^{4} b^{7} c e^{9} + 1068 \, a^{5} b^{5} c^{2} e^{9} - 2324 \, a^{6} b^{3} c^{3} e^{9} + 689 \, a^{7} b c^{4} e^{9}\right)} x}{12 \, {\left(c d^{2} - b d e + a e^{2}\right)}^{5} {\left(c x^{2} + b x + a\right)}^{4} {\left(b^{2} - 4 \, a c\right)}^{4}}"," ",0,"-1/2*e^9*log(c*x^2 + b*x + a)/(c^5*d^10 - 5*b*c^4*d^9*e + 10*b^2*c^3*d^8*e^2 + 5*a*c^4*d^8*e^2 - 10*b^3*c^2*d^7*e^3 - 20*a*b*c^3*d^7*e^3 + 5*b^4*c*d^6*e^4 + 30*a*b^2*c^2*d^6*e^4 + 10*a^2*c^3*d^6*e^4 - b^5*d^5*e^5 - 20*a*b^3*c*d^5*e^5 - 30*a^2*b*c^2*d^5*e^5 + 5*a*b^4*d^4*e^6 + 30*a^2*b^2*c*d^4*e^6 + 10*a^3*c^2*d^4*e^6 - 10*a^2*b^3*d^3*e^7 - 20*a^3*b*c*d^3*e^7 + 10*a^3*b^2*d^2*e^8 + 5*a^4*c*d^2*e^8 - 5*a^4*b*d*e^9 + a^5*e^10) + e^10*log(abs(x*e + d))/(c^5*d^10*e - 5*b*c^4*d^9*e^2 + 10*b^2*c^3*d^8*e^3 + 5*a*c^4*d^8*e^3 - 10*b^3*c^2*d^7*e^4 - 20*a*b*c^3*d^7*e^4 + 5*b^4*c*d^6*e^5 + 30*a*b^2*c^2*d^6*e^5 + 10*a^2*c^3*d^6*e^5 - b^5*d^5*e^6 - 20*a*b^3*c*d^5*e^6 - 30*a^2*b*c^2*d^5*e^6 + 5*a*b^4*d^4*e^7 + 30*a^2*b^2*c*d^4*e^7 + 10*a^3*c^2*d^4*e^7 - 10*a^2*b^3*d^3*e^8 - 20*a^3*b*c*d^3*e^8 + 10*a^3*b^2*d^2*e^9 + 5*a^4*c*d^2*e^9 - 5*a^4*b*d*e^10 + a^5*e^11) + (140*c^9*d^9 - 630*b*c^8*d^8*e + 1080*b^2*c^7*d^7*e^2 + 720*a*c^8*d^7*e^2 - 840*b^3*c^6*d^6*e^3 - 2520*a*b*c^7*d^6*e^3 + 252*b^4*c^5*d^5*e^4 + 3024*a*b^2*c^6*d^5*e^4 + 1512*a^2*c^7*d^5*e^4 - 1260*a*b^3*c^5*d^4*e^5 - 3780*a^2*b*c^6*d^4*e^5 + 2520*a^2*b^2*c^5*d^3*e^6 + 1680*a^3*c^6*d^3*e^6 - 2520*a^3*b*c^5*d^2*e^7 + 1260*a^4*c^5*d*e^8 - b^9*e^9 + 18*a*b^7*c*e^9 - 126*a^2*b^5*c^2*e^9 + 420*a^3*b^3*c^3*e^9 - 630*a^4*b*c^4*e^9)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^8*c^5*d^10 - 16*a*b^6*c^6*d^10 + 96*a^2*b^4*c^7*d^10 - 256*a^3*b^2*c^8*d^10 + 256*a^4*c^9*d^10 - 5*b^9*c^4*d^9*e + 80*a*b^7*c^5*d^9*e - 480*a^2*b^5*c^6*d^9*e + 1280*a^3*b^3*c^7*d^9*e - 1280*a^4*b*c^8*d^9*e + 10*b^10*c^3*d^8*e^2 - 155*a*b^8*c^4*d^8*e^2 + 880*a^2*b^6*c^5*d^8*e^2 - 2080*a^3*b^4*c^6*d^8*e^2 + 1280*a^4*b^2*c^7*d^8*e^2 + 1280*a^5*c^8*d^8*e^2 - 10*b^11*c^2*d^7*e^3 + 140*a*b^9*c^3*d^7*e^3 - 640*a^2*b^7*c^4*d^7*e^3 + 640*a^3*b^5*c^5*d^7*e^3 + 2560*a^4*b^3*c^6*d^7*e^3 - 5120*a^5*b*c^7*d^7*e^3 + 5*b^12*c*d^6*e^4 - 50*a*b^10*c^2*d^6*e^4 + 10*a^2*b^8*c^3*d^6*e^4 + 1440*a^3*b^6*c^4*d^6*e^4 - 5440*a^4*b^4*c^5*d^6*e^4 + 5120*a^5*b^2*c^6*d^6*e^4 + 2560*a^6*c^7*d^6*e^4 - b^13*d^5*e^5 - 4*a*b^11*c*d^5*e^5 + 194*a^2*b^9*c^2*d^5*e^5 - 1184*a^3*b^7*c^3*d^5*e^5 + 1984*a^4*b^5*c^4*d^5*e^5 + 2560*a^5*b^3*c^5*d^5*e^5 - 7680*a^6*b*c^6*d^5*e^5 + 5*a*b^12*d^4*e^6 - 50*a^2*b^10*c*d^4*e^6 + 10*a^3*b^8*c^2*d^4*e^6 + 1440*a^4*b^6*c^3*d^4*e^6 - 5440*a^5*b^4*c^4*d^4*e^6 + 5120*a^6*b^2*c^5*d^4*e^6 + 2560*a^7*c^6*d^4*e^6 - 10*a^2*b^11*d^3*e^7 + 140*a^3*b^9*c*d^3*e^7 - 640*a^4*b^7*c^2*d^3*e^7 + 640*a^5*b^5*c^3*d^3*e^7 + 2560*a^6*b^3*c^4*d^3*e^7 - 5120*a^7*b*c^5*d^3*e^7 + 10*a^3*b^10*d^2*e^8 - 155*a^4*b^8*c*d^2*e^8 + 880*a^5*b^6*c^2*d^2*e^8 - 2080*a^6*b^4*c^3*d^2*e^8 + 1280*a^7*b^2*c^4*d^2*e^8 + 1280*a^8*c^5*d^2*e^8 - 5*a^4*b^9*d*e^9 + 80*a^5*b^7*c*d*e^9 - 480*a^6*b^5*c^2*d*e^9 + 1280*a^7*b^3*c^3*d*e^9 - 1280*a^8*b*c^4*d*e^9 + a^5*b^8*e^10 - 16*a^6*b^6*c*e^10 + 96*a^7*b^4*c^2*e^10 - 256*a^8*b^2*c^3*e^10 + 256*a^9*c^4*e^10)*sqrt(-b^2 + 4*a*c)) - 1/12*(3*b^7*c^5*d^9 - 50*a*b^5*c^6*d^9 + 326*a^2*b^3*c^7*d^9 - 1116*a^3*b*c^8*d^9 - 15*b^8*c^4*d^8*e + 249*a*b^6*c^5*d^8*e - 1611*a^2*b^4*c^6*d^8*e + 5406*a^3*b^2*c^7*d^8*e - 384*a^4*c^8*d^8*e + 30*b^9*c^3*d^7*e^2 - 480*a*b^7*c^4*d^7*e^2 + 2916*a^2*b^5*c^5*d^7*e^2 - 8688*a^3*b^3*c^6*d^7*e^2 - 3984*a^4*b*c^7*d^7*e^2 - 30*b^10*c^2*d^6*e^3 + 430*a*b^8*c^3*d^6*e^3 - 2080*a^2*b^6*c^4*d^6*e^3 + 3132*a^3*b^4*c^5*d^6*e^3 + 19064*a^4*b^2*c^6*d^6*e^3 - 2048*a^5*c^7*d^6*e^3 + 15*b^11*c*d^5*e^4 - 150*a*b^9*c^2*d^5*e^4 + 4800*a^3*b^5*c^4*d^5*e^4 - 25500*a^4*b^3*c^5*d^5*e^4 - 4680*a^5*b*c^6*d^5*e^4 - 3*b^12*d^4*e^5 - 15*a*b^10*c*d^4*e^5 + 639*a^2*b^8*c^2*d^4*e^5 - 3984*a^3*b^6*c^3*d^4*e^5 + 7962*a^4*b^4*c^4*d^4*e^5 + 25524*a^5*b^2*c^5*d^4*e^5 - 4608*a^6*c^6*d^4*e^5 + 16*a*b^11*d^3*e^6 - 154*a^2*b^9*c*d^3*e^6 - 96*a^3*b^7*c^2*d^3*e^6 + 5780*a^4*b^5*c^3*d^3*e^6 - 24368*a^5*b^3*c^4*d^3*e^6 - 1104*a^6*b*c^5*d^3*e^6 - 36*a^2*b^10*d^2*e^7 + 498*a^3*b^8*c*d^2*e^7 - 2172*a^4*b^6*c^2*d^2*e^7 + 1044*a^5*b^4*c^3*d^2*e^7 + 17016*a^6*b^2*c^4*d^2*e^7 - 6144*a^7*c^5*d^2*e^7 + 48*a^3*b^9*d*e^8 - 741*a^4*b^7*c*d*e^8 + 4158*a^5*b^5*c^2*d*e^8 - 9354*a^6*b^3*c^3*d*e^8 + 2244*a^7*b*c^4*d*e^8 - 25*a^4*b^8*e^9 + 385*a^5*b^6*c*e^9 - 2175*a^6*b^4*c^2*e^9 + 5150*a^7*b^2*c^3*e^9 - 3200*a^8*c^4*e^9 - 12*(70*c^12*d^9 - 315*b*c^11*d^8*e + 540*b^2*c^10*d^7*e^2 + 360*a*c^11*d^7*e^2 - 420*b^3*c^9*d^6*e^3 - 1260*a*b*c^10*d^6*e^3 + 126*b^4*c^8*d^5*e^4 + 1512*a*b^2*c^9*d^5*e^4 + 756*a^2*c^10*d^5*e^4 - 630*a*b^3*c^8*d^4*e^5 - 1890*a^2*b*c^9*d^4*e^5 + 1260*a^2*b^2*c^8*d^3*e^6 + 840*a^3*c^9*d^3*e^6 - 1260*a^3*b*c^8*d^2*e^7 - b^8*c^4*d*e^8 + 16*a*b^6*c^5*d*e^8 - 96*a^2*b^4*c^6*d*e^8 + 256*a^3*b^2*c^7*d*e^8 + 374*a^4*c^8*d*e^8 + a*b^7*c^4*e^9 - 15*a^2*b^5*c^5*e^9 + 82*a^3*b^3*c^6*e^9 - 187*a^4*b*c^7*e^9)*x^7 - 6*(490*b*c^11*d^9 - 2205*b^2*c^10*d^8*e + 3780*b^3*c^9*d^7*e^2 + 2520*a*b*c^10*d^7*e^2 - 2940*b^4*c^8*d^6*e^3 - 8820*a*b^2*c^9*d^6*e^3 + 882*b^5*c^7*d^5*e^4 + 10584*a*b^3*c^8*d^5*e^4 + 5292*a^2*b*c^9*d^5*e^4 - 4410*a*b^4*c^7*d^4*e^5 - 13230*a^2*b^2*c^8*d^4*e^5 + 8820*a^2*b^3*c^7*d^3*e^6 + 5880*a^3*b*c^8*d^3*e^6 + b^8*c^4*d^2*e^7 - 16*a*b^6*c^5*d^2*e^7 + 96*a^2*b^4*c^6*d^2*e^7 - 9076*a^3*b^2*c^7*d^2*e^7 + 256*a^4*c^8*d^2*e^7 - 8*b^9*c^3*d*e^8 + 128*a*b^7*c^4*d*e^8 - 768*a^2*b^5*c^5*d*e^8 + 2048*a^3*b^3*c^6*d*e^8 + 2362*a^4*b*c^7*d*e^8 + 8*a*b^8*c^3*e^9 - 121*a^2*b^6*c^4*e^9 + 670*a^3*b^4*c^5*e^9 - 1565*a^4*b^2*c^6*e^9 + 256*a^5*c^7*e^9)*x^6 - 4*(910*b^2*c^10*d^9 + 770*a*c^11*d^9 - 4095*b^3*c^9*d^8*e - 3465*a*b*c^10*d^8*e + 7020*b^4*c^8*d^7*e^2 + 10620*a*b^2*c^9*d^7*e^2 + 3960*a^2*c^10*d^7*e^2 - 5460*b^5*c^7*d^6*e^3 - 21000*a*b^3*c^8*d^6*e^3 - 13860*a^2*b*c^9*d^6*e^3 + 1638*b^6*c^6*d^5*e^4 + 21042*a*b^4*c^7*d^5*e^4 + 26460*a^2*b^2*c^8*d^5*e^4 + 8316*a^3*c^9*d^5*e^4 - 8190*a*b^5*c^6*d^4*e^5 - 31500*a^2*b^3*c^7*d^4*e^5 - 20790*a^3*b*c^8*d^4*e^5 - b^8*c^4*d^3*e^6 + 16*a*b^6*c^5*d^3*e^6 + 16284*a^2*b^4*c^6*d^3*e^6 + 25036*a^3*b^2*c^7*d^3*e^6 + 8984*a^4*c^8*d^3*e^6 + 6*b^9*c^3*d^2*e^7 - 96*a*b^7*c^4*d^2*e^7 + 576*a^2*b^5*c^5*d^2*e^7 - 17916*a^3*b^3*c^6*d^2*e^7 - 12324*a^4*b*c^7*d^2*e^7 - 18*b^10*c^2*d*e^8 + 276*a*b^8*c^3*d*e^8 - 1536*a^2*b^6*c^4*d*e^8 + 3456*a^3*b^4*c^5*d*e^8 + 6654*a^4*b^2*c^6*d*e^8 + 3858*a^5*c^7*d*e^8 + 18*a*b^9*c^2*e^9 - 264*a^2*b^7*c^3*e^9 + 1381*a^3*b^5*c^4*e^9 - 2809*a^4*b^3*c^5*e^9 - 777*a^5*b*c^6*e^9)*x^5 - (1750*b^3*c^9*d^9 + 7700*a*b*c^10*d^9 - 7875*b^4*c^8*d^8*e - 34650*a*b^2*c^9*d^8*e + 13500*b^5*c^7*d^7*e^2 + 68400*a*b^3*c^8*d^7*e^2 + 39600*a^2*b*c^9*d^7*e^2 - 10500*b^6*c^6*d^6*e^3 - 77700*a*b^4*c^7*d^6*e^3 - 138600*a^2*b^2*c^8*d^6*e^3 + 3150*b^7*c^5*d^5*e^4 + 51660*a*b^5*c^6*d^5*e^4 + 185220*a^2*b^3*c^7*d^5*e^4 + 83160*a^3*b*c^8*d^5*e^4 + 3*b^8*c^4*d^4*e^5 - 15798*a*b^6*c^5*d^4*e^5 - 116262*a^2*b^4*c^6*d^4*e^5 - 208668*a^3*b^2*c^7*d^4*e^5 + 768*a^4*c^8*d^4*e^5 - 16*b^9*c^3*d^3*e^6 + 256*a*b^7*c^4*d^3*e^6 + 29964*a^2*b^5*c^5*d^3*e^6 + 163696*a^3*b^3*c^6*d^3*e^6 + 88304*a^4*b*c^7*d^3*e^6 + 36*b^10*c^2*d^2*e^7 - 552*a*b^8*c^3*d^2*e^7 + 3072*a^2*b^6*c^4*d^2*e^7 - 38412*a^3*b^4*c^5*d^2*e^7 - 135528*a^4*b^2*c^6*d^2*e^7 + 6144*a^5*c^7*d^2*e^7 - 48*b^11*c*d*e^8 + 624*a*b^9*c^2*d*e^8 - 2304*a^2*b^7*c^3*d*e^8 - 1536*a^3*b^5*c^4*d*e^8 + 40326*a^4*b^3*c^5*d*e^8 + 32436*a^5*b*c^6*d*e^8 + 48*a*b^10*c*e^9 - 612*a^2*b^8*c^2*e^9 + 2272*a^3*b^6*c^3*e^9 + 473*a^4*b^4*c^4*e^9 - 20058*a^5*b^2*c^5*e^9 + 5376*a^6*c^6*e^9)*x^4 - 4*(42*b^4*c^8*d^9 + 1414*a*b^2*c^9*d^9 + 1022*a^2*c^10*d^9 - 189*b^5*c^7*d^8*e - 6363*a*b^3*c^8*d^8*e - 4599*a^2*b*c^9*d^8*e + 324*b^6*c^6*d^7*e^2 + 11124*a*b^4*c^7*d^7*e^2 + 15156*a^2*b^2*c^8*d^7*e^2 + 5256*a^3*c^9*d^7*e^2 - 252*b^7*c^5*d^6*e^3 - 9240*a*b^5*c^6*d^6*e^3 - 31584*a^2*b^3*c^7*d^6*e^3 - 18396*a^3*b*c^8*d^6*e^3 + 75*b^8*c^4*d^5*e^4 + 3462*a*b^6*c^5*d^5*e^4 + 32778*a^2*b^4*c^6*d^5*e^4 + 37500*a^3*b^2*c^7*d^5*e^4 + 10884*a^4*c^8*d^5*e^4 + 3*b^9*c^3*d^4*e^5 - 426*a*b^7*c^4*d^4*e^5 - 13572*a^2*b^5*c^5*d^4*e^5 - 48144*a^3*b^3*c^6*d^4*e^5 - 26826*a^4*b*c^7*d^4*e^5 - 6*b^10*c^2*d^3*e^6 + 92*a*b^8*c^3*d^3*e^6 + 244*a^2*b^6*c^4*d^3*e^6 + 27108*a^3*b^4*c^5*d^3*e^6 + 34852*a^4*b^2*c^6*d^3*e^6 + 11240*a^5*c^7*d^3*e^6 + 6*b^11*c*d^2*e^7 - 78*a*b^9*c^2*d^2*e^7 + 288*a^2*b^7*c^3*d^2*e^7 - 564*a^3*b^5*c^4*d^2*e^7 - 28524*a^4*b^3*c^5*d^2*e^7 - 13788*a^5*b*c^6*d^2*e^7 - 3*b^12*d*e^8 + 12*a*b^10*c*d*e^8 + 270*a^2*b^8*c^2*d*e^8 - 2400*a^3*b^6*c^3*d*e^8 + 7098*a^4*b^4*c^4*d*e^8 + 8118*a^5*b^2*c^5*d*e^8 + 4590*a^6*c^6*d*e^8 + 3*a*b^11*e^9 - 15*a^2*b^9*c*e^9 - 204*a^3*b^7*c^2*e^9 + 1882*a^4*b^5*c^3*e^9 - 5089*a^5*b^3*c^4*e^9 + 393*a^6*b*c^5*e^9)*x^3 + 2*(14*b^5*c^7*d^9 - 392*a*b^3*c^8*d^9 - 3066*a^2*b*c^9*d^9 - 63*b^6*c^6*d^8*e + 1764*a*b^4*c^7*d^8*e + 13797*a^2*b^2*c^8*d^8*e + 108*b^7*c^5*d^7*e^2 - 2952*a*b^5*c^6*d^7*e^2 - 25668*a^2*b^3*c^7*d^7*e^2 - 15768*a^3*b*c^8*d^7*e^2 - 85*b^8*c^4*d^6*e^3 + 2116*a*b^6*c^5*d^6*e^3 + 25356*a^2*b^4*c^6*d^6*e^3 + 55444*a^3*b^2*c^7*d^6*e^3 - 256*a^4*c^8*d^6*e^3 + 30*b^9*c^3*d^5*e^4 - 480*a*b^7*c^4*d^5*e^4 - 13374*a^2*b^5*c^5*d^5*e^4 - 71688*a^3*b^3*c^6*d^5*e^4 - 31884*a^4*b*c^7*d^5*e^4 - 9*b^10*c^2*d^4*e^5 + 12*a*b^8*c^3*d^4*e^5 + 2382*a^2*b^6*c^4*d^4*e^5 + 39906*a^3*b^4*c^5*d^4*e^5 + 82014*a^4*b^2*c^6*d^4*e^5 - 1536*a^5*c^7*d^4*e^5 + 8*b^11*c*d^3*e^6 - 104*a*b^9*c^2*d^3*e^6 + 636*a^2*b^7*c^3*d^3*e^6 - 6632*a^3*b^5*c^4*d^3*e^6 - 63988*a^4*b^3*c^5*d^3*e^6 - 30648*a^5*b*c^6*d^3*e^6 - 3*b^12*d^2*e^7 + 12*a*b^10*c*d^2*e^7 + 270*a^2*b^8*c^2*d^2*e^7 - 2652*a^3*b^6*c^3*d^2*e^7 + 13776*a^4*b^4*c^4*d^2*e^7 + 50580*a^5*b^2*c^5*d^2*e^7 - 4608*a^6*c^6*d^2*e^7 + 24*a*b^11*d*e^8 - 312*a^2*b^9*c*d*e^8 + 1152*a^3*b^7*c^2*d*e^8 + 894*a^4*b^5*c^3*d*e^8 - 15816*a^5*b^3*c^4*d*e^8 - 9162*a^6*b*c^5*d*e^8 - 21*a^2*b^10*e^9 + 274*a^3*b^8*c*e^9 - 1078*a^4*b^6*c^2*e^9 + 150*a^5*b^4*c^3*e^9 + 7525*a^6*b^2*c^4*e^9 - 3328*a^7*c^5*e^9)*x^2 - 4*(2*b^6*c^6*d^9 - 38*a*b^4*c^7*d^9 + 348*a^2*b^2*c^8*d^9 + 558*a^3*c^9*d^9 - 9*b^7*c^5*d^8*e + 171*a*b^5*c^6*d^8*e - 1566*a^2*b^3*c^7*d^8*e - 2511*a^3*b*c^8*d^8*e + 15*b^8*c^4*d^7*e^2 - 276*a*b^6*c^5*d^7*e^2 + 2448*a^2*b^4*c^6*d^7*e^2 + 6204*a^3*b^2*c^7*d^7*e^2 + 2760*a^4*c^8*d^7*e^2 - 10*b^9*c^3*d^6*e^3 + 160*a*b^7*c^4*d^6*e^3 - 1212*a^2*b^5*c^5*d^6*e^3 - 10124*a^3*b^3*c^6*d^6*e^3 - 9532*a^4*b*c^7*d^6*e^3 + 30*a*b^8*c^3*d^5*e^4 - 480*a^2*b^6*c^4*d^5*e^4 + 8802*a^3*b^4*c^5*d^5*e^4 + 15504*a^4*b^2*c^6*d^5*e^4 + 5412*a^5*c^7*d^5*e^4 + 3*b^11*c*d^4*e^5 - 57*a*b^9*c^2*d^4*e^5 + 432*a^2*b^7*c^3*d^4*e^5 - 2010*a^3*b^5*c^4*d^4*e^5 - 15954*a^4*b^3*c^5*d^4*e^5 - 12762*a^5*b*c^6*d^4*e^5 - b^12*d^3*e^6 + 4*a*b^10*c*d^3*e^6 + 126*a^2*b^8*c^2*d^3*e^6 - 1460*a^3*b^6*c^3*d^3*e^6 + 8048*a^4*b^4*c^4*d^3*e^6 + 12684*a^5*b^2*c^5*d^3*e^6 + 5160*a^6*c^6*d^3*e^6 + 6*a*b^11*d^2*e^7 - 78*a^2*b^9*c*d^2*e^7 + 252*a^3*b^7*c^2*d^2*e^7 + 876*a^4*b^5*c^3*d^2*e^7 - 9336*a^5*b^3*c^4*d^2*e^7 - 5436*a^6*b*c^5*d^2*e^7 - 18*a^2*b^10*d*e^8 + 276*a^3*b^8*c*d*e^8 - 1518*a^4*b^6*c^2*d*e^8 + 3114*a^5*b^4*c^3*d*e^8 + 1596*a^6*b^2*c^4*d*e^8 + 1950*a^7*c^5*d*e^8 + 13*a^3*b^9*e^9 - 196*a^4*b^7*c*e^9 + 1068*a^5*b^5*c^2*e^9 - 2324*a^6*b^3*c^3*e^9 + 689*a^7*b*c^4*e^9)*x)/((c*d^2 - b*d*e + a*e^2)^5*(c*x^2 + b*x + a)^4*(b^2 - 4*a*c)^4)","B",0
2228,1,8036,0,3.055139," ","integrate(1/(e*x+d)^2/(c*x^2+b*x+a)^5,x, algorithm=""giac"")","\frac{5 \, {\left(28 \, c^{10} d^{10} e^{2} - 140 \, b c^{9} d^{9} e^{3} + 270 \, b^{2} c^{8} d^{8} e^{4} + 180 \, a c^{9} d^{8} e^{4} - 240 \, b^{3} c^{7} d^{7} e^{5} - 720 \, a b c^{8} d^{7} e^{5} + 84 \, b^{4} c^{6} d^{6} e^{6} + 1008 \, a b^{2} c^{7} d^{6} e^{6} + 504 \, a^{2} c^{8} d^{6} e^{6} - 504 \, a b^{3} c^{6} d^{5} e^{7} - 1512 \, a^{2} b c^{7} d^{5} e^{7} + 1260 \, a^{2} b^{2} c^{6} d^{4} e^{8} + 840 \, a^{3} c^{7} d^{4} e^{8} - 1680 \, a^{3} b c^{6} d^{3} e^{9} + 1260 \, a^{4} c^{6} d^{2} e^{10} - 2 \, b^{9} c d e^{11} + 36 \, a b^{7} c^{2} d e^{11} - 252 \, a^{2} b^{5} c^{3} d e^{11} + 840 \, a^{3} b^{3} c^{4} d e^{11} - 1260 \, a^{4} b c^{5} d e^{11} + b^{10} e^{12} - 18 \, a b^{8} c e^{12} + 126 \, a^{2} b^{6} c^{2} e^{12} - 420 \, a^{3} b^{4} c^{3} e^{12} + 630 \, a^{4} b^{2} c^{4} e^{12} - 252 \, a^{5} c^{5} e^{12}\right)} \arctan\left(\frac{{\left(2 \, c d - \frac{2 \, c d^{2}}{x e + d} - b e + \frac{2 \, b d e}{x e + d} - \frac{2 \, a e^{2}}{x e + d}\right)} e^{\left(-1\right)}}{\sqrt{-b^{2} + 4 \, a c}}\right) e^{\left(-2\right)}}{{\left(b^{8} c^{6} d^{12} - 16 \, a b^{6} c^{7} d^{12} + 96 \, a^{2} b^{4} c^{8} d^{12} - 256 \, a^{3} b^{2} c^{9} d^{12} + 256 \, a^{4} c^{10} d^{12} - 6 \, b^{9} c^{5} d^{11} e + 96 \, a b^{7} c^{6} d^{11} e - 576 \, a^{2} b^{5} c^{7} d^{11} e + 1536 \, a^{3} b^{3} c^{8} d^{11} e - 1536 \, a^{4} b c^{9} d^{11} e + 15 \, b^{10} c^{4} d^{10} e^{2} - 234 \, a b^{8} c^{5} d^{10} e^{2} + 1344 \, a^{2} b^{6} c^{6} d^{10} e^{2} - 3264 \, a^{3} b^{4} c^{7} d^{10} e^{2} + 2304 \, a^{4} b^{2} c^{8} d^{10} e^{2} + 1536 \, a^{5} c^{9} d^{10} e^{2} - 20 \, b^{11} c^{3} d^{9} e^{3} + 290 \, a b^{9} c^{4} d^{9} e^{3} - 1440 \, a^{2} b^{7} c^{5} d^{9} e^{3} + 2240 \, a^{3} b^{5} c^{6} d^{9} e^{3} + 2560 \, a^{4} b^{3} c^{7} d^{9} e^{3} - 7680 \, a^{5} b c^{8} d^{9} e^{3} + 15 \, b^{12} c^{2} d^{8} e^{4} - 180 \, a b^{10} c^{3} d^{8} e^{4} + 495 \, a^{2} b^{8} c^{4} d^{8} e^{4} + 1680 \, a^{3} b^{6} c^{5} d^{8} e^{4} - 10080 \, a^{4} b^{4} c^{6} d^{8} e^{4} + 11520 \, a^{5} b^{2} c^{7} d^{8} e^{4} + 3840 \, a^{6} c^{8} d^{8} e^{4} - 6 \, b^{13} c d^{7} e^{5} + 36 \, a b^{11} c^{2} d^{7} e^{5} + 324 \, a^{2} b^{9} c^{3} d^{7} e^{5} - 3264 \, a^{3} b^{7} c^{4} d^{7} e^{5} + 8064 \, a^{4} b^{5} c^{5} d^{7} e^{5} - 15360 \, a^{6} b c^{7} d^{7} e^{5} + b^{14} d^{6} e^{6} + 14 \, a b^{12} c d^{6} e^{6} - 294 \, a^{2} b^{10} c^{2} d^{6} e^{6} + 1204 \, a^{3} b^{8} c^{3} d^{6} e^{6} + 896 \, a^{4} b^{6} c^{4} d^{6} e^{6} - 13440 \, a^{5} b^{4} c^{5} d^{6} e^{6} + 17920 \, a^{6} b^{2} c^{6} d^{6} e^{6} + 5120 \, a^{7} c^{7} d^{6} e^{6} - 6 \, a b^{13} d^{5} e^{7} + 36 \, a^{2} b^{11} c d^{5} e^{7} + 324 \, a^{3} b^{9} c^{2} d^{5} e^{7} - 3264 \, a^{4} b^{7} c^{3} d^{5} e^{7} + 8064 \, a^{5} b^{5} c^{4} d^{5} e^{7} - 15360 \, a^{7} b c^{6} d^{5} e^{7} + 15 \, a^{2} b^{12} d^{4} e^{8} - 180 \, a^{3} b^{10} c d^{4} e^{8} + 495 \, a^{4} b^{8} c^{2} d^{4} e^{8} + 1680 \, a^{5} b^{6} c^{3} d^{4} e^{8} - 10080 \, a^{6} b^{4} c^{4} d^{4} e^{8} + 11520 \, a^{7} b^{2} c^{5} d^{4} e^{8} + 3840 \, a^{8} c^{6} d^{4} e^{8} - 20 \, a^{3} b^{11} d^{3} e^{9} + 290 \, a^{4} b^{9} c d^{3} e^{9} - 1440 \, a^{5} b^{7} c^{2} d^{3} e^{9} + 2240 \, a^{6} b^{5} c^{3} d^{3} e^{9} + 2560 \, a^{7} b^{3} c^{4} d^{3} e^{9} - 7680 \, a^{8} b c^{5} d^{3} e^{9} + 15 \, a^{4} b^{10} d^{2} e^{10} - 234 \, a^{5} b^{8} c d^{2} e^{10} + 1344 \, a^{6} b^{6} c^{2} d^{2} e^{10} - 3264 \, a^{7} b^{4} c^{3} d^{2} e^{10} + 2304 \, a^{8} b^{2} c^{4} d^{2} e^{10} + 1536 \, a^{9} c^{5} d^{2} e^{10} - 6 \, a^{5} b^{9} d e^{11} + 96 \, a^{6} b^{7} c d e^{11} - 576 \, a^{7} b^{5} c^{2} d e^{11} + 1536 \, a^{8} b^{3} c^{3} d e^{11} - 1536 \, a^{9} b c^{4} d e^{11} + a^{6} b^{8} e^{12} - 16 \, a^{7} b^{6} c e^{12} + 96 \, a^{8} b^{4} c^{2} e^{12} - 256 \, a^{9} b^{2} c^{3} e^{12} + 256 \, a^{10} c^{4} e^{12}\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{5 \, {\left(2 \, c d e^{9} - b e^{10}\right)} \log\left(c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{b e}{x e + d} - \frac{b d e}{{\left(x e + d\right)}^{2}} + \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right)}{2 \, {\left(c^{6} d^{12} - 6 \, b c^{5} d^{11} e + 15 \, b^{2} c^{4} d^{10} e^{2} + 6 \, a c^{5} d^{10} e^{2} - 20 \, b^{3} c^{3} d^{9} e^{3} - 30 \, a b c^{4} d^{9} e^{3} + 15 \, b^{4} c^{2} d^{8} e^{4} + 60 \, a b^{2} c^{3} d^{8} e^{4} + 15 \, a^{2} c^{4} d^{8} e^{4} - 6 \, b^{5} c d^{7} e^{5} - 60 \, a b^{3} c^{2} d^{7} e^{5} - 60 \, a^{2} b c^{3} d^{7} e^{5} + b^{6} d^{6} e^{6} + 30 \, a b^{4} c d^{6} e^{6} + 90 \, a^{2} b^{2} c^{2} d^{6} e^{6} + 20 \, a^{3} c^{3} d^{6} e^{6} - 6 \, a b^{5} d^{5} e^{7} - 60 \, a^{2} b^{3} c d^{5} e^{7} - 60 \, a^{3} b c^{2} d^{5} e^{7} + 15 \, a^{2} b^{4} d^{4} e^{8} + 60 \, a^{3} b^{2} c d^{4} e^{8} + 15 \, a^{4} c^{2} d^{4} e^{8} - 20 \, a^{3} b^{3} d^{3} e^{9} - 30 \, a^{4} b c d^{3} e^{9} + 15 \, a^{4} b^{2} d^{2} e^{10} + 6 \, a^{5} c d^{2} e^{10} - 6 \, a^{5} b d e^{11} + a^{6} e^{12}\right)}} - \frac{e^{19}}{{\left(c^{5} d^{10} e^{10} - 5 \, b c^{4} d^{9} e^{11} + 10 \, b^{2} c^{3} d^{8} e^{12} + 5 \, a c^{4} d^{8} e^{12} - 10 \, b^{3} c^{2} d^{7} e^{13} - 20 \, a b c^{3} d^{7} e^{13} + 5 \, b^{4} c d^{6} e^{14} + 30 \, a b^{2} c^{2} d^{6} e^{14} + 10 \, a^{2} c^{3} d^{6} e^{14} - b^{5} d^{5} e^{15} - 20 \, a b^{3} c d^{5} e^{15} - 30 \, a^{2} b c^{2} d^{5} e^{15} + 5 \, a b^{4} d^{4} e^{16} + 30 \, a^{2} b^{2} c d^{4} e^{16} + 10 \, a^{3} c^{2} d^{4} e^{16} - 10 \, a^{2} b^{3} d^{3} e^{17} - 20 \, a^{3} b c d^{3} e^{17} + 10 \, a^{3} b^{2} d^{2} e^{18} + 5 \, a^{4} c d^{2} e^{18} - 5 \, a^{4} b d e^{19} + a^{5} e^{20}\right)} {\left(x e + d\right)}} + \frac{840 \, c^{13} d^{9} e - 3780 \, b c^{12} d^{8} e^{2} + 6280 \, b^{2} c^{11} d^{7} e^{3} + 5120 \, a c^{12} d^{7} e^{3} - 4340 \, b^{3} c^{10} d^{6} e^{4} - 17920 \, a b c^{11} d^{6} e^{4} + 738 \, b^{4} c^{9} d^{5} e^{5} + 20136 \, a b^{2} c^{10} d^{5} e^{5} + 13488 \, a^{2} c^{11} d^{5} e^{5} + 185 \, b^{5} c^{8} d^{4} e^{6} - 5540 \, a b^{3} c^{9} d^{4} e^{6} - 33720 \, a^{2} b c^{10} d^{4} e^{6} + 80 \, b^{6} c^{7} d^{3} e^{7} - 1700 \, a b^{4} c^{8} d^{3} e^{7} + 17880 \, a^{2} b^{2} c^{9} d^{3} e^{7} + 21120 \, a^{3} c^{10} d^{3} e^{7} + 45 \, b^{7} c^{6} d^{2} e^{8} - 870 \, a b^{5} c^{7} d^{2} e^{8} + 6900 \, a^{2} b^{3} c^{8} d^{2} e^{8} - 31680 \, a^{3} b c^{9} d^{2} e^{8} - 202 \, b^{8} c^{5} d e^{9} + 3142 \, a b^{6} c^{6} d e^{9} - 17982 \, a^{2} b^{4} c^{7} d e^{9} + 43352 \, a^{3} b^{2} c^{8} d e^{9} - 27512 \, a^{4} c^{9} d e^{9} + 77 \, b^{9} c^{4} e^{10} - 1184 \, a b^{7} c^{5} e^{10} + 6717 \, a^{2} b^{5} c^{6} e^{10} - 16396 \, a^{3} b^{3} c^{7} e^{10} + 13756 \, a^{4} b c^{8} e^{10} - \frac{4 \, {\left(1470 \, c^{13} d^{10} e^{2} - 7350 \, b c^{12} d^{9} e^{3} + 14315 \, b^{2} c^{11} d^{8} e^{4} + 8890 \, a c^{12} d^{8} e^{4} - 13160 \, b^{3} c^{10} d^{7} e^{5} - 35560 \, a b c^{11} d^{7} e^{5} + 5186 \, b^{4} c^{9} d^{6} e^{6} + 50632 \, a b^{2} c^{10} d^{6} e^{6} + 23196 \, a^{2} c^{11} d^{6} e^{6} - 368 \, b^{5} c^{8} d^{5} e^{7} - 27436 \, a b^{3} c^{9} d^{5} e^{7} - 69588 \, a^{2} b c^{10} d^{5} e^{7} - 25 \, b^{6} c^{7} d^{4} e^{8} + 2140 \, a b^{4} c^{8} d^{4} e^{8} + 60030 \, a^{2} b^{2} c^{9} d^{4} e^{8} + 35940 \, a^{3} c^{10} d^{4} e^{8} + 10 \, b^{7} c^{6} d^{3} e^{9} - 40 \, a b^{5} c^{7} d^{3} e^{9} - 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16352 \, b^{5} c^{8} d^{6} e^{8} - 316064 \, a b^{3} c^{9} d^{6} e^{8} - 511532 \, a^{2} b c^{10} d^{6} e^{8} + 744 \, b^{6} c^{7} d^{5} e^{9} + 89184 \, a b^{4} c^{8} d^{5} e^{9} + 591456 \, a^{2} b^{2} c^{9} d^{5} e^{9} + 234456 \, a^{3} c^{10} d^{5} e^{9} + 65 \, b^{7} c^{6} d^{4} e^{10} - 4630 \, a b^{5} c^{7} d^{4} e^{10} - 199810 \, a^{2} b^{3} c^{8} d^{4} e^{10} - 586140 \, a^{3} b c^{9} d^{4} e^{10} - 2816 \, b^{8} c^{5} d^{3} e^{11} + 44796 \, a b^{6} c^{6} d^{3} e^{11} - 259516 \, a^{2} b^{4} c^{7} d^{3} e^{11} + 958456 \, a^{3} b^{2} c^{8} d^{3} e^{11} - 372316 \, a^{4} c^{9} d^{3} e^{11} + 3648 \, b^{9} c^{4} d^{2} e^{12} - 57216 \, a b^{7} c^{5} d^{2} e^{12} + 333318 \, a^{2} b^{5} c^{6} d^{2} e^{12} - 851544 \, a^{3} b^{3} c^{7} d^{2} e^{12} + 558474 \, a^{4} b c^{8} d^{2} e^{12} - 1588 \, b^{10} c^{3} d e^{13} + 24464 \, a b^{8} c^{4} d e^{13} - 138496 \, a^{2} b^{6} c^{5} d e^{13} + 331772 \, a^{3} b^{4} c^{6} d e^{13} - 237772 \, a^{4} b^{2} c^{7} d e^{13} - 33172 \, a^{5} c^{8} d e^{13} + 231 \, b^{11} c^{2} e^{14} - 3494 \, a b^{9} c^{3} e^{14} + 19214 \, a^{2} b^{7} c^{4} e^{14} - 43500 \, a^{3} b^{5} c^{5} e^{14} + 25807 \, a^{4} b^{3} c^{6} e^{14} + 16586 \, a^{5} b c^{7} e^{14}\right)} e^{\left(-2\right)}}{{\left(x e + d\right)}^{2}} - \frac{4 \, {\left(7350 \, c^{13} d^{12} e^{4} - 44100 \, b c^{12} d^{11} e^{5} + 109375 \, b^{2} c^{11} d^{10} e^{6} + 47600 \, a c^{12} d^{10} e^{6} - 142625 \, b^{3} c^{10} d^{9} e^{7} - 238000 \, a b c^{11} d^{9} e^{7} + 101967 \, b^{4} c^{9} d^{8} e^{8} + 467889 \, a b^{2} c^{10} d^{8} e^{8} + 135222 \, a^{2} c^{11} d^{8} e^{8} - 37218 \, b^{5} c^{8} d^{7} e^{9} - 443556 \, a b^{3} c^{9} d^{7} e^{9} - 540888 \, a^{2} b c^{10} d^{7} e^{9} + 5487 \, b^{6} c^{7} d^{6} e^{10} + 194682 \, a b^{4} c^{8} d^{6} e^{10} + 773718 \, a^{2} b^{2} c^{9} d^{6} e^{10} + 230448 \, a^{3} c^{10} d^{6} e^{10} - 123 \, b^{7} c^{6} d^{5} e^{11} - 31200 \, a b^{5} c^{7} d^{5} e^{11} - 428046 \, a^{2} b^{3} c^{8} d^{5} e^{11} - 691344 \, a^{3} b c^{9} d^{5} e^{11} - 2592 \, b^{8} c^{5} d^{4} e^{12} + 42087 \, a b^{6} c^{6} d^{4} e^{12} - 174522 \, a^{2} b^{4} c^{7} d^{4} e^{12} + 1178802 \, a^{3} b^{2} c^{8} d^{4} e^{12} - 314622 \, a^{4} c^{9} d^{4} e^{12} + 4668 \, b^{9} c^{4} d^{3} e^{13} - 73656 \, a b^{7} c^{5} d^{3} e^{13} + 431418 \, a^{2} b^{5} c^{6} d^{3} e^{13} - 1205364 \, a^{3} b^{3} c^{7} d^{3} e^{13} + 629244 \, a^{4} b c^{8} d^{3} e^{13} - 3012 \, b^{10} c^{3} d^{2} e^{14} + 46236 \, a b^{8} c^{4} d^{2} e^{14} - 259404 \, a^{2} b^{6} c^{5} d^{2} e^{14} + 606198 \, a^{3} b^{4} c^{6} d^{2} e^{14} - 308373 \, a^{4} b^{2} c^{7} d^{2} e^{14} - 130848 \, a^{5} c^{8} d^{2} e^{14} + 823 \, b^{11} c^{2} d e^{15} - 12082 \, a b^{9} c^{3} d e^{15} + 62502 \, a^{2} b^{7} c^{4} d e^{15} - 118740 \, a^{3} b^{5} c^{5} d e^{15} - 6249 \, a^{4} b^{3} c^{6} d e^{15} + 130848 \, a^{5} b c^{7} d e^{15} - 77 \, b^{12} c e^{16} + 1025 \, a b^{10} c^{2} e^{16} - 4209 \, a^{2} b^{8} c^{3} e^{16} + 1614 \, a^{3} b^{6} c^{4} e^{16} + 24843 \, a^{4} b^{4} c^{5} e^{16} - 38499 \, a^{5} b^{2} c^{6} e^{16} + 3858 \, a^{6} c^{7} e^{16}\right)} e^{\left(-3\right)}}{{\left(x e + d\right)}^{3}} + \frac{{\left(29400 \, c^{13} d^{13} e^{5} - 191100 \, b c^{12} d^{12} e^{6} + 522200 \, b^{2} c^{11} d^{11} e^{7} + 204400 \, a c^{12} d^{11} e^{7} - 770000 \, b^{3} c^{10} d^{10} e^{8} - 1124200 \, a b c^{11} d^{10} e^{8} + 650450 \, b^{4} c^{9} d^{9} e^{9} + 2496400 \, a b^{2} c^{10} d^{9} e^{9} + 628200 \, a^{2} c^{11} d^{9} e^{9} - 305175 \, b^{5} c^{8} d^{8} e^{10} - 2802300 \, a b^{3} c^{9} d^{8} e^{10} - 2826900 \, a^{2} b c^{10} d^{8} e^{10} + 69600 \, b^{6} c^{7} d^{7} e^{11} + 1606200 \, a b^{4} c^{8} d^{7} e^{11} + 4784400 \, a^{2} b^{2} c^{9} d^{7} e^{11} + 1159200 \, a^{3} c^{10} d^{7} e^{11} - 5250 \, b^{7} c^{6} d^{6} e^{12} - 413700 \, a b^{5} c^{7} d^{6} e^{12} - 3553200 \, a^{2} b^{3} c^{8} d^{6} e^{12} - 4057200 \, a^{3} b c^{9} d^{6} e^{12} - 11544 \, b^{8} c^{5} d^{5} e^{13} + 216204 \, a b^{6} c^{6} d^{5} e^{13} - 56124 \, a^{2} b^{4} c^{7} d^{5} e^{13} + 7256064 \, a^{3} b^{2} c^{8} d^{5} e^{13} - 1170264 \, a^{4} c^{9} d^{5} e^{13} + 26760 \, b^{9} c^{4} d^{4} e^{14} - 423960 \, a b^{7} c^{5} d^{4} e^{14} + 2427210 \, a^{2} b^{5} c^{6} d^{4} e^{14} - 7997160 \, a^{3} b^{3} c^{7} d^{4} e^{14} + 2925660 \, a^{4} b c^{8} d^{4} e^{14} - 22980 \, b^{10} c^{3} d^{3} e^{15} + 352560 \, a b^{8} c^{4} d^{3} e^{15} - 1972560 \, a^{2} b^{6} c^{5} d^{3} e^{15} + 4653960 \, a^{3} b^{4} c^{6} d^{3} e^{15} - 1310760 \, a^{4} b^{2} c^{7} d^{3} e^{15} - 1291920 \, a^{5} c^{8} d^{3} e^{15} + 9035 \, b^{11} c^{2} d^{2} e^{16} - 129830 \, a b^{9} c^{3} d^{2} e^{16} + 639630 \, a^{2} b^{7} c^{4} d^{2} e^{16} - 1012380 \, a^{3} b^{5} c^{5} d^{2} e^{16} - 959520 \, a^{4} b^{3} c^{6} d^{2} e^{16} + 1937880 \, a^{5} b c^{7} d^{2} e^{16} - 1550 \, b^{12} c d e^{17} + 19130 \, a b^{10} c^{2} d e^{17} - 61470 \, a^{2} b^{8} c^{3} d e^{17} - 98580 \, a^{3} b^{6} c^{4} d e^{17} + 801930 \, a^{4} b^{4} c^{5} d e^{17} - 899280 \, a^{5} b^{2} c^{6} d e^{17} - 46440 \, a^{6} c^{7} d e^{17} + 77 \, b^{13} e^{18} - 452 \, a b^{11} c e^{18} - 4593 \, a^{2} b^{9} c^{2} e^{18} + 48048 \, a^{3} b^{7} c^{3} e^{18} - 143523 \, a^{4} b^{5} c^{4} e^{18} + 126660 \, a^{5} b^{3} c^{5} e^{18} + 23220 \, a^{6} b c^{6} e^{18}\right)} e^{\left(-4\right)}}{{\left(x e + d\right)}^{4}} - \frac{20 \, {\left(882 \, c^{13} d^{14} e^{6} - 6174 \, b c^{12} d^{13} e^{7} + 18389 \, b^{2} c^{11} d^{12} e^{8} + 6706 \, a c^{12} d^{12} e^{8} - 30072 \, b^{3} c^{10} d^{11} e^{9} - 40236 \, a b c^{11} d^{11} e^{9} + 28936 \, b^{4} c^{9} d^{10} e^{10} + 99304 \, a b^{2} c^{10} d^{10} e^{10} + 22690 \, a^{2} c^{11} d^{10} e^{10} - 16167 \, b^{5} c^{8} d^{9} e^{11} - 127690 \, a b^{3} c^{9} d^{9} e^{11} - 113450 \, a^{2} b c^{10} d^{9} e^{11} + 4752 \, b^{6} c^{7} d^{8} e^{12} + 88479 \, a b^{4} c^{8} d^{8} e^{12} + 220689 \, a^{2} b^{2} c^{9} d^{8} e^{12} + 46098 \, a^{3} c^{10} d^{8} e^{12} - 546 \, b^{7} c^{6} d^{7} e^{13} - 30372 \, a b^{5} c^{7} d^{7} e^{13} - 202056 \, a^{2} b^{3} c^{8} d^{7} e^{13} - 184392 \, a^{3} b c^{9} d^{7} e^{13} - 393 \, b^{8} c^{5} d^{6} e^{14} + 10110 \, a b^{6} c^{6} d^{6} e^{14} + 45642 \, a^{2} b^{4} c^{7} d^{6} e^{14} + 349752 \, a^{3} b^{2} c^{8} d^{6} e^{14} - 27066 \, a^{4} c^{9} d^{6} e^{14} + 1116 \, b^{9} c^{4} d^{5} e^{15} - 17730 \, a b^{7} c^{5} d^{5} e^{15} + 93780 \, a^{2} b^{5} c^{6} d^{5} e^{15} - 403884 \, a^{3} b^{3} c^{7} d^{5} e^{15} + 81198 \, a^{4} b c^{8} d^{5} e^{15} - 1200 \, b^{10} c^{3} d^{4} e^{16} + 18420 \, a b^{8} c^{4} d^{4} e^{16} - 103035 \, a^{2} b^{6} c^{5} d^{4} e^{16} + 255840 \, a^{3} b^{4} c^{6} d^{4} e^{16} - 6825 \, a^{4} b^{2} c^{7} d^{4} e^{16} - 75738 \, a^{5} c^{8} d^{4} e^{16} + 611 \, b^{11} c^{2} d^{3} e^{17} - 8642 \, a b^{9} c^{3} d^{3} e^{17} + 40938 \, a^{2} b^{7} c^{4} d^{3} e^{17} - 53664 \, a^{3} b^{5} c^{5} d^{3} e^{17} - 121680 \, a^{4} b^{3} c^{6} d^{3} e^{17} + 151476 \, a^{5} b c^{7} d^{3} e^{17} - 147 \, b^{12} c d^{2} e^{18} + 1695 \, a b^{10} c^{2} d^{2} e^{18} - 3987 \, a^{2} b^{8} c^{3} d^{2} e^{18} - 19674 \, a^{3} b^{6} c^{4} d^{2} e^{18} + 99270 \, a^{4} b^{4} c^{5} d^{2} e^{18} - 85824 \, a^{5} b^{2} c^{6} d^{2} e^{18} - 18522 \, a^{6} c^{7} d^{2} e^{18} + 13 \, b^{13} d e^{19} - 44 \, a b^{11} c d e^{19} - 1211 \, a^{2} b^{9} c^{2} d e^{19} + 9924 \, a^{3} b^{7} c^{3} d e^{19} - 24897 \, a^{4} b^{5} c^{4} d e^{19} + 10086 \, a^{5} b^{3} c^{5} d e^{19} + 18522 \, a^{6} b c^{6} d e^{19} - 13 \, a b^{12} e^{20} + 178 \, a^{2} b^{10} c e^{20} - 783 \, a^{3} b^{8} c^{2} e^{20} + 651 \, a^{4} b^{6} c^{3} e^{20} + 3417 \, a^{5} b^{4} c^{4} e^{20} - 6237 \, a^{6} b^{2} c^{5} e^{20} + 918 \, a^{7} c^{6} e^{20}\right)} e^{\left(-5\right)}}{{\left(x e + d\right)}^{5}} + \frac{30 \, {\left(196 \, c^{13} d^{15} e^{7} - 1470 \, b c^{12} d^{14} e^{8} + 4732 \, b^{2} c^{11} d^{13} e^{9} + 1652 \, a c^{12} d^{13} e^{9} - 8463 \, b^{3} c^{10} d^{12} e^{10} - 10738 \, a b c^{11} d^{12} e^{10} + 9058 \, b^{4} c^{9} d^{11} e^{11} + 29092 \, a b^{2} c^{10} d^{11} e^{11} + 6244 \, a^{2} c^{11} d^{11} e^{11} - 5775 \, b^{5} c^{8} d^{10} e^{12} - 41888 \, a b^{3} c^{9} d^{10} e^{12} - 34342 \, a^{2} b c^{10} d^{10} e^{12} + 2016 \, b^{6} c^{7} d^{9} e^{13} + 33558 \, a b^{4} c^{8} d^{9} e^{13} + 75208 \, a^{2} b^{2} c^{9} d^{9} e^{13} + 14196 \, a^{3} c^{10} d^{9} e^{13} - 294 \, b^{7} c^{6} d^{8} e^{14} - 14028 \, a b^{5} c^{7} d^{8} e^{14} - 80871 \, a^{2} b^{3} c^{8} d^{8} e^{14} - 63882 \, a^{3} b c^{9} d^{8} e^{14} - 102 \, b^{8} c^{5} d^{7} e^{15} + 3984 \, a b^{6} c^{6} d^{7} e^{15} + 32208 \, a^{2} b^{4} c^{7} d^{7} e^{15} + 129768 \, a^{3} b^{2} c^{8} d^{7} e^{15} - 2004 \, a^{4} c^{9} d^{7} e^{15} + 343 \, b^{9} c^{4} d^{6} e^{16} - 5460 \, a b^{7} c^{5} d^{6} e^{16} + 24276 \, a^{2} b^{5} c^{6} d^{6} e^{16} - 156072 \, a^{3} b^{3} c^{7} d^{6} e^{16} + 7014 \, a^{4} b c^{8} d^{6} e^{16} - 444 \, b^{10} c^{3} d^{5} e^{17} + 6822 \, a b^{8} c^{4} d^{5} e^{17} - 38196 \, a^{2} b^{6} c^{5} d^{5} e^{17} + 104232 \, a^{3} b^{4} c^{6} d^{5} e^{17} + 25644 \, a^{4} b^{2} c^{7} d^{5} e^{17} - 28932 \, a^{5} c^{8} d^{5} e^{17} + 277 \, b^{11} c^{2} d^{4} e^{18} - 3874 \, a b^{9} c^{3} d^{4} e^{18} + 17811 \, a^{2} b^{7} c^{4} d^{4} e^{18} - 19458 \, a^{3} b^{5} c^{5} d^{4} e^{18} - 81645 \, a^{4} b^{3} c^{6} d^{4} e^{18} + 72330 \, a^{5} b c^{7} d^{4} e^{18} - 84 \, b^{12} c d^{3} e^{19} + 908 \, a b^{10} c^{2} d^{3} e^{19} - 1332 \, a^{2} b^{8} c^{3} d^{3} e^{19} - 16644 \, a^{3} b^{6} c^{4} d^{3} e^{19} + 69390 \, a^{4} b^{4} c^{5} d^{3} e^{19} - 45708 \, a^{5} b^{2} c^{6} d^{3} e^{19} - 17748 \, a^{6} c^{7} d^{3} e^{19} + 10 \, b^{13} d^{2} e^{20} - 8 \, a b^{11} c d^{2} e^{20} - 1274 \, a^{2} b^{9} c^{2} d^{2} e^{20} + 8976 \, a^{3} b^{7} c^{3} d^{2} e^{20} - 18933 \, a^{4} b^{5} c^{4} d^{2} e^{20} - 3768 \, a^{5} b^{3} c^{5} d^{2} e^{20} + 26622 \, a^{6} b c^{6} d^{2} e^{20} - 20 \, a b^{12} d e^{21} + 248 \, a^{2} b^{10} c d e^{21} - 804 \, a^{3} b^{8} c^{2} d e^{21} - 1272 \, a^{4} b^{6} c^{3} d e^{21} + 10626 \, a^{5} b^{4} c^{4} d e^{21} - 12912 \, a^{6} b^{2} c^{5} d e^{21} - 228 \, a^{7} c^{6} d e^{21} + 10 \, a^{2} b^{11} e^{22} - 156 \, a^{3} b^{9} c e^{22} + 903 \, a^{4} b^{7} c^{2} e^{22} - 2274 \, a^{5} b^{5} c^{3} e^{22} + 2019 \, a^{6} b^{3} c^{4} e^{22} + 114 \, a^{7} b c^{5} e^{22}\right)} e^{\left(-6\right)}}{{\left(x e + d\right)}^{6}} - \frac{60 \, {\left(14 \, c^{13} d^{16} e^{8} - 112 \, b c^{12} d^{15} e^{9} + 387 \, b^{2} c^{11} d^{14} e^{10} + 132 \, a c^{12} d^{14} e^{10} - 749 \, b^{3} c^{10} d^{13} e^{11} - 924 \, a b c^{11} d^{13} e^{11} + 877 \, b^{4} c^{9} d^{12} e^{12} + 2721 \, a b^{2} c^{10} d^{12} e^{12} + 564 \, a^{2} c^{11} d^{12} e^{12} - 621 \, b^{5} c^{8} d^{11} e^{13} - 4314 \, a b^{3} c^{9} d^{11} e^{13} - 3384 \, a^{2} b c^{10} d^{11} e^{13} + 246 \, b^{6} c^{7} d^{10} e^{14} + 3879 \, a b^{4} c^{8} d^{10} e^{14} + 8211 \, a^{2} b^{2} c^{9} d^{10} e^{14} + 1460 \, a^{3} c^{10} d^{10} e^{14} - 42 \, b^{7} c^{6} d^{9} e^{15} - 1872 \, a b^{5} c^{7} d^{9} e^{15} - 10035 \, a^{2} b^{3} c^{8} d^{9} e^{15} - 7300 \, a^{3} b c^{9} d^{9} e^{15} - 9 \, b^{8} c^{5} d^{8} e^{16} + 522 \, a b^{6} c^{6} d^{8} e^{16} + 5292 \, a^{2} b^{4} c^{7} d^{8} e^{16} + 15993 \, a^{3} b^{2} c^{8} d^{8} e^{16} + 432 \, a^{4} c^{9} d^{8} e^{16} + 35 \, b^{9} c^{4} d^{7} e^{17} - 558 \, a b^{7} c^{5} d^{7} e^{17} + 1818 \, a^{2} b^{5} c^{6} d^{7} e^{17} - 20172 \, a^{3} b^{3} c^{7} d^{7} e^{17} - 1728 \, a^{4} b c^{8} d^{7} e^{17} - 53 \, b^{10} c^{3} d^{6} e^{18} + 815 \, a b^{8} c^{4} d^{6} e^{18} - 4567 \, a^{2} b^{6} c^{5} d^{6} e^{18} + 14026 \, a^{3} b^{4} c^{6} d^{6} e^{18} + 7249 \, a^{4} b^{2} c^{7} d^{6} e^{18} - 3380 \, a^{5} c^{8} d^{6} e^{18} + 39 \, b^{11} c^{2} d^{5} e^{19} - 540 \, a b^{9} c^{3} d^{5} e^{19} + 2415 \, a^{2} b^{7} c^{4} d^{5} e^{19} - 2136 \, a^{3} b^{5} c^{5} d^{5} e^{19} - 15699 \, a^{4} b^{3} c^{6} d^{5} e^{19} + 10140 \, a^{5} b c^{7} d^{5} e^{19} - 14 \, b^{12} c d^{4} e^{20} + 141 \, a b^{10} c^{2} d^{4} e^{20} - 60 \, a^{2} b^{8} c^{3} d^{4} e^{20} - 3705 \, a^{3} b^{6} c^{4} d^{4} e^{20} + 13785 \, a^{4} b^{4} c^{5} d^{4} e^{20} - 6357 \, a^{5} b^{2} c^{6} d^{4} e^{20} - 4212 \, a^{6} c^{7} d^{4} e^{20} + 2 \, b^{13} d^{3} e^{21} + 4 \, a b^{11} c d^{3} e^{21} - 326 \, a^{2} b^{9} c^{2} d^{3} e^{21} + 2036 \, a^{3} b^{7} c^{3} d^{3} e^{21} - 3421 \, a^{4} b^{5} c^{4} d^{3} e^{21} - 4186 \, a^{5} b^{3} c^{5} d^{3} e^{21} + 8424 \, a^{6} b c^{6} d^{3} e^{21} - 6 \, a b^{12} d^{2} e^{22} + 66 \, a^{2} b^{10} c d^{2} e^{22} - 114 \, a^{3} b^{8} c^{2} d^{2} e^{22} - 1071 \, a^{4} b^{6} c^{3} d^{2} e^{22} + 4623 \, a^{5} b^{4} c^{4} d^{2} e^{22} - 4071 \, a^{6} b^{2} c^{5} d^{2} e^{22} - 1284 \, a^{7} c^{6} d^{2} e^{22} + 6 \, a^{2} b^{11} d e^{23} - 88 \, a^{3} b^{9} c d e^{23} + 453 \, a^{4} b^{7} c^{2} d e^{23} - 840 \, a^{5} b^{5} c^{3} d e^{23} - 141 \, a^{6} b^{3} c^{4} d e^{23} + 1284 \, a^{7} b c^{5} d e^{23} - 2 \, a^{3} b^{10} e^{24} + 32 \, a^{4} b^{8} c e^{24} - 193 \, a^{5} b^{6} c^{2} e^{24} + 526 \, a^{6} b^{4} c^{3} e^{24} - 581 \, a^{7} b^{2} c^{4} e^{24} + 130 \, a^{8} c^{5} e^{24}\right)} e^{\left(-7\right)}}{{\left(x e + d\right)}^{7}}}{12 \, {\left(c d^{2} - b d e + a e^{2}\right)}^{6} {\left(b^{2} - 4 \, a c\right)}^{4} {\left(c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{b e}{x e + d} - \frac{b d e}{{\left(x e + d\right)}^{2}} + \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right)}^{4}}"," ",0,"5*(28*c^10*d^10*e^2 - 140*b*c^9*d^9*e^3 + 270*b^2*c^8*d^8*e^4 + 180*a*c^9*d^8*e^4 - 240*b^3*c^7*d^7*e^5 - 720*a*b*c^8*d^7*e^5 + 84*b^4*c^6*d^6*e^6 + 1008*a*b^2*c^7*d^6*e^6 + 504*a^2*c^8*d^6*e^6 - 504*a*b^3*c^6*d^5*e^7 - 1512*a^2*b*c^7*d^5*e^7 + 1260*a^2*b^2*c^6*d^4*e^8 + 840*a^3*c^7*d^4*e^8 - 1680*a^3*b*c^6*d^3*e^9 + 1260*a^4*c^6*d^2*e^10 - 2*b^9*c*d*e^11 + 36*a*b^7*c^2*d*e^11 - 252*a^2*b^5*c^3*d*e^11 + 840*a^3*b^3*c^4*d*e^11 - 1260*a^4*b*c^5*d*e^11 + b^10*e^12 - 18*a*b^8*c*e^12 + 126*a^2*b^6*c^2*e^12 - 420*a^3*b^4*c^3*e^12 + 630*a^4*b^2*c^4*e^12 - 252*a^5*c^5*e^12)*arctan((2*c*d - 2*c*d^2/(x*e + d) - b*e + 2*b*d*e/(x*e + d) - 2*a*e^2/(x*e + d))*e^(-1)/sqrt(-b^2 + 4*a*c))*e^(-2)/((b^8*c^6*d^12 - 16*a*b^6*c^7*d^12 + 96*a^2*b^4*c^8*d^12 - 256*a^3*b^2*c^9*d^12 + 256*a^4*c^10*d^12 - 6*b^9*c^5*d^11*e + 96*a*b^7*c^6*d^11*e - 576*a^2*b^5*c^7*d^11*e + 1536*a^3*b^3*c^8*d^11*e - 1536*a^4*b*c^9*d^11*e + 15*b^10*c^4*d^10*e^2 - 234*a*b^8*c^5*d^10*e^2 + 1344*a^2*b^6*c^6*d^10*e^2 - 3264*a^3*b^4*c^7*d^10*e^2 + 2304*a^4*b^2*c^8*d^10*e^2 + 1536*a^5*c^9*d^10*e^2 - 20*b^11*c^3*d^9*e^3 + 290*a*b^9*c^4*d^9*e^3 - 1440*a^2*b^7*c^5*d^9*e^3 + 2240*a^3*b^5*c^6*d^9*e^3 + 2560*a^4*b^3*c^7*d^9*e^3 - 7680*a^5*b*c^8*d^9*e^3 + 15*b^12*c^2*d^8*e^4 - 180*a*b^10*c^3*d^8*e^4 + 495*a^2*b^8*c^4*d^8*e^4 + 1680*a^3*b^6*c^5*d^8*e^4 - 10080*a^4*b^4*c^6*d^8*e^4 + 11520*a^5*b^2*c^7*d^8*e^4 + 3840*a^6*c^8*d^8*e^4 - 6*b^13*c*d^7*e^5 + 36*a*b^11*c^2*d^7*e^5 + 324*a^2*b^9*c^3*d^7*e^5 - 3264*a^3*b^7*c^4*d^7*e^5 + 8064*a^4*b^5*c^5*d^7*e^5 - 15360*a^6*b*c^7*d^7*e^5 + b^14*d^6*e^6 + 14*a*b^12*c*d^6*e^6 - 294*a^2*b^10*c^2*d^6*e^6 + 1204*a^3*b^8*c^3*d^6*e^6 + 896*a^4*b^6*c^4*d^6*e^6 - 13440*a^5*b^4*c^5*d^6*e^6 + 17920*a^6*b^2*c^6*d^6*e^6 + 5120*a^7*c^7*d^6*e^6 - 6*a*b^13*d^5*e^7 + 36*a^2*b^11*c*d^5*e^7 + 324*a^3*b^9*c^2*d^5*e^7 - 3264*a^4*b^7*c^3*d^5*e^7 + 8064*a^5*b^5*c^4*d^5*e^7 - 15360*a^7*b*c^6*d^5*e^7 + 15*a^2*b^12*d^4*e^8 - 180*a^3*b^10*c*d^4*e^8 + 495*a^4*b^8*c^2*d^4*e^8 + 1680*a^5*b^6*c^3*d^4*e^8 - 10080*a^6*b^4*c^4*d^4*e^8 + 11520*a^7*b^2*c^5*d^4*e^8 + 3840*a^8*c^6*d^4*e^8 - 20*a^3*b^11*d^3*e^9 + 290*a^4*b^9*c*d^3*e^9 - 1440*a^5*b^7*c^2*d^3*e^9 + 2240*a^6*b^5*c^3*d^3*e^9 + 2560*a^7*b^3*c^4*d^3*e^9 - 7680*a^8*b*c^5*d^3*e^9 + 15*a^4*b^10*d^2*e^10 - 234*a^5*b^8*c*d^2*e^10 + 1344*a^6*b^6*c^2*d^2*e^10 - 3264*a^7*b^4*c^3*d^2*e^10 + 2304*a^8*b^2*c^4*d^2*e^10 + 1536*a^9*c^5*d^2*e^10 - 6*a^5*b^9*d*e^11 + 96*a^6*b^7*c*d*e^11 - 576*a^7*b^5*c^2*d*e^11 + 1536*a^8*b^3*c^3*d*e^11 - 1536*a^9*b*c^4*d*e^11 + a^6*b^8*e^12 - 16*a^7*b^6*c*e^12 + 96*a^8*b^4*c^2*e^12 - 256*a^9*b^2*c^3*e^12 + 256*a^10*c^4*e^12)*sqrt(-b^2 + 4*a*c)) - 5/2*(2*c*d*e^9 - b*e^10)*log(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + b*e/(x*e + d) - b*d*e/(x*e + d)^2 + a*e^2/(x*e + d)^2)/(c^6*d^12 - 6*b*c^5*d^11*e + 15*b^2*c^4*d^10*e^2 + 6*a*c^5*d^10*e^2 - 20*b^3*c^3*d^9*e^3 - 30*a*b*c^4*d^9*e^3 + 15*b^4*c^2*d^8*e^4 + 60*a*b^2*c^3*d^8*e^4 + 15*a^2*c^4*d^8*e^4 - 6*b^5*c*d^7*e^5 - 60*a*b^3*c^2*d^7*e^5 - 60*a^2*b*c^3*d^7*e^5 + b^6*d^6*e^6 + 30*a*b^4*c*d^6*e^6 + 90*a^2*b^2*c^2*d^6*e^6 + 20*a^3*c^3*d^6*e^6 - 6*a*b^5*d^5*e^7 - 60*a^2*b^3*c*d^5*e^7 - 60*a^3*b*c^2*d^5*e^7 + 15*a^2*b^4*d^4*e^8 + 60*a^3*b^2*c*d^4*e^8 + 15*a^4*c^2*d^4*e^8 - 20*a^3*b^3*d^3*e^9 - 30*a^4*b*c*d^3*e^9 + 15*a^4*b^2*d^2*e^10 + 6*a^5*c*d^2*e^10 - 6*a^5*b*d*e^11 + a^6*e^12) - e^19/((c^5*d^10*e^10 - 5*b*c^4*d^9*e^11 + 10*b^2*c^3*d^8*e^12 + 5*a*c^4*d^8*e^12 - 10*b^3*c^2*d^7*e^13 - 20*a*b*c^3*d^7*e^13 + 5*b^4*c*d^6*e^14 + 30*a*b^2*c^2*d^6*e^14 + 10*a^2*c^3*d^6*e^14 - b^5*d^5*e^15 - 20*a*b^3*c*d^5*e^15 - 30*a^2*b*c^2*d^5*e^15 + 5*a*b^4*d^4*e^16 + 30*a^2*b^2*c*d^4*e^16 + 10*a^3*c^2*d^4*e^16 - 10*a^2*b^3*d^3*e^17 - 20*a^3*b*c*d^3*e^17 + 10*a^3*b^2*d^2*e^18 + 5*a^4*c*d^2*e^18 - 5*a^4*b*d*e^19 + a^5*e^20)*(x*e + d)) + 1/12*(840*c^13*d^9*e - 3780*b*c^12*d^8*e^2 + 6280*b^2*c^11*d^7*e^3 + 5120*a*c^12*d^7*e^3 - 4340*b^3*c^10*d^6*e^4 - 17920*a*b*c^11*d^6*e^4 + 738*b^4*c^9*d^5*e^5 + 20136*a*b^2*c^10*d^5*e^5 + 13488*a^2*c^11*d^5*e^5 + 185*b^5*c^8*d^4*e^6 - 5540*a*b^3*c^9*d^4*e^6 - 33720*a^2*b*c^10*d^4*e^6 + 80*b^6*c^7*d^3*e^7 - 1700*a*b^4*c^8*d^3*e^7 + 17880*a^2*b^2*c^9*d^3*e^7 + 21120*a^3*c^10*d^3*e^7 + 45*b^7*c^6*d^2*e^8 - 870*a*b^5*c^7*d^2*e^8 + 6900*a^2*b^3*c^8*d^2*e^8 - 31680*a^3*b*c^9*d^2*e^8 - 202*b^8*c^5*d*e^9 + 3142*a*b^6*c^6*d*e^9 - 17982*a^2*b^4*c^7*d*e^9 + 43352*a^3*b^2*c^8*d*e^9 - 27512*a^4*c^9*d*e^9 + 77*b^9*c^4*e^10 - 1184*a*b^7*c^5*e^10 + 6717*a^2*b^5*c^6*e^10 - 16396*a^3*b^3*c^7*e^10 + 13756*a^4*b*c^8*e^10 - 4*(1470*c^13*d^10*e^2 - 7350*b*c^12*d^9*e^3 + 14315*b^2*c^11*d^8*e^4 + 8890*a*c^12*d^8*e^4 - 13160*b^3*c^10*d^7*e^5 - 35560*a*b*c^11*d^7*e^5 + 5186*b^4*c^9*d^6*e^6 + 50632*a*b^2*c^10*d^6*e^6 + 23196*a^2*c^11*d^6*e^6 - 368*b^5*c^8*d^5*e^7 - 27436*a*b^3*c^9*d^5*e^7 - 69588*a^2*b*c^10*d^5*e^7 - 25*b^6*c^7*d^4*e^8 + 2140*a*b^4*c^8*d^4*e^8 + 60030*a^2*b^2*c^9*d^4*e^8 + 35940*a^3*c^10*d^4*e^8 + 10*b^7*c^6*d^3*e^9 - 40*a*b^5*c^7*d^3*e^9 - 4080*a^2*b^3*c^8*d^3*e^9 - 71880*a^3*b*c^9*d^3*e^9 - 422*b^8*c^5*d^2*e^10 + 6722*a*b^6*c^6*d^2*e^10 - 40272*a^2*b^4*c^7*d^2*e^10 + 111472*a^3*b^2*c^8*d^2*e^10 - 57562*a^4*c^9*d^2*e^10 + 344*b^9*c^4*d*e^11 - 5348*a*b^7*c^5*d*e^11 + 30714*a^2*b^5*c^6*d*e^11 - 75532*a^3*b^3*c^7*d*e^11 + 57562*a^4*b*c^8*d*e^11 - 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294*b^7*c^6*d^8*e^14 - 14028*a*b^5*c^7*d^8*e^14 - 80871*a^2*b^3*c^8*d^8*e^14 - 63882*a^3*b*c^9*d^8*e^14 - 102*b^8*c^5*d^7*e^15 + 3984*a*b^6*c^6*d^7*e^15 + 32208*a^2*b^4*c^7*d^7*e^15 + 129768*a^3*b^2*c^8*d^7*e^15 - 2004*a^4*c^9*d^7*e^15 + 343*b^9*c^4*d^6*e^16 - 5460*a*b^7*c^5*d^6*e^16 + 24276*a^2*b^5*c^6*d^6*e^16 - 156072*a^3*b^3*c^7*d^6*e^16 + 7014*a^4*b*c^8*d^6*e^16 - 444*b^10*c^3*d^5*e^17 + 6822*a*b^8*c^4*d^5*e^17 - 38196*a^2*b^6*c^5*d^5*e^17 + 104232*a^3*b^4*c^6*d^5*e^17 + 25644*a^4*b^2*c^7*d^5*e^17 - 28932*a^5*c^8*d^5*e^17 + 277*b^11*c^2*d^4*e^18 - 3874*a*b^9*c^3*d^4*e^18 + 17811*a^2*b^7*c^4*d^4*e^18 - 19458*a^3*b^5*c^5*d^4*e^18 - 81645*a^4*b^3*c^6*d^4*e^18 + 72330*a^5*b*c^7*d^4*e^18 - 84*b^12*c*d^3*e^19 + 908*a*b^10*c^2*d^3*e^19 - 1332*a^2*b^8*c^3*d^3*e^19 - 16644*a^3*b^6*c^4*d^3*e^19 + 69390*a^4*b^4*c^5*d^3*e^19 - 45708*a^5*b^2*c^6*d^3*e^19 - 17748*a^6*c^7*d^3*e^19 + 10*b^13*d^2*e^20 - 8*a*b^11*c*d^2*e^20 - 1274*a^2*b^9*c^2*d^2*e^20 + 8976*a^3*b^7*c^3*d^2*e^20 - 18933*a^4*b^5*c^4*d^2*e^20 - 3768*a^5*b^3*c^5*d^2*e^20 + 26622*a^6*b*c^6*d^2*e^20 - 20*a*b^12*d*e^21 + 248*a^2*b^10*c*d*e^21 - 804*a^3*b^8*c^2*d*e^21 - 1272*a^4*b^6*c^3*d*e^21 + 10626*a^5*b^4*c^4*d*e^21 - 12912*a^6*b^2*c^5*d*e^21 - 228*a^7*c^6*d*e^21 + 10*a^2*b^11*e^22 - 156*a^3*b^9*c*e^22 + 903*a^4*b^7*c^2*e^22 - 2274*a^5*b^5*c^3*e^22 + 2019*a^6*b^3*c^4*e^22 + 114*a^7*b*c^5*e^22)*e^(-6)/(x*e + d)^6 - 60*(14*c^13*d^16*e^8 - 112*b*c^12*d^15*e^9 + 387*b^2*c^11*d^14*e^10 + 132*a*c^12*d^14*e^10 - 749*b^3*c^10*d^13*e^11 - 924*a*b*c^11*d^13*e^11 + 877*b^4*c^9*d^12*e^12 + 2721*a*b^2*c^10*d^12*e^12 + 564*a^2*c^11*d^12*e^12 - 621*b^5*c^8*d^11*e^13 - 4314*a*b^3*c^9*d^11*e^13 - 3384*a^2*b*c^10*d^11*e^13 + 246*b^6*c^7*d^10*e^14 + 3879*a*b^4*c^8*d^10*e^14 + 8211*a^2*b^2*c^9*d^10*e^14 + 1460*a^3*c^10*d^10*e^14 - 42*b^7*c^6*d^9*e^15 - 1872*a*b^5*c^7*d^9*e^15 - 10035*a^2*b^3*c^8*d^9*e^15 - 7300*a^3*b*c^9*d^9*e^15 - 9*b^8*c^5*d^8*e^16 + 522*a*b^6*c^6*d^8*e^16 + 5292*a^2*b^4*c^7*d^8*e^16 + 15993*a^3*b^2*c^8*d^8*e^16 + 432*a^4*c^9*d^8*e^16 + 35*b^9*c^4*d^7*e^17 - 558*a*b^7*c^5*d^7*e^17 + 1818*a^2*b^5*c^6*d^7*e^17 - 20172*a^3*b^3*c^7*d^7*e^17 - 1728*a^4*b*c^8*d^7*e^17 - 53*b^10*c^3*d^6*e^18 + 815*a*b^8*c^4*d^6*e^18 - 4567*a^2*b^6*c^5*d^6*e^18 + 14026*a^3*b^4*c^6*d^6*e^18 + 7249*a^4*b^2*c^7*d^6*e^18 - 3380*a^5*c^8*d^6*e^18 + 39*b^11*c^2*d^5*e^19 - 540*a*b^9*c^3*d^5*e^19 + 2415*a^2*b^7*c^4*d^5*e^19 - 2136*a^3*b^5*c^5*d^5*e^19 - 15699*a^4*b^3*c^6*d^5*e^19 + 10140*a^5*b*c^7*d^5*e^19 - 14*b^12*c*d^4*e^20 + 141*a*b^10*c^2*d^4*e^20 - 60*a^2*b^8*c^3*d^4*e^20 - 3705*a^3*b^6*c^4*d^4*e^20 + 13785*a^4*b^4*c^5*d^4*e^20 - 6357*a^5*b^2*c^6*d^4*e^20 - 4212*a^6*c^7*d^4*e^20 + 2*b^13*d^3*e^21 + 4*a*b^11*c*d^3*e^21 - 326*a^2*b^9*c^2*d^3*e^21 + 2036*a^3*b^7*c^3*d^3*e^21 - 3421*a^4*b^5*c^4*d^3*e^21 - 4186*a^5*b^3*c^5*d^3*e^21 + 8424*a^6*b*c^6*d^3*e^21 - 6*a*b^12*d^2*e^22 + 66*a^2*b^10*c*d^2*e^22 - 114*a^3*b^8*c^2*d^2*e^22 - 1071*a^4*b^6*c^3*d^2*e^22 + 4623*a^5*b^4*c^4*d^2*e^22 - 4071*a^6*b^2*c^5*d^2*e^22 - 1284*a^7*c^6*d^2*e^22 + 6*a^2*b^11*d*e^23 - 88*a^3*b^9*c*d*e^23 + 453*a^4*b^7*c^2*d*e^23 - 840*a^5*b^5*c^3*d*e^23 - 141*a^6*b^3*c^4*d*e^23 + 1284*a^7*b*c^5*d*e^23 - 2*a^3*b^10*e^24 + 32*a^4*b^8*c*e^24 - 193*a^5*b^6*c^2*e^24 + 526*a^6*b^4*c^3*e^24 - 581*a^7*b^2*c^4*e^24 + 130*a^8*c^5*e^24)*e^(-7)/(x*e + d)^7)/((c*d^2 - b*d*e + a*e^2)^6*(b^2 - 4*a*c)^4*(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + b*e/(x*e + d) - b*d*e/(x*e + d)^2 + a*e^2/(x*e + d)^2)^4)","B",0
2229,1,68,0,0.156132," ","integrate(1/(1+2*x)/(5*x^2+3*x+2)^3,x, algorithm=""giac"")","\frac{125624}{10218313} \, \sqrt{31} \arctan\left(\frac{1}{31} \, \sqrt{31} {\left(10 \, x + 3\right)}\right) + \frac{45800 \, x^{3} + 79660 \, x^{2} + 53968 \, x + 28901}{94178 \, {\left(5 \, x^{2} + 3 \, x + 2\right)}^{2}} - \frac{16}{343} \, \log\left(5 \, x^{2} + 3 \, x + 2\right) + \frac{32}{343} \, \log\left({\left| 2 \, x + 1 \right|}\right)"," ",0,"125624/10218313*sqrt(31)*arctan(1/31*sqrt(31)*(10*x + 3)) + 1/94178*(45800*x^3 + 79660*x^2 + 53968*x + 28901)/(5*x^2 + 3*x + 2)^2 - 16/343*log(5*x^2 + 3*x + 2) + 32/343*log(abs(2*x + 1))","A",0
2230,1,108,0,0.157550," ","integrate(1/(1+2*x)^2/(5*x^2+3*x+2)^3,x, algorithm=""giac"")","-\frac{1065012}{71528191} \, \sqrt{31} \arctan\left(-\frac{1}{31} \, \sqrt{31} {\left(\frac{7}{2 \, x + 1} - 2\right)}\right) - \frac{32}{343 \, {\left(2 \, x + 1\right)}} + \frac{4 \, {\left(\frac{1178375}{2 \, x + 1} - \frac{2320190}{{\left(2 \, x + 1\right)}^{2}} + \frac{87843}{{\left(2 \, x + 1\right)}^{3}} - 1304250\right)}}{2307361 \, {\left(\frac{4}{2 \, x + 1} - \frac{7}{{\left(2 \, x + 1\right)}^{2}} - 5\right)}^{2}} - \frac{192}{2401} \, \log\left(-\frac{4}{2 \, x + 1} + \frac{7}{{\left(2 \, x + 1\right)}^{2}} + 5\right)"," ",0,"-1065012/71528191*sqrt(31)*arctan(-1/31*sqrt(31)*(7/(2*x + 1) - 2)) - 32/343/(2*x + 1) + 4/2307361*(1178375/(2*x + 1) - 2320190/(2*x + 1)^2 + 87843/(2*x + 1)^3 - 1304250)/(4/(2*x + 1) - 7/(2*x + 1)^2 - 5)^2 - 192/2401*log(-4/(2*x + 1) + 7/(2*x + 1)^2 + 5)","A",0
2231,1,78,0,0.159636," ","integrate(1/(1+2*x)/(5*x^2+3*x+2)^4,x, algorithm=""giac"")","\frac{19007376}{2217373921} \, \sqrt{31} \arctan\left(\frac{1}{31} \, \sqrt{31} {\left(10 \, x + 3\right)}\right) + \frac{60969000 \, x^{5} + 127202700 \, x^{4} + 143405620 \, x^{3} + 105257844 \, x^{2} + 44933184 \, x + 13831165}{30654939 \, {\left(5 \, x^{2} + 3 \, x + 2\right)}^{3}} - \frac{64}{2401} \, \log\left(5 \, x^{2} + 3 \, x + 2\right) + \frac{128}{2401} \, \log\left({\left| 2 \, x + 1 \right|}\right)"," ",0,"19007376/2217373921*sqrt(31)*arctan(1/31*sqrt(31)*(10*x + 3)) + 1/30654939*(60969000*x^5 + 127202700*x^4 + 143405620*x^3 + 105257844*x^2 + 44933184*x + 13831165)/(5*x^2 + 3*x + 2)^3 - 64/2401*log(5*x^2 + 3*x + 2) + 128/2401*log(abs(2*x + 1))","A",0
2232,1,126,0,0.155871," ","integrate(1/(1+2*x)^2/(5*x^2+3*x+2)^4,x, algorithm=""giac"")","-\frac{116056984}{15521617447} \, \sqrt{31} \arctan\left(-\frac{1}{31} \, \sqrt{31} {\left(\frac{7}{2 \, x + 1} - 2\right)}\right) - \frac{128}{2401 \, {\left(2 \, x + 1\right)}} - \frac{8 \, {\left(\frac{3841449975}{2 \, x + 1} - \frac{8833663680}{{\left(2 \, x + 1\right)}^{2}} + \frac{7499779568}{{\left(2 \, x + 1\right)}^{3}} - \frac{7050406230}{{\left(2 \, x + 1\right)}^{4}} + \frac{1291725897}{{\left(2 \, x + 1\right)}^{5}} - 2009265250\right)}}{1502092011 \, {\left(\frac{4}{2 \, x + 1} - \frac{7}{{\left(2 \, x + 1\right)}^{2}} - 5\right)}^{3}} - \frac{1024}{16807} \, \log\left(-\frac{4}{2 \, x + 1} + \frac{7}{{\left(2 \, x + 1\right)}^{2}} + 5\right)"," ",0,"-116056984/15521617447*sqrt(31)*arctan(-1/31*sqrt(31)*(7/(2*x + 1) - 2)) - 128/2401/(2*x + 1) - 8/1502092011*(3841449975/(2*x + 1) - 8833663680/(2*x + 1)^2 + 7499779568/(2*x + 1)^3 - 7050406230/(2*x + 1)^4 + 1291725897/(2*x + 1)^5 - 2009265250)/(4/(2*x + 1) - 7/(2*x + 1)^2 - 5)^3 - 1024/16807*log(-4/(2*x + 1) + 7/(2*x + 1)^2 + 5)","A",0
2233,1,44,0,0.183741," ","integrate((7-3*x)/(x^2+2*x-5),x, algorithm=""giac"")","\frac{5}{6} \, \sqrt{6} \log\left(\frac{{\left| 2 \, x - 2 \, \sqrt{6} + 2 \right|}}{{\left| 2 \, x + 2 \, \sqrt{6} + 2 \right|}}\right) - \frac{3}{2} \, \log\left({\left| x^{2} + 2 \, x - 5 \right|}\right)"," ",0,"5/6*sqrt(6)*log(abs(2*x - 2*sqrt(6) + 2)/abs(2*x + 2*sqrt(6) + 2)) - 3/2*log(abs(x^2 + 2*x - 5))","A",0
2234,1,33,0,0.165667," ","integrate(1/(-1+x)/(x^2+x+1),x, algorithm=""giac"")","-\frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) - \frac{1}{6} \, \log\left(x^{2} + x + 1\right) + \frac{1}{3} \, \log\left({\left| x - 1 \right|}\right)"," ",0,"-1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) - 1/6*log(x^2 + x + 1) + 1/3*log(abs(x - 1))","A",0
2235,1,202,0,0.234408," ","integrate(2*((a/b)^(1/n)-x*cos((-1+2*k)*pi/n))/((a/b)^(2/n)+x^2-2*(a/b)^(1/n)*x*cos((-1+2*k)*pi/n)),x, algorithm=""giac"")","-\cos\left(\frac{2 \, \pi k}{n} - \frac{\pi}{n}\right) \log\left(-2 \, x \left(\frac{a}{b}\right)^{\left(\frac{1}{n}\right)} \cos\left(\frac{2 \, \pi k}{n} - \frac{\pi}{n}\right) + x^{2} + \left(\frac{a}{b}\right)^{\frac{2}{n}}\right) - \frac{2 \, {\left(\left(\frac{a}{b}\right)^{\left(\frac{1}{n}\right)} \cos\left(\frac{2 \, \pi k}{n} - \frac{\pi}{n}\right)^{2} - \left(\frac{a}{b}\right)^{\left(\frac{1}{n}\right)}\right)} \arctan\left(-\frac{\left(\frac{a}{b}\right)^{\left(\frac{1}{n}\right)} \cos\left(\frac{2 \, \pi k}{n} - \frac{\pi}{n}\right) - x}{\sqrt{-\cos\left(\frac{2 \, \pi k}{n} - \frac{\pi}{n}\right)^{2} + 1} \left(\frac{a}{b}\right)^{\left(\frac{1}{n}\right)}}\right)}{\sqrt{-\cos\left(\frac{2 \, \pi k}{n} - \frac{\pi}{n}\right)^{2} + 1} \left(\frac{a}{b}\right)^{\left(\frac{1}{n}\right)}}"," ",0,"-cos(2*pi*k/n - pi/n)*log(-2*x*(a/b)^(1/n)*cos(2*pi*k/n - pi/n) + x^2 + (a/b)^(2/n)) - 2*((a/b)^(1/n)*cos(2*pi*k/n - pi/n)^2 - (a/b)^(1/n))*arctan(-((a/b)^(1/n)*cos(2*pi*k/n - pi/n) - x)/(sqrt(-cos(2*pi*k/n - pi/n)^2 + 1)*(a/b)^(1/n)))/(sqrt(-cos(2*pi*k/n - pi/n)^2 + 1)*(a/b)^(1/n))","A",0
2236,1,32,0,0.181647," ","integrate(x^4/(15*x^2+13*x+2),x, algorithm=""giac"")","\frac{1}{45} \, x^{3} - \frac{13}{450} \, x^{2} + \frac{139}{3375} \, x + \frac{1}{4375} \, \log\left({\left| 5 \, x + 1 \right|}\right) - \frac{16}{567} \, \log\left({\left| 3 \, x + 2 \right|}\right)"," ",0,"1/45*x^3 - 13/450*x^2 + 139/3375*x + 1/4375*log(abs(5*x + 1)) - 16/567*log(abs(3*x + 2))","A",0
2237,1,27,0,0.149234," ","integrate(x^3/(15*x^2+13*x+2),x, algorithm=""giac"")","\frac{1}{30} \, x^{2} - \frac{13}{225} \, x - \frac{1}{875} \, \log\left({\left| 5 \, x + 1 \right|}\right) + \frac{8}{189} \, \log\left({\left| 3 \, x + 2 \right|}\right)"," ",0,"1/30*x^2 - 13/225*x - 1/875*log(abs(5*x + 1)) + 8/189*log(abs(3*x + 2))","A",0
2238,1,22,0,0.149655," ","integrate(x^2/(15*x^2+13*x+2),x, algorithm=""giac"")","\frac{1}{15} \, x + \frac{1}{175} \, \log\left({\left| 5 \, x + 1 \right|}\right) - \frac{4}{63} \, \log\left({\left| 3 \, x + 2 \right|}\right)"," ",0,"1/15*x + 1/175*log(abs(5*x + 1)) - 4/63*log(abs(3*x + 2))","A",0
2239,1,19,0,0.160804," ","integrate(x/(15*x^2+13*x+2),x, algorithm=""giac"")","-\frac{1}{35} \, \log\left({\left| 5 \, x + 1 \right|}\right) + \frac{2}{21} \, \log\left({\left| 3 \, x + 2 \right|}\right)"," ",0,"-1/35*log(abs(5*x + 1)) + 2/21*log(abs(3*x + 2))","A",0
2240,1,19,0,0.148600," ","integrate(1/(15*x^2+13*x+2),x, algorithm=""giac"")","\frac{1}{7} \, \log\left({\left| 5 \, x + 1 \right|}\right) - \frac{1}{7} \, \log\left({\left| 3 \, x + 2 \right|}\right)"," ",0,"1/7*log(abs(5*x + 1)) - 1/7*log(abs(3*x + 2))","A",0
2241,1,24,0,0.149835," ","integrate(1/x/(15*x^2+13*x+2),x, algorithm=""giac"")","-\frac{5}{7} \, \log\left({\left| 5 \, x + 1 \right|}\right) + \frac{3}{14} \, \log\left({\left| 3 \, x + 2 \right|}\right) + \frac{1}{2} \, \log\left({\left| x \right|}\right)"," ",0,"-5/7*log(abs(5*x + 1)) + 3/14*log(abs(3*x + 2)) + 1/2*log(abs(x))","A",0
2242,1,29,0,0.170285," ","integrate(1/x^2/(15*x^2+13*x+2),x, algorithm=""giac"")","-\frac{1}{2 \, x} + \frac{25}{7} \, \log\left({\left| 5 \, x + 1 \right|}\right) - \frac{9}{28} \, \log\left({\left| 3 \, x + 2 \right|}\right) - \frac{13}{4} \, \log\left({\left| x \right|}\right)"," ",0,"-1/2/x + 25/7*log(abs(5*x + 1)) - 9/28*log(abs(3*x + 2)) - 13/4*log(abs(x))","A",0
2243,1,34,0,0.173549," ","integrate(1/x^3/(15*x^2+13*x+2),x, algorithm=""giac"")","\frac{13 \, x - 1}{4 \, x^{2}} - \frac{125}{7} \, \log\left({\left| 5 \, x + 1 \right|}\right) + \frac{27}{56} \, \log\left({\left| 3 \, x + 2 \right|}\right) + \frac{139}{8} \, \log\left({\left| x \right|}\right)"," ",0,"1/4*(13*x - 1)/x^2 - 125/7*log(abs(5*x + 1)) + 27/56*log(abs(3*x + 2)) + 139/8*log(abs(x))","A",0
2244,1,39,0,0.172680," ","integrate(1/x^4/(15*x^2+13*x+2),x, algorithm=""giac"")","-\frac{417 \, x^{2} - 39 \, x + 4}{24 \, x^{3}} + \frac{625}{7} \, \log\left({\left| 5 \, x + 1 \right|}\right) - \frac{81}{112} \, \log\left({\left| 3 \, x + 2 \right|}\right) - \frac{1417}{16} \, \log\left({\left| x \right|}\right)"," ",0,"-1/24*(417*x^2 - 39*x + 4)/x^3 + 625/7*log(abs(5*x + 1)) - 81/112*log(abs(3*x + 2)) - 1417/16*log(abs(x))","A",0
2245,1,32,0,0.152316," ","integrate(x^5/(15*x^3+13*x^2+2*x),x, algorithm=""giac"")","\frac{1}{45} \, x^{3} - \frac{13}{450} \, x^{2} + \frac{139}{3375} \, x + \frac{1}{4375} \, \log\left({\left| 5 \, x + 1 \right|}\right) - \frac{16}{567} \, \log\left({\left| 3 \, x + 2 \right|}\right)"," ",0,"1/45*x^3 - 13/450*x^2 + 139/3375*x + 1/4375*log(abs(5*x + 1)) - 16/567*log(abs(3*x + 2))","A",0
2246,1,27,0,0.150286," ","integrate(x^4/(15*x^3+13*x^2+2*x),x, algorithm=""giac"")","\frac{1}{30} \, x^{2} - \frac{13}{225} \, x - \frac{1}{875} \, \log\left({\left| 5 \, x + 1 \right|}\right) + \frac{8}{189} \, \log\left({\left| 3 \, x + 2 \right|}\right)"," ",0,"1/30*x^2 - 13/225*x - 1/875*log(abs(5*x + 1)) + 8/189*log(abs(3*x + 2))","A",0
2247,1,22,0,0.205151," ","integrate(x^3/(15*x^3+13*x^2+2*x),x, algorithm=""giac"")","\frac{1}{15} \, x + \frac{1}{175} \, \log\left({\left| 5 \, x + 1 \right|}\right) - \frac{4}{63} \, \log\left({\left| 3 \, x + 2 \right|}\right)"," ",0,"1/15*x + 1/175*log(abs(5*x + 1)) - 4/63*log(abs(3*x + 2))","A",0
2248,1,19,0,0.151179," ","integrate(x^2/(15*x^3+13*x^2+2*x),x, algorithm=""giac"")","-\frac{1}{35} \, \log\left({\left| 5 \, x + 1 \right|}\right) + \frac{2}{21} \, \log\left({\left| 3 \, x + 2 \right|}\right)"," ",0,"-1/35*log(abs(5*x + 1)) + 2/21*log(abs(3*x + 2))","A",0
2249,1,19,0,0.153580," ","integrate(x/(15*x^3+13*x^2+2*x),x, algorithm=""giac"")","\frac{1}{7} \, \log\left({\left| 5 \, x + 1 \right|}\right) - \frac{1}{7} \, \log\left({\left| 3 \, x + 2 \right|}\right)"," ",0,"1/7*log(abs(5*x + 1)) - 1/7*log(abs(3*x + 2))","A",0
2250,1,24,0,0.203542," ","integrate(1/(15*x^3+13*x^2+2*x),x, algorithm=""giac"")","-\frac{5}{7} \, \log\left({\left| 5 \, x + 1 \right|}\right) + \frac{3}{14} \, \log\left({\left| 3 \, x + 2 \right|}\right) + \frac{1}{2} \, \log\left({\left| x \right|}\right)"," ",0,"-5/7*log(abs(5*x + 1)) + 3/14*log(abs(3*x + 2)) + 1/2*log(abs(x))","A",0
2251,1,29,0,0.148977," ","integrate(1/x/(15*x^3+13*x^2+2*x),x, algorithm=""giac"")","-\frac{1}{2 \, x} + \frac{25}{7} \, \log\left({\left| 5 \, x + 1 \right|}\right) - \frac{9}{28} \, \log\left({\left| 3 \, x + 2 \right|}\right) - \frac{13}{4} \, \log\left({\left| x \right|}\right)"," ",0,"-1/2/x + 25/7*log(abs(5*x + 1)) - 9/28*log(abs(3*x + 2)) - 13/4*log(abs(x))","A",0
2252,1,34,0,0.166683," ","integrate(1/x^2/(15*x^3+13*x^2+2*x),x, algorithm=""giac"")","\frac{13 \, x - 1}{4 \, x^{2}} - \frac{125}{7} \, \log\left({\left| 5 \, x + 1 \right|}\right) + \frac{27}{56} \, \log\left({\left| 3 \, x + 2 \right|}\right) + \frac{139}{8} \, \log\left({\left| x \right|}\right)"," ",0,"1/4*(13*x - 1)/x^2 - 125/7*log(abs(5*x + 1)) + 27/56*log(abs(3*x + 2)) + 139/8*log(abs(x))","A",0
2253,1,39,0,0.151469," ","integrate(1/x^3/(15*x^3+13*x^2+2*x),x, algorithm=""giac"")","-\frac{417 \, x^{2} - 39 \, x + 4}{24 \, x^{3}} + \frac{625}{7} \, \log\left({\left| 5 \, x + 1 \right|}\right) - \frac{81}{112} \, \log\left({\left| 3 \, x + 2 \right|}\right) - \frac{1417}{16} \, \log\left({\left| x \right|}\right)"," ",0,"-1/24*(417*x^2 - 39*x + 4)/x^3 + 625/7*log(abs(5*x + 1)) - 81/112*log(abs(3*x + 2)) - 1417/16*log(abs(x))","A",0
2254,1,13,0,0.150422," ","integrate(x/(x^2+4*x+4),x, algorithm=""giac"")","\frac{2}{x + 2} + \log\left({\left| x + 2 \right|}\right)"," ",0,"2/(x + 2) + log(abs(x + 2))","A",0
2255,1,20,0,0.155400," ","integrate(x/(x^2+2*x+5),x, algorithm=""giac"")","-\frac{1}{2} \, \arctan\left(\frac{1}{2} \, x + \frac{1}{2}\right) + \frac{1}{2} \, \log\left(x^{2} + 2 \, x + 5\right)"," ",0,"-1/2*arctan(1/2*x + 1/2) + 1/2*log(x^2 + 2*x + 5)","A",0
2256,1,15,0,0.169517," ","integrate(x/(x^2-5*x+6),x, algorithm=""giac"")","-2 \, \log\left({\left| x - 2 \right|}\right) + 3 \, \log\left({\left| x - 3 \right|}\right)"," ",0,"-2*log(abs(x - 2)) + 3*log(abs(x - 3))","A",0
2257,1,22,0,0.150041," ","integrate(x/(x^2+2*x+2)^2,x, algorithm=""giac"")","-\frac{x + 2}{2 \, {\left(x^{2} + 2 \, x + 2\right)}} - \frac{1}{2} \, \arctan\left(x + 1\right)"," ",0,"-1/2*(x + 2)/(x^2 + 2*x + 2) - 1/2*arctan(x + 1)","A",0
2258,1,42,0,0.206062," ","integrate(x/(x^2+x+1)^3,x, algorithm=""giac"")","-\frac{2}{9} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) - \frac{2 \, x^{3} + 3 \, x^{2} + 4 \, x + 3}{6 \, {\left(x^{2} + x + 1\right)}^{2}}"," ",0,"-2/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) - 1/6*(2*x^3 + 3*x^2 + 4*x + 3)/(x^2 + x + 1)^2","A",0
2259,1,27,0,0.149689," ","integrate(x^2/(x^2+x+1),x, algorithm=""giac"")","-\frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) + x - \frac{1}{2} \, \log\left(x^{2} + x + 1\right)"," ",0,"-1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) + x - 1/2*log(x^2 + x + 1)","A",0
2260,1,16,0,0.153374," ","integrate(x^2/(x^2-3*x+2),x, algorithm=""giac"")","x - \log\left({\left| x - 1 \right|}\right) + 4 \, \log\left({\left| x - 2 \right|}\right)"," ",0,"x - log(abs(x - 1)) + 4*log(abs(x - 2))","A",0
2261,1,16,0,0.153230," ","integrate(x^2/(x^2+x-6),x, algorithm=""giac"")","x - \frac{9}{5} \, \log\left({\left| x + 3 \right|}\right) + \frac{4}{5} \, \log\left({\left| x - 2 \right|}\right)"," ",0,"x - 9/5*log(abs(x + 3)) + 4/5*log(abs(x - 2))","A",0
2262,1,15,0,0.149719," ","integrate(x^2/(x^2+2*x+2)^2,x, algorithm=""giac"")","\frac{1}{x^{2} + 2 \, x + 2} + \arctan\left(x + 1\right)"," ",0,"1/(x^2 + 2*x + 2) + arctan(x + 1)","A",0
2263,1,23,0,0.147023," ","integrate(x^3/(x^2-3*x+2),x, algorithm=""giac"")","\frac{1}{2} \, x^{2} + 3 \, x - \log\left({\left| x - 1 \right|}\right) + 8 \, \log\left({\left| x - 2 \right|}\right)"," ",0,"1/2*x^2 + 3*x - log(abs(x - 1)) + 8*log(abs(x - 2))","A",0
2264,1,21,0,0.177936," ","integrate(x^3/(x^2+2*x+1),x, algorithm=""giac"")","\frac{1}{2} \, x^{2} - 2 \, x + \frac{1}{x + 1} + 3 \, \log\left({\left| x + 1 \right|}\right)"," ",0,"1/2*x^2 - 2*x + 1/(x + 1) + 3*log(abs(x + 1))","A",0
2265,1,23,0,0.159991," ","integrate(x^3/(x^2-2*x+1),x, algorithm=""giac"")","\frac{1}{2} \, x^{2} + 2 \, x - \frac{1}{x - 1} + 3 \, \log\left({\left| x - 1 \right|}\right)"," ",0,"1/2*x^2 + 2*x - 1/(x - 1) + 3*log(abs(x - 1))","A",0
2266,1,28,0,0.147432," ","integrate(x^4/(x^2+4*x+4),x, algorithm=""giac"")","\frac{1}{3} \, x^{3} - 2 \, x^{2} + 12 \, x - \frac{16}{x + 2} - 32 \, \log\left({\left| x + 2 \right|}\right)"," ",0,"1/3*x^3 - 2*x^2 + 12*x - 16/(x + 2) - 32*log(abs(x + 2))","A",0
2267,1,29,0,0.164251," ","integrate(1/x/(x^2+x+1),x, algorithm=""giac"")","-\frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) - \frac{1}{2} \, \log\left(x^{2} + x + 1\right) + \log\left({\left| x \right|}\right)"," ",0,"-1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) - 1/2*log(x^2 + x + 1) + log(abs(x))","A",0
2268,1,571,0,0.257973," ","integrate((e*x+d)^(5/2)*(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{2}{3465} \, {\left(1155 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} b d^{3} e^{\left(-1\right)} + 231 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} c d^{3} e^{\left(-2\right)} + 693 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} b d^{2} e^{\left(-1\right)} + 297 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} c d^{2} e^{\left(-2\right)} + 3465 \, \sqrt{x e + d} a d^{3} + 3465 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a d^{2} + 297 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b d e^{\left(-1\right)} + 33 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} c d e^{\left(-2\right)} + 693 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a d + 11 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b e^{\left(-1\right)} + 5 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} c e^{\left(-2\right)} + 99 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a\right)} e^{\left(-1\right)}"," ",0,"2/3465*(1155*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*b*d^3*e^(-1) + 231*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*c*d^3*e^(-2) + 693*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*b*d^2*e^(-1) + 297*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*c*d^2*e^(-2) + 3465*sqrt(x*e + d)*a*d^3 + 3465*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a*d^2 + 297*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b*d*e^(-1) + 33*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*c*d*e^(-2) + 693*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a*d + 11*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b*e^(-1) + 5*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*c*e^(-2) + 99*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a)*e^(-1)","B",0
2269,1,365,0,0.174666," ","integrate((e*x+d)^(3/2)*(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{2}{315} \, {\left(105 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} b d^{2} e^{\left(-1\right)} + 21 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} c d^{2} e^{\left(-2\right)} + 42 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} b d e^{\left(-1\right)} + 18 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} c d e^{\left(-2\right)} + 315 \, \sqrt{x e + d} a d^{2} + 210 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a d + 9 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b e^{\left(-1\right)} + {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} c e^{\left(-2\right)} + 21 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a\right)} e^{\left(-1\right)}"," ",0,"2/315*(105*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*b*d^2*e^(-1) + 21*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*c*d^2*e^(-2) + 42*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*b*d*e^(-1) + 18*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*c*d*e^(-2) + 315*sqrt(x*e + d)*a*d^2 + 210*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a*d + 9*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b*e^(-1) + (35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*c*e^(-2) + 21*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a)*e^(-1)","B",0
2270,1,200,0,0.163661," ","integrate((c*x^2+b*x+a)*(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{105} \, {\left(35 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} b d e^{\left(-1\right)} + 7 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} c d e^{\left(-2\right)} + 7 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} b e^{\left(-1\right)} + 3 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} c e^{\left(-2\right)} + 105 \, \sqrt{x e + d} a d + 35 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a\right)} e^{\left(-1\right)}"," ",0,"2/105*(35*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*b*d*e^(-1) + 7*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*c*d*e^(-2) + 7*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*b*e^(-1) + 3*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*c*e^(-2) + 105*sqrt(x*e + d)*a*d + 35*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a)*e^(-1)","B",0
2271,1,80,0,0.169662," ","integrate((c*x^2+b*x+a)/(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{15} \, {\left(5 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} b e^{\left(-1\right)} + {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} c e^{\left(-2\right)} + 15 \, \sqrt{x e + d} a\right)} e^{\left(-1\right)}"," ",0,"2/15*(5*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*b*e^(-1) + (3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*c*e^(-2) + 15*sqrt(x*e + d)*a)*e^(-1)","A",0
2272,1,73,0,0.163156," ","integrate((c*x^2+b*x+a)/(e*x+d)^(3/2),x, algorithm=""giac"")","\frac{2}{3} \, {\left({\left(x e + d\right)}^{\frac{3}{2}} c e^{6} - 6 \, \sqrt{x e + d} c d e^{6} + 3 \, \sqrt{x e + d} b e^{7}\right)} e^{\left(-9\right)} - \frac{2 \, {\left(c d^{2} - b d e + a e^{2}\right)} e^{\left(-3\right)}}{\sqrt{x e + d}}"," ",0,"2/3*((x*e + d)^(3/2)*c*e^6 - 6*sqrt(x*e + d)*c*d*e^6 + 3*sqrt(x*e + d)*b*e^7)*e^(-9) - 2*(c*d^2 - b*d*e + a*e^2)*e^(-3)/sqrt(x*e + d)","A",0
2273,1,64,0,0.167501," ","integrate((c*x^2+b*x+a)/(e*x+d)^(5/2),x, algorithm=""giac"")","2 \, \sqrt{x e + d} c e^{\left(-3\right)} + \frac{2 \, {\left(6 \, {\left(x e + d\right)} c d - c d^{2} - 3 \, {\left(x e + d\right)} b e + b d e - a e^{2}\right)} e^{\left(-3\right)}}{3 \, {\left(x e + d\right)}^{\frac{3}{2}}}"," ",0,"2*sqrt(x*e + d)*c*e^(-3) + 2/3*(6*(x*e + d)*c*d - c*d^2 - 3*(x*e + d)*b*e + b*d*e - a*e^2)*e^(-3)/(x*e + d)^(3/2)","A",0
2274,1,62,0,0.168152," ","integrate((c*x^2+b*x+a)/(e*x+d)^(7/2),x, algorithm=""giac"")","-\frac{2 \, {\left(15 \, {\left(x e + d\right)}^{2} c - 10 \, {\left(x e + d\right)} c d + 3 \, c d^{2} + 5 \, {\left(x e + d\right)} b e - 3 \, b d e + 3 \, a e^{2}\right)} e^{\left(-3\right)}}{15 \, {\left(x e + d\right)}^{\frac{5}{2}}}"," ",0,"-2/15*(15*(x*e + d)^2*c - 10*(x*e + d)*c*d + 3*c*d^2 + 5*(x*e + d)*b*e - 3*b*d*e + 3*a*e^2)*e^(-3)/(x*e + d)^(5/2)","A",0
2275,1,1498,0,0.272891," ","integrate((e*x+d)^(5/2)*(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{2}{45045} \, {\left(30030 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a b d^{3} e^{\left(-1\right)} + 3003 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} b^{2} d^{3} e^{\left(-2\right)} + 6006 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a c d^{3} e^{\left(-2\right)} + 2574 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b c d^{3} e^{\left(-3\right)} + 143 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} c^{2} d^{3} e^{\left(-4\right)} + 18018 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a b d^{2} e^{\left(-1\right)} + 3861 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b^{2} d^{2} e^{\left(-2\right)} + 7722 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a c d^{2} e^{\left(-2\right)} + 858 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b c d^{2} e^{\left(-3\right)} + 195 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} c^{2} d^{2} e^{\left(-4\right)} + 45045 \, \sqrt{x e + d} a^{2} d^{3} + 45045 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{2} d^{2} + 7722 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a b d e^{\left(-1\right)} + 429 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b^{2} d e^{\left(-2\right)} + 858 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a c d e^{\left(-2\right)} + 390 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b c d e^{\left(-3\right)} + 45 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} c^{2} d e^{\left(-4\right)} + 9009 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{2} d + 286 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a b e^{\left(-1\right)} + 65 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b^{2} e^{\left(-2\right)} + 130 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a c e^{\left(-2\right)} + 30 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} b c e^{\left(-3\right)} + 7 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} c^{2} e^{\left(-4\right)} + 1287 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{2}\right)} e^{\left(-1\right)}"," ",0,"2/45045*(30030*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a*b*d^3*e^(-1) + 3003*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*b^2*d^3*e^(-2) + 6006*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a*c*d^3*e^(-2) + 2574*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b*c*d^3*e^(-3) + 143*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*c^2*d^3*e^(-4) + 18018*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a*b*d^2*e^(-1) + 3861*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b^2*d^2*e^(-2) + 7722*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*c*d^2*e^(-2) + 858*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b*c*d^2*e^(-3) + 195*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*c^2*d^2*e^(-4) + 45045*sqrt(x*e + d)*a^2*d^3 + 45045*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^2*d^2 + 7722*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*b*d*e^(-1) + 429*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b^2*d*e^(-2) + 858*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*c*d*e^(-2) + 390*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b*c*d*e^(-3) + 45*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*c^2*d*e^(-4) + 9009*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^2*d + 286*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*b*e^(-1) + 65*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b^2*e^(-2) + 130*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a*c*e^(-2) + 30*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*b*c*e^(-3) + 7*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*c^2*e^(-4) + 1287*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^2)*e^(-1)","B",0
2276,1,999,0,0.230369," ","integrate((e*x+d)^(3/2)*(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{2}{45045} \, {\left(30030 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a b d^{2} e^{\left(-1\right)} + 3003 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} b^{2} d^{2} e^{\left(-2\right)} + 6006 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a c d^{2} e^{\left(-2\right)} + 2574 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b c d^{2} e^{\left(-3\right)} + 143 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} c^{2} d^{2} e^{\left(-4\right)} + 12012 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a b d e^{\left(-1\right)} + 2574 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b^{2} d e^{\left(-2\right)} + 5148 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a c d e^{\left(-2\right)} + 572 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b c d e^{\left(-3\right)} + 130 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} c^{2} d e^{\left(-4\right)} + 45045 \, \sqrt{x e + d} a^{2} d^{2} + 30030 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{2} d + 2574 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a b e^{\left(-1\right)} + 143 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b^{2} e^{\left(-2\right)} + 286 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a c e^{\left(-2\right)} + 130 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b c e^{\left(-3\right)} + 15 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} c^{2} e^{\left(-4\right)} + 3003 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{2}\right)} e^{\left(-1\right)}"," ",0,"2/45045*(30030*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a*b*d^2*e^(-1) + 3003*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*b^2*d^2*e^(-2) + 6006*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a*c*d^2*e^(-2) + 2574*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b*c*d^2*e^(-3) + 143*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*c^2*d^2*e^(-4) + 12012*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a*b*d*e^(-1) + 2574*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b^2*d*e^(-2) + 5148*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*c*d*e^(-2) + 572*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b*c*d*e^(-3) + 130*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*c^2*d*e^(-4) + 45045*sqrt(x*e + d)*a^2*d^2 + 30030*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^2*d + 2574*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*b*e^(-1) + 143*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b^2*e^(-2) + 286*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*c*e^(-2) + 130*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b*c*e^(-3) + 15*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*c^2*e^(-4) + 3003*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^2)*e^(-1)","B",0
2277,1,578,0,0.181492," ","integrate((c*x^2+b*x+a)^2*(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{3465} \, {\left(2310 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a b d e^{\left(-1\right)} + 231 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} b^{2} d e^{\left(-2\right)} + 462 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a c d e^{\left(-2\right)} + 198 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b c d e^{\left(-3\right)} + 11 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} c^{2} d e^{\left(-4\right)} + 462 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a b e^{\left(-1\right)} + 99 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b^{2} e^{\left(-2\right)} + 198 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a c e^{\left(-2\right)} + 22 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b c e^{\left(-3\right)} + 5 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} c^{2} e^{\left(-4\right)} + 3465 \, \sqrt{x e + d} a^{2} d + 1155 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{2}\right)} e^{\left(-1\right)}"," ",0,"2/3465*(2310*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a*b*d*e^(-1) + 231*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*b^2*d*e^(-2) + 462*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a*c*d*e^(-2) + 198*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b*c*d*e^(-3) + 11*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*c^2*d*e^(-4) + 462*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a*b*e^(-1) + 99*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b^2*e^(-2) + 198*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*c*e^(-2) + 22*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b*c*e^(-3) + 5*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*c^2*e^(-4) + 3465*sqrt(x*e + d)*a^2*d + 1155*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^2)*e^(-1)","B",0
2278,1,248,0,0.174565," ","integrate((c*x^2+b*x+a)^2/(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{315} \, {\left(210 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a b e^{\left(-1\right)} + 21 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} b^{2} e^{\left(-2\right)} + 42 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a c e^{\left(-2\right)} + 18 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b c e^{\left(-3\right)} + {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} c^{2} e^{\left(-4\right)} + 315 \, \sqrt{x e + d} a^{2}\right)} e^{\left(-1\right)}"," ",0,"2/315*(210*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a*b*e^(-1) + 21*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*b^2*e^(-2) + 42*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a*c*e^(-2) + 18*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b*c*e^(-3) + (35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*c^2*e^(-4) + 315*sqrt(x*e + d)*a^2)*e^(-1)","A",0
2279,1,253,0,0.229445," ","integrate((c*x^2+b*x+a)^2/(e*x+d)^(3/2),x, algorithm=""giac"")","\frac{2}{105} \, {\left(15 \, {\left(x e + d\right)}^{\frac{7}{2}} c^{2} e^{30} - 84 \, {\left(x e + d\right)}^{\frac{5}{2}} c^{2} d e^{30} + 210 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{2} d^{2} e^{30} - 420 \, \sqrt{x e + d} c^{2} d^{3} e^{30} + 42 \, {\left(x e + d\right)}^{\frac{5}{2}} b c e^{31} - 210 \, {\left(x e + d\right)}^{\frac{3}{2}} b c d e^{31} + 630 \, \sqrt{x e + d} b c d^{2} e^{31} + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{2} e^{32} + 70 \, {\left(x e + d\right)}^{\frac{3}{2}} a c e^{32} - 210 \, \sqrt{x e + d} b^{2} d e^{32} - 420 \, \sqrt{x e + d} a c d e^{32} + 210 \, \sqrt{x e + d} a b e^{33}\right)} e^{\left(-35\right)} - \frac{2 \, {\left(c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2} + 2 \, a c d^{2} e^{2} - 2 \, a b d e^{3} + a^{2} e^{4}\right)} e^{\left(-5\right)}}{\sqrt{x e + d}}"," ",0,"2/105*(15*(x*e + d)^(7/2)*c^2*e^30 - 84*(x*e + d)^(5/2)*c^2*d*e^30 + 210*(x*e + d)^(3/2)*c^2*d^2*e^30 - 420*sqrt(x*e + d)*c^2*d^3*e^30 + 42*(x*e + d)^(5/2)*b*c*e^31 - 210*(x*e + d)^(3/2)*b*c*d*e^31 + 630*sqrt(x*e + d)*b*c*d^2*e^31 + 35*(x*e + d)^(3/2)*b^2*e^32 + 70*(x*e + d)^(3/2)*a*c*e^32 - 210*sqrt(x*e + d)*b^2*d*e^32 - 420*sqrt(x*e + d)*a*c*d*e^32 + 210*sqrt(x*e + d)*a*b*e^33)*e^(-35) - 2*(c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2 + 2*a*c*d^2*e^2 - 2*a*b*d*e^3 + a^2*e^4)*e^(-5)/sqrt(x*e + d)","A",0
2280,1,244,0,0.357811," ","integrate((c*x^2+b*x+a)^2/(e*x+d)^(5/2),x, algorithm=""giac"")","\frac{2}{15} \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} c^{2} e^{20} - 20 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{2} d e^{20} + 90 \, \sqrt{x e + d} c^{2} d^{2} e^{20} + 10 \, {\left(x e + d\right)}^{\frac{3}{2}} b c e^{21} - 90 \, \sqrt{x e + d} b c d e^{21} + 15 \, \sqrt{x e + d} b^{2} e^{22} + 30 \, \sqrt{x e + d} a c e^{22}\right)} e^{\left(-25\right)} + \frac{2 \, {\left(12 \, {\left(x e + d\right)} c^{2} d^{3} - c^{2} d^{4} - 18 \, {\left(x e + d\right)} b c d^{2} e + 2 \, b c d^{3} e + 6 \, {\left(x e + d\right)} b^{2} d e^{2} + 12 \, {\left(x e + d\right)} a c d e^{2} - b^{2} d^{2} e^{2} - 2 \, a c d^{2} e^{2} - 6 \, {\left(x e + d\right)} a b e^{3} + 2 \, a b d e^{3} - a^{2} e^{4}\right)} e^{\left(-5\right)}}{3 \, {\left(x e + d\right)}^{\frac{3}{2}}}"," ",0,"2/15*(3*(x*e + d)^(5/2)*c^2*e^20 - 20*(x*e + d)^(3/2)*c^2*d*e^20 + 90*sqrt(x*e + d)*c^2*d^2*e^20 + 10*(x*e + d)^(3/2)*b*c*e^21 - 90*sqrt(x*e + d)*b*c*d*e^21 + 15*sqrt(x*e + d)*b^2*e^22 + 30*sqrt(x*e + d)*a*c*e^22)*e^(-25) + 2/3*(12*(x*e + d)*c^2*d^3 - c^2*d^4 - 18*(x*e + d)*b*c*d^2*e + 2*b*c*d^3*e + 6*(x*e + d)*b^2*d*e^2 + 12*(x*e + d)*a*c*d*e^2 - b^2*d^2*e^2 - 2*a*c*d^2*e^2 - 6*(x*e + d)*a*b*e^3 + 2*a*b*d*e^3 - a^2*e^4)*e^(-5)/(x*e + d)^(3/2)","A",0
2281,1,241,0,0.193734," ","integrate((c*x^2+b*x+a)^2/(e*x+d)^(7/2),x, algorithm=""giac"")","\frac{2}{3} \, {\left({\left(x e + d\right)}^{\frac{3}{2}} c^{2} e^{10} - 12 \, \sqrt{x e + d} c^{2} d e^{10} + 6 \, \sqrt{x e + d} b c e^{11}\right)} e^{\left(-15\right)} - \frac{2 \, {\left(90 \, {\left(x e + d\right)}^{2} c^{2} d^{2} - 20 \, {\left(x e + d\right)} c^{2} d^{3} + 3 \, c^{2} d^{4} - 90 \, {\left(x e + d\right)}^{2} b c d e + 30 \, {\left(x e + d\right)} b c d^{2} e - 6 \, b c d^{3} e + 15 \, {\left(x e + d\right)}^{2} b^{2} e^{2} + 30 \, {\left(x e + d\right)}^{2} a c e^{2} - 10 \, {\left(x e + d\right)} b^{2} d e^{2} - 20 \, {\left(x e + d\right)} a c d e^{2} + 3 \, b^{2} d^{2} e^{2} + 6 \, a c d^{2} e^{2} + 10 \, {\left(x e + d\right)} a b e^{3} - 6 \, a b d e^{3} + 3 \, a^{2} e^{4}\right)} e^{\left(-5\right)}}{15 \, {\left(x e + d\right)}^{\frac{5}{2}}}"," ",0,"2/3*((x*e + d)^(3/2)*c^2*e^10 - 12*sqrt(x*e + d)*c^2*d*e^10 + 6*sqrt(x*e + d)*b*c*e^11)*e^(-15) - 2/15*(90*(x*e + d)^2*c^2*d^2 - 20*(x*e + d)*c^2*d^3 + 3*c^2*d^4 - 90*(x*e + d)^2*b*c*d*e + 30*(x*e + d)*b*c*d^2*e - 6*b*c*d^3*e + 15*(x*e + d)^2*b^2*e^2 + 30*(x*e + d)^2*a*c*e^2 - 10*(x*e + d)*b^2*d*e^2 - 20*(x*e + d)*a*c*d*e^2 + 3*b^2*d^2*e^2 + 6*a*c*d^2*e^2 + 10*(x*e + d)*a*b*e^3 - 6*a*b*d*e^3 + 3*a^2*e^4)*e^(-5)/(x*e + d)^(5/2)","A",0
2282,1,3066,0,0.360869," ","integrate((e*x+d)^(5/2)*(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{2}{4849845} \, {\left(4849845 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{2} b d^{3} e^{\left(-1\right)} + 969969 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a b^{2} d^{3} e^{\left(-2\right)} + 969969 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{2} c d^{3} e^{\left(-2\right)} + 138567 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b^{3} d^{3} e^{\left(-3\right)} + 831402 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a b c d^{3} e^{\left(-3\right)} + 46189 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b^{2} c d^{3} e^{\left(-4\right)} + 46189 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a c^{2} d^{3} e^{\left(-4\right)} + 20995 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b c^{2} d^{3} e^{\left(-5\right)} + 1615 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} c^{3} d^{3} e^{\left(-6\right)} + 2909907 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{2} b d^{2} e^{\left(-1\right)} + 1247103 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a b^{2} d^{2} e^{\left(-2\right)} + 1247103 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{2} c d^{2} e^{\left(-2\right)} + 46189 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b^{3} d^{2} e^{\left(-3\right)} + 277134 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a b c d^{2} e^{\left(-3\right)} + 62985 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b^{2} c d^{2} e^{\left(-4\right)} + 62985 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a c^{2} d^{2} e^{\left(-4\right)} + 14535 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} b c^{2} d^{2} e^{\left(-5\right)} + 2261 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} c^{3} d^{2} e^{\left(-6\right)} + 4849845 \, \sqrt{x e + d} a^{3} d^{3} + 4849845 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{3} d^{2} + 1247103 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{2} b d e^{\left(-1\right)} + 138567 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a b^{2} d e^{\left(-2\right)} + 138567 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{2} c d e^{\left(-2\right)} + 20995 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b^{3} d e^{\left(-3\right)} + 125970 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a b c d e^{\left(-3\right)} + 14535 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} b^{2} c d e^{\left(-4\right)} + 14535 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} a c^{2} d e^{\left(-4\right)} + 6783 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} b c^{2} d e^{\left(-5\right)} + 133 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} c^{3} d e^{\left(-6\right)} + 969969 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{3} d + 46189 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{2} b e^{\left(-1\right)} + 20995 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a b^{2} e^{\left(-2\right)} + 20995 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a^{2} c e^{\left(-2\right)} + 1615 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} b^{3} e^{\left(-3\right)} + 9690 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} a b c e^{\left(-3\right)} + 2261 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} b^{2} c e^{\left(-4\right)} + 2261 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} a c^{2} e^{\left(-4\right)} + 133 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} b c^{2} e^{\left(-5\right)} + 21 \, {\left(12155 \, {\left(x e + d\right)}^{\frac{19}{2}} - 122265 \, {\left(x e + d\right)}^{\frac{17}{2}} d + 554268 \, {\left(x e + d\right)}^{\frac{15}{2}} d^{2} - 1492260 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{3} + 2645370 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{4} - 3233230 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{5} + 2771340 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{6} - 1662804 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{7} + 692835 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{8} - 230945 \, \sqrt{x e + d} d^{9}\right)} c^{3} e^{\left(-6\right)} + 138567 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{3}\right)} e^{\left(-1\right)}"," ",0,"2/4849845*(4849845*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^2*b*d^3*e^(-1) + 969969*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a*b^2*d^3*e^(-2) + 969969*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^2*c*d^3*e^(-2) + 138567*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b^3*d^3*e^(-3) + 831402*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*b*c*d^3*e^(-3) + 46189*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b^2*c*d^3*e^(-4) + 46189*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*c^2*d^3*e^(-4) + 20995*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b*c^2*d^3*e^(-5) + 1615*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*c^3*d^3*e^(-6) + 2909907*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^2*b*d^2*e^(-1) + 1247103*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*b^2*d^2*e^(-2) + 1247103*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^2*c*d^2*e^(-2) + 46189*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b^3*d^2*e^(-3) + 277134*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*b*c*d^2*e^(-3) + 62985*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b^2*c*d^2*e^(-4) + 62985*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a*c^2*d^2*e^(-4) + 14535*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*b*c^2*d^2*e^(-5) + 2261*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*c^3*d^2*e^(-6) + 4849845*sqrt(x*e + d)*a^3*d^3 + 4849845*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^3*d^2 + 1247103*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^2*b*d*e^(-1) + 138567*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*b^2*d*e^(-2) + 138567*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^2*c*d*e^(-2) + 20995*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b^3*d*e^(-3) + 125970*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a*b*c*d*e^(-3) + 14535*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*b^2*c*d*e^(-4) + 14535*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*a*c^2*d*e^(-4) + 6783*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*b*c^2*d*e^(-5) + 133*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*c^3*d*e^(-6) + 969969*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^3*d + 46189*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^2*b*e^(-1) + 20995*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a*b^2*e^(-2) + 20995*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a^2*c*e^(-2) + 1615*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*b^3*e^(-3) + 9690*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*a*b*c*e^(-3) + 2261*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*b^2*c*e^(-4) + 2261*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*a*c^2*e^(-4) + 133*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*b*c^2*e^(-5) + 21*(12155*(x*e + d)^(19/2) - 122265*(x*e + d)^(17/2)*d + 554268*(x*e + d)^(15/2)*d^2 - 1492260*(x*e + d)^(13/2)*d^3 + 2645370*(x*e + d)^(11/2)*d^4 - 3233230*(x*e + d)^(9/2)*d^5 + 2771340*(x*e + d)^(7/2)*d^6 - 1662804*(x*e + d)^(5/2)*d^7 + 692835*(x*e + d)^(3/2)*d^8 - 230945*sqrt(x*e + d)*d^9)*c^3*e^(-6) + 138567*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^3)*e^(-1)","B",0
2283,1,2092,0,0.615170," ","integrate((e*x+d)^(3/2)*(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{2}{765765} \, {\left(765765 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{2} b d^{2} e^{\left(-1\right)} + 153153 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a b^{2} d^{2} e^{\left(-2\right)} + 153153 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{2} c d^{2} e^{\left(-2\right)} + 21879 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b^{3} d^{2} e^{\left(-3\right)} + 131274 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a b c d^{2} e^{\left(-3\right)} + 7293 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b^{2} c d^{2} e^{\left(-4\right)} + 7293 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a c^{2} d^{2} e^{\left(-4\right)} + 3315 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b c^{2} d^{2} e^{\left(-5\right)} + 255 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} c^{3} d^{2} e^{\left(-6\right)} + 306306 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{2} b d e^{\left(-1\right)} + 131274 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a b^{2} d e^{\left(-2\right)} + 131274 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{2} c d e^{\left(-2\right)} + 4862 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b^{3} d e^{\left(-3\right)} + 29172 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a b c d e^{\left(-3\right)} + 6630 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b^{2} c d e^{\left(-4\right)} + 6630 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a c^{2} d e^{\left(-4\right)} + 1530 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} b c^{2} d e^{\left(-5\right)} + 238 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} c^{3} d e^{\left(-6\right)} + 765765 \, \sqrt{x e + d} a^{3} d^{2} + 510510 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{3} d + 65637 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{2} b e^{\left(-1\right)} + 7293 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a b^{2} e^{\left(-2\right)} + 7293 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a^{2} c e^{\left(-2\right)} + 1105 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b^{3} e^{\left(-3\right)} + 6630 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a b c e^{\left(-3\right)} + 765 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} b^{2} c e^{\left(-4\right)} + 765 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} a c^{2} e^{\left(-4\right)} + 357 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} b c^{2} e^{\left(-5\right)} + 7 \, {\left(6435 \, {\left(x e + d\right)}^{\frac{17}{2}} - 58344 \, {\left(x e + d\right)}^{\frac{15}{2}} d + 235620 \, {\left(x e + d\right)}^{\frac{13}{2}} d^{2} - 556920 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{3} + 850850 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{4} - 875160 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{5} + 612612 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{6} - 291720 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{7} + 109395 \, \sqrt{x e + d} d^{8}\right)} c^{3} e^{\left(-6\right)} + 51051 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{3}\right)} e^{\left(-1\right)}"," ",0,"2/765765*(765765*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^2*b*d^2*e^(-1) + 153153*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a*b^2*d^2*e^(-2) + 153153*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^2*c*d^2*e^(-2) + 21879*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b^3*d^2*e^(-3) + 131274*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*b*c*d^2*e^(-3) + 7293*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b^2*c*d^2*e^(-4) + 7293*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*c^2*d^2*e^(-4) + 3315*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b*c^2*d^2*e^(-5) + 255*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*c^3*d^2*e^(-6) + 306306*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^2*b*d*e^(-1) + 131274*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*b^2*d*e^(-2) + 131274*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^2*c*d*e^(-2) + 4862*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b^3*d*e^(-3) + 29172*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*b*c*d*e^(-3) + 6630*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b^2*c*d*e^(-4) + 6630*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a*c^2*d*e^(-4) + 1530*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*b*c^2*d*e^(-5) + 238*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*c^3*d*e^(-6) + 765765*sqrt(x*e + d)*a^3*d^2 + 510510*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^3*d + 65637*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^2*b*e^(-1) + 7293*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*b^2*e^(-2) + 7293*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a^2*c*e^(-2) + 1105*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b^3*e^(-3) + 6630*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a*b*c*e^(-3) + 765*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*b^2*c*e^(-4) + 765*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*a*c^2*e^(-4) + 357*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*b*c^2*e^(-5) + 7*(6435*(x*e + d)^(17/2) - 58344*(x*e + d)^(15/2)*d + 235620*(x*e + d)^(13/2)*d^2 - 556920*(x*e + d)^(11/2)*d^3 + 850850*(x*e + d)^(9/2)*d^4 - 875160*(x*e + d)^(7/2)*d^5 + 612612*(x*e + d)^(5/2)*d^6 - 291720*(x*e + d)^(3/2)*d^7 + 109395*sqrt(x*e + d)*d^8)*c^3*e^(-6) + 51051*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^3)*e^(-1)","B",0
2284,1,1248,0,0.257039," ","integrate((c*x^2+b*x+a)^3*(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{45045} \, {\left(45045 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{2} b d e^{\left(-1\right)} + 9009 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a b^{2} d e^{\left(-2\right)} + 9009 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{2} c d e^{\left(-2\right)} + 1287 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b^{3} d e^{\left(-3\right)} + 7722 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a b c d e^{\left(-3\right)} + 429 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b^{2} c d e^{\left(-4\right)} + 429 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a c^{2} d e^{\left(-4\right)} + 195 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b c^{2} d e^{\left(-5\right)} + 15 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} c^{3} d e^{\left(-6\right)} + 9009 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{2} b e^{\left(-1\right)} + 3861 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a b^{2} e^{\left(-2\right)} + 3861 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a^{2} c e^{\left(-2\right)} + 143 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b^{3} e^{\left(-3\right)} + 858 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a b c e^{\left(-3\right)} + 195 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b^{2} c e^{\left(-4\right)} + 195 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} a c^{2} e^{\left(-4\right)} + 45 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} b c^{2} e^{\left(-5\right)} + 7 \, {\left(429 \, {\left(x e + d\right)}^{\frac{15}{2}} - 3465 \, {\left(x e + d\right)}^{\frac{13}{2}} d + 12285 \, {\left(x e + d\right)}^{\frac{11}{2}} d^{2} - 25025 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{3} + 32175 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{4} - 27027 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{5} + 15015 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{6} - 6435 \, \sqrt{x e + d} d^{7}\right)} c^{3} e^{\left(-6\right)} + 45045 \, \sqrt{x e + d} a^{3} d + 15015 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{3}\right)} e^{\left(-1\right)}"," ",0,"2/45045*(45045*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^2*b*d*e^(-1) + 9009*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a*b^2*d*e^(-2) + 9009*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^2*c*d*e^(-2) + 1287*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b^3*d*e^(-3) + 7722*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*b*c*d*e^(-3) + 429*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b^2*c*d*e^(-4) + 429*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*c^2*d*e^(-4) + 195*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b*c^2*d*e^(-5) + 15*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*c^3*d*e^(-6) + 9009*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^2*b*e^(-1) + 3861*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*b^2*e^(-2) + 3861*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a^2*c*e^(-2) + 143*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b^3*e^(-3) + 858*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*b*c*e^(-3) + 195*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b^2*c*e^(-4) + 195*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*a*c^2*e^(-4) + 45*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*b*c^2*e^(-5) + 7*(429*(x*e + d)^(15/2) - 3465*(x*e + d)^(13/2)*d + 12285*(x*e + d)^(11/2)*d^2 - 25025*(x*e + d)^(9/2)*d^3 + 32175*(x*e + d)^(7/2)*d^4 - 27027*(x*e + d)^(5/2)*d^5 + 15015*(x*e + d)^(3/2)*d^6 - 6435*sqrt(x*e + d)*d^7)*c^3*e^(-6) + 45045*sqrt(x*e + d)*a^3*d + 15015*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^3)*e^(-1)","B",0
2285,1,556,0,0.213858," ","integrate((c*x^2+b*x+a)^3/(e*x+d)^(1/2),x, algorithm=""giac"")","\frac{2}{15015} \, {\left(15015 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{x e + d} d\right)} a^{2} b e^{\left(-1\right)} + 3003 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a b^{2} e^{\left(-2\right)} + 3003 \, {\left(3 \, {\left(x e + d\right)}^{\frac{5}{2}} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} d + 15 \, \sqrt{x e + d} d^{2}\right)} a^{2} c e^{\left(-2\right)} + 429 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} b^{3} e^{\left(-3\right)} + 2574 \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} - 21 \, {\left(x e + d\right)}^{\frac{5}{2}} d + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{2} - 35 \, \sqrt{x e + d} d^{3}\right)} a b c e^{\left(-3\right)} + 143 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} b^{2} c e^{\left(-4\right)} + 143 \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} - 180 \, {\left(x e + d\right)}^{\frac{7}{2}} d + 378 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{2} - 420 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{3} + 315 \, \sqrt{x e + d} d^{4}\right)} a c^{2} e^{\left(-4\right)} + 65 \, {\left(63 \, {\left(x e + d\right)}^{\frac{11}{2}} - 385 \, {\left(x e + d\right)}^{\frac{9}{2}} d + 990 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{2} - 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{3} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{4} - 693 \, \sqrt{x e + d} d^{5}\right)} b c^{2} e^{\left(-5\right)} + 5 \, {\left(231 \, {\left(x e + d\right)}^{\frac{13}{2}} - 1638 \, {\left(x e + d\right)}^{\frac{11}{2}} d + 5005 \, {\left(x e + d\right)}^{\frac{9}{2}} d^{2} - 8580 \, {\left(x e + d\right)}^{\frac{7}{2}} d^{3} + 9009 \, {\left(x e + d\right)}^{\frac{5}{2}} d^{4} - 6006 \, {\left(x e + d\right)}^{\frac{3}{2}} d^{5} + 3003 \, \sqrt{x e + d} d^{6}\right)} c^{3} e^{\left(-6\right)} + 15015 \, \sqrt{x e + d} a^{3}\right)} e^{\left(-1\right)}"," ",0,"2/15015*(15015*((x*e + d)^(3/2) - 3*sqrt(x*e + d)*d)*a^2*b*e^(-1) + 3003*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a*b^2*e^(-2) + 3003*(3*(x*e + d)^(5/2) - 10*(x*e + d)^(3/2)*d + 15*sqrt(x*e + d)*d^2)*a^2*c*e^(-2) + 429*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*b^3*e^(-3) + 2574*(5*(x*e + d)^(7/2) - 21*(x*e + d)^(5/2)*d + 35*(x*e + d)^(3/2)*d^2 - 35*sqrt(x*e + d)*d^3)*a*b*c*e^(-3) + 143*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*b^2*c*e^(-4) + 143*(35*(x*e + d)^(9/2) - 180*(x*e + d)^(7/2)*d + 378*(x*e + d)^(5/2)*d^2 - 420*(x*e + d)^(3/2)*d^3 + 315*sqrt(x*e + d)*d^4)*a*c^2*e^(-4) + 65*(63*(x*e + d)^(11/2) - 385*(x*e + d)^(9/2)*d + 990*(x*e + d)^(7/2)*d^2 - 1386*(x*e + d)^(5/2)*d^3 + 1155*(x*e + d)^(3/2)*d^4 - 693*sqrt(x*e + d)*d^5)*b*c^2*e^(-5) + 5*(231*(x*e + d)^(13/2) - 1638*(x*e + d)^(11/2)*d + 5005*(x*e + d)^(9/2)*d^2 - 8580*(x*e + d)^(7/2)*d^3 + 9009*(x*e + d)^(5/2)*d^4 - 6006*(x*e + d)^(3/2)*d^5 + 3003*sqrt(x*e + d)*d^6)*c^3*e^(-6) + 15015*sqrt(x*e + d)*a^3)*e^(-1)","B",0
2286,1,631,0,0.242134," ","integrate((c*x^2+b*x+a)^3/(e*x+d)^(3/2),x, algorithm=""giac"")","\frac{2}{1155} \, {\left(105 \, {\left(x e + d\right)}^{\frac{11}{2}} c^{3} e^{70} - 770 \, {\left(x e + d\right)}^{\frac{9}{2}} c^{3} d e^{70} + 2475 \, {\left(x e + d\right)}^{\frac{7}{2}} c^{3} d^{2} e^{70} - 4620 \, {\left(x e + d\right)}^{\frac{5}{2}} c^{3} d^{3} e^{70} + 5775 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{3} d^{4} e^{70} - 6930 \, \sqrt{x e + d} c^{3} d^{5} e^{70} + 385 \, {\left(x e + d\right)}^{\frac{9}{2}} b c^{2} e^{71} - 2475 \, {\left(x e + d\right)}^{\frac{7}{2}} b c^{2} d e^{71} + 6930 \, {\left(x e + d\right)}^{\frac{5}{2}} b c^{2} d^{2} e^{71} - 11550 \, {\left(x e + d\right)}^{\frac{3}{2}} b c^{2} d^{3} e^{71} + 17325 \, \sqrt{x e + d} b c^{2} d^{4} e^{71} + 495 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{2} c e^{72} + 495 \, {\left(x e + d\right)}^{\frac{7}{2}} a c^{2} e^{72} - 2772 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{2} c d e^{72} - 2772 \, {\left(x e + d\right)}^{\frac{5}{2}} a c^{2} d e^{72} + 6930 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{2} c d^{2} e^{72} + 6930 \, {\left(x e + d\right)}^{\frac{3}{2}} a c^{2} d^{2} e^{72} - 13860 \, \sqrt{x e + d} b^{2} c d^{3} e^{72} - 13860 \, \sqrt{x e + d} a c^{2} d^{3} e^{72} + 231 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{3} e^{73} + 1386 \, {\left(x e + d\right)}^{\frac{5}{2}} a b c e^{73} - 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{3} d e^{73} - 6930 \, {\left(x e + d\right)}^{\frac{3}{2}} a b c d e^{73} + 3465 \, \sqrt{x e + d} b^{3} d^{2} e^{73} + 20790 \, \sqrt{x e + d} a b c d^{2} e^{73} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{2} e^{74} + 1155 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} c e^{74} - 6930 \, \sqrt{x e + d} a b^{2} d e^{74} - 6930 \, \sqrt{x e + d} a^{2} c d e^{74} + 3465 \, \sqrt{x e + d} a^{2} b e^{75}\right)} e^{\left(-77\right)} - \frac{2 \, {\left(c^{3} d^{6} - 3 \, b c^{2} d^{5} e + 3 \, b^{2} c d^{4} e^{2} + 3 \, a c^{2} d^{4} e^{2} - b^{3} d^{3} e^{3} - 6 \, a b c d^{3} e^{3} + 3 \, a b^{2} d^{2} e^{4} + 3 \, a^{2} c d^{2} e^{4} - 3 \, a^{2} b d e^{5} + a^{3} e^{6}\right)} e^{\left(-7\right)}}{\sqrt{x e + d}}"," ",0,"2/1155*(105*(x*e + d)^(11/2)*c^3*e^70 - 770*(x*e + d)^(9/2)*c^3*d*e^70 + 2475*(x*e + d)^(7/2)*c^3*d^2*e^70 - 4620*(x*e + d)^(5/2)*c^3*d^3*e^70 + 5775*(x*e + d)^(3/2)*c^3*d^4*e^70 - 6930*sqrt(x*e + d)*c^3*d^5*e^70 + 385*(x*e + d)^(9/2)*b*c^2*e^71 - 2475*(x*e + d)^(7/2)*b*c^2*d*e^71 + 6930*(x*e + d)^(5/2)*b*c^2*d^2*e^71 - 11550*(x*e + d)^(3/2)*b*c^2*d^3*e^71 + 17325*sqrt(x*e + d)*b*c^2*d^4*e^71 + 495*(x*e + d)^(7/2)*b^2*c*e^72 + 495*(x*e + d)^(7/2)*a*c^2*e^72 - 2772*(x*e + d)^(5/2)*b^2*c*d*e^72 - 2772*(x*e + d)^(5/2)*a*c^2*d*e^72 + 6930*(x*e + d)^(3/2)*b^2*c*d^2*e^72 + 6930*(x*e + d)^(3/2)*a*c^2*d^2*e^72 - 13860*sqrt(x*e + d)*b^2*c*d^3*e^72 - 13860*sqrt(x*e + d)*a*c^2*d^3*e^72 + 231*(x*e + d)^(5/2)*b^3*e^73 + 1386*(x*e + d)^(5/2)*a*b*c*e^73 - 1155*(x*e + d)^(3/2)*b^3*d*e^73 - 6930*(x*e + d)^(3/2)*a*b*c*d*e^73 + 3465*sqrt(x*e + d)*b^3*d^2*e^73 + 20790*sqrt(x*e + d)*a*b*c*d^2*e^73 + 1155*(x*e + d)^(3/2)*a*b^2*e^74 + 1155*(x*e + d)^(3/2)*a^2*c*e^74 - 6930*sqrt(x*e + d)*a*b^2*d*e^74 - 6930*sqrt(x*e + d)*a^2*c*d*e^74 + 3465*sqrt(x*e + d)*a^2*b*e^75)*e^(-77) - 2*(c^3*d^6 - 3*b*c^2*d^5*e + 3*b^2*c*d^4*e^2 + 3*a*c^2*d^4*e^2 - b^3*d^3*e^3 - 6*a*b*c*d^3*e^3 + 3*a*b^2*d^2*e^4 + 3*a^2*c*d^2*e^4 - 3*a^2*b*d*e^5 + a^3*e^6)*e^(-7)/sqrt(x*e + d)","B",0
2287,1,612,0,0.242149," ","integrate((c*x^2+b*x+a)^3/(e*x+d)^(5/2),x, algorithm=""giac"")","\frac{2}{315} \, {\left(35 \, {\left(x e + d\right)}^{\frac{9}{2}} c^{3} e^{56} - 270 \, {\left(x e + d\right)}^{\frac{7}{2}} c^{3} d e^{56} + 945 \, {\left(x e + d\right)}^{\frac{5}{2}} c^{3} d^{2} e^{56} - 2100 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{3} d^{3} e^{56} + 4725 \, \sqrt{x e + d} c^{3} d^{4} e^{56} + 135 \, {\left(x e + d\right)}^{\frac{7}{2}} b c^{2} e^{57} - 945 \, {\left(x e + d\right)}^{\frac{5}{2}} b c^{2} d e^{57} + 3150 \, {\left(x e + d\right)}^{\frac{3}{2}} b c^{2} d^{2} e^{57} - 9450 \, \sqrt{x e + d} b c^{2} d^{3} e^{57} + 189 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{2} c e^{58} + 189 \, {\left(x e + d\right)}^{\frac{5}{2}} a c^{2} e^{58} - 1260 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{2} c d e^{58} - 1260 \, {\left(x e + d\right)}^{\frac{3}{2}} a c^{2} d e^{58} + 5670 \, \sqrt{x e + d} b^{2} c d^{2} e^{58} + 5670 \, \sqrt{x e + d} a c^{2} d^{2} e^{58} + 105 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{3} e^{59} + 630 \, {\left(x e + d\right)}^{\frac{3}{2}} a b c e^{59} - 945 \, \sqrt{x e + d} b^{3} d e^{59} - 5670 \, \sqrt{x e + d} a b c d e^{59} + 945 \, \sqrt{x e + d} a b^{2} e^{60} + 945 \, \sqrt{x e + d} a^{2} c e^{60}\right)} e^{\left(-63\right)} + \frac{2 \, {\left(18 \, {\left(x e + d\right)} c^{3} d^{5} - c^{3} d^{6} - 45 \, {\left(x e + d\right)} b c^{2} d^{4} e + 3 \, b c^{2} d^{5} e + 36 \, {\left(x e + d\right)} b^{2} c d^{3} e^{2} + 36 \, {\left(x e + d\right)} a c^{2} d^{3} e^{2} - 3 \, b^{2} c d^{4} e^{2} - 3 \, a c^{2} d^{4} e^{2} - 9 \, {\left(x e + d\right)} b^{3} d^{2} e^{3} - 54 \, {\left(x e + d\right)} a b c d^{2} e^{3} + b^{3} d^{3} e^{3} + 6 \, a b c d^{3} e^{3} + 18 \, {\left(x e + d\right)} a b^{2} d e^{4} + 18 \, {\left(x e + d\right)} a^{2} c d e^{4} - 3 \, a b^{2} d^{2} e^{4} - 3 \, a^{2} c d^{2} e^{4} - 9 \, {\left(x e + d\right)} a^{2} b e^{5} + 3 \, a^{2} b d e^{5} - a^{3} e^{6}\right)} e^{\left(-7\right)}}{3 \, {\left(x e + d\right)}^{\frac{3}{2}}}"," ",0,"2/315*(35*(x*e + d)^(9/2)*c^3*e^56 - 270*(x*e + d)^(7/2)*c^3*d*e^56 + 945*(x*e + d)^(5/2)*c^3*d^2*e^56 - 2100*(x*e + d)^(3/2)*c^3*d^3*e^56 + 4725*sqrt(x*e + d)*c^3*d^4*e^56 + 135*(x*e + d)^(7/2)*b*c^2*e^57 - 945*(x*e + d)^(5/2)*b*c^2*d*e^57 + 3150*(x*e + d)^(3/2)*b*c^2*d^2*e^57 - 9450*sqrt(x*e + d)*b*c^2*d^3*e^57 + 189*(x*e + d)^(5/2)*b^2*c*e^58 + 189*(x*e + d)^(5/2)*a*c^2*e^58 - 1260*(x*e + d)^(3/2)*b^2*c*d*e^58 - 1260*(x*e + d)^(3/2)*a*c^2*d*e^58 + 5670*sqrt(x*e + d)*b^2*c*d^2*e^58 + 5670*sqrt(x*e + d)*a*c^2*d^2*e^58 + 105*(x*e + d)^(3/2)*b^3*e^59 + 630*(x*e + d)^(3/2)*a*b*c*e^59 - 945*sqrt(x*e + d)*b^3*d*e^59 - 5670*sqrt(x*e + d)*a*b*c*d*e^59 + 945*sqrt(x*e + d)*a*b^2*e^60 + 945*sqrt(x*e + d)*a^2*c*e^60)*e^(-63) + 2/3*(18*(x*e + d)*c^3*d^5 - c^3*d^6 - 45*(x*e + d)*b*c^2*d^4*e + 3*b*c^2*d^5*e + 36*(x*e + d)*b^2*c*d^3*e^2 + 36*(x*e + d)*a*c^2*d^3*e^2 - 3*b^2*c*d^4*e^2 - 3*a*c^2*d^4*e^2 - 9*(x*e + d)*b^3*d^2*e^3 - 54*(x*e + d)*a*b*c*d^2*e^3 + b^3*d^3*e^3 + 6*a*b*c*d^3*e^3 + 18*(x*e + d)*a*b^2*d*e^4 + 18*(x*e + d)*a^2*c*d*e^4 - 3*a*b^2*d^2*e^4 - 3*a^2*c*d^2*e^4 - 9*(x*e + d)*a^2*b*e^5 + 3*a^2*b*d*e^5 - a^3*e^6)*e^(-7)/(x*e + d)^(3/2)","B",0
2288,1,609,0,0.242913," ","integrate((c*x^2+b*x+a)^3/(e*x+d)^(7/2),x, algorithm=""giac"")","\frac{2}{35} \, {\left(5 \, {\left(x e + d\right)}^{\frac{7}{2}} c^{3} e^{42} - 42 \, {\left(x e + d\right)}^{\frac{5}{2}} c^{3} d e^{42} + 175 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{3} d^{2} e^{42} - 700 \, \sqrt{x e + d} c^{3} d^{3} e^{42} + 21 \, {\left(x e + d\right)}^{\frac{5}{2}} b c^{2} e^{43} - 175 \, {\left(x e + d\right)}^{\frac{3}{2}} b c^{2} d e^{43} + 1050 \, \sqrt{x e + d} b c^{2} d^{2} e^{43} + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{2} c e^{44} + 35 \, {\left(x e + d\right)}^{\frac{3}{2}} a c^{2} e^{44} - 420 \, \sqrt{x e + d} b^{2} c d e^{44} - 420 \, \sqrt{x e + d} a c^{2} d e^{44} + 35 \, \sqrt{x e + d} b^{3} e^{45} + 210 \, \sqrt{x e + d} a b c e^{45}\right)} e^{\left(-49\right)} - \frac{2 \, {\left(75 \, {\left(x e + d\right)}^{2} c^{3} d^{4} - 10 \, {\left(x e + d\right)} c^{3} d^{5} + c^{3} d^{6} - 150 \, {\left(x e + d\right)}^{2} b c^{2} d^{3} e + 25 \, {\left(x e + d\right)} b c^{2} d^{4} e - 3 \, b c^{2} d^{5} e + 90 \, {\left(x e + d\right)}^{2} b^{2} c d^{2} e^{2} + 90 \, {\left(x e + d\right)}^{2} a c^{2} d^{2} e^{2} - 20 \, {\left(x e + d\right)} b^{2} c d^{3} e^{2} - 20 \, {\left(x e + d\right)} a c^{2} d^{3} e^{2} + 3 \, b^{2} c d^{4} e^{2} + 3 \, a c^{2} d^{4} e^{2} - 15 \, {\left(x e + d\right)}^{2} b^{3} d e^{3} - 90 \, {\left(x e + d\right)}^{2} a b c d e^{3} + 5 \, {\left(x e + d\right)} b^{3} d^{2} e^{3} + 30 \, {\left(x e + d\right)} a b c d^{2} e^{3} - b^{3} d^{3} e^{3} - 6 \, a b c d^{3} e^{3} + 15 \, {\left(x e + d\right)}^{2} a b^{2} e^{4} + 15 \, {\left(x e + d\right)}^{2} a^{2} c e^{4} - 10 \, {\left(x e + d\right)} a b^{2} d e^{4} - 10 \, {\left(x e + d\right)} a^{2} c d e^{4} + 3 \, a b^{2} d^{2} e^{4} + 3 \, a^{2} c d^{2} e^{4} + 5 \, {\left(x e + d\right)} a^{2} b e^{5} - 3 \, a^{2} b d e^{5} + a^{3} e^{6}\right)} e^{\left(-7\right)}}{5 \, {\left(x e + d\right)}^{\frac{5}{2}}}"," ",0,"2/35*(5*(x*e + d)^(7/2)*c^3*e^42 - 42*(x*e + d)^(5/2)*c^3*d*e^42 + 175*(x*e + d)^(3/2)*c^3*d^2*e^42 - 700*sqrt(x*e + d)*c^3*d^3*e^42 + 21*(x*e + d)^(5/2)*b*c^2*e^43 - 175*(x*e + d)^(3/2)*b*c^2*d*e^43 + 1050*sqrt(x*e + d)*b*c^2*d^2*e^43 + 35*(x*e + d)^(3/2)*b^2*c*e^44 + 35*(x*e + d)^(3/2)*a*c^2*e^44 - 420*sqrt(x*e + d)*b^2*c*d*e^44 - 420*sqrt(x*e + d)*a*c^2*d*e^44 + 35*sqrt(x*e + d)*b^3*e^45 + 210*sqrt(x*e + d)*a*b*c*e^45)*e^(-49) - 2/5*(75*(x*e + d)^2*c^3*d^4 - 10*(x*e + d)*c^3*d^5 + c^3*d^6 - 150*(x*e + d)^2*b*c^2*d^3*e + 25*(x*e + d)*b*c^2*d^4*e - 3*b*c^2*d^5*e + 90*(x*e + d)^2*b^2*c*d^2*e^2 + 90*(x*e + d)^2*a*c^2*d^2*e^2 - 20*(x*e + d)*b^2*c*d^3*e^2 - 20*(x*e + d)*a*c^2*d^3*e^2 + 3*b^2*c*d^4*e^2 + 3*a*c^2*d^4*e^2 - 15*(x*e + d)^2*b^3*d*e^3 - 90*(x*e + d)^2*a*b*c*d*e^3 + 5*(x*e + d)*b^3*d^2*e^3 + 30*(x*e + d)*a*b*c*d^2*e^3 - b^3*d^3*e^3 - 6*a*b*c*d^3*e^3 + 15*(x*e + d)^2*a*b^2*e^4 + 15*(x*e + d)^2*a^2*c*e^4 - 10*(x*e + d)*a*b^2*d*e^4 - 10*(x*e + d)*a^2*c*d*e^4 + 3*a*b^2*d^2*e^4 + 3*a^2*c*d^2*e^4 + 5*(x*e + d)*a^2*b*e^5 - 3*a^2*b*d*e^5 + a^3*e^6)*e^(-7)/(x*e + d)^(5/2)","B",0
2289,1,1012,0,0.468543," ","integrate((e*x+d)^(5/2)/(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{{\left({\left(3 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} e^{2} - 3 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d e^{3} + {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} e^{4}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} c^{2} - 2 \, {\left(2 \, \sqrt{b^{2} - 4 \, a c} c^{4} d^{3} e - 3 \, \sqrt{b^{2} - 4 \, a c} b c^{3} d^{2} e^{2} - \sqrt{b^{2} - 4 \, a c} a b c^{2} e^{4} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} \sqrt{b^{2} - 4 \, a c} d e^{3}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left| c \right|} - {\left(4 \, c^{6} d^{4} - 8 \, b c^{5} d^{3} e + 3 \, {\left(3 \, b^{2} c^{4} - 4 \, a c^{5}\right)} d^{2} e^{2} - {\left(5 \, b^{3} c^{3} - 12 \, a b c^{4}\right)} d e^{3} + {\left(b^{4} c^{2} - 3 \, a b^{2} c^{3}\right)} e^{4}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, c^{4} d - b c^{3} e + \sqrt{-4 \, {\left(c^{4} d^{2} - b c^{3} d e + a c^{3} e^{2}\right)} c^{4} + {\left(2 \, c^{4} d - b c^{3} e\right)}^{2}}}{c^{4}}}}\right)}{4 \, {\left(\sqrt{b^{2} - 4 \, a c} c^{5} d^{2} - \sqrt{b^{2} - 4 \, a c} b c^{4} d e + \sqrt{b^{2} - 4 \, a c} a c^{4} e^{2}\right)} c^{2}} - \frac{{\left({\left(3 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} e^{2} - 3 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d e^{3} + {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} e^{4}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} c^{2} + 2 \, {\left(2 \, \sqrt{b^{2} - 4 \, a c} c^{4} d^{3} e - 3 \, \sqrt{b^{2} - 4 \, a c} b c^{3} d^{2} e^{2} - \sqrt{b^{2} - 4 \, a c} a b c^{2} e^{4} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} \sqrt{b^{2} - 4 \, a c} d e^{3}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left| c \right|} - {\left(4 \, c^{6} d^{4} - 8 \, b c^{5} d^{3} e + 3 \, {\left(3 \, b^{2} c^{4} - 4 \, a c^{5}\right)} d^{2} e^{2} - {\left(5 \, b^{3} c^{3} - 12 \, a b c^{4}\right)} d e^{3} + {\left(b^{4} c^{2} - 3 \, a b^{2} c^{3}\right)} e^{4}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, c^{4} d - b c^{3} e - \sqrt{-4 \, {\left(c^{4} d^{2} - b c^{3} d e + a c^{3} e^{2}\right)} c^{4} + {\left(2 \, c^{4} d - b c^{3} e\right)}^{2}}}{c^{4}}}}\right)}{4 \, {\left(\sqrt{b^{2} - 4 \, a c} c^{5} d^{2} - \sqrt{b^{2} - 4 \, a c} b c^{4} d e + \sqrt{b^{2} - 4 \, a c} a c^{4} e^{2}\right)} c^{2}} + \frac{2 \, {\left({\left(x e + d\right)}^{\frac{3}{2}} c^{2} e + 6 \, \sqrt{x e + d} c^{2} d e - 3 \, \sqrt{x e + d} b c e^{2}\right)}}{3 \, c^{3}}"," ",0,"1/4*((3*(b^2*c^2 - 4*a*c^3)*d^2*e^2 - 3*(b^3*c - 4*a*b*c^2)*d*e^3 + (b^4 - 5*a*b^2*c + 4*a^2*c^2)*e^4)*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*c^2 - 2*(2*sqrt(b^2 - 4*a*c)*c^4*d^3*e - 3*sqrt(b^2 - 4*a*c)*b*c^3*d^2*e^2 - sqrt(b^2 - 4*a*c)*a*b*c^2*e^4 + (b^2*c^2 + 2*a*c^3)*sqrt(b^2 - 4*a*c)*d*e^3)*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*abs(c) - (4*c^6*d^4 - 8*b*c^5*d^3*e + 3*(3*b^2*c^4 - 4*a*c^5)*d^2*e^2 - (5*b^3*c^3 - 12*a*b*c^4)*d*e^3 + (b^4*c^2 - 3*a*b^2*c^3)*e^4)*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e))*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*c^4*d - b*c^3*e + sqrt(-4*(c^4*d^2 - b*c^3*d*e + a*c^3*e^2)*c^4 + (2*c^4*d - b*c^3*e)^2))/c^4))/((sqrt(b^2 - 4*a*c)*c^5*d^2 - sqrt(b^2 - 4*a*c)*b*c^4*d*e + sqrt(b^2 - 4*a*c)*a*c^4*e^2)*c^2) - 1/4*((3*(b^2*c^2 - 4*a*c^3)*d^2*e^2 - 3*(b^3*c - 4*a*b*c^2)*d*e^3 + (b^4 - 5*a*b^2*c + 4*a^2*c^2)*e^4)*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*c^2 + 2*(2*sqrt(b^2 - 4*a*c)*c^4*d^3*e - 3*sqrt(b^2 - 4*a*c)*b*c^3*d^2*e^2 - sqrt(b^2 - 4*a*c)*a*b*c^2*e^4 + (b^2*c^2 + 2*a*c^3)*sqrt(b^2 - 4*a*c)*d*e^3)*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*abs(c) - (4*c^6*d^4 - 8*b*c^5*d^3*e + 3*(3*b^2*c^4 - 4*a*c^5)*d^2*e^2 - (5*b^3*c^3 - 12*a*b*c^4)*d*e^3 + (b^4*c^2 - 3*a*b^2*c^3)*e^4)*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e))*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*c^4*d - b*c^3*e - sqrt(-4*(c^4*d^2 - b*c^3*d*e + a*c^3*e^2)*c^4 + (2*c^4*d - b*c^3*e)^2))/c^4))/((sqrt(b^2 - 4*a*c)*c^5*d^2 - sqrt(b^2 - 4*a*c)*b*c^4*d*e + sqrt(b^2 - 4*a*c)*a*c^4*e^2)*c^2) + 2/3*((x*e + d)^(3/2)*c^2*e + 6*sqrt(x*e + d)*c^2*d*e - 3*sqrt(x*e + d)*b*c*e^2)/c^3","B",0
2290,1,783,0,0.408799," ","integrate((e*x+d)^(3/2)/(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{2 \, \sqrt{x e + d} e}{c} + \frac{{\left(\sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d e^{2} - {\left(b^{3} - 4 \, a b c\right)} e^{3}\right)} c^{2} - 2 \, {\left(\sqrt{b^{2} - 4 \, a c} c^{3} d^{2} e - \sqrt{b^{2} - 4 \, a c} b c^{2} d e^{2} + \sqrt{b^{2} - 4 \, a c} a c^{2} e^{3}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left| c \right|} - {\left(4 \, c^{5} d^{3} - 6 \, b c^{4} d^{2} e + 4 \, {\left(b^{2} c^{3} - a c^{4}\right)} d e^{2} - {\left(b^{3} c^{2} - 2 \, a b c^{3}\right)} e^{3}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, c^{2} d - b c e + \sqrt{-4 \, {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} c^{2} + {\left(2 \, c^{2} d - b c e\right)}^{2}}}{c^{2}}}}\right)}{4 \, {\left(\sqrt{b^{2} - 4 \, a c} c^{4} d^{2} - \sqrt{b^{2} - 4 \, a c} b c^{3} d e + \sqrt{b^{2} - 4 \, a c} a c^{3} e^{2}\right)} c^{2}} - \frac{{\left(\sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d e^{2} - {\left(b^{3} - 4 \, a b c\right)} e^{3}\right)} c^{2} + 2 \, {\left(\sqrt{b^{2} - 4 \, a c} c^{3} d^{2} e - \sqrt{b^{2} - 4 \, a c} b c^{2} d e^{2} + \sqrt{b^{2} - 4 \, a c} a c^{2} e^{3}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left| c \right|} - {\left(4 \, c^{5} d^{3} - 6 \, b c^{4} d^{2} e + 4 \, {\left(b^{2} c^{3} - a c^{4}\right)} d e^{2} - {\left(b^{3} c^{2} - 2 \, a b c^{3}\right)} e^{3}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, c^{2} d - b c e - \sqrt{-4 \, {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} c^{2} + {\left(2 \, c^{2} d - b c e\right)}^{2}}}{c^{2}}}}\right)}{4 \, {\left(\sqrt{b^{2} - 4 \, a c} c^{4} d^{2} - \sqrt{b^{2} - 4 \, a c} b c^{3} d e + \sqrt{b^{2} - 4 \, a c} a c^{3} e^{2}\right)} c^{2}}"," ",0,"2*sqrt(x*e + d)*e/c + 1/4*(sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*(2*(b^2*c - 4*a*c^2)*d*e^2 - (b^3 - 4*a*b*c)*e^3)*c^2 - 2*(sqrt(b^2 - 4*a*c)*c^3*d^2*e - sqrt(b^2 - 4*a*c)*b*c^2*d*e^2 + sqrt(b^2 - 4*a*c)*a*c^2*e^3)*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*abs(c) - (4*c^5*d^3 - 6*b*c^4*d^2*e + 4*(b^2*c^3 - a*c^4)*d*e^2 - (b^3*c^2 - 2*a*b*c^3)*e^3)*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e))*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*c^2*d - b*c*e + sqrt(-4*(c^2*d^2 - b*c*d*e + a*c*e^2)*c^2 + (2*c^2*d - b*c*e)^2))/c^2))/((sqrt(b^2 - 4*a*c)*c^4*d^2 - sqrt(b^2 - 4*a*c)*b*c^3*d*e + sqrt(b^2 - 4*a*c)*a*c^3*e^2)*c^2) - 1/4*(sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*(2*(b^2*c - 4*a*c^2)*d*e^2 - (b^3 - 4*a*b*c)*e^3)*c^2 + 2*(sqrt(b^2 - 4*a*c)*c^3*d^2*e - sqrt(b^2 - 4*a*c)*b*c^2*d*e^2 + sqrt(b^2 - 4*a*c)*a*c^2*e^3)*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*abs(c) - (4*c^5*d^3 - 6*b*c^4*d^2*e + 4*(b^2*c^3 - a*c^4)*d*e^2 - (b^3*c^2 - 2*a*b*c^3)*e^3)*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e))*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*c^2*d - b*c*e - sqrt(-4*(c^2*d^2 - b*c*d*e + a*c*e^2)*c^2 + (2*c^2*d - b*c*e)^2))/c^2))/((sqrt(b^2 - 4*a*c)*c^4*d^2 - sqrt(b^2 - 4*a*c)*b*c^3*d*e + sqrt(b^2 - 4*a*c)*a*c^3*e^2)*c^2)","B",0
2291,1,223,0,0.291798," ","integrate((e*x+d)^(1/2)/(c*x^2+b*x+a),x, algorithm=""giac"")","-\frac{\sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, c d - b e + \sqrt{{\left(2 \, c d - b e\right)}^{2} - 4 \, {\left(c d^{2} - b d e + a e^{2}\right)} c}}{c}}}\right)}{\sqrt{b^{2} - 4 \, a c} {\left| c \right|}} + \frac{\sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, c d - b e - \sqrt{{\left(2 \, c d - b e\right)}^{2} - 4 \, {\left(c d^{2} - b d e + a e^{2}\right)} c}}{c}}}\right)}{\sqrt{b^{2} - 4 \, a c} {\left| c \right|}}"," ",0,"-sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*c*d - b*e + sqrt((2*c*d - b*e)^2 - 4*(c*d^2 - b*d*e + a*e^2)*c))/c))/(sqrt(b^2 - 4*a*c)*abs(c)) + sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*c*d - b*e - sqrt((2*c*d - b*e)^2 - 4*(c*d^2 - b*d*e + a*e^2)*c))/c))/(sqrt(b^2 - 4*a*c)*abs(c))","A",0
2292,1,288,0,0.236901," ","integrate(1/(e*x+d)^(1/2)/(c*x^2+b*x+a),x, algorithm=""giac"")","-\frac{2 \, \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} c \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, c d - b e + \sqrt{{\left(2 \, c d - b e\right)}^{2} - 4 \, {\left(c d^{2} - b d e + a e^{2}\right)} c}}{c}}}\right)}{{\left(2 \, \sqrt{b^{2} - 4 \, a c} c d + {\left(b^{2} - 4 \, a c - \sqrt{b^{2} - 4 \, a c} b\right)} e\right)} {\left| c \right|}} + \frac{2 \, \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} c \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, c d - b e - \sqrt{{\left(2 \, c d - b e\right)}^{2} - 4 \, {\left(c d^{2} - b d e + a e^{2}\right)} c}}{c}}}\right)}{{\left(2 \, \sqrt{b^{2} - 4 \, a c} c d - {\left(b^{2} - 4 \, a c + \sqrt{b^{2} - 4 \, a c} b\right)} e\right)} {\left| c \right|}}"," ",0,"-2*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*c*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*c*d - b*e + sqrt((2*c*d - b*e)^2 - 4*(c*d^2 - b*d*e + a*e^2)*c))/c))/((2*sqrt(b^2 - 4*a*c)*c*d + (b^2 - 4*a*c - sqrt(b^2 - 4*a*c)*b)*e)*abs(c)) + 2*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*c*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*c*d - b*e - sqrt((2*c*d - b*e)^2 - 4*(c*d^2 - b*d*e + a*e^2)*c))/c))/((2*sqrt(b^2 - 4*a*c)*c*d - (b^2 - 4*a*c + sqrt(b^2 - 4*a*c)*b)*e)*abs(c))","A",0
2293,1,1458,0,0.746105," ","integrate(1/(e*x+d)^(3/2)/(c*x^2+b*x+a),x, algorithm=""giac"")","-\frac{2 \, e}{{\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{x e + d}} - \frac{{\left({\left(c d^{2} e - b d e^{2} + a e^{3}\right)}^{2} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left(b^{2} - 4 \, a c\right)} e - 2 \, {\left(2 \, \sqrt{b^{2} - 4 \, a c} c^{2} d^{3} e - 3 \, \sqrt{b^{2} - 4 \, a c} b c d^{2} e^{2} - \sqrt{b^{2} - 4 \, a c} a b e^{4} + {\left(b^{2} + 2 \, a c\right)} \sqrt{b^{2} - 4 \, a c} d e^{3}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left| c d^{2} e - b d e^{2} + a e^{3} \right|} + {\left(4 \, c^{4} d^{6} e - 12 \, b c^{3} d^{5} e^{2} + {\left(13 \, b^{2} c^{2} + 8 \, a c^{3}\right)} d^{4} e^{3} + a^{2} b^{2} e^{7} - 2 \, {\left(3 \, b^{3} c + 8 \, a b c^{2}\right)} d^{3} e^{4} + {\left(b^{4} + 10 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} d^{2} e^{5} - 2 \, {\left(a b^{3} + 2 \, a^{2} b c\right)} d e^{6}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, c^{2} d^{3} - 3 \, b c d^{2} e + b^{2} d e^{2} + 2 \, a c d e^{2} - a b e^{3} + \sqrt{{\left(2 \, c^{2} d^{3} - 3 \, b c d^{2} e + b^{2} d e^{2} + 2 \, a c d e^{2} - a b e^{3}\right)}^{2} - 4 \, {\left(c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2} + 2 \, a c d^{2} e^{2} - 2 \, a b d e^{3} + a^{2} e^{4}\right)} {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)}}}{c^{2} d^{2} - b c d e + a c e^{2}}}}\right)}{4 \, {\left(\sqrt{b^{2} - 4 \, a c} c^{3} d^{6} - 3 \, \sqrt{b^{2} - 4 \, a c} b c^{2} d^{5} e + 3 \, {\left(b^{2} c + a c^{2}\right)} \sqrt{b^{2} - 4 \, a c} d^{4} e^{2} - 3 \, \sqrt{b^{2} - 4 \, a c} a^{2} b d e^{5} - {\left(b^{3} + 6 \, a b c\right)} \sqrt{b^{2} - 4 \, a c} d^{3} e^{3} + \sqrt{b^{2} - 4 \, a c} a^{3} e^{6} + 3 \, {\left(a b^{2} + a^{2} c\right)} \sqrt{b^{2} - 4 \, a c} d^{2} e^{4}\right)} {\left| c d^{2} e - b d e^{2} + a e^{3} \right|} {\left| c \right|}} + \frac{{\left({\left(c d^{2} e - b d e^{2} + a e^{3}\right)}^{2} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left(b^{2} - 4 \, a c\right)} e + 2 \, {\left(2 \, \sqrt{b^{2} - 4 \, a c} c^{2} d^{3} e - 3 \, \sqrt{b^{2} - 4 \, a c} b c d^{2} e^{2} - \sqrt{b^{2} - 4 \, a c} a b e^{4} + {\left(b^{2} + 2 \, a c\right)} \sqrt{b^{2} - 4 \, a c} d e^{3}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left| c d^{2} e - b d e^{2} + a e^{3} \right|} + {\left(4 \, c^{4} d^{6} e - 12 \, b c^{3} d^{5} e^{2} + {\left(13 \, b^{2} c^{2} + 8 \, a c^{3}\right)} d^{4} e^{3} + a^{2} b^{2} e^{7} - 2 \, {\left(3 \, b^{3} c + 8 \, a b c^{2}\right)} d^{3} e^{4} + {\left(b^{4} + 10 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} d^{2} e^{5} - 2 \, {\left(a b^{3} + 2 \, a^{2} b c\right)} d e^{6}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, c^{2} d^{3} - 3 \, b c d^{2} e + b^{2} d e^{2} + 2 \, a c d e^{2} - a b e^{3} - \sqrt{{\left(2 \, c^{2} d^{3} - 3 \, b c d^{2} e + b^{2} d e^{2} + 2 \, a c d e^{2} - a b e^{3}\right)}^{2} - 4 \, {\left(c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2} + 2 \, a c d^{2} e^{2} - 2 \, a b d e^{3} + a^{2} e^{4}\right)} {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)}}}{c^{2} d^{2} - b c d e + a c e^{2}}}}\right)}{4 \, {\left(\sqrt{b^{2} - 4 \, a c} c^{3} d^{6} - 3 \, \sqrt{b^{2} - 4 \, a c} b c^{2} d^{5} e + 3 \, {\left(b^{2} c + a c^{2}\right)} \sqrt{b^{2} - 4 \, a c} d^{4} e^{2} - 3 \, \sqrt{b^{2} - 4 \, a c} a^{2} b d e^{5} - {\left(b^{3} + 6 \, a b c\right)} \sqrt{b^{2} - 4 \, a c} d^{3} e^{3} + \sqrt{b^{2} - 4 \, a c} a^{3} e^{6} + 3 \, {\left(a b^{2} + a^{2} c\right)} \sqrt{b^{2} - 4 \, a c} d^{2} e^{4}\right)} {\left| c d^{2} e - b d e^{2} + a e^{3} \right|} {\left| c \right|}}"," ",0,"-2*e/((c*d^2 - b*d*e + a*e^2)*sqrt(x*e + d)) - 1/4*((c*d^2*e - b*d*e^2 + a*e^3)^2*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*(b^2 - 4*a*c)*e - 2*(2*sqrt(b^2 - 4*a*c)*c^2*d^3*e - 3*sqrt(b^2 - 4*a*c)*b*c*d^2*e^2 - sqrt(b^2 - 4*a*c)*a*b*e^4 + (b^2 + 2*a*c)*sqrt(b^2 - 4*a*c)*d*e^3)*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*abs(c*d^2*e - b*d*e^2 + a*e^3) + (4*c^4*d^6*e - 12*b*c^3*d^5*e^2 + (13*b^2*c^2 + 8*a*c^3)*d^4*e^3 + a^2*b^2*e^7 - 2*(3*b^3*c + 8*a*b*c^2)*d^3*e^4 + (b^4 + 10*a*b^2*c + 4*a^2*c^2)*d^2*e^5 - 2*(a*b^3 + 2*a^2*b*c)*d*e^6)*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e))*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*c^2*d^3 - 3*b*c*d^2*e + b^2*d*e^2 + 2*a*c*d*e^2 - a*b*e^3 + sqrt((2*c^2*d^3 - 3*b*c*d^2*e + b^2*d*e^2 + 2*a*c*d*e^2 - a*b*e^3)^2 - 4*(c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2 + 2*a*c*d^2*e^2 - 2*a*b*d*e^3 + a^2*e^4)*(c^2*d^2 - b*c*d*e + a*c*e^2)))/(c^2*d^2 - b*c*d*e + a*c*e^2)))/((sqrt(b^2 - 4*a*c)*c^3*d^6 - 3*sqrt(b^2 - 4*a*c)*b*c^2*d^5*e + 3*(b^2*c + a*c^2)*sqrt(b^2 - 4*a*c)*d^4*e^2 - 3*sqrt(b^2 - 4*a*c)*a^2*b*d*e^5 - (b^3 + 6*a*b*c)*sqrt(b^2 - 4*a*c)*d^3*e^3 + sqrt(b^2 - 4*a*c)*a^3*e^6 + 3*(a*b^2 + a^2*c)*sqrt(b^2 - 4*a*c)*d^2*e^4)*abs(c*d^2*e - b*d*e^2 + a*e^3)*abs(c)) + 1/4*((c*d^2*e - b*d*e^2 + a*e^3)^2*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*(b^2 - 4*a*c)*e + 2*(2*sqrt(b^2 - 4*a*c)*c^2*d^3*e - 3*sqrt(b^2 - 4*a*c)*b*c*d^2*e^2 - sqrt(b^2 - 4*a*c)*a*b*e^4 + (b^2 + 2*a*c)*sqrt(b^2 - 4*a*c)*d*e^3)*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*abs(c*d^2*e - b*d*e^2 + a*e^3) + (4*c^4*d^6*e - 12*b*c^3*d^5*e^2 + (13*b^2*c^2 + 8*a*c^3)*d^4*e^3 + a^2*b^2*e^7 - 2*(3*b^3*c + 8*a*b*c^2)*d^3*e^4 + (b^4 + 10*a*b^2*c + 4*a^2*c^2)*d^2*e^5 - 2*(a*b^3 + 2*a^2*b*c)*d*e^6)*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e))*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*c^2*d^3 - 3*b*c*d^2*e + b^2*d*e^2 + 2*a*c*d*e^2 - a*b*e^3 - sqrt((2*c^2*d^3 - 3*b*c*d^2*e + b^2*d*e^2 + 2*a*c*d*e^2 - a*b*e^3)^2 - 4*(c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2 + 2*a*c*d^2*e^2 - 2*a*b*d*e^3 + a^2*e^4)*(c^2*d^2 - b*c*d*e + a*c*e^2)))/(c^2*d^2 - b*c*d*e + a*c*e^2)))/((sqrt(b^2 - 4*a*c)*c^3*d^6 - 3*sqrt(b^2 - 4*a*c)*b*c^2*d^5*e + 3*(b^2*c + a*c^2)*sqrt(b^2 - 4*a*c)*d^4*e^2 - 3*sqrt(b^2 - 4*a*c)*a^2*b*d*e^5 - (b^3 + 6*a*b*c)*sqrt(b^2 - 4*a*c)*d^3*e^3 + sqrt(b^2 - 4*a*c)*a^3*e^6 + 3*(a*b^2 + a^2*c)*sqrt(b^2 - 4*a*c)*d^2*e^4)*abs(c*d^2*e - b*d*e^2 + a*e^3)*abs(c))","B",0
2294,1,1287,0,3.335093," ","integrate(1/(e*x+d)^(5/2)/(c*x^2+b*x+a),x, algorithm=""giac"")","-\frac{2 \, \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} c^{3} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, c^{3} d^{5} - 5 \, b c^{2} d^{4} e + 4 \, b^{2} c d^{3} e^{2} + 4 \, a c^{2} d^{3} e^{2} - b^{3} d^{2} e^{3} - 6 \, a b c d^{2} e^{3} + 2 \, a b^{2} d e^{4} + 2 \, a^{2} c d e^{4} - a^{2} b e^{5} + \sqrt{{\left(2 \, c^{3} d^{5} - 5 \, b c^{2} d^{4} e + 4 \, b^{2} c d^{3} e^{2} + 4 \, a c^{2} d^{3} e^{2} - b^{3} d^{2} e^{3} - 6 \, a b c d^{2} e^{3} + 2 \, a b^{2} d e^{4} + 2 \, a^{2} c d e^{4} - a^{2} b e^{5}\right)}^{2} - 4 \, {\left(c^{3} d^{6} - 3 \, b c^{2} d^{5} e + 3 \, b^{2} c d^{4} e^{2} + 3 \, a c^{2} d^{4} e^{2} - b^{3} d^{3} e^{3} - 6 \, a b c d^{3} e^{3} + 3 \, a b^{2} d^{2} e^{4} + 3 \, a^{2} c d^{2} e^{4} - 3 \, a^{2} b d e^{5} + a^{3} e^{6}\right)} {\left(c^{3} d^{4} - 2 \, b c^{2} d^{3} e + b^{2} c d^{2} e^{2} + 2 \, a c^{2} d^{2} e^{2} - 2 \, a b c d e^{3} + a^{2} c e^{4}\right)}}}{c^{3} d^{4} - 2 \, b c^{2} d^{3} e + b^{2} c d^{2} e^{2} + 2 \, a c^{2} d^{2} e^{2} - 2 \, a b c d e^{3} + a^{2} c e^{4}}}}\right)}{{\left(2 \, \sqrt{b^{2} - 4 \, a c} c^{3} d^{3} + 3 \, {\left(b^{2} c^{2} - 4 \, a c^{3} - \sqrt{b^{2} - 4 \, a c} b c^{2}\right)} d^{2} e - 3 \, {\left(b^{3} c - 4 \, a b c^{2} - {\left(b^{2} c - 2 \, a c^{2}\right)} \sqrt{b^{2} - 4 \, a c}\right)} d e^{2} + {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2} - {\left(b^{3} - 3 \, a b c\right)} \sqrt{b^{2} - 4 \, a c}\right)} e^{3}\right)} {\left| c \right|}} + \frac{2 \, \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} c^{3} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, c^{3} d^{5} - 5 \, b c^{2} d^{4} e + 4 \, b^{2} c d^{3} e^{2} + 4 \, a c^{2} d^{3} e^{2} - b^{3} d^{2} e^{3} - 6 \, a b c d^{2} e^{3} + 2 \, a b^{2} d e^{4} + 2 \, a^{2} c d e^{4} - a^{2} b e^{5} - \sqrt{{\left(2 \, c^{3} d^{5} - 5 \, b c^{2} d^{4} e + 4 \, b^{2} c d^{3} e^{2} + 4 \, a c^{2} d^{3} e^{2} - b^{3} d^{2} e^{3} - 6 \, a b c d^{2} e^{3} + 2 \, a b^{2} d e^{4} + 2 \, a^{2} c d e^{4} - a^{2} b e^{5}\right)}^{2} - 4 \, {\left(c^{3} d^{6} - 3 \, b c^{2} d^{5} e + 3 \, b^{2} c d^{4} e^{2} + 3 \, a c^{2} d^{4} e^{2} - b^{3} d^{3} e^{3} - 6 \, a b c d^{3} e^{3} + 3 \, a b^{2} d^{2} e^{4} + 3 \, a^{2} c d^{2} e^{4} - 3 \, a^{2} b d e^{5} + a^{3} e^{6}\right)} {\left(c^{3} d^{4} - 2 \, b c^{2} d^{3} e + b^{2} c d^{2} e^{2} + 2 \, a c^{2} d^{2} e^{2} - 2 \, a b c d e^{3} + a^{2} c e^{4}\right)}}}{c^{3} d^{4} - 2 \, b c^{2} d^{3} e + b^{2} c d^{2} e^{2} + 2 \, a c^{2} d^{2} e^{2} - 2 \, a b c d e^{3} + a^{2} c e^{4}}}}\right)}{{\left(2 \, \sqrt{b^{2} - 4 \, a c} c^{3} d^{3} - 3 \, {\left(b^{2} c^{2} - 4 \, a c^{3} + \sqrt{b^{2} - 4 \, a c} b c^{2}\right)} d^{2} e + 3 \, {\left(b^{3} c - 4 \, a b c^{2} + {\left(b^{2} c - 2 \, a c^{2}\right)} \sqrt{b^{2} - 4 \, a c}\right)} d e^{2} - {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2} + {\left(b^{3} - 3 \, a b c\right)} \sqrt{b^{2} - 4 \, a c}\right)} e^{3}\right)} {\left| c \right|}} - \frac{2 \, {\left(6 \, {\left(x e + d\right)} c d e + c d^{2} e - 3 \, {\left(x e + d\right)} b e^{2} - b d e^{2} + a e^{3}\right)}}{3 \, {\left(c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2} + 2 \, a c d^{2} e^{2} - 2 \, a b d e^{3} + a^{2} e^{4}\right)} {\left(x e + d\right)}^{\frac{3}{2}}}"," ",0,"-2*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*c^3*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*c^3*d^5 - 5*b*c^2*d^4*e + 4*b^2*c*d^3*e^2 + 4*a*c^2*d^3*e^2 - b^3*d^2*e^3 - 6*a*b*c*d^2*e^3 + 2*a*b^2*d*e^4 + 2*a^2*c*d*e^4 - a^2*b*e^5 + sqrt((2*c^3*d^5 - 5*b*c^2*d^4*e + 4*b^2*c*d^3*e^2 + 4*a*c^2*d^3*e^2 - b^3*d^2*e^3 - 6*a*b*c*d^2*e^3 + 2*a*b^2*d*e^4 + 2*a^2*c*d*e^4 - a^2*b*e^5)^2 - 4*(c^3*d^6 - 3*b*c^2*d^5*e + 3*b^2*c*d^4*e^2 + 3*a*c^2*d^4*e^2 - b^3*d^3*e^3 - 6*a*b*c*d^3*e^3 + 3*a*b^2*d^2*e^4 + 3*a^2*c*d^2*e^4 - 3*a^2*b*d*e^5 + a^3*e^6)*(c^3*d^4 - 2*b*c^2*d^3*e + b^2*c*d^2*e^2 + 2*a*c^2*d^2*e^2 - 2*a*b*c*d*e^3 + a^2*c*e^4)))/(c^3*d^4 - 2*b*c^2*d^3*e + b^2*c*d^2*e^2 + 2*a*c^2*d^2*e^2 - 2*a*b*c*d*e^3 + a^2*c*e^4)))/((2*sqrt(b^2 - 4*a*c)*c^3*d^3 + 3*(b^2*c^2 - 4*a*c^3 - sqrt(b^2 - 4*a*c)*b*c^2)*d^2*e - 3*(b^3*c - 4*a*b*c^2 - (b^2*c - 2*a*c^2)*sqrt(b^2 - 4*a*c))*d*e^2 + (b^4 - 5*a*b^2*c + 4*a^2*c^2 - (b^3 - 3*a*b*c)*sqrt(b^2 - 4*a*c))*e^3)*abs(c)) + 2*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*c^3*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*c^3*d^5 - 5*b*c^2*d^4*e + 4*b^2*c*d^3*e^2 + 4*a*c^2*d^3*e^2 - b^3*d^2*e^3 - 6*a*b*c*d^2*e^3 + 2*a*b^2*d*e^4 + 2*a^2*c*d*e^4 - a^2*b*e^5 - sqrt((2*c^3*d^5 - 5*b*c^2*d^4*e + 4*b^2*c*d^3*e^2 + 4*a*c^2*d^3*e^2 - b^3*d^2*e^3 - 6*a*b*c*d^2*e^3 + 2*a*b^2*d*e^4 + 2*a^2*c*d*e^4 - a^2*b*e^5)^2 - 4*(c^3*d^6 - 3*b*c^2*d^5*e + 3*b^2*c*d^4*e^2 + 3*a*c^2*d^4*e^2 - b^3*d^3*e^3 - 6*a*b*c*d^3*e^3 + 3*a*b^2*d^2*e^4 + 3*a^2*c*d^2*e^4 - 3*a^2*b*d*e^5 + a^3*e^6)*(c^3*d^4 - 2*b*c^2*d^3*e + b^2*c*d^2*e^2 + 2*a*c^2*d^2*e^2 - 2*a*b*c*d*e^3 + a^2*c*e^4)))/(c^3*d^4 - 2*b*c^2*d^3*e + b^2*c*d^2*e^2 + 2*a*c^2*d^2*e^2 - 2*a*b*c*d*e^3 + a^2*c*e^4)))/((2*sqrt(b^2 - 4*a*c)*c^3*d^3 - 3*(b^2*c^2 - 4*a*c^3 + sqrt(b^2 - 4*a*c)*b*c^2)*d^2*e + 3*(b^3*c - 4*a*b*c^2 + (b^2*c - 2*a*c^2)*sqrt(b^2 - 4*a*c))*d*e^2 - (b^4 - 5*a*b^2*c + 4*a^2*c^2 + (b^3 - 3*a*b*c)*sqrt(b^2 - 4*a*c))*e^3)*abs(c)) - 2/3*(6*(x*e + d)*c*d*e + c*d^2*e - 3*(x*e + d)*b*e^2 - b*d*e^2 + a*e^3)/((c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2 + 2*a*c*d^2*e^2 - 2*a*b*d*e^3 + a^2*e^4)*(x*e + d)^(3/2))","B",0
2295,1,1797,0,3.225254," ","integrate((e*x+d)^(7/2)/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{2 \, \sqrt{x e + d} e^{3}}{c^{2}} - \frac{2 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{3} d^{3} e - 2 \, \sqrt{x e + d} c^{3} d^{4} e - 3 \, {\left(x e + d\right)}^{\frac{3}{2}} b c^{2} d^{2} e^{2} + 4 \, \sqrt{x e + d} b c^{2} d^{3} e^{2} + 3 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{2} c d e^{3} - 6 \, {\left(x e + d\right)}^{\frac{3}{2}} a c^{2} d e^{3} - 3 \, \sqrt{x e + d} b^{2} c d^{2} e^{3} - {\left(x e + d\right)}^{\frac{3}{2}} b^{3} e^{4} + 3 \, {\left(x e + d\right)}^{\frac{3}{2}} a b c e^{4} + \sqrt{x e + d} b^{3} d e^{4} - \sqrt{x e + d} a b^{2} e^{5} + 2 \, \sqrt{x e + d} a^{2} c e^{5}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + {\left(x e + d\right)} b e - b d e + a e^{2}\right)}} - \frac{{\left(16 \, {\left(b^{2} c^{9} - 4 \, a c^{10}\right)} d^{5} e - 40 \, {\left(b^{3} c^{8} - 4 \, a b c^{9}\right)} d^{4} e^{2} + 2 \, {\left(11 \, b^{4} c^{7} - 8 \, a b^{2} c^{8} - 144 \, a^{2} c^{9}\right)} d^{3} e^{3} + {\left(7 \, b^{5} c^{6} - 136 \, a b^{3} c^{7} + 432 \, a^{2} b c^{8}\right)} d^{2} e^{4} - {\left(2 \, c^{3} d^{3} e - 3 \, b c^{2} d^{2} e^{2} - {\left(5 \, b^{2} c - 26 \, a c^{2}\right)} d e^{3} + {\left(3 \, b^{3} - 13 \, a b c\right)} e^{4}\right)} {\left(b^{2} c^{2} e - 4 \, a c^{3} e\right)}^{2} - {\left(11 \, b^{6} c^{5} - 118 \, a b^{4} c^{6} + 336 \, a^{2} b^{2} c^{7} - 160 \, a^{3} c^{8}\right)} d e^{5} - 2 \, {\left(2 \, \sqrt{b^{2} - 4 \, a c} c^{6} d^{4} e - 4 \, \sqrt{b^{2} - 4 \, a c} b c^{5} d^{3} e^{2} + {\left(5 \, b^{2} c^{4} - 8 \, a c^{5}\right)} \sqrt{b^{2} - 4 \, a c} d^{2} e^{3} - {\left(3 \, b^{3} c^{3} - 8 \, a b c^{4}\right)} \sqrt{b^{2} - 4 \, a c} d e^{4} + {\left(3 \, a b^{2} c^{3} - 10 \, a^{2} c^{4}\right)} \sqrt{b^{2} - 4 \, a c} e^{5}\right)} {\left| b^{2} c^{2} e - 4 \, a c^{3} e \right|} + {\left(3 \, b^{7} c^{4} - 31 \, a b^{5} c^{5} + 96 \, a^{2} b^{3} c^{6} - 80 \, a^{3} b c^{7}\right)} e^{6}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, b^{2} c^{3} d - 8 \, a c^{4} d - b^{3} c^{2} e + 4 \, a b c^{3} e + \sqrt{{\left(2 \, b^{2} c^{3} d - 8 \, a c^{4} d - b^{3} c^{2} e + 4 \, a b c^{3} e\right)}^{2} - 4 \, {\left(b^{2} c^{3} d^{2} - 4 \, a c^{4} d^{2} - b^{3} c^{2} d e + 4 \, a b c^{3} d e + a b^{2} c^{2} e^{2} - 4 \, a^{2} c^{3} e^{2}\right)} {\left(b^{2} c^{3} - 4 \, a c^{4}\right)}}}{b^{2} c^{3} - 4 \, a c^{4}}}}\right)}{\sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left(2 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{b^{2} - 4 \, a c} d - {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5} + {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} \sqrt{b^{2} - 4 \, a c}\right)} e\right)} {\left| b^{2} c^{2} e - 4 \, a c^{3} e \right|} {\left| c \right|}} + \frac{{\left(16 \, {\left(b^{2} c^{9} - 4 \, a c^{10}\right)} d^{5} e - 40 \, {\left(b^{3} c^{8} - 4 \, a b c^{9}\right)} d^{4} e^{2} + 2 \, {\left(11 \, b^{4} c^{7} - 8 \, a b^{2} c^{8} - 144 \, a^{2} c^{9}\right)} d^{3} e^{3} + {\left(7 \, b^{5} c^{6} - 136 \, a b^{3} c^{7} + 432 \, a^{2} b c^{8}\right)} d^{2} e^{4} - {\left(2 \, c^{3} d^{3} e - 3 \, b c^{2} d^{2} e^{2} - {\left(5 \, b^{2} c - 26 \, a c^{2}\right)} d e^{3} + {\left(3 \, b^{3} - 13 \, a b c\right)} e^{4}\right)} {\left(b^{2} c^{2} e - 4 \, a c^{3} e\right)}^{2} - {\left(11 \, b^{6} c^{5} - 118 \, a b^{4} c^{6} + 336 \, a^{2} b^{2} c^{7} - 160 \, a^{3} c^{8}\right)} d e^{5} + 2 \, {\left(2 \, \sqrt{b^{2} - 4 \, a c} c^{6} d^{4} e - 4 \, \sqrt{b^{2} - 4 \, a c} b c^{5} d^{3} e^{2} + {\left(5 \, b^{2} c^{4} - 8 \, a c^{5}\right)} \sqrt{b^{2} - 4 \, a c} d^{2} e^{3} - {\left(3 \, b^{3} c^{3} - 8 \, a b c^{4}\right)} \sqrt{b^{2} - 4 \, a c} d e^{4} + {\left(3 \, a b^{2} c^{3} - 10 \, a^{2} c^{4}\right)} \sqrt{b^{2} - 4 \, a c} e^{5}\right)} {\left| b^{2} c^{2} e - 4 \, a c^{3} e \right|} + {\left(3 \, b^{7} c^{4} - 31 \, a b^{5} c^{5} + 96 \, a^{2} b^{3} c^{6} - 80 \, a^{3} b c^{7}\right)} e^{6}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, b^{2} c^{3} d - 8 \, a c^{4} d - b^{3} c^{2} e + 4 \, a b c^{3} e - \sqrt{{\left(2 \, b^{2} c^{3} d - 8 \, a c^{4} d - b^{3} c^{2} e + 4 \, a b c^{3} e\right)}^{2} - 4 \, {\left(b^{2} c^{3} d^{2} - 4 \, a c^{4} d^{2} - b^{3} c^{2} d e + 4 \, a b c^{3} d e + a b^{2} c^{2} e^{2} - 4 \, a^{2} c^{3} e^{2}\right)} {\left(b^{2} c^{3} - 4 \, a c^{4}\right)}}}{b^{2} c^{3} - 4 \, a c^{4}}}}\right)}{\sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left(2 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{b^{2} - 4 \, a c} d + {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5} - {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} \sqrt{b^{2} - 4 \, a c}\right)} e\right)} {\left| b^{2} c^{2} e - 4 \, a c^{3} e \right|} {\left| c \right|}}"," ",0,"2*sqrt(x*e + d)*e^3/c^2 - (2*(x*e + d)^(3/2)*c^3*d^3*e - 2*sqrt(x*e + d)*c^3*d^4*e - 3*(x*e + d)^(3/2)*b*c^2*d^2*e^2 + 4*sqrt(x*e + d)*b*c^2*d^3*e^2 + 3*(x*e + d)^(3/2)*b^2*c*d*e^3 - 6*(x*e + d)^(3/2)*a*c^2*d*e^3 - 3*sqrt(x*e + d)*b^2*c*d^2*e^3 - (x*e + d)^(3/2)*b^3*e^4 + 3*(x*e + d)^(3/2)*a*b*c*e^4 + sqrt(x*e + d)*b^3*d*e^4 - sqrt(x*e + d)*a*b^2*e^5 + 2*sqrt(x*e + d)*a^2*c*e^5)/((b^2*c^2 - 4*a*c^3)*((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + (x*e + d)*b*e - b*d*e + a*e^2)) - (16*(b^2*c^9 - 4*a*c^10)*d^5*e - 40*(b^3*c^8 - 4*a*b*c^9)*d^4*e^2 + 2*(11*b^4*c^7 - 8*a*b^2*c^8 - 144*a^2*c^9)*d^3*e^3 + (7*b^5*c^6 - 136*a*b^3*c^7 + 432*a^2*b*c^8)*d^2*e^4 - (2*c^3*d^3*e - 3*b*c^2*d^2*e^2 - (5*b^2*c - 26*a*c^2)*d*e^3 + (3*b^3 - 13*a*b*c)*e^4)*(b^2*c^2*e - 4*a*c^3*e)^2 - (11*b^6*c^5 - 118*a*b^4*c^6 + 336*a^2*b^2*c^7 - 160*a^3*c^8)*d*e^5 - 2*(2*sqrt(b^2 - 4*a*c)*c^6*d^4*e - 4*sqrt(b^2 - 4*a*c)*b*c^5*d^3*e^2 + (5*b^2*c^4 - 8*a*c^5)*sqrt(b^2 - 4*a*c)*d^2*e^3 - (3*b^3*c^3 - 8*a*b*c^4)*sqrt(b^2 - 4*a*c)*d*e^4 + (3*a*b^2*c^3 - 10*a^2*c^4)*sqrt(b^2 - 4*a*c)*e^5)*abs(b^2*c^2*e - 4*a*c^3*e) + (3*b^7*c^4 - 31*a*b^5*c^5 + 96*a^2*b^3*c^6 - 80*a^3*b*c^7)*e^6)*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*b^2*c^3*d - 8*a*c^4*d - b^3*c^2*e + 4*a*b*c^3*e + sqrt((2*b^2*c^3*d - 8*a*c^4*d - b^3*c^2*e + 4*a*b*c^3*e)^2 - 4*(b^2*c^3*d^2 - 4*a*c^4*d^2 - b^3*c^2*d*e + 4*a*b*c^3*d*e + a*b^2*c^2*e^2 - 4*a^2*c^3*e^2)*(b^2*c^3 - 4*a*c^4)))/(b^2*c^3 - 4*a*c^4)))/(sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*(2*(b^2*c^4 - 4*a*c^5)*sqrt(b^2 - 4*a*c)*d - (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5 + (b^3*c^3 - 4*a*b*c^4)*sqrt(b^2 - 4*a*c))*e)*abs(b^2*c^2*e - 4*a*c^3*e)*abs(c)) + (16*(b^2*c^9 - 4*a*c^10)*d^5*e - 40*(b^3*c^8 - 4*a*b*c^9)*d^4*e^2 + 2*(11*b^4*c^7 - 8*a*b^2*c^8 - 144*a^2*c^9)*d^3*e^3 + (7*b^5*c^6 - 136*a*b^3*c^7 + 432*a^2*b*c^8)*d^2*e^4 - (2*c^3*d^3*e - 3*b*c^2*d^2*e^2 - (5*b^2*c - 26*a*c^2)*d*e^3 + (3*b^3 - 13*a*b*c)*e^4)*(b^2*c^2*e - 4*a*c^3*e)^2 - (11*b^6*c^5 - 118*a*b^4*c^6 + 336*a^2*b^2*c^7 - 160*a^3*c^8)*d*e^5 + 2*(2*sqrt(b^2 - 4*a*c)*c^6*d^4*e - 4*sqrt(b^2 - 4*a*c)*b*c^5*d^3*e^2 + (5*b^2*c^4 - 8*a*c^5)*sqrt(b^2 - 4*a*c)*d^2*e^3 - (3*b^3*c^3 - 8*a*b*c^4)*sqrt(b^2 - 4*a*c)*d*e^4 + (3*a*b^2*c^3 - 10*a^2*c^4)*sqrt(b^2 - 4*a*c)*e^5)*abs(b^2*c^2*e - 4*a*c^3*e) + (3*b^7*c^4 - 31*a*b^5*c^5 + 96*a^2*b^3*c^6 - 80*a^3*b*c^7)*e^6)*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*b^2*c^3*d - 8*a*c^4*d - b^3*c^2*e + 4*a*b*c^3*e - sqrt((2*b^2*c^3*d - 8*a*c^4*d - b^3*c^2*e + 4*a*b*c^3*e)^2 - 4*(b^2*c^3*d^2 - 4*a*c^4*d^2 - b^3*c^2*d*e + 4*a*b*c^3*d*e + a*b^2*c^2*e^2 - 4*a^2*c^3*e^2)*(b^2*c^3 - 4*a*c^4)))/(b^2*c^3 - 4*a*c^4)))/(sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*(2*(b^2*c^4 - 4*a*c^5)*sqrt(b^2 - 4*a*c)*d + (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5 - (b^3*c^3 - 4*a*b*c^4)*sqrt(b^2 - 4*a*c))*e)*abs(b^2*c^2*e - 4*a*c^3*e)*abs(c))","B",0
2296,1,1416,0,2.682050," ","integrate((e*x+d)^(5/2)/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","-\frac{2 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{2} d^{2} e - 2 \, \sqrt{x e + d} c^{2} d^{3} e - 2 \, {\left(x e + d\right)}^{\frac{3}{2}} b c d e^{2} + 3 \, \sqrt{x e + d} b c d^{2} e^{2} + {\left(x e + d\right)}^{\frac{3}{2}} b^{2} e^{3} - 2 \, {\left(x e + d\right)}^{\frac{3}{2}} a c e^{3} - \sqrt{x e + d} b^{2} d e^{3} - 2 \, \sqrt{x e + d} a c d e^{3} + \sqrt{x e + d} a b e^{4}}{{\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + {\left(x e + d\right)} b e - b d e + a e^{2}\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}} - \frac{{\left(16 \, {\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{4} e - 32 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{3} e^{2} + 16 \, {\left(b^{4} c^{4} - 2 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{2} e^{3} - {\left(2 \, c^{2} d^{2} e - 2 \, b c d e^{2} - {\left(b^{2} - 6 \, a c\right)} e^{3}\right)} {\left(b^{2} c e - 4 \, a c^{2} e\right)}^{2} - 32 \, {\left(a b^{3} c^{4} - 4 \, a^{2} b c^{5}\right)} d e^{4} - 2 \, {\left(2 \, \sqrt{b^{2} - 4 \, a c} c^{4} d^{3} e - 3 \, \sqrt{b^{2} - 4 \, a c} b c^{3} d^{2} e^{2} - \sqrt{b^{2} - 4 \, a c} a b c^{2} e^{4} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} \sqrt{b^{2} - 4 \, a c} d e^{3}\right)} {\left| b^{2} c e - 4 \, a c^{2} e \right|} - {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 32 \, a^{2} b^{2} c^{4}\right)} e^{5}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, b^{2} c^{2} d - 8 \, a c^{3} d - b^{3} c e + 4 \, a b c^{2} e + \sqrt{{\left(2 \, b^{2} c^{2} d - 8 \, a c^{3} d - b^{3} c e + 4 \, a b c^{2} e\right)}^{2} - 4 \, {\left(b^{2} c^{2} d^{2} - 4 \, a c^{3} d^{2} - b^{3} c d e + 4 \, a b c^{2} d e + a b^{2} c e^{2} - 4 \, a^{2} c^{2} e^{2}\right)} {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}}}{b^{2} c^{2} - 4 \, a c^{3}}}}\right)}{\sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left(2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{b^{2} - 4 \, a c} d - {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3} + {\left(b^{3} c - 4 \, a b c^{2}\right)} \sqrt{b^{2} - 4 \, a c}\right)} e\right)} {\left| b^{2} c e - 4 \, a c^{2} e \right|} {\left| c \right|}} + \frac{{\left(16 \, {\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{4} e - 32 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{3} e^{2} + 16 \, {\left(b^{4} c^{4} - 2 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{2} e^{3} - {\left(2 \, c^{2} d^{2} e - 2 \, b c d e^{2} - {\left(b^{2} - 6 \, a c\right)} e^{3}\right)} {\left(b^{2} c e - 4 \, a c^{2} e\right)}^{2} - 32 \, {\left(a b^{3} c^{4} - 4 \, a^{2} b c^{5}\right)} d e^{4} + 2 \, {\left(2 \, \sqrt{b^{2} - 4 \, a c} c^{4} d^{3} e - 3 \, \sqrt{b^{2} - 4 \, a c} b c^{3} d^{2} e^{2} - \sqrt{b^{2} - 4 \, a c} a b c^{2} e^{4} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} \sqrt{b^{2} - 4 \, a c} d e^{3}\right)} {\left| b^{2} c e - 4 \, a c^{2} e \right|} - {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 32 \, a^{2} b^{2} c^{4}\right)} e^{5}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, b^{2} c^{2} d - 8 \, a c^{3} d - b^{3} c e + 4 \, a b c^{2} e - \sqrt{{\left(2 \, b^{2} c^{2} d - 8 \, a c^{3} d - b^{3} c e + 4 \, a b c^{2} e\right)}^{2} - 4 \, {\left(b^{2} c^{2} d^{2} - 4 \, a c^{3} d^{2} - b^{3} c d e + 4 \, a b c^{2} d e + a b^{2} c e^{2} - 4 \, a^{2} c^{2} e^{2}\right)} {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}}}{b^{2} c^{2} - 4 \, a c^{3}}}}\right)}{\sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left(2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{b^{2} - 4 \, a c} d + {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3} - {\left(b^{3} c - 4 \, a b c^{2}\right)} \sqrt{b^{2} - 4 \, a c}\right)} e\right)} {\left| b^{2} c e - 4 \, a c^{2} e \right|} {\left| c \right|}}"," ",0,"-(2*(x*e + d)^(3/2)*c^2*d^2*e - 2*sqrt(x*e + d)*c^2*d^3*e - 2*(x*e + d)^(3/2)*b*c*d*e^2 + 3*sqrt(x*e + d)*b*c*d^2*e^2 + (x*e + d)^(3/2)*b^2*e^3 - 2*(x*e + d)^(3/2)*a*c*e^3 - sqrt(x*e + d)*b^2*d*e^3 - 2*sqrt(x*e + d)*a*c*d*e^3 + sqrt(x*e + d)*a*b*e^4)/(((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + (x*e + d)*b*e - b*d*e + a*e^2)*(b^2*c - 4*a*c^2)) - (16*(b^2*c^6 - 4*a*c^7)*d^4*e - 32*(b^3*c^5 - 4*a*b*c^6)*d^3*e^2 + 16*(b^4*c^4 - 2*a*b^2*c^5 - 8*a^2*c^6)*d^2*e^3 - (2*c^2*d^2*e - 2*b*c*d*e^2 - (b^2 - 6*a*c)*e^3)*(b^2*c*e - 4*a*c^2*e)^2 - 32*(a*b^3*c^4 - 4*a^2*b*c^5)*d*e^4 - 2*(2*sqrt(b^2 - 4*a*c)*c^4*d^3*e - 3*sqrt(b^2 - 4*a*c)*b*c^3*d^2*e^2 - sqrt(b^2 - 4*a*c)*a*b*c^2*e^4 + (b^2*c^2 + 2*a*c^3)*sqrt(b^2 - 4*a*c)*d*e^3)*abs(b^2*c*e - 4*a*c^2*e) - (b^6*c^2 - 12*a*b^4*c^3 + 32*a^2*b^2*c^4)*e^5)*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*b^2*c^2*d - 8*a*c^3*d - b^3*c*e + 4*a*b*c^2*e + sqrt((2*b^2*c^2*d - 8*a*c^3*d - b^3*c*e + 4*a*b*c^2*e)^2 - 4*(b^2*c^2*d^2 - 4*a*c^3*d^2 - b^3*c*d*e + 4*a*b*c^2*d*e + a*b^2*c*e^2 - 4*a^2*c^2*e^2)*(b^2*c^2 - 4*a*c^3)))/(b^2*c^2 - 4*a*c^3)))/(sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*(2*(b^2*c^2 - 4*a*c^3)*sqrt(b^2 - 4*a*c)*d - (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3 + (b^3*c - 4*a*b*c^2)*sqrt(b^2 - 4*a*c))*e)*abs(b^2*c*e - 4*a*c^2*e)*abs(c)) + (16*(b^2*c^6 - 4*a*c^7)*d^4*e - 32*(b^3*c^5 - 4*a*b*c^6)*d^3*e^2 + 16*(b^4*c^4 - 2*a*b^2*c^5 - 8*a^2*c^6)*d^2*e^3 - (2*c^2*d^2*e - 2*b*c*d*e^2 - (b^2 - 6*a*c)*e^3)*(b^2*c*e - 4*a*c^2*e)^2 - 32*(a*b^3*c^4 - 4*a^2*b*c^5)*d*e^4 + 2*(2*sqrt(b^2 - 4*a*c)*c^4*d^3*e - 3*sqrt(b^2 - 4*a*c)*b*c^3*d^2*e^2 - sqrt(b^2 - 4*a*c)*a*b*c^2*e^4 + (b^2*c^2 + 2*a*c^3)*sqrt(b^2 - 4*a*c)*d*e^3)*abs(b^2*c*e - 4*a*c^2*e) - (b^6*c^2 - 12*a*b^4*c^3 + 32*a^2*b^2*c^4)*e^5)*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*b^2*c^2*d - 8*a*c^3*d - b^3*c*e + 4*a*b*c^2*e - sqrt((2*b^2*c^2*d - 8*a*c^3*d - b^3*c*e + 4*a*b*c^2*e)^2 - 4*(b^2*c^2*d^2 - 4*a*c^3*d^2 - b^3*c*d*e + 4*a*b*c^2*d*e + a*b^2*c*e^2 - 4*a^2*c^2*e^2)*(b^2*c^2 - 4*a*c^3)))/(b^2*c^2 - 4*a*c^3)))/(sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*(2*(b^2*c^2 - 4*a*c^3)*sqrt(b^2 - 4*a*c)*d + (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3 - (b^3*c - 4*a*b*c^2)*sqrt(b^2 - 4*a*c))*e)*abs(b^2*c*e - 4*a*c^2*e)*abs(c))","B",0
2297,1,1223,0,1.278840," ","integrate((e*x+d)^(3/2)/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","-\frac{2 \, {\left(x e + d\right)}^{\frac{3}{2}} c d e - 2 \, \sqrt{x e + d} c d^{2} e - {\left(x e + d\right)}^{\frac{3}{2}} b e^{2} + 2 \, \sqrt{x e + d} b d e^{2} - 2 \, \sqrt{x e + d} a e^{3}}{{\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + {\left(x e + d\right)} b e - b d e + a e^{2}\right)} {\left(b^{2} - 4 \, a c\right)}} - \frac{{\left(\sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left(b^{2} e - 4 \, a c e\right)}^{2} {\left(2 \, c d e - b e^{2}\right)} + 4 \, {\left(\sqrt{b^{2} - 4 \, a c} c^{2} d^{2} e - \sqrt{b^{2} - 4 \, a c} b c d e^{2} + \sqrt{b^{2} - 4 \, a c} a c e^{3}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left| b^{2} e - 4 \, a c e \right|} - {\left(16 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{3} e - 24 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{2} e^{2} + 2 \, {\left(5 \, b^{4} c - 16 \, a b^{2} c^{2} - 16 \, a^{2} c^{3}\right)} d e^{3} - {\left(b^{5} - 16 \, a^{2} b c^{2}\right)} e^{4}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, b^{2} c d - 8 \, a c^{2} d - b^{3} e + 4 \, a b c e + \sqrt{{\left(2 \, b^{2} c d - 8 \, a c^{2} d - b^{3} e + 4 \, a b c e\right)}^{2} - 4 \, {\left(b^{2} c d^{2} - 4 \, a c^{2} d^{2} - b^{3} d e + 4 \, a b c d e + a b^{2} e^{2} - 4 \, a^{2} c e^{2}\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}}}{b^{2} c - 4 \, a c^{2}}}}\right)}{8 \, {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{b^{2} - 4 \, a c} d^{2} - {\left(b^{3} c - 4 \, a b c^{2}\right)} \sqrt{b^{2} - 4 \, a c} d e + {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} \sqrt{b^{2} - 4 \, a c} e^{2}\right)} {\left| b^{2} e - 4 \, a c e \right|} {\left| c \right|}} + \frac{{\left(\sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left(b^{2} e - 4 \, a c e\right)}^{2} {\left(2 \, c d e - b e^{2}\right)} - 4 \, {\left(\sqrt{b^{2} - 4 \, a c} c^{2} d^{2} e - \sqrt{b^{2} - 4 \, a c} b c d e^{2} + \sqrt{b^{2} - 4 \, a c} a c e^{3}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left| b^{2} e - 4 \, a c e \right|} - {\left(16 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{3} e - 24 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{2} e^{2} + 2 \, {\left(5 \, b^{4} c - 16 \, a b^{2} c^{2} - 16 \, a^{2} c^{3}\right)} d e^{3} - {\left(b^{5} - 16 \, a^{2} b c^{2}\right)} e^{4}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, b^{2} c d - 8 \, a c^{2} d - b^{3} e + 4 \, a b c e - \sqrt{{\left(2 \, b^{2} c d - 8 \, a c^{2} d - b^{3} e + 4 \, a b c e\right)}^{2} - 4 \, {\left(b^{2} c d^{2} - 4 \, a c^{2} d^{2} - b^{3} d e + 4 \, a b c d e + a b^{2} e^{2} - 4 \, a^{2} c e^{2}\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}}}{b^{2} c - 4 \, a c^{2}}}}\right)}{8 \, {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{b^{2} - 4 \, a c} d^{2} - {\left(b^{3} c - 4 \, a b c^{2}\right)} \sqrt{b^{2} - 4 \, a c} d e + {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} \sqrt{b^{2} - 4 \, a c} e^{2}\right)} {\left| b^{2} e - 4 \, a c e \right|} {\left| c \right|}}"," ",0,"-(2*(x*e + d)^(3/2)*c*d*e - 2*sqrt(x*e + d)*c*d^2*e - (x*e + d)^(3/2)*b*e^2 + 2*sqrt(x*e + d)*b*d*e^2 - 2*sqrt(x*e + d)*a*e^3)/(((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + (x*e + d)*b*e - b*d*e + a*e^2)*(b^2 - 4*a*c)) - 1/8*(sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*(b^2*e - 4*a*c*e)^2*(2*c*d*e - b*e^2) + 4*(sqrt(b^2 - 4*a*c)*c^2*d^2*e - sqrt(b^2 - 4*a*c)*b*c*d*e^2 + sqrt(b^2 - 4*a*c)*a*c*e^3)*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*abs(b^2*e - 4*a*c*e) - (16*(b^2*c^3 - 4*a*c^4)*d^3*e - 24*(b^3*c^2 - 4*a*b*c^3)*d^2*e^2 + 2*(5*b^4*c - 16*a*b^2*c^2 - 16*a^2*c^3)*d*e^3 - (b^5 - 16*a^2*b*c^2)*e^4)*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e))*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*b^2*c*d - 8*a*c^2*d - b^3*e + 4*a*b*c*e + sqrt((2*b^2*c*d - 8*a*c^2*d - b^3*e + 4*a*b*c*e)^2 - 4*(b^2*c*d^2 - 4*a*c^2*d^2 - b^3*d*e + 4*a*b*c*d*e + a*b^2*e^2 - 4*a^2*c*e^2)*(b^2*c - 4*a*c^2)))/(b^2*c - 4*a*c^2)))/(((b^2*c^2 - 4*a*c^3)*sqrt(b^2 - 4*a*c)*d^2 - (b^3*c - 4*a*b*c^2)*sqrt(b^2 - 4*a*c)*d*e + (a*b^2*c - 4*a^2*c^2)*sqrt(b^2 - 4*a*c)*e^2)*abs(b^2*e - 4*a*c*e)*abs(c)) + 1/8*(sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*(b^2*e - 4*a*c*e)^2*(2*c*d*e - b*e^2) - 4*(sqrt(b^2 - 4*a*c)*c^2*d^2*e - sqrt(b^2 - 4*a*c)*b*c*d*e^2 + sqrt(b^2 - 4*a*c)*a*c*e^3)*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*abs(b^2*e - 4*a*c*e) - (16*(b^2*c^3 - 4*a*c^4)*d^3*e - 24*(b^3*c^2 - 4*a*b*c^3)*d^2*e^2 + 2*(5*b^4*c - 16*a*b^2*c^2 - 16*a^2*c^3)*d*e^3 - (b^5 - 16*a^2*b*c^2)*e^4)*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e))*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*b^2*c*d - 8*a*c^2*d - b^3*e + 4*a*b*c*e - sqrt((2*b^2*c*d - 8*a*c^2*d - b^3*e + 4*a*b*c*e)^2 - 4*(b^2*c*d^2 - 4*a*c^2*d^2 - b^3*d*e + 4*a*b*c*d*e + a*b^2*e^2 - 4*a^2*c*e^2)*(b^2*c - 4*a*c^2)))/(b^2*c - 4*a*c^2)))/(((b^2*c^2 - 4*a*c^3)*sqrt(b^2 - 4*a*c)*d^2 - (b^3*c - 4*a*b*c^2)*sqrt(b^2 - 4*a*c)*d*e + (a*b^2*c - 4*a^2*c^2)*sqrt(b^2 - 4*a*c)*e^2)*abs(b^2*e - 4*a*c*e)*abs(c))","B",0
2298,1,1041,0,1.278406," ","integrate((e*x+d)^(1/2)/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","-\frac{2 \, {\left(x e + d\right)}^{\frac{3}{2}} c e - 2 \, \sqrt{x e + d} c d e + \sqrt{x e + d} b e^{2}}{{\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + {\left(x e + d\right)} b e - b d e + a e^{2}\right)} {\left(b^{2} - 4 \, a c\right)}} - \frac{{\left(\sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left(b^{2} e - 4 \, a c e\right)}^{2} e + {\left(2 \, \sqrt{b^{2} - 4 \, a c} c d e - \sqrt{b^{2} - 4 \, a c} b e^{2}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left| b^{2} e - 4 \, a c e \right|} - 2 \, {\left(4 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} e - 4 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d e^{2} + {\left(b^{4} - 4 \, a b^{2} c\right)} e^{3}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, b^{2} c d - 8 \, a c^{2} d - b^{3} e + 4 \, a b c e + \sqrt{{\left(2 \, b^{2} c d - 8 \, a c^{2} d - b^{3} e + 4 \, a b c e\right)}^{2} - 4 \, {\left(b^{2} c d^{2} - 4 \, a c^{2} d^{2} - b^{3} d e + 4 \, a b c d e + a b^{2} e^{2} - 4 \, a^{2} c e^{2}\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}}}{b^{2} c - 4 \, a c^{2}}}}\right)}{4 \, {\left({\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{b^{2} - 4 \, a c} d^{2} - {\left(b^{3} - 4 \, a b c\right)} \sqrt{b^{2} - 4 \, a c} d e + {\left(a b^{2} - 4 \, a^{2} c\right)} \sqrt{b^{2} - 4 \, a c} e^{2}\right)} {\left| b^{2} e - 4 \, a c e \right|} {\left| c \right|}} + \frac{{\left(\sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left(b^{2} e - 4 \, a c e\right)}^{2} e - {\left(2 \, \sqrt{b^{2} - 4 \, a c} c d e - \sqrt{b^{2} - 4 \, a c} b e^{2}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left| b^{2} e - 4 \, a c e \right|} - 2 \, {\left(4 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} e - 4 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d e^{2} + {\left(b^{4} - 4 \, a b^{2} c\right)} e^{3}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, b^{2} c d - 8 \, a c^{2} d - b^{3} e + 4 \, a b c e - \sqrt{{\left(2 \, b^{2} c d - 8 \, a c^{2} d - b^{3} e + 4 \, a b c e\right)}^{2} - 4 \, {\left(b^{2} c d^{2} - 4 \, a c^{2} d^{2} - b^{3} d e + 4 \, a b c d e + a b^{2} e^{2} - 4 \, a^{2} c e^{2}\right)} {\left(b^{2} c - 4 \, a c^{2}\right)}}}{b^{2} c - 4 \, a c^{2}}}}\right)}{4 \, {\left({\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{b^{2} - 4 \, a c} d^{2} - {\left(b^{3} - 4 \, a b c\right)} \sqrt{b^{2} - 4 \, a c} d e + {\left(a b^{2} - 4 \, a^{2} c\right)} \sqrt{b^{2} - 4 \, a c} e^{2}\right)} {\left| b^{2} e - 4 \, a c e \right|} {\left| c \right|}}"," ",0,"-(2*(x*e + d)^(3/2)*c*e - 2*sqrt(x*e + d)*c*d*e + sqrt(x*e + d)*b*e^2)/(((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + (x*e + d)*b*e - b*d*e + a*e^2)*(b^2 - 4*a*c)) - 1/4*(sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*(b^2*e - 4*a*c*e)^2*e + (2*sqrt(b^2 - 4*a*c)*c*d*e - sqrt(b^2 - 4*a*c)*b*e^2)*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*abs(b^2*e - 4*a*c*e) - 2*(4*(b^2*c^2 - 4*a*c^3)*d^2*e - 4*(b^3*c - 4*a*b*c^2)*d*e^2 + (b^4 - 4*a*b^2*c)*e^3)*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e))*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*b^2*c*d - 8*a*c^2*d - b^3*e + 4*a*b*c*e + sqrt((2*b^2*c*d - 8*a*c^2*d - b^3*e + 4*a*b*c*e)^2 - 4*(b^2*c*d^2 - 4*a*c^2*d^2 - b^3*d*e + 4*a*b*c*d*e + a*b^2*e^2 - 4*a^2*c*e^2)*(b^2*c - 4*a*c^2)))/(b^2*c - 4*a*c^2)))/(((b^2*c - 4*a*c^2)*sqrt(b^2 - 4*a*c)*d^2 - (b^3 - 4*a*b*c)*sqrt(b^2 - 4*a*c)*d*e + (a*b^2 - 4*a^2*c)*sqrt(b^2 - 4*a*c)*e^2)*abs(b^2*e - 4*a*c*e)*abs(c)) + 1/4*(sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*(b^2*e - 4*a*c*e)^2*e - (2*sqrt(b^2 - 4*a*c)*c*d*e - sqrt(b^2 - 4*a*c)*b*e^2)*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*abs(b^2*e - 4*a*c*e) - 2*(4*(b^2*c^2 - 4*a*c^3)*d^2*e - 4*(b^3*c - 4*a*b*c^2)*d*e^2 + (b^4 - 4*a*b^2*c)*e^3)*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e))*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*b^2*c*d - 8*a*c^2*d - b^3*e + 4*a*b*c*e - sqrt((2*b^2*c*d - 8*a*c^2*d - b^3*e + 4*a*b*c*e)^2 - 4*(b^2*c*d^2 - 4*a*c^2*d^2 - b^3*d*e + 4*a*b*c*d*e + a*b^2*e^2 - 4*a^2*c*e^2)*(b^2*c - 4*a*c^2)))/(b^2*c - 4*a*c^2)))/(((b^2*c - 4*a*c^2)*sqrt(b^2 - 4*a*c)*d^2 - (b^3 - 4*a*b*c)*sqrt(b^2 - 4*a*c)*d*e + (a*b^2 - 4*a^2*c)*sqrt(b^2 - 4*a*c)*e^2)*abs(b^2*e - 4*a*c*e)*abs(c))","B",0
2299,1,2822,0,2.018860," ","integrate(1/(e*x+d)^(1/2)/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","-\frac{2 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{2} d e - 2 \, \sqrt{x e + d} c^{2} d^{2} e - {\left(x e + d\right)}^{\frac{3}{2}} b c e^{2} + 2 \, \sqrt{x e + d} b c d e^{2} - \sqrt{x e + d} b^{2} e^{3} + 2 \, \sqrt{x e + d} a c e^{3}}{{\left(b^{2} c d^{2} - 4 \, a c^{2} d^{2} - b^{3} d e + 4 \, a b c d e + a b^{2} e^{2} - 4 \, a^{2} c e^{2}\right)} {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + {\left(x e + d\right)} b e - b d e + a e^{2}\right)}} - \frac{{\left({\left(b^{2} c d^{2} e - 4 \, a c^{2} d^{2} e - b^{3} d e^{2} + 4 \, a b c d e^{2} + a b^{2} e^{3} - 4 \, a^{2} c e^{3}\right)}^{2} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left(2 \, c d e - b e^{2}\right)} + 2 \, {\left(2 \, \sqrt{b^{2} - 4 \, a c} c^{3} d^{4} e - 4 \, \sqrt{b^{2} - 4 \, a c} b c^{2} d^{3} e^{2} + {\left(b^{2} c + 8 \, a c^{2}\right)} \sqrt{b^{2} - 4 \, a c} d^{2} e^{3} + {\left(b^{3} - 8 \, a b c\right)} \sqrt{b^{2} - 4 \, a c} d e^{4} - {\left(a b^{2} - 6 \, a^{2} c\right)} \sqrt{b^{2} - 4 \, a c} e^{5}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left| b^{2} c d^{2} e - 4 \, a c^{2} d^{2} e - b^{3} d e^{2} + 4 \, a b c d e^{2} + a b^{2} e^{3} - 4 \, a^{2} c e^{3} \right|} - {\left(16 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d^{7} e - 56 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{6} e^{2} + 14 \, {\left(5 \, b^{4} c^{3} - 16 \, a b^{2} c^{4} - 16 \, a^{2} c^{5}\right)} d^{5} e^{3} - 35 \, {\left(b^{5} c^{2} - 16 \, a^{2} b c^{4}\right)} d^{4} e^{4} + 4 \, {\left(b^{6} c + 23 \, a b^{4} c^{2} - 92 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} d^{3} e^{5} + {\left(b^{7} - 26 \, a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 384 \, a^{3} b c^{3}\right)} d^{2} e^{6} - 2 \, {\left(a b^{6} - 19 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} + 48 \, a^{4} c^{3}\right)} d e^{7} + {\left(a^{2} b^{5} - 16 \, a^{3} b^{3} c + 48 \, a^{4} b c^{2}\right)} e^{8}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, b^{2} c^{2} d^{3} - 8 \, a c^{3} d^{3} - 3 \, b^{3} c d^{2} e + 12 \, a b c^{2} d^{2} e + b^{4} d e^{2} - 2 \, a b^{2} c d e^{2} - 8 \, a^{2} c^{2} d e^{2} - a b^{3} e^{3} + 4 \, a^{2} b c e^{3} + \sqrt{{\left(2 \, b^{2} c^{2} d^{3} - 8 \, a c^{3} d^{3} - 3 \, b^{3} c d^{2} e + 12 \, a b c^{2} d^{2} e + b^{4} d e^{2} - 2 \, a b^{2} c d e^{2} - 8 \, a^{2} c^{2} d e^{2} - a b^{3} e^{3} + 4 \, a^{2} b c e^{3}\right)}^{2} - 4 \, {\left(b^{2} c^{2} d^{4} - 4 \, a c^{3} d^{4} - 2 \, b^{3} c d^{3} e + 8 \, a b c^{2} d^{3} e + b^{4} d^{2} e^{2} - 2 \, a b^{2} c d^{2} e^{2} - 8 \, a^{2} c^{2} d^{2} e^{2} - 2 \, a b^{3} d e^{3} + 8 \, a^{2} b c d e^{3} + a^{2} b^{2} e^{4} - 4 \, a^{3} c e^{4}\right)} {\left(b^{2} c^{2} d^{2} - 4 \, a c^{3} d^{2} - b^{3} c d e + 4 \, a b c^{2} d e + a b^{2} c e^{2} - 4 \, a^{2} c^{2} e^{2}\right)}}}{b^{2} c^{2} d^{2} - 4 \, a c^{3} d^{2} - b^{3} c d e + 4 \, a b c^{2} d e + a b^{2} c e^{2} - 4 \, a^{2} c^{2} e^{2}}}}\right)}{8 \, {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{b^{2} - 4 \, a c} d^{6} - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} \sqrt{b^{2} - 4 \, a c} d^{5} e + 3 \, {\left(b^{4} c - 3 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} \sqrt{b^{2} - 4 \, a c} d^{4} e^{2} - {\left(b^{5} + 2 \, a b^{3} c - 24 \, a^{2} b c^{2}\right)} \sqrt{b^{2} - 4 \, a c} d^{3} e^{3} + 3 \, {\left(a b^{4} - 3 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} \sqrt{b^{2} - 4 \, a c} d^{2} e^{4} - 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} \sqrt{b^{2} - 4 \, a c} d e^{5} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{b^{2} - 4 \, a c} e^{6}\right)} {\left| b^{2} c d^{2} e - 4 \, a c^{2} d^{2} e - b^{3} d e^{2} + 4 \, a b c d e^{2} + a b^{2} e^{3} - 4 \, a^{2} c e^{3} \right|} {\left| c \right|}} + \frac{{\left({\left(b^{2} c d^{2} e - 4 \, a c^{2} d^{2} e - b^{3} d e^{2} + 4 \, a b c d e^{2} + a b^{2} e^{3} - 4 \, a^{2} c e^{3}\right)}^{2} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left(2 \, c d e - b e^{2}\right)} - 2 \, {\left(2 \, \sqrt{b^{2} - 4 \, a c} c^{3} d^{4} e - 4 \, \sqrt{b^{2} - 4 \, a c} b c^{2} d^{3} e^{2} + {\left(b^{2} c + 8 \, a c^{2}\right)} \sqrt{b^{2} - 4 \, a c} d^{2} e^{3} + {\left(b^{3} - 8 \, a b c\right)} \sqrt{b^{2} - 4 \, a c} d e^{4} - {\left(a b^{2} - 6 \, a^{2} c\right)} \sqrt{b^{2} - 4 \, a c} e^{5}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left| b^{2} c d^{2} e - 4 \, a c^{2} d^{2} e - b^{3} d e^{2} + 4 \, a b c d e^{2} + a b^{2} e^{3} - 4 \, a^{2} c e^{3} \right|} - {\left(16 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d^{7} e - 56 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{6} e^{2} + 14 \, {\left(5 \, b^{4} c^{3} - 16 \, a b^{2} c^{4} - 16 \, a^{2} c^{5}\right)} d^{5} e^{3} - 35 \, {\left(b^{5} c^{2} - 16 \, a^{2} b c^{4}\right)} d^{4} e^{4} + 4 \, {\left(b^{6} c + 23 \, a b^{4} c^{2} - 92 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} d^{3} e^{5} + {\left(b^{7} - 26 \, a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 384 \, a^{3} b c^{3}\right)} d^{2} e^{6} - 2 \, {\left(a b^{6} - 19 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} + 48 \, a^{4} c^{3}\right)} d e^{7} + {\left(a^{2} b^{5} - 16 \, a^{3} b^{3} c + 48 \, a^{4} b c^{2}\right)} e^{8}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, b^{2} c^{2} d^{3} - 8 \, a c^{3} d^{3} - 3 \, b^{3} c d^{2} e + 12 \, a b c^{2} d^{2} e + b^{4} d e^{2} - 2 \, a b^{2} c d e^{2} - 8 \, a^{2} c^{2} d e^{2} - a b^{3} e^{3} + 4 \, a^{2} b c e^{3} - \sqrt{{\left(2 \, b^{2} c^{2} d^{3} - 8 \, a c^{3} d^{3} - 3 \, b^{3} c d^{2} e + 12 \, a b c^{2} d^{2} e + b^{4} d e^{2} - 2 \, a b^{2} c d e^{2} - 8 \, a^{2} c^{2} d e^{2} - a b^{3} e^{3} + 4 \, a^{2} b c e^{3}\right)}^{2} - 4 \, {\left(b^{2} c^{2} d^{4} - 4 \, a c^{3} d^{4} - 2 \, b^{3} c d^{3} e + 8 \, a b c^{2} d^{3} e + b^{4} d^{2} e^{2} - 2 \, a b^{2} c d^{2} e^{2} - 8 \, a^{2} c^{2} d^{2} e^{2} - 2 \, a b^{3} d e^{3} + 8 \, a^{2} b c d e^{3} + a^{2} b^{2} e^{4} - 4 \, a^{3} c e^{4}\right)} {\left(b^{2} c^{2} d^{2} - 4 \, a c^{3} d^{2} - b^{3} c d e + 4 \, a b c^{2} d e + a b^{2} c e^{2} - 4 \, a^{2} c^{2} e^{2}\right)}}}{b^{2} c^{2} d^{2} - 4 \, a c^{3} d^{2} - b^{3} c d e + 4 \, a b c^{2} d e + a b^{2} c e^{2} - 4 \, a^{2} c^{2} e^{2}}}}\right)}{8 \, {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{b^{2} - 4 \, a c} d^{6} - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} \sqrt{b^{2} - 4 \, a c} d^{5} e + 3 \, {\left(b^{4} c - 3 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} \sqrt{b^{2} - 4 \, a c} d^{4} e^{2} - {\left(b^{5} + 2 \, a b^{3} c - 24 \, a^{2} b c^{2}\right)} \sqrt{b^{2} - 4 \, a c} d^{3} e^{3} + 3 \, {\left(a b^{4} - 3 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} \sqrt{b^{2} - 4 \, a c} d^{2} e^{4} - 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} \sqrt{b^{2} - 4 \, a c} d e^{5} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{b^{2} - 4 \, a c} e^{6}\right)} {\left| b^{2} c d^{2} e - 4 \, a c^{2} d^{2} e - b^{3} d e^{2} + 4 \, a b c d e^{2} + a b^{2} e^{3} - 4 \, a^{2} c e^{3} \right|} {\left| c \right|}}"," ",0,"-(2*(x*e + d)^(3/2)*c^2*d*e - 2*sqrt(x*e + d)*c^2*d^2*e - (x*e + d)^(3/2)*b*c*e^2 + 2*sqrt(x*e + d)*b*c*d*e^2 - sqrt(x*e + d)*b^2*e^3 + 2*sqrt(x*e + d)*a*c*e^3)/((b^2*c*d^2 - 4*a*c^2*d^2 - b^3*d*e + 4*a*b*c*d*e + a*b^2*e^2 - 4*a^2*c*e^2)*((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + (x*e + d)*b*e - b*d*e + a*e^2)) - 1/8*((b^2*c*d^2*e - 4*a*c^2*d^2*e - b^3*d*e^2 + 4*a*b*c*d*e^2 + a*b^2*e^3 - 4*a^2*c*e^3)^2*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*(2*c*d*e - b*e^2) + 2*(2*sqrt(b^2 - 4*a*c)*c^3*d^4*e - 4*sqrt(b^2 - 4*a*c)*b*c^2*d^3*e^2 + (b^2*c + 8*a*c^2)*sqrt(b^2 - 4*a*c)*d^2*e^3 + (b^3 - 8*a*b*c)*sqrt(b^2 - 4*a*c)*d*e^4 - (a*b^2 - 6*a^2*c)*sqrt(b^2 - 4*a*c)*e^5)*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*abs(b^2*c*d^2*e - 4*a*c^2*d^2*e - b^3*d*e^2 + 4*a*b*c*d*e^2 + a*b^2*e^3 - 4*a^2*c*e^3) - (16*(b^2*c^5 - 4*a*c^6)*d^7*e - 56*(b^3*c^4 - 4*a*b*c^5)*d^6*e^2 + 14*(5*b^4*c^3 - 16*a*b^2*c^4 - 16*a^2*c^5)*d^5*e^3 - 35*(b^5*c^2 - 16*a^2*b*c^4)*d^4*e^4 + 4*(b^6*c + 23*a*b^4*c^2 - 92*a^2*b^2*c^3 - 64*a^3*c^4)*d^3*e^5 + (b^7 - 26*a*b^5*c - 8*a^2*b^3*c^2 + 384*a^3*b*c^3)*d^2*e^6 - 2*(a*b^6 - 19*a^2*b^4*c + 48*a^3*b^2*c^2 + 48*a^4*c^3)*d*e^7 + (a^2*b^5 - 16*a^3*b^3*c + 48*a^4*b*c^2)*e^8)*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e))*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*b^2*c^2*d^3 - 8*a*c^3*d^3 - 3*b^3*c*d^2*e + 12*a*b*c^2*d^2*e + b^4*d*e^2 - 2*a*b^2*c*d*e^2 - 8*a^2*c^2*d*e^2 - a*b^3*e^3 + 4*a^2*b*c*e^3 + sqrt((2*b^2*c^2*d^3 - 8*a*c^3*d^3 - 3*b^3*c*d^2*e + 12*a*b*c^2*d^2*e + b^4*d*e^2 - 2*a*b^2*c*d*e^2 - 8*a^2*c^2*d*e^2 - a*b^3*e^3 + 4*a^2*b*c*e^3)^2 - 4*(b^2*c^2*d^4 - 4*a*c^3*d^4 - 2*b^3*c*d^3*e + 8*a*b*c^2*d^3*e + b^4*d^2*e^2 - 2*a*b^2*c*d^2*e^2 - 8*a^2*c^2*d^2*e^2 - 2*a*b^3*d*e^3 + 8*a^2*b*c*d*e^3 + a^2*b^2*e^4 - 4*a^3*c*e^4)*(b^2*c^2*d^2 - 4*a*c^3*d^2 - b^3*c*d*e + 4*a*b*c^2*d*e + a*b^2*c*e^2 - 4*a^2*c^2*e^2)))/(b^2*c^2*d^2 - 4*a*c^3*d^2 - b^3*c*d*e + 4*a*b*c^2*d*e + a*b^2*c*e^2 - 4*a^2*c^2*e^2)))/(((b^2*c^3 - 4*a*c^4)*sqrt(b^2 - 4*a*c)*d^6 - 3*(b^3*c^2 - 4*a*b*c^3)*sqrt(b^2 - 4*a*c)*d^5*e + 3*(b^4*c - 3*a*b^2*c^2 - 4*a^2*c^3)*sqrt(b^2 - 4*a*c)*d^4*e^2 - (b^5 + 2*a*b^3*c - 24*a^2*b*c^2)*sqrt(b^2 - 4*a*c)*d^3*e^3 + 3*(a*b^4 - 3*a^2*b^2*c - 4*a^3*c^2)*sqrt(b^2 - 4*a*c)*d^2*e^4 - 3*(a^2*b^3 - 4*a^3*b*c)*sqrt(b^2 - 4*a*c)*d*e^5 + (a^3*b^2 - 4*a^4*c)*sqrt(b^2 - 4*a*c)*e^6)*abs(b^2*c*d^2*e - 4*a*c^2*d^2*e - b^3*d*e^2 + 4*a*b*c*d*e^2 + a*b^2*e^3 - 4*a^2*c*e^3)*abs(c)) + 1/8*((b^2*c*d^2*e - 4*a*c^2*d^2*e - b^3*d*e^2 + 4*a*b*c*d*e^2 + a*b^2*e^3 - 4*a^2*c*e^3)^2*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*(2*c*d*e - b*e^2) - 2*(2*sqrt(b^2 - 4*a*c)*c^3*d^4*e - 4*sqrt(b^2 - 4*a*c)*b*c^2*d^3*e^2 + (b^2*c + 8*a*c^2)*sqrt(b^2 - 4*a*c)*d^2*e^3 + (b^3 - 8*a*b*c)*sqrt(b^2 - 4*a*c)*d*e^4 - (a*b^2 - 6*a^2*c)*sqrt(b^2 - 4*a*c)*e^5)*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*abs(b^2*c*d^2*e - 4*a*c^2*d^2*e - b^3*d*e^2 + 4*a*b*c*d*e^2 + a*b^2*e^3 - 4*a^2*c*e^3) - (16*(b^2*c^5 - 4*a*c^6)*d^7*e - 56*(b^3*c^4 - 4*a*b*c^5)*d^6*e^2 + 14*(5*b^4*c^3 - 16*a*b^2*c^4 - 16*a^2*c^5)*d^5*e^3 - 35*(b^5*c^2 - 16*a^2*b*c^4)*d^4*e^4 + 4*(b^6*c + 23*a*b^4*c^2 - 92*a^2*b^2*c^3 - 64*a^3*c^4)*d^3*e^5 + (b^7 - 26*a*b^5*c - 8*a^2*b^3*c^2 + 384*a^3*b*c^3)*d^2*e^6 - 2*(a*b^6 - 19*a^2*b^4*c + 48*a^3*b^2*c^2 + 48*a^4*c^3)*d*e^7 + (a^2*b^5 - 16*a^3*b^3*c + 48*a^4*b*c^2)*e^8)*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e))*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*b^2*c^2*d^3 - 8*a*c^3*d^3 - 3*b^3*c*d^2*e + 12*a*b*c^2*d^2*e + b^4*d*e^2 - 2*a*b^2*c*d*e^2 - 8*a^2*c^2*d*e^2 - a*b^3*e^3 + 4*a^2*b*c*e^3 - sqrt((2*b^2*c^2*d^3 - 8*a*c^3*d^3 - 3*b^3*c*d^2*e + 12*a*b*c^2*d^2*e + b^4*d*e^2 - 2*a*b^2*c*d*e^2 - 8*a^2*c^2*d*e^2 - a*b^3*e^3 + 4*a^2*b*c*e^3)^2 - 4*(b^2*c^2*d^4 - 4*a*c^3*d^4 - 2*b^3*c*d^3*e + 8*a*b*c^2*d^3*e + b^4*d^2*e^2 - 2*a*b^2*c*d^2*e^2 - 8*a^2*c^2*d^2*e^2 - 2*a*b^3*d*e^3 + 8*a^2*b*c*d*e^3 + a^2*b^2*e^4 - 4*a^3*c*e^4)*(b^2*c^2*d^2 - 4*a*c^3*d^2 - b^3*c*d*e + 4*a*b*c^2*d*e + a*b^2*c*e^2 - 4*a^2*c^2*e^2)))/(b^2*c^2*d^2 - 4*a*c^3*d^2 - b^3*c*d*e + 4*a*b*c^2*d*e + a*b^2*c*e^2 - 4*a^2*c^2*e^2)))/(((b^2*c^3 - 4*a*c^4)*sqrt(b^2 - 4*a*c)*d^6 - 3*(b^3*c^2 - 4*a*b*c^3)*sqrt(b^2 - 4*a*c)*d^5*e + 3*(b^4*c - 3*a*b^2*c^2 - 4*a^2*c^3)*sqrt(b^2 - 4*a*c)*d^4*e^2 - (b^5 + 2*a*b^3*c - 24*a^2*b*c^2)*sqrt(b^2 - 4*a*c)*d^3*e^3 + 3*(a*b^4 - 3*a^2*b^2*c - 4*a^3*c^2)*sqrt(b^2 - 4*a*c)*d^2*e^4 - 3*(a^2*b^3 - 4*a^3*b*c)*sqrt(b^2 - 4*a*c)*d*e^5 + (a^3*b^2 - 4*a^4*c)*sqrt(b^2 - 4*a*c)*e^6)*abs(b^2*c*d^2*e - 4*a*c^2*d^2*e - b^3*d*e^2 + 4*a*b*c*d*e^2 + a*b^2*e^3 - 4*a^2*c*e^3)*abs(c))","B",0
2300,1,5478,0,6.817907," ","integrate(1/(e*x+d)^(3/2)/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","-\frac{2 \, {\left(x e + d\right)}^{2} c^{3} d^{2} e - 2 \, {\left(x e + d\right)} c^{3} d^{3} e - 2 \, {\left(x e + d\right)}^{2} b c^{2} d e^{2} + 3 \, {\left(x e + d\right)} b c^{2} d^{2} e^{2} + 3 \, {\left(x e + d\right)}^{2} b^{2} c e^{3} - 10 \, {\left(x e + d\right)}^{2} a c^{2} e^{3} - 7 \, {\left(x e + d\right)} b^{2} c d e^{3} + 22 \, {\left(x e + d\right)} a c^{2} d e^{3} + 2 \, b^{2} c d^{2} e^{3} - 8 \, a c^{2} d^{2} e^{3} + 3 \, {\left(x e + d\right)} b^{3} e^{4} - 11 \, {\left(x e + d\right)} a b c e^{4} - 2 \, b^{3} d e^{4} + 8 \, a b c d e^{4} + 2 \, a b^{2} e^{5} - 8 \, a^{2} c e^{5}}{{\left(b^{2} c^{2} d^{4} - 4 \, a c^{3} d^{4} - 2 \, b^{3} c d^{3} e + 8 \, a b c^{2} d^{3} e + b^{4} d^{2} e^{2} - 2 \, a b^{2} c d^{2} e^{2} - 8 \, a^{2} c^{2} d^{2} e^{2} - 2 \, a b^{3} d e^{3} + 8 \, a^{2} b c d e^{3} + a^{2} b^{2} e^{4} - 4 \, a^{3} c e^{4}\right)} {\left({\left(x e + d\right)}^{\frac{5}{2}} c - 2 \, {\left(x e + d\right)}^{\frac{3}{2}} c d + \sqrt{x e + d} c d^{2} + {\left(x e + d\right)}^{\frac{3}{2}} b e - \sqrt{x e + d} b d e + \sqrt{x e + d} a e^{2}\right)}} - \frac{{\left({\left(b^{2} c^{2} d^{4} e - 4 \, a c^{3} d^{4} e - 2 \, b^{3} c d^{3} e^{2} + 8 \, a b c^{2} d^{3} e^{2} + b^{4} d^{2} e^{3} - 2 \, a b^{2} c d^{2} e^{3} - 8 \, a^{2} c^{2} d^{2} e^{3} - 2 \, a b^{3} d e^{4} + 8 \, a^{2} b c d e^{4} + a^{2} b^{2} e^{5} - 4 \, a^{3} c e^{5}\right)}^{2} {\left(2 \, c^{2} d^{2} e - 2 \, b c d e^{2} + {\left(3 \, b^{2} - 10 \, a c\right)} e^{3}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} + 2 \, {\left(2 \, \sqrt{b^{2} - 4 \, a c} c^{5} d^{7} e - 7 \, \sqrt{b^{2} - 4 \, a c} b c^{4} d^{6} e^{2} + 3 \, {\left(b^{2} c^{3} + 10 \, a c^{4}\right)} \sqrt{b^{2} - 4 \, a c} d^{5} e^{3} + 5 \, {\left(2 \, b^{3} c^{2} - 15 \, a b c^{3}\right)} \sqrt{b^{2} - 4 \, a c} d^{4} e^{4} - {\left(11 \, b^{4} c - 48 \, a b^{2} c^{2} - 54 \, a^{2} c^{3}\right)} \sqrt{b^{2} - 4 \, a c} d^{3} e^{5} + 3 \, {\left(b^{5} + a b^{3} c - 27 \, a^{2} b c^{2}\right)} \sqrt{b^{2} - 4 \, a c} d^{2} e^{6} - {\left(6 \, a b^{4} - 21 \, a^{2} b^{2} c - 26 \, a^{3} c^{2}\right)} \sqrt{b^{2} - 4 \, a c} d e^{7} + {\left(3 \, a^{2} b^{3} - 13 \, a^{3} b c\right)} \sqrt{b^{2} - 4 \, a c} e^{8}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left| b^{2} c^{2} d^{4} e - 4 \, a c^{3} d^{4} e - 2 \, b^{3} c d^{3} e^{2} + 8 \, a b c^{2} d^{3} e^{2} + b^{4} d^{2} e^{3} - 2 \, a b^{2} c d^{2} e^{3} - 8 \, a^{2} c^{2} d^{2} e^{3} - 2 \, a b^{3} d e^{4} + 8 \, a^{2} b c d e^{4} + a^{2} b^{2} e^{5} - 4 \, a^{3} c e^{5} \right|} - {\left(16 \, {\left(b^{2} c^{8} - 4 \, a c^{9}\right)} d^{12} e - 96 \, {\left(b^{3} c^{7} - 4 \, a b c^{8}\right)} d^{11} e^{2} + 8 \, {\left(29 \, b^{4} c^{6} - 100 \, a b^{2} c^{7} - 64 \, a^{2} c^{8}\right)} d^{10} e^{3} - 40 \, {\left(7 \, b^{5} c^{5} - 12 \, a b^{3} c^{6} - 64 \, a^{2} b c^{7}\right)} d^{9} e^{4} + {\left(157 \, b^{6} c^{4} + 636 \, a b^{4} c^{5} - 4704 \, a^{2} b^{2} c^{6} - 1408 \, a^{3} c^{7}\right)} d^{8} e^{5} - 4 \, {\left(b^{7} c^{3} + 300 \, a b^{5} c^{4} - 864 \, a^{2} b^{3} c^{5} - 1408 \, a^{3} b c^{6}\right)} d^{7} e^{6} - 14 \, {\left(3 \, b^{8} c^{2} - 50 \, a b^{6} c^{3} + 576 \, a^{3} b^{2} c^{5} + 128 \, a^{4} c^{6}\right)} d^{6} e^{7} + 4 \, {\left(5 \, b^{9} c - 27 \, a b^{7} c^{2} - 336 \, a^{2} b^{5} c^{3} + 1120 \, a^{3} b^{3} c^{4} + 1344 \, a^{4} b c^{5}\right)} d^{5} e^{8} - {\left(3 \, b^{10} + 40 \, a b^{8} c - 590 \, a^{2} b^{6} c^{2} + 120 \, a^{3} b^{4} c^{3} + 5360 \, a^{4} b^{2} c^{4} + 1088 \, a^{5} c^{5}\right)} d^{4} e^{9} + 4 \, {\left(3 \, a b^{9} - 7 \, a^{2} b^{7} c - 164 \, a^{3} b^{5} c^{2} + 440 \, a^{4} b^{3} c^{3} + 544 \, a^{5} b c^{4}\right)} d^{3} e^{10} - 2 \, {\left(9 \, a^{2} b^{8} - 62 \, a^{3} b^{6} c - 60 \, a^{4} b^{4} c^{2} + 624 \, a^{5} b^{2} c^{3} + 128 \, a^{6} c^{4}\right)} d^{2} e^{11} + 4 \, {\left(3 \, a^{3} b^{7} - 26 \, a^{4} b^{5} c + 40 \, a^{5} b^{3} c^{2} + 64 \, a^{6} b c^{3}\right)} d e^{12} - {\left(3 \, a^{4} b^{6} - 28 \, a^{5} b^{4} c + 64 \, a^{6} b^{2} c^{2}\right)} e^{13}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, b^{2} c^{3} d^{5} - 8 \, a c^{4} d^{5} - 5 \, b^{3} c^{2} d^{4} e + 20 \, a b c^{3} d^{4} e + 4 \, b^{4} c d^{3} e^{2} - 12 \, a b^{2} c^{2} d^{3} e^{2} - 16 \, a^{2} c^{3} d^{3} e^{2} - b^{5} d^{2} e^{3} - 2 \, a b^{3} c d^{2} e^{3} + 24 \, a^{2} b c^{2} d^{2} e^{3} + 2 \, a b^{4} d e^{4} - 6 \, a^{2} b^{2} c d e^{4} - 8 \, a^{3} c^{2} d e^{4} - a^{2} b^{3} e^{5} + 4 \, a^{3} b c e^{5} + \sqrt{{\left(2 \, b^{2} c^{3} d^{5} - 8 \, a c^{4} d^{5} - 5 \, b^{3} c^{2} d^{4} e + 20 \, a b c^{3} d^{4} e + 4 \, b^{4} c d^{3} e^{2} - 12 \, a b^{2} c^{2} d^{3} e^{2} - 16 \, a^{2} c^{3} d^{3} e^{2} - b^{5} d^{2} e^{3} - 2 \, a b^{3} c d^{2} e^{3} + 24 \, a^{2} b c^{2} d^{2} e^{3} + 2 \, a b^{4} d e^{4} - 6 \, a^{2} b^{2} c d e^{4} - 8 \, a^{3} c^{2} d e^{4} - a^{2} b^{3} e^{5} + 4 \, a^{3} b c e^{5}\right)}^{2} - 4 \, {\left(b^{2} c^{3} d^{6} - 4 \, a c^{4} d^{6} - 3 \, b^{3} c^{2} d^{5} e + 12 \, a b c^{3} d^{5} e + 3 \, b^{4} c d^{4} e^{2} - 9 \, a b^{2} c^{2} d^{4} e^{2} - 12 \, a^{2} c^{3} d^{4} e^{2} - b^{5} d^{3} e^{3} - 2 \, a b^{3} c d^{3} e^{3} + 24 \, a^{2} b c^{2} d^{3} e^{3} + 3 \, a b^{4} d^{2} e^{4} - 9 \, a^{2} b^{2} c d^{2} e^{4} - 12 \, a^{3} c^{2} d^{2} e^{4} - 3 \, a^{2} b^{3} d e^{5} + 12 \, a^{3} b c d e^{5} + a^{3} b^{2} e^{6} - 4 \, a^{4} c e^{6}\right)} {\left(b^{2} c^{3} d^{4} - 4 \, a c^{4} d^{4} - 2 \, b^{3} c^{2} d^{3} e + 8 \, a b c^{3} d^{3} e + b^{4} c d^{2} e^{2} - 2 \, a b^{2} c^{2} d^{2} e^{2} - 8 \, a^{2} c^{3} d^{2} e^{2} - 2 \, a b^{3} c d e^{3} + 8 \, a^{2} b c^{2} d e^{3} + a^{2} b^{2} c e^{4} - 4 \, a^{3} c^{2} e^{4}\right)}}}{b^{2} c^{3} d^{4} - 4 \, a c^{4} d^{4} - 2 \, b^{3} c^{2} d^{3} e + 8 \, a b c^{3} d^{3} e + b^{4} c d^{2} e^{2} - 2 \, a b^{2} c^{2} d^{2} e^{2} - 8 \, a^{2} c^{3} d^{2} e^{2} - 2 \, a b^{3} c d e^{3} + 8 \, a^{2} b c^{2} d e^{3} + a^{2} b^{2} c e^{4} - 4 \, a^{3} c^{2} e^{4}}}}\right)}{8 \, {\left({\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{b^{2} - 4 \, a c} d^{10} - 5 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} \sqrt{b^{2} - 4 \, a c} d^{9} e + 5 \, {\left(2 \, b^{4} c^{3} - 7 \, a b^{2} c^{4} - 4 \, a^{2} c^{5}\right)} \sqrt{b^{2} - 4 \, a c} d^{8} e^{2} - 10 \, {\left(b^{5} c^{2} - 2 \, a b^{3} c^{3} - 8 \, a^{2} b c^{4}\right)} \sqrt{b^{2} - 4 \, a c} d^{7} e^{3} + 5 \, {\left(b^{6} c + 2 \, a b^{4} c^{2} - 22 \, a^{2} b^{2} c^{3} - 8 \, a^{3} c^{4}\right)} \sqrt{b^{2} - 4 \, a c} d^{6} e^{4} - {\left(b^{7} + 16 \, a b^{5} c - 50 \, a^{2} b^{3} c^{2} - 120 \, a^{3} b c^{3}\right)} \sqrt{b^{2} - 4 \, a c} d^{5} e^{5} + 5 \, {\left(a b^{6} + 2 \, a^{2} b^{4} c - 22 \, a^{3} b^{2} c^{2} - 8 \, a^{4} c^{3}\right)} \sqrt{b^{2} - 4 \, a c} d^{4} e^{6} - 10 \, {\left(a^{2} b^{5} - 2 \, a^{3} b^{3} c - 8 \, a^{4} b c^{2}\right)} \sqrt{b^{2} - 4 \, a c} d^{3} e^{7} + 5 \, {\left(2 \, a^{3} b^{4} - 7 \, a^{4} b^{2} c - 4 \, a^{5} c^{2}\right)} \sqrt{b^{2} - 4 \, a c} d^{2} e^{8} - 5 \, {\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} \sqrt{b^{2} - 4 \, a c} d e^{9} + {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} \sqrt{b^{2} - 4 \, a c} e^{10}\right)} {\left| b^{2} c^{2} d^{4} e - 4 \, a c^{3} d^{4} e - 2 \, b^{3} c d^{3} e^{2} + 8 \, a b c^{2} d^{3} e^{2} + b^{4} d^{2} e^{3} - 2 \, a b^{2} c d^{2} e^{3} - 8 \, a^{2} c^{2} d^{2} e^{3} - 2 \, a b^{3} d e^{4} + 8 \, a^{2} b c d e^{4} + a^{2} b^{2} e^{5} - 4 \, a^{3} c e^{5} \right|} {\left| c \right|}} + \frac{{\left({\left(b^{2} c^{2} d^{4} e - 4 \, a c^{3} d^{4} e - 2 \, b^{3} c d^{3} e^{2} + 8 \, a b c^{2} d^{3} e^{2} + b^{4} d^{2} e^{3} - 2 \, a b^{2} c d^{2} e^{3} - 8 \, a^{2} c^{2} d^{2} e^{3} - 2 \, a b^{3} d e^{4} + 8 \, a^{2} b c d e^{4} + a^{2} b^{2} e^{5} - 4 \, a^{3} c e^{5}\right)}^{2} {\left(2 \, c^{2} d^{2} e - 2 \, b c d e^{2} + {\left(3 \, b^{2} - 10 \, a c\right)} e^{3}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} - 2 \, {\left(2 \, \sqrt{b^{2} - 4 \, a c} c^{5} d^{7} e - 7 \, \sqrt{b^{2} - 4 \, a c} b c^{4} d^{6} e^{2} + 3 \, {\left(b^{2} c^{3} + 10 \, a c^{4}\right)} \sqrt{b^{2} - 4 \, a c} d^{5} e^{3} + 5 \, {\left(2 \, b^{3} c^{2} - 15 \, a b c^{3}\right)} \sqrt{b^{2} - 4 \, a c} d^{4} e^{4} - {\left(11 \, b^{4} c - 48 \, a b^{2} c^{2} - 54 \, a^{2} c^{3}\right)} \sqrt{b^{2} - 4 \, a c} d^{3} e^{5} + 3 \, {\left(b^{5} + a b^{3} c - 27 \, a^{2} b c^{2}\right)} \sqrt{b^{2} - 4 \, a c} d^{2} e^{6} - {\left(6 \, a b^{4} - 21 \, a^{2} b^{2} c - 26 \, a^{3} c^{2}\right)} \sqrt{b^{2} - 4 \, a c} d e^{7} + {\left(3 \, a^{2} b^{3} - 13 \, a^{3} b c\right)} \sqrt{b^{2} - 4 \, a c} e^{8}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left| b^{2} c^{2} d^{4} e - 4 \, a c^{3} d^{4} e - 2 \, b^{3} c d^{3} e^{2} + 8 \, a b c^{2} d^{3} e^{2} + b^{4} d^{2} e^{3} - 2 \, a b^{2} c d^{2} e^{3} - 8 \, a^{2} c^{2} d^{2} e^{3} - 2 \, a b^{3} d e^{4} + 8 \, a^{2} b c d e^{4} + a^{2} b^{2} e^{5} - 4 \, a^{3} c e^{5} \right|} - {\left(16 \, {\left(b^{2} c^{8} - 4 \, a c^{9}\right)} d^{12} e - 96 \, {\left(b^{3} c^{7} - 4 \, a b c^{8}\right)} d^{11} e^{2} + 8 \, {\left(29 \, b^{4} c^{6} - 100 \, a b^{2} c^{7} - 64 \, a^{2} c^{8}\right)} d^{10} e^{3} - 40 \, {\left(7 \, b^{5} c^{5} - 12 \, a b^{3} c^{6} - 64 \, a^{2} b c^{7}\right)} d^{9} e^{4} + {\left(157 \, b^{6} c^{4} + 636 \, a b^{4} c^{5} - 4704 \, a^{2} b^{2} c^{6} - 1408 \, a^{3} c^{7}\right)} d^{8} e^{5} - 4 \, {\left(b^{7} c^{3} + 300 \, a b^{5} c^{4} - 864 \, a^{2} b^{3} c^{5} - 1408 \, a^{3} b c^{6}\right)} d^{7} e^{6} - 14 \, {\left(3 \, b^{8} c^{2} - 50 \, a b^{6} c^{3} + 576 \, a^{3} b^{2} c^{5} + 128 \, a^{4} c^{6}\right)} d^{6} e^{7} + 4 \, {\left(5 \, b^{9} c - 27 \, a b^{7} c^{2} - 336 \, a^{2} b^{5} c^{3} + 1120 \, a^{3} b^{3} c^{4} + 1344 \, a^{4} b c^{5}\right)} d^{5} e^{8} - {\left(3 \, b^{10} + 40 \, a b^{8} c - 590 \, a^{2} b^{6} c^{2} + 120 \, a^{3} b^{4} c^{3} + 5360 \, a^{4} b^{2} c^{4} + 1088 \, a^{5} c^{5}\right)} d^{4} e^{9} + 4 \, {\left(3 \, a b^{9} - 7 \, a^{2} b^{7} c - 164 \, a^{3} b^{5} c^{2} + 440 \, a^{4} b^{3} c^{3} + 544 \, a^{5} b c^{4}\right)} d^{3} e^{10} - 2 \, {\left(9 \, a^{2} b^{8} - 62 \, a^{3} b^{6} c - 60 \, a^{4} b^{4} c^{2} + 624 \, a^{5} b^{2} c^{3} + 128 \, a^{6} c^{4}\right)} d^{2} e^{11} + 4 \, {\left(3 \, a^{3} b^{7} - 26 \, a^{4} b^{5} c + 40 \, a^{5} b^{3} c^{2} + 64 \, a^{6} b c^{3}\right)} d e^{12} - {\left(3 \, a^{4} b^{6} - 28 \, a^{5} b^{4} c + 64 \, a^{6} b^{2} c^{2}\right)} e^{13}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, b^{2} c^{3} d^{5} - 8 \, a c^{4} d^{5} - 5 \, b^{3} c^{2} d^{4} e + 20 \, a b c^{3} d^{4} e + 4 \, b^{4} c d^{3} e^{2} - 12 \, a b^{2} c^{2} d^{3} e^{2} - 16 \, a^{2} c^{3} d^{3} e^{2} - b^{5} d^{2} e^{3} - 2 \, a b^{3} c d^{2} e^{3} + 24 \, a^{2} b c^{2} d^{2} e^{3} + 2 \, a b^{4} d e^{4} - 6 \, a^{2} b^{2} c d e^{4} - 8 \, a^{3} c^{2} d e^{4} - a^{2} b^{3} e^{5} + 4 \, a^{3} b c e^{5} - \sqrt{{\left(2 \, b^{2} c^{3} d^{5} - 8 \, a c^{4} d^{5} - 5 \, b^{3} c^{2} d^{4} e + 20 \, a b c^{3} d^{4} e + 4 \, b^{4} c d^{3} e^{2} - 12 \, a b^{2} c^{2} d^{3} e^{2} - 16 \, a^{2} c^{3} d^{3} e^{2} - b^{5} d^{2} e^{3} - 2 \, a b^{3} c d^{2} e^{3} + 24 \, a^{2} b c^{2} d^{2} e^{3} + 2 \, a b^{4} d e^{4} - 6 \, a^{2} b^{2} c d e^{4} - 8 \, a^{3} c^{2} d e^{4} - a^{2} b^{3} e^{5} + 4 \, a^{3} b c e^{5}\right)}^{2} - 4 \, {\left(b^{2} c^{3} d^{6} - 4 \, a c^{4} d^{6} - 3 \, b^{3} c^{2} d^{5} e + 12 \, a b c^{3} d^{5} e + 3 \, b^{4} c d^{4} e^{2} - 9 \, a b^{2} c^{2} d^{4} e^{2} - 12 \, a^{2} c^{3} d^{4} e^{2} - b^{5} d^{3} e^{3} - 2 \, a b^{3} c d^{3} e^{3} + 24 \, a^{2} b c^{2} d^{3} e^{3} + 3 \, a b^{4} d^{2} e^{4} - 9 \, a^{2} b^{2} c d^{2} e^{4} - 12 \, a^{3} c^{2} d^{2} e^{4} - 3 \, a^{2} b^{3} d e^{5} + 12 \, a^{3} b c d e^{5} + a^{3} b^{2} e^{6} - 4 \, a^{4} c e^{6}\right)} {\left(b^{2} c^{3} d^{4} - 4 \, a c^{4} d^{4} - 2 \, b^{3} c^{2} d^{3} e + 8 \, a b c^{3} d^{3} e + b^{4} c d^{2} e^{2} - 2 \, a b^{2} c^{2} d^{2} e^{2} - 8 \, a^{2} c^{3} d^{2} e^{2} - 2 \, a b^{3} c d e^{3} + 8 \, a^{2} b c^{2} d e^{3} + a^{2} b^{2} c e^{4} - 4 \, a^{3} c^{2} e^{4}\right)}}}{b^{2} c^{3} d^{4} - 4 \, a c^{4} d^{4} - 2 \, b^{3} c^{2} d^{3} e + 8 \, a b c^{3} d^{3} e + b^{4} c d^{2} e^{2} - 2 \, a b^{2} c^{2} d^{2} e^{2} - 8 \, a^{2} c^{3} d^{2} e^{2} - 2 \, a b^{3} c d e^{3} + 8 \, a^{2} b c^{2} d e^{3} + a^{2} b^{2} c e^{4} - 4 \, a^{3} c^{2} e^{4}}}}\right)}{8 \, {\left({\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{b^{2} - 4 \, a c} d^{10} - 5 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} \sqrt{b^{2} - 4 \, a c} d^{9} e + 5 \, {\left(2 \, b^{4} c^{3} - 7 \, a b^{2} c^{4} - 4 \, a^{2} c^{5}\right)} \sqrt{b^{2} - 4 \, a c} d^{8} e^{2} - 10 \, {\left(b^{5} c^{2} - 2 \, a b^{3} c^{3} - 8 \, a^{2} b c^{4}\right)} \sqrt{b^{2} - 4 \, a c} d^{7} e^{3} + 5 \, {\left(b^{6} c + 2 \, a b^{4} c^{2} - 22 \, a^{2} b^{2} c^{3} - 8 \, a^{3} c^{4}\right)} \sqrt{b^{2} - 4 \, a c} d^{6} e^{4} - {\left(b^{7} + 16 \, a b^{5} c - 50 \, a^{2} b^{3} c^{2} - 120 \, a^{3} b c^{3}\right)} \sqrt{b^{2} - 4 \, a c} d^{5} e^{5} + 5 \, {\left(a b^{6} + 2 \, a^{2} b^{4} c - 22 \, a^{3} b^{2} c^{2} - 8 \, a^{4} c^{3}\right)} \sqrt{b^{2} - 4 \, a c} d^{4} e^{6} - 10 \, {\left(a^{2} b^{5} - 2 \, a^{3} b^{3} c - 8 \, a^{4} b c^{2}\right)} \sqrt{b^{2} - 4 \, a c} d^{3} e^{7} + 5 \, {\left(2 \, a^{3} b^{4} - 7 \, a^{4} b^{2} c - 4 \, a^{5} c^{2}\right)} \sqrt{b^{2} - 4 \, a c} d^{2} e^{8} - 5 \, {\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} \sqrt{b^{2} - 4 \, a c} d e^{9} + {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} \sqrt{b^{2} - 4 \, a c} e^{10}\right)} {\left| b^{2} c^{2} d^{4} e - 4 \, a c^{3} d^{4} e - 2 \, b^{3} c d^{3} e^{2} + 8 \, a b c^{2} d^{3} e^{2} + b^{4} d^{2} e^{3} - 2 \, a b^{2} c d^{2} e^{3} - 8 \, a^{2} c^{2} d^{2} e^{3} - 2 \, a b^{3} d e^{4} + 8 \, a^{2} b c d e^{4} + a^{2} b^{2} e^{5} - 4 \, a^{3} c e^{5} \right|} {\left| c \right|}}"," ",0,"-(2*(x*e + d)^2*c^3*d^2*e - 2*(x*e + d)*c^3*d^3*e - 2*(x*e + d)^2*b*c^2*d*e^2 + 3*(x*e + d)*b*c^2*d^2*e^2 + 3*(x*e + d)^2*b^2*c*e^3 - 10*(x*e + d)^2*a*c^2*e^3 - 7*(x*e + d)*b^2*c*d*e^3 + 22*(x*e + d)*a*c^2*d*e^3 + 2*b^2*c*d^2*e^3 - 8*a*c^2*d^2*e^3 + 3*(x*e + d)*b^3*e^4 - 11*(x*e + d)*a*b*c*e^4 - 2*b^3*d*e^4 + 8*a*b*c*d*e^4 + 2*a*b^2*e^5 - 8*a^2*c*e^5)/((b^2*c^2*d^4 - 4*a*c^3*d^4 - 2*b^3*c*d^3*e + 8*a*b*c^2*d^3*e + b^4*d^2*e^2 - 2*a*b^2*c*d^2*e^2 - 8*a^2*c^2*d^2*e^2 - 2*a*b^3*d*e^3 + 8*a^2*b*c*d*e^3 + a^2*b^2*e^4 - 4*a^3*c*e^4)*((x*e + d)^(5/2)*c - 2*(x*e + d)^(3/2)*c*d + sqrt(x*e + d)*c*d^2 + (x*e + d)^(3/2)*b*e - sqrt(x*e + d)*b*d*e + sqrt(x*e + d)*a*e^2)) - 1/8*((b^2*c^2*d^4*e - 4*a*c^3*d^4*e - 2*b^3*c*d^3*e^2 + 8*a*b*c^2*d^3*e^2 + b^4*d^2*e^3 - 2*a*b^2*c*d^2*e^3 - 8*a^2*c^2*d^2*e^3 - 2*a*b^3*d*e^4 + 8*a^2*b*c*d*e^4 + a^2*b^2*e^5 - 4*a^3*c*e^5)^2*(2*c^2*d^2*e - 2*b*c*d*e^2 + (3*b^2 - 10*a*c)*e^3)*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e) + 2*(2*sqrt(b^2 - 4*a*c)*c^5*d^7*e - 7*sqrt(b^2 - 4*a*c)*b*c^4*d^6*e^2 + 3*(b^2*c^3 + 10*a*c^4)*sqrt(b^2 - 4*a*c)*d^5*e^3 + 5*(2*b^3*c^2 - 15*a*b*c^3)*sqrt(b^2 - 4*a*c)*d^4*e^4 - (11*b^4*c - 48*a*b^2*c^2 - 54*a^2*c^3)*sqrt(b^2 - 4*a*c)*d^3*e^5 + 3*(b^5 + a*b^3*c - 27*a^2*b*c^2)*sqrt(b^2 - 4*a*c)*d^2*e^6 - (6*a*b^4 - 21*a^2*b^2*c - 26*a^3*c^2)*sqrt(b^2 - 4*a*c)*d*e^7 + (3*a^2*b^3 - 13*a^3*b*c)*sqrt(b^2 - 4*a*c)*e^8)*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*abs(b^2*c^2*d^4*e - 4*a*c^3*d^4*e - 2*b^3*c*d^3*e^2 + 8*a*b*c^2*d^3*e^2 + b^4*d^2*e^3 - 2*a*b^2*c*d^2*e^3 - 8*a^2*c^2*d^2*e^3 - 2*a*b^3*d*e^4 + 8*a^2*b*c*d*e^4 + a^2*b^2*e^5 - 4*a^3*c*e^5) - (16*(b^2*c^8 - 4*a*c^9)*d^12*e - 96*(b^3*c^7 - 4*a*b*c^8)*d^11*e^2 + 8*(29*b^4*c^6 - 100*a*b^2*c^7 - 64*a^2*c^8)*d^10*e^3 - 40*(7*b^5*c^5 - 12*a*b^3*c^6 - 64*a^2*b*c^7)*d^9*e^4 + (157*b^6*c^4 + 636*a*b^4*c^5 - 4704*a^2*b^2*c^6 - 1408*a^3*c^7)*d^8*e^5 - 4*(b^7*c^3 + 300*a*b^5*c^4 - 864*a^2*b^3*c^5 - 1408*a^3*b*c^6)*d^7*e^6 - 14*(3*b^8*c^2 - 50*a*b^6*c^3 + 576*a^3*b^2*c^5 + 128*a^4*c^6)*d^6*e^7 + 4*(5*b^9*c - 27*a*b^7*c^2 - 336*a^2*b^5*c^3 + 1120*a^3*b^3*c^4 + 1344*a^4*b*c^5)*d^5*e^8 - (3*b^10 + 40*a*b^8*c - 590*a^2*b^6*c^2 + 120*a^3*b^4*c^3 + 5360*a^4*b^2*c^4 + 1088*a^5*c^5)*d^4*e^9 + 4*(3*a*b^9 - 7*a^2*b^7*c - 164*a^3*b^5*c^2 + 440*a^4*b^3*c^3 + 544*a^5*b*c^4)*d^3*e^10 - 2*(9*a^2*b^8 - 62*a^3*b^6*c - 60*a^4*b^4*c^2 + 624*a^5*b^2*c^3 + 128*a^6*c^4)*d^2*e^11 + 4*(3*a^3*b^7 - 26*a^4*b^5*c + 40*a^5*b^3*c^2 + 64*a^6*b*c^3)*d*e^12 - (3*a^4*b^6 - 28*a^5*b^4*c + 64*a^6*b^2*c^2)*e^13)*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e))*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*b^2*c^3*d^5 - 8*a*c^4*d^5 - 5*b^3*c^2*d^4*e + 20*a*b*c^3*d^4*e + 4*b^4*c*d^3*e^2 - 12*a*b^2*c^2*d^3*e^2 - 16*a^2*c^3*d^3*e^2 - b^5*d^2*e^3 - 2*a*b^3*c*d^2*e^3 + 24*a^2*b*c^2*d^2*e^3 + 2*a*b^4*d*e^4 - 6*a^2*b^2*c*d*e^4 - 8*a^3*c^2*d*e^4 - a^2*b^3*e^5 + 4*a^3*b*c*e^5 + sqrt((2*b^2*c^3*d^5 - 8*a*c^4*d^5 - 5*b^3*c^2*d^4*e + 20*a*b*c^3*d^4*e + 4*b^4*c*d^3*e^2 - 12*a*b^2*c^2*d^3*e^2 - 16*a^2*c^3*d^3*e^2 - b^5*d^2*e^3 - 2*a*b^3*c*d^2*e^3 + 24*a^2*b*c^2*d^2*e^3 + 2*a*b^4*d*e^4 - 6*a^2*b^2*c*d*e^4 - 8*a^3*c^2*d*e^4 - a^2*b^3*e^5 + 4*a^3*b*c*e^5)^2 - 4*(b^2*c^3*d^6 - 4*a*c^4*d^6 - 3*b^3*c^2*d^5*e + 12*a*b*c^3*d^5*e + 3*b^4*c*d^4*e^2 - 9*a*b^2*c^2*d^4*e^2 - 12*a^2*c^3*d^4*e^2 - b^5*d^3*e^3 - 2*a*b^3*c*d^3*e^3 + 24*a^2*b*c^2*d^3*e^3 + 3*a*b^4*d^2*e^4 - 9*a^2*b^2*c*d^2*e^4 - 12*a^3*c^2*d^2*e^4 - 3*a^2*b^3*d*e^5 + 12*a^3*b*c*d*e^5 + a^3*b^2*e^6 - 4*a^4*c*e^6)*(b^2*c^3*d^4 - 4*a*c^4*d^4 - 2*b^3*c^2*d^3*e + 8*a*b*c^3*d^3*e + b^4*c*d^2*e^2 - 2*a*b^2*c^2*d^2*e^2 - 8*a^2*c^3*d^2*e^2 - 2*a*b^3*c*d*e^3 + 8*a^2*b*c^2*d*e^3 + a^2*b^2*c*e^4 - 4*a^3*c^2*e^4)))/(b^2*c^3*d^4 - 4*a*c^4*d^4 - 2*b^3*c^2*d^3*e + 8*a*b*c^3*d^3*e + b^4*c*d^2*e^2 - 2*a*b^2*c^2*d^2*e^2 - 8*a^2*c^3*d^2*e^2 - 2*a*b^3*c*d*e^3 + 8*a^2*b*c^2*d*e^3 + a^2*b^2*c*e^4 - 4*a^3*c^2*e^4)))/(((b^2*c^5 - 4*a*c^6)*sqrt(b^2 - 4*a*c)*d^10 - 5*(b^3*c^4 - 4*a*b*c^5)*sqrt(b^2 - 4*a*c)*d^9*e + 5*(2*b^4*c^3 - 7*a*b^2*c^4 - 4*a^2*c^5)*sqrt(b^2 - 4*a*c)*d^8*e^2 - 10*(b^5*c^2 - 2*a*b^3*c^3 - 8*a^2*b*c^4)*sqrt(b^2 - 4*a*c)*d^7*e^3 + 5*(b^6*c + 2*a*b^4*c^2 - 22*a^2*b^2*c^3 - 8*a^3*c^4)*sqrt(b^2 - 4*a*c)*d^6*e^4 - (b^7 + 16*a*b^5*c - 50*a^2*b^3*c^2 - 120*a^3*b*c^3)*sqrt(b^2 - 4*a*c)*d^5*e^5 + 5*(a*b^6 + 2*a^2*b^4*c - 22*a^3*b^2*c^2 - 8*a^4*c^3)*sqrt(b^2 - 4*a*c)*d^4*e^6 - 10*(a^2*b^5 - 2*a^3*b^3*c - 8*a^4*b*c^2)*sqrt(b^2 - 4*a*c)*d^3*e^7 + 5*(2*a^3*b^4 - 7*a^4*b^2*c - 4*a^5*c^2)*sqrt(b^2 - 4*a*c)*d^2*e^8 - 5*(a^4*b^3 - 4*a^5*b*c)*sqrt(b^2 - 4*a*c)*d*e^9 + (a^5*b^2 - 4*a^6*c)*sqrt(b^2 - 4*a*c)*e^10)*abs(b^2*c^2*d^4*e - 4*a*c^3*d^4*e - 2*b^3*c*d^3*e^2 + 8*a*b*c^2*d^3*e^2 + b^4*d^2*e^3 - 2*a*b^2*c*d^2*e^3 - 8*a^2*c^2*d^2*e^3 - 2*a*b^3*d*e^4 + 8*a^2*b*c*d*e^4 + a^2*b^2*e^5 - 4*a^3*c*e^5)*abs(c)) + 1/8*((b^2*c^2*d^4*e - 4*a*c^3*d^4*e - 2*b^3*c*d^3*e^2 + 8*a*b*c^2*d^3*e^2 + b^4*d^2*e^3 - 2*a*b^2*c*d^2*e^3 - 8*a^2*c^2*d^2*e^3 - 2*a*b^3*d*e^4 + 8*a^2*b*c*d*e^4 + a^2*b^2*e^5 - 4*a^3*c*e^5)^2*(2*c^2*d^2*e - 2*b*c*d*e^2 + (3*b^2 - 10*a*c)*e^3)*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e) - 2*(2*sqrt(b^2 - 4*a*c)*c^5*d^7*e - 7*sqrt(b^2 - 4*a*c)*b*c^4*d^6*e^2 + 3*(b^2*c^3 + 10*a*c^4)*sqrt(b^2 - 4*a*c)*d^5*e^3 + 5*(2*b^3*c^2 - 15*a*b*c^3)*sqrt(b^2 - 4*a*c)*d^4*e^4 - (11*b^4*c - 48*a*b^2*c^2 - 54*a^2*c^3)*sqrt(b^2 - 4*a*c)*d^3*e^5 + 3*(b^5 + a*b^3*c - 27*a^2*b*c^2)*sqrt(b^2 - 4*a*c)*d^2*e^6 - (6*a*b^4 - 21*a^2*b^2*c - 26*a^3*c^2)*sqrt(b^2 - 4*a*c)*d*e^7 + (3*a^2*b^3 - 13*a^3*b*c)*sqrt(b^2 - 4*a*c)*e^8)*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*abs(b^2*c^2*d^4*e - 4*a*c^3*d^4*e - 2*b^3*c*d^3*e^2 + 8*a*b*c^2*d^3*e^2 + b^4*d^2*e^3 - 2*a*b^2*c*d^2*e^3 - 8*a^2*c^2*d^2*e^3 - 2*a*b^3*d*e^4 + 8*a^2*b*c*d*e^4 + a^2*b^2*e^5 - 4*a^3*c*e^5) - (16*(b^2*c^8 - 4*a*c^9)*d^12*e - 96*(b^3*c^7 - 4*a*b*c^8)*d^11*e^2 + 8*(29*b^4*c^6 - 100*a*b^2*c^7 - 64*a^2*c^8)*d^10*e^3 - 40*(7*b^5*c^5 - 12*a*b^3*c^6 - 64*a^2*b*c^7)*d^9*e^4 + (157*b^6*c^4 + 636*a*b^4*c^5 - 4704*a^2*b^2*c^6 - 1408*a^3*c^7)*d^8*e^5 - 4*(b^7*c^3 + 300*a*b^5*c^4 - 864*a^2*b^3*c^5 - 1408*a^3*b*c^6)*d^7*e^6 - 14*(3*b^8*c^2 - 50*a*b^6*c^3 + 576*a^3*b^2*c^5 + 128*a^4*c^6)*d^6*e^7 + 4*(5*b^9*c - 27*a*b^7*c^2 - 336*a^2*b^5*c^3 + 1120*a^3*b^3*c^4 + 1344*a^4*b*c^5)*d^5*e^8 - (3*b^10 + 40*a*b^8*c - 590*a^2*b^6*c^2 + 120*a^3*b^4*c^3 + 5360*a^4*b^2*c^4 + 1088*a^5*c^5)*d^4*e^9 + 4*(3*a*b^9 - 7*a^2*b^7*c - 164*a^3*b^5*c^2 + 440*a^4*b^3*c^3 + 544*a^5*b*c^4)*d^3*e^10 - 2*(9*a^2*b^8 - 62*a^3*b^6*c - 60*a^4*b^4*c^2 + 624*a^5*b^2*c^3 + 128*a^6*c^4)*d^2*e^11 + 4*(3*a^3*b^7 - 26*a^4*b^5*c + 40*a^5*b^3*c^2 + 64*a^6*b*c^3)*d*e^12 - (3*a^4*b^6 - 28*a^5*b^4*c + 64*a^6*b^2*c^2)*e^13)*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e))*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*b^2*c^3*d^5 - 8*a*c^4*d^5 - 5*b^3*c^2*d^4*e + 20*a*b*c^3*d^4*e + 4*b^4*c*d^3*e^2 - 12*a*b^2*c^2*d^3*e^2 - 16*a^2*c^3*d^3*e^2 - b^5*d^2*e^3 - 2*a*b^3*c*d^2*e^3 + 24*a^2*b*c^2*d^2*e^3 + 2*a*b^4*d*e^4 - 6*a^2*b^2*c*d*e^4 - 8*a^3*c^2*d*e^4 - a^2*b^3*e^5 + 4*a^3*b*c*e^5 - sqrt((2*b^2*c^3*d^5 - 8*a*c^4*d^5 - 5*b^3*c^2*d^4*e + 20*a*b*c^3*d^4*e + 4*b^4*c*d^3*e^2 - 12*a*b^2*c^2*d^3*e^2 - 16*a^2*c^3*d^3*e^2 - b^5*d^2*e^3 - 2*a*b^3*c*d^2*e^3 + 24*a^2*b*c^2*d^2*e^3 + 2*a*b^4*d*e^4 - 6*a^2*b^2*c*d*e^4 - 8*a^3*c^2*d*e^4 - a^2*b^3*e^5 + 4*a^3*b*c*e^5)^2 - 4*(b^2*c^3*d^6 - 4*a*c^4*d^6 - 3*b^3*c^2*d^5*e + 12*a*b*c^3*d^5*e + 3*b^4*c*d^4*e^2 - 9*a*b^2*c^2*d^4*e^2 - 12*a^2*c^3*d^4*e^2 - b^5*d^3*e^3 - 2*a*b^3*c*d^3*e^3 + 24*a^2*b*c^2*d^3*e^3 + 3*a*b^4*d^2*e^4 - 9*a^2*b^2*c*d^2*e^4 - 12*a^3*c^2*d^2*e^4 - 3*a^2*b^3*d*e^5 + 12*a^3*b*c*d*e^5 + a^3*b^2*e^6 - 4*a^4*c*e^6)*(b^2*c^3*d^4 - 4*a*c^4*d^4 - 2*b^3*c^2*d^3*e + 8*a*b*c^3*d^3*e + b^4*c*d^2*e^2 - 2*a*b^2*c^2*d^2*e^2 - 8*a^2*c^3*d^2*e^2 - 2*a*b^3*c*d*e^3 + 8*a^2*b*c^2*d*e^3 + a^2*b^2*c*e^4 - 4*a^3*c^2*e^4)))/(b^2*c^3*d^4 - 4*a*c^4*d^4 - 2*b^3*c^2*d^3*e + 8*a*b*c^3*d^3*e + b^4*c*d^2*e^2 - 2*a*b^2*c^2*d^2*e^2 - 8*a^2*c^3*d^2*e^2 - 2*a*b^3*c*d*e^3 + 8*a^2*b*c^2*d*e^3 + a^2*b^2*c*e^4 - 4*a^3*c^2*e^4)))/(((b^2*c^5 - 4*a*c^6)*sqrt(b^2 - 4*a*c)*d^10 - 5*(b^3*c^4 - 4*a*b*c^5)*sqrt(b^2 - 4*a*c)*d^9*e + 5*(2*b^4*c^3 - 7*a*b^2*c^4 - 4*a^2*c^5)*sqrt(b^2 - 4*a*c)*d^8*e^2 - 10*(b^5*c^2 - 2*a*b^3*c^3 - 8*a^2*b*c^4)*sqrt(b^2 - 4*a*c)*d^7*e^3 + 5*(b^6*c + 2*a*b^4*c^2 - 22*a^2*b^2*c^3 - 8*a^3*c^4)*sqrt(b^2 - 4*a*c)*d^6*e^4 - (b^7 + 16*a*b^5*c - 50*a^2*b^3*c^2 - 120*a^3*b*c^3)*sqrt(b^2 - 4*a*c)*d^5*e^5 + 5*(a*b^6 + 2*a^2*b^4*c - 22*a^3*b^2*c^2 - 8*a^4*c^3)*sqrt(b^2 - 4*a*c)*d^4*e^6 - 10*(a^2*b^5 - 2*a^3*b^3*c - 8*a^4*b*c^2)*sqrt(b^2 - 4*a*c)*d^3*e^7 + 5*(2*a^3*b^4 - 7*a^4*b^2*c - 4*a^5*c^2)*sqrt(b^2 - 4*a*c)*d^2*e^8 - 5*(a^4*b^3 - 4*a^5*b*c)*sqrt(b^2 - 4*a*c)*d*e^9 + (a^5*b^2 - 4*a^6*c)*sqrt(b^2 - 4*a*c)*e^10)*abs(b^2*c^2*d^4*e - 4*a*c^3*d^4*e - 2*b^3*c*d^3*e^2 + 8*a*b*c^2*d^3*e^2 + b^4*d^2*e^3 - 2*a*b^2*c*d^2*e^3 - 8*a^2*c^2*d^2*e^3 - 2*a*b^3*d*e^4 + 8*a^2*b*c*d*e^4 + a^2*b^2*e^5 - 4*a^3*c*e^5)*abs(c))","B",0
2301,1,3656,0,0.818439," ","integrate(1/x^(5/2)/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{b^{3} c x^{\frac{3}{2}} - 3 \, a b c^{2} x^{\frac{3}{2}} + b^{4} \sqrt{x} - 4 \, a b^{2} c \sqrt{x} + 2 \, a^{2} c^{2} \sqrt{x}}{{\left(a^{3} b^{2} - 4 \, a^{4} c\right)} {\left(c x^{2} + b x + a\right)}} + \frac{{\left(10 \, a^{6} b^{9} c^{2} - 138 \, a^{7} b^{7} c^{3} + 680 \, a^{8} b^{5} c^{4} - 1376 \, a^{9} b^{3} c^{5} + 896 \, a^{10} b c^{6} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{9} + 69 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{7} c + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{8} c - 340 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{5} c^{2} - 98 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{6} c^{2} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{7} c^{2} + 688 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{3} c^{3} + 288 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{4} c^{3} + 49 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{5} c^{3} - 448 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{10} b c^{4} - 224 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{2} c^{4} - 144 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{3} c^{4} + 112 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{9} b c^{5} - 10 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{7} c^{2} + 98 \, {\left(b^{2} - 4 \, a c\right)} a^{7} b^{5} c^{3} - 288 \, {\left(b^{2} - 4 \, a c\right)} a^{8} b^{3} c^{4} + 224 \, {\left(b^{2} - 4 \, a c\right)} a^{9} b c^{5} + {\left(10 \, b^{5} c^{2} - 78 \, a b^{3} c^{3} + 152 \, a^{2} b c^{4} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} + 39 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c - 76 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - 38 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} + 19 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 10 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} + 38 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} {\left(a^{3} b^{2} - 4 \, a^{4} c\right)}^{2} + 2 \, {\left(5 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{8} - 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{6} c - 10 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{7} c - 10 \, a^{3} b^{8} c + 286 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{4} c^{2} + 88 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{5} c^{2} + 5 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} c^{2} + 128 \, a^{4} b^{6} c^{2} - 496 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{2} c^{3} - 220 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{3} c^{3} - 44 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{4} c^{3} - 572 \, a^{5} b^{4} c^{3} + 224 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} c^{4} + 112 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b c^{4} + 110 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{4} + 992 \, a^{6} b^{2} c^{4} - 56 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} c^{5} - 448 \, a^{7} c^{5} + 10 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{6} c - 88 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{4} c^{2} + 220 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{2} c^{3} - 112 \, {\left(b^{2} - 4 \, a c\right)} a^{6} c^{4}\right)} {\left| a^{3} b^{2} - 4 \, a^{4} c \right|}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x}}{\sqrt{\frac{a^{3} b^{3} - 4 \, a^{4} b c + \sqrt{{\left(a^{3} b^{3} - 4 \, a^{4} b c\right)}^{2} - 4 \, {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)}}}{a^{3} b^{2} c - 4 \, a^{4} c^{2}}}}\right)}{8 \, {\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c - 2 \, a^{7} b^{5} c + 48 \, a^{9} b^{2} c^{2} + 16 \, a^{8} b^{3} c^{2} + a^{7} b^{4} c^{2} - 64 \, a^{10} c^{3} - 32 \, a^{9} b c^{3} - 8 \, a^{8} b^{2} c^{3} + 16 \, a^{9} c^{4}\right)} {\left| a^{3} b^{2} - 4 \, a^{4} c \right|} {\left| c \right|}} - \frac{{\left(10 \, a^{6} b^{9} c^{2} - 138 \, a^{7} b^{7} c^{3} + 680 \, a^{8} b^{5} c^{4} - 1376 \, a^{9} b^{3} c^{5} + 896 \, a^{10} b c^{6} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{9} + 69 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{7} c + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{8} c - 340 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{5} c^{2} - 98 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{6} c^{2} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{7} c^{2} + 688 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{3} c^{3} + 288 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{4} c^{3} + 49 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{5} c^{3} - 448 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{10} b c^{4} - 224 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{2} c^{4} - 144 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{3} c^{4} + 112 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{9} b c^{5} - 10 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{7} c^{2} + 98 \, {\left(b^{2} - 4 \, a c\right)} a^{7} b^{5} c^{3} - 288 \, {\left(b^{2} - 4 \, a c\right)} a^{8} b^{3} c^{4} + 224 \, {\left(b^{2} - 4 \, a c\right)} a^{9} b c^{5} + {\left(10 \, b^{5} c^{2} - 78 \, a b^{3} c^{3} + 152 \, a^{2} b c^{4} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} + 39 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c - 76 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{2} - 38 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{2} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{3} c^{2} + 19 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b c^{3} - 10 \, {\left(b^{2} - 4 \, a c\right)} b^{3} c^{2} + 38 \, {\left(b^{2} - 4 \, a c\right)} a b c^{3}\right)} {\left(a^{3} b^{2} - 4 \, a^{4} c\right)}^{2} - 2 \, {\left(5 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{8} - 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{6} c - 10 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{7} c + 10 \, a^{3} b^{8} c + 286 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{4} c^{2} + 88 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{5} c^{2} + 5 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{6} c^{2} - 128 \, a^{4} b^{6} c^{2} - 496 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{2} c^{3} - 220 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{3} c^{3} - 44 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{4} c^{3} + 572 \, a^{5} b^{4} c^{3} + 224 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} c^{4} + 112 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b c^{4} + 110 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{2} c^{4} - 992 \, a^{6} b^{2} c^{4} - 56 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} c^{5} + 448 \, a^{7} c^{5} - 10 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{6} c + 88 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{4} c^{2} - 220 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{2} c^{3} + 112 \, {\left(b^{2} - 4 \, a c\right)} a^{6} c^{4}\right)} {\left| a^{3} b^{2} - 4 \, a^{4} c \right|}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x}}{\sqrt{\frac{a^{3} b^{3} - 4 \, a^{4} b c - \sqrt{{\left(a^{3} b^{3} - 4 \, a^{4} b c\right)}^{2} - 4 \, {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)}}}{a^{3} b^{2} c - 4 \, a^{4} c^{2}}}}\right)}{8 \, {\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c - 2 \, a^{7} b^{5} c + 48 \, a^{9} b^{2} c^{2} + 16 \, a^{8} b^{3} c^{2} + a^{7} b^{4} c^{2} - 64 \, a^{10} c^{3} - 32 \, a^{9} b c^{3} - 8 \, a^{8} b^{2} c^{3} + 16 \, a^{9} c^{4}\right)} {\left| a^{3} b^{2} - 4 \, a^{4} c \right|} {\left| c \right|}} + \frac{2 \, {\left(6 \, b x - a\right)}}{3 \, a^{3} x^{\frac{3}{2}}}"," ",0,"(b^3*c*x^(3/2) - 3*a*b*c^2*x^(3/2) + b^4*sqrt(x) - 4*a*b^2*c*sqrt(x) + 2*a^2*c^2*sqrt(x))/((a^3*b^2 - 4*a^4*c)*(c*x^2 + b*x + a)) + 1/8*(10*a^6*b^9*c^2 - 138*a^7*b^7*c^3 + 680*a^8*b^5*c^4 - 1376*a^9*b^3*c^5 + 896*a^10*b*c^6 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^9 + 69*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^7*c + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^8*c - 340*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^5*c^2 - 98*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^6*c^2 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^7*c^2 + 688*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b^3*c^3 + 288*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^4*c^3 + 49*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^5*c^3 - 448*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^10*b*c^4 - 224*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b^2*c^4 - 144*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^3*c^4 + 112*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b*c^5 - 10*(b^2 - 4*a*c)*a^6*b^7*c^2 + 98*(b^2 - 4*a*c)*a^7*b^5*c^3 - 288*(b^2 - 4*a*c)*a^8*b^3*c^4 + 224*(b^2 - 4*a*c)*a^9*b*c^5 + (10*b^5*c^2 - 78*a*b^3*c^3 + 152*a^2*b*c^4 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5 + 39*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c - 76*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - 38*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^3*c^2 + 19*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - 10*(b^2 - 4*a*c)*b^3*c^2 + 38*(b^2 - 4*a*c)*a*b*c^3)*(a^3*b^2 - 4*a^4*c)^2 + 2*(5*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^8 - 64*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^6*c - 10*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^7*c - 10*a^3*b^8*c + 286*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^4*c^2 + 88*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^5*c^2 + 5*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^6*c^2 + 128*a^4*b^6*c^2 - 496*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^2*c^3 - 220*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^3*c^3 - 44*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c^3 - 572*a^5*b^4*c^3 + 224*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*c^4 + 112*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b*c^4 + 110*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^4 + 992*a^6*b^2*c^4 - 56*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*c^5 - 448*a^7*c^5 + 10*(b^2 - 4*a*c)*a^3*b^6*c - 88*(b^2 - 4*a*c)*a^4*b^4*c^2 + 220*(b^2 - 4*a*c)*a^5*b^2*c^3 - 112*(b^2 - 4*a*c)*a^6*c^4)*abs(a^3*b^2 - 4*a^4*c))*arctan(2*sqrt(1/2)*sqrt(x)/sqrt((a^3*b^3 - 4*a^4*b*c + sqrt((a^3*b^3 - 4*a^4*b*c)^2 - 4*(a^4*b^2 - 4*a^5*c)*(a^3*b^2*c - 4*a^4*c^2)))/(a^3*b^2*c - 4*a^4*c^2)))/((a^7*b^6 - 12*a^8*b^4*c - 2*a^7*b^5*c + 48*a^9*b^2*c^2 + 16*a^8*b^3*c^2 + a^7*b^4*c^2 - 64*a^10*c^3 - 32*a^9*b*c^3 - 8*a^8*b^2*c^3 + 16*a^9*c^4)*abs(a^3*b^2 - 4*a^4*c)*abs(c)) - 1/8*(10*a^6*b^9*c^2 - 138*a^7*b^7*c^3 + 680*a^8*b^5*c^4 - 1376*a^9*b^3*c^5 + 896*a^10*b*c^6 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^9 + 69*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^7*c + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^8*c - 340*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^5*c^2 - 98*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^6*c^2 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^7*c^2 + 688*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b^3*c^3 + 288*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^4*c^3 + 49*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^5*c^3 - 448*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^10*b*c^4 - 224*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b^2*c^4 - 144*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^3*c^4 + 112*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b*c^5 - 10*(b^2 - 4*a*c)*a^6*b^7*c^2 + 98*(b^2 - 4*a*c)*a^7*b^5*c^3 - 288*(b^2 - 4*a*c)*a^8*b^3*c^4 + 224*(b^2 - 4*a*c)*a^9*b*c^5 + (10*b^5*c^2 - 78*a*b^3*c^3 + 152*a^2*b*c^4 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5 + 39*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c - 76*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^2 - 38*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^2 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^3*c^2 + 19*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b*c^3 - 10*(b^2 - 4*a*c)*b^3*c^2 + 38*(b^2 - 4*a*c)*a*b*c^3)*(a^3*b^2 - 4*a^4*c)^2 - 2*(5*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^8 - 64*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^6*c - 10*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^7*c + 10*a^3*b^8*c + 286*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^4*c^2 + 88*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^5*c^2 + 5*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^6*c^2 - 128*a^4*b^6*c^2 - 496*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^2*c^3 - 220*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^3*c^3 - 44*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^4*c^3 + 572*a^5*b^4*c^3 + 224*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*c^4 + 112*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b*c^4 + 110*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^2*c^4 - 992*a^6*b^2*c^4 - 56*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*c^5 + 448*a^7*c^5 - 10*(b^2 - 4*a*c)*a^3*b^6*c + 88*(b^2 - 4*a*c)*a^4*b^4*c^2 - 220*(b^2 - 4*a*c)*a^5*b^2*c^3 + 112*(b^2 - 4*a*c)*a^6*c^4)*abs(a^3*b^2 - 4*a^4*c))*arctan(2*sqrt(1/2)*sqrt(x)/sqrt((a^3*b^3 - 4*a^4*b*c - sqrt((a^3*b^3 - 4*a^4*b*c)^2 - 4*(a^4*b^2 - 4*a^5*c)*(a^3*b^2*c - 4*a^4*c^2)))/(a^3*b^2*c - 4*a^4*c^2)))/((a^7*b^6 - 12*a^8*b^4*c - 2*a^7*b^5*c + 48*a^9*b^2*c^2 + 16*a^8*b^3*c^2 + a^7*b^4*c^2 - 64*a^10*c^3 - 32*a^9*b*c^3 - 8*a^8*b^2*c^3 + 16*a^9*c^4)*abs(a^3*b^2 - 4*a^4*c)*abs(c)) + 2/3*(6*b*x - a)/(a^3*x^(3/2))","B",0
2302,1,3067,0,8.236865," ","integrate((e*x+d)^(7/2)/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{{\left(192 \, {\left(b^{6} c^{7} - 12 \, a b^{4} c^{8} + 48 \, a^{2} b^{2} c^{9} - 64 \, a^{3} c^{10}\right)} d^{5} e - 480 \, {\left(b^{7} c^{6} - 12 \, a b^{5} c^{7} + 48 \, a^{2} b^{3} c^{8} - 64 \, a^{3} b c^{9}\right)} d^{4} e^{2} + 4 \, {\left(101 \, b^{8} c^{5} - 1136 \, a b^{6} c^{6} + 3936 \, a^{2} b^{4} c^{7} - 2816 \, a^{3} b^{2} c^{8} - 4864 \, a^{4} c^{9}\right)} d^{3} e^{3} - 6 \, {\left(21 \, b^{9} c^{4} - 176 \, a b^{7} c^{5} + 96 \, a^{2} b^{5} c^{6} + 2304 \, a^{3} b^{3} c^{7} - 4864 \, a^{4} b c^{8}\right)} d^{2} e^{4} - {\left(24 \, c^{3} d^{3} e - 36 \, b c^{2} d^{2} e^{2} + 2 \, {\left(5 \, b^{2} c + 16 \, a c^{2}\right)} d e^{3} + {\left(b^{3} - 16 \, a b c\right)} e^{4}\right)} {\left(b^{4} c e - 8 \, a b^{2} c^{2} e + 16 \, a^{2} c^{3} e\right)}^{2} + 4 \, {\left(2 \, b^{10} c^{3} + 23 \, a b^{8} c^{4} - 448 \, a^{2} b^{6} c^{5} + 1888 \, a^{3} b^{4} c^{6} - 2048 \, a^{4} b^{2} c^{7} - 1280 \, a^{5} c^{8}\right)} d e^{5} - 2 \, {\left(24 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{b^{2} - 4 \, a c} d^{4} e - 48 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} \sqrt{b^{2} - 4 \, a c} d^{3} e^{2} + {\left(25 \, b^{4} c^{3} - 56 \, a b^{2} c^{4} - 176 \, a^{2} c^{5}\right)} \sqrt{b^{2} - 4 \, a c} d^{2} e^{3} - {\left(b^{5} c^{2} + 40 \, a b^{3} c^{3} - 176 \, a^{2} b c^{4}\right)} \sqrt{b^{2} - 4 \, a c} d e^{4} + {\left(a b^{4} c^{2} + 16 \, a^{2} b^{2} c^{3} - 80 \, a^{3} c^{4}\right)} \sqrt{b^{2} - 4 \, a c} e^{5}\right)} {\left| b^{4} c e - 8 \, a b^{2} c^{2} e + 16 \, a^{2} c^{3} e \right|} + {\left(b^{11} c^{2} - 30 \, a b^{9} c^{3} + 224 \, a^{2} b^{7} c^{4} - 448 \, a^{3} b^{5} c^{5} - 768 \, a^{4} b^{3} c^{6} + 2560 \, a^{5} b c^{7}\right)} e^{6}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, b^{4} c^{2} d - 16 \, a b^{2} c^{3} d + 32 \, a^{2} c^{4} d - b^{5} c e + 8 \, a b^{3} c^{2} e - 16 \, a^{2} b c^{3} e + \sqrt{{\left(2 \, b^{4} c^{2} d - 16 \, a b^{2} c^{3} d + 32 \, a^{2} c^{4} d - b^{5} c e + 8 \, a b^{3} c^{2} e - 16 \, a^{2} b c^{3} e\right)}^{2} - 4 \, {\left(b^{4} c^{2} d^{2} - 8 \, a b^{2} c^{3} d^{2} + 16 \, a^{2} c^{4} d^{2} - b^{5} c d e + 8 \, a b^{3} c^{2} d e - 16 \, a^{2} b c^{3} d e + a b^{4} c e^{2} - 8 \, a^{2} b^{2} c^{2} e^{2} + 16 \, a^{3} c^{3} e^{2}\right)} {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)}}}{b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}}}}\right)}{4 \, \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left(2 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} \sqrt{b^{2} - 4 \, a c} d - {\left(b^{8} c - 16 \, a b^{6} c^{2} + 96 \, a^{2} b^{4} c^{3} - 256 \, a^{3} b^{2} c^{4} + 256 \, a^{4} c^{5} + {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} \sqrt{b^{2} - 4 \, a c}\right)} e\right)} {\left| b^{4} c e - 8 \, a b^{2} c^{2} e + 16 \, a^{2} c^{3} e \right|} {\left| c \right|}} - \frac{{\left(192 \, {\left(b^{6} c^{7} - 12 \, a b^{4} c^{8} + 48 \, a^{2} b^{2} c^{9} - 64 \, a^{3} c^{10}\right)} d^{5} e - 480 \, {\left(b^{7} c^{6} - 12 \, a b^{5} c^{7} + 48 \, a^{2} b^{3} c^{8} - 64 \, a^{3} b c^{9}\right)} d^{4} e^{2} + 4 \, {\left(101 \, b^{8} c^{5} - 1136 \, a b^{6} c^{6} + 3936 \, a^{2} b^{4} c^{7} - 2816 \, a^{3} b^{2} c^{8} - 4864 \, a^{4} c^{9}\right)} d^{3} e^{3} - 6 \, {\left(21 \, b^{9} c^{4} - 176 \, a b^{7} c^{5} + 96 \, a^{2} b^{5} c^{6} + 2304 \, a^{3} b^{3} c^{7} - 4864 \, a^{4} b c^{8}\right)} d^{2} e^{4} - {\left(24 \, c^{3} d^{3} e - 36 \, b c^{2} d^{2} e^{2} + 2 \, {\left(5 \, b^{2} c + 16 \, a c^{2}\right)} d e^{3} + {\left(b^{3} - 16 \, a b c\right)} e^{4}\right)} {\left(b^{4} c e - 8 \, a b^{2} c^{2} e + 16 \, a^{2} c^{3} e\right)}^{2} + 4 \, {\left(2 \, b^{10} c^{3} + 23 \, a b^{8} c^{4} - 448 \, a^{2} b^{6} c^{5} + 1888 \, a^{3} b^{4} c^{6} - 2048 \, a^{4} b^{2} c^{7} - 1280 \, a^{5} c^{8}\right)} d e^{5} + 2 \, {\left(24 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{b^{2} - 4 \, a c} d^{4} e - 48 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} \sqrt{b^{2} - 4 \, a c} d^{3} e^{2} + {\left(25 \, b^{4} c^{3} - 56 \, a b^{2} c^{4} - 176 \, a^{2} c^{5}\right)} \sqrt{b^{2} - 4 \, a c} d^{2} e^{3} - {\left(b^{5} c^{2} + 40 \, a b^{3} c^{3} - 176 \, a^{2} b c^{4}\right)} \sqrt{b^{2} - 4 \, a c} d e^{4} + {\left(a b^{4} c^{2} + 16 \, a^{2} b^{2} c^{3} - 80 \, a^{3} c^{4}\right)} \sqrt{b^{2} - 4 \, a c} e^{5}\right)} {\left| b^{4} c e - 8 \, a b^{2} c^{2} e + 16 \, a^{2} c^{3} e \right|} + {\left(b^{11} c^{2} - 30 \, a b^{9} c^{3} + 224 \, a^{2} b^{7} c^{4} - 448 \, a^{3} b^{5} c^{5} - 768 \, a^{4} b^{3} c^{6} + 2560 \, a^{5} b c^{7}\right)} e^{6}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, b^{4} c^{2} d - 16 \, a b^{2} c^{3} d + 32 \, a^{2} c^{4} d - b^{5} c e + 8 \, a b^{3} c^{2} e - 16 \, a^{2} b c^{3} e - \sqrt{{\left(2 \, b^{4} c^{2} d - 16 \, a b^{2} c^{3} d + 32 \, a^{2} c^{4} d - b^{5} c e + 8 \, a b^{3} c^{2} e - 16 \, a^{2} b c^{3} e\right)}^{2} - 4 \, {\left(b^{4} c^{2} d^{2} - 8 \, a b^{2} c^{3} d^{2} + 16 \, a^{2} c^{4} d^{2} - b^{5} c d e + 8 \, a b^{3} c^{2} d e - 16 \, a^{2} b c^{3} d e + a b^{4} c e^{2} - 8 \, a^{2} b^{2} c^{2} e^{2} + 16 \, a^{3} c^{3} e^{2}\right)} {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)}}}{b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}}}}\right)}{4 \, \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left(2 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} \sqrt{b^{2} - 4 \, a c} d + {\left(b^{8} c - 16 \, a b^{6} c^{2} + 96 \, a^{2} b^{4} c^{3} - 256 \, a^{3} b^{2} c^{4} + 256 \, a^{4} c^{5} - {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} \sqrt{b^{2} - 4 \, a c}\right)} e\right)} {\left| b^{4} c e - 8 \, a b^{2} c^{2} e + 16 \, a^{2} c^{3} e \right|} {\left| c \right|}} + \frac{24 \, {\left(x e + d\right)}^{\frac{7}{2}} c^{4} d^{3} e - 72 \, {\left(x e + d\right)}^{\frac{5}{2}} c^{4} d^{4} e + 72 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{4} d^{5} e - 24 \, \sqrt{x e + d} c^{4} d^{6} e - 36 \, {\left(x e + d\right)}^{\frac{7}{2}} b c^{3} d^{2} e^{2} + 144 \, {\left(x e + d\right)}^{\frac{5}{2}} b c^{3} d^{3} e^{2} - 180 \, {\left(x e + d\right)}^{\frac{3}{2}} b c^{3} d^{4} e^{2} + 72 \, \sqrt{x e + d} b c^{3} d^{5} e^{2} + 10 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{2} c^{2} d e^{3} + 32 \, {\left(x e + d\right)}^{\frac{7}{2}} a c^{3} d e^{3} - 85 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{2} c^{2} d^{2} e^{3} - 92 \, {\left(x e + d\right)}^{\frac{5}{2}} a c^{3} d^{2} e^{3} + 148 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{2} c^{2} d^{3} e^{3} + 128 \, {\left(x e + d\right)}^{\frac{3}{2}} a c^{3} d^{3} e^{3} - 73 \, \sqrt{x e + d} b^{2} c^{2} d^{4} e^{3} - 68 \, \sqrt{x e + d} a c^{3} d^{4} e^{3} + {\left(x e + d\right)}^{\frac{7}{2}} b^{3} c e^{4} - 16 \, {\left(x e + d\right)}^{\frac{7}{2}} a b c^{2} e^{4} + 13 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{3} c d e^{4} + 92 \, {\left(x e + d\right)}^{\frac{5}{2}} a b c^{2} d e^{4} - 42 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{3} c d^{2} e^{4} - 192 \, {\left(x e + d\right)}^{\frac{3}{2}} a b c^{2} d^{2} e^{4} + 26 \, \sqrt{x e + d} b^{3} c d^{3} e^{4} + 136 \, \sqrt{x e + d} a b c^{2} d^{3} e^{4} - {\left(x e + d\right)}^{\frac{5}{2}} b^{4} e^{5} - 5 \, {\left(x e + d\right)}^{\frac{5}{2}} a b^{2} c e^{5} - 36 \, {\left(x e + d\right)}^{\frac{5}{2}} a^{2} c^{2} e^{5} + 2 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{4} d e^{5} + 68 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{2} c d e^{5} + 56 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} c^{2} d e^{5} - \sqrt{x e + d} b^{4} d^{2} e^{5} - 70 \, \sqrt{x e + d} a b^{2} c d^{2} e^{5} - 64 \, \sqrt{x e + d} a^{2} c^{2} d^{2} e^{5} - 2 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{3} e^{6} - 28 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} b c e^{6} + 2 \, \sqrt{x e + d} a b^{3} d e^{6} + 64 \, \sqrt{x e + d} a^{2} b c d e^{6} - \sqrt{x e + d} a^{2} b^{2} e^{7} - 20 \, \sqrt{x e + d} a^{3} c e^{7}}{4 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + {\left(x e + d\right)} b e - b d e + a e^{2}\right)}^{2}}"," ",0,"1/4*(192*(b^6*c^7 - 12*a*b^4*c^8 + 48*a^2*b^2*c^9 - 64*a^3*c^10)*d^5*e - 480*(b^7*c^6 - 12*a*b^5*c^7 + 48*a^2*b^3*c^8 - 64*a^3*b*c^9)*d^4*e^2 + 4*(101*b^8*c^5 - 1136*a*b^6*c^6 + 3936*a^2*b^4*c^7 - 2816*a^3*b^2*c^8 - 4864*a^4*c^9)*d^3*e^3 - 6*(21*b^9*c^4 - 176*a*b^7*c^5 + 96*a^2*b^5*c^6 + 2304*a^3*b^3*c^7 - 4864*a^4*b*c^8)*d^2*e^4 - (24*c^3*d^3*e - 36*b*c^2*d^2*e^2 + 2*(5*b^2*c + 16*a*c^2)*d*e^3 + (b^3 - 16*a*b*c)*e^4)*(b^4*c*e - 8*a*b^2*c^2*e + 16*a^2*c^3*e)^2 + 4*(2*b^10*c^3 + 23*a*b^8*c^4 - 448*a^2*b^6*c^5 + 1888*a^3*b^4*c^6 - 2048*a^4*b^2*c^7 - 1280*a^5*c^8)*d*e^5 - 2*(24*(b^2*c^5 - 4*a*c^6)*sqrt(b^2 - 4*a*c)*d^4*e - 48*(b^3*c^4 - 4*a*b*c^5)*sqrt(b^2 - 4*a*c)*d^3*e^2 + (25*b^4*c^3 - 56*a*b^2*c^4 - 176*a^2*c^5)*sqrt(b^2 - 4*a*c)*d^2*e^3 - (b^5*c^2 + 40*a*b^3*c^3 - 176*a^2*b*c^4)*sqrt(b^2 - 4*a*c)*d*e^4 + (a*b^4*c^2 + 16*a^2*b^2*c^3 - 80*a^3*c^4)*sqrt(b^2 - 4*a*c)*e^5)*abs(b^4*c*e - 8*a*b^2*c^2*e + 16*a^2*c^3*e) + (b^11*c^2 - 30*a*b^9*c^3 + 224*a^2*b^7*c^4 - 448*a^3*b^5*c^5 - 768*a^4*b^3*c^6 + 2560*a^5*b*c^7)*e^6)*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*b^4*c^2*d - 16*a*b^2*c^3*d + 32*a^2*c^4*d - b^5*c*e + 8*a*b^3*c^2*e - 16*a^2*b*c^3*e + sqrt((2*b^4*c^2*d - 16*a*b^2*c^3*d + 32*a^2*c^4*d - b^5*c*e + 8*a*b^3*c^2*e - 16*a^2*b*c^3*e)^2 - 4*(b^4*c^2*d^2 - 8*a*b^2*c^3*d^2 + 16*a^2*c^4*d^2 - b^5*c*d*e + 8*a*b^3*c^2*d*e - 16*a^2*b*c^3*d*e + a*b^4*c*e^2 - 8*a^2*b^2*c^2*e^2 + 16*a^3*c^3*e^2)*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)))/(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)))/(sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*(2*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*sqrt(b^2 - 4*a*c)*d - (b^8*c - 16*a*b^6*c^2 + 96*a^2*b^4*c^3 - 256*a^3*b^2*c^4 + 256*a^4*c^5 + (b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*sqrt(b^2 - 4*a*c))*e)*abs(b^4*c*e - 8*a*b^2*c^2*e + 16*a^2*c^3*e)*abs(c)) - 1/4*(192*(b^6*c^7 - 12*a*b^4*c^8 + 48*a^2*b^2*c^9 - 64*a^3*c^10)*d^5*e - 480*(b^7*c^6 - 12*a*b^5*c^7 + 48*a^2*b^3*c^8 - 64*a^3*b*c^9)*d^4*e^2 + 4*(101*b^8*c^5 - 1136*a*b^6*c^6 + 3936*a^2*b^4*c^7 - 2816*a^3*b^2*c^8 - 4864*a^4*c^9)*d^3*e^3 - 6*(21*b^9*c^4 - 176*a*b^7*c^5 + 96*a^2*b^5*c^6 + 2304*a^3*b^3*c^7 - 4864*a^4*b*c^8)*d^2*e^4 - (24*c^3*d^3*e - 36*b*c^2*d^2*e^2 + 2*(5*b^2*c + 16*a*c^2)*d*e^3 + (b^3 - 16*a*b*c)*e^4)*(b^4*c*e - 8*a*b^2*c^2*e + 16*a^2*c^3*e)^2 + 4*(2*b^10*c^3 + 23*a*b^8*c^4 - 448*a^2*b^6*c^5 + 1888*a^3*b^4*c^6 - 2048*a^4*b^2*c^7 - 1280*a^5*c^8)*d*e^5 + 2*(24*(b^2*c^5 - 4*a*c^6)*sqrt(b^2 - 4*a*c)*d^4*e - 48*(b^3*c^4 - 4*a*b*c^5)*sqrt(b^2 - 4*a*c)*d^3*e^2 + (25*b^4*c^3 - 56*a*b^2*c^4 - 176*a^2*c^5)*sqrt(b^2 - 4*a*c)*d^2*e^3 - (b^5*c^2 + 40*a*b^3*c^3 - 176*a^2*b*c^4)*sqrt(b^2 - 4*a*c)*d*e^4 + (a*b^4*c^2 + 16*a^2*b^2*c^3 - 80*a^3*c^4)*sqrt(b^2 - 4*a*c)*e^5)*abs(b^4*c*e - 8*a*b^2*c^2*e + 16*a^2*c^3*e) + (b^11*c^2 - 30*a*b^9*c^3 + 224*a^2*b^7*c^4 - 448*a^3*b^5*c^5 - 768*a^4*b^3*c^6 + 2560*a^5*b*c^7)*e^6)*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*b^4*c^2*d - 16*a*b^2*c^3*d + 32*a^2*c^4*d - b^5*c*e + 8*a*b^3*c^2*e - 16*a^2*b*c^3*e - sqrt((2*b^4*c^2*d - 16*a*b^2*c^3*d + 32*a^2*c^4*d - b^5*c*e + 8*a*b^3*c^2*e - 16*a^2*b*c^3*e)^2 - 4*(b^4*c^2*d^2 - 8*a*b^2*c^3*d^2 + 16*a^2*c^4*d^2 - b^5*c*d*e + 8*a*b^3*c^2*d*e - 16*a^2*b*c^3*d*e + a*b^4*c*e^2 - 8*a^2*b^2*c^2*e^2 + 16*a^3*c^3*e^2)*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)))/(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)))/(sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*(2*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*sqrt(b^2 - 4*a*c)*d + (b^8*c - 16*a*b^6*c^2 + 96*a^2*b^4*c^3 - 256*a^3*b^2*c^4 + 256*a^4*c^5 - (b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*sqrt(b^2 - 4*a*c))*e)*abs(b^4*c*e - 8*a*b^2*c^2*e + 16*a^2*c^3*e)*abs(c)) + 1/4*(24*(x*e + d)^(7/2)*c^4*d^3*e - 72*(x*e + d)^(5/2)*c^4*d^4*e + 72*(x*e + d)^(3/2)*c^4*d^5*e - 24*sqrt(x*e + d)*c^4*d^6*e - 36*(x*e + d)^(7/2)*b*c^3*d^2*e^2 + 144*(x*e + d)^(5/2)*b*c^3*d^3*e^2 - 180*(x*e + d)^(3/2)*b*c^3*d^4*e^2 + 72*sqrt(x*e + d)*b*c^3*d^5*e^2 + 10*(x*e + d)^(7/2)*b^2*c^2*d*e^3 + 32*(x*e + d)^(7/2)*a*c^3*d*e^3 - 85*(x*e + d)^(5/2)*b^2*c^2*d^2*e^3 - 92*(x*e + d)^(5/2)*a*c^3*d^2*e^3 + 148*(x*e + d)^(3/2)*b^2*c^2*d^3*e^3 + 128*(x*e + d)^(3/2)*a*c^3*d^3*e^3 - 73*sqrt(x*e + d)*b^2*c^2*d^4*e^3 - 68*sqrt(x*e + d)*a*c^3*d^4*e^3 + (x*e + d)^(7/2)*b^3*c*e^4 - 16*(x*e + d)^(7/2)*a*b*c^2*e^4 + 13*(x*e + d)^(5/2)*b^3*c*d*e^4 + 92*(x*e + d)^(5/2)*a*b*c^2*d*e^4 - 42*(x*e + d)^(3/2)*b^3*c*d^2*e^4 - 192*(x*e + d)^(3/2)*a*b*c^2*d^2*e^4 + 26*sqrt(x*e + d)*b^3*c*d^3*e^4 + 136*sqrt(x*e + d)*a*b*c^2*d^3*e^4 - (x*e + d)^(5/2)*b^4*e^5 - 5*(x*e + d)^(5/2)*a*b^2*c*e^5 - 36*(x*e + d)^(5/2)*a^2*c^2*e^5 + 2*(x*e + d)^(3/2)*b^4*d*e^5 + 68*(x*e + d)^(3/2)*a*b^2*c*d*e^5 + 56*(x*e + d)^(3/2)*a^2*c^2*d*e^5 - sqrt(x*e + d)*b^4*d^2*e^5 - 70*sqrt(x*e + d)*a*b^2*c*d^2*e^5 - 64*sqrt(x*e + d)*a^2*c^2*d^2*e^5 - 2*(x*e + d)^(3/2)*a*b^3*e^6 - 28*(x*e + d)^(3/2)*a^2*b*c*e^6 + 2*sqrt(x*e + d)*a*b^3*d*e^6 + 64*sqrt(x*e + d)*a^2*b*c*d*e^6 - sqrt(x*e + d)*a^2*b^2*e^7 - 20*sqrt(x*e + d)*a^3*c*e^7)/((b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + (x*e + d)*b*e - b*d*e + a*e^2)^2)","B",0
2303,1,1392,0,3.985420," ","integrate((e*x+d)^(5/2)/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","-\frac{3 \, {\left(16 \, \sqrt{b^{2} - 4 \, a c} c^{2} d^{2} - 4 \, {\left(b^{2} c - 4 \, a c^{2} + 4 \, \sqrt{b^{2} - 4 \, a c} b c\right)} d e + {\left(2 \, b^{3} - 8 \, a b c + {\left(3 \, b^{2} + 4 \, a c\right)} \sqrt{b^{2} - 4 \, a c}\right)} e^{2}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, b^{4} c d - 16 \, a b^{2} c^{2} d + 32 \, a^{2} c^{3} d - b^{5} e + 8 \, a b^{3} c e - 16 \, a^{2} b c^{2} e + \sqrt{{\left(2 \, b^{4} c d - 16 \, a b^{2} c^{2} d + 32 \, a^{2} c^{3} d - b^{5} e + 8 \, a b^{3} c e - 16 \, a^{2} b c^{2} e\right)}^{2} - 4 \, {\left(b^{4} c d^{2} - 8 \, a b^{2} c^{2} d^{2} + 16 \, a^{2} c^{3} d^{2} - b^{5} d e + 8 \, a b^{3} c d e - 16 \, a^{2} b c^{2} d e + a b^{4} e^{2} - 8 \, a^{2} b^{2} c e^{2} + 16 \, a^{3} c^{2} e^{2}\right)} {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)}}}{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}}}\right)}{8 \, {\left(b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} {\left| c \right|}} + \frac{3 \, {\left(16 \, \sqrt{b^{2} - 4 \, a c} c^{2} d^{2} + 4 \, {\left(b^{2} c - 4 \, a c^{2} - 4 \, \sqrt{b^{2} - 4 \, a c} b c\right)} d e - {\left(2 \, b^{3} - 8 \, a b c - {\left(3 \, b^{2} + 4 \, a c\right)} \sqrt{b^{2} - 4 \, a c}\right)} e^{2}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, b^{4} c d - 16 \, a b^{2} c^{2} d + 32 \, a^{2} c^{3} d - b^{5} e + 8 \, a b^{3} c e - 16 \, a^{2} b c^{2} e - \sqrt{{\left(2 \, b^{4} c d - 16 \, a b^{2} c^{2} d + 32 \, a^{2} c^{3} d - b^{5} e + 8 \, a b^{3} c e - 16 \, a^{2} b c^{2} e\right)}^{2} - 4 \, {\left(b^{4} c d^{2} - 8 \, a b^{2} c^{2} d^{2} + 16 \, a^{2} c^{3} d^{2} - b^{5} d e + 8 \, a b^{3} c d e - 16 \, a^{2} b c^{2} d e + a b^{4} e^{2} - 8 \, a^{2} b^{2} c e^{2} + 16 \, a^{3} c^{2} e^{2}\right)} {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)}}}{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}}}\right)}{8 \, {\left(b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} {\left| c \right|}} + \frac{24 \, {\left(x e + d\right)}^{\frac{7}{2}} c^{3} d^{2} e - 72 \, {\left(x e + d\right)}^{\frac{5}{2}} c^{3} d^{3} e + 72 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{3} d^{4} e - 24 \, \sqrt{x e + d} c^{3} d^{5} e - 24 \, {\left(x e + d\right)}^{\frac{7}{2}} b c^{2} d e^{2} + 108 \, {\left(x e + d\right)}^{\frac{5}{2}} b c^{2} d^{2} e^{2} - 144 \, {\left(x e + d\right)}^{\frac{3}{2}} b c^{2} d^{3} e^{2} + 60 \, \sqrt{x e + d} b c^{2} d^{4} e^{2} + 3 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{2} c e^{3} + 12 \, {\left(x e + d\right)}^{\frac{7}{2}} a c^{2} e^{3} - 46 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{2} c d e^{3} - 32 \, {\left(x e + d\right)}^{\frac{5}{2}} a c^{2} d e^{3} + 91 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{2} c d^{2} e^{3} + 68 \, {\left(x e + d\right)}^{\frac{3}{2}} a c^{2} d^{2} e^{3} - 48 \, \sqrt{x e + d} b^{2} c d^{3} e^{3} - 48 \, \sqrt{x e + d} a c^{2} d^{3} e^{3} + 5 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{3} e^{4} + 16 \, {\left(x e + d\right)}^{\frac{5}{2}} a b c e^{4} - 19 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{3} d e^{4} - 68 \, {\left(x e + d\right)}^{\frac{3}{2}} a b c d e^{4} + 12 \, \sqrt{x e + d} b^{3} d^{2} e^{4} + 72 \, \sqrt{x e + d} a b c d^{2} e^{4} + 19 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{2} e^{5} - 4 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} c e^{5} - 24 \, \sqrt{x e + d} a b^{2} d e^{5} - 24 \, \sqrt{x e + d} a^{2} c d e^{5} + 12 \, \sqrt{x e + d} a^{2} b e^{6}}{4 \, {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + {\left(x e + d\right)} b e - b d e + a e^{2}\right)}^{2}}"," ",0,"-3/8*(16*sqrt(b^2 - 4*a*c)*c^2*d^2 - 4*(b^2*c - 4*a*c^2 + 4*sqrt(b^2 - 4*a*c)*b*c)*d*e + (2*b^3 - 8*a*b*c + (3*b^2 + 4*a*c)*sqrt(b^2 - 4*a*c))*e^2)*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*b^4*c*d - 16*a*b^2*c^2*d + 32*a^2*c^3*d - b^5*e + 8*a*b^3*c*e - 16*a^2*b*c^2*e + sqrt((2*b^4*c*d - 16*a*b^2*c^2*d + 32*a^2*c^3*d - b^5*e + 8*a*b^3*c*e - 16*a^2*b*c^2*e)^2 - 4*(b^4*c*d^2 - 8*a*b^2*c^2*d^2 + 16*a^2*c^3*d^2 - b^5*d*e + 8*a*b^3*c*d*e - 16*a^2*b*c^2*d*e + a*b^4*e^2 - 8*a^2*b^2*c*e^2 + 16*a^3*c^2*e^2)*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)))/(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)))/((b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)*abs(c)) + 3/8*(16*sqrt(b^2 - 4*a*c)*c^2*d^2 + 4*(b^2*c - 4*a*c^2 - 4*sqrt(b^2 - 4*a*c)*b*c)*d*e - (2*b^3 - 8*a*b*c - (3*b^2 + 4*a*c)*sqrt(b^2 - 4*a*c))*e^2)*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*b^4*c*d - 16*a*b^2*c^2*d + 32*a^2*c^3*d - b^5*e + 8*a*b^3*c*e - 16*a^2*b*c^2*e - sqrt((2*b^4*c*d - 16*a*b^2*c^2*d + 32*a^2*c^3*d - b^5*e + 8*a*b^3*c*e - 16*a^2*b*c^2*e)^2 - 4*(b^4*c*d^2 - 8*a*b^2*c^2*d^2 + 16*a^2*c^3*d^2 - b^5*d*e + 8*a*b^3*c*d*e - 16*a^2*b*c^2*d*e + a*b^4*e^2 - 8*a^2*b^2*c*e^2 + 16*a^3*c^2*e^2)*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)))/(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)))/((b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)*abs(c)) + 1/4*(24*(x*e + d)^(7/2)*c^3*d^2*e - 72*(x*e + d)^(5/2)*c^3*d^3*e + 72*(x*e + d)^(3/2)*c^3*d^4*e - 24*sqrt(x*e + d)*c^3*d^5*e - 24*(x*e + d)^(7/2)*b*c^2*d*e^2 + 108*(x*e + d)^(5/2)*b*c^2*d^2*e^2 - 144*(x*e + d)^(3/2)*b*c^2*d^3*e^2 + 60*sqrt(x*e + d)*b*c^2*d^4*e^2 + 3*(x*e + d)^(7/2)*b^2*c*e^3 + 12*(x*e + d)^(7/2)*a*c^2*e^3 - 46*(x*e + d)^(5/2)*b^2*c*d*e^3 - 32*(x*e + d)^(5/2)*a*c^2*d*e^3 + 91*(x*e + d)^(3/2)*b^2*c*d^2*e^3 + 68*(x*e + d)^(3/2)*a*c^2*d^2*e^3 - 48*sqrt(x*e + d)*b^2*c*d^3*e^3 - 48*sqrt(x*e + d)*a*c^2*d^3*e^3 + 5*(x*e + d)^(5/2)*b^3*e^4 + 16*(x*e + d)^(5/2)*a*b*c*e^4 - 19*(x*e + d)^(3/2)*b^3*d*e^4 - 68*(x*e + d)^(3/2)*a*b*c*d*e^4 + 12*sqrt(x*e + d)*b^3*d^2*e^4 + 72*sqrt(x*e + d)*a*b*c*d^2*e^4 + 19*(x*e + d)^(3/2)*a*b^2*e^5 - 4*(x*e + d)^(3/2)*a^2*c*e^5 - 24*sqrt(x*e + d)*a*b^2*d*e^5 - 24*sqrt(x*e + d)*a^2*c*d*e^5 + 12*sqrt(x*e + d)*a^2*b*e^6)/((b^4 - 8*a*b^2*c + 16*a^2*c^2)*((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + (x*e + d)*b*e - b*d*e + a*e^2)^2)","B",0
2304,1,1452,0,4.463577," ","integrate((e*x+d)^(3/2)/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","-\frac{3 \, {\left(16 \, \sqrt{b^{2} - 4 \, a c} c^{3} d^{2} + 4 \, {\left(b^{2} c^{2} - 4 \, a c^{3} - 4 \, \sqrt{b^{2} - 4 \, a c} b c^{2}\right)} d e - {\left(2 \, b^{3} c - 8 \, a b c^{2} - {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} \sqrt{b^{2} - 4 \, a c}\right)} e^{2}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, b^{4} c d - 16 \, a b^{2} c^{2} d + 32 \, a^{2} c^{3} d - b^{5} e + 8 \, a b^{3} c e - 16 \, a^{2} b c^{2} e + \sqrt{{\left(2 \, b^{4} c d - 16 \, a b^{2} c^{2} d + 32 \, a^{2} c^{3} d - b^{5} e + 8 \, a b^{3} c e - 16 \, a^{2} b c^{2} e\right)}^{2} - 4 \, {\left(b^{4} c d^{2} - 8 \, a b^{2} c^{2} d^{2} + 16 \, a^{2} c^{3} d^{2} - b^{5} d e + 8 \, a b^{3} c d e - 16 \, a^{2} b c^{2} d e + a b^{4} e^{2} - 8 \, a^{2} b^{2} c e^{2} + 16 \, a^{3} c^{2} e^{2}\right)} {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)}}}{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}}}\right)}{4 \, {\left(2 \, {\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} d - {\left(b^{7} - 12 \, a b^{5} c + 48 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3} - {\left(b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} \sqrt{b^{2} - 4 \, a c}\right)} e\right)} {\left| c \right|}} + \frac{3 \, {\left(16 \, \sqrt{b^{2} - 4 \, a c} c^{3} d^{2} - 4 \, {\left(b^{2} c^{2} - 4 \, a c^{3} + 4 \, \sqrt{b^{2} - 4 \, a c} b c^{2}\right)} d e + {\left(2 \, b^{3} c - 8 \, a b c^{2} + {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} \sqrt{b^{2} - 4 \, a c}\right)} e^{2}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, b^{4} c d - 16 \, a b^{2} c^{2} d + 32 \, a^{2} c^{3} d - b^{5} e + 8 \, a b^{3} c e - 16 \, a^{2} b c^{2} e - \sqrt{{\left(2 \, b^{4} c d - 16 \, a b^{2} c^{2} d + 32 \, a^{2} c^{3} d - b^{5} e + 8 \, a b^{3} c e - 16 \, a^{2} b c^{2} e\right)}^{2} - 4 \, {\left(b^{4} c d^{2} - 8 \, a b^{2} c^{2} d^{2} + 16 \, a^{2} c^{3} d^{2} - b^{5} d e + 8 \, a b^{3} c d e - 16 \, a^{2} b c^{2} d e + a b^{4} e^{2} - 8 \, a^{2} b^{2} c e^{2} + 16 \, a^{3} c^{2} e^{2}\right)} {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)}}}{b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}}}}\right)}{4 \, {\left(2 \, {\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} d - {\left(b^{7} - 12 \, a b^{5} c + 48 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3} + {\left(b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} \sqrt{b^{2} - 4 \, a c}\right)} e\right)} {\left| c \right|}} + \frac{24 \, {\left(x e + d\right)}^{\frac{7}{2}} c^{3} d e - 72 \, {\left(x e + d\right)}^{\frac{5}{2}} c^{3} d^{2} e + 72 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{3} d^{3} e - 24 \, \sqrt{x e + d} c^{3} d^{4} e - 12 \, {\left(x e + d\right)}^{\frac{7}{2}} b c^{2} e^{2} + 72 \, {\left(x e + d\right)}^{\frac{5}{2}} b c^{2} d e^{2} - 108 \, {\left(x e + d\right)}^{\frac{3}{2}} b c^{2} d^{2} e^{2} + 48 \, \sqrt{x e + d} b c^{2} d^{3} e^{2} - 19 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{2} c e^{3} + 4 \, {\left(x e + d\right)}^{\frac{5}{2}} a c^{2} e^{3} + 46 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{2} c d e^{3} + 32 \, {\left(x e + d\right)}^{\frac{3}{2}} a c^{2} d e^{3} - 27 \, \sqrt{x e + d} b^{2} c d^{2} e^{3} - 36 \, \sqrt{x e + d} a c^{2} d^{2} e^{3} - 5 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{3} e^{4} - 16 \, {\left(x e + d\right)}^{\frac{3}{2}} a b c e^{4} + 3 \, \sqrt{x e + d} b^{3} d e^{4} + 36 \, \sqrt{x e + d} a b c d e^{4} - 3 \, \sqrt{x e + d} a b^{2} e^{5} - 12 \, \sqrt{x e + d} a^{2} c e^{5}}{4 \, {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + {\left(x e + d\right)} b e - b d e + a e^{2}\right)}^{2}}"," ",0,"-3/4*(16*sqrt(b^2 - 4*a*c)*c^3*d^2 + 4*(b^2*c^2 - 4*a*c^3 - 4*sqrt(b^2 - 4*a*c)*b*c^2)*d*e - (2*b^3*c - 8*a*b*c^2 - (3*b^2*c + 4*a*c^2)*sqrt(b^2 - 4*a*c))*e^2)*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*b^4*c*d - 16*a*b^2*c^2*d + 32*a^2*c^3*d - b^5*e + 8*a*b^3*c*e - 16*a^2*b*c^2*e + sqrt((2*b^4*c*d - 16*a*b^2*c^2*d + 32*a^2*c^3*d - b^5*e + 8*a*b^3*c*e - 16*a^2*b*c^2*e)^2 - 4*(b^4*c*d^2 - 8*a*b^2*c^2*d^2 + 16*a^2*c^3*d^2 - b^5*d*e + 8*a*b^3*c*d*e - 16*a^2*b*c^2*d*e + a*b^4*e^2 - 8*a^2*b^2*c*e^2 + 16*a^3*c^2*e^2)*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)))/(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)))/((2*(b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*d - (b^7 - 12*a*b^5*c + 48*a^2*b^3*c^2 - 64*a^3*b*c^3 - (b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)*sqrt(b^2 - 4*a*c))*e)*abs(c)) + 3/4*(16*sqrt(b^2 - 4*a*c)*c^3*d^2 - 4*(b^2*c^2 - 4*a*c^3 + 4*sqrt(b^2 - 4*a*c)*b*c^2)*d*e + (2*b^3*c - 8*a*b*c^2 + (3*b^2*c + 4*a*c^2)*sqrt(b^2 - 4*a*c))*e^2)*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*b^4*c*d - 16*a*b^2*c^2*d + 32*a^2*c^3*d - b^5*e + 8*a*b^3*c*e - 16*a^2*b*c^2*e - sqrt((2*b^4*c*d - 16*a*b^2*c^2*d + 32*a^2*c^3*d - b^5*e + 8*a*b^3*c*e - 16*a^2*b*c^2*e)^2 - 4*(b^4*c*d^2 - 8*a*b^2*c^2*d^2 + 16*a^2*c^3*d^2 - b^5*d*e + 8*a*b^3*c*d*e - 16*a^2*b*c^2*d*e + a*b^4*e^2 - 8*a^2*b^2*c*e^2 + 16*a^3*c^2*e^2)*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)))/(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)))/((2*(b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*d - (b^7 - 12*a*b^5*c + 48*a^2*b^3*c^2 - 64*a^3*b*c^3 + (b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)*sqrt(b^2 - 4*a*c))*e)*abs(c)) + 1/4*(24*(x*e + d)^(7/2)*c^3*d*e - 72*(x*e + d)^(5/2)*c^3*d^2*e + 72*(x*e + d)^(3/2)*c^3*d^3*e - 24*sqrt(x*e + d)*c^3*d^4*e - 12*(x*e + d)^(7/2)*b*c^2*e^2 + 72*(x*e + d)^(5/2)*b*c^2*d*e^2 - 108*(x*e + d)^(3/2)*b*c^2*d^2*e^2 + 48*sqrt(x*e + d)*b*c^2*d^3*e^2 - 19*(x*e + d)^(5/2)*b^2*c*e^3 + 4*(x*e + d)^(5/2)*a*c^2*e^3 + 46*(x*e + d)^(3/2)*b^2*c*d*e^3 + 32*(x*e + d)^(3/2)*a*c^2*d*e^3 - 27*sqrt(x*e + d)*b^2*c*d^2*e^3 - 36*sqrt(x*e + d)*a*c^2*d^2*e^3 - 5*(x*e + d)^(3/2)*b^3*e^4 - 16*(x*e + d)^(3/2)*a*b*c*e^4 + 3*sqrt(x*e + d)*b^3*d*e^4 + 36*sqrt(x*e + d)*a*b*c*d*e^4 - 3*sqrt(x*e + d)*a*b^2*e^5 - 12*sqrt(x*e + d)*a^2*c*e^5)/((b^4 - 8*a*b^2*c + 16*a^2*c^2)*((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + (x*e + d)*b*e - b*d*e + a*e^2)^2)","B",0
2305,1,5117,0,7.975978," ","integrate((e*x+d)^(1/2)/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{{\left({\left(b^{4} c d^{2} e - 8 \, a b^{2} c^{2} d^{2} e + 16 \, a^{2} c^{3} d^{2} e - b^{5} d e^{2} + 8 \, a b^{3} c d e^{2} - 16 \, a^{2} b c^{2} d e^{2} + a b^{4} e^{3} - 8 \, a^{2} b^{2} c e^{3} + 16 \, a^{3} c^{2} e^{3}\right)}^{2} {\left(24 \, c^{2} d^{2} e - 24 \, b c d e^{2} + {\left(b^{2} + 20 \, a c\right)} e^{3}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} + 2 \, {\left(24 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{b^{2} - 4 \, a c} d^{5} e - 60 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} \sqrt{b^{2} - 4 \, a c} d^{4} e^{2} + 2 \, {\left(23 \, b^{4} c^{2} - 64 \, a b^{2} c^{3} - 112 \, a^{2} c^{4}\right)} \sqrt{b^{2} - 4 \, a c} d^{3} e^{3} - 3 \, {\left(3 \, b^{5} c + 16 \, a b^{3} c^{2} - 112 \, a^{2} b c^{3}\right)} \sqrt{b^{2} - 4 \, a c} d^{2} e^{4} - {\left(b^{6} - 30 \, a b^{4} c + 72 \, a^{2} b^{2} c^{2} + 128 \, a^{3} c^{3}\right)} \sqrt{b^{2} - 4 \, a c} d e^{5} + {\left(a b^{5} - 20 \, a^{2} b^{3} c + 64 \, a^{3} b c^{2}\right)} \sqrt{b^{2} - 4 \, a c} e^{6}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left| b^{4} c d^{2} e - 8 \, a b^{2} c^{2} d^{2} e + 16 \, a^{2} c^{3} d^{2} e - b^{5} d e^{2} + 8 \, a b^{3} c d e^{2} - 16 \, a^{2} b c^{2} d e^{2} + a b^{4} e^{3} - 8 \, a^{2} b^{2} c e^{3} + 16 \, a^{3} c^{2} e^{3} \right|} - {\left(192 \, {\left(b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}\right)} d^{8} e - 768 \, {\left(b^{7} c^{5} - 12 \, a b^{5} c^{6} + 48 \, a^{2} b^{3} c^{7} - 64 \, a^{3} b c^{8}\right)} d^{7} e^{2} + 4 \, {\left(299 \, b^{8} c^{4} - 3440 \, a b^{6} c^{5} + 12576 \, a^{2} b^{4} c^{6} - 12032 \, a^{3} b^{2} c^{7} - 9472 \, a^{4} c^{8}\right)} d^{6} e^{3} - 12 \, {\left(75 \, b^{9} c^{3} - 752 \, a b^{7} c^{4} + 1824 \, a^{2} b^{5} c^{5} + 2304 \, a^{3} b^{3} c^{6} - 9472 \, a^{4} b c^{7}\right)} d^{5} e^{4} + {\left(323 \, b^{10} c^{2} - 1960 \, a b^{8} c^{3} - 6880 \, a^{2} b^{6} c^{4} + 64000 \, a^{3} b^{4} c^{5} - 93440 \, a^{4} b^{2} c^{6} - 38912 \, a^{5} c^{7}\right)} d^{4} e^{5} - 2 \, {\left(21 \, b^{11} c + 184 \, a b^{9} c^{2} - 3616 \, a^{2} b^{7} c^{3} + 12288 \, a^{3} b^{5} c^{4} + 1280 \, a^{4} b^{3} c^{5} - 38912 \, a^{5} b c^{6}\right)} d^{3} e^{6} - {\left(b^{12} - 150 \, a b^{10} c + 948 \, a^{2} b^{8} c^{2} + 2176 \, a^{3} b^{6} c^{3} - 24960 \, a^{4} b^{4} c^{4} + 38400 \, a^{5} b^{2} c^{5} + 13312 \, a^{6} c^{6}\right)} d^{2} e^{7} + 2 \, {\left(a b^{11} - 86 \, a^{2} b^{9} c + 832 \, a^{3} b^{7} c^{2} - 2368 \, a^{4} b^{5} c^{3} - 256 \, a^{5} b^{3} c^{4} + 6656 \, a^{6} b c^{5}\right)} d e^{8} - {\left(a^{2} b^{10} - 64 \, a^{3} b^{8} c + 672 \, a^{4} b^{6} c^{2} - 2560 \, a^{5} b^{4} c^{3} + 3328 \, a^{6} b^{2} c^{4}\right)} e^{9}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, b^{4} c^{2} d^{3} - 16 \, a b^{2} c^{3} d^{3} + 32 \, a^{2} c^{4} d^{3} - 3 \, b^{5} c d^{2} e + 24 \, a b^{3} c^{2} d^{2} e - 48 \, a^{2} b c^{3} d^{2} e + b^{6} d e^{2} - 6 \, a b^{4} c d e^{2} + 32 \, a^{3} c^{3} d e^{2} - a b^{5} e^{3} + 8 \, a^{2} b^{3} c e^{3} - 16 \, a^{3} b c^{2} e^{3} + \sqrt{{\left(2 \, b^{4} c^{2} d^{3} - 16 \, a b^{2} c^{3} d^{3} + 32 \, a^{2} c^{4} d^{3} - 3 \, b^{5} c d^{2} e + 24 \, a b^{3} c^{2} d^{2} e - 48 \, a^{2} b c^{3} d^{2} e + b^{6} d e^{2} - 6 \, a b^{4} c d e^{2} + 32 \, a^{3} c^{3} d e^{2} - a b^{5} e^{3} + 8 \, a^{2} b^{3} c e^{3} - 16 \, a^{3} b c^{2} e^{3}\right)}^{2} - 4 \, {\left(b^{4} c^{2} d^{4} - 8 \, a b^{2} c^{3} d^{4} + 16 \, a^{2} c^{4} d^{4} - 2 \, b^{5} c d^{3} e + 16 \, a b^{3} c^{2} d^{3} e - 32 \, a^{2} b c^{3} d^{3} e + b^{6} d^{2} e^{2} - 6 \, a b^{4} c d^{2} e^{2} + 32 \, a^{3} c^{3} d^{2} e^{2} - 2 \, a b^{5} d e^{3} + 16 \, a^{2} b^{3} c d e^{3} - 32 \, a^{3} b c^{2} d e^{3} + a^{2} b^{4} e^{4} - 8 \, a^{3} b^{2} c e^{4} + 16 \, a^{4} c^{2} e^{4}\right)} {\left(b^{4} c^{2} d^{2} - 8 \, a b^{2} c^{3} d^{2} + 16 \, a^{2} c^{4} d^{2} - b^{5} c d e + 8 \, a b^{3} c^{2} d e - 16 \, a^{2} b c^{3} d e + a b^{4} c e^{2} - 8 \, a^{2} b^{2} c^{2} e^{2} + 16 \, a^{3} c^{3} e^{2}\right)}}}{b^{4} c^{2} d^{2} - 8 \, a b^{2} c^{3} d^{2} + 16 \, a^{2} c^{4} d^{2} - b^{5} c d e + 8 \, a b^{3} c^{2} d e - 16 \, a^{2} b c^{3} d e + a b^{4} c e^{2} - 8 \, a^{2} b^{2} c^{2} e^{2} + 16 \, a^{3} c^{3} e^{2}}}}\right)}{32 \, {\left({\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} \sqrt{b^{2} - 4 \, a c} d^{6} - 3 \, {\left(b^{7} c^{2} - 12 \, a b^{5} c^{3} + 48 \, a^{2} b^{3} c^{4} - 64 \, a^{3} b c^{5}\right)} \sqrt{b^{2} - 4 \, a c} d^{5} e + 3 \, {\left(b^{8} c - 11 \, a b^{6} c^{2} + 36 \, a^{2} b^{4} c^{3} - 16 \, a^{3} b^{2} c^{4} - 64 \, a^{4} c^{5}\right)} \sqrt{b^{2} - 4 \, a c} d^{4} e^{2} - {\left(b^{9} - 6 \, a b^{7} c - 24 \, a^{2} b^{5} c^{2} + 224 \, a^{3} b^{3} c^{3} - 384 \, a^{4} b c^{4}\right)} \sqrt{b^{2} - 4 \, a c} d^{3} e^{3} + 3 \, {\left(a b^{8} - 11 \, a^{2} b^{6} c + 36 \, a^{3} b^{4} c^{2} - 16 \, a^{4} b^{2} c^{3} - 64 \, a^{5} c^{4}\right)} \sqrt{b^{2} - 4 \, a c} d^{2} e^{4} - 3 \, {\left(a^{2} b^{7} - 12 \, a^{3} b^{5} c + 48 \, a^{4} b^{3} c^{2} - 64 \, a^{5} b c^{3}\right)} \sqrt{b^{2} - 4 \, a c} d e^{5} + {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}\right)} \sqrt{b^{2} - 4 \, a c} e^{6}\right)} {\left| b^{4} c d^{2} e - 8 \, a b^{2} c^{2} d^{2} e + 16 \, a^{2} c^{3} d^{2} e - b^{5} d e^{2} + 8 \, a b^{3} c d e^{2} - 16 \, a^{2} b c^{2} d e^{2} + a b^{4} e^{3} - 8 \, a^{2} b^{2} c e^{3} + 16 \, a^{3} c^{2} e^{3} \right|} {\left| c \right|}} - \frac{{\left({\left(b^{4} c d^{2} e - 8 \, a b^{2} c^{2} d^{2} e + 16 \, a^{2} c^{3} d^{2} e - b^{5} d e^{2} + 8 \, a b^{3} c d e^{2} - 16 \, a^{2} b c^{2} d e^{2} + a b^{4} e^{3} - 8 \, a^{2} b^{2} c e^{3} + 16 \, a^{3} c^{2} e^{3}\right)}^{2} {\left(24 \, c^{2} d^{2} e - 24 \, b c d e^{2} + {\left(b^{2} + 20 \, a c\right)} e^{3}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} - 2 \, {\left(24 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} \sqrt{b^{2} - 4 \, a c} d^{5} e - 60 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} \sqrt{b^{2} - 4 \, a c} d^{4} e^{2} + 2 \, {\left(23 \, b^{4} c^{2} - 64 \, a b^{2} c^{3} - 112 \, a^{2} c^{4}\right)} \sqrt{b^{2} - 4 \, a c} d^{3} e^{3} - 3 \, {\left(3 \, b^{5} c + 16 \, a b^{3} c^{2} - 112 \, a^{2} b c^{3}\right)} \sqrt{b^{2} - 4 \, a c} d^{2} e^{4} - {\left(b^{6} - 30 \, a b^{4} c + 72 \, a^{2} b^{2} c^{2} + 128 \, a^{3} c^{3}\right)} \sqrt{b^{2} - 4 \, a c} d e^{5} + {\left(a b^{5} - 20 \, a^{2} b^{3} c + 64 \, a^{3} b c^{2}\right)} \sqrt{b^{2} - 4 \, a c} e^{6}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} {\left| b^{4} c d^{2} e - 8 \, a b^{2} c^{2} d^{2} e + 16 \, a^{2} c^{3} d^{2} e - b^{5} d e^{2} + 8 \, a b^{3} c d e^{2} - 16 \, a^{2} b c^{2} d e^{2} + a b^{4} e^{3} - 8 \, a^{2} b^{2} c e^{3} + 16 \, a^{3} c^{2} e^{3} \right|} - {\left(192 \, {\left(b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}\right)} d^{8} e - 768 \, {\left(b^{7} c^{5} - 12 \, a b^{5} c^{6} + 48 \, a^{2} b^{3} c^{7} - 64 \, a^{3} b c^{8}\right)} d^{7} e^{2} + 4 \, {\left(299 \, b^{8} c^{4} - 3440 \, a b^{6} c^{5} + 12576 \, a^{2} b^{4} c^{6} - 12032 \, a^{3} b^{2} c^{7} - 9472 \, a^{4} c^{8}\right)} d^{6} e^{3} - 12 \, {\left(75 \, b^{9} c^{3} - 752 \, a b^{7} c^{4} + 1824 \, a^{2} b^{5} c^{5} + 2304 \, a^{3} b^{3} c^{6} - 9472 \, a^{4} b c^{7}\right)} d^{5} e^{4} + {\left(323 \, b^{10} c^{2} - 1960 \, a b^{8} c^{3} - 6880 \, a^{2} b^{6} c^{4} + 64000 \, a^{3} b^{4} c^{5} - 93440 \, a^{4} b^{2} c^{6} - 38912 \, a^{5} c^{7}\right)} d^{4} e^{5} - 2 \, {\left(21 \, b^{11} c + 184 \, a b^{9} c^{2} - 3616 \, a^{2} b^{7} c^{3} + 12288 \, a^{3} b^{5} c^{4} + 1280 \, a^{4} b^{3} c^{5} - 38912 \, a^{5} b c^{6}\right)} d^{3} e^{6} - {\left(b^{12} - 150 \, a b^{10} c + 948 \, a^{2} b^{8} c^{2} + 2176 \, a^{3} b^{6} c^{3} - 24960 \, a^{4} b^{4} c^{4} + 38400 \, a^{5} b^{2} c^{5} + 13312 \, a^{6} c^{6}\right)} d^{2} e^{7} + 2 \, {\left(a b^{11} - 86 \, a^{2} b^{9} c + 832 \, a^{3} b^{7} c^{2} - 2368 \, a^{4} b^{5} c^{3} - 256 \, a^{5} b^{3} c^{4} + 6656 \, a^{6} b c^{5}\right)} d e^{8} - {\left(a^{2} b^{10} - 64 \, a^{3} b^{8} c + 672 \, a^{4} b^{6} c^{2} - 2560 \, a^{5} b^{4} c^{3} + 3328 \, a^{6} b^{2} c^{4}\right)} e^{9}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, b^{4} c^{2} d^{3} - 16 \, a b^{2} c^{3} d^{3} + 32 \, a^{2} c^{4} d^{3} - 3 \, b^{5} c d^{2} e + 24 \, a b^{3} c^{2} d^{2} e - 48 \, a^{2} b c^{3} d^{2} e + b^{6} d e^{2} - 6 \, a b^{4} c d e^{2} + 32 \, a^{3} c^{3} d e^{2} - a b^{5} e^{3} + 8 \, a^{2} b^{3} c e^{3} - 16 \, a^{3} b c^{2} e^{3} - \sqrt{{\left(2 \, b^{4} c^{2} d^{3} - 16 \, a b^{2} c^{3} d^{3} + 32 \, a^{2} c^{4} d^{3} - 3 \, b^{5} c d^{2} e + 24 \, a b^{3} c^{2} d^{2} e - 48 \, a^{2} b c^{3} d^{2} e + b^{6} d e^{2} - 6 \, a b^{4} c d e^{2} + 32 \, a^{3} c^{3} d e^{2} - a b^{5} e^{3} + 8 \, a^{2} b^{3} c e^{3} - 16 \, a^{3} b c^{2} e^{3}\right)}^{2} - 4 \, {\left(b^{4} c^{2} d^{4} - 8 \, a b^{2} c^{3} d^{4} + 16 \, a^{2} c^{4} d^{4} - 2 \, b^{5} c d^{3} e + 16 \, a b^{3} c^{2} d^{3} e - 32 \, a^{2} b c^{3} d^{3} e + b^{6} d^{2} e^{2} - 6 \, a b^{4} c d^{2} e^{2} + 32 \, a^{3} c^{3} d^{2} e^{2} - 2 \, a b^{5} d e^{3} + 16 \, a^{2} b^{3} c d e^{3} - 32 \, a^{3} b c^{2} d e^{3} + a^{2} b^{4} e^{4} - 8 \, a^{3} b^{2} c e^{4} + 16 \, a^{4} c^{2} e^{4}\right)} {\left(b^{4} c^{2} d^{2} - 8 \, a b^{2} c^{3} d^{2} + 16 \, a^{2} c^{4} d^{2} - b^{5} c d e + 8 \, a b^{3} c^{2} d e - 16 \, a^{2} b c^{3} d e + a b^{4} c e^{2} - 8 \, a^{2} b^{2} c^{2} e^{2} + 16 \, a^{3} c^{3} e^{2}\right)}}}{b^{4} c^{2} d^{2} - 8 \, a b^{2} c^{3} d^{2} + 16 \, a^{2} c^{4} d^{2} - b^{5} c d e + 8 \, a b^{3} c^{2} d e - 16 \, a^{2} b c^{3} d e + a b^{4} c e^{2} - 8 \, a^{2} b^{2} c^{2} e^{2} + 16 \, a^{3} c^{3} e^{2}}}}\right)}{32 \, {\left({\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} \sqrt{b^{2} - 4 \, a c} d^{6} - 3 \, {\left(b^{7} c^{2} - 12 \, a b^{5} c^{3} + 48 \, a^{2} b^{3} c^{4} - 64 \, a^{3} b c^{5}\right)} \sqrt{b^{2} - 4 \, a c} d^{5} e + 3 \, {\left(b^{8} c - 11 \, a b^{6} c^{2} + 36 \, a^{2} b^{4} c^{3} - 16 \, a^{3} b^{2} c^{4} - 64 \, a^{4} c^{5}\right)} \sqrt{b^{2} - 4 \, a c} d^{4} e^{2} - {\left(b^{9} - 6 \, a b^{7} c - 24 \, a^{2} b^{5} c^{2} + 224 \, a^{3} b^{3} c^{3} - 384 \, a^{4} b c^{4}\right)} \sqrt{b^{2} - 4 \, a c} d^{3} e^{3} + 3 \, {\left(a b^{8} - 11 \, a^{2} b^{6} c + 36 \, a^{3} b^{4} c^{2} - 16 \, a^{4} b^{2} c^{3} - 64 \, a^{5} c^{4}\right)} \sqrt{b^{2} - 4 \, a c} d^{2} e^{4} - 3 \, {\left(a^{2} b^{7} - 12 \, a^{3} b^{5} c + 48 \, a^{4} b^{3} c^{2} - 64 \, a^{5} b c^{3}\right)} \sqrt{b^{2} - 4 \, a c} d e^{5} + {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}\right)} \sqrt{b^{2} - 4 \, a c} e^{6}\right)} {\left| b^{4} c d^{2} e - 8 \, a b^{2} c^{2} d^{2} e + 16 \, a^{2} c^{3} d^{2} e - b^{5} d e^{2} + 8 \, a b^{3} c d e^{2} - 16 \, a^{2} b c^{2} d e^{2} + a b^{4} e^{3} - 8 \, a^{2} b^{2} c e^{3} + 16 \, a^{3} c^{2} e^{3} \right|} {\left| c \right|}} + \frac{24 \, {\left(x e + d\right)}^{\frac{7}{2}} c^{4} d^{2} e - 72 \, {\left(x e + d\right)}^{\frac{5}{2}} c^{4} d^{3} e + 72 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{4} d^{4} e - 24 \, \sqrt{x e + d} c^{4} d^{5} e - 24 \, {\left(x e + d\right)}^{\frac{7}{2}} b c^{3} d e^{2} + 108 \, {\left(x e + d\right)}^{\frac{5}{2}} b c^{3} d^{2} e^{2} - 144 \, {\left(x e + d\right)}^{\frac{3}{2}} b c^{3} d^{3} e^{2} + 60 \, \sqrt{x e + d} b c^{3} d^{4} e^{2} + {\left(x e + d\right)}^{\frac{7}{2}} b^{2} c^{2} e^{3} + 20 \, {\left(x e + d\right)}^{\frac{7}{2}} a c^{3} e^{3} - 40 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{2} c^{2} d e^{3} - 56 \, {\left(x e + d\right)}^{\frac{5}{2}} a c^{3} d e^{3} + 85 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{2} c^{2} d^{2} e^{3} + 92 \, {\left(x e + d\right)}^{\frac{3}{2}} a c^{3} d^{2} e^{3} - 46 \, \sqrt{x e + d} b^{2} c^{2} d^{3} e^{3} - 56 \, \sqrt{x e + d} a c^{3} d^{3} e^{3} + 2 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{3} c e^{4} + 28 \, {\left(x e + d\right)}^{\frac{5}{2}} a b c^{2} e^{4} - 13 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{3} c d e^{4} - 92 \, {\left(x e + d\right)}^{\frac{3}{2}} a b c^{2} d e^{4} + 9 \, \sqrt{x e + d} b^{3} c d^{2} e^{4} + 84 \, \sqrt{x e + d} a b c^{2} d^{2} e^{4} + {\left(x e + d\right)}^{\frac{3}{2}} b^{4} e^{5} + 5 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{2} c e^{5} + 36 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} c^{2} e^{5} + \sqrt{x e + d} b^{4} d e^{5} - 26 \, \sqrt{x e + d} a b^{2} c d e^{5} - 32 \, \sqrt{x e + d} a^{2} c^{2} d e^{5} - \sqrt{x e + d} a b^{3} e^{6} + 16 \, \sqrt{x e + d} a^{2} b c e^{6}}{4 \, {\left(b^{4} c d^{2} - 8 \, a b^{2} c^{2} d^{2} + 16 \, a^{2} c^{3} d^{2} - b^{5} d e + 8 \, a b^{3} c d e - 16 \, a^{2} b c^{2} d e + a b^{4} e^{2} - 8 \, a^{2} b^{2} c e^{2} + 16 \, a^{3} c^{2} e^{2}\right)} {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + {\left(x e + d\right)} b e - b d e + a e^{2}\right)}^{2}}"," ",0,"1/32*((b^4*c*d^2*e - 8*a*b^2*c^2*d^2*e + 16*a^2*c^3*d^2*e - b^5*d*e^2 + 8*a*b^3*c*d*e^2 - 16*a^2*b*c^2*d*e^2 + a*b^4*e^3 - 8*a^2*b^2*c*e^3 + 16*a^3*c^2*e^3)^2*(24*c^2*d^2*e - 24*b*c*d*e^2 + (b^2 + 20*a*c)*e^3)*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e) + 2*(24*(b^2*c^4 - 4*a*c^5)*sqrt(b^2 - 4*a*c)*d^5*e - 60*(b^3*c^3 - 4*a*b*c^4)*sqrt(b^2 - 4*a*c)*d^4*e^2 + 2*(23*b^4*c^2 - 64*a*b^2*c^3 - 112*a^2*c^4)*sqrt(b^2 - 4*a*c)*d^3*e^3 - 3*(3*b^5*c + 16*a*b^3*c^2 - 112*a^2*b*c^3)*sqrt(b^2 - 4*a*c)*d^2*e^4 - (b^6 - 30*a*b^4*c + 72*a^2*b^2*c^2 + 128*a^3*c^3)*sqrt(b^2 - 4*a*c)*d*e^5 + (a*b^5 - 20*a^2*b^3*c + 64*a^3*b*c^2)*sqrt(b^2 - 4*a*c)*e^6)*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*abs(b^4*c*d^2*e - 8*a*b^2*c^2*d^2*e + 16*a^2*c^3*d^2*e - b^5*d*e^2 + 8*a*b^3*c*d*e^2 - 16*a^2*b*c^2*d*e^2 + a*b^4*e^3 - 8*a^2*b^2*c*e^3 + 16*a^3*c^2*e^3) - (192*(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)*d^8*e - 768*(b^7*c^5 - 12*a*b^5*c^6 + 48*a^2*b^3*c^7 - 64*a^3*b*c^8)*d^7*e^2 + 4*(299*b^8*c^4 - 3440*a*b^6*c^5 + 12576*a^2*b^4*c^6 - 12032*a^3*b^2*c^7 - 9472*a^4*c^8)*d^6*e^3 - 12*(75*b^9*c^3 - 752*a*b^7*c^4 + 1824*a^2*b^5*c^5 + 2304*a^3*b^3*c^6 - 9472*a^4*b*c^7)*d^5*e^4 + (323*b^10*c^2 - 1960*a*b^8*c^3 - 6880*a^2*b^6*c^4 + 64000*a^3*b^4*c^5 - 93440*a^4*b^2*c^6 - 38912*a^5*c^7)*d^4*e^5 - 2*(21*b^11*c + 184*a*b^9*c^2 - 3616*a^2*b^7*c^3 + 12288*a^3*b^5*c^4 + 1280*a^4*b^3*c^5 - 38912*a^5*b*c^6)*d^3*e^6 - (b^12 - 150*a*b^10*c + 948*a^2*b^8*c^2 + 2176*a^3*b^6*c^3 - 24960*a^4*b^4*c^4 + 38400*a^5*b^2*c^5 + 13312*a^6*c^6)*d^2*e^7 + 2*(a*b^11 - 86*a^2*b^9*c + 832*a^3*b^7*c^2 - 2368*a^4*b^5*c^3 - 256*a^5*b^3*c^4 + 6656*a^6*b*c^5)*d*e^8 - (a^2*b^10 - 64*a^3*b^8*c + 672*a^4*b^6*c^2 - 2560*a^5*b^4*c^3 + 3328*a^6*b^2*c^4)*e^9)*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e))*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*b^4*c^2*d^3 - 16*a*b^2*c^3*d^3 + 32*a^2*c^4*d^3 - 3*b^5*c*d^2*e + 24*a*b^3*c^2*d^2*e - 48*a^2*b*c^3*d^2*e + b^6*d*e^2 - 6*a*b^4*c*d*e^2 + 32*a^3*c^3*d*e^2 - a*b^5*e^3 + 8*a^2*b^3*c*e^3 - 16*a^3*b*c^2*e^3 + sqrt((2*b^4*c^2*d^3 - 16*a*b^2*c^3*d^3 + 32*a^2*c^4*d^3 - 3*b^5*c*d^2*e + 24*a*b^3*c^2*d^2*e - 48*a^2*b*c^3*d^2*e + b^6*d*e^2 - 6*a*b^4*c*d*e^2 + 32*a^3*c^3*d*e^2 - a*b^5*e^3 + 8*a^2*b^3*c*e^3 - 16*a^3*b*c^2*e^3)^2 - 4*(b^4*c^2*d^4 - 8*a*b^2*c^3*d^4 + 16*a^2*c^4*d^4 - 2*b^5*c*d^3*e + 16*a*b^3*c^2*d^3*e - 32*a^2*b*c^3*d^3*e + b^6*d^2*e^2 - 6*a*b^4*c*d^2*e^2 + 32*a^3*c^3*d^2*e^2 - 2*a*b^5*d*e^3 + 16*a^2*b^3*c*d*e^3 - 32*a^3*b*c^2*d*e^3 + a^2*b^4*e^4 - 8*a^3*b^2*c*e^4 + 16*a^4*c^2*e^4)*(b^4*c^2*d^2 - 8*a*b^2*c^3*d^2 + 16*a^2*c^4*d^2 - b^5*c*d*e + 8*a*b^3*c^2*d*e - 16*a^2*b*c^3*d*e + a*b^4*c*e^2 - 8*a^2*b^2*c^2*e^2 + 16*a^3*c^3*e^2)))/(b^4*c^2*d^2 - 8*a*b^2*c^3*d^2 + 16*a^2*c^4*d^2 - b^5*c*d*e + 8*a*b^3*c^2*d*e - 16*a^2*b*c^3*d*e + a*b^4*c*e^2 - 8*a^2*b^2*c^2*e^2 + 16*a^3*c^3*e^2)))/(((b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*sqrt(b^2 - 4*a*c)*d^6 - 3*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*sqrt(b^2 - 4*a*c)*d^5*e + 3*(b^8*c - 11*a*b^6*c^2 + 36*a^2*b^4*c^3 - 16*a^3*b^2*c^4 - 64*a^4*c^5)*sqrt(b^2 - 4*a*c)*d^4*e^2 - (b^9 - 6*a*b^7*c - 24*a^2*b^5*c^2 + 224*a^3*b^3*c^3 - 384*a^4*b*c^4)*sqrt(b^2 - 4*a*c)*d^3*e^3 + 3*(a*b^8 - 11*a^2*b^6*c + 36*a^3*b^4*c^2 - 16*a^4*b^2*c^3 - 64*a^5*c^4)*sqrt(b^2 - 4*a*c)*d^2*e^4 - 3*(a^2*b^7 - 12*a^3*b^5*c + 48*a^4*b^3*c^2 - 64*a^5*b*c^3)*sqrt(b^2 - 4*a*c)*d*e^5 + (a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)*sqrt(b^2 - 4*a*c)*e^6)*abs(b^4*c*d^2*e - 8*a*b^2*c^2*d^2*e + 16*a^2*c^3*d^2*e - b^5*d*e^2 + 8*a*b^3*c*d*e^2 - 16*a^2*b*c^2*d*e^2 + a*b^4*e^3 - 8*a^2*b^2*c*e^3 + 16*a^3*c^2*e^3)*abs(c)) - 1/32*((b^4*c*d^2*e - 8*a*b^2*c^2*d^2*e + 16*a^2*c^3*d^2*e - b^5*d*e^2 + 8*a*b^3*c*d*e^2 - 16*a^2*b*c^2*d*e^2 + a*b^4*e^3 - 8*a^2*b^2*c*e^3 + 16*a^3*c^2*e^3)^2*(24*c^2*d^2*e - 24*b*c*d*e^2 + (b^2 + 20*a*c)*e^3)*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e) - 2*(24*(b^2*c^4 - 4*a*c^5)*sqrt(b^2 - 4*a*c)*d^5*e - 60*(b^3*c^3 - 4*a*b*c^4)*sqrt(b^2 - 4*a*c)*d^4*e^2 + 2*(23*b^4*c^2 - 64*a*b^2*c^3 - 112*a^2*c^4)*sqrt(b^2 - 4*a*c)*d^3*e^3 - 3*(3*b^5*c + 16*a*b^3*c^2 - 112*a^2*b*c^3)*sqrt(b^2 - 4*a*c)*d^2*e^4 - (b^6 - 30*a*b^4*c + 72*a^2*b^2*c^2 + 128*a^3*c^3)*sqrt(b^2 - 4*a*c)*d*e^5 + (a*b^5 - 20*a^2*b^3*c + 64*a^3*b*c^2)*sqrt(b^2 - 4*a*c)*e^6)*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*abs(b^4*c*d^2*e - 8*a*b^2*c^2*d^2*e + 16*a^2*c^3*d^2*e - b^5*d*e^2 + 8*a*b^3*c*d*e^2 - 16*a^2*b*c^2*d*e^2 + a*b^4*e^3 - 8*a^2*b^2*c*e^3 + 16*a^3*c^2*e^3) - (192*(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)*d^8*e - 768*(b^7*c^5 - 12*a*b^5*c^6 + 48*a^2*b^3*c^7 - 64*a^3*b*c^8)*d^7*e^2 + 4*(299*b^8*c^4 - 3440*a*b^6*c^5 + 12576*a^2*b^4*c^6 - 12032*a^3*b^2*c^7 - 9472*a^4*c^8)*d^6*e^3 - 12*(75*b^9*c^3 - 752*a*b^7*c^4 + 1824*a^2*b^5*c^5 + 2304*a^3*b^3*c^6 - 9472*a^4*b*c^7)*d^5*e^4 + (323*b^10*c^2 - 1960*a*b^8*c^3 - 6880*a^2*b^6*c^4 + 64000*a^3*b^4*c^5 - 93440*a^4*b^2*c^6 - 38912*a^5*c^7)*d^4*e^5 - 2*(21*b^11*c + 184*a*b^9*c^2 - 3616*a^2*b^7*c^3 + 12288*a^3*b^5*c^4 + 1280*a^4*b^3*c^5 - 38912*a^5*b*c^6)*d^3*e^6 - (b^12 - 150*a*b^10*c + 948*a^2*b^8*c^2 + 2176*a^3*b^6*c^3 - 24960*a^4*b^4*c^4 + 38400*a^5*b^2*c^5 + 13312*a^6*c^6)*d^2*e^7 + 2*(a*b^11 - 86*a^2*b^9*c + 832*a^3*b^7*c^2 - 2368*a^4*b^5*c^3 - 256*a^5*b^3*c^4 + 6656*a^6*b*c^5)*d*e^8 - (a^2*b^10 - 64*a^3*b^8*c + 672*a^4*b^6*c^2 - 2560*a^5*b^4*c^3 + 3328*a^6*b^2*c^4)*e^9)*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e))*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*b^4*c^2*d^3 - 16*a*b^2*c^3*d^3 + 32*a^2*c^4*d^3 - 3*b^5*c*d^2*e + 24*a*b^3*c^2*d^2*e - 48*a^2*b*c^3*d^2*e + b^6*d*e^2 - 6*a*b^4*c*d*e^2 + 32*a^3*c^3*d*e^2 - a*b^5*e^3 + 8*a^2*b^3*c*e^3 - 16*a^3*b*c^2*e^3 - sqrt((2*b^4*c^2*d^3 - 16*a*b^2*c^3*d^3 + 32*a^2*c^4*d^3 - 3*b^5*c*d^2*e + 24*a*b^3*c^2*d^2*e - 48*a^2*b*c^3*d^2*e + b^6*d*e^2 - 6*a*b^4*c*d*e^2 + 32*a^3*c^3*d*e^2 - a*b^5*e^3 + 8*a^2*b^3*c*e^3 - 16*a^3*b*c^2*e^3)^2 - 4*(b^4*c^2*d^4 - 8*a*b^2*c^3*d^4 + 16*a^2*c^4*d^4 - 2*b^5*c*d^3*e + 16*a*b^3*c^2*d^3*e - 32*a^2*b*c^3*d^3*e + b^6*d^2*e^2 - 6*a*b^4*c*d^2*e^2 + 32*a^3*c^3*d^2*e^2 - 2*a*b^5*d*e^3 + 16*a^2*b^3*c*d*e^3 - 32*a^3*b*c^2*d*e^3 + a^2*b^4*e^4 - 8*a^3*b^2*c*e^4 + 16*a^4*c^2*e^4)*(b^4*c^2*d^2 - 8*a*b^2*c^3*d^2 + 16*a^2*c^4*d^2 - b^5*c*d*e + 8*a*b^3*c^2*d*e - 16*a^2*b*c^3*d*e + a*b^4*c*e^2 - 8*a^2*b^2*c^2*e^2 + 16*a^3*c^3*e^2)))/(b^4*c^2*d^2 - 8*a*b^2*c^3*d^2 + 16*a^2*c^4*d^2 - b^5*c*d*e + 8*a*b^3*c^2*d*e - 16*a^2*b*c^3*d*e + a*b^4*c*e^2 - 8*a^2*b^2*c^2*e^2 + 16*a^3*c^3*e^2)))/(((b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*sqrt(b^2 - 4*a*c)*d^6 - 3*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*sqrt(b^2 - 4*a*c)*d^5*e + 3*(b^8*c - 11*a*b^6*c^2 + 36*a^2*b^4*c^3 - 16*a^3*b^2*c^4 - 64*a^4*c^5)*sqrt(b^2 - 4*a*c)*d^4*e^2 - (b^9 - 6*a*b^7*c - 24*a^2*b^5*c^2 + 224*a^3*b^3*c^3 - 384*a^4*b*c^4)*sqrt(b^2 - 4*a*c)*d^3*e^3 + 3*(a*b^8 - 11*a^2*b^6*c + 36*a^3*b^4*c^2 - 16*a^4*b^2*c^3 - 64*a^5*c^4)*sqrt(b^2 - 4*a*c)*d^2*e^4 - 3*(a^2*b^7 - 12*a^3*b^5*c + 48*a^4*b^3*c^2 - 64*a^5*b*c^3)*sqrt(b^2 - 4*a*c)*d*e^5 + (a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)*sqrt(b^2 - 4*a*c)*e^6)*abs(b^4*c*d^2*e - 8*a*b^2*c^2*d^2*e + 16*a^2*c^3*d^2*e - b^5*d*e^2 + 8*a*b^3*c*d*e^2 - 16*a^2*b*c^2*d*e^2 + a*b^4*e^3 - 8*a^2*b^2*c*e^3 + 16*a^3*c^2*e^3)*abs(c)) + 1/4*(24*(x*e + d)^(7/2)*c^4*d^2*e - 72*(x*e + d)^(5/2)*c^4*d^3*e + 72*(x*e + d)^(3/2)*c^4*d^4*e - 24*sqrt(x*e + d)*c^4*d^5*e - 24*(x*e + d)^(7/2)*b*c^3*d*e^2 + 108*(x*e + d)^(5/2)*b*c^3*d^2*e^2 - 144*(x*e + d)^(3/2)*b*c^3*d^3*e^2 + 60*sqrt(x*e + d)*b*c^3*d^4*e^2 + (x*e + d)^(7/2)*b^2*c^2*e^3 + 20*(x*e + d)^(7/2)*a*c^3*e^3 - 40*(x*e + d)^(5/2)*b^2*c^2*d*e^3 - 56*(x*e + d)^(5/2)*a*c^3*d*e^3 + 85*(x*e + d)^(3/2)*b^2*c^2*d^2*e^3 + 92*(x*e + d)^(3/2)*a*c^3*d^2*e^3 - 46*sqrt(x*e + d)*b^2*c^2*d^3*e^3 - 56*sqrt(x*e + d)*a*c^3*d^3*e^3 + 2*(x*e + d)^(5/2)*b^3*c*e^4 + 28*(x*e + d)^(5/2)*a*b*c^2*e^4 - 13*(x*e + d)^(3/2)*b^3*c*d*e^4 - 92*(x*e + d)^(3/2)*a*b*c^2*d*e^4 + 9*sqrt(x*e + d)*b^3*c*d^2*e^4 + 84*sqrt(x*e + d)*a*b*c^2*d^2*e^4 + (x*e + d)^(3/2)*b^4*e^5 + 5*(x*e + d)^(3/2)*a*b^2*c*e^5 + 36*(x*e + d)^(3/2)*a^2*c^2*e^5 + sqrt(x*e + d)*b^4*d*e^5 - 26*sqrt(x*e + d)*a*b^2*c*d*e^5 - 32*sqrt(x*e + d)*a^2*c^2*d*e^5 - sqrt(x*e + d)*a*b^3*e^6 + 16*sqrt(x*e + d)*a^2*b*c*e^6)/((b^4*c*d^2 - 8*a*b^2*c^2*d^2 + 16*a^2*c^3*d^2 - b^5*d*e + 8*a*b^3*c*d*e - 16*a^2*b*c^2*d*e + a*b^4*e^2 - 8*a^2*b^2*c*e^2 + 16*a^3*c^2*e^2)*((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + (x*e + d)*b*e - b*d*e + a*e^2)^2)","B",0
2306,1,4233,0,24.893891," ","integrate(1/(e*x+d)^(1/2)/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","-\frac{3 \, {\left(16 \, c^{5} d^{2} - 4 \, {\left(4 \, b c^{4} - 5 \, \sqrt{b^{2} - 4 \, a c} c^{4}\right)} d e + {\left(11 \, b^{2} c^{3} - 28 \, a c^{4} - 10 \, \sqrt{b^{2} - 4 \, a c} b c^{3}\right)} e^{2}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c - \sqrt{b^{2} - 4 \, a c} c\right)} e} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, b^{4} c^{3} d^{5} - 16 \, a b^{2} c^{4} d^{5} + 32 \, a^{2} c^{5} d^{5} - 5 \, b^{5} c^{2} d^{4} e + 40 \, a b^{3} c^{3} d^{4} e - 80 \, a^{2} b c^{4} d^{4} e + 4 \, b^{6} c d^{3} e^{2} - 28 \, a b^{4} c^{2} d^{3} e^{2} + 32 \, a^{2} b^{2} c^{3} d^{3} e^{2} + 64 \, a^{3} c^{4} d^{3} e^{2} - b^{7} d^{2} e^{3} + 2 \, a b^{5} c d^{2} e^{3} + 32 \, a^{2} b^{3} c^{2} d^{2} e^{3} - 96 \, a^{3} b c^{3} d^{2} e^{3} + 2 \, a b^{6} d e^{4} - 14 \, a^{2} b^{4} c d e^{4} + 16 \, a^{3} b^{2} c^{2} d e^{4} + 32 \, a^{4} c^{3} d e^{4} - a^{2} b^{5} e^{5} + 8 \, a^{3} b^{3} c e^{5} - 16 \, a^{4} b c^{2} e^{5} + \sqrt{{\left(2 \, b^{4} c^{3} d^{5} - 16 \, a b^{2} c^{4} d^{5} + 32 \, a^{2} c^{5} d^{5} - 5 \, b^{5} c^{2} d^{4} e + 40 \, a b^{3} c^{3} d^{4} e - 80 \, a^{2} b c^{4} d^{4} e + 4 \, b^{6} c d^{3} e^{2} - 28 \, a b^{4} c^{2} d^{3} e^{2} + 32 \, a^{2} b^{2} c^{3} d^{3} e^{2} + 64 \, a^{3} c^{4} d^{3} e^{2} - b^{7} d^{2} e^{3} + 2 \, a b^{5} c d^{2} e^{3} + 32 \, a^{2} b^{3} c^{2} d^{2} e^{3} - 96 \, a^{3} b c^{3} d^{2} e^{3} + 2 \, a b^{6} d e^{4} - 14 \, a^{2} b^{4} c d e^{4} + 16 \, a^{3} b^{2} c^{2} d e^{4} + 32 \, a^{4} c^{3} d e^{4} - a^{2} b^{5} e^{5} + 8 \, a^{3} b^{3} c e^{5} - 16 \, a^{4} b c^{2} e^{5}\right)}^{2} - 4 \, {\left(b^{4} c^{3} d^{6} - 8 \, a b^{2} c^{4} d^{6} + 16 \, a^{2} c^{5} d^{6} - 3 \, b^{5} c^{2} d^{5} e + 24 \, a b^{3} c^{3} d^{5} e - 48 \, a^{2} b c^{4} d^{5} e + 3 \, b^{6} c d^{4} e^{2} - 21 \, a b^{4} c^{2} d^{4} e^{2} + 24 \, a^{2} b^{2} c^{3} d^{4} e^{2} + 48 \, a^{3} c^{4} d^{4} e^{2} - b^{7} d^{3} e^{3} + 2 \, a b^{5} c d^{3} e^{3} + 32 \, a^{2} b^{3} c^{2} d^{3} e^{3} - 96 \, a^{3} b c^{3} d^{3} e^{3} + 3 \, a b^{6} d^{2} e^{4} - 21 \, a^{2} b^{4} c d^{2} e^{4} + 24 \, a^{3} b^{2} c^{2} d^{2} e^{4} + 48 \, a^{4} c^{3} d^{2} e^{4} - 3 \, a^{2} b^{5} d e^{5} + 24 \, a^{3} b^{3} c d e^{5} - 48 \, a^{4} b c^{2} d e^{5} + a^{3} b^{4} e^{6} - 8 \, a^{4} b^{2} c e^{6} + 16 \, a^{5} c^{2} e^{6}\right)} {\left(b^{4} c^{3} d^{4} - 8 \, a b^{2} c^{4} d^{4} + 16 \, a^{2} c^{5} d^{4} - 2 \, b^{5} c^{2} d^{3} e + 16 \, a b^{3} c^{3} d^{3} e - 32 \, a^{2} b c^{4} d^{3} e + b^{6} c d^{2} e^{2} - 6 \, a b^{4} c^{2} d^{2} e^{2} + 32 \, a^{3} c^{4} d^{2} e^{2} - 2 \, a b^{5} c d e^{3} + 16 \, a^{2} b^{3} c^{2} d e^{3} - 32 \, a^{3} b c^{3} d e^{3} + a^{2} b^{4} c e^{4} - 8 \, a^{3} b^{2} c^{2} e^{4} + 16 \, a^{4} c^{3} e^{4}\right)}}}{b^{4} c^{3} d^{4} - 8 \, a b^{2} c^{4} d^{4} + 16 \, a^{2} c^{5} d^{4} - 2 \, b^{5} c^{2} d^{3} e + 16 \, a b^{3} c^{3} d^{3} e - 32 \, a^{2} b c^{4} d^{3} e + b^{6} c d^{2} e^{2} - 6 \, a b^{4} c^{2} d^{2} e^{2} + 32 \, a^{3} c^{4} d^{2} e^{2} - 2 \, a b^{5} c d e^{3} + 16 \, a^{2} b^{3} c^{2} d e^{3} - 32 \, a^{3} b c^{3} d e^{3} + a^{2} b^{4} c e^{4} - 8 \, a^{3} b^{2} c^{2} e^{4} + 16 \, a^{4} c^{3} e^{4}}}}\right)}{4 \, {\left(2 \, {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} \sqrt{b^{2} - 4 \, a c} d^{3} + 3 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5} - {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} \sqrt{b^{2} - 4 \, a c}\right)} d^{2} e - 3 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4} - {\left(b^{6} c - 10 \, a b^{4} c^{2} + 32 \, a^{2} b^{2} c^{3} - 32 \, a^{3} c^{4}\right)} \sqrt{b^{2} - 4 \, a c}\right)} d e^{2} + {\left(b^{8} - 13 \, a b^{6} c + 60 \, a^{2} b^{4} c^{2} - 112 \, a^{3} b^{2} c^{3} + 64 \, a^{4} c^{4} - {\left(b^{7} - 11 \, a b^{5} c + 40 \, a^{2} b^{3} c^{2} - 48 \, a^{3} b c^{3}\right)} \sqrt{b^{2} - 4 \, a c}\right)} e^{3}\right)} {\left| c \right|}} + \frac{3 \, {\left(16 \, c^{5} d^{2} - 4 \, {\left(4 \, b c^{4} + 5 \, \sqrt{b^{2} - 4 \, a c} c^{4}\right)} d e + {\left(11 \, b^{2} c^{3} - 28 \, a c^{4} + 10 \, \sqrt{b^{2} - 4 \, a c} b c^{3}\right)} e^{2}\right)} \sqrt{-4 \, c^{2} d + 2 \, {\left(b c + \sqrt{b^{2} - 4 \, a c} c\right)} e} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x e + d}}{\sqrt{-\frac{2 \, b^{4} c^{3} d^{5} - 16 \, a b^{2} c^{4} d^{5} + 32 \, a^{2} c^{5} d^{5} - 5 \, b^{5} c^{2} d^{4} e + 40 \, a b^{3} c^{3} d^{4} e - 80 \, a^{2} b c^{4} d^{4} e + 4 \, b^{6} c d^{3} e^{2} - 28 \, a b^{4} c^{2} d^{3} e^{2} + 32 \, a^{2} b^{2} c^{3} d^{3} e^{2} + 64 \, a^{3} c^{4} d^{3} e^{2} - b^{7} d^{2} e^{3} + 2 \, a b^{5} c d^{2} e^{3} + 32 \, a^{2} b^{3} c^{2} d^{2} e^{3} - 96 \, a^{3} b c^{3} d^{2} e^{3} + 2 \, a b^{6} d e^{4} - 14 \, a^{2} b^{4} c d e^{4} + 16 \, a^{3} b^{2} c^{2} d e^{4} + 32 \, a^{4} c^{3} d e^{4} - a^{2} b^{5} e^{5} + 8 \, a^{3} b^{3} c e^{5} - 16 \, a^{4} b c^{2} e^{5} - \sqrt{{\left(2 \, b^{4} c^{3} d^{5} - 16 \, a b^{2} c^{4} d^{5} + 32 \, a^{2} c^{5} d^{5} - 5 \, b^{5} c^{2} d^{4} e + 40 \, a b^{3} c^{3} d^{4} e - 80 \, a^{2} b c^{4} d^{4} e + 4 \, b^{6} c d^{3} e^{2} - 28 \, a b^{4} c^{2} d^{3} e^{2} + 32 \, a^{2} b^{2} c^{3} d^{3} e^{2} + 64 \, a^{3} c^{4} d^{3} e^{2} - b^{7} d^{2} e^{3} + 2 \, a b^{5} c d^{2} e^{3} + 32 \, a^{2} b^{3} c^{2} d^{2} e^{3} - 96 \, a^{3} b c^{3} d^{2} e^{3} + 2 \, a b^{6} d e^{4} - 14 \, a^{2} b^{4} c d e^{4} + 16 \, a^{3} b^{2} c^{2} d e^{4} + 32 \, a^{4} c^{3} d e^{4} - a^{2} b^{5} e^{5} + 8 \, a^{3} b^{3} c e^{5} - 16 \, a^{4} b c^{2} e^{5}\right)}^{2} - 4 \, {\left(b^{4} c^{3} d^{6} - 8 \, a b^{2} c^{4} d^{6} + 16 \, a^{2} c^{5} d^{6} - 3 \, b^{5} c^{2} d^{5} e + 24 \, a b^{3} c^{3} d^{5} e - 48 \, a^{2} b c^{4} d^{5} e + 3 \, b^{6} c d^{4} e^{2} - 21 \, a b^{4} c^{2} d^{4} e^{2} + 24 \, a^{2} b^{2} c^{3} d^{4} e^{2} + 48 \, a^{3} c^{4} d^{4} e^{2} - b^{7} d^{3} e^{3} + 2 \, a b^{5} c d^{3} e^{3} + 32 \, a^{2} b^{3} c^{2} d^{3} e^{3} - 96 \, a^{3} b c^{3} d^{3} e^{3} + 3 \, a b^{6} d^{2} e^{4} - 21 \, a^{2} b^{4} c d^{2} e^{4} + 24 \, a^{3} b^{2} c^{2} d^{2} e^{4} + 48 \, a^{4} c^{3} d^{2} e^{4} - 3 \, a^{2} b^{5} d e^{5} + 24 \, a^{3} b^{3} c d e^{5} - 48 \, a^{4} b c^{2} d e^{5} + a^{3} b^{4} e^{6} - 8 \, a^{4} b^{2} c e^{6} + 16 \, a^{5} c^{2} e^{6}\right)} {\left(b^{4} c^{3} d^{4} - 8 \, a b^{2} c^{4} d^{4} + 16 \, a^{2} c^{5} d^{4} - 2 \, b^{5} c^{2} d^{3} e + 16 \, a b^{3} c^{3} d^{3} e - 32 \, a^{2} b c^{4} d^{3} e + b^{6} c d^{2} e^{2} - 6 \, a b^{4} c^{2} d^{2} e^{2} + 32 \, a^{3} c^{4} d^{2} e^{2} - 2 \, a b^{5} c d e^{3} + 16 \, a^{2} b^{3} c^{2} d e^{3} - 32 \, a^{3} b c^{3} d e^{3} + a^{2} b^{4} c e^{4} - 8 \, a^{3} b^{2} c^{2} e^{4} + 16 \, a^{4} c^{3} e^{4}\right)}}}{b^{4} c^{3} d^{4} - 8 \, a b^{2} c^{4} d^{4} + 16 \, a^{2} c^{5} d^{4} - 2 \, b^{5} c^{2} d^{3} e + 16 \, a b^{3} c^{3} d^{3} e - 32 \, a^{2} b c^{4} d^{3} e + b^{6} c d^{2} e^{2} - 6 \, a b^{4} c^{2} d^{2} e^{2} + 32 \, a^{3} c^{4} d^{2} e^{2} - 2 \, a b^{5} c d e^{3} + 16 \, a^{2} b^{3} c^{2} d e^{3} - 32 \, a^{3} b c^{3} d e^{3} + a^{2} b^{4} c e^{4} - 8 \, a^{3} b^{2} c^{2} e^{4} + 16 \, a^{4} c^{3} e^{4}}}}\right)}{4 \, {\left(2 \, {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} \sqrt{b^{2} - 4 \, a c} d^{3} - 3 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5} + {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} \sqrt{b^{2} - 4 \, a c}\right)} d^{2} e + 3 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4} + {\left(b^{6} c - 10 \, a b^{4} c^{2} + 32 \, a^{2} b^{2} c^{3} - 32 \, a^{3} c^{4}\right)} \sqrt{b^{2} - 4 \, a c}\right)} d e^{2} - {\left(b^{8} - 13 \, a b^{6} c + 60 \, a^{2} b^{4} c^{2} - 112 \, a^{3} b^{2} c^{3} + 64 \, a^{4} c^{4} + {\left(b^{7} - 11 \, a b^{5} c + 40 \, a^{2} b^{3} c^{2} - 48 \, a^{3} b c^{3}\right)} \sqrt{b^{2} - 4 \, a c}\right)} e^{3}\right)} {\left| c \right|}} + \frac{24 \, {\left(x e + d\right)}^{\frac{7}{2}} c^{5} d^{3} e - 72 \, {\left(x e + d\right)}^{\frac{5}{2}} c^{5} d^{4} e + 72 \, {\left(x e + d\right)}^{\frac{3}{2}} c^{5} d^{5} e - 24 \, \sqrt{x e + d} c^{5} d^{6} e - 36 \, {\left(x e + d\right)}^{\frac{7}{2}} b c^{4} d^{2} e^{2} + 144 \, {\left(x e + d\right)}^{\frac{5}{2}} b c^{4} d^{3} e^{2} - 180 \, {\left(x e + d\right)}^{\frac{3}{2}} b c^{4} d^{4} e^{2} + 72 \, \sqrt{x e + d} b c^{4} d^{5} e^{2} + 6 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{2} c^{3} d e^{3} + 48 \, {\left(x e + d\right)}^{\frac{7}{2}} a c^{4} d e^{3} - 73 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{2} c^{3} d^{2} e^{3} - 140 \, {\left(x e + d\right)}^{\frac{5}{2}} a c^{4} d^{2} e^{3} + 136 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{2} c^{3} d^{3} e^{3} + 176 \, {\left(x e + d\right)}^{\frac{3}{2}} a c^{4} d^{3} e^{3} - 69 \, \sqrt{x e + d} b^{2} c^{3} d^{4} e^{3} - 84 \, \sqrt{x e + d} a c^{4} d^{4} e^{3} + 3 \, {\left(x e + d\right)}^{\frac{7}{2}} b^{3} c^{2} e^{4} - 24 \, {\left(x e + d\right)}^{\frac{7}{2}} a b c^{3} e^{4} + {\left(x e + d\right)}^{\frac{5}{2}} b^{3} c^{2} d e^{4} + 140 \, {\left(x e + d\right)}^{\frac{5}{2}} a b c^{3} d e^{4} - 24 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{3} c^{2} d^{2} e^{4} - 264 \, {\left(x e + d\right)}^{\frac{3}{2}} a b c^{3} d^{2} e^{4} + 18 \, \sqrt{x e + d} b^{3} c^{2} d^{3} e^{4} + 168 \, \sqrt{x e + d} a b c^{3} d^{3} e^{4} + 6 \, {\left(x e + d\right)}^{\frac{5}{2}} b^{4} c e^{5} - 49 \, {\left(x e + d\right)}^{\frac{5}{2}} a b^{2} c^{2} e^{5} + 28 \, {\left(x e + d\right)}^{\frac{5}{2}} a^{2} c^{3} e^{5} - 10 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{4} c d e^{5} + 128 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{2} c^{2} d e^{5} + 8 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} c^{3} d e^{5} + 8 \, \sqrt{x e + d} b^{4} c d^{2} e^{5} - 118 \, \sqrt{x e + d} a b^{2} c^{2} d^{2} e^{5} - 16 \, \sqrt{x e + d} a^{2} c^{3} d^{2} e^{5} + 3 \, {\left(x e + d\right)}^{\frac{3}{2}} b^{5} e^{6} - 20 \, {\left(x e + d\right)}^{\frac{3}{2}} a b^{3} c e^{6} - 4 \, {\left(x e + d\right)}^{\frac{3}{2}} a^{2} b c^{2} e^{6} - 5 \, \sqrt{x e + d} b^{5} d e^{6} + 34 \, \sqrt{x e + d} a b^{3} c d e^{6} + 16 \, \sqrt{x e + d} a^{2} b c^{2} d e^{6} + 5 \, \sqrt{x e + d} a b^{4} e^{7} - 37 \, \sqrt{x e + d} a^{2} b^{2} c e^{7} + 44 \, \sqrt{x e + d} a^{3} c^{2} e^{7}}{4 \, {\left(b^{4} c^{2} d^{4} - 8 \, a b^{2} c^{3} d^{4} + 16 \, a^{2} c^{4} d^{4} - 2 \, b^{5} c d^{3} e + 16 \, a b^{3} c^{2} d^{3} e - 32 \, a^{2} b c^{3} d^{3} e + b^{6} d^{2} e^{2} - 6 \, a b^{4} c d^{2} e^{2} + 32 \, a^{3} c^{3} d^{2} e^{2} - 2 \, a b^{5} d e^{3} + 16 \, a^{2} b^{3} c d e^{3} - 32 \, a^{3} b c^{2} d e^{3} + a^{2} b^{4} e^{4} - 8 \, a^{3} b^{2} c e^{4} + 16 \, a^{4} c^{2} e^{4}\right)} {\left({\left(x e + d\right)}^{2} c - 2 \, {\left(x e + d\right)} c d + c d^{2} + {\left(x e + d\right)} b e - b d e + a e^{2}\right)}^{2}}"," ",0,"-3/4*(16*c^5*d^2 - 4*(4*b*c^4 - 5*sqrt(b^2 - 4*a*c)*c^4)*d*e + (11*b^2*c^3 - 28*a*c^4 - 10*sqrt(b^2 - 4*a*c)*b*c^3)*e^2)*sqrt(-4*c^2*d + 2*(b*c - sqrt(b^2 - 4*a*c)*c)*e)*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*b^4*c^3*d^5 - 16*a*b^2*c^4*d^5 + 32*a^2*c^5*d^5 - 5*b^5*c^2*d^4*e + 40*a*b^3*c^3*d^4*e - 80*a^2*b*c^4*d^4*e + 4*b^6*c*d^3*e^2 - 28*a*b^4*c^2*d^3*e^2 + 32*a^2*b^2*c^3*d^3*e^2 + 64*a^3*c^4*d^3*e^2 - b^7*d^2*e^3 + 2*a*b^5*c*d^2*e^3 + 32*a^2*b^3*c^2*d^2*e^3 - 96*a^3*b*c^3*d^2*e^3 + 2*a*b^6*d*e^4 - 14*a^2*b^4*c*d*e^4 + 16*a^3*b^2*c^2*d*e^4 + 32*a^4*c^3*d*e^4 - a^2*b^5*e^5 + 8*a^3*b^3*c*e^5 - 16*a^4*b*c^2*e^5 + sqrt((2*b^4*c^3*d^5 - 16*a*b^2*c^4*d^5 + 32*a^2*c^5*d^5 - 5*b^5*c^2*d^4*e + 40*a*b^3*c^3*d^4*e - 80*a^2*b*c^4*d^4*e + 4*b^6*c*d^3*e^2 - 28*a*b^4*c^2*d^3*e^2 + 32*a^2*b^2*c^3*d^3*e^2 + 64*a^3*c^4*d^3*e^2 - b^7*d^2*e^3 + 2*a*b^5*c*d^2*e^3 + 32*a^2*b^3*c^2*d^2*e^3 - 96*a^3*b*c^3*d^2*e^3 + 2*a*b^6*d*e^4 - 14*a^2*b^4*c*d*e^4 + 16*a^3*b^2*c^2*d*e^4 + 32*a^4*c^3*d*e^4 - a^2*b^5*e^5 + 8*a^3*b^3*c*e^5 - 16*a^4*b*c^2*e^5)^2 - 4*(b^4*c^3*d^6 - 8*a*b^2*c^4*d^6 + 16*a^2*c^5*d^6 - 3*b^5*c^2*d^5*e + 24*a*b^3*c^3*d^5*e - 48*a^2*b*c^4*d^5*e + 3*b^6*c*d^4*e^2 - 21*a*b^4*c^2*d^4*e^2 + 24*a^2*b^2*c^3*d^4*e^2 + 48*a^3*c^4*d^4*e^2 - b^7*d^3*e^3 + 2*a*b^5*c*d^3*e^3 + 32*a^2*b^3*c^2*d^3*e^3 - 96*a^3*b*c^3*d^3*e^3 + 3*a*b^6*d^2*e^4 - 21*a^2*b^4*c*d^2*e^4 + 24*a^3*b^2*c^2*d^2*e^4 + 48*a^4*c^3*d^2*e^4 - 3*a^2*b^5*d*e^5 + 24*a^3*b^3*c*d*e^5 - 48*a^4*b*c^2*d*e^5 + a^3*b^4*e^6 - 8*a^4*b^2*c*e^6 + 16*a^5*c^2*e^6)*(b^4*c^3*d^4 - 8*a*b^2*c^4*d^4 + 16*a^2*c^5*d^4 - 2*b^5*c^2*d^3*e + 16*a*b^3*c^3*d^3*e - 32*a^2*b*c^4*d^3*e + b^6*c*d^2*e^2 - 6*a*b^4*c^2*d^2*e^2 + 32*a^3*c^4*d^2*e^2 - 2*a*b^5*c*d*e^3 + 16*a^2*b^3*c^2*d*e^3 - 32*a^3*b*c^3*d*e^3 + a^2*b^4*c*e^4 - 8*a^3*b^2*c^2*e^4 + 16*a^4*c^3*e^4)))/(b^4*c^3*d^4 - 8*a*b^2*c^4*d^4 + 16*a^2*c^5*d^4 - 2*b^5*c^2*d^3*e + 16*a*b^3*c^3*d^3*e - 32*a^2*b*c^4*d^3*e + b^6*c*d^2*e^2 - 6*a*b^4*c^2*d^2*e^2 + 32*a^3*c^4*d^2*e^2 - 2*a*b^5*c*d*e^3 + 16*a^2*b^3*c^2*d*e^3 - 32*a^3*b*c^3*d*e^3 + a^2*b^4*c*e^4 - 8*a^3*b^2*c^2*e^4 + 16*a^4*c^3*e^4)))/((2*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*sqrt(b^2 - 4*a*c)*d^3 + 3*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5 - (b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*sqrt(b^2 - 4*a*c))*d^2*e - 3*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4 - (b^6*c - 10*a*b^4*c^2 + 32*a^2*b^2*c^3 - 32*a^3*c^4)*sqrt(b^2 - 4*a*c))*d*e^2 + (b^8 - 13*a*b^6*c + 60*a^2*b^4*c^2 - 112*a^3*b^2*c^3 + 64*a^4*c^4 - (b^7 - 11*a*b^5*c + 40*a^2*b^3*c^2 - 48*a^3*b*c^3)*sqrt(b^2 - 4*a*c))*e^3)*abs(c)) + 3/4*(16*c^5*d^2 - 4*(4*b*c^4 + 5*sqrt(b^2 - 4*a*c)*c^4)*d*e + (11*b^2*c^3 - 28*a*c^4 + 10*sqrt(b^2 - 4*a*c)*b*c^3)*e^2)*sqrt(-4*c^2*d + 2*(b*c + sqrt(b^2 - 4*a*c)*c)*e)*arctan(2*sqrt(1/2)*sqrt(x*e + d)/sqrt(-(2*b^4*c^3*d^5 - 16*a*b^2*c^4*d^5 + 32*a^2*c^5*d^5 - 5*b^5*c^2*d^4*e + 40*a*b^3*c^3*d^4*e - 80*a^2*b*c^4*d^4*e + 4*b^6*c*d^3*e^2 - 28*a*b^4*c^2*d^3*e^2 + 32*a^2*b^2*c^3*d^3*e^2 + 64*a^3*c^4*d^3*e^2 - b^7*d^2*e^3 + 2*a*b^5*c*d^2*e^3 + 32*a^2*b^3*c^2*d^2*e^3 - 96*a^3*b*c^3*d^2*e^3 + 2*a*b^6*d*e^4 - 14*a^2*b^4*c*d*e^4 + 16*a^3*b^2*c^2*d*e^4 + 32*a^4*c^3*d*e^4 - a^2*b^5*e^5 + 8*a^3*b^3*c*e^5 - 16*a^4*b*c^2*e^5 - sqrt((2*b^4*c^3*d^5 - 16*a*b^2*c^4*d^5 + 32*a^2*c^5*d^5 - 5*b^5*c^2*d^4*e + 40*a*b^3*c^3*d^4*e - 80*a^2*b*c^4*d^4*e + 4*b^6*c*d^3*e^2 - 28*a*b^4*c^2*d^3*e^2 + 32*a^2*b^2*c^3*d^3*e^2 + 64*a^3*c^4*d^3*e^2 - b^7*d^2*e^3 + 2*a*b^5*c*d^2*e^3 + 32*a^2*b^3*c^2*d^2*e^3 - 96*a^3*b*c^3*d^2*e^3 + 2*a*b^6*d*e^4 - 14*a^2*b^4*c*d*e^4 + 16*a^3*b^2*c^2*d*e^4 + 32*a^4*c^3*d*e^4 - a^2*b^5*e^5 + 8*a^3*b^3*c*e^5 - 16*a^4*b*c^2*e^5)^2 - 4*(b^4*c^3*d^6 - 8*a*b^2*c^4*d^6 + 16*a^2*c^5*d^6 - 3*b^5*c^2*d^5*e + 24*a*b^3*c^3*d^5*e - 48*a^2*b*c^4*d^5*e + 3*b^6*c*d^4*e^2 - 21*a*b^4*c^2*d^4*e^2 + 24*a^2*b^2*c^3*d^4*e^2 + 48*a^3*c^4*d^4*e^2 - b^7*d^3*e^3 + 2*a*b^5*c*d^3*e^3 + 32*a^2*b^3*c^2*d^3*e^3 - 96*a^3*b*c^3*d^3*e^3 + 3*a*b^6*d^2*e^4 - 21*a^2*b^4*c*d^2*e^4 + 24*a^3*b^2*c^2*d^2*e^4 + 48*a^4*c^3*d^2*e^4 - 3*a^2*b^5*d*e^5 + 24*a^3*b^3*c*d*e^5 - 48*a^4*b*c^2*d*e^5 + a^3*b^4*e^6 - 8*a^4*b^2*c*e^6 + 16*a^5*c^2*e^6)*(b^4*c^3*d^4 - 8*a*b^2*c^4*d^4 + 16*a^2*c^5*d^4 - 2*b^5*c^2*d^3*e + 16*a*b^3*c^3*d^3*e - 32*a^2*b*c^4*d^3*e + b^6*c*d^2*e^2 - 6*a*b^4*c^2*d^2*e^2 + 32*a^3*c^4*d^2*e^2 - 2*a*b^5*c*d*e^3 + 16*a^2*b^3*c^2*d*e^3 - 32*a^3*b*c^3*d*e^3 + a^2*b^4*c*e^4 - 8*a^3*b^2*c^2*e^4 + 16*a^4*c^3*e^4)))/(b^4*c^3*d^4 - 8*a*b^2*c^4*d^4 + 16*a^2*c^5*d^4 - 2*b^5*c^2*d^3*e + 16*a*b^3*c^3*d^3*e - 32*a^2*b*c^4*d^3*e + b^6*c*d^2*e^2 - 6*a*b^4*c^2*d^2*e^2 + 32*a^3*c^4*d^2*e^2 - 2*a*b^5*c*d*e^3 + 16*a^2*b^3*c^2*d*e^3 - 32*a^3*b*c^3*d*e^3 + a^2*b^4*c*e^4 - 8*a^3*b^2*c^2*e^4 + 16*a^4*c^3*e^4)))/((2*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*sqrt(b^2 - 4*a*c)*d^3 - 3*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5 + (b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*sqrt(b^2 - 4*a*c))*d^2*e + 3*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4 + (b^6*c - 10*a*b^4*c^2 + 32*a^2*b^2*c^3 - 32*a^3*c^4)*sqrt(b^2 - 4*a*c))*d*e^2 - (b^8 - 13*a*b^6*c + 60*a^2*b^4*c^2 - 112*a^3*b^2*c^3 + 64*a^4*c^4 + (b^7 - 11*a*b^5*c + 40*a^2*b^3*c^2 - 48*a^3*b*c^3)*sqrt(b^2 - 4*a*c))*e^3)*abs(c)) + 1/4*(24*(x*e + d)^(7/2)*c^5*d^3*e - 72*(x*e + d)^(5/2)*c^5*d^4*e + 72*(x*e + d)^(3/2)*c^5*d^5*e - 24*sqrt(x*e + d)*c^5*d^6*e - 36*(x*e + d)^(7/2)*b*c^4*d^2*e^2 + 144*(x*e + d)^(5/2)*b*c^4*d^3*e^2 - 180*(x*e + d)^(3/2)*b*c^4*d^4*e^2 + 72*sqrt(x*e + d)*b*c^4*d^5*e^2 + 6*(x*e + d)^(7/2)*b^2*c^3*d*e^3 + 48*(x*e + d)^(7/2)*a*c^4*d*e^3 - 73*(x*e + d)^(5/2)*b^2*c^3*d^2*e^3 - 140*(x*e + d)^(5/2)*a*c^4*d^2*e^3 + 136*(x*e + d)^(3/2)*b^2*c^3*d^3*e^3 + 176*(x*e + d)^(3/2)*a*c^4*d^3*e^3 - 69*sqrt(x*e + d)*b^2*c^3*d^4*e^3 - 84*sqrt(x*e + d)*a*c^4*d^4*e^3 + 3*(x*e + d)^(7/2)*b^3*c^2*e^4 - 24*(x*e + d)^(7/2)*a*b*c^3*e^4 + (x*e + d)^(5/2)*b^3*c^2*d*e^4 + 140*(x*e + d)^(5/2)*a*b*c^3*d*e^4 - 24*(x*e + d)^(3/2)*b^3*c^2*d^2*e^4 - 264*(x*e + d)^(3/2)*a*b*c^3*d^2*e^4 + 18*sqrt(x*e + d)*b^3*c^2*d^3*e^4 + 168*sqrt(x*e + d)*a*b*c^3*d^3*e^4 + 6*(x*e + d)^(5/2)*b^4*c*e^5 - 49*(x*e + d)^(5/2)*a*b^2*c^2*e^5 + 28*(x*e + d)^(5/2)*a^2*c^3*e^5 - 10*(x*e + d)^(3/2)*b^4*c*d*e^5 + 128*(x*e + d)^(3/2)*a*b^2*c^2*d*e^5 + 8*(x*e + d)^(3/2)*a^2*c^3*d*e^5 + 8*sqrt(x*e + d)*b^4*c*d^2*e^5 - 118*sqrt(x*e + d)*a*b^2*c^2*d^2*e^5 - 16*sqrt(x*e + d)*a^2*c^3*d^2*e^5 + 3*(x*e + d)^(3/2)*b^5*e^6 - 20*(x*e + d)^(3/2)*a*b^3*c*e^6 - 4*(x*e + d)^(3/2)*a^2*b*c^2*e^6 - 5*sqrt(x*e + d)*b^5*d*e^6 + 34*sqrt(x*e + d)*a*b^3*c*d*e^6 + 16*sqrt(x*e + d)*a^2*b*c^2*d*e^6 + 5*sqrt(x*e + d)*a*b^4*e^7 - 37*sqrt(x*e + d)*a^2*b^2*c*e^7 + 44*sqrt(x*e + d)*a^3*c^2*e^7)/((b^4*c^2*d^4 - 8*a*b^2*c^3*d^4 + 16*a^2*c^4*d^4 - 2*b^5*c*d^3*e + 16*a*b^3*c^2*d^3*e - 32*a^2*b*c^3*d^3*e + b^6*d^2*e^2 - 6*a*b^4*c*d^2*e^2 + 32*a^3*c^3*d^2*e^2 - 2*a*b^5*d*e^3 + 16*a^2*b^3*c*d*e^3 - 32*a^3*b*c^2*d*e^3 + a^2*b^4*e^4 - 8*a^3*b^2*c*e^4 + 16*a^4*c^2*e^4)*((x*e + d)^2*c - 2*(x*e + d)*c*d + c*d^2 + (x*e + d)*b*e - b*d*e + a*e^2)^2)","B",0
2307,-2,0,0,0.000000," ","integrate((e*x+d)^(1/2)/(a+I*b*x+c*x^2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0,0,0,0,0] was discarded and replaced randomly by 0=[-40,-48,10,-58,31]index.cc index_m operator + Error: Bad Argument ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0,0,0,0,0] was discarded and replaced randomly by 0=[-64,83,-68,-60,2]index.cc index_m operator + Error: Bad Argument ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0,0,0,0,0] was discarded and replaced randomly by 0=[84,-86,82,76,-49]index.cc index_m operator + Error: Bad Argument ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0,0,0,0,0] was discarded and replaced randomly by 0=[17,-70,45,77,-80]index.cc index_m operator + Error: Bad Argument ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0,0,0,0,0] was discarded and replaced randomly by 0=[50,72,91,-18,-31]index.cc index_m operator + Error: Bad Argument ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0,0,0,0,0] was discarded and replaced randomly by 0=[8,-38,11,77,3]index.cc index_m operator + Error: Bad Argument ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0,0,0,0,0] was discarded and replaced randomly by 0=[57,24,19,-14,-32]index.cc index_m operator + Error: Bad Argument ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0,0,0,0,0] was discarded and replaced randomly by 0=[41,20,-42,71,97]index.cc index_m operator + Error: Bad Argument ValueDone","F(-2)",0
2308,-2,0,0,0.000000," ","integrate(1/(e*x+d)^(1/2)/(a+I*b*x+c*x^2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0,0,0,0,0] was discarded and replaced randomly by 0=[-40,-48,10,-58,31]index.cc index_m operator + Error: Bad Argument ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0,0,0,0,0] was discarded and replaced randomly by 0=[-64,83,-68,-60,2]index.cc index_m operator + Error: Bad Argument ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0,0,0,0,0] was discarded and replaced randomly by 0=[84,-86,82,76,-49]index.cc index_m operator + Error: Bad Argument ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0,0,0,0,0] was discarded and replaced randomly by 0=[17,-70,45,77,-80]index.cc index_m operator + Error: Bad Argument ValueDone","F(-2)",0
2309,1,614,0,1.223792," ","integrate((1+2*x)^(7/2)/(5*x^2+3*x+2),x, algorithm=""giac"")","\frac{4}{25} \, {\left(2 \, x + 1\right)}^{\frac{5}{2}} - \frac{1}{1162984375} \, \sqrt{31} {\left(11340 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} - 54 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 108 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 22680 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} - 162925 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450} - 325850 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450}\right)} \arctan\left(\frac{5 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(\left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + \sqrt{2 \, x + 1}\right)}}{7 \, \sqrt{-\frac{1}{35} \, \sqrt{35} + \frac{1}{2}}}\right) - \frac{1}{1162984375} \, \sqrt{31} {\left(11340 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} - 54 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 108 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 22680 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} - 162925 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450} - 325850 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450}\right)} \arctan\left(-\frac{5 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(\left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} - \sqrt{2 \, x + 1}\right)}}{7 \, \sqrt{-\frac{1}{35} \, \sqrt{35} + \frac{1}{2}}}\right) - \frac{1}{2325968750} \, \sqrt{31} {\left(54 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 11340 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} - 22680 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} + 108 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} - 162925 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450} + 325850 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450}\right)} \log\left(2 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{2 \, x + 1} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + 2 \, x + \sqrt{\frac{7}{5}} + 1\right) + \frac{1}{2325968750} \, \sqrt{31} {\left(54 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 11340 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} - 22680 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} + 108 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} - 162925 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450} + 325850 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450}\right)} \log\left(-2 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{2 \, x + 1} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + 2 \, x + \sqrt{\frac{7}{5}} + 1\right) + \frac{16}{75} \, {\left(2 \, x + 1\right)}^{\frac{3}{2}} - \frac{76}{125} \, \sqrt{2 \, x + 1}"," ",0,"4/25*(2*x + 1)^(5/2) - 1/1162984375*sqrt(31)*(11340*sqrt(31)*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) - 54*sqrt(31)*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 108*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 22680*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) - 162925*sqrt(31)*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450) - 325850*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450))*arctan(5/7*(7/5)^(3/4)*((7/5)^(1/4)*sqrt(1/35*sqrt(35) + 1/2) + sqrt(2*x + 1))/sqrt(-1/35*sqrt(35) + 1/2)) - 1/1162984375*sqrt(31)*(11340*sqrt(31)*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) - 54*sqrt(31)*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 108*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 22680*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) - 162925*sqrt(31)*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450) - 325850*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450))*arctan(-5/7*(7/5)^(3/4)*((7/5)^(1/4)*sqrt(1/35*sqrt(35) + 1/2) - sqrt(2*x + 1))/sqrt(-1/35*sqrt(35) + 1/2)) - 1/2325968750*sqrt(31)*(54*sqrt(31)*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 11340*sqrt(31)*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) - 22680*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) + 108*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) - 162925*sqrt(31)*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450) + 325850*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450))*log(2*(7/5)^(1/4)*sqrt(2*x + 1)*sqrt(1/35*sqrt(35) + 1/2) + 2*x + sqrt(7/5) + 1) + 1/2325968750*sqrt(31)*(54*sqrt(31)*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 11340*sqrt(31)*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) - 22680*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) + 108*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) - 162925*sqrt(31)*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450) + 325850*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450))*log(-2*(7/5)^(1/4)*sqrt(2*x + 1)*sqrt(1/35*sqrt(35) + 1/2) + 2*x + sqrt(7/5) + 1) + 16/75*(2*x + 1)^(3/2) - 76/125*sqrt(2*x + 1)","B",0
2310,1,605,0,1.205340," ","integrate((1+2*x)^(5/2)/(5*x^2+3*x+2),x, algorithm=""giac"")","-\frac{1}{930387500} \, \sqrt{31} {\left(3990 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} - 19 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 38 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 7980 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} + 137200 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450} + 274400 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450}\right)} \arctan\left(\frac{5 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(\left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + \sqrt{2 \, x + 1}\right)}}{7 \, \sqrt{-\frac{1}{35} \, \sqrt{35} + \frac{1}{2}}}\right) - \frac{1}{930387500} \, \sqrt{31} {\left(3990 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} - 19 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 38 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 7980 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} + 137200 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450} + 274400 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450}\right)} \arctan\left(-\frac{5 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(\left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} - \sqrt{2 \, x + 1}\right)}}{7 \, \sqrt{-\frac{1}{35} \, \sqrt{35} + \frac{1}{2}}}\right) - \frac{1}{1860775000} \, \sqrt{31} {\left(19 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 3990 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} - 7980 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} + 38 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 137200 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450} - 274400 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450}\right)} \log\left(2 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{2 \, x + 1} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + 2 \, x + \sqrt{\frac{7}{5}} + 1\right) + \frac{1}{1860775000} \, \sqrt{31} {\left(19 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 3990 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} - 7980 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} + 38 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 137200 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450} - 274400 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450}\right)} \log\left(-2 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{2 \, x + 1} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + 2 \, x + \sqrt{\frac{7}{5}} + 1\right) + \frac{4}{15} \, {\left(2 \, x + 1\right)}^{\frac{3}{2}} + \frac{16}{25} \, \sqrt{2 \, x + 1}"," ",0,"-1/930387500*sqrt(31)*(3990*sqrt(31)*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) - 19*sqrt(31)*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 38*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 7980*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) + 137200*sqrt(31)*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450) + 274400*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450))*arctan(5/7*(7/5)^(3/4)*((7/5)^(1/4)*sqrt(1/35*sqrt(35) + 1/2) + sqrt(2*x + 1))/sqrt(-1/35*sqrt(35) + 1/2)) - 1/930387500*sqrt(31)*(3990*sqrt(31)*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) - 19*sqrt(31)*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 38*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 7980*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) + 137200*sqrt(31)*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450) + 274400*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450))*arctan(-5/7*(7/5)^(3/4)*((7/5)^(1/4)*sqrt(1/35*sqrt(35) + 1/2) - sqrt(2*x + 1))/sqrt(-1/35*sqrt(35) + 1/2)) - 1/1860775000*sqrt(31)*(19*sqrt(31)*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 3990*sqrt(31)*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) - 7980*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) + 38*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 137200*sqrt(31)*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450) - 274400*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450))*log(2*(7/5)^(1/4)*sqrt(2*x + 1)*sqrt(1/35*sqrt(35) + 1/2) + 2*x + sqrt(7/5) + 1) + 1/1860775000*sqrt(31)*(19*sqrt(31)*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 3990*sqrt(31)*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) - 7980*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) + 38*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 137200*sqrt(31)*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450) - 274400*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450))*log(-2*(7/5)^(1/4)*sqrt(2*x + 1)*sqrt(1/35*sqrt(35) + 1/2) + 2*x + sqrt(7/5) + 1) + 4/15*(2*x + 1)^(3/2) + 16/25*sqrt(2*x + 1)","B",0
2311,1,594,0,1.179218," ","integrate((1+2*x)^(3/2)/(5*x^2+3*x+2),x, algorithm=""giac"")","\frac{1}{46519375} \, \sqrt{31} {\left(210 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} - \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 2 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 420 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} - 8575 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450} - 17150 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450}\right)} \arctan\left(\frac{5 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(\left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + \sqrt{2 \, x + 1}\right)}}{7 \, \sqrt{-\frac{1}{35} \, \sqrt{35} + \frac{1}{2}}}\right) + \frac{1}{46519375} \, \sqrt{31} {\left(210 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} - \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 2 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 420 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} - 8575 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450} - 17150 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450}\right)} \arctan\left(-\frac{5 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(\left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} - \sqrt{2 \, x + 1}\right)}}{7 \, \sqrt{-\frac{1}{35} \, \sqrt{35} + \frac{1}{2}}}\right) + \frac{1}{93038750} \, \sqrt{31} {\left(\sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 210 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} - 420 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} + 2 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} - 8575 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450} + 17150 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450}\right)} \log\left(2 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{2 \, x + 1} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + 2 \, x + \sqrt{\frac{7}{5}} + 1\right) - \frac{1}{93038750} \, \sqrt{31} {\left(\sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 210 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} - 420 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} + 2 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} - 8575 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450} + 17150 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450}\right)} \log\left(-2 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{2 \, x + 1} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + 2 \, x + \sqrt{\frac{7}{5}} + 1\right) + \frac{4}{5} \, \sqrt{2 \, x + 1}"," ",0,"1/46519375*sqrt(31)*(210*sqrt(31)*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) - sqrt(31)*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 2*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 420*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) - 8575*sqrt(31)*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450) - 17150*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450))*arctan(5/7*(7/5)^(3/4)*((7/5)^(1/4)*sqrt(1/35*sqrt(35) + 1/2) + sqrt(2*x + 1))/sqrt(-1/35*sqrt(35) + 1/2)) + 1/46519375*sqrt(31)*(210*sqrt(31)*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) - sqrt(31)*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 2*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 420*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) - 8575*sqrt(31)*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450) - 17150*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450))*arctan(-5/7*(7/5)^(3/4)*((7/5)^(1/4)*sqrt(1/35*sqrt(35) + 1/2) - sqrt(2*x + 1))/sqrt(-1/35*sqrt(35) + 1/2)) + 1/93038750*sqrt(31)*(sqrt(31)*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 210*sqrt(31)*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) - 420*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) + 2*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) - 8575*sqrt(31)*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450) + 17150*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450))*log(2*(7/5)^(1/4)*sqrt(2*x + 1)*sqrt(1/35*sqrt(35) + 1/2) + 2*x + sqrt(7/5) + 1) - 1/93038750*sqrt(31)*(sqrt(31)*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 210*sqrt(31)*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) - 420*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) + 2*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) - 8575*sqrt(31)*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450) + 17150*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450))*log(-2*(7/5)^(1/4)*sqrt(2*x + 1)*sqrt(1/35*sqrt(35) + 1/2) + 2*x + sqrt(7/5) + 1) + 4/5*sqrt(2*x + 1)","B",0
2312,1,461,0,1.108010," ","integrate((1+2*x)^(1/2)/(5*x^2+3*x+2),x, algorithm=""giac"")","\frac{1}{37215500} \, \sqrt{31} {\left(210 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} - \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 2 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 420 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)}\right)} \arctan\left(\frac{5 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(\left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + \sqrt{2 \, x + 1}\right)}}{7 \, \sqrt{-\frac{1}{35} \, \sqrt{35} + \frac{1}{2}}}\right) + \frac{1}{37215500} \, \sqrt{31} {\left(210 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} - \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 2 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 420 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)}\right)} \arctan\left(-\frac{5 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(\left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} - \sqrt{2 \, x + 1}\right)}}{7 \, \sqrt{-\frac{1}{35} \, \sqrt{35} + \frac{1}{2}}}\right) + \frac{1}{74431000} \, \sqrt{31} {\left(\sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 210 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} - 420 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} + 2 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}}\right)} \log\left(2 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{2 \, x + 1} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + 2 \, x + \sqrt{\frac{7}{5}} + 1\right) - \frac{1}{74431000} \, \sqrt{31} {\left(\sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 210 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} - 420 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} + 2 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}}\right)} \log\left(-2 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{2 \, x + 1} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + 2 \, x + \sqrt{\frac{7}{5}} + 1\right)"," ",0,"1/37215500*sqrt(31)*(210*sqrt(31)*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) - sqrt(31)*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 2*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 420*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35))*arctan(5/7*(7/5)^(3/4)*((7/5)^(1/4)*sqrt(1/35*sqrt(35) + 1/2) + sqrt(2*x + 1))/sqrt(-1/35*sqrt(35) + 1/2)) + 1/37215500*sqrt(31)*(210*sqrt(31)*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) - sqrt(31)*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 2*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 420*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35))*arctan(-5/7*(7/5)^(3/4)*((7/5)^(1/4)*sqrt(1/35*sqrt(35) + 1/2) - sqrt(2*x + 1))/sqrt(-1/35*sqrt(35) + 1/2)) + 1/74431000*sqrt(31)*(sqrt(31)*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 210*sqrt(31)*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) - 420*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) + 2*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2))*log(2*(7/5)^(1/4)*sqrt(2*x + 1)*sqrt(1/35*sqrt(35) + 1/2) + 2*x + sqrt(7/5) + 1) - 1/74431000*sqrt(31)*(sqrt(31)*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 210*sqrt(31)*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) - 420*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) + 2*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2))*log(-2*(7/5)^(1/4)*sqrt(2*x + 1)*sqrt(1/35*sqrt(35) + 1/2) + 2*x + sqrt(7/5) + 1)","B",0
2313,1,279,0,0.630111," ","integrate(1/(1+2*x)^(1/2)/(5*x^2+3*x+2),x, algorithm=""giac"")","\frac{1}{7595} \, \sqrt{31} {\left(\sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450} + 2 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450}\right)} \arctan\left(\frac{5 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(\left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + \sqrt{2 \, x + 1}\right)}}{7 \, \sqrt{-\frac{1}{35} \, \sqrt{35} + \frac{1}{2}}}\right) + \frac{1}{7595} \, \sqrt{31} {\left(\sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450} + 2 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450}\right)} \arctan\left(-\frac{5 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(\left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} - \sqrt{2 \, x + 1}\right)}}{7 \, \sqrt{-\frac{1}{35} \, \sqrt{35} + \frac{1}{2}}}\right) + \frac{1}{15190} \, \sqrt{31} {\left(\sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450} - 2 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450}\right)} \log\left(2 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{2 \, x + 1} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + 2 \, x + \sqrt{\frac{7}{5}} + 1\right) - \frac{1}{15190} \, \sqrt{31} {\left(\sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450} - 2 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450}\right)} \log\left(-2 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{2 \, x + 1} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + 2 \, x + \sqrt{\frac{7}{5}} + 1\right)"," ",0,"1/7595*sqrt(31)*(sqrt(31)*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450) + 2*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450))*arctan(5/7*(7/5)^(3/4)*((7/5)^(1/4)*sqrt(1/35*sqrt(35) + 1/2) + sqrt(2*x + 1))/sqrt(-1/35*sqrt(35) + 1/2)) + 1/7595*sqrt(31)*(sqrt(31)*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450) + 2*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450))*arctan(-5/7*(7/5)^(3/4)*((7/5)^(1/4)*sqrt(1/35*sqrt(35) + 1/2) - sqrt(2*x + 1))/sqrt(-1/35*sqrt(35) + 1/2)) + 1/15190*sqrt(31)*(sqrt(31)*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450) - 2*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450))*log(2*(7/5)^(1/4)*sqrt(2*x + 1)*sqrt(1/35*sqrt(35) + 1/2) + 2*x + sqrt(7/5) + 1) - 1/15190*sqrt(31)*(sqrt(31)*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450) - 2*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450))*log(-2*(7/5)^(1/4)*sqrt(2*x + 1)*sqrt(1/35*sqrt(35) + 1/2) + 2*x + sqrt(7/5) + 1)","A",0
2314,1,594,0,0.817422," ","integrate(1/(1+2*x)^(3/2)/(5*x^2+3*x+2),x, algorithm=""giac"")","-\frac{1}{52101700} \, \sqrt{31} {\left(210 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} - \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 2 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 420 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} - 3920 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450} - 7840 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450}\right)} \arctan\left(\frac{5 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(\left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + \sqrt{2 \, x + 1}\right)}}{7 \, \sqrt{-\frac{1}{35} \, \sqrt{35} + \frac{1}{2}}}\right) - \frac{1}{52101700} \, \sqrt{31} {\left(210 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} - \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 2 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 420 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} - 3920 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450} - 7840 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450}\right)} \arctan\left(-\frac{5 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(\left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} - \sqrt{2 \, x + 1}\right)}}{7 \, \sqrt{-\frac{1}{35} \, \sqrt{35} + \frac{1}{2}}}\right) - \frac{1}{104203400} \, \sqrt{31} {\left(\sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 210 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} - 420 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} + 2 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} - 3920 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450} + 7840 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450}\right)} \log\left(2 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{2 \, x + 1} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + 2 \, x + \sqrt{\frac{7}{5}} + 1\right) + \frac{1}{104203400} \, \sqrt{31} {\left(\sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 210 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} - 420 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} + 2 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} - 3920 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450} + 7840 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450}\right)} \log\left(-2 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{2 \, x + 1} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + 2 \, x + \sqrt{\frac{7}{5}} + 1\right) - \frac{4}{7 \, \sqrt{2 \, x + 1}}"," ",0,"-1/52101700*sqrt(31)*(210*sqrt(31)*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) - sqrt(31)*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 2*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 420*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) - 3920*sqrt(31)*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450) - 7840*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450))*arctan(5/7*(7/5)^(3/4)*((7/5)^(1/4)*sqrt(1/35*sqrt(35) + 1/2) + sqrt(2*x + 1))/sqrt(-1/35*sqrt(35) + 1/2)) - 1/52101700*sqrt(31)*(210*sqrt(31)*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) - sqrt(31)*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 2*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 420*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) - 3920*sqrt(31)*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450) - 7840*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450))*arctan(-5/7*(7/5)^(3/4)*((7/5)^(1/4)*sqrt(1/35*sqrt(35) + 1/2) - sqrt(2*x + 1))/sqrt(-1/35*sqrt(35) + 1/2)) - 1/104203400*sqrt(31)*(sqrt(31)*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 210*sqrt(31)*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) - 420*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) + 2*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) - 3920*sqrt(31)*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450) + 7840*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450))*log(2*(7/5)^(1/4)*sqrt(2*x + 1)*sqrt(1/35*sqrt(35) + 1/2) + 2*x + sqrt(7/5) + 1) + 1/104203400*sqrt(31)*(sqrt(31)*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 210*sqrt(31)*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) - 420*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) + 2*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) - 3920*sqrt(31)*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450) + 7840*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450))*log(-2*(7/5)^(1/4)*sqrt(2*x + 1)*sqrt(1/35*sqrt(35) + 1/2) + 2*x + sqrt(7/5) + 1) - 4/7/sqrt(2*x + 1)","B",0
2315,1,599,0,1.151212," ","integrate(1/(1+2*x)^(5/2)/(5*x^2+3*x+2),x, algorithm=""giac"")","-\frac{1}{91177975} \, \sqrt{31} {\left(210 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} - \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} - 2 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} - 420 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} + 4655 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450} - 9310 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450}\right)} \arctan\left(\frac{5 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(\left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + \sqrt{2 \, x + 1}\right)}}{7 \, \sqrt{-\frac{1}{35} \, \sqrt{35} + \frac{1}{2}}}\right) - \frac{1}{91177975} \, \sqrt{31} {\left(210 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} - \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} - 2 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} - 420 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} + 4655 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450} - 9310 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450}\right)} \arctan\left(-\frac{5 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(\left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} - \sqrt{2 \, x + 1}\right)}}{7 \, \sqrt{-\frac{1}{35} \, \sqrt{35} + \frac{1}{2}}}\right) - \frac{1}{182355950} \, \sqrt{31} {\left(\sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 210 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} + 420 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} - 2 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 4655 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450} + 9310 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450}\right)} \log\left(2 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{2 \, x + 1} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + 2 \, x + \sqrt{\frac{7}{5}} + 1\right) + \frac{1}{182355950} \, \sqrt{31} {\left(\sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 210 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} + 420 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} - 2 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 4655 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450} + 9310 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450}\right)} \log\left(-2 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{2 \, x + 1} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + 2 \, x + \sqrt{\frac{7}{5}} + 1\right) - \frac{4 \, {\left(24 \, x + 19\right)}}{147 \, {\left(2 \, x + 1\right)}^{\frac{3}{2}}}"," ",0,"-1/91177975*sqrt(31)*(210*sqrt(31)*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) - sqrt(31)*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) - 2*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) - 420*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) + 4655*sqrt(31)*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450) - 9310*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450))*arctan(5/7*(7/5)^(3/4)*((7/5)^(1/4)*sqrt(1/35*sqrt(35) + 1/2) + sqrt(2*x + 1))/sqrt(-1/35*sqrt(35) + 1/2)) - 1/91177975*sqrt(31)*(210*sqrt(31)*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) - sqrt(31)*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) - 2*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) - 420*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) + 4655*sqrt(31)*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450) - 9310*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450))*arctan(-5/7*(7/5)^(3/4)*((7/5)^(1/4)*sqrt(1/35*sqrt(35) + 1/2) - sqrt(2*x + 1))/sqrt(-1/35*sqrt(35) + 1/2)) - 1/182355950*sqrt(31)*(sqrt(31)*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 210*sqrt(31)*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) + 420*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) - 2*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 4655*sqrt(31)*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450) + 9310*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450))*log(2*(7/5)^(1/4)*sqrt(2*x + 1)*sqrt(1/35*sqrt(35) + 1/2) + 2*x + sqrt(7/5) + 1) + 1/182355950*sqrt(31)*(sqrt(31)*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 210*sqrt(31)*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) + 420*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) - 2*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 4655*sqrt(31)*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450) + 9310*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450))*log(-2*(7/5)^(1/4)*sqrt(2*x + 1)*sqrt(1/35*sqrt(35) + 1/2) + 2*x + sqrt(7/5) + 1) - 4/147*(24*x + 19)/(2*x + 1)^(3/2)","B",0
2316,1,633,0,1.343427," ","integrate((1+2*x)^(7/2)/(5*x^2+3*x+2)^2,x, algorithm=""giac"")","\frac{1}{14421006250} \, \sqrt{31} {\left(85470 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} - 407 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 814 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 170940 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} - 2589650 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450} - 5179300 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450}\right)} \arctan\left(\frac{5 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(\left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + \sqrt{2 \, x + 1}\right)}}{7 \, \sqrt{-\frac{1}{35} \, \sqrt{35} + \frac{1}{2}}}\right) + \frac{1}{14421006250} \, \sqrt{31} {\left(85470 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} - 407 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 814 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 170940 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} - 2589650 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450} - 5179300 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450}\right)} \arctan\left(-\frac{5 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(\left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} - \sqrt{2 \, x + 1}\right)}}{7 \, \sqrt{-\frac{1}{35} \, \sqrt{35} + \frac{1}{2}}}\right) + \frac{1}{28842012500} \, \sqrt{31} {\left(407 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 85470 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} - 170940 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} + 814 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} - 2589650 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450} + 5179300 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450}\right)} \log\left(2 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{2 \, x + 1} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + 2 \, x + \sqrt{\frac{7}{5}} + 1\right) - \frac{1}{28842012500} \, \sqrt{31} {\left(407 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 85470 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} - 170940 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} + 814 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} - 2589650 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450} + 5179300 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450}\right)} \log\left(-2 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{2 \, x + 1} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + 2 \, x + \sqrt{\frac{7}{5}} + 1\right) + \frac{16}{25} \, \sqrt{2 \, x + 1} - \frac{4 \, {\left(178 \, {\left(2 \, x + 1\right)}^{\frac{3}{2}} - 189 \, \sqrt{2 \, x + 1}\right)}}{775 \, {\left(5 \, {\left(2 \, x + 1\right)}^{2} - 8 \, x + 3\right)}}"," ",0,"1/14421006250*sqrt(31)*(85470*sqrt(31)*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) - 407*sqrt(31)*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 814*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 170940*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) - 2589650*sqrt(31)*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450) - 5179300*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450))*arctan(5/7*(7/5)^(3/4)*((7/5)^(1/4)*sqrt(1/35*sqrt(35) + 1/2) + sqrt(2*x + 1))/sqrt(-1/35*sqrt(35) + 1/2)) + 1/14421006250*sqrt(31)*(85470*sqrt(31)*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) - 407*sqrt(31)*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 814*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 170940*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) - 2589650*sqrt(31)*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450) - 5179300*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450))*arctan(-5/7*(7/5)^(3/4)*((7/5)^(1/4)*sqrt(1/35*sqrt(35) + 1/2) - sqrt(2*x + 1))/sqrt(-1/35*sqrt(35) + 1/2)) + 1/28842012500*sqrt(31)*(407*sqrt(31)*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 85470*sqrt(31)*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) - 170940*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) + 814*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) - 2589650*sqrt(31)*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450) + 5179300*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450))*log(2*(7/5)^(1/4)*sqrt(2*x + 1)*sqrt(1/35*sqrt(35) + 1/2) + 2*x + sqrt(7/5) + 1) - 1/28842012500*sqrt(31)*(407*sqrt(31)*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 85470*sqrt(31)*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) - 170940*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) + 814*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) - 2589650*sqrt(31)*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450) + 5179300*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450))*log(-2*(7/5)^(1/4)*sqrt(2*x + 1)*sqrt(1/35*sqrt(35) + 1/2) + 2*x + sqrt(7/5) + 1) + 16/25*sqrt(2*x + 1) - 4/775*(178*(2*x + 1)^(3/2) - 189*sqrt(2*x + 1))/(5*(2*x + 1)^2 - 8*x + 3)","B",0
2317,1,624,0,1.341046," ","integrate((1+2*x)^(5/2)/(5*x^2+3*x+2)^2,x, algorithm=""giac"")","\frac{1}{5768402500} \, \sqrt{31} {\left(20370 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} - 97 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 194 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 40740 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} + 68600 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450} + 137200 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450}\right)} \arctan\left(\frac{5 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(\left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + \sqrt{2 \, x + 1}\right)}}{7 \, \sqrt{-\frac{1}{35} \, \sqrt{35} + \frac{1}{2}}}\right) + \frac{1}{5768402500} \, \sqrt{31} {\left(20370 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} - 97 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 194 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 40740 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} + 68600 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450} + 137200 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450}\right)} \arctan\left(-\frac{5 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(\left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} - \sqrt{2 \, x + 1}\right)}}{7 \, \sqrt{-\frac{1}{35} \, \sqrt{35} + \frac{1}{2}}}\right) + \frac{1}{11536805000} \, \sqrt{31} {\left(97 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 20370 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} - 40740 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} + 194 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 68600 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450} - 137200 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450}\right)} \log\left(2 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{2 \, x + 1} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + 2 \, x + \sqrt{\frac{7}{5}} + 1\right) - \frac{1}{11536805000} \, \sqrt{31} {\left(97 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 20370 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} - 40740 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} + 194 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 68600 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450} - 137200 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450}\right)} \log\left(-2 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{2 \, x + 1} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + 2 \, x + \sqrt{\frac{7}{5}} + 1\right) - \frac{4 \, {\left(27 \, {\left(2 \, x + 1\right)}^{\frac{3}{2}} + 14 \, \sqrt{2 \, x + 1}\right)}}{155 \, {\left(5 \, {\left(2 \, x + 1\right)}^{2} - 8 \, x + 3\right)}}"," ",0,"1/5768402500*sqrt(31)*(20370*sqrt(31)*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) - 97*sqrt(31)*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 194*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 40740*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) + 68600*sqrt(31)*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450) + 137200*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450))*arctan(5/7*(7/5)^(3/4)*((7/5)^(1/4)*sqrt(1/35*sqrt(35) + 1/2) + sqrt(2*x + 1))/sqrt(-1/35*sqrt(35) + 1/2)) + 1/5768402500*sqrt(31)*(20370*sqrt(31)*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) - 97*sqrt(31)*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 194*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 40740*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) + 68600*sqrt(31)*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450) + 137200*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450))*arctan(-5/7*(7/5)^(3/4)*((7/5)^(1/4)*sqrt(1/35*sqrt(35) + 1/2) - sqrt(2*x + 1))/sqrt(-1/35*sqrt(35) + 1/2)) + 1/11536805000*sqrt(31)*(97*sqrt(31)*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 20370*sqrt(31)*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) - 40740*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) + 194*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 68600*sqrt(31)*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450) - 137200*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450))*log(2*(7/5)^(1/4)*sqrt(2*x + 1)*sqrt(1/35*sqrt(35) + 1/2) + 2*x + sqrt(7/5) + 1) - 1/11536805000*sqrt(31)*(97*sqrt(31)*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 20370*sqrt(31)*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) - 40740*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) + 194*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 68600*sqrt(31)*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450) - 137200*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450))*log(-2*(7/5)^(1/4)*sqrt(2*x + 1)*sqrt(1/35*sqrt(35) + 1/2) + 2*x + sqrt(7/5) + 1) - 4/155*(27*(2*x + 1)^(3/2) + 14*sqrt(2*x + 1))/(5*(2*x + 1)^2 - 8*x + 3)","B",0
2318,1,622,0,1.321506," ","integrate((1+2*x)^(3/2)/(5*x^2+3*x+2)^2,x, algorithm=""giac"")","\frac{1}{576840250} \, \sqrt{31} {\left(210 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} - \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 2 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 420 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} + 17150 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450} + 34300 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450}\right)} \arctan\left(\frac{5 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(\left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + \sqrt{2 \, x + 1}\right)}}{7 \, \sqrt{-\frac{1}{35} \, \sqrt{35} + \frac{1}{2}}}\right) + \frac{1}{576840250} \, \sqrt{31} {\left(210 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} - \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 2 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 420 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} + 17150 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450} + 34300 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450}\right)} \arctan\left(-\frac{5 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(\left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} - \sqrt{2 \, x + 1}\right)}}{7 \, \sqrt{-\frac{1}{35} \, \sqrt{35} + \frac{1}{2}}}\right) + \frac{1}{1153680500} \, \sqrt{31} {\left(\sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 210 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} - 420 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} + 2 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 17150 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450} - 34300 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450}\right)} \log\left(2 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{2 \, x + 1} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + 2 \, x + \sqrt{\frac{7}{5}} + 1\right) - \frac{1}{1153680500} \, \sqrt{31} {\left(\sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 210 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} - 420 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} + 2 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 17150 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450} - 34300 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450}\right)} \log\left(-2 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{2 \, x + 1} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + 2 \, x + \sqrt{\frac{7}{5}} + 1\right) + \frac{4 \, {\left(2 \, {\left(2 \, x + 1\right)}^{\frac{3}{2}} - 7 \, \sqrt{2 \, x + 1}\right)}}{31 \, {\left(5 \, {\left(2 \, x + 1\right)}^{2} - 8 \, x + 3\right)}}"," ",0,"1/576840250*sqrt(31)*(210*sqrt(31)*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) - sqrt(31)*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 2*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 420*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) + 17150*sqrt(31)*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450) + 34300*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450))*arctan(5/7*(7/5)^(3/4)*((7/5)^(1/4)*sqrt(1/35*sqrt(35) + 1/2) + sqrt(2*x + 1))/sqrt(-1/35*sqrt(35) + 1/2)) + 1/576840250*sqrt(31)*(210*sqrt(31)*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) - sqrt(31)*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 2*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 420*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) + 17150*sqrt(31)*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450) + 34300*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450))*arctan(-5/7*(7/5)^(3/4)*((7/5)^(1/4)*sqrt(1/35*sqrt(35) + 1/2) - sqrt(2*x + 1))/sqrt(-1/35*sqrt(35) + 1/2)) + 1/1153680500*sqrt(31)*(sqrt(31)*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 210*sqrt(31)*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) - 420*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) + 2*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 17150*sqrt(31)*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450) - 34300*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450))*log(2*(7/5)^(1/4)*sqrt(2*x + 1)*sqrt(1/35*sqrt(35) + 1/2) + 2*x + sqrt(7/5) + 1) - 1/1153680500*sqrt(31)*(sqrt(31)*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 210*sqrt(31)*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) - 420*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) + 2*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 17150*sqrt(31)*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450) - 34300*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450))*log(-2*(7/5)^(1/4)*sqrt(2*x + 1)*sqrt(1/35*sqrt(35) + 1/2) + 2*x + sqrt(7/5) + 1) + 4/31*(2*(2*x + 1)^(3/2) - 7*sqrt(2*x + 1))/(5*(2*x + 1)^2 - 8*x + 3)","B",0
2319,1,622,0,1.287093," ","integrate((1+2*x)^(1/2)/(5*x^2+3*x+2)^2,x, algorithm=""giac"")","\frac{1}{230736100} \, \sqrt{31} {\left(210 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} - \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 2 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 420 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} + 1960 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450} + 3920 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450}\right)} \arctan\left(\frac{5 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(\left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + \sqrt{2 \, x + 1}\right)}}{7 \, \sqrt{-\frac{1}{35} \, \sqrt{35} + \frac{1}{2}}}\right) + \frac{1}{230736100} \, \sqrt{31} {\left(210 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} - \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 2 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 420 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} + 1960 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450} + 3920 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450}\right)} \arctan\left(-\frac{5 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(\left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} - \sqrt{2 \, x + 1}\right)}}{7 \, \sqrt{-\frac{1}{35} \, \sqrt{35} + \frac{1}{2}}}\right) + \frac{1}{461472200} \, \sqrt{31} {\left(\sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 210 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} - 420 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} + 2 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 1960 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450} - 3920 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450}\right)} \log\left(2 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{2 \, x + 1} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + 2 \, x + \sqrt{\frac{7}{5}} + 1\right) - \frac{1}{461472200} \, \sqrt{31} {\left(\sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 210 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} - 420 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} + 2 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 1960 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450} - 3920 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450}\right)} \log\left(-2 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{2 \, x + 1} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + 2 \, x + \sqrt{\frac{7}{5}} + 1\right) + \frac{4 \, {\left(5 \, {\left(2 \, x + 1\right)}^{\frac{3}{2}} - 2 \, \sqrt{2 \, x + 1}\right)}}{31 \, {\left(5 \, {\left(2 \, x + 1\right)}^{2} - 8 \, x + 3\right)}}"," ",0,"1/230736100*sqrt(31)*(210*sqrt(31)*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) - sqrt(31)*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 2*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 420*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) + 1960*sqrt(31)*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450) + 3920*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450))*arctan(5/7*(7/5)^(3/4)*((7/5)^(1/4)*sqrt(1/35*sqrt(35) + 1/2) + sqrt(2*x + 1))/sqrt(-1/35*sqrt(35) + 1/2)) + 1/230736100*sqrt(31)*(210*sqrt(31)*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) - sqrt(31)*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 2*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 420*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) + 1960*sqrt(31)*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450) + 3920*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450))*arctan(-5/7*(7/5)^(3/4)*((7/5)^(1/4)*sqrt(1/35*sqrt(35) + 1/2) - sqrt(2*x + 1))/sqrt(-1/35*sqrt(35) + 1/2)) + 1/461472200*sqrt(31)*(sqrt(31)*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 210*sqrt(31)*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) - 420*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) + 2*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 1960*sqrt(31)*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450) - 3920*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450))*log(2*(7/5)^(1/4)*sqrt(2*x + 1)*sqrt(1/35*sqrt(35) + 1/2) + 2*x + sqrt(7/5) + 1) - 1/461472200*sqrt(31)*(sqrt(31)*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 210*sqrt(31)*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) - 420*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) + 2*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 1960*sqrt(31)*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450) - 3920*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450))*log(-2*(7/5)^(1/4)*sqrt(2*x + 1)*sqrt(1/35*sqrt(35) + 1/2) + 2*x + sqrt(7/5) + 1) + 4/31*(5*(2*x + 1)^(3/2) - 2*sqrt(2*x + 1))/(5*(2*x + 1)^2 - 8*x + 3)","B",0
2320,1,622,0,0.905740," ","integrate(1/(1+2*x)^(1/2)/(5*x^2+3*x+2)^2,x, algorithm=""giac"")","\frac{1}{807576350} \, \sqrt{31} {\left(210 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} - \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 2 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 420 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} + 47530 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450} + 95060 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450}\right)} \arctan\left(\frac{5 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(\left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + \sqrt{2 \, x + 1}\right)}}{7 \, \sqrt{-\frac{1}{35} \, \sqrt{35} + \frac{1}{2}}}\right) + \frac{1}{807576350} \, \sqrt{31} {\left(210 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} - \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 2 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 420 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} + 47530 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450} + 95060 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450}\right)} \arctan\left(-\frac{5 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(\left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} - \sqrt{2 \, x + 1}\right)}}{7 \, \sqrt{-\frac{1}{35} \, \sqrt{35} + \frac{1}{2}}}\right) + \frac{1}{1615152700} \, \sqrt{31} {\left(\sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 210 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} - 420 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} + 2 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 47530 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450} - 95060 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450}\right)} \log\left(2 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{2 \, x + 1} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + 2 \, x + \sqrt{\frac{7}{5}} + 1\right) - \frac{1}{1615152700} \, \sqrt{31} {\left(\sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 210 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} - 420 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} + 2 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 47530 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450} - 95060 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450}\right)} \log\left(-2 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{2 \, x + 1} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + 2 \, x + \sqrt{\frac{7}{5}} + 1\right) + \frac{4 \, {\left(10 \, {\left(2 \, x + 1\right)}^{\frac{3}{2}} + 27 \, \sqrt{2 \, x + 1}\right)}}{217 \, {\left(5 \, {\left(2 \, x + 1\right)}^{2} - 8 \, x + 3\right)}}"," ",0,"1/807576350*sqrt(31)*(210*sqrt(31)*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) - sqrt(31)*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 2*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 420*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) + 47530*sqrt(31)*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450) + 95060*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450))*arctan(5/7*(7/5)^(3/4)*((7/5)^(1/4)*sqrt(1/35*sqrt(35) + 1/2) + sqrt(2*x + 1))/sqrt(-1/35*sqrt(35) + 1/2)) + 1/807576350*sqrt(31)*(210*sqrt(31)*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) - sqrt(31)*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 2*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 420*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) + 47530*sqrt(31)*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450) + 95060*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450))*arctan(-5/7*(7/5)^(3/4)*((7/5)^(1/4)*sqrt(1/35*sqrt(35) + 1/2) - sqrt(2*x + 1))/sqrt(-1/35*sqrt(35) + 1/2)) + 1/1615152700*sqrt(31)*(sqrt(31)*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 210*sqrt(31)*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) - 420*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) + 2*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 47530*sqrt(31)*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450) - 95060*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450))*log(2*(7/5)^(1/4)*sqrt(2*x + 1)*sqrt(1/35*sqrt(35) + 1/2) + 2*x + sqrt(7/5) + 1) - 1/1615152700*sqrt(31)*(sqrt(31)*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 210*sqrt(31)*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) - 420*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) + 2*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 47530*sqrt(31)*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450) - 95060*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450))*log(-2*(7/5)^(1/4)*sqrt(2*x + 1)*sqrt(1/35*sqrt(35) + 1/2) + 2*x + sqrt(7/5) + 1) + 4/217*(10*(2*x + 1)^(3/2) + 27*sqrt(2*x + 1))/(5*(2*x + 1)^2 - 8*x + 3)","B",0
2321,1,633,0,0.961886," ","integrate(1/(1+2*x)^(3/2)/(5*x^2+3*x+2)^2,x, algorithm=""giac"")","-\frac{1}{11306068900} \, \sqrt{31} {\left(31710 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} - 151 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 302 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 63420 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} - 797720 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450} - 1595440 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450}\right)} \arctan\left(\frac{5 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(\left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + \sqrt{2 \, x + 1}\right)}}{7 \, \sqrt{-\frac{1}{35} \, \sqrt{35} + \frac{1}{2}}}\right) - \frac{1}{11306068900} \, \sqrt{31} {\left(31710 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} - 151 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 302 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 63420 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} - 797720 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450} - 1595440 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450}\right)} \arctan\left(-\frac{5 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(\left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} - \sqrt{2 \, x + 1}\right)}}{7 \, \sqrt{-\frac{1}{35} \, \sqrt{35} + \frac{1}{2}}}\right) - \frac{1}{22612137800} \, \sqrt{31} {\left(151 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 31710 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} - 63420 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} + 302 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} - 797720 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450} + 1595440 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450}\right)} \log\left(2 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{2 \, x + 1} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + 2 \, x + \sqrt{\frac{7}{5}} + 1\right) + \frac{1}{22612137800} \, \sqrt{31} {\left(151 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 31710 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} - 63420 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} + 302 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} - 797720 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450} + 1595440 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450}\right)} \log\left(-2 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{2 \, x + 1} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + 2 \, x + \sqrt{\frac{7}{5}} + 1\right) - \frac{4 \, {\left(755 \, {\left(2 \, x + 1\right)}^{2} - 1348 \, x + 194\right)}}{1519 \, {\left(5 \, {\left(2 \, x + 1\right)}^{\frac{5}{2}} - 4 \, {\left(2 \, x + 1\right)}^{\frac{3}{2}} + 7 \, \sqrt{2 \, x + 1}\right)}}"," ",0,"-1/11306068900*sqrt(31)*(31710*sqrt(31)*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) - 151*sqrt(31)*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 302*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 63420*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) - 797720*sqrt(31)*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450) - 1595440*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450))*arctan(5/7*(7/5)^(3/4)*((7/5)^(1/4)*sqrt(1/35*sqrt(35) + 1/2) + sqrt(2*x + 1))/sqrt(-1/35*sqrt(35) + 1/2)) - 1/11306068900*sqrt(31)*(31710*sqrt(31)*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) - 151*sqrt(31)*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 302*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 63420*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) - 797720*sqrt(31)*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450) - 1595440*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450))*arctan(-5/7*(7/5)^(3/4)*((7/5)^(1/4)*sqrt(1/35*sqrt(35) + 1/2) - sqrt(2*x + 1))/sqrt(-1/35*sqrt(35) + 1/2)) - 1/22612137800*sqrt(31)*(151*sqrt(31)*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 31710*sqrt(31)*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) - 63420*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) + 302*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) - 797720*sqrt(31)*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450) + 1595440*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450))*log(2*(7/5)^(1/4)*sqrt(2*x + 1)*sqrt(1/35*sqrt(35) + 1/2) + 2*x + sqrt(7/5) + 1) + 1/22612137800*sqrt(31)*(151*sqrt(31)*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 31710*sqrt(31)*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) - 63420*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) + 302*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) - 797720*sqrt(31)*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450) + 1595440*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450))*log(-2*(7/5)^(1/4)*sqrt(2*x + 1)*sqrt(1/35*sqrt(35) + 1/2) + 2*x + sqrt(7/5) + 1) - 4/1519*(755*(2*x + 1)^2 - 1348*x + 194)/(5*(2*x + 1)^(5/2) - 4*(2*x + 1)^(3/2) + 7*sqrt(2*x + 1))","B",0
2322,1,638,0,0.994655," ","integrate(1/(1+2*x)^(5/2)/(5*x^2+3*x+2)^2,x, algorithm=""giac"")","-\frac{1}{7914248230} \, \sqrt{31} {\left(24570 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} - 117 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} - 234 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} - 49140 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} + 244510 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450} - 489020 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450}\right)} \arctan\left(\frac{5 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(\left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + \sqrt{2 \, x + 1}\right)}}{7 \, \sqrt{-\frac{1}{35} \, \sqrt{35} + \frac{1}{2}}}\right) - \frac{1}{7914248230} \, \sqrt{31} {\left(24570 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} - 117 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} - 234 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} - 49140 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} + 244510 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450} - 489020 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450}\right)} \arctan\left(-\frac{5 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(\left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} - \sqrt{2 \, x + 1}\right)}}{7 \, \sqrt{-\frac{1}{35} \, \sqrt{35} + \frac{1}{2}}}\right) - \frac{1}{15828496460} \, \sqrt{31} {\left(117 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 24570 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} + 49140 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} - 234 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 244510 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450} + 489020 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450}\right)} \log\left(2 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{2 \, x + 1} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + 2 \, x + \sqrt{\frac{7}{5}} + 1\right) + \frac{1}{15828496460} \, \sqrt{31} {\left(117 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 24570 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} + 49140 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} - 234 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 244510 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450} + 489020 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450}\right)} \log\left(-2 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{2 \, x + 1} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + 2 \, x + \sqrt{\frac{7}{5}} + 1\right) - \frac{4 \, {\left(890 \, {\left(2 \, x + 1\right)}^{\frac{3}{2}} + 233 \, \sqrt{2 \, x + 1}\right)}}{10633 \, {\left(5 \, {\left(2 \, x + 1\right)}^{2} - 8 \, x + 3\right)}} - \frac{16 \, {\left(48 \, x + 31\right)}}{1029 \, {\left(2 \, x + 1\right)}^{\frac{3}{2}}}"," ",0,"-1/7914248230*sqrt(31)*(24570*sqrt(31)*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) - 117*sqrt(31)*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) - 234*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) - 49140*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) + 244510*sqrt(31)*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450) - 489020*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450))*arctan(5/7*(7/5)^(3/4)*((7/5)^(1/4)*sqrt(1/35*sqrt(35) + 1/2) + sqrt(2*x + 1))/sqrt(-1/35*sqrt(35) + 1/2)) - 1/7914248230*sqrt(31)*(24570*sqrt(31)*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) - 117*sqrt(31)*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) - 234*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) - 49140*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) + 244510*sqrt(31)*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450) - 489020*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450))*arctan(-5/7*(7/5)^(3/4)*((7/5)^(1/4)*sqrt(1/35*sqrt(35) + 1/2) - sqrt(2*x + 1))/sqrt(-1/35*sqrt(35) + 1/2)) - 1/15828496460*sqrt(31)*(117*sqrt(31)*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 24570*sqrt(31)*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) + 49140*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) - 234*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 244510*sqrt(31)*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450) + 489020*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450))*log(2*(7/5)^(1/4)*sqrt(2*x + 1)*sqrt(1/35*sqrt(35) + 1/2) + 2*x + sqrt(7/5) + 1) + 1/15828496460*sqrt(31)*(117*sqrt(31)*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 24570*sqrt(31)*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) + 49140*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) - 234*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 244510*sqrt(31)*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450) + 489020*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450))*log(-2*(7/5)^(1/4)*sqrt(2*x + 1)*sqrt(1/35*sqrt(35) + 1/2) + 2*x + sqrt(7/5) + 1) - 4/10633*(890*(2*x + 1)^(3/2) + 233*sqrt(2*x + 1))/(5*(2*x + 1)^2 - 8*x + 3) - 16/1029*(48*x + 31)/(2*x + 1)^(3/2)","B",0
2323,1,642,0,1.439435," ","integrate((1+2*x)^(9/2)/(5*x^2+3*x+2)^3,x, algorithm=""giac"")","\frac{3}{1788204775000} \, \sqrt{31} {\left(1549590 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} - 7379 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 14758 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 3099180 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} + 9055200 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450} + 18110400 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450}\right)} \arctan\left(\frac{5 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(\left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + \sqrt{2 \, x + 1}\right)}}{7 \, \sqrt{-\frac{1}{35} \, \sqrt{35} + \frac{1}{2}}}\right) + \frac{3}{1788204775000} \, \sqrt{31} {\left(1549590 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} - 7379 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 14758 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 3099180 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} + 9055200 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450} + 18110400 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450}\right)} \arctan\left(-\frac{5 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(\left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} - \sqrt{2 \, x + 1}\right)}}{7 \, \sqrt{-\frac{1}{35} \, \sqrt{35} + \frac{1}{2}}}\right) + \frac{3}{3576409550000} \, \sqrt{31} {\left(7379 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 1549590 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} - 3099180 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} + 14758 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 9055200 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450} - 18110400 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450}\right)} \log\left(2 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{2 \, x + 1} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + 2 \, x + \sqrt{\frac{7}{5}} + 1\right) - \frac{3}{3576409550000} \, \sqrt{31} {\left(7379 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 1549590 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} - 3099180 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} + 14758 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 9055200 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450} - 18110400 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450}\right)} \log\left(-2 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{2 \, x + 1} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + 2 \, x + \sqrt{\frac{7}{5}} + 1\right) - \frac{2 \, {\left(43075 \, {\left(2 \, x + 1\right)}^{\frac{7}{2}} + 15332 \, {\left(2 \, x + 1\right)}^{\frac{5}{2}} + 14693 \, {\left(2 \, x + 1\right)}^{\frac{3}{2}} + 38808 \, \sqrt{2 \, x + 1}\right)}}{24025 \, {\left(5 \, {\left(2 \, x + 1\right)}^{2} - 8 \, x + 3\right)}^{2}}"," ",0,"3/1788204775000*sqrt(31)*(1549590*sqrt(31)*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) - 7379*sqrt(31)*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 14758*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 3099180*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) + 9055200*sqrt(31)*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450) + 18110400*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450))*arctan(5/7*(7/5)^(3/4)*((7/5)^(1/4)*sqrt(1/35*sqrt(35) + 1/2) + sqrt(2*x + 1))/sqrt(-1/35*sqrt(35) + 1/2)) + 3/1788204775000*sqrt(31)*(1549590*sqrt(31)*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) - 7379*sqrt(31)*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 14758*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 3099180*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) + 9055200*sqrt(31)*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450) + 18110400*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450))*arctan(-5/7*(7/5)^(3/4)*((7/5)^(1/4)*sqrt(1/35*sqrt(35) + 1/2) - sqrt(2*x + 1))/sqrt(-1/35*sqrt(35) + 1/2)) + 3/3576409550000*sqrt(31)*(7379*sqrt(31)*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 1549590*sqrt(31)*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) - 3099180*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) + 14758*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 9055200*sqrt(31)*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450) - 18110400*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450))*log(2*(7/5)^(1/4)*sqrt(2*x + 1)*sqrt(1/35*sqrt(35) + 1/2) + 2*x + sqrt(7/5) + 1) - 3/3576409550000*sqrt(31)*(7379*sqrt(31)*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 1549590*sqrt(31)*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) - 3099180*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) + 14758*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 9055200*sqrt(31)*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450) - 18110400*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450))*log(-2*(7/5)^(1/4)*sqrt(2*x + 1)*sqrt(1/35*sqrt(35) + 1/2) + 2*x + sqrt(7/5) + 1) - 2/24025*(43075*(2*x + 1)^(7/2) + 15332*(2*x + 1)^(5/2) + 14693*(2*x + 1)^(3/2) + 38808*sqrt(2*x + 1))/(5*(2*x + 1)^2 - 8*x + 3)^2","B",0
2324,1,642,0,1.425881," ","integrate((1+2*x)^(7/2)/(5*x^2+3*x+2)^3,x, algorithm=""giac"")","\frac{1}{89410238750} \, \sqrt{31} {\left(28560 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} - 136 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 272 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 57120 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} + 1534925 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450} + 3069850 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450}\right)} \arctan\left(\frac{5 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(\left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + \sqrt{2 \, x + 1}\right)}}{7 \, \sqrt{-\frac{1}{35} \, \sqrt{35} + \frac{1}{2}}}\right) + \frac{1}{89410238750} \, \sqrt{31} {\left(28560 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} - 136 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 272 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 57120 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} + 1534925 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450} + 3069850 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450}\right)} \arctan\left(-\frac{5 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(\left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} - \sqrt{2 \, x + 1}\right)}}{7 \, \sqrt{-\frac{1}{35} \, \sqrt{35} + \frac{1}{2}}}\right) + \frac{1}{178820477500} \, \sqrt{31} {\left(136 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 28560 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} - 57120 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} + 272 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 1534925 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450} - 3069850 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450}\right)} \log\left(2 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{2 \, x + 1} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + 2 \, x + \sqrt{\frac{7}{5}} + 1\right) - \frac{1}{178820477500} \, \sqrt{31} {\left(136 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 28560 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} - 57120 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} + 272 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 1534925 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450} - 3069850 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450}\right)} \log\left(-2 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{2 \, x + 1} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + 2 \, x + \sqrt{\frac{7}{5}} + 1\right) + \frac{2 \, {\left(2720 \, {\left(2 \, x + 1\right)}^{\frac{7}{2}} - 11789 \, {\left(2 \, x + 1\right)}^{\frac{5}{2}} + 7084 \, {\left(2 \, x + 1\right)}^{\frac{3}{2}} - 8771 \, \sqrt{2 \, x + 1}\right)}}{4805 \, {\left(5 \, {\left(2 \, x + 1\right)}^{2} - 8 \, x + 3\right)}^{2}}"," ",0,"1/89410238750*sqrt(31)*(28560*sqrt(31)*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) - 136*sqrt(31)*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 272*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 57120*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) + 1534925*sqrt(31)*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450) + 3069850*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450))*arctan(5/7*(7/5)^(3/4)*((7/5)^(1/4)*sqrt(1/35*sqrt(35) + 1/2) + sqrt(2*x + 1))/sqrt(-1/35*sqrt(35) + 1/2)) + 1/89410238750*sqrt(31)*(28560*sqrt(31)*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) - 136*sqrt(31)*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 272*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 57120*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) + 1534925*sqrt(31)*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450) + 3069850*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450))*arctan(-5/7*(7/5)^(3/4)*((7/5)^(1/4)*sqrt(1/35*sqrt(35) + 1/2) - sqrt(2*x + 1))/sqrt(-1/35*sqrt(35) + 1/2)) + 1/178820477500*sqrt(31)*(136*sqrt(31)*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 28560*sqrt(31)*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) - 57120*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) + 272*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 1534925*sqrt(31)*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450) - 3069850*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450))*log(2*(7/5)^(1/4)*sqrt(2*x + 1)*sqrt(1/35*sqrt(35) + 1/2) + 2*x + sqrt(7/5) + 1) - 1/178820477500*sqrt(31)*(136*sqrt(31)*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 28560*sqrt(31)*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) - 57120*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) + 272*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 1534925*sqrt(31)*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450) - 3069850*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450))*log(-2*(7/5)^(1/4)*sqrt(2*x + 1)*sqrt(1/35*sqrt(35) + 1/2) + 2*x + sqrt(7/5) + 1) + 2/4805*(2720*(2*x + 1)^(7/2) - 11789*(2*x + 1)^(5/2) + 7084*(2*x + 1)^(3/2) - 8771*sqrt(2*x + 1))/(5*(2*x + 1)^2 - 8*x + 3)^2","B",0
2325,1,642,0,1.427715," ","integrate((1+2*x)^(5/2)/(5*x^2+3*x+2)^3,x, algorithm=""giac"")","\frac{3}{71528191000} \, \sqrt{31} {\left(8190 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} - 39 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 78 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 16380 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} + 137200 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450} + 274400 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450}\right)} \arctan\left(\frac{5 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(\left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + \sqrt{2 \, x + 1}\right)}}{7 \, \sqrt{-\frac{1}{35} \, \sqrt{35} + \frac{1}{2}}}\right) + \frac{3}{71528191000} \, \sqrt{31} {\left(8190 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} - 39 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 78 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 16380 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} + 137200 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450} + 274400 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450}\right)} \arctan\left(-\frac{5 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(\left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} - \sqrt{2 \, x + 1}\right)}}{7 \, \sqrt{-\frac{1}{35} \, \sqrt{35} + \frac{1}{2}}}\right) + \frac{3}{143056382000} \, \sqrt{31} {\left(39 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 8190 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} - 16380 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} + 78 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 137200 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450} - 274400 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450}\right)} \log\left(2 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{2 \, x + 1} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + 2 \, x + \sqrt{\frac{7}{5}} + 1\right) - \frac{3}{143056382000} \, \sqrt{31} {\left(39 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 8190 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} - 16380 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} + 78 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 137200 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450} - 274400 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450}\right)} \log\left(-2 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{2 \, x + 1} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + 2 \, x + \sqrt{\frac{7}{5}} + 1\right) + \frac{2 \, {\left(585 \, {\left(2 \, x + 1\right)}^{\frac{7}{2}} - 640 \, {\left(2 \, x + 1\right)}^{\frac{5}{2}} + 287 \, {\left(2 \, x + 1\right)}^{\frac{3}{2}} - 588 \, \sqrt{2 \, x + 1}\right)}}{961 \, {\left(5 \, {\left(2 \, x + 1\right)}^{2} - 8 \, x + 3\right)}^{2}}"," ",0,"3/71528191000*sqrt(31)*(8190*sqrt(31)*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) - 39*sqrt(31)*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 78*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 16380*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) + 137200*sqrt(31)*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450) + 274400*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450))*arctan(5/7*(7/5)^(3/4)*((7/5)^(1/4)*sqrt(1/35*sqrt(35) + 1/2) + sqrt(2*x + 1))/sqrt(-1/35*sqrt(35) + 1/2)) + 3/71528191000*sqrt(31)*(8190*sqrt(31)*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) - 39*sqrt(31)*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 78*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 16380*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) + 137200*sqrt(31)*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450) + 274400*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450))*arctan(-5/7*(7/5)^(3/4)*((7/5)^(1/4)*sqrt(1/35*sqrt(35) + 1/2) - sqrt(2*x + 1))/sqrt(-1/35*sqrt(35) + 1/2)) + 3/143056382000*sqrt(31)*(39*sqrt(31)*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 8190*sqrt(31)*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) - 16380*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) + 78*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 137200*sqrt(31)*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450) - 274400*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450))*log(2*(7/5)^(1/4)*sqrt(2*x + 1)*sqrt(1/35*sqrt(35) + 1/2) + 2*x + sqrt(7/5) + 1) - 3/143056382000*sqrt(31)*(39*sqrt(31)*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 8190*sqrt(31)*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) - 16380*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) + 78*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 137200*sqrt(31)*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450) - 274400*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450))*log(-2*(7/5)^(1/4)*sqrt(2*x + 1)*sqrt(1/35*sqrt(35) + 1/2) + 2*x + sqrt(7/5) + 1) + 2/961*(585*(2*x + 1)^(7/2) - 640*(2*x + 1)^(5/2) + 287*(2*x + 1)^(3/2) - 588*sqrt(2*x + 1))/(5*(2*x + 1)^2 - 8*x + 3)^2","B",0
2326,1,640,0,1.432577," ","integrate((1+2*x)^(3/2)/(5*x^2+3*x+2)^3,x, algorithm=""giac"")","\frac{3}{3576409550} \, \sqrt{31} {\left(210 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} - \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 2 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 420 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} + 9555 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450} + 19110 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450}\right)} \arctan\left(\frac{5 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(\left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + \sqrt{2 \, x + 1}\right)}}{7 \, \sqrt{-\frac{1}{35} \, \sqrt{35} + \frac{1}{2}}}\right) + \frac{3}{3576409550} \, \sqrt{31} {\left(210 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} - \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 2 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 420 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} + 9555 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450} + 19110 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450}\right)} \arctan\left(-\frac{5 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(\left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} - \sqrt{2 \, x + 1}\right)}}{7 \, \sqrt{-\frac{1}{35} \, \sqrt{35} + \frac{1}{2}}}\right) + \frac{3}{7152819100} \, \sqrt{31} {\left(\sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 210 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} - 420 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} + 2 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 9555 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450} - 19110 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450}\right)} \log\left(2 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{2 \, x + 1} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + 2 \, x + \sqrt{\frac{7}{5}} + 1\right) - \frac{3}{7152819100} \, \sqrt{31} {\left(\sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 210 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} - 420 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} + 2 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 9555 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450} - 19110 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450}\right)} \log\left(-2 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{2 \, x + 1} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + 2 \, x + \sqrt{\frac{7}{5}} + 1\right) + \frac{2 \, {\left(300 \, {\left(2 \, x + 1\right)}^{\frac{7}{2}} - 205 \, {\left(2 \, x + 1\right)}^{\frac{5}{2}} + 640 \, {\left(2 \, x + 1\right)}^{\frac{3}{2}} - 819 \, \sqrt{2 \, x + 1}\right)}}{961 \, {\left(5 \, {\left(2 \, x + 1\right)}^{2} - 8 \, x + 3\right)}^{2}}"," ",0,"3/3576409550*sqrt(31)*(210*sqrt(31)*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) - sqrt(31)*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 2*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 420*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) + 9555*sqrt(31)*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450) + 19110*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450))*arctan(5/7*(7/5)^(3/4)*((7/5)^(1/4)*sqrt(1/35*sqrt(35) + 1/2) + sqrt(2*x + 1))/sqrt(-1/35*sqrt(35) + 1/2)) + 3/3576409550*sqrt(31)*(210*sqrt(31)*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) - sqrt(31)*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 2*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 420*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) + 9555*sqrt(31)*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450) + 19110*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450))*arctan(-5/7*(7/5)^(3/4)*((7/5)^(1/4)*sqrt(1/35*sqrt(35) + 1/2) - sqrt(2*x + 1))/sqrt(-1/35*sqrt(35) + 1/2)) + 3/7152819100*sqrt(31)*(sqrt(31)*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 210*sqrt(31)*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) - 420*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) + 2*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 9555*sqrt(31)*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450) - 19110*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450))*log(2*(7/5)^(1/4)*sqrt(2*x + 1)*sqrt(1/35*sqrt(35) + 1/2) + 2*x + sqrt(7/5) + 1) - 3/7152819100*sqrt(31)*(sqrt(31)*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 210*sqrt(31)*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) - 420*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) + 2*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 9555*sqrt(31)*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450) - 19110*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450))*log(-2*(7/5)^(1/4)*sqrt(2*x + 1)*sqrt(1/35*sqrt(35) + 1/2) + 2*x + sqrt(7/5) + 1) + 2/961*(300*(2*x + 1)^(7/2) - 205*(2*x + 1)^(5/2) + 640*(2*x + 1)^(3/2) - 819*sqrt(2*x + 1))/(5*(2*x + 1)^2 - 8*x + 3)^2","B",0
2327,1,642,0,1.428199," ","integrate((1+2*x)^(1/2)/(5*x^2+3*x+2)^3,x, algorithm=""giac"")","\frac{1}{100139467400} \, \sqrt{31} {\left(37590 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} - 179 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 358 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 75180 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} + 533120 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450} + 1066240 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450}\right)} \arctan\left(\frac{5 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(\left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + \sqrt{2 \, x + 1}\right)}}{7 \, \sqrt{-\frac{1}{35} \, \sqrt{35} + \frac{1}{2}}}\right) + \frac{1}{100139467400} \, \sqrt{31} {\left(37590 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} - 179 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 358 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 75180 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} + 533120 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450} + 1066240 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450}\right)} \arctan\left(-\frac{5 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(\left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} - \sqrt{2 \, x + 1}\right)}}{7 \, \sqrt{-\frac{1}{35} \, \sqrt{35} + \frac{1}{2}}}\right) + \frac{1}{200278934800} \, \sqrt{31} {\left(179 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 37590 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} - 75180 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} + 358 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 533120 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450} - 1066240 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450}\right)} \log\left(2 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{2 \, x + 1} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + 2 \, x + \sqrt{\frac{7}{5}} + 1\right) - \frac{1}{200278934800} \, \sqrt{31} {\left(179 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 37590 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} - 75180 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} + 358 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 533120 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450} - 1066240 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450}\right)} \log\left(-2 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{2 \, x + 1} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + 2 \, x + \sqrt{\frac{7}{5}} + 1\right) + \frac{2 \, {\left(4475 \, {\left(2 \, x + 1\right)}^{\frac{7}{2}} - 5060 \, {\left(2 \, x + 1\right)}^{\frac{5}{2}} + 11789 \, {\left(2 \, x + 1\right)}^{\frac{3}{2}} - 3808 \, \sqrt{2 \, x + 1}\right)}}{6727 \, {\left(5 \, {\left(2 \, x + 1\right)}^{2} - 8 \, x + 3\right)}^{2}}"," ",0,"1/100139467400*sqrt(31)*(37590*sqrt(31)*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) - 179*sqrt(31)*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 358*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 75180*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) + 533120*sqrt(31)*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450) + 1066240*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450))*arctan(5/7*(7/5)^(3/4)*((7/5)^(1/4)*sqrt(1/35*sqrt(35) + 1/2) + sqrt(2*x + 1))/sqrt(-1/35*sqrt(35) + 1/2)) + 1/100139467400*sqrt(31)*(37590*sqrt(31)*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) - 179*sqrt(31)*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 358*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 75180*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) + 533120*sqrt(31)*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450) + 1066240*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450))*arctan(-5/7*(7/5)^(3/4)*((7/5)^(1/4)*sqrt(1/35*sqrt(35) + 1/2) - sqrt(2*x + 1))/sqrt(-1/35*sqrt(35) + 1/2)) + 1/200278934800*sqrt(31)*(179*sqrt(31)*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 37590*sqrt(31)*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) - 75180*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) + 358*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 533120*sqrt(31)*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450) - 1066240*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450))*log(2*(7/5)^(1/4)*sqrt(2*x + 1)*sqrt(1/35*sqrt(35) + 1/2) + 2*x + sqrt(7/5) + 1) - 1/200278934800*sqrt(31)*(179*sqrt(31)*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 37590*sqrt(31)*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) - 75180*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) + 358*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 533120*sqrt(31)*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450) - 1066240*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450))*log(-2*(7/5)^(1/4)*sqrt(2*x + 1)*sqrt(1/35*sqrt(35) + 1/2) + 2*x + sqrt(7/5) + 1) + 2/6727*(4475*(2*x + 1)^(7/2) - 5060*(2*x + 1)^(5/2) + 11789*(2*x + 1)^(3/2) - 3808*sqrt(2*x + 1))/(5*(2*x + 1)^2 - 8*x + 3)^2","B",0
2328,1,642,0,0.990041," ","integrate(1/(1+2*x)^(1/2)/(5*x^2+3*x+2)^3,x, algorithm=""giac"")","\frac{3}{175244067950} \, \sqrt{31} {\left(13860 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} - 66 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 132 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 27720 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} + 1807855 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450} + 3615710 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450}\right)} \arctan\left(\frac{5 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(\left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + \sqrt{2 \, x + 1}\right)}}{7 \, \sqrt{-\frac{1}{35} \, \sqrt{35} + \frac{1}{2}}}\right) + \frac{3}{175244067950} \, \sqrt{31} {\left(13860 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} - 66 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 132 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 27720 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} + 1807855 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450} + 3615710 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450}\right)} \arctan\left(-\frac{5 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(\left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} - \sqrt{2 \, x + 1}\right)}}{7 \, \sqrt{-\frac{1}{35} \, \sqrt{35} + \frac{1}{2}}}\right) + \frac{3}{350488135900} \, \sqrt{31} {\left(66 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 13860 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} - 27720 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} + 132 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 1807855 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450} - 3615710 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450}\right)} \log\left(2 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{2 \, x + 1} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + 2 \, x + \sqrt{\frac{7}{5}} + 1\right) - \frac{3}{350488135900} \, \sqrt{31} {\left(66 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 13860 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} - 27720 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} + 132 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 1807855 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450} - 3615710 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450}\right)} \log\left(-2 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{2 \, x + 1} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + 2 \, x + \sqrt{\frac{7}{5}} + 1\right) + \frac{2 \, {\left(19800 \, {\left(2 \, x + 1\right)}^{\frac{7}{2}} + 10495 \, {\left(2 \, x + 1\right)}^{\frac{5}{2}} + 15332 \, {\left(2 \, x + 1\right)}^{\frac{3}{2}} + 60305 \, \sqrt{2 \, x + 1}\right)}}{47089 \, {\left(5 \, {\left(2 \, x + 1\right)}^{2} - 8 \, x + 3\right)}^{2}}"," ",0,"3/175244067950*sqrt(31)*(13860*sqrt(31)*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) - 66*sqrt(31)*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 132*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 27720*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) + 1807855*sqrt(31)*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450) + 3615710*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450))*arctan(5/7*(7/5)^(3/4)*((7/5)^(1/4)*sqrt(1/35*sqrt(35) + 1/2) + sqrt(2*x + 1))/sqrt(-1/35*sqrt(35) + 1/2)) + 3/175244067950*sqrt(31)*(13860*sqrt(31)*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) - 66*sqrt(31)*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 132*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 27720*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) + 1807855*sqrt(31)*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450) + 3615710*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450))*arctan(-5/7*(7/5)^(3/4)*((7/5)^(1/4)*sqrt(1/35*sqrt(35) + 1/2) - sqrt(2*x + 1))/sqrt(-1/35*sqrt(35) + 1/2)) + 3/350488135900*sqrt(31)*(66*sqrt(31)*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 13860*sqrt(31)*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) - 27720*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) + 132*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 1807855*sqrt(31)*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450) - 3615710*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450))*log(2*(7/5)^(1/4)*sqrt(2*x + 1)*sqrt(1/35*sqrt(35) + 1/2) + 2*x + sqrt(7/5) + 1) - 3/350488135900*sqrt(31)*(66*sqrt(31)*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 13860*sqrt(31)*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) - 27720*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) + 132*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 1807855*sqrt(31)*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450) - 3615710*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450))*log(-2*(7/5)^(1/4)*sqrt(2*x + 1)*sqrt(1/35*sqrt(35) + 1/2) + 2*x + sqrt(7/5) + 1) + 2/47089*(19800*(2*x + 1)^(7/2) + 10495*(2*x + 1)^(5/2) + 15332*(2*x + 1)^(3/2) + 60305*sqrt(2*x + 1))/(5*(2*x + 1)^2 - 8*x + 3)^2","B",0
2329,1,651,0,1.052008," ","integrate(1/(1+2*x)^(3/2)/(5*x^2+3*x+2)^3,x, algorithm=""giac"")","-\frac{3}{981366780520} \, \sqrt{31} {\left(567630 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} - 2703 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 5406 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 1135260 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} - 17730160 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450} - 35460320 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450}\right)} \arctan\left(\frac{5 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(\left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + \sqrt{2 \, x + 1}\right)}}{7 \, \sqrt{-\frac{1}{35} \, \sqrt{35} + \frac{1}{2}}}\right) - \frac{3}{981366780520} \, \sqrt{31} {\left(567630 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} - 2703 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 5406 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 1135260 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} - 17730160 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450} - 35460320 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450}\right)} \arctan\left(-\frac{5 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(\left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} - \sqrt{2 \, x + 1}\right)}}{7 \, \sqrt{-\frac{1}{35} \, \sqrt{35} + \frac{1}{2}}}\right) - \frac{3}{1962733561040} \, \sqrt{31} {\left(2703 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 567630 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} - 1135260 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} + 5406 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} - 17730160 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450} + 35460320 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450}\right)} \log\left(2 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{2 \, x + 1} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + 2 \, x + \sqrt{\frac{7}{5}} + 1\right) + \frac{3}{1962733561040} \, \sqrt{31} {\left(2703 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} + 567630 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{3}{4}} \sqrt{140 \, \sqrt{35} + 2450} {\left(2 \, \sqrt{35} - 35\right)} - 1135260 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(2 \, \sqrt{35} + 35\right)} \sqrt{-140 \, \sqrt{35} + 2450} + 5406 \, \left(\frac{7}{5}\right)^{\frac{3}{4}} {\left(-140 \, \sqrt{35} + 2450\right)}^{\frac{3}{2}} - 17730160 \, \sqrt{31} \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{140 \, \sqrt{35} + 2450} + 35460320 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{-140 \, \sqrt{35} + 2450}\right)} \log\left(-2 \, \left(\frac{7}{5}\right)^{\frac{1}{4}} \sqrt{2 \, x + 1} \sqrt{\frac{1}{35} \, \sqrt{35} + \frac{1}{2}} + 2 \, x + \sqrt{\frac{7}{5}} + 1\right) - \frac{64}{343 \, \sqrt{2 \, x + 1}} - \frac{2 \, {\left(34975 \, {\left(2 \, x + 1\right)}^{\frac{7}{2}} - 81960 \, {\left(2 \, x + 1\right)}^{\frac{5}{2}} + 108889 \, {\left(2 \, x + 1\right)}^{\frac{3}{2}} - 97644 \, \sqrt{2 \, x + 1}\right)}}{47089 \, {\left(5 \, {\left(2 \, x + 1\right)}^{2} - 8 \, x + 3\right)}^{2}}"," ",0,"-3/981366780520*sqrt(31)*(567630*sqrt(31)*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) - 2703*sqrt(31)*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 5406*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 1135260*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) - 17730160*sqrt(31)*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450) - 35460320*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450))*arctan(5/7*(7/5)^(3/4)*((7/5)^(1/4)*sqrt(1/35*sqrt(35) + 1/2) + sqrt(2*x + 1))/sqrt(-1/35*sqrt(35) + 1/2)) - 3/981366780520*sqrt(31)*(567630*sqrt(31)*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) - 2703*sqrt(31)*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) + 5406*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 1135260*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) - 17730160*sqrt(31)*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450) - 35460320*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450))*arctan(-5/7*(7/5)^(3/4)*((7/5)^(1/4)*sqrt(1/35*sqrt(35) + 1/2) - sqrt(2*x + 1))/sqrt(-1/35*sqrt(35) + 1/2)) - 3/1962733561040*sqrt(31)*(2703*sqrt(31)*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 567630*sqrt(31)*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) - 1135260*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) + 5406*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) - 17730160*sqrt(31)*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450) + 35460320*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450))*log(2*(7/5)^(1/4)*sqrt(2*x + 1)*sqrt(1/35*sqrt(35) + 1/2) + 2*x + sqrt(7/5) + 1) + 3/1962733561040*sqrt(31)*(2703*sqrt(31)*(7/5)^(3/4)*(140*sqrt(35) + 2450)^(3/2) + 567630*sqrt(31)*(7/5)^(3/4)*sqrt(140*sqrt(35) + 2450)*(2*sqrt(35) - 35) - 1135260*(7/5)^(3/4)*(2*sqrt(35) + 35)*sqrt(-140*sqrt(35) + 2450) + 5406*(7/5)^(3/4)*(-140*sqrt(35) + 2450)^(3/2) - 17730160*sqrt(31)*(7/5)^(1/4)*sqrt(140*sqrt(35) + 2450) + 35460320*(7/5)^(1/4)*sqrt(-140*sqrt(35) + 2450))*log(-2*(7/5)^(1/4)*sqrt(2*x + 1)*sqrt(1/35*sqrt(35) + 1/2) + 2*x + sqrt(7/5) + 1) - 64/343/sqrt(2*x + 1) - 2/47089*(34975*(2*x + 1)^(7/2) - 81960*(2*x + 1)^(5/2) + 108889*(2*x + 1)^(3/2) - 97644*sqrt(2*x + 1))/(5*(2*x + 1)^2 - 8*x + 3)^2","B",0
2330,1,2436,0,3.238305," ","integrate(x^(9/2)/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{3 \, {\left(\sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{7} - 16 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{5} c - 2 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} c - 2 \, b^{7} c + 80 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} + 24 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} + 32 \, a b^{5} c^{2} - 2 \, b^{6} c^{2} - 128 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 64 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 12 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} - 160 \, a^{2} b^{3} c^{3} + 28 \, a b^{4} c^{3} + 32 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} + 256 \, a^{3} b c^{4} - 192 \, a^{2} b^{2} c^{4} + 448 \, a^{3} c^{5} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} - 14 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c - 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c + 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} + 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} + \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} - 224 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} - 112 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} - 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} + 56 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c - 24 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{2} + 64 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{3} - 20 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} + 112 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x}}{\sqrt{\frac{b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4} + \sqrt{{\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)}^{2} - 4 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)}}}{b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}}}\right)}{16 \, {\left(b^{8} c^{2} - 16 \, a b^{6} c^{3} - 2 \, b^{7} c^{3} + 96 \, a^{2} b^{4} c^{4} + 24 \, a b^{5} c^{4} + b^{6} c^{4} - 256 \, a^{3} b^{2} c^{5} - 96 \, a^{2} b^{3} c^{5} - 12 \, a b^{4} c^{5} + 256 \, a^{4} c^{6} + 128 \, a^{3} b c^{6} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}\right)} {\left| c \right|}} + \frac{3 \, {\left(\sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{7} - 16 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{5} c - 2 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} c + 2 \, b^{7} c + 80 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{3} c^{2} + 24 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c^{2} + \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c^{2} - 32 \, a b^{5} c^{2} + 2 \, b^{6} c^{2} - 128 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b c^{3} - 64 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{3} - 12 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{3} + 160 \, a^{2} b^{3} c^{3} - 28 \, a b^{4} c^{3} + 32 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{4} - 256 \, a^{3} b c^{4} + 192 \, a^{2} b^{2} c^{4} - 448 \, a^{3} c^{5} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} + 14 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c + 2 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c - 96 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 20 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} - \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} + 224 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} + 112 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - 56 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{5} c + 24 \, {\left(b^{2} - 4 \, a c\right)} a b^{3} c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{2} - 64 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b c^{3} + 20 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} - 112 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x}}{\sqrt{\frac{b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4} - \sqrt{{\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)}^{2} - 4 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)}}}{b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}}}\right)}{16 \, {\left(b^{8} c^{2} - 16 \, a b^{6} c^{3} - 2 \, b^{7} c^{3} + 96 \, a^{2} b^{4} c^{4} + 24 \, a b^{5} c^{4} + b^{6} c^{4} - 256 \, a^{3} b^{2} c^{5} - 96 \, a^{2} b^{3} c^{5} - 12 \, a b^{4} c^{5} + 256 \, a^{4} c^{6} + 128 \, a^{3} b c^{6} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}\right)} {\left| c \right|}} - \frac{5 \, b^{4} c x^{\frac{7}{2}} - 37 \, a b^{2} c^{2} x^{\frac{7}{2}} + 44 \, a^{2} c^{3} x^{\frac{7}{2}} + 3 \, b^{5} x^{\frac{5}{2}} - 20 \, a b^{3} c x^{\frac{5}{2}} - 4 \, a^{2} b c^{2} x^{\frac{5}{2}} + 6 \, a b^{4} x^{\frac{3}{2}} - 49 \, a^{2} b^{2} c x^{\frac{3}{2}} + 28 \, a^{3} c^{2} x^{\frac{3}{2}} + 3 \, a^{2} b^{3} \sqrt{x} - 24 \, a^{3} b c \sqrt{x}}{4 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} {\left(c x^{2} + b x + a\right)}^{2}}"," ",0,"3/16*(sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^7 - 16*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^5*c - 2*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6*c - 2*b^7*c + 80*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^2 + 24*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 + sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c^2 + 32*a*b^5*c^2 - 2*b^6*c^2 - 128*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 - 64*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 - 12*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 - 160*a^2*b^3*c^3 + 28*a*b^4*c^3 + 32*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 + 256*a^3*b*c^4 - 192*a^2*b^2*c^4 + 448*a^3*c^5 + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6 - 14*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c - 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c + 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 + 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 + sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^2 - 224*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^3 - 112*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 - 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 + 56*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^4 + 2*(b^2 - 4*a*c)*b^5*c - 24*(b^2 - 4*a*c)*a*b^3*c^2 + 2*(b^2 - 4*a*c)*b^4*c^2 + 64*(b^2 - 4*a*c)*a^2*b*c^3 - 20*(b^2 - 4*a*c)*a*b^2*c^3 + 112*(b^2 - 4*a*c)*a^2*c^4)*arctan(2*sqrt(1/2)*sqrt(x)/sqrt((b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4 + sqrt((b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)^2 - 4*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)))/(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)))/((b^8*c^2 - 16*a*b^6*c^3 - 2*b^7*c^3 + 96*a^2*b^4*c^4 + 24*a*b^5*c^4 + b^6*c^4 - 256*a^3*b^2*c^5 - 96*a^2*b^3*c^5 - 12*a*b^4*c^5 + 256*a^4*c^6 + 128*a^3*b*c^6 + 48*a^2*b^2*c^6 - 64*a^3*c^7)*abs(c)) + 3/16*(sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^7 - 16*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^5*c - 2*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6*c + 2*b^7*c + 80*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^3*c^2 + 24*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c^2 + sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c^2 - 32*a*b^5*c^2 + 2*b^6*c^2 - 128*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b*c^3 - 64*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^3 - 12*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^3 + 160*a^2*b^3*c^3 - 28*a*b^4*c^3 + 32*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^4 - 256*a^3*b*c^4 + 192*a^2*b^2*c^4 - 448*a^3*c^5 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6 + 14*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c + 2*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c - 96*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 - 20*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 - sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^2 + 224*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^3 + 112*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 - 56*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^4 - 2*(b^2 - 4*a*c)*b^5*c + 24*(b^2 - 4*a*c)*a*b^3*c^2 - 2*(b^2 - 4*a*c)*b^4*c^2 - 64*(b^2 - 4*a*c)*a^2*b*c^3 + 20*(b^2 - 4*a*c)*a*b^2*c^3 - 112*(b^2 - 4*a*c)*a^2*c^4)*arctan(2*sqrt(1/2)*sqrt(x)/sqrt((b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4 - sqrt((b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)^2 - 4*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)))/(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)))/((b^8*c^2 - 16*a*b^6*c^3 - 2*b^7*c^3 + 96*a^2*b^4*c^4 + 24*a*b^5*c^4 + b^6*c^4 - 256*a^3*b^2*c^5 - 96*a^2*b^3*c^5 - 12*a*b^4*c^5 + 256*a^4*c^6 + 128*a^3*b*c^6 + 48*a^2*b^2*c^6 - 64*a^3*c^7)*abs(c)) - 1/4*(5*b^4*c*x^(7/2) - 37*a*b^2*c^2*x^(7/2) + 44*a^2*c^3*x^(7/2) + 3*b^5*x^(5/2) - 20*a*b^3*c*x^(5/2) - 4*a^2*b*c^2*x^(5/2) + 6*a*b^4*x^(3/2) - 49*a^2*b^2*c*x^(3/2) + 28*a^3*c^2*x^(3/2) + 3*a^2*b^3*sqrt(x) - 24*a^3*b*c*sqrt(x))/((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*(c*x^2 + b*x + a)^2)","B",0
2331,1,5281,0,1.172354," ","integrate(1/x^(3/2)/(c*x^2+b*x+a)^3,x, algorithm=""giac"")","-\frac{3 \, {\left(10 \, a^{6} b^{14} c^{2} - 254 \, a^{7} b^{12} c^{3} + 2712 \, a^{8} b^{10} c^{4} - 15552 \, a^{9} b^{8} c^{5} + 50432 \, a^{10} b^{6} c^{6} - 87552 \, a^{11} b^{4} c^{7} + 63488 \, a^{12} b^{2} c^{8} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{14} + 127 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{12} c + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{13} c - 1356 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{10} c^{2} - 214 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{11} c^{2} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{12} c^{2} + 7776 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{8} c^{3} + 1856 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{9} c^{3} + 107 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{10} c^{3} - 25216 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{6} c^{4} - 8128 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{7} c^{4} - 928 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{8} c^{4} + 43776 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{11} b^{4} c^{5} + 17920 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{5} c^{5} + 4064 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{6} c^{5} - 31744 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{12} b^{2} c^{6} - 15872 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{11} b^{3} c^{6} - 8960 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{4} c^{6} + 7936 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{11} b^{2} c^{7} - 10 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{12} c^{2} + 214 \, {\left(b^{2} - 4 \, a c\right)} a^{7} b^{10} c^{3} - 1856 \, {\left(b^{2} - 4 \, a c\right)} a^{8} b^{8} c^{4} + 8128 \, {\left(b^{2} - 4 \, a c\right)} a^{9} b^{6} c^{5} - 17920 \, {\left(b^{2} - 4 \, a c\right)} a^{10} b^{4} c^{6} + 15872 \, {\left(b^{2} - 4 \, a c\right)} a^{11} b^{2} c^{7} + {\left(10 \, b^{6} c^{2} - 114 \, a b^{4} c^{3} + 416 \, a^{2} b^{2} c^{4} - 480 \, a^{3} c^{5} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{6} + 57 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{4} c + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{5} c - 208 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 74 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} + 240 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} + 120 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 37 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - 60 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} - 10 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{2} + 74 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} - 120 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4}\right)} {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)}^{2} + 2 \, {\left(5 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{11} - 102 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{9} c - 10 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{10} c - 10 \, a^{3} b^{11} c + 836 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{7} c^{2} + 164 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{8} c^{2} + 5 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{9} c^{2} + 204 \, a^{4} b^{9} c^{2} - 3440 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{5} c^{3} - 1016 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{6} c^{3} - 82 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{7} c^{3} - 1672 \, a^{5} b^{7} c^{3} + 7104 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{3} c^{4} + 2816 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{4} c^{4} + 508 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{5} c^{4} + 6880 \, a^{6} b^{5} c^{4} - 5888 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{8} b c^{5} - 2944 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{2} c^{5} - 1408 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{3} c^{5} - 14208 \, a^{7} b^{3} c^{5} + 1472 \, \sqrt{2} \sqrt{b c + \sqrt{b^{2} - 4 \, a c} c} a^{7} b c^{6} + 11776 \, a^{8} b c^{6} + 10 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{9} c - 164 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{7} c^{2} + 1016 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{5} c^{3} - 2816 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{3} c^{4} + 2944 \, {\left(b^{2} - 4 \, a c\right)} a^{7} b c^{5}\right)} {\left| a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2} \right|}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x}}{\sqrt{\frac{a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2} + \sqrt{{\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)}^{2} - 4 \, {\left(a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2}\right)} {\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)}}}{a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}}}}\right)}{32 \, {\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c - 2 \, a^{7} b^{9} c + 160 \, a^{9} b^{6} c^{2} + 32 \, a^{8} b^{7} c^{2} + a^{7} b^{8} c^{2} - 640 \, a^{10} b^{4} c^{3} - 192 \, a^{9} b^{5} c^{3} - 16 \, a^{8} b^{6} c^{3} + 1280 \, a^{11} b^{2} c^{4} + 512 \, a^{10} b^{3} c^{4} + 96 \, a^{9} b^{4} c^{4} - 1024 \, a^{12} c^{5} - 512 \, a^{11} b c^{5} - 256 \, a^{10} b^{2} c^{5} + 256 \, a^{11} c^{6}\right)} {\left| a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2} \right|} {\left| c \right|}} + \frac{3 \, {\left(10 \, a^{6} b^{14} c^{2} - 254 \, a^{7} b^{12} c^{3} + 2712 \, a^{8} b^{10} c^{4} - 15552 \, a^{9} b^{8} c^{5} + 50432 \, a^{10} b^{6} c^{6} - 87552 \, a^{11} b^{4} c^{7} + 63488 \, a^{12} b^{2} c^{8} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{14} + 127 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{12} c + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{13} c - 1356 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{10} c^{2} - 214 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{11} c^{2} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{12} c^{2} + 7776 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{8} c^{3} + 1856 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{9} c^{3} + 107 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{10} c^{3} - 25216 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{6} c^{4} - 8128 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{7} c^{4} - 928 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b^{8} c^{4} + 43776 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{11} b^{4} c^{5} + 17920 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{5} c^{5} + 4064 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{9} b^{6} c^{5} - 31744 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{12} b^{2} c^{6} - 15872 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{11} b^{3} c^{6} - 8960 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{10} b^{4} c^{6} + 7936 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{11} b^{2} c^{7} - 10 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{12} c^{2} + 214 \, {\left(b^{2} - 4 \, a c\right)} a^{7} b^{10} c^{3} - 1856 \, {\left(b^{2} - 4 \, a c\right)} a^{8} b^{8} c^{4} + 8128 \, {\left(b^{2} - 4 \, a c\right)} a^{9} b^{6} c^{5} - 17920 \, {\left(b^{2} - 4 \, a c\right)} a^{10} b^{4} c^{6} + 15872 \, {\left(b^{2} - 4 \, a c\right)} a^{11} b^{2} c^{7} + {\left(10 \, b^{6} c^{2} - 114 \, a b^{4} c^{3} + 416 \, a^{2} b^{2} c^{4} - 480 \, a^{3} c^{5} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{6} + 57 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{4} c + 10 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{5} c - 208 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b^{2} c^{2} - 74 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{3} c^{2} - 5 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} b^{4} c^{2} + 240 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} c^{3} + 120 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} b c^{3} + 37 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a b^{2} c^{3} - 60 \, \sqrt{2} \sqrt{b^{2} - 4 \, a c} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{2} c^{4} - 10 \, {\left(b^{2} - 4 \, a c\right)} b^{4} c^{2} + 74 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} c^{3} - 120 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c^{4}\right)} {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)}^{2} - 2 \, {\left(5 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{11} - 102 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{9} c - 10 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{10} c + 10 \, a^{3} b^{11} c + 836 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{7} c^{2} + 164 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{8} c^{2} + 5 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{3} b^{9} c^{2} - 204 \, a^{4} b^{9} c^{2} - 3440 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{5} c^{3} - 1016 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{6} c^{3} - 82 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{4} b^{7} c^{3} + 1672 \, a^{5} b^{7} c^{3} + 7104 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{3} c^{4} + 2816 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{4} c^{4} + 508 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{5} b^{5} c^{4} - 6880 \, a^{6} b^{5} c^{4} - 5888 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{8} b c^{5} - 2944 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b^{2} c^{5} - 1408 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{6} b^{3} c^{5} + 14208 \, a^{7} b^{3} c^{5} + 1472 \, \sqrt{2} \sqrt{b c - \sqrt{b^{2} - 4 \, a c} c} a^{7} b c^{6} - 11776 \, a^{8} b c^{6} - 10 \, {\left(b^{2} - 4 \, a c\right)} a^{3} b^{9} c + 164 \, {\left(b^{2} - 4 \, a c\right)} a^{4} b^{7} c^{2} - 1016 \, {\left(b^{2} - 4 \, a c\right)} a^{5} b^{5} c^{3} + 2816 \, {\left(b^{2} - 4 \, a c\right)} a^{6} b^{3} c^{4} - 2944 \, {\left(b^{2} - 4 \, a c\right)} a^{7} b c^{5}\right)} {\left| a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2} \right|}\right)} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{x}}{\sqrt{\frac{a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2} - \sqrt{{\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)}^{2} - 4 \, {\left(a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2}\right)} {\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)}}}{a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}}}}\right)}{32 \, {\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c - 2 \, a^{7} b^{9} c + 160 \, a^{9} b^{6} c^{2} + 32 \, a^{8} b^{7} c^{2} + a^{7} b^{8} c^{2} - 640 \, a^{10} b^{4} c^{3} - 192 \, a^{9} b^{5} c^{3} - 16 \, a^{8} b^{6} c^{3} + 1280 \, a^{11} b^{2} c^{4} + 512 \, a^{10} b^{3} c^{4} + 96 \, a^{9} b^{4} c^{4} - 1024 \, a^{12} c^{5} - 512 \, a^{11} b c^{5} - 256 \, a^{10} b^{2} c^{5} + 256 \, a^{11} c^{6}\right)} {\left| a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2} \right|} {\left| c \right|}} - \frac{7 \, b^{4} c^{2} x^{\frac{7}{2}} - 47 \, a b^{2} c^{3} x^{\frac{7}{2}} + 52 \, a^{2} c^{4} x^{\frac{7}{2}} + 14 \, b^{5} c x^{\frac{5}{2}} - 99 \, a b^{3} c^{2} x^{\frac{5}{2}} + 136 \, a^{2} b c^{3} x^{\frac{5}{2}} + 7 \, b^{6} x^{\frac{3}{2}} - 43 \, a b^{4} c x^{\frac{3}{2}} + 25 \, a^{2} b^{2} c^{2} x^{\frac{3}{2}} + 68 \, a^{3} c^{3} x^{\frac{3}{2}} + 9 \, a b^{5} \sqrt{x} - 66 \, a^{2} b^{3} c \sqrt{x} + 108 \, a^{3} b c^{2} \sqrt{x}}{4 \, {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} {\left(c x^{2} + b x + a\right)}^{2}} - \frac{2}{a^{3} \sqrt{x}}"," ",0,"-3/32*(10*a^6*b^14*c^2 - 254*a^7*b^12*c^3 + 2712*a^8*b^10*c^4 - 15552*a^9*b^8*c^5 + 50432*a^10*b^6*c^6 - 87552*a^11*b^4*c^7 + 63488*a^12*b^2*c^8 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^14 + 127*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^12*c + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^13*c - 1356*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^10*c^2 - 214*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^11*c^2 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^12*c^2 + 7776*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b^8*c^3 + 1856*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^9*c^3 + 107*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^10*c^3 - 25216*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^10*b^6*c^4 - 8128*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b^7*c^4 - 928*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b^8*c^4 + 43776*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^11*b^4*c^5 + 17920*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^10*b^5*c^5 + 4064*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^9*b^6*c^5 - 31744*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^12*b^2*c^6 - 15872*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^11*b^3*c^6 - 8960*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^10*b^4*c^6 + 7936*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^11*b^2*c^7 - 10*(b^2 - 4*a*c)*a^6*b^12*c^2 + 214*(b^2 - 4*a*c)*a^7*b^10*c^3 - 1856*(b^2 - 4*a*c)*a^8*b^8*c^4 + 8128*(b^2 - 4*a*c)*a^9*b^6*c^5 - 17920*(b^2 - 4*a*c)*a^10*b^4*c^6 + 15872*(b^2 - 4*a*c)*a^11*b^2*c^7 + (10*b^6*c^2 - 114*a*b^4*c^3 + 416*a^2*b^2*c^4 - 480*a^3*c^5 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^6 + 57*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^4*c + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^5*c - 208*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 - 74*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*b^4*c^2 + 240*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*c^3 + 120*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 + 37*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 - 60*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^2*c^4 - 10*(b^2 - 4*a*c)*b^4*c^2 + 74*(b^2 - 4*a*c)*a*b^2*c^3 - 120*(b^2 - 4*a*c)*a^2*c^4)*(a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)^2 + 2*(5*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^11 - 102*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^9*c - 10*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^10*c - 10*a^3*b^11*c + 836*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^7*c^2 + 164*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^8*c^2 + 5*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^3*b^9*c^2 + 204*a^4*b^9*c^2 - 3440*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^5*c^3 - 1016*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^6*c^3 - 82*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^4*b^7*c^3 - 1672*a^5*b^7*c^3 + 7104*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^3*c^4 + 2816*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^4*c^4 + 508*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^5*b^5*c^4 + 6880*a^6*b^5*c^4 - 5888*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^8*b*c^5 - 2944*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b^2*c^5 - 1408*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^6*b^3*c^5 - 14208*a^7*b^3*c^5 + 1472*sqrt(2)*sqrt(b*c + sqrt(b^2 - 4*a*c)*c)*a^7*b*c^6 + 11776*a^8*b*c^6 + 10*(b^2 - 4*a*c)*a^3*b^9*c - 164*(b^2 - 4*a*c)*a^4*b^7*c^2 + 1016*(b^2 - 4*a*c)*a^5*b^5*c^3 - 2816*(b^2 - 4*a*c)*a^6*b^3*c^4 + 2944*(b^2 - 4*a*c)*a^7*b*c^5)*abs(a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2))*arctan(2*sqrt(1/2)*sqrt(x)/sqrt((a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2 + sqrt((a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)^2 - 4*(a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2)*(a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)))/(a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)))/((a^7*b^10 - 20*a^8*b^8*c - 2*a^7*b^9*c + 160*a^9*b^6*c^2 + 32*a^8*b^7*c^2 + a^7*b^8*c^2 - 640*a^10*b^4*c^3 - 192*a^9*b^5*c^3 - 16*a^8*b^6*c^3 + 1280*a^11*b^2*c^4 + 512*a^10*b^3*c^4 + 96*a^9*b^4*c^4 - 1024*a^12*c^5 - 512*a^11*b*c^5 - 256*a^10*b^2*c^5 + 256*a^11*c^6)*abs(a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*abs(c)) + 3/32*(10*a^6*b^14*c^2 - 254*a^7*b^12*c^3 + 2712*a^8*b^10*c^4 - 15552*a^9*b^8*c^5 + 50432*a^10*b^6*c^6 - 87552*a^11*b^4*c^7 + 63488*a^12*b^2*c^8 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^14 + 127*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^12*c + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^13*c - 1356*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^10*c^2 - 214*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^11*c^2 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^12*c^2 + 7776*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b^8*c^3 + 1856*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^9*c^3 + 107*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^10*c^3 - 25216*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^10*b^6*c^4 - 8128*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b^7*c^4 - 928*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b^8*c^4 + 43776*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^11*b^4*c^5 + 17920*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^10*b^5*c^5 + 4064*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^9*b^6*c^5 - 31744*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^12*b^2*c^6 - 15872*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^11*b^3*c^6 - 8960*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^10*b^4*c^6 + 7936*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^11*b^2*c^7 - 10*(b^2 - 4*a*c)*a^6*b^12*c^2 + 214*(b^2 - 4*a*c)*a^7*b^10*c^3 - 1856*(b^2 - 4*a*c)*a^8*b^8*c^4 + 8128*(b^2 - 4*a*c)*a^9*b^6*c^5 - 17920*(b^2 - 4*a*c)*a^10*b^4*c^6 + 15872*(b^2 - 4*a*c)*a^11*b^2*c^7 + (10*b^6*c^2 - 114*a*b^4*c^3 + 416*a^2*b^2*c^4 - 480*a^3*c^5 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^6 + 57*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^4*c + 10*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^5*c - 208*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b^2*c^2 - 74*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^3*c^2 - 5*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*b^4*c^2 + 240*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*c^3 + 120*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*b*c^3 + 37*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a*b^2*c^3 - 60*sqrt(2)*sqrt(b^2 - 4*a*c)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^2*c^4 - 10*(b^2 - 4*a*c)*b^4*c^2 + 74*(b^2 - 4*a*c)*a*b^2*c^3 - 120*(b^2 - 4*a*c)*a^2*c^4)*(a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)^2 - 2*(5*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^11 - 102*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^9*c - 10*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^10*c + 10*a^3*b^11*c + 836*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^7*c^2 + 164*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^8*c^2 + 5*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^3*b^9*c^2 - 204*a^4*b^9*c^2 - 3440*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^5*c^3 - 1016*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^6*c^3 - 82*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^4*b^7*c^3 + 1672*a^5*b^7*c^3 + 7104*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^3*c^4 + 2816*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^4*c^4 + 508*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^5*b^5*c^4 - 6880*a^6*b^5*c^4 - 5888*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^8*b*c^5 - 2944*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b^2*c^5 - 1408*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^6*b^3*c^5 + 14208*a^7*b^3*c^5 + 1472*sqrt(2)*sqrt(b*c - sqrt(b^2 - 4*a*c)*c)*a^7*b*c^6 - 11776*a^8*b*c^6 - 10*(b^2 - 4*a*c)*a^3*b^9*c + 164*(b^2 - 4*a*c)*a^4*b^7*c^2 - 1016*(b^2 - 4*a*c)*a^5*b^5*c^3 + 2816*(b^2 - 4*a*c)*a^6*b^3*c^4 - 2944*(b^2 - 4*a*c)*a^7*b*c^5)*abs(a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2))*arctan(2*sqrt(1/2)*sqrt(x)/sqrt((a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2 - sqrt((a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)^2 - 4*(a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2)*(a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)))/(a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)))/((a^7*b^10 - 20*a^8*b^8*c - 2*a^7*b^9*c + 160*a^9*b^6*c^2 + 32*a^8*b^7*c^2 + a^7*b^8*c^2 - 640*a^10*b^4*c^3 - 192*a^9*b^5*c^3 - 16*a^8*b^6*c^3 + 1280*a^11*b^2*c^4 + 512*a^10*b^3*c^4 + 96*a^9*b^4*c^4 - 1024*a^12*c^5 - 512*a^11*b*c^5 - 256*a^10*b^2*c^5 + 256*a^11*c^6)*abs(a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*abs(c)) - 1/4*(7*b^4*c^2*x^(7/2) - 47*a*b^2*c^3*x^(7/2) + 52*a^2*c^4*x^(7/2) + 14*b^5*c*x^(5/2) - 99*a*b^3*c^2*x^(5/2) + 136*a^2*b*c^3*x^(5/2) + 7*b^6*x^(3/2) - 43*a*b^4*c*x^(3/2) + 25*a^2*b^2*c^2*x^(3/2) + 68*a^3*c^3*x^(3/2) + 9*a*b^5*sqrt(x) - 66*a^2*b^3*c*sqrt(x) + 108*a^3*b*c^2*sqrt(x))/((a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*(c*x^2 + b*x + a)^2) - 2/(a^3*sqrt(x))","B",0
2332,1,16,0,0.149632," ","integrate((x^2-x+3)/x^(1/3),x, algorithm=""giac"")","\frac{3}{8} \, x^{\frac{8}{3}} - \frac{3}{5} \, x^{\frac{5}{3}} + \frac{9}{2} \, x^{\frac{2}{3}}"," ",0,"3/8*x^(8/3) - 3/5*x^(5/3) + 9/2*x^(2/3)","A",0
2333,1,380,0,0.228591," ","integrate((e*x+d)^3*(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\frac{1}{1920} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(6 \, {\left(8 \, x e^{3} + \frac{30 \, c^{4} d e^{2} + b c^{3} e^{3}}{c^{4}}\right)} x + \frac{240 \, c^{4} d^{2} e + 30 \, b c^{3} d e^{2} - 7 \, b^{2} c^{2} e^{3} + 16 \, a c^{3} e^{3}}{c^{4}}\right)} x + \frac{480 \, c^{4} d^{3} + 240 \, b c^{3} d^{2} e - 150 \, b^{2} c^{2} d e^{2} + 360 \, a c^{3} d e^{2} + 35 \, b^{3} c e^{3} - 116 \, a b c^{2} e^{3}}{c^{4}}\right)} x + \frac{480 \, b c^{3} d^{3} - 720 \, b^{2} c^{2} d^{2} e + 1920 \, a c^{3} d^{2} e + 450 \, b^{3} c d e^{2} - 1560 \, a b c^{2} d e^{2} - 105 \, b^{4} e^{3} + 460 \, a b^{2} c e^{3} - 256 \, a^{2} c^{2} e^{3}}{c^{4}}\right)} + \frac{{\left(32 \, b^{2} c^{3} d^{3} - 128 \, a c^{4} d^{3} - 48 \, b^{3} c^{2} d^{2} e + 192 \, a b c^{3} d^{2} e + 30 \, b^{4} c d e^{2} - 144 \, a b^{2} c^{2} d e^{2} + 96 \, a^{2} c^{3} d e^{2} - 7 \, b^{5} e^{3} + 40 \, a b^{3} c e^{3} - 48 \, a^{2} b c^{2} e^{3}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{256 \, c^{\frac{9}{2}}}"," ",0,"1/1920*sqrt(c*x^2 + b*x + a)*(2*(4*(6*(8*x*e^3 + (30*c^4*d*e^2 + b*c^3*e^3)/c^4)*x + (240*c^4*d^2*e + 30*b*c^3*d*e^2 - 7*b^2*c^2*e^3 + 16*a*c^3*e^3)/c^4)*x + (480*c^4*d^3 + 240*b*c^3*d^2*e - 150*b^2*c^2*d*e^2 + 360*a*c^3*d*e^2 + 35*b^3*c*e^3 - 116*a*b*c^2*e^3)/c^4)*x + (480*b*c^3*d^3 - 720*b^2*c^2*d^2*e + 1920*a*c^3*d^2*e + 450*b^3*c*d*e^2 - 1560*a*b*c^2*d*e^2 - 105*b^4*e^3 + 460*a*b^2*c*e^3 - 256*a^2*c^2*e^3)/c^4) + 1/256*(32*b^2*c^3*d^3 - 128*a*c^4*d^3 - 48*b^3*c^2*d^2*e + 192*a*b*c^3*d^2*e + 30*b^4*c*d*e^2 - 144*a*b^2*c^2*d*e^2 + 96*a^2*c^3*d*e^2 - 7*b^5*e^3 + 40*a*b^3*c*e^3 - 48*a^2*b*c^2*e^3)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(9/2)","A",0
2334,1,235,0,0.287120," ","integrate((e*x+d)^2*(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\frac{1}{192} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(6 \, x e^{2} + \frac{16 \, c^{3} d e + b c^{2} e^{2}}{c^{3}}\right)} x + \frac{48 \, c^{3} d^{2} + 16 \, b c^{2} d e - 5 \, b^{2} c e^{2} + 12 \, a c^{2} e^{2}}{c^{3}}\right)} x + \frac{48 \, b c^{2} d^{2} - 48 \, b^{2} c d e + 128 \, a c^{2} d e + 15 \, b^{3} e^{2} - 52 \, a b c e^{2}}{c^{3}}\right)} + \frac{{\left(16 \, b^{2} c^{2} d^{2} - 64 \, a c^{3} d^{2} - 16 \, b^{3} c d e + 64 \, a b c^{2} d e + 5 \, b^{4} e^{2} - 24 \, a b^{2} c e^{2} + 16 \, a^{2} c^{2} e^{2}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{128 \, c^{\frac{7}{2}}}"," ",0,"1/192*sqrt(c*x^2 + b*x + a)*(2*(4*(6*x*e^2 + (16*c^3*d*e + b*c^2*e^2)/c^3)*x + (48*c^3*d^2 + 16*b*c^2*d*e - 5*b^2*c*e^2 + 12*a*c^2*e^2)/c^3)*x + (48*b*c^2*d^2 - 48*b^2*c*d*e + 128*a*c^2*d*e + 15*b^3*e^2 - 52*a*b*c*e^2)/c^3) + 1/128*(16*b^2*c^2*d^2 - 64*a*c^3*d^2 - 16*b^3*c*d*e + 64*a*b*c^2*d*e + 5*b^4*e^2 - 24*a*b^2*c*e^2 + 16*a^2*c^2*e^2)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(7/2)","A",0
2335,1,129,0,0.225451," ","integrate((e*x+d)*(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\frac{1}{24} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, x e + \frac{6 \, c^{2} d + b c e}{c^{2}}\right)} x + \frac{6 \, b c d - 3 \, b^{2} e + 8 \, a c e}{c^{2}}\right)} + \frac{{\left(2 \, b^{2} c d - 8 \, a c^{2} d - b^{3} e + 4 \, a b c e\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{16 \, c^{\frac{5}{2}}}"," ",0,"1/24*sqrt(c*x^2 + b*x + a)*(2*(4*x*e + (6*c^2*d + b*c*e)/c^2)*x + (6*b*c*d - 3*b^2*e + 8*a*c*e)/c^2) + 1/16*(2*b^2*c*d - 8*a*c^2*d - b^3*e + 4*a*b*c*e)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(5/2)","A",0
2336,1,68,0,0.173595," ","integrate((c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{c x^{2} + b x + a} {\left(2 \, x + \frac{b}{c}\right)} + \frac{{\left(b^{2} - 4 \, a c\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{8 \, c^{\frac{3}{2}}}"," ",0,"1/4*sqrt(c*x^2 + b*x + a)*(2*x + b/c) + 1/8*(b^2 - 4*a*c)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(3/2)","A",0
2337,-2,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(1/2)/(e*x+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error: Bad Argument Type","F(-2)",0
2338,-2,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(1/2)/(e*x+d)^2,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]Evaluation time: 0.58Error: Bad Argument Type","F(-2)",0
2339,1,686,0,0.310504," ","integrate((c*x^2+b*x+a)^(1/2)/(e*x+d)^3,x, algorithm=""giac"")","-\frac{{\left(b^{2} - 4 \, a c\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} + b d e - a e^{2}}}\right)}{4 \, {\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{-c d^{2} + b d e - a e^{2}}} + \frac{8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} c^{2} d^{2} e + 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} c^{\frac{5}{2}} d^{3} + 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b c^{2} d^{3} - 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b c d e^{2} - 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{2} c d^{2} e - 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a c^{2} d^{2} e + 2 \, b^{2} c^{\frac{3}{2}} d^{3} - 5 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{2} \sqrt{c} d e^{2} - 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a c^{\frac{3}{2}} d e^{2} - b^{3} \sqrt{c} d^{2} e - 4 \, a b c^{\frac{3}{2}} d^{2} e + {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{2} e^{3} + 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a c e^{3} - {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{3} d e^{2} + 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b c d e^{2} + 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a b \sqrt{c} e^{3} + a b^{2} \sqrt{c} d e^{2} + 4 \, a^{2} c^{\frac{3}{2}} d e^{2} + {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{2} e^{3} + 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} c e^{3}}{4 \, {\left(c d^{2} e^{2} - b d e^{3} + a e^{4}\right)} {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} e + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} d + b d - a e\right)}^{2}}"," ",0,"-1/4*(b^2 - 4*a*c)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + b*x + a))*e + sqrt(c)*d)/sqrt(-c*d^2 + b*d*e - a*e^2))/((c*d^2 - b*d*e + a*e^2)*sqrt(-c*d^2 + b*d*e - a*e^2)) + 1/4*(8*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*c^2*d^2*e + 8*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*c^(5/2)*d^3 + 8*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b*c^2*d^3 - 8*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b*c*d*e^2 - 4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^2*c*d^2*e - 8*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*c^2*d^2*e + 2*b^2*c^(3/2)*d^3 - 5*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^2*sqrt(c)*d*e^2 - 4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*c^(3/2)*d*e^2 - b^3*sqrt(c)*d^2*e - 4*a*b*c^(3/2)*d^2*e + (sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^2*e^3 + 4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*c*e^3 - (sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^3*d*e^2 + 4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b*c*d*e^2 + 8*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b*sqrt(c)*e^3 + a*b^2*sqrt(c)*d*e^2 + 4*a^2*c^(3/2)*d*e^2 + (sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^2*e^3 + 4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*c*e^3)/((c*d^2*e^2 - b*d*e^3 + a*e^4)*((sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*e + 2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c)*d + b*d - a*e)^2)","B",0
2340,1,1949,0,0.549706," ","integrate((c*x^2+b*x+a)^(1/2)/(e*x+d)^4,x, algorithm=""giac"")","-\frac{{\left(2 \, b^{2} c d - 8 \, a c^{2} d - b^{3} e + 4 \, a b c e\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} + b d e - a e^{2}}}\right)}{8 \, {\left(c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2} + 2 \, a c d^{2} e^{2} - 2 \, a b d e^{3} + a^{2} e^{4}\right)} \sqrt{-c d^{2} + b d e - a e^{2}}} + \frac{48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} c^{\frac{7}{2}} d^{4} e + 32 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} c^{4} d^{5} + 16 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b c^{3} d^{4} e + 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b c^{\frac{7}{2}} d^{5} - 96 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} b c^{\frac{5}{2}} d^{3} e^{2} - 36 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{2} c^{\frac{5}{2}} d^{4} e - 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a c^{\frac{7}{2}} d^{4} e + 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{2} c^{3} d^{5} - 84 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{2} c^{2} d^{3} e^{2} - 112 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a c^{3} d^{3} e^{2} - 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{3} c^{2} d^{4} e - 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b c^{3} d^{4} e + 4 \, b^{3} c^{\frac{5}{2}} d^{5} + 78 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} b^{2} c^{\frac{3}{2}} d^{2} e^{3} - 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a c^{\frac{5}{2}} d^{2} e^{3} - 6 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{3} c^{\frac{3}{2}} d^{3} e^{2} - 72 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a b c^{\frac{5}{2}} d^{3} e^{2} - 4 \, b^{4} c^{\frac{3}{2}} d^{4} e - 12 \, a b^{2} c^{\frac{5}{2}} d^{4} e + 6 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} b^{2} c d e^{4} - 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a c^{2} d e^{4} + 74 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{3} c d^{2} e^{3} + 120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b c^{2} d^{2} e^{3} + 12 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{4} c d^{3} e^{2} - 12 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{2} c^{2} d^{3} e^{2} + 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} c^{3} d^{3} e^{2} - 15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} b^{3} \sqrt{c} d e^{4} - 36 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a b c^{\frac{3}{2}} d e^{4} + 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{4} \sqrt{c} d^{2} e^{3} + 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a b^{2} c^{\frac{3}{2}} d^{2} e^{3} + 192 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{2} c^{\frac{5}{2}} d^{2} e^{3} + 3 \, b^{5} \sqrt{c} d^{3} e^{2} - 2 \, a b^{3} c^{\frac{3}{2}} d^{3} e^{2} + 24 \, a^{2} b c^{\frac{5}{2}} d^{3} e^{2} - 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} b^{3} e^{5} + 12 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a b c e^{5} - 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{4} d e^{4} - 144 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b^{2} c d e^{4} + 96 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{2} c^{2} d e^{4} + 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{5} d^{2} e^{3} - 18 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{3} c d^{2} e^{3} + 120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} b c^{2} d^{2} e^{3} + 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{2} c^{\frac{3}{2}} e^{5} - 72 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a b^{3} \sqrt{c} d e^{4} - 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{2} b c^{\frac{3}{2}} d e^{4} - 6 \, a b^{4} \sqrt{c} d^{2} e^{3} + 18 \, a^{2} b^{2} c^{\frac{3}{2}} d^{2} e^{3} - 8 \, a^{3} c^{\frac{5}{2}} d^{2} e^{3} + 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b^{3} e^{5} + 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{2} b c e^{5} - 6 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{4} d e^{4} - 30 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} b^{2} c d e^{4} - 72 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{3} c^{2} d e^{4} + 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{2} b^{2} \sqrt{c} e^{5} + 3 \, a^{2} b^{3} \sqrt{c} d e^{4} - 28 \, a^{3} b c^{\frac{3}{2}} d e^{4} + 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} b^{3} e^{5} + 36 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{3} b c e^{5} + 16 \, a^{4} c^{\frac{3}{2}} e^{5}}{24 \, {\left(c^{2} d^{4} e^{2} - 2 \, b c d^{3} e^{3} + b^{2} d^{2} e^{4} + 2 \, a c d^{2} e^{4} - 2 \, a b d e^{5} + a^{2} e^{6}\right)} {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} e + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} d + b d - a e\right)}^{3}}"," ",0,"-1/8*(2*b^2*c*d - 8*a*c^2*d - b^3*e + 4*a*b*c*e)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + b*x + a))*e + sqrt(c)*d)/sqrt(-c*d^2 + b*d*e - a*e^2))/((c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2 + 2*a*c*d^2*e^2 - 2*a*b*d*e^3 + a^2*e^4)*sqrt(-c*d^2 + b*d*e - a*e^2)) + 1/24*(48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*c^(7/2)*d^4*e + 32*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*c^4*d^5 + 16*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b*c^3*d^4*e + 48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b*c^(7/2)*d^5 - 96*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b*c^(5/2)*d^3*e^2 - 36*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^2*c^(5/2)*d^4*e - 48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*c^(7/2)*d^4*e + 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^2*c^3*d^5 - 84*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^2*c^2*d^3*e^2 - 112*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*c^3*d^3*e^2 - 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^3*c^2*d^4*e - 48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b*c^3*d^4*e + 4*b^3*c^(5/2)*d^5 + 78*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^2*c^(3/2)*d^2*e^3 - 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*c^(5/2)*d^2*e^3 - 6*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^3*c^(3/2)*d^3*e^2 - 72*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b*c^(5/2)*d^3*e^2 - 4*b^4*c^(3/2)*d^4*e - 12*a*b^2*c^(5/2)*d^4*e + 6*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b^2*c*d*e^4 - 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*c^2*d*e^4 + 74*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^3*c*d^2*e^3 + 120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b*c^2*d^2*e^3 + 12*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^4*c*d^3*e^2 - 12*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^2*c^2*d^3*e^2 + 48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*c^3*d^3*e^2 - 15*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^3*sqrt(c)*d*e^4 - 36*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*b*c^(3/2)*d*e^4 + 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^4*sqrt(c)*d^2*e^3 + 48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^2*c^(3/2)*d^2*e^3 + 192*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*c^(5/2)*d^2*e^3 + 3*b^5*sqrt(c)*d^3*e^2 - 2*a*b^3*c^(3/2)*d^3*e^2 + 24*a^2*b*c^(5/2)*d^3*e^2 - 3*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b^3*e^5 + 12*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*b*c*e^5 - 8*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^4*d*e^4 - 144*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^2*c*d*e^4 + 96*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*c^2*d*e^4 + 3*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^5*d^2*e^3 - 18*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^3*c*d^2*e^3 + 120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b*c^2*d^2*e^3 + 48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^2*c^(3/2)*e^5 - 72*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^3*sqrt(c)*d*e^4 - 48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*b*c^(3/2)*d*e^4 - 6*a*b^4*sqrt(c)*d^2*e^3 + 18*a^2*b^2*c^(3/2)*d^2*e^3 - 8*a^3*c^(5/2)*d^2*e^3 + 8*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^3*e^5 + 48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*b*c*e^5 - 6*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^4*d*e^4 - 30*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b^2*c*d*e^4 - 72*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*c^2*d*e^4 + 48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*b^2*sqrt(c)*e^5 + 3*a^2*b^3*sqrt(c)*d*e^4 - 28*a^3*b*c^(3/2)*d*e^4 + 3*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b^3*e^5 + 36*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*b*c*e^5 + 16*a^4*c^(3/2)*e^5)/((c^2*d^4*e^2 - 2*b*c*d^3*e^3 + b^2*d^2*e^4 + 2*a*c*d^2*e^4 - 2*a*b*d*e^5 + a^2*e^6)*((sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*e + 2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c)*d + b*d - a*e)^3)","B",0
2341,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(1/2)/(e*x+d)^5,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2342,1,8452,0,2.022942," ","integrate((c*x^2+b*x+a)^(1/2)/(e*x+d)^6,x, algorithm=""giac"")","-\frac{{\left(32 \, b^{2} c^{3} d^{3} - 128 \, a c^{4} d^{3} - 48 \, b^{3} c^{2} d^{2} e + 192 \, a b c^{3} d^{2} e + 30 \, b^{4} c d e^{2} - 144 \, a b^{2} c^{2} d e^{2} + 96 \, a^{2} c^{3} d e^{2} - 7 \, b^{5} e^{3} + 40 \, a b^{3} c e^{3} - 48 \, a^{2} b c^{2} e^{3}\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} + b d e - a e^{2}}}\right)}{128 \, {\left(c^{4} d^{8} - 4 \, b c^{3} d^{7} e + 6 \, b^{2} c^{2} d^{6} e^{2} + 4 \, a c^{3} d^{6} e^{2} - 4 \, b^{3} c d^{5} e^{3} - 12 \, a b c^{2} d^{5} e^{3} + b^{4} d^{4} e^{4} + 12 \, a b^{2} c d^{4} e^{4} + 6 \, a^{2} c^{2} d^{4} e^{4} - 4 \, a b^{3} d^{3} e^{5} - 12 \, a^{2} b c d^{3} e^{5} + 6 \, a^{2} b^{2} d^{2} e^{6} + 4 \, a^{3} c d^{2} e^{6} - 4 \, a^{3} b d e^{7} + a^{4} e^{8}\right)} \sqrt{-c d^{2} + b d e - a e^{2}}} + \frac{7680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} c^{\frac{13}{2}} d^{8} e + 3072 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} c^{7} d^{9} + 9216 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} b c^{6} d^{8} e + 7680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} b c^{\frac{13}{2}} d^{9} - 30720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} b c^{\frac{11}{2}} d^{7} e^{2} - 3840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} b^{2} c^{\frac{11}{2}} d^{8} e - 7680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a c^{\frac{13}{2}} d^{8} e + 7680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{2} c^{6} d^{9} - 50048 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} b^{2} c^{5} d^{7} e^{2} - 57856 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a c^{6} d^{7} e^{2} - 11520 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{3} c^{5} d^{8} e - 15360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b c^{6} d^{8} e + 3840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{3} c^{\frac{11}{2}} d^{9} + 70720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} b^{2} c^{\frac{9}{2}} d^{6} e^{3} - 67840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} a c^{\frac{11}{2}} d^{6} e^{3} - 17600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} b^{3} c^{\frac{9}{2}} d^{7} e^{2} - 113920 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a b c^{\frac{11}{2}} d^{7} e^{2} - 7200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{4} c^{\frac{9}{2}} d^{8} e - 11520 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a b^{2} c^{\frac{11}{2}} d^{8} e + 960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{4} c^{5} d^{9} + 15040 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} b^{2} c^{4} d^{5} e^{4} - 60160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} a c^{5} d^{5} e^{4} + 129280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} b^{3} c^{4} d^{6} e^{3} - 1024 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a b c^{5} d^{6} e^{3} + 14080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{4} c^{4} d^{7} e^{2} - 90880 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b^{2} c^{5} d^{7} e^{2} + 15360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{2} c^{6} d^{7} e^{2} - 1920 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{5} c^{4} d^{8} e - 3840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{3} c^{5} d^{8} e + 96 \, b^{5} c^{\frac{9}{2}} d^{9} + 4320 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} b^{2} c^{\frac{7}{2}} d^{4} e^{5} - 17280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} a c^{\frac{9}{2}} d^{4} e^{5} - 52000 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} b^{3} c^{\frac{7}{2}} d^{5} e^{4} - 7040 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} a b c^{\frac{9}{2}} d^{5} e^{4} + 81920 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} b^{4} c^{\frac{7}{2}} d^{6} e^{3} + 114240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a b^{2} c^{\frac{9}{2}} d^{6} e^{3} + 167680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{2} c^{\frac{11}{2}} d^{6} e^{3} + 13760 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{5} c^{\frac{7}{2}} d^{7} e^{2} - 37760 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a b^{3} c^{\frac{9}{2}} d^{7} e^{2} + 23040 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{2} b c^{\frac{11}{2}} d^{7} e^{2} - 192 \, b^{6} c^{\frac{7}{2}} d^{8} e - 480 \, a b^{4} c^{\frac{9}{2}} d^{8} e + 480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} b^{2} c^{3} d^{3} e^{6} - 1920 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} a c^{4} d^{3} e^{6} - 20320 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} b^{3} c^{3} d^{4} e^{5} + 81280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} a b c^{4} d^{4} e^{5} - 120680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} b^{4} c^{3} d^{5} e^{4} - 122240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a b^{2} c^{4} d^{5} e^{4} + 226432 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{2} c^{5} d^{5} e^{4} + 14080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{5} c^{3} d^{6} e^{3} + 88320 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b^{3} c^{4} d^{6} e^{3} + 281600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{2} b c^{5} d^{6} e^{3} + 4280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{6} c^{3} d^{7} e^{2} - 8480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{4} c^{4} d^{7} e^{2} + 11520 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} b^{2} c^{5} d^{7} e^{2} - 6480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} b^{3} c^{\frac{5}{2}} d^{3} e^{6} + 25920 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} a b c^{\frac{7}{2}} d^{3} e^{6} + 7260 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} b^{4} c^{\frac{5}{2}} d^{4} e^{5} + 59680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} a b^{2} c^{\frac{7}{2}} d^{4} e^{5} + 182720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} a^{2} c^{\frac{9}{2}} d^{4} e^{5} - 85780 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} b^{5} c^{\frac{5}{2}} d^{5} e^{4} - 237120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a b^{3} c^{\frac{7}{2}} d^{5} e^{4} + 63040 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{2} b c^{\frac{9}{2}} d^{5} e^{4} - 6340 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{6} c^{\frac{5}{2}} d^{6} e^{3} + 22000 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a b^{4} c^{\frac{7}{2}} d^{6} e^{3} + 176640 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{2} b^{2} c^{\frac{9}{2}} d^{6} e^{3} - 7680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{3} c^{\frac{11}{2}} d^{6} e^{3} + 476 \, b^{7} c^{\frac{5}{2}} d^{7} e^{2} - 848 \, a b^{5} c^{\frac{7}{2}} d^{7} e^{2} + 1920 \, a^{2} b^{3} c^{\frac{9}{2}} d^{7} e^{2} - 720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} b^{3} c^{2} d^{2} e^{7} + 2880 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} a b c^{3} d^{2} e^{7} + 10740 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} b^{4} c^{2} d^{3} e^{6} - 56480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} a b^{2} c^{3} d^{3} e^{6} + 54080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} a^{2} c^{4} d^{3} e^{6} + 47944 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} b^{5} c^{2} d^{4} e^{5} + 167520 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a b^{3} c^{3} d^{4} e^{5} - 17920 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{2} b c^{4} d^{4} e^{5} - 25220 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{6} c^{2} d^{5} e^{4} - 124960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b^{4} c^{3} d^{5} e^{4} - 239360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{2} b^{2} c^{4} d^{5} e^{4} - 160000 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{3} c^{5} d^{5} e^{4} - 3080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{7} c^{2} d^{6} e^{3} + 480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{5} c^{3} d^{6} e^{3} + 49280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} b^{3} c^{4} d^{6} e^{3} - 7680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{3} b c^{5} d^{6} e^{3} + 4050 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} b^{4} c^{\frac{3}{2}} d^{2} e^{7} - 19440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} a b^{2} c^{\frac{5}{2}} d^{2} e^{7} + 12960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} a^{2} c^{\frac{7}{2}} d^{2} e^{7} + 9310 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} b^{5} c^{\frac{3}{2}} d^{3} e^{6} - 46960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} a b^{3} c^{\frac{5}{2}} d^{3} e^{6} - 176160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} a^{2} b c^{\frac{7}{2}} d^{3} e^{6} + 35330 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} b^{6} c^{\frac{3}{2}} d^{4} e^{5} + 244660 \, {\left(\sqrt{c} x - 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28720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{4} b^{3} c^{\frac{3}{2}} d e^{8} + 160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{5} b c^{\frac{5}{2}} d e^{8} - 420 \, a^{3} b^{6} \sqrt{c} d^{2} e^{7} + 5790 \, a^{4} b^{4} c^{\frac{3}{2}} d^{2} e^{7} + 9008 \, a^{5} b^{2} c^{\frac{5}{2}} d^{2} e^{7} + 2656 \, a^{6} c^{\frac{7}{2}} d^{2} e^{7} + 790 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{3} b^{5} e^{9} + 9200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{4} b^{3} c e^{9} + 12000 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{5} b c^{2} e^{9} - 420 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{3} b^{6} d e^{8} - 9570 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{4} b^{4} c d e^{8} - 13520 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{5} b^{2} c^{2} d e^{8} + 3680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{6} c^{3} d e^{8} + 3840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{4} b^{4} \sqrt{c} e^{9} + 5120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{5} b^{2} c^{\frac{3}{2}} e^{9} + 2560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{6} c^{\frac{5}{2}} e^{9} + 105 \, a^{4} b^{5} \sqrt{c} d e^{8} - 4440 \, a^{5} b^{3} c^{\frac{3}{2}} d e^{8} - 816 \, a^{6} b c^{\frac{5}{2}} d e^{8} + 105 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{4} b^{5} e^{9} + 3240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{5} b^{3} c e^{9} + 720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{6} b c^{2} e^{9} + 1280 \, a^{6} b^{2} c^{\frac{3}{2}} e^{9} - 512 \, a^{7} c^{\frac{5}{2}} e^{9}}{1920 \, {\left(c^{4} d^{8} e^{2} - 4 \, b c^{3} d^{7} e^{3} + 6 \, b^{2} c^{2} d^{6} e^{4} + 4 \, a c^{3} d^{6} e^{4} - 4 \, b^{3} c d^{5} e^{5} - 12 \, a b c^{2} d^{5} e^{5} + b^{4} d^{4} e^{6} + 12 \, a b^{2} c d^{4} e^{6} + 6 \, a^{2} c^{2} d^{4} e^{6} - 4 \, a b^{3} d^{3} e^{7} - 12 \, a^{2} b c d^{3} e^{7} + 6 \, a^{2} b^{2} d^{2} e^{8} + 4 \, a^{3} c d^{2} e^{8} - 4 \, a^{3} b d e^{9} + a^{4} e^{10}\right)} {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} e + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} d + b d - a e\right)}^{5}}"," ",0,"-1/128*(32*b^2*c^3*d^3 - 128*a*c^4*d^3 - 48*b^3*c^2*d^2*e + 192*a*b*c^3*d^2*e + 30*b^4*c*d*e^2 - 144*a*b^2*c^2*d*e^2 + 96*a^2*c^3*d*e^2 - 7*b^5*e^3 + 40*a*b^3*c*e^3 - 48*a^2*b*c^2*e^3)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + b*x + a))*e + sqrt(c)*d)/sqrt(-c*d^2 + b*d*e - a*e^2))/((c^4*d^8 - 4*b*c^3*d^7*e + 6*b^2*c^2*d^6*e^2 + 4*a*c^3*d^6*e^2 - 4*b^3*c*d^5*e^3 - 12*a*b*c^2*d^5*e^3 + b^4*d^4*e^4 + 12*a*b^2*c*d^4*e^4 + 6*a^2*c^2*d^4*e^4 - 4*a*b^3*d^3*e^5 - 12*a^2*b*c*d^3*e^5 + 6*a^2*b^2*d^2*e^6 + 4*a^3*c*d^2*e^6 - 4*a^3*b*d*e^7 + a^4*e^8)*sqrt(-c*d^2 + b*d*e - a*e^2)) + 1/1920*(7680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*c^(13/2)*d^8*e + 3072*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*c^7*d^9 + 9216*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b*c^6*d^8*e + 7680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b*c^(13/2)*d^9 - 30720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*b*c^(11/2)*d^7*e^2 - 3840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^2*c^(11/2)*d^8*e - 7680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*c^(13/2)*d^8*e + 7680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^2*c^6*d^9 - 50048*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b^2*c^5*d^7*e^2 - 57856*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*c^6*d^7*e^2 - 11520*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^3*c^5*d^8*e - 15360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b*c^6*d^8*e + 3840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^3*c^(11/2)*d^9 + 70720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*b^2*c^(9/2)*d^6*e^3 - 67840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a*c^(11/2)*d^6*e^3 - 17600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^3*c^(9/2)*d^7*e^2 - 113920*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*b*c^(11/2)*d^7*e^2 - 7200*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^4*c^(9/2)*d^8*e - 11520*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^2*c^(11/2)*d^8*e + 960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^4*c^5*d^9 + 15040*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*b^2*c^4*d^5*e^4 - 60160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a*c^5*d^5*e^4 + 129280*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b^3*c^4*d^6*e^3 - 1024*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*b*c^5*d^6*e^3 + 14080*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^4*c^4*d^7*e^2 - 90880*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^2*c^5*d^7*e^2 + 15360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*c^6*d^7*e^2 - 1920*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^5*c^4*d^8*e - 3840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^3*c^5*d^8*e + 96*b^5*c^(9/2)*d^9 + 4320*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*b^2*c^(7/2)*d^4*e^5 - 17280*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a*c^(9/2)*d^4*e^5 - 52000*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*b^3*c^(7/2)*d^5*e^4 - 7040*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a*b*c^(9/2)*d^5*e^4 + 81920*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^4*c^(7/2)*d^6*e^3 + 114240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*b^2*c^(9/2)*d^6*e^3 + 167680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^2*c^(11/2)*d^6*e^3 + 13760*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^5*c^(7/2)*d^7*e^2 - 37760*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^3*c^(9/2)*d^7*e^2 + 23040*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*b*c^(11/2)*d^7*e^2 - 192*b^6*c^(7/2)*d^8*e - 480*a*b^4*c^(9/2)*d^8*e + 480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*b^2*c^3*d^3*e^6 - 1920*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*a*c^4*d^3*e^6 - 20320*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*b^3*c^3*d^4*e^5 + 81280*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a*b*c^4*d^4*e^5 - 120680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b^4*c^3*d^5*e^4 - 122240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*b^2*c^4*d^5*e^4 + 226432*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^2*c^5*d^5*e^4 + 14080*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^5*c^3*d^6*e^3 + 88320*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^3*c^4*d^6*e^3 + 281600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*b*c^5*d^6*e^3 + 4280*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^6*c^3*d^7*e^2 - 8480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^4*c^4*d^7*e^2 + 11520*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b^2*c^5*d^7*e^2 - 6480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*b^3*c^(5/2)*d^3*e^6 + 25920*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a*b*c^(7/2)*d^3*e^6 + 7260*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*b^4*c^(5/2)*d^4*e^5 + 59680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a*b^2*c^(7/2)*d^4*e^5 + 182720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^2*c^(9/2)*d^4*e^5 - 85780*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^5*c^(5/2)*d^5*e^4 - 237120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*b^3*c^(7/2)*d^5*e^4 + 63040*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^2*b*c^(9/2)*d^5*e^4 - 6340*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^6*c^(5/2)*d^6*e^3 + 22000*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^4*c^(7/2)*d^6*e^3 + 176640*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*b^2*c^(9/2)*d^6*e^3 - 7680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^3*c^(11/2)*d^6*e^3 + 476*b^7*c^(5/2)*d^7*e^2 - 848*a*b^5*c^(7/2)*d^7*e^2 + 1920*a^2*b^3*c^(9/2)*d^7*e^2 - 720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*b^3*c^2*d^2*e^7 + 2880*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*a*b*c^3*d^2*e^7 + 10740*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*b^4*c^2*d^3*e^6 - 56480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a*b^2*c^3*d^3*e^6 + 54080*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^2*c^4*d^3*e^6 + 47944*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b^5*c^2*d^4*e^5 + 167520*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*b^3*c^3*d^4*e^5 - 17920*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^2*b*c^4*d^4*e^5 - 25220*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^6*c^2*d^5*e^4 - 124960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^4*c^3*d^5*e^4 - 239360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*b^2*c^4*d^5*e^4 - 160000*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^3*c^5*d^5*e^4 - 3080*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^7*c^2*d^6*e^3 + 480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^5*c^3*d^6*e^3 + 49280*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b^3*c^4*d^6*e^3 - 7680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*b*c^5*d^6*e^3 + 4050*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*b^4*c^(3/2)*d^2*e^7 - 19440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a*b^2*c^(5/2)*d^2*e^7 + 12960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a^2*c^(7/2)*d^2*e^7 + 9310*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*b^5*c^(3/2)*d^3*e^6 - 46960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a*b^3*c^(5/2)*d^3*e^6 - 176160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^2*b*c^(7/2)*d^3*e^6 + 35330*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^6*c^(3/2)*d^4*e^5 + 244660*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*b^4*c^(5/2)*d^4*e^5 + 32960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^2*b^2*c^(7/2)*d^4*e^5 - 178880*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^3*c^(9/2)*d^4*e^5 - 1750*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^7*c^(3/2)*d^5*e^4 - 13120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^5*c^(5/2)*d^5*e^4 - 187840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*b^3*c^(7/2)*d^5*e^4 - 216960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^3*b*c^(9/2)*d^5*e^4 - 380*b^8*c^(3/2)*d^6*e^3 - 332*a*b^6*c^(5/2)*d^6*e^3 + 5200*a^2*b^4*c^(7/2)*d^6*e^3 - 1920*a^3*b^2*c^(9/2)*d^6*e^3 + 450*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*b^4*c*d*e^8 - 2160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*a*b^2*c^2*d*e^8 + 1440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*a^2*c^3*d*e^8 - 1190*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*b^5*c*d^2*e^7 + 12080*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a*b^3*c^2*d^2*e^7 - 29280*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^2*b*c^3*d^2*e^7 - 4658*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b^6*c*d^3*e^6 - 80020*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*b^4*c^2*d^3*e^6 - 155840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^2*b^2*c^3*d^3*e^6 - 120640*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^3*c^4*d^3*e^6 + 10510*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^7*c*d^4*e^5 + 120280*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^5*c^2*d^4*e^5 + 200320*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*b^3*c^3*d^4*e^5 + 42240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^3*b*c^4*d^4*e^5 + 600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^8*c*d^5*e^4 + 5380*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^6*c^2*d^5*e^4 - 46840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b^4*c^3*d^5*e^4 - 98880*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*b^2*c^4*d^5*e^4 + 1920*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^4*c^5*d^5*e^4 - 945*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*b^5*sqrt(c)*d*e^8 + 5400*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a*b^3*c^(3/2)*d*e^8 - 6480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a^2*b*c^(5/2)*d*e^8 - 3430*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*b^6*sqrt(c)*d^2*e^7 + 4900*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a*b^4*c^(3/2)*d^2*e^7 + 93120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^2*b^2*c^(5/2)*d^2*e^7 - 16320*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^3*c^(7/2)*d^2*e^7 - 4480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^7*sqrt(c)*d^3*e^6 - 101890*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*b^5*c^(3/2)*d^3*e^6 - 179920*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^2*b^3*c^(5/2)*d^3*e^6 + 56160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^3*b*c^(7/2)*d^3*e^6 + 1470*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^8*sqrt(c)*d^4*e^5 + 16760*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^6*c^(3/2)*d^4*e^5 + 112660*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*b^4*c^(5/2)*d^4*e^5 + 212960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^3*b^2*c^(7/2)*d^4*e^5 + 89920*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^4*c^(9/2)*d^4*e^5 + 105*b^9*sqrt(c)*d^5*e^4 + 990*a*b^7*c^(3/2)*d^5*e^4 - 3244*a^2*b^5*c^(5/2)*d^5*e^4 - 15200*a^3*b^3*c^(7/2)*d^5*e^4 + 960*a^4*b*c^(9/2)*d^5*e^4 - 105*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*b^5*e^9 + 600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*a*b^3*c*e^9 - 720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*a^2*b*c^2*e^9 - 490*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*b^6*d*e^8 + 700*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a*b^4*c*d*e^8 + 6720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^2*b^2*c^2*d*e^8 - 6720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^3*c^3*d*e^8 - 896*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b^7*d^2*e^7 + 5938*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*b^5*c*d^2*e^7 + 105040*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^2*b^3*c^2*d^2*e^7 + 132000*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^3*b*c^3*d^2*e^7 - 790*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^8*d^3*e^6 - 47320*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^6*c*d^3*e^6 - 160420*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*b^4*c^2*d^3*e^6 - 79200*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^3*b^2*c^3*d^3*e^6 + 93120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^4*c^4*d^3*e^6 + 105*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^9*d^4*e^5 - 1950*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^7*c*d^4*e^5 + 16960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b^5*c^2*d^4*e^5 + 96640*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*b^3*c^3*d^4*e^5 + 85120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^4*b*c^4*d^4*e^5 + 3430*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a*b^5*sqrt(c)*d*e^8 - 19600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^2*b^3*c^(3/2)*d*e^8 - 7200*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^3*b*c^(5/2)*d*e^8 + 8960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*b^6*sqrt(c)*d^2*e^7 + 113920*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^2*b^4*c^(3/2)*d^2*e^7 + 51200*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^3*b^2*c^(5/2)*d^2*e^7 + 71680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^4*c^(7/2)*d^2*e^7 - 8250*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^7*sqrt(c)*d^3*e^6 - 46750*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*b^5*c^(3/2)*d^3*e^6 - 154800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^3*b^3*c^(5/2)*d^3*e^6 - 40160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^4*b*c^(7/2)*d^3*e^6 - 420*a*b^8*sqrt(c)*d^4*e^5 - 90*a^2*b^6*c^(3/2)*d^4*e^5 + 11420*a^3*b^4*c^(5/2)*d^4*e^5 + 20320*a^4*b^2*c^(7/2)*d^4*e^5 - 192*a^5*c^(9/2)*d^4*e^5 + 490*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a*b^5*e^9 - 2800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^2*b^3*c*e^9 + 3360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^3*b*c^2*e^9 + 1792*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*b^6*d*e^8 - 6400*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^2*b^4*c*d*e^8 - 92160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^3*b^2*c^2*d*e^8 + 15360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^4*c^3*d*e^8 + 2370*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^7*d^2*e^7 + 72310*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*b^5*c*d^2*e^7 + 71280*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^3*b^3*c^2*d^2*e^7 + 3680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^4*b*c^3*d^2*e^7 - 420*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^8*d^3*e^6 - 990*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b^6*c*d^3*e^6 - 49820*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*b^4*c^2*d^3*e^6 - 74400*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^4*b^2*c^3*d^3*e^6 - 24640*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^5*c^4*d^3*e^6 + 7680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^4*c^(5/2)*e^9 - 4480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^2*b^5*sqrt(c)*d*e^8 - 71680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^3*b^3*c^(3/2)*d*e^8 - 33280*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^4*b*c^(5/2)*d*e^8 + 15930*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*b^6*sqrt(c)*d^2*e^7 + 55340*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^3*b^4*c^(3/2)*d^2*e^7 + 58880*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^4*b^2*c^(5/2)*d^2*e^7 - 20800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^5*c^(7/2)*d^2*e^7 + 630*a^2*b^7*sqrt(c)*d^3*e^6 - 3150*a^3*b^5*c^(3/2)*d^3*e^6 - 16000*a^4*b^3*c^(5/2)*d^3*e^6 - 11936*a^5*b*c^(7/2)*d^3*e^6 - 896*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^2*b^5*e^9 + 5120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^3*b^3*c*e^9 + 15360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^4*b*c^2*e^9 - 2370*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*b^6*d*e^8 - 44700*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^3*b^4*c*d*e^8 - 17920*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^4*b^2*c^2*d*e^8 - 13760*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^5*c^3*d*e^8 + 630*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b^7*d^2*e^7 + 8670*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*b^5*c*d^2*e^7 + 43360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^4*b^3*c^2*d^2*e^7 + 16160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^5*b*c^3*d^2*e^7 + 24320*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^4*b^2*c^(3/2)*e^9 + 2560*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^5*c^(5/2)*e^9 - 12990*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^3*b^5*sqrt(c)*d*e^8 - 28720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^4*b^3*c^(3/2)*d*e^8 + 160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^5*b*c^(5/2)*d*e^8 - 420*a^3*b^6*sqrt(c)*d^2*e^7 + 5790*a^4*b^4*c^(3/2)*d^2*e^7 + 9008*a^5*b^2*c^(5/2)*d^2*e^7 + 2656*a^6*c^(7/2)*d^2*e^7 + 790*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^3*b^5*e^9 + 9200*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^4*b^3*c*e^9 + 12000*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^5*b*c^2*e^9 - 420*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*b^6*d*e^8 - 9570*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^4*b^4*c*d*e^8 - 13520*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^5*b^2*c^2*d*e^8 + 3680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^6*c^3*d*e^8 + 3840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^4*b^4*sqrt(c)*e^9 + 5120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^5*b^2*c^(3/2)*e^9 + 2560*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^6*c^(5/2)*e^9 + 105*a^4*b^5*sqrt(c)*d*e^8 - 4440*a^5*b^3*c^(3/2)*d*e^8 - 816*a^6*b*c^(5/2)*d*e^8 + 105*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^4*b^5*e^9 + 3240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^5*b^3*c*e^9 + 720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^6*b*c^2*e^9 + 1280*a^6*b^2*c^(3/2)*e^9 - 512*a^7*c^(5/2)*e^9)/((c^4*d^8*e^2 - 4*b*c^3*d^7*e^3 + 6*b^2*c^2*d^6*e^4 + 4*a*c^3*d^6*e^4 - 4*b^3*c*d^5*e^5 - 12*a*b*c^2*d^5*e^5 + b^4*d^4*e^6 + 12*a*b^2*c*d^4*e^6 + 6*a^2*c^2*d^4*e^6 - 4*a*b^3*d^3*e^7 - 12*a^2*b*c*d^3*e^7 + 6*a^2*b^2*d^2*e^8 + 4*a^3*c*d^2*e^8 - 4*a^3*b*d*e^9 + a^4*e^10)*((sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*e + 2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c)*d + b*d - a*e)^5)","B",0
2343,1,715,0,0.311035," ","integrate((e*x+d)^3*(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\frac{1}{35840} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(10 \, {\left(4 \, c x e^{3} + \frac{14 \, c^{7} d e^{2} + 5 \, b c^{6} e^{3}}{c^{6}}\right)} x + \frac{168 \, c^{7} d^{2} e + 182 \, b c^{6} d e^{2} + b^{2} c^{5} e^{3} + 64 \, a c^{6} e^{3}}{c^{6}}\right)} x + \frac{560 \, c^{7} d^{3} + 1848 \, b c^{6} d^{2} e + 42 \, b^{2} c^{5} d e^{2} + 1960 \, a c^{6} d e^{2} - 9 \, b^{3} c^{4} e^{3} + 44 \, a b c^{5} e^{3}}{c^{6}}\right)} x + \frac{1680 \, b c^{6} d^{3} + 168 \, b^{2} c^{5} d^{2} e + 5376 \, a c^{6} d^{2} e - 98 \, b^{3} c^{4} d e^{2} + 504 \, a b c^{5} d e^{2} + 21 \, b^{4} c^{3} e^{3} - 124 \, a b^{2} c^{4} e^{3} + 128 \, a^{2} c^{5} e^{3}}{c^{6}}\right)} x + \frac{560 \, b^{2} c^{5} d^{3} + 11200 \, a c^{6} d^{3} - 840 \, b^{3} c^{4} d^{2} e + 4704 \, a b c^{5} d^{2} e + 490 \, b^{4} c^{3} d e^{2} - 3024 \, a b^{2} c^{4} d e^{2} + 3360 \, a^{2} c^{5} d e^{2} - 105 \, b^{5} c^{2} e^{3} + 728 \, a b^{3} c^{3} e^{3} - 1168 \, a^{2} b c^{4} e^{3}}{c^{6}}\right)} x - \frac{1680 \, b^{3} c^{4} d^{3} - 11200 \, a b c^{5} d^{3} - 2520 \, b^{4} c^{3} d^{2} e + 16800 \, a b^{2} c^{4} d^{2} e - 21504 \, a^{2} c^{5} d^{2} e + 1470 \, b^{5} c^{2} d e^{2} - 10640 \, a b^{3} c^{3} d e^{2} + 18144 \, a^{2} b c^{4} d e^{2} - 315 \, b^{6} c e^{3} + 2520 \, a b^{4} c^{2} e^{3} - 5488 \, a^{2} b^{2} c^{3} e^{3} + 2048 \, a^{3} c^{4} e^{3}}{c^{6}}\right)} - \frac{3 \, {\left(16 \, b^{4} c^{3} d^{3} - 128 \, a b^{2} c^{4} d^{3} + 256 \, a^{2} c^{5} d^{3} - 24 \, b^{5} c^{2} d^{2} e + 192 \, a b^{3} c^{3} d^{2} e - 384 \, a^{2} b c^{4} d^{2} e + 14 \, b^{6} c d e^{2} - 120 \, a b^{4} c^{2} d e^{2} + 288 \, a^{2} b^{2} c^{3} d e^{2} - 128 \, a^{3} c^{4} d e^{2} - 3 \, b^{7} e^{3} + 28 \, a b^{5} c e^{3} - 80 \, a^{2} b^{3} c^{2} e^{3} + 64 \, a^{3} b c^{3} e^{3}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{2048 \, c^{\frac{11}{2}}}"," ",0,"1/35840*sqrt(c*x^2 + b*x + a)*(2*(4*(2*(8*(10*(4*c*x*e^3 + (14*c^7*d*e^2 + 5*b*c^6*e^3)/c^6)*x + (168*c^7*d^2*e + 182*b*c^6*d*e^2 + b^2*c^5*e^3 + 64*a*c^6*e^3)/c^6)*x + (560*c^7*d^3 + 1848*b*c^6*d^2*e + 42*b^2*c^5*d*e^2 + 1960*a*c^6*d*e^2 - 9*b^3*c^4*e^3 + 44*a*b*c^5*e^3)/c^6)*x + (1680*b*c^6*d^3 + 168*b^2*c^5*d^2*e + 5376*a*c^6*d^2*e - 98*b^3*c^4*d*e^2 + 504*a*b*c^5*d*e^2 + 21*b^4*c^3*e^3 - 124*a*b^2*c^4*e^3 + 128*a^2*c^5*e^3)/c^6)*x + (560*b^2*c^5*d^3 + 11200*a*c^6*d^3 - 840*b^3*c^4*d^2*e + 4704*a*b*c^5*d^2*e + 490*b^4*c^3*d*e^2 - 3024*a*b^2*c^4*d*e^2 + 3360*a^2*c^5*d*e^2 - 105*b^5*c^2*e^3 + 728*a*b^3*c^3*e^3 - 1168*a^2*b*c^4*e^3)/c^6)*x - (1680*b^3*c^4*d^3 - 11200*a*b*c^5*d^3 - 2520*b^4*c^3*d^2*e + 16800*a*b^2*c^4*d^2*e - 21504*a^2*c^5*d^2*e + 1470*b^5*c^2*d*e^2 - 10640*a*b^3*c^3*d*e^2 + 18144*a^2*b*c^4*d*e^2 - 315*b^6*c*e^3 + 2520*a*b^4*c^2*e^3 - 5488*a^2*b^2*c^3*e^3 + 2048*a^3*c^4*e^3)/c^6) - 3/2048*(16*b^4*c^3*d^3 - 128*a*b^2*c^4*d^3 + 256*a^2*c^5*d^3 - 24*b^5*c^2*d^2*e + 192*a*b^3*c^3*d^2*e - 384*a^2*b*c^4*d^2*e + 14*b^6*c*d*e^2 - 120*a*b^4*c^2*d*e^2 + 288*a^2*b^2*c^3*d*e^2 - 128*a^3*c^4*d*e^2 - 3*b^7*e^3 + 28*a*b^5*c*e^3 - 80*a^2*b^3*c^2*e^3 + 64*a^3*b*c^3*e^3)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(11/2)","B",0
2344,1,463,0,0.318387," ","integrate((e*x+d)^2*(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\frac{1}{7680} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(10 \, c x e^{2} + \frac{24 \, c^{6} d e + 13 \, b c^{5} e^{2}}{c^{5}}\right)} x + \frac{120 \, c^{6} d^{2} + 264 \, b c^{5} d e + 3 \, b^{2} c^{4} e^{2} + 140 \, a c^{5} e^{2}}{c^{5}}\right)} x + \frac{360 \, b c^{5} d^{2} + 24 \, b^{2} c^{4} d e + 768 \, a c^{5} d e - 7 \, b^{3} c^{3} e^{2} + 36 \, a b c^{4} e^{2}}{c^{5}}\right)} x + \frac{120 \, b^{2} c^{4} d^{2} + 2400 \, a c^{5} d^{2} - 120 \, b^{3} c^{3} d e + 672 \, a b c^{4} d e + 35 \, b^{4} c^{2} e^{2} - 216 \, a b^{2} c^{3} e^{2} + 240 \, a^{2} c^{4} e^{2}}{c^{5}}\right)} x - \frac{360 \, b^{3} c^{3} d^{2} - 2400 \, a b c^{4} d^{2} - 360 \, b^{4} c^{2} d e + 2400 \, a b^{2} c^{3} d e - 3072 \, a^{2} c^{4} d e + 105 \, b^{5} c e^{2} - 760 \, a b^{3} c^{2} e^{2} + 1296 \, a^{2} b c^{3} e^{2}}{c^{5}}\right)} - \frac{{\left(24 \, b^{4} c^{2} d^{2} - 192 \, a b^{2} c^{3} d^{2} + 384 \, a^{2} c^{4} d^{2} - 24 \, b^{5} c d e + 192 \, a b^{3} c^{2} d e - 384 \, a^{2} b c^{3} d e + 7 \, b^{6} e^{2} - 60 \, a b^{4} c e^{2} + 144 \, a^{2} b^{2} c^{2} e^{2} - 64 \, a^{3} c^{3} e^{2}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{1024 \, c^{\frac{9}{2}}}"," ",0,"1/7680*sqrt(c*x^2 + b*x + a)*(2*(4*(2*(8*(10*c*x*e^2 + (24*c^6*d*e + 13*b*c^5*e^2)/c^5)*x + (120*c^6*d^2 + 264*b*c^5*d*e + 3*b^2*c^4*e^2 + 140*a*c^5*e^2)/c^5)*x + (360*b*c^5*d^2 + 24*b^2*c^4*d*e + 768*a*c^5*d*e - 7*b^3*c^3*e^2 + 36*a*b*c^4*e^2)/c^5)*x + (120*b^2*c^4*d^2 + 2400*a*c^5*d^2 - 120*b^3*c^3*d*e + 672*a*b*c^4*d*e + 35*b^4*c^2*e^2 - 216*a*b^2*c^3*e^2 + 240*a^2*c^4*e^2)/c^5)*x - (360*b^3*c^3*d^2 - 2400*a*b*c^4*d^2 - 360*b^4*c^2*d*e + 2400*a*b^2*c^3*d*e - 3072*a^2*c^4*d*e + 105*b^5*c*e^2 - 760*a*b^3*c^2*e^2 + 1296*a^2*b*c^3*e^2)/c^5) - 1/1024*(24*b^4*c^2*d^2 - 192*a*b^2*c^3*d^2 + 384*a^2*c^4*d^2 - 24*b^5*c*d*e + 192*a*b^3*c^2*d*e - 384*a^2*b*c^3*d*e + 7*b^6*e^2 - 60*a*b^4*c*e^2 + 144*a^2*b^2*c^2*e^2 - 64*a^3*c^3*e^2)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(9/2)","B",0
2345,1,264,0,0.292199," ","integrate((e*x+d)*(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\frac{1}{640} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, c x e + \frac{10 \, c^{5} d + 11 \, b c^{4} e}{c^{4}}\right)} x + \frac{30 \, b c^{4} d + b^{2} c^{3} e + 32 \, a c^{4} e}{c^{4}}\right)} x + \frac{10 \, b^{2} c^{3} d + 200 \, a c^{4} d - 5 \, b^{3} c^{2} e + 28 \, a b c^{3} e}{c^{4}}\right)} x - \frac{30 \, b^{3} c^{2} d - 200 \, a b c^{3} d - 15 \, b^{4} c e + 100 \, a b^{2} c^{2} e - 128 \, a^{2} c^{3} e}{c^{4}}\right)} - \frac{3 \, {\left(2 \, b^{4} c d - 16 \, a b^{2} c^{2} d + 32 \, a^{2} c^{3} d - b^{5} e + 8 \, a b^{3} c e - 16 \, a^{2} b c^{2} e\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{256 \, c^{\frac{7}{2}}}"," ",0,"1/640*sqrt(c*x^2 + b*x + a)*(2*(4*(2*(8*c*x*e + (10*c^5*d + 11*b*c^4*e)/c^4)*x + (30*b*c^4*d + b^2*c^3*e + 32*a*c^4*e)/c^4)*x + (10*b^2*c^3*d + 200*a*c^4*d - 5*b^3*c^2*e + 28*a*b*c^3*e)/c^4)*x - (30*b^3*c^2*d - 200*a*b*c^3*d - 15*b^4*c*e + 100*a*b^2*c^2*e - 128*a^2*c^3*e)/c^4) - 3/256*(2*b^4*c*d - 16*a*b^2*c^2*d + 32*a^2*c^3*d - b^5*e + 8*a*b^3*c*e - 16*a^2*b*c^2*e)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(7/2)","A",0
2346,1,123,0,0.217586," ","integrate((c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\frac{1}{64} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(2 \, c x + 3 \, b\right)} x + \frac{b^{2} c^{2} + 20 \, a c^{3}}{c^{3}}\right)} x - \frac{3 \, b^{3} c - 20 \, a b c^{2}}{c^{3}}\right)} - \frac{3 \, {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{128 \, c^{\frac{5}{2}}}"," ",0,"1/64*sqrt(c*x^2 + b*x + a)*(2*(4*(2*c*x + 3*b)*x + (b^2*c^2 + 20*a*c^3)/c^3)*x - (3*b^3*c - 20*a*b*c^2)/c^3) - 3/128*(b^4 - 8*a*b^2*c + 16*a^2*c^2)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(5/2)","A",0
2347,-2,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)/(e*x+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error: Bad Argument Type","F(-2)",0
2348,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)/(e*x+d)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2349,-2,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)/(e*x+d)^3,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 0.74Unable to divide, perhaps due to rounding error%%%{1,[6,0,7,0,0]%%%}+%%%{%%{[-6,0]:[1,0,%%%{-1,[1]%%%}]%%},[5,0,6,1,0]%%%}+%%%{3,[4,1,6,1,0]%%%}+%%%{-3,[4,0,7,0,1]%%%}+%%%{%%%{12,[1]%%%},[4,0,5,2,0]%%%}+%%%{%%{[-12,0]:[1,0,%%%{-1,[1]%%%}]%%},[3,1,5,2,0]%%%}+%%%{%%{[12,0]:[1,0,%%%{-1,[1]%%%}]%%},[3,0,6,1,1]%%%}+%%%{%%{[%%%{-8,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,0,4,3,0]%%%}+%%%{3,[2,2,5,2,0]%%%}+%%%{-6,[2,1,6,1,1]%%%}+%%%{%%%{12,[1]%%%},[2,1,4,3,0]%%%}+%%%{3,[2,0,7,0,2]%%%}+%%%{%%%{-12,[1]%%%},[2,0,5,2,1]%%%}+%%%{%%{[-6,0]:[1,0,%%%{-1,[1]%%%}]%%},[1,2,4,3,0]%%%}+%%%{%%{[12,0]:[1,0,%%%{-1,[1]%%%}]%%},[1,1,5,2,1]%%%}+%%%{%%{[-6,0]:[1,0,%%%{-1,[1]%%%}]%%},[1,0,6,1,2]%%%}+%%%{1,[0,3,4,3,0]%%%}+%%%{-3,[0,2,5,2,1]%%%}+%%%{3,[0,1,6,1,2]%%%}+%%%{-1,[0,0,7,0,3]%%%} / %%%{%%{poly1[%%%{1,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[6,0,3,0,0]%%%}+%%%{%%%{-6,[2]%%%},[5,0,2,1,0]%%%}+%%%{%%{[%%%{3,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,1,2,1,0]%%%}+%%%{%%{poly1[%%%{-3,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,3,0,1]%%%}+%%%{%%{poly1[%%%{12,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,1,2,0]%%%}+%%%{%%%{-12,[2]%%%},[3,1,1,2,0]%%%}+%%%{%%%{12,[2]%%%},[3,0,2,1,1]%%%}+%%%{%%%{-8,[3]%%%},[3,0,0,3,0]%%%}+%%%{%%{[%%%{3,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,2,1,2,0]%%%}+%%%{%%{[%%%{-6,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,1,2,1,1]%%%}+%%%{%%{[%%%{12,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,1,0,3,0]%%%}+%%%{%%{poly1[%%%{3,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,3,0,2]%%%}+%%%{%%{poly1[%%%{-12,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,1,2,1]%%%}+%%%{%%%{-6,[2]%%%},[1,2,0,3,0]%%%}+%%%{%%%{12,[2]%%%},[1,1,1,2,1]%%%}+%%%{%%%{-6,[2]%%%},[1,0,2,1,2]%%%}+%%%{%%{[%%%{1,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,3,0,3,0]%%%}+%%%{%%{[%%%{-3,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,2,1,2,1]%%%}+%%%{%%{[%%%{3,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,1,2,1,2]%%%}+%%%{%%{poly1[%%%{-1,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,3,0,3]%%%} Error: Bad Argument Value","F(-2)",0
2350,-2,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)/(e*x+d)^4,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 41.72Unable to divide, perhaps due to rounding error%%%{%%{[-1,0]:[1,0,%%%{-1,[1]%%%}]%%},[8,0,0,8,0]%%%}+%%%{%%%{8,[1]%%%},[7,0,0,7,1]%%%}+%%%{%%{[-4,0]:[1,0,%%%{-1,[1]%%%}]%%},[6,1,0,7,1]%%%}+%%%{%%{[4,0]:[1,0,%%%{-1,[1]%%%}]%%},[6,0,1,8,0]%%%}+%%%{%%{[%%%{-24,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[6,0,0,6,2]%%%}+%%%{%%%{24,[1]%%%},[5,1,0,6,2]%%%}+%%%{%%%{-24,[1]%%%},[5,0,1,7,1]%%%}+%%%{%%%{32,[2]%%%},[5,0,0,5,3]%%%}+%%%{%%{[-6,0]:[1,0,%%%{-1,[1]%%%}]%%},[4,2,0,6,2]%%%}+%%%{%%{[12,0]:[1,0,%%%{-1,[1]%%%}]%%},[4,1,1,7,1]%%%}+%%%{%%{[%%%{-48,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,1,0,5,3]%%%}+%%%{%%{[-6,0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,2,8,0]%%%}+%%%{%%{[%%%{48,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,1,6,2]%%%}+%%%{%%{[%%%{-16,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[4,0,0,4,4]%%%}+%%%{%%%{24,[1]%%%},[3,2,0,5,3]%%%}+%%%{%%%{-48,[1]%%%},[3,1,1,6,2]%%%}+%%%{%%%{32,[2]%%%},[3,1,0,4,4]%%%}+%%%{%%%{24,[1]%%%},[3,0,2,7,1]%%%}+%%%{%%%{-32,[2]%%%},[3,0,1,5,3]%%%}+%%%{%%{[-4,0]:[1,0,%%%{-1,[1]%%%}]%%},[2,3,0,5,3]%%%}+%%%{%%{[12,0]:[1,0,%%%{-1,[1]%%%}]%%},[2,2,1,6,2]%%%}+%%%{%%{[%%%{-24,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,2,0,4,4]%%%}+%%%{%%{[-12,0]:[1,0,%%%{-1,[1]%%%}]%%},[2,1,2,7,1]%%%}+%%%{%%{[%%%{48,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,1,1,5,3]%%%}+%%%{%%{[4,0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,3,8,0]%%%}+%%%{%%{[%%%{-24,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[2,0,2,6,2]%%%}+%%%{%%%{8,[1]%%%},[1,3,0,4,4]%%%}+%%%{%%%{-24,[1]%%%},[1,2,1,5,3]%%%}+%%%{%%%{24,[1]%%%},[1,1,2,6,2]%%%}+%%%{%%%{-8,[1]%%%},[1,0,3,7,1]%%%}+%%%{%%{[-1,0]:[1,0,%%%{-1,[1]%%%}]%%},[0,4,0,4,4]%%%}+%%%{%%{[4,0]:[1,0,%%%{-1,[1]%%%}]%%},[0,3,1,5,3]%%%}+%%%{%%{[-6,0]:[1,0,%%%{-1,[1]%%%}]%%},[0,2,2,6,2]%%%}+%%%{%%{[4,0]:[1,0,%%%{-1,[1]%%%}]%%},[0,1,3,7,1]%%%}+%%%{%%{[-1,0]:[1,0,%%%{-1,[1]%%%}]%%},[0,0,4,8,0]%%%} / %%%{%%%{1,[2]%%%},[8,0,0,4,0]%%%}+%%%{%%{poly1[%%%{-8,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,0,0,3,1]%%%}+%%%{%%%{4,[2]%%%},[6,1,0,3,1]%%%}+%%%{%%%{-4,[2]%%%},[6,0,1,4,0]%%%}+%%%{%%%{24,[3]%%%},[6,0,0,2,2]%%%}+%%%{%%{[%%%{-24,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,1,0,2,2]%%%}+%%%{%%{poly1[%%%{24,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,0,1,3,1]%%%}+%%%{%%{poly1[%%%{-32,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,0,0,1,3]%%%}+%%%{%%%{6,[2]%%%},[4,2,0,2,2]%%%}+%%%{%%%{-12,[2]%%%},[4,1,1,3,1]%%%}+%%%{%%%{48,[3]%%%},[4,1,0,1,3]%%%}+%%%{%%%{6,[2]%%%},[4,0,2,4,0]%%%}+%%%{%%%{-48,[3]%%%},[4,0,1,2,2]%%%}+%%%{%%%{16,[4]%%%},[4,0,0,0,4]%%%}+%%%{%%{poly1[%%%{-24,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,2,0,1,3]%%%}+%%%{%%{[%%%{48,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,1,1,2,2]%%%}+%%%{%%{[%%%{-32,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,1,0,0,4]%%%}+%%%{%%{poly1[%%%{-24,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,0,2,3,1]%%%}+%%%{%%{poly1[%%%{32,[3]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,0,1,1,3]%%%}+%%%{%%%{4,[2]%%%},[2,3,0,1,3]%%%}+%%%{%%%{-12,[2]%%%},[2,2,1,2,2]%%%}+%%%{%%%{24,[3]%%%},[2,2,0,0,4]%%%}+%%%{%%%{12,[2]%%%},[2,1,2,3,1]%%%}+%%%{%%%{-48,[3]%%%},[2,1,1,1,3]%%%}+%%%{%%%{-4,[2]%%%},[2,0,3,4,0]%%%}+%%%{%%%{24,[3]%%%},[2,0,2,2,2]%%%}+%%%{%%{[%%%{-8,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,3,0,0,4]%%%}+%%%{%%{poly1[%%%{24,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,2,1,1,3]%%%}+%%%{%%{[%%%{-24,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,1,2,2,2]%%%}+%%%{%%{poly1[%%%{8,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,0,3,3,1]%%%}+%%%{%%%{1,[2]%%%},[0,4,0,0,4]%%%}+%%%{%%%{-4,[2]%%%},[0,3,1,1,3]%%%}+%%%{%%%{6,[2]%%%},[0,2,2,2,2]%%%}+%%%{%%%{-4,[2]%%%},[0,1,3,3,1]%%%}+%%%{%%%{1,[2]%%%},[0,0,4,4,0]%%%} Error: Bad Argument Value","F(-2)",0
2351,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)/(e*x+d)^5,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2352,1,8184,0,3.692040," ","integrate((c*x^2+b*x+a)^(3/2)/(e*x+d)^6,x, algorithm=""giac"")","\frac{3 \, {\left(2 \, b^{4} c d - 16 \, a b^{2} c^{2} d + 32 \, a^{2} c^{3} d - b^{5} e + 8 \, a b^{3} c e - 16 \, a^{2} b c^{2} e\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} + b d e - a e^{2}}}\right)}{128 \, {\left(c^{3} d^{6} - 3 \, b c^{2} d^{5} e + 3 \, b^{2} c d^{4} e^{2} + 3 \, a c^{2} d^{4} e^{2} - b^{3} d^{3} e^{3} - 6 \, a b c d^{3} e^{3} + 3 \, a b^{2} d^{2} e^{4} + 3 \, a^{2} c d^{2} e^{4} - 3 \, a^{2} b d e^{5} + a^{3} e^{6}\right)} \sqrt{-c d^{2} + b d e - a e^{2}}} + \frac{2560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} c^{\frac{13}{2}} d^{8} e + 1024 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} c^{7} d^{9} + 2560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} c^{6} d^{7} e^{2} + 3072 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} b c^{6} d^{8} e + 2560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} b c^{\frac{13}{2}} d^{9} + 1280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} c^{\frac{11}{2}} d^{6} e^{3} - 1280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} b c^{\frac{11}{2}} d^{7} e^{2} - 1280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} b^{2} c^{\frac{11}{2}} d^{8} e - 2560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a c^{\frac{13}{2}} d^{8} e + 2560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{2} c^{6} d^{9} - 3840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} b c^{5} d^{6} e^{3} - 7936 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} b^{2} c^{5} d^{7} e^{2} - 512 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a c^{6} d^{7} e^{2} - 3840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{3} c^{5} d^{8} e - 5120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b c^{6} d^{8} e + 1280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{3} c^{\frac{11}{2}} d^{9} - 3840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} b c^{\frac{9}{2}} d^{5} e^{4} - 6400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} b^{2} c^{\frac{9}{2}} d^{6} e^{3} + 7680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} a c^{\frac{11}{2}} d^{6} e^{3} - 6400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} b^{3} c^{\frac{9}{2}} d^{7} e^{2} + 8960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a b c^{\frac{11}{2}} d^{7} e^{2} - 2400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{4} c^{\frac{9}{2}} d^{8} e - 3840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a b^{2} c^{\frac{11}{2}} d^{8} e + 320 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{4} c^{5} d^{9} - 3840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} b^{2} c^{4} d^{5} e^{4} + 7680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} a c^{5} d^{5} e^{4} - 1280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} b^{3} c^{4} d^{6} e^{3} + 24832 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a b c^{5} d^{6} e^{3} - 1600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{4} c^{4} d^{7} e^{2} + 17920 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b^{2} c^{5} d^{7} e^{2} + 2560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{2} c^{6} d^{7} e^{2} - 640 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{5} c^{4} d^{8} e - 1280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{3} c^{5} d^{8} e + 32 \, b^{5} c^{\frac{9}{2}} d^{9} + 3840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} b^{2} c^{\frac{7}{2}} d^{4} e^{5} + 3840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} a c^{\frac{9}{2}} d^{4} e^{5} + 1280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} b^{3} c^{\frac{7}{2}} d^{5} e^{4} + 3840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} a b c^{\frac{9}{2}} d^{5} e^{4} + 2400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} b^{4} c^{\frac{7}{2}} d^{6} e^{3} + 19200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a b^{2} c^{\frac{9}{2}} d^{6} e^{3} - 7680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{2} c^{\frac{11}{2}} d^{6} e^{3} + 160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{5} c^{\frac{7}{2}} d^{7} e^{2} + 12800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a b^{3} c^{\frac{9}{2}} d^{7} e^{2} + 3840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{2} b c^{\frac{11}{2}} d^{7} e^{2} - 64 \, b^{6} c^{\frac{7}{2}} d^{8} e - 160 \, a b^{4} c^{\frac{9}{2}} d^{8} e + 8960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} b^{3} c^{3} d^{4} e^{5} - 3840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} a b c^{4} d^{4} e^{5} + 4280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} b^{4} c^{3} d^{5} e^{4} - 18880 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a b^{2} c^{4} d^{5} e^{4} - 25216 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{2} c^{5} d^{5} e^{4} + 2080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{5} c^{3} d^{6} e^{3} - 24320 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{2} b c^{5} d^{6} e^{3} + 120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{6} c^{3} d^{7} e^{2} + 4000 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{4} c^{4} d^{7} e^{2} + 1920 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} b^{2} c^{5} d^{7} e^{2} - 1280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} b^{3} c^{\frac{5}{2}} d^{3} e^{6} - 7680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} a b c^{\frac{7}{2}} d^{3} e^{6} + 7420 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} b^{4} c^{\frac{5}{2}} d^{4} e^{5} - 3040 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} a b^{2} c^{\frac{7}{2}} d^{4} e^{5} - 16960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} a^{2} c^{\frac{9}{2}} d^{4} e^{5} + 2860 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} b^{5} c^{\frac{5}{2}} d^{5} e^{4} - 21600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a b^{3} c^{\frac{7}{2}} d^{5} e^{4} - 40000 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{2} b c^{\frac{9}{2}} d^{5} e^{4} + 860 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{6} c^{\frac{5}{2}} d^{6} e^{3} - 5200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a b^{4} c^{\frac{7}{2}} d^{6} e^{3} - 24000 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{2} b^{2} c^{\frac{9}{2}} d^{6} e^{3} - 1280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{3} c^{\frac{11}{2}} d^{6} e^{3} + 12 \, b^{7} c^{\frac{5}{2}} d^{7} e^{2} + 464 \, a b^{5} c^{\frac{7}{2}} d^{7} e^{2} + 320 \, a^{2} b^{3} c^{\frac{9}{2}} d^{7} e^{2} - 4780 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} b^{4} c^{2} d^{3} e^{6} - 7840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} a b^{2} c^{3} d^{3} e^{6} - 7360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} a^{2} c^{4} d^{3} e^{6} + 1448 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} b^{5} c^{2} d^{4} e^{5} + 8640 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a b^{3} c^{3} d^{4} e^{5} + 12160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{2} b c^{4} d^{4} e^{5} + 540 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{6} c^{2} d^{5} e^{4} - 7520 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b^{4} c^{3} d^{5} e^{4} - 13120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{2} b^{2} c^{4} d^{5} e^{4} + 12800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{3} c^{5} d^{5} e^{4} + 200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{7} c^{2} d^{6} e^{3} - 1920 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{5} c^{3} d^{6} e^{3} - 9600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} b^{3} c^{4} d^{6} e^{3} - 1280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{3} b c^{5} d^{6} e^{3} - 270 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} b^{4} c^{\frac{3}{2}} d^{2} e^{7} + 6000 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} a b^{2} c^{\frac{5}{2}} d^{2} e^{7} - 480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} a^{2} c^{\frac{7}{2}} d^{2} e^{7} - 5330 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} b^{5} c^{\frac{3}{2}} d^{3} e^{6} - 9840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} a b^{3} c^{\frac{5}{2}} d^{3} e^{6} + 8160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} a^{2} b c^{\frac{7}{2}} d^{3} e^{6} - 1390 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} b^{6} c^{\frac{3}{2}} d^{4} e^{5} + 9620 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a b^{4} c^{\frac{5}{2}} d^{4} e^{5} + 37120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{2} b^{2} c^{\frac{7}{2}} d^{4} e^{5} + 37440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{3} c^{\frac{9}{2}} d^{4} e^{5} - 230 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{7} c^{\frac{3}{2}} d^{5} e^{4} - 320 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a b^{5} c^{\frac{5}{2}} d^{5} e^{4} + 5920 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{2} b^{3} c^{\frac{7}{2}} d^{5} e^{4} + 23040 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{3} b c^{\frac{9}{2}} d^{5} e^{4} + 20 \, b^{8} c^{\frac{3}{2}} d^{6} e^{3} - 204 \, a b^{6} c^{\frac{5}{2}} d^{6} e^{3} - 1360 \, a^{2} b^{4} c^{\frac{7}{2}} d^{6} e^{3} - 320 \, a^{3} b^{2} c^{\frac{9}{2}} d^{6} e^{3} - 30 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} b^{4} c d e^{8} + 240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} a b^{2} c^{2} d e^{8} - 480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} a^{2} c^{3} d e^{8} + 330 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} b^{5} c d^{2} e^{7} + 8880 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} a b^{3} c^{2} d^{2} e^{7} + 9120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} a^{2} b c^{3} d^{2} e^{7} - 2626 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} b^{6} c d^{3} e^{6} - 6260 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a b^{4} c^{2} d^{3} e^{6} - 21760 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{2} b^{2} c^{3} d^{3} e^{6} + 29120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{3} c^{4} d^{3} e^{6} - 930 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{7} c d^{4} e^{5} + 4760 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b^{5} c^{2} d^{4} e^{5} + 14240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{2} b^{3} c^{3} d^{4} e^{5} + 42880 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{3} b c^{4} d^{4} e^{5} - 120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{8} c d^{5} e^{4} + 260 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{6} c^{2} d^{5} e^{4} + 3880 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} b^{4} c^{3} d^{5} e^{4} + 12800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{3} b^{2} c^{4} d^{5} e^{4} + 640 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{4} c^{5} d^{5} e^{4} + 135 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} b^{5} \sqrt{c} d e^{8} - 1080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} a b^{3} c^{\frac{3}{2}} d e^{8} - 1680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} a^{2} b c^{\frac{5}{2}} d e^{8} + 490 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} b^{6} \sqrt{c} d^{2} e^{7} + 12420 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} a b^{4} c^{\frac{3}{2}} d^{2} e^{7} - 3840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} a^{2} b^{2} c^{\frac{5}{2}} d^{2} e^{7} + 18240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} a^{3} c^{\frac{7}{2}} d^{2} e^{7} - 640 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} b^{7} \sqrt{c} d^{3} e^{6} + 1390 \, {\left(\sqrt{c} x - 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\sqrt{c x^{2} + b x + a}\right)}^{9} b^{5} e^{9} - 120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} a b^{3} c e^{9} + 240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} a^{2} b c^{2} e^{9} + 70 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} b^{6} d e^{8} - 420 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} a b^{4} c d e^{8} - 11520 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} a^{2} b^{2} c^{2} d e^{8} + 4800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} a^{3} c^{3} d e^{8} + 128 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} b^{7} d^{2} e^{7} + 9026 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a b^{5} c d^{2} e^{7} + 1520 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{2} b^{3} c^{2} d^{2} e^{7} + 11040 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{3} b c^{3} d^{2} e^{7} - 70 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{8} d^{3} e^{6} + 2280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b^{6} c d^{3} e^{6} - 20420 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{2} b^{4} c^{2} d^{3} e^{6} - 20320 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{3} b^{2} c^{3} d^{3} e^{6} - 24640 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{4} c^{4} d^{3} e^{6} - 15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{9} d^{4} e^{5} + 450 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{7} c d^{4} e^{5} - 2080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} b^{5} c^{2} d^{4} e^{5} - 1120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{3} b^{3} c^{3} d^{4} e^{5} - 8960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{4} b c^{4} d^{4} e^{5} + 1280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} a^{3} c^{\frac{5}{2}} e^{9} - 490 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} a b^{5} \sqrt{c} d e^{8} - 11440 \, {\left(\sqrt{c} x - 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330 \, a^{2} b^{6} c^{\frac{3}{2}} d^{4} e^{5} - 260 \, a^{3} b^{4} c^{\frac{5}{2}} d^{4} e^{5} - 2560 \, a^{4} b^{2} c^{\frac{7}{2}} d^{4} e^{5} - 64 \, a^{5} c^{\frac{9}{2}} d^{4} e^{5} - 70 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} a b^{5} e^{9} + 560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} a^{2} b^{3} c e^{9} + 2720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} a^{3} b c^{2} e^{9} - 256 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a b^{6} d e^{8} - 8960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{2} b^{4} c d e^{8} - 7680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{4} c^{3} d e^{8} + 210 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b^{7} d^{2} e^{7} + 230 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{2} b^{5} c d^{2} e^{7} + 26480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{3} b^{3} c^{2} d^{2} e^{7} + 6240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{4} b c^{3} d^{2} e^{7} + 60 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{8} d^{3} e^{6} - 750 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} b^{6} c d^{3} e^{6} + 2820 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{3} b^{4} c^{2} d^{3} e^{6} - 5760 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{4} b^{2} c^{3} d^{3} e^{6} + 2880 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{5} c^{4} d^{3} e^{6} + 5120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} a^{3} b^{2} c^{\frac{3}{2}} e^{9} - 3200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{2} b^{5} \sqrt{c} d e^{8} - 7680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{3} b^{3} c^{\frac{3}{2}} d e^{8} - 3840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{4} b c^{\frac{5}{2}} d e^{8} - 630 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{2} b^{6} \sqrt{c} d^{2} e^{7} + 7180 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{3} b^{4} c^{\frac{3}{2}} d^{2} e^{7} + 7360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{4} b^{2} c^{\frac{5}{2}} d^{2} e^{7} + 11200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{5} c^{\frac{7}{2}} d^{2} e^{7} - 90 \, a^{2} b^{7} \sqrt{c} d^{3} e^{6} + 610 \, a^{3} b^{5} c^{\frac{3}{2}} d^{3} e^{6} - 560 \, a^{4} b^{3} c^{\frac{5}{2}} d^{3} e^{6} + 1568 \, a^{5} b c^{\frac{7}{2}} d^{3} e^{6} + 128 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{2} b^{5} e^{9} + 2560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{3} b^{3} c e^{9} + 3840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{4} b c^{2} e^{9} - 210 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{2} b^{6} d e^{8} - 3580 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{3} b^{4} c d e^{8} - 13760 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{4} b^{2} c^{2} d e^{8} + 5440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{5} c^{3} d e^{8} - 90 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} b^{7} d^{2} e^{7} + 750 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{3} b^{5} c d^{2} e^{7} - 400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{4} b^{3} c^{2} d^{2} e^{7} + 6880 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{5} b c^{3} d^{2} e^{7} + 1280 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{3} b^{4} \sqrt{c} e^{9} + 2560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{4} b^{2} c^{\frac{3}{2}} e^{9} + 2560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{5} c^{\frac{5}{2}} e^{9} + 210 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{3} b^{5} \sqrt{c} d e^{8} - 6800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{4} b^{3} c^{\frac{3}{2}} d e^{8} - 3040 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{5} b c^{\frac{5}{2}} d e^{8} + 60 \, a^{3} b^{6} \sqrt{c} d^{2} e^{7} - 450 \, a^{4} b^{4} c^{\frac{3}{2}} d^{2} e^{7} + 976 \, a^{5} b^{2} c^{\frac{5}{2}} d^{2} e^{7} - 288 \, a^{6} c^{\frac{7}{2}} d^{2} e^{7} + 70 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{3} b^{5} e^{9} + 2000 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{4} b^{3} c e^{9} + 2400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{5} b c^{2} e^{9} + 60 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{3} b^{6} d e^{8} - 450 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{4} b^{4} c d e^{8} - 1840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{5} b^{2} c^{2} d e^{8} - 2080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{6} c^{3} d e^{8} + 2560 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{5} b^{2} c^{\frac{3}{2}} e^{9} - 15 \, a^{4} b^{5} \sqrt{c} d e^{8} + 120 \, a^{5} b^{3} c^{\frac{3}{2}} d e^{8} - 752 \, a^{6} b c^{\frac{5}{2}} d e^{8} - 15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{4} b^{5} e^{9} + 120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{5} b^{3} c e^{9} + 1040 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{6} b c^{2} e^{9} + 256 \, a^{7} c^{\frac{5}{2}} e^{9}}{640 \, {\left(c^{3} d^{6} e^{4} - 3 \, b c^{2} d^{5} e^{5} + 3 \, b^{2} c d^{4} e^{6} + 3 \, a c^{2} d^{4} e^{6} - b^{3} d^{3} e^{7} - 6 \, a b c d^{3} e^{7} + 3 \, a b^{2} d^{2} e^{8} + 3 \, a^{2} c d^{2} e^{8} - 3 \, a^{2} b d e^{9} + a^{3} e^{10}\right)} {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} e + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} d + b d - a e\right)}^{5}}"," ",0,"3/128*(2*b^4*c*d - 16*a*b^2*c^2*d + 32*a^2*c^3*d - b^5*e + 8*a*b^3*c*e - 16*a^2*b*c^2*e)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + b*x + a))*e + sqrt(c)*d)/sqrt(-c*d^2 + b*d*e - a*e^2))/((c^3*d^6 - 3*b*c^2*d^5*e + 3*b^2*c*d^4*e^2 + 3*a*c^2*d^4*e^2 - b^3*d^3*e^3 - 6*a*b*c*d^3*e^3 + 3*a*b^2*d^2*e^4 + 3*a^2*c*d^2*e^4 - 3*a^2*b*d*e^5 + a^3*e^6)*sqrt(-c*d^2 + b*d*e - a*e^2)) + 1/640*(2560*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*c^(13/2)*d^8*e + 1024*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*c^7*d^9 + 2560*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*c^6*d^7*e^2 + 3072*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b*c^6*d^8*e + 2560*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b*c^(13/2)*d^9 + 1280*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*c^(11/2)*d^6*e^3 - 1280*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*b*c^(11/2)*d^7*e^2 - 1280*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^2*c^(11/2)*d^8*e - 2560*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*c^(13/2)*d^8*e + 2560*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^2*c^6*d^9 - 3840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*b*c^5*d^6*e^3 - 7936*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b^2*c^5*d^7*e^2 - 512*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*c^6*d^7*e^2 - 3840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^3*c^5*d^8*e - 5120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b*c^6*d^8*e + 1280*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^3*c^(11/2)*d^9 - 3840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*b*c^(9/2)*d^5*e^4 - 6400*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*b^2*c^(9/2)*d^6*e^3 + 7680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a*c^(11/2)*d^6*e^3 - 6400*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^3*c^(9/2)*d^7*e^2 + 8960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*b*c^(11/2)*d^7*e^2 - 2400*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^4*c^(9/2)*d^8*e - 3840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^2*c^(11/2)*d^8*e + 320*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^4*c^5*d^9 - 3840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*b^2*c^4*d^5*e^4 + 7680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a*c^5*d^5*e^4 - 1280*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b^3*c^4*d^6*e^3 + 24832*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*b*c^5*d^6*e^3 - 1600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^4*c^4*d^7*e^2 + 17920*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^2*c^5*d^7*e^2 + 2560*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*c^6*d^7*e^2 - 640*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^5*c^4*d^8*e - 1280*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^3*c^5*d^8*e + 32*b^5*c^(9/2)*d^9 + 3840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*b^2*c^(7/2)*d^4*e^5 + 3840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a*c^(9/2)*d^4*e^5 + 1280*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*b^3*c^(7/2)*d^5*e^4 + 3840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a*b*c^(9/2)*d^5*e^4 + 2400*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^4*c^(7/2)*d^6*e^3 + 19200*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*b^2*c^(9/2)*d^6*e^3 - 7680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^2*c^(11/2)*d^6*e^3 + 160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^5*c^(7/2)*d^7*e^2 + 12800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^3*c^(9/2)*d^7*e^2 + 3840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*b*c^(11/2)*d^7*e^2 - 64*b^6*c^(7/2)*d^8*e - 160*a*b^4*c^(9/2)*d^8*e + 8960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*b^3*c^3*d^4*e^5 - 3840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a*b*c^4*d^4*e^5 + 4280*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b^4*c^3*d^5*e^4 - 18880*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*b^2*c^4*d^5*e^4 - 25216*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^2*c^5*d^5*e^4 + 2080*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^5*c^3*d^6*e^3 - 24320*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*b*c^5*d^6*e^3 + 120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^6*c^3*d^7*e^2 + 4000*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^4*c^4*d^7*e^2 + 1920*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b^2*c^5*d^7*e^2 - 1280*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*b^3*c^(5/2)*d^3*e^6 - 7680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a*b*c^(7/2)*d^3*e^6 + 7420*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*b^4*c^(5/2)*d^4*e^5 - 3040*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a*b^2*c^(7/2)*d^4*e^5 - 16960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^2*c^(9/2)*d^4*e^5 + 2860*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^5*c^(5/2)*d^5*e^4 - 21600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*b^3*c^(7/2)*d^5*e^4 - 40000*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^2*b*c^(9/2)*d^5*e^4 + 860*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^6*c^(5/2)*d^6*e^3 - 5200*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^4*c^(7/2)*d^6*e^3 - 24000*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*b^2*c^(9/2)*d^6*e^3 - 1280*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^3*c^(11/2)*d^6*e^3 + 12*b^7*c^(5/2)*d^7*e^2 + 464*a*b^5*c^(7/2)*d^7*e^2 + 320*a^2*b^3*c^(9/2)*d^7*e^2 - 4780*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*b^4*c^2*d^3*e^6 - 7840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a*b^2*c^3*d^3*e^6 - 7360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^2*c^4*d^3*e^6 + 1448*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b^5*c^2*d^4*e^5 + 8640*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*b^3*c^3*d^4*e^5 + 12160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^2*b*c^4*d^4*e^5 + 540*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^6*c^2*d^5*e^4 - 7520*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^4*c^3*d^5*e^4 - 13120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*b^2*c^4*d^5*e^4 + 12800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^3*c^5*d^5*e^4 + 200*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^7*c^2*d^6*e^3 - 1920*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^5*c^3*d^6*e^3 - 9600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b^3*c^4*d^6*e^3 - 1280*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*b*c^5*d^6*e^3 - 270*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*b^4*c^(3/2)*d^2*e^7 + 6000*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a*b^2*c^(5/2)*d^2*e^7 - 480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a^2*c^(7/2)*d^2*e^7 - 5330*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*b^5*c^(3/2)*d^3*e^6 - 9840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a*b^3*c^(5/2)*d^3*e^6 + 8160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^2*b*c^(7/2)*d^3*e^6 - 1390*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^6*c^(3/2)*d^4*e^5 + 9620*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*b^4*c^(5/2)*d^4*e^5 + 37120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^2*b^2*c^(7/2)*d^4*e^5 + 37440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^3*c^(9/2)*d^4*e^5 - 230*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^7*c^(3/2)*d^5*e^4 - 320*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^5*c^(5/2)*d^5*e^4 + 5920*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*b^3*c^(7/2)*d^5*e^4 + 23040*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^3*b*c^(9/2)*d^5*e^4 + 20*b^8*c^(3/2)*d^6*e^3 - 204*a*b^6*c^(5/2)*d^6*e^3 - 1360*a^2*b^4*c^(7/2)*d^6*e^3 - 320*a^3*b^2*c^(9/2)*d^6*e^3 - 30*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*b^4*c*d*e^8 + 240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*a*b^2*c^2*d*e^8 - 480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*a^2*c^3*d*e^8 + 330*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*b^5*c*d^2*e^7 + 8880*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a*b^3*c^2*d^2*e^7 + 9120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^2*b*c^3*d^2*e^7 - 2626*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b^6*c*d^3*e^6 - 6260*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*b^4*c^2*d^3*e^6 - 21760*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^2*b^2*c^3*d^3*e^6 + 29120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^3*c^4*d^3*e^6 - 930*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^7*c*d^4*e^5 + 4760*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^5*c^2*d^4*e^5 + 14240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*b^3*c^3*d^4*e^5 + 42880*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^3*b*c^4*d^4*e^5 - 120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^8*c*d^5*e^4 + 260*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^6*c^2*d^5*e^4 + 3880*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b^4*c^3*d^5*e^4 + 12800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*b^2*c^4*d^5*e^4 + 640*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^4*c^5*d^5*e^4 + 135*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*b^5*sqrt(c)*d*e^8 - 1080*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a*b^3*c^(3/2)*d*e^8 - 1680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a^2*b*c^(5/2)*d*e^8 + 490*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*b^6*sqrt(c)*d^2*e^7 + 12420*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a*b^4*c^(3/2)*d^2*e^7 - 3840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^2*b^2*c^(5/2)*d^2*e^7 + 18240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^3*c^(7/2)*d^2*e^7 - 640*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^7*sqrt(c)*d^3*e^6 + 1390*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*b^5*c^(3/2)*d^3*e^6 - 41840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^2*b^3*c^(5/2)*d^3*e^6 - 2080*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^3*b*c^(7/2)*d^3*e^6 - 210*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^8*sqrt(c)*d^4*e^5 + 1720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^6*c^(3/2)*d^4*e^5 - 2380*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*b^4*c^(5/2)*d^4*e^5 + 10720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^3*b^2*c^(7/2)*d^4*e^5 - 7360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^4*c^(9/2)*d^4*e^5 - 15*b^9*sqrt(c)*d^5*e^4 + 30*a*b^7*c^(3/2)*d^5*e^4 + 532*a^2*b^5*c^(5/2)*d^5*e^4 + 2240*a^3*b^3*c^(7/2)*d^5*e^4 + 320*a^4*b*c^(9/2)*d^5*e^4 + 15*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*b^5*e^9 - 120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*a*b^3*c*e^9 + 240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*a^2*b*c^2*e^9 + 70*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*b^6*d*e^8 - 420*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a*b^4*c*d*e^8 - 11520*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^2*b^2*c^2*d*e^8 + 4800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^3*c^3*d*e^8 + 128*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b^7*d^2*e^7 + 9026*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*b^5*c*d^2*e^7 + 1520*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^2*b^3*c^2*d^2*e^7 + 11040*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^3*b*c^3*d^2*e^7 - 70*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^8*d^3*e^6 + 2280*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^6*c*d^3*e^6 - 20420*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*b^4*c^2*d^3*e^6 - 20320*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^3*b^2*c^3*d^3*e^6 - 24640*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^4*c^4*d^3*e^6 - 15*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^9*d^4*e^5 + 450*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^7*c*d^4*e^5 - 2080*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b^5*c^2*d^4*e^5 - 1120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*b^3*c^3*d^4*e^5 - 8960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^4*b*c^4*d^4*e^5 + 1280*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a^3*c^(5/2)*e^9 - 490*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a*b^5*sqrt(c)*d*e^8 - 11440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^2*b^3*c^(3/2)*d*e^8 - 1440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^3*b*c^(5/2)*d*e^8 + 2560*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*b^6*sqrt(c)*d^2*e^7 + 5120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^2*b^4*c^(3/2)*d^2*e^7 + 30720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^3*b^2*c^(5/2)*d^2*e^7 - 15360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^4*c^(7/2)*d^2*e^7 + 630*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^7*sqrt(c)*d^3*e^6 - 4430*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*b^5*c^(3/2)*d^3*e^6 - 2480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^3*b^3*c^(5/2)*d^3*e^6 - 22240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^4*b*c^(7/2)*d^3*e^6 + 60*a*b^8*sqrt(c)*d^4*e^5 - 330*a^2*b^6*c^(3/2)*d^4*e^5 - 260*a^3*b^4*c^(5/2)*d^4*e^5 - 2560*a^4*b^2*c^(7/2)*d^4*e^5 - 64*a^5*c^(9/2)*d^4*e^5 - 70*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a*b^5*e^9 + 560*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^2*b^3*c*e^9 + 2720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^3*b*c^2*e^9 - 256*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*b^6*d*e^8 - 8960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^2*b^4*c*d*e^8 - 7680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^4*c^3*d*e^8 + 210*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^7*d^2*e^7 + 230*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*b^5*c*d^2*e^7 + 26480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^3*b^3*c^2*d^2*e^7 + 6240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^4*b*c^3*d^2*e^7 + 60*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^8*d^3*e^6 - 750*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b^6*c*d^3*e^6 + 2820*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*b^4*c^2*d^3*e^6 - 5760*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^4*b^2*c^3*d^3*e^6 + 2880*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^5*c^4*d^3*e^6 + 5120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^3*b^2*c^(3/2)*e^9 - 3200*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^2*b^5*sqrt(c)*d*e^8 - 7680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^3*b^3*c^(3/2)*d*e^8 - 3840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^4*b*c^(5/2)*d*e^8 - 630*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*b^6*sqrt(c)*d^2*e^7 + 7180*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^3*b^4*c^(3/2)*d^2*e^7 + 7360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^4*b^2*c^(5/2)*d^2*e^7 + 11200*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^5*c^(7/2)*d^2*e^7 - 90*a^2*b^7*sqrt(c)*d^3*e^6 + 610*a^3*b^5*c^(3/2)*d^3*e^6 - 560*a^4*b^3*c^(5/2)*d^3*e^6 + 1568*a^5*b*c^(7/2)*d^3*e^6 + 128*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^2*b^5*e^9 + 2560*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^3*b^3*c*e^9 + 3840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^4*b*c^2*e^9 - 210*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*b^6*d*e^8 - 3580*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^3*b^4*c*d*e^8 - 13760*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^4*b^2*c^2*d*e^8 + 5440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^5*c^3*d*e^8 - 90*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b^7*d^2*e^7 + 750*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*b^5*c*d^2*e^7 - 400*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^4*b^3*c^2*d^2*e^7 + 6880*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^5*b*c^3*d^2*e^7 + 1280*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^3*b^4*sqrt(c)*e^9 + 2560*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^4*b^2*c^(3/2)*e^9 + 2560*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^5*c^(5/2)*e^9 + 210*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^3*b^5*sqrt(c)*d*e^8 - 6800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^4*b^3*c^(3/2)*d*e^8 - 3040*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^5*b*c^(5/2)*d*e^8 + 60*a^3*b^6*sqrt(c)*d^2*e^7 - 450*a^4*b^4*c^(3/2)*d^2*e^7 + 976*a^5*b^2*c^(5/2)*d^2*e^7 - 288*a^6*c^(7/2)*d^2*e^7 + 70*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^3*b^5*e^9 + 2000*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^4*b^3*c*e^9 + 2400*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^5*b*c^2*e^9 + 60*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*b^6*d*e^8 - 450*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^4*b^4*c*d*e^8 - 1840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^5*b^2*c^2*d*e^8 - 2080*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^6*c^3*d*e^8 + 2560*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^5*b^2*c^(3/2)*e^9 - 15*a^4*b^5*sqrt(c)*d*e^8 + 120*a^5*b^3*c^(3/2)*d*e^8 - 752*a^6*b*c^(5/2)*d*e^8 - 15*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^4*b^5*e^9 + 120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^5*b^3*c*e^9 + 1040*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^6*b*c^2*e^9 + 256*a^7*c^(5/2)*e^9)/((c^3*d^6*e^4 - 3*b*c^2*d^5*e^5 + 3*b^2*c*d^4*e^6 + 3*a*c^2*d^4*e^6 - b^3*d^3*e^7 - 6*a*b*c*d^3*e^7 + 3*a*b^2*d^2*e^8 + 3*a^2*c*d^2*e^8 - 3*a^2*b*d*e^9 + a^3*e^10)*((sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*e + 2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c)*d + b*d - a*e)^5)","B",0
2353,1,14083,0,73.466627," ","integrate((c*x^2+b*x+a)^(3/2)/(e*x+d)^7,x, algorithm=""giac"")","\frac{{\left(24 \, b^{4} c^{2} d^{2} - 192 \, a b^{2} c^{3} d^{2} + 384 \, a^{2} c^{4} d^{2} - 24 \, b^{5} c d e + 192 \, a b^{3} c^{2} d e - 384 \, a^{2} b c^{3} d e + 7 \, b^{6} e^{2} - 60 \, a b^{4} c e^{2} + 144 \, a^{2} b^{2} c^{2} e^{2} - 64 \, a^{3} c^{3} e^{2}\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} + b d e - a e^{2}}}\right)}{512 \, {\left(c^{4} d^{8} - 4 \, b c^{3} d^{7} e + 6 \, b^{2} c^{2} d^{6} e^{2} + 4 \, a c^{3} d^{6} e^{2} - 4 \, b^{3} c d^{5} e^{3} - 12 \, a b c^{2} d^{5} e^{3} + b^{4} d^{4} e^{4} + 12 \, a b^{2} c d^{4} e^{4} + 6 \, a^{2} c^{2} d^{4} e^{4} - 4 \, a b^{3} d^{3} e^{5} - 12 \, a^{2} b c d^{3} e^{5} + 6 \, a^{2} b^{2} d^{2} e^{6} + 4 \, a^{3} c d^{2} e^{6} - 4 \, a^{3} b d e^{7} + a^{4} e^{8}\right)} \sqrt{-c d^{2} + b d e - a e^{2}}} + \frac{24576 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} c^{8} d^{10} e + 8192 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} c^{\frac{17}{2}} d^{11} + 30720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} c^{\frac{15}{2}} d^{9} e^{2} + 40960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} b c^{\frac{15}{2}} d^{10} e + 24576 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} b c^{8} d^{11} + 20480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} c^{7} d^{8} e^{3} - 24576 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a c^{8} d^{10} e + 30720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} b^{2} c^{\frac{15}{2}} d^{11} - 46080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} b c^{\frac{13}{2}} d^{8} e^{3} - 101376 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} b^{2} c^{\frac{13}{2}} d^{9} e^{2} - 4096 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} a c^{\frac{15}{2}} d^{9} e^{2} - 46080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} b^{3} c^{\frac{13}{2}} d^{10} e - 61440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a b c^{\frac{15}{2}} d^{10} e + 20480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{3} c^{7} d^{11} - 81920 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} b c^{6} d^{7} e^{4} - 119808 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} b^{2} c^{6} d^{8} e^{3} + 110592 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} a c^{7} d^{8} e^{3} - 119808 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} b^{3} c^{6} d^{9} e^{2} + 110592 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a b c^{7} d^{9} e^{2} - 43520 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{4} c^{6} d^{10} e - 61440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b^{2} c^{7} d^{10} e + 7680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{4} c^{\frac{13}{2}} d^{11} - 122880 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} b^{2} c^{\frac{11}{2}} d^{7} e^{4} + 122880 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} a c^{\frac{13}{2}} d^{7} e^{4} - 55296 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} b^{3} c^{\frac{11}{2}} d^{8} e^{3} + 405504 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} a b c^{\frac{13}{2}} d^{8} e^{3} - 51840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} b^{4} c^{\frac{11}{2}} d^{9} e^{2} + 276480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a b^{2} c^{\frac{13}{2}} d^{9} e^{2} + 30720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{2} c^{\frac{15}{2}} d^{9} e^{2} - 18432 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{5} c^{\frac{11}{2}} d^{10} e - 30720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a b^{3} c^{\frac{13}{2}} d^{10} e + 1536 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{5} c^{6} d^{11} + 122880 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} b^{2} c^{5} d^{6} e^{5} + 81920 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{9} a c^{6} d^{6} e^{5} - 12288 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} b^{3} c^{5} d^{7} e^{4} + 49152 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} a b c^{6} d^{7} e^{4} + 41472 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} b^{4} c^{5} d^{8} e^{3} + 414720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a b^{2} c^{6} d^{8} e^{3} - 110592 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{2} c^{7} d^{8} e^{3} - 3840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{5} c^{5} d^{9} e^{2} + 266240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b^{3} c^{6} d^{9} e^{2} + 61440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{2} b c^{7} d^{9} e^{2} - 3840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{6} c^{5} d^{10} e - 7680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{4} c^{6} d^{10} e + 128 \, b^{6} c^{\frac{11}{2}} d^{11} + 337920 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} b^{3} c^{\frac{9}{2}} d^{6} e^{5} - 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\sqrt{c x^{2} + b x + a}\right)} a^{6} c^{5} d^{4} e^{7} + 76800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{8} a^{4} b c^{\frac{5}{2}} e^{11} - 9702 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} a^{2} b^{6} \sqrt{c} d e^{10} - 367400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} a^{3} b^{4} c^{\frac{3}{2}} d e^{10} - 300960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} a^{4} b^{2} c^{\frac{5}{2}} d e^{10} + 51840 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} a^{5} c^{\frac{7}{2}} d e^{10} + 66870 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{2} b^{7} \sqrt{c} d^{2} e^{9} + 337080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{3} b^{5} c^{\frac{3}{2}} d^{2} e^{9} + 928800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{4} b^{3} c^{\frac{5}{2}} d^{2} e^{9} + 5760 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{5} b c^{\frac{7}{2}} d^{2} e^{9} + 10710 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{2} b^{8} \sqrt{c} d^{3} e^{8} - 104760 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{3} b^{6} c^{\frac{3}{2}} d^{3} e^{8} - 265080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{4} b^{4} c^{\frac{5}{2}} d^{3} e^{8} - 556992 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{5} b^{2} c^{\frac{7}{2}} d^{3} e^{8} - 258432 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{6} c^{\frac{9}{2}} d^{3} e^{8} + 1050 \, a^{2} b^{9} \sqrt{c} d^{4} e^{7} - 5680 \, a^{3} b^{7} c^{\frac{3}{2}} d^{4} e^{7} - 3240 \, a^{4} b^{5} c^{\frac{5}{2}} d^{4} e^{7} + 42048 \, a^{5} b^{3} c^{\frac{7}{2}} d^{4} e^{7} - 11392 \, a^{6} b c^{\frac{9}{2}} d^{4} e^{7} - 1386 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} a^{2} b^{6} e^{11} + 11880 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} a^{3} b^{4} c e^{11} + 97440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} a^{4} b^{2} c^{2} e^{11} + 24960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{7} a^{5} c^{3} e^{11} - 5058 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{2} b^{7} d e^{10} - 190632 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{3} b^{5} c d e^{10} - 305760 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{4} b^{3} c^{2} d e^{10} - 293760 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{5} b c^{3} d e^{10} + 3570 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{2} b^{8} d^{2} e^{9} + 58240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{3} b^{6} c d^{2} e^{9} + 646200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{4} b^{4} c^{2} d^{2} e^{9} + 275520 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{5} b^{2} c^{3} d^{2} e^{9} - 149120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{6} c^{4} d^{2} e^{9} + 1050 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} b^{9} d^{3} e^{8} - 10440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{3} b^{7} c d^{3} e^{8} + 18120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{4} b^{5} c^{2} d^{3} e^{8} - 195264 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{5} b^{3} c^{3} d^{3} e^{8} - 215424 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{6} b c^{4} d^{3} e^{8} + 112640 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} a^{4} b^{3} c^{\frac{3}{2}} e^{11} + 61440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{6} a^{5} b c^{\frac{5}{2}} e^{11} - 53010 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{3} b^{6} \sqrt{c} d e^{10} - 247800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{4} b^{4} c^{\frac{3}{2}} d e^{10} - 280800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{5} b^{2} c^{\frac{5}{2}} d e^{10} - 59520 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{6} c^{\frac{7}{2}} d e^{10} - 7140 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{3} b^{7} \sqrt{c} d^{2} e^{9} + 147240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{4} b^{5} c^{\frac{3}{2}} d^{2} e^{9} + 252288 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{5} b^{3} c^{\frac{5}{2}} d^{2} e^{9} + 163968 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{6} b c^{\frac{7}{2}} d^{2} e^{9} - 1050 \, a^{3} b^{8} \sqrt{c} d^{3} e^{8} + 7270 \, a^{4} b^{6} c^{\frac{3}{2}} d^{3} e^{8} - 11232 \, a^{5} b^{4} c^{\frac{5}{2}} d^{3} e^{8} - 45600 \, a^{6} b^{2} c^{\frac{7}{2}} d^{3} e^{8} + 1792 \, a^{7} c^{\frac{9}{2}} d^{3} e^{8} + 1686 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{3} b^{6} e^{11} + 42600 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{4} b^{4} c e^{11} + 128160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{5} b^{2} c^{2} e^{11} + 24960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a^{6} c^{3} e^{11} - 2380 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{3} b^{7} d e^{10} - 73800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{4} b^{5} c d e^{10} - 309120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{5} b^{3} c^{2} d e^{10} + 30080 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{6} b c^{3} d e^{10} - 1050 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{3} b^{8} d^{2} e^{9} + 8460 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{4} b^{6} c d^{2} e^{9} + 27720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{5} b^{4} c^{2} d^{2} e^{9} + 144768 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{6} b^{2} c^{3} d^{2} e^{9} + 56448 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{7} c^{4} d^{2} e^{9} + 15360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{4} b^{5} \sqrt{c} e^{11} + 61440 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{5} b^{3} c^{\frac{3}{2}} e^{11} + 92160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{6} b c^{\frac{5}{2}} e^{11} + 1785 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{4} b^{6} \sqrt{c} d e^{10} - 107460 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{5} b^{4} c^{\frac{3}{2}} d e^{10} - 95376 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{6} b^{2} c^{\frac{5}{2}} d e^{10} + 20544 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{7} c^{\frac{7}{2}} d e^{10} + 525 \, a^{4} b^{7} \sqrt{c} d^{2} e^{9} - 4140 \, a^{5} b^{5} c^{\frac{3}{2}} d^{2} e^{9} + 17136 \, a^{6} b^{3} c^{\frac{5}{2}} d^{2} e^{9} + 25536 \, a^{7} b c^{\frac{7}{2}} d^{2} e^{9} + 595 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{4} b^{6} e^{11} + 25620 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{5} b^{4} c e^{11} + 58320 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{6} b^{2} c^{2} e^{11} + 15040 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{7} c^{3} e^{11} + 525 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{4} b^{7} d e^{10} - 4140 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{5} b^{5} c d e^{10} - 38160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{6} b^{3} c^{2} d e^{10} - 35904 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{7} b c^{3} d e^{10} + 30720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{6} b^{3} c^{\frac{3}{2}} e^{11} + 12288 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{7} b c^{\frac{5}{2}} e^{11} - 105 \, a^{5} b^{6} \sqrt{c} d e^{10} + 900 \, a^{6} b^{4} c^{\frac{3}{2}} d e^{10} - 11376 \, a^{7} b^{2} c^{\frac{5}{2}} d e^{10} - 5184 \, a^{8} c^{\frac{7}{2}} d e^{10} - 105 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{5} b^{6} e^{11} + 900 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{6} b^{4} c e^{11} + 13200 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{7} b^{2} c^{2} e^{11} + 960 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{8} c^{3} e^{11} + 3072 \, a^{8} b c^{\frac{5}{2}} e^{11}}{7680 \, {\left(c^{4} d^{8} e^{4} - 4 \, b c^{3} d^{7} e^{5} + 6 \, b^{2} c^{2} d^{6} e^{6} + 4 \, a c^{3} d^{6} e^{6} - 4 \, b^{3} c d^{5} e^{7} - 12 \, a b c^{2} d^{5} e^{7} + b^{4} d^{4} e^{8} + 12 \, a b^{2} c d^{4} e^{8} + 6 \, a^{2} c^{2} d^{4} e^{8} - 4 \, a b^{3} d^{3} e^{9} - 12 \, a^{2} b c d^{3} e^{9} + 6 \, a^{2} b^{2} d^{2} e^{10} + 4 \, a^{3} c d^{2} e^{10} - 4 \, a^{3} b d e^{11} + a^{4} e^{12}\right)} {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} e + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} d + b d - a e\right)}^{6}}"," ",0,"1/512*(24*b^4*c^2*d^2 - 192*a*b^2*c^3*d^2 + 384*a^2*c^4*d^2 - 24*b^5*c*d*e + 192*a*b^3*c^2*d*e - 384*a^2*b*c^3*d*e + 7*b^6*e^2 - 60*a*b^4*c*e^2 + 144*a^2*b^2*c^2*e^2 - 64*a^3*c^3*e^2)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + b*x + a))*e + sqrt(c)*d)/sqrt(-c*d^2 + b*d*e - a*e^2))/((c^4*d^8 - 4*b*c^3*d^7*e + 6*b^2*c^2*d^6*e^2 + 4*a*c^3*d^6*e^2 - 4*b^3*c*d^5*e^3 - 12*a*b*c^2*d^5*e^3 + b^4*d^4*e^4 + 12*a*b^2*c*d^4*e^4 + 6*a^2*c^2*d^4*e^4 - 4*a*b^3*d^3*e^5 - 12*a^2*b*c*d^3*e^5 + 6*a^2*b^2*d^2*e^6 + 4*a^3*c*d^2*e^6 - 4*a^3*b*d*e^7 + a^4*e^8)*sqrt(-c*d^2 + b*d*e - a*e^2)) + 1/7680*(24576*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*c^8*d^10*e + 8192*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*c^(17/2)*d^11 + 30720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*c^(15/2)*d^9*e^2 + 40960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*b*c^(15/2)*d^10*e + 24576*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b*c^8*d^11 + 20480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*c^7*d^8*e^3 - 24576*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*c^8*d^10*e + 30720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^2*c^(15/2)*d^11 - 46080*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*b*c^(13/2)*d^8*e^3 - 101376*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*b^2*c^(13/2)*d^9*e^2 - 4096*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a*c^(15/2)*d^9*e^2 - 46080*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^3*c^(13/2)*d^10*e - 61440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*b*c^(15/2)*d^10*e + 20480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^3*c^7*d^11 - 81920*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*b*c^6*d^7*e^4 - 119808*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*b^2*c^6*d^8*e^3 + 110592*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a*c^7*d^8*e^3 - 119808*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b^3*c^6*d^9*e^2 + 110592*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*b*c^7*d^9*e^2 - 43520*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^4*c^6*d^10*e - 61440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^2*c^7*d^10*e + 7680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^4*c^(13/2)*d^11 - 122880*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*b^2*c^(11/2)*d^7*e^4 + 122880*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a*c^(13/2)*d^7*e^4 - 55296*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*b^3*c^(11/2)*d^8*e^3 + 405504*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a*b*c^(13/2)*d^8*e^3 - 51840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^4*c^(11/2)*d^9*e^2 + 276480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*b^2*c^(13/2)*d^9*e^2 + 30720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^2*c^(15/2)*d^9*e^2 - 18432*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^5*c^(11/2)*d^10*e - 30720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^3*c^(13/2)*d^10*e + 1536*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^5*c^6*d^11 + 122880*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*b^2*c^5*d^6*e^5 + 81920*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*a*c^6*d^6*e^5 - 12288*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*b^3*c^5*d^7*e^4 + 49152*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a*b*c^6*d^7*e^4 + 41472*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b^4*c^5*d^8*e^3 + 414720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*b^2*c^6*d^8*e^3 - 110592*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^2*c^7*d^8*e^3 - 3840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^5*c^5*d^9*e^2 + 266240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^3*c^6*d^9*e^2 + 61440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*b*c^7*d^9*e^2 - 3840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^6*c^5*d^10*e - 7680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^4*c^6*d^10*e + 128*b^6*c^(11/2)*d^11 + 337920*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*b^3*c^(9/2)*d^6*e^5 - 61440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a*b*c^(11/2)*d^6*e^5 + 100800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*b^4*c^(9/2)*d^7*e^4 - 450048*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a*b^2*c^(11/2)*d^7*e^4 - 549888*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^2*c^(13/2)*d^7*e^4 + 60480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^5*c^(9/2)*d^8*e^3 + 69120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*b^3*c^(11/2)*d^8*e^3 - 414720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^2*b*c^(13/2)*d^8*e^3 + 3840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^6*c^(9/2)*d^9*e^2 + 126720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^4*c^(11/2)*d^9*e^2 + 46080*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*b^2*c^(13/2)*d^9*e^2 - 320*b^7*c^(9/2)*d^10*e - 768*a*b^5*c^(11/2)*d^10*e - 81920*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*b^3*c^4*d^5*e^6 - 245760*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*a*b*c^5*d^5*e^6 + 336960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*b^4*c^4*d^6*e^5 + 93696*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a*b^2*c^5*d^6*e^5 - 605184*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^2*c^6*d^6*e^5 + 87360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b^5*c^4*d^7*e^4 - 600576*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*b^3*c^5*d^7*e^4 - 1207296*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^2*b*c^6*d^7*e^4 + 33920*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^6*c^4*d^8*e^3 - 130560*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^4*c^5*d^8*e^3 - 537600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*b^2*c^6*d^8*e^3 - 20480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^3*c^7*d^8*e^3 + 1152*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^7*c^4*d^9*e^2 + 29952*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^5*c^5*d^9*e^2 + 15360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b^3*c^6*d^9*e^2 - 317520*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*b^4*c^(7/2)*d^5*e^6 - 224640*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a*b^2*c^(9/2)*d^5*e^6 - 472320*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a^2*c^(11/2)*d^5*e^6 + 95424*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*b^5*c^(7/2)*d^6*e^5 + 698880*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a*b^3*c^(9/2)*d^6*e^5 - 193536*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^2*b*c^(11/2)*d^6*e^5 + 15120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^6*c^(7/2)*d^7*e^4 - 228480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*b^4*c^(9/2)*d^7*e^4 - 864000*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^2*b^2*c^(11/2)*d^7*e^4 + 245760*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^3*c^(13/2)*d^7*e^4 + 11136*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^7*c^(7/2)*d^8*e^3 - 88704*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^5*c^(9/2)*d^8*e^3 - 322560*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*b^3*c^(11/2)*d^8*e^3 - 30720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^3*b*c^(13/2)*d^8*e^3 + 96*b^8*c^(7/2)*d^9*e^2 + 2816*a*b^6*c^(9/2)*d^9*e^2 + 1920*a^2*b^4*c^(11/2)*d^9*e^2 + 2720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*b^4*c^3*d^4*e^7 + 387840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*a*b^2*c^4*d^4*e^7 - 161280*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*a^2*c^5*d^4*e^7 - 419328*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*b^5*c^3*d^5*e^6 - 368640*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a*b^3*c^4*d^5*e^6 - 73728*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^2*b*c^5*d^5*e^6 - 71808*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b^6*c^3*d^6*e^5 + 822720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*b^4*c^4*d^6*e^5 + 907776*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^2*b^2*c^5*d^6*e^5 + 1219584*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^3*c^6*d^6*e^5 - 18080*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^7*c^3*d^7*e^4 + 42240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^5*c^4*d^7*e^4 - 145920*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*b^3*c^5*d^7*e^4 + 573440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^3*b*c^6*d^7*e^4 + 2112*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^8*c^3*d^8*e^3 - 21888*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^6*c^4*d^8*e^3 - 92160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b^4*c^5*d^8*e^3 - 15360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*b^2*c^6*d^8*e^3 - 3960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^10*b^4*c^(5/2)*d^3*e^8 + 31680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^10*a*b^2*c^(7/2)*d^3*e^8 - 63360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^10*a^2*c^(9/2)*d^3*e^8 + 99480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*b^5*c^(5/2)*d^4*e^7 + 617280*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a*b^3*c^(7/2)*d^4*e^7 + 455040*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a^2*b*c^(9/2)*d^4*e^7 - 242840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*b^6*c^(5/2)*d^5*e^6 - 593760*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a*b^4*c^(7/2)*d^5*e^6 - 1011840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^2*b^2*c^(9/2)*d^5*e^6 + 1564160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^3*c^(11/2)*d^5*e^6 - 64440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^7*c^(5/2)*d^6*e^5 + 437280*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*b^5*c^(7/2)*d^6*e^5 + 670080*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^2*b^3*c^(9/2)*d^6*e^5 + 2188800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^3*b*c^(11/2)*d^6*e^5 - 12384*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^8*c^(5/2)*d^7*e^4 + 54816*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^6*c^(7/2)*d^7*e^4 + 89280*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*b^4*c^(9/2)*d^7*e^4 + 476160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^3*b^2*c^(11/2)*d^7*e^4 + 15360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^4*c^(13/2)*d^7*e^4 + 176*b^9*c^(5/2)*d^8*e^3 - 1920*a*b^7*c^(7/2)*d^8*e^3 - 10176*a^2*b^5*c^(9/2)*d^8*e^3 - 2560*a^3*b^3*c^(11/2)*d^8*e^3 - 360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*b^4*c^2*d^2*e^9 + 2880*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*a*b^2*c^3*d^2*e^9 - 5760*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*a^2*c^4*d^2*e^9 + 15720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*b^5*c^2*d^3*e^8 - 207680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*a*b^3*c^3*d^3*e^8 + 5760*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*a^2*b*c^4*d^3*e^8 + 170520*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*b^6*c^2*d^4*e^7 + 846240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a*b^4*c^3*d^4*e^7 + 5760*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^2*b^2*c^4*d^4*e^7 + 1328640*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^3*c^5*d^4*e^7 - 47400*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b^7*c^2*d^5*e^6 - 362592*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*b^5*c^3*d^5*e^6 - 2436480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^2*b^3*c^4*d^5*e^6 + 1033728*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^3*b*c^5*d^5*e^6 - 16320*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^8*c^2*d^6*e^5 + 129920*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^6*c^3*d^6*e^5 - 52800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*b^4*c^4*d^6*e^5 + 1374720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^3*b^2*c^5*d^6*e^5 - 189440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^4*c^6*d^6*e^5 - 3120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^9*c^2*d^7*e^4 + 14496*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^7*c^3*d^7*e^4 + 40896*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b^5*c^4*d^7*e^4 + 168960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*b^3*c^5*d^7*e^4 + 15360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^4*b*c^6*d^7*e^4 + 3960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^10*b^5*c^(3/2)*d^2*e^9 - 31680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^10*a*b^3*c^(5/2)*d^2*e^9 + 63360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^10*a^2*b*c^(7/2)*d^2*e^9 + 6390*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*b^6*c^(3/2)*d^3*e^8 - 333120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a*b^4*c^(5/2)*d^3*e^8 - 836640*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a^2*b^2*c^(7/2)*d^3*e^8 + 526080*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a^3*c^(9/2)*d^3*e^8 + 115328*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*b^7*c^(3/2)*d^4*e^7 + 793248*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a*b^5*c^(5/2)*d^4*e^7 + 480000*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^2*b^3*c^(7/2)*d^4*e^7 + 739840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^3*b*c^(9/2)*d^4*e^7 + 14460*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^8*c^(3/2)*d^5*e^6 - 81720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*b^6*c^(5/2)*d^5*e^6 - 1728000*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^2*b^4*c^(7/2)*d^5*e^6 - 792960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^3*b^2*c^(9/2)*d^5*e^6 - 1198080*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^4*c^(11/2)*d^5*e^6 + 600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^9*c^(3/2)*d^6*e^5 + 26928*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^7*c^(5/2)*d^6*e^5 - 185472*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*b^5*c^(7/2)*d^6*e^5 + 357120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^3*b^3*c^(9/2)*d^6*e^5 - 337920*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^4*b*c^(11/2)*d^6*e^5 - 290*b^10*c^(3/2)*d^7*e^4 + 1272*a*b^8*c^(5/2)*d^7*e^4 + 4752*a^2*b^6*c^(7/2)*d^7*e^4 + 21760*a^3*b^4*c^(9/2)*d^7*e^4 + 3840*a^4*b^2*c^(11/2)*d^7*e^4 + 360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*b^5*c*d*e^10 - 2880*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*a*b^3*c^2*d*e^10 + 5760*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*a^2*b*c^3*d*e^10 - 3140*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*b^6*c*d^2*e^9 + 30120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*a*b^4*c^2*d^2*e^9 + 32640*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*a^2*b^2*c^3*d^2*e^9 + 161920*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*a^3*c^4*d^2*e^9 - 13896*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*b^7*c*d^3*e^8 - 436416*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a*b^5*c^2*d^3*e^8 - 842880*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^2*b^3*c^3*d^3*e^8 - 552960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^3*b*c^4*d^3*e^8 + 38784*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b^8*c*d^4*e^7 + 308424*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*b^6*c^2*d^4*e^7 + 1435680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^2*b^4*c^3*d^4*e^7 + 1192320*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^3*b^2*c^4*d^4*e^7 - 1374720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^4*c^5*d^4*e^7 + 9440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^9*c*d^5*e^6 - 14160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^7*c^2*d^5*e^6 - 454080*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*b^5*c^3*d^5*e^6 - 684800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^3*b^3*c^4*d^5*e^6 - 1827840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^4*b*c^5*d^5*e^6 + 900*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^10*c*d^6*e^5 + 5040*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^8*c^2*d^6*e^5 - 64128*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b^6*c^3*d^6*e^5 + 37440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*b^4*c^4*d^6*e^5 - 192000*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^4*b^2*c^5*d^6*e^5 - 3072*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^5*c^6*d^6*e^5 - 1155*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^10*b^6*sqrt(c)*d*e^10 + 9900*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^10*a*b^4*c^(3/2)*d*e^10 - 23760*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^10*a^2*b^2*c^(5/2)*d*e^10 + 10560*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^10*a^3*c^(7/2)*d*e^10 - 5355*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*b^7*sqrt(c)*d^2*e^9 + 27540*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a*b^5*c^(3/2)*d^2*e^9 + 497520*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a^2*b^3*c^(5/2)*d^2*e^9 - 60480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a^3*b*c^(7/2)*d^2*e^9 - 9702*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*b^8*sqrt(c)*d^3*e^8 - 403352*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a*b^6*c^(3/2)*d^3*e^8 - 693840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^2*b^4*c^(5/2)*d^3*e^8 - 756480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^3*b^2*c^(7/2)*d^3*e^8 - 951040*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^4*c^(9/2)*d^3*e^8 + 6930*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^9*sqrt(c)*d^4*e^7 - 3120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*b^7*c^(3/2)*d^4*e^7 + 997200*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^2*b^5*c^(5/2)*d^4*e^7 + 1948800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^3*b^3*c^(7/2)*d^4*e^7 - 441600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^4*b*c^(9/2)*d^4*e^7 + 1785*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^10*sqrt(c)*d^5*e^6 - 10980*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^8*c^(3/2)*d^5*e^6 - 14184*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*b^6*c^(5/2)*d^5*e^6 - 26400*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^3*b^4*c^(7/2)*d^5*e^6 - 996480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^4*b^2*c^(9/2)*d^5*e^6 + 105984*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^5*c^(11/2)*d^5*e^6 + 105*b^11*sqrt(c)*d^6*e^5 + 620*a*b^9*c^(3/2)*d^6*e^5 - 7512*a^2*b^7*c^(5/2)*d^6*e^5 + 2592*a^3*b^5*c^(7/2)*d^6*e^5 - 35200*a^4*b^3*c^(9/2)*d^6*e^5 - 1536*a^5*b*c^(11/2)*d^6*e^5 - 105*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*b^6*e^11 + 900*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*a*b^4*c*e^11 - 2160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*a^2*b^2*c^2*e^11 + 960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*a^3*c^3*e^11 - 595*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*b^7*d*e^10 + 3060*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*a*b^5*c*d*e^10 + 4080*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*a^2*b^3*c^2*d*e^10 - 109120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*a^3*b*c^3*d*e^10 - 1386*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*b^8*d^2*e^9 + 21024*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a*b^6*c*d^2*e^9 + 638640*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^2*b^4*c^2*d^2*e^9 + 466560*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^3*b^2*c^3*d^2*e^9 - 172800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^4*c^4*d^2*e^9 - 1686*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b^9*d^3*e^8 - 183000*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*b^7*c*d^3*e^8 - 545904*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^2*b^5*c^2*d^3*e^8 - 1482240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^3*b^3*c^3*d^3*e^8 - 103680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^4*b*c^4*d^3*e^8 + 595*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^10*d^4*e^7 - 31380*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^8*c*d^4*e^7 + 280200*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*b^6*c^2*d^4*e^7 + 965600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^3*b^4*c^3*d^4*e^7 + 873600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^4*b^2*c^4*d^4*e^7 + 775680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^5*c^5*d^4*e^7 + 105*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^11*d^5*e^6 - 4140*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^9*c*d^5*e^6 + 11160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b^7*c^2*d^5*e^6 + 66720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*b^5*c^3*d^5*e^6 - 236160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^4*b^3*c^4*d^5*e^6 + 115200*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^5*b*c^5*d^5*e^6 + 5355*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a*b^6*sqrt(c)*d*e^10 - 45900*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a^2*b^4*c^(3/2)*d*e^10 - 197040*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a^3*b^2*c^(5/2)*d*e^10 - 18240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a^4*c^(7/2)*d*e^10 + 19404*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a*b^7*sqrt(c)*d^2*e^9 + 542784*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^2*b^5*c^(3/2)*d^2*e^9 + 374720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^3*b^3*c^(5/2)*d^2*e^9 + 821760*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^4*b*c^(7/2)*d^2*e^9 - 36150*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*b^8*sqrt(c)*d^3*e^8 - 162060*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^2*b^6*c^(3/2)*d^3*e^8 - 1591200*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^3*b^4*c^(5/2)*d^3*e^8 - 619200*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^4*b^2*c^(7/2)*d^3*e^8 + 744960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^5*c^(9/2)*d^3*e^8 - 7140*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^9*sqrt(c)*d^4*e^7 + 44640*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*b^7*c^(3/2)*d^4*e^7 + 95520*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^3*b^5*c^(5/2)*d^4*e^7 + 518400*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^4*b^3*c^(7/2)*d^4*e^7 + 898560*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^5*b*c^(9/2)*d^4*e^7 - 525*a*b^10*sqrt(c)*d^5*e^6 + 1320*a^2*b^8*c^(3/2)*d^5*e^6 + 11704*a^3*b^6*c^(5/2)*d^5*e^6 - 22320*a^4*b^4*c^(7/2)*d^5*e^6 + 30720*a^5*b^2*c^(9/2)*d^5*e^6 + 256*a^6*c^(11/2)*d^5*e^6 + 595*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*a*b^6*e^11 - 5100*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*a^2*b^4*c*e^11 + 12240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*a^3*b^2*c^2*e^11 + 15040*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*a^4*c^3*e^11 + 2772*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a*b^7*d*e^10 - 19008*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^2*b^5*c*d*e^10 - 484800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^3*b^3*c^2*d*e^10 + 99840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^4*b*c^3*d*e^10 + 5058*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*b^8*d^2*e^9 + 292248*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^2*b^6*c*d^2*e^9 + 462480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^3*b^4*c^2*d^2*e^9 + 748800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^4*b^2*c^3*d^2*e^9 + 449280*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^5*c^4*d^2*e^9 - 2380*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^9*d^3*e^8 + 11880*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*b^7*c*d^3*e^8 - 645120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^3*b^5*c^2*d^3*e^8 - 944000*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^4*b^3*c^3*d^3*e^8 - 61440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^5*b*c^4*d^3*e^8 - 525*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^10*d^4*e^7 + 8460*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b^8*c*d^4*e^7 - 33960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*b^6*c^2*d^4*e^7 + 66240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^4*b^4*c^3*d^4*e^7 + 337536*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^5*b^2*c^4*d^4*e^7 - 21504*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^6*c^5*d^4*e^7 + 76800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a^4*b*c^(5/2)*e^11 - 9702*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^2*b^6*sqrt(c)*d*e^10 - 367400*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^3*b^4*c^(3/2)*d*e^10 - 300960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^4*b^2*c^(5/2)*d*e^10 + 51840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^5*c^(7/2)*d*e^10 + 66870*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^2*b^7*sqrt(c)*d^2*e^9 + 337080*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^3*b^5*c^(3/2)*d^2*e^9 + 928800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^4*b^3*c^(5/2)*d^2*e^9 + 5760*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^5*b*c^(7/2)*d^2*e^9 + 10710*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*b^8*sqrt(c)*d^3*e^8 - 104760*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^3*b^6*c^(3/2)*d^3*e^8 - 265080*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^4*b^4*c^(5/2)*d^3*e^8 - 556992*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^5*b^2*c^(7/2)*d^3*e^8 - 258432*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^6*c^(9/2)*d^3*e^8 + 1050*a^2*b^9*sqrt(c)*d^4*e^7 - 5680*a^3*b^7*c^(3/2)*d^4*e^7 - 3240*a^4*b^5*c^(5/2)*d^4*e^7 + 42048*a^5*b^3*c^(7/2)*d^4*e^7 - 11392*a^6*b*c^(9/2)*d^4*e^7 - 1386*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^2*b^6*e^11 + 11880*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^3*b^4*c*e^11 + 97440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^4*b^2*c^2*e^11 + 24960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^5*c^3*e^11 - 5058*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^2*b^7*d*e^10 - 190632*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^3*b^5*c*d*e^10 - 305760*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^4*b^3*c^2*d*e^10 - 293760*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^5*b*c^3*d*e^10 + 3570*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*b^8*d^2*e^9 + 58240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^3*b^6*c*d^2*e^9 + 646200*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^4*b^4*c^2*d^2*e^9 + 275520*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^5*b^2*c^3*d^2*e^9 - 149120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^6*c^4*d^2*e^9 + 1050*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b^9*d^3*e^8 - 10440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*b^7*c*d^3*e^8 + 18120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^4*b^5*c^2*d^3*e^8 - 195264*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^5*b^3*c^3*d^3*e^8 - 215424*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^6*b*c^4*d^3*e^8 + 112640*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^4*b^3*c^(3/2)*e^11 + 61440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^5*b*c^(5/2)*e^11 - 53010*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^3*b^6*sqrt(c)*d*e^10 - 247800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^4*b^4*c^(3/2)*d*e^10 - 280800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^5*b^2*c^(5/2)*d*e^10 - 59520*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^6*c^(7/2)*d*e^10 - 7140*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^3*b^7*sqrt(c)*d^2*e^9 + 147240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^4*b^5*c^(3/2)*d^2*e^9 + 252288*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^5*b^3*c^(5/2)*d^2*e^9 + 163968*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^6*b*c^(7/2)*d^2*e^9 - 1050*a^3*b^8*sqrt(c)*d^3*e^8 + 7270*a^4*b^6*c^(3/2)*d^3*e^8 - 11232*a^5*b^4*c^(5/2)*d^3*e^8 - 45600*a^6*b^2*c^(7/2)*d^3*e^8 + 1792*a^7*c^(9/2)*d^3*e^8 + 1686*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^3*b^6*e^11 + 42600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^4*b^4*c*e^11 + 128160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^5*b^2*c^2*e^11 + 24960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^6*c^3*e^11 - 2380*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^3*b^7*d*e^10 - 73800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^4*b^5*c*d*e^10 - 309120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^5*b^3*c^2*d*e^10 + 30080*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^6*b*c^3*d*e^10 - 1050*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*b^8*d^2*e^9 + 8460*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^4*b^6*c*d^2*e^9 + 27720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^5*b^4*c^2*d^2*e^9 + 144768*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^6*b^2*c^3*d^2*e^9 + 56448*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^7*c^4*d^2*e^9 + 15360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^4*b^5*sqrt(c)*e^11 + 61440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^5*b^3*c^(3/2)*e^11 + 92160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^6*b*c^(5/2)*e^11 + 1785*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^4*b^6*sqrt(c)*d*e^10 - 107460*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^5*b^4*c^(3/2)*d*e^10 - 95376*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^6*b^2*c^(5/2)*d*e^10 + 20544*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^7*c^(7/2)*d*e^10 + 525*a^4*b^7*sqrt(c)*d^2*e^9 - 4140*a^5*b^5*c^(3/2)*d^2*e^9 + 17136*a^6*b^3*c^(5/2)*d^2*e^9 + 25536*a^7*b*c^(7/2)*d^2*e^9 + 595*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^4*b^6*e^11 + 25620*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^5*b^4*c*e^11 + 58320*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^6*b^2*c^2*e^11 + 15040*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^7*c^3*e^11 + 525*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^4*b^7*d*e^10 - 4140*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^5*b^5*c*d*e^10 - 38160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^6*b^3*c^2*d*e^10 - 35904*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^7*b*c^3*d*e^10 + 30720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^6*b^3*c^(3/2)*e^11 + 12288*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^7*b*c^(5/2)*e^11 - 105*a^5*b^6*sqrt(c)*d*e^10 + 900*a^6*b^4*c^(3/2)*d*e^10 - 11376*a^7*b^2*c^(5/2)*d*e^10 - 5184*a^8*c^(7/2)*d*e^10 - 105*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^5*b^6*e^11 + 900*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^6*b^4*c*e^11 + 13200*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^7*b^2*c^2*e^11 + 960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^8*c^3*e^11 + 3072*a^8*b*c^(5/2)*e^11)/((c^4*d^8*e^4 - 4*b*c^3*d^7*e^5 + 6*b^2*c^2*d^6*e^6 + 4*a*c^3*d^6*e^6 - 4*b^3*c*d^5*e^7 - 12*a*b*c^2*d^5*e^7 + b^4*d^4*e^8 + 12*a*b^2*c*d^4*e^8 + 6*a^2*c^2*d^4*e^8 - 4*a*b^3*d^3*e^9 - 12*a^2*b*c*d^3*e^9 + 6*a^2*b^2*d^2*e^10 + 4*a^3*c*d^2*e^10 - 4*a^3*b*d*e^11 + a^4*e^12)*((sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*e + 2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c)*d + b*d - a*e)^6)","B",0
2354,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)/(e*x+d)^8,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2355,1,1160,0,0.334833," ","integrate((e*x+d)^3*(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\frac{1}{2064384} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(2 \, {\left(4 \, {\left(14 \, {\left(16 \, c^{2} x e^{3} + \frac{54 \, c^{10} d e^{2} + 37 \, b c^{9} e^{3}}{c^{8}}\right)} x + \frac{864 \, c^{10} d^{2} e + 1782 \, b c^{9} d e^{2} + 309 \, b^{2} c^{8} e^{3} + 608 \, a c^{9} e^{3}}{c^{8}}\right)} x + \frac{1344 \, c^{10} d^{3} + 8352 \, b c^{9} d^{2} e + 4374 \, b^{2} c^{8} d e^{2} + 8568 \, a c^{9} d e^{2} + 5 \, b^{3} c^{7} e^{3} + 3012 \, a b c^{8} e^{3}}{c^{8}}\right)} x + \frac{6720 \, b c^{9} d^{3} + 10656 \, b^{2} c^{8} d^{2} e + 20736 \, a c^{9} d^{2} e + 54 \, b^{3} c^{7} d e^{2} + 22104 \, a b c^{8} d e^{2} - 11 \, b^{4} c^{6} e^{3} + 84 \, a b^{2} c^{7} e^{3} + 3840 \, a^{2} c^{8} e^{3}}{c^{8}}\right)} x + \frac{36288 \, b^{2} c^{8} d^{3} + 69888 \, a c^{9} d^{3} + 864 \, b^{3} c^{7} d^{2} e + 226944 \, a b c^{8} d^{2} e - 486 \, b^{4} c^{6} d e^{2} + 3888 \, a b^{2} c^{7} d e^{2} + 118944 \, a^{2} c^{8} d e^{2} + 99 \, b^{5} c^{5} e^{3} - 856 \, a b^{3} c^{6} e^{3} + 1968 \, a^{2} b c^{7} e^{3}}{c^{8}}\right)} x + \frac{1344 \, b^{3} c^{7} d^{3} + 209664 \, a b c^{8} d^{3} - 2016 \, b^{4} c^{6} d^{2} e + 17280 \, a b^{2} c^{7} d^{2} e + 331776 \, a^{2} c^{8} d^{2} e + 1134 \, b^{5} c^{5} d e^{2} - 10224 \, a b^{3} c^{6} d e^{2} + 25056 \, a^{2} b c^{7} d e^{2} - 231 \, b^{6} c^{4} e^{3} + 2232 \, a b^{4} c^{5} e^{3} - 6384 \, a^{2} b^{2} c^{6} e^{3} + 4096 \, a^{3} c^{7} e^{3}}{c^{8}}\right)} x - \frac{6720 \, b^{4} c^{6} d^{3} - 64512 \, a b^{2} c^{7} d^{3} - 709632 \, a^{2} c^{8} d^{3} - 10080 \, b^{5} c^{5} d^{2} e + 96768 \, a b^{3} c^{6} d^{2} e - 262656 \, a^{2} b c^{7} d^{2} e + 5670 \, b^{6} c^{4} d e^{2} - 56952 \, a b^{4} c^{5} d e^{2} + 171936 \, a^{2} b^{2} c^{6} d e^{2} - 120960 \, a^{3} c^{7} d e^{2} - 1155 \, b^{7} c^{3} e^{3} + 12348 \, a b^{5} c^{4} e^{3} - 42192 \, a^{2} b^{3} c^{5} e^{3} + 44096 \, a^{3} b c^{6} e^{3}}{c^{8}}\right)} x + \frac{20160 \, b^{5} c^{5} d^{3} - 215040 \, a b^{3} c^{6} d^{3} + 709632 \, a^{2} b c^{7} d^{3} - 30240 \, b^{6} c^{4} d^{2} e + 322560 \, a b^{4} c^{5} d^{2} e - 1064448 \, a^{2} b^{2} c^{6} d^{2} e + 884736 \, a^{3} c^{7} d^{2} e + 17010 \, b^{7} c^{3} d e^{2} - 189000 \, a b^{5} c^{4} d e^{2} + 679392 \, a^{2} b^{3} c^{5} d e^{2} - 763776 \, a^{3} b c^{6} d e^{2} - 3465 \, b^{8} c^{2} e^{3} + 40740 \, a b^{6} c^{3} e^{3} - 162288 \, a^{2} b^{4} c^{4} e^{3} + 234432 \, a^{3} b^{2} c^{5} e^{3} - 65536 \, a^{4} c^{6} e^{3}}{c^{8}}\right)} + \frac{5 \, {\left(64 \, b^{6} c^{3} d^{3} - 768 \, a b^{4} c^{4} d^{3} + 3072 \, a^{2} b^{2} c^{5} d^{3} - 4096 \, a^{3} c^{6} d^{3} - 96 \, b^{7} c^{2} d^{2} e + 1152 \, a b^{5} c^{3} d^{2} e - 4608 \, a^{2} b^{3} c^{4} d^{2} e + 6144 \, a^{3} b c^{5} d^{2} e + 54 \, b^{8} c d e^{2} - 672 \, a b^{6} c^{2} d e^{2} + 2880 \, a^{2} b^{4} c^{3} d e^{2} - 4608 \, a^{3} b^{2} c^{4} d e^{2} + 1536 \, a^{4} c^{5} d e^{2} - 11 \, b^{9} e^{3} + 144 \, a b^{7} c e^{3} - 672 \, a^{2} b^{5} c^{2} e^{3} + 1280 \, a^{3} b^{3} c^{3} e^{3} - 768 \, a^{4} b c^{4} e^{3}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{65536 \, c^{\frac{13}{2}}}"," ",0,"1/2064384*sqrt(c*x^2 + b*x + a)*(2*(4*(2*(8*(2*(4*(14*(16*c^2*x*e^3 + (54*c^10*d*e^2 + 37*b*c^9*e^3)/c^8)*x + (864*c^10*d^2*e + 1782*b*c^9*d*e^2 + 309*b^2*c^8*e^3 + 608*a*c^9*e^3)/c^8)*x + (1344*c^10*d^3 + 8352*b*c^9*d^2*e + 4374*b^2*c^8*d*e^2 + 8568*a*c^9*d*e^2 + 5*b^3*c^7*e^3 + 3012*a*b*c^8*e^3)/c^8)*x + (6720*b*c^9*d^3 + 10656*b^2*c^8*d^2*e + 20736*a*c^9*d^2*e + 54*b^3*c^7*d*e^2 + 22104*a*b*c^8*d*e^2 - 11*b^4*c^6*e^3 + 84*a*b^2*c^7*e^3 + 3840*a^2*c^8*e^3)/c^8)*x + (36288*b^2*c^8*d^3 + 69888*a*c^9*d^3 + 864*b^3*c^7*d^2*e + 226944*a*b*c^8*d^2*e - 486*b^4*c^6*d*e^2 + 3888*a*b^2*c^7*d*e^2 + 118944*a^2*c^8*d*e^2 + 99*b^5*c^5*e^3 - 856*a*b^3*c^6*e^3 + 1968*a^2*b*c^7*e^3)/c^8)*x + (1344*b^3*c^7*d^3 + 209664*a*b*c^8*d^3 - 2016*b^4*c^6*d^2*e + 17280*a*b^2*c^7*d^2*e + 331776*a^2*c^8*d^2*e + 1134*b^5*c^5*d*e^2 - 10224*a*b^3*c^6*d*e^2 + 25056*a^2*b*c^7*d*e^2 - 231*b^6*c^4*e^3 + 2232*a*b^4*c^5*e^3 - 6384*a^2*b^2*c^6*e^3 + 4096*a^3*c^7*e^3)/c^8)*x - (6720*b^4*c^6*d^3 - 64512*a*b^2*c^7*d^3 - 709632*a^2*c^8*d^3 - 10080*b^5*c^5*d^2*e + 96768*a*b^3*c^6*d^2*e - 262656*a^2*b*c^7*d^2*e + 5670*b^6*c^4*d*e^2 - 56952*a*b^4*c^5*d*e^2 + 171936*a^2*b^2*c^6*d*e^2 - 120960*a^3*c^7*d*e^2 - 1155*b^7*c^3*e^3 + 12348*a*b^5*c^4*e^3 - 42192*a^2*b^3*c^5*e^3 + 44096*a^3*b*c^6*e^3)/c^8)*x + (20160*b^5*c^5*d^3 - 215040*a*b^3*c^6*d^3 + 709632*a^2*b*c^7*d^3 - 30240*b^6*c^4*d^2*e + 322560*a*b^4*c^5*d^2*e - 1064448*a^2*b^2*c^6*d^2*e + 884736*a^3*c^7*d^2*e + 17010*b^7*c^3*d*e^2 - 189000*a*b^5*c^4*d*e^2 + 679392*a^2*b^3*c^5*d*e^2 - 763776*a^3*b*c^6*d*e^2 - 3465*b^8*c^2*e^3 + 40740*a*b^6*c^3*e^3 - 162288*a^2*b^4*c^4*e^3 + 234432*a^3*b^2*c^5*e^3 - 65536*a^4*c^6*e^3)/c^8) + 5/65536*(64*b^6*c^3*d^3 - 768*a*b^4*c^4*d^3 + 3072*a^2*b^2*c^5*d^3 - 4096*a^3*c^6*d^3 - 96*b^7*c^2*d^2*e + 1152*a*b^5*c^3*d^2*e - 4608*a^2*b^3*c^4*d^2*e + 6144*a^3*b*c^5*d^2*e + 54*b^8*c*d*e^2 - 672*a*b^6*c^2*d*e^2 + 2880*a^2*b^4*c^3*d*e^2 - 4608*a^3*b^2*c^4*d*e^2 + 1536*a^4*c^5*d*e^2 - 11*b^9*e^3 + 144*a*b^7*c*e^3 - 672*a^2*b^5*c^2*e^3 + 1280*a^3*b^3*c^3*e^3 - 768*a^4*b*c^4*e^3)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(13/2)","B",0
2356,1,767,0,0.307550," ","integrate((e*x+d)^2*(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\frac{1}{344064} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(2 \, {\left(12 \, {\left(14 \, c^{2} x e^{2} + \frac{32 \, c^{9} d e + 33 \, b c^{8} e^{2}}{c^{7}}\right)} x + \frac{224 \, c^{9} d^{2} + 928 \, b c^{8} d e + 243 \, b^{2} c^{7} e^{2} + 476 \, a c^{8} e^{2}}{c^{7}}\right)} x + \frac{1120 \, b c^{8} d^{2} + 1184 \, b^{2} c^{7} d e + 2304 \, a c^{8} d e + 3 \, b^{3} c^{6} e^{2} + 1228 \, a b c^{7} e^{2}}{c^{7}}\right)} x + \frac{6048 \, b^{2} c^{7} d^{2} + 11648 \, a c^{8} d^{2} + 96 \, b^{3} c^{6} d e + 25216 \, a b c^{7} d e - 27 \, b^{4} c^{5} e^{2} + 216 \, a b^{2} c^{6} e^{2} + 6608 \, a^{2} c^{7} e^{2}}{c^{7}}\right)} x + \frac{224 \, b^{3} c^{6} d^{2} + 34944 \, a b c^{7} d^{2} - 224 \, b^{4} c^{5} d e + 1920 \, a b^{2} c^{6} d e + 36864 \, a^{2} c^{7} d e + 63 \, b^{5} c^{4} e^{2} - 568 \, a b^{3} c^{5} e^{2} + 1392 \, a^{2} b c^{6} e^{2}}{c^{7}}\right)} x - \frac{1120 \, b^{4} c^{5} d^{2} - 10752 \, a b^{2} c^{6} d^{2} - 118272 \, a^{2} c^{7} d^{2} - 1120 \, b^{5} c^{4} d e + 10752 \, a b^{3} c^{5} d e - 29184 \, a^{2} b c^{6} d e + 315 \, b^{6} c^{3} e^{2} - 3164 \, a b^{4} c^{4} e^{2} + 9552 \, a^{2} b^{2} c^{5} e^{2} - 6720 \, a^{3} c^{6} e^{2}}{c^{7}}\right)} x + \frac{3360 \, b^{5} c^{4} d^{2} - 35840 \, a b^{3} c^{5} d^{2} + 118272 \, a^{2} b c^{6} d^{2} - 3360 \, b^{6} c^{3} d e + 35840 \, a b^{4} c^{4} d e - 118272 \, a^{2} b^{2} c^{5} d e + 98304 \, a^{3} c^{6} d e + 945 \, b^{7} c^{2} e^{2} - 10500 \, a b^{5} c^{3} e^{2} + 37744 \, a^{2} b^{3} c^{4} e^{2} - 42432 \, a^{3} b c^{5} e^{2}}{c^{7}}\right)} + \frac{5 \, {\left(32 \, b^{6} c^{2} d^{2} - 384 \, a b^{4} c^{3} d^{2} + 1536 \, a^{2} b^{2} c^{4} d^{2} - 2048 \, a^{3} c^{5} d^{2} - 32 \, b^{7} c d e + 384 \, a b^{5} c^{2} d e - 1536 \, a^{2} b^{3} c^{3} d e + 2048 \, a^{3} b c^{4} d e + 9 \, b^{8} e^{2} - 112 \, a b^{6} c e^{2} + 480 \, a^{2} b^{4} c^{2} e^{2} - 768 \, a^{3} b^{2} c^{3} e^{2} + 256 \, a^{4} c^{4} e^{2}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{32768 \, c^{\frac{11}{2}}}"," ",0,"1/344064*sqrt(c*x^2 + b*x + a)*(2*(4*(2*(8*(2*(12*(14*c^2*x*e^2 + (32*c^9*d*e + 33*b*c^8*e^2)/c^7)*x + (224*c^9*d^2 + 928*b*c^8*d*e + 243*b^2*c^7*e^2 + 476*a*c^8*e^2)/c^7)*x + (1120*b*c^8*d^2 + 1184*b^2*c^7*d*e + 2304*a*c^8*d*e + 3*b^3*c^6*e^2 + 1228*a*b*c^7*e^2)/c^7)*x + (6048*b^2*c^7*d^2 + 11648*a*c^8*d^2 + 96*b^3*c^6*d*e + 25216*a*b*c^7*d*e - 27*b^4*c^5*e^2 + 216*a*b^2*c^6*e^2 + 6608*a^2*c^7*e^2)/c^7)*x + (224*b^3*c^6*d^2 + 34944*a*b*c^7*d^2 - 224*b^4*c^5*d*e + 1920*a*b^2*c^6*d*e + 36864*a^2*c^7*d*e + 63*b^5*c^4*e^2 - 568*a*b^3*c^5*e^2 + 1392*a^2*b*c^6*e^2)/c^7)*x - (1120*b^4*c^5*d^2 - 10752*a*b^2*c^6*d^2 - 118272*a^2*c^7*d^2 - 1120*b^5*c^4*d*e + 10752*a*b^3*c^5*d*e - 29184*a^2*b*c^6*d*e + 315*b^6*c^3*e^2 - 3164*a*b^4*c^4*e^2 + 9552*a^2*b^2*c^5*e^2 - 6720*a^3*c^6*e^2)/c^7)*x + (3360*b^5*c^4*d^2 - 35840*a*b^3*c^5*d^2 + 118272*a^2*b*c^6*d^2 - 3360*b^6*c^3*d*e + 35840*a*b^4*c^4*d*e - 118272*a^2*b^2*c^5*d*e + 98304*a^3*c^6*d*e + 945*b^7*c^2*e^2 - 10500*a*b^5*c^3*e^2 + 37744*a^2*b^3*c^4*e^2 - 42432*a^3*b*c^5*e^2)/c^7) + 5/32768*(32*b^6*c^2*d^2 - 384*a*b^4*c^3*d^2 + 1536*a^2*b^2*c^4*d^2 - 2048*a^3*c^5*d^2 - 32*b^7*c*d*e + 384*a*b^5*c^2*d*e - 1536*a^2*b^3*c^3*d*e + 2048*a^3*b*c^4*d*e + 9*b^8*e^2 - 112*a*b^6*c*e^2 + 480*a^2*b^4*c^2*e^2 - 768*a^3*b^2*c^3*e^2 + 256*a^4*c^4*e^2)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(11/2)","B",0
2357,1,445,0,0.253368," ","integrate((e*x+d)*(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\frac{1}{21504} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(2 \, {\left(12 \, c^{2} x e + \frac{14 \, c^{8} d + 29 \, b c^{7} e}{c^{6}}\right)} x + \frac{70 \, b c^{7} d + 37 \, b^{2} c^{6} e + 72 \, a c^{7} e}{c^{6}}\right)} x + \frac{378 \, b^{2} c^{6} d + 728 \, a c^{7} d + 3 \, b^{3} c^{5} e + 788 \, a b c^{6} e}{c^{6}}\right)} x + \frac{14 \, b^{3} c^{5} d + 2184 \, a b c^{6} d - 7 \, b^{4} c^{4} e + 60 \, a b^{2} c^{5} e + 1152 \, a^{2} c^{6} e}{c^{6}}\right)} x - \frac{70 \, b^{4} c^{4} d - 672 \, a b^{2} c^{5} d - 7392 \, a^{2} c^{6} d - 35 \, b^{5} c^{3} e + 336 \, a b^{3} c^{4} e - 912 \, a^{2} b c^{5} e}{c^{6}}\right)} x + \frac{210 \, b^{5} c^{3} d - 2240 \, a b^{3} c^{4} d + 7392 \, a^{2} b c^{5} d - 105 \, b^{6} c^{2} e + 1120 \, a b^{4} c^{3} e - 3696 \, a^{2} b^{2} c^{4} e + 3072 \, a^{3} c^{5} e}{c^{6}}\right)} + \frac{5 \, {\left(2 \, b^{6} c d - 24 \, a b^{4} c^{2} d + 96 \, a^{2} b^{2} c^{3} d - 128 \, a^{3} c^{4} d - b^{7} e + 12 \, a b^{5} c e - 48 \, a^{2} b^{3} c^{2} e + 64 \, a^{3} b c^{3} e\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{2048 \, c^{\frac{9}{2}}}"," ",0,"1/21504*sqrt(c*x^2 + b*x + a)*(2*(4*(2*(8*(2*(12*c^2*x*e + (14*c^8*d + 29*b*c^7*e)/c^6)*x + (70*b*c^7*d + 37*b^2*c^6*e + 72*a*c^7*e)/c^6)*x + (378*b^2*c^6*d + 728*a*c^7*d + 3*b^3*c^5*e + 788*a*b*c^6*e)/c^6)*x + (14*b^3*c^5*d + 2184*a*b*c^6*d - 7*b^4*c^4*e + 60*a*b^2*c^5*e + 1152*a^2*c^6*e)/c^6)*x - (70*b^4*c^4*d - 672*a*b^2*c^5*d - 7392*a^2*c^6*d - 35*b^5*c^3*e + 336*a*b^3*c^4*e - 912*a^2*b*c^5*e)/c^6)*x + (210*b^5*c^3*d - 2240*a*b^3*c^4*d + 7392*a^2*b*c^5*d - 105*b^6*c^2*e + 1120*a*b^4*c^3*e - 3696*a^2*b^2*c^4*e + 3072*a^3*c^5*e)/c^6) + 5/2048*(2*b^6*c*d - 24*a*b^4*c^2*d + 96*a^2*b^2*c^3*d - 128*a^3*c^4*d - b^7*e + 12*a*b^5*c*e - 48*a^2*b^3*c^2*e + 64*a^3*b*c^3*e)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(9/2)","B",0
2358,1,208,0,0.230501," ","integrate((c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\frac{1}{1536} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(2 \, c^{2} x + 5 \, b c\right)} x + \frac{27 \, b^{2} c^{5} + 52 \, a c^{6}}{c^{5}}\right)} x + \frac{b^{3} c^{4} + 156 \, a b c^{5}}{c^{5}}\right)} x - \frac{5 \, b^{4} c^{3} - 48 \, a b^{2} c^{4} - 528 \, a^{2} c^{5}}{c^{5}}\right)} x + \frac{15 \, b^{5} c^{2} - 160 \, a b^{3} c^{3} + 528 \, a^{2} b c^{4}}{c^{5}}\right)} + \frac{5 \, {\left(b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{1024 \, c^{\frac{7}{2}}}"," ",0,"1/1536*sqrt(c*x^2 + b*x + a)*(2*(4*(2*(8*(2*c^2*x + 5*b*c)*x + (27*b^2*c^5 + 52*a*c^6)/c^5)*x + (b^3*c^4 + 156*a*b*c^5)/c^5)*x - (5*b^4*c^3 - 48*a*b^2*c^4 - 528*a^2*c^5)/c^5)*x + (15*b^5*c^2 - 160*a*b^3*c^3 + 528*a^2*b*c^4)/c^5) + 5/1024*(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(7/2)","A",0
2359,-2,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(5/2)/(e*x+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error: Bad Argument Type","F(-2)",0
2360,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(5/2)/(e*x+d)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2361,1,1458,0,1.143915," ","integrate((c*x^2+b*x+a)^(5/2)/(e*x+d)^3,x, algorithm=""giac"")","\frac{5 \, {\left(16 \, c^{3} d^{4} - 32 \, b c^{2} d^{3} e + 19 \, b^{2} c d^{2} e^{2} + 20 \, a c^{2} d^{2} e^{2} - 3 \, b^{3} d e^{3} - 20 \, a b c d e^{3} + 3 \, a b^{2} e^{4} + 4 \, a^{2} c e^{4}\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} + b d e - a e^{2}}}\right) e^{\left(-6\right)}}{4 \, \sqrt{-c d^{2} + b d e - a e^{2}}} + \frac{5 \, {\left(32 \, c^{3} d^{3} - 48 \, b c^{2} d^{2} e + 18 \, b^{2} c d e^{2} + 24 \, a c^{2} d e^{2} - b^{3} e^{3} - 12 \, a b c e^{3}\right)} e^{\left(-6\right)} \log\left({\left| 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} + b \right|}\right)}{16 \, \sqrt{c}} + \frac{1}{24} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, c^{2} x e^{\left(-3\right)} - \frac{{\left(18 \, c^{4} d e^{14} - 13 \, b c^{3} e^{15}\right)} e^{\left(-18\right)}}{c^{2}}\right)} x + \frac{{\left(144 \, c^{4} d^{2} e^{13} - 162 \, b c^{3} d e^{14} + 33 \, b^{2} c^{2} e^{15} + 56 \, a c^{3} e^{15}\right)} e^{\left(-18\right)}}{c^{2}}\right)} + \frac{{\left(40 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} c^{3} d^{4} e + 72 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} c^{\frac{7}{2}} d^{5} - 120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b c^{\frac{5}{2}} d^{4} e + 72 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b c^{3} d^{5} - 80 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b c^{2} d^{3} e^{2} - 124 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{2} c^{2} d^{4} e - 104 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a c^{3} d^{4} e + 18 \, b^{2} c^{\frac{5}{2}} d^{5} + 51 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{2} c^{\frac{3}{2}} d^{3} e^{2} + 36 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a c^{\frac{5}{2}} d^{3} e^{2} - 27 \, b^{3} c^{\frac{3}{2}} d^{4} e - 52 \, a b c^{\frac{5}{2}} d^{4} e + 49 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{2} c d^{2} e^{3} + 44 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a c^{2} d^{2} e^{3} + 59 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{3} c d^{3} e^{2} + 244 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b c^{2} d^{3} e^{2} - 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{3} \sqrt{c} d^{2} e^{3} + 12 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a b c^{\frac{3}{2}} d^{2} e^{3} + 9 \, b^{4} \sqrt{c} d^{3} e^{2} + 95 \, a b^{2} c^{\frac{3}{2}} d^{3} e^{2} + 36 \, a^{2} c^{\frac{5}{2}} d^{3} e^{2} - 9 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{3} d e^{4} - 44 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b c d e^{4} - 7 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{4} d^{2} e^{3} - 127 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{2} c d^{2} e^{3} - 100 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} c^{2} d^{2} e^{3} - 21 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a b^{2} \sqrt{c} d e^{4} - 36 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{2} c^{\frac{3}{2}} d e^{4} - 34 \, a b^{3} \sqrt{c} d^{2} e^{3} - 104 \, a^{2} b c^{\frac{3}{2}} d^{2} e^{3} + 9 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b^{2} e^{5} + 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{2} c e^{5} + 14 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{3} d e^{4} + 64 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} b c d e^{4} + 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{2} b \sqrt{c} e^{5} + 41 \, a^{2} b^{2} \sqrt{c} d e^{4} + 36 \, a^{3} c^{\frac{3}{2}} d e^{4} - 7 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} b^{2} e^{5} + 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{3} c e^{5} - 16 \, a^{3} b \sqrt{c} e^{5}\right)} e^{\left(-6\right)}}{4 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} e + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} d + b d - a e\right)}^{2}}"," ",0,"5/4*(16*c^3*d^4 - 32*b*c^2*d^3*e + 19*b^2*c*d^2*e^2 + 20*a*c^2*d^2*e^2 - 3*b^3*d*e^3 - 20*a*b*c*d*e^3 + 3*a*b^2*e^4 + 4*a^2*c*e^4)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + b*x + a))*e + sqrt(c)*d)/sqrt(-c*d^2 + b*d*e - a*e^2))*e^(-6)/sqrt(-c*d^2 + b*d*e - a*e^2) + 5/16*(32*c^3*d^3 - 48*b*c^2*d^2*e + 18*b^2*c*d*e^2 + 24*a*c^2*d*e^2 - b^3*e^3 - 12*a*b*c*e^3)*e^(-6)*log(abs(2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) + b))/sqrt(c) + 1/24*sqrt(c*x^2 + b*x + a)*(2*(4*c^2*x*e^(-3) - (18*c^4*d*e^14 - 13*b*c^3*e^15)*e^(-18)/c^2)*x + (144*c^4*d^2*e^13 - 162*b*c^3*d*e^14 + 33*b^2*c^2*e^15 + 56*a*c^3*e^15)*e^(-18)/c^2) + 1/4*(40*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*c^3*d^4*e + 72*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*c^(7/2)*d^5 - 120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b*c^(5/2)*d^4*e + 72*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b*c^3*d^5 - 80*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b*c^2*d^3*e^2 - 124*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^2*c^2*d^4*e - 104*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*c^3*d^4*e + 18*b^2*c^(5/2)*d^5 + 51*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^2*c^(3/2)*d^3*e^2 + 36*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*c^(5/2)*d^3*e^2 - 27*b^3*c^(3/2)*d^4*e - 52*a*b*c^(5/2)*d^4*e + 49*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^2*c*d^2*e^3 + 44*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*c^2*d^2*e^3 + 59*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^3*c*d^3*e^2 + 244*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b*c^2*d^3*e^2 - 3*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^3*sqrt(c)*d^2*e^3 + 12*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b*c^(3/2)*d^2*e^3 + 9*b^4*sqrt(c)*d^3*e^2 + 95*a*b^2*c^(3/2)*d^3*e^2 + 36*a^2*c^(5/2)*d^3*e^2 - 9*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^3*d*e^4 - 44*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b*c*d*e^4 - 7*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^4*d^2*e^3 - 127*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^2*c*d^2*e^3 - 100*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*c^2*d^2*e^3 - 21*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^2*sqrt(c)*d*e^4 - 36*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*c^(3/2)*d*e^4 - 34*a*b^3*sqrt(c)*d^2*e^3 - 104*a^2*b*c^(3/2)*d^2*e^3 + 9*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^2*e^5 + 4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*c*e^5 + 14*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^3*d*e^4 + 64*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b*c*d*e^4 + 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*b*sqrt(c)*e^5 + 41*a^2*b^2*sqrt(c)*d*e^4 + 36*a^3*c^(3/2)*d*e^4 - 7*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b^2*e^5 + 4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*c*e^5 - 16*a^3*b*sqrt(c)*e^5)*e^(-6)/((sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*e + 2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c)*d + b*d - a*e)^2","B",0
2362,1,2120,0,24.636490," ","integrate((c*x^2+b*x+a)^(5/2)/(e*x+d)^4,x, algorithm=""giac"")","-\frac{5 \, {\left(32 \, c^{3} d^{3} - 48 \, b c^{2} d^{2} e + 18 \, b^{2} c d e^{2} + 24 \, a c^{2} d e^{2} - b^{3} e^{3} - 12 \, a b c e^{3}\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} + b d e - a e^{2}}}\right) e^{\left(-6\right)}}{8 \, \sqrt{-c d^{2} + b d e - a e^{2}}} - \frac{5 \, {\left(16 \, c^{3} d^{2} - 16 \, b c^{2} d e + 3 \, b^{2} c e^{2} + 4 \, a c^{2} e^{2}\right)} e^{\left(-6\right)} \log\left({\left| 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} + b \right|}\right)}{8 \, \sqrt{c}} + \frac{1}{4} \, {\left(2 \, c^{2} x e^{\left(-4\right)} - \frac{{\left(16 \, c^{3} d e^{10} - 9 \, b c^{2} e^{11}\right)} e^{\left(-15\right)}}{c}\right)} \sqrt{c x^{2} + b x + a} - \frac{{\left(1680 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} c^{4} d^{4} e + 1504 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} c^{\frac{9}{2}} d^{5} + 480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} c^{\frac{7}{2}} d^{3} e^{2} - 400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b c^{\frac{7}{2}} d^{4} e + 2256 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b c^{4} d^{5} - 2160 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} b c^{3} d^{3} e^{2} - 2412 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{2} c^{3} d^{4} e - 2832 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a c^{4} d^{4} e + 1128 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{2} c^{\frac{7}{2}} d^{5} - 720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} b c^{\frac{5}{2}} d^{2} e^{3} - 1308 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{2} c^{\frac{5}{2}} d^{3} e^{2} - 1808 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a c^{\frac{7}{2}} d^{3} e^{2} - 1272 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{3} c^{\frac{5}{2}} d^{4} e - 2832 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b c^{\frac{7}{2}} d^{4} e + 188 \, b^{3} c^{3} d^{5} + 666 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} b^{2} c^{2} d^{2} e^{3} + 216 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a c^{3} d^{2} e^{3} + 462 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{3} c^{2} d^{3} e^{2} + 2952 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a b c^{3} d^{3} e^{2} - 188 \, b^{4} c^{2} d^{4} e - 708 \, a b^{2} c^{3} d^{4} e + 306 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} b^{2} c^{\frac{3}{2}} d e^{4} + 216 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a c^{\frac{5}{2}} d e^{4} + 574 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{3} c^{\frac{3}{2}} d^{2} e^{3} + 3144 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b c^{\frac{5}{2}} d^{2} e^{3} + 324 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{4} c^{\frac{3}{2}} d^{3} e^{2} + 3420 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{2} c^{\frac{5}{2}} d^{3} e^{2} + 1776 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} c^{\frac{7}{2}} d^{3} e^{2} - 21 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} b^{3} c d e^{4} + 324 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a b c^{2} d e^{4} + 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{4} c d^{2} e^{3} + 144 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a b^{2} c^{2} d^{2} e^{3} + 33 \, b^{5} c d^{3} e^{2} + 746 \, a b^{3} c^{2} d^{3} e^{2} + 888 \, a^{2} b c^{3} d^{3} e^{2} - 33 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} b^{3} \sqrt{c} e^{5} - 108 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a b c^{\frac{3}{2}} e^{5} - 40 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{4} \sqrt{c} d e^{4} - 912 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b^{2} c^{\frac{3}{2}} d e^{4} - 672 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{2} c^{\frac{5}{2}} d e^{4} - 15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{5} \sqrt{c} d^{2} e^{3} - 774 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{3} c^{\frac{3}{2}} d^{2} e^{3} - 2664 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} b c^{\frac{5}{2}} d^{2} e^{3} - 144 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a b^{2} c e^{5} - 144 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{2} c^{2} e^{5} - 168 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a b^{3} c d e^{4} - 1008 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{2} b c^{2} d e^{4} - 114 \, a b^{4} c d^{2} e^{3} - 1050 \, a^{2} b^{2} c^{2} d^{2} e^{3} - 376 \, a^{3} c^{3} d^{2} e^{3} + 40 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b^{3} \sqrt{c} e^{5} + 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{2} b c^{\frac{3}{2}} e^{5} + 30 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{4} \sqrt{c} d e^{4} + 486 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} b^{2} c^{\frac{3}{2}} d e^{4} + 456 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{3} c^{\frac{5}{2}} d e^{4} + 144 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{2} b^{2} c e^{5} + 192 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{3} c^{2} e^{5} + 129 \, a^{2} b^{3} c d e^{4} + 604 \, a^{3} b c^{2} d e^{4} - 15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} b^{3} \sqrt{c} e^{5} - 36 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{3} b c^{\frac{3}{2}} e^{5} - 48 \, a^{3} b^{2} c e^{5} - 112 \, a^{4} c^{2} e^{5}\right)} e^{\left(-6\right)}}{24 \, {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} e + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} d + b d - a e\right)}^{3} \sqrt{c}}"," ",0,"-5/8*(32*c^3*d^3 - 48*b*c^2*d^2*e + 18*b^2*c*d*e^2 + 24*a*c^2*d*e^2 - b^3*e^3 - 12*a*b*c*e^3)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + b*x + a))*e + sqrt(c)*d)/sqrt(-c*d^2 + b*d*e - a*e^2))*e^(-6)/sqrt(-c*d^2 + b*d*e - a*e^2) - 5/8*(16*c^3*d^2 - 16*b*c^2*d*e + 3*b^2*c*e^2 + 4*a*c^2*e^2)*e^(-6)*log(abs(2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) + b))/sqrt(c) + 1/4*(2*c^2*x*e^(-4) - (16*c^3*d*e^10 - 9*b*c^2*e^11)*e^(-15)/c)*sqrt(c*x^2 + b*x + a) - 1/24*(1680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*c^4*d^4*e + 1504*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*c^(9/2)*d^5 + 480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*c^(7/2)*d^3*e^2 - 400*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b*c^(7/2)*d^4*e + 2256*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b*c^4*d^5 - 2160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b*c^3*d^3*e^2 - 2412*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^2*c^3*d^4*e - 2832*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*c^4*d^4*e + 1128*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^2*c^(7/2)*d^5 - 720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b*c^(5/2)*d^2*e^3 - 1308*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^2*c^(5/2)*d^3*e^2 - 1808*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*c^(7/2)*d^3*e^2 - 1272*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^3*c^(5/2)*d^4*e - 2832*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b*c^(7/2)*d^4*e + 188*b^3*c^3*d^5 + 666*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^2*c^2*d^2*e^3 + 216*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*c^3*d^2*e^3 + 462*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^3*c^2*d^3*e^2 + 2952*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b*c^3*d^3*e^2 - 188*b^4*c^2*d^4*e - 708*a*b^2*c^3*d^4*e + 306*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b^2*c^(3/2)*d*e^4 + 216*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*c^(5/2)*d*e^4 + 574*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^3*c^(3/2)*d^2*e^3 + 3144*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b*c^(5/2)*d^2*e^3 + 324*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^4*c^(3/2)*d^3*e^2 + 3420*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^2*c^(5/2)*d^3*e^2 + 1776*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*c^(7/2)*d^3*e^2 - 21*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^3*c*d*e^4 + 324*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*b*c^2*d*e^4 + 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^4*c*d^2*e^3 + 144*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^2*c^2*d^2*e^3 + 33*b^5*c*d^3*e^2 + 746*a*b^3*c^2*d^3*e^2 + 888*a^2*b*c^3*d^3*e^2 - 33*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b^3*sqrt(c)*e^5 - 108*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*b*c^(3/2)*e^5 - 40*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^4*sqrt(c)*d*e^4 - 912*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^2*c^(3/2)*d*e^4 - 672*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*c^(5/2)*d*e^4 - 15*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^5*sqrt(c)*d^2*e^3 - 774*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^3*c^(3/2)*d^2*e^3 - 2664*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b*c^(5/2)*d^2*e^3 - 144*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*b^2*c*e^5 - 144*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^2*c^2*e^5 - 168*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^3*c*d*e^4 - 1008*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*b*c^2*d*e^4 - 114*a*b^4*c*d^2*e^3 - 1050*a^2*b^2*c^2*d^2*e^3 - 376*a^3*c^3*d^2*e^3 + 40*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^3*sqrt(c)*e^5 + 48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*b*c^(3/2)*e^5 + 30*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^4*sqrt(c)*d*e^4 + 486*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b^2*c^(3/2)*d*e^4 + 456*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*c^(5/2)*d*e^4 + 144*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*b^2*c*e^5 + 192*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^3*c^2*e^5 + 129*a^2*b^3*c*d*e^4 + 604*a^3*b*c^2*d*e^4 - 15*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b^3*sqrt(c)*e^5 - 36*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*b*c^(3/2)*e^5 - 48*a^3*b^2*c*e^5 - 112*a^4*c^2*e^5)*e^(-6)/(((sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*e + 2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c)*d + b*d - a*e)^3*sqrt(c))","B",0
2363,-2,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(5/2)/(e*x+d)^5,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]Evaluation time: 1.14Unable to divide, perhaps due to rounding error%%%{%%%{1,[0,8,0,0,0]%%%},[4,0]%%%}+%%%{%%%{-2,[0,8,0,0,1]%%%},[2,0]%%%}+%%%{%%%{1,[0,8,0,0,2]%%%},[0,0]%%%} / %%%{%%%{1,[1,2,0,0,0]%%%}+%%%{-1,[0,1,1,1,0]%%%}+%%%{1,[0,0,0,2,1]%%%},[4,0]%%%}+%%%{%%%{-2,[1,2,0,0,1]%%%}+%%%{2,[0,1,1,1,1]%%%}+%%%{-2,[0,0,0,2,2]%%%},[2,0]%%%}+%%%{%%%{1,[1,2,0,0,2]%%%}+%%%{-1,[0,1,1,1,2]%%%}+%%%{1,[0,0,0,2,3]%%%},[0,0]%%%} Error: Bad Argument Value","F(-2)",0
2364,1,77,0,0.190113," ","integrate((5*x^2-3*x-2)^(1/2)/x,x, algorithm=""giac"")","-2 \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{5} x - \sqrt{5 \, x^{2} - 3 \, x - 2}\right)}\right) + \frac{3}{10} \, \sqrt{5} \log\left({\left| -10 \, \sqrt{5} x + 3 \, \sqrt{5} + 10 \, \sqrt{5 \, x^{2} - 3 \, x - 2} \right|}\right) + \sqrt{5 \, x^{2} - 3 \, x - 2}"," ",0,"-2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(5)*x - sqrt(5*x^2 - 3*x - 2))) + 3/10*sqrt(5)*log(abs(-10*sqrt(5)*x + 3*sqrt(5) + 10*sqrt(5*x^2 - 3*x - 2))) + sqrt(5*x^2 - 3*x - 2)","A",0
2365,1,168,0,0.247113," ","integrate((-x^2-x+2)^(1/2)/x^2,x, algorithm=""giac"")","-\frac{1}{4} \, \sqrt{2} \log\left(\frac{{\left| -4 \, \sqrt{2} + \frac{2 \, {\left(2 \, \sqrt{-x^{2} - x + 2} - 3\right)}}{2 \, x + 1} + 6 \right|}}{{\left| 4 \, \sqrt{2} + \frac{2 \, {\left(2 \, \sqrt{-x^{2} - x + 2} - 3\right)}}{2 \, x + 1} + 6 \right|}}\right) + \frac{6 \, {\left(\frac{3 \, {\left(2 \, \sqrt{-x^{2} - x + 2} - 3\right)}}{2 \, x + 1} + 1\right)}}{\frac{6 \, {\left(2 \, \sqrt{-x^{2} - x + 2} - 3\right)}}{2 \, x + 1} + \frac{{\left(2 \, \sqrt{-x^{2} - x + 2} - 3\right)}^{2}}{{\left(2 \, x + 1\right)}^{2}} + 1} - \arcsin\left(\frac{2}{3} \, x + \frac{1}{3}\right)"," ",0,"-1/4*sqrt(2)*log(abs(-4*sqrt(2) + 2*(2*sqrt(-x^2 - x + 2) - 3)/(2*x + 1) + 6)/abs(4*sqrt(2) + 2*(2*sqrt(-x^2 - x + 2) - 3)/(2*x + 1) + 6)) + 6*(3*(2*sqrt(-x^2 - x + 2) - 3)/(2*x + 1) + 1)/(6*(2*sqrt(-x^2 - x + 2) - 3)/(2*x + 1) + (2*sqrt(-x^2 - x + 2) - 3)^2/(2*x + 1)^2 + 1) - arcsin(2/3*x + 1/3)","B",0
2366,1,25,0,0.211348," ","integrate((1+x)^3*(x^2+2*x+2)^(1/2),x, algorithm=""giac"")","\frac{1}{5} \, {\left(x^{2} + 2 \, x + 2\right)}^{\frac{5}{2}} - \frac{1}{3} \, {\left(x^{2} + 2 \, x + 2\right)}^{\frac{3}{2}}"," ",0,"1/5*(x^2 + 2*x + 2)^(5/2) - 1/3*(x^2 + 2*x + 2)^(3/2)","A",0
2367,1,45,0,0.171058," ","integrate((-2+3*x)*(9*x^2+12*x+8)^(1/2),x, algorithm=""giac"")","\frac{1}{9} \, {\left(3 \, {\left(3 \, x - 2\right)} x - 4\right)} \sqrt{9 \, x^{2} + 12 \, x + 8} + \frac{8}{3} \, \log\left(-3 \, x + \sqrt{9 \, x^{2} + 12 \, x + 8} - 2\right)"," ",0,"1/9*(3*(3*x - 2)*x - 4)*sqrt(9*x^2 + 12*x + 8) + 8/3*log(-3*x + sqrt(9*x^2 + 12*x + 8) - 2)","A",0
2368,1,32,0,0.210901," ","integrate((7-2*x)*(-4*x^2+16*x+9)^(1/2),x, algorithm=""giac"")","-\frac{1}{6} \, {\left({\left(4 \, x - 25\right)} x + 9\right)} \sqrt{-4 \, x^{2} + 16 \, x + 9} + \frac{75}{4} \, \arcsin\left(\frac{2}{5} \, x - \frac{4}{5}\right)"," ",0,"-1/6*((4*x - 25)*x + 9)*sqrt(-4*x^2 + 16*x + 9) + 75/4*arcsin(2/5*x - 4/5)","A",0
2369,1,67,0,0.177056," ","integrate((x^2-x-1)^(1/2)/(1+x),x, algorithm=""giac"")","\sqrt{x^{2} - x - 1} - \log\left({\left| -x + \sqrt{x^{2} - x - 1} \right|}\right) + \log\left({\left| -x + \sqrt{x^{2} - x - 1} - 2 \right|}\right) + \frac{3}{2} \, \log\left({\left| -2 \, x + 2 \, \sqrt{x^{2} - x - 1} + 1 \right|}\right)"," ",0,"sqrt(x^2 - x - 1) - log(abs(-x + sqrt(x^2 - x - 1))) + log(abs(-x + sqrt(x^2 - x - 1) - 2)) + 3/2*log(abs(-2*x + 2*sqrt(x^2 - x - 1) + 1))","A",0
2370,1,52,0,0.339327," ","integrate((x^2-x-1)^(1/2)/(1-x),x, algorithm=""giac"")","-\sqrt{x^{2} - x - 1} + 2 \, \arctan\left(-x + \sqrt{x^{2} - x - 1} + 1\right) + \frac{1}{2} \, \log\left({\left| -2 \, x + 2 \, \sqrt{x^{2} - x - 1} + 1 \right|}\right)"," ",0,"-sqrt(x^2 - x - 1) + 2*arctan(-x + sqrt(x^2 - x - 1) + 1) + 1/2*log(abs(-2*x + 2*sqrt(x^2 - x - 1) + 1))","A",0
2371,1,208,0,0.282299," ","integrate(x^6/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\frac{1}{7680} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, x {\left(\frac{10 \, x}{c} - \frac{11 \, b}{c^{2}}\right)} + \frac{99 \, b^{2} c^{3} - 100 \, a c^{4}}{c^{6}}\right)} x - \frac{3 \, {\left(77 \, b^{3} c^{2} - 156 \, a b c^{3}\right)}}{c^{6}}\right)} x + \frac{3 \, {\left(385 \, b^{4} c - 1176 \, a b^{2} c^{2} + 400 \, a^{2} c^{3}\right)}}{c^{6}}\right)} x - \frac{21 \, {\left(165 \, b^{5} - 680 \, a b^{3} c + 528 \, a^{2} b c^{2}\right)}}{c^{6}}\right)} - \frac{{\left(231 \, b^{6} - 1260 \, a b^{4} c + 1680 \, a^{2} b^{2} c^{2} - 320 \, a^{3} c^{3}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{1024 \, c^{\frac{13}{2}}}"," ",0,"1/7680*sqrt(c*x^2 + b*x + a)*(2*(4*(2*(8*x*(10*x/c - 11*b/c^2) + (99*b^2*c^3 - 100*a*c^4)/c^6)*x - 3*(77*b^3*c^2 - 156*a*b*c^3)/c^6)*x + 3*(385*b^4*c - 1176*a*b^2*c^2 + 400*a^2*c^3)/c^6)*x - 21*(165*b^5 - 680*a*b^3*c + 528*a^2*b*c^2)/c^6) - 1/1024*(231*b^6 - 1260*a*b^4*c + 1680*a^2*b^2*c^2 - 320*a^3*c^3)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(13/2)","A",0
2372,1,161,0,0.231238," ","integrate(x^5/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\frac{1}{1920} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, {\left(6 \, x {\left(\frac{8 \, x}{c} - \frac{9 \, b}{c^{2}}\right)} + \frac{63 \, b^{2} c^{2} - 64 \, a c^{3}}{c^{5}}\right)} x - \frac{7 \, {\left(45 \, b^{3} c - 92 \, a b c^{2}\right)}}{c^{5}}\right)} x + \frac{945 \, b^{4} - 2940 \, a b^{2} c + 1024 \, a^{2} c^{2}}{c^{5}}\right)} + \frac{{\left(63 \, b^{5} - 280 \, a b^{3} c + 240 \, a^{2} b c^{2}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{256 \, c^{\frac{11}{2}}}"," ",0,"1/1920*sqrt(c*x^2 + b*x + a)*(2*(4*(6*x*(8*x/c - 9*b/c^2) + (63*b^2*c^2 - 64*a*c^3)/c^5)*x - 7*(45*b^3*c - 92*a*b*c^2)/c^5)*x + (945*b^4 - 2940*a*b^2*c + 1024*a^2*c^2)/c^5) + 1/256*(63*b^5 - 280*a*b^3*c + 240*a^2*b*c^2)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(11/2)","A",0
2373,1,276,0,0.655911," ","integrate((e*x+d)^4/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\frac{1}{192} \, \sqrt{c x^{2} + b x + a} {\left(2 \, {\left(4 \, x {\left(\frac{6 \, x e^{4}}{c} + \frac{32 \, c^{3} d e^{3} - 7 \, b c^{2} e^{4}}{c^{4}}\right)} + \frac{288 \, c^{3} d^{2} e^{2} - 160 \, b c^{2} d e^{3} + 35 \, b^{2} c e^{4} - 36 \, a c^{2} e^{4}}{c^{4}}\right)} x + \frac{768 \, c^{3} d^{3} e - 864 \, b c^{2} d^{2} e^{2} + 480 \, b^{2} c d e^{3} - 512 \, a c^{2} d e^{3} - 105 \, b^{3} e^{4} + 220 \, a b c e^{4}}{c^{4}}\right)} - \frac{{\left(128 \, c^{4} d^{4} - 256 \, b c^{3} d^{3} e + 288 \, b^{2} c^{2} d^{2} e^{2} - 384 \, a c^{3} d^{2} e^{2} - 160 \, b^{3} c d e^{3} + 384 \, a b c^{2} d e^{3} + 35 \, b^{4} e^{4} - 120 \, a b^{2} c e^{4} + 48 \, a^{2} c^{2} e^{4}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{128 \, c^{\frac{9}{2}}}"," ",0,"1/192*sqrt(c*x^2 + b*x + a)*(2*(4*x*(6*x*e^4/c + (32*c^3*d*e^3 - 7*b*c^2*e^4)/c^4) + (288*c^3*d^2*e^2 - 160*b*c^2*d*e^3 + 35*b^2*c*e^4 - 36*a*c^2*e^4)/c^4)*x + (768*c^3*d^3*e - 864*b*c^2*d^2*e^2 + 480*b^2*c*d*e^3 - 512*a*c^2*d*e^3 - 105*b^3*e^4 + 220*a*b*c*e^4)/c^4) - 1/128*(128*c^4*d^4 - 256*b*c^3*d^3*e + 288*b^2*c^2*d^2*e^2 - 384*a*c^3*d^2*e^2 - 160*b^3*c*d*e^3 + 384*a*b*c^2*d*e^3 + 35*b^4*e^4 - 120*a*b^2*c*e^4 + 48*a^2*c^2*e^4)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(9/2)","A",0
2374,1,170,0,0.263250," ","integrate((e*x+d)^3/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\frac{1}{24} \, \sqrt{c x^{2} + b x + a} {\left(2 \, x {\left(\frac{4 \, x e^{3}}{c} + \frac{18 \, c^{2} d e^{2} - 5 \, b c e^{3}}{c^{3}}\right)} + \frac{72 \, c^{2} d^{2} e - 54 \, b c d e^{2} + 15 \, b^{2} e^{3} - 16 \, a c e^{3}}{c^{3}}\right)} - \frac{{\left(16 \, c^{3} d^{3} - 24 \, b c^{2} d^{2} e + 18 \, b^{2} c d e^{2} - 24 \, a c^{2} d e^{2} - 5 \, b^{3} e^{3} + 12 \, a b c e^{3}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{16 \, c^{\frac{7}{2}}}"," ",0,"1/24*sqrt(c*x^2 + b*x + a)*(2*x*(4*x*e^3/c + (18*c^2*d*e^2 - 5*b*c*e^3)/c^3) + (72*c^2*d^2*e - 54*b*c*d*e^2 + 15*b^2*e^3 - 16*a*c*e^3)/c^3) - 1/16*(16*c^3*d^3 - 24*b*c^2*d^2*e + 18*b^2*c*d*e^2 - 24*a*c^2*d*e^2 - 5*b^3*e^3 + 12*a*b*c*e^3)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(7/2)","A",0
2375,1,105,0,0.243770," ","integrate((e*x+d)^2/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{c x^{2} + b x + a} {\left(\frac{2 \, x e^{2}}{c} + \frac{8 \, c d e - 3 \, b e^{2}}{c^{2}}\right)} - \frac{{\left(8 \, c^{2} d^{2} - 8 \, b c d e + 3 \, b^{2} e^{2} - 4 \, a c e^{2}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{8 \, c^{\frac{5}{2}}}"," ",0,"1/4*sqrt(c*x^2 + b*x + a)*(2*x*e^2/c + (8*c*d*e - 3*b*e^2)/c^2) - 1/8*(8*c^2*d^2 - 8*b*c*d*e + 3*b^2*e^2 - 4*a*c*e^2)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(5/2)","A",0
2376,1,65,0,0.257147," ","integrate((e*x+d)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\frac{\sqrt{c x^{2} + b x + a} e}{c} - \frac{{\left(2 \, c d - b e\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{2 \, c^{\frac{3}{2}}}"," ",0,"sqrt(c*x^2 + b*x + a)*e/c - 1/2*(2*c*d - b*e)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(3/2)","A",0
2377,1,36,0,0.207871," ","integrate(1/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","-\frac{\log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{\sqrt{c}}"," ",0,"-log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/sqrt(c)","A",0
2378,1,72,0,0.229419," ","integrate(1/(e*x+d)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\frac{2 \, \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} + b d e - a e^{2}}}\right)}{\sqrt{-c d^{2} + b d e - a e^{2}}}"," ",0,"2*arctan(-((sqrt(c)*x - sqrt(c*x^2 + b*x + a))*e + sqrt(c)*d)/sqrt(-c*d^2 + b*d*e - a*e^2))/sqrt(-c*d^2 + b*d*e - a*e^2)","A",0
2379,-1,0,0,0.000000," ","integrate(1/(e*x+d)^2/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2380,1,785,0,0.363536," ","integrate(1/(e*x+d)^3/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\frac{{\left(8 \, c^{2} d^{2} - 8 \, b c d e + 3 \, b^{2} e^{2} - 4 \, a c e^{2}\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} + b d e - a e^{2}}}\right)}{4 \, {\left(c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2} + 2 \, a c d^{2} e^{2} - 2 \, a b d e^{3} + a^{2} e^{4}\right)} \sqrt{-c d^{2} + b d e - a e^{2}}} - \frac{8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} c^{2} d^{2} e + 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} c^{\frac{5}{2}} d^{3} - 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b c^{\frac{3}{2}} d^{2} e + 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b c^{2} d^{3} - 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b c d e^{2} - 20 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{2} c d^{2} e - 40 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a c^{2} d^{2} e + 6 \, b^{2} c^{\frac{3}{2}} d^{3} + 9 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{2} \sqrt{c} d e^{2} - 12 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a c^{\frac{3}{2}} d e^{2} - 3 \, b^{3} \sqrt{c} d^{2} e - 20 \, a b c^{\frac{3}{2}} d^{2} e + 3 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{2} e^{3} - 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a c e^{3} + 5 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{3} d e^{2} + 28 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b c d e^{2} + 11 \, a b^{2} \sqrt{c} d e^{2} + 12 \, a^{2} c^{\frac{3}{2}} d e^{2} - 5 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{2} e^{3} - 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} c e^{3} - 8 \, a^{2} b \sqrt{c} e^{3}}{4 \, {\left(c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2} + 2 \, a c d^{2} e^{2} - 2 \, a b d e^{3} + a^{2} e^{4}\right)} {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} e + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} d + b d - a e\right)}^{2}}"," ",0,"1/4*(8*c^2*d^2 - 8*b*c*d*e + 3*b^2*e^2 - 4*a*c*e^2)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + b*x + a))*e + sqrt(c)*d)/sqrt(-c*d^2 + b*d*e - a*e^2))/((c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2 + 2*a*c*d^2*e^2 - 2*a*b*d*e^3 + a^2*e^4)*sqrt(-c*d^2 + b*d*e - a*e^2)) - 1/4*(8*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*c^2*d^2*e + 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*c^(5/2)*d^3 - 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b*c^(3/2)*d^2*e + 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b*c^2*d^3 - 8*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b*c*d*e^2 - 20*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^2*c*d^2*e - 40*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*c^2*d^2*e + 6*b^2*c^(3/2)*d^3 + 9*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^2*sqrt(c)*d*e^2 - 12*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*c^(3/2)*d*e^2 - 3*b^3*sqrt(c)*d^2*e - 20*a*b*c^(3/2)*d^2*e + 3*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^2*e^3 - 4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*c*e^3 + 5*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^3*d*e^2 + 28*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b*c*d*e^2 + 11*a*b^2*sqrt(c)*d*e^2 + 12*a^2*c^(3/2)*d*e^2 - 5*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^2*e^3 - 4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*c*e^3 - 8*a^2*b*sqrt(c)*e^3)/((c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2 + 2*a*c*d^2*e^2 - 2*a*b*d*e^3 + a^2*e^4)*((sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*e + 2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c)*d + b*d - a*e)^2)","B",0
2381,1,2079,0,0.474740," ","integrate(1/(e*x+d)^4/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\frac{{\left(16 \, c^{3} d^{3} - 24 \, b c^{2} d^{2} e + 18 \, b^{2} c d e^{2} - 24 \, a c^{2} d e^{2} - 5 \, b^{3} e^{3} + 12 \, a b c e^{3}\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} + b d e - a e^{2}}}\right)}{8 \, {\left(c^{3} d^{6} - 3 \, b c^{2} d^{5} e + 3 \, b^{2} c d^{4} e^{2} + 3 \, a c^{2} d^{4} e^{2} - b^{3} d^{3} e^{3} - 6 \, a b c d^{3} e^{3} + 3 \, a b^{2} d^{2} e^{4} + 3 \, a^{2} c d^{2} e^{4} - 3 \, a^{2} b d e^{5} + a^{3} e^{6}\right)} \sqrt{-c d^{2} + b d e - a e^{2}}} - \frac{240 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} c^{\frac{7}{2}} d^{4} e + 352 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} c^{4} d^{5} + 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} c^{3} d^{3} e^{2} - 400 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b c^{3} d^{4} e + 528 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b c^{\frac{7}{2}} d^{5} - 360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} b c^{\frac{5}{2}} d^{3} e^{2} - 756 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{2} c^{\frac{5}{2}} d^{4} e - 816 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a c^{\frac{7}{2}} d^{4} e + 264 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{2} c^{3} d^{5} - 72 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} b c^{2} d^{2} e^{3} + 204 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{2} c^{2} d^{3} e^{2} - 656 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a c^{3} d^{3} e^{2} - 336 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{3} c^{2} d^{4} e - 816 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b c^{3} d^{4} e + 44 \, b^{3} c^{\frac{5}{2}} d^{5} + 270 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} b^{2} c^{\frac{3}{2}} d^{2} e^{3} - 360 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a c^{\frac{5}{2}} d^{2} e^{3} + 498 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{3} c^{\frac{3}{2}} d^{3} e^{2} + 648 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a b c^{\frac{5}{2}} d^{3} e^{2} - 44 \, b^{4} c^{\frac{3}{2}} d^{4} e - 204 \, a b^{2} c^{\frac{5}{2}} d^{4} e + 54 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} b^{2} c d e^{4} - 72 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a c^{2} d e^{4} + 34 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{3} c d^{2} e^{3} + 264 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b c^{2} d^{2} e^{3} + 180 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{4} c d^{3} e^{2} + 900 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{2} c^{2} d^{3} e^{2} + 480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} c^{3} d^{3} e^{2} - 75 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} b^{3} \sqrt{c} d e^{4} + 180 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a b c^{\frac{3}{2}} d e^{4} - 120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{4} \sqrt{c} d^{2} e^{3} - 432 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a b^{2} c^{\frac{3}{2}} d^{2} e^{3} + 288 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{2} c^{\frac{5}{2}} d^{2} e^{3} + 15 \, b^{5} \sqrt{c} d^{3} e^{2} + 206 \, a b^{3} c^{\frac{3}{2}} d^{3} e^{2} + 240 \, a^{2} b c^{\frac{5}{2}} d^{3} e^{2} - 15 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} b^{3} e^{5} + 36 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a b c e^{5} - 40 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{4} d e^{4} - 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b^{2} c d e^{4} + 192 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{2} c^{2} d e^{4} - 33 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{5} d^{2} e^{3} - 450 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{3} c d^{2} e^{3} - 432 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} b c^{2} d^{2} e^{3} + 120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a b^{3} \sqrt{c} d e^{4} - 78 \, a b^{4} \sqrt{c} d^{2} e^{3} - 222 \, a^{2} b^{2} c^{\frac{3}{2}} d^{2} e^{3} - 88 \, a^{3} c^{\frac{5}{2}} d^{2} e^{3} + 40 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b^{3} e^{5} - 96 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{2} b c e^{5} + 66 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{4} d e^{4} + 306 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} b^{2} c d e^{4} - 120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{3} c^{2} d e^{4} - 96 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{3} c^{\frac{3}{2}} e^{5} + 111 \, a^{2} b^{3} \sqrt{c} d e^{4} + 28 \, a^{3} b c^{\frac{3}{2}} d e^{4} - 33 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} b^{3} e^{5} - 36 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{3} b c e^{5} - 48 \, a^{3} b^{2} \sqrt{c} e^{5} + 32 \, a^{4} c^{\frac{3}{2}} e^{5}}{24 \, {\left(c^{3} d^{6} - 3 \, b c^{2} d^{5} e + 3 \, b^{2} c d^{4} e^{2} + 3 \, a c^{2} d^{4} e^{2} - b^{3} d^{3} e^{3} - 6 \, a b c d^{3} e^{3} + 3 \, a b^{2} d^{2} e^{4} + 3 \, a^{2} c d^{2} e^{4} - 3 \, a^{2} b d e^{5} + a^{3} e^{6}\right)} {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} e + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} d + b d - a e\right)}^{3}}"," ",0,"1/8*(16*c^3*d^3 - 24*b*c^2*d^2*e + 18*b^2*c*d*e^2 - 24*a*c^2*d*e^2 - 5*b^3*e^3 + 12*a*b*c*e^3)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + b*x + a))*e + sqrt(c)*d)/sqrt(-c*d^2 + b*d*e - a*e^2))/((c^3*d^6 - 3*b*c^2*d^5*e + 3*b^2*c*d^4*e^2 + 3*a*c^2*d^4*e^2 - b^3*d^3*e^3 - 6*a*b*c*d^3*e^3 + 3*a*b^2*d^2*e^4 + 3*a^2*c*d^2*e^4 - 3*a^2*b*d*e^5 + a^3*e^6)*sqrt(-c*d^2 + b*d*e - a*e^2)) - 1/24*(240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*c^(7/2)*d^4*e + 352*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*c^4*d^5 + 48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*c^3*d^3*e^2 - 400*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b*c^3*d^4*e + 528*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b*c^(7/2)*d^5 - 360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b*c^(5/2)*d^3*e^2 - 756*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^2*c^(5/2)*d^4*e - 816*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*c^(7/2)*d^4*e + 264*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^2*c^3*d^5 - 72*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b*c^2*d^2*e^3 + 204*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^2*c^2*d^3*e^2 - 656*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*c^3*d^3*e^2 - 336*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^3*c^2*d^4*e - 816*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b*c^3*d^4*e + 44*b^3*c^(5/2)*d^5 + 270*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^2*c^(3/2)*d^2*e^3 - 360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*c^(5/2)*d^2*e^3 + 498*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^3*c^(3/2)*d^3*e^2 + 648*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b*c^(5/2)*d^3*e^2 - 44*b^4*c^(3/2)*d^4*e - 204*a*b^2*c^(5/2)*d^4*e + 54*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b^2*c*d*e^4 - 72*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*c^2*d*e^4 + 34*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^3*c*d^2*e^3 + 264*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b*c^2*d^2*e^3 + 180*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^4*c*d^3*e^2 + 900*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^2*c^2*d^3*e^2 + 480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*c^3*d^3*e^2 - 75*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^3*sqrt(c)*d*e^4 + 180*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*b*c^(3/2)*d*e^4 - 120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^4*sqrt(c)*d^2*e^3 - 432*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^2*c^(3/2)*d^2*e^3 + 288*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*c^(5/2)*d^2*e^3 + 15*b^5*sqrt(c)*d^3*e^2 + 206*a*b^3*c^(3/2)*d^3*e^2 + 240*a^2*b*c^(5/2)*d^3*e^2 - 15*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b^3*e^5 + 36*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*b*c*e^5 - 40*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^4*d*e^4 - 48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^2*c*d*e^4 + 192*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*c^2*d*e^4 - 33*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^5*d^2*e^3 - 450*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^3*c*d^2*e^3 - 432*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b*c^2*d^2*e^3 + 120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^3*sqrt(c)*d*e^4 - 78*a*b^4*sqrt(c)*d^2*e^3 - 222*a^2*b^2*c^(3/2)*d^2*e^3 - 88*a^3*c^(5/2)*d^2*e^3 + 40*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^3*e^5 - 96*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*b*c*e^5 + 66*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^4*d*e^4 + 306*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b^2*c*d*e^4 - 120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*c^2*d*e^4 - 96*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^3*c^(3/2)*e^5 + 111*a^2*b^3*sqrt(c)*d*e^4 + 28*a^3*b*c^(3/2)*d*e^4 - 33*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b^3*e^5 - 36*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*b*c*e^5 - 48*a^3*b^2*sqrt(c)*e^5 + 32*a^4*c^(3/2)*e^5)/((c^3*d^6 - 3*b*c^2*d^5*e + 3*b^2*c*d^4*e^2 + 3*a*c^2*d^4*e^2 - b^3*d^3*e^3 - 6*a*b*c*d^3*e^3 + 3*a*b^2*d^2*e^4 + 3*a^2*c*d^2*e^4 - 3*a^2*b*d*e^5 + a^3*e^6)*((sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*e + 2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c)*d + b*d - a*e)^3)","B",0
2382,1,377,0,0.286981," ","integrate((e*x+d)^4/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\frac{{\left({\left(\frac{2 \, {\left(b^{2} c^{2} e^{4} - 4 \, a c^{3} e^{4}\right)} x}{b^{2} c^{3} - 4 \, a c^{4}} + \frac{16 \, b^{2} c^{2} d e^{3} - 64 \, a c^{3} d e^{3} - 5 \, b^{3} c e^{4} + 20 \, a b c^{2} e^{4}}{b^{2} c^{3} - 4 \, a c^{4}}\right)} x - \frac{16 \, c^{4} d^{4} - 32 \, b c^{3} d^{3} e + 48 \, b^{2} c^{2} d^{2} e^{2} - 96 \, a c^{3} d^{2} e^{2} - 48 \, b^{3} c d e^{3} + 160 \, a b c^{2} d e^{3} + 15 \, b^{4} e^{4} - 62 \, a b^{2} c e^{4} + 24 \, a^{2} c^{2} e^{4}}{b^{2} c^{3} - 4 \, a c^{4}}\right)} x - \frac{8 \, b c^{3} d^{4} - 64 \, a c^{3} d^{3} e + 48 \, a b c^{2} d^{2} e^{2} - 48 \, a b^{2} c d e^{3} + 128 \, a^{2} c^{2} d e^{3} + 15 \, a b^{3} e^{4} - 52 \, a^{2} b c e^{4}}{b^{2} c^{3} - 4 \, a c^{4}}}{4 \, \sqrt{c x^{2} + b x + a}} - \frac{3 \, {\left(16 \, c^{2} d^{2} e^{2} - 16 \, b c d e^{3} + 5 \, b^{2} e^{4} - 4 \, a c e^{4}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{8 \, c^{\frac{7}{2}}}"," ",0,"1/4*(((2*(b^2*c^2*e^4 - 4*a*c^3*e^4)*x/(b^2*c^3 - 4*a*c^4) + (16*b^2*c^2*d*e^3 - 64*a*c^3*d*e^3 - 5*b^3*c*e^4 + 20*a*b*c^2*e^4)/(b^2*c^3 - 4*a*c^4))*x - (16*c^4*d^4 - 32*b*c^3*d^3*e + 48*b^2*c^2*d^2*e^2 - 96*a*c^3*d^2*e^2 - 48*b^3*c*d*e^3 + 160*a*b*c^2*d*e^3 + 15*b^4*e^4 - 62*a*b^2*c*e^4 + 24*a^2*c^2*e^4)/(b^2*c^3 - 4*a*c^4))*x - (8*b*c^3*d^4 - 64*a*c^3*d^3*e + 48*a*b*c^2*d^2*e^2 - 48*a*b^2*c*d*e^3 + 128*a^2*c^2*d*e^3 + 15*a*b^3*e^4 - 52*a^2*b*c*e^4)/(b^2*c^3 - 4*a*c^4))/sqrt(c*x^2 + b*x + a) - 3/8*(16*c^2*d^2*e^2 - 16*b*c*d*e^3 + 5*b^2*e^4 - 4*a*c*e^4)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(7/2)","A",0
2383,1,233,0,0.289662," ","integrate((e*x+d)^3/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\frac{{\left(\frac{{\left(b^{2} c e^{3} - 4 \, a c^{2} e^{3}\right)} x}{b^{2} c^{2} - 4 \, a c^{3}} - \frac{4 \, c^{3} d^{3} - 6 \, b c^{2} d^{2} e + 6 \, b^{2} c d e^{2} - 12 \, a c^{2} d e^{2} - 3 \, b^{3} e^{3} + 10 \, a b c e^{3}}{b^{2} c^{2} - 4 \, a c^{3}}\right)} x - \frac{2 \, b c^{2} d^{3} - 12 \, a c^{2} d^{2} e + 6 \, a b c d e^{2} - 3 \, a b^{2} e^{3} + 8 \, a^{2} c e^{3}}{b^{2} c^{2} - 4 \, a c^{3}}}{\sqrt{c x^{2} + b x + a}} - \frac{3 \, {\left(2 \, c d e^{2} - b e^{3}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{2 \, c^{\frac{5}{2}}}"," ",0,"(((b^2*c*e^3 - 4*a*c^2*e^3)*x/(b^2*c^2 - 4*a*c^3) - (4*c^3*d^3 - 6*b*c^2*d^2*e + 6*b^2*c*d*e^2 - 12*a*c^2*d*e^2 - 3*b^3*e^3 + 10*a*b*c*e^3)/(b^2*c^2 - 4*a*c^3))*x - (2*b*c^2*d^3 - 12*a*c^2*d^2*e + 6*a*b*c*d*e^2 - 3*a*b^2*e^3 + 8*a^2*c*e^3)/(b^2*c^2 - 4*a*c^3))/sqrt(c*x^2 + b*x + a) - 3/2*(2*c*d*e^2 - b*e^3)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(5/2)","A",0
2384,1,132,0,0.261469," ","integrate((e*x+d)^2/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{{\left(2 \, c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2} - 2 \, a c e^{2}\right)} x}{b^{2} c - 4 \, a c^{2}} + \frac{b c d^{2} - 4 \, a c d e + a b e^{2}}{b^{2} c - 4 \, a c^{2}}\right)}}{\sqrt{c x^{2} + b x + a}} - \frac{e^{2} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{c^{\frac{3}{2}}}"," ",0,"-2*((2*c^2*d^2 - 2*b*c*d*e + b^2*e^2 - 2*a*c*e^2)*x/(b^2*c - 4*a*c^2) + (b*c*d^2 - 4*a*c*d*e + a*b*e^2)/(b^2*c - 4*a*c^2))/sqrt(c*x^2 + b*x + a) - e^2*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(3/2)","A",0
2385,1,57,0,0.234394," ","integrate((e*x+d)/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{{\left(2 \, c d - b e\right)} x}{b^{2} - 4 \, a c} + \frac{b d - 2 \, a e}{b^{2} - 4 \, a c}\right)}}{\sqrt{c x^{2} + b x + a}}"," ",0,"-2*((2*c*d - b*e)*x/(b^2 - 4*a*c) + (b*d - 2*a*e)/(b^2 - 4*a*c))/sqrt(c*x^2 + b*x + a)","A",0
2386,1,41,0,0.228264," ","integrate(1/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{2 \, c x}{b^{2} - 4 \, a c} + \frac{b}{b^{2} - 4 \, a c}\right)}}{\sqrt{c x^{2} + b x + a}}"," ",0,"-2*(2*c*x/(b^2 - 4*a*c) + b/(b^2 - 4*a*c))/sqrt(c*x^2 + b*x + a)","A",0
2387,1,447,0,0.272211," ","integrate(1/(e*x+d)/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{{\left(2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e + b^{2} c d e^{2} + 2 \, a c^{2} d e^{2} - a b c e^{3}\right)} x}{b^{2} c^{2} d^{4} - 4 \, a c^{3} d^{4} - 2 \, b^{3} c d^{3} e + 8 \, a b c^{2} d^{3} e + b^{4} d^{2} e^{2} - 2 \, a b^{2} c d^{2} e^{2} - 8 \, a^{2} c^{2} d^{2} e^{2} - 2 \, a b^{3} d e^{3} + 8 \, a^{2} b c d e^{3} + a^{2} b^{2} e^{4} - 4 \, a^{3} c e^{4}} + \frac{b c^{2} d^{3} - 2 \, b^{2} c d^{2} e + 2 \, a c^{2} d^{2} e + b^{3} d e^{2} - a b c d e^{2} - a b^{2} e^{3} + 2 \, a^{2} c e^{3}}{b^{2} c^{2} d^{4} - 4 \, a c^{3} d^{4} - 2 \, b^{3} c d^{3} e + 8 \, a b c^{2} d^{3} e + b^{4} d^{2} e^{2} - 2 \, a b^{2} c d^{2} e^{2} - 8 \, a^{2} c^{2} d^{2} e^{2} - 2 \, a b^{3} d e^{3} + 8 \, a^{2} b c d e^{3} + a^{2} b^{2} e^{4} - 4 \, a^{3} c e^{4}}\right)}}{\sqrt{c x^{2} + b x + a}} + \frac{2 \, \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} + b d e - a e^{2}}}\right) e^{2}}{{\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{-c d^{2} + b d e - a e^{2}}}"," ",0,"-2*((2*c^3*d^3 - 3*b*c^2*d^2*e + b^2*c*d*e^2 + 2*a*c^2*d*e^2 - a*b*c*e^3)*x/(b^2*c^2*d^4 - 4*a*c^3*d^4 - 2*b^3*c*d^3*e + 8*a*b*c^2*d^3*e + b^4*d^2*e^2 - 2*a*b^2*c*d^2*e^2 - 8*a^2*c^2*d^2*e^2 - 2*a*b^3*d*e^3 + 8*a^2*b*c*d*e^3 + a^2*b^2*e^4 - 4*a^3*c*e^4) + (b*c^2*d^3 - 2*b^2*c*d^2*e + 2*a*c^2*d^2*e + b^3*d*e^2 - a*b*c*d*e^2 - a*b^2*e^3 + 2*a^2*c*e^3)/(b^2*c^2*d^4 - 4*a*c^3*d^4 - 2*b^3*c*d^3*e + 8*a*b*c^2*d^3*e + b^4*d^2*e^2 - 2*a*b^2*c*d^2*e^2 - 8*a^2*c^2*d^2*e^2 - 2*a*b^3*d*e^3 + 8*a^2*b*c*d*e^3 + a^2*b^2*e^4 - 4*a^3*c*e^4))/sqrt(c*x^2 + b*x + a) + 2*arctan(-((sqrt(c)*x - sqrt(c*x^2 + b*x + a))*e + sqrt(c)*d)/sqrt(-c*d^2 + b*d*e - a*e^2))*e^2/((c*d^2 - b*d*e + a*e^2)*sqrt(-c*d^2 + b*d*e - a*e^2))","B",0
2388,-1,0,0,0.000000," ","integrate(1/(e*x+d)^2/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2389,1,2574,0,0.672851," ","integrate(1/(e*x+d)^3/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{{\left(2 \, c^{7} d^{9} - 9 \, b c^{6} d^{8} e + 18 \, b^{2} c^{5} d^{7} e^{2} - 21 \, b^{3} c^{4} d^{6} e^{3} + 15 \, b^{4} c^{3} d^{5} e^{4} + 6 \, a b^{2} c^{4} d^{5} e^{4} - 12 \, a^{2} c^{5} d^{5} e^{4} - 6 \, b^{5} c^{2} d^{4} e^{5} - 15 \, a b^{3} c^{3} d^{4} e^{5} + 30 \, a^{2} b c^{4} d^{4} e^{5} + b^{6} c d^{3} e^{6} + 12 \, a b^{4} c^{2} d^{3} e^{6} - 18 \, a^{2} b^{2} c^{3} d^{3} e^{6} - 16 \, a^{3} c^{4} d^{3} e^{6} - 3 \, a b^{5} c d^{2} e^{7} - 3 \, a^{2} b^{3} c^{2} d^{2} e^{7} + 24 \, a^{3} b c^{3} d^{2} e^{7} + 3 \, a^{2} b^{4} c d e^{8} - 6 \, a^{3} b^{2} c^{2} d e^{8} - 6 \, a^{4} c^{3} d e^{8} - a^{3} b^{3} c e^{9} + 3 \, a^{4} b c^{2} e^{9}\right)} x}{b^{2} c^{6} d^{12} - 4 \, a c^{7} d^{12} - 6 \, b^{3} c^{5} d^{11} e + 24 \, a b c^{6} d^{11} e + 15 \, b^{4} c^{4} d^{10} e^{2} - 54 \, a b^{2} c^{5} d^{10} e^{2} - 24 \, a^{2} c^{6} d^{10} e^{2} - 20 \, b^{5} c^{3} d^{9} e^{3} + 50 \, a b^{3} c^{4} d^{9} e^{3} + 120 \, a^{2} b c^{5} d^{9} e^{3} + 15 \, b^{6} c^{2} d^{8} e^{4} - 225 \, a^{2} b^{2} c^{4} d^{8} e^{4} - 60 \, a^{3} c^{5} d^{8} e^{4} - 6 \, b^{7} c d^{7} e^{5} - 36 \, a b^{5} c^{2} d^{7} e^{5} + 180 \, a^{2} b^{3} c^{3} d^{7} e^{5} + 240 \, a^{3} b c^{4} d^{7} e^{5} + b^{8} d^{6} e^{6} + 26 \, a b^{6} c d^{6} e^{6} - 30 \, a^{2} b^{4} c^{2} d^{6} e^{6} - 340 \, a^{3} b^{2} c^{3} d^{6} e^{6} - 80 \, a^{4} c^{4} d^{6} e^{6} - 6 \, a b^{7} d^{5} e^{7} - 36 \, a^{2} b^{5} c d^{5} e^{7} + 180 \, a^{3} b^{3} c^{2} d^{5} e^{7} + 240 \, a^{4} b c^{3} d^{5} e^{7} + 15 \, a^{2} b^{6} d^{4} e^{8} - 225 \, a^{4} b^{2} c^{2} d^{4} e^{8} - 60 \, a^{5} c^{3} d^{4} e^{8} - 20 \, a^{3} b^{5} d^{3} e^{9} + 50 \, a^{4} b^{3} c d^{3} e^{9} + 120 \, a^{5} b c^{2} d^{3} e^{9} + 15 \, a^{4} b^{4} d^{2} e^{10} - 54 \, a^{5} b^{2} c d^{2} e^{10} - 24 \, a^{6} c^{2} d^{2} e^{10} - 6 \, a^{5} b^{3} d e^{11} + 24 \, a^{6} b c d e^{11} + a^{6} b^{2} e^{12} - 4 \, a^{7} c e^{12}} + \frac{b c^{6} d^{9} - 6 \, b^{2} c^{5} d^{8} e + 6 \, a c^{6} d^{8} e + 15 \, b^{3} c^{4} d^{7} e^{2} - 24 \, a b c^{5} d^{7} e^{2} - 20 \, b^{4} c^{3} d^{6} e^{3} + 34 \, a b^{2} c^{4} d^{6} e^{3} + 16 \, a^{2} c^{5} d^{6} e^{3} + 15 \, b^{5} c^{2} d^{5} e^{4} - 15 \, a b^{3} c^{3} d^{5} e^{4} - 54 \, a^{2} b c^{4} d^{5} e^{4} - 6 \, b^{6} c d^{4} e^{5} - 9 \, a b^{4} c^{2} d^{4} e^{5} + 66 \, a^{2} b^{2} c^{3} d^{4} e^{5} + 12 \, a^{3} c^{4} d^{4} e^{5} + b^{7} d^{3} e^{6} + 11 \, a b^{5} c d^{3} e^{6} - 31 \, a^{2} b^{3} c^{2} d^{3} e^{6} - 32 \, a^{3} b c^{3} d^{3} e^{6} - 3 \, a b^{6} d^{2} e^{7} + 30 \, a^{3} b^{2} c^{2} d^{2} e^{7} + 3 \, a^{2} b^{5} d e^{8} - 9 \, a^{3} b^{3} c d e^{8} - 3 \, a^{4} b c^{2} d e^{8} - a^{3} b^{4} e^{9} + 4 \, a^{4} b^{2} c e^{9} - 2 \, a^{5} c^{2} e^{9}}{b^{2} c^{6} d^{12} - 4 \, a c^{7} d^{12} - 6 \, b^{3} c^{5} d^{11} e + 24 \, a b c^{6} d^{11} e + 15 \, b^{4} c^{4} d^{10} e^{2} - 54 \, a b^{2} c^{5} d^{10} e^{2} - 24 \, a^{2} c^{6} d^{10} e^{2} - 20 \, b^{5} c^{3} d^{9} e^{3} + 50 \, a b^{3} c^{4} d^{9} e^{3} + 120 \, a^{2} b c^{5} d^{9} e^{3} + 15 \, b^{6} c^{2} d^{8} e^{4} - 225 \, a^{2} b^{2} c^{4} d^{8} e^{4} - 60 \, a^{3} c^{5} d^{8} e^{4} - 6 \, b^{7} c d^{7} e^{5} - 36 \, a b^{5} c^{2} d^{7} e^{5} + 180 \, a^{2} b^{3} c^{3} d^{7} e^{5} + 240 \, a^{3} b c^{4} d^{7} e^{5} + b^{8} d^{6} e^{6} + 26 \, a b^{6} c d^{6} e^{6} - 30 \, a^{2} b^{4} c^{2} d^{6} e^{6} - 340 \, a^{3} b^{2} c^{3} d^{6} e^{6} - 80 \, a^{4} c^{4} d^{6} e^{6} - 6 \, a b^{7} d^{5} e^{7} - 36 \, a^{2} b^{5} c d^{5} e^{7} + 180 \, a^{3} b^{3} c^{2} d^{5} e^{7} + 240 \, a^{4} b c^{3} d^{5} e^{7} + 15 \, a^{2} b^{6} d^{4} e^{8} - 225 \, a^{4} b^{2} c^{2} d^{4} e^{8} - 60 \, a^{5} c^{3} d^{4} e^{8} - 20 \, a^{3} b^{5} d^{3} e^{9} + 50 \, a^{4} b^{3} c d^{3} e^{9} + 120 \, a^{5} b c^{2} d^{3} e^{9} + 15 \, a^{4} b^{4} d^{2} e^{10} - 54 \, a^{5} b^{2} c d^{2} e^{10} - 24 \, a^{6} c^{2} d^{2} e^{10} - 6 \, a^{5} b^{3} d e^{11} + 24 \, a^{6} b c d e^{11} + a^{6} b^{2} e^{12} - 4 \, a^{7} c e^{12}}\right)}}{\sqrt{c x^{2} + b x + a}} + \frac{3 \, {\left(16 \, c^{2} d^{2} e^{2} - 16 \, b c d e^{3} + 5 \, b^{2} e^{4} - 4 \, a c e^{4}\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} + b d e - a e^{2}}}\right)}{4 \, {\left(c^{3} d^{6} - 3 \, b c^{2} d^{5} e + 3 \, b^{2} c d^{4} e^{2} + 3 \, a c^{2} d^{4} e^{2} - b^{3} d^{3} e^{3} - 6 \, a b c d^{3} e^{3} + 3 \, a b^{2} d^{2} e^{4} + 3 \, a^{2} c d^{2} e^{4} - 3 \, a^{2} b d e^{5} + a^{3} e^{6}\right)} \sqrt{-c d^{2} + b d e - a e^{2}}} - \frac{56 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} c^{\frac{5}{2}} d^{3} e^{2} + 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} c^{2} d^{2} e^{3} + 56 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b c^{2} d^{3} e^{2} - 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b c^{\frac{3}{2}} d^{2} e^{3} + 14 \, b^{2} c^{\frac{3}{2}} d^{3} e^{2} - 24 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b c d e^{4} - 44 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{2} c d^{2} e^{3} - 88 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a c^{2} d^{2} e^{3} + 13 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{2} \sqrt{c} d e^{4} - 28 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a c^{\frac{3}{2}} d e^{4} - 7 \, b^{3} \sqrt{c} d^{2} e^{3} - 44 \, a b c^{\frac{3}{2}} d^{2} e^{3} + 7 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{2} e^{5} - 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a c e^{5} + 9 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{3} d e^{4} + 60 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b c d e^{4} + 8 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a b \sqrt{c} e^{5} + 23 \, a b^{2} \sqrt{c} d e^{4} + 28 \, a^{2} c^{\frac{3}{2}} d e^{4} - 9 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{2} e^{5} - 4 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} c e^{5} - 16 \, a^{2} b \sqrt{c} e^{5}}{4 \, {\left(c^{3} d^{6} - 3 \, b c^{2} d^{5} e + 3 \, b^{2} c d^{4} e^{2} + 3 \, a c^{2} d^{4} e^{2} - b^{3} d^{3} e^{3} - 6 \, a b c d^{3} e^{3} + 3 \, a b^{2} d^{2} e^{4} + 3 \, a^{2} c d^{2} e^{4} - 3 \, a^{2} b d e^{5} + a^{3} e^{6}\right)} {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} e + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} d + b d - a e\right)}^{2}}"," ",0,"-2*((2*c^7*d^9 - 9*b*c^6*d^8*e + 18*b^2*c^5*d^7*e^2 - 21*b^3*c^4*d^6*e^3 + 15*b^4*c^3*d^5*e^4 + 6*a*b^2*c^4*d^5*e^4 - 12*a^2*c^5*d^5*e^4 - 6*b^5*c^2*d^4*e^5 - 15*a*b^3*c^3*d^4*e^5 + 30*a^2*b*c^4*d^4*e^5 + b^6*c*d^3*e^6 + 12*a*b^4*c^2*d^3*e^6 - 18*a^2*b^2*c^3*d^3*e^6 - 16*a^3*c^4*d^3*e^6 - 3*a*b^5*c*d^2*e^7 - 3*a^2*b^3*c^2*d^2*e^7 + 24*a^3*b*c^3*d^2*e^7 + 3*a^2*b^4*c*d*e^8 - 6*a^3*b^2*c^2*d*e^8 - 6*a^4*c^3*d*e^8 - a^3*b^3*c*e^9 + 3*a^4*b*c^2*e^9)*x/(b^2*c^6*d^12 - 4*a*c^7*d^12 - 6*b^3*c^5*d^11*e + 24*a*b*c^6*d^11*e + 15*b^4*c^4*d^10*e^2 - 54*a*b^2*c^5*d^10*e^2 - 24*a^2*c^6*d^10*e^2 - 20*b^5*c^3*d^9*e^3 + 50*a*b^3*c^4*d^9*e^3 + 120*a^2*b*c^5*d^9*e^3 + 15*b^6*c^2*d^8*e^4 - 225*a^2*b^2*c^4*d^8*e^4 - 60*a^3*c^5*d^8*e^4 - 6*b^7*c*d^7*e^5 - 36*a*b^5*c^2*d^7*e^5 + 180*a^2*b^3*c^3*d^7*e^5 + 240*a^3*b*c^4*d^7*e^5 + b^8*d^6*e^6 + 26*a*b^6*c*d^6*e^6 - 30*a^2*b^4*c^2*d^6*e^6 - 340*a^3*b^2*c^3*d^6*e^6 - 80*a^4*c^4*d^6*e^6 - 6*a*b^7*d^5*e^7 - 36*a^2*b^5*c*d^5*e^7 + 180*a^3*b^3*c^2*d^5*e^7 + 240*a^4*b*c^3*d^5*e^7 + 15*a^2*b^6*d^4*e^8 - 225*a^4*b^2*c^2*d^4*e^8 - 60*a^5*c^3*d^4*e^8 - 20*a^3*b^5*d^3*e^9 + 50*a^4*b^3*c*d^3*e^9 + 120*a^5*b*c^2*d^3*e^9 + 15*a^4*b^4*d^2*e^10 - 54*a^5*b^2*c*d^2*e^10 - 24*a^6*c^2*d^2*e^10 - 6*a^5*b^3*d*e^11 + 24*a^6*b*c*d*e^11 + a^6*b^2*e^12 - 4*a^7*c*e^12) + (b*c^6*d^9 - 6*b^2*c^5*d^8*e + 6*a*c^6*d^8*e + 15*b^3*c^4*d^7*e^2 - 24*a*b*c^5*d^7*e^2 - 20*b^4*c^3*d^6*e^3 + 34*a*b^2*c^4*d^6*e^3 + 16*a^2*c^5*d^6*e^3 + 15*b^5*c^2*d^5*e^4 - 15*a*b^3*c^3*d^5*e^4 - 54*a^2*b*c^4*d^5*e^4 - 6*b^6*c*d^4*e^5 - 9*a*b^4*c^2*d^4*e^5 + 66*a^2*b^2*c^3*d^4*e^5 + 12*a^3*c^4*d^4*e^5 + b^7*d^3*e^6 + 11*a*b^5*c*d^3*e^6 - 31*a^2*b^3*c^2*d^3*e^6 - 32*a^3*b*c^3*d^3*e^6 - 3*a*b^6*d^2*e^7 + 30*a^3*b^2*c^2*d^2*e^7 + 3*a^2*b^5*d*e^8 - 9*a^3*b^3*c*d*e^8 - 3*a^4*b*c^2*d*e^8 - a^3*b^4*e^9 + 4*a^4*b^2*c*e^9 - 2*a^5*c^2*e^9)/(b^2*c^6*d^12 - 4*a*c^7*d^12 - 6*b^3*c^5*d^11*e + 24*a*b*c^6*d^11*e + 15*b^4*c^4*d^10*e^2 - 54*a*b^2*c^5*d^10*e^2 - 24*a^2*c^6*d^10*e^2 - 20*b^5*c^3*d^9*e^3 + 50*a*b^3*c^4*d^9*e^3 + 120*a^2*b*c^5*d^9*e^3 + 15*b^6*c^2*d^8*e^4 - 225*a^2*b^2*c^4*d^8*e^4 - 60*a^3*c^5*d^8*e^4 - 6*b^7*c*d^7*e^5 - 36*a*b^5*c^2*d^7*e^5 + 180*a^2*b^3*c^3*d^7*e^5 + 240*a^3*b*c^4*d^7*e^5 + b^8*d^6*e^6 + 26*a*b^6*c*d^6*e^6 - 30*a^2*b^4*c^2*d^6*e^6 - 340*a^3*b^2*c^3*d^6*e^6 - 80*a^4*c^4*d^6*e^6 - 6*a*b^7*d^5*e^7 - 36*a^2*b^5*c*d^5*e^7 + 180*a^3*b^3*c^2*d^5*e^7 + 240*a^4*b*c^3*d^5*e^7 + 15*a^2*b^6*d^4*e^8 - 225*a^4*b^2*c^2*d^4*e^8 - 60*a^5*c^3*d^4*e^8 - 20*a^3*b^5*d^3*e^9 + 50*a^4*b^3*c*d^3*e^9 + 120*a^5*b*c^2*d^3*e^9 + 15*a^4*b^4*d^2*e^10 - 54*a^5*b^2*c*d^2*e^10 - 24*a^6*c^2*d^2*e^10 - 6*a^5*b^3*d*e^11 + 24*a^6*b*c*d*e^11 + a^6*b^2*e^12 - 4*a^7*c*e^12))/sqrt(c*x^2 + b*x + a) + 3/4*(16*c^2*d^2*e^2 - 16*b*c*d*e^3 + 5*b^2*e^4 - 4*a*c*e^4)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + b*x + a))*e + sqrt(c)*d)/sqrt(-c*d^2 + b*d*e - a*e^2))/((c^3*d^6 - 3*b*c^2*d^5*e + 3*b^2*c*d^4*e^2 + 3*a*c^2*d^4*e^2 - b^3*d^3*e^3 - 6*a*b*c*d^3*e^3 + 3*a*b^2*d^2*e^4 + 3*a^2*c*d^2*e^4 - 3*a^2*b*d*e^5 + a^3*e^6)*sqrt(-c*d^2 + b*d*e - a*e^2)) - 1/4*(56*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*c^(5/2)*d^3*e^2 + 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*c^2*d^2*e^3 + 56*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b*c^2*d^3*e^2 - 48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b*c^(3/2)*d^2*e^3 + 14*b^2*c^(3/2)*d^3*e^2 - 24*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b*c*d*e^4 - 44*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^2*c*d^2*e^3 - 88*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*c^2*d^2*e^3 + 13*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^2*sqrt(c)*d*e^4 - 28*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*c^(3/2)*d*e^4 - 7*b^3*sqrt(c)*d^2*e^3 - 44*a*b*c^(3/2)*d^2*e^3 + 7*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^2*e^5 - 4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*c*e^5 + 9*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^3*d*e^4 + 60*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b*c*d*e^4 + 8*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b*sqrt(c)*e^5 + 23*a*b^2*sqrt(c)*d*e^4 + 28*a^2*c^(3/2)*d*e^4 - 9*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^2*e^5 - 4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*c*e^5 - 16*a^2*b*sqrt(c)*e^5)/((c^3*d^6 - 3*b*c^2*d^5*e + 3*b^2*c*d^4*e^2 + 3*a*c^2*d^4*e^2 - b^3*d^3*e^3 - 6*a*b*c*d^3*e^3 + 3*a*b^2*d^2*e^4 + 3*a^2*c*d^2*e^4 - 3*a^2*b*d*e^5 + a^3*e^6)*((sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*e + 2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c)*d + b*d - a*e)^2)","B",0
2390,1,5166,0,1.297436," ","integrate(1/(e*x+d)^4/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{{\left(2 \, c^{9} d^{12} - 12 \, b c^{8} d^{11} e + 34 \, b^{2} c^{7} d^{10} e^{2} - 4 \, a c^{8} d^{10} e^{2} - 60 \, b^{3} c^{6} d^{9} e^{3} + 20 \, a b c^{7} d^{9} e^{3} + 71 \, b^{4} c^{5} d^{8} e^{4} - 28 \, a b^{2} c^{6} d^{8} e^{4} - 34 \, a^{2} c^{7} d^{8} e^{4} - 56 \, b^{5} c^{4} d^{7} e^{5} - 8 \, a b^{3} c^{5} d^{7} e^{5} + 136 \, a^{2} b c^{6} d^{7} e^{5} + 28 \, b^{6} c^{3} d^{6} e^{6} + 56 \, a b^{4} c^{4} d^{6} e^{6} - 196 \, a^{2} b^{2} c^{5} d^{6} e^{6} - 56 \, a^{3} c^{6} d^{6} e^{6} - 8 \, b^{7} c^{2} d^{5} e^{7} - 56 \, a b^{5} c^{3} d^{5} e^{7} + 112 \, a^{2} b^{3} c^{4} d^{5} e^{7} + 168 \, a^{3} b c^{5} d^{5} e^{7} + b^{8} c d^{4} e^{8} + 24 \, a b^{6} c^{2} d^{4} e^{8} - 4 \, a^{2} b^{4} c^{3} d^{4} e^{8} - 176 \, a^{3} b^{2} c^{4} d^{4} e^{8} - 34 \, a^{4} c^{5} d^{4} e^{8} - 4 \, a b^{7} c d^{3} e^{9} - 20 \, a^{2} b^{5} c^{2} d^{3} e^{9} + 72 \, a^{3} b^{3} c^{3} d^{3} e^{9} + 68 \, a^{4} b c^{4} d^{3} e^{9} + 6 \, a^{2} b^{6} c d^{2} e^{10} - 4 \, a^{3} b^{4} c^{2} d^{2} e^{10} - 46 \, a^{4} b^{2} c^{3} d^{2} e^{10} - 4 \, a^{5} c^{4} d^{2} e^{10} - 4 \, a^{3} b^{5} c d e^{11} + 12 \, a^{4} b^{3} c^{2} d e^{11} + 4 \, a^{5} b c^{3} d e^{11} + a^{4} b^{4} c e^{12} - 4 \, a^{5} b^{2} c^{2} e^{12} + 2 \, a^{6} c^{3} e^{12}\right)} x}{b^{2} c^{8} d^{16} - 4 \, a c^{9} d^{16} - 8 \, b^{3} c^{7} d^{15} e + 32 \, a b c^{8} d^{15} e + 28 \, b^{4} c^{6} d^{14} e^{2} - 104 \, a b^{2} c^{7} d^{14} e^{2} - 32 \, a^{2} c^{8} d^{14} e^{2} - 56 \, b^{5} c^{5} d^{13} e^{3} + 168 \, a b^{3} c^{6} d^{13} e^{3} + 224 \, a^{2} b c^{7} d^{13} e^{3} + 70 \, b^{6} c^{4} d^{12} e^{4} - 112 \, a b^{4} c^{5} d^{12} e^{4} - 644 \, a^{2} b^{2} c^{6} d^{12} e^{4} - 112 \, a^{3} c^{7} d^{12} e^{4} - 56 \, b^{7} c^{3} d^{11} e^{5} - 56 \, a b^{5} c^{4} d^{11} e^{5} + 952 \, a^{2} b^{3} c^{5} d^{11} e^{5} + 672 \, a^{3} b c^{6} d^{11} e^{5} + 28 \, b^{8} c^{2} d^{10} e^{6} + 168 \, a b^{6} c^{3} d^{10} e^{6} - 700 \, a^{2} b^{4} c^{4} d^{10} e^{6} - 1624 \, a^{3} b^{2} c^{5} d^{10} e^{6} - 224 \, a^{4} c^{6} d^{10} e^{6} - 8 \, b^{9} c d^{9} e^{7} - 136 \, a b^{7} c^{2} d^{9} e^{7} + 112 \, a^{2} b^{5} c^{3} d^{9} e^{7} + 1960 \, a^{3} b^{3} c^{4} d^{9} e^{7} + 1120 \, a^{4} b c^{5} d^{9} e^{7} + b^{10} d^{8} e^{8} + 52 \, a b^{8} c d^{8} e^{8} + 196 \, a^{2} b^{6} c^{2} d^{8} e^{8} - 1120 \, a^{3} b^{4} c^{3} d^{8} e^{8} - 2170 \, a^{4} b^{2} c^{4} d^{8} e^{8} - 280 \, a^{5} c^{5} d^{8} e^{8} - 8 \, a b^{9} d^{7} e^{9} - 136 \, a^{2} b^{7} c d^{7} e^{9} + 112 \, a^{3} b^{5} c^{2} d^{7} e^{9} + 1960 \, a^{4} b^{3} c^{3} d^{7} e^{9} + 1120 \, a^{5} b c^{4} d^{7} e^{9} + 28 \, a^{2} b^{8} d^{6} e^{10} + 168 \, a^{3} b^{6} c d^{6} e^{10} - 700 \, a^{4} b^{4} c^{2} d^{6} e^{10} - 1624 \, a^{5} b^{2} c^{3} d^{6} e^{10} - 224 \, a^{6} c^{4} d^{6} e^{10} - 56 \, a^{3} b^{7} d^{5} e^{11} - 56 \, a^{4} b^{5} c d^{5} e^{11} + 952 \, a^{5} b^{3} c^{2} d^{5} e^{11} + 672 \, a^{6} b c^{3} d^{5} e^{11} + 70 \, a^{4} b^{6} d^{4} e^{12} - 112 \, a^{5} b^{4} c d^{4} e^{12} - 644 \, a^{6} b^{2} c^{2} d^{4} e^{12} - 112 \, a^{7} c^{3} d^{4} e^{12} - 56 \, a^{5} b^{5} d^{3} e^{13} + 168 \, a^{6} b^{3} c d^{3} e^{13} + 224 \, a^{7} b c^{2} d^{3} e^{13} + 28 \, a^{6} b^{4} d^{2} e^{14} - 104 \, a^{7} b^{2} c d^{2} e^{14} - 32 \, a^{8} c^{2} d^{2} e^{14} - 8 \, a^{7} b^{3} d e^{15} + 32 \, a^{8} b c d e^{15} + a^{8} b^{2} e^{16} - 4 \, a^{9} c e^{16}} + \frac{b c^{8} d^{12} - 8 \, b^{2} c^{7} d^{11} e + 8 \, a c^{8} d^{11} e + 28 \, b^{3} c^{6} d^{10} e^{2} - 46 \, a b c^{7} d^{10} e^{2} - 56 \, b^{4} c^{5} d^{9} e^{3} + 108 \, a b^{2} c^{6} d^{9} e^{3} + 24 \, a^{2} c^{7} d^{9} e^{3} + 70 \, b^{5} c^{4} d^{8} e^{4} - 125 \, a b^{3} c^{5} d^{8} e^{4} - 125 \, a^{2} b c^{6} d^{8} e^{4} - 56 \, b^{6} c^{3} d^{7} e^{5} + 56 \, a b^{4} c^{4} d^{7} e^{5} + 272 \, a^{2} b^{2} c^{5} d^{7} e^{5} + 16 \, a^{3} c^{6} d^{7} e^{5} + 28 \, b^{7} c^{2} d^{6} e^{6} + 28 \, a b^{5} c^{3} d^{6} e^{6} - 308 \, a^{2} b^{3} c^{4} d^{6} e^{6} - 84 \, a^{3} b c^{5} d^{6} e^{6} - 8 \, b^{8} c d^{5} e^{7} - 48 \, a b^{6} c^{2} d^{5} e^{7} + 176 \, a^{2} b^{4} c^{3} d^{5} e^{7} + 184 \, a^{3} b^{2} c^{4} d^{5} e^{7} - 16 \, a^{4} c^{5} d^{5} e^{7} + b^{9} d^{4} e^{8} + 23 \, a b^{7} c d^{4} e^{8} - 29 \, a^{2} b^{5} c^{2} d^{4} e^{8} - 198 \, a^{3} b^{3} c^{3} d^{4} e^{8} + 23 \, a^{4} b c^{4} d^{4} e^{8} - 4 \, a b^{8} d^{3} e^{9} - 16 \, a^{2} b^{6} c d^{3} e^{9} + 96 \, a^{3} b^{4} c^{2} d^{3} e^{9} + 24 \, a^{4} b^{2} c^{3} d^{3} e^{9} - 24 \, a^{5} c^{4} d^{3} e^{9} + 6 \, a^{2} b^{7} d^{2} e^{10} - 10 \, a^{3} b^{5} c d^{2} e^{10} - 48 \, a^{4} b^{3} c^{2} d^{2} e^{10} + 34 \, a^{5} b c^{3} d^{2} e^{10} - 4 \, a^{3} b^{6} d e^{11} + 16 \, a^{4} b^{4} c d e^{11} - 4 \, a^{5} b^{2} c^{2} d e^{11} - 8 \, a^{6} c^{3} d e^{11} + a^{4} b^{5} e^{12} - 5 \, a^{5} b^{3} c e^{12} + 5 \, a^{6} b c^{2} e^{12}}{b^{2} c^{8} d^{16} - 4 \, a c^{9} d^{16} - 8 \, b^{3} c^{7} d^{15} e + 32 \, a b c^{8} d^{15} e + 28 \, b^{4} c^{6} d^{14} e^{2} - 104 \, a b^{2} c^{7} d^{14} e^{2} - 32 \, a^{2} c^{8} d^{14} e^{2} - 56 \, b^{5} c^{5} d^{13} e^{3} + 168 \, a b^{3} c^{6} d^{13} e^{3} + 224 \, a^{2} b c^{7} d^{13} e^{3} + 70 \, b^{6} c^{4} d^{12} e^{4} - 112 \, a b^{4} c^{5} d^{12} e^{4} - 644 \, a^{2} b^{2} c^{6} d^{12} e^{4} - 112 \, a^{3} c^{7} d^{12} e^{4} - 56 \, b^{7} c^{3} d^{11} e^{5} - 56 \, a b^{5} c^{4} d^{11} e^{5} + 952 \, a^{2} b^{3} c^{5} d^{11} e^{5} + 672 \, a^{3} b c^{6} d^{11} e^{5} + 28 \, b^{8} c^{2} d^{10} e^{6} + 168 \, a b^{6} c^{3} d^{10} e^{6} - 700 \, a^{2} b^{4} c^{4} d^{10} e^{6} - 1624 \, a^{3} b^{2} c^{5} d^{10} e^{6} - 224 \, a^{4} c^{6} d^{10} e^{6} - 8 \, b^{9} c d^{9} e^{7} - 136 \, a b^{7} c^{2} d^{9} e^{7} + 112 \, a^{2} b^{5} c^{3} d^{9} e^{7} + 1960 \, a^{3} b^{3} c^{4} d^{9} e^{7} + 1120 \, a^{4} b c^{5} d^{9} e^{7} + b^{10} d^{8} e^{8} + 52 \, a b^{8} c d^{8} e^{8} + 196 \, a^{2} b^{6} c^{2} d^{8} e^{8} - 1120 \, a^{3} b^{4} c^{3} d^{8} e^{8} - 2170 \, a^{4} b^{2} c^{4} d^{8} e^{8} - 280 \, a^{5} c^{5} d^{8} e^{8} - 8 \, a b^{9} d^{7} e^{9} - 136 \, a^{2} b^{7} c d^{7} e^{9} + 112 \, a^{3} b^{5} c^{2} d^{7} e^{9} + 1960 \, a^{4} b^{3} c^{3} d^{7} e^{9} + 1120 \, a^{5} b c^{4} d^{7} e^{9} + 28 \, a^{2} b^{8} d^{6} e^{10} + 168 \, a^{3} b^{6} c d^{6} e^{10} - 700 \, a^{4} b^{4} c^{2} d^{6} e^{10} - 1624 \, a^{5} b^{2} c^{3} d^{6} e^{10} - 224 \, a^{6} c^{4} d^{6} e^{10} - 56 \, a^{3} b^{7} d^{5} e^{11} - 56 \, a^{4} b^{5} c d^{5} e^{11} + 952 \, a^{5} b^{3} c^{2} d^{5} e^{11} + 672 \, a^{6} b c^{3} d^{5} e^{11} + 70 \, a^{4} b^{6} d^{4} e^{12} - 112 \, a^{5} b^{4} c d^{4} e^{12} - 644 \, a^{6} b^{2} c^{2} d^{4} e^{12} - 112 \, a^{7} c^{3} d^{4} e^{12} - 56 \, a^{5} b^{5} d^{3} e^{13} + 168 \, a^{6} b^{3} c d^{3} e^{13} + 224 \, a^{7} b c^{2} d^{3} e^{13} + 28 \, a^{6} b^{4} d^{2} e^{14} - 104 \, a^{7} b^{2} c d^{2} e^{14} - 32 \, a^{8} c^{2} d^{2} e^{14} - 8 \, a^{7} b^{3} d e^{15} + 32 \, a^{8} b c d e^{15} + a^{8} b^{2} e^{16} - 4 \, a^{9} c e^{16}}\right)}}{\sqrt{c x^{2} + b x + a}} + \frac{5 \, {\left(32 \, c^{3} d^{3} e^{2} - 48 \, b c^{2} d^{2} e^{3} + 30 \, b^{2} c d e^{4} - 24 \, a c^{2} d e^{4} - 7 \, b^{3} e^{5} + 12 \, a b c e^{5}\right)} \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} + b d e - a e^{2}}}\right)}{8 \, {\left(c^{4} d^{8} - 4 \, b c^{3} d^{7} e + 6 \, b^{2} c^{2} d^{6} e^{2} + 4 \, a c^{3} d^{6} e^{2} - 4 \, b^{3} c d^{5} e^{3} - 12 \, a b c^{2} d^{5} e^{3} + b^{4} d^{4} e^{4} + 12 \, a b^{2} c d^{4} e^{4} + 6 \, a^{2} c^{2} d^{4} e^{4} - 4 \, a b^{3} d^{3} e^{5} - 12 \, a^{2} b c d^{3} e^{5} + 6 \, a^{2} b^{2} d^{2} e^{6} + 4 \, a^{3} c d^{2} e^{6} - 4 \, a^{3} b d e^{7} + a^{4} e^{8}\right)} \sqrt{-c d^{2} + b d e - a e^{2}}} - \frac{1504 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} c^{4} d^{5} e^{2} + 1296 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} c^{\frac{7}{2}} d^{4} e^{3} + 2256 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b c^{\frac{7}{2}} d^{5} e^{2} + 288 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} c^{3} d^{3} e^{4} - 1168 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b c^{3} d^{4} e^{3} + 1128 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{2} c^{3} d^{5} e^{2} - 1872 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} b c^{\frac{5}{2}} d^{3} e^{4} - 2892 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{2} c^{\frac{5}{2}} d^{4} e^{3} - 3216 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a c^{\frac{7}{2}} d^{4} e^{3} + 188 \, b^{3} c^{\frac{5}{2}} d^{5} e^{2} - 432 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} b c^{2} d^{2} e^{5} - 60 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{2} c^{2} d^{3} e^{4} - 2576 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a c^{3} d^{3} e^{4} - 1368 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{3} c^{2} d^{4} e^{3} - 3216 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b c^{3} d^{4} e^{3} + 1098 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} b^{2} c^{\frac{3}{2}} d^{2} e^{5} - 936 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a c^{\frac{5}{2}} d^{2} e^{5} + 1470 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{3} c^{\frac{3}{2}} d^{3} e^{4} + 2568 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a b c^{\frac{5}{2}} d^{3} e^{4} - 188 \, b^{4} c^{\frac{3}{2}} d^{4} e^{3} - 804 \, a b^{2} c^{\frac{5}{2}} d^{4} e^{3} + 258 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} b^{2} c d e^{6} - 168 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a c^{2} d e^{6} + 430 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{3} c d^{2} e^{5} + 1992 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b c^{2} d^{2} e^{5} + 612 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{4} c d^{3} e^{4} + 3516 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{2} c^{2} d^{3} e^{4} + 1968 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} c^{3} d^{3} e^{4} - 237 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} b^{3} \sqrt{c} d e^{6} + 516 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a b c^{\frac{3}{2}} d e^{6} - 264 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} b^{4} \sqrt{c} d^{2} e^{5} - 1008 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a b^{2} c^{\frac{3}{2}} d^{2} e^{5} + 1152 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{2} c^{\frac{5}{2}} d^{2} e^{5} + 57 \, b^{5} \sqrt{c} d^{3} e^{4} + 794 \, a b^{3} c^{\frac{3}{2}} d^{3} e^{4} + 984 \, a^{2} b c^{\frac{5}{2}} d^{3} e^{4} - 57 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} b^{3} e^{7} + 84 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{5} a b c e^{7} - 136 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} b^{4} d e^{6} - 720 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b^{2} c d e^{6} + 480 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{2} c^{2} d e^{6} - 87 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} b^{5} d^{2} e^{5} - 1494 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{3} c d^{2} e^{5} - 1800 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} b c^{2} d^{2} e^{5} - 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a b^{2} \sqrt{c} e^{7} + 48 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{4} a^{2} c^{\frac{3}{2}} e^{7} + 120 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a b^{3} \sqrt{c} d e^{6} - 432 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{2} b c^{\frac{3}{2}} d e^{6} - 258 \, a b^{4} \sqrt{c} d^{2} e^{5} - 906 \, a^{2} b^{2} c^{\frac{3}{2}} d^{2} e^{5} - 376 \, a^{3} c^{\frac{5}{2}} d^{2} e^{5} + 136 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a b^{3} e^{7} - 144 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{3} a^{2} b c e^{7} + 174 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a b^{4} d e^{6} + 918 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} b^{2} c d e^{6} - 312 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{3} c^{2} d e^{6} + 144 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{2} b^{2} \sqrt{c} e^{7} - 192 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} a^{3} c^{\frac{3}{2}} e^{7} + 345 \, a^{2} b^{3} \sqrt{c} d e^{6} + 220 \, a^{3} b c^{\frac{3}{2}} d e^{6} - 87 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{2} b^{3} e^{7} - 36 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} a^{3} b c e^{7} - 144 \, a^{3} b^{2} \sqrt{c} e^{7} + 80 \, a^{4} c^{\frac{3}{2}} e^{7}}{24 \, {\left(c^{4} d^{8} - 4 \, b c^{3} d^{7} e + 6 \, b^{2} c^{2} d^{6} e^{2} + 4 \, a c^{3} d^{6} e^{2} - 4 \, b^{3} c d^{5} e^{3} - 12 \, a b c^{2} d^{5} e^{3} + b^{4} d^{4} e^{4} + 12 \, a b^{2} c d^{4} e^{4} + 6 \, a^{2} c^{2} d^{4} e^{4} - 4 \, a b^{3} d^{3} e^{5} - 12 \, a^{2} b c d^{3} e^{5} + 6 \, a^{2} b^{2} d^{2} e^{6} + 4 \, a^{3} c d^{2} e^{6} - 4 \, a^{3} b d e^{7} + a^{4} e^{8}\right)} {\left({\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)}^{2} e + 2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} d + b d - a e\right)}^{3}}"," ",0,"-2*((2*c^9*d^12 - 12*b*c^8*d^11*e + 34*b^2*c^7*d^10*e^2 - 4*a*c^8*d^10*e^2 - 60*b^3*c^6*d^9*e^3 + 20*a*b*c^7*d^9*e^3 + 71*b^4*c^5*d^8*e^4 - 28*a*b^2*c^6*d^8*e^4 - 34*a^2*c^7*d^8*e^4 - 56*b^5*c^4*d^7*e^5 - 8*a*b^3*c^5*d^7*e^5 + 136*a^2*b*c^6*d^7*e^5 + 28*b^6*c^3*d^6*e^6 + 56*a*b^4*c^4*d^6*e^6 - 196*a^2*b^2*c^5*d^6*e^6 - 56*a^3*c^6*d^6*e^6 - 8*b^7*c^2*d^5*e^7 - 56*a*b^5*c^3*d^5*e^7 + 112*a^2*b^3*c^4*d^5*e^7 + 168*a^3*b*c^5*d^5*e^7 + b^8*c*d^4*e^8 + 24*a*b^6*c^2*d^4*e^8 - 4*a^2*b^4*c^3*d^4*e^8 - 176*a^3*b^2*c^4*d^4*e^8 - 34*a^4*c^5*d^4*e^8 - 4*a*b^7*c*d^3*e^9 - 20*a^2*b^5*c^2*d^3*e^9 + 72*a^3*b^3*c^3*d^3*e^9 + 68*a^4*b*c^4*d^3*e^9 + 6*a^2*b^6*c*d^2*e^10 - 4*a^3*b^4*c^2*d^2*e^10 - 46*a^4*b^2*c^3*d^2*e^10 - 4*a^5*c^4*d^2*e^10 - 4*a^3*b^5*c*d*e^11 + 12*a^4*b^3*c^2*d*e^11 + 4*a^5*b*c^3*d*e^11 + a^4*b^4*c*e^12 - 4*a^5*b^2*c^2*e^12 + 2*a^6*c^3*e^12)*x/(b^2*c^8*d^16 - 4*a*c^9*d^16 - 8*b^3*c^7*d^15*e + 32*a*b*c^8*d^15*e + 28*b^4*c^6*d^14*e^2 - 104*a*b^2*c^7*d^14*e^2 - 32*a^2*c^8*d^14*e^2 - 56*b^5*c^5*d^13*e^3 + 168*a*b^3*c^6*d^13*e^3 + 224*a^2*b*c^7*d^13*e^3 + 70*b^6*c^4*d^12*e^4 - 112*a*b^4*c^5*d^12*e^4 - 644*a^2*b^2*c^6*d^12*e^4 - 112*a^3*c^7*d^12*e^4 - 56*b^7*c^3*d^11*e^5 - 56*a*b^5*c^4*d^11*e^5 + 952*a^2*b^3*c^5*d^11*e^5 + 672*a^3*b*c^6*d^11*e^5 + 28*b^8*c^2*d^10*e^6 + 168*a*b^6*c^3*d^10*e^6 - 700*a^2*b^4*c^4*d^10*e^6 - 1624*a^3*b^2*c^5*d^10*e^6 - 224*a^4*c^6*d^10*e^6 - 8*b^9*c*d^9*e^7 - 136*a*b^7*c^2*d^9*e^7 + 112*a^2*b^5*c^3*d^9*e^7 + 1960*a^3*b^3*c^4*d^9*e^7 + 1120*a^4*b*c^5*d^9*e^7 + b^10*d^8*e^8 + 52*a*b^8*c*d^8*e^8 + 196*a^2*b^6*c^2*d^8*e^8 - 1120*a^3*b^4*c^3*d^8*e^8 - 2170*a^4*b^2*c^4*d^8*e^8 - 280*a^5*c^5*d^8*e^8 - 8*a*b^9*d^7*e^9 - 136*a^2*b^7*c*d^7*e^9 + 112*a^3*b^5*c^2*d^7*e^9 + 1960*a^4*b^3*c^3*d^7*e^9 + 1120*a^5*b*c^4*d^7*e^9 + 28*a^2*b^8*d^6*e^10 + 168*a^3*b^6*c*d^6*e^10 - 700*a^4*b^4*c^2*d^6*e^10 - 1624*a^5*b^2*c^3*d^6*e^10 - 224*a^6*c^4*d^6*e^10 - 56*a^3*b^7*d^5*e^11 - 56*a^4*b^5*c*d^5*e^11 + 952*a^5*b^3*c^2*d^5*e^11 + 672*a^6*b*c^3*d^5*e^11 + 70*a^4*b^6*d^4*e^12 - 112*a^5*b^4*c*d^4*e^12 - 644*a^6*b^2*c^2*d^4*e^12 - 112*a^7*c^3*d^4*e^12 - 56*a^5*b^5*d^3*e^13 + 168*a^6*b^3*c*d^3*e^13 + 224*a^7*b*c^2*d^3*e^13 + 28*a^6*b^4*d^2*e^14 - 104*a^7*b^2*c*d^2*e^14 - 32*a^8*c^2*d^2*e^14 - 8*a^7*b^3*d*e^15 + 32*a^8*b*c*d*e^15 + a^8*b^2*e^16 - 4*a^9*c*e^16) + (b*c^8*d^12 - 8*b^2*c^7*d^11*e + 8*a*c^8*d^11*e + 28*b^3*c^6*d^10*e^2 - 46*a*b*c^7*d^10*e^2 - 56*b^4*c^5*d^9*e^3 + 108*a*b^2*c^6*d^9*e^3 + 24*a^2*c^7*d^9*e^3 + 70*b^5*c^4*d^8*e^4 - 125*a*b^3*c^5*d^8*e^4 - 125*a^2*b*c^6*d^8*e^4 - 56*b^6*c^3*d^7*e^5 + 56*a*b^4*c^4*d^7*e^5 + 272*a^2*b^2*c^5*d^7*e^5 + 16*a^3*c^6*d^7*e^5 + 28*b^7*c^2*d^6*e^6 + 28*a*b^5*c^3*d^6*e^6 - 308*a^2*b^3*c^4*d^6*e^6 - 84*a^3*b*c^5*d^6*e^6 - 8*b^8*c*d^5*e^7 - 48*a*b^6*c^2*d^5*e^7 + 176*a^2*b^4*c^3*d^5*e^7 + 184*a^3*b^2*c^4*d^5*e^7 - 16*a^4*c^5*d^5*e^7 + b^9*d^4*e^8 + 23*a*b^7*c*d^4*e^8 - 29*a^2*b^5*c^2*d^4*e^8 - 198*a^3*b^3*c^3*d^4*e^8 + 23*a^4*b*c^4*d^4*e^8 - 4*a*b^8*d^3*e^9 - 16*a^2*b^6*c*d^3*e^9 + 96*a^3*b^4*c^2*d^3*e^9 + 24*a^4*b^2*c^3*d^3*e^9 - 24*a^5*c^4*d^3*e^9 + 6*a^2*b^7*d^2*e^10 - 10*a^3*b^5*c*d^2*e^10 - 48*a^4*b^3*c^2*d^2*e^10 + 34*a^5*b*c^3*d^2*e^10 - 4*a^3*b^6*d*e^11 + 16*a^4*b^4*c*d*e^11 - 4*a^5*b^2*c^2*d*e^11 - 8*a^6*c^3*d*e^11 + a^4*b^5*e^12 - 5*a^5*b^3*c*e^12 + 5*a^6*b*c^2*e^12)/(b^2*c^8*d^16 - 4*a*c^9*d^16 - 8*b^3*c^7*d^15*e + 32*a*b*c^8*d^15*e + 28*b^4*c^6*d^14*e^2 - 104*a*b^2*c^7*d^14*e^2 - 32*a^2*c^8*d^14*e^2 - 56*b^5*c^5*d^13*e^3 + 168*a*b^3*c^6*d^13*e^3 + 224*a^2*b*c^7*d^13*e^3 + 70*b^6*c^4*d^12*e^4 - 112*a*b^4*c^5*d^12*e^4 - 644*a^2*b^2*c^6*d^12*e^4 - 112*a^3*c^7*d^12*e^4 - 56*b^7*c^3*d^11*e^5 - 56*a*b^5*c^4*d^11*e^5 + 952*a^2*b^3*c^5*d^11*e^5 + 672*a^3*b*c^6*d^11*e^5 + 28*b^8*c^2*d^10*e^6 + 168*a*b^6*c^3*d^10*e^6 - 700*a^2*b^4*c^4*d^10*e^6 - 1624*a^3*b^2*c^5*d^10*e^6 - 224*a^4*c^6*d^10*e^6 - 8*b^9*c*d^9*e^7 - 136*a*b^7*c^2*d^9*e^7 + 112*a^2*b^5*c^3*d^9*e^7 + 1960*a^3*b^3*c^4*d^9*e^7 + 1120*a^4*b*c^5*d^9*e^7 + b^10*d^8*e^8 + 52*a*b^8*c*d^8*e^8 + 196*a^2*b^6*c^2*d^8*e^8 - 1120*a^3*b^4*c^3*d^8*e^8 - 2170*a^4*b^2*c^4*d^8*e^8 - 280*a^5*c^5*d^8*e^8 - 8*a*b^9*d^7*e^9 - 136*a^2*b^7*c*d^7*e^9 + 112*a^3*b^5*c^2*d^7*e^9 + 1960*a^4*b^3*c^3*d^7*e^9 + 1120*a^5*b*c^4*d^7*e^9 + 28*a^2*b^8*d^6*e^10 + 168*a^3*b^6*c*d^6*e^10 - 700*a^4*b^4*c^2*d^6*e^10 - 1624*a^5*b^2*c^3*d^6*e^10 - 224*a^6*c^4*d^6*e^10 - 56*a^3*b^7*d^5*e^11 - 56*a^4*b^5*c*d^5*e^11 + 952*a^5*b^3*c^2*d^5*e^11 + 672*a^6*b*c^3*d^5*e^11 + 70*a^4*b^6*d^4*e^12 - 112*a^5*b^4*c*d^4*e^12 - 644*a^6*b^2*c^2*d^4*e^12 - 112*a^7*c^3*d^4*e^12 - 56*a^5*b^5*d^3*e^13 + 168*a^6*b^3*c*d^3*e^13 + 224*a^7*b*c^2*d^3*e^13 + 28*a^6*b^4*d^2*e^14 - 104*a^7*b^2*c*d^2*e^14 - 32*a^8*c^2*d^2*e^14 - 8*a^7*b^3*d*e^15 + 32*a^8*b*c*d*e^15 + a^8*b^2*e^16 - 4*a^9*c*e^16))/sqrt(c*x^2 + b*x + a) + 5/8*(32*c^3*d^3*e^2 - 48*b*c^2*d^2*e^3 + 30*b^2*c*d*e^4 - 24*a*c^2*d*e^4 - 7*b^3*e^5 + 12*a*b*c*e^5)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + b*x + a))*e + sqrt(c)*d)/sqrt(-c*d^2 + b*d*e - a*e^2))/((c^4*d^8 - 4*b*c^3*d^7*e + 6*b^2*c^2*d^6*e^2 + 4*a*c^3*d^6*e^2 - 4*b^3*c*d^5*e^3 - 12*a*b*c^2*d^5*e^3 + b^4*d^4*e^4 + 12*a*b^2*c*d^4*e^4 + 6*a^2*c^2*d^4*e^4 - 4*a*b^3*d^3*e^5 - 12*a^2*b*c*d^3*e^5 + 6*a^2*b^2*d^2*e^6 + 4*a^3*c*d^2*e^6 - 4*a^3*b*d*e^7 + a^4*e^8)*sqrt(-c*d^2 + b*d*e - a*e^2)) - 1/24*(1504*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*c^4*d^5*e^2 + 1296*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*c^(7/2)*d^4*e^3 + 2256*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b*c^(7/2)*d^5*e^2 + 288*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*c^3*d^3*e^4 - 1168*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b*c^3*d^4*e^3 + 1128*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^2*c^3*d^5*e^2 - 1872*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b*c^(5/2)*d^3*e^4 - 2892*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^2*c^(5/2)*d^4*e^3 - 3216*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*c^(7/2)*d^4*e^3 + 188*b^3*c^(5/2)*d^5*e^2 - 432*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b*c^2*d^2*e^5 - 60*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^2*c^2*d^3*e^4 - 2576*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*c^3*d^3*e^4 - 1368*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^3*c^2*d^4*e^3 - 3216*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b*c^3*d^4*e^3 + 1098*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^2*c^(3/2)*d^2*e^5 - 936*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*c^(5/2)*d^2*e^5 + 1470*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^3*c^(3/2)*d^3*e^4 + 2568*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b*c^(5/2)*d^3*e^4 - 188*b^4*c^(3/2)*d^4*e^3 - 804*a*b^2*c^(5/2)*d^4*e^3 + 258*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b^2*c*d*e^6 - 168*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*c^2*d*e^6 + 430*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^3*c*d^2*e^5 + 1992*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b*c^2*d^2*e^5 + 612*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^4*c*d^3*e^4 + 3516*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^2*c^2*d^3*e^4 + 1968*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*c^3*d^3*e^4 - 237*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^3*sqrt(c)*d*e^6 + 516*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*b*c^(3/2)*d*e^6 - 264*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^4*sqrt(c)*d^2*e^5 - 1008*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^2*c^(3/2)*d^2*e^5 + 1152*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*c^(5/2)*d^2*e^5 + 57*b^5*sqrt(c)*d^3*e^4 + 794*a*b^3*c^(3/2)*d^3*e^4 + 984*a^2*b*c^(5/2)*d^3*e^4 - 57*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b^3*e^7 + 84*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*b*c*e^7 - 136*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^4*d*e^6 - 720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^2*c*d*e^6 + 480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*c^2*d*e^6 - 87*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^5*d^2*e^5 - 1494*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^3*c*d^2*e^5 - 1800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b*c^2*d^2*e^5 - 48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*b^2*sqrt(c)*e^7 + 48*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^2*c^(3/2)*e^7 + 120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^3*sqrt(c)*d*e^6 - 432*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*b*c^(3/2)*d*e^6 - 258*a*b^4*sqrt(c)*d^2*e^5 - 906*a^2*b^2*c^(3/2)*d^2*e^5 - 376*a^3*c^(5/2)*d^2*e^5 + 136*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^3*e^7 - 144*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*b*c*e^7 + 174*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^4*d*e^6 + 918*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b^2*c*d*e^6 - 312*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*c^2*d*e^6 + 144*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*b^2*sqrt(c)*e^7 - 192*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^3*c^(3/2)*e^7 + 345*a^2*b^3*sqrt(c)*d*e^6 + 220*a^3*b*c^(3/2)*d*e^6 - 87*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b^3*e^7 - 36*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*b*c*e^7 - 144*a^3*b^2*sqrt(c)*e^7 + 80*a^4*c^(3/2)*e^7)/((c^4*d^8 - 4*b*c^3*d^7*e + 6*b^2*c^2*d^6*e^2 + 4*a*c^3*d^6*e^2 - 4*b^3*c*d^5*e^3 - 12*a*b*c^2*d^5*e^3 + b^4*d^4*e^4 + 12*a*b^2*c*d^4*e^4 + 6*a^2*c^2*d^4*e^4 - 4*a*b^3*d^3*e^5 - 12*a^2*b*c*d^3*e^5 + 6*a^2*b^2*d^2*e^6 + 4*a^3*c*d^2*e^6 - 4*a^3*b*d*e^7 + a^4*e^8)*((sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*e + 2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c)*d + b*d - a*e)^3)","B",0
2391,1,788,0,0.362187," ","integrate((e*x+d)^5/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\frac{{\left({\left({\left(\frac{3 \, {\left(b^{4} c^{2} e^{5} - 8 \, a b^{2} c^{3} e^{5} + 16 \, a^{2} c^{4} e^{5}\right)} x}{b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}} + \frac{4 \, {\left(8 \, c^{6} d^{5} - 20 \, b c^{5} d^{4} e + 10 \, b^{2} c^{4} d^{3} e^{2} + 40 \, a c^{5} d^{3} e^{2} + 5 \, b^{3} c^{3} d^{2} e^{3} - 60 \, a b c^{4} d^{2} e^{3} - 10 \, b^{4} c^{2} d e^{4} + 70 \, a b^{2} c^{3} d e^{4} - 80 \, a^{2} c^{4} d e^{4} + 5 \, b^{5} c e^{5} - 37 \, a b^{3} c^{2} e^{5} + 64 \, a^{2} b c^{3} e^{5}\right)}}{b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}\right)} x + \frac{3 \, {\left(16 \, b c^{5} d^{5} - 40 \, b^{2} c^{4} d^{4} e + 20 \, b^{3} c^{3} d^{3} e^{2} + 80 \, a b c^{4} d^{3} e^{2} - 40 \, a b^{2} c^{3} d^{2} e^{3} - 160 \, a^{2} c^{4} d^{2} e^{3} - 10 \, b^{5} c d e^{4} + 60 \, a b^{3} c^{2} d e^{4} + 5 \, b^{6} e^{5} - 30 \, a b^{4} c e^{5} + 16 \, a^{2} b^{2} c^{2} e^{5} + 64 \, a^{3} c^{3} e^{5}\right)}}{b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}\right)} x + \frac{6 \, {\left(2 \, b^{2} c^{4} d^{5} + 8 \, a c^{5} d^{5} - 5 \, b^{3} c^{3} d^{4} e - 20 \, a b c^{4} d^{4} e + 40 \, a b^{2} c^{3} d^{3} e^{2} - 80 \, a^{2} b c^{3} d^{2} e^{3} - 10 \, a b^{4} c d e^{4} + 70 \, a^{2} b^{2} c^{2} d e^{4} - 40 \, a^{3} c^{3} d e^{4} + 5 \, a b^{5} e^{5} - 35 \, a^{2} b^{3} c e^{5} + 52 \, a^{3} b c^{2} e^{5}\right)}}{b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}\right)} x - \frac{2 \, b^{3} c^{3} d^{5} - 24 \, a b c^{4} d^{5} + 20 \, a b^{2} c^{3} d^{4} e + 80 \, a^{2} c^{4} d^{4} e - 160 \, a^{2} b c^{3} d^{3} e^{2} + 320 \, a^{3} c^{3} d^{2} e^{3} + 30 \, a^{2} b^{3} c d e^{4} - 200 \, a^{3} b c^{2} d e^{4} - 15 \, a^{2} b^{4} e^{5} + 100 \, a^{3} b^{2} c e^{5} - 128 \, a^{4} c^{2} e^{5}}{b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}}}{3 \, {\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}} - \frac{5 \, {\left(2 \, c d e^{4} - b e^{5}\right)} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{2 \, c^{\frac{7}{2}}}"," ",0,"1/3*((((3*(b^4*c^2*e^5 - 8*a*b^2*c^3*e^5 + 16*a^2*c^4*e^5)*x/(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5) + 4*(8*c^6*d^5 - 20*b*c^5*d^4*e + 10*b^2*c^4*d^3*e^2 + 40*a*c^5*d^3*e^2 + 5*b^3*c^3*d^2*e^3 - 60*a*b*c^4*d^2*e^3 - 10*b^4*c^2*d*e^4 + 70*a*b^2*c^3*d*e^4 - 80*a^2*c^4*d*e^4 + 5*b^5*c*e^5 - 37*a*b^3*c^2*e^5 + 64*a^2*b*c^3*e^5)/(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5))*x + 3*(16*b*c^5*d^5 - 40*b^2*c^4*d^4*e + 20*b^3*c^3*d^3*e^2 + 80*a*b*c^4*d^3*e^2 - 40*a*b^2*c^3*d^2*e^3 - 160*a^2*c^4*d^2*e^3 - 10*b^5*c*d*e^4 + 60*a*b^3*c^2*d*e^4 + 5*b^6*e^5 - 30*a*b^4*c*e^5 + 16*a^2*b^2*c^2*e^5 + 64*a^3*c^3*e^5)/(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5))*x + 6*(2*b^2*c^4*d^5 + 8*a*c^5*d^5 - 5*b^3*c^3*d^4*e - 20*a*b*c^4*d^4*e + 40*a*b^2*c^3*d^3*e^2 - 80*a^2*b*c^3*d^2*e^3 - 10*a*b^4*c*d*e^4 + 70*a^2*b^2*c^2*d*e^4 - 40*a^3*c^3*d*e^4 + 5*a*b^5*e^5 - 35*a^2*b^3*c*e^5 + 52*a^3*b*c^2*e^5)/(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5))*x - (2*b^3*c^3*d^5 - 24*a*b*c^4*d^5 + 20*a*b^2*c^3*d^4*e + 80*a^2*c^4*d^4*e - 160*a^2*b*c^3*d^3*e^2 + 320*a^3*c^3*d^2*e^3 + 30*a^2*b^3*c*d*e^4 - 200*a^3*b*c^2*d*e^4 - 15*a^2*b^4*e^5 + 100*a^3*b^2*c*e^5 - 128*a^4*c^2*e^5)/(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5))/(c*x^2 + b*x + a)^(3/2) - 5/2*(2*c*d*e^4 - b*e^5)*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(7/2)","B",0
2392,1,549,0,0.359462," ","integrate((e*x+d)^4/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\frac{2 \, {\left({\left({\left(\frac{4 \, {\left(4 \, c^{5} d^{4} - 8 \, b c^{4} d^{3} e + 3 \, b^{2} c^{3} d^{2} e^{2} + 12 \, a c^{4} d^{2} e^{2} + b^{3} c^{2} d e^{3} - 12 \, a b c^{3} d e^{3} - b^{4} c e^{4} + 7 \, a b^{2} c^{2} e^{4} - 8 \, a^{2} c^{3} e^{4}\right)} x}{b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}} + \frac{3 \, {\left(8 \, b c^{4} d^{4} - 16 \, b^{2} c^{3} d^{3} e + 6 \, b^{3} c^{2} d^{2} e^{2} + 24 \, a b c^{3} d^{2} e^{2} - 8 \, a b^{2} c^{2} d e^{3} - 32 \, a^{2} c^{3} d e^{3} - b^{5} e^{4} + 6 \, a b^{3} c e^{4}\right)}}{b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}}\right)} x + \frac{6 \, {\left(b^{2} c^{3} d^{4} + 4 \, a c^{4} d^{4} - 2 \, b^{3} c^{2} d^{3} e - 8 \, a b c^{3} d^{3} e + 12 \, a b^{2} c^{2} d^{2} e^{2} - 16 \, a^{2} b c^{2} d e^{3} - a b^{4} e^{4} + 7 \, a^{2} b^{2} c e^{4} - 4 \, a^{3} c^{2} e^{4}\right)}}{b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}}\right)} x - \frac{b^{3} c^{2} d^{4} - 12 \, a b c^{3} d^{4} + 8 \, a b^{2} c^{2} d^{3} e + 32 \, a^{2} c^{3} d^{3} e - 48 \, a^{2} b c^{2} d^{2} e^{2} + 64 \, a^{3} c^{2} d e^{3} + 3 \, a^{2} b^{3} e^{4} - 20 \, a^{3} b c e^{4}}{b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}}\right)}}{3 \, {\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}} - \frac{e^{4} \log\left({\left| -2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} \sqrt{c} - b \right|}\right)}{c^{\frac{5}{2}}}"," ",0,"2/3*(((4*(4*c^5*d^4 - 8*b*c^4*d^3*e + 3*b^2*c^3*d^2*e^2 + 12*a*c^4*d^2*e^2 + b^3*c^2*d*e^3 - 12*a*b*c^3*d*e^3 - b^4*c*e^4 + 7*a*b^2*c^2*e^4 - 8*a^2*c^3*e^4)*x/(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4) + 3*(8*b*c^4*d^4 - 16*b^2*c^3*d^3*e + 6*b^3*c^2*d^2*e^2 + 24*a*b*c^3*d^2*e^2 - 8*a*b^2*c^2*d*e^3 - 32*a^2*c^3*d*e^3 - b^5*e^4 + 6*a*b^3*c*e^4)/(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4))*x + 6*(b^2*c^3*d^4 + 4*a*c^4*d^4 - 2*b^3*c^2*d^3*e - 8*a*b*c^3*d^3*e + 12*a*b^2*c^2*d^2*e^2 - 16*a^2*b*c^2*d*e^3 - a*b^4*e^4 + 7*a^2*b^2*c*e^4 - 4*a^3*c^2*e^4)/(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4))*x - (b^3*c^2*d^4 - 12*a*b*c^3*d^4 + 8*a*b^2*c^2*d^3*e + 32*a^2*c^3*d^3*e - 48*a^2*b*c^2*d^2*e^2 + 64*a^3*c^2*d*e^3 + 3*a^2*b^3*e^4 - 20*a^3*b*c*e^4)/(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4))/(c*x^2 + b*x + a)^(3/2) - e^4*log(abs(-2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c) - b))/c^(5/2)","A",0
2393,1,327,0,0.306545," ","integrate((e*x+d)^3/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\frac{2 \, {\left({\left({\left(\frac{{\left(16 \, c^{3} d^{3} - 24 \, b c^{2} d^{2} e + 6 \, b^{2} c d e^{2} + 24 \, a c^{2} d e^{2} + b^{3} e^{3} - 12 \, a b c e^{3}\right)} x}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}} + \frac{3 \, {\left(8 \, b c^{2} d^{3} - 12 \, b^{2} c d^{2} e + 3 \, b^{3} d e^{2} + 12 \, a b c d e^{2} - 2 \, a b^{2} e^{3} - 8 \, a^{2} c e^{3}\right)}}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}}\right)} x + \frac{3 \, {\left(2 \, b^{2} c d^{3} + 8 \, a c^{2} d^{3} - 3 \, b^{3} d^{2} e - 12 \, a b c d^{2} e + 12 \, a b^{2} d e^{2} - 8 \, a^{2} b e^{3}\right)}}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}}\right)} x - \frac{b^{3} d^{3} - 12 \, a b c d^{3} + 6 \, a b^{2} d^{2} e + 24 \, a^{2} c d^{2} e - 24 \, a^{2} b d e^{2} + 16 \, a^{3} e^{3}}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}}\right)}}{3 \, {\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}"," ",0,"2/3*((((16*c^3*d^3 - 24*b*c^2*d^2*e + 6*b^2*c*d*e^2 + 24*a*c^2*d*e^2 + b^3*e^3 - 12*a*b*c*e^3)*x/(b^4 - 8*a*b^2*c + 16*a^2*c^2) + 3*(8*b*c^2*d^3 - 12*b^2*c*d^2*e + 3*b^3*d*e^2 + 12*a*b*c*d*e^2 - 2*a*b^2*e^3 - 8*a^2*c*e^3)/(b^4 - 8*a*b^2*c + 16*a^2*c^2))*x + 3*(2*b^2*c*d^3 + 8*a*c^2*d^3 - 3*b^3*d^2*e - 12*a*b*c*d^2*e + 12*a*b^2*d*e^2 - 8*a^2*b*e^3)/(b^4 - 8*a*b^2*c + 16*a^2*c^2))*x - (b^3*d^3 - 12*a*b*c*d^3 + 6*a*b^2*d^2*e + 24*a^2*c*d^2*e - 24*a^2*b*d*e^2 + 16*a^3*e^3)/(b^4 - 8*a*b^2*c + 16*a^2*c^2))/(c*x^2 + b*x + a)^(3/2)","B",0
2394,1,263,0,0.318440," ","integrate((e*x+d)^2/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\frac{2 \, {\left({\left({\left(\frac{2 \, {\left(8 \, c^{3} d^{2} - 8 \, b c^{2} d e + b^{2} c e^{2} + 4 \, a c^{2} e^{2}\right)} x}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}} + \frac{3 \, {\left(8 \, b c^{2} d^{2} - 8 \, b^{2} c d e + b^{3} e^{2} + 4 \, a b c e^{2}\right)}}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}}\right)} x + \frac{6 \, {\left(b^{2} c d^{2} + 4 \, a c^{2} d^{2} - b^{3} d e - 4 \, a b c d e + 2 \, a b^{2} e^{2}\right)}}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}}\right)} x - \frac{b^{3} d^{2} - 12 \, a b c d^{2} + 4 \, a b^{2} d e + 16 \, a^{2} c d e - 8 \, a^{2} b e^{2}}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}}\right)}}{3 \, {\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}"," ",0,"2/3*(((2*(8*c^3*d^2 - 8*b*c^2*d*e + b^2*c*e^2 + 4*a*c^2*e^2)*x/(b^4 - 8*a*b^2*c + 16*a^2*c^2) + 3*(8*b*c^2*d^2 - 8*b^2*c*d*e + b^3*e^2 + 4*a*b*c*e^2)/(b^4 - 8*a*b^2*c + 16*a^2*c^2))*x + 6*(b^2*c*d^2 + 4*a*c^2*d^2 - b^3*d*e - 4*a*b*c*d*e + 2*a*b^2*e^2)/(b^4 - 8*a*b^2*c + 16*a^2*c^2))*x - (b^3*d^2 - 12*a*b*c*d^2 + 4*a*b^2*d*e + 16*a^2*c*d*e - 8*a^2*b*e^2)/(b^4 - 8*a*b^2*c + 16*a^2*c^2))/(c*x^2 + b*x + a)^(3/2)","B",0
2395,1,203,0,0.308010," ","integrate((e*x+d)/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\frac{2 \, {\left({\left(4 \, {\left(\frac{2 \, {\left(2 \, c^{3} d - b c^{2} e\right)} x}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}} + \frac{3 \, {\left(2 \, b c^{2} d - b^{2} c e\right)}}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}}\right)} x + \frac{3 \, {\left(2 \, b^{2} c d + 8 \, a c^{2} d - b^{3} e - 4 \, a b c e\right)}}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}}\right)} x - \frac{b^{3} d - 12 \, a b c d + 2 \, a b^{2} e + 8 \, a^{2} c e}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}}\right)}}{3 \, {\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}"," ",0,"2/3*((4*(2*(2*c^3*d - b*c^2*e)*x/(b^4 - 8*a*b^2*c + 16*a^2*c^2) + 3*(2*b*c^2*d - b^2*c*e)/(b^4 - 8*a*b^2*c + 16*a^2*c^2))*x + 3*(2*b^2*c*d + 8*a*c^2*d - b^3*e - 4*a*b*c*e)/(b^4 - 8*a*b^2*c + 16*a^2*c^2))*x - (b^3*d - 12*a*b*c*d + 2*a*b^2*e + 8*a^2*c*e)/(b^4 - 8*a*b^2*c + 16*a^2*c^2))/(c*x^2 + b*x + a)^(3/2)","B",0
2396,1,144,0,0.300311," ","integrate(1/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\frac{2 \, {\left(2 \, {\left(4 \, {\left(\frac{2 \, c^{3} x}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}} + \frac{3 \, b c^{2}}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}}\right)} x + \frac{3 \, {\left(b^{2} c + 4 \, a c^{2}\right)}}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}}\right)} x - \frac{b^{3} - 12 \, a b c}{b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}}\right)}}{3 \, {\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}"," ",0,"2/3*(2*(4*(2*c^3*x/(b^4 - 8*a*b^2*c + 16*a^2*c^2) + 3*b*c^2/(b^4 - 8*a*b^2*c + 16*a^2*c^2))*x + 3*(b^2*c + 4*a*c^2)/(b^4 - 8*a*b^2*c + 16*a^2*c^2))*x - (b^3 - 12*a*b*c)/(b^4 - 8*a*b^2*c + 16*a^2*c^2))/(c*x^2 + b*x + a)^(3/2)","B",0
2397,1,7942,0,0.785827," ","integrate(1/(e*x+d)/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\frac{2 \, \arctan\left(-\frac{{\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} e + \sqrt{c} d}{\sqrt{-c d^{2} + b d e - a e^{2}}}\right) e^{4}}{{\left(c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2} + 2 \, a c d^{2} e^{2} - 2 \, a b d e^{3} + a^{2} e^{4}\right)} \sqrt{-c d^{2} + b d e - a e^{2}}} + \frac{2 \, {\left({\left({\left(\frac{{\left(16 \, c^{11} d^{15} - 120 \, b c^{10} d^{14} e + 386 \, b^{2} c^{9} d^{13} e^{2} + 136 \, a c^{10} d^{13} e^{2} - 689 \, b^{3} c^{8} d^{12} e^{3} - 884 \, a b c^{9} d^{12} e^{3} + 732 \, b^{4} c^{7} d^{11} e^{4} + 2412 \, a b^{2} c^{8} d^{11} e^{4} + 480 \, a^{2} c^{9} d^{11} e^{4} - 451 \, b^{5} c^{6} d^{10} e^{5} - 3542 \, a b^{3} c^{7} d^{10} e^{5} - 2640 \, a^{2} b c^{8} d^{10} e^{5} + 130 \, b^{6} c^{5} d^{9} e^{6} + 2950 \, a b^{4} c^{6} d^{9} e^{6} + 5910 \, a^{2} b^{2} c^{7} d^{9} e^{6} + 920 \, a^{3} c^{8} d^{9} e^{6} + 9 \, b^{7} c^{4} d^{8} e^{7} - 1296 \, a b^{5} c^{5} d^{8} e^{7} - 6795 \, a^{2} b^{3} c^{6} d^{8} e^{7} - 4140 \, a^{3} b c^{7} d^{8} e^{7} - 16 \, b^{8} c^{3} d^{7} e^{8} + 184 \, a b^{6} c^{4} d^{7} e^{8} + 4080 \, a^{2} b^{4} c^{5} d^{7} e^{8} + 7240 \, a^{3} b^{2} c^{6} d^{7} e^{8} + 1040 \, a^{4} c^{7} d^{7} e^{8} + 3 \, b^{9} c^{2} d^{6} e^{9} + 58 \, a b^{7} c^{3} d^{6} e^{9} - 1050 \, a^{2} b^{5} c^{4} d^{6} e^{9} - 6020 \, a^{3} b^{3} c^{5} d^{6} e^{9} - 3640 \, a^{4} b c^{6} d^{6} e^{9} - 18 \, a b^{8} c^{2} d^{5} e^{10} - 30 \, a^{2} b^{6} c^{3} d^{5} e^{10} + 2220 \, a^{3} b^{4} c^{4} d^{5} e^{10} + 4590 \, a^{4} b^{2} c^{5} d^{5} e^{10} + 696 \, a^{5} c^{6} d^{5} e^{10} + 45 \, a^{2} b^{7} c^{2} d^{4} e^{11} - 160 \, a^{3} b^{5} c^{3} d^{4} e^{11} - 2375 \, a^{4} b^{3} c^{4} d^{4} e^{11} - 1740 \, a^{5} b c^{5} d^{4} e^{11} - 60 \, a^{3} b^{6} c^{2} d^{3} e^{12} + 340 \, a^{4} b^{4} c^{3} d^{3} e^{12} + 1356 \, a^{5} b^{2} c^{4} d^{3} e^{12} + 256 \, a^{6} c^{5} d^{3} e^{12} + 45 \, a^{4} b^{5} c^{2} d^{2} e^{13} - 294 \, a^{5} b^{3} c^{3} d^{2} e^{13} - 384 \, a^{6} b c^{4} d^{2} e^{13} - 18 \, a^{5} b^{4} c^{2} d e^{14} + 122 \, a^{6} b^{2} c^{3} d e^{14} + 40 \, a^{7} c^{4} d e^{14} + 3 \, a^{6} b^{3} c^{2} e^{15} - 20 \, a^{7} b c^{3} e^{15}\right)} x}{b^{4} c^{8} d^{16} - 8 \, a b^{2} c^{9} d^{16} + 16 \, a^{2} c^{10} d^{16} - 8 \, b^{5} c^{7} d^{15} e + 64 \, a b^{3} c^{8} d^{15} e - 128 \, a^{2} b c^{9} d^{15} e + 28 \, b^{6} c^{6} d^{14} e^{2} - 216 \, a b^{4} c^{7} d^{14} e^{2} + 384 \, a^{2} b^{2} c^{8} d^{14} e^{2} + 128 \, a^{3} c^{9} d^{14} e^{2} - 56 \, b^{7} c^{5} d^{13} e^{3} + 392 \, a b^{5} c^{6} d^{13} e^{3} - 448 \, a^{2} b^{3} c^{7} d^{13} e^{3} - 896 \, a^{3} b c^{8} d^{13} e^{3} + 70 \, b^{8} c^{4} d^{12} e^{4} - 392 \, a b^{6} c^{5} d^{12} e^{4} - 196 \, a^{2} b^{4} c^{6} d^{12} e^{4} + 2464 \, a^{3} b^{2} c^{7} d^{12} e^{4} + 448 \, a^{4} c^{8} d^{12} e^{4} - 56 \, b^{9} c^{3} d^{11} e^{5} + 168 \, a b^{7} c^{4} d^{11} e^{5} + 1176 \, a^{2} b^{5} c^{5} d^{11} e^{5} - 3136 \, a^{3} b^{3} c^{6} d^{11} e^{5} - 2688 \, a^{4} b c^{7} d^{11} e^{5} + 28 \, b^{10} c^{2} d^{10} e^{6} + 56 \, a b^{8} c^{3} d^{10} e^{6} - 1372 \, a^{2} b^{6} c^{4} d^{10} e^{6} + 1176 \, a^{3} b^{4} c^{5} d^{10} e^{6} + 6272 \, a^{4} b^{2} c^{6} d^{10} e^{6} + 896 \, a^{5} c^{7} d^{10} e^{6} - 8 \, b^{11} c d^{9} e^{7} - 104 \, a b^{9} c^{2} d^{9} e^{7} + 656 \, a^{2} b^{7} c^{3} d^{9} e^{7} + 1512 \, a^{3} b^{5} c^{4} d^{9} e^{7} - 6720 \, a^{4} b^{3} c^{5} d^{9} e^{7} - 4480 \, a^{5} b c^{6} d^{9} e^{7} + b^{12} d^{8} e^{8} + 48 \, a b^{10} c d^{8} e^{8} - 12 \, a^{2} b^{8} c^{2} d^{8} e^{8} - 1904 \, a^{3} b^{6} c^{3} d^{8} e^{8} + 2310 \, a^{4} b^{4} c^{4} d^{8} e^{8} + 8400 \, a^{5} b^{2} c^{5} d^{8} e^{8} + 1120 \, a^{6} c^{6} d^{8} e^{8} - 8 \, a b^{11} d^{7} e^{9} - 104 \, a^{2} b^{9} c d^{7} e^{9} + 656 \, a^{3} b^{7} c^{2} d^{7} e^{9} + 1512 \, a^{4} b^{5} c^{3} d^{7} e^{9} - 6720 \, a^{5} b^{3} c^{4} d^{7} e^{9} - 4480 \, a^{6} b c^{5} d^{7} e^{9} + 28 \, a^{2} b^{10} d^{6} e^{10} + 56 \, a^{3} b^{8} c d^{6} e^{10} - 1372 \, a^{4} b^{6} c^{2} d^{6} e^{10} + 1176 \, a^{5} b^{4} c^{3} d^{6} e^{10} + 6272 \, a^{6} b^{2} c^{4} d^{6} e^{10} + 896 \, a^{7} c^{5} d^{6} e^{10} - 56 \, a^{3} b^{9} d^{5} e^{11} + 168 \, a^{4} b^{7} c d^{5} e^{11} + 1176 \, a^{5} b^{5} c^{2} d^{5} e^{11} - 3136 \, a^{6} b^{3} c^{3} d^{5} e^{11} - 2688 \, a^{7} b c^{4} d^{5} e^{11} + 70 \, a^{4} b^{8} d^{4} e^{12} - 392 \, a^{5} b^{6} c d^{4} e^{12} - 196 \, a^{6} b^{4} c^{2} d^{4} e^{12} + 2464 \, a^{7} b^{2} c^{3} d^{4} e^{12} + 448 \, a^{8} c^{4} d^{4} e^{12} - 56 \, a^{5} b^{7} d^{3} e^{13} + 392 \, a^{6} b^{5} c d^{3} e^{13} - 448 \, a^{7} b^{3} c^{2} d^{3} e^{13} - 896 \, a^{8} b c^{3} d^{3} e^{13} + 28 \, a^{6} b^{6} d^{2} e^{14} - 216 \, a^{7} b^{4} c d^{2} e^{14} + 384 \, a^{8} b^{2} c^{2} d^{2} e^{14} + 128 \, a^{9} c^{3} d^{2} e^{14} - 8 \, a^{7} b^{5} d e^{15} + 64 \, a^{8} b^{3} c d e^{15} - 128 \, a^{9} b c^{2} d e^{15} + a^{8} b^{4} e^{16} - 8 \, a^{9} b^{2} c e^{16} + 16 \, a^{10} c^{2} e^{16}} + \frac{3 \, {\left(8 \, b c^{10} d^{15} - 60 \, b^{2} c^{9} d^{14} e + 193 \, b^{3} c^{8} d^{13} e^{2} + 68 \, a b c^{9} d^{13} e^{2} - 344 \, b^{4} c^{7} d^{12} e^{3} - 446 \, a b^{2} c^{8} d^{12} e^{3} + 8 \, a^{2} c^{9} d^{12} e^{3} + 363 \, b^{5} c^{6} d^{11} e^{4} + 1230 \, a b^{3} c^{7} d^{11} e^{4} + 192 \, a^{2} b c^{8} d^{11} e^{4} - 218 \, b^{6} c^{5} d^{10} e^{5} - 1828 \, a b^{4} c^{6} d^{10} e^{5} - 1224 \, a^{2} b^{2} c^{7} d^{10} e^{5} + 48 \, a^{3} c^{8} d^{10} e^{5} + 55 \, b^{7} c^{4} d^{9} e^{6} + 1540 \, a b^{5} c^{5} d^{9} e^{6} + 2915 \, a^{2} b^{3} c^{6} d^{9} e^{6} + 220 \, a^{3} b c^{7} d^{9} e^{6} + 12 \, b^{8} c^{3} d^{8} e^{7} - 678 \, a b^{6} c^{4} d^{8} e^{7} - 3510 \, a^{2} b^{4} c^{5} d^{8} e^{7} - 1650 \, a^{3} b^{2} c^{6} d^{8} e^{7} + 120 \, a^{4} c^{7} d^{8} e^{7} - 11 \, b^{9} c^{2} d^{7} e^{8} + 86 \, a b^{7} c^{3} d^{7} e^{8} + 2202 \, a^{2} b^{5} c^{4} d^{7} e^{8} + 3380 \, a^{3} b^{3} c^{5} d^{7} e^{8} + 40 \, a^{4} b c^{6} d^{7} e^{8} + 2 \, b^{10} c d^{6} e^{9} + 40 \, a b^{8} c^{2} d^{6} e^{9} - 592 \, a^{2} b^{6} c^{3} d^{6} e^{9} - 3120 \, a^{3} b^{4} c^{4} d^{6} e^{9} - 1180 \, a^{4} b^{2} c^{5} d^{6} e^{9} + 160 \, a^{5} c^{6} d^{6} e^{9} - 12 \, a b^{9} c d^{5} e^{10} - 21 \, a^{2} b^{7} c^{2} d^{5} e^{10} + 1272 \, a^{3} b^{5} c^{3} d^{5} e^{10} + 2055 \, a^{4} b^{3} c^{4} d^{5} e^{10} - 132 \, a^{5} b c^{5} d^{5} e^{10} + 30 \, a^{2} b^{8} c d^{4} e^{11} - 110 \, a^{3} b^{6} c^{2} d^{4} e^{11} - 1300 \, a^{4} b^{4} c^{3} d^{4} e^{11} - 450 \, a^{5} b^{2} c^{4} d^{4} e^{11} + 120 \, a^{6} c^{5} d^{4} e^{11} - 40 \, a^{3} b^{7} c d^{3} e^{12} + 235 \, a^{4} b^{5} c^{2} d^{3} e^{12} + 638 \, a^{5} b^{3} c^{3} d^{3} e^{12} - 112 \, a^{6} b c^{4} d^{3} e^{12} + 30 \, a^{4} b^{6} c d^{2} e^{13} - 204 \, a^{5} b^{4} c^{2} d^{2} e^{13} - 96 \, a^{6} b^{2} c^{3} d^{2} e^{13} + 48 \, a^{7} c^{4} d^{2} e^{13} - 12 \, a^{5} b^{5} c d e^{14} + 85 \, a^{6} b^{3} c^{2} d e^{14} - 28 \, a^{7} b c^{3} d e^{14} + 2 \, a^{6} b^{4} c e^{15} - 14 \, a^{7} b^{2} c^{2} e^{15} + 8 \, a^{8} c^{3} e^{15}\right)}}{b^{4} c^{8} d^{16} - 8 \, a b^{2} c^{9} d^{16} + 16 \, a^{2} c^{10} d^{16} - 8 \, b^{5} c^{7} d^{15} e + 64 \, a b^{3} c^{8} d^{15} e - 128 \, a^{2} b c^{9} d^{15} e + 28 \, b^{6} c^{6} d^{14} e^{2} - 216 \, a b^{4} c^{7} d^{14} e^{2} + 384 \, a^{2} b^{2} c^{8} d^{14} e^{2} + 128 \, a^{3} c^{9} d^{14} e^{2} - 56 \, b^{7} c^{5} d^{13} e^{3} + 392 \, a b^{5} c^{6} d^{13} e^{3} - 448 \, a^{2} b^{3} c^{7} d^{13} e^{3} - 896 \, a^{3} b c^{8} d^{13} e^{3} + 70 \, b^{8} c^{4} d^{12} e^{4} - 392 \, a b^{6} c^{5} d^{12} e^{4} - 196 \, a^{2} b^{4} c^{6} d^{12} e^{4} + 2464 \, a^{3} b^{2} c^{7} d^{12} e^{4} + 448 \, a^{4} c^{8} d^{12} e^{4} - 56 \, b^{9} c^{3} d^{11} e^{5} + 168 \, a b^{7} c^{4} d^{11} e^{5} + 1176 \, a^{2} b^{5} c^{5} d^{11} e^{5} - 3136 \, a^{3} b^{3} c^{6} d^{11} e^{5} - 2688 \, a^{4} b c^{7} d^{11} e^{5} + 28 \, b^{10} c^{2} d^{10} e^{6} + 56 \, a b^{8} c^{3} d^{10} e^{6} - 1372 \, a^{2} b^{6} c^{4} d^{10} e^{6} + 1176 \, a^{3} b^{4} c^{5} d^{10} e^{6} + 6272 \, a^{4} b^{2} c^{6} d^{10} e^{6} + 896 \, a^{5} c^{7} d^{10} e^{6} - 8 \, b^{11} c d^{9} e^{7} - 104 \, a b^{9} c^{2} d^{9} e^{7} + 656 \, a^{2} b^{7} c^{3} d^{9} e^{7} + 1512 \, a^{3} b^{5} c^{4} d^{9} e^{7} - 6720 \, a^{4} b^{3} c^{5} d^{9} e^{7} - 4480 \, a^{5} b c^{6} d^{9} e^{7} + b^{12} d^{8} e^{8} + 48 \, a b^{10} c d^{8} e^{8} - 12 \, a^{2} b^{8} c^{2} d^{8} e^{8} - 1904 \, a^{3} b^{6} c^{3} d^{8} e^{8} + 2310 \, a^{4} b^{4} c^{4} d^{8} e^{8} + 8400 \, a^{5} b^{2} c^{5} d^{8} e^{8} + 1120 \, a^{6} c^{6} d^{8} e^{8} - 8 \, a b^{11} d^{7} e^{9} - 104 \, a^{2} b^{9} c d^{7} e^{9} + 656 \, a^{3} b^{7} c^{2} d^{7} e^{9} + 1512 \, a^{4} b^{5} c^{3} d^{7} e^{9} - 6720 \, a^{5} b^{3} c^{4} d^{7} e^{9} - 4480 \, a^{6} b c^{5} d^{7} e^{9} + 28 \, a^{2} b^{10} d^{6} e^{10} + 56 \, a^{3} b^{8} c d^{6} e^{10} - 1372 \, a^{4} b^{6} c^{2} d^{6} e^{10} + 1176 \, a^{5} b^{4} c^{3} d^{6} e^{10} + 6272 \, a^{6} b^{2} c^{4} d^{6} e^{10} + 896 \, a^{7} c^{5} d^{6} e^{10} - 56 \, a^{3} b^{9} d^{5} e^{11} + 168 \, a^{4} b^{7} c d^{5} e^{11} + 1176 \, a^{5} b^{5} c^{2} d^{5} e^{11} - 3136 \, a^{6} b^{3} c^{3} d^{5} e^{11} - 2688 \, a^{7} b c^{4} d^{5} e^{11} + 70 \, a^{4} b^{8} d^{4} e^{12} - 392 \, a^{5} b^{6} c d^{4} e^{12} - 196 \, a^{6} b^{4} c^{2} d^{4} e^{12} + 2464 \, a^{7} b^{2} c^{3} d^{4} e^{12} + 448 \, a^{8} c^{4} d^{4} e^{12} - 56 \, a^{5} b^{7} d^{3} e^{13} + 392 \, a^{6} b^{5} c d^{3} e^{13} - 448 \, a^{7} b^{3} c^{2} d^{3} e^{13} - 896 \, a^{8} b c^{3} d^{3} e^{13} + 28 \, a^{6} b^{6} d^{2} e^{14} - 216 \, a^{7} b^{4} c d^{2} e^{14} + 384 \, a^{8} b^{2} c^{2} d^{2} e^{14} + 128 \, a^{9} c^{3} d^{2} e^{14} - 8 \, a^{7} b^{5} d e^{15} + 64 \, a^{8} b^{3} c d e^{15} - 128 \, a^{9} b c^{2} d e^{15} + a^{8} b^{4} e^{16} - 8 \, a^{9} b^{2} c e^{16} + 16 \, a^{10} c^{2} e^{16}}\right)} x + \frac{3 \, {\left(2 \, b^{2} c^{9} d^{15} + 8 \, a c^{10} d^{15} - 15 \, b^{3} c^{8} d^{14} e - 60 \, a b c^{9} d^{14} e + 48 \, b^{4} c^{7} d^{13} e^{2} + 212 \, a b^{2} c^{8} d^{13} e^{2} + 64 \, a^{2} c^{9} d^{13} e^{2} - 84 \, b^{5} c^{6} d^{12} e^{3} - 472 \, a b^{3} c^{7} d^{12} e^{3} - 408 \, a^{2} b c^{8} d^{12} e^{3} + 84 \, b^{6} c^{5} d^{11} e^{4} + 726 \, a b^{4} c^{6} d^{11} e^{4} + 1158 \, a^{2} b^{2} c^{7} d^{11} e^{4} + 216 \, a^{3} c^{8} d^{11} e^{4} - 42 \, b^{7} c^{4} d^{10} e^{5} - 772 \, a b^{5} c^{5} d^{10} e^{5} - 1961 \, a^{2} b^{3} c^{6} d^{10} e^{5} - 1140 \, a^{3} b c^{7} d^{10} e^{5} + 530 \, a b^{6} c^{4} d^{9} e^{6} + 2220 \, a^{2} b^{4} c^{5} d^{9} e^{6} + 2560 \, a^{3} b^{2} c^{6} d^{9} e^{6} + 400 \, a^{4} c^{7} d^{9} e^{6} + 12 \, b^{9} c^{2} d^{8} e^{7} - 192 \, a b^{7} c^{3} d^{8} e^{7} - 1719 \, a^{2} b^{5} c^{4} d^{8} e^{7} - 3270 \, a^{3} b^{3} c^{5} d^{8} e^{7} - 1680 \, a^{4} b c^{6} d^{8} e^{7} - 6 \, b^{10} c d^{7} e^{8} + 2 \, a b^{8} c^{2} d^{7} e^{8} + 838 \, a^{2} b^{6} c^{3} d^{7} e^{8} + 2700 \, a^{3} b^{4} c^{4} d^{7} e^{8} + 2830 \, a^{4} b^{2} c^{5} d^{7} e^{8} + 440 \, a^{5} c^{6} d^{7} e^{8} + b^{11} d^{6} e^{9} + 24 \, a b^{9} c d^{6} e^{9} - 183 \, a^{2} b^{7} c^{2} d^{6} e^{9} - 1496 \, a^{3} b^{5} c^{3} d^{6} e^{9} - 2545 \, a^{4} b^{3} c^{4} d^{6} e^{9} - 1380 \, a^{5} b c^{5} d^{6} e^{9} - 6 \, a b^{10} d^{5} e^{10} - 24 \, a^{2} b^{8} c d^{5} e^{10} + 480 \, a^{3} b^{6} c^{2} d^{5} e^{10} + 1440 \, a^{4} b^{4} c^{3} d^{5} e^{10} + 1572 \, a^{5} b^{2} c^{4} d^{5} e^{10} + 288 \, a^{6} c^{5} d^{5} e^{10} + 15 \, a^{2} b^{9} d^{4} e^{11} - 30 \, a^{3} b^{7} c d^{4} e^{11} - 550 \, a^{4} b^{5} c^{2} d^{4} e^{11} - 860 \, a^{5} b^{3} c^{3} d^{4} e^{11} - 600 \, a^{6} b c^{4} d^{4} e^{11} - 20 \, a^{3} b^{8} d^{3} e^{12} + 90 \, a^{4} b^{6} c d^{3} e^{12} + 318 \, a^{5} b^{4} c^{2} d^{3} e^{12} + 362 \, a^{6} b^{2} c^{3} d^{3} e^{12} + 104 \, a^{7} c^{4} d^{3} e^{12} + 15 \, a^{4} b^{7} d^{2} e^{13} - 84 \, a^{5} b^{5} c d^{2} e^{13} - 87 \, a^{6} b^{3} c^{2} d^{2} e^{13} - 108 \, a^{7} b c^{3} d^{2} e^{13} - 6 \, a^{5} b^{6} d e^{14} + 36 \, a^{6} b^{4} c d e^{14} + 8 \, a^{7} b^{2} c^{2} d e^{14} + 16 \, a^{8} c^{3} d e^{14} + a^{6} b^{5} e^{15} - 6 \, a^{7} b^{3} c e^{15}\right)}}{b^{4} c^{8} d^{16} - 8 \, a b^{2} c^{9} d^{16} + 16 \, a^{2} c^{10} d^{16} - 8 \, b^{5} c^{7} d^{15} e + 64 \, a b^{3} c^{8} d^{15} e - 128 \, a^{2} b c^{9} d^{15} e + 28 \, b^{6} c^{6} d^{14} e^{2} - 216 \, a b^{4} c^{7} d^{14} e^{2} + 384 \, a^{2} b^{2} c^{8} d^{14} e^{2} + 128 \, a^{3} c^{9} d^{14} e^{2} - 56 \, b^{7} c^{5} d^{13} e^{3} + 392 \, a b^{5} c^{6} d^{13} e^{3} - 448 \, a^{2} b^{3} c^{7} d^{13} e^{3} - 896 \, a^{3} b c^{8} d^{13} e^{3} + 70 \, b^{8} c^{4} d^{12} e^{4} - 392 \, a b^{6} c^{5} d^{12} e^{4} - 196 \, a^{2} b^{4} c^{6} d^{12} e^{4} + 2464 \, a^{3} b^{2} c^{7} d^{12} e^{4} + 448 \, a^{4} c^{8} d^{12} e^{4} - 56 \, b^{9} c^{3} d^{11} e^{5} + 168 \, a b^{7} c^{4} d^{11} e^{5} + 1176 \, a^{2} b^{5} c^{5} d^{11} e^{5} - 3136 \, a^{3} b^{3} c^{6} d^{11} e^{5} - 2688 \, a^{4} b c^{7} d^{11} e^{5} + 28 \, b^{10} c^{2} d^{10} e^{6} + 56 \, a b^{8} c^{3} d^{10} e^{6} - 1372 \, a^{2} b^{6} c^{4} d^{10} e^{6} + 1176 \, a^{3} b^{4} c^{5} d^{10} e^{6} + 6272 \, a^{4} b^{2} c^{6} d^{10} e^{6} + 896 \, a^{5} c^{7} d^{10} e^{6} - 8 \, b^{11} c d^{9} e^{7} - 104 \, a b^{9} c^{2} d^{9} e^{7} + 656 \, a^{2} b^{7} c^{3} d^{9} e^{7} + 1512 \, a^{3} b^{5} c^{4} d^{9} e^{7} - 6720 \, a^{4} b^{3} c^{5} d^{9} e^{7} - 4480 \, a^{5} b c^{6} d^{9} e^{7} + b^{12} d^{8} e^{8} + 48 \, a b^{10} c d^{8} e^{8} - 12 \, a^{2} b^{8} c^{2} d^{8} e^{8} - 1904 \, a^{3} b^{6} c^{3} d^{8} e^{8} + 2310 \, a^{4} b^{4} c^{4} d^{8} e^{8} + 8400 \, a^{5} b^{2} c^{5} d^{8} e^{8} + 1120 \, a^{6} c^{6} d^{8} e^{8} - 8 \, a b^{11} d^{7} e^{9} - 104 \, a^{2} b^{9} c d^{7} e^{9} + 656 \, a^{3} b^{7} c^{2} d^{7} e^{9} + 1512 \, a^{4} b^{5} c^{3} d^{7} e^{9} - 6720 \, a^{5} b^{3} c^{4} d^{7} e^{9} - 4480 \, a^{6} b c^{5} d^{7} e^{9} + 28 \, a^{2} b^{10} d^{6} e^{10} + 56 \, a^{3} b^{8} c d^{6} e^{10} - 1372 \, a^{4} b^{6} c^{2} d^{6} e^{10} + 1176 \, a^{5} b^{4} c^{3} d^{6} e^{10} + 6272 \, a^{6} b^{2} c^{4} d^{6} e^{10} + 896 \, a^{7} c^{5} d^{6} e^{10} - 56 \, a^{3} b^{9} d^{5} e^{11} + 168 \, a^{4} b^{7} c d^{5} e^{11} + 1176 \, a^{5} b^{5} c^{2} d^{5} e^{11} - 3136 \, a^{6} b^{3} c^{3} d^{5} e^{11} - 2688 \, a^{7} b c^{4} d^{5} e^{11} + 70 \, a^{4} b^{8} d^{4} e^{12} - 392 \, a^{5} b^{6} c d^{4} e^{12} - 196 \, a^{6} b^{4} c^{2} d^{4} e^{12} + 2464 \, a^{7} b^{2} c^{3} d^{4} e^{12} + 448 \, a^{8} c^{4} d^{4} e^{12} - 56 \, a^{5} b^{7} d^{3} e^{13} + 392 \, a^{6} b^{5} c d^{3} e^{13} - 448 \, a^{7} b^{3} c^{2} d^{3} e^{13} - 896 \, a^{8} b c^{3} d^{3} e^{13} + 28 \, a^{6} b^{6} d^{2} e^{14} - 216 \, a^{7} b^{4} c d^{2} e^{14} + 384 \, a^{8} b^{2} c^{2} d^{2} e^{14} + 128 \, a^{9} c^{3} d^{2} e^{14} - 8 \, a^{7} b^{5} d e^{15} + 64 \, a^{8} b^{3} c d e^{15} - 128 \, a^{9} b c^{2} d e^{15} + a^{8} b^{4} e^{16} - 8 \, a^{9} b^{2} c e^{16} + 16 \, a^{10} c^{2} e^{16}}\right)} x - \frac{b^{3} c^{8} d^{15} - 12 \, a b c^{9} d^{15} - 8 \, b^{4} c^{7} d^{14} e + 94 \, a b^{2} c^{8} d^{14} e - 8 \, a^{2} c^{9} d^{14} e + 28 \, b^{5} c^{6} d^{13} e^{2} - 312 \, a b^{3} c^{7} d^{13} e^{2} - 40 \, a^{2} b c^{8} d^{13} e^{2} - 56 \, b^{6} c^{5} d^{12} e^{3} + 560 \, a b^{4} c^{6} d^{12} e^{3} + 496 \, a^{2} b^{2} c^{7} d^{12} e^{3} - 80 \, a^{3} c^{8} d^{12} e^{3} + 70 \, b^{7} c^{4} d^{11} e^{4} - 560 \, a b^{5} c^{5} d^{11} e^{4} - 1649 \, a^{2} b^{3} c^{6} d^{11} e^{4} + 156 \, a^{3} b c^{7} d^{11} e^{4} - 56 \, b^{8} c^{3} d^{10} e^{5} + 252 \, a b^{6} c^{4} d^{10} e^{5} + 2726 \, a^{2} b^{4} c^{5} d^{10} e^{5} + 738 \, a^{3} b^{2} c^{6} d^{10} e^{5} - 312 \, a^{4} c^{7} d^{10} e^{5} + 28 \, b^{9} c^{2} d^{9} e^{6} + 56 \, a b^{7} c^{3} d^{9} e^{6} - 2447 \, a^{2} b^{5} c^{4} d^{9} e^{6} - 3150 \, a^{3} b^{3} c^{5} d^{9} e^{6} + 960 \, a^{4} b c^{6} d^{9} e^{6} - 8 \, b^{10} c d^{8} e^{7} - 128 \, a b^{8} c^{2} d^{8} e^{7} + 1060 \, a^{2} b^{6} c^{3} d^{8} e^{7} + 4820 \, a^{3} b^{4} c^{4} d^{8} e^{7} - 100 \, a^{4} b^{2} c^{5} d^{8} e^{7} - 640 \, a^{5} c^{6} d^{8} e^{7} + b^{11} d^{7} e^{8} + 60 \, a b^{9} c d^{7} e^{8} - 31 \, a^{2} b^{7} c^{2} d^{7} e^{8} - 3520 \, a^{3} b^{5} c^{3} d^{7} e^{8} - 2865 \, a^{4} b^{3} c^{4} d^{7} e^{8} + 1900 \, a^{5} b c^{5} d^{7} e^{8} - 10 \, a b^{10} d^{6} e^{9} - 146 \, a^{2} b^{8} c d^{6} e^{9} + 1034 \, a^{3} b^{6} c^{2} d^{6} e^{9} + 4180 \, a^{4} b^{4} c^{3} d^{6} e^{9} - 1150 \, a^{5} b^{2} c^{4} d^{6} e^{9} - 760 \, a^{6} c^{5} d^{6} e^{9} + 39 \, a^{2} b^{9} d^{5} e^{10} + 82 \, a^{3} b^{7} c d^{5} e^{10} - 2198 \, a^{4} b^{5} c^{2} d^{5} e^{10} - 1484 \, a^{5} b^{3} c^{3} d^{5} e^{10} + 1848 \, a^{6} b c^{4} d^{5} e^{10} - 80 \, a^{3} b^{8} d^{4} e^{11} + 240 \, a^{4} b^{6} c d^{4} e^{11} + 1952 \, a^{5} b^{4} c^{2} d^{4} e^{11} - 936 \, a^{6} b^{2} c^{3} d^{4} e^{11} - 528 \, a^{7} c^{4} d^{4} e^{11} + 95 \, a^{4} b^{7} d^{3} e^{12} - 512 \, a^{5} b^{5} c d^{3} e^{12} - 607 \, a^{6} b^{3} c^{2} d^{3} e^{12} + 900 \, a^{7} b c^{3} d^{3} e^{12} - 66 \, a^{5} b^{6} d^{2} e^{13} + 430 \, a^{6} b^{4} c d^{2} e^{13} - 194 \, a^{7} b^{2} c^{2} d^{2} e^{13} - 200 \, a^{8} c^{3} d^{2} e^{13} + 25 \, a^{6} b^{5} d e^{14} - 174 \, a^{7} b^{3} c d e^{14} + 176 \, a^{8} b c^{2} d e^{14} - 4 \, a^{7} b^{4} e^{15} + 28 \, a^{8} b^{2} c e^{15} - 32 \, a^{9} c^{2} e^{15}}{b^{4} c^{8} d^{16} - 8 \, a b^{2} c^{9} d^{16} + 16 \, a^{2} c^{10} d^{16} - 8 \, b^{5} c^{7} d^{15} e + 64 \, a b^{3} c^{8} d^{15} e - 128 \, a^{2} b c^{9} d^{15} e + 28 \, b^{6} c^{6} d^{14} e^{2} - 216 \, a b^{4} c^{7} d^{14} e^{2} + 384 \, a^{2} b^{2} c^{8} d^{14} e^{2} + 128 \, a^{3} c^{9} d^{14} e^{2} - 56 \, b^{7} c^{5} d^{13} e^{3} + 392 \, a b^{5} c^{6} d^{13} e^{3} - 448 \, a^{2} b^{3} c^{7} d^{13} e^{3} - 896 \, a^{3} b c^{8} d^{13} e^{3} + 70 \, b^{8} c^{4} d^{12} e^{4} - 392 \, a b^{6} c^{5} d^{12} e^{4} - 196 \, a^{2} b^{4} c^{6} d^{12} e^{4} + 2464 \, a^{3} b^{2} c^{7} d^{12} e^{4} + 448 \, a^{4} c^{8} d^{12} e^{4} - 56 \, b^{9} c^{3} d^{11} e^{5} + 168 \, a b^{7} c^{4} d^{11} e^{5} + 1176 \, a^{2} b^{5} c^{5} d^{11} e^{5} - 3136 \, a^{3} b^{3} c^{6} d^{11} e^{5} - 2688 \, a^{4} b c^{7} d^{11} e^{5} + 28 \, b^{10} c^{2} d^{10} e^{6} + 56 \, a b^{8} c^{3} d^{10} e^{6} - 1372 \, a^{2} b^{6} c^{4} d^{10} e^{6} + 1176 \, a^{3} b^{4} c^{5} d^{10} e^{6} + 6272 \, a^{4} b^{2} c^{6} d^{10} e^{6} + 896 \, a^{5} c^{7} d^{10} e^{6} - 8 \, b^{11} c d^{9} e^{7} - 104 \, a b^{9} c^{2} d^{9} e^{7} + 656 \, a^{2} b^{7} c^{3} d^{9} e^{7} + 1512 \, a^{3} b^{5} c^{4} d^{9} e^{7} - 6720 \, a^{4} b^{3} c^{5} d^{9} e^{7} - 4480 \, a^{5} b c^{6} d^{9} e^{7} + b^{12} d^{8} e^{8} + 48 \, a b^{10} c d^{8} e^{8} - 12 \, a^{2} b^{8} c^{2} d^{8} e^{8} - 1904 \, a^{3} b^{6} c^{3} d^{8} e^{8} + 2310 \, a^{4} b^{4} c^{4} d^{8} e^{8} + 8400 \, a^{5} b^{2} c^{5} d^{8} e^{8} + 1120 \, a^{6} c^{6} d^{8} e^{8} - 8 \, a b^{11} d^{7} e^{9} - 104 \, a^{2} b^{9} c d^{7} e^{9} + 656 \, a^{3} b^{7} c^{2} d^{7} e^{9} + 1512 \, a^{4} b^{5} c^{3} d^{7} e^{9} - 6720 \, a^{5} b^{3} c^{4} d^{7} e^{9} - 4480 \, a^{6} b c^{5} d^{7} e^{9} + 28 \, a^{2} b^{10} d^{6} e^{10} + 56 \, a^{3} b^{8} c d^{6} e^{10} - 1372 \, a^{4} b^{6} c^{2} d^{6} e^{10} + 1176 \, a^{5} b^{4} c^{3} d^{6} e^{10} + 6272 \, a^{6} b^{2} c^{4} d^{6} e^{10} + 896 \, a^{7} c^{5} d^{6} e^{10} - 56 \, a^{3} b^{9} d^{5} e^{11} + 168 \, a^{4} b^{7} c d^{5} e^{11} + 1176 \, a^{5} b^{5} c^{2} d^{5} e^{11} - 3136 \, a^{6} b^{3} c^{3} d^{5} e^{11} - 2688 \, a^{7} b c^{4} d^{5} e^{11} + 70 \, a^{4} b^{8} d^{4} e^{12} - 392 \, a^{5} b^{6} c d^{4} e^{12} - 196 \, a^{6} b^{4} c^{2} d^{4} e^{12} + 2464 \, a^{7} b^{2} c^{3} d^{4} e^{12} + 448 \, a^{8} c^{4} d^{4} e^{12} - 56 \, a^{5} b^{7} d^{3} e^{13} + 392 \, a^{6} b^{5} c d^{3} e^{13} - 448 \, a^{7} b^{3} c^{2} d^{3} e^{13} - 896 \, a^{8} b c^{3} d^{3} e^{13} + 28 \, a^{6} b^{6} d^{2} e^{14} - 216 \, a^{7} b^{4} c d^{2} e^{14} + 384 \, a^{8} b^{2} c^{2} d^{2} e^{14} + 128 \, a^{9} c^{3} d^{2} e^{14} - 8 \, a^{7} b^{5} d e^{15} + 64 \, a^{8} b^{3} c d e^{15} - 128 \, a^{9} b c^{2} d e^{15} + a^{8} b^{4} e^{16} - 8 \, a^{9} b^{2} c e^{16} + 16 \, a^{10} c^{2} e^{16}}\right)}}{3 \, {\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}"," ",0,"2*arctan(-((sqrt(c)*x - sqrt(c*x^2 + b*x + a))*e + sqrt(c)*d)/sqrt(-c*d^2 + b*d*e - a*e^2))*e^4/((c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2 + 2*a*c*d^2*e^2 - 2*a*b*d*e^3 + a^2*e^4)*sqrt(-c*d^2 + b*d*e - a*e^2)) + 2/3*((((16*c^11*d^15 - 120*b*c^10*d^14*e + 386*b^2*c^9*d^13*e^2 + 136*a*c^10*d^13*e^2 - 689*b^3*c^8*d^12*e^3 - 884*a*b*c^9*d^12*e^3 + 732*b^4*c^7*d^11*e^4 + 2412*a*b^2*c^8*d^11*e^4 + 480*a^2*c^9*d^11*e^4 - 451*b^5*c^6*d^10*e^5 - 3542*a*b^3*c^7*d^10*e^5 - 2640*a^2*b*c^8*d^10*e^5 + 130*b^6*c^5*d^9*e^6 + 2950*a*b^4*c^6*d^9*e^6 + 5910*a^2*b^2*c^7*d^9*e^6 + 920*a^3*c^8*d^9*e^6 + 9*b^7*c^4*d^8*e^7 - 1296*a*b^5*c^5*d^8*e^7 - 6795*a^2*b^3*c^6*d^8*e^7 - 4140*a^3*b*c^7*d^8*e^7 - 16*b^8*c^3*d^7*e^8 + 184*a*b^6*c^4*d^7*e^8 + 4080*a^2*b^4*c^5*d^7*e^8 + 7240*a^3*b^2*c^6*d^7*e^8 + 1040*a^4*c^7*d^7*e^8 + 3*b^9*c^2*d^6*e^9 + 58*a*b^7*c^3*d^6*e^9 - 1050*a^2*b^5*c^4*d^6*e^9 - 6020*a^3*b^3*c^5*d^6*e^9 - 3640*a^4*b*c^6*d^6*e^9 - 18*a*b^8*c^2*d^5*e^10 - 30*a^2*b^6*c^3*d^5*e^10 + 2220*a^3*b^4*c^4*d^5*e^10 + 4590*a^4*b^2*c^5*d^5*e^10 + 696*a^5*c^6*d^5*e^10 + 45*a^2*b^7*c^2*d^4*e^11 - 160*a^3*b^5*c^3*d^4*e^11 - 2375*a^4*b^3*c^4*d^4*e^11 - 1740*a^5*b*c^5*d^4*e^11 - 60*a^3*b^6*c^2*d^3*e^12 + 340*a^4*b^4*c^3*d^3*e^12 + 1356*a^5*b^2*c^4*d^3*e^12 + 256*a^6*c^5*d^3*e^12 + 45*a^4*b^5*c^2*d^2*e^13 - 294*a^5*b^3*c^3*d^2*e^13 - 384*a^6*b*c^4*d^2*e^13 - 18*a^5*b^4*c^2*d*e^14 + 122*a^6*b^2*c^3*d*e^14 + 40*a^7*c^4*d*e^14 + 3*a^6*b^3*c^2*e^15 - 20*a^7*b*c^3*e^15)*x/(b^4*c^8*d^16 - 8*a*b^2*c^9*d^16 + 16*a^2*c^10*d^16 - 8*b^5*c^7*d^15*e + 64*a*b^3*c^8*d^15*e - 128*a^2*b*c^9*d^15*e + 28*b^6*c^6*d^14*e^2 - 216*a*b^4*c^7*d^14*e^2 + 384*a^2*b^2*c^8*d^14*e^2 + 128*a^3*c^9*d^14*e^2 - 56*b^7*c^5*d^13*e^3 + 392*a*b^5*c^6*d^13*e^3 - 448*a^2*b^3*c^7*d^13*e^3 - 896*a^3*b*c^8*d^13*e^3 + 70*b^8*c^4*d^12*e^4 - 392*a*b^6*c^5*d^12*e^4 - 196*a^2*b^4*c^6*d^12*e^4 + 2464*a^3*b^2*c^7*d^12*e^4 + 448*a^4*c^8*d^12*e^4 - 56*b^9*c^3*d^11*e^5 + 168*a*b^7*c^4*d^11*e^5 + 1176*a^2*b^5*c^5*d^11*e^5 - 3136*a^3*b^3*c^6*d^11*e^5 - 2688*a^4*b*c^7*d^11*e^5 + 28*b^10*c^2*d^10*e^6 + 56*a*b^8*c^3*d^10*e^6 - 1372*a^2*b^6*c^4*d^10*e^6 + 1176*a^3*b^4*c^5*d^10*e^6 + 6272*a^4*b^2*c^6*d^10*e^6 + 896*a^5*c^7*d^10*e^6 - 8*b^11*c*d^9*e^7 - 104*a*b^9*c^2*d^9*e^7 + 656*a^2*b^7*c^3*d^9*e^7 + 1512*a^3*b^5*c^4*d^9*e^7 - 6720*a^4*b^3*c^5*d^9*e^7 - 4480*a^5*b*c^6*d^9*e^7 + b^12*d^8*e^8 + 48*a*b^10*c*d^8*e^8 - 12*a^2*b^8*c^2*d^8*e^8 - 1904*a^3*b^6*c^3*d^8*e^8 + 2310*a^4*b^4*c^4*d^8*e^8 + 8400*a^5*b^2*c^5*d^8*e^8 + 1120*a^6*c^6*d^8*e^8 - 8*a*b^11*d^7*e^9 - 104*a^2*b^9*c*d^7*e^9 + 656*a^3*b^7*c^2*d^7*e^9 + 1512*a^4*b^5*c^3*d^7*e^9 - 6720*a^5*b^3*c^4*d^7*e^9 - 4480*a^6*b*c^5*d^7*e^9 + 28*a^2*b^10*d^6*e^10 + 56*a^3*b^8*c*d^6*e^10 - 1372*a^4*b^6*c^2*d^6*e^10 + 1176*a^5*b^4*c^3*d^6*e^10 + 6272*a^6*b^2*c^4*d^6*e^10 + 896*a^7*c^5*d^6*e^10 - 56*a^3*b^9*d^5*e^11 + 168*a^4*b^7*c*d^5*e^11 + 1176*a^5*b^5*c^2*d^5*e^11 - 3136*a^6*b^3*c^3*d^5*e^11 - 2688*a^7*b*c^4*d^5*e^11 + 70*a^4*b^8*d^4*e^12 - 392*a^5*b^6*c*d^4*e^12 - 196*a^6*b^4*c^2*d^4*e^12 + 2464*a^7*b^2*c^3*d^4*e^12 + 448*a^8*c^4*d^4*e^12 - 56*a^5*b^7*d^3*e^13 + 392*a^6*b^5*c*d^3*e^13 - 448*a^7*b^3*c^2*d^3*e^13 - 896*a^8*b*c^3*d^3*e^13 + 28*a^6*b^6*d^2*e^14 - 216*a^7*b^4*c*d^2*e^14 + 384*a^8*b^2*c^2*d^2*e^14 + 128*a^9*c^3*d^2*e^14 - 8*a^7*b^5*d*e^15 + 64*a^8*b^3*c*d*e^15 - 128*a^9*b*c^2*d*e^15 + a^8*b^4*e^16 - 8*a^9*b^2*c*e^16 + 16*a^10*c^2*e^16) + 3*(8*b*c^10*d^15 - 60*b^2*c^9*d^14*e + 193*b^3*c^8*d^13*e^2 + 68*a*b*c^9*d^13*e^2 - 344*b^4*c^7*d^12*e^3 - 446*a*b^2*c^8*d^12*e^3 + 8*a^2*c^9*d^12*e^3 + 363*b^5*c^6*d^11*e^4 + 1230*a*b^3*c^7*d^11*e^4 + 192*a^2*b*c^8*d^11*e^4 - 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1372*a^2*b^6*c^4*d^10*e^6 + 1176*a^3*b^4*c^5*d^10*e^6 + 6272*a^4*b^2*c^6*d^10*e^6 + 896*a^5*c^7*d^10*e^6 - 8*b^11*c*d^9*e^7 - 104*a*b^9*c^2*d^9*e^7 + 656*a^2*b^7*c^3*d^9*e^7 + 1512*a^3*b^5*c^4*d^9*e^7 - 6720*a^4*b^3*c^5*d^9*e^7 - 4480*a^5*b*c^6*d^9*e^7 + b^12*d^8*e^8 + 48*a*b^10*c*d^8*e^8 - 12*a^2*b^8*c^2*d^8*e^8 - 1904*a^3*b^6*c^3*d^8*e^8 + 2310*a^4*b^4*c^4*d^8*e^8 + 8400*a^5*b^2*c^5*d^8*e^8 + 1120*a^6*c^6*d^8*e^8 - 8*a*b^11*d^7*e^9 - 104*a^2*b^9*c*d^7*e^9 + 656*a^3*b^7*c^2*d^7*e^9 + 1512*a^4*b^5*c^3*d^7*e^9 - 6720*a^5*b^3*c^4*d^7*e^9 - 4480*a^6*b*c^5*d^7*e^9 + 28*a^2*b^10*d^6*e^10 + 56*a^3*b^8*c*d^6*e^10 - 1372*a^4*b^6*c^2*d^6*e^10 + 1176*a^5*b^4*c^3*d^6*e^10 + 6272*a^6*b^2*c^4*d^6*e^10 + 896*a^7*c^5*d^6*e^10 - 56*a^3*b^9*d^5*e^11 + 168*a^4*b^7*c*d^5*e^11 + 1176*a^5*b^5*c^2*d^5*e^11 - 3136*a^6*b^3*c^3*d^5*e^11 - 2688*a^7*b*c^4*d^5*e^11 + 70*a^4*b^8*d^4*e^12 - 392*a^5*b^6*c*d^4*e^12 - 196*a^6*b^4*c^2*d^4*e^12 + 2464*a^7*b^2*c^3*d^4*e^12 + 448*a^8*c^4*d^4*e^12 - 56*a^5*b^7*d^3*e^13 + 392*a^6*b^5*c*d^3*e^13 - 448*a^7*b^3*c^2*d^3*e^13 - 896*a^8*b*c^3*d^3*e^13 + 28*a^6*b^6*d^2*e^14 - 216*a^7*b^4*c*d^2*e^14 + 384*a^8*b^2*c^2*d^2*e^14 + 128*a^9*c^3*d^2*e^14 - 8*a^7*b^5*d*e^15 + 64*a^8*b^3*c*d*e^15 - 128*a^9*b*c^2*d*e^15 + a^8*b^4*e^16 - 8*a^9*b^2*c*e^16 + 16*a^10*c^2*e^16))*x - (b^3*c^8*d^15 - 12*a*b*c^9*d^15 - 8*b^4*c^7*d^14*e + 94*a*b^2*c^8*d^14*e - 8*a^2*c^9*d^14*e + 28*b^5*c^6*d^13*e^2 - 312*a*b^3*c^7*d^13*e^2 - 40*a^2*b*c^8*d^13*e^2 - 56*b^6*c^5*d^12*e^3 + 560*a*b^4*c^6*d^12*e^3 + 496*a^2*b^2*c^7*d^12*e^3 - 80*a^3*c^8*d^12*e^3 + 70*b^7*c^4*d^11*e^4 - 560*a*b^5*c^5*d^11*e^4 - 1649*a^2*b^3*c^6*d^11*e^4 + 156*a^3*b*c^7*d^11*e^4 - 56*b^8*c^3*d^10*e^5 + 252*a*b^6*c^4*d^10*e^5 + 2726*a^2*b^4*c^5*d^10*e^5 + 738*a^3*b^2*c^6*d^10*e^5 - 312*a^4*c^7*d^10*e^5 + 28*b^9*c^2*d^9*e^6 + 56*a*b^7*c^3*d^9*e^6 - 2447*a^2*b^5*c^4*d^9*e^6 - 3150*a^3*b^3*c^5*d^9*e^6 + 960*a^4*b*c^6*d^9*e^6 - 8*b^10*c*d^8*e^7 - 128*a*b^8*c^2*d^8*e^7 + 1060*a^2*b^6*c^3*d^8*e^7 + 4820*a^3*b^4*c^4*d^8*e^7 - 100*a^4*b^2*c^5*d^8*e^7 - 640*a^5*c^6*d^8*e^7 + b^11*d^7*e^8 + 60*a*b^9*c*d^7*e^8 - 31*a^2*b^7*c^2*d^7*e^8 - 3520*a^3*b^5*c^3*d^7*e^8 - 2865*a^4*b^3*c^4*d^7*e^8 + 1900*a^5*b*c^5*d^7*e^8 - 10*a*b^10*d^6*e^9 - 146*a^2*b^8*c*d^6*e^9 + 1034*a^3*b^6*c^2*d^6*e^9 + 4180*a^4*b^4*c^3*d^6*e^9 - 1150*a^5*b^2*c^4*d^6*e^9 - 760*a^6*c^5*d^6*e^9 + 39*a^2*b^9*d^5*e^10 + 82*a^3*b^7*c*d^5*e^10 - 2198*a^4*b^5*c^2*d^5*e^10 - 1484*a^5*b^3*c^3*d^5*e^10 + 1848*a^6*b*c^4*d^5*e^10 - 80*a^3*b^8*d^4*e^11 + 240*a^4*b^6*c*d^4*e^11 + 1952*a^5*b^4*c^2*d^4*e^11 - 936*a^6*b^2*c^3*d^4*e^11 - 528*a^7*c^4*d^4*e^11 + 95*a^4*b^7*d^3*e^12 - 512*a^5*b^5*c*d^3*e^12 - 607*a^6*b^3*c^2*d^3*e^12 + 900*a^7*b*c^3*d^3*e^12 - 66*a^5*b^6*d^2*e^13 + 430*a^6*b^4*c*d^2*e^13 - 194*a^7*b^2*c^2*d^2*e^13 - 200*a^8*c^3*d^2*e^13 + 25*a^6*b^5*d*e^14 - 174*a^7*b^3*c*d*e^14 + 176*a^8*b*c^2*d*e^14 - 4*a^7*b^4*e^15 + 28*a^8*b^2*c*e^15 - 32*a^9*c^2*e^15)/(b^4*c^8*d^16 - 8*a*b^2*c^9*d^16 + 16*a^2*c^10*d^16 - 8*b^5*c^7*d^15*e + 64*a*b^3*c^8*d^15*e - 128*a^2*b*c^9*d^15*e + 28*b^6*c^6*d^14*e^2 - 216*a*b^4*c^7*d^14*e^2 + 384*a^2*b^2*c^8*d^14*e^2 + 128*a^3*c^9*d^14*e^2 - 56*b^7*c^5*d^13*e^3 + 392*a*b^5*c^6*d^13*e^3 - 448*a^2*b^3*c^7*d^13*e^3 - 896*a^3*b*c^8*d^13*e^3 + 70*b^8*c^4*d^12*e^4 - 392*a*b^6*c^5*d^12*e^4 - 196*a^2*b^4*c^6*d^12*e^4 + 2464*a^3*b^2*c^7*d^12*e^4 + 448*a^4*c^8*d^12*e^4 - 56*b^9*c^3*d^11*e^5 + 168*a*b^7*c^4*d^11*e^5 + 1176*a^2*b^5*c^5*d^11*e^5 - 3136*a^3*b^3*c^6*d^11*e^5 - 2688*a^4*b*c^7*d^11*e^5 + 28*b^10*c^2*d^10*e^6 + 56*a*b^8*c^3*d^10*e^6 - 1372*a^2*b^6*c^4*d^10*e^6 + 1176*a^3*b^4*c^5*d^10*e^6 + 6272*a^4*b^2*c^6*d^10*e^6 + 896*a^5*c^7*d^10*e^6 - 8*b^11*c*d^9*e^7 - 104*a*b^9*c^2*d^9*e^7 + 656*a^2*b^7*c^3*d^9*e^7 + 1512*a^3*b^5*c^4*d^9*e^7 - 6720*a^4*b^3*c^5*d^9*e^7 - 4480*a^5*b*c^6*d^9*e^7 + b^12*d^8*e^8 + 48*a*b^10*c*d^8*e^8 - 12*a^2*b^8*c^2*d^8*e^8 - 1904*a^3*b^6*c^3*d^8*e^8 + 2310*a^4*b^4*c^4*d^8*e^8 + 8400*a^5*b^2*c^5*d^8*e^8 + 1120*a^6*c^6*d^8*e^8 - 8*a*b^11*d^7*e^9 - 104*a^2*b^9*c*d^7*e^9 + 656*a^3*b^7*c^2*d^7*e^9 + 1512*a^4*b^5*c^3*d^7*e^9 - 6720*a^5*b^3*c^4*d^7*e^9 - 4480*a^6*b*c^5*d^7*e^9 + 28*a^2*b^10*d^6*e^10 + 56*a^3*b^8*c*d^6*e^10 - 1372*a^4*b^6*c^2*d^6*e^10 + 1176*a^5*b^4*c^3*d^6*e^10 + 6272*a^6*b^2*c^4*d^6*e^10 + 896*a^7*c^5*d^6*e^10 - 56*a^3*b^9*d^5*e^11 + 168*a^4*b^7*c*d^5*e^11 + 1176*a^5*b^5*c^2*d^5*e^11 - 3136*a^6*b^3*c^3*d^5*e^11 - 2688*a^7*b*c^4*d^5*e^11 + 70*a^4*b^8*d^4*e^12 - 392*a^5*b^6*c*d^4*e^12 - 196*a^6*b^4*c^2*d^4*e^12 + 2464*a^7*b^2*c^3*d^4*e^12 + 448*a^8*c^4*d^4*e^12 - 56*a^5*b^7*d^3*e^13 + 392*a^6*b^5*c*d^3*e^13 - 448*a^7*b^3*c^2*d^3*e^13 - 896*a^8*b*c^3*d^3*e^13 + 28*a^6*b^6*d^2*e^14 - 216*a^7*b^4*c*d^2*e^14 + 384*a^8*b^2*c^2*d^2*e^14 + 128*a^9*c^3*d^2*e^14 - 8*a^7*b^5*d*e^15 + 64*a^8*b^3*c*d*e^15 - 128*a^9*b*c^2*d*e^15 + a^8*b^4*e^16 - 8*a^9*b^2*c*e^16 + 16*a^10*c^2*e^16))/(c*x^2 + b*x + a)^(3/2)","B",0
2398,1,5122,0,2.679836," ","integrate(1/(e*x+d)^2/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","-\frac{1}{6} \, {\left(\frac{{\left(64 \, \sqrt{c d^{2} - b d e + a e^{2}} c^{5} d^{4} e^{2} - 128 \, \sqrt{c d^{2} - b d e + a e^{2}} b c^{4} d^{3} e^{3} + 24 \, \sqrt{c d^{2} - b d e + a e^{2}} b^{2} c^{3} d^{2} e^{4} + 288 \, \sqrt{c d^{2} - b d e + a e^{2}} a c^{4} d^{2} e^{4} - 30 \, b^{4} c^{\frac{3}{2}} d e^{6} \log\left({\left| -2 \, c d + b e + 2 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c} \right|}\right) + 240 \, a b^{2} c^{\frac{5}{2}} d e^{6} \log\left({\left| -2 \, c d + b e + 2 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c} \right|}\right) - 480 \, a^{2} c^{\frac{7}{2}} d e^{6} \log\left({\left| -2 \, c d + b e + 2 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c} \right|}\right) + 40 \, \sqrt{c d^{2} - b d e + a e^{2}} b^{3} c^{2} d e^{5} - 288 \, \sqrt{c d^{2} - b d e + a e^{2}} a b c^{3} d e^{5} + 15 \, b^{5} \sqrt{c} e^{7} \log\left({\left| -2 \, c d + b e + 2 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c} \right|}\right) - 120 \, a b^{3} c^{\frac{3}{2}} e^{7} \log\left({\left| -2 \, c d + b e + 2 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c} \right|}\right) + 240 \, a^{2} b c^{\frac{5}{2}} e^{7} \log\left({\left| -2 \, c d + b e + 2 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c} \right|}\right) - 30 \, \sqrt{c d^{2} - b d e + a e^{2}} b^{4} c e^{6} + 200 \, \sqrt{c d^{2} - b d e + a e^{2}} a b^{2} c^{2} e^{6} - 256 \, \sqrt{c d^{2} - b d e + a e^{2}} a^{2} c^{3} e^{6}\right)} \mathrm{sgn}\left(\frac{1}{x e + d}\right)}{\sqrt{c d^{2} - b d e + a e^{2}} b^{4} c^{\frac{7}{2}} d^{6} - 8 \, \sqrt{c d^{2} - b d e + a e^{2}} a b^{2} c^{\frac{9}{2}} d^{6} + 16 \, \sqrt{c d^{2} - b d e + a e^{2}} a^{2} c^{\frac{11}{2}} d^{6} - 3 \, \sqrt{c d^{2} - b d e + a e^{2}} b^{5} c^{\frac{5}{2}} d^{5} e + 24 \, \sqrt{c d^{2} - b d e + a e^{2}} a b^{3} c^{\frac{7}{2}} d^{5} e - 48 \, \sqrt{c d^{2} - b d e + a e^{2}} a^{2} b c^{\frac{9}{2}} d^{5} e + 3 \, \sqrt{c d^{2} - b d e + a e^{2}} b^{6} c^{\frac{3}{2}} d^{4} e^{2} - 21 \, \sqrt{c d^{2} - b d e + a e^{2}} a b^{4} c^{\frac{5}{2}} d^{4} e^{2} + 24 \, \sqrt{c d^{2} - b d e + a e^{2}} a^{2} b^{2} c^{\frac{7}{2}} d^{4} e^{2} + 48 \, \sqrt{c d^{2} - b d e + a e^{2}} a^{3} c^{\frac{9}{2}} d^{4} e^{2} - \sqrt{c d^{2} - b d e + a e^{2}} b^{7} \sqrt{c} d^{3} e^{3} + 2 \, \sqrt{c d^{2} - b d e + a e^{2}} a b^{5} c^{\frac{3}{2}} d^{3} e^{3} + 32 \, \sqrt{c d^{2} - b d e + a e^{2}} a^{2} b^{3} c^{\frac{5}{2}} d^{3} e^{3} - 96 \, \sqrt{c d^{2} - b d e + a e^{2}} a^{3} b c^{\frac{7}{2}} d^{3} e^{3} + 3 \, \sqrt{c d^{2} - b d e + a e^{2}} a b^{6} \sqrt{c} d^{2} e^{4} - 21 \, \sqrt{c d^{2} - b d e + a e^{2}} a^{2} b^{4} c^{\frac{3}{2}} d^{2} e^{4} + 24 \, \sqrt{c d^{2} - b d e + a e^{2}} a^{3} b^{2} c^{\frac{5}{2}} d^{2} e^{4} + 48 \, \sqrt{c d^{2} - b d e + a e^{2}} a^{4} c^{\frac{7}{2}} d^{2} e^{4} - 3 \, \sqrt{c d^{2} - b d e + a e^{2}} a^{2} b^{5} \sqrt{c} d e^{5} + 24 \, \sqrt{c d^{2} - b d e + a e^{2}} a^{3} b^{3} c^{\frac{3}{2}} d e^{5} - 48 \, \sqrt{c d^{2} - b d e + a e^{2}} a^{4} b c^{\frac{5}{2}} d e^{5} + \sqrt{c d^{2} - b d e + a e^{2}} a^{3} b^{4} \sqrt{c} e^{6} - 8 \, \sqrt{c d^{2} - b d e + a e^{2}} a^{4} b^{2} c^{\frac{3}{2}} e^{6} + 16 \, \sqrt{c d^{2} - b d e + a e^{2}} a^{5} c^{\frac{5}{2}} e^{6}} + \frac{2 \, {\left(\frac{{\left(\frac{{\left(\frac{{\left(\frac{4 \, {\left(8 \, c^{6} d^{7} e^{16} - 28 \, b c^{5} d^{6} e^{17} + 30 \, b^{2} c^{4} d^{5} e^{18} + 48 \, a c^{5} d^{5} e^{18} - 5 \, b^{3} c^{3} d^{4} e^{19} - 120 \, a b c^{4} d^{4} e^{19} - 18 \, b^{4} c^{2} d^{3} e^{20} + 164 \, a b^{2} c^{3} d^{3} e^{20} - 88 \, a^{2} c^{4} d^{3} e^{20} + 18 \, b^{5} c d^{2} e^{21} - 126 \, a b^{3} c^{2} d^{2} e^{21} + 132 \, a^{2} b c^{3} d^{2} e^{21} - 5 \, b^{6} d e^{22} + 24 \, a b^{4} c d e^{22} + 30 \, a^{2} b^{2} c^{2} d e^{22} - 128 \, a^{3} c^{3} d e^{22} + 5 \, a b^{5} e^{23} - 37 \, a^{2} b^{3} c e^{23} + 64 \, a^{3} b c^{2} e^{23}\right)}}{b^{4} c^{3} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 8 \, a b^{2} c^{4} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 16 \, a^{2} c^{5} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 3 \, b^{5} c^{2} d^{5} e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 24 \, a b^{3} c^{3} d^{5} e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 48 \, a^{2} b c^{4} d^{5} e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 3 \, b^{6} c d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 21 \, a b^{4} c^{2} d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 24 \, a^{2} b^{2} c^{3} d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 48 \, a^{3} c^{4} d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - b^{7} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 2 \, a b^{5} c d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 32 \, a^{2} b^{3} c^{2} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 96 \, a^{3} b c^{3} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 3 \, a b^{6} d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 21 \, a^{2} b^{4} c d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 24 \, a^{3} b^{2} c^{2} d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 48 \, a^{4} c^{3} d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 3 \, a^{2} b^{5} d e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 24 \, a^{3} b^{3} c d e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 48 \, a^{4} b c^{2} d e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + a^{3} b^{4} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 8 \, a^{4} b^{2} c e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 16 \, a^{5} c^{2} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right)} + \frac{3 \, {\left(b^{4} c^{2} d^{4} e^{21} - 8 \, a b^{2} c^{3} d^{4} e^{21} + 16 \, a^{2} c^{4} d^{4} e^{21} - 2 \, b^{5} c d^{3} e^{22} + 16 \, a b^{3} c^{2} d^{3} e^{22} - 32 \, a^{2} b c^{3} d^{3} e^{22} + b^{6} d^{2} e^{23} - 6 \, a b^{4} c d^{2} e^{23} + 32 \, a^{3} c^{3} d^{2} e^{23} - 2 \, a b^{5} d e^{24} + 16 \, a^{2} b^{3} c d e^{24} - 32 \, a^{3} b c^{2} d e^{24} + a^{2} b^{4} e^{25} - 8 \, a^{3} b^{2} c e^{25} + 16 \, a^{4} c^{2} e^{25}\right)} e^{\left(-1\right)}}{{\left(b^{4} c^{3} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 8 \, a b^{2} c^{4} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 16 \, a^{2} c^{5} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 3 \, b^{5} c^{2} d^{5} e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 24 \, a b^{3} c^{3} d^{5} e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 48 \, a^{2} b c^{4} d^{5} e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 3 \, b^{6} c d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 21 \, a b^{4} c^{2} d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 24 \, a^{2} b^{2} c^{3} d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 48 \, a^{3} c^{4} d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - b^{7} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 2 \, a b^{5} c d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 32 \, a^{2} b^{3} c^{2} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 96 \, a^{3} b c^{3} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 3 \, a b^{6} d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 21 \, a^{2} b^{4} c d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 24 \, a^{3} b^{2} c^{2} d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 48 \, a^{4} c^{3} d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 3 \, a^{2} b^{5} d e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 24 \, a^{3} b^{3} c d e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 48 \, a^{4} b c^{2} d e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + a^{3} b^{4} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 8 \, a^{4} b^{2} c e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 16 \, a^{5} c^{2} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right)\right)} {\left(x e + d\right)}}\right)} e^{\left(-1\right)}}{x e + d} - \frac{3 \, {\left(32 \, c^{6} d^{6} e^{15} - 96 \, b c^{5} d^{5} e^{16} + 80 \, b^{2} c^{4} d^{4} e^{17} + 160 \, a c^{5} d^{4} e^{17} - 320 \, a b c^{4} d^{3} e^{18} - 46 \, b^{4} c^{2} d^{2} e^{19} + 368 \, a b^{2} c^{3} d^{2} e^{19} - 256 \, a^{2} c^{4} d^{2} e^{19} + 30 \, b^{5} c d e^{20} - 208 \, a b^{3} c^{2} d e^{20} + 256 \, a^{2} b c^{3} d e^{20} - 5 \, b^{6} e^{21} + 30 \, a b^{4} c e^{21} - 16 \, a^{2} b^{2} c^{2} e^{21} - 64 \, a^{3} c^{3} e^{21}\right)}}{b^{4} c^{3} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 8 \, a b^{2} c^{4} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 16 \, a^{2} c^{5} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 3 \, b^{5} c^{2} d^{5} e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 24 \, a b^{3} c^{3} d^{5} e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 48 \, a^{2} b c^{4} d^{5} e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 3 \, b^{6} c d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 21 \, a b^{4} c^{2} d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 24 \, a^{2} b^{2} c^{3} d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 48 \, a^{3} c^{4} d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - b^{7} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 2 \, a b^{5} c d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 32 \, a^{2} b^{3} c^{2} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 96 \, a^{3} b c^{3} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 3 \, a b^{6} d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 21 \, a^{2} b^{4} c d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 24 \, a^{3} b^{2} c^{2} d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 48 \, a^{4} c^{3} d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 3 \, a^{2} b^{5} d e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 24 \, a^{3} b^{3} c d e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 48 \, a^{4} b c^{2} d e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + a^{3} b^{4} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 8 \, a^{4} b^{2} c e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 16 \, a^{5} c^{2} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right)}\right)} e^{\left(-1\right)}}{x e + d} + \frac{6 \, {\left(16 \, c^{6} d^{5} e^{14} - 40 \, b c^{5} d^{4} e^{15} + 22 \, b^{2} c^{4} d^{3} e^{16} + 72 \, a c^{5} d^{3} e^{16} + 7 \, b^{3} c^{3} d^{2} e^{17} - 108 \, a b c^{4} d^{2} e^{17} - 15 \, b^{4} c^{2} d e^{18} + 106 \, a b^{2} c^{3} d e^{18} - 104 \, a^{2} c^{4} d e^{18} + 5 \, b^{5} c e^{19} - 35 \, a b^{3} c^{2} e^{19} + 52 \, a^{2} b c^{3} e^{19}\right)}}{b^{4} c^{3} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 8 \, a b^{2} c^{4} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 16 \, a^{2} c^{5} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 3 \, b^{5} c^{2} d^{5} e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 24 \, a b^{3} c^{3} d^{5} e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 48 \, a^{2} b c^{4} d^{5} e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 3 \, b^{6} c d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 21 \, a b^{4} c^{2} d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 24 \, a^{2} b^{2} c^{3} d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 48 \, a^{3} c^{4} d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - b^{7} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 2 \, a b^{5} c d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 32 \, a^{2} b^{3} c^{2} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 96 \, a^{3} b c^{3} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 3 \, a b^{6} d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 21 \, a^{2} b^{4} c d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 24 \, a^{3} b^{2} c^{2} d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 48 \, a^{4} c^{3} d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 3 \, a^{2} b^{5} d e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 24 \, a^{3} b^{3} c d e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 48 \, a^{4} b c^{2} d e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + a^{3} b^{4} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 8 \, a^{4} b^{2} c e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 16 \, a^{5} c^{2} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right)}\right)} e^{\left(-1\right)}}{x e + d} - \frac{32 \, c^{6} d^{4} e^{13} - 64 \, b c^{5} d^{3} e^{14} + 12 \, b^{2} c^{4} d^{2} e^{15} + 144 \, a c^{5} d^{2} e^{15} + 20 \, b^{3} c^{3} d e^{16} - 144 \, a b c^{4} d e^{16} - 15 \, b^{4} c^{2} e^{17} + 100 \, a b^{2} c^{3} e^{17} - 128 \, a^{2} c^{4} e^{17}}{b^{4} c^{3} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 8 \, a b^{2} c^{4} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 16 \, a^{2} c^{5} d^{6} e^{11} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 3 \, b^{5} c^{2} d^{5} e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 24 \, a b^{3} c^{3} d^{5} e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 48 \, a^{2} b c^{4} d^{5} e^{12} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 3 \, b^{6} c d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 21 \, a b^{4} c^{2} d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 24 \, a^{2} b^{2} c^{3} d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 48 \, a^{3} c^{4} d^{4} e^{13} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - b^{7} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 2 \, a b^{5} c d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 32 \, a^{2} b^{3} c^{2} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 96 \, a^{3} b c^{3} d^{3} e^{14} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 3 \, a b^{6} d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 21 \, a^{2} b^{4} c d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 24 \, a^{3} b^{2} c^{2} d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 48 \, a^{4} c^{3} d^{2} e^{15} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 3 \, a^{2} b^{5} d e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 24 \, a^{3} b^{3} c d e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 48 \, a^{4} b c^{2} d e^{16} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + a^{3} b^{4} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right) - 8 \, a^{4} b^{2} c e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right) + 16 \, a^{5} c^{2} e^{17} \mathrm{sgn}\left(\frac{1}{x e + d}\right)}\right)}}{{\left(c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{b e}{x e + d} - \frac{b d e}{{\left(x e + d\right)}^{2}} + \frac{a e^{2}}{{\left(x e + d\right)}^{2}}\right)}^{\frac{3}{2}}} + \frac{15 \, {\left(2 \, c d e^{7} - b e^{8}\right)} \log\left({\left| -2 \, c d + b e + 2 \, \sqrt{c d^{2} - b d e + a e^{2}} {\left(\sqrt{c - \frac{2 \, c d}{x e + d} + \frac{c d^{2}}{{\left(x e + d\right)}^{2}} + \frac{b e}{x e + d} - \frac{b d e}{{\left(x e + d\right)}^{2}} + \frac{a e^{2}}{{\left(x e + d\right)}^{2}}} + \frac{\sqrt{c d^{2} e^{2} - b d e^{3} + a e^{4}} e^{\left(-1\right)}}{x e + d}\right)} \right|}\right)}{{\left(c^{3} d^{6} e - 3 \, b c^{2} d^{5} e^{2} + 3 \, b^{2} c d^{4} e^{3} + 3 \, a c^{2} d^{4} e^{3} - b^{3} d^{3} e^{4} - 6 \, a b c d^{3} e^{4} + 3 \, a b^{2} d^{2} e^{5} + 3 \, a^{2} c d^{2} e^{5} - 3 \, a^{2} b d e^{6} + a^{3} e^{7}\right)} \sqrt{c d^{2} - b d e + a e^{2}} \mathrm{sgn}\left(\frac{1}{x e + d}\right)}\right)} e^{\left(-2\right)}"," ",0,"-1/6*((64*sqrt(c*d^2 - b*d*e + a*e^2)*c^5*d^4*e^2 - 128*sqrt(c*d^2 - b*d*e + a*e^2)*b*c^4*d^3*e^3 + 24*sqrt(c*d^2 - b*d*e + a*e^2)*b^2*c^3*d^2*e^4 + 288*sqrt(c*d^2 - b*d*e + a*e^2)*a*c^4*d^2*e^4 - 30*b^4*c^(3/2)*d*e^6*log(abs(-2*c*d + b*e + 2*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c))) + 240*a*b^2*c^(5/2)*d*e^6*log(abs(-2*c*d + b*e + 2*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c))) - 480*a^2*c^(7/2)*d*e^6*log(abs(-2*c*d + b*e + 2*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c))) + 40*sqrt(c*d^2 - b*d*e + a*e^2)*b^3*c^2*d*e^5 - 288*sqrt(c*d^2 - b*d*e + a*e^2)*a*b*c^3*d*e^5 + 15*b^5*sqrt(c)*e^7*log(abs(-2*c*d + b*e + 2*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c))) - 120*a*b^3*c^(3/2)*e^7*log(abs(-2*c*d + b*e + 2*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c))) + 240*a^2*b*c^(5/2)*e^7*log(abs(-2*c*d + b*e + 2*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c))) - 30*sqrt(c*d^2 - b*d*e + a*e^2)*b^4*c*e^6 + 200*sqrt(c*d^2 - b*d*e + a*e^2)*a*b^2*c^2*e^6 - 256*sqrt(c*d^2 - b*d*e + a*e^2)*a^2*c^3*e^6)*sgn(1/(x*e + d))/(sqrt(c*d^2 - b*d*e + a*e^2)*b^4*c^(7/2)*d^6 - 8*sqrt(c*d^2 - b*d*e + a*e^2)*a*b^2*c^(9/2)*d^6 + 16*sqrt(c*d^2 - b*d*e + a*e^2)*a^2*c^(11/2)*d^6 - 3*sqrt(c*d^2 - b*d*e + a*e^2)*b^5*c^(5/2)*d^5*e + 24*sqrt(c*d^2 - b*d*e + a*e^2)*a*b^3*c^(7/2)*d^5*e - 48*sqrt(c*d^2 - b*d*e + a*e^2)*a^2*b*c^(9/2)*d^5*e + 3*sqrt(c*d^2 - b*d*e + a*e^2)*b^6*c^(3/2)*d^4*e^2 - 21*sqrt(c*d^2 - b*d*e + a*e^2)*a*b^4*c^(5/2)*d^4*e^2 + 24*sqrt(c*d^2 - b*d*e + a*e^2)*a^2*b^2*c^(7/2)*d^4*e^2 + 48*sqrt(c*d^2 - b*d*e + a*e^2)*a^3*c^(9/2)*d^4*e^2 - sqrt(c*d^2 - b*d*e + a*e^2)*b^7*sqrt(c)*d^3*e^3 + 2*sqrt(c*d^2 - b*d*e + a*e^2)*a*b^5*c^(3/2)*d^3*e^3 + 32*sqrt(c*d^2 - b*d*e + a*e^2)*a^2*b^3*c^(5/2)*d^3*e^3 - 96*sqrt(c*d^2 - b*d*e + a*e^2)*a^3*b*c^(7/2)*d^3*e^3 + 3*sqrt(c*d^2 - b*d*e + a*e^2)*a*b^6*sqrt(c)*d^2*e^4 - 21*sqrt(c*d^2 - b*d*e + a*e^2)*a^2*b^4*c^(3/2)*d^2*e^4 + 24*sqrt(c*d^2 - b*d*e + a*e^2)*a^3*b^2*c^(5/2)*d^2*e^4 + 48*sqrt(c*d^2 - b*d*e + a*e^2)*a^4*c^(7/2)*d^2*e^4 - 3*sqrt(c*d^2 - b*d*e + a*e^2)*a^2*b^5*sqrt(c)*d*e^5 + 24*sqrt(c*d^2 - b*d*e + a*e^2)*a^3*b^3*c^(3/2)*d*e^5 - 48*sqrt(c*d^2 - b*d*e + a*e^2)*a^4*b*c^(5/2)*d*e^5 + sqrt(c*d^2 - b*d*e + a*e^2)*a^3*b^4*sqrt(c)*e^6 - 8*sqrt(c*d^2 - b*d*e + a*e^2)*a^4*b^2*c^(3/2)*e^6 + 16*sqrt(c*d^2 - b*d*e + a*e^2)*a^5*c^(5/2)*e^6) + 2*((((4*(8*c^6*d^7*e^16 - 28*b*c^5*d^6*e^17 + 30*b^2*c^4*d^5*e^18 + 48*a*c^5*d^5*e^18 - 5*b^3*c^3*d^4*e^19 - 120*a*b*c^4*d^4*e^19 - 18*b^4*c^2*d^3*e^20 + 164*a*b^2*c^3*d^3*e^20 - 88*a^2*c^4*d^3*e^20 + 18*b^5*c*d^2*e^21 - 126*a*b^3*c^2*d^2*e^21 + 132*a^2*b*c^3*d^2*e^21 - 5*b^6*d*e^22 + 24*a*b^4*c*d*e^22 + 30*a^2*b^2*c^2*d*e^22 - 128*a^3*c^3*d*e^22 + 5*a*b^5*e^23 - 37*a^2*b^3*c*e^23 + 64*a^3*b*c^2*e^23)/(b^4*c^3*d^6*e^11*sgn(1/(x*e + d)) - 8*a*b^2*c^4*d^6*e^11*sgn(1/(x*e + d)) + 16*a^2*c^5*d^6*e^11*sgn(1/(x*e + d)) - 3*b^5*c^2*d^5*e^12*sgn(1/(x*e + d)) + 24*a*b^3*c^3*d^5*e^12*sgn(1/(x*e + d)) - 48*a^2*b*c^4*d^5*e^12*sgn(1/(x*e + d)) + 3*b^6*c*d^4*e^13*sgn(1/(x*e + d)) - 21*a*b^4*c^2*d^4*e^13*sgn(1/(x*e + d)) + 24*a^2*b^2*c^3*d^4*e^13*sgn(1/(x*e + d)) + 48*a^3*c^4*d^4*e^13*sgn(1/(x*e + d)) - b^7*d^3*e^14*sgn(1/(x*e + d)) + 2*a*b^5*c*d^3*e^14*sgn(1/(x*e + d)) + 32*a^2*b^3*c^2*d^3*e^14*sgn(1/(x*e + d)) - 96*a^3*b*c^3*d^3*e^14*sgn(1/(x*e + d)) + 3*a*b^6*d^2*e^15*sgn(1/(x*e + d)) - 21*a^2*b^4*c*d^2*e^15*sgn(1/(x*e + d)) + 24*a^3*b^2*c^2*d^2*e^15*sgn(1/(x*e + d)) + 48*a^4*c^3*d^2*e^15*sgn(1/(x*e + d)) - 3*a^2*b^5*d*e^16*sgn(1/(x*e + d)) + 24*a^3*b^3*c*d*e^16*sgn(1/(x*e + d)) - 48*a^4*b*c^2*d*e^16*sgn(1/(x*e + d)) + a^3*b^4*e^17*sgn(1/(x*e + d)) - 8*a^4*b^2*c*e^17*sgn(1/(x*e + d)) + 16*a^5*c^2*e^17*sgn(1/(x*e + d))) + 3*(b^4*c^2*d^4*e^21 - 8*a*b^2*c^3*d^4*e^21 + 16*a^2*c^4*d^4*e^21 - 2*b^5*c*d^3*e^22 + 16*a*b^3*c^2*d^3*e^22 - 32*a^2*b*c^3*d^3*e^22 + b^6*d^2*e^23 - 6*a*b^4*c*d^2*e^23 + 32*a^3*c^3*d^2*e^23 - 2*a*b^5*d*e^24 + 16*a^2*b^3*c*d*e^24 - 32*a^3*b*c^2*d*e^24 + a^2*b^4*e^25 - 8*a^3*b^2*c*e^25 + 16*a^4*c^2*e^25)*e^(-1)/((b^4*c^3*d^6*e^11*sgn(1/(x*e + d)) - 8*a*b^2*c^4*d^6*e^11*sgn(1/(x*e + d)) + 16*a^2*c^5*d^6*e^11*sgn(1/(x*e + d)) - 3*b^5*c^2*d^5*e^12*sgn(1/(x*e + d)) + 24*a*b^3*c^3*d^5*e^12*sgn(1/(x*e + d)) - 48*a^2*b*c^4*d^5*e^12*sgn(1/(x*e + d)) + 3*b^6*c*d^4*e^13*sgn(1/(x*e + d)) - 21*a*b^4*c^2*d^4*e^13*sgn(1/(x*e + d)) + 24*a^2*b^2*c^3*d^4*e^13*sgn(1/(x*e + d)) + 48*a^3*c^4*d^4*e^13*sgn(1/(x*e + d)) - b^7*d^3*e^14*sgn(1/(x*e + d)) + 2*a*b^5*c*d^3*e^14*sgn(1/(x*e + d)) + 32*a^2*b^3*c^2*d^3*e^14*sgn(1/(x*e + d)) - 96*a^3*b*c^3*d^3*e^14*sgn(1/(x*e + d)) + 3*a*b^6*d^2*e^15*sgn(1/(x*e + d)) - 21*a^2*b^4*c*d^2*e^15*sgn(1/(x*e + d)) + 24*a^3*b^2*c^2*d^2*e^15*sgn(1/(x*e + d)) + 48*a^4*c^3*d^2*e^15*sgn(1/(x*e + d)) - 3*a^2*b^5*d*e^16*sgn(1/(x*e + d)) + 24*a^3*b^3*c*d*e^16*sgn(1/(x*e + d)) - 48*a^4*b*c^2*d*e^16*sgn(1/(x*e + d)) + a^3*b^4*e^17*sgn(1/(x*e + d)) - 8*a^4*b^2*c*e^17*sgn(1/(x*e + d)) + 16*a^5*c^2*e^17*sgn(1/(x*e + d)))*(x*e + d)))*e^(-1)/(x*e + d) - 3*(32*c^6*d^6*e^15 - 96*b*c^5*d^5*e^16 + 80*b^2*c^4*d^4*e^17 + 160*a*c^5*d^4*e^17 - 320*a*b*c^4*d^3*e^18 - 46*b^4*c^2*d^2*e^19 + 368*a*b^2*c^3*d^2*e^19 - 256*a^2*c^4*d^2*e^19 + 30*b^5*c*d*e^20 - 208*a*b^3*c^2*d*e^20 + 256*a^2*b*c^3*d*e^20 - 5*b^6*e^21 + 30*a*b^4*c*e^21 - 16*a^2*b^2*c^2*e^21 - 64*a^3*c^3*e^21)/(b^4*c^3*d^6*e^11*sgn(1/(x*e + d)) - 8*a*b^2*c^4*d^6*e^11*sgn(1/(x*e + d)) + 16*a^2*c^5*d^6*e^11*sgn(1/(x*e + d)) - 3*b^5*c^2*d^5*e^12*sgn(1/(x*e + d)) + 24*a*b^3*c^3*d^5*e^12*sgn(1/(x*e + d)) - 48*a^2*b*c^4*d^5*e^12*sgn(1/(x*e + d)) + 3*b^6*c*d^4*e^13*sgn(1/(x*e + d)) - 21*a*b^4*c^2*d^4*e^13*sgn(1/(x*e + d)) + 24*a^2*b^2*c^3*d^4*e^13*sgn(1/(x*e + d)) + 48*a^3*c^4*d^4*e^13*sgn(1/(x*e + d)) - b^7*d^3*e^14*sgn(1/(x*e + d)) + 2*a*b^5*c*d^3*e^14*sgn(1/(x*e + d)) + 32*a^2*b^3*c^2*d^3*e^14*sgn(1/(x*e + d)) - 96*a^3*b*c^3*d^3*e^14*sgn(1/(x*e + d)) + 3*a*b^6*d^2*e^15*sgn(1/(x*e + d)) - 21*a^2*b^4*c*d^2*e^15*sgn(1/(x*e + d)) + 24*a^3*b^2*c^2*d^2*e^15*sgn(1/(x*e + d)) + 48*a^4*c^3*d^2*e^15*sgn(1/(x*e + d)) - 3*a^2*b^5*d*e^16*sgn(1/(x*e + d)) + 24*a^3*b^3*c*d*e^16*sgn(1/(x*e + d)) - 48*a^4*b*c^2*d*e^16*sgn(1/(x*e + d)) + a^3*b^4*e^17*sgn(1/(x*e + d)) - 8*a^4*b^2*c*e^17*sgn(1/(x*e + d)) + 16*a^5*c^2*e^17*sgn(1/(x*e + d))))*e^(-1)/(x*e + d) + 6*(16*c^6*d^5*e^14 - 40*b*c^5*d^4*e^15 + 22*b^2*c^4*d^3*e^16 + 72*a*c^5*d^3*e^16 + 7*b^3*c^3*d^2*e^17 - 108*a*b*c^4*d^2*e^17 - 15*b^4*c^2*d*e^18 + 106*a*b^2*c^3*d*e^18 - 104*a^2*c^4*d*e^18 + 5*b^5*c*e^19 - 35*a*b^3*c^2*e^19 + 52*a^2*b*c^3*e^19)/(b^4*c^3*d^6*e^11*sgn(1/(x*e + d)) - 8*a*b^2*c^4*d^6*e^11*sgn(1/(x*e + d)) + 16*a^2*c^5*d^6*e^11*sgn(1/(x*e + d)) - 3*b^5*c^2*d^5*e^12*sgn(1/(x*e + d)) + 24*a*b^3*c^3*d^5*e^12*sgn(1/(x*e + d)) - 48*a^2*b*c^4*d^5*e^12*sgn(1/(x*e + d)) + 3*b^6*c*d^4*e^13*sgn(1/(x*e + d)) - 21*a*b^4*c^2*d^4*e^13*sgn(1/(x*e + d)) + 24*a^2*b^2*c^3*d^4*e^13*sgn(1/(x*e + d)) + 48*a^3*c^4*d^4*e^13*sgn(1/(x*e + d)) - b^7*d^3*e^14*sgn(1/(x*e + d)) + 2*a*b^5*c*d^3*e^14*sgn(1/(x*e + d)) + 32*a^2*b^3*c^2*d^3*e^14*sgn(1/(x*e + d)) - 96*a^3*b*c^3*d^3*e^14*sgn(1/(x*e + d)) + 3*a*b^6*d^2*e^15*sgn(1/(x*e + d)) - 21*a^2*b^4*c*d^2*e^15*sgn(1/(x*e + d)) + 24*a^3*b^2*c^2*d^2*e^15*sgn(1/(x*e + d)) + 48*a^4*c^3*d^2*e^15*sgn(1/(x*e + d)) - 3*a^2*b^5*d*e^16*sgn(1/(x*e + d)) + 24*a^3*b^3*c*d*e^16*sgn(1/(x*e + d)) - 48*a^4*b*c^2*d*e^16*sgn(1/(x*e + d)) + a^3*b^4*e^17*sgn(1/(x*e + d)) - 8*a^4*b^2*c*e^17*sgn(1/(x*e + d)) + 16*a^5*c^2*e^17*sgn(1/(x*e + d))))*e^(-1)/(x*e + d) - (32*c^6*d^4*e^13 - 64*b*c^5*d^3*e^14 + 12*b^2*c^4*d^2*e^15 + 144*a*c^5*d^2*e^15 + 20*b^3*c^3*d*e^16 - 144*a*b*c^4*d*e^16 - 15*b^4*c^2*e^17 + 100*a*b^2*c^3*e^17 - 128*a^2*c^4*e^17)/(b^4*c^3*d^6*e^11*sgn(1/(x*e + d)) - 8*a*b^2*c^4*d^6*e^11*sgn(1/(x*e + d)) + 16*a^2*c^5*d^6*e^11*sgn(1/(x*e + d)) - 3*b^5*c^2*d^5*e^12*sgn(1/(x*e + d)) + 24*a*b^3*c^3*d^5*e^12*sgn(1/(x*e + d)) - 48*a^2*b*c^4*d^5*e^12*sgn(1/(x*e + d)) + 3*b^6*c*d^4*e^13*sgn(1/(x*e + d)) - 21*a*b^4*c^2*d^4*e^13*sgn(1/(x*e + d)) + 24*a^2*b^2*c^3*d^4*e^13*sgn(1/(x*e + d)) + 48*a^3*c^4*d^4*e^13*sgn(1/(x*e + d)) - b^7*d^3*e^14*sgn(1/(x*e + d)) + 2*a*b^5*c*d^3*e^14*sgn(1/(x*e + d)) + 32*a^2*b^3*c^2*d^3*e^14*sgn(1/(x*e + d)) - 96*a^3*b*c^3*d^3*e^14*sgn(1/(x*e + d)) + 3*a*b^6*d^2*e^15*sgn(1/(x*e + d)) - 21*a^2*b^4*c*d^2*e^15*sgn(1/(x*e + d)) + 24*a^3*b^2*c^2*d^2*e^15*sgn(1/(x*e + d)) + 48*a^4*c^3*d^2*e^15*sgn(1/(x*e + d)) - 3*a^2*b^5*d*e^16*sgn(1/(x*e + d)) + 24*a^3*b^3*c*d*e^16*sgn(1/(x*e + d)) - 48*a^4*b*c^2*d*e^16*sgn(1/(x*e + d)) + a^3*b^4*e^17*sgn(1/(x*e + d)) - 8*a^4*b^2*c*e^17*sgn(1/(x*e + d)) + 16*a^5*c^2*e^17*sgn(1/(x*e + d))))/(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + b*e/(x*e + d) - b*d*e/(x*e + d)^2 + a*e^2/(x*e + d)^2)^(3/2) + 15*(2*c*d*e^7 - b*e^8)*log(abs(-2*c*d + b*e + 2*sqrt(c*d^2 - b*d*e + a*e^2)*(sqrt(c - 2*c*d/(x*e + d) + c*d^2/(x*e + d)^2 + b*e/(x*e + d) - b*d*e/(x*e + d)^2 + a*e^2/(x*e + d)^2) + sqrt(c*d^2*e^2 - b*d*e^3 + a*e^4)*e^(-1)/(x*e + d))))/((c^3*d^6*e - 3*b*c^2*d^5*e^2 + 3*b^2*c*d^4*e^3 + 3*a*c^2*d^4*e^3 - b^3*d^3*e^4 - 6*a*b*c*d^3*e^4 + 3*a*b^2*d^2*e^5 + 3*a^2*c*d^2*e^5 - 3*a^2*b*d*e^6 + a^3*e^7)*sqrt(c*d^2 - b*d*e + a*e^2)*sgn(1/(x*e + d))))*e^(-2)","B",0
2399,-1,0,0,0.000000," ","integrate(1/(e*x+d)^3/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2400,1,21,0,0.187980," ","integrate((3+x)/(-x^2-4*x+5)^(1/2),x, algorithm=""giac"")","-\sqrt{-x^{2} - 4 \, x + 5} + \arcsin\left(\frac{1}{3} \, x + \frac{2}{3}\right)"," ",0,"-sqrt(-x^2 - 4*x + 5) + arcsin(1/3*x + 2/3)","A",0
2401,1,23,0,0.239575," ","integrate(1/2*(5-4*x)/(-x^2+3*x-2)^(1/2),x, algorithm=""giac"")","2 \, \sqrt{-x^{2} + 3 \, x - 2} - \frac{1}{2} \, \arcsin\left(2 \, x - 3\right)"," ",0,"2*sqrt(-x^2 + 3*x - 2) - 1/2*arcsin(2*x - 3)","A",0
2402,1,31,0,0.173507," ","integrate((3+2*x)/(x^2+2*x+5)^(1/2),x, algorithm=""giac"")","2 \, \sqrt{x^{2} + 2 \, x + 5} - \log\left(-x + \sqrt{x^{2} + 2 \, x + 5} - 1\right)"," ",0,"2*sqrt(x^2 + 2*x + 5) - log(-x + sqrt(x^2 + 2*x + 5) - 1)","A",0
2403,1,30,0,0.226463," ","integrate((-1+x)/(x^2-4*x+3)^(1/2),x, algorithm=""giac"")","\sqrt{x^{2} - 4 \, x + 3} - \log\left({\left| -x + \sqrt{x^{2} - 4 \, x + 3} + 2 \right|}\right)"," ",0,"sqrt(x^2 - 4*x + 3) - log(abs(-x + sqrt(x^2 - 4*x + 3) + 2))","A",0
2404,1,18,0,0.174069," ","integrate(1/(1-x)/(x^2+2*x-4)^(1/2),x, algorithm=""giac"")","-2 \, \arctan\left(-x + \sqrt{x^{2} + 2 \, x - 4} + 1\right)"," ",0,"-2*arctan(-x + sqrt(x^2 + 2*x - 4) + 1)","A",0
2405,1,18,0,0.173794," ","integrate(1/(-2+x)/(x^2-4*x+3)^(1/2),x, algorithm=""giac"")","2 \, \arctan\left(-x + \sqrt{x^{2} - 4 \, x + 3} + 2\right)"," ",0,"2*arctan(-x + sqrt(x^2 - 4*x + 3) + 2)","A",0
2406,1,19,0,0.237095," ","integrate((1+x)/(x^2+3*x+2)^(3/2),x, algorithm=""giac"")","\frac{2}{x - \sqrt{x^{2} + 3 \, x + 2} + 2}"," ",0,"2/(x - sqrt(x^2 + 3*x + 2) + 2)","A",0
2407,-2,0,0,0.000000," ","integrate(2/(e*x+d)/(1/c*b^2+4*b*x+4*c*x^2)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(2*c*t_nostep+b)]Discontinuities at zeroes of 2*c*t_nostep+b were not checkedsym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
2408,1,65,0,0.235600," ","integrate(1/(1/2*b*e/c+e*x)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\frac{4 \, c \arctan\left(-\frac{2 \, {\left(\sqrt{c} x - \sqrt{c x^{2} + b x + a}\right)} c + b \sqrt{c}}{\sqrt{b^{2} c - 4 \, a c^{2}}}\right) e^{\left(-1\right)}}{\sqrt{b^{2} c - 4 \, a c^{2}}}"," ",0,"4*c*arctan(-(2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*c + b*sqrt(c))/sqrt(b^2*c - 4*a*c^2))*e^(-1)/sqrt(b^2*c - 4*a*c^2)","A",0
2409,-2,0,0,0.000000," ","integrate(1/(e*x+d)/((b*d*e-c*d^2)/e^2+b*x+c*x^2)^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: 2*exp(2)*2/2/sqrt(-c*d^2*exp(2)^2-b*d*exp(1)^3*exp(2)+b*d*exp(1)*exp(2)^2+c*d^2*exp(1)^2*exp(2))*atan((-d*sqrt(c)*exp(2)+(sqrt(c*x^2+b*x-(c*d^2-b*d*exp(1))/exp(2))-sqrt(c)*x)*exp(1)*exp(2))/sqrt(-c*d^2*exp(2)^2-b*d*exp(1)^3*exp(2)+b*d*exp(1)*exp(2)^2+c*d^2*exp(1)^2*exp(2)))","F(-2)",0
2410,1,44,0,0.200685," ","integrate(2/(1/2*b*e/c+e*x)/(1/c*b^2+4*b*x+4*c*x^2)^(1/2),x, algorithm=""giac"")","\frac{4 \, \sqrt{c} e^{\left(-1\right)}}{{\left(2 \, \sqrt{c} x - \sqrt{4 \, c x^{2} + 4 \, b x + \frac{b^{2}}{c}}\right)} \sqrt{c} + b}"," ",0,"4*sqrt(c)*e^(-1)/((2*sqrt(c)*x - sqrt(4*c*x^2 + 4*b*x + b^2/c))*sqrt(c) + b)","A",0
2411,1,48,0,0.181697," ","integrate(x/(3*x^2+4*x+2)^(1/2),x, algorithm=""giac"")","\frac{2}{9} \, \sqrt{3} \log\left(-\sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 4 \, x + 2}\right)} - 2\right) + \frac{1}{3} \, \sqrt{3 \, x^{2} + 4 \, x + 2}"," ",0,"2/9*sqrt(3)*log(-sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 4*x + 2)) - 2) + 1/3*sqrt(3*x^2 + 4*x + 2)","A",0
2412,1,31,0,0.198940," ","integrate(x/(-3*x^2+4*x+2)^(1/2),x, algorithm=""giac"")","\frac{2}{9} \, \sqrt{3} \arcsin\left(\frac{1}{10} \, \sqrt{10} {\left(3 \, x - 2\right)}\right) - \frac{1}{3} \, \sqrt{-3 \, x^{2} + 4 \, x + 2}"," ",0,"2/9*sqrt(3)*arcsin(1/10*sqrt(10)*(3*x - 2)) - 1/3*sqrt(-3*x^2 + 4*x + 2)","A",0
2413,1,49,0,0.211852," ","integrate(x/(3*x^2+5*x+2)^(1/2),x, algorithm=""giac"")","\frac{5}{18} \, \sqrt{3} \log\left({\left| -2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x + 2}\right)} - 5 \right|}\right) + \frac{1}{3} \, \sqrt{3 \, x^{2} + 5 \, x + 2}"," ",0,"5/18*sqrt(3)*log(abs(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x + 2)) - 5)) + 1/3*sqrt(3*x^2 + 5*x + 2)","A",0
2414,1,26,0,0.210069," ","integrate(x/(-3*x^2+5*x+2)^(1/2),x, algorithm=""giac"")","\frac{5}{18} \, \sqrt{3} \arcsin\left(\frac{6}{7} \, x - \frac{5}{7}\right) - \frac{1}{3} \, \sqrt{-3 \, x^{2} + 5 \, x + 2}"," ",0,"5/18*sqrt(3)*arcsin(6/7*x - 5/7) - 1/3*sqrt(-3*x^2 + 5*x + 2)","A",0
2415,1,49,0,0.227652," ","integrate(x/(3*x^2+4*x-2)^(1/2),x, algorithm=""giac"")","\frac{2}{9} \, \sqrt{3} \log\left({\left| -\sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 4 \, x - 2}\right)} - 2 \right|}\right) + \frac{1}{3} \, \sqrt{3 \, x^{2} + 4 \, x - 2}"," ",0,"2/9*sqrt(3)*log(abs(-sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 4*x - 2)) - 2)) + 1/3*sqrt(3*x^2 + 4*x - 2)","A",0
2416,0,0,0,0.000000," ","integrate(x/(-3*x^2+4*x-2)^(1/2),x, algorithm=""giac"")","\int \frac{x}{\sqrt{-3 \, x^{2} + 4 \, x - 2}}\,{d x}"," ",0,"integrate(x/sqrt(-3*x^2 + 4*x - 2), x)","F",0
2417,1,49,0,0.217775," ","integrate(x/(3*x^2+5*x-2)^(1/2),x, algorithm=""giac"")","\frac{5}{18} \, \sqrt{3} \log\left({\left| -2 \, \sqrt{3} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x - 2}\right)} - 5 \right|}\right) + \frac{1}{3} \, \sqrt{3 \, x^{2} + 5 \, x - 2}"," ",0,"5/18*sqrt(3)*log(abs(-2*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 5*x - 2)) - 5)) + 1/3*sqrt(3*x^2 + 5*x - 2)","A",0
2418,1,26,0,0.289103," ","integrate(x/(-3*x^2+5*x-2)^(1/2),x, algorithm=""giac"")","\frac{5}{18} \, \sqrt{3} \arcsin\left(6 \, x - 5\right) - \frac{1}{3} \, \sqrt{-3 \, x^{2} + 5 \, x - 2}"," ",0,"5/18*sqrt(3)*arcsin(6*x - 5) - 1/3*sqrt(-3*x^2 + 5*x - 2)","A",0
2419,1,21,0,0.197785," ","integrate(1/x/((2+3*x)^2)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \, {\left(\log\left({\left| 3 \, x + 2 \right|}\right) - \log\left({\left| x \right|}\right)\right)} \mathrm{sgn}\left(3 \, x + 2\right)"," ",0,"-1/2*(log(abs(3*x + 2)) - log(abs(x)))*sgn(3*x + 2)","A",0
2420,1,21,0,0.153986," ","integrate(1/x/((-2+3*x)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, {\left(\log\left({\left| 3 \, x - 2 \right|}\right) - \log\left({\left| x \right|}\right)\right)} \mathrm{sgn}\left(3 \, x - 2\right)"," ",0,"1/2*(log(abs(3*x - 2)) - log(abs(x)))*sgn(3*x - 2)","A",0
2421,0,0,0,0.000000," ","integrate(1/x/(-(-2+3*x)^2)^(1/2),x, algorithm=""giac"")","\mathit{undef}"," ",0,"undef","F",0
2422,0,0,0,0.000000," ","integrate(1/x/(-(2+3*x)^2)^(1/2),x, algorithm=""giac"")","\mathit{undef}"," ",0,"undef","F",0
2423,1,28,0,0.149012," ","integrate(1/x/((b*x+a)^2)^(1/2),x, algorithm=""giac"")","-{\left(\frac{\log\left({\left| b x + a \right|}\right)}{a} - \frac{\log\left({\left| x \right|}\right)}{a}\right)} \mathrm{sgn}\left(b x + a\right)"," ",0,"-(log(abs(b*x + a))/a - log(abs(x))/a)*sgn(b*x + a)","A",0
2424,1,31,0,0.154518," ","integrate(1/x/((b*x-a)^2)^(1/2),x, algorithm=""giac"")","{\left(\frac{\log\left({\left| b x - a \right|}\right)}{a} - \frac{\log\left({\left| x \right|}\right)}{a}\right)} \mathrm{sgn}\left(b x - a\right)"," ",0,"(log(abs(b*x - a))/a - log(abs(x))/a)*sgn(b*x - a)","A",0
2425,0,0,0,0.000000," ","integrate(1/x/(-(b*x-a)^2)^(1/2),x, algorithm=""giac"")","\mathit{undef}"," ",0,"undef","F",0
2426,0,0,0,0.000000," ","integrate(1/x/(-(b*x+a)^2)^(1/2),x, algorithm=""giac"")","\mathit{undef}"," ",0,"undef","F",0
2427,1,32,0,0.163996," ","integrate(x*(-x^2-2*x+3)^(1/2),x, algorithm=""giac"")","\frac{1}{6} \, {\left({\left(2 \, x + 1\right)} x - 9\right)} \sqrt{-x^{2} - 2 \, x + 3} - 2 \, \arcsin\left(\frac{1}{2} \, x + \frac{1}{2}\right)"," ",0,"1/6*((2*x + 1)*x - 9)*sqrt(-x^2 - 2*x + 3) - 2*arcsin(1/2*x + 1/2)","A",0
2428,1,32,0,0.164812," ","integrate(x*(-x^2+2*x+8)^(1/2),x, algorithm=""giac"")","\frac{1}{6} \, {\left({\left(2 \, x - 1\right)} x - 19\right)} \sqrt{-x^{2} + 2 \, x + 8} + \frac{9}{2} \, \arcsin\left(\frac{1}{3} \, x - \frac{1}{3}\right)"," ",0,"1/6*((2*x - 1)*x - 19)*sqrt(-x^2 + 2*x + 8) + 9/2*arcsin(1/3*x - 1/3)","A",0
2429,1,40,0,0.187908," ","integrate(x*(x^2+2*x+4)^(1/2),x, algorithm=""giac"")","\frac{1}{6} \, {\left({\left(2 \, x + 1\right)} x + 5\right)} \sqrt{x^{2} + 2 \, x + 4} + \frac{3}{2} \, \log\left(-x + \sqrt{x^{2} + 2 \, x + 4} - 1\right)"," ",0,"1/6*((2*x + 1)*x + 5)*sqrt(x^2 + 2*x + 4) + 3/2*log(-x + sqrt(x^2 + 2*x + 4) - 1)","A",0
2430,1,60,0,0.223185," ","integrate(1/x/(3*x^2+4*x+2)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{2} \log\left(-\sqrt{3} x + \sqrt{2} + \sqrt{3 \, x^{2} + 4 \, x + 2}\right) + \frac{1}{2} \, \sqrt{2} \log\left({\left| -\sqrt{3} x - \sqrt{2} + \sqrt{3 \, x^{2} + 4 \, x + 2} \right|}\right)"," ",0,"-1/2*sqrt(2)*log(-sqrt(3)*x + sqrt(2) + sqrt(3*x^2 + 4*x + 2)) + 1/2*sqrt(2)*log(abs(-sqrt(3)*x - sqrt(2) + sqrt(3*x^2 + 4*x + 2)))","B",0
2431,1,98,0,0.352190," ","integrate(1/x/(-3*x^2+4*x+2)^(1/2),x, algorithm=""giac"")","-\frac{1}{6} \, \sqrt{6} \sqrt{3} \log\left(\frac{{\left| -14 \, \sqrt{10} - 14 \, \sqrt{6} + \frac{28 \, {\left(\sqrt{3} \sqrt{-3 \, x^{2} + 4 \, x + 2} - \sqrt{10}\right)}}{3 \, x - 2} \right|}}{{\left| -14 \, \sqrt{10} + 14 \, \sqrt{6} + \frac{28 \, {\left(\sqrt{3} \sqrt{-3 \, x^{2} + 4 \, x + 2} - \sqrt{10}\right)}}{3 \, x - 2} \right|}}\right)"," ",0,"-1/6*sqrt(6)*sqrt(3)*log(abs(-14*sqrt(10) - 14*sqrt(6) + 28*(sqrt(3)*sqrt(-3*x^2 + 4*x + 2) - sqrt(10))/(3*x - 2))/abs(-14*sqrt(10) + 14*sqrt(6) + 28*(sqrt(3)*sqrt(-3*x^2 + 4*x + 2) - sqrt(10))/(3*x - 2)))","B",0
2432,1,61,0,0.282597," ","integrate(1/x/(3*x^2+5*x+2)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{2} \log\left({\left| -\sqrt{3} x + \sqrt{2} + \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}\right) + \frac{1}{2} \, \sqrt{2} \log\left({\left| -\sqrt{3} x - \sqrt{2} + \sqrt{3 \, x^{2} + 5 \, x + 2} \right|}\right)"," ",0,"-1/2*sqrt(2)*log(abs(-sqrt(3)*x + sqrt(2) + sqrt(3*x^2 + 5*x + 2))) + 1/2*sqrt(2)*log(abs(-sqrt(3)*x - sqrt(2) + sqrt(3*x^2 + 5*x + 2)))","B",0
2433,1,84,0,0.302024," ","integrate(1/x/(-3*x^2+5*x+2)^(1/2),x, algorithm=""giac"")","-\frac{1}{6} \, \sqrt{6} \sqrt{3} \log\left(\frac{{\left| -4 \, \sqrt{6} + \frac{10 \, {\left(2 \, \sqrt{3} \sqrt{-3 \, x^{2} + 5 \, x + 2} - 7\right)}}{6 \, x - 5} - 14 \right|}}{{\left| 4 \, \sqrt{6} + \frac{10 \, {\left(2 \, \sqrt{3} \sqrt{-3 \, x^{2} + 5 \, x + 2} - 7\right)}}{6 \, x - 5} - 14 \right|}}\right)"," ",0,"-1/6*sqrt(6)*sqrt(3)*log(abs(-4*sqrt(6) + 10*(2*sqrt(3)*sqrt(-3*x^2 + 5*x + 2) - 7)/(6*x - 5) - 14)/abs(4*sqrt(6) + 10*(2*sqrt(3)*sqrt(-3*x^2 + 5*x + 2) - 7)/(6*x - 5) - 14))","B",0
2434,1,30,0,0.203832," ","integrate(1/x/(3*x^2+4*x-2)^(1/2),x, algorithm=""giac"")","\sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 4 \, x - 2}\right)}\right)"," ",0,"sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(3)*x - sqrt(3*x^2 + 4*x - 2)))","A",0
2435,0,0,0,0.000000," ","integrate(1/x/(-3*x^2+4*x-2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-3 \, x^{2} + 4 \, x - 2} x}\,{d x}"," ",0,"integrate(1/(sqrt(-3*x^2 + 4*x - 2)*x), x)","F",0
2436,1,30,0,0.200256," ","integrate(1/x/(3*x^2+5*x-2)^(1/2),x, algorithm=""giac"")","\sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{3} x - \sqrt{3 \, x^{2} + 5 \, x - 2}\right)}\right)"," ",0,"sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(3)*x - sqrt(3*x^2 + 5*x - 2)))","A",0
2437,1,44,0,0.211577," ","integrate(1/x/(-3*x^2+5*x-2)^(1/2),x, algorithm=""giac"")","-\frac{1}{3} \, \sqrt{6} \sqrt{3} \arctan\left(\frac{1}{12} \, \sqrt{6} {\left(\frac{5 \, {\left(2 \, \sqrt{3} \sqrt{-3 \, x^{2} + 5 \, x - 2} - 1\right)}}{6 \, x - 5} - 1\right)}\right)"," ",0,"-1/3*sqrt(6)*sqrt(3)*arctan(1/12*sqrt(6)*(5*(2*sqrt(3)*sqrt(-3*x^2 + 5*x - 2) - 1)/(6*x - 5) - 1))","A",0
2438,1,84,0,0.184659," ","integrate(1/x^3/(x^2+x+1)^(1/2),x, algorithm=""giac"")","\frac{{\left(x - \sqrt{x^{2} + x + 1}\right)}^{3} + 9 \, x - 9 \, \sqrt{x^{2} + x + 1} + 8}{4 \, {\left({\left(x - \sqrt{x^{2} + x + 1}\right)}^{2} - 1\right)}^{2}} + \frac{1}{8} \, \log\left({\left| -x + \sqrt{x^{2} + x + 1} + 1 \right|}\right) - \frac{1}{8} \, \log\left({\left| -x + \sqrt{x^{2} + x + 1} - 1 \right|}\right)"," ",0,"1/4*((x - sqrt(x^2 + x + 1))^3 + 9*x - 9*sqrt(x^2 + x + 1) + 8)/((x - sqrt(x^2 + x + 1))^2 - 1)^2 + 1/8*log(abs(-x + sqrt(x^2 + x + 1) + 1)) - 1/8*log(abs(-x + sqrt(x^2 + x + 1) - 1))","A",0
2439,1,50,0,0.257377," ","integrate(1/x-1/x/(c*x^2+b*x+1)^(1/2),x, algorithm=""giac"")","\log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + b x + 1} + 1 \right|}\right) - \log\left({\left| -\sqrt{c} x + \sqrt{c x^{2} + b x + 1} - 1 \right|}\right) + \log\left({\left| x \right|}\right)"," ",0,"log(abs(-sqrt(c)*x + sqrt(c*x^2 + b*x + 1) + 1)) - log(abs(-sqrt(c)*x + sqrt(c*x^2 + b*x + 1) - 1)) + log(abs(x))","B",0
2440,0,0,0,0.000000," ","integrate((d*x)^(5/2)*(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int \sqrt{c x^{2} + b x + a} \left(d x\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + b*x + a)*(d*x)^(5/2), x)","F",0
2441,0,0,0,0.000000," ","integrate((e*x+d)^(3/2)*(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int \sqrt{c x^{2} + b x + a} {\left(e x + d\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + b*x + a)*(e*x + d)^(3/2), x)","F",0
2442,0,0,0,0.000000," ","integrate((e*x+d)^(1/2)*(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int \sqrt{c x^{2} + b x + a} \sqrt{e x + d}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + b*x + a)*sqrt(e*x + d), x)","F",0
2443,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(1/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{c x^{2} + b x + a}}{\sqrt{e x + d}}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + b*x + a)/sqrt(e*x + d), x)","F",0
2444,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(1/2)/(e*x+d)^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{c x^{2} + b x + a}}{{\left(e x + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + b*x + a)/(e*x + d)^(3/2), x)","F",0
2445,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(1/2)/(e*x+d)^(5/2),x, algorithm=""giac"")","\int \frac{\sqrt{c x^{2} + b x + a}}{{\left(e x + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + b*x + a)/(e*x + d)^(5/2), x)","F",0
2446,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(1/2)/(e*x+d)^(7/2),x, algorithm=""giac"")","\int \frac{\sqrt{c x^{2} + b x + a}}{{\left(e x + d\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + b*x + a)/(e*x + d)^(7/2), x)","F",0
2447,0,0,0,0.000000," ","integrate((e*x+d)^(3/2)*(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\int {\left(c x^{2} + b x + a\right)}^{\frac{3}{2}} {\left(e x + d\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(3/2)*(e*x + d)^(3/2), x)","F",0
2448,0,0,0,0.000000," ","integrate((e*x+d)^(1/2)*(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\int {\left(c x^{2} + b x + a\right)}^{\frac{3}{2}} \sqrt{e x + d}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(3/2)*sqrt(e*x + d), x)","F",0
2449,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}{\sqrt{e x + d}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(3/2)/sqrt(e*x + d), x)","F",0
2450,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)/(e*x+d)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}{{\left(e x + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(3/2)/(e*x + d)^(3/2), x)","F",0
2451,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)/(e*x+d)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}{{\left(e x + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(3/2)/(e*x + d)^(5/2), x)","F",0
2452,-2,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)/(e*x+d)^(7/2),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(d*exp(1)+x*exp(1)^2)]integrate()  Bad Argument Typeintegrate()  Bad Argument TypeEvaluation time: 4.09Unable to transpose Error: Bad Argument Value","F(-2)",0
2453,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)/(e*x+d)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}{{\left(e x + d\right)}^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(3/2)/(e*x + d)^(9/2), x)","F",0
2454,0,0,0,0.000000," ","integrate((d*x)^(1/2)*(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\int {\left(c x^{2} + b x + a\right)}^{\frac{5}{2}} \sqrt{d x}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(5/2)*sqrt(d*x), x)","F",0
2455,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(5/2)/(e*x+d)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{\frac{5}{2}}}{\sqrt{e x + d}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(5/2)/sqrt(e*x + d), x)","F",0
2456,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(5/2)/(e*x+d)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{\frac{5}{2}}}{{\left(e x + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(5/2)/(e*x + d)^(3/2), x)","F",0
2457,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(5/2)/(e*x+d)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{\frac{5}{2}}}{{\left(e x + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(5/2)/(e*x + d)^(5/2), x)","F",0
2458,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(5/2)/(e*x+d)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{\frac{5}{2}}}{{\left(e x + d\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(5/2)/(e*x + d)^(7/2), x)","F",0
2459,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(5/2)/(e*x+d)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{\frac{5}{2}}}{{\left(e x + d\right)}^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(5/2)/(e*x + d)^(9/2), x)","F",0
2460,-2,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(5/2)/(e*x+d)^(11/2),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(d*exp(1)+x*exp(1)^2)]integrate()  Bad Argument Typeintegrate()  Bad Argument TypeEvaluation time: 28.18Unable to transpose Error: Bad Argument Value","F(-2)",0
2461,0,0,0,0.000000," ","integrate((e*x+d)^(7/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{\frac{7}{2}}}{\sqrt{c x^{2} + b x + a}}\,{d x}"," ",0,"integrate((e*x + d)^(7/2)/sqrt(c*x^2 + b*x + a), x)","F",0
2462,0,0,0,0.000000," ","integrate((e*x+d)^(5/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{\frac{5}{2}}}{\sqrt{c x^{2} + b x + a}}\,{d x}"," ",0,"integrate((e*x + d)^(5/2)/sqrt(c*x^2 + b*x + a), x)","F",0
2463,0,0,0,0.000000," ","integrate((e*x+d)^(3/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{\frac{3}{2}}}{\sqrt{c x^{2} + b x + a}}\,{d x}"," ",0,"integrate((e*x + d)^(3/2)/sqrt(c*x^2 + b*x + a), x)","F",0
2464,0,0,0,0.000000," ","integrate((e*x+d)^(1/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{e x + d}}{\sqrt{c x^{2} + b x + a}}\,{d x}"," ",0,"integrate(sqrt(e*x + d)/sqrt(c*x^2 + b*x + a), x)","F",0
2465,0,0,0,0.000000," ","integrate(1/(e*x+d)^(1/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{c x^{2} + b x + a} \sqrt{e x + d}}\,{d x}"," ",0,"integrate(1/(sqrt(c*x^2 + b*x + a)*sqrt(e*x + d)), x)","F",0
2466,0,0,0,0.000000," ","integrate(1/(e*x+d)^(3/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{c x^{2} + b x + a} {\left(e x + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(c*x^2 + b*x + a)*(e*x + d)^(3/2)), x)","F",0
2467,0,0,0,0.000000," ","integrate(1/(e*x+d)^(5/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{c x^{2} + b x + a} {\left(e x + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(c*x^2 + b*x + a)*(e*x + d)^(5/2)), x)","F",0
2468,0,0,0,0.000000," ","integrate(1/(e*x+d)^(7/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{c x^{2} + b x + a} {\left(e x + d\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(c*x^2 + b*x + a)*(e*x + d)^(7/2)), x)","F",0
2469,0,0,0,0.000000," ","integrate((e*x+d)^(7/2)/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{\frac{7}{2}}}{{\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((e*x + d)^(7/2)/(c*x^2 + b*x + a)^(3/2), x)","F",0
2470,0,0,0,0.000000," ","integrate((e*x+d)^(5/2)/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{\frac{5}{2}}}{{\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((e*x + d)^(5/2)/(c*x^2 + b*x + a)^(3/2), x)","F",0
2471,0,0,0,0.000000," ","integrate((e*x+d)^(3/2)/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{\frac{3}{2}}}{{\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((e*x + d)^(3/2)/(c*x^2 + b*x + a)^(3/2), x)","F",0
2472,0,0,0,0.000000," ","integrate((e*x+d)^(1/2)/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{e x + d}}{{\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(e*x + d)/(c*x^2 + b*x + a)^(3/2), x)","F",0
2473,0,0,0,0.000000," ","integrate(1/(e*x+d)^(1/2)/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{2} + b x + a\right)}^{\frac{3}{2}} \sqrt{e x + d}}\,{d x}"," ",0,"integrate(1/((c*x^2 + b*x + a)^(3/2)*sqrt(e*x + d)), x)","F",0
2474,-2,0,0,0.000000," ","integrate(1/(e*x+d)^(3/2)/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:integrate()  Bad Argument Typeintegrate()  Bad Argument TypeEvaluation time: 155.09Unable to transpose Error: Bad Argument Value","F(-2)",0
2475,-1,0,0,0.000000," ","integrate(1/(e*x+d)^(5/2)/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2476,0,0,0,0.000000," ","integrate((e*x+d)^(7/2)/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{\frac{7}{2}}}{{\left(c x^{2} + b x + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((e*x + d)^(7/2)/(c*x^2 + b*x + a)^(5/2), x)","F",0
2477,0,0,0,0.000000," ","integrate((e*x+d)^(5/2)/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{\frac{5}{2}}}{{\left(c x^{2} + b x + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((e*x + d)^(5/2)/(c*x^2 + b*x + a)^(5/2), x)","F",0
2478,0,0,0,0.000000," ","integrate((e*x+d)^(3/2)/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{\frac{3}{2}}}{{\left(c x^{2} + b x + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((e*x + d)^(3/2)/(c*x^2 + b*x + a)^(5/2), x)","F",0
2479,0,0,0,0.000000," ","integrate((e*x+d)^(1/2)/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\int \frac{\sqrt{e x + d}}{{\left(c x^{2} + b x + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(e*x + d)/(c*x^2 + b*x + a)^(5/2), x)","F",0
2480,0,0,0,0.000000," ","integrate(1/(e*x+d)^(1/2)/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{2} + b x + a\right)}^{\frac{5}{2}} \sqrt{e x + d}}\,{d x}"," ",0,"integrate(1/((c*x^2 + b*x + a)^(5/2)*sqrt(e*x + d)), x)","F",0
2481,-2,0,0,0.000000," ","integrate(1/(e*x+d)^(3/2)/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Evaluation time: 97.54Unable to transpose Error: Bad Argument Value","F(-2)",0
2482,0,0,0,0.000000," ","integrate((3+5*x)^(1/2)/(-12*x^2+5*x+2)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{5 \, x + 3}}{\sqrt{-12 \, x^{2} + 5 \, x + 2}}\,{d x}"," ",0,"integrate(sqrt(5*x + 3)/sqrt(-12*x^2 + 5*x + 2), x)","F",0
2483,0,0,0,0.000000," ","integrate((e*x+d)^2*(c*x^2+b*x+a)^(4/3),x, algorithm=""giac"")","\int {\left(c x^{2} + b x + a\right)}^{\frac{4}{3}} {\left(e x + d\right)}^{2}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(4/3)*(e*x + d)^2, x)","F",0
2484,0,0,0,0.000000," ","integrate((e*x+d)*(c*x^2+b*x+a)^(4/3),x, algorithm=""giac"")","\int {\left(c x^{2} + b x + a\right)}^{\frac{4}{3}} {\left(e x + d\right)}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(4/3)*(e*x + d), x)","F",0
2485,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(4/3),x, algorithm=""giac"")","\int {\left(c x^{2} + b x + a\right)}^{\frac{4}{3}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(4/3), x)","F",0
2486,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(4/3)/(e*x+d),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{\frac{4}{3}}}{e x + d}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(4/3)/(e*x + d), x)","F",0
2487,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(4/3)/(e*x+d)^2,x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{\frac{4}{3}}}{{\left(e x + d\right)}^{2}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(4/3)/(e*x + d)^2, x)","F",0
2488,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(4/3)/(e*x+d)^3,x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{\frac{4}{3}}}{{\left(e x + d\right)}^{3}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(4/3)/(e*x + d)^3, x)","F",0
2489,0,0,0,0.000000," ","integrate((e*x+d)^3/(c*x^2+b*x+a)^(7/3),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{3}}{{\left(c x^{2} + b x + a\right)}^{\frac{7}{3}}}\,{d x}"," ",0,"integrate((e*x + d)^3/(c*x^2 + b*x + a)^(7/3), x)","F",0
2490,0,0,0,0.000000," ","integrate((e*x+d)^2/(c*x^2+b*x+a)^(7/3),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{2}}{{\left(c x^{2} + b x + a\right)}^{\frac{7}{3}}}\,{d x}"," ",0,"integrate((e*x + d)^2/(c*x^2 + b*x + a)^(7/3), x)","F",0
2491,0,0,0,0.000000," ","integrate((e*x+d)/(c*x^2+b*x+a)^(7/3),x, algorithm=""giac"")","\int \frac{e x + d}{{\left(c x^{2} + b x + a\right)}^{\frac{7}{3}}}\,{d x}"," ",0,"integrate((e*x + d)/(c*x^2 + b*x + a)^(7/3), x)","F",0
2492,0,0,0,0.000000," ","integrate(1/(c*x^2+b*x+a)^(7/3),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{2} + b x + a\right)}^{\frac{7}{3}}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(-7/3), x)","F",0
2493,0,0,0,0.000000," ","integrate(1/(e*x+d)/(c*x^2+b*x+a)^(7/3),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{2} + b x + a\right)}^{\frac{7}{3}} {\left(e x + d\right)}}\,{d x}"," ",0,"integrate(1/((c*x^2 + b*x + a)^(7/3)*(e*x + d)), x)","F",0
2494,0,0,0,0.000000," ","integrate(1/(e*x+d)^2/(c*x^2+b*x+a)^(7/3),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{2} + b x + a\right)}^{\frac{7}{3}} {\left(e x + d\right)}^{2}}\,{d x}"," ",0,"integrate(1/((c*x^2 + b*x + a)^(7/3)*(e*x + d)^2), x)","F",0
2495,0,0,0,0.000000," ","integrate(1/(e*x+d)^3/(c*x^2+b*x+a)^(7/3),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{2} + b x + a\right)}^{\frac{7}{3}} {\left(e x + d\right)}^{3}}\,{d x}"," ",0,"integrate(1/((c*x^2 + b*x + a)^(7/3)*(e*x + d)^3), x)","F",0
2496,0,0,0,0.000000," ","integrate(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, algorithm=""giac"")","\int \frac{1}{{\left(3 \, c^{2} e^{2} x^{2} + 3 \, b c e^{2} x + c^{2} d^{2} - b c d e + b^{2} e^{2}\right)}^{\frac{1}{3}} {\left(e x + d\right)}}\,{d x}"," ",0,"integrate(1/((3*c^2*e^2*x^2 + 3*b*c*e^2*x + c^2*d^2 - b*c*d*e + b^2*e^2)^(1/3)*(e*x + d)), x)","F",0
2497,0,0,0,0.000000," ","integrate((2+3*x)^3/(27*x^2-54*x+52)^(1/3),x, algorithm=""giac"")","\int \frac{{\left(3 \, x + 2\right)}^{3}}{{\left(27 \, x^{2} - 54 \, x + 52\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((3*x + 2)^3/(27*x^2 - 54*x + 52)^(1/3), x)","F",0
2498,0,0,0,0.000000," ","integrate((2+3*x)^2/(27*x^2-54*x+52)^(1/3),x, algorithm=""giac"")","\int \frac{{\left(3 \, x + 2\right)}^{2}}{{\left(27 \, x^{2} - 54 \, x + 52\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((3*x + 2)^2/(27*x^2 - 54*x + 52)^(1/3), x)","F",0
2499,0,0,0,0.000000," ","integrate((2+3*x)/(27*x^2-54*x+52)^(1/3),x, algorithm=""giac"")","\int \frac{3 \, x + 2}{{\left(27 \, x^{2} - 54 \, x + 52\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((3*x + 2)/(27*x^2 - 54*x + 52)^(1/3), x)","F",0
2500,0,0,0,0.000000," ","integrate(1/(2+3*x)/(27*x^2-54*x+52)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(27 \, x^{2} - 54 \, x + 52\right)}^{\frac{1}{3}} {\left(3 \, x + 2\right)}}\,{d x}"," ",0,"integrate(1/((27*x^2 - 54*x + 52)^(1/3)*(3*x + 2)), x)","F",0
2501,0,0,0,0.000000," ","integrate(1/(2+3*x)^2/(27*x^2-54*x+52)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(27 \, x^{2} - 54 \, x + 52\right)}^{\frac{1}{3}} {\left(3 \, x + 2\right)}^{2}}\,{d x}"," ",0,"integrate(1/((27*x^2 - 54*x + 52)^(1/3)*(3*x + 2)^2), x)","F",0
2502,0,0,0,0.000000," ","integrate(1/(2+3*x)^3/(27*x^2-54*x+52)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(27 \, x^{2} - 54 \, x + 52\right)}^{\frac{1}{3}} {\left(3 \, x + 2\right)}^{3}}\,{d x}"," ",0,"integrate(1/((27*x^2 - 54*x + 52)^(1/3)*(3*x + 2)^3), x)","F",0
2503,0,0,0,0.000000," ","integrate((2+3*x)^3/(27*x^2+54*x+28)^(1/3),x, algorithm=""giac"")","\int \frac{{\left(3 \, x + 2\right)}^{3}}{{\left(27 \, x^{2} + 54 \, x + 28\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((3*x + 2)^3/(27*x^2 + 54*x + 28)^(1/3), x)","F",0
2504,0,0,0,0.000000," ","integrate((2+3*x)^2/(27*x^2+54*x+28)^(1/3),x, algorithm=""giac"")","\int \frac{{\left(3 \, x + 2\right)}^{2}}{{\left(27 \, x^{2} + 54 \, x + 28\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((3*x + 2)^2/(27*x^2 + 54*x + 28)^(1/3), x)","F",0
2505,0,0,0,0.000000," ","integrate((2+3*x)/(27*x^2+54*x+28)^(1/3),x, algorithm=""giac"")","\int \frac{3 \, x + 2}{{\left(27 \, x^{2} + 54 \, x + 28\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((3*x + 2)/(27*x^2 + 54*x + 28)^(1/3), x)","F",0
2506,0,0,0,0.000000," ","integrate(1/(2+3*x)/(27*x^2+54*x+28)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(27 \, x^{2} + 54 \, x + 28\right)}^{\frac{1}{3}} {\left(3 \, x + 2\right)}}\,{d x}"," ",0,"integrate(1/((27*x^2 + 54*x + 28)^(1/3)*(3*x + 2)), x)","F",0
2507,0,0,0,0.000000," ","integrate(1/(2+3*x)^2/(27*x^2+54*x+28)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(27 \, x^{2} + 54 \, x + 28\right)}^{\frac{1}{3}} {\left(3 \, x + 2\right)}^{2}}\,{d x}"," ",0,"integrate(1/((27*x^2 + 54*x + 28)^(1/3)*(3*x + 2)^2), x)","F",0
2508,0,0,0,0.000000," ","integrate(1/(2+3*x)^3/(27*x^2+54*x+28)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(27 \, x^{2} + 54 \, x + 28\right)}^{\frac{1}{3}} {\left(3 \, x + 2\right)}^{3}}\,{d x}"," ",0,"integrate(1/((27*x^2 + 54*x + 28)^(1/3)*(3*x + 2)^3), x)","F",0
2509,0,0,0,0.000000," ","integrate(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, algorithm=""giac"")","\int \frac{1}{{\left(9 \, c^{2} e^{2} x^{2} + 9 \, b c e^{2} x - c^{2} d^{2} + b c d e + 2 \, b^{2} e^{2}\right)}^{\frac{1}{3}} {\left(e x + d\right)}}\,{d x}"," ",0,"integrate(1/((9*c^2*e^2*x^2 + 9*b*c*e^2*x - c^2*d^2 + b*c*d*e + 2*b^2*e^2)^(1/3)*(e*x + d)), x)","F",0
2510,0,0,0,0.000000," ","integrate((e*x+d)^3*(c*x^2+b*x+a)^(1/4),x, algorithm=""giac"")","\int {\left(c x^{2} + b x + a\right)}^{\frac{1}{4}} {\left(e x + d\right)}^{3}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(1/4)*(e*x + d)^3, x)","F",0
2511,0,0,0,0.000000," ","integrate((e*x+d)^2*(c*x^2+b*x+a)^(1/4),x, algorithm=""giac"")","\int {\left(c x^{2} + b x + a\right)}^{\frac{1}{4}} {\left(e x + d\right)}^{2}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(1/4)*(e*x + d)^2, x)","F",0
2512,0,0,0,0.000000," ","integrate((e*x+d)*(c*x^2+b*x+a)^(1/4),x, algorithm=""giac"")","\int {\left(c x^{2} + b x + a\right)}^{\frac{1}{4}} {\left(e x + d\right)}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(1/4)*(e*x + d), x)","F",0
2513,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(1/4),x, algorithm=""giac"")","\int {\left(c x^{2} + b x + a\right)}^{\frac{1}{4}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(1/4), x)","F",0
2514,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(1/4)/(e*x+d),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{\frac{1}{4}}}{e x + d}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(1/4)/(e*x + d), x)","F",0
2515,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(1/4)/(e*x+d)^2,x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{\frac{1}{4}}}{{\left(e x + d\right)}^{2}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(1/4)/(e*x + d)^2, x)","F",0
2516,0,0,0,0.000000," ","integrate((e*x+d)^3*(c*x^2+b*x+a)^(3/4),x, algorithm=""giac"")","\int {\left(c x^{2} + b x + a\right)}^{\frac{3}{4}} {\left(e x + d\right)}^{3}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(3/4)*(e*x + d)^3, x)","F",0
2517,0,0,0,0.000000," ","integrate((e*x+d)^2*(c*x^2+b*x+a)^(3/4),x, algorithm=""giac"")","\int {\left(c x^{2} + b x + a\right)}^{\frac{3}{4}} {\left(e x + d\right)}^{2}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(3/4)*(e*x + d)^2, x)","F",0
2518,0,0,0,0.000000," ","integrate((e*x+d)*(c*x^2+b*x+a)^(3/4),x, algorithm=""giac"")","\int {\left(c x^{2} + b x + a\right)}^{\frac{3}{4}} {\left(e x + d\right)}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(3/4)*(e*x + d), x)","F",0
2519,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/4),x, algorithm=""giac"")","\int {\left(c x^{2} + b x + a\right)}^{\frac{3}{4}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(3/4), x)","F",0
2520,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/4)/(e*x+d),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{\frac{3}{4}}}{e x + d}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(3/4)/(e*x + d), x)","F",0
2521,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/4)/(e*x+d)^2,x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{\frac{3}{4}}}{{\left(e x + d\right)}^{2}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(3/4)/(e*x + d)^2, x)","F",0
2522,0,0,0,0.000000," ","integrate((e*x+d)^3*(c*x^2+b*x+a)^(5/4),x, algorithm=""giac"")","\int {\left(c x^{2} + b x + a\right)}^{\frac{5}{4}} {\left(e x + d\right)}^{3}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(5/4)*(e*x + d)^3, x)","F",0
2523,0,0,0,0.000000," ","integrate((e*x+d)^2*(c*x^2+b*x+a)^(5/4),x, algorithm=""giac"")","\int {\left(c x^{2} + b x + a\right)}^{\frac{5}{4}} {\left(e x + d\right)}^{2}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(5/4)*(e*x + d)^2, x)","F",0
2524,0,0,0,0.000000," ","integrate((e*x+d)*(c*x^2+b*x+a)^(5/4),x, algorithm=""giac"")","\int {\left(c x^{2} + b x + a\right)}^{\frac{5}{4}} {\left(e x + d\right)}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(5/4)*(e*x + d), x)","F",0
2525,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(5/4),x, algorithm=""giac"")","\int {\left(c x^{2} + b x + a\right)}^{\frac{5}{4}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(5/4), x)","F",0
2526,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(5/4)/(e*x+d),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{\frac{5}{4}}}{e x + d}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(5/4)/(e*x + d), x)","F",0
2527,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(5/4)/(e*x+d)^2,x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{\frac{5}{4}}}{{\left(e x + d\right)}^{2}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(5/4)/(e*x + d)^2, x)","F",0
2528,0,0,0,0.000000," ","integrate((e*x+d)^3/(c*x^2+b*x+a)^(1/4),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{3}}{{\left(c x^{2} + b x + a\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((e*x + d)^3/(c*x^2 + b*x + a)^(1/4), x)","F",0
2529,0,0,0,0.000000," ","integrate((e*x+d)^2/(c*x^2+b*x+a)^(1/4),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{2}}{{\left(c x^{2} + b x + a\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((e*x + d)^2/(c*x^2 + b*x + a)^(1/4), x)","F",0
2530,0,0,0,0.000000," ","integrate((e*x+d)/(c*x^2+b*x+a)^(1/4),x, algorithm=""giac"")","\int \frac{e x + d}{{\left(c x^{2} + b x + a\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((e*x + d)/(c*x^2 + b*x + a)^(1/4), x)","F",0
2531,0,0,0,0.000000," ","integrate(1/(c*x^2+b*x+a)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{2} + b x + a\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(-1/4), x)","F",0
2532,0,0,0,0.000000," ","integrate(1/(e*x+d)/(c*x^2+b*x+a)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{2} + b x + a\right)}^{\frac{1}{4}} {\left(e x + d\right)}}\,{d x}"," ",0,"integrate(1/((c*x^2 + b*x + a)^(1/4)*(e*x + d)), x)","F",0
2533,0,0,0,0.000000," ","integrate(1/(e*x+d)^2/(c*x^2+b*x+a)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{2} + b x + a\right)}^{\frac{1}{4}} {\left(e x + d\right)}^{2}}\,{d x}"," ",0,"integrate(1/((c*x^2 + b*x + a)^(1/4)*(e*x + d)^2), x)","F",0
2534,0,0,0,0.000000," ","integrate(1/(e*x+d)^3/(c*x^2+b*x+a)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{2} + b x + a\right)}^{\frac{1}{4}} {\left(e x + d\right)}^{3}}\,{d x}"," ",0,"integrate(1/((c*x^2 + b*x + a)^(1/4)*(e*x + d)^3), x)","F",0
2535,0,0,0,0.000000," ","integrate((e*x+d)^3/(c*x^2+b*x+a)^(3/4),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{3}}{{\left(c x^{2} + b x + a\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate((e*x + d)^3/(c*x^2 + b*x + a)^(3/4), x)","F",0
2536,0,0,0,0.000000," ","integrate((e*x+d)^2/(c*x^2+b*x+a)^(3/4),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{2}}{{\left(c x^{2} + b x + a\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate((e*x + d)^2/(c*x^2 + b*x + a)^(3/4), x)","F",0
2537,0,0,0,0.000000," ","integrate((e*x+d)/(c*x^2+b*x+a)^(3/4),x, algorithm=""giac"")","\int \frac{e x + d}{{\left(c x^{2} + b x + a\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate((e*x + d)/(c*x^2 + b*x + a)^(3/4), x)","F",0
2538,0,0,0,0.000000," ","integrate(1/(c*x^2+b*x+a)^(3/4),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{2} + b x + a\right)}^{\frac{3}{4}}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(-3/4), x)","F",0
2539,0,0,0,0.000000," ","integrate(1/(e*x+d)/(c*x^2+b*x+a)^(3/4),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{2} + b x + a\right)}^{\frac{3}{4}} {\left(e x + d\right)}}\,{d x}"," ",0,"integrate(1/((c*x^2 + b*x + a)^(3/4)*(e*x + d)), x)","F",0
2540,0,0,0,0.000000," ","integrate(1/(e*x+d)^2/(c*x^2+b*x+a)^(3/4),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{2} + b x + a\right)}^{\frac{3}{4}} {\left(e x + d\right)}^{2}}\,{d x}"," ",0,"integrate(1/((c*x^2 + b*x + a)^(3/4)*(e*x + d)^2), x)","F",0
2541,0,0,0,0.000000," ","integrate(1/(e*x+d)^3/(c*x^2+b*x+a)^(3/4),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{2} + b x + a\right)}^{\frac{3}{4}} {\left(e x + d\right)}^{3}}\,{d x}"," ",0,"integrate(1/((c*x^2 + b*x + a)^(3/4)*(e*x + d)^3), x)","F",0
2542,0,0,0,0.000000," ","integrate((e*x+d)^3/(c*x^2+b*x+a)^(5/4),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{3}}{{\left(c x^{2} + b x + a\right)}^{\frac{5}{4}}}\,{d x}"," ",0,"integrate((e*x + d)^3/(c*x^2 + b*x + a)^(5/4), x)","F",0
2543,0,0,0,0.000000," ","integrate((e*x+d)^2/(c*x^2+b*x+a)^(5/4),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{2}}{{\left(c x^{2} + b x + a\right)}^{\frac{5}{4}}}\,{d x}"," ",0,"integrate((e*x + d)^2/(c*x^2 + b*x + a)^(5/4), x)","F",0
2544,0,0,0,0.000000," ","integrate((e*x+d)/(c*x^2+b*x+a)^(5/4),x, algorithm=""giac"")","\int \frac{e x + d}{{\left(c x^{2} + b x + a\right)}^{\frac{5}{4}}}\,{d x}"," ",0,"integrate((e*x + d)/(c*x^2 + b*x + a)^(5/4), x)","F",0
2545,0,0,0,0.000000," ","integrate(1/(c*x^2+b*x+a)^(5/4),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{2} + b x + a\right)}^{\frac{5}{4}}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(-5/4), x)","F",0
2546,0,0,0,0.000000," ","integrate(1/(e*x+d)/(c*x^2+b*x+a)^(5/4),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{2} + b x + a\right)}^{\frac{5}{4}} {\left(e x + d\right)}}\,{d x}"," ",0,"integrate(1/((c*x^2 + b*x + a)^(5/4)*(e*x + d)), x)","F",0
2547,0,0,0,0.000000," ","integrate(1/(e*x+d)^2/(c*x^2+b*x+a)^(5/4),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{2} + b x + a\right)}^{\frac{5}{4}} {\left(e x + d\right)}^{2}}\,{d x}"," ",0,"integrate(1/((c*x^2 + b*x + a)^(5/4)*(e*x + d)^2), x)","F",0
2548,0,0,0,0.000000," ","integrate(1/(e*x+d)^(3/2)/(c*x^2+b*x+a)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(c x^{2} + b x + a\right)}^{\frac{1}{4}} {\left(e x + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((c*x^2 + b*x + a)^(1/4)*(e*x + d)^(3/2)), x)","F",0
2549,1,13143,0,0.855701," ","integrate((e*x+d)^m*(c*x^2+b*x+a)^4,x, algorithm=""giac"")","\frac{{\left(x e + d\right)}^{m} c^{4} m^{8} x^{9} e^{9} + {\left(x e + d\right)}^{m} c^{4} d m^{8} x^{8} e^{8} + 4 \, {\left(x e + d\right)}^{m} b c^{3} m^{8} x^{8} e^{9} + 36 \, {\left(x e + d\right)}^{m} c^{4} m^{7} x^{9} e^{9} + 4 \, {\left(x e + d\right)}^{m} b c^{3} d m^{8} x^{7} e^{8} + 28 \, {\left(x e + d\right)}^{m} c^{4} d m^{7} x^{8} e^{8} - 8 \, {\left(x e + d\right)}^{m} c^{4} d^{2} m^{7} x^{7} e^{7} + 6 \, {\left(x e + d\right)}^{m} b^{2} c^{2} m^{8} x^{7} e^{9} + 4 \, {\left(x e + d\right)}^{m} a c^{3} m^{8} x^{7} e^{9} + 148 \, {\left(x e + d\right)}^{m} b c^{3} m^{7} x^{8} e^{9} + 546 \, {\left(x e + d\right)}^{m} c^{4} m^{6} x^{9} e^{9} + 6 \, {\left(x e + d\right)}^{m} b^{2} c^{2} d m^{8} x^{6} e^{8} + 4 \, {\left(x e + d\right)}^{m} a c^{3} d m^{8} x^{6} e^{8} + 120 \, {\left(x e + d\right)}^{m} b c^{3} d m^{7} x^{7} e^{8} + 322 \, {\left(x e + d\right)}^{m} c^{4} d m^{6} x^{8} e^{8} - 28 \, {\left(x e + d\right)}^{m} b c^{3} d^{2} m^{7} x^{6} e^{7} - 168 \, {\left(x e + d\right)}^{m} c^{4} d^{2} m^{6} x^{7} e^{7} + 56 \, {\left(x e + d\right)}^{m} c^{4} d^{3} m^{6} x^{6} e^{6} + 4 \, {\left(x e + d\right)}^{m} b^{3} c m^{8} x^{6} e^{9} + 12 \, {\left(x e + d\right)}^{m} a b c^{2} m^{8} x^{6} e^{9} + 228 \, {\left(x e + d\right)}^{m} b^{2} c^{2} m^{7} x^{7} e^{9} + 152 \, {\left(x e + d\right)}^{m} a c^{3} m^{7} x^{7} e^{9} + 2296 \, {\left(x e + d\right)}^{m} b c^{3} m^{6} x^{8} e^{9} + 4536 \, {\left(x e + d\right)}^{m} c^{4} m^{5} x^{9} e^{9} + 4 \, {\left(x e + d\right)}^{m} b^{3} c d m^{8} x^{5} e^{8} + 12 \, {\left(x e + d\right)}^{m} a b c^{2} d m^{8} x^{5} e^{8} + 192 \, {\left(x e + d\right)}^{m} b^{2} c^{2} d m^{7} x^{6} e^{8} + 128 \, {\left(x e + d\right)}^{m} a c^{3} d m^{7} x^{6} e^{8} + 1456 \, {\left(x e + d\right)}^{m} b c^{3} d m^{6} x^{7} e^{8} + 1960 \, {\left(x e + d\right)}^{m} c^{4} d m^{5} x^{8} e^{8} - 36 \, {\left(x e + d\right)}^{m} b^{2} c^{2} d^{2} m^{7} x^{5} e^{7} - 24 \, {\left(x e + d\right)}^{m} a c^{3} d^{2} m^{7} x^{5} e^{7} - 672 \, {\left(x e + d\right)}^{m} b c^{3} d^{2} m^{6} x^{6} e^{7} - 1400 \, {\left(x e + d\right)}^{m} c^{4} d^{2} m^{5} x^{7} e^{7} + 168 \, {\left(x e + d\right)}^{m} b c^{3} d^{3} m^{6} x^{5} e^{6} + 840 \, {\left(x e + d\right)}^{m} c^{4} d^{3} m^{5} x^{6} e^{6} - 336 \, {\left(x e + d\right)}^{m} c^{4} d^{4} m^{5} x^{5} e^{5} + {\left(x e + d\right)}^{m} b^{4} m^{8} x^{5} e^{9} + 12 \, {\left(x e + d\right)}^{m} a b^{2} c m^{8} x^{5} e^{9} + 6 \, {\left(x e + d\right)}^{m} a^{2} c^{2} m^{8} x^{5} e^{9} + 156 \, {\left(x e + d\right)}^{m} b^{3} c m^{7} x^{6} e^{9} + 468 \, {\left(x e + d\right)}^{m} a b c^{2} m^{7} x^{6} e^{9} + 3624 \, {\left(x e + d\right)}^{m} b^{2} c^{2} m^{6} x^{7} e^{9} + 2416 \, {\left(x e + d\right)}^{m} a c^{3} m^{6} x^{7} e^{9} + 19432 \, {\left(x e + d\right)}^{m} b c^{3} m^{5} x^{8} e^{9} + 22449 \, {\left(x e + d\right)}^{m} c^{4} m^{4} x^{9} e^{9} + {\left(x e + d\right)}^{m} b^{4} d m^{8} x^{4} e^{8} + 12 \, {\left(x e + d\right)}^{m} a b^{2} c d m^{8} x^{4} e^{8} + 6 \, {\left(x e + d\right)}^{m} a^{2} c^{2} d m^{8} x^{4} e^{8} + 136 \, {\left(x e + d\right)}^{m} b^{3} c d m^{7} x^{5} e^{8} + 408 \, {\left(x e + d\right)}^{m} a b c^{2} d m^{7} x^{5} e^{8} + 2472 \, {\left(x e + d\right)}^{m} b^{2} c^{2} d m^{6} x^{6} e^{8} + 1648 \, {\left(x e + d\right)}^{m} a c^{3} d m^{6} x^{6} e^{8} + 9240 \, {\left(x e + d\right)}^{m} b c^{3} d m^{5} x^{7} e^{8} + 6769 \, {\left(x e + d\right)}^{m} c^{4} d m^{4} x^{8} e^{8} - 20 \, {\left(x e + d\right)}^{m} b^{3} c d^{2} m^{7} x^{4} e^{7} - 60 \, {\left(x e + d\right)}^{m} a b c^{2} d^{2} m^{7} x^{4} e^{7} - 972 \, {\left(x e + d\right)}^{m} b^{2} c^{2} d^{2} m^{6} x^{5} e^{7} - 648 \, {\left(x e + d\right)}^{m} a c^{3} d^{2} m^{6} x^{5} e^{7} - 6160 \, {\left(x e + d\right)}^{m} b c^{3} d^{2} m^{5} x^{6} e^{7} - 5880 \, {\left(x e + d\right)}^{m} c^{4} d^{2} m^{4} x^{7} e^{7} + 180 \, {\left(x e + d\right)}^{m} b^{2} c^{2} d^{3} m^{6} x^{4} e^{6} + 120 \, {\left(x e + d\right)}^{m} a c^{3} d^{3} m^{6} x^{4} e^{6} + 3192 \, {\left(x e + d\right)}^{m} b c^{3} d^{3} m^{5} x^{5} e^{6} + 4760 \, {\left(x e + d\right)}^{m} c^{4} d^{3} m^{4} x^{6} e^{6} - 840 \, {\left(x e + d\right)}^{m} b c^{3} d^{4} m^{5} x^{4} e^{5} - 3360 \, {\left(x e + d\right)}^{m} c^{4} d^{4} m^{4} x^{5} e^{5} + 1680 \, {\left(x e + d\right)}^{m} c^{4} d^{5} m^{4} x^{4} e^{4} + 4 \, {\left(x e + d\right)}^{m} a b^{3} m^{8} x^{4} e^{9} + 12 \, {\left(x e + d\right)}^{m} a^{2} b c m^{8} x^{4} e^{9} + 40 \, {\left(x e + d\right)}^{m} b^{4} m^{7} x^{5} e^{9} + 480 \, {\left(x e + d\right)}^{m} a b^{2} c m^{7} x^{5} e^{9} + 240 \, {\left(x e + d\right)}^{m} a^{2} c^{2} m^{7} x^{5} e^{9} + 2544 \, {\left(x e + d\right)}^{m} b^{3} c m^{6} x^{6} e^{9} + 7632 \, {\left(x e + d\right)}^{m} a b c^{2} m^{6} x^{6} e^{9} + 31332 \, {\left(x e + d\right)}^{m} b^{2} c^{2} m^{5} x^{7} e^{9} + 20888 \, {\left(x e + d\right)}^{m} a c^{3} m^{5} x^{7} e^{9} + 97636 \, {\left(x e + d\right)}^{m} b c^{3} m^{4} x^{8} e^{9} + 67284 \, {\left(x e + d\right)}^{m} c^{4} m^{3} x^{9} e^{9} + 4 \, {\left(x e + d\right)}^{m} a b^{3} d m^{8} x^{3} e^{8} + 12 \, {\left(x e + d\right)}^{m} a^{2} b c d m^{8} x^{3} e^{8} + 36 \, {\left(x e + d\right)}^{m} b^{4} d m^{7} x^{4} e^{8} + 432 \, {\left(x e + d\right)}^{m} a b^{2} c d m^{7} x^{4} e^{8} + 216 \, {\left(x e + d\right)}^{m} a^{2} c^{2} d m^{7} x^{4} e^{8} + 1864 \, {\left(x e + d\right)}^{m} b^{3} c d m^{6} x^{5} e^{8} + 5592 \, {\left(x e + d\right)}^{m} a b c^{2} d m^{6} x^{5} e^{8} + 16500 \, {\left(x e + d\right)}^{m} b^{2} c^{2} d m^{5} x^{6} e^{8} + 11000 \, {\left(x e + d\right)}^{m} a c^{3} d m^{5} x^{6} e^{8} + 32956 \, {\left(x e + d\right)}^{m} b c^{3} d m^{4} x^{7} e^{8} + 13132 \, {\left(x e + d\right)}^{m} c^{4} d m^{3} x^{8} e^{8} - 4 \, {\left(x e + d\right)}^{m} b^{4} d^{2} m^{7} x^{3} e^{7} - 48 \, {\left(x e + d\right)}^{m} a b^{2} c d^{2} m^{7} x^{3} e^{7} - 24 \, {\left(x e + d\right)}^{m} a^{2} c^{2} d^{2} m^{7} x^{3} e^{7} - 600 \, {\left(x e + d\right)}^{m} b^{3} c d^{2} m^{6} x^{4} e^{7} - 1800 \, {\left(x e + d\right)}^{m} a b c^{2} d^{2} m^{6} x^{4} e^{7} - 9972 \, {\left(x e + d\right)}^{m} b^{2} c^{2} d^{2} m^{5} x^{5} e^{7} - 6648 \, {\left(x e + d\right)}^{m} a c^{3} d^{2} m^{5} x^{5} e^{7} - 27720 \, {\left(x e + d\right)}^{m} b c^{3} d^{2} m^{4} x^{6} e^{7} - 12992 \, {\left(x e + d\right)}^{m} c^{4} d^{2} m^{3} x^{7} e^{7} + 80 \, {\left(x e + d\right)}^{m} b^{3} c d^{3} m^{6} x^{3} e^{6} + 240 \, {\left(x e + d\right)}^{m} a b c^{2} d^{3} m^{6} x^{3} e^{6} + 4140 \, {\left(x e + d\right)}^{m} b^{2} c^{2} d^{3} m^{5} x^{4} e^{6} + 2760 \, {\left(x e + d\right)}^{m} a c^{3} d^{3} m^{5} x^{4} e^{6} + 21000 \, {\left(x e + d\right)}^{m} b c^{3} d^{3} m^{4} x^{5} e^{6} + 12600 \, {\left(x e + d\right)}^{m} c^{4} d^{3} m^{3} x^{6} e^{6} - 720 \, {\left(x e + d\right)}^{m} b^{2} c^{2} d^{4} m^{5} x^{3} e^{5} - 480 \, {\left(x e + d\right)}^{m} a c^{3} d^{4} m^{5} x^{3} e^{5} - 12600 \, {\left(x e + d\right)}^{m} b c^{3} d^{4} m^{4} x^{4} e^{5} - 11760 \, {\left(x e + d\right)}^{m} c^{4} d^{4} m^{3} x^{5} e^{5} + 3360 \, {\left(x e + d\right)}^{m} b c^{3} d^{5} m^{4} x^{3} e^{4} + 10080 \, {\left(x e + d\right)}^{m} c^{4} d^{5} m^{3} x^{4} e^{4} - 6720 \, {\left(x e + d\right)}^{m} c^{4} d^{6} m^{3} x^{3} e^{3} + 6 \, {\left(x e + d\right)}^{m} a^{2} b^{2} m^{8} x^{3} e^{9} + 4 \, {\left(x e + d\right)}^{m} a^{3} c m^{8} x^{3} e^{9} + 164 \, {\left(x e + d\right)}^{m} a b^{3} m^{7} x^{4} e^{9} + 492 \, {\left(x e + d\right)}^{m} a^{2} b c m^{7} x^{4} e^{9} + 670 \, {\left(x e + d\right)}^{m} b^{4} m^{6} x^{5} e^{9} + 8040 \, {\left(x e + d\right)}^{m} a b^{2} c m^{6} x^{5} e^{9} + 4020 \, {\left(x e + d\right)}^{m} a^{2} c^{2} m^{6} x^{5} e^{9} + 22536 \, {\left(x e + d\right)}^{m} b^{3} c m^{5} x^{6} e^{9} + 67608 \, {\left(x e + d\right)}^{m} a b c^{2} m^{5} x^{6} e^{9} + 160314 \, {\left(x e + d\right)}^{m} b^{2} c^{2} m^{4} x^{7} e^{9} + 106876 \, {\left(x e + d\right)}^{m} a c^{3} m^{4} x^{7} e^{9} + 296212 \, {\left(x e + d\right)}^{m} b c^{3} m^{3} x^{8} e^{9} + 118124 \, {\left(x e + d\right)}^{m} c^{4} m^{2} x^{9} e^{9} + 6 \, {\left(x e + d\right)}^{m} a^{2} b^{2} d m^{8} x^{2} e^{8} + 4 \, {\left(x e + d\right)}^{m} a^{3} c d m^{8} x^{2} e^{8} + 152 \, {\left(x e + d\right)}^{m} a b^{3} d m^{7} x^{3} e^{8} + 456 \, {\left(x e + d\right)}^{m} a^{2} b c d m^{7} x^{3} e^{8} + 526 \, {\left(x e + d\right)}^{m} b^{4} d m^{6} x^{4} e^{8} + 6312 \, {\left(x e + d\right)}^{m} a b^{2} c d m^{6} x^{4} e^{8} + 3156 \, {\left(x e + d\right)}^{m} a^{2} c^{2} d m^{6} x^{4} e^{8} + 13216 \, {\left(x e + d\right)}^{m} b^{3} c d m^{5} x^{5} e^{8} + 39648 \, {\left(x e + d\right)}^{m} a b c^{2} d m^{5} x^{5} e^{8} + 61314 \, {\left(x e + d\right)}^{m} b^{2} c^{2} d m^{4} x^{6} e^{8} + 40876 \, {\left(x e + d\right)}^{m} a c^{3} d m^{4} x^{6} e^{8} + 65520 \, {\left(x e + d\right)}^{m} b c^{3} d m^{3} x^{7} e^{8} + 13068 \, {\left(x e + d\right)}^{m} c^{4} d m^{2} x^{8} e^{8} - 12 \, {\left(x e + d\right)}^{m} a b^{3} d^{2} m^{7} x^{2} e^{7} - 36 \, {\left(x e + d\right)}^{m} a^{2} b c d^{2} m^{7} x^{2} e^{7} - 132 \, {\left(x e + d\right)}^{m} b^{4} d^{2} m^{6} x^{3} e^{7} - 1584 \, {\left(x e + d\right)}^{m} a b^{2} c d^{2} m^{6} x^{3} e^{7} - 792 \, {\left(x e + d\right)}^{m} a^{2} c^{2} d^{2} m^{6} x^{3} e^{7} - 6920 \, {\left(x e + d\right)}^{m} b^{3} c d^{2} m^{5} x^{4} e^{7} - 20760 \, {\left(x e + d\right)}^{m} a b c^{2} d^{2} m^{5} x^{4} e^{7} - 49140 \, {\left(x e + d\right)}^{m} b^{2} c^{2} d^{2} m^{4} x^{5} e^{7} - 32760 \, {\left(x e + d\right)}^{m} a c^{3} d^{2} m^{4} x^{5} e^{7} - 64372 \, {\left(x e + d\right)}^{m} b c^{3} d^{2} m^{3} x^{6} e^{7} - 14112 \, {\left(x e + d\right)}^{m} c^{4} d^{2} m^{2} x^{7} e^{7} + 12 \, {\left(x e + d\right)}^{m} b^{4} d^{3} m^{6} x^{2} e^{6} + 144 \, {\left(x e + d\right)}^{m} a b^{2} c d^{3} m^{6} x^{2} e^{6} + 72 \, {\left(x e + d\right)}^{m} a^{2} c^{2} d^{3} m^{6} x^{2} e^{6} + 2160 \, {\left(x e + d\right)}^{m} b^{3} c d^{3} m^{5} x^{3} e^{6} + 6480 \, {\left(x e + d\right)}^{m} a b c^{2} d^{3} m^{5} x^{3} e^{6} + 33300 \, {\left(x e + d\right)}^{m} b^{2} c^{2} d^{3} m^{4} x^{4} e^{6} + 22200 \, {\left(x e + d\right)}^{m} a c^{3} d^{3} m^{4} x^{4} e^{6} + 61320 \, {\left(x e + d\right)}^{m} b c^{3} d^{3} m^{3} x^{5} e^{6} + 15344 \, {\left(x e + d\right)}^{m} c^{4} d^{3} m^{2} x^{6} e^{6} - 240 \, {\left(x e + d\right)}^{m} b^{3} c d^{4} m^{5} x^{2} e^{5} - 720 \, {\left(x e + d\right)}^{m} a b c^{2} d^{4} m^{5} x^{2} e^{5} - 14400 \, {\left(x e + d\right)}^{m} b^{2} c^{2} d^{4} m^{4} x^{3} e^{5} - 9600 \, {\left(x e + d\right)}^{m} a c^{3} d^{4} m^{4} x^{3} e^{5} - 54600 \, {\left(x e + d\right)}^{m} b c^{3} d^{4} m^{3} x^{4} e^{5} - 16800 \, {\left(x e + d\right)}^{m} c^{4} d^{4} m^{2} x^{5} e^{5} + 2160 \, {\left(x e + d\right)}^{m} b^{2} c^{2} d^{5} m^{4} x^{2} e^{4} + 1440 \, {\left(x e + d\right)}^{m} a c^{3} d^{5} m^{4} x^{2} e^{4} + 40320 \, {\left(x e + d\right)}^{m} b c^{3} d^{5} m^{3} x^{3} e^{4} + 18480 \, {\left(x e + d\right)}^{m} c^{4} d^{5} m^{2} x^{4} e^{4} - 10080 \, {\left(x e + d\right)}^{m} b c^{3} d^{6} m^{3} x^{2} e^{3} - 20160 \, {\left(x e + d\right)}^{m} c^{4} d^{6} m^{2} x^{3} e^{3} + 20160 \, {\left(x e + d\right)}^{m} c^{4} d^{7} m^{2} x^{2} e^{2} + 4 \, {\left(x e + d\right)}^{m} a^{3} b m^{8} x^{2} e^{9} + 252 \, {\left(x e + d\right)}^{m} a^{2} b^{2} m^{7} x^{3} e^{9} + 168 \, {\left(x e + d\right)}^{m} a^{3} c m^{7} x^{3} e^{9} + 2824 \, {\left(x e + d\right)}^{m} a b^{3} m^{6} x^{4} e^{9} + 8472 \, {\left(x e + d\right)}^{m} a^{2} b c m^{6} x^{4} e^{9} + 6100 \, {\left(x e + d\right)}^{m} b^{4} m^{5} x^{5} e^{9} + 73200 \, {\left(x e + d\right)}^{m} a b^{2} c m^{5} x^{5} e^{9} + 36600 \, {\left(x e + d\right)}^{m} a^{2} c^{2} m^{5} x^{5} e^{9} + 117876 \, {\left(x e + d\right)}^{m} b^{3} c m^{4} x^{6} e^{9} + 353628 \, {\left(x e + d\right)}^{m} a b c^{2} m^{4} x^{6} e^{9} + 493752 \, {\left(x e + d\right)}^{m} b^{2} c^{2} m^{3} x^{7} e^{9} + 329168 \, {\left(x e + d\right)}^{m} a c^{3} m^{3} x^{7} e^{9} + 525024 \, {\left(x e + d\right)}^{m} b c^{3} m^{2} x^{8} e^{9} + 109584 \, {\left(x e + d\right)}^{m} c^{4} m x^{9} e^{9} + 4 \, {\left(x e + d\right)}^{m} a^{3} b d m^{8} x e^{8} + 240 \, {\left(x e + d\right)}^{m} a^{2} b^{2} d m^{7} x^{2} e^{8} + 160 \, {\left(x e + d\right)}^{m} a^{3} c d m^{7} x^{2} e^{8} + 2368 \, {\left(x e + d\right)}^{m} a b^{3} d m^{6} x^{3} e^{8} + 7104 \, {\left(x e + d\right)}^{m} a^{2} b c d m^{6} x^{3} e^{8} + 3996 \, {\left(x e + d\right)}^{m} b^{4} d m^{5} x^{4} e^{8} + 47952 \, {\left(x e + d\right)}^{m} a b^{2} c d m^{5} x^{4} e^{8} + 23976 \, {\left(x e + d\right)}^{m} a^{2} c^{2} d m^{5} x^{4} e^{8} + 51796 \, {\left(x e + d\right)}^{m} b^{3} c d m^{4} x^{5} e^{8} + 155388 \, {\left(x e + d\right)}^{m} a b c^{2} d m^{4} x^{5} e^{8} + 125868 \, {\left(x e + d\right)}^{m} b^{2} c^{2} d m^{3} x^{6} e^{8} + 83912 \, {\left(x e + d\right)}^{m} a c^{3} d m^{3} x^{6} e^{8} + 66384 \, {\left(x e + d\right)}^{m} b c^{3} d m^{2} x^{7} e^{8} + 5040 \, {\left(x e + d\right)}^{m} c^{4} d m x^{8} e^{8} - 12 \, {\left(x e + d\right)}^{m} a^{2} b^{2} d^{2} m^{7} x e^{7} - 8 \, {\left(x e + d\right)}^{m} a^{3} c d^{2} m^{7} x e^{7} - 432 \, {\left(x e + d\right)}^{m} a b^{3} d^{2} m^{6} x^{2} e^{7} - 1296 \, {\left(x e + d\right)}^{m} a^{2} b c d^{2} m^{6} x^{2} e^{7} - 1708 \, {\left(x e + d\right)}^{m} b^{4} d^{2} m^{5} x^{3} e^{7} - 20496 \, {\left(x e + d\right)}^{m} a b^{2} c d^{2} m^{5} x^{3} e^{7} - 10248 \, {\left(x e + d\right)}^{m} a^{2} c^{2} d^{2} m^{5} x^{3} e^{7} - 38400 \, {\left(x e + d\right)}^{m} b^{3} c d^{2} m^{4} x^{4} e^{7} - 115200 \, {\left(x e + d\right)}^{m} a b c^{2} d^{2} m^{4} x^{4} e^{7} - 122184 \, {\left(x e + d\right)}^{m} b^{2} c^{2} d^{2} m^{3} x^{5} e^{7} - 81456 \, {\left(x e + d\right)}^{m} a c^{3} d^{2} m^{3} x^{5} e^{7} - 72408 \, {\left(x e + d\right)}^{m} b c^{3} d^{2} m^{2} x^{6} e^{7} - 5760 \, {\left(x e + d\right)}^{m} c^{4} d^{2} m x^{7} e^{7} + 24 \, {\left(x e + d\right)}^{m} a b^{3} d^{3} m^{6} x e^{6} + 72 \, {\left(x e + d\right)}^{m} a^{2} b c d^{3} m^{6} x e^{6} + 372 \, {\left(x e + d\right)}^{m} b^{4} d^{3} m^{5} x^{2} e^{6} + 4464 \, {\left(x e + d\right)}^{m} a b^{2} c d^{3} m^{5} x^{2} e^{6} + 2232 \, {\left(x e + d\right)}^{m} a^{2} c^{2} d^{3} m^{5} x^{2} e^{6} + 21200 \, {\left(x e + d\right)}^{m} b^{3} c d^{3} m^{4} x^{3} e^{6} + 63600 \, {\left(x e + d\right)}^{m} a b c^{2} d^{3} m^{4} x^{3} e^{6} + 112500 \, {\left(x e + d\right)}^{m} b^{2} c^{2} d^{3} m^{3} x^{4} e^{6} + 75000 \, {\left(x e + d\right)}^{m} a c^{3} d^{3} m^{3} x^{4} e^{6} + 79632 \, {\left(x e + d\right)}^{m} b c^{3} d^{3} m^{2} x^{5} e^{6} + 6720 \, {\left(x e + d\right)}^{m} c^{4} d^{3} m x^{6} e^{6} - 24 \, {\left(x e + d\right)}^{m} b^{4} d^{4} m^{5} x e^{5} - 288 \, {\left(x e + d\right)}^{m} a b^{2} c d^{4} m^{5} x e^{5} - 144 \, {\left(x e + d\right)}^{m} a^{2} c^{2} d^{4} m^{5} x e^{5} - 6000 \, {\left(x e + d\right)}^{m} b^{3} c d^{4} m^{4} x^{2} e^{5} - 18000 \, {\left(x e + d\right)}^{m} a b c^{2} d^{4} m^{4} x^{2} e^{5} - 90000 \, {\left(x e + d\right)}^{m} b^{2} c^{2} d^{4} m^{3} x^{3} e^{5} - 60000 \, {\left(x e + d\right)}^{m} a c^{3} d^{4} m^{3} x^{3} e^{5} - 88200 \, {\left(x e + d\right)}^{m} b c^{3} d^{4} m^{2} x^{4} e^{5} - 8064 \, {\left(x e + d\right)}^{m} c^{4} d^{4} m x^{5} e^{5} + 480 \, {\left(x e + d\right)}^{m} b^{3} c d^{5} m^{4} x e^{4} + 1440 \, {\left(x e + d\right)}^{m} a b c^{2} d^{5} m^{4} x e^{4} + 38880 \, {\left(x e + d\right)}^{m} b^{2} c^{2} d^{5} m^{3} x^{2} e^{4} + 25920 \, {\left(x e + d\right)}^{m} a c^{3} d^{5} m^{3} x^{2} e^{4} + 97440 \, {\left(x e + d\right)}^{m} b c^{3} d^{5} m^{2} x^{3} e^{4} + 10080 \, {\left(x e + d\right)}^{m} c^{4} d^{5} m x^{4} e^{4} - 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11640 \, {\left(x e + d\right)}^{m} a b^{3} d^{4} m^{3} e^{5} - 34920 \, {\left(x e + d\right)}^{m} a^{2} b c d^{4} m^{3} e^{5} - 39600 \, {\left(x e + d\right)}^{m} b^{4} d^{4} m^{2} x e^{5} - 475200 \, {\left(x e + d\right)}^{m} a b^{2} c d^{4} m^{2} x e^{5} - 237600 \, {\left(x e + d\right)}^{m} a^{2} c^{2} d^{4} m^{2} x e^{5} - 120960 \, {\left(x e + d\right)}^{m} b^{3} c d^{4} m x^{2} e^{5} - 362880 \, {\left(x e + d\right)}^{m} a b c^{2} d^{4} m x^{2} e^{5} + 8040 \, {\left(x e + d\right)}^{m} b^{4} d^{5} m^{2} e^{4} + 96480 \, {\left(x e + d\right)}^{m} a b^{2} c d^{5} m^{2} e^{4} + 48240 \, {\left(x e + d\right)}^{m} a^{2} c^{2} d^{5} m^{2} e^{4} + 241920 \, {\left(x e + d\right)}^{m} b^{3} c d^{5} m x e^{4} + 725760 \, {\left(x e + d\right)}^{m} a b c^{2} d^{5} m x e^{4} - 91680 \, {\left(x e + d\right)}^{m} b^{3} c d^{6} m e^{3} - 275040 \, {\left(x e + d\right)}^{m} a b c^{2} d^{6} m e^{3} + 311040 \, {\left(x e + d\right)}^{m} b^{2} c^{2} d^{7} e^{2} + 207360 \, {\left(x e + d\right)}^{m} a c^{3} d^{7} e^{2} + 8624 \, {\left(x e + d\right)}^{m} a^{4} m^{5} x e^{9} + 190036 \, {\left(x e + d\right)}^{m} a^{3} b m^{4} x^{2} e^{9} + 866808 \, {\left(x e + d\right)}^{m} a^{2} b^{2} m^{3} x^{3} e^{9} + 577872 \, {\left(x e + d\right)}^{m} a^{3} c m^{3} x^{3} e^{9} + 938736 \, {\left(x e + d\right)}^{m} a b^{3} m^{2} x^{4} e^{9} + 2816208 \, {\left(x e + d\right)}^{m} a^{2} b c m^{2} x^{4} e^{9} + 190800 \, {\left(x e + d\right)}^{m} b^{4} m x^{5} e^{9} + 2289600 \, {\left(x e + d\right)}^{m} a b^{2} c m x^{5} e^{9} + 1144800 \, {\left(x e + d\right)}^{m} a^{2} c^{2} m x^{5} e^{9} + 241920 \, {\left(x e + d\right)}^{m} b^{3} c x^{6} e^{9} + 725760 \, {\left(x e + d\right)}^{m} a b c^{2} x^{6} e^{9} + 8624 \, {\left(x e + d\right)}^{m} a^{4} d m^{5} e^{8} + 161476 \, {\left(x e + d\right)}^{m} a^{3} b d m^{4} x e^{8} + 508740 \, {\left(x e + d\right)}^{m} a^{2} b^{2} d m^{3} x^{2} e^{8} + 339160 \, {\left(x e + d\right)}^{m} a^{3} c d m^{3} x^{2} e^{8} + 271632 \, {\left(x e + d\right)}^{m} a b^{3} d m^{2} x^{3} e^{8} + 814896 \, {\left(x e + d\right)}^{m} a^{2} b c d m^{2} x^{3} e^{8} + 18144 \, {\left(x e + d\right)}^{m} b^{4} d m x^{4} e^{8} + 217728 \, {\left(x e + d\right)}^{m} a b^{2} c d m x^{4} e^{8} + 108864 \, {\left(x e + d\right)}^{m} a^{2} c^{2} d m x^{4} e^{8} - 28560 \, {\left(x e + d\right)}^{m} a^{3} b d^{2} m^{4} e^{7} - 294888 \, {\left(x e + d\right)}^{m} a^{2} b^{2} d^{2} m^{3} x e^{7} - 196592 \, {\left(x e + d\right)}^{m} a^{3} c d^{2} m^{3} x e^{7} - 316728 \, {\left(x e + d\right)}^{m} a b^{3} d^{2} m^{2} x^{2} e^{7} - 950184 \, {\left(x e + d\right)}^{m} a^{2} b c d^{2} m^{2} x^{2} e^{7} - 24192 \, {\left(x e + d\right)}^{m} b^{4} d^{2} m x^{3} e^{7} - 290304 \, {\left(x e + d\right)}^{m} a b^{2} c d^{2} m x^{3} e^{7} - 145152 \, {\left(x e + d\right)}^{m} a^{2} c^{2} d^{2} m x^{3} e^{7} + 63180 \, {\left(x e + d\right)}^{m} a^{2} b^{2} d^{3} m^{3} e^{6} + 42120 \, {\left(x e + d\right)}^{m} a^{3} c d^{3} m^{3} e^{6} + 270576 \, {\left(x e + d\right)}^{m} a b^{3} d^{3} m^{2} x e^{6} + 811728 \, {\left(x e + d\right)}^{m} a^{2} b c d^{3} m^{2} x e^{6} + 36288 \, {\left(x e + d\right)}^{m} b^{4} d^{3} m x^{2} e^{6} + 435456 \, {\left(x e + d\right)}^{m} a b^{2} c d^{3} m x^{2} e^{6} + 217728 \, {\left(x e + d\right)}^{m} a^{2} c^{2} d^{3} m x^{2} e^{6} - 79800 \, {\left(x e + d\right)}^{m} a b^{3} d^{4} m^{2} e^{5} - 239400 \, {\left(x e + d\right)}^{m} a^{2} b c d^{4} m^{2} e^{5} - 72576 \, {\left(x e + d\right)}^{m} b^{4} d^{4} m x e^{5} - 870912 \, {\left(x e + d\right)}^{m} a b^{2} c d^{4} m x e^{5} - 435456 \, {\left(x e + d\right)}^{m} a^{2} c^{2} d^{4} m x e^{5} + 39600 \, {\left(x e + d\right)}^{m} b^{4} d^{5} m e^{4} + 475200 \, {\left(x e + d\right)}^{m} a b^{2} c d^{5} m e^{4} + 237600 \, {\left(x e + d\right)}^{m} a^{2} c^{2} d^{5} m e^{4} - 241920 \, {\left(x e + d\right)}^{m} b^{3} c d^{6} e^{3} - 725760 \, {\left(x e + d\right)}^{m} a b c^{2} d^{6} e^{3} + 54649 \, {\left(x e + d\right)}^{m} a^{4} m^{4} x e^{9} + 697228 \, {\left(x e + d\right)}^{m} a^{3} b m^{3} x^{2} e^{9} + 1741656 \, {\left(x e + d\right)}^{m} a^{2} b^{2} m^{2} x^{3} e^{9} + 1161104 \, {\left(x e + d\right)}^{m} a^{3} c m^{2} x^{3} e^{9} + 935856 \, {\left(x e + d\right)}^{m} a b^{3} m x^{4} e^{9} + 2807568 \, {\left(x e + d\right)}^{m} a^{2} b c m x^{4} e^{9} + 72576 \, {\left(x e + d\right)}^{m} b^{4} x^{5} e^{9} + 870912 \, {\left(x e + d\right)}^{m} a b^{2} c x^{5} e^{9} + 435456 \, {\left(x e + d\right)}^{m} a^{2} c^{2} x^{5} e^{9} + 54649 \, {\left(x e + d\right)}^{m} a^{4} d m^{4} e^{8} + 535752 \, {\left(x e + d\right)}^{m} a^{3} b d m^{3} x e^{8} + 724176 \, {\left(x e + d\right)}^{m} a^{2} b^{2} d m^{2} x^{2} e^{8} + 482784 \, {\left(x e + d\right)}^{m} a^{3} c d m^{2} x^{2} e^{8} + 120960 \, {\left(x e + d\right)}^{m} a b^{3} d m x^{3} e^{8} + 362880 \, {\left(x e + d\right)}^{m} a^{2} b c d m x^{3} e^{8} - 161476 \, {\left(x e + d\right)}^{m} a^{3} b d^{2} m^{3} e^{7} - 722592 \, {\left(x e + d\right)}^{m} a^{2} b^{2} d^{2} m^{2} x e^{7} - 481728 \, {\left(x e + d\right)}^{m} a^{3} c d^{2} m^{2} x e^{7} - 181440 \, {\left(x e + d\right)}^{m} a b^{3} d^{2} m x^{2} e^{7} - 544320 \, {\left(x e + d\right)}^{m} a^{2} b c d^{2} m x^{2} e^{7} + 294888 \, {\left(x e + d\right)}^{m} a^{2} b^{2} d^{3} m^{2} e^{6} + 196592 \, {\left(x e + d\right)}^{m} a^{3} c d^{3} m^{2} e^{6} + 362880 \, {\left(x e + d\right)}^{m} a b^{3} d^{3} m x e^{6} + 1088640 \, {\left(x e + d\right)}^{m} a^{2} b c d^{3} m x e^{6} - 270576 \, {\left(x e + d\right)}^{m} a b^{3} d^{4} m e^{5} - 811728 \, {\left(x e + d\right)}^{m} a^{2} b c d^{4} m e^{5} + 72576 \, {\left(x e + d\right)}^{m} b^{4} d^{5} e^{4} + 870912 \, {\left(x e + d\right)}^{m} a b^{2} c d^{5} e^{4} + 435456 \, {\left(x e + d\right)}^{m} a^{2} c^{2} d^{5} e^{4} + 214676 \, {\left(x e + d\right)}^{m} a^{4} m^{3} x e^{9} + 1500264 \, {\left(x e + d\right)}^{m} a^{3} b m^{2} x^{2} e^{9} + 1811232 \, {\left(x e + d\right)}^{m} a^{2} b^{2} m x^{3} e^{9} + 1207488 \, {\left(x e + d\right)}^{m} a^{3} c m x^{3} e^{9} + 362880 \, {\left(x e + d\right)}^{m} a b^{3} x^{4} e^{9} + 1088640 \, {\left(x e + d\right)}^{m} a^{2} b c x^{4} e^{9} + 214676 \, {\left(x e + d\right)}^{m} a^{4} d m^{3} e^{8} + 964512 \, {\left(x e + d\right)}^{m} a^{3} b d m^{2} x e^{8} + 362880 \, {\left(x e + d\right)}^{m} a^{2} b^{2} d m x^{2} e^{8} + 241920 \, {\left(x e + d\right)}^{m} a^{3} c d m x^{2} e^{8} - 535752 \, {\left(x e + d\right)}^{m} a^{3} b d^{2} m^{2} e^{7} - 725760 \, {\left(x e + d\right)}^{m} a^{2} b^{2} d^{2} m x e^{7} - 483840 \, {\left(x e + d\right)}^{m} a^{3} c d^{2} m x e^{7} + 722592 \, {\left(x e + d\right)}^{m} a^{2} b^{2} d^{3} m e^{6} + 481728 \, {\left(x e + d\right)}^{m} a^{3} c d^{3} m e^{6} - 362880 \, {\left(x e + d\right)}^{m} a b^{3} d^{4} e^{5} - 1088640 \, {\left(x e + d\right)}^{m} a^{2} b c d^{4} e^{5} + 509004 \, {\left(x e + d\right)}^{m} a^{4} m^{2} x e^{9} + 1690272 \, {\left(x e + d\right)}^{m} a^{3} b m x^{2} e^{9} + 725760 \, {\left(x e + d\right)}^{m} a^{2} b^{2} x^{3} e^{9} + 483840 \, {\left(x e + d\right)}^{m} a^{3} c x^{3} e^{9} + 509004 \, {\left(x e + d\right)}^{m} a^{4} d m^{2} e^{8} + 725760 \, {\left(x e + d\right)}^{m} a^{3} b d m x e^{8} - 964512 \, {\left(x e + d\right)}^{m} a^{3} b d^{2} m e^{7} + 725760 \, {\left(x e + d\right)}^{m} a^{2} b^{2} d^{3} e^{6} + 483840 \, {\left(x e + d\right)}^{m} a^{3} c d^{3} e^{6} + 663696 \, {\left(x e + d\right)}^{m} a^{4} m x e^{9} + 725760 \, {\left(x e + d\right)}^{m} a^{3} b x^{2} e^{9} + 663696 \, {\left(x e + d\right)}^{m} a^{4} d m e^{8} - 725760 \, {\left(x e + d\right)}^{m} a^{3} b d^{2} e^{7} + 362880 \, {\left(x e + d\right)}^{m} a^{4} x e^{9} + 362880 \, {\left(x e + d\right)}^{m} a^{4} d e^{8}}{m^{9} e^{9} + 45 \, m^{8} e^{9} + 870 \, m^{7} e^{9} + 9450 \, m^{6} e^{9} + 63273 \, m^{5} e^{9} + 269325 \, m^{4} e^{9} + 723680 \, m^{3} e^{9} + 1172700 \, m^{2} e^{9} + 1026576 \, m e^{9} + 362880 \, e^{9}}"," ",0,"((x*e + d)^m*c^4*m^8*x^9*e^9 + (x*e + d)^m*c^4*d*m^8*x^8*e^8 + 4*(x*e + d)^m*b*c^3*m^8*x^8*e^9 + 36*(x*e + d)^m*c^4*m^7*x^9*e^9 + 4*(x*e + d)^m*b*c^3*d*m^8*x^7*e^8 + 28*(x*e + d)^m*c^4*d*m^7*x^8*e^8 - 8*(x*e + d)^m*c^4*d^2*m^7*x^7*e^7 + 6*(x*e + d)^m*b^2*c^2*m^8*x^7*e^9 + 4*(x*e + d)^m*a*c^3*m^8*x^7*e^9 + 148*(x*e + d)^m*b*c^3*m^7*x^8*e^9 + 546*(x*e + d)^m*c^4*m^6*x^9*e^9 + 6*(x*e + d)^m*b^2*c^2*d*m^8*x^6*e^8 + 4*(x*e + d)^m*a*c^3*d*m^8*x^6*e^8 + 120*(x*e + d)^m*b*c^3*d*m^7*x^7*e^8 + 322*(x*e + d)^m*c^4*d*m^6*x^8*e^8 - 28*(x*e + d)^m*b*c^3*d^2*m^7*x^6*e^7 - 168*(x*e + d)^m*c^4*d^2*m^6*x^7*e^7 + 56*(x*e + d)^m*c^4*d^3*m^6*x^6*e^6 + 4*(x*e + d)^m*b^3*c*m^8*x^6*e^9 + 12*(x*e + d)^m*a*b*c^2*m^8*x^6*e^9 + 228*(x*e + d)^m*b^2*c^2*m^7*x^7*e^9 + 152*(x*e + d)^m*a*c^3*m^7*x^7*e^9 + 2296*(x*e + d)^m*b*c^3*m^6*x^8*e^9 + 4536*(x*e + d)^m*c^4*m^5*x^9*e^9 + 4*(x*e + d)^m*b^3*c*d*m^8*x^5*e^8 + 12*(x*e + d)^m*a*b*c^2*d*m^8*x^5*e^8 + 192*(x*e + d)^m*b^2*c^2*d*m^7*x^6*e^8 + 128*(x*e + d)^m*a*c^3*d*m^7*x^6*e^8 + 1456*(x*e + d)^m*b*c^3*d*m^6*x^7*e^8 + 1960*(x*e + d)^m*c^4*d*m^5*x^8*e^8 - 36*(x*e + d)^m*b^2*c^2*d^2*m^7*x^5*e^7 - 24*(x*e + d)^m*a*c^3*d^2*m^7*x^5*e^7 - 672*(x*e + d)^m*b*c^3*d^2*m^6*x^6*e^7 - 1400*(x*e + d)^m*c^4*d^2*m^5*x^7*e^7 + 168*(x*e + d)^m*b*c^3*d^3*m^6*x^5*e^6 + 840*(x*e + d)^m*c^4*d^3*m^5*x^6*e^6 - 336*(x*e + d)^m*c^4*d^4*m^5*x^5*e^5 + (x*e + d)^m*b^4*m^8*x^5*e^9 + 12*(x*e + d)^m*a*b^2*c*m^8*x^5*e^9 + 6*(x*e + d)^m*a^2*c^2*m^8*x^5*e^9 + 156*(x*e + d)^m*b^3*c*m^7*x^6*e^9 + 468*(x*e + d)^m*a*b*c^2*m^7*x^6*e^9 + 3624*(x*e + d)^m*b^2*c^2*m^6*x^7*e^9 + 2416*(x*e + d)^m*a*c^3*m^6*x^7*e^9 + 19432*(x*e + d)^m*b*c^3*m^5*x^8*e^9 + 22449*(x*e + d)^m*c^4*m^4*x^9*e^9 + (x*e + d)^m*b^4*d*m^8*x^4*e^8 + 12*(x*e + d)^m*a*b^2*c*d*m^8*x^4*e^8 + 6*(x*e + d)^m*a^2*c^2*d*m^8*x^4*e^8 + 136*(x*e + d)^m*b^3*c*d*m^7*x^5*e^8 + 408*(x*e + d)^m*a*b*c^2*d*m^7*x^5*e^8 + 2472*(x*e + d)^m*b^2*c^2*d*m^6*x^6*e^8 + 1648*(x*e + d)^m*a*c^3*d*m^6*x^6*e^8 + 9240*(x*e + d)^m*b*c^3*d*m^5*x^7*e^8 + 6769*(x*e + d)^m*c^4*d*m^4*x^8*e^8 - 20*(x*e + d)^m*b^3*c*d^2*m^7*x^4*e^7 - 60*(x*e + d)^m*a*b*c^2*d^2*m^7*x^4*e^7 - 972*(x*e + d)^m*b^2*c^2*d^2*m^6*x^5*e^7 - 648*(x*e + d)^m*a*c^3*d^2*m^6*x^5*e^7 - 6160*(x*e + d)^m*b*c^3*d^2*m^5*x^6*e^7 - 5880*(x*e + d)^m*c^4*d^2*m^4*x^7*e^7 + 180*(x*e + d)^m*b^2*c^2*d^3*m^6*x^4*e^6 + 120*(x*e + d)^m*a*c^3*d^3*m^6*x^4*e^6 + 3192*(x*e + d)^m*b*c^3*d^3*m^5*x^5*e^6 + 4760*(x*e + d)^m*c^4*d^3*m^4*x^6*e^6 - 840*(x*e + d)^m*b*c^3*d^4*m^5*x^4*e^5 - 3360*(x*e + d)^m*c^4*d^4*m^4*x^5*e^5 + 1680*(x*e + d)^m*c^4*d^5*m^4*x^4*e^4 + 4*(x*e + d)^m*a*b^3*m^8*x^4*e^9 + 12*(x*e + d)^m*a^2*b*c*m^8*x^4*e^9 + 40*(x*e + d)^m*b^4*m^7*x^5*e^9 + 480*(x*e + d)^m*a*b^2*c*m^7*x^5*e^9 + 240*(x*e + d)^m*a^2*c^2*m^7*x^5*e^9 + 2544*(x*e + d)^m*b^3*c*m^6*x^6*e^9 + 7632*(x*e + d)^m*a*b*c^2*m^6*x^6*e^9 + 31332*(x*e + d)^m*b^2*c^2*m^5*x^7*e^9 + 20888*(x*e + d)^m*a*c^3*m^5*x^7*e^9 + 97636*(x*e + d)^m*b*c^3*m^4*x^8*e^9 + 67284*(x*e + d)^m*c^4*m^3*x^9*e^9 + 4*(x*e + d)^m*a*b^3*d*m^8*x^3*e^8 + 12*(x*e + d)^m*a^2*b*c*d*m^8*x^3*e^8 + 36*(x*e + d)^m*b^4*d*m^7*x^4*e^8 + 432*(x*e + d)^m*a*b^2*c*d*m^7*x^4*e^8 + 216*(x*e + d)^m*a^2*c^2*d*m^7*x^4*e^8 + 1864*(x*e + d)^m*b^3*c*d*m^6*x^5*e^8 + 5592*(x*e + d)^m*a*b*c^2*d*m^6*x^5*e^8 + 16500*(x*e + d)^m*b^2*c^2*d*m^5*x^6*e^8 + 11000*(x*e + d)^m*a*c^3*d*m^5*x^6*e^8 + 32956*(x*e + d)^m*b*c^3*d*m^4*x^7*e^8 + 13132*(x*e + d)^m*c^4*d*m^3*x^8*e^8 - 4*(x*e + d)^m*b^4*d^2*m^7*x^3*e^7 - 48*(x*e + d)^m*a*b^2*c*d^2*m^7*x^3*e^7 - 24*(x*e + d)^m*a^2*c^2*d^2*m^7*x^3*e^7 - 600*(x*e + d)^m*b^3*c*d^2*m^6*x^4*e^7 - 1800*(x*e + d)^m*a*b*c^2*d^2*m^6*x^4*e^7 - 9972*(x*e + d)^m*b^2*c^2*d^2*m^5*x^5*e^7 - 6648*(x*e + d)^m*a*c^3*d^2*m^5*x^5*e^7 - 27720*(x*e + d)^m*b*c^3*d^2*m^4*x^6*e^7 - 12992*(x*e + d)^m*c^4*d^2*m^3*x^7*e^7 + 80*(x*e + d)^m*b^3*c*d^3*m^6*x^3*e^6 + 240*(x*e + d)^m*a*b*c^2*d^3*m^6*x^3*e^6 + 4140*(x*e + d)^m*b^2*c^2*d^3*m^5*x^4*e^6 + 2760*(x*e + d)^m*a*c^3*d^3*m^5*x^4*e^6 + 21000*(x*e + d)^m*b*c^3*d^3*m^4*x^5*e^6 + 12600*(x*e + d)^m*c^4*d^3*m^3*x^6*e^6 - 720*(x*e + d)^m*b^2*c^2*d^4*m^5*x^3*e^5 - 480*(x*e + d)^m*a*c^3*d^4*m^5*x^3*e^5 - 12600*(x*e + d)^m*b*c^3*d^4*m^4*x^4*e^5 - 11760*(x*e + d)^m*c^4*d^4*m^3*x^5*e^5 + 3360*(x*e + d)^m*b*c^3*d^5*m^4*x^3*e^4 + 10080*(x*e + d)^m*c^4*d^5*m^3*x^4*e^4 - 6720*(x*e + d)^m*c^4*d^6*m^3*x^3*e^3 + 6*(x*e + d)^m*a^2*b^2*m^8*x^3*e^9 + 4*(x*e + d)^m*a^3*c*m^8*x^3*e^9 + 164*(x*e + d)^m*a*b^3*m^7*x^4*e^9 + 492*(x*e + d)^m*a^2*b*c*m^7*x^4*e^9 + 670*(x*e + d)^m*b^4*m^6*x^5*e^9 + 8040*(x*e + d)^m*a*b^2*c*m^6*x^5*e^9 + 4020*(x*e + d)^m*a^2*c^2*m^6*x^5*e^9 + 22536*(x*e + d)^m*b^3*c*m^5*x^6*e^9 + 67608*(x*e + d)^m*a*b*c^2*m^5*x^6*e^9 + 160314*(x*e + d)^m*b^2*c^2*m^4*x^7*e^9 + 106876*(x*e + d)^m*a*c^3*m^4*x^7*e^9 + 296212*(x*e + d)^m*b*c^3*m^3*x^8*e^9 + 118124*(x*e + d)^m*c^4*m^2*x^9*e^9 + 6*(x*e + d)^m*a^2*b^2*d*m^8*x^2*e^8 + 4*(x*e + d)^m*a^3*c*d*m^8*x^2*e^8 + 152*(x*e + d)^m*a*b^3*d*m^7*x^3*e^8 + 456*(x*e + d)^m*a^2*b*c*d*m^7*x^3*e^8 + 526*(x*e + d)^m*b^4*d*m^6*x^4*e^8 + 6312*(x*e + d)^m*a*b^2*c*d*m^6*x^4*e^8 + 3156*(x*e + d)^m*a^2*c^2*d*m^6*x^4*e^8 + 13216*(x*e + d)^m*b^3*c*d*m^5*x^5*e^8 + 39648*(x*e + d)^m*a*b*c^2*d*m^5*x^5*e^8 + 61314*(x*e + d)^m*b^2*c^2*d*m^4*x^6*e^8 + 40876*(x*e + d)^m*a*c^3*d*m^4*x^6*e^8 + 65520*(x*e + d)^m*b*c^3*d*m^3*x^7*e^8 + 13068*(x*e + d)^m*c^4*d*m^2*x^8*e^8 - 12*(x*e + d)^m*a*b^3*d^2*m^7*x^2*e^7 - 36*(x*e + d)^m*a^2*b*c*d^2*m^7*x^2*e^7 - 132*(x*e + d)^m*b^4*d^2*m^6*x^3*e^7 - 1584*(x*e + d)^m*a*b^2*c*d^2*m^6*x^3*e^7 - 792*(x*e + d)^m*a^2*c^2*d^2*m^6*x^3*e^7 - 6920*(x*e + d)^m*b^3*c*d^2*m^5*x^4*e^7 - 20760*(x*e + d)^m*a*b*c^2*d^2*m^5*x^4*e^7 - 49140*(x*e + d)^m*b^2*c^2*d^2*m^4*x^5*e^7 - 32760*(x*e + d)^m*a*c^3*d^2*m^4*x^5*e^7 - 64372*(x*e + d)^m*b*c^3*d^2*m^3*x^6*e^7 - 14112*(x*e + d)^m*c^4*d^2*m^2*x^7*e^7 + 12*(x*e + d)^m*b^4*d^3*m^6*x^2*e^6 + 144*(x*e + d)^m*a*b^2*c*d^3*m^6*x^2*e^6 + 72*(x*e + d)^m*a^2*c^2*d^3*m^6*x^2*e^6 + 2160*(x*e + d)^m*b^3*c*d^3*m^5*x^3*e^6 + 6480*(x*e + d)^m*a*b*c^2*d^3*m^5*x^3*e^6 + 33300*(x*e + d)^m*b^2*c^2*d^3*m^4*x^4*e^6 + 22200*(x*e + d)^m*a*c^3*d^3*m^4*x^4*e^6 + 61320*(x*e + d)^m*b*c^3*d^3*m^3*x^5*e^6 + 15344*(x*e + d)^m*c^4*d^3*m^2*x^6*e^6 - 240*(x*e + d)^m*b^3*c*d^4*m^5*x^2*e^5 - 720*(x*e + d)^m*a*b*c^2*d^4*m^5*x^2*e^5 - 14400*(x*e + d)^m*b^2*c^2*d^4*m^4*x^3*e^5 - 9600*(x*e + d)^m*a*c^3*d^4*m^4*x^3*e^5 - 54600*(x*e + d)^m*b*c^3*d^4*m^3*x^4*e^5 - 16800*(x*e + d)^m*c^4*d^4*m^2*x^5*e^5 + 2160*(x*e + d)^m*b^2*c^2*d^5*m^4*x^2*e^4 + 1440*(x*e + d)^m*a*c^3*d^5*m^4*x^2*e^4 + 40320*(x*e + d)^m*b*c^3*d^5*m^3*x^3*e^4 + 18480*(x*e + d)^m*c^4*d^5*m^2*x^4*e^4 - 10080*(x*e + d)^m*b*c^3*d^6*m^3*x^2*e^3 - 20160*(x*e + d)^m*c^4*d^6*m^2*x^3*e^3 + 20160*(x*e + d)^m*c^4*d^7*m^2*x^2*e^2 + 4*(x*e + d)^m*a^3*b*m^8*x^2*e^9 + 252*(x*e + d)^m*a^2*b^2*m^7*x^3*e^9 + 168*(x*e + d)^m*a^3*c*m^7*x^3*e^9 + 2824*(x*e + d)^m*a*b^3*m^6*x^4*e^9 + 8472*(x*e + d)^m*a^2*b*c*m^6*x^4*e^9 + 6100*(x*e + d)^m*b^4*m^5*x^5*e^9 + 73200*(x*e + d)^m*a*b^2*c*m^5*x^5*e^9 + 36600*(x*e + d)^m*a^2*c^2*m^5*x^5*e^9 + 117876*(x*e + d)^m*b^3*c*m^4*x^6*e^9 + 353628*(x*e + d)^m*a*b*c^2*m^4*x^6*e^9 + 493752*(x*e + d)^m*b^2*c^2*m^3*x^7*e^9 + 329168*(x*e + d)^m*a*c^3*m^3*x^7*e^9 + 525024*(x*e + d)^m*b*c^3*m^2*x^8*e^9 + 109584*(x*e + d)^m*c^4*m*x^9*e^9 + 4*(x*e + d)^m*a^3*b*d*m^8*x*e^8 + 240*(x*e + d)^m*a^2*b^2*d*m^7*x^2*e^8 + 160*(x*e + d)^m*a^3*c*d*m^7*x^2*e^8 + 2368*(x*e + d)^m*a*b^3*d*m^6*x^3*e^8 + 7104*(x*e + d)^m*a^2*b*c*d*m^6*x^3*e^8 + 3996*(x*e + d)^m*b^4*d*m^5*x^4*e^8 + 47952*(x*e + d)^m*a*b^2*c*d*m^5*x^4*e^8 + 23976*(x*e + d)^m*a^2*c^2*d*m^5*x^4*e^8 + 51796*(x*e + d)^m*b^3*c*d*m^4*x^5*e^8 + 155388*(x*e + d)^m*a*b*c^2*d*m^4*x^5*e^8 + 125868*(x*e + d)^m*b^2*c^2*d*m^3*x^6*e^8 + 83912*(x*e + d)^m*a*c^3*d*m^3*x^6*e^8 + 66384*(x*e + d)^m*b*c^3*d*m^2*x^7*e^8 + 5040*(x*e + d)^m*c^4*d*m*x^8*e^8 - 12*(x*e + d)^m*a^2*b^2*d^2*m^7*x*e^7 - 8*(x*e + d)^m*a^3*c*d^2*m^7*x*e^7 - 432*(x*e + d)^m*a*b^3*d^2*m^6*x^2*e^7 - 1296*(x*e + d)^m*a^2*b*c*d^2*m^6*x^2*e^7 - 1708*(x*e + d)^m*b^4*d^2*m^5*x^3*e^7 - 20496*(x*e + d)^m*a*b^2*c*d^2*m^5*x^3*e^7 - 10248*(x*e + d)^m*a^2*c^2*d^2*m^5*x^3*e^7 - 38400*(x*e + d)^m*b^3*c*d^2*m^4*x^4*e^7 - 115200*(x*e + d)^m*a*b*c^2*d^2*m^4*x^4*e^7 - 122184*(x*e + d)^m*b^2*c^2*d^2*m^3*x^5*e^7 - 81456*(x*e + d)^m*a*c^3*d^2*m^3*x^5*e^7 - 72408*(x*e + d)^m*b*c^3*d^2*m^2*x^6*e^7 - 5760*(x*e + d)^m*c^4*d^2*m*x^7*e^7 + 24*(x*e + d)^m*a*b^3*d^3*m^6*x*e^6 + 72*(x*e + d)^m*a^2*b*c*d^3*m^6*x*e^6 + 372*(x*e + d)^m*b^4*d^3*m^5*x^2*e^6 + 4464*(x*e + d)^m*a*b^2*c*d^3*m^5*x^2*e^6 + 2232*(x*e + d)^m*a^2*c^2*d^3*m^5*x^2*e^6 + 21200*(x*e + d)^m*b^3*c*d^3*m^4*x^3*e^6 + 63600*(x*e + d)^m*a*b*c^2*d^3*m^4*x^3*e^6 + 112500*(x*e + d)^m*b^2*c^2*d^3*m^3*x^4*e^6 + 75000*(x*e + d)^m*a*c^3*d^3*m^3*x^4*e^6 + 79632*(x*e + d)^m*b*c^3*d^3*m^2*x^5*e^6 + 6720*(x*e + d)^m*c^4*d^3*m*x^6*e^6 - 24*(x*e + d)^m*b^4*d^4*m^5*x*e^5 - 288*(x*e + d)^m*a*b^2*c*d^4*m^5*x*e^5 - 144*(x*e + d)^m*a^2*c^2*d^4*m^5*x*e^5 - 6000*(x*e + d)^m*b^3*c*d^4*m^4*x^2*e^5 - 18000*(x*e + d)^m*a*b*c^2*d^4*m^4*x^2*e^5 - 90000*(x*e + d)^m*b^2*c^2*d^4*m^3*x^3*e^5 - 60000*(x*e + d)^m*a*c^3*d^4*m^3*x^3*e^5 - 88200*(x*e + d)^m*b*c^3*d^4*m^2*x^4*e^5 - 8064*(x*e + d)^m*c^4*d^4*m*x^5*e^5 + 480*(x*e + d)^m*b^3*c*d^5*m^4*x*e^4 + 1440*(x*e + d)^m*a*b*c^2*d^5*m^4*x*e^4 + 38880*(x*e + d)^m*b^2*c^2*d^5*m^3*x^2*e^4 + 25920*(x*e + d)^m*a*c^3*d^5*m^3*x^2*e^4 + 97440*(x*e + d)^m*b*c^3*d^5*m^2*x^3*e^4 + 10080*(x*e + d)^m*c^4*d^5*m*x^4*e^4 - 4320*(x*e + d)^m*b^2*c^2*d^6*m^3*x*e^3 - 2880*(x*e + d)^m*a*c^3*d^6*m^3*x*e^3 - 100800*(x*e + d)^m*b*c^3*d^6*m^2*x^2*e^3 - 13440*(x*e + d)^m*c^4*d^6*m*x^3*e^3 + 20160*(x*e + d)^m*b*c^3*d^7*m^2*x*e^2 + 20160*(x*e + d)^m*c^4*d^7*m*x^2*e^2 - 40320*(x*e + d)^m*c^4*d^8*m*x*e + (x*e + d)^m*a^4*m^8*x*e^9 + 172*(x*e + d)^m*a^3*b*m^7*x^2*e^9 + 4464*(x*e + d)^m*a^2*b^2*m^6*x^3*e^9 + 2976*(x*e + d)^m*a^3*c*m^6*x^3*e^9 + 26504*(x*e + d)^m*a*b^3*m^5*x^4*e^9 + 79512*(x*e + d)^m*a^2*b*c*m^5*x^4*e^9 + 32773*(x*e + d)^m*b^4*m^4*x^5*e^9 + 393276*(x*e + d)^m*a*b^2*c*m^4*x^5*e^9 + 196638*(x*e + d)^m*a^2*c^2*m^4*x^5*e^9 + 370044*(x*e + d)^m*b^3*c*m^3*x^6*e^9 + 1110132*(x*e + d)^m*a*b*c^2*m^3*x^6*e^9 + 885816*(x*e + d)^m*b^2*c^2*m^2*x^7*e^9 + 590544*(x*e + d)^m*a*c^3*m^2*x^7*e^9 + 490608*(x*e + d)^m*b*c^3*m*x^8*e^9 + 40320*(x*e + d)^m*c^4*x^9*e^9 + (x*e + d)^m*a^4*d*m^8*e^8 + 168*(x*e + d)^m*a^3*b*d*m^7*x*e^8 + 3984*(x*e + d)^m*a^2*b^2*d*m^6*x^2*e^8 + 2656*(x*e + d)^m*a^3*c*d*m^6*x^2*e^8 + 19400*(x*e + d)^m*a*b^3*d*m^5*x^3*e^8 + 58200*(x*e + d)^m*a^2*b*c*d*m^5*x^3*e^8 + 16789*(x*e + d)^m*b^4*d*m^4*x^4*e^8 + 201468*(x*e + d)^m*a*b^2*c*d*m^4*x^4*e^8 + 100734*(x*e + d)^m*a^2*c^2*d*m^4*x^4*e^8 + 111064*(x*e + d)^m*b^3*c*d*m^3*x^5*e^8 + 333192*(x*e + d)^m*a*b*c^2*d*m^3*x^5*e^8 + 130608*(x*e + d)^m*b^2*c^2*d*m^2*x^6*e^8 + 87072*(x*e + d)^m*a*c^3*d*m^2*x^6*e^8 + 25920*(x*e + d)^m*b*c^3*d*m*x^7*e^8 - 4*(x*e + d)^m*a^3*b*d^2*m^7*e^7 - 468*(x*e + d)^m*a^2*b^2*d^2*m^6*x*e^7 - 312*(x*e + d)^m*a^3*c*d^2*m^6*x*e^7 - 6240*(x*e + d)^m*a*b^3*d^2*m^5*x^2*e^7 - 18720*(x*e + d)^m*a^2*b*c*d^2*m^5*x^2*e^7 - 10860*(x*e + d)^m*b^4*d^2*m^4*x^3*e^7 - 130320*(x*e + d)^m*a*b^2*c*d^2*m^4*x^3*e^7 - 65160*(x*e + d)^m*a^2*c^2*d^2*m^4*x^3*e^7 - 105380*(x*e + d)^m*b^3*c*d^2*m^3*x^4*e^7 - 316140*(x*e + d)^m*a*b*c^2*d^2*m^3*x^4*e^7 - 144288*(x*e + d)^m*b^2*c^2*d^2*m^2*x^5*e^7 - 96192*(x*e + d)^m*a*c^3*d^2*m^2*x^5*e^7 - 30240*(x*e + d)^m*b*c^3*d^2*m*x^6*e^7 + 12*(x*e + d)^m*a^2*b^2*d^3*m^6*e^6 + 8*(x*e + d)^m*a^3*c*d^3*m^6*e^6 + 840*(x*e + d)^m*a*b^3*d^3*m^5*x*e^6 + 2520*(x*e + d)^m*a^2*b*c*d^3*m^5*x*e^6 + 4380*(x*e + d)^m*b^4*d^3*m^4*x^2*e^6 + 52560*(x*e + d)^m*a*b^2*c*d^3*m^4*x^2*e^6 + 26280*(x*e + d)^m*a^2*c^2*d^3*m^4*x^2*e^6 + 90000*(x*e + d)^m*b^3*c*d^3*m^3*x^3*e^6 + 270000*(x*e + d)^m*a*b*c^2*d^3*m^3*x^3*e^6 + 160920*(x*e + d)^m*b^2*c^2*d^3*m^2*x^4*e^6 + 107280*(x*e + d)^m*a*c^3*d^3*m^2*x^4*e^6 + 36288*(x*e + d)^m*b*c^3*d^3*m*x^5*e^6 - 24*(x*e + d)^m*a*b^3*d^4*m^5*e^5 - 72*(x*e + d)^m*a^2*b*c*d^4*m^5*e^5 - 720*(x*e + d)^m*b^4*d^4*m^4*x*e^5 - 8640*(x*e + d)^m*a*b^2*c*d^4*m^4*x*e^5 - 4320*(x*e + d)^m*a^2*c^2*d^4*m^4*x*e^5 - 51600*(x*e + d)^m*b^3*c*d^4*m^3*x^2*e^5 - 154800*(x*e + d)^m*a*b*c^2*d^4*m^3*x^2*e^5 - 180000*(x*e + d)^m*b^2*c^2*d^4*m^2*x^3*e^5 - 120000*(x*e + d)^m*a*c^3*d^4*m^2*x^3*e^5 - 45360*(x*e + d)^m*b*c^3*d^4*m*x^4*e^5 + 24*(x*e + d)^m*b^4*d^5*m^4*e^4 + 288*(x*e + d)^m*a*b^2*c*d^5*m^4*e^4 + 144*(x*e + d)^m*a^2*c^2*d^5*m^4*e^4 + 11520*(x*e + d)^m*b^3*c*d^5*m^3*x*e^4 + 34560*(x*e + d)^m*a*b*c^2*d^5*m^3*x*e^4 + 192240*(x*e + d)^m*b^2*c^2*d^5*m^2*x^2*e^4 + 128160*(x*e + d)^m*a*c^3*d^5*m^2*x^2*e^4 + 60480*(x*e + d)^m*b*c^3*d^5*m*x^3*e^4 - 480*(x*e + d)^m*b^3*c*d^6*m^3*e^3 - 1440*(x*e + d)^m*a*b*c^2*d^6*m^3*e^3 - 73440*(x*e + d)^m*b^2*c^2*d^6*m^2*x*e^3 - 48960*(x*e + d)^m*a*c^3*d^6*m^2*x*e^3 - 90720*(x*e + d)^m*b*c^3*d^6*m*x^2*e^3 + 4320*(x*e + d)^m*b^2*c^2*d^7*m^2*e^2 + 2880*(x*e + d)^m*a*c^3*d^7*m^2*e^2 + 181440*(x*e + d)^m*b*c^3*d^7*m*x*e^2 - 20160*(x*e + d)^m*b*c^3*d^8*m*e + 40320*(x*e + d)^m*c^4*d^9 + 44*(x*e + d)^m*a^4*m^7*x*e^9 + 3136*(x*e + d)^m*a^3*b*m^6*x^2*e^9 + 43308*(x*e + d)^m*a^2*b^2*m^5*x^3*e^9 + 28872*(x*e + d)^m*a^3*c*m^5*x^3*e^9 + 147076*(x*e + d)^m*a*b^3*m^4*x^4*e^9 + 441228*(x*e + d)^m*a^2*b*c*m^4*x^4*e^9 + 105460*(x*e + d)^m*b^4*m^3*x^5*e^9 + 1265520*(x*e + d)^m*a*b^2*c*m^3*x^5*e^9 + 632760*(x*e + d)^m*a^2*c^2*m^3*x^5*e^9 + 674456*(x*e + d)^m*b^3*c*m^2*x^6*e^9 + 2023368*(x*e + d)^m*a*b*c^2*m^2*x^6*e^9 + 835488*(x*e + d)^m*b^2*c^2*m*x^7*e^9 + 556992*(x*e + d)^m*a*c^3*m*x^7*e^9 + 181440*(x*e + d)^m*b*c^3*x^8*e^9 + 44*(x*e + d)^m*a^4*d*m^7*e^8 + 2968*(x*e + d)^m*a^3*b*d*m^6*x*e^8 + 35340*(x*e + d)^m*a^2*b^2*d*m^5*x^2*e^8 + 23560*(x*e + d)^m*a^3*c*d*m^5*x^2*e^8 + 88876*(x*e + d)^m*a*b^3*d*m^4*x^3*e^8 + 266628*(x*e + d)^m*a^2*b*c*d*m^4*x^3*e^8 + 38304*(x*e + d)^m*b^4*d*m^3*x^4*e^8 + 459648*(x*e + d)^m*a*b^2*c*d*m^3*x^4*e^8 + 229824*(x*e + d)^m*a^2*c^2*d*m^3*x^4*e^8 + 119136*(x*e + d)^m*b^3*c*d*m^2*x^5*e^8 + 357408*(x*e + d)^m*a*b*c^2*d*m^2*x^5*e^8 + 51840*(x*e + d)^m*b^2*c^2*d*m*x^6*e^8 + 34560*(x*e + d)^m*a*c^3*d*m*x^6*e^8 - 168*(x*e + d)^m*a^3*b*d^2*m^6*e^7 - 7500*(x*e + d)^m*a^2*b^2*d^2*m^5*x*e^7 - 5000*(x*e + d)^m*a^3*c*d^2*m^5*x*e^7 - 45720*(x*e + d)^m*a*b^3*d^2*m^4*x^2*e^7 - 137160*(x*e + d)^m*a^2*b*c*d^2*m^4*x^2*e^7 - 34576*(x*e + d)^m*b^4*d^2*m^3*x^3*e^7 - 414912*(x*e + d)^m*a*b^2*c*d^2*m^3*x^3*e^7 - 207456*(x*e + d)^m*a^2*c^2*d^2*m^3*x^3*e^7 - 133800*(x*e + d)^m*b^3*c*d^2*m^2*x^4*e^7 - 401400*(x*e + d)^m*a*b*c^2*d^2*m^2*x^4*e^7 - 62208*(x*e + d)^m*b^2*c^2*d^2*m*x^5*e^7 - 41472*(x*e + d)^m*a*c^3*d^2*m*x^5*e^7 + 468*(x*e + d)^m*a^2*b^2*d^3*m^5*e^6 + 312*(x*e + d)^m*a^3*c*d^3*m^5*e^6 + 11640*(x*e + d)^m*a*b^3*d^3*m^4*x*e^6 + 34920*(x*e + d)^m*a^2*b*c*d^3*m^4*x*e^6 + 23820*(x*e + d)^m*b^4*d^3*m^3*x^2*e^6 + 285840*(x*e + d)^m*a*b^2*c*d^3*m^3*x^2*e^6 + 142920*(x*e + d)^m*a^2*c^2*d^3*m^3*x^2*e^6 + 151520*(x*e + d)^m*b^3*c*d^3*m^2*x^3*e^6 + 454560*(x*e + d)^m*a*b*c^2*d^3*m^2*x^3*e^6 + 77760*(x*e + d)^m*b^2*c^2*d^3*m*x^4*e^6 + 51840*(x*e + d)^m*a*c^3*d^3*m*x^4*e^6 - 840*(x*e + d)^m*a*b^3*d^4*m^4*e^5 - 2520*(x*e + d)^m*a^2*b*c*d^4*m^4*e^5 - 8040*(x*e + d)^m*b^4*d^4*m^3*x*e^5 - 96480*(x*e + d)^m*a*b^2*c*d^4*m^3*x*e^5 - 48240*(x*e + d)^m*a^2*c^2*d^4*m^3*x*e^5 - 166800*(x*e + d)^m*b^3*c*d^4*m^2*x^2*e^5 - 500400*(x*e + d)^m*a*b*c^2*d^4*m^2*x^2*e^5 - 103680*(x*e + d)^m*b^2*c^2*d^4*m*x^3*e^5 - 69120*(x*e + d)^m*a*c^3*d^4*m*x^3*e^5 + 720*(x*e + d)^m*b^4*d^5*m^3*e^4 + 8640*(x*e + d)^m*a*b^2*c*d^5*m^3*e^4 + 4320*(x*e + d)^m*a^2*c^2*d^5*m^3*e^4 + 91680*(x*e + d)^m*b^3*c*d^5*m^2*x*e^4 + 275040*(x*e + d)^m*a*b*c^2*d^5*m^2*x*e^4 + 155520*(x*e + d)^m*b^2*c^2*d^5*m*x^2*e^4 + 103680*(x*e + d)^m*a*c^3*d^5*m*x^2*e^4 - 11520*(x*e + d)^m*b^3*c*d^6*m^2*e^3 - 34560*(x*e + d)^m*a*b*c^2*d^6*m^2*e^3 - 311040*(x*e + d)^m*b^2*c^2*d^6*m*x*e^3 - 207360*(x*e + d)^m*a*c^3*d^6*m*x*e^3 + 73440*(x*e + d)^m*b^2*c^2*d^7*m*e^2 + 48960*(x*e + d)^m*a*c^3*d^7*m*e^2 - 181440*(x*e + d)^m*b*c^3*d^8*e + 826*(x*e + d)^m*a^4*m^6*x*e^9 + 31528*(x*e + d)^m*a^3*b*m^5*x^2*e^9 + 249714*(x*e + d)^m*a^2*b^2*m^4*x^3*e^9 + 166476*(x*e + d)^m*a^3*c*m^4*x^3*e^9 + 488996*(x*e + d)^m*a*b^3*m^3*x^4*e^9 + 1466988*(x*e + d)^m*a^2*b*c*m^3*x^4*e^9 + 196380*(x*e + d)^m*b^4*m^2*x^5*e^9 + 2356560*(x*e + d)^m*a*b^2*c*m^2*x^5*e^9 + 1178280*(x*e + d)^m*a^2*c^2*m^2*x^5*e^9 + 644064*(x*e + d)^m*b^3*c*m*x^6*e^9 + 1932192*(x*e + d)^m*a*b*c^2*m*x^6*e^9 + 311040*(x*e + d)^m*b^2*c^2*x^7*e^9 + 207360*(x*e + d)^m*a*c^3*x^7*e^9 + 826*(x*e + d)^m*a^4*d*m^6*e^8 + 28560*(x*e + d)^m*a^3*b*d*m^5*x*e^8 + 179034*(x*e + d)^m*a^2*b^2*d*m^4*x^2*e^8 + 119356*(x*e + d)^m*a^3*c*d*m^4*x^2*e^8 + 222368*(x*e + d)^m*a*b^3*d*m^3*x^3*e^8 + 667104*(x*e + d)^m*a^2*b*c*d*m^3*x^3*e^8 + 43164*(x*e + d)^m*b^4*d*m^2*x^4*e^8 + 517968*(x*e + d)^m*a*b^2*c*d*m^2*x^4*e^8 + 258984*(x*e + d)^m*a^2*c^2*d*m^2*x^4*e^8 + 48384*(x*e + d)^m*b^3*c*d*m*x^5*e^8 + 145152*(x*e + d)^m*a*b*c^2*d*m*x^5*e^8 - 2968*(x*e + d)^m*a^3*b*d^2*m^5*e^7 - 63180*(x*e + d)^m*a^2*b^2*d^2*m^4*x*e^7 - 42120*(x*e + d)^m*a^3*c*d^2*m^4*x*e^7 - 175188*(x*e + d)^m*a*b^3*d^2*m^3*x^2*e^7 - 525564*(x*e + d)^m*a^2*b*c*d^2*m^3*x^2*e^7 - 49488*(x*e + d)^m*b^4*d^2*m^2*x^3*e^7 - 593856*(x*e + d)^m*a*b^2*c*d^2*m^2*x^3*e^7 - 296928*(x*e + d)^m*a^2*c^2*d^2*m^2*x^3*e^7 - 60480*(x*e + d)^m*b^3*c*d^2*m*x^4*e^7 - 181440*(x*e + d)^m*a*b*c^2*d^2*m*x^4*e^7 + 7500*(x*e + d)^m*a^2*b^2*d^3*m^4*e^6 + 5000*(x*e + d)^m*a^3*c*d^3*m^4*e^6 + 79800*(x*e + d)^m*a*b^3*d^3*m^3*x*e^6 + 239400*(x*e + d)^m*a^2*b*c*d^3*m^3*x*e^6 + 56088*(x*e + d)^m*b^4*d^3*m^2*x^2*e^6 + 673056*(x*e + d)^m*a*b^2*c*d^3*m^2*x^2*e^6 + 336528*(x*e + d)^m*a^2*c^2*d^3*m^2*x^2*e^6 + 80640*(x*e + d)^m*b^3*c*d^3*m*x^3*e^6 + 241920*(x*e + d)^m*a*b*c^2*d^3*m*x^3*e^6 - 11640*(x*e + d)^m*a*b^3*d^4*m^3*e^5 - 34920*(x*e + d)^m*a^2*b*c*d^4*m^3*e^5 - 39600*(x*e + d)^m*b^4*d^4*m^2*x*e^5 - 475200*(x*e + d)^m*a*b^2*c*d^4*m^2*x*e^5 - 237600*(x*e + d)^m*a^2*c^2*d^4*m^2*x*e^5 - 120960*(x*e + d)^m*b^3*c*d^4*m*x^2*e^5 - 362880*(x*e + d)^m*a*b*c^2*d^4*m*x^2*e^5 + 8040*(x*e + d)^m*b^4*d^5*m^2*e^4 + 96480*(x*e + d)^m*a*b^2*c*d^5*m^2*e^4 + 48240*(x*e + d)^m*a^2*c^2*d^5*m^2*e^4 + 241920*(x*e + d)^m*b^3*c*d^5*m*x*e^4 + 725760*(x*e + d)^m*a*b*c^2*d^5*m*x*e^4 - 91680*(x*e + d)^m*b^3*c*d^6*m*e^3 - 275040*(x*e + d)^m*a*b*c^2*d^6*m*e^3 + 311040*(x*e + d)^m*b^2*c^2*d^7*e^2 + 207360*(x*e + d)^m*a*c^3*d^7*e^2 + 8624*(x*e + d)^m*a^4*m^5*x*e^9 + 190036*(x*e + d)^m*a^3*b*m^4*x^2*e^9 + 866808*(x*e + d)^m*a^2*b^2*m^3*x^3*e^9 + 577872*(x*e + d)^m*a^3*c*m^3*x^3*e^9 + 938736*(x*e + d)^m*a*b^3*m^2*x^4*e^9 + 2816208*(x*e + d)^m*a^2*b*c*m^2*x^4*e^9 + 190800*(x*e + d)^m*b^4*m*x^5*e^9 + 2289600*(x*e + d)^m*a*b^2*c*m*x^5*e^9 + 1144800*(x*e + d)^m*a^2*c^2*m*x^5*e^9 + 241920*(x*e + d)^m*b^3*c*x^6*e^9 + 725760*(x*e + d)^m*a*b*c^2*x^6*e^9 + 8624*(x*e + d)^m*a^4*d*m^5*e^8 + 161476*(x*e + d)^m*a^3*b*d*m^4*x*e^8 + 508740*(x*e + d)^m*a^2*b^2*d*m^3*x^2*e^8 + 339160*(x*e + d)^m*a^3*c*d*m^3*x^2*e^8 + 271632*(x*e + d)^m*a*b^3*d*m^2*x^3*e^8 + 814896*(x*e + d)^m*a^2*b*c*d*m^2*x^3*e^8 + 18144*(x*e + d)^m*b^4*d*m*x^4*e^8 + 217728*(x*e + d)^m*a*b^2*c*d*m*x^4*e^8 + 108864*(x*e + d)^m*a^2*c^2*d*m*x^4*e^8 - 28560*(x*e + d)^m*a^3*b*d^2*m^4*e^7 - 294888*(x*e + d)^m*a^2*b^2*d^2*m^3*x*e^7 - 196592*(x*e + d)^m*a^3*c*d^2*m^3*x*e^7 - 316728*(x*e + d)^m*a*b^3*d^2*m^2*x^2*e^7 - 950184*(x*e + d)^m*a^2*b*c*d^2*m^2*x^2*e^7 - 24192*(x*e + d)^m*b^4*d^2*m*x^3*e^7 - 290304*(x*e + d)^m*a*b^2*c*d^2*m*x^3*e^7 - 145152*(x*e + d)^m*a^2*c^2*d^2*m*x^3*e^7 + 63180*(x*e + d)^m*a^2*b^2*d^3*m^3*e^6 + 42120*(x*e + d)^m*a^3*c*d^3*m^3*e^6 + 270576*(x*e + d)^m*a*b^3*d^3*m^2*x*e^6 + 811728*(x*e + d)^m*a^2*b*c*d^3*m^2*x*e^6 + 36288*(x*e + d)^m*b^4*d^3*m*x^2*e^6 + 435456*(x*e + d)^m*a*b^2*c*d^3*m*x^2*e^6 + 217728*(x*e + d)^m*a^2*c^2*d^3*m*x^2*e^6 - 79800*(x*e + d)^m*a*b^3*d^4*m^2*e^5 - 239400*(x*e + d)^m*a^2*b*c*d^4*m^2*e^5 - 72576*(x*e + d)^m*b^4*d^4*m*x*e^5 - 870912*(x*e + d)^m*a*b^2*c*d^4*m*x*e^5 - 435456*(x*e + d)^m*a^2*c^2*d^4*m*x*e^5 + 39600*(x*e + d)^m*b^4*d^5*m*e^4 + 475200*(x*e + d)^m*a*b^2*c*d^5*m*e^4 + 237600*(x*e + d)^m*a^2*c^2*d^5*m*e^4 - 241920*(x*e + d)^m*b^3*c*d^6*e^3 - 725760*(x*e + d)^m*a*b*c^2*d^6*e^3 + 54649*(x*e + d)^m*a^4*m^4*x*e^9 + 697228*(x*e + d)^m*a^3*b*m^3*x^2*e^9 + 1741656*(x*e + d)^m*a^2*b^2*m^2*x^3*e^9 + 1161104*(x*e + d)^m*a^3*c*m^2*x^3*e^9 + 935856*(x*e + d)^m*a*b^3*m*x^4*e^9 + 2807568*(x*e + d)^m*a^2*b*c*m*x^4*e^9 + 72576*(x*e + d)^m*b^4*x^5*e^9 + 870912*(x*e + d)^m*a*b^2*c*x^5*e^9 + 435456*(x*e + d)^m*a^2*c^2*x^5*e^9 + 54649*(x*e + d)^m*a^4*d*m^4*e^8 + 535752*(x*e + d)^m*a^3*b*d*m^3*x*e^8 + 724176*(x*e + d)^m*a^2*b^2*d*m^2*x^2*e^8 + 482784*(x*e + d)^m*a^3*c*d*m^2*x^2*e^8 + 120960*(x*e + d)^m*a*b^3*d*m*x^3*e^8 + 362880*(x*e + d)^m*a^2*b*c*d*m*x^3*e^8 - 161476*(x*e + d)^m*a^3*b*d^2*m^3*e^7 - 722592*(x*e + d)^m*a^2*b^2*d^2*m^2*x*e^7 - 481728*(x*e + d)^m*a^3*c*d^2*m^2*x*e^7 - 181440*(x*e + d)^m*a*b^3*d^2*m*x^2*e^7 - 544320*(x*e + d)^m*a^2*b*c*d^2*m*x^2*e^7 + 294888*(x*e + d)^m*a^2*b^2*d^3*m^2*e^6 + 196592*(x*e + d)^m*a^3*c*d^3*m^2*e^6 + 362880*(x*e + d)^m*a*b^3*d^3*m*x*e^6 + 1088640*(x*e + d)^m*a^2*b*c*d^3*m*x*e^6 - 270576*(x*e + d)^m*a*b^3*d^4*m*e^5 - 811728*(x*e + d)^m*a^2*b*c*d^4*m*e^5 + 72576*(x*e + d)^m*b^4*d^5*e^4 + 870912*(x*e + d)^m*a*b^2*c*d^5*e^4 + 435456*(x*e + d)^m*a^2*c^2*d^5*e^4 + 214676*(x*e + d)^m*a^4*m^3*x*e^9 + 1500264*(x*e + d)^m*a^3*b*m^2*x^2*e^9 + 1811232*(x*e + d)^m*a^2*b^2*m*x^3*e^9 + 1207488*(x*e + d)^m*a^3*c*m*x^3*e^9 + 362880*(x*e + d)^m*a*b^3*x^4*e^9 + 1088640*(x*e + d)^m*a^2*b*c*x^4*e^9 + 214676*(x*e + d)^m*a^4*d*m^3*e^8 + 964512*(x*e + d)^m*a^3*b*d*m^2*x*e^8 + 362880*(x*e + d)^m*a^2*b^2*d*m*x^2*e^8 + 241920*(x*e + d)^m*a^3*c*d*m*x^2*e^8 - 535752*(x*e + d)^m*a^3*b*d^2*m^2*e^7 - 725760*(x*e + d)^m*a^2*b^2*d^2*m*x*e^7 - 483840*(x*e + d)^m*a^3*c*d^2*m*x*e^7 + 722592*(x*e + d)^m*a^2*b^2*d^3*m*e^6 + 481728*(x*e + d)^m*a^3*c*d^3*m*e^6 - 362880*(x*e + d)^m*a*b^3*d^4*e^5 - 1088640*(x*e + d)^m*a^2*b*c*d^4*e^5 + 509004*(x*e + d)^m*a^4*m^2*x*e^9 + 1690272*(x*e + d)^m*a^3*b*m*x^2*e^9 + 725760*(x*e + d)^m*a^2*b^2*x^3*e^9 + 483840*(x*e + d)^m*a^3*c*x^3*e^9 + 509004*(x*e + d)^m*a^4*d*m^2*e^8 + 725760*(x*e + d)^m*a^3*b*d*m*x*e^8 - 964512*(x*e + d)^m*a^3*b*d^2*m*e^7 + 725760*(x*e + d)^m*a^2*b^2*d^3*e^6 + 483840*(x*e + d)^m*a^3*c*d^3*e^6 + 663696*(x*e + d)^m*a^4*m*x*e^9 + 725760*(x*e + d)^m*a^3*b*x^2*e^9 + 663696*(x*e + d)^m*a^4*d*m*e^8 - 725760*(x*e + d)^m*a^3*b*d^2*e^7 + 362880*(x*e + d)^m*a^4*x*e^9 + 362880*(x*e + d)^m*a^4*d*e^8)/(m^9*e^9 + 45*m^8*e^9 + 870*m^7*e^9 + 9450*m^6*e^9 + 63273*m^5*e^9 + 269325*m^4*e^9 + 723680*m^3*e^9 + 1172700*m^2*e^9 + 1026576*m*e^9 + 362880*e^9)","B",0
2550,1,5387,0,0.349334," ","integrate((e*x+d)^m*(c*x^2+b*x+a)^3,x, algorithm=""giac"")","\frac{{\left(x e + d\right)}^{m} c^{3} m^{6} x^{7} e^{7} + {\left(x e + d\right)}^{m} c^{3} d m^{6} x^{6} e^{6} + 3 \, {\left(x e + d\right)}^{m} b c^{2} m^{6} x^{6} e^{7} + 21 \, {\left(x e + d\right)}^{m} c^{3} m^{5} x^{7} e^{7} + 3 \, {\left(x e + d\right)}^{m} b c^{2} d m^{6} x^{5} e^{6} + 15 \, {\left(x e + d\right)}^{m} c^{3} d m^{5} x^{6} e^{6} - 6 \, {\left(x e + d\right)}^{m} c^{3} d^{2} m^{5} x^{5} e^{5} + 3 \, {\left(x e + d\right)}^{m} b^{2} c m^{6} x^{5} e^{7} + 3 \, {\left(x e + d\right)}^{m} a c^{2} m^{6} x^{5} e^{7} + 66 \, {\left(x e + d\right)}^{m} b c^{2} m^{5} x^{6} e^{7} + 175 \, {\left(x e + d\right)}^{m} c^{3} m^{4} x^{7} e^{7} + 3 \, {\left(x e + d\right)}^{m} b^{2} c d m^{6} x^{4} e^{6} + 3 \, {\left(x e + d\right)}^{m} a c^{2} d m^{6} x^{4} e^{6} + 51 \, {\left(x e + d\right)}^{m} b c^{2} d m^{5} x^{5} e^{6} + 85 \, {\left(x e + d\right)}^{m} c^{3} d m^{4} x^{6} e^{6} - 15 \, {\left(x e + d\right)}^{m} b c^{2} d^{2} m^{5} x^{4} e^{5} - 60 \, {\left(x e + d\right)}^{m} c^{3} d^{2} m^{4} x^{5} e^{5} + 30 \, {\left(x e + d\right)}^{m} c^{3} d^{3} m^{4} x^{4} e^{4} + {\left(x e + d\right)}^{m} b^{3} m^{6} x^{4} e^{7} + 6 \, {\left(x e + d\right)}^{m} a b c m^{6} x^{4} e^{7} + 69 \, {\left(x e + d\right)}^{m} b^{2} c m^{5} x^{5} e^{7} + 69 \, {\left(x e + d\right)}^{m} a c^{2} m^{5} x^{5} e^{7} + 570 \, {\left(x e + d\right)}^{m} b c^{2} m^{4} x^{6} e^{7} + 735 \, {\left(x e + d\right)}^{m} c^{3} m^{3} x^{7} e^{7} + {\left(x e + d\right)}^{m} b^{3} d m^{6} x^{3} e^{6} + 6 \, {\left(x e + d\right)}^{m} a b c d m^{6} x^{3} e^{6} + 57 \, {\left(x e + d\right)}^{m} b^{2} c d m^{5} x^{4} e^{6} + 57 \, {\left(x e + d\right)}^{m} a c^{2} d m^{5} x^{4} e^{6} + 315 \, {\left(x e + d\right)}^{m} b c^{2} d m^{4} x^{5} e^{6} + 225 \, {\left(x e + d\right)}^{m} c^{3} d m^{3} x^{6} e^{6} - 12 \, {\left(x e + d\right)}^{m} b^{2} c d^{2} m^{5} x^{3} e^{5} - 12 \, {\left(x e + d\right)}^{m} a c^{2} d^{2} m^{5} x^{3} e^{5} - 195 \, {\left(x e + d\right)}^{m} b c^{2} d^{2} m^{4} x^{4} e^{5} - 210 \, {\left(x e + d\right)}^{m} c^{3} d^{2} m^{3} x^{5} e^{5} + 60 \, {\left(x e + d\right)}^{m} b c^{2} d^{3} m^{4} x^{3} e^{4} + 180 \, {\left(x e + d\right)}^{m} c^{3} d^{3} m^{3} x^{4} e^{4} - 120 \, {\left(x e + d\right)}^{m} c^{3} d^{4} m^{3} x^{3} e^{3} + 3 \, {\left(x e + d\right)}^{m} a b^{2} m^{6} x^{3} e^{7} + 3 \, {\left(x e + d\right)}^{m} a^{2} c m^{6} x^{3} e^{7} + 24 \, {\left(x e + d\right)}^{m} b^{3} m^{5} x^{4} e^{7} + 144 \, {\left(x e + d\right)}^{m} a b c m^{5} x^{4} e^{7} + 621 \, {\left(x e + d\right)}^{m} b^{2} c m^{4} x^{5} e^{7} + 621 \, {\left(x e + d\right)}^{m} a c^{2} m^{4} x^{5} e^{7} + 2460 \, {\left(x e + d\right)}^{m} b c^{2} m^{3} x^{6} e^{7} + 1624 \, {\left(x e + d\right)}^{m} c^{3} m^{2} x^{7} e^{7} + 3 \, {\left(x e + d\right)}^{m} a b^{2} d m^{6} x^{2} e^{6} + 3 \, {\left(x e + d\right)}^{m} a^{2} c d m^{6} x^{2} e^{6} + 21 \, {\left(x e + d\right)}^{m} b^{3} d m^{5} x^{3} e^{6} + 126 \, {\left(x e + d\right)}^{m} a b c d m^{5} x^{3} e^{6} + 393 \, {\left(x e + d\right)}^{m} b^{2} c d m^{4} x^{4} e^{6} + 393 \, {\left(x e + d\right)}^{m} a c^{2} d m^{4} x^{4} e^{6} + 885 \, {\left(x e + d\right)}^{m} b c^{2} d m^{3} x^{5} e^{6} + 274 \, {\left(x e + d\right)}^{m} c^{3} d m^{2} x^{6} e^{6} - 3 \, {\left(x e + d\right)}^{m} b^{3} d^{2} m^{5} x^{2} e^{5} - 18 \, {\left(x e + d\right)}^{m} a b c d^{2} m^{5} x^{2} e^{5} - 192 \, {\left(x e + d\right)}^{m} b^{2} c d^{2} m^{4} x^{3} e^{5} - 192 \, {\left(x e + d\right)}^{m} a c^{2} d^{2} m^{4} x^{3} e^{5} - 795 \, {\left(x e + d\right)}^{m} b c^{2} d^{2} m^{3} x^{4} e^{5} - 300 \, {\left(x e + d\right)}^{m} c^{3} d^{2} m^{2} x^{5} e^{5} + 36 \, {\left(x e + d\right)}^{m} b^{2} c d^{3} m^{4} x^{2} e^{4} + 36 \, {\left(x e + d\right)}^{m} a c^{2} d^{3} m^{4} x^{2} e^{4} + 600 \, {\left(x e + d\right)}^{m} b c^{2} d^{3} m^{3} x^{3} e^{4} + 330 \, {\left(x e + d\right)}^{m} c^{3} d^{3} m^{2} x^{4} e^{4} - 180 \, {\left(x e + d\right)}^{m} b c^{2} d^{4} m^{3} x^{2} e^{3} - 360 \, {\left(x e + d\right)}^{m} c^{3} d^{4} m^{2} x^{3} e^{3} + 360 \, {\left(x e + d\right)}^{m} c^{3} d^{5} m^{2} x^{2} e^{2} + 3 \, {\left(x e + d\right)}^{m} a^{2} b m^{6} x^{2} e^{7} + 75 \, {\left(x e + d\right)}^{m} a b^{2} m^{5} x^{3} e^{7} + 75 \, {\left(x e + d\right)}^{m} a^{2} c m^{5} x^{3} e^{7} + 226 \, {\left(x e + d\right)}^{m} b^{3} m^{4} x^{4} e^{7} + 1356 \, {\left(x e + d\right)}^{m} a b c m^{4} x^{4} e^{7} + 2775 \, {\left(x e + d\right)}^{m} b^{2} c m^{3} x^{5} e^{7} + 2775 \, {\left(x e + d\right)}^{m} a c^{2} m^{3} x^{5} e^{7} + 5547 \, {\left(x e + d\right)}^{m} b c^{2} m^{2} x^{6} e^{7} + 1764 \, {\left(x e + d\right)}^{m} c^{3} m x^{7} e^{7} + 3 \, {\left(x e + d\right)}^{m} a^{2} b d m^{6} x e^{6} + 69 \, {\left(x e + d\right)}^{m} a b^{2} d m^{5} x^{2} e^{6} + 69 \, {\left(x e + d\right)}^{m} a^{2} c d m^{5} x^{2} e^{6} + 163 \, {\left(x e + d\right)}^{m} b^{3} d m^{4} x^{3} e^{6} + 978 \, {\left(x e + d\right)}^{m} a b c d m^{4} x^{3} e^{6} + 1203 \, {\left(x e + d\right)}^{m} b^{2} c d m^{3} x^{4} e^{6} + 1203 \, {\left(x e + d\right)}^{m} a c^{2} d m^{3} x^{4} e^{6} + 1122 \, {\left(x e + d\right)}^{m} b c^{2} d m^{2} x^{5} e^{6} + 120 \, {\left(x e + d\right)}^{m} c^{3} d m x^{6} e^{6} - 6 \, {\left(x e + d\right)}^{m} a b^{2} d^{2} m^{5} x e^{5} - 6 \, {\left(x e + d\right)}^{m} a^{2} c d^{2} m^{5} x e^{5} - 57 \, {\left(x e + d\right)}^{m} b^{3} d^{2} m^{4} x^{2} e^{5} - 342 \, {\left(x e + d\right)}^{m} a b c d^{2} m^{4} x^{2} e^{5} - 996 \, {\left(x e + d\right)}^{m} b^{2} c d^{2} m^{3} x^{3} e^{5} - 996 \, {\left(x e + d\right)}^{m} a c^{2} d^{2} m^{3} x^{3} e^{5} - 1245 \, {\left(x e + d\right)}^{m} b c^{2} d^{2} m^{2} x^{4} e^{5} - 144 \, {\left(x e + d\right)}^{m} c^{3} d^{2} m x^{5} e^{5} + 6 \, {\left(x e + d\right)}^{m} b^{3} d^{3} m^{4} x e^{4} + 36 \, {\left(x e + d\right)}^{m} a b c d^{3} m^{4} x e^{4} + 504 \, {\left(x e + d\right)}^{m} b^{2} c d^{3} m^{3} x^{2} e^{4} + 504 \, {\left(x e + d\right)}^{m} a c^{2} d^{3} m^{3} x^{2} e^{4} + 1380 \, {\left(x e + d\right)}^{m} b c^{2} d^{3} m^{2} x^{3} e^{4} + 180 \, {\left(x e + d\right)}^{m} c^{3} d^{3} m x^{4} e^{4} - 72 \, {\left(x e + d\right)}^{m} b^{2} c d^{4} m^{3} x e^{3} - 72 \, {\left(x e + d\right)}^{m} a c^{2} d^{4} m^{3} x e^{3} - 1440 \, {\left(x e + d\right)}^{m} b c^{2} d^{4} m^{2} x^{2} e^{3} - 240 \, {\left(x e + d\right)}^{m} c^{3} d^{4} m x^{3} e^{3} + 360 \, {\left(x e + d\right)}^{m} b c^{2} d^{5} m^{2} x e^{2} + 360 \, {\left(x e + d\right)}^{m} c^{3} d^{5} m x^{2} e^{2} - 720 \, {\left(x e + d\right)}^{m} c^{3} d^{6} m x e + {\left(x e + d\right)}^{m} a^{3} m^{6} x e^{7} + 78 \, {\left(x e + d\right)}^{m} a^{2} b m^{5} x^{2} e^{7} + 741 \, {\left(x e + d\right)}^{m} a b^{2} m^{4} x^{3} e^{7} + 741 \, {\left(x e + d\right)}^{m} a^{2} c m^{4} x^{3} e^{7} + 1056 \, {\left(x e + d\right)}^{m} b^{3} m^{3} x^{4} e^{7} + 6336 \, {\left(x e + d\right)}^{m} a b c m^{3} x^{4} e^{7} + 6432 \, {\left(x e + d\right)}^{m} b^{2} c m^{2} x^{5} e^{7} + 6432 \, {\left(x e + d\right)}^{m} a c^{2} m^{2} x^{5} e^{7} + 6114 \, {\left(x e + d\right)}^{m} b c^{2} m x^{6} e^{7} + 720 \, {\left(x e + d\right)}^{m} c^{3} x^{7} e^{7} + {\left(x e + d\right)}^{m} a^{3} d m^{6} e^{6} + 75 \, {\left(x e + d\right)}^{m} a^{2} b d m^{5} x e^{6} + 603 \, {\left(x e + d\right)}^{m} a b^{2} d m^{4} x^{2} e^{6} + 603 \, {\left(x e + d\right)}^{m} a^{2} c d m^{4} x^{2} e^{6} + 567 \, {\left(x e + d\right)}^{m} b^{3} d m^{3} x^{3} e^{6} + 3402 \, {\left(x e + d\right)}^{m} a b c d m^{3} x^{3} e^{6} + 1620 \, {\left(x e + d\right)}^{m} b^{2} c d m^{2} x^{4} e^{6} + 1620 \, {\left(x e + d\right)}^{m} a c^{2} d m^{2} x^{4} e^{6} + 504 \, {\left(x e + d\right)}^{m} b c^{2} d m x^{5} e^{6} - 3 \, {\left(x e + d\right)}^{m} a^{2} b d^{2} m^{5} e^{5} - 132 \, {\left(x e + d\right)}^{m} a b^{2} d^{2} m^{4} x e^{5} - 132 \, {\left(x e + d\right)}^{m} a^{2} c d^{2} m^{4} x e^{5} - 375 \, {\left(x e + d\right)}^{m} b^{3} d^{2} m^{3} x^{2} e^{5} - 2250 \, {\left(x e + d\right)}^{m} a b c d^{2} m^{3} x^{2} e^{5} - 1824 \, {\left(x e + d\right)}^{m} b^{2} c d^{2} m^{2} x^{3} e^{5} - 1824 \, {\left(x e + d\right)}^{m} a c^{2} d^{2} m^{2} x^{3} e^{5} - 630 \, {\left(x e + d\right)}^{m} b c^{2} d^{2} m x^{4} e^{5} + 6 \, {\left(x e + d\right)}^{m} a b^{2} d^{3} m^{4} e^{4} + 6 \, {\left(x e + d\right)}^{m} a^{2} c d^{3} m^{4} e^{4} + 108 \, {\left(x e + d\right)}^{m} b^{3} d^{3} m^{3} x e^{4} + 648 \, {\left(x e + d\right)}^{m} a b c d^{3} m^{3} x e^{4} + 1980 \, {\left(x e + d\right)}^{m} b^{2} c d^{3} m^{2} x^{2} e^{4} + 1980 \, {\left(x e + d\right)}^{m} a c^{2} d^{3} m^{2} x^{2} e^{4} + 840 \, {\left(x e + d\right)}^{m} b c^{2} d^{3} m x^{3} e^{4} - 6 \, {\left(x e + d\right)}^{m} b^{3} d^{4} m^{3} e^{3} - 36 \, {\left(x e + d\right)}^{m} a b c d^{4} m^{3} e^{3} - 936 \, {\left(x e + d\right)}^{m} b^{2} c d^{4} m^{2} x e^{3} - 936 \, {\left(x e + d\right)}^{m} a c^{2} d^{4} m^{2} x e^{3} - 1260 \, {\left(x e + d\right)}^{m} b c^{2} d^{4} m x^{2} e^{3} + 72 \, {\left(x e + d\right)}^{m} b^{2} c d^{5} m^{2} e^{2} + 72 \, {\left(x e + d\right)}^{m} a c^{2} d^{5} m^{2} e^{2} + 2520 \, {\left(x e + d\right)}^{m} b c^{2} d^{5} m x e^{2} - 360 \, {\left(x e + d\right)}^{m} b c^{2} d^{6} m e + 720 \, {\left(x e + d\right)}^{m} c^{3} d^{7} + 27 \, {\left(x e + d\right)}^{m} a^{3} m^{5} x e^{7} + 810 \, {\left(x e + d\right)}^{m} a^{2} b m^{4} x^{2} e^{7} + 3657 \, {\left(x e + d\right)}^{m} a b^{2} m^{3} x^{3} e^{7} + 3657 \, {\left(x e + d\right)}^{m} a^{2} c m^{3} x^{3} e^{7} + 2545 \, {\left(x e + d\right)}^{m} b^{3} m^{2} x^{4} e^{7} + 15270 \, {\left(x e + d\right)}^{m} a b c m^{2} x^{4} e^{7} + 7236 \, {\left(x e + d\right)}^{m} b^{2} c m x^{5} e^{7} + 7236 \, {\left(x e + d\right)}^{m} a c^{2} m x^{5} e^{7} + 2520 \, {\left(x e + d\right)}^{m} b c^{2} x^{6} e^{7} + 27 \, {\left(x e + d\right)}^{m} a^{3} d m^{5} e^{6} + 735 \, {\left(x e + d\right)}^{m} a^{2} b d m^{4} x e^{6} + 2451 \, {\left(x e + d\right)}^{m} a b^{2} d m^{3} x^{2} e^{6} + 2451 \, {\left(x e + d\right)}^{m} a^{2} c d m^{3} x^{2} e^{6} + 844 \, {\left(x e + d\right)}^{m} b^{3} d m^{2} x^{3} e^{6} + 5064 \, {\left(x e + d\right)}^{m} a b c d m^{2} x^{3} e^{6} + 756 \, {\left(x e + d\right)}^{m} b^{2} c d m x^{4} e^{6} + 756 \, {\left(x e + d\right)}^{m} a c^{2} d m x^{4} e^{6} - 75 \, {\left(x e + d\right)}^{m} a^{2} b d^{2} m^{4} e^{5} - 1074 \, {\left(x e + d\right)}^{m} a b^{2} d^{2} m^{3} x e^{5} - 1074 \, {\left(x e + d\right)}^{m} a^{2} c d^{2} m^{3} x e^{5} - 951 \, {\left(x e + d\right)}^{m} b^{3} d^{2} m^{2} x^{2} e^{5} - 5706 \, {\left(x e + d\right)}^{m} a b c d^{2} m^{2} x^{2} e^{5} - 1008 \, {\left(x e + d\right)}^{m} b^{2} c d^{2} m x^{3} e^{5} - 1008 \, {\left(x e + d\right)}^{m} a c^{2} d^{2} m x^{3} e^{5} + 132 \, {\left(x e + d\right)}^{m} a b^{2} d^{3} m^{3} e^{4} + 132 \, {\left(x e + d\right)}^{m} a^{2} c d^{3} m^{3} e^{4} + 642 \, {\left(x e + d\right)}^{m} b^{3} d^{3} m^{2} x e^{4} + 3852 \, {\left(x e + d\right)}^{m} a b c d^{3} m^{2} x e^{4} + 1512 \, {\left(x e + d\right)}^{m} b^{2} c d^{3} m x^{2} e^{4} + 1512 \, {\left(x e + d\right)}^{m} a c^{2} d^{3} m x^{2} e^{4} - 108 \, {\left(x e + d\right)}^{m} b^{3} d^{4} m^{2} e^{3} - 648 \, {\left(x e + d\right)}^{m} a b c d^{4} m^{2} e^{3} - 3024 \, {\left(x e + d\right)}^{m} b^{2} c d^{4} m x e^{3} - 3024 \, {\left(x e + d\right)}^{m} a c^{2} d^{4} m x e^{3} + 936 \, {\left(x e + d\right)}^{m} b^{2} c d^{5} m e^{2} + 936 \, {\left(x e + d\right)}^{m} a c^{2} d^{5} m e^{2} - 2520 \, {\left(x e + d\right)}^{m} b c^{2} d^{6} e + 295 \, {\left(x e + d\right)}^{m} a^{3} m^{4} x e^{7} + 4260 \, {\left(x e + d\right)}^{m} a^{2} b m^{3} x^{2} e^{7} + 9336 \, {\left(x e + d\right)}^{m} a b^{2} m^{2} x^{3} e^{7} + 9336 \, {\left(x e + d\right)}^{m} a^{2} c m^{2} x^{3} e^{7} + 2952 \, {\left(x e + d\right)}^{m} b^{3} m x^{4} e^{7} + 17712 \, {\left(x e + d\right)}^{m} a b c m x^{4} e^{7} + 3024 \, {\left(x e + d\right)}^{m} b^{2} c x^{5} e^{7} + 3024 \, {\left(x e + d\right)}^{m} a c^{2} x^{5} e^{7} + 295 \, {\left(x e + d\right)}^{m} a^{3} d m^{4} e^{6} + 3525 \, {\left(x e + d\right)}^{m} a^{2} b d m^{3} x e^{6} + 4434 \, {\left(x e + d\right)}^{m} a b^{2} d m^{2} x^{2} e^{6} + 4434 \, {\left(x e + d\right)}^{m} a^{2} c d m^{2} x^{2} e^{6} + 420 \, {\left(x e + d\right)}^{m} b^{3} d m x^{3} e^{6} + 2520 \, {\left(x e + d\right)}^{m} a b c d m x^{3} e^{6} - 735 \, {\left(x e + d\right)}^{m} a^{2} b d^{2} m^{3} e^{5} - 3828 \, {\left(x e + d\right)}^{m} a b^{2} d^{2} m^{2} x e^{5} - 3828 \, {\left(x e + d\right)}^{m} a^{2} c d^{2} m^{2} x e^{5} - 630 \, {\left(x e + d\right)}^{m} b^{3} d^{2} m x^{2} e^{5} - 3780 \, {\left(x e + d\right)}^{m} a b c d^{2} m x^{2} e^{5} + 1074 \, {\left(x e + d\right)}^{m} a b^{2} d^{3} m^{2} e^{4} + 1074 \, {\left(x e + d\right)}^{m} a^{2} c d^{3} m^{2} e^{4} + 1260 \, {\left(x e + d\right)}^{m} b^{3} d^{3} m x e^{4} + 7560 \, {\left(x e + d\right)}^{m} a b c d^{3} m x e^{4} - 642 \, {\left(x e + d\right)}^{m} b^{3} d^{4} m e^{3} - 3852 \, {\left(x e + d\right)}^{m} a b c d^{4} m e^{3} + 3024 \, {\left(x e + d\right)}^{m} b^{2} c d^{5} e^{2} + 3024 \, {\left(x e + d\right)}^{m} a c^{2} d^{5} e^{2} + 1665 \, {\left(x e + d\right)}^{m} a^{3} m^{3} x e^{7} + 11787 \, {\left(x e + d\right)}^{m} a^{2} b m^{2} x^{2} e^{7} + 11388 \, {\left(x e + d\right)}^{m} a b^{2} m x^{3} e^{7} + 11388 \, {\left(x e + d\right)}^{m} a^{2} c m x^{3} e^{7} + 1260 \, {\left(x e + d\right)}^{m} b^{3} x^{4} e^{7} + 7560 \, {\left(x e + d\right)}^{m} a b c x^{4} e^{7} + 1665 \, {\left(x e + d\right)}^{m} a^{3} d m^{3} e^{6} + 8262 \, {\left(x e + d\right)}^{m} a^{2} b d m^{2} x e^{6} + 2520 \, {\left(x e + d\right)}^{m} a b^{2} d m x^{2} e^{6} + 2520 \, {\left(x e + d\right)}^{m} a^{2} c d m x^{2} e^{6} - 3525 \, {\left(x e + d\right)}^{m} a^{2} b d^{2} m^{2} e^{5} - 5040 \, {\left(x e + d\right)}^{m} a b^{2} d^{2} m x e^{5} - 5040 \, {\left(x e + d\right)}^{m} a^{2} c d^{2} m x e^{5} + 3828 \, {\left(x e + d\right)}^{m} a b^{2} d^{3} m e^{4} + 3828 \, {\left(x e + d\right)}^{m} a^{2} c d^{3} m e^{4} - 1260 \, {\left(x e + d\right)}^{m} b^{3} d^{4} e^{3} - 7560 \, {\left(x e + d\right)}^{m} a b c d^{4} e^{3} + 5104 \, {\left(x e + d\right)}^{m} a^{3} m^{2} x e^{7} + 15822 \, {\left(x e + d\right)}^{m} a^{2} b m x^{2} e^{7} + 5040 \, {\left(x e + d\right)}^{m} a b^{2} x^{3} e^{7} + 5040 \, {\left(x e + d\right)}^{m} a^{2} c x^{3} e^{7} + 5104 \, {\left(x e + d\right)}^{m} a^{3} d m^{2} e^{6} + 7560 \, {\left(x e + d\right)}^{m} a^{2} b d m x e^{6} - 8262 \, {\left(x e + d\right)}^{m} a^{2} b d^{2} m e^{5} + 5040 \, {\left(x e + d\right)}^{m} a b^{2} d^{3} e^{4} + 5040 \, {\left(x e + d\right)}^{m} a^{2} c d^{3} e^{4} + 8028 \, {\left(x e + d\right)}^{m} a^{3} m x e^{7} + 7560 \, {\left(x e + d\right)}^{m} a^{2} b x^{2} e^{7} + 8028 \, {\left(x e + d\right)}^{m} a^{3} d m e^{6} - 7560 \, {\left(x e + d\right)}^{m} a^{2} b d^{2} e^{5} + 5040 \, {\left(x e + d\right)}^{m} a^{3} x e^{7} + 5040 \, {\left(x e + d\right)}^{m} a^{3} d e^{6}}{m^{7} e^{7} + 28 \, m^{6} e^{7} + 322 \, m^{5} e^{7} + 1960 \, m^{4} e^{7} + 6769 \, m^{3} e^{7} + 13132 \, m^{2} e^{7} + 13068 \, m e^{7} + 5040 \, e^{7}}"," ",0,"((x*e + d)^m*c^3*m^6*x^7*e^7 + (x*e + d)^m*c^3*d*m^6*x^6*e^6 + 3*(x*e + d)^m*b*c^2*m^6*x^6*e^7 + 21*(x*e + d)^m*c^3*m^5*x^7*e^7 + 3*(x*e + d)^m*b*c^2*d*m^6*x^5*e^6 + 15*(x*e + d)^m*c^3*d*m^5*x^6*e^6 - 6*(x*e + d)^m*c^3*d^2*m^5*x^5*e^5 + 3*(x*e + d)^m*b^2*c*m^6*x^5*e^7 + 3*(x*e + d)^m*a*c^2*m^6*x^5*e^7 + 66*(x*e + d)^m*b*c^2*m^5*x^6*e^7 + 175*(x*e + d)^m*c^3*m^4*x^7*e^7 + 3*(x*e + d)^m*b^2*c*d*m^6*x^4*e^6 + 3*(x*e + d)^m*a*c^2*d*m^6*x^4*e^6 + 51*(x*e + d)^m*b*c^2*d*m^5*x^5*e^6 + 85*(x*e + d)^m*c^3*d*m^4*x^6*e^6 - 15*(x*e + d)^m*b*c^2*d^2*m^5*x^4*e^5 - 60*(x*e + d)^m*c^3*d^2*m^4*x^5*e^5 + 30*(x*e + d)^m*c^3*d^3*m^4*x^4*e^4 + (x*e + d)^m*b^3*m^6*x^4*e^7 + 6*(x*e + d)^m*a*b*c*m^6*x^4*e^7 + 69*(x*e + d)^m*b^2*c*m^5*x^5*e^7 + 69*(x*e + d)^m*a*c^2*m^5*x^5*e^7 + 570*(x*e + d)^m*b*c^2*m^4*x^6*e^7 + 735*(x*e + d)^m*c^3*m^3*x^7*e^7 + (x*e + d)^m*b^3*d*m^6*x^3*e^6 + 6*(x*e + d)^m*a*b*c*d*m^6*x^3*e^6 + 57*(x*e + d)^m*b^2*c*d*m^5*x^4*e^6 + 57*(x*e + d)^m*a*c^2*d*m^5*x^4*e^6 + 315*(x*e + d)^m*b*c^2*d*m^4*x^5*e^6 + 225*(x*e + d)^m*c^3*d*m^3*x^6*e^6 - 12*(x*e + d)^m*b^2*c*d^2*m^5*x^3*e^5 - 12*(x*e + d)^m*a*c^2*d^2*m^5*x^3*e^5 - 195*(x*e + d)^m*b*c^2*d^2*m^4*x^4*e^5 - 210*(x*e + d)^m*c^3*d^2*m^3*x^5*e^5 + 60*(x*e + d)^m*b*c^2*d^3*m^4*x^3*e^4 + 180*(x*e + d)^m*c^3*d^3*m^3*x^4*e^4 - 120*(x*e + d)^m*c^3*d^4*m^3*x^3*e^3 + 3*(x*e + d)^m*a*b^2*m^6*x^3*e^7 + 3*(x*e + d)^m*a^2*c*m^6*x^3*e^7 + 24*(x*e + d)^m*b^3*m^5*x^4*e^7 + 144*(x*e + d)^m*a*b*c*m^5*x^4*e^7 + 621*(x*e + d)^m*b^2*c*m^4*x^5*e^7 + 621*(x*e + d)^m*a*c^2*m^4*x^5*e^7 + 2460*(x*e + d)^m*b*c^2*m^3*x^6*e^7 + 1624*(x*e + d)^m*c^3*m^2*x^7*e^7 + 3*(x*e + d)^m*a*b^2*d*m^6*x^2*e^6 + 3*(x*e + d)^m*a^2*c*d*m^6*x^2*e^6 + 21*(x*e + d)^m*b^3*d*m^5*x^3*e^6 + 126*(x*e + d)^m*a*b*c*d*m^5*x^3*e^6 + 393*(x*e + d)^m*b^2*c*d*m^4*x^4*e^6 + 393*(x*e + d)^m*a*c^2*d*m^4*x^4*e^6 + 885*(x*e + d)^m*b*c^2*d*m^3*x^5*e^6 + 274*(x*e + d)^m*c^3*d*m^2*x^6*e^6 - 3*(x*e + d)^m*b^3*d^2*m^5*x^2*e^5 - 18*(x*e + d)^m*a*b*c*d^2*m^5*x^2*e^5 - 192*(x*e + d)^m*b^2*c*d^2*m^4*x^3*e^5 - 192*(x*e + d)^m*a*c^2*d^2*m^4*x^3*e^5 - 795*(x*e + d)^m*b*c^2*d^2*m^3*x^4*e^5 - 300*(x*e + d)^m*c^3*d^2*m^2*x^5*e^5 + 36*(x*e + d)^m*b^2*c*d^3*m^4*x^2*e^4 + 36*(x*e + d)^m*a*c^2*d^3*m^4*x^2*e^4 + 600*(x*e + d)^m*b*c^2*d^3*m^3*x^3*e^4 + 330*(x*e + d)^m*c^3*d^3*m^2*x^4*e^4 - 180*(x*e + d)^m*b*c^2*d^4*m^3*x^2*e^3 - 360*(x*e + d)^m*c^3*d^4*m^2*x^3*e^3 + 360*(x*e + d)^m*c^3*d^5*m^2*x^2*e^2 + 3*(x*e + d)^m*a^2*b*m^6*x^2*e^7 + 75*(x*e + d)^m*a*b^2*m^5*x^3*e^7 + 75*(x*e + d)^m*a^2*c*m^5*x^3*e^7 + 226*(x*e + d)^m*b^3*m^4*x^4*e^7 + 1356*(x*e + d)^m*a*b*c*m^4*x^4*e^7 + 2775*(x*e + d)^m*b^2*c*m^3*x^5*e^7 + 2775*(x*e + d)^m*a*c^2*m^3*x^5*e^7 + 5547*(x*e + d)^m*b*c^2*m^2*x^6*e^7 + 1764*(x*e + d)^m*c^3*m*x^7*e^7 + 3*(x*e + d)^m*a^2*b*d*m^6*x*e^6 + 69*(x*e + d)^m*a*b^2*d*m^5*x^2*e^6 + 69*(x*e + d)^m*a^2*c*d*m^5*x^2*e^6 + 163*(x*e + d)^m*b^3*d*m^4*x^3*e^6 + 978*(x*e + d)^m*a*b*c*d*m^4*x^3*e^6 + 1203*(x*e + d)^m*b^2*c*d*m^3*x^4*e^6 + 1203*(x*e + d)^m*a*c^2*d*m^3*x^4*e^6 + 1122*(x*e + d)^m*b*c^2*d*m^2*x^5*e^6 + 120*(x*e + d)^m*c^3*d*m*x^6*e^6 - 6*(x*e + d)^m*a*b^2*d^2*m^5*x*e^5 - 6*(x*e + d)^m*a^2*c*d^2*m^5*x*e^5 - 57*(x*e + d)^m*b^3*d^2*m^4*x^2*e^5 - 342*(x*e + d)^m*a*b*c*d^2*m^4*x^2*e^5 - 996*(x*e + d)^m*b^2*c*d^2*m^3*x^3*e^5 - 996*(x*e + d)^m*a*c^2*d^2*m^3*x^3*e^5 - 1245*(x*e + d)^m*b*c^2*d^2*m^2*x^4*e^5 - 144*(x*e + d)^m*c^3*d^2*m*x^5*e^5 + 6*(x*e + d)^m*b^3*d^3*m^4*x*e^4 + 36*(x*e + d)^m*a*b*c*d^3*m^4*x*e^4 + 504*(x*e + d)^m*b^2*c*d^3*m^3*x^2*e^4 + 504*(x*e + d)^m*a*c^2*d^3*m^3*x^2*e^4 + 1380*(x*e + d)^m*b*c^2*d^3*m^2*x^3*e^4 + 180*(x*e + d)^m*c^3*d^3*m*x^4*e^4 - 72*(x*e + d)^m*b^2*c*d^4*m^3*x*e^3 - 72*(x*e + d)^m*a*c^2*d^4*m^3*x*e^3 - 1440*(x*e + d)^m*b*c^2*d^4*m^2*x^2*e^3 - 240*(x*e + d)^m*c^3*d^4*m*x^3*e^3 + 360*(x*e + d)^m*b*c^2*d^5*m^2*x*e^2 + 360*(x*e + d)^m*c^3*d^5*m*x^2*e^2 - 720*(x*e + d)^m*c^3*d^6*m*x*e + (x*e + d)^m*a^3*m^6*x*e^7 + 78*(x*e + d)^m*a^2*b*m^5*x^2*e^7 + 741*(x*e + d)^m*a*b^2*m^4*x^3*e^7 + 741*(x*e + d)^m*a^2*c*m^4*x^3*e^7 + 1056*(x*e + d)^m*b^3*m^3*x^4*e^7 + 6336*(x*e + d)^m*a*b*c*m^3*x^4*e^7 + 6432*(x*e + d)^m*b^2*c*m^2*x^5*e^7 + 6432*(x*e + d)^m*a*c^2*m^2*x^5*e^7 + 6114*(x*e + d)^m*b*c^2*m*x^6*e^7 + 720*(x*e + d)^m*c^3*x^7*e^7 + (x*e + d)^m*a^3*d*m^6*e^6 + 75*(x*e + d)^m*a^2*b*d*m^5*x*e^6 + 603*(x*e + d)^m*a*b^2*d*m^4*x^2*e^6 + 603*(x*e + d)^m*a^2*c*d*m^4*x^2*e^6 + 567*(x*e + d)^m*b^3*d*m^3*x^3*e^6 + 3402*(x*e + d)^m*a*b*c*d*m^3*x^3*e^6 + 1620*(x*e + d)^m*b^2*c*d*m^2*x^4*e^6 + 1620*(x*e + d)^m*a*c^2*d*m^2*x^4*e^6 + 504*(x*e + d)^m*b*c^2*d*m*x^5*e^6 - 3*(x*e + d)^m*a^2*b*d^2*m^5*e^5 - 132*(x*e + d)^m*a*b^2*d^2*m^4*x*e^5 - 132*(x*e + d)^m*a^2*c*d^2*m^4*x*e^5 - 375*(x*e + d)^m*b^3*d^2*m^3*x^2*e^5 - 2250*(x*e + d)^m*a*b*c*d^2*m^3*x^2*e^5 - 1824*(x*e + d)^m*b^2*c*d^2*m^2*x^3*e^5 - 1824*(x*e + d)^m*a*c^2*d^2*m^2*x^3*e^5 - 630*(x*e + d)^m*b*c^2*d^2*m*x^4*e^5 + 6*(x*e + d)^m*a*b^2*d^3*m^4*e^4 + 6*(x*e + d)^m*a^2*c*d^3*m^4*e^4 + 108*(x*e + d)^m*b^3*d^3*m^3*x*e^4 + 648*(x*e + d)^m*a*b*c*d^3*m^3*x*e^4 + 1980*(x*e + d)^m*b^2*c*d^3*m^2*x^2*e^4 + 1980*(x*e + d)^m*a*c^2*d^3*m^2*x^2*e^4 + 840*(x*e + d)^m*b*c^2*d^3*m*x^3*e^4 - 6*(x*e + d)^m*b^3*d^4*m^3*e^3 - 36*(x*e + d)^m*a*b*c*d^4*m^3*e^3 - 936*(x*e + d)^m*b^2*c*d^4*m^2*x*e^3 - 936*(x*e + d)^m*a*c^2*d^4*m^2*x*e^3 - 1260*(x*e + d)^m*b*c^2*d^4*m*x^2*e^3 + 72*(x*e + d)^m*b^2*c*d^5*m^2*e^2 + 72*(x*e + d)^m*a*c^2*d^5*m^2*e^2 + 2520*(x*e + d)^m*b*c^2*d^5*m*x*e^2 - 360*(x*e + d)^m*b*c^2*d^6*m*e + 720*(x*e + d)^m*c^3*d^7 + 27*(x*e + d)^m*a^3*m^5*x*e^7 + 810*(x*e + d)^m*a^2*b*m^4*x^2*e^7 + 3657*(x*e + d)^m*a*b^2*m^3*x^3*e^7 + 3657*(x*e + d)^m*a^2*c*m^3*x^3*e^7 + 2545*(x*e + d)^m*b^3*m^2*x^4*e^7 + 15270*(x*e + d)^m*a*b*c*m^2*x^4*e^7 + 7236*(x*e + d)^m*b^2*c*m*x^5*e^7 + 7236*(x*e + d)^m*a*c^2*m*x^5*e^7 + 2520*(x*e + d)^m*b*c^2*x^6*e^7 + 27*(x*e + d)^m*a^3*d*m^5*e^6 + 735*(x*e + d)^m*a^2*b*d*m^4*x*e^6 + 2451*(x*e + d)^m*a*b^2*d*m^3*x^2*e^6 + 2451*(x*e + d)^m*a^2*c*d*m^3*x^2*e^6 + 844*(x*e + d)^m*b^3*d*m^2*x^3*e^6 + 5064*(x*e + d)^m*a*b*c*d*m^2*x^3*e^6 + 756*(x*e + d)^m*b^2*c*d*m*x^4*e^6 + 756*(x*e + d)^m*a*c^2*d*m*x^4*e^6 - 75*(x*e + d)^m*a^2*b*d^2*m^4*e^5 - 1074*(x*e + d)^m*a*b^2*d^2*m^3*x*e^5 - 1074*(x*e + d)^m*a^2*c*d^2*m^3*x*e^5 - 951*(x*e + d)^m*b^3*d^2*m^2*x^2*e^5 - 5706*(x*e + d)^m*a*b*c*d^2*m^2*x^2*e^5 - 1008*(x*e + d)^m*b^2*c*d^2*m*x^3*e^5 - 1008*(x*e + d)^m*a*c^2*d^2*m*x^3*e^5 + 132*(x*e + d)^m*a*b^2*d^3*m^3*e^4 + 132*(x*e + d)^m*a^2*c*d^3*m^3*e^4 + 642*(x*e + d)^m*b^3*d^3*m^2*x*e^4 + 3852*(x*e + d)^m*a*b*c*d^3*m^2*x*e^4 + 1512*(x*e + d)^m*b^2*c*d^3*m*x^2*e^4 + 1512*(x*e + d)^m*a*c^2*d^3*m*x^2*e^4 - 108*(x*e + d)^m*b^3*d^4*m^2*e^3 - 648*(x*e + d)^m*a*b*c*d^4*m^2*e^3 - 3024*(x*e + d)^m*b^2*c*d^4*m*x*e^3 - 3024*(x*e + d)^m*a*c^2*d^4*m*x*e^3 + 936*(x*e + d)^m*b^2*c*d^5*m*e^2 + 936*(x*e + d)^m*a*c^2*d^5*m*e^2 - 2520*(x*e + d)^m*b*c^2*d^6*e + 295*(x*e + d)^m*a^3*m^4*x*e^7 + 4260*(x*e + d)^m*a^2*b*m^3*x^2*e^7 + 9336*(x*e + d)^m*a*b^2*m^2*x^3*e^7 + 9336*(x*e + d)^m*a^2*c*m^2*x^3*e^7 + 2952*(x*e + d)^m*b^3*m*x^4*e^7 + 17712*(x*e + d)^m*a*b*c*m*x^4*e^7 + 3024*(x*e + d)^m*b^2*c*x^5*e^7 + 3024*(x*e + d)^m*a*c^2*x^5*e^7 + 295*(x*e + d)^m*a^3*d*m^4*e^6 + 3525*(x*e + d)^m*a^2*b*d*m^3*x*e^6 + 4434*(x*e + d)^m*a*b^2*d*m^2*x^2*e^6 + 4434*(x*e + d)^m*a^2*c*d*m^2*x^2*e^6 + 420*(x*e + d)^m*b^3*d*m*x^3*e^6 + 2520*(x*e + d)^m*a*b*c*d*m*x^3*e^6 - 735*(x*e + d)^m*a^2*b*d^2*m^3*e^5 - 3828*(x*e + d)^m*a*b^2*d^2*m^2*x*e^5 - 3828*(x*e + d)^m*a^2*c*d^2*m^2*x*e^5 - 630*(x*e + d)^m*b^3*d^2*m*x^2*e^5 - 3780*(x*e + d)^m*a*b*c*d^2*m*x^2*e^5 + 1074*(x*e + d)^m*a*b^2*d^3*m^2*e^4 + 1074*(x*e + d)^m*a^2*c*d^3*m^2*e^4 + 1260*(x*e + d)^m*b^3*d^3*m*x*e^4 + 7560*(x*e + d)^m*a*b*c*d^3*m*x*e^4 - 642*(x*e + d)^m*b^3*d^4*m*e^3 - 3852*(x*e + d)^m*a*b*c*d^4*m*e^3 + 3024*(x*e + d)^m*b^2*c*d^5*e^2 + 3024*(x*e + d)^m*a*c^2*d^5*e^2 + 1665*(x*e + d)^m*a^3*m^3*x*e^7 + 11787*(x*e + d)^m*a^2*b*m^2*x^2*e^7 + 11388*(x*e + d)^m*a*b^2*m*x^3*e^7 + 11388*(x*e + d)^m*a^2*c*m*x^3*e^7 + 1260*(x*e + d)^m*b^3*x^4*e^7 + 7560*(x*e + d)^m*a*b*c*x^4*e^7 + 1665*(x*e + d)^m*a^3*d*m^3*e^6 + 8262*(x*e + d)^m*a^2*b*d*m^2*x*e^6 + 2520*(x*e + d)^m*a*b^2*d*m*x^2*e^6 + 2520*(x*e + d)^m*a^2*c*d*m*x^2*e^6 - 3525*(x*e + d)^m*a^2*b*d^2*m^2*e^5 - 5040*(x*e + d)^m*a*b^2*d^2*m*x*e^5 - 5040*(x*e + d)^m*a^2*c*d^2*m*x*e^5 + 3828*(x*e + d)^m*a*b^2*d^3*m*e^4 + 3828*(x*e + d)^m*a^2*c*d^3*m*e^4 - 1260*(x*e + d)^m*b^3*d^4*e^3 - 7560*(x*e + d)^m*a*b*c*d^4*e^3 + 5104*(x*e + d)^m*a^3*m^2*x*e^7 + 15822*(x*e + d)^m*a^2*b*m*x^2*e^7 + 5040*(x*e + d)^m*a*b^2*x^3*e^7 + 5040*(x*e + d)^m*a^2*c*x^3*e^7 + 5104*(x*e + d)^m*a^3*d*m^2*e^6 + 7560*(x*e + d)^m*a^2*b*d*m*x*e^6 - 8262*(x*e + d)^m*a^2*b*d^2*m*e^5 + 5040*(x*e + d)^m*a*b^2*d^3*e^4 + 5040*(x*e + d)^m*a^2*c*d^3*e^4 + 8028*(x*e + d)^m*a^3*m*x*e^7 + 7560*(x*e + d)^m*a^2*b*x^2*e^7 + 8028*(x*e + d)^m*a^3*d*m*e^6 - 7560*(x*e + d)^m*a^2*b*d^2*e^5 + 5040*(x*e + d)^m*a^3*x*e^7 + 5040*(x*e + d)^m*a^3*d*e^6)/(m^7*e^7 + 28*m^6*e^7 + 322*m^5*e^7 + 1960*m^4*e^7 + 6769*m^3*e^7 + 13132*m^2*e^7 + 13068*m*e^7 + 5040*e^7)","B",0
2551,1,1717,0,0.229216," ","integrate((e*x+d)^m*(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{{\left(x e + d\right)}^{m} c^{2} m^{4} x^{5} e^{5} + {\left(x e + d\right)}^{m} c^{2} d m^{4} x^{4} e^{4} + 2 \, {\left(x e + d\right)}^{m} b c m^{4} x^{4} e^{5} + 10 \, {\left(x e + d\right)}^{m} c^{2} m^{3} x^{5} e^{5} + 2 \, {\left(x e + d\right)}^{m} b c d m^{4} x^{3} e^{4} + 6 \, {\left(x e + d\right)}^{m} c^{2} d m^{3} x^{4} e^{4} - 4 \, {\left(x e + d\right)}^{m} c^{2} d^{2} m^{3} x^{3} e^{3} + {\left(x e + d\right)}^{m} b^{2} m^{4} x^{3} e^{5} + 2 \, {\left(x e + d\right)}^{m} a c m^{4} x^{3} e^{5} + 22 \, {\left(x e + d\right)}^{m} b c m^{3} x^{4} e^{5} + 35 \, {\left(x e + d\right)}^{m} c^{2} m^{2} x^{5} e^{5} + {\left(x e + d\right)}^{m} b^{2} d m^{4} x^{2} e^{4} + 2 \, {\left(x e + d\right)}^{m} a c d m^{4} x^{2} e^{4} + 16 \, {\left(x e + d\right)}^{m} b c d m^{3} x^{3} e^{4} + 11 \, {\left(x e + d\right)}^{m} c^{2} d m^{2} x^{4} e^{4} - 6 \, {\left(x e + d\right)}^{m} b c d^{2} m^{3} x^{2} e^{3} - 12 \, {\left(x e + d\right)}^{m} c^{2} d^{2} m^{2} x^{3} e^{3} + 12 \, {\left(x e + d\right)}^{m} c^{2} d^{3} m^{2} x^{2} e^{2} + 2 \, {\left(x e + d\right)}^{m} a b m^{4} x^{2} e^{5} + 12 \, {\left(x e + d\right)}^{m} b^{2} m^{3} x^{3} e^{5} + 24 \, {\left(x e + d\right)}^{m} a c m^{3} x^{3} e^{5} + 82 \, {\left(x e + d\right)}^{m} b c m^{2} x^{4} e^{5} + 50 \, {\left(x e + d\right)}^{m} c^{2} m x^{5} e^{5} + 2 \, {\left(x e + d\right)}^{m} a b d m^{4} x e^{4} + 10 \, {\left(x e + d\right)}^{m} b^{2} d m^{3} x^{2} e^{4} + 20 \, {\left(x e + d\right)}^{m} a c d m^{3} x^{2} e^{4} + 34 \, {\left(x e + d\right)}^{m} b c d m^{2} x^{3} e^{4} + 6 \, {\left(x e + d\right)}^{m} c^{2} d m x^{4} e^{4} - 2 \, {\left(x e + d\right)}^{m} b^{2} d^{2} m^{3} x e^{3} - 4 \, {\left(x e + d\right)}^{m} a c d^{2} m^{3} x e^{3} - 36 \, {\left(x e + d\right)}^{m} b c d^{2} m^{2} x^{2} e^{3} - 8 \, {\left(x e + d\right)}^{m} c^{2} d^{2} m x^{3} e^{3} + 12 \, {\left(x e + d\right)}^{m} b c d^{3} m^{2} x e^{2} + 12 \, {\left(x e + d\right)}^{m} c^{2} d^{3} m x^{2} e^{2} - 24 \, {\left(x e + d\right)}^{m} c^{2} d^{4} m x e + {\left(x e + d\right)}^{m} a^{2} m^{4} x e^{5} + 26 \, {\left(x e + d\right)}^{m} a b m^{3} x^{2} e^{5} + 49 \, {\left(x e + d\right)}^{m} b^{2} m^{2} x^{3} e^{5} + 98 \, {\left(x e + d\right)}^{m} a c m^{2} x^{3} e^{5} + 122 \, {\left(x e + d\right)}^{m} b c m x^{4} e^{5} + 24 \, {\left(x e + d\right)}^{m} c^{2} x^{5} e^{5} + {\left(x e + d\right)}^{m} a^{2} d m^{4} e^{4} + 24 \, {\left(x e + d\right)}^{m} a b d m^{3} x e^{4} + 29 \, {\left(x e + d\right)}^{m} b^{2} d m^{2} x^{2} e^{4} + 58 \, {\left(x e + d\right)}^{m} a c d m^{2} x^{2} e^{4} + 20 \, {\left(x e + d\right)}^{m} b c d m x^{3} e^{4} - 2 \, {\left(x e + d\right)}^{m} a b d^{2} m^{3} e^{3} - 18 \, {\left(x e + d\right)}^{m} b^{2} d^{2} m^{2} x e^{3} - 36 \, {\left(x e + d\right)}^{m} a c d^{2} m^{2} x e^{3} - 30 \, {\left(x e + d\right)}^{m} b c d^{2} m x^{2} e^{3} + 2 \, {\left(x e + d\right)}^{m} b^{2} d^{3} m^{2} e^{2} + 4 \, {\left(x e + d\right)}^{m} a c d^{3} m^{2} e^{2} + 60 \, {\left(x e + d\right)}^{m} b c d^{3} m x e^{2} - 12 \, {\left(x e + d\right)}^{m} b c d^{4} m e + 24 \, {\left(x e + d\right)}^{m} c^{2} d^{5} + 14 \, {\left(x e + d\right)}^{m} a^{2} m^{3} x e^{5} + 118 \, {\left(x e + d\right)}^{m} a b m^{2} x^{2} e^{5} + 78 \, {\left(x e + d\right)}^{m} b^{2} m x^{3} e^{5} + 156 \, {\left(x e + d\right)}^{m} a c m x^{3} e^{5} + 60 \, {\left(x e + d\right)}^{m} b c x^{4} e^{5} + 14 \, {\left(x e + d\right)}^{m} a^{2} d m^{3} e^{4} + 94 \, {\left(x e + d\right)}^{m} a b d m^{2} x e^{4} + 20 \, {\left(x e + d\right)}^{m} b^{2} d m x^{2} e^{4} + 40 \, {\left(x e + d\right)}^{m} a c d m x^{2} e^{4} - 24 \, {\left(x e + d\right)}^{m} a b d^{2} m^{2} e^{3} - 40 \, {\left(x e + d\right)}^{m} b^{2} d^{2} m x e^{3} - 80 \, {\left(x e + d\right)}^{m} a c d^{2} m x e^{3} + 18 \, {\left(x e + d\right)}^{m} b^{2} d^{3} m e^{2} + 36 \, {\left(x e + d\right)}^{m} a c d^{3} m e^{2} - 60 \, {\left(x e + d\right)}^{m} b c d^{4} e + 71 \, {\left(x e + d\right)}^{m} a^{2} m^{2} x e^{5} + 214 \, {\left(x e + d\right)}^{m} a b m x^{2} e^{5} + 40 \, {\left(x e + d\right)}^{m} b^{2} x^{3} e^{5} + 80 \, {\left(x e + d\right)}^{m} a c x^{3} e^{5} + 71 \, {\left(x e + d\right)}^{m} a^{2} d m^{2} e^{4} + 120 \, {\left(x e + d\right)}^{m} a b d m x e^{4} - 94 \, {\left(x e + d\right)}^{m} a b d^{2} m e^{3} + 40 \, {\left(x e + d\right)}^{m} b^{2} d^{3} e^{2} + 80 \, {\left(x e + d\right)}^{m} a c d^{3} e^{2} + 154 \, {\left(x e + d\right)}^{m} a^{2} m x e^{5} + 120 \, {\left(x e + d\right)}^{m} a b x^{2} e^{5} + 154 \, {\left(x e + d\right)}^{m} a^{2} d m e^{4} - 120 \, {\left(x e + d\right)}^{m} a b d^{2} e^{3} + 120 \, {\left(x e + d\right)}^{m} a^{2} x e^{5} + 120 \, {\left(x e + d\right)}^{m} a^{2} d e^{4}}{m^{5} e^{5} + 15 \, m^{4} e^{5} + 85 \, m^{3} e^{5} + 225 \, m^{2} e^{5} + 274 \, m e^{5} + 120 \, e^{5}}"," ",0,"((x*e + d)^m*c^2*m^4*x^5*e^5 + (x*e + d)^m*c^2*d*m^4*x^4*e^4 + 2*(x*e + d)^m*b*c*m^4*x^4*e^5 + 10*(x*e + d)^m*c^2*m^3*x^5*e^5 + 2*(x*e + d)^m*b*c*d*m^4*x^3*e^4 + 6*(x*e + d)^m*c^2*d*m^3*x^4*e^4 - 4*(x*e + d)^m*c^2*d^2*m^3*x^3*e^3 + (x*e + d)^m*b^2*m^4*x^3*e^5 + 2*(x*e + d)^m*a*c*m^4*x^3*e^5 + 22*(x*e + d)^m*b*c*m^3*x^4*e^5 + 35*(x*e + d)^m*c^2*m^2*x^5*e^5 + (x*e + d)^m*b^2*d*m^4*x^2*e^4 + 2*(x*e + d)^m*a*c*d*m^4*x^2*e^4 + 16*(x*e + d)^m*b*c*d*m^3*x^3*e^4 + 11*(x*e + d)^m*c^2*d*m^2*x^4*e^4 - 6*(x*e + d)^m*b*c*d^2*m^3*x^2*e^3 - 12*(x*e + d)^m*c^2*d^2*m^2*x^3*e^3 + 12*(x*e + d)^m*c^2*d^3*m^2*x^2*e^2 + 2*(x*e + d)^m*a*b*m^4*x^2*e^5 + 12*(x*e + d)^m*b^2*m^3*x^3*e^5 + 24*(x*e + d)^m*a*c*m^3*x^3*e^5 + 82*(x*e + d)^m*b*c*m^2*x^4*e^5 + 50*(x*e + d)^m*c^2*m*x^5*e^5 + 2*(x*e + d)^m*a*b*d*m^4*x*e^4 + 10*(x*e + d)^m*b^2*d*m^3*x^2*e^4 + 20*(x*e + d)^m*a*c*d*m^3*x^2*e^4 + 34*(x*e + d)^m*b*c*d*m^2*x^3*e^4 + 6*(x*e + d)^m*c^2*d*m*x^4*e^4 - 2*(x*e + d)^m*b^2*d^2*m^3*x*e^3 - 4*(x*e + d)^m*a*c*d^2*m^3*x*e^3 - 36*(x*e + d)^m*b*c*d^2*m^2*x^2*e^3 - 8*(x*e + d)^m*c^2*d^2*m*x^3*e^3 + 12*(x*e + d)^m*b*c*d^3*m^2*x*e^2 + 12*(x*e + d)^m*c^2*d^3*m*x^2*e^2 - 24*(x*e + d)^m*c^2*d^4*m*x*e + (x*e + d)^m*a^2*m^4*x*e^5 + 26*(x*e + d)^m*a*b*m^3*x^2*e^5 + 49*(x*e + d)^m*b^2*m^2*x^3*e^5 + 98*(x*e + d)^m*a*c*m^2*x^3*e^5 + 122*(x*e + d)^m*b*c*m*x^4*e^5 + 24*(x*e + d)^m*c^2*x^5*e^5 + (x*e + d)^m*a^2*d*m^4*e^4 + 24*(x*e + d)^m*a*b*d*m^3*x*e^4 + 29*(x*e + d)^m*b^2*d*m^2*x^2*e^4 + 58*(x*e + d)^m*a*c*d*m^2*x^2*e^4 + 20*(x*e + d)^m*b*c*d*m*x^3*e^4 - 2*(x*e + d)^m*a*b*d^2*m^3*e^3 - 18*(x*e + d)^m*b^2*d^2*m^2*x*e^3 - 36*(x*e + d)^m*a*c*d^2*m^2*x*e^3 - 30*(x*e + d)^m*b*c*d^2*m*x^2*e^3 + 2*(x*e + d)^m*b^2*d^3*m^2*e^2 + 4*(x*e + d)^m*a*c*d^3*m^2*e^2 + 60*(x*e + d)^m*b*c*d^3*m*x*e^2 - 12*(x*e + d)^m*b*c*d^4*m*e + 24*(x*e + d)^m*c^2*d^5 + 14*(x*e + d)^m*a^2*m^3*x*e^5 + 118*(x*e + d)^m*a*b*m^2*x^2*e^5 + 78*(x*e + d)^m*b^2*m*x^3*e^5 + 156*(x*e + d)^m*a*c*m*x^3*e^5 + 60*(x*e + d)^m*b*c*x^4*e^5 + 14*(x*e + d)^m*a^2*d*m^3*e^4 + 94*(x*e + d)^m*a*b*d*m^2*x*e^4 + 20*(x*e + d)^m*b^2*d*m*x^2*e^4 + 40*(x*e + d)^m*a*c*d*m*x^2*e^4 - 24*(x*e + d)^m*a*b*d^2*m^2*e^3 - 40*(x*e + d)^m*b^2*d^2*m*x*e^3 - 80*(x*e + d)^m*a*c*d^2*m*x*e^3 + 18*(x*e + d)^m*b^2*d^3*m*e^2 + 36*(x*e + d)^m*a*c*d^3*m*e^2 - 60*(x*e + d)^m*b*c*d^4*e + 71*(x*e + d)^m*a^2*m^2*x*e^5 + 214*(x*e + d)^m*a*b*m*x^2*e^5 + 40*(x*e + d)^m*b^2*x^3*e^5 + 80*(x*e + d)^m*a*c*x^3*e^5 + 71*(x*e + d)^m*a^2*d*m^2*e^4 + 120*(x*e + d)^m*a*b*d*m*x*e^4 - 94*(x*e + d)^m*a*b*d^2*m*e^3 + 40*(x*e + d)^m*b^2*d^3*e^2 + 80*(x*e + d)^m*a*c*d^3*e^2 + 154*(x*e + d)^m*a^2*m*x*e^5 + 120*(x*e + d)^m*a*b*x^2*e^5 + 154*(x*e + d)^m*a^2*d*m*e^4 - 120*(x*e + d)^m*a*b*d^2*e^3 + 120*(x*e + d)^m*a^2*x*e^5 + 120*(x*e + d)^m*a^2*d*e^4)/(m^5*e^5 + 15*m^4*e^5 + 85*m^3*e^5 + 225*m^2*e^5 + 274*m*e^5 + 120*e^5)","B",0
2552,1,353,0,0.202013," ","integrate((e*x+d)^m*(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{{\left(x e + d\right)}^{m} c m^{2} x^{3} e^{3} + {\left(x e + d\right)}^{m} c d m^{2} x^{2} e^{2} + {\left(x e + d\right)}^{m} b m^{2} x^{2} e^{3} + 3 \, {\left(x e + d\right)}^{m} c m x^{3} e^{3} + {\left(x e + d\right)}^{m} b d m^{2} x e^{2} + {\left(x e + d\right)}^{m} c d m x^{2} e^{2} - 2 \, {\left(x e + d\right)}^{m} c d^{2} m x e + {\left(x e + d\right)}^{m} a m^{2} x e^{3} + 4 \, {\left(x e + d\right)}^{m} b m x^{2} e^{3} + 2 \, {\left(x e + d\right)}^{m} c x^{3} e^{3} + {\left(x e + d\right)}^{m} a d m^{2} e^{2} + 3 \, {\left(x e + d\right)}^{m} b d m x e^{2} - {\left(x e + d\right)}^{m} b d^{2} m e + 2 \, {\left(x e + d\right)}^{m} c d^{3} + 5 \, {\left(x e + d\right)}^{m} a m x e^{3} + 3 \, {\left(x e + d\right)}^{m} b x^{2} e^{3} + 5 \, {\left(x e + d\right)}^{m} a d m e^{2} - 3 \, {\left(x e + d\right)}^{m} b d^{2} e + 6 \, {\left(x e + d\right)}^{m} a x e^{3} + 6 \, {\left(x e + d\right)}^{m} a d e^{2}}{m^{3} e^{3} + 6 \, m^{2} e^{3} + 11 \, m e^{3} + 6 \, e^{3}}"," ",0,"((x*e + d)^m*c*m^2*x^3*e^3 + (x*e + d)^m*c*d*m^2*x^2*e^2 + (x*e + d)^m*b*m^2*x^2*e^3 + 3*(x*e + d)^m*c*m*x^3*e^3 + (x*e + d)^m*b*d*m^2*x*e^2 + (x*e + d)^m*c*d*m*x^2*e^2 - 2*(x*e + d)^m*c*d^2*m*x*e + (x*e + d)^m*a*m^2*x*e^3 + 4*(x*e + d)^m*b*m*x^2*e^3 + 2*(x*e + d)^m*c*x^3*e^3 + (x*e + d)^m*a*d*m^2*e^2 + 3*(x*e + d)^m*b*d*m*x*e^2 - (x*e + d)^m*b*d^2*m*e + 2*(x*e + d)^m*c*d^3 + 5*(x*e + d)^m*a*m*x*e^3 + 3*(x*e + d)^m*b*x^2*e^3 + 5*(x*e + d)^m*a*d*m*e^2 - 3*(x*e + d)^m*b*d^2*e + 6*(x*e + d)^m*a*x*e^3 + 6*(x*e + d)^m*a*d*e^2)/(m^3*e^3 + 6*m^2*e^3 + 11*m*e^3 + 6*e^3)","B",0
2553,0,0,0,0.000000," ","integrate((e*x+d)^m/(c*x^2+b*x+a),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{m}}{c x^{2} + b x + a}\,{d x}"," ",0,"integrate((e*x + d)^m/(c*x^2 + b*x + a), x)","F",0
2554,0,0,0,0.000000," ","integrate((e*x+d)^m/(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{m}}{{\left(c x^{2} + b x + a\right)}^{2}}\,{d x}"," ",0,"integrate((e*x + d)^m/(c*x^2 + b*x + a)^2, x)","F",0
2555,0,0,0,0.000000," ","integrate((e*x+d)^m*(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\int {\left(c x^{2} + b x + a\right)}^{\frac{5}{2}} {\left(e x + d\right)}^{m}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(5/2)*(e*x + d)^m, x)","F",0
2556,0,0,0,0.000000," ","integrate((e*x+d)^m*(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\int {\left(c x^{2} + b x + a\right)}^{\frac{3}{2}} {\left(e x + d\right)}^{m}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^(3/2)*(e*x + d)^m, x)","F",0
2557,0,0,0,0.000000," ","integrate((e*x+d)^m*(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int \sqrt{c x^{2} + b x + a} {\left(e x + d\right)}^{m}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + b*x + a)*(e*x + d)^m, x)","F",0
2558,0,0,0,0.000000," ","integrate((e*x+d)^m/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{m}}{\sqrt{c x^{2} + b x + a}}\,{d x}"," ",0,"integrate((e*x + d)^m/sqrt(c*x^2 + b*x + a), x)","F",0
2559,0,0,0,0.000000," ","integrate((e*x+d)^m/(c*x^2+b*x+a)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{m}}{{\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((e*x + d)^m/(c*x^2 + b*x + a)^(3/2), x)","F",0
2560,0,0,0,0.000000," ","integrate((e*x+d)^m/(c*x^2+b*x+a)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(e x + d\right)}^{m}}{{\left(c x^{2} + b x + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((e*x + d)^m/(c*x^2 + b*x + a)^(5/2), x)","F",0
2561,0,0,0,0.000000," ","integrate((d*x)^m*(c*x^2+b*x+a)^p,x, algorithm=""giac"")","\int {\left(c x^{2} + b x + a\right)}^{p} \left(d x\right)^{m}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^p*(d*x)^m, x)","F",0
2562,0,0,0,0.000000," ","integrate((e*x+d)^m*(c*x^2+b*x+a)^p,x, algorithm=""giac"")","\int {\left(c x^{2} + b x + a\right)}^{p} {\left(e x + d\right)}^{m}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^p*(e*x + d)^m, x)","F",0
2563,0,0,0,0.000000," ","integrate((e*x+d)^3*(c*x^2+b*x+a)^p,x, algorithm=""giac"")","\int {\left(e x + d\right)}^{3} {\left(c x^{2} + b x + a\right)}^{p}\,{d x}"," ",0,"integrate((e*x + d)^3*(c*x^2 + b*x + a)^p, x)","F",0
2564,0,0,0,0.000000," ","integrate((e*x+d)^2*(c*x^2+b*x+a)^p,x, algorithm=""giac"")","\int {\left(e x + d\right)}^{2} {\left(c x^{2} + b x + a\right)}^{p}\,{d x}"," ",0,"integrate((e*x + d)^2*(c*x^2 + b*x + a)^p, x)","F",0
2565,0,0,0,0.000000," ","integrate((e*x+d)*(c*x^2+b*x+a)^p,x, algorithm=""giac"")","\int {\left(e x + d\right)} {\left(c x^{2} + b x + a\right)}^{p}\,{d x}"," ",0,"integrate((e*x + d)*(c*x^2 + b*x + a)^p, x)","F",0
2566,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^p,x, algorithm=""giac"")","\int {\left(c x^{2} + b x + a\right)}^{p}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^p, x)","F",0
2567,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^p/(e*x+d),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{p}}{e x + d}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^p/(e*x + d), x)","F",0
2568,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^p/(e*x+d)^2,x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{p}}{{\left(e x + d\right)}^{2}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^p/(e*x + d)^2, x)","F",0
2569,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^p/(e*x+d)^3,x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{p}}{{\left(e x + d\right)}^{3}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^p/(e*x + d)^3, x)","F",0
2570,0,0,0,0.000000," ","integrate((e*x+d)^(3/2)*(c*x^2+b*x+a)^p,x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
2571,0,0,0,0.000000," ","integrate((e*x+d)^(1/2)*(c*x^2+b*x+a)^p,x, algorithm=""giac"")","\int \sqrt{e x + d} {\left(c x^{2} + b x + a\right)}^{p}\,{d x}"," ",0,"integrate(sqrt(e*x + d)*(c*x^2 + b*x + a)^p, x)","F",0
2572,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^p/(e*x+d)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{p}}{\sqrt{e x + d}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^p/sqrt(e*x + d), x)","F",0
2573,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^p/(e*x+d)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{p}}{{\left(e x + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^p/(e*x + d)^(3/2), x)","F",0
2574,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^p/((e*x+d)^(2*p)),x, algorithm=""giac"")","\int \frac{{\left(c x^{2} + b x + a\right)}^{p}}{{\left(e x + d\right)}^{2 \, p}}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^p/(e*x + d)^(2*p), x)","F",0
2575,0,0,0,0.000000," ","integrate((e*x+d)^(-1-2*p)*(c*x^2+b*x+a)^p,x, algorithm=""giac"")","\int {\left(c x^{2} + b x + a\right)}^{p} {\left(e x + d\right)}^{-2 \, p - 1}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^p*(e*x + d)^(-2*p - 1), x)","F",0
2576,0,0,0,0.000000," ","integrate((e*x+d)^(-2-2*p)*(c*x^2+b*x+a)^p,x, algorithm=""giac"")","\int {\left(c x^{2} + b x + a\right)}^{p} {\left(e x + d\right)}^{-2 \, p - 2}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^p*(e*x + d)^(-2*p - 2), x)","F",0
2577,0,0,0,0.000000," ","integrate((e*x+d)^(-3-2*p)*(c*x^2+b*x+a)^p,x, algorithm=""giac"")","\int {\left(c x^{2} + b x + a\right)}^{p} {\left(e x + d\right)}^{-2 \, p - 3}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^p*(e*x + d)^(-2*p - 3), x)","F",0
2578,0,0,0,0.000000," ","integrate((e*x+d)^(-4-2*p)*(c*x^2+b*x+a)^p,x, algorithm=""giac"")","\int {\left(c x^{2} + b x + a\right)}^{p} {\left(e x + d\right)}^{-2 \, p - 4}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^p*(e*x + d)^(-2*p - 4), x)","F",0
2579,0,0,0,0.000000," ","integrate((e*x+d)^(-5-2*p)*(c*x^2+b*x+a)^p,x, algorithm=""giac"")","\int {\left(c x^{2} + b x + a\right)}^{p} {\left(e x + d\right)}^{-2 \, p - 5}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^p*(e*x + d)^(-2*p - 5), x)","F",0
2580,0,0,0,0.000000," ","integrate((e*x+d)^(-6-2*p)*(c*x^2+b*x+a)^p,x, algorithm=""giac"")","\int {\left(c x^{2} + b x + a\right)}^{p} {\left(e x + d\right)}^{-2 \, p - 6}\,{d x}"," ",0,"integrate((c*x^2 + b*x + a)^p*(e*x + d)^(-2*p - 6), x)","F",0
2581,-1,0,0,0.000000," ","integrate((e*x+d)^m*(c*x^2+b*x+a)^(-2-1/2*m),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2582,0,0,0,0.000000," ","integrate(1/(1+x)^(1/3)/(x^2-x+1)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{2} - x + 1\right)}^{\frac{1}{3}} {\left(x + 1\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/((x^2 - x + 1)^(1/3)*(x + 1)^(1/3)), x)","F",0
2583,0,0,0,0.000000," ","integrate(1/(1+x)^(2/3)/(x^2-x+1)^(2/3),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{2} - x + 1\right)}^{\frac{2}{3}} {\left(x + 1\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(1/((x^2 - x + 1)^(2/3)*(x + 1)^(2/3)), x)","F",0
2584,0,0,0,0.000000," ","integrate((1+x)^p*(x^2-x+1)^p,x, algorithm=""giac"")","\int {\left(x^{2} - x + 1\right)}^{p} {\left(x + 1\right)}^{p}\,{d x}"," ",0,"integrate((x^2 - x + 1)^p*(x + 1)^p, x)","F",0
2585,0,0,0,0.000000," ","integrate(1/(1-x)^(1/3)/(x^2+x+1)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{2} + x + 1\right)}^{\frac{1}{3}} {\left(-x + 1\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/((x^2 + x + 1)^(1/3)*(-x + 1)^(1/3)), x)","F",0
2586,0,0,0,0.000000," ","integrate(1/(1-x)^(2/3)/(x^2+x+1)^(2/3),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{2} + x + 1\right)}^{\frac{2}{3}} {\left(-x + 1\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(1/((x^2 + x + 1)^(2/3)*(-x + 1)^(2/3)), x)","F",0
2587,0,0,0,0.000000," ","integrate((1-x)^p*(x^2+x+1)^p,x, algorithm=""giac"")","\int {\left(x^{2} + x + 1\right)}^{p} {\left(-x + 1\right)}^{p}\,{d x}"," ",0,"integrate((x^2 + x + 1)^p*(-x + 1)^p, x)","F",0
2588,0,0,0,0.000000," ","integrate(1/(-c*e*x+b*e)^(1/3)/(c^2*x^2+b*c*x+b^2)^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(c^{2} x^{2} + b c x + b^{2}\right)}^{\frac{1}{3}} {\left(-c e x + b e\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/((c^2*x^2 + b*c*x + b^2)^(1/3)*(-c*e*x + b*e)^(1/3)), x)","F",0
2589,0,0,0,0.000000," ","integrate(1/(-c*e*x+b*e)^(2/3)/(c^2*x^2+b*c*x+b^2)^(2/3),x, algorithm=""giac"")","\int \frac{1}{{\left(c^{2} x^{2} + b c x + b^{2}\right)}^{\frac{2}{3}} {\left(-c e x + b e\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(1/((c^2*x^2 + b*c*x + b^2)^(2/3)*(-c*e*x + b*e)^(2/3)), x)","F",0
2590,0,0,0,0.000000," ","integrate((-c*e*x+b*e)^p*(c^2*x^2+b*c*x+b^2)^p,x, algorithm=""giac"")","\int {\left(c^{2} x^{2} + b c x + b^{2}\right)}^{p} {\left(-c e x + b e\right)}^{p}\,{d x}"," ",0,"integrate((c^2*x^2 + b*c*x + b^2)^p*(-c*e*x + b*e)^p, x)","F",0
